LMFDB - Embedded newform 8041.2.a.j.1.21

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			1.21
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56353 q^{2} -0.440346 q^{3} +0.444615 q^{4} -3.20854 q^{5} +0.688493 q^{6} -3.01743 q^{7} +2.43189 q^{8} -2.80610 q^{9} +O(q^{10})$	\(q-1.56353 q^{2} -0.440346 q^{3} +0.444615 q^{4} -3.20854 q^{5} +0.688493 q^{6} -3.01743 q^{7} +2.43189 q^{8} -2.80610 q^{9} +5.01664 q^{10} +1.00000 q^{11} -0.195784 q^{12} -1.07827 q^{13} +4.71783 q^{14} +1.41287 q^{15} -4.69155 q^{16} +1.00000 q^{17} +4.38740 q^{18} +1.71104 q^{19} -1.42656 q^{20} +1.32871 q^{21} -1.56353 q^{22} -3.83958 q^{23} -1.07087 q^{24} +5.29473 q^{25} +1.68590 q^{26} +2.55669 q^{27} -1.34159 q^{28} +4.93512 q^{29} -2.20906 q^{30} +9.73856 q^{31} +2.47158 q^{32} -0.440346 q^{33} -1.56353 q^{34} +9.68154 q^{35} -1.24763 q^{36} -7.78668 q^{37} -2.67525 q^{38} +0.474810 q^{39} -7.80280 q^{40} +6.21957 q^{41} -2.07748 q^{42} +1.00000 q^{43} +0.444615 q^{44} +9.00347 q^{45} +6.00328 q^{46} -9.79189 q^{47} +2.06591 q^{48} +2.10487 q^{49} -8.27845 q^{50} -0.440346 q^{51} -0.479412 q^{52} -11.9804 q^{53} -3.99746 q^{54} -3.20854 q^{55} -7.33804 q^{56} -0.753448 q^{57} -7.71620 q^{58} -10.3384 q^{59} +0.628182 q^{60} -6.55723 q^{61} -15.2265 q^{62} +8.46719 q^{63} +5.51871 q^{64} +3.45966 q^{65} +0.688493 q^{66} -9.99052 q^{67} +0.444615 q^{68} +1.69074 q^{69} -15.1373 q^{70} -4.39278 q^{71} -6.82410 q^{72} -10.3751 q^{73} +12.1747 q^{74} -2.33151 q^{75} +0.760751 q^{76} -3.01743 q^{77} -0.742378 q^{78} +0.595901 q^{79} +15.0530 q^{80} +7.29246 q^{81} -9.72446 q^{82} +1.27937 q^{83} +0.590765 q^{84} -3.20854 q^{85} -1.56353 q^{86} -2.17316 q^{87} +2.43189 q^{88} +1.37471 q^{89} -14.0772 q^{90} +3.25359 q^{91} -1.70713 q^{92} -4.28834 q^{93} +15.3099 q^{94} -5.48993 q^{95} -1.08835 q^{96} -13.3342 q^{97} -3.29102 q^{98} -2.80610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.56353	−1.10558	−0.552790	−	0.833321i	$-0.686437\pi$
$2$	−1.56353	−1.10558	−0.552790	+	0.833321i	$0.686437\pi$
$3$	−0.440346	−0.254234	−0.127117	−	0.991888i	$-0.540572\pi$
$3$	−0.440346	−0.254234	−0.127117	+	0.991888i	$0.540572\pi$
$4$	0.444615	0.222307
$5$	−3.20854	−1.43490	−0.717451	−	0.696609i	$-0.754691\pi$
$5$	−3.20854	−1.43490	−0.717451	+	0.696609i	$0.754691\pi$
$6$	0.688493	0.281076
$7$	−3.01743	−1.14048	−0.570240	−	0.821478i	$-0.693150\pi$
$7$	−3.01743	−1.14048	−0.570240	+	0.821478i	$0.693150\pi$
$8$	2.43189	0.859802
$9$	−2.80610	−0.935365
$10$	5.01664	1.58640
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.195784	−0.0565181
$13$	−1.07827	−0.299057	−0.149529	−	0.988757i	$-0.547776\pi$
$13$	−1.07827	−0.299057	−0.149529	+	0.988757i	$0.547776\pi$
$14$	4.71783	1.26089
$15$	1.41287	0.364801
$16$	−4.69155	−1.17289
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.38740	1.03412
$19$	1.71104	0.392539	0.196269	−	0.980550i	$-0.437117\pi$
$19$	1.71104	0.392539	0.196269	+	0.980550i	$0.437117\pi$
$20$	−1.42656	−0.318989
$21$	1.32871	0.289949
$22$	−1.56353	−0.333345
$23$	−3.83958	−0.800607	−0.400304	−	0.916383i	$-0.631095\pi$
$23$	−3.83958	−0.800607	−0.400304	+	0.916383i	$0.631095\pi$
$24$	−1.07087	−0.218591
$25$	5.29473	1.05895
$26$	1.68590	0.330631
$27$	2.55669	0.492036
$28$	−1.34159	−0.253537
$29$	4.93512	0.916429	0.458215	−	0.888842i	$-0.348489\pi$
$29$	4.93512	0.916429	0.458215	+	0.888842i	$0.348489\pi$
$30$	−2.20906	−0.403317
$31$	9.73856	1.74910	0.874548	−	0.484938i	$-0.161158\pi$
$31$	9.73856	1.74910	0.874548	+	0.484938i	$0.161158\pi$
$32$	2.47158	0.436919
$33$	−0.440346	−0.0766545
$34$	−1.56353	−0.268143
$35$	9.68154	1.63648
$36$	−1.24763	−0.207938
$37$	−7.78668	−1.28012	−0.640061	−	0.768324i	$-0.721091\pi$
$37$	−7.78668	−1.28012	−0.640061	+	0.768324i	$0.721091\pi$
$38$	−2.67525	−0.433983
$39$	0.474810	0.0760305
$40$	−7.80280	−1.23373
$41$	6.21957	0.971334	0.485667	−	0.874144i	$-0.338577\pi$
$41$	6.21957	0.971334	0.485667	+	0.874144i	$0.338577\pi$
$42$	−2.07748	−0.320562
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.444615	0.0670282
$45$	9.00347	1.34216
$46$	6.00328	0.885136
$47$	−9.79189	−1.42829	−0.714147	−	0.699996i	$-0.753185\pi$
$47$	−9.79189	−1.42829	−0.714147	+	0.699996i	$0.753185\pi$
$48$	2.06591	0.298188
$49$	2.10487	0.300696
$50$	−8.27845	−1.17075
$51$	−0.440346	−0.0616608
$52$	−0.479412	−0.0664825
$53$	−11.9804	−1.64564	−0.822819	−	0.568303i	$-0.807600\pi$
$53$	−11.9804	−1.64564	−0.822819	+	0.568303i	$0.807600\pi$
$54$	−3.99746	−0.543985
$55$	−3.20854	−0.432639
$56$	−7.33804	−0.980587
$57$	−0.753448	−0.0997967
$58$	−7.71620	−1.01319
$59$	−10.3384	−1.34595	−0.672975	−	0.739665i	$-0.734984\pi$
$59$	−10.3384	−1.34595	−0.672975	+	0.739665i	$0.734984\pi$
$60$	0.628182	0.0810979
$61$	−6.55723	−0.839568	−0.419784	−	0.907624i	$-0.637894\pi$
$61$	−6.55723	−0.839568	−0.419784	+	0.907624i	$0.637894\pi$
$62$	−15.2265	−1.93377
$63$	8.46719	1.06677
$64$	5.51871	0.689838
$65$	3.45966	0.429118
$66$	0.688493	0.0847476
$67$	−9.99052	−1.22054	−0.610268	−	0.792195i	$-0.708938\pi$
$67$	−9.99052	−1.22054	−0.610268	+	0.792195i	$0.708938\pi$
$68$	0.444615	0.0539174
$69$	1.69074	0.203542
$70$	−15.1373	−1.80926
$71$	−4.39278	−0.521327	−0.260663	−	0.965430i	$-0.583941\pi$
$71$	−4.39278	−0.521327	−0.260663	+	0.965430i	$0.583941\pi$
$72$	−6.82410	−0.804228
$73$	−10.3751	−1.21431	−0.607156	−	0.794583i	$-0.707690\pi$
$73$	−10.3751	−1.21431	−0.607156	+	0.794583i	$0.707690\pi$
$74$	12.1747	1.41528
$75$	−2.33151	−0.269220
$76$	0.760751	0.0872642
$77$	−3.01743	−0.343868
$78$	−0.742378	−0.0840578
$79$	0.595901	0.0670441	0.0335221	−	0.999438i	$-0.489328\pi$
$79$	0.595901	0.0670441	0.0335221	+	0.999438i	$0.489328\pi$
$80$	15.0530	1.68298
$81$	7.29246	0.810273
$82$	−9.72446	−1.07389
$83$	1.27937	0.140429	0.0702144	−	0.997532i	$-0.477632\pi$
$83$	1.27937	0.140429	0.0702144	+	0.997532i	$0.477632\pi$
$84$	0.590765	0.0644578
$85$	−3.20854	−0.348015
$86$	−1.56353	−0.168599
$87$	−2.17316	−0.232988
$88$	2.43189	0.259240
$89$	1.37471	0.145719	0.0728594	−	0.997342i	$-0.476788\pi$
$89$	1.37471	0.145719	0.0728594	+	0.997342i	$0.476788\pi$
$90$	−14.0772	−1.48386
$91$	3.25359	0.341069
$92$	−1.70713	−0.177981
$93$	−4.28834	−0.444680
$94$	15.3099	1.57909
$95$	−5.48993	−0.563255
$96$	−1.08835	−0.111080
$97$	−13.3342	−1.35388	−0.676942	−	0.736036i	$-0.736695\pi$
$97$	−13.3342	−1.35388	−0.676942	+	0.736036i	$0.736695\pi$
$98$	−3.29102	−0.332443
$99$	−2.80610	−0.282023
$100$	2.35411	0.235411
$101$	8.18692	0.814629	0.407314	−	0.913288i	$-0.366465\pi$
$101$	8.18692	0.814629	0.407314	+	0.913288i	$0.366465\pi$
$102$	0.688493	0.0681710
$103$	−2.14339	−0.211194	−0.105597	−	0.994409i	$-0.533675\pi$
$103$	−2.14339	−0.211194	−0.105597	+	0.994409i	$0.533675\pi$
$104$	−2.62222	−0.257130
$105$	−4.26323	−0.416049
$106$	18.7317	1.81939
$107$	−17.1645	−1.65936	−0.829679	−	0.558240i	$-0.811477\pi$
$107$	−17.1645	−1.65936	−0.829679	+	0.558240i	$0.811477\pi$
$108$	1.13674	0.109383
$109$	0.363365	0.0348040	0.0174020	−	0.999849i	$-0.494460\pi$
$109$	0.363365	0.0348040	0.0174020	+	0.999849i	$0.494460\pi$
$110$	5.01664	0.478318
$111$	3.42883	0.325450
$112$	14.1564	1.33765
$113$	−10.5404	−0.991555	−0.495777	−	0.868450i	$-0.665117\pi$
$113$	−10.5404	−0.991555	−0.495777	+	0.868450i	$0.665117\pi$
$114$	1.17804	0.110333
$115$	12.3194	1.14879
$116$	2.19423	0.203729
$117$	3.02572	0.279727
$118$	16.1644	1.48806
$119$	−3.01743	−0.276607
$120$	3.43594	0.313657
$121$	1.00000	0.0909091
$122$	10.2524	0.928210
$123$	−2.73876	−0.246946
$124$	4.32990	0.388837
$125$	−0.945648	−0.0845813
$126$	−13.2387	−1.17939
$127$	7.45545	0.661564	0.330782	−	0.943707i	$-0.392688\pi$
$127$	7.45545	0.661564	0.330782	+	0.943707i	$0.392688\pi$
$128$	−13.5718	−1.19959
$129$	−0.440346	−0.0387703
$130$	−5.40927	−0.474424
$131$	−0.643014	−0.0561804	−0.0280902	−	0.999605i	$-0.508943\pi$
$131$	−0.643014	−0.0561804	−0.0280902	+	0.999605i	$0.508943\pi$
$132$	−0.195784	−0.0170408
$133$	−5.16293	−0.447683
$134$	15.6204	1.34940
$135$	−8.20325	−0.706023
$136$	2.43189	0.208533
$137$	−0.477864	−0.0408267	−0.0204133	−	0.999792i	$-0.506498\pi$
$137$	−0.477864	−0.0408267	−0.0204133	+	0.999792i	$0.506498\pi$
$138$	−2.64352	−0.225032
$139$	−9.29946	−0.788770	−0.394385	−	0.918945i	$-0.629042\pi$
$139$	−9.29946	−0.788770	−0.394385	+	0.918945i	$0.629042\pi$
$140$	4.30455	0.363801
$141$	4.31182	0.363121
$142$	6.86822	0.576369
$143$	−1.07827	−0.0901691
$144$	13.1649	1.09708
$145$	−15.8345	−1.31499
$146$	16.2217	1.34252
$147$	−0.926872	−0.0764471
$148$	−3.46207	−0.284580
$149$	−11.1073	−0.909942	−0.454971	−	0.890506i	$-0.650350\pi$
$149$	−11.1073	−0.909942	−0.454971	+	0.890506i	$0.650350\pi$
$150$	3.64538	0.297644
$151$	20.5497	1.67231	0.836157	−	0.548491i	$-0.184797\pi$
$151$	20.5497	1.67231	0.836157	+	0.548491i	$0.184797\pi$
$152$	4.16104	0.337505
$153$	−2.80610	−0.226859
$154$	4.71783	0.380173
$155$	−31.2466	−2.50978
$156$	0.211108	0.0169021
$157$	8.97237	0.716073	0.358037	−	0.933708i	$-0.383446\pi$
$157$	8.97237	0.716073	0.358037	+	0.933708i	$0.383446\pi$
$158$	−0.931707	−0.0741226
$159$	5.27554	0.418377
$160$	−7.93018	−0.626936
$161$	11.5857	0.913077
$162$	−11.4019	−0.895821
$163$	−21.0731	−1.65057	−0.825286	−	0.564715i	$-0.808986\pi$
$163$	−21.0731	−1.65057	−0.825286	+	0.564715i	$0.808986\pi$
$164$	2.76531	0.215935
$165$	1.41287	0.109992
$166$	−2.00032	−0.155255
$167$	24.3572	1.88482	0.942410	−	0.334459i	$-0.108554\pi$
$167$	24.3572	1.88482	0.942410	+	0.334459i	$0.108554\pi$
$168$	3.23128	0.249299
$169$	−11.8373	−0.910565
$170$	5.01664	0.384758
$171$	−4.80133	−0.367167
$172$	0.444615	0.0339015
$173$	−5.70504	−0.433746	−0.216873	−	0.976200i	$-0.569586\pi$
$173$	−5.70504	−0.433746	−0.216873	+	0.976200i	$0.569586\pi$
$174$	3.39780	0.257586
$175$	−15.9765	−1.20771
$176$	−4.69155	−0.353639
$177$	4.55249	0.342186
$178$	−2.14939	−0.161104
$179$	−3.47071	−0.259413	−0.129707	−	0.991552i	$-0.541404\pi$
$179$	−3.47071	−0.259413	−0.129707	+	0.991552i	$0.541404\pi$
$180$	4.00307	0.298371
$181$	8.52724	0.633825	0.316912	−	0.948455i	$-0.397354\pi$
$181$	8.52724	0.633825	0.316912	+	0.948455i	$0.397354\pi$
$182$	−5.08707	−0.377079
$183$	2.88745	0.213447
$184$	−9.33742	−0.688364
$185$	24.9839	1.83685
$186$	6.70493	0.491629
$187$	1.00000	0.0731272
$188$	−4.35361	−0.317520
$189$	−7.71464	−0.561157
$190$	8.58365	0.622723
$191$	−20.4067	−1.47658	−0.738288	−	0.674486i	$-0.764365\pi$
$191$	−20.4067	−1.47658	−0.738288	+	0.674486i	$0.764365\pi$
$192$	−2.43014	−0.175380
$193$	−13.2939	−0.956913	−0.478457	−	0.878111i	$-0.658804\pi$
$193$	−13.2939	−0.956913	−0.478457	+	0.878111i	$0.658804\pi$
$194$	20.8484	1.49683
$195$	−1.52345	−0.109096
$196$	0.935856	0.0668469
$197$	0.0142793	0.00101736	0.000508678	−	1.00000i	$-0.499838\pi$
$197$	0.0142793	0.00101736	0.000508678		1.00000i	$0.499838\pi$
$198$	4.38740	0.311799
$199$	−21.2910	−1.50928	−0.754640	−	0.656139i	$-0.772188\pi$
$199$	−21.2910	−1.50928	−0.754640	+	0.656139i	$0.772188\pi$
$200$	12.8762	0.910483
$201$	4.39929	0.310302
$202$	−12.8005	−0.900638
$203$	−14.8914	−1.04517
$204$	−0.195784	−0.0137076
$205$	−19.9557	−1.39377
$206$	3.35125	0.233492
$207$	10.7742	0.748860
$208$	5.05873	0.350760
$209$	1.71104	0.118355
$210$	6.66567	0.459975
$211$	−0.631022	−0.0434413	−0.0217207	−	0.999764i	$-0.506914\pi$
$211$	−0.631022	−0.0434413	−0.0217207	+	0.999764i	$0.506914\pi$
$212$	−5.32667	−0.365837
$213$	1.93434	0.132539
$214$	26.8372	1.83455
$215$	−3.20854	−0.218821
$216$	6.21759	0.423053
$217$	−29.3854	−1.99481
$218$	−0.568130	−0.0384786
$219$	4.56863	0.308719
$220$	−1.42656	−0.0961789
$221$	−1.07827	−0.0725320
$222$	−5.36107	−0.359812
$223$	−4.21147	−0.282021	−0.141011	−	0.990008i	$-0.545035\pi$
$223$	−4.21147	−0.282021	−0.141011	+	0.990008i	$0.545035\pi$
$224$	−7.45783	−0.498297
$225$	−14.8575	−0.990501
$226$	16.4801	1.09624
$227$	−7.95323	−0.527875	−0.263937	−	0.964540i	$-0.585021\pi$
$227$	−7.95323	−0.527875	−0.263937	+	0.964540i	$0.585021\pi$
$228$	−0.334994	−0.0221855
$229$	6.35506	0.419954	0.209977	−	0.977706i	$-0.432661\pi$
$229$	6.35506	0.419954	0.209977	+	0.977706i	$0.432661\pi$
$230$	−19.2618	−1.27008
$231$	1.32871	0.0874229
$232$	12.0017	0.787947
$233$	24.9037	1.63149	0.815747	−	0.578408i	$-0.196326\pi$
$233$	24.9037	1.63149	0.815747	+	0.578408i	$0.196326\pi$
$234$	−4.73079	−0.309261
$235$	31.4177	2.04946
$236$	−4.59662	−0.299214
$237$	−0.262403	−0.0170449
$238$	4.71783	0.305811
$239$	−22.8366	−1.47718	−0.738590	−	0.674155i	$-0.764508\pi$
$239$	−22.8366	−1.47718	−0.738590	+	0.674155i	$0.764508\pi$
$240$	−6.62854	−0.427870
$241$	−3.66039	−0.235786	−0.117893	−	0.993026i	$-0.537614\pi$
$241$	−3.66039	−0.235786	−0.117893	+	0.993026i	$0.537614\pi$
$242$	−1.56353	−0.100507
$243$	−10.8813	−0.698035
$244$	−2.91544	−0.186642
$245$	−6.75356	−0.431469
$246$	4.28213	0.273019
$247$	−1.84495	−0.117391
$248$	23.6831	1.50388
$249$	−0.563365	−0.0357018
$250$	1.47855	0.0935114
$251$	−9.10192	−0.574508	−0.287254	−	0.957854i	$-0.592742\pi$
$251$	−9.10192	−0.574508	−0.287254	+	0.957854i	$0.592742\pi$
$252$	3.76464	0.237150
$253$	−3.83958	−0.241392
$254$	−11.6568	−0.731412
$255$	1.41287	0.0884773
$256$	10.1825	0.636405
$257$	−4.76589	−0.297288	−0.148644	−	0.988891i	$-0.547491\pi$
$257$	−4.76589	−0.297288	−0.148644	+	0.988891i	$0.547491\pi$
$258$	0.688493	0.0428637
$259$	23.4957	1.45995
$260$	1.53821	0.0953960
$261$	−13.8484	−0.857196
$262$	1.00537	0.0621119
$263$	9.36935	0.577739	0.288869	−	0.957369i	$-0.406721\pi$
$263$	9.36935	0.577739	0.288869	+	0.957369i	$0.406721\pi$
$264$	−1.07087	−0.0659076
$265$	38.4397	2.36133
$266$	8.07237	0.494949
$267$	−0.605348	−0.0370467
$268$	−4.44193	−0.271334
$269$	−2.76687	−0.168699	−0.0843495	−	0.996436i	$-0.526881\pi$
$269$	−2.76687	−0.168699	−0.0843495	+	0.996436i	$0.526881\pi$
$270$	12.8260	0.780565
$271$	8.03510	0.488098	0.244049	−	0.969763i	$-0.421524\pi$
$271$	8.03510	0.488098	0.244049	+	0.969763i	$0.421524\pi$
$272$	−4.69155	−0.284467
$273$	−1.43271	−0.0867113
$274$	0.747153	0.0451372
$275$	5.29473	0.319284
$276$	0.751729	0.0452488
$277$	−26.6098	−1.59883	−0.799415	−	0.600780i	$-0.794857\pi$
$277$	−26.6098	−1.59883	−0.799415	+	0.600780i	$0.794857\pi$
$278$	14.5399	0.872048
$279$	−27.3273	−1.63604
$280$	23.5444	1.40705
$281$	8.70585	0.519347	0.259674	−	0.965696i	$-0.416385\pi$
$281$	8.70585	0.519347	0.259674	+	0.965696i	$0.416385\pi$
$282$	−6.74164	−0.401459
$283$	−20.4342	−1.21469	−0.607344	−	0.794439i	$-0.707765\pi$
$283$	−20.4342	−1.21469	−0.607344	+	0.794439i	$0.707765\pi$
$284$	−1.95309	−0.115895
$285$	2.41747	0.143199
$286$	1.68590	0.0996891
$287$	−18.7671	−1.10779
$288$	−6.93550	−0.408678
$289$	1.00000	0.0588235
$290$	24.7577	1.45382
$291$	5.87167	0.344203
$292$	−4.61291	−0.269950
$293$	14.8208	0.865841	0.432920	−	0.901432i	$-0.357483\pi$
$293$	14.8208	0.865841	0.432920	+	0.901432i	$0.357483\pi$
$294$	1.44919	0.0845184
$295$	33.1713	1.93131
$296$	−18.9363	−1.10065
$297$	2.55669	0.148354
$298$	17.3665	1.00601
$299$	4.14008	0.239427
$300$	−1.03663	−0.0598496
$301$	−3.01743	−0.173922
$302$	−32.1300	−1.84888
$303$	−3.60508	−0.207106
$304$	−8.02741	−0.460403
$305$	21.0392	1.20470
$306$	4.38740	0.250811
$307$	33.3553	1.90369	0.951844	−	0.306583i	$-0.0991857\pi$
$307$	33.3553	1.90369	0.951844	+	0.306583i	$0.0991857\pi$
$308$	−1.34159	−0.0764443
$309$	0.943834	0.0536928
$310$	48.8548	2.77477
$311$	26.4824	1.50168	0.750838	−	0.660486i	$-0.229650\pi$
$311$	26.4824	1.50168	0.750838	+	0.660486i	$0.229650\pi$
$312$	1.15468	0.0653711
$313$	10.2900	0.581627	0.290814	−	0.956780i	$-0.406074\pi$
$313$	10.2900	0.581627	0.290814	+	0.956780i	$0.406074\pi$
$314$	−14.0285	−0.791676
$315$	−27.1673	−1.53070
$316$	0.264946	0.0149044
$317$	−1.66501	−0.0935161	−0.0467581	−	0.998906i	$-0.514889\pi$
$317$	−1.66501	−0.0935161	−0.0467581	+	0.998906i	$0.514889\pi$
$318$	−8.24844	−0.462550
$319$	4.93512	0.276314
$320$	−17.7070	−0.989851
$321$	7.55834	0.421865
$322$	−18.1145	−1.00948
$323$	1.71104	0.0952046
$324$	3.24233	0.180130
$325$	−5.70912	−0.316685
$326$	32.9483	1.82484
$327$	−0.160006	−0.00884837
$328$	15.1253	0.835154
$329$	29.5463	1.62894
$330$	−2.20906	−0.121605
$331$	−20.7463	−1.14032	−0.570161	−	0.821533i	$-0.693119\pi$
$331$	−20.7463	−1.14032	−0.570161	+	0.821533i	$0.693119\pi$
$332$	0.568825	0.0312183
$333$	21.8502	1.19738
$334$	−38.0832	−2.08382
$335$	32.0550	1.75135
$336$	−6.23372	−0.340077
$337$	−0.324523	−0.0176779	−0.00883894	−	0.999961i	$-0.502814\pi$
$337$	−0.324523	−0.0176779	−0.00883894	+	0.999961i	$0.502814\pi$
$338$	18.5080	1.00670
$339$	4.64141	0.252087
$340$	−1.42656	−0.0773663
$341$	9.73856	0.527372
$342$	7.50700	0.405932
$343$	14.7707	0.797543
$344$	2.43189	0.131119
$345$	−5.42482	−0.292063
$346$	8.91998	0.479541
$347$	25.1534	1.35030	0.675152	−	0.737679i	$-0.264078\pi$
$347$	25.1534	1.35030	0.675152	+	0.737679i	$0.264078\pi$
$348$	−0.966220	−0.0517948
$349$	−10.3438	−0.553691	−0.276846	−	0.960914i	$-0.589289\pi$
$349$	−10.3438	−0.553691	−0.276846	+	0.960914i	$0.589289\pi$
$350$	24.9796	1.33522
$351$	−2.75679	−0.147147
$352$	2.47158	0.131736
$353$	−8.61080	−0.458307	−0.229153	−	0.973390i	$-0.573596\pi$
$353$	−8.61080	−0.458307	−0.229153	+	0.973390i	$0.573596\pi$
$354$	−7.11794	−0.378314
$355$	14.0944	0.748053
$356$	0.611215	0.0323943
$357$	1.32871	0.0703230
$358$	5.42655	0.286802
$359$	−3.05970	−0.161485	−0.0807424	−	0.996735i	$-0.525729\pi$
$359$	−3.05970	−0.161485	−0.0807424	+	0.996735i	$0.525729\pi$
$360$	21.8954	1.15399
$361$	−16.0724	−0.845913
$362$	−13.3326	−0.700744
$363$	−0.440346	−0.0231122
$364$	1.44659	0.0758221
$365$	33.2889	1.74242
$366$	−4.51461	−0.235982
$367$	−20.3694	−1.06328	−0.531638	−	0.846972i	$-0.678423\pi$
$367$	−20.3694	−1.06328	−0.531638	+	0.846972i	$0.678423\pi$
$368$	18.0136	0.939022
$369$	−17.4527	−0.908552
$370$	−39.0629	−2.03078
$371$	36.1501	1.87682
$372$	−1.90666	−0.0988556
$373$	−6.66775	−0.345243	−0.172622	−	0.984988i	$-0.555224\pi$
$373$	−6.66775	−0.345243	−0.172622	+	0.984988i	$0.555224\pi$
$374$	−1.56353	−0.0808480
$375$	0.416413	0.0215034
$376$	−23.8127	−1.22805
$377$	−5.32137	−0.274065
$378$	12.0620	0.620404
$379$	−12.1485	−0.624026	−0.312013	−	0.950078i	$-0.601003\pi$
$379$	−12.1485	−0.624026	−0.312013	+	0.950078i	$0.601003\pi$
$380$	−2.44090	−0.125216
$381$	−3.28298	−0.168192
$382$	31.9064	1.63247
$383$	−15.6362	−0.798974	−0.399487	−	0.916739i	$-0.630812\pi$
$383$	−15.6362	−0.798974	−0.399487	+	0.916739i	$0.630812\pi$
$384$	5.97630	0.304977
$385$	9.68154	0.493417
$386$	20.7853	1.05794
$387$	−2.80610	−0.142642
$388$	−5.92858	−0.300978
$389$	−37.4532	−1.89895	−0.949476	−	0.313840i	$-0.898384\pi$
$389$	−37.4532	−1.89895	−0.949476	+	0.313840i	$0.898384\pi$
$390$	2.38195	0.120615
$391$	−3.83958	−0.194176
$392$	5.11881	0.258539
$393$	0.283149	0.0142830
$394$	−0.0223260	−0.00112477
$395$	−1.91197	−0.0962018
$396$	−1.24763	−0.0626958
$397$	4.24690	0.213146	0.106573	−	0.994305i	$-0.466012\pi$
$397$	4.24690	0.213146	0.106573	+	0.994305i	$0.466012\pi$
$398$	33.2891	1.66863
$399$	2.27348	0.113816
$400$	−24.8405	−1.24202
$401$	−4.71005	−0.235209	−0.117604	−	0.993061i	$-0.537521\pi$
$401$	−4.71005	−0.235209	−0.117604	+	0.993061i	$0.537521\pi$
$402$	−6.87840	−0.343064
$403$	−10.5008	−0.523080
$404$	3.64002	0.181098
$405$	−23.3981	−1.16266
$406$	23.2831	1.15552
$407$	−7.78668	−0.385971
$408$	−1.07087	−0.0530161
$409$	20.7525	1.02614	0.513072	−	0.858345i	$-0.328507\pi$
$409$	20.7525	1.02614	0.513072	+	0.858345i	$0.328507\pi$
$410$	31.2013	1.54092
$411$	0.210426	0.0103795
$412$	−0.952982	−0.0469500
$413$	31.1955	1.53503
$414$	−16.8458	−0.827925
$415$	−4.10490	−0.201502
$416$	−2.66502	−0.130664
$417$	4.09498	0.200532
$418$	−2.67525	−0.130851
$419$	−27.4919	−1.34307	−0.671535	−	0.740973i	$-0.734365\pi$
$419$	−27.4919	−1.34307	−0.671535	+	0.740973i	$0.734365\pi$
$420$	−1.89549	−0.0924906
$421$	−6.30617	−0.307344	−0.153672	−	0.988122i	$-0.549110\pi$
$421$	−6.30617	−0.307344	−0.153672	+	0.988122i	$0.549110\pi$
$422$	0.986619	0.0480279
$423$	27.4770	1.33598
$424$	−29.1350	−1.41492
$425$	5.29473	0.256832
$426$	−3.02440	−0.146533
$427$	19.7860	0.957511
$428$	−7.63160	−0.368887
$429$	0.474810	0.0229241
$430$	5.01664	0.241924
$431$	12.0200	0.578983	0.289492	−	0.957181i	$-0.406514\pi$
$431$	12.0200	0.578983	0.289492	+	0.957181i	$0.406514\pi$
$432$	−11.9948	−0.577102
$433$	6.74614	0.324199	0.162099	−	0.986774i	$-0.448173\pi$
$433$	6.74614	0.324199	0.162099	+	0.986774i	$0.448173\pi$
$434$	45.9448	2.20542
$435$	6.97268	0.334314
$436$	0.161557	0.00773718
$437$	−6.56966	−0.314269
$438$	−7.14317	−0.341314
$439$	1.34282	0.0640895	0.0320447	−	0.999486i	$-0.489798\pi$
$439$	1.34282	0.0640895	0.0320447	+	0.999486i	$0.489798\pi$
$440$	−7.80280	−0.371984
$441$	−5.90647	−0.281260
$442$	1.68590	0.0801899
$443$	−1.90507	−0.0905128	−0.0452564	−	0.998975i	$-0.514410\pi$
$443$	−1.90507	−0.0905128	−0.0452564	+	0.998975i	$0.514410\pi$
$444$	1.52451	0.0723500
$445$	−4.41081	−0.209092
$446$	6.58475	0.311797
$447$	4.89104	0.231338
$448$	−16.6523	−0.786747
$449$	18.8736	0.890699	0.445350	−	0.895357i	$-0.353079\pi$
$449$	18.8736	0.890699	0.445350	+	0.895357i	$0.353079\pi$
$450$	23.2301	1.09508
$451$	6.21957	0.292868
$452$	−4.68640	−0.220430
$453$	−9.04900	−0.425159
$454$	12.4351	0.583608
$455$	−10.4393	−0.489400
$456$	−1.83230	−0.0858053
$457$	−22.9911	−1.07548	−0.537739	−	0.843111i	$-0.680721\pi$
$457$	−22.9911	−1.07548	−0.537739	+	0.843111i	$0.680721\pi$
$458$	−9.93631	−0.464293
$459$	2.55669	0.119336
$460$	5.47740	0.255385
$461$	11.9440	0.556286	0.278143	−	0.960540i	$-0.410281\pi$
$461$	11.9440	0.556286	0.278143	+	0.960540i	$0.410281\pi$
$462$	−2.07748	−0.0966530
$463$	−39.0220	−1.81351	−0.906754	−	0.421661i	$-0.861447\pi$
$463$	−39.0220	−1.81351	−0.906754	+	0.421661i	$0.861447\pi$
$464$	−23.1534	−1.07487
$465$	13.7593	0.638072
$466$	−38.9376	−1.80375
$467$	29.2415	1.35313	0.676567	−	0.736381i	$-0.263467\pi$
$467$	29.2415	1.35313	0.676567	+	0.736381i	$0.263467\pi$
$468$	1.34528	0.0621855
$469$	30.1457	1.39200
$470$	−49.1223	−2.26584
$471$	−3.95095	−0.182050
$472$	−25.1419	−1.15725
$473$	1.00000	0.0459800
$474$	0.410274	0.0188445
$475$	9.05947	0.415677
$476$	−1.34159	−0.0614918
$477$	33.6182	1.53927
$478$	35.7057	1.63314
$479$	4.84508	0.221377	0.110689	−	0.993855i	$-0.464694\pi$
$479$	4.84508	0.221377	0.110689	+	0.993855i	$0.464694\pi$
$480$	3.49202	0.159388
$481$	8.39610	0.382829
$482$	5.72311	0.260681
$483$	−5.10170	−0.232135
$484$	0.444615	0.0202098
$485$	42.7833	1.94269
$486$	17.0132	0.771733
$487$	11.4084	0.516964	0.258482	−	0.966016i	$-0.416778\pi$
$487$	11.4084	0.516964	0.258482	+	0.966016i	$0.416778\pi$
$488$	−15.9464	−0.721862
$489$	9.27946	0.419632
$490$	10.5594	0.477024
$491$	25.8750	1.16772	0.583860	−	0.811854i	$-0.301542\pi$
$491$	25.8750	1.16772	0.583860	+	0.811854i	$0.301542\pi$
$492$	−1.21769	−0.0548979
$493$	4.93512	0.222267
$494$	2.88463	0.129786
$495$	9.00347	0.404676
$496$	−45.6889	−2.05149
$497$	13.2549	0.594563
$498$	0.880835	0.0394712
$499$	−35.6148	−1.59434	−0.797169	−	0.603756i	$-0.793670\pi$
$499$	−35.6148	−1.59434	−0.797169	+	0.603756i	$0.793670\pi$
$500$	−0.420449	−0.0188030
$501$	−10.7256	−0.479186
$502$	14.2311	0.635165
$503$	−38.6075	−1.72142	−0.860711	−	0.509094i	$-0.829980\pi$
$503$	−38.6075	−1.72142	−0.860711	+	0.509094i	$0.829980\pi$
$504$	20.5912	0.917207
$505$	−26.2681	−1.16891
$506$	6.00328	0.266878
$507$	5.21253	0.231497
$508$	3.31480	0.147070
$509$	31.0435	1.37598	0.687989	−	0.725721i	$-0.258494\pi$
$509$	31.0435	1.37598	0.687989	+	0.725721i	$0.258494\pi$
$510$	−2.20906	−0.0978187
$511$	31.3061	1.38490
$512$	11.2231	0.495994
$513$	4.37459	0.193143
$514$	7.45159	0.328675
$515$	6.87715	0.303043
$516$	−0.195784	−0.00861893
$517$	−9.79189	−0.430647
$518$	−36.7362	−1.61410
$519$	2.51219	0.110273
$520$	8.41349	0.368956
$521$	−28.7588	−1.25995	−0.629973	−	0.776617i	$-0.716934\pi$
$521$	−28.7588	−1.25995	−0.629973	+	0.776617i	$0.716934\pi$
$522$	21.6524	0.947699
$523$	28.5746	1.24948	0.624741	−	0.780832i	$-0.285205\pi$
$523$	28.5746	1.24948	0.624741	+	0.780832i	$0.285205\pi$
$524$	−0.285893	−0.0124893
$525$	7.03518	0.307040
$526$	−14.6492	−0.638736
$527$	9.73856	0.424218
$528$	2.06591	0.0899070
$529$	−8.25764	−0.359028
$530$	−60.1015	−2.61064
$531$	29.0106	1.25895
$532$	−2.29551	−0.0995231
$533$	−6.70635	−0.290484
$534$	0.946477	0.0409581
$535$	55.0731	2.38102
$536$	−24.2958	−1.04942
$537$	1.52832	0.0659517
$538$	4.32607	0.186510
$539$	2.10487	0.0906632
$540$	−3.64728	−0.156954
$541$	33.4995	1.44026	0.720129	−	0.693840i	$-0.244083\pi$
$541$	33.4995	1.44026	0.720129	+	0.693840i	$0.244083\pi$
$542$	−12.5631	−0.539631
$543$	−3.75494	−0.161140
$544$	2.47158	0.105968
$545$	−1.16587	−0.0499404
$546$	2.24007	0.0958663
$547$	3.28794	0.140582	0.0702911	−	0.997527i	$-0.477607\pi$
$547$	3.28794	0.140582	0.0702911	+	0.997527i	$0.477607\pi$
$548$	−0.212465	−0.00907607
$549$	18.4002	0.785302
$550$	−8.27845	−0.352994
$551$	8.44417	0.359734
$552$	4.11170	0.175005
$553$	−1.79809	−0.0764625
$554$	41.6052	1.76763
$555$	−11.0015	−0.466990
$556$	−4.13467	−0.175349
$557$	8.92391	0.378118	0.189059	−	0.981966i	$-0.439456\pi$
$557$	8.92391	0.378118	0.189059	+	0.981966i	$0.439456\pi$
$558$	42.7270	1.80878
$559$	−1.07827	−0.0456058
$560$	−45.4214	−1.91940
$561$	−0.440346	−0.0185914
$562$	−13.6118	−0.574180
$563$	−26.2338	−1.10562	−0.552811	−	0.833307i	$-0.686445\pi$
$563$	−26.2338	−1.10562	−0.552811	+	0.833307i	$0.686445\pi$
$564$	1.91710	0.0807244
$565$	33.8192	1.42278
$566$	31.9494	1.34293
$567$	−22.0045	−0.924100
$568$	−10.6827	−0.448238
$569$	−10.2612	−0.430171	−0.215085	−	0.976595i	$-0.569003\pi$
$569$	−10.2612	−0.430171	−0.215085	+	0.976595i	$0.569003\pi$
$570$	−3.77978	−0.158317
$571$	5.05351	0.211483	0.105741	−	0.994394i	$-0.466278\pi$
$571$	5.05351	0.211483	0.105741	+	0.994394i	$0.466278\pi$
$572$	−0.479412	−0.0200452
$573$	8.98601	0.375396
$574$	29.3429	1.22475
$575$	−20.3295	−0.847800
$576$	−15.4860	−0.645251
$577$	23.9591	0.997429	0.498714	−	0.866766i	$-0.333806\pi$
$577$	23.9591	0.997429	0.498714	+	0.866766i	$0.333806\pi$
$578$	−1.56353	−0.0650341
$579$	5.85390	0.243280
$580$	−7.04027	−0.292331
$581$	−3.86040	−0.160156
$582$	−9.18051	−0.380544
$583$	−11.9804	−0.496179
$584$	−25.2310	−1.04407
$585$	−9.70813	−0.401382
$586$	−23.1727	−0.957257
$587$	−31.2226	−1.28869	−0.644347	−	0.764734i	$-0.722871\pi$
$587$	−31.2226	−1.28869	−0.644347	+	0.764734i	$0.722871\pi$
$588$	−0.412101	−0.0169948
$589$	16.6630	0.686588
$590$	−51.8642	−2.13521
$591$	−0.00628782	−0.000258646 0
$592$	36.5316	1.50144
$593$	−15.2295	−0.625399	−0.312699	−	0.949852i	$-0.601233\pi$
$593$	−15.2295	−0.625399	−0.312699	+	0.949852i	$0.601233\pi$
$594$	−3.99746	−0.164018
$595$	9.68154	0.396904
$596$	−4.93845	−0.202287
$597$	9.37542	0.383710
$598$	−6.47313	−0.264706
$599$	11.8895	0.485792	0.242896	−	0.970052i	$-0.421903\pi$
$599$	11.8895	0.485792	0.242896	+	0.970052i	$0.421903\pi$
$600$	−5.66998	−0.231476
$601$	−34.5679	−1.41005	−0.705026	−	0.709181i	$-0.749065\pi$
$601$	−34.5679	−1.41005	−0.705026	+	0.709181i	$0.749065\pi$
$602$	4.71783	0.192284
$603$	28.0343	1.14165
$604$	9.13671	0.371767
$605$	−3.20854	−0.130446
$606$	5.63664	0.228973
$607$	−9.05139	−0.367385	−0.183692	−	0.982984i	$-0.558805\pi$
$607$	−9.05139	−0.367385	−0.183692	+	0.982984i	$0.558805\pi$
$608$	4.22897	0.171507
$609$	6.55736	0.265718
$610$	−32.8953	−1.33189
$611$	10.5583	0.427141
$612$	−1.24763	−0.0504325
$613$	36.8663	1.48902	0.744508	−	0.667614i	$-0.232684\pi$
$613$	36.8663	1.48902	0.744508	+	0.667614i	$0.232684\pi$
$614$	−52.1519	−2.10468
$615$	8.78744	0.354344
$616$	−7.33804	−0.295658
$617$	33.7786	1.35988	0.679938	−	0.733270i	$-0.262007\pi$
$617$	33.7786	1.35988	0.679938	+	0.733270i	$0.262007\pi$
$618$	−1.47571	−0.0593617
$619$	−10.6245	−0.427036	−0.213518	−	0.976939i	$-0.568492\pi$
$619$	−10.6245	−0.427036	−0.213518	+	0.976939i	$0.568492\pi$
$620$	−13.8927	−0.557943
$621$	−9.81662	−0.393927
$622$	−41.4059	−1.66022
$623$	−4.14808	−0.166189
$624$	−2.22759	−0.0891752
$625$	−23.4395	−0.937580
$626$	−16.0887	−0.643035
$627$	−0.753448	−0.0300898
$628$	3.98925	0.159188
$629$	−7.78668	−0.310475
$630$	42.4768	1.69232
$631$	−32.3171	−1.28652	−0.643261	−	0.765647i	$-0.722419\pi$
$631$	−32.3171	−1.28652	−0.643261	+	0.765647i	$0.722419\pi$
$632$	1.44916	0.0576446
$633$	0.277868	0.0110443
$634$	2.60328	0.103390
$635$	−23.9211	−0.949280
$636$	2.34558	0.0930083
$637$	−2.26961	−0.0899252
$638$	−7.71620	−0.305487
$639$	12.3266	0.487631
$640$	43.5457	1.72129
$641$	39.1659	1.54696	0.773480	−	0.633820i	$-0.218514\pi$
$641$	39.1659	1.54696	0.773480	+	0.633820i	$0.218514\pi$
$642$	−11.8177	−0.466406
$643$	−6.43500	−0.253772	−0.126886	−	0.991917i	$-0.540498\pi$
$643$	−6.43500	−0.253772	−0.126886	+	0.991917i	$0.540498\pi$
$644$	5.15115	0.202984
$645$	1.41287	0.0556317
$646$	−2.67525	−0.105256
$647$	−17.2489	−0.678126	−0.339063	−	0.940764i	$-0.610110\pi$
$647$	−17.2489	−0.678126	−0.339063	+	0.940764i	$0.610110\pi$
$648$	17.7344	0.696674
$649$	−10.3384	−0.405819
$650$	8.92636	0.350121
$651$	12.9398	0.507149
$652$	−9.36941	−0.366934
$653$	6.11279	0.239212	0.119606	−	0.992821i	$-0.461837\pi$
$653$	6.11279	0.239212	0.119606	+	0.992821i	$0.461837\pi$
$654$	0.250174	0.00978258
$655$	2.06314	0.0806134
$656$	−29.1794	−1.13926
$657$	29.1135	1.13582
$658$	−46.1964	−1.80092
$659$	31.2304	1.21656	0.608282	−	0.793721i	$-0.291859\pi$
$659$	31.2304	1.21656	0.608282	+	0.793721i	$0.291859\pi$
$660$	0.628182	0.0244519
$661$	−40.9808	−1.59397	−0.796984	−	0.604000i	$-0.793573\pi$
$661$	−40.9808	−1.59397	−0.796984	+	0.604000i	$0.793573\pi$
$662$	32.4375	1.26072
$663$	0.474810	0.0184401
$664$	3.11128	0.120741
$665$	16.5655	0.642381
$666$	−34.1633	−1.32380
$667$	−18.9488	−0.733700
$668$	10.8296	0.419009
$669$	1.85451	0.0716994
$670$	−50.1188	−1.93626
$671$	−6.55723	−0.253139
$672$	3.28403	0.126684
$673$	−35.2980	−1.36064	−0.680319	−	0.732916i	$-0.738159\pi$
$673$	−35.2980	−1.36064	−0.680319	+	0.732916i	$0.738159\pi$
$674$	0.507400	0.0195443
$675$	13.5370	0.521039
$676$	−5.26305	−0.202425
$677$	−9.69710	−0.372690	−0.186345	−	0.982484i	$-0.559664\pi$
$677$	−9.69710	−0.372690	−0.186345	+	0.982484i	$0.559664\pi$
$678$	−7.25697	−0.278702
$679$	40.2350	1.54408
$680$	−7.80280	−0.299224
$681$	3.50218	0.134204
$682$	−15.2265	−0.583052
$683$	5.10466	0.195324	0.0976621	−	0.995220i	$-0.468864\pi$
$683$	5.10466	0.195324	0.0976621	+	0.995220i	$0.468864\pi$
$684$	−2.13474	−0.0816238
$685$	1.53325	0.0585823
$686$	−23.0944	−0.881747
$687$	−2.79843	−0.106767
$688$	−4.69155	−0.178864
$689$	12.9181	0.492140
$690$	8.48185	0.322898
$691$	3.49085	0.132798	0.0663990	−	0.997793i	$-0.478849\pi$
$691$	3.49085	0.132798	0.0663990	+	0.997793i	$0.478849\pi$
$692$	−2.53654	−0.0964249
$693$	8.46719	0.321642
$694$	−39.3280	−1.49287
$695$	29.8377	1.13181
$696$	−5.28489	−0.200323
$697$	6.21957	0.235583
$698$	16.1728	0.612150
$699$	−10.9662	−0.414782
$700$	−7.10337	−0.268482
$701$	41.3030	1.55999	0.779996	−	0.625785i	$-0.215221\pi$
$701$	41.3030	1.55999	0.779996	+	0.625785i	$0.215221\pi$
$702$	4.31032	0.162683
$703$	−13.3233	−0.502497
$704$	5.51871	0.207994
$705$	−13.8346	−0.521043
$706$	13.4632	0.506695
$707$	−24.7034	−0.929068
$708$	2.02410	0.0760705
$709$	15.9452	0.598835	0.299417	−	0.954122i	$-0.403208\pi$
$709$	15.9452	0.598835	0.299417	+	0.954122i	$0.403208\pi$
$710$	−22.0370	−0.827033
$711$	−1.67215	−0.0627107
$712$	3.34313	0.125289
$713$	−37.3920	−1.40034
$714$	−2.07748	−0.0777477
$715$	3.45966	0.129384
$716$	−1.54313	−0.0576695
$717$	10.0560	0.375549
$718$	4.78392	0.178534
$719$	48.3823	1.80435	0.902177	−	0.431366i	$-0.141968\pi$
$719$	48.3823	1.80435	0.902177	+	0.431366i	$0.141968\pi$
$720$	−42.2402	−1.57420
$721$	6.46752	0.240863
$722$	25.1296	0.935225
$723$	1.61184	0.0599449
$724$	3.79133	0.140904
$725$	26.1301	0.970449
$726$	0.688493	0.0255524
$727$	44.1939	1.63906	0.819530	−	0.573036i	$-0.194235\pi$
$727$	44.1939	1.63906	0.819530	+	0.573036i	$0.194235\pi$
$728$	7.91236	0.293251
$729$	−17.0858	−0.632809
$730$	−52.0480	−1.92638
$731$	1.00000	0.0369863
$732$	1.28380	0.0474508
$733$	−18.7014	−0.690750	−0.345375	−	0.938465i	$-0.612248\pi$
$733$	−18.7014	−0.690750	−0.345375	+	0.938465i	$0.612248\pi$
$734$	31.8482	1.17554
$735$	2.97391	0.109694
$736$	−9.48984	−0.349800
$737$	−9.99052	−0.368005
$738$	27.2878	1.00448
$739$	−0.0473672	−0.00174243	−0.000871216	−	1.00000i	$-0.500277\pi$
$739$	−0.0473672	−0.00174243	−0.000871216		1.00000i	$0.500277\pi$
$740$	11.1082	0.408345
$741$	0.812417	0.0298449
$742$	−56.5216	−2.07497
$743$	34.3450	1.26000	0.629998	−	0.776597i	$-0.283056\pi$
$743$	34.3450	1.26000	0.629998	+	0.776597i	$0.283056\pi$
$744$	−10.4288	−0.382337
$745$	35.6381	1.30568
$746$	10.4252	0.381694
$747$	−3.59003	−0.131352
$748$	0.444615	0.0162567
$749$	51.7928	1.89247
$750$	−0.651072	−0.0237738
$751$	20.4373	0.745769	0.372884	−	0.927878i	$-0.378369\pi$
$751$	20.4373	0.745769	0.372884	+	0.927878i	$0.378369\pi$
$752$	45.9391	1.67523
$753$	4.00800	0.146060
$754$	8.32011	0.303000
$755$	−65.9346	−2.39961
$756$	−3.43004	−0.124749
$757$	50.3336	1.82940	0.914702	−	0.404129i	$-0.132425\pi$
$757$	50.3336	1.82940	0.914702	+	0.404129i	$0.132425\pi$
$758$	18.9945	0.689911
$759$	1.69074	0.0613701
$760$	−13.3509	−0.484287
$761$	−39.9363	−1.44769	−0.723845	−	0.689963i	$-0.757627\pi$
$761$	−39.9363	−1.44769	−0.723845	+	0.689963i	$0.757627\pi$
$762$	5.13302	0.185950
$763$	−1.09643	−0.0396933
$764$	−9.07311	−0.328253
$765$	9.00347	0.325521
$766$	24.4476	0.883329
$767$	11.1476	0.402516
$768$	−4.48381	−0.161796
$769$	−22.8736	−0.824843	−0.412421	−	0.910993i	$-0.635317\pi$
$769$	−22.8736	−0.824843	−0.412421	+	0.910993i	$0.635317\pi$
$770$	−15.1373	−0.545512
$771$	2.09864	0.0755807
$772$	−5.91064	−0.212729
$773$	17.1108	0.615432	0.307716	−	0.951478i	$-0.400435\pi$
$773$	17.1108	0.615432	0.307716	+	0.951478i	$0.400435\pi$
$774$	4.38740	0.157702
$775$	51.5630	1.85220
$776$	−32.4273	−1.16407
$777$	−10.3463	−0.371170
$778$	58.5590	2.09944
$779$	10.6419	0.381286
$780$	−0.677347	−0.0242529
$781$	−4.39278	−0.157186
$782$	6.00328	0.214677
$783$	12.6176	0.450916
$784$	−9.87510	−0.352682
$785$	−28.7882	−1.02750
$786$	−0.442711	−0.0157910
$787$	−41.5507	−1.48112	−0.740562	−	0.671988i	$-0.765441\pi$
$787$	−41.5507	−1.48112	−0.740562	+	0.671988i	$0.765441\pi$
$788$	0.00634877	0.000226166 0
$789$	−4.12576	−0.146881
$790$	2.98942	0.106359
$791$	31.8048	1.13085
$792$	−6.82410	−0.242484
$793$	7.07044	0.251079
$794$	−6.64013	−0.235650
$795$	−16.9268	−0.600331
$796$	−9.46629	−0.335524
$797$	5.14360	0.182196	0.0910978	−	0.995842i	$-0.470962\pi$
$797$	5.14360	0.182196	0.0910978	+	0.995842i	$0.470962\pi$
$798$	−3.55464	−0.125833
$799$	−9.79189	−0.346412
$800$	13.0864	0.462673
$801$	−3.85756	−0.136300
$802$	7.36429	0.260042
$803$	−10.3751	−0.366129
$804$	1.95599	0.0689824
$805$	−37.1730	−1.31018
$806$	16.4182	0.578306
$807$	1.21838	0.0428890
$808$	19.9097	0.700419
$809$	−28.0238	−0.985265	−0.492632	−	0.870237i	$-0.663965\pi$
$809$	−28.0238	−0.985265	−0.492632	+	0.870237i	$0.663965\pi$
$810$	36.5836	1.28542
$811$	−22.5008	−0.790109	−0.395055	−	0.918658i	$-0.629274\pi$
$811$	−22.5008	−0.790109	−0.395055	+	0.918658i	$0.629274\pi$
$812$	−6.62092	−0.232349
$813$	−3.53823	−0.124091
$814$	12.1747	0.426722
$815$	67.6139	2.36841
$816$	2.06591	0.0723212
$817$	1.71104	0.0598616
$818$	−32.4471	−1.13448
$819$	−9.12988	−0.319024
$820$	−8.87261	−0.309845
$821$	6.29027	0.219532	0.109766	−	0.993957i	$-0.464990\pi$
$821$	6.29027	0.219532	0.109766	+	0.993957i	$0.464990\pi$
$822$	−0.329006	−0.0114754
$823$	−25.8850	−0.902294	−0.451147	−	0.892450i	$-0.648985\pi$
$823$	−25.8850	−0.902294	−0.451147	+	0.892450i	$0.648985\pi$
$824$	−5.21248	−0.181585
$825$	−2.33151	−0.0811729
$826$	−48.7750	−1.69710
$827$	52.7781	1.83527	0.917637	−	0.397420i	$-0.130094\pi$
$827$	52.7781	1.83527	0.917637	+	0.397420i	$0.130094\pi$
$828$	4.79038	0.166477
$829$	13.4481	0.467072	0.233536	−	0.972348i	$-0.424970\pi$
$829$	13.4481	0.467072	0.233536	+	0.972348i	$0.424970\pi$
$830$	6.41812	0.222776
$831$	11.7175	0.406477
$832$	−5.95063	−0.206301
$833$	2.10487	0.0729295
$834$	−6.40261	−0.221704
$835$	−78.1512	−2.70453
$836$	0.760751	0.0263111
$837$	24.8985	0.860618
$838$	42.9844	1.48487
$839$	16.5050	0.569817	0.284909	−	0.958555i	$-0.408037\pi$
$839$	16.5050	0.569817	0.284909	+	0.958555i	$0.408037\pi$
$840$	−10.3677	−0.357719
$841$	−4.64456	−0.160157
$842$	9.85987	0.339793
$843$	−3.83359	−0.132036
$844$	−0.280561	−0.00965732
$845$	37.9806	1.30657
$846$	−42.9610	−1.47703
$847$	−3.01743	−0.103680
$848$	56.2067	1.93015
$849$	8.99812	0.308815
$850$	−8.27845	−0.283948
$851$	29.8975	1.02487
$852$	0.860037	0.0294644
$853$	35.6388	1.22025	0.610124	−	0.792306i	$-0.291120\pi$
$853$	35.6388	1.22025	0.610124	+	0.792306i	$0.291120\pi$
$854$	−30.9359	−1.05860
$855$	15.4053	0.526849
$856$	−41.7422	−1.42672
$857$	34.5437	1.17999	0.589995	−	0.807407i	$-0.299130\pi$
$857$	34.5437	1.17999	0.589995	+	0.807407i	$0.299130\pi$
$858$	−0.742378	−0.0253444
$859$	−42.7504	−1.45863	−0.729313	−	0.684180i	$-0.760160\pi$
$859$	−42.7504	−1.45863	−0.729313	+	0.684180i	$0.760160\pi$
$860$	−1.42656	−0.0486454
$861$	8.26403	0.281637
$862$	−18.7936	−0.640113
$863$	−31.8884	−1.08550	−0.542748	−	0.839896i	$-0.682616\pi$
$863$	−31.8884	−1.08550	−0.542748	+	0.839896i	$0.682616\pi$
$864$	6.31908	0.214980
$865$	18.3048	0.622383
$866$	−10.5478	−0.358428
$867$	−0.440346	−0.0149549
$868$	−13.0652	−0.443461
$869$	0.595901	0.0202146
$870$	−10.9020	−0.369611
$871$	10.7724	0.365010
$872$	0.883661	0.0299245
$873$	37.4171	1.26638
$874$	10.2718	0.347450
$875$	2.85342	0.0964633
$876$	2.03128	0.0686305
$877$	−13.5433	−0.457324	−0.228662	−	0.973506i	$-0.573435\pi$
$877$	−13.5433	−0.457324	−0.228662	+	0.973506i	$0.573435\pi$
$878$	−2.09954	−0.0708560
$879$	−6.52629	−0.220126
$880$	15.0530	0.507437
$881$	17.6420	0.594373	0.297186	−	0.954820i	$-0.403952\pi$
$881$	17.6420	0.594373	0.297186	+	0.954820i	$0.403952\pi$
$882$	9.23492	0.310956
$883$	−3.78304	−0.127310	−0.0636548	−	0.997972i	$-0.520276\pi$
$883$	−3.78304	−0.127310	−0.0636548	+	0.997972i	$0.520276\pi$
$884$	−0.479412	−0.0161244
$885$	−14.6069	−0.491004
$886$	2.97863	0.100069
$887$	34.1269	1.14587	0.572935	−	0.819601i	$-0.305805\pi$
$887$	34.1269	1.14587	0.572935	+	0.819601i	$0.305805\pi$
$888$	8.33853	0.279823
$889$	−22.4963	−0.754501
$890$	6.89641	0.231168
$891$	7.29246	0.244306
$892$	−1.87248	−0.0626954
$893$	−16.7543	−0.560660
$894$	−7.64727	−0.255763
$895$	11.1359	0.372233
$896$	40.9520	1.36811
$897$	−1.82307	−0.0608706
$898$	−29.5093	−0.984739
$899$	48.0610	1.60292
$900$	−6.60587	−0.220196
$901$	−11.9804	−0.399126
$902$	−9.72446	−0.323789
$903$	1.32871	0.0442168
$904$	−25.6330	−0.852540
$905$	−27.3600	−0.909476
$906$	14.1483	0.470047
$907$	−56.2615	−1.86813	−0.934066	−	0.357100i	$-0.883765\pi$
$907$	−56.2615	−1.86813	−0.934066	+	0.357100i	$0.883765\pi$
$908$	−3.53612	−0.117350
$909$	−22.9733	−0.761975
$910$	16.3221	0.541071
$911$	1.81780	0.0602264	0.0301132	−	0.999546i	$-0.490413\pi$
$911$	1.81780	0.0602264	0.0301132	+	0.999546i	$0.490413\pi$
$912$	3.53484	0.117050
$913$	1.27937	0.0423409
$914$	35.9472	1.18903
$915$	−9.26451	−0.306275
$916$	2.82555	0.0933589
$917$	1.94025	0.0640726
$918$	−3.99746	−0.131936
$919$	−6.65570	−0.219551	−0.109776	−	0.993956i	$-0.535013\pi$
$919$	−6.65570	−0.219551	−0.109776	+	0.993956i	$0.535013\pi$
$920$	29.9595	0.987735
$921$	−14.6879	−0.483982
$922$	−18.6747	−0.615019
$923$	4.73658	0.155906
$924$	0.590765	0.0194347
$925$	−41.2283	−1.35558
$926$	61.0120	2.00498
$927$	6.01455	0.197544
$928$	12.1976	0.400405
$929$	−11.3351	−0.371892	−0.185946	−	0.982560i	$-0.559535\pi$
$929$	−11.3351	−0.371892	−0.185946	+	0.982560i	$0.559535\pi$
$930$	−21.5130	−0.705440
$931$	3.60151	0.118035
$932$	11.0725	0.362693
$933$	−11.6614	−0.381777
$934$	−45.7198	−1.49600
$935$	−3.20854	−0.104930
$936$	7.35820	0.240510
$937$	−7.54062	−0.246341	−0.123171	−	0.992386i	$-0.539306\pi$
$937$	−7.54062	−0.246341	−0.123171	+	0.992386i	$0.539306\pi$
$938$	−47.1335	−1.53896
$939$	−4.53118	−0.147869
$940$	13.9687	0.455610
$941$	20.9521	0.683018	0.341509	−	0.939879i	$-0.389062\pi$
$941$	20.9521	0.683018	0.341509	+	0.939879i	$0.389062\pi$
$942$	6.17742	0.201271
$943$	−23.8805	−0.777657
$944$	48.5033	1.57865
$945$	24.7527	0.805206
$946$	−1.56353	−0.0508346
$947$	−32.6602	−1.06131	−0.530657	−	0.847587i	$-0.678055\pi$
$947$	−32.6602	−1.06131	−0.530657	+	0.847587i	$0.678055\pi$
$948$	−0.116668	−0.00378920
$949$	11.1871	0.363148
$950$	−14.1647	−0.459564
$951$	0.733180	0.0237750
$952$	−7.33804	−0.237827
$953$	18.1681	0.588522	0.294261	−	0.955725i	$-0.404927\pi$
$953$	18.1681	0.588522	0.294261	+	0.955725i	$0.404927\pi$
$954$	−52.5630	−1.70179
$955$	65.4757	2.11874
$956$	−10.1535	−0.328388
$957$	−2.17316	−0.0702484
$958$	−7.57541	−0.244750
$959$	1.44192	0.0465620
$960$	7.79721	0.251654
$961$	63.8395	2.05934
$962$	−13.1275	−0.423248
$963$	48.1653	1.55211
$964$	−1.62746	−0.0524170
$965$	42.6539	1.37308
$966$	7.97664	0.256644
$967$	10.0610	0.323540	0.161770	−	0.986829i	$-0.448280\pi$
$967$	10.0610	0.323540	0.161770	+	0.986829i	$0.448280\pi$
$968$	2.43189	0.0781638
$969$	−0.753448	−0.0242042
$970$	−66.8929	−2.14780
$971$	19.3627	0.621377	0.310689	−	0.950512i	$-0.399440\pi$
$971$	19.3627	0.621377	0.310689	+	0.950512i	$0.399440\pi$
$972$	−4.83798	−0.155178
$973$	28.0604	0.899576
$974$	−17.8373	−0.571545
$975$	2.51399	0.0805122
$976$	30.7636	0.984718
$977$	−24.3772	−0.779897	−0.389948	−	0.920837i	$-0.627507\pi$
$977$	−24.3772	−0.779897	−0.389948	+	0.920837i	$0.627507\pi$
$978$	−14.5087	−0.463937
$979$	1.37471	0.0439359
$980$	−3.00273	−0.0959188
$981$	−1.01964	−0.0325545
$982$	−40.4562	−1.29101
$983$	20.6700	0.659271	0.329635	−	0.944108i	$-0.393074\pi$
$983$	20.6700	0.659271	0.329635	+	0.944108i	$0.393074\pi$
$984$	−6.66036	−0.212325
$985$	−0.0458156	−0.00145981
$986$	−7.71620	−0.245734
$987$	−13.0106	−0.414132
$988$	−0.820292	−0.0260970
$989$	−3.83958	−0.122091
$990$	−14.0772	−0.447401
$991$	1.51440	0.0481065	0.0240533	−	0.999711i	$-0.492343\pi$
$991$	1.51440	0.0481065	0.0240533	+	0.999711i	$0.492343\pi$
$992$	24.0697	0.764213
$993$	9.13558	0.289909
$994$	−20.7244	−0.657337
$995$	68.3130	2.16567
$996$	−0.250480	−0.00793676
$997$	−17.7295	−0.561499	−0.280750	−	0.959781i	$-0.590583\pi$
$997$	−17.7295	−0.561499	−0.280750	+	0.959781i	$0.590583\pi$
$998$	55.6847	1.76267
$999$	−19.9081	−0.629866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.21	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.21	✓	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)

\(f(q)\)	\(=\)	\(q-1.56353 q^{2} -0.440346 q^{3} +0.444615 q^{4} -3.20854 q^{5} +0.688493 q^{6} -3.01743 q^{7} +2.43189 q^{8} -2.80610 q^{9} +O(q^{10})\)	\(q-1.56353 q^{2} -0.440346 q^{3} +0.444615 q^{4} -3.20854 q^{5} +0.688493 q^{6} -3.01743 q^{7} +2.43189 q^{8} -2.80610 q^{9} +5.01664 q^{10} +1.00000 q^{11} -0.195784 q^{12} -1.07827 q^{13} +4.71783 q^{14} +1.41287 q^{15} -4.69155 q^{16} +1.00000 q^{17} +4.38740 q^{18} +1.71104 q^{19} -1.42656 q^{20} +1.32871 q^{21} -1.56353 q^{22} -3.83958 q^{23} -1.07087 q^{24} +5.29473 q^{25} +1.68590 q^{26} +2.55669 q^{27} -1.34159 q^{28} +4.93512 q^{29} -2.20906 q^{30} +9.73856 q^{31} +2.47158 q^{32} -0.440346 q^{33} -1.56353 q^{34} +9.68154 q^{35} -1.24763 q^{36} -7.78668 q^{37} -2.67525 q^{38} +0.474810 q^{39} -7.80280 q^{40} +6.21957 q^{41} -2.07748 q^{42} +1.00000 q^{43} +0.444615 q^{44} +9.00347 q^{45} +6.00328 q^{46} -9.79189 q^{47} +2.06591 q^{48} +2.10487 q^{49} -8.27845 q^{50} -0.440346 q^{51} -0.479412 q^{52} -11.9804 q^{53} -3.99746 q^{54} -3.20854 q^{55} -7.33804 q^{56} -0.753448 q^{57} -7.71620 q^{58} -10.3384 q^{59} +0.628182 q^{60} -6.55723 q^{61} -15.2265 q^{62} +8.46719 q^{63} +5.51871 q^{64} +3.45966 q^{65} +0.688493 q^{66} -9.99052 q^{67} +0.444615 q^{68} +1.69074 q^{69} -15.1373 q^{70} -4.39278 q^{71} -6.82410 q^{72} -10.3751 q^{73} +12.1747 q^{74} -2.33151 q^{75} +0.760751 q^{76} -3.01743 q^{77} -0.742378 q^{78} +0.595901 q^{79} +15.0530 q^{80} +7.29246 q^{81} -9.72446 q^{82} +1.27937 q^{83} +0.590765 q^{84} -3.20854 q^{85} -1.56353 q^{86} -2.17316 q^{87} +2.43189 q^{88} +1.37471 q^{89} -14.0772 q^{90} +3.25359 q^{91} -1.70713 q^{92} -4.28834 q^{93} +15.3099 q^{94} -5.48993 q^{95} -1.08835 q^{96} -13.3342 q^{97} -3.29102 q^{98} -2.80610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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