LMFDB - Embedded newform 8041.2.a.j.1.9

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			1.9
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30854 q^{2} -0.184135 q^{3} +3.32934 q^{4} -0.542742 q^{5} +0.425082 q^{6} -0.304747 q^{7} -3.06883 q^{8} -2.96609 q^{9} +O(q^{10})$	\(q-2.30854 q^{2} -0.184135 q^{3} +3.32934 q^{4} -0.542742 q^{5} +0.425082 q^{6} -0.304747 q^{7} -3.06883 q^{8} -2.96609 q^{9} +1.25294 q^{10} +1.00000 q^{11} -0.613048 q^{12} -5.72441 q^{13} +0.703519 q^{14} +0.0999378 q^{15} +0.425823 q^{16} +1.00000 q^{17} +6.84734 q^{18} +1.89879 q^{19} -1.80697 q^{20} +0.0561145 q^{21} -2.30854 q^{22} -4.78957 q^{23} +0.565079 q^{24} -4.70543 q^{25} +13.2150 q^{26} +1.09857 q^{27} -1.01461 q^{28} -8.33283 q^{29} -0.230710 q^{30} +0.864559 q^{31} +5.15463 q^{32} -0.184135 q^{33} -2.30854 q^{34} +0.165399 q^{35} -9.87513 q^{36} +6.24616 q^{37} -4.38342 q^{38} +1.05406 q^{39} +1.66558 q^{40} -3.09302 q^{41} -0.129542 q^{42} +1.00000 q^{43} +3.32934 q^{44} +1.60982 q^{45} +11.0569 q^{46} -7.40841 q^{47} -0.0784089 q^{48} -6.90713 q^{49} +10.8627 q^{50} -0.184135 q^{51} -19.0585 q^{52} +0.618875 q^{53} -2.53608 q^{54} -0.542742 q^{55} +0.935215 q^{56} -0.349633 q^{57} +19.2366 q^{58} -6.68953 q^{59} +0.332727 q^{60} -0.290764 q^{61} -1.99587 q^{62} +0.903907 q^{63} -12.7513 q^{64} +3.10688 q^{65} +0.425082 q^{66} -11.3482 q^{67} +3.32934 q^{68} +0.881927 q^{69} -0.381829 q^{70} +16.0839 q^{71} +9.10243 q^{72} -8.64826 q^{73} -14.4195 q^{74} +0.866435 q^{75} +6.32171 q^{76} -0.304747 q^{77} -2.43334 q^{78} +6.41459 q^{79} -0.231112 q^{80} +8.69600 q^{81} +7.14034 q^{82} -5.43137 q^{83} +0.186824 q^{84} -0.542742 q^{85} -2.30854 q^{86} +1.53437 q^{87} -3.06883 q^{88} -13.4338 q^{89} -3.71634 q^{90} +1.74449 q^{91} -15.9461 q^{92} -0.159196 q^{93} +17.1026 q^{94} -1.03055 q^{95} -0.949148 q^{96} +0.218025 q^{97} +15.9454 q^{98} -2.96609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.30854	−1.63238	−0.816191	−	0.577782i	$-0.803918\pi$
$2$	−2.30854	−1.63238	−0.816191	+	0.577782i	$0.803918\pi$
$3$	−0.184135	−0.106310	−0.0531552	−	0.998586i	$-0.516928\pi$
$3$	−0.184135	−0.106310	−0.0531552	+	0.998586i	$0.516928\pi$
$4$	3.32934	1.66467
$5$	−0.542742	−0.242722	−0.121361	−	0.992608i	$-0.538726\pi$
$5$	−0.542742	−0.242722	−0.121361	+	0.992608i	$0.538726\pi$
$6$	0.425082	0.173539
$7$	−0.304747	−0.115183	−0.0575917	−	0.998340i	$-0.518342\pi$
$7$	−0.304747	−0.115183	−0.0575917	+	0.998340i	$0.518342\pi$
$8$	−3.06883	−1.08499
$9$	−2.96609	−0.988698
$10$	1.25294	0.396214
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.613048	−0.176972
$13$	−5.72441	−1.58766	−0.793832	−	0.608137i	$-0.791917\pi$
$13$	−5.72441	−1.58766	−0.793832	+	0.608137i	$0.791917\pi$
$14$	0.703519	0.188023
$15$	0.0999378	0.0258038
$16$	0.425823	0.106456
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.84734	1.61393
$19$	1.89879	0.435612	0.217806	−	0.975992i	$-0.430110\pi$
$19$	1.89879	0.435612	0.217806	+	0.975992i	$0.430110\pi$
$20$	−1.80697	−0.404051
$21$	0.0561145	0.0122452
$22$	−2.30854	−0.492182
$23$	−4.78957	−0.998694	−0.499347	−	0.866402i	$-0.666427\pi$
$23$	−4.78957	−0.998694	−0.499347	+	0.866402i	$0.666427\pi$
$24$	0.565079	0.115346
$25$	−4.70543	−0.941086
$26$	13.2150	2.59167
$27$	1.09857	0.211419
$28$	−1.01461	−0.191742
$29$	−8.33283	−1.54737	−0.773684	−	0.633572i	$-0.781588\pi$
$29$	−8.33283	−1.54737	−0.773684	+	0.633572i	$0.781588\pi$
$30$	−0.230710	−0.0421217
$31$	0.864559	0.155279	0.0776397	−	0.996981i	$-0.475262\pi$
$31$	0.864559	0.155279	0.0776397	+	0.996981i	$0.475262\pi$
$32$	5.15463	0.911218
$33$	−0.184135	−0.0320538
$34$	−2.30854	−0.395911
$35$	0.165399	0.0279575
$36$	−9.87513	−1.64586
$37$	6.24616	1.02686	0.513431	−	0.858131i	$-0.328374\pi$
$37$	6.24616	1.02686	0.513431	+	0.858131i	$0.328374\pi$
$38$	−4.38342	−0.711085
$39$	1.05406	0.168785
$40$	1.66558	0.263352
$41$	−3.09302	−0.483048	−0.241524	−	0.970395i	$-0.577647\pi$
$41$	−3.09302	−0.483048	−0.241524	+	0.970395i	$0.577647\pi$
$42$	−0.129542	−0.0199888
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.32934	0.501917
$45$	1.60982	0.239978
$46$	11.0569	1.63025
$47$	−7.40841	−1.08063	−0.540314	−	0.841464i	$-0.681694\pi$
$47$	−7.40841	−1.08063	−0.540314	+	0.841464i	$0.681694\pi$
$48$	−0.0784089	−0.0113173
$49$	−6.90713	−0.986733
$50$	10.8627	1.53621
$51$	−0.184135	−0.0257841
$52$	−19.0585	−2.64294
$53$	0.618875	0.0850090	0.0425045	−	0.999096i	$-0.486466\pi$
$53$	0.618875	0.0850090	0.0425045	+	0.999096i	$0.486466\pi$
$54$	−2.53608	−0.345117
$55$	−0.542742	−0.0731833
$56$	0.935215	0.124973
$57$	−0.349633	−0.0463101
$58$	19.2366	2.52590
$59$	−6.68953	−0.870903	−0.435451	−	0.900212i	$-0.643411\pi$
$59$	−6.68953	−0.870903	−0.435451	+	0.900212i	$0.643411\pi$
$60$	0.332727	0.0429549
$61$	−0.290764	−0.0372285	−0.0186142	−	0.999827i	$-0.505925\pi$
$61$	−0.290764	−0.0372285	−0.0186142	+	0.999827i	$0.505925\pi$
$62$	−1.99587	−0.253475
$63$	0.903907	0.113882
$64$	−12.7513	−1.59391
$65$	3.10688	0.385361
$66$	0.425082	0.0523240
$67$	−11.3482	−1.38640	−0.693201	−	0.720744i	$-0.743800\pi$
$67$	−11.3482	−1.38640	−0.693201	+	0.720744i	$0.743800\pi$
$68$	3.32934	0.403742
$69$	0.881927	0.106172
$70$	−0.381829	−0.0456373
$71$	16.0839	1.90881	0.954403	−	0.298522i	$-0.0964937\pi$
$71$	16.0839	1.90881	0.954403	+	0.298522i	$0.0964937\pi$
$72$	9.10243	1.07273
$73$	−8.64826	−1.01220	−0.506101	−	0.862474i	$-0.668914\pi$
$73$	−8.64826	−1.01220	−0.506101	+	0.862474i	$0.668914\pi$
$74$	−14.4195	−1.67623
$75$	0.866435	0.100047
$76$	6.32171	0.725150
$77$	−0.304747	−0.0347291
$78$	−2.43334	−0.275522
$79$	6.41459	0.721698	0.360849	−	0.932624i	$-0.382487\pi$
$79$	6.41459	0.721698	0.360849	+	0.932624i	$0.382487\pi$
$80$	−0.231112	−0.0258391
$81$	8.69600	0.966222
$82$	7.14034	0.788519
$83$	−5.43137	−0.596170	−0.298085	−	0.954539i	$-0.596348\pi$
$83$	−5.43137	−0.596170	−0.298085	+	0.954539i	$0.596348\pi$
$84$	0.186824	0.0203842
$85$	−0.542742	−0.0588686
$86$	−2.30854	−0.248936
$87$	1.53437	0.164501
$88$	−3.06883	−0.327138
$89$	−13.4338	−1.42398	−0.711990	−	0.702190i	$-0.752206\pi$
$89$	−13.4338	−1.42398	−0.711990	+	0.702190i	$0.752206\pi$
$90$	−3.71634	−0.391736
$91$	1.74449	0.182873
$92$	−15.9461	−1.66250
$93$	−0.159196	−0.0165078
$94$	17.1026	1.76400
$95$	−1.03055	−0.105732
$96$	−0.949148	−0.0968720
$97$	0.218025	0.0221370	0.0110685	−	0.999939i	$-0.496477\pi$
$97$	0.218025	0.0221370	0.0110685	+	0.999939i	$0.496477\pi$
$98$	15.9454	1.61072
$99$	−2.96609	−0.298104
$100$	−15.6660	−1.56660
$101$	2.59099	0.257813	0.128907	−	0.991657i	$-0.458853\pi$
$101$	2.59099	0.257813	0.128907	+	0.991657i	$0.458853\pi$
$102$	0.425082	0.0420894
$103$	−6.08702	−0.599772	−0.299886	−	0.953975i	$-0.596949\pi$
$103$	−6.08702	−0.599772	−0.299886	+	0.953975i	$0.596949\pi$
$104$	17.5672	1.72261
$105$	−0.0304557	−0.00297217
$106$	−1.42870	−0.138767
$107$	−14.2140	−1.37412	−0.687061	−	0.726599i	$-0.741100\pi$
$107$	−14.2140	−1.37412	−0.687061	+	0.726599i	$0.741100\pi$
$108$	3.65750	0.351943
$109$	−7.35830	−0.704797	−0.352399	−	0.935850i	$-0.614634\pi$
$109$	−7.35830	−0.704797	−0.352399	+	0.935850i	$0.614634\pi$
$110$	1.25294	0.119463
$111$	−1.15014	−0.109166
$112$	−0.129768	−0.0122619
$113$	12.4767	1.17371	0.586853	−	0.809694i	$-0.300367\pi$
$113$	12.4767	1.17371	0.586853	+	0.809694i	$0.300367\pi$
$114$	0.807142	0.0755957
$115$	2.59950	0.242405
$116$	−27.7428	−2.57586
$117$	16.9791	1.56972
$118$	15.4430	1.42165
$119$	−0.304747	−0.0279361
$120$	−0.306692	−0.0279970
$121$	1.00000	0.0909091
$122$	0.671239	0.0607711
$123$	0.569533	0.0513531
$124$	2.87841	0.258489
$125$	5.26755	0.471144
$126$	−2.08670	−0.185898
$127$	−5.67904	−0.503933	−0.251967	−	0.967736i	$-0.581077\pi$
$127$	−5.67904	−0.503933	−0.251967	+	0.967736i	$0.581077\pi$
$128$	19.1276	1.69065
$129$	−0.184135	−0.0162122
$130$	−7.17234	−0.629056
$131$	−10.2293	−0.893736	−0.446868	−	0.894600i	$-0.647461\pi$
$131$	−10.2293	−0.893736	−0.446868	+	0.894600i	$0.647461\pi$
$132$	−0.613048	−0.0533590
$133$	−0.578649	−0.0501753
$134$	26.1977	2.26314
$135$	−0.596239	−0.0513160
$136$	−3.06883	−0.263150
$137$	14.9785	1.27970	0.639848	−	0.768502i	$-0.278997\pi$
$137$	14.9785	1.27970	0.639848	+	0.768502i	$0.278997\pi$
$138$	−2.03596	−0.173313
$139$	1.37038	0.116234	0.0581170	−	0.998310i	$-0.481490\pi$
$139$	1.37038	0.116234	0.0581170	+	0.998310i	$0.481490\pi$
$140$	0.550669	0.0465400
$141$	1.36415	0.114882
$142$	−37.1302	−3.11590
$143$	−5.72441	−0.478699
$144$	−1.26303	−0.105252
$145$	4.52258	0.375580
$146$	19.9648	1.65230
$147$	1.27184	0.104900
$148$	20.7956	1.70939
$149$	9.65315	0.790817	0.395408	−	0.918505i	$-0.370603\pi$
$149$	9.65315	0.790817	0.395408	+	0.918505i	$0.370603\pi$
$150$	−2.00020	−0.163315
$151$	−19.2433	−1.56600	−0.782999	−	0.622023i	$-0.786311\pi$
$151$	−19.2433	−1.56600	−0.782999	+	0.622023i	$0.786311\pi$
$152$	−5.82706	−0.472637
$153$	−2.96609	−0.239795
$154$	0.703519	0.0566911
$155$	−0.469233	−0.0376897
$156$	3.50934	0.280972
$157$	−21.0854	−1.68280	−0.841400	−	0.540413i	$-0.818268\pi$
$157$	−21.0854	−1.68280	−0.841400	+	0.540413i	$0.818268\pi$
$158$	−14.8083	−1.17809
$159$	−0.113957	−0.00903734
$160$	−2.79763	−0.221172
$161$	1.45961	0.115033
$162$	−20.0750	−1.57724
$163$	14.9433	1.17045	0.585224	−	0.810872i	$-0.301007\pi$
$163$	14.9433	1.17045	0.585224	+	0.810872i	$0.301007\pi$
$164$	−10.2977	−0.804116
$165$	0.0999378	0.00778015
$166$	12.5385	0.973177
$167$	−4.50817	−0.348853	−0.174426	−	0.984670i	$-0.555807\pi$
$167$	−4.50817	−0.348853	−0.174426	+	0.984670i	$0.555807\pi$
$168$	−0.172206	−0.0132860
$169$	19.7688	1.52068
$170$	1.25294	0.0960961
$171$	−5.63199	−0.430689
$172$	3.32934	0.253860
$173$	21.4508	1.63087	0.815437	−	0.578846i	$-0.196497\pi$
$173$	21.4508	1.63087	0.815437	+	0.578846i	$0.196497\pi$
$174$	−3.54214	−0.268529
$175$	1.43396	0.108398
$176$	0.425823	0.0320976
$177$	1.23178	0.0925860
$178$	31.0124	2.32448
$179$	−17.7072	−1.32350	−0.661749	−	0.749726i	$-0.730185\pi$
$179$	−17.7072	−1.32350	−0.661749	+	0.749726i	$0.730185\pi$
$180$	5.35965	0.399485
$181$	−3.26694	−0.242829	−0.121415	−	0.992602i	$-0.538743\pi$
$181$	−3.26694	−0.242829	−0.121415	+	0.992602i	$0.538743\pi$
$182$	−4.02723	−0.298518
$183$	0.0535398	0.00395777
$184$	14.6984	1.08358
$185$	−3.39006	−0.249242
$186$	0.367509	0.0269471
$187$	1.00000	0.0731272
$188$	−24.6651	−1.79889
$189$	−0.334785	−0.0243520
$190$	2.37907	0.172596
$191$	20.7606	1.50218	0.751092	−	0.660197i	$-0.229527\pi$
$191$	20.7606	1.50218	0.751092	+	0.660197i	$0.229527\pi$
$192$	2.34796	0.169449
$193$	18.0198	1.29709	0.648546	−	0.761175i	$-0.275377\pi$
$193$	18.0198	1.29709	0.648546	+	0.761175i	$0.275377\pi$
$194$	−0.503318	−0.0361361
$195$	−0.572085	−0.0409678
$196$	−22.9962	−1.64258
$197$	−13.4070	−0.955208	−0.477604	−	0.878575i	$-0.658495\pi$
$197$	−13.4070	−0.955208	−0.477604	+	0.878575i	$0.658495\pi$
$198$	6.84734	0.486619
$199$	17.5992	1.24757	0.623787	−	0.781594i	$-0.285593\pi$
$199$	17.5992	1.24757	0.623787	+	0.781594i	$0.285593\pi$
$200$	14.4402	1.02107
$201$	2.08960	0.147389
$202$	−5.98140	−0.420850
$203$	2.53940	0.178231
$204$	−0.613048	−0.0429219
$205$	1.67871	0.117246
$206$	14.0521	0.979057
$207$	14.2063	0.987407
$208$	−2.43758	−0.169016
$209$	1.89879	0.131342
$210$	0.0703081	0.00485172
$211$	4.29967	0.296002	0.148001	−	0.988987i	$-0.452716\pi$
$211$	4.29967	0.296002	0.148001	+	0.988987i	$0.452716\pi$
$212$	2.06045	0.141512
$213$	−2.96161	−0.202926
$214$	32.8136	2.24309
$215$	−0.542742	−0.0370147
$216$	−3.37131	−0.229389
$217$	−0.263472	−0.0178856
$218$	16.9869	1.15050
$219$	1.59245	0.107608
$220$	−1.80697	−0.121826
$221$	−5.72441	−0.385065
$222$	2.65513	0.178201
$223$	−22.2114	−1.48738	−0.743692	−	0.668522i	$-0.766927\pi$
$223$	−22.2114	−1.48738	−0.743692	+	0.668522i	$0.766927\pi$
$224$	−1.57086	−0.104957
$225$	13.9568	0.930450
$226$	−28.8028	−1.91593
$227$	−14.6353	−0.971376	−0.485688	−	0.874132i	$-0.661431\pi$
$227$	−14.6353	−0.971376	−0.485688	+	0.874132i	$0.661431\pi$
$228$	−1.16405	−0.0770910
$229$	−25.1737	−1.66352	−0.831762	−	0.555132i	$-0.812668\pi$
$229$	−25.1737	−1.66352	−0.831762	+	0.555132i	$0.812668\pi$
$230$	−6.00104	−0.395697
$231$	0.0561145	0.00369207
$232$	25.5720	1.67889
$233$	17.5381	1.14896	0.574480	−	0.818519i	$-0.305204\pi$
$233$	17.5381	1.14896	0.574480	+	0.818519i	$0.305204\pi$
$234$	−39.1969	−2.56238
$235$	4.02086	0.262292
$236$	−22.2717	−1.44977
$237$	−1.18115	−0.0767240
$238$	0.703519	0.0456023
$239$	−1.97029	−0.127447	−0.0637236	−	0.997968i	$-0.520298\pi$
$239$	−1.97029	−0.127447	−0.0637236	+	0.997968i	$0.520298\pi$
$240$	0.0425558	0.00274696
$241$	23.4376	1.50975	0.754875	−	0.655869i	$-0.227698\pi$
$241$	23.4376	1.50975	0.754875	+	0.655869i	$0.227698\pi$
$242$	−2.30854	−0.148398
$243$	−4.89694	−0.314139
$244$	−0.968051	−0.0619731
$245$	3.74879	0.239501
$246$	−1.31479	−0.0838278
$247$	−10.8694	−0.691606
$248$	−2.65318	−0.168477
$249$	1.00011	0.0633791
$250$	−12.1603	−0.769086
$251$	23.0204	1.45303	0.726517	−	0.687149i	$-0.241138\pi$
$251$	23.0204	1.45303	0.726517	+	0.687149i	$0.241138\pi$
$252$	3.00941	0.189575
$253$	−4.78957	−0.301118
$254$	13.1103	0.822611
$255$	0.0999378	0.00625835
$256$	−18.6541	−1.16588
$257$	−13.2455	−0.826233	−0.413116	−	0.910678i	$-0.635560\pi$
$257$	−13.2455	−0.826233	−0.413116	+	0.910678i	$0.635560\pi$
$258$	0.425082	0.0264645
$259$	−1.90350	−0.118278
$260$	10.3438	0.641498
$261$	24.7160	1.52988
$262$	23.6147	1.45892
$263$	8.76348	0.540379	0.270190	−	0.962807i	$-0.412914\pi$
$263$	8.76348	0.540379	0.270190	+	0.962807i	$0.412914\pi$
$264$	0.565079	0.0347782
$265$	−0.335890	−0.0206335
$266$	1.33583	0.0819052
$267$	2.47363	0.151384
$268$	−37.7820	−2.30790
$269$	31.7833	1.93786	0.968930	−	0.247336i	$-0.0795551\pi$
$269$	31.7833	1.93786	0.968930	+	0.247336i	$0.0795551\pi$
$270$	1.37644	0.0837674
$271$	−16.0076	−0.972395	−0.486197	−	0.873849i	$-0.661616\pi$
$271$	−16.0076	−0.972395	−0.486197	+	0.873849i	$0.661616\pi$
$272$	0.425823	0.0258193
$273$	−0.321222	−0.0194413
$274$	−34.5783	−2.08895
$275$	−4.70543	−0.283748
$276$	2.93624	0.176741
$277$	−14.9075	−0.895704	−0.447852	−	0.894108i	$-0.647811\pi$
$277$	−14.9075	−0.895704	−0.447852	+	0.894108i	$0.647811\pi$
$278$	−3.16357	−0.189738
$279$	−2.56436	−0.153524
$280$	−0.507581	−0.0303337
$281$	20.0100	1.19370	0.596849	−	0.802354i	$-0.296419\pi$
$281$	20.0100	1.19370	0.596849	+	0.802354i	$0.296419\pi$
$282$	−3.14918	−0.187531
$283$	−24.7266	−1.46984	−0.734921	−	0.678152i	$-0.762781\pi$
$283$	−24.7266	−1.46984	−0.734921	+	0.678152i	$0.762781\pi$
$284$	53.5487	3.17753
$285$	0.189761	0.0112405
$286$	13.2150	0.781419
$287$	0.942587	0.0556391
$288$	−15.2891	−0.900920
$289$	1.00000	0.0588235
$290$	−10.4405	−0.613089
$291$	−0.0401460	−0.00235340
$292$	−28.7930	−1.68498
$293$	−12.9573	−0.756972	−0.378486	−	0.925607i	$-0.623555\pi$
$293$	−12.9573	−0.756972	−0.378486	+	0.925607i	$0.623555\pi$
$294$	−2.93610	−0.171237
$295$	3.63069	0.211387
$296$	−19.1684	−1.11414
$297$	1.09857	0.0637453
$298$	−22.2846	−1.29091
$299$	27.4174	1.58559
$300$	2.88466	0.166546
$301$	−0.304747	−0.0175653
$302$	44.4239	2.55631
$303$	−0.477092	−0.0274082
$304$	0.808547	0.0463734
$305$	0.157810	0.00903616
$306$	6.84734	0.391436
$307$	4.53338	0.258733	0.129367	−	0.991597i	$-0.458706\pi$
$307$	4.53338	0.258733	0.129367	+	0.991597i	$0.458706\pi$
$308$	−1.01461	−0.0578125
$309$	1.12083	0.0637620
$310$	1.08324	0.0615239
$311$	−11.8619	−0.672627	−0.336313	−	0.941750i	$-0.609180\pi$
$311$	−11.8619	−0.672627	−0.336313	+	0.941750i	$0.609180\pi$
$312$	−3.23474	−0.183131
$313$	6.73806	0.380858	0.190429	−	0.981701i	$-0.439012\pi$
$313$	6.73806	0.380858	0.190429	+	0.981701i	$0.439012\pi$
$314$	48.6765	2.74697
$315$	−0.490588	−0.0276415
$316$	21.3563	1.20139
$317$	2.35683	0.132373	0.0661865	−	0.997807i	$-0.478917\pi$
$317$	2.35683	0.132373	0.0661865	+	0.997807i	$0.478917\pi$
$318$	0.263073	0.0147524
$319$	−8.33283	−0.466549
$320$	6.92066	0.386877
$321$	2.61730	0.146084
$322$	−3.36955	−0.187778
$323$	1.89879	0.105651
$324$	28.9519	1.60844
$325$	26.9358	1.49413
$326$	−34.4971	−1.91062
$327$	1.35492	0.0749273
$328$	9.49194	0.524105
$329$	2.25769	0.124470
$330$	−0.230710	−0.0127002
$331$	16.3735	0.899969	0.449984	−	0.893036i	$-0.351430\pi$
$331$	16.3735	0.899969	0.449984	+	0.893036i	$0.351430\pi$
$332$	−18.0829	−0.992426
$333$	−18.5267	−1.01526
$334$	10.4073	0.569461
$335$	6.15914	0.336510
$336$	0.0238948	0.00130357
$337$	−12.7380	−0.693885	−0.346942	−	0.937886i	$-0.612780\pi$
$337$	−12.7380	−0.693885	−0.346942	+	0.937886i	$0.612780\pi$
$338$	−45.6371	−2.48233
$339$	−2.29739	−0.124777
$340$	−1.80697	−0.0979969
$341$	0.864559	0.0468185
$342$	13.0016	0.703048
$343$	4.23815	0.228839
$344$	−3.06883	−0.165460
$345$	−0.478659	−0.0257701
$346$	−49.5200	−2.66221
$347$	−33.1422	−1.77917	−0.889583	−	0.456774i	$-0.849005\pi$
$347$	−33.1422	−1.77917	−0.889583	+	0.456774i	$0.849005\pi$
$348$	5.10843	0.273840
$349$	−30.3445	−1.62430	−0.812151	−	0.583447i	$-0.801704\pi$
$349$	−30.3445	−1.62430	−0.812151	+	0.583447i	$0.801704\pi$
$350$	−3.31036	−0.176946
$351$	−6.28864	−0.335663
$352$	5.15463	0.274743
$353$	−4.96394	−0.264204	−0.132102	−	0.991236i	$-0.542173\pi$
$353$	−4.96394	−0.264204	−0.132102	+	0.991236i	$0.542173\pi$
$354$	−2.84360	−0.151136
$355$	−8.72940	−0.463308
$356$	−44.7257	−2.37046
$357$	0.0561145	0.00296990
$358$	40.8777	2.16045
$359$	−23.0991	−1.21912	−0.609562	−	0.792738i	$-0.708655\pi$
$359$	−23.0991	−1.21912	−0.609562	+	0.792738i	$0.708655\pi$
$360$	−4.94027	−0.260375
$361$	−15.3946	−0.810242
$362$	7.54184	0.396390
$363$	−0.184135	−0.00966458
$364$	5.80801	0.304423
$365$	4.69378	0.245683
$366$	−0.123599	−0.00646060
$367$	33.7485	1.76166	0.880828	−	0.473436i	$-0.156986\pi$
$367$	33.7485	1.76166	0.880828	+	0.473436i	$0.156986\pi$
$368$	−2.03951	−0.106317
$369$	9.17418	0.477589
$370$	7.82607	0.406858
$371$	−0.188600	−0.00979163
$372$	−0.530016	−0.0274801
$373$	12.0955	0.626282	0.313141	−	0.949707i	$-0.398619\pi$
$373$	12.0955	0.626282	0.313141	+	0.949707i	$0.398619\pi$
$374$	−2.30854	−0.119372
$375$	−0.969940	−0.0500875
$376$	22.7351	1.17248
$377$	47.7005	2.45670
$378$	0.772862	0.0397517
$379$	18.0263	0.925950	0.462975	−	0.886371i	$-0.346782\pi$
$379$	18.0263	0.925950	0.462975	+	0.886371i	$0.346782\pi$
$380$	−3.43106	−0.176010
$381$	1.04571	0.0535733
$382$	−47.9266	−2.45214
$383$	−21.2909	−1.08792	−0.543958	−	0.839112i	$-0.683075\pi$
$383$	−21.2909	−1.08792	−0.543958	+	0.839112i	$0.683075\pi$
$384$	−3.52206	−0.179734
$385$	0.165399	0.00842950
$386$	−41.5993	−2.11735
$387$	−2.96609	−0.150775
$388$	0.725878	0.0368509
$389$	25.4585	1.29080	0.645398	−	0.763847i	$-0.276692\pi$
$389$	25.4585	1.29080	0.645398	+	0.763847i	$0.276692\pi$
$390$	1.32068	0.0668752
$391$	−4.78957	−0.242219
$392$	21.1968	1.07060
$393$	1.88357	0.0950135
$394$	30.9505	1.55926
$395$	−3.48147	−0.175172
$396$	−9.87513	−0.496244
$397$	−13.0162	−0.653262	−0.326631	−	0.945152i	$-0.605913\pi$
$397$	−13.0162	−0.653262	−0.326631	+	0.945152i	$0.605913\pi$
$398$	−40.6284	−2.03652
$399$	0.106550	0.00533415
$400$	−2.00368	−0.100184
$401$	−33.5385	−1.67483	−0.837416	−	0.546566i	$-0.815935\pi$
$401$	−33.5385	−1.67483	−0.837416	+	0.546566i	$0.815935\pi$
$402$	−4.82392	−0.240595
$403$	−4.94909	−0.246532
$404$	8.62629	0.429174
$405$	−4.71968	−0.234523
$406$	−5.86230	−0.290941
$407$	6.24616	0.309611
$408$	0.565079	0.0279756
$409$	−16.2233	−0.802189	−0.401095	−	0.916037i	$-0.631370\pi$
$409$	−16.2233	−0.802189	−0.401095	+	0.916037i	$0.631370\pi$
$410$	−3.87536	−0.191391
$411$	−2.75806	−0.136045
$412$	−20.2658	−0.998422
$413$	2.03861	0.100314
$414$	−32.7958	−1.61183
$415$	2.94783	0.144703
$416$	−29.5072	−1.44671
$417$	−0.252335	−0.0123569
$418$	−4.38342	−0.214400
$419$	31.4749	1.53765	0.768824	−	0.639460i	$-0.220842\pi$
$419$	31.4749	1.53765	0.768824	+	0.639460i	$0.220842\pi$
$420$	−0.101397	−0.00494769
$421$	32.9680	1.60676	0.803382	−	0.595464i	$-0.203032\pi$
$421$	32.9680	1.60676	0.803382	+	0.595464i	$0.203032\pi$
$422$	−9.92595	−0.483188
$423$	21.9740	1.06841
$424$	−1.89922	−0.0922343
$425$	−4.70543	−0.228247
$426$	6.83697	0.331252
$427$	0.0886093	0.00428810
$428$	−47.3234	−2.28746
$429$	1.05406	0.0508907
$430$	1.25294	0.0604221
$431$	−16.6396	−0.801502	−0.400751	−	0.916187i	$-0.631251\pi$
$431$	−16.6396	−0.801502	−0.400751	+	0.916187i	$0.631251\pi$
$432$	0.467795	0.0225068
$433$	−25.0432	−1.20350	−0.601750	−	0.798685i	$-0.705530\pi$
$433$	−25.0432	−1.20350	−0.601750	+	0.798685i	$0.705530\pi$
$434$	0.608234	0.0291961
$435$	−0.832765	−0.0399280
$436$	−24.4983	−1.17325
$437$	−9.09438	−0.435043
$438$	−3.67622	−0.175657
$439$	−12.4601	−0.594688	−0.297344	−	0.954770i	$-0.596101\pi$
$439$	−12.4601	−0.594688	−0.297344	+	0.954770i	$0.596101\pi$
$440$	1.66558	0.0794035
$441$	20.4872	0.975581
$442$	13.2150	0.628573
$443$	−5.16365	−0.245332	−0.122666	−	0.992448i	$-0.539144\pi$
$443$	−5.16365	−0.245332	−0.122666	+	0.992448i	$0.539144\pi$
$444$	−3.82920	−0.181726
$445$	7.29108	0.345631
$446$	51.2758	2.42798
$447$	−1.77748	−0.0840720
$448$	3.88591	0.183592
$449$	14.4908	0.683865	0.341933	−	0.939724i	$-0.388919\pi$
$449$	14.4908	0.683865	0.341933	+	0.939724i	$0.388919\pi$
$450$	−32.2197	−1.51885
$451$	−3.09302	−0.145645
$452$	41.5390	1.95383
$453$	3.54337	0.166482
$454$	33.7860	1.58566
$455$	−0.946810	−0.0443871
$456$	1.07297	0.0502462
$457$	−26.4648	−1.23797	−0.618985	−	0.785402i	$-0.712456\pi$
$457$	−26.4648	−1.23797	−0.618985	+	0.785402i	$0.712456\pi$
$458$	58.1144	2.71551
$459$	1.09857	0.0512767
$460$	8.65462	0.403524
$461$	−4.18075	−0.194717	−0.0973585	−	0.995249i	$-0.531039\pi$
$461$	−4.18075	−0.194717	−0.0973585	+	0.995249i	$0.531039\pi$
$462$	−0.129542	−0.00602686
$463$	15.0713	0.700424	0.350212	−	0.936670i	$-0.386110\pi$
$463$	15.0713	0.700424	0.350212	+	0.936670i	$0.386110\pi$
$464$	−3.54831	−0.164726
$465$	0.0864022	0.00400680
$466$	−40.4874	−1.87554
$467$	3.97247	0.183824	0.0919121	−	0.995767i	$-0.470702\pi$
$467$	3.97247	0.183824	0.0919121	+	0.995767i	$0.470702\pi$
$468$	56.5293	2.61307
$469$	3.45832	0.159691
$470$	−9.28229	−0.428160
$471$	3.88257	0.178899
$472$	20.5290	0.944925
$473$	1.00000	0.0459800
$474$	2.72673	0.125243
$475$	−8.93462	−0.409948
$476$	−1.01461	−0.0465043
$477$	−1.83564	−0.0840483
$478$	4.54848	0.208043
$479$	−4.96724	−0.226959	−0.113479	−	0.993540i	$-0.536200\pi$
$479$	−4.96724	−0.226959	−0.113479	+	0.993540i	$0.536200\pi$
$480$	0.515143	0.0235129
$481$	−35.7556	−1.63031
$482$	−54.1066	−2.46449
$483$	−0.268764	−0.0122292
$484$	3.32934	0.151334
$485$	−0.118331	−0.00537314
$486$	11.3048	0.512794
$487$	−32.3995	−1.46816	−0.734081	−	0.679062i	$-0.762387\pi$
$487$	−32.3995	−1.46816	−0.734081	+	0.679062i	$0.762387\pi$
$488$	0.892304	0.0403927
$489$	−2.75158	−0.124431
$490$	−8.65422	−0.390958
$491$	25.5740	1.15414	0.577069	−	0.816695i	$-0.304196\pi$
$491$	25.5740	1.15414	0.577069	+	0.816695i	$0.304196\pi$
$492$	1.89617	0.0854859
$493$	−8.33283	−0.375292
$494$	25.0925	1.12896
$495$	1.60982	0.0723562
$496$	0.368149	0.0165304
$497$	−4.90151	−0.219863
$498$	−2.30878	−0.103459
$499$	−8.40594	−0.376302	−0.188151	−	0.982140i	$-0.560249\pi$
$499$	−8.40594	−0.376302	−0.188151	+	0.982140i	$0.560249\pi$
$500$	17.5374	0.784299
$501$	0.830112	0.0370867
$502$	−53.1434	−2.37191
$503$	8.07205	0.359915	0.179957	−	0.983674i	$-0.442404\pi$
$503$	8.07205	0.359915	0.179957	+	0.983674i	$0.442404\pi$
$504$	−2.77394	−0.123561
$505$	−1.40624	−0.0625769
$506$	11.0569	0.491539
$507$	−3.64013	−0.161664
$508$	−18.9074	−0.838882
$509$	44.1180	1.95550	0.977748	−	0.209782i	$-0.0672756\pi$
$509$	44.1180	1.95550	0.977748	+	0.209782i	$0.0672756\pi$
$510$	−0.230710	−0.0102160
$511$	2.63553	0.116589
$512$	4.80851	0.212508
$513$	2.08595	0.0920968
$514$	30.5778	1.34873
$515$	3.30368	0.145578
$516$	−0.613048	−0.0269879
$517$	−7.40841	−0.325822
$518$	4.39429	0.193074
$519$	−3.94984	−0.173379
$520$	−9.53447	−0.418114
$521$	−2.04995	−0.0898101	−0.0449050	−	0.998991i	$-0.514299\pi$
$521$	−2.04995	−0.0898101	−0.0449050	+	0.998991i	$0.514299\pi$
$522$	−57.0577	−2.49735
$523$	10.7757	0.471189	0.235595	−	0.971851i	$-0.424296\pi$
$523$	10.7757	0.471189	0.235595	+	0.971851i	$0.424296\pi$
$524$	−34.0567	−1.48778
$525$	−0.264043	−0.0115238
$526$	−20.2308	−0.882105
$527$	0.864559	0.0376608
$528$	−0.0784089	−0.00341231
$529$	−0.0600275	−0.00260989
$530$	0.775413	0.0336818
$531$	19.8418	0.861060
$532$	−1.92652	−0.0835252
$533$	17.7057	0.766919
$534$	−5.71047	−0.247116
$535$	7.71456	0.333529
$536$	34.8257	1.50424
$537$	3.26051	0.140702
$538$	−73.3728	−3.16333
$539$	−6.90713	−0.297511
$540$	−1.98508	−0.0854243
$541$	16.0124	0.688426	0.344213	−	0.938892i	$-0.388146\pi$
$541$	16.0124	0.688426	0.344213	+	0.938892i	$0.388146\pi$
$542$	36.9542	1.58732
$543$	0.601557	0.0258153
$544$	5.15463	0.221003
$545$	3.99366	0.171070
$546$	0.741554	0.0317356
$547$	−3.92698	−0.167906	−0.0839528	−	0.996470i	$-0.526755\pi$
$547$	−3.92698	−0.167906	−0.0839528	+	0.996470i	$0.526755\pi$
$548$	49.8684	2.13027
$549$	0.862433	0.0368077
$550$	10.8627	0.463185
$551$	−15.8223	−0.674052
$552$	−2.70648	−0.115196
$553$	−1.95482	−0.0831276
$554$	34.4145	1.46213
$555$	0.624228	0.0264970
$556$	4.56245	0.193491
$557$	20.3925	0.864060	0.432030	−	0.901859i	$-0.357797\pi$
$557$	20.3925	0.864060	0.432030	+	0.901859i	$0.357797\pi$
$558$	5.91993	0.250611
$559$	−5.72441	−0.242117
$560$	0.0704306	0.00297623
$561$	−0.184135	−0.00777419
$562$	−46.1939	−1.94857
$563$	14.1735	0.597342	0.298671	−	0.954356i	$-0.403457\pi$
$563$	14.1735	0.597342	0.298671	+	0.954356i	$0.403457\pi$
$564$	4.54171	0.191241
$565$	−6.77161	−0.284884
$566$	57.0822	2.39934
$567$	−2.65008	−0.111293
$568$	−49.3587	−2.07104
$569$	−22.0930	−0.926188	−0.463094	−	0.886309i	$-0.653261\pi$
$569$	−22.0930	−0.926188	−0.463094	+	0.886309i	$0.653261\pi$
$570$	−0.438070	−0.0183487
$571$	10.0568	0.420862	0.210431	−	0.977609i	$-0.432513\pi$
$571$	10.0568	0.420862	0.210431	+	0.977609i	$0.432513\pi$
$572$	−19.0585	−0.796876
$573$	−3.82275	−0.159698
$574$	−2.17600	−0.0908243
$575$	22.5370	0.939857
$576$	37.8215	1.57590
$577$	−1.79973	−0.0749237	−0.0374619	−	0.999298i	$-0.511927\pi$
$577$	−1.79973	−0.0749237	−0.0374619	+	0.999298i	$0.511927\pi$
$578$	−2.30854	−0.0960224
$579$	−3.31807	−0.137894
$580$	15.0572	0.625216
$581$	1.65519	0.0686689
$582$	0.0926784	0.00384164
$583$	0.618875	0.0256312
$584$	26.5400	1.09823
$585$	−9.21529	−0.381005
$586$	29.9124	1.23567
$587$	26.7244	1.10303	0.551517	−	0.834164i	$-0.314049\pi$
$587$	26.7244	1.10303	0.551517	+	0.834164i	$0.314049\pi$
$588$	4.23440	0.174624
$589$	1.64162	0.0676416
$590$	−8.38158	−0.345064
$591$	2.46869	0.101549
$592$	2.65976	0.109315
$593$	40.7115	1.67182	0.835911	−	0.548866i	$-0.184940\pi$
$593$	40.7115	1.67182	0.835911	+	0.548866i	$0.184940\pi$
$594$	−2.53608	−0.104057
$595$	0.165399	0.00678069
$596$	32.1386	1.31645
$597$	−3.24063	−0.132630
$598$	−63.2942	−2.58829
$599$	0.153486	0.00627128	0.00313564	−	0.999995i	$-0.499002\pi$
$599$	0.153486	0.00627128	0.00313564	+	0.999995i	$0.499002\pi$
$600$	−2.65894	−0.108551
$601$	31.9944	1.30508	0.652539	−	0.757755i	$-0.273704\pi$
$601$	31.9944	1.30508	0.652539	+	0.757755i	$0.273704\pi$
$602$	0.703519	0.0286733
$603$	33.6598	1.37073
$604$	−64.0675	−2.60687
$605$	−0.542742	−0.0220656
$606$	1.10139	0.0447407
$607$	6.47739	0.262909	0.131455	−	0.991322i	$-0.458035\pi$
$607$	6.47739	0.262909	0.131455	+	0.991322i	$0.458035\pi$
$608$	9.78755	0.396938
$609$	−0.467593	−0.0189478
$610$	−0.364309	−0.0147505
$611$	42.4088	1.71567
$612$	−9.87513	−0.399179
$613$	−30.0752	−1.21473	−0.607363	−	0.794425i	$-0.707773\pi$
$613$	−30.0752	−1.21473	−0.607363	+	0.794425i	$0.707773\pi$
$614$	−10.4655	−0.422352
$615$	−0.309109	−0.0124645
$616$	0.935215	0.0376809
$617$	31.0786	1.25118	0.625588	−	0.780153i	$-0.284859\pi$
$617$	31.0786	1.25118	0.625588	+	0.780153i	$0.284859\pi$
$618$	−2.58749	−0.104084
$619$	−38.7555	−1.55771	−0.778857	−	0.627202i	$-0.784200\pi$
$619$	−38.7555	−1.55771	−0.778857	+	0.627202i	$0.784200\pi$
$620$	−1.56223	−0.0627409
$621$	−5.26166	−0.211143
$622$	27.3836	1.09798
$623$	4.09390	0.164019
$624$	0.448844	0.0179681
$625$	20.6682	0.826729
$626$	−15.5551	−0.621705
$627$	−0.349633	−0.0139630
$628$	−70.2005	−2.80131
$629$	6.24616	0.249051
$630$	1.13254	0.0451215
$631$	−3.14018	−0.125009	−0.0625043	−	0.998045i	$-0.519909\pi$
$631$	−3.14018	−0.125009	−0.0625043	+	0.998045i	$0.519909\pi$
$632$	−19.6853	−0.783038
$633$	−0.791721	−0.0314681
$634$	−5.44083	−0.216083
$635$	3.08225	0.122315
$636$	−0.379400	−0.0150442
$637$	39.5392	1.56660
$638$	19.2366	0.761586
$639$	−47.7063	−1.88723
$640$	−10.3813	−0.410358
$641$	0.960447	0.0379354	0.0189677	−	0.999820i	$-0.493962\pi$
$641$	0.960447	0.0379354	0.0189677	+	0.999820i	$0.493962\pi$
$642$	−6.04214	−0.238464
$643$	4.15672	0.163925	0.0819625	−	0.996635i	$-0.473881\pi$
$643$	4.15672	0.163925	0.0819625	+	0.996635i	$0.473881\pi$
$644$	4.85952	0.191492
$645$	0.0999378	0.00393505
$646$	−4.38342	−0.172463
$647$	−16.9879	−0.667862	−0.333931	−	0.942598i	$-0.608375\pi$
$647$	−16.9879	−0.667862	−0.333931	+	0.942598i	$0.608375\pi$
$648$	−26.6865	−1.04835
$649$	−6.68953	−0.262587
$650$	−62.1823	−2.43899
$651$	0.0485143	0.00190143
$652$	49.7512	1.94841
$653$	−47.4106	−1.85532	−0.927661	−	0.373424i	$-0.878184\pi$
$653$	−47.4106	−1.85532	−0.927661	+	0.373424i	$0.878184\pi$
$654$	−3.12788	−0.122310
$655$	5.55186	0.216929
$656$	−1.31708	−0.0514232
$657$	25.6516	1.00076
$658$	−5.21195	−0.203183
$659$	30.5211	1.18893	0.594467	−	0.804120i	$-0.297363\pi$
$659$	30.5211	1.18893	0.594467	+	0.804120i	$0.297363\pi$
$660$	0.332727	0.0129514
$661$	10.1689	0.395525	0.197763	−	0.980250i	$-0.436632\pi$
$661$	10.1689	0.395525	0.197763	+	0.980250i	$0.436632\pi$
$662$	−37.7988	−1.46909
$663$	1.05406	0.0409364
$664$	16.6679	0.646841
$665$	0.314057	0.0121786
$666$	42.7696	1.65729
$667$	39.9107	1.54535
$668$	−15.0092	−0.580725
$669$	4.08989	0.158124
$670$	−14.2186	−0.549313
$671$	−0.290764	−0.0112248
$672$	0.289250	0.0111580
$673$	14.6631	0.565221	0.282611	−	0.959235i	$-0.408800\pi$
$673$	14.6631	0.565221	0.282611	+	0.959235i	$0.408800\pi$
$674$	29.4062	1.13268
$675$	−5.16923	−0.198964
$676$	65.8172	2.53143
$677$	−50.0425	−1.92329	−0.961645	−	0.274296i	$-0.911555\pi$
$677$	−50.0425	−1.92329	−0.961645	+	0.274296i	$0.911555\pi$
$678$	5.30361	0.203684
$679$	−0.0664423	−0.00254982
$680$	1.66558	0.0638722
$681$	2.69486	0.103267
$682$	−1.99587	−0.0764257
$683$	35.6463	1.36397	0.681983	−	0.731368i	$-0.261118\pi$
$683$	35.6463	1.36397	0.681983	+	0.731368i	$0.261118\pi$
$684$	−18.7508	−0.716954
$685$	−8.12944	−0.310610
$686$	−9.78392	−0.373552
$687$	4.63536	0.176850
$688$	0.425823	0.0162343
$689$	−3.54269	−0.134966
$690$	1.10500	0.0420667
$691$	10.0335	0.381693	0.190847	−	0.981620i	$-0.438877\pi$
$691$	10.0335	0.381693	0.190847	+	0.981620i	$0.438877\pi$
$692$	71.4170	2.71487
$693$	0.903907	0.0343366
$694$	76.5099	2.90428
$695$	−0.743762	−0.0282125
$696$	−4.70871	−0.178483
$697$	−3.09302	−0.117156
$698$	70.0513	2.65148
$699$	−3.22938	−0.122146
$700$	4.77415	0.180446
$701$	21.3942	0.808049	0.404024	−	0.914748i	$-0.367611\pi$
$701$	21.3942	0.808049	0.404024	+	0.914748i	$0.367611\pi$
$702$	14.5176	0.547930
$703$	11.8601	0.447314
$704$	−12.7513	−0.480583
$705$	−0.740380	−0.0278843
$706$	11.4594	0.431281
$707$	−0.789596	−0.0296958
$708$	4.10100	0.154125
$709$	38.5450	1.44759	0.723794	−	0.690016i	$-0.242396\pi$
$709$	38.5450	1.44759	0.723794	+	0.690016i	$0.242396\pi$
$710$	20.1521	0.756296
$711$	−19.0263	−0.713541
$712$	41.2260	1.54501
$713$	−4.14087	−0.155077
$714$	−0.129542	−0.00484800
$715$	3.10688	0.116191
$716$	−58.9532	−2.20319
$717$	0.362799	0.0135490
$718$	53.3252	1.99008
$719$	32.3961	1.20817	0.604085	−	0.796920i	$-0.293539\pi$
$719$	32.3961	1.20817	0.604085	+	0.796920i	$0.293539\pi$
$720$	0.685500	0.0255471
$721$	1.85500	0.0690838
$722$	35.5390	1.32262
$723$	−4.31569	−0.160502
$724$	−10.8767	−0.404231
$725$	39.2096	1.45621
$726$	0.425082	0.0157763
$727$	−44.2866	−1.64250	−0.821250	−	0.570569i	$-0.806723\pi$
$727$	−44.2866	−1.64250	−0.821250	+	0.570569i	$0.806723\pi$
$728$	−5.35355	−0.198416
$729$	−25.1863	−0.932826
$730$	−10.8358	−0.401049
$731$	1.00000	0.0369863
$732$	0.178252	0.00658839
$733$	−52.9772	−1.95676	−0.978380	−	0.206817i	$-0.933689\pi$
$733$	−52.9772	−1.95676	−0.978380	+	0.206817i	$0.933689\pi$
$734$	−77.9096	−2.87570
$735$	−0.690284	−0.0254615
$736$	−24.6885	−0.910029
$737$	−11.3482	−0.418016
$738$	−21.1789	−0.779607
$739$	0.595312	0.0218989	0.0109494	−	0.999940i	$-0.496515\pi$
$739$	0.595312	0.0218989	0.0109494	+	0.999940i	$0.496515\pi$
$740$	−11.2866	−0.414905
$741$	2.00144	0.0735249
$742$	0.435390	0.0159837
$743$	12.1942	0.447361	0.223680	−	0.974663i	$-0.428193\pi$
$743$	12.1942	0.447361	0.223680	+	0.974663i	$0.428193\pi$
$744$	0.488544	0.0179109
$745$	−5.23917	−0.191948
$746$	−27.9229	−1.02233
$747$	16.1100	0.589432
$748$	3.32934	0.121733
$749$	4.33168	0.158276
$750$	2.23914	0.0817619
$751$	−32.0834	−1.17074	−0.585370	−	0.810766i	$-0.699051\pi$
$751$	−32.0834	−1.17074	−0.585370	+	0.810766i	$0.699051\pi$
$752$	−3.15467	−0.115039
$753$	−4.23886	−0.154473
$754$	−110.118	−4.01027
$755$	10.4442	0.380102
$756$	−1.11461	−0.0405380
$757$	5.83715	0.212155	0.106077	−	0.994358i	$-0.466171\pi$
$757$	5.83715	0.212155	0.106077	+	0.994358i	$0.466171\pi$
$758$	−41.6144	−1.51150
$759$	0.881927	0.0320119
$760$	3.16259	0.114719
$761$	−32.2084	−1.16755	−0.583777	−	0.811914i	$-0.698426\pi$
$761$	−32.2084	−1.16755	−0.583777	+	0.811914i	$0.698426\pi$
$762$	−2.41406	−0.0874521
$763$	2.24242	0.0811810
$764$	69.1191	2.50064
$765$	1.60982	0.0582033
$766$	49.1509	1.77589
$767$	38.2936	1.38270
$768$	3.43487	0.123945
$769$	−5.83271	−0.210333	−0.105166	−	0.994455i	$-0.533538\pi$
$769$	−5.83271	−0.210333	−0.105166	+	0.994455i	$0.533538\pi$
$770$	−0.381829	−0.0137602
$771$	2.43896	0.0878371
$772$	59.9940	2.15923
$773$	44.3557	1.59536	0.797681	−	0.603079i	$-0.206060\pi$
$773$	44.3557	1.59536	0.797681	+	0.603079i	$0.206060\pi$
$774$	6.84734	0.246122
$775$	−4.06812	−0.146131
$776$	−0.669080	−0.0240186
$777$	0.350500	0.0125741
$778$	−58.7718	−2.10707
$779$	−5.87299	−0.210422
$780$	−1.90466	−0.0681979
$781$	16.0839	0.575526
$782$	11.0569	0.395394
$783$	−9.15417	−0.327143
$784$	−2.94121	−0.105043
$785$	11.4439	0.408452
$786$	−4.34829	−0.155098
$787$	11.7245	0.417934	0.208967	−	0.977923i	$-0.432990\pi$
$787$	11.7245	0.417934	0.208967	+	0.977923i	$0.432990\pi$
$788$	−44.6364	−1.59011
$789$	−1.61366	−0.0574479
$790$	8.03709	0.285947
$791$	−3.80222	−0.135191
$792$	9.10243	0.323441
$793$	1.66445	0.0591063
$794$	30.0483	1.06637
$795$	0.0618490	0.00219356
$796$	58.5937	2.07680
$797$	−5.06072	−0.179260	−0.0896300	−	0.995975i	$-0.528568\pi$
$797$	−5.06072	−0.179260	−0.0896300	+	0.995975i	$0.528568\pi$
$798$	−0.245974	−0.00870737
$799$	−7.40841	−0.262091
$800$	−24.2548	−0.857535
$801$	39.8459	1.40789
$802$	77.4248	2.73397
$803$	−8.64826	−0.305191
$804$	6.95699	0.245354
$805$	−0.792189	−0.0279210
$806$	11.4252	0.402434
$807$	−5.85241	−0.206015
$808$	−7.95131	−0.279726
$809$	15.5561	0.546924	0.273462	−	0.961883i	$-0.411831\pi$
$809$	15.5561	0.546924	0.273462	+	0.961883i	$0.411831\pi$
$810$	10.8956	0.382831
$811$	−19.9142	−0.699281	−0.349641	−	0.936884i	$-0.613696\pi$
$811$	−19.9142	−0.699281	−0.349641	+	0.936884i	$0.613696\pi$
$812$	8.45453	0.296696
$813$	2.94757	0.103376
$814$	−14.4195	−0.505403
$815$	−8.11034	−0.284093
$816$	−0.0784089	−0.00274486
$817$	1.89879	0.0664302
$818$	37.4520	1.30948
$819$	−5.17433	−0.180806
$820$	5.58900	0.195176
$821$	44.9752	1.56965	0.784823	−	0.619721i	$-0.212754\pi$
$821$	44.9752	1.56965	0.784823	+	0.619721i	$0.212754\pi$
$822$	6.36708	0.222077
$823$	49.0247	1.70889	0.854447	−	0.519539i	$-0.173896\pi$
$823$	49.0247	1.70889	0.854447	+	0.519539i	$0.173896\pi$
$824$	18.6800	0.650749
$825$	0.866435	0.0301654
$826$	−4.70621	−0.163750
$827$	−27.8507	−0.968463	−0.484232	−	0.874940i	$-0.660901\pi$
$827$	−27.8507	−0.968463	−0.484232	+	0.874940i	$0.660901\pi$
$828$	47.2976	1.64371
$829$	17.7690	0.617142	0.308571	−	0.951201i	$-0.400149\pi$
$829$	17.7690	0.617142	0.308571	+	0.951201i	$0.400149\pi$
$830$	−6.80518	−0.236211
$831$	2.74499	0.0952226
$832$	72.9936	2.53060
$833$	−6.90713	−0.239318
$834$	0.582523	0.0201711
$835$	2.44677	0.0846741
$836$	6.32171	0.218641
$837$	0.949776	0.0328291
$838$	−72.6609	−2.51003
$839$	1.05401	0.0363884	0.0181942	−	0.999834i	$-0.494208\pi$
$839$	1.05401	0.0363884	0.0181942	+	0.999834i	$0.494208\pi$
$840$	0.0934634	0.00322479
$841$	40.4361	1.39435
$842$	−76.1079	−2.62285
$843$	−3.68455	−0.126903
$844$	14.3151	0.492745
$845$	−10.7294	−0.369102
$846$	−50.7279	−1.74406
$847$	−0.304747	−0.0104712
$848$	0.263531	0.00904969
$849$	4.55303	0.156260
$850$	10.8627	0.372586
$851$	−29.9164	−1.02552
$852$	−9.86019	−0.337805
$853$	17.9631	0.615044	0.307522	−	0.951541i	$-0.400500\pi$
$853$	17.9631	0.615044	0.307522	+	0.951541i	$0.400500\pi$
$854$	−0.204558	−0.00699982
$855$	3.05672	0.104537
$856$	43.6204	1.49092
$857$	43.2990	1.47906	0.739532	−	0.673121i	$-0.235047\pi$
$857$	43.2990	1.47906	0.739532	+	0.673121i	$0.235047\pi$
$858$	−2.43334	−0.0830730
$859$	−0.793772	−0.0270832	−0.0135416	−	0.999908i	$-0.504311\pi$
$859$	−0.793772	−0.0270832	−0.0135416	+	0.999908i	$0.504311\pi$
$860$	−1.80697	−0.0616173
$861$	−0.173563	−0.00591502
$862$	38.4131	1.30836
$863$	36.2640	1.23444	0.617221	−	0.786790i	$-0.288258\pi$
$863$	36.2640	1.23444	0.617221	+	0.786790i	$0.288258\pi$
$864$	5.66271	0.192649
$865$	−11.6423	−0.395848
$866$	57.8132	1.96457
$867$	−0.184135	−0.00625355
$868$	−0.877186	−0.0297736
$869$	6.41459	0.217600
$870$	1.92247	0.0651778
$871$	64.9617	2.20114
$872$	22.5814	0.764701
$873$	−0.646681	−0.0218868
$874$	20.9947	0.710156
$875$	−1.60527	−0.0542679
$876$	5.30180	0.179131
$877$	−25.4954	−0.860917	−0.430459	−	0.902610i	$-0.641648\pi$
$877$	−25.4954	−0.860917	−0.430459	+	0.902610i	$0.641648\pi$
$878$	28.7646	0.970757
$879$	2.38589	0.0804740
$880$	−0.231112	−0.00779078
$881$	33.5368	1.12988	0.564941	−	0.825131i	$-0.308899\pi$
$881$	33.5368	1.12988	0.564941	+	0.825131i	$0.308899\pi$
$882$	−47.2954	−1.59252
$883$	−2.87100	−0.0966168	−0.0483084	−	0.998832i	$-0.515383\pi$
$883$	−2.87100	−0.0966168	−0.0483084	+	0.998832i	$0.515383\pi$
$884$	−19.0585	−0.641007
$885$	−0.668537	−0.0224726
$886$	11.9205	0.400476
$887$	16.4315	0.551716	0.275858	−	0.961198i	$-0.411038\pi$
$887$	16.4315	0.551716	0.275858	+	0.961198i	$0.411038\pi$
$888$	3.52957	0.118445
$889$	1.73067	0.0580447
$890$	−16.8317	−0.564201
$891$	8.69600	0.291327
$892$	−73.9492	−2.47600
$893$	−14.0670	−0.470734
$894$	4.10338	0.137238
$895$	9.61044	0.321241
$896$	−5.82906	−0.194735
$897$	−5.04851	−0.168565
$898$	−33.4526	−1.11633
$899$	−7.20423	−0.240274
$900$	46.4668	1.54889
$901$	0.618875	0.0206177
$902$	7.14034	0.237747
$903$	0.0561145	0.00186737
$904$	−38.2887	−1.27346
$905$	1.77310	0.0589400
$906$	−8.17999	−0.271762
$907$	11.3865	0.378084	0.189042	−	0.981969i	$-0.439462\pi$
$907$	11.3865	0.378084	0.189042	+	0.981969i	$0.439462\pi$
$908$	−48.7257	−1.61702
$909$	−7.68513	−0.254900
$910$	2.18575	0.0724568
$911$	43.9993	1.45776	0.728881	−	0.684641i	$-0.240041\pi$
$911$	43.9993	1.45776	0.728881	+	0.684641i	$0.240041\pi$
$912$	−0.148882	−0.00492997
$913$	−5.43137	−0.179752
$914$	61.0949	2.02084
$915$	−0.0290583	−0.000960638 0
$916$	−83.8118	−2.76922
$917$	3.11734	0.102944
$918$	−2.53608	−0.0837032
$919$	−39.4141	−1.30015	−0.650076	−	0.759869i	$-0.725263\pi$
$919$	−39.4141	−1.30015	−0.650076	+	0.759869i	$0.725263\pi$
$920$	−7.97742	−0.263008
$921$	−0.834753	−0.0275061
$922$	9.65142	0.317852
$923$	−92.0707	−3.03054
$924$	0.186824	0.00614607
$925$	−29.3909	−0.966366
$926$	−34.7927	−1.14336
$927$	18.0547	0.592993
$928$	−42.9527	−1.40999
$929$	−18.0027	−0.590651	−0.295325	−	0.955397i	$-0.595428\pi$
$929$	−18.0027	−0.590651	−0.295325	+	0.955397i	$0.595428\pi$
$930$	−0.199463	−0.00654063
$931$	−13.1152	−0.429833
$932$	58.3903	1.91264
$933$	2.18419	0.0715072
$934$	−9.17060	−0.300071
$935$	−0.542742	−0.0177496
$936$	−52.1060	−1.70314
$937$	−30.0806	−0.982689	−0.491345	−	0.870965i	$-0.663494\pi$
$937$	−30.0806	−0.982689	−0.491345	+	0.870965i	$0.663494\pi$
$938$	−7.98367	−0.260676
$939$	−1.24071	−0.0404892
$940$	13.3868	0.436629
$941$	37.5416	1.22382	0.611910	−	0.790927i	$-0.290401\pi$
$941$	37.5416	1.22382	0.611910	+	0.790927i	$0.290401\pi$
$942$	−8.96304	−0.292032
$943$	14.8142	0.482417
$944$	−2.84855	−0.0927125
$945$	0.181702	0.00591076
$946$	−2.30854	−0.0750570
$947$	48.4971	1.57595	0.787973	−	0.615710i	$-0.211131\pi$
$947$	48.4971	1.57595	0.787973	+	0.615710i	$0.211131\pi$
$948$	−3.93245	−0.127720
$949$	49.5062	1.60704
$950$	20.6259	0.669192
$951$	−0.433975	−0.0140726
$952$	0.935215	0.0303105
$953$	32.8759	1.06496	0.532478	−	0.846444i	$-0.321261\pi$
$953$	32.8759	1.06496	0.532478	+	0.846444i	$0.321261\pi$
$954$	4.23765	0.137199
$955$	−11.2677	−0.364613
$956$	−6.55975	−0.212158
$957$	1.53437	0.0495990
$958$	11.4670	0.370483
$959$	−4.56463	−0.147400
$960$	−1.27434	−0.0411290
$961$	−30.2525	−0.975888
$962$	82.5430	2.66129
$963$	42.1602	1.35859
$964$	78.0318	2.51323
$965$	−9.78009	−0.314832
$966$	0.620452	0.0199627
$967$	−19.9999	−0.643155	−0.321577	−	0.946883i	$-0.604213\pi$
$967$	−19.9999	−0.643155	−0.321577	+	0.946883i	$0.604213\pi$
$968$	−3.06883	−0.0986359
$969$	−0.349633	−0.0112318
$970$	0.273172	0.00877101
$971$	−41.0066	−1.31597	−0.657983	−	0.753033i	$-0.728590\pi$
$971$	−41.0066	−1.31597	−0.657983	+	0.753033i	$0.728590\pi$
$972$	−16.3036	−0.522937
$973$	−0.417618	−0.0133882
$974$	74.7954	2.39660
$975$	−4.95982	−0.158842
$976$	−0.123814	−0.00396318
$977$	11.2811	0.360914	0.180457	−	0.983583i	$-0.442242\pi$
$977$	11.2811	0.360914	0.180457	+	0.983583i	$0.442242\pi$
$978$	6.35212	0.203118
$979$	−13.4338	−0.429346
$980$	12.4810	0.398691
$981$	21.8254	0.696832
$982$	−59.0385	−1.88399
$983$	−30.9156	−0.986054	−0.493027	−	0.870014i	$-0.664110\pi$
$983$	−30.9156	−0.986054	−0.493027	+	0.870014i	$0.664110\pi$
$984$	−1.74780	−0.0557178
$985$	7.27653	0.231850
$986$	19.2366	0.612620
$987$	−0.415719	−0.0132325
$988$	−36.1880	−1.15130
$989$	−4.78957	−0.152299
$990$	−3.71634	−0.118113
$991$	−3.28294	−0.104286	−0.0521430	−	0.998640i	$-0.516605\pi$
$991$	−3.28294	−0.104286	−0.0521430	+	0.998640i	$0.516605\pi$
$992$	4.45648	0.141493
$993$	−3.01493	−0.0956760
$994$	11.3153	0.358900
$995$	−9.55183	−0.302813
$996$	3.32969	0.105505
$997$	6.74732	0.213690	0.106845	−	0.994276i	$-0.465925\pi$
$997$	6.74732	0.213690	0.106845	+	0.994276i	$0.465925\pi$
$998$	19.4054	0.614268
$999$	6.86183	0.217099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.9	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.30854 q^{2} -0.184135 q^{3} +3.32934 q^{4} -0.542742 q^{5} +0.425082 q^{6} -0.304747 q^{7} -3.06883 q^{8} -2.96609 q^{9} +O(q^{10})\)	\(q-2.30854 q^{2} -0.184135 q^{3} +3.32934 q^{4} -0.542742 q^{5} +0.425082 q^{6} -0.304747 q^{7} -3.06883 q^{8} -2.96609 q^{9} +1.25294 q^{10} +1.00000 q^{11} -0.613048 q^{12} -5.72441 q^{13} +0.703519 q^{14} +0.0999378 q^{15} +0.425823 q^{16} +1.00000 q^{17} +6.84734 q^{18} +1.89879 q^{19} -1.80697 q^{20} +0.0561145 q^{21} -2.30854 q^{22} -4.78957 q^{23} +0.565079 q^{24} -4.70543 q^{25} +13.2150 q^{26} +1.09857 q^{27} -1.01461 q^{28} -8.33283 q^{29} -0.230710 q^{30} +0.864559 q^{31} +5.15463 q^{32} -0.184135 q^{33} -2.30854 q^{34} +0.165399 q^{35} -9.87513 q^{36} +6.24616 q^{37} -4.38342 q^{38} +1.05406 q^{39} +1.66558 q^{40} -3.09302 q^{41} -0.129542 q^{42} +1.00000 q^{43} +3.32934 q^{44} +1.60982 q^{45} +11.0569 q^{46} -7.40841 q^{47} -0.0784089 q^{48} -6.90713 q^{49} +10.8627 q^{50} -0.184135 q^{51} -19.0585 q^{52} +0.618875 q^{53} -2.53608 q^{54} -0.542742 q^{55} +0.935215 q^{56} -0.349633 q^{57} +19.2366 q^{58} -6.68953 q^{59} +0.332727 q^{60} -0.290764 q^{61} -1.99587 q^{62} +0.903907 q^{63} -12.7513 q^{64} +3.10688 q^{65} +0.425082 q^{66} -11.3482 q^{67} +3.32934 q^{68} +0.881927 q^{69} -0.381829 q^{70} +16.0839 q^{71} +9.10243 q^{72} -8.64826 q^{73} -14.4195 q^{74} +0.866435 q^{75} +6.32171 q^{76} -0.304747 q^{77} -2.43334 q^{78} +6.41459 q^{79} -0.231112 q^{80} +8.69600 q^{81} +7.14034 q^{82} -5.43137 q^{83} +0.186824 q^{84} -0.542742 q^{85} -2.30854 q^{86} +1.53437 q^{87} -3.06883 q^{88} -13.4338 q^{89} -3.71634 q^{90} +1.74449 q^{91} -15.9461 q^{92} -0.159196 q^{93} +17.1026 q^{94} -1.03055 q^{95} -0.949148 q^{96} +0.218025 q^{97} +15.9454 q^{98} -2.96609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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