LMFDB - Embedded newform 8041.2.a.j.1.33

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			1.33
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.449851 q^{2} +1.97290 q^{3} -1.79763 q^{4} -2.37738 q^{5} -0.887509 q^{6} -0.236897 q^{7} +1.70837 q^{8} +0.892318 q^{9} +O(q^{10})$	\(q-0.449851 q^{2} +1.97290 q^{3} -1.79763 q^{4} -2.37738 q^{5} -0.887509 q^{6} -0.236897 q^{7} +1.70837 q^{8} +0.892318 q^{9} +1.06947 q^{10} +1.00000 q^{11} -3.54654 q^{12} -0.980591 q^{13} +0.106568 q^{14} -4.69032 q^{15} +2.82676 q^{16} +1.00000 q^{17} -0.401410 q^{18} -3.74615 q^{19} +4.27366 q^{20} -0.467373 q^{21} -0.449851 q^{22} -6.39424 q^{23} +3.37043 q^{24} +0.651934 q^{25} +0.441119 q^{26} -4.15824 q^{27} +0.425854 q^{28} +3.57993 q^{29} +2.10995 q^{30} -0.645633 q^{31} -4.68836 q^{32} +1.97290 q^{33} -0.449851 q^{34} +0.563194 q^{35} -1.60406 q^{36} +8.80964 q^{37} +1.68521 q^{38} -1.93460 q^{39} -4.06144 q^{40} +8.73024 q^{41} +0.210248 q^{42} +1.00000 q^{43} -1.79763 q^{44} -2.12138 q^{45} +2.87645 q^{46} -10.5569 q^{47} +5.57690 q^{48} -6.94388 q^{49} -0.293273 q^{50} +1.97290 q^{51} +1.76274 q^{52} +3.26819 q^{53} +1.87059 q^{54} -2.37738 q^{55} -0.404707 q^{56} -7.39077 q^{57} -1.61043 q^{58} -3.34474 q^{59} +8.43148 q^{60} -5.42657 q^{61} +0.290438 q^{62} -0.211387 q^{63} -3.54445 q^{64} +2.33124 q^{65} -0.887509 q^{66} +10.9784 q^{67} -1.79763 q^{68} -12.6152 q^{69} -0.253353 q^{70} -6.83018 q^{71} +1.52441 q^{72} +1.94030 q^{73} -3.96302 q^{74} +1.28620 q^{75} +6.73421 q^{76} -0.236897 q^{77} +0.870283 q^{78} +9.75683 q^{79} -6.72028 q^{80} -10.8807 q^{81} -3.92730 q^{82} -1.37097 q^{83} +0.840166 q^{84} -2.37738 q^{85} -0.449851 q^{86} +7.06283 q^{87} +1.70837 q^{88} +3.78318 q^{89} +0.954304 q^{90} +0.232299 q^{91} +11.4945 q^{92} -1.27377 q^{93} +4.74902 q^{94} +8.90602 q^{95} -9.24964 q^{96} -14.3597 q^{97} +3.12371 q^{98} +0.892318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.449851	−0.318093	−0.159046	−	0.987271i	$-0.550842\pi$
$2$	−0.449851	−0.318093	−0.159046	+	0.987271i	$0.550842\pi$
$3$	1.97290	1.13905	0.569526	−	0.821973i	$-0.307127\pi$
$3$	1.97290	1.13905	0.569526	+	0.821973i	$0.307127\pi$
$4$	−1.79763	−0.898817
$5$	−2.37738	−1.06320	−0.531598	−	0.846997i	$-0.678408\pi$
$5$	−2.37738	−1.06320	−0.531598	+	0.846997i	$0.678408\pi$
$6$	−0.887509	−0.362324
$7$	−0.236897	−0.0895387	−0.0447693	−	0.998997i	$-0.514255\pi$
$7$	−0.236897	−0.0895387	−0.0447693	+	0.998997i	$0.514255\pi$
$8$	1.70837	0.604000
$9$	0.892318	0.297439
$10$	1.06947	0.338195
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.54654	−1.02380
$13$	−0.980591	−0.271967	−0.135983	−	0.990711i	$-0.543419\pi$
$13$	−0.980591	−0.271967	−0.135983	+	0.990711i	$0.543419\pi$
$14$	0.106568	0.0284816
$15$	−4.69032	−1.21104
$16$	2.82676	0.706689
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.401410	−0.0946132
$19$	−3.74615	−0.859426	−0.429713	−	0.902966i	$-0.641385\pi$
$19$	−3.74615	−0.859426	−0.429713	+	0.902966i	$0.641385\pi$
$20$	4.27366	0.955619
$21$	−0.467373	−0.101989
$22$	−0.449851	−0.0959085
$23$	−6.39424	−1.33329	−0.666645	−	0.745375i	$-0.732270\pi$
$23$	−6.39424	−1.33329	−0.666645	+	0.745375i	$0.732270\pi$
$24$	3.37043	0.687987
$25$	0.651934	0.130387
$26$	0.441119	0.0865106
$27$	−4.15824	−0.800253
$28$	0.425854	0.0804789
$29$	3.57993	0.664776	0.332388	−	0.943143i	$-0.392146\pi$
$29$	3.57993	0.664776	0.332388	+	0.943143i	$0.392146\pi$
$30$	2.10995	0.385222
$31$	−0.645633	−0.115959	−0.0579795	−	0.998318i	$-0.518466\pi$
$31$	−0.645633	−0.115959	−0.0579795	+	0.998318i	$0.518466\pi$
$32$	−4.68836	−0.828792
$33$	1.97290	0.343437
$34$	−0.449851	−0.0771488
$35$	0.563194	0.0951972
$36$	−1.60406	−0.267343
$37$	8.80964	1.44830	0.724148	−	0.689645i	$-0.242233\pi$
$37$	8.80964	1.44830	0.724148	+	0.689645i	$0.242233\pi$
$38$	1.68521	0.273377
$39$	−1.93460	−0.309784
$40$	−4.06144	−0.642170
$41$	8.73024	1.36343	0.681717	−	0.731616i	$-0.261234\pi$
$41$	8.73024	1.36343	0.681717	+	0.731616i	$0.261234\pi$
$42$	0.210248	0.0324420
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.79763	−0.271004
$45$	−2.12138	−0.316236
$46$	2.87645	0.424110
$47$	−10.5569	−1.53988	−0.769939	−	0.638117i	$-0.779713\pi$
$47$	−10.5569	−1.53988	−0.769939	+	0.638117i	$0.779713\pi$
$48$	5.57690	0.804956
$49$	−6.94388	−0.991983
$50$	−0.293273	−0.0414751
$51$	1.97290	0.276261
$52$	1.76274	0.244448
$53$	3.26819	0.448920	0.224460	−	0.974483i	$-0.427938\pi$
$53$	3.26819	0.448920	0.224460	+	0.974483i	$0.427938\pi$
$54$	1.87059	0.254555
$55$	−2.37738	−0.320566
$56$	−0.404707	−0.0540813
$57$	−7.39077	−0.978931
$58$	−1.61043	−0.211460
$59$	−3.34474	−0.435448	−0.217724	−	0.976010i	$-0.569863\pi$
$59$	−3.34474	−0.435448	−0.217724	+	0.976010i	$0.569863\pi$
$60$	8.43148	1.08850
$61$	−5.42657	−0.694801	−0.347400	−	0.937717i	$-0.612936\pi$
$61$	−5.42657	−0.694801	−0.347400	+	0.937717i	$0.612936\pi$
$62$	0.290438	0.0368857
$63$	−0.211387	−0.0266323
$64$	−3.54445	−0.443057
$65$	2.33124	0.289154
$66$	−0.887509	−0.109245
$67$	10.9784	1.34122	0.670612	−	0.741809i	$-0.266032\pi$
$67$	10.9784	1.34122	0.670612	+	0.741809i	$0.266032\pi$
$68$	−1.79763	−0.217995
$69$	−12.6152	−1.51869
$70$	−0.253353	−0.0302815
$71$	−6.83018	−0.810593	−0.405297	−	0.914185i	$-0.632832\pi$
$71$	−6.83018	−0.810593	−0.405297	+	0.914185i	$0.632832\pi$
$72$	1.52441	0.179653
$73$	1.94030	0.227094	0.113547	−	0.993533i	$-0.463779\pi$
$73$	1.94030	0.227094	0.113547	+	0.993533i	$0.463779\pi$
$74$	−3.96302	−0.460692
$75$	1.28620	0.148517
$76$	6.73421	0.772467
$77$	−0.236897	−0.0269969
$78$	0.870283	0.0985401
$79$	9.75683	1.09773	0.548864	−	0.835911i	$-0.315060\pi$
$79$	9.75683	1.09773	0.548864	+	0.835911i	$0.315060\pi$
$80$	−6.72028	−0.751350
$81$	−10.8807	−1.20897
$82$	−3.92730	−0.433698
$83$	−1.37097	−0.150484	−0.0752418	−	0.997165i	$-0.523973\pi$
$83$	−1.37097	−0.150484	−0.0752418	+	0.997165i	$0.523973\pi$
$84$	0.840166	0.0916696
$85$	−2.37738	−0.257863
$86$	−0.449851	−0.0485087
$87$	7.06283	0.757214
$88$	1.70837	0.182113
$89$	3.78318	0.401017	0.200508	−	0.979692i	$-0.435741\pi$
$89$	3.78318	0.401017	0.200508	+	0.979692i	$0.435741\pi$
$90$	0.954304	0.100592
$91$	0.232299	0.0243515
$92$	11.4945	1.19838
$93$	−1.27377	−0.132083
$94$	4.74902	0.489824
$95$	8.90602	0.913739
$96$	−9.24964	−0.944037
$97$	−14.3597	−1.45800	−0.729001	−	0.684512i	$-0.760015\pi$
$97$	−14.3597	−1.45800	−0.729001	+	0.684512i	$0.760015\pi$
$98$	3.12371	0.315542
$99$	0.892318	0.0896813
$100$	−1.17194	−0.117194
$101$	18.3336	1.82426	0.912131	−	0.409898i	$-0.134436\pi$
$101$	18.3336	1.82426	0.912131	+	0.409898i	$0.134436\pi$
$102$	−0.887509	−0.0878765
$103$	1.46521	0.144371	0.0721856	−	0.997391i	$-0.477003\pi$
$103$	1.46521	0.144371	0.0721856	+	0.997391i	$0.477003\pi$
$104$	−1.67521	−0.164268
$105$	1.11112	0.108435
$106$	−1.47020	−0.142798
$107$	−5.42869	−0.524812	−0.262406	−	0.964958i	$-0.584516\pi$
$107$	−5.42869	−0.524812	−0.262406	+	0.964958i	$0.584516\pi$
$108$	7.47499	0.719281
$109$	−13.3382	−1.27757	−0.638784	−	0.769386i	$-0.720562\pi$
$109$	−13.3382	−1.27757	−0.638784	+	0.769386i	$0.720562\pi$
$110$	1.06947	0.101970
$111$	17.3805	1.64968
$112$	−0.669650	−0.0632760
$113$	15.1745	1.42750	0.713748	−	0.700403i	$-0.246996\pi$
$113$	15.1745	1.42750	0.713748	+	0.700403i	$0.246996\pi$
$114$	3.32474	0.311391
$115$	15.2015	1.41755
$116$	−6.43540	−0.597512
$117$	−0.874998	−0.0808936
$118$	1.50463	0.138513
$119$	−0.236897	−0.0217163
$120$	−8.01280	−0.731465
$121$	1.00000	0.0909091
$122$	2.44115	0.221011
$123$	17.2238	1.55302
$124$	1.16061	0.104226
$125$	10.3370	0.924570
$126$	0.0950928	0.00847154
$127$	−10.5878	−0.939514	−0.469757	−	0.882796i	$-0.655658\pi$
$127$	−10.5878	−0.939514	−0.469757	+	0.882796i	$0.655658\pi$
$128$	10.9712	0.969725
$129$	1.97290	0.173704
$130$	−1.04871	−0.0919778
$131$	−0.496350	−0.0433663	−0.0216832	−	0.999765i	$-0.506903\pi$
$131$	−0.496350	−0.0433663	−0.0216832	+	0.999765i	$0.506903\pi$
$132$	−3.54654	−0.308687
$133$	0.887452	0.0769519
$134$	−4.93864	−0.426633
$135$	9.88571	0.850826
$136$	1.70837	0.146491
$137$	−16.6273	−1.42057	−0.710284	−	0.703915i	$-0.751434\pi$
$137$	−16.6273	−1.42057	−0.710284	+	0.703915i	$0.751434\pi$
$138$	5.67494	0.483083
$139$	10.9372	0.927682	0.463841	−	0.885918i	$-0.346471\pi$
$139$	10.9372	0.927682	0.463841	+	0.885918i	$0.346471\pi$
$140$	−1.01242	−0.0855649
$141$	−20.8276	−1.75400
$142$	3.07256	0.257844
$143$	−0.980591	−0.0820011
$144$	2.52237	0.210197
$145$	−8.51085	−0.706788
$146$	−0.872844	−0.0722371
$147$	−13.6996	−1.12992
$148$	−15.8365	−1.30175
$149$	3.27543	0.268333	0.134167	−	0.990959i	$-0.457164\pi$
$149$	3.27543	0.268333	0.134167	+	0.990959i	$0.457164\pi$
$150$	−0.578597	−0.0472422
$151$	0.558277	0.0454319	0.0227160	−	0.999742i	$-0.492769\pi$
$151$	0.558277	0.0454319	0.0227160	+	0.999742i	$0.492769\pi$
$152$	−6.39981	−0.519093
$153$	0.892318	0.0721396
$154$	0.106568	0.00858752
$155$	1.53491	0.123287
$156$	3.47771	0.278440
$157$	20.9211	1.66968	0.834842	−	0.550490i	$-0.185559\pi$
$157$	20.9211	1.66968	0.834842	+	0.550490i	$0.185559\pi$
$158$	−4.38912	−0.349179
$159$	6.44779	0.511343
$160$	11.1460	0.881169
$161$	1.51478	0.119381
$162$	4.89470	0.384564
$163$	11.2932	0.884549	0.442274	−	0.896880i	$-0.354172\pi$
$163$	11.2932	0.884549	0.442274	+	0.896880i	$0.354172\pi$
$164$	−15.6938	−1.22548
$165$	−4.69032	−0.365141
$166$	0.616733	0.0478677
$167$	8.80631	0.681453	0.340726	−	0.940162i	$-0.389327\pi$
$167$	8.80631	0.681453	0.340726	+	0.940162i	$0.389327\pi$
$168$	−0.798446	−0.0616014
$169$	−12.0384	−0.926034
$170$	1.06947	0.0820243
$171$	−3.34276	−0.255627
$172$	−1.79763	−0.137068
$173$	4.71830	0.358726	0.179363	−	0.983783i	$-0.442596\pi$
$173$	4.71830	0.358726	0.179363	+	0.983783i	$0.442596\pi$
$174$	−3.17722	−0.240864
$175$	−0.154441	−0.0116747
$176$	2.82676	0.213075
$177$	−6.59882	−0.495998
$178$	−1.70187	−0.127560
$179$	−6.80564	−0.508677	−0.254339	−	0.967115i	$-0.581858\pi$
$179$	−6.80564	−0.508677	−0.254339	+	0.967115i	$0.581858\pi$
$180$	3.81346	0.284239
$181$	6.87848	0.511273	0.255637	−	0.966773i	$-0.417715\pi$
$181$	6.87848	0.511273	0.255637	+	0.966773i	$0.417715\pi$
$182$	−0.104500	−0.00774605
$183$	−10.7061	−0.791414
$184$	−10.9237	−0.805307
$185$	−20.9438	−1.53982
$186$	0.573005	0.0420147
$187$	1.00000	0.0731272
$188$	18.9774	1.38407
$189$	0.985074	0.0716536
$190$	−4.00638	−0.290654
$191$	−9.50817	−0.687987	−0.343993	−	0.938972i	$-0.611780\pi$
$191$	−9.50817	−0.687987	−0.343993	+	0.938972i	$0.611780\pi$
$192$	−6.99284	−0.504665
$193$	7.52703	0.541807	0.270904	−	0.962606i	$-0.412678\pi$
$193$	7.52703	0.541807	0.270904	+	0.962606i	$0.412678\pi$
$194$	6.45970	0.463780
$195$	4.59929	0.329362
$196$	12.4826	0.891611
$197$	26.8321	1.91171	0.955854	−	0.293844i	$-0.0949345\pi$
$197$	26.8321	1.91171	0.955854	+	0.293844i	$0.0949345\pi$
$198$	−0.401410	−0.0285270
$199$	24.8192	1.75939	0.879693	−	0.475543i	$-0.157748\pi$
$199$	24.8192	1.75939	0.879693	+	0.475543i	$0.157748\pi$
$200$	1.11374	0.0787536
$201$	21.6592	1.52772
$202$	−8.24739	−0.580284
$203$	−0.848074	−0.0595231
$204$	−3.54654	−0.248308
$205$	−20.7551	−1.44960
$206$	−0.659125	−0.0459234
$207$	−5.70569	−0.396573
$208$	−2.77189	−0.192196
$209$	−3.74615	−0.259127
$210$	−0.499840	−0.0344922
$211$	11.0895	0.763431	0.381715	−	0.924280i	$-0.375333\pi$
$211$	11.0895	0.763431	0.381715	+	0.924280i	$0.375333\pi$
$212$	−5.87500	−0.403497
$213$	−13.4752	−0.923308
$214$	2.44210	0.166939
$215$	−2.37738	−0.162136
$216$	−7.10380	−0.483353
$217$	0.152948	0.0103828
$218$	6.00020	0.406385
$219$	3.82800	0.258672
$220$	4.27366	0.288130
$221$	−0.980591	−0.0659617
$222$	−7.81863	−0.524752
$223$	5.33316	0.357135	0.178567	−	0.983928i	$-0.442854\pi$
$223$	5.33316	0.357135	0.178567	+	0.983928i	$0.442854\pi$
$224$	1.11066	0.0742089
$225$	0.581732	0.0387821
$226$	−6.82626	−0.454076
$227$	12.8570	0.853352	0.426676	−	0.904404i	$-0.359684\pi$
$227$	12.8570	0.853352	0.426676	+	0.904404i	$0.359684\pi$
$228$	13.2859	0.879880
$229$	−14.8378	−0.980509	−0.490255	−	0.871579i	$-0.663096\pi$
$229$	−14.8378	−0.980509	−0.490255	+	0.871579i	$0.663096\pi$
$230$	−6.83842	−0.450912
$231$	−0.467373	−0.0307509
$232$	6.11584	0.401524
$233$	−27.8563	−1.82493	−0.912465	−	0.409156i	$-0.865823\pi$
$233$	−27.8563	−1.82493	−0.912465	+	0.409156i	$0.865823\pi$
$234$	0.393619	0.0257317
$235$	25.0977	1.63719
$236$	6.01262	0.391388
$237$	19.2492	1.25037
$238$	0.106568	0.00690780
$239$	5.16191	0.333896	0.166948	−	0.985966i	$-0.446609\pi$
$239$	5.16191	0.333896	0.166948	+	0.985966i	$0.446609\pi$
$240$	−13.2584	−0.855826
$241$	17.4877	1.12648	0.563240	−	0.826293i	$-0.309555\pi$
$241$	17.4877	1.12648	0.563240	+	0.826293i	$0.309555\pi$
$242$	−0.449851	−0.0289175
$243$	−8.99182	−0.576825
$244$	9.75499	0.624499
$245$	16.5082	1.05467
$246$	−7.74816	−0.494005
$247$	3.67344	0.233735
$248$	−1.10298	−0.0700392
$249$	−2.70478	−0.171409
$250$	−4.65011	−0.294099
$251$	16.6345	1.04996	0.524981	−	0.851114i	$-0.324072\pi$
$251$	16.6345	1.04996	0.524981	+	0.851114i	$0.324072\pi$
$252$	0.379997	0.0239376
$253$	−6.39424	−0.402002
$254$	4.76292	0.298852
$255$	−4.69032	−0.293719
$256$	2.15351	0.134594
$257$	−15.5139	−0.967729	−0.483865	−	0.875143i	$-0.660767\pi$
$257$	−15.5139	−0.967729	−0.483865	+	0.875143i	$0.660767\pi$
$258$	−0.887509	−0.0552539
$259$	−2.08698	−0.129678
$260$	−4.19071	−0.259897
$261$	3.19443	0.197730
$262$	0.223284	0.0137945
$263$	22.4171	1.38230	0.691148	−	0.722713i	$-0.257105\pi$
$263$	22.4171	1.38230	0.691148	+	0.722713i	$0.257105\pi$
$264$	3.37043	0.207436
$265$	−7.76972	−0.477290
$266$	−0.399221	−0.0244778
$267$	7.46383	0.456779
$268$	−19.7351	−1.20551
$269$	−13.5888	−0.828524	−0.414262	−	0.910158i	$-0.635960\pi$
$269$	−13.5888	−0.828524	−0.414262	+	0.910158i	$0.635960\pi$
$270$	−4.44709	−0.270642
$271$	0.223357	0.0135680	0.00678398	−	0.999977i	$-0.497841\pi$
$271$	0.223357	0.0135680	0.00678398	+	0.999977i	$0.497841\pi$
$272$	2.82676	0.171397
$273$	0.458302	0.0277377
$274$	7.47982	0.451872
$275$	0.651934	0.0393131
$276$	22.6774	1.36502
$277$	−28.8613	−1.73411	−0.867054	−	0.498214i	$-0.833989\pi$
$277$	−28.8613	−1.73411	−0.867054	+	0.498214i	$0.833989\pi$
$278$	−4.92011	−0.295089
$279$	−0.576109	−0.0344908
$280$	0.962143	0.0574991
$281$	−3.20480	−0.191183	−0.0955913	−	0.995421i	$-0.530474\pi$
$281$	−3.20480	−0.191183	−0.0955913	+	0.995421i	$0.530474\pi$
$282$	9.36932	0.557935
$283$	−11.8618	−0.705112	−0.352556	−	0.935791i	$-0.614687\pi$
$283$	−11.8618	−0.705112	−0.352556	+	0.935791i	$0.614687\pi$
$284$	12.2782	0.728575
$285$	17.5707	1.04080
$286$	0.441119	0.0260839
$287$	−2.06817	−0.122080
$288$	−4.18350	−0.246515
$289$	1.00000	0.0588235
$290$	3.82861	0.224824
$291$	−28.3301	−1.66074
$292$	−3.48794	−0.204116
$293$	22.1482	1.29391	0.646956	−	0.762528i	$-0.276042\pi$
$293$	22.1482	1.29391	0.646956	+	0.762528i	$0.276042\pi$
$294$	6.16275	0.359419
$295$	7.95171	0.462967
$296$	15.0501	0.874770
$297$	−4.15824	−0.241285
$298$	−1.47345	−0.0853549
$299$	6.27013	0.362611
$300$	−2.31211	−0.133490
$301$	−0.236897	−0.0136545
$302$	−0.251141	−0.0144516
$303$	36.1703	2.07793
$304$	−10.5895	−0.607347
$305$	12.9010	0.738710
$306$	−0.401410	−0.0229471
$307$	2.16515	0.123572	0.0617859	−	0.998089i	$-0.480320\pi$
$307$	2.16515	0.123572	0.0617859	+	0.998089i	$0.480320\pi$
$308$	0.425854	0.0242653
$309$	2.89070	0.164446
$310$	−0.690482	−0.0392168
$311$	19.4134	1.10083	0.550415	−	0.834891i	$-0.314469\pi$
$311$	19.4134	1.10083	0.550415	+	0.834891i	$0.314469\pi$
$312$	−3.30502	−0.187110
$313$	−8.67189	−0.490164	−0.245082	−	0.969502i	$-0.578815\pi$
$313$	−8.67189	−0.490164	−0.245082	+	0.969502i	$0.578815\pi$
$314$	−9.41136	−0.531114
$315$	0.502548	0.0283154
$316$	−17.5392	−0.986657
$317$	−5.93403	−0.333288	−0.166644	−	0.986017i	$-0.553293\pi$
$317$	−5.93403	−0.333288	−0.166644	+	0.986017i	$0.553293\pi$
$318$	−2.90054	−0.162654
$319$	3.57993	0.200438
$320$	8.42651	0.471056
$321$	−10.7102	−0.597788
$322$	−0.681423	−0.0379742
$323$	−3.74615	−0.208441
$324$	19.5596	1.08664
$325$	−0.639280	−0.0354609
$326$	−5.08024	−0.281368
$327$	−26.3149	−1.45522
$328$	14.9145	0.823514
$329$	2.50089	0.137879
$330$	2.10995	0.116149
$331$	24.5501	1.34939	0.674697	−	0.738095i	$-0.264274\pi$
$331$	24.5501	1.34939	0.674697	+	0.738095i	$0.264274\pi$
$332$	2.46451	0.135257
$333$	7.86099	0.430780
$334$	−3.96153	−0.216765
$335$	−26.0998	−1.42598
$336$	−1.32115	−0.0720747
$337$	22.0103	1.19898	0.599488	−	0.800384i	$-0.295371\pi$
$337$	22.0103	1.19898	0.599488	+	0.800384i	$0.295371\pi$
$338$	5.41550	0.294565
$339$	29.9377	1.62599
$340$	4.27366	0.231772
$341$	−0.645633	−0.0349630
$342$	1.50374	0.0813131
$343$	3.30326	0.178359
$344$	1.70837	0.0921091
$345$	29.9910	1.61466
$346$	−2.12253	−0.114108
$347$	18.6475	1.00105	0.500524	−	0.865722i	$-0.333141\pi$
$347$	18.6475	1.00105	0.500524	+	0.865722i	$0.333141\pi$
$348$	−12.6964	−0.680597
$349$	20.8635	1.11680	0.558398	−	0.829573i	$-0.311416\pi$
$349$	20.8635	1.11680	0.558398	+	0.829573i	$0.311416\pi$
$350$	0.0694755	0.00371362
$351$	4.07753	0.217642
$352$	−4.68836	−0.249890
$353$	−37.3934	−1.99025	−0.995124	−	0.0986271i	$-0.968555\pi$
$353$	−37.3934	−1.99025	−0.995124	+	0.0986271i	$0.968555\pi$
$354$	2.96849	0.157773
$355$	16.2379	0.861820
$356$	−6.80078	−0.360441
$357$	−0.467373	−0.0247360
$358$	3.06152	0.161806
$359$	−13.4338	−0.709010	−0.354505	−	0.935054i	$-0.615351\pi$
$359$	−13.4338	−0.709010	−0.354505	+	0.935054i	$0.615351\pi$
$360$	−3.62410	−0.191007
$361$	−4.96635	−0.261387
$362$	−3.09429	−0.162632
$363$	1.97290	0.103550
$364$	−0.417589	−0.0218876
$365$	−4.61282	−0.241446
$366$	4.81613	0.251743
$367$	28.5963	1.49271	0.746357	−	0.665546i	$-0.231801\pi$
$367$	28.5963	1.49271	0.746357	+	0.665546i	$0.231801\pi$
$368$	−18.0750	−0.942222
$369$	7.79015	0.405539
$370$	9.42161	0.489806
$371$	−0.774224	−0.0401957
$372$	2.28977	0.118719
$373$	14.6443	0.758256	0.379128	−	0.925344i	$-0.376224\pi$
$373$	14.6443	0.758256	0.379128	+	0.925344i	$0.376224\pi$
$374$	−0.449851	−0.0232612
$375$	20.3938	1.05313
$376$	−18.0350	−0.930086
$377$	−3.51044	−0.180797
$378$	−0.443136	−0.0227925
$379$	38.0838	1.95623	0.978117	−	0.208054i	$-0.0667129\pi$
$379$	38.0838	1.95623	0.978117	+	0.208054i	$0.0667129\pi$
$380$	−16.0098	−0.821284
$381$	−20.8886	−1.07016
$382$	4.27726	0.218844
$383$	14.5377	0.742844	0.371422	−	0.928464i	$-0.378870\pi$
$383$	14.5377	0.742844	0.371422	+	0.928464i	$0.378870\pi$
$384$	21.6450	1.10457
$385$	0.563194	0.0287030
$386$	−3.38604	−0.172345
$387$	0.892318	0.0453591
$388$	25.8134	1.31048
$389$	6.95182	0.352471	0.176236	−	0.984348i	$-0.443608\pi$
$389$	6.95182	0.352471	0.176236	+	0.984348i	$0.443608\pi$
$390$	−2.06899	−0.104768
$391$	−6.39424	−0.323370
$392$	−11.8627	−0.599157
$393$	−0.979247	−0.0493965
$394$	−12.0704	−0.608100
$395$	−23.1957	−1.16710
$396$	−1.60406	−0.0806071
$397$	−11.6923	−0.586821	−0.293411	−	0.955986i	$-0.594790\pi$
$397$	−11.6923	−0.586821	−0.293411	+	0.955986i	$0.594790\pi$
$398$	−11.1649	−0.559647
$399$	1.75085	0.0876522
$400$	1.84286	0.0921429
$401$	10.2092	0.509823	0.254912	−	0.966964i	$-0.417954\pi$
$401$	10.2092	0.509823	0.254912	+	0.966964i	$0.417954\pi$
$402$	−9.74342	−0.485957
$403$	0.633101	0.0315370
$404$	−32.9571	−1.63968
$405$	25.8676	1.28537
$406$	0.381507	0.0189339
$407$	8.80964	0.436677
$408$	3.37043	0.166861
$409$	1.87917	0.0929188	0.0464594	−	0.998920i	$-0.485206\pi$
$409$	1.87917	0.0929188	0.0464594	+	0.998920i	$0.485206\pi$
$410$	9.33669	0.461106
$411$	−32.8040	−1.61810
$412$	−2.63391	−0.129763
$413$	0.792359	0.0389894
$414$	2.56671	0.126147
$415$	3.25932	0.159994
$416$	4.59736	0.225404
$417$	21.5780	1.05668
$418$	1.68521	0.0824263
$419$	14.0895	0.688316	0.344158	−	0.938912i	$-0.388164\pi$
$419$	14.0895	0.688316	0.344158	+	0.938912i	$0.388164\pi$
$420$	−1.99739	−0.0974628
$421$	28.7100	1.39924	0.699621	−	0.714514i	$-0.253352\pi$
$421$	28.7100	1.39924	0.699621	+	0.714514i	$0.253352\pi$
$422$	−4.98861	−0.242842
$423$	−9.42008	−0.458020
$424$	5.58327	0.271148
$425$	0.651934	0.0316234
$426$	6.06185	0.293697
$427$	1.28554	0.0622115
$428$	9.75881	0.471710
$429$	−1.93460	−0.0934035
$430$	1.06947	0.0515742
$431$	6.42259	0.309365	0.154683	−	0.987964i	$-0.450564\pi$
$431$	6.42259	0.309365	0.154683	+	0.987964i	$0.450564\pi$
$432$	−11.7543	−0.565530
$433$	−23.7310	−1.14044	−0.570219	−	0.821493i	$-0.693142\pi$
$433$	−23.7310	−1.14044	−0.570219	+	0.821493i	$0.693142\pi$
$434$	−0.0688040	−0.00330270
$435$	−16.7910	−0.805068
$436$	23.9772	1.14830
$437$	23.9538	1.14586
$438$	−1.72203	−0.0822818
$439$	−7.85213	−0.374762	−0.187381	−	0.982287i	$-0.560000\pi$
$439$	−7.85213	−0.374762	−0.187381	+	0.982287i	$0.560000\pi$
$440$	−4.06144	−0.193622
$441$	−6.19615	−0.295055
$442$	0.441119	0.0209819
$443$	13.6370	0.647914	0.323957	−	0.946072i	$-0.394987\pi$
$443$	13.6370	0.647914	0.323957	+	0.946072i	$0.394987\pi$
$444$	−31.2438	−1.48276
$445$	−8.99406	−0.426359
$446$	−2.39912	−0.113602
$447$	6.46208	0.305646
$448$	0.839670	0.0396707
$449$	21.5006	1.01468	0.507339	−	0.861747i	$-0.330629\pi$
$449$	21.5006	1.01468	0.507339	+	0.861747i	$0.330629\pi$
$450$	−0.261693	−0.0123363
$451$	8.73024	0.411091
$452$	−27.2782	−1.28306
$453$	1.10142	0.0517493
$454$	−5.78375	−0.271445
$455$	−0.552263	−0.0258905
$456$	−12.6262	−0.591274
$457$	17.2247	0.805736	0.402868	−	0.915258i	$-0.368013\pi$
$457$	17.2247	0.805736	0.402868	+	0.915258i	$0.368013\pi$
$458$	6.67480	0.311893
$459$	−4.15824	−0.194090
$460$	−27.3268	−1.27412
$461$	12.5856	0.586172	0.293086	−	0.956086i	$-0.405318\pi$
$461$	12.5856	0.586172	0.293086	+	0.956086i	$0.405318\pi$
$462$	0.210248	0.00978163
$463$	−4.18176	−0.194343	−0.0971714	−	0.995268i	$-0.530980\pi$
$463$	−4.18176	−0.194343	−0.0971714	+	0.995268i	$0.530980\pi$
$464$	10.1196	0.469790
$465$	3.02822	0.140431
$466$	12.5312	0.580496
$467$	−4.27575	−0.197858	−0.0989291	−	0.995094i	$-0.531542\pi$
$467$	−4.27575	−0.197858	−0.0989291	+	0.995094i	$0.531542\pi$
$468$	1.57293	0.0727086
$469$	−2.60075	−0.120091
$470$	−11.2902	−0.520779
$471$	41.2751	1.90186
$472$	−5.71405	−0.263010
$473$	1.00000	0.0459800
$474$	−8.65927	−0.397733
$475$	−2.44224	−0.112058
$476$	0.425854	0.0195190
$477$	2.91626	0.133526
$478$	−2.32209	−0.106210
$479$	30.7340	1.40427	0.702137	−	0.712042i	$-0.252230\pi$
$479$	30.7340	1.40427	0.702137	+	0.712042i	$0.252230\pi$
$480$	21.9899	1.00370
$481$	−8.63865	−0.393888
$482$	−7.86685	−0.358325
$483$	2.98849	0.135981
$484$	−1.79763	−0.0817106
$485$	34.1384	1.55014
$486$	4.04498	0.183484
$487$	4.97162	0.225286	0.112643	−	0.993636i	$-0.464068\pi$
$487$	4.97162	0.225286	0.112643	+	0.993636i	$0.464068\pi$
$488$	−9.27058	−0.419659
$489$	22.2802	1.00755
$490$	−7.42624	−0.335484
$491$	2.92090	0.131818	0.0659091	−	0.997826i	$-0.479005\pi$
$491$	2.92090	0.131818	0.0659091	+	0.997826i	$0.479005\pi$
$492$	−30.9622	−1.39588
$493$	3.57993	0.161232
$494$	−1.65250	−0.0743495
$495$	−2.12138	−0.0953488
$496$	−1.82505	−0.0819470
$497$	1.61805	0.0725794
$498$	1.21675	0.0545238
$499$	3.73581	0.167238	0.0836188	−	0.996498i	$-0.473352\pi$
$499$	3.73581	0.167238	0.0836188	+	0.996498i	$0.473352\pi$
$500$	−18.5822	−0.831019
$501$	17.3739	0.776210
$502$	−7.48306	−0.333985
$503$	24.8969	1.11010	0.555049	−	0.831817i	$-0.312699\pi$
$503$	24.8969	1.11010	0.555049	+	0.831817i	$0.312699\pi$
$504$	−0.361128	−0.0160859
$505$	−43.5860	−1.93955
$506$	2.87645	0.127874
$507$	−23.7506	−1.05480
$508$	19.0330	0.844451
$509$	1.66180	0.0736582	0.0368291	−	0.999322i	$-0.488274\pi$
$509$	1.66180	0.0736582	0.0368291	+	0.999322i	$0.488274\pi$
$510$	2.10995	0.0934299
$511$	−0.459650	−0.0203337
$512$	−22.9111	−1.01254
$513$	15.5774	0.687758
$514$	6.97893	0.307827
$515$	−3.48336	−0.153495
$516$	−3.54654	−0.156128
$517$	−10.5569	−0.464291
$518$	0.938828	0.0412497
$519$	9.30872	0.408608
$520$	3.98261	0.174649
$521$	29.2604	1.28192	0.640962	−	0.767573i	$-0.278536\pi$
$521$	29.2604	1.28192	0.640962	+	0.767573i	$0.278536\pi$
$522$	−1.43702	−0.0628966
$523$	18.5249	0.810035	0.405018	−	0.914309i	$-0.367265\pi$
$523$	18.5249	0.810035	0.405018	+	0.914309i	$0.367265\pi$
$524$	0.892256	0.0389784
$525$	−0.304696	−0.0132980
$526$	−10.0843	−0.439698
$527$	−0.645633	−0.0281242
$528$	5.57690	0.242703
$529$	17.8862	0.777663
$530$	3.49522	0.151822
$531$	−2.98457	−0.129519
$532$	−1.59531	−0.0691656
$533$	−8.56079	−0.370809
$534$	−3.35761	−0.145298
$535$	12.9061	0.557978
$536$	18.7551	0.810099
$537$	−13.4268	−0.579410
$538$	6.11294	0.263547
$539$	−6.94388	−0.299094
$540$	−17.7709	−0.764737
$541$	−8.55497	−0.367807	−0.183903	−	0.982944i	$-0.558873\pi$
$541$	−8.55497	−0.367807	−0.183903	+	0.982944i	$0.558873\pi$
$542$	−0.100477	−0.00431586
$543$	13.5705	0.582367
$544$	−4.68836	−0.201012
$545$	31.7099	1.35830
$546$	−0.206167	−0.00882315
$547$	11.6578	0.498451	0.249225	−	0.968446i	$-0.419824\pi$
$547$	11.6578	0.498451	0.249225	+	0.968446i	$0.419824\pi$
$548$	29.8899	1.27683
$549$	−4.84222	−0.206661
$550$	−0.293273	−0.0125052
$551$	−13.4110	−0.571326
$552$	−21.5513	−0.917286
$553$	−2.31136	−0.0982892
$554$	12.9833	0.551607
$555$	−41.3200	−1.75394
$556$	−19.6611	−0.833816
$557$	5.81720	0.246483	0.123241	−	0.992377i	$-0.460671\pi$
$557$	5.81720	0.246483	0.123241	+	0.992377i	$0.460671\pi$
$558$	0.259163	0.0109713
$559$	−0.980591	−0.0414746
$560$	1.59201	0.0672748
$561$	1.97290	0.0832957
$562$	1.44168	0.0608138
$563$	−11.8498	−0.499410	−0.249705	−	0.968322i	$-0.580334\pi$
$563$	−11.8498	−0.499410	−0.249705	+	0.968322i	$0.580334\pi$
$564$	37.4404	1.57653
$565$	−36.0755	−1.51771
$566$	5.33605	0.224291
$567$	2.57761	0.108249
$568$	−11.6685	−0.489598
$569$	20.9095	0.876571	0.438285	−	0.898836i	$-0.355586\pi$
$569$	20.9095	0.876571	0.438285	+	0.898836i	$0.355586\pi$
$570$	−7.90417	−0.331069
$571$	−21.2833	−0.890679	−0.445339	−	0.895362i	$-0.646917\pi$
$571$	−21.2833	−0.890679	−0.445339	+	0.895362i	$0.646917\pi$
$572$	1.76274	0.0737040
$573$	−18.7586	−0.783653
$574$	0.930367	0.0388328
$575$	−4.16862	−0.173843
$576$	−3.16278	−0.131782
$577$	−17.7632	−0.739492	−0.369746	−	0.929133i	$-0.620555\pi$
$577$	−17.7632	−0.739492	−0.369746	+	0.929133i	$0.620555\pi$
$578$	−0.449851	−0.0187113
$579$	14.8500	0.617147
$580$	15.2994	0.635273
$581$	0.324779	0.0134741
$582$	12.7443	0.528269
$583$	3.26819	0.135354
$584$	3.31474	0.137165
$585$	2.08020	0.0860058
$586$	−9.96338	−0.411584
$587$	−4.38511	−0.180993	−0.0904965	−	0.995897i	$-0.528845\pi$
$587$	−4.38511	−0.180993	−0.0904965	+	0.995897i	$0.528845\pi$
$588$	24.6268	1.01559
$589$	2.41864	0.0996582
$590$	−3.57709	−0.147266
$591$	52.9369	2.17753
$592$	24.9027	1.02349
$593$	−25.3750	−1.04203	−0.521013	−	0.853549i	$-0.674446\pi$
$593$	−25.3750	−1.04203	−0.521013	+	0.853549i	$0.674446\pi$
$594$	1.87059	0.0767511
$595$	0.563194	0.0230887
$596$	−5.88802	−0.241183
$597$	48.9657	2.00403
$598$	−2.82062	−0.115344
$599$	−17.8864	−0.730820	−0.365410	−	0.930847i	$-0.619071\pi$
$599$	−17.8864	−0.730820	−0.365410	+	0.930847i	$0.619071\pi$
$600$	2.19730	0.0897044
$601$	−46.4206	−1.89354	−0.946769	−	0.321914i	$-0.895674\pi$
$601$	−46.4206	−1.89354	−0.946769	+	0.321914i	$0.895674\pi$
$602$	0.106568	0.00434340
$603$	9.79621	0.398932
$604$	−1.00358	−0.0408350
$605$	−2.37738	−0.0966542
$606$	−16.2712	−0.660974
$607$	4.31492	0.175137	0.0875686	−	0.996158i	$-0.472090\pi$
$607$	4.31492	0.175137	0.0875686	+	0.996158i	$0.472090\pi$
$608$	17.5633	0.712286
$609$	−1.67316	−0.0678000
$610$	−5.80353	−0.234978
$611$	10.3520	0.418796
$612$	−1.60406	−0.0648403
$613$	2.25043	0.0908940	0.0454470	−	0.998967i	$-0.485529\pi$
$613$	2.25043	0.0908940	0.0454470	+	0.998967i	$0.485529\pi$
$614$	−0.973996	−0.0393073
$615$	−40.9476	−1.65117
$616$	−0.404707	−0.0163061
$617$	−1.74083	−0.0700831	−0.0350416	−	0.999386i	$-0.511156\pi$
$617$	−1.74083	−0.0700831	−0.0350416	+	0.999386i	$0.511156\pi$
$618$	−1.30039	−0.0523092
$619$	−6.66170	−0.267756	−0.133878	−	0.990998i	$-0.542743\pi$
$619$	−6.66170	−0.267756	−0.133878	+	0.990998i	$0.542743\pi$
$620$	−2.75921	−0.110813
$621$	26.5888	1.06697
$622$	−8.73311	−0.350166
$623$	−0.896225	−0.0359065
$624$	−5.46865	−0.218921
$625$	−27.8347	−1.11339
$626$	3.90106	0.155918
$627$	−7.39077	−0.295159
$628$	−37.6084	−1.50074
$629$	8.80964	0.351263
$630$	−0.226072	−0.00900691
$631$	−10.8140	−0.430497	−0.215248	−	0.976559i	$-0.569056\pi$
$631$	−10.8140	−0.430497	−0.215248	+	0.976559i	$0.569056\pi$
$632$	16.6683	0.663028
$633$	21.8784	0.869587
$634$	2.66943	0.106017
$635$	25.1712	0.998888
$636$	−11.5908	−0.459604
$637$	6.80910	0.269786
$638$	−1.61043	−0.0637577
$639$	−6.09469	−0.241102
$640$	−26.0827	−1.03101
$641$	37.5543	1.48331	0.741653	−	0.670784i	$-0.234042\pi$
$641$	37.5543	1.48331	0.741653	+	0.670784i	$0.234042\pi$
$642$	4.81801	0.190152
$643$	−10.1907	−0.401883	−0.200942	−	0.979603i	$-0.564400\pi$
$643$	−10.1907	−0.401883	−0.200942	+	0.979603i	$0.564400\pi$
$644$	−2.72301	−0.107302
$645$	−4.69032	−0.184681
$646$	1.68521	0.0663037
$647$	25.8631	1.01678	0.508391	−	0.861126i	$-0.330241\pi$
$647$	25.8631	1.01678	0.508391	+	0.861126i	$0.330241\pi$
$648$	−18.5883	−0.730217
$649$	−3.34474	−0.131292
$650$	0.287581	0.0112798
$651$	0.301751	0.0118266
$652$	−20.3010	−0.795048
$653$	1.74567	0.0683132	0.0341566	−	0.999416i	$-0.489126\pi$
$653$	1.74567	0.0683132	0.0341566	+	0.999416i	$0.489126\pi$
$654$	11.8378	0.462893
$655$	1.18001	0.0461069
$656$	24.6783	0.963524
$657$	1.73136	0.0675468
$658$	−1.12503	−0.0438582
$659$	−26.6372	−1.03764	−0.518818	−	0.854885i	$-0.673628\pi$
$659$	−26.6372	−1.03764	−0.518818	+	0.854885i	$0.673628\pi$
$660$	8.43148	0.328195
$661$	21.6782	0.843184	0.421592	−	0.906786i	$-0.361472\pi$
$661$	21.6782	0.843184	0.421592	+	0.906786i	$0.361472\pi$
$662$	−11.0439	−0.429232
$663$	−1.93460	−0.0751338
$664$	−2.34213	−0.0908921
$665$	−2.10981	−0.0818149
$666$	−3.53627	−0.137028
$667$	−22.8909	−0.886339
$668$	−15.8305	−0.612502
$669$	10.5218	0.406795
$670$	11.7410	0.453595
$671$	−5.42657	−0.209490
$672$	2.19121	0.0845278
$673$	26.6574	1.02757	0.513783	−	0.857920i	$-0.328243\pi$
$673$	26.6574	1.02757	0.513783	+	0.857920i	$0.328243\pi$
$674$	−9.90133	−0.381385
$675$	−2.71090	−0.104342
$676$	21.6407	0.832335
$677$	7.25261	0.278740	0.139370	−	0.990240i	$-0.455492\pi$
$677$	7.25261	0.278740	0.139370	+	0.990240i	$0.455492\pi$
$678$	−13.4675	−0.517216
$679$	3.40176	0.130548
$680$	−4.06144	−0.155749
$681$	25.3656	0.972013
$682$	0.290438	0.0111215
$683$	10.4900	0.401389	0.200694	−	0.979654i	$-0.435680\pi$
$683$	10.4900	0.401389	0.200694	+	0.979654i	$0.435680\pi$
$684$	6.00905	0.229762
$685$	39.5295	1.51034
$686$	−1.48598	−0.0567348
$687$	−29.2734	−1.11685
$688$	2.82676	0.107769
$689$	−3.20475	−0.122091
$690$	−13.4915	−0.513612
$691$	−28.2541	−1.07484	−0.537419	−	0.843316i	$-0.680601\pi$
$691$	−28.2541	−1.07484	−0.537419	+	0.843316i	$0.680601\pi$
$692$	−8.48179	−0.322429
$693$	−0.211387	−0.00802994
$694$	−8.38858	−0.318426
$695$	−26.0019	−0.986308
$696$	12.0659	0.457357
$697$	8.73024	0.330681
$698$	−9.38545	−0.355244
$699$	−54.9576	−2.07869
$700$	0.277629	0.0104934
$701$	20.1645	0.761602	0.380801	−	0.924657i	$-0.375648\pi$
$701$	20.1645	0.761602	0.380801	+	0.924657i	$0.375648\pi$
$702$	−1.83428	−0.0692304
$703$	−33.0022	−1.24470
$704$	−3.54445	−0.133587
$705$	49.5151	1.86485
$706$	16.8214	0.633083
$707$	−4.34318	−0.163342
$708$	11.8623	0.445811
$709$	−32.6293	−1.22542	−0.612710	−	0.790308i	$-0.709921\pi$
$709$	−32.6293	−1.22542	−0.612710	+	0.790308i	$0.709921\pi$
$710$	−7.30465	−0.274139
$711$	8.70619	0.326508
$712$	6.46307	0.242214
$713$	4.12833	0.154607
$714$	0.210248	0.00786834
$715$	2.33124	0.0871833
$716$	12.2340	0.457208
$717$	10.1839	0.380325
$718$	6.04322	0.225531
$719$	−29.5762	−1.10301	−0.551503	−	0.834173i	$-0.685945\pi$
$719$	−29.5762	−1.10301	−0.551503	+	0.834173i	$0.685945\pi$
$720$	−5.99662	−0.223481
$721$	−0.347103	−0.0129268
$722$	2.23412	0.0831452
$723$	34.5014	1.28312
$724$	−12.3650	−0.459541
$725$	2.33388	0.0866780
$726$	−0.887509	−0.0329385
$727$	−31.5440	−1.16990	−0.584950	−	0.811069i	$-0.698886\pi$
$727$	−31.5440	−1.16990	−0.584950	+	0.811069i	$0.698886\pi$
$728$	0.396852	0.0147083
$729$	14.9022	0.551935
$730$	2.07508	0.0768022
$731$	1.00000	0.0369863
$732$	19.2456	0.711337
$733$	30.9400	1.14279	0.571397	−	0.820674i	$-0.306402\pi$
$733$	30.9400	1.14279	0.571397	+	0.820674i	$0.306402\pi$
$734$	−12.8641	−0.474821
$735$	32.5690	1.20133
$736$	29.9785	1.10502
$737$	10.9784	0.404394
$738$	−3.50440	−0.128999
$739$	−6.15380	−0.226371	−0.113186	−	0.993574i	$-0.536105\pi$
$739$	−6.15380	−0.226371	−0.113186	+	0.993574i	$0.536105\pi$
$740$	37.6494	1.38402
$741$	7.24732	0.266237
$742$	0.348285	0.0127860
$743$	−29.7998	−1.09325	−0.546625	−	0.837378i	$-0.684088\pi$
$743$	−29.7998	−1.09325	−0.546625	+	0.837378i	$0.684088\pi$
$744$	−2.17606	−0.0797783
$745$	−7.78693	−0.285291
$746$	−6.58777	−0.241195
$747$	−1.22334	−0.0447597
$748$	−1.79763	−0.0657280
$749$	1.28604	0.0469909
$750$	−9.17418	−0.334994
$751$	−18.7251	−0.683288	−0.341644	−	0.939829i	$-0.610984\pi$
$751$	−18.7251	−0.683288	−0.341644	+	0.939829i	$0.610984\pi$
$752$	−29.8417	−1.08822
$753$	32.8182	1.19596
$754$	1.57918	0.0575102
$755$	−1.32724	−0.0483031
$756$	−1.77080	−0.0644035
$757$	−24.2472	−0.881280	−0.440640	−	0.897684i	$-0.645248\pi$
$757$	−24.2472	−0.881280	−0.440640	+	0.897684i	$0.645248\pi$
$758$	−17.1320	−0.622264
$759$	−12.6152	−0.457901
$760$	15.2148	0.551898
$761$	42.0465	1.52418	0.762091	−	0.647470i	$-0.224173\pi$
$761$	42.0465	1.52418	0.762091	+	0.647470i	$0.224173\pi$
$762$	9.39675	0.340408
$763$	3.15978	0.114392
$764$	17.0922	0.618374
$765$	−2.12138	−0.0766986
$766$	−6.53982	−0.236293
$767$	3.27982	0.118427
$768$	4.24865	0.153310
$769$	−43.5572	−1.57071	−0.785356	−	0.619044i	$-0.787520\pi$
$769$	−43.5572	−1.57071	−0.785356	+	0.619044i	$0.787520\pi$
$770$	−0.253353	−0.00913022
$771$	−30.6073	−1.10229
$772$	−13.5308	−0.486986
$773$	−43.7987	−1.57533	−0.787665	−	0.616104i	$-0.788710\pi$
$773$	−43.7987	−1.57533	−0.787665	+	0.616104i	$0.788710\pi$
$774$	−0.401410	−0.0144284
$775$	−0.420910	−0.0151195
$776$	−24.5316	−0.880633
$777$	−4.11739	−0.147710
$778$	−3.12728	−0.112119
$779$	−32.7048	−1.17177
$780$	−8.26783	−0.296036
$781$	−6.83018	−0.244403
$782$	2.87645	0.102862
$783$	−14.8862	−0.531989
$784$	−19.6287	−0.701024
$785$	−49.7373	−1.77520
$786$	0.440515	0.0157127
$787$	21.0767	0.751302	0.375651	−	0.926761i	$-0.377419\pi$
$787$	21.0767	0.751302	0.375651	+	0.926761i	$0.377419\pi$
$788$	−48.2343	−1.71827
$789$	44.2265	1.57451
$790$	10.4346	0.371246
$791$	−3.59479	−0.127816
$792$	1.52441	0.0541675
$793$	5.32124	0.188963
$794$	5.25981	0.186664
$795$	−15.3288	−0.543658
$796$	−44.6158	−1.58137
$797$	−7.83452	−0.277513	−0.138757	−	0.990327i	$-0.544311\pi$
$797$	−7.83452	−0.277513	−0.138757	+	0.990327i	$0.544311\pi$
$798$	−0.787621	−0.0278815
$799$	−10.5569	−0.373475
$800$	−3.05650	−0.108064
$801$	3.37580	0.119278
$802$	−4.59262	−0.162171
$803$	1.94030	0.0684716
$804$	−38.9353	−1.37314
$805$	−3.60120	−0.126925
$806$	−0.284801	−0.0100317
$807$	−26.8093	−0.943732
$808$	31.3206	1.10185
$809$	−29.5437	−1.03870	−0.519351	−	0.854561i	$-0.673826\pi$
$809$	−29.5437	−1.03870	−0.519351	+	0.854561i	$0.673826\pi$
$810$	−11.6366	−0.408867
$811$	2.69120	0.0945008	0.0472504	−	0.998883i	$-0.484954\pi$
$811$	2.69120	0.0945008	0.0472504	+	0.998883i	$0.484954\pi$
$812$	1.52453	0.0535004
$813$	0.440659	0.0154546
$814$	−3.96302	−0.138904
$815$	−26.8481	−0.940449
$816$	5.57690	0.195230
$817$	−3.74615	−0.131061
$818$	−0.845345	−0.0295568
$819$	0.207284	0.00724311
$820$	37.3101	1.30292
$821$	6.19626	0.216251	0.108125	−	0.994137i	$-0.465515\pi$
$821$	6.19626	0.216251	0.108125	+	0.994137i	$0.465515\pi$
$822$	14.7569	0.514706
$823$	19.7568	0.688680	0.344340	−	0.938845i	$-0.388103\pi$
$823$	19.7568	0.688680	0.344340	+	0.938845i	$0.388103\pi$
$824$	2.50312	0.0872002
$825$	1.28620	0.0447796
$826$	−0.356443	−0.0124022
$827$	−23.9621	−0.833244	−0.416622	−	0.909080i	$-0.636786\pi$
$827$	−23.9621	−0.833244	−0.416622	+	0.909080i	$0.636786\pi$
$828$	10.2567	0.356446
$829$	−5.79663	−0.201325	−0.100663	−	0.994921i	$-0.532096\pi$
$829$	−5.79663	−0.201325	−0.100663	+	0.994921i	$0.532096\pi$
$830$	−1.46621	−0.0508928
$831$	−56.9404	−1.97524
$832$	3.47566	0.120497
$833$	−6.94388	−0.240591
$834$	−9.70687	−0.336121
$835$	−20.9359	−0.724518
$836$	6.73421	0.232908
$837$	2.68469	0.0927966
$838$	−6.33816	−0.218948
$839$	−0.192863	−0.00665838	−0.00332919	−	0.999994i	$-0.501060\pi$
$839$	−0.192863	−0.00665838	−0.00332919	+	0.999994i	$0.501060\pi$
$840$	1.89821	0.0654944
$841$	−16.1841	−0.558073
$842$	−12.9152	−0.445088
$843$	−6.32275	−0.217767
$844$	−19.9348	−0.686184
$845$	28.6199	0.984556
$846$	4.23763	0.145693
$847$	−0.236897	−0.00813988
$848$	9.23837	0.317247
$849$	−23.4021	−0.803159
$850$	−0.293273	−0.0100592
$851$	−56.3309	−1.93100
$852$	24.2235	0.829885
$853$	−1.24165	−0.0425132	−0.0212566	−	0.999774i	$-0.506767\pi$
$853$	−1.24165	−0.0425132	−0.0212566	+	0.999774i	$0.506767\pi$
$854$	−0.578300	−0.0197890
$855$	7.94700	0.271782
$856$	−9.27421	−0.316986
$857$	−51.7481	−1.76768	−0.883840	−	0.467789i	$-0.845051\pi$
$857$	−51.7481	−1.76768	−0.883840	+	0.467789i	$0.845051\pi$
$858$	0.870283	0.0297110
$859$	39.9460	1.36294	0.681470	−	0.731846i	$-0.261341\pi$
$859$	39.9460	1.36294	0.681470	+	0.731846i	$0.261341\pi$
$860$	4.27366	0.145731
$861$	−4.08028	−0.139056
$862$	−2.88921	−0.0984068
$863$	9.52844	0.324352	0.162176	−	0.986762i	$-0.448149\pi$
$863$	9.52844	0.324352	0.162176	+	0.986762i	$0.448149\pi$
$864$	19.4953	0.663244
$865$	−11.2172	−0.381396
$866$	10.6754	0.362765
$867$	1.97290	0.0670031
$868$	−0.274945	−0.00933225
$869$	9.75683	0.330978
$870$	7.55345	0.256086
$871$	−10.7653	−0.364768
$872$	−22.7866	−0.771650
$873$	−12.8134	−0.433667
$874$	−10.7756	−0.364491
$875$	−2.44881	−0.0827847
$876$	−6.88135	−0.232499
$877$	−36.9397	−1.24737	−0.623683	−	0.781678i	$-0.714364\pi$
$877$	−36.9397	−1.24737	−0.623683	+	0.781678i	$0.714364\pi$
$878$	3.53229	0.119209
$879$	43.6961	1.47383
$880$	−6.72028	−0.226540
$881$	5.27633	0.177764	0.0888820	−	0.996042i	$-0.471671\pi$
$881$	5.27633	0.177764	0.0888820	+	0.996042i	$0.471671\pi$
$882$	2.78734	0.0938547
$883$	−22.5158	−0.757718	−0.378859	−	0.925454i	$-0.623683\pi$
$883$	−22.5158	−0.757718	−0.378859	+	0.925454i	$0.623683\pi$
$884$	1.76274	0.0592875
$885$	15.6879	0.527343
$886$	−6.13462	−0.206097
$887$	37.8064	1.26942	0.634708	−	0.772752i	$-0.281121\pi$
$887$	37.8064	1.26942	0.634708	+	0.772752i	$0.281121\pi$
$888$	29.6923	0.996408
$889$	2.50821	0.0841228
$890$	4.04599	0.135622
$891$	−10.8807	−0.364518
$892$	−9.58706	−0.320999
$893$	39.5476	1.32341
$894$	−2.90697	−0.0972236
$895$	16.1796	0.540824
$896$	−2.59904	−0.0868279
$897$	12.3703	0.413033
$898$	−9.67208	−0.322762
$899$	−2.31132	−0.0770868
$900$	−1.04574	−0.0348580
$901$	3.26819	0.108879
$902$	−3.92730	−0.130765
$903$	−0.467373	−0.0155532
$904$	25.9236	0.862207
$905$	−16.3528	−0.543584
$906$	−0.495476	−0.0164611
$907$	−1.78610	−0.0593064	−0.0296532	−	0.999560i	$-0.509440\pi$
$907$	−1.78610	−0.0593064	−0.0296532	+	0.999560i	$0.509440\pi$
$908$	−23.1123	−0.767008
$909$	16.3594	0.542607
$910$	0.248436	0.00823557
$911$	40.7280	1.34938	0.674689	−	0.738102i	$-0.264278\pi$
$911$	40.7280	1.34938	0.674689	+	0.738102i	$0.264278\pi$
$912$	−20.8919	−0.691800
$913$	−1.37097	−0.0453725
$914$	−7.74853	−0.256299
$915$	25.4524	0.841429
$916$	26.6729	0.881299
$917$	0.117584	0.00388296
$918$	1.87059	0.0617386
$919$	−1.12067	−0.0369677	−0.0184838	−	0.999829i	$-0.505884\pi$
$919$	−1.12067	−0.0369677	−0.0184838	+	0.999829i	$0.505884\pi$
$920$	25.9698	0.856199
$921$	4.27162	0.140755
$922$	−5.66166	−0.186457
$923$	6.69761	0.220455
$924$	0.840166	0.0276394
$925$	5.74330	0.188839
$926$	1.88117	0.0618190
$927$	1.30743	0.0429417
$928$	−16.7840	−0.550961
$929$	−29.6381	−0.972395	−0.486198	−	0.873849i	$-0.661617\pi$
$929$	−29.6381	−0.972395	−0.486198	+	0.873849i	$0.661617\pi$
$930$	−1.36225	−0.0446699
$931$	26.0128	0.852536
$932$	50.0755	1.64028
$933$	38.3005	1.25390
$934$	1.92345	0.0629372
$935$	−2.37738	−0.0777486
$936$	−1.49482	−0.0488597
$937$	7.58390	0.247755	0.123878	−	0.992298i	$-0.460467\pi$
$937$	7.58390	0.247755	0.123878	+	0.992298i	$0.460467\pi$
$938$	1.16995	0.0382002
$939$	−17.1087	−0.558323
$940$	−45.1165	−1.47154
$941$	50.6208	1.65019	0.825095	−	0.564993i	$-0.191121\pi$
$941$	50.6208	1.65019	0.825095	+	0.564993i	$0.191121\pi$
$942$	−18.5676	−0.604966
$943$	−55.8232	−1.81785
$944$	−9.45477	−0.307726
$945$	−2.34189	−0.0761818
$946$	−0.449851	−0.0146259
$947$	−6.39606	−0.207844	−0.103922	−	0.994585i	$-0.533139\pi$
$947$	−6.39606	−0.207844	−0.103922	+	0.994585i	$0.533139\pi$
$948$	−34.6030	−1.12385
$949$	−1.90264	−0.0617622
$950$	1.09864	0.0356447
$951$	−11.7072	−0.379633
$952$	−0.404707	−0.0131166
$953$	−24.3297	−0.788116	−0.394058	−	0.919086i	$-0.628929\pi$
$953$	−24.3297	−0.788116	−0.394058	+	0.919086i	$0.628929\pi$
$954$	−1.31188	−0.0424738
$955$	22.6045	0.731465
$956$	−9.27923	−0.300112
$957$	7.06283	0.228309
$958$	−13.8257	−0.446689
$959$	3.93896	0.127196
$960$	16.6246	0.536558
$961$	−30.5832	−0.986554
$962$	3.88610	0.125293
$963$	−4.84412	−0.156100
$964$	−31.4364	−1.01250
$965$	−17.8946	−0.576048
$966$	−1.34438	−0.0432546
$967$	18.7502	0.602967	0.301483	−	0.953471i	$-0.402518\pi$
$967$	18.7502	0.602967	0.301483	+	0.953471i	$0.402518\pi$
$968$	1.70837	0.0549091
$969$	−7.39077	−0.237426
$970$	−15.3572	−0.493089
$971$	−5.11793	−0.164242	−0.0821210	−	0.996622i	$-0.526169\pi$
$971$	−5.11793	−0.164242	−0.0821210	+	0.996622i	$0.526169\pi$
$972$	16.1640	0.518461
$973$	−2.59099	−0.0830634
$974$	−2.23649	−0.0716617
$975$	−1.26123	−0.0403918
$976$	−15.3396	−0.491008
$977$	32.7276	1.04705	0.523524	−	0.852011i	$-0.324617\pi$
$977$	32.7276	1.04705	0.523524	+	0.852011i	$0.324617\pi$
$978$	−10.0228	−0.320493
$979$	3.78318	0.120911
$980$	−29.6758	−0.947958
$981$	−11.9019	−0.379999
$982$	−1.31397	−0.0419304
$983$	−24.7713	−0.790082	−0.395041	−	0.918663i	$-0.629270\pi$
$983$	−24.7713	−0.790082	−0.395041	+	0.918663i	$0.629270\pi$
$984$	29.4247	0.938025
$985$	−63.7901	−2.03252
$986$	−1.61043	−0.0512867
$987$	4.93400	0.157051
$988$	−6.60350	−0.210085
$989$	−6.39424	−0.203325
$990$	0.954304	0.0303298
$991$	3.76537	0.119611	0.0598054	−	0.998210i	$-0.480952\pi$
$991$	3.76537	0.119611	0.0598054	+	0.998210i	$0.480952\pi$
$992$	3.02696	0.0961060
$993$	48.4347	1.53703
$994$	−0.727881	−0.0230870
$995$	−59.0046	−1.87057
$996$	4.86221	0.154065
$997$	−41.2587	−1.30668	−0.653339	−	0.757066i	$-0.726632\pi$
$997$	−41.2587	−1.30668	−0.653339	+	0.757066i	$0.726632\pi$
$998$	−1.68056	−0.0531971
$999$	−36.6326	−1.15900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.33	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.33	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.449851 q^{2} +1.97290 q^{3} -1.79763 q^{4} -2.37738 q^{5} -0.887509 q^{6} -0.236897 q^{7} +1.70837 q^{8} +0.892318 q^{9} +O(q^{10})\)	\(q-0.449851 q^{2} +1.97290 q^{3} -1.79763 q^{4} -2.37738 q^{5} -0.887509 q^{6} -0.236897 q^{7} +1.70837 q^{8} +0.892318 q^{9} +1.06947 q^{10} +1.00000 q^{11} -3.54654 q^{12} -0.980591 q^{13} +0.106568 q^{14} -4.69032 q^{15} +2.82676 q^{16} +1.00000 q^{17} -0.401410 q^{18} -3.74615 q^{19} +4.27366 q^{20} -0.467373 q^{21} -0.449851 q^{22} -6.39424 q^{23} +3.37043 q^{24} +0.651934 q^{25} +0.441119 q^{26} -4.15824 q^{27} +0.425854 q^{28} +3.57993 q^{29} +2.10995 q^{30} -0.645633 q^{31} -4.68836 q^{32} +1.97290 q^{33} -0.449851 q^{34} +0.563194 q^{35} -1.60406 q^{36} +8.80964 q^{37} +1.68521 q^{38} -1.93460 q^{39} -4.06144 q^{40} +8.73024 q^{41} +0.210248 q^{42} +1.00000 q^{43} -1.79763 q^{44} -2.12138 q^{45} +2.87645 q^{46} -10.5569 q^{47} +5.57690 q^{48} -6.94388 q^{49} -0.293273 q^{50} +1.97290 q^{51} +1.76274 q^{52} +3.26819 q^{53} +1.87059 q^{54} -2.37738 q^{55} -0.404707 q^{56} -7.39077 q^{57} -1.61043 q^{58} -3.34474 q^{59} +8.43148 q^{60} -5.42657 q^{61} +0.290438 q^{62} -0.211387 q^{63} -3.54445 q^{64} +2.33124 q^{65} -0.887509 q^{66} +10.9784 q^{67} -1.79763 q^{68} -12.6152 q^{69} -0.253353 q^{70} -6.83018 q^{71} +1.52441 q^{72} +1.94030 q^{73} -3.96302 q^{74} +1.28620 q^{75} +6.73421 q^{76} -0.236897 q^{77} +0.870283 q^{78} +9.75683 q^{79} -6.72028 q^{80} -10.8807 q^{81} -3.92730 q^{82} -1.37097 q^{83} +0.840166 q^{84} -2.37738 q^{85} -0.449851 q^{86} +7.06283 q^{87} +1.70837 q^{88} +3.78318 q^{89} +0.954304 q^{90} +0.232299 q^{91} +11.4945 q^{92} -1.27377 q^{93} +4.74902 q^{94} +8.90602 q^{95} -9.24964 q^{96} -14.3597 q^{97} +3.12371 q^{98} +0.892318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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