LMFDB - Embedded newform 8011.2.a.b.1.154

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.154
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.356440 q^{2} -1.47323 q^{3} -1.87295 q^{4} -3.48561 q^{5} +0.525116 q^{6} -2.23893 q^{7} +1.38047 q^{8} -0.829603 q^{9} +O(q^{10})$	\(q-0.356440 q^{2} -1.47323 q^{3} -1.87295 q^{4} -3.48561 q^{5} +0.525116 q^{6} -2.23893 q^{7} +1.38047 q^{8} -0.829603 q^{9} +1.24241 q^{10} +6.17030 q^{11} +2.75928 q^{12} +6.08686 q^{13} +0.798043 q^{14} +5.13510 q^{15} +3.25385 q^{16} -7.86003 q^{17} +0.295703 q^{18} -0.253187 q^{19} +6.52838 q^{20} +3.29845 q^{21} -2.19934 q^{22} -2.26625 q^{23} -2.03375 q^{24} +7.14949 q^{25} -2.16960 q^{26} +5.64187 q^{27} +4.19340 q^{28} +8.55443 q^{29} -1.83035 q^{30} +9.96445 q^{31} -3.92075 q^{32} -9.09025 q^{33} +2.80162 q^{34} +7.80404 q^{35} +1.55381 q^{36} -2.82214 q^{37} +0.0902458 q^{38} -8.96733 q^{39} -4.81179 q^{40} +2.31404 q^{41} -1.17570 q^{42} +8.30899 q^{43} -11.5567 q^{44} +2.89167 q^{45} +0.807781 q^{46} -0.223727 q^{47} -4.79365 q^{48} -1.98720 q^{49} -2.54836 q^{50} +11.5796 q^{51} -11.4004 q^{52} -5.42151 q^{53} -2.01099 q^{54} -21.5073 q^{55} -3.09078 q^{56} +0.373002 q^{57} -3.04914 q^{58} +13.9337 q^{59} -9.61779 q^{60} -7.48052 q^{61} -3.55172 q^{62} +1.85742 q^{63} -5.11018 q^{64} -21.2164 q^{65} +3.24013 q^{66} +2.18793 q^{67} +14.7214 q^{68} +3.33870 q^{69} -2.78167 q^{70} +7.10663 q^{71} -1.14524 q^{72} -12.0902 q^{73} +1.00592 q^{74} -10.5328 q^{75} +0.474206 q^{76} -13.8149 q^{77} +3.19631 q^{78} -2.41600 q^{79} -11.3416 q^{80} -5.82295 q^{81} -0.824816 q^{82} -6.77046 q^{83} -6.17783 q^{84} +27.3970 q^{85} -2.96165 q^{86} -12.6026 q^{87} +8.51793 q^{88} +11.7850 q^{89} -1.03071 q^{90} -13.6280 q^{91} +4.24457 q^{92} -14.6799 q^{93} +0.0797452 q^{94} +0.882511 q^{95} +5.77615 q^{96} -16.7724 q^{97} +0.708317 q^{98} -5.11890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−0.356440	−0.252041	−0.126020	−	0.992028i	$-0.540220\pi$
$2$	−0.356440	−0.252041	−0.126020	+	0.992028i	$0.540220\pi$
$3$	−1.47323	−0.850568	−0.425284	−	0.905060i	$-0.639826\pi$
$3$	−1.47323	−0.850568	−0.425284	+	0.905060i	$0.639826\pi$
$4$	−1.87295	−0.936475
$5$	−3.48561	−1.55881	−0.779407	−	0.626518i	$-0.784479\pi$
$5$	−3.48561	−1.55881	−0.779407	+	0.626518i	$0.784479\pi$
$6$	0.525116	0.214378
$7$	−2.23893	−0.846235	−0.423118	−	0.906075i	$-0.639064\pi$
$7$	−2.23893	−0.846235	−0.423118	+	0.906075i	$0.639064\pi$
$8$	1.38047	0.488071
$9$	−0.829603	−0.276534
$10$	1.24241	0.392885
$11$	6.17030	1.86042	0.930208	−	0.367033i	$-0.119626\pi$
$11$	6.17030	1.86042	0.930208	+	0.367033i	$0.119626\pi$
$12$	2.75928	0.796536
$13$	6.08686	1.68819	0.844096	−	0.536192i	$-0.180138\pi$
$13$	6.08686	1.68819	0.844096	+	0.536192i	$0.180138\pi$
$14$	0.798043	0.213286
$15$	5.13510	1.32588
$16$	3.25385	0.813462
$17$	−7.86003	−1.90634	−0.953168	−	0.302440i	$-0.902199\pi$
$17$	−7.86003	−1.90634	−0.953168	+	0.302440i	$0.902199\pi$
$18$	0.295703	0.0696979
$19$	−0.253187	−0.0580850	−0.0290425	−	0.999578i	$-0.509246\pi$
$19$	−0.253187	−0.0580850	−0.0290425	+	0.999578i	$0.509246\pi$
$20$	6.52838	1.45979
$21$	3.29845	0.719781
$22$	−2.19934	−0.468901
$23$	−2.26625	−0.472546	−0.236273	−	0.971687i	$-0.575926\pi$
$23$	−2.26625	−0.472546	−0.236273	+	0.971687i	$0.575926\pi$
$24$	−2.03375	−0.415137
$25$	7.14949	1.42990
$26$	−2.16960	−0.425493
$27$	5.64187	1.08578
$28$	4.19340	0.792479
$29$	8.55443	1.58852	0.794258	−	0.607580i	$-0.207860\pi$
$29$	8.55443	1.58852	0.794258	+	0.607580i	$0.207860\pi$
$30$	−1.83035	−0.334175
$31$	9.96445	1.78967	0.894834	−	0.446399i	$-0.147294\pi$
$31$	9.96445	1.78967	0.894834	+	0.446399i	$0.147294\pi$
$32$	−3.92075	−0.693096
$33$	−9.09025	−1.58241
$34$	2.80162	0.480475
$35$	7.80404	1.31912
$36$	1.55381	0.258968
$37$	−2.82214	−0.463956	−0.231978	−	0.972721i	$-0.574520\pi$
$37$	−2.82214	−0.463956	−0.231978	+	0.972721i	$0.574520\pi$
$38$	0.0902458	0.0146398
$39$	−8.96733	−1.43592
$40$	−4.81179	−0.760811
$41$	2.31404	0.361393	0.180696	−	0.983539i	$-0.442165\pi$
$41$	2.31404	0.361393	0.180696	+	0.983539i	$0.442165\pi$
$42$	−1.17570	−0.181414
$43$	8.30899	1.26711	0.633555	−	0.773698i	$-0.281595\pi$
$43$	8.30899	1.26711	0.633555	+	0.773698i	$0.281595\pi$
$44$	−11.5567	−1.74223
$45$	2.89167	0.431065
$46$	0.807781	0.119101
$47$	−0.223727	−0.0326339	−0.0163170	−	0.999867i	$-0.505194\pi$
$47$	−0.223727	−0.0326339	−0.0163170	+	0.999867i	$0.505194\pi$
$48$	−4.79365	−0.691904
$49$	−1.98720	−0.283886
$50$	−2.54836	−0.360393
$51$	11.5796	1.62147
$52$	−11.4004	−1.58095
$53$	−5.42151	−0.744702	−0.372351	−	0.928092i	$-0.621448\pi$
$53$	−5.42151	−0.744702	−0.372351	+	0.928092i	$0.621448\pi$
$54$	−2.01099	−0.273661
$55$	−21.5073	−2.90004
$56$	−3.09078	−0.413023
$57$	0.373002	0.0494053
$58$	−3.04914	−0.400371
$59$	13.9337	1.81401	0.907004	−	0.421122i	$-0.138364\pi$
$59$	13.9337	1.81401	0.907004	+	0.421122i	$0.138364\pi$
$60$	−9.61779	−1.24165
$61$	−7.48052	−0.957783	−0.478891	−	0.877874i	$-0.658961\pi$
$61$	−7.48052	−0.957783	−0.478891	+	0.877874i	$0.658961\pi$
$62$	−3.55172	−0.451069
$63$	1.85742	0.234013
$64$	−5.11018	−0.638773
$65$	−21.2164	−2.63158
$66$	3.24013	0.398832
$67$	2.18793	0.267299	0.133649	−	0.991029i	$-0.457330\pi$
$67$	2.18793	0.267299	0.133649	+	0.991029i	$0.457330\pi$
$68$	14.7214	1.78524
$69$	3.33870	0.401932
$70$	−2.78167	−0.332473
$71$	7.10663	0.843402	0.421701	−	0.906735i	$-0.361433\pi$
$71$	7.10663	0.843402	0.421701	+	0.906735i	$0.361433\pi$
$72$	−1.14524	−0.134968
$73$	−12.0902	−1.41505	−0.707527	−	0.706686i	$-0.750189\pi$
$73$	−12.0902	−1.41505	−0.707527	+	0.706686i	$0.750189\pi$
$74$	1.00592	0.116936
$75$	−10.5328	−1.21623
$76$	0.474206	0.0543952
$77$	−13.8149	−1.57435
$78$	3.19631	0.361911
$79$	−2.41600	−0.271821	−0.135911	−	0.990721i	$-0.543396\pi$
$79$	−2.41600	−0.271821	−0.135911	+	0.990721i	$0.543396\pi$
$80$	−11.3416	−1.26803
$81$	−5.82295	−0.646994
$82$	−0.824816	−0.0910857
$83$	−6.77046	−0.743155	−0.371577	−	0.928402i	$-0.621183\pi$
$83$	−6.77046	−0.743155	−0.371577	+	0.928402i	$0.621183\pi$
$84$	−6.17783	−0.674057
$85$	27.3970	2.97162
$86$	−2.96165	−0.319363
$87$	−12.6026	−1.35114
$88$	8.51793	0.908015
$89$	11.7850	1.24921	0.624606	−	0.780940i	$-0.285259\pi$
$89$	11.7850	1.24921	0.624606	+	0.780940i	$0.285259\pi$
$90$	−1.03071	−0.108646
$91$	−13.6280	−1.42861
$92$	4.24457	0.442527
$93$	−14.6799	−1.52223
$94$	0.0797452	0.00822509
$95$	0.882511	0.0905437
$96$	5.77615	0.589526
$97$	−16.7724	−1.70298	−0.851491	−	0.524369i	$-0.824301\pi$
$97$	−16.7724	−1.70298	−0.851491	+	0.524369i	$0.824301\pi$
$98$	0.708317	0.0715508
$99$	−5.11890	−0.514469
$100$	−13.3907	−1.33907
$101$	6.29553	0.626429	0.313214	−	0.949682i	$-0.398594\pi$
$101$	6.29553	0.626429	0.313214	+	0.949682i	$0.398594\pi$
$102$	−4.12743	−0.408676
$103$	14.8978	1.46792	0.733961	−	0.679192i	$-0.237670\pi$
$103$	14.8978	1.46792	0.733961	+	0.679192i	$0.237670\pi$
$104$	8.40275	0.823957
$105$	−11.4971	−1.12200
$106$	1.93244	0.187695
$107$	−13.3723	−1.29275	−0.646376	−	0.763019i	$-0.723716\pi$
$107$	−13.3723	−1.29275	−0.646376	+	0.763019i	$0.723716\pi$
$108$	−10.5670	−1.01681
$109$	−12.9058	−1.23616	−0.618078	−	0.786117i	$-0.712088\pi$
$109$	−12.9058	−1.23616	−0.618078	+	0.786117i	$0.712088\pi$
$110$	7.66604	0.730929
$111$	4.15765	0.394626
$112$	−7.28513	−0.688380
$113$	−0.287559	−0.0270513	−0.0135256	−	0.999909i	$-0.504305\pi$
$113$	−0.287559	−0.0270513	−0.0135256	+	0.999909i	$0.504305\pi$
$114$	−0.132953	−0.0124521
$115$	7.89927	0.736610
$116$	−16.0220	−1.48761
$117$	−5.04968	−0.466843
$118$	−4.96651	−0.457204
$119$	17.5980	1.61321
$120$	7.08886	0.647122
$121$	27.0726	2.46115
$122$	2.66635	0.241400
$123$	−3.40911	−0.307389
$124$	−18.6629	−1.67598
$125$	−7.49231	−0.670132
$126$	−0.662059	−0.0589809
$127$	6.14793	0.545541	0.272770	−	0.962079i	$-0.412060\pi$
$127$	6.14793	0.545541	0.272770	+	0.962079i	$0.412060\pi$
$128$	9.66296	0.854093
$129$	−12.2410	−1.07776
$130$	7.56238	0.663265
$131$	−2.80785	−0.245323	−0.122662	−	0.992449i	$-0.539143\pi$
$131$	−2.80785	−0.245323	−0.122662	+	0.992449i	$0.539143\pi$
$132$	17.0256	1.48189
$133$	0.566867	0.0491536
$134$	−0.779866	−0.0673701
$135$	−19.6654	−1.69253
$136$	−10.8506	−0.930427
$137$	3.18809	0.272377	0.136189	−	0.990683i	$-0.456515\pi$
$137$	3.18809	0.272377	0.136189	+	0.990683i	$0.456515\pi$
$138$	−1.19004	−0.101303
$139$	−15.7817	−1.33858	−0.669292	−	0.742999i	$-0.733402\pi$
$139$	−15.7817	−1.33858	−0.669292	+	0.742999i	$0.733402\pi$
$140$	−14.6166	−1.23533
$141$	0.329601	0.0277574
$142$	−2.53308	−0.212572
$143$	37.5578	3.14074
$144$	−2.69940	−0.224950
$145$	−29.8174	−2.47620
$146$	4.30944	0.356652
$147$	2.92760	0.241464
$148$	5.28572	0.434484
$149$	10.0931	0.826862	0.413431	−	0.910535i	$-0.364330\pi$
$149$	10.0931	0.826862	0.413431	+	0.910535i	$0.364330\pi$
$150$	3.75432	0.306539
$151$	15.1157	1.23010	0.615049	−	0.788489i	$-0.289136\pi$
$151$	15.1157	1.23010	0.615049	+	0.788489i	$0.289136\pi$
$152$	−0.349518	−0.0283496
$153$	6.52070	0.527168
$154$	4.92416	0.396800
$155$	−34.7322	−2.78976
$156$	16.7954	1.34471
$157$	−14.0356	−1.12016	−0.560081	−	0.828438i	$-0.689230\pi$
$157$	−14.0356	−1.12016	−0.560081	+	0.828438i	$0.689230\pi$
$158$	0.861158	0.0685101
$159$	7.98711	0.633419
$160$	13.6662	1.08041
$161$	5.07397	0.399885
$162$	2.07553	0.163069
$163$	3.54904	0.277982	0.138991	−	0.990294i	$-0.455614\pi$
$163$	3.54904	0.277982	0.138991	+	0.990294i	$0.455614\pi$
$164$	−4.33409	−0.338435
$165$	31.6851	2.46668
$166$	2.41326	0.187305
$167$	−19.1754	−1.48384	−0.741920	−	0.670489i	$-0.766084\pi$
$167$	−19.1754	−1.48384	−0.741920	+	0.670489i	$0.766084\pi$
$168$	4.55342	0.351304
$169$	24.0499	1.84999
$170$	−9.76538	−0.748970
$171$	0.210045	0.0160625
$172$	−15.5623	−1.18662
$173$	−18.1375	−1.37897	−0.689486	−	0.724299i	$-0.742163\pi$
$173$	−18.1375	−1.37897	−0.689486	+	0.724299i	$0.742163\pi$
$174$	4.49207	0.340543
$175$	−16.0072	−1.21003
$176$	20.0772	1.51338
$177$	−20.5274	−1.54294
$178$	−4.20066	−0.314853
$179$	15.9147	1.18952	0.594762	−	0.803902i	$-0.297246\pi$
$179$	15.9147	1.18952	0.594762	+	0.803902i	$0.297246\pi$
$180$	−5.41596	−0.403682
$181$	−22.0272	−1.63727	−0.818633	−	0.574316i	$-0.805268\pi$
$181$	−22.0272	−1.63727	−0.818633	+	0.574316i	$0.805268\pi$
$182$	4.85758	0.360067
$183$	11.0205	0.814659
$184$	−3.12850	−0.230636
$185$	9.83687	0.723221
$186$	5.23249	0.383665
$187$	−48.4987	−3.54658
$188$	0.419030	0.0305609
$189$	−12.6318	−0.918825
$190$	−0.314562	−0.0228207
$191$	1.00868	0.0729857	0.0364929	−	0.999334i	$-0.488381\pi$
$191$	1.00868	0.0729857	0.0364929	+	0.999334i	$0.488381\pi$
$192$	7.52846	0.543320
$193$	11.5781	0.833407	0.416703	−	0.909043i	$-0.363185\pi$
$193$	11.5781	0.833407	0.416703	+	0.909043i	$0.363185\pi$
$194$	5.97836	0.429221
$195$	31.2566	2.23833
$196$	3.72193	0.265852
$197$	17.9932	1.28196	0.640981	−	0.767557i	$-0.278528\pi$
$197$	17.9932	1.28196	0.640981	+	0.767557i	$0.278528\pi$
$198$	1.82458	0.129667
$199$	10.0096	0.709563	0.354781	−	0.934949i	$-0.384555\pi$
$199$	10.0096	0.709563	0.354781	+	0.934949i	$0.384555\pi$
$200$	9.86968	0.697892
$201$	−3.22332	−0.227356
$202$	−2.24398	−0.157886
$203$	−19.1527	−1.34426
$204$	−21.6880	−1.51847
$205$	−8.06585	−0.563344
$206$	−5.31016	−0.369976
$207$	1.88009	0.130675
$208$	19.8057	1.37328
$209$	−1.56224	−0.108062
$210$	4.09803	0.282791
$211$	0.607441	0.0418179	0.0209090	−	0.999781i	$-0.493344\pi$
$211$	0.607441	0.0418179	0.0209090	+	0.999781i	$0.493344\pi$
$212$	10.1542	0.697395
$213$	−10.4697	−0.717371
$214$	4.76642	0.325826
$215$	−28.9619	−1.97519
$216$	7.78845	0.529937
$217$	−22.3097	−1.51448
$218$	4.60015	0.311562
$219$	17.8117	1.20360
$220$	40.2821	2.71582
$221$	−47.8429	−3.21826
$222$	−1.48195	−0.0994620
$223$	−2.90043	−0.194227	−0.0971137	−	0.995273i	$-0.530961\pi$
$223$	−2.90043	−0.194227	−0.0971137	+	0.995273i	$0.530961\pi$
$224$	8.77827	0.586523
$225$	−5.93124	−0.395416
$226$	0.102497	0.00681802
$227$	7.45393	0.494735	0.247367	−	0.968922i	$-0.420435\pi$
$227$	7.45393	0.494735	0.247367	+	0.968922i	$0.420435\pi$
$228$	−0.698614	−0.0462668
$229$	−7.05682	−0.466327	−0.233164	−	0.972437i	$-0.574908\pi$
$229$	−7.05682	−0.466327	−0.233164	+	0.972437i	$0.574908\pi$
$230$	−2.81561	−0.185656
$231$	20.3524	1.33909
$232$	11.8092	0.775309
$233$	−8.23334	−0.539384	−0.269692	−	0.962947i	$-0.586922\pi$
$233$	−8.23334	−0.539384	−0.269692	+	0.962947i	$0.586922\pi$
$234$	1.79991	0.117664
$235$	0.779826	0.0508702
$236$	−26.0971	−1.69877
$237$	3.55932	0.231202
$238$	−6.27264	−0.406595
$239$	17.9811	1.16310	0.581550	−	0.813511i	$-0.302447\pi$
$239$	17.9811	1.16310	0.581550	+	0.813511i	$0.302447\pi$
$240$	16.7088	1.07855
$241$	−16.8994	−1.08859	−0.544294	−	0.838895i	$-0.683202\pi$
$241$	−16.8994	−1.08859	−0.544294	+	0.838895i	$0.683202\pi$
$242$	−9.64975	−0.620309
$243$	−8.34710	−0.535466
$244$	14.0107	0.896940
$245$	6.92661	0.442525
$246$	1.21514	0.0774746
$247$	−1.54111	−0.0980587
$248$	13.7557	0.873485
$249$	9.97443	0.632104
$250$	2.67055	0.168901
$251$	20.2486	1.27808	0.639040	−	0.769174i	$-0.279332\pi$
$251$	20.2486	1.27808	0.639040	+	0.769174i	$0.279332\pi$
$252$	−3.47886	−0.219148
$253$	−13.9834	−0.879131
$254$	−2.19137	−0.137499
$255$	−40.3620	−2.52757
$256$	6.77611	0.423507
$257$	12.2461	0.763890	0.381945	−	0.924185i	$-0.375254\pi$
$257$	12.2461	0.763890	0.381945	+	0.924185i	$0.375254\pi$
$258$	4.36319	0.271640
$259$	6.31856	0.392616
$260$	39.7374	2.46441
$261$	−7.09678	−0.439280
$262$	1.00083	0.0618314
$263$	26.1580	1.61297	0.806484	−	0.591256i	$-0.201368\pi$
$263$	26.1580	1.61297	0.806484	+	0.591256i	$0.201368\pi$
$264$	−12.5488	−0.772328
$265$	18.8973	1.16085
$266$	−0.202054	−0.0123887
$267$	−17.3620	−1.06254
$268$	−4.09789	−0.250318
$269$	15.8626	0.967161	0.483581	−	0.875300i	$-0.339336\pi$
$269$	15.8626	0.967161	0.483581	+	0.875300i	$0.339336\pi$
$270$	7.00952	0.426586
$271$	−11.7192	−0.711889	−0.355945	−	0.934507i	$-0.615841\pi$
$271$	−11.7192	−0.711889	−0.355945	+	0.934507i	$0.615841\pi$
$272$	−25.5753	−1.55073
$273$	20.0772	1.21513
$274$	−1.13636	−0.0686502
$275$	44.1145	2.66021
$276$	−6.25322	−0.376400
$277$	−21.2191	−1.27493	−0.637467	−	0.770478i	$-0.720018\pi$
$277$	−21.2191	−1.27493	−0.637467	+	0.770478i	$0.720018\pi$
$278$	5.62521	0.337378
$279$	−8.26654	−0.494905
$280$	10.7733	0.643826
$281$	−5.81862	−0.347110	−0.173555	−	0.984824i	$-0.555525\pi$
$281$	−5.81862	−0.347110	−0.173555	+	0.984824i	$0.555525\pi$
$282$	−0.117483	−0.00699599
$283$	23.6889	1.40816	0.704080	−	0.710121i	$-0.251360\pi$
$283$	23.6889	1.40816	0.704080	+	0.710121i	$0.251360\pi$
$284$	−13.3104	−0.789825
$285$	−1.30014	−0.0770136
$286$	−13.3871	−0.791594
$287$	−5.18097	−0.305823
$288$	3.25266	0.191665
$289$	44.7800	2.63412
$290$	10.6281	0.624104
$291$	24.7096	1.44850
$292$	22.6444	1.32516
$293$	−19.2334	−1.12363	−0.561813	−	0.827264i	$-0.689896\pi$
$293$	−19.2334	−1.12363	−0.561813	+	0.827264i	$0.689896\pi$
$294$	−1.04351	−0.0608588
$295$	−48.5673	−2.82770
$296$	−3.89588	−0.226444
$297$	34.8121	2.02000
$298$	−3.59759	−0.208403
$299$	−13.7943	−0.797748
$300$	19.7275	1.13897
$301$	−18.6032	−1.07227
$302$	−5.38784	−0.310035
$303$	−9.27474	−0.532820
$304$	−0.823831	−0.0472500
$305$	26.0742	1.49300
$306$	−2.32424	−0.132868
$307$	1.37917	0.0787135	0.0393567	−	0.999225i	$-0.487469\pi$
$307$	1.37917	0.0787135	0.0393567	+	0.999225i	$0.487469\pi$
$308$	25.8746	1.47434
$309$	−21.9478	−1.24857
$310$	12.3799	0.703133
$311$	9.22872	0.523313	0.261656	−	0.965161i	$-0.415731\pi$
$311$	9.22872	0.523313	0.261656	+	0.965161i	$0.415731\pi$
$312$	−12.3792	−0.700832
$313$	0.944259	0.0533727	0.0266863	−	0.999644i	$-0.491504\pi$
$313$	0.944259	0.0533727	0.0266863	+	0.999644i	$0.491504\pi$
$314$	5.00284	0.282326
$315$	−6.47425	−0.364783
$316$	4.52505	0.254554
$317$	−18.6457	−1.04724	−0.523622	−	0.851950i	$-0.675420\pi$
$317$	−18.6457	−1.04724	−0.523622	+	0.851950i	$0.675420\pi$
$318$	−2.84692	−0.159648
$319$	52.7834	2.95530
$320$	17.8121	0.995728
$321$	19.7005	1.09957
$322$	−1.80856	−0.100787
$323$	1.99006	0.110730
$324$	10.9061	0.605894
$325$	43.5180	2.41394
$326$	−1.26502	−0.0700629
$327$	19.0132	1.05143
$328$	3.19447	0.176385
$329$	0.500909	0.0276160
$330$	−11.2938	−0.621704
$331$	2.17841	0.119736	0.0598681	−	0.998206i	$-0.480932\pi$
$331$	2.17841	0.119736	0.0598681	+	0.998206i	$0.480932\pi$
$332$	12.6807	0.695946
$333$	2.34125	0.128300
$334$	6.83488	0.373988
$335$	−7.62629	−0.416668
$336$	10.7326	0.585514
$337$	14.7028	0.800910	0.400455	−	0.916316i	$-0.368852\pi$
$337$	14.7028	0.800910	0.400455	+	0.916316i	$0.368852\pi$
$338$	−8.57233	−0.466273
$339$	0.423639	0.0230089
$340$	−51.3133	−2.78285
$341$	61.4836	3.32953
$342$	−0.0748682	−0.00404841
$343$	20.1217	1.08647
$344$	11.4703	0.618439
$345$	−11.6374	−0.626537
$346$	6.46493	0.347557
$347$	2.03905	0.109462	0.0547310	−	0.998501i	$-0.482570\pi$
$347$	2.03905	0.109462	0.0547310	+	0.998501i	$0.482570\pi$
$348$	23.6041	1.26531
$349$	16.7829	0.898365	0.449183	−	0.893440i	$-0.351715\pi$
$349$	16.7829	0.898365	0.449183	+	0.893440i	$0.351715\pi$
$350$	5.70560	0.304977
$351$	34.3413	1.83300
$352$	−24.1922	−1.28945
$353$	21.5689	1.14800	0.573998	−	0.818857i	$-0.305392\pi$
$353$	21.5689	1.14800	0.573998	+	0.818857i	$0.305392\pi$
$354$	7.31679	0.388883
$355$	−24.7710	−1.31471
$356$	−22.0728	−1.16986
$357$	−25.9259	−1.37214
$358$	−5.67265	−0.299809
$359$	−32.0868	−1.69348	−0.846738	−	0.532010i	$-0.821437\pi$
$359$	−32.0868	−1.69348	−0.846738	+	0.532010i	$0.821437\pi$
$360$	3.99188	0.210390
$361$	−18.9359	−0.996626
$362$	7.85136	0.412658
$363$	−39.8841	−2.09337
$364$	25.5247	1.33786
$365$	42.1419	2.20581
$366$	−3.92814	−0.205327
$367$	21.1572	1.10440	0.552199	−	0.833712i	$-0.313789\pi$
$367$	21.1572	1.10440	0.552199	+	0.833712i	$0.313789\pi$
$368$	−7.37403	−0.384398
$369$	−1.91974	−0.0999375
$370$	−3.50625	−0.182281
$371$	12.1384	0.630193
$372$	27.4947	1.42553
$373$	−33.4125	−1.73003	−0.865017	−	0.501743i	$-0.832692\pi$
$373$	−33.4125	−1.73003	−0.865017	+	0.501743i	$0.832692\pi$
$374$	17.2869	0.893883
$375$	11.0379	0.569993
$376$	−0.308849	−0.0159277
$377$	52.0696	2.68172
$378$	4.50246	0.231581
$379$	20.8609	1.07155	0.535776	−	0.844360i	$-0.320019\pi$
$379$	20.8609	1.07155	0.535776	+	0.844360i	$0.320019\pi$
$380$	−1.65290	−0.0847920
$381$	−9.05730	−0.464019
$382$	−0.359534	−0.0183954
$383$	−10.0991	−0.516042	−0.258021	−	0.966139i	$-0.583070\pi$
$383$	−10.0991	−0.516042	−0.258021	+	0.966139i	$0.583070\pi$
$384$	−14.2357	−0.726464
$385$	48.1533	2.45412
$386$	−4.12688	−0.210052
$387$	−6.89316	−0.350399
$388$	31.4139	1.59480
$389$	6.72132	0.340784	0.170392	−	0.985376i	$-0.445497\pi$
$389$	6.72132	0.340784	0.170392	+	0.985376i	$0.445497\pi$
$390$	−11.1411	−0.564152
$391$	17.8128	0.900831
$392$	−2.74328	−0.138556
$393$	4.13660	0.208664
$394$	−6.41348	−0.323107
$395$	8.42124	0.423719
$396$	9.58745	0.481787
$397$	−17.4041	−0.873486	−0.436743	−	0.899586i	$-0.643868\pi$
$397$	−17.4041	−0.873486	−0.436743	+	0.899586i	$0.643868\pi$
$398$	−3.56782	−0.178839
$399$	−0.835124	−0.0418085
$400$	23.2634	1.16317
$401$	−17.1101	−0.854436	−0.427218	−	0.904149i	$-0.640506\pi$
$401$	−17.1101	−0.854436	−0.427218	+	0.904149i	$0.640506\pi$
$402$	1.14892	0.0573029
$403$	60.6522	3.02130
$404$	−11.7912	−0.586635
$405$	20.2965	1.00854
$406$	6.82680	0.338808
$407$	−17.4134	−0.863152
$408$	15.9853	0.791392
$409$	28.5903	1.41370	0.706850	−	0.707363i	$-0.250115\pi$
$409$	28.5903	1.41370	0.706850	+	0.707363i	$0.250115\pi$
$410$	2.87499	0.141986
$411$	−4.69679	−0.231675
$412$	−27.9028	−1.37467
$413$	−31.1965	−1.53508
$414$	−0.670137	−0.0329355
$415$	23.5992	1.15844
$416$	−23.8650	−1.17008
$417$	23.2500	1.13856
$418$	0.556844	0.0272361
$419$	16.5296	0.807525	0.403762	−	0.914864i	$-0.367702\pi$
$419$	16.5296	0.807525	0.403762	+	0.914864i	$0.367702\pi$
$420$	21.5335	1.05073
$421$	−15.2834	−0.744865	−0.372433	−	0.928059i	$-0.621476\pi$
$421$	−15.2834	−0.744865	−0.372433	+	0.928059i	$0.621476\pi$
$422$	−0.216516	−0.0105398
$423$	0.185605	0.00902441
$424$	−7.48425	−0.363467
$425$	−56.1952	−2.72587
$426$	3.73181	0.180807
$427$	16.7484	0.810510
$428$	25.0457	1.21063
$429$	−55.3311	−2.67141
$430$	10.3232	0.497828
$431$	3.33342	0.160565	0.0802827	−	0.996772i	$-0.474418\pi$
$431$	3.33342	0.160565	0.0802827	+	0.996772i	$0.474418\pi$
$432$	18.3578	0.883240
$433$	3.77005	0.181177	0.0905885	−	0.995888i	$-0.471125\pi$
$433$	3.77005	0.181177	0.0905885	+	0.995888i	$0.471125\pi$
$434$	7.95205	0.381711
$435$	43.9278	2.10618
$436$	24.1720	1.15763
$437$	0.573784	0.0274478
$438$	−6.34878	−0.303356
$439$	−22.6296	−1.08005	−0.540026	−	0.841648i	$-0.681586\pi$
$439$	−22.6296	−1.08005	−0.540026	+	0.841648i	$0.681586\pi$
$440$	−29.6902	−1.41543
$441$	1.64859	0.0785041
$442$	17.0531	0.811133
$443$	4.77569	0.226900	0.113450	−	0.993544i	$-0.463810\pi$
$443$	4.77569	0.226900	0.113450	+	0.993544i	$0.463810\pi$
$444$	−7.78707	−0.369558
$445$	−41.0781	−1.94729
$446$	1.03383	0.0489532
$447$	−14.8695	−0.703302
$448$	11.4413	0.540552
$449$	−11.4606	−0.540861	−0.270431	−	0.962739i	$-0.587166\pi$
$449$	−11.4606	−0.540861	−0.270431	+	0.962739i	$0.587166\pi$
$450$	2.11413	0.0996610
$451$	14.2783	0.672341
$452$	0.538583	0.0253328
$453$	−22.2689	−1.04628
$454$	−2.65688	−0.124693
$455$	47.5021	2.22693
$456$	0.514919	0.0241133
$457$	28.9065	1.35219	0.676095	−	0.736815i	$-0.263671\pi$
$457$	28.9065	1.35219	0.676095	+	0.736815i	$0.263671\pi$
$458$	2.51533	0.117534
$459$	−44.3453	−2.06986
$460$	−14.7949	−0.689818
$461$	22.3024	1.03872	0.519362	−	0.854554i	$-0.326170\pi$
$461$	22.3024	1.03872	0.519362	+	0.854554i	$0.326170\pi$
$462$	−7.25441	−0.337506
$463$	13.6826	0.635887	0.317943	−	0.948110i	$-0.397008\pi$
$463$	13.6826	0.635887	0.317943	+	0.948110i	$0.397008\pi$
$464$	27.8348	1.29220
$465$	51.1684	2.37288
$466$	2.93469	0.135947
$467$	16.8717	0.780729	0.390365	−	0.920660i	$-0.372349\pi$
$467$	16.8717	0.780729	0.390365	+	0.920660i	$0.372349\pi$
$468$	9.45780	0.437187
$469$	−4.89862	−0.226197
$470$	−0.277961	−0.0128214
$471$	20.6776	0.952773
$472$	19.2350	0.885364
$473$	51.2690	2.35735
$474$	−1.26868	−0.0582724
$475$	−1.81016	−0.0830557
$476$	−32.9603	−1.51073
$477$	4.49770	0.205936
$478$	−6.40917	−0.293148
$479$	−3.35370	−0.153234	−0.0766172	−	0.997061i	$-0.524412\pi$
$479$	−3.35370	−0.153234	−0.0766172	+	0.997061i	$0.524412\pi$
$480$	−20.1334	−0.918960
$481$	−17.1780	−0.783247
$482$	6.02362	0.274369
$483$	−7.47511	−0.340129
$484$	−50.7057	−2.30480
$485$	58.4622	2.65463
$486$	2.97524	0.134959
$487$	−5.70881	−0.258691	−0.129346	−	0.991600i	$-0.541288\pi$
$487$	−5.70881	−0.258691	−0.129346	+	0.991600i	$0.541288\pi$
$488$	−10.3267	−0.467466
$489$	−5.22854	−0.236443
$490$	−2.46892	−0.111534
$491$	3.08252	0.139112	0.0695562	−	0.997578i	$-0.477842\pi$
$491$	3.08252	0.139112	0.0695562	+	0.997578i	$0.477842\pi$
$492$	6.38509	0.287862
$493$	−67.2380	−3.02825
$494$	0.549314	0.0247148
$495$	17.8425	0.801961
$496$	32.4228	1.45583
$497$	−15.9112	−0.713717
$498$	−3.55528	−0.159316
$499$	−4.03045	−0.180428	−0.0902140	−	0.995922i	$-0.528755\pi$
$499$	−4.03045	−0.180428	−0.0902140	+	0.995922i	$0.528755\pi$
$500$	14.0327	0.627562
$501$	28.2498	1.26211
$502$	−7.21740	−0.322128
$503$	−28.2019	−1.25746	−0.628731	−	0.777623i	$-0.716425\pi$
$503$	−28.2019	−1.25746	−0.628731	+	0.777623i	$0.716425\pi$
$504$	2.56412	0.114215
$505$	−21.9438	−0.976485
$506$	4.98425	0.221577
$507$	−35.4309	−1.57354
$508$	−11.5148	−0.510885
$509$	36.6242	1.62334	0.811669	−	0.584117i	$-0.198559\pi$
$509$	36.6242	1.62334	0.811669	+	0.584117i	$0.198559\pi$
$510$	14.3866	0.637050
$511$	27.0692	1.19747
$512$	−21.7412	−0.960834
$513$	−1.42845	−0.0630675
$514$	−4.36499	−0.192532
$515$	−51.9279	−2.28822
$516$	22.9268	1.00930
$517$	−1.38046	−0.0607127
$518$	−2.25219	−0.0989553
$519$	26.7207	1.17291
$520$	−29.2887	−1.28440
$521$	12.0283	0.526969	0.263484	−	0.964664i	$-0.415128\pi$
$521$	12.0283	0.526969	0.263484	+	0.964664i	$0.415128\pi$
$522$	2.52957	0.110716
$523$	−6.05769	−0.264884	−0.132442	−	0.991191i	$-0.542282\pi$
$523$	−6.05769	−0.264884	−0.132442	+	0.991191i	$0.542282\pi$
$524$	5.25897	0.229739
$525$	23.5822	1.02921
$526$	−9.32373	−0.406534
$527$	−78.3208	−3.41171
$528$	−29.5783	−1.28723
$529$	−17.8641	−0.776701
$530$	−6.73574	−0.292582
$531$	−11.5594	−0.501635
$532$	−1.06171	−0.0460312
$533$	14.0853	0.610100
$534$	6.18852	0.267803
$535$	46.6107	2.01516
$536$	3.02038	0.130461
$537$	−23.4460	−1.01177
$538$	−5.65407	−0.243764
$539$	−12.2616	−0.528145
$540$	36.8323	1.58501
$541$	−28.3509	−1.21890	−0.609449	−	0.792825i	$-0.708609\pi$
$541$	−28.3509	−1.21890	−0.609449	+	0.792825i	$0.708609\pi$
$542$	4.17718	0.179425
$543$	32.4510	1.39261
$544$	30.8172	1.32128
$545$	44.9848	1.92694
$546$	−7.15631	−0.306262
$547$	−6.18228	−0.264335	−0.132168	−	0.991227i	$-0.542194\pi$
$547$	−6.18228	−0.264335	−0.132168	+	0.991227i	$0.542194\pi$
$548$	−5.97114	−0.255075
$549$	6.20586	0.264860
$550$	−15.7242	−0.670481
$551$	−2.16587	−0.0922691
$552$	4.60898	0.196171
$553$	5.40925	0.230025
$554$	7.56333	0.321335
$555$	−14.4919	−0.615149
$556$	29.5583	1.25355
$557$	23.1333	0.980189	0.490095	−	0.871669i	$-0.336962\pi$
$557$	23.1333	0.980189	0.490095	+	0.871669i	$0.336962\pi$
$558$	2.94652	0.124736
$559$	50.5757	2.13912
$560$	25.3931	1.07306
$561$	71.4496	3.01661
$562$	2.07399	0.0874859
$563$	25.9922	1.09544	0.547721	−	0.836661i	$-0.315496\pi$
$563$	25.9922	1.09544	0.547721	+	0.836661i	$0.315496\pi$
$564$	−0.617326	−0.0259941
$565$	1.00232	0.0421679
$566$	−8.44366	−0.354914
$567$	13.0372	0.547510
$568$	9.81051	0.411640
$569$	−7.56083	−0.316966	−0.158483	−	0.987362i	$-0.550660\pi$
$569$	−7.56083	−0.316966	−0.158483	+	0.987362i	$0.550660\pi$
$570$	0.463421	0.0194106
$571$	−34.8344	−1.45778	−0.728888	−	0.684633i	$-0.759962\pi$
$571$	−34.8344	−1.45778	−0.728888	+	0.684633i	$0.759962\pi$
$572$	−70.3439	−2.94122
$573$	−1.48602	−0.0620793
$574$	1.84670	0.0770799
$575$	−16.2025	−0.675692
$576$	4.23942	0.176643
$577$	−33.4816	−1.39386	−0.696928	−	0.717141i	$-0.745450\pi$
$577$	−33.4816	−1.39386	−0.696928	+	0.717141i	$0.745450\pi$
$578$	−15.9614	−0.663906
$579$	−17.0571	−0.708869
$580$	55.8465	2.31890
$581$	15.1586	0.628884
$582$	−8.80748	−0.365082
$583$	−33.4523	−1.38545
$584$	−16.6902	−0.690647
$585$	17.6012	0.727721
$586$	6.85554	0.283200
$587$	−37.2237	−1.53639	−0.768193	−	0.640218i	$-0.778844\pi$
$587$	−37.2237	−1.53639	−0.768193	+	0.640218i	$0.778844\pi$
$588$	−5.48324	−0.226125
$589$	−2.52287	−0.103953
$590$	17.3113	0.712696
$591$	−26.5080	−1.09039
$592$	−9.18280	−0.377411
$593$	−27.3043	−1.12125	−0.560627	−	0.828068i	$-0.689440\pi$
$593$	−27.3043	−1.12125	−0.560627	+	0.828068i	$0.689440\pi$
$594$	−12.4084	−0.509123
$595$	−61.3399	−2.51469
$596$	−18.9040	−0.774336
$597$	−14.7464	−0.603531
$598$	4.91685	0.201065
$599$	−17.5271	−0.716136	−0.358068	−	0.933695i	$-0.616564\pi$
$599$	−17.5271	−0.716136	−0.358068	+	0.933695i	$0.616564\pi$
$600$	−14.5403	−0.593605
$601$	−7.29439	−0.297544	−0.148772	−	0.988872i	$-0.547532\pi$
$601$	−7.29439	−0.297544	−0.148772	+	0.988872i	$0.547532\pi$
$602$	6.63093	0.270256
$603$	−1.81512	−0.0739172
$604$	−28.3110	−1.15196
$605$	−94.3646	−3.83647
$606$	3.30589	0.134292
$607$	−10.9207	−0.443257	−0.221629	−	0.975131i	$-0.571137\pi$
$607$	−10.9207	−0.443257	−0.221629	+	0.975131i	$0.571137\pi$
$608$	0.992681	0.0402585
$609$	28.2163	1.14338
$610$	−9.29388	−0.376298
$611$	−1.36180	−0.0550924
$612$	−12.2130	−0.493679
$613$	17.2465	0.696579	0.348289	−	0.937387i	$-0.386763\pi$
$613$	17.2465	0.696579	0.348289	+	0.937387i	$0.386763\pi$
$614$	−0.491591	−0.0198390
$615$	11.8828	0.479162
$616$	−19.0710	−0.768394
$617$	−28.7152	−1.15603	−0.578016	−	0.816025i	$-0.696173\pi$
$617$	−28.7152	−1.15603	−0.578016	+	0.816025i	$0.696173\pi$
$618$	7.82307	0.314690
$619$	−4.10249	−0.164893	−0.0824464	−	0.996595i	$-0.526273\pi$
$619$	−4.10249	−0.164893	−0.0824464	+	0.996595i	$0.526273\pi$
$620$	65.0517	2.61254
$621$	−12.7859	−0.513080
$622$	−3.28948	−0.131896
$623$	−26.3859	−1.05713
$624$	−29.1783	−1.16807
$625$	−9.63220	−0.385288
$626$	−0.336571	−0.0134521
$627$	2.30153	0.0919143
$628$	26.2880	1.04900
$629$	22.1821	0.884457
$630$	2.30768	0.0919402
$631$	−12.6290	−0.502754	−0.251377	−	0.967889i	$-0.580883\pi$
$631$	−12.6290	−0.502754	−0.251377	+	0.967889i	$0.580883\pi$
$632$	−3.33522	−0.132668
$633$	−0.894898	−0.0355690
$634$	6.64605	0.263948
$635$	−21.4293	−0.850396
$636$	−14.9595	−0.593182
$637$	−12.0958	−0.479254
$638$	−18.8141	−0.744857
$639$	−5.89568	−0.233230
$640$	−33.6813	−1.33137
$641$	−32.1471	−1.26973	−0.634867	−	0.772621i	$-0.718945\pi$
$641$	−32.1471	−1.26973	−0.634867	+	0.772621i	$0.718945\pi$
$642$	−7.02202	−0.277137
$643$	44.6435	1.76057	0.880284	−	0.474446i	$-0.157352\pi$
$643$	44.6435	1.76057	0.880284	+	0.474446i	$0.157352\pi$
$644$	−9.50330	−0.374482
$645$	42.6675	1.68003
$646$	−0.709334	−0.0279084
$647$	−8.80372	−0.346110	−0.173055	−	0.984912i	$-0.555364\pi$
$647$	−8.80372	−0.346110	−0.173055	+	0.984912i	$0.555364\pi$
$648$	−8.03842	−0.315779
$649$	85.9749	3.37481
$650$	−15.5115	−0.608412
$651$	32.8672	1.28817
$652$	−6.64718	−0.260324
$653$	33.5097	1.31134	0.655669	−	0.755049i	$-0.272387\pi$
$653$	33.5097	1.31134	0.655669	+	0.755049i	$0.272387\pi$
$654$	−6.77707	−0.265004
$655$	9.78708	0.382413
$656$	7.52954	0.293979
$657$	10.0301	0.391311
$658$	−0.178544	−0.00696036
$659$	−16.6013	−0.646697	−0.323348	−	0.946280i	$-0.604809\pi$
$659$	−16.6013	−0.646697	−0.323348	+	0.946280i	$0.604809\pi$
$660$	−59.3446	−2.30999
$661$	−18.4108	−0.716096	−0.358048	−	0.933703i	$-0.616558\pi$
$661$	−18.4108	−0.716096	−0.358048	+	0.933703i	$0.616558\pi$
$662$	−0.776471	−0.0301784
$663$	70.4834	2.73735
$664$	−9.34644	−0.362712
$665$	−1.97588	−0.0766213
$666$	−0.834515	−0.0323368
$667$	−19.3865	−0.750647
$668$	35.9146	1.38958
$669$	4.27300	0.165204
$670$	2.71831	0.105017
$671$	−46.1571	−1.78187
$672$	−12.9324	−0.498877
$673$	8.21205	0.316551	0.158276	−	0.987395i	$-0.449407\pi$
$673$	8.21205	0.316551	0.158276	+	0.987395i	$0.449407\pi$
$674$	−5.24064	−0.201862
$675$	40.3365	1.55255
$676$	−45.0443	−1.73247
$677$	16.9870	0.652862	0.326431	−	0.945221i	$-0.394154\pi$
$677$	16.9870	0.652862	0.326431	+	0.945221i	$0.394154\pi$
$678$	−0.151002	−0.00579919
$679$	37.5523	1.44112
$680$	37.8208	1.45036
$681$	−10.9813	−0.420806
$682$	−21.9152	−0.839177
$683$	−45.7338	−1.74995	−0.874977	−	0.484165i	$-0.839123\pi$
$683$	−45.7338	−1.74995	−0.874977	+	0.484165i	$0.839123\pi$
$684$	−0.393403	−0.0150421
$685$	−11.1125	−0.424585
$686$	−7.17217	−0.273835
$687$	10.3963	0.396643
$688$	27.0362	1.03074
$689$	−33.0000	−1.25720
$690$	4.14803	0.157913
$691$	−10.0269	−0.381440	−0.190720	−	0.981644i	$-0.561082\pi$
$691$	−10.0269	−0.381440	−0.190720	+	0.981644i	$0.561082\pi$
$692$	33.9707	1.29137
$693$	11.4609	0.435362
$694$	−0.726799	−0.0275889
$695$	55.0088	2.08660
$696$	−17.3976	−0.659453
$697$	−18.1884	−0.688936
$698$	−5.98207	−0.226425
$699$	12.1296	0.458783
$700$	29.9807	1.13316
$701$	−28.4421	−1.07424	−0.537122	−	0.843504i	$-0.680489\pi$
$701$	−28.4421	−1.07424	−0.537122	+	0.843504i	$0.680489\pi$
$702$	−12.2406	−0.461992
$703$	0.714528	0.0269489
$704$	−31.5314	−1.18838
$705$	−1.14886	−0.0432686
$706$	−7.68801	−0.289342
$707$	−14.0952	−0.530106
$708$	38.4469	1.44492
$709$	24.7979	0.931305	0.465652	−	0.884968i	$-0.345820\pi$
$709$	24.7979	0.931305	0.465652	+	0.884968i	$0.345820\pi$
$710$	8.82935	0.331360
$711$	2.00432	0.0751679
$712$	16.2689	0.609704
$713$	−22.5819	−0.845700
$714$	9.24102	0.345836
$715$	−130.912	−4.89583
$716$	−29.8075	−1.11396
$717$	−26.4902	−0.989295
$718$	11.4370	0.426825
$719$	−29.9790	−1.11803	−0.559013	−	0.829159i	$-0.688820\pi$
$719$	−29.9790	−1.11803	−0.559013	+	0.829159i	$0.688820\pi$
$720$	9.40907	0.350655
$721$	−33.3551	−1.24221
$722$	6.74950	0.251190
$723$	24.8967	0.925918
$724$	41.2558	1.53326
$725$	61.1598	2.27142
$726$	14.2163	0.527615
$727$	12.7160	0.471610	0.235805	−	0.971800i	$-0.424227\pi$
$727$	12.7160	0.471610	0.235805	+	0.971800i	$0.424227\pi$
$728$	−18.8132	−0.697262
$729$	29.7660	1.10244
$730$	−15.0210	−0.555953
$731$	−65.3089	−2.41554
$732$	−20.6409	−0.762908
$733$	0.595292	0.0219876	0.0109938	−	0.999940i	$-0.496500\pi$
$733$	0.595292	0.0219876	0.0109938	+	0.999940i	$0.496500\pi$
$734$	−7.54128	−0.278354
$735$	−10.2045	−0.376397
$736$	8.88539	0.327520
$737$	13.5002	0.497286
$738$	0.684270	0.0251883
$739$	−7.65317	−0.281527	−0.140763	−	0.990043i	$-0.544956\pi$
$739$	−7.65317	−0.281527	−0.140763	+	0.990043i	$0.544956\pi$
$740$	−18.4240	−0.677279
$741$	2.27041	0.0834056
$742$	−4.32660	−0.158834
$743$	−23.6051	−0.865988	−0.432994	−	0.901397i	$-0.642543\pi$
$743$	−23.6051	−0.865988	−0.432994	+	0.901397i	$0.642543\pi$
$744$	−20.2652	−0.742958
$745$	−35.1808	−1.28892
$746$	11.9095	0.436039
$747$	5.61680	0.205508
$748$	90.8357	3.32128
$749$	29.9397	1.09397
$750$	−3.93433	−0.143661
$751$	43.6212	1.59176	0.795880	−	0.605454i	$-0.207009\pi$
$751$	43.6212	1.59176	0.795880	+	0.605454i	$0.207009\pi$
$752$	−0.727974	−0.0265465
$753$	−29.8308	−1.08709
$754$	−18.5597	−0.675903
$755$	−52.6875	−1.91749
$756$	23.6586	0.860457
$757$	−45.7138	−1.66150	−0.830748	−	0.556649i	$-0.812087\pi$
$757$	−45.7138	−1.66150	−0.830748	+	0.556649i	$0.812087\pi$
$758$	−7.43565	−0.270075
$759$	20.6008	0.747761
$760$	1.21828	0.0441918
$761$	36.9968	1.34113	0.670566	−	0.741849i	$-0.266051\pi$
$761$	36.9968	1.34113	0.670566	+	0.741849i	$0.266051\pi$
$762$	3.22838	0.116952
$763$	28.8953	1.04608
$764$	−1.88921	−0.0683493
$765$	−22.7286	−0.821756
$766$	3.59973	0.130064
$767$	84.8123	3.06239
$768$	−9.98274	−0.360221
$769$	−40.5275	−1.46146	−0.730729	−	0.682668i	$-0.760820\pi$
$769$	−40.5275	−1.46146	−0.730729	+	0.682668i	$0.760820\pi$
$770$	−17.1637	−0.618538
$771$	−18.0413	−0.649741
$772$	−21.6851	−0.780465
$773$	4.66186	0.167676	0.0838378	−	0.996479i	$-0.473282\pi$
$773$	4.66186	0.167676	0.0838378	+	0.996479i	$0.473282\pi$
$774$	2.45700	0.0883149
$775$	71.2408	2.55904
$776$	−23.1539	−0.831176
$777$	−9.30867	−0.333947
$778$	−2.39574	−0.0858916
$779$	−0.585885	−0.0209915
$780$	−58.5421	−2.09614
$781$	43.8501	1.56908
$782$	−6.34918	−0.227046
$783$	48.2630	1.72478
$784$	−6.46604	−0.230930
$785$	48.9226	1.74612
$786$	−1.47445	−0.0525918
$787$	36.0743	1.28591	0.642954	−	0.765904i	$-0.277708\pi$
$787$	36.0743	1.28591	0.642954	+	0.765904i	$0.277708\pi$
$788$	−33.7003	−1.20053
$789$	−38.5366	−1.37194
$790$	−3.00166	−0.106794
$791$	0.643824	0.0228917
$792$	−7.06650	−0.251097
$793$	−45.5329	−1.61692
$794$	6.20350	0.220154
$795$	−27.8400	−0.987382
$796$	−18.7475	−0.664488
$797$	0.955482	0.0338449	0.0169225	−	0.999857i	$-0.494613\pi$
$797$	0.955482	0.0338449	0.0169225	+	0.999857i	$0.494613\pi$
$798$	0.297671	0.0105374
$799$	1.75850	0.0622113
$800$	−28.0313	−0.991058
$801$	−9.77691	−0.345450
$802$	6.09870	0.215353
$803$	−74.6004	−2.63259
$804$	6.03712	0.212913
$805$	−17.6859	−0.623346
$806$	−21.6189	−0.761492
$807$	−23.3692	−0.822636
$808$	8.69081	0.305742
$809$	−25.4363	−0.894291	−0.447145	−	0.894461i	$-0.647559\pi$
$809$	−25.4363	−0.894291	−0.447145	+	0.894461i	$0.647559\pi$
$810$	−7.23449	−0.254194
$811$	17.8228	0.625844	0.312922	−	0.949779i	$-0.398692\pi$
$811$	17.8228	0.625844	0.312922	+	0.949779i	$0.398692\pi$
$812$	35.8722	1.25887
$813$	17.2650	0.605510
$814$	6.20684	0.217549
$815$	−12.3706	−0.433322
$816$	37.6782	1.31900
$817$	−2.10373	−0.0736001
$818$	−10.1907	−0.356310
$819$	11.3059	0.395059
$820$	15.1069	0.527557
$821$	13.5821	0.474017	0.237009	−	0.971508i	$-0.423833\pi$
$821$	13.5821	0.474017	0.237009	+	0.971508i	$0.423833\pi$
$822$	1.67412	0.0583916
$823$	34.3758	1.19827	0.599133	−	0.800649i	$-0.295512\pi$
$823$	34.3758	1.19827	0.599133	+	0.800649i	$0.295512\pi$
$824$	20.5660	0.716450
$825$	−64.9907	−2.26269
$826$	11.1197	0.386902
$827$	26.5713	0.923976	0.461988	−	0.886886i	$-0.347136\pi$
$827$	26.5713	0.923976	0.461988	+	0.886886i	$0.347136\pi$
$828$	−3.52131	−0.122374
$829$	−2.20920	−0.0767288	−0.0383644	−	0.999264i	$-0.512215\pi$
$829$	−2.20920	−0.0767288	−0.0383644	+	0.999264i	$0.512215\pi$
$830$	−8.41169	−0.291974
$831$	31.2606	1.08442
$832$	−31.1050	−1.07837
$833$	15.6194	0.541182
$834$	−8.28721	−0.286963
$835$	66.8381	2.31303
$836$	2.92600	0.101198
$837$	56.2182	1.94318
$838$	−5.89181	−0.203529
$839$	−0.493122	−0.0170244	−0.00851222	−	0.999964i	$-0.502710\pi$
$839$	−0.493122	−0.0170244	−0.00851222	+	0.999964i	$0.502710\pi$
$840$	−15.8715	−0.547617
$841$	44.1782	1.52339
$842$	5.44759	0.187736
$843$	8.57215	0.295241
$844$	−1.13771	−0.0391615
$845$	−83.8286	−2.88379
$846$	−0.0661568	−0.00227452
$847$	−60.6136	−2.08271
$848$	−17.6408	−0.605786
$849$	−34.8991	−1.19773
$850$	20.0302	0.687030
$851$	6.39566	0.219241
$852$	19.6092	0.671800
$853$	39.2042	1.34233	0.671163	−	0.741310i	$-0.265795\pi$
$853$	39.2042	1.34233	0.671163	+	0.741310i	$0.265795\pi$
$854$	−5.96978	−0.204282
$855$	−0.732134	−0.0250385
$856$	−18.4601	−0.630954
$857$	−45.2448	−1.54553	−0.772766	−	0.634691i	$-0.781127\pi$
$857$	−45.2448	−1.54553	−0.772766	+	0.634691i	$0.781127\pi$
$858$	19.7222	0.673305
$859$	−38.4000	−1.31019	−0.655095	−	0.755546i	$-0.727372\pi$
$859$	−38.4000	−1.31019	−0.655095	+	0.755546i	$0.727372\pi$
$860$	54.2443	1.84971
$861$	7.63275	0.260123
$862$	−1.18816	−0.0404690
$863$	33.5810	1.14311	0.571555	−	0.820563i	$-0.306340\pi$
$863$	33.5810	1.14311	0.571555	+	0.820563i	$0.306340\pi$
$864$	−22.1203	−0.752550
$865$	63.2204	2.14956
$866$	−1.34380	−0.0456640
$867$	−65.9711	−2.24050
$868$	41.7849	1.41827
$869$	−14.9074	−0.505701
$870$	−15.6576	−0.530843
$871$	13.3176	0.451251
$872$	−17.8162	−0.603332
$873$	13.9145	0.470933
$874$	−0.204519	−0.00691797
$875$	16.7747	0.567090
$876$	−33.3603	−1.12714
$877$	53.4837	1.80602	0.903008	−	0.429623i	$-0.141354\pi$
$877$	53.4837	1.80602	0.903008	+	0.429623i	$0.141354\pi$
$878$	8.06609	0.272217
$879$	28.3351	0.955720
$880$	−69.9814	−2.35907
$881$	24.7082	0.832440	0.416220	−	0.909264i	$-0.363355\pi$
$881$	24.7082	0.832440	0.416220	+	0.909264i	$0.363355\pi$
$882$	−0.587622	−0.0197862
$883$	9.11637	0.306790	0.153395	−	0.988165i	$-0.450979\pi$
$883$	9.11637	0.306790	0.153395	+	0.988165i	$0.450979\pi$
$884$	89.6074	3.01382
$885$	71.5507	2.40515
$886$	−1.70225	−0.0571881
$887$	30.0985	1.01061	0.505305	−	0.862941i	$-0.331380\pi$
$887$	30.0985	1.01061	0.505305	+	0.862941i	$0.331380\pi$
$888$	5.73952	0.192606
$889$	−13.7648	−0.461656
$890$	14.6419	0.490796
$891$	−35.9294	−1.20368
$892$	5.43237	0.181889
$893$	0.0566447	0.00189554
$894$	5.30007	0.177261
$895$	−55.4727	−1.85425
$896$	−21.6347	−0.722764
$897$	20.3222	0.678539
$898$	4.08503	0.136319
$899$	85.2401	2.84292
$900$	11.1089	0.370298
$901$	42.6132	1.41965
$902$	−5.08936	−0.169457
$903$	27.4068	0.912041
$904$	−0.396967	−0.0132029
$905$	76.7782	2.55219
$906$	7.93750	0.263706
$907$	−6.20178	−0.205927	−0.102963	−	0.994685i	$-0.532832\pi$
$907$	−6.20178	−0.205927	−0.102963	+	0.994685i	$0.532832\pi$
$908$	−13.9609	−0.463307
$909$	−5.22279	−0.173229
$910$	−16.9316	−0.561278
$911$	42.6606	1.41341	0.706705	−	0.707508i	$-0.250181\pi$
$911$	42.6606	1.41341	0.706705	+	0.707508i	$0.250181\pi$
$912$	1.21369	0.0401893
$913$	−41.7758	−1.38258
$914$	−10.3034	−0.340807
$915$	−38.4132	−1.26990
$916$	13.2171	0.436704
$917$	6.28658	0.207601
$918$	15.8064	0.521689
$919$	−39.2008	−1.29312	−0.646558	−	0.762865i	$-0.723792\pi$
$919$	−39.2008	−1.29312	−0.646558	+	0.762865i	$0.723792\pi$
$920$	10.9047	0.359518
$921$	−2.03183	−0.0669511
$922$	−7.94944	−0.261801
$923$	43.2571	1.42382
$924$	−38.1191	−1.25403
$925$	−20.1768	−0.663411
$926$	−4.87704	−0.160269
$927$	−12.3592	−0.405931
$928$	−33.5397	−1.10100
$929$	−15.4994	−0.508519	−0.254259	−	0.967136i	$-0.581832\pi$
$929$	−15.4994	−0.508519	−0.254259	+	0.967136i	$0.581832\pi$
$930$	−18.2384	−0.598062
$931$	0.503133	0.0164895
$932$	15.4206	0.505120
$933$	−13.5960	−0.445113
$934$	−6.01374	−0.196776
$935$	169.048	5.52845
$936$	−6.97095	−0.227852
$937$	29.3514	0.958868	0.479434	−	0.877578i	$-0.340842\pi$
$937$	29.3514	0.958868	0.479434	+	0.877578i	$0.340842\pi$
$938$	1.74606	0.0570110
$939$	−1.39111	−0.0453971
$940$	−1.46058	−0.0476387
$941$	6.50421	0.212031	0.106016	−	0.994364i	$-0.466191\pi$
$941$	6.50421	0.212031	0.106016	+	0.994364i	$0.466191\pi$
$942$	−7.37031	−0.240138
$943$	−5.24420	−0.170774
$944$	45.3380	1.47563
$945$	44.0294	1.43228
$946$	−18.2743	−0.594148
$947$	54.0585	1.75667	0.878333	−	0.478049i	$-0.158656\pi$
$947$	54.0585	1.75667	0.878333	+	0.478049i	$0.158656\pi$
$948$	−6.66642	−0.216515
$949$	−73.5916	−2.38888
$950$	0.645212	0.0209334
$951$	27.4693	0.890753
$952$	24.2936	0.787361
$953$	−55.3338	−1.79244	−0.896218	−	0.443613i	$-0.853696\pi$
$953$	−55.3338	−1.79244	−0.896218	+	0.443613i	$0.853696\pi$
$954$	−1.60316	−0.0519042
$955$	−3.51588	−0.113771
$956$	−33.6777	−1.08921
$957$	−77.7619	−2.51368
$958$	1.19539	0.0386213
$959$	−7.13791	−0.230495
$960$	−26.2413	−0.846934
$961$	68.2902	2.20291
$962$	6.12290	0.197410
$963$	11.0937	0.357490
$964$	31.6518	1.01944
$965$	−40.3566	−1.29913
$966$	2.66442	0.0857264
$967$	5.06839	0.162988	0.0814942	−	0.996674i	$-0.474031\pi$
$967$	5.06839	0.162988	0.0814942	+	0.996674i	$0.474031\pi$
$968$	37.3730	1.20121
$969$	−2.93180	−0.0941831
$970$	−20.8382	−0.669076
$971$	50.0989	1.60775	0.803875	−	0.594798i	$-0.202768\pi$
$971$	50.0989	1.60775	0.803875	+	0.594798i	$0.202768\pi$
$972$	15.6337	0.501451
$973$	35.3340	1.13276
$974$	2.03485	0.0652007
$975$	−64.1119	−2.05322
$976$	−24.3405	−0.779119
$977$	45.0003	1.43969	0.719844	−	0.694136i	$-0.244213\pi$
$977$	45.0003	1.43969	0.719844	+	0.694136i	$0.244213\pi$
$978$	1.86366	0.0595932
$979$	72.7173	2.32405
$980$	−12.9732	−0.414414
$981$	10.7067	0.341840
$982$	−1.09873	−0.0350620
$983$	33.4794	1.06783	0.533913	−	0.845539i	$-0.320721\pi$
$983$	33.4794	1.06783	0.533913	+	0.845539i	$0.320721\pi$
$984$	−4.70618	−0.150028
$985$	−62.7173	−1.99834
$986$	23.9663	0.763242
$987$	−0.737952	−0.0234893
$988$	2.88643	0.0918296
$989$	−18.8302	−0.598767
$990$	−6.35977	−0.202127
$991$	17.3560	0.551333	0.275666	−	0.961253i	$-0.411101\pi$
$991$	17.3560	0.551333	0.275666	+	0.961253i	$0.411101\pi$
$992$	−39.0681	−1.24041
$993$	−3.20929	−0.101844
$994$	5.67139	0.179886
$995$	−34.8896	−1.10608
$996$	−18.6816	−0.591949
$997$	−56.2374	−1.78106	−0.890528	−	0.454929i	$-0.849665\pi$
$997$	−56.2374	−1.78106	−0.890528	+	0.454929i	$0.849665\pi$
$998$	1.43661	0.0454752
$999$	−15.9221	−0.503754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.154	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.154	✓	358	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.356440 q^{2} -1.47323 q^{3} -1.87295 q^{4} -3.48561 q^{5} +0.525116 q^{6} -2.23893 q^{7} +1.38047 q^{8} -0.829603 q^{9} +O(q^{10})\)	\(q-0.356440 q^{2} -1.47323 q^{3} -1.87295 q^{4} -3.48561 q^{5} +0.525116 q^{6} -2.23893 q^{7} +1.38047 q^{8} -0.829603 q^{9} +1.24241 q^{10} +6.17030 q^{11} +2.75928 q^{12} +6.08686 q^{13} +0.798043 q^{14} +5.13510 q^{15} +3.25385 q^{16} -7.86003 q^{17} +0.295703 q^{18} -0.253187 q^{19} +6.52838 q^{20} +3.29845 q^{21} -2.19934 q^{22} -2.26625 q^{23} -2.03375 q^{24} +7.14949 q^{25} -2.16960 q^{26} +5.64187 q^{27} +4.19340 q^{28} +8.55443 q^{29} -1.83035 q^{30} +9.96445 q^{31} -3.92075 q^{32} -9.09025 q^{33} +2.80162 q^{34} +7.80404 q^{35} +1.55381 q^{36} -2.82214 q^{37} +0.0902458 q^{38} -8.96733 q^{39} -4.81179 q^{40} +2.31404 q^{41} -1.17570 q^{42} +8.30899 q^{43} -11.5567 q^{44} +2.89167 q^{45} +0.807781 q^{46} -0.223727 q^{47} -4.79365 q^{48} -1.98720 q^{49} -2.54836 q^{50} +11.5796 q^{51} -11.4004 q^{52} -5.42151 q^{53} -2.01099 q^{54} -21.5073 q^{55} -3.09078 q^{56} +0.373002 q^{57} -3.04914 q^{58} +13.9337 q^{59} -9.61779 q^{60} -7.48052 q^{61} -3.55172 q^{62} +1.85742 q^{63} -5.11018 q^{64} -21.2164 q^{65} +3.24013 q^{66} +2.18793 q^{67} +14.7214 q^{68} +3.33870 q^{69} -2.78167 q^{70} +7.10663 q^{71} -1.14524 q^{72} -12.0902 q^{73} +1.00592 q^{74} -10.5328 q^{75} +0.474206 q^{76} -13.8149 q^{77} +3.19631 q^{78} -2.41600 q^{79} -11.3416 q^{80} -5.82295 q^{81} -0.824816 q^{82} -6.77046 q^{83} -6.17783 q^{84} +27.3970 q^{85} -2.96165 q^{86} -12.6026 q^{87} +8.51793 q^{88} +11.7850 q^{89} -1.03071 q^{90} -13.6280 q^{91} +4.24457 q^{92} -14.6799 q^{93} +0.0797452 q^{94} +0.882511 q^{95} +5.77615 q^{96} -16.7724 q^{97} +0.708317 q^{98} -5.11890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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