LMFDB - Embedded newform 8041.2.a.i.1.11

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:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} +O(q^{10})$	\(q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} -2.91829 q^{10} +1.00000 q^{11} +7.63653 q^{12} +5.45777 q^{13} -8.75577 q^{14} +3.25019 q^{15} -0.793731 q^{16} -1.00000 q^{17} -7.33817 q^{18} +5.05012 q^{19} +3.96163 q^{20} +9.75157 q^{21} -2.24742 q^{22} +6.25714 q^{23} -5.91180 q^{24} -3.31389 q^{25} -12.2659 q^{26} +0.663664 q^{27} +11.8861 q^{28} -3.12906 q^{29} -7.30455 q^{30} +1.86183 q^{31} +6.50757 q^{32} +2.50303 q^{33} +2.24742 q^{34} +5.05885 q^{35} +9.96169 q^{36} -6.20357 q^{37} -11.3498 q^{38} +13.6609 q^{39} -3.06688 q^{40} -5.29435 q^{41} -21.9159 q^{42} -1.00000 q^{43} +3.05092 q^{44} +4.23980 q^{45} -14.0624 q^{46} +1.06975 q^{47} -1.98673 q^{48} +8.17812 q^{49} +7.44772 q^{50} -2.50303 q^{51} +16.6512 q^{52} +12.4670 q^{53} -1.49153 q^{54} +1.29850 q^{55} -9.20160 q^{56} +12.6406 q^{57} +7.03232 q^{58} +8.63365 q^{59} +9.91606 q^{60} -3.21326 q^{61} -4.18432 q^{62} +12.7207 q^{63} -13.0378 q^{64} +7.08693 q^{65} -5.62537 q^{66} -7.84936 q^{67} -3.05092 q^{68} +15.6618 q^{69} -11.3694 q^{70} +9.27564 q^{71} -7.71182 q^{72} -11.4308 q^{73} +13.9421 q^{74} -8.29476 q^{75} +15.4075 q^{76} +3.89591 q^{77} -30.7019 q^{78} -10.2426 q^{79} -1.03066 q^{80} -8.13427 q^{81} +11.8987 q^{82} +3.46832 q^{83} +29.7513 q^{84} -1.29850 q^{85} +2.24742 q^{86} -7.83212 q^{87} -2.36186 q^{88} +6.43379 q^{89} -9.52863 q^{90} +21.2630 q^{91} +19.0900 q^{92} +4.66021 q^{93} -2.40418 q^{94} +6.55760 q^{95} +16.2886 q^{96} +1.16747 q^{97} -18.3797 q^{98} +3.26514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.24742	−1.58917	−0.794585	−	0.607153i	$-0.792311\pi$
$2$	−2.24742	−1.58917	−0.794585	+	0.607153i	$0.792311\pi$
$3$	2.50303	1.44512	0.722562	−	0.691306i	$-0.242965\pi$
$3$	2.50303	1.44512	0.722562	+	0.691306i	$0.242965\pi$
$4$	3.05092	1.52546
$5$	1.29850	0.580708	0.290354	−	0.956919i	$-0.406227\pi$
$5$	1.29850	0.580708	0.290354	+	0.956919i	$0.406227\pi$
$6$	−5.62537	−2.29655
$7$	3.89591	1.47252	0.736258	−	0.676701i	$-0.236591\pi$
$7$	3.89591	1.47252	0.736258	+	0.676701i	$0.236591\pi$
$8$	−2.36186	−0.835044
$9$	3.26514	1.08838
$10$	−2.91829	−0.922843
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.63653	2.20448
$13$	5.45777	1.51371	0.756856	−	0.653581i	$-0.226734\pi$
$13$	5.45777	1.51371	0.756856	+	0.653581i	$0.226734\pi$
$14$	−8.75577	−2.34008
$15$	3.25019	0.839195
$16$	−0.793731	−0.198433
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.33817	−1.72962
$19$	5.05012	1.15858	0.579289	−	0.815122i	$-0.303330\pi$
$19$	5.05012	1.15858	0.579289	+	0.815122i	$0.303330\pi$
$20$	3.96163	0.885847
$21$	9.75157	2.12797
$22$	−2.24742	−0.479153
$23$	6.25714	1.30470	0.652352	−	0.757917i	$-0.273783\pi$
$23$	6.25714	1.30470	0.652352	+	0.757917i	$0.273783\pi$
$24$	−5.91180	−1.20674
$25$	−3.31389	−0.662778
$26$	−12.2659	−2.40555
$27$	0.663664	0.127722
$28$	11.8861	2.24626
$29$	−3.12906	−0.581051	−0.290526	−	0.956867i	$-0.593830\pi$
$29$	−3.12906	−0.581051	−0.290526	+	0.956867i	$0.593830\pi$
$30$	−7.30455	−1.33362
$31$	1.86183	0.334394	0.167197	−	0.985923i	$-0.446528\pi$
$31$	1.86183	0.334394	0.167197	+	0.985923i	$0.446528\pi$
$32$	6.50757	1.15039
$33$	2.50303	0.435721
$34$	2.24742	0.385430
$35$	5.05885	0.855102
$36$	9.96169	1.66028
$37$	−6.20357	−1.01986	−0.509930	−	0.860216i	$-0.670329\pi$
$37$	−6.20357	−1.01986	−0.509930	+	0.860216i	$0.670329\pi$
$38$	−11.3498	−1.84118
$39$	13.6609	2.18750
$40$	−3.06688	−0.484917
$41$	−5.29435	−0.826839	−0.413419	−	0.910541i	$-0.635666\pi$
$41$	−5.29435	−0.826839	−0.413419	+	0.910541i	$0.635666\pi$
$42$	−21.9159	−3.38170
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	3.05092	0.459943
$45$	4.23980	0.632032
$46$	−14.0624	−2.07339
$47$	1.06975	0.156039	0.0780196	−	0.996952i	$-0.475140\pi$
$47$	1.06975	0.156039	0.0780196	+	0.996952i	$0.475140\pi$
$48$	−1.98673	−0.286760
$49$	8.17812	1.16830
$50$	7.44772	1.05327
$51$	−2.50303	−0.350494
$52$	16.6512	2.30911
$53$	12.4670	1.71248	0.856240	−	0.516578i	$-0.172794\pi$
$53$	12.4670	1.71248	0.856240	+	0.516578i	$0.172794\pi$
$54$	−1.49153	−0.202972
$55$	1.29850	0.175090
$56$	−9.20160	−1.22962
$57$	12.6406	1.67429
$58$	7.03232	0.923389
$59$	8.63365	1.12401	0.562003	−	0.827135i	$-0.310031\pi$
$59$	8.63365	1.12401	0.562003	+	0.827135i	$0.310031\pi$
$60$	9.91606	1.28016
$61$	−3.21326	−0.411416	−0.205708	−	0.978613i	$-0.565950\pi$
$61$	−3.21326	−0.411416	−0.205708	+	0.978613i	$0.565950\pi$
$62$	−4.18432	−0.531409
$63$	12.7207	1.60266
$64$	−13.0378	−1.62973
$65$	7.08693	0.879025
$66$	−5.62537	−0.692435
$67$	−7.84936	−0.958952	−0.479476	−	0.877555i	$-0.659173\pi$
$67$	−7.84936	−0.958952	−0.479476	+	0.877555i	$0.659173\pi$
$68$	−3.05092	−0.369978
$69$	15.6618	1.88546
$70$	−11.3694	−1.35890
$71$	9.27564	1.10082	0.550408	−	0.834896i	$-0.314472\pi$
$71$	9.27564	1.10082	0.550408	+	0.834896i	$0.314472\pi$
$72$	−7.71182	−0.908847
$73$	−11.4308	−1.33787	−0.668936	−	0.743320i	$-0.733250\pi$
$73$	−11.4308	−1.33787	−0.668936	+	0.743320i	$0.733250\pi$
$74$	13.9421	1.62073
$75$	−8.29476	−0.957796
$76$	15.4075	1.76736
$77$	3.89591	0.443980
$78$	−30.7019	−3.47631
$79$	−10.2426	−1.15239	−0.576193	−	0.817314i	$-0.695462\pi$
$79$	−10.2426	−1.15239	−0.576193	+	0.817314i	$0.695462\pi$
$80$	−1.03066	−0.115231
$81$	−8.13427	−0.903807
$82$	11.8987	1.31399
$83$	3.46832	0.380697	0.190349	−	0.981717i	$-0.439038\pi$
$83$	3.46832	0.380697	0.190349	+	0.981717i	$0.439038\pi$
$84$	29.7513	3.24613
$85$	−1.29850	−0.140842
$86$	2.24742	0.242346
$87$	−7.83212	−0.839691
$88$	−2.36186	−0.251775
$89$	6.43379	0.681980	0.340990	−	0.940067i	$-0.389238\pi$
$89$	6.43379	0.681980	0.340990	+	0.940067i	$0.389238\pi$
$90$	−9.52863	−1.00441
$91$	21.2630	2.22897
$92$	19.0900	1.99027
$93$	4.66021	0.483241
$94$	−2.40418	−0.247973
$95$	6.55760	0.672795
$96$	16.2886	1.66245
$97$	1.16747	0.118539	0.0592693	−	0.998242i	$-0.481123\pi$
$97$	1.16747	0.118539	0.0592693	+	0.998242i	$0.481123\pi$
$98$	−18.3797	−1.85663
$99$	3.26514	0.328159
$100$	−10.1104	−1.01104
$101$	3.52949	0.351197	0.175599	−	0.984462i	$-0.443814\pi$
$101$	3.52949	0.351197	0.175599	+	0.984462i	$0.443814\pi$
$102$	5.62537	0.556994
$103$	−7.70041	−0.758744	−0.379372	−	0.925244i	$-0.623860\pi$
$103$	−7.70041	−0.758744	−0.379372	+	0.925244i	$0.623860\pi$
$104$	−12.8905	−1.26402
$105$	12.6624	1.23573
$106$	−28.0188	−2.72142
$107$	2.14806	0.207661	0.103830	−	0.994595i	$-0.466890\pi$
$107$	2.14806	0.207661	0.103830	+	0.994595i	$0.466890\pi$
$108$	2.02478	0.194835
$109$	−10.4562	−1.00152	−0.500760	−	0.865586i	$-0.666946\pi$
$109$	−10.4562	−1.00152	−0.500760	+	0.865586i	$0.666946\pi$
$110$	−2.91829	−0.278248
$111$	−15.5277	−1.47382
$112$	−3.09230	−0.292195
$113$	1.95017	0.183456	0.0917282	−	0.995784i	$-0.470761\pi$
$113$	1.95017	0.183456	0.0917282	+	0.995784i	$0.470761\pi$
$114$	−28.4088	−2.66073
$115$	8.12491	0.757652
$116$	−9.54650	−0.886370
$117$	17.8204	1.64750
$118$	−19.4035	−1.78623
$119$	−3.89591	−0.357138
$120$	−7.67649	−0.700765
$121$	1.00000	0.0909091
$122$	7.22156	0.653809
$123$	−13.2519	−1.19488
$124$	5.68029	0.510105
$125$	−10.7956	−0.965589
$126$	−28.5888	−2.54690
$127$	18.4418	1.63645	0.818223	−	0.574901i	$-0.194960\pi$
$127$	18.4418	1.63645	0.818223	+	0.574901i	$0.194960\pi$
$128$	16.2864	1.43953
$129$	−2.50303	−0.220379
$130$	−15.9273	−1.39692
$131$	9.06011	0.791586	0.395793	−	0.918340i	$-0.370470\pi$
$131$	9.06011	0.791586	0.395793	+	0.918340i	$0.370470\pi$
$132$	7.63653	0.664675
$133$	19.6748	1.70602
$134$	17.6408	1.52394
$135$	0.861769	0.0741693
$136$	2.36186	0.202528
$137$	13.4506	1.14916	0.574580	−	0.818448i	$-0.305165\pi$
$137$	13.4506	1.14916	0.574580	+	0.818448i	$0.305165\pi$
$138$	−35.1987	−2.99631
$139$	−18.2149	−1.54497	−0.772485	−	0.635033i	$-0.780987\pi$
$139$	−18.2149	−1.54497	−0.772485	+	0.635033i	$0.780987\pi$
$140$	15.4341	1.30442
$141$	2.67761	0.225496
$142$	−20.8463	−1.74938
$143$	5.45777	0.456402
$144$	−2.59165	−0.215970
$145$	−4.06309	−0.337421
$146$	25.6898	2.12611
$147$	20.4701	1.68834
$148$	−18.9266	−1.55576
$149$	7.74413	0.634424	0.317212	−	0.948355i	$-0.397253\pi$
$149$	7.74413	0.634424	0.317212	+	0.948355i	$0.397253\pi$
$150$	18.6418	1.52210
$151$	−23.3657	−1.90148	−0.950738	−	0.309996i	$-0.899672\pi$
$151$	−23.3657	−1.90148	−0.950738	+	0.309996i	$0.899672\pi$
$152$	−11.9277	−0.967464
$153$	−3.26514	−0.263971
$154$	−8.75577	−0.705560
$155$	2.41759	0.194186
$156$	41.6784	3.33695
$157$	5.08626	0.405928	0.202964	−	0.979186i	$-0.434943\pi$
$157$	5.08626	0.405928	0.202964	+	0.979186i	$0.434943\pi$
$158$	23.0196	1.83134
$159$	31.2054	2.47475
$160$	8.45010	0.668039
$161$	24.3772	1.92120
$162$	18.2812	1.43630
$163$	−1.41971	−0.111200	−0.0556001	−	0.998453i	$-0.517707\pi$
$163$	−1.41971	−0.111200	−0.0556001	+	0.998453i	$0.517707\pi$
$164$	−16.1526	−1.26131
$165$	3.25019	0.253027
$166$	−7.79478	−0.604992
$167$	5.40974	0.418618	0.209309	−	0.977850i	$-0.432878\pi$
$167$	5.40974	0.418618	0.209309	+	0.977850i	$0.432878\pi$
$168$	−23.0319	−1.77695
$169$	16.7872	1.29133
$170$	2.91829	0.223822
$171$	16.4894	1.26097
$172$	−3.05092	−0.232630
$173$	−4.26716	−0.324426	−0.162213	−	0.986756i	$-0.551863\pi$
$173$	−4.26716	−0.324426	−0.162213	+	0.986756i	$0.551863\pi$
$174$	17.6021	1.33441
$175$	−12.9106	−0.975951
$176$	−0.793731	−0.0598297
$177$	21.6103	1.62433
$178$	−14.4595	−1.08378
$179$	−13.2461	−0.990060	−0.495030	−	0.868876i	$-0.664843\pi$
$179$	−13.2461	−0.990060	−0.495030	+	0.868876i	$0.664843\pi$
$180$	12.9353	0.964139
$181$	11.2586	0.836846	0.418423	−	0.908252i	$-0.362583\pi$
$181$	11.2586	0.836846	0.418423	+	0.908252i	$0.362583\pi$
$182$	−47.7870	−3.54221
$183$	−8.04288	−0.594546
$184$	−14.7785	−1.08948
$185$	−8.05535	−0.592241
$186$	−10.4735	−0.767952
$187$	−1.00000	−0.0731272
$188$	3.26372	0.238031
$189$	2.58557	0.188073
$190$	−14.7377	−1.06919
$191$	−9.65206	−0.698398	−0.349199	−	0.937049i	$-0.613546\pi$
$191$	−9.65206	−0.698398	−0.349199	+	0.937049i	$0.613546\pi$
$192$	−32.6340	−2.35516
$193$	−9.66911	−0.695998	−0.347999	−	0.937495i	$-0.613139\pi$
$193$	−9.66911	−0.695998	−0.347999	+	0.937495i	$0.613139\pi$
$194$	−2.62380	−0.188378
$195$	17.7388	1.27030
$196$	24.9508	1.78220
$197$	−26.0453	−1.85565	−0.927826	−	0.373012i	$-0.878325\pi$
$197$	−26.0453	−1.85565	−0.927826	+	0.373012i	$0.878325\pi$
$198$	−7.33817	−0.521501
$199$	5.26448	0.373189	0.186595	−	0.982437i	$-0.440255\pi$
$199$	5.26448	0.373189	0.186595	+	0.982437i	$0.440255\pi$
$200$	7.82695	0.553449
$201$	−19.6472	−1.38580
$202$	−7.93226	−0.558112
$203$	−12.1905	−0.855607
$204$	−7.63653	−0.534664
$205$	−6.87473	−0.480152
$206$	17.3061	1.20577
$207$	20.4305	1.42001
$208$	−4.33200	−0.300370
$209$	5.05012	0.349324
$210$	−28.4579	−1.96378
$211$	−20.2874	−1.39664	−0.698321	−	0.715784i	$-0.746069\pi$
$211$	−20.2874	−1.39664	−0.698321	+	0.715784i	$0.746069\pi$
$212$	38.0360	2.61232
$213$	23.2172	1.59081
$214$	−4.82760	−0.330008
$215$	−1.29850	−0.0885571
$216$	−1.56748	−0.106654
$217$	7.25352	0.492401
$218$	23.4995	1.59158
$219$	−28.6116	−1.93339
$220$	3.96163	0.267093
$221$	−5.45777	−0.367129
$222$	34.8973	2.34216
$223$	−9.08984	−0.608701	−0.304350	−	0.952560i	$-0.598439\pi$
$223$	−9.08984	−0.608701	−0.304350	+	0.952560i	$0.598439\pi$
$224$	25.3529	1.69396
$225$	−10.8203	−0.721355
$226$	−4.38286	−0.291543
$227$	20.1651	1.33841	0.669203	−	0.743079i	$-0.266635\pi$
$227$	20.1651	1.33841	0.669203	+	0.743079i	$0.266635\pi$
$228$	38.5654	2.55406
$229$	10.0428	0.663650	0.331825	−	0.943341i	$-0.392336\pi$
$229$	10.0428	0.663650	0.331825	+	0.943341i	$0.392336\pi$
$230$	−18.2601	−1.20404
$231$	9.75157	0.641606
$232$	7.39040	0.485204
$233$	−6.51859	−0.427047	−0.213524	−	0.976938i	$-0.568494\pi$
$233$	−6.51859	−0.427047	−0.213524	+	0.976938i	$0.568494\pi$
$234$	−40.0500	−2.61815
$235$	1.38907	0.0906132
$236$	26.3406	1.71462
$237$	−25.6376	−1.66534
$238$	8.75577	0.567552
$239$	−18.4861	−1.19577	−0.597883	−	0.801583i	$-0.703991\pi$
$239$	−18.4861	−1.19577	−0.597883	+	0.801583i	$0.703991\pi$
$240$	−2.57977	−0.166524
$241$	3.24031	0.208727	0.104364	−	0.994539i	$-0.466719\pi$
$241$	3.24031	0.208727	0.104364	+	0.994539i	$0.466719\pi$
$242$	−2.24742	−0.144470
$243$	−22.3513	−1.43384
$244$	−9.80339	−0.627598
$245$	10.6193	0.678443
$246$	29.7827	1.89887
$247$	27.5624	1.75375
$248$	−4.39738	−0.279234
$249$	8.68129	0.550154
$250$	24.2623	1.53448
$251$	20.5238	1.29545	0.647726	−	0.761873i	$-0.275720\pi$
$251$	20.5238	1.29545	0.647726	+	0.761873i	$0.275720\pi$
$252$	38.8099	2.44479
$253$	6.25714	0.393383
$254$	−41.4466	−2.60059
$255$	−3.25019	−0.203535
$256$	−10.5268	−0.657923
$257$	10.1027	0.630188	0.315094	−	0.949060i	$-0.397964\pi$
$257$	10.1027	0.630188	0.315094	+	0.949060i	$0.397964\pi$
$258$	5.62537	0.350220
$259$	−24.1685	−1.50176
$260$	21.6216	1.34092
$261$	−10.2168	−0.632406
$262$	−20.3619	−1.25796
$263$	8.50347	0.524347	0.262173	−	0.965021i	$-0.415561\pi$
$263$	8.50347	0.524347	0.262173	+	0.965021i	$0.415561\pi$
$264$	−5.91180	−0.363846
$265$	16.1885	0.994451
$266$	−44.2177	−2.71116
$267$	16.1040	0.985546
$268$	−23.9478	−1.46284
$269$	−2.60052	−0.158557	−0.0792784	−	0.996853i	$-0.525262\pi$
$269$	−2.60052	−0.158557	−0.0792784	+	0.996853i	$0.525262\pi$
$270$	−1.93676	−0.117868
$271$	−12.1214	−0.736323	−0.368162	−	0.929762i	$-0.620013\pi$
$271$	−12.1214	−0.736323	−0.368162	+	0.929762i	$0.620013\pi$
$272$	0.793731	0.0481270
$273$	53.2218	3.22113
$274$	−30.2292	−1.82621
$275$	−3.31389	−0.199835
$276$	47.7828	2.87619
$277$	17.9928	1.08108	0.540541	−	0.841317i	$-0.318219\pi$
$277$	17.9928	1.08108	0.540541	+	0.841317i	$0.318219\pi$
$278$	40.9367	2.45522
$279$	6.07914	0.363949
$280$	−11.9483	−0.714048
$281$	−25.8853	−1.54419	−0.772093	−	0.635510i	$-0.780790\pi$
$281$	−25.8853	−1.54419	−0.772093	+	0.635510i	$0.780790\pi$
$282$	−6.01774	−0.358351
$283$	18.0848	1.07503	0.537515	−	0.843254i	$-0.319363\pi$
$283$	18.0848	1.07503	0.537515	+	0.843254i	$0.319363\pi$
$284$	28.2992	1.67925
$285$	16.4138	0.972272
$286$	−12.2659	−0.725300
$287$	−20.6263	−1.21753
$288$	21.2482	1.25206
$289$	1.00000	0.0588235
$290$	9.13149	0.536220
$291$	2.92221	0.171303
$292$	−34.8744	−2.04087
$293$	−1.40597	−0.0821375	−0.0410688	−	0.999156i	$-0.513076\pi$
$293$	−1.40597	−0.0821375	−0.0410688	+	0.999156i	$0.513076\pi$
$294$	−46.0049	−2.68306
$295$	11.2108	0.652719
$296$	14.6520	0.851629
$297$	0.663664	0.0385097
$298$	−17.4044	−1.00821
$299$	34.1500	1.97495
$300$	−25.3066	−1.46108
$301$	−3.89591	−0.224557
$302$	52.5127	3.02177
$303$	8.83440	0.507523
$304$	−4.00844	−0.229900
$305$	−4.17243	−0.238912
$306$	7.33817	0.419495
$307$	−10.6707	−0.609012	−0.304506	−	0.952510i	$-0.598491\pi$
$307$	−10.6707	−0.609012	−0.304506	+	0.952510i	$0.598491\pi$
$308$	11.8861	0.677274
$309$	−19.2743	−1.09648
$310$	−5.43335	−0.308594
$311$	−19.1958	−1.08850	−0.544248	−	0.838924i	$-0.683185\pi$
$311$	−19.1958	−1.08850	−0.544248	+	0.838924i	$0.683185\pi$
$312$	−32.2653	−1.82666
$313$	19.0190	1.07502	0.537508	−	0.843259i	$-0.319366\pi$
$313$	19.0190	1.07502	0.537508	+	0.843259i	$0.319366\pi$
$314$	−11.4310	−0.645089
$315$	16.5179	0.930677
$316$	−31.2494	−1.75792
$317$	0.322116	0.0180918	0.00904591	−	0.999959i	$-0.497121\pi$
$317$	0.322116	0.0180918	0.00904591	+	0.999959i	$0.497121\pi$
$318$	−70.1317	−3.93279
$319$	−3.12906	−0.175194
$320$	−16.9296	−0.946396
$321$	5.37665	0.300095
$322$	−54.7860	−3.05311
$323$	−5.05012	−0.280996
$324$	−24.8170	−1.37872
$325$	−18.0865	−1.00326
$326$	3.19069	0.176716
$327$	−26.1721	−1.44732
$328$	12.5045	0.690447
$329$	4.16765	0.229770
$330$	−7.30455	−0.402102
$331$	17.6260	0.968815	0.484407	−	0.874843i	$-0.339035\pi$
$331$	17.6260	0.968815	0.484407	+	0.874843i	$0.339035\pi$
$332$	10.5816	0.580738
$333$	−20.2555	−1.11000
$334$	−12.1580	−0.665256
$335$	−10.1924	−0.556871
$336$	−7.74012	−0.422258
$337$	32.0174	1.74410	0.872050	−	0.489417i	$-0.162790\pi$
$337$	32.0174	1.74410	0.872050	+	0.489417i	$0.162790\pi$
$338$	−37.7281	−2.05214
$339$	4.88133	0.265117
$340$	−3.96163	−0.214849
$341$	1.86183	0.100824
$342$	−37.0586	−2.00390
$343$	4.58985	0.247829
$344$	2.36186	0.127343
$345$	20.3369	1.09490
$346$	9.59012	0.515568
$347$	−6.91527	−0.371231	−0.185616	−	0.982622i	$-0.559428\pi$
$347$	−6.91527	−0.371231	−0.185616	+	0.982622i	$0.559428\pi$
$348$	−23.8952	−1.28091
$349$	15.2322	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$349$	15.2322	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$350$	29.0157	1.55095
$351$	3.62212	0.193335
$352$	6.50757	0.346855
$353$	31.3606	1.66915	0.834577	−	0.550891i	$-0.185712\pi$
$353$	31.3606	1.66915	0.834577	+	0.550891i	$0.185712\pi$
$354$	−48.5674	−2.58133
$355$	12.0444	0.639252
$356$	19.6290	1.04033
$357$	−9.75157	−0.516108
$358$	29.7696	1.57337
$359$	−11.4855	−0.606183	−0.303091	−	0.952961i	$-0.598019\pi$
$359$	−11.4855	−0.606183	−0.303091	+	0.952961i	$0.598019\pi$
$360$	−10.0138	−0.527775
$361$	6.50374	0.342302
$362$	−25.3029	−1.32989
$363$	2.50303	0.131375
$364$	64.8716	3.40020
$365$	−14.8429	−0.776913
$366$	18.0758	0.944835
$367$	−33.4544	−1.74631	−0.873153	−	0.487446i	$-0.837928\pi$
$367$	−33.4544	−1.74631	−0.873153	+	0.487446i	$0.837928\pi$
$368$	−4.96648	−0.258896
$369$	−17.2868	−0.899916
$370$	18.1038	0.941171
$371$	48.5705	2.52166
$372$	14.2179	0.737165
$373$	−26.8485	−1.39016	−0.695082	−	0.718931i	$-0.744632\pi$
$373$	−26.8485	−1.39016	−0.695082	+	0.718931i	$0.744632\pi$
$374$	2.24742	0.116212
$375$	−27.0217	−1.39539
$376$	−2.52660	−0.130300
$377$	−17.0777	−0.879545
$378$	−5.81088	−0.298880
$379$	15.2165	0.781618	0.390809	−	0.920472i	$-0.372195\pi$
$379$	15.2165	0.781618	0.390809	+	0.920472i	$0.372195\pi$
$380$	20.0067	1.02632
$381$	46.1603	2.36487
$382$	21.6923	1.10987
$383$	−34.7631	−1.77631	−0.888155	−	0.459543i	$-0.848013\pi$
$383$	−34.7631	−1.77631	−0.888155	+	0.459543i	$0.848013\pi$
$384$	40.7653	2.08029
$385$	5.05885	0.257823
$386$	21.7306	1.10606
$387$	−3.26514	−0.165977
$388$	3.56186	0.180826
$389$	16.7497	0.849241	0.424621	−	0.905371i	$-0.360407\pi$
$389$	16.7497	0.849241	0.424621	+	0.905371i	$0.360407\pi$
$390$	−39.8666	−2.01872
$391$	−6.25714	−0.316437
$392$	−19.3156	−0.975585
$393$	22.6777	1.14394
$394$	58.5349	2.94895
$395$	−13.3001	−0.669200
$396$	9.96169	0.500594
$397$	−6.08086	−0.305190	−0.152595	−	0.988289i	$-0.548763\pi$
$397$	−6.08086	−0.305190	−0.152595	+	0.988289i	$0.548763\pi$
$398$	−11.8315	−0.593061
$399$	49.2466	2.46542
$400$	2.63034	0.131517
$401$	−19.0965	−0.953636	−0.476818	−	0.879002i	$-0.658210\pi$
$401$	−19.0965	−0.953636	−0.476818	+	0.879002i	$0.658210\pi$
$402$	44.1555	2.20228
$403$	10.1614	0.506177
$404$	10.7682	0.535737
$405$	−10.5624	−0.524848
$406$	27.3973	1.35971
$407$	−6.20357	−0.307499
$408$	5.91180	0.292678
$409$	3.61284	0.178643	0.0893216	−	0.996003i	$-0.471530\pi$
$409$	3.61284	0.178643	0.0893216	+	0.996003i	$0.471530\pi$
$410$	15.4504	0.763043
$411$	33.6672	1.66068
$412$	−23.4933	−1.15743
$413$	33.6359	1.65512
$414$	−45.9159	−2.25664
$415$	4.50362	0.221074
$416$	35.5168	1.74136
$417$	−45.5925	−2.23267
$418$	−11.3498	−0.555136
$419$	−33.8980	−1.65603	−0.828013	−	0.560709i	$-0.810528\pi$
$419$	−33.8980	−1.65603	−0.828013	+	0.560709i	$0.810528\pi$
$420$	38.6321	1.88505
$421$	−1.22532	−0.0597186	−0.0298593	−	0.999554i	$-0.509506\pi$
$421$	−1.22532	−0.0597186	−0.0298593	+	0.999554i	$0.509506\pi$
$422$	45.5944	2.21950
$423$	3.49289	0.169830
$424$	−29.4454	−1.43000
$425$	3.31389	0.160747
$426$	−52.1788	−2.52807
$427$	−12.5186	−0.605816
$428$	6.55355	0.316778
$429$	13.6609	0.659557
$430$	2.91829	0.140732
$431$	−27.0231	−1.30166	−0.650830	−	0.759224i	$-0.725579\pi$
$431$	−27.0231	−1.30166	−0.650830	+	0.759224i	$0.725579\pi$
$432$	−0.526770	−0.0253442
$433$	4.86248	0.233676	0.116838	−	0.993151i	$-0.462724\pi$
$433$	4.86248	0.233676	0.116838	+	0.993151i	$0.462724\pi$
$434$	−16.3017	−0.782509
$435$	−10.1700	−0.487615
$436$	−31.9009	−1.52778
$437$	31.5993	1.51160
$438$	64.3024	3.07249
$439$	−16.5288	−0.788878	−0.394439	−	0.918922i	$-0.629061\pi$
$439$	−16.5288	−0.788878	−0.394439	+	0.918922i	$0.629061\pi$
$440$	−3.06688	−0.146208
$441$	26.7027	1.27156
$442$	12.2659	0.583431
$443$	4.21628	0.200322	0.100161	−	0.994971i	$-0.468064\pi$
$443$	4.21628	0.200322	0.100161	+	0.994971i	$0.468064\pi$
$444$	−47.3738	−2.24826
$445$	8.35429	0.396031
$446$	20.4287	0.967329
$447$	19.3838	0.916821
$448$	−50.7942	−2.39980
$449$	3.19480	0.150772	0.0753860	−	0.997154i	$-0.475981\pi$
$449$	3.19480	0.150772	0.0753860	+	0.997154i	$0.475981\pi$
$450$	24.3179	1.14636
$451$	−5.29435	−0.249301
$452$	5.94981	0.279855
$453$	−58.4850	−2.74787
$454$	−45.3196	−2.12696
$455$	27.6100	1.29438
$456$	−29.8553	−1.39810
$457$	12.3202	0.576314	0.288157	−	0.957583i	$-0.406958\pi$
$457$	12.3202	0.576314	0.288157	+	0.957583i	$0.406958\pi$
$458$	−22.5705	−1.05465
$459$	−0.663664	−0.0309772
$460$	24.7884	1.15577
$461$	−19.8534	−0.924663	−0.462331	−	0.886707i	$-0.652987\pi$
$461$	−19.8534	−0.924663	−0.462331	+	0.886707i	$0.652987\pi$
$462$	−21.9159	−1.01962
$463$	−15.1086	−0.702155	−0.351078	−	0.936346i	$-0.614185\pi$
$463$	−15.1086	−0.702155	−0.351078	+	0.936346i	$0.614185\pi$
$464$	2.48363	0.115300
$465$	6.05129	0.280622
$466$	14.6500	0.678650
$467$	19.6309	0.908412	0.454206	−	0.890897i	$-0.349923\pi$
$467$	19.6309	0.908412	0.454206	+	0.890897i	$0.349923\pi$
$468$	54.3686	2.51319
$469$	−30.5804	−1.41207
$470$	−3.12184	−0.144000
$471$	12.7311	0.586616
$472$	−20.3915	−0.938594
$473$	−1.00000	−0.0459800
$474$	57.6186	2.64651
$475$	−16.7356	−0.767880
$476$	−11.8861	−0.544799
$477$	40.7067	1.86383
$478$	41.5461	1.90028
$479$	16.1951	0.739971	0.369986	−	0.929037i	$-0.379363\pi$
$479$	16.1951	0.739971	0.369986	+	0.929037i	$0.379363\pi$
$480$	21.1508	0.965399
$481$	−33.8576	−1.54378
$482$	−7.28236	−0.331703
$483$	61.0169	2.77637
$484$	3.05092	0.138678
$485$	1.51596	0.0688363
$486$	50.2328	2.27861
$487$	8.50186	0.385256	0.192628	−	0.981272i	$-0.438299\pi$
$487$	8.50186	0.385256	0.192628	+	0.981272i	$0.438299\pi$
$488$	7.58927	0.343550
$489$	−3.55357	−0.160698
$490$	−23.8661	−1.07816
$491$	−27.4917	−1.24068	−0.620341	−	0.784332i	$-0.713006\pi$
$491$	−27.4917	−1.24068	−0.620341	+	0.784332i	$0.713006\pi$
$492$	−40.4305	−1.82275
$493$	3.12906	0.140926
$494$	−61.9444	−2.78701
$495$	4.23980	0.190565
$496$	−1.47779	−0.0663548
$497$	36.1371	1.62097
$498$	−19.5105	−0.874289
$499$	−39.1081	−1.75072	−0.875360	−	0.483472i	$-0.839376\pi$
$499$	−39.1081	−1.75072	−0.875360	+	0.483472i	$0.839376\pi$
$500$	−32.9365	−1.47297
$501$	13.5407	0.604955
$502$	−46.1258	−2.05869
$503$	13.7303	0.612202	0.306101	−	0.951999i	$-0.400975\pi$
$503$	13.7303	0.612202	0.306101	+	0.951999i	$0.400975\pi$
$504$	−30.0446	−1.33829
$505$	4.58305	0.203943
$506$	−14.0624	−0.625152
$507$	42.0189	1.86613
$508$	56.2645	2.49633
$509$	−29.6756	−1.31535	−0.657673	−	0.753303i	$-0.728459\pi$
$509$	−29.6756	−1.31535	−0.657673	+	0.753303i	$0.728459\pi$
$510$	7.30455	0.323451
$511$	−44.5333	−1.97004
$512$	−8.91463	−0.393975
$513$	3.35158	0.147976
$514$	−22.7050	−1.00148
$515$	−9.99901	−0.440609
$516$	−7.63653	−0.336180
$517$	1.06975	0.0470476
$518$	54.3170	2.38655
$519$	−10.6808	−0.468836
$520$	−16.7383	−0.734025
$521$	0.758394	0.0332258	0.0166129	−	0.999862i	$-0.494712\pi$
$521$	0.758394	0.0332258	0.0166129	+	0.999862i	$0.494712\pi$
$522$	22.9615	1.00500
$523$	−15.7541	−0.688877	−0.344439	−	0.938809i	$-0.611931\pi$
$523$	−15.7541	−0.688877	−0.344439	+	0.938809i	$0.611931\pi$
$524$	27.6417	1.20753
$525$	−32.3156	−1.41037
$526$	−19.1109	−0.833276
$527$	−1.86183	−0.0811026
$528$	−1.98673	−0.0864613
$529$	16.1518	0.702250
$530$	−36.3824	−1.58035
$531$	28.1901	1.22335
$532$	60.0263	2.60247
$533$	−28.8953	−1.25160
$534$	−36.1924	−1.56620
$535$	2.78926	0.120590
$536$	18.5391	0.800767
$537$	−33.1553	−1.43076
$538$	5.84448	0.251973
$539$	8.17812	0.352257
$540$	2.62919	0.113142
$541$	−15.4550	−0.664463	−0.332232	−	0.943198i	$-0.607802\pi$
$541$	−15.4550	−0.664463	−0.332232	+	0.943198i	$0.607802\pi$
$542$	27.2420	1.17014
$543$	28.1806	1.20935
$544$	−6.50757	−0.279010
$545$	−13.5774	−0.581590
$546$	−119.612	−5.11892
$547$	9.90966	0.423707	0.211853	−	0.977301i	$-0.432050\pi$
$547$	9.90966	0.423707	0.211853	+	0.977301i	$0.432050\pi$
$548$	41.0366	1.75300
$549$	−10.4918	−0.447777
$550$	7.44772	0.317572
$551$	−15.8021	−0.673193
$552$	−36.9910	−1.57444
$553$	−39.9044	−1.69691
$554$	−40.4375	−1.71802
$555$	−20.1628	−0.855861
$556$	−55.5723	−2.35679
$557$	−23.3130	−0.987803	−0.493901	−	0.869518i	$-0.664430\pi$
$557$	−23.3130	−0.987803	−0.493901	+	0.869518i	$0.664430\pi$
$558$	−13.6624	−0.578376
$559$	−5.45777	−0.230839
$560$	−4.01537	−0.169680
$561$	−2.50303	−0.105678
$562$	58.1752	2.45397
$563$	24.7387	1.04261	0.521306	−	0.853370i	$-0.325445\pi$
$563$	24.7387	1.04261	0.521306	+	0.853370i	$0.325445\pi$
$564$	8.16918	0.343985
$565$	2.53230	0.106535
$566$	−40.6442	−1.70840
$567$	−31.6904	−1.33087
$568$	−21.9078	−0.919230
$569$	9.37413	0.392984	0.196492	−	0.980505i	$-0.437045\pi$
$569$	9.37413	0.392984	0.196492	+	0.980505i	$0.437045\pi$
$570$	−36.8889	−1.54511
$571$	−16.6403	−0.696374	−0.348187	−	0.937425i	$-0.613203\pi$
$571$	−16.6403	−0.696374	−0.348187	+	0.937425i	$0.613203\pi$
$572$	16.6512	0.696222
$573$	−24.1594	−1.00927
$574$	46.3561	1.93487
$575$	−20.7355	−0.864729
$576$	−42.5704	−1.77377
$577$	−14.5126	−0.604166	−0.302083	−	0.953282i	$-0.597682\pi$
$577$	−14.5126	−0.604166	−0.302083	+	0.953282i	$0.597682\pi$
$578$	−2.24742	−0.0934806
$579$	−24.2020	−1.00580
$580$	−12.3962	−0.514722
$581$	13.5123	0.560583
$582$	−6.56744	−0.272229
$583$	12.4670	0.516332
$584$	26.9979	1.11718
$585$	23.1398	0.956715
$586$	3.15981	0.130530
$587$	1.96415	0.0810693	0.0405347	−	0.999178i	$-0.487094\pi$
$587$	1.96415	0.0810693	0.0405347	+	0.999178i	$0.487094\pi$
$588$	62.4525	2.57550
$589$	9.40247	0.387422
$590$	−25.1955	−1.03728
$591$	−65.1922	−2.68165
$592$	4.92396	0.202374
$593$	29.1849	1.19848	0.599240	−	0.800569i	$-0.295469\pi$
$593$	29.1849	1.19848	0.599240	+	0.800569i	$0.295469\pi$
$594$	−1.49153	−0.0611984
$595$	−5.05885	−0.207393
$596$	23.6267	0.967788
$597$	13.1771	0.539305
$598$	−76.7496	−3.13852
$599$	−0.721406	−0.0294759	−0.0147379	−	0.999891i	$-0.504691\pi$
$599$	−0.721406	−0.0294759	−0.0147379	+	0.999891i	$0.504691\pi$
$600$	19.5911	0.799802
$601$	−46.5021	−1.89686	−0.948431	−	0.316985i	$-0.897330\pi$
$601$	−46.5021	−1.89686	−0.948431	+	0.316985i	$0.897330\pi$
$602$	8.75577	0.356858
$603$	−25.6293	−1.04371
$604$	−71.2869	−2.90062
$605$	1.29850	0.0527916
$606$	−19.8547	−0.806540
$607$	43.8105	1.77821	0.889107	−	0.457699i	$-0.151326\pi$
$607$	43.8105	1.77821	0.889107	+	0.457699i	$0.151326\pi$
$608$	32.8641	1.33281
$609$	−30.5132	−1.23646
$610$	9.37721	0.379672
$611$	5.83845	0.236198
$612$	−9.96169	−0.402678
$613$	−43.1007	−1.74082	−0.870411	−	0.492326i	$-0.836147\pi$
$613$	−43.1007	−1.74082	−0.870411	+	0.492326i	$0.836147\pi$
$614$	23.9817	0.967823
$615$	−17.2076	−0.693879
$616$	−9.20160	−0.370743
$617$	26.7367	1.07638	0.538189	−	0.842824i	$-0.319109\pi$
$617$	26.7367	1.07638	0.538189	+	0.842824i	$0.319109\pi$
$618$	43.3176	1.74249
$619$	−12.7618	−0.512940	−0.256470	−	0.966552i	$-0.582559\pi$
$619$	−12.7618	−0.512940	−0.256470	+	0.966552i	$0.582559\pi$
$620$	7.37587	0.296222
$621$	4.15263	0.166639
$622$	43.1412	1.72980
$623$	25.0655	1.00423
$624$	−10.8431	−0.434072
$625$	2.55133	0.102053
$626$	−42.7437	−1.70838
$627$	12.6406	0.504817
$628$	15.5178	0.619227
$629$	6.20357	0.247352
$630$	−37.1227	−1.47900
$631$	36.4173	1.44975	0.724875	−	0.688881i	$-0.241898\pi$
$631$	36.4173	1.44975	0.724875	+	0.688881i	$0.241898\pi$
$632$	24.1917	0.962294
$633$	−50.7799	−2.01832
$634$	−0.723930	−0.0287510
$635$	23.9467	0.950297
$636$	95.2050	3.77512
$637$	44.6343	1.76848
$638$	7.03232	0.278412
$639$	30.2863	1.19811
$640$	21.1479	0.835945
$641$	−45.6000	−1.80109	−0.900547	−	0.434759i	$-0.856834\pi$
$641$	−45.6000	−1.80109	−0.900547	+	0.434759i	$0.856834\pi$
$642$	−12.0836	−0.476902
$643$	11.5233	0.454436	0.227218	−	0.973844i	$-0.427037\pi$
$643$	11.5233	0.454436	0.227218	+	0.973844i	$0.427037\pi$
$644$	74.3730	2.93071
$645$	−3.25019	−0.127976
$646$	11.3498	0.446551
$647$	−42.6096	−1.67515	−0.837577	−	0.546319i	$-0.816029\pi$
$647$	−42.6096	−1.67515	−0.837577	+	0.546319i	$0.816029\pi$
$648$	19.2120	0.754719
$649$	8.63365	0.338900
$650$	40.6479	1.59434
$651$	18.1558	0.711580
$652$	−4.33142	−0.169631
$653$	−30.8010	−1.20533	−0.602667	−	0.797993i	$-0.705895\pi$
$653$	−30.8010	−1.20533	−0.602667	+	0.797993i	$0.705895\pi$
$654$	58.8198	2.30004
$655$	11.7646	0.459680
$656$	4.20229	0.164072
$657$	−37.3232	−1.45612
$658$	−9.36648	−0.365144
$659$	−23.8832	−0.930357	−0.465179	−	0.885217i	$-0.654010\pi$
$659$	−23.8832	−0.930357	−0.465179	+	0.885217i	$0.654010\pi$
$660$	9.91606	0.385982
$661$	37.7122	1.46684	0.733418	−	0.679778i	$-0.237924\pi$
$661$	37.7122	1.46684	0.733418	+	0.679778i	$0.237924\pi$
$662$	−39.6132	−1.53961
$663$	−13.6609	−0.530547
$664$	−8.19169	−0.317899
$665$	25.5478	0.990702
$666$	45.5228	1.76397
$667$	−19.5789	−0.758100
$668$	16.5047	0.638585
$669$	−22.7521	−0.879648
$670$	22.9067	0.884962
$671$	−3.21326	−0.124047
$672$	63.4591	2.44799
$673$	22.1018	0.851960	0.425980	−	0.904733i	$-0.359929\pi$
$673$	22.1018	0.851960	0.425980	+	0.904733i	$0.359929\pi$
$674$	−71.9567	−2.77167
$675$	−2.19931	−0.0846514
$676$	51.2165	1.96987
$677$	45.0030	1.72961	0.864803	−	0.502111i	$-0.167443\pi$
$677$	45.0030	1.72961	0.864803	+	0.502111i	$0.167443\pi$
$678$	−10.9704	−0.421316
$679$	4.54836	0.174550
$680$	3.06688	0.117610
$681$	50.4739	1.93416
$682$	−4.18432	−0.160226
$683$	17.9007	0.684953	0.342476	−	0.939526i	$-0.388734\pi$
$683$	17.9007	0.684953	0.342476	+	0.939526i	$0.388734\pi$
$684$	50.3078	1.92357
$685$	17.4656	0.667327
$686$	−10.3153	−0.393842
$687$	25.1375	0.959056
$688$	0.793731	0.0302607
$689$	68.0423	2.59220
$690$	−45.7056	−1.73998
$691$	3.89552	0.148192	0.0740962	−	0.997251i	$-0.476393\pi$
$691$	3.89552	0.148192	0.0740962	+	0.997251i	$0.476393\pi$
$692$	−13.0188	−0.494899
$693$	12.7207	0.483220
$694$	15.5415	0.589949
$695$	−23.6521	−0.897177
$696$	18.4984	0.701179
$697$	5.29435	0.200538
$698$	−34.2333	−1.29575
$699$	−16.3162	−0.617136
$700$	−39.3893	−1.48877
$701$	−17.3023	−0.653498	−0.326749	−	0.945111i	$-0.605953\pi$
$701$	−17.3023	−0.653498	−0.326749	+	0.945111i	$0.605953\pi$
$702$	−8.14045	−0.307242
$703$	−31.3288	−1.18159
$704$	−13.0378	−0.491381
$705$	3.47689	0.130947
$706$	−70.4805	−2.65257
$707$	13.7506	0.517143
$708$	65.9311	2.47784
$709$	29.8795	1.12215	0.561075	−	0.827765i	$-0.310388\pi$
$709$	29.8795	1.12215	0.561075	+	0.827765i	$0.310388\pi$
$710$	−27.0690	−1.01588
$711$	−33.4437	−1.25424
$712$	−15.1957	−0.569484
$713$	11.6497	0.436285
$714$	21.9159	0.820183
$715$	7.08693	0.265036
$716$	−40.4128	−1.51030
$717$	−46.2712	−1.72803
$718$	25.8129	0.963327
$719$	28.8517	1.07599	0.537993	−	0.842950i	$-0.319183\pi$
$719$	28.8517	1.07599	0.537993	+	0.842950i	$0.319183\pi$
$720$	−3.36526	−0.125416
$721$	−30.0001	−1.11726
$722$	−14.6167	−0.543976
$723$	8.11059	0.301636
$724$	34.3491	1.27657
$725$	10.3694	0.385108
$726$	−5.62537	−0.208777
$727$	10.8843	0.403675	0.201838	−	0.979419i	$-0.435309\pi$
$727$	10.8843	0.403675	0.201838	+	0.979419i	$0.435309\pi$
$728$	−50.2202	−1.86129
$729$	−31.5431	−1.16826
$730$	33.3583	1.23465
$731$	1.00000	0.0369863
$732$	−24.5382	−0.906957
$733$	−22.7745	−0.841195	−0.420597	−	0.907247i	$-0.638180\pi$
$733$	−22.7745	−0.841195	−0.420597	+	0.907247i	$0.638180\pi$
$734$	75.1863	2.77518
$735$	26.5804	0.980434
$736$	40.7188	1.50091
$737$	−7.84936	−0.289135
$738$	38.8508	1.43012
$739$	−6.55869	−0.241265	−0.120633	−	0.992697i	$-0.538492\pi$
$739$	−6.55869	−0.241265	−0.120633	+	0.992697i	$0.538492\pi$
$740$	−24.5762	−0.903440
$741$	68.9895	2.53439
$742$	−109.159	−4.00734
$743$	9.89598	0.363048	0.181524	−	0.983386i	$-0.441897\pi$
$743$	9.89598	0.363048	0.181524	+	0.983386i	$0.441897\pi$
$744$	−11.0068	−0.403528
$745$	10.0558	0.368415
$746$	60.3400	2.20921
$747$	11.3246	0.414344
$748$	−3.05092	−0.111553
$749$	8.36865	0.305784
$750$	60.7292	2.21752
$751$	40.9101	1.49283	0.746415	−	0.665481i	$-0.231774\pi$
$751$	40.9101	1.49283	0.746415	+	0.665481i	$0.231774\pi$
$752$	−0.849094	−0.0309633
$753$	51.3717	1.87209
$754$	38.3808	1.39775
$755$	−30.3405	−1.10420
$756$	7.88838	0.286898
$757$	−6.70267	−0.243613	−0.121806	−	0.992554i	$-0.538869\pi$
$757$	−6.70267	−0.243613	−0.121806	+	0.992554i	$0.538869\pi$
$758$	−34.1979	−1.24212
$759$	15.6618	0.568487
$760$	−15.4881	−0.561814
$761$	−37.1265	−1.34584	−0.672918	−	0.739717i	$-0.734959\pi$
$761$	−37.1265	−1.34584	−0.672918	+	0.739717i	$0.734959\pi$
$762$	−103.742	−3.75817
$763$	−40.7363	−1.47475
$764$	−29.4477	−1.06538
$765$	−4.23980	−0.153290
$766$	78.1274	2.82286
$767$	47.1205	1.70142
$768$	−26.3488	−0.950780
$769$	−22.2466	−0.802233	−0.401117	−	0.916027i	$-0.631378\pi$
$769$	−22.2466	−0.802233	−0.401117	+	0.916027i	$0.631378\pi$
$770$	−11.3694	−0.409724
$771$	25.2873	0.910700
$772$	−29.4997	−1.06172
$773$	−5.65323	−0.203333	−0.101666	−	0.994819i	$-0.532417\pi$
$773$	−5.65323	−0.203333	−0.101666	+	0.994819i	$0.532417\pi$
$774$	7.33817	0.263765
$775$	−6.16990	−0.221629
$776$	−2.75740	−0.0989850
$777$	−60.4945	−2.17023
$778$	−37.6436	−1.34959
$779$	−26.7371	−0.957957
$780$	54.1196	1.93779
$781$	9.27564	0.331908
$782$	14.0624	0.502872
$783$	−2.07664	−0.0742131
$784$	−6.49123	−0.231829
$785$	6.60453	0.235726
$786$	−50.9664	−1.81791
$787$	14.9658	0.533474	0.266737	−	0.963769i	$-0.414055\pi$
$787$	14.9658	0.533474	0.266737	+	0.963769i	$0.414055\pi$
$788$	−79.4622	−2.83072
$789$	21.2844	0.757746
$790$	29.8909	1.06347
$791$	7.59769	0.270143
$792$	−7.71182	−0.274028
$793$	−17.5372	−0.622765
$794$	13.6663	0.484998
$795$	40.5202	1.43710
$796$	16.0615	0.569285
$797$	−2.78234	−0.0985556	−0.0492778	−	0.998785i	$-0.515692\pi$
$797$	−2.78234	−0.0985556	−0.0492778	+	0.998785i	$0.515692\pi$
$798$	−110.678	−3.91796
$799$	−1.06975	−0.0378450
$800$	−21.5654	−0.762452
$801$	21.0073	0.742255
$802$	42.9181	1.51549
$803$	−11.4308	−0.403384
$804$	−59.9419	−2.11399
$805$	31.6539	1.11565
$806$	−22.8371	−0.804401
$807$	−6.50918	−0.229134
$808$	−8.33616	−0.293265
$809$	11.2250	0.394650	0.197325	−	0.980338i	$-0.436775\pi$
$809$	11.2250	0.394650	0.197325	+	0.980338i	$0.436775\pi$
$810$	23.7381	0.834073
$811$	−17.5173	−0.615117	−0.307558	−	0.951529i	$-0.599512\pi$
$811$	−17.5173	−0.615117	−0.307558	+	0.951529i	$0.599512\pi$
$812$	−37.1923	−1.30519
$813$	−30.3402	−1.06408
$814$	13.9421	0.488669
$815$	−1.84350	−0.0645749
$816$	1.98673	0.0695495
$817$	−5.05012	−0.176681
$818$	−8.11958	−0.283894
$819$	69.4267	2.42597
$820$	−20.9742	−0.732452
$821$	19.7865	0.690554	0.345277	−	0.938501i	$-0.387785\pi$
$821$	19.7865	0.690554	0.345277	+	0.938501i	$0.387785\pi$
$822$	−75.6644	−2.63910
$823$	24.6735	0.860064	0.430032	−	0.902814i	$-0.358502\pi$
$823$	24.6735	0.860064	0.430032	+	0.902814i	$0.358502\pi$
$824$	18.1873	0.633585
$825$	−8.29476	−0.288786
$826$	−75.5942	−2.63026
$827$	8.80854	0.306303	0.153152	−	0.988203i	$-0.451058\pi$
$827$	8.80854	0.306303	0.153152	+	0.988203i	$0.451058\pi$
$828$	62.3317	2.16618
$829$	9.55607	0.331896	0.165948	−	0.986135i	$-0.446932\pi$
$829$	9.55607	0.331896	0.165948	+	0.986135i	$0.446932\pi$
$830$	−10.1215	−0.351324
$831$	45.0365	1.56230
$832$	−71.1574	−2.46694
$833$	−8.17812	−0.283355
$834$	102.466	3.54810
$835$	7.02456	0.243095
$836$	15.4075	0.532880
$837$	1.23563	0.0427096
$838$	76.1832	2.63170
$839$	40.6984	1.40506	0.702532	−	0.711652i	$-0.252053\pi$
$839$	40.6984	1.40506	0.702532	+	0.711652i	$0.252053\pi$
$840$	−29.9069	−1.03189
$841$	−19.2090	−0.662379
$842$	2.75382	0.0949029
$843$	−64.7915	−2.23154
$844$	−61.8952	−2.13052
$845$	21.7983	0.749884
$846$	−7.85001	−0.269889
$847$	3.89591	0.133865
$848$	−9.89548	−0.339812
$849$	45.2667	1.55355
$850$	−7.44772	−0.255455
$851$	−38.8166	−1.33062
$852$	70.8337	2.42672
$853$	37.9370	1.29894	0.649468	−	0.760389i	$-0.274991\pi$
$853$	37.9370	1.29894	0.649468	+	0.760389i	$0.274991\pi$
$854$	28.1345	0.962744
$855$	21.4115	0.732258
$856$	−5.07342	−0.173406
$857$	−54.0819	−1.84740	−0.923701	−	0.383114i	$-0.874852\pi$
$857$	−54.0819	−1.84740	−0.923701	+	0.383114i	$0.874852\pi$
$858$	−30.7019	−1.04815
$859$	11.0328	0.376434	0.188217	−	0.982127i	$-0.439729\pi$
$859$	11.0328	0.376434	0.188217	+	0.982127i	$0.439729\pi$
$860$	−3.96163	−0.135090
$861$	−51.6282	−1.75949
$862$	60.7325	2.06856
$863$	−29.0166	−0.987736	−0.493868	−	0.869537i	$-0.664417\pi$
$863$	−29.0166	−0.987736	−0.493868	+	0.869537i	$0.664417\pi$
$864$	4.31884	0.146930
$865$	−5.54092	−0.188397
$866$	−10.9281	−0.371350
$867$	2.50303	0.0850073
$868$	22.1299	0.751138
$869$	−10.2426	−0.347458
$870$	22.8564	0.774903
$871$	−42.8400	−1.45158
$872$	24.6960	0.836313
$873$	3.81196	0.129015
$874$	−71.0171	−2.40219
$875$	−42.0587	−1.42184
$876$	−87.2916	−2.94931
$877$	49.2283	1.66232	0.831161	−	0.556031i	$-0.187677\pi$
$877$	49.2283	1.66232	0.831161	+	0.556031i	$0.187677\pi$
$878$	37.1473	1.25366
$879$	−3.51918	−0.118699
$880$	−1.03066	−0.0347436
$881$	−4.53190	−0.152684	−0.0763418	−	0.997082i	$-0.524324\pi$
$881$	−4.53190	−0.152684	−0.0763418	+	0.997082i	$0.524324\pi$
$882$	−60.0124	−2.02072
$883$	−2.86139	−0.0962933	−0.0481466	−	0.998840i	$-0.515331\pi$
$883$	−2.86139	−0.0962933	−0.0481466	+	0.998840i	$0.515331\pi$
$884$	−16.6512	−0.560041
$885$	28.0610	0.943259
$886$	−9.47577	−0.318345
$887$	50.6299	1.69999	0.849993	−	0.526794i	$-0.176606\pi$
$887$	50.6299	1.69999	0.849993	+	0.526794i	$0.176606\pi$
$888$	36.6743	1.23071
$889$	71.8476	2.40969
$890$	−18.7756	−0.629361
$891$	−8.13427	−0.272508
$892$	−27.7324	−0.928548
$893$	5.40237	0.180783
$894$	−43.5636	−1.45698
$895$	−17.2001	−0.574936
$896$	63.4503	2.11973
$897$	85.4784	2.85404
$898$	−7.18008	−0.239602
$899$	−5.82577	−0.194300
$900$	−33.0120	−1.10040
$901$	−12.4670	−0.415338
$902$	11.8987	0.396182
$903$	−9.75157	−0.324512
$904$	−4.60603	−0.153194
$905$	14.6193	0.485963
$906$	131.441	4.36683
$907$	43.7426	1.45245	0.726224	−	0.687458i	$-0.241273\pi$
$907$	43.7426	1.45245	0.726224	+	0.687458i	$0.241273\pi$
$908$	61.5222	2.04169
$909$	11.5243	0.382236
$910$	−62.0515	−2.05699
$911$	47.5104	1.57409	0.787045	−	0.616896i	$-0.211610\pi$
$911$	47.5104	1.57409	0.787045	+	0.616896i	$0.211610\pi$
$912$	−10.0332	−0.332233
$913$	3.46832	0.114785
$914$	−27.6887	−0.915860
$915$	−10.4437	−0.345258
$916$	30.6399	1.01237
$917$	35.2974	1.16562
$918$	1.49153	0.0492280
$919$	41.0831	1.35521	0.677603	−	0.735428i	$-0.263019\pi$
$919$	41.0831	1.35521	0.677603	+	0.735428i	$0.263019\pi$
$920$	−19.1899	−0.632673
$921$	−26.7092	−0.880097
$922$	44.6189	1.46945
$923$	50.6243	1.66632
$924$	29.7513	0.978744
$925$	20.5579	0.675941
$926$	33.9554	1.11584
$927$	−25.1430	−0.825803
$928$	−20.3626	−0.668434
$929$	29.0175	0.952032	0.476016	−	0.879437i	$-0.342080\pi$
$929$	29.0175	0.952032	0.476016	+	0.879437i	$0.342080\pi$
$930$	−13.5998	−0.445956
$931$	41.3005	1.35357
$932$	−19.8877	−0.651443
$933$	−48.0477	−1.57301
$934$	−44.1191	−1.44362
$935$	−1.29850	−0.0424656
$936$	−42.0893	−1.37573
$937$	−11.3659	−0.371308	−0.185654	−	0.982615i	$-0.559440\pi$
$937$	−11.3659	−0.371308	−0.185654	+	0.982615i	$0.559440\pi$
$938$	68.7271	2.24402
$939$	47.6050	1.55353
$940$	4.23795	0.138227
$941$	−34.3599	−1.12010	−0.560051	−	0.828458i	$-0.689218\pi$
$941$	−34.3599	−1.12010	−0.560051	+	0.828458i	$0.689218\pi$
$942$	−28.6121	−0.932232
$943$	−33.1275	−1.07878
$944$	−6.85279	−0.223039
$945$	3.35738	0.109215
$946$	2.24742	0.0730701
$947$	6.66073	0.216445	0.108222	−	0.994127i	$-0.465484\pi$
$947$	6.66073	0.216445	0.108222	+	0.994127i	$0.465484\pi$
$948$	−78.2182	−2.54041
$949$	−62.3866	−2.02516
$950$	37.6119	1.22029
$951$	0.806264	0.0261449
$952$	9.20160	0.298226
$953$	−27.0813	−0.877250	−0.438625	−	0.898670i	$-0.644534\pi$
$953$	−27.0813	−0.877250	−0.438625	+	0.898670i	$0.644534\pi$
$954$	−91.4853	−2.96195
$955$	−12.5332	−0.405566
$956$	−56.3996	−1.82409
$957$	−7.83212	−0.253176
$958$	−36.3972	−1.17594
$959$	52.4022	1.69216
$960$	−42.3754	−1.36766
$961$	−27.5336	−0.888180
$962$	76.0925	2.45332
$963$	7.01372	0.226014
$964$	9.88594	0.318405
$965$	−12.5554	−0.404172
$966$	−137.131	−4.41211
$967$	−23.4339	−0.753584	−0.376792	−	0.926298i	$-0.622973\pi$
$967$	−23.4339	−0.753584	−0.376792	+	0.926298i	$0.622973\pi$
$968$	−2.36186	−0.0759131
$969$	−12.6406	−0.406074
$970$	−3.40701	−0.109393
$971$	33.0060	1.05921	0.529607	−	0.848243i	$-0.322340\pi$
$971$	33.0060	1.05921	0.529607	+	0.848243i	$0.322340\pi$
$972$	−68.1919	−2.18726
$973$	−70.9638	−2.27499
$974$	−19.1073	−0.612237
$975$	−45.2709	−1.44983
$976$	2.55046	0.0816383
$977$	50.0477	1.60117	0.800583	−	0.599221i	$-0.204523\pi$
$977$	50.0477	1.60117	0.800583	+	0.599221i	$0.204523\pi$
$978$	7.98639	0.255376
$979$	6.43379	0.205625
$980$	32.3987	1.03494
$981$	−34.1409	−1.09004
$982$	61.7855	1.97166
$983$	−49.5716	−1.58109	−0.790544	−	0.612405i	$-0.790202\pi$
$983$	−49.5716	−1.58109	−0.790544	+	0.612405i	$0.790202\pi$
$984$	31.2992	0.997781
$985$	−33.8199	−1.07759
$986$	−7.03232	−0.223955
$987$	10.4317	0.332046
$988$	84.0907	2.67528
$989$	−6.25714	−0.198965
$990$	−9.52863	−0.302840
$991$	−13.1785	−0.418628	−0.209314	−	0.977848i	$-0.567123\pi$
$991$	−13.1785	−0.418628	−0.209314	+	0.977848i	$0.567123\pi$
$992$	12.1160	0.384683
$993$	44.1185	1.40006
$994$	−81.2153	−2.57599
$995$	6.83595	0.216714
$996$	26.4859	0.839238
$997$	47.6776	1.50996	0.754982	−	0.655745i	$-0.227646\pi$
$997$	47.6776	1.50996	0.754982	+	0.655745i	$0.227646\pi$
$998$	87.8926	2.78219
$999$	−4.11708	−0.130259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.11	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.11	✓	78	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} +O(q^{10})\)	\(q-2.24742 q^{2} +2.50303 q^{3} +3.05092 q^{4} +1.29850 q^{5} -5.62537 q^{6} +3.89591 q^{7} -2.36186 q^{8} +3.26514 q^{9} -2.91829 q^{10} +1.00000 q^{11} +7.63653 q^{12} +5.45777 q^{13} -8.75577 q^{14} +3.25019 q^{15} -0.793731 q^{16} -1.00000 q^{17} -7.33817 q^{18} +5.05012 q^{19} +3.96163 q^{20} +9.75157 q^{21} -2.24742 q^{22} +6.25714 q^{23} -5.91180 q^{24} -3.31389 q^{25} -12.2659 q^{26} +0.663664 q^{27} +11.8861 q^{28} -3.12906 q^{29} -7.30455 q^{30} +1.86183 q^{31} +6.50757 q^{32} +2.50303 q^{33} +2.24742 q^{34} +5.05885 q^{35} +9.96169 q^{36} -6.20357 q^{37} -11.3498 q^{38} +13.6609 q^{39} -3.06688 q^{40} -5.29435 q^{41} -21.9159 q^{42} -1.00000 q^{43} +3.05092 q^{44} +4.23980 q^{45} -14.0624 q^{46} +1.06975 q^{47} -1.98673 q^{48} +8.17812 q^{49} +7.44772 q^{50} -2.50303 q^{51} +16.6512 q^{52} +12.4670 q^{53} -1.49153 q^{54} +1.29850 q^{55} -9.20160 q^{56} +12.6406 q^{57} +7.03232 q^{58} +8.63365 q^{59} +9.91606 q^{60} -3.21326 q^{61} -4.18432 q^{62} +12.7207 q^{63} -13.0378 q^{64} +7.08693 q^{65} -5.62537 q^{66} -7.84936 q^{67} -3.05092 q^{68} +15.6618 q^{69} -11.3694 q^{70} +9.27564 q^{71} -7.71182 q^{72} -11.4308 q^{73} +13.9421 q^{74} -8.29476 q^{75} +15.4075 q^{76} +3.89591 q^{77} -30.7019 q^{78} -10.2426 q^{79} -1.03066 q^{80} -8.13427 q^{81} +11.8987 q^{82} +3.46832 q^{83} +29.7513 q^{84} -1.29850 q^{85} +2.24742 q^{86} -7.83212 q^{87} -2.36186 q^{88} +6.43379 q^{89} -9.52863 q^{90} +21.2630 q^{91} +19.0900 q^{92} +4.66021 q^{93} -2.40418 q^{94} +6.55760 q^{95} +16.2886 q^{96} +1.16747 q^{97} -18.3797 q^{98} +3.26514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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