LMFDB - Embedded newform 8033.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57712 q^{2} -3.09746 q^{3} +4.64157 q^{4} -1.30860 q^{5} +7.98254 q^{6} +0.204481 q^{7} -6.80764 q^{8} +6.59427 q^{9} +O(q^{10})$	\(q-2.57712 q^{2} -3.09746 q^{3} +4.64157 q^{4} -1.30860 q^{5} +7.98254 q^{6} +0.204481 q^{7} -6.80764 q^{8} +6.59427 q^{9} +3.37243 q^{10} +4.00900 q^{11} -14.3771 q^{12} -1.31047 q^{13} -0.526974 q^{14} +4.05335 q^{15} +8.26100 q^{16} -2.43653 q^{17} -16.9943 q^{18} -0.259978 q^{19} -6.07396 q^{20} -0.633373 q^{21} -10.3317 q^{22} +5.35846 q^{23} +21.0864 q^{24} -3.28756 q^{25} +3.37723 q^{26} -11.1331 q^{27} +0.949113 q^{28} -1.00000 q^{29} -10.4460 q^{30} +10.7673 q^{31} -7.67434 q^{32} -12.4177 q^{33} +6.27925 q^{34} -0.267585 q^{35} +30.6077 q^{36} -2.45462 q^{37} +0.669995 q^{38} +4.05912 q^{39} +8.90849 q^{40} +12.1841 q^{41} +1.63228 q^{42} +5.15576 q^{43} +18.6080 q^{44} -8.62928 q^{45} -13.8094 q^{46} -4.67417 q^{47} -25.5881 q^{48} -6.95819 q^{49} +8.47245 q^{50} +7.54707 q^{51} -6.08261 q^{52} +7.17011 q^{53} +28.6914 q^{54} -5.24619 q^{55} -1.39204 q^{56} +0.805272 q^{57} +2.57712 q^{58} -13.0190 q^{59} +18.8139 q^{60} -8.81390 q^{61} -27.7488 q^{62} +1.34841 q^{63} +3.25572 q^{64} +1.71488 q^{65} +32.0020 q^{66} +7.78682 q^{67} -11.3093 q^{68} -16.5976 q^{69} +0.689599 q^{70} -3.19052 q^{71} -44.8914 q^{72} -7.68693 q^{73} +6.32586 q^{74} +10.1831 q^{75} -1.20670 q^{76} +0.819766 q^{77} -10.4608 q^{78} +3.89730 q^{79} -10.8104 q^{80} +14.7016 q^{81} -31.3999 q^{82} -4.79724 q^{83} -2.93984 q^{84} +3.18845 q^{85} -13.2870 q^{86} +3.09746 q^{87} -27.2918 q^{88} +6.10285 q^{89} +22.2387 q^{90} -0.267966 q^{91} +24.8716 q^{92} -33.3514 q^{93} +12.0459 q^{94} +0.340208 q^{95} +23.7710 q^{96} -14.5801 q^{97} +17.9321 q^{98} +26.4364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.57712	−1.82230	−0.911151	−	0.412073i	$-0.864805\pi$
$2$	−2.57712	−1.82230	−0.911151	+	0.412073i	$0.864805\pi$
$3$	−3.09746	−1.78832	−0.894160	−	0.447747i	$-0.852227\pi$
$3$	−3.09746	−1.78832	−0.894160	+	0.447747i	$0.852227\pi$
$4$	4.64157	2.32078
$5$	−1.30860	−0.585225	−0.292612	−	0.956231i	$-0.594525\pi$
$5$	−1.30860	−0.585225	−0.292612	+	0.956231i	$0.594525\pi$
$6$	7.98254	3.25886
$7$	0.204481	0.0772867	0.0386433	−	0.999253i	$-0.487696\pi$
$7$	0.204481	0.0772867	0.0386433	+	0.999253i	$0.487696\pi$
$8$	−6.80764	−2.40686
$9$	6.59427	2.19809
$10$	3.37243	1.06646
$11$	4.00900	1.20876	0.604380	−	0.796696i	$-0.293421\pi$
$11$	4.00900	1.20876	0.604380	+	0.796696i	$0.293421\pi$
$12$	−14.3771	−4.15030
$13$	−1.31047	−0.363458	−0.181729	−	0.983349i	$-0.558169\pi$
$13$	−1.31047	−0.363458	−0.181729	+	0.983349i	$0.558169\pi$
$14$	−0.526974	−0.140840
$15$	4.05335	1.04657
$16$	8.26100	2.06525
$17$	−2.43653	−0.590946	−0.295473	−	0.955351i	$-0.595477\pi$
$17$	−2.43653	−0.590946	−0.295473	+	0.955351i	$0.595477\pi$
$18$	−16.9943	−4.00558
$19$	−0.259978	−0.0596430	−0.0298215	−	0.999555i	$-0.509494\pi$
$19$	−0.259978	−0.0596430	−0.0298215	+	0.999555i	$0.509494\pi$
$20$	−6.07396	−1.35818
$21$	−0.633373	−0.138213
$22$	−10.3317	−2.20272
$23$	5.35846	1.11732	0.558658	−	0.829398i	$-0.311317\pi$
$23$	5.35846	1.11732	0.558658	+	0.829398i	$0.311317\pi$
$24$	21.0864	4.30425
$25$	−3.28756	−0.657512
$26$	3.37723	0.662330
$27$	−11.1331	−2.14257
$28$	0.949113	0.179366
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−10.4460	−1.90717
$31$	10.7673	1.93387	0.966935	−	0.255022i	$-0.0820827\pi$
$31$	10.7673	1.93387	0.966935	+	0.255022i	$0.0820827\pi$
$32$	−7.67434	−1.35664
$33$	−12.4177	−2.16165
$34$	6.27925	1.07688
$35$	−0.267585	−0.0452301
$36$	30.6077	5.10129
$37$	−2.45462	−0.403537	−0.201769	−	0.979433i	$-0.564669\pi$
$37$	−2.45462	−0.403537	−0.201769	+	0.979433i	$0.564669\pi$
$38$	0.669995	0.108688
$39$	4.05912	0.649979
$40$	8.90849	1.40856
$41$	12.1841	1.90284	0.951418	−	0.307902i	$-0.0996268\pi$
$41$	12.1841	1.90284	0.951418	+	0.307902i	$0.0996268\pi$
$42$	1.63228	0.251866
$43$	5.15576	0.786247	0.393123	−	0.919486i	$-0.371395\pi$
$43$	5.15576	0.786247	0.393123	+	0.919486i	$0.371395\pi$
$44$	18.6080	2.80527
$45$	−8.62928	−1.28638
$46$	−13.8094	−2.03609
$47$	−4.67417	−0.681798	−0.340899	−	0.940100i	$-0.610731\pi$
$47$	−4.67417	−0.681798	−0.340899	+	0.940100i	$0.610731\pi$
$48$	−25.5881	−3.69333
$49$	−6.95819	−0.994027
$50$	8.47245	1.19819
$51$	7.54707	1.05680
$52$	−6.08261	−0.843507
$53$	7.17011	0.984890	0.492445	−	0.870343i	$-0.336103\pi$
$53$	7.17011	0.984890	0.492445	+	0.870343i	$0.336103\pi$
$54$	28.6914	3.90441
$55$	−5.24619	−0.707396
$56$	−1.39204	−0.186019
$57$	0.805272	0.106661
$58$	2.57712	0.338393
$59$	−13.0190	−1.69493	−0.847463	−	0.530854i	$-0.821871\pi$
$59$	−13.0190	−1.69493	−0.847463	+	0.530854i	$0.821871\pi$
$60$	18.8139	2.42886
$61$	−8.81390	−1.12850	−0.564252	−	0.825603i	$-0.690835\pi$
$61$	−8.81390	−1.12850	−0.564252	+	0.825603i	$0.690835\pi$
$62$	−27.7488	−3.52410
$63$	1.34841	0.169883
$64$	3.25572	0.406964
$65$	1.71488	0.212705
$66$	32.0020	3.93918
$67$	7.78682	0.951311	0.475655	−	0.879632i	$-0.342211\pi$
$67$	7.78682	0.951311	0.475655	+	0.879632i	$0.342211\pi$
$68$	−11.3093	−1.37146
$69$	−16.5976	−1.99812
$70$	0.689599	0.0824228
$71$	−3.19052	−0.378645	−0.189323	−	0.981915i	$-0.560629\pi$
$71$	−3.19052	−0.378645	−0.189323	+	0.981915i	$0.560629\pi$
$72$	−44.8914	−5.29051
$73$	−7.68693	−0.899687	−0.449844	−	0.893107i	$-0.648520\pi$
$73$	−7.68693	−0.899687	−0.449844	+	0.893107i	$0.648520\pi$
$74$	6.32586	0.735366
$75$	10.1831	1.17584
$76$	−1.20670	−0.138419
$77$	0.819766	0.0934210
$78$	−10.4608	−1.18446
$79$	3.89730	0.438480	0.219240	−	0.975671i	$-0.429642\pi$
$79$	3.89730	0.438480	0.219240	+	0.975671i	$0.429642\pi$
$80$	−10.8104	−1.20864
$81$	14.7016	1.63351
$82$	−31.3999	−3.46754
$83$	−4.79724	−0.526565	−0.263283	−	0.964719i	$-0.584805\pi$
$83$	−4.79724	−0.526565	−0.263283	+	0.964719i	$0.584805\pi$
$84$	−2.93984	−0.320763
$85$	3.18845	0.345836
$86$	−13.2870	−1.43278
$87$	3.09746	0.332083
$88$	−27.2918	−2.90932
$89$	6.10285	0.646901	0.323451	−	0.946245i	$-0.395157\pi$
$89$	6.10285	0.646901	0.323451	+	0.946245i	$0.395157\pi$
$90$	22.2387	2.34417
$91$	−0.267966	−0.0280904
$92$	24.8716	2.59305
$93$	−33.3514	−3.45838
$94$	12.0459	1.24244
$95$	0.340208	0.0349046
$96$	23.7710	2.42611
$97$	−14.5801	−1.48038	−0.740192	−	0.672395i	$-0.765266\pi$
$97$	−14.5801	−1.48038	−0.740192	+	0.672395i	$0.765266\pi$
$98$	17.9321	1.81142
$99$	26.4364	2.65696
$100$	−15.2594	−1.52594
$101$	15.3998	1.53234	0.766170	−	0.642638i	$-0.222160\pi$
$101$	15.3998	1.53234	0.766170	+	0.642638i	$0.222160\pi$
$102$	−19.4497	−1.92581
$103$	−13.7653	−1.35634	−0.678169	−	0.734906i	$-0.737226\pi$
$103$	−13.7653	−1.35634	−0.678169	+	0.734906i	$0.737226\pi$
$104$	8.92118	0.874794
$105$	0.828833	0.0808859
$106$	−18.4783	−1.79477
$107$	−0.756912	−0.0731734	−0.0365867	−	0.999330i	$-0.511649\pi$
$107$	−0.756912	−0.0731734	−0.0365867	+	0.999330i	$0.511649\pi$
$108$	−51.6751	−4.97244
$109$	−13.5757	−1.30032	−0.650158	−	0.759799i	$-0.725297\pi$
$109$	−13.5757	−1.30032	−0.650158	+	0.759799i	$0.725297\pi$
$110$	13.5201	1.28909
$111$	7.60309	0.721654
$112$	1.68922	0.159616
$113$	−14.7141	−1.38418	−0.692092	−	0.721810i	$-0.743311\pi$
$113$	−14.7141	−1.38418	−0.692092	+	0.721810i	$0.743311\pi$
$114$	−2.07529	−0.194368
$115$	−7.01209	−0.653881
$116$	−4.64157	−0.430959
$117$	−8.64157	−0.798913
$118$	33.5515	3.08867
$119$	−0.498226	−0.0456723
$120$	−27.5937	−2.51895
$121$	5.07209	0.461099
$122$	22.7145	2.05647
$123$	−37.7398	−3.40288
$124$	49.9773	4.48809
$125$	10.8451	0.970017
$126$	−3.47501	−0.309578
$127$	7.80216	0.692330	0.346165	−	0.938174i	$-0.387484\pi$
$127$	7.80216	0.692330	0.346165	+	0.938174i	$0.387484\pi$
$128$	6.95830	0.615032
$129$	−15.9698	−1.40606
$130$	−4.41945	−0.387612
$131$	−15.6916	−1.37098	−0.685492	−	0.728081i	$-0.740413\pi$
$131$	−15.6916	−1.37098	−0.685492	+	0.728081i	$0.740413\pi$
$132$	−57.6377	−5.01672
$133$	−0.0531606	−0.00460961
$134$	−20.0676	−1.73358
$135$	14.5688	1.25389
$136$	16.5870	1.42233
$137$	−15.3633	−1.31258	−0.656289	−	0.754509i	$-0.727875\pi$
$137$	−15.3633	−1.31258	−0.656289	+	0.754509i	$0.727875\pi$
$138$	42.7741	3.64117
$139$	−11.7864	−0.999713	−0.499856	−	0.866108i	$-0.666614\pi$
$139$	−11.7864	−0.999713	−0.499856	+	0.866108i	$0.666614\pi$
$140$	−1.24201	−0.104969
$141$	14.4781	1.21927
$142$	8.22236	0.690005
$143$	−5.25366	−0.439333
$144$	54.4753	4.53961
$145$	1.30860	0.108674
$146$	19.8102	1.63950
$147$	21.5527	1.77764
$148$	−11.3933	−0.936522
$149$	21.3881	1.75218	0.876092	−	0.482145i	$-0.160142\pi$
$149$	21.3881	1.75218	0.876092	+	0.482145i	$0.160142\pi$
$150$	−26.2431	−2.14274
$151$	−18.1154	−1.47421	−0.737104	−	0.675779i	$-0.763807\pi$
$151$	−18.1154	−1.47421	−0.737104	+	0.675779i	$0.763807\pi$
$152$	1.76984	0.143553
$153$	−16.0672	−1.29895
$154$	−2.11264	−0.170241
$155$	−14.0902	−1.13175
$156$	18.8407	1.50846
$157$	13.1339	1.04820	0.524098	−	0.851658i	$-0.324402\pi$
$157$	13.1339	1.04820	0.524098	+	0.851658i	$0.324402\pi$
$158$	−10.0438	−0.799043
$159$	−22.2091	−1.76130
$160$	10.0427	0.793942
$161$	1.09570	0.0863536
$162$	−37.8879	−2.97675
$163$	8.19341	0.641757	0.320879	−	0.947120i	$-0.396022\pi$
$163$	8.19341	0.641757	0.320879	+	0.947120i	$0.396022\pi$
$164$	56.5533	4.41607
$165$	16.2499	1.26505
$166$	12.3631	0.959561
$167$	−7.79939	−0.603535	−0.301767	−	0.953382i	$-0.597577\pi$
$167$	−7.79939	−0.603535	−0.301767	+	0.953382i	$0.597577\pi$
$168$	4.31178	0.332661
$169$	−11.2827	−0.867898
$170$	−8.21704	−0.630218
$171$	−1.71437	−0.131101
$172$	23.9308	1.82471
$173$	5.62881	0.427950	0.213975	−	0.976839i	$-0.431359\pi$
$173$	5.62881	0.427950	0.213975	+	0.976839i	$0.431359\pi$
$174$	−7.98254	−0.605155
$175$	−0.672245	−0.0508169
$176$	33.1184	2.49639
$177$	40.3258	3.03107
$178$	−15.7278	−1.17885
$179$	19.2361	1.43777	0.718887	−	0.695127i	$-0.244652\pi$
$179$	19.2361	1.43777	0.718887	+	0.695127i	$0.244652\pi$
$180$	−40.0534	−2.98540
$181$	14.4617	1.07493	0.537466	−	0.843285i	$-0.319381\pi$
$181$	14.4617	1.07493	0.537466	+	0.843285i	$0.319381\pi$
$182$	0.690581	0.0511893
$183$	27.3007	2.01813
$184$	−36.4784	−2.68923
$185$	3.21212	0.236160
$186$	85.9507	6.30221
$187$	−9.76807	−0.714312
$188$	−21.6955	−1.58231
$189$	−2.27652	−0.165592
$190$	−0.876757	−0.0636067
$191$	7.19894	0.520897	0.260449	−	0.965488i	$-0.416130\pi$
$191$	7.19894	0.520897	0.260449	+	0.965488i	$0.416130\pi$
$192$	−10.0845	−0.727783
$193$	−5.81124	−0.418302	−0.209151	−	0.977883i	$-0.567070\pi$
$193$	−5.81124	−0.418302	−0.209151	+	0.977883i	$0.567070\pi$
$194$	37.5747	2.69771
$195$	−5.31177	−0.380384
$196$	−32.2969	−2.30692
$197$	3.88172	0.276561	0.138280	−	0.990393i	$-0.455842\pi$
$197$	3.88172	0.276561	0.138280	+	0.990393i	$0.455842\pi$
$198$	−68.1300	−4.84179
$199$	8.09984	0.574182	0.287091	−	0.957903i	$-0.407312\pi$
$199$	8.09984	0.574182	0.287091	+	0.957903i	$0.407312\pi$
$200$	22.3805	1.58254
$201$	−24.1194	−1.70125
$202$	−39.6872	−2.79238
$203$	−0.204481	−0.0143518
$204$	35.0302	2.45261
$205$	−15.9441	−1.11359
$206$	35.4750	2.47166
$207$	35.3351	2.45596
$208$	−10.8258	−0.750631
$209$	−1.04225	−0.0720941
$210$	−2.13601	−0.147398
$211$	27.9589	1.92477	0.962386	−	0.271686i	$-0.0875812\pi$
$211$	27.9589	1.92477	0.962386	+	0.271686i	$0.0875812\pi$
$212$	33.2805	2.28572
$213$	9.88252	0.677139
$214$	1.95066	0.133344
$215$	−6.74684	−0.460131
$216$	75.7903	5.15688
$217$	2.20172	0.149462
$218$	34.9862	2.36957
$219$	23.8100	1.60893
$220$	−24.3505	−1.64171
$221$	3.19299	0.214784
$222$	−19.5941	−1.31507
$223$	−18.9632	−1.26987	−0.634935	−	0.772565i	$-0.718973\pi$
$223$	−18.9632	−1.26987	−0.634935	+	0.772565i	$0.718973\pi$
$224$	−1.56926	−0.104851
$225$	−21.6791	−1.44527
$226$	37.9200	2.52240
$227$	19.9741	1.32573	0.662865	−	0.748739i	$-0.269340\pi$
$227$	19.9741	1.32573	0.662865	+	0.748739i	$0.269340\pi$
$228$	3.73772	0.247537
$229$	−19.0476	−1.25870	−0.629350	−	0.777122i	$-0.716679\pi$
$229$	−19.0476	−1.25870	−0.629350	+	0.777122i	$0.716679\pi$
$230$	18.0710	1.19157
$231$	−2.53919	−0.167067
$232$	6.80764	0.446944
$233$	−11.5047	−0.753700	−0.376850	−	0.926274i	$-0.622993\pi$
$233$	−11.5047	−0.753700	−0.376850	+	0.926274i	$0.622993\pi$
$234$	22.2704	1.45586
$235$	6.11663	0.399005
$236$	−60.4284	−3.93356
$237$	−12.0717	−0.784143
$238$	1.28399	0.0832286
$239$	1.19707	0.0774319	0.0387160	−	0.999250i	$-0.487673\pi$
$239$	1.19707	0.0774319	0.0387160	+	0.999250i	$0.487673\pi$
$240$	33.4847	2.16143
$241$	−24.2006	−1.55890	−0.779449	−	0.626466i	$-0.784501\pi$
$241$	−24.2006	−1.55890	−0.779449	+	0.626466i	$0.784501\pi$
$242$	−13.0714	−0.840262
$243$	−12.1383	−0.778673
$244$	−40.9103	−2.61901
$245$	9.10550	0.581729
$246$	97.2601	6.20108
$247$	0.340692	0.0216777
$248$	−73.3002	−4.65456
$249$	14.8593	0.941668
$250$	−27.9492	−1.76766
$251$	−11.1628	−0.704588	−0.352294	−	0.935889i	$-0.614598\pi$
$251$	−11.1628	−0.704588	−0.352294	+	0.935889i	$0.614598\pi$
$252$	6.25871	0.394262
$253$	21.4821	1.35057
$254$	−20.1071	−1.26163
$255$	−9.87611	−0.618466
$256$	−24.4438	−1.52774
$257$	−28.7417	−1.79286	−0.896430	−	0.443185i	$-0.853848\pi$
$257$	−28.7417	−1.79286	−0.896430	+	0.443185i	$0.853848\pi$
$258$	41.1561	2.56227
$259$	−0.501924	−0.0311880
$260$	7.95972	0.493641
$261$	−6.59427	−0.408175
$262$	40.4392	2.49834
$263$	−4.94322	−0.304812	−0.152406	−	0.988318i	$-0.548702\pi$
$263$	−4.94322	−0.304812	−0.152406	+	0.988318i	$0.548702\pi$
$264$	84.5355	5.20280
$265$	−9.38282	−0.576382
$266$	0.137002	0.00840010
$267$	−18.9034	−1.15687
$268$	36.1430	2.20779
$269$	−10.5622	−0.643986	−0.321993	−	0.946742i	$-0.604353\pi$
$269$	−10.5622	−0.643986	−0.321993	+	0.946742i	$0.604353\pi$
$270$	−37.5457	−2.28496
$271$	13.9672	0.848444	0.424222	−	0.905558i	$-0.360548\pi$
$271$	13.9672	0.848444	0.424222	+	0.905558i	$0.360548\pi$
$272$	−20.1282	−1.22045
$273$	0.830014	0.0502347
$274$	39.5932	2.39191
$275$	−13.1798	−0.794774
$276$	−77.0389	−4.63720
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	30.3751	1.82178
$279$	71.0027	4.25082
$280$	1.82162	0.108863
$281$	22.7195	1.35533	0.677666	−	0.735370i	$-0.262992\pi$
$281$	22.7195	1.35533	0.677666	+	0.735370i	$0.262992\pi$
$282$	−37.3118	−2.22188
$283$	−17.4272	−1.03594	−0.517969	−	0.855400i	$-0.673312\pi$
$283$	−17.4272	−1.03594	−0.517969	+	0.855400i	$0.673312\pi$
$284$	−14.8090	−0.878753
$285$	−1.05378	−0.0624206
$286$	13.5393	0.800597
$287$	2.49142	0.147064
$288$	−50.6067	−2.98203
$289$	−11.0633	−0.650783
$290$	−3.37243	−0.198036
$291$	45.1613	2.64740
$292$	−35.6794	−2.08798
$293$	12.9631	0.757315	0.378657	−	0.925537i	$-0.376386\pi$
$293$	12.9631	0.757315	0.378657	+	0.925537i	$0.376386\pi$
$294$	−55.5440	−3.23939
$295$	17.0367	0.991913
$296$	16.7102	0.971259
$297$	−44.6327	−2.58985
$298$	−55.1198	−3.19301
$299$	−7.02207	−0.406097
$300$	47.2655	2.72887
$301$	1.05426	0.0607664
$302$	46.6856	2.68645
$303$	−47.7004	−2.74031
$304$	−2.14768	−0.123178
$305$	11.5339	0.660429
$306$	41.4071	2.36708
$307$	20.0043	1.14170	0.570852	−	0.821053i	$-0.306613\pi$
$307$	20.0043	1.14170	0.570852	+	0.821053i	$0.306613\pi$
$308$	3.80500	0.216810
$309$	42.6376	2.42557
$310$	36.3121	2.06239
$311$	16.6184	0.942344	0.471172	−	0.882041i	$-0.343831\pi$
$311$	16.6184	0.942344	0.471172	+	0.882041i	$0.343831\pi$
$312$	−27.6330	−1.56441
$313$	0.918882	0.0519383	0.0259691	−	0.999663i	$-0.491733\pi$
$313$	0.918882	0.0519383	0.0259691	+	0.999663i	$0.491733\pi$
$314$	−33.8476	−1.91013
$315$	−1.76453	−0.0994198
$316$	18.0896	1.01762
$317$	19.7089	1.10696	0.553482	−	0.832861i	$-0.313299\pi$
$317$	19.7089	1.10696	0.553482	+	0.832861i	$0.313299\pi$
$318$	57.2357	3.20962
$319$	−4.00900	−0.224461
$320$	−4.26044	−0.238166
$321$	2.34451	0.130858
$322$	−2.82376	−0.157362
$323$	0.633445	0.0352458
$324$	68.2385	3.79103
$325$	4.30824	0.238978
$326$	−21.1154	−1.16948
$327$	42.0502	2.32538
$328$	−82.9450	−4.57987
$329$	−0.955781	−0.0526939
$330$	−41.8779	−2.30530
$331$	3.01057	0.165476	0.0827380	−	0.996571i	$-0.473634\pi$
$331$	3.01057	0.165476	0.0827380	+	0.996571i	$0.473634\pi$
$332$	−22.2667	−1.22204
$333$	−16.1864	−0.887011
$334$	20.1000	1.09982
$335$	−10.1898	−0.556731
$336$	−5.23230	−0.285445
$337$	25.5256	1.39047	0.695233	−	0.718785i	$-0.255301\pi$
$337$	25.5256	1.39047	0.695233	+	0.718785i	$0.255301\pi$
$338$	29.0769	1.58157
$339$	45.5763	2.47536
$340$	14.7994	0.802611
$341$	43.1663	2.33758
$342$	4.41813	0.238905
$343$	−2.85419	−0.154112
$344$	−35.0986	−1.89239
$345$	21.7197	1.16935
$346$	−14.5061	−0.779854
$347$	30.6289	1.64425	0.822123	−	0.569309i	$-0.192789\pi$
$347$	30.6289	1.64425	0.822123	+	0.569309i	$0.192789\pi$
$348$	14.3771	0.770692
$349$	−13.6945	−0.733048	−0.366524	−	0.930409i	$-0.619452\pi$
$349$	−13.6945	−0.733048	−0.366524	+	0.930409i	$0.619452\pi$
$350$	1.73246	0.0926037
$351$	14.5896	0.778734
$352$	−30.7664	−1.63986
$353$	9.74112	0.518468	0.259234	−	0.965815i	$-0.416530\pi$
$353$	9.74112	0.518468	0.259234	+	0.965815i	$0.416530\pi$
$354$	−103.925	−5.52353
$355$	4.17512	0.221592
$356$	28.3268	1.50132
$357$	1.54324	0.0816767
$358$	−49.5738	−2.62006
$359$	9.46344	0.499461	0.249731	−	0.968315i	$-0.419658\pi$
$359$	9.46344	0.499461	0.249731	+	0.968315i	$0.419658\pi$
$360$	58.7450	3.09614
$361$	−18.9324	−0.996443
$362$	−37.2697	−1.95885
$363$	−15.7106	−0.824594
$364$	−1.24378	−0.0651918
$365$	10.0591	0.526519
$366$	−70.3573	−3.67764
$367$	1.56732	0.0818135	0.0409067	−	0.999163i	$-0.486975\pi$
$367$	1.56732	0.0818135	0.0409067	+	0.999163i	$0.486975\pi$
$368$	44.2662	2.30754
$369$	80.3453	4.18261
$370$	−8.27803	−0.430354
$371$	1.46615	0.0761189
$372$	−154.803	−8.02615
$373$	−30.3059	−1.56918	−0.784589	−	0.620016i	$-0.787126\pi$
$373$	−30.3059	−1.56918	−0.784589	+	0.620016i	$0.787126\pi$
$374$	25.1735	1.30169
$375$	−33.5923	−1.73470
$376$	31.8201	1.64100
$377$	1.31047	0.0674924
$378$	5.86686	0.301759
$379$	−37.0542	−1.90335	−0.951674	−	0.307109i	$-0.900638\pi$
$379$	−37.0542	−1.90335	−0.951674	+	0.307109i	$0.900638\pi$
$380$	1.57910	0.0810059
$381$	−24.1669	−1.23811
$382$	−18.5526	−0.949232
$383$	−22.6103	−1.15533	−0.577665	−	0.816274i	$-0.696036\pi$
$383$	−22.6103	−1.15533	−0.577665	+	0.816274i	$0.696036\pi$
$384$	−21.5531	−1.09987
$385$	−1.07275	−0.0546723
$386$	14.9763	0.762273
$387$	33.9985	1.72824
$388$	−67.6745	−3.43565
$389$	18.8765	0.957079	0.478539	−	0.878066i	$-0.341166\pi$
$389$	18.8765	0.957079	0.478539	+	0.878066i	$0.341166\pi$
$390$	13.6891	0.693174
$391$	−13.0561	−0.660273
$392$	47.3688	2.39249
$393$	48.6042	2.45176
$394$	−10.0037	−0.503977
$395$	−5.10001	−0.256610
$396$	122.707	6.16623
$397$	17.7859	0.892647	0.446323	−	0.894872i	$-0.352733\pi$
$397$	17.7859	0.892647	0.446323	+	0.894872i	$0.352733\pi$
$398$	−20.8743	−1.04633
$399$	0.164663	0.00824346
$400$	−27.1585	−1.35793
$401$	8.20211	0.409594	0.204797	−	0.978804i	$-0.434347\pi$
$401$	8.20211	0.409594	0.204797	+	0.978804i	$0.434347\pi$
$402$	62.1586	3.10019
$403$	−14.1102	−0.702880
$404$	71.4793	3.55623
$405$	−19.2386	−0.955972
$406$	0.526974	0.0261533
$407$	−9.84058	−0.487779
$408$	−51.3778	−2.54358
$409$	38.7555	1.91633	0.958167	−	0.286210i	$-0.0923955\pi$
$409$	38.7555	1.91633	0.958167	+	0.286210i	$0.0923955\pi$
$410$	41.0900	2.02929
$411$	47.5874	2.34731
$412$	−63.8927	−3.14777
$413$	−2.66214	−0.130995
$414$	−91.0630	−4.47550
$415$	6.27768	0.308159
$416$	10.0570	0.493083
$417$	36.5081	1.78781
$418$	2.68601	0.131377
$419$	−4.37384	−0.213676	−0.106838	−	0.994276i	$-0.534073\pi$
$419$	−4.37384	−0.213676	−0.106838	+	0.994276i	$0.534073\pi$
$420$	3.84709	0.187719
$421$	28.7957	1.40342	0.701709	−	0.712464i	$-0.252421\pi$
$421$	28.7957	1.40342	0.701709	+	0.712464i	$0.252421\pi$
$422$	−72.0536	−3.50751
$423$	−30.8228	−1.49865
$424$	−48.8115	−2.37050
$425$	8.01025	0.388554
$426$	−25.4685	−1.23395
$427$	−1.80228	−0.0872183
$428$	−3.51326	−0.169820
$429$	16.2730	0.785668
$430$	17.3875	0.838497
$431$	29.9402	1.44217	0.721084	−	0.692848i	$-0.243644\pi$
$431$	29.9402	1.44217	0.721084	+	0.692848i	$0.243644\pi$
$432$	−91.9707	−4.42494
$433$	23.2484	1.11725	0.558624	−	0.829421i	$-0.311330\pi$
$433$	23.2484	1.11725	0.558624	+	0.829421i	$0.311330\pi$
$434$	−5.67410	−0.272366
$435$	−4.05335	−0.194343
$436$	−63.0125	−3.01775
$437$	−1.39308	−0.0666401
$438$	−61.3613	−2.93195
$439$	−11.7545	−0.561010	−0.280505	−	0.959853i	$-0.590502\pi$
$439$	−11.7545	−0.561010	−0.280505	+	0.959853i	$0.590502\pi$
$440$	35.7142	1.70261
$441$	−45.8842	−2.18496
$442$	−8.22874	−0.391401
$443$	−0.753676	−0.0358082	−0.0179041	−	0.999840i	$-0.505699\pi$
$443$	−0.753676	−0.0358082	−0.0179041	+	0.999840i	$0.505699\pi$
$444$	35.2903	1.67480
$445$	−7.98621	−0.378583
$446$	48.8705	2.31409
$447$	−66.2489	−3.13347
$448$	0.665733	0.0314529
$449$	−16.6133	−0.784030	−0.392015	−	0.919959i	$-0.628222\pi$
$449$	−16.6133	−0.784030	−0.392015	+	0.919959i	$0.628222\pi$
$450$	55.8696	2.63372
$451$	48.8461	2.30007
$452$	−68.2963	−3.21239
$453$	56.1117	2.63636
$454$	−51.4758	−2.41588
$455$	0.350661	0.0164392
$456$	−5.48200	−0.256718
$457$	−16.8395	−0.787717	−0.393858	−	0.919171i	$-0.628860\pi$
$457$	−16.8395	−0.787717	−0.393858	+	0.919171i	$0.628860\pi$
$458$	49.0880	2.29373
$459$	27.1262	1.26614
$460$	−32.5471	−1.51751
$461$	−40.8703	−1.90352	−0.951759	−	0.306848i	$-0.900726\pi$
$461$	−40.8703	−1.90352	−0.951759	+	0.306848i	$0.900726\pi$
$462$	6.54382	0.304446
$463$	−9.49223	−0.441141	−0.220571	−	0.975371i	$-0.570792\pi$
$463$	−9.49223	−0.441141	−0.220571	+	0.975371i	$0.570792\pi$
$464$	−8.26100	−0.383507
$465$	43.6437	2.02393
$466$	29.6491	1.37347
$467$	−27.3376	−1.26503	−0.632517	−	0.774546i	$-0.717978\pi$
$467$	−27.3376	−1.26503	−0.632517	+	0.774546i	$0.717978\pi$
$468$	−40.1104	−1.85410
$469$	1.59226	0.0735236
$470$	−15.7633	−0.727108
$471$	−40.6816	−1.87451
$472$	88.6285	4.07946
$473$	20.6695	0.950383
$474$	31.1104	1.42895
$475$	0.854693	0.0392160
$476$	−2.31255	−0.105995
$477$	47.2817	2.16488
$478$	−3.08499	−0.141104
$479$	−31.0993	−1.42096	−0.710481	−	0.703716i	$-0.751523\pi$
$479$	−31.0993	−1.42096	−0.710481	+	0.703716i	$0.751523\pi$
$480$	−31.1067	−1.41982
$481$	3.21670	0.146669
$482$	62.3679	2.84078
$483$	−3.39390	−0.154428
$484$	23.5425	1.07011
$485$	19.0796	0.866358
$486$	31.2819	1.41898
$487$	32.4202	1.46910	0.734550	−	0.678555i	$-0.237393\pi$
$487$	32.4202	1.46910	0.734550	+	0.678555i	$0.237393\pi$
$488$	60.0019	2.71616
$489$	−25.3788	−1.14767
$490$	−23.4660	−1.06009
$491$	−29.9993	−1.35385	−0.676925	−	0.736052i	$-0.736688\pi$
$491$	−29.9993	−1.35385	−0.676925	+	0.736052i	$0.736688\pi$
$492$	−175.172	−7.89735
$493$	2.43653	0.109736
$494$	−0.878006	−0.0395034
$495$	−34.5948	−1.55492
$496$	88.9490	3.99393
$497$	−0.652402	−0.0292642
$498$	−38.2942	−1.71600
$499$	1.97947	0.0886131	0.0443065	−	0.999018i	$-0.485892\pi$
$499$	1.97947	0.0886131	0.0443065	+	0.999018i	$0.485892\pi$
$500$	50.3383	2.25120
$501$	24.1583	1.07931
$502$	28.7679	1.28397
$503$	29.1157	1.29820	0.649102	−	0.760701i	$-0.275145\pi$
$503$	29.1157	1.29820	0.649102	+	0.760701i	$0.275145\pi$
$504$	−9.17946	−0.408886
$505$	−20.1522	−0.896763
$506$	−55.3619	−2.46114
$507$	34.9477	1.55208
$508$	36.2142	1.60675
$509$	39.6554	1.75769	0.878847	−	0.477104i	$-0.158314\pi$
$509$	39.6554	1.75769	0.878847	+	0.477104i	$0.158314\pi$
$510$	25.4520	1.12703
$511$	−1.57183	−0.0695338
$512$	49.0781	2.16897
$513$	2.89437	0.127789
$514$	74.0710	3.26713
$515$	18.0133	0.793763
$516$	−74.1248	−3.26316
$517$	−18.7388	−0.824130
$518$	1.29352	0.0568340
$519$	−17.4350	−0.765312
$520$	−11.6743	−0.511951
$521$	18.2555	0.799789	0.399894	−	0.916561i	$-0.369047\pi$
$521$	18.2555	0.799789	0.399894	+	0.916561i	$0.369047\pi$
$522$	16.9943	0.743818
$523$	38.1325	1.66742	0.833708	−	0.552206i	$-0.186214\pi$
$523$	38.1325	1.66742	0.833708	+	0.552206i	$0.186214\pi$
$524$	−72.8337	−3.18175
$525$	2.08225	0.0908769
$526$	12.7393	0.555460
$527$	−26.2350	−1.14281
$528$	−102.583	−4.46435
$529$	5.71305	0.248394
$530$	24.1807	1.05034
$531$	−85.8507	−3.72560
$532$	−0.246749	−0.0106979
$533$	−15.9668	−0.691601
$534$	48.7163	2.10816
$535$	0.990497	0.0428229
$536$	−53.0098	−2.28968
$537$	−59.5831	−2.57120
$538$	27.2200	1.17354
$539$	−27.8954	−1.20154
$540$	67.6222	2.91000
$541$	21.8539	0.939574	0.469787	−	0.882780i	$-0.344331\pi$
$541$	21.8539	0.939574	0.469787	+	0.882780i	$0.344331\pi$
$542$	−35.9951	−1.54612
$543$	−44.7947	−1.92232
$544$	18.6988	0.801704
$545$	17.7652	0.760977
$546$	−2.13905	−0.0915428
$547$	−14.2909	−0.611036	−0.305518	−	0.952186i	$-0.598830\pi$
$547$	−14.2909	−0.611036	−0.305518	+	0.952186i	$0.598830\pi$
$548$	−71.3100	−3.04621
$549$	−58.1213	−2.48055
$550$	33.9661	1.44832
$551$	0.259978	0.0110754
$552$	112.991	4.80920
$553$	0.796925	0.0338887
$554$	2.57712	0.109491
$555$	−9.94942	−0.422330
$556$	−54.7075	−2.32012
$557$	2.47782	0.104989	0.0524944	−	0.998621i	$-0.483283\pi$
$557$	2.47782	0.104989	0.0524944	+	0.998621i	$0.483283\pi$
$558$	−182.983	−7.74628
$559$	−6.75645	−0.285767
$560$	−2.21052	−0.0934114
$561$	30.2562	1.27742
$562$	−58.5509	−2.46982
$563$	−8.10766	−0.341697	−0.170849	−	0.985297i	$-0.554651\pi$
$563$	−8.10766	−0.341697	−0.170849	+	0.985297i	$0.554651\pi$
$564$	67.2009	2.82967
$565$	19.2549	0.810058
$566$	44.9120	1.88779
$567$	3.00620	0.126249
$568$	21.7199	0.911347
$569$	25.0093	1.04844	0.524222	−	0.851582i	$-0.324356\pi$
$569$	25.0093	1.04844	0.524222	+	0.851582i	$0.324356\pi$
$570$	2.71572	0.113749
$571$	−26.7907	−1.12115	−0.560577	−	0.828102i	$-0.689421\pi$
$571$	−26.7907	−1.12115	−0.560577	+	0.828102i	$0.689421\pi$
$572$	−24.3852	−1.01960
$573$	−22.2985	−0.931532
$574$	−6.42070	−0.267995
$575$	−17.6162	−0.734648
$576$	21.4691	0.894545
$577$	31.0153	1.29118	0.645592	−	0.763683i	$-0.276611\pi$
$577$	31.0153	1.29118	0.645592	+	0.763683i	$0.276611\pi$
$578$	28.5115	1.18592
$579$	18.0001	0.748059
$580$	6.07396	0.252208
$581$	−0.980946	−0.0406965
$582$	−116.386	−4.82437
$583$	28.7450	1.19050
$584$	52.3299	2.16543
$585$	11.3084	0.467544
$586$	−33.4076	−1.38006
$587$	22.1219	0.913070	0.456535	−	0.889705i	$-0.349090\pi$
$587$	22.1219	0.913070	0.456535	+	0.889705i	$0.349090\pi$
$588$	100.038	4.12551
$589$	−2.79927	−0.115342
$590$	−43.9056	−1.80756
$591$	−12.0235	−0.494580
$592$	−20.2776	−0.833405
$593$	−36.3891	−1.49432	−0.747161	−	0.664643i	$-0.768583\pi$
$593$	−36.3891	−1.49432	−0.747161	+	0.664643i	$0.768583\pi$
$594$	115.024	4.71949
$595$	0.651979	0.0267285
$596$	99.2744	4.06644
$597$	−25.0889	−1.02682
$598$	18.0968	0.740031
$599$	−5.70825	−0.233233	−0.116616	−	0.993177i	$-0.537205\pi$
$599$	−5.70825	−0.233233	−0.116616	+	0.993177i	$0.537205\pi$
$600$	−69.3228	−2.83009
$601$	−13.3118	−0.542998	−0.271499	−	0.962439i	$-0.587519\pi$
$601$	−13.3118	−0.542998	−0.271499	+	0.962439i	$0.587519\pi$
$602$	−2.71695	−0.110735
$603$	51.3484	2.09107
$604$	−84.0837	−3.42132
$605$	−6.63735	−0.269847
$606$	122.930	4.99368
$607$	−23.4146	−0.950371	−0.475185	−	0.879886i	$-0.657619\pi$
$607$	−23.4146	−0.950371	−0.475185	+	0.879886i	$0.657619\pi$
$608$	1.99516	0.0809144
$609$	0.633373	0.0256656
$610$	−29.7243	−1.20350
$611$	6.12534	0.247805
$612$	−74.5768	−3.01459
$613$	−12.2570	−0.495054	−0.247527	−	0.968881i	$-0.579618\pi$
$613$	−12.2570	−0.495054	−0.247527	+	0.968881i	$0.579618\pi$
$614$	−51.5535	−2.08053
$615$	49.3864	1.99145
$616$	−5.58067	−0.224852
$617$	21.5291	0.866730	0.433365	−	0.901218i	$-0.357326\pi$
$617$	21.5291	0.866730	0.433365	+	0.901218i	$0.357326\pi$
$618$	−109.882	−4.42012
$619$	−22.6271	−0.909459	−0.454729	−	0.890630i	$-0.650264\pi$
$619$	−22.6271	−0.909459	−0.454729	+	0.890630i	$0.650264\pi$
$620$	−65.4004	−2.62654
$621$	−59.6563	−2.39393
$622$	−42.8277	−1.71723
$623$	1.24792	0.0499968
$624$	33.5324	1.34237
$625$	2.24585	0.0898341
$626$	−2.36807	−0.0946472
$627$	3.22834	0.128927
$628$	60.9617	2.43264
$629$	5.98076	0.238469
$630$	4.54740	0.181173
$631$	−12.5654	−0.500221	−0.250110	−	0.968217i	$-0.580467\pi$
$631$	−12.5654	−0.500221	−0.250110	+	0.968217i	$0.580467\pi$
$632$	−26.5314	−1.05536
$633$	−86.6017	−3.44211
$634$	−50.7923	−2.01722
$635$	−10.2099	−0.405168
$636$	−103.085	−4.08759
$637$	9.11847	0.361287
$638$	10.3317	0.409036
$639$	−21.0392	−0.832296
$640$	−9.10564	−0.359932
$641$	−19.6555	−0.776344	−0.388172	−	0.921587i	$-0.626893\pi$
$641$	−19.6555	−0.776344	−0.388172	+	0.921587i	$0.626893\pi$
$642$	−6.04208	−0.238462
$643$	−3.23789	−0.127690	−0.0638451	−	0.997960i	$-0.520336\pi$
$643$	−3.23789	−0.127690	−0.0638451	+	0.997960i	$0.520336\pi$
$644$	5.08578	0.200408
$645$	20.8981	0.822862
$646$	−1.63247	−0.0642285
$647$	−6.10354	−0.239955	−0.119977	−	0.992777i	$-0.538282\pi$
$647$	−6.10354	−0.239955	−0.119977	+	0.992777i	$0.538282\pi$
$648$	−100.083	−3.93164
$649$	−52.1931	−2.04876
$650$	−11.1029	−0.435490
$651$	−6.81974	−0.267287
$652$	38.0303	1.48938
$653$	−20.0254	−0.783653	−0.391827	−	0.920039i	$-0.628157\pi$
$653$	−20.0254	−0.783653	−0.391827	+	0.920039i	$0.628157\pi$
$654$	−108.369	−4.23755
$655$	20.5341	0.802333
$656$	100.653	3.92983
$657$	−50.6897	−1.97759
$658$	2.46317	0.0960242
$659$	12.7541	0.496829	0.248414	−	0.968654i	$-0.420091\pi$
$659$	12.7541	0.496829	0.248414	+	0.968654i	$0.420091\pi$
$660$	75.4248	2.93591
$661$	−26.9761	−1.04925	−0.524624	−	0.851334i	$-0.675794\pi$
$661$	−26.9761	−1.04925	−0.524624	+	0.851334i	$0.675794\pi$
$662$	−7.75862	−0.301547
$663$	−9.89018	−0.384103
$664$	32.6579	1.26737
$665$	0.0695661	0.00269766
$666$	41.7144	1.61640
$667$	−5.35846	−0.207480
$668$	−36.2014	−1.40067
$669$	58.7378	2.27094
$670$	26.2605	1.01453
$671$	−35.3349	−1.36409
$672$	4.86072	0.187506
$673$	−18.5687	−0.715770	−0.357885	−	0.933766i	$-0.616502\pi$
$673$	−18.5687	−0.715770	−0.357885	+	0.933766i	$0.616502\pi$
$674$	−65.7825	−2.53385
$675$	36.6008	1.40877
$676$	−52.3693	−2.01420
$677$	49.7760	1.91305	0.956524	−	0.291654i	$-0.0942055\pi$
$677$	49.7760	1.91305	0.956524	+	0.291654i	$0.0942055\pi$
$678$	−117.456	−4.51086
$679$	−2.98136	−0.114414
$680$	−21.7058	−0.832381
$681$	−61.8691	−2.37083
$682$	−111.245	−4.25978
$683$	−39.0215	−1.49312	−0.746558	−	0.665320i	$-0.768295\pi$
$683$	−39.0215	−1.49312	−0.746558	+	0.665320i	$0.768295\pi$
$684$	−7.95734	−0.304257
$685$	20.1045	0.768154
$686$	7.35560	0.280838
$687$	58.9992	2.25096
$688$	42.5918	1.62380
$689$	−9.39619	−0.357966
$690$	−55.9743	−2.13090
$691$	6.74489	0.256588	0.128294	−	0.991736i	$-0.459050\pi$
$691$	6.74489	0.256588	0.128294	+	0.991736i	$0.459050\pi$
$692$	26.1265	0.993180
$693$	5.40576	0.205348
$694$	−78.9345	−2.99631
$695$	15.4238	0.585057
$696$	−21.0864	−0.799278
$697$	−29.6870	−1.12447
$698$	35.2923	1.33583
$699$	35.6355	1.34786
$700$	−3.12027	−0.117935
$701$	9.41730	0.355687	0.177843	−	0.984059i	$-0.443088\pi$
$701$	9.41730	0.355687	0.177843	+	0.984059i	$0.443088\pi$
$702$	−37.5991	−1.41909
$703$	0.638147	0.0240682
$704$	13.0522	0.491922
$705$	−18.9460	−0.713549
$706$	−25.1041	−0.944804
$707$	3.14898	0.118429
$708$	187.175	7.03446
$709$	23.0615	0.866091	0.433046	−	0.901372i	$-0.357439\pi$
$709$	23.0615	0.866091	0.433046	+	0.901372i	$0.357439\pi$
$710$	−10.7598	−0.403808
$711$	25.6998	0.963820
$712$	−41.5460	−1.55700
$713$	57.6963	2.16074
$714$	−3.97711	−0.148839
$715$	6.87495	0.257109
$716$	89.2857	3.33676
$717$	−3.70787	−0.138473
$718$	−24.3885	−0.910169
$719$	0.324938	0.0121181	0.00605906	−	0.999982i	$-0.498071\pi$
$719$	0.324938	0.0121181	0.00605906	+	0.999982i	$0.498071\pi$
$720$	−71.2865	−2.65669
$721$	−2.81475	−0.104827
$722$	48.7912	1.81582
$723$	74.9605	2.78781
$724$	67.1251	2.49469
$725$	3.28756	0.122097
$726$	40.4882	1.50266
$727$	−36.5667	−1.35618	−0.678091	−	0.734978i	$-0.737193\pi$
$727$	−36.5667	−1.35618	−0.678091	+	0.734978i	$0.737193\pi$
$728$	1.82421	0.0676099
$729$	−6.50686	−0.240995
$730$	−25.9236	−0.959477
$731$	−12.5622	−0.464629
$732$	126.718	4.68364
$733$	−2.44456	−0.0902917	−0.0451459	−	0.998980i	$-0.514375\pi$
$733$	−2.44456	−0.0902917	−0.0451459	+	0.998980i	$0.514375\pi$
$734$	−4.03918	−0.149089
$735$	−28.2039	−1.04032
$736$	−41.1226	−1.51580
$737$	31.2174	1.14991
$738$	−207.060	−7.62197
$739$	−40.4644	−1.48851	−0.744254	−	0.667897i	$-0.767195\pi$
$739$	−40.4644	−1.48851	−0.744254	+	0.667897i	$0.767195\pi$
$740$	14.9093	0.548076
$741$	−1.05528	−0.0387667
$742$	−3.77846	−0.138712
$743$	−36.5077	−1.33934	−0.669669	−	0.742659i	$-0.733564\pi$
$743$	−36.5077	−1.33934	−0.669669	+	0.742659i	$0.733564\pi$
$744$	227.044	8.32385
$745$	−27.9885	−1.02542
$746$	78.1020	2.85952
$747$	−31.6343	−1.15744
$748$	−45.3391	−1.65776
$749$	−0.154774	−0.00565533
$750$	86.5716	3.16115
$751$	−47.3599	−1.72819	−0.864094	−	0.503330i	$-0.832108\pi$
$751$	−47.3599	−1.72819	−0.864094	+	0.503330i	$0.832108\pi$
$752$	−38.6134	−1.40808
$753$	34.5763	1.26003
$754$	−3.37723	−0.122992
$755$	23.7058	0.862743
$756$	−10.5666	−0.384303
$757$	10.6387	0.386672	0.193336	−	0.981133i	$-0.438069\pi$
$757$	10.6387	0.386672	0.193336	+	0.981133i	$0.438069\pi$
$758$	95.4934	3.46848
$759$	−66.5399	−2.41524
$760$	−2.31601	−0.0840106
$761$	−31.6291	−1.14655	−0.573277	−	0.819362i	$-0.694328\pi$
$761$	−31.6291	−1.14655	−0.573277	+	0.819362i	$0.694328\pi$
$762$	62.2811	2.25621
$763$	−2.77598	−0.100497
$764$	33.4144	1.20889
$765$	21.0255	0.760180
$766$	58.2695	2.10536
$767$	17.0609	0.616034
$768$	75.7138	2.73209
$769$	14.7743	0.532773	0.266387	−	0.963866i	$-0.414170\pi$
$769$	14.7743	0.532773	0.266387	+	0.963866i	$0.414170\pi$
$770$	2.76460	0.0996294
$771$	89.0264	3.20621
$772$	−26.9733	−0.970789
$773$	16.7572	0.602714	0.301357	−	0.953511i	$-0.402560\pi$
$773$	16.7572	0.602714	0.301357	+	0.953511i	$0.402560\pi$
$774$	−87.6184	−3.14938
$775$	−35.3983	−1.27154
$776$	99.2561	3.56309
$777$	1.55469	0.0557742
$778$	−48.6472	−1.74409
$779$	−3.16760	−0.113491
$780$	−24.6549	−0.882788
$781$	−12.7908	−0.457691
$782$	33.6471	1.20322
$783$	11.1331	0.397865
$784$	−57.4816	−2.05291
$785$	−17.1870	−0.613430
$786$	−125.259	−4.46784
$787$	6.30365	0.224701	0.112350	−	0.993669i	$-0.464162\pi$
$787$	6.30365	0.224701	0.112350	+	0.993669i	$0.464162\pi$
$788$	18.0172	0.641838
$789$	15.3114	0.545102
$790$	13.1434	0.467620
$791$	−3.00875	−0.106979
$792$	−179.970	−6.39495
$793$	11.5503	0.410164
$794$	−45.8364	−1.62667
$795$	29.0629	1.03076
$796$	37.5959	1.33255
$797$	16.1233	0.571116	0.285558	−	0.958361i	$-0.407821\pi$
$797$	16.1233	0.571116	0.285558	+	0.958361i	$0.407821\pi$
$798$	−0.424357	−0.0150221
$799$	11.3888	0.402906
$800$	25.2299	0.892010
$801$	40.2439	1.42195
$802$	−21.1378	−0.746403
$803$	−30.8169	−1.08751
$804$	−111.952	−3.94823
$805$	−1.43384	−0.0505363
$806$	36.3638	1.28086
$807$	32.7159	1.15165
$808$	−104.836	−3.68813
$809$	44.5853	1.56754	0.783768	−	0.621054i	$-0.213295\pi$
$809$	44.5853	1.56754	0.783768	+	0.621054i	$0.213295\pi$
$810$	49.5801	1.74207
$811$	−12.7607	−0.448089	−0.224045	−	0.974579i	$-0.571926\pi$
$811$	−12.7607	−0.448089	−0.224045	+	0.974579i	$0.571926\pi$
$812$	−0.949113	−0.0333074
$813$	−43.2627	−1.51729
$814$	25.3604	0.888881
$815$	−10.7219	−0.375572
$816$	62.3464	2.18256
$817$	−1.34038	−0.0468941
$818$	−99.8776	−3.49214
$819$	−1.76704	−0.0617453
$820$	−74.0058	−2.58439
$821$	0.881934	0.0307797	0.0153899	−	0.999882i	$-0.495101\pi$
$821$	0.881934	0.0307797	0.0153899	+	0.999882i	$0.495101\pi$
$822$	−122.639	−4.27751
$823$	5.03086	0.175365	0.0876824	−	0.996148i	$-0.472054\pi$
$823$	5.03086	0.175365	0.0876824	+	0.996148i	$0.472054\pi$
$824$	93.7095	3.26452
$825$	40.8240	1.42131
$826$	6.86066	0.238713
$827$	2.60551	0.0906023	0.0453012	−	0.998973i	$-0.485575\pi$
$827$	2.60551	0.0906023	0.0453012	+	0.998973i	$0.485575\pi$
$828$	164.010	5.69975
$829$	−7.87430	−0.273486	−0.136743	−	0.990607i	$-0.543663\pi$
$829$	−7.87430	−0.273486	−0.136743	+	0.990607i	$0.543663\pi$
$830$	−16.1784	−0.561559
$831$	3.09746	0.107450
$832$	−4.26650	−0.147914
$833$	16.9539	0.587416
$834$	−94.0858	−3.25792
$835$	10.2063	0.353204
$836$	−4.83768	−0.167315
$837$	−119.874	−4.14345
$838$	11.2719	0.389382
$839$	−39.9011	−1.37754	−0.688770	−	0.724980i	$-0.741849\pi$
$839$	−39.9011	−1.37754	−0.688770	+	0.724980i	$0.741849\pi$
$840$	−5.64240	−0.194681
$841$	1.00000	0.0344828
$842$	−74.2102	−2.55745
$843$	−70.3728	−2.42377
$844$	129.773	4.46698
$845$	14.7645	0.507916
$846$	79.4341	2.73100
$847$	1.03715	0.0356368
$848$	59.2323	2.03405
$849$	53.9800	1.85259
$850$	−20.6434	−0.708063
$851$	−13.1530	−0.450878
$852$	45.8703	1.57149
$853$	−4.81021	−0.164698	−0.0823492	−	0.996604i	$-0.526242\pi$
$853$	−4.81021	−0.164698	−0.0823492	+	0.996604i	$0.526242\pi$
$854$	4.64469	0.158938
$855$	2.24342	0.0767234
$856$	5.15278	0.176119
$857$	−14.4360	−0.493123	−0.246561	−	0.969127i	$-0.579301\pi$
$857$	−14.4360	−0.493123	−0.246561	+	0.969127i	$0.579301\pi$
$858$	−41.9376	−1.43172
$859$	−23.5366	−0.803057	−0.401529	−	0.915847i	$-0.631521\pi$
$859$	−23.5366	−0.803057	−0.401529	+	0.915847i	$0.631521\pi$
$860$	−31.3159	−1.06786
$861$	−7.71708	−0.262997
$862$	−77.1595	−2.62806
$863$	−32.9227	−1.12070	−0.560351	−	0.828255i	$-0.689334\pi$
$863$	−32.9227	−1.12070	−0.560351	+	0.828255i	$0.689334\pi$
$864$	85.4394	2.90671
$865$	−7.36587	−0.250447
$866$	−59.9140	−2.03596
$867$	34.2682	1.16381
$868$	10.2194	0.346870
$869$	15.6243	0.530017
$870$	10.4460	0.354152
$871$	−10.2044	−0.345761
$872$	92.4185	3.12968
$873$	−96.1452	−3.25402
$874$	3.59014	0.121438
$875$	2.21762	0.0749694
$876$	110.516	3.73398
$877$	−31.3035	−1.05705	−0.528523	−	0.848919i	$-0.677254\pi$
$877$	−31.3035	−1.05705	−0.528523	+	0.848919i	$0.677254\pi$
$878$	30.2927	1.02233
$879$	−40.1528	−1.35432
$880$	−43.3388	−1.46095
$881$	−18.8098	−0.633720	−0.316860	−	0.948472i	$-0.602628\pi$
$881$	−18.8098	−0.633720	−0.316860	+	0.948472i	$0.602628\pi$
$882$	118.249	3.98166
$883$	−12.6561	−0.425913	−0.212956	−	0.977062i	$-0.568309\pi$
$883$	−12.6561	−0.425913	−0.212956	+	0.977062i	$0.568309\pi$
$884$	14.8205	0.498467
$885$	−52.7704	−1.77386
$886$	1.94232	0.0652534
$887$	−16.5093	−0.554327	−0.277163	−	0.960823i	$-0.589394\pi$
$887$	−16.5093	−0.554327	−0.277163	+	0.960823i	$0.589394\pi$
$888$	−51.7591	−1.73692
$889$	1.59540	0.0535079
$890$	20.5814	0.689892
$891$	58.9388	1.97452
$892$	−88.0190	−2.94709
$893$	1.21518	0.0406645
$894$	170.732	5.71012
$895$	−25.1724	−0.841421
$896$	1.42284	0.0475338
$897$	21.7506	0.726232
$898$	42.8145	1.42874
$899$	−10.7673	−0.359111
$900$	−100.625	−3.35416
$901$	−17.4702	−0.582017
$902$	−125.882	−4.19142
$903$	−3.26552	−0.108670
$904$	100.168	3.33154
$905$	−18.9247	−0.629077
$906$	−144.607	−4.80424
$907$	45.6523	1.51586	0.757930	−	0.652336i	$-0.226211\pi$
$907$	45.6523	1.51586	0.757930	+	0.652336i	$0.226211\pi$
$908$	92.7113	3.07673
$909$	101.551	3.36822
$910$	−0.903696	−0.0299572
$911$	42.7306	1.41573	0.707863	−	0.706349i	$-0.249659\pi$
$911$	42.7306	1.41573	0.707863	+	0.706349i	$0.249659\pi$
$912$	6.65235	0.220281
$913$	−19.2321	−0.636491
$914$	43.3974	1.43546
$915$	−35.7258	−1.18106
$916$	−88.4107	−2.92117
$917$	−3.20864	−0.105959
$918$	−69.9076	−2.30730
$919$	−42.7265	−1.40942	−0.704708	−	0.709497i	$-0.748922\pi$
$919$	−42.7265	−1.40942	−0.704708	+	0.709497i	$0.748922\pi$
$920$	47.7358	1.57380
$921$	−61.9625	−2.04173
$922$	105.328	3.46878
$923$	4.18107	0.137622
$924$	−11.7858	−0.387726
$925$	8.06971	0.265330
$926$	24.4627	0.803893
$927$	−90.7724	−2.98136
$928$	7.67434	0.251923
$929$	−57.3392	−1.88124	−0.940618	−	0.339466i	$-0.889754\pi$
$929$	−57.3392	−1.88124	−0.940618	+	0.339466i	$0.889754\pi$
$930$	−112.475	−3.68821
$931$	1.80898	0.0592868
$932$	−53.3999	−1.74917
$933$	−51.4749	−1.68521
$934$	70.4524	2.30527
$935$	12.7825	0.418033
$936$	58.8287	1.92288
$937$	−2.61724	−0.0855014	−0.0427507	−	0.999086i	$-0.513612\pi$
$937$	−2.61724	−0.0855014	−0.0427507	+	0.999086i	$0.513612\pi$
$938$	−4.10345	−0.133982
$939$	−2.84620	−0.0928823
$940$	28.3908	0.926004
$941$	23.0530	0.751507	0.375753	−	0.926720i	$-0.377384\pi$
$941$	23.0530	0.751507	0.375753	+	0.926720i	$0.377384\pi$
$942$	104.842	3.41592
$943$	65.2880	2.12607
$944$	−107.550	−3.50045
$945$	2.97905	0.0969086
$946$	−53.2678	−1.73188
$947$	−46.2413	−1.50264	−0.751319	−	0.659939i	$-0.770582\pi$
$947$	−46.2413	−1.50264	−0.751319	+	0.659939i	$0.770582\pi$
$948$	−56.0317	−1.81983
$949$	10.0735	0.326998
$950$	−2.20265	−0.0714634
$951$	−61.0476	−1.97961
$952$	3.39174	0.109927
$953$	4.69231	0.151999	0.0759993	−	0.997108i	$-0.475785\pi$
$953$	4.69231	0.151999	0.0759993	+	0.997108i	$0.475785\pi$
$954$	−121.851	−3.94506
$955$	−9.42056	−0.304842
$956$	5.55627	0.179703
$957$	12.4177	0.401408
$958$	80.1467	2.58942
$959$	−3.14152	−0.101445
$960$	13.1965	0.425917
$961$	84.9355	2.73985
$962$	−8.28982	−0.267275
$963$	−4.99128	−0.160842
$964$	−112.329	−3.61786
$965$	7.60461	0.244801
$966$	8.74651	0.281414
$967$	−14.0075	−0.450450	−0.225225	−	0.974307i	$-0.572312\pi$
$967$	−14.0075	−0.450450	−0.225225	+	0.974307i	$0.572312\pi$
$968$	−34.5290	−1.10980
$969$	−1.96207	−0.0630308
$970$	−49.1704	−1.57877
$971$	−30.6185	−0.982595	−0.491297	−	0.870992i	$-0.663477\pi$
$971$	−30.6185	−0.982595	−0.491297	+	0.870992i	$0.663477\pi$
$972$	−56.3408	−1.80713
$973$	−2.41011	−0.0772645
$974$	−83.5509	−2.67714
$975$	−13.3446	−0.427369
$976$	−72.8116	−2.33064
$977$	6.42463	0.205542	0.102771	−	0.994705i	$-0.467229\pi$
$977$	6.42463	0.205542	0.102771	+	0.994705i	$0.467229\pi$
$978$	65.4043	2.09140
$979$	24.4664	0.781948
$980$	42.2638	1.35007
$981$	−89.5218	−2.85821
$982$	77.3119	2.46712
$983$	21.9220	0.699204	0.349602	−	0.936898i	$-0.386317\pi$
$983$	21.9220	0.699204	0.349602	+	0.936898i	$0.386317\pi$
$984$	256.919	8.19028
$985$	−5.07962	−0.161850
$986$	−6.27925	−0.199972
$987$	2.96050	0.0942336
$988$	1.58135	0.0503093
$989$	27.6269	0.878485
$990$	89.1551	2.83353
$991$	6.57622	0.208900	0.104450	−	0.994530i	$-0.466692\pi$
$991$	6.57622	0.208900	0.104450	+	0.994530i	$0.466692\pi$
$992$	−82.6322	−2.62357
$993$	−9.32513	−0.295924
$994$	1.68132	0.0533282
$995$	−10.5995	−0.336026
$996$	68.9703	2.18541
$997$	−25.1934	−0.797882	−0.398941	−	0.916977i	$-0.630622\pi$
$997$	−25.1934	−0.797882	−0.398941	+	0.916977i	$0.630622\pi$
$998$	−5.10133	−0.161480
$999$	27.3276	0.864607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.10	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.10	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57712 q^{2} -3.09746 q^{3} +4.64157 q^{4} -1.30860 q^{5} +7.98254 q^{6} +0.204481 q^{7} -6.80764 q^{8} +6.59427 q^{9} +O(q^{10})\)	\(q-2.57712 q^{2} -3.09746 q^{3} +4.64157 q^{4} -1.30860 q^{5} +7.98254 q^{6} +0.204481 q^{7} -6.80764 q^{8} +6.59427 q^{9} +3.37243 q^{10} +4.00900 q^{11} -14.3771 q^{12} -1.31047 q^{13} -0.526974 q^{14} +4.05335 q^{15} +8.26100 q^{16} -2.43653 q^{17} -16.9943 q^{18} -0.259978 q^{19} -6.07396 q^{20} -0.633373 q^{21} -10.3317 q^{22} +5.35846 q^{23} +21.0864 q^{24} -3.28756 q^{25} +3.37723 q^{26} -11.1331 q^{27} +0.949113 q^{28} -1.00000 q^{29} -10.4460 q^{30} +10.7673 q^{31} -7.67434 q^{32} -12.4177 q^{33} +6.27925 q^{34} -0.267585 q^{35} +30.6077 q^{36} -2.45462 q^{37} +0.669995 q^{38} +4.05912 q^{39} +8.90849 q^{40} +12.1841 q^{41} +1.63228 q^{42} +5.15576 q^{43} +18.6080 q^{44} -8.62928 q^{45} -13.8094 q^{46} -4.67417 q^{47} -25.5881 q^{48} -6.95819 q^{49} +8.47245 q^{50} +7.54707 q^{51} -6.08261 q^{52} +7.17011 q^{53} +28.6914 q^{54} -5.24619 q^{55} -1.39204 q^{56} +0.805272 q^{57} +2.57712 q^{58} -13.0190 q^{59} +18.8139 q^{60} -8.81390 q^{61} -27.7488 q^{62} +1.34841 q^{63} +3.25572 q^{64} +1.71488 q^{65} +32.0020 q^{66} +7.78682 q^{67} -11.3093 q^{68} -16.5976 q^{69} +0.689599 q^{70} -3.19052 q^{71} -44.8914 q^{72} -7.68693 q^{73} +6.32586 q^{74} +10.1831 q^{75} -1.20670 q^{76} +0.819766 q^{77} -10.4608 q^{78} +3.89730 q^{79} -10.8104 q^{80} +14.7016 q^{81} -31.3999 q^{82} -4.79724 q^{83} -2.93984 q^{84} +3.18845 q^{85} -13.2870 q^{86} +3.09746 q^{87} -27.2918 q^{88} +6.10285 q^{89} +22.2387 q^{90} -0.267966 q^{91} +24.8716 q^{92} -33.3514 q^{93} +12.0459 q^{94} +0.340208 q^{95} +23.7710 q^{96} -14.5801 q^{97} +17.9321 q^{98} +26.4364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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