LMFDB - Embedded newform 8033.2.a.e.1.4

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:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.75139 q^{2} -3.04076 q^{3} +5.57013 q^{4} +1.50173 q^{5} +8.36631 q^{6} +3.15937 q^{7} -9.82282 q^{8} +6.24621 q^{9} +O(q^{10})$	\(q-2.75139 q^{2} -3.04076 q^{3} +5.57013 q^{4} +1.50173 q^{5} +8.36631 q^{6} +3.15937 q^{7} -9.82282 q^{8} +6.24621 q^{9} -4.13185 q^{10} -4.17909 q^{11} -16.9374 q^{12} -2.69173 q^{13} -8.69264 q^{14} -4.56640 q^{15} +15.8861 q^{16} +4.25225 q^{17} -17.1858 q^{18} +1.04094 q^{19} +8.36485 q^{20} -9.60687 q^{21} +11.4983 q^{22} +7.43738 q^{23} +29.8688 q^{24} -2.74480 q^{25} +7.40600 q^{26} -9.87095 q^{27} +17.5981 q^{28} -1.00000 q^{29} +12.5639 q^{30} -3.16754 q^{31} -24.0632 q^{32} +12.7076 q^{33} -11.6996 q^{34} +4.74452 q^{35} +34.7922 q^{36} -2.66546 q^{37} -2.86404 q^{38} +8.18492 q^{39} -14.7512 q^{40} -5.89794 q^{41} +26.4322 q^{42} +7.87723 q^{43} -23.2781 q^{44} +9.38014 q^{45} -20.4631 q^{46} -6.32241 q^{47} -48.3059 q^{48} +2.98160 q^{49} +7.55201 q^{50} -12.9301 q^{51} -14.9933 q^{52} -4.55429 q^{53} +27.1588 q^{54} -6.27587 q^{55} -31.0339 q^{56} -3.16526 q^{57} +2.75139 q^{58} -3.32368 q^{59} -25.4355 q^{60} +3.46071 q^{61} +8.71513 q^{62} +19.7341 q^{63} +34.4350 q^{64} -4.04226 q^{65} -34.9635 q^{66} +6.24548 q^{67} +23.6856 q^{68} -22.6153 q^{69} -13.0540 q^{70} -0.152742 q^{71} -61.3554 q^{72} -2.04011 q^{73} +7.33372 q^{74} +8.34628 q^{75} +5.79819 q^{76} -13.2033 q^{77} -22.5199 q^{78} +0.923996 q^{79} +23.8567 q^{80} +11.2765 q^{81} +16.2275 q^{82} -10.8684 q^{83} -53.5116 q^{84} +6.38573 q^{85} -21.6733 q^{86} +3.04076 q^{87} +41.0504 q^{88} -8.30890 q^{89} -25.8084 q^{90} -8.50418 q^{91} +41.4272 q^{92} +9.63173 q^{93} +17.3954 q^{94} +1.56322 q^{95} +73.1705 q^{96} +14.9881 q^{97} -8.20354 q^{98} -26.1035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.75139	−1.94552	−0.972762	−	0.231805i	$-0.925537\pi$
$2$	−2.75139	−1.94552	−0.972762	+	0.231805i	$0.925537\pi$
$3$	−3.04076	−1.75558	−0.877791	−	0.479043i	$-0.840984\pi$
$3$	−3.04076	−1.75558	−0.877791	+	0.479043i	$0.840984\pi$
$4$	5.57013	2.78507
$5$	1.50173	0.671595	0.335797	−	0.941934i	$-0.390994\pi$
$5$	1.50173	0.671595	0.335797	+	0.941934i	$0.390994\pi$
$6$	8.36631	3.41553
$7$	3.15937	1.19413	0.597064	−	0.802193i	$-0.296334\pi$
$7$	3.15937	1.19413	0.597064	+	0.802193i	$0.296334\pi$
$8$	−9.82282	−3.47289
$9$	6.24621	2.08207
$10$	−4.13185	−1.30660
$11$	−4.17909	−1.26004	−0.630021	−	0.776578i	$-0.716954\pi$
$11$	−4.17909	−1.26004	−0.630021	+	0.776578i	$0.716954\pi$
$12$	−16.9374	−4.88942
$13$	−2.69173	−0.746553	−0.373276	−	0.927720i	$-0.621766\pi$
$13$	−2.69173	−0.746553	−0.373276	+	0.927720i	$0.621766\pi$
$14$	−8.69264	−2.32321
$15$	−4.56640	−1.17904
$16$	15.8861	3.97153
$17$	4.25225	1.03132	0.515661	−	0.856793i	$-0.327547\pi$
$17$	4.25225	1.03132	0.515661	+	0.856793i	$0.327547\pi$
$18$	−17.1858	−4.05072
$19$	1.04094	0.238809	0.119404	−	0.992846i	$-0.461902\pi$
$19$	1.04094	0.238809	0.119404	+	0.992846i	$0.461902\pi$
$20$	8.36485	1.87044
$21$	−9.60687	−2.09639
$22$	11.4983	2.45144
$23$	7.43738	1.55080	0.775401	−	0.631469i	$-0.217548\pi$
$23$	7.43738	1.55080	0.775401	+	0.631469i	$0.217548\pi$
$24$	29.8688	6.09695
$25$	−2.74480	−0.548960
$26$	7.40600	1.45244
$27$	−9.87095	−1.89967
$28$	17.5981	3.32573
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	12.5639	2.29385
$31$	−3.16754	−0.568907	−0.284454	−	0.958690i	$-0.591812\pi$
$31$	−3.16754	−0.568907	−0.284454	+	0.958690i	$0.591812\pi$
$32$	−24.0632	−4.25382
$33$	12.7076	2.21211
$34$	−11.6996	−2.00646
$35$	4.74452	0.801971
$36$	34.7922	5.79871
$37$	−2.66546	−0.438199	−0.219100	−	0.975703i	$-0.570312\pi$
$37$	−2.66546	−0.438199	−0.219100	+	0.975703i	$0.570312\pi$
$38$	−2.86404	−0.464608
$39$	8.18492	1.31064
$40$	−14.7512	−2.33238
$41$	−5.89794	−0.921104	−0.460552	−	0.887633i	$-0.652349\pi$
$41$	−5.89794	−0.921104	−0.460552	+	0.887633i	$0.652349\pi$
$42$	26.4322	4.07858
$43$	7.87723	1.20127	0.600633	−	0.799525i	$-0.294915\pi$
$43$	7.87723	1.20127	0.600633	+	0.799525i	$0.294915\pi$
$44$	−23.2781	−3.50930
$45$	9.38014	1.39831
$46$	−20.4631	−3.01712
$47$	−6.32241	−0.922218	−0.461109	−	0.887344i	$-0.652548\pi$
$47$	−6.32241	−0.922218	−0.461109	+	0.887344i	$0.652548\pi$
$48$	−48.3059	−6.97235
$49$	2.98160	0.425943
$50$	7.55201	1.06802
$51$	−12.9301	−1.81057
$52$	−14.9933	−2.07920
$53$	−4.55429	−0.625580	−0.312790	−	0.949822i	$-0.601264\pi$
$53$	−4.55429	−0.625580	−0.312790	+	0.949822i	$0.601264\pi$
$54$	27.1588	3.69585
$55$	−6.27587	−0.846238
$56$	−31.0339	−4.14708
$57$	−3.16526	−0.419249
$58$	2.75139	0.361275
$59$	−3.32368	−0.432706	−0.216353	−	0.976315i	$-0.569416\pi$
$59$	−3.32368	−0.432706	−0.216353	+	0.976315i	$0.569416\pi$
$60$	−25.4355	−3.28371
$61$	3.46071	0.443098	0.221549	−	0.975149i	$-0.428889\pi$
$61$	3.46071	0.443098	0.221549	+	0.975149i	$0.428889\pi$
$62$	8.71513	1.10682
$63$	19.7341	2.48626
$64$	34.4350	4.30438
$65$	−4.04226	−0.501381
$66$	−34.9635	−4.30371
$67$	6.24548	0.763006	0.381503	−	0.924368i	$-0.375407\pi$
$67$	6.24548	0.763006	0.381503	+	0.924368i	$0.375407\pi$
$68$	23.6856	2.87230
$69$	−22.6153	−2.72256
$70$	−13.0540	−1.56025
$71$	−0.152742	−0.0181272	−0.00906359	−	0.999959i	$-0.502885\pi$
$71$	−0.152742	−0.0181272	−0.00906359	+	0.999959i	$0.502885\pi$
$72$	−61.3554	−7.23081
$73$	−2.04011	−0.238777	−0.119389	−	0.992848i	$-0.538093\pi$
$73$	−2.04011	−0.238777	−0.119389	+	0.992848i	$0.538093\pi$
$74$	7.33372	0.852527
$75$	8.34628	0.963745
$76$	5.79819	0.665098
$77$	−13.2033	−1.50465
$78$	−22.5199	−2.54987
$79$	0.923996	0.103958	0.0519788	−	0.998648i	$-0.483447\pi$
$79$	0.923996	0.103958	0.0519788	+	0.998648i	$0.483447\pi$
$80$	23.8567	2.66726
$81$	11.2765	1.25295
$82$	16.2275	1.79203
$83$	−10.8684	−1.19296	−0.596482	−	0.802627i	$-0.703435\pi$
$83$	−10.8684	−1.19296	−0.596482	+	0.802627i	$0.703435\pi$
$84$	−53.5116	−5.83859
$85$	6.38573	0.692630
$86$	−21.6733	−2.33709
$87$	3.04076	0.326004
$88$	41.0504	4.37599
$89$	−8.30890	−0.880742	−0.440371	−	0.897816i	$-0.645153\pi$
$89$	−8.30890	−0.880742	−0.440371	+	0.897816i	$0.645153\pi$
$90$	−25.8084	−2.72044
$91$	−8.50418	−0.891480
$92$	41.4272	4.31909
$93$	9.63173	0.998764
$94$	17.3954	1.79420
$95$	1.56322	0.160383
$96$	73.1705	7.46793
$97$	14.9881	1.52181	0.760906	−	0.648862i	$-0.224755\pi$
$97$	14.9881	1.52181	0.760906	+	0.648862i	$0.224755\pi$
$98$	−8.20354	−0.828683
$99$	−26.1035	−2.62350
$100$	−15.2889	−1.52889
$101$	2.41333	0.240135	0.120067	−	0.992766i	$-0.461689\pi$
$101$	2.41333	0.240135	0.120067	+	0.992766i	$0.461689\pi$
$102$	35.5756	3.52251
$103$	−0.700284	−0.0690010	−0.0345005	−	0.999405i	$-0.510984\pi$
$103$	−0.700284	−0.0690010	−0.0345005	+	0.999405i	$0.510984\pi$
$104$	26.4404	2.59270
$105$	−14.4269	−1.40793
$106$	12.5306	1.21708
$107$	0.0324105	0.00313324	0.00156662	−	0.999999i	$-0.499501\pi$
$107$	0.0324105	0.00313324	0.00156662	+	0.999999i	$0.499501\pi$
$108$	−54.9825	−5.29069
$109$	−8.23522	−0.788791	−0.394395	−	0.918941i	$-0.629046\pi$
$109$	−8.23522	−0.788791	−0.394395	+	0.918941i	$0.629046\pi$
$110$	17.2673	1.64638
$111$	8.10502	0.769295
$112$	50.1901	4.74252
$113$	15.8895	1.49476	0.747381	−	0.664395i	$-0.231311\pi$
$113$	15.8895	1.49476	0.747381	+	0.664395i	$0.231311\pi$
$114$	8.70885	0.815659
$115$	11.1690	1.04151
$116$	−5.57013	−0.517174
$117$	−16.8131	−1.55438
$118$	9.14473	0.841840
$119$	13.4344	1.23153
$120$	44.8550	4.09468
$121$	6.46476	0.587705
$122$	−9.52174	−0.862058
$123$	17.9342	1.61707
$124$	−17.6436	−1.58444
$125$	−11.6306	−1.04027
$126$	−54.2961	−4.83708
$127$	−5.80288	−0.514922	−0.257461	−	0.966289i	$-0.582886\pi$
$127$	−5.80288	−0.514922	−0.257461	+	0.966289i	$0.582886\pi$
$128$	−46.6176	−4.12046
$129$	−23.9527	−2.10892
$130$	11.1218	0.975449
$131$	13.2214	1.15516	0.577580	−	0.816334i	$-0.303997\pi$
$131$	13.2214	1.15516	0.577580	+	0.816334i	$0.303997\pi$
$132$	70.7830	6.16087
$133$	3.28872	0.285168
$134$	−17.1837	−1.48445
$135$	−14.8235	−1.27581
$136$	−41.7691	−3.58167
$137$	21.0594	1.79923	0.899613	−	0.436688i	$-0.143849\pi$
$137$	21.0594	1.79923	0.899613	+	0.436688i	$0.143849\pi$
$138$	62.2234	5.29681
$139$	15.3816	1.30465	0.652324	−	0.757940i	$-0.273794\pi$
$139$	15.3816	1.30465	0.652324	+	0.757940i	$0.273794\pi$
$140$	26.4276	2.23354
$141$	19.2249	1.61903
$142$	0.420253	0.0352669
$143$	11.2490	0.940688
$144$	99.2281	8.26901
$145$	−1.50173	−0.124712
$146$	5.61315	0.464547
$147$	−9.06633	−0.747778
$148$	−14.8470	−1.22041
$149$	−20.3604	−1.66799	−0.833993	−	0.551775i	$-0.813951\pi$
$149$	−20.3604	−1.66799	−0.833993	+	0.551775i	$0.813951\pi$
$150$	−22.9638	−1.87499
$151$	14.3671	1.16918	0.584589	−	0.811330i	$-0.301256\pi$
$151$	14.3671	1.16918	0.584589	+	0.811330i	$0.301256\pi$
$152$	−10.2250	−0.829357
$153$	26.5604	2.14728
$154$	36.3273	2.92734
$155$	−4.75680	−0.382075
$156$	45.5911	3.65021
$157$	24.0485	1.91928	0.959641	−	0.281227i	$-0.0907413\pi$
$157$	24.0485	1.91928	0.959641	+	0.281227i	$0.0907413\pi$
$158$	−2.54227	−0.202252
$159$	13.8485	1.09826
$160$	−36.1365	−2.85684
$161$	23.4974	1.85186
$162$	−31.0261	−2.43764
$163$	−9.08232	−0.711382	−0.355691	−	0.934604i	$-0.615754\pi$
$163$	−9.08232	−0.711382	−0.355691	+	0.934604i	$0.615754\pi$
$164$	−32.8523	−2.56534
$165$	19.0834	1.48564
$166$	29.9032	2.32094
$167$	4.74960	0.367535	0.183768	−	0.982970i	$-0.441171\pi$
$167$	4.74960	0.367535	0.183768	+	0.982970i	$0.441171\pi$
$168$	94.3666	7.28054
$169$	−5.75457	−0.442659
$170$	−17.5696	−1.34753
$171$	6.50195	0.497217
$172$	43.8772	3.34561
$173$	5.52603	0.420136	0.210068	−	0.977687i	$-0.432631\pi$
$173$	5.52603	0.420136	0.210068	+	0.977687i	$0.432631\pi$
$174$	−8.36631	−0.634248
$175$	−8.67183	−0.655529
$176$	−66.3895	−5.00429
$177$	10.1065	0.759651
$178$	22.8610	1.71350
$179$	−10.2073	−0.762926	−0.381463	−	0.924384i	$-0.624580\pi$
$179$	−10.2073	−0.762926	−0.381463	+	0.924384i	$0.624580\pi$
$180$	52.2486	3.89438
$181$	8.97249	0.666920	0.333460	−	0.942764i	$-0.391784\pi$
$181$	8.97249	0.666920	0.333460	+	0.942764i	$0.391784\pi$
$182$	23.3983	1.73440
$183$	−10.5232	−0.777895
$184$	−73.0561	−5.38577
$185$	−4.00281	−0.294292
$186$	−26.5006	−1.94312
$187$	−17.7705	−1.29951
$188$	−35.2166	−2.56844
$189$	−31.1860	−2.26844
$190$	−4.30102	−0.312029
$191$	−14.5514	−1.05290	−0.526452	−	0.850205i	$-0.676478\pi$
$191$	−14.5514	−1.05290	−0.526452	+	0.850205i	$0.676478\pi$
$192$	−104.709	−7.55669
$193$	13.6840	0.984994	0.492497	−	0.870314i	$-0.336084\pi$
$193$	13.6840	0.984994	0.492497	+	0.870314i	$0.336084\pi$
$194$	−41.2381	−2.96072
$195$	12.2915	0.880216
$196$	16.6079	1.18628
$197$	0.154878	0.0110346	0.00551731	−	0.999985i	$-0.498244\pi$
$197$	0.154878	0.0110346	0.00551731	+	0.999985i	$0.498244\pi$
$198$	71.8207	5.10408
$199$	12.7455	0.903507	0.451753	−	0.892143i	$-0.350799\pi$
$199$	12.7455	0.903507	0.451753	+	0.892143i	$0.350799\pi$
$200$	26.9617	1.90648
$201$	−18.9910	−1.33952
$202$	−6.64000	−0.467189
$203$	−3.15937	−0.221744
$204$	−72.0221	−5.04256
$205$	−8.85713	−0.618609
$206$	1.92675	0.134243
$207$	46.4555	3.22888
$208$	−42.7612	−2.96496
$209$	−4.35019	−0.300909
$210$	39.6941	2.73916
$211$	21.7171	1.49507	0.747534	−	0.664223i	$-0.231238\pi$
$211$	21.7171	1.49507	0.747534	+	0.664223i	$0.231238\pi$
$212$	−25.3680	−1.74228
$213$	0.464453	0.0318238
$214$	−0.0891737	−0.00609579
$215$	11.8295	0.806764
$216$	96.9606	6.59733
$217$	−10.0074	−0.679348
$218$	22.6583	1.53461
$219$	6.20350	0.419193
$220$	−34.9574	−2.35683
$221$	−11.4459	−0.769936
$222$	−22.3001	−1.49668
$223$	20.2373	1.35519	0.677594	−	0.735436i	$-0.263023\pi$
$223$	20.2373	1.35519	0.677594	+	0.735436i	$0.263023\pi$
$224$	−76.0246	−5.07961
$225$	−17.1446	−1.14297
$226$	−43.7183	−2.90810
$227$	−18.7810	−1.24654	−0.623271	−	0.782006i	$-0.714197\pi$
$227$	−18.7810	−1.24654	−0.623271	+	0.782006i	$0.714197\pi$
$228$	−17.6309	−1.16764
$229$	4.32646	0.285901	0.142950	−	0.989730i	$-0.454341\pi$
$229$	4.32646	0.285901	0.142950	+	0.989730i	$0.454341\pi$
$230$	−30.7301	−2.02628
$231$	40.1479	2.64154
$232$	9.82282	0.644900
$233$	22.9542	1.50378	0.751889	−	0.659290i	$-0.229143\pi$
$233$	22.9542	1.50378	0.751889	+	0.659290i	$0.229143\pi$
$234$	46.2595	3.02408
$235$	−9.49456	−0.619357
$236$	−18.5133	−1.20512
$237$	−2.80965	−0.182506
$238$	−36.9633	−2.39597
$239$	−20.8538	−1.34892	−0.674459	−	0.738313i	$-0.735623\pi$
$239$	−20.8538	−1.34892	−0.674459	+	0.738313i	$0.735623\pi$
$240$	−72.5424	−4.68259
$241$	6.47490	0.417085	0.208542	−	0.978013i	$-0.433128\pi$
$241$	6.47490	0.417085	0.208542	+	0.978013i	$0.433128\pi$
$242$	−17.7871	−1.14340
$243$	−4.67638	−0.299990
$244$	19.2766	1.23406
$245$	4.47757	0.286061
$246$	−49.3440	−3.14606
$247$	−2.80194	−0.178283
$248$	31.1142	1.97575
$249$	33.0482	2.09435
$250$	32.0003	2.02388
$251$	−12.8235	−0.809411	−0.404705	−	0.914447i	$-0.632626\pi$
$251$	−12.8235	−0.809411	−0.404705	+	0.914447i	$0.632626\pi$
$252$	109.921	6.92440
$253$	−31.0815	−1.95408
$254$	15.9660	1.00179
$255$	−19.4175	−1.21597
$256$	59.3932	3.71207
$257$	−24.2731	−1.51411	−0.757056	−	0.653350i	$-0.773363\pi$
$257$	−24.2731	−1.51411	−0.757056	+	0.653350i	$0.773363\pi$
$258$	65.9033	4.10296
$259$	−8.42117	−0.523266
$260$	−22.5159	−1.39638
$261$	−6.24621	−0.386631
$262$	−36.3772	−2.24739
$263$	−3.67384	−0.226539	−0.113269	−	0.993564i	$-0.536132\pi$
$263$	−3.67384	−0.226539	−0.113269	+	0.993564i	$0.536132\pi$
$264$	−124.824	−7.68241
$265$	−6.83933	−0.420136
$266$	−9.04855	−0.554802
$267$	25.2654	1.54622
$268$	34.7881	2.12502
$269$	10.7355	0.654552	0.327276	−	0.944929i	$-0.393869\pi$
$269$	10.7355	0.654552	0.327276	+	0.944929i	$0.393869\pi$
$270$	40.7853	2.48211
$271$	16.7828	1.01948	0.509741	−	0.860328i	$-0.329741\pi$
$271$	16.7828	1.01948	0.509741	+	0.860328i	$0.329741\pi$
$272$	67.5517	4.09592
$273$	25.8592	1.56507
$274$	−57.9426	−3.50044
$275$	11.4708	0.691713
$276$	−125.970	−7.58251
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−42.3207	−2.53823
$279$	−19.7851	−1.18451
$280$	−46.6046	−2.78516
$281$	−21.8395	−1.30283	−0.651417	−	0.758720i	$-0.725825\pi$
$281$	−21.8395	−1.30283	−0.651417	+	0.758720i	$0.725825\pi$
$282$	−52.8952	−3.14986
$283$	22.0298	1.30954	0.654768	−	0.755829i	$-0.272766\pi$
$283$	22.0298	1.30954	0.654768	+	0.755829i	$0.272766\pi$
$284$	−0.850795	−0.0504854
$285$	−4.75337	−0.281565
$286$	−30.9503	−1.83013
$287$	−18.6338	−1.09992
$288$	−150.304	−8.85675
$289$	1.08160	0.0636236
$290$	4.13185	0.242630
$291$	−45.5752	−2.67167
$292$	−11.3637	−0.665011
$293$	−29.8364	−1.74306	−0.871532	−	0.490339i	$-0.836873\pi$
$293$	−29.8364	−1.74306	−0.871532	+	0.490339i	$0.836873\pi$
$294$	24.9450	1.45482
$295$	−4.99127	−0.290603
$296$	26.1823	1.52182
$297$	41.2516	2.39366
$298$	56.0193	3.24511
$299$	−20.0195	−1.15776
$300$	46.4899	2.68409
$301$	24.8871	1.43447
$302$	−39.5294	−2.27466
$303$	−7.33834	−0.421577
$304$	16.5365	0.948436
$305$	5.19705	0.297582
$306$	−73.0781	−4.17759
$307$	14.7416	0.841350	0.420675	−	0.907211i	$-0.361793\pi$
$307$	14.7416	0.841350	0.420675	+	0.907211i	$0.361793\pi$
$308$	−73.5440	−4.19056
$309$	2.12939	0.121137
$310$	13.0878	0.743337
$311$	22.8353	1.29487	0.647435	−	0.762121i	$-0.275842\pi$
$311$	22.8353	1.29487	0.647435	+	0.762121i	$0.275842\pi$
$312$	−80.3989	−4.55169
$313$	−21.5394	−1.21748	−0.608740	−	0.793370i	$-0.708325\pi$
$313$	−21.5394	−1.21748	−0.608740	+	0.793370i	$0.708325\pi$
$314$	−66.1669	−3.73401
$315$	29.6353	1.66976
$316$	5.14678	0.289529
$317$	11.2558	0.632187	0.316093	−	0.948728i	$-0.397629\pi$
$317$	11.2558	0.632187	0.316093	+	0.948728i	$0.397629\pi$
$318$	−38.1026	−2.13669
$319$	4.17909	0.233984
$320$	51.7122	2.89080
$321$	−0.0985524	−0.00550066
$322$	−64.6505	−3.60283
$323$	4.42635	0.246289
$324$	62.8118	3.48955
$325$	7.38828	0.409828
$326$	24.9890	1.38401
$327$	25.0413	1.38479
$328$	57.9344	3.19889
$329$	−19.9748	−1.10125
$330$	−52.5058	−2.89035
$331$	−27.0832	−1.48863	−0.744314	−	0.667829i	$-0.767224\pi$
$331$	−27.0832	−1.48863	−0.744314	+	0.667829i	$0.767224\pi$
$332$	−60.5385	−3.32248
$333$	−16.6490	−0.912362
$334$	−13.0680	−0.715049
$335$	9.37903	0.512431
$336$	−152.616	−8.32588
$337$	14.9970	0.816938	0.408469	−	0.912772i	$-0.366063\pi$
$337$	14.9970	0.816938	0.408469	+	0.912772i	$0.366063\pi$
$338$	15.8330	0.861204
$339$	−48.3163	−2.62418
$340$	35.5694	1.92902
$341$	13.2374	0.716847
$342$	−17.8894	−0.967348
$343$	−12.6956	−0.685498
$344$	−77.3766	−4.17187
$345$	−33.9621	−1.82846
$346$	−15.2042	−0.817385
$347$	20.1456	1.08147	0.540737	−	0.841192i	$-0.318145\pi$
$347$	20.1456	1.08147	0.540737	+	0.841192i	$0.318145\pi$
$348$	16.9374	0.907942
$349$	−29.5049	−1.57936	−0.789680	−	0.613519i	$-0.789753\pi$
$349$	−29.5049	−1.57936	−0.789680	+	0.613519i	$0.789753\pi$
$350$	23.8596	1.27535
$351$	26.5700	1.41820
$352$	100.562	5.35999
$353$	−12.5312	−0.666966	−0.333483	−	0.942756i	$-0.608224\pi$
$353$	−12.5312	−0.666966	−0.333483	+	0.942756i	$0.608224\pi$
$354$	−27.8069	−1.47792
$355$	−0.229378	−0.0121741
$356$	−46.2817	−2.45292
$357$	−40.8508	−2.16205
$358$	28.0841	1.48429
$359$	1.70669	0.0900755	0.0450377	−	0.998985i	$-0.485659\pi$
$359$	1.70669	0.0900755	0.0450377	+	0.998985i	$0.485659\pi$
$360$	−92.1394	−4.85617
$361$	−17.9164	−0.942970
$362$	−24.6868	−1.29751
$363$	−19.6578	−1.03177
$364$	−47.3694	−2.48283
$365$	−3.06371	−0.160362
$366$	28.9533	1.51341
$367$	10.6006	0.553349	0.276674	−	0.960964i	$-0.410768\pi$
$367$	10.6006	0.553349	0.276674	+	0.960964i	$0.410768\pi$
$368$	118.151	6.15906
$369$	−36.8398	−1.91780
$370$	11.0133	0.572553
$371$	−14.3887	−0.747023
$372$	53.6500	2.78162
$373$	0.672033	0.0347966	0.0173983	−	0.999849i	$-0.494462\pi$
$373$	0.672033	0.0347966	0.0173983	+	0.999849i	$0.494462\pi$
$374$	48.8935	2.52822
$375$	35.3659	1.82629
$376$	62.1038	3.20276
$377$	2.69173	0.138631
$378$	85.8047	4.41332
$379$	5.38179	0.276444	0.138222	−	0.990401i	$-0.455861\pi$
$379$	5.38179	0.276444	0.138222	+	0.990401i	$0.455861\pi$
$380$	8.70733	0.446677
$381$	17.6452	0.903989
$382$	40.0366	2.04845
$383$	32.2567	1.64824	0.824121	−	0.566414i	$-0.191670\pi$
$383$	32.2567	1.64824	0.824121	+	0.566414i	$0.191670\pi$
$384$	141.753	7.23380
$385$	−19.8278	−1.01052
$386$	−37.6499	−1.91633
$387$	49.2028	2.50112
$388$	83.4858	4.23835
$389$	−34.3596	−1.74210	−0.871052	−	0.491191i	$-0.836562\pi$
$389$	−34.3596	−1.74210	−0.871052	+	0.491191i	$0.836562\pi$
$390$	−33.8188	−1.71248
$391$	31.6256	1.59937
$392$	−29.2877	−1.47925
$393$	−40.2031	−2.02798
$394$	−0.426130	−0.0214681
$395$	1.38759	0.0698174
$396$	−145.400	−7.30661
$397$	5.73241	0.287701	0.143851	−	0.989599i	$-0.454052\pi$
$397$	5.73241	0.287701	0.143851	+	0.989599i	$0.454052\pi$
$398$	−35.0679	−1.75779
$399$	−10.0002	−0.500637
$400$	−43.6042	−2.18021
$401$	33.2295	1.65940	0.829702	−	0.558207i	$-0.188510\pi$
$401$	33.2295	1.65940	0.829702	+	0.558207i	$0.188510\pi$
$402$	52.2516	2.60607
$403$	8.52618	0.424719
$404$	13.4426	0.668792
$405$	16.9343	0.841474
$406$	8.69264	0.431409
$407$	11.1392	0.552149
$408$	127.010	6.28791
$409$	16.9940	0.840301	0.420150	−	0.907454i	$-0.361977\pi$
$409$	16.9940	0.840301	0.420150	+	0.907454i	$0.361977\pi$
$410$	24.3694	1.20352
$411$	−64.0366	−3.15869
$412$	−3.90067	−0.192172
$413$	−10.5007	−0.516707
$414$	−127.817	−6.28187
$415$	−16.3214	−0.801188
$416$	64.7718	3.17570
$417$	−46.7717	−2.29042
$418$	11.9691	0.585426
$419$	26.4093	1.29018	0.645088	−	0.764108i	$-0.276821\pi$
$419$	26.4093	1.29018	0.645088	+	0.764108i	$0.276821\pi$
$420$	−80.3600	−3.92117
$421$	−4.44208	−0.216494	−0.108247	−	0.994124i	$-0.534524\pi$
$421$	−4.44208	−0.216494	−0.108247	+	0.994124i	$0.534524\pi$
$422$	−59.7522	−2.90869
$423$	−39.4911	−1.92012
$424$	44.7360	2.17257
$425$	−11.6716	−0.566154
$426$	−1.27789	−0.0619139
$427$	10.9336	0.529116
$428$	0.180531	0.00872627
$429$	−34.2055	−1.65146
$430$	−32.5475	−1.56958
$431$	26.6267	1.28256	0.641281	−	0.767306i	$-0.278403\pi$
$431$	26.6267	1.28256	0.641281	+	0.767306i	$0.278403\pi$
$432$	−156.811	−7.54458
$433$	−23.2724	−1.11840	−0.559201	−	0.829032i	$-0.688892\pi$
$433$	−23.2724	−1.11840	−0.559201	+	0.829032i	$0.688892\pi$
$434$	27.5343	1.32169
$435$	4.56640	0.218942
$436$	−45.8713	−2.19684
$437$	7.74190	0.370345
$438$	−17.0682	−0.815551
$439$	13.2296	0.631413	0.315707	−	0.948857i	$-0.397758\pi$
$439$	13.2296	0.631413	0.315707	+	0.948857i	$0.397758\pi$
$440$	61.6467	2.93889
$441$	18.6237	0.886844
$442$	31.4922	1.49793
$443$	15.9484	0.757732	0.378866	−	0.925452i	$-0.376314\pi$
$443$	15.9484	0.757732	0.378866	+	0.925452i	$0.376314\pi$
$444$	45.1461	2.14254
$445$	−12.4777	−0.591502
$446$	−55.6806	−2.63655
$447$	61.9110	2.92829
$448$	108.793	5.13998
$449$	16.4107	0.774470	0.387235	−	0.921981i	$-0.373430\pi$
$449$	16.4107	0.774470	0.387235	+	0.921981i	$0.373430\pi$
$450$	47.1715	2.22368
$451$	24.6480	1.16063
$452$	88.5069	4.16301
$453$	−43.6869	−2.05259
$454$	51.6739	2.42518
$455$	−12.7710	−0.598714
$456$	31.0918	1.45600
$457$	−30.4428	−1.42405	−0.712027	−	0.702152i	$-0.752223\pi$
$457$	−30.4428	−1.42405	−0.712027	+	0.702152i	$0.752223\pi$
$458$	−11.9038	−0.556227
$459$	−41.9737	−1.95917
$460$	62.2126	2.90068
$461$	−19.8221	−0.923209	−0.461604	−	0.887086i	$-0.652726\pi$
$461$	−19.8221	−0.923209	−0.461604	+	0.887086i	$0.652726\pi$
$462$	−110.463	−5.13918
$463$	−29.6536	−1.37812	−0.689060	−	0.724704i	$-0.741976\pi$
$463$	−29.6536	−1.37812	−0.689060	+	0.724704i	$0.741976\pi$
$464$	−15.8861	−0.737495
$465$	14.4643	0.670765
$466$	−63.1558	−2.92564
$467$	−14.2439	−0.659130	−0.329565	−	0.944133i	$-0.606902\pi$
$467$	−14.2439	−0.659130	−0.329565	+	0.944133i	$0.606902\pi$
$468$	−93.6515	−4.32904
$469$	19.7318	0.911128
$470$	26.1232	1.20497
$471$	−73.1258	−3.36946
$472$	32.6479	1.50274
$473$	−32.9196	−1.51365
$474$	7.73043	0.355070
$475$	−2.85718	−0.131097
$476$	74.8314	3.42989
$477$	−28.4471	−1.30250
$478$	57.3768	2.62435
$479$	35.5489	1.62427	0.812136	−	0.583468i	$-0.198304\pi$
$479$	35.5489	1.62427	0.812136	+	0.583468i	$0.198304\pi$
$480$	109.882	5.01542
$481$	7.17471	0.327139
$482$	−17.8150	−0.811449
$483$	−71.4500	−3.25109
$484$	36.0096	1.63680
$485$	22.5081	1.02204
$486$	12.8665	0.583638
$487$	14.2342	0.645011	0.322505	−	0.946568i	$-0.395475\pi$
$487$	14.2342	0.645011	0.322505	+	0.946568i	$0.395475\pi$
$488$	−33.9939	−1.53883
$489$	27.6171	1.24889
$490$	−12.3195	−0.556539
$491$	−43.4408	−1.96046	−0.980229	−	0.197868i	$-0.936598\pi$
$491$	−43.4408	−1.96046	−0.980229	+	0.197868i	$0.936598\pi$
$492$	99.8960	4.50366
$493$	−4.25225	−0.191512
$494$	7.70923	0.346855
$495$	−39.2004	−1.76193
$496$	−50.3199	−2.25943
$497$	−0.482569	−0.0216462
$498$	−90.9284	−4.07460
$499$	37.4442	1.67623	0.838117	−	0.545491i	$-0.183657\pi$
$499$	37.4442	1.67623	0.838117	+	0.545491i	$0.183657\pi$
$500$	−64.7841	−2.89723
$501$	−14.4424	−0.645238
$502$	35.2824	1.57473
$503$	−3.87360	−0.172715	−0.0863576	−	0.996264i	$-0.527523\pi$
$503$	−3.87360	−0.172715	−0.0863576	+	0.996264i	$0.527523\pi$
$504$	−193.844	−8.63451
$505$	3.62417	0.161273
$506$	85.5172	3.80170
$507$	17.4982	0.777124
$508$	−32.3228	−1.43409
$509$	−5.21218	−0.231026	−0.115513	−	0.993306i	$-0.536851\pi$
$509$	−5.21218	−0.231026	−0.115513	+	0.993306i	$0.536851\pi$
$510$	53.4250	2.36570
$511$	−6.44547	−0.285131
$512$	−70.1783	−3.10147
$513$	−10.2751	−0.453657
$514$	66.7846	2.94574
$515$	−1.05164	−0.0463407
$516$	−133.420	−5.87349
$517$	26.4219	1.16203
$518$	23.1699	1.01803
$519$	−16.8033	−0.737584
$520$	39.7064	1.74124
$521$	−28.1925	−1.23514	−0.617569	−	0.786517i	$-0.711882\pi$
$521$	−28.1925	−1.23514	−0.617569	+	0.786517i	$0.711882\pi$
$522$	17.1858	0.752200
$523$	0.134998	0.00590305	0.00295152	−	0.999996i	$-0.499060\pi$
$523$	0.134998	0.00590305	0.00295152	+	0.999996i	$0.499060\pi$
$524$	73.6450	3.21720
$525$	26.3690	1.15084
$526$	10.1082	0.440737
$527$	−13.4692	−0.586726
$528$	201.874	8.78545
$529$	32.3147	1.40499
$530$	18.8176	0.817386
$531$	−20.7604	−0.900925
$532$	18.3186	0.794213
$533$	15.8757	0.687653
$534$	−69.5148	−3.00820
$535$	0.0486718	0.00210427
$536$	−61.3482	−2.64984
$537$	31.0378	1.33938
$538$	−29.5374	−1.27345
$539$	−12.4604	−0.536706
$540$	−82.5690	−3.55320
$541$	−9.18112	−0.394727	−0.197364	−	0.980330i	$-0.563238\pi$
$541$	−9.18112	−0.394727	−0.197364	+	0.980330i	$0.563238\pi$
$542$	−46.1760	−1.98343
$543$	−27.2832	−1.17083
$544$	−102.323	−4.38705
$545$	−12.3671	−0.529748
$546$	−71.1486	−3.04488
$547$	39.3004	1.68036	0.840182	−	0.542304i	$-0.182448\pi$
$547$	39.3004	1.68036	0.840182	+	0.542304i	$0.182448\pi$
$548$	117.304	5.01096
$549$	21.6163	0.922562
$550$	−31.5605	−1.34574
$551$	−1.04094	−0.0443457
$552$	222.146	9.45516
$553$	2.91924	0.124139
$554$	−2.75139	−0.116895
$555$	12.1716	0.516655
$556$	85.6774	3.63353
$557$	27.3805	1.16015	0.580074	−	0.814564i	$-0.303024\pi$
$557$	27.3805	1.16015	0.580074	+	0.814564i	$0.303024\pi$
$558$	54.4366	2.30448
$559$	−21.2034	−0.896808
$560$	75.3721	3.18505
$561$	54.0358	2.28139
$562$	60.0889	2.53470
$563$	21.2589	0.895955	0.447978	−	0.894045i	$-0.352144\pi$
$563$	21.2589	0.895955	0.447978	+	0.894045i	$0.352144\pi$
$564$	107.085	4.50910
$565$	23.8618	1.00387
$566$	−60.6126	−2.54774
$567$	35.6267	1.49618
$568$	1.50036	0.0629537
$569$	19.9195	0.835070	0.417535	−	0.908661i	$-0.362894\pi$
$569$	19.9195	0.835070	0.417535	+	0.908661i	$0.362894\pi$
$570$	13.0784	0.547792
$571$	−41.9741	−1.75656	−0.878280	−	0.478147i	$-0.841309\pi$
$571$	−41.9741	−1.75656	−0.878280	+	0.478147i	$0.841309\pi$
$572$	62.6584	2.61988
$573$	44.2474	1.84846
$574$	51.2687	2.13992
$575$	−20.4141	−0.851328
$576$	215.089	8.96202
$577$	11.7236	0.488060	0.244030	−	0.969768i	$-0.421530\pi$
$577$	11.7236	0.488060	0.244030	+	0.969768i	$0.421530\pi$
$578$	−2.97590	−0.123781
$579$	−41.6097	−1.72924
$580$	−8.36485	−0.347331
$581$	−34.3373	−1.42455
$582$	125.395	5.19779
$583$	19.0328	0.788257
$584$	20.0397	0.829248
$585$	−25.2488	−1.04391
$586$	82.0916	3.39117
$587$	5.68901	0.234811	0.117405	−	0.993084i	$-0.462542\pi$
$587$	5.68901	0.234811	0.117405	+	0.993084i	$0.462542\pi$
$588$	−50.5007	−2.08261
$589$	−3.29723	−0.135860
$590$	13.7329	0.565376
$591$	−0.470948	−0.0193722
$592$	−42.3438	−1.74032
$593$	−4.91996	−0.202038	−0.101019	−	0.994884i	$-0.532210\pi$
$593$	−4.91996	−0.202038	−0.101019	+	0.994884i	$0.532210\pi$
$594$	−113.499	−4.65692
$595$	20.1749	0.827090
$596$	−113.410	−4.64545
$597$	−38.7561	−1.58618
$598$	55.0813	2.25244
$599$	29.0932	1.18872	0.594358	−	0.804201i	$-0.297406\pi$
$599$	29.0932	1.18872	0.594358	+	0.804201i	$0.297406\pi$
$600$	−81.9840	−3.34698
$601$	−21.9878	−0.896903	−0.448451	−	0.893807i	$-0.648024\pi$
$601$	−21.9878	−0.896903	−0.448451	+	0.893807i	$0.648024\pi$
$602$	−68.4739	−2.79079
$603$	39.0106	1.58863
$604$	80.0266	3.25624
$605$	9.70833	0.394700
$606$	20.1906	0.820188
$607$	33.4497	1.35768	0.678841	−	0.734285i	$-0.262482\pi$
$607$	33.4497	1.35768	0.678841	+	0.734285i	$0.262482\pi$
$608$	−25.0485	−1.01585
$609$	9.60687	0.389290
$610$	−14.2991	−0.578954
$611$	17.0182	0.688484
$612$	147.945	5.98033
$613$	−36.6632	−1.48081	−0.740406	−	0.672160i	$-0.765367\pi$
$613$	−36.6632	−1.48081	−0.740406	+	0.672160i	$0.765367\pi$
$614$	−40.5600	−1.63687
$615$	26.9324	1.08602
$616$	129.693	5.22549
$617$	19.7368	0.794573	0.397286	−	0.917695i	$-0.369952\pi$
$617$	19.7368	0.794573	0.397286	+	0.917695i	$0.369952\pi$
$618$	−5.85879	−0.235675
$619$	−42.8916	−1.72396	−0.861979	−	0.506944i	$-0.830775\pi$
$619$	−42.8916	−1.72396	−0.861979	+	0.506944i	$0.830775\pi$
$620$	−26.4960	−1.06411
$621$	−73.4141	−2.94600
$622$	−62.8287	−2.51920
$623$	−26.2509	−1.05172
$624$	130.027	5.20523
$625$	−3.74206	−0.149683
$626$	59.2633	2.36864
$627$	13.2279	0.528271
$628$	133.954	5.34533
$629$	−11.3342	−0.451924
$630$	−81.5382	−3.24856
$631$	15.5051	0.617246	0.308623	−	0.951184i	$-0.400132\pi$
$631$	15.5051	0.617246	0.308623	+	0.951184i	$0.400132\pi$
$632$	−9.07624	−0.361034
$633$	−66.0365	−2.62472
$634$	−30.9690	−1.22994
$635$	−8.71437	−0.345819
$636$	77.1380	3.05872
$637$	−8.02568	−0.317989
$638$	−11.4983	−0.455221
$639$	−0.954061	−0.0377421
$640$	−70.0072	−2.76728
$641$	7.45222	0.294345	0.147172	−	0.989111i	$-0.452983\pi$
$641$	7.45222	0.294345	0.147172	+	0.989111i	$0.452983\pi$
$642$	0.271156	0.0107017
$643$	24.8443	0.979762	0.489881	−	0.871789i	$-0.337040\pi$
$643$	24.8443	0.979762	0.489881	+	0.871789i	$0.337040\pi$
$644$	130.884	5.15754
$645$	−35.9706	−1.41634
$646$	−12.1786	−0.479161
$647$	22.7342	0.893774	0.446887	−	0.894591i	$-0.352533\pi$
$647$	22.7342	0.893774	0.446887	+	0.894591i	$0.352533\pi$
$648$	−110.767	−4.35136
$649$	13.8899	0.545228
$650$	−20.3280	−0.797330
$651$	30.4302	1.19265
$652$	−50.5897	−1.98125
$653$	−23.4145	−0.916278	−0.458139	−	0.888880i	$-0.651484\pi$
$653$	−23.4145	−0.916278	−0.458139	+	0.888880i	$0.651484\pi$
$654$	−68.8984	−2.69414
$655$	19.8550	0.775800
$656$	−93.6954	−3.65819
$657$	−12.7430	−0.497151
$658$	54.9584	2.14250
$659$	35.5100	1.38327	0.691636	−	0.722246i	$-0.256890\pi$
$659$	35.5100	1.38327	0.691636	+	0.722246i	$0.256890\pi$
$660$	106.297	4.13761
$661$	14.1763	0.551395	0.275698	−	0.961244i	$-0.411091\pi$
$661$	14.1763	0.551395	0.275698	+	0.961244i	$0.411091\pi$
$662$	74.5164	2.89616
$663$	34.8043	1.35169
$664$	106.758	4.14303
$665$	4.93878	0.191518
$666$	45.8080	1.77502
$667$	−7.43738	−0.287977
$668$	26.4559	1.02361
$669$	−61.5367	−2.37915
$670$	−25.8053	−0.996947
$671$	−14.4626	−0.558322
$672$	231.172	8.91767
$673$	27.9021	1.07555	0.537774	−	0.843089i	$-0.319266\pi$
$673$	27.9021	1.07555	0.537774	+	0.843089i	$0.319266\pi$
$674$	−41.2625	−1.58937
$675$	27.0938	1.04284
$676$	−32.0537	−1.23283
$677$	−20.6797	−0.794785	−0.397393	−	0.917649i	$-0.630085\pi$
$677$	−20.6797	−0.794785	−0.397393	+	0.917649i	$0.630085\pi$
$678$	132.937	5.10541
$679$	47.3529	1.81724
$680$	−62.7259	−2.40543
$681$	57.1086	2.18841
$682$	−36.4213	−1.39464
$683$	40.3646	1.54451	0.772255	−	0.635313i	$-0.219129\pi$
$683$	40.3646	1.54451	0.772255	+	0.635313i	$0.219129\pi$
$684$	36.2168	1.38478
$685$	31.6256	1.20835
$686$	34.9305	1.33365
$687$	−13.1557	−0.501922
$688$	125.139	4.77086
$689$	12.2589	0.467029
$690$	93.4429	3.55731
$691$	−27.7748	−1.05660	−0.528302	−	0.849056i	$-0.677171\pi$
$691$	−27.7748	−1.05660	−0.528302	+	0.849056i	$0.677171\pi$
$692$	30.7807	1.17011
$693$	−82.4704	−3.13279
$694$	−55.4284	−2.10403
$695$	23.0990	0.876195
$696$	−29.8688	−1.13217
$697$	−25.0795	−0.949954
$698$	81.1793	3.07268
$699$	−69.7981	−2.64001
$700$	−48.3033	−1.82569
$701$	13.7887	0.520794	0.260397	−	0.965502i	$-0.416147\pi$
$701$	13.7887	0.520794	0.260397	+	0.965502i	$0.416147\pi$
$702$	−73.1043	−2.75914
$703$	−2.77459	−0.104646
$704$	−143.907	−5.42370
$705$	28.8707	1.08733
$706$	34.4781	1.29760
$707$	7.62459	0.286752
$708$	56.2946	2.11568
$709$	−35.2647	−1.32439	−0.662197	−	0.749330i	$-0.730376\pi$
$709$	−35.2647	−1.32439	−0.662197	+	0.749330i	$0.730376\pi$
$710$	0.631108	0.0236851
$711$	5.77147	0.216447
$712$	81.6168	3.05872
$713$	−23.5582	−0.882262
$714$	112.396	4.20633
$715$	16.8930	0.631761
$716$	−56.8558	−2.12480
$717$	63.4112	2.36814
$718$	−4.69576	−0.175244
$719$	14.6956	0.548053	0.274027	−	0.961722i	$-0.411644\pi$
$719$	14.6956	0.548053	0.274027	+	0.961722i	$0.411644\pi$
$720$	149.014	5.55342
$721$	−2.21245	−0.0823961
$722$	49.2951	1.83457
$723$	−19.6886	−0.732227
$724$	49.9779	1.85742
$725$	2.74480	0.101939
$726$	54.0861	2.00732
$727$	22.0630	0.818272	0.409136	−	0.912473i	$-0.365830\pi$
$727$	22.0630	0.818272	0.409136	+	0.912473i	$0.365830\pi$
$728$	83.5350	3.09601
$729$	−19.6099	−0.726291
$730$	8.42944	0.311988
$731$	33.4959	1.23889
$732$	−58.6155	−2.16649
$733$	−22.8774	−0.844997	−0.422499	−	0.906364i	$-0.638847\pi$
$733$	−22.8774	−0.844997	−0.422499	+	0.906364i	$0.638847\pi$
$734$	−29.1664	−1.07655
$735$	−13.6152	−0.502204
$736$	−178.967	−6.59683
$737$	−26.1004	−0.961420
$738$	101.361	3.73114
$739$	21.2122	0.780303	0.390151	−	0.920751i	$-0.372423\pi$
$739$	21.2122	0.780303	0.390151	+	0.920751i	$0.372423\pi$
$740$	−22.2962	−0.819624
$741$	8.52003	0.312991
$742$	39.5888	1.45335
$743$	−51.1572	−1.87678	−0.938388	−	0.345584i	$-0.887681\pi$
$743$	−51.1572	−1.87678	−0.938388	+	0.345584i	$0.887681\pi$
$744$	−94.6108	−3.46860
$745$	−30.5758	−1.12021
$746$	−1.84902	−0.0676976
$747$	−67.8864	−2.48383
$748$	−98.9841	−3.61922
$749$	0.102397	0.00374149
$750$	−97.3053	−3.55309
$751$	−44.2616	−1.61513	−0.807564	−	0.589780i	$-0.799214\pi$
$751$	−44.2616	−1.61513	−0.807564	+	0.589780i	$0.799214\pi$
$752$	−100.438	−3.66261
$753$	38.9931	1.42099
$754$	−7.40600	−0.269711
$755$	21.5755	0.785213
$756$	−173.710	−6.31777
$757$	9.22622	0.335333	0.167666	−	0.985844i	$-0.446377\pi$
$757$	9.22622	0.335333	0.167666	+	0.985844i	$0.446377\pi$
$758$	−14.8074	−0.537829
$759$	94.5112	3.43054
$760$	−15.3552	−0.556992
$761$	21.6576	0.785086	0.392543	−	0.919734i	$-0.371595\pi$
$761$	21.6576	0.785086	0.392543	+	0.919734i	$0.371595\pi$
$762$	−48.5487	−1.75873
$763$	−26.0181	−0.941918
$764$	−81.0534	−2.93241
$765$	39.8867	1.44211
$766$	−88.7508	−3.20670
$767$	8.94646	0.323038
$768$	−180.600	−6.51685
$769$	−35.8953	−1.29442	−0.647209	−	0.762312i	$-0.724064\pi$
$769$	−35.8953	−1.29442	−0.647209	+	0.762312i	$0.724064\pi$
$770$	54.5539	1.96599
$771$	73.8085	2.65815
$772$	76.2216	2.74327
$773$	−33.9467	−1.22098	−0.610490	−	0.792024i	$-0.709027\pi$
$773$	−33.9467	−1.22098	−0.610490	+	0.792024i	$0.709027\pi$
$774$	−135.376	−4.86599
$775$	8.69427	0.312307
$776$	−147.226	−5.28509
$777$	25.6067	0.918637
$778$	94.5367	3.38931
$779$	−6.13943	−0.219968
$780$	68.4656	2.45146
$781$	0.638323	0.0228410
$782$	−87.0143	−3.11162
$783$	9.87095	0.352759
$784$	47.3661	1.69165
$785$	36.1145	1.28898
$786$	110.614	3.94548
$787$	4.56540	0.162739	0.0813695	−	0.996684i	$-0.474071\pi$
$787$	4.56540	0.162739	0.0813695	+	0.996684i	$0.474071\pi$
$788$	0.862693	0.0307322
$789$	11.1713	0.397708
$790$	−3.81781	−0.135832
$791$	50.2009	1.78494
$792$	256.410	9.11112
$793$	−9.31530	−0.330796
$794$	−15.7721	−0.559730
$795$	20.7967	0.737584
$796$	70.9943	2.51633
$797$	−10.8817	−0.385451	−0.192726	−	0.981253i	$-0.561733\pi$
$797$	−10.8817	−0.385451	−0.192726	+	0.981253i	$0.561733\pi$
$798$	27.5145	0.974001
$799$	−26.8844	−0.951103
$800$	66.0488	2.33518
$801$	−51.8992	−1.83377
$802$	−91.4273	−3.22841
$803$	8.52581	0.300869
$804$	−105.782	−3.73065
$805$	35.2868	1.24370
$806$	−23.4588	−0.826302
$807$	−32.6439	−1.14912
$808$	−23.7057	−0.833963
$809$	7.37387	0.259251	0.129626	−	0.991563i	$-0.458622\pi$
$809$	7.37387	0.259251	0.129626	+	0.991563i	$0.458622\pi$
$810$	−46.5929	−1.63711
$811$	39.7598	1.39616	0.698078	−	0.716022i	$-0.254039\pi$
$811$	39.7598	1.39616	0.698078	+	0.716022i	$0.254039\pi$
$812$	−17.5981	−0.617572
$813$	−51.0324	−1.78978
$814$	−30.6482	−1.07422
$815$	−13.6392	−0.477761
$816$	−205.408	−7.19073
$817$	8.19975	0.286873
$818$	−46.7572	−1.63483
$819$	−53.1189	−1.85612
$820$	−49.3354	−1.72287
$821$	5.74564	0.200524	0.100262	−	0.994961i	$-0.468032\pi$
$821$	5.74564	0.200524	0.100262	+	0.994961i	$0.468032\pi$
$822$	176.189	6.14531
$823$	−43.1343	−1.50357	−0.751784	−	0.659409i	$-0.770806\pi$
$823$	−43.1343	−1.50357	−0.751784	+	0.659409i	$0.770806\pi$
$824$	6.87876	0.239633
$825$	−34.8798	−1.21436
$826$	28.8916	1.00527
$827$	−16.9417	−0.589120	−0.294560	−	0.955633i	$-0.595173\pi$
$827$	−16.9417	−0.589120	−0.294560	+	0.955633i	$0.595173\pi$
$828$	258.763	8.99264
$829$	−38.8991	−1.35102	−0.675510	−	0.737351i	$-0.736077\pi$
$829$	−38.8991	−1.35102	−0.675510	+	0.737351i	$0.736077\pi$
$830$	44.9066	1.55873
$831$	−3.04076	−0.105483
$832$	−92.6900	−3.21345
$833$	12.6785	0.439284
$834$	128.687	4.45607
$835$	7.13263	0.246835
$836$	−24.2311	−0.838052
$837$	31.2666	1.08073
$838$	−72.6621	−2.51007
$839$	37.9081	1.30873	0.654367	−	0.756177i	$-0.272935\pi$
$839$	37.9081	1.30873	0.654367	+	0.756177i	$0.272935\pi$
$840$	141.713	4.88957
$841$	1.00000	0.0344828
$842$	12.2219	0.421194
$843$	66.4086	2.28723
$844$	120.967	4.16386
$845$	−8.64181	−0.297287
$846$	108.655	3.73565
$847$	20.4245	0.701796
$848$	−72.3500	−2.48451
$849$	−66.9874	−2.29900
$850$	32.1130	1.10147
$851$	−19.8241	−0.679560
$852$	2.58706	0.0886313
$853$	−33.8854	−1.16022	−0.580108	−	0.814540i	$-0.696990\pi$
$853$	−33.8854	−1.16022	−0.580108	+	0.814540i	$0.696990\pi$
$854$	−30.0827	−1.02941
$855$	9.76419	0.333928
$856$	−0.318362	−0.0108814
$857$	−39.1387	−1.33695	−0.668477	−	0.743733i	$-0.733053\pi$
$857$	−39.1387	−1.33695	−0.668477	+	0.743733i	$0.733053\pi$
$858$	94.1125	3.21295
$859$	−12.8496	−0.438423	−0.219211	−	0.975677i	$-0.570348\pi$
$859$	−12.8496	−0.438423	−0.219211	+	0.975677i	$0.570348\pi$
$860$	65.8918	2.24689
$861$	56.6608	1.93099
$862$	−73.2603	−2.49526
$863$	−0.0677821	−0.00230733	−0.00115366	−	0.999999i	$-0.500367\pi$
$863$	−0.0677821	−0.00230733	−0.00115366	+	0.999999i	$0.500367\pi$
$864$	237.527	8.08083
$865$	8.29861	0.282161
$866$	64.0315	2.17588
$867$	−3.28889	−0.111697
$868$	−55.7427	−1.89203
$869$	−3.86146	−0.130991
$870$	−12.5639	−0.425958
$871$	−16.8112	−0.569624
$872$	80.8931	2.73939
$873$	93.6189	3.16852
$874$	−21.3010	−0.720516
$875$	−36.7454	−1.24222
$876$	34.5543	1.16748
$877$	−43.9777	−1.48502	−0.742510	−	0.669835i	$-0.766365\pi$
$877$	−43.9777	−1.48502	−0.742510	+	0.669835i	$0.766365\pi$
$878$	−36.3997	−1.22843
$879$	90.7254	3.06009
$880$	−99.6992	−3.36086
$881$	44.8493	1.51101	0.755506	−	0.655142i	$-0.227391\pi$
$881$	44.8493	1.51101	0.755506	+	0.655142i	$0.227391\pi$
$882$	−51.2411	−1.72538
$883$	19.0273	0.640321	0.320161	−	0.947363i	$-0.396263\pi$
$883$	19.0273	0.640321	0.320161	+	0.947363i	$0.396263\pi$
$884$	−63.7553	−2.14432
$885$	15.1773	0.510178
$886$	−43.8803	−1.47419
$887$	−13.6034	−0.456758	−0.228379	−	0.973572i	$-0.573343\pi$
$887$	−13.6034	−0.456758	−0.228379	+	0.973572i	$0.573343\pi$
$888$	−79.6142	−2.67168
$889$	−18.3334	−0.614884
$890$	34.3311	1.15078
$891$	−47.1256	−1.57877
$892$	112.724	3.77429
$893$	−6.58127	−0.220234
$894$	−170.341	−5.69706
$895$	−15.3286	−0.512378
$896$	−147.282	−4.92036
$897$	60.8744	2.03254
$898$	−45.1522	−1.50675
$899$	3.16754	0.105643
$900$	−95.4978	−3.18326
$901$	−19.3660	−0.645174
$902$	−67.8162	−2.25803
$903$	−75.6755	−2.51832
$904$	−156.080	−5.19115
$905$	13.4743	0.447900
$906$	120.199	3.99336
$907$	−44.0065	−1.46121	−0.730605	−	0.682800i	$-0.760762\pi$
$907$	−44.0065	−1.46121	−0.730605	+	0.682800i	$0.760762\pi$
$908$	−104.613	−3.47170
$909$	15.0742	0.499978
$910$	35.1380	1.16481
$911$	−11.9951	−0.397416	−0.198708	−	0.980059i	$-0.563675\pi$
$911$	−11.9951	−0.397416	−0.198708	+	0.980059i	$0.563675\pi$
$912$	−50.2837	−1.66506
$913$	45.4200	1.50318
$914$	83.7600	2.77053
$915$	−15.8030	−0.522431
$916$	24.0990	0.796253
$917$	41.7713	1.37941
$918$	115.486	3.81160
$919$	−32.8561	−1.08382	−0.541911	−	0.840436i	$-0.682299\pi$
$919$	−32.8561	−1.08382	−0.541911	+	0.840436i	$0.682299\pi$
$920$	−109.711	−3.61705
$921$	−44.8258	−1.47706
$922$	54.5384	1.79613
$923$	0.411142	0.0135329
$924$	223.629	7.35687
$925$	7.31616	0.240554
$926$	81.5886	2.68117
$927$	−4.37412	−0.143665
$928$	24.0632	0.789914
$929$	−40.9328	−1.34296	−0.671481	−	0.741022i	$-0.734341\pi$
$929$	−40.9328	−1.34296	−0.671481	+	0.741022i	$0.734341\pi$
$930$	−39.7968	−1.30499
$931$	3.10368	0.101719
$932$	127.858	4.18812
$933$	−69.4366	−2.27325
$934$	39.1906	1.28235
$935$	−26.6865	−0.872743
$936$	165.153	5.39818
$937$	0.429886	0.0140438	0.00702188	−	0.999975i	$-0.497765\pi$
$937$	0.429886	0.0140438	0.00702188	+	0.999975i	$0.497765\pi$
$938$	−54.2897	−1.77262
$939$	65.4962	2.13739
$940$	−52.8860	−1.72495
$941$	51.0874	1.66540	0.832700	−	0.553724i	$-0.186794\pi$
$941$	51.0874	1.66540	0.832700	+	0.553724i	$0.186794\pi$
$942$	201.197	6.55537
$943$	−43.8653	−1.42845
$944$	−52.8003	−1.71850
$945$	−46.8330	−1.52348
$946$	90.5746	2.94483
$947$	0.985476	0.0320237	0.0160118	−	0.999872i	$-0.494903\pi$
$947$	0.985476	0.0320237	0.0160118	+	0.999872i	$0.494903\pi$
$948$	−15.6501	−0.508292
$949$	5.49145	0.178260
$950$	7.86122	0.255052
$951$	−34.2261	−1.10986
$952$	−131.964	−4.27697
$953$	22.7802	0.737923	0.368961	−	0.929445i	$-0.379713\pi$
$953$	22.7802	0.737923	0.368961	+	0.929445i	$0.379713\pi$
$954$	78.2689	2.53405
$955$	−21.8524	−0.707126
$956$	−116.158	−3.75682
$957$	−12.7076	−0.410778
$958$	−97.8089	−3.16006
$959$	66.5344	2.14851
$960$	−157.244	−5.07504
$961$	−20.9667	−0.676344
$962$	−19.7404	−0.636457
$963$	0.202443	0.00652362
$964$	36.0661	1.16161
$965$	20.5497	0.661517
$966$	196.587	6.32507
$967$	49.9899	1.60757	0.803783	−	0.594923i	$-0.202817\pi$
$967$	49.9899	1.60757	0.803783	+	0.594923i	$0.202817\pi$
$968$	−63.5022	−2.04104
$969$	−13.4595	−0.432380
$970$	−61.9286	−1.98841
$971$	−20.9051	−0.670878	−0.335439	−	0.942062i	$-0.608885\pi$
$971$	−20.9051	−0.670878	−0.335439	+	0.942062i	$0.608885\pi$
$972$	−26.0481	−0.835493
$973$	48.5961	1.55792
$974$	−39.1637	−1.25488
$975$	−22.4660	−0.719487
$976$	54.9772	1.75978
$977$	54.2340	1.73510	0.867550	−	0.497350i	$-0.165693\pi$
$977$	54.2340	1.73510	0.867550	+	0.497350i	$0.165693\pi$
$978$	−75.9854	−2.42975
$979$	34.7236	1.10977
$980$	24.9406	0.796700
$981$	−51.4389	−1.64232
$982$	119.523	3.81412
$983$	13.7808	0.439538	0.219769	−	0.975552i	$-0.429470\pi$
$983$	13.7808	0.439538	0.219769	+	0.975552i	$0.429470\pi$
$984$	−176.165	−5.61592
$985$	0.232586	0.00741080
$986$	11.6996	0.372590
$987$	60.7385	1.93333
$988$	−15.6072	−0.496531
$989$	58.5860	1.86293
$990$	107.855	3.42787
$991$	26.3107	0.835786	0.417893	−	0.908496i	$-0.362769\pi$
$991$	26.3107	0.835786	0.417893	+	0.908496i	$0.362769\pi$
$992$	76.2213	2.42003
$993$	82.3535	2.61341
$994$	1.32773	0.0421132
$995$	19.1404	0.606791
$996$	184.083	5.83289
$997$	32.3364	1.02410	0.512052	−	0.858954i	$-0.328886\pi$
$997$	32.3364	1.02410	0.512052	+	0.858954i	$0.328886\pi$
$998$	−103.024	−3.26115
$999$	26.3106	0.832432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.4	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.4	✓	169	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)

\(f(q)\)	\(=\)	\(q-2.75139 q^{2} -3.04076 q^{3} +5.57013 q^{4} +1.50173 q^{5} +8.36631 q^{6} +3.15937 q^{7} -9.82282 q^{8} +6.24621 q^{9} +O(q^{10})\)	\(q-2.75139 q^{2} -3.04076 q^{3} +5.57013 q^{4} +1.50173 q^{5} +8.36631 q^{6} +3.15937 q^{7} -9.82282 q^{8} +6.24621 q^{9} -4.13185 q^{10} -4.17909 q^{11} -16.9374 q^{12} -2.69173 q^{13} -8.69264 q^{14} -4.56640 q^{15} +15.8861 q^{16} +4.25225 q^{17} -17.1858 q^{18} +1.04094 q^{19} +8.36485 q^{20} -9.60687 q^{21} +11.4983 q^{22} +7.43738 q^{23} +29.8688 q^{24} -2.74480 q^{25} +7.40600 q^{26} -9.87095 q^{27} +17.5981 q^{28} -1.00000 q^{29} +12.5639 q^{30} -3.16754 q^{31} -24.0632 q^{32} +12.7076 q^{33} -11.6996 q^{34} +4.74452 q^{35} +34.7922 q^{36} -2.66546 q^{37} -2.86404 q^{38} +8.18492 q^{39} -14.7512 q^{40} -5.89794 q^{41} +26.4322 q^{42} +7.87723 q^{43} -23.2781 q^{44} +9.38014 q^{45} -20.4631 q^{46} -6.32241 q^{47} -48.3059 q^{48} +2.98160 q^{49} +7.55201 q^{50} -12.9301 q^{51} -14.9933 q^{52} -4.55429 q^{53} +27.1588 q^{54} -6.27587 q^{55} -31.0339 q^{56} -3.16526 q^{57} +2.75139 q^{58} -3.32368 q^{59} -25.4355 q^{60} +3.46071 q^{61} +8.71513 q^{62} +19.7341 q^{63} +34.4350 q^{64} -4.04226 q^{65} -34.9635 q^{66} +6.24548 q^{67} +23.6856 q^{68} -22.6153 q^{69} -13.0540 q^{70} -0.152742 q^{71} -61.3554 q^{72} -2.04011 q^{73} +7.33372 q^{74} +8.34628 q^{75} +5.79819 q^{76} -13.2033 q^{77} -22.5199 q^{78} +0.923996 q^{79} +23.8567 q^{80} +11.2765 q^{81} +16.2275 q^{82} -10.8684 q^{83} -53.5116 q^{84} +6.38573 q^{85} -21.6733 q^{86} +3.04076 q^{87} +41.0504 q^{88} -8.30890 q^{89} -25.8084 q^{90} -8.50418 q^{91} +41.4272 q^{92} +9.63173 q^{93} +17.3954 q^{94} +1.56322 q^{95} +73.1705 q^{96} +14.9881 q^{97} -8.20354 q^{98} -26.1035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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