LMFDB - Embedded newform 8033.2.a.c.1.12

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:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-2.49784 q^{2} +3.18584 q^{3} +4.23922 q^{4} -0.569133 q^{5} -7.95772 q^{6} -1.98471 q^{7} -5.59321 q^{8} +7.14957 q^{9} +O(q^{10})$	\(q-2.49784 q^{2} +3.18584 q^{3} +4.23922 q^{4} -0.569133 q^{5} -7.95772 q^{6} -1.98471 q^{7} -5.59321 q^{8} +7.14957 q^{9} +1.42160 q^{10} -3.53354 q^{11} +13.5055 q^{12} +2.05553 q^{13} +4.95749 q^{14} -1.81317 q^{15} +5.49253 q^{16} +1.43703 q^{17} -17.8585 q^{18} +1.03608 q^{19} -2.41268 q^{20} -6.32296 q^{21} +8.82622 q^{22} -8.08488 q^{23} -17.8191 q^{24} -4.67609 q^{25} -5.13439 q^{26} +13.2199 q^{27} -8.41361 q^{28} +1.00000 q^{29} +4.52900 q^{30} -1.26648 q^{31} -2.53305 q^{32} -11.2573 q^{33} -3.58948 q^{34} +1.12956 q^{35} +30.3086 q^{36} +2.54580 q^{37} -2.58796 q^{38} +6.54859 q^{39} +3.18328 q^{40} +10.9466 q^{41} +15.7938 q^{42} -7.66181 q^{43} -14.9794 q^{44} -4.06906 q^{45} +20.1948 q^{46} +3.44535 q^{47} +17.4983 q^{48} -3.06094 q^{49} +11.6801 q^{50} +4.57815 q^{51} +8.71384 q^{52} +4.88572 q^{53} -33.0211 q^{54} +2.01105 q^{55} +11.1009 q^{56} +3.30078 q^{57} -2.49784 q^{58} +1.14006 q^{59} -7.68640 q^{60} -5.01342 q^{61} +3.16347 q^{62} -14.1898 q^{63} -4.65791 q^{64} -1.16987 q^{65} +28.1189 q^{66} +3.74888 q^{67} +6.09189 q^{68} -25.7571 q^{69} -2.82147 q^{70} +7.04983 q^{71} -39.9891 q^{72} -17.0037 q^{73} -6.35902 q^{74} -14.8973 q^{75} +4.39217 q^{76} +7.01304 q^{77} -16.3573 q^{78} -7.44154 q^{79} -3.12598 q^{80} +20.6676 q^{81} -27.3429 q^{82} +6.01330 q^{83} -26.8044 q^{84} -0.817862 q^{85} +19.1380 q^{86} +3.18584 q^{87} +19.7638 q^{88} +13.2715 q^{89} +10.1639 q^{90} -4.07963 q^{91} -34.2736 q^{92} -4.03481 q^{93} -8.60594 q^{94} -0.589667 q^{95} -8.06988 q^{96} -16.5999 q^{97} +7.64574 q^{98} -25.2633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.49784	−1.76624	−0.883121	−	0.469146i	$-0.844562\pi$
$2$	−2.49784	−1.76624	−0.883121	+	0.469146i	$0.844562\pi$
$3$	3.18584	1.83934	0.919672	−	0.392686i	$-0.128454\pi$
$3$	3.18584	1.83934	0.919672	+	0.392686i	$0.128454\pi$
$4$	4.23922	2.11961
$5$	−0.569133	−0.254524	−0.127262	−	0.991869i	$-0.540619\pi$
$5$	−0.569133	−0.254524	−0.127262	+	0.991869i	$0.540619\pi$
$6$	−7.95772	−3.24873
$7$	−1.98471	−0.750149	−0.375074	−	0.926995i	$-0.622383\pi$
$7$	−1.98471	−0.750149	−0.375074	+	0.926995i	$0.622383\pi$
$8$	−5.59321	−1.97750
$9$	7.14957	2.38319
$10$	1.42160	0.449551
$11$	−3.53354	−1.06540	−0.532701	−	0.846304i	$-0.678823\pi$
$11$	−3.53354	−1.06540	−0.532701	+	0.846304i	$0.678823\pi$
$12$	13.5055	3.89869
$13$	2.05553	0.570102	0.285051	−	0.958512i	$-0.407990\pi$
$13$	2.05553	0.570102	0.285051	+	0.958512i	$0.407990\pi$
$14$	4.95749	1.32494
$15$	−1.81317	−0.468157
$16$	5.49253	1.37313
$17$	1.43703	0.348531	0.174266	−	0.984699i	$-0.444245\pi$
$17$	1.43703	0.348531	0.174266	+	0.984699i	$0.444245\pi$
$18$	−17.8585	−4.20929
$19$	1.03608	0.237693	0.118846	−	0.992913i	$-0.462080\pi$
$19$	1.03608	0.237693	0.118846	+	0.992913i	$0.462080\pi$
$20$	−2.41268	−0.539491
$21$	−6.32296	−1.37978
$22$	8.82622	1.88176
$23$	−8.08488	−1.68581	−0.842907	−	0.538059i	$-0.819158\pi$
$23$	−8.08488	−1.68581	−0.842907	+	0.538059i	$0.819158\pi$
$24$	−17.8191	−3.63730
$25$	−4.67609	−0.935218
$26$	−5.13439	−1.00694
$27$	13.2199	2.54416
$28$	−8.41361	−1.59002
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	4.52900	0.826879
$31$	−1.26648	−0.227467	−0.113733	−	0.993511i	$-0.536281\pi$
$31$	−1.26648	−0.227467	−0.113733	+	0.993511i	$0.536281\pi$
$32$	−2.53305	−0.447783
$33$	−11.2573	−1.95964
$34$	−3.58948	−0.615591
$35$	1.12956	0.190931
$36$	30.3086	5.05143
$37$	2.54580	0.418528	0.209264	−	0.977859i	$-0.432893\pi$
$37$	2.54580	0.418528	0.209264	+	0.977859i	$0.432893\pi$
$38$	−2.58796	−0.419823
$39$	6.54859	1.04861
$40$	3.18328	0.503321
$41$	10.9466	1.70957	0.854787	−	0.518979i	$-0.173688\pi$
$41$	10.9466	1.70957	0.854787	+	0.518979i	$0.173688\pi$
$42$	15.7938	2.43703
$43$	−7.66181	−1.16841	−0.584207	−	0.811604i	$-0.698595\pi$
$43$	−7.66181	−1.16841	−0.584207	+	0.811604i	$0.698595\pi$
$44$	−14.9794	−2.25823
$45$	−4.06906	−0.606579
$46$	20.1948	2.97756
$47$	3.44535	0.502556	0.251278	−	0.967915i	$-0.419149\pi$
$47$	3.44535	0.502556	0.251278	+	0.967915i	$0.419149\pi$
$48$	17.4983	2.52566
$49$	−3.06094	−0.437277
$50$	11.6801	1.65182
$51$	4.57815	0.641070
$52$	8.71384	1.20839
$53$	4.88572	0.671105	0.335552	−	0.942022i	$-0.391077\pi$
$53$	4.88572	0.671105	0.335552	+	0.942022i	$0.391077\pi$
$54$	−33.0211	−4.49361
$55$	2.01105	0.271170
$56$	11.1009	1.48342
$57$	3.30078	0.437199
$58$	−2.49784	−0.327983
$59$	1.14006	0.148423	0.0742116	−	0.997243i	$-0.476356\pi$
$59$	1.14006	0.148423	0.0742116	+	0.997243i	$0.476356\pi$
$60$	−7.68640	−0.992310
$61$	−5.01342	−0.641903	−0.320951	−	0.947096i	$-0.604003\pi$
$61$	−5.01342	−0.641903	−0.320951	+	0.947096i	$0.604003\pi$
$62$	3.16347	0.401761
$63$	−14.1898	−1.78775
$64$	−4.65791	−0.582238
$65$	−1.16987	−0.145105
$66$	28.1189	3.46120
$67$	3.74888	0.457999	0.228999	−	0.973427i	$-0.426455\pi$
$67$	3.74888	0.457999	0.228999	+	0.973427i	$0.426455\pi$
$68$	6.09189	0.738750
$69$	−25.7571	−3.10080
$70$	−2.82147	−0.337230
$71$	7.04983	0.836661	0.418330	−	0.908295i	$-0.362615\pi$
$71$	7.04983	0.836661	0.418330	+	0.908295i	$0.362615\pi$
$72$	−39.9891	−4.71276
$73$	−17.0037	−1.99013	−0.995066	−	0.0992110i	$-0.968368\pi$
$73$	−17.0037	−1.99013	−0.995066	+	0.0992110i	$0.968368\pi$
$74$	−6.35902	−0.739221
$75$	−14.8973	−1.72019
$76$	4.39217	0.503816
$77$	7.01304	0.799210
$78$	−16.3573	−1.85210
$79$	−7.44154	−0.837238	−0.418619	−	0.908162i	$-0.637486\pi$
$79$	−7.44154	−0.837238	−0.418619	+	0.908162i	$0.637486\pi$
$80$	−3.12598	−0.349495
$81$	20.6676	2.29640
$82$	−27.3429	−3.01952
$83$	6.01330	0.660045	0.330023	−	0.943973i	$-0.392944\pi$
$83$	6.01330	0.660045	0.330023	+	0.943973i	$0.392944\pi$
$84$	−26.8044	−2.92460
$85$	−0.817862	−0.0887096
$86$	19.1380	2.06370
$87$	3.18584	0.341558
$88$	19.7638	2.10683
$89$	13.2715	1.40677	0.703386	−	0.710808i	$-0.251671\pi$
$89$	13.2715	1.40677	0.703386	+	0.710808i	$0.251671\pi$
$90$	10.1639	1.07136
$91$	−4.07963	−0.427661
$92$	−34.2736	−3.57327
$93$	−4.03481	−0.418390
$94$	−8.60594	−0.887635
$95$	−0.589667	−0.0604986
$96$	−8.06988	−0.823628
$97$	−16.5999	−1.68546	−0.842732	−	0.538334i	$-0.819054\pi$
$97$	−16.5999	−1.68546	−0.842732	+	0.538334i	$0.819054\pi$
$98$	7.64574	0.772336
$99$	−25.2633	−2.53905
$100$	−19.8230	−1.98230
$101$	−3.91737	−0.389793	−0.194897	−	0.980824i	$-0.562437\pi$
$101$	−3.91737	−0.389793	−0.194897	+	0.980824i	$0.562437\pi$
$102$	−11.4355	−1.13228
$103$	−18.3554	−1.80862	−0.904308	−	0.426880i	$-0.859613\pi$
$103$	−18.3554	−1.80862	−0.904308	+	0.426880i	$0.859613\pi$
$104$	−11.4970	−1.12738
$105$	3.59860	0.351188
$106$	−12.2038	−1.18533
$107$	−13.6211	−1.31680	−0.658400	−	0.752668i	$-0.728766\pi$
$107$	−13.6211	−1.31680	−0.658400	+	0.752668i	$0.728766\pi$
$108$	56.0419	5.39263
$109$	6.86379	0.657432	0.328716	−	0.944429i	$-0.393384\pi$
$109$	6.86379	0.657432	0.328716	+	0.944429i	$0.393384\pi$
$110$	−5.02329	−0.478952
$111$	8.11052	0.769817
$112$	−10.9011	−1.03005
$113$	−1.90752	−0.179445	−0.0897223	−	0.995967i	$-0.528598\pi$
$113$	−1.90752	−0.179445	−0.0897223	+	0.995967i	$0.528598\pi$
$114$	−8.24484	−0.772200
$115$	4.60137	0.429080
$116$	4.23922	0.393601
$117$	14.6962	1.35866
$118$	−2.84769	−0.262151
$119$	−2.85209	−0.261450
$120$	10.1414	0.925781
$121$	1.48588	0.135080
$122$	12.5227	1.13376
$123$	34.8742	3.14450
$124$	−5.36889	−0.482141
$125$	5.50698	0.492559
$126$	35.4439	3.15759
$127$	16.3148	1.44771	0.723854	−	0.689954i	$-0.242369\pi$
$127$	16.3148	1.44771	0.723854	+	0.689954i	$0.242369\pi$
$128$	16.7008	1.47616
$129$	−24.4093	−2.14912
$130$	2.92215	0.256290
$131$	−15.8108	−1.38139	−0.690696	−	0.723145i	$-0.742696\pi$
$131$	−15.8108	−1.38139	−0.690696	+	0.723145i	$0.742696\pi$
$132$	−47.7220	−4.15367
$133$	−2.05631	−0.178305
$134$	−9.36412	−0.808937
$135$	−7.52386	−0.647551
$136$	−8.03762	−0.689221
$137$	2.16173	0.184689	0.0923444	−	0.995727i	$-0.470564\pi$
$137$	2.16173	0.184689	0.0923444	+	0.995727i	$0.470564\pi$
$138$	64.3373	5.47675
$139$	0.559459	0.0474527	0.0237264	−	0.999718i	$-0.492447\pi$
$139$	0.559459	0.0474527	0.0237264	+	0.999718i	$0.492447\pi$
$140$	4.78846	0.404699
$141$	10.9763	0.924374
$142$	−17.6094	−1.47774
$143$	−7.26329	−0.607387
$144$	39.2692	3.27243
$145$	−0.569133	−0.0472639
$146$	42.4726	3.51505
$147$	−9.75165	−0.804303
$148$	10.7922	0.887115
$149$	−12.9211	−1.05853	−0.529267	−	0.848455i	$-0.677533\pi$
$149$	−12.9211	−1.05853	−0.529267	+	0.848455i	$0.677533\pi$
$150$	37.2110	3.03827
$151$	−1.64440	−0.133819	−0.0669096	−	0.997759i	$-0.521314\pi$
$151$	−1.64440	−0.133819	−0.0669096	+	0.997759i	$0.521314\pi$
$152$	−5.79501	−0.470038
$153$	10.2742	0.830617
$154$	−17.5175	−1.41160
$155$	0.720797	0.0578958
$156$	27.7609	2.22265
$157$	−5.01433	−0.400187	−0.200093	−	0.979777i	$-0.564125\pi$
$157$	−5.01433	−0.400187	−0.200093	+	0.979777i	$0.564125\pi$
$158$	18.5878	1.47877
$159$	15.5651	1.23439
$160$	1.44164	0.113972
$161$	16.0461	1.26461
$162$	−51.6245	−4.05600
$163$	17.2789	1.35339	0.676694	−	0.736265i	$-0.263412\pi$
$163$	17.2789	1.35339	0.676694	+	0.736265i	$0.263412\pi$
$164$	46.4051	3.62363
$165$	6.40689	0.498775
$166$	−15.0203	−1.16580
$167$	−17.2679	−1.33623	−0.668114	−	0.744059i	$-0.732898\pi$
$167$	−17.2679	−1.33623	−0.668114	+	0.744059i	$0.732898\pi$
$168$	35.3656	2.72852
$169$	−8.77479	−0.674984
$170$	2.04289	0.156683
$171$	7.40752	0.566468
$172$	−32.4801	−2.47658
$173$	−13.5985	−1.03388	−0.516938	−	0.856023i	$-0.672928\pi$
$173$	−13.5985	−1.03388	−0.516938	+	0.856023i	$0.672928\pi$
$174$	−7.95772	−0.603273
$175$	9.28067	0.701552
$176$	−19.4080	−1.46294
$177$	3.63205	0.273001
$178$	−33.1500	−2.48470
$179$	0.00409165	0.000305825 0	0.000152912	−	1.00000i	$-0.499951\pi$
$179$	0.00409165	0.000305825 0	0.000152912		1.00000i	$0.499951\pi$
$180$	−17.2496	−1.28571
$181$	−9.49092	−0.705455	−0.352727	−	0.935726i	$-0.614746\pi$
$181$	−9.49092	−0.705455	−0.352727	+	0.935726i	$0.614746\pi$
$182$	10.1903	0.755353
$183$	−15.9720	−1.18068
$184$	45.2205	3.33370
$185$	−1.44890	−0.106525
$186$	10.0783	0.738978
$187$	−5.07780	−0.371326
$188$	14.6056	1.06522
$189$	−26.2376	−1.90850
$190$	1.47290	0.106855
$191$	24.4653	1.77025	0.885125	−	0.465353i	$-0.154073\pi$
$191$	24.4653	1.77025	0.885125	+	0.465353i	$0.154073\pi$
$192$	−14.8393	−1.07094
$193$	1.48092	0.106599	0.0532995	−	0.998579i	$-0.483026\pi$
$193$	1.48092	0.106599	0.0532995	+	0.998579i	$0.483026\pi$
$194$	41.4639	2.97693
$195$	−3.72702	−0.266897
$196$	−12.9760	−0.926855
$197$	−8.68494	−0.618776	−0.309388	−	0.950936i	$-0.600124\pi$
$197$	−8.68494	−0.618776	−0.309388	+	0.950936i	$0.600124\pi$
$198$	63.1037	4.48458
$199$	−5.85888	−0.415325	−0.207662	−	0.978201i	$-0.566586\pi$
$199$	−5.85888	−0.415325	−0.207662	+	0.978201i	$0.566586\pi$
$200$	26.1543	1.84939
$201$	11.9433	0.842418
$202$	9.78498	0.688469
$203$	−1.98471	−0.139299
$204$	19.4078	1.35882
$205$	−6.23008	−0.435128
$206$	45.8490	3.19445
$207$	−57.8034	−4.01762
$208$	11.2901	0.782825
$209$	−3.66103	−0.253238
$210$	−8.98874	−0.620282
$211$	1.06169	0.0730900	0.0365450	−	0.999332i	$-0.488365\pi$
$211$	1.06169	0.0730900	0.0365450	+	0.999332i	$0.488365\pi$
$212$	20.7116	1.42248
$213$	22.4596	1.53891
$214$	34.0233	2.32579
$215$	4.36059	0.297390
$216$	−73.9415	−5.03108
$217$	2.51360	0.170634
$218$	−17.1447	−1.16118
$219$	−54.1711	−3.66054
$220$	8.52529	0.574775
$221$	2.95386	0.198698
$222$	−20.2588	−1.35968
$223$	1.97111	0.131995	0.0659976	−	0.997820i	$-0.478977\pi$
$223$	1.97111	0.131995	0.0659976	+	0.997820i	$0.478977\pi$
$224$	5.02735	0.335904
$225$	−33.4320	−2.22880
$226$	4.76469	0.316943
$227$	−3.47107	−0.230383	−0.115192	−	0.993343i	$-0.536748\pi$
$227$	−3.47107	−0.230383	−0.115192	+	0.993343i	$0.536748\pi$
$228$	13.9927	0.926692
$229$	−23.3880	−1.54552	−0.772762	−	0.634696i	$-0.781125\pi$
$229$	−23.3880	−1.54552	−0.772762	+	0.634696i	$0.781125\pi$
$230$	−11.4935	−0.757859
$231$	22.3424	1.47002
$232$	−5.59321	−0.367212
$233$	0.774937	0.0507678	0.0253839	−	0.999678i	$-0.491919\pi$
$233$	0.774937	0.0507678	0.0253839	+	0.999678i	$0.491919\pi$
$234$	−36.7087	−2.39972
$235$	−1.96086	−0.127913
$236$	4.83296	0.314599
$237$	−23.7075	−1.53997
$238$	7.12407	0.461785
$239$	20.4659	1.32383	0.661915	−	0.749579i	$-0.269744\pi$
$239$	20.4659	1.32383	0.661915	+	0.749579i	$0.269744\pi$
$240$	−9.95886	−0.642842
$241$	−21.8378	−1.40669	−0.703347	−	0.710846i	$-0.748312\pi$
$241$	−21.8378	−1.40669	−0.703347	+	0.710846i	$0.748312\pi$
$242$	−3.71149	−0.238584
$243$	26.1842	1.67972
$244$	−21.2530	−1.36058
$245$	1.74208	0.111297
$246$	−87.1101	−5.55394
$247$	2.12969	0.135509
$248$	7.08370	0.449816
$249$	19.1574	1.21405
$250$	−13.7556	−0.869979
$251$	−5.20479	−0.328524	−0.164262	−	0.986417i	$-0.552524\pi$
$251$	−5.20479	−0.328524	−0.164262	+	0.986417i	$0.552524\pi$
$252$	−60.1537	−3.78932
$253$	28.5682	1.79607
$254$	−40.7519	−2.55700
$255$	−2.60558	−0.163168
$256$	−32.4002	−2.02501
$257$	15.6122	0.973861	0.486930	−	0.873441i	$-0.338117\pi$
$257$	15.6122	0.973861	0.486930	+	0.873441i	$0.338117\pi$
$258$	60.9706	3.79586
$259$	−5.05268	−0.313958
$260$	−4.95933	−0.307565
$261$	7.14957	0.442547
$262$	39.4928	2.43987
$263$	−20.5038	−1.26432	−0.632161	−	0.774837i	$-0.717832\pi$
$263$	−20.5038	−1.26432	−0.632161	+	0.774837i	$0.717832\pi$
$264$	62.9643	3.87519
$265$	−2.78062	−0.170812
$266$	5.13635	0.314930
$267$	42.2807	2.58754
$268$	15.8923	0.970778
$269$	20.8380	1.27051	0.635257	−	0.772300i	$-0.280894\pi$
$269$	20.8380	1.27051	0.635257	+	0.772300i	$0.280894\pi$
$270$	18.7934	1.14373
$271$	−6.01303	−0.365266	−0.182633	−	0.983181i	$-0.558462\pi$
$271$	−6.01303	−0.365266	−0.182633	+	0.983181i	$0.558462\pi$
$272$	7.89294	0.478580
$273$	−12.9970	−0.786616
$274$	−5.39965	−0.326205
$275$	16.5231	0.996382
$276$	−109.190	−6.57247
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−1.39744	−0.0838130
$279$	−9.05480	−0.542097
$280$	−6.31788	−0.377566
$281$	−15.0999	−0.900783	−0.450392	−	0.892831i	$-0.648716\pi$
$281$	−15.0999	−0.900783	−0.450392	+	0.892831i	$0.648716\pi$
$282$	−27.4171	−1.63267
$283$	−2.58613	−0.153729	−0.0768647	−	0.997042i	$-0.524491\pi$
$283$	−2.58613	−0.153729	−0.0768647	+	0.997042i	$0.524491\pi$
$284$	29.8858	1.77339
$285$	−1.87858	−0.111278
$286$	18.1426	1.07279
$287$	−21.7258	−1.28243
$288$	−18.1102	−1.06715
$289$	−14.9349	−0.878526
$290$	1.42160	0.0834795
$291$	−52.8846	−3.10015
$292$	−72.0824	−4.21830
$293$	−29.1762	−1.70449	−0.852247	−	0.523140i	$-0.824761\pi$
$293$	−29.1762	−1.70449	−0.852247	+	0.523140i	$0.824761\pi$
$294$	24.3581	1.42059
$295$	−0.648845	−0.0377772
$296$	−14.2392	−0.827638
$297$	−46.7129	−2.71056
$298$	32.2748	1.86963
$299$	−16.6187	−0.961086
$300$	−63.1527	−3.64612
$301$	15.2064	0.876485
$302$	4.10745	0.236357
$303$	−12.4801	−0.716964
$304$	5.69070	0.326384
$305$	2.85330	0.163380
$306$	−25.6632	−1.46707
$307$	−4.84709	−0.276638	−0.138319	−	0.990388i	$-0.544170\pi$
$307$	−4.84709	−0.276638	−0.138319	+	0.990388i	$0.544170\pi$
$308$	29.7298	1.69401
$309$	−58.4775	−3.32667
$310$	−1.80044	−0.102258
$311$	−18.2793	−1.03652	−0.518262	−	0.855222i	$-0.673421\pi$
$311$	−18.2793	−1.03652	−0.518262	+	0.855222i	$0.673421\pi$
$312$	−36.6277	−2.07363
$313$	−0.422197	−0.0238640	−0.0119320	−	0.999929i	$-0.503798\pi$
$313$	−0.422197	−0.0238640	−0.0119320	+	0.999929i	$0.503798\pi$
$314$	12.5250	0.706826
$315$	8.07588	0.455025
$316$	−31.5463	−1.77462
$317$	−2.67503	−0.150245	−0.0751224	−	0.997174i	$-0.523935\pi$
$317$	−2.67503	−0.150245	−0.0751224	+	0.997174i	$0.523935\pi$
$318$	−38.8792	−2.18024
$319$	−3.53354	−0.197840
$320$	2.65097	0.148194
$321$	−43.3946	−2.42205
$322$	−40.0807	−2.23361
$323$	1.48888	0.0828435
$324$	87.6146	4.86748
$325$	−9.61184	−0.533169
$326$	−43.1600	−2.39041
$327$	21.8669	1.20924
$328$	−61.2267	−3.38068
$329$	−6.83801	−0.376992
$330$	−16.0034	−0.880958
$331$	13.8780	0.762801	0.381401	−	0.924410i	$-0.375442\pi$
$331$	13.8780	0.762801	0.381401	+	0.924410i	$0.375442\pi$
$332$	25.4917	1.39904
$333$	18.2014	0.997431
$334$	43.1324	2.36010
$335$	−2.13361	−0.116572
$336$	−34.7290	−1.89462
$337$	−17.1454	−0.933968	−0.466984	−	0.884266i	$-0.654659\pi$
$337$	−17.1454	−0.933968	−0.466984	+	0.884266i	$0.654659\pi$
$338$	21.9180	1.19218
$339$	−6.07706	−0.330061
$340$	−3.46710	−0.188030
$341$	4.47516	0.242344
$342$	−18.5028	−1.00052
$343$	19.9680	1.07817
$344$	42.8541	2.31054
$345$	14.6592	0.789227
$346$	33.9669	1.82607
$347$	−2.11466	−0.113521	−0.0567604	−	0.998388i	$-0.518077\pi$
$347$	−2.11466	−0.113521	−0.0567604	+	0.998388i	$0.518077\pi$
$348$	13.5055	0.723969
$349$	−11.7867	−0.630930	−0.315465	−	0.948937i	$-0.602160\pi$
$349$	−11.7867	−0.630930	−0.315465	+	0.948937i	$0.602160\pi$
$350$	−23.1816	−1.23911
$351$	27.1738	1.45043
$352$	8.95061	0.477069
$353$	13.1500	0.699903	0.349952	−	0.936768i	$-0.386198\pi$
$353$	13.1500	0.699903	0.349952	+	0.936768i	$0.386198\pi$
$354$	−9.07228	−0.482186
$355$	−4.01229	−0.212950
$356$	56.2606	2.98181
$357$	−9.08629	−0.480898
$358$	−0.0102203	−0.000540160 0
$359$	−24.0814	−1.27097	−0.635485	−	0.772113i	$-0.719200\pi$
$359$	−24.0814	−1.27097	−0.635485	+	0.772113i	$0.719200\pi$
$360$	22.7591	1.19951
$361$	−17.9265	−0.943502
$362$	23.7068	1.24600
$363$	4.73377	0.248458
$364$	−17.2944	−0.906474
$365$	9.67737	0.506537
$366$	39.8954	2.08537
$367$	−31.8300	−1.66151	−0.830756	−	0.556637i	$-0.812092\pi$
$367$	−31.8300	−1.66151	−0.830756	+	0.556637i	$0.812092\pi$
$368$	−44.4065	−2.31485
$369$	78.2636	4.07424
$370$	3.61913	0.188149
$371$	−9.69672	−0.503428
$372$	−17.1044	−0.886823
$373$	24.5920	1.27333	0.636663	−	0.771142i	$-0.280314\pi$
$373$	24.5920	1.27333	0.636663	+	0.771142i	$0.280314\pi$
$374$	12.6836	0.655851
$375$	17.5444	0.905986
$376$	−19.2706	−0.993804
$377$	2.05553	0.105865
$378$	65.5373	3.37087
$379$	28.4709	1.46245	0.731227	−	0.682134i	$-0.238948\pi$
$379$	28.4709	1.46245	0.731227	+	0.682134i	$0.238948\pi$
$380$	−2.49973	−0.128233
$381$	51.9764	2.66283
$382$	−61.1106	−3.12669
$383$	−22.2197	−1.13538	−0.567688	−	0.823244i	$-0.692162\pi$
$383$	−22.2197	−1.13538	−0.567688	+	0.823244i	$0.692162\pi$
$384$	53.2061	2.71516
$385$	−3.99135	−0.203418
$386$	−3.69911	−0.188280
$387$	−54.7786	−2.78455
$388$	−70.3705	−3.57252
$389$	−8.64947	−0.438546	−0.219273	−	0.975664i	$-0.570368\pi$
$389$	−8.64947	−0.438546	−0.219273	+	0.975664i	$0.570368\pi$
$390$	9.30951	0.471405
$391$	−11.6182	−0.587559
$392$	17.1205	0.864714
$393$	−50.3705	−2.54086
$394$	21.6936	1.09291
$395$	4.23522	0.213097
$396$	−107.096	−5.38180
$397$	9.00910	0.452154	0.226077	−	0.974109i	$-0.427410\pi$
$397$	9.00910	0.452154	0.226077	+	0.974109i	$0.427410\pi$
$398$	14.6346	0.733564
$399$	−6.55109	−0.327965
$400$	−25.6835	−1.28418
$401$	30.8227	1.53921	0.769606	−	0.638519i	$-0.220453\pi$
$401$	30.8227	1.53921	0.769606	+	0.638519i	$0.220453\pi$
$402$	−29.8326	−1.48791
$403$	−2.60329	−0.129679
$404$	−16.6066	−0.826209
$405$	−11.7626	−0.584490
$406$	4.95749	0.246036
$407$	−8.99569	−0.445900
$408$	−25.6066	−1.26771
$409$	19.4596	0.962215	0.481108	−	0.876662i	$-0.340235\pi$
$409$	19.4596	0.962215	0.481108	+	0.876662i	$0.340235\pi$
$410$	15.5618	0.768540
$411$	6.88691	0.339706
$412$	−77.8127	−3.83356
$413$	−2.26268	−0.111339
$414$	144.384	7.09608
$415$	−3.42236	−0.167997
$416$	−5.20675	−0.255282
$417$	1.78235	0.0872819
$418$	9.14466	0.447280
$419$	−0.167858	−0.00820038	−0.00410019	−	0.999992i	$-0.501305\pi$
$419$	−0.167858	−0.00820038	−0.00410019	+	0.999992i	$0.501305\pi$
$420$	15.2553	0.744381
$421$	2.95486	0.144011	0.0720055	−	0.997404i	$-0.477060\pi$
$421$	2.95486	0.144011	0.0720055	+	0.997404i	$0.477060\pi$
$422$	−2.65194	−0.129095
$423$	24.6328	1.19769
$424$	−27.3268	−1.32711
$425$	−6.71969	−0.325953
$426$	−56.1006	−2.71808
$427$	9.95017	0.481523
$428$	−57.7427	−2.79110
$429$	−23.1397	−1.11719
$430$	−10.8921	−0.525262
$431$	−28.9051	−1.39231	−0.696154	−	0.717892i	$-0.745107\pi$
$431$	−28.9051	−1.39231	−0.696154	+	0.717892i	$0.745107\pi$
$432$	72.6105	3.49347
$433$	0.841027	0.0404172	0.0202086	−	0.999796i	$-0.493567\pi$
$433$	0.841027	0.0404172	0.0202086	+	0.999796i	$0.493567\pi$
$434$	−6.27857	−0.301381
$435$	−1.81317	−0.0869346
$436$	29.0971	1.39350
$437$	−8.37659	−0.400706
$438$	135.311	6.46540
$439$	−24.2839	−1.15901	−0.579503	−	0.814970i	$-0.696753\pi$
$439$	−24.2839	−1.15901	−0.579503	+	0.814970i	$0.696753\pi$
$440$	−11.2482	−0.536239
$441$	−21.8844	−1.04211
$442$	−7.37829	−0.350949
$443$	−22.8157	−1.08401	−0.542003	−	0.840377i	$-0.682334\pi$
$443$	−22.8157	−1.08401	−0.542003	+	0.840377i	$0.682334\pi$
$444$	34.3823	1.63171
$445$	−7.55323	−0.358057
$446$	−4.92352	−0.233135
$447$	−41.1644	−1.94701
$448$	9.24458	0.436765
$449$	37.9002	1.78862	0.894309	−	0.447449i	$-0.147667\pi$
$449$	37.9002	1.78862	0.894309	+	0.447449i	$0.147667\pi$
$450$	83.5079	3.93660
$451$	−38.6803	−1.82138
$452$	−8.08640	−0.380352
$453$	−5.23878	−0.246140
$454$	8.67019	0.406912
$455$	2.32185	0.108850
$456$	−18.4620	−0.864561
$457$	1.98596	0.0928992	0.0464496	−	0.998921i	$-0.485209\pi$
$457$	1.98596	0.0928992	0.0464496	+	0.998921i	$0.485209\pi$
$458$	58.4196	2.72977
$459$	18.9974	0.886721
$460$	19.5062	0.909482
$461$	−28.2330	−1.31494	−0.657472	−	0.753479i	$-0.728374\pi$
$461$	−28.2330	−1.31494	−0.657472	+	0.753479i	$0.728374\pi$
$462$	−55.8078	−2.59641
$463$	8.79709	0.408835	0.204418	−	0.978884i	$-0.434470\pi$
$463$	8.79709	0.408835	0.204418	+	0.978884i	$0.434470\pi$
$464$	5.49253	0.254984
$465$	2.29634	0.106490
$466$	−1.93567	−0.0896682
$467$	21.0625	0.974656	0.487328	−	0.873219i	$-0.337972\pi$
$467$	21.0625	0.974656	0.487328	+	0.873219i	$0.337972\pi$
$468$	62.3002	2.87983
$469$	−7.44043	−0.343567
$470$	4.89792	0.225924
$471$	−15.9748	−0.736081
$472$	−6.37659	−0.293507
$473$	27.0733	1.24483
$474$	59.2177	2.71996
$475$	−4.84480	−0.222295
$476$	−12.0906	−0.554173
$477$	34.9308	1.59937
$478$	−51.1206	−2.33820
$479$	−9.69887	−0.443153	−0.221576	−	0.975143i	$-0.571120\pi$
$479$	−9.69887	−0.443153	−0.221576	+	0.975143i	$0.571120\pi$
$480$	4.59283	0.209633
$481$	5.23298	0.238603
$482$	54.5473	2.48456
$483$	51.1204	2.32606
$484$	6.29896	0.286316
$485$	9.44754	0.428991
$486$	−65.4040	−2.96678
$487$	30.8029	1.39581	0.697906	−	0.716189i	$-0.254115\pi$
$487$	30.8029	1.39581	0.697906	+	0.716189i	$0.254115\pi$
$488$	28.0411	1.26936
$489$	55.0478	2.48935
$490$	−4.35144	−0.196578
$491$	3.11471	0.140565	0.0702824	−	0.997527i	$-0.477610\pi$
$491$	3.11471	0.140565	0.0702824	+	0.997527i	$0.477610\pi$
$492$	147.839	6.66510
$493$	1.43703	0.0647207
$494$	−5.31964	−0.239342
$495$	14.3782	0.646250
$496$	−6.95619	−0.312342
$497$	−13.9918	−0.627620
$498$	−47.8522	−2.14431
$499$	24.6129	1.10182	0.550911	−	0.834564i	$-0.314280\pi$
$499$	24.6129	1.10182	0.550911	+	0.834564i	$0.314280\pi$
$500$	23.3453	1.04403
$501$	−55.0127	−2.45778
$502$	13.0008	0.580252
$503$	−32.2647	−1.43861	−0.719305	−	0.694694i	$-0.755540\pi$
$503$	−32.2647	−1.43861	−0.719305	+	0.694694i	$0.755540\pi$
$504$	79.3666	3.53527
$505$	2.22951	0.0992117
$506$	−71.3589	−3.17229
$507$	−27.9551	−1.24153
$508$	69.1621	3.06857
$509$	−13.4396	−0.595699	−0.297849	−	0.954613i	$-0.596269\pi$
$509$	−13.4396	−0.595699	−0.297849	+	0.954613i	$0.596269\pi$
$510$	6.50832	0.288193
$511$	33.7474	1.49290
$512$	47.5289	2.10050
$513$	13.6968	0.604730
$514$	−38.9968	−1.72007
$515$	10.4467	0.460336
$516$	−103.476	−4.55529
$517$	−12.1743	−0.535424
$518$	12.6208	0.554526
$519$	−43.3227	−1.90165
$520$	6.54333	0.286944
$521$	40.0225	1.75342	0.876709	−	0.481021i	$-0.159734\pi$
$521$	40.0225	1.75342	0.876709	+	0.481021i	$0.159734\pi$
$522$	−17.8585	−0.781645
$523$	28.6453	1.25257	0.626286	−	0.779594i	$-0.284574\pi$
$523$	28.6453	1.25257	0.626286	+	0.779594i	$0.284574\pi$
$524$	−67.0252	−2.92801
$525$	29.5667	1.29040
$526$	51.2154	2.23310
$527$	−1.81998	−0.0792794
$528$	−61.8309	−2.69084
$529$	42.3654	1.84197
$530$	6.94556	0.301696
$531$	8.15094	0.353720
$532$	−8.71717	−0.377937
$533$	22.5011	0.974631
$534$	−105.611	−4.57022
$535$	7.75221	0.335157
$536$	−20.9683	−0.905692
$537$	0.0130354	0.000562517 0
$538$	−52.0500	−2.24404
$539$	10.8159	0.465875
$540$	−31.8953	−1.37255
$541$	21.0491	0.904970	0.452485	−	0.891772i	$-0.350538\pi$
$541$	21.0491	0.904970	0.452485	+	0.891772i	$0.350538\pi$
$542$	15.0196	0.645148
$543$	−30.2366	−1.29757
$544$	−3.64007	−0.156067
$545$	−3.90641	−0.167332
$546$	32.4645	1.38935
$547$	−0.674947	−0.0288587	−0.0144293	−	0.999896i	$-0.504593\pi$
$547$	−0.674947	−0.0288587	−0.0144293	+	0.999896i	$0.504593\pi$
$548$	9.16403	0.391468
$549$	−35.8438	−1.52978
$550$	−41.2722	−1.75985
$551$	1.03608	0.0441385
$552$	144.065	6.13182
$553$	14.7693	0.628053
$554$	−2.49784	−0.106123
$555$	−4.61597	−0.195937
$556$	2.37167	0.100581
$557$	−15.7839	−0.668787	−0.334393	−	0.942434i	$-0.608531\pi$
$557$	−15.7839	−0.668787	−0.334393	+	0.942434i	$0.608531\pi$
$558$	22.6175	0.957474
$559$	−15.7491	−0.666115
$560$	6.20415	0.262173
$561$	−16.1771	−0.682996
$562$	37.7171	1.59100
$563$	18.5811	0.783100	0.391550	−	0.920157i	$-0.371939\pi$
$563$	18.5811	0.783100	0.391550	+	0.920157i	$0.371939\pi$
$564$	46.5310	1.95931
$565$	1.08563	0.0456730
$566$	6.45974	0.271523
$567$	−41.0192	−1.72265
$568$	−39.4312	−1.65450
$569$	−7.31841	−0.306804	−0.153402	−	0.988164i	$-0.549023\pi$
$569$	−7.31841	−0.306804	−0.153402	+	0.988164i	$0.549023\pi$
$570$	4.69241	0.196543
$571$	0.0881010	0.00368691	0.00184346	−	0.999998i	$-0.499413\pi$
$571$	0.0881010	0.00368691	0.00184346	+	0.999998i	$0.499413\pi$
$572$	−30.7907	−1.28742
$573$	77.9426	3.25610
$574$	54.2677	2.26509
$575$	37.8056	1.57660
$576$	−33.3020	−1.38758
$577$	26.1304	1.08782	0.543911	−	0.839143i	$-0.316943\pi$
$577$	26.1304	1.08782	0.543911	+	0.839143i	$0.316943\pi$
$578$	37.3051	1.55169
$579$	4.71798	0.196072
$580$	−2.41268	−0.100181
$581$	−11.9346	−0.495132
$582$	132.097	5.47561
$583$	−17.2639	−0.714996
$584$	95.1053	3.93549
$585$	−8.36407	−0.345812
$586$	72.8776	3.01055
$587$	1.63199	0.0673594	0.0336797	−	0.999433i	$-0.489277\pi$
$587$	1.63199	0.0673594	0.0336797	+	0.999433i	$0.489277\pi$
$588$	−41.3394	−1.70481
$589$	−1.31218	−0.0540673
$590$	1.62071	0.0667237
$591$	−27.6688	−1.13814
$592$	13.9829	0.574694
$593$	−5.32599	−0.218712	−0.109356	−	0.994003i	$-0.534879\pi$
$593$	−5.32599	−0.218712	−0.109356	+	0.994003i	$0.534879\pi$
$594$	116.681	4.78749
$595$	1.62322	0.0665454
$596$	−54.7752	−2.24368
$597$	−18.6654	−0.763926
$598$	41.5110	1.69751
$599$	−34.6747	−1.41677	−0.708384	−	0.705827i	$-0.750576\pi$
$599$	−34.6747	−1.41677	−0.708384	+	0.705827i	$0.750576\pi$
$600$	83.3235	3.40167
$601$	14.9146	0.608381	0.304191	−	0.952611i	$-0.401614\pi$
$601$	14.9146	0.608381	0.304191	+	0.952611i	$0.401614\pi$
$602$	−37.9833	−1.54808
$603$	26.8029	1.09150
$604$	−6.97096	−0.283644
$605$	−0.845662	−0.0343811
$606$	31.1734	1.26633
$607$	−3.78511	−0.153633	−0.0768165	−	0.997045i	$-0.524476\pi$
$607$	−3.78511	−0.153633	−0.0768165	+	0.997045i	$0.524476\pi$
$608$	−2.62444	−0.106435
$609$	−6.32296	−0.256219
$610$	−7.12710	−0.288568
$611$	7.08202	0.286508
$612$	43.5544	1.76058
$613$	−45.2591	−1.82800	−0.913999	−	0.405717i	$-0.867022\pi$
$613$	−45.2591	−1.82800	−0.913999	+	0.405717i	$0.867022\pi$
$614$	12.1073	0.488610
$615$	−19.8480	−0.800350
$616$	−39.2254	−1.58044
$617$	25.0906	1.01011	0.505055	−	0.863087i	$-0.331472\pi$
$617$	25.0906	1.01011	0.505055	+	0.863087i	$0.331472\pi$
$618$	146.068	5.87570
$619$	−44.8431	−1.80240	−0.901198	−	0.433408i	$-0.857311\pi$
$619$	−44.8431	−1.80240	−0.901198	+	0.433408i	$0.857311\pi$
$620$	3.05561	0.122716
$621$	−106.881	−4.28899
$622$	45.6588	1.83075
$623$	−26.3400	−1.05529
$624$	35.9683	1.43989
$625$	20.2462	0.809849
$626$	1.05458	0.0421495
$627$	−11.6634	−0.465793
$628$	−21.2568	−0.848239
$629$	3.65840	0.145870
$630$	−20.1723	−0.803683
$631$	44.2642	1.76213	0.881064	−	0.472997i	$-0.156828\pi$
$631$	44.2642	1.76213	0.881064	+	0.472997i	$0.156828\pi$
$632$	41.6221	1.65564
$633$	3.38238	0.134438
$634$	6.68181	0.265369
$635$	−9.28531	−0.368476
$636$	65.9839	2.61643
$637$	−6.29185	−0.249292
$638$	8.82622	0.349433
$639$	50.4032	1.99392
$640$	−9.50498	−0.375717
$641$	38.1151	1.50546	0.752728	−	0.658332i	$-0.228738\pi$
$641$	38.1151	1.50546	0.752728	+	0.658332i	$0.228738\pi$
$642$	108.393	4.27792
$643$	−24.3567	−0.960533	−0.480267	−	0.877123i	$-0.659460\pi$
$643$	−24.3567	−0.960533	−0.480267	+	0.877123i	$0.659460\pi$
$644$	68.0230	2.68048
$645$	13.8921	0.547002
$646$	−3.71899	−0.146322
$647$	−48.4088	−1.90315	−0.951573	−	0.307422i	$-0.900534\pi$
$647$	−48.4088	−1.90315	−0.951573	+	0.307422i	$0.900534\pi$
$648$	−115.598	−4.54114
$649$	−4.02844	−0.158130
$650$	24.0089	0.941705
$651$	8.00791	0.313855
$652$	73.2490	2.86865
$653$	−10.5626	−0.413346	−0.206673	−	0.978410i	$-0.566264\pi$
$653$	−10.5626	−0.413346	−0.206673	+	0.978410i	$0.566264\pi$
$654$	−54.6201	−2.13582
$655$	8.99842	0.351597
$656$	60.1246	2.34747
$657$	−121.569	−4.74286
$658$	17.0803	0.665858
$659$	44.2129	1.72229	0.861144	−	0.508361i	$-0.169748\pi$
$659$	44.2129	1.72229	0.861144	+	0.508361i	$0.169748\pi$
$660$	27.1602	1.05721
$661$	8.90088	0.346204	0.173102	−	0.984904i	$-0.444621\pi$
$661$	8.90088	0.346204	0.173102	+	0.984904i	$0.444621\pi$
$662$	−34.6649	−1.34729
$663$	9.41053	0.365475
$664$	−33.6336	−1.30524
$665$	1.17032	0.0453829
$666$	−45.4643	−1.76170
$667$	−8.08488	−0.313048
$668$	−73.2023	−2.83228
$669$	6.27963	0.242785
$670$	5.32943	0.205894
$671$	17.7151	0.683884
$672$	16.0163	0.617844
$673$	27.0052	1.04097	0.520487	−	0.853869i	$-0.325750\pi$
$673$	27.0052	1.04097	0.520487	+	0.853869i	$0.325750\pi$
$674$	42.8264	1.64961
$675$	−61.8172	−2.37935
$676$	−37.1983	−1.43070
$677$	10.7444	0.412942	0.206471	−	0.978453i	$-0.433802\pi$
$677$	10.7444	0.412942	0.206471	+	0.978453i	$0.433802\pi$
$678$	15.1795	0.582967
$679$	32.9459	1.26435
$680$	4.57448	0.175423
$681$	−11.0583	−0.423754
$682$	−11.1782	−0.428037
$683$	−10.9036	−0.417216	−0.208608	−	0.977999i	$-0.566893\pi$
$683$	−10.9036	−0.417216	−0.208608	+	0.977999i	$0.566893\pi$
$684$	31.4021	1.20069
$685$	−1.23031	−0.0470077
$686$	−49.8770	−1.90431
$687$	−74.5105	−2.84275
$688$	−42.0827	−1.60439
$689$	10.0427	0.382598
$690$	−36.6165	−1.39396
$691$	−38.1309	−1.45057	−0.725284	−	0.688450i	$-0.758292\pi$
$691$	−38.1309	−1.45057	−0.725284	+	0.688450i	$0.758292\pi$
$692$	−57.6470	−2.19141
$693$	50.1402	1.90467
$694$	5.28208	0.200505
$695$	−0.318407	−0.0120779
$696$	−17.8191	−0.675430
$697$	15.7306	0.595840
$698$	29.4414	1.11437
$699$	2.46883	0.0933795
$700$	39.3428	1.48702
$701$	−7.33146	−0.276905	−0.138453	−	0.990369i	$-0.544213\pi$
$701$	−7.33146	−0.276905	−0.138453	+	0.990369i	$0.544213\pi$
$702$	−67.8760	−2.56181
$703$	2.63766	0.0994811
$704$	16.4589	0.620317
$705$	−6.24699	−0.235275
$706$	−32.8466	−1.23620
$707$	7.77484	0.292403
$708$	15.3970	0.578656
$709$	−2.49331	−0.0936382	−0.0468191	−	0.998903i	$-0.514908\pi$
$709$	−2.49331	−0.0936382	−0.0468191	+	0.998903i	$0.514908\pi$
$710$	10.0221	0.376122
$711$	−53.2038	−1.99530
$712$	−74.2301	−2.78189
$713$	10.2394	0.383467
$714$	22.6961	0.849381
$715$	4.13378	0.154595
$716$	0.0173454	0.000648228 0
$717$	65.2011	2.43498
$718$	60.1517	2.24484
$719$	−19.2448	−0.717709	−0.358855	−	0.933393i	$-0.616833\pi$
$719$	−19.2448	−0.717709	−0.358855	+	0.933393i	$0.616833\pi$
$720$	−22.3494	−0.832913
$721$	36.4302	1.35673
$722$	44.7777	1.66645
$723$	−69.5716	−2.58740
$724$	−40.2341	−1.49529
$725$	−4.67609	−0.173666
$726$	−11.8242	−0.438838
$727$	29.7010	1.10155	0.550775	−	0.834654i	$-0.314332\pi$
$727$	29.7010	1.10155	0.550775	+	0.834654i	$0.314332\pi$
$728$	22.8182	0.845699
$729$	21.4157	0.793174
$730$	−24.1725	−0.894666
$731$	−11.0103	−0.407229
$732$	−67.7086	−2.50258
$733$	−22.6074	−0.835022	−0.417511	−	0.908672i	$-0.637098\pi$
$733$	−22.6074	−0.835022	−0.417511	+	0.908672i	$0.637098\pi$
$734$	79.5063	2.93463
$735$	5.54999	0.204714
$736$	20.4794	0.754880
$737$	−13.2468	−0.487953
$738$	−195.490	−7.19609
$739$	−52.2573	−1.92231	−0.961157	−	0.276001i	$-0.910991\pi$
$739$	−52.2573	−1.92231	−0.961157	+	0.276001i	$0.910991\pi$
$740$	−6.14221	−0.225792
$741$	6.78486	0.249248
$742$	24.2209	0.889176
$743$	15.3651	0.563692	0.281846	−	0.959460i	$-0.409053\pi$
$743$	15.3651	0.563692	0.281846	+	0.959460i	$0.409053\pi$
$744$	22.5675	0.827366
$745$	7.35380	0.269422
$746$	−61.4270	−2.24900
$747$	42.9925	1.57301
$748$	−21.5259	−0.787065
$749$	27.0339	0.987796
$750$	−43.8230	−1.60019
$751$	−10.9198	−0.398470	−0.199235	−	0.979952i	$-0.563846\pi$
$751$	−10.9198	−0.398470	−0.199235	+	0.979952i	$0.563846\pi$
$752$	18.9237	0.690075
$753$	−16.5816	−0.604268
$754$	−5.13439	−0.186984
$755$	0.935881	0.0340602
$756$	−111.227	−4.04528
$757$	40.4709	1.47094	0.735469	−	0.677558i	$-0.236962\pi$
$757$	40.4709	1.47094	0.735469	+	0.677558i	$0.236962\pi$
$758$	−71.1159	−2.58305
$759$	91.0138	3.30359
$760$	3.29813	0.119636
$761$	13.2504	0.480327	0.240163	−	0.970732i	$-0.422799\pi$
$761$	13.2504	0.480327	0.240163	+	0.970732i	$0.422799\pi$
$762$	−129.829	−4.70321
$763$	−13.6226	−0.493172
$764$	103.714	3.75224
$765$	−5.84736	−0.211412
$766$	55.5014	2.00535
$767$	2.34343	0.0846163
$768$	−103.222	−3.72469
$769$	3.50527	0.126403	0.0632016	−	0.998001i	$-0.479869\pi$
$769$	3.50527	0.126403	0.0632016	+	0.998001i	$0.479869\pi$
$770$	9.96976	0.359285
$771$	49.7379	1.79127
$772$	6.27795	0.225948
$773$	−14.1464	−0.508811	−0.254406	−	0.967098i	$-0.581880\pi$
$773$	−14.1464	−0.508811	−0.254406	+	0.967098i	$0.581880\pi$
$774$	136.828	4.91820
$775$	5.92218	0.212731
$776$	92.8467	3.33300
$777$	−16.0970	−0.577477
$778$	21.6050	0.774577
$779$	11.3416	0.406354
$780$	−15.7996	−0.565718
$781$	−24.9108	−0.891379
$782$	29.0205	1.03777
$783$	13.2199	0.472439
$784$	−16.8123	−0.600439
$785$	2.85382	0.101857
$786$	125.818	4.48777
$787$	0.871428	0.0310631	0.0155315	−	0.999879i	$-0.495056\pi$
$787$	0.871428	0.0310631	0.0155315	+	0.999879i	$0.495056\pi$
$788$	−36.8173	−1.31156
$789$	−65.3219	−2.32552
$790$	−10.5789	−0.376381
$791$	3.78587	0.134610
$792$	141.303	5.02098
$793$	−10.3052	−0.365950
$794$	−22.5033	−0.798613
$795$	−8.85861	−0.314183
$796$	−24.8371	−0.880326
$797$	54.0951	1.91615	0.958073	−	0.286526i	$-0.0925004\pi$
$797$	54.0951	1.91615	0.958073	+	0.286526i	$0.0925004\pi$
$798$	16.3636	0.579265
$799$	4.95108	0.175156
$800$	11.8447	0.418775
$801$	94.8852	3.35260
$802$	−76.9902	−2.71862
$803$	60.0832	2.12029
$804$	50.6304	1.78560
$805$	−9.13238	−0.321874
$806$	6.50262	0.229045
$807$	66.3865	2.33692
$808$	21.9107	0.770816
$809$	13.9028	0.488798	0.244399	−	0.969675i	$-0.421409\pi$
$809$	13.9028	0.488798	0.244399	+	0.969675i	$0.421409\pi$
$810$	29.3812	1.03235
$811$	−28.5254	−1.00166	−0.500832	−	0.865545i	$-0.666972\pi$
$811$	−28.5254	−1.00166	−0.500832	+	0.865545i	$0.666972\pi$
$812$	−8.41361	−0.295260
$813$	−19.1566	−0.671850
$814$	22.4698	0.787567
$815$	−9.83399	−0.344470
$816$	25.1456	0.880273
$817$	−7.93825	−0.277724
$818$	−48.6070	−1.69950
$819$	−29.1676	−1.01920
$820$	−26.4107	−0.922300
$821$	19.9630	0.696714	0.348357	−	0.937362i	$-0.386740\pi$
$821$	19.9630	0.696714	0.348357	+	0.937362i	$0.386740\pi$
$822$	−17.2024	−0.600004
$823$	−4.06513	−0.141702	−0.0708508	−	0.997487i	$-0.522571\pi$
$823$	−4.06513	−0.141702	−0.0708508	+	0.997487i	$0.522571\pi$
$824$	102.666	3.57654
$825$	52.6400	1.83269
$826$	5.65183	0.196652
$827$	−6.23783	−0.216911	−0.108455	−	0.994101i	$-0.534590\pi$
$827$	−6.23783	−0.216911	−0.108455	+	0.994101i	$0.534590\pi$
$828$	−245.041	−8.51578
$829$	−10.2755	−0.356882	−0.178441	−	0.983951i	$-0.557105\pi$
$829$	−10.2755	−0.356882	−0.178441	+	0.983951i	$0.557105\pi$
$830$	8.54853	0.296724
$831$	3.18584	0.110516
$832$	−9.57447	−0.331935
$833$	−4.39866	−0.152405
$834$	−4.45202	−0.154161
$835$	9.82771	0.340102
$836$	−15.5199	−0.536766
$837$	−16.7427	−0.578713
$838$	0.419282	0.0144838
$839$	−46.0509	−1.58985	−0.794927	−	0.606705i	$-0.792491\pi$
$839$	−46.0509	−1.58985	−0.794927	+	0.606705i	$0.792491\pi$
$840$	−20.1278	−0.694473
$841$	1.00000	0.0344828
$842$	−7.38077	−0.254358
$843$	−48.1058	−1.65685
$844$	4.50075	0.154922
$845$	4.99402	0.171800
$846$	−61.5288	−2.11540
$847$	−2.94903	−0.101330
$848$	26.8349	0.921515
$849$	−8.23899	−0.282761
$850$	16.7847	0.575711
$851$	−20.5825	−0.705560
$852$	95.2112	3.26188
$853$	9.70527	0.332302	0.166151	−	0.986100i	$-0.446866\pi$
$853$	9.70527	0.332302	0.166151	+	0.986100i	$0.446866\pi$
$854$	−24.8540	−0.850485
$855$	−4.21587	−0.144180
$856$	76.1856	2.60397
$857$	−20.5389	−0.701597	−0.350798	−	0.936451i	$-0.614090\pi$
$857$	−20.5389	−0.701597	−0.350798	+	0.936451i	$0.614090\pi$
$858$	57.7993	1.97323
$859$	5.25351	0.179248	0.0896238	−	0.995976i	$-0.471434\pi$
$859$	5.25351	0.179248	0.0896238	+	0.995976i	$0.471434\pi$
$860$	18.4855	0.630350
$861$	−69.2150	−2.35884
$862$	72.2003	2.45915
$863$	27.5495	0.937797	0.468899	−	0.883252i	$-0.344651\pi$
$863$	27.5495	0.937797	0.468899	+	0.883252i	$0.344651\pi$
$864$	−33.4865	−1.13923
$865$	7.73936	0.263146
$866$	−2.10075	−0.0713865
$867$	−47.5803	−1.61591
$868$	10.6557	0.361677
$869$	26.2949	0.891995
$870$	4.52900	0.153548
$871$	7.70594	0.261106
$872$	−38.3906	−1.30007
$873$	−118.682	−4.01678
$874$	20.9234	0.707744
$875$	−10.9297	−0.369493
$876$	−229.643	−7.75891
$877$	19.3560	0.653604	0.326802	−	0.945093i	$-0.394029\pi$
$877$	19.3560	0.653604	0.326802	+	0.945093i	$0.394029\pi$
$878$	60.6573	2.04708
$879$	−92.9508	−3.13515
$880$	11.0458	0.372352
$881$	38.7113	1.30422	0.652109	−	0.758125i	$-0.273884\pi$
$881$	38.7113	1.30422	0.652109	+	0.758125i	$0.273884\pi$
$882$	54.6637	1.84062
$883$	45.7638	1.54007	0.770037	−	0.637999i	$-0.220238\pi$
$883$	45.7638	1.54007	0.770037	+	0.637999i	$0.220238\pi$
$884$	12.5221	0.421163
$885$	−2.06712	−0.0694854
$886$	56.9900	1.91462
$887$	−55.2712	−1.85583	−0.927913	−	0.372797i	$-0.878399\pi$
$887$	−55.2712	−1.85583	−0.927913	+	0.372797i	$0.878399\pi$
$888$	−45.3639	−1.52231
$889$	−32.3802	−1.08600
$890$	18.8668	0.632415
$891$	−73.0299	−2.44659
$892$	8.35596	0.279778
$893$	3.56966	0.119454
$894$	102.822	3.43889
$895$	−0.00232870	−7.78397e−5 0
$896$	−33.1462	−1.10734
$897$	−52.9446	−1.76777
$898$	−94.6686	−3.15913
$899$	−1.26648	−0.0422395
$900$	−141.726	−4.72419
$901$	7.02093	0.233901
$902$	96.6172	3.21700
$903$	48.4453	1.61216
$904$	10.6692	0.354852
$905$	5.40160	0.179555
$906$	13.0857	0.434742
$907$	−26.8285	−0.890825	−0.445412	−	0.895326i	$-0.646943\pi$
$907$	−26.8285	−0.890825	−0.445412	+	0.895326i	$0.646943\pi$
$908$	−14.7146	−0.488322
$909$	−28.0075	−0.928951
$910$	−5.79962	−0.192255
$911$	50.8339	1.68420	0.842100	−	0.539321i	$-0.181319\pi$
$911$	50.8339	1.68420	0.842100	+	0.539321i	$0.181319\pi$
$912$	18.1296	0.600332
$913$	−21.2482	−0.703213
$914$	−4.96061	−0.164082
$915$	9.09017	0.300512
$916$	−99.1469	−3.27591
$917$	31.3797	1.03625
$918$	−47.4524	−1.56616
$919$	−34.0539	−1.12334	−0.561668	−	0.827363i	$-0.689840\pi$
$919$	−34.0539	−1.12334	−0.561668	+	0.827363i	$0.689840\pi$
$920$	−25.7365	−0.848506
$921$	−15.4421	−0.508833
$922$	70.5217	2.32251
$923$	14.4911	0.476982
$924$	94.7143	3.11587
$925$	−11.9044	−0.391414
$926$	−21.9737	−0.722102
$927$	−131.234	−4.31028
$928$	−2.53305	−0.0831513
$929$	50.5351	1.65800	0.829001	−	0.559248i	$-0.188910\pi$
$929$	50.5351	1.65800	0.829001	+	0.559248i	$0.188910\pi$
$930$	−5.73590	−0.188088
$931$	−3.17137	−0.103938
$932$	3.28513	0.107608
$933$	−58.2349	−1.90652
$934$	−52.6108	−1.72148
$935$	2.88995	0.0945113
$936$	−82.1987	−2.68675
$937$	21.2920	0.695578	0.347789	−	0.937573i	$-0.386932\pi$
$937$	21.2920	0.695578	0.347789	+	0.937573i	$0.386932\pi$
$938$	18.5850	0.606823
$939$	−1.34505	−0.0438941
$940$	−8.31252	−0.271124
$941$	12.5372	0.408702	0.204351	−	0.978898i	$-0.434492\pi$
$941$	12.5372	0.408702	0.204351	+	0.978898i	$0.434492\pi$
$942$	39.9026	1.30010
$943$	−88.5021	−2.88203
$944$	6.26181	0.203805
$945$	14.9327	0.485759
$946$	−67.6248	−2.19867
$947$	36.7919	1.19558	0.597789	−	0.801654i	$-0.296046\pi$
$947$	36.7919	1.19558	0.597789	+	0.801654i	$0.296046\pi$
$948$	−100.501	−3.26413
$949$	−34.9516	−1.13458
$950$	12.1015	0.392626
$951$	−8.52222	−0.276352
$952$	15.9523	0.517018
$953$	5.43765	0.176143	0.0880714	−	0.996114i	$-0.471930\pi$
$953$	5.43765	0.176143	0.0880714	+	0.996114i	$0.471930\pi$
$954$	−87.2516	−2.82487
$955$	−13.9240	−0.450571
$956$	86.7595	2.80600
$957$	−11.2573	−0.363896
$958$	24.2263	0.782715
$959$	−4.29040	−0.138544
$960$	8.44556	0.272579
$961$	−29.3960	−0.948259
$962$	−13.0712	−0.421431
$963$	−97.3849	−3.13819
$964$	−92.5751	−2.98164
$965$	−0.842841	−0.0271320
$966$	−127.691	−4.10838
$967$	−45.6290	−1.46733	−0.733665	−	0.679511i	$-0.762192\pi$
$967$	−45.6290	−1.46733	−0.733665	+	0.679511i	$0.762192\pi$
$968$	−8.31083	−0.267120
$969$	4.74333	0.152378
$970$	−23.5985	−0.757701
$971$	−18.2818	−0.586690	−0.293345	−	0.956007i	$-0.594768\pi$
$971$	−18.2818	−0.586690	−0.293345	+	0.956007i	$0.594768\pi$
$972$	111.000	3.56034
$973$	−1.11036	−0.0355966
$974$	−76.9408	−2.46534
$975$	−30.6218	−0.980682
$976$	−27.5364	−0.881417
$977$	−32.9439	−1.05397	−0.526985	−	0.849875i	$-0.676678\pi$
$977$	−32.9439	−1.05397	−0.526985	+	0.849875i	$0.676678\pi$
$978$	−137.501	−4.39679
$979$	−46.8952	−1.49878
$980$	7.38506	0.235907
$981$	49.0731	1.56678
$982$	−7.78005	−0.248271
$983$	−42.0468	−1.34108	−0.670542	−	0.741871i	$-0.733938\pi$
$983$	−42.0468	−1.34108	−0.670542	+	0.741871i	$0.733938\pi$
$984$	−195.059	−6.21824
$985$	4.94289	0.157493
$986$	−3.58948	−0.114312
$987$	−21.7848	−0.693418
$988$	9.02824	0.287226
$989$	61.9448	1.96973
$990$	−35.9144	−1.14143
$991$	40.2243	1.27777	0.638883	−	0.769304i	$-0.279397\pi$
$991$	40.2243	1.27777	0.638883	+	0.769304i	$0.279397\pi$
$992$	3.20806	0.101856
$993$	44.2129	1.40305
$994$	34.9494	1.10853
$995$	3.33448	0.105710
$996$	81.2124	2.57331
$997$	−36.5957	−1.15900	−0.579498	−	0.814974i	$-0.696751\pi$
$997$	−36.5957	−1.15900	−0.579498	+	0.814974i	$0.696751\pi$
$998$	−61.4790	−1.94608
$999$	33.6552	1.06480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.12	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.12	✓	154	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)

\(f(q)\)	\(=\)	\(q-2.49784 q^{2} +3.18584 q^{3} +4.23922 q^{4} -0.569133 q^{5} -7.95772 q^{6} -1.98471 q^{7} -5.59321 q^{8} +7.14957 q^{9} +O(q^{10})\)	\(q-2.49784 q^{2} +3.18584 q^{3} +4.23922 q^{4} -0.569133 q^{5} -7.95772 q^{6} -1.98471 q^{7} -5.59321 q^{8} +7.14957 q^{9} +1.42160 q^{10} -3.53354 q^{11} +13.5055 q^{12} +2.05553 q^{13} +4.95749 q^{14} -1.81317 q^{15} +5.49253 q^{16} +1.43703 q^{17} -17.8585 q^{18} +1.03608 q^{19} -2.41268 q^{20} -6.32296 q^{21} +8.82622 q^{22} -8.08488 q^{23} -17.8191 q^{24} -4.67609 q^{25} -5.13439 q^{26} +13.2199 q^{27} -8.41361 q^{28} +1.00000 q^{29} +4.52900 q^{30} -1.26648 q^{31} -2.53305 q^{32} -11.2573 q^{33} -3.58948 q^{34} +1.12956 q^{35} +30.3086 q^{36} +2.54580 q^{37} -2.58796 q^{38} +6.54859 q^{39} +3.18328 q^{40} +10.9466 q^{41} +15.7938 q^{42} -7.66181 q^{43} -14.9794 q^{44} -4.06906 q^{45} +20.1948 q^{46} +3.44535 q^{47} +17.4983 q^{48} -3.06094 q^{49} +11.6801 q^{50} +4.57815 q^{51} +8.71384 q^{52} +4.88572 q^{53} -33.0211 q^{54} +2.01105 q^{55} +11.1009 q^{56} +3.30078 q^{57} -2.49784 q^{58} +1.14006 q^{59} -7.68640 q^{60} -5.01342 q^{61} +3.16347 q^{62} -14.1898 q^{63} -4.65791 q^{64} -1.16987 q^{65} +28.1189 q^{66} +3.74888 q^{67} +6.09189 q^{68} -25.7571 q^{69} -2.82147 q^{70} +7.04983 q^{71} -39.9891 q^{72} -17.0037 q^{73} -6.35902 q^{74} -14.8973 q^{75} +4.39217 q^{76} +7.01304 q^{77} -16.3573 q^{78} -7.44154 q^{79} -3.12598 q^{80} +20.6676 q^{81} -27.3429 q^{82} +6.01330 q^{83} -26.8044 q^{84} -0.817862 q^{85} +19.1380 q^{86} +3.18584 q^{87} +19.7638 q^{88} +13.2715 q^{89} +10.1639 q^{90} -4.07963 q^{91} -34.2736 q^{92} -4.03481 q^{93} -8.60594 q^{94} -0.589667 q^{95} -8.06988 q^{96} -16.5999 q^{97} +7.64574 q^{98} -25.2633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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