LMFDB - Embedded newform 8018.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +2.51574 q^{10} -0.0753521 q^{11} +0.846820 q^{12} -5.73702 q^{13} -3.73115 q^{14} +2.13038 q^{15} +1.00000 q^{16} +3.44373 q^{17} -2.28290 q^{18} +1.00000 q^{19} +2.51574 q^{20} -3.15962 q^{21} -0.0753521 q^{22} +6.79036 q^{23} +0.846820 q^{24} +1.32895 q^{25} -5.73702 q^{26} -4.47366 q^{27} -3.73115 q^{28} +1.05848 q^{29} +2.13038 q^{30} -3.37751 q^{31} +1.00000 q^{32} -0.0638097 q^{33} +3.44373 q^{34} -9.38662 q^{35} -2.28290 q^{36} +0.0136820 q^{37} +1.00000 q^{38} -4.85823 q^{39} +2.51574 q^{40} -5.23820 q^{41} -3.15962 q^{42} -8.50526 q^{43} -0.0753521 q^{44} -5.74317 q^{45} +6.79036 q^{46} -6.20848 q^{47} +0.846820 q^{48} +6.92151 q^{49} +1.32895 q^{50} +2.91622 q^{51} -5.73702 q^{52} +3.31645 q^{53} -4.47366 q^{54} -0.189566 q^{55} -3.73115 q^{56} +0.846820 q^{57} +1.05848 q^{58} +8.85589 q^{59} +2.13038 q^{60} -1.05386 q^{61} -3.37751 q^{62} +8.51784 q^{63} +1.00000 q^{64} -14.4329 q^{65} -0.0638097 q^{66} -14.4792 q^{67} +3.44373 q^{68} +5.75021 q^{69} -9.38662 q^{70} -10.5764 q^{71} -2.28290 q^{72} -10.5869 q^{73} +0.0136820 q^{74} +1.12539 q^{75} +1.00000 q^{76} +0.281150 q^{77} -4.85823 q^{78} +9.08302 q^{79} +2.51574 q^{80} +3.06030 q^{81} -5.23820 q^{82} +0.661023 q^{83} -3.15962 q^{84} +8.66354 q^{85} -8.50526 q^{86} +0.896345 q^{87} -0.0753521 q^{88} -4.15153 q^{89} -5.74317 q^{90} +21.4057 q^{91} +6.79036 q^{92} -2.86015 q^{93} -6.20848 q^{94} +2.51574 q^{95} +0.846820 q^{96} -0.682779 q^{97} +6.92151 q^{98} +0.172021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.846820	0.488912	0.244456	−	0.969660i	$-0.421391\pi$
$3$	0.846820	0.488912	0.244456	+	0.969660i	$0.421391\pi$
$4$	1.00000	0.500000
$5$	2.51574	1.12507	0.562537	−	0.826772i	$-0.309825\pi$
$5$	2.51574	1.12507	0.562537	+	0.826772i	$0.309825\pi$
$6$	0.846820	0.345713
$7$	−3.73115	−1.41024	−0.705122	−	0.709086i	$-0.749108\pi$
$7$	−3.73115	−1.41024	−0.705122	+	0.709086i	$0.749108\pi$
$8$	1.00000	0.353553
$9$	−2.28290	−0.760965
$10$	2.51574	0.795547
$11$	−0.0753521	−0.0227195	−0.0113598	−	0.999935i	$-0.503616\pi$
$11$	−0.0753521	−0.0227195	−0.0113598	+	0.999935i	$0.503616\pi$
$12$	0.846820	0.244456
$13$	−5.73702	−1.59116	−0.795582	−	0.605846i	$-0.792835\pi$
$13$	−5.73702	−1.59116	−0.795582	+	0.605846i	$0.792835\pi$
$14$	−3.73115	−0.997193
$15$	2.13038	0.550062
$16$	1.00000	0.250000
$17$	3.44373	0.835228	0.417614	−	0.908625i	$-0.362866\pi$
$17$	3.44373	0.835228	0.417614	+	0.908625i	$0.362866\pi$
$18$	−2.28290	−0.538084
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.51574	0.562537
$21$	−3.15962	−0.689485
$22$	−0.0753521	−0.0160651
$23$	6.79036	1.41589	0.707944	−	0.706269i	$-0.249623\pi$
$23$	6.79036	1.41589	0.707944	+	0.706269i	$0.249623\pi$
$24$	0.846820	0.172856
$25$	1.32895	0.265791
$26$	−5.73702	−1.12512
$27$	−4.47366	−0.860957
$28$	−3.73115	−0.705122
$29$	1.05848	0.196555	0.0982777	−	0.995159i	$-0.468667\pi$
$29$	1.05848	0.196555	0.0982777	+	0.995159i	$0.468667\pi$
$30$	2.13038	0.388952
$31$	−3.37751	−0.606619	−0.303310	−	0.952892i	$-0.598092\pi$
$31$	−3.37751	−0.606619	−0.303310	+	0.952892i	$0.598092\pi$
$32$	1.00000	0.176777
$33$	−0.0638097	−0.0111078
$34$	3.44373	0.590595
$35$	−9.38662	−1.58663
$36$	−2.28290	−0.380483
$37$	0.0136820	0.00224930	0.00112465	−	0.999999i	$-0.499642\pi$
$37$	0.0136820	0.00224930	0.00112465	+	0.999999i	$0.499642\pi$
$38$	1.00000	0.162221
$39$	−4.85823	−0.777939
$40$	2.51574	0.397774
$41$	−5.23820	−0.818069	−0.409034	−	0.912519i	$-0.634134\pi$
$41$	−5.23820	−0.818069	−0.409034	+	0.912519i	$0.634134\pi$
$42$	−3.15962	−0.487539
$43$	−8.50526	−1.29704	−0.648520	−	0.761198i	$-0.724612\pi$
$43$	−8.50526	−1.29704	−0.648520	+	0.761198i	$0.724612\pi$
$44$	−0.0753521	−0.0113598
$45$	−5.74317	−0.856142
$46$	6.79036	1.00118
$47$	−6.20848	−0.905600	−0.452800	−	0.891612i	$-0.649575\pi$
$47$	−6.20848	−0.905600	−0.452800	+	0.891612i	$0.649575\pi$
$48$	0.846820	0.122228
$49$	6.92151	0.988788
$50$	1.32895	0.187943
$51$	2.91622	0.408353
$52$	−5.73702	−0.795582
$53$	3.31645	0.455550	0.227775	−	0.973714i	$-0.426855\pi$
$53$	3.31645	0.455550	0.227775	+	0.973714i	$0.426855\pi$
$54$	−4.47366	−0.608788
$55$	−0.189566	−0.0255611
$56$	−3.73115	−0.498596
$57$	0.846820	0.112164
$58$	1.05848	0.138986
$59$	8.85589	1.15294	0.576469	−	0.817119i	$-0.304430\pi$
$59$	8.85589	1.15294	0.576469	+	0.817119i	$0.304430\pi$
$60$	2.13038	0.275031
$61$	−1.05386	−0.134933	−0.0674665	−	0.997722i	$-0.521492\pi$
$61$	−1.05386	−0.134933	−0.0674665	+	0.997722i	$0.521492\pi$
$62$	−3.37751	−0.428944
$63$	8.51784	1.07315
$64$	1.00000	0.125000
$65$	−14.4329	−1.79018
$66$	−0.0638097	−0.00785443
$67$	−14.4792	−1.76891	−0.884455	−	0.466625i	$-0.845470\pi$
$67$	−14.4792	−1.76891	−0.884455	+	0.466625i	$0.845470\pi$
$68$	3.44373	0.417614
$69$	5.75021	0.692244
$70$	−9.38662	−1.12192
$71$	−10.5764	−1.25518	−0.627592	−	0.778542i	$-0.715960\pi$
$71$	−10.5764	−1.25518	−0.627592	+	0.778542i	$0.715960\pi$
$72$	−2.28290	−0.269042
$73$	−10.5869	−1.23910	−0.619550	−	0.784957i	$-0.712685\pi$
$73$	−10.5869	−1.23910	−0.619550	+	0.784957i	$0.712685\pi$
$74$	0.0136820	0.00159050
$75$	1.12539	0.129948
$76$	1.00000	0.114708
$77$	0.281150	0.0320400
$78$	−4.85823	−0.550086
$79$	9.08302	1.02192	0.510960	−	0.859604i	$-0.329290\pi$
$79$	9.08302	1.02192	0.510960	+	0.859604i	$0.329290\pi$
$80$	2.51574	0.281268
$81$	3.06030	0.340033
$82$	−5.23820	−0.578462
$83$	0.661023	0.0725567	0.0362784	−	0.999342i	$-0.488450\pi$
$83$	0.661023	0.0725567	0.0362784	+	0.999342i	$0.488450\pi$
$84$	−3.15962	−0.344742
$85$	8.66354	0.939693
$86$	−8.50526	−0.917145
$87$	0.896345	0.0960983
$88$	−0.0753521	−0.00803256
$89$	−4.15153	−0.440061	−0.220030	−	0.975493i	$-0.570616\pi$
$89$	−4.15153	−0.440061	−0.220030	+	0.975493i	$0.570616\pi$
$90$	−5.74317	−0.605384
$91$	21.4057	2.24393
$92$	6.79036	0.707944
$93$	−2.86015	−0.296583
$94$	−6.20848	−0.640356
$95$	2.51574	0.258110
$96$	0.846820	0.0864282
$97$	−0.682779	−0.0693257	−0.0346628	−	0.999399i	$-0.511036\pi$
$97$	−0.682779	−0.0693257	−0.0346628	+	0.999399i	$0.511036\pi$
$98$	6.92151	0.699178
$99$	0.172021	0.0172888
$100$	1.32895	0.132895
$101$	−6.09314	−0.606290	−0.303145	−	0.952944i	$-0.598037\pi$
$101$	−6.09314	−0.606290	−0.303145	+	0.952944i	$0.598037\pi$
$102$	2.91622	0.288749
$103$	−16.5270	−1.62846	−0.814228	−	0.580545i	$-0.802840\pi$
$103$	−16.5270	−1.62846	−0.814228	+	0.580545i	$0.802840\pi$
$104$	−5.73702	−0.562561
$105$	−7.94878	−0.775721
$106$	3.31645	0.322122
$107$	9.14029	0.883625	0.441813	−	0.897107i	$-0.354336\pi$
$107$	9.14029	0.883625	0.441813	+	0.897107i	$0.354336\pi$
$108$	−4.47366	−0.430478
$109$	4.48298	0.429392	0.214696	−	0.976681i	$-0.431124\pi$
$109$	4.48298	0.429392	0.214696	+	0.976681i	$0.431124\pi$
$110$	−0.189566	−0.0180744
$111$	0.0115862	0.00109971
$112$	−3.73115	−0.352561
$113$	−19.2161	−1.80770	−0.903850	−	0.427849i	$-0.859271\pi$
$113$	−19.2161	−1.80770	−0.903850	+	0.427849i	$0.859271\pi$
$114$	0.846820	0.0793120
$115$	17.0828	1.59298
$116$	1.05848	0.0982777
$117$	13.0970	1.21082
$118$	8.85589	0.815250
$119$	−12.8491	−1.17787
$120$	2.13038	0.194476
$121$	−10.9943	−0.999484
$122$	−1.05386	−0.0954121
$123$	−4.43581	−0.399964
$124$	−3.37751	−0.303310
$125$	−9.23540	−0.826039
$126$	8.51784	0.758829
$127$	−13.1175	−1.16399	−0.581995	−	0.813192i	$-0.697728\pi$
$127$	−13.1175	−1.16399	−0.581995	+	0.813192i	$0.697728\pi$
$128$	1.00000	0.0883883
$129$	−7.20242	−0.634138
$130$	−14.4329	−1.26585
$131$	13.7876	1.20463	0.602316	−	0.798258i	$-0.294245\pi$
$131$	13.7876	1.20463	0.602316	+	0.798258i	$0.294245\pi$
$132$	−0.0638097	−0.00555392
$133$	−3.73115	−0.323532
$134$	−14.4792	−1.25081
$135$	−11.2546	−0.968640
$136$	3.44373	0.295298
$137$	−3.46483	−0.296020	−0.148010	−	0.988986i	$-0.547287\pi$
$137$	−3.46483	−0.296020	−0.148010	+	0.988986i	$0.547287\pi$
$138$	5.75021	0.489491
$139$	−4.06379	−0.344686	−0.172343	−	0.985037i	$-0.555134\pi$
$139$	−4.06379	−0.344686	−0.172343	+	0.985037i	$0.555134\pi$
$140$	−9.38662	−0.793314
$141$	−5.25747	−0.442759
$142$	−10.5764	−0.887550
$143$	0.432297	0.0361505
$144$	−2.28290	−0.190241
$145$	2.66287	0.221139
$146$	−10.5869	−0.876176
$147$	5.86128	0.483430
$148$	0.0136820	0.00112465
$149$	3.68372	0.301782	0.150891	−	0.988550i	$-0.451786\pi$
$149$	3.68372	0.301782	0.150891	+	0.988550i	$0.451786\pi$
$150$	1.12539	0.0918873
$151$	7.08380	0.576472	0.288236	−	0.957559i	$-0.406931\pi$
$151$	7.08380	0.576472	0.288236	+	0.957559i	$0.406931\pi$
$152$	1.00000	0.0811107
$153$	−7.86168	−0.635579
$154$	0.281150	0.0226557
$155$	−8.49695	−0.682491
$156$	−4.85823	−0.388969
$157$	−1.84050	−0.146888	−0.0734439	−	0.997299i	$-0.523399\pi$
$157$	−1.84050	−0.146888	−0.0734439	+	0.997299i	$0.523399\pi$
$158$	9.08302	0.722607
$159$	2.80844	0.222724
$160$	2.51574	0.198887
$161$	−25.3359	−1.99675
$162$	3.06030	0.240440
$163$	−9.61863	−0.753390	−0.376695	−	0.926337i	$-0.622939\pi$
$163$	−9.61863	−0.753390	−0.376695	+	0.926337i	$0.622939\pi$
$164$	−5.23820	−0.409034
$165$	−0.160529	−0.0124971
$166$	0.661023	0.0513053
$167$	10.5078	0.813120	0.406560	−	0.913624i	$-0.366728\pi$
$167$	10.5078	0.813120	0.406560	+	0.913624i	$0.366728\pi$
$168$	−3.15962	−0.243770
$169$	19.9134	1.53180
$170$	8.66354	0.664463
$171$	−2.28290	−0.174577
$172$	−8.50526	−0.648520
$173$	−10.9446	−0.832099	−0.416049	−	0.909342i	$-0.636586\pi$
$173$	−10.9446	−0.832099	−0.416049	+	0.909342i	$0.636586\pi$
$174$	0.896345	0.0679517
$175$	−4.95853	−0.374830
$176$	−0.0753521	−0.00567988
$177$	7.49934	0.563685
$178$	−4.15153	−0.311170
$179$	6.23538	0.466054	0.233027	−	0.972470i	$-0.425137\pi$
$179$	6.23538	0.466054	0.233027	+	0.972470i	$0.425137\pi$
$180$	−5.74317	−0.428071
$181$	9.18136	0.682445	0.341223	−	0.939982i	$-0.389159\pi$
$181$	9.18136	0.682445	0.341223	+	0.939982i	$0.389159\pi$
$182$	21.4057	1.58670
$183$	−0.892431	−0.0659704
$184$	6.79036	0.500592
$185$	0.0344203	0.00253063
$186$	−2.86015	−0.209716
$187$	−0.259492	−0.0189760
$188$	−6.20848	−0.452800
$189$	16.6919	1.21416
$190$	2.51574	0.182511
$191$	−4.66074	−0.337239	−0.168619	−	0.985681i	$-0.553931\pi$
$191$	−4.66074	−0.337239	−0.168619	+	0.985681i	$0.553931\pi$
$192$	0.846820	0.0611140
$193$	2.69972	0.194330	0.0971650	−	0.995268i	$-0.469023\pi$
$193$	2.69972	0.194330	0.0971650	+	0.995268i	$0.469023\pi$
$194$	−0.682779	−0.0490207
$195$	−12.2220	−0.875238
$196$	6.92151	0.494394
$197$	−17.6195	−1.25534	−0.627668	−	0.778481i	$-0.715990\pi$
$197$	−17.6195	−1.25534	−0.627668	+	0.778481i	$0.715990\pi$
$198$	0.172021	0.0122250
$199$	11.3966	0.807887	0.403943	−	0.914784i	$-0.367639\pi$
$199$	11.3966	0.807887	0.403943	+	0.914784i	$0.367639\pi$
$200$	1.32895	0.0939713
$201$	−12.2612	−0.864841
$202$	−6.09314	−0.428712
$203$	−3.94936	−0.277191
$204$	2.91622	0.204176
$205$	−13.1779	−0.920388
$206$	−16.5270	−1.15149
$207$	−15.5017	−1.07744
$208$	−5.73702	−0.397791
$209$	−0.0753521	−0.00521221
$210$	−7.94878	−0.548518
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.31645	0.227775
$213$	−8.95629	−0.613675
$214$	9.14029	0.624817
$215$	−21.3970	−1.45927
$216$	−4.47366	−0.304394
$217$	12.6020	0.855481
$218$	4.48298	0.303626
$219$	−8.96518	−0.605811
$220$	−0.189566	−0.0127806
$221$	−19.7568	−1.32898
$222$	0.0115862	0.000777614 0
$223$	−22.9125	−1.53434	−0.767169	−	0.641446i	$-0.778335\pi$
$223$	−22.9125	−1.53434	−0.767169	+	0.641446i	$0.778335\pi$
$224$	−3.73115	−0.249298
$225$	−3.03386	−0.202258
$226$	−19.2161	−1.27824
$227$	−14.4216	−0.957196	−0.478598	−	0.878034i	$-0.658855\pi$
$227$	−14.4216	−0.957196	−0.478598	+	0.878034i	$0.658855\pi$
$228$	0.846820	0.0560820
$229$	−23.6041	−1.55980	−0.779902	−	0.625901i	$-0.784731\pi$
$229$	−23.6041	−1.55980	−0.779902	+	0.625901i	$0.784731\pi$
$230$	17.0828	1.12641
$231$	0.238084	0.0156648
$232$	1.05848	0.0694928
$233$	−25.4543	−1.66757	−0.833784	−	0.552090i	$-0.813830\pi$
$233$	−25.4543	−1.66757	−0.833784	+	0.552090i	$0.813830\pi$
$234$	13.0970	0.856179
$235$	−15.6189	−1.01887
$236$	8.85589	0.576469
$237$	7.69169	0.499629
$238$	−12.8491	−0.832883
$239$	−8.55439	−0.553338	−0.276669	−	0.960965i	$-0.589230\pi$
$239$	−8.55439	−0.553338	−0.276669	+	0.960965i	$0.589230\pi$
$240$	2.13038	0.137515
$241$	25.2877	1.62893	0.814463	−	0.580215i	$-0.197031\pi$
$241$	25.2877	1.62893	0.814463	+	0.580215i	$0.197031\pi$
$242$	−10.9943	−0.706742
$243$	16.0125	1.02720
$244$	−1.05386	−0.0674665
$245$	17.4127	1.11246
$246$	−4.43581	−0.282817
$247$	−5.73702	−0.365038
$248$	−3.37751	−0.214472
$249$	0.559768	0.0354738
$250$	−9.23540	−0.584098
$251$	13.8372	0.873394	0.436697	−	0.899609i	$-0.356148\pi$
$251$	13.8372	0.873394	0.436697	+	0.899609i	$0.356148\pi$
$252$	8.51784	0.536573
$253$	−0.511668	−0.0321683
$254$	−13.1175	−0.823066
$255$	7.33646	0.459427
$256$	1.00000	0.0625000
$257$	1.16464	0.0726482	0.0363241	−	0.999340i	$-0.488435\pi$
$257$	1.16464	0.0726482	0.0363241	+	0.999340i	$0.488435\pi$
$258$	−7.20242	−0.448403
$259$	−0.0510496	−0.00317207
$260$	−14.4329	−0.895088
$261$	−2.41641	−0.149572
$262$	13.7876	0.851804
$263$	17.2266	1.06224	0.531120	−	0.847297i	$-0.321771\pi$
$263$	17.2266	1.06224	0.531120	+	0.847297i	$0.321771\pi$
$264$	−0.0638097	−0.00392721
$265$	8.34333	0.512527
$266$	−3.73115	−0.228772
$267$	−3.51560	−0.215151
$268$	−14.4792	−0.884455
$269$	−5.59641	−0.341219	−0.170610	−	0.985339i	$-0.554574\pi$
$269$	−5.59641	−0.341219	−0.170610	+	0.985339i	$0.554574\pi$
$270$	−11.2546	−0.684932
$271$	−6.36372	−0.386568	−0.193284	−	0.981143i	$-0.561914\pi$
$271$	−6.36372	−0.386568	−0.193284	+	0.981143i	$0.561914\pi$
$272$	3.44373	0.208807
$273$	18.1268	1.09708
$274$	−3.46483	−0.209318
$275$	−0.100139	−0.00603864
$276$	5.75021	0.346122
$277$	23.2939	1.39959	0.699797	−	0.714342i	$-0.253274\pi$
$277$	23.2939	1.39959	0.699797	+	0.714342i	$0.253274\pi$
$278$	−4.06379	−0.243730
$279$	7.71051	0.461616
$280$	−9.38662	−0.560958
$281$	30.9071	1.84376	0.921880	−	0.387475i	$-0.126653\pi$
$281$	30.9071	1.84376	0.921880	+	0.387475i	$0.126653\pi$
$282$	−5.25747	−0.313078
$283$	7.88482	0.468704	0.234352	−	0.972152i	$-0.424703\pi$
$283$	7.88482	0.468704	0.234352	+	0.972152i	$0.424703\pi$
$284$	−10.5764	−0.627592
$285$	2.13038	0.126193
$286$	0.432297	0.0255622
$287$	19.5445	1.15368
$288$	−2.28290	−0.134521
$289$	−5.14071	−0.302394
$290$	2.66287	0.156369
$291$	−0.578191	−0.0338942
$292$	−10.5869	−0.619550
$293$	−26.7684	−1.56382	−0.781912	−	0.623389i	$-0.785755\pi$
$293$	−26.7684	−1.56382	−0.781912	+	0.623389i	$0.785755\pi$
$294$	5.86128	0.341837
$295$	22.2791	1.29714
$296$	0.0136820	0.000795249 0
$297$	0.337100	0.0195605
$298$	3.68372	0.213392
$299$	−38.9564	−2.25291
$300$	1.12539	0.0649741
$301$	31.7344	1.82914
$302$	7.08380	0.407627
$303$	−5.15979	−0.296422
$304$	1.00000	0.0573539
$305$	−2.65124	−0.151810
$306$	−7.86168	−0.449422
$307$	21.6088	1.23328	0.616638	−	0.787247i	$-0.288494\pi$
$307$	21.6088	1.23328	0.616638	+	0.787247i	$0.288494\pi$
$308$	0.281150	0.0160200
$309$	−13.9954	−0.796172
$310$	−8.49695	−0.482594
$311$	4.23255	0.240006	0.120003	−	0.992774i	$-0.461710\pi$
$311$	4.23255	0.240006	0.120003	+	0.992774i	$0.461710\pi$
$312$	−4.85823	−0.275043
$313$	21.2458	1.20088	0.600442	−	0.799668i	$-0.294991\pi$
$313$	21.2458	1.20088	0.600442	+	0.799668i	$0.294991\pi$
$314$	−1.84050	−0.103865
$315$	21.4287	1.20737
$316$	9.08302	0.510960
$317$	24.3234	1.36614	0.683070	−	0.730353i	$-0.260644\pi$
$317$	24.3234	1.36614	0.683070	+	0.730353i	$0.260644\pi$
$318$	2.80844	0.157489
$319$	−0.0797589	−0.00446564
$320$	2.51574	0.140634
$321$	7.74018	0.432015
$322$	−25.3359	−1.41191
$323$	3.44373	0.191614
$324$	3.06030	0.170017
$325$	−7.62424	−0.422917
$326$	−9.61863	−0.532727
$327$	3.79628	0.209935
$328$	−5.23820	−0.289231
$329$	23.1648	1.27712
$330$	−0.160529	−0.00883681
$331$	9.82654	0.540115	0.270058	−	0.962844i	$-0.412957\pi$
$331$	9.82654	0.540115	0.270058	+	0.962844i	$0.412957\pi$
$332$	0.661023	0.0362784
$333$	−0.0312345	−0.00171164
$334$	10.5078	0.574962
$335$	−36.4258	−1.99015
$336$	−3.15962	−0.172371
$337$	16.0274	0.873070	0.436535	−	0.899687i	$-0.356206\pi$
$337$	16.0274	0.873070	0.436535	+	0.899687i	$0.356206\pi$
$338$	19.9134	1.08315
$339$	−16.2726	−0.883806
$340$	8.66354	0.469846
$341$	0.254503	0.0137821
$342$	−2.28290	−0.123445
$343$	0.292848	0.0158123
$344$	−8.50526	−0.458573
$345$	14.4661	0.778826
$346$	−10.9446	−0.588383
$347$	3.93856	0.211433	0.105717	−	0.994396i	$-0.466286\pi$
$347$	3.93856	0.211433	0.105717	+	0.994396i	$0.466286\pi$
$348$	0.896345	0.0480491
$349$	1.23767	0.0662512	0.0331256	−	0.999451i	$-0.489454\pi$
$349$	1.23767	0.0662512	0.0331256	+	0.999451i	$0.489454\pi$
$350$	−4.95853	−0.265045
$351$	25.6655	1.36992
$352$	−0.0753521	−0.00401628
$353$	5.65440	0.300953	0.150477	−	0.988614i	$-0.451919\pi$
$353$	5.65440	0.300953	0.150477	+	0.988614i	$0.451919\pi$
$354$	7.49934	0.398586
$355$	−26.6074	−1.41218
$356$	−4.15153	−0.220030
$357$	−10.8809	−0.575877
$358$	6.23538	0.329550
$359$	9.74840	0.514501	0.257250	−	0.966345i	$-0.417184\pi$
$359$	9.74840	0.514501	0.257250	+	0.966345i	$0.417184\pi$
$360$	−5.74317	−0.302692
$361$	1.00000	0.0526316
$362$	9.18136	0.482562
$363$	−9.31021	−0.488660
$364$	21.4057	1.12196
$365$	−26.6339	−1.39408
$366$	−0.892431	−0.0466481
$367$	−8.60189	−0.449015	−0.224507	−	0.974472i	$-0.572077\pi$
$367$	−8.60189	−0.449015	−0.224507	+	0.974472i	$0.572077\pi$
$368$	6.79036	0.353972
$369$	11.9583	0.622522
$370$	0.0344203	0.00178943
$371$	−12.3742	−0.642436
$372$	−2.86015	−0.148292
$373$	6.05625	0.313581	0.156790	−	0.987632i	$-0.449885\pi$
$373$	6.05625	0.313581	0.156790	+	0.987632i	$0.449885\pi$
$374$	−0.259492	−0.0134180
$375$	−7.82072	−0.403860
$376$	−6.20848	−0.320178
$377$	−6.07254	−0.312752
$378$	16.6919	0.858540
$379$	20.3044	1.04296	0.521482	−	0.853262i	$-0.325379\pi$
$379$	20.3044	1.04296	0.521482	+	0.853262i	$0.325379\pi$
$380$	2.51574	0.129055
$381$	−11.1082	−0.569089
$382$	−4.66074	−0.238464
$383$	31.1049	1.58939	0.794694	−	0.607011i	$-0.207632\pi$
$383$	31.1049	1.58939	0.794694	+	0.607011i	$0.207632\pi$
$384$	0.846820	0.0432141
$385$	0.707301	0.0360474
$386$	2.69972	0.137412
$387$	19.4166	0.987002
$388$	−0.682779	−0.0346628
$389$	−7.23787	−0.366974	−0.183487	−	0.983022i	$-0.558739\pi$
$389$	−7.23787	−0.366974	−0.183487	+	0.983022i	$0.558739\pi$
$390$	−12.2220	−0.618887
$391$	23.3842	1.18259
$392$	6.92151	0.349589
$393$	11.6757	0.588959
$394$	−17.6195	−0.887657
$395$	22.8505	1.14974
$396$	0.172021	0.00864438
$397$	22.1359	1.11097	0.555483	−	0.831528i	$-0.312533\pi$
$397$	22.1359	1.11097	0.555483	+	0.831528i	$0.312533\pi$
$398$	11.3966	0.571262
$399$	−3.15962	−0.158179
$400$	1.32895	0.0664477
$401$	13.9938	0.698816	0.349408	−	0.936971i	$-0.386383\pi$
$401$	13.9938	0.698816	0.349408	+	0.936971i	$0.386383\pi$
$402$	−12.2612	−0.611535
$403$	19.3769	0.965230
$404$	−6.09314	−0.303145
$405$	7.69892	0.382562
$406$	−3.94936	−0.196004
$407$	−0.00103097	−5.11031e−5 0
$408$	2.91622	0.144375
$409$	25.7319	1.27236	0.636180	−	0.771540i	$-0.280513\pi$
$409$	25.7319	1.27236	0.636180	+	0.771540i	$0.280513\pi$
$410$	−13.1779	−0.650812
$411$	−2.93408	−0.144728
$412$	−16.5270	−0.814228
$413$	−33.0427	−1.62592
$414$	−15.5017	−0.761866
$415$	1.66296	0.0816316
$416$	−5.73702	−0.281281
$417$	−3.44130	−0.168521
$418$	−0.0753521	−0.00368559
$419$	1.36340	0.0666064	0.0333032	−	0.999445i	$-0.489397\pi$
$419$	1.36340	0.0666064	0.0333032	+	0.999445i	$0.489397\pi$
$420$	−7.94878	−0.387861
$421$	−2.18984	−0.106726	−0.0533632	−	0.998575i	$-0.516994\pi$
$421$	−2.18984	−0.106726	−0.0533632	+	0.998575i	$0.516994\pi$
$422$	−1.00000	−0.0486792
$423$	14.1733	0.689130
$424$	3.31645	0.161061
$425$	4.57656	0.221996
$426$	−8.95629	−0.433934
$427$	3.93212	0.190288
$428$	9.14029	0.441813
$429$	0.366077	0.0176744
$430$	−21.3970	−1.03186
$431$	8.48009	0.408471	0.204236	−	0.978922i	$-0.434529\pi$
$431$	8.48009	0.408471	0.204236	+	0.978922i	$0.434529\pi$
$432$	−4.47366	−0.215239
$433$	−10.4229	−0.500893	−0.250446	−	0.968130i	$-0.580577\pi$
$433$	−10.4229	−0.500893	−0.250446	+	0.968130i	$0.580577\pi$
$434$	12.6020	0.604916
$435$	2.25497	0.108118
$436$	4.48298	0.214696
$437$	6.79036	0.324827
$438$	−8.96518	−0.428373
$439$	−12.6496	−0.603733	−0.301866	−	0.953350i	$-0.597610\pi$
$439$	−12.6496	−0.603733	−0.301866	+	0.953350i	$0.597610\pi$
$440$	−0.189566	−0.00903722
$441$	−15.8011	−0.752433
$442$	−19.7568	−0.939734
$443$	−35.3294	−1.67855	−0.839276	−	0.543705i	$-0.817021\pi$
$443$	−35.3294	−1.67855	−0.839276	+	0.543705i	$0.817021\pi$
$444$	0.0115862	0.000549856 0
$445$	−10.4442	−0.495101
$446$	−22.9125	−1.08494
$447$	3.11945	0.147545
$448$	−3.73115	−0.176280
$449$	−9.46560	−0.446710	−0.223355	−	0.974737i	$-0.571701\pi$
$449$	−9.46560	−0.446710	−0.223355	+	0.974737i	$0.571701\pi$
$450$	−3.03386	−0.143018
$451$	0.394709	0.0185861
$452$	−19.2161	−0.903850
$453$	5.99871	0.281844
$454$	−14.4216	−0.676840
$455$	53.8512	2.52459
$456$	0.846820	0.0396560
$457$	−32.0612	−1.49976	−0.749879	−	0.661575i	$-0.769889\pi$
$457$	−32.0612	−1.49976	−0.749879	+	0.661575i	$0.769889\pi$
$458$	−23.6041	−1.10295
$459$	−15.4061	−0.719095
$460$	17.0828	0.796489
$461$	27.2979	1.27139	0.635696	−	0.771940i	$-0.280713\pi$
$461$	27.2979	1.27139	0.635696	+	0.771940i	$0.280713\pi$
$462$	0.238084	0.0110767
$463$	32.4611	1.50859	0.754297	−	0.656533i	$-0.227978\pi$
$463$	32.4611	1.50859	0.754297	+	0.656533i	$0.227978\pi$
$464$	1.05848	0.0491388
$465$	−7.19539	−0.333678
$466$	−25.4543	−1.17915
$467$	−31.2049	−1.44399	−0.721996	−	0.691897i	$-0.756775\pi$
$467$	−31.2049	−1.44399	−0.721996	+	0.691897i	$0.756775\pi$
$468$	13.0970	0.605410
$469$	54.0240	2.49459
$470$	−15.6189	−0.720448
$471$	−1.55857	−0.0718152
$472$	8.85589	0.407625
$473$	0.640889	0.0294681
$474$	7.69169	0.353291
$475$	1.32895	0.0609766
$476$	−12.8491	−0.588937
$477$	−7.57111	−0.346657
$478$	−8.55439	−0.391269
$479$	−22.2905	−1.01848	−0.509240	−	0.860625i	$-0.670073\pi$
$479$	−22.2905	−1.01848	−0.509240	+	0.860625i	$0.670073\pi$
$480$	2.13038	0.0972381
$481$	−0.0784939	−0.00357901
$482$	25.2877	1.15183
$483$	−21.4549	−0.976233
$484$	−10.9943	−0.499742
$485$	−1.71770	−0.0779965
$486$	16.0125	0.726342
$487$	4.50007	0.203918	0.101959	−	0.994789i	$-0.467489\pi$
$487$	4.50007	0.203918	0.101959	+	0.994789i	$0.467489\pi$
$488$	−1.05386	−0.0477060
$489$	−8.14525	−0.368341
$490$	17.4127	0.786627
$491$	−39.6320	−1.78857	−0.894284	−	0.447499i	$-0.852315\pi$
$491$	−39.6320	−1.78857	−0.894284	+	0.447499i	$0.852315\pi$
$492$	−4.43581	−0.199982
$493$	3.64513	0.164169
$494$	−5.73702	−0.258121
$495$	0.432760	0.0194511
$496$	−3.37751	−0.151655
$497$	39.4621	1.77012
$498$	0.559768	0.0250838
$499$	17.7075	0.792696	0.396348	−	0.918100i	$-0.370277\pi$
$499$	17.7075	0.792696	0.396348	+	0.918100i	$0.370277\pi$
$500$	−9.23540	−0.413020
$501$	8.89823	0.397544
$502$	13.8372	0.617583
$503$	40.0337	1.78501	0.892507	−	0.451034i	$-0.148945\pi$
$503$	40.0337	1.78501	0.892507	+	0.451034i	$0.148945\pi$
$504$	8.51784	0.379415
$505$	−15.3288	−0.682121
$506$	−0.511668	−0.0227464
$507$	16.8631	0.748916
$508$	−13.1175	−0.581995
$509$	9.74155	0.431786	0.215893	−	0.976417i	$-0.430734\pi$
$509$	9.74155	0.431786	0.215893	+	0.976417i	$0.430734\pi$
$510$	7.33646	0.324864
$511$	39.5013	1.74743
$512$	1.00000	0.0441942
$513$	−4.47366	−0.197517
$514$	1.16464	0.0513700
$515$	−41.5777	−1.83213
$516$	−7.20242	−0.317069
$517$	0.467822	0.0205748
$518$	−0.0510496	−0.00224299
$519$	−9.26807	−0.406823
$520$	−14.4329	−0.632923
$521$	−16.2677	−0.712700	−0.356350	−	0.934353i	$-0.615979\pi$
$521$	−16.2677	−0.712700	−0.356350	+	0.934353i	$0.615979\pi$
$522$	−2.41641	−0.105763
$523$	34.1150	1.49174	0.745872	−	0.666090i	$-0.232033\pi$
$523$	34.1150	1.49174	0.745872	+	0.666090i	$0.232033\pi$
$524$	13.7876	0.602316
$525$	−4.19899	−0.183259
$526$	17.2266	0.751117
$527$	−11.6312	−0.506665
$528$	−0.0638097	−0.00277696
$529$	23.1090	1.00474
$530$	8.34333	0.362411
$531$	−20.2171	−0.877346
$532$	−3.73115	−0.161766
$533$	30.0516	1.30168
$534$	−3.51560	−0.152135
$535$	22.9946	0.994143
$536$	−14.4792	−0.625404
$537$	5.28024	0.227859
$538$	−5.59641	−0.241278
$539$	−0.521550	−0.0224648
$540$	−11.2546	−0.484320
$541$	−14.8874	−0.640059	−0.320029	−	0.947408i	$-0.603693\pi$
$541$	−14.8874	−0.640059	−0.320029	+	0.947408i	$0.603693\pi$
$542$	−6.36372	−0.273345
$543$	7.77496	0.333656
$544$	3.44373	0.147649
$545$	11.2780	0.483097
$546$	18.1268	0.775755
$547$	−33.1241	−1.41628	−0.708142	−	0.706070i	$-0.750467\pi$
$547$	−33.1241	−1.41628	−0.708142	+	0.706070i	$0.750467\pi$
$548$	−3.46483	−0.148010
$549$	2.40585	0.102679
$550$	−0.100139	−0.00426996
$551$	1.05848	0.0450929
$552$	5.75021	0.244745
$553$	−33.8902	−1.44116
$554$	23.2939	0.989662
$555$	0.0291478	0.00123726
$556$	−4.06379	−0.172343
$557$	−19.4433	−0.823839	−0.411920	−	0.911220i	$-0.635142\pi$
$557$	−19.4433	−0.823839	−0.411920	+	0.911220i	$0.635142\pi$
$558$	7.71051	0.326412
$559$	48.7948	2.06380
$560$	−9.38662	−0.396657
$561$	−0.219743	−0.00927758
$562$	30.9071	1.30374
$563$	27.6601	1.16573	0.582867	−	0.812568i	$-0.301931\pi$
$563$	27.6601	1.16573	0.582867	+	0.812568i	$0.301931\pi$
$564$	−5.25747	−0.221379
$565$	−48.3428	−2.03380
$566$	7.88482	0.331424
$567$	−11.4184	−0.479530
$568$	−10.5764	−0.443775
$569$	−25.2610	−1.05900	−0.529499	−	0.848311i	$-0.677620\pi$
$569$	−25.2610	−1.05900	−0.529499	+	0.848311i	$0.677620\pi$
$570$	2.13038	0.0892318
$571$	−2.57697	−0.107843	−0.0539213	−	0.998545i	$-0.517172\pi$
$571$	−2.57697	−0.107843	−0.0539213	+	0.998545i	$0.517172\pi$
$572$	0.432297	0.0180752
$573$	−3.94681	−0.164880
$574$	19.5445	0.815772
$575$	9.02408	0.376330
$576$	−2.28290	−0.0951206
$577$	12.0125	0.500087	0.250043	−	0.968235i	$-0.419555\pi$
$577$	12.0125	0.500087	0.250043	+	0.968235i	$0.419555\pi$
$578$	−5.14071	−0.213825
$579$	2.28618	0.0950102
$580$	2.66287	0.110570
$581$	−2.46638	−0.102323
$582$	−0.578191	−0.0239668
$583$	−0.249902	−0.0103499
$584$	−10.5869	−0.438088
$585$	32.9487	1.36226
$586$	−26.7684	−1.10579
$587$	−20.3688	−0.840710	−0.420355	−	0.907360i	$-0.638095\pi$
$587$	−20.3688	−0.840710	−0.420355	+	0.907360i	$0.638095\pi$
$588$	5.86128	0.241715
$589$	−3.37751	−0.139168
$590$	22.2791	0.917217
$591$	−14.9205	−0.613749
$592$	0.0136820	0.000562326 0
$593$	17.1310	0.703486	0.351743	−	0.936097i	$-0.385589\pi$
$593$	17.1310	0.703486	0.351743	+	0.936097i	$0.385589\pi$
$594$	0.337100	0.0138314
$595$	−32.3250	−1.32520
$596$	3.68372	0.150891
$597$	9.65091	0.394985
$598$	−38.9564	−1.59305
$599$	5.99149	0.244806	0.122403	−	0.992481i	$-0.460940\pi$
$599$	5.99149	0.244806	0.122403	+	0.992481i	$0.460940\pi$
$600$	1.12539	0.0459437
$601$	28.3842	1.15782	0.578908	−	0.815393i	$-0.303479\pi$
$601$	28.3842	1.15782	0.578908	+	0.815393i	$0.303479\pi$
$602$	31.7344	1.29340
$603$	33.0544	1.34608
$604$	7.08380	0.288236
$605$	−27.6589	−1.12449
$606$	−5.15979	−0.209602
$607$	36.1322	1.46656	0.733281	−	0.679926i	$-0.237988\pi$
$607$	36.1322	1.46656	0.733281	+	0.679926i	$0.237988\pi$
$608$	1.00000	0.0405554
$609$	−3.34440	−0.135522
$610$	−2.65124	−0.107346
$611$	35.6182	1.44096
$612$	−7.86168	−0.317790
$613$	−19.6460	−0.793496	−0.396748	−	0.917928i	$-0.629861\pi$
$613$	−19.6460	−0.793496	−0.396748	+	0.917928i	$0.629861\pi$
$614$	21.6088	0.872058
$615$	−11.1594	−0.449988
$616$	0.281150	0.0113279
$617$	−25.6886	−1.03419	−0.517093	−	0.855929i	$-0.672986\pi$
$617$	−25.6886	−1.03419	−0.517093	+	0.855929i	$0.672986\pi$
$618$	−13.9954	−0.562978
$619$	40.6099	1.63225	0.816124	−	0.577876i	$-0.196118\pi$
$619$	40.6099	1.63225	0.816124	+	0.577876i	$0.196118\pi$
$620$	−8.49695	−0.341246
$621$	−30.3778	−1.21902
$622$	4.23255	0.169710
$623$	15.4900	0.620593
$624$	−4.85823	−0.194485
$625$	−29.8787	−1.19515
$626$	21.2458	0.849153
$627$	−0.0638097	−0.00254831
$628$	−1.84050	−0.0734439
$629$	0.0471171	0.00187868
$630$	21.4287	0.853739
$631$	−30.5871	−1.21766	−0.608828	−	0.793303i	$-0.708360\pi$
$631$	−30.5871	−1.21766	−0.608828	+	0.793303i	$0.708360\pi$
$632$	9.08302	0.361303
$633$	−0.846820	−0.0336581
$634$	24.3234	0.966007
$635$	−33.0003	−1.30958
$636$	2.80844	0.111362
$637$	−39.7089	−1.57332
$638$	−0.0797589	−0.00315769
$639$	24.1448	0.955152
$640$	2.51574	0.0994434
$641$	−16.0251	−0.632954	−0.316477	−	0.948600i	$-0.602500\pi$
$641$	−16.0251	−0.632954	−0.316477	+	0.948600i	$0.602500\pi$
$642$	7.74018	0.305481
$643$	4.93100	0.194460	0.0972299	−	0.995262i	$-0.469002\pi$
$643$	4.93100	0.194460	0.0972299	+	0.995262i	$0.469002\pi$
$644$	−25.3359	−0.998374
$645$	−18.1194	−0.713452
$646$	3.44373	0.135492
$647$	25.6515	1.00847	0.504233	−	0.863568i	$-0.331775\pi$
$647$	25.6515	1.00847	0.504233	+	0.863568i	$0.331775\pi$
$648$	3.06030	0.120220
$649$	−0.667309	−0.0261942
$650$	−7.62424	−0.299047
$651$	10.6716	0.418255
$652$	−9.61863	−0.376695
$653$	−27.2836	−1.06769	−0.533844	−	0.845583i	$-0.679253\pi$
$653$	−27.2836	−1.06769	−0.533844	+	0.845583i	$0.679253\pi$
$654$	3.79628	0.148446
$655$	34.6862	1.35530
$656$	−5.23820	−0.204517
$657$	24.1687	0.942912
$658$	23.1648	0.903058
$659$	−41.1158	−1.60164	−0.800821	−	0.598904i	$-0.795603\pi$
$659$	−41.1158	−1.60164	−0.800821	+	0.598904i	$0.795603\pi$
$660$	−0.160529	−0.00624857
$661$	18.2616	0.710294	0.355147	−	0.934811i	$-0.384431\pi$
$661$	18.2616	0.710294	0.355147	+	0.934811i	$0.384431\pi$
$662$	9.82654	0.381919
$663$	−16.7304	−0.649756
$664$	0.661023	0.0256527
$665$	−9.38662	−0.363997
$666$	−0.0312345	−0.00121031
$667$	7.18748	0.278300
$668$	10.5078	0.406560
$669$	−19.4028	−0.750156
$670$	−36.4258	−1.40725
$671$	0.0794106	0.00306561
$672$	−3.15962	−0.121885
$673$	−5.97396	−0.230279	−0.115140	−	0.993349i	$-0.536732\pi$
$673$	−5.97396	−0.230279	−0.115140	+	0.993349i	$0.536732\pi$
$674$	16.0274	0.617353
$675$	−5.94529	−0.228834
$676$	19.9134	0.765901
$677$	9.51990	0.365880	0.182940	−	0.983124i	$-0.441439\pi$
$677$	9.51990	0.365880	0.182940	+	0.983124i	$0.441439\pi$
$678$	−16.2726	−0.624945
$679$	2.54755	0.0977661
$680$	8.66354	0.332232
$681$	−12.2125	−0.467984
$682$	0.254503	0.00974541
$683$	32.9274	1.25993	0.629966	−	0.776623i	$-0.283069\pi$
$683$	32.9274	1.25993	0.629966	+	0.776623i	$0.283069\pi$
$684$	−2.28290	−0.0872887
$685$	−8.71660	−0.333044
$686$	0.292848	0.0111810
$687$	−19.9885	−0.762607
$688$	−8.50526	−0.324260
$689$	−19.0266	−0.724854
$690$	14.4661	0.550713
$691$	−34.0226	−1.29428	−0.647140	−	0.762371i	$-0.724035\pi$
$691$	−34.0226	−1.29428	−0.647140	+	0.762371i	$0.724035\pi$
$692$	−10.9446	−0.416049
$693$	−0.641837	−0.0243814
$694$	3.93856	0.149506
$695$	−10.2234	−0.387797
$696$	0.896345	0.0339759
$697$	−18.0389	−0.683274
$698$	1.23767	0.0468467
$699$	−21.5552	−0.815294
$700$	−4.95853	−0.187415
$701$	−25.5674	−0.965668	−0.482834	−	0.875712i	$-0.660392\pi$
$701$	−25.5674	−0.965668	−0.482834	+	0.875712i	$0.660392\pi$
$702$	25.6655	0.968682
$703$	0.0136820	0.000516026 0
$704$	−0.0753521	−0.00283994
$705$	−13.2264	−0.498136
$706$	5.65440	0.212806
$707$	22.7344	0.855016
$708$	7.49934	0.281843
$709$	10.2425	0.384663	0.192332	−	0.981330i	$-0.438395\pi$
$709$	10.2425	0.384663	0.192332	+	0.981330i	$0.438395\pi$
$710$	−26.6074	−0.998559
$711$	−20.7356	−0.777646
$712$	−4.15153	−0.155585
$713$	−22.9345	−0.858905
$714$	−10.8809	−0.407207
$715$	1.08755	0.0406719
$716$	6.23538	0.233027
$717$	−7.24403	−0.270533
$718$	9.74840	0.363807
$719$	−18.3629	−0.684820	−0.342410	−	0.939551i	$-0.611243\pi$
$719$	−18.3629	−0.684820	−0.342410	+	0.939551i	$0.611243\pi$
$720$	−5.74317	−0.214035
$721$	61.6649	2.29652
$722$	1.00000	0.0372161
$723$	21.4142	0.796402
$724$	9.18136	0.341223
$725$	1.40668	0.0522426
$726$	−9.31021	−0.345534
$727$	13.9659	0.517967	0.258983	−	0.965882i	$-0.416613\pi$
$727$	13.9659	0.517967	0.258983	+	0.965882i	$0.416613\pi$
$728$	21.4057	0.793349
$729$	4.37882	0.162179
$730$	−26.6339	−0.985763
$731$	−29.2898	−1.08332
$732$	−0.892431	−0.0329852
$733$	−11.4936	−0.424526	−0.212263	−	0.977213i	$-0.568083\pi$
$733$	−11.4936	−0.424526	−0.212263	+	0.977213i	$0.568083\pi$
$734$	−8.60189	−0.317502
$735$	14.7455	0.543894
$736$	6.79036	0.250296
$737$	1.09103	0.0401888
$738$	11.9583	0.440189
$739$	−8.84645	−0.325422	−0.162711	−	0.986674i	$-0.552024\pi$
$739$	−8.84645	−0.325422	−0.162711	+	0.986674i	$0.552024\pi$
$740$	0.0344203	0.00126532
$741$	−4.85823	−0.178471
$742$	−12.3742	−0.454271
$743$	19.4815	0.714708	0.357354	−	0.933969i	$-0.383679\pi$
$743$	19.4815	0.714708	0.357354	+	0.933969i	$0.383679\pi$
$744$	−2.86015	−0.104858
$745$	9.26729	0.339527
$746$	6.05625	0.221735
$747$	−1.50905	−0.0552131
$748$	−0.259492	−0.00948798
$749$	−34.1038	−1.24613
$750$	−7.82072	−0.285572
$751$	−37.7993	−1.37932	−0.689658	−	0.724135i	$-0.742239\pi$
$751$	−37.7993	−1.37932	−0.689658	+	0.724135i	$0.742239\pi$
$752$	−6.20848	−0.226400
$753$	11.7176	0.427013
$754$	−6.07254	−0.221149
$755$	17.8210	0.648573
$756$	16.6919	0.607079
$757$	−21.6737	−0.787745	−0.393873	−	0.919165i	$-0.628865\pi$
$757$	−21.6737	−0.787745	−0.393873	+	0.919165i	$0.628865\pi$
$758$	20.3044	0.737487
$759$	−0.433291	−0.0157275
$760$	2.51574	0.0912555
$761$	3.87589	0.140501	0.0702505	−	0.997529i	$-0.477620\pi$
$761$	3.87589	0.140501	0.0702505	+	0.997529i	$0.477620\pi$
$762$	−11.1082	−0.402407
$763$	−16.7267	−0.605547
$764$	−4.66074	−0.168619
$765$	−19.7780	−0.715074
$766$	31.1049	1.12387
$767$	−50.8064	−1.83451
$768$	0.846820	0.0305570
$769$	−49.1946	−1.77400	−0.887002	−	0.461766i	$-0.847216\pi$
$769$	−49.1946	−1.77400	−0.887002	+	0.461766i	$0.847216\pi$
$770$	0.707301	0.0254894
$771$	0.986240	0.0355186
$772$	2.69972	0.0971650
$773$	30.8200	1.10852	0.554260	−	0.832344i	$-0.313001\pi$
$773$	30.8200	1.10852	0.554260	+	0.832344i	$0.313001\pi$
$774$	19.4166	0.697916
$775$	−4.48856	−0.161234
$776$	−0.682779	−0.0245103
$777$	−0.0432298	−0.00155086
$778$	−7.23787	−0.259490
$779$	−5.23820	−0.187678
$780$	−12.2220	−0.437619
$781$	0.796952	0.0285172
$782$	23.3842	0.836217
$783$	−4.73530	−0.169226
$784$	6.92151	0.247197
$785$	−4.63022	−0.165260
$786$	11.6757	0.416457
$787$	−20.2589	−0.722153	−0.361077	−	0.932536i	$-0.617591\pi$
$787$	−20.2589	−0.722153	−0.361077	+	0.932536i	$0.617591\pi$
$788$	−17.6195	−0.627668
$789$	14.5879	0.519342
$790$	22.8505	0.812986
$791$	71.6983	2.54930
$792$	0.172021	0.00611250
$793$	6.04602	0.214701
$794$	22.1359	0.785572
$795$	7.06530	0.250580
$796$	11.3966	0.403943
$797$	42.7498	1.51428	0.757139	−	0.653254i	$-0.226597\pi$
$797$	42.7498	1.51428	0.757139	+	0.653254i	$0.226597\pi$
$798$	−3.15962	−0.111849
$799$	−21.3803	−0.756382
$800$	1.32895	0.0469856
$801$	9.47750	0.334871
$802$	13.9938	0.494138
$803$	0.797744	0.0281518
$804$	−12.2612	−0.432421
$805$	−63.7385	−2.24649
$806$	19.3769	0.682521
$807$	−4.73915	−0.166826
$808$	−6.09314	−0.214356
$809$	−21.8005	−0.766465	−0.383232	−	0.923652i	$-0.625189\pi$
$809$	−21.8005	−0.766465	−0.383232	+	0.923652i	$0.625189\pi$
$810$	7.69892	0.270512
$811$	39.8101	1.39792	0.698962	−	0.715159i	$-0.253646\pi$
$811$	39.8101	1.39792	0.698962	+	0.715159i	$0.253646\pi$
$812$	−3.94936	−0.138595
$813$	−5.38892	−0.188998
$814$	−0.00103097	−3.61354e−5 0
$815$	−24.1980	−0.847619
$816$	2.91622	0.102088
$817$	−8.50526	−0.297561
$818$	25.7319	0.899695
$819$	−48.8670	−1.70755
$820$	−13.1779	−0.460194
$821$	34.0338	1.18779	0.593895	−	0.804543i	$-0.297590\pi$
$821$	34.0338	1.18779	0.593895	+	0.804543i	$0.297590\pi$
$822$	−2.93408	−0.102338
$823$	36.5418	1.27377	0.636883	−	0.770960i	$-0.280223\pi$
$823$	36.5418	1.27377	0.636883	+	0.770960i	$0.280223\pi$
$824$	−16.5270	−0.575746
$825$	−0.0848001	−0.00295236
$826$	−33.0427	−1.14970
$827$	50.5007	1.75608	0.878041	−	0.478585i	$-0.158850\pi$
$827$	50.5007	1.75608	0.878041	+	0.478585i	$0.158850\pi$
$828$	−15.5017	−0.538721
$829$	−5.06039	−0.175755	−0.0878773	−	0.996131i	$-0.528008\pi$
$829$	−5.06039	−0.175755	−0.0878773	+	0.996131i	$0.528008\pi$
$830$	1.66296	0.0577223
$831$	19.7257	0.684278
$832$	−5.73702	−0.198895
$833$	23.8358	0.825863
$834$	−3.44130	−0.119162
$835$	26.4350	0.914819
$836$	−0.0753521	−0.00260611
$837$	15.1099	0.522273
$838$	1.36340	0.0470978
$839$	−12.8972	−0.445261	−0.222630	−	0.974903i	$-0.571464\pi$
$839$	−12.8972	−0.445261	−0.222630	+	0.974903i	$0.571464\pi$
$840$	−7.94878	−0.274259
$841$	−27.8796	−0.961366
$842$	−2.18984	−0.0754670
$843$	26.1727	0.901437
$844$	−1.00000	−0.0344214
$845$	50.0970	1.72339
$846$	14.1733	0.487288
$847$	41.0215	1.40952
$848$	3.31645	0.113887
$849$	6.67703	0.229155
$850$	4.57656	0.156975
$851$	0.0929056	0.00318476
$852$	−8.95629	−0.306837
$853$	13.0874	0.448103	0.224052	−	0.974577i	$-0.428072\pi$
$853$	13.0874	0.448103	0.224052	+	0.974577i	$0.428072\pi$
$854$	3.93212	0.134554
$855$	−5.74317	−0.196412
$856$	9.14029	0.312409
$857$	−3.57872	−0.122247	−0.0611234	−	0.998130i	$-0.519468\pi$
$857$	−3.57872	−0.122247	−0.0611234	+	0.998130i	$0.519468\pi$
$858$	0.366077	0.0124977
$859$	35.9009	1.22492	0.612461	−	0.790501i	$-0.290180\pi$
$859$	35.9009	1.22492	0.612461	+	0.790501i	$0.290180\pi$
$860$	−21.3970	−0.729633
$861$	16.5507	0.564046
$862$	8.48009	0.288833
$863$	51.2372	1.74414	0.872068	−	0.489385i	$-0.162779\pi$
$863$	51.2372	1.74414	0.872068	+	0.489385i	$0.162779\pi$
$864$	−4.47366	−0.152197
$865$	−27.5337	−0.936172
$866$	−10.4229	−0.354185
$867$	−4.35325	−0.147844
$868$	12.6020	0.427740
$869$	−0.684425	−0.0232175
$870$	2.25497	0.0764507
$871$	83.0672	2.81463
$872$	4.48298	0.151813
$873$	1.55871	0.0527544
$874$	6.79036	0.229687
$875$	34.4587	1.16492
$876$	−8.96518	−0.302906
$877$	2.74250	0.0926076	0.0463038	−	0.998927i	$-0.485256\pi$
$877$	2.74250	0.0926076	0.0463038	+	0.998927i	$0.485256\pi$
$878$	−12.6496	−0.426904
$879$	−22.6680	−0.764572
$880$	−0.189566	−0.00639028
$881$	−28.3894	−0.956462	−0.478231	−	0.878234i	$-0.658722\pi$
$881$	−28.3894	−0.956462	−0.478231	+	0.878234i	$0.658722\pi$
$882$	−15.8011	−0.532050
$883$	43.2360	1.45501	0.727504	−	0.686103i	$-0.240680\pi$
$883$	43.2360	1.45501	0.727504	+	0.686103i	$0.240680\pi$
$884$	−19.7568	−0.664492
$885$	18.8664	0.634187
$886$	−35.3294	−1.18692
$887$	−51.4742	−1.72834	−0.864168	−	0.503204i	$-0.832154\pi$
$887$	−51.4742	−1.72834	−0.864168	+	0.503204i	$0.832154\pi$
$888$	0.0115862	0.000388807 0
$889$	48.9434	1.64151
$890$	−10.4442	−0.350089
$891$	−0.230600	−0.00772539
$892$	−22.9125	−0.767169
$893$	−6.20848	−0.207759
$894$	3.11945	0.104330
$895$	15.6866	0.524345
$896$	−3.73115	−0.124649
$897$	−32.9891	−1.10147
$898$	−9.46560	−0.315871
$899$	−3.57504	−0.119234
$900$	−3.03386	−0.101129
$901$	11.4210	0.380488
$902$	0.394709	0.0131424
$903$	26.8734	0.894289
$904$	−19.2161	−0.639118
$905$	23.0979	0.767801
$906$	5.99871	0.199294
$907$	2.28392	0.0758365	0.0379182	−	0.999281i	$-0.487927\pi$
$907$	2.28392	0.0758365	0.0379182	+	0.999281i	$0.487927\pi$
$908$	−14.4216	−0.478598
$909$	13.9100	0.461365
$910$	53.8512	1.78515
$911$	−45.5629	−1.50956	−0.754782	−	0.655975i	$-0.772258\pi$
$911$	−45.5629	−1.50956	−0.754782	+	0.655975i	$0.772258\pi$
$912$	0.846820	0.0280410
$913$	−0.0498095	−0.00164845
$914$	−32.0612	−1.06049
$915$	−2.24512	−0.0742215
$916$	−23.6041	−0.779902
$917$	−51.4438	−1.69883
$918$	−15.4061	−0.508477
$919$	−48.0167	−1.58392	−0.791962	−	0.610571i	$-0.790940\pi$
$919$	−48.0167	−1.58392	−0.791962	+	0.610571i	$0.790940\pi$
$920$	17.0828	0.563203
$921$	18.2987	0.602964
$922$	27.2979	0.899009
$923$	60.6769	1.99720
$924$	0.238084	0.00783238
$925$	0.0181827	0.000597845 0
$926$	32.4611	1.06674
$927$	37.7295	1.23920
$928$	1.05848	0.0347464
$929$	−42.4245	−1.39190	−0.695951	−	0.718089i	$-0.745017\pi$
$929$	−42.4245	−1.39190	−0.695951	+	0.718089i	$0.745017\pi$
$930$	−7.19539	−0.235946
$931$	6.92151	0.226843
$932$	−25.4543	−0.833784
$933$	3.58421	0.117342
$934$	−31.2049	−1.02106
$935$	−0.652816	−0.0213494
$936$	13.0970	0.428090
$937$	−49.6572	−1.62223	−0.811115	−	0.584886i	$-0.801139\pi$
$937$	−49.6572	−1.62223	−0.811115	+	0.584886i	$0.801139\pi$
$938$	54.0240	1.76394
$939$	17.9914	0.587126
$940$	−15.6189	−0.509433
$941$	−45.4562	−1.48183	−0.740915	−	0.671599i	$-0.765608\pi$
$941$	−45.4562	−1.48183	−0.740915	+	0.671599i	$0.765608\pi$
$942$	−1.55857	−0.0507810
$943$	−35.5692	−1.15829
$944$	8.85589	0.288235
$945$	41.9926	1.36602
$946$	0.640889	0.0208371
$947$	−16.2142	−0.526892	−0.263446	−	0.964674i	$-0.584859\pi$
$947$	−16.2142	−0.526892	−0.263446	+	0.964674i	$0.584859\pi$
$948$	7.69169	0.249814
$949$	60.7372	1.97161
$950$	1.32895	0.0431170
$951$	20.5976	0.667922
$952$	−12.8491	−0.416442
$953$	−32.2726	−1.04541	−0.522706	−	0.852513i	$-0.675078\pi$
$953$	−32.2726	−1.04541	−0.522706	+	0.852513i	$0.675078\pi$
$954$	−7.57111	−0.245124
$955$	−11.7252	−0.379419
$956$	−8.55439	−0.276669
$957$	−0.0675415	−0.00218331
$958$	−22.2905	−0.720174
$959$	12.9278	0.417460
$960$	2.13038	0.0687577
$961$	−19.5924	−0.632013
$962$	−0.0784939	−0.00253074
$963$	−20.8663	−0.672408
$964$	25.2877	0.814463
$965$	6.79179	0.218636
$966$	−21.4549	−0.690301
$967$	17.3653	0.558431	0.279216	−	0.960228i	$-0.409926\pi$
$967$	17.3653	0.558431	0.279216	+	0.960228i	$0.409926\pi$
$968$	−10.9943	−0.353371
$969$	2.91622	0.0936826
$970$	−1.71770	−0.0551519
$971$	−3.71071	−0.119082	−0.0595412	−	0.998226i	$-0.518964\pi$
$971$	−3.71071	−0.119082	−0.0595412	+	0.998226i	$0.518964\pi$
$972$	16.0125	0.513602
$973$	15.1626	0.486091
$974$	4.50007	0.144192
$975$	−6.45636	−0.206769
$976$	−1.05386	−0.0337333
$977$	−30.3366	−0.970554	−0.485277	−	0.874360i	$-0.661281\pi$
$977$	−30.3366	−0.970554	−0.485277	+	0.874360i	$0.661281\pi$
$978$	−8.14525	−0.260456
$979$	0.312826	0.00999797
$980$	17.4127	0.556229
$981$	−10.2342	−0.326752
$982$	−39.6320	−1.26471
$983$	0.696013	0.0221994	0.0110997	−	0.999938i	$-0.496467\pi$
$983$	0.696013	0.0221994	0.0110997	+	0.999938i	$0.496467\pi$
$984$	−4.43581	−0.141408
$985$	−44.3261	−1.41235
$986$	3.64513	0.116085
$987$	19.6164	0.624397
$988$	−5.73702	−0.182519
$989$	−57.7538	−1.83646
$990$	0.432760	0.0137540
$991$	8.15308	0.258991	0.129496	−	0.991580i	$-0.458664\pi$
$991$	8.15308	0.258991	0.129496	+	0.991580i	$0.458664\pi$
$992$	−3.37751	−0.107236
$993$	8.32131	0.264069
$994$	39.4621	1.25166
$995$	28.6710	0.908932
$996$	0.559768	0.0177369
$997$	−22.6110	−0.716098	−0.358049	−	0.933703i	$-0.616558\pi$
$997$	−22.6110	−0.716098	−0.358049	+	0.933703i	$0.616558\pi$
$998$	17.7075	0.560521
$999$	−0.0612086	−0.00193655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.20	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.20	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.846820 q^{3} +1.00000 q^{4} +2.51574 q^{5} +0.846820 q^{6} -3.73115 q^{7} +1.00000 q^{8} -2.28290 q^{9} +2.51574 q^{10} -0.0753521 q^{11} +0.846820 q^{12} -5.73702 q^{13} -3.73115 q^{14} +2.13038 q^{15} +1.00000 q^{16} +3.44373 q^{17} -2.28290 q^{18} +1.00000 q^{19} +2.51574 q^{20} -3.15962 q^{21} -0.0753521 q^{22} +6.79036 q^{23} +0.846820 q^{24} +1.32895 q^{25} -5.73702 q^{26} -4.47366 q^{27} -3.73115 q^{28} +1.05848 q^{29} +2.13038 q^{30} -3.37751 q^{31} +1.00000 q^{32} -0.0638097 q^{33} +3.44373 q^{34} -9.38662 q^{35} -2.28290 q^{36} +0.0136820 q^{37} +1.00000 q^{38} -4.85823 q^{39} +2.51574 q^{40} -5.23820 q^{41} -3.15962 q^{42} -8.50526 q^{43} -0.0753521 q^{44} -5.74317 q^{45} +6.79036 q^{46} -6.20848 q^{47} +0.846820 q^{48} +6.92151 q^{49} +1.32895 q^{50} +2.91622 q^{51} -5.73702 q^{52} +3.31645 q^{53} -4.47366 q^{54} -0.189566 q^{55} -3.73115 q^{56} +0.846820 q^{57} +1.05848 q^{58} +8.85589 q^{59} +2.13038 q^{60} -1.05386 q^{61} -3.37751 q^{62} +8.51784 q^{63} +1.00000 q^{64} -14.4329 q^{65} -0.0638097 q^{66} -14.4792 q^{67} +3.44373 q^{68} +5.75021 q^{69} -9.38662 q^{70} -10.5764 q^{71} -2.28290 q^{72} -10.5869 q^{73} +0.0136820 q^{74} +1.12539 q^{75} +1.00000 q^{76} +0.281150 q^{77} -4.85823 q^{78} +9.08302 q^{79} +2.51574 q^{80} +3.06030 q^{81} -5.23820 q^{82} +0.661023 q^{83} -3.15962 q^{84} +8.66354 q^{85} -8.50526 q^{86} +0.896345 q^{87} -0.0753521 q^{88} -4.15153 q^{89} -5.74317 q^{90} +21.4057 q^{91} +6.79036 q^{92} -2.86015 q^{93} -6.20848 q^{94} +2.51574 q^{95} +0.846820 q^{96} -0.682779 q^{97} +6.92151 q^{98} +0.172021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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