LMFDB - Embedded newform 8018.2.a.d.1.16

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			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +2.27443 q^{10} +3.87014 q^{11} -0.219326 q^{12} -1.48964 q^{13} -3.32577 q^{14} -0.498840 q^{15} +1.00000 q^{16} +0.776211 q^{17} -2.95190 q^{18} +1.00000 q^{19} +2.27443 q^{20} +0.729426 q^{21} +3.87014 q^{22} -8.89752 q^{23} -0.219326 q^{24} +0.173023 q^{25} -1.48964 q^{26} +1.30540 q^{27} -3.32577 q^{28} +4.85906 q^{29} -0.498840 q^{30} +2.88048 q^{31} +1.00000 q^{32} -0.848822 q^{33} +0.776211 q^{34} -7.56422 q^{35} -2.95190 q^{36} -7.10422 q^{37} +1.00000 q^{38} +0.326715 q^{39} +2.27443 q^{40} -7.81788 q^{41} +0.729426 q^{42} +0.180535 q^{43} +3.87014 q^{44} -6.71388 q^{45} -8.89752 q^{46} +3.93186 q^{47} -0.219326 q^{48} +4.06072 q^{49} +0.173023 q^{50} -0.170243 q^{51} -1.48964 q^{52} +2.43017 q^{53} +1.30540 q^{54} +8.80236 q^{55} -3.32577 q^{56} -0.219326 q^{57} +4.85906 q^{58} -9.44317 q^{59} -0.498840 q^{60} -5.88140 q^{61} +2.88048 q^{62} +9.81732 q^{63} +1.00000 q^{64} -3.38807 q^{65} -0.848822 q^{66} -0.157168 q^{67} +0.776211 q^{68} +1.95145 q^{69} -7.56422 q^{70} +4.50788 q^{71} -2.95190 q^{72} -8.65662 q^{73} -7.10422 q^{74} -0.0379485 q^{75} +1.00000 q^{76} -12.8712 q^{77} +0.326715 q^{78} -7.31318 q^{79} +2.27443 q^{80} +8.56938 q^{81} -7.81788 q^{82} -11.8891 q^{83} +0.729426 q^{84} +1.76544 q^{85} +0.180535 q^{86} -1.06572 q^{87} +3.87014 q^{88} +6.08863 q^{89} -6.71388 q^{90} +4.95418 q^{91} -8.89752 q^{92} -0.631762 q^{93} +3.93186 q^{94} +2.27443 q^{95} -0.219326 q^{96} -0.915773 q^{97} +4.06072 q^{98} -11.4243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.219326	−0.126628	−0.0633139	−	0.997994i	$-0.520167\pi$
$3$	−0.219326	−0.126628	−0.0633139	+	0.997994i	$0.520167\pi$
$4$	1.00000	0.500000
$5$	2.27443	1.01716	0.508578	−	0.861016i	$-0.330171\pi$
$5$	2.27443	1.01716	0.508578	+	0.861016i	$0.330171\pi$
$6$	−0.219326	−0.0895393
$7$	−3.32577	−1.25702	−0.628511	−	0.777801i	$-0.716335\pi$
$7$	−3.32577	−1.25702	−0.628511	+	0.777801i	$0.716335\pi$
$8$	1.00000	0.353553
$9$	−2.95190	−0.983965
$10$	2.27443	0.719237
$11$	3.87014	1.16689	0.583446	−	0.812152i	$-0.301704\pi$
$11$	3.87014	1.16689	0.583446	+	0.812152i	$0.301704\pi$
$12$	−0.219326	−0.0633139
$13$	−1.48964	−0.413150	−0.206575	−	0.978431i	$-0.566232\pi$
$13$	−1.48964	−0.413150	−0.206575	+	0.978431i	$0.566232\pi$
$14$	−3.32577	−0.888849
$15$	−0.498840	−0.128800
$16$	1.00000	0.250000
$17$	0.776211	0.188259	0.0941294	−	0.995560i	$-0.469993\pi$
$17$	0.776211	0.188259	0.0941294	+	0.995560i	$0.469993\pi$
$18$	−2.95190	−0.695769
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.27443	0.508578
$21$	0.729426	0.159174
$22$	3.87014	0.825117
$23$	−8.89752	−1.85526	−0.927631	−	0.373498i	$-0.878158\pi$
$23$	−8.89752	−1.85526	−0.927631	+	0.373498i	$0.878158\pi$
$24$	−0.219326	−0.0447697
$25$	0.173023	0.0346047
$26$	−1.48964	−0.292141
$27$	1.30540	0.251225
$28$	−3.32577	−0.628511
$29$	4.85906	0.902305	0.451153	−	0.892447i	$-0.351013\pi$
$29$	4.85906	0.902305	0.451153	+	0.892447i	$0.351013\pi$
$30$	−0.498840	−0.0910754
$31$	2.88048	0.517349	0.258674	−	0.965965i	$-0.416714\pi$
$31$	2.88048	0.517349	0.258674	+	0.965965i	$0.416714\pi$
$32$	1.00000	0.176777
$33$	−0.848822	−0.147761
$34$	0.776211	0.133119
$35$	−7.56422	−1.27859
$36$	−2.95190	−0.491983
$37$	−7.10422	−1.16793	−0.583964	−	0.811780i	$-0.698499\pi$
$37$	−7.10422	−1.16793	−0.583964	+	0.811780i	$0.698499\pi$
$38$	1.00000	0.162221
$39$	0.326715	0.0523163
$40$	2.27443	0.359619
$41$	−7.81788	−1.22095	−0.610474	−	0.792036i	$-0.709021\pi$
$41$	−7.81788	−1.22095	−0.610474	+	0.792036i	$0.709021\pi$
$42$	0.729426	0.112553
$43$	0.180535	0.0275314	0.0137657	−	0.999905i	$-0.495618\pi$
$43$	0.180535	0.0275314	0.0137657	+	0.999905i	$0.495618\pi$
$44$	3.87014	0.583446
$45$	−6.71388	−1.00085
$46$	−8.89752	−1.31187
$47$	3.93186	0.573521	0.286761	−	0.958002i	$-0.407422\pi$
$47$	3.93186	0.573521	0.286761	+	0.958002i	$0.407422\pi$
$48$	−0.219326	−0.0316569
$49$	4.06072	0.580103
$50$	0.173023	0.0244692
$51$	−0.170243	−0.0238388
$52$	−1.48964	−0.206575
$53$	2.43017	0.333809	0.166905	−	0.985973i	$-0.446623\pi$
$53$	2.43017	0.333809	0.166905	+	0.985973i	$0.446623\pi$
$54$	1.30540	0.177643
$55$	8.80236	1.18691
$56$	−3.32577	−0.444424
$57$	−0.219326	−0.0290504
$58$	4.85906	0.638026
$59$	−9.44317	−1.22940	−0.614698	−	0.788763i	$-0.710722\pi$
$59$	−9.44317	−1.22940	−0.614698	+	0.788763i	$0.710722\pi$
$60$	−0.498840	−0.0644000
$61$	−5.88140	−0.753036	−0.376518	−	0.926409i	$-0.622879\pi$
$61$	−5.88140	−0.753036	−0.376518	+	0.926409i	$0.622879\pi$
$62$	2.88048	0.365821
$63$	9.81732	1.23687
$64$	1.00000	0.125000
$65$	−3.38807	−0.420238
$66$	−0.848822	−0.104483
$67$	−0.157168	−0.0192011	−0.00960056	−	0.999954i	$-0.503056\pi$
$67$	−0.157168	−0.0192011	−0.00960056	+	0.999954i	$0.503056\pi$
$68$	0.776211	0.0941294
$69$	1.95145	0.234928
$70$	−7.56422	−0.904097
$71$	4.50788	0.534987	0.267494	−	0.963560i	$-0.413805\pi$
$71$	4.50788	0.534987	0.267494	+	0.963560i	$0.413805\pi$
$72$	−2.95190	−0.347884
$73$	−8.65662	−1.01318	−0.506590	−	0.862187i	$-0.669094\pi$
$73$	−8.65662	−1.01318	−0.506590	+	0.862187i	$0.669094\pi$
$74$	−7.10422	−0.825849
$75$	−0.0379485	−0.00438191
$76$	1.00000	0.114708
$77$	−12.8712	−1.46681
$78$	0.326715	0.0369932
$79$	−7.31318	−0.822797	−0.411399	−	0.911455i	$-0.634960\pi$
$79$	−7.31318	−0.822797	−0.411399	+	0.911455i	$0.634960\pi$
$80$	2.27443	0.254289
$81$	8.56938	0.952153
$82$	−7.81788	−0.863341
$83$	−11.8891	−1.30500	−0.652498	−	0.757790i	$-0.726279\pi$
$83$	−11.8891	−1.30500	−0.652498	+	0.757790i	$0.726279\pi$
$84$	0.729426	0.0795869
$85$	1.76544	0.191488
$86$	0.180535	0.0194676
$87$	−1.06572	−0.114257
$88$	3.87014	0.412559
$89$	6.08863	0.645393	0.322697	−	0.946502i	$-0.395411\pi$
$89$	6.08863	0.645393	0.322697	+	0.946502i	$0.395411\pi$
$90$	−6.71388	−0.707705
$91$	4.95418	0.519339
$92$	−8.89752	−0.927631
$93$	−0.631762	−0.0655107
$94$	3.93186	0.405541
$95$	2.27443	0.233351
$96$	−0.219326	−0.0223848
$97$	−0.915773	−0.0929826	−0.0464913	−	0.998919i	$-0.514804\pi$
$97$	−0.915773	−0.0929826	−0.0464913	+	0.998919i	$0.514804\pi$
$98$	4.06072	0.410195
$99$	−11.4243	−1.14818
$100$	0.173023	0.0173023
$101$	13.9362	1.38670	0.693352	−	0.720599i	$-0.256133\pi$
$101$	13.9362	1.38670	0.693352	+	0.720599i	$0.256133\pi$
$102$	−0.170243	−0.0168566
$103$	0.216189	0.0213018	0.0106509	−	0.999943i	$-0.496610\pi$
$103$	0.216189	0.0213018	0.0106509	+	0.999943i	$0.496610\pi$
$104$	−1.48964	−0.146071
$105$	1.65903	0.161904
$106$	2.43017	0.236039
$107$	−8.87146	−0.857636	−0.428818	−	0.903391i	$-0.641070\pi$
$107$	−8.87146	−0.857636	−0.428818	+	0.903391i	$0.641070\pi$
$108$	1.30540	0.125613
$109$	−14.8224	−1.41973	−0.709866	−	0.704336i	$-0.751245\pi$
$109$	−14.8224	−1.41973	−0.709866	+	0.704336i	$0.751245\pi$
$110$	8.80236	0.839272
$111$	1.55814	0.147892
$112$	−3.32577	−0.314255
$113$	8.48491	0.798193	0.399096	−	0.916909i	$-0.369324\pi$
$113$	8.48491	0.798193	0.399096	+	0.916909i	$0.369324\pi$
$114$	−0.219326	−0.0205417
$115$	−20.2368	−1.88709
$116$	4.85906	0.451153
$117$	4.39725	0.406526
$118$	−9.44317	−0.869314
$119$	−2.58150	−0.236645
$120$	−0.498840	−0.0455377
$121$	3.97800	0.361637
$122$	−5.88140	−0.532477
$123$	1.71466	0.154606
$124$	2.88048	0.258674
$125$	−10.9786	−0.981957
$126$	9.81732	0.874596
$127$	−5.31550	−0.471675	−0.235837	−	0.971793i	$-0.575783\pi$
$127$	−5.31550	−0.471675	−0.235837	+	0.971793i	$0.575783\pi$
$128$	1.00000	0.0883883
$129$	−0.0395960	−0.00348623
$130$	−3.38807	−0.297153
$131$	2.03558	0.177849	0.0889245	−	0.996038i	$-0.471657\pi$
$131$	2.03558	0.177849	0.0889245	+	0.996038i	$0.471657\pi$
$132$	−0.848822	−0.0738804
$133$	−3.32577	−0.288381
$134$	−0.157168	−0.0135772
$135$	2.96905	0.255535
$136$	0.776211	0.0665595
$137$	0.269241	0.0230028	0.0115014	−	0.999934i	$-0.496339\pi$
$137$	0.269241	0.0230028	0.0115014	+	0.999934i	$0.496339\pi$
$138$	1.95145	0.166119
$139$	13.5163	1.14644	0.573221	−	0.819401i	$-0.305694\pi$
$139$	13.5163	1.14644	0.573221	+	0.819401i	$0.305694\pi$
$140$	−7.56422	−0.639293
$141$	−0.862358	−0.0726237
$142$	4.50788	0.378293
$143$	−5.76510	−0.482102
$144$	−2.95190	−0.245991
$145$	11.0516	0.917784
$146$	−8.65662	−0.716427
$147$	−0.890621	−0.0734572
$148$	−7.10422	−0.583964
$149$	16.1543	1.32342	0.661708	−	0.749762i	$-0.269832\pi$
$149$	16.1543	1.32342	0.661708	+	0.749762i	$0.269832\pi$
$150$	−0.0379485	−0.00309848
$151$	−2.60227	−0.211770	−0.105885	−	0.994378i	$-0.533768\pi$
$151$	−2.60227	−0.211770	−0.105885	+	0.994378i	$0.533768\pi$
$152$	1.00000	0.0811107
$153$	−2.29129	−0.185240
$154$	−12.8712	−1.03719
$155$	6.55143	0.526224
$156$	0.326715	0.0261581
$157$	−22.9956	−1.83525	−0.917623	−	0.397452i	$-0.869895\pi$
$157$	−22.9956	−1.83525	−0.917623	+	0.397452i	$0.869895\pi$
$158$	−7.31318	−0.581806
$159$	−0.532998	−0.0422695
$160$	2.27443	0.179809
$161$	29.5911	2.33210
$162$	8.56938	0.673274
$163$	−0.813102	−0.0636870	−0.0318435	−	0.999493i	$-0.510138\pi$
$163$	−0.813102	−0.0636870	−0.0318435	+	0.999493i	$0.510138\pi$
$164$	−7.81788	−0.610474
$165$	−1.93058	−0.150296
$166$	−11.8891	−0.922772
$167$	−0.224287	−0.0173558	−0.00867791	−	0.999962i	$-0.502762\pi$
$167$	−0.224287	−0.0173558	−0.00867791	+	0.999962i	$0.502762\pi$
$168$	0.729426	0.0562764
$169$	−10.7810	−0.829307
$170$	1.76544	0.135403
$171$	−2.95190	−0.225737
$172$	0.180535	0.0137657
$173$	−3.97111	−0.301918	−0.150959	−	0.988540i	$-0.548236\pi$
$173$	−3.97111	−0.301918	−0.150959	+	0.988540i	$0.548236\pi$
$174$	−1.06572	−0.0807918
$175$	−0.575435	−0.0434988
$176$	3.87014	0.291723
$177$	2.07113	0.155676
$178$	6.08863	0.456362
$179$	−1.17036	−0.0874768	−0.0437384	−	0.999043i	$-0.513927\pi$
$179$	−1.17036	−0.0874768	−0.0437384	+	0.999043i	$0.513927\pi$
$180$	−6.71388	−0.500423
$181$	−8.51244	−0.632725	−0.316362	−	0.948638i	$-0.602462\pi$
$181$	−8.51244	−0.632725	−0.316362	+	0.948638i	$0.602462\pi$
$182$	4.95418	0.367228
$183$	1.28994	0.0953553
$184$	−8.89752	−0.655934
$185$	−16.1580	−1.18796
$186$	−0.631762	−0.0463230
$187$	3.00405	0.219678
$188$	3.93186	0.286761
$189$	−4.34147	−0.315795
$190$	2.27443	0.165004
$191$	−26.5812	−1.92335	−0.961674	−	0.274196i	$-0.911588\pi$
$191$	−26.5812	−1.92335	−0.961674	+	0.274196i	$0.911588\pi$
$192$	−0.219326	−0.0158285
$193$	2.02726	0.145925	0.0729627	−	0.997335i	$-0.476755\pi$
$193$	2.02726	0.145925	0.0729627	+	0.997335i	$0.476755\pi$
$194$	−0.915773	−0.0657486
$195$	0.743090	0.0532138
$196$	4.06072	0.290052
$197$	−23.4024	−1.66735	−0.833676	−	0.552254i	$-0.813768\pi$
$197$	−23.4024	−1.66735	−0.833676	+	0.552254i	$0.813768\pi$
$198$	−11.4243	−0.811887
$199$	12.2850	0.870860	0.435430	−	0.900223i	$-0.356596\pi$
$199$	12.2850	0.870860	0.435430	+	0.900223i	$0.356596\pi$
$200$	0.173023	0.0122346
$201$	0.0344710	0.00243139
$202$	13.9362	0.980547
$203$	−16.1601	−1.13422
$204$	−0.170243	−0.0119194
$205$	−17.7812	−1.24189
$206$	0.216189	0.0150626
$207$	26.2646	1.82551
$208$	−1.48964	−0.103288
$209$	3.87014	0.267703
$210$	1.65903	0.114484
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	2.43017	0.166905
$213$	−0.988694	−0.0677442
$214$	−8.87146	−0.606440
$215$	0.410614	0.0280037
$216$	1.30540	0.0888215
$217$	−9.57979	−0.650318
$218$	−14.8224	−1.00390
$219$	1.89862	0.128297
$220$	8.80236	0.593455
$221$	−1.15627	−0.0777792
$222$	1.55814	0.104575
$223$	9.42269	0.630990	0.315495	−	0.948927i	$-0.397829\pi$
$223$	9.42269	0.630990	0.315495	+	0.948927i	$0.397829\pi$
$224$	−3.32577	−0.222212
$225$	−0.510747	−0.0340498
$226$	8.48491	0.564408
$227$	−23.2406	−1.54254	−0.771268	−	0.636511i	$-0.780377\pi$
$227$	−23.2406	−1.54254	−0.771268	+	0.636511i	$0.780377\pi$
$228$	−0.219326	−0.0145252
$229$	5.04393	0.333312	0.166656	−	0.986015i	$-0.446703\pi$
$229$	5.04393	0.333312	0.166656	+	0.986015i	$0.446703\pi$
$230$	−20.2368	−1.33437
$231$	2.82298	0.185739
$232$	4.85906	0.319013
$233$	0.0399453	0.00261690	0.00130845	−	0.999999i	$-0.499584\pi$
$233$	0.0399453	0.00261690	0.00130845	+	0.999999i	$0.499584\pi$
$234$	4.39725	0.287457
$235$	8.94274	0.583360
$236$	−9.44317	−0.614698
$237$	1.60397	0.104189
$238$	−2.58150	−0.167334
$239$	18.8370	1.21847	0.609233	−	0.792992i	$-0.291478\pi$
$239$	18.8370	1.21847	0.609233	+	0.792992i	$0.291478\pi$
$240$	−0.498840	−0.0322000
$241$	−17.3048	−1.11470	−0.557352	−	0.830277i	$-0.688182\pi$
$241$	−17.3048	−1.11470	−0.557352	+	0.830277i	$0.688182\pi$
$242$	3.97800	0.255716
$243$	−5.79570	−0.371794
$244$	−5.88140	−0.376518
$245$	9.23582	0.590055
$246$	1.71466	0.109323
$247$	−1.48964	−0.0947832
$248$	2.88048	0.182910
$249$	2.60758	0.165249
$250$	−10.9786	−0.694348
$251$	0.183589	0.0115880	0.00579402	−	0.999983i	$-0.498156\pi$
$251$	0.183589	0.0115880	0.00579402	+	0.999983i	$0.498156\pi$
$252$	9.81732	0.618433
$253$	−34.4347	−2.16489
$254$	−5.31550	−0.333524
$255$	−0.387205	−0.0242477
$256$	1.00000	0.0625000
$257$	−28.6461	−1.78690	−0.893448	−	0.449166i	$-0.851721\pi$
$257$	−28.6461	−1.78690	−0.893448	+	0.449166i	$0.851721\pi$
$258$	−0.0395960	−0.00246514
$259$	23.6270	1.46811
$260$	−3.38807	−0.210119
$261$	−14.3434	−0.887837
$262$	2.03558	0.125758
$263$	−13.6178	−0.839710	−0.419855	−	0.907591i	$-0.637919\pi$
$263$	−13.6178	−0.839710	−0.419855	+	0.907591i	$0.637919\pi$
$264$	−0.848822	−0.0522414
$265$	5.52724	0.339536
$266$	−3.32577	−0.203916
$267$	−1.33539	−0.0817247
$268$	−0.157168	−0.00960056
$269$	−3.95941	−0.241410	−0.120705	−	0.992688i	$-0.538515\pi$
$269$	−3.95941	−0.241410	−0.120705	+	0.992688i	$0.538515\pi$
$270$	2.96905	0.180690
$271$	−4.17077	−0.253356	−0.126678	−	0.991944i	$-0.540432\pi$
$271$	−4.17077	−0.253356	−0.126678	+	0.991944i	$0.540432\pi$
$272$	0.776211	0.0470647
$273$	−1.08658	−0.0657627
$274$	0.269241	0.0162655
$275$	0.669625	0.0403799
$276$	1.95145	0.117464
$277$	17.6128	1.05825	0.529126	−	0.848543i	$-0.322520\pi$
$277$	17.6128	1.05825	0.529126	+	0.848543i	$0.322520\pi$
$278$	13.5163	0.810656
$279$	−8.50286	−0.509053
$280$	−7.56422	−0.452048
$281$	−15.1516	−0.903866	−0.451933	−	0.892052i	$-0.649265\pi$
$281$	−15.1516	−0.903866	−0.451933	+	0.892052i	$0.649265\pi$
$282$	−0.862358	−0.0513527
$283$	32.2846	1.91912	0.959559	−	0.281506i	$-0.0908339\pi$
$283$	32.2846	1.91912	0.959559	+	0.281506i	$0.0908339\pi$
$284$	4.50788	0.267494
$285$	−0.498840	−0.0295488
$286$	−5.76510	−0.340898
$287$	26.0005	1.53476
$288$	−2.95190	−0.173942
$289$	−16.3975	−0.964559
$290$	11.0516	0.648972
$291$	0.200852	0.0117742
$292$	−8.65662	−0.506590
$293$	26.6325	1.55589	0.777945	−	0.628332i	$-0.216262\pi$
$293$	26.6325	1.55589	0.777945	+	0.628332i	$0.216262\pi$
$294$	−0.890621	−0.0519421
$295$	−21.4778	−1.25049
$296$	−7.10422	−0.412925
$297$	5.05210	0.293152
$298$	16.1543	0.935796
$299$	13.2541	0.766502
$300$	−0.0379485	−0.00219096
$301$	−0.600418	−0.0346075
$302$	−2.60227	−0.149744
$303$	−3.05657	−0.175595
$304$	1.00000	0.0573539
$305$	−13.3768	−0.765955
$306$	−2.29129	−0.130985
$307$	17.8341	1.01784	0.508922	−	0.860813i	$-0.330044\pi$
$307$	17.8341	1.01784	0.508922	+	0.860813i	$0.330044\pi$
$308$	−12.8712	−0.733404
$309$	−0.0474159	−0.00269739
$310$	6.55143	0.372096
$311$	−23.3430	−1.32366	−0.661830	−	0.749654i	$-0.730220\pi$
$311$	−23.3430	−1.32366	−0.661830	+	0.749654i	$0.730220\pi$
$312$	0.326715	0.0184966
$313$	0.540099	0.0305282	0.0152641	−	0.999883i	$-0.495141\pi$
$313$	0.540099	0.0305282	0.0152641	+	0.999883i	$0.495141\pi$
$314$	−22.9956	−1.29771
$315$	22.3288	1.25808
$316$	−7.31318	−0.411399
$317$	17.0554	0.957925	0.478963	−	0.877835i	$-0.341013\pi$
$317$	17.0554	0.957925	0.478963	+	0.877835i	$0.341013\pi$
$318$	−0.532998	−0.0298890
$319$	18.8053	1.05289
$320$	2.27443	0.127144
$321$	1.94574	0.108600
$322$	29.5911	1.64905
$323$	0.776211	0.0431895
$324$	8.56938	0.476077
$325$	−0.257742	−0.0142969
$326$	−0.813102	−0.0450335
$327$	3.25094	0.179777
$328$	−7.81788	−0.431670
$329$	−13.0765	−0.720929
$330$	−1.93058	−0.106275
$331$	34.0474	1.87142	0.935708	−	0.352776i	$-0.114762\pi$
$331$	34.0474	1.87142	0.935708	+	0.352776i	$0.114762\pi$
$332$	−11.8891	−0.652498
$333$	20.9709	1.14920
$334$	−0.224287	−0.0122724
$335$	−0.357467	−0.0195305
$336$	0.729426	0.0397934
$337$	−9.48533	−0.516699	−0.258350	−	0.966052i	$-0.583179\pi$
$337$	−9.48533	−0.516699	−0.258350	+	0.966052i	$0.583179\pi$
$338$	−10.7810	−0.586408
$339$	−1.86096	−0.101073
$340$	1.76544	0.0957442
$341$	11.1478	0.603690
$342$	−2.95190	−0.159620
$343$	9.77535	0.527819
$344$	0.180535	0.00973381
$345$	4.43844	0.238958
$346$	−3.97111	−0.213488
$347$	−36.5159	−1.96028	−0.980139	−	0.198313i	$-0.936454\pi$
$347$	−36.5159	−1.96028	−0.980139	+	0.198313i	$0.936454\pi$
$348$	−1.06572	−0.0571284
$349$	5.10461	0.273243	0.136622	−	0.990623i	$-0.456376\pi$
$349$	5.10461	0.273243	0.136622	+	0.990623i	$0.456376\pi$
$350$	−0.575435	−0.0307583
$351$	−1.94457	−0.103794
$352$	3.87014	0.206279
$353$	−9.06775	−0.482628	−0.241314	−	0.970447i	$-0.577578\pi$
$353$	−9.06775	−0.482628	−0.241314	+	0.970447i	$0.577578\pi$
$354$	2.07113	0.110079
$355$	10.2529	0.544165
$356$	6.08863	0.322697
$357$	0.566188	0.0299659
$358$	−1.17036	−0.0618554
$359$	15.4124	0.813434	0.406717	−	0.913554i	$-0.366673\pi$
$359$	15.4124	0.813434	0.406717	+	0.913554i	$0.366673\pi$
$360$	−6.71388	−0.353852
$361$	1.00000	0.0526316
$362$	−8.51244	−0.447404
$363$	−0.872478	−0.0457932
$364$	4.95418	0.259670
$365$	−19.6889	−1.03056
$366$	1.28994	0.0674264
$367$	−23.5461	−1.22910	−0.614548	−	0.788880i	$-0.710661\pi$
$367$	−23.5461	−1.22910	−0.614548	+	0.788880i	$0.710661\pi$
$368$	−8.89752	−0.463815
$369$	23.0776	1.20137
$370$	−16.1580	−0.840017
$371$	−8.08217	−0.419605
$372$	−0.631762	−0.0327553
$373$	18.0439	0.934280	0.467140	−	0.884183i	$-0.345284\pi$
$373$	18.0439	0.934280	0.467140	+	0.884183i	$0.345284\pi$
$374$	3.00405	0.155336
$375$	2.40789	0.124343
$376$	3.93186	0.202770
$377$	−7.23823	−0.372788
$378$	−4.34147	−0.223301
$379$	25.5307	1.31143	0.655713	−	0.755010i	$-0.272368\pi$
$379$	25.5307	1.31143	0.655713	+	0.755010i	$0.272368\pi$
$380$	2.27443	0.116676
$381$	1.16583	0.0597271
$382$	−26.5812	−1.36001
$383$	10.9443	0.559226	0.279613	−	0.960113i	$-0.409794\pi$
$383$	10.9443	0.559226	0.279613	+	0.960113i	$0.409794\pi$
$384$	−0.219326	−0.0111924
$385$	−29.2746	−1.49197
$386$	2.02726	0.103185
$387$	−0.532921	−0.0270899
$388$	−0.915773	−0.0464913
$389$	11.8152	0.599054	0.299527	−	0.954088i	$-0.403171\pi$
$389$	11.8152	0.599054	0.299527	+	0.954088i	$0.403171\pi$
$390$	0.743090	0.0376278
$391$	−6.90635	−0.349269
$392$	4.06072	0.205098
$393$	−0.446454	−0.0225206
$394$	−23.4024	−1.17900
$395$	−16.6333	−0.836913
$396$	−11.4243	−0.574091
$397$	−25.4826	−1.27893	−0.639467	−	0.768819i	$-0.720845\pi$
$397$	−25.4826	−1.27893	−0.639467	+	0.768819i	$0.720845\pi$
$398$	12.2850	0.615791
$399$	0.729426	0.0365170
$400$	0.173023	0.00865117
$401$	−26.9100	−1.34382	−0.671911	−	0.740632i	$-0.734526\pi$
$401$	−26.9100	−1.34382	−0.671911	+	0.740632i	$0.734526\pi$
$402$	0.0344710	0.00171926
$403$	−4.29086	−0.213743
$404$	13.9362	0.693352
$405$	19.4904	0.968488
$406$	−16.1601	−0.802013
$407$	−27.4944	−1.36284
$408$	−0.170243	−0.00842828
$409$	−17.8779	−0.884007	−0.442003	−	0.897013i	$-0.645732\pi$
$409$	−17.8779	−0.884007	−0.442003	+	0.897013i	$0.645732\pi$
$410$	−17.7812	−0.878152
$411$	−0.0590515	−0.00291280
$412$	0.216189	0.0106509
$413$	31.4058	1.54538
$414$	26.2646	1.29083
$415$	−27.0409	−1.32738
$416$	−1.48964	−0.0730354
$417$	−2.96448	−0.145171
$418$	3.87014	0.189295
$419$	1.95105	0.0953150	0.0476575	−	0.998864i	$-0.484824\pi$
$419$	1.95105	0.0953150	0.0476575	+	0.998864i	$0.484824\pi$
$420$	1.65903	0.0809522
$421$	7.76004	0.378201	0.189101	−	0.981958i	$-0.439443\pi$
$421$	7.76004	0.378201	0.189101	+	0.981958i	$0.439443\pi$
$422$	−1.00000	−0.0486792
$423$	−11.6065	−0.564325
$424$	2.43017	0.118019
$425$	0.134303	0.00651464
$426$	−0.988694	−0.0479024
$427$	19.5602	0.946583
$428$	−8.87146	−0.428818
$429$	1.26443	0.0610475
$430$	0.410614	0.0198016
$431$	−12.2312	−0.589156	−0.294578	−	0.955627i	$-0.595179\pi$
$431$	−12.2312	−0.589156	−0.294578	+	0.955627i	$0.595179\pi$
$432$	1.30540	0.0628063
$433$	18.6933	0.898342	0.449171	−	0.893446i	$-0.351719\pi$
$433$	18.6933	0.898342	0.449171	+	0.893446i	$0.351719\pi$
$434$	−9.57979	−0.459845
$435$	−2.42390	−0.116217
$436$	−14.8224	−0.709866
$437$	−8.89752	−0.425626
$438$	1.89862	0.0907195
$439$	−10.4972	−0.501005	−0.250502	−	0.968116i	$-0.580596\pi$
$439$	−10.4972	−0.501005	−0.250502	+	0.968116i	$0.580596\pi$
$440$	8.80236	0.419636
$441$	−11.9868	−0.570802
$442$	−1.15627	−0.0549982
$443$	38.5842	1.83319	0.916596	−	0.399814i	$-0.130925\pi$
$443$	38.5842	1.83319	0.916596	+	0.399814i	$0.130925\pi$
$444$	1.55814	0.0739460
$445$	13.8481	0.656465
$446$	9.42269	0.446178
$447$	−3.54306	−0.167581
$448$	−3.32577	−0.157128
$449$	−30.0086	−1.41619	−0.708096	−	0.706116i	$-0.750446\pi$
$449$	−30.0086	−1.41619	−0.708096	+	0.706116i	$0.750446\pi$
$450$	−0.510747	−0.0240769
$451$	−30.2563	−1.42471
$452$	8.48491	0.399096
$453$	0.570745	0.0268159
$454$	−23.2406	−1.09074
$455$	11.2679	0.528248
$456$	−0.219326	−0.0102709
$457$	34.4348	1.61079	0.805397	−	0.592736i	$-0.201952\pi$
$457$	34.4348	1.61079	0.805397	+	0.592736i	$0.201952\pi$
$458$	5.04393	0.235687
$459$	1.01327	0.0472953
$460$	−20.2368	−0.943545
$461$	−8.96726	−0.417647	−0.208823	−	0.977953i	$-0.566963\pi$
$461$	−8.96726	−0.417647	−0.208823	+	0.977953i	$0.566963\pi$
$462$	2.82298	0.131337
$463$	−12.2753	−0.570480	−0.285240	−	0.958456i	$-0.592073\pi$
$463$	−12.2753	−0.570480	−0.285240	+	0.958456i	$0.592073\pi$
$464$	4.85906	0.225576
$465$	−1.43690	−0.0666345
$466$	0.0399453	0.00185043
$467$	37.4755	1.73416	0.867079	−	0.498171i	$-0.165995\pi$
$467$	37.4755	1.73416	0.867079	+	0.498171i	$0.165995\pi$
$468$	4.39725	0.203263
$469$	0.522704	0.0241362
$470$	8.94274	0.412498
$471$	5.04352	0.232393
$472$	−9.44317	−0.434657
$473$	0.698697	0.0321261
$474$	1.60397	0.0736727
$475$	0.173023	0.00793886
$476$	−2.58150	−0.118323
$477$	−7.17360	−0.328457
$478$	18.8370	0.861585
$479$	−0.888395	−0.0405918	−0.0202959	−	0.999794i	$-0.506461\pi$
$479$	−0.888395	−0.0405918	−0.0202959	+	0.999794i	$0.506461\pi$
$480$	−0.498840	−0.0227688
$481$	10.5827	0.482530
$482$	−17.3048	−0.788214
$483$	−6.49008	−0.295309
$484$	3.97800	0.180818
$485$	−2.08286	−0.0945777
$486$	−5.79570	−0.262898
$487$	−22.8576	−1.03578	−0.517888	−	0.855448i	$-0.673282\pi$
$487$	−22.8576	−1.03578	−0.517888	+	0.855448i	$0.673282\pi$
$488$	−5.88140	−0.266239
$489$	0.178334	0.00806454
$490$	9.23582	0.417232
$491$	12.6592	0.571303	0.285652	−	0.958334i	$-0.407790\pi$
$491$	12.6592	0.571303	0.285652	+	0.958334i	$0.407790\pi$
$492$	1.71466	0.0773030
$493$	3.77166	0.169867
$494$	−1.48964	−0.0670218
$495$	−25.9837	−1.16788
$496$	2.88048	0.129337
$497$	−14.9922	−0.672490
$498$	2.60758	0.116849
$499$	43.5023	1.94743	0.973715	−	0.227768i	$-0.0731427\pi$
$499$	43.5023	1.94743	0.973715	+	0.227768i	$0.0731427\pi$
$500$	−10.9786	−0.490978
$501$	0.0491918	0.00219773
$502$	0.183589	0.00819398
$503$	3.62671	0.161707	0.0808534	−	0.996726i	$-0.474235\pi$
$503$	3.62671	0.161707	0.0808534	+	0.996726i	$0.474235\pi$
$504$	9.81732	0.437298
$505$	31.6969	1.41049
$506$	−34.4347	−1.53081
$507$	2.36455	0.105013
$508$	−5.31550	−0.235837
$509$	−24.9347	−1.10521	−0.552606	−	0.833443i	$-0.686366\pi$
$509$	−24.9347	−1.10521	−0.552606	+	0.833443i	$0.686366\pi$
$510$	−0.387205	−0.0171457
$511$	28.7899	1.27359
$512$	1.00000	0.0441942
$513$	1.30540	0.0576350
$514$	−28.6461	−1.26353
$515$	0.491707	0.0216672
$516$	−0.0395960	−0.00174312
$517$	15.2169	0.669237
$518$	23.6270	1.03811
$519$	0.870965	0.0382311
$520$	−3.38807	−0.148577
$521$	3.44440	0.150902	0.0754510	−	0.997150i	$-0.475960\pi$
$521$	3.44440	0.150902	0.0754510	+	0.997150i	$0.475960\pi$
$522$	−14.3434	−0.627796
$523$	18.8977	0.826341	0.413170	−	0.910654i	$-0.364421\pi$
$523$	18.8977	0.826341	0.413170	+	0.910654i	$0.364421\pi$
$524$	2.03558	0.0889245
$525$	0.126208	0.00550816
$526$	−13.6178	−0.593765
$527$	2.23586	0.0973954
$528$	−0.848822	−0.0369402
$529$	56.1659	2.44200
$530$	5.52724	0.240088
$531$	27.8753	1.20968
$532$	−3.32577	−0.144190
$533$	11.6458	0.504435
$534$	−1.33539	−0.0577881
$535$	−20.1775	−0.872349
$536$	−0.157168	−0.00678862
$537$	0.256690	0.0110770
$538$	−3.95941	−0.170702
$539$	15.7156	0.676918
$540$	2.96905	0.127767
$541$	16.7703	0.721011	0.360505	−	0.932757i	$-0.382604\pi$
$541$	16.7703	0.721011	0.360505	+	0.932757i	$0.382604\pi$
$542$	−4.17077	−0.179150
$543$	1.86700	0.0801205
$544$	0.776211	0.0332798
$545$	−33.7126	−1.44409
$546$	−1.08658	−0.0465013
$547$	−25.6690	−1.09753	−0.548764	−	0.835977i	$-0.684902\pi$
$547$	−25.6690	−1.09753	−0.548764	+	0.835977i	$0.684902\pi$
$548$	0.269241	0.0115014
$549$	17.3613	0.740962
$550$	0.669625	0.0285529
$551$	4.85906	0.207003
$552$	1.95145	0.0830594
$553$	24.3219	1.03427
$554$	17.6128	0.748297
$555$	3.54387	0.150429
$556$	13.5163	0.573221
$557$	−30.3522	−1.28607	−0.643033	−	0.765838i	$-0.722324\pi$
$557$	−30.3522	−1.28607	−0.643033	+	0.765838i	$0.722324\pi$
$558$	−8.50286	−0.359955
$559$	−0.268932	−0.0113746
$560$	−7.56422	−0.319647
$561$	−0.658865	−0.0278173
$562$	−15.1516	−0.639130
$563$	−15.3643	−0.647528	−0.323764	−	0.946138i	$-0.604948\pi$
$563$	−15.3643	−0.647528	−0.323764	+	0.946138i	$0.604948\pi$
$564$	−0.862358	−0.0363118
$565$	19.2983	0.811886
$566$	32.2846	1.35702
$567$	−28.4998	−1.19688
$568$	4.50788	0.189147
$569$	2.41097	0.101073	0.0505366	−	0.998722i	$-0.483907\pi$
$569$	2.41097	0.101073	0.0505366	+	0.998722i	$0.483907\pi$
$570$	−0.498840	−0.0208941
$571$	13.9963	0.585725	0.292863	−	0.956155i	$-0.405392\pi$
$571$	13.9963	0.585725	0.292863	+	0.956155i	$0.405392\pi$
$572$	−5.76510	−0.241051
$573$	5.82994	0.243549
$574$	26.0005	1.08524
$575$	−1.53948	−0.0642007
$576$	−2.95190	−0.122996
$577$	6.63098	0.276051	0.138026	−	0.990429i	$-0.455924\pi$
$577$	6.63098	0.276051	0.138026	+	0.990429i	$0.455924\pi$
$578$	−16.3975	−0.682046
$579$	−0.444630	−0.0184782
$580$	11.0516	0.458892
$581$	39.5403	1.64041
$582$	0.200852	0.00832560
$583$	9.40509	0.389519
$584$	−8.65662	−0.358213
$585$	10.0012	0.413500
$586$	26.6325	1.10018
$587$	−37.7032	−1.55618	−0.778088	−	0.628155i	$-0.783810\pi$
$587$	−37.7032	−1.55618	−0.778088	+	0.628155i	$0.783810\pi$
$588$	−0.890621	−0.0367286
$589$	2.88048	0.118688
$590$	−21.4778	−0.884227
$591$	5.13275	0.211133
$592$	−7.10422	−0.291982
$593$	−2.24240	−0.0920845	−0.0460422	−	0.998939i	$-0.514661\pi$
$593$	−2.24240	−0.0920845	−0.0460422	+	0.998939i	$0.514661\pi$
$594$	5.05210	0.207290
$595$	−5.87143	−0.240705
$596$	16.1543	0.661708
$597$	−2.69441	−0.110275
$598$	13.2541	0.541999
$599$	37.6138	1.53686	0.768430	−	0.639934i	$-0.221038\pi$
$599$	37.6138	1.53686	0.768430	+	0.639934i	$0.221038\pi$
$600$	−0.0379485	−0.00154924
$601$	−21.9816	−0.896650	−0.448325	−	0.893871i	$-0.647979\pi$
$601$	−21.9816	−0.896650	−0.448325	+	0.893871i	$0.647979\pi$
$602$	−0.600418	−0.0244712
$603$	0.463943	0.0188932
$604$	−2.60227	−0.105885
$605$	9.04768	0.367841
$606$	−3.05657	−0.124164
$607$	18.8259	0.764118	0.382059	−	0.924138i	$-0.375215\pi$
$607$	18.8259	0.764118	0.382059	+	0.924138i	$0.375215\pi$
$608$	1.00000	0.0405554
$609$	3.54433	0.143623
$610$	−13.3768	−0.541612
$611$	−5.85704	−0.236951
$612$	−2.29129	−0.0926201
$613$	−34.1263	−1.37835	−0.689174	−	0.724596i	$-0.742027\pi$
$613$	−34.1263	−1.37835	−0.689174	+	0.724596i	$0.742027\pi$
$614$	17.8341	0.719725
$615$	3.89988	0.157258
$616$	−12.8712	−0.518595
$617$	−8.79088	−0.353907	−0.176954	−	0.984219i	$-0.556624\pi$
$617$	−8.79088	−0.353907	−0.176954	+	0.984219i	$0.556624\pi$
$618$	−0.0474159	−0.00190735
$619$	−13.6216	−0.547500	−0.273750	−	0.961801i	$-0.588264\pi$
$619$	−13.6216	−0.547500	−0.273750	+	0.961801i	$0.588264\pi$
$620$	6.55143	0.263112
$621$	−11.6149	−0.466088
$622$	−23.3430	−0.935969
$623$	−20.2494	−0.811273
$624$	0.326715	0.0130791
$625$	−25.8352	−1.03341
$626$	0.540099	0.0215867
$627$	−0.848822	−0.0338987
$628$	−22.9956	−0.917623
$629$	−5.51438	−0.219873
$630$	22.3288	0.889600
$631$	16.0179	0.637664	0.318832	−	0.947811i	$-0.396709\pi$
$631$	16.0179	0.637664	0.318832	+	0.947811i	$0.396709\pi$
$632$	−7.31318	−0.290903
$633$	0.219326	0.00871741
$634$	17.0554	0.677356
$635$	−12.0897	−0.479766
$636$	−0.532998	−0.0211347
$637$	−6.04900	−0.239670
$638$	18.8053	0.744507
$639$	−13.3068	−0.526409
$640$	2.27443	0.0899047
$641$	−7.21015	−0.284784	−0.142392	−	0.989810i	$-0.545479\pi$
$641$	−7.21015	−0.284784	−0.142392	+	0.989810i	$0.545479\pi$
$642$	1.94574	0.0767921
$643$	4.15506	0.163860	0.0819298	−	0.996638i	$-0.473892\pi$
$643$	4.15506	0.163860	0.0819298	+	0.996638i	$0.473892\pi$
$644$	29.5911	1.16605
$645$	−0.0900583	−0.00354604
$646$	0.776211	0.0305396
$647$	40.2218	1.58128	0.790642	−	0.612279i	$-0.209747\pi$
$647$	40.2218	1.58128	0.790642	+	0.612279i	$0.209747\pi$
$648$	8.56938	0.336637
$649$	−36.5464	−1.43457
$650$	−0.257742	−0.0101095
$651$	2.10109	0.0823483
$652$	−0.813102	−0.0318435
$653$	−16.0758	−0.629096	−0.314548	−	0.949242i	$-0.601853\pi$
$653$	−16.0758	−0.629096	−0.314548	+	0.949242i	$0.601853\pi$
$654$	3.25094	0.127122
$655$	4.62977	0.180900
$656$	−7.81788	−0.305237
$657$	25.5534	0.996934
$658$	−13.0765	−0.509773
$659$	−32.3698	−1.26095	−0.630473	−	0.776211i	$-0.717139\pi$
$659$	−32.3698	−1.26095	−0.630473	+	0.776211i	$0.717139\pi$
$660$	−1.93058	−0.0751479
$661$	28.3297	1.10190	0.550948	−	0.834539i	$-0.314266\pi$
$661$	28.3297	1.10190	0.550948	+	0.834539i	$0.314266\pi$
$662$	34.0474	1.32329
$663$	0.253600	0.00984900
$664$	−11.8891	−0.461386
$665$	−7.56422	−0.293328
$666$	20.9709	0.812607
$667$	−43.2336	−1.67401
$668$	−0.224287	−0.00867791
$669$	−2.06664	−0.0799009
$670$	−0.357467	−0.0138102
$671$	−22.7619	−0.878712
$672$	0.729426	0.0281382
$673$	5.58056	0.215115	0.107557	−	0.994199i	$-0.465697\pi$
$673$	5.58056	0.215115	0.107557	+	0.994199i	$0.465697\pi$
$674$	−9.48533	−0.365361
$675$	0.225865	0.00869356
$676$	−10.7810	−0.414653
$677$	36.5549	1.40492	0.702459	−	0.711724i	$-0.252085\pi$
$677$	36.5549	1.40492	0.702459	+	0.711724i	$0.252085\pi$
$678$	−1.86096	−0.0714696
$679$	3.04565	0.116881
$680$	1.76544	0.0677014
$681$	5.09727	0.195328
$682$	11.1478	0.426873
$683$	−5.59207	−0.213975	−0.106987	−	0.994260i	$-0.534120\pi$
$683$	−5.59207	−0.213975	−0.106987	+	0.994260i	$0.534120\pi$
$684$	−2.95190	−0.112869
$685$	0.612370	0.0233975
$686$	9.77535	0.373224
$687$	−1.10626	−0.0422066
$688$	0.180535	0.00688284
$689$	−3.62006	−0.137913
$690$	4.43844	0.168969
$691$	7.35685	0.279868	0.139934	−	0.990161i	$-0.455311\pi$
$691$	7.35685	0.279868	0.139934	+	0.990161i	$0.455311\pi$
$692$	−3.97111	−0.150959
$693$	37.9944	1.44329
$694$	−36.5159	−1.38613
$695$	30.7420	1.16611
$696$	−1.06572	−0.0403959
$697$	−6.06833	−0.229854
$698$	5.10461	0.193212
$699$	−0.00876102	−0.000331372 0
$700$	−0.575435	−0.0217494
$701$	42.9081	1.62062	0.810308	−	0.586004i	$-0.199300\pi$
$701$	42.9081	1.62062	0.810308	+	0.586004i	$0.199300\pi$
$702$	−1.94457	−0.0733932
$703$	−7.10422	−0.267941
$704$	3.87014	0.145861
$705$	−1.96137	−0.0738696
$706$	−9.06775	−0.341269
$707$	−46.3485	−1.74312
$708$	2.07113	0.0778378
$709$	1.97574	0.0742004	0.0371002	−	0.999312i	$-0.488188\pi$
$709$	1.97574	0.0742004	0.0371002	+	0.999312i	$0.488188\pi$
$710$	10.2529	0.384783
$711$	21.5878	0.809604
$712$	6.08863	0.228181
$713$	−25.6291	−0.959817
$714$	0.566188	0.0211891
$715$	−13.1123	−0.490372
$716$	−1.17036	−0.0437384
$717$	−4.13144	−0.154291
$718$	15.4124	0.575185
$719$	8.80075	0.328213	0.164106	−	0.986443i	$-0.447526\pi$
$719$	8.80075	0.328213	0.164106	+	0.986443i	$0.447526\pi$
$720$	−6.71388	−0.250211
$721$	−0.718995	−0.0267768
$722$	1.00000	0.0372161
$723$	3.79540	0.141152
$724$	−8.51244	−0.316362
$725$	0.840731	0.0312240
$726$	−0.872478	−0.0323807
$727$	−2.66065	−0.0986782	−0.0493391	−	0.998782i	$-0.515711\pi$
$727$	−2.66065	−0.0986782	−0.0493391	+	0.998782i	$0.515711\pi$
$728$	4.95418	0.183614
$729$	−24.4370	−0.905074
$730$	−19.6889	−0.728717
$731$	0.140133	0.00518302
$732$	1.28994	0.0476776
$733$	−29.0243	−1.07204	−0.536018	−	0.844207i	$-0.680072\pi$
$733$	−29.0243	−1.07204	−0.536018	+	0.844207i	$0.680072\pi$
$734$	−23.5461	−0.869102
$735$	−2.02565	−0.0747173
$736$	−8.89752	−0.327967
$737$	−0.608262	−0.0224056
$738$	23.0776	0.849498
$739$	33.7327	1.24088	0.620440	−	0.784254i	$-0.286954\pi$
$739$	33.7327	1.24088	0.620440	+	0.784254i	$0.286954\pi$
$740$	−16.1580	−0.593982
$741$	0.326715	0.0120022
$742$	−8.08217	−0.296706
$743$	−33.7006	−1.23636	−0.618178	−	0.786038i	$-0.712129\pi$
$743$	−33.7006	−1.23636	−0.618178	+	0.786038i	$0.712129\pi$
$744$	−0.631762	−0.0231615
$745$	36.7419	1.34612
$746$	18.0439	0.660635
$747$	35.0954	1.28407
$748$	3.00405	0.109839
$749$	29.5044	1.07807
$750$	2.40789	0.0879237
$751$	46.4367	1.69450	0.847250	−	0.531194i	$-0.178256\pi$
$751$	46.4367	1.69450	0.847250	+	0.531194i	$0.178256\pi$
$752$	3.93186	0.143380
$753$	−0.0402658	−0.00146737
$754$	−7.23823	−0.263601
$755$	−5.91868	−0.215403
$756$	−4.34147	−0.157898
$757$	14.3009	0.519775	0.259887	−	0.965639i	$-0.416315\pi$
$757$	14.3009	0.519775	0.259887	+	0.965639i	$0.416315\pi$
$758$	25.5307	0.927318
$759$	7.55241	0.274135
$760$	2.27443	0.0825022
$761$	−16.1913	−0.586936	−0.293468	−	0.955969i	$-0.594809\pi$
$761$	−16.1913	−0.586936	−0.293468	+	0.955969i	$0.594809\pi$
$762$	1.16583	0.0422334
$763$	49.2960	1.78463
$764$	−26.5812	−0.961674
$765$	−5.21138	−0.188418
$766$	10.9443	0.395433
$767$	14.0669	0.507925
$768$	−0.219326	−0.00791423
$769$	−35.2375	−1.27070	−0.635349	−	0.772225i	$-0.719144\pi$
$769$	−35.2375	−1.27070	−0.635349	+	0.772225i	$0.719144\pi$
$770$	−29.2746	−1.05498
$771$	6.28283	0.226271
$772$	2.02726	0.0729627
$773$	−16.6163	−0.597646	−0.298823	−	0.954308i	$-0.596594\pi$
$773$	−16.6163	−0.597646	−0.298823	+	0.954308i	$0.596594\pi$
$774$	−0.532921	−0.0191555
$775$	0.498390	0.0179027
$776$	−0.915773	−0.0328743
$777$	−5.18200	−0.185903
$778$	11.8152	0.423595
$779$	−7.81788	−0.280105
$780$	0.743090	0.0266069
$781$	17.4461	0.624272
$782$	−6.90635	−0.246971
$783$	6.34304	0.226682
$784$	4.06072	0.145026
$785$	−52.3018	−1.86673
$786$	−0.446454	−0.0159245
$787$	55.4813	1.97769	0.988847	−	0.148932i	$-0.0475835\pi$
$787$	55.4813	1.97769	0.988847	+	0.148932i	$0.0475835\pi$
$788$	−23.4024	−0.833676
$789$	2.98674	0.106331
$790$	−16.6333	−0.591787
$791$	−28.2188	−1.00335
$792$	−11.4243	−0.405943
$793$	8.76114	0.311117
$794$	−25.4826	−0.904343
$795$	−1.21227	−0.0429946
$796$	12.2850	0.435430
$797$	−22.0708	−0.781786	−0.390893	−	0.920436i	$-0.627834\pi$
$797$	−22.0708	−0.781786	−0.390893	+	0.920436i	$0.627834\pi$
$798$	0.729426	0.0258214
$799$	3.05196	0.107970
$800$	0.173023	0.00611730
$801$	−17.9730	−0.635045
$802$	−26.9100	−0.950226
$803$	−33.5023	−1.18227
$804$	0.0344710	0.00121570
$805$	67.3028	2.37211
$806$	−4.29086	−0.151139
$807$	0.868401	0.0305692
$808$	13.9362	0.490274
$809$	−25.6910	−0.903248	−0.451624	−	0.892208i	$-0.649155\pi$
$809$	−25.6910	−0.903248	−0.451624	+	0.892208i	$0.649155\pi$
$810$	19.4904	0.684824
$811$	11.5579	0.405854	0.202927	−	0.979194i	$-0.434955\pi$
$811$	11.5579	0.405854	0.202927	+	0.979194i	$0.434955\pi$
$812$	−16.1601	−0.567109
$813$	0.914757	0.0320819
$814$	−27.4944	−0.963677
$815$	−1.84934	−0.0647796
$816$	−0.170243	−0.00595970
$817$	0.180535	0.00631613
$818$	−17.8779	−0.625087
$819$	−14.6242	−0.511012
$820$	−17.7812	−0.620947
$821$	9.87345	0.344586	0.172293	−	0.985046i	$-0.444882\pi$
$821$	9.87345	0.344586	0.172293	+	0.985046i	$0.444882\pi$
$822$	−0.0590515	−0.00205966
$823$	39.6575	1.38237	0.691186	−	0.722677i	$-0.257088\pi$
$823$	39.6575	1.38237	0.691186	+	0.722677i	$0.257088\pi$
$824$	0.216189	0.00753131
$825$	−0.146866	−0.00511322
$826$	31.4058	1.09275
$827$	−28.3694	−0.986501	−0.493250	−	0.869887i	$-0.664191\pi$
$827$	−28.3694	−0.986501	−0.493250	+	0.869887i	$0.664191\pi$
$828$	26.2646	0.912757
$829$	−4.82781	−0.167677	−0.0838383	−	0.996479i	$-0.526718\pi$
$829$	−4.82781	−0.167677	−0.0838383	+	0.996479i	$0.526718\pi$
$830$	−27.0409	−0.938603
$831$	−3.86294	−0.134004
$832$	−1.48964	−0.0516438
$833$	3.15198	0.109210
$834$	−2.96448	−0.102652
$835$	−0.510124	−0.0176536
$836$	3.87014	0.133852
$837$	3.76018	0.129971
$838$	1.95105	0.0673979
$839$	−5.59719	−0.193237	−0.0966183	−	0.995322i	$-0.530803\pi$
$839$	−5.59719	−0.193237	−0.0966183	+	0.995322i	$0.530803\pi$
$840$	1.65903	0.0572419
$841$	−5.38952	−0.185845
$842$	7.76004	0.267429
$843$	3.32313	0.114455
$844$	−1.00000	−0.0344214
$845$	−24.5206	−0.843534
$846$	−11.6065	−0.399038
$847$	−13.2299	−0.454585
$848$	2.43017	0.0834523
$849$	−7.08084	−0.243014
$850$	0.134303	0.00460654
$851$	63.2100	2.16681
$852$	−0.988694	−0.0338721
$853$	44.5474	1.52527	0.762637	−	0.646827i	$-0.223904\pi$
$853$	44.5474	1.52527	0.762637	+	0.646827i	$0.223904\pi$
$854$	19.5602	0.669335
$855$	−6.71388	−0.229610
$856$	−8.87146	−0.303220
$857$	−17.4083	−0.594656	−0.297328	−	0.954775i	$-0.596096\pi$
$857$	−17.4083	−0.594656	−0.297328	+	0.954775i	$0.596096\pi$
$858$	1.26443	0.0431671
$859$	−32.1652	−1.09746	−0.548731	−	0.835999i	$-0.684889\pi$
$859$	−32.1652	−1.09746	−0.548731	+	0.835999i	$0.684889\pi$
$860$	0.410614	0.0140018
$861$	−5.70257	−0.194343
$862$	−12.2312	−0.416596
$863$	44.8554	1.52689	0.763447	−	0.645870i	$-0.223505\pi$
$863$	44.8554	1.52689	0.763447	+	0.645870i	$0.223505\pi$
$864$	1.30540	0.0444107
$865$	−9.03200	−0.307097
$866$	18.6933	0.635224
$867$	3.59639	0.122140
$868$	−9.57979	−0.325159
$869$	−28.3031	−0.960116
$870$	−2.42390	−0.0821778
$871$	0.234123	0.00793295
$872$	−14.8224	−0.501951
$873$	2.70327	0.0914917
$874$	−8.89752	−0.300963
$875$	36.5123	1.23434
$876$	1.89862	0.0641484
$877$	32.1443	1.08544	0.542718	−	0.839915i	$-0.317395\pi$
$877$	32.1443	1.08544	0.542718	+	0.839915i	$0.317395\pi$
$878$	−10.4972	−0.354264
$879$	−5.84120	−0.197019
$880$	8.80236	0.296728
$881$	14.7435	0.496721	0.248361	−	0.968668i	$-0.420108\pi$
$881$	14.7435	0.496721	0.248361	+	0.968668i	$0.420108\pi$
$882$	−11.9868	−0.403618
$883$	−53.3082	−1.79396	−0.896981	−	0.442068i	$-0.854245\pi$
$883$	−53.3082	−1.79396	−0.896981	+	0.442068i	$0.854245\pi$
$884$	−1.15627	−0.0388896
$885$	4.71063	0.158346
$886$	38.5842	1.29626
$887$	−15.3308	−0.514757	−0.257379	−	0.966311i	$-0.582859\pi$
$887$	−15.3308	−0.514757	−0.257379	+	0.966311i	$0.582859\pi$
$888$	1.55814	0.0522877
$889$	17.6781	0.592905
$890$	13.8481	0.464191
$891$	33.1647	1.11106
$892$	9.42269	0.315495
$893$	3.93186	0.131575
$894$	−3.54306	−0.118498
$895$	−2.66190	−0.0889775
$896$	−3.32577	−0.111106
$897$	−2.90696	−0.0970604
$898$	−30.0086	−1.00140
$899$	13.9964	0.466806
$900$	−0.510747	−0.0170249
$901$	1.88632	0.0628425
$902$	−30.2563	−1.00743
$903$	0.131687	0.00438227
$904$	8.48491	0.282204
$905$	−19.3609	−0.643579
$906$	0.570745	0.0189617
$907$	−55.8503	−1.85448	−0.927240	−	0.374467i	$-0.877826\pi$
$907$	−55.8503	−1.85448	−0.927240	+	0.374467i	$0.877826\pi$
$908$	−23.2406	−0.771268
$909$	−41.1382	−1.36447
$910$	11.2679	0.373528
$911$	8.85277	0.293305	0.146653	−	0.989188i	$-0.453150\pi$
$911$	8.85277	0.293305	0.146653	+	0.989188i	$0.453150\pi$
$912$	−0.219326	−0.00726260
$913$	−46.0125	−1.52279
$914$	34.4348	1.13900
$915$	2.93388	0.0969911
$916$	5.04393	0.166656
$917$	−6.76985	−0.223560
$918$	1.01327	0.0334428
$919$	42.5615	1.40397	0.701987	−	0.712190i	$-0.252297\pi$
$919$	42.5615	1.40397	0.701987	+	0.712190i	$0.252297\pi$
$920$	−20.2368	−0.667187
$921$	−3.91147	−0.128887
$922$	−8.96726	−0.295321
$923$	−6.71510	−0.221030
$924$	2.82298	0.0928693
$925$	−1.22920	−0.0404157
$926$	−12.2753	−0.403391
$927$	−0.638168	−0.0209602
$928$	4.85906	0.159507
$929$	−2.58457	−0.0847969	−0.0423984	−	0.999101i	$-0.513500\pi$
$929$	−2.58457	−0.0847969	−0.0423984	+	0.999101i	$0.513500\pi$
$930$	−1.43690	−0.0471177
$931$	4.06072	0.133085
$932$	0.0399453	0.00130845
$933$	5.11972	0.167612
$934$	37.4755	1.22623
$935$	6.83249	0.223446
$936$	4.39725	0.143729
$937$	−41.7399	−1.36358	−0.681792	−	0.731546i	$-0.738799\pi$
$937$	−41.7399	−1.36358	−0.681792	+	0.731546i	$0.738799\pi$
$938$	0.522704	0.0170669
$939$	−0.118457	−0.00386571
$940$	8.94274	0.291680
$941$	47.6551	1.55351	0.776756	−	0.629801i	$-0.216864\pi$
$941$	47.6551	1.55351	0.776756	+	0.629801i	$0.216864\pi$
$942$	5.04352	0.164327
$943$	69.5598	2.26518
$944$	−9.44317	−0.307349
$945$	−9.87436	−0.321213
$946$	0.698697	0.0227166
$947$	19.9334	0.647747	0.323874	−	0.946100i	$-0.395015\pi$
$947$	19.9334	0.647747	0.323874	+	0.946100i	$0.395015\pi$
$948$	1.60397	0.0520945
$949$	12.8952	0.418596
$950$	0.173023	0.00561362
$951$	−3.74068	−0.121300
$952$	−2.58150	−0.0836668
$953$	−8.20450	−0.265770	−0.132885	−	0.991131i	$-0.542424\pi$
$953$	−8.20450	−0.265770	−0.132885	+	0.991131i	$0.542424\pi$
$954$	−7.17360	−0.232254
$955$	−60.4570	−1.95634
$956$	18.8370	0.609233
$957$	−4.12448	−0.133325
$958$	−0.888395	−0.0287027
$959$	−0.895434	−0.0289151
$960$	−0.498840	−0.0161000
$961$	−22.7029	−0.732350
$962$	10.5827	0.341200
$963$	26.1876	0.843884
$964$	−17.3048	−0.557352
$965$	4.61086	0.148429
$966$	−6.49008	−0.208815
$967$	−3.43780	−0.110552	−0.0552762	−	0.998471i	$-0.517604\pi$
$967$	−3.43780	−0.110552	−0.0552762	+	0.998471i	$0.517604\pi$
$968$	3.97800	0.127858
$969$	−0.170243	−0.00546899
$970$	−2.08286	−0.0668766
$971$	28.9208	0.928112	0.464056	−	0.885806i	$-0.346394\pi$
$971$	28.9208	0.928112	0.464056	+	0.885806i	$0.346394\pi$
$972$	−5.79570	−0.185897
$973$	−44.9522	−1.44110
$974$	−22.8576	−0.732404
$975$	0.0565294	0.00181039
$976$	−5.88140	−0.188259
$977$	8.58772	0.274746	0.137373	−	0.990519i	$-0.456134\pi$
$977$	8.58772	0.274746	0.137373	+	0.990519i	$0.456134\pi$
$978$	0.178334	0.00570249
$979$	23.5639	0.753104
$980$	9.23582	0.295028
$981$	43.7543	1.39697
$982$	12.6592	0.403972
$983$	−19.0744	−0.608378	−0.304189	−	0.952612i	$-0.598385\pi$
$983$	−19.0744	−0.608378	−0.304189	+	0.952612i	$0.598385\pi$
$984$	1.71466	0.0546614
$985$	−53.2271	−1.69596
$986$	3.77166	0.120114
$987$	2.86800	0.0912895
$988$	−1.48964	−0.0473916
$989$	−1.60632	−0.0510779
$990$	−25.9837	−0.825815
$991$	54.0756	1.71777	0.858884	−	0.512170i	$-0.171158\pi$
$991$	54.0756	1.71777	0.858884	+	0.512170i	$0.171158\pi$
$992$	2.88048	0.0914552
$993$	−7.46747	−0.236973
$994$	−14.9922	−0.475523
$995$	27.9413	0.885799
$996$	2.60758	0.0826244
$997$	−29.1666	−0.923714	−0.461857	−	0.886954i	$-0.652817\pi$
$997$	−29.1666	−0.923714	−0.461857	+	0.886954i	$0.652817\pi$
$998$	43.5023	1.37704
$999$	−9.27388	−0.293412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.16	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.219326 q^{3} +1.00000 q^{4} +2.27443 q^{5} -0.219326 q^{6} -3.32577 q^{7} +1.00000 q^{8} -2.95190 q^{9} +2.27443 q^{10} +3.87014 q^{11} -0.219326 q^{12} -1.48964 q^{13} -3.32577 q^{14} -0.498840 q^{15} +1.00000 q^{16} +0.776211 q^{17} -2.95190 q^{18} +1.00000 q^{19} +2.27443 q^{20} +0.729426 q^{21} +3.87014 q^{22} -8.89752 q^{23} -0.219326 q^{24} +0.173023 q^{25} -1.48964 q^{26} +1.30540 q^{27} -3.32577 q^{28} +4.85906 q^{29} -0.498840 q^{30} +2.88048 q^{31} +1.00000 q^{32} -0.848822 q^{33} +0.776211 q^{34} -7.56422 q^{35} -2.95190 q^{36} -7.10422 q^{37} +1.00000 q^{38} +0.326715 q^{39} +2.27443 q^{40} -7.81788 q^{41} +0.729426 q^{42} +0.180535 q^{43} +3.87014 q^{44} -6.71388 q^{45} -8.89752 q^{46} +3.93186 q^{47} -0.219326 q^{48} +4.06072 q^{49} +0.173023 q^{50} -0.170243 q^{51} -1.48964 q^{52} +2.43017 q^{53} +1.30540 q^{54} +8.80236 q^{55} -3.32577 q^{56} -0.219326 q^{57} +4.85906 q^{58} -9.44317 q^{59} -0.498840 q^{60} -5.88140 q^{61} +2.88048 q^{62} +9.81732 q^{63} +1.00000 q^{64} -3.38807 q^{65} -0.848822 q^{66} -0.157168 q^{67} +0.776211 q^{68} +1.95145 q^{69} -7.56422 q^{70} +4.50788 q^{71} -2.95190 q^{72} -8.65662 q^{73} -7.10422 q^{74} -0.0379485 q^{75} +1.00000 q^{76} -12.8712 q^{77} +0.326715 q^{78} -7.31318 q^{79} +2.27443 q^{80} +8.56938 q^{81} -7.81788 q^{82} -11.8891 q^{83} +0.729426 q^{84} +1.76544 q^{85} +0.180535 q^{86} -1.06572 q^{87} +3.87014 q^{88} +6.08863 q^{89} -6.71388 q^{90} +4.95418 q^{91} -8.89752 q^{92} -0.631762 q^{93} +3.93186 q^{94} +2.27443 q^{95} -0.219326 q^{96} -0.915773 q^{97} +4.06072 q^{98} -11.4243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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