LMFDB - Embedded newform 8029.2.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50294 q^{2} +0.107359 q^{3} +0.258826 q^{4} +3.46915 q^{5} -0.161355 q^{6} -1.00000 q^{7} +2.61688 q^{8} -2.98847 q^{9} +O(q^{10})$	\(q-1.50294 q^{2} +0.107359 q^{3} +0.258826 q^{4} +3.46915 q^{5} -0.161355 q^{6} -1.00000 q^{7} +2.61688 q^{8} -2.98847 q^{9} -5.21392 q^{10} +5.32483 q^{11} +0.0277874 q^{12} -6.03656 q^{13} +1.50294 q^{14} +0.372446 q^{15} -4.45066 q^{16} -5.58595 q^{17} +4.49149 q^{18} -2.85408 q^{19} +0.897905 q^{20} -0.107359 q^{21} -8.00289 q^{22} +1.45164 q^{23} +0.280947 q^{24} +7.03498 q^{25} +9.07259 q^{26} -0.642919 q^{27} -0.258826 q^{28} +7.35014 q^{29} -0.559763 q^{30} -1.00000 q^{31} +1.45531 q^{32} +0.571670 q^{33} +8.39535 q^{34} -3.46915 q^{35} -0.773494 q^{36} +1.00000 q^{37} +4.28950 q^{38} -0.648082 q^{39} +9.07834 q^{40} -4.20889 q^{41} +0.161355 q^{42} -11.8812 q^{43} +1.37820 q^{44} -10.3675 q^{45} -2.18173 q^{46} +1.15815 q^{47} -0.477820 q^{48} +1.00000 q^{49} -10.5732 q^{50} -0.599705 q^{51} -1.56242 q^{52} -5.08040 q^{53} +0.966268 q^{54} +18.4726 q^{55} -2.61688 q^{56} -0.306412 q^{57} -11.0468 q^{58} +1.51953 q^{59} +0.0963986 q^{60} -2.06634 q^{61} +1.50294 q^{62} +2.98847 q^{63} +6.71407 q^{64} -20.9417 q^{65} -0.859186 q^{66} +1.14572 q^{67} -1.44579 q^{68} +0.155848 q^{69} +5.21392 q^{70} -2.04144 q^{71} -7.82047 q^{72} -0.104578 q^{73} -1.50294 q^{74} +0.755272 q^{75} -0.738708 q^{76} -5.32483 q^{77} +0.974028 q^{78} +11.2581 q^{79} -15.4400 q^{80} +8.89640 q^{81} +6.32571 q^{82} +11.3931 q^{83} -0.0277874 q^{84} -19.3785 q^{85} +17.8567 q^{86} +0.789107 q^{87} +13.9344 q^{88} +1.04650 q^{89} +15.5817 q^{90} +6.03656 q^{91} +0.375722 q^{92} -0.107359 q^{93} -1.74062 q^{94} -9.90121 q^{95} +0.156242 q^{96} +11.6485 q^{97} -1.50294 q^{98} -15.9131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−1.50294	−1.06274	−0.531369	−	0.847140i	$-0.678322\pi$
$2$	−1.50294	−1.06274	−0.531369	+	0.847140i	$0.678322\pi$
$3$	0.107359	0.0619840	0.0309920	−	0.999520i	$-0.490133\pi$
$3$	0.107359	0.0619840	0.0309920	+	0.999520i	$0.490133\pi$
$4$	0.258826	0.129413
$5$	3.46915	1.55145	0.775725	−	0.631071i	$-0.217384\pi$
$5$	3.46915	1.55145	0.775725	+	0.631071i	$0.217384\pi$
$6$	−0.161355	−0.0658728
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.61688	0.925206
$9$	−2.98847	−0.996158
$10$	−5.21392	−1.64879
$11$	5.32483	1.60550	0.802748	−	0.596319i	$-0.203371\pi$
$11$	5.32483	1.60550	0.802748	+	0.596319i	$0.203371\pi$
$12$	0.0277874	0.00802153
$13$	−6.03656	−1.67424	−0.837121	−	0.547018i	$-0.815763\pi$
$13$	−6.03656	−1.67424	−0.837121	+	0.547018i	$0.815763\pi$
$14$	1.50294	0.401677
$15$	0.372446	0.0961651
$16$	−4.45066	−1.11267
$17$	−5.58595	−1.35479	−0.677396	−	0.735618i	$-0.736892\pi$
$17$	−5.58595	−1.35479	−0.677396	+	0.735618i	$0.736892\pi$
$18$	4.49149	1.05866
$19$	−2.85408	−0.654770	−0.327385	−	0.944891i	$-0.606167\pi$
$19$	−2.85408	−0.654770	−0.327385	+	0.944891i	$0.606167\pi$
$20$	0.897905	0.200778
$21$	−0.107359	−0.0234278
$22$	−8.00289	−1.70622
$23$	1.45164	0.302688	0.151344	−	0.988481i	$-0.451640\pi$
$23$	1.45164	0.302688	0.151344	+	0.988481i	$0.451640\pi$
$24$	0.280947	0.0573480
$25$	7.03498	1.40700
$26$	9.07259	1.77928
$27$	−0.642919	−0.123730
$28$	−0.258826	−0.0489135
$29$	7.35014	1.36489	0.682443	−	0.730939i	$-0.260917\pi$
$29$	7.35014	1.36489	0.682443	+	0.730939i	$0.260917\pi$
$30$	−0.559763	−0.102198
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.45531	0.257266
$33$	0.571670	0.0995151
$34$	8.39535	1.43979
$35$	−3.46915	−0.586393
$36$	−0.773494	−0.128916
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	4.28950	0.695849
$39$	−0.648082	−0.103776
$40$	9.07834	1.43541
$41$	−4.20889	−0.657318	−0.328659	−	0.944449i	$-0.606597\pi$
$41$	−4.20889	−0.657318	−0.328659	+	0.944449i	$0.606597\pi$
$42$	0.161355	0.0248976
$43$	−11.8812	−1.81186	−0.905932	−	0.423423i	$-0.860828\pi$
$43$	−11.8812	−1.81186	−0.905932	+	0.423423i	$0.860828\pi$
$44$	1.37820	0.207772
$45$	−10.3675	−1.54549
$46$	−2.18173	−0.321679
$47$	1.15815	0.168933	0.0844665	−	0.996426i	$-0.473081\pi$
$47$	1.15815	0.168933	0.0844665	+	0.996426i	$0.473081\pi$
$48$	−0.477820	−0.0689674
$49$	1.00000	0.142857
$50$	−10.5732	−1.49527
$51$	−0.599705	−0.0839755
$52$	−1.56242	−0.216668
$53$	−5.08040	−0.697846	−0.348923	−	0.937151i	$-0.613453\pi$
$53$	−5.08040	−0.697846	−0.348923	+	0.937151i	$0.613453\pi$
$54$	0.966268	0.131492
$55$	18.4726	2.49085
$56$	−2.61688	−0.349695
$57$	−0.306412	−0.0405853
$58$	−11.0468	−1.45052
$59$	1.51953	0.197826	0.0989129	−	0.995096i	$-0.468463\pi$
$59$	1.51953	0.197826	0.0989129	+	0.995096i	$0.468463\pi$
$60$	0.0963986	0.0124450
$61$	−2.06634	−0.264567	−0.132284	−	0.991212i	$-0.542231\pi$
$61$	−2.06634	−0.264567	−0.132284	+	0.991212i	$0.542231\pi$
$62$	1.50294	0.190873
$63$	2.98847	0.376512
$64$	6.71407	0.839259
$65$	−20.9417	−2.59750
$66$	−0.859186	−0.105758
$67$	1.14572	0.139971	0.0699857	−	0.997548i	$-0.477705\pi$
$67$	1.14572	0.139971	0.0699857	+	0.997548i	$0.477705\pi$
$68$	−1.44579	−0.175328
$69$	0.155848	0.0187618
$70$	5.21392	0.623182
$71$	−2.04144	−0.242274	−0.121137	−	0.992636i	$-0.538654\pi$
$71$	−2.04144	−0.242274	−0.121137	+	0.992636i	$0.538654\pi$
$72$	−7.82047	−0.921652
$73$	−0.104578	−0.0122399	−0.00611994	−	0.999981i	$-0.501948\pi$
$73$	−0.104578	−0.0122399	−0.00611994	+	0.999981i	$0.501948\pi$
$74$	−1.50294	−0.174713
$75$	0.755272	0.0872113
$76$	−0.738708	−0.0847356
$77$	−5.32483	−0.606820
$78$	0.974028	0.110287
$79$	11.2581	1.26663	0.633317	−	0.773893i	$-0.281693\pi$
$79$	11.2581	1.26663	0.633317	+	0.773893i	$0.281693\pi$
$80$	−15.4400	−1.72624
$81$	8.89640	0.988489
$82$	6.32571	0.698557
$83$	11.3931	1.25056	0.625278	−	0.780402i	$-0.284986\pi$
$83$	11.3931	1.25056	0.625278	+	0.780402i	$0.284986\pi$
$84$	−0.0277874	−0.00303185
$85$	−19.3785	−2.10189
$86$	17.8567	1.92554
$87$	0.789107	0.0846011
$88$	13.9344	1.48541
$89$	1.04650	0.110929	0.0554644	−	0.998461i	$-0.482336\pi$
$89$	1.04650	0.110929	0.0554644	+	0.998461i	$0.482336\pi$
$90$	15.5817	1.64245
$91$	6.03656	0.632804
$92$	0.375722	0.0391718
$93$	−0.107359	−0.0111327
$94$	−1.74062	−0.179532
$95$	−9.90121	−1.01584
$96$	0.156242	0.0159464
$97$	11.6485	1.18272	0.591361	−	0.806407i	$-0.298591\pi$
$97$	11.6485	1.18272	0.591361	+	0.806407i	$0.298591\pi$
$98$	−1.50294	−0.151820
$99$	−15.9131	−1.59933
$100$	1.82084	0.182084
$101$	11.9128	1.18537	0.592684	−	0.805435i	$-0.298068\pi$
$101$	11.9128	1.18537	0.592684	+	0.805435i	$0.298068\pi$
$102$	0.901320	0.0892440
$103$	−10.3945	−1.02420	−0.512102	−	0.858925i	$-0.671133\pi$
$103$	−10.3945	−1.02420	−0.512102	+	0.858925i	$0.671133\pi$
$104$	−15.7970	−1.54902
$105$	−0.372446	−0.0363470
$106$	7.63553	0.741628
$107$	−0.637579	−0.0616371	−0.0308185	−	0.999525i	$-0.509811\pi$
$107$	−0.637579	−0.0616371	−0.0308185	+	0.999525i	$0.509811\pi$
$108$	−0.166404	−0.0160122
$109$	14.0197	1.34284	0.671421	−	0.741076i	$-0.265684\pi$
$109$	14.0197	1.34284	0.671421	+	0.741076i	$0.265684\pi$
$110$	−27.7632	−2.64712
$111$	0.107359	0.0101901
$112$	4.45066	0.420548
$113$	3.59787	0.338459	0.169230	−	0.985577i	$-0.445872\pi$
$113$	3.59787	0.338459	0.169230	+	0.985577i	$0.445872\pi$
$114$	0.460518	0.0431315
$115$	5.03596	0.469606
$116$	1.90240	0.176634
$117$	18.0401	1.66781
$118$	−2.28376	−0.210237
$119$	5.58595	0.512063
$120$	0.974645	0.0889725
$121$	17.3538	1.57762
$122$	3.10558	0.281166
$123$	−0.451864	−0.0407432
$124$	−0.258826	−0.0232432
$125$	7.05966	0.631435
$126$	−4.49149	−0.400134
$127$	8.54322	0.758088	0.379044	−	0.925379i	$-0.376253\pi$
$127$	8.54322	0.758088	0.379044	+	0.925379i	$0.376253\pi$
$128$	−13.0015	−1.14918
$129$	−1.27556	−0.112307
$130$	31.4741	2.76047
$131$	9.34278	0.816282	0.408141	−	0.912919i	$-0.366177\pi$
$131$	9.34278	0.816282	0.408141	+	0.912919i	$0.366177\pi$
$132$	0.147963	0.0128785
$133$	2.85408	0.247480
$134$	−1.72194	−0.148753
$135$	−2.23038	−0.191961
$136$	−14.6178	−1.25346
$137$	20.2763	1.73232	0.866162	−	0.499764i	$-0.166580\pi$
$137$	20.2763	1.73232	0.866162	+	0.499764i	$0.166580\pi$
$138$	−0.234229	−0.0199389
$139$	12.6512	1.07306	0.536529	−	0.843882i	$-0.319735\pi$
$139$	12.6512	1.07306	0.536529	+	0.843882i	$0.319735\pi$
$140$	−0.897905	−0.0758868
$141$	0.124338	0.0104711
$142$	3.06816	0.257474
$143$	−32.1437	−2.68799
$144$	13.3007	1.10839
$145$	25.4987	2.11755
$146$	0.157174	0.0130078
$147$	0.107359	0.00885486
$148$	0.258826	0.0212753
$149$	22.6892	1.85878	0.929388	−	0.369105i	$-0.120336\pi$
$149$	22.6892	1.85878	0.929388	+	0.369105i	$0.120336\pi$
$150$	−1.13513	−0.0926828
$151$	1.12627	0.0916542	0.0458271	−	0.998949i	$-0.485408\pi$
$151$	1.12627	0.0916542	0.0458271	+	0.998949i	$0.485408\pi$
$152$	−7.46877	−0.605797
$153$	16.6935	1.34959
$154$	8.00289	0.644891
$155$	−3.46915	−0.278649
$156$	−0.167740	−0.0134300
$157$	−8.18356	−0.653119	−0.326560	−	0.945177i	$-0.605889\pi$
$157$	−8.18356	−0.653119	−0.326560	+	0.945177i	$0.605889\pi$
$158$	−16.9202	−1.34610
$159$	−0.545429	−0.0432553
$160$	5.04870	0.399135
$161$	−1.45164	−0.114405
$162$	−13.3707	−1.05050
$163$	22.0793	1.72938	0.864691	−	0.502304i	$-0.167514\pi$
$163$	22.0793	1.72938	0.864691	+	0.502304i	$0.167514\pi$
$164$	−1.08937	−0.0850654
$165$	1.98321	0.154393
$166$	−17.1231	−1.32901
$167$	−21.2718	−1.64606	−0.823030	−	0.567998i	$-0.807718\pi$
$167$	−21.2718	−1.64606	−0.823030	+	0.567998i	$0.807718\pi$
$168$	−0.280947	−0.0216755
$169$	23.4401	1.80308
$170$	29.1247	2.23376
$171$	8.52933	0.652254
$172$	−3.07516	−0.234479
$173$	1.81556	0.138034	0.0690171	−	0.997615i	$-0.478014\pi$
$173$	1.81556	0.138034	0.0690171	+	0.997615i	$0.478014\pi$
$174$	−1.18598	−0.0899089
$175$	−7.03498	−0.531795
$176$	−23.6990	−1.78638
$177$	0.163136	0.0122620
$178$	−1.57283	−0.117888
$179$	4.59760	0.343640	0.171820	−	0.985128i	$-0.445035\pi$
$179$	4.59760	0.343640	0.171820	+	0.985128i	$0.445035\pi$
$180$	−2.68336	−0.200006
$181$	−0.864042	−0.0642238	−0.0321119	−	0.999484i	$-0.510223\pi$
$181$	−0.864042	−0.0642238	−0.0321119	+	0.999484i	$0.510223\pi$
$182$	−9.07259	−0.672505
$183$	−0.221841	−0.0163989
$184$	3.79877	0.280049
$185$	3.46915	0.255057
$186$	0.161355	0.0118311
$187$	−29.7442	−2.17511
$188$	0.299758	0.0218621
$189$	0.642919	0.0467655
$190$	14.8809	1.07957
$191$	−13.3655	−0.967094	−0.483547	−	0.875319i	$-0.660652\pi$
$191$	−13.3655	−0.967094	−0.483547	+	0.875319i	$0.660652\pi$
$192$	0.720819	0.0520206
$193$	25.7192	1.85131	0.925654	−	0.378371i	$-0.123515\pi$
$193$	25.7192	1.85131	0.925654	+	0.378371i	$0.123515\pi$
$194$	−17.5069	−1.25692
$195$	−2.24829	−0.161004
$196$	0.258826	0.0184876
$197$	9.57737	0.682360	0.341180	−	0.939998i	$-0.389173\pi$
$197$	9.57737	0.682360	0.341180	+	0.939998i	$0.389173\pi$
$198$	23.9164	1.69967
$199$	15.2202	1.07893	0.539467	−	0.842007i	$-0.318626\pi$
$199$	15.2202	1.07893	0.539467	+	0.842007i	$0.318626\pi$
$200$	18.4097	1.30176
$201$	0.123003	0.00867599
$202$	−17.9042	−1.25974
$203$	−7.35014	−0.515879
$204$	−0.155219	−0.0108675
$205$	−14.6013	−1.01980
$206$	15.6223	1.08846
$207$	−4.33820	−0.301525
$208$	26.8667	1.86287
$209$	−15.1975	−1.05123
$210$	0.559763	0.0386273
$211$	−8.02880	−0.552726	−0.276363	−	0.961053i	$-0.589129\pi$
$211$	−8.02880	−0.552726	−0.276363	+	0.961053i	$0.589129\pi$
$212$	−1.31494	−0.0903103
$213$	−0.219168	−0.0150171
$214$	0.958243	0.0655041
$215$	−41.2176	−2.81102
$216$	−1.68244	−0.114476
$217$	1.00000	0.0678844
$218$	−21.0707	−1.42709
$219$	−0.0112274	−0.000758677 0
$220$	4.78119	0.322348
$221$	33.7200	2.26825
$222$	−0.161355	−0.0108294
$223$	2.54455	0.170396	0.0851978	−	0.996364i	$-0.472848\pi$
$223$	2.54455	0.170396	0.0851978	+	0.996364i	$0.472848\pi$
$224$	−1.45531	−0.0972373
$225$	−21.0239	−1.40159
$226$	−5.40738	−0.359694
$227$	−29.8340	−1.98015	−0.990077	−	0.140524i	$-0.955121\pi$
$227$	−29.8340	−1.98015	−0.990077	+	0.140524i	$0.955121\pi$
$228$	−0.0793073	−0.00525225
$229$	1.18141	0.0780700	0.0390350	−	0.999238i	$-0.487572\pi$
$229$	1.18141	0.0780700	0.0390350	+	0.999238i	$0.487572\pi$
$230$	−7.56874	−0.499068
$231$	−0.571670	−0.0376132
$232$	19.2344	1.26280
$233$	−25.6614	−1.68113	−0.840566	−	0.541709i	$-0.817778\pi$
$233$	−25.6614	−1.68113	−0.840566	+	0.541709i	$0.817778\pi$
$234$	−27.1132	−1.77244
$235$	4.01778	0.262091
$236$	0.393293	0.0256012
$237$	1.20866	0.0785110
$238$	−8.39535	−0.544189
$239$	−23.2583	−1.50445	−0.752227	−	0.658904i	$-0.771020\pi$
$239$	−23.2583	−1.50445	−0.752227	+	0.658904i	$0.771020\pi$
$240$	−1.65763	−0.107000
$241$	−20.9945	−1.35238	−0.676188	−	0.736729i	$-0.736370\pi$
$241$	−20.9945	−1.35238	−0.676188	+	0.736729i	$0.736370\pi$
$242$	−26.0817	−1.67659
$243$	2.88387	0.185000
$244$	−0.534821	−0.0342384
$245$	3.46915	0.221636
$246$	0.679124	0.0432994
$247$	17.2288	1.09624
$248$	−2.61688	−0.166172
$249$	1.22316	0.0775144
$250$	−10.6102	−0.671050
$251$	−4.47869	−0.282693	−0.141346	−	0.989960i	$-0.545143\pi$
$251$	−4.47869	−0.282693	−0.141346	+	0.989960i	$0.545143\pi$
$252$	0.773494	0.0487255
$253$	7.72974	0.485965
$254$	−12.8399	−0.805649
$255$	−2.08046	−0.130284
$256$	6.11227	0.382017
$257$	4.50935	0.281286	0.140643	−	0.990060i	$-0.455083\pi$
$257$	4.50935	0.281286	0.140643	+	0.990060i	$0.455083\pi$
$258$	1.91709	0.119353
$259$	−1.00000	−0.0621370
$260$	−5.42026	−0.336150
$261$	−21.9657	−1.35964
$262$	−14.0416	−0.867495
$263$	6.98016	0.430415	0.215208	−	0.976568i	$-0.430957\pi$
$263$	6.98016	0.430415	0.215208	+	0.976568i	$0.430957\pi$
$264$	1.49599	0.0920720
$265$	−17.6246	−1.08267
$266$	−4.28950	−0.263006
$267$	0.112352	0.00687581
$268$	0.296541	0.0181141
$269$	10.0269	0.611351	0.305675	−	0.952136i	$-0.401118\pi$
$269$	10.0269	0.611351	0.305675	+	0.952136i	$0.401118\pi$
$270$	3.35213	0.204004
$271$	19.8275	1.20443	0.602216	−	0.798333i	$-0.294285\pi$
$271$	19.8275	1.20443	0.602216	+	0.798333i	$0.294285\pi$
$272$	24.8612	1.50743
$273$	0.648082	0.0392237
$274$	−30.4741	−1.84101
$275$	37.4601	2.25893
$276$	0.0403374	0.00242802
$277$	−8.15494	−0.489983	−0.244991	−	0.969525i	$-0.578785\pi$
$277$	−8.15494	−0.489983	−0.244991	+	0.969525i	$0.578785\pi$
$278$	−19.0139	−1.14038
$279$	2.98847	0.178915
$280$	−9.07834	−0.542534
$281$	31.4110	1.87382	0.936911	−	0.349568i	$-0.113672\pi$
$281$	31.4110	1.87382	0.936911	+	0.349568i	$0.113672\pi$
$282$	−0.186872	−0.0111281
$283$	−18.9201	−1.12468	−0.562341	−	0.826905i	$-0.690099\pi$
$283$	−18.9201	−1.12468	−0.562341	+	0.826905i	$0.690099\pi$
$284$	−0.528377	−0.0313534
$285$	−1.06299	−0.0629660
$286$	48.3100	2.85663
$287$	4.20889	0.248443
$288$	−4.34917	−0.256277
$289$	14.2029	0.835463
$290$	−38.3230	−2.25040
$291$	1.25057	0.0733099
$292$	−0.0270674	−0.00158400
$293$	−3.71870	−0.217249	−0.108624	−	0.994083i	$-0.534645\pi$
$293$	−3.71870	−0.217249	−0.108624	+	0.994083i	$0.534645\pi$
$294$	−0.161355	−0.00941040
$295$	5.27147	0.306917
$296$	2.61688	0.152103
$297$	−3.42343	−0.198648
$298$	−34.1006	−1.97539
$299$	−8.76293	−0.506773
$300$	0.195484	0.0112863
$301$	11.8812	0.684820
$302$	−1.69271	−0.0974045
$303$	1.27895	0.0734739
$304$	12.7025	0.728540
$305$	−7.16842	−0.410463
$306$	−25.0893	−1.43426
$307$	24.1503	1.37833	0.689166	−	0.724603i	$-0.257977\pi$
$307$	24.1503	1.37833	0.689166	+	0.724603i	$0.257977\pi$
$308$	−1.37820	−0.0785304
$309$	−1.11595	−0.0634842
$310$	5.21392	0.296131
$311$	−11.4759	−0.650740	−0.325370	−	0.945587i	$-0.605489\pi$
$311$	−11.4759	−0.650740	−0.325370	+	0.945587i	$0.605489\pi$
$312$	−1.69595	−0.0960144
$313$	−2.36669	−0.133773	−0.0668867	−	0.997761i	$-0.521307\pi$
$313$	−2.36669	−0.133773	−0.0668867	+	0.997761i	$0.521307\pi$
$314$	12.2994	0.694095
$315$	10.3675	0.584140
$316$	2.91388	0.163919
$317$	7.31445	0.410820	0.205410	−	0.978676i	$-0.434147\pi$
$317$	7.31445	0.410820	0.205410	+	0.978676i	$0.434147\pi$
$318$	0.819746	0.0459691
$319$	39.1382	2.19132
$320$	23.2921	1.30207
$321$	−0.0684501	−0.00382051
$322$	2.18173	0.121583
$323$	15.9427	0.887077
$324$	2.30262	0.127923
$325$	−42.4671	−2.35565
$326$	−33.1838	−1.83788
$327$	1.50514	0.0832347
$328$	−11.0142	−0.608155
$329$	−1.15815	−0.0638507
$330$	−2.98064	−0.164079
$331$	14.8128	0.814183	0.407091	−	0.913387i	$-0.366543\pi$
$331$	14.8128	0.814183	0.407091	+	0.913387i	$0.366543\pi$
$332$	2.94883	0.161838
$333$	−2.98847	−0.163767
$334$	31.9702	1.74933
$335$	3.97466	0.217159
$336$	0.477820	0.0260672
$337$	−6.93654	−0.377857	−0.188929	−	0.981991i	$-0.560501\pi$
$337$	−6.93654	−0.377857	−0.188929	+	0.981991i	$0.560501\pi$
$338$	−35.2290	−1.91621
$339$	0.386266	0.0209791
$340$	−5.01565	−0.272012
$341$	−5.32483	−0.288356
$342$	−12.8191	−0.693176
$343$	−1.00000	−0.0539949
$344$	−31.0916	−1.67635
$345$	0.540658	0.0291081
$346$	−2.72867	−0.146694
$347$	−2.62472	−0.140902	−0.0704511	−	0.997515i	$-0.522444\pi$
$347$	−2.62472	−0.140902	−0.0704511	+	0.997515i	$0.522444\pi$
$348$	0.204241	0.0109485
$349$	3.00476	0.160841	0.0804204	−	0.996761i	$-0.474374\pi$
$349$	3.00476	0.160841	0.0804204	+	0.996761i	$0.474374\pi$
$350$	10.5732	0.565159
$351$	3.88102	0.207154
$352$	7.74930	0.413039
$353$	−10.3302	−0.549819	−0.274910	−	0.961470i	$-0.588648\pi$
$353$	−10.3302	−0.549819	−0.274910	+	0.961470i	$0.588648\pi$
$354$	−0.245183	−0.0130313
$355$	−7.08206	−0.375877
$356$	0.270861	0.0143556
$357$	0.599705	0.0317397
$358$	−6.90991	−0.365200
$359$	−3.67089	−0.193742	−0.0968712	−	0.995297i	$-0.530883\pi$
$359$	−3.67089	−0.193742	−0.0968712	+	0.995297i	$0.530883\pi$
$360$	−27.1304	−1.42990
$361$	−10.8543	−0.571277
$362$	1.29860	0.0682531
$363$	1.86309	0.0977870
$364$	1.56242	0.0818930
$365$	−0.362795	−0.0189896
$366$	0.333413	0.0174278
$367$	12.1814	0.635864	0.317932	−	0.948114i	$-0.397012\pi$
$367$	12.1814	0.635864	0.317932	+	0.948114i	$0.397012\pi$
$368$	−6.46077	−0.336791
$369$	12.5782	0.654793
$370$	−5.21392	−0.271059
$371$	5.08040	0.263761
$372$	−0.0277874	−0.00144071
$373$	13.2508	0.686102	0.343051	−	0.939317i	$-0.388540\pi$
$373$	13.2508	0.686102	0.343051	+	0.939317i	$0.388540\pi$
$374$	44.7038	2.31158
$375$	0.757921	0.0391389
$376$	3.03073	0.156298
$377$	−44.3696	−2.28515
$378$	−0.966268	−0.0496995
$379$	12.4348	0.638734	0.319367	−	0.947631i	$-0.396530\pi$
$379$	12.4348	0.638734	0.319367	+	0.947631i	$0.396530\pi$
$380$	−2.56269	−0.131463
$381$	0.917195	0.0469893
$382$	20.0875	1.02777
$383$	9.47186	0.483989	0.241995	−	0.970278i	$-0.422198\pi$
$383$	9.47186	0.483989	0.241995	+	0.970278i	$0.422198\pi$
$384$	−1.39583	−0.0712307
$385$	−18.4726	−0.941451
$386$	−38.6544	−1.96746
$387$	35.5066	1.80490
$388$	3.01492	0.153060
$389$	−0.347894	−0.0176389	−0.00881946	−	0.999961i	$-0.502807\pi$
$389$	−0.347894	−0.0176389	−0.00881946	+	0.999961i	$0.502807\pi$
$390$	3.37905	0.171105
$391$	−8.10881	−0.410080
$392$	2.61688	0.132172
$393$	1.00304	0.0505965
$394$	−14.3942	−0.725170
$395$	39.0559	1.96512
$396$	−4.11872	−0.206974
$397$	6.08158	0.305226	0.152613	−	0.988286i	$-0.451231\pi$
$397$	6.08158	0.305226	0.152613	+	0.988286i	$0.451231\pi$
$398$	−22.8751	−1.14662
$399$	0.306412	0.0153398
$400$	−31.3103	−1.56552
$401$	−0.395034	−0.0197271	−0.00986353	−	0.999951i	$-0.503140\pi$
$401$	−0.395034	−0.0197271	−0.00986353	+	0.999951i	$0.503140\pi$
$402$	−0.184867	−0.00922031
$403$	6.03656	0.300703
$404$	3.08334	0.153402
$405$	30.8629	1.53359
$406$	11.0468	0.548244
$407$	5.32483	0.263942
$408$	−1.56935	−0.0776946
$409$	−12.2335	−0.604906	−0.302453	−	0.953164i	$-0.597806\pi$
$409$	−12.2335	−0.604906	−0.302453	+	0.953164i	$0.597806\pi$
$410$	21.9448	1.08378
$411$	2.17685	0.107376
$412$	−2.69037	−0.132545
$413$	−1.51953	−0.0747711
$414$	6.52004	0.320443
$415$	39.5243	1.94017
$416$	−8.78510	−0.430725
$417$	1.35822	0.0665125
$418$	22.8409	1.11718
$419$	10.7634	0.525825	0.262912	−	0.964820i	$-0.415317\pi$
$419$	10.7634	0.525825	0.262912	+	0.964820i	$0.415317\pi$
$420$	−0.0963986	−0.00470377
$421$	5.25157	0.255946	0.127973	−	0.991778i	$-0.459153\pi$
$421$	5.25157	0.255946	0.127973	+	0.991778i	$0.459153\pi$
$422$	12.0668	0.587403
$423$	−3.46109	−0.168284
$424$	−13.2948	−0.645652
$425$	−39.2971	−1.90619
$426$	0.329396	0.0159593
$427$	2.06634	0.0999970
$428$	−0.165022	−0.00797663
$429$	−3.45093	−0.166612
$430$	61.9475	2.98738
$431$	1.46532	0.0705821	0.0352911	−	0.999377i	$-0.488764\pi$
$431$	1.46532	0.0705821	0.0352911	+	0.999377i	$0.488764\pi$
$432$	2.86142	0.137670
$433$	31.0200	1.49072	0.745362	−	0.666660i	$-0.232277\pi$
$433$	31.0200	1.49072	0.745362	+	0.666660i	$0.232277\pi$
$434$	−1.50294	−0.0721434
$435$	2.73753	0.131254
$436$	3.62865	0.173781
$437$	−4.14310	−0.198191
$438$	0.0168741	0.000806275 0
$439$	14.2662	0.680888	0.340444	−	0.940265i	$-0.389423\pi$
$439$	14.2662	0.680888	0.340444	+	0.940265i	$0.389423\pi$
$440$	48.3406	2.30455
$441$	−2.98847	−0.142308
$442$	−50.6790	−2.41056
$443$	6.54404	0.310917	0.155458	−	0.987842i	$-0.450315\pi$
$443$	6.54404	0.310917	0.155458	+	0.987842i	$0.450315\pi$
$444$	0.0277874	0.00131873
$445$	3.63046	0.172100
$446$	−3.82430	−0.181086
$447$	2.43590	0.115214
$448$	−6.71407	−0.317210
$449$	30.6650	1.44717	0.723587	−	0.690234i	$-0.242492\pi$
$449$	30.6650	1.44717	0.723587	+	0.690234i	$0.242492\pi$
$450$	31.5976	1.48952
$451$	−22.4116	−1.05532
$452$	0.931222	0.0438010
$453$	0.120915	0.00568110
$454$	44.8387	2.10439
$455$	20.9417	0.981763
$456$	−0.801843	−0.0375497
$457$	−30.1752	−1.41154	−0.705768	−	0.708443i	$-0.749398\pi$
$457$	−30.1752	−1.41154	−0.705768	+	0.708443i	$0.749398\pi$
$458$	−1.77559	−0.0829680
$459$	3.59132	0.167628
$460$	1.30344	0.0607730
$461$	−29.4394	−1.37113	−0.685566	−	0.728011i	$-0.740445\pi$
$461$	−29.4394	−1.37113	−0.685566	+	0.728011i	$0.740445\pi$
$462$	0.859186	0.0399729
$463$	−30.4245	−1.41395	−0.706974	−	0.707240i	$-0.749940\pi$
$463$	−30.4245	−1.41395	−0.706974	+	0.707240i	$0.749940\pi$
$464$	−32.7130	−1.51866
$465$	−0.372446	−0.0172718
$466$	38.5675	1.78660
$467$	14.3545	0.664246	0.332123	−	0.943236i	$-0.392235\pi$
$467$	14.3545	0.664246	0.332123	+	0.943236i	$0.392235\pi$
$468$	4.66925	0.215836
$469$	−1.14572	−0.0529042
$470$	−6.03848	−0.278534
$471$	−0.878583	−0.0404830
$472$	3.97642	0.183030
$473$	−63.2653	−2.90894
$474$	−1.81654	−0.0834366
$475$	−20.0784	−0.921259
$476$	1.44579	0.0662676
$477$	15.1826	0.695165
$478$	34.9558	1.59884
$479$	26.9541	1.23156	0.615782	−	0.787916i	$-0.288840\pi$
$479$	26.9541	1.23156	0.615782	+	0.787916i	$0.288840\pi$
$480$	0.542026	0.0247400
$481$	−6.03656	−0.275244
$482$	31.5535	1.43722
$483$	−0.155848	−0.00709131
$484$	4.49161	0.204164
$485$	40.4102	1.83493
$486$	−4.33428	−0.196607
$487$	−0.211560	−0.00958670	−0.00479335	−	0.999989i	$-0.501526\pi$
$487$	−0.211560	−0.00958670	−0.00479335	+	0.999989i	$0.501526\pi$
$488$	−5.40735	−0.244779
$489$	2.37042	0.107194
$490$	−5.21392	−0.235541
$491$	−14.1271	−0.637546	−0.318773	−	0.947831i	$-0.603271\pi$
$491$	−14.1271	−0.637546	−0.318773	+	0.947831i	$0.603271\pi$
$492$	−0.116954	−0.00527270
$493$	−41.0575	−1.84914
$494$	−25.8938	−1.16502
$495$	−55.2049	−2.48128
$496$	4.45066	0.199841
$497$	2.04144	0.0915711
$498$	−1.83833	−0.0823775
$499$	23.0436	1.03157	0.515786	−	0.856718i	$-0.327500\pi$
$499$	23.0436	1.03157	0.515786	+	0.856718i	$0.327500\pi$
$500$	1.82722	0.0817158
$501$	−2.28373	−0.102029
$502$	6.73120	0.300428
$503$	20.6752	0.921860	0.460930	−	0.887437i	$-0.347516\pi$
$503$	20.6752	0.921860	0.460930	+	0.887437i	$0.347516\pi$
$504$	7.82047	0.348352
$505$	41.3273	1.83904
$506$	−11.6173	−0.516454
$507$	2.51652	0.111762
$508$	2.21120	0.0981063
$509$	3.60439	0.159762	0.0798809	−	0.996804i	$-0.474546\pi$
$509$	3.60439	0.159762	0.0798809	+	0.996804i	$0.474546\pi$
$510$	3.12681	0.138458
$511$	0.104578	0.00462624
$512$	16.8166	0.743194
$513$	1.83494	0.0810146
$514$	−6.77728	−0.298933
$515$	−36.0602	−1.58900
$516$	−0.330147	−0.0145339
$517$	6.16693	0.271221
$518$	1.50294	0.0660354
$519$	0.194917	0.00855591
$520$	−54.8020	−2.40323
$521$	2.31335	0.101350	0.0506748	−	0.998715i	$-0.483863\pi$
$521$	2.31335	0.101350	0.0506748	+	0.998715i	$0.483863\pi$
$522$	33.0131	1.44494
$523$	−0.879700	−0.0384666	−0.0192333	−	0.999815i	$-0.506123\pi$
$523$	−0.879700	−0.0384666	−0.0192333	+	0.999815i	$0.506123\pi$
$524$	2.41815	0.105637
$525$	−0.755272	−0.0329628
$526$	−10.4908	−0.457419
$527$	5.58595	0.243328
$528$	−2.54431	−0.110727
$529$	−20.8927	−0.908380
$530$	26.4888	1.15060
$531$	−4.54107	−0.197066
$532$	0.738708	0.0320271
$533$	25.4072	1.10051
$534$	−0.168858	−0.00730719
$535$	−2.21186	−0.0956269
$536$	2.99820	0.129502
$537$	0.493595	0.0213002
$538$	−15.0698	−0.649706
$539$	5.32483	0.229357
$540$	−0.577280	−0.0248422
$541$	8.29695	0.356714	0.178357	−	0.983966i	$-0.442922\pi$
$541$	8.29695	0.356714	0.178357	+	0.983966i	$0.442922\pi$
$542$	−29.7995	−1.28000
$543$	−0.0927631	−0.00398085
$544$	−8.12932	−0.348542
$545$	48.6363	2.08335
$546$	−0.974028	−0.0416845
$547$	−1.65265	−0.0706623	−0.0353312	−	0.999376i	$-0.511249\pi$
$547$	−1.65265	−0.0706623	−0.0353312	+	0.999376i	$0.511249\pi$
$548$	5.24803	0.224185
$549$	6.17519	0.263551
$550$	−56.3002	−2.40065
$551$	−20.9778	−0.893686
$552$	0.407834	0.0173586
$553$	−11.2581	−0.478742
$554$	12.2564	0.520724
$555$	0.372446	0.0158094
$556$	3.27445	0.138868
$557$	−16.1230	−0.683151	−0.341576	−	0.939854i	$-0.610961\pi$
$557$	−16.1230	−0.683151	−0.341576	+	0.939854i	$0.610961\pi$
$558$	−4.49149	−0.190140
$559$	71.7216	3.03350
$560$	15.4400	0.652459
$561$	−3.19332	−0.134822
$562$	−47.2088	−1.99138
$563$	−40.6151	−1.71172	−0.855862	−	0.517205i	$-0.826973\pi$
$563$	−40.6151	−1.71172	−0.855862	+	0.517205i	$0.826973\pi$
$564$	0.0321819	0.00135510
$565$	12.4815	0.525103
$566$	28.4357	1.19524
$567$	−8.89640	−0.373614
$568$	−5.34220	−0.224154
$569$	5.10443	0.213989	0.106994	−	0.994260i	$-0.465877\pi$
$569$	5.10443	0.213989	0.106994	+	0.994260i	$0.465877\pi$
$570$	1.59761	0.0669164
$571$	−30.2597	−1.26633	−0.633164	−	0.774018i	$-0.718244\pi$
$571$	−30.2597	−1.26633	−0.633164	+	0.774018i	$0.718244\pi$
$572$	−8.31961	−0.347860
$573$	−1.43491	−0.0599443
$574$	−6.32571	−0.264030
$575$	10.2123	0.425882
$576$	−20.0648	−0.836035
$577$	−41.8891	−1.74386	−0.871932	−	0.489626i	$-0.837133\pi$
$577$	−41.8891	−1.74386	−0.871932	+	0.489626i	$0.837133\pi$
$578$	−21.3460	−0.887878
$579$	2.76120	0.114752
$580$	6.59972	0.274039
$581$	−11.3931	−0.472665
$582$	−1.87953	−0.0779092
$583$	−27.0522	−1.12039
$584$	−0.273667	−0.0113244
$585$	62.5838	2.58752
$586$	5.58898	0.230879
$587$	27.5846	1.13854	0.569270	−	0.822151i	$-0.307226\pi$
$587$	27.5846	1.13854	0.569270	+	0.822151i	$0.307226\pi$
$588$	0.0277874	0.00114593
$589$	2.85408	0.117600
$590$	−7.92270	−0.326172
$591$	1.02822	0.0422954
$592$	−4.45066	−0.182921
$593$	−13.2955	−0.545980	−0.272990	−	0.962017i	$-0.588013\pi$
$593$	−13.2955	−0.545980	−0.272990	+	0.962017i	$0.588013\pi$
$594$	5.14521	0.211111
$595$	19.3785	0.794441
$596$	5.87256	0.240549
$597$	1.63404	0.0668766
$598$	13.1702	0.538568
$599$	−32.5497	−1.32995	−0.664973	−	0.746868i	$-0.731557\pi$
$599$	−32.5497	−1.32995	−0.664973	+	0.746868i	$0.731557\pi$
$600$	1.97646	0.0806884
$601$	−45.9486	−1.87428	−0.937142	−	0.348949i	$-0.886539\pi$
$601$	−45.9486	−1.87428	−0.937142	+	0.348949i	$0.886539\pi$
$602$	−17.8567	−0.727785
$603$	−3.42394	−0.139434
$604$	0.291507	0.0118612
$605$	60.2028	2.44759
$606$	−1.92219	−0.0780835
$607$	33.6939	1.36759	0.683797	−	0.729672i	$-0.260327\pi$
$607$	33.6939	1.36759	0.683797	+	0.729672i	$0.260327\pi$
$608$	−4.15358	−0.168450
$609$	−0.789107	−0.0319762
$610$	10.7737	0.436215
$611$	−6.99123	−0.282835
$612$	4.32070	0.174654
$613$	20.5074	0.828288	0.414144	−	0.910211i	$-0.364081\pi$
$613$	20.5074	0.828288	0.414144	+	0.910211i	$0.364081\pi$
$614$	−36.2965	−1.46481
$615$	−1.56758	−0.0632111
$616$	−13.9344	−0.561434
$617$	3.19453	0.128607	0.0643035	−	0.997930i	$-0.479517\pi$
$617$	3.19453	0.128607	0.0643035	+	0.997930i	$0.479517\pi$
$618$	1.67721	0.0674671
$619$	−3.59351	−0.144435	−0.0722177	−	0.997389i	$-0.523008\pi$
$619$	−3.59351	−0.144435	−0.0722177	+	0.997389i	$0.523008\pi$
$620$	−0.897905	−0.0360607
$621$	−0.933289	−0.0374516
$622$	17.2476	0.691566
$623$	−1.04650	−0.0419271
$624$	2.88439	0.115468
$625$	−10.6839	−0.427357
$626$	3.55699	0.142166
$627$	−1.63159	−0.0651594
$628$	−2.11812	−0.0845221
$629$	−5.58595	−0.222727
$630$	−15.5817	−0.620788
$631$	13.7343	0.546754	0.273377	−	0.961907i	$-0.411859\pi$
$631$	13.7343	0.546754	0.273377	+	0.961907i	$0.411859\pi$
$632$	29.4610	1.17190
$633$	−0.861968	−0.0342601
$634$	−10.9932	−0.436594
$635$	29.6377	1.17614
$636$	−0.141171	−0.00559779
$637$	−6.03656	−0.239177
$638$	−58.8223	−2.32880
$639$	6.10079	0.241344
$640$	−45.1040	−1.78289
$641$	−8.85062	−0.349579	−0.174789	−	0.984606i	$-0.555924\pi$
$641$	−8.85062	−0.349579	−0.174789	+	0.984606i	$0.555924\pi$
$642$	0.102876	0.00406021
$643$	−21.3499	−0.841958	−0.420979	−	0.907070i	$-0.638313\pi$
$643$	−21.3499	−0.841958	−0.420979	+	0.907070i	$0.638313\pi$
$644$	−0.375722	−0.0148055
$645$	−4.42510	−0.174238
$646$	−23.9609	−0.942731
$647$	41.2401	1.62132	0.810658	−	0.585520i	$-0.199110\pi$
$647$	41.2401	1.62132	0.810658	+	0.585520i	$0.199110\pi$
$648$	23.2808	0.914556
$649$	8.09123	0.317608
$650$	63.8255	2.50344
$651$	0.107359	0.00420775
$652$	5.71468	0.223804
$653$	−38.0267	−1.48810	−0.744049	−	0.668125i	$-0.767097\pi$
$653$	−38.0267	−1.48810	−0.744049	+	0.668125i	$0.767097\pi$
$654$	−2.26214	−0.0884567
$655$	32.4115	1.26642
$656$	18.7323	0.731375
$657$	0.312527	0.0121929
$658$	1.74062	0.0678566
$659$	35.5518	1.38490	0.692450	−	0.721466i	$-0.256531\pi$
$659$	35.5518	1.38490	0.692450	+	0.721466i	$0.256531\pi$
$660$	0.513306	0.0199804
$661$	−6.30630	−0.245286	−0.122643	−	0.992451i	$-0.539137\pi$
$661$	−6.30630	−0.245286	−0.122643	+	0.992451i	$0.539137\pi$
$662$	−22.2627	−0.865263
$663$	3.62016	0.140595
$664$	29.8144	1.15702
$665$	9.90121	0.383952
$666$	4.49149	0.174042
$667$	10.6698	0.413135
$668$	−5.50568	−0.213021
$669$	0.273181	0.0105618
$670$	−5.97367	−0.230783
$671$	−11.0029	−0.424762
$672$	−0.156242	−0.00602716
$673$	33.4280	1.28855	0.644276	−	0.764793i	$-0.277159\pi$
$673$	33.4280	1.28855	0.644276	+	0.764793i	$0.277159\pi$
$674$	10.4252	0.401563
$675$	−4.52293	−0.174088
$676$	6.06690	0.233342
$677$	−5.94922	−0.228647	−0.114324	−	0.993444i	$-0.536470\pi$
$677$	−5.94922	−0.228647	−0.114324	+	0.993444i	$0.536470\pi$
$678$	−0.580534	−0.0222953
$679$	−11.6485	−0.447027
$680$	−50.7112	−1.94468
$681$	−3.20297	−0.122738
$682$	8.00289	0.306446
$683$	34.5731	1.32290	0.661451	−	0.749989i	$-0.269941\pi$
$683$	34.5731	1.32290	0.661451	+	0.749989i	$0.269941\pi$
$684$	2.20761	0.0844101
$685$	70.3415	2.68761
$686$	1.50294	0.0573825
$687$	0.126836	0.00483909
$688$	52.8791	2.01600
$689$	30.6681	1.16836
$690$	−0.812576	−0.0309342
$691$	25.1571	0.957022	0.478511	−	0.878081i	$-0.341177\pi$
$691$	25.1571	0.957022	0.478511	+	0.878081i	$0.341177\pi$
$692$	0.469913	0.0178634
$693$	15.9131	0.604489
$694$	3.94479	0.149742
$695$	43.8888	1.66480
$696$	2.06500	0.0782735
$697$	23.5107	0.890530
$698$	−4.51596	−0.170932
$699$	−2.75499	−0.104203
$700$	−1.82084	−0.0688211
$701$	−6.31261	−0.238424	−0.119212	−	0.992869i	$-0.538037\pi$
$701$	−6.31261	−0.238424	−0.119212	+	0.992869i	$0.538037\pi$
$702$	−5.83294	−0.220150
$703$	−2.85408	−0.107643
$704$	35.7513	1.34743
$705$	0.431347	0.0162455
$706$	15.5256	0.584314
$707$	−11.9128	−0.448027
$708$	0.0422237	0.00158687
$709$	44.8482	1.68431	0.842154	−	0.539237i	$-0.181287\pi$
$709$	44.8482	1.68431	0.842154	+	0.539237i	$0.181287\pi$
$710$	10.6439	0.399459
$711$	−33.6445	−1.26177
$712$	2.73856	0.102632
$713$	−1.45164	−0.0543644
$714$	−0.901320	−0.0337310
$715$	−111.511	−4.17028
$716$	1.18998	0.0444715
$717$	−2.49700	−0.0932521
$718$	5.51713	0.205898
$719$	30.4710	1.13637	0.568187	−	0.822899i	$-0.307645\pi$
$719$	30.4710	1.13637	0.568187	+	0.822899i	$0.307645\pi$
$720$	46.1420	1.71961
$721$	10.3945	0.387112
$722$	16.3133	0.607118
$723$	−2.25396	−0.0838257
$724$	−0.223636	−0.00831138
$725$	51.7081	1.92039
$726$	−2.80011	−0.103922
$727$	−42.2210	−1.56589	−0.782945	−	0.622091i	$-0.786284\pi$
$727$	−42.2210	−1.56589	−0.782945	+	0.622091i	$0.786284\pi$
$728$	15.7970	0.585474
$729$	−26.3796	−0.977022
$730$	0.545259	0.0201809
$731$	66.3678	2.45470
$732$	−0.0574181	−0.00212223
$733$	−29.7625	−1.09930	−0.549651	−	0.835394i	$-0.685239\pi$
$733$	−29.7625	−1.09930	−0.549651	+	0.835394i	$0.685239\pi$
$734$	−18.3079	−0.675757
$735$	0.372446	0.0137379
$736$	2.11260	0.0778713
$737$	6.10074	0.224724
$738$	−18.9042	−0.695873
$739$	−19.4162	−0.714235	−0.357118	−	0.934059i	$-0.616240\pi$
$739$	−19.4162	−0.714235	−0.357118	+	0.934059i	$0.616240\pi$
$740$	0.897905	0.0330076
$741$	1.84968	0.0679495
$742$	−7.63553	−0.280309
$743$	33.2274	1.21900	0.609498	−	0.792788i	$-0.291371\pi$
$743$	33.2274	1.21900	0.609498	+	0.792788i	$0.291371\pi$
$744$	−0.280947	−0.0103000
$745$	78.7123	2.88380
$746$	−19.9152	−0.729147
$747$	−34.0480	−1.24575
$748$	−7.69857	−0.281488
$749$	0.637579	0.0232966
$750$	−1.13911	−0.0415944
$751$	−46.5230	−1.69765	−0.848824	−	0.528675i	$-0.822689\pi$
$751$	−46.5230	−1.69765	−0.848824	+	0.528675i	$0.822689\pi$
$752$	−5.15452	−0.187966
$753$	−0.480830	−0.0175224
$754$	66.6848	2.42852
$755$	3.90718	0.142197
$756$	0.166404	0.00605206
$757$	7.63640	0.277550	0.138775	−	0.990324i	$-0.455684\pi$
$757$	7.63640	0.277550	0.138775	+	0.990324i	$0.455684\pi$
$758$	−18.6888	−0.678808
$759$	0.829861	0.0301220
$760$	−25.9103	−0.939864
$761$	−42.8019	−1.55157	−0.775783	−	0.630999i	$-0.782645\pi$
$761$	−42.8019	−1.55157	−0.775783	+	0.630999i	$0.782645\pi$
$762$	−1.37849	−0.0499374
$763$	−14.0197	−0.507546
$764$	−3.45934	−0.125154
$765$	57.9121	2.09382
$766$	−14.2356	−0.514354
$767$	−9.17273	−0.331208
$768$	0.656210	0.0236789
$769$	3.53475	0.127466	0.0637331	−	0.997967i	$-0.479699\pi$
$769$	3.53475	0.127466	0.0637331	+	0.997967i	$0.479699\pi$
$770$	27.7632	1.00052
$771$	0.484121	0.0174352
$772$	6.65679	0.239583
$773$	−13.1675	−0.473601	−0.236801	−	0.971558i	$-0.576099\pi$
$773$	−13.1675	−0.473601	−0.236801	+	0.971558i	$0.576099\pi$
$774$	−53.3643	−1.91814
$775$	−7.03498	−0.252704
$776$	30.4826	1.09426
$777$	−0.107359	−0.00385150
$778$	0.522863	0.0187456
$779$	12.0125	0.430392
$780$	−0.581916	−0.0208359
$781$	−10.8703	−0.388971
$782$	12.1870	0.435808
$783$	−4.72554	−0.168877
$784$	−4.45066	−0.158952
$785$	−28.3900	−1.01328
$786$	−1.50750	−0.0537708
$787$	16.3962	0.584461	0.292230	−	0.956348i	$-0.405603\pi$
$787$	16.3962	0.584461	0.292230	+	0.956348i	$0.405603\pi$
$788$	2.47887	0.0883061
$789$	0.749386	0.0266788
$790$	−58.6987	−2.08841
$791$	−3.59787	−0.127926
$792$	−41.6427	−1.47971
$793$	12.4736	0.442949
$794$	−9.14024	−0.324375
$795$	−1.89217	−0.0671084
$796$	3.93939	0.139628
$797$	3.56862	0.126407	0.0632035	−	0.998001i	$-0.479868\pi$
$797$	3.56862	0.126407	0.0632035	+	0.998001i	$0.479868\pi$
$798$	−0.460518	−0.0163022
$799$	−6.46935	−0.228869
$800$	10.2381	0.361972
$801$	−3.12744	−0.110503
$802$	0.593712	0.0209647
$803$	−0.556857	−0.0196511
$804$	0.0318364	0.00112278
$805$	−5.03596	−0.177494
$806$	−9.07259	−0.319568
$807$	1.07648	0.0378940
$808$	31.1744	1.09671
$809$	5.58772	0.196454	0.0982269	−	0.995164i	$-0.468683\pi$
$809$	5.58772	0.196454	0.0982269	+	0.995164i	$0.468683\pi$
$810$	−46.3851	−1.62981
$811$	47.9456	1.68360	0.841800	−	0.539790i	$-0.181496\pi$
$811$	47.9456	1.68360	0.841800	+	0.539790i	$0.181496\pi$
$812$	−1.90240	−0.0667613
$813$	2.12866	0.0746555
$814$	−8.00289	−0.280501
$815$	76.5963	2.68305
$816$	2.66908	0.0934366
$817$	33.9098	1.18635
$818$	18.3862	0.642857
$819$	−18.0401	−0.630373
$820$	−3.77918	−0.131975
$821$	53.5850	1.87013	0.935064	−	0.354479i	$-0.115342\pi$
$821$	53.5850	1.87013	0.935064	+	0.354479i	$0.115342\pi$
$822$	−3.27168	−0.114113
$823$	41.7102	1.45393	0.726964	−	0.686676i	$-0.240931\pi$
$823$	41.7102	1.45393	0.726964	+	0.686676i	$0.240931\pi$
$824$	−27.2012	−0.947599
$825$	4.02169	0.140017
$826$	2.28376	0.0794621
$827$	16.7234	0.581531	0.290766	−	0.956794i	$-0.406090\pi$
$827$	16.7234	0.581531	0.290766	+	0.956794i	$0.406090\pi$
$828$	−1.12284	−0.0390213
$829$	−45.9012	−1.59421	−0.797107	−	0.603839i	$-0.793637\pi$
$829$	−45.9012	−1.59421	−0.797107	+	0.603839i	$0.793637\pi$
$830$	−59.4027	−2.06190
$831$	−0.875510	−0.0303711
$832$	−40.5299	−1.40512
$833$	−5.58595	−0.193542
$834$	−2.04133	−0.0706853
$835$	−73.7949	−2.55378
$836$	−3.93349	−0.136043
$837$	0.642919	0.0222225
$838$	−16.1767	−0.558814
$839$	6.19853	0.213997	0.106999	−	0.994259i	$-0.465876\pi$
$839$	6.19853	0.213997	0.106999	+	0.994259i	$0.465876\pi$
$840$	−0.974645	−0.0336285
$841$	25.0245	0.862914
$842$	−7.89279	−0.272003
$843$	3.37227	0.116147
$844$	−2.07806	−0.0715298
$845$	81.3172	2.79740
$846$	5.20181	0.178842
$847$	−17.3538	−0.596283
$848$	22.6111	0.776469
$849$	−2.03125	−0.0697123
$850$	59.0611	2.02578
$851$	1.45164	0.0497617
$852$	−0.0567263	−0.00194341
$853$	−44.2316	−1.51446	−0.757230	−	0.653148i	$-0.773448\pi$
$853$	−44.2316	−1.51446	−0.757230	+	0.653148i	$0.773448\pi$
$854$	−3.10558	−0.106271
$855$	29.5895	1.01194
$856$	−1.66847	−0.0570270
$857$	47.2174	1.61292	0.806458	−	0.591291i	$-0.201382\pi$
$857$	47.2174	1.61292	0.806458	+	0.591291i	$0.201382\pi$
$858$	5.18653	0.177065
$859$	6.97968	0.238144	0.119072	−	0.992886i	$-0.462008\pi$
$859$	6.97968	0.238144	0.119072	+	0.992886i	$0.462008\pi$
$860$	−10.6682	−0.363782
$861$	0.451864	0.0153995
$862$	−2.20229	−0.0750103
$863$	−33.5306	−1.14139	−0.570697	−	0.821161i	$-0.693327\pi$
$863$	−33.5306	−1.14139	−0.570697	+	0.821161i	$0.693327\pi$
$864$	−0.935650	−0.0318314
$865$	6.29843	0.214153
$866$	−46.6211	−1.58425
$867$	1.52481	0.0517853
$868$	0.258826	0.00878512
$869$	59.9473	2.03357
$870$	−4.11434	−0.139489
$871$	−6.91618	−0.234346
$872$	36.6878	1.24241
$873$	−34.8111	−1.17818
$874$	6.22682	0.210625
$875$	−7.05966	−0.238660
$876$	−0.00290594	−9.81825e−5 0
$877$	42.6850	1.44137	0.720685	−	0.693263i	$-0.243827\pi$
$877$	42.6850	1.44137	0.720685	+	0.693263i	$0.243827\pi$
$878$	−21.4412	−0.723606
$879$	−0.399238	−0.0134660
$880$	−82.2153	−2.77148
$881$	−41.3834	−1.39424	−0.697122	−	0.716953i	$-0.745536\pi$
$881$	−41.3834	−1.39424	−0.697122	+	0.716953i	$0.745536\pi$
$882$	4.49149	0.151236
$883$	17.2414	0.580220	0.290110	−	0.956993i	$-0.406308\pi$
$883$	17.2414	0.580220	0.290110	+	0.956993i	$0.406308\pi$
$884$	8.72759	0.293541
$885$	0.565942	0.0190239
$886$	−9.83530	−0.330423
$887$	24.2552	0.814410	0.407205	−	0.913337i	$-0.366504\pi$
$887$	24.2552	0.814410	0.407205	+	0.913337i	$0.366504\pi$
$888$	0.280947	0.00942795
$889$	−8.54322	−0.286530
$890$	−5.45636	−0.182898
$891$	47.3718	1.58701
$892$	0.658595	0.0220514
$893$	−3.30544	−0.110612
$894$	−3.66102	−0.122443
$895$	15.9497	0.533141
$896$	13.0015	0.434349
$897$	−0.940784	−0.0314118
$898$	−46.0877	−1.53797
$899$	−7.35014	−0.245141
$900$	−5.44152	−0.181384
$901$	28.3789	0.945437
$902$	33.6833	1.12153
$903$	1.27556	0.0424479
$904$	9.41520	0.313145
$905$	−2.99749	−0.0996399
$906$	−0.181728	−0.00603752
$907$	−30.3863	−1.00896	−0.504481	−	0.863423i	$-0.668316\pi$
$907$	−30.3863	−1.00896	−0.504481	+	0.863423i	$0.668316\pi$
$908$	−7.72182	−0.256257
$909$	−35.6011	−1.18081
$910$	−31.4741	−1.04336
$911$	26.0023	0.861495	0.430748	−	0.902472i	$-0.358250\pi$
$911$	26.0023	0.861495	0.430748	+	0.902472i	$0.358250\pi$
$912$	1.36374	0.0451578
$913$	60.6663	2.00776
$914$	45.3515	1.50009
$915$	−0.769598	−0.0254421
$916$	0.305780	0.0101033
$917$	−9.34278	−0.308526
$918$	−5.39753	−0.178145
$919$	47.3423	1.56168	0.780839	−	0.624733i	$-0.214792\pi$
$919$	47.3423	1.56168	0.780839	+	0.624733i	$0.214792\pi$
$920$	13.1785	0.434482
$921$	2.59277	0.0854346
$922$	44.2457	1.45715
$923$	12.3233	0.405626
$924$	−0.147963	−0.00486763
$925$	7.03498	0.231309
$926$	45.7262	1.50266
$927$	31.0638	1.02027
$928$	10.6968	0.351138
$929$	32.5238	1.06707	0.533535	−	0.845778i	$-0.320863\pi$
$929$	32.5238	1.06707	0.533535	+	0.845778i	$0.320863\pi$
$930$	0.559763	0.0183554
$931$	−2.85408	−0.0935385
$932$	−6.64183	−0.217560
$933$	−1.23205	−0.0403355
$934$	−21.5739	−0.705920
$935$	−103.187	−3.37458
$936$	47.2088	1.54307
$937$	−51.4895	−1.68209	−0.841044	−	0.540967i	$-0.818058\pi$
$937$	−51.4895	−1.68209	−0.841044	+	0.540967i	$0.818058\pi$
$938$	1.72194	0.0562234
$939$	−0.254087	−0.00829181
$940$	1.03991	0.0339180
$941$	−1.57726	−0.0514171	−0.0257085	−	0.999669i	$-0.508184\pi$
$941$	−1.57726	−0.0514171	−0.0257085	+	0.999669i	$0.508184\pi$
$942$	1.32046	0.0430228
$943$	−6.10980	−0.198963
$944$	−6.76291	−0.220114
$945$	2.23038	0.0725543
$946$	95.0839	3.09144
$947$	2.38129	0.0773816	0.0386908	−	0.999251i	$-0.487681\pi$
$947$	2.38129	0.0773816	0.0386908	+	0.999251i	$0.487681\pi$
$948$	0.312833	0.0101603
$949$	0.631289	0.0204925
$950$	30.1766	0.979057
$951$	0.785275	0.0254643
$952$	14.6178	0.473764
$953$	−27.5081	−0.891075	−0.445538	−	0.895263i	$-0.646987\pi$
$953$	−27.5081	−0.891075	−0.445538	+	0.895263i	$0.646987\pi$
$954$	−22.8186	−0.738779
$955$	−46.3669	−1.50040
$956$	−6.01985	−0.194696
$957$	4.20186	0.135827
$958$	−40.5104	−1.30883
$959$	−20.2763	−0.654757
$960$	2.50063	0.0807074
$961$	1.00000	0.0322581
$962$	9.07259	0.292512
$963$	1.90539	0.0614003
$964$	−5.43393	−0.175015
$965$	89.2237	2.87221
$966$	0.234229	0.00753621
$967$	17.1583	0.551772	0.275886	−	0.961190i	$-0.411029\pi$
$967$	17.1583	0.551772	0.275886	+	0.961190i	$0.411029\pi$
$968$	45.4127	1.45962
$969$	1.71160	0.0549846
$970$	−60.7341	−1.95006
$971$	−5.56968	−0.178740	−0.0893698	−	0.995999i	$-0.528485\pi$
$971$	−5.56968	−0.178740	−0.0893698	+	0.995999i	$0.528485\pi$
$972$	0.746420	0.0239414
$973$	−12.6512	−0.405578
$974$	0.317962	0.0101882
$975$	−4.55925	−0.146013
$976$	9.19656	0.294375
$977$	25.1017	0.803074	0.401537	−	0.915843i	$-0.368476\pi$
$977$	25.1017	0.803074	0.401537	+	0.915843i	$0.368476\pi$
$978$	−3.56259	−0.113919
$979$	5.57243	0.178096
$980$	0.897905	0.0286825
$981$	−41.8974	−1.33768
$982$	21.2321	0.677544
$983$	3.50755	0.111874	0.0559368	−	0.998434i	$-0.482185\pi$
$983$	3.50755	0.111874	0.0559368	+	0.998434i	$0.482185\pi$
$984$	−1.18247	−0.0376959
$985$	33.2253	1.05865
$986$	61.7069	1.96515
$987$	−0.124338	−0.00395772
$988$	4.45926	0.141868
$989$	−17.2472	−0.548430
$990$	82.9696	2.63695
$991$	18.0896	0.574634	0.287317	−	0.957836i	$-0.407237\pi$
$991$	18.0896	0.574634	0.287317	+	0.957836i	$0.407237\pi$
$992$	−1.45531	−0.0462063
$993$	1.59029	0.0504663
$994$	−3.06816	−0.0973161
$995$	52.8012	1.67391
$996$	0.316584	0.0100314
$997$	36.5484	1.15750	0.578749	−	0.815506i	$-0.303541\pi$
$997$	36.5484	1.15750	0.578749	+	0.815506i	$0.303541\pi$
$998$	−34.6331	−1.09629
$999$	−0.642919	−0.0203411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.18	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.18	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50294 q^{2} +0.107359 q^{3} +0.258826 q^{4} +3.46915 q^{5} -0.161355 q^{6} -1.00000 q^{7} +2.61688 q^{8} -2.98847 q^{9} +O(q^{10})\)	\(q-1.50294 q^{2} +0.107359 q^{3} +0.258826 q^{4} +3.46915 q^{5} -0.161355 q^{6} -1.00000 q^{7} +2.61688 q^{8} -2.98847 q^{9} -5.21392 q^{10} +5.32483 q^{11} +0.0277874 q^{12} -6.03656 q^{13} +1.50294 q^{14} +0.372446 q^{15} -4.45066 q^{16} -5.58595 q^{17} +4.49149 q^{18} -2.85408 q^{19} +0.897905 q^{20} -0.107359 q^{21} -8.00289 q^{22} +1.45164 q^{23} +0.280947 q^{24} +7.03498 q^{25} +9.07259 q^{26} -0.642919 q^{27} -0.258826 q^{28} +7.35014 q^{29} -0.559763 q^{30} -1.00000 q^{31} +1.45531 q^{32} +0.571670 q^{33} +8.39535 q^{34} -3.46915 q^{35} -0.773494 q^{36} +1.00000 q^{37} +4.28950 q^{38} -0.648082 q^{39} +9.07834 q^{40} -4.20889 q^{41} +0.161355 q^{42} -11.8812 q^{43} +1.37820 q^{44} -10.3675 q^{45} -2.18173 q^{46} +1.15815 q^{47} -0.477820 q^{48} +1.00000 q^{49} -10.5732 q^{50} -0.599705 q^{51} -1.56242 q^{52} -5.08040 q^{53} +0.966268 q^{54} +18.4726 q^{55} -2.61688 q^{56} -0.306412 q^{57} -11.0468 q^{58} +1.51953 q^{59} +0.0963986 q^{60} -2.06634 q^{61} +1.50294 q^{62} +2.98847 q^{63} +6.71407 q^{64} -20.9417 q^{65} -0.859186 q^{66} +1.14572 q^{67} -1.44579 q^{68} +0.155848 q^{69} +5.21392 q^{70} -2.04144 q^{71} -7.82047 q^{72} -0.104578 q^{73} -1.50294 q^{74} +0.755272 q^{75} -0.738708 q^{76} -5.32483 q^{77} +0.974028 q^{78} +11.2581 q^{79} -15.4400 q^{80} +8.89640 q^{81} +6.32571 q^{82} +11.3931 q^{83} -0.0277874 q^{84} -19.3785 q^{85} +17.8567 q^{86} +0.789107 q^{87} +13.9344 q^{88} +1.04650 q^{89} +15.5817 q^{90} +6.03656 q^{91} +0.375722 q^{92} -0.107359 q^{93} -1.74062 q^{94} -9.90121 q^{95} +0.156242 q^{96} +11.6485 q^{97} -1.50294 q^{98} -15.9131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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