LMFDB - Embedded newform 8002.2.a.e.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0959021 q^{3} +1.00000 q^{4} -2.77140 q^{5} +0.0959021 q^{6} +2.92426 q^{7} -1.00000 q^{8} -2.99080 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0959021 q^{3} +1.00000 q^{4} -2.77140 q^{5} +0.0959021 q^{6} +2.92426 q^{7} -1.00000 q^{8} -2.99080 q^{9} +2.77140 q^{10} +6.48636 q^{11} -0.0959021 q^{12} -0.946829 q^{13} -2.92426 q^{14} +0.265783 q^{15} +1.00000 q^{16} -5.63298 q^{17} +2.99080 q^{18} -5.83340 q^{19} -2.77140 q^{20} -0.280442 q^{21} -6.48636 q^{22} -4.06839 q^{23} +0.0959021 q^{24} +2.68067 q^{25} +0.946829 q^{26} +0.574530 q^{27} +2.92426 q^{28} -5.77262 q^{29} -0.265783 q^{30} +3.86154 q^{31} -1.00000 q^{32} -0.622055 q^{33} +5.63298 q^{34} -8.10430 q^{35} -2.99080 q^{36} -8.15595 q^{37} +5.83340 q^{38} +0.0908028 q^{39} +2.77140 q^{40} +4.85327 q^{41} +0.280442 q^{42} -2.76149 q^{43} +6.48636 q^{44} +8.28872 q^{45} +4.06839 q^{46} +10.9102 q^{47} -0.0959021 q^{48} +1.55129 q^{49} -2.68067 q^{50} +0.540214 q^{51} -0.946829 q^{52} +5.50958 q^{53} -0.574530 q^{54} -17.9763 q^{55} -2.92426 q^{56} +0.559435 q^{57} +5.77262 q^{58} +1.84067 q^{59} +0.265783 q^{60} -13.7919 q^{61} -3.86154 q^{62} -8.74588 q^{63} +1.00000 q^{64} +2.62404 q^{65} +0.622055 q^{66} +8.92362 q^{67} -5.63298 q^{68} +0.390167 q^{69} +8.10430 q^{70} +13.8776 q^{71} +2.99080 q^{72} +9.52886 q^{73} +8.15595 q^{74} -0.257082 q^{75} -5.83340 q^{76} +18.9678 q^{77} -0.0908028 q^{78} +5.90230 q^{79} -2.77140 q^{80} +8.91731 q^{81} -4.85327 q^{82} -4.57584 q^{83} -0.280442 q^{84} +15.6113 q^{85} +2.76149 q^{86} +0.553606 q^{87} -6.48636 q^{88} -1.28188 q^{89} -8.28872 q^{90} -2.76877 q^{91} -4.06839 q^{92} -0.370330 q^{93} -10.9102 q^{94} +16.1667 q^{95} +0.0959021 q^{96} -14.7881 q^{97} -1.55129 q^{98} -19.3994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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
$3$	−0.0959021	−0.0553691	−0.0276845	−	0.999617i	$-0.508813\pi$
$3$	−0.0959021	−0.0553691	−0.0276845	+	0.999617i	$0.508813\pi$
$4$	1.00000	0.500000
$5$	−2.77140	−1.23941	−0.619705	−	0.784835i	$-0.712748\pi$
$5$	−2.77140	−1.23941	−0.619705	+	0.784835i	$0.712748\pi$
$6$	0.0959021	0.0391519
$7$	2.92426	1.10527	0.552633	−	0.833425i	$-0.313623\pi$
$7$	2.92426	1.10527	0.552633	+	0.833425i	$0.313623\pi$
$8$	−1.00000	−0.353553
$9$	−2.99080	−0.996934
$10$	2.77140	0.876395
$11$	6.48636	1.95571	0.977855	−	0.209282i	$-0.0671125\pi$
$11$	6.48636	1.95571	0.977855	+	0.209282i	$0.0671125\pi$
$12$	−0.0959021	−0.0276845
$13$	−0.946829	−0.262603	−0.131302	−	0.991342i	$-0.541916\pi$
$13$	−0.946829	−0.262603	−0.131302	+	0.991342i	$0.541916\pi$
$14$	−2.92426	−0.781541
$15$	0.265783	0.0686249
$16$	1.00000	0.250000
$17$	−5.63298	−1.36620	−0.683099	−	0.730326i	$-0.739368\pi$
$17$	−5.63298	−1.36620	−0.683099	+	0.730326i	$0.739368\pi$
$18$	2.99080	0.704939
$19$	−5.83340	−1.33827	−0.669137	−	0.743139i	$-0.733336\pi$
$19$	−5.83340	−1.33827	−0.669137	+	0.743139i	$0.733336\pi$
$20$	−2.77140	−0.619705
$21$	−0.280442	−0.0611976
$22$	−6.48636	−1.38290
$23$	−4.06839	−0.848317	−0.424159	−	0.905588i	$-0.639430\pi$
$23$	−4.06839	−0.848317	−0.424159	+	0.905588i	$0.639430\pi$
$24$	0.0959021	0.0195759
$25$	2.68067	0.536135
$26$	0.946829	0.185688
$27$	0.574530	0.110568
$28$	2.92426	0.552633
$29$	−5.77262	−1.07195	−0.535974	−	0.844235i	$-0.680055\pi$
$29$	−5.77262	−1.07195	−0.535974	+	0.844235i	$0.680055\pi$
$30$	−0.265783	−0.0485252
$31$	3.86154	0.693553	0.346777	−	0.937948i	$-0.387276\pi$
$31$	3.86154	0.693553	0.346777	+	0.937948i	$0.387276\pi$
$32$	−1.00000	−0.176777
$33$	−0.622055	−0.108286
$34$	5.63298	0.966048
$35$	−8.10430	−1.36988
$36$	−2.99080	−0.498467
$37$	−8.15595	−1.34083	−0.670415	−	0.741986i	$-0.733884\pi$
$37$	−8.15595	−1.34083	−0.670415	+	0.741986i	$0.733884\pi$
$38$	5.83340	0.946302
$39$	0.0908028	0.0145401
$40$	2.77140	0.438197
$41$	4.85327	0.757953	0.378977	−	0.925406i	$-0.376276\pi$
$41$	4.85327	0.757953	0.378977	+	0.925406i	$0.376276\pi$
$42$	0.280442	0.0432732
$43$	−2.76149	−0.421123	−0.210561	−	0.977581i	$-0.567529\pi$
$43$	−2.76149	−0.421123	−0.210561	+	0.977581i	$0.567529\pi$
$44$	6.48636	0.977855
$45$	8.28872	1.23561
$46$	4.06839	0.599851
$47$	10.9102	1.59141	0.795705	−	0.605684i	$-0.207101\pi$
$47$	10.9102	1.59141	0.795705	+	0.605684i	$0.207101\pi$
$48$	−0.0959021	−0.0138423
$49$	1.55129	0.221613
$50$	−2.68067	−0.379105
$51$	0.540214	0.0756452
$52$	−0.946829	−0.131302
$53$	5.50958	0.756799	0.378400	−	0.925642i	$-0.376475\pi$
$53$	5.50958	0.756799	0.378400	+	0.925642i	$0.376475\pi$
$54$	−0.574530	−0.0781837
$55$	−17.9763	−2.42393
$56$	−2.92426	−0.390771
$57$	0.559435	0.0740990
$58$	5.77262	0.757982
$59$	1.84067	0.239635	0.119817	−	0.992796i	$-0.461769\pi$
$59$	1.84067	0.239635	0.119817	+	0.992796i	$0.461769\pi$
$60$	0.265783	0.0343125
$61$	−13.7919	−1.76587	−0.882933	−	0.469498i	$-0.844435\pi$
$61$	−13.7919	−1.76587	−0.882933	+	0.469498i	$0.844435\pi$
$62$	−3.86154	−0.490416
$63$	−8.74588	−1.10188
$64$	1.00000	0.125000
$65$	2.62404	0.325473
$66$	0.622055	0.0765697
$67$	8.92362	1.09019	0.545097	−	0.838373i	$-0.316493\pi$
$67$	8.92362	1.09019	0.545097	+	0.838373i	$0.316493\pi$
$68$	−5.63298	−0.683099
$69$	0.390167	0.0469705
$70$	8.10430	0.968649
$71$	13.8776	1.64697	0.823487	−	0.567336i	$-0.192026\pi$
$71$	13.8776	1.64697	0.823487	+	0.567336i	$0.192026\pi$
$72$	2.99080	0.352469
$73$	9.52886	1.11527	0.557634	−	0.830087i	$-0.311709\pi$
$73$	9.52886	1.11527	0.557634	+	0.830087i	$0.311709\pi$
$74$	8.15595	0.948110
$75$	−0.257082	−0.0296853
$76$	−5.83340	−0.669137
$77$	18.9678	2.16158
$78$	−0.0908028	−0.0102814
$79$	5.90230	0.664061	0.332030	−	0.943269i	$-0.392266\pi$
$79$	5.90230	0.664061	0.332030	+	0.943269i	$0.392266\pi$
$80$	−2.77140	−0.309852
$81$	8.91731	0.990812
$82$	−4.85327	−0.535954
$83$	−4.57584	−0.502263	−0.251132	−	0.967953i	$-0.580803\pi$
$83$	−4.57584	−0.502263	−0.251132	+	0.967953i	$0.580803\pi$
$84$	−0.280442	−0.0305988
$85$	15.6113	1.69328
$86$	2.76149	0.297779
$87$	0.553606	0.0593528
$88$	−6.48636	−0.691448
$89$	−1.28188	−0.135879	−0.0679396	−	0.997689i	$-0.521643\pi$
$89$	−1.28188	−0.135879	−0.0679396	+	0.997689i	$0.521643\pi$
$90$	−8.28872	−0.873708
$91$	−2.76877	−0.290246
$92$	−4.06839	−0.424159
$93$	−0.370330	−0.0384014
$94$	−10.9102	−1.12530
$95$	16.1667	1.65867
$96$	0.0959021	0.00978796
$97$	−14.7881	−1.50150	−0.750752	−	0.660584i	$-0.770309\pi$
$97$	−14.7881	−1.50150	−0.750752	+	0.660584i	$0.770309\pi$
$98$	−1.55129	−0.156704
$99$	−19.3994	−1.94972
$100$	2.68067	0.268067
$101$	−2.12792	−0.211736	−0.105868	−	0.994380i	$-0.533762\pi$
$101$	−2.12792	−0.211736	−0.105868	+	0.994380i	$0.533762\pi$
$102$	−0.540214	−0.0534892
$103$	18.5453	1.82732	0.913660	−	0.406478i	$-0.133243\pi$
$103$	18.5453	1.82732	0.913660	+	0.406478i	$0.133243\pi$
$104$	0.946829	0.0928442
$105$	0.777219	0.0758488
$106$	−5.50958	−0.535138
$107$	−17.4041	−1.68251	−0.841257	−	0.540636i	$-0.818184\pi$
$107$	−17.4041	−1.68251	−0.841257	+	0.540636i	$0.818184\pi$
$108$	0.574530	0.0552842
$109$	−10.9158	−1.04554	−0.522772	−	0.852472i	$-0.675102\pi$
$109$	−10.9158	−1.04554	−0.522772	+	0.852472i	$0.675102\pi$
$110$	17.9763	1.71397
$111$	0.782172	0.0742405
$112$	2.92426	0.276317
$113$	9.75638	0.917803	0.458902	−	0.888487i	$-0.348243\pi$
$113$	9.75638	0.917803	0.458902	+	0.888487i	$0.348243\pi$
$114$	−0.559435	−0.0523959
$115$	11.2751	1.05141
$116$	−5.77262	−0.535974
$117$	2.83178	0.261798
$118$	−1.84067	−0.169447
$119$	−16.4723	−1.51001
$120$	−0.265783	−0.0242626
$121$	31.0729	2.82480
$122$	13.7919	1.24866
$123$	−0.465438	−0.0419672
$124$	3.86154	0.346777
$125$	6.42779	0.574919
$126$	8.74588	0.779145
$127$	−15.9075	−1.41156	−0.705782	−	0.708429i	$-0.749404\pi$
$127$	−15.9075	−1.41156	−0.705782	+	0.708429i	$0.749404\pi$
$128$	−1.00000	−0.0883883
$129$	0.264832	0.0233172
$130$	−2.62404	−0.230144
$131$	−6.72858	−0.587879	−0.293939	−	0.955824i	$-0.594966\pi$
$131$	−6.72858	−0.587879	−0.293939	+	0.955824i	$0.594966\pi$
$132$	−0.622055	−0.0541430
$133$	−17.0584	−1.47915
$134$	−8.92362	−0.770884
$135$	−1.59225	−0.137039
$136$	5.63298	0.483024
$137$	14.4459	1.23419	0.617097	−	0.786887i	$-0.288308\pi$
$137$	14.4459	1.23419	0.617097	+	0.786887i	$0.288308\pi$
$138$	−0.390167	−0.0332132
$139$	13.9063	1.17952	0.589759	−	0.807579i	$-0.299223\pi$
$139$	13.9063	1.17952	0.589759	+	0.807579i	$0.299223\pi$
$140$	−8.10430	−0.684938
$141$	−1.04631	−0.0881149
$142$	−13.8776	−1.16459
$143$	−6.14147	−0.513576
$144$	−2.99080	−0.249234
$145$	15.9982	1.32858
$146$	−9.52886	−0.788614
$147$	−0.148772	−0.0122705
$148$	−8.15595	−0.670415
$149$	7.62742	0.624863	0.312431	−	0.949940i	$-0.398857\pi$
$149$	7.62742	0.624863	0.312431	+	0.949940i	$0.398857\pi$
$150$	0.257082	0.0209907
$151$	−19.7725	−1.60906	−0.804532	−	0.593909i	$-0.797584\pi$
$151$	−19.7725	−1.60906	−0.804532	+	0.593909i	$0.797584\pi$
$152$	5.83340	0.473151
$153$	16.8471	1.36201
$154$	−18.9678	−1.52847
$155$	−10.7019	−0.859596
$156$	0.0908028	0.00727005
$157$	10.7466	0.857670	0.428835	−	0.903383i	$-0.358924\pi$
$157$	10.7466	0.857670	0.428835	+	0.903383i	$0.358924\pi$
$158$	−5.90230	−0.469562
$159$	−0.528380	−0.0419033
$160$	2.77140	0.219099
$161$	−11.8970	−0.937616
$162$	−8.91731	−0.700610
$163$	−21.3763	−1.67432	−0.837159	−	0.546959i	$-0.815785\pi$
$163$	−21.3763	−1.67432	−0.837159	+	0.546959i	$0.815785\pi$
$164$	4.85327	0.378977
$165$	1.72397	0.134211
$166$	4.57584	0.355154
$167$	9.91633	0.767349	0.383674	−	0.923468i	$-0.374658\pi$
$167$	9.91633	0.767349	0.383674	+	0.923468i	$0.374658\pi$
$168$	0.280442	0.0216366
$169$	−12.1035	−0.931040
$170$	−15.6113	−1.19733
$171$	17.4466	1.33417
$172$	−2.76149	−0.210561
$173$	0.910896	0.0692541	0.0346271	−	0.999400i	$-0.488976\pi$
$173$	0.910896	0.0692541	0.0346271	+	0.999400i	$0.488976\pi$
$174$	−0.553606	−0.0419687
$175$	7.83899	0.592572
$176$	6.48636	0.488928
$177$	−0.176524	−0.0132683
$178$	1.28188	0.0960811
$179$	6.32701	0.472903	0.236452	−	0.971643i	$-0.424016\pi$
$179$	6.32701	0.472903	0.236452	+	0.971643i	$0.424016\pi$
$180$	8.28872	0.617805
$181$	−20.9934	−1.56043	−0.780213	−	0.625514i	$-0.784889\pi$
$181$	−20.9934	−1.56043	−0.780213	+	0.625514i	$0.784889\pi$
$182$	2.76877	0.205235
$183$	1.32267	0.0977744
$184$	4.06839	0.299925
$185$	22.6034	1.66184
$186$	0.370330	0.0271539
$187$	−36.5375	−2.67189
$188$	10.9102	0.795705
$189$	1.68008	0.122208
$190$	−16.1667	−1.17286
$191$	−8.92746	−0.645968	−0.322984	−	0.946404i	$-0.604686\pi$
$191$	−8.92746	−0.645968	−0.322984	+	0.946404i	$0.604686\pi$
$192$	−0.0959021	−0.00692113
$193$	−7.76842	−0.559183	−0.279591	−	0.960119i	$-0.590199\pi$
$193$	−7.76842	−0.559183	−0.279591	+	0.960119i	$0.590199\pi$
$194$	14.7881	1.06172
$195$	−0.251651	−0.0180211
$196$	1.55129	0.110807
$197$	23.1819	1.65164	0.825821	−	0.563933i	$-0.190712\pi$
$197$	23.1819	1.65164	0.825821	+	0.563933i	$0.190712\pi$
$198$	19.3994	1.37866
$199$	−20.1553	−1.42877	−0.714385	−	0.699753i	$-0.753293\pi$
$199$	−20.1553	−1.42877	−0.714385	+	0.699753i	$0.753293\pi$
$200$	−2.68067	−0.189552
$201$	−0.855794	−0.0603630
$202$	2.12792	0.149720
$203$	−16.8806	−1.18479
$204$	0.540214	0.0378226
$205$	−13.4504	−0.939414
$206$	−18.5453	−1.29211
$207$	12.1677	0.845717
$208$	−0.946829	−0.0656508
$209$	−37.8375	−2.61728
$210$	−0.777219	−0.0536332
$211$	2.59635	0.178740	0.0893702	−	0.995998i	$-0.471515\pi$
$211$	2.59635	0.178740	0.0893702	+	0.995998i	$0.471515\pi$
$212$	5.50958	0.378400
$213$	−1.33089	−0.0911914
$214$	17.4041	1.18972
$215$	7.65319	0.521943
$216$	−0.574530	−0.0390918
$217$	11.2921	0.766561
$218$	10.9158	0.739312
$219$	−0.913837	−0.0617514
$220$	−17.9763	−1.21196
$221$	5.33347	0.358768
$222$	−0.782172	−0.0524960
$223$	4.79504	0.321100	0.160550	−	0.987028i	$-0.448673\pi$
$223$	4.79504	0.321100	0.160550	+	0.987028i	$0.448673\pi$
$224$	−2.92426	−0.195385
$225$	−8.01737	−0.534491
$226$	−9.75638	−0.648985
$227$	16.4166	1.08961	0.544805	−	0.838563i	$-0.316604\pi$
$227$	16.4166	1.08961	0.544805	+	0.838563i	$0.316604\pi$
$228$	0.559435	0.0370495
$229$	−3.93044	−0.259731	−0.129865	−	0.991532i	$-0.541454\pi$
$229$	−3.93044	−0.259731	−0.129865	+	0.991532i	$0.541454\pi$
$230$	−11.2751	−0.743461
$231$	−1.81905	−0.119685
$232$	5.77262	0.378991
$233$	0.444946	0.0291494	0.0145747	−	0.999894i	$-0.495361\pi$
$233$	0.444946	0.0291494	0.0145747	+	0.999894i	$0.495361\pi$
$234$	−2.83178	−0.185119
$235$	−30.2364	−1.97241
$236$	1.84067	0.119817
$237$	−0.566043	−0.0367684
$238$	16.4723	1.06774
$239$	1.11162	0.0719046	0.0359523	−	0.999354i	$-0.488554\pi$
$239$	1.11162	0.0719046	0.0359523	+	0.999354i	$0.488554\pi$
$240$	0.265783	0.0171562
$241$	16.2045	1.04382	0.521911	−	0.853000i	$-0.325219\pi$
$241$	16.2045	1.04382	0.521911	+	0.853000i	$0.325219\pi$
$242$	−31.0729	−1.99744
$243$	−2.57878	−0.165429
$244$	−13.7919	−0.882933
$245$	−4.29926	−0.274669
$246$	0.465438	0.0296753
$247$	5.52323	0.351435
$248$	−3.86154	−0.245208
$249$	0.438832	0.0278099
$250$	−6.42779	−0.406529
$251$	1.97412	0.124605	0.0623026	−	0.998057i	$-0.480156\pi$
$251$	1.97412	0.124605	0.0623026	+	0.998057i	$0.480156\pi$
$252$	−8.74588	−0.550939
$253$	−26.3890	−1.65906
$254$	15.9075	0.998127
$255$	−1.49715	−0.0937553
$256$	1.00000	0.0625000
$257$	−10.3465	−0.645394	−0.322697	−	0.946502i	$-0.604589\pi$
$257$	−10.3465	−0.645394	−0.322697	+	0.946502i	$0.604589\pi$
$258$	−0.264832	−0.0164877
$259$	−23.8501	−1.48197
$260$	2.62404	0.162736
$261$	17.2648	1.06866
$262$	6.72858	0.415693
$263$	−0.358033	−0.0220773	−0.0110386	−	0.999939i	$-0.503514\pi$
$263$	−0.358033	−0.0220773	−0.0110386	+	0.999939i	$0.503514\pi$
$264$	0.622055	0.0382848
$265$	−15.2693	−0.937984
$266$	17.0584	1.04592
$267$	0.122935	0.00752351
$268$	8.92362	0.545097
$269$	21.3995	1.30475	0.652375	−	0.757897i	$-0.273773\pi$
$269$	21.3995	1.30475	0.652375	+	0.757897i	$0.273773\pi$
$270$	1.59225	0.0969016
$271$	16.2497	0.987098	0.493549	−	0.869718i	$-0.335699\pi$
$271$	16.2497	0.987098	0.493549	+	0.869718i	$0.335699\pi$
$272$	−5.63298	−0.341550
$273$	0.265531	0.0160707
$274$	−14.4459	−0.872708
$275$	17.3878	1.04852
$276$	0.390167	0.0234853
$277$	23.6368	1.42020	0.710099	−	0.704102i	$-0.248650\pi$
$277$	23.6368	1.42020	0.710099	+	0.704102i	$0.248650\pi$
$278$	−13.9063	−0.834045
$279$	−11.5491	−0.691427
$280$	8.10430	0.484325
$281$	3.74204	0.223232	0.111616	−	0.993751i	$-0.464397\pi$
$281$	3.74204	0.223232	0.111616	+	0.993751i	$0.464397\pi$
$282$	1.04631	0.0623067
$283$	30.9372	1.83903	0.919514	−	0.393057i	$-0.128582\pi$
$283$	30.9372	1.83903	0.919514	+	0.393057i	$0.128582\pi$
$284$	13.8776	0.823487
$285$	−1.55042	−0.0918390
$286$	6.14147	0.363153
$287$	14.1922	0.837740
$288$	2.99080	0.176235
$289$	14.7305	0.866498
$290$	−15.9982	−0.939449
$291$	1.41821	0.0831369
$292$	9.52886	0.557634
$293$	−5.41506	−0.316351	−0.158176	−	0.987411i	$-0.550561\pi$
$293$	−5.41506	−0.316351	−0.158176	+	0.987411i	$0.550561\pi$
$294$	0.148772	0.00867657
$295$	−5.10123	−0.297005
$296$	8.15595	0.474055
$297$	3.72661	0.216240
$298$	−7.62742	−0.441845
$299$	3.85207	0.222771
$300$	−0.257082	−0.0148426
$301$	−8.07530	−0.465453
$302$	19.7725	1.13778
$303$	0.204072	0.0117236
$304$	−5.83340	−0.334568
$305$	38.2228	2.18863
$306$	−16.8471	−0.963087
$307$	17.7878	1.01520	0.507602	−	0.861591i	$-0.330532\pi$
$307$	17.7878	1.01520	0.507602	+	0.861591i	$0.330532\pi$
$308$	18.9678	1.08079
$309$	−1.77853	−0.101177
$310$	10.7019	0.607826
$311$	5.17349	0.293362	0.146681	−	0.989184i	$-0.453141\pi$
$311$	5.17349	0.293362	0.146681	+	0.989184i	$0.453141\pi$
$312$	−0.0908028	−0.00514070
$313$	32.4356	1.83337	0.916685	−	0.399611i	$-0.130855\pi$
$313$	32.4356	1.83337	0.916685	+	0.399611i	$0.130855\pi$
$314$	−10.7466	−0.606464
$315$	24.2384	1.36568
$316$	5.90230	0.332030
$317$	−19.0834	−1.07183	−0.535916	−	0.844271i	$-0.680034\pi$
$317$	−19.0834	−1.07183	−0.535916	+	0.844271i	$0.680034\pi$
$318$	0.528380	0.0296301
$319$	−37.4433	−2.09642
$320$	−2.77140	−0.154926
$321$	1.66908	0.0931592
$322$	11.8970	0.662995
$323$	32.8594	1.82835
$324$	8.91731	0.495406
$325$	−2.53814	−0.140791
$326$	21.3763	1.18392
$327$	1.04685	0.0578908
$328$	−4.85327	−0.267977
$329$	31.9041	1.75893
$330$	−1.72397	−0.0949012
$331$	−8.03473	−0.441629	−0.220814	−	0.975316i	$-0.570871\pi$
$331$	−8.03473	−0.441629	−0.220814	+	0.975316i	$0.570871\pi$
$332$	−4.57584	−0.251132
$333$	24.3928	1.33672
$334$	−9.91633	−0.542598
$335$	−24.7310	−1.35120
$336$	−0.280442	−0.0152994
$337$	24.9873	1.36114	0.680572	−	0.732681i	$-0.261731\pi$
$337$	24.9873	1.36114	0.680572	+	0.732681i	$0.261731\pi$
$338$	12.1035	0.658344
$339$	−0.935657	−0.0508179
$340$	15.6113	0.846639
$341$	25.0473	1.35639
$342$	−17.4466	−0.943401
$343$	−15.9334	−0.860325
$344$	2.76149	0.148889
$345$	−1.08131	−0.0582157
$346$	−0.910896	−0.0489701
$347$	20.9311	1.12364	0.561820	−	0.827260i	$-0.310102\pi$
$347$	20.9311	1.12364	0.561820	+	0.827260i	$0.310102\pi$
$348$	0.553606	0.0296764
$349$	27.0525	1.44809	0.724043	−	0.689754i	$-0.242281\pi$
$349$	27.0525	1.44809	0.724043	+	0.689754i	$0.242281\pi$
$350$	−7.83899	−0.419011
$351$	−0.543982	−0.0290356
$352$	−6.48636	−0.345724
$353$	7.73744	0.411822	0.205911	−	0.978571i	$-0.433984\pi$
$353$	7.73744	0.411822	0.205911	+	0.978571i	$0.433984\pi$
$354$	0.176524	0.00938214
$355$	−38.4605	−2.04127
$356$	−1.28188	−0.0679396
$357$	1.57973	0.0836080
$358$	−6.32701	−0.334393
$359$	0.0105153	0.000554975 0	0.000277487	−	1.00000i	$-0.499912\pi$
$359$	0.0105153	0.000554975 0	0.000277487		1.00000i	$0.499912\pi$
$360$	−8.28872	−0.436854
$361$	15.0286	0.790977
$362$	20.9934	1.10339
$363$	−2.97995	−0.156407
$364$	−2.76877	−0.145123
$365$	−26.4083	−1.38227
$366$	−1.32267	−0.0691370
$367$	13.4346	0.701281	0.350641	−	0.936510i	$-0.385964\pi$
$367$	13.4346	0.701281	0.350641	+	0.936510i	$0.385964\pi$
$368$	−4.06839	−0.212079
$369$	−14.5152	−0.755629
$370$	−22.6034	−1.17510
$371$	16.1114	0.836464
$372$	−0.370330	−0.0192007
$373$	28.4689	1.47406	0.737031	−	0.675859i	$-0.236227\pi$
$373$	28.4689	1.47406	0.737031	+	0.675859i	$0.236227\pi$
$374$	36.5375	1.88931
$375$	−0.616438	−0.0318327
$376$	−10.9102	−0.562648
$377$	5.46568	0.281497
$378$	−1.68008	−0.0864138
$379$	−33.7912	−1.73574	−0.867869	−	0.496793i	$-0.834511\pi$
$379$	−33.7912	−1.73574	−0.867869	+	0.496793i	$0.834511\pi$
$380$	16.1667	0.829334
$381$	1.52556	0.0781570
$382$	8.92746	0.456768
$383$	−0.754075	−0.0385314	−0.0192657	−	0.999814i	$-0.506133\pi$
$383$	−0.754075	−0.0385314	−0.0192657	+	0.999814i	$0.506133\pi$
$384$	0.0959021	0.00489398
$385$	−52.5674	−2.67908
$386$	7.76842	0.395402
$387$	8.25906	0.419832
$388$	−14.7881	−0.750752
$389$	12.4833	0.632927	0.316464	−	0.948605i	$-0.397504\pi$
$389$	12.4833	0.632927	0.316464	+	0.948605i	$0.397504\pi$
$390$	0.251651	0.0127429
$391$	22.9171	1.15897
$392$	−1.55129	−0.0783521
$393$	0.645285	0.0325503
$394$	−23.1819	−1.16789
$395$	−16.3576	−0.823043
$396$	−19.3994	−0.974858
$397$	−23.4913	−1.17900	−0.589498	−	0.807770i	$-0.700674\pi$
$397$	−23.4913	−1.17900	−0.589498	+	0.807770i	$0.700674\pi$
$398$	20.1553	1.01029
$399$	1.63593	0.0818991
$400$	2.68067	0.134034
$401$	16.8513	0.841516	0.420758	−	0.907173i	$-0.361764\pi$
$401$	16.8513	0.841516	0.420758	+	0.907173i	$0.361764\pi$
$402$	0.855794	0.0426831
$403$	−3.65622	−0.182129
$404$	−2.12792	−0.105868
$405$	−24.7135	−1.22802
$406$	16.8806	0.837771
$407$	−52.9024	−2.62228
$408$	−0.540214	−0.0267446
$409$	−10.9555	−0.541714	−0.270857	−	0.962620i	$-0.587307\pi$
$409$	−10.9555	−0.541714	−0.270857	+	0.962620i	$0.587307\pi$
$410$	13.4504	0.664266
$411$	−1.38539	−0.0683362
$412$	18.5453	0.913660
$413$	5.38259	0.264860
$414$	−12.1677	−0.598012
$415$	12.6815	0.622510
$416$	0.946829	0.0464221
$417$	−1.33364	−0.0653088
$418$	37.8375	1.85069
$419$	5.95729	0.291033	0.145516	−	0.989356i	$-0.453516\pi$
$419$	5.95729	0.291033	0.145516	+	0.989356i	$0.453516\pi$
$420$	0.777219	0.0379244
$421$	33.1195	1.61415	0.807073	−	0.590452i	$-0.201050\pi$
$421$	33.1195	1.61415	0.807073	+	0.590452i	$0.201050\pi$
$422$	−2.59635	−0.126389
$423$	−32.6301	−1.58653
$424$	−5.50958	−0.267569
$425$	−15.1002	−0.732467
$426$	1.33089	0.0644820
$427$	−40.3310	−1.95175
$428$	−17.4041	−0.841257
$429$	0.588980	0.0284362
$430$	−7.65319	−0.369070
$431$	−8.06502	−0.388478	−0.194239	−	0.980954i	$-0.562224\pi$
$431$	−8.06502	−0.388478	−0.194239	+	0.980954i	$0.562224\pi$
$432$	0.574530	0.0276421
$433$	−15.4396	−0.741982	−0.370991	−	0.928636i	$-0.620982\pi$
$433$	−15.4396	−0.741982	−0.370991	+	0.928636i	$0.620982\pi$
$434$	−11.2921	−0.542041
$435$	−1.53426	−0.0735624
$436$	−10.9158	−0.522772
$437$	23.7325	1.13528
$438$	0.913837	0.0436648
$439$	15.1690	0.723975	0.361987	−	0.932183i	$-0.382098\pi$
$439$	15.1690	0.723975	0.361987	+	0.932183i	$0.382098\pi$
$440$	17.9763	0.856987
$441$	−4.63961	−0.220934
$442$	−5.33347	−0.253687
$443$	17.7517	0.843410	0.421705	−	0.906733i	$-0.361432\pi$
$443$	17.7517	0.843410	0.421705	+	0.906733i	$0.361432\pi$
$444$	0.782172	0.0371203
$445$	3.55261	0.168410
$446$	−4.79504	−0.227052
$447$	−0.731485	−0.0345981
$448$	2.92426	0.138158
$449$	4.46836	0.210875	0.105438	−	0.994426i	$-0.466376\pi$
$449$	4.46836	0.210875	0.105438	+	0.994426i	$0.466376\pi$
$450$	8.01737	0.377942
$451$	31.4800	1.48234
$452$	9.75638	0.458902
$453$	1.89622	0.0890924
$454$	−16.4166	−0.770470
$455$	7.67339	0.359734
$456$	−0.559435	−0.0261979
$457$	−2.68712	−0.125698	−0.0628491	−	0.998023i	$-0.520019\pi$
$457$	−2.68712	−0.125698	−0.0628491	+	0.998023i	$0.520019\pi$
$458$	3.93044	0.183657
$459$	−3.23632	−0.151058
$460$	11.2751	0.525706
$461$	22.2273	1.03523	0.517614	−	0.855614i	$-0.326820\pi$
$461$	22.2273	1.03523	0.517614	+	0.855614i	$0.326820\pi$
$462$	1.81905	0.0846299
$463$	−40.7332	−1.89303	−0.946515	−	0.322659i	$-0.895423\pi$
$463$	−40.7332	−1.89303	−0.946515	+	0.322659i	$0.895423\pi$
$464$	−5.77262	−0.267987
$465$	1.02633	0.0475951
$466$	−0.444946	−0.0206117
$467$	30.1353	1.39450	0.697248	−	0.716830i	$-0.254407\pi$
$467$	30.1353	1.39450	0.697248	+	0.716830i	$0.254407\pi$
$468$	2.83178	0.130899
$469$	26.0950	1.20495
$470$	30.2364	1.39470
$471$	−1.03062	−0.0474884
$472$	−1.84067	−0.0847236
$473$	−17.9120	−0.823594
$474$	0.566043	0.0259992
$475$	−15.6374	−0.717495
$476$	−16.4723	−0.755006
$477$	−16.4781	−0.754479
$478$	−1.11162	−0.0508442
$479$	11.4997	0.525433	0.262716	−	0.964873i	$-0.415382\pi$
$479$	11.4997	0.525433	0.262716	+	0.964873i	$0.415382\pi$
$480$	−0.265783	−0.0121313
$481$	7.72229	0.352106
$482$	−16.2045	−0.738093
$483$	1.14095	0.0519150
$484$	31.0729	1.41240
$485$	40.9838	1.86098
$486$	2.57878	0.116976
$487$	18.1518	0.822538	0.411269	−	0.911514i	$-0.365086\pi$
$487$	18.1518	0.822538	0.411269	+	0.911514i	$0.365086\pi$
$488$	13.7919	0.624328
$489$	2.05003	0.0927055
$490$	4.29926	0.194221
$491$	−23.8875	−1.07803	−0.539014	−	0.842297i	$-0.681203\pi$
$491$	−23.8875	−1.07803	−0.539014	+	0.842297i	$0.681203\pi$
$492$	−0.465438	−0.0209836
$493$	32.5170	1.46449
$494$	−5.52323	−0.248502
$495$	53.7636	2.41649
$496$	3.86154	0.173388
$497$	40.5818	1.82034
$498$	−0.438832	−0.0196645
$499$	10.3466	0.463176	0.231588	−	0.972814i	$-0.425608\pi$
$499$	10.3466	0.463176	0.231588	+	0.972814i	$0.425608\pi$
$500$	6.42779	0.287459
$501$	−0.950997	−0.0424874
$502$	−1.97412	−0.0881092
$503$	33.9422	1.51341	0.756703	−	0.653759i	$-0.226809\pi$
$503$	33.9422	1.51341	0.756703	+	0.653759i	$0.226809\pi$
$504$	8.74588	0.389573
$505$	5.89732	0.262427
$506$	26.3890	1.17313
$507$	1.16075	0.0515508
$508$	−15.9075	−0.705782
$509$	−9.58311	−0.424764	−0.212382	−	0.977187i	$-0.568122\pi$
$509$	−9.58311	−0.424764	−0.212382	+	0.977187i	$0.568122\pi$
$510$	1.49715	0.0662950
$511$	27.8649	1.23267
$512$	−1.00000	−0.0441942
$513$	−3.35147	−0.147971
$514$	10.3465	0.456362
$515$	−51.3964	−2.26480
$516$	0.264832	0.0116586
$517$	70.7672	3.11234
$518$	23.8501	1.04791
$519$	−0.0873568	−0.00383454
$520$	−2.62404	−0.115072
$521$	−11.0228	−0.482919	−0.241459	−	0.970411i	$-0.577626\pi$
$521$	−11.0228	−0.482919	−0.241459	+	0.970411i	$0.577626\pi$
$522$	−17.2648	−0.755658
$523$	−36.7850	−1.60850	−0.804248	−	0.594294i	$-0.797432\pi$
$523$	−36.7850	−1.60850	−0.804248	+	0.594294i	$0.797432\pi$
$524$	−6.72858	−0.293939
$525$	−0.751775	−0.0328101
$526$	0.358033	0.0156110
$527$	−21.7520	−0.947532
$528$	−0.622055	−0.0270715
$529$	−6.44823	−0.280358
$530$	15.2693	0.663255
$531$	−5.50508	−0.238900
$532$	−17.0584	−0.739574
$533$	−4.59521	−0.199041
$534$	−0.122935	−0.00531992
$535$	48.2336	2.08532
$536$	−8.92362	−0.385442
$537$	−0.606774	−0.0261842
$538$	−21.3995	−0.922597
$539$	10.0622	0.433411
$540$	−1.59225	−0.0685197
$541$	33.6118	1.44508	0.722541	−	0.691328i	$-0.242974\pi$
$541$	33.6118	1.44508	0.722541	+	0.691328i	$0.242974\pi$
$542$	−16.2497	−0.697984
$543$	2.01331	0.0863993
$544$	5.63298	0.241512
$545$	30.2521	1.29586
$546$	−0.265531	−0.0113637
$547$	10.3937	0.444403	0.222202	−	0.975001i	$-0.428676\pi$
$547$	10.3937	0.444403	0.222202	+	0.975001i	$0.428676\pi$
$548$	14.4459	0.617097
$549$	41.2487	1.76045
$550$	−17.3878	−0.741419
$551$	33.6740	1.43456
$552$	−0.390167	−0.0166066
$553$	17.2599	0.733964
$554$	−23.6368	−1.00423
$555$	−2.16771	−0.0920144
$556$	13.9063	0.589759
$557$	−44.4587	−1.88378	−0.941888	−	0.335927i	$-0.890950\pi$
$557$	−44.4587	−1.88378	−0.941888	+	0.335927i	$0.890950\pi$
$558$	11.5491	0.488913
$559$	2.61466	0.110588
$560$	−8.10430	−0.342469
$561$	3.50402	0.147940
$562$	−3.74204	−0.157849
$563$	29.7629	1.25436	0.627178	−	0.778876i	$-0.284210\pi$
$563$	29.7629	1.25436	0.627178	+	0.778876i	$0.284210\pi$
$564$	−1.04631	−0.0440575
$565$	−27.0389	−1.13753
$566$	−30.9372	−1.30039
$567$	26.0765	1.09511
$568$	−13.8776	−0.582293
$569$	−17.2806	−0.724441	−0.362220	−	0.932092i	$-0.617981\pi$
$569$	−17.2806	−0.724441	−0.362220	+	0.932092i	$0.617981\pi$
$570$	1.55042	0.0649399
$571$	−1.38870	−0.0581151	−0.0290575	−	0.999578i	$-0.509251\pi$
$571$	−1.38870	−0.0581151	−0.0290575	+	0.999578i	$0.509251\pi$
$572$	−6.14147	−0.256788
$573$	0.856161	0.0357667
$574$	−14.1922	−0.592372
$575$	−10.9060	−0.454812
$576$	−2.99080	−0.124617
$577$	16.0017	0.666160	0.333080	−	0.942899i	$-0.391912\pi$
$577$	16.0017	0.666160	0.333080	+	0.942899i	$0.391912\pi$
$578$	−14.7305	−0.612707
$579$	0.745007	0.0309614
$580$	15.9982	0.664291
$581$	−13.3809	−0.555135
$582$	−1.41821	−0.0587867
$583$	35.7371	1.48008
$584$	−9.52886	−0.394307
$585$	−7.84800	−0.324475
$586$	5.41506	0.223694
$587$	−20.1988	−0.833694	−0.416847	−	0.908977i	$-0.636865\pi$
$587$	−20.1988	−0.833694	−0.416847	+	0.908977i	$0.636865\pi$
$588$	−0.148772	−0.00613526
$589$	−22.5259	−0.928164
$590$	5.10123	0.210014
$591$	−2.22319	−0.0914498
$592$	−8.15595	−0.335207
$593$	−29.1146	−1.19559	−0.597796	−	0.801648i	$-0.703957\pi$
$593$	−29.1146	−1.19559	−0.597796	+	0.801648i	$0.703957\pi$
$594$	−3.72661	−0.152905
$595$	45.6514	1.87152
$596$	7.62742	0.312431
$597$	1.93293	0.0791097
$598$	−3.85207	−0.157523
$599$	−24.8465	−1.01520	−0.507600	−	0.861593i	$-0.669467\pi$
$599$	−24.8465	−1.01520	−0.507600	+	0.861593i	$0.669467\pi$
$600$	0.257082	0.0104953
$601$	−16.9793	−0.692600	−0.346300	−	0.938124i	$-0.612562\pi$
$601$	−16.9793	−0.692600	−0.346300	+	0.938124i	$0.612562\pi$
$602$	8.07530	0.329125
$603$	−26.6888	−1.08685
$604$	−19.7725	−0.804532
$605$	−86.1154	−3.50109
$606$	−0.204072	−0.00828985
$607$	18.3595	0.745187	0.372594	−	0.927995i	$-0.378469\pi$
$607$	18.3595	0.745187	0.372594	+	0.927995i	$0.378469\pi$
$608$	5.83340	0.236576
$609$	1.61889	0.0656006
$610$	−38.2228	−1.54760
$611$	−10.3301	−0.417909
$612$	16.8471	0.681005
$613$	−11.9066	−0.480901	−0.240451	−	0.970661i	$-0.577295\pi$
$613$	−11.9066	−0.480901	−0.240451	+	0.970661i	$0.577295\pi$
$614$	−17.7878	−0.717858
$615$	1.28992	0.0520145
$616$	−18.9678	−0.764234
$617$	−0.145219	−0.00584628	−0.00292314	−	0.999996i	$-0.500930\pi$
$617$	−0.145219	−0.00584628	−0.00292314	+	0.999996i	$0.500930\pi$
$618$	1.77853	0.0715430
$619$	−6.45433	−0.259422	−0.129711	−	0.991552i	$-0.541405\pi$
$619$	−6.45433	−0.259422	−0.129711	+	0.991552i	$0.541405\pi$
$620$	−10.7019	−0.429798
$621$	−2.33741	−0.0937971
$622$	−5.17349	−0.207438
$623$	−3.74855	−0.150183
$624$	0.0908028	0.00363502
$625$	−31.2174	−1.24869
$626$	−32.4356	−1.29639
$627$	3.62870	0.144916
$628$	10.7466	0.428835
$629$	45.9423	1.83184
$630$	−24.2384	−0.965680
$631$	−15.1684	−0.603843	−0.301921	−	0.953333i	$-0.597628\pi$
$631$	−15.1684	−0.603843	−0.301921	+	0.953333i	$0.597628\pi$
$632$	−5.90230	−0.234781
$633$	−0.248996	−0.00989669
$634$	19.0834	0.757900
$635$	44.0861	1.74951
$636$	−0.528380	−0.0209516
$637$	−1.46881	−0.0581963
$638$	37.4433	1.48239
$639$	−41.5053	−1.64192
$640$	2.77140	0.109549
$641$	40.8276	1.61259	0.806297	−	0.591511i	$-0.201468\pi$
$641$	40.8276	1.61259	0.806297	+	0.591511i	$0.201468\pi$
$642$	−1.66908	−0.0658735
$643$	8.75576	0.345294	0.172647	−	0.984984i	$-0.444768\pi$
$643$	8.75576	0.345294	0.172647	+	0.984984i	$0.444768\pi$
$644$	−11.8970	−0.468808
$645$	−0.733957	−0.0288995
$646$	−32.8594	−1.29284
$647$	16.6154	0.653219	0.326609	−	0.945159i	$-0.394094\pi$
$647$	16.6154	0.653219	0.326609	+	0.945159i	$0.394094\pi$
$648$	−8.91731	−0.350305
$649$	11.9392	0.468656
$650$	2.53814	0.0995540
$651$	−1.08294	−0.0424438
$652$	−21.3763	−0.837159
$653$	41.0651	1.60700	0.803500	−	0.595305i	$-0.202969\pi$
$653$	41.0651	1.60700	0.803500	+	0.595305i	$0.202969\pi$
$654$	−1.04685	−0.0409350
$655$	18.6476	0.728622
$656$	4.85327	0.189488
$657$	−28.4989	−1.11185
$658$	−31.9041	−1.24375
$659$	−17.4992	−0.681671	−0.340835	−	0.940123i	$-0.610710\pi$
$659$	−17.4992	−0.681671	−0.340835	+	0.940123i	$0.610710\pi$
$660$	1.72397	0.0671053
$661$	−24.3785	−0.948212	−0.474106	−	0.880468i	$-0.657229\pi$
$661$	−24.3785	−0.948212	−0.474106	+	0.880468i	$0.657229\pi$
$662$	8.03473	0.312279
$663$	−0.511491	−0.0198647
$664$	4.57584	0.177577
$665$	47.2756	1.83327
$666$	−24.3928	−0.945203
$667$	23.4852	0.909352
$668$	9.91633	0.383674
$669$	−0.459854	−0.0177790
$670$	24.7310	0.955440
$671$	−89.4590	−3.45353
$672$	0.280442	0.0108183
$673$	5.31058	0.204708	0.102354	−	0.994748i	$-0.467363\pi$
$673$	5.31058	0.204708	0.102354	+	0.994748i	$0.467363\pi$
$674$	−24.9873	−0.962474
$675$	1.54013	0.0592796
$676$	−12.1035	−0.465520
$677$	−32.0582	−1.23210	−0.616049	−	0.787708i	$-0.711268\pi$
$677$	−32.0582	−1.23210	−0.616049	+	0.787708i	$0.711268\pi$
$678$	0.935657	0.0359337
$679$	−43.2442	−1.65956
$680$	−15.6113	−0.598664
$681$	−1.57439	−0.0603306
$682$	−25.0473	−0.959112
$683$	25.7753	0.986263	0.493132	−	0.869955i	$-0.335852\pi$
$683$	25.7753	0.986263	0.493132	+	0.869955i	$0.335852\pi$
$684$	17.4466	0.667086
$685$	−40.0354	−1.52967
$686$	15.9334	0.608341
$687$	0.376937	0.0143810
$688$	−2.76149	−0.105281
$689$	−5.21663	−0.198738
$690$	1.08131	0.0411647
$691$	−13.6570	−0.519535	−0.259767	−	0.965671i	$-0.583646\pi$
$691$	−13.6570	−0.519535	−0.259767	+	0.965671i	$0.583646\pi$
$692$	0.910896	0.0346271
$693$	−56.7289	−2.15495
$694$	−20.9311	−0.794533
$695$	−38.5400	−1.46190
$696$	−0.553606	−0.0209844
$697$	−27.3384	−1.03551
$698$	−27.0525	−1.02395
$699$	−0.0426713	−0.00161398
$700$	7.83899	0.296286
$701$	39.8456	1.50495	0.752473	−	0.658623i	$-0.228861\pi$
$701$	39.8456	1.50495	0.752473	+	0.658623i	$0.228861\pi$
$702$	0.543982	0.0205313
$703$	47.5769	1.79440
$704$	6.48636	0.244464
$705$	2.89974	0.109210
$706$	−7.73744	−0.291202
$707$	−6.22259	−0.234025
$708$	−0.176524	−0.00663417
$709$	−41.3418	−1.55262	−0.776312	−	0.630349i	$-0.782912\pi$
$709$	−41.3418	−1.55262	−0.776312	+	0.630349i	$0.782912\pi$
$710$	38.4605	1.44340
$711$	−17.6526	−0.662025
$712$	1.28188	0.0480405
$713$	−15.7102	−0.588353
$714$	−1.57973	−0.0591198
$715$	17.0205	0.636530
$716$	6.32701	0.236452
$717$	−0.106606	−0.00398129
$718$	−0.0105153	−0.000392426 0
$719$	−37.7175	−1.40662	−0.703312	−	0.710882i	$-0.748296\pi$
$719$	−37.7175	−1.40662	−0.703312	+	0.710882i	$0.748296\pi$
$720$	8.28872	0.308902
$721$	54.2312	2.01968
$722$	−15.0286	−0.559305
$723$	−1.55404	−0.0577954
$724$	−20.9934	−0.780213
$725$	−15.4745	−0.574709
$726$	2.97995	0.110596
$727$	47.5770	1.76453	0.882267	−	0.470750i	$-0.156017\pi$
$727$	47.5770	1.76453	0.882267	+	0.470750i	$0.156017\pi$
$728$	2.76877	0.102618
$729$	−26.5046	−0.981653
$730$	26.4083	0.977416
$731$	15.5554	0.575337
$732$	1.32267	0.0488872
$733$	29.7932	1.10044	0.550218	−	0.835021i	$-0.314544\pi$
$733$	29.7932	1.10044	0.550218	+	0.835021i	$0.314544\pi$
$734$	−13.4346	−0.495881
$735$	0.412308	0.0152082
$736$	4.06839	0.149963
$737$	57.8818	2.13210
$738$	14.5152	0.534311
$739$	−17.2914	−0.636073	−0.318037	−	0.948078i	$-0.603023\pi$
$739$	−17.2914	−0.636073	−0.318037	+	0.948078i	$0.603023\pi$
$740$	22.6034	0.830918
$741$	−0.529689	−0.0194586
$742$	−16.1114	−0.591470
$743$	10.1866	0.373711	0.186855	−	0.982387i	$-0.440170\pi$
$743$	10.1866	0.373711	0.186855	+	0.982387i	$0.440170\pi$
$744$	0.370330	0.0135769
$745$	−21.1387	−0.774460
$746$	−28.4689	−1.04232
$747$	13.6854	0.500724
$748$	−36.5375	−1.33594
$749$	−50.8940	−1.85963
$750$	0.616438	0.0225091
$751$	46.4103	1.69354	0.846768	−	0.531962i	$-0.178545\pi$
$751$	46.4103	1.69354	0.846768	+	0.531962i	$0.178545\pi$
$752$	10.9102	0.397853
$753$	−0.189322	−0.00689928
$754$	−5.46568	−0.199048
$755$	54.7976	1.99429
$756$	1.68008	0.0611038
$757$	−24.7075	−0.898010	−0.449005	−	0.893529i	$-0.648221\pi$
$757$	−24.7075	−0.898010	−0.449005	+	0.893529i	$0.648221\pi$
$758$	33.7912	1.22735
$759$	2.53076	0.0918608
$760$	−16.1667	−0.586428
$761$	13.8073	0.500513	0.250256	−	0.968180i	$-0.419485\pi$
$761$	13.8073	0.500513	0.250256	+	0.968180i	$0.419485\pi$
$762$	−1.52556	−0.0552653
$763$	−31.9207	−1.15561
$764$	−8.92746	−0.322984
$765$	−46.6902	−1.68809
$766$	0.754075	0.0272458
$767$	−1.74280	−0.0629288
$768$	−0.0959021	−0.00346057
$769$	12.5890	0.453971	0.226986	−	0.973898i	$-0.427113\pi$
$769$	12.5890	0.453971	0.226986	+	0.973898i	$0.427113\pi$
$770$	52.5674	1.89440
$771$	0.992246	0.0357349
$772$	−7.76842	−0.279591
$773$	38.1793	1.37321	0.686607	−	0.727028i	$-0.259099\pi$
$773$	38.1793	1.37321	0.686607	+	0.727028i	$0.259099\pi$
$774$	−8.25906	−0.296866
$775$	10.3515	0.371838
$776$	14.7881	0.530862
$777$	2.28727	0.0820555
$778$	−12.4833	−0.447547
$779$	−28.3111	−1.01435
$780$	−0.251651	−0.00901056
$781$	90.0154	3.22100
$782$	−22.9171	−0.819515
$783$	−3.31654	−0.118524
$784$	1.55129	0.0554033
$785$	−29.7831	−1.06300
$786$	−0.645285	−0.0230165
$787$	−16.0519	−0.572188	−0.286094	−	0.958202i	$-0.592357\pi$
$787$	−16.0519	−0.572188	−0.286094	+	0.958202i	$0.592357\pi$
$788$	23.1819	0.825821
$789$	0.0343361	0.00122240
$790$	16.3576	0.581979
$791$	28.5302	1.01442
$792$	19.3994	0.689328
$793$	13.0585	0.463722
$794$	23.4913	0.833675
$795$	1.46435	0.0519353
$796$	−20.1553	−0.714385
$797$	−26.8354	−0.950560	−0.475280	−	0.879835i	$-0.657653\pi$
$797$	−26.8354	−0.950560	−0.475280	+	0.879835i	$0.657653\pi$
$798$	−1.63593	−0.0579114
$799$	−61.4567	−2.17418
$800$	−2.68067	−0.0947761
$801$	3.83386	0.135463
$802$	−16.8513	−0.595042
$803$	61.8076	2.18114
$804$	−0.855794	−0.0301815
$805$	32.9714	1.16209
$806$	3.65622	0.128785
$807$	−2.05225	−0.0722428
$808$	2.12792	0.0748600
$809$	20.2617	0.712364	0.356182	−	0.934417i	$-0.384078\pi$
$809$	20.2617	0.712364	0.356182	+	0.934417i	$0.384078\pi$
$810$	24.7135	0.868342
$811$	35.7167	1.25418	0.627092	−	0.778945i	$-0.284245\pi$
$811$	35.7167	1.25418	0.627092	+	0.778945i	$0.284245\pi$
$812$	−16.8806	−0.592394
$813$	−1.55838	−0.0546547
$814$	52.9024	1.85423
$815$	59.2423	2.07517
$816$	0.540214	0.0189113
$817$	16.1089	0.563578
$818$	10.9555	0.383050
$819$	8.28086	0.289357
$820$	−13.4504	−0.469707
$821$	46.1330	1.61005	0.805026	−	0.593240i	$-0.202152\pi$
$821$	46.1330	1.61005	0.805026	+	0.593240i	$0.202152\pi$
$822$	1.38539	0.0483210
$823$	−37.8019	−1.31769	−0.658846	−	0.752278i	$-0.728955\pi$
$823$	−37.8019	−1.31769	−0.658846	+	0.752278i	$0.728955\pi$
$824$	−18.5453	−0.646055
$825$	−1.66753	−0.0580558
$826$	−5.38259	−0.187284
$827$	−52.0453	−1.80979	−0.904897	−	0.425632i	$-0.860052\pi$
$827$	−52.0453	−1.80979	−0.904897	+	0.425632i	$0.860052\pi$
$828$	12.1677	0.422858
$829$	50.6397	1.75879	0.879395	−	0.476092i	$-0.157947\pi$
$829$	50.6397	1.75879	0.879395	+	0.476092i	$0.157947\pi$
$830$	−12.6815	−0.440181
$831$	−2.26682	−0.0786351
$832$	−0.946829	−0.0328254
$833$	−8.73840	−0.302768
$834$	1.33364	0.0461803
$835$	−27.4822	−0.951059
$836$	−37.8375	−1.30864
$837$	2.21857	0.0766851
$838$	−5.95729	−0.205791
$839$	−45.3607	−1.56602	−0.783012	−	0.622006i	$-0.786318\pi$
$839$	−45.3607	−1.56602	−0.783012	+	0.622006i	$0.786318\pi$
$840$	−0.777219	−0.0268166
$841$	4.32309	0.149072
$842$	−33.1195	−1.14137
$843$	−0.358870	−0.0123601
$844$	2.59635	0.0893702
$845$	33.5437	1.15394
$846$	32.6301	1.12185
$847$	90.8651	3.12216
$848$	5.50958	0.189200
$849$	−2.96695	−0.101825
$850$	15.1002	0.517932
$851$	33.1816	1.13745
$852$	−1.33089	−0.0455957
$853$	−56.6548	−1.93982	−0.969911	−	0.243459i	$-0.921718\pi$
$853$	−56.6548	−1.93982	−0.969911	+	0.243459i	$0.921718\pi$
$854$	40.3310	1.38010
$855$	−48.3514	−1.65358
$856$	17.4041	0.594858
$857$	10.1087	0.345307	0.172654	−	0.984983i	$-0.444766\pi$
$857$	10.1087	0.345307	0.172654	+	0.984983i	$0.444766\pi$
$858$	−0.588980	−0.0201074
$859$	15.6886	0.535289	0.267645	−	0.963518i	$-0.413755\pi$
$859$	15.6886	0.535289	0.267645	+	0.963518i	$0.413755\pi$
$860$	7.65319	0.260972
$861$	−1.36106	−0.0463849
$862$	8.06502	0.274696
$863$	10.6381	0.362126	0.181063	−	0.983471i	$-0.442046\pi$
$863$	10.6381	0.362126	0.181063	+	0.983471i	$0.442046\pi$
$864$	−0.574530	−0.0195459
$865$	−2.52446	−0.0858342
$866$	15.4396	0.524661
$867$	−1.41268	−0.0479772
$868$	11.2921	0.383281
$869$	38.2844	1.29871
$870$	1.53426	0.0520164
$871$	−8.44914	−0.286288
$872$	10.9158	0.369656
$873$	44.2283	1.49690
$874$	−23.7325	−0.802765
$875$	18.7965	0.635438
$876$	−0.913837	−0.0308757
$877$	−18.6346	−0.629246	−0.314623	−	0.949217i	$-0.601878\pi$
$877$	−18.6346	−0.629246	−0.314623	+	0.949217i	$0.601878\pi$
$878$	−15.1690	−0.511927
$879$	0.519316	0.0175161
$880$	−17.9763	−0.605981
$881$	−35.0945	−1.18236	−0.591182	−	0.806538i	$-0.701339\pi$
$881$	−35.0945	−1.18236	−0.591182	+	0.806538i	$0.701339\pi$
$882$	4.63961	0.156224
$883$	−1.22938	−0.0413718	−0.0206859	−	0.999786i	$-0.506585\pi$
$883$	−1.22938	−0.0413718	−0.0206859	+	0.999786i	$0.506585\pi$
$884$	5.33347	0.179384
$885$	0.489219	0.0164449
$886$	−17.7517	−0.596381
$887$	18.8188	0.631874	0.315937	−	0.948780i	$-0.397681\pi$
$887$	18.8188	0.631874	0.315937	+	0.948780i	$0.397681\pi$
$888$	−0.782172	−0.0262480
$889$	−46.5177	−1.56015
$890$	−3.55261	−0.119084
$891$	57.8409	1.93774
$892$	4.79504	0.160550
$893$	−63.6433	−2.12974
$894$	0.731485	0.0244645
$895$	−17.5347	−0.586121
$896$	−2.92426	−0.0976926
$897$	−0.369421	−0.0123346
$898$	−4.46836	−0.149111
$899$	−22.2912	−0.743453
$900$	−8.01737	−0.267246
$901$	−31.0354	−1.03394
$902$	−31.4800	−1.04817
$903$	0.774438	0.0257717
$904$	−9.75638	−0.324492
$905$	58.1811	1.93401
$906$	−1.89622	−0.0629978
$907$	−21.8871	−0.726749	−0.363374	−	0.931643i	$-0.618375\pi$
$907$	−21.8871	−0.726749	−0.363374	+	0.931643i	$0.618375\pi$
$908$	16.4166	0.544805
$909$	6.36419	0.211087
$910$	−7.67339	−0.254370
$911$	31.8715	1.05595	0.527975	−	0.849260i	$-0.322951\pi$
$911$	31.8715	1.05595	0.527975	+	0.849260i	$0.322951\pi$
$912$	0.559435	0.0185247
$913$	−29.6805	−0.982282
$914$	2.68712	0.0888820
$915$	−3.66565	−0.121183
$916$	−3.93044	−0.129865
$917$	−19.6761	−0.649763
$918$	3.23632	0.106814
$919$	47.4749	1.56605	0.783026	−	0.621989i	$-0.213675\pi$
$919$	47.4749	1.56605	0.783026	+	0.621989i	$0.213675\pi$
$920$	−11.2751	−0.371730
$921$	−1.70589	−0.0562110
$922$	−22.2273	−0.732017
$923$	−13.1398	−0.432500
$924$	−1.81905	−0.0598424
$925$	−21.8634	−0.718866
$926$	40.7332	1.33857
$927$	−55.4653	−1.82172
$928$	5.77262	0.189495
$929$	4.14509	0.135996	0.0679980	−	0.997685i	$-0.478339\pi$
$929$	4.14509	0.135996	0.0679980	+	0.997685i	$0.478339\pi$
$930$	−1.02633	−0.0336548
$931$	−9.04931	−0.296579
$932$	0.444946	0.0145747
$933$	−0.496148	−0.0162432
$934$	−30.1353	−0.986058
$935$	101.260	3.31156
$936$	−2.83178	−0.0925596
$937$	49.3407	1.61189	0.805945	−	0.591991i	$-0.201658\pi$
$937$	49.3407	1.61189	0.805945	+	0.591991i	$0.201658\pi$
$938$	−26.0950	−0.852032
$939$	−3.11064	−0.101512
$940$	−30.2364	−0.986204
$941$	54.2123	1.76727	0.883636	−	0.468175i	$-0.155088\pi$
$941$	54.2123	1.76727	0.883636	+	0.468175i	$0.155088\pi$
$942$	1.03062	0.0335794
$943$	−19.7450	−0.642985
$944$	1.84067	0.0599087
$945$	−4.65617	−0.151465
$946$	17.9120	0.582369
$947$	30.0828	0.977560	0.488780	−	0.872407i	$-0.337442\pi$
$947$	30.0828	0.977560	0.488780	+	0.872407i	$0.337442\pi$
$948$	−0.566043	−0.0183842
$949$	−9.02220	−0.292873
$950$	15.6374	0.507346
$951$	1.83014	0.0593464
$952$	16.4723	0.533870
$953$	48.5932	1.57409	0.787044	−	0.616897i	$-0.211611\pi$
$953$	48.5932	1.57409	0.787044	+	0.616897i	$0.211611\pi$
$954$	16.4781	0.533497
$955$	24.7416	0.800619
$956$	1.11162	0.0359523
$957$	3.59089	0.116077
$958$	−11.4997	−0.371537
$959$	42.2435	1.36411
$960$	0.265783	0.00857812
$961$	−16.0885	−0.518984
$962$	−7.72229	−0.248977
$963$	52.0521	1.67736
$964$	16.2045	0.521911
$965$	21.5294	0.693056
$966$	−1.14095	−0.0367094
$967$	52.6299	1.69246	0.846232	−	0.532814i	$-0.178865\pi$
$967$	52.6299	1.69246	0.846232	+	0.532814i	$0.178865\pi$
$968$	−31.0729	−0.998719
$969$	−3.15129	−0.101234
$970$	−40.9838	−1.31591
$971$	5.64316	0.181098	0.0905489	−	0.995892i	$-0.471138\pi$
$971$	5.64316	0.181098	0.0905489	+	0.995892i	$0.471138\pi$
$972$	−2.57878	−0.0827144
$973$	40.6656	1.30368
$974$	−18.1518	−0.581622
$975$	0.243413	0.00779545
$976$	−13.7919	−0.441467
$977$	24.7994	0.793402	0.396701	−	0.917948i	$-0.370155\pi$
$977$	24.7994	0.793402	0.396701	+	0.917948i	$0.370155\pi$
$978$	−2.05003	−0.0655527
$979$	−8.31475	−0.265740
$980$	−4.29926	−0.137335
$981$	32.6470	1.04234
$982$	23.8875	0.762280
$983$	−18.3581	−0.585533	−0.292767	−	0.956184i	$-0.594576\pi$
$983$	−18.3581	−0.585533	−0.292767	+	0.956184i	$0.594576\pi$
$984$	0.465438	0.0148376
$985$	−64.2464	−2.04706
$986$	−32.5170	−1.03555
$987$	−3.05967	−0.0973904
$988$	5.52323	0.175717
$989$	11.2348	0.357246
$990$	−53.7636	−1.70872
$991$	24.6742	0.783801	0.391900	−	0.920008i	$-0.371818\pi$
$991$	24.6742	0.783801	0.391900	+	0.920008i	$0.371818\pi$
$992$	−3.86154	−0.122604
$993$	0.770547	0.0244526
$994$	−40.5818	−1.28718
$995$	55.8584	1.77083
$996$	0.438832	0.0139049
$997$	−3.43956	−0.108932	−0.0544660	−	0.998516i	$-0.517346\pi$
$997$	−3.43956	−0.108932	−0.0544660	+	0.998516i	$0.517346\pi$
$998$	−10.3466	−0.327515
$999$	−4.68584	−0.148253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.38	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.38	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0959021 q^{3} +1.00000 q^{4} -2.77140 q^{5} +0.0959021 q^{6} +2.92426 q^{7} -1.00000 q^{8} -2.99080 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0959021 q^{3} +1.00000 q^{4} -2.77140 q^{5} +0.0959021 q^{6} +2.92426 q^{7} -1.00000 q^{8} -2.99080 q^{9} +2.77140 q^{10} +6.48636 q^{11} -0.0959021 q^{12} -0.946829 q^{13} -2.92426 q^{14} +0.265783 q^{15} +1.00000 q^{16} -5.63298 q^{17} +2.99080 q^{18} -5.83340 q^{19} -2.77140 q^{20} -0.280442 q^{21} -6.48636 q^{22} -4.06839 q^{23} +0.0959021 q^{24} +2.68067 q^{25} +0.946829 q^{26} +0.574530 q^{27} +2.92426 q^{28} -5.77262 q^{29} -0.265783 q^{30} +3.86154 q^{31} -1.00000 q^{32} -0.622055 q^{33} +5.63298 q^{34} -8.10430 q^{35} -2.99080 q^{36} -8.15595 q^{37} +5.83340 q^{38} +0.0908028 q^{39} +2.77140 q^{40} +4.85327 q^{41} +0.280442 q^{42} -2.76149 q^{43} +6.48636 q^{44} +8.28872 q^{45} +4.06839 q^{46} +10.9102 q^{47} -0.0959021 q^{48} +1.55129 q^{49} -2.68067 q^{50} +0.540214 q^{51} -0.946829 q^{52} +5.50958 q^{53} -0.574530 q^{54} -17.9763 q^{55} -2.92426 q^{56} +0.559435 q^{57} +5.77262 q^{58} +1.84067 q^{59} +0.265783 q^{60} -13.7919 q^{61} -3.86154 q^{62} -8.74588 q^{63} +1.00000 q^{64} +2.62404 q^{65} +0.622055 q^{66} +8.92362 q^{67} -5.63298 q^{68} +0.390167 q^{69} +8.10430 q^{70} +13.8776 q^{71} +2.99080 q^{72} +9.52886 q^{73} +8.15595 q^{74} -0.257082 q^{75} -5.83340 q^{76} +18.9678 q^{77} -0.0908028 q^{78} +5.90230 q^{79} -2.77140 q^{80} +8.91731 q^{81} -4.85327 q^{82} -4.57584 q^{83} -0.280442 q^{84} +15.6113 q^{85} +2.76149 q^{86} +0.553606 q^{87} -6.48636 q^{88} -1.28188 q^{89} -8.28872 q^{90} -2.76877 q^{91} -4.06839 q^{92} -0.370330 q^{93} -10.9102 q^{94} +16.1667 q^{95} +0.0959021 q^{96} -14.7881 q^{97} -1.55129 q^{98} -19.3994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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