LMFDB - Embedded newform 4031.2.a.c.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.292455 q^{2} +2.53585 q^{3} -1.91447 q^{4} -1.96622 q^{5} -0.741621 q^{6} -4.61679 q^{7} +1.14481 q^{8} +3.43052 q^{9} +O(q^{10})$	\(q-0.292455 q^{2} +2.53585 q^{3} -1.91447 q^{4} -1.96622 q^{5} -0.741621 q^{6} -4.61679 q^{7} +1.14481 q^{8} +3.43052 q^{9} +0.575030 q^{10} -0.331348 q^{11} -4.85480 q^{12} +4.15773 q^{13} +1.35020 q^{14} -4.98602 q^{15} +3.49414 q^{16} +3.51043 q^{17} -1.00327 q^{18} +1.05721 q^{19} +3.76426 q^{20} -11.7075 q^{21} +0.0969044 q^{22} +4.53125 q^{23} +2.90305 q^{24} -1.13399 q^{25} -1.21595 q^{26} +1.09174 q^{27} +8.83870 q^{28} -1.00000 q^{29} +1.45819 q^{30} +6.81243 q^{31} -3.31149 q^{32} -0.840249 q^{33} -1.02664 q^{34} +9.07760 q^{35} -6.56764 q^{36} -1.35149 q^{37} -0.309188 q^{38} +10.5434 q^{39} -2.25094 q^{40} -5.44493 q^{41} +3.42391 q^{42} -10.6634 q^{43} +0.634356 q^{44} -6.74515 q^{45} -1.32519 q^{46} -4.81889 q^{47} +8.86060 q^{48} +14.3147 q^{49} +0.331642 q^{50} +8.90191 q^{51} -7.95986 q^{52} -1.33388 q^{53} -0.319286 q^{54} +0.651502 q^{55} -5.28532 q^{56} +2.68094 q^{57} +0.292455 q^{58} -5.18768 q^{59} +9.54560 q^{60} -12.3497 q^{61} -1.99233 q^{62} -15.8380 q^{63} -6.01981 q^{64} -8.17500 q^{65} +0.245735 q^{66} -4.63655 q^{67} -6.72061 q^{68} +11.4906 q^{69} -2.65479 q^{70} +5.80156 q^{71} +3.92729 q^{72} +2.83001 q^{73} +0.395249 q^{74} -2.87564 q^{75} -2.02401 q^{76} +1.52976 q^{77} -3.08346 q^{78} -1.76502 q^{79} -6.87023 q^{80} -7.52308 q^{81} +1.59240 q^{82} -2.86315 q^{83} +22.4136 q^{84} -6.90226 q^{85} +3.11856 q^{86} -2.53585 q^{87} -0.379330 q^{88} -2.46780 q^{89} +1.97265 q^{90} -19.1954 q^{91} -8.67494 q^{92} +17.2753 q^{93} +1.40931 q^{94} -2.07871 q^{95} -8.39743 q^{96} +0.822927 q^{97} -4.18641 q^{98} -1.13670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−0.292455	−0.206797	−0.103398	−	0.994640i	$-0.532972\pi$
$2$	−0.292455	−0.206797	−0.103398	+	0.994640i	$0.532972\pi$
$3$	2.53585	1.46407	0.732036	−	0.681266i	$-0.238570\pi$
$3$	2.53585	1.46407	0.732036	+	0.681266i	$0.238570\pi$
$4$	−1.91447	−0.957235
$5$	−1.96622	−0.879319	−0.439659	−	0.898165i	$-0.644901\pi$
$5$	−1.96622	−0.879319	−0.439659	+	0.898165i	$0.644901\pi$
$6$	−0.741621	−0.302766
$7$	−4.61679	−1.74498	−0.872490	−	0.488631i	$-0.837496\pi$
$7$	−4.61679	−1.74498	−0.872490	+	0.488631i	$0.837496\pi$
$8$	1.14481	0.404750
$9$	3.43052	1.14351
$10$	0.575030	0.181840
$11$	−0.331348	−0.0999053	−0.0499526	−	0.998752i	$-0.515907\pi$
$11$	−0.331348	−0.0999053	−0.0499526	+	0.998752i	$0.515907\pi$
$12$	−4.85480	−1.40146
$13$	4.15773	1.15315	0.576574	−	0.817045i	$-0.304389\pi$
$13$	4.15773	1.15315	0.576574	+	0.817045i	$0.304389\pi$
$14$	1.35020	0.360857
$15$	−4.98602	−1.28739
$16$	3.49414	0.873534
$17$	3.51043	0.851404	0.425702	−	0.904863i	$-0.360027\pi$
$17$	3.51043	0.851404	0.425702	+	0.904863i	$0.360027\pi$
$18$	−1.00327	−0.236474
$19$	1.05721	0.242542	0.121271	−	0.992619i	$-0.461303\pi$
$19$	1.05721	0.242542	0.121271	+	0.992619i	$0.461303\pi$
$20$	3.76426	0.841715
$21$	−11.7075	−2.55478
$22$	0.0969044	0.0206601
$23$	4.53125	0.944830	0.472415	−	0.881376i	$-0.343382\pi$
$23$	4.53125	0.944830	0.472415	+	0.881376i	$0.343382\pi$
$24$	2.90305	0.592583
$25$	−1.13399	−0.226799
$26$	−1.21595	−0.238467
$27$	1.09174	0.210106
$28$	8.83870	1.67036
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.45819	0.266227
$31$	6.81243	1.22355	0.611775	−	0.791032i	$-0.290456\pi$
$31$	6.81243	1.22355	0.611775	+	0.791032i	$0.290456\pi$
$32$	−3.31149	−0.585394
$33$	−0.840249	−0.146269
$34$	−1.02664	−0.176068
$35$	9.07760	1.53439
$36$	−6.56764	−1.09461
$37$	−1.35149	−0.222183	−0.111092	−	0.993810i	$-0.535435\pi$
$37$	−1.35149	−0.222183	−0.111092	+	0.993810i	$0.535435\pi$
$38$	−0.309188	−0.0501569
$39$	10.5434	1.68829
$40$	−2.25094	−0.355904
$41$	−5.44493	−0.850355	−0.425178	−	0.905110i	$-0.639788\pi$
$41$	−5.44493	−0.850355	−0.425178	+	0.905110i	$0.639788\pi$
$42$	3.42391	0.528320
$43$	−10.6634	−1.62615	−0.813075	−	0.582159i	$-0.802208\pi$
$43$	−10.6634	−1.62615	−0.813075	+	0.582159i	$0.802208\pi$
$44$	0.634356	0.0956328
$45$	−6.74515	−1.00551
$46$	−1.32519	−0.195388
$47$	−4.81889	−0.702908	−0.351454	−	0.936205i	$-0.614313\pi$
$47$	−4.81889	−0.702908	−0.351454	+	0.936205i	$0.614313\pi$
$48$	8.86060	1.27892
$49$	14.3147	2.04496
$50$	0.331642	0.0469013
$51$	8.90191	1.24652
$52$	−7.95986	−1.10383
$53$	−1.33388	−0.183223	−0.0916114	−	0.995795i	$-0.529202\pi$
$53$	−1.33388	−0.183223	−0.0916114	+	0.995795i	$0.529202\pi$
$54$	−0.319286	−0.0434493
$55$	0.651502	0.0878486
$56$	−5.28532	−0.706281
$57$	2.68094	0.355099
$58$	0.292455	0.0384012
$59$	−5.18768	−0.675378	−0.337689	−	0.941258i	$-0.609645\pi$
$59$	−5.18768	−0.675378	−0.337689	+	0.941258i	$0.609645\pi$
$60$	9.54560	1.23233
$61$	−12.3497	−1.58122	−0.790610	−	0.612320i	$-0.790236\pi$
$61$	−12.3497	−1.58122	−0.790610	+	0.612320i	$0.790236\pi$
$62$	−1.99233	−0.253026
$63$	−15.8380	−1.99540
$64$	−6.01981	−0.752476
$65$	−8.17500	−1.01398
$66$	0.245735	0.0302479
$67$	−4.63655	−0.566445	−0.283222	−	0.959054i	$-0.591403\pi$
$67$	−4.63655	−0.566445	−0.283222	+	0.959054i	$0.591403\pi$
$68$	−6.72061	−0.814994
$69$	11.4906	1.38330
$70$	−2.65479	−0.317308
$71$	5.80156	0.688519	0.344259	−	0.938875i	$-0.388130\pi$
$71$	5.80156	0.688519	0.344259	+	0.938875i	$0.388130\pi$
$72$	3.92729	0.462835
$73$	2.83001	0.331228	0.165614	−	0.986191i	$-0.447039\pi$
$73$	2.83001	0.331228	0.165614	+	0.986191i	$0.447039\pi$
$74$	0.395249	0.0459468
$75$	−2.87564	−0.332050
$76$	−2.02401	−0.232169
$77$	1.52976	0.174333
$78$	−3.08346	−0.349134
$79$	−1.76502	−0.198580	−0.0992901	−	0.995059i	$-0.531657\pi$
$79$	−1.76502	−0.198580	−0.0992901	+	0.995059i	$0.531657\pi$
$80$	−6.87023	−0.768115
$81$	−7.52308	−0.835897
$82$	1.59240	0.175851
$83$	−2.86315	−0.314271	−0.157136	−	0.987577i	$-0.550226\pi$
$83$	−2.86315	−0.314271	−0.157136	+	0.987577i	$0.550226\pi$
$84$	22.4136	2.44552
$85$	−6.90226	−0.748655
$86$	3.11856	0.336283
$87$	−2.53585	−0.271871
$88$	−0.379330	−0.0404367
$89$	−2.46780	−0.261587	−0.130793	−	0.991410i	$-0.541752\pi$
$89$	−2.46780	−0.261587	−0.130793	+	0.991410i	$0.541752\pi$
$90$	1.97265	0.207936
$91$	−19.1954	−2.01222
$92$	−8.67494	−0.904425
$93$	17.2753	1.79136
$94$	1.40931	0.145359
$95$	−2.07871	−0.213271
$96$	−8.39743	−0.857060
$97$	0.822927	0.0835556	0.0417778	−	0.999127i	$-0.486698\pi$
$97$	0.822927	0.0835556	0.0417778	+	0.999127i	$0.486698\pi$
$98$	−4.18641	−0.422891
$99$	−1.13670	−0.114242
$100$	2.17100	0.217100
$101$	−4.94699	−0.492244	−0.246122	−	0.969239i	$-0.579156\pi$
$101$	−4.94699	−0.492244	−0.246122	+	0.969239i	$0.579156\pi$
$102$	−2.60341	−0.257776
$103$	13.8919	1.36881	0.684406	−	0.729101i	$-0.260062\pi$
$103$	13.8919	1.36881	0.684406	+	0.729101i	$0.260062\pi$
$104$	4.75980	0.466737
$105$	23.0194	2.24646
$106$	0.390100	0.0378899
$107$	−4.37695	−0.423136	−0.211568	−	0.977363i	$-0.567857\pi$
$107$	−4.37695	−0.423136	−0.211568	+	0.977363i	$0.567857\pi$
$108$	−2.09011	−0.201121
$109$	−3.26051	−0.312300	−0.156150	−	0.987733i	$-0.549908\pi$
$109$	−3.26051	−0.312300	−0.156150	+	0.987733i	$0.549908\pi$
$110$	−0.190535	−0.0181668
$111$	−3.42717	−0.325292
$112$	−16.1317	−1.52430
$113$	7.96240	0.749040	0.374520	−	0.927219i	$-0.377808\pi$
$113$	7.96240	0.749040	0.374520	+	0.927219i	$0.377808\pi$
$114$	−0.784053	−0.0734333
$115$	−8.90941	−0.830807
$116$	1.91447	0.177754
$117$	14.2632	1.31863
$118$	1.51716	0.139666
$119$	−16.2069	−1.48568
$120$	−5.70803	−0.521070
$121$	−10.8902	−0.990019
$122$	3.61174	0.326991
$123$	−13.8075	−1.24498
$124$	−13.0422	−1.17122
$125$	12.0608	1.07875
$126$	4.63190	0.412642
$127$	−12.6055	−1.11856	−0.559280	−	0.828979i	$-0.688922\pi$
$127$	−12.6055	−1.11856	−0.559280	+	0.828979i	$0.688922\pi$
$128$	8.38350	0.741004
$129$	−27.0407	−2.38080
$130$	2.39082	0.209689
$131$	−8.41020	−0.734803	−0.367401	−	0.930063i	$-0.619752\pi$
$131$	−8.41020	−0.734803	−0.367401	+	0.930063i	$0.619752\pi$
$132$	1.60863	0.140013
$133$	−4.88093	−0.423231
$134$	1.35598	0.117139
$135$	−2.14660	−0.184750
$136$	4.01876	0.344606
$137$	−17.5566	−1.49996	−0.749979	−	0.661462i	$-0.769936\pi$
$137$	−17.5566	−1.49996	−0.749979	+	0.661462i	$0.769936\pi$
$138$	−3.36047	−0.286062
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−17.3788	−1.46878
$141$	−12.2200	−1.02911
$142$	−1.69670	−0.142384
$143$	−1.37766	−0.115206
$144$	11.9867	0.998893
$145$	1.96622	0.163285
$146$	−0.827650	−0.0684968
$147$	36.2999	2.99397
$148$	2.58738	0.212682
$149$	14.7199	1.20590	0.602952	−	0.797777i	$-0.293991\pi$
$149$	14.7199	1.20590	0.602952	+	0.797777i	$0.293991\pi$
$150$	0.840994	0.0686669
$151$	5.32636	0.433453	0.216726	−	0.976232i	$-0.430462\pi$
$151$	5.32636	0.433453	0.216726	+	0.976232i	$0.430462\pi$
$152$	1.21031	0.0981688
$153$	12.0426	0.973587
$154$	−0.447387	−0.0360515
$155$	−13.3947	−1.07589
$156$	−20.1850	−1.61609
$157$	0.0872165	0.00696063	0.00348032	−	0.999994i	$-0.498892\pi$
$157$	0.0872165	0.00696063	0.00348032	+	0.999994i	$0.498892\pi$
$158$	0.516189	0.0410658
$159$	−3.38252	−0.268251
$160$	6.51110	0.514748
$161$	−20.9198	−1.64871
$162$	2.20016	0.172861
$163$	8.56099	0.670549	0.335274	−	0.942121i	$-0.391171\pi$
$163$	8.56099	0.670549	0.335274	+	0.942121i	$0.391171\pi$
$164$	10.4242	0.813990
$165$	1.65211	0.128617
$166$	0.837342	0.0649903
$167$	−23.0464	−1.78338	−0.891690	−	0.452646i	$-0.850480\pi$
$167$	−23.0464	−1.78338	−0.891690	+	0.452646i	$0.850480\pi$
$168$	−13.4028	−1.03405
$169$	4.28675	0.329750
$170$	2.01860	0.154820
$171$	3.62680	0.277348
$172$	20.4147	1.55661
$173$	−15.9959	−1.21615	−0.608073	−	0.793881i	$-0.708057\pi$
$173$	−15.9959	−1.21615	−0.608073	+	0.793881i	$0.708057\pi$
$174$	0.741621	0.0562222
$175$	5.23541	0.395760
$176$	−1.15778	−0.0872706
$177$	−13.1552	−0.988802
$178$	0.721721	0.0540953
$179$	−0.733589	−0.0548310	−0.0274155	−	0.999624i	$-0.508728\pi$
$179$	−0.733589	−0.0548310	−0.0274155	+	0.999624i	$0.508728\pi$
$180$	12.9134	0.962507
$181$	2.88905	0.214741	0.107371	−	0.994219i	$-0.465757\pi$
$181$	2.88905	0.214741	0.107371	+	0.994219i	$0.465757\pi$
$182$	5.61378	0.416121
$183$	−31.3170	−2.31502
$184$	5.18740	0.382420
$185$	2.65732	0.195370
$186$	−5.05225	−0.370449
$187$	−1.16317	−0.0850597
$188$	9.22563	0.672848
$189$	−5.04034	−0.366631
$190$	0.607930	0.0441039
$191$	−12.1144	−0.876566	−0.438283	−	0.898837i	$-0.644413\pi$
$191$	−12.1144	−0.876566	−0.438283	+	0.898837i	$0.644413\pi$
$192$	−15.2653	−1.10168
$193$	1.27598	0.0918471	0.0459235	−	0.998945i	$-0.485377\pi$
$193$	1.27598	0.0918471	0.0459235	+	0.998945i	$0.485377\pi$
$194$	−0.240669	−0.0172790
$195$	−20.7306	−1.48455
$196$	−27.4051	−1.95751
$197$	5.92294	0.421992	0.210996	−	0.977487i	$-0.432329\pi$
$197$	5.92294	0.421992	0.210996	+	0.977487i	$0.432329\pi$
$198$	0.332433	0.0236250
$199$	−16.5882	−1.17591	−0.587953	−	0.808895i	$-0.700066\pi$
$199$	−16.5882	−1.17591	−0.587953	+	0.808895i	$0.700066\pi$
$200$	−1.29820	−0.0917969
$201$	−11.7576	−0.829316
$202$	1.44677	0.101794
$203$	4.61679	0.324035
$204$	−17.0424	−1.19321
$205$	10.7059	0.747733
$206$	−4.06276	−0.283066
$207$	15.5446	1.08042
$208$	14.5277	1.00731
$209$	−0.350306	−0.0242312
$210$	−6.73214	−0.464562
$211$	−8.07054	−0.555599	−0.277800	−	0.960639i	$-0.589605\pi$
$211$	−8.07054	−0.555599	−0.277800	+	0.960639i	$0.589605\pi$
$212$	2.55368	0.175387
$213$	14.7119	1.00804
$214$	1.28006	0.0875032
$215$	20.9665	1.42990
$216$	1.24983	0.0850405
$217$	−31.4515	−2.13507
$218$	0.953551	0.0645826
$219$	7.17647	0.484941
$220$	−1.24728	−0.0840917
$221$	14.5954	0.981795
$222$	1.00229	0.0672694
$223$	26.5047	1.77488	0.887442	−	0.460920i	$-0.152481\pi$
$223$	26.5047	1.77488	0.887442	+	0.460920i	$0.152481\pi$
$224$	15.2884	1.02150
$225$	−3.89019	−0.259346
$226$	−2.32864	−0.154899
$227$	−10.2506	−0.680358	−0.340179	−	0.940361i	$-0.610488\pi$
$227$	−10.2506	−0.680358	−0.340179	+	0.940361i	$0.610488\pi$
$228$	−5.13257	−0.339913
$229$	−10.1741	−0.672325	−0.336162	−	0.941804i	$-0.609129\pi$
$229$	−10.1741	−0.672325	−0.336162	+	0.941804i	$0.609129\pi$
$230$	2.60560	0.171808
$231$	3.87925	0.255236
$232$	−1.14481	−0.0751602
$233$	−20.3907	−1.33584	−0.667919	−	0.744234i	$-0.732815\pi$
$233$	−20.3907	−1.33584	−0.667919	+	0.744234i	$0.732815\pi$
$234$	−4.17135	−0.272689
$235$	9.47498	0.618080
$236$	9.93165	0.646495
$237$	−4.47582	−0.290736
$238$	4.73979	0.307235
$239$	−12.3490	−0.798794	−0.399397	−	0.916778i	$-0.630780\pi$
$239$	−12.3490	−0.798794	−0.399397	+	0.916778i	$0.630780\pi$
$240$	−17.4218	−1.12458
$241$	−4.79548	−0.308904	−0.154452	−	0.988000i	$-0.549361\pi$
$241$	−4.79548	−0.308904	−0.154452	+	0.988000i	$0.549361\pi$
$242$	3.18490	0.204733
$243$	−22.3526	−1.43392
$244$	23.6432	1.51360
$245$	−28.1458	−1.79817
$246$	4.03808	0.257458
$247$	4.39562	0.279686
$248$	7.79892	0.495232
$249$	−7.26050	−0.460116
$250$	−3.52723	−0.223082
$251$	−1.22590	−0.0773784	−0.0386892	−	0.999251i	$-0.512318\pi$
$251$	−1.22590	−0.0773784	−0.0386892	+	0.999251i	$0.512318\pi$
$252$	30.3214	1.91007
$253$	−1.50142	−0.0943935
$254$	3.68655	0.231315
$255$	−17.5031	−1.09609
$256$	9.58782	0.599239
$257$	−13.0249	−0.812469	−0.406234	−	0.913769i	$-0.633158\pi$
$257$	−13.0249	−0.812469	−0.406234	+	0.913769i	$0.633158\pi$
$258$	7.90819	0.492342
$259$	6.23953	0.387705
$260$	15.6508	0.970621
$261$	−3.43052	−0.212344
$262$	2.45960	0.151955
$263$	−6.77892	−0.418006	−0.209003	−	0.977915i	$-0.567022\pi$
$263$	−6.77892	−0.418006	−0.209003	+	0.977915i	$0.567022\pi$
$264$	−0.961922	−0.0592022
$265$	2.62270	0.161111
$266$	1.42745	0.0875228
$267$	−6.25797	−0.382982
$268$	8.87654	0.542221
$269$	17.6647	1.07703	0.538517	−	0.842615i	$-0.318985\pi$
$269$	17.6647	1.07703	0.538517	+	0.842615i	$0.318985\pi$
$270$	0.627785	0.0382058
$271$	24.0976	1.46383	0.731914	−	0.681397i	$-0.238627\pi$
$271$	24.0976	1.46383	0.731914	+	0.681397i	$0.238627\pi$
$272$	12.2659	0.743730
$273$	−48.6765	−2.94604
$274$	5.13450	0.310187
$275$	0.375747	0.0226584
$276$	−21.9983	−1.32414
$277$	−20.1752	−1.21221	−0.606105	−	0.795385i	$-0.707269\pi$
$277$	−20.1752	−1.21221	−0.606105	+	0.795385i	$0.707269\pi$
$278$	0.292455	0.0175403
$279$	23.3702	1.39914
$280$	10.3921	0.621046
$281$	−7.64666	−0.456161	−0.228081	−	0.973642i	$-0.573245\pi$
$281$	−7.64666	−0.456161	−0.228081	+	0.973642i	$0.573245\pi$
$282$	3.57379	0.212816
$283$	−13.1415	−0.781181	−0.390591	−	0.920564i	$-0.627729\pi$
$283$	−13.1415	−0.781181	−0.390591	+	0.920564i	$0.627729\pi$
$284$	−11.1069	−0.659074
$285$	−5.27130	−0.312245
$286$	0.402903	0.0238241
$287$	25.1381	1.48385
$288$	−11.3601	−0.669403
$289$	−4.67690	−0.275112
$290$	−0.575030	−0.0337669
$291$	2.08682	0.122331
$292$	−5.41797	−0.317063
$293$	2.37073	0.138499	0.0692497	−	0.997599i	$-0.477939\pi$
$293$	2.37073	0.138499	0.0692497	+	0.997599i	$0.477939\pi$
$294$	−10.6161	−0.619143
$295$	10.2001	0.593872
$296$	−1.54719	−0.0899287
$297$	−0.361747	−0.0209907
$298$	−4.30492	−0.249377
$299$	18.8397	1.08953
$300$	5.50532	0.317850
$301$	49.2305	2.83760
$302$	−1.55772	−0.0896367
$303$	−12.5448	−0.720680
$304$	3.69405	0.211868
$305$	24.2822	1.39040
$306$	−3.52192	−0.201335
$307$	26.1848	1.49444	0.747222	−	0.664575i	$-0.231387\pi$
$307$	26.1848	1.49444	0.747222	+	0.664575i	$0.231387\pi$
$308$	−2.92869	−0.166877
$309$	35.2278	2.00404
$310$	3.91735	0.222491
$311$	1.53747	0.0871818	0.0435909	−	0.999049i	$-0.486120\pi$
$311$	1.53747	0.0871818	0.0435909	+	0.999049i	$0.486120\pi$
$312$	12.0701	0.683336
$313$	−30.3572	−1.71589	−0.857945	−	0.513742i	$-0.828259\pi$
$313$	−30.3572	−1.71589	−0.857945	+	0.513742i	$0.828259\pi$
$314$	−0.0255069	−0.00143944
$315$	31.1409	1.75459
$316$	3.37908	0.190088
$317$	18.8951	1.06126	0.530628	−	0.847605i	$-0.321956\pi$
$317$	18.8951	1.06126	0.530628	+	0.847605i	$0.321956\pi$
$318$	0.989235	0.0554736
$319$	0.331348	0.0185519
$320$	11.8362	0.661666
$321$	−11.0993	−0.619502
$322$	6.11810	0.340948
$323$	3.71128	0.206501
$324$	14.4027	0.800150
$325$	−4.71485	−0.261533
$326$	−2.50371	−0.138667
$327$	−8.26815	−0.457230
$328$	−6.23339	−0.344181
$329$	22.2478	1.22656
$330$	−0.483168	−0.0265975
$331$	11.0149	0.605436	0.302718	−	0.953080i	$-0.402106\pi$
$331$	11.0149	0.605436	0.302718	+	0.953080i	$0.402106\pi$
$332$	5.48141	0.300831
$333$	−4.63631	−0.254068
$334$	6.74002	0.368798
$335$	9.11646	0.498086
$336$	−40.9075	−2.23169
$337$	1.99443	0.108643	0.0543217	−	0.998523i	$-0.482700\pi$
$337$	1.99443	0.108643	0.0543217	+	0.998523i	$0.482700\pi$
$338$	−1.25368	−0.0681913
$339$	20.1914	1.09665
$340$	13.2142	0.716639
$341$	−2.25729	−0.122239
$342$	−1.06068	−0.0573548
$343$	−33.7704	−1.82343
$344$	−12.2075	−0.658184
$345$	−22.5929	−1.21636
$346$	4.67808	0.251495
$347$	29.0328	1.55856	0.779282	−	0.626674i	$-0.215584\pi$
$347$	29.0328	1.55856	0.779282	+	0.626674i	$0.215584\pi$
$348$	4.85480	0.260245
$349$	36.8971	1.97506	0.987528	−	0.157442i	$-0.0503246\pi$
$349$	36.8971	1.97506	0.987528	+	0.157442i	$0.0503246\pi$
$350$	−1.53112	−0.0818419
$351$	4.53918	0.242283
$352$	1.09726	0.0584840
$353$	21.6562	1.15264	0.576322	−	0.817222i	$-0.304487\pi$
$353$	21.6562	1.15264	0.576322	+	0.817222i	$0.304487\pi$
$354$	3.84729	0.204481
$355$	−11.4071	−0.605427
$356$	4.72454	0.250400
$357$	−41.0982	−2.17515
$358$	0.214542	0.0113389
$359$	15.0368	0.793613	0.396806	−	0.917902i	$-0.370118\pi$
$359$	15.0368	0.793613	0.396806	+	0.917902i	$0.370118\pi$
$360$	−7.72189	−0.406979
$361$	−17.8823	−0.941174
$362$	−0.844917	−0.0444078
$363$	−27.6159	−1.44946
$364$	36.7490	1.92617
$365$	−5.56441	−0.291255
$366$	9.15882	0.478739
$367$	5.52912	0.288618	0.144309	−	0.989533i	$-0.453904\pi$
$367$	5.52912	0.288618	0.144309	+	0.989533i	$0.453904\pi$
$368$	15.8328	0.825341
$369$	−18.6790	−0.972388
$370$	−0.777145	−0.0404019
$371$	6.15825	0.319720
$372$	−33.0730	−1.71476
$373$	−14.9805	−0.775660	−0.387830	−	0.921731i	$-0.626775\pi$
$373$	−14.9805	−0.775660	−0.387830	+	0.921731i	$0.626775\pi$
$374$	0.340176	0.0175901
$375$	30.5842	1.57936
$376$	−5.51670	−0.284502
$377$	−4.15773	−0.214134
$378$	1.47407	0.0758182
$379$	9.11519	0.468216	0.234108	−	0.972211i	$-0.424783\pi$
$379$	9.11519	0.468216	0.234108	+	0.972211i	$0.424783\pi$
$380$	3.97963	0.204151
$381$	−31.9657	−1.63765
$382$	3.54291	0.181271
$383$	−4.73716	−0.242058	−0.121029	−	0.992649i	$-0.538619\pi$
$383$	−4.73716	−0.242058	−0.121029	+	0.992649i	$0.538619\pi$
$384$	21.2593	1.08488
$385$	−3.00785	−0.153294
$386$	−0.373167	−0.0189937
$387$	−36.5810	−1.85951
$388$	−1.57547	−0.0799823
$389$	−15.1377	−0.767513	−0.383757	−	0.923434i	$-0.625370\pi$
$389$	−15.1377	−0.767513	−0.383757	+	0.923434i	$0.625370\pi$
$390$	6.06276	0.307000
$391$	15.9066	0.804432
$392$	16.3876	0.827697
$393$	−21.3270	−1.07580
$394$	−1.73219	−0.0872666
$395$	3.47041	0.174615
$396$	2.17617	0.109357
$397$	−0.873039	−0.0438165	−0.0219083	−	0.999760i	$-0.506974\pi$
$397$	−0.873039	−0.0438165	−0.0219083	+	0.999760i	$0.506974\pi$
$398$	4.85130	0.243174
$399$	−12.3773	−0.619640
$400$	−3.96233	−0.198117
$401$	−28.2176	−1.40912	−0.704560	−	0.709645i	$-0.748855\pi$
$401$	−28.2176	−1.40912	−0.704560	+	0.709645i	$0.748855\pi$
$402$	3.43856	0.171500
$403$	28.3243	1.41093
$404$	9.47086	0.471193
$405$	14.7920	0.735020
$406$	−1.35020	−0.0670094
$407$	0.447813	0.0221973
$408$	10.1910	0.504528
$409$	−17.9385	−0.887003	−0.443501	−	0.896274i	$-0.646264\pi$
$409$	−17.9385	−0.887003	−0.443501	+	0.896274i	$0.646264\pi$
$410$	−3.13100	−0.154629
$411$	−44.5208	−2.19605
$412$	−26.5957	−1.31027
$413$	23.9504	1.17852
$414$	−4.54608	−0.223428
$415$	5.62957	0.276345
$416$	−13.7683	−0.675046
$417$	−2.53585	−0.124181
$418$	0.102449	0.00501093
$419$	−3.89020	−0.190049	−0.0950244	−	0.995475i	$-0.530293\pi$
$419$	−3.89020	−0.190049	−0.0950244	+	0.995475i	$0.530293\pi$
$420$	−44.0700	−2.15039
$421$	−0.0543379	−0.00264827	−0.00132413	−	0.999999i	$-0.500421\pi$
$421$	−0.0543379	−0.00264827	−0.00132413	+	0.999999i	$0.500421\pi$
$422$	2.36027	0.114896
$423$	−16.5313	−0.803781
$424$	−1.52704	−0.0741595
$425$	−3.98081	−0.193097
$426$	−4.30256	−0.208460
$427$	57.0160	2.75920
$428$	8.37954	0.405040
$429$	−3.49353	−0.168669
$430$	−6.13176	−0.295700
$431$	11.4619	0.552099	0.276050	−	0.961143i	$-0.410975\pi$
$431$	11.4619	0.552099	0.276050	+	0.961143i	$0.410975\pi$
$432$	3.81470	0.183535
$433$	−34.1345	−1.64040	−0.820199	−	0.572078i	$-0.806137\pi$
$433$	−34.1345	−1.64040	−0.820199	+	0.572078i	$0.806137\pi$
$434$	9.19816	0.441526
$435$	4.98602	0.239062
$436$	6.24214	0.298944
$437$	4.79050	0.229161
$438$	−2.09880	−0.100284
$439$	−16.0684	−0.766902	−0.383451	−	0.923561i	$-0.625264\pi$
$439$	−16.0684	−0.766902	−0.383451	+	0.923561i	$0.625264\pi$
$440$	0.745844	0.0355567
$441$	49.1069	2.33843
$442$	−4.26850	−0.203032
$443$	5.57939	0.265085	0.132542	−	0.991177i	$-0.457686\pi$
$443$	5.57939	0.265085	0.132542	+	0.991177i	$0.457686\pi$
$444$	6.56121	0.311381
$445$	4.85224	0.230018
$446$	−7.75142	−0.367040
$447$	37.3275	1.76553
$448$	27.7922	1.31306
$449$	31.7906	1.50029	0.750146	−	0.661273i	$-0.229983\pi$
$449$	31.7906	1.50029	0.750146	+	0.661273i	$0.229983\pi$
$450$	1.13771	0.0536320
$451$	1.80417	0.0849550
$452$	−15.2438	−0.717007
$453$	13.5068	0.634607
$454$	2.99785	0.140696
$455$	37.7422	1.76938
$456$	3.06915	0.143726
$457$	15.7517	0.736833	0.368417	−	0.929661i	$-0.379900\pi$
$457$	15.7517	0.736833	0.368417	+	0.929661i	$0.379900\pi$
$458$	2.97547	0.139035
$459$	3.83249	0.178885
$460$	17.0568	0.795277
$461$	−3.83105	−0.178430	−0.0892149	−	0.996012i	$-0.528436\pi$
$461$	−3.83105	−0.178430	−0.0892149	+	0.996012i	$0.528436\pi$
$462$	−1.13451	−0.0527820
$463$	40.9663	1.90386	0.951932	−	0.306310i	$-0.0990944\pi$
$463$	40.9663	1.90386	0.951932	+	0.306310i	$0.0990944\pi$
$464$	−3.49414	−0.162211
$465$	−33.9670	−1.57518
$466$	5.96336	0.276247
$467$	9.12911	0.422445	0.211222	−	0.977438i	$-0.432256\pi$
$467$	9.12911	0.422445	0.211222	+	0.977438i	$0.432256\pi$
$468$	−27.3065	−1.26224
$469$	21.4060	0.988435
$470$	−2.77101	−0.127817
$471$	0.221168	0.0101909
$472$	−5.93888	−0.273359
$473$	3.53329	0.162461
$474$	1.30898	0.0601232
$475$	−1.19888	−0.0550082
$476$	31.0276	1.42215
$477$	−4.57592	−0.209517
$478$	3.61154	0.165188
$479$	3.90430	0.178392	0.0891960	−	0.996014i	$-0.471570\pi$
$479$	3.90430	0.178392	0.0891960	+	0.996014i	$0.471570\pi$
$480$	16.5112	0.753628
$481$	−5.61913	−0.256210
$482$	1.40246	0.0638804
$483$	−53.0494	−2.41383
$484$	20.8490	0.947681
$485$	−1.61805	−0.0734720
$486$	6.53713	0.296530
$487$	6.25958	0.283648	0.141824	−	0.989892i	$-0.454703\pi$
$487$	6.25958	0.283648	0.141824	+	0.989892i	$0.454703\pi$
$488$	−14.1380	−0.639999
$489$	21.7094	0.981732
$490$	8.23138	0.371856
$491$	0.560012	0.0252730	0.0126365	−	0.999920i	$-0.495978\pi$
$491$	0.560012	0.0252730	0.0126365	+	0.999920i	$0.495978\pi$
$492$	26.4341	1.19174
$493$	−3.51043	−0.158102
$494$	−1.28552	−0.0578383
$495$	2.23499	0.100456
$496$	23.8036	1.06881
$497$	−26.7846	−1.20145
$498$	2.12337	0.0951505
$499$	−18.9733	−0.849361	−0.424681	−	0.905343i	$-0.639614\pi$
$499$	−18.9733	−0.849361	−0.424681	+	0.905343i	$0.639614\pi$
$500$	−23.0900	−1.03261
$501$	−58.4421	−2.61100
$502$	0.358522	0.0160016
$503$	14.2519	0.635459	0.317729	−	0.948181i	$-0.397080\pi$
$503$	14.2519	0.635459	0.317729	+	0.948181i	$0.397080\pi$
$504$	−18.1314	−0.807638
$505$	9.72684	0.432839
$506$	0.439098	0.0195203
$507$	10.8706	0.482778
$508$	24.1329	1.07073
$509$	12.8060	0.567617	0.283809	−	0.958881i	$-0.408402\pi$
$509$	12.8060	0.567617	0.283809	+	0.958881i	$0.408402\pi$
$510$	5.11886	0.226667
$511$	−13.0655	−0.577986
$512$	−19.5710	−0.864925
$513$	1.15421	0.0509595
$514$	3.80919	0.168016
$515$	−27.3145	−1.20362
$516$	51.7686	2.27899
$517$	1.59673	0.0702242
$518$	−1.82478	−0.0801763
$519$	−40.5632	−1.78053
$520$	−9.35879	−0.410410
$521$	−29.4654	−1.29090	−0.645451	−	0.763801i	$-0.723331\pi$
$521$	−29.4654	−1.29090	−0.645451	+	0.763801i	$0.723331\pi$
$522$	1.00327	0.0439121
$523$	15.6314	0.683513	0.341757	−	0.939789i	$-0.388978\pi$
$523$	15.6314	0.683513	0.341757	+	0.939789i	$0.388978\pi$
$524$	16.1011	0.703379
$525$	13.2762	0.579421
$526$	1.98253	0.0864424
$527$	23.9146	1.04173
$528$	−2.93594	−0.127771
$529$	−2.46780	−0.107296
$530$	−0.767022	−0.0333173
$531$	−17.7964	−0.772300
$532$	9.34440	0.405131
$533$	−22.6386	−0.980586
$534$	1.83018	0.0791994
$535$	8.60603	0.372071
$536$	−5.30795	−0.229269
$537$	−1.86027	−0.0802766
$538$	−5.16612	−0.222727
$539$	−4.74315	−0.204302
$540$	4.10961	0.176849
$541$	−23.3989	−1.00600	−0.502998	−	0.864288i	$-0.667770\pi$
$541$	−23.3989	−1.00600	−0.502998	+	0.864288i	$0.667770\pi$
$542$	−7.04748	−0.302715
$543$	7.32619	0.314397
$544$	−11.6247	−0.498407
$545$	6.41086	0.274611
$546$	14.2357	0.609231
$547$	9.17370	0.392239	0.196119	−	0.980580i	$-0.437166\pi$
$547$	9.17370	0.392239	0.196119	+	0.980580i	$0.437166\pi$
$548$	33.6115	1.43581
$549$	−42.3660	−1.80814
$550$	−0.109889	−0.00468569
$551$	−1.05721	−0.0450389
$552$	13.1545	0.559891
$553$	8.14871	0.346519
$554$	5.90033	0.250681
$555$	6.73855	0.286036
$556$	1.91447	0.0811916
$557$	37.3965	1.58454	0.792271	−	0.610170i	$-0.208899\pi$
$557$	37.3965	1.58454	0.792271	+	0.610170i	$0.208899\pi$
$558$	−6.83474	−0.289337
$559$	−44.3355	−1.87519
$560$	31.7184	1.34035
$561$	−2.94963	−0.124534
$562$	2.23630	0.0943327
$563$	−23.3136	−0.982549	−0.491275	−	0.871005i	$-0.663469\pi$
$563$	−23.3136	−0.982549	−0.491275	+	0.871005i	$0.663469\pi$
$564$	23.3948	0.985098
$565$	−15.6558	−0.658644
$566$	3.84330	0.161546
$567$	34.7324	1.45863
$568$	6.64167	0.278678
$569$	36.2314	1.51890	0.759450	−	0.650565i	$-0.225468\pi$
$569$	36.2314	1.51890	0.759450	+	0.650565i	$0.225468\pi$
$570$	1.54162	0.0645712
$571$	30.1237	1.26064	0.630318	−	0.776337i	$-0.282924\pi$
$571$	30.1237	1.26064	0.630318	+	0.776337i	$0.282924\pi$
$572$	2.63749	0.110279
$573$	−30.7202	−1.28336
$574$	−7.35176	−0.306856
$575$	−5.13841	−0.214286
$576$	−20.6511	−0.860463
$577$	1.10749	0.0461054	0.0230527	−	0.999734i	$-0.492661\pi$
$577$	1.10749	0.0461054	0.0230527	+	0.999734i	$0.492661\pi$
$578$	1.36778	0.0568922
$579$	3.23569	0.134471
$580$	−3.76426	−0.156302
$581$	13.2185	0.548397
$582$	−0.610300	−0.0252978
$583$	0.441980	0.0183049
$584$	3.23981	0.134064
$585$	−28.0445	−1.15950
$586$	−0.693331	−0.0286413
$587$	−0.891766	−0.0368071	−0.0184036	−	0.999831i	$-0.505858\pi$
$587$	−0.891766	−0.0368071	−0.0184036	+	0.999831i	$0.505858\pi$
$588$	−69.4951	−2.86593
$589$	7.20221	0.296762
$590$	−2.98307	−0.122811
$591$	15.0197	0.617827
$592$	−4.72228	−0.194085
$593$	−39.0708	−1.60445	−0.802223	−	0.597025i	$-0.796349\pi$
$593$	−39.0708	−1.60445	−0.802223	+	0.597025i	$0.796349\pi$
$594$	0.105795	0.00434081
$595$	31.8663	1.30639
$596$	−28.1809	−1.15433
$597$	−42.0652	−1.72161
$598$	−5.50977	−0.225311
$599$	−44.7373	−1.82792	−0.913958	−	0.405809i	$-0.866990\pi$
$599$	−44.7373	−1.82792	−0.913958	+	0.405809i	$0.866990\pi$
$600$	−3.29205	−0.134397
$601$	−22.8653	−0.932696	−0.466348	−	0.884601i	$-0.654430\pi$
$601$	−22.8653	−0.932696	−0.466348	+	0.884601i	$0.654430\pi$
$602$	−14.3977	−0.586807
$603$	−15.9058	−0.647734
$604$	−10.1972	−0.414916
$605$	21.4125	0.870542
$606$	3.66879	0.149034
$607$	−19.3447	−0.785179	−0.392589	−	0.919714i	$-0.628421\pi$
$607$	−19.3447	−0.785179	−0.392589	+	0.919714i	$0.628421\pi$
$608$	−3.50096	−0.141982
$609$	11.7075	0.474410
$610$	−7.10146	−0.287530
$611$	−20.0357	−0.810557
$612$	−23.0552	−0.931952
$613$	−47.4410	−1.91612	−0.958062	−	0.286560i	$-0.907488\pi$
$613$	−47.4410	−1.91612	−0.958062	+	0.286560i	$0.907488\pi$
$614$	−7.65786	−0.309046
$615$	27.1486	1.09474
$616$	1.75128	0.0705612
$617$	26.7735	1.07786	0.538931	−	0.842350i	$-0.318828\pi$
$617$	26.7735	1.07786	0.538931	+	0.842350i	$0.318828\pi$
$618$	−10.3025	−0.414429
$619$	−39.0102	−1.56795	−0.783975	−	0.620792i	$-0.786811\pi$
$619$	−39.0102	−1.56795	−0.783975	+	0.620792i	$0.786811\pi$
$620$	25.6438	1.02988
$621$	4.94696	0.198515
$622$	−0.449640	−0.0180289
$623$	11.3933	0.456464
$624$	36.8400	1.47478
$625$	−18.0441	−0.721763
$626$	8.87811	0.354841
$627$	−0.888323	−0.0354762
$628$	−0.166973	−0.00666296
$629$	−4.74430	−0.189168
$630$	−9.10732	−0.362844
$631$	−40.9520	−1.63028	−0.815138	−	0.579267i	$-0.803339\pi$
$631$	−40.9520	−1.63028	−0.815138	+	0.579267i	$0.803339\pi$
$632$	−2.02060	−0.0803753
$633$	−20.4657	−0.813437
$634$	−5.52597	−0.219464
$635$	24.7852	0.983571
$636$	6.47574	0.256780
$637$	59.5167	2.35814
$638$	−0.0969044	−0.00383648
$639$	19.9024	0.787327
$640$	−16.4838	−0.651579
$641$	11.2214	0.443218	0.221609	−	0.975136i	$-0.428869\pi$
$641$	11.2214	0.443218	0.221609	+	0.975136i	$0.428869\pi$
$642$	3.24604	0.128111
$643$	24.9173	0.982642	0.491321	−	0.870979i	$-0.336514\pi$
$643$	24.9173	0.982642	0.491321	+	0.870979i	$0.336514\pi$
$644$	40.0503	1.57820
$645$	53.1679	2.09348
$646$	−1.08538	−0.0427037
$647$	5.87159	0.230836	0.115418	−	0.993317i	$-0.463179\pi$
$647$	5.87159	0.230836	0.115418	+	0.993317i	$0.463179\pi$
$648$	−8.61247	−0.338330
$649$	1.71893	0.0674738
$650$	1.37888	0.0540841
$651$	−79.7563	−3.12590
$652$	−16.3898	−0.641873
$653$	0.224998	0.00880485	0.00440242	−	0.999990i	$-0.498599\pi$
$653$	0.224998	0.00880485	0.00440242	+	0.999990i	$0.498599\pi$
$654$	2.41806	0.0945537
$655$	16.5363	0.646126
$656$	−19.0253	−0.742814
$657$	9.70842	0.378761
$658$	−6.50648	−0.253649
$659$	−27.4660	−1.06992	−0.534962	−	0.844876i	$-0.679674\pi$
$659$	−27.4660	−1.06992	−0.534962	+	0.844876i	$0.679674\pi$
$660$	−3.16292	−0.123116
$661$	−8.41548	−0.327324	−0.163662	−	0.986516i	$-0.552331\pi$
$661$	−8.41548	−0.327324	−0.163662	+	0.986516i	$0.552331\pi$
$662$	−3.22138	−0.125202
$663$	37.0118	1.43742
$664$	−3.27775	−0.127201
$665$	9.59697	0.372154
$666$	1.35591	0.0525405
$667$	−4.53125	−0.175451
$668$	44.1216	1.70711
$669$	67.2118	2.59856
$670$	−2.66615	−0.103003
$671$	4.09206	0.157972
$672$	38.7692	1.49555
$673$	−13.3130	−0.513179	−0.256590	−	0.966520i	$-0.582599\pi$
$673$	−13.3130	−0.513179	−0.256590	+	0.966520i	$0.582599\pi$
$674$	−0.583280	−0.0224671
$675$	−1.23803	−0.0476518
$676$	−8.20686	−0.315649
$677$	−45.7645	−1.75887	−0.879436	−	0.476017i	$-0.842080\pi$
$677$	−45.7645	−1.75887	−0.879436	+	0.476017i	$0.842080\pi$
$678$	−5.90508	−0.226783
$679$	−3.79928	−0.145803
$680$	−7.90175	−0.303018
$681$	−25.9940	−0.996093
$682$	0.660155	0.0252786
$683$	−50.1900	−1.92047	−0.960233	−	0.279200i	$-0.909931\pi$
$683$	−50.1900	−1.92047	−0.960233	+	0.279200i	$0.909931\pi$
$684$	−6.94340	−0.265488
$685$	34.5200	1.31894
$686$	9.87633	0.377080
$687$	−25.8000	−0.984332
$688$	−37.2593	−1.42050
$689$	−5.54593	−0.211283
$690$	6.60741	0.251540
$691$	7.26583	0.276405	0.138203	−	0.990404i	$-0.455867\pi$
$691$	7.26583	0.276405	0.138203	+	0.990404i	$0.455867\pi$
$692$	30.6237	1.16414
$693$	5.24789	0.199351
$694$	−8.49079	−0.322306
$695$	1.96622	0.0745828
$696$	−2.90305	−0.110040
$697$	−19.1140	−0.723996
$698$	−10.7907	−0.408436
$699$	−51.7077	−1.95576
$700$	−10.0230	−0.378835
$701$	28.8673	1.09030	0.545151	−	0.838338i	$-0.316472\pi$
$701$	28.8673	1.09030	0.545151	+	0.838338i	$0.316472\pi$
$702$	−1.32751	−0.0501035
$703$	−1.42881	−0.0538887
$704$	1.99465	0.0751763
$705$	24.0271	0.904914
$706$	−6.33347	−0.238363
$707$	22.8392	0.858956
$708$	25.1852	0.946516
$709$	−1.81175	−0.0680417	−0.0340208	−	0.999421i	$-0.510831\pi$
$709$	−1.81175	−0.0680417	−0.0340208	+	0.999421i	$0.510831\pi$
$710$	3.33607	0.125201
$711$	−6.05494	−0.227078
$712$	−2.82516	−0.105877
$713$	30.8688	1.15605
$714$	12.0194	0.449814
$715$	2.70877	0.101302
$716$	1.40443	0.0524862
$717$	−31.3153	−1.16949
$718$	−4.39759	−0.164117
$719$	25.4698	0.949862	0.474931	−	0.880023i	$-0.342473\pi$
$719$	25.4698	0.949862	0.474931	+	0.880023i	$0.342473\pi$
$720$	−23.5685	−0.878345
$721$	−64.1360	−2.38855
$722$	5.22977	0.194632
$723$	−12.1606	−0.452258
$724$	−5.53100	−0.205558
$725$	1.13399	0.0421155
$726$	8.07641	0.299744
$727$	−7.11060	−0.263717	−0.131859	−	0.991269i	$-0.542095\pi$
$727$	−7.11060	−0.263717	−0.131859	+	0.991269i	$0.542095\pi$
$728$	−21.9750	−0.814447
$729$	−34.1136	−1.26347
$730$	1.62734	0.0602305
$731$	−37.4330	−1.38451
$732$	59.9555	2.21602
$733$	2.46111	0.0909033	0.0454517	−	0.998967i	$-0.485527\pi$
$733$	2.46111	0.0909033	0.0454517	+	0.998967i	$0.485527\pi$
$734$	−1.61702	−0.0596853
$735$	−71.3735	−2.63265
$736$	−15.0052	−0.553098
$737$	1.53631	0.0565908
$738$	5.46276	0.201087
$739$	24.8965	0.915834	0.457917	−	0.888995i	$-0.348596\pi$
$739$	24.8965	0.915834	0.457917	+	0.888995i	$0.348596\pi$
$740$	−5.08735	−0.187015
$741$	11.1466	0.409481
$742$	−1.80101	−0.0661172
$743$	17.5299	0.643110	0.321555	−	0.946891i	$-0.395794\pi$
$743$	17.5299	0.643110	0.321555	+	0.946891i	$0.395794\pi$
$744$	19.7769	0.725055
$745$	−28.9426	−1.06037
$746$	4.38112	0.160404
$747$	−9.82209	−0.359372
$748$	2.22686	0.0814221
$749$	20.2074	0.738364
$750$	−8.94451	−0.326607
$751$	11.1698	0.407593	0.203797	−	0.979013i	$-0.434672\pi$
$751$	11.1698	0.407593	0.203797	+	0.979013i	$0.434672\pi$
$752$	−16.8379	−0.614014
$753$	−3.10871	−0.113288
$754$	1.21595	0.0442823
$755$	−10.4728	−0.381143
$756$	9.64959	0.350952
$757$	−46.7178	−1.69799	−0.848993	−	0.528404i	$-0.822791\pi$
$757$	−46.7178	−1.69799	−0.848993	+	0.528404i	$0.822791\pi$
$758$	−2.66578	−0.0968256
$759$	−3.80737	−0.138199
$760$	−2.37972	−0.0863216
$761$	25.4482	0.922498	0.461249	−	0.887271i	$-0.347401\pi$
$761$	25.4482	0.922498	0.461249	+	0.887271i	$0.347401\pi$
$762$	9.34853	0.338662
$763$	15.0531	0.544957
$764$	23.1926	0.839080
$765$	−23.6784	−0.856093
$766$	1.38541	0.0500568
$767$	−21.5690	−0.778811
$768$	24.3133	0.877329
$769$	−38.3658	−1.38351	−0.691754	−	0.722133i	$-0.743162\pi$
$769$	−38.3658	−1.38351	−0.691754	+	0.722133i	$0.743162\pi$
$770$	0.879660	0.0317007
$771$	−33.0291	−1.18951
$772$	−2.44283	−0.0879192
$773$	−50.6714	−1.82252	−0.911262	−	0.411828i	$-0.864891\pi$
$773$	−50.6714	−1.82252	−0.911262	+	0.411828i	$0.864891\pi$
$774$	10.6983	0.384542
$775$	−7.72526	−0.277500
$776$	0.942092	0.0338191
$777$	15.8225	0.567629
$778$	4.42710	0.158719
$779$	−5.75646	−0.206247
$780$	39.6880	1.42106
$781$	−1.92234	−0.0687867
$782$	−4.65197	−0.166354
$783$	−1.09174	−0.0390157
$784$	50.0175	1.78634
$785$	−0.171486	−0.00612061
$786$	6.23718	0.222473
$787$	−17.4777	−0.623011	−0.311506	−	0.950244i	$-0.600833\pi$
$787$	−17.4777	−0.623011	−0.311506	+	0.950244i	$0.600833\pi$
$788$	−11.3393	−0.403945
$789$	−17.1903	−0.611991
$790$	−1.01494	−0.0361099
$791$	−36.7607	−1.30706
$792$	−1.30130	−0.0462396
$793$	−51.3469	−1.82338
$794$	0.255324	0.00906113
$795$	6.65077	0.235879
$796$	31.7576	1.12562
$797$	32.8805	1.16469	0.582343	−	0.812943i	$-0.302136\pi$
$797$	32.8805	1.16469	0.582343	+	0.812943i	$0.302136\pi$
$798$	3.61980	0.128140
$799$	−16.9164	−0.598458
$800$	3.75521	0.132767
$801$	−8.46586	−0.299126
$802$	8.25237	0.291401
$803$	−0.937719	−0.0330914
$804$	22.5096	0.793851
$805$	41.1328	1.44974
$806$	−8.28358	−0.291777
$807$	44.7949	1.57685
$808$	−5.66334	−0.199236
$809$	−13.1484	−0.462272	−0.231136	−	0.972921i	$-0.574244\pi$
$809$	−13.1484	−0.462272	−0.231136	+	0.972921i	$0.574244\pi$
$810$	−4.32599	−0.152000
$811$	−9.84115	−0.345569	−0.172785	−	0.984960i	$-0.555276\pi$
$811$	−9.84115	−0.345569	−0.172785	+	0.984960i	$0.555276\pi$
$812$	−8.83870	−0.310177
$813$	61.1080	2.14315
$814$	−0.130965	−0.00459033
$815$	−16.8328	−0.589626
$816$	31.1045	1.08887
$817$	−11.2735	−0.394409
$818$	5.24621	0.183429
$819$	−65.8502	−2.30099
$820$	−20.4961	−0.715757
$821$	−28.2754	−0.986818	−0.493409	−	0.869797i	$-0.664249\pi$
$821$	−28.2754	−0.986818	−0.493409	+	0.869797i	$0.664249\pi$
$822$	13.0203	0.454136
$823$	7.24496	0.252544	0.126272	−	0.991996i	$-0.459699\pi$
$823$	7.24496	0.252544	0.126272	+	0.991996i	$0.459699\pi$
$824$	15.9036	0.554027
$825$	0.952837	0.0331735
$826$	−7.00441	−0.243715
$827$	29.8436	1.03777	0.518883	−	0.854846i	$-0.326348\pi$
$827$	29.8436	1.03777	0.518883	+	0.854846i	$0.326348\pi$
$828$	−29.7596	−1.03422
$829$	17.4189	0.604983	0.302491	−	0.953152i	$-0.402182\pi$
$829$	17.4189	0.604983	0.302491	+	0.953152i	$0.402182\pi$
$830$	−1.64639	−0.0571472
$831$	−51.1612	−1.77476
$832$	−25.0288	−0.867717
$833$	50.2507	1.74109
$834$	0.741621	0.0256802
$835$	45.3141	1.56816
$836$	0.670651	0.0231949
$837$	7.43743	0.257075
$838$	1.13771	0.0393015
$839$	−19.8197	−0.684254	−0.342127	−	0.939654i	$-0.611147\pi$
$839$	−19.8197	−0.684254	−0.342127	+	0.939654i	$0.611147\pi$
$840$	26.3528	0.909257
$841$	1.00000	0.0344828
$842$	0.0158914	0.000547654 0
$843$	−19.3908	−0.667853
$844$	15.4508	0.531839
$845$	−8.42868	−0.289956
$846$	4.83467	0.166219
$847$	50.2778	1.72756
$848$	−4.66077	−0.160051
$849$	−33.3248	−1.14371
$850$	1.16421	0.0399319
$851$	−6.12392	−0.209925
$852$	−28.1655	−0.964933
$853$	4.04593	0.138530	0.0692650	−	0.997598i	$-0.477935\pi$
$853$	4.04593	0.138530	0.0692650	+	0.997598i	$0.477935\pi$
$854$	−16.6746	−0.570594
$855$	−7.13107	−0.243878
$856$	−5.01076	−0.171264
$857$	1.69049	0.0577459	0.0288729	−	0.999583i	$-0.490808\pi$
$857$	1.69049	0.0577459	0.0288729	+	0.999583i	$0.490808\pi$
$858$	1.02170	0.0348803
$859$	−14.7158	−0.502097	−0.251048	−	0.967975i	$-0.580775\pi$
$859$	−14.7158	−0.502097	−0.251048	+	0.967975i	$0.580775\pi$
$860$	−40.1397	−1.36875
$861$	63.7463	2.17247
$862$	−3.35208	−0.114172
$863$	35.3814	1.20440	0.602199	−	0.798346i	$-0.294291\pi$
$863$	35.3814	1.20440	0.602199	+	0.798346i	$0.294291\pi$
$864$	−3.61530	−0.122995
$865$	31.4514	1.06938
$866$	9.98280	0.339229
$867$	−11.8599	−0.402783
$868$	60.2130	2.04376
$869$	0.584836	0.0198392
$870$	−1.45819	−0.0494372
$871$	−19.2775	−0.653195
$872$	−3.73265	−0.126403
$873$	2.82307	0.0955465
$874$	−1.40101	−0.0473897
$875$	−55.6819	−1.88239
$876$	−13.7391	−0.464203
$877$	36.7505	1.24098	0.620488	−	0.784216i	$-0.286935\pi$
$877$	36.7505	1.24098	0.620488	+	0.784216i	$0.286935\pi$
$878$	4.69927	0.158593
$879$	6.01181	0.202773
$880$	2.27644	0.0767387
$881$	8.68694	0.292670	0.146335	−	0.989235i	$-0.453252\pi$
$881$	8.68694	0.292670	0.146335	+	0.989235i	$0.453252\pi$
$882$	−14.3616	−0.483579
$883$	−22.0666	−0.742600	−0.371300	−	0.928513i	$-0.621088\pi$
$883$	−22.0666	−0.742600	−0.371300	+	0.928513i	$0.621088\pi$
$884$	−27.9425	−0.939808
$885$	25.8659	0.869472
$886$	−1.63172	−0.0548188
$887$	−27.4261	−0.920878	−0.460439	−	0.887691i	$-0.652308\pi$
$887$	−27.4261	−0.920878	−0.460439	+	0.887691i	$0.652308\pi$
$888$	−3.92344	−0.131662
$889$	58.1971	1.95187
$890$	−1.41906	−0.0475670
$891$	2.49276	0.0835106
$892$	−50.7424	−1.69898
$893$	−5.09460	−0.170484
$894$	−10.9166	−0.365106
$895$	1.44240	0.0482140
$896$	−38.7048	−1.29304
$897$	47.7747	1.59515
$898$	−9.29732	−0.310256
$899$	−6.81243	−0.227207
$900$	7.44766	0.248255
$901$	−4.68250	−0.155997
$902$	−0.527638	−0.0175684
$903$	124.841	4.15445
$904$	9.11540	0.303174
$905$	−5.68049	−0.188826
$906$	−3.95014	−0.131235
$907$	29.2551	0.971399	0.485700	−	0.874126i	$-0.338565\pi$
$907$	29.2551	0.971399	0.485700	+	0.874126i	$0.338565\pi$
$908$	19.6245	0.651262
$909$	−16.9708	−0.562884
$910$	−11.0379	−0.365903
$911$	−33.8920	−1.12289	−0.561447	−	0.827513i	$-0.689755\pi$
$911$	−33.8920	−1.12289	−0.561447	+	0.827513i	$0.689755\pi$
$912$	9.36755	0.310191
$913$	0.948699	0.0313973
$914$	−4.60666	−0.152375
$915$	61.5760	2.03564
$916$	19.4780	0.643573
$917$	38.8281	1.28222
$918$	−1.12083	−0.0369929
$919$	22.4756	0.741403	0.370702	−	0.928752i	$-0.379117\pi$
$919$	22.4756	0.741403	0.370702	+	0.928752i	$0.379117\pi$
$920$	−10.1995	−0.336269
$921$	66.4006	2.18797
$922$	1.12041	0.0368987
$923$	24.1214	0.793964
$924$	−7.42670	−0.244321
$925$	1.53258	0.0503909
$926$	−11.9808	−0.393713
$927$	47.6566	1.56525
$928$	3.31149	0.108705
$929$	45.2062	1.48317	0.741584	−	0.670860i	$-0.234075\pi$
$929$	45.2062	1.48317	0.741584	+	0.670860i	$0.234075\pi$
$930$	9.93381	0.325742
$931$	15.1337	0.495988
$932$	39.0374	1.27871
$933$	3.89879	0.127641
$934$	−2.66985	−0.0873603
$935$	2.28705	0.0747946
$936$	16.3286	0.533717
$937$	−44.7687	−1.46253	−0.731264	−	0.682094i	$-0.761069\pi$
$937$	−44.7687	−1.46253	−0.731264	+	0.682094i	$0.761069\pi$
$938$	−6.26028	−0.204405
$939$	−76.9812	−2.51219
$940$	−18.1396	−0.591648
$941$	56.1405	1.83013	0.915065	−	0.403307i	$-0.132139\pi$
$941$	56.1405	1.83013	0.915065	+	0.403307i	$0.132139\pi$
$942$	−0.0646816	−0.00210744
$943$	−24.6723	−0.803442
$944$	−18.1264	−0.589966
$945$	9.91041	0.322386
$946$	−1.03333	−0.0335964
$947$	−12.8824	−0.418623	−0.209311	−	0.977849i	$-0.567122\pi$
$947$	−12.8824	−0.418623	−0.209311	+	0.977849i	$0.567122\pi$
$948$	8.56882	0.278302
$949$	11.7664	0.381954
$950$	0.350617	0.0113755
$951$	47.9152	1.55376
$952$	−18.5537	−0.601330
$953$	44.6861	1.44752	0.723762	−	0.690049i	$-0.242411\pi$
$953$	44.6861	1.44752	0.723762	+	0.690049i	$0.242411\pi$
$954$	1.33825	0.0433274
$955$	23.8195	0.770781
$956$	23.6419	0.764633
$957$	0.840249	0.0271614
$958$	−1.14183	−0.0368909
$959$	81.0549	2.61740
$960$	30.0149	0.968727
$961$	15.4093	0.497073
$962$	1.64334	0.0529834
$963$	−15.0152	−0.483859
$964$	9.18080	0.295694
$965$	−2.50885	−0.0807628
$966$	15.5146	0.499173
$967$	−18.7622	−0.603353	−0.301677	−	0.953410i	$-0.597546\pi$
$967$	−18.7622	−0.603353	−0.301677	+	0.953410i	$0.597546\pi$
$968$	−12.4672	−0.400710
$969$	9.41123	0.302332
$970$	0.473207	0.0151938
$971$	−4.86689	−0.156186	−0.0780930	−	0.996946i	$-0.524883\pi$
$971$	−4.86689	−0.156186	−0.0780930	+	0.996946i	$0.524883\pi$
$972$	42.7934	1.37260
$973$	4.61679	0.148007
$974$	−1.83064	−0.0586576
$975$	−11.9561	−0.382903
$976$	−43.1516	−1.38125
$977$	−30.8820	−0.988004	−0.494002	−	0.869461i	$-0.664466\pi$
$977$	−30.8820	−0.988004	−0.494002	+	0.869461i	$0.664466\pi$
$978$	−6.34902	−0.203019
$979$	0.817702	0.0261339
$980$	53.8843	1.72127
$981$	−11.1852	−0.357117
$982$	−0.163778	−0.00522637
$983$	35.2942	1.12571	0.562855	−	0.826556i	$-0.309703\pi$
$983$	35.2942	1.12571	0.562855	+	0.826556i	$0.309703\pi$
$984$	−15.8069	−0.503907
$985$	−11.6458	−0.371065
$986$	1.02664	0.0326949
$987$	56.4170	1.79577
$988$	−8.41528	−0.267726
$989$	−48.3184	−1.53644
$990$	−0.653635	−0.0207739
$991$	57.7165	1.83342	0.916712	−	0.399549i	$-0.130833\pi$
$991$	57.7165	1.83342	0.916712	+	0.399549i	$0.130833\pi$
$992$	−22.5593	−0.716259
$993$	27.9322	0.886403
$994$	7.83328	0.248457
$995$	32.6160	1.03400
$996$	13.9000	0.440439
$997$	10.8829	0.344666	0.172333	−	0.985039i	$-0.444869\pi$
$997$	10.8829	0.344666	0.172333	+	0.985039i	$0.444869\pi$
$998$	5.54883	0.175645
$999$	−1.47548	−0.0466820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.29	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.29	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-0.292455 q^{2} +2.53585 q^{3} -1.91447 q^{4} -1.96622 q^{5} -0.741621 q^{6} -4.61679 q^{7} +1.14481 q^{8} +3.43052 q^{9} +O(q^{10})\)	\(q-0.292455 q^{2} +2.53585 q^{3} -1.91447 q^{4} -1.96622 q^{5} -0.741621 q^{6} -4.61679 q^{7} +1.14481 q^{8} +3.43052 q^{9} +0.575030 q^{10} -0.331348 q^{11} -4.85480 q^{12} +4.15773 q^{13} +1.35020 q^{14} -4.98602 q^{15} +3.49414 q^{16} +3.51043 q^{17} -1.00327 q^{18} +1.05721 q^{19} +3.76426 q^{20} -11.7075 q^{21} +0.0969044 q^{22} +4.53125 q^{23} +2.90305 q^{24} -1.13399 q^{25} -1.21595 q^{26} +1.09174 q^{27} +8.83870 q^{28} -1.00000 q^{29} +1.45819 q^{30} +6.81243 q^{31} -3.31149 q^{32} -0.840249 q^{33} -1.02664 q^{34} +9.07760 q^{35} -6.56764 q^{36} -1.35149 q^{37} -0.309188 q^{38} +10.5434 q^{39} -2.25094 q^{40} -5.44493 q^{41} +3.42391 q^{42} -10.6634 q^{43} +0.634356 q^{44} -6.74515 q^{45} -1.32519 q^{46} -4.81889 q^{47} +8.86060 q^{48} +14.3147 q^{49} +0.331642 q^{50} +8.90191 q^{51} -7.95986 q^{52} -1.33388 q^{53} -0.319286 q^{54} +0.651502 q^{55} -5.28532 q^{56} +2.68094 q^{57} +0.292455 q^{58} -5.18768 q^{59} +9.54560 q^{60} -12.3497 q^{61} -1.99233 q^{62} -15.8380 q^{63} -6.01981 q^{64} -8.17500 q^{65} +0.245735 q^{66} -4.63655 q^{67} -6.72061 q^{68} +11.4906 q^{69} -2.65479 q^{70} +5.80156 q^{71} +3.92729 q^{72} +2.83001 q^{73} +0.395249 q^{74} -2.87564 q^{75} -2.02401 q^{76} +1.52976 q^{77} -3.08346 q^{78} -1.76502 q^{79} -6.87023 q^{80} -7.52308 q^{81} +1.59240 q^{82} -2.86315 q^{83} +22.4136 q^{84} -6.90226 q^{85} +3.11856 q^{86} -2.53585 q^{87} -0.379330 q^{88} -2.46780 q^{89} +1.97265 q^{90} -19.1954 q^{91} -8.67494 q^{92} +17.2753 q^{93} +1.40931 q^{94} -2.07871 q^{95} -8.39743 q^{96} +0.822927 q^{97} -4.18641 q^{98} -1.13670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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