LMFDB - Embedded newform 8029.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.91066 q^{2} -1.87934 q^{3} +1.65063 q^{4} -2.89304 q^{5} +3.59078 q^{6} +1.00000 q^{7} +0.667519 q^{8} +0.531906 q^{9} +O(q^{10})$	\(q-1.91066 q^{2} -1.87934 q^{3} +1.65063 q^{4} -2.89304 q^{5} +3.59078 q^{6} +1.00000 q^{7} +0.667519 q^{8} +0.531906 q^{9} +5.52763 q^{10} +6.05267 q^{11} -3.10210 q^{12} +0.237991 q^{13} -1.91066 q^{14} +5.43700 q^{15} -4.57667 q^{16} -7.47734 q^{17} -1.01629 q^{18} +3.12677 q^{19} -4.77536 q^{20} -1.87934 q^{21} -11.5646 q^{22} -7.52590 q^{23} -1.25449 q^{24} +3.36970 q^{25} -0.454721 q^{26} +4.63838 q^{27} +1.65063 q^{28} +2.41144 q^{29} -10.3883 q^{30} +1.00000 q^{31} +7.40945 q^{32} -11.3750 q^{33} +14.2867 q^{34} -2.89304 q^{35} +0.877982 q^{36} +1.00000 q^{37} -5.97420 q^{38} -0.447265 q^{39} -1.93116 q^{40} +10.7000 q^{41} +3.59078 q^{42} -6.11113 q^{43} +9.99075 q^{44} -1.53883 q^{45} +14.3795 q^{46} +4.46173 q^{47} +8.60111 q^{48} +1.00000 q^{49} -6.43837 q^{50} +14.0524 q^{51} +0.392836 q^{52} -3.94983 q^{53} -8.86238 q^{54} -17.5106 q^{55} +0.667519 q^{56} -5.87625 q^{57} -4.60744 q^{58} +13.6142 q^{59} +8.97451 q^{60} -10.6738 q^{61} -1.91066 q^{62} +0.531906 q^{63} -5.00361 q^{64} -0.688519 q^{65} +21.7338 q^{66} -15.8820 q^{67} -12.3424 q^{68} +14.1437 q^{69} +5.52763 q^{70} +14.0914 q^{71} +0.355057 q^{72} +11.0475 q^{73} -1.91066 q^{74} -6.33281 q^{75} +5.16115 q^{76} +6.05267 q^{77} +0.854574 q^{78} +4.35115 q^{79} +13.2405 q^{80} -10.3128 q^{81} -20.4442 q^{82} +11.7105 q^{83} -3.10210 q^{84} +21.6323 q^{85} +11.6763 q^{86} -4.53190 q^{87} +4.04027 q^{88} -0.360581 q^{89} +2.94018 q^{90} +0.237991 q^{91} -12.4225 q^{92} -1.87934 q^{93} -8.52487 q^{94} -9.04588 q^{95} -13.9248 q^{96} +14.5570 q^{97} -1.91066 q^{98} +3.21945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−1.91066	−1.35104	−0.675522	−	0.737340i	$-0.736081\pi$
$2$	−1.91066	−1.35104	−0.675522	+	0.737340i	$0.736081\pi$
$3$	−1.87934	−1.08504	−0.542518	−	0.840044i	$-0.682529\pi$
$3$	−1.87934	−1.08504	−0.542518	+	0.840044i	$0.682529\pi$
$4$	1.65063	0.825317
$5$	−2.89304	−1.29381	−0.646904	−	0.762571i	$-0.723937\pi$
$5$	−2.89304	−1.29381	−0.646904	+	0.762571i	$0.723937\pi$
$6$	3.59078	1.46593
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.667519	0.236004
$9$	0.531906	0.177302
$10$	5.52763	1.74799
$11$	6.05267	1.82495	0.912474	−	0.409134i	$-0.134169\pi$
$11$	6.05267	1.82495	0.912474	+	0.409134i	$0.134169\pi$
$12$	−3.10210	−0.895499
$13$	0.237991	0.0660069	0.0330034	−	0.999455i	$-0.489493\pi$
$13$	0.237991	0.0660069	0.0330034	+	0.999455i	$0.489493\pi$
$14$	−1.91066	−0.510646
$15$	5.43700	1.40383
$16$	−4.57667	−1.14417
$17$	−7.47734	−1.81352	−0.906760	−	0.421647i	$-0.861452\pi$
$17$	−7.47734	−1.81352	−0.906760	+	0.421647i	$0.861452\pi$
$18$	−1.01629	−0.239543
$19$	3.12677	0.717330	0.358665	−	0.933466i	$-0.383232\pi$
$19$	3.12677	0.717330	0.358665	+	0.933466i	$0.383232\pi$
$20$	−4.77536	−1.06780
$21$	−1.87934	−0.410105
$22$	−11.5646	−2.46558
$23$	−7.52590	−1.56926	−0.784630	−	0.619965i	$-0.787147\pi$
$23$	−7.52590	−1.56926	−0.784630	+	0.619965i	$0.787147\pi$
$24$	−1.25449	−0.256072
$25$	3.36970	0.673941
$26$	−0.454721	−0.0891781
$27$	4.63838	0.892657
$28$	1.65063	0.311941
$29$	2.41144	0.447793	0.223896	−	0.974613i	$-0.428122\pi$
$29$	2.41144	0.447793	0.223896	+	0.974613i	$0.428122\pi$
$30$	−10.3883	−1.89663
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.40945	1.30982
$33$	−11.3750	−1.98013
$34$	14.2867	2.45014
$35$	−2.89304	−0.489014
$36$	0.877982	0.146330
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−5.97420	−0.969144
$39$	−0.447265	−0.0716198
$40$	−1.93116	−0.305344
$41$	10.7000	1.67106	0.835532	−	0.549441i	$-0.185159\pi$
$41$	10.7000	1.67106	0.835532	+	0.549441i	$0.185159\pi$
$42$	3.59078	0.554069
$43$	−6.11113	−0.931939	−0.465969	−	0.884801i	$-0.654294\pi$
$43$	−6.11113	−0.931939	−0.465969	+	0.884801i	$0.654294\pi$
$44$	9.99075	1.50616
$45$	−1.53883	−0.229395
$46$	14.3795	2.12014
$47$	4.46173	0.650810	0.325405	−	0.945575i	$-0.394499\pi$
$47$	4.46173	0.650810	0.325405	+	0.945575i	$0.394499\pi$
$48$	8.60111	1.24146
$49$	1.00000	0.142857
$50$	−6.43837	−0.910523
$51$	14.0524	1.96773
$52$	0.392836	0.0544766
$53$	−3.94983	−0.542550	−0.271275	−	0.962502i	$-0.587445\pi$
$53$	−3.94983	−0.542550	−0.271275	+	0.962502i	$0.587445\pi$
$54$	−8.86238	−1.20602
$55$	−17.5106	−2.36113
$56$	0.667519	0.0892010
$57$	−5.87625	−0.778329
$58$	−4.60744	−0.604987
$59$	13.6142	1.77242	0.886208	−	0.463287i	$-0.153330\pi$
$59$	13.6142	1.77242	0.886208	+	0.463287i	$0.153330\pi$
$60$	8.97451	1.15860
$61$	−10.6738	−1.36664	−0.683321	−	0.730118i	$-0.739465\pi$
$61$	−10.6738	−1.36664	−0.683321	+	0.730118i	$0.739465\pi$
$62$	−1.91066	−0.242655
$63$	0.531906	0.0670138
$64$	−5.00361	−0.625451
$65$	−0.688519	−0.0854002
$66$	21.7338	2.67525
$67$	−15.8820	−1.94029	−0.970146	−	0.242520i	$-0.922026\pi$
$67$	−15.8820	−1.94029	−0.970146	+	0.242520i	$0.922026\pi$
$68$	−12.3424	−1.49673
$69$	14.1437	1.70270
$70$	5.52763	0.660679
$71$	14.0914	1.67235	0.836174	−	0.548465i	$-0.184788\pi$
$71$	14.0914	1.67235	0.836174	+	0.548465i	$0.184788\pi$
$72$	0.355057	0.0418439
$73$	11.0475	1.29301	0.646507	−	0.762908i	$-0.276229\pi$
$73$	11.0475	1.29301	0.646507	+	0.762908i	$0.276229\pi$
$74$	−1.91066	−0.222110
$75$	−6.33281	−0.731250
$76$	5.16115	0.592025
$77$	6.05267	0.689766
$78$	0.854574	0.0967614
$79$	4.35115	0.489543	0.244771	−	0.969581i	$-0.421287\pi$
$79$	4.35115	0.489543	0.244771	+	0.969581i	$0.421287\pi$
$80$	13.2405	1.48034
$81$	−10.3128	−1.14587
$82$	−20.4442	−2.25768
$83$	11.7105	1.28539	0.642697	−	0.766120i	$-0.277815\pi$
$83$	11.7105	1.28539	0.642697	+	0.766120i	$0.277815\pi$
$84$	−3.10210	−0.338467
$85$	21.6323	2.34635
$86$	11.6763	1.25909
$87$	−4.53190	−0.485871
$88$	4.04027	0.430695
$89$	−0.360581	−0.0382215	−0.0191108	−	0.999817i	$-0.506084\pi$
$89$	−0.360581	−0.0382215	−0.0191108	+	0.999817i	$0.506084\pi$
$90$	2.94018	0.309922
$91$	0.237991	0.0249482
$92$	−12.4225	−1.29514
$93$	−1.87934	−0.194878
$94$	−8.52487	−0.879273
$95$	−9.04588	−0.928088
$96$	−13.9248	−1.42120
$97$	14.5570	1.47804	0.739020	−	0.673683i	$-0.235289\pi$
$97$	14.5570	1.47804	0.739020	+	0.673683i	$0.235289\pi$
$98$	−1.91066	−0.193006
$99$	3.21945	0.323567
$100$	5.56215	0.556215
$101$	−7.51864	−0.748133	−0.374066	−	0.927402i	$-0.622037\pi$
$101$	−7.51864	−0.748133	−0.374066	+	0.927402i	$0.622037\pi$
$102$	−26.8495	−2.65849
$103$	−10.6923	−1.05354	−0.526770	−	0.850008i	$-0.676597\pi$
$103$	−10.6923	−1.05354	−0.526770	+	0.850008i	$0.676597\pi$
$104$	0.158864	0.0155779
$105$	5.43700	0.530597
$106$	7.54679	0.733009
$107$	4.46330	0.431483	0.215742	−	0.976451i	$-0.430783\pi$
$107$	4.46330	0.431483	0.215742	+	0.976451i	$0.430783\pi$
$108$	7.65627	0.736725
$109$	−2.23491	−0.214065	−0.107033	−	0.994256i	$-0.534135\pi$
$109$	−2.23491	−0.214065	−0.107033	+	0.994256i	$0.534135\pi$
$110$	33.4569	3.18999
$111$	−1.87934	−0.178379
$112$	−4.57667	−0.432455
$113$	−15.1755	−1.42759	−0.713796	−	0.700354i	$-0.753026\pi$
$113$	−15.1755	−1.42759	−0.713796	+	0.700354i	$0.753026\pi$
$114$	11.2275	1.05156
$115$	21.7728	2.03032
$116$	3.98040	0.369571
$117$	0.126589	0.0117031
$118$	−26.0121	−2.39461
$119$	−7.47734	−0.685446
$120$	3.62930	0.331309
$121$	25.6348	2.33044
$122$	20.3941	1.84639
$123$	−20.1090	−1.81316
$124$	1.65063	0.148231
$125$	4.71652	0.421858
$126$	−1.01629	−0.0905386
$127$	1.07494	0.0953858	0.0476929	−	0.998862i	$-0.484813\pi$
$127$	1.07494	0.0953858	0.0476929	+	0.998862i	$0.484813\pi$
$128$	−5.25868	−0.464806
$129$	11.4849	1.01119
$130$	1.31553	0.115379
$131$	1.18457	0.103496	0.0517481	−	0.998660i	$-0.483521\pi$
$131$	1.18457	0.103496	0.0517481	+	0.998660i	$0.483521\pi$
$132$	−18.7760	−1.63424
$133$	3.12677	0.271125
$134$	30.3451	2.62142
$135$	−13.4190	−1.15493
$136$	−4.99126	−0.427997
$137$	−3.35209	−0.286389	−0.143194	−	0.989695i	$-0.545737\pi$
$137$	−3.35209	−0.286389	−0.143194	+	0.989695i	$0.545737\pi$
$138$	−27.0239	−2.30042
$139$	−13.8880	−1.17797	−0.588984	−	0.808145i	$-0.700472\pi$
$139$	−13.8880	−1.17797	−0.588984	+	0.808145i	$0.700472\pi$
$140$	−4.77536	−0.403592
$141$	−8.38509	−0.706152
$142$	−26.9240	−2.25941
$143$	1.44048	0.120459
$144$	−2.43436	−0.202863
$145$	−6.97639	−0.579358
$146$	−21.1081	−1.74692
$147$	−1.87934	−0.155005
$148$	1.65063	0.135681
$149$	2.29734	0.188206	0.0941029	−	0.995562i	$-0.470002\pi$
$149$	2.29734	0.188206	0.0941029	+	0.995562i	$0.470002\pi$
$150$	12.0999	0.987950
$151$	3.17327	0.258237	0.129118	−	0.991629i	$-0.458785\pi$
$151$	3.17327	0.258237	0.129118	+	0.991629i	$0.458785\pi$
$152$	2.08718	0.169293
$153$	−3.97724	−0.321541
$154$	−11.5646	−0.931903
$155$	−2.89304	−0.232375
$156$	−0.738272	−0.0591091
$157$	10.4227	0.831826	0.415913	−	0.909404i	$-0.363462\pi$
$157$	10.4227	0.831826	0.415913	+	0.909404i	$0.363462\pi$
$158$	−8.31358	−0.661393
$159$	7.42305	0.588686
$160$	−21.4359	−1.69465
$161$	−7.52590	−0.593124
$162$	19.7043	1.54811
$163$	−24.6885	−1.93375	−0.966876	−	0.255245i	$-0.917844\pi$
$163$	−24.6885	−1.93375	−0.966876	+	0.255245i	$0.917844\pi$
$164$	17.6619	1.37916
$165$	32.9084	2.56191
$166$	−22.3748	−1.73662
$167$	−18.8878	−1.46158	−0.730792	−	0.682601i	$-0.760849\pi$
$167$	−18.8878	−1.46158	−0.730792	+	0.682601i	$0.760849\pi$
$168$	−1.25449	−0.0967862
$169$	−12.9434	−0.995643
$170$	−41.3320	−3.17002
$171$	1.66315	0.127184
$172$	−10.0872	−0.769145
$173$	−3.14542	−0.239142	−0.119571	−	0.992826i	$-0.538152\pi$
$173$	−3.14542	−0.239142	−0.119571	+	0.992826i	$0.538152\pi$
$174$	8.65894	0.656432
$175$	3.36970	0.254726
$176$	−27.7011	−2.08805
$177$	−25.5857	−1.92314
$178$	0.688949	0.0516389
$179$	−3.12570	−0.233626	−0.116813	−	0.993154i	$-0.537268\pi$
$179$	−3.12570	−0.233626	−0.116813	+	0.993154i	$0.537268\pi$
$180$	−2.54004	−0.189323
$181$	1.47787	0.109849	0.0549246	−	0.998491i	$-0.482508\pi$
$181$	1.47787	0.109849	0.0549246	+	0.998491i	$0.482508\pi$
$182$	−0.454721	−0.0337062
$183$	20.0597	1.48286
$184$	−5.02368	−0.370351
$185$	−2.89304	−0.212701
$186$	3.59078	0.263289
$187$	−45.2578	−3.30958
$188$	7.36469	0.537125
$189$	4.63838	0.337392
$190$	17.2836	1.25389
$191$	1.59731	0.115577	0.0577885	−	0.998329i	$-0.481595\pi$
$191$	1.59731	0.115577	0.0577885	+	0.998329i	$0.481595\pi$
$192$	9.40347	0.678637
$193$	−16.7881	−1.20843	−0.604217	−	0.796820i	$-0.706514\pi$
$193$	−16.7881	−1.20843	−0.604217	+	0.796820i	$0.706514\pi$
$194$	−27.8135	−1.99690
$195$	1.29396	0.0926623
$196$	1.65063	0.117902
$197$	19.0391	1.35648	0.678240	−	0.734840i	$-0.262743\pi$
$197$	19.0391	1.35648	0.678240	+	0.734840i	$0.262743\pi$
$198$	−6.15128	−0.437153
$199$	6.36446	0.451165	0.225582	−	0.974224i	$-0.427572\pi$
$199$	6.36446	0.451165	0.225582	+	0.974224i	$0.427572\pi$
$200$	2.24934	0.159052
$201$	29.8476	2.10529
$202$	14.3656	1.01076
$203$	2.41144	0.169250
$204$	23.1954	1.62401
$205$	−30.9557	−2.16204
$206$	20.4293	1.42338
$207$	−4.00307	−0.278233
$208$	−1.08921	−0.0755230
$209$	18.9253	1.30909
$210$	−10.3883	−0.716860
$211$	−26.6179	−1.83245	−0.916225	−	0.400664i	$-0.868780\pi$
$211$	−26.6179	−1.83245	−0.916225	+	0.400664i	$0.868780\pi$
$212$	−6.51972	−0.447776
$213$	−26.4826	−1.81456
$214$	−8.52786	−0.582952
$215$	17.6798	1.20575
$216$	3.09621	0.210670
$217$	1.00000	0.0678844
$218$	4.27015	0.289211
$219$	−20.7620	−1.40297
$220$	−28.9037	−1.94869
$221$	−1.77954	−0.119705
$222$	3.59078	0.240997
$223$	4.54055	0.304057	0.152029	−	0.988376i	$-0.451419\pi$
$223$	4.54055	0.304057	0.152029	+	0.988376i	$0.451419\pi$
$224$	7.40945	0.495064
$225$	1.79236	0.119491
$226$	28.9953	1.92874
$227$	−14.4493	−0.959034	−0.479517	−	0.877532i	$-0.659188\pi$
$227$	−14.4493	−0.959034	−0.479517	+	0.877532i	$0.659188\pi$
$228$	−9.69955	−0.642368
$229$	−3.79740	−0.250939	−0.125470	−	0.992097i	$-0.540044\pi$
$229$	−3.79740	−0.250939	−0.125470	+	0.992097i	$0.540044\pi$
$230$	−41.6004	−2.74305
$231$	−11.3750	−0.748420
$232$	1.60968	0.105681
$233$	13.6034	0.891187	0.445594	−	0.895235i	$-0.352993\pi$
$233$	13.6034	0.891187	0.445594	+	0.895235i	$0.352993\pi$
$234$	−0.241869	−0.0158114
$235$	−12.9080	−0.842024
$236$	22.4721	1.46281
$237$	−8.17727	−0.531171
$238$	14.2867	0.926067
$239$	0.617504	0.0399430	0.0199715	−	0.999801i	$-0.493642\pi$
$239$	0.617504	0.0399430	0.0199715	+	0.999801i	$0.493642\pi$
$240$	−24.8834	−1.60622
$241$	−10.9229	−0.703608	−0.351804	−	0.936074i	$-0.614432\pi$
$241$	−10.9229	−0.703608	−0.351804	+	0.936074i	$0.614432\pi$
$242$	−48.9795	−3.14852
$243$	5.46607	0.350649
$244$	−17.6186	−1.12791
$245$	−2.89304	−0.184830
$246$	38.4215	2.44966
$247$	0.744143	0.0473487
$248$	0.667519	0.0423875
$249$	−22.0080	−1.39470
$250$	−9.01168	−0.569949
$251$	17.9394	1.13233	0.566163	−	0.824293i	$-0.308427\pi$
$251$	17.9394	1.13233	0.566163	+	0.824293i	$0.308427\pi$
$252$	0.877982	0.0553077
$253$	−45.5518	−2.86382
$254$	−2.05385	−0.128870
$255$	−40.6543	−2.54587
$256$	20.0548	1.25342
$257$	−3.89623	−0.243040	−0.121520	−	0.992589i	$-0.538777\pi$
$257$	−3.89623	−0.243040	−0.121520	+	0.992589i	$0.538777\pi$
$258$	−21.9437	−1.36616
$259$	1.00000	0.0621370
$260$	−1.13649	−0.0704823
$261$	1.28266	0.0793945
$262$	−2.26331	−0.139828
$263$	−13.0707	−0.805974	−0.402987	−	0.915206i	$-0.632028\pi$
$263$	−13.0707	−0.805974	−0.402987	+	0.915206i	$0.632028\pi$
$264$	−7.59303	−0.467319
$265$	11.4270	0.701956
$266$	−5.97420	−0.366302
$267$	0.677653	0.0414717
$268$	−26.2154	−1.60136
$269$	−15.1698	−0.924920	−0.462460	−	0.886640i	$-0.653033\pi$
$269$	−15.1698	−0.924920	−0.462460	+	0.886640i	$0.653033\pi$
$270$	25.6393	1.56036
$271$	−13.2602	−0.805502	−0.402751	−	0.915310i	$-0.631946\pi$
$271$	−13.2602	−0.805502	−0.402751	+	0.915310i	$0.631946\pi$
$272$	34.2213	2.07497
$273$	−0.447265	−0.0270697
$274$	6.40472	0.386924
$275$	20.3957	1.22991
$276$	23.3461	1.40527
$277$	23.9664	1.44000	0.720000	−	0.693974i	$-0.244142\pi$
$277$	23.9664	1.44000	0.720000	+	0.693974i	$0.244142\pi$
$278$	26.5354	1.59149
$279$	0.531906	0.0318444
$280$	−1.93116	−0.115409
$281$	19.2313	1.14724	0.573621	−	0.819121i	$-0.305538\pi$
$281$	19.2313	1.14724	0.573621	+	0.819121i	$0.305538\pi$
$282$	16.0211	0.954042
$283$	15.8308	0.941041	0.470520	−	0.882389i	$-0.344066\pi$
$283$	15.8308	0.941041	0.470520	+	0.882389i	$0.344066\pi$
$284$	23.2598	1.38022
$285$	17.0003	1.00701
$286$	−2.75228	−0.162745
$287$	10.7000	0.631603
$288$	3.94113	0.232233
$289$	38.9106	2.28886
$290$	13.3295	0.782737
$291$	−27.3575	−1.60373
$292$	18.2354	1.06715
$293$	23.9764	1.40072	0.700359	−	0.713791i	$-0.253023\pi$
$293$	23.9764	1.40072	0.700359	+	0.713791i	$0.253023\pi$
$294$	3.59078	0.209419
$295$	−39.3865	−2.29317
$296$	0.667519	0.0387988
$297$	28.0746	1.62905
$298$	−4.38945	−0.254274
$299$	−1.79110	−0.103582
$300$	−10.4532	−0.603513
$301$	−6.11113	−0.352240
$302$	−6.06305	−0.348889
$303$	14.1301	0.811751
$304$	−14.3102	−0.820747
$305$	30.8798	1.76817
$306$	7.59916	0.434415
$307$	−14.1092	−0.805256	−0.402628	−	0.915364i	$-0.631903\pi$
$307$	−14.1092	−0.805256	−0.402628	+	0.915364i	$0.631903\pi$
$308$	9.99075	0.569276
$309$	20.0944	1.14313
$310$	5.52763	0.313948
$311$	−12.8329	−0.727688	−0.363844	−	0.931460i	$-0.618536\pi$
$311$	−12.8329	−0.727688	−0.363844	+	0.931460i	$0.618536\pi$
$312$	−0.298558	−0.0169025
$313$	22.9750	1.29863	0.649313	−	0.760521i	$-0.275057\pi$
$313$	22.9750	1.29863	0.649313	+	0.760521i	$0.275057\pi$
$314$	−19.9144	−1.12383
$315$	−1.53883	−0.0867031
$316$	7.18216	0.404028
$317$	−17.1280	−0.962006	−0.481003	−	0.876719i	$-0.659727\pi$
$317$	−17.1280	−0.962006	−0.481003	+	0.876719i	$0.659727\pi$
$318$	−14.1830	−0.795340
$319$	14.5956	0.817198
$320$	14.4757	0.809214
$321$	−8.38804	−0.468174
$322$	14.3795	0.801337
$323$	−23.3799	−1.30089
$324$	−17.0227	−0.945703
$325$	0.801959	0.0444847
$326$	47.1714	2.61258
$327$	4.20014	0.232268
$328$	7.14248	0.394377
$329$	4.46173	0.245983
$330$	−62.8768	−3.46126
$331$	5.64666	0.310368	0.155184	−	0.987886i	$-0.450403\pi$
$331$	5.64666	0.310368	0.155184	+	0.987886i	$0.450403\pi$
$332$	19.3298	1.06086
$333$	0.531906	0.0291483
$334$	36.0883	1.97466
$335$	45.9473	2.51037
$336$	8.60111	0.469229
$337$	−11.6930	−0.636961	−0.318480	−	0.947929i	$-0.603173\pi$
$337$	−11.6930	−0.636961	−0.318480	+	0.947929i	$0.603173\pi$
$338$	24.7304	1.34516
$339$	28.5199	1.54899
$340$	35.7070	1.93648
$341$	6.05267	0.327770
$342$	−3.17771	−0.171831
$343$	1.00000	0.0539949
$344$	−4.07930	−0.219941
$345$	−40.9184	−2.20297
$346$	6.00984	0.323091
$347$	−0.0790947	−0.00424603	−0.00212301	−	0.999998i	$-0.500676\pi$
$347$	−0.0790947	−0.00424603	−0.00212301	+	0.999998i	$0.500676\pi$
$348$	−7.48051	−0.400998
$349$	−21.6877	−1.16092	−0.580458	−	0.814290i	$-0.697127\pi$
$349$	−21.6877	−1.16092	−0.580458	+	0.814290i	$0.697127\pi$
$350$	−6.43837	−0.344145
$351$	1.10389	0.0589215
$352$	44.8469	2.39035
$353$	−1.30470	−0.0694422	−0.0347211	−	0.999397i	$-0.511054\pi$
$353$	−1.30470	−0.0694422	−0.0347211	+	0.999397i	$0.511054\pi$
$354$	48.8856	2.59824
$355$	−40.7672	−2.16370
$356$	−0.595188	−0.0315449
$357$	14.0524	0.743734
$358$	5.97216	0.315638
$359$	14.3478	0.757246	0.378623	−	0.925551i	$-0.376398\pi$
$359$	14.3478	0.757246	0.378623	+	0.925551i	$0.376398\pi$
$360$	−1.02720	−0.0541380
$361$	−9.22331	−0.485438
$362$	−2.82371	−0.148411
$363$	−48.1764	−2.52861
$364$	0.392836	0.0205902
$365$	−31.9610	−1.67291
$366$	−38.3273	−2.00340
$367$	17.0953	0.892370	0.446185	−	0.894941i	$-0.352782\pi$
$367$	17.0953	0.892370	0.446185	+	0.894941i	$0.352782\pi$
$368$	34.4436	1.79550
$369$	5.69141	0.296283
$370$	5.52763	0.287368
$371$	−3.94983	−0.205065
$372$	−3.10210	−0.160836
$373$	−8.33411	−0.431524	−0.215762	−	0.976446i	$-0.569224\pi$
$373$	−8.33411	−0.431524	−0.215762	+	0.976446i	$0.569224\pi$
$374$	86.4725	4.47139
$375$	−8.86393	−0.457731
$376$	2.97829	0.153594
$377$	0.573901	0.0295574
$378$	−8.86238	−0.455832
$379$	−13.5731	−0.697202	−0.348601	−	0.937271i	$-0.613343\pi$
$379$	−13.5731	−0.697202	−0.348601	+	0.937271i	$0.613343\pi$
$380$	−14.9314	−0.765967
$381$	−2.02018	−0.103497
$382$	−3.05192	−0.156150
$383$	3.97183	0.202951	0.101475	−	0.994838i	$-0.467644\pi$
$383$	3.97183	0.202951	0.101475	+	0.994838i	$0.467644\pi$
$384$	9.88283	0.504331
$385$	−17.5106	−0.892425
$386$	32.0764	1.63265
$387$	−3.25055	−0.165235
$388$	24.0283	1.21985
$389$	−14.9850	−0.759769	−0.379885	−	0.925034i	$-0.624036\pi$
$389$	−14.9850	−0.759769	−0.379885	+	0.925034i	$0.624036\pi$
$390$	−2.47232	−0.125191
$391$	56.2737	2.84588
$392$	0.667519	0.0337148
$393$	−2.22620	−0.112297
$394$	−36.3773	−1.83266
$395$	−12.5881	−0.633374
$396$	5.31414	0.267045
$397$	31.5738	1.58464	0.792321	−	0.610104i	$-0.208873\pi$
$397$	31.5738	1.58464	0.792321	+	0.610104i	$0.208873\pi$
$398$	−12.1603	−0.609543
$399$	−5.87625	−0.294181
$400$	−15.4220	−0.771102
$401$	−0.232236	−0.0115973	−0.00579867	−	0.999983i	$-0.501846\pi$
$401$	−0.232236	−0.0115973	−0.00579867	+	0.999983i	$0.501846\pi$
$402$	−57.0287	−2.84433
$403$	0.237991	0.0118552
$404$	−12.4105	−0.617447
$405$	29.8354	1.48253
$406$	−4.60744	−0.228664
$407$	6.05267	0.300020
$408$	9.38027	0.464392
$409$	21.8079	1.07833	0.539165	−	0.842200i	$-0.318740\pi$
$409$	21.8079	1.07833	0.539165	+	0.842200i	$0.318740\pi$
$410$	59.1459	2.92101
$411$	6.29971	0.310742
$412$	−17.6490	−0.869505
$413$	13.6142	0.669911
$414$	7.64852	0.375904
$415$	−33.8790	−1.66305
$416$	1.76338	0.0864569
$417$	26.1003	1.27814
$418$	−36.1599	−1.76864
$419$	−8.30435	−0.405694	−0.202847	−	0.979210i	$-0.565019\pi$
$419$	−8.30435	−0.405694	−0.202847	+	0.979210i	$0.565019\pi$
$420$	8.97451	0.437911
$421$	−10.4552	−0.509556	−0.254778	−	0.967000i	$-0.582002\pi$
$421$	−10.4552	−0.509556	−0.254778	+	0.967000i	$0.582002\pi$
$422$	50.8578	2.47572
$423$	2.37322	0.115390
$424$	−2.63658	−0.128044
$425$	−25.1964	−1.22221
$426$	50.5993	2.45154
$427$	−10.6738	−0.516542
$428$	7.36727	0.356111
$429$	−2.70715	−0.130702
$430$	−33.7801	−1.62902
$431$	−11.6705	−0.562149	−0.281075	−	0.959686i	$-0.590691\pi$
$431$	−11.6705	−0.562149	−0.281075	+	0.959686i	$0.590691\pi$
$432$	−21.2284	−1.02135
$433$	14.7921	0.710861	0.355430	−	0.934703i	$-0.384334\pi$
$433$	14.7921	0.710861	0.355430	+	0.934703i	$0.384334\pi$
$434$	−1.91066	−0.0917148
$435$	13.1110	0.628624
$436$	−3.68901	−0.176672
$437$	−23.5318	−1.12568
$438$	39.6692	1.89547
$439$	−23.4737	−1.12034	−0.560169	−	0.828378i	$-0.689264\pi$
$439$	−23.4737	−1.12034	−0.560169	+	0.828378i	$0.689264\pi$
$440$	−11.6887	−0.557236
$441$	0.531906	0.0253288
$442$	3.40010	0.161726
$443$	3.78334	0.179752	0.0898759	−	0.995953i	$-0.471353\pi$
$443$	3.78334	0.179752	0.0898759	+	0.995953i	$0.471353\pi$
$444$	−3.10210	−0.147219
$445$	1.04318	0.0494513
$446$	−8.67546	−0.410795
$447$	−4.31748	−0.204210
$448$	−5.00361	−0.236398
$449$	36.6905	1.73153	0.865767	−	0.500447i	$-0.166831\pi$
$449$	36.6905	1.73153	0.865767	+	0.500447i	$0.166831\pi$
$450$	−3.42461	−0.161437
$451$	64.7638	3.04961
$452$	−25.0492	−1.17822
$453$	−5.96364	−0.280196
$454$	27.6078	1.29570
$455$	−0.688519	−0.0322783
$456$	−3.92251	−0.183688
$457$	−23.2909	−1.08950	−0.544752	−	0.838597i	$-0.683376\pi$
$457$	−23.2909	−1.08950	−0.544752	+	0.838597i	$0.683376\pi$
$458$	7.25556	0.339030
$459$	−34.6827	−1.61885
$460$	35.9389	1.67566
$461$	−13.9775	−0.650996	−0.325498	−	0.945543i	$-0.605532\pi$
$461$	−13.9775	−0.650996	−0.325498	+	0.945543i	$0.605532\pi$
$462$	21.7338	1.01115
$463$	−37.6938	−1.75178	−0.875889	−	0.482512i	$-0.839724\pi$
$463$	−37.6938	−1.75178	−0.875889	+	0.482512i	$0.839724\pi$
$464$	−11.0364	−0.512350
$465$	5.43700	0.252135
$466$	−25.9915	−1.20403
$467$	−24.0537	−1.11307	−0.556536	−	0.830824i	$-0.687870\pi$
$467$	−24.0537	−1.11307	−0.556536	+	0.830824i	$0.687870\pi$
$468$	0.208952	0.00965881
$469$	−15.8820	−0.733362
$470$	24.6628	1.13761
$471$	−19.5879	−0.902561
$472$	9.08773	0.418297
$473$	−36.9887	−1.70074
$474$	15.6240	0.717635
$475$	10.5363	0.483438
$476$	−12.3424	−0.565711
$477$	−2.10093	−0.0961952
$478$	−1.17984	−0.0539647
$479$	−23.5063	−1.07403	−0.537016	−	0.843572i	$-0.680448\pi$
$479$	−23.5063	−1.07403	−0.537016	+	0.843572i	$0.680448\pi$
$480$	40.2852	1.83876
$481$	0.237991	0.0108515
$482$	20.8701	0.950605
$483$	14.1437	0.643561
$484$	42.3137	1.92335
$485$	−42.1141	−1.91230
$486$	−10.4438	−0.473741
$487$	21.7149	0.983997	0.491999	−	0.870596i	$-0.336267\pi$
$487$	21.7149	0.983997	0.491999	+	0.870596i	$0.336267\pi$
$488$	−7.12498	−0.322533
$489$	46.3980	2.09819
$490$	5.52763	0.249713
$491$	38.3527	1.73083	0.865417	−	0.501052i	$-0.167053\pi$
$491$	38.3527	1.73083	0.865417	+	0.501052i	$0.167053\pi$
$492$	−33.1926	−1.49644
$493$	−18.0311	−0.812081
$494$	−1.42181	−0.0639701
$495$	−9.31401	−0.418634
$496$	−4.57667	−0.205499
$497$	14.0914	0.632088
$498$	42.0498	1.88430
$499$	−5.43784	−0.243431	−0.121716	−	0.992565i	$-0.538840\pi$
$499$	−5.43784	−0.243431	−0.121716	+	0.992565i	$0.538840\pi$
$500$	7.78525	0.348167
$501$	35.4966	1.58587
$502$	−34.2762	−1.52982
$503$	6.81426	0.303833	0.151916	−	0.988393i	$-0.451456\pi$
$503$	6.81426	0.303833	0.151916	+	0.988393i	$0.451456\pi$
$504$	0.355057	0.0158155
$505$	21.7518	0.967941
$506$	87.0342	3.86914
$507$	24.3249	1.08031
$508$	1.77434	0.0787236
$509$	15.6395	0.693210	0.346605	−	0.938011i	$-0.387334\pi$
$509$	15.6395	0.693210	0.346605	+	0.938011i	$0.387334\pi$
$510$	77.6767	3.43958
$511$	11.0475	0.488714
$512$	−27.8006	−1.22862
$513$	14.5031	0.640329
$514$	7.44439	0.328358
$515$	30.9332	1.36308
$516$	18.9573	0.834550
$517$	27.0054	1.18770
$518$	−1.91066	−0.0839497
$519$	5.91130	0.259477
$520$	−0.459599	−0.0201548
$521$	−10.8816	−0.476733	−0.238366	−	0.971175i	$-0.576612\pi$
$521$	−10.8816	−0.476733	−0.238366	+	0.971175i	$0.576612\pi$
$522$	−2.45073	−0.107265
$523$	38.4692	1.68214	0.841071	−	0.540925i	$-0.181926\pi$
$523$	38.4692	1.68214	0.841071	+	0.540925i	$0.181926\pi$
$524$	1.95529	0.0854172
$525$	−6.33281	−0.276386
$526$	24.9737	1.08891
$527$	−7.47734	−0.325718
$528$	52.0597	2.26561
$529$	33.6392	1.46258
$530$	−21.8332	−0.948373
$531$	7.24147	0.314253
$532$	5.16115	0.223764
$533$	2.54651	0.110302
$534$	−1.29477	−0.0560301
$535$	−12.9125	−0.558257
$536$	−10.6015	−0.457916
$537$	5.87424	0.253492
$538$	28.9844	1.24961
$539$	6.05267	0.260707
$540$	−22.1499	−0.953181
$541$	−14.1271	−0.607370	−0.303685	−	0.952773i	$-0.598217\pi$
$541$	−14.1271	−0.607370	−0.303685	+	0.952773i	$0.598217\pi$
$542$	25.3359	1.08827
$543$	−2.77741	−0.119190
$544$	−55.4029	−2.37538
$545$	6.46568	0.276959
$546$	0.854574	0.0365724
$547$	−5.83986	−0.249694	−0.124847	−	0.992176i	$-0.539844\pi$
$547$	−5.83986	−0.249694	−0.124847	+	0.992176i	$0.539844\pi$
$548$	−5.53308	−0.236362
$549$	−5.67746	−0.242308
$550$	−38.9693	−1.66166
$551$	7.54001	0.321215
$552$	9.44119	0.401844
$553$	4.35115	0.185030
$554$	−45.7917	−1.94550
$555$	5.43700	0.230788
$556$	−22.9241	−0.972198
$557$	24.0065	1.01719	0.508593	−	0.861007i	$-0.330166\pi$
$557$	24.0065	1.01719	0.508593	+	0.861007i	$0.330166\pi$
$558$	−1.01629	−0.0430231
$559$	−1.45439	−0.0615143
$560$	13.2405	0.559514
$561$	85.0547	3.59101
$562$	−36.7445	−1.54997
$563$	30.1995	1.27276	0.636378	−	0.771377i	$-0.280432\pi$
$563$	30.1995	1.27276	0.636378	+	0.771377i	$0.280432\pi$
$564$	−13.8407	−0.582800
$565$	43.9034	1.84703
$566$	−30.2472	−1.27139
$567$	−10.3128	−0.433097
$568$	9.40631	0.394680
$569$	−19.4337	−0.814701	−0.407351	−	0.913272i	$-0.633547\pi$
$569$	−19.4337	−0.814701	−0.407351	+	0.913272i	$0.633547\pi$
$570$	−32.4818	−1.36051
$571$	−40.9559	−1.71395	−0.856975	−	0.515358i	$-0.827659\pi$
$571$	−40.9559	−1.71395	−0.856975	+	0.515358i	$0.827659\pi$
$572$	2.37771	0.0994170
$573$	−3.00188	−0.125405
$574$	−20.4442	−0.853323
$575$	−25.3601	−1.05759
$576$	−2.66145	−0.110894
$577$	44.5725	1.85558	0.927788	−	0.373107i	$-0.121707\pi$
$577$	44.5725	1.85558	0.927788	+	0.373107i	$0.121707\pi$
$578$	−74.3450	−3.09234
$579$	31.5505	1.31119
$580$	−11.5155	−0.478154
$581$	11.7105	0.485833
$582$	52.2710	2.16670
$583$	−23.9070	−0.990126
$584$	7.37443	0.305156
$585$	−0.366227	−0.0151416
$586$	−45.8109	−1.89243
$587$	−7.53998	−0.311208	−0.155604	−	0.987819i	$-0.549732\pi$
$587$	−7.53998	−0.311208	−0.155604	+	0.987819i	$0.549732\pi$
$588$	−3.10210	−0.127928
$589$	3.12677	0.128836
$590$	75.2543	3.09817
$591$	−35.7809	−1.47183
$592$	−4.57667	−0.188100
$593$	−1.83851	−0.0754987	−0.0377494	−	0.999287i	$-0.512019\pi$
$593$	−1.83851	−0.0754987	−0.0377494	+	0.999287i	$0.512019\pi$
$594$	−53.6411	−2.20092
$595$	21.6323	0.886836
$596$	3.79208	0.155329
$597$	−11.9610	−0.489530
$598$	3.42219	0.139944
$599$	38.7213	1.58211	0.791054	−	0.611746i	$-0.209532\pi$
$599$	38.7213	1.58211	0.791054	+	0.611746i	$0.209532\pi$
$600$	−4.22727	−0.172578
$601$	−1.09888	−0.0448242	−0.0224121	−	0.999749i	$-0.507135\pi$
$601$	−1.09888	−0.0448242	−0.0224121	+	0.999749i	$0.507135\pi$
$602$	11.6763	0.475891
$603$	−8.44772	−0.344018
$604$	5.23791	0.213127
$605$	−74.1626	−3.01514
$606$	−26.9978	−1.09671
$607$	6.93905	0.281647	0.140824	−	0.990035i	$-0.455025\pi$
$607$	6.93905	0.281647	0.140824	+	0.990035i	$0.455025\pi$
$608$	23.1676	0.939571
$609$	−4.53190	−0.183642
$610$	−59.0009	−2.38888
$611$	1.06185	0.0429580
$612$	−6.56497	−0.265373
$613$	−36.3824	−1.46947	−0.734735	−	0.678354i	$-0.762694\pi$
$613$	−36.3824	−1.46947	−0.734735	+	0.678354i	$0.762694\pi$
$614$	26.9580	1.08794
$615$	58.1761	2.34589
$616$	4.04027	0.162787
$617$	−2.25150	−0.0906421	−0.0453210	−	0.998972i	$-0.514431\pi$
$617$	−2.25150	−0.0906421	−0.0453210	+	0.998972i	$0.514431\pi$
$618$	−38.3936	−1.54442
$619$	28.8149	1.15817	0.579084	−	0.815268i	$-0.303410\pi$
$619$	28.8149	1.15817	0.579084	+	0.815268i	$0.303410\pi$
$620$	−4.77536	−0.191783
$621$	−34.9080	−1.40081
$622$	24.5194	0.983137
$623$	−0.360581	−0.0144464
$624$	2.04699	0.0819451
$625$	−30.4936	−1.21974
$626$	−43.8976	−1.75450
$627$	−35.5670	−1.42041
$628$	17.2042	0.686520
$629$	−7.47734	−0.298141
$630$	2.94018	0.117140
$631$	−36.5215	−1.45390	−0.726950	−	0.686691i	$-0.759063\pi$
$631$	−36.5215	−1.45390	−0.726950	+	0.686691i	$0.759063\pi$
$632$	2.90448	0.115534
$633$	50.0240	1.98827
$634$	32.7259	1.29971
$635$	−3.10986	−0.123411
$636$	12.2527	0.485853
$637$	0.237991	0.00942955
$638$	−27.8873	−1.10407
$639$	7.49532	0.296510
$640$	15.2136	0.601370
$641$	41.1934	1.62704	0.813521	−	0.581535i	$-0.197548\pi$
$641$	41.1934	1.62704	0.813521	+	0.581535i	$0.197548\pi$
$642$	16.0267	0.632524
$643$	−3.96602	−0.156404	−0.0782022	−	0.996938i	$-0.524918\pi$
$643$	−3.96602	−0.156404	−0.0782022	+	0.996938i	$0.524918\pi$
$644$	−12.4225	−0.489516
$645$	−33.2262	−1.30828
$646$	44.6711	1.75756
$647$	22.3852	0.880054	0.440027	−	0.897985i	$-0.354969\pi$
$647$	22.3852	0.880054	0.440027	+	0.897985i	$0.354969\pi$
$648$	−6.88399	−0.270429
$649$	82.4022	3.23457
$650$	−1.53227	−0.0601008
$651$	−1.87934	−0.0736570
$652$	−40.7517	−1.59596
$653$	−46.2356	−1.80934	−0.904669	−	0.426115i	$-0.859882\pi$
$653$	−46.2356	−1.80934	−0.904669	+	0.426115i	$0.859882\pi$
$654$	−8.02505	−0.313804
$655$	−3.42701	−0.133904
$656$	−48.9706	−1.91198
$657$	5.87624	0.229254
$658$	−8.52487	−0.332334
$659$	−31.4595	−1.22549	−0.612745	−	0.790281i	$-0.709935\pi$
$659$	−31.4595	−1.22549	−0.612745	+	0.790281i	$0.709935\pi$
$660$	54.3197	2.11439
$661$	−12.3661	−0.480986	−0.240493	−	0.970651i	$-0.577309\pi$
$661$	−12.3661	−0.480986	−0.240493	+	0.970651i	$0.577309\pi$
$662$	−10.7889	−0.419321
$663$	3.34435	0.129884
$664$	7.81698	0.303358
$665$	−9.04588	−0.350784
$666$	−1.01629	−0.0393805
$667$	−18.1482	−0.702703
$668$	−31.1769	−1.20627
$669$	−8.53322	−0.329913
$670$	−87.7898	−3.39161
$671$	−64.6051	−2.49405
$672$	−13.9248	−0.537162
$673$	27.4886	1.05961	0.529804	−	0.848120i	$-0.322266\pi$
$673$	27.4886	1.05961	0.529804	+	0.848120i	$0.322266\pi$
$674$	22.3415	0.860562
$675$	15.6300	0.601598
$676$	−21.3648	−0.821722
$677$	9.44482	0.362994	0.181497	−	0.983392i	$-0.441906\pi$
$677$	9.44482	0.362994	0.181497	+	0.983392i	$0.441906\pi$
$678$	−54.4919	−2.09275
$679$	14.5570	0.558647
$680$	14.4399	0.553747
$681$	27.1551	1.04059
$682$	−11.5646	−0.442832
$683$	6.09411	0.233185	0.116592	−	0.993180i	$-0.462803\pi$
$683$	6.09411	0.233185	0.116592	+	0.993180i	$0.462803\pi$
$684$	2.74525	0.104967
$685$	9.69776	0.370532
$686$	−1.91066	−0.0729495
$687$	7.13660	0.272278
$688$	27.9687	1.06629
$689$	−0.940023	−0.0358120
$690$	78.1812	2.97631
$691$	42.7286	1.62547	0.812736	−	0.582632i	$-0.197977\pi$
$691$	42.7286	1.62547	0.812736	+	0.582632i	$0.197977\pi$
$692$	−5.19194	−0.197368
$693$	3.21945	0.122297
$694$	0.151123	0.00573657
$695$	40.1787	1.52407
$696$	−3.02513	−0.114667
$697$	−80.0078	−3.03051
$698$	41.4379	1.56845
$699$	−25.5653	−0.966970
$700$	5.56215	0.210230
$701$	−31.9080	−1.20515	−0.602575	−	0.798062i	$-0.705858\pi$
$701$	−31.9080	−1.20515	−0.602575	+	0.798062i	$0.705858\pi$
$702$	−2.10917	−0.0796054
$703$	3.12677	0.117928
$704$	−30.2852	−1.14142
$705$	24.2584	0.913626
$706$	2.49284	0.0938194
$707$	−7.51864	−0.282768
$708$	−42.2326	−1.58720
$709$	32.4628	1.21916	0.609582	−	0.792723i	$-0.291337\pi$
$709$	32.4628	1.21916	0.609582	+	0.792723i	$0.291337\pi$
$710$	77.8924	2.92325
$711$	2.31440	0.0867968
$712$	−0.240695	−0.00902042
$713$	−7.52590	−0.281847
$714$	−26.8495	−1.00482
$715$	−4.16738	−0.155851
$716$	−5.15939	−0.192815
$717$	−1.16050	−0.0433396
$718$	−27.4137	−1.02307
$719$	−14.6690	−0.547063	−0.273532	−	0.961863i	$-0.588192\pi$
$719$	−14.6690	−0.547063	−0.273532	+	0.961863i	$0.588192\pi$
$720$	7.04271	0.262466
$721$	−10.6923	−0.398201
$722$	17.6226	0.655847
$723$	20.5279	0.763440
$724$	2.43942	0.0906604
$725$	8.12583	0.301786
$726$	92.0490	3.41626
$727$	−1.50835	−0.0559416	−0.0279708	−	0.999609i	$-0.508905\pi$
$727$	−1.50835	−0.0559416	−0.0279708	+	0.999609i	$0.508905\pi$
$728$	0.158864	0.00588788
$729$	20.6658	0.765400
$730$	61.0667	2.26018
$731$	45.6950	1.69009
$732$	33.1112	1.22383
$733$	−49.2007	−1.81727	−0.908634	−	0.417593i	$-0.862874\pi$
$733$	−49.2007	−1.81727	−0.908634	+	0.417593i	$0.862874\pi$
$734$	−32.6634	−1.20563
$735$	5.43700	0.200547
$736$	−55.7628	−2.05544
$737$	−96.1284	−3.54093
$738$	−10.8744	−0.400291
$739$	39.2842	1.44509	0.722546	−	0.691323i	$-0.242972\pi$
$739$	39.2842	1.44509	0.722546	+	0.691323i	$0.242972\pi$
$740$	−4.77536	−0.175546
$741$	−1.39850	−0.0513750
$742$	7.54679	0.277051
$743$	42.2339	1.54941	0.774707	−	0.632321i	$-0.217898\pi$
$743$	42.2339	1.54941	0.774707	+	0.632321i	$0.217898\pi$
$744$	−1.25449	−0.0459919
$745$	−6.64632	−0.243502
$746$	15.9237	0.583007
$747$	6.22888	0.227903
$748$	−74.7042	−2.73146
$749$	4.46330	0.163085
$750$	16.9360	0.618415
$751$	−10.1823	−0.371556	−0.185778	−	0.982592i	$-0.559481\pi$
$751$	−10.1823	−0.371556	−0.185778	+	0.982592i	$0.559481\pi$
$752$	−20.4199	−0.744637
$753$	−33.7142	−1.22861
$754$	−1.09653	−0.0399333
$755$	−9.18040	−0.334109
$756$	7.65627	0.278456
$757$	3.69354	0.134244	0.0671219	−	0.997745i	$-0.478618\pi$
$757$	3.69354	0.134244	0.0671219	+	0.997745i	$0.478618\pi$
$758$	25.9336	0.941950
$759$	85.6072	3.10734
$760$	−6.03830	−0.219032
$761$	−9.01049	−0.326630	−0.163315	−	0.986574i	$-0.552219\pi$
$761$	−9.01049	−0.326630	−0.163315	+	0.986574i	$0.552219\pi$
$762$	3.85988	0.139829
$763$	−2.23491	−0.0809090
$764$	2.63657	0.0953878
$765$	11.5063	0.416012
$766$	−7.58883	−0.274196
$767$	3.24006	0.116992
$768$	−37.6897	−1.36001
$769$	30.5552	1.10185	0.550925	−	0.834555i	$-0.314275\pi$
$769$	30.5552	1.10185	0.550925	+	0.834555i	$0.314275\pi$
$770$	33.4569	1.20570
$771$	7.32233	0.263707
$772$	−27.7110	−0.997341
$773$	18.9702	0.682311	0.341155	−	0.940007i	$-0.389182\pi$
$773$	18.9702	0.682311	0.341155	+	0.940007i	$0.389182\pi$
$774$	6.21070	0.223239
$775$	3.36970	0.121043
$776$	9.71708	0.348823
$777$	−1.87934	−0.0674208
$778$	28.6313	1.02648
$779$	33.4565	1.19870
$780$	2.13585	0.0764758
$781$	85.2909	3.05195
$782$	−107.520	−3.84491
$783$	11.1852	0.399725
$784$	−4.57667	−0.163453
$785$	−30.1535	−1.07622
$786$	4.25352	0.151718
$787$	16.3949	0.584416	0.292208	−	0.956355i	$-0.405610\pi$
$787$	16.3949	0.584416	0.292208	+	0.956355i	$0.405610\pi$
$788$	31.4266	1.11953
$789$	24.5642	0.874510
$790$	24.0516	0.855716
$791$	−15.1755	−0.539579
$792$	2.14904	0.0763630
$793$	−2.54027	−0.0902078
$794$	−60.3268	−2.14092
$795$	−21.4752	−0.761647
$796$	10.5054	0.372354
$797$	45.9029	1.62596	0.812982	−	0.582289i	$-0.197843\pi$
$797$	45.9029	1.62596	0.812982	+	0.582289i	$0.197843\pi$
$798$	11.2275	0.397451
$799$	−33.3619	−1.18026
$800$	24.9676	0.882739
$801$	−0.191795	−0.00677675
$802$	0.443726	0.0156685
$803$	66.8670	2.35969
$804$	49.2675	1.73753
$805$	21.7728	0.767389
$806$	−0.454721	−0.0160169
$807$	28.5092	1.00357
$808$	−5.01884	−0.176562
$809$	19.3756	0.681211	0.340605	−	0.940206i	$-0.389368\pi$
$809$	19.3756	0.681211	0.340605	+	0.940206i	$0.389368\pi$
$810$	−57.0053	−2.00296
$811$	−47.1999	−1.65741	−0.828706	−	0.559684i	$-0.810922\pi$
$811$	−47.1999	−1.65741	−0.828706	+	0.559684i	$0.810922\pi$
$812$	3.98040	0.139685
$813$	24.9205	0.873999
$814$	−11.5646	−0.405340
$815$	71.4249	2.50191
$816$	−64.3134	−2.25142
$817$	−19.1081	−0.668508
$818$	−41.6675	−1.45687
$819$	0.126589	0.00442337
$820$	−51.0965	−1.78437
$821$	45.0153	1.57104	0.785522	−	0.618834i	$-0.212395\pi$
$821$	45.0153	1.57104	0.785522	+	0.618834i	$0.212395\pi$
$822$	−12.0366	−0.419826
$823$	−44.5362	−1.55244	−0.776218	−	0.630465i	$-0.782864\pi$
$823$	−44.5362	−1.55244	−0.776218	+	0.630465i	$0.782864\pi$
$824$	−7.13729	−0.248639
$825$	−38.3304	−1.33449
$826$	−26.0121	−0.905078
$827$	−18.5926	−0.646529	−0.323265	−	0.946309i	$-0.604780\pi$
$827$	−18.5926	−0.646529	−0.323265	+	0.946309i	$0.604780\pi$
$828$	−6.60761	−0.229630
$829$	−11.8242	−0.410671	−0.205336	−	0.978692i	$-0.565829\pi$
$829$	−11.8242	−0.410671	−0.205336	+	0.978692i	$0.565829\pi$
$830$	64.7313	2.24686
$831$	−45.0409	−1.56245
$832$	−1.19081	−0.0412841
$833$	−7.47734	−0.259074
$834$	−49.8689	−1.72682
$835$	54.6433	1.89101
$836$	31.2388	1.08042
$837$	4.63838	0.160326
$838$	15.8668	0.548110
$839$	−31.2012	−1.07719	−0.538593	−	0.842566i	$-0.681044\pi$
$839$	−31.2012	−1.07719	−0.538593	+	0.842566i	$0.681044\pi$
$840$	3.62930	0.125223
$841$	−23.1850	−0.799482
$842$	19.9764	0.688433
$843$	−36.1420	−1.24480
$844$	−43.9364	−1.51235
$845$	37.4457	1.28817
$846$	−4.53443	−0.155897
$847$	25.6348	0.880822
$848$	18.0771	0.620769
$849$	−29.7513	−1.02106
$850$	48.1419	1.65125
$851$	−7.52590	−0.257985
$852$	−43.7131	−1.49758
$853$	48.5458	1.66218	0.831088	−	0.556140i	$-0.187718\pi$
$853$	48.5458	1.66218	0.831088	+	0.556140i	$0.187718\pi$
$854$	20.3941	0.697871
$855$	−4.81156	−0.164552
$856$	2.97934	0.101832
$857$	18.4778	0.631189	0.315594	−	0.948894i	$-0.397796\pi$
$857$	18.4778	0.631189	0.315594	+	0.948894i	$0.397796\pi$
$858$	5.17245	0.176585
$859$	−42.9543	−1.46558	−0.732791	−	0.680454i	$-0.761783\pi$
$859$	−42.9543	−1.46558	−0.732791	+	0.680454i	$0.761783\pi$
$860$	29.1828	0.995127
$861$	−20.1090	−0.685312
$862$	22.2984	0.759488
$863$	46.9779	1.59915	0.799573	−	0.600569i	$-0.205059\pi$
$863$	46.9779	1.59915	0.799573	+	0.600569i	$0.205059\pi$
$864$	34.3678	1.16922
$865$	9.09984	0.309404
$866$	−28.2626	−0.960404
$867$	−73.1260	−2.48349
$868$	1.65063	0.0560262
$869$	26.3361	0.893390
$870$	−25.0507	−0.849298
$871$	−3.77977	−0.128073
$872$	−1.49184	−0.0505202
$873$	7.74296	0.262059
$874$	44.9613	1.52084
$875$	4.71652	0.159447
$876$	−34.2705	−1.15789
$877$	29.6534	1.00132	0.500662	−	0.865643i	$-0.333090\pi$
$877$	29.6534	1.00132	0.500662	+	0.865643i	$0.333090\pi$
$878$	44.8503	1.51363
$879$	−45.0598	−1.51983
$880$	80.1405	2.70154
$881$	18.5125	0.623700	0.311850	−	0.950131i	$-0.399051\pi$
$881$	18.5125	0.623700	0.311850	+	0.950131i	$0.399051\pi$
$882$	−1.01629	−0.0342204
$883$	38.1777	1.28478	0.642391	−	0.766377i	$-0.277943\pi$
$883$	38.1777	1.28478	0.642391	+	0.766377i	$0.277943\pi$
$884$	−2.93737	−0.0987945
$885$	74.0204	2.48817
$886$	−7.22868	−0.242852
$887$	−35.3724	−1.18769	−0.593844	−	0.804580i	$-0.702390\pi$
$887$	−35.3724	−1.18769	−0.593844	+	0.804580i	$0.702390\pi$
$888$	−1.25449	−0.0420980
$889$	1.07494	0.0360524
$890$	−1.99316	−0.0668109
$891$	−62.4199	−2.09115
$892$	7.49478	0.250944
$893$	13.9508	0.466846
$894$	8.24926	0.275896
$895$	9.04279	0.302267
$896$	−5.25868	−0.175680
$897$	3.36608	0.112390
$898$	−70.1033	−2.33938
$899$	2.41144	0.0804259
$900$	2.95854	0.0986180
$901$	29.5342	0.983926
$902$	−123.742	−4.12015
$903$	11.4849	0.382193
$904$	−10.1299	−0.336917
$905$	−4.27554	−0.142124
$906$	11.3945	0.378557
$907$	15.6259	0.518851	0.259426	−	0.965763i	$-0.416467\pi$
$907$	15.6259	0.518851	0.259426	+	0.965763i	$0.416467\pi$
$908$	−23.8505	−0.791508
$909$	−3.99921	−0.132645
$910$	1.31553	0.0436093
$911$	6.48738	0.214936	0.107468	−	0.994209i	$-0.465726\pi$
$911$	6.48738	0.214936	0.107468	+	0.994209i	$0.465726\pi$
$912$	26.8937	0.890539
$913$	70.8798	2.34578
$914$	44.5011	1.47197
$915$	−58.0336	−1.91853
$916$	−6.26812	−0.207105
$917$	1.18457	0.0391179
$918$	66.2670	2.18714
$919$	47.7466	1.57501	0.787507	−	0.616305i	$-0.211371\pi$
$919$	47.7466	1.57501	0.787507	+	0.616305i	$0.211371\pi$
$920$	14.5337	0.479163
$921$	26.5160	0.873732
$922$	26.7063	0.879524
$923$	3.35364	0.110386
$924$	−18.7760	−0.617684
$925$	3.36970	0.110795
$926$	72.0201	2.36673
$927$	−5.68728	−0.186795
$928$	17.8674	0.586526
$929$	29.5664	0.970043	0.485022	−	0.874502i	$-0.338812\pi$
$929$	29.5664	0.970043	0.485022	+	0.874502i	$0.338812\pi$
$930$	−10.3883	−0.340645
$931$	3.12677	0.102476
$932$	22.4542	0.735512
$933$	24.1174	0.789567
$934$	45.9585	1.50381
$935$	130.933	4.28196
$936$	0.0845005	0.00276198
$937$	12.5491	0.409961	0.204980	−	0.978766i	$-0.434287\pi$
$937$	12.5491	0.409961	0.204980	+	0.978766i	$0.434287\pi$
$938$	30.3451	0.990803
$939$	−43.1778	−1.40905
$940$	−21.3064	−0.694937
$941$	−31.5826	−1.02956	−0.514781	−	0.857322i	$-0.672127\pi$
$941$	−31.5826	−1.02956	−0.514781	+	0.857322i	$0.672127\pi$
$942$	37.4258	1.21940
$943$	−80.5274	−2.62233
$944$	−62.3077	−2.02794
$945$	−13.4190	−0.436521
$946$	70.6729	2.29777
$947$	36.7760	1.19506	0.597530	−	0.801847i	$-0.296149\pi$
$947$	36.7760	1.19506	0.597530	+	0.801847i	$0.296149\pi$
$948$	−13.4977	−0.438385
$949$	2.62921	0.0853478
$950$	−20.1313	−0.653145
$951$	32.1893	1.04381
$952$	−4.99126	−0.161768
$953$	−45.7384	−1.48161	−0.740806	−	0.671719i	$-0.765556\pi$
$953$	−45.7384	−1.48161	−0.740806	+	0.671719i	$0.765556\pi$
$954$	4.01418	0.129964
$955$	−4.62108	−0.149535
$956$	1.01927	0.0329656
$957$	−27.4301	−0.886689
$958$	44.9127	1.45106
$959$	−3.35209	−0.108245
$960$	−27.2046	−0.878026
$961$	1.00000	0.0322581
$962$	−0.454721	−0.0146608
$963$	2.37405	0.0765028
$964$	−18.0298	−0.580700
$965$	48.5687	1.56348
$966$	−27.0239	−0.869479
$967$	41.3663	1.33025	0.665126	−	0.746731i	$-0.268378\pi$
$967$	41.3663	1.33025	0.665126	+	0.746731i	$0.268378\pi$
$968$	17.1117	0.549992
$969$	43.9387	1.41151
$970$	80.4658	2.58360
$971$	54.9858	1.76458	0.882290	−	0.470707i	$-0.156001\pi$
$971$	54.9858	1.76458	0.882290	+	0.470707i	$0.156001\pi$
$972$	9.02249	0.289396
$973$	−13.8880	−0.445230
$974$	−41.4899	−1.32942
$975$	−1.50715	−0.0482675
$976$	48.8506	1.56367
$977$	−51.0329	−1.63269	−0.816343	−	0.577567i	$-0.804002\pi$
$977$	−51.0329	−1.63269	−0.816343	+	0.577567i	$0.804002\pi$
$978$	−88.6510	−2.83475
$979$	−2.18248	−0.0697523
$980$	−4.77536	−0.152543
$981$	−1.18876	−0.0379542
$982$	−73.2792	−2.33843
$983$	−26.8469	−0.856283	−0.428142	−	0.903712i	$-0.640832\pi$
$983$	−26.8469	−0.856283	−0.428142	+	0.903712i	$0.640832\pi$
$984$	−13.4231	−0.427913
$985$	−55.0810	−1.75503
$986$	34.4514	1.09716
$987$	−8.38509	−0.266900
$988$	1.22831	0.0390777
$989$	45.9918	1.46245
$990$	17.7959	0.565592
$991$	−5.56936	−0.176916	−0.0884582	−	0.996080i	$-0.528194\pi$
$991$	−5.56936	−0.176916	−0.0884582	+	0.996080i	$0.528194\pi$
$992$	7.40945	0.235250
$993$	−10.6120	−0.336761
$994$	−26.9240	−0.853978
$995$	−18.4127	−0.583721
$996$	−36.3271	−1.15107
$997$	55.8329	1.76825	0.884123	−	0.467254i	$-0.154757\pi$
$997$	55.8329	1.76825	0.884123	+	0.467254i	$0.154757\pi$
$998$	10.3899	0.328886
$999$	4.63838	0.146752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.15	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.15	✓	70	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.91066 q^{2} -1.87934 q^{3} +1.65063 q^{4} -2.89304 q^{5} +3.59078 q^{6} +1.00000 q^{7} +0.667519 q^{8} +0.531906 q^{9} +O(q^{10})\)	\(q-1.91066 q^{2} -1.87934 q^{3} +1.65063 q^{4} -2.89304 q^{5} +3.59078 q^{6} +1.00000 q^{7} +0.667519 q^{8} +0.531906 q^{9} +5.52763 q^{10} +6.05267 q^{11} -3.10210 q^{12} +0.237991 q^{13} -1.91066 q^{14} +5.43700 q^{15} -4.57667 q^{16} -7.47734 q^{17} -1.01629 q^{18} +3.12677 q^{19} -4.77536 q^{20} -1.87934 q^{21} -11.5646 q^{22} -7.52590 q^{23} -1.25449 q^{24} +3.36970 q^{25} -0.454721 q^{26} +4.63838 q^{27} +1.65063 q^{28} +2.41144 q^{29} -10.3883 q^{30} +1.00000 q^{31} +7.40945 q^{32} -11.3750 q^{33} +14.2867 q^{34} -2.89304 q^{35} +0.877982 q^{36} +1.00000 q^{37} -5.97420 q^{38} -0.447265 q^{39} -1.93116 q^{40} +10.7000 q^{41} +3.59078 q^{42} -6.11113 q^{43} +9.99075 q^{44} -1.53883 q^{45} +14.3795 q^{46} +4.46173 q^{47} +8.60111 q^{48} +1.00000 q^{49} -6.43837 q^{50} +14.0524 q^{51} +0.392836 q^{52} -3.94983 q^{53} -8.86238 q^{54} -17.5106 q^{55} +0.667519 q^{56} -5.87625 q^{57} -4.60744 q^{58} +13.6142 q^{59} +8.97451 q^{60} -10.6738 q^{61} -1.91066 q^{62} +0.531906 q^{63} -5.00361 q^{64} -0.688519 q^{65} +21.7338 q^{66} -15.8820 q^{67} -12.3424 q^{68} +14.1437 q^{69} +5.52763 q^{70} +14.0914 q^{71} +0.355057 q^{72} +11.0475 q^{73} -1.91066 q^{74} -6.33281 q^{75} +5.16115 q^{76} +6.05267 q^{77} +0.854574 q^{78} +4.35115 q^{79} +13.2405 q^{80} -10.3128 q^{81} -20.4442 q^{82} +11.7105 q^{83} -3.10210 q^{84} +21.6323 q^{85} +11.6763 q^{86} -4.53190 q^{87} +4.04027 q^{88} -0.360581 q^{89} +2.94018 q^{90} +0.237991 q^{91} -12.4225 q^{92} -1.87934 q^{93} -8.52487 q^{94} -9.04588 q^{95} -13.9248 q^{96} +14.5570 q^{97} -1.91066 q^{98} +3.21945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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