LMFDB - Embedded newform 8027.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77862 q^{2} +1.96044 q^{3} +5.72072 q^{4} -1.21161 q^{5} -5.44733 q^{6} +1.22758 q^{7} -10.3385 q^{8} +0.843341 q^{9} +O(q^{10})$	\(q-2.77862 q^{2} +1.96044 q^{3} +5.72072 q^{4} -1.21161 q^{5} -5.44733 q^{6} +1.22758 q^{7} -10.3385 q^{8} +0.843341 q^{9} +3.36659 q^{10} +3.35372 q^{11} +11.2152 q^{12} +0.751744 q^{13} -3.41097 q^{14} -2.37529 q^{15} +17.2852 q^{16} +1.77465 q^{17} -2.34332 q^{18} -7.47908 q^{19} -6.93126 q^{20} +2.40660 q^{21} -9.31872 q^{22} -1.00000 q^{23} -20.2680 q^{24} -3.53201 q^{25} -2.08881 q^{26} -4.22801 q^{27} +7.02263 q^{28} +4.36311 q^{29} +6.60002 q^{30} -4.76051 q^{31} -27.3521 q^{32} +6.57479 q^{33} -4.93108 q^{34} -1.48734 q^{35} +4.82452 q^{36} +8.53185 q^{37} +20.7815 q^{38} +1.47375 q^{39} +12.5262 q^{40} +8.02573 q^{41} -6.68702 q^{42} -4.87555 q^{43} +19.1857 q^{44} -1.02180 q^{45} +2.77862 q^{46} +2.96683 q^{47} +33.8867 q^{48} -5.49305 q^{49} +9.81410 q^{50} +3.47911 q^{51} +4.30052 q^{52} +2.50512 q^{53} +11.7480 q^{54} -4.06339 q^{55} -12.6913 q^{56} -14.6623 q^{57} -12.1234 q^{58} -13.6556 q^{59} -13.5884 q^{60} -2.11592 q^{61} +13.2276 q^{62} +1.03527 q^{63} +41.4305 q^{64} -0.910818 q^{65} -18.2688 q^{66} -2.57166 q^{67} +10.1523 q^{68} -1.96044 q^{69} +4.13275 q^{70} +4.37449 q^{71} -8.71885 q^{72} -12.0282 q^{73} -23.7067 q^{74} -6.92431 q^{75} -42.7857 q^{76} +4.11696 q^{77} -4.09500 q^{78} -9.96762 q^{79} -20.9429 q^{80} -10.8188 q^{81} -22.3004 q^{82} +12.0098 q^{83} +13.7675 q^{84} -2.15018 q^{85} +13.5473 q^{86} +8.55363 q^{87} -34.6723 q^{88} -8.39684 q^{89} +2.83919 q^{90} +0.922824 q^{91} -5.72072 q^{92} -9.33272 q^{93} -8.24369 q^{94} +9.06170 q^{95} -53.6222 q^{96} -5.34106 q^{97} +15.2631 q^{98} +2.82833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.77862	−1.96478	−0.982390	−	0.186842i	$-0.940175\pi$
$2$	−2.77862	−1.96478	−0.982390	+	0.186842i	$0.940175\pi$
$3$	1.96044	1.13186	0.565931	−	0.824452i	$-0.308517\pi$
$3$	1.96044	1.13186	0.565931	+	0.824452i	$0.308517\pi$
$4$	5.72072	2.86036
$5$	−1.21161	−0.541847	−0.270924	−	0.962601i	$-0.587329\pi$
$5$	−1.21161	−0.541847	−0.270924	+	0.962601i	$0.587329\pi$
$6$	−5.44733	−2.22386
$7$	1.22758	0.463981	0.231990	−	0.972718i	$-0.425476\pi$
$7$	1.22758	0.463981	0.231990	+	0.972718i	$0.425476\pi$
$8$	−10.3385	−3.65520
$9$	0.843341	0.281114
$10$	3.36659	1.06461
$11$	3.35372	1.01119	0.505593	−	0.862772i	$-0.331274\pi$
$11$	3.35372	1.01119	0.505593	+	0.862772i	$0.331274\pi$
$12$	11.2152	3.23754
$13$	0.751744	0.208496	0.104248	−	0.994551i	$-0.466756\pi$
$13$	0.751744	0.208496	0.104248	+	0.994551i	$0.466756\pi$
$14$	−3.41097	−0.911620
$15$	−2.37529	−0.613297
$16$	17.2852	4.32130
$17$	1.77465	0.430416	0.215208	−	0.976568i	$-0.430957\pi$
$17$	1.77465	0.430416	0.215208	+	0.976568i	$0.430957\pi$
$18$	−2.34332	−0.552326
$19$	−7.47908	−1.71582	−0.857909	−	0.513802i	$-0.828237\pi$
$19$	−7.47908	−1.71582	−0.857909	+	0.513802i	$0.828237\pi$
$20$	−6.93126	−1.54988
$21$	2.40660	0.525163
$22$	−9.31872	−1.98676
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−20.2680	−4.13718
$25$	−3.53201	−0.706402
$26$	−2.08881	−0.409649
$27$	−4.22801	−0.813681
$28$	7.02263	1.32715
$29$	4.36311	0.810209	0.405104	−	0.914270i	$-0.367235\pi$
$29$	4.36311	0.810209	0.405104	+	0.914270i	$0.367235\pi$
$30$	6.60002	1.20499
$31$	−4.76051	−0.855013	−0.427507	−	0.904012i	$-0.640608\pi$
$31$	−4.76051	−0.855013	−0.427507	+	0.904012i	$0.640608\pi$
$32$	−27.3521	−4.83521
$33$	6.57479	1.14452
$34$	−4.93108	−0.845673
$35$	−1.48734	−0.251407
$36$	4.82452	0.804086
$37$	8.53185	1.40263	0.701314	−	0.712853i	$-0.252597\pi$
$37$	8.53185	1.40263	0.701314	+	0.712853i	$0.252597\pi$
$38$	20.7815	3.37120
$39$	1.47375	0.235989
$40$	12.5262	1.98056
$41$	8.02573	1.25341	0.626704	−	0.779257i	$-0.284403\pi$
$41$	8.02573	1.25341	0.626704	+	0.779257i	$0.284403\pi$
$42$	−6.68702	−1.03183
$43$	−4.87555	−0.743514	−0.371757	−	0.928330i	$-0.621245\pi$
$43$	−4.87555	−0.743514	−0.371757	+	0.928330i	$0.621245\pi$
$44$	19.1857	2.89235
$45$	−1.02180	−0.152321
$46$	2.77862	0.409685
$47$	2.96683	0.432756	0.216378	−	0.976310i	$-0.430576\pi$
$47$	2.96683	0.432756	0.216378	+	0.976310i	$0.430576\pi$
$48$	33.8867	4.89112
$49$	−5.49305	−0.784722
$50$	9.81410	1.38792
$51$	3.47911	0.487172
$52$	4.30052	0.596375
$53$	2.50512	0.344105	0.172053	−	0.985088i	$-0.444960\pi$
$53$	2.50512	0.344105	0.172053	+	0.985088i	$0.444960\pi$
$54$	11.7480	1.59870
$55$	−4.06339	−0.547908
$56$	−12.6913	−1.69594
$57$	−14.6623	−1.94207
$58$	−12.1234	−1.59188
$59$	−13.6556	−1.77781	−0.888903	−	0.458096i	$-0.848532\pi$
$59$	−13.6556	−1.77781	−0.888903	+	0.458096i	$0.848532\pi$
$60$	−13.5884	−1.75425
$61$	−2.11592	−0.270915	−0.135458	−	0.990783i	$-0.543250\pi$
$61$	−2.11592	−0.270915	−0.135458	+	0.990783i	$0.543250\pi$
$62$	13.2276	1.67991
$63$	1.03527	0.130431
$64$	41.4305	5.17881
$65$	−0.910818	−0.112973
$66$	−18.2688	−2.24874
$67$	−2.57166	−0.314178	−0.157089	−	0.987584i	$-0.550211\pi$
$67$	−2.57166	−0.314178	−0.157089	+	0.987584i	$0.550211\pi$
$68$	10.1523	1.23115
$69$	−1.96044	−0.236010
$70$	4.13275	0.493959
$71$	4.37449	0.519157	0.259578	−	0.965722i	$-0.416416\pi$
$71$	4.37449	0.519157	0.259578	+	0.965722i	$0.416416\pi$
$72$	−8.71885	−1.02753
$73$	−12.0282	−1.40779	−0.703896	−	0.710303i	$-0.748558\pi$
$73$	−12.0282	−1.40779	−0.703896	+	0.710303i	$0.748558\pi$
$74$	−23.7067	−2.75585
$75$	−6.92431	−0.799550
$76$	−42.7857	−4.90786
$77$	4.11696	0.469171
$78$	−4.09500	−0.463667
$79$	−9.96762	−1.12145	−0.560723	−	0.828004i	$-0.689477\pi$
$79$	−9.96762	−1.12145	−0.560723	+	0.828004i	$0.689477\pi$
$80$	−20.9429	−2.34148
$81$	−10.8188	−1.20209
$82$	−22.3004	−2.46267
$83$	12.0098	1.31825	0.659125	−	0.752033i	$-0.270927\pi$
$83$	12.0098	1.31825	0.659125	+	0.752033i	$0.270927\pi$
$84$	13.7675	1.50215
$85$	−2.15018	−0.233220
$86$	13.5473	1.46084
$87$	8.55363	0.917045
$88$	−34.6723	−3.69608
$89$	−8.39684	−0.890063	−0.445032	−	0.895515i	$-0.646808\pi$
$89$	−8.39684	−0.890063	−0.445032	+	0.895515i	$0.646808\pi$
$90$	2.83919	0.299276
$91$	0.922824	0.0967383
$92$	−5.72072	−0.596426
$93$	−9.33272	−0.967758
$94$	−8.24369	−0.850271
$95$	9.06170	0.929711
$96$	−53.6222	−5.47279
$97$	−5.34106	−0.542303	−0.271151	−	0.962537i	$-0.587404\pi$
$97$	−5.34106	−0.542303	−0.271151	+	0.962537i	$0.587404\pi$
$98$	15.2631	1.54181
$99$	2.82833	0.284258
$100$	−20.2056	−2.02056
$101$	15.5335	1.54564	0.772820	−	0.634625i	$-0.218845\pi$
$101$	15.5335	1.54564	0.772820	+	0.634625i	$0.218845\pi$
$102$	−9.66711	−0.957186
$103$	7.41904	0.731020	0.365510	−	0.930807i	$-0.380895\pi$
$103$	7.41904	0.731020	0.365510	+	0.930807i	$0.380895\pi$
$104$	−7.77188	−0.762095
$105$	−2.91585	−0.284558
$106$	−6.96078	−0.676091
$107$	−5.05696	−0.488875	−0.244437	−	0.969665i	$-0.578603\pi$
$107$	−5.05696	−0.488875	−0.244437	+	0.969665i	$0.578603\pi$
$108$	−24.1873	−2.32742
$109$	−12.4347	−1.19103	−0.595515	−	0.803344i	$-0.703052\pi$
$109$	−12.4347	−1.19103	−0.595515	+	0.803344i	$0.703052\pi$
$110$	11.2906	1.07652
$111$	16.7262	1.58758
$112$	21.2189	2.00500
$113$	18.0009	1.69338	0.846690	−	0.532087i	$-0.178592\pi$
$113$	18.0009	1.69338	0.846690	+	0.532087i	$0.178592\pi$
$114$	40.7410	3.81574
$115$	1.21161	0.112983
$116$	24.9601	2.31749
$117$	0.633977	0.0586112
$118$	37.9437	3.49300
$119$	2.17852	0.199705
$120$	24.5568	2.24172
$121$	0.247457	0.0224960
$122$	5.87932	0.532289
$123$	15.7340	1.41869
$124$	−27.2336	−2.44565
$125$	10.3374	0.924609
$126$	−2.87661	−0.256269
$127$	−5.60775	−0.497607	−0.248804	−	0.968554i	$-0.580037\pi$
$127$	−5.60775	−0.497607	−0.248804	+	0.968554i	$0.580037\pi$
$128$	−60.4155	−5.34002
$129$	−9.55824	−0.841556
$130$	2.53082	0.221967
$131$	−12.1847	−1.06458	−0.532292	−	0.846561i	$-0.678669\pi$
$131$	−12.1847	−1.06458	−0.532292	+	0.846561i	$0.678669\pi$
$132$	37.6125	3.27375
$133$	−9.18115	−0.796106
$134$	7.14565	0.617290
$135$	5.12269	0.440891
$136$	−18.3472	−1.57326
$137$	−22.5881	−1.92983	−0.964914	−	0.262565i	$-0.915432\pi$
$137$	−22.5881	−1.92983	−0.964914	+	0.262565i	$0.915432\pi$
$138$	5.44733	0.463707
$139$	−4.29549	−0.364339	−0.182170	−	0.983267i	$-0.558312\pi$
$139$	−4.29549	−0.364339	−0.182170	+	0.983267i	$0.558312\pi$
$140$	−8.50867	−0.719113
$141$	5.81630	0.489821
$142$	−12.1550	−1.02003
$143$	2.52114	0.210828
$144$	14.5773	1.21478
$145$	−5.28637	−0.439009
$146$	33.4217	2.76600
$147$	−10.7688	−0.888198
$148$	48.8083	4.01202
$149$	0.351990	0.0288362	0.0144181	−	0.999896i	$-0.495410\pi$
$149$	0.351990	0.0288362	0.0144181	+	0.999896i	$0.495410\pi$
$150$	19.2400	1.57094
$151$	23.4316	1.90684	0.953420	−	0.301646i	$-0.0975360\pi$
$151$	23.4316	1.90684	0.953420	+	0.301646i	$0.0975360\pi$
$152$	77.3221	6.27165
$153$	1.49664	0.120996
$154$	−11.4394	−0.921817
$155$	5.76787	0.463286
$156$	8.43092	0.675014
$157$	3.32873	0.265661	0.132831	−	0.991139i	$-0.457593\pi$
$157$	3.32873	0.265661	0.132831	+	0.991139i	$0.457593\pi$
$158$	27.6962	2.20339
$159$	4.91116	0.389480
$160$	33.1399	2.61994
$161$	−1.22758	−0.0967467
$162$	30.0613	2.36184
$163$	−10.9979	−0.861420	−0.430710	−	0.902490i	$-0.641737\pi$
$163$	−10.9979	−0.861420	−0.430710	+	0.902490i	$0.641737\pi$
$164$	45.9130	3.58520
$165$	−7.96606	−0.620157
$166$	−33.3707	−2.59007
$167$	−13.6340	−1.05503	−0.527517	−	0.849545i	$-0.676877\pi$
$167$	−13.6340	−1.05503	−0.527517	+	0.849545i	$0.676877\pi$
$168$	−24.8805	−1.91957
$169$	−12.4349	−0.956529
$170$	5.97453	0.458226
$171$	−6.30741	−0.482340
$172$	−27.8916	−2.12672
$173$	2.41901	0.183914	0.0919568	−	0.995763i	$-0.470688\pi$
$173$	2.41901	0.183914	0.0919568	+	0.995763i	$0.470688\pi$
$174$	−23.7673	−1.80179
$175$	−4.33582	−0.327757
$176$	57.9698	4.36964
$177$	−26.7710	−2.01223
$178$	23.3316	1.74878
$179$	14.3942	1.07587	0.537937	−	0.842985i	$-0.319204\pi$
$179$	14.3942	1.07587	0.537937	+	0.842985i	$0.319204\pi$
$180$	−5.84542	−0.435692
$181$	−5.71217	−0.424582	−0.212291	−	0.977206i	$-0.568093\pi$
$181$	−5.71217	−0.424582	−0.212291	+	0.977206i	$0.568093\pi$
$182$	−2.56418	−0.190069
$183$	−4.14814	−0.306639
$184$	10.3385	0.762162
$185$	−10.3372	−0.760009
$186$	25.9321	1.90143
$187$	5.95169	0.435231
$188$	16.9724	1.23784
$189$	−5.19021	−0.377532
$190$	−25.1790	−1.82668
$191$	−7.62000	−0.551364	−0.275682	−	0.961249i	$-0.588904\pi$
$191$	−7.62000	−0.551364	−0.275682	+	0.961249i	$0.588904\pi$
$192$	81.2222	5.86171
$193$	−13.0578	−0.939918	−0.469959	−	0.882688i	$-0.655731\pi$
$193$	−13.0578	−0.939918	−0.469959	+	0.882688i	$0.655731\pi$
$194$	14.8408	1.06551
$195$	−1.78561	−0.127870
$196$	−31.4242	−2.24459
$197$	−6.28274	−0.447627	−0.223813	−	0.974632i	$-0.571851\pi$
$197$	−6.28274	−0.447627	−0.223813	+	0.974632i	$0.571851\pi$
$198$	−7.85885	−0.558504
$199$	14.9089	1.05687	0.528433	−	0.848975i	$-0.322780\pi$
$199$	14.9089	1.05687	0.528433	+	0.848975i	$0.322780\pi$
$200$	36.5155	2.58204
$201$	−5.04159	−0.355606
$202$	−43.1617	−3.03684
$203$	5.35605	0.375921
$204$	19.9030	1.39349
$205$	−9.72403	−0.679156
$206$	−20.6147	−1.43629
$207$	−0.843341	−0.0586162
$208$	12.9940	0.900975
$209$	−25.0827	−1.73501
$210$	8.10203	0.559094
$211$	0.869340	0.0598478	0.0299239	−	0.999552i	$-0.490474\pi$
$211$	0.869340	0.0598478	0.0299239	+	0.999552i	$0.490474\pi$
$212$	14.3311	0.984265
$213$	8.57594	0.587614
$214$	14.0514	0.960531
$215$	5.90725	0.402871
$216$	43.7111	2.97416
$217$	−5.84390	−0.396710
$218$	34.5513	2.34011
$219$	−23.5806	−1.59343
$220$	−23.2455	−1.56721
$221$	1.33408	0.0897402
$222$	−46.4758	−3.11925
$223$	−25.8713	−1.73247	−0.866236	−	0.499636i	$-0.833467\pi$
$223$	−25.8713	−1.73247	−0.866236	+	0.499636i	$0.833467\pi$
$224$	−33.5768	−2.24344
$225$	−2.97869	−0.198579
$226$	−50.0176	−3.32712
$227$	−16.6452	−1.10478	−0.552390	−	0.833586i	$-0.686284\pi$
$227$	−16.6452	−1.10478	−0.552390	+	0.833586i	$0.686284\pi$
$228$	−83.8790	−5.55502
$229$	15.0741	0.996125	0.498063	−	0.867141i	$-0.334045\pi$
$229$	15.0741	0.996125	0.498063	+	0.867141i	$0.334045\pi$
$230$	−3.36659	−0.221987
$231$	8.07106	0.531037
$232$	−45.1078	−2.96147
$233$	−6.81762	−0.446637	−0.223319	−	0.974746i	$-0.571689\pi$
$233$	−6.81762	−0.446637	−0.223319	+	0.974746i	$0.571689\pi$
$234$	−1.76158	−0.115158
$235$	−3.59463	−0.234488
$236$	−78.1198	−5.08516
$237$	−19.5410	−1.26932
$238$	−6.05329	−0.392376
$239$	18.3554	1.18731	0.593657	−	0.804718i	$-0.297683\pi$
$239$	18.3554	1.18731	0.593657	+	0.804718i	$0.297683\pi$
$240$	−41.0573	−2.65024
$241$	−1.50493	−0.0969412	−0.0484706	−	0.998825i	$-0.515435\pi$
$241$	−1.50493	−0.0969412	−0.0484706	+	0.998825i	$0.515435\pi$
$242$	−0.687587	−0.0441998
$243$	−8.52562	−0.546919
$244$	−12.1046	−0.774915
$245$	6.65542	0.425199
$246$	−43.7188	−2.78741
$247$	−5.62235	−0.357742
$248$	49.2164	3.12524
$249$	23.5446	1.49208
$250$	−28.7238	−1.81665
$251$	0.332157	0.0209655	0.0104828	−	0.999945i	$-0.496663\pi$
$251$	0.332157	0.0209655	0.0104828	+	0.999945i	$0.496663\pi$
$252$	5.92247	0.373081
$253$	−3.35372	−0.210847
$254$	15.5818	0.977688
$255$	−4.21531	−0.263973
$256$	85.0105	5.31316
$257$	−25.8017	−1.60946	−0.804732	−	0.593638i	$-0.797691\pi$
$257$	−25.8017	−1.60946	−0.804732	+	0.593638i	$0.797691\pi$
$258$	26.5587	1.65347
$259$	10.4735	0.650792
$260$	−5.21054	−0.323144
$261$	3.67959	0.227761
$262$	33.8567	2.09167
$263$	−15.3217	−0.944775	−0.472387	−	0.881391i	$-0.656608\pi$
$263$	−15.3217	−0.944775	−0.472387	+	0.881391i	$0.656608\pi$
$264$	−67.9732	−4.18346
$265$	−3.03523	−0.186452
$266$	25.5109	1.56417
$267$	−16.4615	−1.00743
$268$	−14.7117	−0.898661
$269$	−1.78202	−0.108652	−0.0543259	−	0.998523i	$-0.517301\pi$
$269$	−1.78202	−0.108652	−0.0543259	+	0.998523i	$0.517301\pi$
$270$	−14.2340	−0.866253
$271$	18.6887	1.13526	0.567629	−	0.823284i	$-0.307861\pi$
$271$	18.6887	1.13526	0.567629	+	0.823284i	$0.307861\pi$
$272$	30.6752	1.85996
$273$	1.80915	0.109494
$274$	62.7636	3.79169
$275$	−11.8454	−0.714303
$276$	−11.2152	−0.675073
$277$	23.9583	1.43952	0.719758	−	0.694225i	$-0.244253\pi$
$277$	23.9583	1.43952	0.719758	+	0.694225i	$0.244253\pi$
$278$	11.9355	0.715846
$279$	−4.01473	−0.240356
$280$	15.3768	0.918941
$281$	−18.5278	−1.10527	−0.552637	−	0.833422i	$-0.686379\pi$
$281$	−18.5278	−1.10527	−0.552637	+	0.833422i	$0.686379\pi$
$282$	−16.1613	−0.962390
$283$	30.9969	1.84258	0.921289	−	0.388879i	$-0.127138\pi$
$283$	30.9969	1.84258	0.921289	+	0.388879i	$0.127138\pi$
$284$	25.0252	1.48497
$285$	17.7650	1.05231
$286$	−7.00529	−0.414231
$287$	9.85221	0.581558
$288$	−23.0671	−1.35924
$289$	−13.8506	−0.814742
$290$	14.6888	0.862557
$291$	−10.4709	−0.613812
$292$	−68.8099	−4.02679
$293$	−30.6901	−1.79294	−0.896468	−	0.443108i	$-0.853876\pi$
$293$	−30.6901	−1.79294	−0.896468	+	0.443108i	$0.853876\pi$
$294$	29.9225	1.74511
$295$	16.5452	0.963299
$296$	−88.2062	−5.12688
$297$	−14.1796	−0.822782
$298$	−0.978047	−0.0566568
$299$	−0.751744	−0.0434745
$300$	−39.6120	−2.28700
$301$	−5.98511	−0.344976
$302$	−65.1076	−3.74652
$303$	30.4525	1.74945
$304$	−129.277	−7.41456
$305$	2.56366	0.146795
$306$	−4.15858	−0.237730
$307$	10.7294	0.612359	0.306180	−	0.951974i	$-0.400949\pi$
$307$	10.7294	0.612359	0.306180	+	0.951974i	$0.400949\pi$
$308$	23.5519	1.34200
$309$	14.5446	0.827414
$310$	−16.0267	−0.910256
$311$	7.57764	0.429688	0.214844	−	0.976648i	$-0.431076\pi$
$311$	7.57764	0.429688	0.214844	+	0.976648i	$0.431076\pi$
$312$	−15.2363	−0.862587
$313$	−5.16772	−0.292097	−0.146048	−	0.989277i	$-0.546656\pi$
$313$	−5.16772	−0.292097	−0.146048	+	0.989277i	$0.546656\pi$
$314$	−9.24926	−0.521966
$315$	−1.25434	−0.0706738
$316$	−57.0220	−3.20774
$317$	−24.3805	−1.36934	−0.684672	−	0.728852i	$-0.740054\pi$
$317$	−24.3805	−1.36934	−0.684672	+	0.728852i	$0.740054\pi$
$318$	−13.6462	−0.765242
$319$	14.6327	0.819271
$320$	−50.1975	−2.80613
$321$	−9.91388	−0.553339
$322$	3.41097	0.190086
$323$	−13.2728	−0.738516
$324$	−61.8913	−3.43841
$325$	−2.65517	−0.147282
$326$	30.5589	1.69250
$327$	−24.3776	−1.34808
$328$	−82.9737	−4.58146
$329$	3.64201	0.200791
$330$	22.1346	1.21847
$331$	−5.58177	−0.306802	−0.153401	−	0.988164i	$-0.549023\pi$
$331$	−5.58177	−0.306802	−0.153401	+	0.988164i	$0.549023\pi$
$332$	68.7049	3.77067
$333$	7.19526	0.394298
$334$	37.8838	2.07291
$335$	3.11584	0.170236
$336$	41.5985	2.26939
$337$	16.3804	0.892298	0.446149	−	0.894959i	$-0.352795\pi$
$337$	16.3804	0.892298	0.446149	+	0.894959i	$0.352795\pi$
$338$	34.5518	1.87937
$339$	35.2897	1.91667
$340$	−12.3006	−0.667093
$341$	−15.9654	−0.864577
$342$	17.5259	0.947691
$343$	−15.3362	−0.828077
$344$	50.4057	2.71769
$345$	2.37529	0.127881
$346$	−6.72150	−0.361350
$347$	−7.53163	−0.404319	−0.202160	−	0.979353i	$-0.564796\pi$
$347$	−7.53163	−0.404319	−0.202160	+	0.979353i	$0.564796\pi$
$348$	48.9329	2.62308
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	12.0476	0.643970
$351$	−3.17838	−0.169649
$352$	−91.7312	−4.88929
$353$	11.7355	0.624618	0.312309	−	0.949981i	$-0.398898\pi$
$353$	11.7355	0.624618	0.312309	+	0.949981i	$0.398898\pi$
$354$	74.3864	3.95359
$355$	−5.30016	−0.281303
$356$	−48.0360	−2.54590
$357$	4.27087	0.226039
$358$	−39.9961	−2.11386
$359$	18.2413	0.962737	0.481368	−	0.876518i	$-0.340140\pi$
$359$	18.2413	0.962737	0.481368	+	0.876518i	$0.340140\pi$
$360$	10.5638	0.556762
$361$	36.9366	1.94403
$362$	15.8719	0.834211
$363$	0.485125	0.0254624
$364$	5.27922	0.276706
$365$	14.5734	0.762808
$366$	11.5261	0.602478
$367$	−27.3202	−1.42610	−0.713051	−	0.701112i	$-0.752687\pi$
$367$	−27.3202	−1.42610	−0.713051	+	0.701112i	$0.752687\pi$
$368$	−17.2852	−0.901053
$369$	6.76843	0.352350
$370$	28.7233	1.49325
$371$	3.07523	0.159658
$372$	−53.3899	−2.76814
$373$	−10.7036	−0.554209	−0.277104	−	0.960840i	$-0.589375\pi$
$373$	−10.7036	−0.554209	−0.277104	+	0.960840i	$0.589375\pi$
$374$	−16.5375	−0.855133
$375$	20.2660	1.04653
$376$	−30.6724	−1.58181
$377$	3.27994	0.168926
$378$	14.4216	0.741768
$379$	5.28721	0.271586	0.135793	−	0.990737i	$-0.456642\pi$
$379$	5.28721	0.271586	0.135793	+	0.990737i	$0.456642\pi$
$380$	51.8394	2.65931
$381$	−10.9937	−0.563223
$382$	21.1731	1.08331
$383$	35.3059	1.80405	0.902023	−	0.431687i	$-0.142082\pi$
$383$	35.3059	1.80405	0.902023	+	0.431687i	$0.142082\pi$
$384$	−118.441	−6.04418
$385$	−4.98813	−0.254219
$386$	36.2825	1.84673
$387$	−4.11175	−0.209012
$388$	−30.5547	−1.55118
$389$	−33.6796	−1.70762	−0.853812	−	0.520582i	$-0.825715\pi$
$389$	−33.6796	−1.70762	−0.853812	+	0.520582i	$0.825715\pi$
$390$	4.96152	0.251237
$391$	−1.77465	−0.0897480
$392$	56.7897	2.86831
$393$	−23.8875	−1.20496
$394$	17.4573	0.879488
$395$	12.0768	0.607652
$396$	16.1801	0.813080
$397$	−9.42976	−0.473266	−0.236633	−	0.971599i	$-0.576044\pi$
$397$	−9.42976	−0.473266	−0.236633	+	0.971599i	$0.576044\pi$
$398$	−41.4262	−2.07651
$399$	−17.9991	−0.901083
$400$	−61.0515	−3.05257
$401$	9.61399	0.480100	0.240050	−	0.970761i	$-0.422836\pi$
$401$	9.61399	0.480100	0.240050	+	0.970761i	$0.422836\pi$
$402$	14.0086	0.698688
$403$	−3.57869	−0.178267
$404$	88.8628	4.42109
$405$	13.1081	0.651348
$406$	−14.8824	−0.738603
$407$	28.6135	1.41832
$408$	−35.9686	−1.78071
$409$	−1.56008	−0.0771411	−0.0385705	−	0.999256i	$-0.512280\pi$
$409$	−1.56008	−0.0771411	−0.0385705	+	0.999256i	$0.512280\pi$
$410$	27.0194	1.33439
$411$	−44.2826	−2.18430
$412$	42.4423	2.09098
$413$	−16.7633	−0.824868
$414$	2.34332	0.115168
$415$	−14.5512	−0.714290
$416$	−20.5617	−1.00812
$417$	−8.42108	−0.412382
$418$	69.6954	3.40891
$419$	27.6729	1.35191	0.675956	−	0.736942i	$-0.263731\pi$
$419$	27.6729	1.35191	0.675956	+	0.736942i	$0.263731\pi$
$420$	−16.6808	−0.813938
$421$	−6.99567	−0.340948	−0.170474	−	0.985362i	$-0.554530\pi$
$421$	−6.99567	−0.340948	−0.170474	+	0.985362i	$0.554530\pi$
$422$	−2.41556	−0.117588
$423$	2.50205	0.121654
$424$	−25.8991	−1.25777
$425$	−6.26809	−0.304047
$426$	−23.8293	−1.15453
$427$	−2.59745	−0.125699
$428$	−28.9294	−1.39836
$429$	4.94256	0.238629
$430$	−16.4140	−0.791553
$431$	−16.6100	−0.800075	−0.400038	−	0.916499i	$-0.631003\pi$
$431$	−16.6100	−0.800075	−0.400038	+	0.916499i	$0.631003\pi$
$432$	−73.0820	−3.51616
$433$	−1.96779	−0.0945659	−0.0472830	−	0.998882i	$-0.515056\pi$
$433$	−1.96779	−0.0945659	−0.0472830	+	0.998882i	$0.515056\pi$
$434$	16.2380	0.779447
$435$	−10.3636	−0.496898
$436$	−71.1355	−3.40677
$437$	7.47908	0.357773
$438$	65.5215	3.13074
$439$	1.78978	0.0854214	0.0427107	−	0.999087i	$-0.486401\pi$
$439$	1.78978	0.0854214	0.0427107	+	0.999087i	$0.486401\pi$
$440$	42.0092	2.00271
$441$	−4.63252	−0.220596
$442$	−3.70691	−0.176320
$443$	23.5255	1.11773	0.558866	−	0.829258i	$-0.311237\pi$
$443$	23.5255	1.11773	0.558866	+	0.829258i	$0.311237\pi$
$444$	95.6860	4.54106
$445$	10.1737	0.482278
$446$	71.8865	3.40393
$447$	0.690058	0.0326386
$448$	50.8592	2.40287
$449$	7.19485	0.339546	0.169773	−	0.985483i	$-0.445697\pi$
$449$	7.19485	0.339546	0.169773	+	0.985483i	$0.445697\pi$
$450$	8.27664	0.390164
$451$	26.9161	1.26743
$452$	102.978	4.84368
$453$	45.9364	2.15828
$454$	46.2507	2.17065
$455$	−1.11810	−0.0524174
$456$	151.586	7.09865
$457$	−1.22393	−0.0572529	−0.0286264	−	0.999590i	$-0.509113\pi$
$457$	−1.22393	−0.0572529	−0.0286264	+	0.999590i	$0.509113\pi$
$458$	−41.8852	−1.95717
$459$	−7.50325	−0.350222
$460$	6.93126	0.323172
$461$	7.76376	0.361594	0.180797	−	0.983520i	$-0.442132\pi$
$461$	7.76376	0.361594	0.180797	+	0.983520i	$0.442132\pi$
$462$	−22.4264	−1.04337
$463$	−26.7567	−1.24349	−0.621744	−	0.783221i	$-0.713575\pi$
$463$	−26.7567	−1.24349	−0.621744	+	0.783221i	$0.713575\pi$
$464$	75.4172	3.50116
$465$	11.3076	0.524377
$466$	18.9436	0.877544
$467$	−34.3950	−1.59161	−0.795805	−	0.605553i	$-0.792952\pi$
$467$	−34.3950	−1.59161	−0.795805	+	0.605553i	$0.792952\pi$
$468$	3.62680	0.167649
$469$	−3.15691	−0.145772
$470$	9.98811	0.460717
$471$	6.52578	0.300692
$472$	141.178	6.49823
$473$	−16.3512	−0.751830
$474$	54.2969	2.49394
$475$	26.4162	1.21206
$476$	12.4627	0.571228
$477$	2.11267	0.0967327
$478$	−51.0028	−2.33281
$479$	−38.2450	−1.74746	−0.873730	−	0.486411i	$-0.838306\pi$
$479$	−38.2450	−1.74746	−0.873730	+	0.486411i	$0.838306\pi$
$480$	64.9690	2.96541
$481$	6.41377	0.292443
$482$	4.18163	0.190468
$483$	−2.40660	−0.109504
$484$	1.41563	0.0643468
$485$	6.47127	0.293845
$486$	23.6894	1.07458
$487$	−16.7711	−0.759972	−0.379986	−	0.924992i	$-0.624071\pi$
$487$	−16.7711	−0.759972	−0.379986	+	0.924992i	$0.624071\pi$
$488$	21.8753	0.990249
$489$	−21.5607	−0.975010
$490$	−18.4929	−0.835423
$491$	42.1945	1.90421	0.952105	−	0.305770i	$-0.0989139\pi$
$491$	42.1945	1.90421	0.952105	+	0.305770i	$0.0989139\pi$
$492$	90.0098	4.05796
$493$	7.74300	0.348727
$494$	15.6224	0.702884
$495$	−3.42683	−0.154024
$496$	−82.2864	−3.69477
$497$	5.37003	0.240879
$498$	−65.4215	−2.93161
$499$	−23.2728	−1.04183	−0.520916	−	0.853608i	$-0.674410\pi$
$499$	−23.2728	−1.04183	−0.520916	+	0.853608i	$0.674410\pi$
$500$	59.1376	2.64471
$501$	−26.7288	−1.19415
$502$	−0.922937	−0.0411927
$503$	−11.7710	−0.524842	−0.262421	−	0.964953i	$-0.584521\pi$
$503$	−11.7710	−0.524842	−0.262421	+	0.964953i	$0.584521\pi$
$504$	−10.7031	−0.476752
$505$	−18.8205	−0.837501
$506$	9.31872	0.414267
$507$	−24.3779	−1.08266
$508$	−32.0803	−1.42334
$509$	−25.6840	−1.13842	−0.569212	−	0.822191i	$-0.692752\pi$
$509$	−25.6840	−1.13842	−0.569212	+	0.822191i	$0.692752\pi$
$510$	11.7127	0.518649
$511$	−14.7655	−0.653189
$512$	−115.381	−5.09916
$513$	31.6216	1.39613
$514$	71.6930	3.16224
$515$	−8.98896	−0.396101
$516$	−54.6800	−2.40715
$517$	9.94992	0.437597
$518$	−29.1019	−1.27866
$519$	4.74233	0.208165
$520$	9.41646	0.412939
$521$	3.91295	0.171430	0.0857148	−	0.996320i	$-0.472683\pi$
$521$	3.91295	0.171430	0.0857148	+	0.996320i	$0.472683\pi$
$522$	−10.2242	−0.447500
$523$	22.1270	0.967545	0.483773	−	0.875194i	$-0.339266\pi$
$523$	22.1270	0.967545	0.483773	+	0.875194i	$0.339266\pi$
$524$	−69.7054	−3.04509
$525$	−8.50012	−0.370976
$526$	42.5731	1.85627
$527$	−8.44825	−0.368012
$528$	113.646	4.94583
$529$	1.00000	0.0434783
$530$	8.43373	0.366338
$531$	−11.5163	−0.499765
$532$	−52.5228	−2.27715
$533$	6.03330	0.261331
$534$	45.7403	1.97938
$535$	6.12705	0.264895
$536$	26.5870	1.14838
$537$	28.2191	1.21774
$538$	4.95156	0.213477
$539$	−18.4222	−0.793499
$540$	29.3055	1.26111
$541$	2.37087	0.101932	0.0509659	−	0.998700i	$-0.483770\pi$
$541$	2.37087	0.101932	0.0509659	+	0.998700i	$0.483770\pi$
$542$	−51.9288	−2.23053
$543$	−11.1984	−0.480569
$544$	−48.5404	−2.08115
$545$	15.0660	0.645356
$546$	−5.02692	−0.215133
$547$	−42.3787	−1.81198	−0.905990	−	0.423299i	$-0.860872\pi$
$547$	−42.3787	−1.81198	−0.905990	+	0.423299i	$0.860872\pi$
$548$	−129.220	−5.52001
$549$	−1.78444	−0.0761580
$550$	32.9138	1.40345
$551$	−32.6320	−1.39017
$552$	20.2680	0.862662
$553$	−12.2360	−0.520329
$554$	−66.5710	−2.82833
$555$	−20.2656	−0.860226
$556$	−24.5733	−1.04214
$557$	−18.9898	−0.804624	−0.402312	−	0.915503i	$-0.631793\pi$
$557$	−18.9898	−0.804624	−0.402312	+	0.915503i	$0.631793\pi$
$558$	11.1554	0.472246
$559$	−3.66516	−0.155020
$560$	−25.7090	−1.08640
$561$	11.6680	0.492622
$562$	51.4816	2.17162
$563$	43.3532	1.82712	0.913560	−	0.406705i	$-0.133322\pi$
$563$	43.3532	1.82712	0.913560	+	0.406705i	$0.133322\pi$
$564$	33.2734	1.40106
$565$	−21.8100	−0.917553
$566$	−86.1287	−3.62026
$567$	−13.2809	−0.557746
$568$	−45.2255	−1.89762
$569$	33.8433	1.41879	0.709393	−	0.704814i	$-0.248969\pi$
$569$	33.8433	1.41879	0.709393	+	0.704814i	$0.248969\pi$
$570$	−49.3620	−2.06755
$571$	5.64097	0.236067	0.118034	−	0.993010i	$-0.462341\pi$
$571$	5.64097	0.236067	0.118034	+	0.993010i	$0.462341\pi$
$572$	14.4227	0.603045
$573$	−14.9386	−0.624068
$574$	−27.3755	−1.14263
$575$	3.53201	0.147295
$576$	34.9400	1.45584
$577$	23.8689	0.993674	0.496837	−	0.867844i	$-0.334495\pi$
$577$	23.8689	0.993674	0.496837	+	0.867844i	$0.334495\pi$
$578$	38.4856	1.60079
$579$	−25.5990	−1.06386
$580$	−30.2419	−1.25572
$581$	14.7430	0.611643
$582$	29.0945	1.20601
$583$	8.40149	0.347954
$584$	124.353	5.14576
$585$	−0.768130	−0.0317583
$586$	85.2762	3.52273
$587$	11.2374	0.463816	0.231908	−	0.972738i	$-0.425503\pi$
$587$	11.2374	0.463816	0.231908	+	0.972738i	$0.425503\pi$
$588$	−61.6054	−2.54056
$589$	35.6042	1.46705
$590$	−45.9728	−1.89267
$591$	−12.3170	−0.506652
$592$	147.475	6.06117
$593$	−40.2829	−1.65422	−0.827111	−	0.562039i	$-0.810017\pi$
$593$	−40.2829	−1.65422	−0.827111	+	0.562039i	$0.810017\pi$
$594$	39.3996	1.61659
$595$	−2.63951	−0.108210
$596$	2.01364	0.0824819
$597$	29.2281	1.19623
$598$	2.08881	0.0854178
$599$	−12.7177	−0.519630	−0.259815	−	0.965658i	$-0.583662\pi$
$599$	−12.7177	−0.519630	−0.259815	+	0.965658i	$0.583662\pi$
$600$	71.5867	2.92251
$601$	2.25444	0.0919606	0.0459803	−	0.998942i	$-0.485359\pi$
$601$	2.25444	0.0919606	0.0459803	+	0.998942i	$0.485359\pi$
$602$	16.6303	0.677802
$603$	−2.16878	−0.0883196
$604$	134.046	5.45425
$605$	−0.299820	−0.0121894
$606$	−84.6160	−3.43729
$607$	−9.52231	−0.386499	−0.193249	−	0.981150i	$-0.561903\pi$
$607$	−9.52231	−0.386499	−0.193249	+	0.981150i	$0.561903\pi$
$608$	204.568	8.29633
$609$	10.5002	0.425491
$610$	−7.12343	−0.288419
$611$	2.23030	0.0902281
$612$	8.56184	0.346092
$613$	4.62804	0.186925	0.0934624	−	0.995623i	$-0.470207\pi$
$613$	4.62804	0.186925	0.0934624	+	0.995623i	$0.470207\pi$
$614$	−29.8129	−1.20315
$615$	−19.0634	−0.768711
$616$	−42.5630	−1.71491
$617$	24.9571	1.00473	0.502367	−	0.864655i	$-0.332463\pi$
$617$	24.9571	1.00473	0.502367	+	0.864655i	$0.332463\pi$
$618$	−40.4139	−1.62569
$619$	16.4772	0.662275	0.331137	−	0.943583i	$-0.392568\pi$
$619$	16.4772	0.662275	0.331137	+	0.943583i	$0.392568\pi$
$620$	32.9964	1.32517
$621$	4.22801	0.169664
$622$	−21.0554	−0.844243
$623$	−10.3078	−0.412972
$624$	25.4741	1.01978
$625$	5.13513	0.205405
$626$	14.3591	0.573906
$627$	−49.1733	−1.96379
$628$	19.0427	0.759887
$629$	15.1411	0.603714
$630$	3.48532	0.138859
$631$	−14.3964	−0.573111	−0.286555	−	0.958064i	$-0.592510\pi$
$631$	−14.3964	−0.573111	−0.286555	+	0.958064i	$0.592510\pi$
$632$	103.050	4.09910
$633$	1.70429	0.0677395
$634$	67.7440	2.69046
$635$	6.79438	0.269627
$636$	28.0953	1.11405
$637$	−4.12937	−0.163612
$638$	−40.6586	−1.60969
$639$	3.68919	0.145942
$640$	73.1998	2.89348
$641$	2.79339	0.110332	0.0551661	−	0.998477i	$-0.482431\pi$
$641$	2.79339	0.110332	0.0551661	+	0.998477i	$0.482431\pi$
$642$	27.5469	1.08719
$643$	−32.5770	−1.28471	−0.642356	−	0.766406i	$-0.722043\pi$
$643$	−32.5770	−1.28471	−0.642356	+	0.766406i	$0.722043\pi$
$644$	−7.02263	−0.276730
$645$	11.5808	0.455995
$646$	36.8799	1.45102
$647$	18.4979	0.727226	0.363613	−	0.931550i	$-0.381543\pi$
$647$	18.4979	0.727226	0.363613	+	0.931550i	$0.381543\pi$
$648$	111.850	4.39387
$649$	−45.7970	−1.79769
$650$	7.37770	0.289377
$651$	−11.4566	−0.449021
$652$	−62.9158	−2.46397
$653$	−16.4953	−0.645510	−0.322755	−	0.946483i	$-0.604609\pi$
$653$	−16.4953	−0.645510	−0.322755	+	0.946483i	$0.604609\pi$
$654$	67.7360	2.64869
$655$	14.7631	0.576842
$656$	138.726	5.41636
$657$	−10.1439	−0.395750
$658$	−10.1198	−0.394509
$659$	8.09343	0.315275	0.157638	−	0.987497i	$-0.449612\pi$
$659$	8.09343	0.315275	0.157638	+	0.987497i	$0.449612\pi$
$660$	−45.5716	−1.77387
$661$	−41.7332	−1.62323	−0.811616	−	0.584191i	$-0.801412\pi$
$661$	−41.7332	−1.62323	−0.811616	+	0.584191i	$0.801412\pi$
$662$	15.5096	0.602798
$663$	2.61540	0.101574
$664$	−124.163	−4.81847
$665$	11.1239	0.431368
$666$	−19.9929	−0.774708
$667$	−4.36311	−0.168940
$668$	−77.9965	−3.01777
$669$	−50.7193	−1.96092
$670$	−8.65772	−0.334477
$671$	−7.09620	−0.273946
$672$	−65.8254	−2.53927
$673$	−5.19940	−0.200422	−0.100211	−	0.994966i	$-0.531952\pi$
$673$	−5.19940	−0.200422	−0.100211	+	0.994966i	$0.531952\pi$
$674$	−45.5149	−1.75317
$675$	14.9334	0.574786
$676$	−71.1365	−2.73602
$677$	8.87269	0.341005	0.170503	−	0.985357i	$-0.445461\pi$
$677$	8.87269	0.341005	0.170503	+	0.985357i	$0.445461\pi$
$678$	−98.0566	−3.76584
$679$	−6.55657	−0.251618
$680$	22.2296	0.852465
$681$	−32.6320	−1.25046
$682$	44.3619	1.69870
$683$	16.1686	0.618675	0.309338	−	0.950952i	$-0.399893\pi$
$683$	16.1686	0.618675	0.309338	+	0.950952i	$0.399893\pi$
$684$	−36.0829	−1.37967
$685$	27.3679	1.04567
$686$	42.6134	1.62699
$687$	29.5520	1.12748
$688$	−84.2748	−3.21295
$689$	1.88321	0.0717447
$690$	−6.60002	−0.251258
$691$	37.4121	1.42322	0.711611	−	0.702573i	$-0.247966\pi$
$691$	37.4121	1.42322	0.711611	+	0.702573i	$0.247966\pi$
$692$	13.8385	0.526059
$693$	3.47200	0.131890
$694$	20.9275	0.794398
$695$	5.20445	0.197416
$696$	−88.4314	−3.35198
$697$	14.2429	0.539488
$698$	2.77862	0.105172
$699$	−13.3656	−0.505532
$700$	−24.8040	−0.937503
$701$	32.9610	1.24492	0.622459	−	0.782652i	$-0.286134\pi$
$701$	32.9610	1.24492	0.622459	+	0.782652i	$0.286134\pi$
$702$	8.83151	0.333324
$703$	−63.8103	−2.40665
$704$	138.946	5.23674
$705$	−7.04707	−0.265408
$706$	−32.6085	−1.22724
$707$	19.0686	0.717147
$708$	−153.149	−5.75571
$709$	22.5645	0.847429	0.423715	−	0.905796i	$-0.360726\pi$
$709$	22.5645	0.847429	0.423715	+	0.905796i	$0.360726\pi$
$710$	14.7271	0.552699
$711$	−8.40610	−0.315253
$712$	86.8104	3.25336
$713$	4.76051	0.178283
$714$	−11.8671	−0.444116
$715$	−3.05463	−0.114237
$716$	82.3453	3.07739
$717$	35.9848	1.34388
$718$	−50.6855	−1.89157
$719$	−48.5640	−1.81113	−0.905566	−	0.424206i	$-0.860553\pi$
$719$	−48.5640	−1.81113	−0.905566	+	0.424206i	$0.860553\pi$
$720$	−17.6620	−0.658223
$721$	9.10745	0.339179
$722$	−102.633	−3.81959
$723$	−2.95034	−0.109724
$724$	−32.6777	−1.21446
$725$	−15.4105	−0.572333
$726$	−1.34798	−0.0500281
$727$	15.1762	0.562853	0.281426	−	0.959583i	$-0.409192\pi$
$727$	15.1762	0.562853	0.281426	+	0.959583i	$0.409192\pi$
$728$	−9.54058	−0.353598
$729$	15.7424	0.583052
$730$	−40.4940	−1.49875
$731$	−8.65240	−0.320021
$732$	−23.7303	−0.877098
$733$	9.35450	0.345516	0.172758	−	0.984964i	$-0.444732\pi$
$733$	9.35450	0.345516	0.172758	+	0.984964i	$0.444732\pi$
$734$	75.9123	2.80198
$735$	13.0476	0.481267
$736$	27.3521	1.00821
$737$	−8.62462	−0.317692
$738$	−18.8069	−0.692291
$739$	31.5469	1.16047	0.580236	−	0.814448i	$-0.302960\pi$
$739$	31.5469	1.16047	0.580236	+	0.814448i	$0.302960\pi$
$740$	−59.1365	−2.17390
$741$	−11.0223	−0.404914
$742$	−8.54490	−0.313693
$743$	−14.4373	−0.529654	−0.264827	−	0.964296i	$-0.585315\pi$
$743$	−14.4373	−0.529654	−0.264827	+	0.964296i	$0.585315\pi$
$744$	96.4859	3.53735
$745$	−0.426474	−0.0156248
$746$	29.7411	1.08890
$747$	10.1284	0.370578
$748$	34.0480	1.24492
$749$	−6.20781	−0.226828
$750$	−56.3114	−2.05620
$751$	0.885929	0.0323280	0.0161640	−	0.999869i	$-0.494855\pi$
$751$	0.885929	0.0323280	0.0161640	+	0.999869i	$0.494855\pi$
$752$	51.2822	1.87007
$753$	0.651174	0.0237301
$754$	−9.11370	−0.331902
$755$	−28.3899	−1.03322
$756$	−29.6917	−1.07988
$757$	−49.1000	−1.78457	−0.892285	−	0.451473i	$-0.850899\pi$
$757$	−49.1000	−1.78457	−0.892285	+	0.451473i	$0.850899\pi$
$758$	−14.6911	−0.533606
$759$	−6.57479	−0.238650
$760$	−93.6840	−3.39828
$761$	−13.6327	−0.494183	−0.247092	−	0.968992i	$-0.579475\pi$
$761$	−13.6327	−0.494183	−0.247092	+	0.968992i	$0.579475\pi$
$762$	30.5472	1.10661
$763$	−15.2646	−0.552615
$764$	−43.5919	−1.57710
$765$	−1.81334	−0.0655613
$766$	−98.1016	−3.54455
$767$	−10.2655	−0.370666
$768$	166.658	6.01377
$769$	18.8087	0.678260	0.339130	−	0.940740i	$-0.389867\pi$
$769$	18.8087	0.678260	0.339130	+	0.940740i	$0.389867\pi$
$770$	13.8601	0.499484
$771$	−50.5827	−1.82169
$772$	−74.6998	−2.68850
$773$	−32.4553	−1.16734	−0.583668	−	0.811993i	$-0.698383\pi$
$773$	−32.4553	−1.16734	−0.583668	+	0.811993i	$0.698383\pi$
$774$	11.4250	0.410662
$775$	16.8142	0.603983
$776$	55.2184	1.98222
$777$	20.5327	0.736607
$778$	93.5828	3.35510
$779$	−60.0251	−2.15062
$780$	−10.2150	−0.365754
$781$	14.6708	0.524964
$782$	4.93108	0.176335
$783$	−18.4473	−0.659251
$784$	−94.9485	−3.39102
$785$	−4.03311	−0.143948
$786$	66.3741	2.36749
$787$	43.7274	1.55871	0.779356	−	0.626581i	$-0.215546\pi$
$787$	43.7274	1.55871	0.779356	+	0.626581i	$0.215546\pi$
$788$	−35.9418	−1.28037
$789$	−30.0373	−1.06936
$790$	−33.5569	−1.19390
$791$	22.0975	0.785696
$792$	−29.2406	−1.03902
$793$	−1.59063	−0.0564848
$794$	26.2017	0.929864
$795$	−5.95039	−0.211039
$796$	85.2898	3.02302
$797$	−34.7191	−1.22981	−0.614907	−	0.788599i	$-0.710807\pi$
$797$	−34.7191	−1.22981	−0.614907	+	0.788599i	$0.710807\pi$
$798$	50.0127	1.77043
$799$	5.26509	0.186265
$800$	96.6077	3.41560
$801$	−7.08140	−0.250209
$802$	−26.7136	−0.943291
$803$	−40.3392	−1.42354
$804$	−28.8415	−1.01716
$805$	1.48734	0.0524219
$806$	9.94381	0.350256
$807$	−3.49356	−0.122979
$808$	−160.592	−5.64962
$809$	22.2695	0.782955	0.391477	−	0.920188i	$-0.371964\pi$
$809$	22.2695	0.782955	0.391477	+	0.920188i	$0.371964\pi$
$810$	−36.4225	−1.27976
$811$	−34.0797	−1.19670	−0.598351	−	0.801234i	$-0.704177\pi$
$811$	−34.0797	−1.19670	−0.598351	+	0.801234i	$0.704177\pi$
$812$	30.6405	1.07527
$813$	36.6382	1.28496
$814$	−79.5059	−2.78668
$815$	13.3251	0.466758
$816$	60.1370	2.10522
$817$	36.4646	1.27573
$818$	4.33487	0.151565
$819$	0.778255	0.0271944
$820$	−55.6285	−1.94263
$821$	−50.5657	−1.76476	−0.882378	−	0.470541i	$-0.844059\pi$
$821$	−50.5657	−1.76476	−0.882378	+	0.470541i	$0.844059\pi$
$822$	123.045	4.29167
$823$	−20.8578	−0.727059	−0.363529	−	0.931583i	$-0.618428\pi$
$823$	−20.8578	−0.727059	−0.363529	+	0.931583i	$0.618428\pi$
$824$	−76.7015	−2.67202
$825$	−23.2222	−0.808493
$826$	46.5788	1.62068
$827$	48.3644	1.68179	0.840897	−	0.541195i	$-0.182028\pi$
$827$	48.3644	1.68179	0.840897	+	0.541195i	$0.182028\pi$
$828$	−4.82452	−0.167664
$829$	37.5563	1.30438	0.652191	−	0.758054i	$-0.273850\pi$
$829$	37.5563	1.30438	0.652191	+	0.758054i	$0.273850\pi$
$830$	40.4322	1.40342
$831$	46.9689	1.62933
$832$	31.1451	1.07976
$833$	−9.74826	−0.337757
$834$	23.3990	0.810240
$835$	16.5191	0.571667
$836$	−143.491	−4.96275
$837$	20.1275	0.695708
$838$	−76.8926	−2.65621
$839$	−22.4198	−0.774019	−0.387009	−	0.922076i	$-0.626492\pi$
$839$	−22.4198	−0.774019	−0.387009	+	0.922076i	$0.626492\pi$
$840$	30.1454	1.04012
$841$	−9.96329	−0.343562
$842$	19.4383	0.669888
$843$	−36.3227	−1.25102
$844$	4.97325	0.171186
$845$	15.0662	0.518293
$846$	−6.95224	−0.239023
$847$	0.303772	0.0104377
$848$	43.3016	1.48698
$849$	60.7678	2.08554
$850$	17.4166	0.597385
$851$	−8.53185	−0.292468
$852$	49.0606	1.68079
$853$	2.68614	0.0919717	0.0459858	−	0.998942i	$-0.485357\pi$
$853$	2.68614	0.0919717	0.0459858	+	0.998942i	$0.485357\pi$
$854$	7.21733	0.246972
$855$	7.64210	0.261354
$856$	52.2812	1.78693
$857$	5.32220	0.181803	0.0909015	−	0.995860i	$-0.471025\pi$
$857$	5.32220	0.181803	0.0909015	+	0.995860i	$0.471025\pi$
$858$	−13.7335	−0.468853
$859$	−1.62011	−0.0552774	−0.0276387	−	0.999618i	$-0.508799\pi$
$859$	−1.62011	−0.0552774	−0.0276387	+	0.999618i	$0.508799\pi$
$860$	33.7937	1.15236
$861$	19.3147	0.658243
$862$	46.1528	1.57197
$863$	17.9129	0.609763	0.304882	−	0.952390i	$-0.401383\pi$
$863$	17.9129	0.609763	0.304882	+	0.952390i	$0.401383\pi$
$864$	115.645	3.93431
$865$	−2.93089	−0.0996531
$866$	5.46774	0.185801
$867$	−27.1533	−0.922176
$868$	−33.4313	−1.13473
$869$	−33.4286	−1.13399
$870$	28.7966	0.976296
$871$	−1.93323	−0.0655049
$872$	128.556	4.35345
$873$	−4.50434	−0.152449
$874$	−20.7815	−0.702945
$875$	12.6900	0.429001
$876$	−134.898	−4.55778
$877$	9.47815	0.320054	0.160027	−	0.987113i	$-0.448842\pi$
$877$	9.47815	0.320054	0.160027	+	0.987113i	$0.448842\pi$
$878$	−4.97311	−0.167834
$879$	−60.1663	−2.02936
$880$	−70.2366	−2.36767
$881$	20.5211	0.691375	0.345687	−	0.938350i	$-0.387646\pi$
$881$	20.5211	0.691375	0.345687	+	0.938350i	$0.387646\pi$
$882$	12.8720	0.433423
$883$	−54.1839	−1.82343	−0.911716	−	0.410821i	$-0.865242\pi$
$883$	−54.1839	−1.82343	−0.911716	+	0.410821i	$0.865242\pi$
$884$	7.63192	0.256689
$885$	32.4359	1.09032
$886$	−65.3685	−2.19610
$887$	57.7971	1.94064	0.970319	−	0.241830i	$-0.0777477\pi$
$887$	57.7971	1.94064	0.970319	+	0.241830i	$0.0777477\pi$
$888$	−172.923	−5.80293
$889$	−6.88394	−0.230880
$890$	−28.2688	−0.947571
$891$	−36.2833	−1.21553
$892$	−148.003	−4.95549
$893$	−22.1891	−0.742531
$894$	−1.91741	−0.0641277
$895$	−17.4401	−0.582960
$896$	−74.1647	−2.47767
$897$	−1.47375	−0.0492072
$898$	−19.9918	−0.667133
$899$	−20.7706	−0.692739
$900$	−17.0402	−0.568008
$901$	4.44572	0.148109
$902$	−74.7895	−2.49022
$903$	−11.7335	−0.390466
$904$	−186.101	−6.18964
$905$	6.92090	0.230059
$906$	−127.640	−4.24055
$907$	−16.9019	−0.561218	−0.280609	−	0.959822i	$-0.590536\pi$
$907$	−16.9019	−0.561218	−0.280609	+	0.959822i	$0.590536\pi$
$908$	−95.2225	−3.16007
$909$	13.1000	0.434501
$910$	3.10677	0.102989
$911$	15.3337	0.508028	0.254014	−	0.967201i	$-0.418249\pi$
$911$	15.3337	0.508028	0.254014	+	0.967201i	$0.418249\pi$
$912$	−253.441	−8.39227
$913$	40.2776	1.33300
$914$	3.40082	0.112489
$915$	5.02591	0.166151
$916$	86.2348	2.84928
$917$	−14.9577	−0.493947
$918$	20.8487	0.688108
$919$	−23.8272	−0.785987	−0.392993	−	0.919541i	$-0.628560\pi$
$919$	−23.8272	−0.785987	−0.392993	+	0.919541i	$0.628560\pi$
$920$	−12.5262	−0.412975
$921$	21.0344	0.693107
$922$	−21.5725	−0.710454
$923$	3.28850	0.108242
$924$	46.1723	1.51896
$925$	−30.1346	−0.990818
$926$	74.3466	2.44318
$927$	6.25678	0.205500
$928$	−119.340	−3.91753
$929$	0.809747	0.0265669	0.0132835	−	0.999912i	$-0.495772\pi$
$929$	0.809747	0.0265669	0.0132835	+	0.999912i	$0.495772\pi$
$930$	−31.4195	−1.03028
$931$	41.0830	1.34644
$932$	−39.0017	−1.27754
$933$	14.8555	0.486348
$934$	95.5706	3.12716
$935$	−7.21111	−0.235829
$936$	−6.55434	−0.214235
$937$	51.4516	1.68085	0.840425	−	0.541927i	$-0.182305\pi$
$937$	51.4516	1.68085	0.840425	+	0.541927i	$0.182305\pi$
$938$	8.77184	0.286411
$939$	−10.1310	−0.330614
$940$	−20.5639	−0.670720
$941$	22.3590	0.728882	0.364441	−	0.931226i	$-0.381260\pi$
$941$	22.3590	0.728882	0.364441	+	0.931226i	$0.381260\pi$
$942$	−18.1327	−0.590794
$943$	−8.02573	−0.261354
$944$	−236.039	−7.68243
$945$	6.28849	0.204565
$946$	45.4338	1.47718
$947$	−17.6756	−0.574378	−0.287189	−	0.957874i	$-0.592721\pi$
$947$	−17.6756	−0.574378	−0.287189	+	0.957874i	$0.592721\pi$
$948$	−111.788	−3.63072
$949$	−9.04212	−0.293520
$950$	−73.4004	−2.38142
$951$	−47.7965	−1.54991
$952$	−22.5226	−0.729961
$953$	18.5638	0.601340	0.300670	−	0.953728i	$-0.402790\pi$
$953$	18.5638	0.601340	0.300670	+	0.953728i	$0.402790\pi$
$954$	−5.87031	−0.190058
$955$	9.23244	0.298755
$956$	105.006	3.39615
$957$	28.6865	0.927303
$958$	106.268	3.43338
$959$	−27.7286	−0.895403
$960$	−98.4094	−3.17615
$961$	−8.33753	−0.268953
$962$	−17.8214	−0.574585
$963$	−4.26474	−0.137429
$964$	−8.60930	−0.277287
$965$	15.8209	0.509292
$966$	6.68702	0.215151
$967$	−0.642020	−0.0206460	−0.0103230	−	0.999947i	$-0.503286\pi$
$967$	−0.642020	−0.0206460	−0.0103230	+	0.999947i	$0.503286\pi$
$968$	−2.55832	−0.0822275
$969$	−26.0205	−0.835899
$970$	−17.9812	−0.577341
$971$	−28.6676	−0.919986	−0.459993	−	0.887923i	$-0.652148\pi$
$971$	−28.6676	−0.919986	−0.459993	+	0.887923i	$0.652148\pi$
$972$	−48.7727	−1.56438
$973$	−5.27305	−0.169046
$974$	46.6006	1.49318
$975$	−5.20531	−0.166703
$976$	−36.5740	−1.17071
$977$	−51.0518	−1.63329	−0.816645	−	0.577140i	$-0.804169\pi$
$977$	−51.0518	−1.63329	−0.816645	+	0.577140i	$0.804169\pi$
$978$	59.9090	1.91568
$979$	−28.1607	−0.900019
$980$	38.0738	1.21622
$981$	−10.4867	−0.334815
$982$	−117.242	−3.74135
$983$	−3.94636	−0.125869	−0.0629346	−	0.998018i	$-0.520046\pi$
$983$	−3.94636	−0.125869	−0.0629346	+	0.998018i	$0.520046\pi$
$984$	−162.665	−5.18558
$985$	7.61221	0.242545
$986$	−21.5148	−0.685172
$987$	7.13996	0.227268
$988$	−32.1639	−1.02327
$989$	4.87555	0.155033
$990$	9.52184	0.302624
$991$	−21.7391	−0.690567	−0.345283	−	0.938498i	$-0.612217\pi$
$991$	−21.7391	−0.690567	−0.345283	+	0.938498i	$0.612217\pi$
$992$	130.210	4.13416
$993$	−10.9427	−0.347258
$994$	−14.9213	−0.473274
$995$	−18.0638	−0.572659
$996$	134.692	4.26788
$997$	−42.7586	−1.35418	−0.677090	−	0.735900i	$-0.736759\pi$
$997$	−42.7586	−1.35418	−0.677090	+	0.735900i	$0.736759\pi$
$998$	64.6661	2.04697
$999$	−36.0727	−1.14129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.1	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.1	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77862 q^{2} +1.96044 q^{3} +5.72072 q^{4} -1.21161 q^{5} -5.44733 q^{6} +1.22758 q^{7} -10.3385 q^{8} +0.843341 q^{9} +O(q^{10})\)	\(q-2.77862 q^{2} +1.96044 q^{3} +5.72072 q^{4} -1.21161 q^{5} -5.44733 q^{6} +1.22758 q^{7} -10.3385 q^{8} +0.843341 q^{9} +3.36659 q^{10} +3.35372 q^{11} +11.2152 q^{12} +0.751744 q^{13} -3.41097 q^{14} -2.37529 q^{15} +17.2852 q^{16} +1.77465 q^{17} -2.34332 q^{18} -7.47908 q^{19} -6.93126 q^{20} +2.40660 q^{21} -9.31872 q^{22} -1.00000 q^{23} -20.2680 q^{24} -3.53201 q^{25} -2.08881 q^{26} -4.22801 q^{27} +7.02263 q^{28} +4.36311 q^{29} +6.60002 q^{30} -4.76051 q^{31} -27.3521 q^{32} +6.57479 q^{33} -4.93108 q^{34} -1.48734 q^{35} +4.82452 q^{36} +8.53185 q^{37} +20.7815 q^{38} +1.47375 q^{39} +12.5262 q^{40} +8.02573 q^{41} -6.68702 q^{42} -4.87555 q^{43} +19.1857 q^{44} -1.02180 q^{45} +2.77862 q^{46} +2.96683 q^{47} +33.8867 q^{48} -5.49305 q^{49} +9.81410 q^{50} +3.47911 q^{51} +4.30052 q^{52} +2.50512 q^{53} +11.7480 q^{54} -4.06339 q^{55} -12.6913 q^{56} -14.6623 q^{57} -12.1234 q^{58} -13.6556 q^{59} -13.5884 q^{60} -2.11592 q^{61} +13.2276 q^{62} +1.03527 q^{63} +41.4305 q^{64} -0.910818 q^{65} -18.2688 q^{66} -2.57166 q^{67} +10.1523 q^{68} -1.96044 q^{69} +4.13275 q^{70} +4.37449 q^{71} -8.71885 q^{72} -12.0282 q^{73} -23.7067 q^{74} -6.92431 q^{75} -42.7857 q^{76} +4.11696 q^{77} -4.09500 q^{78} -9.96762 q^{79} -20.9429 q^{80} -10.8188 q^{81} -22.3004 q^{82} +12.0098 q^{83} +13.7675 q^{84} -2.15018 q^{85} +13.5473 q^{86} +8.55363 q^{87} -34.6723 q^{88} -8.39684 q^{89} +2.83919 q^{90} +0.922824 q^{91} -5.72072 q^{92} -9.33272 q^{93} -8.24369 q^{94} +9.06170 q^{95} -53.6222 q^{96} -5.34106 q^{97} +15.2631 q^{98} +2.82833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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