LMFDB - Embedded newform 8027.2.a.e.1.17

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:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.35712 q^{2} +0.851105 q^{3} +3.55600 q^{4} +1.53859 q^{5} -2.00615 q^{6} +0.407410 q^{7} -3.66768 q^{8} -2.27562 q^{9} +O(q^{10})$	\(q-2.35712 q^{2} +0.851105 q^{3} +3.55600 q^{4} +1.53859 q^{5} -2.00615 q^{6} +0.407410 q^{7} -3.66768 q^{8} -2.27562 q^{9} -3.62663 q^{10} -5.12862 q^{11} +3.02653 q^{12} -2.08905 q^{13} -0.960313 q^{14} +1.30950 q^{15} +1.53314 q^{16} -5.38316 q^{17} +5.36390 q^{18} -5.17161 q^{19} +5.47122 q^{20} +0.346749 q^{21} +12.0888 q^{22} -1.00000 q^{23} -3.12158 q^{24} -2.63275 q^{25} +4.92414 q^{26} -4.49011 q^{27} +1.44875 q^{28} +6.92140 q^{29} -3.08664 q^{30} +5.31350 q^{31} +3.72156 q^{32} -4.36499 q^{33} +12.6887 q^{34} +0.626835 q^{35} -8.09211 q^{36} +4.62975 q^{37} +12.1901 q^{38} -1.77800 q^{39} -5.64304 q^{40} +3.47997 q^{41} -0.817327 q^{42} -1.49920 q^{43} -18.2374 q^{44} -3.50124 q^{45} +2.35712 q^{46} +3.13345 q^{47} +1.30486 q^{48} -6.83402 q^{49} +6.20570 q^{50} -4.58164 q^{51} -7.42867 q^{52} +0.524278 q^{53} +10.5837 q^{54} -7.89082 q^{55} -1.49425 q^{56} -4.40159 q^{57} -16.3145 q^{58} -13.8479 q^{59} +4.65658 q^{60} +2.81994 q^{61} -12.5245 q^{62} -0.927110 q^{63} -11.8384 q^{64} -3.21419 q^{65} +10.2888 q^{66} -5.65390 q^{67} -19.1425 q^{68} -0.851105 q^{69} -1.47752 q^{70} -0.182071 q^{71} +8.34624 q^{72} +12.2820 q^{73} -10.9129 q^{74} -2.24075 q^{75} -18.3903 q^{76} -2.08945 q^{77} +4.19096 q^{78} +4.01594 q^{79} +2.35887 q^{80} +3.00531 q^{81} -8.20270 q^{82} -11.2101 q^{83} +1.23304 q^{84} -8.28246 q^{85} +3.53379 q^{86} +5.89084 q^{87} +18.8101 q^{88} +4.20902 q^{89} +8.25283 q^{90} -0.851100 q^{91} -3.55600 q^{92} +4.52235 q^{93} -7.38591 q^{94} -7.95698 q^{95} +3.16744 q^{96} +16.2134 q^{97} +16.1086 q^{98} +11.6708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.35712	−1.66673	−0.833367	−	0.552720i	$-0.813590\pi$
$2$	−2.35712	−1.66673	−0.833367	+	0.552720i	$0.813590\pi$
$3$	0.851105	0.491386	0.245693	−	0.969348i	$-0.420985\pi$
$3$	0.851105	0.491386	0.245693	+	0.969348i	$0.420985\pi$
$4$	3.55600	1.77800
$5$	1.53859	0.688077	0.344038	−	0.938956i	$-0.388205\pi$
$5$	1.53859	0.688077	0.344038	+	0.938956i	$0.388205\pi$
$6$	−2.00615	−0.819009
$7$	0.407410	0.153986	0.0769932	−	0.997032i	$-0.475468\pi$
$7$	0.407410	0.153986	0.0769932	+	0.997032i	$0.475468\pi$
$8$	−3.66768	−1.29672
$9$	−2.27562	−0.758540
$10$	−3.62663	−1.14684
$11$	−5.12862	−1.54634	−0.773168	−	0.634201i	$-0.781329\pi$
$11$	−5.12862	−1.54634	−0.773168	+	0.634201i	$0.781329\pi$
$12$	3.02653	0.873684
$13$	−2.08905	−0.579399	−0.289699	−	0.957118i	$-0.593555\pi$
$13$	−2.08905	−0.579399	−0.289699	+	0.957118i	$0.593555\pi$
$14$	−0.960313	−0.256654
$15$	1.30950	0.338111
$16$	1.53314	0.383285
$17$	−5.38316	−1.30561	−0.652804	−	0.757527i	$-0.726408\pi$
$17$	−5.38316	−1.30561	−0.652804	+	0.757527i	$0.726408\pi$
$18$	5.36390	1.26428
$19$	−5.17161	−1.18645	−0.593225	−	0.805037i	$-0.702145\pi$
$19$	−5.17161	−1.18645	−0.593225	+	0.805037i	$0.702145\pi$
$20$	5.47122	1.22340
$21$	0.346749	0.0756667
$22$	12.0888	2.57733
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.12158	−0.637189
$25$	−2.63275	−0.526550
$26$	4.92414	0.965703
$27$	−4.49011	−0.864121
$28$	1.44875	0.273788
$29$	6.92140	1.28527	0.642636	−	0.766172i	$-0.277841\pi$
$29$	6.92140	1.28527	0.642636	+	0.766172i	$0.277841\pi$
$30$	−3.08664	−0.563541
$31$	5.31350	0.954333	0.477166	−	0.878813i	$-0.341664\pi$
$31$	5.31350	0.954333	0.477166	+	0.878813i	$0.341664\pi$
$32$	3.72156	0.657886
$33$	−4.36499	−0.759848
$34$	12.6887	2.17610
$35$	0.626835	0.105955
$36$	−8.09211	−1.34868
$37$	4.62975	0.761126	0.380563	−	0.924755i	$-0.375730\pi$
$37$	4.62975	0.761126	0.380563	+	0.924755i	$0.375730\pi$
$38$	12.1901	1.97749
$39$	−1.77800	−0.284708
$40$	−5.64304	−0.892242
$41$	3.47997	0.543480	0.271740	−	0.962371i	$-0.412401\pi$
$41$	3.47997	0.543480	0.271740	+	0.962371i	$0.412401\pi$
$42$	−0.817327	−0.126116
$43$	−1.49920	−0.228626	−0.114313	−	0.993445i	$-0.536467\pi$
$43$	−1.49920	−0.228626	−0.114313	+	0.993445i	$0.536467\pi$
$44$	−18.2374	−2.74939
$45$	−3.50124	−0.521934
$46$	2.35712	0.347538
$47$	3.13345	0.457060	0.228530	−	0.973537i	$-0.426608\pi$
$47$	3.13345	0.457060	0.228530	+	0.973537i	$0.426608\pi$
$48$	1.30486	0.188341
$49$	−6.83402	−0.976288
$50$	6.20570	0.877619
$51$	−4.58164	−0.641557
$52$	−7.42867	−1.03017
$53$	0.524278	0.0720152	0.0360076	−	0.999352i	$-0.488536\pi$
$53$	0.524278	0.0720152	0.0360076	+	0.999352i	$0.488536\pi$
$54$	10.5837	1.44026
$55$	−7.89082	−1.06400
$56$	−1.49425	−0.199677
$57$	−4.40159	−0.583004
$58$	−16.3145	−2.14220
$59$	−13.8479	−1.80284	−0.901420	−	0.432945i	$-0.857474\pi$
$59$	−13.8479	−1.80284	−0.901420	+	0.432945i	$0.857474\pi$
$60$	4.65658	0.601162
$61$	2.81994	0.361056	0.180528	−	0.983570i	$-0.442219\pi$
$61$	2.81994	0.361056	0.180528	+	0.983570i	$0.442219\pi$
$62$	−12.5245	−1.59062
$63$	−0.927110	−0.116805
$64$	−11.8384	−1.47980
$65$	−3.21419	−0.398671
$66$	10.2888	1.26646
$67$	−5.65390	−0.690733	−0.345367	−	0.938468i	$-0.612245\pi$
$67$	−5.65390	−0.690733	−0.345367	+	0.938468i	$0.612245\pi$
$68$	−19.1425	−2.32137
$69$	−0.851105	−0.102461
$70$	−1.47752	−0.176598
$71$	−0.182071	−0.0216078	−0.0108039	−	0.999942i	$-0.503439\pi$
$71$	−0.182071	−0.0216078	−0.0108039	+	0.999942i	$0.503439\pi$
$72$	8.34624	0.983613
$73$	12.2820	1.43750	0.718750	−	0.695269i	$-0.244715\pi$
$73$	12.2820	1.43750	0.718750	+	0.695269i	$0.244715\pi$
$74$	−10.9129	−1.26859
$75$	−2.24075	−0.258739
$76$	−18.3903	−2.10951
$77$	−2.08945	−0.238115
$78$	4.19096	0.474533
$79$	4.01594	0.451829	0.225914	−	0.974147i	$-0.427463\pi$
$79$	4.01594	0.451829	0.225914	+	0.974147i	$0.427463\pi$
$80$	2.35887	0.263729
$81$	3.00531	0.333923
$82$	−8.20270	−0.905837
$83$	−11.2101	−1.23047	−0.615233	−	0.788345i	$-0.710938\pi$
$83$	−11.2101	−1.23047	−0.615233	+	0.788345i	$0.710938\pi$
$84$	1.23304	0.134535
$85$	−8.28246	−0.898359
$86$	3.53379	0.381059
$87$	5.89084	0.631564
$88$	18.8101	2.00516
$89$	4.20902	0.446156	0.223078	−	0.974801i	$-0.428390\pi$
$89$	4.20902	0.446156	0.223078	+	0.974801i	$0.428390\pi$
$90$	8.25283	0.869925
$91$	−0.851100	−0.0892195
$92$	−3.55600	−0.370739
$93$	4.52235	0.468945
$94$	−7.38591	−0.761798
$95$	−7.95698	−0.816368
$96$	3.16744	0.323276
$97$	16.2134	1.64622	0.823109	−	0.567883i	$-0.192238\pi$
$97$	16.2134	1.64622	0.823109	+	0.567883i	$0.192238\pi$
$98$	16.1086	1.62721
$99$	11.6708	1.17296
$100$	−9.36206	−0.936206
$101$	10.9272	1.08729	0.543647	−	0.839314i	$-0.317043\pi$
$101$	10.9272	1.08729	0.543647	+	0.839314i	$0.317043\pi$
$102$	10.7995	1.06931
$103$	−9.77543	−0.963202	−0.481601	−	0.876391i	$-0.659945\pi$
$103$	−9.77543	−0.963202	−0.481601	+	0.876391i	$0.659945\pi$
$104$	7.66196	0.751317
$105$	0.533503	0.0520645
$106$	−1.23579	−0.120030
$107$	−4.77935	−0.462038	−0.231019	−	0.972949i	$-0.574206\pi$
$107$	−4.77935	−0.462038	−0.231019	+	0.972949i	$0.574206\pi$
$108$	−15.9668	−1.53641
$109$	−2.52597	−0.241944	−0.120972	−	0.992656i	$-0.538601\pi$
$109$	−2.52597	−0.241944	−0.120972	+	0.992656i	$0.538601\pi$
$110$	18.5996	1.77340
$111$	3.94040	0.374006
$112$	0.624616	0.0590206
$113$	−8.18365	−0.769853	−0.384927	−	0.922947i	$-0.625773\pi$
$113$	−8.18365	−0.769853	−0.384927	+	0.922947i	$0.625773\pi$
$114$	10.3751	0.971713
$115$	−1.53859	−0.143474
$116$	24.6125	2.28521
$117$	4.75389	0.439497
$118$	32.6411	3.00485
$119$	−2.19315	−0.201046
$120$	−4.80282	−0.438435
$121$	15.3027	1.39116
$122$	−6.64693	−0.601785
$123$	2.96182	0.267058
$124$	18.8948	1.69680
$125$	−11.7436	−1.05038
$126$	2.18531	0.194683
$127$	−1.65530	−0.146884	−0.0734422	−	0.997299i	$-0.523398\pi$
$127$	−1.65530	−0.146884	−0.0734422	+	0.997299i	$0.523398\pi$
$128$	20.4615	1.80855
$129$	−1.27598	−0.112344
$130$	7.57621	0.664478
$131$	−1.73616	−0.151689	−0.0758446	−	0.997120i	$-0.524165\pi$
$131$	−1.73616	−0.151689	−0.0758446	+	0.997120i	$0.524165\pi$
$132$	−15.5219	−1.35101
$133$	−2.10697	−0.182697
$134$	13.3269	1.15127
$135$	−6.90842	−0.594582
$136$	19.7437	1.69301
$137$	−1.76653	−0.150925	−0.0754623	−	0.997149i	$-0.524043\pi$
$137$	−1.76653	−0.150925	−0.0754623	+	0.997149i	$0.524043\pi$
$138$	2.00615	0.170775
$139$	1.07210	0.0909342	0.0454671	−	0.998966i	$-0.485522\pi$
$139$	1.07210	0.0909342	0.0454671	+	0.998966i	$0.485522\pi$
$140$	2.22903	0.188387
$141$	2.66689	0.224593
$142$	0.429162	0.0360145
$143$	10.7139	0.895945
$144$	−3.48884	−0.290737
$145$	10.6492	0.884366
$146$	−28.9501	−2.39593
$147$	−5.81647	−0.479734
$148$	16.4634	1.35328
$149$	−19.9538	−1.63468	−0.817340	−	0.576156i	$-0.804552\pi$
$149$	−19.9538	−1.63468	−0.817340	+	0.576156i	$0.804552\pi$
$150$	5.28170	0.431249
$151$	−5.45465	−0.443893	−0.221946	−	0.975059i	$-0.571241\pi$
$151$	−5.45465	−0.443893	−0.221946	+	0.975059i	$0.571241\pi$
$152$	18.9678	1.53849
$153$	12.2500	0.990356
$154$	4.92508	0.396874
$155$	8.17528	0.656654
$156$	−6.32258	−0.506211
$157$	15.5619	1.24198	0.620988	−	0.783820i	$-0.286731\pi$
$157$	15.5619	1.24198	0.620988	+	0.783820i	$0.286731\pi$
$158$	−9.46604	−0.753078
$159$	0.446216	0.0353872
$160$	5.72595	0.452676
$161$	−0.407410	−0.0321084
$162$	−7.08386	−0.556561
$163$	−14.3243	−1.12197	−0.560983	−	0.827827i	$-0.689577\pi$
$163$	−14.3243	−1.12197	−0.560983	+	0.827827i	$0.689577\pi$
$164$	12.3748	0.966308
$165$	−6.71592	−0.522834
$166$	26.4235	2.05086
$167$	8.36141	0.647025	0.323513	−	0.946224i	$-0.395136\pi$
$167$	8.36141	0.647025	0.323513	+	0.946224i	$0.395136\pi$
$168$	−1.27176	−0.0981185
$169$	−8.63587	−0.664297
$170$	19.5227	1.49733
$171$	11.7686	0.899969
$172$	−5.33116	−0.406497
$173$	−9.11427	−0.692945	−0.346473	−	0.938060i	$-0.612621\pi$
$173$	−9.11427	−0.692945	−0.346473	+	0.938060i	$0.612621\pi$
$174$	−13.8854	−1.05265
$175$	−1.07261	−0.0810816
$176$	−7.86288	−0.592687
$177$	−11.7860	−0.885890
$178$	−9.92116	−0.743622
$179$	5.07735	0.379499	0.189749	−	0.981833i	$-0.439232\pi$
$179$	5.07735	0.379499	0.189749	+	0.981833i	$0.439232\pi$
$180$	−12.4504	−0.927999
$181$	23.7916	1.76842	0.884209	−	0.467091i	$-0.154698\pi$
$181$	23.7916	1.76842	0.884209	+	0.467091i	$0.154698\pi$
$182$	2.00614	0.148705
$183$	2.40007	0.177418
$184$	3.66768	0.270385
$185$	7.12327	0.523713
$186$	−10.6597	−0.781607
$187$	27.6082	2.01891
$188$	11.1425	0.812654
$189$	−1.82931	−0.133063
$190$	18.7555	1.36067
$191$	−4.01477	−0.290499	−0.145249	−	0.989395i	$-0.546398\pi$
$191$	−4.01477	−0.290499	−0.145249	+	0.989395i	$0.546398\pi$
$192$	−10.0758	−0.727155
$193$	1.21764	0.0876477	0.0438238	−	0.999039i	$-0.486046\pi$
$193$	1.21764	0.0876477	0.0438238	+	0.999039i	$0.486046\pi$
$194$	−38.2168	−2.74381
$195$	−2.73561	−0.195901
$196$	−24.3018	−1.73584
$197$	8.56426	0.610178	0.305089	−	0.952324i	$-0.401314\pi$
$197$	8.56426	0.610178	0.305089	+	0.952324i	$0.401314\pi$
$198$	−27.5094	−1.95501
$199$	20.2434	1.43502	0.717510	−	0.696548i	$-0.245282\pi$
$199$	20.2434	1.43502	0.717510	+	0.696548i	$0.245282\pi$
$200$	9.65607	0.682788
$201$	−4.81206	−0.339417
$202$	−25.7566	−1.81223
$203$	2.81985	0.197914
$204$	−16.2923	−1.14069
$205$	5.35424	0.373956
$206$	23.0418	1.60540
$207$	2.27562	0.158167
$208$	−3.20281	−0.222075
$209$	26.5232	1.83465
$210$	−1.25753	−0.0867777
$211$	15.4163	1.06130	0.530650	−	0.847591i	$-0.321948\pi$
$211$	15.4163	1.06130	0.530650	+	0.847591i	$0.321948\pi$
$212$	1.86433	0.128043
$213$	−0.154961	−0.0106178
$214$	11.2655	0.770094
$215$	−2.30665	−0.157312
$216$	16.4683	1.12052
$217$	2.16477	0.146954
$218$	5.95400	0.403256
$219$	10.4533	0.706367
$220$	−28.0598	−1.89179
$221$	11.2457	0.756468
$222$	−9.28798	−0.623369
$223$	−8.62974	−0.577890	−0.288945	−	0.957346i	$-0.593305\pi$
$223$	−8.62974	−0.577890	−0.288945	+	0.957346i	$0.593305\pi$
$224$	1.51620	0.101305
$225$	5.99114	0.399409
$226$	19.2898	1.28314
$227$	19.7272	1.30934	0.654670	−	0.755915i	$-0.272808\pi$
$227$	19.7272	1.30934	0.654670	+	0.755915i	$0.272808\pi$
$228$	−15.6520	−1.03658
$229$	27.3336	1.80626	0.903129	−	0.429369i	$-0.141264\pi$
$229$	27.3336	1.80626	0.903129	+	0.429369i	$0.141264\pi$
$230$	3.62663	0.239133
$231$	−1.77834	−0.117006
$232$	−25.3854	−1.66664
$233$	−15.2021	−0.995920	−0.497960	−	0.867200i	$-0.665917\pi$
$233$	−15.2021	−0.995920	−0.497960	+	0.867200i	$0.665917\pi$
$234$	−11.2055	−0.732524
$235$	4.82108	0.314493
$236$	−49.2431	−3.20545
$237$	3.41799	0.222022
$238$	5.16952	0.335090
$239$	−5.42184	−0.350710	−0.175355	−	0.984505i	$-0.556107\pi$
$239$	−5.42184	−0.350710	−0.175355	+	0.984505i	$0.556107\pi$
$240$	2.00764	0.129593
$241$	17.8961	1.15279	0.576393	−	0.817172i	$-0.304460\pi$
$241$	17.8961	1.15279	0.576393	+	0.817172i	$0.304460\pi$
$242$	−36.0703	−2.31869
$243$	16.0282	1.02821
$244$	10.0277	0.641958
$245$	−10.5147	−0.671761
$246$	−6.98136	−0.445115
$247$	10.8038	0.687427
$248$	−19.4882	−1.23750
$249$	−9.54095	−0.604633
$250$	27.6812	1.75071
$251$	20.2443	1.27781	0.638904	−	0.769286i	$-0.279388\pi$
$251$	20.2443	1.27781	0.638904	+	0.769286i	$0.279388\pi$
$252$	−3.29680	−0.207679
$253$	5.12862	0.322433
$254$	3.90174	0.244817
$255$	−7.04925	−0.441441
$256$	−24.5532	−1.53457
$257$	14.8865	0.928595	0.464297	−	0.885679i	$-0.346307\pi$
$257$	14.8865	0.928595	0.464297	+	0.885679i	$0.346307\pi$
$258$	3.00763	0.187247
$259$	1.88620	0.117203
$260$	−11.4296	−0.708837
$261$	−15.7505	−0.974930
$262$	4.09234	0.252826
$263$	3.68107	0.226985	0.113492	−	0.993539i	$-0.463796\pi$
$263$	3.68107	0.226985	0.113492	+	0.993539i	$0.463796\pi$
$264$	16.0094	0.985309
$265$	0.806648	0.0495520
$266$	4.96636	0.304507
$267$	3.58232	0.219234
$268$	−20.1053	−1.22812
$269$	5.61128	0.342126	0.171063	−	0.985260i	$-0.445280\pi$
$269$	5.61128	0.342126	0.171063	+	0.985260i	$0.445280\pi$
$270$	16.2840	0.991010
$271$	2.23959	0.136045	0.0680226	−	0.997684i	$-0.478331\pi$
$271$	2.23959	0.136045	0.0680226	+	0.997684i	$0.478331\pi$
$272$	−8.25313	−0.500420
$273$	−0.724375	−0.0438412
$274$	4.16391	0.251551
$275$	13.5024	0.814224
$276$	−3.02653	−0.182176
$277$	2.61964	0.157399	0.0786995	−	0.996898i	$-0.474923\pi$
$277$	2.61964	0.157399	0.0786995	+	0.996898i	$0.474923\pi$
$278$	−2.52706	−0.151563
$279$	−12.0915	−0.723899
$280$	−2.29903	−0.137393
$281$	−23.8489	−1.42271	−0.711353	−	0.702835i	$-0.751917\pi$
$281$	−23.8489	−1.42271	−0.711353	+	0.702835i	$0.751917\pi$
$282$	−6.28618	−0.374337
$283$	6.10593	0.362960	0.181480	−	0.983395i	$-0.441911\pi$
$283$	6.10593	0.362960	0.181480	+	0.983395i	$0.441911\pi$
$284$	−0.647444	−0.0384187
$285$	−6.77222	−0.401152
$286$	−25.2540	−1.49330
$287$	1.41777	0.0836886
$288$	−8.46886	−0.499033
$289$	11.9784	0.704614
$290$	−25.1013	−1.47400
$291$	13.7993	0.808928
$292$	43.6748	2.55587
$293$	3.28173	0.191721	0.0958604	−	0.995395i	$-0.469440\pi$
$293$	3.28173	0.191721	0.0958604	+	0.995395i	$0.469440\pi$
$294$	13.7101	0.799589
$295$	−21.3062	−1.24049
$296$	−16.9804	−0.986966
$297$	23.0280	1.33622
$298$	47.0335	2.72457
$299$	2.08905	0.120813
$300$	−7.96810	−0.460038
$301$	−0.610789	−0.0352053
$302$	12.8572	0.739851
$303$	9.30017	0.534281
$304$	−7.92880	−0.454748
$305$	4.33872	0.248435
$306$	−28.8748	−1.65066
$307$	15.3789	0.877718	0.438859	−	0.898556i	$-0.355383\pi$
$307$	15.3789	0.877718	0.438859	+	0.898556i	$0.355383\pi$
$308$	−7.43008	−0.423368
$309$	−8.31992	−0.473304
$310$	−19.2701	−1.09447
$311$	5.04206	0.285909	0.142955	−	0.989729i	$-0.454340\pi$
$311$	5.04206	0.285909	0.142955	+	0.989729i	$0.454340\pi$
$312$	6.52113	0.369187
$313$	9.61655	0.543560	0.271780	−	0.962359i	$-0.412388\pi$
$313$	9.61655	0.543560	0.271780	+	0.962359i	$0.412388\pi$
$314$	−36.6813	−2.07004
$315$	−1.42644	−0.0803707
$316$	14.2807	0.803351
$317$	−13.3098	−0.747551	−0.373776	−	0.927519i	$-0.621937\pi$
$317$	−13.3098	−0.747551	−0.373776	+	0.927519i	$0.621937\pi$
$318$	−1.05178	−0.0589811
$319$	−35.4972	−1.98746
$320$	−18.2145	−1.01822
$321$	−4.06773	−0.227039
$322$	0.960313	0.0535161
$323$	27.8396	1.54904
$324$	10.6869	0.593715
$325$	5.49995	0.305082
$326$	33.7640	1.87002
$327$	−2.14986	−0.118888
$328$	−12.7634	−0.704741
$329$	1.27660	0.0703811
$330$	15.8302	0.871424
$331$	−16.4230	−0.902689	−0.451344	−	0.892350i	$-0.649055\pi$
$331$	−16.4230	−0.902689	−0.451344	+	0.892350i	$0.649055\pi$
$332$	−39.8630	−2.18777
$333$	−10.5355	−0.577344
$334$	−19.7088	−1.07842
$335$	−8.69901	−0.475278
$336$	0.531614	0.0290019
$337$	−9.03148	−0.491976	−0.245988	−	0.969273i	$-0.579112\pi$
$337$	−9.03148	−0.491976	−0.245988	+	0.969273i	$0.579112\pi$
$338$	20.3557	1.10721
$339$	−6.96515	−0.378295
$340$	−29.4524	−1.59728
$341$	−27.2509	−1.47572
$342$	−27.7400	−1.50001
$343$	−5.63611	−0.304322
$344$	5.49858	0.296464
$345$	−1.30950	−0.0705011
$346$	21.4834	1.15496
$347$	−0.226462	−0.0121571	−0.00607856	−	0.999982i	$-0.501935\pi$
$347$	−0.226462	−0.0121571	−0.00607856	+	0.999982i	$0.501935\pi$
$348$	20.9478	1.12292
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	2.52826	0.135141
$351$	9.38006	0.500671
$352$	−19.0865	−1.01731
$353$	−14.1658	−0.753969	−0.376984	−	0.926220i	$-0.623039\pi$
$353$	−14.1658	−0.753969	−0.376984	+	0.926220i	$0.623039\pi$
$354$	27.7810	1.47654
$355$	−0.280132	−0.0148679
$356$	14.9673	0.793265
$357$	−1.86660	−0.0987911
$358$	−11.9679	−0.632524
$359$	−2.85429	−0.150644	−0.0753218	−	0.997159i	$-0.523998\pi$
$359$	−2.85429	−0.150644	−0.0753218	+	0.997159i	$0.523998\pi$
$360$	12.8414	0.676802
$361$	7.74558	0.407662
$362$	−56.0797	−2.94748
$363$	13.0242	0.683595
$364$	−3.02651	−0.158632
$365$	18.8969	0.989110
$366$	−5.65724	−0.295708
$367$	16.2144	0.846386	0.423193	−	0.906039i	$-0.360909\pi$
$367$	16.2144	0.846386	0.423193	+	0.906039i	$0.360909\pi$
$368$	−1.53314	−0.0799204
$369$	−7.91909	−0.412252
$370$	−16.7904	−0.872890
$371$	0.213596	0.0110894
$372$	16.0815	0.833785
$373$	23.4890	1.21621	0.608106	−	0.793856i	$-0.291929\pi$
$373$	23.4890	1.21621	0.608106	+	0.793856i	$0.291929\pi$
$374$	−65.0757	−3.36499
$375$	−9.99508	−0.516144
$376$	−11.4925	−0.592679
$377$	−14.4592	−0.744684
$378$	4.31191	0.221781
$379$	37.6834	1.93567	0.967833	−	0.251592i	$-0.0809540\pi$
$379$	37.6834	1.93567	0.967833	+	0.251592i	$0.0809540\pi$
$380$	−28.2950	−1.45150
$381$	−1.40884	−0.0721769
$382$	9.46329	0.484184
$383$	−13.8646	−0.708446	−0.354223	−	0.935161i	$-0.615255\pi$
$383$	−13.8646	−0.708446	−0.354223	+	0.935161i	$0.615255\pi$
$384$	17.4148	0.888698
$385$	−3.21480	−0.163841
$386$	−2.87012	−0.146085
$387$	3.41161	0.173422
$388$	57.6547	2.92698
$389$	15.2018	0.770762	0.385381	−	0.922757i	$-0.374070\pi$
$389$	15.2018	0.770762	0.385381	+	0.922757i	$0.374070\pi$
$390$	6.44815	0.326515
$391$	5.38316	0.272238
$392$	25.0650	1.26597
$393$	−1.47766	−0.0745380
$394$	−20.1870	−1.01700
$395$	6.17887	0.310893
$396$	41.5013	2.08552
$397$	0.842926	0.0423052	0.0211526	−	0.999776i	$-0.493266\pi$
$397$	0.842926	0.0423052	0.0211526	+	0.999776i	$0.493266\pi$
$398$	−47.7162	−2.39180
$399$	−1.79325	−0.0897747
$400$	−4.03637	−0.201819
$401$	−24.6438	−1.23065	−0.615326	−	0.788273i	$-0.710975\pi$
$401$	−24.6438	−1.23065	−0.615326	+	0.788273i	$0.710975\pi$
$402$	11.3426	0.565717
$403$	−11.1002	−0.552939
$404$	38.8570	1.93321
$405$	4.62393	0.229765
$406$	−6.64671	−0.329870
$407$	−23.7442	−1.17696
$408$	16.8040	0.831920
$409$	−18.3480	−0.907252	−0.453626	−	0.891192i	$-0.649870\pi$
$409$	−18.3480	−0.907252	−0.453626	+	0.891192i	$0.649870\pi$
$410$	−12.6206	−0.623285
$411$	−1.50350	−0.0741622
$412$	−34.7614	−1.71257
$413$	−5.64176	−0.277613
$414$	−5.36390	−0.263621
$415$	−17.2477	−0.846655
$416$	−7.77454	−0.381178
$417$	0.912469	0.0446838
$418$	−62.5183	−3.05787
$419$	26.1461	1.27732	0.638659	−	0.769490i	$-0.279489\pi$
$419$	26.1461	1.27732	0.638659	+	0.769490i	$0.279489\pi$
$420$	1.89714	0.0925708
$421$	−19.2827	−0.939780	−0.469890	−	0.882725i	$-0.655706\pi$
$421$	−19.2827	−0.939780	−0.469890	+	0.882725i	$0.655706\pi$
$422$	−36.3379	−1.76890
$423$	−7.13054	−0.346699
$424$	−1.92288	−0.0933834
$425$	14.1725	0.687468
$426$	0.365262	0.0176970
$427$	1.14887	0.0555978
$428$	−16.9954	−0.821503
$429$	9.11869	0.440255
$430$	5.43705	0.262198
$431$	−25.8291	−1.24414	−0.622072	−	0.782960i	$-0.713709\pi$
$431$	−25.8291	−1.24414	−0.622072	+	0.782960i	$0.713709\pi$
$432$	−6.88396	−0.331205
$433$	−15.5960	−0.749495	−0.374748	−	0.927127i	$-0.622271\pi$
$433$	−15.5960	−0.749495	−0.374748	+	0.927127i	$0.622271\pi$
$434$	−5.10262	−0.244934
$435$	9.06356	0.434565
$436$	−8.98233	−0.430176
$437$	5.17161	0.247392
$438$	−24.6396	−1.17732
$439$	36.9804	1.76498	0.882490	−	0.470331i	$-0.155866\pi$
$439$	36.9804	1.76498	0.882490	+	0.470331i	$0.155866\pi$
$440$	28.9410	1.37971
$441$	15.5516	0.740554
$442$	−26.5074	−1.26083
$443$	−18.1715	−0.863352	−0.431676	−	0.902029i	$-0.642078\pi$
$443$	−18.1715	−0.863352	−0.431676	+	0.902029i	$0.642078\pi$
$444$	14.0121	0.664983
$445$	6.47595	0.306989
$446$	20.3413	0.963189
$447$	−16.9828	−0.803258
$448$	−4.82310	−0.227870
$449$	37.2485	1.75786	0.878932	−	0.476947i	$-0.158257\pi$
$449$	37.2485	1.75786	0.878932	+	0.476947i	$0.158257\pi$
$450$	−14.1218	−0.665709
$451$	−17.8474	−0.840404
$452$	−29.1011	−1.36880
$453$	−4.64248	−0.218123
$454$	−46.4993	−2.18232
$455$	−1.30949	−0.0613899
$456$	16.1436	0.755993
$457$	8.73537	0.408624	0.204312	−	0.978906i	$-0.434504\pi$
$457$	8.73537	0.408624	0.204312	+	0.978906i	$0.434504\pi$
$458$	−64.4286	−3.01055
$459$	24.1710	1.12820
$460$	−5.47122	−0.255097
$461$	−38.0734	−1.77326	−0.886628	−	0.462484i	$-0.846958\pi$
$461$	−38.0734	−1.77326	−0.886628	+	0.462484i	$0.846958\pi$
$462$	4.19176	0.195018
$463$	13.7913	0.640937	0.320469	−	0.947259i	$-0.396160\pi$
$463$	13.7913	0.640937	0.320469	+	0.947259i	$0.396160\pi$
$464$	10.6115	0.492625
$465$	6.95802	0.322671
$466$	35.8330	1.65993
$467$	36.7710	1.70156	0.850780	−	0.525522i	$-0.176130\pi$
$467$	36.7710	1.70156	0.850780	+	0.525522i	$0.176130\pi$
$468$	16.9048	0.781426
$469$	−2.30345	−0.106364
$470$	−11.3639	−0.524176
$471$	13.2448	0.610289
$472$	50.7895	2.33778
$473$	7.68883	0.353533
$474$	−8.05660	−0.370052
$475$	13.6156	0.624725
$476$	−7.79885	−0.357460
$477$	−1.19306	−0.0546264
$478$	12.7799	0.584540
$479$	28.8588	1.31859	0.659297	−	0.751883i	$-0.270854\pi$
$479$	28.8588	1.31859	0.659297	+	0.751883i	$0.270854\pi$
$480$	4.87338	0.222439
$481$	−9.67178	−0.440995
$482$	−42.1831	−1.92139
$483$	−0.346749	−0.0157776
$484$	54.4165	2.47348
$485$	24.9457	1.13272
$486$	−37.7802	−1.71375
$487$	−15.0259	−0.680890	−0.340445	−	0.940264i	$-0.610578\pi$
$487$	−15.0259	−0.680890	−0.340445	+	0.940264i	$0.610578\pi$
$488$	−10.3426	−0.468189
$489$	−12.1915	−0.551318
$490$	24.7844	1.11965
$491$	−29.6893	−1.33986	−0.669929	−	0.742425i	$-0.733675\pi$
$491$	−29.6893	−1.33986	−0.669929	+	0.742425i	$0.733675\pi$
$492$	10.5322	0.474830
$493$	−37.2590	−1.67806
$494$	−25.4657	−1.14576
$495$	17.9565	0.807086
$496$	8.14633	0.365781
$497$	−0.0741775	−0.00332731
$498$	22.4891	1.00776
$499$	16.5077	0.738988	0.369494	−	0.929233i	$-0.379531\pi$
$499$	16.5077	0.738988	0.369494	+	0.929233i	$0.379531\pi$
$500$	−41.7604	−1.86758
$501$	7.11644	0.317939
$502$	−47.7182	−2.12977
$503$	−17.4255	−0.776963	−0.388482	−	0.921456i	$-0.627000\pi$
$503$	−17.4255	−0.776963	−0.388482	+	0.921456i	$0.627000\pi$
$504$	3.40034	0.151463
$505$	16.8124	0.748142
$506$	−12.0888	−0.537411
$507$	−7.35003	−0.326426
$508$	−5.88626	−0.261160
$509$	30.5069	1.35220	0.676098	−	0.736812i	$-0.263670\pi$
$509$	30.5069	1.35220	0.676098	+	0.736812i	$0.263670\pi$
$510$	16.6159	0.735764
$511$	5.00381	0.221355
$512$	16.9518	0.749170
$513$	23.2211	1.02524
$514$	−35.0892	−1.54772
$515$	−15.0404	−0.662757
$516$	−4.53738	−0.199747
$517$	−16.0703	−0.706769
$518$	−4.44600	−0.195346
$519$	−7.75720	−0.340503
$520$	11.7886	0.516964
$521$	11.0957	0.486113	0.243057	−	0.970012i	$-0.421850\pi$
$521$	11.0957	0.486113	0.243057	+	0.970012i	$0.421850\pi$
$522$	37.1257	1.62495
$523$	−3.84126	−0.167967	−0.0839834	−	0.996467i	$-0.526764\pi$
$523$	−3.84126	−0.167967	−0.0839834	+	0.996467i	$0.526764\pi$
$524$	−6.17380	−0.269704
$525$	−0.912902	−0.0398423
$526$	−8.67672	−0.378323
$527$	−28.6034	−1.24598
$528$	−6.69214	−0.291238
$529$	1.00000	0.0434783
$530$	−1.90136	−0.0825899
$531$	31.5125	1.36753
$532$	−7.49237	−0.324835
$533$	−7.26984	−0.314892
$534$	−8.44395	−0.365405
$535$	−7.35345	−0.317917
$536$	20.7367	0.895687
$537$	4.32136	0.186480
$538$	−13.2264	−0.570232
$539$	35.0491	1.50967
$540$	−24.5663	−1.05717
$541$	−0.355562	−0.0152868	−0.00764340	−	0.999971i	$-0.502433\pi$
$541$	−0.355562	−0.0152868	−0.00764340	+	0.999971i	$0.502433\pi$
$542$	−5.27897	−0.226751
$543$	20.2492	0.868975
$544$	−20.0338	−0.858941
$545$	−3.88642	−0.166476
$546$	1.70744	0.0730716
$547$	−32.4171	−1.38605	−0.693027	−	0.720911i	$-0.743723\pi$
$547$	−32.4171	−1.38605	−0.693027	+	0.720911i	$0.743723\pi$
$548$	−6.28177	−0.268344
$549$	−6.41711	−0.273876
$550$	−31.8267	−1.35709
$551$	−35.7948	−1.52491
$552$	3.12158	0.132863
$553$	1.63613	0.0695755
$554$	−6.17480	−0.262342
$555$	6.06265	0.257345
$556$	3.81238	0.161681
$557$	8.59925	0.364362	0.182181	−	0.983265i	$-0.441684\pi$
$557$	8.59925	0.364362	0.182181	+	0.983265i	$0.441684\pi$
$558$	28.5011	1.20655
$559$	3.13191	0.132466
$560$	0.961025	0.0406107
$561$	23.4975	0.992064
$562$	56.2147	2.37127
$563$	11.0063	0.463859	0.231929	−	0.972733i	$-0.425496\pi$
$563$	11.0063	0.463859	0.231929	+	0.972733i	$0.425496\pi$
$564$	9.48348	0.399326
$565$	−12.5913	−0.529718
$566$	−14.3924	−0.604957
$567$	1.22439	0.0514196
$568$	0.667777	0.0280193
$569$	−11.0418	−0.462898	−0.231449	−	0.972847i	$-0.574347\pi$
$569$	−11.0418	−0.462898	−0.231449	+	0.972847i	$0.574347\pi$
$570$	15.9629	0.668613
$571$	13.4416	0.562514	0.281257	−	0.959633i	$-0.409249\pi$
$571$	13.4416	0.562514	0.281257	+	0.959633i	$0.409249\pi$
$572$	38.0988	1.59299
$573$	−3.41699	−0.142747
$574$	−3.34186	−0.139487
$575$	2.63275	0.109793
$576$	26.9398	1.12249
$577$	42.7331	1.77900	0.889500	−	0.456934i	$-0.151053\pi$
$577$	42.7331	1.77900	0.889500	+	0.456934i	$0.151053\pi$
$578$	−28.2346	−1.17440
$579$	1.03634	0.0430688
$580$	37.8685	1.57240
$581$	−4.56709	−0.189475
$582$	−32.5265	−1.34827
$583$	−2.68882	−0.111360
$584$	−45.0464	−1.86403
$585$	7.31427	0.302408
$586$	−7.73542	−0.319547
$587$	1.10234	0.0454984	0.0227492	−	0.999741i	$-0.492758\pi$
$587$	1.10234	0.0454984	0.0227492	+	0.999741i	$0.492758\pi$
$588$	−20.6834	−0.852967
$589$	−27.4794	−1.13227
$590$	50.2211	2.06757
$591$	7.28909	0.299833
$592$	7.09804	0.291728
$593$	11.9395	0.490295	0.245147	−	0.969486i	$-0.421164\pi$
$593$	11.9395	0.490295	0.245147	+	0.969486i	$0.421164\pi$
$594$	−54.2798	−2.22713
$595$	−3.37436	−0.138335
$596$	−70.9557	−2.90646
$597$	17.2293	0.705148
$598$	−4.92414	−0.201363
$599$	−12.0326	−0.491640	−0.245820	−	0.969316i	$-0.579057\pi$
$599$	−12.0326	−0.491640	−0.245820	+	0.969316i	$0.579057\pi$
$600$	8.21833	0.335512
$601$	−24.6138	−1.00402	−0.502010	−	0.864862i	$-0.667406\pi$
$601$	−24.6138	−1.00402	−0.502010	+	0.864862i	$0.667406\pi$
$602$	1.43970	0.0586778
$603$	12.8661	0.523949
$604$	−19.3967	−0.789242
$605$	23.5446	0.957223
$606$	−21.9216	−0.890504
$607$	−38.6710	−1.56961	−0.784803	−	0.619745i	$-0.787236\pi$
$607$	−38.6710	−1.56961	−0.784803	+	0.619745i	$0.787236\pi$
$608$	−19.2465	−0.780548
$609$	2.39998	0.0972523
$610$	−10.2269	−0.414074
$611$	−6.54593	−0.264820
$612$	43.5611	1.76085
$613$	11.2754	0.455410	0.227705	−	0.973730i	$-0.426878\pi$
$613$	11.2754	0.455410	0.227705	+	0.973730i	$0.426878\pi$
$614$	−36.2498	−1.46292
$615$	4.55702	0.183757
$616$	7.66342	0.308768
$617$	2.09069	0.0841681	0.0420841	−	0.999114i	$-0.486600\pi$
$617$	2.09069	0.0841681	0.0420841	+	0.999114i	$0.486600\pi$
$618$	19.6110	0.788871
$619$	−22.8083	−0.916744	−0.458372	−	0.888760i	$-0.651567\pi$
$619$	−22.8083	−0.916744	−0.458372	+	0.888760i	$0.651567\pi$
$620$	29.0713	1.16753
$621$	4.49011	0.180182
$622$	−11.8847	−0.476534
$623$	1.71480	0.0687019
$624$	−2.72592	−0.109124
$625$	−4.90487	−0.196195
$626$	−22.6673	−0.905969
$627$	22.5741	0.901521
$628$	55.3382	2.20823
$629$	−24.9227	−0.993732
$630$	3.36228	0.133957
$631$	8.89076	0.353936	0.176968	−	0.984217i	$-0.443371\pi$
$631$	8.89076	0.353936	0.176968	+	0.984217i	$0.443371\pi$
$632$	−14.7292	−0.585895
$633$	13.1209	0.521507
$634$	31.3727	1.24597
$635$	−2.54683	−0.101068
$636$	1.58674	0.0629185
$637$	14.2766	0.565660
$638$	83.6711	3.31257
$639$	0.414324	0.0163904
$640$	31.4817	1.24442
$641$	10.3222	0.407703	0.203852	−	0.979002i	$-0.434654\pi$
$641$	10.3222	0.407703	0.203852	+	0.979002i	$0.434654\pi$
$642$	9.58812	0.378413
$643$	43.6495	1.72137	0.860684	−	0.509139i	$-0.170036\pi$
$643$	43.6495	1.72137	0.860684	+	0.509139i	$0.170036\pi$
$644$	−1.44875	−0.0570887
$645$	−1.96320	−0.0773010
$646$	−65.6213	−2.58183
$647$	20.1820	0.793438	0.396719	−	0.917940i	$-0.370149\pi$
$647$	20.1820	0.793438	0.396719	+	0.917940i	$0.370149\pi$
$648$	−11.0225	−0.433004
$649$	71.0205	2.78780
$650$	−12.9640	−0.508491
$651$	1.84245	0.0722112
$652$	−50.9372	−1.99485
$653$	−11.7407	−0.459450	−0.229725	−	0.973256i	$-0.573783\pi$
$653$	−11.7407	−0.459450	−0.229725	+	0.973256i	$0.573783\pi$
$654$	5.06748	0.198154
$655$	−2.67124	−0.104374
$656$	5.33528	0.208308
$657$	−27.9492	−1.09040
$658$	−3.00909	−0.117307
$659$	−24.8896	−0.969563	−0.484781	−	0.874635i	$-0.661101\pi$
$659$	−24.8896	−0.969563	−0.484781	+	0.874635i	$0.661101\pi$
$660$	−23.8818	−0.929598
$661$	−2.95275	−0.114849	−0.0574244	−	0.998350i	$-0.518289\pi$
$661$	−2.95275	−0.114849	−0.0574244	+	0.998350i	$0.518289\pi$
$662$	38.7109	1.50454
$663$	9.57127	0.371717
$664$	41.1149	1.59557
$665$	−3.24175	−0.125710
$666$	24.8335	0.962279
$667$	−6.92140	−0.267998
$668$	29.7332	1.15041
$669$	−7.34482	−0.283967
$670$	20.5046	0.792161
$671$	−14.4624	−0.558315
$672$	1.29045	0.0497801
$673$	47.1058	1.81580	0.907898	−	0.419192i	$-0.137686\pi$
$673$	47.1058	1.81580	0.907898	+	0.419192i	$0.137686\pi$
$674$	21.2882	0.819993
$675$	11.8213	0.455003
$676$	−30.7091	−1.18112
$677$	−24.3799	−0.936998	−0.468499	−	0.883464i	$-0.655205\pi$
$677$	−24.3799	−0.936998	−0.468499	+	0.883464i	$0.655205\pi$
$678$	16.4177	0.630517
$679$	6.60548	0.253495
$680$	30.3774	1.16492
$681$	16.7899	0.643391
$682$	64.2336	2.45963
$683$	28.9873	1.10917	0.554583	−	0.832128i	$-0.312878\pi$
$683$	28.9873	1.10917	0.554583	+	0.832128i	$0.312878\pi$
$684$	41.8492	1.60015
$685$	−2.71796	−0.103848
$686$	13.2850	0.507223
$687$	23.2638	0.887569
$688$	−2.29848	−0.0876288
$689$	−1.09524	−0.0417255
$690$	3.08664	0.117506
$691$	0.505236	0.0192201	0.00961004	−	0.999954i	$-0.496941\pi$
$691$	0.505236	0.0192201	0.00961004	+	0.999954i	$0.496941\pi$
$692$	−32.4104	−1.23206
$693$	4.75479	0.180620
$694$	0.533798	0.0202627
$695$	1.64952	0.0625698
$696$	−21.6057	−0.818961
$697$	−18.7333	−0.709573
$698$	−2.35712	−0.0892182
$699$	−12.9386	−0.489381
$700$	−3.81420	−0.144163
$701$	−26.1706	−0.988450	−0.494225	−	0.869334i	$-0.664548\pi$
$701$	−26.1706	−0.988450	−0.494225	+	0.869334i	$0.664548\pi$
$702$	−22.1099	−0.834485
$703$	−23.9433	−0.903037
$704$	60.7148	2.28828
$705$	4.10325	0.154537
$706$	33.3904	1.25667
$707$	4.45184	0.167429
$708$	−41.9110	−1.57511
$709$	15.7312	0.590797	0.295399	−	0.955374i	$-0.404548\pi$
$709$	15.7312	0.590797	0.295399	+	0.955374i	$0.404548\pi$
$710$	0.660304	0.0247808
$711$	−9.13876	−0.342730
$712$	−15.4373	−0.578538
$713$	−5.31350	−0.198992
$714$	4.39980	0.164658
$715$	16.4843	0.616479
$716$	18.0551	0.674749
$717$	−4.61456	−0.172334
$718$	6.72789	0.251083
$719$	0.735281	0.0274213	0.0137107	−	0.999906i	$-0.495636\pi$
$719$	0.735281	0.0274213	0.0137107	+	0.999906i	$0.495636\pi$
$720$	−5.36789	−0.200049
$721$	−3.98261	−0.148320
$722$	−18.2572	−0.679464
$723$	15.2314	0.566463
$724$	84.6031	3.14425
$725$	−18.2223	−0.676760
$726$	−30.6996	−1.13937
$727$	12.4972	0.463497	0.231749	−	0.972776i	$-0.425555\pi$
$727$	12.4972	0.463497	0.231749	+	0.972776i	$0.425555\pi$
$728$	3.12156	0.115693
$729$	4.62572	0.171323
$730$	−44.5423	−1.64858
$731$	8.07044	0.298496
$732$	8.53463	0.315449
$733$	38.9210	1.43758	0.718791	−	0.695227i	$-0.244696\pi$
$733$	38.9210	1.43758	0.718791	+	0.695227i	$0.244696\pi$
$734$	−38.2193	−1.41070
$735$	−8.94914	−0.330094
$736$	−3.72156	−0.137179
$737$	28.9967	1.06811
$738$	18.6662	0.687114
$739$	−36.7318	−1.35120	−0.675601	−	0.737267i	$-0.736116\pi$
$739$	−36.7318	−1.35120	−0.675601	+	0.737267i	$0.736116\pi$
$740$	25.3303	0.931162
$741$	9.19514	0.337792
$742$	−0.503471	−0.0184830
$743$	43.0713	1.58013	0.790066	−	0.613022i	$-0.210046\pi$
$743$	43.0713	1.58013	0.790066	+	0.613022i	$0.210046\pi$
$744$	−16.5865	−0.608090
$745$	−30.7007	−1.12479
$746$	−55.3663	−2.02710
$747$	25.5099	0.933358
$748$	98.1747	3.58962
$749$	−1.94716	−0.0711475
$750$	23.5596	0.860274
$751$	−2.51305	−0.0917024	−0.0458512	−	0.998948i	$-0.514600\pi$
$751$	−2.51305	−0.0917024	−0.0458512	+	0.998948i	$0.514600\pi$
$752$	4.80401	0.175184
$753$	17.2300	0.627897
$754$	34.0819	1.24119
$755$	−8.39245	−0.305432
$756$	−6.50504	−0.236586
$757$	30.1948	1.09745	0.548725	−	0.836003i	$-0.315114\pi$
$757$	30.1948	1.09745	0.548725	+	0.836003i	$0.315114\pi$
$758$	−88.8242	−3.22624
$759$	4.36499	0.158439
$760$	29.1836	1.05860
$761$	1.82455	0.0661398	0.0330699	−	0.999453i	$-0.489472\pi$
$761$	1.82455	0.0661398	0.0330699	+	0.999453i	$0.489472\pi$
$762$	3.32079	0.120300
$763$	−1.02910	−0.0372560
$764$	−14.2765	−0.516507
$765$	18.8477	0.681441
$766$	32.6804	1.18079
$767$	28.9289	1.04456
$768$	−20.8973	−0.754067
$769$	−10.4581	−0.377130	−0.188565	−	0.982061i	$-0.560384\pi$
$769$	−10.4581	−0.377130	−0.188565	+	0.982061i	$0.560384\pi$
$770$	7.57766	0.273080
$771$	12.6700	0.456298
$772$	4.32993	0.155838
$773$	13.7864	0.495863	0.247931	−	0.968778i	$-0.420249\pi$
$773$	13.7864	0.495863	0.247931	+	0.968778i	$0.420249\pi$
$774$	−8.04157	−0.289048
$775$	−13.9891	−0.502504
$776$	−59.4654	−2.13468
$777$	1.60536	0.0575919
$778$	−35.8324	−1.28466
$779$	−17.9971	−0.644812
$780$	−9.72783	−0.348312
$781$	0.933772	0.0334130
$782$	−12.6887	−0.453749
$783$	−31.0778	−1.11063
$784$	−10.4775	−0.374196
$785$	23.9434	0.854575
$786$	3.48301	0.124235
$787$	39.5234	1.40886	0.704429	−	0.709775i	$-0.251203\pi$
$787$	39.5234	1.40886	0.704429	+	0.709775i	$0.251203\pi$
$788$	30.4545	1.08490
$789$	3.13298	0.111537
$790$	−14.5643	−0.518176
$791$	−3.33410	−0.118547
$792$	−42.8047	−1.52100
$793$	−5.89100	−0.209196
$794$	−1.98688	−0.0705116
$795$	0.686542	0.0243491
$796$	71.9857	2.55147
$797$	32.2737	1.14319	0.571596	−	0.820535i	$-0.306324\pi$
$797$	32.2737	1.14319	0.571596	+	0.820535i	$0.306324\pi$
$798$	4.22690	0.149631
$799$	−16.8679	−0.596742
$800$	−9.79795	−0.346410
$801$	−9.57814	−0.338427
$802$	58.0882	2.05117
$803$	−62.9897	−2.22286
$804$	−17.1117	−0.603483
$805$	−0.626835	−0.0220930
$806$	26.1644	0.921602
$807$	4.77579	0.168116
$808$	−40.0773	−1.40991
$809$	−22.1733	−0.779573	−0.389787	−	0.920905i	$-0.627451\pi$
$809$	−22.1733	−0.779573	−0.389787	+	0.920905i	$0.627451\pi$
$810$	−10.8991	−0.382957
$811$	−43.5215	−1.52825	−0.764124	−	0.645070i	$-0.776828\pi$
$811$	−43.5215	−1.52825	−0.764124	+	0.645070i	$0.776828\pi$
$812$	10.0274	0.351892
$813$	1.90612	0.0668506
$814$	55.9679	1.96167
$815$	−22.0392	−0.771999
$816$	−7.02428	−0.245899
$817$	7.75329	0.271253
$818$	43.2485	1.51215
$819$	1.93678	0.0676766
$820$	19.0397	0.664894
$821$	35.1273	1.22595	0.612976	−	0.790102i	$-0.289972\pi$
$821$	35.1273	1.22595	0.612976	+	0.790102i	$0.289972\pi$
$822$	3.54393	0.123609
$823$	4.55552	0.158795	0.0793977	−	0.996843i	$-0.474700\pi$
$823$	4.55552	0.158795	0.0793977	+	0.996843i	$0.474700\pi$
$824$	35.8531	1.24900
$825$	11.4919	0.400098
$826$	13.2983	0.462707
$827$	−26.9372	−0.936700	−0.468350	−	0.883543i	$-0.655151\pi$
$827$	−26.9372	−0.936700	−0.468350	+	0.883543i	$0.655151\pi$
$828$	8.09211	0.281220
$829$	15.7109	0.545662	0.272831	−	0.962062i	$-0.412040\pi$
$829$	15.7109	0.545662	0.272831	+	0.962062i	$0.412040\pi$
$830$	40.6548	1.41115
$831$	2.22959	0.0773436
$832$	24.7311	0.857397
$833$	36.7886	1.27465
$834$	−2.15080	−0.0744760
$835$	12.8648	0.445203
$836$	94.3166	3.26201
$837$	−23.8582	−0.824659
$838$	−61.6293	−2.12895
$839$	−25.7863	−0.890243	−0.445121	−	0.895470i	$-0.646839\pi$
$839$	−25.7863	−0.890243	−0.445121	+	0.895470i	$0.646839\pi$
$840$	−1.95671	−0.0675131
$841$	18.9058	0.651922
$842$	45.4515	1.56636
$843$	−20.2979	−0.699098
$844$	54.8202	1.88699
$845$	−13.2870	−0.457088
$846$	16.8075	0.577854
$847$	6.23448	0.214219
$848$	0.803791	0.0276023
$849$	5.19678	0.178353
$850$	−33.4063	−1.14583
$851$	−4.62975	−0.158706
$852$	−0.551043	−0.0188784
$853$	−25.2437	−0.864328	−0.432164	−	0.901795i	$-0.642250\pi$
$853$	−25.2437	−0.864328	−0.432164	+	0.901795i	$0.642250\pi$
$854$	−2.70802	−0.0926667
$855$	18.1071	0.619248
$856$	17.5291	0.599133
$857$	29.6624	1.01325	0.506625	−	0.862167i	$-0.330893\pi$
$857$	29.6624	1.01325	0.506625	+	0.862167i	$0.330893\pi$
$858$	−21.4938	−0.733787
$859$	21.9671	0.749509	0.374754	−	0.927124i	$-0.377727\pi$
$859$	21.9671	0.749509	0.374754	+	0.927124i	$0.377727\pi$
$860$	−8.20245	−0.279701
$861$	1.20668	0.0411234
$862$	60.8823	2.07366
$863$	−41.3691	−1.40822	−0.704110	−	0.710091i	$-0.748654\pi$
$863$	−41.3691	−1.40822	−0.704110	+	0.710091i	$0.748654\pi$
$864$	−16.7102	−0.568493
$865$	−14.0231	−0.476800
$866$	36.7616	1.24921
$867$	10.1949	0.346237
$868$	7.69793	0.261285
$869$	−20.5962	−0.698679
$870$	−21.3639	−0.724303
$871$	11.8113	0.400210
$872$	9.26442	0.313733
$873$	−36.8955	−1.24872
$874$	−12.1901	−0.412336
$875$	−4.78448	−0.161745
$876$	37.1718	1.25592
$877$	−36.6339	−1.23704	−0.618520	−	0.785769i	$-0.712267\pi$
$877$	−36.6339	−1.23704	−0.618520	+	0.785769i	$0.712267\pi$
$878$	−87.1672	−2.94175
$879$	2.79310	0.0942088
$880$	−12.0977	−0.407814
$881$	3.83298	0.129136	0.0645681	−	0.997913i	$-0.479433\pi$
$881$	3.83298	0.129136	0.0645681	+	0.997913i	$0.479433\pi$
$882$	−36.6570	−1.23431
$883$	2.24389	0.0755128	0.0377564	−	0.999287i	$-0.487979\pi$
$883$	2.24389	0.0755128	0.0377564	+	0.999287i	$0.487979\pi$
$884$	39.9897	1.34500
$885$	−18.1338	−0.609561
$886$	42.8323	1.43898
$887$	0.121217	0.00407007	0.00203503	−	0.999998i	$-0.499352\pi$
$887$	0.121217	0.00407007	0.00203503	+	0.999998i	$0.499352\pi$
$888$	−14.4521	−0.484981
$889$	−0.674386	−0.0226182
$890$	−15.2646	−0.511669
$891$	−15.4131	−0.516358
$892$	−30.6874	−1.02749
$893$	−16.2050	−0.542279
$894$	40.0304	1.33882
$895$	7.81194	0.261124
$896$	8.33620	0.278493
$897$	1.77800	0.0593658
$898$	−87.7990	−2.92989
$899$	36.7768	1.22658
$900$	21.3045	0.710150
$901$	−2.82228	−0.0940236
$902$	42.0685	1.40073
$903$	−0.519846	−0.0172994
$904$	30.0150	0.998284
$905$	36.6055	1.21681
$906$	10.9429	0.363552
$907$	27.7880	0.922685	0.461343	−	0.887222i	$-0.347368\pi$
$907$	27.7880	0.922685	0.461343	+	0.887222i	$0.347368\pi$
$908$	70.1499	2.32801
$909$	−24.8661	−0.824756
$910$	3.08662	0.102321
$911$	−7.01267	−0.232340	−0.116170	−	0.993229i	$-0.537062\pi$
$911$	−7.01267	−0.232340	−0.116170	+	0.993229i	$0.537062\pi$
$912$	−6.74824	−0.223457
$913$	57.4922	1.90271
$914$	−20.5903	−0.681067
$915$	3.69271	0.122077
$916$	97.1985	3.21153
$917$	−0.707330	−0.0233581
$918$	−56.9738	−1.88042
$919$	−26.0207	−0.858343	−0.429171	−	0.903223i	$-0.641194\pi$
$919$	−26.0207	−0.858343	−0.429171	+	0.903223i	$0.641194\pi$
$920$	5.64304	0.186045
$921$	13.0890	0.431298
$922$	89.7435	2.95554
$923$	0.380355	0.0125196
$924$	−6.32378	−0.208037
$925$	−12.1890	−0.400771
$926$	−32.5078	−1.06827
$927$	22.2452	0.730627
$928$	25.7584	0.845562
$929$	38.0801	1.24937	0.624685	−	0.780877i	$-0.285228\pi$
$929$	38.0801	1.24937	0.624685	+	0.780877i	$0.285228\pi$
$930$	−16.4009	−0.537806
$931$	35.3429	1.15832
$932$	−54.0586	−1.77075
$933$	4.29132	0.140492
$934$	−86.6736	−2.83605
$935$	42.4776	1.38917
$936$	−17.4357	−0.569904
$937$	−9.74121	−0.318232	−0.159116	−	0.987260i	$-0.550864\pi$
$937$	−9.74121	−0.318232	−0.159116	+	0.987260i	$0.550864\pi$
$938$	5.42951	0.177280
$939$	8.18470	0.267098
$940$	17.1438	0.559168
$941$	6.68470	0.217915	0.108957	−	0.994046i	$-0.465249\pi$
$941$	6.68470	0.217915	0.108957	+	0.994046i	$0.465249\pi$
$942$	−31.2196	−1.01719
$943$	−3.47997	−0.113323
$944$	−21.2307	−0.691001
$945$	−2.81456	−0.0915576
$946$	−18.1235	−0.589245
$947$	−3.97455	−0.129156	−0.0645778	−	0.997913i	$-0.520570\pi$
$947$	−3.97455	−0.129156	−0.0645778	+	0.997913i	$0.520570\pi$
$948$	12.1544	0.394755
$949$	−25.6577	−0.832885
$950$	−32.0935	−1.04125
$951$	−11.3280	−0.367336
$952$	8.04377	0.260700
$953$	−28.6101	−0.926771	−0.463386	−	0.886157i	$-0.653366\pi$
$953$	−28.6101	−0.926771	−0.463386	+	0.886157i	$0.653366\pi$
$954$	2.81218	0.0910476
$955$	−6.17707	−0.199885
$956$	−19.2801	−0.623562
$957$	−30.2119	−0.976611
$958$	−68.0237	−2.19774
$959$	−0.719701	−0.0232403
$960$	−15.5024	−0.500339
$961$	−2.76673	−0.0892494
$962$	22.7975	0.735021
$963$	10.8760	0.350474
$964$	63.6384	2.04965
$965$	1.87345	0.0603084
$966$	0.817327	0.0262971
$967$	6.56408	0.211087	0.105543	−	0.994415i	$-0.466342\pi$
$967$	6.56408	0.211087	0.105543	+	0.994415i	$0.466342\pi$
$968$	−56.1254	−1.80394
$969$	23.6944	0.761175
$970$	−58.7999	−1.88795
$971$	−51.8724	−1.66467	−0.832333	−	0.554276i	$-0.812995\pi$
$971$	−51.8724	−1.66467	−0.832333	+	0.554276i	$0.812995\pi$
$972$	56.9961	1.82815
$973$	0.436784	0.0140026
$974$	35.4179	1.13486
$975$	4.68104	0.149913
$976$	4.32336	0.138387
$977$	3.61044	0.115508	0.0577541	−	0.998331i	$-0.481606\pi$
$977$	3.61044	0.115508	0.0577541	+	0.998331i	$0.481606\pi$
$978$	28.7367	0.918900
$979$	−21.5865	−0.689907
$980$	−37.3904	−1.19439
$981$	5.74814	0.183524
$982$	69.9811	2.23319
$983$	17.5164	0.558686	0.279343	−	0.960191i	$-0.409883\pi$
$983$	17.5164	0.558686	0.279343	+	0.960191i	$0.409883\pi$
$984$	−10.8630	−0.346300
$985$	13.1769	0.419850
$986$	87.8238	2.79688
$987$	1.08652	0.0345843
$988$	38.4182	1.22225
$989$	1.49920	0.0476718
$990$	−42.3256	−1.34520
$991$	−20.2046	−0.641821	−0.320910	−	0.947110i	$-0.603989\pi$
$991$	−20.2046	−0.641821	−0.320910	+	0.947110i	$0.603989\pi$
$992$	19.7745	0.627842
$993$	−13.9777	−0.443568
$994$	0.174845	0.00554575
$995$	31.1463	0.987404
$996$	−33.9276	−1.07504
$997$	−33.7534	−1.06898	−0.534490	−	0.845175i	$-0.679496\pi$
$997$	−33.7534	−1.06898	−0.534490	+	0.845175i	$0.679496\pi$
$998$	−38.9107	−1.23170
$999$	−20.7881	−0.657705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.17	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.17	✓	169	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)

\(f(q)\)	\(=\)	\(q-2.35712 q^{2} +0.851105 q^{3} +3.55600 q^{4} +1.53859 q^{5} -2.00615 q^{6} +0.407410 q^{7} -3.66768 q^{8} -2.27562 q^{9} +O(q^{10})\)	\(q-2.35712 q^{2} +0.851105 q^{3} +3.55600 q^{4} +1.53859 q^{5} -2.00615 q^{6} +0.407410 q^{7} -3.66768 q^{8} -2.27562 q^{9} -3.62663 q^{10} -5.12862 q^{11} +3.02653 q^{12} -2.08905 q^{13} -0.960313 q^{14} +1.30950 q^{15} +1.53314 q^{16} -5.38316 q^{17} +5.36390 q^{18} -5.17161 q^{19} +5.47122 q^{20} +0.346749 q^{21} +12.0888 q^{22} -1.00000 q^{23} -3.12158 q^{24} -2.63275 q^{25} +4.92414 q^{26} -4.49011 q^{27} +1.44875 q^{28} +6.92140 q^{29} -3.08664 q^{30} +5.31350 q^{31} +3.72156 q^{32} -4.36499 q^{33} +12.6887 q^{34} +0.626835 q^{35} -8.09211 q^{36} +4.62975 q^{37} +12.1901 q^{38} -1.77800 q^{39} -5.64304 q^{40} +3.47997 q^{41} -0.817327 q^{42} -1.49920 q^{43} -18.2374 q^{44} -3.50124 q^{45} +2.35712 q^{46} +3.13345 q^{47} +1.30486 q^{48} -6.83402 q^{49} +6.20570 q^{50} -4.58164 q^{51} -7.42867 q^{52} +0.524278 q^{53} +10.5837 q^{54} -7.89082 q^{55} -1.49425 q^{56} -4.40159 q^{57} -16.3145 q^{58} -13.8479 q^{59} +4.65658 q^{60} +2.81994 q^{61} -12.5245 q^{62} -0.927110 q^{63} -11.8384 q^{64} -3.21419 q^{65} +10.2888 q^{66} -5.65390 q^{67} -19.1425 q^{68} -0.851105 q^{69} -1.47752 q^{70} -0.182071 q^{71} +8.34624 q^{72} +12.2820 q^{73} -10.9129 q^{74} -2.24075 q^{75} -18.3903 q^{76} -2.08945 q^{77} +4.19096 q^{78} +4.01594 q^{79} +2.35887 q^{80} +3.00531 q^{81} -8.20270 q^{82} -11.2101 q^{83} +1.23304 q^{84} -8.28246 q^{85} +3.53379 q^{86} +5.89084 q^{87} +18.8101 q^{88} +4.20902 q^{89} +8.25283 q^{90} -0.851100 q^{91} -3.55600 q^{92} +4.52235 q^{93} -7.38591 q^{94} -7.95698 q^{95} +3.16744 q^{96} +16.2134 q^{97} +16.1086 q^{98} +11.6708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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