LMFDB - Embedded newform 8027.2.a.e.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.57271 q^{2} +0.131094 q^{3} +4.61881 q^{4} +4.05012 q^{5} -0.337267 q^{6} -4.42802 q^{7} -6.73744 q^{8} -2.98281 q^{9} +O(q^{10})$	\(q-2.57271 q^{2} +0.131094 q^{3} +4.61881 q^{4} +4.05012 q^{5} -0.337267 q^{6} -4.42802 q^{7} -6.73744 q^{8} -2.98281 q^{9} -10.4198 q^{10} +2.70141 q^{11} +0.605500 q^{12} +6.77346 q^{13} +11.3920 q^{14} +0.530948 q^{15} +8.09582 q^{16} -5.30168 q^{17} +7.67390 q^{18} -5.19452 q^{19} +18.7068 q^{20} -0.580488 q^{21} -6.94992 q^{22} -1.00000 q^{23} -0.883240 q^{24} +11.4035 q^{25} -17.4261 q^{26} -0.784313 q^{27} -20.4522 q^{28} +3.77715 q^{29} -1.36597 q^{30} +2.75335 q^{31} -7.35329 q^{32} +0.354139 q^{33} +13.6397 q^{34} -17.9340 q^{35} -13.7771 q^{36} +8.25863 q^{37} +13.3640 q^{38} +0.887962 q^{39} -27.2874 q^{40} -6.76071 q^{41} +1.49342 q^{42} -11.9360 q^{43} +12.4773 q^{44} -12.0808 q^{45} +2.57271 q^{46} +10.7953 q^{47} +1.06132 q^{48} +12.6073 q^{49} -29.3378 q^{50} -0.695020 q^{51} +31.2853 q^{52} +10.4371 q^{53} +2.01781 q^{54} +10.9410 q^{55} +29.8335 q^{56} -0.680973 q^{57} -9.71749 q^{58} -1.59549 q^{59} +2.45235 q^{60} +8.20957 q^{61} -7.08355 q^{62} +13.2080 q^{63} +2.72620 q^{64} +27.4333 q^{65} -0.911095 q^{66} +3.89013 q^{67} -24.4875 q^{68} -0.131094 q^{69} +46.1389 q^{70} -4.25456 q^{71} +20.0965 q^{72} -6.85087 q^{73} -21.2470 q^{74} +1.49493 q^{75} -23.9925 q^{76} -11.9619 q^{77} -2.28446 q^{78} -15.3025 q^{79} +32.7891 q^{80} +8.84562 q^{81} +17.3933 q^{82} +11.6067 q^{83} -2.68117 q^{84} -21.4724 q^{85} +30.7079 q^{86} +0.495163 q^{87} -18.2006 q^{88} -3.03851 q^{89} +31.0802 q^{90} -29.9930 q^{91} -4.61881 q^{92} +0.360948 q^{93} -27.7732 q^{94} -21.0385 q^{95} -0.963974 q^{96} +0.526724 q^{97} -32.4350 q^{98} -8.05779 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57271	−1.81918	−0.909589	−	0.415509i	$-0.863603\pi$
$2$	−2.57271	−1.81918	−0.909589	+	0.415509i	$0.863603\pi$
$3$	0.131094	0.0756873	0.0378437	−	0.999284i	$-0.487951\pi$
$3$	0.131094	0.0756873	0.0378437	+	0.999284i	$0.487951\pi$
$4$	4.61881	2.30941
$5$	4.05012	1.81127	0.905635	−	0.424059i	$-0.139395\pi$
$5$	4.05012	1.81127	0.905635	+	0.424059i	$0.139395\pi$
$6$	−0.337267	−0.137689
$7$	−4.42802	−1.67363	−0.836817	−	0.547483i	$-0.815586\pi$
$7$	−4.42802	−1.67363	−0.836817	+	0.547483i	$0.815586\pi$
$8$	−6.73744	−2.38204
$9$	−2.98281	−0.994271
$10$	−10.4198	−3.29502
$11$	2.70141	0.814504	0.407252	−	0.913316i	$-0.366487\pi$
$11$	2.70141	0.814504	0.407252	+	0.913316i	$0.366487\pi$
$12$	0.605500	0.174793
$13$	6.77346	1.87862	0.939309	−	0.343072i	$-0.111467\pi$
$13$	6.77346	1.87862	0.939309	+	0.343072i	$0.111467\pi$
$14$	11.3920	3.04464
$15$	0.530948	0.137090
$16$	8.09582	2.02396
$17$	−5.30168	−1.28585	−0.642923	−	0.765931i	$-0.722278\pi$
$17$	−5.30168	−1.28585	−0.642923	+	0.765931i	$0.722278\pi$
$18$	7.67390	1.80876
$19$	−5.19452	−1.19171	−0.595853	−	0.803094i	$-0.703186\pi$
$19$	−5.19452	−1.19171	−0.595853	+	0.803094i	$0.703186\pi$
$20$	18.7068	4.18296
$21$	−0.580488	−0.126673
$22$	−6.94992	−1.48173
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.883240	−0.180291
$25$	11.4035	2.28070
$26$	−17.4261	−3.41754
$27$	−0.784313	−0.150941
$28$	−20.4522	−3.86510
$29$	3.77715	0.701399	0.350700	−	0.936488i	$-0.385944\pi$
$29$	3.77715	0.701399	0.350700	+	0.936488i	$0.385944\pi$
$30$	−1.36597	−0.249391
$31$	2.75335	0.494516	0.247258	−	0.968950i	$-0.420471\pi$
$31$	2.75335	0.494516	0.247258	+	0.968950i	$0.420471\pi$
$32$	−7.35329	−1.29989
$33$	0.354139	0.0616477
$34$	13.6397	2.33918
$35$	−17.9340	−3.03140
$36$	−13.7771	−2.29618
$37$	8.25863	1.35771	0.678855	−	0.734272i	$-0.262476\pi$
$37$	8.25863	1.35771	0.678855	+	0.734272i	$0.262476\pi$
$38$	13.3640	2.16792
$39$	0.887962	0.142188
$40$	−27.2874	−4.31452
$41$	−6.76071	−1.05585	−0.527923	−	0.849292i	$-0.677029\pi$
$41$	−6.76071	−1.05585	−0.527923	+	0.849292i	$0.677029\pi$
$42$	1.49342	0.230440
$43$	−11.9360	−1.82023	−0.910113	−	0.414360i	$-0.864005\pi$
$43$	−11.9360	−1.82023	−0.910113	+	0.414360i	$0.864005\pi$
$44$	12.4773	1.88102
$45$	−12.0808	−1.80089
$46$	2.57271	0.379325
$47$	10.7953	1.57466	0.787329	−	0.616533i	$-0.211463\pi$
$47$	10.7953	1.57466	0.787329	+	0.616533i	$0.211463\pi$
$48$	1.06132	0.153188
$49$	12.6073	1.80105
$50$	−29.3378	−4.14899
$51$	−0.695020	−0.0973222
$52$	31.2853	4.33850
$53$	10.4371	1.43365	0.716825	−	0.697253i	$-0.245594\pi$
$53$	10.4371	1.43365	0.716825	+	0.697253i	$0.245594\pi$
$54$	2.01781	0.274589
$55$	10.9410	1.47529
$56$	29.8335	3.98667
$57$	−0.680973	−0.0901970
$58$	−9.71749	−1.27597
$59$	−1.59549	−0.207715	−0.103857	−	0.994592i	$-0.533119\pi$
$59$	−1.59549	−0.207715	−0.103857	+	0.994592i	$0.533119\pi$
$60$	2.45235	0.316597
$61$	8.20957	1.05113	0.525564	−	0.850754i	$-0.323854\pi$
$61$	8.20957	1.05113	0.525564	+	0.850754i	$0.323854\pi$
$62$	−7.08355	−0.899612
$63$	13.2080	1.66405
$64$	2.72620	0.340775
$65$	27.4333	3.40268
$66$	−0.911095	−0.112148
$67$	3.89013	0.475254	0.237627	−	0.971356i	$-0.423630\pi$
$67$	3.89013	0.475254	0.237627	+	0.971356i	$0.423630\pi$
$68$	−24.4875	−2.96954
$69$	−0.131094	−0.0157819
$70$	46.1389	5.51465
$71$	−4.25456	−0.504923	−0.252462	−	0.967607i	$-0.581240\pi$
$71$	−4.25456	−0.504923	−0.252462	+	0.967607i	$0.581240\pi$
$72$	20.0965	2.36840
$73$	−6.85087	−0.801834	−0.400917	−	0.916114i	$-0.631308\pi$
$73$	−6.85087	−0.801834	−0.400917	+	0.916114i	$0.631308\pi$
$74$	−21.2470	−2.46992
$75$	1.49493	0.172620
$76$	−23.9925	−2.75213
$77$	−11.9619	−1.36318
$78$	−2.28446	−0.258665
$79$	−15.3025	−1.72166	−0.860832	−	0.508888i	$-0.830057\pi$
$79$	−15.3025	−1.72166	−0.860832	+	0.508888i	$0.830057\pi$
$80$	32.7891	3.66593
$81$	8.84562	0.982847
$82$	17.3933	1.92077
$83$	11.6067	1.27400	0.637002	−	0.770862i	$-0.280174\pi$
$83$	11.6067	1.27400	0.637002	+	0.770862i	$0.280174\pi$
$84$	−2.68117	−0.292539
$85$	−21.4724	−2.32901
$86$	30.7079	3.31131
$87$	0.495163	0.0530870
$88$	−18.2006	−1.94019
$89$	−3.03851	−0.322082	−0.161041	−	0.986948i	$-0.551485\pi$
$89$	−3.03851	−0.322082	−0.161041	+	0.986948i	$0.551485\pi$
$90$	31.0802	3.27614
$91$	−29.9930	−3.14412
$92$	−4.61881	−0.481545
$93$	0.360948	0.0374286
$94$	−27.7732	−2.86458
$95$	−21.0385	−2.15850
$96$	−0.963974	−0.0983852
$97$	0.526724	0.0534807	0.0267403	−	0.999642i	$-0.491487\pi$
$97$	0.526724	0.0534807	0.0267403	+	0.999642i	$0.491487\pi$
$98$	−32.4350	−3.27643
$99$	−8.05779	−0.809838
$100$	52.6706	5.26706
$101$	−19.0740	−1.89793	−0.948966	−	0.315380i	$-0.897868\pi$
$101$	−19.0740	−1.89793	−0.948966	+	0.315380i	$0.897868\pi$
$102$	1.78808	0.177046
$103$	−1.91620	−0.188809	−0.0944044	−	0.995534i	$-0.530095\pi$
$103$	−1.91620	−0.188809	−0.0944044	+	0.995534i	$0.530095\pi$
$104$	−45.6357	−4.47495
$105$	−2.35105	−0.229439
$106$	−26.8517	−2.60807
$107$	6.83741	0.660997	0.330499	−	0.943806i	$-0.392783\pi$
$107$	6.83741	0.660997	0.330499	+	0.943806i	$0.392783\pi$
$108$	−3.62260	−0.348585
$109$	4.45928	0.427122	0.213561	−	0.976930i	$-0.431494\pi$
$109$	4.45928	0.427122	0.213561	+	0.976930i	$0.431494\pi$
$110$	−28.1480	−2.68381
$111$	1.08266	0.102762
$112$	−35.8484	−3.38736
$113$	−11.2768	−1.06083	−0.530417	−	0.847737i	$-0.677965\pi$
$113$	−11.2768	−1.06083	−0.530417	+	0.847737i	$0.677965\pi$
$114$	1.75194	0.164084
$115$	−4.05012	−0.377676
$116$	17.4460	1.61982
$117$	−20.2040	−1.86786
$118$	4.10472	0.377870
$119$	23.4759	2.15203
$120$	−3.57723	−0.326555
$121$	−3.70241	−0.336583
$122$	−21.1208	−1.91219
$123$	−0.886291	−0.0799142
$124$	12.7172	1.14204
$125$	25.9349	2.31968
$126$	−33.9802	−3.02719
$127$	3.81161	0.338225	0.169113	−	0.985597i	$-0.445910\pi$
$127$	3.81161	0.338225	0.169113	+	0.985597i	$0.445910\pi$
$128$	7.69287	0.679960
$129$	−1.56474	−0.137768
$130$	−70.5778	−6.19009
$131$	8.89335	0.777015	0.388508	−	0.921445i	$-0.372991\pi$
$131$	8.89335	0.777015	0.388508	+	0.921445i	$0.372991\pi$
$132$	1.63570	0.142370
$133$	23.0014	1.99448
$134$	−10.0081	−0.864572
$135$	−3.17656	−0.273395
$136$	35.7197	3.06294
$137$	−14.8643	−1.26994	−0.634970	−	0.772537i	$-0.718987\pi$
$137$	−14.8643	−1.26994	−0.634970	+	0.772537i	$0.718987\pi$
$138$	0.337267	0.0287101
$139$	10.2729	0.871334	0.435667	−	0.900108i	$-0.356512\pi$
$139$	10.2729	0.871334	0.435667	+	0.900108i	$0.356512\pi$
$140$	−82.8338	−7.00074
$141$	1.41520	0.119182
$142$	10.9457	0.918545
$143$	18.2978	1.53014
$144$	−24.1483	−2.01236
$145$	15.2979	1.27042
$146$	17.6253	1.45868
$147$	1.65275	0.136316
$148$	38.1451	3.13551
$149$	18.7727	1.53792	0.768959	−	0.639298i	$-0.220775\pi$
$149$	18.7727	1.53792	0.768959	+	0.639298i	$0.220775\pi$
$150$	−3.84602	−0.314026
$151$	−16.7601	−1.36392	−0.681958	−	0.731392i	$-0.738871\pi$
$151$	−16.7601	−1.36392	−0.681958	+	0.731392i	$0.738871\pi$
$152$	34.9978	2.83870
$153$	15.8139	1.27848
$154$	30.7744	2.47987
$155$	11.1514	0.895701
$156$	4.10133	0.328369
$157$	−8.51555	−0.679615	−0.339807	−	0.940495i	$-0.610362\pi$
$157$	−8.51555	−0.679615	−0.339807	+	0.940495i	$0.610362\pi$
$158$	39.3688	3.13201
$159$	1.36825	0.108509
$160$	−29.7817	−2.35445
$161$	4.42802	0.348977
$162$	−22.7572	−1.78797
$163$	3.56417	0.279167	0.139584	−	0.990210i	$-0.455424\pi$
$163$	3.56417	0.279167	0.139584	+	0.990210i	$0.455424\pi$
$164$	−31.2265	−2.43838
$165$	1.43431	0.111661
$166$	−29.8607	−2.31764
$167$	−14.0782	−1.08941	−0.544704	−	0.838629i	$-0.683358\pi$
$167$	−14.0782	−1.08941	−0.544704	+	0.838629i	$0.683358\pi$
$168$	3.91100	0.301740
$169$	32.8797	2.52921
$170$	55.2423	4.23689
$171$	15.4943	1.18488
$172$	−55.1303	−4.20364
$173$	21.1992	1.61175	0.805874	−	0.592086i	$-0.201696\pi$
$173$	21.1992	1.61175	0.805874	+	0.592086i	$0.201696\pi$
$174$	−1.27391	−0.0965747
$175$	−50.4948	−3.81705
$176$	21.8701	1.64852
$177$	−0.209159	−0.0157214
$178$	7.81720	0.585924
$179$	7.63898	0.570964	0.285482	−	0.958384i	$-0.407846\pi$
$179$	7.63898	0.570964	0.285482	+	0.958384i	$0.407846\pi$
$180$	−55.7988	−4.15900
$181$	13.3310	0.990888	0.495444	−	0.868640i	$-0.335005\pi$
$181$	13.3310	0.990888	0.495444	+	0.868640i	$0.335005\pi$
$182$	77.1631	5.71971
$183$	1.07623	0.0795571
$184$	6.73744	0.496691
$185$	33.4485	2.45918
$186$	−0.928613	−0.0680892
$187$	−14.3220	−1.04733
$188$	49.8616	3.63653
$189$	3.47295	0.252620
$190$	54.1257	3.92669
$191$	1.52673	0.110470	0.0552351	−	0.998473i	$-0.482409\pi$
$191$	1.52673	0.110470	0.0552351	+	0.998473i	$0.482409\pi$
$192$	0.357389	0.0257923
$193$	−4.80160	−0.345627	−0.172813	−	0.984955i	$-0.555286\pi$
$193$	−4.80160	−0.345627	−0.172813	+	0.984955i	$0.555286\pi$
$194$	−1.35510	−0.0972908
$195$	3.59635	0.257540
$196$	58.2309	4.15935
$197$	12.7348	0.907320	0.453660	−	0.891175i	$-0.350118\pi$
$197$	12.7348	0.907320	0.453660	+	0.891175i	$0.350118\pi$
$198$	20.7303	1.47324
$199$	7.13624	0.505875	0.252937	−	0.967483i	$-0.418603\pi$
$199$	7.13624	0.505875	0.252937	+	0.967483i	$0.418603\pi$
$200$	−76.8303	−5.43272
$201$	0.509973	0.0359707
$202$	49.0717	3.45267
$203$	−16.7253	−1.17388
$204$	−3.21017	−0.224757
$205$	−27.3817	−1.91242
$206$	4.92982	0.343477
$207$	2.98281	0.207320
$208$	54.8367	3.80224
$209$	−14.0325	−0.970650
$210$	6.04855	0.417390
$211$	0.935797	0.0644229	0.0322115	−	0.999481i	$-0.489745\pi$
$211$	0.935797	0.0644229	0.0322115	+	0.999481i	$0.489745\pi$
$212$	48.2072	3.31088
$213$	−0.557749	−0.0382163
$214$	−17.5906	−1.20247
$215$	−48.3423	−3.29692
$216$	5.28426	0.359548
$217$	−12.1919	−0.827638
$218$	−11.4724	−0.777011
$219$	−0.898111	−0.0606887
$220$	50.5345	3.40704
$221$	−35.9107	−2.41561
$222$	−2.78536	−0.186941
$223$	12.4580	0.834246	0.417123	−	0.908850i	$-0.363038\pi$
$223$	12.4580	0.834246	0.417123	+	0.908850i	$0.363038\pi$
$224$	32.5605	2.17554
$225$	−34.0145	−2.26763
$226$	29.0119	1.92985
$227$	0.548450	0.0364019	0.0182009	−	0.999834i	$-0.494206\pi$
$227$	0.548450	0.0364019	0.0182009	+	0.999834i	$0.494206\pi$
$228$	−3.14529	−0.208302
$229$	15.6722	1.03565	0.517825	−	0.855487i	$-0.326742\pi$
$229$	15.6722	1.03565	0.517825	+	0.855487i	$0.326742\pi$
$230$	10.4198	0.687059
$231$	−1.56813	−0.103176
$232$	−25.4483	−1.67076
$233$	19.0373	1.24718	0.623588	−	0.781753i	$-0.285674\pi$
$233$	19.0373	1.24718	0.623588	+	0.781753i	$0.285674\pi$
$234$	51.9788	3.39796
$235$	43.7223	2.85213
$236$	−7.36926	−0.479698
$237$	−2.00607	−0.130308
$238$	−60.3966	−3.91493
$239$	3.92516	0.253897	0.126949	−	0.991909i	$-0.459482\pi$
$239$	3.92516	0.253897	0.126949	+	0.991909i	$0.459482\pi$
$240$	4.29846	0.277464
$241$	−7.09856	−0.457258	−0.228629	−	0.973514i	$-0.573424\pi$
$241$	−7.09856	−0.457258	−0.228629	+	0.973514i	$0.573424\pi$
$242$	9.52521	0.612303
$243$	3.51255	0.225330
$244$	37.9185	2.42748
$245$	51.0612	3.26218
$246$	2.28017	0.145378
$247$	−35.1849	−2.23876
$248$	−18.5505	−1.17796
$249$	1.52158	0.0964259
$250$	−66.7228	−4.21992
$251$	1.23666	0.0780572	0.0390286	−	0.999238i	$-0.487574\pi$
$251$	1.23666	0.0780572	0.0390286	+	0.999238i	$0.487574\pi$
$252$	61.0051	3.84296
$253$	−2.70141	−0.169836
$254$	−9.80614	−0.615292
$255$	−2.81491	−0.176277
$256$	−25.2439	−1.57774
$257$	4.42712	0.276156	0.138078	−	0.990421i	$-0.455907\pi$
$257$	4.42712	0.276156	0.138078	+	0.990421i	$0.455907\pi$
$258$	4.02563	0.250625
$259$	−36.5694	−2.27231
$260$	126.709	7.85818
$261$	−11.2665	−0.697381
$262$	−22.8800	−1.41353
$263$	3.58105	0.220817	0.110409	−	0.993886i	$-0.464784\pi$
$263$	3.58105	0.220817	0.110409	+	0.993886i	$0.464784\pi$
$264$	−2.38599	−0.146848
$265$	42.2717	2.59673
$266$	−59.1759	−3.62831
$267$	−0.398332	−0.0243775
$268$	17.9678	1.09756
$269$	7.73893	0.471851	0.235925	−	0.971771i	$-0.424188\pi$
$269$	7.73893	0.471851	0.235925	+	0.971771i	$0.424188\pi$
$270$	8.17236	0.497354
$271$	−13.0268	−0.791322	−0.395661	−	0.918397i	$-0.629485\pi$
$271$	−13.0268	−0.791322	−0.395661	+	0.918397i	$0.629485\pi$
$272$	−42.9214	−2.60249
$273$	−3.93191	−0.237970
$274$	38.2414	2.31025
$275$	30.8054	1.85764
$276$	−0.605500	−0.0364468
$277$	27.9029	1.67652	0.838260	−	0.545270i	$-0.183573\pi$
$277$	27.9029	1.67652	0.838260	+	0.545270i	$0.183573\pi$
$278$	−26.4291	−1.58511
$279$	−8.21272	−0.491683
$280$	120.829	7.22093
$281$	−18.6061	−1.10995	−0.554973	−	0.831869i	$-0.687271\pi$
$281$	−18.6061	−1.10995	−0.554973	+	0.831869i	$0.687271\pi$
$282$	−3.64090	−0.216813
$283$	31.0652	1.84663	0.923317	−	0.384038i	$-0.125467\pi$
$283$	31.0652	1.84663	0.923317	+	0.384038i	$0.125467\pi$
$284$	−19.6510	−1.16607
$285$	−2.75802	−0.163371
$286$	−47.0750	−2.78360
$287$	29.9365	1.76710
$288$	21.9335	1.29244
$289$	11.1078	0.653399
$290$	−39.3570	−2.31112
$291$	0.0690505	0.00404781
$292$	−31.6429	−1.85176
$293$	5.69212	0.332537	0.166269	−	0.986080i	$-0.446828\pi$
$293$	5.69212	0.332537	0.166269	+	0.986080i	$0.446828\pi$
$294$	−4.25204	−0.247984
$295$	−6.46191	−0.376227
$296$	−55.6420	−3.23413
$297$	−2.11875	−0.122942
$298$	−48.2966	−2.79775
$299$	−6.77346	−0.391719
$300$	6.90481	0.398649
$301$	52.8529	3.04639
$302$	43.1187	2.48120
$303$	−2.50049	−0.143649
$304$	−42.0539	−2.41196
$305$	33.2498	1.90388
$306$	−40.6846	−2.32578
$307$	0.186827	0.0106628	0.00533138	−	0.999986i	$-0.498303\pi$
$307$	0.186827	0.0106628	0.00533138	+	0.999986i	$0.498303\pi$
$308$	−55.2497	−3.14814
$309$	−0.251203	−0.0142904
$310$	−28.6892	−1.62944
$311$	0.856995	0.0485957	0.0242979	−	0.999705i	$-0.492265\pi$
$311$	0.856995	0.0485957	0.0242979	+	0.999705i	$0.492265\pi$
$312$	−5.98259	−0.338697
$313$	−17.0239	−0.962245	−0.481123	−	0.876653i	$-0.659771\pi$
$313$	−17.0239	−0.962245	−0.481123	+	0.876653i	$0.659771\pi$
$314$	21.9080	1.23634
$315$	53.4938	3.01403
$316$	−70.6794	−3.97603
$317$	−5.96766	−0.335177	−0.167589	−	0.985857i	$-0.553598\pi$
$317$	−5.96766	−0.335177	−0.167589	+	0.985857i	$0.553598\pi$
$318$	−3.52010	−0.197398
$319$	10.2036	0.571293
$320$	11.0414	0.617235
$321$	0.896345	0.0500291
$322$	−11.3920	−0.634850
$323$	27.5397	1.53235
$324$	40.8563	2.26979
$325$	77.2410	4.28456
$326$	−9.16956	−0.507855
$327$	0.584587	0.0323277
$328$	45.5499	2.51507
$329$	−47.8018	−2.63540
$330$	−3.69005	−0.203130
$331$	−34.7595	−1.91055	−0.955276	−	0.295715i	$-0.904442\pi$
$331$	−34.7595	−1.91055	−0.955276	+	0.295715i	$0.904442\pi$
$332$	53.6093	2.94219
$333$	−24.6340	−1.34993
$334$	36.2192	1.98182
$335$	15.7555	0.860814
$336$	−4.69953	−0.256380
$337$	19.9058	1.08434	0.542169	−	0.840270i	$-0.317603\pi$
$337$	19.9058	1.08434	0.542169	+	0.840270i	$0.317603\pi$
$338$	−84.5898	−4.60108
$339$	−1.47833	−0.0802917
$340$	−99.1772	−5.37864
$341$	7.43791	0.402785
$342$	−39.8623	−2.15551
$343$	−24.8294	−1.34066
$344$	80.4182	4.33586
$345$	−0.530948	−0.0285853
$346$	−54.5394	−2.93206
$347$	−9.29247	−0.498846	−0.249423	−	0.968395i	$-0.580241\pi$
$347$	−9.29247	−0.498846	−0.249423	+	0.968395i	$0.580241\pi$
$348$	2.28707	0.122600
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	129.908	6.94389
$351$	−5.31251	−0.283561
$352$	−19.8642	−1.05877
$353$	21.1511	1.12576	0.562880	−	0.826539i	$-0.309693\pi$
$353$	21.1511	1.12576	0.562880	+	0.826539i	$0.309693\pi$
$354$	0.538105	0.0286000
$355$	−17.2315	−0.914552
$356$	−14.0343	−0.743817
$357$	3.07756	0.162882
$358$	−19.6529	−1.03869
$359$	−20.8519	−1.10052	−0.550260	−	0.834993i	$-0.685472\pi$
$359$	−20.8519	−1.10052	−0.550260	+	0.834993i	$0.685472\pi$
$360$	81.3934	4.28981
$361$	7.98308	0.420162
$362$	−34.2968	−1.80260
$363$	−0.485365	−0.0254750
$364$	−138.532	−7.26105
$365$	−27.7469	−1.45234
$366$	−2.76882	−0.144728
$367$	18.5112	0.966277	0.483138	−	0.875544i	$-0.339497\pi$
$367$	18.5112	0.966277	0.483138	+	0.875544i	$0.339497\pi$
$368$	−8.09582	−0.422024
$369$	20.1659	1.04980
$370$	−86.0530	−4.47368
$371$	−46.2158	−2.39941
$372$	1.66715	0.0864378
$373$	25.3199	1.31101	0.655507	−	0.755189i	$-0.272455\pi$
$373$	25.3199	1.31101	0.655507	+	0.755189i	$0.272455\pi$
$374$	36.8462	1.90527
$375$	3.39991	0.175571
$376$	−72.7328	−3.75091
$377$	25.5844	1.31766
$378$	−8.93488	−0.459561
$379$	27.9205	1.43418	0.717091	−	0.696980i	$-0.245473\pi$
$379$	27.9205	1.43418	0.717091	+	0.696980i	$0.245473\pi$
$380$	−97.1727	−4.98486
$381$	0.499680	0.0255994
$382$	−3.92782	−0.200965
$383$	−11.1250	−0.568461	−0.284230	−	0.958756i	$-0.591738\pi$
$383$	−11.1250	−0.568461	−0.284230	+	0.958756i	$0.591738\pi$
$384$	1.00849	0.0514643
$385$	−48.4470	−2.46909
$386$	12.3531	0.628756
$387$	35.6029	1.80980
$388$	2.43284	0.123509
$389$	−7.01234	−0.355540	−0.177770	−	0.984072i	$-0.556888\pi$
$389$	−7.01234	−0.355540	−0.177770	+	0.984072i	$0.556888\pi$
$390$	−9.25235	−0.468511
$391$	5.30168	0.268117
$392$	−84.9411	−4.29018
$393$	1.16587	0.0588102
$394$	−32.7630	−1.65058
$395$	−61.9769	−3.11840
$396$	−37.2174	−1.87025
$397$	24.4227	1.22574	0.612870	−	0.790183i	$-0.290015\pi$
$397$	24.4227	1.22574	0.612870	+	0.790183i	$0.290015\pi$
$398$	−18.3595	−0.920276
$399$	3.01536	0.150957
$400$	92.3205	4.61603
$401$	−22.3716	−1.11718	−0.558592	−	0.829442i	$-0.688658\pi$
$401$	−22.3716	−1.11718	−0.558592	+	0.829442i	$0.688658\pi$
$402$	−1.31201	−0.0654372
$403$	18.6497	0.929006
$404$	−88.0992	−4.38310
$405$	35.8258	1.78020
$406$	43.0292	2.13550
$407$	22.3099	1.10586
$408$	4.68265	0.231826
$409$	27.9598	1.38252	0.691262	−	0.722604i	$-0.257055\pi$
$409$	27.9598	1.38252	0.691262	+	0.722604i	$0.257055\pi$
$410$	70.4451	3.47903
$411$	−1.94862	−0.0961183
$412$	−8.85057	−0.436036
$413$	7.06484	0.347638
$414$	−7.67390	−0.377152
$415$	47.0086	2.30756
$416$	−49.8072	−2.44200
$417$	1.34672	0.0659490
$418$	36.1015	1.76578
$419$	34.3708	1.67912	0.839562	−	0.543264i	$-0.182812\pi$
$419$	34.3708	1.67912	0.839562	+	0.543264i	$0.182812\pi$
$420$	−10.8590	−0.529867
$421$	19.1625	0.933923	0.466962	−	0.884278i	$-0.345349\pi$
$421$	19.1625	0.933923	0.466962	+	0.884278i	$0.345349\pi$
$422$	−2.40753	−0.117197
$423$	−32.2004	−1.56564
$424$	−70.3196	−3.41502
$425$	−60.4576	−2.93262
$426$	1.43492	0.0695222
$427$	−36.3521	−1.75920
$428$	31.5807	1.52651
$429$	2.39874	0.115812
$430$	124.371	5.99768
$431$	15.1623	0.730342	0.365171	−	0.930940i	$-0.381011\pi$
$431$	15.1623	0.730342	0.365171	+	0.930940i	$0.381011\pi$
$432$	−6.34966	−0.305498
$433$	9.39307	0.451402	0.225701	−	0.974197i	$-0.427533\pi$
$433$	9.39307	0.451402	0.225701	+	0.974197i	$0.427533\pi$
$434$	31.3661	1.50562
$435$	2.00547	0.0961549
$436$	20.5966	0.986399
$437$	5.19452	0.248488
$438$	2.31057	0.110404
$439$	−13.7351	−0.655540	−0.327770	−	0.944758i	$-0.606297\pi$
$439$	−13.7351	−0.655540	−0.327770	+	0.944758i	$0.606297\pi$
$440$	−73.7145	−3.51420
$441$	−37.6053	−1.79073
$442$	92.3876	4.39443
$443$	15.5239	0.737563	0.368781	−	0.929516i	$-0.379775\pi$
$443$	15.5239	0.737563	0.368781	+	0.929516i	$0.379775\pi$
$444$	5.00060	0.237318
$445$	−12.3063	−0.583376
$446$	−32.0507	−1.51764
$447$	2.46099	0.116401
$448$	−12.0716	−0.570332
$449$	−12.0856	−0.570356	−0.285178	−	0.958475i	$-0.592053\pi$
$449$	−12.0856	−0.570356	−0.285178	+	0.958475i	$0.592053\pi$
$450$	87.5092	4.12522
$451$	−18.2634	−0.859991
$452$	−52.0855	−2.44990
$453$	−2.19715	−0.103231
$454$	−1.41100	−0.0662215
$455$	−121.475	−5.69484
$456$	4.58801	0.214853
$457$	17.0967	0.799752	0.399876	−	0.916569i	$-0.369053\pi$
$457$	17.0967	0.799752	0.399876	+	0.916569i	$0.369053\pi$
$458$	−40.3200	−1.88403
$459$	4.15817	0.194087
$460$	−18.7068	−0.872207
$461$	2.24712	0.104659	0.0523294	−	0.998630i	$-0.483335\pi$
$461$	2.24712	0.104659	0.0523294	+	0.998630i	$0.483335\pi$
$462$	4.03435	0.187695
$463$	−1.35473	−0.0629598	−0.0314799	−	0.999504i	$-0.510022\pi$
$463$	−1.35473	−0.0629598	−0.0314799	+	0.999504i	$0.510022\pi$
$464$	30.5791	1.41960
$465$	1.46188	0.0677932
$466$	−48.9774	−2.26884
$467$	17.2714	0.799227	0.399614	−	0.916684i	$-0.369144\pi$
$467$	17.2714	0.799227	0.399614	+	0.916684i	$0.369144\pi$
$468$	−93.3183	−4.31364
$469$	−17.2255	−0.795402
$470$	−112.485	−5.18853
$471$	−1.11634	−0.0514382
$472$	10.7495	0.494786
$473$	−32.2440	−1.48258
$474$	5.16103	0.237054
$475$	−59.2357	−2.71792
$476$	108.431	4.96992
$477$	−31.1320	−1.42544
$478$	−10.0983	−0.461885
$479$	−16.7067	−0.763347	−0.381673	−	0.924297i	$-0.624652\pi$
$479$	−16.7067	−0.763347	−0.381673	+	0.924297i	$0.624652\pi$
$480$	−3.90421	−0.178202
$481$	55.9395	2.55062
$482$	18.2625	0.831834
$483$	0.580488	0.0264131
$484$	−17.1007	−0.777306
$485$	2.13329	0.0968679
$486$	−9.03676	−0.409916
$487$	−16.4099	−0.743603	−0.371802	−	0.928312i	$-0.621260\pi$
$487$	−16.4099	−0.743603	−0.371802	+	0.928312i	$0.621260\pi$
$488$	−55.3115	−2.50383
$489$	0.467242	0.0211294
$490$	−131.365	−5.93449
$491$	−30.7762	−1.38891	−0.694455	−	0.719536i	$-0.744354\pi$
$491$	−30.7762	−1.38891	−0.694455	+	0.719536i	$0.744354\pi$
$492$	−4.09361	−0.184554
$493$	−20.0252	−0.901891
$494$	90.5203	4.07270
$495$	−32.6350	−1.46684
$496$	22.2906	1.00088
$497$	18.8393	0.845056
$498$	−3.91457	−0.175416
$499$	−25.6742	−1.14934	−0.574668	−	0.818386i	$-0.694869\pi$
$499$	−25.6742	−1.14934	−0.574668	+	0.818386i	$0.694869\pi$
$500$	119.788	5.35710
$501$	−1.84558	−0.0824543
$502$	−3.18156	−0.142000
$503$	−5.11148	−0.227910	−0.113955	−	0.993486i	$-0.536352\pi$
$503$	−5.11148	−0.227910	−0.113955	+	0.993486i	$0.536352\pi$
$504$	−88.9878	−3.96383
$505$	−77.2519	−3.43766
$506$	6.94992	0.308962
$507$	4.31034	0.191429
$508$	17.6051	0.781100
$509$	−8.48542	−0.376110	−0.188055	−	0.982159i	$-0.560218\pi$
$509$	−8.48542	−0.376110	−0.188055	+	0.982159i	$0.560218\pi$
$510$	7.24195	0.320679
$511$	30.3358	1.34198
$512$	49.5593	2.19023
$513$	4.07413	0.179877
$514$	−11.3897	−0.502378
$515$	−7.76084	−0.341984
$516$	−7.22726	−0.318163
$517$	29.1625	1.28257
$518$	94.0822	4.13373
$519$	2.77910	0.121989
$520$	−184.830	−8.10534
$521$	24.3928	1.06867	0.534334	−	0.845274i	$-0.320563\pi$
$521$	24.3928	1.06867	0.534334	+	0.845274i	$0.320563\pi$
$522$	28.9855	1.26866
$523$	17.4178	0.761627	0.380813	−	0.924652i	$-0.375644\pi$
$523$	17.4178	0.761627	0.380813	+	0.924652i	$0.375644\pi$
$524$	41.0767	1.79445
$525$	−6.61958	−0.288902
$526$	−9.21300	−0.401706
$527$	−14.5974	−0.635871
$528$	2.86705	0.124772
$529$	1.00000	0.0434783
$530$	−108.753	−4.72391
$531$	4.75904	0.206525
$532$	106.239	4.60606
$533$	−45.7934	−1.98353
$534$	1.02479	0.0443470
$535$	27.6923	1.19724
$536$	−26.2095	−1.13208
$537$	1.00143	0.0432148
$538$	−19.9100	−0.858381
$539$	34.0575	1.46696
$540$	−14.6720	−0.631380
$541$	14.8306	0.637618	0.318809	−	0.947819i	$-0.396717\pi$
$541$	14.8306	0.637618	0.318809	+	0.947819i	$0.396717\pi$
$542$	33.5141	1.43956
$543$	1.74762	0.0749977
$544$	38.9848	1.67146
$545$	18.0606	0.773633
$546$	10.1156	0.432910
$547$	27.8733	1.19178	0.595888	−	0.803068i	$-0.296800\pi$
$547$	27.8733	1.19178	0.595888	+	0.803068i	$0.296800\pi$
$548$	−68.6553	−2.93281
$549$	−24.4876	−1.04511
$550$	−79.2533	−3.37937
$551$	−19.6205	−0.835861
$552$	0.883240	0.0375932
$553$	67.7597	2.88144
$554$	−71.7859	−3.04989
$555$	4.38490	0.186129
$556$	47.4485	2.01227
$557$	32.6721	1.38436	0.692181	−	0.721724i	$-0.256650\pi$
$557$	32.6721	1.38436	0.692181	+	0.721724i	$0.256650\pi$
$558$	21.1289	0.894458
$559$	−80.8481	−3.41951
$560$	−145.190	−6.13542
$561$	−1.87753	−0.0792694
$562$	47.8679	2.01919
$563$	−7.52385	−0.317093	−0.158546	−	0.987352i	$-0.550681\pi$
$563$	−7.52385	−0.317093	−0.158546	+	0.987352i	$0.550681\pi$
$564$	6.53657	0.275239
$565$	−45.6725	−1.92146
$566$	−79.9216	−3.35936
$567$	−39.1686	−1.64493
$568$	28.6648	1.20275
$569$	21.5373	0.902892	0.451446	−	0.892298i	$-0.350908\pi$
$569$	21.5373	0.902892	0.451446	+	0.892298i	$0.350908\pi$
$570$	7.09558	0.297201
$571$	3.63993	0.152326	0.0761631	−	0.997095i	$-0.475733\pi$
$571$	3.63993	0.152326	0.0761631	+	0.997095i	$0.475733\pi$
$572$	84.5144	3.53372
$573$	0.200145	0.00836119
$574$	−77.0179	−3.21467
$575$	−11.4035	−0.475558
$576$	−8.13174	−0.338823
$577$	−45.5745	−1.89729	−0.948646	−	0.316339i	$-0.897546\pi$
$577$	−45.5745	−1.89729	−0.948646	+	0.316339i	$0.897546\pi$
$578$	−28.5771	−1.18865
$579$	−0.629462	−0.0261596
$580$	70.6582	2.93392
$581$	−51.3948	−2.13221
$582$	−0.177647	−0.00736369
$583$	28.1949	1.16772
$584$	46.1573	1.91000
$585$	−81.8285	−3.38319
$586$	−14.6442	−0.604945
$587$	−16.0132	−0.660935	−0.330468	−	0.943817i	$-0.607206\pi$
$587$	−16.0132	−0.660935	−0.330468	+	0.943817i	$0.607206\pi$
$588$	7.63374	0.314810
$589$	−14.3023	−0.589317
$590$	16.6246	0.684424
$591$	1.66947	0.0686727
$592$	66.8604	2.74795
$593$	29.0330	1.19224	0.596121	−	0.802894i	$-0.296708\pi$
$593$	29.0330	1.19224	0.596121	+	0.802894i	$0.296708\pi$
$594$	5.45091	0.223654
$595$	95.0803	3.89791
$596$	86.7075	3.55168
$597$	0.935521	0.0382883
$598$	17.4261	0.712607
$599$	−4.24169	−0.173311	−0.0866554	−	0.996238i	$-0.527618\pi$
$599$	−4.24169	−0.173311	−0.0866554	+	0.996238i	$0.527618\pi$
$600$	−10.0720	−0.411188
$601$	2.33851	0.0953897	0.0476948	−	0.998862i	$-0.484813\pi$
$601$	2.33851	0.0953897	0.0476948	+	0.998862i	$0.484813\pi$
$602$	−135.975	−5.54192
$603$	−11.6035	−0.472532
$604$	−77.4117	−3.14984
$605$	−14.9952	−0.609642
$606$	6.43302	0.261324
$607$	−8.68644	−0.352572	−0.176286	−	0.984339i	$-0.556408\pi$
$607$	−8.68644	−0.352572	−0.176286	+	0.984339i	$0.556408\pi$
$608$	38.1968	1.54909
$609$	−2.19259	−0.0888482
$610$	−85.5418	−3.46349
$611$	73.1216	2.95818
$612$	73.0416	2.95253
$613$	10.2486	0.413938	0.206969	−	0.978348i	$-0.433640\pi$
$613$	10.2486	0.413938	0.206969	+	0.978348i	$0.433640\pi$
$614$	−0.480650	−0.0193975
$615$	−3.58959	−0.144746
$616$	80.5924	3.24716
$617$	−31.6579	−1.27450	−0.637249	−	0.770658i	$-0.719928\pi$
$617$	−31.6579	−1.27450	−0.637249	+	0.770658i	$0.719928\pi$
$618$	0.646271	0.0259968
$619$	19.0256	0.764705	0.382352	−	0.924017i	$-0.375114\pi$
$619$	19.0256	0.764705	0.382352	+	0.924017i	$0.375114\pi$
$620$	51.5062	2.06854
$621$	0.784313	0.0314734
$622$	−2.20480	−0.0884043
$623$	13.4546	0.539046
$624$	7.18878	0.287781
$625$	48.0219	1.92088
$626$	43.7974	1.75049
$627$	−1.83958	−0.0734659
$628$	−39.3318	−1.56951
$629$	−43.7846	−1.74581
$630$	−137.624	−5.48306
$631$	12.2089	0.486029	0.243015	−	0.970023i	$-0.421864\pi$
$631$	12.2089	0.486029	0.243015	+	0.970023i	$0.421864\pi$
$632$	103.100	4.10108
$633$	0.122678	0.00487600
$634$	15.3530	0.609747
$635$	15.4375	0.612617
$636$	6.31969	0.250592
$637$	85.3952	3.38348
$638$	−26.2509	−1.03928
$639$	12.6906	0.502031
$640$	31.1570	1.23159
$641$	−25.5717	−1.01002	−0.505011	−	0.863113i	$-0.668512\pi$
$641$	−25.5717	−1.01002	−0.505011	+	0.863113i	$0.668512\pi$
$642$	−2.30603	−0.0910119
$643$	45.3691	1.78918	0.894591	−	0.446886i	$-0.147467\pi$
$643$	45.3691	1.78918	0.894591	+	0.446886i	$0.147467\pi$
$644$	20.4522	0.805929
$645$	−6.33740	−0.249535
$646$	−70.8515	−2.78762
$647$	−16.7911	−0.660125	−0.330062	−	0.943959i	$-0.607070\pi$
$647$	−16.7911	−0.660125	−0.330062	+	0.943959i	$0.607070\pi$
$648$	−59.5969	−2.34119
$649$	−4.31006	−0.169184
$650$	−198.718	−7.79437
$651$	−1.59828	−0.0626417
$652$	16.4622	0.644711
$653$	−25.5788	−1.00098	−0.500489	−	0.865743i	$-0.666846\pi$
$653$	−25.5788	−1.00098	−0.500489	+	0.865743i	$0.666846\pi$
$654$	−1.50397	−0.0588099
$655$	36.0191	1.40738
$656$	−54.7335	−2.13698
$657$	20.4349	0.797241
$658$	122.980	4.79426
$659$	13.9690	0.544157	0.272078	−	0.962275i	$-0.412289\pi$
$659$	13.9690	0.544157	0.272078	+	0.962275i	$0.412289\pi$
$660$	6.62479	0.257870
$661$	−8.85675	−0.344488	−0.172244	−	0.985054i	$-0.555102\pi$
$661$	−8.85675	−0.344488	−0.172244	+	0.985054i	$0.555102\pi$
$662$	89.4258	3.47563
$663$	−4.70769	−0.182831
$664$	−78.1996	−3.03473
$665$	93.1586	3.61254
$666$	63.3759	2.45577
$667$	−3.77715	−0.146252
$668$	−65.0248	−2.51588
$669$	1.63317	0.0631419
$670$	−40.5342	−1.56597
$671$	22.1774	0.856148
$672$	4.26849	0.164661
$673$	−3.26911	−0.126015	−0.0630075	−	0.998013i	$-0.520069\pi$
$673$	−3.26911	−0.126015	−0.0630075	+	0.998013i	$0.520069\pi$
$674$	−51.2117	−1.97260
$675$	−8.94390	−0.344251
$676$	151.865	5.84097
$677$	17.2912	0.664556	0.332278	−	0.943182i	$-0.392183\pi$
$677$	17.2912	0.664556	0.332278	+	0.943182i	$0.392183\pi$
$678$	3.80330	0.146065
$679$	−2.33234	−0.0895070
$680$	144.669	5.54781
$681$	0.0718986	0.00275516
$682$	−19.1355	−0.732738
$683$	−15.1467	−0.579572	−0.289786	−	0.957092i	$-0.593584\pi$
$683$	−15.1467	−0.579572	−0.289786	+	0.957092i	$0.593584\pi$
$684$	71.5653	2.73637
$685$	−60.2020	−2.30020
$686$	63.8786	2.43890
$687$	2.05454	0.0783855
$688$	−96.6319	−3.68406
$689$	70.6955	2.69328
$690$	1.36597	0.0520017
$691$	16.5915	0.631171	0.315585	−	0.948897i	$-0.397799\pi$
$691$	16.5915	0.631171	0.315585	+	0.948897i	$0.397799\pi$
$692$	97.9154	3.72219
$693$	35.6800	1.35537
$694$	23.9068	0.907489
$695$	41.6064	1.57822
$696$	−3.33613	−0.126456
$697$	35.8431	1.35765
$698$	−2.57271	−0.0973783
$699$	2.49569	0.0943955
$700$	−233.226	−8.81512
$701$	−22.1876	−0.838015	−0.419007	−	0.907983i	$-0.637622\pi$
$701$	−22.1876	−0.838015	−0.419007	+	0.907983i	$0.637622\pi$
$702$	13.6675	0.515847
$703$	−42.8997	−1.61799
$704$	7.36457	0.277563
$705$	5.73175	0.215870
$706$	−54.4156	−2.04796
$707$	84.4599	3.17644
$708$	−0.966068	−0.0363070
$709$	−0.700975	−0.0263257	−0.0131628	−	0.999913i	$-0.504190\pi$
$709$	−0.700975	−0.0263257	−0.0131628	+	0.999913i	$0.504190\pi$
$710$	44.3315	1.66373
$711$	45.6445	1.71180
$712$	20.4718	0.767213
$713$	−2.75335	−0.103114
$714$	−7.91765	−0.296311
$715$	74.1085	2.77150
$716$	35.2831	1.31859
$717$	0.514566	0.0192168
$718$	53.6458	2.00204
$719$	−34.1898	−1.27506	−0.637532	−	0.770424i	$-0.720045\pi$
$719$	−34.1898	−1.27506	−0.637532	+	0.770424i	$0.720045\pi$
$720$	−97.8037	−3.64493
$721$	8.48497	0.315997
$722$	−20.5381	−0.764350
$723$	−0.930580	−0.0346087
$724$	61.5736	2.28837
$725$	43.0726	1.59968
$726$	1.24870	0.0463436
$727$	−24.1194	−0.894538	−0.447269	−	0.894399i	$-0.647603\pi$
$727$	−24.1194	−0.894538	−0.447269	+	0.894399i	$0.647603\pi$
$728$	202.076	7.48943
$729$	−26.0764	−0.965792
$730$	71.3845	2.64206
$731$	63.2809	2.34053
$732$	4.97090	0.183730
$733$	17.1328	0.632816	0.316408	−	0.948623i	$-0.397523\pi$
$733$	17.1328	0.632816	0.316408	+	0.948623i	$0.397523\pi$
$734$	−47.6239	−1.75783
$735$	6.69384	0.246906
$736$	7.35329	0.271046
$737$	10.5088	0.387097
$738$	−51.8811	−1.90977
$739$	40.8754	1.50362	0.751812	−	0.659377i	$-0.229180\pi$
$739$	40.8754	1.50362	0.751812	+	0.659377i	$0.229180\pi$
$740$	154.492	5.67925
$741$	−4.61254	−0.169446
$742$	118.900	4.36495
$743$	−4.61189	−0.169194	−0.0845969	−	0.996415i	$-0.526960\pi$
$743$	−4.61189	−0.169194	−0.0845969	+	0.996415i	$0.526960\pi$
$744$	−2.43187	−0.0891565
$745$	76.0316	2.78558
$746$	−65.1406	−2.38497
$747$	−34.6207	−1.26671
$748$	−66.1506	−2.41870
$749$	−30.2762	−1.10627
$750$	−8.74698	−0.319394
$751$	−28.2085	−1.02934	−0.514671	−	0.857387i	$-0.672086\pi$
$751$	−28.2085	−1.02934	−0.514671	+	0.857387i	$0.672086\pi$
$752$	87.3969	3.18704
$753$	0.162119	0.00590794
$754$	−65.8210	−2.39706
$755$	−67.8803	−2.47042
$756$	16.0409	0.583403
$757$	22.1180	0.803892	0.401946	−	0.915663i	$-0.368334\pi$
$757$	22.1180	0.803892	0.401946	+	0.915663i	$0.368334\pi$
$758$	−71.8313	−2.60903
$759$	−0.354139	−0.0128544
$760$	141.745	5.14164
$761$	−34.4654	−1.24937	−0.624685	−	0.780877i	$-0.714773\pi$
$761$	−34.4654	−1.24937	−0.624685	+	0.780877i	$0.714773\pi$
$762$	−1.28553	−0.0465698
$763$	−19.7458	−0.714845
$764$	7.05167	0.255121
$765$	64.0483	2.31567
$766$	28.6213	1.03413
$767$	−10.8070	−0.390217
$768$	−3.30933	−0.119415
$769$	3.94475	0.142251	0.0711256	−	0.997467i	$-0.477341\pi$
$769$	3.94475	0.142251	0.0711256	+	0.997467i	$0.477341\pi$
$770$	124.640	4.49171
$771$	0.580371	0.0209015
$772$	−22.1777	−0.798192
$773$	14.2939	0.514115	0.257057	−	0.966396i	$-0.417247\pi$
$773$	14.2939	0.514115	0.257057	+	0.966396i	$0.417247\pi$
$774$	−91.5959	−3.29235
$775$	31.3977	1.12784
$776$	−3.54877	−0.127393
$777$	−4.79403	−0.171985
$778$	18.0407	0.646790
$779$	35.1187	1.25826
$780$	16.6109	0.594765
$781$	−11.4933	−0.411262
$782$	−13.6397	−0.487753
$783$	−2.96247	−0.105870
$784$	102.067	3.64524
$785$	−34.4890	−1.23097
$786$	−2.99943	−0.106986
$787$	51.1476	1.82321	0.911607	−	0.411063i	$-0.134842\pi$
$787$	51.1476	1.82321	0.911607	+	0.411063i	$0.134842\pi$
$788$	58.8199	2.09537
$789$	0.469456	0.0167131
$790$	159.448	5.67292
$791$	49.9339	1.77545
$792$	54.2889	1.92907
$793$	55.6072	1.97467
$794$	−62.8325	−2.22984
$795$	5.54158	0.196539
$796$	32.9610	1.16827
$797$	8.67210	0.307181	0.153591	−	0.988135i	$-0.450916\pi$
$797$	8.67210	0.307181	0.153591	+	0.988135i	$0.450916\pi$
$798$	−7.75763	−0.274617
$799$	−57.2333	−2.02477
$800$	−83.8530	−2.96465
$801$	9.06331	0.320236
$802$	57.5555	2.03236
$803$	−18.5070	−0.653097
$804$	2.35547	0.0830711
$805$	17.9340	0.632091
$806$	−47.9801	−1.69003
$807$	1.01453	0.0357131
$808$	128.510	4.52096
$809$	29.1770	1.02581	0.512905	−	0.858445i	$-0.328569\pi$
$809$	29.1770	1.02581	0.512905	+	0.858445i	$0.328569\pi$
$810$	−92.1694	−3.23850
$811$	36.0503	1.26590	0.632948	−	0.774194i	$-0.281845\pi$
$811$	36.0503	1.26590	0.632948	+	0.774194i	$0.281845\pi$
$812$	−77.2510	−2.71098
$813$	−1.70774	−0.0598931
$814$	−57.3968	−2.01176
$815$	14.4353	0.505647
$816$	−5.62676	−0.196976
$817$	62.0019	2.16917
$818$	−71.9324	−2.51506
$819$	89.4635	3.12611
$820$	−126.471	−4.41656
$821$	−47.1173	−1.64441	−0.822203	−	0.569194i	$-0.807255\pi$
$821$	−47.1173	−1.64441	−0.822203	+	0.569194i	$0.807255\pi$
$822$	5.01323	0.174856
$823$	−42.8123	−1.49234	−0.746172	−	0.665753i	$-0.768110\pi$
$823$	−42.8123	−1.49234	−0.746172	+	0.665753i	$0.768110\pi$
$824$	12.9103	0.449751
$825$	4.03842	0.140600
$826$	−18.1758	−0.632415
$827$	12.1253	0.421637	0.210818	−	0.977525i	$-0.432387\pi$
$827$	12.1253	0.421637	0.210818	+	0.977525i	$0.432387\pi$
$828$	13.7771	0.478786
$829$	−21.3472	−0.741420	−0.370710	−	0.928749i	$-0.620886\pi$
$829$	−21.3472	−0.741420	−0.370710	+	0.928749i	$0.620886\pi$
$830$	−120.939	−4.19787
$831$	3.65791	0.126891
$832$	18.4658	0.640186
$833$	−66.8400	−2.31587
$834$	−3.46470	−0.119973
$835$	−57.0186	−1.97321
$836$	−64.8136	−2.24163
$837$	−2.15949	−0.0746427
$838$	−88.4260	−3.05462
$839$	29.1294	1.00566	0.502829	−	0.864386i	$-0.332293\pi$
$839$	29.1294	1.00566	0.502829	+	0.864386i	$0.332293\pi$
$840$	15.8400	0.546533
$841$	−14.7331	−0.508039
$842$	−49.2995	−1.69897
$843$	−2.43915	−0.0840088
$844$	4.32227	0.148779
$845$	133.167	4.58108
$846$	82.8422	2.84817
$847$	16.3943	0.563316
$848$	84.4972	2.90165
$849$	4.07247	0.139767
$850$	155.540	5.33496
$851$	−8.25863	−0.283102
$852$	−2.57614	−0.0882570
$853$	−12.1894	−0.417356	−0.208678	−	0.977984i	$-0.566916\pi$
$853$	−12.1894	−0.417356	−0.208678	+	0.977984i	$0.566916\pi$
$854$	93.5233	3.20030
$855$	62.7538	2.14613
$856$	−46.0666	−1.57453
$857$	6.13178	0.209458	0.104729	−	0.994501i	$-0.466603\pi$
$857$	6.13178	0.209458	0.104729	+	0.994501i	$0.466603\pi$
$858$	−6.17126	−0.210683
$859$	47.9178	1.63494	0.817468	−	0.575974i	$-0.195377\pi$
$859$	47.9178	1.63494	0.817468	+	0.575974i	$0.195377\pi$
$860$	−223.284	−7.61393
$861$	3.92451	0.133747
$862$	−39.0081	−1.32862
$863$	−38.7217	−1.31810	−0.659050	−	0.752099i	$-0.729042\pi$
$863$	−38.7217	−1.31810	−0.659050	+	0.752099i	$0.729042\pi$
$864$	5.76728	0.196207
$865$	85.8595	2.91931
$866$	−24.1656	−0.821181
$867$	1.45617	0.0494540
$868$	−56.3120	−1.91135
$869$	−41.3382	−1.40230
$870$	−5.15948	−0.174923
$871$	26.3496	0.892822
$872$	−30.0442	−1.01742
$873$	−1.57112	−0.0531743
$874$	−13.3640	−0.452043
$875$	−114.840	−3.88230
$876$	−4.14821	−0.140155
$877$	−5.10733	−0.172462	−0.0862311	−	0.996275i	$-0.527482\pi$
$877$	−5.10733	−0.172462	−0.0862311	+	0.996275i	$0.527482\pi$
$878$	35.3363	1.19254
$879$	0.746205	0.0251689
$880$	88.5765	2.98591
$881$	45.2627	1.52494	0.762470	−	0.647024i	$-0.223987\pi$
$881$	45.2627	1.52494	0.762470	+	0.647024i	$0.223987\pi$
$882$	96.7475	3.25766
$883$	49.0503	1.65067	0.825336	−	0.564641i	$-0.190986\pi$
$883$	49.0503	1.65067	0.825336	+	0.564641i	$0.190986\pi$
$884$	−165.865	−5.57864
$885$	−0.847120	−0.0284756
$886$	−39.9384	−1.34176
$887$	−34.9767	−1.17440	−0.587201	−	0.809441i	$-0.699770\pi$
$887$	−34.9767	−1.17440	−0.587201	+	0.809441i	$0.699770\pi$
$888$	−7.29435	−0.244783
$889$	−16.8779	−0.566065
$890$	31.6606	1.06127
$891$	23.8956	0.800533
$892$	57.5410	1.92661
$893$	−56.0765	−1.87653
$894$	−6.33141	−0.211754
$895$	30.9388	1.03417
$896$	−34.0641	−1.13800
$897$	−0.887962	−0.0296482
$898$	31.0927	1.03758
$899$	10.3998	0.346853
$900$	−157.106	−5.23688
$901$	−55.3343	−1.84345
$902$	46.9864	1.56448
$903$	6.92871	0.230573
$904$	75.9769	2.52695
$905$	53.9923	1.79477
$906$	5.65262	0.187796
$907$	39.0540	1.29677	0.648383	−	0.761314i	$-0.275446\pi$
$907$	39.0540	1.29677	0.648383	+	0.761314i	$0.275446\pi$
$908$	2.53319	0.0840668
$909$	56.8941	1.88706
$910$	312.520	10.3599
$911$	−9.06583	−0.300364	−0.150182	−	0.988658i	$-0.547986\pi$
$911$	−9.06583	−0.300364	−0.150182	+	0.988658i	$0.547986\pi$
$912$	−5.51303	−0.182555
$913$	31.3545	1.03768
$914$	−43.9849	−1.45489
$915$	4.35885	0.144099
$916$	72.3871	2.39174
$917$	−39.3799	−1.30044
$918$	−10.6978	−0.353079
$919$	32.9876	1.08816	0.544080	−	0.839033i	$-0.316879\pi$
$919$	32.9876	1.08816	0.544080	+	0.839033i	$0.316879\pi$
$920$	27.2874	0.899640
$921$	0.0244919	0.000807036 0
$922$	−5.78118	−0.190393
$923$	−28.8181	−0.948558
$924$	−7.24292	−0.238274
$925$	94.1771	3.09652
$926$	3.48533	0.114535
$927$	5.71567	0.187727
$928$	−27.7745	−0.911741
$929$	−12.8994	−0.423214	−0.211607	−	0.977355i	$-0.567870\pi$
$929$	−12.8994	−0.423214	−0.211607	+	0.977355i	$0.567870\pi$
$930$	−3.76100	−0.123328
$931$	−65.4891	−2.14632
$932$	87.9299	2.88024
$933$	0.112347	0.00367808
$934$	−44.4344	−1.45394
$935$	−58.0058	−1.89699
$936$	136.123	4.44932
$937$	−15.2166	−0.497105	−0.248552	−	0.968618i	$-0.579955\pi$
$937$	−15.2166	−0.497105	−0.248552	+	0.968618i	$0.579955\pi$
$938$	44.3162	1.44698
$939$	−2.23173	−0.0728298
$940$	201.945	6.58673
$941$	−39.5278	−1.28857	−0.644285	−	0.764786i	$-0.722845\pi$
$941$	−39.5278	−1.28857	−0.644285	+	0.764786i	$0.722845\pi$
$942$	2.87202	0.0935753
$943$	6.76071	0.220159
$944$	−12.9168	−0.420405
$945$	14.0659	0.457563
$946$	82.9544	2.69708
$947$	−48.1446	−1.56449	−0.782245	−	0.622971i	$-0.785926\pi$
$947$	−48.1446	−1.56449	−0.782245	+	0.622971i	$0.785926\pi$
$948$	−9.26567	−0.300935
$949$	−46.4041	−1.50634
$950$	152.396	4.94438
$951$	−0.782327	−0.0253687
$952$	−158.168	−5.12624
$953$	−38.8168	−1.25740	−0.628700	−	0.777648i	$-0.716413\pi$
$953$	−38.8168	−1.25740	−0.628700	+	0.777648i	$0.716413\pi$
$954$	80.0936	2.59313
$955$	6.18343	0.200091
$956$	18.1296	0.586353
$957$	1.33764	0.0432396
$958$	42.9813	1.38866
$959$	65.8192	2.12541
$960$	1.44747	0.0467169
$961$	−23.4191	−0.755454
$962$	−143.916	−4.64003
$963$	−20.3947	−0.657211
$964$	−32.7869	−1.05600
$965$	−19.4470	−0.626023
$966$	−1.49342	−0.0480501
$967$	28.4015	0.913329	0.456665	−	0.889639i	$-0.349044\pi$
$967$	28.4015	0.913329	0.456665	+	0.889639i	$0.349044\pi$
$968$	24.9448	0.801755
$969$	3.61030	0.115979
$970$	−5.48834	−0.176220
$971$	−6.25678	−0.200790	−0.100395	−	0.994948i	$-0.532011\pi$
$971$	−6.25678	−0.200790	−0.100395	+	0.994948i	$0.532011\pi$
$972$	16.2238	0.520379
$973$	−45.4885	−1.45829
$974$	42.2178	1.35275
$975$	10.1259	0.324287
$976$	66.4632	2.12744
$977$	49.3774	1.57972	0.789861	−	0.613286i	$-0.210153\pi$
$977$	49.3774	1.57972	0.789861	+	0.613286i	$0.210153\pi$
$978$	−1.20208	−0.0384382
$979$	−8.20825	−0.262337
$980$	235.842	7.53371
$981$	−13.3012	−0.424675
$982$	79.1780	2.52667
$983$	−38.6794	−1.23368	−0.616841	−	0.787088i	$-0.711588\pi$
$983$	−38.6794	−1.23368	−0.616841	+	0.787088i	$0.711588\pi$
$984$	5.97133	0.190359
$985$	51.5777	1.64340
$986$	51.5190	1.64070
$987$	−6.26655	−0.199466
$988$	−162.512	−5.17021
$989$	11.9360	0.379543
$990$	83.9603	2.66843
$991$	48.8435	1.55157	0.775783	−	0.631000i	$-0.217355\pi$
$991$	48.8435	1.55157	0.775783	+	0.631000i	$0.217355\pi$
$992$	−20.2461	−0.642816
$993$	−4.55677	−0.144605
$994$	−48.4679	−1.53731
$995$	28.9026	0.916275
$996$	7.02787	0.222687
$997$	53.0918	1.68143	0.840717	−	0.541474i	$-0.182134\pi$
$997$	53.0918	1.68143	0.840717	+	0.541474i	$0.182134\pi$
$998$	66.0523	2.09085
$999$	−6.47735	−0.204934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.11	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.57271 q^{2} +0.131094 q^{3} +4.61881 q^{4} +4.05012 q^{5} -0.337267 q^{6} -4.42802 q^{7} -6.73744 q^{8} -2.98281 q^{9} +O(q^{10})\)	\(q-2.57271 q^{2} +0.131094 q^{3} +4.61881 q^{4} +4.05012 q^{5} -0.337267 q^{6} -4.42802 q^{7} -6.73744 q^{8} -2.98281 q^{9} -10.4198 q^{10} +2.70141 q^{11} +0.605500 q^{12} +6.77346 q^{13} +11.3920 q^{14} +0.530948 q^{15} +8.09582 q^{16} -5.30168 q^{17} +7.67390 q^{18} -5.19452 q^{19} +18.7068 q^{20} -0.580488 q^{21} -6.94992 q^{22} -1.00000 q^{23} -0.883240 q^{24} +11.4035 q^{25} -17.4261 q^{26} -0.784313 q^{27} -20.4522 q^{28} +3.77715 q^{29} -1.36597 q^{30} +2.75335 q^{31} -7.35329 q^{32} +0.354139 q^{33} +13.6397 q^{34} -17.9340 q^{35} -13.7771 q^{36} +8.25863 q^{37} +13.3640 q^{38} +0.887962 q^{39} -27.2874 q^{40} -6.76071 q^{41} +1.49342 q^{42} -11.9360 q^{43} +12.4773 q^{44} -12.0808 q^{45} +2.57271 q^{46} +10.7953 q^{47} +1.06132 q^{48} +12.6073 q^{49} -29.3378 q^{50} -0.695020 q^{51} +31.2853 q^{52} +10.4371 q^{53} +2.01781 q^{54} +10.9410 q^{55} +29.8335 q^{56} -0.680973 q^{57} -9.71749 q^{58} -1.59549 q^{59} +2.45235 q^{60} +8.20957 q^{61} -7.08355 q^{62} +13.2080 q^{63} +2.72620 q^{64} +27.4333 q^{65} -0.911095 q^{66} +3.89013 q^{67} -24.4875 q^{68} -0.131094 q^{69} +46.1389 q^{70} -4.25456 q^{71} +20.0965 q^{72} -6.85087 q^{73} -21.2470 q^{74} +1.49493 q^{75} -23.9925 q^{76} -11.9619 q^{77} -2.28446 q^{78} -15.3025 q^{79} +32.7891 q^{80} +8.84562 q^{81} +17.3933 q^{82} +11.6067 q^{83} -2.68117 q^{84} -21.4724 q^{85} +30.7079 q^{86} +0.495163 q^{87} -18.2006 q^{88} -3.03851 q^{89} +31.0802 q^{90} -29.9930 q^{91} -4.61881 q^{92} +0.360948 q^{93} -27.7732 q^{94} -21.0385 q^{95} -0.963974 q^{96} +0.526724 q^{97} -32.4350 q^{98} -8.05779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 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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