LMFDB - Embedded newform 5077.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46112 q^{2} -3.25745 q^{3} +4.05713 q^{4} -3.21291 q^{5} +8.01698 q^{6} -0.720862 q^{7} -5.06284 q^{8} +7.61098 q^{9} +O(q^{10})$	\(q-2.46112 q^{2} -3.25745 q^{3} +4.05713 q^{4} -3.21291 q^{5} +8.01698 q^{6} -0.720862 q^{7} -5.06284 q^{8} +7.61098 q^{9} +7.90737 q^{10} +6.51846 q^{11} -13.2159 q^{12} -0.723399 q^{13} +1.77413 q^{14} +10.4659 q^{15} +4.34602 q^{16} -4.23921 q^{17} -18.7315 q^{18} -0.671570 q^{19} -13.0352 q^{20} +2.34817 q^{21} -16.0427 q^{22} +4.96700 q^{23} +16.4919 q^{24} +5.32281 q^{25} +1.78037 q^{26} -15.0200 q^{27} -2.92463 q^{28} +8.16219 q^{29} -25.7579 q^{30} +6.04817 q^{31} -0.570403 q^{32} -21.2336 q^{33} +10.4332 q^{34} +2.31607 q^{35} +30.8787 q^{36} -3.23482 q^{37} +1.65282 q^{38} +2.35644 q^{39} +16.2665 q^{40} -11.8544 q^{41} -5.77914 q^{42} +8.16513 q^{43} +26.4462 q^{44} -24.4534 q^{45} -12.2244 q^{46} -11.1630 q^{47} -14.1569 q^{48} -6.48036 q^{49} -13.1001 q^{50} +13.8090 q^{51} -2.93492 q^{52} -8.55688 q^{53} +36.9661 q^{54} -20.9433 q^{55} +3.64961 q^{56} +2.18760 q^{57} -20.0882 q^{58} -10.5691 q^{59} +42.4615 q^{60} +4.98703 q^{61} -14.8853 q^{62} -5.48646 q^{63} -7.28820 q^{64} +2.32422 q^{65} +52.2584 q^{66} -1.24382 q^{67} -17.1990 q^{68} -16.1798 q^{69} -5.70012 q^{70} -8.74277 q^{71} -38.5331 q^{72} +12.7774 q^{73} +7.96128 q^{74} -17.3388 q^{75} -2.72464 q^{76} -4.69891 q^{77} -5.79948 q^{78} +10.1389 q^{79} -13.9634 q^{80} +26.0940 q^{81} +29.1751 q^{82} +1.32162 q^{83} +9.52682 q^{84} +13.6202 q^{85} -20.0954 q^{86} -26.5879 q^{87} -33.0019 q^{88} +5.73221 q^{89} +60.1828 q^{90} +0.521471 q^{91} +20.1518 q^{92} -19.7016 q^{93} +27.4736 q^{94} +2.15769 q^{95} +1.85806 q^{96} -9.60734 q^{97} +15.9490 q^{98} +49.6119 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.46112	−1.74028	−0.870138	−	0.492808i	$-0.835971\pi$
$2$	−2.46112	−1.74028	−0.870138	+	0.492808i	$0.835971\pi$
$3$	−3.25745	−1.88069	−0.940345	−	0.340224i	$-0.889497\pi$
$3$	−3.25745	−1.88069	−0.940345	+	0.340224i	$0.889497\pi$
$4$	4.05713	2.02856
$5$	−3.21291	−1.43686	−0.718429	−	0.695600i	$-0.755139\pi$
$5$	−3.21291	−1.43686	−0.718429	+	0.695600i	$0.755139\pi$
$6$	8.01698	3.27292
$7$	−0.720862	−0.272460	−0.136230	−	0.990677i	$-0.543499\pi$
$7$	−0.720862	−0.272460	−0.136230	+	0.990677i	$0.543499\pi$
$8$	−5.06284	−1.78998
$9$	7.61098	2.53699
$10$	7.90737	2.50053
$11$	6.51846	1.96539	0.982695	−	0.185229i	$-0.0593028\pi$
$11$	6.51846	1.96539	0.982695	+	0.185229i	$0.0593028\pi$
$12$	−13.2159	−3.81510
$13$	−0.723399	−0.200635	−0.100317	−	0.994955i	$-0.531986\pi$
$13$	−0.723399	−0.200635	−0.100317	+	0.994955i	$0.531986\pi$
$14$	1.77413	0.474156
$15$	10.4659	2.70228
$16$	4.34602	1.08650
$17$	−4.23921	−1.02816	−0.514079	−	0.857743i	$-0.671866\pi$
$17$	−4.23921	−1.02816	−0.514079	+	0.857743i	$0.671866\pi$
$18$	−18.7315	−4.41507
$19$	−0.671570	−0.154069	−0.0770343	−	0.997028i	$-0.524545\pi$
$19$	−0.671570	−0.154069	−0.0770343	+	0.997028i	$0.524545\pi$
$20$	−13.0352	−2.91476
$21$	2.34817	0.512413
$22$	−16.0427	−3.42032
$23$	4.96700	1.03569	0.517846	−	0.855474i	$-0.326734\pi$
$23$	4.96700	1.03569	0.517846	+	0.855474i	$0.326734\pi$
$24$	16.4919	3.36640
$25$	5.32281	1.06456
$26$	1.78037	0.349160
$27$	−15.0200	−2.89060
$28$	−2.92463	−0.552702
$29$	8.16219	1.51568	0.757841	−	0.652440i	$-0.226254\pi$
$29$	8.16219	1.51568	0.757841	+	0.652440i	$0.226254\pi$
$30$	−25.7579	−4.70272
$31$	6.04817	1.08628	0.543141	−	0.839641i	$-0.317235\pi$
$31$	6.04817	1.08628	0.543141	+	0.839641i	$0.317235\pi$
$32$	−0.570403	−0.100834
$33$	−21.2336	−3.69629
$34$	10.4332	1.78928
$35$	2.31607	0.391487
$36$	30.8787	5.14645
$37$	−3.23482	−0.531801	−0.265900	−	0.964001i	$-0.585669\pi$
$37$	−3.23482	−0.531801	−0.265900	+	0.964001i	$0.585669\pi$
$38$	1.65282	0.268122
$39$	2.35644	0.377332
$40$	16.2665	2.57195
$41$	−11.8544	−1.85135	−0.925674	−	0.378323i	$-0.876501\pi$
$41$	−11.8544	−1.85135	−0.925674	+	0.378323i	$0.876501\pi$
$42$	−5.77914	−0.891740
$43$	8.16513	1.24517	0.622585	−	0.782552i	$-0.286082\pi$
$43$	8.16513	1.24517	0.622585	+	0.782552i	$0.286082\pi$
$44$	26.4462	3.98692
$45$	−24.4534	−3.64530
$46$	−12.2244	−1.80239
$47$	−11.1630	−1.62829	−0.814147	−	0.580659i	$-0.802795\pi$
$47$	−11.1630	−1.62829	−0.814147	+	0.580659i	$0.802795\pi$
$48$	−14.1569	−2.04338
$49$	−6.48036	−0.925765
$50$	−13.1001	−1.85263
$51$	13.8090	1.93365
$52$	−2.93492	−0.407000
$53$	−8.55688	−1.17538	−0.587689	−	0.809087i	$-0.699962\pi$
$53$	−8.55688	−1.17538	−0.587689	+	0.809087i	$0.699962\pi$
$54$	36.9661	5.03045
$55$	−20.9433	−2.82399
$56$	3.64961	0.487699
$57$	2.18760	0.289755
$58$	−20.0882	−2.63770
$59$	−10.5691	−1.37599	−0.687993	−	0.725718i	$-0.741508\pi$
$59$	−10.5691	−1.37599	−0.687993	+	0.725718i	$0.741508\pi$
$60$	42.4615	5.48175
$61$	4.98703	0.638523	0.319262	−	0.947667i	$-0.396565\pi$
$61$	4.98703	0.638523	0.319262	+	0.947667i	$0.396565\pi$
$62$	−14.8853	−1.89043
$63$	−5.48646	−0.691229
$64$	−7.28820	−0.911025
$65$	2.32422	0.288284
$66$	52.2584	6.43257
$67$	−1.24382	−0.151957	−0.0759786	−	0.997109i	$-0.524208\pi$
$67$	−1.24382	−0.151957	−0.0759786	+	0.997109i	$0.524208\pi$
$68$	−17.1990	−2.08568
$69$	−16.1798	−1.94781
$70$	−5.70012	−0.681295
$71$	−8.74277	−1.03758	−0.518788	−	0.854903i	$-0.673617\pi$
$71$	−8.74277	−1.03758	−0.518788	+	0.854903i	$0.673617\pi$
$72$	−38.5331	−4.54117
$73$	12.7774	1.49548	0.747739	−	0.663993i	$-0.231139\pi$
$73$	12.7774	1.49548	0.747739	+	0.663993i	$0.231139\pi$
$74$	7.96128	0.925480
$75$	−17.3388	−2.00211
$76$	−2.72464	−0.312538
$77$	−4.69891	−0.535491
$78$	−5.79948	−0.656661
$79$	10.1389	1.14071	0.570355	−	0.821398i	$-0.306806\pi$
$79$	10.1389	1.14071	0.570355	+	0.821398i	$0.306806\pi$
$80$	−13.9634	−1.56115
$81$	26.0940	2.89934
$82$	29.1751	3.22186
$83$	1.32162	0.145067	0.0725334	−	0.997366i	$-0.476892\pi$
$83$	1.32162	0.145067	0.0725334	+	0.997366i	$0.476892\pi$
$84$	9.52682	1.03946
$85$	13.6202	1.47732
$86$	−20.0954	−2.16694
$87$	−26.5879	−2.85053
$88$	−33.0019	−3.51802
$89$	5.73221	0.607613	0.303807	−	0.952734i	$-0.401742\pi$
$89$	5.73221	0.607613	0.303807	+	0.952734i	$0.401742\pi$
$90$	60.1828	6.34383
$91$	0.521471	0.0546650
$92$	20.1518	2.10097
$93$	−19.7016	−2.04296
$94$	27.4736	2.83368
$95$	2.15769	0.221375
$96$	1.85806	0.189637
$97$	−9.60734	−0.975478	−0.487739	−	0.872990i	$-0.662178\pi$
$97$	−9.60734	−0.975478	−0.487739	+	0.872990i	$0.662178\pi$
$98$	15.9490	1.61109
$99$	49.6119	4.98618
$100$	21.5953	2.15953
$101$	−13.7326	−1.36644	−0.683221	−	0.730212i	$-0.739421\pi$
$101$	−13.7326	−1.36644	−0.683221	+	0.730212i	$0.739421\pi$
$102$	−33.9856	−3.36508
$103$	16.0131	1.57782	0.788908	−	0.614512i	$-0.210647\pi$
$103$	16.0131	1.57782	0.788908	+	0.614512i	$0.210647\pi$
$104$	3.66245	0.359133
$105$	−7.54447	−0.736265
$106$	21.0595	2.04548
$107$	−11.1968	−1.08243	−0.541216	−	0.840884i	$-0.682036\pi$
$107$	−11.1968	−1.08243	−0.541216	+	0.840884i	$0.682036\pi$
$108$	−60.9381	−5.86377
$109$	−19.7497	−1.89168	−0.945840	−	0.324633i	$-0.894759\pi$
$109$	−19.7497	−1.89168	−0.945840	+	0.324633i	$0.894759\pi$
$110$	51.5439	4.91452
$111$	10.5373	1.00015
$112$	−3.13288	−0.296029
$113$	8.05750	0.757986	0.378993	−	0.925400i	$-0.376270\pi$
$113$	8.05750	0.757986	0.378993	+	0.925400i	$0.376270\pi$
$114$	−5.38396	−0.504254
$115$	−15.9585	−1.48814
$116$	33.1150	3.07465
$117$	−5.50577	−0.509009
$118$	26.0120	2.39460
$119$	3.05588	0.280132
$120$	−52.9872	−4.83704
$121$	31.4904	2.86276
$122$	−12.2737	−1.11121
$123$	38.6151	3.48181
$124$	24.5382	2.20359
$125$	−1.03716	−0.0927665
$126$	13.5029	1.20293
$127$	−1.30328	−0.115648	−0.0578238	−	0.998327i	$-0.518416\pi$
$127$	−1.30328	−0.115648	−0.0578238	+	0.998327i	$0.518416\pi$
$128$	19.0780	1.68627
$129$	−26.5975	−2.34178
$130$	−5.72019	−0.501693
$131$	17.4648	1.52590	0.762952	−	0.646456i	$-0.223749\pi$
$131$	17.4648	1.52590	0.762952	+	0.646456i	$0.223749\pi$
$132$	−86.1472	−7.49815
$133$	0.484109	0.0419776
$134$	3.06120	0.264448
$135$	48.2580	4.15339
$136$	21.4624	1.84039
$137$	14.7409	1.25940	0.629698	−	0.776840i	$-0.283179\pi$
$137$	14.7409	1.25940	0.629698	+	0.776840i	$0.283179\pi$
$138$	39.8204	3.38974
$139$	13.7038	1.16234	0.581172	−	0.813781i	$-0.302594\pi$
$139$	13.7038	1.16234	0.581172	+	0.813781i	$0.302594\pi$
$140$	9.39657	0.794155
$141$	36.3630	3.06231
$142$	21.5170	1.80567
$143$	−4.71545	−0.394326
$144$	33.0774	2.75645
$145$	−26.2244	−2.17782
$146$	−31.4467	−2.60255
$147$	21.1094	1.74108
$148$	−13.1241	−1.07879
$149$	−13.4239	−1.09973	−0.549863	−	0.835255i	$-0.685320\pi$
$149$	−13.4239	−1.09973	−0.549863	+	0.835255i	$0.685320\pi$
$150$	42.6729	3.48423
$151$	−20.3991	−1.66006	−0.830028	−	0.557721i	$-0.811676\pi$
$151$	−20.3991	−1.66006	−0.830028	+	0.557721i	$0.811676\pi$
$152$	3.40005	0.275780
$153$	−32.2645	−2.60843
$154$	11.5646	0.931902
$155$	−19.4322	−1.56083
$156$	9.56035	0.765441
$157$	18.9800	1.51477	0.757384	−	0.652970i	$-0.226477\pi$
$157$	18.9800	1.51477	0.757384	+	0.652970i	$0.226477\pi$
$158$	−24.9530	−1.98515
$159$	27.8736	2.21052
$160$	1.83266	0.144884
$161$	−3.58052	−0.282185
$162$	−64.2206	−5.04565
$163$	−6.93539	−0.543222	−0.271611	−	0.962407i	$-0.587556\pi$
$163$	−6.93539	−0.543222	−0.271611	+	0.962407i	$0.587556\pi$
$164$	−48.0948	−3.75557
$165$	68.2216	5.31104
$166$	−3.25267	−0.252456
$167$	14.3234	1.10837	0.554187	−	0.832392i	$-0.313029\pi$
$167$	14.3234	1.10837	0.554187	+	0.832392i	$0.313029\pi$
$168$	−11.8884	−0.917211
$169$	−12.4767	−0.959746
$170$	−33.5210	−2.57094
$171$	−5.11130	−0.390871
$172$	33.1269	2.52591
$173$	3.95718	0.300859	0.150430	−	0.988621i	$-0.451934\pi$
$173$	3.95718	0.300859	0.150430	+	0.988621i	$0.451934\pi$
$174$	65.4362	4.96070
$175$	−3.83701	−0.290051
$176$	28.3293	2.13540
$177$	34.4285	2.58780
$178$	−14.1077	−1.05742
$179$	−2.16452	−0.161784	−0.0808919	−	0.996723i	$-0.525777\pi$
$179$	−2.16452	−0.161784	−0.0808919	+	0.996723i	$0.525777\pi$
$180$	−99.2105	−7.39472
$181$	5.84721	0.434620	0.217310	−	0.976103i	$-0.430272\pi$
$181$	5.84721	0.434620	0.217310	+	0.976103i	$0.430272\pi$
$182$	−1.28340	−0.0951322
$183$	−16.2450	−1.20086
$184$	−25.1471	−1.85387
$185$	10.3932	0.764122
$186$	48.4880	3.55532
$187$	−27.6331	−2.02073
$188$	−45.2898	−3.30310
$189$	10.8274	0.787574
$190$	−5.31035	−0.385253
$191$	1.40539	0.101690	0.0508451	−	0.998707i	$-0.483809\pi$
$191$	1.40539	0.101690	0.0508451	+	0.998707i	$0.483809\pi$
$192$	23.7409	1.71336
$193$	4.16092	0.299509	0.149755	−	0.988723i	$-0.452152\pi$
$193$	4.16092	0.299509	0.149755	+	0.988723i	$0.452152\pi$
$194$	23.6448	1.69760
$195$	−7.57102	−0.542172
$196$	−26.2916	−1.87797
$197$	−12.2177	−0.870472	−0.435236	−	0.900316i	$-0.643335\pi$
$197$	−12.2177	−0.870472	−0.435236	+	0.900316i	$0.643335\pi$
$198$	−122.101	−8.67733
$199$	20.5331	1.45555	0.727775	−	0.685816i	$-0.240554\pi$
$199$	20.5331	1.45555	0.727775	+	0.685816i	$0.240554\pi$
$200$	−26.9485	−1.90555
$201$	4.05169	0.285784
$202$	33.7975	2.37799
$203$	−5.88381	−0.412963
$204$	56.0248	3.92252
$205$	38.0872	2.66012
$206$	−39.4102	−2.74584
$207$	37.8037	2.62754
$208$	−3.14390	−0.217991
$209$	−4.37760	−0.302805
$210$	18.5679	1.28130
$211$	18.9626	1.30544	0.652721	−	0.757598i	$-0.273627\pi$
$211$	18.9626	1.30544	0.652721	+	0.757598i	$0.273627\pi$
$212$	−34.7163	−2.38433
$213$	28.4791	1.95136
$214$	27.5566	1.88373
$215$	−26.2338	−1.78913
$216$	76.0439	5.17413
$217$	−4.35989	−0.295969
$218$	48.6065	3.29205
$219$	−41.6216	−2.81253
$220$	−84.9694	−5.72864
$221$	3.06664	0.206284
$222$	−25.9335	−1.74054
$223$	−8.76177	−0.586732	−0.293366	−	0.956000i	$-0.594775\pi$
$223$	−8.76177	−0.586732	−0.293366	+	0.956000i	$0.594775\pi$
$224$	0.411182	0.0274732
$225$	40.5118	2.70079
$226$	−19.8305	−1.31911
$227$	−4.88465	−0.324205	−0.162103	−	0.986774i	$-0.551828\pi$
$227$	−4.88465	−0.324205	−0.162103	+	0.986774i	$0.551828\pi$
$228$	8.87538	0.587787
$229$	−12.3060	−0.813205	−0.406603	−	0.913605i	$-0.633287\pi$
$229$	−12.3060	−0.813205	−0.406603	+	0.913605i	$0.633287\pi$
$230$	39.2759	2.58978
$231$	15.3065	1.00709
$232$	−41.3239	−2.71304
$233$	−7.46782	−0.489233	−0.244617	−	0.969620i	$-0.578662\pi$
$233$	−7.46782	−0.489233	−0.244617	+	0.969620i	$0.578662\pi$
$234$	13.5504	0.885816
$235$	35.8658	2.33963
$236$	−42.8803	−2.79127
$237$	−33.0268	−2.14532
$238$	−7.52090	−0.487507
$239$	0.428295	0.0277041	0.0138521	−	0.999904i	$-0.495591\pi$
$239$	0.428295	0.0277041	0.0138521	+	0.999904i	$0.495591\pi$
$240$	45.4850	2.93604
$241$	−11.1451	−0.717922	−0.358961	−	0.933353i	$-0.616869\pi$
$241$	−11.1451	−0.717922	−0.358961	+	0.933353i	$0.616869\pi$
$242$	−77.5016	−4.98199
$243$	−39.9399	−2.56215
$244$	20.2330	1.29528
$245$	20.8208	1.33019
$246$	−95.0366	−6.05931
$247$	0.485813	0.0309115
$248$	−30.6209	−1.94443
$249$	−4.30511	−0.272825
$250$	2.55258	0.161439
$251$	−23.2090	−1.46494	−0.732470	−	0.680799i	$-0.761633\pi$
$251$	−23.2090	−1.46494	−0.732470	+	0.680799i	$0.761633\pi$
$252$	−22.2593	−1.40220
$253$	32.3772	2.03554
$254$	3.20754	0.201259
$255$	−44.3671	−2.77838
$256$	−32.3768	−2.02355
$257$	10.7887	0.672978	0.336489	−	0.941687i	$-0.390761\pi$
$257$	10.7887	0.672978	0.336489	+	0.941687i	$0.390761\pi$
$258$	65.4597	4.07534
$259$	2.33186	0.144894
$260$	9.42964	0.584802
$261$	62.1223	3.84527
$262$	−42.9829	−2.65549
$263$	2.15733	0.133026	0.0665132	−	0.997786i	$-0.478813\pi$
$263$	2.15733	0.133026	0.0665132	+	0.997786i	$0.478813\pi$
$264$	107.502	6.61630
$265$	27.4925	1.68885
$266$	−1.19145	−0.0730526
$267$	−18.6724	−1.14273
$268$	−5.04635	−0.308255
$269$	7.53715	0.459548	0.229774	−	0.973244i	$-0.426201\pi$
$269$	7.53715	0.459548	0.229774	+	0.973244i	$0.426201\pi$
$270$	−118.769	−7.22804
$271$	27.0185	1.64126	0.820629	−	0.571461i	$-0.193623\pi$
$271$	27.0185	1.64126	0.820629	+	0.571461i	$0.193623\pi$
$272$	−18.4237	−1.11710
$273$	−1.69866	−0.102808
$274$	−36.2790	−2.19170
$275$	34.6965	2.09228
$276$	−65.6433	−3.95126
$277$	4.64065	0.278830	0.139415	−	0.990234i	$-0.455478\pi$
$277$	4.64065	0.278830	0.139415	+	0.990234i	$0.455478\pi$
$278$	−33.7268	−2.02280
$279$	46.0324	2.75589
$280$	−11.7259	−0.700755
$281$	−10.0202	−0.597754	−0.298877	−	0.954292i	$-0.596612\pi$
$281$	−10.0202	−0.597754	−0.298877	+	0.954292i	$0.596612\pi$
$282$	−89.4937	−5.32927
$283$	7.33611	0.436086	0.218043	−	0.975939i	$-0.430033\pi$
$283$	7.33611	0.436086	0.218043	+	0.975939i	$0.430033\pi$
$284$	−35.4705	−2.10479
$285$	−7.02858	−0.416337
$286$	11.6053	0.686236
$287$	8.54539	0.504418
$288$	−4.34132	−0.255815
$289$	0.970861	0.0571095
$290$	64.5415	3.79001
$291$	31.2954	1.83457
$292$	51.8394	3.03367
$293$	−17.2303	−1.00661	−0.503304	−	0.864110i	$-0.667882\pi$
$293$	−17.2303	−1.00661	−0.503304	+	0.864110i	$0.667882\pi$
$294$	−51.9529	−3.02996
$295$	33.9577	1.97710
$296$	16.3774	0.951914
$297$	−97.9074	−5.68117
$298$	33.0378	1.91383
$299$	−3.59312	−0.207796
$300$	−70.3456	−4.06141
$301$	−5.88593	−0.339259
$302$	50.2047	2.88896
$303$	44.7331	2.56985
$304$	−2.91865	−0.167396
$305$	−16.0229	−0.917468
$306$	79.4069	4.53939
$307$	−23.1948	−1.32380	−0.661898	−	0.749594i	$-0.730249\pi$
$307$	−23.1948	−1.32380	−0.661898	+	0.749594i	$0.730249\pi$
$308$	−19.0641	−1.08628
$309$	−52.1618	−2.96738
$310$	47.8251	2.71628
$311$	−20.0904	−1.13922	−0.569611	−	0.821914i	$-0.692906\pi$
$311$	−20.0904	−1.13922	−0.569611	+	0.821914i	$0.692906\pi$
$312$	−11.9303	−0.675418
$313$	10.5647	0.597149	0.298575	−	0.954386i	$-0.403489\pi$
$313$	10.5647	0.597149	0.298575	+	0.954386i	$0.403489\pi$
$314$	−46.7121	−2.63612
$315$	17.6275	0.993198
$316$	41.1346	2.31400
$317$	−4.68749	−0.263276	−0.131638	−	0.991298i	$-0.542024\pi$
$317$	−4.68749	−0.263276	−0.131638	+	0.991298i	$0.542024\pi$
$318$	−68.6003	−3.84692
$319$	53.2050	2.97891
$320$	23.4164	1.30901
$321$	36.4729	2.03572
$322$	8.81210	0.491079
$323$	2.84692	0.158407
$324$	105.867	5.88148
$325$	−3.85052	−0.213588
$326$	17.0689	0.945356
$327$	64.3337	3.55766
$328$	60.0169	3.31388
$329$	8.04699	0.443645
$330$	−167.902	−9.24269
$331$	0.937678	0.0515394	0.0257697	−	0.999668i	$-0.491796\pi$
$331$	0.937678	0.0515394	0.0257697	+	0.999668i	$0.491796\pi$
$332$	5.36198	0.294277
$333$	−24.6201	−1.34917
$334$	−35.2515	−1.92888
$335$	3.99630	0.218341
$336$	10.2052	0.556739
$337$	−12.6936	−0.691467	−0.345733	−	0.938333i	$-0.612370\pi$
$337$	−12.6936	−0.691467	−0.345733	+	0.938333i	$0.612370\pi$
$338$	30.7067	1.67022
$339$	−26.2469	−1.42554
$340$	55.2589	2.99683
$341$	39.4247	2.13497
$342$	12.5795	0.680223
$343$	9.71747	0.524694
$344$	−41.3387	−2.22883
$345$	51.9842	2.79873
$346$	−9.73911	−0.523578
$347$	−33.7692	−1.81283	−0.906413	−	0.422393i	$-0.861190\pi$
$347$	−33.7692	−1.81283	−0.906413	+	0.422393i	$0.861190\pi$
$348$	−107.871	−5.78247
$349$	−8.48295	−0.454082	−0.227041	−	0.973885i	$-0.572905\pi$
$349$	−8.48295	−0.454082	−0.227041	+	0.973885i	$0.572905\pi$
$350$	9.44335	0.504768
$351$	10.8655	0.579956
$352$	−3.71815	−0.198178
$353$	27.0574	1.44012	0.720061	−	0.693911i	$-0.244114\pi$
$353$	27.0574	1.44012	0.720061	+	0.693911i	$0.244114\pi$
$354$	−84.7327	−4.50349
$355$	28.0898	1.49085
$356$	23.2563	1.23258
$357$	−9.95438	−0.526842
$358$	5.32715	0.281549
$359$	−19.5460	−1.03160	−0.515800	−	0.856709i	$-0.672505\pi$
$359$	−19.5460	−1.03160	−0.515800	+	0.856709i	$0.672505\pi$
$360$	123.804	6.52502
$361$	−18.5490	−0.976263
$362$	−14.3907	−0.756359
$363$	−102.578	−5.38396
$364$	2.11567	0.110891
$365$	−41.0526	−2.14879
$366$	39.9809	2.08984
$367$	−2.89279	−0.151002	−0.0755011	−	0.997146i	$-0.524056\pi$
$367$	−2.89279	−0.151002	−0.0755011	+	0.997146i	$0.524056\pi$
$368$	21.5867	1.12528
$369$	−90.2236	−4.69685
$370$	−25.5789	−1.32978
$371$	6.16833	0.320244
$372$	−79.9318	−4.14427
$373$	19.0813	0.987994	0.493997	−	0.869464i	$-0.335535\pi$
$373$	19.0813	0.987994	0.493997	+	0.869464i	$0.335535\pi$
$374$	68.0085	3.51663
$375$	3.37850	0.174465
$376$	56.5166	2.91462
$377$	−5.90452	−0.304098
$378$	−26.6475	−1.37060
$379$	5.15909	0.265005	0.132502	−	0.991183i	$-0.457699\pi$
$379$	5.15909	0.265005	0.132502	+	0.991183i	$0.457699\pi$
$380$	8.75404	0.449073
$381$	4.24538	0.217497
$382$	−3.45883	−0.176969
$383$	18.4108	0.940750	0.470375	−	0.882467i	$-0.344119\pi$
$383$	18.4108	0.940750	0.470375	+	0.882467i	$0.344119\pi$
$384$	−62.1455	−3.17135
$385$	15.0972	0.769424
$386$	−10.2405	−0.521229
$387$	62.1446	3.15899
$388$	−38.9782	−1.97882
$389$	−6.99538	−0.354680	−0.177340	−	0.984150i	$-0.556749\pi$
$389$	−6.99538	−0.354680	−0.177340	+	0.984150i	$0.556749\pi$
$390$	18.6332	0.943530
$391$	−21.0561	−1.06485
$392$	32.8090	1.65711
$393$	−56.8906	−2.86975
$394$	30.0692	1.51486
$395$	−32.5753	−1.63904
$396$	201.282	10.1148
$397$	14.1668	0.711010	0.355505	−	0.934674i	$-0.384309\pi$
$397$	14.1668	0.711010	0.355505	+	0.934674i	$0.384309\pi$
$398$	−50.5344	−2.53306
$399$	−1.57696	−0.0789468
$400$	23.1330	1.15665
$401$	6.35140	0.317174	0.158587	−	0.987345i	$-0.449306\pi$
$401$	6.35140	0.317174	0.158587	+	0.987345i	$0.449306\pi$
$402$	−9.97171	−0.497344
$403$	−4.37524	−0.217946
$404$	−55.7148	−2.77191
$405$	−83.8378	−4.16593
$406$	14.4808	0.718669
$407$	−21.0860	−1.04520
$408$	−69.9127	−3.46120
$409$	−2.80524	−0.138710	−0.0693550	−	0.997592i	$-0.522094\pi$
$409$	−2.80524	−0.138710	−0.0693550	+	0.997592i	$0.522094\pi$
$410$	−93.7372	−4.62935
$411$	−48.0176	−2.36853
$412$	64.9671	3.20070
$413$	7.61889	0.374901
$414$	−93.0396	−4.57265
$415$	−4.24625	−0.208440
$416$	0.412629	0.0202308
$417$	−44.6395	−2.18601
$418$	10.7738	0.526965
$419$	5.24261	0.256118	0.128059	−	0.991767i	$-0.459125\pi$
$419$	5.24261	0.256118	0.128059	+	0.991767i	$0.459125\pi$
$420$	−30.6089	−1.49356
$421$	18.2579	0.889834	0.444917	−	0.895572i	$-0.353233\pi$
$421$	18.2579	0.889834	0.444917	+	0.895572i	$0.353233\pi$
$422$	−46.6694	−2.27183
$423$	−84.9615	−4.13097
$424$	43.3221	2.10391
$425$	−22.5645	−1.09454
$426$	−70.0907	−3.39590
$427$	−3.59496	−0.173972
$428$	−45.4267	−2.19578
$429$	15.3603	0.741604
$430$	64.5647	3.11359
$431$	−17.4605	−0.841041	−0.420521	−	0.907283i	$-0.638153\pi$
$431$	−17.4605	−0.841041	−0.420521	+	0.907283i	$0.638153\pi$
$432$	−65.2772	−3.14065
$433$	14.7843	0.710487	0.355243	−	0.934774i	$-0.384398\pi$
$433$	14.7843	0.710487	0.355243	+	0.934774i	$0.384398\pi$
$434$	10.7302	0.515067
$435$	85.4247	4.09580
$436$	−80.1271	−3.83739
$437$	−3.33569	−0.159568
$438$	102.436	4.89458
$439$	−4.23647	−0.202196	−0.101098	−	0.994876i	$-0.532236\pi$
$439$	−4.23647	−0.202196	−0.101098	+	0.994876i	$0.532236\pi$
$440$	106.032	5.05489
$441$	−49.3218	−2.34866
$442$	−7.54737	−0.358992
$443$	22.1687	1.05326	0.526632	−	0.850093i	$-0.323454\pi$
$443$	22.1687	1.05326	0.526632	+	0.850093i	$0.323454\pi$
$444$	42.7510	2.02887
$445$	−18.4171	−0.873054
$446$	21.5638	1.02108
$447$	43.7276	2.06824
$448$	5.25379	0.248218
$449$	−0.570849	−0.0269401	−0.0134700	−	0.999909i	$-0.504288\pi$
$449$	−0.570849	−0.0269401	−0.0134700	+	0.999909i	$0.504288\pi$
$450$	−99.7045	−4.70011
$451$	−77.2725	−3.63862
$452$	32.6903	1.53762
$453$	66.4491	3.12205
$454$	12.0217	0.564207
$455$	−1.67544	−0.0785458
$456$	−11.0755	−0.518657
$457$	11.2132	0.524531	0.262266	−	0.964996i	$-0.415530\pi$
$457$	11.2132	0.524531	0.262266	+	0.964996i	$0.415530\pi$
$458$	30.2867	1.41520
$459$	63.6729	2.97200
$460$	−64.7458	−3.01879
$461$	1.40876	0.0656123	0.0328061	−	0.999462i	$-0.489556\pi$
$461$	1.40876	0.0656123	0.0328061	+	0.999462i	$0.489556\pi$
$462$	−37.6711	−1.75262
$463$	1.34817	0.0626548	0.0313274	−	0.999509i	$-0.490027\pi$
$463$	1.34817	0.0626548	0.0313274	+	0.999509i	$0.490027\pi$
$464$	35.4730	1.64679
$465$	63.2995	2.93544
$466$	18.3792	0.851401
$467$	−14.0761	−0.651365	−0.325682	−	0.945479i	$-0.605594\pi$
$467$	−14.0761	−0.651365	−0.325682	+	0.945479i	$0.605594\pi$
$468$	−22.3376	−1.03256
$469$	0.896625	0.0414023
$470$	−88.2702	−4.07160
$471$	−61.8264	−2.84881
$472$	53.5099	2.46299
$473$	53.2241	2.44725
$474$	81.2830	3.73345
$475$	−3.57464	−0.164016
$476$	12.3981	0.568266
$477$	−65.1262	−2.98192
$478$	−1.05409	−0.0482128
$479$	4.62798	0.211458	0.105729	−	0.994395i	$-0.466282\pi$
$479$	4.62798	0.211458	0.105729	+	0.994395i	$0.466282\pi$
$480$	−5.96978	−0.272482
$481$	2.34006	0.106698
$482$	27.4296	1.24938
$483$	11.6634	0.530702
$484$	127.760	5.80729
$485$	30.8675	1.40162
$486$	98.2970	4.45884
$487$	27.8877	1.26371	0.631857	−	0.775085i	$-0.282293\pi$
$487$	27.8877	1.26371	0.631857	+	0.775085i	$0.282293\pi$
$488$	−25.2485	−1.14295
$489$	22.5917	1.02163
$490$	−51.2426	−2.31491
$491$	−33.8071	−1.52569	−0.762846	−	0.646580i	$-0.776199\pi$
$491$	−33.8071	−1.52569	−0.762846	+	0.646580i	$0.776199\pi$
$492$	156.666	7.06307
$493$	−34.6012	−1.55836
$494$	−1.19564	−0.0537946
$495$	−159.399	−7.16443
$496$	26.2854	1.18025
$497$	6.30233	0.282698
$498$	10.5954	0.474792
$499$	0.749366	0.0335462	0.0167731	−	0.999859i	$-0.494661\pi$
$499$	0.749366	0.0335462	0.0167731	+	0.999859i	$0.494661\pi$
$500$	−4.20789	−0.188183
$501$	−46.6576	−2.08451
$502$	57.1202	2.54940
$503$	5.78357	0.257877	0.128938	−	0.991653i	$-0.458843\pi$
$503$	5.78357	0.257877	0.128938	+	0.991653i	$0.458843\pi$
$504$	27.7771	1.23729
$505$	44.1216	1.96338
$506$	−79.6843	−3.54240
$507$	40.6422	1.80498
$508$	−5.28758	−0.234599
$509$	43.9877	1.94972	0.974861	−	0.222814i	$-0.0715243\pi$
$509$	43.9877	1.94972	0.974861	+	0.222814i	$0.0715243\pi$
$510$	109.193	4.83514
$511$	−9.21072	−0.407458
$512$	41.5274	1.83527
$513$	10.0870	0.445351
$514$	−26.5522	−1.17117
$515$	−51.4486	−2.26710
$516$	−107.909	−4.75044
$517$	−72.7657	−3.20023
$518$	−5.73898	−0.252156
$519$	−12.8903	−0.565822
$520$	−11.7671	−0.516023
$521$	13.6361	0.597409	0.298704	−	0.954346i	$-0.403446\pi$
$521$	13.6361	0.597409	0.298704	+	0.954346i	$0.403446\pi$
$522$	−152.890	−6.69183
$523$	−41.7447	−1.82537	−0.912684	−	0.408666i	$-0.865994\pi$
$523$	−41.7447	−1.82537	−0.912684	+	0.408666i	$0.865994\pi$
$524$	70.8567	3.09539
$525$	12.4989	0.545495
$526$	−5.30944	−0.231503
$527$	−25.6394	−1.11687
$528$	−92.2814	−4.01603
$529$	1.67111	0.0726572
$530$	−67.6624	−2.93907
$531$	−80.4415	−3.49086
$532$	1.96409	0.0851541
$533$	8.57546	0.371445
$534$	45.9551	1.98867
$535$	35.9742	1.55530
$536$	6.29728	0.272001
$537$	7.05082	0.304265
$538$	−18.5499	−0.799741
$539$	−42.2420	−1.81949
$540$	195.789	8.42541
$541$	30.3987	1.30694	0.653471	−	0.756952i	$-0.273312\pi$
$541$	30.3987	1.30694	0.653471	+	0.756952i	$0.273312\pi$
$542$	−66.4959	−2.85624
$543$	−19.0470	−0.817385
$544$	2.41806	0.103673
$545$	63.4541	2.71808
$546$	4.18062	0.178914
$547$	−6.17485	−0.264017	−0.132009	−	0.991249i	$-0.542143\pi$
$547$	−6.17485	−0.264017	−0.132009	+	0.991249i	$0.542143\pi$
$548$	59.8055	2.55476
$549$	37.9561	1.61993
$550$	−85.3925	−3.64115
$551$	−5.48148	−0.233519
$552$	81.9155	3.48656
$553$	−7.30871	−0.310798
$554$	−11.4212	−0.485241
$555$	−33.8553	−1.43708
$556$	55.5982	2.35789
$557$	−4.12130	−0.174625	−0.0873126	−	0.996181i	$-0.527828\pi$
$557$	−4.12130	−0.174625	−0.0873126	+	0.996181i	$0.527828\pi$
$558$	−113.291	−4.79601
$559$	−5.90664	−0.249824
$560$	10.0657	0.425352
$561$	90.0134	3.80037
$562$	24.6609	1.04026
$563$	−21.3717	−0.900708	−0.450354	−	0.892850i	$-0.648702\pi$
$563$	−21.3717	−0.900708	−0.450354	+	0.892850i	$0.648702\pi$
$564$	147.529	6.21210
$565$	−25.8881	−1.08912
$566$	−18.0551	−0.758911
$567$	−18.8102	−0.789953
$568$	44.2632	1.85724
$569$	33.6721	1.41161	0.705804	−	0.708407i	$-0.250586\pi$
$569$	33.6721	1.41161	0.705804	+	0.708407i	$0.250586\pi$
$570$	17.2982	0.724542
$571$	−41.2603	−1.72669	−0.863346	−	0.504613i	$-0.831635\pi$
$571$	−41.2603	−1.72669	−0.863346	+	0.504613i	$0.831635\pi$
$572$	−19.1312	−0.799914
$573$	−4.57798	−0.191248
$574$	−21.0312	−0.877827
$575$	26.4384	1.10256
$576$	−55.4703	−2.31126
$577$	17.0133	0.708274	0.354137	−	0.935194i	$-0.384775\pi$
$577$	17.0133	0.708274	0.354137	+	0.935194i	$0.384775\pi$
$578$	−2.38941	−0.0993863
$579$	−13.5540	−0.563284
$580$	−106.396	−4.41784
$581$	−0.952706	−0.0395249
$582$	−77.0219	−3.19266
$583$	−55.7777	−2.31008
$584$	−64.6898	−2.67688
$585$	17.6896	0.731374
$586$	42.4060	1.75178
$587$	21.2859	0.878565	0.439282	−	0.898349i	$-0.355233\pi$
$587$	21.2859	0.878565	0.439282	+	0.898349i	$0.355233\pi$
$588$	85.6436	3.53188
$589$	−4.06176	−0.167362
$590$	−83.5742	−3.44069
$591$	39.7984	1.63709
$592$	−14.0586	−0.577804
$593$	−21.9222	−0.900237	−0.450118	−	0.892969i	$-0.648618\pi$
$593$	−21.9222	−0.900237	−0.450118	+	0.892969i	$0.648618\pi$
$594$	240.962	9.88680
$595$	−9.81828	−0.402510
$596$	−54.4623	−2.23086
$597$	−66.8854	−2.73744
$598$	8.84312	0.361622
$599$	−15.7458	−0.643354	−0.321677	−	0.946849i	$-0.604247\pi$
$599$	−15.7458	−0.643354	−0.321677	+	0.946849i	$0.604247\pi$
$600$	87.7835	3.58374
$601$	−13.7151	−0.559449	−0.279724	−	0.960080i	$-0.590243\pi$
$601$	−13.7151	−0.559449	−0.279724	+	0.960080i	$0.590243\pi$
$602$	14.4860	0.590405
$603$	−9.46671	−0.385514
$604$	−82.7618	−3.36753
$605$	−101.176	−4.11338
$606$	−110.094	−4.47225
$607$	−11.9050	−0.483211	−0.241605	−	0.970375i	$-0.577674\pi$
$607$	−11.9050	−0.483211	−0.241605	+	0.970375i	$0.577674\pi$
$608$	0.383065	0.0155354
$609$	19.1662	0.776655
$610$	39.4343	1.59665
$611$	8.07532	0.326692
$612$	−130.901	−5.29136
$613$	−0.905612	−0.0365773	−0.0182887	−	0.999833i	$-0.505822\pi$
$613$	−0.905612	−0.0365773	−0.0182887	+	0.999833i	$0.505822\pi$
$614$	57.0852	2.30377
$615$	−124.067	−5.00287
$616$	23.7898	0.958519
$617$	21.0758	0.848478	0.424239	−	0.905550i	$-0.360542\pi$
$617$	21.0758	0.848478	0.424239	+	0.905550i	$0.360542\pi$
$618$	128.377	5.16406
$619$	−35.5781	−1.43000	−0.715002	−	0.699122i	$-0.753574\pi$
$619$	−35.5781	−1.43000	−0.715002	+	0.699122i	$0.753574\pi$
$620$	−78.8390	−3.16625
$621$	−74.6045	−2.99377
$622$	49.4449	1.98256
$623$	−4.13213	−0.165550
$624$	10.2411	0.409972
$625$	−23.2817	−0.931270
$626$	−26.0009	−1.03921
$627$	14.2598	0.569482
$628$	77.0042	3.07280
$629$	13.7131	0.546775
$630$	−43.3835	−1.72844
$631$	−8.57104	−0.341208	−0.170604	−	0.985340i	$-0.554572\pi$
$631$	−8.57104	−0.341208	−0.170604	+	0.985340i	$0.554572\pi$
$632$	−51.3314	−2.04185
$633$	−61.7699	−2.45513
$634$	11.5365	0.458173
$635$	4.18733	0.166169
$636$	113.087	4.48418
$637$	4.68788	0.185741
$638$	−130.944	−5.18412
$639$	−66.5410	−2.63232
$640$	−61.2958	−2.42293
$641$	16.4036	0.647903	0.323951	−	0.946074i	$-0.394989\pi$
$641$	16.4036	0.647903	0.323951	+	0.946074i	$0.394989\pi$
$642$	−89.7642	−3.54271
$643$	−14.9491	−0.589536	−0.294768	−	0.955569i	$-0.595242\pi$
$643$	−14.9491	−0.589536	−0.294768	+	0.955569i	$0.595242\pi$
$644$	−14.5266	−0.572429
$645$	85.4554	3.36480
$646$	−7.00662	−0.275672
$647$	−5.92481	−0.232928	−0.116464	−	0.993195i	$-0.537156\pi$
$647$	−5.92481	−0.232928	−0.116464	+	0.993195i	$0.537156\pi$
$648$	−132.110	−5.18976
$649$	−68.8946	−2.70435
$650$	9.47659	0.371702
$651$	14.2021	0.556625
$652$	−28.1378	−1.10196
$653$	4.28008	0.167492	0.0837462	−	0.996487i	$-0.473312\pi$
$653$	4.28008	0.167492	0.0837462	+	0.996487i	$0.473312\pi$
$654$	−158.333	−6.19132
$655$	−56.1128	−2.19251
$656$	−51.5194	−2.01150
$657$	97.2482	3.79402
$658$	−19.8046	−0.772065
$659$	25.4053	0.989649	0.494824	−	0.868993i	$-0.335232\pi$
$659$	25.4053	0.989649	0.494824	+	0.868993i	$0.335232\pi$
$660$	276.784	10.7738
$661$	−28.6551	−1.11456	−0.557278	−	0.830326i	$-0.688154\pi$
$661$	−28.6551	−1.11456	−0.557278	+	0.830326i	$0.688154\pi$
$662$	−2.30774	−0.0896929
$663$	−9.98941	−0.387957
$664$	−6.69115	−0.259667
$665$	−1.55540	−0.0603158
$666$	60.5931	2.34794
$667$	40.5416	1.56978
$668$	58.1117	2.24841
$669$	28.5410	1.10346
$670$	−9.83538	−0.379974
$671$	32.5078	1.25495
$672$	−1.33940	−0.0516686
$673$	6.28021	0.242084	0.121042	−	0.992647i	$-0.461376\pi$
$673$	6.28021	0.242084	0.121042	+	0.992647i	$0.461376\pi$
$674$	31.2406	1.20334
$675$	−79.9487	−3.07723
$676$	−50.6195	−1.94690
$677$	−14.6524	−0.563138	−0.281569	−	0.959541i	$-0.590855\pi$
$677$	−14.6524	−0.563138	−0.281569	+	0.959541i	$0.590855\pi$
$678$	64.5969	2.48083
$679$	6.92556	0.265779
$680$	−68.9569	−2.64437
$681$	15.9115	0.609730
$682$	−97.0291	−3.71544
$683$	24.9561	0.954917	0.477459	−	0.878654i	$-0.341558\pi$
$683$	24.9561	0.954917	0.477459	+	0.878654i	$0.341558\pi$
$684$	−20.7372	−0.792906
$685$	−47.3611	−1.80957
$686$	−23.9159	−0.913113
$687$	40.0863	1.52939
$688$	35.4858	1.35288
$689$	6.19004	0.235822
$690$	−127.939	−4.87057
$691$	−33.1694	−1.26182	−0.630912	−	0.775854i	$-0.717319\pi$
$691$	−33.1694	−1.26182	−0.630912	+	0.775854i	$0.717319\pi$
$692$	16.0548	0.610311
$693$	−35.7633	−1.35854
$694$	83.1102	3.15482
$695$	−44.0292	−1.67012
$696$	134.610	5.10239
$697$	50.2533	1.90348
$698$	20.8776	0.790228
$699$	24.3260	0.920095
$700$	−15.5672	−0.588386
$701$	12.8543	0.485499	0.242750	−	0.970089i	$-0.421951\pi$
$701$	12.8543	0.485499	0.242750	+	0.970089i	$0.421951\pi$
$702$	−26.7412	−1.00928
$703$	2.17240	0.0819338
$704$	−47.5079	−1.79052
$705$	−116.831	−4.40011
$706$	−66.5917	−2.50621
$707$	9.89928	0.372301
$708$	139.681	5.24952
$709$	41.8362	1.57119	0.785595	−	0.618741i	$-0.212357\pi$
$709$	41.8362	1.57119	0.785595	+	0.618741i	$0.212357\pi$
$710$	−69.1324	−2.59449
$711$	77.1666	2.89397
$712$	−29.0213	−1.08762
$713$	30.0413	1.12505
$714$	24.4989	0.916850
$715$	15.1503	0.566590
$716$	−8.78173	−0.328189
$717$	−1.39515	−0.0521028
$718$	48.1052	1.79527
$719$	−28.0475	−1.04600	−0.522999	−	0.852334i	$-0.675187\pi$
$719$	−28.0475	−1.04600	−0.522999	+	0.852334i	$0.675187\pi$
$720$	−106.275	−3.96063
$721$	−11.5432	−0.429892
$722$	45.6514	1.69897
$723$	36.3047	1.35019
$724$	23.7229	0.881654
$725$	43.4458	1.61354
$726$	252.458	9.36958
$727$	31.2342	1.15841	0.579207	−	0.815181i	$-0.303362\pi$
$727$	31.2342	1.15841	0.579207	+	0.815181i	$0.303362\pi$
$728$	−2.64012	−0.0978494
$729$	51.8201	1.91926
$730$	101.035	3.73949
$731$	−34.6137	−1.28023
$732$	−65.9079	−2.43603
$733$	−34.5937	−1.27775	−0.638873	−	0.769312i	$-0.720599\pi$
$733$	−34.5937	−1.27775	−0.638873	+	0.769312i	$0.720599\pi$
$734$	7.11950	0.262786
$735$	−67.8228	−2.50168
$736$	−2.83319	−0.104433
$737$	−8.10782	−0.298655
$738$	222.051	8.17382
$739$	12.3966	0.456016	0.228008	−	0.973659i	$-0.426779\pi$
$739$	12.3966	0.456016	0.228008	+	0.973659i	$0.426779\pi$
$740$	42.1665	1.55007
$741$	−1.58251	−0.0581350
$742$	−15.1810	−0.557312
$743$	−40.5205	−1.48655	−0.743277	−	0.668984i	$-0.766730\pi$
$743$	−40.5205	−1.48655	−0.743277	+	0.668984i	$0.766730\pi$
$744$	99.7460	3.65687
$745$	43.1297	1.58015
$746$	−46.9615	−1.71938
$747$	10.0588	0.368033
$748$	−112.111	−4.09918
$749$	8.07132	0.294919
$750$	−8.31491	−0.303617
$751$	32.2620	1.17726	0.588629	−	0.808403i	$-0.299668\pi$
$751$	32.2620	1.17726	0.588629	+	0.808403i	$0.299668\pi$
$752$	−48.5147	−1.76915
$753$	75.6022	2.75510
$754$	14.5318	0.529215
$755$	65.5406	2.38527
$756$	43.9279	1.59764
$757$	19.6886	0.715596	0.357798	−	0.933799i	$-0.383528\pi$
$757$	19.6886	0.715596	0.357798	+	0.933799i	$0.383528\pi$
$758$	−12.6972	−0.461181
$759$	−105.467	−3.82822
$760$	−10.9241	−0.396257
$761$	12.1249	0.439528	0.219764	−	0.975553i	$-0.429471\pi$
$761$	12.1249	0.439528	0.219764	+	0.975553i	$0.429471\pi$
$762$	−10.4484	−0.378505
$763$	14.2368	0.515407
$764$	5.70183	0.206285
$765$	103.663	3.74794
$766$	−45.3113	−1.63717
$767$	7.64571	0.276071
$768$	105.466	3.80567
$769$	1.39472	0.0502949	0.0251475	−	0.999684i	$-0.491994\pi$
$769$	1.39472	0.0502949	0.0251475	+	0.999684i	$0.491994\pi$
$770$	−37.1560	−1.33901
$771$	−35.1435	−1.26566
$772$	16.8814	0.607574
$773$	−51.6757	−1.85865	−0.929323	−	0.369268i	$-0.879608\pi$
$773$	−51.6757	−1.85865	−0.929323	+	0.369268i	$0.879608\pi$
$774$	−152.945	−5.49751
$775$	32.1932	1.15642
$776$	48.6404	1.74609
$777$	−7.59590	−0.272501
$778$	17.2165	0.617241
$779$	7.96106	0.285235
$780$	−30.7166	−1.09983
$781$	−56.9894	−2.03924
$782$	51.8218	1.85314
$783$	−122.596	−4.38123
$784$	−28.1637	−1.00585
$785$	−60.9811	−2.17651
$786$	140.015	4.99416
$787$	20.0657	0.715264	0.357632	−	0.933863i	$-0.383584\pi$
$787$	20.0657	0.715264	0.357632	+	0.933863i	$0.383584\pi$
$788$	−49.5686	−1.76581
$789$	−7.02738	−0.250181
$790$	80.1717	2.85238
$791$	−5.80835	−0.206521
$792$	−251.177	−8.92518
$793$	−3.60761	−0.128110
$794$	−34.8662	−1.23735
$795$	−89.5554	−3.17620
$796$	83.3052	2.95267
$797$	−9.38819	−0.332547	−0.166273	−	0.986080i	$-0.553173\pi$
$797$	−9.38819	−0.332547	−0.166273	+	0.986080i	$0.553173\pi$
$798$	3.88109	0.137389
$799$	47.3223	1.67414
$800$	−3.03615	−0.107344
$801$	43.6277	1.54151
$802$	−15.6316	−0.551970
$803$	83.2888	2.93920
$804$	16.4382	0.579731
$805$	11.5039	0.405459
$806$	10.7680	0.379286
$807$	−24.5519	−0.864267
$808$	69.5258	2.44591
$809$	22.9821	0.808009	0.404005	−	0.914757i	$-0.367618\pi$
$809$	22.9821	0.808009	0.404005	+	0.914757i	$0.367618\pi$
$810$	206.335	7.24988
$811$	38.6017	1.35549	0.677744	−	0.735298i	$-0.262958\pi$
$811$	38.6017	1.35549	0.677744	+	0.735298i	$0.262958\pi$
$812$	−23.8714	−0.837721
$813$	−88.0115	−3.08670
$814$	51.8953	1.81893
$815$	22.2828	0.780533
$816$	60.0141	2.10091
$817$	−5.48345	−0.191842
$818$	6.90403	0.241394
$819$	3.96890	0.138685
$820$	154.524	5.39623
$821$	24.7338	0.863217	0.431608	−	0.902061i	$-0.357946\pi$
$821$	24.7338	0.863217	0.431608	+	0.902061i	$0.357946\pi$
$822$	118.177	4.12190
$823$	2.24953	0.0784137	0.0392069	−	0.999231i	$-0.487517\pi$
$823$	2.24953	0.0784137	0.0392069	+	0.999231i	$0.487517\pi$
$824$	−81.0716	−2.82426
$825$	−113.022	−3.93493
$826$	−18.7510	−0.652432
$827$	−21.2555	−0.739127	−0.369563	−	0.929206i	$-0.620493\pi$
$827$	−21.2555	−0.739127	−0.369563	+	0.929206i	$0.620493\pi$
$828$	153.374	5.33013
$829$	31.6913	1.10068	0.550342	−	0.834939i	$-0.314497\pi$
$829$	31.6913	1.10068	0.550342	+	0.834939i	$0.314497\pi$
$830$	10.4506	0.362744
$831$	−15.1167	−0.524392
$832$	5.27228	0.182783
$833$	27.4716	0.951833
$834$	109.863	3.80426
$835$	−46.0197	−1.59258
$836$	−17.7605	−0.614259
$837$	−90.8436	−3.14001
$838$	−12.9027	−0.445717
$839$	−5.98421	−0.206598	−0.103299	−	0.994650i	$-0.532940\pi$
$839$	−5.98421	−0.206598	−0.103299	+	0.994650i	$0.532940\pi$
$840$	38.1964	1.31790
$841$	37.6214	1.29729
$842$	−44.9349	−1.54856
$843$	32.6402	1.12419
$844$	76.9338	2.64817
$845$	40.0865	1.37902
$846$	209.101	7.18903
$847$	−22.7002	−0.779988
$848$	−37.1883	−1.27705
$849$	−23.8970	−0.820143
$850$	55.5340	1.90480
$851$	−16.0673	−0.550781
$852$	115.543	3.95845
$853$	32.3762	1.10854	0.554269	−	0.832337i	$-0.312998\pi$
$853$	32.3762	1.10854	0.554269	+	0.832337i	$0.312998\pi$
$854$	8.84763	0.302760
$855$	16.4222	0.561626
$856$	56.6874	1.93754
$857$	−47.6070	−1.62623	−0.813113	−	0.582106i	$-0.802229\pi$
$857$	−47.6070	−1.62623	−0.813113	+	0.582106i	$0.802229\pi$
$858$	−37.8037	−1.29060
$859$	−35.9394	−1.22623	−0.613117	−	0.789992i	$-0.710085\pi$
$859$	−35.9394	−1.22623	−0.613117	+	0.789992i	$0.710085\pi$
$860$	−106.434	−3.62937
$861$	−27.8362	−0.948654
$862$	42.9724	1.46364
$863$	13.8418	0.471180	0.235590	−	0.971852i	$-0.424298\pi$
$863$	13.8418	0.471180	0.235590	+	0.971852i	$0.424298\pi$
$864$	8.56746	0.291471
$865$	−12.7141	−0.432292
$866$	−36.3859	−1.23644
$867$	−3.16253	−0.107405
$868$	−17.6886	−0.600391
$869$	66.0897	2.24194
$870$	−210.241	−7.12783
$871$	0.899780	0.0304879
$872$	99.9896	3.38608
$873$	−73.1212	−2.47478
$874$	8.20954	0.277692
$875$	0.747650	0.0252752
$876$	−168.864	−5.70539
$877$	32.0405	1.08193	0.540965	−	0.841045i	$-0.318059\pi$
$877$	32.0405	1.08193	0.540965	+	0.841045i	$0.318059\pi$
$878$	10.4265	0.351877
$879$	56.1270	1.89312
$880$	−91.0197	−3.06827
$881$	3.68241	0.124063	0.0620317	−	0.998074i	$-0.480242\pi$
$881$	3.68241	0.124063	0.0620317	+	0.998074i	$0.480242\pi$
$882$	121.387	4.08732
$883$	3.41462	0.114911	0.0574556	−	0.998348i	$-0.481701\pi$
$883$	3.41462	0.114911	0.0574556	+	0.998348i	$0.481701\pi$
$884$	12.4417	0.418461
$885$	−110.616	−3.71830
$886$	−54.5598	−1.83297
$887$	−30.4915	−1.02381	−0.511903	−	0.859043i	$-0.671059\pi$
$887$	−30.4915	−1.02381	−0.511903	+	0.859043i	$0.671059\pi$
$888$	−53.3484	−1.79026
$889$	0.939487	0.0315094
$890$	45.3268	1.51936
$891$	170.093	5.69833
$892$	−35.5476	−1.19022
$893$	7.49675	0.250869
$894$	−107.619	−3.59931
$895$	6.95442	0.232461
$896$	−13.7526	−0.459441
$897$	11.7044	0.390799
$898$	1.40493	0.0468831
$899$	49.3663	1.64646
$900$	164.361	5.47871
$901$	36.2744	1.20847
$902$	190.177	6.33221
$903$	19.1731	0.638041
$904$	−40.7938	−1.35678
$905$	−18.7866	−0.624487
$906$	−163.539	−5.43323
$907$	−29.8662	−0.991690	−0.495845	−	0.868411i	$-0.665142\pi$
$907$	−29.8662	−0.991690	−0.495845	+	0.868411i	$0.665142\pi$
$908$	−19.8176	−0.657671
$909$	−104.518	−3.46665
$910$	4.12346	0.136691
$911$	19.4874	0.645647	0.322824	−	0.946459i	$-0.395368\pi$
$911$	19.4874	0.645647	0.322824	+	0.946459i	$0.395368\pi$
$912$	9.50736	0.314820
$913$	8.61494	0.285113
$914$	−27.5971	−0.912829
$915$	52.1937	1.72547
$916$	−49.9271	−1.64964
$917$	−12.5897	−0.415748
$918$	−156.707	−5.17210
$919$	32.0908	1.05858	0.529289	−	0.848442i	$-0.322459\pi$
$919$	32.0908	1.05858	0.529289	+	0.848442i	$0.322459\pi$
$920$	80.7955	2.66375
$921$	75.5558	2.48965
$922$	−3.46712	−0.114184
$923$	6.32451	0.208174
$924$	62.1002	2.04295
$925$	−17.2183	−0.566135
$926$	−3.31801	−0.109037
$927$	121.875	4.00290
$928$	−4.65574	−0.152832
$929$	8.86571	0.290874	0.145437	−	0.989367i	$-0.453541\pi$
$929$	8.86571	0.290874	0.145437	+	0.989367i	$0.453541\pi$
$930$	−155.788	−5.10848
$931$	4.35201	0.142631
$932$	−30.2979	−0.992440
$933$	65.4435	2.14252
$934$	34.6430	1.13356
$935$	88.7828	2.90351
$936$	27.8748	0.911117
$937$	5.45192	0.178106	0.0890532	−	0.996027i	$-0.471616\pi$
$937$	5.45192	0.178106	0.0890532	+	0.996027i	$0.471616\pi$
$938$	−2.20670	−0.0720514
$939$	−34.4138	−1.12305
$940$	145.512	4.74608
$941$	−9.67421	−0.315370	−0.157685	−	0.987489i	$-0.550403\pi$
$941$	−9.67421	−0.315370	−0.157685	+	0.987489i	$0.550403\pi$
$942$	152.162	4.95771
$943$	−58.8809	−1.91742
$944$	−45.9337	−1.49501
$945$	−34.7874	−1.13163
$946$	−130.991	−4.25888
$947$	23.2003	0.753907	0.376954	−	0.926232i	$-0.376972\pi$
$947$	23.2003	0.753907	0.376954	+	0.926232i	$0.376972\pi$
$948$	−133.994	−4.35192
$949$	−9.24314	−0.300045
$950$	8.79762	0.285433
$951$	15.2693	0.495140
$952$	−15.4714	−0.501432
$953$	−8.94448	−0.289740	−0.144870	−	0.989451i	$-0.546276\pi$
$953$	−8.94448	−0.289740	−0.144870	+	0.989451i	$0.546276\pi$
$954$	160.284	5.18937
$955$	−4.51539	−0.146114
$956$	1.73765	0.0561995
$957$	−173.312	−5.60240
$958$	−11.3900	−0.367995
$959$	−10.6261	−0.343135
$960$	−76.2776	−2.46185
$961$	5.58031	0.180010
$962$	−5.75918	−0.185684
$963$	−85.2183	−2.74612
$964$	−45.2172	−1.45635
$965$	−13.3687	−0.430353
$966$	−28.7050	−0.923568
$967$	13.5208	0.434800	0.217400	−	0.976083i	$-0.430242\pi$
$967$	13.5208	0.434800	0.217400	+	0.976083i	$0.430242\pi$
$968$	−159.431	−5.12429
$969$	−9.27370	−0.297914
$970$	−75.9688	−2.43921
$971$	−28.3649	−0.910272	−0.455136	−	0.890422i	$-0.650409\pi$
$971$	−28.3649	−0.910272	−0.455136	+	0.890422i	$0.650409\pi$
$972$	−162.041	−5.19747
$973$	−9.87857	−0.316692
$974$	−68.6351	−2.19921
$975$	12.5429	0.401693
$976$	21.6737	0.693758
$977$	−11.4045	−0.364862	−0.182431	−	0.983219i	$-0.558397\pi$
$977$	−11.4045	−0.364862	−0.182431	+	0.983219i	$0.558397\pi$
$978$	−55.6009	−1.77792
$979$	37.3652	1.19420
$980$	84.4727	2.69838
$981$	−150.315	−4.79918
$982$	83.2034	2.65513
$983$	15.8430	0.505315	0.252657	−	0.967556i	$-0.418695\pi$
$983$	15.8430	0.505315	0.252657	+	0.967556i	$0.418695\pi$
$984$	−195.502	−6.23238
$985$	39.2543	1.25075
$986$	85.1578	2.71198
$987$	−26.2127	−0.834359
$988$	1.97100	0.0627060
$989$	40.5562	1.28961
$990$	392.300	12.4681
$991$	−47.9015	−1.52164	−0.760821	−	0.648962i	$-0.775203\pi$
$991$	−47.9015	−1.52164	−0.760821	+	0.648962i	$0.775203\pi$
$992$	−3.44989	−0.109534
$993$	−3.05444	−0.0969297
$994$	−15.5108	−0.491973
$995$	−65.9709	−2.09142
$996$	−17.4664	−0.553444
$997$	52.6301	1.66681	0.833406	−	0.552661i	$-0.186388\pi$
$997$	52.6301	1.66681	0.833406	+	0.552661i	$0.186388\pi$
$998$	−1.84428	−0.0583797
$999$	48.5870	1.53722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.20	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.20	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46112 q^{2} -3.25745 q^{3} +4.05713 q^{4} -3.21291 q^{5} +8.01698 q^{6} -0.720862 q^{7} -5.06284 q^{8} +7.61098 q^{9} +O(q^{10})\)	\(q-2.46112 q^{2} -3.25745 q^{3} +4.05713 q^{4} -3.21291 q^{5} +8.01698 q^{6} -0.720862 q^{7} -5.06284 q^{8} +7.61098 q^{9} +7.90737 q^{10} +6.51846 q^{11} -13.2159 q^{12} -0.723399 q^{13} +1.77413 q^{14} +10.4659 q^{15} +4.34602 q^{16} -4.23921 q^{17} -18.7315 q^{18} -0.671570 q^{19} -13.0352 q^{20} +2.34817 q^{21} -16.0427 q^{22} +4.96700 q^{23} +16.4919 q^{24} +5.32281 q^{25} +1.78037 q^{26} -15.0200 q^{27} -2.92463 q^{28} +8.16219 q^{29} -25.7579 q^{30} +6.04817 q^{31} -0.570403 q^{32} -21.2336 q^{33} +10.4332 q^{34} +2.31607 q^{35} +30.8787 q^{36} -3.23482 q^{37} +1.65282 q^{38} +2.35644 q^{39} +16.2665 q^{40} -11.8544 q^{41} -5.77914 q^{42} +8.16513 q^{43} +26.4462 q^{44} -24.4534 q^{45} -12.2244 q^{46} -11.1630 q^{47} -14.1569 q^{48} -6.48036 q^{49} -13.1001 q^{50} +13.8090 q^{51} -2.93492 q^{52} -8.55688 q^{53} +36.9661 q^{54} -20.9433 q^{55} +3.64961 q^{56} +2.18760 q^{57} -20.0882 q^{58} -10.5691 q^{59} +42.4615 q^{60} +4.98703 q^{61} -14.8853 q^{62} -5.48646 q^{63} -7.28820 q^{64} +2.32422 q^{65} +52.2584 q^{66} -1.24382 q^{67} -17.1990 q^{68} -16.1798 q^{69} -5.70012 q^{70} -8.74277 q^{71} -38.5331 q^{72} +12.7774 q^{73} +7.96128 q^{74} -17.3388 q^{75} -2.72464 q^{76} -4.69891 q^{77} -5.79948 q^{78} +10.1389 q^{79} -13.9634 q^{80} +26.0940 q^{81} +29.1751 q^{82} +1.32162 q^{83} +9.52682 q^{84} +13.6202 q^{85} -20.0954 q^{86} -26.5879 q^{87} -33.0019 q^{88} +5.73221 q^{89} +60.1828 q^{90} +0.521471 q^{91} +20.1518 q^{92} -19.7016 q^{93} +27.4736 q^{94} +2.15769 q^{95} +1.85806 q^{96} -9.60734 q^{97} +15.9490 q^{98} +49.6119 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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