LMFDB - Embedded newform 8029.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29618 q^{2} -2.98190 q^{3} +3.27246 q^{4} +2.81992 q^{5} +6.84699 q^{6} +1.00000 q^{7} -2.92179 q^{8} +5.89173 q^{9} +O(q^{10})$	\(q-2.29618 q^{2} -2.98190 q^{3} +3.27246 q^{4} +2.81992 q^{5} +6.84699 q^{6} +1.00000 q^{7} -2.92179 q^{8} +5.89173 q^{9} -6.47505 q^{10} -3.72818 q^{11} -9.75814 q^{12} +4.45108 q^{13} -2.29618 q^{14} -8.40871 q^{15} +0.164061 q^{16} +0.549742 q^{17} -13.5285 q^{18} -2.16577 q^{19} +9.22806 q^{20} -2.98190 q^{21} +8.56058 q^{22} -4.66333 q^{23} +8.71250 q^{24} +2.95194 q^{25} -10.2205 q^{26} -8.62284 q^{27} +3.27246 q^{28} -0.161770 q^{29} +19.3079 q^{30} +1.00000 q^{31} +5.46687 q^{32} +11.1170 q^{33} -1.26231 q^{34} +2.81992 q^{35} +19.2804 q^{36} -1.00000 q^{37} +4.97302 q^{38} -13.2727 q^{39} -8.23922 q^{40} +7.54439 q^{41} +6.84699 q^{42} -2.46148 q^{43} -12.2003 q^{44} +16.6142 q^{45} +10.7079 q^{46} +5.40613 q^{47} -0.489214 q^{48} +1.00000 q^{49} -6.77819 q^{50} -1.63928 q^{51} +14.5660 q^{52} -14.2886 q^{53} +19.7996 q^{54} -10.5132 q^{55} -2.92179 q^{56} +6.45812 q^{57} +0.371453 q^{58} +9.49842 q^{59} -27.5172 q^{60} +4.93308 q^{61} -2.29618 q^{62} +5.89173 q^{63} -12.8811 q^{64} +12.5517 q^{65} -25.5268 q^{66} -7.50007 q^{67} +1.79901 q^{68} +13.9056 q^{69} -6.47505 q^{70} +4.04551 q^{71} -17.2144 q^{72} +14.0290 q^{73} +2.29618 q^{74} -8.80239 q^{75} -7.08740 q^{76} -3.72818 q^{77} +30.4765 q^{78} -6.83858 q^{79} +0.462639 q^{80} +8.03726 q^{81} -17.3233 q^{82} -12.4540 q^{83} -9.75814 q^{84} +1.55023 q^{85} +5.65201 q^{86} +0.482381 q^{87} +10.8930 q^{88} -2.54383 q^{89} -38.1492 q^{90} +4.45108 q^{91} -15.2605 q^{92} -2.98190 q^{93} -12.4135 q^{94} -6.10731 q^{95} -16.3017 q^{96} +13.7140 q^{97} -2.29618 q^{98} -21.9654 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−2.29618	−1.62365	−0.811823	−	0.583903i	$-0.801525\pi$
$2$	−2.29618	−1.62365	−0.811823	+	0.583903i	$0.801525\pi$
$3$	−2.98190	−1.72160	−0.860800	−	0.508943i	$-0.830036\pi$
$3$	−2.98190	−1.72160	−0.860800	+	0.508943i	$0.830036\pi$
$4$	3.27246	1.63623
$5$	2.81992	1.26111	0.630553	−	0.776146i	$-0.282828\pi$
$5$	2.81992	1.26111	0.630553	+	0.776146i	$0.282828\pi$
$6$	6.84699	2.79527
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.92179	−1.03301
$9$	5.89173	1.96391
$10$	−6.47505	−2.04759
$11$	−3.72818	−1.12409	−0.562044	−	0.827108i	$-0.689985\pi$
$11$	−3.72818	−1.12409	−0.562044	+	0.827108i	$0.689985\pi$
$12$	−9.75814	−2.81693
$13$	4.45108	1.23451	0.617253	−	0.786765i	$-0.288245\pi$
$13$	4.45108	1.23451	0.617253	+	0.786765i	$0.288245\pi$
$14$	−2.29618	−0.613681
$15$	−8.40871	−2.17112
$16$	0.164061	0.0410153
$17$	0.549742	0.133332	0.0666660	−	0.997775i	$-0.478764\pi$
$17$	0.549742	0.133332	0.0666660	+	0.997775i	$0.478764\pi$
$18$	−13.5285	−3.18869
$19$	−2.16577	−0.496863	−0.248431	−	0.968649i	$-0.579915\pi$
$19$	−2.16577	−0.496863	−0.248431	+	0.968649i	$0.579915\pi$
$20$	9.22806	2.06346
$21$	−2.98190	−0.650704
$22$	8.56058	1.82512
$23$	−4.66333	−0.972371	−0.486186	−	0.873856i	$-0.661612\pi$
$23$	−4.66333	−0.972371	−0.486186	+	0.873856i	$0.661612\pi$
$24$	8.71250	1.77843
$25$	2.95194	0.590388
$26$	−10.2205	−2.00440
$27$	−8.62284	−1.65947
$28$	3.27246	0.618436
$29$	−0.161770	−0.0300399	−0.0150199	−	0.999887i	$-0.504781\pi$
$29$	−0.161770	−0.0300399	−0.0150199	+	0.999887i	$0.504781\pi$
$30$	19.3079	3.52513
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.46687	0.966416
$33$	11.1170	1.93523
$34$	−1.26231	−0.216484
$35$	2.81992	0.476653
$36$	19.2804	3.21340
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.97302	0.806730
$39$	−13.2727	−2.12533
$40$	−8.23922	−1.30274
$41$	7.54439	1.17824	0.589118	−	0.808047i	$-0.299475\pi$
$41$	7.54439	1.17824	0.589118	+	0.808047i	$0.299475\pi$
$42$	6.84699	1.05651
$43$	−2.46148	−0.375372	−0.187686	−	0.982229i	$-0.560099\pi$
$43$	−2.46148	−0.375372	−0.187686	+	0.982229i	$0.560099\pi$
$44$	−12.2003	−1.83926
$45$	16.6142	2.47670
$46$	10.7079	1.57879
$47$	5.40613	0.788566	0.394283	−	0.918989i	$-0.370993\pi$
$47$	5.40613	0.788566	0.394283	+	0.918989i	$0.370993\pi$
$48$	−0.489214	−0.0706119
$49$	1.00000	0.142857
$50$	−6.77819	−0.958581
$51$	−1.63928	−0.229545
$52$	14.5660	2.01993
$53$	−14.2886	−1.96270	−0.981348	−	0.192241i	$-0.938425\pi$
$53$	−14.2886	−1.96270	−0.981348	+	0.192241i	$0.938425\pi$
$54$	19.7996	2.69439
$55$	−10.5132	−1.41759
$56$	−2.92179	−0.390441
$57$	6.45812	0.855399
$58$	0.371453	0.0487742
$59$	9.49842	1.23659	0.618295	−	0.785946i	$-0.287824\pi$
$59$	9.49842	1.23659	0.618295	+	0.785946i	$0.287824\pi$
$60$	−27.5172	−3.55245
$61$	4.93308	0.631616	0.315808	−	0.948823i	$-0.397725\pi$
$61$	4.93308	0.631616	0.315808	+	0.948823i	$0.397725\pi$
$62$	−2.29618	−0.291616
$63$	5.89173	0.742288
$64$	−12.8811	−1.61013
$65$	12.5517	1.55684
$66$	−25.5268	−3.14213
$67$	−7.50007	−0.916279	−0.458140	−	0.888880i	$-0.651484\pi$
$67$	−7.50007	−0.916279	−0.458140	+	0.888880i	$0.651484\pi$
$68$	1.79901	0.218162
$69$	13.9056	1.67403
$70$	−6.47505	−0.773916
$71$	4.04551	0.480113	0.240057	−	0.970759i	$-0.422834\pi$
$71$	4.04551	0.480113	0.240057	+	0.970759i	$0.422834\pi$
$72$	−17.2144	−2.02874
$73$	14.0290	1.64198	0.820988	−	0.570946i	$-0.193423\pi$
$73$	14.0290	1.64198	0.820988	+	0.570946i	$0.193423\pi$
$74$	2.29618	0.266926
$75$	−8.80239	−1.01641
$76$	−7.08740	−0.812981
$77$	−3.72818	−0.424865
$78$	30.4765	3.45078
$79$	−6.83858	−0.769400	−0.384700	−	0.923042i	$-0.625695\pi$
$79$	−6.83858	−0.769400	−0.384700	+	0.923042i	$0.625695\pi$
$80$	0.462639	0.0517246
$81$	8.03726	0.893029
$82$	−17.3233	−1.91304
$83$	−12.4540	−1.36700	−0.683501	−	0.729950i	$-0.739544\pi$
$83$	−12.4540	−1.36700	−0.683501	+	0.729950i	$0.739544\pi$
$84$	−9.75814	−1.06470
$85$	1.55023	0.168146
$86$	5.65201	0.609472
$87$	0.482381	0.0517167
$88$	10.8930	1.16119
$89$	−2.54383	−0.269646	−0.134823	−	0.990870i	$-0.543047\pi$
$89$	−2.54383	−0.269646	−0.134823	+	0.990870i	$0.543047\pi$
$90$	−38.1492	−4.02128
$91$	4.45108	0.466600
$92$	−15.2605	−1.59102
$93$	−2.98190	−0.309209
$94$	−12.4135	−1.28035
$95$	−6.10731	−0.626597
$96$	−16.3017	−1.66378
$97$	13.7140	1.39244	0.696221	−	0.717828i	$-0.254864\pi$
$97$	13.7140	1.39244	0.696221	+	0.717828i	$0.254864\pi$
$98$	−2.29618	−0.231950
$99$	−21.9654	−2.20761
$100$	9.66010	0.966010
$101$	−14.5440	−1.44718	−0.723590	−	0.690230i	$-0.757509\pi$
$101$	−14.5440	−1.44718	−0.723590	+	0.690230i	$0.757509\pi$
$102$	3.76408	0.372699
$103$	5.69642	0.561285	0.280643	−	0.959812i	$-0.409452\pi$
$103$	5.69642	0.561285	0.280643	+	0.959812i	$0.409452\pi$
$104$	−13.0051	−1.27526
$105$	−8.40871	−0.820606
$106$	32.8093	3.18672
$107$	−12.0202	−1.16204	−0.581019	−	0.813890i	$-0.697346\pi$
$107$	−12.0202	−1.16204	−0.581019	+	0.813890i	$0.697346\pi$
$108$	−28.2179	−2.71527
$109$	−9.32594	−0.893263	−0.446631	−	0.894718i	$-0.647376\pi$
$109$	−9.32594	−0.893263	−0.446631	+	0.894718i	$0.647376\pi$
$110$	24.1401	2.30167
$111$	2.98190	0.283029
$112$	0.164061	0.0155023
$113$	11.8763	1.11723	0.558615	−	0.829427i	$-0.311333\pi$
$113$	11.8763	1.11723	0.558615	+	0.829427i	$0.311333\pi$
$114$	−14.8290	−1.38887
$115$	−13.1502	−1.22626
$116$	−0.529384	−0.0491521
$117$	26.2245	2.42446
$118$	−21.8101	−2.00778
$119$	0.549742	0.0503948
$120$	24.5685	2.24279
$121$	2.89930	0.263572
$122$	−11.3272	−1.02552
$123$	−22.4966	−2.02845
$124$	3.27246	0.293875
$125$	−5.77536	−0.516564
$126$	−13.5285	−1.20521
$127$	−4.59668	−0.407890	−0.203945	−	0.978982i	$-0.565376\pi$
$127$	−4.59668	−0.407890	−0.203945	+	0.978982i	$0.565376\pi$
$128$	18.6435	1.64787
$129$	7.33989	0.646242
$130$	−28.8209	−2.52776
$131$	−11.7412	−1.02583	−0.512915	−	0.858440i	$-0.671434\pi$
$131$	−11.7412	−1.02583	−0.512915	+	0.858440i	$0.671434\pi$
$132$	36.3801	3.16648
$133$	−2.16577	−0.187796
$134$	17.2215	1.48771
$135$	−24.3157	−2.09276
$136$	−1.60623	−0.137733
$137$	−17.1953	−1.46909	−0.734547	−	0.678558i	$-0.762605\pi$
$137$	−17.1953	−1.46909	−0.734547	+	0.678558i	$0.762605\pi$
$138$	−31.9298	−2.71804
$139$	14.1140	1.19713	0.598567	−	0.801073i	$-0.295737\pi$
$139$	14.1140	1.19713	0.598567	+	0.801073i	$0.295737\pi$
$140$	9.22806	0.779914
$141$	−16.1205	−1.35760
$142$	−9.28922	−0.779534
$143$	−16.5944	−1.38769
$144$	0.966603	0.0805503
$145$	−0.456177	−0.0378835
$146$	−32.2132	−2.66599
$147$	−2.98190	−0.245943
$148$	−3.27246	−0.268994
$149$	−20.8771	−1.71032	−0.855160	−	0.518365i	$-0.826541\pi$
$149$	−20.8771	−1.71032	−0.855160	+	0.518365i	$0.826541\pi$
$150$	20.2119	1.65029
$151$	−14.9824	−1.21925	−0.609627	−	0.792688i	$-0.708681\pi$
$151$	−14.9824	−1.21925	−0.609627	+	0.792688i	$0.708681\pi$
$152$	6.32795	0.513264
$153$	3.23893	0.261852
$154$	8.56058	0.689831
$155$	2.81992	0.226501
$156$	−43.4342	−3.47752
$157$	11.8206	0.943389	0.471694	−	0.881762i	$-0.343643\pi$
$157$	11.8206	0.943389	0.471694	+	0.881762i	$0.343643\pi$
$158$	15.7026	1.24923
$159$	42.6073	3.37898
$160$	15.4161	1.21875
$161$	−4.66333	−0.367522
$162$	−18.4550	−1.44996
$163$	9.11838	0.714206	0.357103	−	0.934065i	$-0.383764\pi$
$163$	9.11838	0.714206	0.357103	+	0.934065i	$0.383764\pi$
$164$	24.6887	1.92786
$165$	31.3492	2.44053
$166$	28.5966	2.21953
$167$	−20.1227	−1.55714	−0.778572	−	0.627555i	$-0.784056\pi$
$167$	−20.1227	−1.55714	−0.778572	+	0.627555i	$0.784056\pi$
$168$	8.71250	0.672184
$169$	6.81208	0.524006
$170$	−3.55961	−0.273009
$171$	−12.7602	−0.975793
$172$	−8.05509	−0.614195
$173$	16.1261	1.22604	0.613022	−	0.790065i	$-0.289953\pi$
$173$	16.1261	1.22604	0.613022	+	0.790065i	$0.289953\pi$
$174$	−1.10764	−0.0839696
$175$	2.95194	0.223146
$176$	−0.611649	−0.0461047
$177$	−28.3233	−2.12891
$178$	5.84110	0.437809
$179$	−5.22387	−0.390451	−0.195225	−	0.980758i	$-0.562544\pi$
$179$	−5.22387	−0.390451	−0.195225	+	0.980758i	$0.562544\pi$
$180$	54.3692	4.05244
$181$	−9.92895	−0.738013	−0.369007	−	0.929427i	$-0.620302\pi$
$181$	−9.92895	−0.738013	−0.369007	+	0.929427i	$0.620302\pi$
$182$	−10.2205	−0.757593
$183$	−14.7099	−1.08739
$184$	13.6253	1.00447
$185$	−2.81992	−0.207325
$186$	6.84699	0.502046
$187$	−2.04954	−0.149877
$188$	17.6913	1.29027
$189$	−8.62284	−0.627219
$190$	14.0235	1.01737
$191$	16.2731	1.17748	0.588740	−	0.808322i	$-0.299624\pi$
$191$	16.2731	1.17748	0.588740	+	0.808322i	$0.299624\pi$
$192$	38.4101	2.77201
$193$	−1.65027	−0.118789	−0.0593946	−	0.998235i	$-0.518917\pi$
$193$	−1.65027	−0.118789	−0.0593946	+	0.998235i	$0.518917\pi$
$194$	−31.4898	−2.26083
$195$	−37.4278	−2.68026
$196$	3.27246	0.233747
$197$	13.2106	0.941219	0.470610	−	0.882342i	$-0.344034\pi$
$197$	13.2106	0.941219	0.470610	+	0.882342i	$0.344034\pi$
$198$	50.4366	3.58437
$199$	−21.6294	−1.53327	−0.766635	−	0.642083i	$-0.778070\pi$
$199$	−21.6294	−1.53327	−0.766635	+	0.642083i	$0.778070\pi$
$200$	−8.62496	−0.609877
$201$	22.3645	1.57747
$202$	33.3956	2.34971
$203$	−0.161770	−0.0113540
$204$	−5.36446	−0.375587
$205$	21.2746	1.48588
$206$	−13.0800	−0.911329
$207$	−27.4751	−1.90965
$208$	0.730248	0.0506336
$209$	8.07439	0.558517
$210$	19.3079	1.33237
$211$	−3.24981	−0.223726	−0.111863	−	0.993724i	$-0.535682\pi$
$211$	−3.24981	−0.223726	−0.111863	+	0.993724i	$0.535682\pi$
$212$	−46.7590	−3.21142
$213$	−12.0633	−0.826563
$214$	27.6006	1.88674
$215$	−6.94118	−0.473384
$216$	25.1942	1.71425
$217$	1.00000	0.0678844
$218$	21.4141	1.45034
$219$	−41.8332	−2.82683
$220$	−34.4038	−2.31951
$221$	2.44694	0.164599
$222$	−6.84699	−0.459540
$223$	14.8072	0.991561	0.495780	−	0.868448i	$-0.334882\pi$
$223$	14.8072	0.991561	0.495780	+	0.868448i	$0.334882\pi$
$224$	5.46687	0.365271
$225$	17.3920	1.15947
$226$	−27.2702	−1.81399
$227$	8.33994	0.553541	0.276771	−	0.960936i	$-0.410736\pi$
$227$	8.33994	0.553541	0.276771	+	0.960936i	$0.410736\pi$
$228$	21.1339	1.39963
$229$	−11.5101	−0.760609	−0.380305	−	0.924861i	$-0.624181\pi$
$229$	−11.5101	−0.760609	−0.380305	+	0.924861i	$0.624181\pi$
$230$	30.1953	1.99102
$231$	11.1170	0.731448
$232$	0.472658	0.0310315
$233$	20.4052	1.33679	0.668396	−	0.743805i	$-0.266981\pi$
$233$	20.4052	1.33679	0.668396	+	0.743805i	$0.266981\pi$
$234$	−60.2163	−3.93646
$235$	15.2449	0.994465
$236$	31.0832	2.02334
$237$	20.3919	1.32460
$238$	−1.26231	−0.0818233
$239$	16.8685	1.09114	0.545568	−	0.838067i	$-0.316314\pi$
$239$	16.8685	1.09114	0.545568	+	0.838067i	$0.316314\pi$
$240$	−1.37954	−0.0890491
$241$	−6.08055	−0.391682	−0.195841	−	0.980636i	$-0.562744\pi$
$241$	−6.08055	−0.391682	−0.195841	+	0.980636i	$0.562744\pi$
$242$	−6.65732	−0.427949
$243$	1.90220	0.122026
$244$	16.1433	1.03347
$245$	2.81992	0.180158
$246$	51.6563	3.29349
$247$	−9.64003	−0.613380
$248$	−2.92179	−0.185534
$249$	37.1365	2.35343
$250$	13.2613	0.838718
$251$	6.90063	0.435564	0.217782	−	0.975997i	$-0.430118\pi$
$251$	6.90063	0.435564	0.217782	+	0.975997i	$0.430118\pi$
$252$	19.2804	1.21455
$253$	17.3857	1.09303
$254$	10.5548	0.662269
$255$	−4.62262	−0.289480
$256$	−17.0468	−1.06543
$257$	−7.21350	−0.449966	−0.224983	−	0.974363i	$-0.572233\pi$
$257$	−7.21350	−0.449966	−0.224983	+	0.974363i	$0.572233\pi$
$258$	−16.8537	−1.04927
$259$	−1.00000	−0.0621370
$260$	41.0748	2.54735
$261$	−0.953103	−0.0589956
$262$	26.9598	1.66558
$263$	13.4500	0.829360	0.414680	−	0.909967i	$-0.363894\pi$
$263$	13.4500	0.829360	0.414680	+	0.909967i	$0.363894\pi$
$264$	−32.4817	−1.99911
$265$	−40.2928	−2.47517
$266$	4.97302	0.304915
$267$	7.58545	0.464222
$268$	−24.5436	−1.49924
$269$	−23.8727	−1.45554	−0.727771	−	0.685821i	$-0.759443\pi$
$269$	−23.8727	−1.45554	−0.727771	+	0.685821i	$0.759443\pi$
$270$	55.8333	3.39791
$271$	23.3447	1.41809	0.709045	−	0.705164i	$-0.249127\pi$
$271$	23.3447	1.41809	0.709045	+	0.705164i	$0.249127\pi$
$272$	0.0901913	0.00546865
$273$	−13.2727	−0.803298
$274$	39.4836	2.38529
$275$	−11.0054	−0.663648
$276$	45.5054	2.73910
$277$	−13.7086	−0.823668	−0.411834	−	0.911259i	$-0.635112\pi$
$277$	−13.7086	−0.823668	−0.411834	+	0.911259i	$0.635112\pi$
$278$	−32.4083	−1.94372
$279$	5.89173	0.352728
$280$	−8.23922	−0.492388
$281$	−21.8659	−1.30441	−0.652205	−	0.758043i	$-0.726156\pi$
$281$	−21.8659	−1.30441	−0.652205	+	0.758043i	$0.726156\pi$
$282$	37.0157	2.20425
$283$	−9.03140	−0.536861	−0.268431	−	0.963299i	$-0.586505\pi$
$283$	−9.03140	−0.536861	−0.268431	+	0.963299i	$0.586505\pi$
$284$	13.2387	0.785575
$285$	18.2114	1.07875
$286$	38.1038	2.25312
$287$	7.54439	0.445331
$288$	32.2093	1.89795
$289$	−16.6978	−0.982223
$290$	1.04747	0.0615094
$291$	−40.8936	−2.39723
$292$	45.9094	2.68665
$293$	−17.0294	−0.994867	−0.497434	−	0.867502i	$-0.665724\pi$
$293$	−17.0294	−0.994867	−0.497434	+	0.867502i	$0.665724\pi$
$294$	6.84699	0.399324
$295$	26.7848	1.55947
$296$	2.92179	0.169826
$297$	32.1475	1.86539
$298$	47.9377	2.77695
$299$	−20.7568	−1.20040
$300$	−28.8054	−1.66308
$301$	−2.46148	−0.141877
$302$	34.4024	1.97964
$303$	43.3687	2.49147
$304$	−0.355319	−0.0203790
$305$	13.9109	0.796534
$306$	−7.43718	−0.425155
$307$	9.04666	0.516320	0.258160	−	0.966102i	$-0.416884\pi$
$307$	9.04666	0.516320	0.258160	+	0.966102i	$0.416884\pi$
$308$	−12.2003	−0.695176
$309$	−16.9862	−0.966309
$310$	−6.47505	−0.367758
$311$	−26.5868	−1.50760	−0.753800	−	0.657104i	$-0.771781\pi$
$311$	−26.5868	−1.50760	−0.753800	+	0.657104i	$0.771781\pi$
$312$	38.7800	2.19548
$313$	17.8389	1.00831	0.504156	−	0.863613i	$-0.331804\pi$
$313$	17.8389	1.00831	0.504156	+	0.863613i	$0.331804\pi$
$314$	−27.1423	−1.53173
$315$	16.6142	0.936103
$316$	−22.3789	−1.25891
$317$	20.0962	1.12872	0.564358	−	0.825530i	$-0.309124\pi$
$317$	20.0962	1.12872	0.564358	+	0.825530i	$0.309124\pi$
$318$	−97.8341	−5.48627
$319$	0.603106	0.0337675
$320$	−36.3236	−2.03055
$321$	35.8431	2.00057
$322$	10.7079	0.596725
$323$	−1.19062	−0.0662477
$324$	26.3016	1.46120
$325$	13.1393	0.728838
$326$	−20.9375	−1.15962
$327$	27.8090	1.53784
$328$	−22.0432	−1.21713
$329$	5.40613	0.298050
$330$	−71.9834	−3.96256
$331$	−21.5471	−1.18434	−0.592168	−	0.805814i	$-0.701728\pi$
$331$	−21.5471	−1.18434	−0.592168	+	0.805814i	$0.701728\pi$
$332$	−40.7551	−2.23673
$333$	−5.89173	−0.322865
$334$	46.2055	2.52825
$335$	−21.1496	−1.15552
$336$	−0.489214	−0.0266888
$337$	30.8656	1.68136	0.840679	−	0.541533i	$-0.182156\pi$
$337$	30.8656	1.68136	0.840679	+	0.541533i	$0.182156\pi$
$338$	−15.6418	−0.850801
$339$	−35.4140	−1.92342
$340$	5.07305	0.275125
$341$	−3.72818	−0.201892
$342$	29.2996	1.58434
$343$	1.00000	0.0539949
$344$	7.19194	0.387764
$345$	39.2126	2.11113
$346$	−37.0285	−1.99066
$347$	27.2107	1.46074	0.730372	−	0.683049i	$-0.239347\pi$
$347$	27.2107	1.46074	0.730372	+	0.683049i	$0.239347\pi$
$348$	1.57857	0.0846203
$349$	14.4532	0.773662	0.386831	−	0.922151i	$-0.373570\pi$
$349$	14.4532	0.773662	0.386831	+	0.922151i	$0.373570\pi$
$350$	−6.77819	−0.362310
$351$	−38.3809	−2.04862
$352$	−20.3815	−1.08634
$353$	−0.894279	−0.0475977	−0.0237988	−	0.999717i	$-0.507576\pi$
$353$	−0.894279	−0.0475977	−0.0237988	+	0.999717i	$0.507576\pi$
$354$	65.0356	3.45660
$355$	11.4080	0.605474
$356$	−8.32458	−0.441202
$357$	−1.63928	−0.0867597
$358$	11.9950	0.633954
$359$	−12.4438	−0.656759	−0.328380	−	0.944546i	$-0.606503\pi$
$359$	−12.4438	−0.656759	−0.328380	+	0.944546i	$0.606503\pi$
$360$	−48.5432	−2.55845
$361$	−14.3094	−0.753127
$362$	22.7987	1.19827
$363$	−8.64541	−0.453767
$364$	14.5660	0.763464
$365$	39.5608	2.07070
$366$	33.7767	1.76554
$367$	−7.73589	−0.403810	−0.201905	−	0.979405i	$-0.564713\pi$
$367$	−7.73589	−0.403810	−0.201905	+	0.979405i	$0.564713\pi$
$368$	−0.765071	−0.0398821
$369$	44.4495	2.31395
$370$	6.47505	0.336622
$371$	−14.2886	−0.741829
$372$	−9.75814	−0.505936
$373$	−19.7641	−1.02335	−0.511673	−	0.859180i	$-0.670974\pi$
$373$	−19.7641	−1.02335	−0.511673	+	0.859180i	$0.670974\pi$
$374$	4.70611	0.243347
$375$	17.2216	0.889317
$376$	−15.7956	−0.814596
$377$	−0.720049	−0.0370844
$378$	19.7996	1.01838
$379$	27.8191	1.42897	0.714486	−	0.699650i	$-0.246661\pi$
$379$	27.8191	1.42897	0.714486	+	0.699650i	$0.246661\pi$
$380$	−19.9859	−1.02526
$381$	13.7068	0.702223
$382$	−37.3660	−1.91181
$383$	−8.77751	−0.448510	−0.224255	−	0.974531i	$-0.571995\pi$
$383$	−8.77751	−0.448510	−0.224255	+	0.974531i	$0.571995\pi$
$384$	−55.5932	−2.83698
$385$	−10.5132	−0.535800
$386$	3.78933	0.192872
$387$	−14.5024	−0.737197
$388$	44.8783	2.27835
$389$	14.2436	0.722181	0.361091	−	0.932531i	$-0.382404\pi$
$389$	14.2436	0.722181	0.361091	+	0.932531i	$0.382404\pi$
$390$	85.9412	4.35180
$391$	−2.56363	−0.129648
$392$	−2.92179	−0.147573
$393$	35.0109	1.76607
$394$	−30.3340	−1.52821
$395$	−19.2842	−0.970295
$396$	−71.8808	−3.61215
$397$	−2.69858	−0.135438	−0.0677190	−	0.997704i	$-0.521572\pi$
$397$	−2.69858	−0.135438	−0.0677190	+	0.997704i	$0.521572\pi$
$398$	49.6651	2.48949
$399$	6.45812	0.323311
$400$	0.484298	0.0242149
$401$	−21.0117	−1.04928	−0.524638	−	0.851326i	$-0.675799\pi$
$401$	−21.0117	−1.04928	−0.524638	+	0.851326i	$0.675799\pi$
$402$	−51.3529	−2.56125
$403$	4.45108	0.221724
$404$	−47.5945	−2.36792
$405$	22.6644	1.12620
$406$	0.371453	0.0184349
$407$	3.72818	0.184799
$408$	4.78963	0.237122
$409$	29.5613	1.46171	0.730855	−	0.682533i	$-0.239122\pi$
$409$	29.5613	1.46171	0.730855	+	0.682533i	$0.239122\pi$
$410$	−48.8503	−2.41254
$411$	51.2747	2.52919
$412$	18.6413	0.918391
$413$	9.49842	0.467387
$414$	63.0878	3.10059
$415$	−35.1192	−1.72393
$416$	24.3335	1.19305
$417$	−42.0865	−2.06099
$418$	−18.5403	−0.906835
$419$	−13.8934	−0.678737	−0.339368	−	0.940654i	$-0.610213\pi$
$419$	−13.8934	−0.678737	−0.339368	+	0.940654i	$0.610213\pi$
$420$	−27.5172	−1.34270
$421$	−7.51839	−0.366424	−0.183212	−	0.983073i	$-0.558649\pi$
$421$	−7.51839	−0.366424	−0.183212	+	0.983073i	$0.558649\pi$
$422$	7.46215	0.363252
$423$	31.8515	1.54867
$424$	41.7485	2.02748
$425$	1.62281	0.0787176
$426$	27.6995	1.34205
$427$	4.93308	0.238728
$428$	−39.3357	−1.90136
$429$	49.4828	2.38905
$430$	15.9382	0.768609
$431$	2.82523	0.136087	0.0680433	−	0.997682i	$-0.478324\pi$
$431$	2.82523	0.136087	0.0680433	+	0.997682i	$0.478324\pi$
$432$	−1.41467	−0.0680635
$433$	−38.0131	−1.82679	−0.913397	−	0.407069i	$-0.866551\pi$
$433$	−38.0131	−1.82679	−0.913397	+	0.407069i	$0.866551\pi$
$434$	−2.29618	−0.110220
$435$	1.36028	0.0652202
$436$	−30.5187	−1.46158
$437$	10.0997	0.483135
$438$	96.0567	4.58977
$439$	17.4343	0.832092	0.416046	−	0.909344i	$-0.363416\pi$
$439$	17.4343	0.832092	0.416046	+	0.909344i	$0.363416\pi$
$440$	30.7173	1.46439
$441$	5.89173	0.280558
$442$	−5.61863	−0.267251
$443$	−34.6637	−1.64692	−0.823462	−	0.567372i	$-0.807960\pi$
$443$	−34.6637	−1.64692	−0.823462	+	0.567372i	$0.807960\pi$
$444$	9.75814	0.463101
$445$	−7.17340	−0.340052
$446$	−34.0000	−1.60994
$447$	62.2534	2.94449
$448$	−12.8811	−0.608573
$449$	−16.9826	−0.801460	−0.400730	−	0.916196i	$-0.631244\pi$
$449$	−16.9826	−0.801460	−0.400730	+	0.916196i	$0.631244\pi$
$450$	−39.9353	−1.88257
$451$	−28.1268	−1.32444
$452$	38.8648	1.82804
$453$	44.6761	2.09907
$454$	−19.1500	−0.898755
$455$	12.5517	0.588431
$456$	−18.8693	−0.883636
$457$	12.8462	0.600922	0.300461	−	0.953794i	$-0.402860\pi$
$457$	12.8462	0.600922	0.300461	+	0.953794i	$0.402860\pi$
$458$	26.4293	1.23496
$459$	−4.74034	−0.221260
$460$	−43.0335	−2.00645
$461$	−1.83151	−0.0853019	−0.0426510	−	0.999090i	$-0.513580\pi$
$461$	−1.83151	−0.0853019	−0.0426510	+	0.999090i	$0.513580\pi$
$462$	−25.5268	−1.18761
$463$	22.6140	1.05096	0.525481	−	0.850805i	$-0.323885\pi$
$463$	22.6140	1.05096	0.525481	+	0.850805i	$0.323885\pi$
$464$	−0.0265401	−0.00123209
$465$	−8.40871	−0.389945
$466$	−46.8542	−2.17048
$467$	5.12304	0.237066	0.118533	−	0.992950i	$-0.462181\pi$
$467$	5.12304	0.237066	0.118533	+	0.992950i	$0.462181\pi$
$468$	85.8186	3.96697
$469$	−7.50007	−0.346321
$470$	−35.0050	−1.61466
$471$	−35.2479	−1.62414
$472$	−27.7524	−1.27741
$473$	9.17684	0.421951
$474$	−46.8236	−2.15068
$475$	−6.39324	−0.293342
$476$	1.79901	0.0824574
$477$	−84.1848	−3.85456
$478$	−38.7333	−1.77162
$479$	20.9827	0.958723	0.479362	−	0.877617i	$-0.340868\pi$
$479$	20.9827	0.958723	0.479362	+	0.877617i	$0.340868\pi$
$480$	−45.9694	−2.09821
$481$	−4.45108	−0.202952
$482$	13.9620	0.635954
$483$	13.9056	0.632726
$484$	9.48782	0.431265
$485$	38.6722	1.75602
$486$	−4.36781	−0.198128
$487$	13.3479	0.604850	0.302425	−	0.953173i	$-0.402204\pi$
$487$	13.3479	0.604850	0.302425	+	0.953173i	$0.402204\pi$
$488$	−14.4134	−0.652465
$489$	−27.1901	−1.22958
$490$	−6.47505	−0.292513
$491$	−17.2371	−0.777900	−0.388950	−	0.921259i	$-0.627162\pi$
$491$	−17.2371	−0.777900	−0.388950	+	0.921259i	$0.627162\pi$
$492$	−73.6192	−3.31901
$493$	−0.0889316	−0.00400528
$494$	22.1353	0.995913
$495$	−61.9406	−2.78402
$496$	0.164061	0.00736656
$497$	4.04551	0.181466
$498$	−85.2723	−3.82114
$499$	34.9548	1.56479	0.782396	−	0.622781i	$-0.213997\pi$
$499$	34.9548	1.56479	0.782396	+	0.622781i	$0.213997\pi$
$500$	−18.8996	−0.845217
$501$	60.0040	2.68078
$502$	−15.8451	−0.707202
$503$	−31.0653	−1.38514	−0.692568	−	0.721353i	$-0.743521\pi$
$503$	−31.0653	−1.38514	−0.692568	+	0.721353i	$0.743521\pi$
$504$	−17.2144	−0.766791
$505$	−41.0128	−1.82505
$506$	−39.9208	−1.77469
$507$	−20.3129	−0.902130
$508$	−15.0424	−0.667401
$509$	8.91104	0.394975	0.197487	−	0.980305i	$-0.436722\pi$
$509$	8.91104	0.394975	0.197487	+	0.980305i	$0.436722\pi$
$510$	10.6144	0.470013
$511$	14.0290	0.620608
$512$	1.85561	0.0820070
$513$	18.6751	0.824527
$514$	16.5635	0.730586
$515$	16.0634	0.707840
$516$	24.0195	1.05740
$517$	−20.1550	−0.886417
$518$	2.29618	0.100888
$519$	−48.0864	−2.11076
$520$	−36.6734	−1.60824
$521$	20.4821	0.897336	0.448668	−	0.893699i	$-0.351899\pi$
$521$	20.4821	0.897336	0.448668	+	0.893699i	$0.351899\pi$
$522$	2.18850	0.0957880
$523$	−22.5222	−0.984828	−0.492414	−	0.870361i	$-0.663885\pi$
$523$	−22.5222	−0.984828	−0.492414	+	0.870361i	$0.663885\pi$
$524$	−38.4224	−1.67849
$525$	−8.80239	−0.384168
$526$	−30.8836	−1.34659
$527$	0.549742	0.0239471
$528$	1.82387	0.0793740
$529$	−1.25337	−0.0544945
$530$	92.5196	4.01880
$531$	55.9621	2.42855
$532$	−7.08740	−0.307278
$533$	33.5807	1.45454
$534$	−17.4176	−0.753733
$535$	−33.8961	−1.46545
$536$	21.9137	0.946526
$537$	15.5771	0.672200
$538$	54.8160	2.36328
$539$	−3.72818	−0.160584
$540$	−79.5721	−3.42424
$541$	8.36049	0.359445	0.179723	−	0.983717i	$-0.442480\pi$
$541$	8.36049	0.359445	0.179723	+	0.983717i	$0.442480\pi$
$542$	−53.6037	−2.30248
$543$	29.6071	1.27056
$544$	3.00537	0.128854
$545$	−26.2984	−1.12650
$546$	30.4765	1.30427
$547$	−6.50705	−0.278221	−0.139111	−	0.990277i	$-0.544424\pi$
$547$	−6.50705	−0.278221	−0.139111	+	0.990277i	$0.544424\pi$
$548$	−56.2709	−2.40377
$549$	29.0643	1.24044
$550$	25.2703	1.07753
$551$	0.350357	0.0149257
$552$	−40.6292	−1.72930
$553$	−6.83858	−0.290806
$554$	31.4774	1.33735
$555$	8.40871	0.356930
$556$	46.1875	1.95878
$557$	−25.4406	−1.07795	−0.538977	−	0.842321i	$-0.681189\pi$
$557$	−25.4406	−1.07795	−0.538977	+	0.842321i	$0.681189\pi$
$558$	−13.5285	−0.572706
$559$	−10.9562	−0.463400
$560$	0.462639	0.0195501
$561$	6.11151	0.258028
$562$	50.2081	2.11790
$563$	12.8702	0.542414	0.271207	−	0.962521i	$-0.412577\pi$
$563$	12.8702	0.542414	0.271207	+	0.962521i	$0.412577\pi$
$564$	−52.7538	−2.22134
$565$	33.4903	1.40895
$566$	20.7378	0.871673
$567$	8.03726	0.337533
$568$	−11.8201	−0.495962
$569$	−38.1026	−1.59734	−0.798672	−	0.601767i	$-0.794464\pi$
$569$	−38.1026	−1.59734	−0.798672	+	0.601767i	$0.794464\pi$
$570$	−41.8167	−1.75151
$571$	−44.8548	−1.87711	−0.938557	−	0.345125i	$-0.887837\pi$
$571$	−44.8548	−1.87711	−0.938557	+	0.345125i	$0.887837\pi$
$572$	−54.3045	−2.27058
$573$	−48.5248	−2.02715
$574$	−17.3233	−0.723060
$575$	−13.7659	−0.574076
$576$	−75.8917	−3.16216
$577$	27.9926	1.16535	0.582674	−	0.812706i	$-0.302006\pi$
$577$	27.9926	1.16535	0.582674	+	0.812706i	$0.302006\pi$
$578$	38.3412	1.59478
$579$	4.92094	0.204507
$580$	−1.49282	−0.0619860
$581$	−12.4540	−0.516678
$582$	93.8993	3.89225
$583$	53.2706	2.20624
$584$	−40.9900	−1.69618
$585$	73.9510	3.05750
$586$	39.1026	1.61531
$587$	26.7105	1.10246	0.551230	−	0.834353i	$-0.314159\pi$
$587$	26.7105	1.10246	0.551230	+	0.834353i	$0.314159\pi$
$588$	−9.75814	−0.402419
$589$	−2.16577	−0.0892392
$590$	−61.5028	−2.53203
$591$	−39.3928	−1.62040
$592$	−0.164061	−0.00674287
$593$	1.69931	0.0697825	0.0348912	−	0.999391i	$-0.488892\pi$
$593$	1.69931	0.0697825	0.0348912	+	0.999391i	$0.488892\pi$
$594$	−73.8165	−3.02873
$595$	1.55023	0.0635532
$596$	−68.3194	−2.79847
$597$	64.4968	2.63968
$598$	47.6615	1.94902
$599$	−31.9307	−1.30465	−0.652327	−	0.757938i	$-0.726207\pi$
$599$	−31.9307	−1.30465	−0.652327	+	0.757938i	$0.726207\pi$
$600$	25.7188	1.04996
$601$	13.2884	0.542046	0.271023	−	0.962573i	$-0.412638\pi$
$601$	13.2884	0.542046	0.271023	+	0.962573i	$0.412638\pi$
$602$	5.65201	0.230359
$603$	−44.1883	−1.79949
$604$	−49.0294	−1.99498
$605$	8.17578	0.332393
$606$	−99.5824	−4.04526
$607$	−2.18600	−0.0887271	−0.0443636	−	0.999015i	$-0.514126\pi$
$607$	−2.18600	−0.0887271	−0.0443636	+	0.999015i	$0.514126\pi$
$608$	−11.8400	−0.480176
$609$	0.482381	0.0195471
$610$	−31.9419	−1.29329
$611$	24.0631	0.973489
$612$	10.5993	0.428450
$613$	−7.53468	−0.304323	−0.152161	−	0.988356i	$-0.548623\pi$
$613$	−7.53468	−0.304323	−0.152161	+	0.988356i	$0.548623\pi$
$614$	−20.7728	−0.838321
$615$	−63.4386	−2.55809
$616$	10.8930	0.438890
$617$	12.4491	0.501183	0.250592	−	0.968093i	$-0.419375\pi$
$617$	12.4491	0.501183	0.250592	+	0.968093i	$0.419375\pi$
$618$	39.0033	1.56894
$619$	−9.35009	−0.375812	−0.187906	−	0.982187i	$-0.560170\pi$
$619$	−9.35009	−0.375812	−0.187906	+	0.982187i	$0.560170\pi$
$620$	9.22806	0.370608
$621$	40.2111	1.61362
$622$	61.0482	2.44781
$623$	−2.54383	−0.101916
$624$	−2.17753	−0.0871709
$625$	−31.0458	−1.24183
$626$	−40.9613	−1.63714
$627$	−24.0770	−0.961544
$628$	38.6825	1.54360
$629$	−0.549742	−0.0219197
$630$	−38.1492	−1.51990
$631$	−13.6944	−0.545165	−0.272583	−	0.962132i	$-0.587878\pi$
$631$	−13.6944	−0.545165	−0.272583	+	0.962132i	$0.587878\pi$
$632$	19.9809	0.794798
$633$	9.69060	0.385167
$634$	−46.1446	−1.83264
$635$	−12.9623	−0.514392
$636$	139.431	5.52878
$637$	4.45108	0.176358
$638$	−1.38484	−0.0548264
$639$	23.8350	0.942899
$640$	52.5733	2.07814
$641$	−21.4099	−0.845639	−0.422820	−	0.906214i	$-0.638960\pi$
$641$	−21.4099	−0.845639	−0.422820	+	0.906214i	$0.638960\pi$
$642$	−82.3023	−3.24821
$643$	15.9954	0.630796	0.315398	−	0.948960i	$-0.397862\pi$
$643$	15.9954	0.630796	0.315398	+	0.948960i	$0.397862\pi$
$644$	−15.2605	−0.601350
$645$	20.6979	0.814979
$646$	2.73388	0.107563
$647$	8.04776	0.316390	0.158195	−	0.987408i	$-0.449433\pi$
$647$	8.04776	0.316390	0.158195	+	0.987408i	$0.449433\pi$
$648$	−23.4832	−0.922509
$649$	−35.4118	−1.39003
$650$	−30.1703	−1.18337
$651$	−2.98190	−0.116870
$652$	29.8395	1.16860
$653$	9.38500	0.367264	0.183632	−	0.982995i	$-0.441215\pi$
$653$	9.38500	0.367264	0.183632	+	0.982995i	$0.441215\pi$
$654$	−63.8546	−2.49691
$655$	−33.1091	−1.29368
$656$	1.23774	0.0483256
$657$	82.6553	3.22469
$658$	−12.4135	−0.483928
$659$	−24.3423	−0.948241	−0.474120	−	0.880460i	$-0.657234\pi$
$659$	−24.3423	−0.948241	−0.474120	+	0.880460i	$0.657234\pi$
$660$	102.589	3.99326
$661$	−23.1868	−0.901863	−0.450932	−	0.892558i	$-0.648908\pi$
$661$	−23.1868	−0.901863	−0.450932	+	0.892558i	$0.648908\pi$
$662$	49.4761	1.92294
$663$	−7.29654	−0.283374
$664$	36.3880	1.41213
$665$	−6.10731	−0.236831
$666$	13.5285	0.524218
$667$	0.754385	0.0292099
$668$	−65.8508	−2.54784
$669$	−44.1535	−1.70707
$670$	48.5633	1.87616
$671$	−18.3914	−0.709991
$672$	−16.3017	−0.628851
$673$	−49.5275	−1.90915	−0.954573	−	0.297977i	$-0.903688\pi$
$673$	−49.5275	−1.90915	−0.954573	+	0.297977i	$0.903688\pi$
$674$	−70.8732	−2.72993
$675$	−25.4541	−0.979729
$676$	22.2922	0.857394
$677$	26.8846	1.03326	0.516630	−	0.856209i	$-0.327186\pi$
$677$	26.8846	1.03326	0.516630	+	0.856209i	$0.327186\pi$
$678$	81.3170	3.12296
$679$	13.7140	0.526293
$680$	−4.52945	−0.173696
$681$	−24.8689	−0.952977
$682$	8.56058	0.327801
$683$	−8.02133	−0.306928	−0.153464	−	0.988154i	$-0.549043\pi$
$683$	−8.02133	−0.306928	−0.153464	+	0.988154i	$0.549043\pi$
$684$	−41.7570	−1.59662
$685$	−48.4893	−1.85268
$686$	−2.29618	−0.0876687
$687$	34.3220	1.30947
$688$	−0.403833	−0.0153960
$689$	−63.5998	−2.42296
$690$	−90.0393	−3.42774
$691$	−35.7975	−1.36180	−0.680900	−	0.732377i	$-0.738411\pi$
$691$	−35.7975	−1.36180	−0.680900	+	0.732377i	$0.738411\pi$
$692$	52.7720	2.00609
$693$	−21.9654	−0.834396
$694$	−62.4807	−2.37173
$695$	39.8003	1.50971
$696$	−1.40942	−0.0534239
$697$	4.14747	0.157097
$698$	−33.1872	−1.25615
$699$	−60.8464	−2.30142
$700$	9.66010	0.365117
$701$	16.3584	0.617848	0.308924	−	0.951087i	$-0.400031\pi$
$701$	16.3584	0.617848	0.308924	+	0.951087i	$0.400031\pi$
$702$	88.1296	3.32624
$703$	2.16577	0.0816837
$704$	48.0229	1.80993
$705$	−45.4586	−1.71207
$706$	2.05343	0.0772818
$707$	−14.5440	−0.546983
$708$	−92.6869	−3.48339
$709$	13.1842	0.495141	0.247571	−	0.968870i	$-0.420368\pi$
$709$	13.1842	0.495141	0.247571	+	0.968870i	$0.420368\pi$
$710$	−26.1948	−0.983075
$711$	−40.2910	−1.51103
$712$	7.43255	0.278547
$713$	−4.66333	−0.174643
$714$	3.76408	0.140867
$715$	−46.7948	−1.75003
$716$	−17.0949	−0.638866
$717$	−50.3003	−1.87850
$718$	28.5733	1.06634
$719$	−38.4759	−1.43491	−0.717454	−	0.696606i	$-0.754693\pi$
$719$	−38.4759	−1.43491	−0.717454	+	0.696606i	$0.754693\pi$
$720$	2.72574	0.101582
$721$	5.69642	0.212146
$722$	32.8571	1.22281
$723$	18.1316	0.674321
$724$	−32.4921	−1.20756
$725$	−0.477534	−0.0177352
$726$	19.8515	0.736756
$727$	34.3859	1.27530	0.637652	−	0.770325i	$-0.279906\pi$
$727$	34.3859	1.27530	0.637652	+	0.770325i	$0.279906\pi$
$728$	−13.0051	−0.482002
$729$	−29.7840	−1.10311
$730$	−90.8387	−3.36209
$731$	−1.35318	−0.0500492
$732$	−48.1376	−1.77922
$733$	−34.7510	−1.28356	−0.641779	−	0.766890i	$-0.721803\pi$
$733$	−34.7510	−1.28356	−0.641779	+	0.766890i	$0.721803\pi$
$734$	17.7630	0.655645
$735$	−8.40871	−0.310160
$736$	−25.4938	−0.939715
$737$	27.9616	1.02998
$738$	−102.064	−3.75703
$739$	2.82119	0.103779	0.0518896	−	0.998653i	$-0.483476\pi$
$739$	2.82119	0.103779	0.0518896	+	0.998653i	$0.483476\pi$
$740$	−9.22806	−0.339230
$741$	28.7456	1.05600
$742$	32.8093	1.20447
$743$	−9.01687	−0.330797	−0.165398	−	0.986227i	$-0.552891\pi$
$743$	−9.01687	−0.330797	−0.165398	+	0.986227i	$0.552891\pi$
$744$	8.71250	0.319416
$745$	−58.8717	−2.15689
$746$	45.3820	1.66155
$747$	−73.3755	−2.68467
$748$	−6.70702	−0.245233
$749$	−12.0202	−0.439209
$750$	−39.5438	−1.44394
$751$	14.9617	0.545961	0.272981	−	0.962020i	$-0.411991\pi$
$751$	14.9617	0.545961	0.272981	+	0.962020i	$0.411991\pi$
$752$	0.886936	0.0323432
$753$	−20.5770	−0.749868
$754$	1.65337	0.0602120
$755$	−42.2493	−1.53761
$756$	−28.2179	−1.02627
$757$	−9.15632	−0.332792	−0.166396	−	0.986059i	$-0.553213\pi$
$757$	−9.15632	−0.332792	−0.166396	+	0.986059i	$0.553213\pi$
$758$	−63.8778	−2.32015
$759$	−51.8424	−1.88176
$760$	17.8443	0.647281
$761$	35.0245	1.26964	0.634819	−	0.772661i	$-0.281075\pi$
$761$	35.0245	1.26964	0.634819	+	0.772661i	$0.281075\pi$
$762$	−31.4734	−1.14016
$763$	−9.32594	−0.337622
$764$	53.2530	1.92663
$765$	9.13352	0.330223
$766$	20.1548	0.728222
$767$	42.2782	1.52658
$768$	50.8320	1.83424
$769$	10.1015	0.364271	0.182135	−	0.983273i	$-0.441699\pi$
$769$	10.1015	0.364271	0.182135	+	0.983273i	$0.441699\pi$
$770$	24.1401	0.869950
$771$	21.5099	0.774662
$772$	−5.40044	−0.194366
$773$	36.5529	1.31472	0.657358	−	0.753578i	$-0.271674\pi$
$773$	36.5529	1.31472	0.657358	+	0.753578i	$0.271674\pi$
$774$	33.3001	1.19695
$775$	2.95194	0.106037
$776$	−40.0694	−1.43841
$777$	2.98190	0.106975
$778$	−32.7060	−1.17257
$779$	−16.3394	−0.585421
$780$	−122.481	−4.38552
$781$	−15.0824	−0.539689
$782$	5.88656	0.210503
$783$	1.39491	0.0498502
$784$	0.164061	0.00585932
$785$	33.3332	1.18971
$786$	−80.3915	−2.86747
$787$	−23.5228	−0.838497	−0.419249	−	0.907871i	$-0.637706\pi$
$787$	−23.5228	−0.838497	−0.419249	+	0.907871i	$0.637706\pi$
$788$	43.2312	1.54005
$789$	−40.1064	−1.42783
$790$	44.2801	1.57542
$791$	11.8763	0.422273
$792$	64.1784	2.28048
$793$	21.9575	0.779734
$794$	6.19644	0.219903
$795$	120.149	4.26125
$796$	−70.7814	−2.50878
$797$	−23.4282	−0.829868	−0.414934	−	0.909851i	$-0.636195\pi$
$797$	−23.4282	−0.829868	−0.414934	+	0.909851i	$0.636195\pi$
$798$	−14.8290	−0.524942
$799$	2.97198	0.105141
$800$	16.1379	0.570560
$801$	−14.9876	−0.529559
$802$	48.2468	1.70365
$803$	−52.3027	−1.84572
$804$	73.1867	2.58110
$805$	−13.1502	−0.463484
$806$	−10.2205	−0.360001
$807$	71.1859	2.50586
$808$	42.4945	1.49495
$809$	12.8995	0.453521	0.226761	−	0.973951i	$-0.427187\pi$
$809$	12.8995	0.453521	0.226761	+	0.973951i	$0.427187\pi$
$810$	−52.0417	−1.82856
$811$	9.93811	0.348974	0.174487	−	0.984659i	$-0.444173\pi$
$811$	9.93811	0.348974	0.174487	+	0.984659i	$0.444173\pi$
$812$	−0.529384	−0.0185778
$813$	−69.6115	−2.44138
$814$	−8.56058	−0.300048
$815$	25.7131	0.900690
$816$	−0.268941	−0.00941483
$817$	5.33101	0.186509
$818$	−67.8781	−2.37330
$819$	26.2245	0.916359
$820$	69.6201	2.43124
$821$	−6.36920	−0.222287	−0.111143	−	0.993804i	$-0.535451\pi$
$821$	−6.36920	−0.222287	−0.111143	+	0.993804i	$0.535451\pi$
$822$	−117.736	−4.10651
$823$	13.4616	0.469241	0.234620	−	0.972087i	$-0.424615\pi$
$823$	13.4616	0.469241	0.234620	+	0.972087i	$0.424615\pi$
$824$	−16.6438	−0.579813
$825$	32.8169	1.14254
$826$	−21.8101	−0.758871
$827$	−29.0920	−1.01163	−0.505814	−	0.862643i	$-0.668808\pi$
$827$	−29.0920	−1.01163	−0.505814	+	0.862643i	$0.668808\pi$
$828$	−89.9109	−3.12462
$829$	40.3678	1.40203	0.701016	−	0.713145i	$-0.252730\pi$
$829$	40.3678	1.40203	0.701016	+	0.713145i	$0.252730\pi$
$830$	80.6401	2.79906
$831$	40.8776	1.41803
$832$	−57.3346	−1.98772
$833$	0.549742	0.0190474
$834$	96.6384	3.34631
$835$	−56.7445	−1.96372
$836$	26.4231	0.913862
$837$	−8.62284	−0.298049
$838$	31.9018	1.10203
$839$	−51.5326	−1.77910	−0.889552	−	0.456834i	$-0.848983\pi$
$839$	−51.5326	−1.77910	−0.889552	+	0.456834i	$0.848983\pi$
$840$	24.5685	0.847695
$841$	−28.9738	−0.999098
$842$	17.2636	0.594943
$843$	65.2019	2.24567
$844$	−10.6349	−0.366067
$845$	19.2095	0.660827
$846$	−73.1368	−2.51449
$847$	2.89930	0.0996210
$848$	−2.34421	−0.0805005
$849$	26.9307	0.924261
$850$	−3.72626	−0.127810
$851$	4.66333	0.159857
$852$	−39.4766	−1.35245
$853$	55.3130	1.89388	0.946940	−	0.321409i	$-0.104157\pi$
$853$	55.3130	1.89388	0.946940	+	0.321409i	$0.104157\pi$
$854$	−11.3272	−0.387610
$855$	−35.9826	−1.23058
$856$	35.1206	1.20040
$857$	−3.69444	−0.126200	−0.0630998	−	0.998007i	$-0.520099\pi$
$857$	−3.69444	−0.126200	−0.0630998	+	0.998007i	$0.520099\pi$
$858$	−113.622	−3.87898
$859$	39.4729	1.34680	0.673400	−	0.739279i	$-0.264833\pi$
$859$	39.4729	1.34680	0.673400	+	0.739279i	$0.264833\pi$
$860$	−22.7147	−0.774565
$861$	−22.4966	−0.766682
$862$	−6.48724	−0.220956
$863$	−24.5150	−0.834502	−0.417251	−	0.908791i	$-0.637006\pi$
$863$	−24.5150	−0.834502	−0.417251	+	0.908791i	$0.637006\pi$
$864$	−47.1400	−1.60373
$865$	45.4743	1.54617
$866$	87.2851	2.96607
$867$	49.7911	1.69100
$868$	3.27246	0.111074
$869$	25.4954	0.864873
$870$	−3.12344	−0.105895
$871$	−33.3834	−1.13115
$872$	27.2485	0.922750
$873$	80.7989	2.73463
$874$	−23.1908	−0.784441
$875$	−5.77536	−0.195243
$876$	−136.897	−4.62533
$877$	34.2573	1.15679	0.578394	−	0.815757i	$-0.303680\pi$
$877$	34.2573	1.15679	0.578394	+	0.815757i	$0.303680\pi$
$878$	−40.0323	−1.35102
$879$	50.7799	1.71276
$880$	−1.72480	−0.0581430
$881$	−38.3541	−1.29218	−0.646092	−	0.763260i	$-0.723598\pi$
$881$	−38.3541	−1.29218	−0.646092	+	0.763260i	$0.723598\pi$
$882$	−13.5285	−0.455528
$883$	−28.4554	−0.957602	−0.478801	−	0.877924i	$-0.658928\pi$
$883$	−28.4554	−0.957602	−0.478801	+	0.877924i	$0.658928\pi$
$884$	8.00752	0.269322
$885$	−79.8695	−2.68478
$886$	79.5943	2.67402
$887$	−40.9151	−1.37379	−0.686897	−	0.726754i	$-0.741028\pi$
$887$	−40.9151	−1.37379	−0.686897	+	0.726754i	$0.741028\pi$
$888$	−8.71250	−0.292372
$889$	−4.59668	−0.154168
$890$	16.4714	0.552124
$891$	−29.9643	−1.00384
$892$	48.4558	1.62242
$893$	−11.7085	−0.391809
$894$	−142.945	−4.78081
$895$	−14.7309	−0.492399
$896$	18.6435	0.622837
$897$	61.8948	2.06661
$898$	38.9953	1.30129
$899$	−0.161770	−0.00539532
$900$	56.9146	1.89715
$901$	−7.85507	−0.261690
$902$	64.5843	2.15042
$903$	7.33989	0.244256
$904$	−34.7002	−1.15411
$905$	−27.9988	−0.930713
$906$	−102.585	−3.40815
$907$	24.3528	0.808623	0.404311	−	0.914621i	$-0.367511\pi$
$907$	24.3528	0.808623	0.404311	+	0.914621i	$0.367511\pi$
$908$	27.2921	0.905720
$909$	−85.6891	−2.84213
$910$	−28.8209	−0.955405
$911$	46.1287	1.52831	0.764156	−	0.645031i	$-0.223156\pi$
$911$	46.1287	1.52831	0.764156	+	0.645031i	$0.223156\pi$
$912$	1.05953	0.0350844
$913$	46.4306	1.53663
$914$	−29.4973	−0.975685
$915$	−41.4808	−1.37131
$916$	−37.6663	−1.24453
$917$	−11.7412	−0.387727
$918$	10.8847	0.359248
$919$	38.2226	1.26085	0.630423	−	0.776252i	$-0.282881\pi$
$919$	38.2226	1.26085	0.630423	+	0.776252i	$0.282881\pi$
$920$	38.4222	1.26674
$921$	−26.9762	−0.888897
$922$	4.20548	0.138500
$923$	18.0069	0.592703
$924$	36.3801	1.19682
$925$	−2.95194	−0.0970592
$926$	−51.9259	−1.70639
$927$	33.5618	1.10231
$928$	−0.884375	−0.0290310
$929$	54.6318	1.79241	0.896205	−	0.443640i	$-0.146313\pi$
$929$	54.6318	1.79241	0.896205	+	0.443640i	$0.146313\pi$
$930$	19.3079	0.633133
$931$	−2.16577	−0.0709804
$932$	66.7753	2.18730
$933$	79.2792	2.59548
$934$	−11.7634	−0.384912
$935$	−5.77952	−0.189011
$936$	−76.6227	−2.50449
$937$	1.62524	0.0530943	0.0265471	−	0.999648i	$-0.491549\pi$
$937$	1.62524	0.0530943	0.0265471	+	0.999648i	$0.491549\pi$
$938$	17.2215	0.562303
$939$	−53.1937	−1.73591
$940$	49.8881	1.62717
$941$	−13.1936	−0.430098	−0.215049	−	0.976603i	$-0.568991\pi$
$941$	−13.1936	−0.430098	−0.215049	+	0.976603i	$0.568991\pi$
$942$	80.9357	2.63703
$943$	−35.1820	−1.14568
$944$	1.55832	0.0507190
$945$	−24.3157	−0.790990
$946$	−21.0717	−0.685100
$947$	−25.5523	−0.830338	−0.415169	−	0.909744i	$-0.636278\pi$
$947$	−25.5523	−0.830338	−0.415169	+	0.909744i	$0.636278\pi$
$948$	66.7318	2.16735
$949$	62.4443	2.02703
$950$	14.6800	0.476283
$951$	−59.9249	−1.94320
$952$	−1.60623	−0.0520583
$953$	−48.4123	−1.56823	−0.784115	−	0.620616i	$-0.786883\pi$
$953$	−48.4123	−1.56823	−0.784115	+	0.620616i	$0.786883\pi$
$954$	193.304	6.25844
$955$	45.8888	1.48493
$956$	55.2016	1.78535
$957$	−1.79840	−0.0581341
$958$	−48.1801	−1.55663
$959$	−17.1953	−0.555265
$960$	108.313	3.49579
$961$	1.00000	0.0322581
$962$	10.2205	0.329522
$963$	−70.8199	−2.28214
$964$	−19.8983	−0.640882
$965$	−4.65363	−0.149806
$966$	−31.9298	−1.02732
$967$	2.37479	0.0763681	0.0381841	−	0.999271i	$-0.487843\pi$
$967$	2.37479	0.0763681	0.0381841	+	0.999271i	$0.487843\pi$
$968$	−8.47115	−0.272273
$969$	3.55030	0.114052
$970$	−88.7985	−2.85115
$971$	25.5638	0.820381	0.410190	−	0.912000i	$-0.365462\pi$
$971$	25.5638	0.820381	0.410190	+	0.912000i	$0.365462\pi$
$972$	6.22488	0.199663
$973$	14.1140	0.452474
$974$	−30.6492	−0.982063
$975$	−39.1801	−1.25477
$976$	0.809326	0.0259059
$977$	29.1521	0.932659	0.466329	−	0.884611i	$-0.345576\pi$
$977$	29.1521	0.932659	0.466329	+	0.884611i	$0.345576\pi$
$978$	62.4334	1.99640
$979$	9.48385	0.303105
$980$	9.22806	0.294780
$981$	−54.9459	−1.75429
$982$	39.5796	1.26303
$983$	−38.0174	−1.21257	−0.606284	−	0.795249i	$-0.707340\pi$
$983$	−38.0174	−1.21257	−0.606284	+	0.795249i	$0.707340\pi$
$984$	65.7305	2.09541
$985$	37.2529	1.18698
$986$	0.204203	0.00650316
$987$	−16.1205	−0.513123
$988$	−31.5466	−1.00363
$989$	11.4787	0.365001
$990$	142.227	4.52027
$991$	14.2083	0.451343	0.225671	−	0.974203i	$-0.427542\pi$
$991$	14.2083	0.451343	0.225671	+	0.974203i	$0.427542\pi$
$992$	5.46687	0.173573
$993$	64.2513	2.03895
$994$	−9.28922	−0.294636
$995$	−60.9932	−1.93362
$996$	121.528	3.85075
$997$	18.9752	0.600951	0.300475	−	0.953790i	$-0.402855\pi$
$997$	18.9752	0.600951	0.300475	+	0.953790i	$0.402855\pi$
$998$	−80.2626	−2.54067
$999$	8.62284	0.272815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.8	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.8	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.29618 q^{2} -2.98190 q^{3} +3.27246 q^{4} +2.81992 q^{5} +6.84699 q^{6} +1.00000 q^{7} -2.92179 q^{8} +5.89173 q^{9} +O(q^{10})\)	\(q-2.29618 q^{2} -2.98190 q^{3} +3.27246 q^{4} +2.81992 q^{5} +6.84699 q^{6} +1.00000 q^{7} -2.92179 q^{8} +5.89173 q^{9} -6.47505 q^{10} -3.72818 q^{11} -9.75814 q^{12} +4.45108 q^{13} -2.29618 q^{14} -8.40871 q^{15} +0.164061 q^{16} +0.549742 q^{17} -13.5285 q^{18} -2.16577 q^{19} +9.22806 q^{20} -2.98190 q^{21} +8.56058 q^{22} -4.66333 q^{23} +8.71250 q^{24} +2.95194 q^{25} -10.2205 q^{26} -8.62284 q^{27} +3.27246 q^{28} -0.161770 q^{29} +19.3079 q^{30} +1.00000 q^{31} +5.46687 q^{32} +11.1170 q^{33} -1.26231 q^{34} +2.81992 q^{35} +19.2804 q^{36} -1.00000 q^{37} +4.97302 q^{38} -13.2727 q^{39} -8.23922 q^{40} +7.54439 q^{41} +6.84699 q^{42} -2.46148 q^{43} -12.2003 q^{44} +16.6142 q^{45} +10.7079 q^{46} +5.40613 q^{47} -0.489214 q^{48} +1.00000 q^{49} -6.77819 q^{50} -1.63928 q^{51} +14.5660 q^{52} -14.2886 q^{53} +19.7996 q^{54} -10.5132 q^{55} -2.92179 q^{56} +6.45812 q^{57} +0.371453 q^{58} +9.49842 q^{59} -27.5172 q^{60} +4.93308 q^{61} -2.29618 q^{62} +5.89173 q^{63} -12.8811 q^{64} +12.5517 q^{65} -25.5268 q^{66} -7.50007 q^{67} +1.79901 q^{68} +13.9056 q^{69} -6.47505 q^{70} +4.04551 q^{71} -17.2144 q^{72} +14.0290 q^{73} +2.29618 q^{74} -8.80239 q^{75} -7.08740 q^{76} -3.72818 q^{77} +30.4765 q^{78} -6.83858 q^{79} +0.462639 q^{80} +8.03726 q^{81} -17.3233 q^{82} -12.4540 q^{83} -9.75814 q^{84} +1.55023 q^{85} +5.65201 q^{86} +0.482381 q^{87} +10.8930 q^{88} -2.54383 q^{89} -38.1492 q^{90} +4.45108 q^{91} -15.2605 q^{92} -2.98190 q^{93} -12.4135 q^{94} -6.10731 q^{95} -16.3017 q^{96} +13.7140 q^{97} -2.29618 q^{98} -21.9654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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