LMFDB - Embedded newform 4034.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.264302 q^{3} +1.00000 q^{4} +2.82441 q^{5} -0.264302 q^{6} -2.96778 q^{7} +1.00000 q^{8} -2.93014 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.264302 q^{3} +1.00000 q^{4} +2.82441 q^{5} -0.264302 q^{6} -2.96778 q^{7} +1.00000 q^{8} -2.93014 q^{9} +2.82441 q^{10} +0.928107 q^{11} -0.264302 q^{12} -5.11315 q^{13} -2.96778 q^{14} -0.746498 q^{15} +1.00000 q^{16} -0.891104 q^{17} -2.93014 q^{18} -0.528674 q^{19} +2.82441 q^{20} +0.784392 q^{21} +0.928107 q^{22} -0.169859 q^{23} -0.264302 q^{24} +2.97729 q^{25} -5.11315 q^{26} +1.56735 q^{27} -2.96778 q^{28} +9.39363 q^{29} -0.746498 q^{30} -1.82113 q^{31} +1.00000 q^{32} -0.245301 q^{33} -0.891104 q^{34} -8.38223 q^{35} -2.93014 q^{36} -8.30737 q^{37} -0.528674 q^{38} +1.35142 q^{39} +2.82441 q^{40} -5.33554 q^{41} +0.784392 q^{42} +1.68414 q^{43} +0.928107 q^{44} -8.27593 q^{45} -0.169859 q^{46} -4.82276 q^{47} -0.264302 q^{48} +1.80772 q^{49} +2.97729 q^{50} +0.235521 q^{51} -5.11315 q^{52} -0.389249 q^{53} +1.56735 q^{54} +2.62136 q^{55} -2.96778 q^{56} +0.139730 q^{57} +9.39363 q^{58} -9.17369 q^{59} -0.746498 q^{60} -6.54017 q^{61} -1.82113 q^{62} +8.69603 q^{63} +1.00000 q^{64} -14.4416 q^{65} -0.245301 q^{66} -7.24006 q^{67} -0.891104 q^{68} +0.0448941 q^{69} -8.38223 q^{70} +8.41456 q^{71} -2.93014 q^{72} +7.83999 q^{73} -8.30737 q^{74} -0.786905 q^{75} -0.528674 q^{76} -2.75442 q^{77} +1.35142 q^{78} -8.66522 q^{79} +2.82441 q^{80} +8.37618 q^{81} -5.33554 q^{82} -11.1768 q^{83} +0.784392 q^{84} -2.51684 q^{85} +1.68414 q^{86} -2.48276 q^{87} +0.928107 q^{88} -17.0726 q^{89} -8.27593 q^{90} +15.1747 q^{91} -0.169859 q^{92} +0.481329 q^{93} -4.82276 q^{94} -1.49319 q^{95} -0.264302 q^{96} -12.2767 q^{97} +1.80772 q^{98} -2.71949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.264302	−0.152595	−0.0762975	−	0.997085i	$-0.524310\pi$
$3$	−0.264302	−0.152595	−0.0762975	+	0.997085i	$0.524310\pi$
$4$	1.00000	0.500000
$5$	2.82441	1.26311	0.631557	−	0.775329i	$-0.282416\pi$
$5$	2.82441	1.26311	0.631557	+	0.775329i	$0.282416\pi$
$6$	−0.264302	−0.107901
$7$	−2.96778	−1.12172	−0.560858	−	0.827912i	$-0.689529\pi$
$7$	−2.96778	−1.12172	−0.560858	+	0.827912i	$0.689529\pi$
$8$	1.00000	0.353553
$9$	−2.93014	−0.976715
$10$	2.82441	0.893157
$11$	0.928107	0.279835	0.139917	−	0.990163i	$-0.455316\pi$
$11$	0.928107	0.279835	0.139917	+	0.990163i	$0.455316\pi$
$12$	−0.264302	−0.0762975
$13$	−5.11315	−1.41813	−0.709066	−	0.705142i	$-0.750883\pi$
$13$	−5.11315	−1.41813	−0.709066	+	0.705142i	$0.750883\pi$
$14$	−2.96778	−0.793173
$15$	−0.746498	−0.192745
$16$	1.00000	0.250000
$17$	−0.891104	−0.216124	−0.108062	−	0.994144i	$-0.534465\pi$
$17$	−0.891104	−0.216124	−0.108062	+	0.994144i	$0.534465\pi$
$18$	−2.93014	−0.690642
$19$	−0.528674	−0.121286	−0.0606431	−	0.998160i	$-0.519315\pi$
$19$	−0.528674	−0.121286	−0.0606431	+	0.998160i	$0.519315\pi$
$20$	2.82441	0.631557
$21$	0.784392	0.171168
$22$	0.928107	0.197873
$23$	−0.169859	−0.0354180	−0.0177090	−	0.999843i	$-0.505637\pi$
$23$	−0.169859	−0.0354180	−0.0177090	+	0.999843i	$0.505637\pi$
$24$	−0.264302	−0.0539505
$25$	2.97729	0.595458
$26$	−5.11315	−1.00277
$27$	1.56735	0.301637
$28$	−2.96778	−0.560858
$29$	9.39363	1.74435	0.872177	−	0.489191i	$-0.162708\pi$
$29$	9.39363	1.74435	0.872177	+	0.489191i	$0.162708\pi$
$30$	−0.746498	−0.136291
$31$	−1.82113	−0.327084	−0.163542	−	0.986536i	$-0.552292\pi$
$31$	−1.82113	−0.327084	−0.163542	+	0.986536i	$0.552292\pi$
$32$	1.00000	0.176777
$33$	−0.245301	−0.0427014
$34$	−0.891104	−0.152823
$35$	−8.38223	−1.41686
$36$	−2.93014	−0.488357
$37$	−8.30737	−1.36572	−0.682861	−	0.730548i	$-0.739265\pi$
$37$	−8.30737	−1.36572	−0.682861	+	0.730548i	$0.739265\pi$
$38$	−0.528674	−0.0857623
$39$	1.35142	0.216400
$40$	2.82441	0.446578
$41$	−5.33554	−0.833271	−0.416636	−	0.909074i	$-0.636791\pi$
$41$	−5.33554	−0.833271	−0.416636	+	0.909074i	$0.636791\pi$
$42$	0.784392	0.121034
$43$	1.68414	0.256828	0.128414	−	0.991721i	$-0.459011\pi$
$43$	1.68414	0.256828	0.128414	+	0.991721i	$0.459011\pi$
$44$	0.928107	0.139917
$45$	−8.27593	−1.23370
$46$	−0.169859	−0.0250443
$47$	−4.82276	−0.703472	−0.351736	−	0.936099i	$-0.614408\pi$
$47$	−4.82276	−0.703472	−0.351736	+	0.936099i	$0.614408\pi$
$48$	−0.264302	−0.0381488
$49$	1.80772	0.258246
$50$	2.97729	0.421053
$51$	0.235521	0.0329795
$52$	−5.11315	−0.709066
$53$	−0.389249	−0.0534675	−0.0267338	−	0.999643i	$-0.508511\pi$
$53$	−0.389249	−0.0534675	−0.0267338	+	0.999643i	$0.508511\pi$
$54$	1.56735	0.213289
$55$	2.62136	0.353463
$56$	−2.96778	−0.396586
$57$	0.139730	0.0185077
$58$	9.39363	1.23344
$59$	−9.17369	−1.19431	−0.597156	−	0.802125i	$-0.703703\pi$
$59$	−9.17369	−1.19431	−0.597156	+	0.802125i	$0.703703\pi$
$60$	−0.746498	−0.0963725
$61$	−6.54017	−0.837383	−0.418691	−	0.908129i	$-0.637511\pi$
$61$	−6.54017	−0.837383	−0.418691	+	0.908129i	$0.637511\pi$
$62$	−1.82113	−0.231284
$63$	8.69603	1.09560
$64$	1.00000	0.125000
$65$	−14.4416	−1.79126
$66$	−0.245301	−0.0301945
$67$	−7.24006	−0.884514	−0.442257	−	0.896888i	$-0.645822\pi$
$67$	−7.24006	−0.884514	−0.442257	+	0.896888i	$0.645822\pi$
$68$	−0.891104	−0.108062
$69$	0.0448941	0.00540461
$70$	−8.38223	−1.00187
$71$	8.41456	0.998625	0.499313	−	0.866422i	$-0.333586\pi$
$71$	8.41456	0.998625	0.499313	+	0.866422i	$0.333586\pi$
$72$	−2.93014	−0.345321
$73$	7.83999	0.917602	0.458801	−	0.888539i	$-0.348279\pi$
$73$	7.83999	0.917602	0.458801	+	0.888539i	$0.348279\pi$
$74$	−8.30737	−0.965712
$75$	−0.786905	−0.0908640
$76$	−0.528674	−0.0606431
$77$	−2.75442	−0.313895
$78$	1.35142	0.153018
$79$	−8.66522	−0.974913	−0.487457	−	0.873147i	$-0.662075\pi$
$79$	−8.66522	−0.974913	−0.487457	+	0.873147i	$0.662075\pi$
$80$	2.82441	0.315779
$81$	8.37618	0.930686
$82$	−5.33554	−0.589212
$83$	−11.1768	−1.22682	−0.613408	−	0.789766i	$-0.710202\pi$
$83$	−11.1768	−1.22682	−0.613408	+	0.789766i	$0.710202\pi$
$84$	0.784392	0.0855841
$85$	−2.51684	−0.272990
$86$	1.68414	0.181605
$87$	−2.48276	−0.266180
$88$	0.928107	0.0989366
$89$	−17.0726	−1.80969	−0.904844	−	0.425743i	$-0.860013\pi$
$89$	−17.0726	−1.80969	−0.904844	+	0.425743i	$0.860013\pi$
$90$	−8.27593	−0.872359
$91$	15.1747	1.59074
$92$	−0.169859	−0.0177090
$93$	0.481329	0.0499114
$94$	−4.82276	−0.497430
$95$	−1.49319	−0.153198
$96$	−0.264302	−0.0269752
$97$	−12.2767	−1.24651	−0.623255	−	0.782018i	$-0.714190\pi$
$97$	−12.2767	−1.24651	−0.623255	+	0.782018i	$0.714190\pi$
$98$	1.80772	0.182608
$99$	−2.71949	−0.273319
$100$	2.97729	0.297729
$101$	−17.1604	−1.70752	−0.853760	−	0.520666i	$-0.825684\pi$
$101$	−17.1604	−1.70752	−0.853760	+	0.520666i	$0.825684\pi$
$102$	0.235521	0.0233200
$103$	5.53963	0.545836	0.272918	−	0.962037i	$-0.412011\pi$
$103$	5.53963	0.545836	0.272918	+	0.962037i	$0.412011\pi$
$104$	−5.11315	−0.501385
$105$	2.21544	0.216205
$106$	−0.389249	−0.0378072
$107$	10.0755	0.974040	0.487020	−	0.873391i	$-0.338084\pi$
$107$	10.0755	0.974040	0.487020	+	0.873391i	$0.338084\pi$
$108$	1.56735	0.150818
$109$	−8.15628	−0.781230	−0.390615	−	0.920554i	$-0.627738\pi$
$109$	−8.15628	−0.781230	−0.390615	+	0.920554i	$0.627738\pi$
$110$	2.62136	0.249936
$111$	2.19566	0.208402
$112$	−2.96778	−0.280429
$113$	−3.30351	−0.310768	−0.155384	−	0.987854i	$-0.549661\pi$
$113$	−3.30351	−0.310768	−0.155384	+	0.987854i	$0.549661\pi$
$114$	0.139730	0.0130869
$115$	−0.479751	−0.0447370
$116$	9.39363	0.872177
$117$	14.9823	1.38511
$118$	−9.17369	−0.844506
$119$	2.64460	0.242430
$120$	−0.746498	−0.0681457
$121$	−10.1386	−0.921692
$122$	−6.54017	−0.592119
$123$	1.41020	0.127153
$124$	−1.82113	−0.163542
$125$	−5.71296	−0.510983
$126$	8.69603	0.774704
$127$	−3.22996	−0.286613	−0.143306	−	0.989678i	$-0.545773\pi$
$127$	−3.22996	−0.286613	−0.143306	+	0.989678i	$0.545773\pi$
$128$	1.00000	0.0883883
$129$	−0.445121	−0.0391907
$130$	−14.4416	−1.26661
$131$	−4.36677	−0.381526	−0.190763	−	0.981636i	$-0.561096\pi$
$131$	−4.36677	−0.381526	−0.190763	+	0.981636i	$0.561096\pi$
$132$	−0.245301	−0.0213507
$133$	1.56899	0.136049
$134$	−7.24006	−0.625446
$135$	4.42684	0.381002
$136$	−0.891104	−0.0764115
$137$	16.6263	1.42048	0.710241	−	0.703958i	$-0.248586\pi$
$137$	16.6263	1.42048	0.710241	+	0.703958i	$0.248586\pi$
$138$	0.0448941	0.00382164
$139$	18.8746	1.60092	0.800460	−	0.599386i	$-0.204589\pi$
$139$	18.8746	1.60092	0.800460	+	0.599386i	$0.204589\pi$
$140$	−8.38223	−0.708428
$141$	1.27467	0.107346
$142$	8.41456	0.706135
$143$	−4.74555	−0.396843
$144$	−2.93014	−0.244179
$145$	26.5315	2.20332
$146$	7.83999	0.648843
$147$	−0.477786	−0.0394071
$148$	−8.30737	−0.682861
$149$	−9.06313	−0.742480	−0.371240	−	0.928537i	$-0.621067\pi$
$149$	−9.06313	−0.742480	−0.371240	+	0.928537i	$0.621067\pi$
$150$	−0.786905	−0.0642505
$151$	−2.81156	−0.228801	−0.114401	−	0.993435i	$-0.536495\pi$
$151$	−2.81156	−0.228801	−0.114401	+	0.993435i	$0.536495\pi$
$152$	−0.528674	−0.0428811
$153$	2.61106	0.211092
$154$	−2.75442	−0.221957
$155$	−5.14361	−0.413145
$156$	1.35142	0.108200
$157$	17.6000	1.40463	0.702316	−	0.711865i	$-0.252149\pi$
$157$	17.6000	1.40463	0.702316	+	0.711865i	$0.252149\pi$
$158$	−8.66522	−0.689368
$159$	0.102880	0.00815888
$160$	2.82441	0.223289
$161$	0.504103	0.0397289
$162$	8.37618	0.658095
$163$	17.3553	1.35938	0.679688	−	0.733502i	$-0.262115\pi$
$163$	17.3553	1.35938	0.679688	+	0.733502i	$0.262115\pi$
$164$	−5.33554	−0.416636
$165$	−0.692830	−0.0539368
$166$	−11.1768	−0.867490
$167$	−0.827985	−0.0640714	−0.0320357	−	0.999487i	$-0.510199\pi$
$167$	−0.827985	−0.0640714	−0.0320357	+	0.999487i	$0.510199\pi$
$168$	0.784392	0.0605171
$169$	13.1443	1.01110
$170$	−2.51684	−0.193033
$171$	1.54909	0.118462
$172$	1.68414	0.128414
$173$	7.92745	0.602713	0.301357	−	0.953512i	$-0.402561\pi$
$173$	7.92745	0.602713	0.301357	+	0.953512i	$0.402561\pi$
$174$	−2.48276	−0.188217
$175$	−8.83595	−0.667935
$176$	0.928107	0.0699587
$177$	2.42463	0.182246
$178$	−17.0726	−1.27964
$179$	20.4978	1.53208	0.766039	−	0.642794i	$-0.222225\pi$
$179$	20.4978	1.53208	0.766039	+	0.642794i	$0.222225\pi$
$180$	−8.27593	−0.616851
$181$	9.14006	0.679376	0.339688	−	0.940538i	$-0.389679\pi$
$181$	9.14006	0.679376	0.339688	+	0.940538i	$0.389679\pi$
$182$	15.1747	1.12482
$183$	1.72858	0.127780
$184$	−0.169859	−0.0125222
$185$	−23.4634	−1.72506
$186$	0.481329	0.0352927
$187$	−0.827040	−0.0604792
$188$	−4.82276	−0.351736
$189$	−4.65156	−0.338351
$190$	−1.49319	−0.108328
$191$	−12.6132	−0.912661	−0.456331	−	0.889810i	$-0.650837\pi$
$191$	−12.6132	−0.912661	−0.456331	+	0.889810i	$0.650837\pi$
$192$	−0.264302	−0.0190744
$193$	22.2551	1.60195	0.800977	−	0.598695i	$-0.204314\pi$
$193$	22.2551	1.60195	0.800977	+	0.598695i	$0.204314\pi$
$194$	−12.2767	−0.881416
$195$	3.81696	0.273338
$196$	1.80772	0.129123
$197$	16.4612	1.17281	0.586407	−	0.810016i	$-0.300542\pi$
$197$	16.4612	1.17281	0.586407	+	0.810016i	$0.300542\pi$
$198$	−2.71949	−0.193266
$199$	5.49339	0.389416	0.194708	−	0.980861i	$-0.437624\pi$
$199$	5.49339	0.389416	0.194708	+	0.980861i	$0.437624\pi$
$200$	2.97729	0.210526
$201$	1.91356	0.134972
$202$	−17.1604	−1.20740
$203$	−27.8782	−1.95667
$204$	0.235521	0.0164898
$205$	−15.0698	−1.05252
$206$	5.53963	0.385964
$207$	0.497711	0.0345933
$208$	−5.11315	−0.354533
$209$	−0.490666	−0.0339401
$210$	2.21544	0.152880
$211$	7.67099	0.528093	0.264046	−	0.964510i	$-0.414943\pi$
$211$	7.67099	0.528093	0.264046	+	0.964510i	$0.414943\pi$
$212$	−0.389249	−0.0267338
$213$	−2.22399	−0.152385
$214$	10.0755	0.688750
$215$	4.75669	0.324404
$216$	1.56735	0.106645
$217$	5.40471	0.366896
$218$	−8.15628	−0.552413
$219$	−2.07213	−0.140022
$220$	2.62136	0.176732
$221$	4.55635	0.306493
$222$	2.19566	0.147363
$223$	18.7937	1.25852	0.629259	−	0.777195i	$-0.283358\pi$
$223$	18.7937	1.25852	0.629259	+	0.777195i	$0.283358\pi$
$224$	−2.96778	−0.198293
$225$	−8.72389	−0.581593
$226$	−3.30351	−0.219746
$227$	−8.55819	−0.568027	−0.284014	−	0.958820i	$-0.591666\pi$
$227$	−8.55819	−0.568027	−0.284014	+	0.958820i	$0.591666\pi$
$228$	0.139730	0.00925383
$229$	−14.5324	−0.960327	−0.480163	−	0.877179i	$-0.659423\pi$
$229$	−14.5324	−0.960327	−0.480163	+	0.877179i	$0.659423\pi$
$230$	−0.479751	−0.0316338
$231$	0.727999	0.0478988
$232$	9.39363	0.616722
$233$	−3.24068	−0.212304	−0.106152	−	0.994350i	$-0.533853\pi$
$233$	−3.24068	−0.212304	−0.106152	+	0.994350i	$0.533853\pi$
$234$	14.9823	0.979421
$235$	−13.6214	−0.888565
$236$	−9.17369	−0.597156
$237$	2.29024	0.148767
$238$	2.64460	0.171424
$239$	−3.75282	−0.242750	−0.121375	−	0.992607i	$-0.538730\pi$
$239$	−3.75282	−0.242750	−0.121375	+	0.992607i	$0.538730\pi$
$240$	−0.746498	−0.0481863
$241$	−23.9268	−1.54126	−0.770631	−	0.637282i	$-0.780059\pi$
$241$	−23.9268	−1.54126	−0.770631	+	0.637282i	$0.780059\pi$
$242$	−10.1386	−0.651735
$243$	−6.91590	−0.443655
$244$	−6.54017	−0.418691
$245$	5.10575	0.326194
$246$	1.41020	0.0899108
$247$	2.70319	0.172000
$248$	−1.82113	−0.115642
$249$	2.95406	0.187206
$250$	−5.71296	−0.361319
$251$	8.65141	0.546072	0.273036	−	0.962004i	$-0.411972\pi$
$251$	8.65141	0.546072	0.273036	+	0.962004i	$0.411972\pi$
$252$	8.69603	0.547798
$253$	−0.157647	−0.00991119
$254$	−3.22996	−0.202666
$255$	0.665208	0.0416569
$256$	1.00000	0.0625000
$257$	2.51246	0.156723	0.0783614	−	0.996925i	$-0.475031\pi$
$257$	2.51246	0.156723	0.0783614	+	0.996925i	$0.475031\pi$
$258$	−0.445121	−0.0277120
$259$	24.6544	1.53195
$260$	−14.4416	−0.895632
$261$	−27.5247	−1.70374
$262$	−4.36677	−0.269780
$263$	9.23690	0.569572	0.284786	−	0.958591i	$-0.408077\pi$
$263$	9.23690	0.569572	0.284786	+	0.958591i	$0.408077\pi$
$264$	−0.245301	−0.0150972
$265$	−1.09940	−0.0675356
$266$	1.56899	0.0962009
$267$	4.51232	0.276150
$268$	−7.24006	−0.442257
$269$	−23.2579	−1.41806	−0.709028	−	0.705180i	$-0.750866\pi$
$269$	−23.2579	−1.41806	−0.709028	+	0.705180i	$0.750866\pi$
$270$	4.42684	0.269409
$271$	−21.2873	−1.29311	−0.646554	−	0.762868i	$-0.723791\pi$
$271$	−21.2873	−1.29311	−0.646554	+	0.762868i	$0.723791\pi$
$272$	−0.891104	−0.0540311
$273$	−4.01071	−0.242739
$274$	16.6263	1.00443
$275$	2.76324	0.166630
$276$	0.0448941	0.00270231
$277$	13.5672	0.815171	0.407586	−	0.913167i	$-0.366371\pi$
$277$	13.5672	0.815171	0.407586	+	0.913167i	$0.366371\pi$
$278$	18.8746	1.13202
$279$	5.33617	0.319468
$280$	−8.38223	−0.500934
$281$	1.20152	0.0716767	0.0358384	−	0.999358i	$-0.488590\pi$
$281$	1.20152	0.0716767	0.0358384	+	0.999358i	$0.488590\pi$
$282$	1.27467	0.0759053
$283$	−21.3034	−1.26636	−0.633178	−	0.774006i	$-0.718250\pi$
$283$	−21.3034	−1.26636	−0.633178	+	0.774006i	$0.718250\pi$
$284$	8.41456	0.499313
$285$	0.394654	0.0233773
$286$	−4.74555	−0.280610
$287$	15.8347	0.934694
$288$	−2.93014	−0.172660
$289$	−16.2059	−0.953290
$290$	26.5315	1.55798
$291$	3.24476	0.190211
$292$	7.83999	0.458801
$293$	1.45477	0.0849888	0.0424944	−	0.999097i	$-0.486470\pi$
$293$	1.45477	0.0849888	0.0424944	+	0.999097i	$0.486470\pi$
$294$	−0.477786	−0.0278650
$295$	−25.9102	−1.50855
$296$	−8.30737	−0.482856
$297$	1.45467	0.0844085
$298$	−9.06313	−0.525013
$299$	0.868513	0.0502274
$300$	−0.786905	−0.0454320
$301$	−4.99815	−0.288088
$302$	−2.81156	−0.161787
$303$	4.53553	0.260559
$304$	−0.528674	−0.0303215
$305$	−18.4721	−1.05771
$306$	2.61106	0.149265
$307$	30.8055	1.75817	0.879083	−	0.476670i	$-0.158156\pi$
$307$	30.8055	1.75817	0.879083	+	0.476670i	$0.158156\pi$
$308$	−2.75442	−0.156948
$309$	−1.46414	−0.0832919
$310$	−5.14361	−0.292138
$311$	15.0779	0.854991	0.427495	−	0.904018i	$-0.359396\pi$
$311$	15.0779	0.854991	0.427495	+	0.904018i	$0.359396\pi$
$312$	1.35142	0.0765089
$313$	6.64914	0.375831	0.187916	−	0.982185i	$-0.439827\pi$
$313$	6.64914	0.375831	0.187916	+	0.982185i	$0.439827\pi$
$314$	17.6000	0.993225
$315$	24.5611	1.38386
$316$	−8.66522	−0.487457
$317$	16.3120	0.916174	0.458087	−	0.888907i	$-0.348535\pi$
$317$	16.3120	0.916174	0.458087	+	0.888907i	$0.348535\pi$
$318$	0.102880	0.00576920
$319$	8.71829	0.488131
$320$	2.82441	0.157889
$321$	−2.66299	−0.148634
$322$	0.504103	0.0280926
$323$	0.471104	0.0262129
$324$	8.37618	0.465343
$325$	−15.2233	−0.844438
$326$	17.3553	0.961223
$327$	2.15572	0.119212
$328$	−5.33554	−0.294606
$329$	14.3129	0.789095
$330$	−0.692830	−0.0381391
$331$	−23.6403	−1.29939	−0.649696	−	0.760194i	$-0.725104\pi$
$331$	−23.6403	−1.29939	−0.649696	+	0.760194i	$0.725104\pi$
$332$	−11.1768	−0.613408
$333$	24.3418	1.33392
$334$	−0.827985	−0.0453053
$335$	−20.4489	−1.11724
$336$	0.784392	0.0427921
$337$	−14.4516	−0.787227	−0.393614	−	0.919276i	$-0.628775\pi$
$337$	−14.4516	−0.787227	−0.393614	+	0.919276i	$0.628775\pi$
$338$	13.1443	0.714955
$339$	0.873125	0.0474216
$340$	−2.51684	−0.136495
$341$	−1.69020	−0.0915296
$342$	1.54909	0.0837653
$343$	15.4095	0.832037
$344$	1.68414	0.0908026
$345$	0.126799	0.00682664
$346$	7.92745	0.426183
$347$	−33.1123	−1.77756	−0.888782	−	0.458330i	$-0.848448\pi$
$347$	−33.1123	−1.77756	−0.888782	+	0.458330i	$0.848448\pi$
$348$	−2.48276	−0.133090
$349$	7.86636	0.421077	0.210538	−	0.977586i	$-0.432478\pi$
$349$	7.86636	0.421077	0.210538	+	0.977586i	$0.432478\pi$
$350$	−8.83595	−0.472301
$351$	−8.01410	−0.427761
$352$	0.928107	0.0494683
$353$	−19.3220	−1.02841	−0.514204	−	0.857668i	$-0.671912\pi$
$353$	−19.3220	−1.02841	−0.514204	+	0.857668i	$0.671912\pi$
$354$	2.42463	0.128867
$355$	23.7662	1.26138
$356$	−17.0726	−0.904844
$357$	−0.698974	−0.0369937
$358$	20.4978	1.08334
$359$	11.7188	0.618496	0.309248	−	0.950981i	$-0.399923\pi$
$359$	11.7188	0.618496	0.309248	+	0.950981i	$0.399923\pi$
$360$	−8.27593	−0.436180
$361$	−18.7205	−0.985290
$362$	9.14006	0.480391
$363$	2.67966	0.140646
$364$	15.1747	0.795371
$365$	22.1434	1.15904
$366$	1.72858	0.0903545
$367$	31.8628	1.66322	0.831611	−	0.555358i	$-0.187419\pi$
$367$	31.8628	1.66322	0.831611	+	0.555358i	$0.187419\pi$
$368$	−0.169859	−0.00885450
$369$	15.6339	0.813868
$370$	−23.4634	−1.21980
$371$	1.15521	0.0599754
$372$	0.481329	0.0249557
$373$	5.49297	0.284415	0.142207	−	0.989837i	$-0.454580\pi$
$373$	5.49297	0.284415	0.142207	+	0.989837i	$0.454580\pi$
$374$	−0.827040	−0.0427652
$375$	1.50995	0.0779734
$376$	−4.82276	−0.248715
$377$	−48.0310	−2.47372
$378$	−4.65156	−0.239250
$379$	25.7365	1.32199	0.660997	−	0.750389i	$-0.270134\pi$
$379$	25.7365	1.32199	0.660997	+	0.750389i	$0.270134\pi$
$380$	−1.49319	−0.0765991
$381$	0.853687	0.0437357
$382$	−12.6132	−0.645349
$383$	−28.9635	−1.47996	−0.739982	−	0.672626i	$-0.765166\pi$
$383$	−28.9635	−1.47996	−0.739982	+	0.672626i	$0.765166\pi$
$384$	−0.264302	−0.0134876
$385$	−7.77961	−0.396485
$386$	22.2551	1.13275
$387$	−4.93476	−0.250848
$388$	−12.2767	−0.623255
$389$	−33.6214	−1.70467	−0.852336	−	0.522994i	$-0.824815\pi$
$389$	−33.6214	−1.70467	−0.852336	+	0.522994i	$0.824815\pi$
$390$	3.81696	0.193279
$391$	0.151362	0.00765469
$392$	1.80772	0.0913038
$393$	1.15415	0.0582190
$394$	16.4612	0.829305
$395$	−24.4741	−1.23143
$396$	−2.71949	−0.136659
$397$	28.2857	1.41962	0.709809	−	0.704394i	$-0.248781\pi$
$397$	28.2857	1.41962	0.709809	+	0.704394i	$0.248781\pi$
$398$	5.49339	0.275359
$399$	−0.414687	−0.0207603
$400$	2.97729	0.148865
$401$	14.8038	0.739267	0.369634	−	0.929178i	$-0.379483\pi$
$401$	14.8038	0.739267	0.369634	+	0.929178i	$0.379483\pi$
$402$	1.91356	0.0954399
$403$	9.31170	0.463849
$404$	−17.1604	−0.853760
$405$	23.6578	1.17556
$406$	−27.8782	−1.38357
$407$	−7.71013	−0.382177
$408$	0.235521	0.0116600
$409$	−10.5998	−0.524127	−0.262063	−	0.965051i	$-0.584403\pi$
$409$	−10.5998	−0.524127	−0.262063	+	0.965051i	$0.584403\pi$
$410$	−15.0698	−0.744242
$411$	−4.39438	−0.216759
$412$	5.53963	0.272918
$413$	27.2255	1.33968
$414$	0.497711	0.0244611
$415$	−31.5679	−1.54961
$416$	−5.11315	−0.250693
$417$	−4.98859	−0.244293
$418$	−0.490666	−0.0239993
$419$	14.5161	0.709159	0.354579	−	0.935026i	$-0.384624\pi$
$419$	14.5161	0.709159	0.354579	+	0.935026i	$0.384624\pi$
$420$	2.21544	0.108103
$421$	−8.16891	−0.398128	−0.199064	−	0.979986i	$-0.563790\pi$
$421$	−8.16891	−0.398128	−0.199064	+	0.979986i	$0.563790\pi$
$422$	7.67099	0.373418
$423$	14.1314	0.687091
$424$	−0.389249	−0.0189036
$425$	−2.65308	−0.128693
$426$	−2.22399	−0.107753
$427$	19.4098	0.939306
$428$	10.0755	0.487020
$429$	1.25426	0.0605562
$430$	4.75669	0.229388
$431$	−15.5519	−0.749110	−0.374555	−	0.927205i	$-0.622204\pi$
$431$	−15.5519	−0.749110	−0.374555	+	0.927205i	$0.622204\pi$
$432$	1.56735	0.0754092
$433$	−28.5967	−1.37427	−0.687134	−	0.726530i	$-0.741132\pi$
$433$	−28.5967	−1.37427	−0.687134	+	0.726530i	$0.741132\pi$
$434$	5.40471	0.259434
$435$	−7.01233	−0.336215
$436$	−8.15628	−0.390615
$437$	0.0897999	0.00429571
$438$	−2.07213	−0.0990102
$439$	16.3080	0.778336	0.389168	−	0.921167i	$-0.372763\pi$
$439$	16.3080	0.778336	0.389168	+	0.921167i	$0.372763\pi$
$440$	2.62136	0.124968
$441$	−5.29689	−0.252233
$442$	4.55635	0.216723
$443$	30.7121	1.45917	0.729587	−	0.683888i	$-0.239712\pi$
$443$	30.7121	1.45917	0.729587	+	0.683888i	$0.239712\pi$
$444$	2.19566	0.104201
$445$	−48.2199	−2.28584
$446$	18.7937	0.889907
$447$	2.39541	0.113299
$448$	−2.96778	−0.140214
$449$	14.5633	0.687286	0.343643	−	0.939100i	$-0.388339\pi$
$449$	14.5633	0.687286	0.343643	+	0.939100i	$0.388339\pi$
$450$	−8.72389	−0.411248
$451$	−4.95195	−0.233178
$452$	−3.30351	−0.155384
$453$	0.743101	0.0349139
$454$	−8.55819	−0.401656
$455$	42.8596	2.00929
$456$	0.139730	0.00654345
$457$	37.5481	1.75642	0.878212	−	0.478272i	$-0.158737\pi$
$457$	37.5481	1.75642	0.878212	+	0.478272i	$0.158737\pi$
$458$	−14.5324	−0.679053
$459$	−1.39667	−0.0651911
$460$	−0.479751	−0.0223685
$461$	18.6425	0.868269	0.434134	−	0.900848i	$-0.357054\pi$
$461$	18.6425	0.868269	0.434134	+	0.900848i	$0.357054\pi$
$462$	0.727999	0.0338696
$463$	28.7542	1.33632	0.668161	−	0.744017i	$-0.267082\pi$
$463$	28.7542	1.33632	0.668161	+	0.744017i	$0.267082\pi$
$464$	9.39363	0.436088
$465$	1.35947	0.0630439
$466$	−3.24068	−0.150122
$467$	−34.8651	−1.61337	−0.806683	−	0.590985i	$-0.798739\pi$
$467$	−34.8651	−1.61337	−0.806683	+	0.590985i	$0.798739\pi$
$468$	14.9823	0.692555
$469$	21.4869	0.992173
$470$	−13.6214	−0.628310
$471$	−4.65172	−0.214340
$472$	−9.17369	−0.422253
$473$	1.56306	0.0718695
$474$	2.29024	0.105194
$475$	−1.57402	−0.0722208
$476$	2.64460	0.121215
$477$	1.14056	0.0522225
$478$	−3.75282	−0.171650
$479$	−2.76222	−0.126209	−0.0631045	−	0.998007i	$-0.520100\pi$
$479$	−2.76222	−0.126209	−0.0631045	+	0.998007i	$0.520100\pi$
$480$	−0.746498	−0.0340728
$481$	42.4768	1.93677
$482$	−23.9268	−1.08984
$483$	−0.133236	−0.00606244
$484$	−10.1386	−0.460846
$485$	−34.6745	−1.57449
$486$	−6.91590	−0.313711
$487$	10.0022	0.453244	0.226622	−	0.973983i	$-0.427232\pi$
$487$	10.0022	0.453244	0.226622	+	0.973983i	$0.427232\pi$
$488$	−6.54017	−0.296060
$489$	−4.58706	−0.207434
$490$	5.10575	0.230654
$491$	−15.8070	−0.713361	−0.356680	−	0.934226i	$-0.616092\pi$
$491$	−15.8070	−0.713361	−0.356680	+	0.934226i	$0.616092\pi$
$492$	1.41020	0.0635765
$493$	−8.37070	−0.376997
$494$	2.70319	0.121622
$495$	−7.68095	−0.345233
$496$	−1.82113	−0.0817711
$497$	−24.9726	−1.12017
$498$	2.95406	0.132375
$499$	9.05673	0.405435	0.202718	−	0.979237i	$-0.435023\pi$
$499$	9.05673	0.405435	0.202718	+	0.979237i	$0.435023\pi$
$500$	−5.71296	−0.255491
$501$	0.218839	0.00977698
$502$	8.65141	0.386131
$503$	23.8385	1.06290	0.531452	−	0.847088i	$-0.321646\pi$
$503$	23.8385	1.06290	0.531452	+	0.847088i	$0.321646\pi$
$504$	8.69603	0.387352
$505$	−48.4679	−2.15679
$506$	−0.157647	−0.00700827
$507$	−3.47406	−0.154289
$508$	−3.22996	−0.143306
$509$	2.86660	0.127060	0.0635299	−	0.997980i	$-0.479764\pi$
$509$	2.86660	0.127060	0.0635299	+	0.997980i	$0.479764\pi$
$510$	0.665208	0.0294559
$511$	−23.2674	−1.02929
$512$	1.00000	0.0441942
$513$	−0.828618	−0.0365844
$514$	2.51246	0.110820
$515$	15.6462	0.689453
$516$	−0.445121	−0.0195954
$517$	−4.47604	−0.196856
$518$	24.6544	1.08325
$519$	−2.09525	−0.0919711
$520$	−14.4416	−0.633307
$521$	−14.6537	−0.641990	−0.320995	−	0.947081i	$-0.604017\pi$
$521$	−14.6537	−0.641990	−0.320995	+	0.947081i	$0.604017\pi$
$522$	−27.5247	−1.20472
$523$	4.46175	0.195099	0.0975493	−	0.995231i	$-0.468900\pi$
$523$	4.46175	0.195099	0.0975493	+	0.995231i	$0.468900\pi$
$524$	−4.36677	−0.190763
$525$	2.33536	0.101924
$526$	9.23690	0.402748
$527$	1.62281	0.0706909
$528$	−0.245301	−0.0106754
$529$	−22.9711	−0.998746
$530$	−1.09940	−0.0477549
$531$	26.8802	1.16650
$532$	1.56899	0.0680243
$533$	27.2814	1.18169
$534$	4.51232	0.195267
$535$	28.4575	1.23032
$536$	−7.24006	−0.312723
$537$	−5.41762	−0.233788
$538$	−23.2579	−1.00272
$539$	1.67776	0.0722663
$540$	4.42684	0.190501
$541$	−25.6237	−1.10165	−0.550825	−	0.834621i	$-0.685687\pi$
$541$	−25.6237	−1.10165	−0.550825	+	0.834621i	$0.685687\pi$
$542$	−21.2873	−0.914366
$543$	−2.41574	−0.103669
$544$	−0.891104	−0.0382058
$545$	−23.0367	−0.986783
$546$	−4.01071	−0.171643
$547$	38.4098	1.64228	0.821142	−	0.570724i	$-0.193337\pi$
$547$	38.4098	1.64228	0.821142	+	0.570724i	$0.193337\pi$
$548$	16.6263	0.710241
$549$	19.1636	0.817884
$550$	2.76324	0.117825
$551$	−4.96617	−0.211566
$552$	0.0448941	0.00191082
$553$	25.7165	1.09358
$554$	13.5672	0.576413
$555$	6.20143	0.263236
$556$	18.8746	0.800460
$557$	9.51872	0.403321	0.201661	−	0.979455i	$-0.435366\pi$
$557$	9.51872	0.403321	0.201661	+	0.979455i	$0.435366\pi$
$558$	5.33617	0.225898
$559$	−8.61124	−0.364217
$560$	−8.38223	−0.354214
$561$	0.218589	0.00922882
$562$	1.20152	0.0506831
$563$	2.69016	0.113377	0.0566885	−	0.998392i	$-0.481946\pi$
$563$	2.69016	0.113377	0.0566885	+	0.998392i	$0.481946\pi$
$564$	1.27467	0.0536731
$565$	−9.33046	−0.392535
$566$	−21.3034	−0.895449
$567$	−24.8587	−1.04397
$568$	8.41456	0.353067
$569$	−22.0157	−0.922948	−0.461474	−	0.887154i	$-0.652679\pi$
$569$	−22.0157	−0.922948	−0.461474	+	0.887154i	$0.652679\pi$
$570$	0.394654	0.0165302
$571$	18.9090	0.791319	0.395659	−	0.918397i	$-0.370516\pi$
$571$	18.9090	0.791319	0.395659	+	0.918397i	$0.370516\pi$
$572$	−4.74555	−0.198421
$573$	3.33371	0.139268
$574$	15.8347	0.660928
$575$	−0.505719	−0.0210899
$576$	−2.93014	−0.122089
$577$	−46.8824	−1.95174	−0.975871	−	0.218349i	$-0.929933\pi$
$577$	−46.8824	−1.95174	−0.975871	+	0.218349i	$0.929933\pi$
$578$	−16.2059	−0.674078
$579$	−5.88207	−0.244450
$580$	26.5315	1.10166
$581$	33.1704	1.37614
$582$	3.24476	0.134500
$583$	−0.361265	−0.0149621
$584$	7.83999	0.324421
$585$	42.3160	1.74955
$586$	1.45477	0.0600962
$587$	10.5398	0.435023	0.217511	−	0.976058i	$-0.430206\pi$
$587$	10.5398	0.435023	0.217511	+	0.976058i	$0.430206\pi$
$588$	−0.477786	−0.0197035
$589$	0.962783	0.0396708
$590$	−25.9102	−1.06671
$591$	−4.35074	−0.178966
$592$	−8.30737	−0.341431
$593$	−13.8199	−0.567514	−0.283757	−	0.958896i	$-0.591581\pi$
$593$	−13.8199	−0.567514	−0.283757	+	0.958896i	$0.591581\pi$
$594$	1.45467	0.0596858
$595$	7.46944	0.306217
$596$	−9.06313	−0.371240
$597$	−1.45192	−0.0594230
$598$	0.868513	0.0355161
$599$	3.98297	0.162740	0.0813699	−	0.996684i	$-0.474070\pi$
$599$	3.98297	0.162740	0.0813699	+	0.996684i	$0.474070\pi$
$600$	−0.786905	−0.0321253
$601$	−38.5726	−1.57341	−0.786704	−	0.617331i	$-0.788214\pi$
$601$	−38.5726	−1.57341	−0.786704	+	0.617331i	$0.788214\pi$
$602$	−4.99815	−0.203709
$603$	21.2144	0.863918
$604$	−2.81156	−0.114401
$605$	−28.6356	−1.16420
$606$	4.53553	0.184243
$607$	−5.57388	−0.226237	−0.113118	−	0.993582i	$-0.536084\pi$
$607$	−5.57388	−0.226237	−0.113118	+	0.993582i	$0.536084\pi$
$608$	−0.528674	−0.0214406
$609$	7.36828	0.298578
$610$	−18.4721	−0.747914
$611$	24.6595	0.997616
$612$	2.61106	0.105546
$613$	2.61682	0.105692	0.0528462	−	0.998603i	$-0.483171\pi$
$613$	2.61682	0.105692	0.0528462	+	0.998603i	$0.483171\pi$
$614$	30.8055	1.24321
$615$	3.98297	0.160609
$616$	−2.75442	−0.110979
$617$	−47.6470	−1.91819	−0.959097	−	0.283077i	$-0.908645\pi$
$617$	−47.6470	−1.91819	−0.959097	+	0.283077i	$0.908645\pi$
$618$	−1.46414	−0.0588962
$619$	29.0661	1.16826	0.584132	−	0.811659i	$-0.301435\pi$
$619$	29.0661	1.16826	0.584132	+	0.811659i	$0.301435\pi$
$620$	−5.14361	−0.206572
$621$	−0.266228	−0.0106834
$622$	15.0779	0.604570
$623$	50.6676	2.02996
$624$	1.35142	0.0541000
$625$	−31.0222	−1.24089
$626$	6.64914	0.265753
$627$	0.129684	0.00517909
$628$	17.6000	0.702316
$629$	7.40273	0.295166
$630$	24.5611	0.978539
$631$	−43.0013	−1.71186	−0.855928	−	0.517095i	$-0.827013\pi$
$631$	−43.0013	−1.71186	−0.855928	+	0.517095i	$0.827013\pi$
$632$	−8.66522	−0.344684
$633$	−2.02746	−0.0805844
$634$	16.3120	0.647833
$635$	−9.12274	−0.362025
$636$	0.102880	0.00407944
$637$	−9.24316	−0.366227
$638$	8.71829	0.345161
$639$	−24.6559	−0.975372
$640$	2.82441	0.111645
$641$	20.5106	0.810121	0.405060	−	0.914290i	$-0.367251\pi$
$641$	20.5106	0.810121	0.405060	+	0.914290i	$0.367251\pi$
$642$	−2.66299	−0.105100
$643$	20.5311	0.809668	0.404834	−	0.914390i	$-0.367329\pi$
$643$	20.5311	0.809668	0.404834	+	0.914390i	$0.367329\pi$
$644$	0.504103	0.0198645
$645$	−1.25720	−0.0495024
$646$	0.471104	0.0185353
$647$	7.53166	0.296100	0.148050	−	0.988980i	$-0.452700\pi$
$647$	7.53166	0.296100	0.148050	+	0.988980i	$0.452700\pi$
$648$	8.37618	0.329047
$649$	−8.51416	−0.334210
$650$	−15.2233	−0.597108
$651$	−1.42848	−0.0559865
$652$	17.3553	0.679688
$653$	−21.3929	−0.837167	−0.418584	−	0.908178i	$-0.637473\pi$
$653$	−21.3929	−0.837167	−0.418584	+	0.908178i	$0.637473\pi$
$654$	2.15572	0.0842955
$655$	−12.3335	−0.481911
$656$	−5.33554	−0.208318
$657$	−22.9723	−0.896235
$658$	14.3129	0.557975
$659$	−42.7365	−1.66478	−0.832388	−	0.554193i	$-0.813027\pi$
$659$	−42.7365	−1.66478	−0.832388	+	0.554193i	$0.813027\pi$
$660$	−0.692830	−0.0269684
$661$	9.13199	0.355193	0.177597	−	0.984103i	$-0.443168\pi$
$661$	9.13199	0.355193	0.177597	+	0.984103i	$0.443168\pi$
$662$	−23.6403	−0.918808
$663$	−1.20425	−0.0467693
$664$	−11.1768	−0.433745
$665$	4.43147	0.171845
$666$	24.3418	0.943225
$667$	−1.59559	−0.0617815
$668$	−0.827985	−0.0320357
$669$	−4.96722	−0.192044
$670$	−20.4489	−0.790009
$671$	−6.06998	−0.234329
$672$	0.784392	0.0302586
$673$	17.8439	0.687833	0.343917	−	0.939000i	$-0.388246\pi$
$673$	17.8439	0.687833	0.343917	+	0.939000i	$0.388246\pi$
$674$	−14.4516	−0.556654
$675$	4.66646	0.179612
$676$	13.1443	0.505549
$677$	−27.9318	−1.07350	−0.536752	−	0.843740i	$-0.680349\pi$
$677$	−27.9318	−1.07350	−0.536752	+	0.843740i	$0.680349\pi$
$678$	0.873125	0.0335322
$679$	36.4346	1.39823
$680$	−2.51684	−0.0965165
$681$	2.26195	0.0866781
$682$	−1.69020	−0.0647212
$683$	−4.60873	−0.176348	−0.0881741	−	0.996105i	$-0.528103\pi$
$683$	−4.60873	−0.176348	−0.0881741	+	0.996105i	$0.528103\pi$
$684$	1.54909	0.0592310
$685$	46.9595	1.79423
$686$	15.4095	0.588339
$687$	3.84094	0.146541
$688$	1.68414	0.0642071
$689$	1.99029	0.0758240
$690$	0.126799	0.00482716
$691$	8.72839	0.332044	0.166022	−	0.986122i	$-0.446908\pi$
$691$	8.72839	0.332044	0.166022	+	0.986122i	$0.446908\pi$
$692$	7.92745	0.301357
$693$	8.07084	0.306586
$694$	−33.1123	−1.25693
$695$	53.3095	2.02215
$696$	−2.48276	−0.0941087
$697$	4.75452	0.180090
$698$	7.86636	0.297746
$699$	0.856520	0.0323966
$700$	−8.83595	−0.333967
$701$	−7.52070	−0.284053	−0.142026	−	0.989863i	$-0.545362\pi$
$701$	−7.52070	−0.284053	−0.142026	+	0.989863i	$0.545362\pi$
$702$	−8.01410	−0.302473
$703$	4.39189	0.165643
$704$	0.928107	0.0349794
$705$	3.60018	0.135591
$706$	−19.3220	−0.727194
$707$	50.9282	1.91535
$708$	2.42463	0.0911231
$709$	−40.7493	−1.53037	−0.765187	−	0.643808i	$-0.777353\pi$
$709$	−40.7493	−1.53037	−0.765187	+	0.643808i	$0.777353\pi$
$710$	23.7662	0.891929
$711$	25.3903	0.952212
$712$	−17.0726	−0.639822
$713$	0.309334	0.0115847
$714$	−0.698974	−0.0261585
$715$	−13.4034	−0.501258
$716$	20.4978	0.766039
$717$	0.991879	0.0370424
$718$	11.7188	0.437343
$719$	50.4524	1.88156	0.940778	−	0.339023i	$-0.110096\pi$
$719$	50.4524	1.88156	0.940778	+	0.339023i	$0.110096\pi$
$720$	−8.27593	−0.308426
$721$	−16.4404	−0.612273
$722$	−18.7205	−0.696705
$723$	6.32391	0.235189
$724$	9.14006	0.339688
$725$	27.9676	1.03869
$726$	2.67966	0.0994515
$727$	−28.7121	−1.06487	−0.532436	−	0.846470i	$-0.678723\pi$
$727$	−28.7121	−1.06487	−0.532436	+	0.846470i	$0.678723\pi$
$728$	15.1747	0.562412
$729$	−23.3006	−0.862987
$730$	22.1434	0.819562
$731$	−1.50074	−0.0555069
$732$	1.72858	0.0638902
$733$	4.68297	0.172969	0.0864847	−	0.996253i	$-0.472437\pi$
$733$	4.68297	0.172969	0.0864847	+	0.996253i	$0.472437\pi$
$734$	31.8628	1.17608
$735$	−1.34946	−0.0497757
$736$	−0.169859	−0.00626108
$737$	−6.71955	−0.247518
$738$	15.6339	0.575492
$739$	41.3910	1.52259	0.761296	−	0.648405i	$-0.224563\pi$
$739$	41.3910	1.52259	0.761296	+	0.648405i	$0.224563\pi$
$740$	−23.4634	−0.862532
$741$	−0.714459	−0.0262463
$742$	1.15521	0.0424090
$743$	−14.5858	−0.535101	−0.267551	−	0.963544i	$-0.586214\pi$
$743$	−14.5858	−0.535101	−0.267551	+	0.963544i	$0.586214\pi$
$744$	0.481329	0.0176464
$745$	−25.5980	−0.937838
$746$	5.49297	0.201112
$747$	32.7497	1.19825
$748$	−0.827040	−0.0302396
$749$	−29.9020	−1.09260
$750$	1.50995	0.0551355
$751$	−42.0233	−1.53345	−0.766726	−	0.641975i	$-0.778115\pi$
$751$	−42.0233	−1.53345	−0.766726	+	0.641975i	$0.778115\pi$
$752$	−4.82276	−0.175868
$753$	−2.28659	−0.0833279
$754$	−48.0310	−1.74919
$755$	−7.94099	−0.289002
$756$	−4.65156	−0.169175
$757$	−22.1164	−0.803833	−0.401916	−	0.915676i	$-0.631656\pi$
$757$	−22.1164	−0.803833	−0.401916	+	0.915676i	$0.631656\pi$
$758$	25.7365	0.934791
$759$	0.0416665	0.00151240
$760$	−1.49319	−0.0541638
$761$	31.6108	1.14589	0.572946	−	0.819593i	$-0.305801\pi$
$761$	31.6108	1.14589	0.572946	+	0.819593i	$0.305801\pi$
$762$	0.853687	0.0309258
$763$	24.2061	0.876318
$764$	−12.6132	−0.456331
$765$	7.37471	0.266633
$766$	−28.9635	−1.04649
$767$	46.9064	1.69369
$768$	−0.264302	−0.00953719
$769$	44.1484	1.59203	0.796016	−	0.605276i	$-0.206937\pi$
$769$	44.1484	1.59203	0.796016	+	0.605276i	$0.206937\pi$
$770$	−7.77961	−0.280358
$771$	−0.664048	−0.0239151
$772$	22.2551	0.800977
$773$	29.9404	1.07688	0.538440	−	0.842664i	$-0.319014\pi$
$773$	29.9404	1.07688	0.538440	+	0.842664i	$0.319014\pi$
$774$	−4.93476	−0.177376
$775$	−5.42203	−0.194765
$776$	−12.2767	−0.440708
$777$	−6.51623	−0.233768
$778$	−33.6214	−1.20539
$779$	2.82076	0.101064
$780$	3.81696	0.136669
$781$	7.80962	0.279450
$782$	0.151362	0.00541269
$783$	14.7231	0.526161
$784$	1.80772	0.0645615
$785$	49.7096	1.77421
$786$	1.15415	0.0411670
$787$	−12.8098	−0.456619	−0.228309	−	0.973589i	$-0.573320\pi$
$787$	−12.8098	−0.456619	−0.228309	+	0.973589i	$0.573320\pi$
$788$	16.4612	0.586407
$789$	−2.44134	−0.0869139
$790$	−24.4741	−0.870750
$791$	9.80409	0.348593
$792$	−2.71949	−0.0966328
$793$	33.4409	1.18752
$794$	28.2857	1.00382
$795$	0.290574	0.0103056
$796$	5.49339	0.194708
$797$	−19.3503	−0.685423	−0.342711	−	0.939441i	$-0.611345\pi$
$797$	−19.3503	−0.685423	−0.342711	+	0.939441i	$0.611345\pi$
$798$	−0.414687	−0.0146798
$799$	4.29758	0.152037
$800$	2.97729	0.105263
$801$	50.0251	1.76755
$802$	14.8038	0.522741
$803$	7.27635	0.256777
$804$	1.91356	0.0674862
$805$	1.42379	0.0501822
$806$	9.31170	0.327991
$807$	6.14711	0.216388
$808$	−17.1604	−0.603700
$809$	−1.12892	−0.0396907	−0.0198454	−	0.999803i	$-0.506317\pi$
$809$	−1.12892	−0.0396907	−0.0198454	+	0.999803i	$0.506317\pi$
$810$	23.6578	0.831249
$811$	14.1674	0.497486	0.248743	−	0.968569i	$-0.419982\pi$
$811$	14.1674	0.497486	0.248743	+	0.968569i	$0.419982\pi$
$812$	−27.8782	−0.978334
$813$	5.62627	0.197322
$814$	−7.71013	−0.270240
$815$	49.0186	1.71705
$816$	0.235521	0.00824488
$817$	−0.890359	−0.0311497
$818$	−10.5998	−0.370614
$819$	−44.4641	−1.55370
$820$	−15.0698	−0.526259
$821$	14.1160	0.492651	0.246326	−	0.969187i	$-0.420777\pi$
$821$	14.1160	0.492651	0.246326	+	0.969187i	$0.420777\pi$
$822$	−4.39438	−0.153271
$823$	25.4001	0.885390	0.442695	−	0.896672i	$-0.354022\pi$
$823$	25.4001	0.885390	0.442695	+	0.896672i	$0.354022\pi$
$824$	5.53963	0.192982
$825$	−0.730332	−0.0254269
$826$	27.2255	0.947296
$827$	1.23266	0.0428639	0.0214320	−	0.999770i	$-0.493177\pi$
$827$	1.23266	0.0428639	0.0214320	+	0.999770i	$0.493177\pi$
$828$	0.497711	0.0172966
$829$	11.9511	0.415078	0.207539	−	0.978227i	$-0.433455\pi$
$829$	11.9511	0.415078	0.207539	+	0.978227i	$0.433455\pi$
$830$	−31.5679	−1.09574
$831$	−3.58583	−0.124391
$832$	−5.11315	−0.177267
$833$	−1.61087	−0.0558133
$834$	−4.98859	−0.172741
$835$	−2.33857	−0.0809295
$836$	−0.490666	−0.0169700
$837$	−2.85435	−0.0986607
$838$	14.5161	0.501451
$839$	−37.5677	−1.29698	−0.648491	−	0.761223i	$-0.724599\pi$
$839$	−37.5677	−1.29698	−0.648491	+	0.761223i	$0.724599\pi$
$840$	2.21544	0.0764401
$841$	59.2403	2.04277
$842$	−8.16891	−0.281519
$843$	−0.317565	−0.0109375
$844$	7.67099	0.264046
$845$	37.1248	1.27713
$846$	14.1314	0.485847
$847$	30.0892	1.03388
$848$	−0.389249	−0.0133669
$849$	5.63054	0.193240
$850$	−2.65308	−0.0909997
$851$	1.41108	0.0483711
$852$	−2.22399	−0.0761926
$853$	−12.9990	−0.445077	−0.222538	−	0.974924i	$-0.571434\pi$
$853$	−12.9990	−0.445077	−0.222538	+	0.974924i	$0.571434\pi$
$854$	19.4098	0.664189
$855$	4.37527	0.149631
$856$	10.0755	0.344375
$857$	25.7561	0.879813	0.439906	−	0.898044i	$-0.355012\pi$
$857$	25.7561	0.879813	0.439906	+	0.898044i	$0.355012\pi$
$858$	1.25426	0.0428197
$859$	21.3065	0.726967	0.363484	−	0.931601i	$-0.381587\pi$
$859$	21.3065	0.726967	0.363484	+	0.931601i	$0.381587\pi$
$860$	4.75669	0.162202
$861$	−4.18515	−0.142630
$862$	−15.5519	−0.529701
$863$	−8.40809	−0.286215	−0.143107	−	0.989707i	$-0.545709\pi$
$863$	−8.40809	−0.286215	−0.143107	+	0.989707i	$0.545709\pi$
$864$	1.56735	0.0533224
$865$	22.3904	0.761296
$866$	−28.5967	−0.971755
$867$	4.28327	0.145467
$868$	5.40471	0.183448
$869$	−8.04225	−0.272815
$870$	−7.01233	−0.237740
$871$	37.0195	1.25436
$872$	−8.15628	−0.276207
$873$	35.9725	1.21749
$874$	0.0897999	0.00303753
$875$	16.9548	0.573177
$876$	−2.07213	−0.0700108
$877$	37.0129	1.24984	0.624918	−	0.780691i	$-0.285132\pi$
$877$	37.0129	1.24984	0.624918	+	0.780691i	$0.285132\pi$
$878$	16.3080	0.550367
$879$	−0.384500	−0.0129689
$880$	2.62136	0.0883659
$881$	−28.5434	−0.961651	−0.480826	−	0.876816i	$-0.659663\pi$
$881$	−28.5434	−0.961651	−0.480826	+	0.876816i	$0.659663\pi$
$882$	−5.29689	−0.178356
$883$	34.9990	1.17781	0.588905	−	0.808203i	$-0.299559\pi$
$883$	34.9990	1.17781	0.588905	+	0.808203i	$0.299559\pi$
$884$	4.55635	0.153247
$885$	6.84814	0.230198
$886$	30.7121	1.03179
$887$	11.1294	0.373690	0.186845	−	0.982389i	$-0.440174\pi$
$887$	11.1294	0.373690	0.186845	+	0.982389i	$0.440174\pi$
$888$	2.19566	0.0736814
$889$	9.58583	0.321498
$890$	−48.2199	−1.61634
$891$	7.77399	0.260438
$892$	18.7937	0.629259
$893$	2.54967	0.0853214
$894$	2.39541	0.0801144
$895$	57.8942	1.93519
$896$	−2.96778	−0.0991466
$897$	−0.229550	−0.00766445
$898$	14.5633	0.485984
$899$	−17.1070	−0.570550
$900$	−8.72389	−0.290796
$901$	0.346862	0.0115556
$902$	−4.95195	−0.164882
$903$	1.32102	0.0439609
$904$	−3.30351	−0.109873
$905$	25.8153	0.858129
$906$	0.743101	0.0246879
$907$	1.24654	0.0413906	0.0206953	−	0.999786i	$-0.493412\pi$
$907$	1.24654	0.0413906	0.0206953	+	0.999786i	$0.493412\pi$
$908$	−8.55819	−0.284014
$909$	50.2824	1.66776
$910$	42.8596	1.42078
$911$	−23.7653	−0.787380	−0.393690	−	0.919243i	$-0.628802\pi$
$911$	−23.7653	−0.787380	−0.393690	+	0.919243i	$0.628802\pi$
$912$	0.139730	0.00462692
$913$	−10.3733	−0.343306
$914$	37.5481	1.24198
$915$	4.88223	0.161401
$916$	−14.5324	−0.480163
$917$	12.9596	0.427964
$918$	−1.39667	−0.0460971
$919$	−46.4609	−1.53260	−0.766301	−	0.642482i	$-0.777905\pi$
$919$	−46.4609	−1.53260	−0.766301	+	0.642482i	$0.777905\pi$
$920$	−0.479751	−0.0158169
$921$	−8.14198	−0.268287
$922$	18.6425	0.613959
$923$	−43.0249	−1.41618
$924$	0.727999	0.0239494
$925$	−24.7334	−0.813231
$926$	28.7542	0.944922
$927$	−16.2319	−0.533126
$928$	9.39363	0.308361
$929$	27.3433	0.897105	0.448553	−	0.893756i	$-0.351940\pi$
$929$	27.3433	0.897105	0.448553	+	0.893756i	$0.351940\pi$
$930$	1.35947	0.0445787
$931$	−0.955696	−0.0313217
$932$	−3.24068	−0.106152
$933$	−3.98513	−0.130467
$934$	−34.8651	−1.14082
$935$	−2.33590	−0.0763921
$936$	14.9823	0.489711
$937$	−31.1545	−1.01777	−0.508887	−	0.860834i	$-0.669943\pi$
$937$	−31.1545	−1.01777	−0.508887	+	0.860834i	$0.669943\pi$
$938$	21.4869	0.701572
$939$	−1.75738	−0.0573500
$940$	−13.6214	−0.444283
$941$	−13.5466	−0.441606	−0.220803	−	0.975318i	$-0.570868\pi$
$941$	−13.5466	−0.441606	−0.220803	+	0.975318i	$0.570868\pi$
$942$	−4.65172	−0.151561
$943$	0.906288	0.0295128
$944$	−9.17369	−0.298578
$945$	−13.1379	−0.427376
$946$	1.56306	0.0508194
$947$	9.88310	0.321158	0.160579	−	0.987023i	$-0.448664\pi$
$947$	9.88310	0.321158	0.160579	+	0.987023i	$0.448664\pi$
$948$	2.29024	0.0743835
$949$	−40.0870	−1.30128
$950$	−1.57402	−0.0510678
$951$	−4.31130	−0.139804
$952$	2.64460	0.0857120
$953$	−9.12023	−0.295433	−0.147717	−	0.989030i	$-0.547192\pi$
$953$	−9.12023	−0.295433	−0.147717	+	0.989030i	$0.547192\pi$
$954$	1.14056	0.0369269
$955$	−35.6249	−1.15280
$956$	−3.75282	−0.121375
$957$	−2.30427	−0.0744863
$958$	−2.76222	−0.0892432
$959$	−49.3433	−1.59338
$960$	−0.746498	−0.0240931
$961$	−27.6835	−0.893016
$962$	42.4768	1.36951
$963$	−29.5228	−0.951359
$964$	−23.9268	−0.770631
$965$	62.8574	2.02345
$966$	−0.133236	−0.00428679
$967$	−53.1193	−1.70820	−0.854101	−	0.520107i	$-0.825892\pi$
$967$	−53.1193	−1.70820	−0.854101	+	0.520107i	$0.825892\pi$
$968$	−10.1386	−0.325867
$969$	−0.124514	−0.00399996
$970$	−34.6745	−1.11333
$971$	−20.3264	−0.652306	−0.326153	−	0.945317i	$-0.605752\pi$
$971$	−20.3264	−0.652306	−0.326153	+	0.945317i	$0.605752\pi$
$972$	−6.91590	−0.221828
$973$	−56.0156	−1.79578
$974$	10.0022	0.320492
$975$	4.02356	0.128857
$976$	−6.54017	−0.209346
$977$	36.3851	1.16406	0.582031	−	0.813167i	$-0.302258\pi$
$977$	36.3851	1.16406	0.582031	+	0.813167i	$0.302258\pi$
$978$	−4.58706	−0.146678
$979$	−15.8452	−0.506414
$980$	5.10575	0.163097
$981$	23.8991	0.763039
$982$	−15.8070	−0.504422
$983$	−13.5968	−0.433670	−0.216835	−	0.976208i	$-0.569573\pi$
$983$	−13.5968	−0.433670	−0.216835	+	0.976208i	$0.569573\pi$
$984$	1.41020	0.0449554
$985$	46.4933	1.48140
$986$	−8.37070	−0.266577
$987$	−3.78293	−0.120412
$988$	2.70319	0.0859999
$989$	−0.286065	−0.00909635
$990$	−7.68095	−0.244117
$991$	25.8167	0.820096	0.410048	−	0.912064i	$-0.365512\pi$
$991$	25.8167	0.820096	0.410048	+	0.912064i	$0.365512\pi$
$992$	−1.82113	−0.0578209
$993$	6.24820	0.198281
$994$	−24.9726	−0.792082
$995$	15.5156	0.491877
$996$	2.95406	0.0936031
$997$	21.1411	0.669545	0.334773	−	0.942299i	$-0.391340\pi$
$997$	21.1411	0.669545	0.334773	+	0.942299i	$0.391340\pi$
$998$	9.05673	0.286686
$999$	−13.0206	−0.411952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.19	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.19	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.264302 q^{3} +1.00000 q^{4} +2.82441 q^{5} -0.264302 q^{6} -2.96778 q^{7} +1.00000 q^{8} -2.93014 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.264302 q^{3} +1.00000 q^{4} +2.82441 q^{5} -0.264302 q^{6} -2.96778 q^{7} +1.00000 q^{8} -2.93014 q^{9} +2.82441 q^{10} +0.928107 q^{11} -0.264302 q^{12} -5.11315 q^{13} -2.96778 q^{14} -0.746498 q^{15} +1.00000 q^{16} -0.891104 q^{17} -2.93014 q^{18} -0.528674 q^{19} +2.82441 q^{20} +0.784392 q^{21} +0.928107 q^{22} -0.169859 q^{23} -0.264302 q^{24} +2.97729 q^{25} -5.11315 q^{26} +1.56735 q^{27} -2.96778 q^{28} +9.39363 q^{29} -0.746498 q^{30} -1.82113 q^{31} +1.00000 q^{32} -0.245301 q^{33} -0.891104 q^{34} -8.38223 q^{35} -2.93014 q^{36} -8.30737 q^{37} -0.528674 q^{38} +1.35142 q^{39} +2.82441 q^{40} -5.33554 q^{41} +0.784392 q^{42} +1.68414 q^{43} +0.928107 q^{44} -8.27593 q^{45} -0.169859 q^{46} -4.82276 q^{47} -0.264302 q^{48} +1.80772 q^{49} +2.97729 q^{50} +0.235521 q^{51} -5.11315 q^{52} -0.389249 q^{53} +1.56735 q^{54} +2.62136 q^{55} -2.96778 q^{56} +0.139730 q^{57} +9.39363 q^{58} -9.17369 q^{59} -0.746498 q^{60} -6.54017 q^{61} -1.82113 q^{62} +8.69603 q^{63} +1.00000 q^{64} -14.4416 q^{65} -0.245301 q^{66} -7.24006 q^{67} -0.891104 q^{68} +0.0448941 q^{69} -8.38223 q^{70} +8.41456 q^{71} -2.93014 q^{72} +7.83999 q^{73} -8.30737 q^{74} -0.786905 q^{75} -0.528674 q^{76} -2.75442 q^{77} +1.35142 q^{78} -8.66522 q^{79} +2.82441 q^{80} +8.37618 q^{81} -5.33554 q^{82} -11.1768 q^{83} +0.784392 q^{84} -2.51684 q^{85} +1.68414 q^{86} -2.48276 q^{87} +0.928107 q^{88} -17.0726 q^{89} -8.27593 q^{90} +15.1747 q^{91} -0.169859 q^{92} +0.481329 q^{93} -4.82276 q^{94} -1.49319 q^{95} -0.264302 q^{96} -12.2767 q^{97} +1.80772 q^{98} -2.71949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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