LMFDB - Embedded newform 4029.2.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.23345 q^{2} -1.00000 q^{3} -0.478591 q^{4} +1.09712 q^{5} -1.23345 q^{6} +2.41639 q^{7} -3.05723 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.23345 q^{2} -1.00000 q^{3} -0.478591 q^{4} +1.09712 q^{5} -1.23345 q^{6} +2.41639 q^{7} -3.05723 q^{8} +1.00000 q^{9} +1.35325 q^{10} +4.37271 q^{11} +0.478591 q^{12} -4.47582 q^{13} +2.98051 q^{14} -1.09712 q^{15} -2.81377 q^{16} -1.00000 q^{17} +1.23345 q^{18} -4.39471 q^{19} -0.525072 q^{20} -2.41639 q^{21} +5.39354 q^{22} -3.08077 q^{23} +3.05723 q^{24} -3.79633 q^{25} -5.52072 q^{26} -1.00000 q^{27} -1.15646 q^{28} -2.64634 q^{29} -1.35325 q^{30} -1.07482 q^{31} +2.64380 q^{32} -4.37271 q^{33} -1.23345 q^{34} +2.65107 q^{35} -0.478591 q^{36} -2.84224 q^{37} -5.42067 q^{38} +4.47582 q^{39} -3.35414 q^{40} -10.3130 q^{41} -2.98051 q^{42} +12.1285 q^{43} -2.09274 q^{44} +1.09712 q^{45} -3.79999 q^{46} -0.00757624 q^{47} +2.81377 q^{48} -1.16105 q^{49} -4.68260 q^{50} +1.00000 q^{51} +2.14209 q^{52} +1.68572 q^{53} -1.23345 q^{54} +4.79739 q^{55} -7.38746 q^{56} +4.39471 q^{57} -3.26414 q^{58} -4.86874 q^{59} +0.525072 q^{60} +10.7177 q^{61} -1.32575 q^{62} +2.41639 q^{63} +8.88855 q^{64} -4.91051 q^{65} -5.39354 q^{66} +2.54540 q^{67} +0.478591 q^{68} +3.08077 q^{69} +3.26997 q^{70} -1.25447 q^{71} -3.05723 q^{72} -0.544334 q^{73} -3.50578 q^{74} +3.79633 q^{75} +2.10327 q^{76} +10.5662 q^{77} +5.52072 q^{78} -1.00000 q^{79} -3.08704 q^{80} +1.00000 q^{81} -12.7206 q^{82} -12.8571 q^{83} +1.15646 q^{84} -1.09712 q^{85} +14.9599 q^{86} +2.64634 q^{87} -13.3684 q^{88} -1.35116 q^{89} +1.35325 q^{90} -10.8153 q^{91} +1.47443 q^{92} +1.07482 q^{93} -0.00934494 q^{94} -4.82152 q^{95} -2.64380 q^{96} -11.0473 q^{97} -1.43210 q^{98} +4.37271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	1.23345	0.872184	0.436092	−	0.899902i	$-0.356362\pi$
$2$	1.23345	0.872184	0.436092	+	0.899902i	$0.356362\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.478591	−0.239296
$5$	1.09712	0.490646	0.245323	−	0.969441i	$-0.421106\pi$
$5$	1.09712	0.490646	0.245323	+	0.969441i	$0.421106\pi$
$6$	−1.23345	−0.503555
$7$	2.41639	0.913310	0.456655	−	0.889644i	$-0.349047\pi$
$7$	2.41639	0.913310	0.456655	+	0.889644i	$0.349047\pi$
$8$	−3.05723	−1.08089
$9$	1.00000	0.333333
$10$	1.35325	0.427934
$11$	4.37271	1.31842	0.659211	−	0.751958i	$-0.270890\pi$
$11$	4.37271	1.31842	0.659211	+	0.751958i	$0.270890\pi$
$12$	0.478591	0.138157
$13$	−4.47582	−1.24137	−0.620685	−	0.784060i	$-0.713145\pi$
$13$	−4.47582	−1.24137	−0.620685	+	0.784060i	$0.713145\pi$
$14$	2.98051	0.796574
$15$	−1.09712	−0.283275
$16$	−2.81377	−0.703442
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.23345	0.290728
$19$	−4.39471	−1.00821	−0.504107	−	0.863641i	$-0.668178\pi$
$19$	−4.39471	−1.00821	−0.504107	+	0.863641i	$0.668178\pi$
$20$	−0.525072	−0.117410
$21$	−2.41639	−0.527300
$22$	5.39354	1.14991
$23$	−3.08077	−0.642385	−0.321193	−	0.947014i	$-0.604084\pi$
$23$	−3.08077	−0.642385	−0.321193	+	0.947014i	$0.604084\pi$
$24$	3.05723	0.624054
$25$	−3.79633	−0.759266
$26$	−5.52072	−1.08270
$27$	−1.00000	−0.192450
$28$	−1.15646	−0.218551
$29$	−2.64634	−0.491413	−0.245706	−	0.969344i	$-0.579020\pi$
$29$	−2.64634	−0.491413	−0.245706	+	0.969344i	$0.579020\pi$
$30$	−1.35325	−0.247068
$31$	−1.07482	−0.193044	−0.0965221	−	0.995331i	$-0.530772\pi$
$31$	−1.07482	−0.193044	−0.0965221	+	0.995331i	$0.530772\pi$
$32$	2.64380	0.467363
$33$	−4.37271	−0.761192
$34$	−1.23345	−0.211536
$35$	2.65107	0.448113
$36$	−0.478591	−0.0797652
$37$	−2.84224	−0.467262	−0.233631	−	0.972325i	$-0.575061\pi$
$37$	−2.84224	−0.467262	−0.233631	+	0.972325i	$0.575061\pi$
$38$	−5.42067	−0.879349
$39$	4.47582	0.716705
$40$	−3.35414	−0.530337
$41$	−10.3130	−1.61062	−0.805309	−	0.592856i	$-0.798000\pi$
$41$	−10.3130	−1.61062	−0.805309	+	0.592856i	$0.798000\pi$
$42$	−2.98051	−0.459902
$43$	12.1285	1.84958	0.924788	−	0.380482i	$-0.124242\pi$
$43$	12.1285	1.84958	0.924788	+	0.380482i	$0.124242\pi$
$44$	−2.09274	−0.315493
$45$	1.09712	0.163549
$46$	−3.79999	−0.560278
$47$	−0.00757624	−0.00110511	−0.000552554	−	1.00000i	$-0.500176\pi$
$47$	−0.00757624	−0.00110511	−0.000552554		1.00000i	$0.500176\pi$
$48$	2.81377	0.406132
$49$	−1.16105	−0.165864
$50$	−4.68260	−0.662219
$51$	1.00000	0.140028
$52$	2.14209	0.297054
$53$	1.68572	0.231551	0.115776	−	0.993275i	$-0.463065\pi$
$53$	1.68572	0.231551	0.115776	+	0.993275i	$0.463065\pi$
$54$	−1.23345	−0.167852
$55$	4.79739	0.646879
$56$	−7.38746	−0.987191
$57$	4.39471	0.582093
$58$	−3.26414	−0.428602
$59$	−4.86874	−0.633856	−0.316928	−	0.948450i	$-0.602651\pi$
$59$	−4.86874	−0.633856	−0.316928	+	0.948450i	$0.602651\pi$
$60$	0.525072	0.0677864
$61$	10.7177	1.37226	0.686132	−	0.727477i	$-0.259307\pi$
$61$	10.7177	1.37226	0.686132	+	0.727477i	$0.259307\pi$
$62$	−1.32575	−0.168370
$63$	2.41639	0.304437
$64$	8.88855	1.11107
$65$	−4.91051	−0.609074
$66$	−5.39354	−0.663899
$67$	2.54540	0.310970	0.155485	−	0.987838i	$-0.450306\pi$
$67$	2.54540	0.310970	0.155485	+	0.987838i	$0.450306\pi$
$68$	0.478591	0.0580377
$69$	3.08077	0.370881
$70$	3.26997	0.390836
$71$	−1.25447	−0.148878	−0.0744392	−	0.997226i	$-0.523717\pi$
$71$	−1.25447	−0.148878	−0.0744392	+	0.997226i	$0.523717\pi$
$72$	−3.05723	−0.360298
$73$	−0.544334	−0.0637095	−0.0318547	−	0.999493i	$-0.510141\pi$
$73$	−0.544334	−0.0637095	−0.0318547	+	0.999493i	$0.510141\pi$
$74$	−3.50578	−0.407538
$75$	3.79633	0.438362
$76$	2.10327	0.241261
$77$	10.5662	1.20413
$78$	5.52072	0.625099
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−3.08704	−0.345141
$81$	1.00000	0.111111
$82$	−12.7206	−1.40475
$83$	−12.8571	−1.41126	−0.705628	−	0.708583i	$-0.749335\pi$
$83$	−12.8571	−1.41126	−0.705628	+	0.708583i	$0.749335\pi$
$84$	1.15646	0.126181
$85$	−1.09712	−0.118999
$86$	14.9599	1.61317
$87$	2.64634	0.283717
$88$	−13.3684	−1.42507
$89$	−1.35116	−0.143223	−0.0716115	−	0.997433i	$-0.522814\pi$
$89$	−1.35116	−0.143223	−0.0716115	+	0.997433i	$0.522814\pi$
$90$	1.35325	0.142645
$91$	−10.8153	−1.13376
$92$	1.47443	0.153720
$93$	1.07482	0.111454
$94$	−0.00934494	−0.000963857 0
$95$	−4.82152	−0.494677
$96$	−2.64380	−0.269832
$97$	−11.0473	−1.12168	−0.560840	−	0.827924i	$-0.689522\pi$
$97$	−11.0473	−1.12168	−0.560840	+	0.827924i	$0.689522\pi$
$98$	−1.43210	−0.144664
$99$	4.37271	0.439474
$100$	1.81689	0.181689
$101$	−4.20018	−0.417933	−0.208967	−	0.977923i	$-0.567010\pi$
$101$	−4.20018	−0.417933	−0.208967	+	0.977923i	$0.567010\pi$
$102$	1.23345	0.122130
$103$	−2.67111	−0.263193	−0.131596	−	0.991303i	$-0.542010\pi$
$103$	−2.67111	−0.263193	−0.131596	+	0.991303i	$0.542010\pi$
$104$	13.6836	1.34179
$105$	−2.65107	−0.258718
$106$	2.07926	0.201955
$107$	3.07303	0.297081	0.148540	−	0.988906i	$-0.452542\pi$
$107$	3.07303	0.297081	0.148540	+	0.988906i	$0.452542\pi$
$108$	0.478591	0.0460525
$109$	−10.3265	−0.989098	−0.494549	−	0.869150i	$-0.664667\pi$
$109$	−10.3265	−0.989098	−0.494549	+	0.869150i	$0.664667\pi$
$110$	5.91736	0.564198
$111$	2.84224	0.269774
$112$	−6.79917	−0.642461
$113$	−10.2654	−0.965692	−0.482846	−	0.875705i	$-0.660397\pi$
$113$	−10.2654	−0.965692	−0.482846	+	0.875705i	$0.660397\pi$
$114$	5.42067	0.507692
$115$	−3.37997	−0.315184
$116$	1.26651	0.117593
$117$	−4.47582	−0.413790
$118$	−6.00537	−0.552839
$119$	−2.41639	−0.221510
$120$	3.35414	0.306190
$121$	8.12063	0.738239
$122$	13.2198	1.19687
$123$	10.3130	0.929890
$124$	0.514402	0.0461946
$125$	−9.65062	−0.863178
$126$	2.98051	0.265525
$127$	−11.3538	−1.00749	−0.503743	−	0.863854i	$-0.668044\pi$
$127$	−11.3538	−1.00749	−0.503743	+	0.863854i	$0.668044\pi$
$128$	5.67600	0.501693
$129$	−12.1285	−1.06785
$130$	−6.05689	−0.531224
$131$	7.74108	0.676341	0.338171	−	0.941085i	$-0.390192\pi$
$131$	7.74108	0.676341	0.338171	+	0.941085i	$0.390192\pi$
$132$	2.09274	0.182150
$133$	−10.6193	−0.920813
$134$	3.13963	0.271223
$135$	−1.09712	−0.0944250
$136$	3.05723	0.262155
$137$	0.831255	0.0710189	0.0355095	−	0.999369i	$-0.488695\pi$
$137$	0.831255	0.0710189	0.0355095	+	0.999369i	$0.488695\pi$
$138$	3.79999	0.323477
$139$	−8.90848	−0.755607	−0.377804	−	0.925886i	$-0.623321\pi$
$139$	−8.90848	−0.755607	−0.377804	+	0.925886i	$0.623321\pi$
$140$	−1.26878	−0.107231
$141$	0.00757624	0.000638034 0
$142$	−1.54733	−0.129849
$143$	−19.5715	−1.63665
$144$	−2.81377	−0.234481
$145$	−2.90335	−0.241110
$146$	−0.671411	−0.0555664
$147$	1.16105	0.0957617
$148$	1.36027	0.111814
$149$	−8.58595	−0.703389	−0.351694	−	0.936115i	$-0.614394\pi$
$149$	−8.58595	−0.703389	−0.351694	+	0.936115i	$0.614394\pi$
$150$	4.68260	0.382333
$151$	−4.33681	−0.352925	−0.176462	−	0.984307i	$-0.556465\pi$
$151$	−4.33681	−0.352925	−0.176462	+	0.984307i	$0.556465\pi$
$152$	13.4356	1.08977
$153$	−1.00000	−0.0808452
$154$	13.0329	1.05022
$155$	−1.17921	−0.0947165
$156$	−2.14209	−0.171504
$157$	12.0823	0.964269	0.482135	−	0.876097i	$-0.339862\pi$
$157$	12.0823	0.964269	0.482135	+	0.876097i	$0.339862\pi$
$158$	−1.23345	−0.0981283
$159$	−1.68572	−0.133686
$160$	2.90057	0.229310
$161$	−7.44435	−0.586697
$162$	1.23345	0.0969093
$163$	0.355165	0.0278187	0.0139093	−	0.999903i	$-0.495572\pi$
$163$	0.355165	0.0278187	0.0139093	+	0.999903i	$0.495572\pi$
$164$	4.93570	0.385414
$165$	−4.79739	−0.373476
$166$	−15.8587	−1.23087
$167$	−4.79417	−0.370984	−0.185492	−	0.982646i	$-0.559388\pi$
$167$	−4.79417	−0.370984	−0.185492	+	0.982646i	$0.559388\pi$
$168$	7.38746	0.569955
$169$	7.03300	0.541000
$170$	−1.35325	−0.103789
$171$	−4.39471	−0.336072
$172$	−5.80459	−0.442596
$173$	−19.2216	−1.46139	−0.730697	−	0.682702i	$-0.760805\pi$
$173$	−19.2216	−1.46139	−0.730697	+	0.682702i	$0.760805\pi$
$174$	3.26414	0.247454
$175$	−9.17342	−0.693446
$176$	−12.3038	−0.927434
$177$	4.86874	0.365957
$178$	−1.66660	−0.124917
$179$	12.4267	0.928812	0.464406	−	0.885622i	$-0.346268\pi$
$179$	12.4267	0.928812	0.464406	+	0.885622i	$0.346268\pi$
$180$	−0.525072	−0.0391365
$181$	−25.6064	−1.90331	−0.951655	−	0.307168i	$-0.900619\pi$
$181$	−25.6064	−1.90331	−0.951655	+	0.307168i	$0.900619\pi$
$182$	−13.3402	−0.988844
$183$	−10.7177	−0.792277
$184$	9.41862	0.694350
$185$	−3.11828	−0.229260
$186$	1.32575	0.0972085
$187$	−4.37271	−0.319765
$188$	0.00362592	0.000264447 0
$189$	−2.41639	−0.175767
$190$	−5.94712	−0.431449
$191$	16.9840	1.22892	0.614460	−	0.788948i	$-0.289374\pi$
$191$	16.9840	1.22892	0.614460	+	0.788948i	$0.289374\pi$
$192$	−8.88855	−0.641476
$193$	−4.16013	−0.299453	−0.149726	−	0.988727i	$-0.547839\pi$
$193$	−4.16013	−0.299453	−0.149726	+	0.988727i	$0.547839\pi$
$194$	−13.6263	−0.978311
$195$	4.91051	0.351649
$196$	0.555668	0.0396906
$197$	−4.98288	−0.355015	−0.177508	−	0.984119i	$-0.556803\pi$
$197$	−4.98288	−0.355015	−0.177508	+	0.984119i	$0.556803\pi$
$198$	5.39354	0.383302
$199$	19.9525	1.41440	0.707199	−	0.707015i	$-0.249959\pi$
$199$	19.9525	1.41440	0.707199	+	0.707015i	$0.249959\pi$
$200$	11.6062	0.820686
$201$	−2.54540	−0.179539
$202$	−5.18073	−0.364515
$203$	−6.39459	−0.448812
$204$	−0.478591	−0.0335081
$205$	−11.3146	−0.790244
$206$	−3.29470	−0.229552
$207$	−3.08077	−0.214128
$208$	12.5939	0.873232
$209$	−19.2168	−1.32925
$210$	−3.26997	−0.225650
$211$	15.7962	1.08746	0.543728	−	0.839261i	$-0.317012\pi$
$211$	15.7962	1.08746	0.543728	+	0.839261i	$0.317012\pi$
$212$	−0.806770	−0.0554092
$213$	1.25447	0.0859550
$214$	3.79044	0.259109
$215$	13.3064	0.907488
$216$	3.05723	0.208018
$217$	−2.59720	−0.176309
$218$	−12.7372	−0.862675
$219$	0.544334	0.0367827
$220$	−2.29599	−0.154795
$221$	4.47582	0.301076
$222$	3.50578	0.235292
$223$	−24.1795	−1.61918	−0.809588	−	0.586998i	$-0.800310\pi$
$223$	−24.1795	−1.61918	−0.809588	+	0.586998i	$0.800310\pi$
$224$	6.38847	0.426847
$225$	−3.79633	−0.253089
$226$	−12.6620	−0.842261
$227$	1.64530	0.109203	0.0546013	−	0.998508i	$-0.482611\pi$
$227$	1.64530	0.109203	0.0546013	+	0.998508i	$0.482611\pi$
$228$	−2.10327	−0.139292
$229$	17.1487	1.13322	0.566608	−	0.823987i	$-0.308255\pi$
$229$	17.1487	1.13322	0.566608	+	0.823987i	$0.308255\pi$
$230$	−4.16904	−0.274898
$231$	−10.5662	−0.695204
$232$	8.09046	0.531165
$233$	3.28775	0.215388	0.107694	−	0.994184i	$-0.465653\pi$
$233$	3.28775	0.215388	0.107694	+	0.994184i	$0.465653\pi$
$234$	−5.52072	−0.360901
$235$	−0.00831203	−0.000542217 0
$236$	2.33014	0.151679
$237$	1.00000	0.0649570
$238$	−2.98051	−0.193198
$239$	−2.42596	−0.156922	−0.0784610	−	0.996917i	$-0.525001\pi$
$239$	−2.42596	−0.156922	−0.0784610	+	0.996917i	$0.525001\pi$
$240$	3.08704	0.199267
$241$	−19.7247	−1.27058	−0.635291	−	0.772273i	$-0.719120\pi$
$241$	−19.7247	−1.27058	−0.635291	+	0.772273i	$0.719120\pi$
$242$	10.0164	0.643880
$243$	−1.00000	−0.0641500
$244$	−5.12941	−0.328377
$245$	−1.27381	−0.0813806
$246$	12.7206	0.811035
$247$	19.6699	1.25157
$248$	3.28598	0.208660
$249$	12.8571	0.814789
$250$	−11.9036	−0.752849
$251$	−14.5273	−0.916957	−0.458479	−	0.888705i	$-0.651605\pi$
$251$	−14.5273	−0.916957	−0.458479	+	0.888705i	$0.651605\pi$
$252$	−1.15646	−0.0728504
$253$	−13.4713	−0.846936
$254$	−14.0044	−0.878713
$255$	1.09712	0.0687042
$256$	−10.7760	−0.673500
$257$	27.3050	1.70324	0.851621	−	0.524158i	$-0.175620\pi$
$257$	27.3050	1.70324	0.851621	+	0.524158i	$0.175620\pi$
$258$	−14.9599	−0.931365
$259$	−6.86797	−0.426755
$260$	2.35013	0.145749
$261$	−2.64634	−0.163804
$262$	9.54826	0.589894
$263$	6.84103	0.421836	0.210918	−	0.977504i	$-0.432355\pi$
$263$	6.84103	0.421836	0.210918	+	0.977504i	$0.432355\pi$
$264$	13.3684	0.822767
$265$	1.84943	0.113610
$266$	−13.0985	−0.803118
$267$	1.35116	0.0826899
$268$	−1.21821	−0.0744138
$269$	−2.35494	−0.143583	−0.0717916	−	0.997420i	$-0.522872\pi$
$269$	−2.35494	−0.143583	−0.0717916	+	0.997420i	$0.522872\pi$
$270$	−1.35325	−0.0823559
$271$	−19.4689	−1.18265	−0.591324	−	0.806434i	$-0.701395\pi$
$271$	−19.4689	−1.18265	−0.591324	+	0.806434i	$0.701395\pi$
$272$	2.81377	0.170610
$273$	10.8153	0.654574
$274$	1.02531	0.0619415
$275$	−16.6003	−1.00103
$276$	−1.47443	−0.0887503
$277$	11.6894	0.702349	0.351174	−	0.936310i	$-0.385782\pi$
$277$	11.6894	0.702349	0.351174	+	0.936310i	$0.385782\pi$
$278$	−10.9882	−0.659028
$279$	−1.07482	−0.0643481
$280$	−8.10492	−0.484362
$281$	0.217392	0.0129685	0.00648426	−	0.999979i	$-0.497936\pi$
$281$	0.217392	0.0129685	0.00648426	+	0.999979i	$0.497936\pi$
$282$	0.00934494	0.000556483 0
$283$	−10.2970	−0.612094	−0.306047	−	0.952016i	$-0.599006\pi$
$283$	−10.2970	−0.612094	−0.306047	+	0.952016i	$0.599006\pi$
$284$	0.600380	0.0356260
$285$	4.82152	0.285602
$286$	−24.1405	−1.42746
$287$	−24.9202	−1.47099
$288$	2.64380	0.155788
$289$	1.00000	0.0588235
$290$	−3.58115	−0.210292
$291$	11.0473	0.647602
$292$	0.260514	0.0152454
$293$	−11.1973	−0.654153	−0.327077	−	0.944998i	$-0.606064\pi$
$293$	−11.1973	−0.654153	−0.327077	+	0.944998i	$0.606064\pi$
$294$	1.43210	0.0835218
$295$	−5.34159	−0.310999
$296$	8.68939	0.505060
$297$	−4.37271	−0.253731
$298$	−10.5904	−0.613484
$299$	13.7890	0.797438
$300$	−1.81689	−0.104898
$301$	29.3072	1.68924
$302$	−5.34926	−0.307815
$303$	4.20018	0.241294
$304$	12.3657	0.709221
$305$	11.7586	0.673297
$306$	−1.23345	−0.0705119
$307$	18.4937	1.05549	0.527745	−	0.849403i	$-0.323038\pi$
$307$	18.4937	1.05549	0.527745	+	0.849403i	$0.323038\pi$
$308$	−5.05689	−0.288143
$309$	2.67111	0.151954
$310$	−1.45450	−0.0826102
$311$	19.5374	1.10787	0.553933	−	0.832561i	$-0.313126\pi$
$311$	19.5374	1.10787	0.553933	+	0.832561i	$0.313126\pi$
$312$	−13.6836	−0.774682
$313$	2.65965	0.150332	0.0751661	−	0.997171i	$-0.476051\pi$
$313$	2.65965	0.150332	0.0751661	+	0.997171i	$0.476051\pi$
$314$	14.9029	0.841020
$315$	2.65107	0.149371
$316$	0.478591	0.0269229
$317$	18.5652	1.04272	0.521362	−	0.853336i	$-0.325424\pi$
$317$	18.5652	1.04272	0.521362	+	0.853336i	$0.325424\pi$
$318$	−2.07926	−0.116599
$319$	−11.5717	−0.647890
$320$	9.75179	0.545142
$321$	−3.07303	−0.171520
$322$	−9.18227	−0.511708
$323$	4.39471	0.244528
$324$	−0.478591	−0.0265884
$325$	16.9917	0.942530
$326$	0.438080	0.0242630
$327$	10.3265	0.571056
$328$	31.5291	1.74091
$329$	−0.0183072	−0.00100931
$330$	−5.91736	−0.325740
$331$	−15.3551	−0.843990	−0.421995	−	0.906598i	$-0.638670\pi$
$331$	−15.3551	−0.843990	−0.421995	+	0.906598i	$0.638670\pi$
$332$	6.15332	0.337707
$333$	−2.84224	−0.155754
$334$	−5.91338	−0.323566
$335$	2.79261	0.152576
$336$	6.79917	0.370925
$337$	−5.12600	−0.279231	−0.139616	−	0.990206i	$-0.544587\pi$
$337$	−5.12600	−0.279231	−0.139616	+	0.990206i	$0.544587\pi$
$338$	8.67488	0.471851
$339$	10.2654	0.557543
$340$	0.525072	0.0284760
$341$	−4.69990	−0.254514
$342$	−5.42067	−0.293116
$343$	−19.7203	−1.06480
$344$	−37.0796	−1.99920
$345$	3.37997	0.181972
$346$	−23.7090	−1.27460
$347$	−17.6370	−0.946804	−0.473402	−	0.880847i	$-0.656974\pi$
$347$	−17.6370	−0.946804	−0.473402	+	0.880847i	$0.656974\pi$
$348$	−1.26651	−0.0678923
$349$	6.97597	0.373415	0.186707	−	0.982416i	$-0.440218\pi$
$349$	6.97597	0.373415	0.186707	+	0.982416i	$0.440218\pi$
$350$	−11.3150	−0.604812
$351$	4.47582	0.238902
$352$	11.5606	0.616182
$353$	33.6212	1.78947	0.894737	−	0.446593i	$-0.147363\pi$
$353$	33.6212	1.78947	0.894737	+	0.446593i	$0.147363\pi$
$354$	6.00537	0.319182
$355$	−1.37631	−0.0730467
$356$	0.646655	0.0342727
$357$	2.41639	0.127889
$358$	15.3277	0.810095
$359$	2.26984	0.119798	0.0598989	−	0.998204i	$-0.480922\pi$
$359$	2.26984	0.119798	0.0598989	+	0.998204i	$0.480922\pi$
$360$	−3.35414	−0.176779
$361$	0.313452	0.0164975
$362$	−31.5843	−1.66004
$363$	−8.12063	−0.426222
$364$	5.17613	0.271303
$365$	−0.597199	−0.0312588
$366$	−13.2198	−0.691011
$367$	1.28073	0.0668535	0.0334268	−	0.999441i	$-0.489358\pi$
$367$	1.28073	0.0668535	0.0334268	+	0.999441i	$0.489358\pi$
$368$	8.66858	0.451881
$369$	−10.3130	−0.536872
$370$	−3.84625	−0.199957
$371$	4.07336	0.211478
$372$	−0.514402	−0.0266705
$373$	24.9724	1.29302	0.646512	−	0.762904i	$-0.276227\pi$
$373$	24.9724	1.29302	0.646512	+	0.762904i	$0.276227\pi$
$374$	−5.39354	−0.278893
$375$	9.65062	0.498356
$376$	0.0231623	0.00119450
$377$	11.8445	0.610025
$378$	−2.98051	−0.153301
$379$	16.0440	0.824127	0.412064	−	0.911155i	$-0.364808\pi$
$379$	16.0440	0.824127	0.412064	+	0.911155i	$0.364808\pi$
$380$	2.30754	0.118374
$381$	11.3538	0.581672
$382$	20.9490	1.07184
$383$	−19.8287	−1.01320	−0.506600	−	0.862181i	$-0.669098\pi$
$383$	−19.8287	−1.01320	−0.506600	+	0.862181i	$0.669098\pi$
$384$	−5.67600	−0.289652
$385$	11.5924	0.590802
$386$	−5.13133	−0.261178
$387$	12.1285	0.616526
$388$	5.28713	0.268413
$389$	1.94436	0.0985828	0.0492914	−	0.998784i	$-0.484304\pi$
$389$	1.94436	0.0985828	0.0492914	+	0.998784i	$0.484304\pi$
$390$	6.05689	0.306702
$391$	3.08077	0.155801
$392$	3.54959	0.179281
$393$	−7.74108	−0.390486
$394$	−6.14615	−0.309639
$395$	−1.09712	−0.0552020
$396$	−2.09274	−0.105164
$397$	−6.11642	−0.306974	−0.153487	−	0.988151i	$-0.549050\pi$
$397$	−6.11642	−0.306974	−0.153487	+	0.988151i	$0.549050\pi$
$398$	24.6105	1.23361
$399$	10.6193	0.531632
$400$	10.6820	0.534100
$401$	−9.72440	−0.485613	−0.242807	−	0.970075i	$-0.578068\pi$
$401$	−9.72440	−0.485613	−0.242807	+	0.970075i	$0.578068\pi$
$402$	−3.13963	−0.156591
$403$	4.81073	0.239639
$404$	2.01017	0.100010
$405$	1.09712	0.0545163
$406$	−7.88743	−0.391447
$407$	−12.4283	−0.616049
$408$	−3.05723	−0.151355
$409$	34.9243	1.72689	0.863447	−	0.504439i	$-0.168301\pi$
$409$	34.9243	1.72689	0.863447	+	0.504439i	$0.168301\pi$
$410$	−13.9560	−0.689238
$411$	−0.831255	−0.0410028
$412$	1.27837	0.0629809
$413$	−11.7648	−0.578907
$414$	−3.79999	−0.186759
$415$	−14.1058	−0.692427
$416$	−11.8332	−0.580170
$417$	8.90848	0.436250
$418$	−23.7030	−1.15935
$419$	27.6724	1.35188	0.675942	−	0.736954i	$-0.263737\pi$
$419$	27.6724	1.35188	0.675942	+	0.736954i	$0.263737\pi$
$420$	1.26878	0.0619101
$421$	5.95306	0.290134	0.145067	−	0.989422i	$-0.453660\pi$
$421$	5.95306	0.290134	0.145067	+	0.989422i	$0.453660\pi$
$422$	19.4839	0.948462
$423$	−0.00757624	−0.000368369 0
$424$	−5.15363	−0.250282
$425$	3.79633	0.184149
$426$	1.54733	0.0749686
$427$	25.8982	1.25330
$428$	−1.47072	−0.0710902
$429$	19.5715	0.944921
$430$	16.4128	0.791496
$431$	−13.3089	−0.641066	−0.320533	−	0.947237i	$-0.603862\pi$
$431$	−13.3089	−0.641066	−0.320533	+	0.947237i	$0.603862\pi$
$432$	2.81377	0.135377
$433$	−26.0593	−1.25233	−0.626166	−	0.779690i	$-0.715377\pi$
$433$	−26.0593	−1.25233	−0.626166	+	0.779690i	$0.715377\pi$
$434$	−3.20352	−0.153774
$435$	2.90335	0.139205
$436$	4.94217	0.236687
$437$	13.5391	0.647663
$438$	0.671411	0.0320813
$439$	−22.4418	−1.07109	−0.535544	−	0.844507i	$-0.679893\pi$
$439$	−22.4418	−1.07109	−0.535544	+	0.844507i	$0.679893\pi$
$440$	−14.6667	−0.699208
$441$	−1.16105	−0.0552880
$442$	5.52072	0.262594
$443$	−2.91961	−0.138715	−0.0693573	−	0.997592i	$-0.522095\pi$
$443$	−2.91961	−0.138715	−0.0693573	+	0.997592i	$0.522095\pi$
$444$	−1.36027	−0.0645557
$445$	−1.48239	−0.0702719
$446$	−29.8243	−1.41222
$447$	8.58595	0.406102
$448$	21.4782	1.01475
$449$	−6.03263	−0.284697	−0.142349	−	0.989817i	$-0.545465\pi$
$449$	−6.03263	−0.284697	−0.142349	+	0.989817i	$0.545465\pi$
$450$	−4.68260	−0.220740
$451$	−45.0957	−2.12347
$452$	4.91295	0.231086
$453$	4.33681	0.203761
$454$	2.02941	0.0952448
$455$	−11.8657	−0.556274
$456$	−13.4356	−0.629181
$457$	10.2843	0.481078	0.240539	−	0.970639i	$-0.422676\pi$
$457$	10.2843	0.481078	0.240539	+	0.970639i	$0.422676\pi$
$458$	21.1521	0.988373
$459$	1.00000	0.0466760
$460$	1.61763	0.0754222
$461$	−20.1495	−0.938456	−0.469228	−	0.883077i	$-0.655468\pi$
$461$	−20.1495	−0.938456	−0.469228	+	0.883077i	$0.655468\pi$
$462$	−13.0329	−0.606346
$463$	38.2626	1.77821	0.889107	−	0.457700i	$-0.151327\pi$
$463$	38.2626	1.77821	0.889107	+	0.457700i	$0.151327\pi$
$464$	7.44618	0.345680
$465$	1.17921	0.0546846
$466$	4.05529	0.187858
$467$	−4.82866	−0.223444	−0.111722	−	0.993740i	$-0.535637\pi$
$467$	−4.82866	−0.223444	−0.111722	+	0.993740i	$0.535637\pi$
$468$	2.14209	0.0990182
$469$	6.15068	0.284012
$470$	−0.0102525	−0.000472913 0
$471$	−12.0823	−0.556721
$472$	14.8849	0.685131
$473$	53.0344	2.43852
$474$	1.23345	0.0566544
$475$	16.6838	0.765503
$476$	1.15646	0.0530065
$477$	1.68572	0.0771838
$478$	−2.99231	−0.136865
$479$	31.0487	1.41865	0.709326	−	0.704881i	$-0.248999\pi$
$479$	31.0487	1.41865	0.709326	+	0.704881i	$0.248999\pi$
$480$	−2.90057	−0.132392
$481$	12.7214	0.580045
$482$	−24.3295	−1.10818
$483$	7.44435	0.338730
$484$	−3.88646	−0.176657
$485$	−12.1202	−0.550348
$486$	−1.23345	−0.0559506
$487$	−4.25959	−0.193021	−0.0965103	−	0.995332i	$-0.530768\pi$
$487$	−4.25959	−0.193021	−0.0965103	+	0.995332i	$0.530768\pi$
$488$	−32.7665	−1.48327
$489$	−0.355165	−0.0160611
$490$	−1.57118	−0.0709789
$491$	−21.4393	−0.967543	−0.483772	−	0.875194i	$-0.660733\pi$
$491$	−21.4393	−0.967543	−0.483772	+	0.875194i	$0.660733\pi$
$492$	−4.93570	−0.222519
$493$	2.64634	0.119185
$494$	24.2620	1.09160
$495$	4.79739	0.215626
$496$	3.02431	0.135795
$497$	−3.03130	−0.135972
$498$	15.8587	0.710645
$499$	4.97402	0.222667	0.111334	−	0.993783i	$-0.464488\pi$
$499$	4.97402	0.222667	0.111334	+	0.993783i	$0.464488\pi$
$500$	4.61870	0.206555
$501$	4.79417	0.214188
$502$	−17.9188	−0.799755
$503$	−2.12982	−0.0949641	−0.0474821	−	0.998872i	$-0.515120\pi$
$503$	−2.12982	−0.0949641	−0.0474821	+	0.998872i	$0.515120\pi$
$504$	−7.38746	−0.329064
$505$	−4.60810	−0.205058
$506$	−16.6163	−0.738683
$507$	−7.03300	−0.312346
$508$	5.43382	0.241087
$509$	0.370084	0.0164037	0.00820184	−	0.999966i	$-0.497389\pi$
$509$	0.370084	0.0164037	0.00820184	+	0.999966i	$0.497389\pi$
$510$	1.35325	0.0599227
$511$	−1.31532	−0.0581865
$512$	−24.6437	−1.08911
$513$	4.39471	0.194031
$514$	33.6795	1.48554
$515$	−2.93053	−0.129135
$516$	5.80459	0.255533
$517$	−0.0331287	−0.00145700
$518$	−8.47133	−0.372209
$519$	19.2216	0.843736
$520$	15.0126	0.658344
$521$	14.5156	0.635939	0.317970	−	0.948101i	$-0.396999\pi$
$521$	14.5156	0.635939	0.317970	+	0.948101i	$0.396999\pi$
$522$	−3.26414	−0.142867
$523$	−16.2273	−0.709568	−0.354784	−	0.934948i	$-0.615446\pi$
$523$	−16.2273	−0.709568	−0.354784	+	0.934948i	$0.615446\pi$
$524$	−3.70481	−0.161845
$525$	9.17342	0.400361
$526$	8.43810	0.367919
$527$	1.07482	0.0468201
$528$	12.3038	0.535454
$529$	−13.5088	−0.587341
$530$	2.28119	0.0990886
$531$	−4.86874	−0.211285
$532$	5.08232	0.220347
$533$	46.1591	1.99937
$534$	1.66660	0.0721208
$535$	3.37148	0.145762
$536$	−7.78187	−0.336125
$537$	−12.4267	−0.536250
$538$	−2.90471	−0.125231
$539$	−5.07693	−0.218679
$540$	0.525072	0.0225955
$541$	−37.6619	−1.61921	−0.809606	−	0.586973i	$-0.800319\pi$
$541$	−37.6619	−1.61921	−0.809606	+	0.586973i	$0.800319\pi$
$542$	−24.0139	−1.03149
$543$	25.6064	1.09888
$544$	−2.64380	−0.113352
$545$	−11.3294	−0.485297
$546$	13.3402	0.570909
$547$	26.2506	1.12240	0.561198	−	0.827681i	$-0.310341\pi$
$547$	26.2506	1.12240	0.561198	+	0.827681i	$0.310341\pi$
$548$	−0.397831	−0.0169945
$549$	10.7177	0.457422
$550$	−20.4757	−0.873085
$551$	11.6299	0.495450
$552$	−9.41862	−0.400883
$553$	−2.41639	−0.102755
$554$	14.4184	0.612577
$555$	3.11828	0.132364
$556$	4.26352	0.180813
$557$	37.4947	1.58870	0.794350	−	0.607460i	$-0.207811\pi$
$557$	37.4947	1.58870	0.794350	+	0.607460i	$0.207811\pi$
$558$	−1.32575	−0.0561233
$559$	−54.2850	−2.29601
$560$	−7.45949	−0.315221
$561$	4.37271	0.184616
$562$	0.268143	0.0113109
$563$	−19.7661	−0.833040	−0.416520	−	0.909127i	$-0.636750\pi$
$563$	−19.7661	−0.833040	−0.416520	+	0.909127i	$0.636750\pi$
$564$	−0.00362592	−0.000152679 0
$565$	−11.2624	−0.473813
$566$	−12.7009	−0.533858
$567$	2.41639	0.101479
$568$	3.83521	0.160922
$569$	6.15618	0.258081	0.129040	−	0.991639i	$-0.458810\pi$
$569$	6.15618	0.258081	0.129040	+	0.991639i	$0.458810\pi$
$570$	5.94712	0.249097
$571$	−35.2536	−1.47532	−0.737659	−	0.675173i	$-0.764069\pi$
$571$	−35.2536	−1.47532	−0.737659	+	0.675173i	$0.764069\pi$
$572$	9.36675	0.391643
$573$	−16.9840	−0.709517
$574$	−30.7379	−1.28298
$575$	11.6956	0.487741
$576$	8.88855	0.370356
$577$	−23.0394	−0.959143	−0.479572	−	0.877503i	$-0.659208\pi$
$577$	−23.0394	−0.959143	−0.479572	+	0.877503i	$0.659208\pi$
$578$	1.23345	0.0513049
$579$	4.16013	0.172889
$580$	1.38952	0.0576965
$581$	−31.0679	−1.28891
$582$	13.6263	0.564828
$583$	7.37117	0.305282
$584$	1.66415	0.0688632
$585$	−4.91051	−0.203025
$586$	−13.8114	−0.570542
$587$	−5.90037	−0.243534	−0.121767	−	0.992559i	$-0.538856\pi$
$587$	−5.90037	−0.243534	−0.121767	+	0.992559i	$0.538856\pi$
$588$	−0.555668	−0.0229154
$589$	4.72354	0.194630
$590$	−6.58860	−0.271248
$591$	4.98288	0.204968
$592$	7.99741	0.328692
$593$	15.6673	0.643380	0.321690	−	0.946845i	$-0.395749\pi$
$593$	15.6673	0.643380	0.321690	+	0.946845i	$0.395749\pi$
$594$	−5.39354	−0.221300
$595$	−2.65107	−0.108683
$596$	4.10916	0.168318
$597$	−19.9525	−0.816603
$598$	17.0081	0.695513
$599$	14.7351	0.602058	0.301029	−	0.953615i	$-0.402670\pi$
$599$	14.7351	0.602058	0.301029	+	0.953615i	$0.402670\pi$
$600$	−11.6062	−0.473823
$601$	−6.96920	−0.284280	−0.142140	−	0.989847i	$-0.545398\pi$
$601$	−6.96920	−0.284280	−0.142140	+	0.989847i	$0.545398\pi$
$602$	36.1491	1.47333
$603$	2.54540	0.103657
$604$	2.07556	0.0844534
$605$	8.90929	0.362214
$606$	5.18073	0.210453
$607$	23.4796	0.953007	0.476504	−	0.879173i	$-0.341904\pi$
$607$	23.4796	0.953007	0.476504	+	0.879173i	$0.341904\pi$
$608$	−11.6187	−0.471202
$609$	6.39459	0.259122
$610$	14.5037	0.587238
$611$	0.0339099	0.00137185
$612$	0.478591	0.0193459
$613$	25.4375	1.02741	0.513706	−	0.857966i	$-0.328272\pi$
$613$	25.4375	1.02741	0.513706	+	0.857966i	$0.328272\pi$
$614$	22.8111	0.920582
$615$	11.3146	0.456247
$616$	−32.3033	−1.30154
$617$	36.4887	1.46898	0.734489	−	0.678620i	$-0.237422\pi$
$617$	36.4887	1.46898	0.734489	+	0.678620i	$0.237422\pi$
$618$	3.29470	0.132532
$619$	−8.75237	−0.351787	−0.175894	−	0.984409i	$-0.556281\pi$
$619$	−8.75237	−0.351787	−0.175894	+	0.984409i	$0.556281\pi$
$620$	0.564360	0.0226652
$621$	3.08077	0.123627
$622$	24.0985	0.966263
$623$	−3.26494	−0.130807
$624$	−12.5939	−0.504161
$625$	8.39378	0.335751
$626$	3.28055	0.131117
$627$	19.2168	0.767445
$628$	−5.78246	−0.230745
$629$	2.84224	0.113328
$630$	3.26997	0.130279
$631$	−35.7662	−1.42383	−0.711914	−	0.702266i	$-0.752172\pi$
$631$	−35.7662	−1.42383	−0.711914	+	0.702266i	$0.752172\pi$
$632$	3.05723	0.121610
$633$	−15.7962	−0.627843
$634$	22.8993	0.909447
$635$	−12.4565	−0.494319
$636$	0.806770	0.0319905
$637$	5.19665	0.205899
$638$	−14.2731	−0.565079
$639$	−1.25447	−0.0496262
$640$	6.22725	0.246154
$641$	22.2081	0.877168	0.438584	−	0.898690i	$-0.355480\pi$
$641$	22.2081	0.877168	0.438584	+	0.898690i	$0.355480\pi$
$642$	−3.79044	−0.149597
$643$	−37.2598	−1.46938	−0.734691	−	0.678402i	$-0.762673\pi$
$643$	−37.2598	−1.46938	−0.734691	+	0.678402i	$0.762673\pi$
$644$	3.56280	0.140394
$645$	−13.3064	−0.523939
$646$	5.42067	0.213273
$647$	−12.5079	−0.491738	−0.245869	−	0.969303i	$-0.579073\pi$
$647$	−12.5079	−0.491738	−0.245869	+	0.969303i	$0.579073\pi$
$648$	−3.05723	−0.120099
$649$	−21.2896	−0.835690
$650$	20.9585	0.822059
$651$	2.59720	0.101792
$652$	−0.169979	−0.00665689
$653$	−1.18454	−0.0463548	−0.0231774	−	0.999731i	$-0.507378\pi$
$653$	−1.18454	−0.0463548	−0.0231774	+	0.999731i	$0.507378\pi$
$654$	12.7372	0.498066
$655$	8.49288	0.331844
$656$	29.0183	1.13298
$657$	−0.544334	−0.0212365
$658$	−0.0225810	−0.000880300 0
$659$	1.51096	0.0588587	0.0294293	−	0.999567i	$-0.490631\pi$
$659$	1.51096	0.0588587	0.0294293	+	0.999567i	$0.490631\pi$
$660$	2.29599	0.0893712
$661$	19.1412	0.744505	0.372252	−	0.928132i	$-0.378586\pi$
$661$	19.1412	0.744505	0.372252	+	0.928132i	$0.378586\pi$
$662$	−18.9398	−0.736115
$663$	−4.47582	−0.173827
$664$	39.3072	1.52542
$665$	−11.6507	−0.451794
$666$	−3.50578	−0.135846
$667$	8.15277	0.315676
$668$	2.29445	0.0887748
$669$	24.1795	0.934832
$670$	3.44455	0.133075
$671$	46.8656	1.80923
$672$	−6.38847	−0.246440
$673$	32.9355	1.26957	0.634785	−	0.772689i	$-0.281089\pi$
$673$	32.9355	1.26957	0.634785	+	0.772689i	$0.281089\pi$
$674$	−6.32269	−0.243541
$675$	3.79633	0.146121
$676$	−3.36593	−0.129459
$677$	13.2093	0.507673	0.253836	−	0.967247i	$-0.418308\pi$
$677$	13.2093	0.507673	0.253836	+	0.967247i	$0.418308\pi$
$678$	12.6620	0.486280
$679$	−26.6945	−1.02444
$680$	3.35414	0.128626
$681$	−1.64530	−0.0630482
$682$	−5.79711	−0.221983
$683$	−15.4741	−0.592102	−0.296051	−	0.955172i	$-0.595670\pi$
$683$	−15.4741	−0.592102	−0.296051	+	0.955172i	$0.595670\pi$
$684$	2.10327	0.0804205
$685$	0.911986	0.0348452
$686$	−24.3241	−0.928698
$687$	−17.1487	−0.654263
$688$	−34.1267	−1.30107
$689$	−7.54498	−0.287441
$690$	4.16904	0.158713
$691$	−1.49000	−0.0566822	−0.0283411	−	0.999598i	$-0.509022\pi$
$691$	−1.49000	−0.0566822	−0.0283411	+	0.999598i	$0.509022\pi$
$692$	9.19931	0.349705
$693$	10.5662	0.401376
$694$	−21.7544	−0.825787
$695$	−9.77366	−0.370736
$696$	−8.09046	−0.306668
$697$	10.3130	0.390632
$698$	8.60453	0.325686
$699$	−3.28775	−0.124354
$700$	4.39032	0.165939
$701$	−28.3126	−1.06935	−0.534676	−	0.845057i	$-0.679566\pi$
$701$	−28.3126	−1.06935	−0.534676	+	0.845057i	$0.679566\pi$
$702$	5.52072	0.208366
$703$	12.4908	0.471100
$704$	38.8671	1.46486
$705$	0.00831203	0.000313049 0
$706$	41.4702	1.56075
$707$	−10.1493	−0.381703
$708$	−2.33014	−0.0875719
$709$	−23.3171	−0.875693	−0.437847	−	0.899050i	$-0.644259\pi$
$709$	−23.3171	−0.875693	−0.437847	+	0.899050i	$0.644259\pi$
$710$	−1.69761	−0.0637101
$711$	−1.00000	−0.0375029
$712$	4.13082	0.154809
$713$	3.31129	0.124009
$714$	2.98051	0.111543
$715$	−21.4723	−0.803017
$716$	−5.94729	−0.222261
$717$	2.42596	0.0905990
$718$	2.79975	0.104486
$719$	53.1645	1.98270	0.991350	−	0.131242i	$-0.0418965\pi$
$719$	53.1645	1.98270	0.991350	+	0.131242i	$0.0418965\pi$
$720$	−3.08704	−0.115047
$721$	−6.45446	−0.240377
$722$	0.386629	0.0143888
$723$	19.7247	0.733571
$724$	12.2550	0.455454
$725$	10.0464	0.373113
$726$	−10.0164	−0.371744
$727$	34.7258	1.28791	0.643955	−	0.765063i	$-0.277292\pi$
$727$	34.7258	1.28791	0.643955	+	0.765063i	$0.277292\pi$
$728$	33.0650	1.22547
$729$	1.00000	0.0370370
$730$	−0.736618	−0.0272634
$731$	−12.1285	−0.448588
$732$	5.12941	0.189589
$733$	−14.7233	−0.543818	−0.271909	−	0.962323i	$-0.587655\pi$
$733$	−14.7233	−0.543818	−0.271909	+	0.962323i	$0.587655\pi$
$734$	1.57972	0.0583085
$735$	1.27381	0.0469851
$736$	−8.14496	−0.300227
$737$	11.1303	0.409990
$738$	−12.7206	−0.468251
$739$	−15.9514	−0.586783	−0.293391	−	0.955992i	$-0.594784\pi$
$739$	−15.9514	−0.586783	−0.293391	+	0.955992i	$0.594784\pi$
$740$	1.49238	0.0548610
$741$	−19.6699	−0.722593
$742$	5.02430	0.184448
$743$	12.4120	0.455354	0.227677	−	0.973737i	$-0.426887\pi$
$743$	12.4120	0.455354	0.227677	+	0.973737i	$0.426887\pi$
$744$	−3.28598	−0.120470
$745$	−9.41981	−0.345115
$746$	30.8023	1.12775
$747$	−12.8571	−0.470418
$748$	2.09274	0.0765183
$749$	7.42564	0.271327
$750$	11.9036	0.434658
$751$	−0.135357	−0.00493927	−0.00246963	−	0.999997i	$-0.500786\pi$
$751$	−0.135357	−0.00493927	−0.00246963	+	0.999997i	$0.500786\pi$
$752$	0.0213178	0.000777379 0
$753$	14.5273	0.529406
$754$	14.6097	0.532054
$755$	−4.75800	−0.173161
$756$	1.15646	0.0420602
$757$	5.62820	0.204560	0.102280	−	0.994756i	$-0.467386\pi$
$757$	5.62820	0.204560	0.102280	+	0.994756i	$0.467386\pi$
$758$	19.7896	0.718790
$759$	13.4713	0.488979
$760$	14.7405	0.534693
$761$	48.2448	1.74887	0.874437	−	0.485140i	$-0.161231\pi$
$761$	48.2448	1.74887	0.874437	+	0.485140i	$0.161231\pi$
$762$	14.0044	0.507325
$763$	−24.9528	−0.903353
$764$	−8.12840	−0.294075
$765$	−1.09712	−0.0396664
$766$	−24.4578	−0.883697
$767$	21.7916	0.786850
$768$	10.7760	0.388845
$769$	−2.68720	−0.0969030	−0.0484515	−	0.998826i	$-0.515429\pi$
$769$	−2.68720	−0.0969030	−0.0484515	+	0.998826i	$0.515429\pi$
$770$	14.2987	0.515288
$771$	−27.3050	−0.983367
$772$	1.99100	0.0716577
$773$	6.72568	0.241906	0.120953	−	0.992658i	$-0.461405\pi$
$773$	6.72568	0.241906	0.120953	+	0.992658i	$0.461405\pi$
$774$	14.9599	0.537724
$775$	4.08039	0.146572
$776$	33.7740	1.21242
$777$	6.86797	0.246387
$778$	2.39827	0.0859823
$779$	45.3225	1.62385
$780$	−2.35013	−0.0841481
$781$	−5.48545	−0.196285
$782$	3.79999	0.135887
$783$	2.64634	0.0945724
$784$	3.26692	0.116676
$785$	13.2557	0.473115
$786$	−9.54826	−0.340575
$787$	25.2228	0.899095	0.449547	−	0.893256i	$-0.351585\pi$
$787$	25.2228	0.899095	0.449547	+	0.893256i	$0.351585\pi$
$788$	2.38476	0.0849536
$789$	−6.84103	−0.243547
$790$	−1.35325	−0.0481463
$791$	−24.8053	−0.881977
$792$	−13.3684	−0.475025
$793$	−47.9707	−1.70349
$794$	−7.54432	−0.267738
$795$	−1.84943	−0.0655927
$796$	−9.54911	−0.338459
$797$	28.8482	1.02185	0.510927	−	0.859624i	$-0.329302\pi$
$797$	28.8482	1.02185	0.510927	+	0.859624i	$0.329302\pi$
$798$	13.0985	0.463681
$799$	0.00757624	0.000268028 0
$800$	−10.0368	−0.354853
$801$	−1.35116	−0.0477410
$802$	−11.9946	−0.423544
$803$	−2.38022	−0.0839960
$804$	1.21821	0.0429628
$805$	−8.16734	−0.287861
$806$	5.93381	0.209010
$807$	2.35494	0.0828978
$808$	12.8409	0.451742
$809$	35.9572	1.26419	0.632095	−	0.774891i	$-0.282195\pi$
$809$	35.9572	1.26419	0.632095	+	0.774891i	$0.282195\pi$
$810$	1.35325	0.0475482
$811$	39.0365	1.37076	0.685379	−	0.728186i	$-0.259636\pi$
$811$	39.0365	1.37076	0.685379	+	0.728186i	$0.259636\pi$
$812$	3.06040	0.107399
$813$	19.4689	0.682803
$814$	−15.3298	−0.537308
$815$	0.389659	0.0136491
$816$	−2.81377	−0.0985016
$817$	−53.3011	−1.86477
$818$	43.0775	1.50617
$819$	−10.8153	−0.377919
$820$	5.41505	0.189102
$821$	−2.24726	−0.0784299	−0.0392149	−	0.999231i	$-0.512486\pi$
$821$	−2.24726	−0.0784299	−0.0392149	+	0.999231i	$0.512486\pi$
$822$	−1.02531	−0.0357620
$823$	25.0926	0.874673	0.437337	−	0.899298i	$-0.355922\pi$
$823$	25.0926	0.874673	0.437337	+	0.899298i	$0.355922\pi$
$824$	8.16620	0.284483
$825$	16.6003	0.577947
$826$	−14.5113	−0.504913
$827$	26.3802	0.917328	0.458664	−	0.888610i	$-0.348328\pi$
$827$	26.3802	0.917328	0.458664	+	0.888610i	$0.348328\pi$
$828$	1.47443	0.0512400
$829$	−49.5777	−1.72190	−0.860952	−	0.508687i	$-0.830131\pi$
$829$	−49.5777	−1.72190	−0.860952	+	0.508687i	$0.830131\pi$
$830$	−17.3989	−0.603924
$831$	−11.6894	−0.405501
$832$	−39.7836	−1.37925
$833$	1.16105	0.0402280
$834$	10.9882	0.380490
$835$	−5.25977	−0.182022
$836$	9.19699	0.318085
$837$	1.07482	0.0371514
$838$	34.1326	1.17909
$839$	−12.3551	−0.426544	−0.213272	−	0.976993i	$-0.568412\pi$
$839$	−12.3551	−0.426544	−0.213272	+	0.976993i	$0.568412\pi$
$840$	8.10492	0.279646
$841$	−21.9969	−0.758514
$842$	7.34282	0.253050
$843$	−0.217392	−0.00748738
$844$	−7.55993	−0.260224
$845$	7.71604	0.265440
$846$	−0.00934494	−0.000321286 0
$847$	19.6226	0.674241
$848$	−4.74322	−0.162883
$849$	10.2970	0.353393
$850$	4.68260	0.160612
$851$	8.75630	0.300162
$852$	−0.600380	−0.0205687
$853$	1.94184	0.0664873	0.0332436	−	0.999447i	$-0.489416\pi$
$853$	1.94184	0.0664873	0.0332436	+	0.999447i	$0.489416\pi$
$854$	31.9443	1.09311
$855$	−4.82152	−0.164892
$856$	−9.39495	−0.321113
$857$	−34.0851	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$857$	−34.0851	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$858$	24.1405	0.824144
$859$	−47.0185	−1.60425	−0.802125	−	0.597156i	$-0.796297\pi$
$859$	−47.0185	−1.60425	−0.802125	+	0.597156i	$0.796297\pi$
$860$	−6.36832	−0.217158
$861$	24.9202	0.849279
$862$	−16.4159	−0.559127
$863$	35.4450	1.20656	0.603280	−	0.797529i	$-0.293860\pi$
$863$	35.4450	1.20656	0.603280	+	0.797529i	$0.293860\pi$
$864$	−2.64380	−0.0899440
$865$	−21.0884	−0.717028
$866$	−32.1430	−1.09226
$867$	−1.00000	−0.0339618
$868$	1.24300	0.0421900
$869$	−4.37271	−0.148334
$870$	3.58115	0.121412
$871$	−11.3928	−0.386029
$872$	31.5704	1.06911
$873$	−11.0473	−0.373893
$874$	16.6998	0.564881
$875$	−23.3197	−0.788349
$876$	−0.260514	−0.00880194
$877$	−7.45408	−0.251706	−0.125853	−	0.992049i	$-0.540167\pi$
$877$	−7.45408	−0.251706	−0.125853	+	0.992049i	$0.540167\pi$
$878$	−27.6809	−0.934185
$879$	11.1973	0.377676
$880$	−13.4987	−0.455042
$881$	25.5255	0.859976	0.429988	−	0.902835i	$-0.358518\pi$
$881$	25.5255	0.859976	0.429988	+	0.902835i	$0.358518\pi$
$882$	−1.43210	−0.0482213
$883$	−6.77699	−0.228064	−0.114032	−	0.993477i	$-0.536377\pi$
$883$	−6.77699	−0.228064	−0.114032	+	0.993477i	$0.536377\pi$
$884$	−2.14209	−0.0720463
$885$	5.34159	0.179555
$886$	−3.60120	−0.120985
$887$	18.1212	0.608450	0.304225	−	0.952600i	$-0.401602\pi$
$887$	18.1212	0.608450	0.304225	+	0.952600i	$0.401602\pi$
$888$	−8.68939	−0.291597
$889$	−27.4352	−0.920147
$890$	−1.82846	−0.0612900
$891$	4.37271	0.146491
$892$	11.5721	0.387462
$893$	0.0332953	0.00111419
$894$	10.5904	0.354195
$895$	13.6335	0.455718
$896$	13.7155	0.458201
$897$	−13.7890	−0.460401
$898$	−7.44097	−0.248308
$899$	2.84435	0.0948644
$900$	1.81689	0.0605630
$901$	−1.68572	−0.0561594
$902$	−55.6235	−1.85206
$903$	−29.3072	−0.975282
$904$	31.3838	1.04381
$905$	−28.0933	−0.933852
$906$	5.34926	0.177717
$907$	−47.4498	−1.57555	−0.787773	−	0.615966i	$-0.788766\pi$
$907$	−47.4498	−1.57555	−0.787773	+	0.615966i	$0.788766\pi$
$908$	−0.787428	−0.0261317
$909$	−4.20018	−0.139311
$910$	−14.6358	−0.485173
$911$	32.5868	1.07965	0.539824	−	0.841778i	$-0.318491\pi$
$911$	32.5868	1.07965	0.539824	+	0.841778i	$0.318491\pi$
$912$	−12.3657	−0.409469
$913$	−56.2206	−1.86063
$914$	12.6852	0.419589
$915$	−11.7586	−0.388728
$916$	−8.20721	−0.271174
$917$	18.7055	0.617709
$918$	1.23345	0.0407100
$919$	−28.8100	−0.950353	−0.475176	−	0.879891i	$-0.657616\pi$
$919$	−28.8100	−0.950353	−0.475176	+	0.879891i	$0.657616\pi$
$920$	10.3334	0.340680
$921$	−18.4937	−0.609388
$922$	−24.8535	−0.818506
$923$	5.61480	0.184813
$924$	5.05689	0.166359
$925$	10.7901	0.354776
$926$	47.1951	1.55093
$927$	−2.67111	−0.0877309
$928$	−6.99640	−0.229668
$929$	−12.7441	−0.418119	−0.209059	−	0.977903i	$-0.567040\pi$
$929$	−12.7441	−0.418119	−0.209059	+	0.977903i	$0.567040\pi$
$930$	1.45450	0.0476950
$931$	5.10247	0.167227
$932$	−1.57349	−0.0515413
$933$	−19.5374	−0.639627
$934$	−5.95593	−0.194884
$935$	−4.79739	−0.156891
$936$	13.6836	0.447263
$937$	44.2354	1.44511	0.722554	−	0.691314i	$-0.242968\pi$
$937$	44.2354	1.44511	0.722554	+	0.691314i	$0.242968\pi$
$938$	7.58658	0.247711
$939$	−2.65965	−0.0867944
$940$	0.00397807	0.000129750 0
$941$	39.9359	1.30187	0.650937	−	0.759132i	$-0.274376\pi$
$941$	39.9359	1.30187	0.650937	+	0.759132i	$0.274376\pi$
$942$	−14.9029	−0.485563
$943$	31.7720	1.03464
$944$	13.6995	0.445881
$945$	−2.65107	−0.0862393
$946$	65.4155	2.12684
$947$	0.656909	0.0213467	0.0106733	−	0.999943i	$-0.496603\pi$
$947$	0.656909	0.0213467	0.0106733	+	0.999943i	$0.496603\pi$
$948$	−0.478591	−0.0155439
$949$	2.43634	0.0790871
$950$	20.5787	0.667660
$951$	−18.5652	−0.602017
$952$	7.38746	0.239429
$953$	−48.0661	−1.55701	−0.778506	−	0.627637i	$-0.784022\pi$
$953$	−48.0661	−1.55701	−0.778506	+	0.627637i	$0.784022\pi$
$954$	2.07926	0.0673184
$955$	18.6335	0.602965
$956$	1.16104	0.0375508
$957$	11.5717	0.374059
$958$	38.2972	1.23733
$959$	2.00864	0.0648623
$960$	−9.75179	−0.314738
$961$	−29.8448	−0.962734
$962$	15.6912	0.505906
$963$	3.07303	0.0990270
$964$	9.44008	0.304045
$965$	−4.56416	−0.146925
$966$	9.18227	0.295435
$967$	0.0549829	0.00176813	0.000884066	−	1.00000i	$-0.499719\pi$
$967$	0.0549829	0.00176813	0.000884066		1.00000i	$0.499719\pi$
$968$	−24.8266	−0.797957
$969$	−4.39471	−0.141178
$970$	−14.9497	−0.480005
$971$	15.0545	0.483122	0.241561	−	0.970386i	$-0.422341\pi$
$971$	15.0545	0.483122	0.241561	+	0.970386i	$0.422341\pi$
$972$	0.478591	0.0153508
$973$	−21.5264	−0.690104
$974$	−5.25401	−0.168349
$975$	−16.9917	−0.544170
$976$	−30.1572	−0.965309
$977$	−53.5592	−1.71351	−0.856756	−	0.515722i	$-0.827524\pi$
$977$	−53.5592	−1.71351	−0.856756	+	0.515722i	$0.827524\pi$
$978$	−0.438080	−0.0140083
$979$	−5.90825	−0.188829
$980$	0.609634	0.0194740
$981$	−10.3265	−0.329699
$982$	−26.4444	−0.843875
$983$	32.1100	1.02415	0.512075	−	0.858941i	$-0.328877\pi$
$983$	32.1100	1.02415	0.512075	+	0.858941i	$0.328877\pi$
$984$	−31.5291	−1.00511
$985$	−5.46681	−0.174187
$986$	3.26414	0.103951
$987$	0.0183072	0.000582723 0
$988$	−9.41386	−0.299495
$989$	−37.3651	−1.18814
$990$	5.91736	0.188066
$991$	−33.2881	−1.05743	−0.528716	−	0.848799i	$-0.677326\pi$
$991$	−33.2881	−1.05743	−0.528716	+	0.848799i	$0.677326\pi$
$992$	−2.84163	−0.0902217
$993$	15.3551	0.487278
$994$	−3.73897	−0.118593
$995$	21.8903	0.693969
$996$	−6.15332	−0.194975
$997$	−5.62358	−0.178101	−0.0890503	−	0.996027i	$-0.528383\pi$
$997$	−5.62358	−0.178101	−0.0890503	+	0.996027i	$0.528383\pi$
$998$	6.13522	0.194207
$999$	2.84224	0.0899246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.16	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.16	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.23345 q^{2} -1.00000 q^{3} -0.478591 q^{4} +1.09712 q^{5} -1.23345 q^{6} +2.41639 q^{7} -3.05723 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.23345 q^{2} -1.00000 q^{3} -0.478591 q^{4} +1.09712 q^{5} -1.23345 q^{6} +2.41639 q^{7} -3.05723 q^{8} +1.00000 q^{9} +1.35325 q^{10} +4.37271 q^{11} +0.478591 q^{12} -4.47582 q^{13} +2.98051 q^{14} -1.09712 q^{15} -2.81377 q^{16} -1.00000 q^{17} +1.23345 q^{18} -4.39471 q^{19} -0.525072 q^{20} -2.41639 q^{21} +5.39354 q^{22} -3.08077 q^{23} +3.05723 q^{24} -3.79633 q^{25} -5.52072 q^{26} -1.00000 q^{27} -1.15646 q^{28} -2.64634 q^{29} -1.35325 q^{30} -1.07482 q^{31} +2.64380 q^{32} -4.37271 q^{33} -1.23345 q^{34} +2.65107 q^{35} -0.478591 q^{36} -2.84224 q^{37} -5.42067 q^{38} +4.47582 q^{39} -3.35414 q^{40} -10.3130 q^{41} -2.98051 q^{42} +12.1285 q^{43} -2.09274 q^{44} +1.09712 q^{45} -3.79999 q^{46} -0.00757624 q^{47} +2.81377 q^{48} -1.16105 q^{49} -4.68260 q^{50} +1.00000 q^{51} +2.14209 q^{52} +1.68572 q^{53} -1.23345 q^{54} +4.79739 q^{55} -7.38746 q^{56} +4.39471 q^{57} -3.26414 q^{58} -4.86874 q^{59} +0.525072 q^{60} +10.7177 q^{61} -1.32575 q^{62} +2.41639 q^{63} +8.88855 q^{64} -4.91051 q^{65} -5.39354 q^{66} +2.54540 q^{67} +0.478591 q^{68} +3.08077 q^{69} +3.26997 q^{70} -1.25447 q^{71} -3.05723 q^{72} -0.544334 q^{73} -3.50578 q^{74} +3.79633 q^{75} +2.10327 q^{76} +10.5662 q^{77} +5.52072 q^{78} -1.00000 q^{79} -3.08704 q^{80} +1.00000 q^{81} -12.7206 q^{82} -12.8571 q^{83} +1.15646 q^{84} -1.09712 q^{85} +14.9599 q^{86} +2.64634 q^{87} -13.3684 q^{88} -1.35116 q^{89} +1.35325 q^{90} -10.8153 q^{91} +1.47443 q^{92} +1.07482 q^{93} -0.00934494 q^{94} -4.82152 q^{95} -2.64380 q^{96} -11.0473 q^{97} -1.43210 q^{98} +4.37271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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