LMFDB - Embedded newform 4022.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.97777 q^{3} +1.00000 q^{4} -2.48115 q^{5} -2.97777 q^{6} +4.88773 q^{7} +1.00000 q^{8} +5.86711 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.97777 q^{3} +1.00000 q^{4} -2.48115 q^{5} -2.97777 q^{6} +4.88773 q^{7} +1.00000 q^{8} +5.86711 q^{9} -2.48115 q^{10} +1.65983 q^{11} -2.97777 q^{12} +4.91476 q^{13} +4.88773 q^{14} +7.38828 q^{15} +1.00000 q^{16} +4.32695 q^{17} +5.86711 q^{18} +1.98481 q^{19} -2.48115 q^{20} -14.5545 q^{21} +1.65983 q^{22} +4.62047 q^{23} -2.97777 q^{24} +1.15608 q^{25} +4.91476 q^{26} -8.53759 q^{27} +4.88773 q^{28} -1.48970 q^{29} +7.38828 q^{30} +0.164647 q^{31} +1.00000 q^{32} -4.94259 q^{33} +4.32695 q^{34} -12.1272 q^{35} +5.86711 q^{36} +0.0499696 q^{37} +1.98481 q^{38} -14.6350 q^{39} -2.48115 q^{40} +2.74657 q^{41} -14.5545 q^{42} -0.530368 q^{43} +1.65983 q^{44} -14.5572 q^{45} +4.62047 q^{46} +7.52651 q^{47} -2.97777 q^{48} +16.8899 q^{49} +1.15608 q^{50} -12.8847 q^{51} +4.91476 q^{52} -9.24138 q^{53} -8.53759 q^{54} -4.11828 q^{55} +4.88773 q^{56} -5.91031 q^{57} -1.48970 q^{58} -8.61237 q^{59} +7.38828 q^{60} +13.1269 q^{61} +0.164647 q^{62} +28.6768 q^{63} +1.00000 q^{64} -12.1942 q^{65} -4.94259 q^{66} -7.60968 q^{67} +4.32695 q^{68} -13.7587 q^{69} -12.1272 q^{70} -13.7830 q^{71} +5.86711 q^{72} -10.0180 q^{73} +0.0499696 q^{74} -3.44255 q^{75} +1.98481 q^{76} +8.11280 q^{77} -14.6350 q^{78} +4.66957 q^{79} -2.48115 q^{80} +7.82164 q^{81} +2.74657 q^{82} -14.4264 q^{83} -14.5545 q^{84} -10.7358 q^{85} -0.530368 q^{86} +4.43598 q^{87} +1.65983 q^{88} +12.5130 q^{89} -14.5572 q^{90} +24.0220 q^{91} +4.62047 q^{92} -0.490281 q^{93} +7.52651 q^{94} -4.92461 q^{95} -2.97777 q^{96} -0.564799 q^{97} +16.8899 q^{98} +9.73840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−2.97777	−1.71922	−0.859608	−	0.510954i	$-0.829292\pi$
$3$	−2.97777	−1.71922	−0.859608	+	0.510954i	$0.829292\pi$
$4$	1.00000	0.500000
$5$	−2.48115	−1.10960	−0.554801	−	0.831983i	$-0.687206\pi$
$5$	−2.48115	−1.10960	−0.554801	+	0.831983i	$0.687206\pi$
$6$	−2.97777	−1.21567
$7$	4.88773	1.84739	0.923694	−	0.383131i	$-0.125154\pi$
$7$	4.88773	1.84739	0.923694	+	0.383131i	$0.125154\pi$
$8$	1.00000	0.353553
$9$	5.86711	1.95570
$10$	−2.48115	−0.784607
$11$	1.65983	0.500458	0.250229	−	0.968187i	$-0.419494\pi$
$11$	1.65983	0.500458	0.250229	+	0.968187i	$0.419494\pi$
$12$	−2.97777	−0.859608
$13$	4.91476	1.36311	0.681554	−	0.731768i	$-0.261305\pi$
$13$	4.91476	1.36311	0.681554	+	0.731768i	$0.261305\pi$
$14$	4.88773	1.30630
$15$	7.38828	1.90765
$16$	1.00000	0.250000
$17$	4.32695	1.04944	0.524720	−	0.851275i	$-0.324170\pi$
$17$	4.32695	1.04944	0.524720	+	0.851275i	$0.324170\pi$
$18$	5.86711	1.38289
$19$	1.98481	0.455347	0.227674	−	0.973738i	$-0.426888\pi$
$19$	1.98481	0.455347	0.227674	+	0.973738i	$0.426888\pi$
$20$	−2.48115	−0.554801
$21$	−14.5545	−3.17606
$22$	1.65983	0.353877
$23$	4.62047	0.963435	0.481718	−	0.876327i	$-0.340013\pi$
$23$	4.62047	0.963435	0.481718	+	0.876327i	$0.340013\pi$
$24$	−2.97777	−0.607835
$25$	1.15608	0.231217
$26$	4.91476	0.963863
$27$	−8.53759	−1.64306
$28$	4.88773	0.923694
$29$	−1.48970	−0.276630	−0.138315	−	0.990388i	$-0.544169\pi$
$29$	−1.48970	−0.276630	−0.138315	+	0.990388i	$0.544169\pi$
$30$	7.38828	1.34891
$31$	0.164647	0.0295715	0.0147858	−	0.999891i	$-0.495293\pi$
$31$	0.164647	0.0295715	0.0147858	+	0.999891i	$0.495293\pi$
$32$	1.00000	0.176777
$33$	−4.94259	−0.860395
$34$	4.32695	0.742067
$35$	−12.1272	−2.04987
$36$	5.86711	0.977852
$37$	0.0499696	0.00821495	0.00410747	−	0.999992i	$-0.498693\pi$
$37$	0.0499696	0.00821495	0.00410747	+	0.999992i	$0.498693\pi$
$38$	1.98481	0.321979
$39$	−14.6350	−2.34348
$40$	−2.48115	−0.392304
$41$	2.74657	0.428942	0.214471	−	0.976730i	$-0.431197\pi$
$41$	2.74657	0.428942	0.214471	+	0.976730i	$0.431197\pi$
$42$	−14.5545	−2.24581
$43$	−0.530368	−0.0808804	−0.0404402	−	0.999182i	$-0.512876\pi$
$43$	−0.530368	−0.0808804	−0.0404402	+	0.999182i	$0.512876\pi$
$44$	1.65983	0.250229
$45$	−14.5572	−2.17005
$46$	4.62047	0.681251
$47$	7.52651	1.09785	0.548927	−	0.835870i	$-0.315036\pi$
$47$	7.52651	1.09785	0.548927	+	0.835870i	$0.315036\pi$
$48$	−2.97777	−0.429804
$49$	16.8899	2.41284
$50$	1.15608	0.163495
$51$	−12.8847	−1.80421
$52$	4.91476	0.681554
$53$	−9.24138	−1.26940	−0.634700	−	0.772758i	$-0.718876\pi$
$53$	−9.24138	−1.26940	−0.634700	+	0.772758i	$0.718876\pi$
$54$	−8.53759	−1.16182
$55$	−4.11828	−0.555309
$56$	4.88773	0.653150
$57$	−5.91031	−0.782840
$58$	−1.48970	−0.195607
$59$	−8.61237	−1.12124	−0.560618	−	0.828075i	$-0.689436\pi$
$59$	−8.61237	−1.12124	−0.560618	+	0.828075i	$0.689436\pi$
$60$	7.38828	0.953823
$61$	13.1269	1.68073	0.840366	−	0.542019i	$-0.182340\pi$
$61$	13.1269	1.68073	0.840366	+	0.542019i	$0.182340\pi$
$62$	0.164647	0.0209102
$63$	28.6768	3.61294
$64$	1.00000	0.125000
$65$	−12.1942	−1.51251
$66$	−4.94259	−0.608391
$67$	−7.60968	−0.929670	−0.464835	−	0.885397i	$-0.653886\pi$
$67$	−7.60968	−0.929670	−0.464835	+	0.885397i	$0.653886\pi$
$68$	4.32695	0.524720
$69$	−13.7587	−1.65635
$70$	−12.1272	−1.44947
$71$	−13.7830	−1.63574	−0.817868	−	0.575405i	$-0.804844\pi$
$71$	−13.7830	−1.63574	−0.817868	+	0.575405i	$0.804844\pi$
$72$	5.86711	0.691445
$73$	−10.0180	−1.17252	−0.586259	−	0.810123i	$-0.699400\pi$
$73$	−10.0180	−1.17252	−0.586259	+	0.810123i	$0.699400\pi$
$74$	0.0499696	0.00580885
$75$	−3.44255	−0.397511
$76$	1.98481	0.227674
$77$	8.11280	0.924539
$78$	−14.6350	−1.65709
$79$	4.66957	0.525368	0.262684	−	0.964882i	$-0.415392\pi$
$79$	4.66957	0.525368	0.262684	+	0.964882i	$0.415392\pi$
$80$	−2.48115	−0.277401
$81$	7.82164	0.869072
$82$	2.74657	0.303308
$83$	−14.4264	−1.58351	−0.791754	−	0.610840i	$-0.790832\pi$
$83$	−14.4264	−1.58351	−0.791754	+	0.610840i	$0.790832\pi$
$84$	−14.5545	−1.58803
$85$	−10.7358	−1.16446
$86$	−0.530368	−0.0571911
$87$	4.43598	0.475587
$88$	1.65983	0.176938
$89$	12.5130	1.32638	0.663190	−	0.748451i	$-0.269202\pi$
$89$	12.5130	1.32638	0.663190	+	0.748451i	$0.269202\pi$
$90$	−14.5572	−1.53446
$91$	24.0220	2.51819
$92$	4.62047	0.481718
$93$	−0.490281	−0.0508398
$94$	7.52651	0.776300
$95$	−4.92461	−0.505254
$96$	−2.97777	−0.303917
$97$	−0.564799	−0.0573467	−0.0286733	−	0.999589i	$-0.509128\pi$
$97$	−0.564799	−0.0573467	−0.0286733	+	0.999589i	$0.509128\pi$
$98$	16.8899	1.70614
$99$	9.73840	0.978746
$100$	1.15608	0.115608
$101$	4.61456	0.459166	0.229583	−	0.973289i	$-0.426264\pi$
$101$	4.61456	0.459166	0.229583	+	0.973289i	$0.426264\pi$
$102$	−12.8847	−1.27577
$103$	6.64751	0.654999	0.327500	−	0.944851i	$-0.393794\pi$
$103$	6.64751	0.654999	0.327500	+	0.944851i	$0.393794\pi$
$104$	4.91476	0.481931
$105$	36.1119	3.52416
$106$	−9.24138	−0.897602
$107$	0.829332	0.0801746	0.0400873	−	0.999196i	$-0.487236\pi$
$107$	0.829332	0.0801746	0.0400873	+	0.999196i	$0.487236\pi$
$108$	−8.53759	−0.821530
$109$	−1.86654	−0.178782	−0.0893908	−	0.995997i	$-0.528492\pi$
$109$	−1.86654	−0.178782	−0.0893908	+	0.995997i	$0.528492\pi$
$110$	−4.11828	−0.392663
$111$	−0.148798	−0.0141233
$112$	4.88773	0.461847
$113$	−20.8708	−1.96336	−0.981678	−	0.190548i	$-0.938974\pi$
$113$	−20.8708	−1.96336	−0.981678	+	0.190548i	$0.938974\pi$
$114$	−5.91031	−0.553551
$115$	−11.4641	−1.06903
$116$	−1.48970	−0.138315
$117$	28.8354	2.66583
$118$	−8.61237	−0.792833
$119$	21.1490	1.93872
$120$	7.38828	0.674454
$121$	−8.24496	−0.749542
$122$	13.1269	1.18846
$123$	−8.17865	−0.737444
$124$	0.164647	0.0147858
$125$	9.53732	0.853044
$126$	28.6768	2.55474
$127$	10.5161	0.933151	0.466575	−	0.884481i	$-0.345488\pi$
$127$	10.5161	0.933151	0.466575	+	0.884481i	$0.345488\pi$
$128$	1.00000	0.0883883
$129$	1.57931	0.139051
$130$	−12.1942	−1.06950
$131$	11.1935	0.977983	0.488992	−	0.872288i	$-0.337365\pi$
$131$	11.1935	0.977983	0.488992	+	0.872288i	$0.337365\pi$
$132$	−4.94259	−0.430197
$133$	9.70122	0.841203
$134$	−7.60968	−0.657376
$135$	21.1830	1.82314
$136$	4.32695	0.371033
$137$	11.8716	1.01426	0.507130	−	0.861870i	$-0.330706\pi$
$137$	11.8716	1.01426	0.507130	+	0.861870i	$0.330706\pi$
$138$	−13.7587	−1.17122
$139$	9.02382	0.765390	0.382695	−	0.923875i	$-0.374996\pi$
$139$	9.02382	0.765390	0.382695	+	0.923875i	$0.374996\pi$
$140$	−12.1272	−1.02493
$141$	−22.4122	−1.88745
$142$	−13.7830	−1.15664
$143$	8.15766	0.682178
$144$	5.86711	0.488926
$145$	3.69616	0.306949
$146$	−10.0180	−0.829096
$147$	−50.2942	−4.14820
$148$	0.0499696	0.00410747
$149$	−5.99410	−0.491055	−0.245528	−	0.969390i	$-0.578961\pi$
$149$	−5.99410	−0.491055	−0.245528	+	0.969390i	$0.578961\pi$
$150$	−3.44255	−0.281083
$151$	10.0428	0.817273	0.408636	−	0.912697i	$-0.366004\pi$
$151$	10.0428	0.817273	0.408636	+	0.912697i	$0.366004\pi$
$152$	1.98481	0.160989
$153$	25.3867	2.05239
$154$	8.11280	0.653748
$155$	−0.408514	−0.0328126
$156$	−14.6350	−1.17174
$157$	18.0852	1.44335	0.721676	−	0.692230i	$-0.243372\pi$
$157$	18.0852	1.44335	0.721676	+	0.692230i	$0.243372\pi$
$158$	4.66957	0.371491
$159$	27.5187	2.18237
$160$	−2.48115	−0.196152
$161$	22.5836	1.77984
$162$	7.82164	0.614526
$163$	−7.20207	−0.564109	−0.282055	−	0.959398i	$-0.591016\pi$
$163$	−7.20207	−0.564109	−0.282055	+	0.959398i	$0.591016\pi$
$164$	2.74657	0.214471
$165$	12.2633	0.954696
$166$	−14.4264	−1.11971
$167$	21.5291	1.66597	0.832986	−	0.553294i	$-0.186629\pi$
$167$	21.5291	1.66597	0.832986	+	0.553294i	$0.186629\pi$
$168$	−14.5545	−1.12291
$169$	11.1548	0.858063
$170$	−10.7358	−0.823399
$171$	11.6451	0.890524
$172$	−0.530368	−0.0404402
$173$	−19.5382	−1.48546	−0.742732	−	0.669589i	$-0.766470\pi$
$173$	−19.5382	−1.48546	−0.742732	+	0.669589i	$0.766470\pi$
$174$	4.43598	0.336291
$175$	5.65062	0.427147
$176$	1.65983	0.125114
$177$	25.6457	1.92765
$178$	12.5130	0.937892
$179$	15.4318	1.15343	0.576713	−	0.816947i	$-0.304335\pi$
$179$	15.4318	1.15343	0.576713	+	0.816947i	$0.304335\pi$
$180$	−14.5572	−1.08503
$181$	0.313819	0.0233260	0.0116630	−	0.999932i	$-0.496287\pi$
$181$	0.313819	0.0233260	0.0116630	+	0.999932i	$0.496287\pi$
$182$	24.0220	1.78063
$183$	−39.0890	−2.88954
$184$	4.62047	0.340626
$185$	−0.123982	−0.00911532
$186$	−0.490281	−0.0359492
$187$	7.18201	0.525200
$188$	7.52651	0.548927
$189$	−41.7294	−3.03537
$190$	−4.92461	−0.357269
$191$	1.44125	0.104285	0.0521425	−	0.998640i	$-0.483395\pi$
$191$	1.44125	0.104285	0.0521425	+	0.998640i	$0.483395\pi$
$192$	−2.97777	−0.214902
$193$	6.57378	0.473191	0.236596	−	0.971608i	$-0.423968\pi$
$193$	6.57378	0.473191	0.236596	+	0.971608i	$0.423968\pi$
$194$	−0.564799	−0.0405502
$195$	36.3116	2.60033
$196$	16.8899	1.20642
$197$	4.07409	0.290267	0.145134	−	0.989412i	$-0.453639\pi$
$197$	4.07409	0.290267	0.145134	+	0.989412i	$0.453639\pi$
$198$	9.73840	0.692078
$199$	−3.36709	−0.238687	−0.119343	−	0.992853i	$-0.538079\pi$
$199$	−3.36709	−0.238687	−0.119343	+	0.992853i	$0.538079\pi$
$200$	1.15608	0.0817474
$201$	22.6599	1.59830
$202$	4.61456	0.324680
$203$	−7.28125	−0.511043
$204$	−12.8847	−0.902107
$205$	−6.81464	−0.475955
$206$	6.64751	0.463154
$207$	27.1088	1.88419
$208$	4.91476	0.340777
$209$	3.29445	0.227882
$210$	36.1119	2.49196
$211$	12.2887	0.845990	0.422995	−	0.906132i	$-0.360979\pi$
$211$	12.2887	0.845990	0.422995	+	0.906132i	$0.360979\pi$
$212$	−9.24138	−0.634700
$213$	41.0425	2.81218
$214$	0.829332	0.0566920
$215$	1.31592	0.0897451
$216$	−8.53759	−0.580909
$217$	0.804751	0.0546301
$218$	−1.86654	−0.126418
$219$	29.8313	2.01581
$220$	−4.11828	−0.277654
$221$	21.2659	1.43050
$222$	−0.148798	−0.00998666
$223$	−14.8872	−0.996920	−0.498460	−	0.866913i	$-0.666101\pi$
$223$	−14.8872	−0.996920	−0.498460	+	0.866913i	$0.666101\pi$
$224$	4.88773	0.326575
$225$	6.78287	0.452191
$226$	−20.8708	−1.38830
$227$	−1.01835	−0.0675903	−0.0337952	−	0.999429i	$-0.510759\pi$
$227$	−1.01835	−0.0675903	−0.0337952	+	0.999429i	$0.510759\pi$
$228$	−5.91031	−0.391420
$229$	−23.9040	−1.57962	−0.789809	−	0.613352i	$-0.789821\pi$
$229$	−23.9040	−1.57962	−0.789809	+	0.613352i	$0.789821\pi$
$230$	−11.4641	−0.755918
$231$	−24.1580	−1.58948
$232$	−1.48970	−0.0978035
$233$	−15.1825	−0.994637	−0.497319	−	0.867568i	$-0.665682\pi$
$233$	−15.1825	−0.994637	−0.497319	+	0.867568i	$0.665682\pi$
$234$	28.8354	1.88503
$235$	−18.6744	−1.21818
$236$	−8.61237	−0.560618
$237$	−13.9049	−0.903221
$238$	21.1490	1.37089
$239$	−22.7323	−1.47043	−0.735217	−	0.677832i	$-0.762920\pi$
$239$	−22.7323	−1.47043	−0.735217	+	0.677832i	$0.762920\pi$
$240$	7.38828	0.476911
$241$	0.307193	0.0197880	0.00989401	−	0.999951i	$-0.496851\pi$
$241$	0.307193	0.0197880	0.00989401	+	0.999951i	$0.496851\pi$
$242$	−8.24496	−0.530006
$243$	2.32172	0.148938
$244$	13.1269	0.840366
$245$	−41.9063	−2.67730
$246$	−8.17865	−0.521452
$247$	9.75486	0.620687
$248$	0.164647	0.0104551
$249$	42.9586	2.72239
$250$	9.53732	0.603193
$251$	−25.6993	−1.62213	−0.811063	−	0.584959i	$-0.801111\pi$
$251$	−25.6993	−1.62213	−0.811063	+	0.584959i	$0.801111\pi$
$252$	28.6768	1.80647
$253$	7.66920	0.482158
$254$	10.5161	0.659837
$255$	31.9687	2.00196
$256$	1.00000	0.0625000
$257$	−29.2690	−1.82575	−0.912875	−	0.408240i	$-0.866143\pi$
$257$	−29.2690	−1.82575	−0.912875	+	0.408240i	$0.866143\pi$
$258$	1.57931	0.0983238
$259$	0.244238	0.0151762
$260$	−12.1942	−0.756254
$261$	−8.74023	−0.541006
$262$	11.1935	0.691539
$263$	−1.73162	−0.106776	−0.0533880	−	0.998574i	$-0.517002\pi$
$263$	−1.73162	−0.106776	−0.0533880	+	0.998574i	$0.517002\pi$
$264$	−4.94259	−0.304195
$265$	22.9292	1.40853
$266$	9.70122	0.594820
$267$	−37.2610	−2.28033
$268$	−7.60968	−0.464835
$269$	2.40948	0.146908	0.0734542	−	0.997299i	$-0.476598\pi$
$269$	2.40948	0.146908	0.0734542	+	0.997299i	$0.476598\pi$
$270$	21.1830	1.28916
$271$	9.45179	0.574155	0.287078	−	0.957907i	$-0.407316\pi$
$271$	9.45179	0.574155	0.287078	+	0.957907i	$0.407316\pi$
$272$	4.32695	0.262360
$273$	−71.5320	−4.32931
$274$	11.8716	0.717190
$275$	1.91890	0.115714
$276$	−13.7587	−0.828176
$277$	2.53448	0.152282	0.0761411	−	0.997097i	$-0.475740\pi$
$277$	2.53448	0.152282	0.0761411	+	0.997097i	$0.475740\pi$
$278$	9.02382	0.541213
$279$	0.966003	0.0578331
$280$	−12.1272	−0.724737
$281$	−1.98212	−0.118243	−0.0591216	−	0.998251i	$-0.518830\pi$
$281$	−1.98212	−0.118243	−0.0591216	+	0.998251i	$0.518830\pi$
$282$	−22.4122	−1.33463
$283$	−19.2185	−1.14242	−0.571212	−	0.820803i	$-0.693526\pi$
$283$	−19.2185	−1.14242	−0.571212	+	0.820803i	$0.693526\pi$
$284$	−13.7830	−0.817868
$285$	14.6643	0.868641
$286$	8.15766	0.482372
$287$	13.4245	0.792423
$288$	5.86711	0.345723
$289$	1.72254	0.101326
$290$	3.69616	0.217046
$291$	1.68184	0.0985913
$292$	−10.0180	−0.586259
$293$	−19.6336	−1.14701	−0.573505	−	0.819202i	$-0.694417\pi$
$293$	−19.6336	−1.14701	−0.573505	+	0.819202i	$0.694417\pi$
$294$	−50.2942	−2.93322
$295$	21.3686	1.24413
$296$	0.0499696	0.00290442
$297$	−14.1709	−0.822282
$298$	−5.99410	−0.347229
$299$	22.7085	1.31327
$300$	−3.44255	−0.198756
$301$	−2.59230	−0.149418
$302$	10.0428	0.577899
$303$	−13.7411	−0.789406
$304$	1.98481	0.113837
$305$	−32.5698	−1.86494
$306$	25.3867	1.45126
$307$	15.7591	0.899421	0.449711	−	0.893174i	$-0.351527\pi$
$307$	15.7591	0.899421	0.449711	+	0.893174i	$0.351527\pi$
$308$	8.11280	0.462270
$309$	−19.7948	−1.12608
$310$	−0.408514	−0.0232020
$311$	22.6432	1.28398	0.641990	−	0.766713i	$-0.278109\pi$
$311$	22.6432	1.28398	0.641990	+	0.766713i	$0.278109\pi$
$312$	−14.6350	−0.828544
$313$	13.3409	0.754072	0.377036	−	0.926199i	$-0.376943\pi$
$313$	13.3409	0.754072	0.377036	+	0.926199i	$0.376943\pi$
$314$	18.0852	1.02060
$315$	−71.1514	−4.00893
$316$	4.66957	0.262684
$317$	15.5186	0.871614	0.435807	−	0.900040i	$-0.356463\pi$
$317$	15.5186	0.871614	0.435807	+	0.900040i	$0.356463\pi$
$318$	27.5187	1.54317
$319$	−2.47265	−0.138442
$320$	−2.48115	−0.138700
$321$	−2.46956	−0.137837
$322$	22.5836	1.25854
$323$	8.58819	0.477860
$324$	7.82164	0.434536
$325$	5.68187	0.315173
$326$	−7.20207	−0.398886
$327$	5.55811	0.307364
$328$	2.74657	0.151654
$329$	36.7876	2.02816
$330$	12.2633	0.675072
$331$	−28.5387	−1.56863	−0.784313	−	0.620365i	$-0.786984\pi$
$331$	−28.5387	−1.56863	−0.784313	+	0.620365i	$0.786984\pi$
$332$	−14.4264	−0.791754
$333$	0.293177	0.0160660
$334$	21.5291	1.17802
$335$	18.8807	1.03156
$336$	−14.5545	−0.794015
$337$	−14.0029	−0.762785	−0.381392	−	0.924413i	$-0.624555\pi$
$337$	−14.0029	−0.762785	−0.381392	+	0.924413i	$0.624555\pi$
$338$	11.1548	0.606742
$339$	62.1483	3.37543
$340$	−10.7358	−0.582231
$341$	0.273286	0.0147993
$342$	11.6451	0.629695
$343$	48.3392	2.61007
$344$	−0.530368	−0.0285955
$345$	34.1373	1.83789
$346$	−19.5382	−1.05038
$347$	27.1412	1.45702	0.728509	−	0.685036i	$-0.240214\pi$
$347$	27.1412	1.45702	0.728509	+	0.685036i	$0.240214\pi$
$348$	4.43598	0.237793
$349$	−10.1433	−0.542956	−0.271478	−	0.962445i	$-0.587512\pi$
$349$	−10.1433	−0.542956	−0.271478	+	0.962445i	$0.587512\pi$
$350$	5.65062	0.302039
$351$	−41.9602	−2.23967
$352$	1.65983	0.0884692
$353$	3.36254	0.178970	0.0894849	−	0.995988i	$-0.471478\pi$
$353$	3.36254	0.178970	0.0894849	+	0.995988i	$0.471478\pi$
$354$	25.6457	1.36305
$355$	34.1975	1.81502
$356$	12.5130	0.663190
$357$	−62.9768	−3.33309
$358$	15.4318	0.815596
$359$	−31.9560	−1.68657	−0.843287	−	0.537464i	$-0.819382\pi$
$359$	−31.9560	−1.68657	−0.843287	+	0.537464i	$0.819382\pi$
$360$	−14.5572	−0.767229
$361$	−15.0605	−0.792659
$362$	0.313819	0.0164940
$363$	24.5516	1.28862
$364$	24.0220	1.25909
$365$	24.8561	1.30103
$366$	−39.0890	−2.04321
$367$	24.6470	1.28656	0.643281	−	0.765630i	$-0.277573\pi$
$367$	24.6470	1.28656	0.643281	+	0.765630i	$0.277573\pi$
$368$	4.62047	0.240859
$369$	16.1144	0.838884
$370$	−0.123982	−0.00644551
$371$	−45.1694	−2.34508
$372$	−0.490281	−0.0254199
$373$	22.4677	1.16334	0.581668	−	0.813426i	$-0.302400\pi$
$373$	22.4677	1.16334	0.581668	+	0.813426i	$0.302400\pi$
$374$	7.18201	0.371373
$375$	−28.3999	−1.46657
$376$	7.52651	0.388150
$377$	−7.32151	−0.377077
$378$	−41.7294	−2.14633
$379$	−7.33839	−0.376948	−0.188474	−	0.982078i	$-0.560354\pi$
$379$	−7.33839	−0.376948	−0.188474	+	0.982078i	$0.560354\pi$
$380$	−4.92461	−0.252627
$381$	−31.3144	−1.60429
$382$	1.44125	0.0737407
$383$	−18.4303	−0.941743	−0.470872	−	0.882202i	$-0.656060\pi$
$383$	−18.4303	−0.941743	−0.470872	+	0.882202i	$0.656060\pi$
$384$	−2.97777	−0.151959
$385$	−20.1290	−1.02587
$386$	6.57378	0.334597
$387$	−3.11173	−0.158178
$388$	−0.564799	−0.0286733
$389$	−15.1914	−0.770234	−0.385117	−	0.922868i	$-0.625839\pi$
$389$	−15.1914	−0.770234	−0.385117	+	0.922868i	$0.625839\pi$
$390$	36.3116	1.83871
$391$	19.9926	1.01107
$392$	16.8899	0.853069
$393$	−33.3318	−1.68136
$394$	4.07409	0.205250
$395$	−11.5859	−0.582950
$396$	9.73840	0.489373
$397$	−25.8874	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$397$	−25.8874	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$398$	−3.36709	−0.168777
$399$	−28.8880	−1.44621
$400$	1.15608	0.0578042
$401$	8.80464	0.439683	0.219841	−	0.975536i	$-0.429446\pi$
$401$	8.80464	0.439683	0.219841	+	0.975536i	$0.429446\pi$
$402$	22.6599	1.13017
$403$	0.809201	0.0403092
$404$	4.61456	0.229583
$405$	−19.4066	−0.964324
$406$	−7.28125	−0.361362
$407$	0.0829410	0.00411123
$408$	−12.8847	−0.637886
$409$	14.7189	0.727801	0.363900	−	0.931438i	$-0.381445\pi$
$409$	14.7189	0.727801	0.363900	+	0.931438i	$0.381445\pi$
$410$	−6.81464	−0.336551
$411$	−35.3509	−1.74373
$412$	6.64751	0.327500
$413$	−42.0950	−2.07136
$414$	27.1088	1.33233
$415$	35.7941	1.75706
$416$	4.91476	0.240966
$417$	−26.8709	−1.31587
$418$	3.29445	0.161137
$419$	11.6333	0.568326	0.284163	−	0.958776i	$-0.408284\pi$
$419$	11.6333	0.568326	0.284163	+	0.958776i	$0.408284\pi$
$420$	36.1119	1.76208
$421$	−13.6002	−0.662833	−0.331417	−	0.943484i	$-0.607527\pi$
$421$	−13.6002	−0.662833	−0.331417	+	0.943484i	$0.607527\pi$
$422$	12.2887	0.598205
$423$	44.1589	2.14708
$424$	−9.24138	−0.448801
$425$	5.00232	0.242648
$426$	41.0425	1.98851
$427$	64.1609	3.10497
$428$	0.829332	0.0400873
$429$	−24.2916	−1.17281
$430$	1.31592	0.0634594
$431$	20.4742	0.986206	0.493103	−	0.869971i	$-0.335863\pi$
$431$	20.4742	0.986206	0.493103	+	0.869971i	$0.335863\pi$
$432$	−8.53759	−0.410765
$433$	17.1401	0.823702	0.411851	−	0.911251i	$-0.364882\pi$
$433$	17.1401	0.823702	0.411851	+	0.911251i	$0.364882\pi$
$434$	0.804751	0.0386293
$435$	−11.0063	−0.527712
$436$	−1.86654	−0.0893908
$437$	9.17077	0.438697
$438$	29.8313	1.42540
$439$	30.8397	1.47190	0.735949	−	0.677037i	$-0.236736\pi$
$439$	30.8397	1.47190	0.735949	+	0.677037i	$0.236736\pi$
$440$	−4.11828	−0.196331
$441$	99.0949	4.71881
$442$	21.2659	1.01152
$443$	−24.8697	−1.18160	−0.590798	−	0.806820i	$-0.701187\pi$
$443$	−24.8697	−1.18160	−0.590798	+	0.806820i	$0.701187\pi$
$444$	−0.148798	−0.00706164
$445$	−31.0467	−1.47175
$446$	−14.8872	−0.704929
$447$	17.8490	0.844230
$448$	4.88773	0.230924
$449$	−7.44174	−0.351197	−0.175599	−	0.984462i	$-0.556186\pi$
$449$	−7.44174	−0.351197	−0.175599	+	0.984462i	$0.556186\pi$
$450$	6.78287	0.319747
$451$	4.55884	0.214667
$452$	−20.8708	−0.981678
$453$	−29.9052	−1.40507
$454$	−1.01835	−0.0477936
$455$	−59.6021	−2.79419
$456$	−5.91031	−0.276776
$457$	17.0074	0.795572	0.397786	−	0.917478i	$-0.369779\pi$
$457$	17.0074	0.795572	0.397786	+	0.917478i	$0.369779\pi$
$458$	−23.9040	−1.11696
$459$	−36.9418	−1.72429
$460$	−11.4641	−0.534515
$461$	−6.23888	−0.290574	−0.145287	−	0.989390i	$-0.546410\pi$
$461$	−6.23888	−0.290574	−0.145287	+	0.989390i	$0.546410\pi$
$462$	−24.1580	−1.12393
$463$	35.0308	1.62802	0.814010	−	0.580851i	$-0.197280\pi$
$463$	35.0308	1.62802	0.814010	+	0.580851i	$0.197280\pi$
$464$	−1.48970	−0.0691575
$465$	1.21646	0.0564120
$466$	−15.1825	−0.703315
$467$	41.9172	1.93970	0.969849	−	0.243705i	$-0.0783629\pi$
$467$	41.9172	1.93970	0.969849	+	0.243705i	$0.0783629\pi$
$468$	28.8354	1.33292
$469$	−37.1941	−1.71746
$470$	−18.6744	−0.861384
$471$	−53.8534	−2.48144
$472$	−8.61237	−0.396417
$473$	−0.880321	−0.0404772
$474$	−13.9049	−0.638674
$475$	2.29461	0.105284
$476$	21.1490	0.969362
$477$	−54.2202	−2.48257
$478$	−22.7323	−1.03975
$479$	30.4447	1.39105	0.695527	−	0.718500i	$-0.255171\pi$
$479$	30.4447	1.39105	0.695527	+	0.718500i	$0.255171\pi$
$480$	7.38828	0.337227
$481$	0.245588	0.0111979
$482$	0.307193	0.0139922
$483$	−67.2488	−3.05993
$484$	−8.24496	−0.374771
$485$	1.40135	0.0636320
$486$	2.32172	0.105315
$487$	−15.6333	−0.708411	−0.354205	−	0.935168i	$-0.615249\pi$
$487$	−15.6333	−0.708411	−0.354205	+	0.935168i	$0.615249\pi$
$488$	13.1269	0.594229
$489$	21.4461	0.969826
$490$	−41.9063	−1.89313
$491$	5.99820	0.270695	0.135347	−	0.990798i	$-0.456785\pi$
$491$	5.99820	0.270695	0.135347	+	0.990798i	$0.456785\pi$
$492$	−8.17865	−0.368722
$493$	−6.44586	−0.290307
$494$	9.75486	0.438892
$495$	−24.1624	−1.08602
$496$	0.164647	0.00739288
$497$	−67.3674	−3.02184
$498$	42.9586	1.92502
$499$	31.1415	1.39408	0.697042	−	0.717031i	$-0.254499\pi$
$499$	31.1415	1.39408	0.697042	+	0.717031i	$0.254499\pi$
$500$	9.53732	0.426522
$501$	−64.1087	−2.86417
$502$	−25.6993	−1.14702
$503$	−28.1618	−1.25567	−0.627837	−	0.778345i	$-0.716059\pi$
$503$	−28.1618	−1.25567	−0.627837	+	0.778345i	$0.716059\pi$
$504$	28.6768	1.27737
$505$	−11.4494	−0.509492
$506$	7.66920	0.340937
$507$	−33.2165	−1.47520
$508$	10.5161	0.466575
$509$	−29.0656	−1.28831	−0.644156	−	0.764894i	$-0.722791\pi$
$509$	−29.0656	−1.28831	−0.644156	+	0.764894i	$0.722791\pi$
$510$	31.9687	1.41560
$511$	−48.9653	−2.16610
$512$	1.00000	0.0441942
$513$	−16.9455	−0.748162
$514$	−29.2690	−1.29100
$515$	−16.4935	−0.726788
$516$	1.57931	0.0695255
$517$	12.4927	0.549430
$518$	0.244238	0.0107312
$519$	58.1803	2.55383
$520$	−12.1942	−0.534752
$521$	−16.4026	−0.718609	−0.359305	−	0.933220i	$-0.616986\pi$
$521$	−16.4026	−0.718609	−0.359305	+	0.933220i	$0.616986\pi$
$522$	−8.74023	−0.382549
$523$	−22.8805	−1.00049	−0.500246	−	0.865883i	$-0.666757\pi$
$523$	−22.8805	−1.00049	−0.500246	+	0.865883i	$0.666757\pi$
$524$	11.1935	0.488992
$525$	−16.8263	−0.734358
$526$	−1.73162	−0.0755020
$527$	0.712421	0.0310335
$528$	−4.94259	−0.215099
$529$	−1.65124	−0.0717929
$530$	22.9292	0.995981
$531$	−50.5297	−2.19280
$532$	9.70122	0.420601
$533$	13.4987	0.584695
$534$	−37.2610	−1.61244
$535$	−2.05769	−0.0889619
$536$	−7.60968	−0.328688
$537$	−45.9523	−1.98299
$538$	2.40948	0.103880
$539$	28.0344	1.20753
$540$	21.1830	0.911571
$541$	−10.7399	−0.461746	−0.230873	−	0.972984i	$-0.574158\pi$
$541$	−10.7399	−0.461746	−0.230873	+	0.972984i	$0.574158\pi$
$542$	9.45179	0.405989
$543$	−0.934480	−0.0401024
$544$	4.32695	0.185517
$545$	4.63115	0.198376
$546$	−71.5320	−3.06129
$547$	−20.8491	−0.891444	−0.445722	−	0.895171i	$-0.647053\pi$
$547$	−20.8491	−0.891444	−0.445722	+	0.895171i	$0.647053\pi$
$548$	11.8716	0.507130
$549$	77.0172	3.28701
$550$	1.91890	0.0818222
$551$	−2.95677	−0.125963
$552$	−13.7587	−0.585609
$553$	22.8236	0.970559
$554$	2.53448	0.107680
$555$	0.369189	0.0156712
$556$	9.02382	0.382695
$557$	−14.6884	−0.622368	−0.311184	−	0.950350i	$-0.600726\pi$
$557$	−14.6884	−0.622368	−0.311184	+	0.950350i	$0.600726\pi$
$558$	0.966003	0.0408942
$559$	−2.60663	−0.110249
$560$	−12.1272	−0.512466
$561$	−21.3864	−0.902933
$562$	−1.98212	−0.0836106
$563$	10.7967	0.455026	0.227513	−	0.973775i	$-0.426941\pi$
$563$	10.7967	0.455026	0.227513	+	0.973775i	$0.426941\pi$
$564$	−22.4122	−0.943724
$565$	51.7834	2.17854
$566$	−19.2185	−0.807815
$567$	38.2301	1.60551
$568$	−13.7830	−0.578320
$569$	−34.9208	−1.46396	−0.731979	−	0.681327i	$-0.761403\pi$
$569$	−34.9208	−1.46396	−0.731979	+	0.681327i	$0.761403\pi$
$570$	14.6643	0.614222
$571$	−28.1831	−1.17942	−0.589712	−	0.807613i	$-0.700759\pi$
$571$	−28.1831	−1.17942	−0.589712	+	0.807613i	$0.700759\pi$
$572$	8.15766	0.341089
$573$	−4.29170	−0.179288
$574$	13.4245	0.560328
$575$	5.34165	0.222762
$576$	5.86711	0.244463
$577$	−4.85275	−0.202023	−0.101011	−	0.994885i	$-0.532208\pi$
$577$	−4.85275	−0.202023	−0.101011	+	0.994885i	$0.532208\pi$
$578$	1.72254	0.0716480
$579$	−19.5752	−0.813518
$580$	3.69616	0.153475
$581$	−70.5126	−2.92535
$582$	1.68184	0.0697146
$583$	−15.3391	−0.635281
$584$	−10.0180	−0.414548
$585$	−71.5448	−2.95802
$586$	−19.6336	−0.811058
$587$	10.9050	0.450097	0.225049	−	0.974348i	$-0.427746\pi$
$587$	10.9050	0.450097	0.225049	+	0.974348i	$0.427746\pi$
$588$	−50.2942	−2.07410
$589$	0.326794	0.0134653
$590$	21.3686	0.879729
$591$	−12.1317	−0.499032
$592$	0.0499696	0.00205374
$593$	25.4503	1.04512	0.522559	−	0.852603i	$-0.324977\pi$
$593$	25.4503	1.04512	0.522559	+	0.852603i	$0.324977\pi$
$594$	−14.1709	−0.581441
$595$	−52.4737	−2.15121
$596$	−5.99410	−0.245528
$597$	10.0264	0.410354
$598$	22.7085	0.928619
$599$	2.92151	0.119370	0.0596848	−	0.998217i	$-0.480990\pi$
$599$	2.92151	0.119370	0.0596848	+	0.998217i	$0.480990\pi$
$600$	−3.44255	−0.140541
$601$	1.49126	0.0608296	0.0304148	−	0.999537i	$-0.490317\pi$
$601$	1.49126	0.0608296	0.0304148	+	0.999537i	$0.490317\pi$
$602$	−2.59230	−0.105654
$603$	−44.6468	−1.81816
$604$	10.0428	0.408636
$605$	20.4570	0.831694
$606$	−13.7411	−0.558194
$607$	19.3148	0.783963	0.391982	−	0.919973i	$-0.371790\pi$
$607$	19.3148	0.783963	0.391982	+	0.919973i	$0.371790\pi$
$608$	1.98481	0.0804947
$609$	21.6819	0.878594
$610$	−32.5698	−1.31871
$611$	36.9910	1.49649
$612$	25.3867	1.02620
$613$	46.2072	1.86629	0.933147	−	0.359496i	$-0.117051\pi$
$613$	46.2072	1.86629	0.933147	+	0.359496i	$0.117051\pi$
$614$	15.7591	0.635987
$615$	20.2924	0.818270
$616$	8.11280	0.326874
$617$	−6.13107	−0.246828	−0.123414	−	0.992355i	$-0.539384\pi$
$617$	−6.13107	−0.246828	−0.123414	+	0.992355i	$0.539384\pi$
$618$	−19.7948	−0.796262
$619$	11.4536	0.460358	0.230179	−	0.973148i	$-0.426069\pi$
$619$	11.4536	0.460358	0.230179	+	0.973148i	$0.426069\pi$
$620$	−0.408514	−0.0164063
$621$	−39.4477	−1.58298
$622$	22.6432	0.907911
$623$	61.1604	2.45034
$624$	−14.6350	−0.585869
$625$	−29.4439	−1.17776
$626$	13.3409	0.533209
$627$	−9.81011	−0.391778
$628$	18.0852	0.721676
$629$	0.216216	0.00862110
$630$	−71.1514	−2.83474
$631$	42.7426	1.70156	0.850778	−	0.525525i	$-0.176131\pi$
$631$	42.7426	1.70156	0.850778	+	0.525525i	$0.176131\pi$
$632$	4.66957	0.185746
$633$	−36.5930	−1.45444
$634$	15.5186	0.616324
$635$	−26.0919	−1.03543
$636$	27.5187	1.09119
$637$	83.0098	3.28897
$638$	−2.47265	−0.0978930
$639$	−80.8662	−3.19902
$640$	−2.48115	−0.0980759
$641$	−45.1201	−1.78214	−0.891068	−	0.453870i	$-0.850043\pi$
$641$	−45.1201	−1.78214	−0.891068	+	0.453870i	$0.850043\pi$
$642$	−2.46956	−0.0974658
$643$	17.0057	0.670639	0.335319	−	0.942104i	$-0.391156\pi$
$643$	17.0057	0.670639	0.335319	+	0.942104i	$0.391156\pi$
$644$	22.5836	0.889919
$645$	−3.91851	−0.154291
$646$	8.58819	0.337898
$647$	−7.34983	−0.288952	−0.144476	−	0.989508i	$-0.546150\pi$
$647$	−7.34983	−0.288952	−0.144476	+	0.989508i	$0.546150\pi$
$648$	7.82164	0.307263
$649$	−14.2951	−0.561131
$650$	5.68187	0.222861
$651$	−2.39636	−0.0939209
$652$	−7.20207	−0.282055
$653$	28.1001	1.09964	0.549822	−	0.835282i	$-0.314696\pi$
$653$	28.1001	1.09964	0.549822	+	0.835282i	$0.314696\pi$
$654$	5.55811	0.217339
$655$	−27.7728	−1.08517
$656$	2.74657	0.107236
$657$	−58.7767	−2.29310
$658$	36.7876	1.43413
$659$	2.39498	0.0932951	0.0466475	−	0.998911i	$-0.485146\pi$
$659$	2.39498	0.0932951	0.0466475	+	0.998911i	$0.485146\pi$
$660$	12.2633	0.477348
$661$	50.2720	1.95535	0.977677	−	0.210112i	$-0.0673830\pi$
$661$	50.2720	1.95535	0.977677	+	0.210112i	$0.0673830\pi$
$662$	−28.5387	−1.10919
$663$	−63.3250	−2.45934
$664$	−14.4264	−0.559855
$665$	−24.0701	−0.933400
$666$	0.293177	0.0113604
$667$	−6.88311	−0.266515
$668$	21.5291	0.832986
$669$	44.3306	1.71392
$670$	18.8807	0.729426
$671$	21.7885	0.841135
$672$	−14.5545	−0.561453
$673$	13.5749	0.523276	0.261638	−	0.965166i	$-0.415737\pi$
$673$	13.5749	0.523276	0.261638	+	0.965166i	$0.415737\pi$
$674$	−14.0029	−0.539370
$675$	−9.87016	−0.379903
$676$	11.1548	0.429031
$677$	−34.8409	−1.33904	−0.669522	−	0.742792i	$-0.733501\pi$
$677$	−34.8409	−1.33904	−0.669522	+	0.742792i	$0.733501\pi$
$678$	62.1483	2.38679
$679$	−2.76059	−0.105942
$680$	−10.7358	−0.411699
$681$	3.03241	0.116202
$682$	0.273286	0.0104647
$683$	5.55084	0.212397	0.106199	−	0.994345i	$-0.466132\pi$
$683$	5.55084	0.212397	0.106199	+	0.994345i	$0.466132\pi$
$684$	11.6451	0.445262
$685$	−29.4552	−1.12542
$686$	48.3392	1.84560
$687$	71.1805	2.71571
$688$	−0.530368	−0.0202201
$689$	−45.4191	−1.73033
$690$	34.1373	1.29959
$691$	35.6432	1.35593	0.677966	−	0.735093i	$-0.262862\pi$
$691$	35.6432	1.35593	0.677966	+	0.735093i	$0.262862\pi$
$692$	−19.5382	−0.742732
$693$	47.5987	1.80812
$694$	27.1412	1.03027
$695$	−22.3894	−0.849279
$696$	4.43598	0.168145
$697$	11.8843	0.450149
$698$	−10.1433	−0.383928
$699$	45.2099	1.71000
$700$	5.65062	0.213573
$701$	1.11508	0.0421159	0.0210580	−	0.999778i	$-0.493297\pi$
$701$	1.11508	0.0421159	0.0210580	+	0.999778i	$0.493297\pi$
$702$	−41.9602	−1.58368
$703$	0.0991802	0.00374065
$704$	1.65983	0.0625572
$705$	55.6080	2.09432
$706$	3.36254	0.126551
$707$	22.5547	0.848258
$708$	25.6457	0.963823
$709$	−14.2037	−0.533432	−0.266716	−	0.963775i	$-0.585939\pi$
$709$	−14.2037	−0.533432	−0.266716	+	0.963775i	$0.585939\pi$
$710$	34.1975	1.28341
$711$	27.3969	1.02746
$712$	12.5130	0.468946
$713$	0.760748	0.0284902
$714$	−62.9768	−2.35685
$715$	−20.2403	−0.756946
$716$	15.4318	0.576713
$717$	67.6917	2.52799
$718$	−31.9560	−1.19259
$719$	4.75192	0.177217	0.0886083	−	0.996067i	$-0.471758\pi$
$719$	4.75192	0.177217	0.0886083	+	0.996067i	$0.471758\pi$
$720$	−14.5572	−0.542513
$721$	32.4913	1.21004
$722$	−15.0605	−0.560495
$723$	−0.914749	−0.0340199
$724$	0.313819	0.0116630
$725$	−1.72222	−0.0639615
$726$	24.5516	0.911195
$727$	−33.3212	−1.23581	−0.617907	−	0.786251i	$-0.712019\pi$
$727$	−33.3212	−1.23581	−0.617907	+	0.786251i	$0.712019\pi$
$728$	24.0220	0.890314
$729$	−30.3785	−1.12513
$730$	24.8561	0.919967
$731$	−2.29488	−0.0848792
$732$	−39.0890	−1.44477
$733$	18.6666	0.689468	0.344734	−	0.938700i	$-0.387969\pi$
$733$	18.6666	0.689468	0.344734	+	0.938700i	$0.387969\pi$
$734$	24.6470	0.909737
$735$	124.787	4.60285
$736$	4.62047	0.170313
$737$	−12.6308	−0.465260
$738$	16.1144	0.593180
$739$	−18.4281	−0.677890	−0.338945	−	0.940806i	$-0.610070\pi$
$739$	−18.4281	−0.677890	−0.338945	+	0.940806i	$0.610070\pi$
$740$	−0.123982	−0.00455766
$741$	−29.0477	−1.06710
$742$	−45.1694	−1.65822
$743$	−5.44254	−0.199667	−0.0998337	−	0.995004i	$-0.531831\pi$
$743$	−5.44254	−0.199667	−0.0998337	+	0.995004i	$0.531831\pi$
$744$	−0.490281	−0.0179746
$745$	14.8722	0.544876
$746$	22.4677	0.822603
$747$	−84.6415	−3.09687
$748$	7.18201	0.262600
$749$	4.05355	0.148114
$750$	−28.3999	−1.03702
$751$	45.3796	1.65592	0.827962	−	0.560784i	$-0.189500\pi$
$751$	45.3796	1.65592	0.827962	+	0.560784i	$0.189500\pi$
$752$	7.52651	0.274464
$753$	76.5266	2.78878
$754$	−7.32151	−0.266634
$755$	−24.9177	−0.906848
$756$	−41.7294	−1.51768
$757$	−15.6580	−0.569100	−0.284550	−	0.958661i	$-0.591844\pi$
$757$	−15.6580	−0.569100	−0.284550	+	0.958661i	$0.591844\pi$
$758$	−7.33839	−0.266542
$759$	−22.8371	−0.828934
$760$	−4.92461	−0.178634
$761$	48.2963	1.75074	0.875370	−	0.483453i	$-0.160618\pi$
$761$	48.2963	1.75074	0.875370	+	0.483453i	$0.160618\pi$
$762$	−31.3144	−1.13440
$763$	−9.12312	−0.330279
$764$	1.44125	0.0521425
$765$	−62.9881	−2.27734
$766$	−18.4303	−0.665913
$767$	−42.3277	−1.52836
$768$	−2.97777	−0.107451
$769$	−13.9656	−0.503614	−0.251807	−	0.967777i	$-0.581025\pi$
$769$	−13.9656	−0.503614	−0.251807	+	0.967777i	$0.581025\pi$
$770$	−20.1290	−0.725400
$771$	87.1563	3.13886
$772$	6.57378	0.236596
$773$	−20.7204	−0.745261	−0.372630	−	0.927980i	$-0.621544\pi$
$773$	−20.7204	−0.745261	−0.372630	+	0.927980i	$0.621544\pi$
$774$	−3.11173	−0.111849
$775$	0.190346	0.00683743
$776$	−0.564799	−0.0202751
$777$	−0.727284	−0.0260912
$778$	−15.1914	−0.544637
$779$	5.45143	0.195318
$780$	36.3116	1.30016
$781$	−22.8774	−0.818617
$782$	19.9926	0.714933
$783$	12.7184	0.454520
$784$	16.8899	0.603211
$785$	−44.8719	−1.60155
$786$	−33.3318	−1.18890
$787$	−42.4962	−1.51482	−0.757412	−	0.652937i	$-0.773537\pi$
$787$	−42.4962	−1.51482	−0.757412	+	0.652937i	$0.773537\pi$
$788$	4.07409	0.145134
$789$	5.15635	0.183571
$790$	−11.5859	−0.412208
$791$	−102.011	−3.62708
$792$	9.73840	0.346039
$793$	64.5157	2.29102
$794$	−25.8874	−0.918709
$795$	−68.2779	−2.42157
$796$	−3.36709	−0.119343
$797$	53.3638	1.89024	0.945121	−	0.326719i	$-0.105943\pi$
$797$	53.3638	1.89024	0.945121	+	0.326719i	$0.105943\pi$
$798$	−28.8880	−1.02262
$799$	32.5669	1.15213
$800$	1.15608	0.0408737
$801$	73.4154	2.59401
$802$	8.80464	0.310903
$803$	−16.6282	−0.586796
$804$	22.6599	0.799152
$805$	−56.0333	−1.97491
$806$	0.809201	0.0285029
$807$	−7.17486	−0.252567
$808$	4.61456	0.162340
$809$	36.9726	1.29989	0.649944	−	0.759982i	$-0.274792\pi$
$809$	36.9726	1.29989	0.649944	+	0.759982i	$0.274792\pi$
$810$	−19.4066	−0.681880
$811$	−2.73637	−0.0960870	−0.0480435	−	0.998845i	$-0.515299\pi$
$811$	−2.73637	−0.0960870	−0.0480435	+	0.998845i	$0.515299\pi$
$812$	−7.28125	−0.255522
$813$	−28.1452	−0.987096
$814$	0.0829410	0.00290708
$815$	17.8694	0.625937
$816$	−12.8847	−0.451054
$817$	−1.05268	−0.0368287
$818$	14.7189	0.514633
$819$	140.940	4.92483
$820$	−6.81464	−0.237978
$821$	−36.4366	−1.27165	−0.635824	−	0.771834i	$-0.719339\pi$
$821$	−36.4366	−1.27165	−0.635824	+	0.771834i	$0.719339\pi$
$822$	−35.3509	−1.23300
$823$	−13.0322	−0.454275	−0.227138	−	0.973863i	$-0.572937\pi$
$823$	−13.0322	−0.454275	−0.227138	+	0.973863i	$0.572937\pi$
$824$	6.64751	0.231577
$825$	−5.71405	−0.198938
$826$	−42.0950	−1.46467
$827$	12.2905	0.427382	0.213691	−	0.976901i	$-0.431451\pi$
$827$	12.2905	0.427382	0.213691	+	0.976901i	$0.431451\pi$
$828$	27.1088	0.942096
$829$	33.6778	1.16968	0.584840	−	0.811149i	$-0.301157\pi$
$829$	33.6778	1.16968	0.584840	+	0.811149i	$0.301157\pi$
$830$	35.7941	1.24243
$831$	−7.54710	−0.261806
$832$	4.91476	0.170388
$833$	73.0819	2.53214
$834$	−26.8709	−0.930462
$835$	−53.4169	−1.84857
$836$	3.29445	0.113941
$837$	−1.40569	−0.0485878
$838$	11.6333	0.401867
$839$	−14.2450	−0.491793	−0.245897	−	0.969296i	$-0.579082\pi$
$839$	−14.2450	−0.491793	−0.245897	+	0.969296i	$0.579082\pi$
$840$	36.1119	1.24598
$841$	−26.7808	−0.923476
$842$	−13.6002	−0.468694
$843$	5.90229	0.203286
$844$	12.2887	0.422995
$845$	−27.6767	−0.952108
$846$	44.1589	1.51821
$847$	−40.2992	−1.38470
$848$	−9.24138	−0.317350
$849$	57.2284	1.96407
$850$	5.00232	0.171578
$851$	0.230883	0.00791457
$852$	41.0425	1.40609
$853$	1.45119	0.0496878	0.0248439	−	0.999691i	$-0.492091\pi$
$853$	1.45119	0.0496878	0.0248439	+	0.999691i	$0.492091\pi$
$854$	64.1609	2.19554
$855$	−28.8932	−0.988127
$856$	0.829332	0.0283460
$857$	−19.3350	−0.660471	−0.330236	−	0.943899i	$-0.607128\pi$
$857$	−19.3350	−0.660471	−0.330236	+	0.943899i	$0.607128\pi$
$858$	−24.2916	−0.829302
$859$	−45.9310	−1.56714	−0.783572	−	0.621301i	$-0.786604\pi$
$859$	−45.9310	−1.56714	−0.783572	+	0.621301i	$0.786604\pi$
$860$	1.31592	0.0448725
$861$	−39.9751	−1.36235
$862$	20.4742	0.697353
$863$	11.6107	0.395232	0.197616	−	0.980280i	$-0.436680\pi$
$863$	11.6107	0.395232	0.197616	+	0.980280i	$0.436680\pi$
$864$	−8.53759	−0.290455
$865$	48.4772	1.64827
$866$	17.1401	0.582445
$867$	−5.12931	−0.174201
$868$	0.804751	0.0273150
$869$	7.75070	0.262924
$870$	−11.0063	−0.373149
$871$	−37.3997	−1.26724
$872$	−1.86654	−0.0632089
$873$	−3.31374	−0.112153
$874$	9.17077	0.310206
$875$	46.6158	1.57590
$876$	29.8313	1.00791
$877$	52.1935	1.76245	0.881225	−	0.472697i	$-0.156719\pi$
$877$	52.1935	1.76245	0.881225	+	0.472697i	$0.156719\pi$
$878$	30.8397	1.04079
$879$	58.4644	1.97196
$880$	−4.11828	−0.138827
$881$	−49.3656	−1.66317	−0.831585	−	0.555397i	$-0.812566\pi$
$881$	−49.3656	−1.66317	−0.831585	+	0.555397i	$0.812566\pi$
$882$	99.0949	3.33670
$883$	14.6936	0.494479	0.247239	−	0.968954i	$-0.420477\pi$
$883$	14.6936	0.494479	0.247239	+	0.968954i	$0.420477\pi$
$884$	21.2659	0.715250
$885$	−63.6306	−2.13892
$886$	−24.8697	−0.835514
$887$	−22.8664	−0.767779	−0.383890	−	0.923379i	$-0.625416\pi$
$887$	−22.8664	−0.767779	−0.383890	+	0.923379i	$0.625416\pi$
$888$	−0.148798	−0.00499333
$889$	51.3997	1.72389
$890$	−31.0467	−1.04069
$891$	12.9826	0.434933
$892$	−14.8872	−0.498460
$893$	14.9387	0.499905
$894$	17.8490	0.596961
$895$	−38.2885	−1.27984
$896$	4.88773	0.163288
$897$	−67.6206	−2.25779
$898$	−7.44174	−0.248334
$899$	−0.245275	−0.00818037
$900$	6.78287	0.226096
$901$	−39.9870	−1.33216
$902$	4.55884	0.151793
$903$	7.71926	0.256881
$904$	−20.8708	−0.694151
$905$	−0.778630	−0.0258825
$906$	−29.9052	−0.993533
$907$	53.1054	1.76333	0.881667	−	0.471872i	$-0.156421\pi$
$907$	53.1054	1.76333	0.881667	+	0.471872i	$0.156421\pi$
$908$	−1.01835	−0.0337952
$909$	27.0741	0.897993
$910$	−59.6021	−1.97579
$911$	14.2415	0.471841	0.235921	−	0.971772i	$-0.424189\pi$
$911$	14.2415	0.471841	0.235921	+	0.971772i	$0.424189\pi$
$912$	−5.91031	−0.195710
$913$	−23.9454	−0.792479
$914$	17.0074	0.562555
$915$	96.9855	3.20624
$916$	−23.9040	−0.789809
$917$	54.7110	1.80672
$918$	−36.9418	−1.21926
$919$	−5.21512	−0.172031	−0.0860154	−	0.996294i	$-0.527413\pi$
$919$	−5.21512	−0.172031	−0.0860154	+	0.996294i	$0.527413\pi$
$920$	−11.4641	−0.377959
$921$	−46.9271	−1.54630
$922$	−6.23888	−0.205467
$923$	−67.7399	−2.22969
$924$	−24.1580	−0.794741
$925$	0.0577690	0.00189943
$926$	35.0308	1.15118
$927$	39.0017	1.28098
$928$	−1.48970	−0.0489018
$929$	−52.3650	−1.71804	−0.859021	−	0.511941i	$-0.828927\pi$
$929$	−52.3650	−1.71804	−0.859021	+	0.511941i	$0.828927\pi$
$930$	1.21646	0.0398893
$931$	33.5233	1.09868
$932$	−15.1825	−0.497319
$933$	−67.4264	−2.20744
$934$	41.9172	1.37157
$935$	−17.8196	−0.582764
$936$	28.8354	0.942515
$937$	5.76848	0.188448	0.0942240	−	0.995551i	$-0.469963\pi$
$937$	5.76848	0.188448	0.0942240	+	0.995551i	$0.469963\pi$
$938$	−37.1941	−1.21443
$939$	−39.7261	−1.29641
$940$	−18.6744	−0.609091
$941$	31.1153	1.01433	0.507164	−	0.861849i	$-0.330694\pi$
$941$	31.1153	1.01433	0.507164	+	0.861849i	$0.330694\pi$
$942$	−53.8534	−1.75464
$943$	12.6905	0.413258
$944$	−8.61237	−0.280309
$945$	103.537	3.36805
$946$	−0.880321	−0.0286217
$947$	14.5420	0.472552	0.236276	−	0.971686i	$-0.424073\pi$
$947$	14.5420	0.472552	0.236276	+	0.971686i	$0.424073\pi$
$948$	−13.9049	−0.451611
$949$	−49.2360	−1.59827
$950$	2.29461	0.0744469
$951$	−46.2109	−1.49849
$952$	21.1490	0.685443
$953$	−41.4071	−1.34131	−0.670654	−	0.741771i	$-0.733986\pi$
$953$	−41.4071	−1.34131	−0.670654	+	0.741771i	$0.733986\pi$
$954$	−54.2202	−1.75544
$955$	−3.57595	−0.115715
$956$	−22.7323	−0.735217
$957$	7.36297	0.238011
$958$	30.4447	0.983624
$959$	58.0252	1.87373
$960$	7.38828	0.238456
$961$	−30.9729	−0.999126
$962$	0.245588	0.00791808
$963$	4.86578	0.156798
$964$	0.307193	0.00989401
$965$	−16.3105	−0.525054
$966$	−67.2488	−2.16370
$967$	28.8225	0.926868	0.463434	−	0.886131i	$-0.346617\pi$
$967$	28.8225	0.926868	0.463434	+	0.886131i	$0.346617\pi$
$968$	−8.24496	−0.265003
$969$	−25.5736	−0.821544
$970$	1.40135	0.0449946
$971$	33.4059	1.07205	0.536024	−	0.844203i	$-0.319926\pi$
$971$	33.4059	1.07205	0.536024	+	0.844203i	$0.319926\pi$
$972$	2.32172	0.0744692
$973$	44.1060	1.41397
$974$	−15.6333	−0.500922
$975$	−16.9193	−0.541851
$976$	13.1269	0.420183
$977$	39.1001	1.25092	0.625461	−	0.780255i	$-0.284911\pi$
$977$	39.1001	1.25092	0.625461	+	0.780255i	$0.284911\pi$
$978$	21.4461	0.685770
$979$	20.7695	0.663797
$980$	−41.9063	−1.33865
$981$	−10.9512	−0.349644
$982$	5.99820	0.191410
$983$	−16.7685	−0.534831	−0.267416	−	0.963581i	$-0.586170\pi$
$983$	−16.7685	−0.534831	−0.267416	+	0.963581i	$0.586170\pi$
$984$	−8.17865	−0.260726
$985$	−10.1084	−0.322081
$986$	−6.44586	−0.205278
$987$	−109.545	−3.48685
$988$	9.75486	0.310344
$989$	−2.45055	−0.0779230
$990$	−24.1624	−0.767931
$991$	−25.4338	−0.807932	−0.403966	−	0.914774i	$-0.632369\pi$
$991$	−25.4338	−0.807932	−0.403966	+	0.914774i	$0.632369\pi$
$992$	0.164647	0.00522755
$993$	84.9815	2.69681
$994$	−67.3674	−2.13676
$995$	8.35424	0.264847
$996$	42.9586	1.36120
$997$	13.9420	0.441548	0.220774	−	0.975325i	$-0.429142\pi$
$997$	13.9420	0.441548	0.220774	+	0.975325i	$0.429142\pi$
$998$	31.1415	0.985766
$999$	−0.426620	−0.0134977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.2	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.2	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.97777 q^{3} +1.00000 q^{4} -2.48115 q^{5} -2.97777 q^{6} +4.88773 q^{7} +1.00000 q^{8} +5.86711 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.97777 q^{3} +1.00000 q^{4} -2.48115 q^{5} -2.97777 q^{6} +4.88773 q^{7} +1.00000 q^{8} +5.86711 q^{9} -2.48115 q^{10} +1.65983 q^{11} -2.97777 q^{12} +4.91476 q^{13} +4.88773 q^{14} +7.38828 q^{15} +1.00000 q^{16} +4.32695 q^{17} +5.86711 q^{18} +1.98481 q^{19} -2.48115 q^{20} -14.5545 q^{21} +1.65983 q^{22} +4.62047 q^{23} -2.97777 q^{24} +1.15608 q^{25} +4.91476 q^{26} -8.53759 q^{27} +4.88773 q^{28} -1.48970 q^{29} +7.38828 q^{30} +0.164647 q^{31} +1.00000 q^{32} -4.94259 q^{33} +4.32695 q^{34} -12.1272 q^{35} +5.86711 q^{36} +0.0499696 q^{37} +1.98481 q^{38} -14.6350 q^{39} -2.48115 q^{40} +2.74657 q^{41} -14.5545 q^{42} -0.530368 q^{43} +1.65983 q^{44} -14.5572 q^{45} +4.62047 q^{46} +7.52651 q^{47} -2.97777 q^{48} +16.8899 q^{49} +1.15608 q^{50} -12.8847 q^{51} +4.91476 q^{52} -9.24138 q^{53} -8.53759 q^{54} -4.11828 q^{55} +4.88773 q^{56} -5.91031 q^{57} -1.48970 q^{58} -8.61237 q^{59} +7.38828 q^{60} +13.1269 q^{61} +0.164647 q^{62} +28.6768 q^{63} +1.00000 q^{64} -12.1942 q^{65} -4.94259 q^{66} -7.60968 q^{67} +4.32695 q^{68} -13.7587 q^{69} -12.1272 q^{70} -13.7830 q^{71} +5.86711 q^{72} -10.0180 q^{73} +0.0499696 q^{74} -3.44255 q^{75} +1.98481 q^{76} +8.11280 q^{77} -14.6350 q^{78} +4.66957 q^{79} -2.48115 q^{80} +7.82164 q^{81} +2.74657 q^{82} -14.4264 q^{83} -14.5545 q^{84} -10.7358 q^{85} -0.530368 q^{86} +4.43598 q^{87} +1.65983 q^{88} +12.5130 q^{89} -14.5572 q^{90} +24.0220 q^{91} +4.62047 q^{92} -0.490281 q^{93} +7.52651 q^{94} -4.92461 q^{95} -2.97777 q^{96} -0.564799 q^{97} +16.8899 q^{98} +9.73840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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