LMFDB - Embedded newform 4334.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.68443 q^{3} +1.00000 q^{4} +2.21213 q^{5} -2.68443 q^{6} +4.45954 q^{7} +1.00000 q^{8} +4.20617 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.68443 q^{3} +1.00000 q^{4} +2.21213 q^{5} -2.68443 q^{6} +4.45954 q^{7} +1.00000 q^{8} +4.20617 q^{9} +2.21213 q^{10} -1.00000 q^{11} -2.68443 q^{12} -0.0499536 q^{13} +4.45954 q^{14} -5.93830 q^{15} +1.00000 q^{16} +2.30875 q^{17} +4.20617 q^{18} +3.92697 q^{19} +2.21213 q^{20} -11.9713 q^{21} -1.00000 q^{22} +2.67113 q^{23} -2.68443 q^{24} -0.106494 q^{25} -0.0499536 q^{26} -3.23787 q^{27} +4.45954 q^{28} -4.38772 q^{29} -5.93830 q^{30} +4.46633 q^{31} +1.00000 q^{32} +2.68443 q^{33} +2.30875 q^{34} +9.86508 q^{35} +4.20617 q^{36} +11.1664 q^{37} +3.92697 q^{38} +0.134097 q^{39} +2.21213 q^{40} +0.808342 q^{41} -11.9713 q^{42} -1.84462 q^{43} -1.00000 q^{44} +9.30458 q^{45} +2.67113 q^{46} -1.34682 q^{47} -2.68443 q^{48} +12.8875 q^{49} -0.106494 q^{50} -6.19767 q^{51} -0.0499536 q^{52} +4.19224 q^{53} -3.23787 q^{54} -2.21213 q^{55} +4.45954 q^{56} -10.5417 q^{57} -4.38772 q^{58} -12.7581 q^{59} -5.93830 q^{60} -7.78077 q^{61} +4.46633 q^{62} +18.7576 q^{63} +1.00000 q^{64} -0.110504 q^{65} +2.68443 q^{66} +9.32145 q^{67} +2.30875 q^{68} -7.17046 q^{69} +9.86508 q^{70} -13.4642 q^{71} +4.20617 q^{72} -7.02630 q^{73} +11.1664 q^{74} +0.285875 q^{75} +3.92697 q^{76} -4.45954 q^{77} +0.134097 q^{78} +4.15520 q^{79} +2.21213 q^{80} -3.92665 q^{81} +0.808342 q^{82} +13.7085 q^{83} -11.9713 q^{84} +5.10724 q^{85} -1.84462 q^{86} +11.7785 q^{87} -1.00000 q^{88} -2.44827 q^{89} +9.30458 q^{90} -0.222770 q^{91} +2.67113 q^{92} -11.9896 q^{93} -1.34682 q^{94} +8.68696 q^{95} -2.68443 q^{96} -10.7345 q^{97} +12.8875 q^{98} -4.20617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	−2.68443	−1.54986	−0.774928	−	0.632049i	$-0.782214\pi$
$3$	−2.68443	−1.54986	−0.774928	+	0.632049i	$0.782214\pi$
$4$	1.00000	0.500000
$5$	2.21213	0.989293	0.494647	−	0.869094i	$-0.335297\pi$
$5$	2.21213	0.989293	0.494647	+	0.869094i	$0.335297\pi$
$6$	−2.68443	−1.09591
$7$	4.45954	1.68555	0.842775	−	0.538267i	$-0.180921\pi$
$7$	4.45954	1.68555	0.842775	+	0.538267i	$0.180921\pi$
$8$	1.00000	0.353553
$9$	4.20617	1.40206
$10$	2.21213	0.699536
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.68443	−0.774928
$13$	−0.0499536	−0.0138546	−0.00692732	−	0.999976i	$-0.502205\pi$
$13$	−0.0499536	−0.0138546	−0.00692732	+	0.999976i	$0.502205\pi$
$14$	4.45954	1.19186
$15$	−5.93830	−1.53326
$16$	1.00000	0.250000
$17$	2.30875	0.559953	0.279977	−	0.960007i	$-0.409673\pi$
$17$	2.30875	0.559953	0.279977	+	0.960007i	$0.409673\pi$
$18$	4.20617	0.991403
$19$	3.92697	0.900909	0.450454	−	0.892799i	$-0.351262\pi$
$19$	3.92697	0.900909	0.450454	+	0.892799i	$0.351262\pi$
$20$	2.21213	0.494647
$21$	−11.9713	−2.61236
$22$	−1.00000	−0.213201
$23$	2.67113	0.556969	0.278484	−	0.960441i	$-0.410168\pi$
$23$	2.67113	0.556969	0.278484	+	0.960441i	$0.410168\pi$
$24$	−2.68443	−0.547957
$25$	−0.106494	−0.0212987
$26$	−0.0499536	−0.00979672
$27$	−3.23787	−0.623129
$28$	4.45954	0.842775
$29$	−4.38772	−0.814779	−0.407389	−	0.913255i	$-0.633561\pi$
$29$	−4.38772	−0.814779	−0.407389	+	0.913255i	$0.633561\pi$
$30$	−5.93830	−1.08418
$31$	4.46633	0.802177	0.401088	−	0.916039i	$-0.368632\pi$
$31$	4.46633	0.802177	0.401088	+	0.916039i	$0.368632\pi$
$32$	1.00000	0.176777
$33$	2.68443	0.467299
$34$	2.30875	0.395947
$35$	9.86508	1.66750
$36$	4.20617	0.701028
$37$	11.1664	1.83575	0.917876	−	0.396867i	$-0.129902\pi$
$37$	11.1664	1.83575	0.917876	+	0.396867i	$0.129902\pi$
$38$	3.92697	0.637039
$39$	0.134097	0.0214727
$40$	2.21213	0.349768
$41$	0.808342	0.126242	0.0631209	−	0.998006i	$-0.479895\pi$
$41$	0.808342	0.126242	0.0631209	+	0.998006i	$0.479895\pi$
$42$	−11.9713	−1.84722
$43$	−1.84462	−0.281302	−0.140651	−	0.990059i	$-0.544920\pi$
$43$	−1.84462	−0.281302	−0.140651	+	0.990059i	$0.544920\pi$
$44$	−1.00000	−0.150756
$45$	9.30458	1.38704
$46$	2.67113	0.393836
$47$	−1.34682	−0.196453	−0.0982266	−	0.995164i	$-0.531317\pi$
$47$	−1.34682	−0.196453	−0.0982266	+	0.995164i	$0.531317\pi$
$48$	−2.68443	−0.387464
$49$	12.8875	1.84108
$50$	−0.106494	−0.0150605
$51$	−6.19767	−0.867847
$52$	−0.0499536	−0.00692732
$53$	4.19224	0.575848	0.287924	−	0.957653i	$-0.407035\pi$
$53$	4.19224	0.575848	0.287924	+	0.957653i	$0.407035\pi$
$54$	−3.23787	−0.440619
$55$	−2.21213	−0.298283
$56$	4.45954	0.595932
$57$	−10.5417	−1.39628
$58$	−4.38772	−0.576135
$59$	−12.7581	−1.66096	−0.830482	−	0.557046i	$-0.811935\pi$
$59$	−12.7581	−1.66096	−0.830482	+	0.557046i	$0.811935\pi$
$60$	−5.93830	−0.766631
$61$	−7.78077	−0.996225	−0.498113	−	0.867112i	$-0.665973\pi$
$61$	−7.78077	−0.996225	−0.498113	+	0.867112i	$0.665973\pi$
$62$	4.46633	0.567225
$63$	18.7576	2.36323
$64$	1.00000	0.125000
$65$	−0.110504	−0.0137063
$66$	2.68443	0.330431
$67$	9.32145	1.13880	0.569398	−	0.822062i	$-0.307176\pi$
$67$	9.32145	1.13880	0.569398	+	0.822062i	$0.307176\pi$
$68$	2.30875	0.279977
$69$	−7.17046	−0.863222
$70$	9.86508	1.17910
$71$	−13.4642	−1.59791	−0.798955	−	0.601391i	$-0.794613\pi$
$71$	−13.4642	−1.59791	−0.798955	+	0.601391i	$0.794613\pi$
$72$	4.20617	0.495702
$73$	−7.02630	−0.822366	−0.411183	−	0.911553i	$-0.634884\pi$
$73$	−7.02630	−0.822366	−0.411183	+	0.911553i	$0.634884\pi$
$74$	11.1664	1.29807
$75$	0.285875	0.0330100
$76$	3.92697	0.450454
$77$	−4.45954	−0.508212
$78$	0.134097	0.0151835
$79$	4.15520	0.467497	0.233748	−	0.972297i	$-0.424901\pi$
$79$	4.15520	0.467497	0.233748	+	0.972297i	$0.424901\pi$
$80$	2.21213	0.247323
$81$	−3.92665	−0.436295
$82$	0.808342	0.0892665
$83$	13.7085	1.50471	0.752353	−	0.658760i	$-0.228919\pi$
$83$	13.7085	1.50471	0.752353	+	0.658760i	$0.228919\pi$
$84$	−11.9713	−1.30618
$85$	5.10724	0.553958
$86$	−1.84462	−0.198911
$87$	11.7785	1.26279
$88$	−1.00000	−0.106600
$89$	−2.44827	−0.259516	−0.129758	−	0.991546i	$-0.541420\pi$
$89$	−2.44827	−0.259516	−0.129758	+	0.991546i	$0.541420\pi$
$90$	9.30458	0.980789
$91$	−0.222770	−0.0233527
$92$	2.67113	0.278484
$93$	−11.9896	−1.24326
$94$	−1.34682	−0.138913
$95$	8.68696	0.891263
$96$	−2.68443	−0.273979
$97$	−10.7345	−1.08992	−0.544960	−	0.838462i	$-0.683455\pi$
$97$	−10.7345	−1.08992	−0.544960	+	0.838462i	$0.683455\pi$
$98$	12.8875	1.30184
$99$	−4.20617	−0.422736
$100$	−0.106494	−0.0106494
$101$	−10.2954	−1.02443	−0.512216	−	0.858857i	$-0.671175\pi$
$101$	−10.2954	−1.02443	−0.512216	+	0.858857i	$0.671175\pi$
$102$	−6.19767	−0.613661
$103$	−7.48432	−0.737452	−0.368726	−	0.929538i	$-0.620206\pi$
$103$	−7.48432	−0.737452	−0.368726	+	0.929538i	$0.620206\pi$
$104$	−0.0499536	−0.00489836
$105$	−26.4821	−2.58439
$106$	4.19224	0.407186
$107$	−0.621729	−0.0601048	−0.0300524	−	0.999548i	$-0.509567\pi$
$107$	−0.621729	−0.0601048	−0.0300524	+	0.999548i	$0.509567\pi$
$108$	−3.23787	−0.311565
$109$	5.09458	0.487972	0.243986	−	0.969779i	$-0.421545\pi$
$109$	5.09458	0.487972	0.243986	+	0.969779i	$0.421545\pi$
$110$	−2.21213	−0.210918
$111$	−29.9756	−2.84515
$112$	4.45954	0.421387
$113$	−18.0873	−1.70151	−0.850757	−	0.525559i	$-0.823856\pi$
$113$	−18.0873	−1.70151	−0.850757	+	0.525559i	$0.823856\pi$
$114$	−10.5417	−0.987319
$115$	5.90888	0.551006
$116$	−4.38772	−0.407389
$117$	−0.210113	−0.0194250
$118$	−12.7581	−1.17448
$119$	10.2960	0.943829
$120$	−5.93830	−0.542090
$121$	1.00000	0.0909091
$122$	−7.78077	−0.704438
$123$	−2.16994	−0.195657
$124$	4.46633	0.401088
$125$	−11.2962	−1.01036
$126$	18.7576	1.67106
$127$	−2.92947	−0.259948	−0.129974	−	0.991517i	$-0.541489\pi$
$127$	−2.92947	−0.259948	−0.129974	+	0.991517i	$0.541489\pi$
$128$	1.00000	0.0883883
$129$	4.95176	0.435979
$130$	−0.110504	−0.00969183
$131$	17.4944	1.52849	0.764246	−	0.644925i	$-0.223111\pi$
$131$	17.4944	1.52849	0.764246	+	0.644925i	$0.223111\pi$
$132$	2.68443	0.233650
$133$	17.5125	1.51853
$134$	9.32145	0.805250
$135$	−7.16259	−0.616458
$136$	2.30875	0.197973
$137$	2.44222	0.208653	0.104327	−	0.994543i	$-0.466731\pi$
$137$	2.44222	0.208653	0.104327	+	0.994543i	$0.466731\pi$
$138$	−7.17046	−0.610390
$139$	14.8639	1.26074	0.630368	−	0.776297i	$-0.282904\pi$
$139$	14.8639	1.26074	0.630368	+	0.776297i	$0.282904\pi$
$140$	9.86508	0.833751
$141$	3.61543	0.304474
$142$	−13.4642	−1.12989
$143$	0.0499536	0.00417733
$144$	4.20617	0.350514
$145$	−9.70619	−0.806055
$146$	−7.02630	−0.581500
$147$	−34.5957	−2.85340
$148$	11.1664	0.917876
$149$	3.39816	0.278388	0.139194	−	0.990265i	$-0.455549\pi$
$149$	3.39816	0.278388	0.139194	+	0.990265i	$0.455549\pi$
$150$	0.285875	0.0233416
$151$	−1.09000	−0.0887032	−0.0443516	−	0.999016i	$-0.514122\pi$
$151$	−1.09000	−0.0887032	−0.0443516	+	0.999016i	$0.514122\pi$
$152$	3.92697	0.318519
$153$	9.71097	0.785086
$154$	−4.45954	−0.359360
$155$	9.88009	0.793588
$156$	0.134097	0.0107364
$157$	21.3066	1.70045	0.850225	−	0.526420i	$-0.176466\pi$
$157$	21.3066	1.70045	0.850225	+	0.526420i	$0.176466\pi$
$158$	4.15520	0.330570
$159$	−11.2538	−0.892483
$160$	2.21213	0.174884
$161$	11.9120	0.938798
$162$	−3.92665	−0.308507
$163$	20.2406	1.58537	0.792684	−	0.609633i	$-0.208683\pi$
$163$	20.2406	1.58537	0.792684	+	0.609633i	$0.208683\pi$
$164$	0.808342	0.0631209
$165$	5.93830	0.462296
$166$	13.7085	1.06399
$167$	−5.75084	−0.445014	−0.222507	−	0.974931i	$-0.571424\pi$
$167$	−5.75084	−0.445014	−0.222507	+	0.974931i	$0.571424\pi$
$168$	−11.9713	−0.923609
$169$	−12.9975	−0.999808
$170$	5.10724	0.391707
$171$	16.5175	1.26312
$172$	−1.84462	−0.140651
$173$	20.2207	1.53735	0.768675	−	0.639639i	$-0.220916\pi$
$173$	20.2207	1.53735	0.768675	+	0.639639i	$0.220916\pi$
$174$	11.7785	0.892927
$175$	−0.474914	−0.0359001
$176$	−1.00000	−0.0753778
$177$	34.2482	2.57426
$178$	−2.44827	−0.183506
$179$	12.0962	0.904109	0.452055	−	0.891990i	$-0.350691\pi$
$179$	12.0962	0.904109	0.452055	+	0.891990i	$0.350691\pi$
$180$	9.30458	0.693522
$181$	−10.2771	−0.763893	−0.381947	−	0.924184i	$-0.624746\pi$
$181$	−10.2771	−0.763893	−0.381947	+	0.924184i	$0.624746\pi$
$182$	−0.222770	−0.0165128
$183$	20.8869	1.54401
$184$	2.67113	0.196918
$185$	24.7016	1.81610
$186$	−11.9896	−0.879117
$187$	−2.30875	−0.168832
$188$	−1.34682	−0.0982266
$189$	−14.4394	−1.05032
$190$	8.68696	0.630218
$191$	−2.25144	−0.162909	−0.0814543	−	0.996677i	$-0.525956\pi$
$191$	−2.25144	−0.162909	−0.0814543	+	0.996677i	$0.525956\pi$
$192$	−2.68443	−0.193732
$193$	−12.5770	−0.905309	−0.452655	−	0.891686i	$-0.649523\pi$
$193$	−12.5770	−0.905309	−0.452655	+	0.891686i	$0.649523\pi$
$194$	−10.7345	−0.770689
$195$	0.296640	0.0212428
$196$	12.8875	0.920538
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−4.20617	−0.298919
$199$	4.84998	0.343806	0.171903	−	0.985114i	$-0.445008\pi$
$199$	4.84998	0.343806	0.171903	+	0.985114i	$0.445008\pi$
$200$	−0.106494	−0.00753024
$201$	−25.0228	−1.76497
$202$	−10.2954	−0.724383
$203$	−19.5672	−1.37335
$204$	−6.19767	−0.433924
$205$	1.78816	0.124890
$206$	−7.48432	−0.521457
$207$	11.2352	0.780901
$208$	−0.0499536	−0.00346366
$209$	−3.92697	−0.271634
$210$	−26.4821	−1.82744
$211$	−12.1866	−0.838958	−0.419479	−	0.907765i	$-0.637787\pi$
$211$	−12.1866	−0.838958	−0.419479	+	0.907765i	$0.637787\pi$
$212$	4.19224	0.287924
$213$	36.1438	2.47653
$214$	−0.621729	−0.0425005
$215$	−4.08054	−0.278291
$216$	−3.23787	−0.220309
$217$	19.9178	1.35211
$218$	5.09458	0.345048
$219$	18.8616	1.27455
$220$	−2.21213	−0.149142
$221$	−0.115330	−0.00775795
$222$	−29.9756	−2.01183
$223$	7.79077	0.521708	0.260854	−	0.965378i	$-0.415996\pi$
$223$	7.79077	0.521708	0.260854	+	0.965378i	$0.415996\pi$
$224$	4.45954	0.297966
$225$	−0.447931	−0.0298620
$226$	−18.0873	−1.20315
$227$	4.47245	0.296847	0.148423	−	0.988924i	$-0.452580\pi$
$227$	4.47245	0.296847	0.148423	+	0.988924i	$0.452580\pi$
$228$	−10.5417	−0.698140
$229$	26.5637	1.75538	0.877689	−	0.479231i	$-0.159084\pi$
$229$	26.5637	1.75538	0.877689	+	0.479231i	$0.159084\pi$
$230$	5.90888	0.389620
$231$	11.9713	0.787656
$232$	−4.38772	−0.288068
$233$	11.0628	0.724751	0.362375	−	0.932032i	$-0.381966\pi$
$233$	11.0628	0.724751	0.362375	+	0.932032i	$0.381966\pi$
$234$	−0.210113	−0.0137355
$235$	−2.97933	−0.194350
$236$	−12.7581	−0.830482
$237$	−11.1543	−0.724553
$238$	10.2960	0.667388
$239$	−3.06114	−0.198008	−0.0990042	−	0.995087i	$-0.531566\pi$
$239$	−3.06114	−0.198008	−0.0990042	+	0.995087i	$0.531566\pi$
$240$	−5.93830	−0.383316
$241$	5.35500	0.344946	0.172473	−	0.985014i	$-0.444824\pi$
$241$	5.35500	0.344946	0.172473	+	0.985014i	$0.444824\pi$
$242$	1.00000	0.0642824
$243$	20.2545	1.29932
$244$	−7.78077	−0.498113
$245$	28.5089	1.82136
$246$	−2.16994	−0.138350
$247$	−0.196166	−0.0124818
$248$	4.46633	0.283612
$249$	−36.7996	−2.33208
$250$	−11.2962	−0.714435
$251$	4.46708	0.281960	0.140980	−	0.990012i	$-0.454975\pi$
$251$	4.46708	0.281960	0.140980	+	0.990012i	$0.454975\pi$
$252$	18.7576	1.18162
$253$	−2.67113	−0.167932
$254$	−2.92947	−0.183811
$255$	−13.7100	−0.858555
$256$	1.00000	0.0625000
$257$	−8.70521	−0.543016	−0.271508	−	0.962436i	$-0.587522\pi$
$257$	−8.70521	−0.543016	−0.271508	+	0.962436i	$0.587522\pi$
$258$	4.95176	0.308283
$259$	49.7973	3.09425
$260$	−0.110504	−0.00685316
$261$	−18.4555	−1.14237
$262$	17.4944	1.08081
$263$	1.56043	0.0962201	0.0481101	−	0.998842i	$-0.484680\pi$
$263$	1.56043	0.0962201	0.0481101	+	0.998842i	$0.484680\pi$
$264$	2.68443	0.165215
$265$	9.27377	0.569683
$266$	17.5125	1.07376
$267$	6.57221	0.402213
$268$	9.32145	0.569398
$269$	−3.36730	−0.205308	−0.102654	−	0.994717i	$-0.532733\pi$
$269$	−3.36730	−0.205308	−0.102654	+	0.994717i	$0.532733\pi$
$270$	−7.16259	−0.435901
$271$	23.6189	1.43475	0.717374	−	0.696688i	$-0.245344\pi$
$271$	23.6189	1.43475	0.717374	+	0.696688i	$0.245344\pi$
$272$	2.30875	0.139988
$273$	0.598012	0.0361933
$274$	2.44222	0.147540
$275$	0.106494	0.00642181
$276$	−7.17046	−0.431611
$277$	−4.42502	−0.265874	−0.132937	−	0.991125i	$-0.542441\pi$
$277$	−4.42502	−0.265874	−0.132937	+	0.991125i	$0.542441\pi$
$278$	14.8639	0.891475
$279$	18.7861	1.12470
$280$	9.86508	0.589551
$281$	−21.9074	−1.30688	−0.653442	−	0.756977i	$-0.726676\pi$
$281$	−21.9074	−1.30688	−0.653442	+	0.756977i	$0.726676\pi$
$282$	3.61543	0.215296
$283$	−27.0931	−1.61052	−0.805260	−	0.592922i	$-0.797974\pi$
$283$	−27.0931	−1.61052	−0.805260	+	0.592922i	$0.797974\pi$
$284$	−13.4642	−0.798955
$285$	−23.3195	−1.38133
$286$	0.0499536	0.00295382
$287$	3.60484	0.212787
$288$	4.20617	0.247851
$289$	−11.6697	−0.686452
$290$	−9.70619	−0.569967
$291$	28.8159	1.68922
$292$	−7.02630	−0.411183
$293$	1.27144	0.0742780	0.0371390	−	0.999310i	$-0.488176\pi$
$293$	1.27144	0.0742780	0.0371390	+	0.999310i	$0.488176\pi$
$294$	−34.5957	−2.01766
$295$	−28.2225	−1.64318
$296$	11.1664	0.649037
$297$	3.23787	0.187881
$298$	3.39816	0.196850
$299$	−0.133433	−0.00771661
$300$	0.285875	0.0165050
$301$	−8.22618	−0.474149
$302$	−1.09000	−0.0627227
$303$	27.6373	1.58772
$304$	3.92697	0.225227
$305$	−17.2120	−0.985559
$306$	9.71097	0.555139
$307$	−22.0761	−1.25995	−0.629974	−	0.776616i	$-0.716934\pi$
$307$	−22.0761	−1.25995	−0.629974	+	0.776616i	$0.716934\pi$
$308$	−4.45954	−0.254106
$309$	20.0911	1.14295
$310$	9.88009	0.561152
$311$	−18.3309	−1.03945	−0.519726	−	0.854333i	$-0.673966\pi$
$311$	−18.3309	−1.03945	−0.519726	+	0.854333i	$0.673966\pi$
$312$	0.134097	0.00759175
$313$	−14.4768	−0.818278	−0.409139	−	0.912472i	$-0.634171\pi$
$313$	−14.4768	−0.818278	−0.409139	+	0.912472i	$0.634171\pi$
$314$	21.3066	1.20240
$315$	41.4942	2.33793
$316$	4.15520	0.233748
$317$	7.27339	0.408514	0.204257	−	0.978917i	$-0.434522\pi$
$317$	7.27339	0.408514	0.204257	+	0.978917i	$0.434522\pi$
$318$	−11.2538	−0.631080
$319$	4.38772	0.245665
$320$	2.21213	0.123662
$321$	1.66899	0.0931539
$322$	11.9120	0.663831
$323$	9.06638	0.504467
$324$	−3.92665	−0.218147
$325$	0.00531975	0.000295087 0
$326$	20.2406	1.12102
$327$	−13.6760	−0.756287
$328$	0.808342	0.0446332
$329$	−6.00618	−0.331132
$330$	5.93830	0.326893
$331$	4.21926	0.231912	0.115956	−	0.993254i	$-0.463007\pi$
$331$	4.21926	0.231912	0.115956	+	0.993254i	$0.463007\pi$
$332$	13.7085	0.752353
$333$	46.9680	2.57383
$334$	−5.75084	−0.314672
$335$	20.6202	1.12660
$336$	−11.9713	−0.653090
$337$	−17.4640	−0.951324	−0.475662	−	0.879628i	$-0.657791\pi$
$337$	−17.4640	−0.951324	−0.475662	+	0.879628i	$0.657791\pi$
$338$	−12.9975	−0.706971
$339$	48.5542	2.63710
$340$	5.10724	0.276979
$341$	−4.46633	−0.241865
$342$	16.5175	0.893164
$343$	26.2557	1.41768
$344$	−1.84462	−0.0994554
$345$	−15.8620	−0.853980
$346$	20.2207	1.08707
$347$	9.40787	0.505041	0.252520	−	0.967592i	$-0.418741\pi$
$347$	9.40787	0.505041	0.252520	+	0.967592i	$0.418741\pi$
$348$	11.7785	0.631395
$349$	−0.682681	−0.0365431	−0.0182715	−	0.999833i	$-0.505816\pi$
$349$	−0.682681	−0.0365431	−0.0182715	+	0.999833i	$0.505816\pi$
$350$	−0.474914	−0.0253852
$351$	0.161744	0.00863324
$352$	−1.00000	−0.0533002
$353$	−1.97132	−0.104923	−0.0524614	−	0.998623i	$-0.516707\pi$
$353$	−1.97132	−0.104923	−0.0524614	+	0.998623i	$0.516707\pi$
$354$	34.2482	1.82027
$355$	−29.7846	−1.58080
$356$	−2.44827	−0.129758
$357$	−27.6388	−1.46280
$358$	12.0962	0.639302
$359$	7.87847	0.415810	0.207905	−	0.978149i	$-0.433336\pi$
$359$	7.87847	0.415810	0.207905	+	0.978149i	$0.433336\pi$
$360$	9.30458	0.490394
$361$	−3.57891	−0.188364
$362$	−10.2771	−0.540154
$363$	−2.68443	−0.140896
$364$	−0.222770	−0.0116763
$365$	−15.5431	−0.813561
$366$	20.8869	1.09178
$367$	29.2478	1.52672	0.763361	−	0.645972i	$-0.223548\pi$
$367$	29.2478	1.52672	0.763361	+	0.645972i	$0.223548\pi$
$368$	2.67113	0.139242
$369$	3.40002	0.176998
$370$	24.7016	1.28418
$371$	18.6955	0.970621
$372$	−11.9896	−0.621630
$373$	3.11076	0.161069	0.0805346	−	0.996752i	$-0.474337\pi$
$373$	3.11076	0.161069	0.0805346	+	0.996752i	$0.474337\pi$
$374$	−2.30875	−0.119382
$375$	30.3239	1.56592
$376$	−1.34682	−0.0694567
$377$	0.219182	0.0112885
$378$	−14.4394	−0.742685
$379$	27.7425	1.42504	0.712518	−	0.701654i	$-0.247555\pi$
$379$	27.7425	1.42504	0.712518	+	0.701654i	$0.247555\pi$
$380$	8.68696	0.445631
$381$	7.86396	0.402883
$382$	−2.25144	−0.115194
$383$	14.8989	0.761297	0.380648	−	0.924720i	$-0.375701\pi$
$383$	14.8989	0.761297	0.380648	+	0.924720i	$0.375701\pi$
$384$	−2.68443	−0.136989
$385$	−9.86508	−0.502771
$386$	−12.5770	−0.640150
$387$	−7.75880	−0.394402
$388$	−10.7345	−0.544960
$389$	−14.8110	−0.750946	−0.375473	−	0.926833i	$-0.622520\pi$
$389$	−14.8110	−0.750946	−0.375473	+	0.926833i	$0.622520\pi$
$390$	0.296640	0.0150209
$391$	6.16696	0.311876
$392$	12.8875	0.650919
$393$	−46.9625	−2.36894
$394$	−1.00000	−0.0503793
$395$	9.19183	0.462491
$396$	−4.20617	−0.211368
$397$	0.644823	0.0323627	0.0161814	−	0.999869i	$-0.494849\pi$
$397$	0.644823	0.0323627	0.0161814	+	0.999869i	$0.494849\pi$
$398$	4.84998	0.243108
$399$	−47.0111	−2.35350
$400$	−0.106494	−0.00532469
$401$	−3.91068	−0.195290	−0.0976450	−	0.995221i	$-0.531131\pi$
$401$	−3.91068	−0.195290	−0.0976450	+	0.995221i	$0.531131\pi$
$402$	−25.0228	−1.24802
$403$	−0.223110	−0.0111139
$404$	−10.2954	−0.512216
$405$	−8.68626	−0.431624
$406$	−19.5672	−0.971105
$407$	−11.1664	−0.553500
$408$	−6.19767	−0.306830
$409$	−6.47831	−0.320332	−0.160166	−	0.987090i	$-0.551203\pi$
$409$	−6.47831	−0.320332	−0.160166	+	0.987090i	$0.551203\pi$
$410$	1.78816	0.0883107
$411$	−6.55598	−0.323383
$412$	−7.48432	−0.368726
$413$	−56.8953	−2.79964
$414$	11.2352	0.552181
$415$	30.3250	1.48860
$416$	−0.0499536	−0.00244918
$417$	−39.9010	−1.95396
$418$	−3.92697	−0.192074
$419$	10.4551	0.510765	0.255383	−	0.966840i	$-0.417799\pi$
$419$	10.4551	0.510765	0.255383	+	0.966840i	$0.417799\pi$
$420$	−26.4821	−1.29220
$421$	12.4443	0.606497	0.303249	−	0.952911i	$-0.401929\pi$
$421$	12.4443	0.606497	0.303249	+	0.952911i	$0.401929\pi$
$422$	−12.1866	−0.593233
$423$	−5.66493	−0.275438
$424$	4.19224	0.203593
$425$	−0.245867	−0.0119263
$426$	36.1438	1.75117
$427$	−34.6987	−1.67919
$428$	−0.621729	−0.0300524
$429$	−0.134097	−0.00647427
$430$	−4.08054	−0.196781
$431$	40.0542	1.92934	0.964671	−	0.263456i	$-0.0848625\pi$
$431$	40.0542	1.92934	0.964671	+	0.263456i	$0.0848625\pi$
$432$	−3.23787	−0.155782
$433$	35.3222	1.69748	0.848738	−	0.528813i	$-0.177363\pi$
$433$	35.3222	1.69748	0.848738	+	0.528813i	$0.177363\pi$
$434$	19.9178	0.956085
$435$	26.0556	1.24927
$436$	5.09458	0.243986
$437$	10.4894	0.501778
$438$	18.8616	0.901242
$439$	11.5766	0.552523	0.276261	−	0.961083i	$-0.410904\pi$
$439$	11.5766	0.552523	0.276261	+	0.961083i	$0.410904\pi$
$440$	−2.21213	−0.105459
$441$	54.2071	2.58129
$442$	−0.115330	−0.00548570
$443$	−5.48117	−0.260418	−0.130209	−	0.991487i	$-0.541565\pi$
$443$	−5.48117	−0.260418	−0.130209	+	0.991487i	$0.541565\pi$
$444$	−29.9756	−1.42258
$445$	−5.41588	−0.256738
$446$	7.79077	0.368904
$447$	−9.12213	−0.431462
$448$	4.45954	0.210694
$449$	23.9530	1.13041	0.565206	−	0.824950i	$-0.308797\pi$
$449$	23.9530	1.13041	0.565206	+	0.824950i	$0.308797\pi$
$450$	−0.447931	−0.0211157
$451$	−0.808342	−0.0380633
$452$	−18.0873	−0.850757
$453$	2.92604	0.137477
$454$	4.47245	0.209902
$455$	−0.492797	−0.0231027
$456$	−10.5417	−0.493659
$457$	−21.5716	−1.00908	−0.504538	−	0.863389i	$-0.668337\pi$
$457$	−21.5716	−1.00908	−0.504538	+	0.863389i	$0.668337\pi$
$458$	26.5637	1.24124
$459$	−7.47543	−0.348923
$460$	5.90888	0.275503
$461$	−33.2628	−1.54920	−0.774602	−	0.632450i	$-0.782050\pi$
$461$	−33.2628	−1.54920	−0.774602	+	0.632450i	$0.782050\pi$
$462$	11.9713	0.556957
$463$	16.3477	0.759744	0.379872	−	0.925039i	$-0.375968\pi$
$463$	16.3477	0.759744	0.379872	+	0.925039i	$0.375968\pi$
$464$	−4.38772	−0.203695
$465$	−26.5224	−1.22995
$466$	11.0628	0.512476
$467$	−29.5182	−1.36594	−0.682969	−	0.730448i	$-0.739312\pi$
$467$	−29.5182	−1.36594	−0.682969	+	0.730448i	$0.739312\pi$
$468$	−0.210113	−0.00971250
$469$	41.5694	1.91950
$470$	−2.97933	−0.137426
$471$	−57.1960	−2.63545
$472$	−12.7581	−0.587239
$473$	1.84462	0.0848159
$474$	−11.1543	−0.512336
$475$	−0.418198	−0.0191882
$476$	10.2960	0.471914
$477$	17.6333	0.807372
$478$	−3.06114	−0.140013
$479$	−41.6202	−1.90168	−0.950838	−	0.309688i	$-0.899775\pi$
$479$	−41.6202	−1.90168	−0.950838	+	0.309688i	$0.899775\pi$
$480$	−5.93830	−0.271045
$481$	−0.557805	−0.0254337
$482$	5.35500	0.243914
$483$	−31.9770	−1.45500
$484$	1.00000	0.0454545
$485$	−23.7460	−1.07825
$486$	20.2545	0.918761
$487$	−8.43538	−0.382243	−0.191122	−	0.981566i	$-0.561213\pi$
$487$	−8.43538	−0.382243	−0.191122	+	0.981566i	$0.561213\pi$
$488$	−7.78077	−0.352219
$489$	−54.3346	−2.45709
$490$	28.5089	1.28790
$491$	−6.30386	−0.284489	−0.142245	−	0.989832i	$-0.545432\pi$
$491$	−6.30386	−0.284489	−0.142245	+	0.989832i	$0.545432\pi$
$492$	−2.16994	−0.0978284
$493$	−10.1301	−0.456238
$494$	−0.196166	−0.00882595
$495$	−9.30458	−0.418210
$496$	4.46633	0.200544
$497$	−60.0443	−2.69336
$498$	−36.7996	−1.64903
$499$	39.1272	1.75157	0.875787	−	0.482697i	$-0.160343\pi$
$499$	39.1272	1.75157	0.875787	+	0.482697i	$0.160343\pi$
$500$	−11.2962	−0.505182
$501$	15.4377	0.689707
$502$	4.46708	0.199376
$503$	32.5061	1.44938	0.724688	−	0.689077i	$-0.241984\pi$
$503$	32.5061	1.44938	0.724688	+	0.689077i	$0.241984\pi$
$504$	18.7576	0.835530
$505$	−22.7748	−1.01346
$506$	−2.67113	−0.118746
$507$	34.8909	1.54956
$508$	−2.92947	−0.129974
$509$	−10.1356	−0.449253	−0.224626	−	0.974445i	$-0.572116\pi$
$509$	−10.1356	−0.449253	−0.224626	+	0.974445i	$0.572116\pi$
$510$	−13.7100	−0.607090
$511$	−31.3341	−1.38614
$512$	1.00000	0.0441942
$513$	−12.7150	−0.561383
$514$	−8.70521	−0.383970
$515$	−16.5563	−0.729557
$516$	4.95176	0.217989
$517$	1.34682	0.0592329
$518$	49.7973	2.18797
$519$	−54.2810	−2.38267
$520$	−0.110504	−0.00484591
$521$	1.27357	0.0557962	0.0278981	−	0.999611i	$-0.491119\pi$
$521$	1.27357	0.0557962	0.0278981	+	0.999611i	$0.491119\pi$
$522$	−18.4555	−0.807774
$523$	14.4973	0.633922	0.316961	−	0.948438i	$-0.397337\pi$
$523$	14.4973	0.633922	0.316961	+	0.948438i	$0.397337\pi$
$524$	17.4944	0.764246
$525$	1.27487	0.0556400
$526$	1.56043	0.0680379
$527$	10.3116	0.449182
$528$	2.68443	0.116825
$529$	−15.8651	−0.689786
$530$	9.27377	0.402827
$531$	−53.6627	−2.32876
$532$	17.5125	0.759263
$533$	−0.0403796	−0.00174904
$534$	6.57221	0.284407
$535$	−1.37534	−0.0594613
$536$	9.32145	0.402625
$537$	−32.4713	−1.40124
$538$	−3.36730	−0.145175
$539$	−12.8875	−0.555105
$540$	−7.16259	−0.308229
$541$	−23.8991	−1.02750	−0.513752	−	0.857939i	$-0.671745\pi$
$541$	−23.8991	−1.02750	−0.513752	+	0.857939i	$0.671745\pi$
$542$	23.6189	1.01452
$543$	27.5883	1.18393
$544$	2.30875	0.0989867
$545$	11.2699	0.482748
$546$	0.598012	0.0255925
$547$	−7.48686	−0.320115	−0.160057	−	0.987108i	$-0.551168\pi$
$547$	−7.48686	−0.320115	−0.160057	+	0.987108i	$0.551168\pi$
$548$	2.44222	0.104327
$549$	−32.7272	−1.39676
$550$	0.106494	0.00454091
$551$	−17.2304	−0.734041
$552$	−7.17046	−0.305195
$553$	18.5303	0.787988
$554$	−4.42502	−0.188001
$555$	−66.3097	−2.81469
$556$	14.8639	0.630368
$557$	4.23340	0.179375	0.0896874	−	0.995970i	$-0.471413\pi$
$557$	4.23340	0.179375	0.0896874	+	0.995970i	$0.471413\pi$
$558$	18.7861	0.795281
$559$	0.0921457	0.00389735
$560$	9.86508	0.416876
$561$	6.19767	0.261666
$562$	−21.9074	−0.924106
$563$	−13.1430	−0.553912	−0.276956	−	0.960883i	$-0.589326\pi$
$563$	−13.1430	−0.553912	−0.276956	+	0.960883i	$0.589326\pi$
$564$	3.61543	0.152237
$565$	−40.0115	−1.68330
$566$	−27.0931	−1.13881
$567$	−17.5111	−0.735396
$568$	−13.4642	−0.564946
$569$	−43.7049	−1.83221	−0.916103	−	0.400942i	$-0.868683\pi$
$569$	−43.7049	−1.83221	−0.916103	+	0.400942i	$0.868683\pi$
$570$	−23.3195	−0.976748
$571$	15.1602	0.634436	0.317218	−	0.948353i	$-0.397251\pi$
$571$	15.1602	0.634436	0.317218	+	0.948353i	$0.397251\pi$
$572$	0.0499536	0.00208867
$573$	6.04384	0.252485
$574$	3.60484	0.150463
$575$	−0.284458	−0.0118627
$576$	4.20617	0.175257
$577$	−27.3076	−1.13683	−0.568416	−	0.822742i	$-0.692443\pi$
$577$	−27.3076	−1.13683	−0.568416	+	0.822742i	$0.692443\pi$
$578$	−11.6697	−0.485395
$579$	33.7620	1.40310
$580$	−9.70619	−0.403027
$581$	61.1338	2.53626
$582$	28.8159	1.19446
$583$	−4.19224	−0.173625
$584$	−7.02630	−0.290750
$585$	−0.464798	−0.0192170
$586$	1.27144	0.0525225
$587$	−31.1562	−1.28595	−0.642976	−	0.765886i	$-0.722301\pi$
$587$	−31.1562	−1.28595	−0.642976	+	0.765886i	$0.722301\pi$
$588$	−34.5957	−1.42670
$589$	17.5392	0.722688
$590$	−28.2225	−1.16190
$591$	2.68443	0.110423
$592$	11.1664	0.458938
$593$	32.0293	1.31529	0.657644	−	0.753329i	$-0.271553\pi$
$593$	32.0293	1.31529	0.657644	+	0.753329i	$0.271553\pi$
$594$	3.23787	0.132852
$595$	22.7760	0.933723
$596$	3.39816	0.139194
$597$	−13.0194	−0.532850
$598$	−0.133433	−0.00545646
$599$	−13.3016	−0.543487	−0.271743	−	0.962370i	$-0.587600\pi$
$599$	−13.3016	−0.543487	−0.271743	+	0.962370i	$0.587600\pi$
$600$	0.285875	0.0116708
$601$	15.6524	0.638475	0.319237	−	0.947675i	$-0.396573\pi$
$601$	15.6524	0.638475	0.319237	+	0.947675i	$0.396573\pi$
$602$	−8.22618	−0.335274
$603$	39.2076	1.59666
$604$	−1.09000	−0.0443516
$605$	2.21213	0.0899358
$606$	27.6373	1.12269
$607$	3.64612	0.147991	0.0739957	−	0.997259i	$-0.476425\pi$
$607$	3.64612	0.147991	0.0739957	+	0.997259i	$0.476425\pi$
$608$	3.92697	0.159260
$609$	52.5268	2.12849
$610$	−17.2120	−0.696896
$611$	0.0672783	0.00272179
$612$	9.71097	0.392543
$613$	−34.1518	−1.37938	−0.689689	−	0.724105i	$-0.742253\pi$
$613$	−34.1518	−1.37938	−0.689689	+	0.724105i	$0.742253\pi$
$614$	−22.0761	−0.890917
$615$	−4.80018	−0.193562
$616$	−4.45954	−0.179680
$617$	−4.28860	−0.172653	−0.0863264	−	0.996267i	$-0.527513\pi$
$617$	−4.28860	−0.172653	−0.0863264	+	0.996267i	$0.527513\pi$
$618$	20.0911	0.808184
$619$	−0.333229	−0.0133936	−0.00669680	−	0.999978i	$-0.502132\pi$
$619$	−0.333229	−0.0133936	−0.00669680	+	0.999978i	$0.502132\pi$
$620$	9.88009	0.396794
$621$	−8.64878	−0.347064
$622$	−18.3309	−0.735004
$623$	−10.9182	−0.437427
$624$	0.134097	0.00536818
$625$	−24.4562	−0.978248
$626$	−14.4768	−0.578610
$627$	10.5417	0.420994
$628$	21.3066	0.850225
$629$	25.7805	1.02794
$630$	41.4942	1.65317
$631$	−0.812491	−0.0323447	−0.0161724	−	0.999869i	$-0.505148\pi$
$631$	−0.812491	−0.0323447	−0.0161724	+	0.999869i	$0.505148\pi$
$632$	4.15520	0.165285
$633$	32.7140	1.30026
$634$	7.27339	0.288863
$635$	−6.48036	−0.257165
$636$	−11.2538	−0.446241
$637$	−0.643779	−0.0255075
$638$	4.38772	0.173711
$639$	−56.6328	−2.24036
$640$	2.21213	0.0874420
$641$	4.98919	0.197061	0.0985307	−	0.995134i	$-0.468586\pi$
$641$	4.98919	0.197061	0.0985307	+	0.995134i	$0.468586\pi$
$642$	1.66899	0.0658697
$643$	−28.0276	−1.10530	−0.552651	−	0.833413i	$-0.686384\pi$
$643$	−28.0276	−1.10530	−0.552651	+	0.833413i	$0.686384\pi$
$644$	11.9120	0.469399
$645$	10.9539	0.431311
$646$	9.06638	0.356712
$647$	23.6508	0.929809	0.464905	−	0.885361i	$-0.346089\pi$
$647$	23.6508	0.929809	0.464905	+	0.885361i	$0.346089\pi$
$648$	−3.92665	−0.154254
$649$	12.7581	0.500799
$650$	0.00531975	0.000208658 0
$651$	−53.4680	−2.09557
$652$	20.2406	0.792684
$653$	41.8979	1.63959	0.819796	−	0.572656i	$-0.194087\pi$
$653$	41.8979	1.63959	0.819796	+	0.572656i	$0.194087\pi$
$654$	−13.6760	−0.534776
$655$	38.6998	1.51213
$656$	0.808342	0.0315605
$657$	−29.5538	−1.15300
$658$	−6.00618	−0.234145
$659$	−40.1580	−1.56433	−0.782167	−	0.623069i	$-0.785886\pi$
$659$	−40.1580	−1.56433	−0.782167	+	0.623069i	$0.785886\pi$
$660$	5.93830	0.231148
$661$	12.6835	0.493332	0.246666	−	0.969101i	$-0.420665\pi$
$661$	12.6835	0.493332	0.246666	+	0.969101i	$0.420665\pi$
$662$	4.21926	0.163986
$663$	0.309596	0.0120237
$664$	13.7085	0.531994
$665$	38.7399	1.50227
$666$	46.9680	1.81997
$667$	−11.7202	−0.453806
$668$	−5.75084	−0.222507
$669$	−20.9138	−0.808573
$670$	20.6202	0.796629
$671$	7.78077	0.300373
$672$	−11.9713	−0.461804
$673$	16.4845	0.635432	0.317716	−	0.948186i	$-0.397084\pi$
$673$	16.4845	0.635432	0.317716	+	0.948186i	$0.397084\pi$
$674$	−17.4640	−0.672687
$675$	0.344813	0.0132719
$676$	−12.9975	−0.499904
$677$	−49.0497	−1.88513	−0.942567	−	0.334016i	$-0.891596\pi$
$677$	−49.0497	−1.88513	−0.942567	+	0.334016i	$0.891596\pi$
$678$	48.5542	1.86471
$679$	−47.8708	−1.83711
$680$	5.10724	0.195854
$681$	−12.0060	−0.460070
$682$	−4.46633	−0.171025
$683$	45.6210	1.74564	0.872820	−	0.488043i	$-0.162289\pi$
$683$	45.6210	1.74564	0.872820	+	0.488043i	$0.162289\pi$
$684$	16.5175	0.631562
$685$	5.40251	0.206419
$686$	26.2557	1.00245
$687$	−71.3084	−2.72058
$688$	−1.84462	−0.0703256
$689$	−0.209418	−0.00797818
$690$	−15.8620	−0.603855
$691$	−19.4315	−0.739208	−0.369604	−	0.929189i	$-0.620507\pi$
$691$	−19.4315	−0.739208	−0.369604	+	0.929189i	$0.620507\pi$
$692$	20.2207	0.768675
$693$	−18.7576	−0.712542
$694$	9.40787	0.357118
$695$	32.8807	1.24724
$696$	11.7785	0.446464
$697$	1.86626	0.0706895
$698$	−0.682681	−0.0258399
$699$	−29.6974	−1.12326
$700$	−0.474914	−0.0179500
$701$	8.09771	0.305846	0.152923	−	0.988238i	$-0.451131\pi$
$701$	8.09771	0.305846	0.152923	+	0.988238i	$0.451131\pi$
$702$	0.161744	0.00610462
$703$	43.8503	1.65385
$704$	−1.00000	−0.0376889
$705$	7.99780	0.301214
$706$	−1.97132	−0.0741916
$707$	−45.9128	−1.72673
$708$	34.2482	1.28713
$709$	−20.7873	−0.780685	−0.390342	−	0.920670i	$-0.627643\pi$
$709$	−20.7873	−0.780685	−0.390342	+	0.920670i	$0.627643\pi$
$710$	−29.7846	−1.11780
$711$	17.4775	0.655456
$712$	−2.44827	−0.0917528
$713$	11.9301	0.446788
$714$	−27.6388	−1.03436
$715$	0.110504	0.00413261
$716$	12.0962	0.452055
$717$	8.21741	0.306885
$718$	7.87847	0.294022
$719$	−13.1789	−0.491491	−0.245745	−	0.969334i	$-0.579033\pi$
$719$	−13.1789	−0.491491	−0.245745	+	0.969334i	$0.579033\pi$
$720$	9.30458	0.346761
$721$	−33.3767	−1.24301
$722$	−3.57891	−0.133193
$723$	−14.3751	−0.534617
$724$	−10.2771	−0.381947
$725$	0.467264	0.0173538
$726$	−2.68443	−0.0996286
$727$	47.4272	1.75898	0.879489	−	0.475918i	$-0.157884\pi$
$727$	47.4272	1.75898	0.879489	+	0.475918i	$0.157884\pi$
$728$	−0.222770	−0.00825642
$729$	−42.5917	−1.57747
$730$	−15.5431	−0.575275
$731$	−4.25877	−0.157516
$732$	20.8869	0.772003
$733$	−34.0100	−1.25619	−0.628095	−	0.778137i	$-0.716165\pi$
$733$	−34.0100	−1.25619	−0.628095	+	0.778137i	$0.716165\pi$
$734$	29.2478	1.07956
$735$	−76.5301	−2.82285
$736$	2.67113	0.0984591
$737$	−9.32145	−0.343360
$738$	3.40002	0.125157
$739$	−9.39539	−0.345615	−0.172808	−	0.984956i	$-0.555284\pi$
$739$	−9.39539	−0.345615	−0.172808	+	0.984956i	$0.555284\pi$
$740$	24.7016	0.908049
$741$	0.526595	0.0193450
$742$	18.6955	0.686333
$743$	−24.5271	−0.899811	−0.449905	−	0.893076i	$-0.648542\pi$
$743$	−24.5271	−0.899811	−0.449905	+	0.893076i	$0.648542\pi$
$744$	−11.9896	−0.439559
$745$	7.51717	0.275408
$746$	3.11076	0.113893
$747$	57.6604	2.10968
$748$	−2.30875	−0.0844161
$749$	−2.77263	−0.101310
$750$	30.3239	1.10727
$751$	−46.3498	−1.69133	−0.845664	−	0.533716i	$-0.820795\pi$
$751$	−46.3498	−1.69133	−0.845664	+	0.533716i	$0.820795\pi$
$752$	−1.34682	−0.0491133
$753$	−11.9916	−0.436997
$754$	0.219182	0.00798215
$755$	−2.41123	−0.0877535
$756$	−14.4394	−0.525158
$757$	−4.47486	−0.162641	−0.0813207	−	0.996688i	$-0.525914\pi$
$757$	−4.47486	−0.162641	−0.0813207	+	0.996688i	$0.525914\pi$
$758$	27.7425	1.00765
$759$	7.17046	0.260271
$760$	8.68696	0.315109
$761$	32.6907	1.18504	0.592518	−	0.805557i	$-0.298134\pi$
$761$	32.6907	1.18504	0.592518	+	0.805557i	$0.298134\pi$
$762$	7.86396	0.284881
$763$	22.7195	0.822501
$764$	−2.25144	−0.0814543
$765$	21.4819	0.776680
$766$	14.8989	0.538318
$767$	0.637314	0.0230121
$768$	−2.68443	−0.0968660
$769$	29.4142	1.06070	0.530351	−	0.847778i	$-0.322060\pi$
$769$	29.4142	1.06070	0.530351	+	0.847778i	$0.322060\pi$
$770$	−9.86508	−0.355513
$771$	23.3685	0.841597
$772$	−12.5770	−0.452655
$773$	−37.6981	−1.35591	−0.677953	−	0.735105i	$-0.737133\pi$
$773$	−37.6981	−1.35591	−0.677953	+	0.735105i	$0.737133\pi$
$774$	−7.75880	−0.278884
$775$	−0.475636	−0.0170854
$776$	−10.7345	−0.385345
$777$	−133.677	−4.79565
$778$	−14.8110	−0.530999
$779$	3.17434	0.113732
$780$	0.296640	0.0106214
$781$	13.4642	0.481788
$782$	6.16696	0.220530
$783$	14.2069	0.507712
$784$	12.8875	0.460269
$785$	47.1328	1.68224
$786$	−46.9625	−1.67510
$787$	30.6278	1.09176	0.545882	−	0.837862i	$-0.316195\pi$
$787$	30.6278	1.09176	0.545882	+	0.837862i	$0.316195\pi$
$788$	−1.00000	−0.0356235
$789$	−4.18886	−0.149127
$790$	9.19183	0.327031
$791$	−80.6613	−2.86799
$792$	−4.20617	−0.149460
$793$	0.388678	0.0138024
$794$	0.644823	0.0228839
$795$	−24.8948	−0.882927
$796$	4.84998	0.171903
$797$	−19.3495	−0.685395	−0.342697	−	0.939446i	$-0.611341\pi$
$797$	−19.3495	−0.685395	−0.342697	+	0.939446i	$0.611341\pi$
$798$	−47.0111	−1.66417
$799$	−3.10945	−0.110005
$800$	−0.106494	−0.00376512
$801$	−10.2978	−0.363856
$802$	−3.91068	−0.138091
$803$	7.02630	0.247953
$804$	−25.0228	−0.882485
$805$	26.3509	0.928747
$806$	−0.223110	−0.00785870
$807$	9.03928	0.318198
$808$	−10.2954	−0.362191
$809$	−18.5650	−0.652711	−0.326355	−	0.945247i	$-0.605821\pi$
$809$	−18.5650	−0.652711	−0.326355	+	0.945247i	$0.605821\pi$
$810$	−8.68626	−0.305204
$811$	24.5934	0.863592	0.431796	−	0.901971i	$-0.357880\pi$
$811$	24.5934	0.863592	0.431796	+	0.901971i	$0.357880\pi$
$812$	−19.5672	−0.686675
$813$	−63.4034	−2.22365
$814$	−11.1664	−0.391384
$815$	44.7748	1.56839
$816$	−6.19767	−0.216962
$817$	−7.24378	−0.253428
$818$	−6.47831	−0.226509
$819$	−0.937010	−0.0327418
$820$	1.78816	0.0624451
$821$	21.0187	0.733558	0.366779	−	0.930308i	$-0.380460\pi$
$821$	21.0187	0.733558	0.366779	+	0.930308i	$0.380460\pi$
$822$	−6.55598	−0.228666
$823$	−32.8778	−1.14605	−0.573025	−	0.819538i	$-0.694230\pi$
$823$	−32.8778	−1.14605	−0.573025	+	0.819538i	$0.694230\pi$
$824$	−7.48432	−0.260729
$825$	−0.285875	−0.00995289
$826$	−56.8953	−1.97964
$827$	−32.3642	−1.12541	−0.562707	−	0.826656i	$-0.690240\pi$
$827$	−32.3642	−1.12541	−0.562707	+	0.826656i	$0.690240\pi$
$828$	11.2352	0.390451
$829$	49.2894	1.71189	0.855946	−	0.517065i	$-0.172975\pi$
$829$	49.2894	1.71189	0.855946	+	0.517065i	$0.172975\pi$
$830$	30.3250	1.05260
$831$	11.8787	0.412066
$832$	−0.0499536	−0.00173183
$833$	29.7540	1.03092
$834$	−39.9010	−1.38166
$835$	−12.7216	−0.440249
$836$	−3.92697	−0.135817
$837$	−14.4614	−0.499860
$838$	10.4551	0.361165
$839$	15.2131	0.525214	0.262607	−	0.964903i	$-0.415418\pi$
$839$	15.2131	0.525214	0.262607	+	0.964903i	$0.415418\pi$
$840$	−26.4821	−0.913720
$841$	−9.74794	−0.336136
$842$	12.4443	0.428858
$843$	58.8088	2.02548
$844$	−12.1866	−0.419479
$845$	−28.7521	−0.989103
$846$	−5.66493	−0.194764
$847$	4.45954	0.153232
$848$	4.19224	0.143962
$849$	72.7296	2.49607
$850$	−0.245867	−0.00843317
$851$	29.8270	1.02246
$852$	36.1438	1.23827
$853$	−50.0067	−1.71220	−0.856098	−	0.516813i	$-0.827118\pi$
$853$	−50.0067	−1.71220	−0.856098	+	0.516813i	$0.827118\pi$
$854$	−34.6987	−1.18736
$855$	36.5388	1.24960
$856$	−0.621729	−0.0212503
$857$	−24.9914	−0.853691	−0.426845	−	0.904325i	$-0.640375\pi$
$857$	−24.9914	−0.853691	−0.426845	+	0.904325i	$0.640375\pi$
$858$	−0.134097	−0.00457800
$859$	−47.6678	−1.62641	−0.813203	−	0.581980i	$-0.802278\pi$
$859$	−47.6678	−1.62641	−0.813203	+	0.581980i	$0.802278\pi$
$860$	−4.08054	−0.139145
$861$	−9.67694	−0.329789
$862$	40.0542	1.36425
$863$	−33.6781	−1.14642	−0.573209	−	0.819410i	$-0.694302\pi$
$863$	−33.6781	−1.14642	−0.573209	+	0.819410i	$0.694302\pi$
$864$	−3.23787	−0.110155
$865$	44.7307	1.52089
$866$	35.3222	1.20030
$867$	31.3265	1.06390
$868$	19.9178	0.676054
$869$	−4.15520	−0.140956
$870$	26.0556	0.883367
$871$	−0.465640	−0.0157776
$872$	5.09458	0.172524
$873$	−45.1509	−1.52813
$874$	10.4894	0.354811
$875$	−50.3760	−1.70302
$876$	18.8616	0.637275
$877$	−36.5044	−1.23266	−0.616332	−	0.787486i	$-0.711382\pi$
$877$	−36.5044	−1.23266	−0.616332	+	0.787486i	$0.711382\pi$
$878$	11.5766	0.390693
$879$	−3.41308	−0.115120
$880$	−2.21213	−0.0745708
$881$	37.2565	1.25520	0.627601	−	0.778535i	$-0.284037\pi$
$881$	37.2565	1.25520	0.627601	+	0.778535i	$0.284037\pi$
$882$	54.2071	1.82525
$883$	14.7757	0.497243	0.248621	−	0.968601i	$-0.420022\pi$
$883$	14.7757	0.497243	0.248621	+	0.968601i	$0.420022\pi$
$884$	−0.115330	−0.00387898
$885$	75.7615	2.54669
$886$	−5.48117	−0.184144
$887$	−32.6500	−1.09628	−0.548140	−	0.836386i	$-0.684664\pi$
$887$	−32.6500	−1.09628	−0.548140	+	0.836386i	$0.684664\pi$
$888$	−29.9756	−1.00591
$889$	−13.0641	−0.438156
$890$	−5.41588	−0.181541
$891$	3.92665	0.131548
$892$	7.79077	0.260854
$893$	−5.28890	−0.176986
$894$	−9.12213	−0.305090
$895$	26.7582	0.894429
$896$	4.45954	0.148983
$897$	0.358191	0.0119596
$898$	23.9530	0.799323
$899$	−19.5970	−0.653597
$900$	−0.447931	−0.0149310
$901$	9.67882	0.322448
$902$	−0.808342	−0.0269149
$903$	22.0826	0.734863
$904$	−18.0873	−0.601576
$905$	−22.7343	−0.755715
$906$	2.92604	0.0972112
$907$	−31.7642	−1.05471	−0.527356	−	0.849644i	$-0.676817\pi$
$907$	−31.7642	−1.05471	−0.527356	+	0.849644i	$0.676817\pi$
$908$	4.47245	0.148423
$909$	−43.3042	−1.43631
$910$	−0.492797	−0.0163360
$911$	−48.0546	−1.59212	−0.796060	−	0.605218i	$-0.793086\pi$
$911$	−48.0546	−1.59212	−0.796060	+	0.605218i	$0.793086\pi$
$912$	−10.5417	−0.349070
$913$	−13.7085	−0.453686
$914$	−21.5716	−0.713525
$915$	46.2046	1.52748
$916$	26.5637	0.877689
$917$	78.0170	2.57635
$918$	−7.47543	−0.246726
$919$	28.1344	0.928067	0.464033	−	0.885818i	$-0.346402\pi$
$919$	28.1344	0.928067	0.464033	+	0.885818i	$0.346402\pi$
$920$	5.90888	0.194810
$921$	59.2617	1.95274
$922$	−33.2628	−1.09545
$923$	0.672587	0.0221385
$924$	11.9713	0.393828
$925$	−1.18916	−0.0390992
$926$	16.3477	0.537220
$927$	−31.4803	−1.03395
$928$	−4.38772	−0.144034
$929$	23.4285	0.768666	0.384333	−	0.923195i	$-0.374431\pi$
$929$	23.4285	0.768666	0.384333	+	0.923195i	$0.374431\pi$
$930$	−26.5224	−0.869705
$931$	50.6089	1.65864
$932$	11.0628	0.362375
$933$	49.2081	1.61100
$934$	−29.5182	−0.965864
$935$	−5.10724	−0.167025
$936$	−0.210113	−0.00686777
$937$	11.4682	0.374650	0.187325	−	0.982298i	$-0.440018\pi$
$937$	11.4682	0.374650	0.187325	+	0.982298i	$0.440018\pi$
$938$	41.5694	1.35729
$939$	38.8620	1.26821
$940$	−2.97933	−0.0971749
$941$	−5.19188	−0.169250	−0.0846252	−	0.996413i	$-0.526969\pi$
$941$	−5.19188	−0.169250	−0.0846252	+	0.996413i	$0.526969\pi$
$942$	−57.1960	−1.86355
$943$	2.15919	0.0703128
$944$	−12.7581	−0.415241
$945$	−31.9419	−1.03907
$946$	1.84462	0.0599739
$947$	1.03061	0.0334904	0.0167452	−	0.999860i	$-0.494670\pi$
$947$	1.03061	0.0334904	0.0167452	+	0.999860i	$0.494670\pi$
$948$	−11.1543	−0.362276
$949$	0.350989	0.0113936
$950$	−0.418198	−0.0135681
$951$	−19.5249	−0.633139
$952$	10.2960	0.333694
$953$	10.2253	0.331229	0.165615	−	0.986191i	$-0.447039\pi$
$953$	10.2253	0.331229	0.165615	+	0.986191i	$0.447039\pi$
$954$	17.6333	0.570898
$955$	−4.98048	−0.161164
$956$	−3.06114	−0.0990042
$957$	−11.7785	−0.380746
$958$	−41.6202	−1.34469
$959$	10.8912	0.351695
$960$	−5.93830	−0.191658
$961$	−11.0519	−0.356512
$962$	−0.557805	−0.0179843
$963$	−2.61510	−0.0842703
$964$	5.35500	0.172473
$965$	−27.8218	−0.895616
$966$	−31.9770	−1.02884
$967$	−27.4056	−0.881306	−0.440653	−	0.897678i	$-0.645253\pi$
$967$	−27.4056	−0.881306	−0.440653	+	0.897678i	$0.645253\pi$
$968$	1.00000	0.0321412
$969$	−24.3381	−0.781851
$970$	−23.7460	−0.762438
$971$	1.36481	0.0437989	0.0218994	−	0.999760i	$-0.493029\pi$
$971$	1.36481	0.0437989	0.0218994	+	0.999760i	$0.493029\pi$
$972$	20.2545	0.649662
$973$	66.2860	2.12503
$974$	−8.43538	−0.270287
$975$	−0.0142805	−0.000457342 0
$976$	−7.78077	−0.249056
$977$	−41.4923	−1.32746	−0.663728	−	0.747974i	$-0.731027\pi$
$977$	−41.4923	−1.32746	−0.663728	+	0.747974i	$0.731027\pi$
$978$	−54.3346	−1.73743
$979$	2.44827	0.0782470
$980$	28.5089	0.910682
$981$	21.4287	0.684164
$982$	−6.30386	−0.201164
$983$	−36.0601	−1.15014	−0.575070	−	0.818104i	$-0.695025\pi$
$983$	−36.0601	−1.15014	−0.575070	+	0.818104i	$0.695025\pi$
$984$	−2.16994	−0.0691751
$985$	−2.21213	−0.0704842
$986$	−10.1301	−0.322609
$987$	16.1232	0.513207
$988$	−0.196166	−0.00624089
$989$	−4.92723	−0.156677
$990$	−9.30458	−0.295719
$991$	−16.1902	−0.514300	−0.257150	−	0.966372i	$-0.582783\pi$
$991$	−16.1902	−0.514300	−0.257150	+	0.966372i	$0.582783\pi$
$992$	4.46633	0.141806
$993$	−11.3263	−0.359430
$994$	−60.0443	−1.90449
$995$	10.7288	0.340125
$996$	−36.7996	−1.16604
$997$	22.6653	0.717818	0.358909	−	0.933372i	$-0.383149\pi$
$997$	22.6653	0.717818	0.358909	+	0.933372i	$0.383149\pi$
$998$	39.1272	1.23855
$999$	−36.1556	−1.14391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.2	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.68443 q^{3} +1.00000 q^{4} +2.21213 q^{5} -2.68443 q^{6} +4.45954 q^{7} +1.00000 q^{8} +4.20617 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.68443 q^{3} +1.00000 q^{4} +2.21213 q^{5} -2.68443 q^{6} +4.45954 q^{7} +1.00000 q^{8} +4.20617 q^{9} +2.21213 q^{10} -1.00000 q^{11} -2.68443 q^{12} -0.0499536 q^{13} +4.45954 q^{14} -5.93830 q^{15} +1.00000 q^{16} +2.30875 q^{17} +4.20617 q^{18} +3.92697 q^{19} +2.21213 q^{20} -11.9713 q^{21} -1.00000 q^{22} +2.67113 q^{23} -2.68443 q^{24} -0.106494 q^{25} -0.0499536 q^{26} -3.23787 q^{27} +4.45954 q^{28} -4.38772 q^{29} -5.93830 q^{30} +4.46633 q^{31} +1.00000 q^{32} +2.68443 q^{33} +2.30875 q^{34} +9.86508 q^{35} +4.20617 q^{36} +11.1664 q^{37} +3.92697 q^{38} +0.134097 q^{39} +2.21213 q^{40} +0.808342 q^{41} -11.9713 q^{42} -1.84462 q^{43} -1.00000 q^{44} +9.30458 q^{45} +2.67113 q^{46} -1.34682 q^{47} -2.68443 q^{48} +12.8875 q^{49} -0.106494 q^{50} -6.19767 q^{51} -0.0499536 q^{52} +4.19224 q^{53} -3.23787 q^{54} -2.21213 q^{55} +4.45954 q^{56} -10.5417 q^{57} -4.38772 q^{58} -12.7581 q^{59} -5.93830 q^{60} -7.78077 q^{61} +4.46633 q^{62} +18.7576 q^{63} +1.00000 q^{64} -0.110504 q^{65} +2.68443 q^{66} +9.32145 q^{67} +2.30875 q^{68} -7.17046 q^{69} +9.86508 q^{70} -13.4642 q^{71} +4.20617 q^{72} -7.02630 q^{73} +11.1664 q^{74} +0.285875 q^{75} +3.92697 q^{76} -4.45954 q^{77} +0.134097 q^{78} +4.15520 q^{79} +2.21213 q^{80} -3.92665 q^{81} +0.808342 q^{82} +13.7085 q^{83} -11.9713 q^{84} +5.10724 q^{85} -1.84462 q^{86} +11.7785 q^{87} -1.00000 q^{88} -2.44827 q^{89} +9.30458 q^{90} -0.222770 q^{91} +2.67113 q^{92} -11.9896 q^{93} -1.34682 q^{94} +8.68696 q^{95} -2.68443 q^{96} -10.7345 q^{97} +12.8875 q^{98} -4.20617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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