LMFDB - Embedded newform 1441.4.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57727 q^{2} +6.26190 q^{3} +4.79686 q^{4} -11.2090 q^{5} -22.4005 q^{6} -24.1930 q^{7} +11.4585 q^{8} +12.2114 q^{9} +O(q^{10})$	\(q-3.57727 q^{2} +6.26190 q^{3} +4.79686 q^{4} -11.2090 q^{5} -22.4005 q^{6} -24.1930 q^{7} +11.4585 q^{8} +12.2114 q^{9} +40.0975 q^{10} -11.0000 q^{11} +30.0375 q^{12} -57.7974 q^{13} +86.5449 q^{14} -70.1894 q^{15} -79.3650 q^{16} -104.747 q^{17} -43.6834 q^{18} -37.5792 q^{19} -53.7679 q^{20} -151.494 q^{21} +39.3500 q^{22} -20.1650 q^{23} +71.7519 q^{24} +0.640928 q^{25} +206.757 q^{26} -92.6049 q^{27} -116.050 q^{28} -46.9543 q^{29} +251.086 q^{30} -176.335 q^{31} +192.242 q^{32} -68.8809 q^{33} +374.708 q^{34} +271.179 q^{35} +58.5763 q^{36} +336.935 q^{37} +134.431 q^{38} -361.922 q^{39} -128.438 q^{40} -497.809 q^{41} +541.935 q^{42} +239.614 q^{43} -52.7655 q^{44} -136.877 q^{45} +72.1355 q^{46} -47.2443 q^{47} -496.976 q^{48} +242.301 q^{49} -2.29277 q^{50} -655.915 q^{51} -277.246 q^{52} +123.342 q^{53} +331.273 q^{54} +123.299 q^{55} -277.215 q^{56} -235.317 q^{57} +167.968 q^{58} -434.845 q^{59} -336.689 q^{60} -878.216 q^{61} +630.797 q^{62} -295.430 q^{63} -52.7820 q^{64} +647.850 q^{65} +246.406 q^{66} +242.200 q^{67} -502.457 q^{68} -126.271 q^{69} -970.079 q^{70} -778.053 q^{71} +139.924 q^{72} -342.919 q^{73} -1205.31 q^{74} +4.01343 q^{75} -180.262 q^{76} +266.123 q^{77} +1294.69 q^{78} +392.147 q^{79} +889.600 q^{80} -909.589 q^{81} +1780.80 q^{82} +692.624 q^{83} -726.696 q^{84} +1174.11 q^{85} -857.164 q^{86} -294.023 q^{87} -126.043 q^{88} -311.708 q^{89} +489.646 q^{90} +1398.29 q^{91} -96.7285 q^{92} -1104.19 q^{93} +169.006 q^{94} +421.223 q^{95} +1203.80 q^{96} +1048.91 q^{97} -866.777 q^{98} -134.325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−3.57727	−1.26476	−0.632378	−	0.774660i	$-0.717921\pi$
$2$	−3.57727	−1.26476	−0.632378	+	0.774660i	$0.717921\pi$
$3$	6.26190	1.20510	0.602551	−	0.798080i	$-0.294151\pi$
$3$	6.26190	1.20510	0.602551	+	0.798080i	$0.294151\pi$
$4$	4.79686	0.599608
$5$	−11.2090	−1.00256	−0.501280	−	0.865285i	$-0.667137\pi$
$5$	−11.2090	−1.00256	−0.501280	+	0.865285i	$0.667137\pi$
$6$	−22.4005	−1.52416
$7$	−24.1930	−1.30630	−0.653150	−	0.757229i	$-0.726553\pi$
$7$	−24.1930	−1.30630	−0.653150	+	0.757229i	$0.726553\pi$
$8$	11.4585	0.506399
$9$	12.2114	0.452273
$10$	40.0975	1.26799
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	30.0375	0.722589
$13$	−57.7974	−1.23309	−0.616543	−	0.787321i	$-0.711467\pi$
$13$	−57.7974	−1.23309	−0.616543	+	0.787321i	$0.711467\pi$
$14$	86.5449	1.65215
$15$	−70.1894	−1.20819
$16$	−79.3650	−1.24008
$17$	−104.747	−1.49440	−0.747202	−	0.664597i	$-0.768603\pi$
$17$	−104.747	−1.49440	−0.747202	+	0.664597i	$0.768603\pi$
$18$	−43.6834	−0.572015
$19$	−37.5792	−0.453750	−0.226875	−	0.973924i	$-0.572851\pi$
$19$	−37.5792	−0.453750	−0.226875	+	0.973924i	$0.572851\pi$
$20$	−53.7679	−0.601143
$21$	−151.494	−1.57423
$22$	39.3500	0.381338
$23$	−20.1650	−0.182812	−0.0914062	−	0.995814i	$-0.529136\pi$
$23$	−20.1650	−0.182812	−0.0914062	+	0.995814i	$0.529136\pi$
$24$	71.7519	0.610262
$25$	0.640928	0.00512742
$26$	206.757	1.55955
$27$	−92.6049	−0.660067
$28$	−116.050	−0.783267
$29$	−46.9543	−0.300662	−0.150331	−	0.988636i	$-0.548034\pi$
$29$	−46.9543	−0.300662	−0.150331	+	0.988636i	$0.548034\pi$
$30$	251.086	1.52806
$31$	−176.335	−1.02163	−0.510817	−	0.859689i	$-0.670657\pi$
$31$	−176.335	−1.02163	−0.510817	+	0.859689i	$0.670657\pi$
$32$	192.242	1.06200
$33$	−68.8809	−0.363352
$34$	374.708	1.89006
$35$	271.179	1.30964
$36$	58.5763	0.271186
$37$	336.935	1.49708	0.748538	−	0.663092i	$-0.230756\pi$
$37$	336.935	1.49708	0.748538	+	0.663092i	$0.230756\pi$
$38$	134.431	0.573883
$39$	−361.922	−1.48600
$40$	−128.438	−0.507695
$41$	−497.809	−1.89621	−0.948106	−	0.317953i	$-0.897005\pi$
$41$	−497.809	−1.89621	−0.948106	+	0.317953i	$0.897005\pi$
$42$	541.935	1.99101
$43$	239.614	0.849786	0.424893	−	0.905244i	$-0.360312\pi$
$43$	239.614	0.849786	0.424893	+	0.905244i	$0.360312\pi$
$44$	−52.7655	−0.180789
$45$	−136.877	−0.453431
$46$	72.1355	0.231213
$47$	−47.2443	−0.146623	−0.0733115	−	0.997309i	$-0.523357\pi$
$47$	−47.2443	−0.146623	−0.0733115	+	0.997309i	$0.523357\pi$
$48$	−496.976	−1.49442
$49$	242.301	0.706418
$50$	−2.29277	−0.00648494
$51$	−655.915	−1.80091
$52$	−277.246	−0.739368
$53$	123.342	0.319667	0.159834	−	0.987144i	$-0.448904\pi$
$53$	123.342	0.319667	0.159834	+	0.987144i	$0.448904\pi$
$54$	331.273	0.834824
$55$	123.299	0.302283
$56$	−277.215	−0.661508
$57$	−235.317	−0.546815
$58$	167.968	0.380264
$59$	−434.845	−0.959526	−0.479763	−	0.877398i	$-0.659277\pi$
$59$	−434.845	−0.959526	−0.479763	+	0.877398i	$0.659277\pi$
$60$	−336.689	−0.724439
$61$	−878.216	−1.84335	−0.921673	−	0.387968i	$-0.873177\pi$
$61$	−878.216	−1.84335	−0.921673	+	0.387968i	$0.873177\pi$
$62$	630.797	1.29212
$63$	−295.430	−0.590804
$64$	−52.7820	−0.103090
$65$	647.850	1.23624
$66$	246.406	0.459552
$67$	242.200	0.441634	0.220817	−	0.975315i	$-0.429128\pi$
$67$	242.200	0.441634	0.220817	+	0.975315i	$0.429128\pi$
$68$	−502.457	−0.896056
$69$	−126.271	−0.220308
$70$	−970.079	−1.65638
$71$	−778.053	−1.30053	−0.650267	−	0.759706i	$-0.725343\pi$
$71$	−778.053	−1.30053	−0.650267	+	0.759706i	$0.725343\pi$
$72$	139.924	0.229030
$73$	−342.919	−0.549803	−0.274901	−	0.961472i	$-0.588645\pi$
$73$	−342.919	−0.549803	−0.274901	+	0.961472i	$0.588645\pi$
$74$	−1205.31	−1.89344
$75$	4.01343	0.00617907
$76$	−180.262	−0.272072
$77$	266.123	0.393864
$78$	1294.69	1.87942
$79$	392.147	0.558481	0.279240	−	0.960221i	$-0.409917\pi$
$79$	392.147	0.558481	0.279240	+	0.960221i	$0.409917\pi$
$80$	889.600	1.24325
$81$	−909.589	−1.24772
$82$	1780.80	2.39825
$83$	692.624	0.915969	0.457984	−	0.888960i	$-0.348572\pi$
$83$	692.624	0.915969	0.457984	+	0.888960i	$0.348572\pi$
$84$	−726.696	−0.943917
$85$	1174.11	1.49823
$86$	−857.164	−1.07477
$87$	−294.023	−0.362329
$88$	−126.043	−0.152685
$89$	−311.708	−0.371246	−0.185623	−	0.982621i	$-0.559430\pi$
$89$	−311.708	−0.371246	−0.185623	+	0.982621i	$0.559430\pi$
$90$	489.646	0.573480
$91$	1398.29	1.61078
$92$	−96.7285	−0.109616
$93$	−1104.19	−1.23117
$94$	169.006	0.185442
$95$	421.223	0.454912
$96$	1203.80	1.27982
$97$	1048.91	1.09794	0.548972	−	0.835841i	$-0.315019\pi$
$97$	1048.91	1.09794	0.548972	+	0.835841i	$0.315019\pi$
$98$	−866.777	−0.893446
$99$	−134.325	−0.136365
$100$	3.07444	0.00307444
$101$	408.637	0.402583	0.201292	−	0.979531i	$-0.435486\pi$
$101$	408.637	0.402583	0.201292	+	0.979531i	$0.435486\pi$
$102$	2346.38	2.27771
$103$	517.556	0.495110	0.247555	−	0.968874i	$-0.420373\pi$
$103$	517.556	0.495110	0.247555	+	0.968874i	$0.420373\pi$
$104$	−662.271	−0.624433
$105$	1698.09	1.57826
$106$	−441.229	−0.404301
$107$	−691.582	−0.624839	−0.312419	−	0.949944i	$-0.601139\pi$
$107$	−691.582	−0.624839	−0.312419	+	0.949944i	$0.601139\pi$
$108$	−444.213	−0.395781
$109$	−779.715	−0.685166	−0.342583	−	0.939487i	$-0.611302\pi$
$109$	−779.715	−0.685166	−0.342583	+	0.939487i	$0.611302\pi$
$110$	−441.073	−0.382315
$111$	2109.86	1.80413
$112$	1920.08	1.61991
$113$	973.726	0.810623	0.405312	−	0.914179i	$-0.367163\pi$
$113$	973.726	0.810623	0.405312	+	0.914179i	$0.367163\pi$
$114$	841.792	0.691588
$115$	226.028	0.183280
$116$	−225.233	−0.180279
$117$	−705.786	−0.557692
$118$	1555.56	1.21357
$119$	2534.14	1.95214
$120$	−804.265	−0.611825
$121$	121.000	0.0909091
$122$	3141.62	2.33138
$123$	−3117.23	−2.28513
$124$	−845.853	−0.612580
$125$	1393.94	0.997420
$126$	1056.83	0.747223
$127$	−2296.95	−1.60489	−0.802445	−	0.596726i	$-0.796468\pi$
$127$	−2296.95	−1.60489	−0.802445	+	0.596726i	$0.796468\pi$
$128$	−1349.12	−0.931614
$129$	1500.44	1.02408
$130$	−2317.53	−1.56355
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	−330.412	−0.217869
$133$	909.152	0.592733
$134$	−866.416	−0.558559
$135$	1038.00	0.661757
$136$	−1200.24	−0.756764
$137$	−1058.38	−0.660028	−0.330014	−	0.943976i	$-0.607053\pi$
$137$	−1058.38	−0.660028	−0.330014	+	0.943976i	$0.607053\pi$
$138$	451.705	0.278635
$139$	−978.167	−0.596885	−0.298442	−	0.954428i	$-0.596467\pi$
$139$	−978.167	−0.596885	−0.298442	+	0.954428i	$0.596467\pi$
$140$	1300.81	0.785273
$141$	−295.839	−0.176696
$142$	2783.31	1.64486
$143$	635.772	0.371790
$144$	−969.156	−0.560854
$145$	526.310	0.301432
$146$	1226.71	0.695366
$147$	1517.27	0.851306
$148$	1616.23	0.897659
$149$	1079.25	0.593394	0.296697	−	0.954972i	$-0.404115\pi$
$149$	1079.25	0.593394	0.296697	+	0.954972i	$0.404115\pi$
$150$	−14.3571	−0.00781502
$151$	1238.35	0.667389	0.333694	−	0.942681i	$-0.391705\pi$
$151$	1238.35	0.667389	0.333694	+	0.942681i	$0.391705\pi$
$152$	−430.600	−0.229778
$153$	−1279.10	−0.675879
$154$	−951.994	−0.498142
$155$	1976.53	1.02425
$156$	−1736.09	−0.891015
$157$	1231.36	0.625942	0.312971	−	0.949763i	$-0.398676\pi$
$157$	1231.36	0.625942	0.312971	+	0.949763i	$0.398676\pi$
$158$	−1402.82	−0.706342
$159$	772.357	0.385232
$160$	−2154.84	−1.06472
$161$	487.851	0.238808
$162$	3253.85	1.57806
$163$	−3665.08	−1.76117	−0.880585	−	0.473887i	$-0.842850\pi$
$163$	−3665.08	−1.76117	−0.880585	+	0.473887i	$0.842850\pi$
$164$	−2387.92	−1.13698
$165$	772.084	0.364283
$166$	−2477.70	−1.15848
$167$	−489.329	−0.226739	−0.113370	−	0.993553i	$-0.536164\pi$
$167$	−489.329	−0.226739	−0.113370	+	0.993553i	$0.536164\pi$
$168$	−1735.89	−0.797185
$169$	1143.54	0.520502
$170$	−4200.09	−1.89490
$171$	−458.893	−0.205219
$172$	1149.39	0.509538
$173$	−1863.63	−0.819011	−0.409506	−	0.912308i	$-0.634299\pi$
$173$	−1863.63	−0.819011	−0.409506	+	0.912308i	$0.634299\pi$
$174$	1051.80	0.458258
$175$	−15.5060	−0.00669795
$176$	873.015	0.373898
$177$	−2722.96	−1.15633
$178$	1115.06	0.469536
$179$	736.493	0.307531	0.153765	−	0.988107i	$-0.450860\pi$
$179$	736.493	0.307531	0.153765	+	0.988107i	$0.450860\pi$
$180$	−656.579	−0.271881
$181$	−2951.61	−1.21211	−0.606054	−	0.795424i	$-0.707248\pi$
$181$	−2951.61	−1.21211	−0.606054	+	0.795424i	$0.707248\pi$
$182$	−5002.07	−2.03724
$183$	−5499.30	−2.22142
$184$	−231.060	−0.0925759
$185$	−3776.70	−1.50091
$186$	3949.99	1.55713
$187$	1152.22	0.450580
$188$	−226.624	−0.0879163
$189$	2240.39	0.862245
$190$	−1506.83	−0.575352
$191$	159.061	0.0602577	0.0301288	−	0.999546i	$-0.490408\pi$
$191$	159.061	0.0602577	0.0301288	+	0.999546i	$0.490408\pi$
$192$	−330.515	−0.124234
$193$	−2854.19	−1.06450	−0.532252	−	0.846586i	$-0.678654\pi$
$193$	−2854.19	−1.06450	−0.532252	+	0.846586i	$0.678654\pi$
$194$	−3752.23	−1.38863
$195$	4056.77	1.48980
$196$	1162.29	0.423573
$197$	−228.737	−0.0827252	−0.0413626	−	0.999144i	$-0.513170\pi$
$197$	−228.737	−0.0827252	−0.0413626	+	0.999144i	$0.513170\pi$
$198$	480.517	0.172469
$199$	−3102.46	−1.10516	−0.552582	−	0.833458i	$-0.686358\pi$
$199$	−3102.46	−1.10516	−0.552582	+	0.833458i	$0.686358\pi$
$200$	7.34407	0.00259652
$201$	1516.63	0.532215
$202$	−1461.81	−0.509170
$203$	1135.97	0.392755
$204$	−3146.33	−1.07984
$205$	5579.93	1.90107
$206$	−1851.44	−0.626193
$207$	−246.242	−0.0826811
$208$	4587.09	1.52912
$209$	413.371	0.136811
$210$	−6074.54	−1.99611
$211$	407.371	0.132913	0.0664563	−	0.997789i	$-0.478831\pi$
$211$	407.371	0.132913	0.0664563	+	0.997789i	$0.478831\pi$
$212$	591.656	0.191675
$213$	−4872.09	−1.56728
$214$	2473.97	0.790268
$215$	−2685.82	−0.851961
$216$	−1061.11	−0.334257
$217$	4266.07	1.33456
$218$	2789.25	0.866568
$219$	−2147.32	−0.662569
$220$	591.446	0.181251
$221$	6054.11	1.84273
$222$	−7547.52	−2.28179
$223$	−2331.07	−0.700001	−0.350001	−	0.936749i	$-0.613819\pi$
$223$	−2331.07	−0.700001	−0.350001	+	0.936749i	$0.613819\pi$
$224$	−4650.91	−1.38729
$225$	7.82661	0.00231900
$226$	−3483.28	−1.02524
$227$	4845.33	1.41672	0.708361	−	0.705850i	$-0.249435\pi$
$227$	4845.33	1.41672	0.708361	+	0.705850i	$0.249435\pi$
$228$	−1128.78	−0.327875
$229$	5459.13	1.57532	0.787662	−	0.616107i	$-0.211291\pi$
$229$	5459.13	1.57532	0.787662	+	0.616107i	$0.211291\pi$
$230$	−808.564	−0.231805
$231$	1666.44	0.474647
$232$	−538.026	−0.152255
$233$	955.388	0.268625	0.134312	−	0.990939i	$-0.457117\pi$
$233$	955.388	0.268625	0.134312	+	0.990939i	$0.457117\pi$
$234$	2524.79	0.705344
$235$	529.559	0.146999
$236$	−2085.89	−0.575339
$237$	2455.58	0.673027
$238$	−9065.32	−2.46898
$239$	4403.52	1.19180	0.595900	−	0.803059i	$-0.296796\pi$
$239$	4403.52	1.19180	0.595900	+	0.803059i	$0.296796\pi$
$240$	5570.58	1.49825
$241$	646.924	0.172913	0.0864565	−	0.996256i	$-0.472446\pi$
$241$	646.924	0.172913	0.0864565	+	0.996256i	$0.472446\pi$
$242$	−432.850	−0.114978
$243$	−3195.43	−0.843566
$244$	−4212.68	−1.10528
$245$	−2715.95	−0.708226
$246$	11151.2	2.89013
$247$	2171.98	0.559513
$248$	−2020.53	−0.517354
$249$	4337.14	1.10384
$250$	−4986.49	−1.26149
$251$	4819.79	1.21204	0.606021	−	0.795449i	$-0.292765\pi$
$251$	4819.79	1.21204	0.606021	+	0.795449i	$0.292765\pi$
$252$	−1417.14	−0.354251
$253$	221.815	0.0551200
$254$	8216.79	2.02979
$255$	7352.13	1.80552
$256$	5248.43	1.28135
$257$	−4955.77	−1.20285	−0.601425	−	0.798929i	$-0.705400\pi$
$257$	−4955.77	−1.20285	−0.601425	+	0.798929i	$0.705400\pi$
$258$	−5367.47	−1.29521
$259$	−8151.48	−1.95563
$260$	3107.64	0.741261
$261$	−573.377	−0.135981
$262$	468.622	0.110502
$263$	3441.57	0.806906	0.403453	−	0.915000i	$-0.367810\pi$
$263$	3441.57	0.806906	0.403453	+	0.915000i	$0.367810\pi$
$264$	−789.271	−0.184001
$265$	−1382.54	−0.320486
$266$	−3252.28	−0.749663
$267$	−1951.88	−0.447390
$268$	1161.80	0.264807
$269$	7541.94	1.70944	0.854721	−	0.519087i	$-0.173728\pi$
$269$	7541.94	1.70944	0.854721	+	0.519087i	$0.173728\pi$
$270$	−3713.22	−0.836962
$271$	−5118.77	−1.14739	−0.573696	−	0.819068i	$-0.694491\pi$
$271$	−5118.77	−1.14739	−0.573696	+	0.819068i	$0.694491\pi$
$272$	8313.24	1.85318
$273$	8755.97	1.94116
$274$	3786.12	0.834774
$275$	−7.05021	−0.00154598
$276$	−605.704	−0.132098
$277$	806.111	0.174854	0.0874270	−	0.996171i	$-0.472136\pi$
$277$	806.111	0.174854	0.0874270	+	0.996171i	$0.472136\pi$
$278$	3499.17	0.754914
$279$	−2153.29	−0.462058
$280$	3107.30	0.663202
$281$	−7112.13	−1.50987	−0.754936	−	0.655799i	$-0.772332\pi$
$281$	−7112.13	−1.50987	−0.754936	+	0.655799i	$0.772332\pi$
$282$	1058.30	0.223477
$283$	−6559.77	−1.37787	−0.688936	−	0.724822i	$-0.741922\pi$
$283$	−6559.77	−1.37787	−0.688936	+	0.724822i	$0.741922\pi$
$284$	−3732.21	−0.779810
$285$	2637.66	0.548215
$286$	−2274.33	−0.470223
$287$	12043.5	2.47702
$288$	2347.54	0.480313
$289$	6058.93	1.23324
$290$	−1882.75	−0.381238
$291$	6568.16	1.32314
$292$	−1644.93	−0.329666
$293$	5265.36	1.04985	0.524924	−	0.851149i	$-0.324094\pi$
$293$	5265.36	1.04985	0.524924	+	0.851149i	$0.324094\pi$
$294$	−5427.67	−1.07669
$295$	4874.17	0.961983
$296$	3860.77	0.758118
$297$	1018.65	0.199018
$298$	−3860.77	−0.750498
$299$	1165.48	0.225423
$300$	19.2518	0.00370502
$301$	−5796.98	−1.11007
$302$	−4429.92	−0.844084
$303$	2558.84	0.485154
$304$	2982.47	0.562685
$305$	9843.90	1.84807
$306$	4575.70	0.854822
$307$	−1824.99	−0.339275	−0.169638	−	0.985507i	$-0.554260\pi$
$307$	−1824.99	−0.339275	−0.169638	+	0.985507i	$0.554260\pi$
$308$	1276.56	0.236164
$309$	3240.89	0.596659
$310$	−7070.58	−1.29543
$311$	−5178.01	−0.944109	−0.472055	−	0.881569i	$-0.656488\pi$
$311$	−5178.01	−0.944109	−0.472055	+	0.881569i	$0.656488\pi$
$312$	−4147.08	−0.752506
$313$	1673.78	0.302261	0.151131	−	0.988514i	$-0.451709\pi$
$313$	1673.78	0.302261	0.151131	+	0.988514i	$0.451709\pi$
$314$	−4404.89	−0.791663
$315$	3311.46	0.592317
$316$	1881.07	0.334869
$317$	−2047.26	−0.362730	−0.181365	−	0.983416i	$-0.558052\pi$
$317$	−2047.26	−0.362730	−0.181365	+	0.983416i	$0.558052\pi$
$318$	−2762.93	−0.487224
$319$	516.498	0.0906531
$320$	591.631	0.103354
$321$	−4330.61	−0.752995
$322$	−1745.17	−0.302033
$323$	3936.30	0.678086
$324$	−4363.17	−0.748144
$325$	−37.0440	−0.00632256
$326$	13111.0	2.22745
$327$	−4882.50	−0.825696
$328$	−5704.14	−0.960240
$329$	1142.98	0.191534
$330$	−2761.95	−0.460729
$331$	9212.80	1.52985	0.764926	−	0.644118i	$-0.222775\pi$
$331$	9212.80	1.52985	0.764926	+	0.644118i	$0.222775\pi$
$332$	3322.42	0.549222
$333$	4114.44	0.677088
$334$	1750.46	0.286770
$335$	−2714.82	−0.442765
$336$	12023.3	1.95216
$337$	−11827.0	−1.91174	−0.955872	−	0.293783i	$-0.905086\pi$
$337$	−11827.0	−1.91174	−0.955872	+	0.293783i	$0.905086\pi$
$338$	−4090.76	−0.658308
$339$	6097.37	0.976884
$340$	5632.02	0.898351
$341$	1939.68	0.308034
$342$	1641.58	0.259552
$343$	2436.20	0.383506
$344$	2745.61	0.430330
$345$	1415.37	0.220872
$346$	6666.70	1.03585
$347$	666.104	0.103050	0.0515250	−	0.998672i	$-0.483592\pi$
$347$	666.104	0.103050	0.0515250	+	0.998672i	$0.483592\pi$
$348$	−1410.39	−0.217255
$349$	7744.48	1.18783	0.593914	−	0.804528i	$-0.297582\pi$
$349$	7744.48	1.18783	0.593914	+	0.804528i	$0.297582\pi$
$350$	55.4690	0.00847127
$351$	5352.32	0.813920
$352$	−2114.66	−0.320204
$353$	8043.18	1.21273	0.606367	−	0.795185i	$-0.292626\pi$
$353$	8043.18	1.21273	0.606367	+	0.795185i	$0.292626\pi$
$354$	9740.76	1.46247
$355$	8721.17	1.30386
$356$	−1495.22	−0.222602
$357$	15868.5	2.35253
$358$	−2634.63	−0.388952
$359$	−256.149	−0.0376575	−0.0188287	−	0.999823i	$-0.505994\pi$
$359$	−256.149	−0.0376575	−0.0188287	+	0.999823i	$0.505994\pi$
$360$	−1568.40	−0.229617
$361$	−5446.81	−0.794111
$362$	10558.7	1.53302
$363$	757.690	0.109555
$364$	6707.42	0.965836
$365$	3843.76	0.551210
$366$	19672.5	2.80956
$367$	9577.71	1.36227	0.681134	−	0.732159i	$-0.261487\pi$
$367$	9577.71	1.36227	0.681134	+	0.732159i	$0.261487\pi$
$368$	1600.39	0.226702
$369$	−6078.93	−0.857606
$370$	13510.3	1.89828
$371$	−2984.02	−0.417581
$372$	−5296.65	−0.738221
$373$	−7145.22	−0.991864	−0.495932	−	0.868361i	$-0.665174\pi$
$373$	−7145.22	−0.991864	−0.495932	+	0.868361i	$0.665174\pi$
$374$	−4121.79	−0.569874
$375$	8728.69	1.20199
$376$	−541.348	−0.0742497
$377$	2713.84	0.370742
$378$	−8014.48	−1.09053
$379$	3152.89	0.427316	0.213658	−	0.976908i	$-0.431462\pi$
$379$	3152.89	0.427316	0.213658	+	0.976908i	$0.431462\pi$
$380$	2020.55	0.272769
$381$	−14383.2	−1.93406
$382$	−569.003	−0.0762113
$383$	126.689	0.0169021	0.00845107	−	0.999964i	$-0.497310\pi$
$383$	126.689	0.0169021	0.00845107	+	0.999964i	$0.497310\pi$
$384$	−8448.06	−1.12269
$385$	−2982.96	−0.394872
$386$	10210.2	1.34634
$387$	2926.01	0.384335
$388$	5031.47	0.658336
$389$	2926.09	0.381384	0.190692	−	0.981650i	$-0.438927\pi$
$389$	2926.09	0.381384	0.190692	+	0.981650i	$0.438927\pi$
$390$	−14512.2	−1.88423
$391$	2112.22	0.273196
$392$	2776.41	0.357729
$393$	−820.309	−0.105290
$394$	818.255	0.104627
$395$	−4395.56	−0.559911
$396$	−644.339	−0.0817658
$397$	−6068.01	−0.767115	−0.383557	−	0.923517i	$-0.625301\pi$
$397$	−6068.01	−0.767115	−0.383557	+	0.923517i	$0.625301\pi$
$398$	11098.3	1.39776
$399$	5693.02	0.714304
$400$	−50.8673	−0.00635841
$401$	−866.894	−0.107957	−0.0539784	−	0.998542i	$-0.517190\pi$
$401$	−866.894	−0.107957	−0.0539784	+	0.998542i	$0.517190\pi$
$402$	−5425.41	−0.673122
$403$	10191.7	1.25976
$404$	1960.18	0.241392
$405$	10195.6	1.25092
$406$	−4063.66	−0.496739
$407$	−3706.29	−0.451386
$408$	−7515.80	−0.911979
$409$	−5316.98	−0.642807	−0.321403	−	0.946942i	$-0.604155\pi$
$409$	−5316.98	−0.642807	−0.321403	+	0.946942i	$0.604155\pi$
$410$	−19960.9	−2.40439
$411$	−6627.49	−0.795401
$412$	2482.65	0.296872
$413$	10520.2	1.25343
$414$	880.873	0.104571
$415$	−7763.60	−0.918314
$416$	−11111.1	−1.30954
$417$	−6125.18	−0.719308
$418$	−1478.74	−0.173032
$419$	−10676.9	−1.24487	−0.622437	−	0.782670i	$-0.713857\pi$
$419$	−10676.9	−1.24487	−0.622437	+	0.782670i	$0.713857\pi$
$420$	8145.51	0.946334
$421$	7264.48	0.840972	0.420486	−	0.907299i	$-0.361860\pi$
$421$	7264.48	0.840972	0.420486	+	0.907299i	$0.361860\pi$
$422$	−1457.28	−0.168102
$423$	−576.917	−0.0663137
$424$	1413.32	0.161879
$425$	−67.1353	−0.00766244
$426$	17428.8	1.98222
$427$	21246.7	2.40796
$428$	−3317.42	−0.374658
$429$	3981.14	0.448045
$430$	9607.92	1.07752
$431$	−13202.0	−1.47545	−0.737724	−	0.675103i	$-0.764099\pi$
$431$	−13202.0	−1.47545	−0.737724	+	0.675103i	$0.764099\pi$
$432$	7349.59	0.818535
$433$	−8686.69	−0.964101	−0.482051	−	0.876143i	$-0.660108\pi$
$433$	−8686.69	−0.964101	−0.482051	+	0.876143i	$0.660108\pi$
$434$	−15260.9	−1.68789
$435$	3295.70	0.363257
$436$	−3740.18	−0.410831
$437$	757.782	0.0829511
$438$	7681.55	0.837988
$439$	−15613.3	−1.69746	−0.848729	−	0.528828i	$-0.822632\pi$
$439$	−15613.3	−1.69746	−0.848729	+	0.528828i	$0.822632\pi$
$440$	1412.82	0.153076
$441$	2958.83	0.319494
$442$	−21657.2	−2.33060
$443$	1937.72	0.207819	0.103909	−	0.994587i	$-0.466865\pi$
$443$	1937.72	0.207819	0.103909	+	0.994587i	$0.466865\pi$
$444$	10120.7	1.08177
$445$	3493.92	0.372197
$446$	8338.88	0.885331
$447$	6758.16	0.715101
$448$	1276.95	0.134666
$449$	−6576.08	−0.691190	−0.345595	−	0.938384i	$-0.612323\pi$
$449$	−6576.08	−0.691190	−0.345595	+	0.938384i	$0.612323\pi$
$450$	−27.9979	−0.00293296
$451$	5475.90	0.571730
$452$	4670.83	0.486056
$453$	7754.44	0.804272
$454$	−17333.1	−1.79181
$455$	−15673.4	−1.61490
$456$	−2696.38	−0.276907
$457$	−8997.64	−0.920988	−0.460494	−	0.887663i	$-0.652328\pi$
$457$	−8997.64	−0.920988	−0.460494	+	0.887663i	$0.652328\pi$
$458$	−19528.8	−1.99240
$459$	9700.08	0.986407
$460$	1084.23	0.109896
$461$	6773.02	0.684275	0.342138	−	0.939650i	$-0.388849\pi$
$461$	6773.02	0.684275	0.342138	+	0.939650i	$0.388849\pi$
$462$	−5961.29	−0.600312
$463$	−14031.2	−1.40840	−0.704198	−	0.710004i	$-0.748693\pi$
$463$	−14031.2	−1.40840	−0.704198	+	0.710004i	$0.748693\pi$
$464$	3726.53	0.372845
$465$	12376.8	1.23433
$466$	−3417.68	−0.339745
$467$	6605.78	0.654559	0.327280	−	0.944928i	$-0.393868\pi$
$467$	6605.78	0.654559	0.327280	+	0.944928i	$0.393868\pi$
$468$	−3385.56	−0.334396
$469$	−5859.55	−0.576906
$470$	−1894.38	−0.185917
$471$	7710.62	0.754324
$472$	−4982.67	−0.485903
$473$	−2635.75	−0.256220
$474$	−8784.29	−0.851215
$475$	−24.0855	−0.00232657
$476$	12155.9	1.17052
$477$	1506.18	0.144577
$478$	−15752.6	−1.50734
$479$	72.5548	0.00692090	0.00346045	−	0.999994i	$-0.498899\pi$
$479$	72.5548	0.00692090	0.00346045	+	0.999994i	$0.498899\pi$
$480$	−13493.4	−1.28309
$481$	−19474.0	−1.84603
$482$	−2314.22	−0.218693
$483$	3054.87	0.287788
$484$	580.420	0.0545098
$485$	−11757.2	−1.10076
$486$	11430.9	1.06691
$487$	14509.0	1.35003	0.675014	−	0.737805i	$-0.264138\pi$
$487$	14509.0	1.35003	0.675014	+	0.737805i	$0.264138\pi$
$488$	−10063.0	−0.933468
$489$	−22950.3	−2.12239
$490$	9715.67	0.895734
$491$	1819.89	0.167272	0.0836360	−	0.996496i	$-0.473347\pi$
$491$	1819.89	0.167272	0.0836360	+	0.996496i	$0.473347\pi$
$492$	−14952.9	−1.37018
$493$	4918.33	0.449311
$494$	−7769.75	−0.707647
$495$	1505.65	0.136715
$496$	13994.8	1.26691
$497$	18823.4	1.69889
$498$	−15515.1	−1.39608
$499$	−6688.45	−0.600033	−0.300016	−	0.953934i	$-0.596992\pi$
$499$	−6688.45	−0.600033	−0.300016	+	0.953934i	$0.596992\pi$
$500$	6686.52	0.598061
$501$	−3064.13	−0.273244
$502$	−17241.7	−1.53294
$503$	−8710.80	−0.772158	−0.386079	−	0.922466i	$-0.626171\pi$
$503$	−8710.80	−0.772158	−0.386079	+	0.922466i	$0.626171\pi$
$504$	−3385.18	−0.299182
$505$	−4580.40	−0.403614
$506$	−793.490	−0.0697133
$507$	7160.75	0.627259
$508$	−11018.1	−0.962304
$509$	11719.0	1.02050	0.510250	−	0.860026i	$-0.329553\pi$
$509$	11719.0	1.02050	0.510250	+	0.860026i	$0.329553\pi$
$510$	−26300.5	−2.28354
$511$	8296.23	0.718207
$512$	−7982.07	−0.688987
$513$	3480.01	0.299505
$514$	17728.1	1.52131
$515$	−5801.27	−0.496378
$516$	7197.39	0.614046
$517$	519.687	0.0442085
$518$	29160.0	2.47339
$519$	−11669.8	−0.986993
$520$	7423.38	0.626032
$521$	2126.71	0.178835	0.0894175	−	0.995994i	$-0.471499\pi$
$521$	2126.71	0.178835	0.0894175	+	0.995994i	$0.471499\pi$
$522$	2051.12	0.171983
$523$	−75.9947	−0.00635376	−0.00317688	−	0.999995i	$-0.501011\pi$
$523$	−75.9947	−0.00635376	−0.00317688	+	0.999995i	$0.501011\pi$
$524$	−628.389	−0.0523880
$525$	−97.0968	−0.00807172
$526$	−12311.4	−1.02054
$527$	18470.5	1.52673
$528$	5466.73	0.450585
$529$	−11760.4	−0.966580
$530$	4945.72	0.405336
$531$	−5310.06	−0.433968
$532$	4361.08	0.355407
$533$	28772.1	2.33819
$534$	6982.41	0.565839
$535$	7751.92	0.626438
$536$	2775.25	0.223643
$537$	4611.84	0.370606
$538$	−26979.5	−2.16203
$539$	−2665.31	−0.212993
$540$	4979.17	0.396795
$541$	12920.8	1.02682	0.513409	−	0.858144i	$-0.328382\pi$
$541$	12920.8	1.02682	0.513409	+	0.858144i	$0.328382\pi$
$542$	18311.2	1.45117
$543$	−18482.7	−1.46071
$544$	−20136.8	−1.58705
$545$	8739.80	0.686921
$546$	−31322.5	−2.45509
$547$	−14561.8	−1.13824	−0.569119	−	0.822255i	$-0.692716\pi$
$547$	−14561.8	−1.13824	−0.569119	+	0.822255i	$0.692716\pi$
$548$	−5076.92	−0.395758
$549$	−10724.2	−0.833696
$550$	25.2205	0.00195528
$551$	1764.50	0.136425
$552$	−1446.87	−0.111564
$553$	−9487.21	−0.729543
$554$	−2883.68	−0.221148
$555$	−23649.3	−1.80875
$556$	−4692.13	−0.357897
$557$	5419.01	0.412228	0.206114	−	0.978528i	$-0.433918\pi$
$557$	5419.01	0.412228	0.206114	+	0.978528i	$0.433918\pi$
$558$	7702.90	0.584390
$559$	−13849.1	−1.04786
$560$	−21522.1	−1.62406
$561$	7215.06	0.542995
$562$	25442.0	1.90962
$563$	−7575.84	−0.567111	−0.283556	−	0.958956i	$-0.591514\pi$
$563$	−7575.84	−0.567111	−0.283556	+	0.958956i	$0.591514\pi$
$564$	−1419.10	−0.105948
$565$	−10914.5	−0.812699
$566$	23466.1	1.74267
$567$	22005.7	1.62990
$568$	−8915.32	−0.658589
$569$	2977.99	0.219409	0.109705	−	0.993964i	$-0.465010\pi$
$569$	2977.99	0.219409	0.109705	+	0.993964i	$0.465010\pi$
$570$	−9435.62	−0.693359
$571$	−711.616	−0.0521545	−0.0260772	−	0.999660i	$-0.508302\pi$
$571$	−711.616	−0.0521545	−0.0260772	+	0.999660i	$0.508302\pi$
$572$	3049.71	0.222928
$573$	996.021	0.0726167
$574$	−43082.8	−3.13283
$575$	−12.9243	−0.000937356 0
$576$	−644.540	−0.0466247
$577$	17559.3	1.26691	0.633453	−	0.773781i	$-0.281637\pi$
$577$	17559.3	1.26691	0.633453	+	0.773781i	$0.281637\pi$
$578$	−21674.4	−1.55975
$579$	−17872.6	−1.28284
$580$	2524.63	0.180741
$581$	−16756.7	−1.19653
$582$	−23496.1	−1.67344
$583$	−1356.76	−0.0963833
$584$	−3929.33	−0.278419
$585$	7911.13	0.559120
$586$	−18835.6	−1.32780
$587$	−8693.60	−0.611283	−0.305642	−	0.952147i	$-0.598871\pi$
$587$	−8693.60	−0.611283	−0.305642	+	0.952147i	$0.598871\pi$
$588$	7278.11	0.510450
$589$	6626.51	0.463566
$590$	−17436.2	−1.21667
$591$	−1432.33	−0.0996924
$592$	−26740.9	−1.85649
$593$	−20380.3	−1.41133	−0.705664	−	0.708546i	$-0.749351\pi$
$593$	−20380.3	−1.41133	−0.705664	+	0.708546i	$0.749351\pi$
$594$	−3644.00	−0.251709
$595$	−28405.1	−1.95714
$596$	5177.02	0.355803
$597$	−19427.3	−1.33184
$598$	−4169.25	−0.285106
$599$	25170.4	1.71692	0.858459	−	0.512882i	$-0.171422\pi$
$599$	25170.4	1.71692	0.858459	+	0.512882i	$0.171422\pi$
$600$	45.9878	0.00312907
$601$	22052.2	1.49672	0.748358	−	0.663295i	$-0.230843\pi$
$601$	22052.2	1.49672	0.748358	+	0.663295i	$0.230843\pi$
$602$	20737.4	1.40397
$603$	2957.60	0.199739
$604$	5940.21	0.400171
$605$	−1356.28	−0.0911419
$606$	−9153.67	−0.613602
$607$	−20044.4	−1.34033	−0.670164	−	0.742213i	$-0.733776\pi$
$607$	−20044.4	−1.34033	−0.670164	+	0.742213i	$0.733776\pi$
$608$	−7224.30	−0.481881
$609$	7113.31	0.473310
$610$	−35214.3	−2.33735
$611$	2730.60	0.180799
$612$	−6135.69	−0.405262
$613$	−46.1430	−0.00304029	−0.00152014	−	0.999999i	$-0.500484\pi$
$613$	−46.1430	−0.00304029	−0.00152014	+	0.999999i	$0.500484\pi$
$614$	6528.47	0.429100
$615$	34940.9	2.29098
$616$	3049.37	0.199452
$617$	−2028.07	−0.132329	−0.0661644	−	0.997809i	$-0.521076\pi$
$617$	−2028.07	−0.132329	−0.0661644	+	0.997809i	$0.521076\pi$
$618$	−11593.5	−0.754628
$619$	−11993.2	−0.778751	−0.389376	−	0.921079i	$-0.627309\pi$
$619$	−11993.2	−0.778751	−0.389376	+	0.921079i	$0.627309\pi$
$620$	9481.14	0.614148
$621$	1867.37	0.120668
$622$	18523.1	1.19407
$623$	7541.14	0.484959
$624$	28723.9	1.84275
$625$	−15704.7	−1.00510
$626$	−5987.57	−0.382287
$627$	2588.49	0.164871
$628$	5906.64	0.375319
$629$	−35293.0	−2.23724
$630$	−11846.0	−0.749136
$631$	−2119.71	−0.133731	−0.0668656	−	0.997762i	$-0.521300\pi$
$631$	−2119.71	−0.133731	−0.0668656	+	0.997762i	$0.521300\pi$
$632$	4493.41	0.282814
$633$	2550.92	0.160173
$634$	7323.59	0.458765
$635$	25746.4	1.60900
$636$	3704.89	0.230988
$637$	−14004.4	−0.871074
$638$	−1847.65	−0.114654
$639$	−9501.10	−0.588197
$640$	15122.3	0.934000
$641$	25313.0	1.55976	0.779879	−	0.625931i	$-0.215281\pi$
$641$	25313.0	1.55976	0.779879	+	0.625931i	$0.215281\pi$
$642$	15491.8	0.952355
$643$	19659.6	1.20576	0.602878	−	0.797834i	$-0.294021\pi$
$643$	19659.6	1.20576	0.602878	+	0.797834i	$0.294021\pi$
$644$	2340.15	0.143191
$645$	−16818.4	−1.02670
$646$	−14081.2	−0.857613
$647$	−27063.1	−1.64445	−0.822227	−	0.569159i	$-0.807269\pi$
$647$	−27063.1	−1.64445	−0.822227	+	0.569159i	$0.807269\pi$
$648$	−10422.5	−0.631845
$649$	4783.30	0.289308
$650$	132.516	0.00799649
$651$	26713.7	1.60828
$652$	−17580.9	−1.05601
$653$	15595.8	0.934628	0.467314	−	0.884092i	$-0.345222\pi$
$653$	15595.8	0.934628	0.467314	+	0.884092i	$0.345222\pi$
$654$	17466.0	1.04430
$655$	1468.37	0.0875941
$656$	39508.6	2.35145
$657$	−4187.51	−0.248661
$658$	−4088.75	−0.242243
$659$	24419.6	1.44348	0.721740	−	0.692164i	$-0.243342\pi$
$659$	24419.6	1.44348	0.721740	+	0.692164i	$0.243342\pi$
$660$	3703.58	0.218427
$661$	11755.4	0.691729	0.345864	−	0.938285i	$-0.387586\pi$
$661$	11755.4	0.691729	0.345864	+	0.938285i	$0.387586\pi$
$662$	−32956.7	−1.93489
$663$	37910.2	2.22068
$664$	7936.43	0.463845
$665$	−10190.7	−0.594251
$666$	−14718.5	−0.856351
$667$	946.832	0.0549648
$668$	−2347.25	−0.135955
$669$	−14596.9	−0.843573
$670$	9711.63	0.559989
$671$	9660.38	0.555790
$672$	−29123.6	−1.67182
$673$	−13233.9	−0.757996	−0.378998	−	0.925398i	$-0.623731\pi$
$673$	−13233.9	−0.757996	−0.378998	+	0.925398i	$0.623731\pi$
$674$	42308.4	2.41789
$675$	−59.3531	−0.00338444
$676$	5485.42	0.312097
$677$	−26202.4	−1.48750	−0.743752	−	0.668456i	$-0.766956\pi$
$677$	−26202.4	−1.48750	−0.743752	+	0.668456i	$0.766956\pi$
$678$	−21811.9	−1.23552
$679$	−25376.3	−1.43424
$680$	13453.5	0.758702
$681$	30341.0	1.70730
$682$	−6938.77	−0.389588
$683$	−14512.6	−0.813047	−0.406523	−	0.913640i	$-0.633259\pi$
$683$	−14512.6	−0.813047	−0.406523	+	0.913640i	$0.633259\pi$
$684$	−2201.25	−0.123051
$685$	11863.4	0.661718
$686$	−8714.96	−0.485042
$687$	34184.5	1.89843
$688$	−19017.0	−1.05380
$689$	−7128.87	−0.394177
$690$	−5063.15	−0.279349
$691$	3727.47	0.205209	0.102605	−	0.994722i	$-0.467282\pi$
$691$	3727.47	0.205209	0.102605	+	0.994722i	$0.467282\pi$
$692$	−8939.56	−0.491085
$693$	3249.73	0.178134
$694$	−2382.83	−0.130333
$695$	10964.2	0.598413
$696$	−3369.06	−0.183483
$697$	52144.0	2.83371
$698$	−27704.1	−1.50231
$699$	5982.54	0.323720
$700$	−74.3800	−0.00401614
$701$	−11090.9	−0.597570	−0.298785	−	0.954321i	$-0.596581\pi$
$701$	−11090.9	−0.597570	−0.298785	+	0.954321i	$0.596581\pi$
$702$	−19146.7	−1.02941
$703$	−12661.7	−0.679298
$704$	580.602	0.0310827
$705$	3316.05	0.177148
$706$	−28772.6	−1.53381
$707$	−9886.16	−0.525894
$708$	−13061.7	−0.693343
$709$	−35137.8	−1.86125	−0.930625	−	0.365974i	$-0.880736\pi$
$709$	−35137.8	−1.86125	−0.930625	+	0.365974i	$0.880736\pi$
$710$	−31198.0	−1.64907
$711$	4788.65	0.252586
$712$	−3571.70	−0.187999
$713$	3555.78	0.186767
$714$	−56766.1	−2.97537
$715$	−7126.34	−0.372742
$716$	3532.85	0.184398
$717$	27574.4	1.43624
$718$	916.315	0.0476275
$719$	−8130.30	−0.421709	−0.210855	−	0.977517i	$-0.567625\pi$
$719$	−8130.30	−0.421709	−0.210855	+	0.977517i	$0.567625\pi$
$720$	10863.2	0.562290
$721$	−12521.2	−0.646762
$722$	19484.7	1.00436
$723$	4050.97	0.208378
$724$	−14158.5	−0.726789
$725$	−30.0944	−0.00154162
$726$	−2710.46	−0.138560
$727$	−15402.1	−0.785737	−0.392869	−	0.919595i	$-0.628517\pi$
$727$	−15402.1	−0.785737	−0.392869	+	0.919595i	$0.628517\pi$
$728$	16022.3	0.815697
$729$	4549.49	0.231138
$730$	−13750.2	−0.697147
$731$	−25098.8	−1.26992
$732$	−26379.4	−1.33198
$733$	−4466.16	−0.225050	−0.112525	−	0.993649i	$-0.535894\pi$
$733$	−4466.16	−0.225050	−0.112525	+	0.993649i	$0.535894\pi$
$734$	−34262.1	−1.72294
$735$	−17007.0	−0.853486
$736$	−3876.55	−0.194146
$737$	−2664.20	−0.133158
$738$	21746.0	1.08466
$739$	−28359.0	−1.41164	−0.705820	−	0.708392i	$-0.749421\pi$
$739$	−28359.0	−1.41164	−0.705820	+	0.708392i	$0.749421\pi$
$740$	−18116.3	−0.899957
$741$	13600.7	0.674271
$742$	10674.6	0.528138
$743$	9301.53	0.459273	0.229637	−	0.973276i	$-0.426246\pi$
$743$	9301.53	0.459273	0.229637	+	0.973276i	$0.426246\pi$
$744$	−12652.4	−0.623465
$745$	−12097.3	−0.594913
$746$	25560.4	1.25447
$747$	8457.89	0.414268
$748$	5527.02	0.270171
$749$	16731.4	0.816226
$750$	−31224.9	−1.52023
$751$	−23907.5	−1.16165	−0.580823	−	0.814030i	$-0.697269\pi$
$751$	−23907.5	−1.16165	−0.580823	+	0.814030i	$0.697269\pi$
$752$	3749.54	0.181824
$753$	30181.1	1.46064
$754$	−9708.14	−0.468899
$755$	−13880.7	−0.669098
$756$	10746.8	0.517009
$757$	−6950.39	−0.333707	−0.166854	−	0.985982i	$-0.553361\pi$
$757$	−6950.39	−0.333707	−0.166854	+	0.985982i	$0.553361\pi$
$758$	−11278.7	−0.540451
$759$	1388.98	0.0664253
$760$	4826.59	0.230367
$761$	111.776	0.00532440	0.00266220	−	0.999996i	$-0.499153\pi$
$761$	111.776	0.00532440	0.00266220	+	0.999996i	$0.499153\pi$
$762$	51452.7	2.44611
$763$	18863.6	0.895032
$764$	762.992	0.0361310
$765$	14337.4	0.677609
$766$	−453.202	−0.0213771
$767$	25133.0	1.18318
$768$	32865.1	1.54416
$769$	−17081.1	−0.800987	−0.400493	−	0.916300i	$-0.631161\pi$
$769$	−17081.1	−0.800987	−0.400493	+	0.916300i	$0.631161\pi$
$770$	10670.9	0.499417
$771$	−31032.6	−1.44956
$772$	−13691.2	−0.638284
$773$	−39041.9	−1.81661	−0.908305	−	0.418308i	$-0.862623\pi$
$773$	−39041.9	−1.81661	−0.908305	+	0.418308i	$0.862623\pi$
$774$	−10467.1	−0.486090
$775$	−113.018	−0.00523835
$776$	12018.9	0.555998
$777$	−51043.7	−2.35674
$778$	−10467.4	−0.482358
$779$	18707.2	0.860406
$780$	19459.8	0.893296
$781$	8558.59	0.392126
$782$	−7555.97	−0.345526
$783$	4348.20	0.198457
$784$	−19230.2	−0.876013
$785$	−13802.2	−0.627544
$786$	2934.47	0.133167
$787$	−2338.59	−0.105924	−0.0529618	−	0.998597i	$-0.516866\pi$
$787$	−2338.59	−0.105924	−0.0529618	+	0.998597i	$0.516866\pi$
$788$	−1097.22	−0.0496027
$789$	21550.8	0.972405
$790$	15724.1	0.708150
$791$	−23557.3	−1.05892
$792$	−1539.16	−0.0690553
$793$	50758.6	2.27300
$794$	21706.9	0.970213
$795$	−8657.32	−0.386218
$796$	−14882.1	−0.662665
$797$	23923.6	1.06326	0.531629	−	0.846977i	$-0.321580\pi$
$797$	23923.6	1.06326	0.531629	+	0.846977i	$0.321580\pi$
$798$	−20365.5	−0.903421
$799$	4948.69	0.219114
$800$	123.213	0.00544531
$801$	−3806.38	−0.167905
$802$	3101.12	0.136539
$803$	3772.11	0.165772
$804$	7275.08	0.319120
$805$	−5468.30	−0.239419
$806$	−36458.4	−1.59329
$807$	47226.8	2.06005
$808$	4682.36	0.203868
$809$	−24163.4	−1.05011	−0.525056	−	0.851068i	$-0.675956\pi$
$809$	−24163.4	−1.05011	−0.525056	+	0.851068i	$0.675956\pi$
$810$	−36472.3	−1.58210
$811$	−30732.2	−1.33065	−0.665324	−	0.746555i	$-0.731706\pi$
$811$	−30732.2	−1.33065	−0.665324	+	0.746555i	$0.731706\pi$
$812$	5449.07	0.235499
$813$	−32053.2	−1.38273
$814$	13258.4	0.570893
$815$	41081.7	1.76568
$816$	52056.7	2.23327
$817$	−9004.49	−0.385590
$818$	19020.3	0.812994
$819$	17075.1	0.728512
$820$	26766.1	1.13989
$821$	−16591.7	−0.705304	−0.352652	−	0.935755i	$-0.614720\pi$
$821$	−16591.7	−0.705304	−0.352652	+	0.935755i	$0.614720\pi$
$822$	23708.3	1.00599
$823$	−31516.6	−1.33487	−0.667436	−	0.744667i	$-0.732608\pi$
$823$	−31516.6	−1.33487	−0.667436	+	0.744667i	$0.732608\pi$
$824$	5930.42	0.250723
$825$	−44.1477	−0.00186306
$826$	−37633.7	−1.58528
$827$	−33466.6	−1.40719	−0.703596	−	0.710600i	$-0.748424\pi$
$827$	−33466.6	−1.40719	−0.703596	+	0.710600i	$0.748424\pi$
$828$	−1181.19	−0.0495762
$829$	25245.9	1.05769	0.528846	−	0.848718i	$-0.322625\pi$
$829$	25245.9	1.05769	0.528846	+	0.848718i	$0.322625\pi$
$830$	27772.5	1.16144
$831$	5047.79	0.210717
$832$	3050.66	0.127119
$833$	−25380.3	−1.05567
$834$	21911.4	0.909749
$835$	5484.88	0.227320
$836$	1982.88	0.0820328
$837$	16329.5	0.674347
$838$	38194.3	1.57446
$839$	6167.18	0.253772	0.126886	−	0.991917i	$-0.459502\pi$
$839$	6167.18	0.253772	0.126886	+	0.991917i	$0.459502\pi$
$840$	19457.6	0.799227
$841$	−22184.3	−0.909602
$842$	−25987.0	−1.06362
$843$	−44535.4	−1.81955
$844$	1954.10	0.0796954
$845$	−12817.9	−0.521835
$846$	2063.79	0.0838706
$847$	−2927.35	−0.118754
$848$	−9789.06	−0.396412
$849$	−41076.6	−1.66048
$850$	240.161	0.00969112
$851$	−6794.29	−0.273684
$852$	−23370.7	−0.939752
$853$	−29559.4	−1.18651	−0.593255	−	0.805014i	$-0.702157\pi$
$853$	−29559.4	−1.18651	−0.593255	+	0.805014i	$0.702157\pi$
$854$	−76005.1	−3.04548
$855$	5143.72	0.205744
$856$	−7924.48	−0.316417
$857$	−27420.6	−1.09296	−0.546482	−	0.837471i	$-0.684033\pi$
$857$	−27420.6	−1.09296	−0.546482	+	0.837471i	$0.684033\pi$
$858$	−14241.6	−0.566667
$859$	−43876.7	−1.74279	−0.871393	−	0.490585i	$-0.836783\pi$
$859$	−43876.7	−1.74279	−0.871393	+	0.490585i	$0.836783\pi$
$860$	−12883.5	−0.510843
$861$	75415.2	2.98507
$862$	47227.1	1.86608
$863$	28565.3	1.12674	0.563368	−	0.826206i	$-0.309505\pi$
$863$	28565.3	1.12674	0.563368	+	0.826206i	$0.309505\pi$
$864$	−17802.6	−0.700990
$865$	20889.3	0.821108
$866$	31074.6	1.21935
$867$	37940.4	1.48619
$868$	20463.7	0.800212
$869$	−4313.62	−0.168388
$870$	−11789.6	−0.459431
$871$	−13998.6	−0.544573
$872$	−8934.36	−0.346967
$873$	12808.6	0.496571
$874$	−2710.79	−0.104913
$875$	−33723.5	−1.30293
$876$	−10300.4	−0.397281
$877$	44285.0	1.70513	0.852564	−	0.522623i	$-0.175046\pi$
$877$	44285.0	1.70513	0.852564	+	0.522623i	$0.175046\pi$
$878$	55853.1	2.14687
$879$	32971.1	1.26517
$880$	−9785.60	−0.374855
$881$	−6465.23	−0.247241	−0.123620	−	0.992330i	$-0.539450\pi$
$881$	−6465.23	−0.247241	−0.123620	+	0.992330i	$0.539450\pi$
$882$	−10584.5	−0.404082
$883$	−47183.3	−1.79824	−0.899120	−	0.437702i	$-0.855792\pi$
$883$	−47183.3	−1.79824	−0.899120	+	0.437702i	$0.855792\pi$
$884$	29040.7	1.10491
$885$	30521.5	1.15929
$886$	−6931.74	−0.262840
$887$	−38193.4	−1.44578	−0.722892	−	0.690961i	$-0.757188\pi$
$887$	−38193.4	−1.44578	−0.722892	+	0.690961i	$0.757188\pi$
$888$	24175.8	0.913610
$889$	55570.0	2.09647
$890$	−12498.7	−0.470738
$891$	10005.5	0.376202
$892$	−11181.8	−0.419726
$893$	1775.40	0.0665302
$894$	−24175.8	−0.904428
$895$	−8255.32	−0.308318
$896$	32639.3	1.21697
$897$	7298.13	0.271658
$898$	23524.4	0.874187
$899$	8279.68	0.307167
$900$	37.5432	0.00139049
$901$	−12919.7	−0.477712
$902$	−19588.8	−0.723099
$903$	−36300.1	−1.33775
$904$	11157.4	0.410498
$905$	33084.5	1.21521
$906$	−27739.7	−1.01721
$907$	25869.9	0.947075	0.473537	−	0.880774i	$-0.342977\pi$
$907$	25869.9	0.947075	0.473537	+	0.880774i	$0.342977\pi$
$908$	23242.4	0.849478
$909$	4990.02	0.182078
$910$	56068.1	2.04246
$911$	−1992.67	−0.0724699	−0.0362349	−	0.999343i	$-0.511536\pi$
$911$	−1992.67	−0.0724699	−0.0362349	+	0.999343i	$0.511536\pi$
$912$	18675.9	0.678094
$913$	−7618.87	−0.276175
$914$	32187.0	1.16483
$915$	61641.5	2.22711
$916$	26186.7	0.944577
$917$	3169.28	0.114132
$918$	−34699.8	−1.24756
$919$	4474.98	0.160627	0.0803134	−	0.996770i	$-0.474408\pi$
$919$	4474.98	0.160627	0.0803134	+	0.996770i	$0.474408\pi$
$920$	2589.94	0.0928129
$921$	−11427.9	−0.408861
$922$	−24228.9	−0.865441
$923$	44969.5	1.60367
$924$	7993.66	0.284602
$925$	215.951	0.00767615
$926$	50193.6	1.78128
$927$	6320.07	0.223925
$928$	−9026.60	−0.319303
$929$	2011.29	0.0710314	0.0355157	−	0.999369i	$-0.488693\pi$
$929$	2011.29	0.0710314	0.0355157	+	0.999369i	$0.488693\pi$
$930$	−44275.3	−1.56112
$931$	−9105.48	−0.320537
$932$	4582.86	0.161069
$933$	−32424.2	−1.13775
$934$	−23630.7	−0.827858
$935$	−12915.2	−0.451734
$936$	−8087.24	−0.282414
$937$	−33686.1	−1.17447	−0.587234	−	0.809417i	$-0.699783\pi$
$937$	−33686.1	−1.17447	−0.587234	+	0.809417i	$0.699783\pi$
$938$	20961.2	0.729646
$939$	10481.1	0.364256
$940$	2540.22	0.0881414
$941$	27137.5	0.940126	0.470063	−	0.882633i	$-0.344231\pi$
$941$	27137.5	0.940126	0.470063	+	0.882633i	$0.344231\pi$
$942$	−27583.0	−0.954036
$943$	10038.3	0.346651
$944$	34511.5	1.18989
$945$	−25112.5	−0.864453
$946$	9428.80	0.324056
$947$	−43728.7	−1.50052	−0.750260	−	0.661143i	$-0.770072\pi$
$947$	−43728.7	−1.50052	−0.750260	+	0.661143i	$0.770072\pi$
$948$	11779.1	0.403552
$949$	19819.8	0.677954
$950$	86.1604	0.00294254
$951$	−12819.7	−0.437127
$952$	29037.5	0.988561
$953$	−6133.31	−0.208476	−0.104238	−	0.994552i	$-0.533240\pi$
$953$	−6133.31	−0.208476	−0.104238	+	0.994552i	$0.533240\pi$
$954$	−5388.01	−0.182854
$955$	−1782.90	−0.0604120
$956$	21123.1	0.714612
$957$	3234.26	0.109246
$958$	−259.548	−0.00875325
$959$	25605.5	0.862194
$960$	3704.74	0.124552
$961$	1302.94	0.0437360
$962$	69663.8	2.33477
$963$	−8445.16	−0.282598
$964$	3103.20	0.103680
$965$	31992.5	1.06723
$966$	−10928.1	−0.363981
$967$	−2484.68	−0.0826285	−0.0413143	−	0.999146i	$-0.513154\pi$
$967$	−2484.68	−0.0826285	−0.0413143	+	0.999146i	$0.513154\pi$
$968$	1386.48	0.0460362
$969$	24648.7	0.817163
$970$	42058.6	1.39219
$971$	−48668.6	−1.60850	−0.804248	−	0.594294i	$-0.797431\pi$
$971$	−48668.6	−1.60850	−0.804248	+	0.594294i	$0.797431\pi$
$972$	−15328.0	−0.505809
$973$	23664.8	0.779710
$974$	−51902.4	−1.70746
$975$	−231.966	−0.00761933
$976$	69699.6	2.28589
$977$	−15241.9	−0.499110	−0.249555	−	0.968361i	$-0.580284\pi$
$977$	−15241.9	−0.499110	−0.249555	+	0.968361i	$0.580284\pi$
$978$	82099.5	2.68431
$979$	3428.78	0.111935
$980$	−13028.0	−0.424658
$981$	−9521.39	−0.309882
$982$	−6510.24	−0.211558
$983$	28167.7	0.913946	0.456973	−	0.889481i	$-0.348934\pi$
$983$	28167.7	0.913946	0.456973	+	0.889481i	$0.348934\pi$
$984$	−35718.8	−1.15719
$985$	2563.91	0.0829370
$986$	−17594.2	−0.568269
$987$	7157.23	0.230818
$988$	10418.7	0.335488
$989$	−4831.80	−0.155351
$990$	−5386.10	−0.172911
$991$	8444.93	0.270698	0.135349	−	0.990798i	$-0.456784\pi$
$991$	8444.93	0.270698	0.135349	+	0.990798i	$0.456784\pi$
$992$	−33899.0	−1.08497
$993$	57689.6	1.84363
$994$	−67336.5	−2.14868
$995$	34775.4	1.10799
$996$	20804.7	0.661869
$997$	3534.26	0.112268	0.0561340	−	0.998423i	$-0.482123\pi$
$997$	3534.26	0.112268	0.0561340	+	0.998423i	$0.482123\pi$
$998$	23926.4	0.758895
$999$	−31201.9	−0.988171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.18	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.18	✓	84	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-3.57727 q^{2} +6.26190 q^{3} +4.79686 q^{4} -11.2090 q^{5} -22.4005 q^{6} -24.1930 q^{7} +11.4585 q^{8} +12.2114 q^{9} +O(q^{10})\)	\(q-3.57727 q^{2} +6.26190 q^{3} +4.79686 q^{4} -11.2090 q^{5} -22.4005 q^{6} -24.1930 q^{7} +11.4585 q^{8} +12.2114 q^{9} +40.0975 q^{10} -11.0000 q^{11} +30.0375 q^{12} -57.7974 q^{13} +86.5449 q^{14} -70.1894 q^{15} -79.3650 q^{16} -104.747 q^{17} -43.6834 q^{18} -37.5792 q^{19} -53.7679 q^{20} -151.494 q^{21} +39.3500 q^{22} -20.1650 q^{23} +71.7519 q^{24} +0.640928 q^{25} +206.757 q^{26} -92.6049 q^{27} -116.050 q^{28} -46.9543 q^{29} +251.086 q^{30} -176.335 q^{31} +192.242 q^{32} -68.8809 q^{33} +374.708 q^{34} +271.179 q^{35} +58.5763 q^{36} +336.935 q^{37} +134.431 q^{38} -361.922 q^{39} -128.438 q^{40} -497.809 q^{41} +541.935 q^{42} +239.614 q^{43} -52.7655 q^{44} -136.877 q^{45} +72.1355 q^{46} -47.2443 q^{47} -496.976 q^{48} +242.301 q^{49} -2.29277 q^{50} -655.915 q^{51} -277.246 q^{52} +123.342 q^{53} +331.273 q^{54} +123.299 q^{55} -277.215 q^{56} -235.317 q^{57} +167.968 q^{58} -434.845 q^{59} -336.689 q^{60} -878.216 q^{61} +630.797 q^{62} -295.430 q^{63} -52.7820 q^{64} +647.850 q^{65} +246.406 q^{66} +242.200 q^{67} -502.457 q^{68} -126.271 q^{69} -970.079 q^{70} -778.053 q^{71} +139.924 q^{72} -342.919 q^{73} -1205.31 q^{74} +4.01343 q^{75} -180.262 q^{76} +266.123 q^{77} +1294.69 q^{78} +392.147 q^{79} +889.600 q^{80} -909.589 q^{81} +1780.80 q^{82} +692.624 q^{83} -726.696 q^{84} +1174.11 q^{85} -857.164 q^{86} -294.023 q^{87} -126.043 q^{88} -311.708 q^{89} +489.646 q^{90} +1398.29 q^{91} -96.7285 q^{92} -1104.19 q^{93} +169.006 q^{94} +421.223 q^{95} +1203.80 q^{96} +1048.91 q^{97} -866.777 q^{98} -134.325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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