LMFDB - Embedded newform 547.4.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2740447731$
Analytic rank:	$1$
Dimension:	$65$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.41983 q^{2} +7.59300 q^{3} +3.69524 q^{4} +4.48488 q^{5} -25.9668 q^{6} -4.49298 q^{7} +14.7215 q^{8} +30.6536 q^{9} +O(q^{10})$	\(q-3.41983 q^{2} +7.59300 q^{3} +3.69524 q^{4} +4.48488 q^{5} -25.9668 q^{6} -4.49298 q^{7} +14.7215 q^{8} +30.6536 q^{9} -15.3375 q^{10} -23.1279 q^{11} +28.0580 q^{12} -37.2904 q^{13} +15.3652 q^{14} +34.0536 q^{15} -79.9071 q^{16} +18.7211 q^{17} -104.830 q^{18} -96.2157 q^{19} +16.5727 q^{20} -34.1152 q^{21} +79.0936 q^{22} +99.8235 q^{23} +111.781 q^{24} -104.886 q^{25} +127.527 q^{26} +27.7418 q^{27} -16.6027 q^{28} -104.960 q^{29} -116.458 q^{30} -180.598 q^{31} +155.497 q^{32} -175.610 q^{33} -64.0230 q^{34} -20.1505 q^{35} +113.272 q^{36} +98.3432 q^{37} +329.041 q^{38} -283.146 q^{39} +66.0243 q^{40} -100.529 q^{41} +116.668 q^{42} -145.429 q^{43} -85.4633 q^{44} +137.478 q^{45} -341.380 q^{46} -67.7241 q^{47} -606.735 q^{48} -322.813 q^{49} +358.692 q^{50} +142.149 q^{51} -137.797 q^{52} -27.8771 q^{53} -94.8721 q^{54} -103.726 q^{55} -66.1436 q^{56} -730.565 q^{57} +358.944 q^{58} -34.0999 q^{59} +125.836 q^{60} +797.662 q^{61} +617.616 q^{62} -137.726 q^{63} +107.485 q^{64} -167.243 q^{65} +600.557 q^{66} +797.053 q^{67} +69.1790 q^{68} +757.960 q^{69} +68.9112 q^{70} -672.198 q^{71} +451.268 q^{72} +525.961 q^{73} -336.317 q^{74} -796.398 q^{75} -355.540 q^{76} +103.913 q^{77} +968.310 q^{78} -641.526 q^{79} -358.374 q^{80} -617.004 q^{81} +343.794 q^{82} +822.967 q^{83} -126.064 q^{84} +83.9619 q^{85} +497.344 q^{86} -796.959 q^{87} -340.479 q^{88} -1257.88 q^{89} -470.150 q^{90} +167.545 q^{91} +368.872 q^{92} -1371.28 q^{93} +231.605 q^{94} -431.515 q^{95} +1180.68 q^{96} +240.164 q^{97} +1103.97 q^{98} -708.954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) $ 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * 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 $

$2$	−3.41983	−1.20909	−0.604546	−	0.796570i	$-0.706646\pi$
$2$	−3.41983	−1.20909	−0.604546	+	0.796570i	$0.706646\pi$
$3$	7.59300	1.46127	0.730636	−	0.682767i	$-0.239223\pi$
$3$	7.59300	1.46127	0.730636	+	0.682767i	$0.239223\pi$
$4$	3.69524	0.461905
$5$	4.48488	0.401140	0.200570	−	0.979679i	$-0.435721\pi$
$5$	4.48488	0.401140	0.200570	+	0.979679i	$0.435721\pi$
$6$	−25.9668	−1.76681
$7$	−4.49298	−0.242598	−0.121299	−	0.992616i	$-0.538706\pi$
$7$	−4.49298	−0.242598	−0.121299	+	0.992616i	$0.538706\pi$
$8$	14.7215	0.650606
$9$	30.6536	1.13532
$10$	−15.3375	−0.485015
$11$	−23.1279	−0.633939	−0.316970	−	0.948436i	$-0.602665\pi$
$11$	−23.1279	−0.633939	−0.316970	+	0.948436i	$0.602665\pi$
$12$	28.0580	0.674970
$13$	−37.2904	−0.795576	−0.397788	−	0.917477i	$-0.630222\pi$
$13$	−37.2904	−0.795576	−0.397788	+	0.917477i	$0.630222\pi$
$14$	15.3652	0.293324
$15$	34.0536	0.586174
$16$	−79.9071	−1.24855
$17$	18.7211	0.267090	0.133545	−	0.991043i	$-0.457364\pi$
$17$	18.7211	0.267090	0.133545	+	0.991043i	$0.457364\pi$
$18$	−104.830	−1.37271
$19$	−96.2157	−1.16176	−0.580879	−	0.813990i	$-0.697291\pi$
$19$	−96.2157	−1.16176	−0.580879	+	0.813990i	$0.697291\pi$
$20$	16.5727	0.185288
$21$	−34.1152	−0.354502
$22$	79.0936	0.766491
$23$	99.8235	0.904984	0.452492	−	0.891768i	$-0.350535\pi$
$23$	99.8235	0.904984	0.452492	+	0.891768i	$0.350535\pi$
$24$	111.781	0.950713
$25$	−104.886	−0.839087
$26$	127.527	0.961925
$27$	27.7418	0.197737
$28$	−16.6027	−0.112057
$29$	−104.960	−0.672087	−0.336044	−	0.941846i	$-0.609089\pi$
$29$	−104.960	−0.672087	−0.336044	+	0.941846i	$0.609089\pi$
$30$	−116.458	−0.708739
$31$	−180.598	−1.04634	−0.523168	−	0.852230i	$-0.675250\pi$
$31$	−180.598	−1.04634	−0.523168	+	0.852230i	$0.675250\pi$
$32$	155.497	0.859005
$33$	−175.610	−0.926358
$34$	−64.0230	−0.322937
$35$	−20.1505	−0.0973157
$36$	113.272	0.524410
$37$	98.3432	0.436960	0.218480	−	0.975841i	$-0.429890\pi$
$37$	98.3432	0.436960	0.218480	+	0.975841i	$0.429890\pi$
$38$	329.041	1.40467
$39$	−283.146	−1.16255
$40$	66.0243	0.260984
$41$	−100.529	−0.382928	−0.191464	−	0.981500i	$-0.561324\pi$
$41$	−100.529	−0.382928	−0.191464	+	0.981500i	$0.561324\pi$
$42$	116.668	0.428626
$43$	−145.429	−0.515762	−0.257881	−	0.966177i	$-0.583024\pi$
$43$	−145.429	−0.515762	−0.257881	+	0.966177i	$0.583024\pi$
$44$	−85.4633	−0.292820
$45$	137.478	0.455421
$46$	−341.380	−1.09421
$47$	−67.7241	−0.210182	−0.105091	−	0.994463i	$-0.533513\pi$
$47$	−67.7241	−0.210182	−0.105091	+	0.994463i	$0.533513\pi$
$48$	−606.735	−1.82447
$49$	−322.813	−0.941146
$50$	358.692	1.01453
$51$	142.149	0.390292
$52$	−137.797	−0.367481
$53$	−27.8771	−0.0722492	−0.0361246	−	0.999347i	$-0.511501\pi$
$53$	−27.8771	−0.0722492	−0.0361246	+	0.999347i	$0.511501\pi$
$54$	−94.8721	−0.239083
$55$	−103.726	−0.254298
$56$	−66.1436	−0.157836
$57$	−730.565	−1.69764
$58$	358.944	0.812616
$59$	−34.0999	−0.0752446	−0.0376223	−	0.999292i	$-0.511978\pi$
$59$	−34.0999	−0.0752446	−0.0376223	+	0.999292i	$0.511978\pi$
$60$	125.836	0.270757
$61$	797.662	1.67426	0.837132	−	0.547001i	$-0.184231\pi$
$61$	797.662	1.67426	0.837132	+	0.547001i	$0.184231\pi$
$62$	617.616	1.26512
$63$	−137.726	−0.275426
$64$	107.485	0.209932
$65$	−167.243	−0.319137
$66$	600.557	1.12005
$67$	797.053	1.45337	0.726683	−	0.686973i	$-0.241061\pi$
$67$	797.053	1.45337	0.726683	+	0.686973i	$0.241061\pi$
$68$	69.1790	0.123370
$69$	757.960	1.32243
$70$	68.9112	0.117664
$71$	−672.198	−1.12359	−0.561797	−	0.827275i	$-0.689890\pi$
$71$	−672.198	−1.12359	−0.561797	+	0.827275i	$0.689890\pi$
$72$	451.268	0.738645
$73$	525.961	0.843275	0.421638	−	0.906764i	$-0.361455\pi$
$73$	525.961	0.843275	0.421638	+	0.906764i	$0.361455\pi$
$74$	−336.317	−0.528325
$75$	−796.398	−1.22614
$76$	−355.540	−0.536622
$77$	103.913	0.153792
$78$	968.310	1.40563
$79$	−641.526	−0.913636	−0.456818	−	0.889560i	$-0.651011\pi$
$79$	−641.526	−0.913636	−0.456818	+	0.889560i	$0.651011\pi$
$80$	−358.374	−0.500842
$81$	−617.004	−0.846370
$82$	343.794	0.462996
$83$	822.967	1.08834	0.544171	−	0.838974i	$-0.316844\pi$
$83$	822.967	1.08834	0.544171	+	0.838974i	$0.316844\pi$
$84$	−126.064	−0.163746
$85$	83.9619	0.107140
$86$	497.344	0.623604
$87$	−796.959	−0.982103
$88$	−340.479	−0.412445
$89$	−1257.88	−1.49815	−0.749075	−	0.662486i	$-0.769502\pi$
$89$	−1257.88	−1.49815	−0.749075	+	0.662486i	$0.769502\pi$
$90$	−470.150	−0.550646
$91$	167.545	0.193005
$92$	368.872	0.418017
$93$	−1371.28	−1.52898
$94$	231.605	0.254130
$95$	−431.515	−0.466027
$96$	1180.68	1.25524
$97$	240.164	0.251391	0.125696	−	0.992069i	$-0.459884\pi$
$97$	240.164	0.251391	0.125696	+	0.992069i	$0.459884\pi$
$98$	1103.97	1.13793
$99$	−708.954	−0.719723
$100$	−387.579	−0.387579
$101$	431.758	0.425362	0.212681	−	0.977122i	$-0.431781\pi$
$101$	431.758	0.425362	0.212681	+	0.977122i	$0.431781\pi$
$102$	−486.127	−0.471899
$103$	−1146.61	−1.09688	−0.548440	−	0.836190i	$-0.684778\pi$
$103$	−1146.61	−1.09688	−0.548440	+	0.836190i	$0.684778\pi$
$104$	−548.972	−0.517607
$105$	−153.002	−0.142205
$106$	95.3349	0.0873560
$107$	1836.16	1.65895	0.829476	−	0.558542i	$-0.188639\pi$
$107$	1836.16	1.65895	0.829476	+	0.558542i	$0.188639\pi$
$108$	102.513	0.0913358
$109$	−1574.58	−1.38365	−0.691823	−	0.722067i	$-0.743192\pi$
$109$	−1574.58	−1.38365	−0.691823	+	0.722067i	$0.743192\pi$
$110$	354.725	0.307470
$111$	746.720	0.638518
$112$	359.021	0.302896
$113$	−1770.79	−1.47418	−0.737090	−	0.675795i	$-0.763800\pi$
$113$	−1770.79	−1.47418	−0.737090	+	0.675795i	$0.763800\pi$
$114$	2498.41	2.05261
$115$	447.696	0.363025
$116$	−387.852	−0.310441
$117$	−1143.08	−0.903232
$118$	116.616	0.0909776
$119$	−84.1136	−0.0647956
$120$	501.322	0.381369
$121$	−796.099	−0.598121
$122$	−2727.87	−2.02434
$123$	−763.320	−0.559563
$124$	−667.355	−0.483308
$125$	−1031.01	−0.737730
$126$	471.000	0.333016
$127$	−1939.73	−1.35530	−0.677652	−	0.735383i	$-0.737002\pi$
$127$	−1939.73	−1.35530	−0.677652	+	0.735383i	$0.737002\pi$
$128$	−1611.55	−1.11283
$129$	−1104.24	−0.753669
$130$	571.941	0.385866
$131$	−591.852	−0.394735	−0.197368	−	0.980330i	$-0.563239\pi$
$131$	−591.852	−0.394735	−0.197368	+	0.980330i	$0.563239\pi$
$132$	−648.922	−0.427890
$133$	432.295	0.281840
$134$	−2725.79	−1.75726
$135$	124.418	0.0793202
$136$	275.604	0.173771
$137$	−893.686	−0.557320	−0.278660	−	0.960390i	$-0.589890\pi$
$137$	−893.686	−0.557320	−0.278660	+	0.960390i	$0.589890\pi$
$138$	−2592.09	−1.59894
$139$	−2380.75	−1.45275	−0.726376	−	0.687297i	$-0.758797\pi$
$139$	−2380.75	−1.45275	−0.726376	+	0.687297i	$0.758797\pi$
$140$	−74.4608	−0.0449506
$141$	−514.229	−0.307134
$142$	2298.80	1.35853
$143$	862.449	0.504347
$144$	−2449.44	−1.41750
$145$	−470.731	−0.269601
$146$	−1798.70	−1.01960
$147$	−2451.12	−1.37527
$148$	363.402	0.201834
$149$	−524.091	−0.288156	−0.144078	−	0.989566i	$-0.546022\pi$
$149$	−524.091	−0.288156	−0.144078	+	0.989566i	$0.546022\pi$
$150$	2723.55	1.48251
$151$	1969.90	1.06164	0.530822	−	0.847483i	$-0.321883\pi$
$151$	1969.90	1.06164	0.530822	+	0.847483i	$0.321883\pi$
$152$	−1416.44	−0.755847
$153$	573.869	0.303233
$154$	−355.366	−0.185949
$155$	−809.961	−0.419727
$156$	−1046.29	−0.536989
$157$	1116.28	0.567444	0.283722	−	0.958907i	$-0.408431\pi$
$157$	1116.28	0.567444	0.283722	+	0.958907i	$0.408431\pi$
$158$	2193.91	1.10467
$159$	−211.670	−0.105576
$160$	697.383	0.344581
$161$	−448.505	−0.219548
$162$	2110.05	1.02334
$163$	1508.59	0.724918	0.362459	−	0.932000i	$-0.381937\pi$
$163$	1508.59	0.724918	0.362459	+	0.932000i	$0.381937\pi$
$164$	−371.481	−0.176877
$165$	−787.590	−0.371599
$166$	−2814.41	−1.31591
$167$	287.805	0.133359	0.0666797	−	0.997774i	$-0.478759\pi$
$167$	287.805	0.133359	0.0666797	+	0.997774i	$0.478759\pi$
$168$	−502.228	−0.230641
$169$	−806.429	−0.367059
$170$	−287.135	−0.129543
$171$	−2949.36	−1.31896
$172$	−537.397	−0.238233
$173$	2165.75	0.951785	0.475893	−	0.879503i	$-0.342125\pi$
$173$	2165.75	0.951785	0.475893	+	0.879503i	$0.342125\pi$
$174$	2725.46	1.18745
$175$	471.250	0.203561
$176$	1848.09	0.791504
$177$	−258.920	−0.109953
$178$	4301.75	1.81140
$179$	−1657.80	−0.692235	−0.346118	−	0.938191i	$-0.612500\pi$
$179$	−1657.80	−0.692235	−0.346118	+	0.938191i	$0.612500\pi$
$180$	508.013	0.210361
$181$	2537.57	1.04208	0.521039	−	0.853533i	$-0.325545\pi$
$181$	2537.57	1.04208	0.521039	+	0.853533i	$0.325545\pi$
$182$	−572.975	−0.233361
$183$	6056.64	2.44656
$184$	1469.56	0.588789
$185$	441.057	0.175282
$186$	4689.55	1.84868
$187$	−432.980	−0.169319
$188$	−250.257	−0.0970843
$189$	−124.643	−0.0479707
$190$	1475.71	0.563470
$191$	2198.82	0.832991	0.416496	−	0.909138i	$-0.363258\pi$
$191$	2198.82	0.832991	0.416496	+	0.909138i	$0.363258\pi$
$192$	816.135	0.306768
$193$	−764.782	−0.285234	−0.142617	−	0.989778i	$-0.545552\pi$
$193$	−764.782	−0.285234	−0.142617	+	0.989778i	$0.545552\pi$
$194$	−821.319	−0.303955
$195$	−1269.87	−0.466346
$196$	−1192.87	−0.434720
$197$	−2516.70	−0.910189	−0.455094	−	0.890443i	$-0.650394\pi$
$197$	−2516.70	−0.910189	−0.455094	+	0.890443i	$0.650394\pi$
$198$	2424.50	0.870212
$199$	−1531.20	−0.545448	−0.272724	−	0.962092i	$-0.587925\pi$
$199$	−1531.20	−0.545448	−0.272724	+	0.962092i	$0.587925\pi$
$200$	−1544.08	−0.545915
$201$	6052.02	2.12377
$202$	−1476.54	−0.514302
$203$	471.582	0.163047
$204$	525.276	0.180278
$205$	−450.862	−0.153608
$206$	3921.21	1.32623
$207$	3059.95	1.02745
$208$	2979.77	0.993315
$209$	2225.27	0.736484
$210$	523.242	0.171939
$211$	131.314	0.0428436	0.0214218	−	0.999771i	$-0.493181\pi$
$211$	131.314	0.0428436	0.0214218	+	0.999771i	$0.493181\pi$
$212$	−103.013	−0.0333723
$213$	−5104.00	−1.64188
$214$	−6279.34	−2.00583
$215$	−652.233	−0.206893
$216$	408.401	0.128649
$217$	811.425	0.253839
$218$	5384.80	1.67296
$219$	3993.62	1.23226
$220$	−383.292	−0.117462
$221$	−698.117	−0.212491
$222$	−2553.65	−0.772027
$223$	4264.48	1.28059	0.640293	−	0.768131i	$-0.278813\pi$
$223$	4264.48	1.28059	0.640293	+	0.768131i	$0.278813\pi$
$224$	−698.643	−0.208393
$225$	−3215.13	−0.952631
$226$	6055.82	1.78242
$227$	4193.06	1.22600	0.613002	−	0.790081i	$-0.289962\pi$
$227$	4193.06	1.22600	0.613002	+	0.790081i	$0.289962\pi$
$228$	−2699.62	−0.784151
$229$	3610.08	1.04175	0.520874	−	0.853633i	$-0.325606\pi$
$229$	3610.08	1.04175	0.520874	+	0.853633i	$0.325606\pi$
$230$	−1531.04	−0.438931
$231$	789.013	0.224733
$232$	−1545.17	−0.437264
$233$	−3372.39	−0.948209	−0.474104	−	0.880469i	$-0.657228\pi$
$233$	−3372.39	−0.948209	−0.474104	+	0.880469i	$0.657228\pi$
$234$	3909.15	1.09209
$235$	−303.734	−0.0843124
$236$	−126.007	−0.0347559
$237$	−4871.10	−1.33507
$238$	287.654	0.0783439
$239$	−4110.51	−1.11250	−0.556249	−	0.831016i	$-0.687760\pi$
$239$	−4110.51	−1.11250	−0.556249	+	0.831016i	$0.687760\pi$
$240$	−2721.13	−0.731867
$241$	4191.98	1.12045	0.560227	−	0.828339i	$-0.310714\pi$
$241$	4191.98	1.12045	0.560227	+	0.828339i	$0.310714\pi$
$242$	2722.52	0.723184
$243$	−5433.94	−1.43452
$244$	2947.55	0.773351
$245$	−1447.78	−0.377531
$246$	2610.42	0.676563
$247$	3587.92	0.924266
$248$	−2658.69	−0.680753
$249$	6248.79	1.59036
$250$	3525.88	0.891985
$251$	−2045.83	−0.514469	−0.257234	−	0.966349i	$-0.582811\pi$
$251$	−2045.83	−0.514469	−0.257234	+	0.966349i	$0.582811\pi$
$252$	−508.931	−0.127221
$253$	−2308.71	−0.573705
$254$	6633.56	1.63869
$255$	637.522	0.156562
$256$	4651.36	1.13559
$257$	−987.369	−0.239651	−0.119826	−	0.992795i	$-0.538234\pi$
$257$	−987.369	−0.239651	−0.119826	+	0.992795i	$0.538234\pi$
$258$	3776.33	0.911256
$259$	−441.854	−0.106006
$260$	−618.002	−0.147411
$261$	−3217.39	−0.763033
$262$	2024.03	0.477271
$263$	2170.18	0.508818	0.254409	−	0.967097i	$-0.418119\pi$
$263$	2170.18	0.508818	0.254409	+	0.967097i	$0.418119\pi$
$264$	−2585.25	−0.602695
$265$	−125.025	−0.0289820
$266$	−1478.38	−0.340771
$267$	−9551.10	−2.18920
$268$	2945.31	0.671318
$269$	1182.08	0.267928	0.133964	−	0.990986i	$-0.457229\pi$
$269$	1182.08	0.267928	0.133964	+	0.990986i	$0.457229\pi$
$270$	−425.490	−0.0959055
$271$	−3373.42	−0.756165	−0.378082	−	0.925772i	$-0.623416\pi$
$271$	−3373.42	−0.756165	−0.378082	+	0.925772i	$0.623416\pi$
$272$	−1495.95	−0.333475
$273$	1272.17	0.282033
$274$	3056.26	0.673851
$275$	2425.79	0.531930
$276$	2800.84	0.610837
$277$	3789.49	0.821979	0.410989	−	0.911640i	$-0.365183\pi$
$277$	3789.49	0.821979	0.410989	+	0.911640i	$0.365183\pi$
$278$	8141.77	1.75651
$279$	−5535.99	−1.18792
$280$	−296.646	−0.0633142
$281$	88.8440	0.0188612	0.00943059	−	0.999956i	$-0.496998\pi$
$281$	88.8440	0.0188612	0.00943059	+	0.999956i	$0.496998\pi$
$282$	1758.57	0.371353
$283$	3973.01	0.834526	0.417263	−	0.908786i	$-0.362989\pi$
$283$	3973.01	0.834526	0.417263	+	0.908786i	$0.362989\pi$
$284$	−2483.93	−0.518994
$285$	−3276.49	−0.680992
$286$	−2949.43	−0.609802
$287$	451.677	0.0928977
$288$	4766.53	0.975244
$289$	−4562.52	−0.928663
$290$	1609.82	0.325972
$291$	1823.56	0.367351
$292$	1943.55	0.389513
$293$	4843.77	0.965789	0.482895	−	0.875679i	$-0.339585\pi$
$293$	4843.77	0.965789	0.482895	+	0.875679i	$0.339585\pi$
$294$	8382.41	1.66283
$295$	−152.934	−0.0301836
$296$	1447.76	0.284289
$297$	−641.609	−0.125353
$298$	1792.30	0.348407
$299$	−3722.45	−0.719984
$300$	−2942.88	−0.566358
$301$	653.411	0.125123
$302$	−6736.72	−1.28363
$303$	3278.34	0.621569
$304$	7688.32	1.45051
$305$	3577.41	0.671613
$306$	−1962.54	−0.366636
$307$	6337.29	1.17814	0.589069	−	0.808083i	$-0.299495\pi$
$307$	6337.29	1.17814	0.589069	+	0.808083i	$0.299495\pi$
$308$	383.985	0.0710376
$309$	−8706.19	−1.60284
$310$	2769.93	0.507489
$311$	−9169.10	−1.67181	−0.835903	−	0.548877i	$-0.815056\pi$
$311$	−9169.10	−1.67181	−0.835903	+	0.548877i	$0.815056\pi$
$312$	−4168.34	−0.756365
$313$	5924.56	1.06989	0.534946	−	0.844886i	$-0.320332\pi$
$313$	5924.56	1.06989	0.534946	+	0.844886i	$0.320332\pi$
$314$	−3817.49	−0.686093
$315$	−617.684	−0.110484
$316$	−2370.59	−0.422013
$317$	−6891.69	−1.22106	−0.610529	−	0.791994i	$-0.709043\pi$
$317$	−6891.69	−1.22106	−0.610529	+	0.791994i	$0.709043\pi$
$318$	723.877	0.127651
$319$	2427.50	0.426062
$320$	482.058	0.0842121
$321$	13941.9	2.42418
$322$	1533.81	0.265453
$323$	−1801.26	−0.310294
$324$	−2279.98	−0.390943
$325$	3911.23	0.667557
$326$	−5159.11	−0.876493
$327$	−11955.8	−2.02189
$328$	−1479.95	−0.249136
$329$	304.283	0.0509898
$330$	2693.43	0.449298
$331$	2796.66	0.464406	0.232203	−	0.972667i	$-0.425407\pi$
$331$	2796.66	0.464406	0.232203	+	0.972667i	$0.425407\pi$
$332$	3041.06	0.502711
$333$	3014.57	0.496089
$334$	−984.244	−0.161244
$335$	3574.69	0.583003
$336$	2726.05	0.442613
$337$	10225.6	1.65289	0.826446	−	0.563015i	$-0.190359\pi$
$337$	10225.6	1.65289	0.826446	+	0.563015i	$0.190359\pi$
$338$	2757.85	0.443809
$339$	−13445.6	−2.15418
$340$	310.259	0.0494888
$341$	4176.87	0.663314
$342$	10086.3	1.59475
$343$	2991.49	0.470918
$344$	−2140.94	−0.335558
$345$	3399.36	0.530479
$346$	−7406.49	−1.15080
$347$	5834.05	0.902559	0.451280	−	0.892383i	$-0.350968\pi$
$347$	5834.05	0.902559	0.451280	+	0.892383i	$0.350968\pi$
$348$	−2944.96	−0.453639
$349$	−6169.85	−0.946317	−0.473158	−	0.880977i	$-0.656886\pi$
$349$	−6169.85	−0.946317	−0.473158	+	0.880977i	$0.656886\pi$
$350$	−1611.60	−0.246124
$351$	−1034.50	−0.157315
$352$	−3596.31	−0.544557
$353$	7617.21	1.14851	0.574254	−	0.818678i	$-0.305292\pi$
$353$	7617.21	1.14851	0.574254	+	0.818678i	$0.305292\pi$
$354$	885.464	0.132943
$355$	−3014.72	−0.450718
$356$	−4648.18	−0.692003
$357$	−638.674	−0.0946841
$358$	5669.41	0.836977
$359$	7570.87	1.11302	0.556511	−	0.830840i	$-0.312140\pi$
$359$	7570.87	1.11302	0.556511	+	0.830840i	$0.312140\pi$
$360$	2023.88	0.296300
$361$	2398.46	0.349680
$362$	−8678.06	−1.25997
$363$	−6044.78	−0.874018
$364$	619.119	0.0891501
$365$	2358.87	0.338271
$366$	−20712.7	−2.95811
$367$	−1586.25	−0.225618	−0.112809	−	0.993617i	$-0.535985\pi$
$367$	−1586.25	−0.225618	−0.112809	+	0.993617i	$0.535985\pi$
$368$	−7976.61	−1.12992
$369$	−3081.59	−0.434746
$370$	−1508.34	−0.211932
$371$	125.251	0.0175275
$372$	−5067.22	−0.706245
$373$	7364.40	1.02229	0.511145	−	0.859495i	$-0.329222\pi$
$373$	7364.40	1.02229	0.511145	+	0.859495i	$0.329222\pi$
$374$	1480.72	0.204722
$375$	−7828.45	−1.07803
$376$	−997.003	−0.136746
$377$	3913.99	0.534696
$378$	426.259	0.0580010
$379$	−1930.18	−0.261600	−0.130800	−	0.991409i	$-0.541755\pi$
$379$	−1930.18	−0.261600	−0.130800	+	0.991409i	$0.541755\pi$
$380$	−1594.55	−0.215260
$381$	−14728.4	−1.98047
$382$	−7519.61	−1.00716
$383$	−1814.29	−0.242052	−0.121026	−	0.992649i	$-0.538618\pi$
$383$	−1814.29	−0.242052	−0.121026	+	0.992649i	$0.538618\pi$
$384$	−12236.5	−1.62615
$385$	466.038	0.0616922
$386$	2615.43	0.344875
$387$	−4457.93	−0.585554
$388$	887.463	0.116119
$389$	−7356.06	−0.958784	−0.479392	−	0.877601i	$-0.659143\pi$
$389$	−7356.06	−0.958784	−0.479392	+	0.877601i	$0.659143\pi$
$390$	4342.75	0.563856
$391$	1868.81	0.241713
$392$	−4752.31	−0.612316
$393$	−4493.93	−0.576816
$394$	8606.68	1.10050
$395$	−2877.16	−0.366496
$396$	−2619.76	−0.332444
$397$	2010.50	0.254167	0.127083	−	0.991892i	$-0.459438\pi$
$397$	2010.50	0.254167	0.127083	+	0.991892i	$0.459438\pi$
$398$	5236.46	0.659497
$399$	3282.42	0.411845
$400$	8381.13	1.04764
$401$	−6947.28	−0.865164	−0.432582	−	0.901595i	$-0.642397\pi$
$401$	−6947.28	−0.865164	−0.432582	+	0.901595i	$0.642397\pi$
$402$	−20696.9	−2.56783
$403$	6734.58	0.832440
$404$	1595.45	0.196477
$405$	−2767.19	−0.339513
$406$	−1612.73	−0.197139
$407$	−2274.47	−0.277006
$408$	2092.66	0.253926
$409$	−1281.62	−0.154944	−0.0774720	−	0.996995i	$-0.524685\pi$
$409$	−1281.62	−0.154944	−0.0774720	+	0.996995i	$0.524685\pi$
$410$	1541.87	0.185726
$411$	−6785.76	−0.814396
$412$	−4236.99	−0.506655
$413$	153.210	0.0182542
$414$	−10464.5	−1.24228
$415$	3690.91	0.436577
$416$	−5798.52	−0.683403
$417$	−18077.0	−2.12287
$418$	−7610.04	−0.890477
$419$	−919.432	−0.107201	−0.0536005	−	0.998562i	$-0.517070\pi$
$419$	−919.432	−0.107201	−0.0536005	+	0.998562i	$0.517070\pi$
$420$	−565.381	−0.0656851
$421$	2929.56	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$421$	2929.56	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$422$	−449.070	−0.0518019
$423$	−2075.99	−0.238624
$424$	−410.393	−0.0470058
$425$	−1963.58	−0.224112
$426$	17454.8	1.98518
$427$	−3583.88	−0.406173
$428$	6785.04	0.766279
$429$	6548.57	0.736988
$430$	2230.53	0.250152
$431$	−2656.81	−0.296924	−0.148462	−	0.988918i	$-0.547432\pi$
$431$	−2656.81	−0.296924	−0.148462	+	0.988918i	$0.547432\pi$
$432$	−2216.76	−0.246884
$433$	8934.58	0.991614	0.495807	−	0.868433i	$-0.334872\pi$
$433$	8934.58	0.991614	0.495807	+	0.868433i	$0.334872\pi$
$434$	−2774.94	−0.306915
$435$	−3574.26	−0.393960
$436$	−5818.46	−0.639114
$437$	−9604.59	−1.05137
$438$	−13657.5	−1.48991
$439$	75.1861	0.00817411	0.00408706	−	0.999992i	$-0.498699\pi$
$439$	75.1861	0.00817411	0.00408706	+	0.999992i	$0.498699\pi$
$440$	−1527.00	−0.165448
$441$	−9895.38	−1.06850
$442$	2387.44	0.256921
$443$	−6028.41	−0.646542	−0.323271	−	0.946306i	$-0.604783\pi$
$443$	−6028.41	−0.646542	−0.323271	+	0.946306i	$0.604783\pi$
$444$	2759.31	0.294935
$445$	−5641.45	−0.600967
$446$	−14583.8	−1.54835
$447$	−3979.42	−0.421074
$448$	−482.929	−0.0509291
$449$	4426.22	0.465225	0.232613	−	0.972569i	$-0.425273\pi$
$449$	4426.22	0.465225	0.232613	+	0.972569i	$0.425273\pi$
$450$	10995.2	1.15182
$451$	2325.04	0.242753
$452$	−6543.51	−0.680931
$453$	14957.4	1.55135
$454$	−14339.5	−1.48235
$455$	751.418	0.0774220
$456$	−10755.0	−1.10450
$457$	13598.8	1.39196	0.695978	−	0.718063i	$-0.254971\pi$
$457$	13598.8	1.39196	0.695978	+	0.718063i	$0.254971\pi$
$458$	−12345.8	−1.25957
$459$	519.356	0.0528137
$460$	1654.35	0.167683
$461$	−1350.99	−0.136490	−0.0682452	−	0.997669i	$-0.521740\pi$
$461$	−1350.99	−0.136490	−0.0682452	+	0.997669i	$0.521740\pi$
$462$	−2698.29	−0.271723
$463$	8646.11	0.867860	0.433930	−	0.900947i	$-0.357127\pi$
$463$	8646.11	0.867860	0.433930	+	0.900947i	$0.357127\pi$
$464$	8387.03	0.839134
$465$	−6150.03	−0.613335
$466$	11533.0	1.14647
$467$	−3674.90	−0.364141	−0.182071	−	0.983285i	$-0.558280\pi$
$467$	−3674.90	−0.364141	−0.182071	+	0.983285i	$0.558280\pi$
$468$	−4223.97	−0.417208
$469$	−3581.14	−0.352584
$470$	1038.72	0.101942
$471$	8475.90	0.829191
$472$	−502.003	−0.0489546
$473$	3363.48	0.326962
$474$	16658.3	1.61423
$475$	10091.7	0.974816
$476$	−310.820	−0.0299294
$477$	−854.532	−0.0820259
$478$	14057.3	1.34511
$479$	−6093.25	−0.581227	−0.290614	−	0.956840i	$-0.593859\pi$
$479$	−6093.25	−0.581227	−0.290614	+	0.956840i	$0.593859\pi$
$480$	5295.22	0.503527
$481$	−3667.25	−0.347635
$482$	−14335.9	−1.35473
$483$	−3405.50	−0.320819
$484$	−2941.78	−0.276275
$485$	1077.10	0.100843
$486$	18583.1	1.73446
$487$	−11023.4	−1.02571	−0.512853	−	0.858476i	$-0.671412\pi$
$487$	−11023.4	−1.02571	−0.512853	+	0.858476i	$0.671412\pi$
$488$	11742.8	1.08929
$489$	11454.7	1.05930
$490$	4951.15	0.456470
$491$	8415.45	0.773491	0.386746	−	0.922186i	$-0.373599\pi$
$491$	8415.45	0.773491	0.386746	+	0.922186i	$0.373599\pi$
$492$	−2820.65	−0.258465
$493$	−1964.96	−0.179508
$494$	−12270.1	−1.11752
$495$	−3179.57	−0.288709
$496$	14431.1	1.30640
$497$	3020.17	0.272582
$498$	−21369.8	−1.92290
$499$	3966.54	0.355845	0.177922	−	0.984045i	$-0.443062\pi$
$499$	3966.54	0.355845	0.177922	+	0.984045i	$0.443062\pi$
$500$	−3809.83	−0.340762
$501$	2185.30	0.194874
$502$	6996.40	0.622041
$503$	−2941.03	−0.260704	−0.130352	−	0.991468i	$-0.541611\pi$
$503$	−2941.03	−0.260704	−0.130352	+	0.991468i	$0.541611\pi$
$504$	−2027.54	−0.179194
$505$	1936.38	0.170629
$506$	7895.40	0.693663
$507$	−6123.22	−0.536374
$508$	−7167.79	−0.626022
$509$	−8783.80	−0.764902	−0.382451	−	0.923976i	$-0.624920\pi$
$509$	−8783.80	−0.764902	−0.382451	+	0.923976i	$0.624920\pi$
$510$	−2180.22	−0.189297
$511$	−2363.13	−0.204577
$512$	−3014.43	−0.260196
$513$	−2669.19	−0.229723
$514$	3376.63	0.289761
$515$	−5142.39	−0.440002
$516$	−4080.45	−0.348124
$517$	1566.32	0.133243
$518$	1511.07	0.128171
$519$	16444.5	1.39082
$520$	−2462.07	−0.207632
$521$	−23627.9	−1.98687	−0.993435	−	0.114402i	$-0.963505\pi$
$521$	−23627.9	−1.98687	−0.993435	+	0.114402i	$0.963505\pi$
$522$	11002.9	0.922578
$523$	−8175.81	−0.683562	−0.341781	−	0.939780i	$-0.611030\pi$
$523$	−8175.81	−0.683562	−0.341781	+	0.939780i	$0.611030\pi$
$524$	−2187.03	−0.182330
$525$	3578.20	0.297458
$526$	−7421.65	−0.615208
$527$	−3381.00	−0.279466
$528$	14032.5	1.15660
$529$	−2202.27	−0.181003
$530$	427.565	0.0350420
$531$	−1045.28	−0.0854265
$532$	1597.44	0.130183
$533$	3748.78	0.304649
$534$	32663.1	2.64695
$535$	8234.93	0.665471
$536$	11733.9	0.945570
$537$	−12587.7	−1.01154
$538$	−4042.51	−0.323950
$539$	7466.00	0.596629
$540$	459.756	0.0366384
$541$	5151.27	0.409372	0.204686	−	0.978828i	$-0.434383\pi$
$541$	5151.27	0.409372	0.204686	+	0.978828i	$0.434383\pi$
$542$	11536.5	0.914273
$543$	19267.8	1.52276
$544$	2911.07	0.229432
$545$	−7061.80	−0.555035
$546$	−4350.60	−0.341004
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	−3302.39	−0.257429
$549$	24451.2	1.90082
$550$	−8295.80	−0.643153
$551$	10098.8	0.780802
$552$	11158.3	0.860381
$553$	2882.36	0.221646
$554$	−12959.4	−0.993849
$555$	3348.94	0.256135
$556$	−8797.45	−0.671034
$557$	3918.51	0.298083	0.149042	−	0.988831i	$-0.452381\pi$
$557$	3918.51	0.298083	0.149042	+	0.988831i	$0.452381\pi$
$558$	18932.1	1.43631
$559$	5423.11	0.410328
$560$	1610.17	0.121503
$561$	−3287.62	−0.247421
$562$	−303.832	−0.0228049
$563$	−19053.6	−1.42631	−0.713156	−	0.701006i	$-0.752735\pi$
$563$	−19053.6	−1.42631	−0.713156	+	0.701006i	$0.752735\pi$
$564$	−1900.20	−0.141867
$565$	−7941.79	−0.591352
$566$	−13587.0	−1.00902
$567$	2772.19	0.205328
$568$	−9895.79	−0.731018
$569$	23448.5	1.72761	0.863806	−	0.503824i	$-0.168074\pi$
$569$	23448.5	1.72761	0.863806	+	0.503824i	$0.168074\pi$
$570$	11205.1	0.823383
$571$	−7307.76	−0.535587	−0.267794	−	0.963476i	$-0.586294\pi$
$571$	−7307.76	−0.535587	−0.267794	+	0.963476i	$0.586294\pi$
$572$	3186.96	0.232960
$573$	16695.7	1.21723
$574$	−1544.66	−0.112322
$575$	−10470.1	−0.759361
$576$	3294.81	0.238340
$577$	−7494.63	−0.540737	−0.270369	−	0.962757i	$-0.587146\pi$
$577$	−7494.63	−0.540737	−0.270369	+	0.962757i	$0.587146\pi$
$578$	15603.0	1.12284
$579$	−5806.99	−0.416805
$580$	−1739.47	−0.124530
$581$	−3697.58	−0.264030
$582$	−6236.27	−0.444161
$583$	644.739	0.0458016
$584$	7742.96	0.548640
$585$	−5126.59	−0.362322
$586$	−16564.9	−1.16773
$587$	18184.6	1.27864	0.639319	−	0.768942i	$-0.279217\pi$
$587$	18184.6	1.27864	0.639319	+	0.768942i	$0.279217\pi$
$588$	−9057.48	−0.635245
$589$	17376.4	1.21559
$590$	523.008	0.0364947
$591$	−19109.3	−1.33003
$592$	−7858.32	−0.545566
$593$	25357.5	1.75600	0.877999	−	0.478662i	$-0.158878\pi$
$593$	25357.5	1.75600	0.877999	+	0.478662i	$0.158878\pi$
$594$	2194.19	0.151564
$595$	−377.239	−0.0259921
$596$	−1936.64	−0.133101
$597$	−11626.4	−0.797048
$598$	12730.2	0.870527
$599$	−3945.48	−0.269128	−0.134564	−	0.990905i	$-0.542963\pi$
$599$	−3945.48	−0.269128	−0.134564	+	0.990905i	$0.542963\pi$
$600$	−11724.2	−0.797731
$601$	22411.9	1.52113	0.760567	−	0.649260i	$-0.224921\pi$
$601$	22411.9	1.52113	0.760567	+	0.649260i	$0.224921\pi$
$602$	−2234.56	−0.151285
$603$	24432.6	1.65003
$604$	7279.26	0.490379
$605$	−3570.41	−0.239930
$606$	−11211.4	−0.751535
$607$	−24850.7	−1.66171	−0.830856	−	0.556488i	$-0.812149\pi$
$607$	−24850.7	−1.66171	−0.830856	+	0.556488i	$0.812149\pi$
$608$	−14961.2	−0.997955
$609$	3580.72	0.238256
$610$	−12234.1	−0.812043
$611$	2525.45	0.167216
$612$	2120.59	0.140065
$613$	−28087.7	−1.85066	−0.925328	−	0.379167i	$-0.876211\pi$
$613$	−28087.7	−1.85066	−0.925328	+	0.379167i	$0.876211\pi$
$614$	−21672.5	−1.42448
$615$	−3423.40	−0.224463
$616$	1529.76	0.100058
$617$	18050.5	1.17777	0.588886	−	0.808216i	$-0.299567\pi$
$617$	18050.5	1.17777	0.588886	+	0.808216i	$0.299567\pi$
$618$	29773.7	1.93798
$619$	−21524.0	−1.39761	−0.698807	−	0.715310i	$-0.746285\pi$
$619$	−21524.0	−1.39761	−0.698807	+	0.715310i	$0.746285\pi$
$620$	−2993.00	−0.193874
$621$	2769.28	0.178949
$622$	31356.8	2.02137
$623$	5651.64	0.363448
$624$	22625.3	1.45150
$625$	8486.79	0.543154
$626$	−20261.0	−1.29360
$627$	16896.5	1.07620
$628$	4124.92	0.262106
$629$	1841.09	0.116708
$630$	2112.38	0.133586
$631$	−1168.63	−0.0737280	−0.0368640	−	0.999320i	$-0.511737\pi$
$631$	−1168.63	−0.0737280	−0.0368640	+	0.999320i	$0.511737\pi$
$632$	−9444.25	−0.594418
$633$	997.064	0.0626062
$634$	23568.4	1.47637
$635$	−8699.47	−0.543666
$636$	−782.174	−0.0487660
$637$	12037.8	0.748753
$638$	−8301.64	−0.515149
$639$	−20605.3	−1.27564
$640$	−7227.62	−0.446401
$641$	17049.9	1.05059	0.525296	−	0.850920i	$-0.323955\pi$
$641$	17049.9	1.05059	0.525296	+	0.850920i	$0.323955\pi$
$642$	−47679.0	−2.93106
$643$	5795.26	0.355432	0.177716	−	0.984082i	$-0.443129\pi$
$643$	5795.26	0.355432	0.177716	+	0.984082i	$0.443129\pi$
$644$	−1657.34	−0.101410
$645$	−4952.40	−0.302326
$646$	6160.02	0.375174
$647$	5419.78	0.329326	0.164663	−	0.986350i	$-0.447346\pi$
$647$	5419.78	0.329326	0.164663	+	0.986350i	$0.447346\pi$
$648$	−9083.25	−0.550654
$649$	788.660	0.0477005
$650$	−13375.8	−0.807139
$651$	6161.15	0.370928
$652$	5574.59	0.334843
$653$	−11276.7	−0.675788	−0.337894	−	0.941184i	$-0.609715\pi$
$653$	−11276.7	−0.675788	−0.337894	+	0.941184i	$0.609715\pi$
$654$	40886.8	2.44465
$655$	−2654.38	−0.158344
$656$	8033.02	0.478105
$657$	16122.6	0.957386
$658$	−1040.60	−0.0616514
$659$	22784.8	1.34685	0.673423	−	0.739257i	$-0.264823\pi$
$659$	22784.8	1.34685	0.673423	+	0.739257i	$0.264823\pi$
$660$	−2910.34	−0.171644
$661$	6037.97	0.355295	0.177648	−	0.984094i	$-0.443151\pi$
$661$	6037.97	0.355295	0.177648	+	0.984094i	$0.443151\pi$
$662$	−9564.11	−0.561510
$663$	−5300.80	−0.310507
$664$	12115.3	0.708082
$665$	1938.79	0.113057
$666$	−10309.3	−0.599817
$667$	−10477.4	−0.608229
$668$	1063.51	0.0615994
$669$	32380.2	1.87129
$670$	−12224.8	−0.704904
$671$	−18448.3	−1.06138
$672$	−5304.79	−0.304519
$673$	−13508.4	−0.773716	−0.386858	−	0.922139i	$-0.626440\pi$
$673$	−13508.4	−0.773716	−0.386858	+	0.922139i	$0.626440\pi$
$674$	−34969.9	−1.99850
$675$	−2909.72	−0.165919
$676$	−2979.95	−0.169547
$677$	−30871.2	−1.75255	−0.876276	−	0.481810i	$-0.839980\pi$
$677$	−30871.2	−1.75255	−0.876276	+	0.481810i	$0.839980\pi$
$678$	45981.8	2.60460
$679$	−1079.05	−0.0609870
$680$	1236.05	0.0697063
$681$	31837.9	1.79153
$682$	−14284.2	−0.802008
$683$	10593.3	0.593472	0.296736	−	0.954960i	$-0.404102\pi$
$683$	10593.3	0.593472	0.296736	+	0.954960i	$0.404102\pi$
$684$	−10898.6	−0.609237
$685$	−4008.07	−0.223563
$686$	−10230.4	−0.569384
$687$	27411.3	1.52228
$688$	11620.8	0.643954
$689$	1039.55	0.0574797
$690$	−11625.2	−0.641398
$691$	16173.2	0.890389	0.445195	−	0.895434i	$-0.353134\pi$
$691$	16173.2	0.890389	0.445195	+	0.895434i	$0.353134\pi$
$692$	8002.97	0.439635
$693$	3185.32	0.174603
$694$	−19951.5	−1.09128
$695$	−10677.4	−0.582757
$696$	−11732.5	−0.638962
$697$	−1882.02	−0.102276
$698$	21099.8	1.14418
$699$	−25606.6	−1.38559
$700$	1741.38	0.0940259
$701$	4672.81	0.251768	0.125884	−	0.992045i	$-0.459823\pi$
$701$	4672.81	0.251768	0.125884	+	0.992045i	$0.459823\pi$
$702$	3537.81	0.190208
$703$	−9462.16	−0.507642
$704$	−2485.91	−0.133084
$705$	−2306.25	−0.123203
$706$	−26049.6	−1.38865
$707$	−1939.88	−0.103192
$708$	−956.774	−0.0507878
$709$	−18423.8	−0.975910	−0.487955	−	0.872869i	$-0.662257\pi$
$709$	−18423.8	−0.975910	−0.487955	+	0.872869i	$0.662257\pi$
$710$	10309.8	0.544960
$711$	−19665.1	−1.03727
$712$	−18518.0	−0.974705
$713$	−18028.0	−0.946918
$714$	2184.16	0.114482
$715$	3867.97	0.202313
$716$	−6125.99	−0.319747
$717$	−31211.1	−1.62566
$718$	−25891.1	−1.34575
$719$	2004.44	0.103968	0.0519840	−	0.998648i	$-0.483446\pi$
$719$	2004.44	0.103968	0.0519840	+	0.998648i	$0.483446\pi$
$720$	−10985.4	−0.568615
$721$	5151.69	0.266101
$722$	−8202.32	−0.422796
$723$	31829.7	1.63729
$724$	9376.93	0.481341
$725$	11008.8	0.563940
$726$	20672.1	1.05677
$727$	−1848.91	−0.0943223	−0.0471611	−	0.998887i	$-0.515017\pi$
$727$	−1848.91	−0.0943223	−0.0471611	+	0.998887i	$0.515017\pi$
$728$	2466.52	0.125570
$729$	−24600.8	−1.24985
$730$	−8066.94	−0.409001
$731$	−2722.60	−0.137755
$732$	22380.8	1.13008
$733$	−10393.5	−0.523730	−0.261865	−	0.965104i	$-0.584338\pi$
$733$	−10393.5	−0.523730	−0.261865	+	0.965104i	$0.584338\pi$
$734$	5424.71	0.272792
$735$	−10993.0	−0.551676
$736$	15522.2	0.777386
$737$	−18434.2	−0.921346
$738$	10538.5	0.525648
$739$	−19636.9	−0.977476	−0.488738	−	0.872431i	$-0.662543\pi$
$739$	−19636.9	−0.977476	−0.488738	+	0.872431i	$0.662543\pi$
$740$	1629.81	0.0809637
$741$	27243.0	1.35060
$742$	−428.338	−0.0211924
$743$	−11866.4	−0.585915	−0.292957	−	0.956126i	$-0.594639\pi$
$743$	−11866.4	−0.585915	−0.292957	+	0.956126i	$0.594639\pi$
$744$	−20187.4	−0.994766
$745$	−2350.48	−0.115591
$746$	−25185.0	−1.23604
$747$	25226.9	1.23561
$748$	−1599.97	−0.0782094
$749$	−8249.81	−0.402459
$750$	26772.0	1.30343
$751$	−2675.53	−0.130002	−0.0650009	−	0.997885i	$-0.520705\pi$
$751$	−2675.53	−0.130002	−0.0650009	+	0.997885i	$0.520705\pi$
$752$	5411.63	0.262423
$753$	−15534.0	−0.751780
$754$	−13385.2	−0.646497
$755$	8834.76	0.425867
$756$	−460.587	−0.0221579
$757$	98.5237	0.00473039	0.00236520	−	0.999997i	$-0.499247\pi$
$757$	98.5237	0.00473039	0.00236520	+	0.999997i	$0.499247\pi$
$758$	6600.87	0.316299
$759$	−17530.0	−0.838340
$760$	−6352.57	−0.303200
$761$	−32041.2	−1.52627	−0.763137	−	0.646237i	$-0.776342\pi$
$761$	−32041.2	−1.52627	−0.763137	+	0.646237i	$0.776342\pi$
$762$	50368.6	2.39457
$763$	7074.56	0.335670
$764$	8125.19	0.384763
$765$	2573.73	0.121639
$766$	6204.56	0.292663
$767$	1271.60	0.0598627
$768$	35317.7	1.65940
$769$	−19007.6	−0.891328	−0.445664	−	0.895200i	$-0.647032\pi$
$769$	−19007.6	−0.891328	−0.445664	+	0.895200i	$0.647032\pi$
$770$	−1593.77	−0.0745916
$771$	−7497.09	−0.350196
$772$	−2826.06	−0.131751
$773$	−8805.59	−0.409722	−0.204861	−	0.978791i	$-0.565674\pi$
$773$	−8805.59	−0.409722	−0.204861	+	0.978791i	$0.565674\pi$
$774$	15245.4	0.707989
$775$	18942.2	0.877967
$776$	3535.58	0.163557
$777$	−3355.00	−0.154903
$778$	25156.5	1.15926
$779$	9672.51	0.444870
$780$	−4692.49	−0.215408
$781$	15546.5	0.712291
$782$	−6391.00	−0.292253
$783$	−2911.77	−0.132897
$784$	25795.1	1.17507
$785$	5006.37	0.227624
$786$	15368.5	0.697424
$787$	9893.22	0.448101	0.224050	−	0.974578i	$-0.428072\pi$
$787$	9893.22	0.448101	0.224050	+	0.974578i	$0.428072\pi$
$788$	−9299.80	−0.420421
$789$	16478.2	0.743522
$790$	9839.41	0.443127
$791$	7956.14	0.357633
$792$	−10436.9	−0.468256
$793$	−29745.1	−1.33200
$794$	−6875.58	−0.307311
$795$	−949.316	−0.0423506
$796$	−5658.17	−0.251945
$797$	1519.65	0.0675393	0.0337697	−	0.999430i	$-0.489249\pi$
$797$	1519.65	0.0675393	0.0337697	+	0.999430i	$0.489249\pi$
$798$	−11225.3	−0.497959
$799$	−1267.87	−0.0561377
$800$	−16309.4	−0.720780
$801$	−38558.6	−1.70088
$802$	23758.5	1.04606
$803$	−12164.4	−0.534585
$804$	22363.7	0.980978
$805$	−2011.49	−0.0880692
$806$	−23031.1	−1.00650
$807$	8975.52	0.391516
$808$	6356.14	0.276743
$809$	32571.4	1.41551	0.707755	−	0.706458i	$-0.249708\pi$
$809$	32571.4	1.41551	0.707755	+	0.706458i	$0.249708\pi$
$810$	9463.31	0.410502
$811$	−1786.60	−0.0773565	−0.0386783	−	0.999252i	$-0.512315\pi$
$811$	−1786.60	−0.0773565	−0.0386783	+	0.999252i	$0.512315\pi$
$812$	1742.61	0.0753123
$813$	−25614.4	−1.10496
$814$	7778.32	0.334926
$815$	6765.82	0.290793
$816$	−11358.7	−0.487298
$817$	13992.6	0.599190
$818$	4382.93	0.187342
$819$	5135.85	0.219122
$820$	−1666.05	−0.0709522
$821$	−24313.2	−1.03354	−0.516769	−	0.856125i	$-0.672865\pi$
$821$	−24313.2	−1.03354	−0.516769	+	0.856125i	$0.672865\pi$
$822$	23206.1	0.984680
$823$	4875.45	0.206498	0.103249	−	0.994656i	$-0.467076\pi$
$823$	4875.45	0.206498	0.103249	+	0.994656i	$0.467076\pi$
$824$	−16879.8	−0.713637
$825$	18419.0	0.777295
$826$	−523.953	−0.0220710
$827$	39757.3	1.67170	0.835850	−	0.548957i	$-0.184975\pi$
$827$	39757.3	1.67170	0.835850	+	0.548957i	$0.184975\pi$
$828$	11307.3	0.474583
$829$	−11069.4	−0.463757	−0.231879	−	0.972745i	$-0.574487\pi$
$829$	−11069.4	−0.463757	−0.231879	+	0.972745i	$0.574487\pi$
$830$	−12622.3	−0.527862
$831$	28773.6	1.20114
$832$	−4008.16	−0.167017
$833$	−6043.42	−0.251371
$834$	61820.4	2.56674
$835$	1290.77	0.0534957
$836$	8222.91	0.340186
$837$	−5010.12	−0.206900
$838$	3144.30	0.129616
$839$	36434.5	1.49924	0.749618	−	0.661871i	$-0.230237\pi$
$839$	36434.5	1.49924	0.749618	+	0.661871i	$0.230237\pi$
$840$	−2252.43	−0.0925193
$841$	−13372.5	−0.548299
$842$	−10018.6	−0.410052
$843$	674.593	0.0275613
$844$	485.236	0.0197897
$845$	−3616.74	−0.147242
$846$	7099.52	0.288518
$847$	3576.86	0.145103
$848$	2227.58	0.0902067
$849$	30167.1	1.21947
$850$	6715.11	0.270972
$851$	9816.96	0.395442
$852$	−18860.5	−0.758392
$853$	−40447.6	−1.62356	−0.811781	−	0.583961i	$-0.801502\pi$
$853$	−40447.6	−1.62356	−0.811781	+	0.583961i	$0.801502\pi$
$854$	12256.3	0.491101
$855$	−13227.5	−0.529089
$856$	27031.0	1.07932
$857$	−31018.7	−1.23638	−0.618191	−	0.786028i	$-0.712134\pi$
$857$	−31018.7	−1.23638	−0.618191	+	0.786028i	$0.712134\pi$
$858$	−22395.0	−0.891087
$859$	30742.7	1.22110	0.610552	−	0.791976i	$-0.290948\pi$
$859$	30742.7	1.22110	0.610552	+	0.791976i	$0.290948\pi$
$860$	−2410.16	−0.0955648
$861$	3429.58	0.135749
$862$	9085.85	0.359008
$863$	−35126.1	−1.38552	−0.692761	−	0.721168i	$-0.743606\pi$
$863$	−35126.1	−1.38552	−0.692761	+	0.721168i	$0.743606\pi$
$864$	4313.75	0.169857
$865$	9713.11	0.381799
$866$	−30554.8	−1.19895
$867$	−34643.2	−1.35703
$868$	2998.41	0.117250
$869$	14837.2	0.579190
$870$	12223.4	0.476334
$871$	−29722.4	−1.15626
$872$	−23180.3	−0.900209
$873$	7361.88	0.285409
$874$	32846.1	1.27121
$875$	4632.31	0.178972
$876$	14757.4	0.569185
$877$	−19665.7	−0.757199	−0.378599	−	0.925561i	$-0.623594\pi$
$877$	−19665.7	−0.757199	−0.378599	+	0.925561i	$0.623594\pi$
$878$	−257.124	−0.00988326
$879$	36778.7	1.41128
$880$	8288.44	0.317504
$881$	15989.5	0.611465	0.305733	−	0.952117i	$-0.401099\pi$
$881$	15989.5	0.611465	0.305733	+	0.952117i	$0.401099\pi$
$882$	33840.5	1.29192
$883$	−2656.23	−0.101234	−0.0506169	−	0.998718i	$-0.516119\pi$
$883$	−2656.23	−0.101234	−0.0506169	+	0.998718i	$0.516119\pi$
$884$	−2579.71	−0.0981505
$885$	−1161.23	−0.0441064
$886$	20616.1	0.781730
$887$	−8166.49	−0.309136	−0.154568	−	0.987982i	$-0.549399\pi$
$887$	−8166.49	−0.309136	−0.154568	+	0.987982i	$0.549399\pi$
$888$	10992.9	0.415424
$889$	8715.19	0.328794
$890$	19292.8	0.726625
$891$	14270.0	0.536547
$892$	15758.3	0.591509
$893$	6516.12	0.244181
$894$	13609.0	0.509118
$895$	−7435.05	−0.277683
$896$	7240.68	0.269971
$897$	−28264.6	−1.05209
$898$	−15136.9	−0.562501
$899$	18955.6	0.703229
$900$	−11880.7	−0.440025
$901$	−521.890	−0.0192971
$902$	−7951.24	−0.293511
$903$	4961.35	0.182839
$904$	−26068.8	−0.959110
$905$	11380.7	0.418018
$906$	−51151.9	−1.87573
$907$	−16456.4	−0.602456	−0.301228	−	0.953552i	$-0.597396\pi$
$907$	−16456.4	−0.602456	−0.301228	+	0.953552i	$0.597396\pi$
$908$	15494.4	0.566298
$909$	13234.9	0.482921
$910$	−2569.72	−0.0936104
$911$	−21020.4	−0.764473	−0.382237	−	0.924064i	$-0.624846\pi$
$911$	−21020.4	−0.764473	−0.382237	+	0.924064i	$0.624846\pi$
$912$	58377.4	2.11959
$913$	−19033.5	−0.689943
$914$	−46505.5	−1.68301
$915$	27163.3	0.981410
$916$	13340.1	0.481189
$917$	2659.18	0.0957620
$918$	−1776.11	−0.0638566
$919$	−30767.5	−1.10438	−0.552190	−	0.833718i	$-0.686208\pi$
$919$	−30767.5	−1.10438	−0.552190	+	0.833718i	$0.686208\pi$
$920$	6590.78	0.236186
$921$	48119.0	1.72158
$922$	4620.17	0.165030
$923$	25066.5	0.893904
$924$	2915.60	0.103805
$925$	−10314.8	−0.366648
$926$	−29568.2	−1.04932
$927$	−35147.7	−1.24531
$928$	−16320.9	−0.577326
$929$	5638.47	0.199130	0.0995652	−	0.995031i	$-0.468255\pi$
$929$	5638.47	0.199130	0.0995652	+	0.995031i	$0.468255\pi$
$930$	21032.1	0.741579
$931$	31059.7	1.09338
$932$	−12461.8	−0.437983
$933$	−69620.9	−2.44297
$934$	12567.5	0.440281
$935$	−1941.86	−0.0679206
$936$	−16828.0	−0.587648
$937$	−41920.4	−1.46156	−0.730780	−	0.682614i	$-0.760843\pi$
$937$	−41920.4	−1.46156	−0.730780	+	0.682614i	$0.760843\pi$
$938$	12246.9	0.426307
$939$	44985.2	1.56340
$940$	−1122.37	−0.0389444
$941$	54387.4	1.88414	0.942071	−	0.335414i	$-0.108876\pi$
$941$	54387.4	1.88414	0.942071	+	0.335414i	$0.108876\pi$
$942$	−28986.2	−1.00257
$943$	−10035.2	−0.346544
$944$	2724.82	0.0939465
$945$	−559.009	−0.0192429
$946$	−11502.5	−0.395327
$947$	−29126.4	−0.999451	−0.499726	−	0.866184i	$-0.666566\pi$
$947$	−29126.4	−0.999451	−0.499726	+	0.866184i	$0.666566\pi$
$948$	−17999.9	−0.616677
$949$	−19613.3	−0.670889
$950$	−34511.8	−1.17864
$951$	−52328.5	−1.78430
$952$	−1238.28	−0.0421564
$953$	7953.31	0.270339	0.135169	−	0.990822i	$-0.456842\pi$
$953$	7953.31	0.270339	0.135169	+	0.990822i	$0.456842\pi$
$954$	2922.36	0.0991769
$955$	9861.45	0.334146
$956$	−15189.3	−0.513869
$957$	18432.0	0.622594
$958$	20837.9	0.702758
$959$	4015.32	0.135205
$960$	3660.27	0.123057
$961$	2824.77	0.0948195
$962$	12541.4	0.420323
$963$	56284.8	1.88344
$964$	15490.4	0.517544
$965$	−3429.95	−0.114419
$966$	11646.2	0.387900
$967$	34419.0	1.14461	0.572306	−	0.820040i	$-0.306049\pi$
$967$	34419.0	1.14461	0.572306	+	0.820040i	$0.306049\pi$
$968$	−11719.8	−0.389141
$969$	−13677.0	−0.453425
$970$	−3683.52	−0.121928
$971$	−45735.5	−1.51156	−0.755779	−	0.654827i	$-0.772742\pi$
$971$	−45735.5	−1.51156	−0.755779	+	0.654827i	$0.772742\pi$
$972$	−20079.7	−0.662610
$973$	10696.7	0.352435
$974$	37698.3	1.24017
$975$	29698.0	0.975483
$976$	−63738.8	−2.09040
$977$	−43118.0	−1.41194	−0.705971	−	0.708240i	$-0.749489\pi$
$977$	−43118.0	−1.41194	−0.705971	+	0.708240i	$0.749489\pi$
$978$	−39173.1	−1.28080
$979$	29092.2	0.949736
$980$	−5349.89	−0.174384
$981$	−48266.6	−1.57088
$982$	−28779.4	−0.935222
$983$	19739.7	0.640488	0.320244	−	0.947335i	$-0.396235\pi$
$983$	19739.7	0.640488	0.320244	+	0.947335i	$0.396235\pi$
$984$	−11237.2	−0.364055
$985$	−11287.1	−0.365113
$986$	6719.84	0.217042
$987$	2310.42	0.0745101
$988$	13258.2	0.426923
$989$	−14517.3	−0.466757
$990$	10873.6	0.349076
$991$	13373.3	0.428675	0.214337	−	0.976760i	$-0.431241\pi$
$991$	13373.3	0.428675	0.214337	+	0.976760i	$0.431241\pi$
$992$	−28082.4	−0.898808
$993$	21235.0	0.678624
$994$	−10328.5	−0.329577
$995$	−6867.26	−0.218801
$996$	23090.8	0.734598
$997$	−31515.2	−1.00110	−0.500550	−	0.865708i	$-0.666869\pi$
$997$	−31515.2	−1.00110	−0.500550	+	0.865708i	$0.666869\pi$
$998$	−13564.9	−0.430249
$999$	2728.21	0.0864032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.17	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.17	✓	65	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-3.41983 q^{2} +7.59300 q^{3} +3.69524 q^{4} +4.48488 q^{5} -25.9668 q^{6} -4.49298 q^{7} +14.7215 q^{8} +30.6536 q^{9} +O(q^{10})\)	\(q-3.41983 q^{2} +7.59300 q^{3} +3.69524 q^{4} +4.48488 q^{5} -25.9668 q^{6} -4.49298 q^{7} +14.7215 q^{8} +30.6536 q^{9} -15.3375 q^{10} -23.1279 q^{11} +28.0580 q^{12} -37.2904 q^{13} +15.3652 q^{14} +34.0536 q^{15} -79.9071 q^{16} +18.7211 q^{17} -104.830 q^{18} -96.2157 q^{19} +16.5727 q^{20} -34.1152 q^{21} +79.0936 q^{22} +99.8235 q^{23} +111.781 q^{24} -104.886 q^{25} +127.527 q^{26} +27.7418 q^{27} -16.6027 q^{28} -104.960 q^{29} -116.458 q^{30} -180.598 q^{31} +155.497 q^{32} -175.610 q^{33} -64.0230 q^{34} -20.1505 q^{35} +113.272 q^{36} +98.3432 q^{37} +329.041 q^{38} -283.146 q^{39} +66.0243 q^{40} -100.529 q^{41} +116.668 q^{42} -145.429 q^{43} -85.4633 q^{44} +137.478 q^{45} -341.380 q^{46} -67.7241 q^{47} -606.735 q^{48} -322.813 q^{49} +358.692 q^{50} +142.149 q^{51} -137.797 q^{52} -27.8771 q^{53} -94.8721 q^{54} -103.726 q^{55} -66.1436 q^{56} -730.565 q^{57} +358.944 q^{58} -34.0999 q^{59} +125.836 q^{60} +797.662 q^{61} +617.616 q^{62} -137.726 q^{63} +107.485 q^{64} -167.243 q^{65} +600.557 q^{66} +797.053 q^{67} +69.1790 q^{68} +757.960 q^{69} +68.9112 q^{70} -672.198 q^{71} +451.268 q^{72} +525.961 q^{73} -336.317 q^{74} -796.398 q^{75} -355.540 q^{76} +103.913 q^{77} +968.310 q^{78} -641.526 q^{79} -358.374 q^{80} -617.004 q^{81} +343.794 q^{82} +822.967 q^{83} -126.064 q^{84} +83.9619 q^{85} +497.344 q^{86} -796.959 q^{87} -340.479 q^{88} -1257.88 q^{89} -470.150 q^{90} +167.545 q^{91} +368.872 q^{92} -1371.28 q^{93} +231.605 q^{94} -431.515 q^{95} +1180.68 q^{96} +240.164 q^{97} +1103.97 q^{98} -708.954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * q^99

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