LMFDB - Embedded newform 2013.4.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70549 q^{2} +3.00000 q^{3} -5.09131 q^{4} -1.03329 q^{5} -5.11647 q^{6} +1.91271 q^{7} +22.3271 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.70549 q^{2} +3.00000 q^{3} -5.09131 q^{4} -1.03329 q^{5} -5.11647 q^{6} +1.91271 q^{7} +22.3271 q^{8} +9.00000 q^{9} +1.76227 q^{10} -11.0000 q^{11} -15.2739 q^{12} +24.2208 q^{13} -3.26210 q^{14} -3.09988 q^{15} +2.65188 q^{16} +33.3685 q^{17} -15.3494 q^{18} +11.9220 q^{19} +5.26082 q^{20} +5.73812 q^{21} +18.7604 q^{22} -174.078 q^{23} +66.9812 q^{24} -123.932 q^{25} -41.3084 q^{26} +27.0000 q^{27} -9.73817 q^{28} +290.454 q^{29} +5.28682 q^{30} +125.559 q^{31} -183.139 q^{32} -33.0000 q^{33} -56.9096 q^{34} -1.97639 q^{35} -45.8218 q^{36} +238.644 q^{37} -20.3328 q^{38} +72.6625 q^{39} -23.0705 q^{40} +34.5692 q^{41} -9.78629 q^{42} -141.886 q^{43} +56.0044 q^{44} -9.29965 q^{45} +296.888 q^{46} +355.714 q^{47} +7.95565 q^{48} -339.342 q^{49} +211.365 q^{50} +100.106 q^{51} -123.316 q^{52} +168.386 q^{53} -46.0482 q^{54} +11.3662 q^{55} +42.7051 q^{56} +35.7659 q^{57} -495.365 q^{58} -208.326 q^{59} +15.7825 q^{60} +61.0000 q^{61} -214.140 q^{62} +17.2143 q^{63} +291.127 q^{64} -25.0273 q^{65} +56.2811 q^{66} -472.418 q^{67} -169.889 q^{68} -522.235 q^{69} +3.37071 q^{70} -280.960 q^{71} +200.944 q^{72} +15.3551 q^{73} -407.004 q^{74} -371.797 q^{75} -60.6984 q^{76} -21.0398 q^{77} -123.925 q^{78} +1027.42 q^{79} -2.74018 q^{80} +81.0000 q^{81} -58.9573 q^{82} +267.377 q^{83} -29.2145 q^{84} -34.4795 q^{85} +241.986 q^{86} +871.361 q^{87} -245.598 q^{88} -1493.91 q^{89} +15.8605 q^{90} +46.3273 q^{91} +886.286 q^{92} +376.678 q^{93} -606.667 q^{94} -12.3189 q^{95} -549.418 q^{96} +360.610 q^{97} +578.743 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.70549	−0.602981	−0.301491	−	0.953469i	$-0.597484\pi$
$2$	−1.70549	−0.602981	−0.301491	+	0.953469i	$0.597484\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.09131	−0.636414
$5$	−1.03329	−0.0924207	−0.0462104	−	0.998932i	$-0.514714\pi$
$5$	−1.03329	−0.0924207	−0.0462104	+	0.998932i	$0.514714\pi$
$6$	−5.11647	−0.348131
$7$	1.91271	0.103276	0.0516382	−	0.998666i	$-0.483556\pi$
$7$	1.91271	0.103276	0.0516382	+	0.998666i	$0.483556\pi$
$8$	22.3271	0.986727
$9$	9.00000	0.333333
$10$	1.76227	0.0557280
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−15.2739	−0.367434
$13$	24.2208	0.516743	0.258371	−	0.966046i	$-0.416814\pi$
$13$	24.2208	0.516743	0.258371	+	0.966046i	$0.416814\pi$
$14$	−3.26210	−0.0622737
$15$	−3.09988	−0.0533591
$16$	2.65188	0.0414357
$17$	33.3685	0.476062	0.238031	−	0.971258i	$-0.423498\pi$
$17$	33.3685	0.476062	0.238031	+	0.971258i	$0.423498\pi$
$18$	−15.3494	−0.200994
$19$	11.9220	0.143952	0.0719760	−	0.997406i	$-0.477070\pi$
$19$	11.9220	0.143952	0.0719760	+	0.997406i	$0.477070\pi$
$20$	5.26082	0.0588178
$21$	5.73812	0.0596267
$22$	18.7604	0.181806
$23$	−174.078	−1.57817	−0.789083	−	0.614287i	$-0.789444\pi$
$23$	−174.078	−1.57817	−0.789083	+	0.614287i	$0.789444\pi$
$24$	66.9812	0.569687
$25$	−123.932	−0.991458
$26$	−41.3084	−0.311586
$27$	27.0000	0.192450
$28$	−9.73817	−0.0657265
$29$	290.454	1.85986	0.929929	−	0.367738i	$-0.119868\pi$
$29$	290.454	1.85986	0.929929	+	0.367738i	$0.119868\pi$
$30$	5.28682	0.0321746
$31$	125.559	0.727456	0.363728	−	0.931505i	$-0.381504\pi$
$31$	125.559	0.727456	0.363728	+	0.931505i	$0.381504\pi$
$32$	−183.139	−1.01171
$33$	−33.0000	−0.174078
$34$	−56.9096	−0.287056
$35$	−1.97639	−0.00954488
$36$	−45.8218	−0.212138
$37$	238.644	1.06034	0.530172	−	0.847890i	$-0.322127\pi$
$37$	238.644	1.06034	0.530172	+	0.847890i	$0.322127\pi$
$38$	−20.3328	−0.0868003
$39$	72.6625	0.298341
$40$	−23.0705	−0.0911940
$41$	34.5692	0.131678	0.0658390	−	0.997830i	$-0.479028\pi$
$41$	34.5692	0.131678	0.0658390	+	0.997830i	$0.479028\pi$
$42$	−9.78629	−0.0359538
$43$	−141.886	−0.503197	−0.251598	−	0.967832i	$-0.580956\pi$
$43$	−141.886	−0.503197	−0.251598	+	0.967832i	$0.580956\pi$
$44$	56.0044	0.191886
$45$	−9.29965	−0.0308069
$46$	296.888	0.951605
$47$	355.714	1.10396	0.551982	−	0.833856i	$-0.313872\pi$
$47$	355.714	1.10396	0.551982	+	0.833856i	$0.313872\pi$
$48$	7.95565	0.0239229
$49$	−339.342	−0.989334
$50$	211.365	0.597831
$51$	100.106	0.274854
$52$	−123.316	−0.328862
$53$	168.386	0.436407	0.218204	−	0.975903i	$-0.429980\pi$
$53$	168.386	0.436407	0.218204	+	0.975903i	$0.429980\pi$
$54$	−46.0482	−0.116044
$55$	11.3662	0.0278659
$56$	42.7051	0.101906
$57$	35.7659	0.0831107
$58$	−495.365	−1.12146
$59$	−208.326	−0.459691	−0.229846	−	0.973227i	$-0.573822\pi$
$59$	−208.326	−0.459691	−0.229846	+	0.973227i	$0.573822\pi$
$60$	15.7825	0.0339585
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−214.140	−0.438643
$63$	17.2143	0.0344255
$64$	291.127	0.568608
$65$	−25.0273	−0.0477577
$66$	56.2811	0.104966
$67$	−472.418	−0.861418	−0.430709	−	0.902491i	$-0.641736\pi$
$67$	−472.418	−0.861418	−0.430709	+	0.902491i	$0.641736\pi$
$68$	−169.889	−0.302972
$69$	−522.235	−0.911155
$70$	3.37071	0.00575538
$71$	−280.960	−0.469631	−0.234815	−	0.972040i	$-0.575449\pi$
$71$	−280.960	−0.469631	−0.234815	+	0.972040i	$0.575449\pi$
$72$	200.944	0.328909
$73$	15.3551	0.0246188	0.0123094	−	0.999924i	$-0.496082\pi$
$73$	15.3551	0.0246188	0.0123094	+	0.999924i	$0.496082\pi$
$74$	−407.004	−0.639368
$75$	−371.797	−0.572419
$76$	−60.6984	−0.0916130
$77$	−21.0398	−0.0311390
$78$	−123.925	−0.179894
$79$	1027.42	1.46321	0.731603	−	0.681731i	$-0.238772\pi$
$79$	1027.42	1.46321	0.731603	+	0.681731i	$0.238772\pi$
$80$	−2.74018	−0.00382951
$81$	81.0000	0.111111
$82$	−58.9573	−0.0793993
$83$	267.377	0.353596	0.176798	−	0.984247i	$-0.443426\pi$
$83$	267.377	0.353596	0.176798	+	0.984247i	$0.443426\pi$
$84$	−29.2145	−0.0379472
$85$	−34.4795	−0.0439980
$86$	241.986	0.303418
$87$	871.361	1.07379
$88$	−245.598	−0.297509
$89$	−1493.91	−1.77925	−0.889627	−	0.456687i	$-0.849036\pi$
$89$	−1493.91	−1.77925	−0.889627	+	0.456687i	$0.849036\pi$
$90$	15.8605	0.0185760
$91$	46.3273	0.0533673
$92$	886.286	1.00437
$93$	376.678	0.419997
$94$	−606.667	−0.665669
$95$	−12.3189	−0.0133041
$96$	−549.418	−0.584112
$97$	360.610	0.377468	0.188734	−	0.982028i	$-0.439562\pi$
$97$	360.610	0.377468	0.188734	+	0.982028i	$0.439562\pi$
$98$	578.743	0.596550
$99$	−99.0000	−0.100504
$100$	630.978	0.630978
$101$	499.384	0.491985	0.245993	−	0.969272i	$-0.420886\pi$
$101$	499.384	0.491985	0.245993	+	0.969272i	$0.420886\pi$
$102$	−170.729	−0.165732
$103$	−1001.30	−0.957873	−0.478937	−	0.877850i	$-0.658978\pi$
$103$	−1001.30	−0.957873	−0.478937	+	0.877850i	$0.658978\pi$
$104$	540.781	0.509884
$105$	−5.92917	−0.00551074
$106$	−287.180	−0.263145
$107$	−815.788	−0.737058	−0.368529	−	0.929616i	$-0.620139\pi$
$107$	−815.788	−0.737058	−0.368529	+	0.929616i	$0.620139\pi$
$108$	−137.465	−0.122478
$109$	364.812	0.320575	0.160287	−	0.987070i	$-0.448758\pi$
$109$	364.812	0.320575	0.160287	+	0.987070i	$0.448758\pi$
$110$	−19.3850	−0.0168026
$111$	715.931	0.612190
$112$	5.07227	0.00427933
$113$	−1886.32	−1.57035	−0.785175	−	0.619274i	$-0.787427\pi$
$113$	−1886.32	−1.57035	−0.785175	+	0.619274i	$0.787427\pi$
$114$	−60.9984	−0.0501142
$115$	179.874	0.145855
$116$	−1478.79	−1.18364
$117$	217.988	0.172248
$118$	355.298	0.277185
$119$	63.8241	0.0491660
$120$	−69.2114	−0.0526509
$121$	121.000	0.0909091
$122$	−104.035	−0.0772038
$123$	103.707	0.0760243
$124$	−639.262	−0.462963
$125$	257.220	0.184052
$126$	−29.3589	−0.0207579
$127$	1437.61	1.00446	0.502232	−	0.864733i	$-0.332512\pi$
$127$	1437.61	1.00446	0.502232	+	0.864733i	$0.332512\pi$
$128$	968.601	0.668852
$129$	−425.659	−0.290521
$130$	42.6837	0.0287970
$131$	−1101.66	−0.734753	−0.367376	−	0.930072i	$-0.619744\pi$
$131$	−1101.66	−0.734753	−0.367376	+	0.930072i	$0.619744\pi$
$132$	168.013	0.110785
$133$	22.8032	0.0148668
$134$	805.703	0.519419
$135$	−27.8990	−0.0177864
$136$	745.021	0.469743
$137$	749.159	0.467190	0.233595	−	0.972334i	$-0.424951\pi$
$137$	749.159	0.467190	0.233595	+	0.972334i	$0.424951\pi$
$138$	890.665	0.549409
$139$	1833.02	1.11852	0.559260	−	0.828992i	$-0.311085\pi$
$139$	1833.02	1.11852	0.559260	+	0.828992i	$0.311085\pi$
$140$	10.0624	0.00607449
$141$	1067.14	0.637374
$142$	479.174	0.283179
$143$	−266.429	−0.155804
$144$	23.8670	0.0138119
$145$	−300.124	−0.171889
$146$	−26.1879	−0.0148447
$147$	−1018.02	−0.571192
$148$	−1215.01	−0.674818
$149$	−107.176	−0.0589276	−0.0294638	−	0.999566i	$-0.509380\pi$
$149$	−107.176	−0.0589276	−0.0294638	+	0.999566i	$0.509380\pi$
$150$	634.095	0.345158
$151$	−1729.24	−0.931942	−0.465971	−	0.884800i	$-0.654295\pi$
$151$	−1729.24	−0.931942	−0.465971	+	0.884800i	$0.654295\pi$
$152$	266.183	0.142041
$153$	300.317	0.158687
$154$	35.8831	0.0187762
$155$	−129.740	−0.0672320
$156$	−369.947	−0.189869
$157$	1786.89	0.908340	0.454170	−	0.890915i	$-0.349936\pi$
$157$	1786.89	0.908340	0.454170	+	0.890915i	$0.349936\pi$
$158$	−1752.25	−0.882286
$159$	505.158	0.251960
$160$	189.237	0.0935031
$161$	−332.960	−0.162987
$162$	−138.145	−0.0669979
$163$	−26.4953	−0.0127317	−0.00636587	−	0.999980i	$-0.502026\pi$
$163$	−26.4953	−0.0127317	−0.00636587	+	0.999980i	$0.502026\pi$
$164$	−176.002	−0.0838016
$165$	34.0987	0.0160884
$166$	−456.009	−0.213212
$167$	3871.11	1.79374	0.896872	−	0.442289i	$-0.145834\pi$
$167$	3871.11	1.79374	0.896872	+	0.442289i	$0.145834\pi$
$168$	128.115	0.0588352
$169$	−1610.35	−0.732977
$170$	58.8044	0.0265300
$171$	107.298	0.0479840
$172$	722.387	0.320241
$173$	2952.88	1.29771	0.648853	−	0.760914i	$-0.275249\pi$
$173$	2952.88	1.29771	0.648853	+	0.760914i	$0.275249\pi$
$174$	−1486.10	−0.647475
$175$	−237.046	−0.102394
$176$	−29.1707	−0.0124933
$177$	−624.979	−0.265403
$178$	2547.84	1.07286
$179$	3981.96	1.66271	0.831356	−	0.555740i	$-0.187565\pi$
$179$	3981.96	1.66271	0.831356	+	0.555740i	$0.187565\pi$
$180$	47.3474	0.0196059
$181$	−3718.73	−1.52713	−0.763567	−	0.645729i	$-0.776554\pi$
$181$	−3718.73	−1.52713	−0.763567	+	0.645729i	$0.776554\pi$
$182$	−79.0108	−0.0321795
$183$	183.000	0.0739221
$184$	−3886.66	−1.55722
$185$	−246.589	−0.0979978
$186$	−642.421	−0.253250
$187$	−367.054	−0.143538
$188$	−1811.05	−0.702577
$189$	51.6430	0.0198756
$190$	21.0098	0.00802215
$191$	3338.69	1.26481	0.632407	−	0.774636i	$-0.282067\pi$
$191$	3338.69	1.26481	0.632407	+	0.774636i	$0.282067\pi$
$192$	873.381	0.328286
$193$	3673.51	1.37008	0.685038	−	0.728507i	$-0.259785\pi$
$193$	3673.51	1.37008	0.685038	+	0.728507i	$0.259785\pi$
$194$	−615.017	−0.227606
$195$	−75.0818	−0.0275729
$196$	1727.69	0.629626
$197$	−1126.60	−0.407447	−0.203724	−	0.979028i	$-0.565304\pi$
$197$	−1126.60	−0.407447	−0.203724	+	0.979028i	$0.565304\pi$
$198$	168.843	0.0606019
$199$	3476.09	1.23826	0.619129	−	0.785290i	$-0.287486\pi$
$199$	3476.09	1.23826	0.619129	+	0.785290i	$0.287486\pi$
$200$	−2767.05	−0.978299
$201$	−1417.25	−0.497340
$202$	−851.693	−0.296658
$203$	555.552	0.192079
$204$	−509.668	−0.174921
$205$	−35.7201	−0.0121698
$206$	1707.70	0.577580
$207$	−1566.70	−0.526055
$208$	64.2309	0.0214116
$209$	−131.142	−0.0434032
$210$	10.1121	0.00332287
$211$	102.414	0.0334146	0.0167073	−	0.999860i	$-0.494682\pi$
$211$	102.414	0.0334146	0.0167073	+	0.999860i	$0.494682\pi$
$212$	−857.304	−0.277735
$213$	−842.879	−0.271141
$214$	1391.32	0.444432
$215$	146.610	0.0465058
$216$	602.831	0.189896
$217$	240.158	0.0751291
$218$	−622.183	−0.193301
$219$	46.0652	0.0142137
$220$	−57.8690	−0.0177342
$221$	808.214	0.246002
$222$	−1221.01	−0.369139
$223$	3688.64	1.10767	0.553833	−	0.832628i	$-0.313165\pi$
$223$	3688.64	1.10767	0.553833	+	0.832628i	$0.313165\pi$
$224$	−350.292	−0.104486
$225$	−1115.39	−0.330486
$226$	3217.09	0.946892
$227$	3449.94	1.00873	0.504363	−	0.863492i	$-0.331727\pi$
$227$	3449.94	1.00873	0.504363	+	0.863492i	$0.331727\pi$
$228$	−182.095	−0.0528928
$229$	−1068.07	−0.308211	−0.154106	−	0.988054i	$-0.549250\pi$
$229$	−1068.07	−0.308211	−0.154106	+	0.988054i	$0.549250\pi$
$230$	−306.773	−0.0879480
$231$	−63.1193	−0.0179781
$232$	6484.98	1.83517
$233$	−822.732	−0.231326	−0.115663	−	0.993289i	$-0.536899\pi$
$233$	−822.732	−0.231326	−0.115663	+	0.993289i	$0.536899\pi$
$234$	−371.775	−0.103862
$235$	−367.558	−0.102029
$236$	1060.65	0.292554
$237$	3082.25	0.844783
$238$	−108.851	−0.0296462
$239$	3744.31	1.01339	0.506693	−	0.862127i	$-0.330868\pi$
$239$	3744.31	1.01339	0.506693	+	0.862127i	$0.330868\pi$
$240$	−8.22053	−0.00221097
$241$	1436.65	0.383996	0.191998	−	0.981395i	$-0.438503\pi$
$241$	1436.65	0.383996	0.191998	+	0.981395i	$0.438503\pi$
$242$	−206.364	−0.0548165
$243$	243.000	0.0641500
$244$	−310.570	−0.0814844
$245$	350.640	0.0914349
$246$	−176.872	−0.0458412
$247$	288.760	0.0743861
$248$	2803.38	0.717801
$249$	802.132	0.204149
$250$	−438.687	−0.110980
$251$	−776.198	−0.195192	−0.0975960	−	0.995226i	$-0.531115\pi$
$251$	−776.198	−0.195192	−0.0975960	+	0.995226i	$0.531115\pi$
$252$	−87.6436	−0.0219088
$253$	1914.86	0.475835
$254$	−2451.82	−0.605674
$255$	−103.439	−0.0254022
$256$	−3980.96	−0.971913
$257$	2489.39	0.604217	0.302108	−	0.953274i	$-0.402310\pi$
$257$	2489.39	0.604217	0.302108	+	0.953274i	$0.402310\pi$
$258$	725.957	0.175179
$259$	456.455	0.109509
$260$	127.422	0.0303937
$261$	2614.08	0.619953
$262$	1878.87	0.443042
$263$	4630.00	1.08554	0.542772	−	0.839880i	$-0.317375\pi$
$263$	4630.00	1.08554	0.542772	+	0.839880i	$0.317375\pi$
$264$	−736.794	−0.171767
$265$	−173.992	−0.0403331
$266$	−38.8906	−0.00896443
$267$	−4481.72	−1.02725
$268$	2405.22	0.548218
$269$	−4662.60	−1.05682	−0.528409	−	0.848990i	$-0.677211\pi$
$269$	−4662.60	−1.05682	−0.528409	+	0.848990i	$0.677211\pi$
$270$	47.5814	0.0107249
$271$	5966.32	1.33737	0.668686	−	0.743545i	$-0.266857\pi$
$271$	5966.32	1.33737	0.668686	+	0.743545i	$0.266857\pi$
$272$	88.4894	0.0197260
$273$	138.982	0.0308116
$274$	−1277.68	−0.281707
$275$	1363.26	0.298936
$276$	2658.86	0.579871
$277$	1572.63	0.341119	0.170559	−	0.985347i	$-0.445443\pi$
$277$	1572.63	0.341119	0.170559	+	0.985347i	$0.445443\pi$
$278$	−3126.19	−0.674447
$279$	1130.04	0.242485
$280$	−44.1270	−0.00941819
$281$	2699.97	0.573191	0.286596	−	0.958052i	$-0.407476\pi$
$281$	2699.97	0.573191	0.286596	+	0.958052i	$0.407476\pi$
$282$	−1820.00	−0.384324
$283$	−6180.13	−1.29813	−0.649065	−	0.760733i	$-0.724840\pi$
$283$	−6180.13	−1.29813	−0.649065	+	0.760733i	$0.724840\pi$
$284$	1430.45	0.298879
$285$	−36.9567	−0.00768115
$286$	454.392	0.0939468
$287$	66.1206	0.0135992
$288$	−1648.25	−0.337237
$289$	−3799.54	−0.773365
$290$	511.859	0.103646
$291$	1081.83	0.217931
$292$	−78.1774	−0.0156678
$293$	4777.93	0.952661	0.476331	−	0.879266i	$-0.341967\pi$
$293$	4777.93	0.952661	0.476331	+	0.879266i	$0.341967\pi$
$294$	1736.23	0.344418
$295$	215.262	0.0424850
$296$	5328.21	1.04627
$297$	−297.000	−0.0580259
$298$	182.788	0.0355322
$299$	−4216.32	−0.815506
$300$	1892.93	0.364295
$301$	−271.387	−0.0519684
$302$	2949.19	0.561944
$303$	1498.15	0.284048
$304$	31.6157	0.00596475
$305$	−63.0310	−0.0118333
$306$	−512.187	−0.0956855
$307$	−1824.73	−0.339227	−0.169614	−	0.985511i	$-0.554252\pi$
$307$	−1824.73	−0.339227	−0.169614	+	0.985511i	$0.554252\pi$
$308$	107.120	0.0198173
$309$	−3003.90	−0.553028
$310$	221.270	0.0405397
$311$	9187.69	1.67520	0.837599	−	0.546286i	$-0.183959\pi$
$311$	9187.69	1.67520	0.837599	+	0.546286i	$0.183959\pi$
$312$	1622.34	0.294382
$313$	2875.55	0.519284	0.259642	−	0.965705i	$-0.416396\pi$
$313$	2875.55	0.519284	0.259642	+	0.965705i	$0.416396\pi$
$314$	−3047.52	−0.547712
$315$	−17.7875	−0.00318163
$316$	−5230.89	−0.931205
$317$	−7299.89	−1.29338	−0.646692	−	0.762751i	$-0.723848\pi$
$317$	−7299.89	−1.29338	−0.646692	+	0.762751i	$0.723848\pi$
$318$	−861.541	−0.151927
$319$	−3194.99	−0.560768
$320$	−300.820	−0.0525511
$321$	−2447.37	−0.425541
$322$	567.860	0.0982783
$323$	397.818	0.0685301
$324$	−412.396	−0.0707126
$325$	−3001.75	−0.512329
$326$	45.1875	0.00767700
$327$	1094.44	0.185084
$328$	771.828	0.129930
$329$	680.377	0.114013
$330$	−58.1550	−0.00970099
$331$	−4647.94	−0.771824	−0.385912	−	0.922536i	$-0.626113\pi$
$331$	−4647.94	−0.771824	−0.385912	+	0.922536i	$0.626113\pi$
$332$	−1361.30	−0.225033
$333$	2147.79	0.353448
$334$	−6602.13	−1.08159
$335$	488.147	0.0796128
$336$	15.2168	0.00247067
$337$	−7319.36	−1.18312	−0.591559	−	0.806261i	$-0.701487\pi$
$337$	−7319.36	−1.18312	−0.591559	+	0.806261i	$0.701487\pi$
$338$	2746.43	0.441971
$339$	−5658.95	−0.906642
$340$	175.546	0.0280009
$341$	−1381.15	−0.219336
$342$	−182.995	−0.0289334
$343$	−1305.12	−0.205451
$344$	−3167.91	−0.496518
$345$	539.622	0.0842095
$346$	−5036.10	−0.782492
$347$	4616.51	0.714200	0.357100	−	0.934066i	$-0.383766\pi$
$347$	4616.51	0.714200	0.357100	+	0.934066i	$0.383766\pi$
$348$	−4436.37	−0.683374
$349$	5222.57	0.801025	0.400513	−	0.916291i	$-0.368832\pi$
$349$	5222.57	0.801025	0.400513	+	0.916291i	$0.368832\pi$
$350$	404.279	0.0617418
$351$	653.963	0.0994472
$352$	2014.53	0.305043
$353$	−54.4797	−0.00821434	−0.00410717	−	0.999992i	$-0.501307\pi$
$353$	−54.4797	−0.00821434	−0.00410717	+	0.999992i	$0.501307\pi$
$354$	1065.89	0.160033
$355$	290.314	0.0434036
$356$	7605.93	1.13234
$357$	191.472	0.0283860
$358$	−6791.18	−1.00258
$359$	1178.99	0.173328	0.0866640	−	0.996238i	$-0.472379\pi$
$359$	1178.99	0.173328	0.0866640	+	0.996238i	$0.472379\pi$
$360$	−207.634	−0.0303980
$361$	−6716.87	−0.979278
$362$	6342.25	0.920833
$363$	363.000	0.0524864
$364$	−235.867	−0.0339637
$365$	−15.8663	−0.00227529
$366$	−312.104	−0.0445737
$367$	−2700.63	−0.384119	−0.192059	−	0.981383i	$-0.561517\pi$
$367$	−2700.63	−0.384119	−0.192059	+	0.981383i	$0.561517\pi$
$368$	−461.635	−0.0653924
$369$	311.122	0.0438926
$370$	420.555	0.0590908
$371$	322.073	0.0450706
$372$	−1917.79	−0.267292
$373$	7652.81	1.06233	0.531163	−	0.847270i	$-0.321755\pi$
$373$	7652.81	1.06233	0.531163	+	0.847270i	$0.321755\pi$
$374$	626.006	0.0865508
$375$	771.661	0.106262
$376$	7942.06	1.08931
$377$	7035.03	0.961068
$378$	−88.0766	−0.0119846
$379$	2294.01	0.310912	0.155456	−	0.987843i	$-0.450315\pi$
$379$	2294.01	0.310912	0.155456	+	0.987843i	$0.450315\pi$
$380$	62.7194	0.00846694
$381$	4312.82	0.579928
$382$	−5694.11	−0.762659
$383$	−1595.66	−0.212883	−0.106442	−	0.994319i	$-0.533946\pi$
$383$	−1595.66	−0.212883	−0.106442	+	0.994319i	$0.533946\pi$
$384$	2905.80	0.386162
$385$	21.7403	0.00287789
$386$	−6265.12	−0.826131
$387$	−1276.98	−0.167732
$388$	−1835.98	−0.240226
$389$	8650.33	1.12748	0.563739	−	0.825953i	$-0.309362\pi$
$389$	8650.33	1.12748	0.563739	+	0.825953i	$0.309362\pi$
$390$	128.051	0.0166260
$391$	−5808.73	−0.751305
$392$	−7576.51	−0.976202
$393$	−3304.98	−0.424210
$394$	1921.41	0.245683
$395$	−1061.62	−0.135231
$396$	504.040	0.0639620
$397$	12149.4	1.53592	0.767961	−	0.640496i	$-0.221271\pi$
$397$	12149.4	1.53592	0.767961	+	0.640496i	$0.221271\pi$
$398$	−5928.43	−0.746646
$399$	68.4097	0.00858337
$400$	−328.654	−0.0410818
$401$	7412.31	0.923075	0.461538	−	0.887121i	$-0.347298\pi$
$401$	7412.31	0.923075	0.461538	+	0.887121i	$0.347298\pi$
$402$	2417.11	0.299887
$403$	3041.16	0.375908
$404$	−2542.52	−0.313106
$405$	−83.6969	−0.0102690
$406$	−947.488	−0.115820
$407$	−2625.08	−0.319706
$408$	2235.06	0.271206
$409$	−8944.91	−1.08141	−0.540706	−	0.841212i	$-0.681843\pi$
$409$	−8944.91	−1.08141	−0.540706	+	0.841212i	$0.681843\pi$
$410$	60.9203	0.00733814
$411$	2247.48	0.269732
$412$	5097.92	0.609603
$413$	−398.467	−0.0474752
$414$	2672.00	0.317202
$415$	−276.280	−0.0326796
$416$	−4435.79	−0.522795
$417$	5499.05	0.645778
$418$	223.661	0.0261713
$419$	16299.9	1.90049	0.950244	−	0.311506i	$-0.100833\pi$
$419$	16299.9	1.90049	0.950244	+	0.311506i	$0.100833\pi$
$420$	30.1872	0.00350711
$421$	6121.78	0.708687	0.354344	−	0.935115i	$-0.384704\pi$
$421$	6121.78	0.708687	0.354344	+	0.935115i	$0.384704\pi$
$422$	−174.666	−0.0201484
$423$	3201.43	0.367988
$424$	3759.57	0.430615
$425$	−4135.44	−0.471996
$426$	1437.52	0.163493
$427$	116.675	0.0132232
$428$	4153.43	0.469074
$429$	−799.288	−0.0899533
$430$	−250.042	−0.0280421
$431$	4052.67	0.452924	0.226462	−	0.974020i	$-0.427284\pi$
$431$	4052.67	0.452924	0.226462	+	0.974020i	$0.427284\pi$
$432$	71.6009	0.00797430
$433$	9215.07	1.02274	0.511372	−	0.859360i	$-0.329138\pi$
$433$	9215.07	1.02274	0.511372	+	0.859360i	$0.329138\pi$
$434$	−409.587	−0.0453014
$435$	−900.373	−0.0992404
$436$	−1857.37	−0.204018
$437$	−2075.36	−0.227180
$438$	−78.5637	−0.00857059
$439$	−7504.44	−0.815871	−0.407935	−	0.913011i	$-0.633751\pi$
$439$	−7504.44	−0.815871	−0.407935	+	0.913011i	$0.633751\pi$
$440$	253.775	0.0274960
$441$	−3054.07	−0.329778
$442$	−1378.40	−0.148334
$443$	7627.17	0.818009	0.409004	−	0.912532i	$-0.365876\pi$
$443$	7627.17	0.818009	0.409004	+	0.912532i	$0.365876\pi$
$444$	−3645.02	−0.389606
$445$	1543.65	0.164440
$446$	−6290.93	−0.667902
$447$	−321.528	−0.0340219
$448$	556.840	0.0587237
$449$	3364.79	0.353662	0.176831	−	0.984241i	$-0.443415\pi$
$449$	3364.79	0.353662	0.176831	+	0.984241i	$0.443415\pi$
$450$	1902.29	0.199277
$451$	−380.261	−0.0397024
$452$	9603.81	0.999392
$453$	−5187.71	−0.538057
$454$	−5883.84	−0.608243
$455$	−47.8698	−0.00493224
$456$	798.548	0.0820076
$457$	−17926.9	−1.83498	−0.917489	−	0.397762i	$-0.869787\pi$
$457$	−17926.9	−1.83498	−0.917489	+	0.397762i	$0.869787\pi$
$458$	1821.59	0.185846
$459$	900.950	0.0916182
$460$	−915.795	−0.0928242
$461$	8894.15	0.898572	0.449286	−	0.893388i	$-0.351678\pi$
$461$	8894.15	0.898572	0.449286	+	0.893388i	$0.351678\pi$
$462$	107.649	0.0108405
$463$	10209.9	1.02483	0.512415	−	0.858738i	$-0.328751\pi$
$463$	10209.9	1.02483	0.512415	+	0.858738i	$0.328751\pi$
$464$	770.249	0.0770645
$465$	−389.220	−0.0388164
$466$	1403.16	0.139485
$467$	4194.12	0.415591	0.207795	−	0.978172i	$-0.433371\pi$
$467$	4194.12	0.415591	0.207795	+	0.978172i	$0.433371\pi$
$468$	−1109.84	−0.109621
$469$	−903.596	−0.0889641
$470$	626.866	0.0615216
$471$	5360.67	0.524430
$472$	−4651.32	−0.453589
$473$	1560.75	0.151720
$474$	−5256.74	−0.509388
$475$	−1477.52	−0.142722
$476$	−324.948	−0.0312899
$477$	1515.47	0.145469
$478$	−6385.87	−0.611052
$479$	4672.27	0.445682	0.222841	−	0.974855i	$-0.428467\pi$
$479$	4672.27	0.445682	0.222841	+	0.974855i	$0.428467\pi$
$480$	567.711	0.0539840
$481$	5780.15	0.547925
$482$	−2450.20	−0.231542
$483$	−998.881	−0.0941008
$484$	−616.048	−0.0578558
$485$	−372.617	−0.0348859
$486$	−414.434	−0.0386813
$487$	12603.1	1.17270	0.586348	−	0.810059i	$-0.300565\pi$
$487$	12603.1	1.17270	0.586348	+	0.810059i	$0.300565\pi$
$488$	1361.95	0.126337
$489$	−79.4859	−0.00735067
$490$	−598.012	−0.0551336
$491$	17948.7	1.64972	0.824861	−	0.565336i	$-0.191253\pi$
$491$	17948.7	1.64972	0.824861	+	0.565336i	$0.191253\pi$
$492$	−528.007	−0.0483829
$493$	9692.01	0.885408
$494$	−492.477	−0.0448534
$495$	102.296	0.00928863
$496$	332.969	0.0301426
$497$	−537.393	−0.0485018
$498$	−1368.03	−0.123098
$499$	10074.3	0.903781	0.451891	−	0.892073i	$-0.350750\pi$
$499$	10074.3	0.903781	0.451891	+	0.892073i	$0.350750\pi$
$500$	−1309.59	−0.117133
$501$	11613.3	1.03562
$502$	1323.80	0.117697
$503$	14670.1	1.30042	0.650208	−	0.759756i	$-0.274682\pi$
$503$	14670.1	1.30042	0.650208	+	0.759756i	$0.274682\pi$
$504$	384.346	0.0339685
$505$	−516.010	−0.0454696
$506$	−3265.77	−0.286920
$507$	−4831.05	−0.423185
$508$	−7319.30	−0.639255
$509$	−17995.1	−1.56703	−0.783517	−	0.621371i	$-0.786576\pi$
$509$	−17995.1	−1.56703	−0.783517	+	0.621371i	$0.786576\pi$
$510$	176.413	0.0153171
$511$	29.3697	0.00254255
$512$	−959.335	−0.0828067
$513$	321.893	0.0277036
$514$	−4245.62	−0.364332
$515$	1034.64	0.0885273
$516$	2167.16	0.184891
$517$	−3912.86	−0.332857
$518$	−778.478	−0.0660316
$519$	8858.63	0.749231
$520$	−558.786	−0.0471238
$521$	2663.06	0.223936	0.111968	−	0.993712i	$-0.464285\pi$
$521$	2663.06	0.223936	0.111968	+	0.993712i	$0.464285\pi$
$522$	−4458.29	−0.373820
$523$	−13224.5	−1.10568	−0.552838	−	0.833289i	$-0.686455\pi$
$523$	−13224.5	−1.10568	−0.552838	+	0.833289i	$0.686455\pi$
$524$	5608.90	0.467606
$525$	−711.138	−0.0591173
$526$	−7896.42	−0.654563
$527$	4189.73	0.346314
$528$	−87.5122	−0.00721303
$529$	18136.2	1.49061
$530$	296.742	0.0243201
$531$	−1874.94	−0.153230
$532$	−116.098	−0.00946146
$533$	837.294	0.0680436
$534$	7643.52	0.619415
$535$	842.950	0.0681195
$536$	−10547.7	−0.849984
$537$	11945.9	0.959967
$538$	7952.01	0.637241
$539$	3732.76	0.298295
$540$	142.042	0.0113195
$541$	9350.73	0.743104	0.371552	−	0.928412i	$-0.378826\pi$
$541$	9350.73	0.743104	0.371552	+	0.928412i	$0.378826\pi$
$542$	−10175.5	−0.806411
$543$	−11156.2	−0.881691
$544$	−6111.09	−0.481637
$545$	−376.959	−0.0296278
$546$	−237.032	−0.0185788
$547$	−12411.5	−0.970158	−0.485079	−	0.874470i	$-0.661209\pi$
$547$	−12411.5	−0.970158	−0.485079	+	0.874470i	$0.661209\pi$
$548$	−3814.20	−0.297326
$549$	549.000	0.0426790
$550$	−2325.02	−0.180253
$551$	3462.78	0.267730
$552$	−11660.0	−0.899061
$553$	1965.14	0.151115
$554$	−2682.10	−0.205688
$555$	−739.767	−0.0565791
$556$	−9332.45	−0.711842
$557$	2461.12	0.187219	0.0936097	−	0.995609i	$-0.470159\pi$
$557$	2461.12	0.187219	0.0936097	+	0.995609i	$0.470159\pi$
$558$	−1927.26	−0.146214
$559$	−3436.61	−0.260023
$560$	−5.24115	−0.000395498 0
$561$	−1101.16	−0.0828717
$562$	−4604.77	−0.345624
$563$	6694.90	0.501166	0.250583	−	0.968095i	$-0.419378\pi$
$563$	6694.90	0.501166	0.250583	+	0.968095i	$0.419378\pi$
$564$	−5433.15	−0.405633
$565$	1949.12	0.145133
$566$	10540.1	0.782748
$567$	154.929	0.0114752
$568$	−6273.01	−0.463397
$569$	−1582.49	−0.116593	−0.0582965	−	0.998299i	$-0.518567\pi$
$569$	−1582.49	−0.116593	−0.0582965	+	0.998299i	$0.518567\pi$
$570$	63.0293	0.00463159
$571$	7613.72	0.558011	0.279005	−	0.960290i	$-0.409995\pi$
$571$	7613.72	0.558011	0.279005	+	0.960290i	$0.409995\pi$
$572$	1356.47	0.0991556
$573$	10016.1	0.730241
$574$	−112.768	−0.00820008
$575$	21573.9	1.56469
$576$	2620.14	0.189536
$577$	−10304.8	−0.743490	−0.371745	−	0.928335i	$-0.621240\pi$
$577$	−10304.8	−0.743490	−0.371745	+	0.928335i	$0.621240\pi$
$578$	6480.08	0.466325
$579$	11020.5	0.791014
$580$	1528.03	0.109393
$581$	511.414	0.0365181
$582$	−1845.05	−0.131409
$583$	−1852.24	−0.131582
$584$	342.834	0.0242921
$585$	−225.245	−0.0159192
$586$	−8148.71	−0.574437
$587$	−20468.8	−1.43924	−0.719622	−	0.694366i	$-0.755685\pi$
$587$	−20468.8	−1.43924	−0.719622	+	0.694366i	$0.755685\pi$
$588$	5183.08	0.363514
$589$	1496.92	0.104719
$590$	−367.128	−0.0256176
$591$	−3379.81	−0.235240
$592$	632.855	0.0439361
$593$	28516.6	1.97476	0.987382	−	0.158357i	$-0.0506197\pi$
$593$	28516.6	1.97476	0.987382	+	0.158357i	$0.0506197\pi$
$594$	506.530	0.0349885
$595$	−65.9492	−0.00454395
$596$	545.667	0.0375023
$597$	10428.3	0.714908
$598$	7190.89	0.491735
$599$	19695.9	1.34349	0.671747	−	0.740781i	$-0.265544\pi$
$599$	19695.9	1.34349	0.671747	+	0.740781i	$0.265544\pi$
$600$	−8301.14	−0.564821
$601$	−2927.84	−0.198718	−0.0993588	−	0.995052i	$-0.531679\pi$
$601$	−2927.84	−0.198718	−0.0993588	+	0.995052i	$0.531679\pi$
$602$	462.847	0.0313360
$603$	−4251.76	−0.287139
$604$	8804.07	0.593100
$605$	−125.029	−0.00840188
$606$	−2555.08	−0.171276
$607$	−5395.47	−0.360783	−0.180392	−	0.983595i	$-0.557737\pi$
$607$	−5395.47	−0.360783	−0.180392	+	0.983595i	$0.557737\pi$
$608$	−2183.38	−0.145638
$609$	1666.66	0.110897
$610$	107.499	0.00713523
$611$	8615.70	0.570465
$612$	−1529.00	−0.100991
$613$	−3769.08	−0.248339	−0.124169	−	0.992261i	$-0.539627\pi$
$613$	−3769.08	−0.248339	−0.124169	+	0.992261i	$0.539627\pi$
$614$	3112.05	0.204548
$615$	−107.160	−0.00702622
$616$	−469.756	−0.0307257
$617$	16632.6	1.08526	0.542628	−	0.839973i	$-0.317429\pi$
$617$	16632.6	1.08526	0.542628	+	0.839973i	$0.317429\pi$
$618$	5123.11	0.333466
$619$	13334.3	0.865836	0.432918	−	0.901433i	$-0.357484\pi$
$619$	13334.3	0.865836	0.432918	+	0.901433i	$0.357484\pi$
$620$	660.546	0.0427874
$621$	−4700.11	−0.303718
$622$	−15669.5	−1.01011
$623$	−2857.40	−0.183755
$624$	192.693	0.0123620
$625$	15225.8	0.974448
$626$	−4904.22	−0.313118
$627$	−393.425	−0.0250588
$628$	−9097.61	−0.578080
$629$	7963.18	0.504790
$630$	30.3364	0.00191846
$631$	−16270.4	−1.02649	−0.513246	−	0.858242i	$-0.671557\pi$
$631$	−16270.4	−1.02649	−0.513246	+	0.858242i	$0.671557\pi$
$632$	22939.2	1.44379
$633$	307.242	0.0192919
$634$	12449.9	0.779886
$635$	−1485.47	−0.0928334
$636$	−2571.91	−0.160351
$637$	−8219.14	−0.511231
$638$	5449.02	0.338133
$639$	−2528.64	−0.156544
$640$	−1000.85	−0.0618158
$641$	7926.70	0.488434	0.244217	−	0.969721i	$-0.421469\pi$
$641$	7926.70	0.488434	0.244217	+	0.969721i	$0.421469\pi$
$642$	4173.95	0.256593
$643$	−7198.55	−0.441498	−0.220749	−	0.975331i	$-0.570850\pi$
$643$	−7198.55	−0.441498	−0.220749	+	0.975331i	$0.570850\pi$
$644$	1695.20	0.103727
$645$	439.831	0.0268501
$646$	−678.475	−0.0413223
$647$	13843.2	0.841166	0.420583	−	0.907254i	$-0.361826\pi$
$647$	13843.2	0.841166	0.420583	+	0.907254i	$0.361826\pi$
$648$	1808.49	0.109636
$649$	2291.59	0.138602
$650$	5119.44	0.308925
$651$	720.475	0.0433758
$652$	134.896	0.00810265
$653$	−20532.8	−1.23049	−0.615246	−	0.788335i	$-0.710944\pi$
$653$	−20532.8	−1.23049	−0.615246	+	0.788335i	$0.710944\pi$
$654$	−1866.55	−0.111602
$655$	1138.34	0.0679063
$656$	91.6734	0.00545617
$657$	138.196	0.00820628
$658$	−1160.38	−0.0687479
$659$	−6948.62	−0.410744	−0.205372	−	0.978684i	$-0.565840\pi$
$659$	−6948.62	−0.410744	−0.205372	+	0.978684i	$0.565840\pi$
$660$	−173.607	−0.0102389
$661$	−13179.5	−0.775528	−0.387764	−	0.921759i	$-0.626753\pi$
$661$	−13179.5	−0.775528	−0.387764	+	0.921759i	$0.626753\pi$
$662$	7927.00	0.465395
$663$	2424.64	0.142029
$664$	5969.76	0.348903
$665$	−23.5624	−0.00137400
$666$	−3663.03	−0.213123
$667$	−50561.7	−2.93517
$668$	−19709.0	−1.14156
$669$	11065.9	0.639511
$670$	−832.529	−0.0480051
$671$	−671.000	−0.0386046
$672$	−1050.88	−0.0603250
$673$	16137.9	0.924322	0.462161	−	0.886796i	$-0.347074\pi$
$673$	16137.9	0.924322	0.462161	+	0.886796i	$0.347074\pi$
$674$	12483.1	0.713399
$675$	−3346.17	−0.190806
$676$	8198.79	0.466477
$677$	−20376.6	−1.15677	−0.578387	−	0.815763i	$-0.696318\pi$
$677$	−20376.6	−1.15677	−0.578387	+	0.815763i	$0.696318\pi$
$678$	9651.27	0.546688
$679$	689.741	0.0389836
$680$	−769.827	−0.0434140
$681$	10349.8	0.582388
$682$	2355.54	0.132256
$683$	−21989.0	−1.23190	−0.615950	−	0.787785i	$-0.711228\pi$
$683$	−21989.0	−1.23190	−0.615950	+	0.787785i	$0.711228\pi$
$684$	−546.286	−0.0305377
$685$	−774.102	−0.0431780
$686$	2225.86	0.123883
$687$	−3204.22	−0.177946
$688$	−376.266	−0.0208503
$689$	4078.45	0.225510
$690$	−920.320	−0.0507768
$691$	−25988.7	−1.43076	−0.715382	−	0.698734i	$-0.753747\pi$
$691$	−25988.7	−1.43076	−0.715382	+	0.698734i	$0.753747\pi$
$692$	−15034.0	−0.825877
$693$	−189.358	−0.0103797
$694$	−7873.41	−0.430649
$695$	−1894.05	−0.103374
$696$	19454.9	1.05954
$697$	1153.52	0.0626869
$698$	−8907.04	−0.483003
$699$	−2468.20	−0.133556
$700$	1206.87	0.0651651
$701$	−3288.44	−0.177179	−0.0885897	−	0.996068i	$-0.528236\pi$
$701$	−3288.44	−0.177179	−0.0885897	+	0.996068i	$0.528236\pi$
$702$	−1115.33	−0.0599648
$703$	2845.10	0.152639
$704$	−3202.40	−0.171442
$705$	−1102.67	−0.0589065
$706$	92.9145	0.00495309
$707$	955.174	0.0508105
$708$	3181.96	0.168906
$709$	−31307.5	−1.65836	−0.829181	−	0.558981i	$-0.811193\pi$
$709$	−31307.5	−1.65836	−0.829181	+	0.558981i	$0.811193\pi$
$710$	−495.128	−0.0261716
$711$	9246.74	0.487736
$712$	−33354.6	−1.75564
$713$	−21857.2	−1.14805
$714$	−326.554	−0.0171162
$715$	275.300	0.0143995
$716$	−20273.4	−1.05817
$717$	11232.9	0.585078
$718$	−2010.76	−0.104514
$719$	−28708.7	−1.48909	−0.744544	−	0.667573i	$-0.767333\pi$
$719$	−28708.7	−1.48909	−0.744544	+	0.667573i	$0.767333\pi$
$720$	−24.6616	−0.00127650
$721$	−1915.19	−0.0989257
$722$	11455.5	0.590486
$723$	4309.96	0.221700
$724$	18933.2	0.971888
$725$	−35996.6	−1.84397
$726$	−619.092	−0.0316483
$727$	−13770.7	−0.702511	−0.351255	−	0.936280i	$-0.614245\pi$
$727$	−13770.7	−0.702511	−0.351255	+	0.936280i	$0.614245\pi$
$728$	1034.35	0.0526590
$729$	729.000	0.0370370
$730$	27.0598	0.00137196
$731$	−4734.54	−0.239553
$732$	−931.709	−0.0470450
$733$	−13713.7	−0.691034	−0.345517	−	0.938412i	$-0.612296\pi$
$733$	−13713.7	−0.691034	−0.345517	+	0.938412i	$0.612296\pi$
$734$	4605.89	0.231617
$735$	1051.92	0.0527900
$736$	31880.6	1.59665
$737$	5196.59	0.259727
$738$	−530.616	−0.0264664
$739$	13503.7	0.672180	0.336090	−	0.941830i	$-0.390895\pi$
$739$	13503.7	0.672180	0.336090	+	0.941830i	$0.390895\pi$
$740$	1255.46	0.0623671
$741$	866.281	0.0429468
$742$	−549.291	−0.0271767
$743$	11108.2	0.548479	0.274240	−	0.961661i	$-0.411574\pi$
$743$	11108.2	0.548479	0.274240	+	0.961661i	$0.411574\pi$
$744$	8410.13	0.414422
$745$	110.745	0.00544613
$746$	−13051.8	−0.640562
$747$	2406.40	0.117865
$748$	1868.78	0.0913496
$749$	−1560.36	−0.0761207
$750$	−1316.06	−0.0640743
$751$	−4741.52	−0.230387	−0.115193	−	0.993343i	$-0.536749\pi$
$751$	−4741.52	−0.230387	−0.115193	+	0.993343i	$0.536749\pi$
$752$	943.313	0.0457435
$753$	−2328.60	−0.112694
$754$	−11998.2	−0.579506
$755$	1786.81	0.0861307
$756$	−262.931	−0.0126491
$757$	−38382.5	−1.84285	−0.921424	−	0.388559i	$-0.872973\pi$
$757$	−38382.5	−1.84285	−0.921424	+	0.388559i	$0.872973\pi$
$758$	−3912.41	−0.187474
$759$	5744.58	0.274723
$760$	−275.045	−0.0131276
$761$	−31965.9	−1.52268	−0.761342	−	0.648351i	$-0.775459\pi$
$761$	−31965.9	−1.52268	−0.761342	+	0.648351i	$0.775459\pi$
$762$	−7355.47	−0.349686
$763$	697.778	0.0331078
$764$	−16998.3	−0.804945
$765$	−310.316	−0.0146660
$766$	2721.38	0.128365
$767$	−5045.84	−0.237542
$768$	−11942.9	−0.561134
$769$	9157.24	0.429413	0.214706	−	0.976679i	$-0.431121\pi$
$769$	9157.24	0.429413	0.214706	+	0.976679i	$0.431121\pi$
$770$	−37.0778	−0.00173531
$771$	7468.16	0.348845
$772$	−18703.0	−0.871935
$773$	−10953.4	−0.509659	−0.254829	−	0.966986i	$-0.582019\pi$
$773$	−10953.4	−0.509659	−0.254829	+	0.966986i	$0.582019\pi$
$774$	2177.87	0.101139
$775$	−15560.9	−0.721243
$776$	8051.37	0.372458
$777$	1369.36	0.0632248
$778$	−14753.0	−0.679848
$779$	412.132	0.0189553
$780$	382.265	0.0175478
$781$	3090.56	0.141599
$782$	9906.73	0.453023
$783$	7842.25	0.357930
$784$	−899.894	−0.0409937
$785$	−1846.38	−0.0839494
$786$	5636.61	0.255790
$787$	−7711.06	−0.349262	−0.174631	−	0.984634i	$-0.555873\pi$
$787$	−7711.06	−0.349262	−0.174631	+	0.984634i	$0.555873\pi$
$788$	5735.88	0.259305
$789$	13890.0	0.626739
$790$	1810.59	0.0815415
$791$	−3607.97	−0.162180
$792$	−2210.38	−0.0991698
$793$	1477.47	0.0661621
$794$	−20720.7	−0.926133
$795$	−521.977	−0.0232863
$796$	−17697.8	−0.788044
$797$	32743.4	1.45525	0.727623	−	0.685977i	$-0.240625\pi$
$797$	32743.4	1.45525	0.727623	+	0.685977i	$0.240625\pi$
$798$	−116.672	−0.00517561
$799$	11869.7	0.525555
$800$	22696.9	1.00307
$801$	−13445.2	−0.593085
$802$	−12641.6	−0.556597
$803$	−168.906	−0.00742286
$804$	7215.67	0.316514
$805$	344.046	0.0150634
$806$	−5186.66	−0.226665
$807$	−13987.8	−0.610154
$808$	11149.8	0.485455
$809$	−17377.8	−0.755220	−0.377610	−	0.925965i	$-0.623254\pi$
$809$	−17377.8	−0.755220	−0.377610	+	0.925965i	$0.623254\pi$
$810$	142.744	0.00619200
$811$	−12376.5	−0.535877	−0.267938	−	0.963436i	$-0.586342\pi$
$811$	−12376.5	−0.535877	−0.267938	+	0.963436i	$0.586342\pi$
$812$	−2828.49	−0.122242
$813$	17898.9	0.772132
$814$	4477.04	0.192777
$815$	27.3775	0.00117668
$816$	265.468	0.0113888
$817$	−1691.57	−0.0724362
$818$	15255.4	0.652071
$819$	416.946	0.0177891
$820$	181.862	0.00774500
$821$	14131.7	0.600731	0.300366	−	0.953824i	$-0.402891\pi$
$821$	14131.7	0.600731	0.300366	+	0.953824i	$0.402891\pi$
$822$	−3833.05	−0.162643
$823$	8927.45	0.378118	0.189059	−	0.981966i	$-0.439456\pi$
$823$	8927.45	0.378118	0.189059	+	0.981966i	$0.439456\pi$
$824$	−22356.1	−0.945159
$825$	4089.77	0.172591
$826$	679.581	0.0286267
$827$	−12589.8	−0.529373	−0.264687	−	0.964334i	$-0.585269\pi$
$827$	−12589.8	−0.529373	−0.264687	+	0.964334i	$0.585269\pi$
$828$	7976.57	0.334789
$829$	5819.60	0.243816	0.121908	−	0.992541i	$-0.461099\pi$
$829$	5819.60	0.243816	0.121908	+	0.992541i	$0.461099\pi$
$830$	471.192	0.0197052
$831$	4717.88	0.196945
$832$	7051.34	0.293824
$833$	−11323.3	−0.470984
$834$	−9378.56	−0.389392
$835$	−4000.00	−0.165779
$836$	667.683	0.0276224
$837$	3390.11	0.139999
$838$	−27799.4	−1.14596
$839$	44301.2	1.82294	0.911471	−	0.411365i	$-0.134948\pi$
$839$	44301.2	1.82294	0.911471	+	0.411365i	$0.134948\pi$
$840$	−132.381	−0.00543759
$841$	59974.3	2.45907
$842$	−10440.6	−0.427325
$843$	8099.91	0.330932
$844$	−521.421	−0.0212655
$845$	1663.97	0.0677423
$846$	−5460.00	−0.221890
$847$	231.437	0.00938876
$848$	446.540	0.0180828
$849$	−18540.4	−0.749476
$850$	7052.94	0.284605
$851$	−41542.6	−1.67340
$852$	4291.36	0.172558
$853$	16539.0	0.663874	0.331937	−	0.943302i	$-0.392298\pi$
$853$	16539.0	0.663874	0.331937	+	0.943302i	$0.392298\pi$
$854$	−198.988	−0.00797333
$855$	−110.870	−0.00443471
$856$	−18214.2	−0.727275
$857$	46202.2	1.84158	0.920792	−	0.390055i	$-0.127544\pi$
$857$	46202.2	1.84158	0.920792	+	0.390055i	$0.127544\pi$
$858$	1363.18	0.0542402
$859$	−4437.88	−0.176273	−0.0881364	−	0.996108i	$-0.528091\pi$
$859$	−4437.88	−0.176273	−0.0881364	+	0.996108i	$0.528091\pi$
$860$	−746.439	−0.0295969
$861$	198.362	0.00785151
$862$	−6911.79	−0.273105
$863$	−31754.8	−1.25254	−0.626272	−	0.779605i	$-0.715420\pi$
$863$	−31754.8	−1.25254	−0.626272	+	0.779605i	$0.715420\pi$
$864$	−4944.76	−0.194704
$865$	−3051.19	−0.119935
$866$	−15716.2	−0.616695
$867$	−11398.6	−0.446502
$868$	−1222.72	−0.0478131
$869$	−11301.6	−0.441173
$870$	1535.58	0.0598401
$871$	−11442.4	−0.445131
$872$	8145.19	0.316320
$873$	3245.49	0.125823
$874$	3539.50	0.136985
$875$	491.987	0.0190082
$876$	−234.532	−0.00904579
$877$	−10923.6	−0.420597	−0.210299	−	0.977637i	$-0.567444\pi$
$877$	−10923.6	−0.420597	−0.210299	+	0.977637i	$0.567444\pi$
$878$	12798.7	0.491955
$879$	14333.8	0.550019
$880$	30.1420	0.00115464
$881$	2250.56	0.0860650	0.0430325	−	0.999074i	$-0.486298\pi$
$881$	2250.56	0.0860650	0.0430325	+	0.999074i	$0.486298\pi$
$882$	5208.69	0.198850
$883$	−27518.1	−1.04876	−0.524382	−	0.851483i	$-0.675703\pi$
$883$	−27518.1	−1.04876	−0.524382	+	0.851483i	$0.675703\pi$
$884$	−4114.86	−0.156559
$885$	645.787	0.0245287
$886$	−13008.1	−0.493244
$887$	−8769.73	−0.331971	−0.165986	−	0.986128i	$-0.553081\pi$
$887$	−8769.73	−0.331971	−0.165986	+	0.986128i	$0.553081\pi$
$888$	15984.6	0.604065
$889$	2749.72	0.103738
$890$	−2632.67	−0.0991542
$891$	−891.000	−0.0335013
$892$	−18780.0	−0.704934
$893$	4240.82	0.158918
$894$	548.363	0.0205145
$895$	−4114.54	−0.153669
$896$	1852.65	0.0690766
$897$	−12649.0	−0.470832
$898$	−5738.61	−0.213252
$899$	36469.2	1.35297
$900$	5678.80	0.210326
$901$	5618.79	0.207757
$902$	648.530	0.0239398
$903$	−814.161	−0.0300039
$904$	−42115.9	−1.54951
$905$	3842.55	0.141139
$906$	8847.58	0.324438
$907$	16741.2	0.612880	0.306440	−	0.951890i	$-0.400862\pi$
$907$	16741.2	0.612880	0.306440	+	0.951890i	$0.400862\pi$
$908$	−17564.7	−0.641967
$909$	4494.45	0.163995
$910$	81.6414	0.00297405
$911$	37244.8	1.35453	0.677265	−	0.735739i	$-0.263165\pi$
$911$	37244.8	1.35453	0.677265	+	0.735739i	$0.263165\pi$
$912$	94.8470	0.00344375
$913$	−2941.15	−0.106613
$914$	30574.1	1.10646
$915$	−189.093	−0.00683194
$916$	5437.90	0.196150
$917$	−2107.15	−0.0758826
$918$	−1536.56	−0.0552440
$919$	49969.1	1.79361	0.896805	−	0.442426i	$-0.145882\pi$
$919$	49969.1	1.79361	0.896805	+	0.442426i	$0.145882\pi$
$920$	4016.06	0.143919
$921$	−5474.18	−0.195853
$922$	−15168.9	−0.541822
$923$	−6805.08	−0.242678
$924$	321.360	0.0114415
$925$	−29575.6	−1.05129
$926$	−17412.9	−0.617953
$927$	−9011.69	−0.319291
$928$	−53193.5	−1.88164
$929$	−19876.4	−0.701963	−0.350982	−	0.936382i	$-0.614152\pi$
$929$	−19876.4	−0.701963	−0.350982	+	0.936382i	$0.614152\pi$
$930$	663.810	0.0234056
$931$	−4045.62	−0.142417
$932$	4188.78	0.147219
$933$	27563.1	0.967175
$934$	−7153.03	−0.250593
$935$	379.275	0.0132659
$936$	4867.03	0.169961
$937$	−26350.6	−0.918715	−0.459358	−	0.888251i	$-0.651920\pi$
$937$	−26350.6	−0.918715	−0.459358	+	0.888251i	$0.651920\pi$
$938$	1541.07	0.0536437
$939$	8626.65	0.299809
$940$	1871.35	0.0649327
$941$	−33212.4	−1.15058	−0.575289	−	0.817950i	$-0.695110\pi$
$941$	−33212.4	−1.15058	−0.575289	+	0.817950i	$0.695110\pi$
$942$	−9142.56	−0.316222
$943$	−6017.74	−0.207810
$944$	−552.457	−0.0190476
$945$	−53.3625	−0.00183691
$946$	−2661.84	−0.0914841
$947$	24240.5	0.831795	0.415898	−	0.909411i	$-0.363468\pi$
$947$	24240.5	0.831795	0.415898	+	0.909411i	$0.363468\pi$
$948$	−15692.7	−0.537631
$949$	371.913	0.0127216
$950$	2519.89	0.0860589
$951$	−21899.7	−0.746735
$952$	1425.01	0.0485134
$953$	27790.0	0.944604	0.472302	−	0.881437i	$-0.343423\pi$
$953$	27790.0	0.944604	0.472302	+	0.881437i	$0.343423\pi$
$954$	−2584.62	−0.0877151
$955$	−3449.86	−0.116895
$956$	−19063.4	−0.644932
$957$	−9584.97	−0.323760
$958$	−7968.50	−0.268738
$959$	1432.92	0.0482497
$960$	−902.460	−0.0303404
$961$	−14025.8	−0.470807
$962$	−9857.98	−0.330389
$963$	−7342.10	−0.245686
$964$	−7314.44	−0.244380
$965$	−3795.81	−0.126623
$966$	1703.58	0.0567410
$967$	−18587.9	−0.618146	−0.309073	−	0.951038i	$-0.600019\pi$
$967$	−18587.9	−0.618146	−0.309073	+	0.951038i	$0.600019\pi$
$968$	2701.58	0.0897024
$969$	1193.46	0.0395658
$970$	635.494	0.0210355
$971$	−30187.0	−0.997680	−0.498840	−	0.866694i	$-0.666240\pi$
$971$	−30187.0	−0.997680	−0.498840	+	0.866694i	$0.666240\pi$
$972$	−1237.19	−0.0408259
$973$	3506.02	0.115517
$974$	−21494.5	−0.707113
$975$	−9005.24	−0.295793
$976$	161.765	0.00530530
$977$	−19511.0	−0.638909	−0.319454	−	0.947602i	$-0.603500\pi$
$977$	−19511.0	−0.638909	−0.319454	+	0.947602i	$0.603500\pi$
$978$	135.562	0.00443232
$979$	16433.0	0.536466
$980$	−1785.22	−0.0581904
$981$	3283.31	0.106858
$982$	−30611.3	−0.994752
$983$	30350.2	0.984762	0.492381	−	0.870380i	$-0.336127\pi$
$983$	30350.2	0.984762	0.492381	+	0.870380i	$0.336127\pi$
$984$	2315.48	0.0750152
$985$	1164.11	0.0376566
$986$	−16529.6	−0.533884
$987$	2041.13	0.0658256
$988$	−1470.17	−0.0473403
$989$	24699.3	0.794128
$990$	−174.465	−0.00560087
$991$	−57869.1	−1.85497	−0.927483	−	0.373865i	$-0.878032\pi$
$991$	−57869.1	−1.85497	−0.927483	+	0.373865i	$0.878032\pi$
$992$	−22994.9	−0.735976
$993$	−13943.8	−0.445613
$994$	916.518	0.0292457
$995$	−3591.82	−0.114441
$996$	−4083.90	−0.129923
$997$	−46220.3	−1.46822	−0.734109	−	0.679032i	$-0.762400\pi$
$997$	−46220.3	−1.46822	−0.734109	+	0.679032i	$0.762400\pi$
$998$	−17181.6	−0.544963
$999$	6443.37	0.204063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.14	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.14	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70549 q^{2} +3.00000 q^{3} -5.09131 q^{4} -1.03329 q^{5} -5.11647 q^{6} +1.91271 q^{7} +22.3271 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.70549 q^{2} +3.00000 q^{3} -5.09131 q^{4} -1.03329 q^{5} -5.11647 q^{6} +1.91271 q^{7} +22.3271 q^{8} +9.00000 q^{9} +1.76227 q^{10} -11.0000 q^{11} -15.2739 q^{12} +24.2208 q^{13} -3.26210 q^{14} -3.09988 q^{15} +2.65188 q^{16} +33.3685 q^{17} -15.3494 q^{18} +11.9220 q^{19} +5.26082 q^{20} +5.73812 q^{21} +18.7604 q^{22} -174.078 q^{23} +66.9812 q^{24} -123.932 q^{25} -41.3084 q^{26} +27.0000 q^{27} -9.73817 q^{28} +290.454 q^{29} +5.28682 q^{30} +125.559 q^{31} -183.139 q^{32} -33.0000 q^{33} -56.9096 q^{34} -1.97639 q^{35} -45.8218 q^{36} +238.644 q^{37} -20.3328 q^{38} +72.6625 q^{39} -23.0705 q^{40} +34.5692 q^{41} -9.78629 q^{42} -141.886 q^{43} +56.0044 q^{44} -9.29965 q^{45} +296.888 q^{46} +355.714 q^{47} +7.95565 q^{48} -339.342 q^{49} +211.365 q^{50} +100.106 q^{51} -123.316 q^{52} +168.386 q^{53} -46.0482 q^{54} +11.3662 q^{55} +42.7051 q^{56} +35.7659 q^{57} -495.365 q^{58} -208.326 q^{59} +15.7825 q^{60} +61.0000 q^{61} -214.140 q^{62} +17.2143 q^{63} +291.127 q^{64} -25.0273 q^{65} +56.2811 q^{66} -472.418 q^{67} -169.889 q^{68} -522.235 q^{69} +3.37071 q^{70} -280.960 q^{71} +200.944 q^{72} +15.3551 q^{73} -407.004 q^{74} -371.797 q^{75} -60.6984 q^{76} -21.0398 q^{77} -123.925 q^{78} +1027.42 q^{79} -2.74018 q^{80} +81.0000 q^{81} -58.9573 q^{82} +267.377 q^{83} -29.2145 q^{84} -34.4795 q^{85} +241.986 q^{86} +871.361 q^{87} -245.598 q^{88} -1493.91 q^{89} +15.8605 q^{90} +46.3273 q^{91} +886.286 q^{92} +376.678 q^{93} -606.667 q^{94} -12.3189 q^{95} -549.418 q^{96} +360.610 q^{97} +578.743 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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