LMFDB - Embedded newform 2013.4.a.d.1.9

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:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-3.73288 q^{2} -3.00000 q^{3} +5.93441 q^{4} -18.1575 q^{5} +11.1986 q^{6} +21.4866 q^{7} +7.71060 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.73288 q^{2} -3.00000 q^{3} +5.93441 q^{4} -18.1575 q^{5} +11.1986 q^{6} +21.4866 q^{7} +7.71060 q^{8} +9.00000 q^{9} +67.7799 q^{10} +11.0000 q^{11} -17.8032 q^{12} +11.6529 q^{13} -80.2069 q^{14} +54.4725 q^{15} -76.2581 q^{16} +64.7204 q^{17} -33.5959 q^{18} -151.422 q^{19} -107.754 q^{20} -64.4598 q^{21} -41.0617 q^{22} +94.8450 q^{23} -23.1318 q^{24} +204.695 q^{25} -43.4989 q^{26} -27.0000 q^{27} +127.510 q^{28} +41.8412 q^{29} -203.340 q^{30} +112.578 q^{31} +222.978 q^{32} -33.0000 q^{33} -241.594 q^{34} -390.143 q^{35} +53.4097 q^{36} -242.007 q^{37} +565.240 q^{38} -34.9587 q^{39} -140.005 q^{40} -107.306 q^{41} +240.621 q^{42} -365.711 q^{43} +65.2785 q^{44} -163.418 q^{45} -354.045 q^{46} -115.766 q^{47} +228.774 q^{48} +118.673 q^{49} -764.104 q^{50} -194.161 q^{51} +69.1531 q^{52} +401.473 q^{53} +100.788 q^{54} -199.733 q^{55} +165.674 q^{56} +454.265 q^{57} -156.188 q^{58} -649.263 q^{59} +323.262 q^{60} -61.0000 q^{61} -420.240 q^{62} +193.379 q^{63} -222.285 q^{64} -211.588 q^{65} +123.185 q^{66} -54.2713 q^{67} +384.077 q^{68} -284.535 q^{69} +1456.36 q^{70} -249.652 q^{71} +69.3954 q^{72} +27.8992 q^{73} +903.382 q^{74} -614.086 q^{75} -898.599 q^{76} +236.352 q^{77} +130.497 q^{78} -1126.95 q^{79} +1384.66 q^{80} +81.0000 q^{81} +400.561 q^{82} +1316.73 q^{83} -382.531 q^{84} -1175.16 q^{85} +1365.16 q^{86} -125.524 q^{87} +84.8166 q^{88} +497.622 q^{89} +610.019 q^{90} +250.381 q^{91} +562.849 q^{92} -337.734 q^{93} +432.140 q^{94} +2749.44 q^{95} -668.933 q^{96} +1534.52 q^{97} -442.993 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−3.73288	−1.31977	−0.659887	−	0.751365i	$-0.729396\pi$
$2$	−3.73288	−1.31977	−0.659887	+	0.751365i	$0.729396\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	5.93441	0.741801
$5$	−18.1575	−1.62406	−0.812029	−	0.583617i	$-0.801637\pi$
$5$	−18.1575	−1.62406	−0.812029	+	0.583617i	$0.801637\pi$
$6$	11.1986	0.761971
$7$	21.4866	1.16017	0.580083	−	0.814557i	$-0.303020\pi$
$7$	21.4866	1.16017	0.580083	+	0.814557i	$0.303020\pi$
$8$	7.71060	0.340764
$9$	9.00000	0.333333
$10$	67.7799	2.14339
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−17.8032	−0.428279
$13$	11.6529	0.248610	0.124305	−	0.992244i	$-0.460330\pi$
$13$	11.6529	0.248610	0.124305	+	0.992244i	$0.460330\pi$
$14$	−80.2069	−1.53116
$15$	54.4725	0.937650
$16$	−76.2581	−1.19153
$17$	64.7204	0.923353	0.461676	−	0.887048i	$-0.347248\pi$
$17$	64.7204	0.923353	0.461676	+	0.887048i	$0.347248\pi$
$18$	−33.5959	−0.439924
$19$	−151.422	−1.82834	−0.914172	−	0.405327i	$-0.867158\pi$
$19$	−151.422	−1.82834	−0.914172	+	0.405327i	$0.867158\pi$
$20$	−107.754	−1.20473
$21$	−64.4598	−0.669822
$22$	−41.0617	−0.397927
$23$	94.8450	0.859850	0.429925	−	0.902865i	$-0.358540\pi$
$23$	94.8450	0.859850	0.429925	+	0.902865i	$0.358540\pi$
$24$	−23.1318	−0.196740
$25$	204.695	1.63756
$26$	−43.4989	−0.328109
$27$	−27.0000	−0.192450
$28$	127.510	0.860613
$29$	41.8412	0.267921	0.133961	−	0.990987i	$-0.457230\pi$
$29$	41.8412	0.267921	0.133961	+	0.990987i	$0.457230\pi$
$30$	−203.340	−1.23749
$31$	112.578	0.652244	0.326122	−	0.945328i	$-0.394258\pi$
$31$	112.578	0.652244	0.326122	+	0.945328i	$0.394258\pi$
$32$	222.978	1.23179
$33$	−33.0000	−0.174078
$34$	−241.594	−1.21862
$35$	−390.143	−1.88418
$36$	53.4097	0.247267
$37$	−242.007	−1.07529	−0.537644	−	0.843172i	$-0.680686\pi$
$37$	−242.007	−1.07529	−0.537644	+	0.843172i	$0.680686\pi$
$38$	565.240	2.41300
$39$	−34.9587	−0.143535
$40$	−140.005	−0.553420
$41$	−107.306	−0.408741	−0.204371	−	0.978894i	$-0.565515\pi$
$41$	−107.306	−0.408741	−0.204371	+	0.978894i	$0.565515\pi$
$42$	240.621	0.884014
$43$	−365.711	−1.29699	−0.648493	−	0.761221i	$-0.724600\pi$
$43$	−365.711	−1.29699	−0.648493	+	0.761221i	$0.724600\pi$
$44$	65.2785	0.223662
$45$	−163.418	−0.541352
$46$	−354.045	−1.13481
$47$	−115.766	−0.359280	−0.179640	−	0.983732i	$-0.557493\pi$
$47$	−115.766	−0.359280	−0.179640	+	0.983732i	$0.557493\pi$
$48$	228.774	0.687931
$49$	118.673	0.345986
$50$	−764.104	−2.16121
$51$	−194.161	−0.533098
$52$	69.1531	0.184419
$53$	401.473	1.04050	0.520250	−	0.854014i	$-0.325839\pi$
$53$	401.473	1.04050	0.520250	+	0.854014i	$0.325839\pi$
$54$	100.788	0.253990
$55$	−199.733	−0.489672
$56$	165.674	0.395343
$57$	454.265	1.05559
$58$	−156.188	−0.353595
$59$	−649.263	−1.43266	−0.716329	−	0.697763i	$-0.754179\pi$
$59$	−649.263	−1.43266	−0.716329	+	0.697763i	$0.754179\pi$
$60$	323.262	0.695550
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−420.240	−0.860815
$63$	193.379	0.386722
$64$	−222.285	−0.434149
$65$	−211.588	−0.403757
$66$	123.185	0.229743
$67$	−54.2713	−0.0989595	−0.0494798	−	0.998775i	$-0.515756\pi$
$67$	−54.2713	−0.0989595	−0.0494798	+	0.998775i	$0.515756\pi$
$68$	384.077	0.684945
$69$	−284.535	−0.496434
$70$	1456.36	2.48669
$71$	−249.652	−0.417300	−0.208650	−	0.977990i	$-0.566907\pi$
$71$	−249.652	−0.417300	−0.208650	+	0.977990i	$0.566907\pi$
$72$	69.3954	0.113588
$73$	27.8992	0.0447309	0.0223654	−	0.999750i	$-0.492880\pi$
$73$	27.8992	0.0447309	0.0223654	+	0.999750i	$0.492880\pi$
$74$	903.382	1.41914
$75$	−614.086	−0.945447
$76$	−898.599	−1.35627
$77$	236.352	0.349803
$78$	130.497	0.189434
$79$	−1126.95	−1.60496	−0.802480	−	0.596679i	$-0.796487\pi$
$79$	−1126.95	−1.60496	−0.802480	+	0.596679i	$0.796487\pi$
$80$	1384.66	1.93512
$81$	81.0000	0.111111
$82$	400.561	0.539446
$83$	1316.73	1.74132	0.870662	−	0.491881i	$-0.163691\pi$
$83$	1316.73	1.74132	0.870662	+	0.491881i	$0.163691\pi$
$84$	−382.531	−0.496875
$85$	−1175.16	−1.49958
$86$	1365.16	1.71173
$87$	−125.524	−0.154684
$88$	84.8166	0.102744
$89$	497.622	0.592672	0.296336	−	0.955084i	$-0.404235\pi$
$89$	497.622	0.592672	0.296336	+	0.955084i	$0.404235\pi$
$90$	610.019	0.714463
$91$	250.381	0.288429
$92$	562.849	0.637838
$93$	−337.734	−0.376573
$94$	432.140	0.474168
$95$	2749.44	2.96934
$96$	−668.933	−0.711173
$97$	1534.52	1.60626	0.803128	−	0.595807i	$-0.203168\pi$
$97$	1534.52	1.60626	0.803128	+	0.595807i	$0.203168\pi$
$98$	−442.993	−0.456623
$99$	99.0000	0.100504
$100$	1214.75	1.21475
$101$	765.893	0.754547	0.377273	−	0.926102i	$-0.376862\pi$
$101$	765.893	0.754547	0.377273	+	0.926102i	$0.376862\pi$
$102$	724.781	0.703569
$103$	−1746.41	−1.67067	−0.835334	−	0.549743i	$-0.814726\pi$
$103$	−1746.41	−1.67067	−0.835334	+	0.549743i	$0.814726\pi$
$104$	89.8509	0.0847173
$105$	1170.43	1.08783
$106$	−1498.65	−1.37322
$107$	2149.47	1.94203	0.971015	−	0.239020i	$-0.0768261\pi$
$107$	2149.47	1.94203	0.971015	+	0.239020i	$0.0768261\pi$
$108$	−160.229	−0.142760
$109$	1952.43	1.71567	0.857837	−	0.513922i	$-0.171808\pi$
$109$	1952.43	1.71567	0.857837	+	0.513922i	$0.171808\pi$
$110$	745.579	0.646256
$111$	726.020	0.620818
$112$	−1638.53	−1.38238
$113$	1000.13	0.832604	0.416302	−	0.909226i	$-0.363326\pi$
$113$	1000.13	0.832604	0.416302	+	0.909226i	$0.363326\pi$
$114$	−1695.72	−1.39315
$115$	−1722.15	−1.39645
$116$	248.303	0.198744
$117$	104.876	0.0828701
$118$	2423.62	1.89078
$119$	1390.62	1.07124
$120$	420.016	0.319517
$121$	121.000	0.0909091
$122$	227.706	0.168980
$123$	321.918	0.235987
$124$	668.083	0.483836
$125$	−1447.07	−1.03544
$126$	−721.862	−0.510386
$127$	1418.44	0.991074	0.495537	−	0.868587i	$-0.334971\pi$
$127$	1418.44	0.991074	0.495537	+	0.868587i	$0.334971\pi$
$128$	−954.058	−0.658810
$129$	1097.13	0.748815
$130$	789.832	0.532868
$131$	−2121.37	−1.41485	−0.707425	−	0.706788i	$-0.750143\pi$
$131$	−2121.37	−1.41485	−0.707425	+	0.706788i	$0.750143\pi$
$132$	−195.836	−0.129131
$133$	−3253.54	−2.12118
$134$	202.588	0.130604
$135$	490.253	0.312550
$136$	499.033	0.314645
$137$	2207.16	1.37643	0.688214	−	0.725508i	$-0.258395\pi$
$137$	2207.16	1.37643	0.688214	+	0.725508i	$0.258395\pi$
$138$	1062.14	0.655181
$139$	−719.896	−0.439286	−0.219643	−	0.975580i	$-0.570489\pi$
$139$	−719.896	−0.439286	−0.219643	+	0.975580i	$0.570489\pi$
$140$	−2315.27	−1.39769
$141$	347.297	0.207430
$142$	931.923	0.550741
$143$	128.182	0.0749588
$144$	−686.322	−0.397177
$145$	−759.733	−0.435120
$146$	−104.144	−0.0590346
$147$	−356.020	−0.199755
$148$	−1436.17	−0.797650
$149$	−1737.93	−0.955549	−0.477775	−	0.878482i	$-0.658556\pi$
$149$	−1737.93	−0.955549	−0.477775	+	0.878482i	$0.658556\pi$
$150$	2292.31	1.24778
$151$	1188.67	0.640611	0.320306	−	0.947314i	$-0.396214\pi$
$151$	1188.67	0.640611	0.320306	+	0.947314i	$0.396214\pi$
$152$	−1167.55	−0.623033
$153$	582.484	0.307784
$154$	−882.276	−0.461661
$155$	−2044.13	−1.05928
$156$	−207.459	−0.106475
$157$	785.227	0.399159	0.199579	−	0.979882i	$-0.436042\pi$
$157$	785.227	0.399159	0.199579	+	0.979882i	$0.436042\pi$
$158$	4206.77	2.11818
$159$	−1204.42	−0.600733
$160$	−4048.72	−2.00050
$161$	2037.89	0.997569
$162$	−302.363	−0.146641
$163$	−69.3788	−0.0333384	−0.0166692	−	0.999861i	$-0.505306\pi$
$163$	−69.3788	−0.0333384	−0.0166692	+	0.999861i	$0.505306\pi$
$164$	−636.798	−0.303205
$165$	599.198	0.282712
$166$	−4915.20	−2.29815
$167$	−3830.53	−1.77494	−0.887471	−	0.460864i	$-0.847540\pi$
$167$	−3830.53	−1.77494	−0.887471	+	0.460864i	$0.847540\pi$
$168$	−497.023	−0.228251
$169$	−2061.21	−0.938193
$170$	4386.74	1.97910
$171$	−1362.80	−0.609448
$172$	−2170.28	−0.962105
$173$	3946.31	1.73429	0.867145	−	0.498055i	$-0.165952\pi$
$173$	3946.31	1.73429	0.867145	+	0.498055i	$0.165952\pi$
$174$	468.565	0.204148
$175$	4398.20	1.89985
$176$	−838.839	−0.359260
$177$	1947.79	0.827145
$178$	−1857.56	−0.782193
$179$	−3911.05	−1.63311	−0.816553	−	0.577271i	$-0.804118\pi$
$179$	−3911.05	−1.63311	−0.816553	+	0.577271i	$0.804118\pi$
$180$	−969.787	−0.401576
$181$	−3864.59	−1.58703	−0.793515	−	0.608550i	$-0.791751\pi$
$181$	−3864.59	−1.58703	−0.793515	+	0.608550i	$0.791751\pi$
$182$	−934.643	−0.380661
$183$	183.000	0.0739221
$184$	731.312	0.293005
$185$	4394.24	1.74633
$186$	1260.72	0.496992
$187$	711.924	0.278401
$188$	−687.001	−0.266514
$189$	−580.138	−0.223274
$190$	−10263.3	−3.91885
$191$	−233.194	−0.0883421	−0.0441710	−	0.999024i	$-0.514065\pi$
$191$	−233.194	−0.0883421	−0.0441710	+	0.999024i	$0.514065\pi$
$192$	666.854	0.250656
$193$	686.304	0.255965	0.127983	−	0.991776i	$-0.459150\pi$
$193$	686.304	0.255965	0.127983	+	0.991776i	$0.459150\pi$
$194$	−5728.18	−2.11989
$195$	634.763	0.233109
$196$	704.256	0.256653
$197$	4247.97	1.53632	0.768160	−	0.640258i	$-0.221172\pi$
$197$	4247.97	1.53632	0.768160	+	0.640258i	$0.221172\pi$
$198$	−369.555	−0.132642
$199$	−2443.54	−0.870443	−0.435222	−	0.900323i	$-0.643330\pi$
$199$	−2443.54	−0.870443	−0.435222	+	0.900323i	$0.643330\pi$
$200$	1578.32	0.558022
$201$	162.814	0.0571343
$202$	−2858.99	−0.995831
$203$	899.025	0.310833
$204$	−1152.23	−0.395453
$205$	1948.41	0.663819
$206$	6519.14	2.20490
$207$	853.605	0.286617
$208$	−888.628	−0.296227
$209$	−1665.64	−0.551266
$210$	−4369.07	−1.43569
$211$	3881.21	1.26632	0.633160	−	0.774021i	$-0.281758\pi$
$211$	3881.21	1.26632	0.633160	+	0.774021i	$0.281758\pi$
$212$	2382.50	0.771845
$213$	748.957	0.240928
$214$	−8023.72	−2.56304
$215$	6640.40	2.10638
$216$	−208.186	−0.0655800
$217$	2418.91	0.756712
$218$	−7288.17	−2.26430
$219$	−83.6976	−0.0258254
$220$	−1185.30	−0.363239
$221$	754.180	0.229555
$222$	−2710.15	−0.819339
$223$	5931.69	1.78124	0.890618	−	0.454753i	$-0.150272\pi$
$223$	5931.69	1.78124	0.890618	+	0.454753i	$0.150272\pi$
$224$	4791.03	1.42908
$225$	1842.26	0.545854
$226$	−3733.37	−1.09885
$227$	−2743.26	−0.802099	−0.401050	−	0.916056i	$-0.631354\pi$
$227$	−2743.26	−0.802099	−0.401050	+	0.916056i	$0.631354\pi$
$228$	2695.80	0.783042
$229$	−2515.23	−0.725813	−0.362907	−	0.931826i	$-0.618216\pi$
$229$	−2515.23	−0.725813	−0.362907	+	0.931826i	$0.618216\pi$
$230$	6428.58	1.84299
$231$	−709.057	−0.201959
$232$	322.621	0.0912979
$233$	−3823.71	−1.07510	−0.537552	−	0.843230i	$-0.680651\pi$
$233$	−3823.71	−1.07510	−0.537552	+	0.843230i	$0.680651\pi$
$234$	−391.490	−0.109370
$235$	2102.02	0.583492
$236$	−3852.99	−1.06275
$237$	3380.85	0.926624
$238$	−5191.02	−1.41380
$239$	5045.30	1.36549	0.682747	−	0.730655i	$-0.260785\pi$
$239$	5045.30	1.36549	0.682747	+	0.730655i	$0.260785\pi$
$240$	−4153.97	−1.11724
$241$	−1106.95	−0.295872	−0.147936	−	0.988997i	$-0.547263\pi$
$241$	−1106.95	−0.295872	−0.147936	+	0.988997i	$0.547263\pi$
$242$	−451.679	−0.119979
$243$	−243.000	−0.0641500
$244$	−361.999	−0.0949779
$245$	−2154.81	−0.561901
$246$	−1201.68	−0.311449
$247$	−1764.50	−0.454545
$248$	868.043	0.222261
$249$	−3950.19	−1.00535
$250$	5401.74	1.36654
$251$	1306.74	0.328609	0.164305	−	0.986410i	$-0.447462\pi$
$251$	1306.74	0.328609	0.164305	+	0.986410i	$0.447462\pi$
$252$	1147.59	0.286871
$253$	1043.29	0.259254
$254$	−5294.88	−1.30799
$255$	3525.48	0.865782
$256$	5339.66	1.30363
$257$	2328.26	0.565107	0.282554	−	0.959252i	$-0.408818\pi$
$257$	2328.26	0.565107	0.282554	+	0.959252i	$0.408818\pi$
$258$	−4095.47	−0.988266
$259$	−5199.90	−1.24751
$260$	−1255.65	−0.299508
$261$	376.571	0.0893071
$262$	7918.84	1.86728
$263$	−676.529	−0.158618	−0.0793090	−	0.996850i	$-0.525271\pi$
$263$	−676.529	−0.158618	−0.0793090	+	0.996850i	$0.525271\pi$
$264$	−254.450	−0.0593193
$265$	−7289.75	−1.68983
$266$	12145.1	2.79948
$267$	−1492.87	−0.342179
$268$	−322.068	−0.0734083
$269$	−6204.71	−1.40635	−0.703174	−	0.711018i	$-0.748235\pi$
$269$	−6204.71	−1.40635	−0.703174	+	0.711018i	$0.748235\pi$
$270$	−1830.06	−0.412495
$271$	1214.61	0.272259	0.136130	−	0.990691i	$-0.456534\pi$
$271$	1214.61	0.272259	0.136130	+	0.990691i	$0.456534\pi$
$272$	−4935.45	−1.10020
$273$	−751.143	−0.166525
$274$	−8239.08	−1.81657
$275$	2251.65	0.493744
$276$	−1688.55	−0.368256
$277$	6347.79	1.37690	0.688451	−	0.725283i	$-0.258291\pi$
$277$	6347.79	1.37690	0.688451	+	0.725283i	$0.258291\pi$
$278$	2687.29	0.579758
$279$	1013.20	0.217415
$280$	−3008.24	−0.642059
$281$	−7725.09	−1.64000	−0.820000	−	0.572363i	$-0.806027\pi$
$281$	−7725.09	−1.64000	−0.820000	+	0.572363i	$0.806027\pi$
$282$	−1296.42	−0.273761
$283$	320.144	0.0672459	0.0336229	−	0.999435i	$-0.489295\pi$
$283$	320.144	0.0672459	0.0336229	+	0.999435i	$0.489295\pi$
$284$	−1481.54	−0.309554
$285$	−8248.33	−1.71435
$286$	−478.488	−0.0989286
$287$	−2305.64	−0.474208
$288$	2006.80	0.410596
$289$	−724.271	−0.147419
$290$	2835.99	0.574259
$291$	−4603.56	−0.927372
$292$	165.565	0.0331814
$293$	−96.0420	−0.0191496	−0.00957480	−	0.999954i	$-0.503048\pi$
$293$	−96.0420	−0.0191496	−0.00957480	+	0.999954i	$0.503048\pi$
$294$	1328.98	0.263632
$295$	11789.0	2.32672
$296$	−1866.02	−0.366419
$297$	−297.000	−0.0580259
$298$	6487.49	1.26111
$299$	1105.22	0.213767
$300$	−3644.24	−0.701334
$301$	−7857.87	−1.50472
$302$	−4437.15	−0.845461
$303$	−2297.68	−0.435638
$304$	11547.1	2.17853
$305$	1107.61	0.207939
$306$	−2174.34	−0.406206
$307$	2657.00	0.493950	0.246975	−	0.969022i	$-0.420563\pi$
$307$	2657.00	0.493950	0.246975	+	0.969022i	$0.420563\pi$
$308$	1402.61	0.259485
$309$	5239.23	0.964560
$310$	7630.51	1.39801
$311$	−3088.48	−0.563125	−0.281563	−	0.959543i	$-0.590853\pi$
$311$	−3088.48	−0.563125	−0.281563	+	0.959543i	$0.590853\pi$
$312$	−269.553	−0.0489116
$313$	−5691.27	−1.02776	−0.513881	−	0.857861i	$-0.671793\pi$
$313$	−5691.27	−1.02776	−0.513881	+	0.857861i	$0.671793\pi$
$314$	−2931.16	−0.526799
$315$	−3511.29	−0.628059
$316$	−6687.79	−1.19056
$317$	−7101.48	−1.25823	−0.629115	−	0.777312i	$-0.716583\pi$
$317$	−7101.48	−1.25823	−0.629115	+	0.777312i	$0.716583\pi$
$318$	4495.95	0.792832
$319$	460.253	0.0807813
$320$	4036.13	0.705084
$321$	−6448.41	−1.12123
$322$	−7607.22	−1.31656
$323$	−9800.08	−1.68821
$324$	480.687	0.0824224
$325$	2385.29	0.407115
$326$	258.983	0.0439992
$327$	−5857.28	−0.990545
$328$	−827.394	−0.139284
$329$	−2487.41	−0.416825
$330$	−2236.74	−0.373116
$331$	−9787.78	−1.62533	−0.812666	−	0.582730i	$-0.801985\pi$
$331$	−9787.78	−1.62533	−0.812666	+	0.582730i	$0.801985\pi$
$332$	7814.02	1.29172
$333$	−2178.06	−0.358429
$334$	14298.9	2.34252
$335$	985.431	0.160716
$336$	4915.58	0.798115
$337$	5433.84	0.878339	0.439169	−	0.898404i	$-0.355273\pi$
$337$	5433.84	0.878339	0.439169	+	0.898404i	$0.355273\pi$
$338$	7694.25	1.23820
$339$	−3000.39	−0.480704
$340$	−6973.89	−1.11239
$341$	1238.36	0.196659
$342$	5087.16	0.804333
$343$	−4820.02	−0.758765
$344$	−2819.85	−0.441965
$345$	5166.45	0.806238
$346$	−14731.1	−2.28887
$347$	−2638.30	−0.408159	−0.204080	−	0.978954i	$-0.565420\pi$
$347$	−2638.30	−0.408159	−0.204080	+	0.978954i	$0.565420\pi$
$348$	−744.909	−0.114745
$349$	−2715.34	−0.416472	−0.208236	−	0.978079i	$-0.566772\pi$
$349$	−2715.34	−0.416472	−0.208236	+	0.978079i	$0.566772\pi$
$350$	−16418.0	−2.50737
$351$	−314.628	−0.0478451
$352$	2452.75	0.371398
$353$	6035.11	0.909962	0.454981	−	0.890501i	$-0.349646\pi$
$353$	6035.11	0.909962	0.454981	+	0.890501i	$0.349646\pi$
$354$	−7270.87	−1.09164
$355$	4533.07	0.677719
$356$	2953.09	0.439645
$357$	−4171.86	−0.618483
$358$	14599.5	2.15533
$359$	4325.46	0.635903	0.317951	−	0.948107i	$-0.397005\pi$
$359$	4325.46	0.635903	0.317951	+	0.948107i	$0.397005\pi$
$360$	−1260.05	−0.184473
$361$	16069.6	2.34284
$362$	14426.1	2.09452
$363$	−363.000	−0.0524864
$364$	1485.86	0.213957
$365$	−506.580	−0.0726455
$366$	−683.117	−0.0975604
$367$	10547.0	1.50013	0.750064	−	0.661365i	$-0.230023\pi$
$367$	10547.0	1.50013	0.750064	+	0.661365i	$0.230023\pi$
$368$	−7232.69	−1.02454
$369$	−965.754	−0.136247
$370$	−16403.2	−2.30476
$371$	8626.28	1.20715
$372$	−2004.25	−0.279343
$373$	−6215.00	−0.862736	−0.431368	−	0.902176i	$-0.641969\pi$
$373$	−6215.00	−0.862736	−0.431368	+	0.902176i	$0.641969\pi$
$374$	−2657.53	−0.367427
$375$	4341.21	0.597811
$376$	−892.623	−0.122430
$377$	487.572	0.0666080
$378$	2165.59	0.294671
$379$	−3789.43	−0.513588	−0.256794	−	0.966466i	$-0.582666\pi$
$379$	−3789.43	−0.513588	−0.256794	+	0.966466i	$0.582666\pi$
$380$	16316.3	2.20266
$381$	−4255.33	−0.572197
$382$	870.486	0.116592
$383$	−9328.85	−1.24460	−0.622301	−	0.782778i	$-0.713802\pi$
$383$	−9328.85	−1.24460	−0.622301	+	0.782778i	$0.713802\pi$
$384$	2862.18	0.380364
$385$	−4291.57	−0.568101
$386$	−2561.89	−0.337816
$387$	−3291.40	−0.432328
$388$	9106.46	1.19152
$389$	4920.42	0.641324	0.320662	−	0.947194i	$-0.396095\pi$
$389$	4920.42	0.641324	0.320662	+	0.947194i	$0.396095\pi$
$390$	−2369.50	−0.307652
$391$	6138.40	0.793945
$392$	915.042	0.117900
$393$	6364.12	0.816864
$394$	−15857.2	−2.02759
$395$	20462.6	2.60655
$396$	587.507	0.0745538
$397$	−12225.8	−1.54558	−0.772792	−	0.634660i	$-0.781140\pi$
$397$	−12225.8	−1.54558	−0.772792	+	0.634660i	$0.781140\pi$
$398$	9121.46	1.14879
$399$	9760.61	1.22467
$400$	−15609.7	−1.95121
$401$	9584.80	1.19362	0.596810	−	0.802382i	$-0.296434\pi$
$401$	9584.80	1.19362	0.596810	+	0.802382i	$0.296434\pi$
$402$	−607.765	−0.0754043
$403$	1311.86	0.162155
$404$	4545.13	0.559724
$405$	−1470.76	−0.180451
$406$	−3355.95	−0.410230
$407$	−2662.07	−0.324212
$408$	−1497.10	−0.181660
$409$	10936.2	1.32215	0.661077	−	0.750318i	$-0.270100\pi$
$409$	10936.2	1.32215	0.661077	+	0.750318i	$0.270100\pi$
$410$	−7273.19	−0.876091
$411$	−6621.49	−0.794681
$412$	−10363.9	−1.23930
$413$	−13950.4	−1.66212
$414$	−3186.41	−0.378269
$415$	−23908.6	−2.82801
$416$	2598.34	0.306235
$417$	2159.69	0.253622
$418$	6217.64	0.727547
$419$	−7094.16	−0.827141	−0.413571	−	0.910472i	$-0.635719\pi$
$419$	−7094.16	−0.827141	−0.413571	+	0.910472i	$0.635719\pi$
$420$	6945.81	0.806954
$421$	6789.59	0.785996	0.392998	−	0.919539i	$-0.371438\pi$
$421$	6789.59	0.785996	0.392998	+	0.919539i	$0.371438\pi$
$422$	−14488.1	−1.67125
$423$	−1041.89	−0.119760
$424$	3095.60	0.354565
$425$	13248.0	1.51205
$426$	−2795.77	−0.317971
$427$	−1310.68	−0.148544
$428$	12755.8	1.44060
$429$	−384.546	−0.0432775
$430$	−24787.8	−2.77994
$431$	−11516.2	−1.28704	−0.643520	−	0.765429i	$-0.722527\pi$
$431$	−11516.2	−1.28704	−0.643520	+	0.765429i	$0.722527\pi$
$432$	2058.97	0.229310
$433$	−8961.67	−0.994620	−0.497310	−	0.867573i	$-0.665679\pi$
$433$	−8961.67	−0.994620	−0.497310	+	0.867573i	$0.665679\pi$
$434$	−9029.52	−0.998688
$435$	2279.20	0.251217
$436$	11586.5	1.27269
$437$	−14361.6	−1.57210
$438$	312.433	0.0340836
$439$	−3798.71	−0.412989	−0.206495	−	0.978448i	$-0.566206\pi$
$439$	−3798.71	−0.412989	−0.206495	+	0.978448i	$0.566206\pi$
$440$	−1540.06	−0.166862
$441$	1068.06	0.115329
$442$	−2815.27	−0.302961
$443$	13781.9	1.47810	0.739049	−	0.673652i	$-0.235275\pi$
$443$	13781.9	1.47810	0.739049	+	0.673652i	$0.235275\pi$
$444$	4308.50	0.460523
$445$	−9035.58	−0.962533
$446$	−22142.3	−2.35083
$447$	5213.79	0.551687
$448$	−4776.13	−0.503686
$449$	−7650.38	−0.804107	−0.402053	−	0.915616i	$-0.631703\pi$
$449$	−7650.38	−0.804107	−0.402053	+	0.915616i	$0.631703\pi$
$450$	−6876.93	−0.720404
$451$	−1180.37	−0.123240
$452$	5935.18	0.617627
$453$	−3566.00	−0.369857
$454$	10240.3	1.05859
$455$	−4546.30	−0.468426
$456$	3502.66	0.359708
$457$	−8743.02	−0.894926	−0.447463	−	0.894302i	$-0.647672\pi$
$457$	−8743.02	−0.894926	−0.447463	+	0.894302i	$0.647672\pi$
$458$	9389.07	0.957909
$459$	−1747.45	−0.177699
$460$	−10219.9	−1.03589
$461$	−13667.9	−1.38086	−0.690432	−	0.723398i	$-0.742579\pi$
$461$	−13667.9	−1.38086	−0.690432	+	0.723398i	$0.742579\pi$
$462$	2646.83	0.266540
$463$	2366.21	0.237510	0.118755	−	0.992924i	$-0.462110\pi$
$463$	2366.21	0.237510	0.118755	+	0.992924i	$0.462110\pi$
$464$	−3190.73	−0.319237
$465$	6132.40	0.611577
$466$	14273.4	1.41889
$467$	929.525	0.0921055	0.0460528	−	0.998939i	$-0.485336\pi$
$467$	929.525	0.0921055	0.0460528	+	0.998939i	$0.485336\pi$
$468$	622.378	0.0614731
$469$	−1166.10	−0.114810
$470$	−7846.58	−0.770077
$471$	−2355.68	−0.230454
$472$	−5006.21	−0.488198
$473$	−4022.82	−0.391056
$474$	−12620.3	−1.22293
$475$	−30995.3	−2.99403
$476$	8252.51	0.794650
$477$	3613.26	0.346834
$478$	−18833.5	−1.80214
$479$	7575.07	0.722576	0.361288	−	0.932454i	$-0.382337\pi$
$479$	7575.07	0.722576	0.361288	+	0.932454i	$0.382337\pi$
$480$	12146.2	1.15499
$481$	−2820.08	−0.267328
$482$	4132.13	0.390484
$483$	−6113.68	−0.575947
$484$	718.064	0.0674365
$485$	−27863.0	−2.60865
$486$	907.090	0.0846635
$487$	−15756.3	−1.46609	−0.733046	−	0.680179i	$-0.761902\pi$
$487$	−15756.3	−1.46609	−0.733046	+	0.680179i	$0.761902\pi$
$488$	−470.347	−0.0436303
$489$	208.136	0.0192480
$490$	8043.66	0.741583
$491$	15307.7	1.40698	0.703491	−	0.710704i	$-0.251623\pi$
$491$	15307.7	1.40698	0.703491	+	0.710704i	$0.251623\pi$
$492$	1910.39	0.175055
$493$	2707.98	0.247386
$494$	6586.68	0.599896
$495$	−1797.59	−0.163224
$496$	−8584.97	−0.777170
$497$	−5364.18	−0.484137
$498$	14745.6	1.32684
$499$	−9158.28	−0.821605	−0.410802	−	0.911724i	$-0.634751\pi$
$499$	−9158.28	−0.821605	−0.410802	+	0.911724i	$0.634751\pi$
$500$	−8587.50	−0.768090
$501$	11491.6	1.02476
$502$	−4877.92	−0.433690
$503$	−2947.05	−0.261237	−0.130619	−	0.991433i	$-0.541696\pi$
$503$	−2947.05	−0.261237	−0.130619	+	0.991433i	$0.541696\pi$
$504$	1491.07	0.131781
$505$	−13906.7	−1.22543
$506$	−3894.50	−0.342157
$507$	6183.63	0.541666
$508$	8417.62	0.735180
$509$	17085.8	1.48785	0.743926	−	0.668262i	$-0.232961\pi$
$509$	17085.8	1.48785	0.743926	+	0.668262i	$0.232961\pi$
$510$	−13160.2	−1.14264
$511$	599.458	0.0518952
$512$	−12299.9	−1.06168
$513$	4088.39	0.351865
$514$	−8691.10	−0.745813
$515$	31710.4	2.71326
$516$	6510.83	0.555472
$517$	−1273.42	−0.108327
$518$	19410.6	1.64643
$519$	−11838.9	−1.00129
$520$	−1631.47	−0.137586
$521$	10368.6	0.871893	0.435947	−	0.899972i	$-0.356414\pi$
$521$	10368.6	0.871893	0.435947	+	0.899972i	$0.356414\pi$
$522$	−1405.70	−0.117865
$523$	21702.5	1.81450	0.907252	−	0.420587i	$-0.138176\pi$
$523$	21702.5	1.81450	0.907252	+	0.420587i	$0.138176\pi$
$524$	−12589.1	−1.04954
$525$	−13194.6	−1.09688
$526$	2525.40	0.209340
$527$	7286.08	0.602252
$528$	2516.52	0.207419
$529$	−3171.43	−0.260659
$530$	27211.8	2.23020
$531$	−5843.37	−0.477553
$532$	−19307.8	−1.57350
$533$	−1250.43	−0.101617
$534$	5572.69	0.451599
$535$	−39029.0	−3.15397
$536$	−418.464	−0.0337218
$537$	11733.2	0.942874
$538$	23161.4	1.85606
$539$	1305.41	0.104319
$540$	2909.36	0.231850
$541$	2010.90	0.159807	0.0799033	−	0.996803i	$-0.474539\pi$
$541$	2010.90	0.159807	0.0799033	+	0.996803i	$0.474539\pi$
$542$	−4533.99	−0.359321
$543$	11593.8	0.916273
$544$	14431.2	1.13738
$545$	−35451.2	−2.78635
$546$	2803.93	0.219775
$547$	10624.3	0.830461	0.415230	−	0.909716i	$-0.363701\pi$
$547$	10624.3	0.830461	0.415230	+	0.909716i	$0.363701\pi$
$548$	13098.2	1.02104
$549$	−549.000	−0.0426790
$550$	−8405.14	−0.651630
$551$	−6335.67	−0.489852
$552$	−2193.93	−0.169167
$553$	−24214.3	−1.86202
$554$	−23695.5	−1.81720
$555$	−13182.7	−1.00824
$556$	−4272.16	−0.325863
$557$	−25554.1	−1.94391	−0.971957	−	0.235157i	$-0.924439\pi$
$557$	−25554.1	−1.94391	−0.971957	+	0.235157i	$0.924439\pi$
$558$	−3782.16	−0.286938
$559$	−4261.59	−0.322444
$560$	29751.5	2.24506
$561$	−2135.77	−0.160735
$562$	28836.8	2.16443
$563$	−1061.83	−0.0794864	−0.0397432	−	0.999210i	$-0.512654\pi$
$563$	−1061.83	−0.0794864	−0.0397432	+	0.999210i	$0.512654\pi$
$564$	2061.00	0.153872
$565$	−18159.9	−1.35220
$566$	−1195.06	−0.0887493
$567$	1740.41	0.128907
$568$	−1924.97	−0.142201
$569$	−4511.54	−0.332397	−0.166198	−	0.986092i	$-0.553149\pi$
$569$	−4511.54	−0.332397	−0.166198	+	0.986092i	$0.553149\pi$
$570$	30790.0	2.26255
$571$	−12374.0	−0.906893	−0.453447	−	0.891283i	$-0.649806\pi$
$571$	−12374.0	−0.906893	−0.453447	+	0.891283i	$0.649806\pi$
$572$	760.684	0.0556045
$573$	699.582	0.0510043
$574$	8606.68	0.625847
$575$	19414.3	1.40806
$576$	−2000.56	−0.144716
$577$	613.557	0.0442682	0.0221341	−	0.999755i	$-0.492954\pi$
$577$	613.557	0.0442682	0.0221341	+	0.999755i	$0.492954\pi$
$578$	2703.62	0.194560
$579$	−2058.91	−0.147782
$580$	−4508.57	−0.322772
$581$	28292.0	2.02023
$582$	17184.5	1.22392
$583$	4416.20	0.313723
$584$	215.119	0.0152426
$585$	−1904.29	−0.134586
$586$	358.513	0.0252731
$587$	2129.32	0.149721	0.0748607	−	0.997194i	$-0.476149\pi$
$587$	2129.32	0.149721	0.0748607	+	0.997194i	$0.476149\pi$
$588$	−2112.77	−0.148179
$589$	−17046.7	−1.19253
$590$	−44006.9	−3.07074
$591$	−12743.9	−0.886995
$592$	18455.0	1.28124
$593$	8843.05	0.612378	0.306189	−	0.951971i	$-0.400946\pi$
$593$	8843.05	0.612378	0.306189	+	0.951971i	$0.400946\pi$
$594$	1108.67	0.0765810
$595$	−25250.2	−1.73976
$596$	−10313.6	−0.708828
$597$	7330.63	0.502551
$598$	−4125.65	−0.282125
$599$	11081.6	0.755896	0.377948	−	0.925827i	$-0.376630\pi$
$599$	11081.6	0.755896	0.377948	+	0.925827i	$0.376630\pi$
$600$	−4734.97	−0.322174
$601$	12687.6	0.861126	0.430563	−	0.902560i	$-0.358315\pi$
$601$	12687.6	0.861126	0.430563	+	0.902560i	$0.358315\pi$
$602$	29332.5	1.98589
$603$	−488.441	−0.0329865
$604$	7054.03	0.475206
$605$	−2197.06	−0.147642
$606$	8576.97	0.574943
$607$	−7565.39	−0.505881	−0.252941	−	0.967482i	$-0.581398\pi$
$607$	−7565.39	−0.505881	−0.252941	+	0.967482i	$0.581398\pi$
$608$	−33763.7	−2.25213
$609$	−2697.07	−0.179460
$610$	−4134.57	−0.274433
$611$	−1349.01	−0.0893207
$612$	3456.70	0.228315
$613$	21206.1	1.39724	0.698619	−	0.715493i	$-0.253798\pi$
$613$	21206.1	1.39724	0.698619	+	0.715493i	$0.253798\pi$
$614$	−9918.25	−0.651902
$615$	−5845.23	−0.383256
$616$	1822.42	0.119200
$617$	20705.3	1.35099	0.675496	−	0.737363i	$-0.263929\pi$
$617$	20705.3	1.35099	0.675496	+	0.737363i	$0.263929\pi$
$618$	−19557.4	−1.27300
$619$	8171.54	0.530601	0.265300	−	0.964166i	$-0.414529\pi$
$619$	8171.54	0.530601	0.265300	+	0.964166i	$0.414529\pi$
$620$	−12130.7	−0.785777
$621$	−2560.81	−0.165478
$622$	11528.9	0.743197
$623$	10692.2	0.687598
$624$	2665.88	0.171027
$625$	688.265	0.0440489
$626$	21244.8	1.35641
$627$	4996.92	0.318274
$628$	4659.86	0.296096
$629$	−15662.8	−0.992870
$630$	13107.2	0.828895
$631$	3962.05	0.249963	0.124982	−	0.992159i	$-0.460113\pi$
$631$	3962.05	0.249963	0.124982	+	0.992159i	$0.460113\pi$
$632$	−8689.47	−0.546912
$633$	−11643.6	−0.731110
$634$	26509.0	1.66058
$635$	−25755.4	−1.60956
$636$	−7147.51	−0.445625
$637$	1382.89	0.0860157
$638$	−1718.07	−0.106613
$639$	−2246.87	−0.139100
$640$	17323.3	1.06994
$641$	3809.39	0.234730	0.117365	−	0.993089i	$-0.462555\pi$
$641$	3809.39	0.234730	0.117365	+	0.993089i	$0.462555\pi$
$642$	24071.2	1.47977
$643$	−12226.6	−0.749873	−0.374937	−	0.927050i	$-0.622336\pi$
$643$	−12226.6	−0.749873	−0.374937	+	0.927050i	$0.622336\pi$
$644$	12093.7	0.739998
$645$	−19921.2	−1.21612
$646$	36582.5	2.22805
$647$	−13009.5	−0.790502	−0.395251	−	0.918573i	$-0.629342\pi$
$647$	−13009.5	−0.790502	−0.395251	+	0.918573i	$0.629342\pi$
$648$	624.559	0.0378626
$649$	−7141.89	−0.431963
$650$	−8904.02	−0.537299
$651$	−7256.74	−0.436888
$652$	−411.722	−0.0247305
$653$	−18126.5	−1.08629	−0.543143	−	0.839640i	$-0.682766\pi$
$653$	−18126.5	−1.08629	−0.543143	+	0.839640i	$0.682766\pi$
$654$	21864.5	1.30729
$655$	38518.9	2.29780
$656$	8182.95	0.487028
$657$	251.093	0.0149103
$658$	9285.21	0.550114
$659$	−12223.8	−0.722567	−0.361284	−	0.932456i	$-0.617661\pi$
$659$	−12223.8	−0.722567	−0.361284	+	0.932456i	$0.617661\pi$
$660$	3555.89	0.209716
$661$	−88.8900	−0.00523059	−0.00261530	−	0.999997i	$-0.500832\pi$
$661$	−88.8900	−0.00523059	−0.00261530	+	0.999997i	$0.500832\pi$
$662$	36536.6	2.14507
$663$	−2262.54	−0.132534
$664$	10152.8	0.593380
$665$	59076.1	3.44492
$666$	8130.44	0.473045
$667$	3968.43	0.230372
$668$	−22731.9	−1.31665
$669$	−17795.1	−1.02840
$670$	−3678.50	−0.212109
$671$	−671.000	−0.0386046
$672$	−14373.1	−0.825080
$673$	20690.7	1.18509	0.592547	−	0.805536i	$-0.298122\pi$
$673$	20690.7	1.18509	0.592547	+	0.805536i	$0.298122\pi$
$674$	−20283.9	−1.15921
$675$	−5526.77	−0.315149
$676$	−12232.1	−0.695953
$677$	−22685.1	−1.28783	−0.643915	−	0.765097i	$-0.722691\pi$
$677$	−22685.1	−1.28783	−0.643915	+	0.765097i	$0.722691\pi$
$678$	11200.1	0.634421
$679$	32971.6	1.86352
$680$	−9061.20	−0.511002
$681$	8229.78	0.463092
$682$	−4622.64	−0.259545
$683$	−24154.3	−1.35320	−0.676602	−	0.736349i	$-0.736548\pi$
$683$	−24154.3	−1.35320	−0.676602	+	0.736349i	$0.736548\pi$
$684$	−8087.39	−0.452089
$685$	−40076.6	−2.23540
$686$	17992.5	1.00140
$687$	7545.70	0.419048
$688$	27888.4	1.54540
$689$	4678.32	0.258679
$690$	−19285.7	−1.06405
$691$	−26243.8	−1.44481	−0.722403	−	0.691472i	$-0.756962\pi$
$691$	−26243.8	−1.44481	−0.722403	+	0.691472i	$0.756962\pi$
$692$	23419.0	1.28650
$693$	2127.17	0.116601
$694$	9848.46	0.538678
$695$	13071.5	0.713426
$696$	−967.863	−0.0527108
$697$	−6944.89	−0.377412
$698$	10136.0	0.549649
$699$	11471.1	0.620712
$700$	26100.7	1.40931
$701$	575.408	0.0310027	0.0155013	−	0.999880i	$-0.495066\pi$
$701$	575.408	0.0310027	0.0155013	+	0.999880i	$0.495066\pi$
$702$	1174.47	0.0631446
$703$	36645.1	1.96600
$704$	−2445.13	−0.130901
$705$	−6306.05	−0.336879
$706$	−22528.4	−1.20094
$707$	16456.4	0.875400
$708$	11559.0	0.613578
$709$	−32812.4	−1.73808	−0.869038	−	0.494746i	$-0.835261\pi$
$709$	−32812.4	−1.73808	−0.869038	+	0.494746i	$0.835261\pi$
$710$	−16921.4	−0.894435
$711$	−10142.6	−0.534987
$712$	3836.96	0.201961
$713$	10677.4	0.560832
$714$	15573.1	0.816257
$715$	−2327.46	−0.121737
$716$	−23209.8	−1.21144
$717$	−15135.9	−0.788368
$718$	−16146.4	−0.839248
$719$	28306.6	1.46823	0.734114	−	0.679026i	$-0.237598\pi$
$719$	28306.6	1.46823	0.734114	+	0.679026i	$0.237598\pi$
$720$	12461.9	0.645039
$721$	−37524.4	−1.93825
$722$	−59985.7	−3.09202
$723$	3320.86	0.170822
$724$	−22934.1	−1.17726
$725$	8564.70	0.438738
$726$	1355.04	0.0692701
$727$	−2693.45	−0.137406	−0.0687032	−	0.997637i	$-0.521886\pi$
$727$	−2693.45	−0.137406	−0.0687032	+	0.997637i	$0.521886\pi$
$728$	1930.59	0.0982862
$729$	729.000	0.0370370
$730$	1891.00	0.0958756
$731$	−23668.9	−1.19758
$732$	1086.00	0.0548355
$733$	−33679.6	−1.69711	−0.848557	−	0.529104i	$-0.822528\pi$
$733$	−33679.6	−1.69711	−0.848557	+	0.529104i	$0.822528\pi$
$734$	−39370.6	−1.97983
$735$	6464.43	0.324414
$736$	21148.3	1.05915
$737$	−596.984	−0.0298374
$738$	3605.05	0.179815
$739$	−31746.4	−1.58026	−0.790128	−	0.612942i	$-0.789986\pi$
$739$	−31746.4	−1.58026	−0.790128	+	0.612942i	$0.789986\pi$
$740$	26077.2	1.29543
$741$	5293.51	0.262432
$742$	−32200.9	−1.59317
$743$	6207.35	0.306495	0.153247	−	0.988188i	$-0.451027\pi$
$743$	6207.35	0.306495	0.153247	+	0.988188i	$0.451027\pi$
$744$	−2604.13	−0.128323
$745$	31556.5	1.55187
$746$	23199.9	1.13862
$747$	11850.6	0.580442
$748$	4224.85	0.206519
$749$	46184.8	2.25308
$750$	−16205.2	−0.788975
$751$	29579.7	1.43726	0.718628	−	0.695395i	$-0.244771\pi$
$751$	29579.7	1.43726	0.718628	+	0.695395i	$0.244771\pi$
$752$	8828.07	0.428094
$753$	−3920.23	−0.189723
$754$	−1820.05	−0.0879075
$755$	−21583.2	−1.04039
$756$	−3442.78	−0.165625
$757$	−12812.7	−0.615175	−0.307587	−	0.951520i	$-0.599522\pi$
$757$	−12812.7	−0.615175	−0.307587	+	0.951520i	$0.599522\pi$
$758$	14145.5	0.677819
$759$	−3129.88	−0.149681
$760$	21199.9	1.01184
$761$	23959.6	1.14131	0.570653	−	0.821191i	$-0.306690\pi$
$761$	23959.6	1.14131	0.570653	+	0.821191i	$0.306690\pi$
$762$	15884.6	0.755170
$763$	41950.9	1.99047
$764$	−1383.87	−0.0655323
$765$	−10576.5	−0.499859
$766$	34823.5	1.64259
$767$	−7565.80	−0.356173
$768$	−16019.0	−0.752650
$769$	−18171.3	−0.852111	−0.426055	−	0.904697i	$-0.640097\pi$
$769$	−18171.3	−0.852111	−0.426055	+	0.904697i	$0.640097\pi$
$770$	16019.9	0.749764
$771$	−6984.77	−0.326265
$772$	4072.81	0.189875
$773$	−9799.78	−0.455982	−0.227991	−	0.973663i	$-0.573216\pi$
$773$	−9799.78	−0.455982	−0.227991	+	0.973663i	$0.573216\pi$
$774$	12286.4	0.570575
$775$	23044.2	1.06809
$776$	11832.1	0.547353
$777$	15599.7	0.720252
$778$	−18367.3	−0.846402
$779$	16248.5	0.747320
$780$	3766.95	0.172921
$781$	−2746.18	−0.125821
$782$	−22913.9	−1.04783
$783$	−1129.71	−0.0515615
$784$	−9049.79	−0.412254
$785$	−14257.8	−0.648257
$786$	−23756.5	−1.07808
$787$	−35736.0	−1.61862	−0.809308	−	0.587384i	$-0.800158\pi$
$787$	−35736.0	−1.61862	−0.809308	+	0.587384i	$0.800158\pi$
$788$	25209.2	1.13964
$789$	2029.59	0.0915782
$790$	−76384.6	−3.44005
$791$	21489.4	0.965959
$792$	763.349	0.0342480
$793$	−710.827	−0.0318313
$794$	45637.6	2.03982
$795$	21869.2	0.975625
$796$	−14501.0	−0.645696
$797$	−16976.2	−0.754490	−0.377245	−	0.926114i	$-0.623128\pi$
$797$	−16976.2	−0.754490	−0.377245	+	0.926114i	$0.623128\pi$
$798$	−36435.2	−1.61628
$799$	−7492.40	−0.331742
$800$	45642.5	2.01713
$801$	4478.60	0.197557
$802$	−35778.9	−1.57531
$803$	306.891	0.0134869
$804$	966.204	0.0423823
$805$	−37003.1	−1.62011
$806$	−4897.01	−0.214007
$807$	18614.1	0.811956
$808$	5905.50	0.257122
$809$	31523.3	1.36996	0.684982	−	0.728560i	$-0.259810\pi$
$809$	31523.3	1.36996	0.684982	+	0.728560i	$0.259810\pi$
$810$	5490.17	0.238154
$811$	16284.0	0.705068	0.352534	−	0.935799i	$-0.385320\pi$
$811$	16284.0	0.705068	0.352534	+	0.935799i	$0.385320\pi$
$812$	5335.18	0.230577
$813$	−3643.83	−0.157189
$814$	9937.21	0.427886
$815$	1259.75	0.0541435
$816$	14806.4	0.635203
$817$	55376.6	2.37133
$818$	−40823.6	−1.74494
$819$	2253.43	0.0961431
$820$	11562.7	0.492422
$821$	34644.1	1.47270	0.736351	−	0.676600i	$-0.236547\pi$
$821$	34644.1	1.47270	0.736351	+	0.676600i	$0.236547\pi$
$822$	24717.2	1.04880
$823$	1822.31	0.0771833	0.0385917	−	0.999255i	$-0.487713\pi$
$823$	1822.31	0.0771833	0.0385917	+	0.999255i	$0.487713\pi$
$824$	−13465.9	−0.569303
$825$	−6754.95	−0.285063
$826$	52075.4	2.19362
$827$	−27079.9	−1.13864	−0.569322	−	0.822114i	$-0.692794\pi$
$827$	−27079.9	−1.13864	−0.569322	+	0.822114i	$0.692794\pi$
$828$	5065.64	0.212613
$829$	−21092.7	−0.883690	−0.441845	−	0.897092i	$-0.645676\pi$
$829$	−21092.7	−0.883690	−0.441845	+	0.897092i	$0.645676\pi$
$830$	89247.8	3.73233
$831$	−19043.4	−0.794954
$832$	−2590.26	−0.107934
$833$	7680.58	0.319467
$834$	−8061.86	−0.334724
$835$	69552.9	2.88261
$836$	−9884.59	−0.408930
$837$	−3039.60	−0.125524
$838$	26481.6	1.09164
$839$	−13650.7	−0.561709	−0.280854	−	0.959750i	$-0.590618\pi$
$839$	−13650.7	−0.561709	−0.280854	+	0.959750i	$0.590618\pi$
$840$	9024.71	0.370693
$841$	−22638.3	−0.928218
$842$	−25344.7	−1.03734
$843$	23175.3	0.946855
$844$	23032.7	0.939358
$845$	37426.4	1.52368
$846$	3889.26	0.158056
$847$	2599.88	0.105470
$848$	−30615.5	−1.23979
$849$	−960.432	−0.0388244
$850$	−49453.1	−1.99556
$851$	−22953.1	−0.924586
$852$	4444.62	0.178721
$853$	−20881.2	−0.838169	−0.419085	−	0.907947i	$-0.637649\pi$
$853$	−20881.2	−0.838169	−0.419085	+	0.907947i	$0.637649\pi$
$854$	4892.62	0.196045
$855$	24745.0	0.989779
$856$	16573.7	0.661773
$857$	19566.5	0.779904	0.389952	−	0.920835i	$-0.372492\pi$
$857$	19566.5	0.779904	0.389952	+	0.920835i	$0.372492\pi$
$858$	1435.46	0.0571165
$859$	35364.2	1.40467	0.702336	−	0.711846i	$-0.252141\pi$
$859$	35364.2	1.40467	0.702336	+	0.711846i	$0.252141\pi$
$860$	39406.8	1.56251
$861$	6916.92	0.273784
$862$	42988.5	1.69860
$863$	25043.7	0.987831	0.493915	−	0.869510i	$-0.335565\pi$
$863$	25043.7	0.987831	0.493915	+	0.869510i	$0.335565\pi$
$864$	−6020.39	−0.237058
$865$	−71655.1	−2.81659
$866$	33452.9	1.31267
$867$	2172.81	0.0851126
$868$	14354.8	0.561330
$869$	−12396.5	−0.483914
$870$	−8507.98	−0.331549
$871$	−632.417	−0.0246024
$872$	15054.4	0.584639
$873$	13810.7	0.535418
$874$	53610.1	2.07482
$875$	−31092.6	−1.20128
$876$	−496.696	−0.0191573
$877$	−1236.74	−0.0476188	−0.0238094	−	0.999717i	$-0.507579\pi$
$877$	−1236.74	−0.0476188	−0.0238094	+	0.999717i	$0.507579\pi$
$878$	14180.1	0.545052
$879$	288.126	0.0110560
$880$	15231.2	0.583460
$881$	−24475.3	−0.935977	−0.467988	−	0.883735i	$-0.655021\pi$
$881$	−24475.3	−0.935977	−0.467988	+	0.883735i	$0.655021\pi$
$882$	−3986.94	−0.152208
$883$	2176.53	0.0829516	0.0414758	−	0.999140i	$-0.486794\pi$
$883$	2176.53	0.0829516	0.0414758	+	0.999140i	$0.486794\pi$
$884$	4475.62	0.170284
$885$	−35367.0	−1.34333
$886$	−51446.2	−1.95075
$887$	−6214.01	−0.235226	−0.117613	−	0.993059i	$-0.537524\pi$
$887$	−6214.01	−0.235226	−0.117613	+	0.993059i	$0.537524\pi$
$888$	5598.05	0.211552
$889$	30477.5	1.14981
$890$	33728.7	1.27033
$891$	891.000	0.0335013
$892$	35201.1	1.32132
$893$	17529.4	0.656888
$894$	−19462.5	−0.728101
$895$	71015.0	2.65226
$896$	−20499.5	−0.764329
$897$	−3315.66	−0.123419
$898$	28558.0	1.06124
$899$	4710.39	0.174750
$900$	10932.7	0.404915
$901$	25983.5	0.960749
$902$	4406.17	0.162649
$903$	23573.6	0.868750
$904$	7711.60	0.283721
$905$	70171.3	2.57743
$906$	13311.5	0.488127
$907$	19056.9	0.697657	0.348828	−	0.937187i	$-0.386580\pi$
$907$	19056.9	0.697657	0.348828	+	0.937187i	$0.386580\pi$
$908$	−16279.6	−0.594998
$909$	6893.04	0.251516
$910$	16970.8	0.618216
$911$	1157.05	0.0420800	0.0210400	−	0.999779i	$-0.493302\pi$
$911$	1157.05	0.0420800	0.0210400	+	0.999779i	$0.493302\pi$
$912$	−34641.4	−1.25778
$913$	14484.0	0.525029
$914$	32636.7	1.18110
$915$	−3322.83	−0.120054
$916$	−14926.4	−0.538409
$917$	−45581.1	−1.64146
$918$	6523.03	0.234523
$919$	23983.0	0.860856	0.430428	−	0.902625i	$-0.358363\pi$
$919$	23983.0	0.860856	0.430428	+	0.902625i	$0.358363\pi$
$920$	−13278.8	−0.475858
$921$	−7970.99	−0.285182
$922$	51020.7	1.82243
$923$	−2909.17	−0.103745
$924$	−4207.84	−0.149814
$925$	−49537.6	−1.76085
$926$	−8832.77	−0.313459
$927$	−15717.7	−0.556889
$928$	9329.65	0.330023
$929$	45349.4	1.60158	0.800788	−	0.598948i	$-0.204414\pi$
$929$	45349.4	1.60158	0.800788	+	0.598948i	$0.204414\pi$
$930$	−22891.5	−0.807143
$931$	−17969.7	−0.632582
$932$	−22691.5	−0.797514
$933$	9265.45	0.325120
$934$	−3469.81	−0.121558
$935$	−12926.8	−0.452140
$936$	808.658	0.0282391
$937$	−34987.0	−1.21982	−0.609912	−	0.792469i	$-0.708795\pi$
$937$	−34987.0	−1.21982	−0.609912	+	0.792469i	$0.708795\pi$
$938$	4352.93	0.151523
$939$	17073.8	0.593379
$940$	12474.2	0.432835
$941$	−11745.0	−0.406881	−0.203441	−	0.979087i	$-0.565212\pi$
$941$	−11745.0	−0.406881	−0.203441	+	0.979087i	$0.565212\pi$
$942$	8793.48	0.304148
$943$	−10177.4	−0.351456
$944$	49511.5	1.70706
$945$	10533.9	0.362610
$946$	15016.7	0.516105
$947$	8633.78	0.296262	0.148131	−	0.988968i	$-0.452674\pi$
$947$	8633.78	0.296262	0.148131	+	0.988968i	$0.452674\pi$
$948$	20063.4	0.687371
$949$	325.106	0.0111205
$950$	115702.	3.95144
$951$	21304.4	0.726439
$952$	10722.5	0.365041
$953$	−45101.2	−1.53302	−0.766512	−	0.642230i	$-0.778009\pi$
$953$	−45101.2	−1.53302	−0.766512	+	0.642230i	$0.778009\pi$
$954$	−13487.9	−0.457742
$955$	4234.23	0.143473
$956$	29940.9	1.01293
$957$	−1380.76	−0.0466391
$958$	−28276.9	−0.953636
$959$	47424.4	1.59689
$960$	−12108.4	−0.407080
$961$	−17117.2	−0.574577
$962$	10527.0	0.352812
$963$	19345.2	0.647343
$964$	−6569.12	−0.219478
$965$	−12461.6	−0.415702
$966$	22821.7	0.760119
$967$	−46013.2	−1.53018	−0.765090	−	0.643924i	$-0.777305\pi$
$967$	−46013.2	−1.53018	−0.765090	+	0.643924i	$0.777305\pi$
$968$	932.983	0.0309785
$969$	29400.2	0.974687
$970$	104009.	3.44283
$971$	22609.1	0.747232	0.373616	−	0.927584i	$-0.378118\pi$
$971$	22609.1	0.747232	0.373616	+	0.927584i	$0.378118\pi$
$972$	−1442.06	−0.0475866
$973$	−15468.1	−0.509645
$974$	58816.5	1.93491
$975$	−7155.88	−0.235048
$976$	4651.74	0.152560
$977$	−1821.95	−0.0596616	−0.0298308	−	0.999555i	$-0.509497\pi$
$977$	−1821.95	−0.0596616	−0.0298308	+	0.999555i	$0.509497\pi$
$978$	−776.949	−0.0254029
$979$	5473.84	0.178697
$980$	−12787.5	−0.416819
$981$	17571.8	0.571891
$982$	−57142.0	−1.85690
$983$	6596.08	0.214021	0.107010	−	0.994258i	$-0.465872\pi$
$983$	6596.08	0.214021	0.107010	+	0.994258i	$0.465872\pi$
$984$	2482.18	0.0804157
$985$	−77132.5	−2.49507
$986$	−10108.6	−0.326493
$987$	7462.23	0.240654
$988$	−10471.3	−0.337182
$989$	−34685.8	−1.11521
$990$	6710.21	0.215419
$991$	−7601.18	−0.243652	−0.121826	−	0.992551i	$-0.538875\pi$
$991$	−7601.18	−0.243652	−0.121826	+	0.992551i	$0.538875\pi$
$992$	25102.3	0.803427
$993$	29363.3	0.938386
$994$	20023.8	0.638951
$995$	44368.7	1.41365
$996$	−23442.1	−0.745773
$997$	33274.3	1.05698	0.528490	−	0.848940i	$-0.322758\pi$
$997$	33274.3	1.05698	0.528490	+	0.848940i	$0.322758\pi$
$998$	34186.8	1.08433
$999$	6534.18	0.206939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.9	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.9	✓	37	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)

\(f(q)\)	\(=\)	\(q-3.73288 q^{2} -3.00000 q^{3} +5.93441 q^{4} -18.1575 q^{5} +11.1986 q^{6} +21.4866 q^{7} +7.71060 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.73288 q^{2} -3.00000 q^{3} +5.93441 q^{4} -18.1575 q^{5} +11.1986 q^{6} +21.4866 q^{7} +7.71060 q^{8} +9.00000 q^{9} +67.7799 q^{10} +11.0000 q^{11} -17.8032 q^{12} +11.6529 q^{13} -80.2069 q^{14} +54.4725 q^{15} -76.2581 q^{16} +64.7204 q^{17} -33.5959 q^{18} -151.422 q^{19} -107.754 q^{20} -64.4598 q^{21} -41.0617 q^{22} +94.8450 q^{23} -23.1318 q^{24} +204.695 q^{25} -43.4989 q^{26} -27.0000 q^{27} +127.510 q^{28} +41.8412 q^{29} -203.340 q^{30} +112.578 q^{31} +222.978 q^{32} -33.0000 q^{33} -241.594 q^{34} -390.143 q^{35} +53.4097 q^{36} -242.007 q^{37} +565.240 q^{38} -34.9587 q^{39} -140.005 q^{40} -107.306 q^{41} +240.621 q^{42} -365.711 q^{43} +65.2785 q^{44} -163.418 q^{45} -354.045 q^{46} -115.766 q^{47} +228.774 q^{48} +118.673 q^{49} -764.104 q^{50} -194.161 q^{51} +69.1531 q^{52} +401.473 q^{53} +100.788 q^{54} -199.733 q^{55} +165.674 q^{56} +454.265 q^{57} -156.188 q^{58} -649.263 q^{59} +323.262 q^{60} -61.0000 q^{61} -420.240 q^{62} +193.379 q^{63} -222.285 q^{64} -211.588 q^{65} +123.185 q^{66} -54.2713 q^{67} +384.077 q^{68} -284.535 q^{69} +1456.36 q^{70} -249.652 q^{71} +69.3954 q^{72} +27.8992 q^{73} +903.382 q^{74} -614.086 q^{75} -898.599 q^{76} +236.352 q^{77} +130.497 q^{78} -1126.95 q^{79} +1384.66 q^{80} +81.0000 q^{81} +400.561 q^{82} +1316.73 q^{83} -382.531 q^{84} -1175.16 q^{85} +1365.16 q^{86} -125.524 q^{87} +84.8166 q^{88} +497.622 q^{89} +610.019 q^{90} +250.381 q^{91} +562.849 q^{92} -337.734 q^{93} +432.140 q^{94} +2749.44 q^{95} -668.933 q^{96} +1534.52 q^{97} -442.993 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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