LMFDB - Embedded newform 2001.4.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61295 q^{2} +3.00000 q^{3} -5.39841 q^{4} -4.25187 q^{5} -4.83884 q^{6} -1.08998 q^{7} +21.6109 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.61295 q^{2} +3.00000 q^{3} -5.39841 q^{4} -4.25187 q^{5} -4.83884 q^{6} -1.08998 q^{7} +21.6109 q^{8} +9.00000 q^{9} +6.85803 q^{10} +22.8896 q^{11} -16.1952 q^{12} -68.3858 q^{13} +1.75808 q^{14} -12.7556 q^{15} +8.33005 q^{16} +31.2425 q^{17} -14.5165 q^{18} -35.7402 q^{19} +22.9533 q^{20} -3.26994 q^{21} -36.9197 q^{22} +23.0000 q^{23} +64.8327 q^{24} -106.922 q^{25} +110.303 q^{26} +27.0000 q^{27} +5.88416 q^{28} -29.0000 q^{29} +20.5741 q^{30} +222.093 q^{31} -186.323 q^{32} +68.6688 q^{33} -50.3924 q^{34} +4.63445 q^{35} -48.5857 q^{36} -215.756 q^{37} +57.6471 q^{38} -205.157 q^{39} -91.8866 q^{40} +241.952 q^{41} +5.27424 q^{42} -151.590 q^{43} -123.567 q^{44} -38.2668 q^{45} -37.0977 q^{46} +573.095 q^{47} +24.9902 q^{48} -341.812 q^{49} +172.459 q^{50} +93.7274 q^{51} +369.174 q^{52} +272.743 q^{53} -43.5495 q^{54} -97.3235 q^{55} -23.5555 q^{56} -107.221 q^{57} +46.7754 q^{58} -136.221 q^{59} +68.8599 q^{60} -522.676 q^{61} -358.224 q^{62} -9.80983 q^{63} +233.889 q^{64} +290.767 q^{65} -110.759 q^{66} +102.378 q^{67} -168.660 q^{68} +69.0000 q^{69} -7.47512 q^{70} -883.564 q^{71} +194.498 q^{72} +685.056 q^{73} +348.003 q^{74} -320.765 q^{75} +192.940 q^{76} -24.9492 q^{77} +330.908 q^{78} -374.025 q^{79} -35.4183 q^{80} +81.0000 q^{81} -390.255 q^{82} +338.449 q^{83} +17.6525 q^{84} -132.839 q^{85} +244.506 q^{86} -87.0000 q^{87} +494.665 q^{88} +547.883 q^{89} +61.7222 q^{90} +74.5392 q^{91} -124.163 q^{92} +666.280 q^{93} -924.371 q^{94} +151.963 q^{95} -558.969 q^{96} -1766.64 q^{97} +551.324 q^{98} +206.006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) $ 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * 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 $

$2$	−1.61295	−0.570262	−0.285131	−	0.958489i	$-0.592037\pi$
$2$	−1.61295	−0.570262	−0.285131	+	0.958489i	$0.592037\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.39841	−0.674801
$5$	−4.25187	−0.380298	−0.190149	−	0.981755i	$-0.560897\pi$
$5$	−4.25187	−0.380298	−0.190149	+	0.981755i	$0.560897\pi$
$6$	−4.83884	−0.329241
$7$	−1.08998	−0.0588534	−0.0294267	−	0.999567i	$-0.509368\pi$
$7$	−1.08998	−0.0588534	−0.0294267	+	0.999567i	$0.509368\pi$
$8$	21.6109	0.955076
$9$	9.00000	0.333333
$10$	6.85803	0.216870
$11$	22.8896	0.627406	0.313703	−	0.949521i	$-0.398430\pi$
$11$	22.8896	0.627406	0.313703	+	0.949521i	$0.398430\pi$
$12$	−16.1952	−0.389596
$13$	−68.3858	−1.45899	−0.729493	−	0.683989i	$-0.760244\pi$
$13$	−68.3858	−1.45899	−0.729493	+	0.683989i	$0.760244\pi$
$14$	1.75808	0.0335619
$15$	−12.7556	−0.219565
$16$	8.33005	0.130157
$17$	31.2425	0.445730	0.222865	−	0.974849i	$-0.428459\pi$
$17$	31.2425	0.445730	0.222865	+	0.974849i	$0.428459\pi$
$18$	−14.5165	−0.190087
$19$	−35.7402	−0.431546	−0.215773	−	0.976444i	$-0.569227\pi$
$19$	−35.7402	−0.431546	−0.215773	+	0.976444i	$0.569227\pi$
$20$	22.9533	0.256626
$21$	−3.26994	−0.0339791
$22$	−36.9197	−0.357786
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	64.8327	0.551413
$25$	−106.922	−0.855373
$26$	110.303	0.832004
$27$	27.0000	0.192450
$28$	5.88416	0.0397144
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	20.5741	0.125210
$31$	222.093	1.28675	0.643373	−	0.765553i	$-0.277534\pi$
$31$	222.093	1.28675	0.643373	+	0.765553i	$0.277534\pi$
$32$	−186.323	−1.02930
$33$	68.6688	0.362233
$34$	−50.3924	−0.254183
$35$	4.63445	0.0223819
$36$	−48.5857	−0.224934
$37$	−215.756	−0.958650	−0.479325	−	0.877637i	$-0.659119\pi$
$37$	−215.756	−0.958650	−0.479325	+	0.877637i	$0.659119\pi$
$38$	57.6471	0.246094
$39$	−205.157	−0.842345
$40$	−91.8866	−0.363214
$41$	241.952	0.921623	0.460812	−	0.887498i	$-0.347558\pi$
$41$	241.952	0.921623	0.460812	+	0.887498i	$0.347558\pi$
$42$	5.27424	0.0193770
$43$	−151.590	−0.537609	−0.268804	−	0.963195i	$-0.586629\pi$
$43$	−151.590	−0.537609	−0.268804	+	0.963195i	$0.586629\pi$
$44$	−123.567	−0.423374
$45$	−38.2668	−0.126766
$46$	−37.0977	−0.118908
$47$	573.095	1.77861	0.889303	−	0.457319i	$-0.151190\pi$
$47$	573.095	1.77861	0.889303	+	0.457319i	$0.151190\pi$
$48$	24.9902	0.0751462
$49$	−341.812	−0.996536
$50$	172.459	0.487787
$51$	93.7274	0.257342
$52$	369.174	0.984524
$53$	272.743	0.706870	0.353435	−	0.935459i	$-0.385013\pi$
$53$	272.743	0.706870	0.353435	+	0.935459i	$0.385013\pi$
$54$	−43.5495	−0.109747
$55$	−97.3235	−0.238602
$56$	−23.5555	−0.0562095
$57$	−107.221	−0.249153
$58$	46.7754	0.105895
$59$	−136.221	−0.300585	−0.150293	−	0.988642i	$-0.548022\pi$
$59$	−136.221	−0.300585	−0.150293	+	0.988642i	$0.548022\pi$
$60$	68.8599	0.148163
$61$	−522.676	−1.09708	−0.548539	−	0.836125i	$-0.684816\pi$
$61$	−522.676	−1.09708	−0.548539	+	0.836125i	$0.684816\pi$
$62$	−358.224	−0.733783
$63$	−9.80983	−0.0196178
$64$	233.889	0.456814
$65$	290.767	0.554850
$66$	−110.759	−0.206568
$67$	102.378	0.186679	0.0933394	−	0.995634i	$-0.470246\pi$
$67$	102.378	0.186679	0.0933394	+	0.995634i	$0.470246\pi$
$68$	−168.660	−0.300779
$69$	69.0000	0.120386
$70$	−7.47512	−0.0127635
$71$	−883.564	−1.47690	−0.738449	−	0.674309i	$-0.764442\pi$
$71$	−883.564	−1.47690	−0.738449	+	0.674309i	$0.764442\pi$
$72$	194.498	0.318359
$73$	685.056	1.09835	0.549176	−	0.835707i	$-0.314942\pi$
$73$	685.056	1.09835	0.549176	+	0.835707i	$0.314942\pi$
$74$	348.003	0.546682
$75$	−320.765	−0.493850
$76$	192.940	0.291208
$77$	−24.9492	−0.0369250
$78$	330.908	0.480358
$79$	−374.025	−0.532673	−0.266336	−	0.963880i	$-0.585813\pi$
$79$	−374.025	−0.532673	−0.266336	+	0.963880i	$0.585813\pi$
$80$	−35.4183	−0.0494985
$81$	81.0000	0.111111
$82$	−390.255	−0.525567
$83$	338.449	0.447585	0.223793	−	0.974637i	$-0.428156\pi$
$83$	338.449	0.447585	0.223793	+	0.974637i	$0.428156\pi$
$84$	17.6525	0.0229291
$85$	−132.839	−0.169510
$86$	244.506	0.306578
$87$	−87.0000	−0.107211
$88$	494.665	0.599221
$89$	547.883	0.652534	0.326267	−	0.945278i	$-0.394209\pi$
$89$	547.883	0.652534	0.326267	+	0.945278i	$0.394209\pi$
$90$	61.7222	0.0722899
$91$	74.5392	0.0858663
$92$	−124.163	−0.140706
$93$	666.280	0.742904
$94$	−924.371	−1.01427
$95$	151.963	0.164116
$96$	−558.969	−0.594266
$97$	−1766.64	−1.84923	−0.924613	−	0.380909i	$-0.875611\pi$
$97$	−1766.64	−1.84923	−0.924613	+	0.380909i	$0.875611\pi$
$98$	551.324	0.568287
$99$	206.006	0.209135
$100$	577.207	0.577207
$101$	1340.30	1.32044	0.660222	−	0.751070i	$-0.270462\pi$
$101$	1340.30	1.32044	0.660222	+	0.751070i	$0.270462\pi$
$102$	−151.177	−0.146753
$103$	425.222	0.406781	0.203390	−	0.979098i	$-0.434804\pi$
$103$	425.222	0.406781	0.203390	+	0.979098i	$0.434804\pi$
$104$	−1477.88	−1.39344
$105$	13.9034	0.0129222
$106$	−439.920	−0.403102
$107$	−2030.68	−1.83471	−0.917353	−	0.398076i	$-0.869678\pi$
$107$	−2030.68	−1.83471	−0.917353	+	0.398076i	$0.869678\pi$
$108$	−145.757	−0.129865
$109$	−847.197	−0.744466	−0.372233	−	0.928139i	$-0.621408\pi$
$109$	−847.197	−0.744466	−0.372233	+	0.928139i	$0.621408\pi$
$110$	156.977	0.136066
$111$	−647.268	−0.553477
$112$	−9.07960	−0.00766019
$113$	−637.405	−0.530637	−0.265319	−	0.964161i	$-0.585477\pi$
$113$	−637.405	−0.530637	−0.265319	+	0.964161i	$0.585477\pi$
$114$	172.941	0.142083
$115$	−97.7929	−0.0792977
$116$	156.554	0.125307
$117$	−615.472	−0.486328
$118$	219.718	0.171412
$119$	−34.0537	−0.0262328
$120$	−275.660	−0.209702
$121$	−807.067	−0.606361
$122$	843.047	0.625622
$123$	725.856	0.532099
$124$	−1198.95	−0.868298
$125$	986.100	0.705595
$126$	15.8227	0.0111873
$127$	−1391.00	−0.971897	−0.485948	−	0.873988i	$-0.661526\pi$
$127$	−1391.00	−0.971897	−0.485948	+	0.873988i	$0.661526\pi$
$128$	1113.34	0.768796
$129$	−454.769	−0.310389
$130$	−468.992	−0.316410
$131$	647.135	0.431606	0.215803	−	0.976437i	$-0.430763\pi$
$131$	647.135	0.431606	0.215803	+	0.976437i	$0.430763\pi$
$132$	−370.702	−0.244435
$133$	38.9562	0.0253980
$134$	−165.130	−0.106456
$135$	−114.800	−0.0731885
$136$	675.178	0.425706
$137$	2025.55	1.26317	0.631587	−	0.775305i	$-0.282404\pi$
$137$	2025.55	1.26317	0.631587	+	0.775305i	$0.282404\pi$
$138$	−111.293	−0.0686515
$139$	1085.59	0.662434	0.331217	−	0.943555i	$-0.392541\pi$
$139$	1085.59	0.662434	0.331217	+	0.943555i	$0.392541\pi$
$140$	−25.0187	−0.0151033
$141$	1719.28	1.02688
$142$	1425.14	0.842220
$143$	−1565.32	−0.915377
$144$	74.9705	0.0433857
$145$	123.304	0.0706196
$146$	−1104.96	−0.626349
$147$	−1025.44	−0.575350
$148$	1164.74	0.646898
$149$	−148.545	−0.0816728	−0.0408364	−	0.999166i	$-0.513002\pi$
$149$	−148.545	−0.0816728	−0.0408364	+	0.999166i	$0.513002\pi$
$150$	517.376	0.281624
$151$	474.108	0.255512	0.127756	−	0.991806i	$-0.459223\pi$
$151$	474.108	0.255512	0.127756	+	0.991806i	$0.459223\pi$
$152$	−772.379	−0.412159
$153$	281.182	0.148577
$154$	40.2417	0.0210570
$155$	−944.311	−0.489348
$156$	1107.52	0.568415
$157$	3537.02	1.79799	0.898996	−	0.437956i	$-0.144297\pi$
$157$	3537.02	1.79799	0.898996	+	0.437956i	$0.144297\pi$
$158$	603.283	0.303763
$159$	818.229	0.408112
$160$	792.221	0.391441
$161$	−25.0696	−0.0122718
$162$	−130.649	−0.0633625
$163$	1543.88	0.741877	0.370939	−	0.928657i	$-0.379036\pi$
$163$	1543.88	0.741877	0.370939	+	0.928657i	$0.379036\pi$
$164$	−1306.16	−0.621912
$165$	−291.970	−0.137757
$166$	−545.899	−0.255241
$167$	543.383	0.251786	0.125893	−	0.992044i	$-0.459820\pi$
$167$	543.383	0.251786	0.125893	+	0.992044i	$0.459820\pi$
$168$	−70.6664	−0.0324526
$169$	2479.62	1.12864
$170$	214.262	0.0966654
$171$	−321.662	−0.143849
$172$	818.342	0.362779
$173$	1420.72	0.624365	0.312183	−	0.950022i	$-0.398940\pi$
$173$	1420.72	0.624365	0.312183	+	0.950022i	$0.398940\pi$
$174$	140.326	0.0611385
$175$	116.543	0.0503417
$176$	190.671	0.0816614
$177$	−408.664	−0.173543
$178$	−883.706	−0.372116
$179$	545.197	0.227653	0.113827	−	0.993501i	$-0.463689\pi$
$179$	545.197	0.227653	0.113827	+	0.993501i	$0.463689\pi$
$180$	206.580	0.0855419
$181$	−520.582	−0.213782	−0.106891	−	0.994271i	$-0.534090\pi$
$181$	−520.582	−0.213782	−0.106891	+	0.994271i	$0.534090\pi$
$182$	−120.228	−0.0489663
$183$	−1568.03	−0.633398
$184$	497.051	0.199147
$185$	917.365	0.364573
$186$	−1074.67	−0.423650
$187$	715.127	0.279654
$188$	−3093.80	−1.20020
$189$	−29.4295	−0.0113264
$190$	−245.107	−0.0935893
$191$	−15.3094	−0.00579973	−0.00289986	−	0.999996i	$-0.500923\pi$
$191$	−15.3094	−0.00579973	−0.00289986	+	0.999996i	$0.500923\pi$
$192$	701.666	0.263742
$193$	2736.54	1.02062	0.510311	−	0.859990i	$-0.329530\pi$
$193$	2736.54	1.02062	0.510311	+	0.859990i	$0.329530\pi$
$194$	2849.49	1.05454
$195$	872.302	0.320343
$196$	1845.24	0.672464
$197$	3145.36	1.13755	0.568776	−	0.822492i	$-0.307417\pi$
$197$	3145.36	1.13755	0.568776	+	0.822492i	$0.307417\pi$
$198$	−332.277	−0.119262
$199$	4618.16	1.64509	0.822544	−	0.568702i	$-0.192554\pi$
$199$	4618.16	1.64509	0.822544	+	0.568702i	$0.192554\pi$
$200$	−2310.67	−0.816946
$201$	307.134	0.107779
$202$	−2161.83	−0.753000
$203$	31.6094	0.0109288
$204$	−505.979	−0.173655
$205$	−1028.75	−0.350492
$206$	−685.861	−0.231972
$207$	207.000	0.0695048
$208$	−569.657	−0.189897
$209$	−818.079	−0.270755
$210$	−22.4254	−0.00736903
$211$	398.425	0.129994	0.0649970	−	0.997885i	$-0.479296\pi$
$211$	398.425	0.129994	0.0649970	+	0.997885i	$0.479296\pi$
$212$	−1472.38	−0.476997
$213$	−2650.69	−0.852688
$214$	3275.38	1.04626
$215$	644.538	0.204452
$216$	583.494	0.183804
$217$	−242.078	−0.0757295
$218$	1366.48	0.424541
$219$	2055.17	0.634134
$220$	525.392	0.161009
$221$	−2136.54	−0.650314
$222$	1044.01	0.315627
$223$	799.181	0.239987	0.119994	−	0.992775i	$-0.461713\pi$
$223$	799.181	0.239987	0.119994	+	0.992775i	$0.461713\pi$
$224$	203.089	0.0605778
$225$	−962.295	−0.285124
$226$	1028.10	0.302602
$227$	−1122.13	−0.328098	−0.164049	−	0.986452i	$-0.552455\pi$
$227$	−1122.13	−0.328098	−0.164049	+	0.986452i	$0.552455\pi$
$228$	578.821	0.168129
$229$	3868.84	1.11642	0.558209	−	0.829700i	$-0.311489\pi$
$229$	3868.84	1.11642	0.558209	+	0.829700i	$0.311489\pi$
$230$	157.735	0.0452205
$231$	−74.8477	−0.0213187
$232$	−626.716	−0.177353
$233$	3117.16	0.876447	0.438223	−	0.898866i	$-0.355608\pi$
$233$	3117.16	0.876447	0.438223	+	0.898866i	$0.355608\pi$
$234$	992.723	0.277335
$235$	−2436.72	−0.676401
$236$	735.379	0.202835
$237$	−1122.08	−0.307539
$238$	54.9268	0.0149596
$239$	−1046.12	−0.283128	−0.141564	−	0.989929i	$-0.545213\pi$
$239$	−1046.12	−0.283128	−0.141564	+	0.989929i	$0.545213\pi$
$240$	−106.255	−0.0285780
$241$	6937.72	1.85435	0.927174	−	0.374630i	$-0.122230\pi$
$241$	6937.72	1.85435	0.927174	+	0.374630i	$0.122230\pi$
$242$	1301.75	0.345785
$243$	243.000	0.0641500
$244$	2821.62	0.740309
$245$	1453.34	0.378981
$246$	−1170.77	−0.303436
$247$	2444.12	0.629619
$248$	4799.64	1.22894
$249$	1015.35	0.258413
$250$	−1590.52	−0.402374
$251$	304.501	0.0765733	0.0382867	−	0.999267i	$-0.487810\pi$
$251$	304.501	0.0765733	0.0382867	+	0.999267i	$0.487810\pi$
$252$	52.9574	0.0132381
$253$	526.461	0.130823
$254$	2243.60	0.554236
$255$	−398.516	−0.0978669
$256$	−3666.86	−0.895229
$257$	3143.20	0.762909	0.381454	−	0.924388i	$-0.375423\pi$
$257$	3143.20	0.762909	0.381454	+	0.924388i	$0.375423\pi$
$258$	733.517	0.177003
$259$	235.170	0.0564199
$260$	−1569.68	−0.374413
$261$	−261.000	−0.0618984
$262$	−1043.79	−0.246129
$263$	−976.563	−0.228964	−0.114482	−	0.993425i	$-0.536521\pi$
$263$	−976.563	−0.228964	−0.114482	+	0.993425i	$0.536521\pi$
$264$	1483.99	0.345960
$265$	−1159.67	−0.268822
$266$	−62.8342	−0.0144835
$267$	1643.65	0.376741
$268$	−552.679	−0.125971
$269$	6429.80	1.45737	0.728683	−	0.684851i	$-0.240133\pi$
$269$	6429.80	1.45737	0.728683	+	0.684851i	$0.240133\pi$
$270$	185.167	0.0417366
$271$	−48.5457	−0.0108817	−0.00544086	−	0.999985i	$-0.501732\pi$
$271$	−48.5457	−0.0108817	−0.00544086	+	0.999985i	$0.501732\pi$
$272$	260.251	0.0580149
$273$	223.618	0.0495749
$274$	−3267.11	−0.720340
$275$	−2447.39	−0.536667
$276$	−372.490	−0.0812365
$277$	−6975.44	−1.51305	−0.756523	−	0.653967i	$-0.773103\pi$
$277$	−6975.44	−1.51305	−0.756523	+	0.653967i	$0.773103\pi$
$278$	−1750.99	−0.377761
$279$	1998.84	0.428916
$280$	100.155	0.0213764
$281$	205.255	0.0435747	0.0217873	−	0.999763i	$-0.493064\pi$
$281$	205.255	0.0435747	0.0217873	+	0.999763i	$0.493064\pi$
$282$	−2773.11	−0.585590
$283$	−2008.42	−0.421865	−0.210933	−	0.977501i	$-0.567650\pi$
$283$	−2008.42	−0.421865	−0.210933	+	0.977501i	$0.567650\pi$
$284$	4769.84	0.996612
$285$	455.888	0.0947525
$286$	2524.78	0.522005
$287$	−263.723	−0.0542407
$288$	−1676.91	−0.343100
$289$	−3936.91	−0.801325
$290$	−198.883	−0.0402717
$291$	−5299.91	−1.06765
$292$	−3698.21	−0.741169
$293$	3348.02	0.667554	0.333777	−	0.942652i	$-0.391677\pi$
$293$	3348.02	0.667554	0.333777	+	0.942652i	$0.391677\pi$
$294$	1653.97	0.328101
$295$	579.195	0.114312
$296$	−4662.68	−0.915584
$297$	618.019	0.120744
$298$	239.594	0.0465749
$299$	−1572.87	−0.304219
$300$	1731.62	0.333250
$301$	165.230	0.0316401
$302$	−764.710	−0.145709
$303$	4020.90	0.762359
$304$	−297.718	−0.0561687
$305$	2222.35	0.417217
$306$	−453.532	−0.0847277
$307$	4556.89	0.847151	0.423575	−	0.905861i	$-0.360775\pi$
$307$	4556.89	0.847151	0.423575	+	0.905861i	$0.360775\pi$
$308$	134.686	0.0249170
$309$	1275.67	0.234855
$310$	1523.12	0.279057
$311$	264.284	0.0481871	0.0240935	−	0.999710i	$-0.492330\pi$
$311$	264.284	0.0481871	0.0240935	+	0.999710i	$0.492330\pi$
$312$	−4433.64	−0.804504
$313$	−2934.07	−0.529851	−0.264925	−	0.964269i	$-0.585347\pi$
$313$	−2934.07	−0.529851	−0.264925	+	0.964269i	$0.585347\pi$
$314$	−5705.02	−1.02533
$315$	41.7101	0.00746062
$316$	2019.14	0.359448
$317$	−9227.56	−1.63492	−0.817462	−	0.575982i	$-0.804620\pi$
$317$	−9227.56	−1.63492	−0.817462	+	0.575982i	$0.804620\pi$
$318$	−1319.76	−0.232731
$319$	−663.798	−0.116506
$320$	−994.463	−0.173726
$321$	−6092.05	−1.05927
$322$	40.4358	0.00699814
$323$	−1116.61	−0.192353
$324$	−437.271	−0.0749779
$325$	7311.92	1.24798
$326$	−2490.19	−0.423065
$327$	−2541.59	−0.429817
$328$	5228.80	0.880220
$329$	−624.662	−0.104677
$330$	470.932	0.0785575
$331$	6883.56	1.14307	0.571533	−	0.820579i	$-0.306349\pi$
$331$	6883.56	1.14307	0.571533	+	0.820579i	$0.306349\pi$
$332$	−1827.08	−0.302031
$333$	−1941.80	−0.319550
$334$	−876.447	−0.143584
$335$	−435.298	−0.0709936
$336$	−27.2388	−0.00442261
$337$	−1102.15	−0.178154	−0.0890772	−	0.996025i	$-0.528392\pi$
$337$	−1102.15	−0.178154	−0.0890772	+	0.996025i	$0.528392\pi$
$338$	−3999.49	−0.643620
$339$	−1912.21	−0.306364
$340$	717.118	0.114386
$341$	5083.63	0.807313
$342$	518.823	0.0820315
$343$	746.432	0.117503
$344$	−3275.99	−0.513457
$345$	−293.379	−0.0457825
$346$	−2291.54	−0.356052
$347$	−502.782	−0.0777831	−0.0388916	−	0.999243i	$-0.512383\pi$
$347$	−502.782	−0.0777831	−0.0388916	+	0.999243i	$0.512383\pi$
$348$	469.661	0.0723462
$349$	12539.3	1.92325	0.961624	−	0.274372i	$-0.0884700\pi$
$349$	12539.3	1.92325	0.961624	+	0.274372i	$0.0884700\pi$
$350$	−187.977	−0.0287079
$351$	−1846.42	−0.280782
$352$	−4264.86	−0.645789
$353$	2370.75	0.357456	0.178728	−	0.983898i	$-0.442802\pi$
$353$	2370.75	0.357456	0.178728	+	0.983898i	$0.442802\pi$
$354$	659.153	0.0989650
$355$	3756.80	0.561662
$356$	−2957.70	−0.440330
$357$	−102.161	−0.0151455
$358$	−879.373	−0.129822
$359$	−3727.83	−0.548042	−0.274021	−	0.961724i	$-0.588354\pi$
$359$	−3727.83	−0.548042	−0.274021	+	0.961724i	$0.588354\pi$
$360$	−826.980	−0.121071
$361$	−5581.64	−0.813768
$362$	839.671	0.121912
$363$	−2421.20	−0.350083
$364$	−402.393	−0.0579427
$365$	−2912.77	−0.417702
$366$	2529.14	0.361203
$367$	5040.68	0.716953	0.358476	−	0.933539i	$-0.383296\pi$
$367$	5040.68	0.716953	0.358476	+	0.933539i	$0.383296\pi$
$368$	191.591	0.0271396
$369$	2177.57	0.307208
$370$	−1479.66	−0.207902
$371$	−297.285	−0.0416018
$372$	−3596.85	−0.501312
$373$	5786.14	0.803203	0.401602	−	0.915815i	$-0.368454\pi$
$373$	5786.14	0.803203	0.401602	+	0.915815i	$0.368454\pi$
$374$	−1153.46	−0.159476
$375$	2958.30	0.407376
$376$	12385.1	1.69870
$377$	1983.19	0.270927
$378$	47.4682	0.00645899
$379$	3250.22	0.440508	0.220254	−	0.975443i	$-0.429311\pi$
$379$	3250.22	0.440508	0.220254	+	0.975443i	$0.429311\pi$
$380$	−820.356	−0.110746
$381$	−4172.99	−0.561125
$382$	24.6932	0.00330737
$383$	4689.80	0.625685	0.312843	−	0.949805i	$-0.398719\pi$
$383$	4689.80	0.625685	0.312843	+	0.949805i	$0.398719\pi$
$384$	3340.01	0.443865
$385$	106.081	0.0140425
$386$	−4413.88	−0.582023
$387$	−1364.31	−0.179203
$388$	9537.03	1.24786
$389$	−2790.76	−0.363746	−0.181873	−	0.983322i	$-0.558216\pi$
$389$	−2790.76	−0.363746	−0.181873	+	0.983322i	$0.558216\pi$
$390$	−1406.97	−0.182679
$391$	718.577	0.0929412
$392$	−7386.86	−0.951768
$393$	1941.40	0.249188
$394$	−5073.30	−0.648703
$395$	1590.31	0.202575
$396$	−1112.11	−0.141125
$397$	−10249.6	−1.29575	−0.647873	−	0.761748i	$-0.724341\pi$
$397$	−10249.6	−1.29575	−0.647873	+	0.761748i	$0.724341\pi$
$398$	−7448.84	−0.938132
$399$	116.869	0.0146635
$400$	−890.663	−0.111333
$401$	13109.7	1.63259	0.816296	−	0.577634i	$-0.196024\pi$
$401$	13109.7	1.63259	0.816296	+	0.577634i	$0.196024\pi$
$402$	−495.391	−0.0614623
$403$	−15188.0	−1.87734
$404$	−7235.49	−0.891037
$405$	−344.401	−0.0422554
$406$	−50.9843	−0.00623229
$407$	−4938.57	−0.601463
$408$	2025.53	0.245782
$409$	11156.5	1.34879	0.674396	−	0.738370i	$-0.264404\pi$
$409$	11156.5	1.34879	0.674396	+	0.738370i	$0.264404\pi$
$410$	1659.31	0.199872
$411$	6076.66	0.729294
$412$	−2295.52	−0.274496
$413$	148.479	0.0176905
$414$	−333.880	−0.0396360
$415$	−1439.04	−0.170216
$416$	12741.9	1.50173
$417$	3256.76	0.382456
$418$	1319.52	0.154401
$419$	14938.6	1.74176	0.870882	−	0.491492i	$-0.163548\pi$
$419$	14938.6	1.74176	0.870882	+	0.491492i	$0.163548\pi$
$420$	−75.0560	−0.00871990
$421$	−119.874	−0.0138772	−0.00693861	−	0.999976i	$-0.502209\pi$
$421$	−119.874	−0.0138772	−0.00693861	+	0.999976i	$0.502209\pi$
$422$	−642.639	−0.0741307
$423$	5157.85	0.592869
$424$	5894.22	0.675115
$425$	−3340.50	−0.381266
$426$	4275.42	0.486256
$427$	569.706	0.0645668
$428$	10962.4	1.23806
$429$	−4695.97	−0.528493
$430$	−1039.60	−0.116591
$431$	9603.35	1.07326	0.536632	−	0.843816i	$-0.319696\pi$
$431$	9603.35	1.07326	0.536632	+	0.843816i	$0.319696\pi$
$432$	224.911	0.0250487
$433$	4206.70	0.466885	0.233442	−	0.972371i	$-0.425001\pi$
$433$	4206.70	0.466885	0.233442	+	0.972371i	$0.425001\pi$
$434$	390.458	0.0431857
$435$	369.912	0.0407723
$436$	4573.51	0.502366
$437$	−822.025	−0.0899835
$438$	−3314.87	−0.361623
$439$	−4779.32	−0.519600	−0.259800	−	0.965662i	$-0.583657\pi$
$439$	−4779.32	−0.519600	−0.259800	+	0.965662i	$0.583657\pi$
$440$	−2103.25	−0.227883
$441$	−3076.31	−0.332179
$442$	3446.12	0.370849
$443$	3809.10	0.408523	0.204262	−	0.978916i	$-0.434521\pi$
$443$	3809.10	0.408523	0.204262	+	0.978916i	$0.434521\pi$
$444$	3494.22	0.373487
$445$	−2329.53	−0.248158
$446$	−1289.04	−0.136856
$447$	−445.634	−0.0471538
$448$	−254.934	−0.0268851
$449$	−10526.3	−1.10639	−0.553194	−	0.833052i	$-0.686591\pi$
$449$	−10526.3	−1.10639	−0.553194	+	0.833052i	$0.686591\pi$
$450$	1552.13	0.162596
$451$	5538.18	0.578232
$452$	3440.97	0.358074
$453$	1422.32	0.147520
$454$	1809.93	0.187102
$455$	−316.931	−0.0326548
$456$	−2317.14	−0.237960
$457$	13571.1	1.38912	0.694561	−	0.719434i	$-0.255599\pi$
$457$	13571.1	1.38912	0.694561	+	0.719434i	$0.255599\pi$
$458$	−6240.22	−0.636651
$459$	843.547	0.0857808
$460$	527.926	0.0535102
$461$	−1622.93	−0.163964	−0.0819821	−	0.996634i	$-0.526125\pi$
$461$	−1622.93	−0.163964	−0.0819821	+	0.996634i	$0.526125\pi$
$462$	120.725	0.0121572
$463$	17796.9	1.78638	0.893189	−	0.449682i	$-0.148463\pi$
$463$	17796.9	1.78638	0.893189	+	0.449682i	$0.148463\pi$
$464$	−241.571	−0.0241696
$465$	−2832.93	−0.282525
$466$	−5027.81	−0.499805
$467$	−14312.2	−1.41818	−0.709088	−	0.705120i	$-0.750893\pi$
$467$	−14312.2	−1.41818	−0.709088	+	0.705120i	$0.750893\pi$
$468$	3322.57	0.328175
$469$	−111.590	−0.0109867
$470$	3930.30	0.385726
$471$	10611.1	1.03807
$472$	−2943.87	−0.287082
$473$	−3469.82	−0.337299
$474$	1809.85	0.175378
$475$	3821.40	0.369133
$476$	183.836	0.0177019
$477$	2454.69	0.235623
$478$	1687.33	0.161457
$479$	5256.58	0.501418	0.250709	−	0.968062i	$-0.419336\pi$
$479$	5256.58	0.501418	0.250709	+	0.968062i	$0.419336\pi$
$480$	2376.66	0.225999
$481$	14754.6	1.39866
$482$	−11190.2	−1.05747
$483$	−75.2087	−0.00708512
$484$	4356.87	0.409173
$485$	7511.50	0.703257
$486$	−391.946	−0.0365823
$487$	13150.3	1.22360	0.611802	−	0.791011i	$-0.290445\pi$
$487$	13150.3	1.22360	0.611802	+	0.791011i	$0.290445\pi$
$488$	−11295.5	−1.04779
$489$	4631.64	0.428323
$490$	−2344.16	−0.216119
$491$	12601.5	1.15825	0.579124	−	0.815239i	$-0.303395\pi$
$491$	12601.5	1.15825	0.579124	+	0.815239i	$0.303395\pi$
$492$	−3918.47	−0.359061
$493$	−906.032	−0.0827700
$494$	−3942.24	−0.359048
$495$	−875.911	−0.0795339
$496$	1850.05	0.167479
$497$	963.068	0.0869206
$498$	−1637.70	−0.147363
$499$	−20081.1	−1.80151	−0.900756	−	0.434326i	$-0.856987\pi$
$499$	−20081.1	−1.80151	−0.900756	+	0.434326i	$0.856987\pi$
$500$	−5323.37	−0.476136
$501$	1630.15	0.145369
$502$	−491.143	−0.0436669
$503$	10363.1	0.918628	0.459314	−	0.888274i	$-0.348095\pi$
$503$	10363.1	0.918628	0.459314	+	0.888274i	$0.348095\pi$
$504$	−211.999	−0.0187365
$505$	−5698.78	−0.502163
$506$	−849.152	−0.0746036
$507$	7438.85	0.651619
$508$	7509.16	0.655837
$509$	9838.89	0.856781	0.428390	−	0.903594i	$-0.359081\pi$
$509$	9838.89	0.856781	0.428390	+	0.903594i	$0.359081\pi$
$510$	642.785	0.0558098
$511$	−746.698	−0.0646418
$512$	−2992.24	−0.258280
$513$	−964.986	−0.0830511
$514$	−5069.81	−0.435058
$515$	−1807.99	−0.154698
$516$	2455.03	0.209451
$517$	13117.9	1.11591
$518$	−379.316	−0.0321741
$519$	4262.16	0.360478
$520$	6283.74	0.529924
$521$	18499.1	1.55558	0.777792	−	0.628522i	$-0.216340\pi$
$521$	18499.1	1.55558	0.777792	+	0.628522i	$0.216340\pi$
$522$	420.979	0.0352984
$523$	−16117.5	−1.34755	−0.673777	−	0.738934i	$-0.735329\pi$
$523$	−16117.5	−1.34755	−0.673777	+	0.738934i	$0.735329\pi$
$524$	−3493.50	−0.291248
$525$	349.628	0.0290648
$526$	1575.14	0.130569
$527$	6938.75	0.573542
$528$	572.014	0.0471472
$529$	529.000	0.0434783
$530$	1870.48	0.153299
$531$	−1225.99	−0.100195
$532$	−210.301	−0.0171386
$533$	−16546.1	−1.34463
$534$	−2651.12	−0.214841
$535$	8634.19	0.697735
$536$	2212.48	0.178292
$537$	1635.59	0.131436
$538$	−10370.9	−0.831081
$539$	−7823.94	−0.625233
$540$	619.739	0.0493876
$541$	−9773.37	−0.776691	−0.388346	−	0.921514i	$-0.626953\pi$
$541$	−9773.37	−0.776691	−0.388346	+	0.921514i	$0.626953\pi$
$542$	78.3016	0.00620543
$543$	−1561.75	−0.123427
$544$	−5821.20	−0.458790
$545$	3602.17	0.283119
$546$	−360.683	−0.0282707
$547$	−1982.14	−0.154936	−0.0774682	−	0.996995i	$-0.524684\pi$
$547$	−1982.14	−0.154936	−0.0774682	+	0.996995i	$0.524684\pi$
$548$	−10934.8	−0.852391
$549$	−4704.08	−0.365693
$550$	3947.51	0.306041
$551$	1036.47	0.0801361
$552$	1491.15	0.114978
$553$	407.681	0.0313496
$554$	11251.0	0.862833
$555$	2752.10	0.210486
$556$	−5860.44	−0.447011
$557$	−6982.02	−0.531127	−0.265564	−	0.964093i	$-0.585558\pi$
$557$	−6982.02	−0.531127	−0.265564	+	0.964093i	$0.585558\pi$
$558$	−3224.02	−0.244594
$559$	10366.6	0.784363
$560$	38.6052	0.00291316
$561$	2145.38	0.161458
$562$	−331.065	−0.0248490
$563$	−8583.89	−0.642571	−0.321286	−	0.946982i	$-0.604115\pi$
$563$	−8583.89	−0.642571	−0.321286	+	0.946982i	$0.604115\pi$
$564$	−9281.40	−0.692938
$565$	2710.16	0.201800
$566$	3239.46	0.240574
$567$	−88.2885	−0.00653927
$568$	−19094.6	−1.41055
$569$	19273.3	1.42000	0.709998	−	0.704204i	$-0.248696\pi$
$569$	19273.3	1.42000	0.709998	+	0.704204i	$0.248696\pi$
$570$	−735.322	−0.0540338
$571$	−9773.14	−0.716275	−0.358138	−	0.933669i	$-0.616588\pi$
$571$	−9773.14	−0.716275	−0.358138	+	0.933669i	$0.616588\pi$
$572$	8450.25	0.617697
$573$	−45.9281	−0.00334847
$574$	425.371	0.0309314
$575$	−2459.20	−0.178358
$576$	2105.00	0.152271
$577$	7560.77	0.545510	0.272755	−	0.962084i	$-0.412065\pi$
$577$	7560.77	0.545510	0.272755	+	0.962084i	$0.412065\pi$
$578$	6350.02	0.456965
$579$	8209.61	0.589257
$580$	−665.646	−0.0476542
$581$	−368.903	−0.0263419
$582$	8548.47	0.608841
$583$	6242.98	0.443495
$584$	14804.7	1.04901
$585$	2616.90	0.184950
$586$	−5400.17	−0.380681
$587$	−12574.4	−0.884157	−0.442079	−	0.896976i	$-0.645759\pi$
$587$	−12574.4	−0.884157	−0.442079	+	0.896976i	$0.645759\pi$
$588$	5535.72	0.388247
$589$	−7937.67	−0.555290
$590$	−934.210	−0.0651878
$591$	9436.09	0.656766
$592$	−1797.26	−0.124775
$593$	6814.52	0.471904	0.235952	−	0.971765i	$-0.424179\pi$
$593$	6814.52	0.471904	0.235952	+	0.971765i	$0.424179\pi$
$594$	−996.831	−0.0688560
$595$	144.792	0.00997627
$596$	801.904	0.0551129
$597$	13854.5	0.949792
$598$	2536.96	0.173485
$599$	−20362.2	−1.38895	−0.694473	−	0.719519i	$-0.744362\pi$
$599$	−20362.2	−1.38895	−0.694473	+	0.719519i	$0.744362\pi$
$600$	−6932.02	−0.471664
$601$	9813.03	0.666026	0.333013	−	0.942922i	$-0.391935\pi$
$601$	9813.03	0.666026	0.333013	+	0.942922i	$0.391935\pi$
$602$	−266.506	−0.0180432
$603$	921.403	0.0622263
$604$	−2559.43	−0.172420
$605$	3431.54	0.230598
$606$	−6485.50	−0.434745
$607$	9725.74	0.650339	0.325169	−	0.945656i	$-0.394579\pi$
$607$	9725.74	0.650339	0.325169	+	0.945656i	$0.394579\pi$
$608$	6659.23	0.444190
$609$	94.8283	0.00630975
$610$	−3584.52	−0.237923
$611$	−39191.5	−2.59496
$612$	−1517.94	−0.100260
$613$	−4750.62	−0.313011	−0.156505	−	0.987677i	$-0.550023\pi$
$613$	−4750.62	−0.313011	−0.156505	+	0.987677i	$0.550023\pi$
$614$	−7350.01	−0.483098
$615$	−3086.24	−0.202357
$616$	−539.175	−0.0352662
$617$	10168.0	0.663450	0.331725	−	0.943376i	$-0.392369\pi$
$617$	10168.0	0.663450	0.331725	+	0.943376i	$0.392369\pi$
$618$	−2057.58	−0.133929
$619$	−3398.99	−0.220706	−0.110353	−	0.993892i	$-0.535198\pi$
$619$	−3398.99	−0.220706	−0.110353	+	0.993892i	$0.535198\pi$
$620$	5097.78	0.330212
$621$	621.000	0.0401286
$622$	−426.276	−0.0274793
$623$	−597.182	−0.0384039
$624$	−1708.97	−0.109637
$625$	9172.44	0.587036
$626$	4732.49	0.302154
$627$	−2454.24	−0.156320
$628$	−19094.3	−1.21329
$629$	−6740.75	−0.427299
$630$	−67.2761	−0.00425451
$631$	−9137.70	−0.576491	−0.288246	−	0.957556i	$-0.593072\pi$
$631$	−9137.70	−0.576491	−0.288246	+	0.957556i	$0.593072\pi$
$632$	−8083.03	−0.508743
$633$	1195.28	0.0750521
$634$	14883.5	0.932336
$635$	5914.32	0.369611
$636$	−4417.13	−0.275394
$637$	23375.1	1.45393
$638$	1070.67	0.0664392
$639$	−7952.08	−0.492300
$640$	−4733.75	−0.292372
$641$	−26373.1	−1.62508	−0.812539	−	0.582907i	$-0.801915\pi$
$641$	−26373.1	−1.62508	−0.812539	+	0.582907i	$0.801915\pi$
$642$	9826.14	0.604060
$643$	29005.5	1.77895	0.889474	−	0.456985i	$-0.151071\pi$
$643$	29005.5	1.77895	0.889474	+	0.456985i	$0.151071\pi$
$644$	135.336	0.00828102
$645$	1933.61	0.118040
$646$	1801.04	0.109692
$647$	−10655.3	−0.647457	−0.323728	−	0.946150i	$-0.604936\pi$
$647$	−10655.3	−0.647457	−0.323728	+	0.946150i	$0.604936\pi$
$648$	1750.48	0.106120
$649$	−3118.05	−0.188589
$650$	−11793.7	−0.711674
$651$	−726.233	−0.0437224
$652$	−8334.49	−0.500619
$653$	−9657.16	−0.578735	−0.289368	−	0.957218i	$-0.593445\pi$
$653$	−9657.16	−0.578735	−0.289368	+	0.957218i	$0.593445\pi$
$654$	4099.45	0.245109
$655$	−2751.53	−0.164139
$656$	2015.47	0.119956
$657$	6165.50	0.366117
$658$	1007.55	0.0596934
$659$	−28114.8	−1.66191	−0.830953	−	0.556342i	$-0.812204\pi$
$659$	−28114.8	−1.66191	−0.830953	+	0.556342i	$0.812204\pi$
$660$	1576.17	0.0929584
$661$	29442.5	1.73249	0.866247	−	0.499615i	$-0.166525\pi$
$661$	29442.5	1.73249	0.866247	+	0.499615i	$0.166525\pi$
$662$	−11102.8	−0.651847
$663$	−6409.62	−0.375459
$664$	7314.18	0.427478
$665$	−165.636	−0.00965880
$666$	3132.02	0.182227
$667$	−667.000	−0.0387202
$668$	−2933.40	−0.169905
$669$	2397.54	0.138557
$670$	702.112	0.0404850
$671$	−11963.8	−0.688314
$672$	609.266	0.0349746
$673$	−17702.2	−1.01392	−0.506962	−	0.861968i	$-0.669232\pi$
$673$	−17702.2	−1.01392	−0.506962	+	0.861968i	$0.669232\pi$
$674$	1777.71	0.101595
$675$	−2886.88	−0.164617
$676$	−13386.0	−0.761606
$677$	18130.4	1.02926	0.514630	−	0.857412i	$-0.327929\pi$
$677$	18130.4	1.02926	0.514630	+	0.857412i	$0.327929\pi$
$678$	3084.30	0.174708
$679$	1925.60	0.108833
$680$	−2870.77	−0.161895
$681$	−3366.38	−0.189427
$682$	−8199.61	−0.460380
$683$	−2048.97	−0.114790	−0.0573951	−	0.998352i	$-0.518279\pi$
$683$	−2048.97	−0.114790	−0.0573951	+	0.998352i	$0.518279\pi$
$684$	1736.46	0.0970692
$685$	−8612.38	−0.480383
$686$	−1203.95	−0.0670076
$687$	11606.5	0.644565
$688$	−1262.75	−0.0699736
$689$	−18651.7	−1.03131
$690$	473.204	0.0261081
$691$	23959.5	1.31905	0.659525	−	0.751682i	$-0.270757\pi$
$691$	23959.5	1.31905	0.659525	+	0.751682i	$0.270757\pi$
$692$	−7669.62	−0.421322
$693$	−224.543	−0.0123083
$694$	810.960	0.0443568
$695$	−4615.77	−0.251922
$696$	−1880.15	−0.102395
$697$	7559.18	0.410795
$698$	−20225.2	−1.09676
$699$	9351.49	0.506017
$700$	−629.144	−0.0339706
$701$	−1623.30	−0.0874627	−0.0437313	−	0.999043i	$-0.513925\pi$
$701$	−1623.30	−0.0874627	−0.0437313	+	0.999043i	$0.513925\pi$
$702$	2978.17	0.160119
$703$	7711.17	0.413702
$704$	5353.61	0.286608
$705$	−7310.16	−0.390520
$706$	−3823.88	−0.203844
$707$	−1460.90	−0.0777127
$708$	2206.14	0.117107
$709$	4962.49	0.262864	0.131432	−	0.991325i	$-0.458043\pi$
$709$	4962.49	0.262864	0.131432	+	0.991325i	$0.458043\pi$
$710$	−6059.51	−0.320295
$711$	−3366.23	−0.177558
$712$	11840.3	0.623219
$713$	5108.15	0.268305
$714$	164.780	0.00863690
$715$	6655.54	0.348116
$716$	−2943.20	−0.153621
$717$	−3138.35	−0.163464
$718$	6012.78	0.312528
$719$	2695.17	0.139795	0.0698976	−	0.997554i	$-0.477733\pi$
$719$	2695.17	0.139795	0.0698976	+	0.997554i	$0.477733\pi$
$720$	−318.764	−0.0164995
$721$	−463.484	−0.0239404
$722$	9002.87	0.464061
$723$	20813.2	1.07061
$724$	2810.31	0.144260
$725$	3100.73	0.158839
$726$	3905.26	0.199639
$727$	−963.542	−0.0491552	−0.0245776	−	0.999698i	$-0.507824\pi$
$727$	−963.542	−0.0491552	−0.0245776	+	0.999698i	$0.507824\pi$
$728$	1610.86	0.0820088
$729$	729.000	0.0370370
$730$	4698.13	0.238200
$731$	−4736.03	−0.239629
$732$	8464.85	0.427418
$733$	−9241.44	−0.465676	−0.232838	−	0.972516i	$-0.574801\pi$
$733$	−9241.44	−0.465676	−0.232838	+	0.972516i	$0.574801\pi$
$734$	−8130.35	−0.408851
$735$	4360.01	0.218805
$736$	−4285.43	−0.214624
$737$	2343.39	0.117123
$738$	−3512.30	−0.175189
$739$	−23802.9	−1.18485	−0.592426	−	0.805625i	$-0.701830\pi$
$739$	−23802.9	−1.18485	−0.592426	+	0.805625i	$0.701830\pi$
$740$	−4952.31	−0.246014
$741$	7332.37	0.363511
$742$	479.504	0.0237239
$743$	−15368.1	−0.758817	−0.379409	−	0.925229i	$-0.623873\pi$
$743$	−15368.1	−0.758817	−0.379409	+	0.925229i	$0.623873\pi$
$744$	14398.9	0.709529
$745$	631.592	0.0310600
$746$	−9332.72	−0.458036
$747$	3046.04	0.149195
$748$	−3860.55	−0.188711
$749$	2213.41	0.107979
$750$	−4771.57	−0.232311
$751$	16637.4	0.808400	0.404200	−	0.914671i	$-0.367550\pi$
$751$	16637.4	0.808400	0.404200	+	0.914671i	$0.367550\pi$
$752$	4773.91	0.231498
$753$	913.502	0.0442096
$754$	−3198.77	−0.154499
$755$	−2015.84	−0.0971709
$756$	158.872	0.00764303
$757$	28921.9	1.38862	0.694310	−	0.719677i	$-0.255710\pi$
$757$	28921.9	1.38862	0.694310	+	0.719677i	$0.255710\pi$
$758$	−5242.43	−0.251205
$759$	1579.38	0.0755309
$760$	3284.05	0.156743
$761$	−26378.0	−1.25651	−0.628255	−	0.778008i	$-0.716230\pi$
$761$	−26378.0	−1.25651	−0.628255	+	0.778008i	$0.716230\pi$
$762$	6730.80	0.319988
$763$	923.428	0.0438144
$764$	82.6463	0.00391366
$765$	−1195.55	−0.0565035
$766$	−7564.39	−0.356805
$767$	9315.61	0.438549
$768$	−11000.6	−0.516861
$769$	−20197.1	−0.947108	−0.473554	−	0.880765i	$-0.657029\pi$
$769$	−20197.1	−0.947108	−0.473554	+	0.880765i	$0.657029\pi$
$770$	−171.102	−0.00800793
$771$	9429.60	0.440466
$772$	−14772.9	−0.688717
$773$	−12515.0	−0.582322	−0.291161	−	0.956674i	$-0.594042\pi$
$773$	−12515.0	−0.582322	−0.291161	+	0.956674i	$0.594042\pi$
$774$	2200.55	0.102193
$775$	−23746.6	−1.10065
$776$	−38178.6	−1.76615
$777$	705.510	0.0325740
$778$	4501.35	0.207431
$779$	−8647.42	−0.397723
$780$	−4709.04	−0.216167
$781$	−20224.4	−0.926616
$782$	−1159.03	−0.0530008
$783$	−783.000	−0.0357371
$784$	−2847.31	−0.129706
$785$	−15038.9	−0.683774
$786$	−3131.38	−0.142103
$787$	31629.2	1.43260	0.716301	−	0.697791i	$-0.245834\pi$
$787$	31629.2	1.43260	0.716301	+	0.697791i	$0.245834\pi$
$788$	−16979.9	−0.767621
$789$	−2929.69	−0.132192
$790$	−2565.08	−0.115521
$791$	694.759	0.0312298
$792$	4451.98	0.199740
$793$	35743.6	1.60062
$794$	16532.0	0.738916
$795$	−3479.00	−0.155204
$796$	−24930.7	−1.11011
$797$	−21243.2	−0.944133	−0.472066	−	0.881563i	$-0.656492\pi$
$797$	−21243.2	−0.944133	−0.472066	+	0.881563i	$0.656492\pi$
$798$	−188.503	−0.00836205
$799$	17904.9	0.792778
$800$	19922.0	0.880435
$801$	4930.95	0.217511
$802$	−21145.3	−0.931006
$803$	15680.6	0.689113
$804$	−1658.04	−0.0727294
$805$	106.592	0.00466694
$806$	24497.5	1.07058
$807$	19289.4	0.841411
$808$	28965.1	1.26113
$809$	27674.8	1.20271	0.601356	−	0.798981i	$-0.294627\pi$
$809$	27674.8	1.20271	0.601356	+	0.798981i	$0.294627\pi$
$810$	555.500	0.0240966
$811$	25869.4	1.12009	0.560047	−	0.828461i	$-0.310783\pi$
$811$	25869.4	1.12009	0.560047	+	0.828461i	$0.310783\pi$
$812$	−170.641	−0.00737477
$813$	−145.637	−0.00628256
$814$	7965.64	0.342992
$815$	−6564.37	−0.282135
$816$	780.754	0.0334949
$817$	5417.85	0.232003
$818$	−17994.9	−0.769165
$819$	670.853	0.0286221
$820$	5553.60	0.236512
$821$	−1173.99	−0.0499059	−0.0249529	−	0.999689i	$-0.507944\pi$
$821$	−1173.99	−0.0499059	−0.0249529	+	0.999689i	$0.507944\pi$
$822$	−9801.33	−0.415889
$823$	26667.8	1.12950	0.564751	−	0.825262i	$-0.308972\pi$
$823$	26667.8	1.12950	0.564751	+	0.825262i	$0.308972\pi$
$824$	9189.44	0.388506
$825$	−7342.18	−0.309845
$826$	−239.488	−0.0100882
$827$	−40206.9	−1.69061	−0.845303	−	0.534287i	$-0.820580\pi$
$827$	−40206.9	−1.69061	−0.845303	+	0.534287i	$0.820580\pi$
$828$	−1117.47	−0.0469019
$829$	−29089.0	−1.21870	−0.609349	−	0.792902i	$-0.708569\pi$
$829$	−29089.0	−1.21870	−0.609349	+	0.792902i	$0.708569\pi$
$830$	2321.09	0.0970677
$831$	−20926.3	−0.873557
$832$	−15994.7	−0.666484
$833$	−10679.1	−0.444186
$834$	−5252.98	−0.218100
$835$	−2310.39	−0.0957537
$836$	4416.33	0.182706
$837$	5996.52	0.247635
$838$	−24095.2	−0.993263
$839$	−4362.11	−0.179496	−0.0897478	−	0.995965i	$-0.528606\pi$
$839$	−4362.11	−0.179496	−0.0897478	+	0.995965i	$0.528606\pi$
$840$	300.464	0.0123417
$841$	841.000	0.0344828
$842$	193.350	0.00791365
$843$	615.765	0.0251579
$844$	−2150.86	−0.0877201
$845$	−10543.0	−0.429219
$846$	−8319.34	−0.338091
$847$	879.687	0.0356864
$848$	2271.96	0.0920042
$849$	−6025.25	−0.243564
$850$	5388.04	0.217421
$851$	−4962.39	−0.199892
$852$	14309.5	0.575394
$853$	−885.553	−0.0355460	−0.0177730	−	0.999842i	$-0.505658\pi$
$853$	−885.553	−0.0355460	−0.0177730	+	0.999842i	$0.505658\pi$
$854$	−918.905	−0.0368200
$855$	1367.66	0.0547054
$856$	−43884.9	−1.75228
$857$	−17384.1	−0.692919	−0.346459	−	0.938065i	$-0.612616\pi$
$857$	−17384.1	−0.692919	−0.346459	+	0.938065i	$0.612616\pi$
$858$	7574.34	0.301380
$859$	−12786.0	−0.507863	−0.253931	−	0.967222i	$-0.581724\pi$
$859$	−12786.0	−0.507863	−0.253931	+	0.967222i	$0.581724\pi$
$860$	−3479.48	−0.137964
$861$	−791.169	−0.0313159
$862$	−15489.7	−0.612042
$863$	−32091.0	−1.26581	−0.632904	−	0.774230i	$-0.718137\pi$
$863$	−32091.0	−1.26581	−0.632904	+	0.774230i	$0.718137\pi$
$864$	−5030.72	−0.198089
$865$	−6040.70	−0.237445
$866$	−6785.18	−0.266247
$867$	−11810.7	−0.462645
$868$	1306.83	0.0511023
$869$	−8561.29	−0.334202
$870$	−596.648	−0.0232509
$871$	−7001.21	−0.272362
$872$	−18308.7	−0.711021
$873$	−15899.7	−0.616408
$874$	1325.88	0.0513142
$875$	−1074.83	−0.0415267
$876$	−11094.6	−0.427914
$877$	−1416.37	−0.0545353	−0.0272677	−	0.999628i	$-0.508681\pi$
$877$	−1416.37	−0.0545353	−0.0272677	+	0.999628i	$0.508681\pi$
$878$	7708.78	0.296308
$879$	10044.1	0.385413
$880$	−810.709	−0.0310557
$881$	−28446.9	−1.08785	−0.543927	−	0.839132i	$-0.683063\pi$
$881$	−28446.9	−1.08785	−0.543927	+	0.839132i	$0.683063\pi$
$882$	4961.92	0.189429
$883$	−37602.6	−1.43310	−0.716551	−	0.697535i	$-0.754280\pi$
$883$	−37602.6	−1.43310	−0.716551	+	0.697535i	$0.754280\pi$
$884$	11533.9	0.438832
$885$	1737.59	0.0659981
$886$	−6143.87	−0.232965
$887$	−7840.22	−0.296786	−0.148393	−	0.988929i	$-0.547410\pi$
$887$	−7840.22	−0.296786	−0.148393	+	0.988929i	$0.547410\pi$
$888$	−13988.0	−0.528613
$889$	1516.16	0.0571995
$890$	3757.40	0.141515
$891$	1854.06	0.0697118
$892$	−4314.31	−0.161944
$893$	−20482.5	−0.767550
$894$	718.783	0.0268900
$895$	−2318.10	−0.0865762
$896$	−1213.51	−0.0452463
$897$	−4718.62	−0.175641
$898$	16978.4	0.630932
$899$	−6440.71	−0.238943
$900$	5194.86	0.192402
$901$	8521.17	0.315073
$902$	−8932.79	−0.329744
$903$	495.689	0.0182674
$904$	−13774.9	−0.506799
$905$	2213.44	0.0813010
$906$	−2294.13	−0.0841251
$907$	4420.34	0.161825	0.0809123	−	0.996721i	$-0.474217\pi$
$907$	4420.34	0.161825	0.0809123	+	0.996721i	$0.474217\pi$
$908$	6057.70	0.221401
$909$	12062.7	0.440148
$910$	511.192	0.0186218
$911$	−5727.62	−0.208304	−0.104152	−	0.994561i	$-0.533213\pi$
$911$	−5727.62	−0.208304	−0.104152	+	0.994561i	$0.533213\pi$
$912$	−893.154	−0.0324290
$913$	7746.95	0.280818
$914$	−21889.4	−0.792164
$915$	6667.04	0.240880
$916$	−20885.5	−0.753360
$917$	−705.365	−0.0254015
$918$	−1360.60	−0.0489176
$919$	−51233.1	−1.83898	−0.919492	−	0.393110i	$-0.871399\pi$
$919$	−51233.1	−1.83898	−0.919492	+	0.393110i	$0.871399\pi$
$920$	−2113.39	−0.0757353
$921$	13670.7	0.489103
$922$	2617.70	0.0935026
$923$	60423.3	2.15477
$924$	404.058	0.0143859
$925$	23069.0	0.820004
$926$	−28705.5	−1.01870
$927$	3827.00	0.135594
$928$	5403.37	0.191136
$929$	9928.61	0.350643	0.175321	−	0.984511i	$-0.443904\pi$
$929$	9928.61	0.350643	0.175321	+	0.984511i	$0.443904\pi$
$930$	4569.37	0.161113
$931$	12216.4	0.430051
$932$	−16827.7	−0.591427
$933$	792.853	0.0278208
$934$	23084.7	0.808732
$935$	−3040.63	−0.106352
$936$	−13300.9	−0.464481
$937$	−13269.9	−0.462656	−0.231328	−	0.972876i	$-0.574307\pi$
$937$	−13269.9	−0.462656	−0.231328	+	0.972876i	$0.574307\pi$
$938$	179.989	0.00626529
$939$	−8802.20	−0.305909
$940$	13154.4	0.456436
$941$	51676.0	1.79021	0.895106	−	0.445853i	$-0.147099\pi$
$941$	51676.0	1.79021	0.895106	+	0.445853i	$0.147099\pi$
$942$	−17115.1	−0.591973
$943$	5564.90	0.192172
$944$	−1134.73	−0.0391233
$945$	125.130	0.00430739
$946$	5596.63	0.192349
$947$	16466.8	0.565047	0.282524	−	0.959260i	$-0.408828\pi$
$947$	16466.8	0.565047	0.282524	+	0.959260i	$0.408828\pi$
$948$	6057.43	0.207527
$949$	−46848.1	−1.60248
$950$	−6163.72	−0.210503
$951$	−27682.7	−0.943924
$952$	−735.931	−0.0250543
$953$	37296.4	1.26773	0.633867	−	0.773442i	$-0.281467\pi$
$953$	37296.4	1.26773	0.633867	+	0.773442i	$0.281467\pi$
$954$	−3959.28	−0.134367
$955$	65.0934	0.00220563
$956$	5647.36	0.191055
$957$	−1991.39	−0.0672650
$958$	−8478.58	−0.285940
$959$	−2207.82	−0.0743421
$960$	−2983.39	−0.100300
$961$	19534.5	0.655717
$962$	−23798.4	−0.797601
$963$	−18276.1	−0.611568
$964$	−37452.7	−1.25132
$965$	−11635.4	−0.388141
$966$	121.308	0.00404038
$967$	−15637.5	−0.520030	−0.260015	−	0.965605i	$-0.583727\pi$
$967$	−15637.5	−0.520030	−0.260015	+	0.965605i	$0.583727\pi$
$968$	−17441.4	−0.579121
$969$	−3349.84	−0.111055
$970$	−12115.6	−0.401041
$971$	−11260.7	−0.372165	−0.186083	−	0.982534i	$-0.559579\pi$
$971$	−11260.7	−0.372165	−0.186083	+	0.982534i	$0.559579\pi$
$972$	−1311.81	−0.0432885
$973$	−1183.27	−0.0389865
$974$	−21210.7	−0.697776
$975$	21935.8	0.720520
$976$	−4353.91	−0.142792
$977$	28500.9	0.933290	0.466645	−	0.884445i	$-0.345463\pi$
$977$	28500.9	0.933290	0.466645	+	0.884445i	$0.345463\pi$
$978$	−7470.58	−0.244256
$979$	12540.8	0.409404
$980$	−7845.71	−0.255737
$981$	−7624.77	−0.248155
$982$	−20325.6	−0.660505
$983$	21935.4	0.711730	0.355865	−	0.934537i	$-0.384186\pi$
$983$	21935.4	0.711730	0.355865	+	0.934537i	$0.384186\pi$
$984$	15686.4	0.508195
$985$	−13373.7	−0.432609
$986$	1461.38	0.0472006
$987$	−1873.99	−0.0604353
$988$	−13194.4	−0.424868
$989$	−3486.56	−0.112099
$990$	1412.80	0.0453552
$991$	2256.44	0.0723292	0.0361646	−	0.999346i	$-0.488486\pi$
$991$	2256.44	0.0723292	0.0361646	+	0.999346i	$0.488486\pi$
$992$	−41381.1	−1.32445
$993$	20650.7	0.659949
$994$	−1553.38	−0.0495675
$995$	−19635.8	−0.625624
$996$	−5481.25	−0.174378
$997$	−5289.97	−0.168039	−0.0840196	−	0.996464i	$-0.526776\pi$
$997$	−5289.97	−0.168039	−0.0840196	+	0.996464i	$0.526776\pi$
$998$	32389.8	1.02733
$999$	−5825.41	−0.184492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.h.1.17	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.h.1.17	✓	44	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61295 q^{2} +3.00000 q^{3} -5.39841 q^{4} -4.25187 q^{5} -4.83884 q^{6} -1.08998 q^{7} +21.6109 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.61295 q^{2} +3.00000 q^{3} -5.39841 q^{4} -4.25187 q^{5} -4.83884 q^{6} -1.08998 q^{7} +21.6109 q^{8} +9.00000 q^{9} +6.85803 q^{10} +22.8896 q^{11} -16.1952 q^{12} -68.3858 q^{13} +1.75808 q^{14} -12.7556 q^{15} +8.33005 q^{16} +31.2425 q^{17} -14.5165 q^{18} -35.7402 q^{19} +22.9533 q^{20} -3.26994 q^{21} -36.9197 q^{22} +23.0000 q^{23} +64.8327 q^{24} -106.922 q^{25} +110.303 q^{26} +27.0000 q^{27} +5.88416 q^{28} -29.0000 q^{29} +20.5741 q^{30} +222.093 q^{31} -186.323 q^{32} +68.6688 q^{33} -50.3924 q^{34} +4.63445 q^{35} -48.5857 q^{36} -215.756 q^{37} +57.6471 q^{38} -205.157 q^{39} -91.8866 q^{40} +241.952 q^{41} +5.27424 q^{42} -151.590 q^{43} -123.567 q^{44} -38.2668 q^{45} -37.0977 q^{46} +573.095 q^{47} +24.9902 q^{48} -341.812 q^{49} +172.459 q^{50} +93.7274 q^{51} +369.174 q^{52} +272.743 q^{53} -43.5495 q^{54} -97.3235 q^{55} -23.5555 q^{56} -107.221 q^{57} +46.7754 q^{58} -136.221 q^{59} +68.8599 q^{60} -522.676 q^{61} -358.224 q^{62} -9.80983 q^{63} +233.889 q^{64} +290.767 q^{65} -110.759 q^{66} +102.378 q^{67} -168.660 q^{68} +69.0000 q^{69} -7.47512 q^{70} -883.564 q^{71} +194.498 q^{72} +685.056 q^{73} +348.003 q^{74} -320.765 q^{75} +192.940 q^{76} -24.9492 q^{77} +330.908 q^{78} -374.025 q^{79} -35.4183 q^{80} +81.0000 q^{81} -390.255 q^{82} +338.449 q^{83} +17.6525 q^{84} -132.839 q^{85} +244.506 q^{86} -87.0000 q^{87} +494.665 q^{88} +547.883 q^{89} +61.7222 q^{90} +74.5392 q^{91} -124.163 q^{92} +666.280 q^{93} -924.371 q^{94} +151.963 q^{95} -558.969 q^{96} -1766.64 q^{97} +551.324 q^{98} +206.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9}+O(q^{10}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9	\( 44 q + 6 q^{2} + 132 q^{3} + 210 q^{4} + 15 q^{5} + 18 q^{6} + 78 q^{7} + 12 q^{8} + 396 q^{9} + 214 q^{10} + 111 q^{11} + 630 q^{12} + 275 q^{13} + 104 q^{14} + 45 q^{15} + 1062 q^{16} - 58 q^{17} + 54 q^{18} + 331 q^{19} + 287 q^{20} + 234 q^{21} + 285 q^{22} + 1012 q^{23} + 36 q^{24} + 1903 q^{25} + 1084 q^{26} + 1188 q^{27} + 222 q^{28} - 1276 q^{29} + 642 q^{30} + 1394 q^{31} + 42 q^{32} + 333 q^{33} + 373 q^{34} + 567 q^{35} + 1890 q^{36} + 1229 q^{37} + 733 q^{38} + 825 q^{39} + 2483 q^{40} - 107 q^{41} + 312 q^{42} + 1165 q^{43} + 1639 q^{44} + 135 q^{45} + 138 q^{46} + 964 q^{47} + 3186 q^{48} + 4264 q^{49} + 495 q^{50} - 174 q^{51} + 2679 q^{52} - 380 q^{53} + 162 q^{54} + 1260 q^{55} + 2229 q^{56} + 993 q^{57} - 174 q^{58} + 897 q^{59} + 861 q^{60} + 2584 q^{61} + 3034 q^{62} + 702 q^{63} + 6866 q^{64} - 286 q^{65} + 855 q^{66} + 2277 q^{67} - 1554 q^{68} + 3036 q^{69} + 689 q^{70} + 4304 q^{71} + 108 q^{72} + 4712 q^{73} - 1005 q^{74} + 5709 q^{75} + 2877 q^{76} + 919 q^{77} + 3252 q^{78} + 3864 q^{79} + 2593 q^{80} + 3564 q^{81} + 3297 q^{82} - 540 q^{83} + 666 q^{84} + 6537 q^{85} + 3789 q^{86} - 3828 q^{87} + 1707 q^{88} - 331 q^{89} + 1926 q^{90} + 4311 q^{91} + 4830 q^{92} + 4182 q^{93} + 6189 q^{94} + 3267 q^{95} + 126 q^{96} + 5572 q^{97} + 2588 q^{98} + 999 q^{99}+O(q^{100}) \) 44 * q + 6 * q^2 + 132 * q^3 + 210 * q^4 + 15 * q^5 + 18 * q^6 + 78 * q^7 + 12 * q^8 + 396 * q^9 + 214 * q^10 + 111 * q^11 + 630 * q^12 + 275 * q^13 + 104 * q^14 + 45 * q^15 + 1062 * q^16 - 58 * q^17 + 54 * q^18 + 331 * q^19 + 287 * q^20 + 234 * q^21 + 285 * q^22 + 1012 * q^23 + 36 * q^24 + 1903 * q^25 + 1084 * q^26 + 1188 * q^27 + 222 * q^28 - 1276 * q^29 + 642 * q^30 + 1394 * q^31 + 42 * q^32 + 333 * q^33 + 373 * q^34 + 567 * q^35 + 1890 * q^36 + 1229 * q^37 + 733 * q^38 + 825 * q^39 + 2483 * q^40 - 107 * q^41 + 312 * q^42 + 1165 * q^43 + 1639 * q^44 + 135 * q^45 + 138 * q^46 + 964 * q^47 + 3186 * q^48 + 4264 * q^49 + 495 * q^50 - 174 * q^51 + 2679 * q^52 - 380 * q^53 + 162 * q^54 + 1260 * q^55 + 2229 * q^56 + 993 * q^57 - 174 * q^58 + 897 * q^59 + 861 * q^60 + 2584 * q^61 + 3034 * q^62 + 702 * q^63 + 6866 * q^64 - 286 * q^65 + 855 * q^66 + 2277 * q^67 - 1554 * q^68 + 3036 * q^69 + 689 * q^70 + 4304 * q^71 + 108 * q^72 + 4712 * q^73 - 1005 * q^74 + 5709 * q^75 + 2877 * q^76 + 919 * q^77 + 3252 * q^78 + 3864 * q^79 + 2593 * q^80 + 3564 * q^81 + 3297 * q^82 - 540 * q^83 + 666 * q^84 + 6537 * q^85 + 3789 * q^86 - 3828 * q^87 + 1707 * q^88 - 331 * q^89 + 1926 * q^90 + 4311 * q^91 + 4830 * q^92 + 4182 * q^93 + 6189 * q^94 + 3267 * q^95 + 126 * q^96 + 5572 * q^97 + 2588 * q^98 + 999 * q^99

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