LMFDB - Embedded newform 2001.4.a.a.1.1

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:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-5.54277 q^{2} +3.00000 q^{3} +22.7223 q^{4} +9.48245 q^{5} -16.6283 q^{6} -7.42459 q^{7} -81.6022 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.54277 q^{2} +3.00000 q^{3} +22.7223 q^{4} +9.48245 q^{5} -16.6283 q^{6} -7.42459 q^{7} -81.6022 q^{8} +9.00000 q^{9} -52.5591 q^{10} +19.9969 q^{11} +68.1668 q^{12} +8.70861 q^{13} +41.1528 q^{14} +28.4474 q^{15} +270.524 q^{16} -57.9162 q^{17} -49.8849 q^{18} -46.5744 q^{19} +215.463 q^{20} -22.2738 q^{21} -110.838 q^{22} +23.0000 q^{23} -244.807 q^{24} -35.0830 q^{25} -48.2698 q^{26} +27.0000 q^{27} -168.704 q^{28} +29.0000 q^{29} -157.677 q^{30} -320.682 q^{31} -846.634 q^{32} +59.9906 q^{33} +321.016 q^{34} -70.4034 q^{35} +204.501 q^{36} +38.9531 q^{37} +258.151 q^{38} +26.1258 q^{39} -773.789 q^{40} +354.803 q^{41} +123.458 q^{42} +465.715 q^{43} +454.374 q^{44} +85.3421 q^{45} -127.484 q^{46} +196.282 q^{47} +811.572 q^{48} -287.875 q^{49} +194.457 q^{50} -173.749 q^{51} +197.879 q^{52} +255.222 q^{53} -149.655 q^{54} +189.619 q^{55} +605.863 q^{56} -139.723 q^{57} -160.740 q^{58} -672.716 q^{59} +646.389 q^{60} +458.541 q^{61} +1777.47 q^{62} -66.8213 q^{63} +2528.50 q^{64} +82.5790 q^{65} -332.514 q^{66} -749.263 q^{67} -1315.99 q^{68} +69.0000 q^{69} +390.230 q^{70} -879.384 q^{71} -734.420 q^{72} +381.607 q^{73} -215.908 q^{74} -105.249 q^{75} -1058.28 q^{76} -148.468 q^{77} -144.809 q^{78} -1187.32 q^{79} +2565.23 q^{80} +81.0000 q^{81} -1966.59 q^{82} +990.301 q^{83} -506.111 q^{84} -549.188 q^{85} -2581.35 q^{86} +87.0000 q^{87} -1631.79 q^{88} +1432.92 q^{89} -473.031 q^{90} -64.6579 q^{91} +522.612 q^{92} -962.046 q^{93} -1087.94 q^{94} -441.640 q^{95} -2539.90 q^{96} -418.890 q^{97} +1595.63 q^{98} +179.972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9}+O(q^{10}) $ 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9} - 6 q^{10} - 109 q^{11} + 222 q^{12} - 317 q^{13} - 159 q^{14} - 75 q^{15} + 54 q^{16} - 180 q^{17} - 90 q^{18} - 217 q^{19} - 193 q^{20} - 228 q^{21} - 160 q^{22} + 713 q^{23} - 351 q^{24} + 208 q^{25} + 211 q^{26} + 837 q^{27} + 5 q^{28} + 899 q^{29} - 18 q^{30} - 622 q^{31} - 696 q^{32} - 327 q^{33} + 126 q^{34} - 627 q^{35} + 666 q^{36} - 539 q^{37} + 35 q^{38} - 951 q^{39} + 371 q^{40} - 459 q^{41} - 477 q^{42} - 719 q^{43} - 876 q^{44} - 225 q^{45} - 230 q^{46} - 1384 q^{47} + 162 q^{48} - 747 q^{49} - 2005 q^{50} - 540 q^{51} - 2190 q^{52} - 730 q^{53} - 270 q^{54} - 1408 q^{55} - 1107 q^{56} - 651 q^{57} - 290 q^{58} - 3765 q^{59} - 579 q^{60} - 1300 q^{61} - 70 q^{62} - 684 q^{63} - 813 q^{64} - 2490 q^{65} - 480 q^{66} - 2735 q^{67} - 2031 q^{68} + 2139 q^{69} - 2581 q^{70} - 4800 q^{71} - 1053 q^{72} - 1858 q^{73} - 801 q^{74} + 624 q^{75} - 2699 q^{76} - 1661 q^{77} + 633 q^{78} - 4466 q^{79} + 3587 q^{80} + 2511 q^{81} - 5615 q^{82} - 1234 q^{83} + 15 q^{84} - 3623 q^{85} - 1873 q^{86} + 2697 q^{87} - 6893 q^{88} - 455 q^{89} - 54 q^{90} - 2425 q^{91} + 1702 q^{92} - 1866 q^{93} - 3912 q^{94} - 1851 q^{95} - 2088 q^{96} - 2114 q^{97} + 1769 q^{98} - 981 q^{99}+O(q^{100}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9 - 6 * q^10 - 109 * q^11 + 222 * q^12 - 317 * q^13 - 159 * q^14 - 75 * q^15 + 54 * q^16 - 180 * q^17 - 90 * q^18 - 217 * q^19 - 193 * q^20 - 228 * q^21 - 160 * q^22 + 713 * q^23 - 351 * q^24 + 208 * q^25 + 211 * q^26 + 837 * q^27 + 5 * q^28 + 899 * q^29 - 18 * q^30 - 622 * q^31 - 696 * q^32 - 327 * q^33 + 126 * q^34 - 627 * q^35 + 666 * q^36 - 539 * q^37 + 35 * q^38 - 951 * q^39 + 371 * q^40 - 459 * q^41 - 477 * q^42 - 719 * q^43 - 876 * q^44 - 225 * q^45 - 230 * q^46 - 1384 * q^47 + 162 * q^48 - 747 * q^49 - 2005 * q^50 - 540 * q^51 - 2190 * q^52 - 730 * q^53 - 270 * q^54 - 1408 * q^55 - 1107 * q^56 - 651 * q^57 - 290 * q^58 - 3765 * q^59 - 579 * q^60 - 1300 * q^61 - 70 * q^62 - 684 * q^63 - 813 * q^64 - 2490 * q^65 - 480 * q^66 - 2735 * q^67 - 2031 * q^68 + 2139 * q^69 - 2581 * q^70 - 4800 * q^71 - 1053 * q^72 - 1858 * q^73 - 801 * q^74 + 624 * q^75 - 2699 * q^76 - 1661 * q^77 + 633 * q^78 - 4466 * q^79 + 3587 * q^80 + 2511 * q^81 - 5615 * q^82 - 1234 * q^83 + 15 * q^84 - 3623 * q^85 - 1873 * q^86 + 2697 * q^87 - 6893 * q^88 - 455 * q^89 - 54 * q^90 - 2425 * q^91 + 1702 * q^92 - 1866 * q^93 - 3912 * q^94 - 1851 * q^95 - 2088 * q^96 - 2114 * q^97 + 1769 * q^98 - 981 * 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 $

$2$	−5.54277	−1.95966	−0.979832	−	0.199822i	$-0.935964\pi$
$2$	−5.54277	−1.95966	−0.979832	+	0.199822i	$0.935964\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	22.7223	2.84029
$5$	9.48245	0.848137	0.424068	−	0.905630i	$-0.360602\pi$
$5$	9.48245	0.848137	0.424068	+	0.905630i	$0.360602\pi$
$6$	−16.6283	−1.13141
$7$	−7.42459	−0.400890	−0.200445	−	0.979705i	$-0.564239\pi$
$7$	−7.42459	−0.400890	−0.200445	+	0.979705i	$0.564239\pi$
$8$	−81.6022	−3.60634
$9$	9.00000	0.333333
$10$	−52.5591	−1.66206
$11$	19.9969	0.548116	0.274058	−	0.961713i	$-0.411634\pi$
$11$	19.9969	0.548116	0.274058	+	0.961713i	$0.411634\pi$
$12$	68.1668	1.63984
$13$	8.70861	0.185795	0.0928974	−	0.995676i	$-0.470387\pi$
$13$	8.70861	0.185795	0.0928974	+	0.995676i	$0.470387\pi$
$14$	41.1528	0.785611
$15$	28.4474	0.489672
$16$	270.524	4.22694
$17$	−57.9162	−0.826279	−0.413140	−	0.910668i	$-0.635568\pi$
$17$	−57.9162	−0.826279	−0.413140	+	0.910668i	$0.635568\pi$
$18$	−49.8849	−0.653222
$19$	−46.5744	−0.562364	−0.281182	−	0.959655i	$-0.590726\pi$
$19$	−46.5744	−0.562364	−0.281182	+	0.959655i	$0.590726\pi$
$20$	215.463	2.40895
$21$	−22.2738	−0.231454
$22$	−110.838	−1.07412
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−244.807	−2.08212
$25$	−35.0830	−0.280664
$26$	−48.2698	−0.364096
$27$	27.0000	0.192450
$28$	−168.704	−1.13864
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−157.677	−0.959593
$31$	−320.682	−1.85794	−0.928970	−	0.370154i	$-0.879305\pi$
$31$	−320.682	−1.85794	−0.928970	+	0.370154i	$0.879305\pi$
$32$	−846.634	−4.67703
$33$	59.9906	0.316455
$34$	321.016	1.61923
$35$	−70.4034	−0.340010
$36$	204.501	0.946762
$37$	38.9531	0.173077	0.0865386	−	0.996248i	$-0.472419\pi$
$37$	38.9531	0.173077	0.0865386	+	0.996248i	$0.472419\pi$
$38$	258.151	1.10204
$39$	26.1258	0.107269
$40$	−773.789	−3.05867
$41$	354.803	1.35148	0.675742	−	0.737138i	$-0.263823\pi$
$41$	354.803	1.35148	0.675742	+	0.737138i	$0.263823\pi$
$42$	123.458	0.453572
$43$	465.715	1.65165	0.825823	−	0.563929i	$-0.190711\pi$
$43$	465.715	1.65165	0.825823	+	0.563929i	$0.190711\pi$
$44$	454.374	1.55681
$45$	85.3421	0.282712
$46$	−127.484	−0.408618
$47$	196.282	0.609163	0.304581	−	0.952486i	$-0.401483\pi$
$47$	196.282	0.609163	0.304581	+	0.952486i	$0.401483\pi$
$48$	811.572	2.44042
$49$	−287.875	−0.839287
$50$	194.457	0.550008
$51$	−173.749	−0.477053
$52$	197.879	0.527710
$53$	255.222	0.661462	0.330731	−	0.943725i	$-0.392705\pi$
$53$	255.222	0.661462	0.330731	+	0.943725i	$0.392705\pi$
$54$	−149.655	−0.377138
$55$	189.619	0.464877
$56$	605.863	1.44575
$57$	−139.723	−0.324681
$58$	−160.740	−0.363901
$59$	−672.716	−1.48441	−0.742205	−	0.670173i	$-0.766220\pi$
$59$	−672.716	−1.48441	−0.742205	+	0.670173i	$0.766220\pi$
$60$	646.389	1.39081
$61$	458.541	0.962461	0.481231	−	0.876594i	$-0.340190\pi$
$61$	458.541	0.962461	0.481231	+	0.876594i	$0.340190\pi$
$62$	1777.47	3.64094
$63$	−66.8213	−0.133630
$64$	2528.50	4.93848
$65$	82.5790	0.157579
$66$	−332.514	−0.620146
$67$	−749.263	−1.36622	−0.683112	−	0.730314i	$-0.739374\pi$
$67$	−749.263	−1.36622	−0.683112	+	0.730314i	$0.739374\pi$
$68$	−1315.99	−2.34687
$69$	69.0000	0.120386
$70$	390.230	0.666305
$71$	−879.384	−1.46991	−0.734956	−	0.678115i	$-0.762797\pi$
$71$	−879.384	−1.46991	−0.734956	+	0.678115i	$0.762797\pi$
$72$	−734.420	−1.20211
$73$	381.607	0.611832	0.305916	−	0.952059i	$-0.401037\pi$
$73$	381.607	0.611832	0.305916	+	0.952059i	$0.401037\pi$
$74$	−215.908	−0.339173
$75$	−105.249	−0.162042
$76$	−1058.28	−1.59727
$77$	−148.468	−0.219734
$78$	−144.809	−0.210211
$79$	−1187.32	−1.69093	−0.845466	−	0.534029i	$-0.820677\pi$
$79$	−1187.32	−1.69093	−0.845466	+	0.534029i	$0.820677\pi$
$80$	2565.23	3.58502
$81$	81.0000	0.111111
$82$	−1966.59	−2.64846
$83$	990.301	1.30963	0.654817	−	0.755787i	$-0.272746\pi$
$83$	990.301	1.30963	0.654817	+	0.755787i	$0.272746\pi$
$84$	−506.111	−0.657396
$85$	−549.188	−0.700798
$86$	−2581.35	−3.23667
$87$	87.0000	0.107211
$88$	−1631.79	−1.97669
$89$	1432.92	1.70662	0.853309	−	0.521406i	$-0.174592\pi$
$89$	1432.92	1.70662	0.853309	+	0.521406i	$0.174592\pi$
$90$	−473.031	−0.554021
$91$	−64.6579	−0.0744834
$92$	522.612	0.592240
$93$	−962.046	−1.07268
$94$	−1087.94	−1.19375
$95$	−441.640	−0.476961
$96$	−2539.90	−2.70029
$97$	−418.890	−0.438472	−0.219236	−	0.975672i	$-0.570356\pi$
$97$	−418.890	−0.438472	−0.219236	+	0.975672i	$0.570356\pi$
$98$	1595.63	1.64472
$99$	179.972	0.182705
$100$	−797.167	−0.797167
$101$	−279.990	−0.275842	−0.137921	−	0.990443i	$-0.544042\pi$
$101$	−279.990	−0.275842	−0.137921	+	0.990443i	$0.544042\pi$
$102$	963.049	0.934863
$103$	−1363.53	−1.30440	−0.652199	−	0.758048i	$-0.726153\pi$
$103$	−1363.53	−1.30440	−0.652199	+	0.758048i	$0.726153\pi$
$104$	−710.642	−0.670040
$105$	−211.210	−0.196305
$106$	−1414.64	−1.29624
$107$	−764.831	−0.691019	−0.345509	−	0.938415i	$-0.612294\pi$
$107$	−764.831	−0.691019	−0.345509	+	0.938415i	$0.612294\pi$
$108$	613.502	0.546613
$109$	−558.926	−0.491151	−0.245575	−	0.969378i	$-0.578977\pi$
$109$	−558.926	−0.491151	−0.245575	+	0.969378i	$0.578977\pi$
$110$	−1051.02	−0.911004
$111$	116.859	0.0999262
$112$	−2008.53	−1.69454
$113$	−1697.96	−1.41354	−0.706772	−	0.707442i	$-0.749849\pi$
$113$	−1697.96	−1.41354	−0.706772	+	0.707442i	$0.749849\pi$
$114$	774.454	0.636266
$115$	218.096	0.176849
$116$	658.946	0.527428
$117$	78.3775	0.0619316
$118$	3728.71	2.90894
$119$	430.004	0.331247
$120$	−2321.37	−1.76592
$121$	−931.126	−0.699569
$122$	−2541.59	−1.88610
$123$	1064.41	0.780280
$124$	−7286.62	−5.27708
$125$	−1517.98	−1.08618
$126$	370.375	0.261870
$127$	−2624.07	−1.83345	−0.916725	−	0.399519i	$-0.869177\pi$
$127$	−2624.07	−1.83345	−0.916725	+	0.399519i	$0.869177\pi$
$128$	−7241.84	−5.00073
$129$	1397.14	0.953579
$130$	−457.716	−0.308803
$131$	940.616	0.627343	0.313672	−	0.949532i	$-0.398441\pi$
$131$	940.616	0.627343	0.313672	+	0.949532i	$0.398441\pi$
$132$	1363.12	0.898822
$133$	345.796	0.225446
$134$	4152.99	2.67734
$135$	256.026	0.163224
$136$	4726.09	2.97985
$137$	2651.32	1.65341	0.826706	−	0.562634i	$-0.190212\pi$
$137$	2651.32	1.65341	0.826706	+	0.562634i	$0.190212\pi$
$138$	−382.451	−0.235916
$139$	2011.09	1.22718	0.613591	−	0.789624i	$-0.289724\pi$
$139$	2011.09	1.22718	0.613591	+	0.789624i	$0.289724\pi$
$140$	−1599.73	−0.965725
$141$	588.845	0.351700
$142$	4874.22	2.88053
$143$	174.145	0.101837
$144$	2434.71	1.40898
$145$	274.991	0.157495
$146$	−2115.16	−1.19898
$147$	−863.626	−0.484563
$148$	885.104	0.491589
$149$	−976.007	−0.536628	−0.268314	−	0.963331i	$-0.586467\pi$
$149$	−976.007	−0.536628	−0.268314	+	0.963331i	$0.586467\pi$
$150$	583.372	0.317547
$151$	−219.029	−0.118042	−0.0590209	−	0.998257i	$-0.518798\pi$
$151$	−219.029	−0.118042	−0.0590209	+	0.998257i	$0.518798\pi$
$152$	3800.58	2.02808
$153$	−521.246	−0.275426
$154$	822.926	0.430606
$155$	−3040.85	−1.57579
$156$	593.638	0.304674
$157$	−234.671	−0.119292	−0.0596458	−	0.998220i	$-0.518997\pi$
$157$	−234.671	−0.119292	−0.0596458	+	0.998220i	$0.518997\pi$
$158$	6581.03	3.31366
$159$	765.667	0.381895
$160$	−8028.16	−3.96676
$161$	−170.766	−0.0835914
$162$	−448.964	−0.217741
$163$	578.321	0.277899	0.138950	−	0.990299i	$-0.455627\pi$
$163$	578.321	0.277899	0.138950	+	0.990299i	$0.455627\pi$
$164$	8061.93	3.83860
$165$	568.858	0.268397
$166$	−5489.01	−2.56644
$167$	−781.901	−0.362307	−0.181154	−	0.983455i	$-0.557983\pi$
$167$	−781.901	−0.362307	−0.181154	+	0.983455i	$0.557983\pi$
$168$	1817.59	0.834703
$169$	−2121.16	−0.965480
$170$	3044.02	1.37333
$171$	−419.170	−0.187455
$172$	10582.1	4.69115
$173$	632.454	0.277945	0.138973	−	0.990296i	$-0.455620\pi$
$173$	632.454	0.277945	0.138973	+	0.990296i	$0.455620\pi$
$174$	−482.221	−0.210098
$175$	260.477	0.112516
$176$	5409.63	2.31685
$177$	−2018.15	−0.857024
$178$	−7942.33	−3.34440
$179$	−1586.67	−0.662534	−0.331267	−	0.943537i	$-0.607476\pi$
$179$	−1586.67	−0.662534	−0.331267	+	0.943537i	$0.607476\pi$
$180$	1939.17	0.802983
$181$	−2229.23	−0.915455	−0.457727	−	0.889093i	$-0.651336\pi$
$181$	−2229.23	−0.915455	−0.457727	+	0.889093i	$0.651336\pi$
$182$	358.384	0.145962
$183$	1375.62	0.555677
$184$	−1876.85	−0.751974
$185$	369.371	0.146793
$186$	5332.40	2.10210
$187$	−1158.14	−0.452897
$188$	4459.97	1.73020
$189$	−200.464	−0.0771514
$190$	2447.91	0.934684
$191$	−613.849	−0.232547	−0.116274	−	0.993217i	$-0.537095\pi$
$191$	−613.849	−0.232547	−0.116274	+	0.993217i	$0.537095\pi$
$192$	7585.51	2.85123
$193$	4583.05	1.70930	0.854652	−	0.519202i	$-0.173771\pi$
$193$	4583.05	1.70930	0.854652	+	0.519202i	$0.173771\pi$
$194$	2321.81	0.859258
$195$	247.737	0.0909785
$196$	−6541.19	−2.38381
$197$	−91.6095	−0.0331315	−0.0165657	−	0.999863i	$-0.505273\pi$
$197$	−91.6095	−0.0331315	−0.0165657	+	0.999863i	$0.505273\pi$
$198$	−997.541	−0.358041
$199$	−4161.75	−1.48250	−0.741252	−	0.671227i	$-0.765768\pi$
$199$	−4161.75	−1.48250	−0.741252	+	0.671227i	$0.765768\pi$
$200$	2862.85	1.01217
$201$	−2247.79	−0.788790
$202$	1551.92	0.540558
$203$	−215.313	−0.0744435
$204$	−3947.97	−1.35497
$205$	3364.40	1.14624
$206$	7557.75	2.55618
$207$	207.000	0.0695048
$208$	2355.89	0.785343
$209$	−931.342	−0.308241
$210$	1170.69	0.384691
$211$	−2250.81	−0.734369	−0.367184	−	0.930148i	$-0.619678\pi$
$211$	−2250.81	−0.734369	−0.367184	+	0.930148i	$0.619678\pi$
$212$	5799.24	1.87874
$213$	−2638.15	−0.848654
$214$	4239.28	1.35416
$215$	4416.12	1.40082
$216$	−2203.26	−0.694041
$217$	2380.93	0.744830
$218$	3098.00	0.962490
$219$	1144.82	0.353241
$220$	4308.58	1.32038
$221$	−504.370	−0.153518
$222$	−647.725	−0.195822
$223$	5178.99	1.55520	0.777602	−	0.628757i	$-0.216436\pi$
$223$	5178.99	1.55520	0.777602	+	0.628757i	$0.216436\pi$
$224$	6285.91	1.87498
$225$	−315.747	−0.0935548
$226$	9411.38	2.77007
$227$	−826.327	−0.241609	−0.120805	−	0.992676i	$-0.538547\pi$
$227$	−826.327	−0.241609	−0.120805	+	0.992676i	$0.538547\pi$
$228$	−3174.83	−0.922186
$229$	−4346.93	−1.25438	−0.627190	−	0.778866i	$-0.715795\pi$
$229$	−4346.93	−1.25438	−0.627190	+	0.778866i	$0.715795\pi$
$230$	−1208.86	−0.346564
$231$	−445.405	−0.126864
$232$	−2366.46	−0.669681
$233$	−4645.75	−1.30624	−0.653118	−	0.757256i	$-0.726539\pi$
$233$	−4645.75	−1.30624	−0.653118	+	0.757256i	$0.726539\pi$
$234$	−434.428	−0.121365
$235$	1861.23	0.516653
$236$	−15285.6	−4.21615
$237$	−3561.95	−0.976260
$238$	−2383.41	−0.649134
$239$	2666.32	0.721632	0.360816	−	0.932637i	$-0.382498\pi$
$239$	2666.32	0.721632	0.360816	+	0.932637i	$0.382498\pi$
$240$	7695.69	2.06981
$241$	−3730.09	−0.996996	−0.498498	−	0.866891i	$-0.666115\pi$
$241$	−3730.09	−0.996996	−0.498498	+	0.866891i	$0.666115\pi$
$242$	5161.02	1.37092
$243$	243.000	0.0641500
$244$	10419.1	2.73366
$245$	−2729.77	−0.711830
$246$	−5899.77	−1.52909
$247$	−405.599	−0.104484
$248$	26168.3	6.70037
$249$	2970.90	0.756118
$250$	8413.81	2.12855
$251$	1273.45	0.320237	0.160119	−	0.987098i	$-0.448812\pi$
$251$	1273.45	0.320237	0.160119	+	0.987098i	$0.448812\pi$
$252$	−1518.33	−0.379548
$253$	459.928	0.114290
$254$	14544.6	3.59295
$255$	−1647.56	−0.404606
$256$	19911.8	4.86128
$257$	3080.42	0.747670	0.373835	−	0.927495i	$-0.378043\pi$
$257$	3080.42	0.747670	0.373835	+	0.927495i	$0.378043\pi$
$258$	−7744.04	−1.86869
$259$	−289.211	−0.0693850
$260$	1876.38	0.447570
$261$	261.000	0.0618984
$262$	−5213.61	−1.22938
$263$	6415.04	1.50406	0.752031	−	0.659127i	$-0.229074\pi$
$263$	6415.04	1.50406	0.752031	+	0.659127i	$0.229074\pi$
$264$	−4895.36	−1.14124
$265$	2420.14	0.561010
$266$	−1916.67	−0.441799
$267$	4298.75	0.985316
$268$	−17025.0	−3.88047
$269$	−4384.77	−0.993843	−0.496922	−	0.867795i	$-0.665536\pi$
$269$	−4384.77	−0.993843	−0.496922	+	0.867795i	$0.665536\pi$
$270$	−1419.09	−0.319864
$271$	−2114.06	−0.473874	−0.236937	−	0.971525i	$-0.576143\pi$
$271$	−2114.06	−0.473874	−0.236937	+	0.971525i	$0.576143\pi$
$272$	−15667.7	−3.49263
$273$	−193.974	−0.0430030
$274$	−14695.6	−3.24013
$275$	−701.550	−0.153837
$276$	1567.84	0.341930
$277$	7679.40	1.66574	0.832870	−	0.553468i	$-0.186696\pi$
$277$	7679.40	1.66574	0.832870	+	0.553468i	$0.186696\pi$
$278$	−11147.0	−2.40487
$279$	−2886.14	−0.619314
$280$	5745.07	1.22619
$281$	4770.23	1.01270	0.506349	−	0.862328i	$-0.330995\pi$
$281$	4770.23	1.01270	0.506349	+	0.862328i	$0.330995\pi$
$282$	−3263.83	−0.689215
$283$	−1370.07	−0.287782	−0.143891	−	0.989594i	$-0.545961\pi$
$283$	−1370.07	−0.287782	−0.143891	+	0.989594i	$0.545961\pi$
$284$	−19981.6	−4.17497
$285$	−1324.92	−0.275374
$286$	−965.244	−0.199567
$287$	−2634.26	−0.541797
$288$	−7619.70	−1.55901
$289$	−1558.71	−0.317262
$290$	−1524.21	−0.308637
$291$	−1256.67	−0.253152
$292$	8670.98	1.73778
$293$	−5666.81	−1.12989	−0.564946	−	0.825128i	$-0.691103\pi$
$293$	−5666.81	−1.12989	−0.564946	+	0.825128i	$0.691103\pi$
$294$	4786.88	0.949580
$295$	−6379.00	−1.25898
$296$	−3178.66	−0.624176
$297$	539.915	0.105485
$298$	5409.78	1.05161
$299$	200.298	0.0387409
$300$	−2391.50	−0.460245
$301$	−3457.74	−0.662129
$302$	1214.03	0.231322
$303$	−839.970	−0.159257
$304$	−12599.5	−2.37707
$305$	4348.09	0.816299
$306$	2889.15	0.539744
$307$	6923.55	1.28713	0.643563	−	0.765393i	$-0.277455\pi$
$307$	6923.55	1.28713	0.643563	+	0.765393i	$0.277455\pi$
$308$	−3373.54	−0.624108
$309$	−4090.60	−0.753095
$310$	16854.7	3.08802
$311$	7946.81	1.44895	0.724473	−	0.689304i	$-0.242083\pi$
$311$	7946.81	1.44895	0.724473	+	0.689304i	$0.242083\pi$
$312$	−2131.92	−0.386848
$313$	−10357.6	−1.87043	−0.935217	−	0.354074i	$-0.884796\pi$
$313$	−10357.6	−1.87043	−0.935217	+	0.354074i	$0.884796\pi$
$314$	1300.73	0.233772
$315$	−633.630	−0.113337
$316$	−26978.6	−4.80273
$317$	9043.77	1.60236	0.801181	−	0.598422i	$-0.204206\pi$
$317$	9043.77	1.60236	0.801181	+	0.598422i	$0.204206\pi$
$318$	−4243.92	−0.748387
$319$	579.909	0.101783
$320$	23976.4	4.18851
$321$	−2294.49	−0.398960
$322$	946.514	0.163811
$323$	2697.42	0.464670
$324$	1840.50	0.315587
$325$	−305.524	−0.0521460
$326$	−3205.50	−0.544589
$327$	−1676.78	−0.283566
$328$	−28952.7	−4.87391
$329$	−1457.31	−0.244207
$330$	−3153.05	−0.525968
$331$	4862.80	0.807504	0.403752	−	0.914868i	$-0.367706\pi$
$331$	4862.80	0.807504	0.403752	+	0.914868i	$0.367706\pi$
$332$	22501.9	3.71973
$333$	350.578	0.0576924
$334$	4333.89	0.710000
$335$	−7104.85	−1.15874
$336$	−6025.59	−0.978342
$337$	2645.24	0.427582	0.213791	−	0.976879i	$-0.431419\pi$
$337$	2645.24	0.427582	0.213791	+	0.976879i	$0.431419\pi$
$338$	11757.1	1.89202
$339$	−5093.87	−0.816109
$340$	−12478.8	−1.99047
$341$	−6412.63	−1.01837
$342$	2323.36	0.367348
$343$	4683.99	0.737352
$344$	−38003.3	−5.95640
$345$	654.289	0.102104
$346$	−3505.54	−0.544680
$347$	−4315.99	−0.667707	−0.333853	−	0.942625i	$-0.608349\pi$
$347$	−4315.99	−0.667707	−0.333853	+	0.942625i	$0.608349\pi$
$348$	1976.84	0.304511
$349$	−10369.7	−1.59047	−0.795236	−	0.606299i	$-0.792653\pi$
$349$	−10369.7	−1.59047	−0.795236	+	0.606299i	$0.792653\pi$
$350$	−1443.77	−0.220493
$351$	235.132	0.0357562
$352$	−16930.0	−2.56356
$353$	2774.54	0.418339	0.209170	−	0.977879i	$-0.432924\pi$
$353$	2774.54	0.418339	0.209170	+	0.977879i	$0.432924\pi$
$354$	11186.1	1.67948
$355$	−8338.72	−1.24669
$356$	32559.2	4.84728
$357$	1290.01	0.191246
$358$	8794.57	1.29835
$359$	−10355.2	−1.52236	−0.761178	−	0.648543i	$-0.775379\pi$
$359$	−10355.2	−1.52236	−0.761178	+	0.648543i	$0.775379\pi$
$360$	−6964.10	−1.01956
$361$	−4689.82	−0.683747
$362$	12356.1	1.79398
$363$	−2793.38	−0.403896
$364$	−1469.17	−0.211554
$365$	3618.57	0.518917
$366$	−7624.76	−1.08894
$367$	−11892.9	−1.69156	−0.845781	−	0.533530i	$-0.820865\pi$
$367$	−11892.9	−1.69156	−0.845781	+	0.533530i	$0.820865\pi$
$368$	6222.05	0.881377
$369$	3193.22	0.450495
$370$	−2047.34	−0.287665
$371$	−1894.92	−0.265174
$372$	−21859.9	−3.04672
$373$	−3518.70	−0.488449	−0.244225	−	0.969719i	$-0.578533\pi$
$373$	−3518.70	−0.488449	−0.244225	+	0.969719i	$0.578533\pi$
$374$	6419.31	0.887526
$375$	−4553.94	−0.627105
$376$	−16017.0	−2.19685
$377$	252.550	0.0345012
$378$	1111.13	0.151191
$379$	−10881.3	−1.47476	−0.737380	−	0.675478i	$-0.763937\pi$
$379$	−10881.3	−1.47476	−0.737380	+	0.675478i	$0.763937\pi$
$380$	−10035.1	−1.35471
$381$	−7872.20	−1.05854
$382$	3402.42	0.455715
$383$	196.413	0.0262043	0.0131021	−	0.999914i	$-0.495829\pi$
$383$	196.413	0.0262043	0.0131021	+	0.999914i	$0.495829\pi$
$384$	−21725.5	−2.88718
$385$	−1407.85	−0.186365
$386$	−25402.8	−3.34966
$387$	4191.43	0.550549
$388$	−9518.13	−1.24539
$389$	11583.5	1.50979	0.754894	−	0.655847i	$-0.227688\pi$
$389$	11583.5	1.50979	0.754894	+	0.655847i	$0.227688\pi$
$390$	−1373.15	−0.178287
$391$	−1332.07	−0.172291
$392$	23491.3	3.02676
$393$	2821.85	0.362197
$394$	507.770	0.0649266
$395$	−11258.7	−1.43414
$396$	4089.37	0.518935
$397$	−1175.40	−0.148594	−0.0742970	−	0.997236i	$-0.523671\pi$
$397$	−1175.40	−0.148594	−0.0742970	+	0.997236i	$0.523671\pi$
$398$	23067.6	2.90521
$399$	1037.39	0.130161
$400$	−9490.80	−1.18635
$401$	−13129.1	−1.63500	−0.817500	−	0.575928i	$-0.804641\pi$
$401$	−13129.1	−1.63500	−0.817500	+	0.575928i	$0.804641\pi$
$402$	12459.0	1.54576
$403$	−2792.69	−0.345196
$404$	−6362.01	−0.783470
$405$	768.079	0.0942374
$406$	1193.43	0.145884
$407$	778.940	0.0948664
$408$	14178.3	1.72042
$409$	3687.66	0.445826	0.222913	−	0.974838i	$-0.428443\pi$
$409$	3687.66	0.445826	0.222913	+	0.974838i	$0.428443\pi$
$410$	−18648.1	−2.24625
$411$	7953.96	0.954598
$412$	−30982.6	−3.70486
$413$	4994.64	0.595085
$414$	−1147.35	−0.136206
$415$	9390.48	1.11075
$416$	−7373.00	−0.868969
$417$	6033.27	0.708514
$418$	5162.21	0.604048
$419$	−3140.47	−0.366162	−0.183081	−	0.983098i	$-0.558607\pi$
$419$	−3140.47	−0.366162	−0.183081	+	0.983098i	$0.558607\pi$
$420$	−4799.18	−0.557561
$421$	3105.28	0.359482	0.179741	−	0.983714i	$-0.442474\pi$
$421$	3105.28	0.359482	0.179741	+	0.983714i	$0.442474\pi$
$422$	12475.7	1.43912
$423$	1766.54	0.203054
$424$	−20826.7	−2.38546
$425$	2031.88	0.231907
$426$	14622.7	1.66308
$427$	−3404.48	−0.385841
$428$	−17378.7	−1.96269
$429$	522.434	0.0587957
$430$	−24477.5	−2.74514
$431$	12555.3	1.40317	0.701585	−	0.712585i	$-0.252476\pi$
$431$	12555.3	1.40317	0.701585	+	0.712585i	$0.252476\pi$
$432$	7304.14	0.813474
$433$	9280.57	1.03001	0.515006	−	0.857186i	$-0.327790\pi$
$433$	9280.57	1.03001	0.515006	+	0.857186i	$0.327790\pi$
$434$	−13197.0	−1.45962
$435$	824.974	0.0909298
$436$	−12700.1	−1.39501
$437$	−1071.21	−0.117261
$438$	−6345.48	−0.692234
$439$	−8705.18	−0.946413	−0.473207	−	0.880951i	$-0.656904\pi$
$439$	−8705.18	−0.946413	−0.473207	+	0.880951i	$0.656904\pi$
$440$	−15473.3	−1.67651
$441$	−2590.88	−0.279762
$442$	2795.60	0.300845
$443$	−2751.38	−0.295083	−0.147542	−	0.989056i	$-0.547136\pi$
$443$	−2751.38	−0.295083	−0.147542	+	0.989056i	$0.547136\pi$
$444$	2655.31	0.283819
$445$	13587.6	1.44744
$446$	−28705.9	−3.04768
$447$	−2928.02	−0.309823
$448$	−18773.1	−1.97979
$449$	−3510.66	−0.368994	−0.184497	−	0.982833i	$-0.559066\pi$
$449$	−3510.66	−0.368994	−0.184497	+	0.982833i	$0.559066\pi$
$450$	1750.11	0.183336
$451$	7094.93	0.740770
$452$	−38581.5	−4.01487
$453$	−657.086	−0.0681514
$454$	4580.14	0.473473
$455$	−613.115	−0.0631721
$456$	11401.7	1.17091
$457$	−8347.64	−0.854456	−0.427228	−	0.904144i	$-0.640510\pi$
$457$	−8347.64	−0.854456	−0.427228	+	0.904144i	$0.640510\pi$
$458$	24094.0	2.45816
$459$	−1563.74	−0.159018
$460$	4955.65	0.502301
$461$	−7576.07	−0.765407	−0.382704	−	0.923871i	$-0.625007\pi$
$461$	−7576.07	−0.765407	−0.382704	+	0.923871i	$0.625007\pi$
$462$	2468.78	0.248610
$463$	19027.0	1.90985	0.954924	−	0.296851i	$-0.0959366\pi$
$463$	19027.0	1.90985	0.954924	+	0.296851i	$0.0959366\pi$
$464$	7845.19	0.784922
$465$	−9122.55	−0.909781
$466$	25750.3	2.55978
$467$	−5805.05	−0.575216	−0.287608	−	0.957748i	$-0.592860\pi$
$467$	−5805.05	−0.575216	−0.287608	+	0.957748i	$0.592860\pi$
$468$	1780.91	0.175903
$469$	5562.97	0.547706
$470$	−10316.4	−1.01247
$471$	−704.013	−0.0688731
$472$	54895.1	5.35329
$473$	9312.83	0.905294
$474$	19743.1	1.91314
$475$	1633.97	0.157835
$476$	9770.68	0.940837
$477$	2297.00	0.220487
$478$	−14778.8	−1.41416
$479$	−1428.04	−0.136219	−0.0681096	−	0.997678i	$-0.521697\pi$
$479$	−1428.04	−0.136219	−0.0681096	+	0.997678i	$0.521697\pi$
$480$	−24084.5	−2.29021
$481$	339.228	0.0321569
$482$	20675.0	1.95378
$483$	−512.297	−0.0482615
$484$	−21157.3	−1.98697
$485$	−3972.10	−0.371884
$486$	−1346.89	−0.125713
$487$	−12178.9	−1.13322	−0.566610	−	0.823986i	$-0.691745\pi$
$487$	−12178.9	−1.13322	−0.566610	+	0.823986i	$0.691745\pi$
$488$	−37417.9	−3.47096
$489$	1734.96	0.160445
$490$	15130.5	1.39495
$491$	51.2236	0.00470812	0.00235406	−	0.999997i	$-0.499251\pi$
$491$	51.2236	0.00470812	0.00235406	+	0.999997i	$0.499251\pi$
$492$	24185.8	2.21622
$493$	−1679.57	−0.153436
$494$	2248.14	0.204754
$495$	1706.57	0.154959
$496$	−86752.1	−7.85340
$497$	6529.07	0.589273
$498$	−16467.0	−1.48174
$499$	15304.9	1.37303	0.686517	−	0.727114i	$-0.259139\pi$
$499$	15304.9	1.37303	0.686517	+	0.727114i	$0.259139\pi$
$500$	−34492.0	−3.08506
$501$	−2345.70	−0.209178
$502$	−7058.45	−0.627558
$503$	1672.77	0.148281	0.0741405	−	0.997248i	$-0.476379\pi$
$503$	1672.77	0.148281	0.0741405	+	0.997248i	$0.476379\pi$
$504$	5452.77	0.481916
$505$	−2654.99	−0.233952
$506$	−2549.27	−0.223970
$507$	−6363.48	−0.557420
$508$	−59624.8	−5.20752
$509$	−6256.67	−0.544837	−0.272419	−	0.962179i	$-0.587824\pi$
$509$	−6256.67	−0.544837	−0.272419	+	0.962179i	$0.587824\pi$
$510$	9132.07	0.792892
$511$	−2833.28	−0.245277
$512$	−52431.8	−4.52574
$513$	−1257.51	−0.108227
$514$	−17074.1	−1.46518
$515$	−12929.7	−1.10631
$516$	31746.3	2.70844
$517$	3925.02	0.333892
$518$	1603.03	0.135971
$519$	1897.36	0.160472
$520$	−6738.63	−0.568285
$521$	−5707.06	−0.479906	−0.239953	−	0.970785i	$-0.577132\pi$
$521$	−5707.06	−0.479906	−0.239953	+	0.970785i	$0.577132\pi$
$522$	−1446.66	−0.121300
$523$	8557.79	0.715500	0.357750	−	0.933817i	$-0.383544\pi$
$523$	8557.79	0.715500	0.357750	+	0.933817i	$0.383544\pi$
$524$	21372.9	1.78183
$525$	781.432	0.0649609
$526$	−35557.1	−2.94746
$527$	18572.7	1.53518
$528$	16228.9	1.33763
$529$	529.000	0.0434783
$530$	−13414.2	−1.09939
$531$	−6054.44	−0.494803
$532$	7857.28	0.640331
$533$	3089.84	0.251099
$534$	−23827.0	−1.93089
$535$	−7252.47	−0.586078
$536$	61141.5	4.92707
$537$	−4760.02	−0.382514
$538$	24303.7	1.94760
$539$	−5756.60	−0.460027
$540$	5817.50	0.463603
$541$	24241.9	1.92651	0.963253	−	0.268595i	$-0.0865592\pi$
$541$	24241.9	1.92651	0.963253	+	0.268595i	$0.0865592\pi$
$542$	11717.7	0.928633
$543$	−6687.69	−0.528538
$544$	49033.8	3.86454
$545$	−5299.99	−0.416563
$546$	1075.15	0.0842714
$547$	−20161.5	−1.57594	−0.787972	−	0.615710i	$-0.788869\pi$
$547$	−20161.5	−1.57594	−0.787972	+	0.615710i	$0.788869\pi$
$548$	60244.0	4.69616
$549$	4126.87	0.320820
$550$	3888.53	0.301468
$551$	−1350.66	−0.104428
$552$	−5630.55	−0.434153
$553$	8815.35	0.677878
$554$	−42565.1	−3.26429
$555$	1108.11	0.0847510
$556$	45696.5	3.48555
$557$	−10191.2	−0.775251	−0.387626	−	0.921817i	$-0.626705\pi$
$557$	−10191.2	−0.775251	−0.387626	+	0.921817i	$0.626705\pi$
$558$	15997.2	1.21365
$559$	4055.73	0.306867
$560$	−19045.8	−1.43720
$561$	−3474.43	−0.261480
$562$	−26440.3	−1.98455
$563$	6071.87	0.454527	0.227264	−	0.973833i	$-0.427022\pi$
$563$	6071.87	0.454527	0.227264	+	0.973833i	$0.427022\pi$
$564$	13379.9	0.998929
$565$	−16100.8	−1.19888
$566$	7593.99	0.563956
$567$	−601.392	−0.0445434
$568$	71759.7	5.30100
$569$	−12230.2	−0.901086	−0.450543	−	0.892755i	$-0.648770\pi$
$569$	−12230.2	−0.901086	−0.450543	+	0.892755i	$0.648770\pi$
$570$	7343.73	0.539640
$571$	5289.15	0.387643	0.193821	−	0.981037i	$-0.437912\pi$
$571$	5289.15	0.387643	0.193821	+	0.981037i	$0.437912\pi$
$572$	3956.97	0.289247
$573$	−1841.55	−0.134261
$574$	14601.1	1.06174
$575$	−806.910	−0.0585226
$576$	22756.5	1.64616
$577$	−12955.0	−0.934702	−0.467351	−	0.884072i	$-0.654792\pi$
$577$	−12955.0	−0.934702	−0.467351	+	0.884072i	$0.654792\pi$
$578$	8639.57	0.621728
$579$	13749.2	0.986867
$580$	6248.43	0.447331
$581$	−7352.58	−0.525020
$582$	6965.42	0.496093
$583$	5103.64	0.362558
$584$	−31140.0	−2.20647
$585$	743.211	0.0525265
$586$	31409.8	2.21421
$587$	−1379.49	−0.0969975	−0.0484988	−	0.998823i	$-0.515444\pi$
$587$	−1379.49	−0.0969975	−0.0484988	+	0.998823i	$0.515444\pi$
$588$	−19623.6	−1.37630
$589$	14935.6	1.04484
$590$	35357.3	2.46718
$591$	−274.828	−0.0191285
$592$	10537.8	0.731586
$593$	−16785.4	−1.16238	−0.581192	−	0.813766i	$-0.697414\pi$
$593$	−16785.4	−1.16238	−0.581192	+	0.813766i	$0.697414\pi$
$594$	−2992.62	−0.206715
$595$	4077.50	0.280943
$596$	−22177.1	−1.52418
$597$	−12485.2	−0.855924
$598$	−1110.21	−0.0759192
$599$	−11058.0	−0.754288	−0.377144	−	0.926155i	$-0.623094\pi$
$599$	−11058.0	−0.754288	−0.377144	+	0.926155i	$0.623094\pi$
$600$	8588.56	0.584378
$601$	−19273.4	−1.30812	−0.654060	−	0.756443i	$-0.726936\pi$
$601$	−19273.4	−1.30812	−0.654060	+	0.756443i	$0.726936\pi$
$602$	19165.5	1.29755
$603$	−6743.36	−0.455408
$604$	−4976.83	−0.335272
$605$	−8829.36	−0.593330
$606$	4655.76	0.312091
$607$	−1371.58	−0.0917146	−0.0458573	−	0.998948i	$-0.514602\pi$
$607$	−1371.58	−0.0917146	−0.0458573	+	0.998948i	$0.514602\pi$
$608$	39431.5	2.63019
$609$	−645.940	−0.0429800
$610$	−24100.5	−1.59967
$611$	1709.34	0.113179
$612$	−11843.9	−0.782290
$613$	9543.86	0.628830	0.314415	−	0.949286i	$-0.398192\pi$
$613$	9543.86	0.628830	0.314415	+	0.949286i	$0.398192\pi$
$614$	−38375.6	−2.52234
$615$	10093.2	0.661784
$616$	12115.4	0.792437
$617$	−5103.48	−0.332995	−0.166498	−	0.986042i	$-0.553246\pi$
$617$	−5103.48	−0.332995	−0.166498	+	0.986042i	$0.553246\pi$
$618$	22673.3	1.47581
$619$	−7801.27	−0.506558	−0.253279	−	0.967393i	$-0.581509\pi$
$619$	−7801.27	−0.506558	−0.253279	+	0.967393i	$0.581509\pi$
$620$	−69095.1	−4.47569
$621$	621.000	0.0401286
$622$	−44047.3	−2.83945
$623$	−10638.8	−0.684166
$624$	7067.66	0.453418
$625$	−10008.8	−0.640563
$626$	57409.8	3.66543
$627$	−2794.03	−0.177963
$628$	−5332.26	−0.338822
$629$	−2256.02	−0.143010
$630$	3512.07	0.222102
$631$	15256.4	0.962516	0.481258	−	0.876579i	$-0.340180\pi$
$631$	15256.4	0.962516	0.481258	+	0.876579i	$0.340180\pi$
$632$	96887.7	6.09808
$633$	−6752.42	−0.423988
$634$	−50127.5	−3.14009
$635$	−24882.6	−1.55502
$636$	17397.7	1.08469
$637$	−2506.99	−0.155935
$638$	−3214.30	−0.199460
$639$	−7914.46	−0.489971
$640$	−68670.4	−4.24131
$641$	2038.41	0.125604	0.0628021	−	0.998026i	$-0.479996\pi$
$641$	2038.41	0.125604	0.0628021	+	0.998026i	$0.479996\pi$
$642$	12717.8	0.781827
$643$	11175.3	0.685398	0.342699	−	0.939445i	$-0.388659\pi$
$643$	11175.3	0.685398	0.342699	+	0.939445i	$0.388659\pi$
$644$	−3880.18	−0.237423
$645$	13248.4	0.808765
$646$	−14951.2	−0.910596
$647$	−3620.94	−0.220021	−0.110011	−	0.993930i	$-0.535088\pi$
$647$	−3620.94	−0.220021	−0.110011	+	0.993930i	$0.535088\pi$
$648$	−6609.78	−0.400705
$649$	−13452.2	−0.813629
$650$	1693.45	0.102189
$651$	7142.80	0.430028
$652$	13140.8	0.789313
$653$	−26443.9	−1.58473	−0.792366	−	0.610045i	$-0.791151\pi$
$653$	−26443.9	−1.58473	−0.792366	+	0.610045i	$0.791151\pi$
$654$	9293.99	0.555694
$655$	8919.34	0.532073
$656$	95982.6	5.71264
$657$	3434.46	0.203944
$658$	8077.55	0.478565
$659$	−22582.9	−1.33491	−0.667454	−	0.744651i	$-0.732616\pi$
$659$	−22582.9	−1.33491	−0.667454	+	0.744651i	$0.732616\pi$
$660$	12925.7	0.762324
$661$	601.526	0.0353959	0.0176979	−	0.999843i	$-0.494366\pi$
$661$	601.526	0.0353959	0.0176979	+	0.999843i	$0.494366\pi$
$662$	−26953.4	−1.58244
$663$	−1513.11	−0.0886339
$664$	−80810.7	−4.72299
$665$	3279.00	0.191209
$666$	−1943.17	−0.113058
$667$	667.000	0.0387202
$668$	−17766.6	−1.02906
$669$	15537.0	0.897898
$670$	39380.5	2.27075
$671$	9169.37	0.527541
$672$	18857.7	1.08252
$673$	19215.4	1.10059	0.550295	−	0.834970i	$-0.314515\pi$
$673$	19215.4	1.10059	0.550295	+	0.834970i	$0.314515\pi$
$674$	−14661.9	−0.837918
$675$	−947.242	−0.0540139
$676$	−48197.6	−2.74224
$677$	−29022.0	−1.64757	−0.823787	−	0.566900i	$-0.808143\pi$
$677$	−29022.0	−1.64757	−0.823787	+	0.566900i	$0.808143\pi$
$678$	28234.2	1.59930
$679$	3110.08	0.175779
$680$	44815.0	2.52732
$681$	−2478.98	−0.139493
$682$	35543.7	1.99566
$683$	−17781.8	−0.996197	−0.498099	−	0.867120i	$-0.665968\pi$
$683$	−17781.8	−0.996197	−0.498099	+	0.867120i	$0.665968\pi$
$684$	−9524.50	−0.532424
$685$	25141.0	1.40232
$686$	−25962.3	−1.44496
$687$	−13040.8	−0.724217
$688$	125987.	6.98140
$689$	2222.63	0.122896
$690$	−3626.57	−0.200089
$691$	−4018.41	−0.221227	−0.110613	−	0.993864i	$-0.535282\pi$
$691$	−4018.41	−0.221227	−0.110613	+	0.993864i	$0.535282\pi$
$692$	14370.8	0.789444
$693$	−1336.22	−0.0732448
$694$	23922.5	1.30848
$695$	19070.1	1.04082
$696$	−7099.39	−0.386640
$697$	−20548.8	−1.11670
$698$	57476.6	3.11679
$699$	−13937.2	−0.754156
$700$	5918.64	0.319576
$701$	31301.8	1.68653	0.843263	−	0.537501i	$-0.180632\pi$
$701$	31301.8	1.68653	0.843263	+	0.537501i	$0.180632\pi$
$702$	−1303.28	−0.0700702
$703$	−1814.22	−0.0973323
$704$	50562.1	2.70686
$705$	5583.70	0.298290
$706$	−15378.6	−0.819805
$707$	2078.81	0.110582
$708$	−45856.9	−2.43419
$709$	−17818.9	−0.943870	−0.471935	−	0.881633i	$-0.656444\pi$
$709$	−17818.9	−0.943870	−0.471935	+	0.881633i	$0.656444\pi$
$710$	46219.6	2.44309
$711$	−10685.9	−0.563644
$712$	−116929.	−6.15465
$713$	−7375.68	−0.387407
$714$	−7150.24	−0.374778
$715$	1651.32	0.0863718
$716$	−36052.9	−1.88179
$717$	7998.97	0.416635
$718$	57396.4	2.98331
$719$	−35769.4	−1.85532	−0.927660	−	0.373426i	$-0.878183\pi$
$719$	−35769.4	−1.85532	−0.927660	+	0.373426i	$0.878183\pi$
$720$	23087.1	1.19501
$721$	10123.7	0.522921
$722$	25994.6	1.33991
$723$	−11190.3	−0.575616
$724$	−50653.2	−2.60015
$725$	−1017.41	−0.0521181
$726$	15483.0	0.791501
$727$	8859.65	0.451976	0.225988	−	0.974130i	$-0.427439\pi$
$727$	8859.65	0.451976	0.225988	+	0.974130i	$0.427439\pi$
$728$	5276.22	0.268612
$729$	729.000	0.0370370
$730$	−20056.9	−1.01690
$731$	−26972.4	−1.36472
$732$	31257.3	1.57828
$733$	−15698.3	−0.791034	−0.395517	−	0.918459i	$-0.629435\pi$
$733$	−15698.3	−0.791034	−0.395517	+	0.918459i	$0.629435\pi$
$734$	65919.5	3.31489
$735$	−8189.30	−0.410975
$736$	−19472.6	−0.975229
$737$	−14982.9	−0.748849
$738$	−17699.3	−0.882819
$739$	−17071.7	−0.849785	−0.424893	−	0.905244i	$-0.639688\pi$
$739$	−17071.7	−0.849785	−0.424893	+	0.905244i	$0.639688\pi$
$740$	8392.96	0.416934
$741$	−1216.80	−0.0603240
$742$	10503.1	0.519652
$743$	−25079.7	−1.23834	−0.619169	−	0.785258i	$-0.712530\pi$
$743$	−25079.7	−1.23834	−0.619169	+	0.785258i	$0.712530\pi$
$744$	78505.0	3.86846
$745$	−9254.95	−0.455134
$746$	19503.4	0.957197
$747$	8912.71	0.436545
$748$	−26315.6	−1.28636
$749$	5678.56	0.277023
$750$	25241.4	1.22892
$751$	19230.3	0.934388	0.467194	−	0.884155i	$-0.345265\pi$
$751$	19230.3	0.934388	0.467194	+	0.884155i	$0.345265\pi$
$752$	53098.9	2.57489
$753$	3820.36	0.184889
$754$	−1399.82	−0.0676109
$755$	−2076.93	−0.100115
$756$	−4555.00	−0.219132
$757$	−23521.7	−1.12934	−0.564671	−	0.825316i	$-0.690997\pi$
$757$	−23521.7	−1.12934	−0.564671	+	0.825316i	$0.690997\pi$
$758$	60312.5	2.89004
$759$	1379.78	0.0659854
$760$	36038.8	1.72009
$761$	26141.4	1.24524	0.622619	−	0.782525i	$-0.286069\pi$
$761$	26141.4	1.24524	0.622619	+	0.782525i	$0.286069\pi$
$762$	43633.8	2.07439
$763$	4149.80	0.196898
$764$	−13948.0	−0.660501
$765$	−4942.69	−0.233599
$766$	−1088.67	−0.0513516
$767$	−5858.42	−0.275796
$768$	59735.4	2.80666
$769$	3010.33	0.141164	0.0705822	−	0.997506i	$-0.477514\pi$
$769$	3010.33	0.141164	0.0705822	+	0.997506i	$0.477514\pi$
$770$	7803.36	0.365212
$771$	9241.26	0.431668
$772$	104137.	4.85491
$773$	−6781.30	−0.315532	−0.157766	−	0.987477i	$-0.550429\pi$
$773$	−6781.30	−0.315532	−0.157766	+	0.987477i	$0.550429\pi$
$774$	−23232.1	−1.07889
$775$	11250.5	0.521458
$776$	34182.3	1.58128
$777$	−867.633	−0.0400594
$778$	−64204.7	−2.95868
$779$	−16524.7	−0.760026
$780$	5629.15	0.258405
$781$	−17584.9	−0.805682
$782$	7383.37	0.337633
$783$	783.000	0.0357371
$784$	−77877.2	−3.54761
$785$	−2225.26	−0.101176
$786$	−15640.8	−0.709784
$787$	−23044.9	−1.04379	−0.521896	−	0.853009i	$-0.674775\pi$
$787$	−23044.9	−1.04379	−0.521896	+	0.853009i	$0.674775\pi$
$788$	−2081.58	−0.0941029
$789$	19245.1	0.868371
$790$	62404.3	2.81044
$791$	12606.6	0.566676
$792$	−14686.1	−0.658898
$793$	3993.25	0.178820
$794$	6514.99	0.291194
$795$	7260.41	0.323899
$796$	−94564.4	−4.21074
$797$	35771.9	1.58984	0.794922	−	0.606712i	$-0.207512\pi$
$797$	35771.9	1.58984	0.794922	+	0.606712i	$0.207512\pi$
$798$	−5750.01	−0.255073
$799$	−11367.9	−0.503339
$800$	29702.5	1.31268
$801$	12896.3	0.568873
$802$	72771.5	3.20405
$803$	7630.94	0.335355
$804$	−51074.9	−2.24039
$805$	−1619.28	−0.0708969
$806$	15479.2	0.676468
$807$	−13154.3	−0.573796
$808$	22847.8	0.994781
$809$	36327.8	1.57876	0.789379	−	0.613906i	$-0.210403\pi$
$809$	36327.8	1.57876	0.789379	+	0.613906i	$0.210403\pi$
$810$	−4257.28	−0.184674
$811$	9475.22	0.410259	0.205129	−	0.978735i	$-0.434238\pi$
$811$	9475.22	0.410259	0.205129	+	0.978735i	$0.434238\pi$
$812$	−4892.41	−0.211441
$813$	−6342.17	−0.273591
$814$	−4317.48	−0.185906
$815$	5483.90	0.235697
$816$	−47003.2	−2.01647
$817$	−21690.4	−0.928826
$818$	−20439.8	−0.873670
$819$	−581.921	−0.0248278
$820$	76446.8	3.25566
$821$	9335.77	0.396858	0.198429	−	0.980115i	$-0.436416\pi$
$821$	9335.77	0.396858	0.198429	+	0.980115i	$0.436416\pi$
$822$	−44086.9	−1.87069
$823$	−10468.3	−0.443380	−0.221690	−	0.975117i	$-0.571157\pi$
$823$	−10468.3	−0.443380	−0.221690	+	0.975117i	$0.571157\pi$
$824$	111267.	4.70411
$825$	−2104.65	−0.0888176
$826$	−27684.1	−1.16617
$827$	−34455.7	−1.44878	−0.724390	−	0.689391i	$-0.757878\pi$
$827$	−34455.7	−1.44878	−0.724390	+	0.689391i	$0.757878\pi$
$828$	4703.51	0.197413
$829$	−25561.8	−1.07092	−0.535462	−	0.844559i	$-0.679863\pi$
$829$	−25561.8	−1.07092	−0.535462	+	0.844559i	$0.679863\pi$
$830$	−52049.3	−2.17669
$831$	23038.2	0.961716
$832$	22019.7	0.917544
$833$	16672.7	0.693486
$834$	−33441.0	−1.38845
$835$	−7414.34	−0.307286
$836$	−21162.2	−0.875491
$837$	−8658.41	−0.357561
$838$	17406.9	0.717555
$839$	2263.07	0.0931226	0.0465613	−	0.998915i	$-0.485174\pi$
$839$	2263.07	0.0931226	0.0465613	+	0.998915i	$0.485174\pi$
$840$	17235.2	0.707942
$841$	841.000	0.0344828
$842$	−17211.8	−0.704464
$843$	14310.7	0.584682
$844$	−51143.4	−2.08582
$845$	−20113.8	−0.818859
$846$	−9791.50	−0.397918
$847$	6913.23	0.280450
$848$	69043.8	2.79596
$849$	−4110.22	−0.166151
$850$	−11262.2	−0.454460
$851$	895.922	0.0360891
$852$	−59944.9	−2.41042
$853$	33.0606	0.00132705	0.000663525	−	1.00000i	$-0.499789\pi$
$853$	33.0606	0.00132705	0.000663525		1.00000i	$0.499789\pi$
$854$	18870.2	0.756120
$855$	−3974.76	−0.158987
$856$	62411.9	2.49205
$857$	−9817.15	−0.391304	−0.195652	−	0.980673i	$-0.562682\pi$
$857$	−9817.15	−0.391304	−0.195652	+	0.980673i	$0.562682\pi$
$858$	−2895.73	−0.115220
$859$	2435.39	0.0967338	0.0483669	−	0.998830i	$-0.484598\pi$
$859$	2435.39	0.0967338	0.0483669	+	0.998830i	$0.484598\pi$
$860$	100344.	3.97873
$861$	−7902.79	−0.312807
$862$	−69591.0	−2.74974
$863$	−12208.3	−0.481549	−0.240774	−	0.970581i	$-0.577401\pi$
$863$	−12208.3	−0.481549	−0.240774	+	0.970581i	$0.577401\pi$
$864$	−22859.1	−0.900096
$865$	5997.21	0.235736
$866$	−51440.0	−2.01848
$867$	−4676.13	−0.183171
$868$	54100.2	2.11553
$869$	−23742.6	−0.926827
$870$	−4572.64	−0.178192
$871$	−6525.03	−0.253837
$872$	45609.6	1.77126
$873$	−3770.01	−0.146157
$874$	5937.48	0.229792
$875$	11270.4	0.435438
$876$	26012.9	1.00331
$877$	8686.49	0.334461	0.167230	−	0.985918i	$-0.446518\pi$
$877$	8686.49	0.334461	0.167230	+	0.985918i	$0.446518\pi$
$878$	48250.8	1.85465
$879$	−17000.4	−0.652344
$880$	51296.5	1.96501
$881$	13560.5	0.518574	0.259287	−	0.965800i	$-0.416512\pi$
$881$	13560.5	0.518574	0.259287	+	0.965800i	$0.416512\pi$
$882$	14360.6	0.548240
$883$	13793.4	0.525692	0.262846	−	0.964838i	$-0.415339\pi$
$883$	13793.4	0.525692	0.262846	+	0.964838i	$0.415339\pi$
$884$	−11460.4	−0.436036
$885$	−19137.0	−0.726873
$886$	15250.2	0.578264
$887$	−42361.2	−1.60355	−0.801775	−	0.597625i	$-0.796111\pi$
$887$	−42361.2	−1.60355	−0.801775	+	0.597625i	$0.796111\pi$
$888$	−9535.99	−0.360368
$889$	19482.6	0.735012
$890$	−75312.8	−2.83651
$891$	1619.74	0.0609018
$892$	117678.	4.41722
$893$	−9141.72	−0.342571
$894$	16229.3	0.607148
$895$	−15045.6	−0.561920
$896$	53767.7	2.00475
$897$	600.894	0.0223671
$898$	19458.8	0.723105
$899$	−9299.77	−0.345011
$900$	−7174.50	−0.265722
$901$	−14781.5	−0.546553
$902$	−39325.6	−1.45166
$903$	−10373.2	−0.382280
$904$	138557.	5.09772
$905$	−21138.6	−0.776430
$906$	3642.08	0.133554
$907$	30452.8	1.11485	0.557425	−	0.830227i	$-0.311789\pi$
$907$	30452.8	1.11485	0.557425	+	0.830227i	$0.311789\pi$
$908$	−18776.0	−0.686239
$909$	−2519.91	−0.0919473
$910$	3398.36	0.123796
$911$	3123.73	0.113604	0.0568022	−	0.998385i	$-0.481910\pi$
$911$	3123.73	0.113604	0.0568022	+	0.998385i	$0.481910\pi$
$912$	−37798.5	−1.37240
$913$	19802.9	0.717832
$914$	46269.1	1.67445
$915$	13044.3	0.471290
$916$	−98772.1	−3.56280
$917$	−6983.69	−0.251496
$918$	8667.44	0.311621
$919$	−14185.4	−0.509177	−0.254588	−	0.967049i	$-0.581940\pi$
$919$	−14185.4	−0.509177	−0.254588	+	0.967049i	$0.581940\pi$
$920$	−17797.2	−0.637777
$921$	20770.7	0.743123
$922$	41992.4	1.49994
$923$	−7658.21	−0.273102
$924$	−10120.6	−0.360329
$925$	−1366.59	−0.0485766
$926$	−105462.	−3.74266
$927$	−12271.8	−0.434799
$928$	−24552.4	−0.868503
$929$	42230.2	1.49142	0.745709	−	0.666271i	$-0.232111\pi$
$929$	42230.2	1.49142	0.745709	+	0.666271i	$0.232111\pi$
$930$	50564.2	1.78287
$931$	13407.6	0.471985
$932$	−105562.	−3.71008
$933$	23840.4	0.836549
$934$	32176.1	1.12723
$935$	−10982.0	−0.384119
$936$	−6395.77	−0.223347
$937$	−4187.64	−0.146002	−0.0730012	−	0.997332i	$-0.523258\pi$
$937$	−4187.64	−0.146002	−0.0730012	+	0.997332i	$0.523258\pi$
$938$	−30834.2	−1.07332
$939$	−31072.8	−1.07990
$940$	42291.5	1.46744
$941$	42146.8	1.46009	0.730046	−	0.683398i	$-0.239499\pi$
$941$	42146.8	1.46009	0.730046	+	0.683398i	$0.239499\pi$
$942$	3902.18	0.134968
$943$	8160.46	0.281804
$944$	−181986.	−6.27450
$945$	−1900.89	−0.0654349
$946$	−51618.8	−1.77407
$947$	−48996.8	−1.68129	−0.840646	−	0.541585i	$-0.817824\pi$
$947$	−48996.8	−1.68129	−0.840646	+	0.541585i	$0.817824\pi$
$948$	−80935.7	−2.77286
$949$	3323.27	0.113675
$950$	−9056.74	−0.309305
$951$	27131.3	0.925124
$952$	−35089.3	−1.19459
$953$	26147.6	0.888776	0.444388	−	0.895834i	$-0.353421\pi$
$953$	26147.6	0.888776	0.444388	+	0.895834i	$0.353421\pi$
$954$	−12731.8	−0.432081
$955$	−5820.79	−0.197232
$956$	60585.0	2.04964
$957$	1739.73	0.0587642
$958$	7915.32	0.266944
$959$	−19685.0	−0.662837
$960$	71929.2	2.41824
$961$	73045.9	2.45194
$962$	−1880.26	−0.0630166
$963$	−6883.48	−0.230340
$964$	−84756.1	−2.83175
$965$	43458.6	1.44972
$966$	2839.54	0.0945764
$967$	−430.511	−0.0143168	−0.00715838	−	0.999974i	$-0.502279\pi$
$967$	−430.511	−0.0143168	−0.00715838	+	0.999974i	$0.502279\pi$
$968$	75981.9	2.52288
$969$	8092.25	0.268277
$970$	22016.4	0.728768
$971$	−15065.5	−0.497916	−0.248958	−	0.968514i	$-0.580088\pi$
$971$	−15065.5	−0.497916	−0.248958	+	0.968514i	$0.580088\pi$
$972$	5521.51	0.182204
$973$	−14931.5	−0.491966
$974$	67504.7	2.22073
$975$	−916.573	−0.0301065
$976$	124046.	4.06826
$977$	52519.1	1.71979	0.859896	−	0.510470i	$-0.170529\pi$
$977$	52519.1	1.71979	0.859896	+	0.510470i	$0.170529\pi$
$978$	−9616.49	−0.314419
$979$	28653.8	0.935425
$980$	−62026.5	−2.02180
$981$	−5030.34	−0.163717
$982$	−283.921	−0.00922634
$983$	10208.4	0.331229	0.165614	−	0.986191i	$-0.447039\pi$
$983$	10208.4	0.331229	0.165614	+	0.986191i	$0.447039\pi$
$984$	−86858.0	−2.81396
$985$	−868.683	−0.0281000
$986$	9309.47	0.300684
$987$	−4371.94	−0.140993
$988$	−9216.12	−0.296765
$989$	10711.4	0.344392
$990$	−9459.14	−0.303668
$991$	33639.7	1.07830	0.539152	−	0.842208i	$-0.318745\pi$
$991$	33639.7	1.07830	0.539152	+	0.842208i	$0.318745\pi$
$992$	271500.	8.68965
$993$	14588.4	0.466213
$994$	−36189.1	−1.15478
$995$	−39463.6	−1.25737
$996$	67505.7	2.14759
$997$	7044.77	0.223781	0.111891	−	0.993721i	$-0.464309\pi$
$997$	7044.77	0.223781	0.111891	+	0.993721i	$0.464309\pi$
$998$	−84831.8	−2.69068
$999$	1051.73	0.0333087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.a.1.1	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.a.1.1	✓	31	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)

\(f(q)\)	\(=\)	\(q-5.54277 q^{2} +3.00000 q^{3} +22.7223 q^{4} +9.48245 q^{5} -16.6283 q^{6} -7.42459 q^{7} -81.6022 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.54277 q^{2} +3.00000 q^{3} +22.7223 q^{4} +9.48245 q^{5} -16.6283 q^{6} -7.42459 q^{7} -81.6022 q^{8} +9.00000 q^{9} -52.5591 q^{10} +19.9969 q^{11} +68.1668 q^{12} +8.70861 q^{13} +41.1528 q^{14} +28.4474 q^{15} +270.524 q^{16} -57.9162 q^{17} -49.8849 q^{18} -46.5744 q^{19} +215.463 q^{20} -22.2738 q^{21} -110.838 q^{22} +23.0000 q^{23} -244.807 q^{24} -35.0830 q^{25} -48.2698 q^{26} +27.0000 q^{27} -168.704 q^{28} +29.0000 q^{29} -157.677 q^{30} -320.682 q^{31} -846.634 q^{32} +59.9906 q^{33} +321.016 q^{34} -70.4034 q^{35} +204.501 q^{36} +38.9531 q^{37} +258.151 q^{38} +26.1258 q^{39} -773.789 q^{40} +354.803 q^{41} +123.458 q^{42} +465.715 q^{43} +454.374 q^{44} +85.3421 q^{45} -127.484 q^{46} +196.282 q^{47} +811.572 q^{48} -287.875 q^{49} +194.457 q^{50} -173.749 q^{51} +197.879 q^{52} +255.222 q^{53} -149.655 q^{54} +189.619 q^{55} +605.863 q^{56} -139.723 q^{57} -160.740 q^{58} -672.716 q^{59} +646.389 q^{60} +458.541 q^{61} +1777.47 q^{62} -66.8213 q^{63} +2528.50 q^{64} +82.5790 q^{65} -332.514 q^{66} -749.263 q^{67} -1315.99 q^{68} +69.0000 q^{69} +390.230 q^{70} -879.384 q^{71} -734.420 q^{72} +381.607 q^{73} -215.908 q^{74} -105.249 q^{75} -1058.28 q^{76} -148.468 q^{77} -144.809 q^{78} -1187.32 q^{79} +2565.23 q^{80} +81.0000 q^{81} -1966.59 q^{82} +990.301 q^{83} -506.111 q^{84} -549.188 q^{85} -2581.35 q^{86} +87.0000 q^{87} -1631.79 q^{88} +1432.92 q^{89} -473.031 q^{90} -64.6579 q^{91} +522.612 q^{92} -962.046 q^{93} -1087.94 q^{94} -441.640 q^{95} -2539.90 q^{96} -418.890 q^{97} +1595.63 q^{98} +179.972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9}+O(q^{10}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9	\( 31 q - 10 q^{2} + 93 q^{3} + 74 q^{4} - 25 q^{5} - 30 q^{6} - 76 q^{7} - 117 q^{8} + 279 q^{9} - 6 q^{10} - 109 q^{11} + 222 q^{12} - 317 q^{13} - 159 q^{14} - 75 q^{15} + 54 q^{16} - 180 q^{17} - 90 q^{18} - 217 q^{19} - 193 q^{20} - 228 q^{21} - 160 q^{22} + 713 q^{23} - 351 q^{24} + 208 q^{25} + 211 q^{26} + 837 q^{27} + 5 q^{28} + 899 q^{29} - 18 q^{30} - 622 q^{31} - 696 q^{32} - 327 q^{33} + 126 q^{34} - 627 q^{35} + 666 q^{36} - 539 q^{37} + 35 q^{38} - 951 q^{39} + 371 q^{40} - 459 q^{41} - 477 q^{42} - 719 q^{43} - 876 q^{44} - 225 q^{45} - 230 q^{46} - 1384 q^{47} + 162 q^{48} - 747 q^{49} - 2005 q^{50} - 540 q^{51} - 2190 q^{52} - 730 q^{53} - 270 q^{54} - 1408 q^{55} - 1107 q^{56} - 651 q^{57} - 290 q^{58} - 3765 q^{59} - 579 q^{60} - 1300 q^{61} - 70 q^{62} - 684 q^{63} - 813 q^{64} - 2490 q^{65} - 480 q^{66} - 2735 q^{67} - 2031 q^{68} + 2139 q^{69} - 2581 q^{70} - 4800 q^{71} - 1053 q^{72} - 1858 q^{73} - 801 q^{74} + 624 q^{75} - 2699 q^{76} - 1661 q^{77} + 633 q^{78} - 4466 q^{79} + 3587 q^{80} + 2511 q^{81} - 5615 q^{82} - 1234 q^{83} + 15 q^{84} - 3623 q^{85} - 1873 q^{86} + 2697 q^{87} - 6893 q^{88} - 455 q^{89} - 54 q^{90} - 2425 q^{91} + 1702 q^{92} - 1866 q^{93} - 3912 q^{94} - 1851 q^{95} - 2088 q^{96} - 2114 q^{97} + 1769 q^{98} - 981 q^{99}+O(q^{100}) \) 31 * q - 10 * q^2 + 93 * q^3 + 74 * q^4 - 25 * q^5 - 30 * q^6 - 76 * q^7 - 117 * q^8 + 279 * q^9 - 6 * q^10 - 109 * q^11 + 222 * q^12 - 317 * q^13 - 159 * q^14 - 75 * q^15 + 54 * q^16 - 180 * q^17 - 90 * q^18 - 217 * q^19 - 193 * q^20 - 228 * q^21 - 160 * q^22 + 713 * q^23 - 351 * q^24 + 208 * q^25 + 211 * q^26 + 837 * q^27 + 5 * q^28 + 899 * q^29 - 18 * q^30 - 622 * q^31 - 696 * q^32 - 327 * q^33 + 126 * q^34 - 627 * q^35 + 666 * q^36 - 539 * q^37 + 35 * q^38 - 951 * q^39 + 371 * q^40 - 459 * q^41 - 477 * q^42 - 719 * q^43 - 876 * q^44 - 225 * q^45 - 230 * q^46 - 1384 * q^47 + 162 * q^48 - 747 * q^49 - 2005 * q^50 - 540 * q^51 - 2190 * q^52 - 730 * q^53 - 270 * q^54 - 1408 * q^55 - 1107 * q^56 - 651 * q^57 - 290 * q^58 - 3765 * q^59 - 579 * q^60 - 1300 * q^61 - 70 * q^62 - 684 * q^63 - 813 * q^64 - 2490 * q^65 - 480 * q^66 - 2735 * q^67 - 2031 * q^68 + 2139 * q^69 - 2581 * q^70 - 4800 * q^71 - 1053 * q^72 - 1858 * q^73 - 801 * q^74 + 624 * q^75 - 2699 * q^76 - 1661 * q^77 + 633 * q^78 - 4466 * q^79 + 3587 * q^80 + 2511 * q^81 - 5615 * q^82 - 1234 * q^83 + 15 * q^84 - 3623 * q^85 - 1873 * q^86 + 2697 * q^87 - 6893 * q^88 - 455 * q^89 - 54 * q^90 - 2425 * q^91 + 1702 * q^92 - 1866 * q^93 - 3912 * q^94 - 1851 * q^95 - 2088 * q^96 - 2114 * q^97 + 1769 * q^98 - 981 * q^99

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