LMFDB - Embedded newform 2001.4.a.g.1.41

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:	$43$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
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)

$f(q)$	$=$	$q+5.28814 q^{2} +3.00000 q^{3} +19.9645 q^{4} +4.18300 q^{5} +15.8644 q^{6} -2.80401 q^{7} +63.2698 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.28814 q^{2} +3.00000 q^{3} +19.9645 q^{4} +4.18300 q^{5} +15.8644 q^{6} -2.80401 q^{7} +63.2698 q^{8} +9.00000 q^{9} +22.1203 q^{10} +3.76713 q^{11} +59.8934 q^{12} +43.6724 q^{13} -14.8280 q^{14} +12.5490 q^{15} +174.864 q^{16} +33.0896 q^{17} +47.5933 q^{18} +82.9357 q^{19} +83.5114 q^{20} -8.41203 q^{21} +19.9211 q^{22} -23.0000 q^{23} +189.809 q^{24} -107.502 q^{25} +230.946 q^{26} +27.0000 q^{27} -55.9805 q^{28} +29.0000 q^{29} +66.3610 q^{30} +185.018 q^{31} +418.547 q^{32} +11.3014 q^{33} +174.983 q^{34} -11.7292 q^{35} +179.680 q^{36} -239.983 q^{37} +438.576 q^{38} +131.017 q^{39} +264.658 q^{40} -344.479 q^{41} -44.4840 q^{42} -40.3736 q^{43} +75.2086 q^{44} +37.6470 q^{45} -121.627 q^{46} -337.164 q^{47} +524.592 q^{48} -335.138 q^{49} -568.489 q^{50} +99.2689 q^{51} +871.896 q^{52} +430.576 q^{53} +142.780 q^{54} +15.7579 q^{55} -177.409 q^{56} +248.807 q^{57} +153.356 q^{58} +528.991 q^{59} +250.534 q^{60} -30.2410 q^{61} +978.399 q^{62} -25.2361 q^{63} +814.427 q^{64} +182.682 q^{65} +59.7633 q^{66} +85.5260 q^{67} +660.616 q^{68} -69.0000 q^{69} -62.0256 q^{70} -463.619 q^{71} +569.428 q^{72} +810.128 q^{73} -1269.07 q^{74} -322.507 q^{75} +1655.77 q^{76} -10.5631 q^{77} +692.838 q^{78} +343.607 q^{79} +731.456 q^{80} +81.0000 q^{81} -1821.65 q^{82} -904.210 q^{83} -167.942 q^{84} +138.414 q^{85} -213.501 q^{86} +87.0000 q^{87} +238.345 q^{88} +375.401 q^{89} +199.083 q^{90} -122.458 q^{91} -459.183 q^{92} +555.053 q^{93} -1782.97 q^{94} +346.920 q^{95} +1255.64 q^{96} +1665.21 q^{97} -1772.26 q^{98} +33.9041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9}+O(q^{10}) $ 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9} + 32 q^{10} + 109 q^{11} + 630 q^{12} + 235 q^{13} + 205 q^{14} + 75 q^{15} + 1190 q^{16} + 228 q^{17} + 18 q^{18} + 291 q^{19} + 407 q^{20} + 318 q^{21} + 808 q^{22} - 989 q^{23} + 81 q^{24} + 1656 q^{25} - 289 q^{26} + 1161 q^{27} + 1831 q^{28} + 1247 q^{29} + 96 q^{30} + 694 q^{31} + 88 q^{32} + 327 q^{33} + 1158 q^{34} - 43 q^{35} + 1890 q^{36} + 1167 q^{37} + 35 q^{38} + 705 q^{39} + 1117 q^{40} + 977 q^{41} + 615 q^{42} + 1361 q^{43} + 798 q^{44} + 225 q^{45} - 46 q^{46} + 684 q^{47} + 3570 q^{48} + 3417 q^{49} + 267 q^{50} + 684 q^{51} + 3054 q^{52} + 1344 q^{53} + 54 q^{54} + 1072 q^{55} + 1741 q^{56} + 873 q^{57} + 58 q^{58} - 313 q^{59} + 1221 q^{60} + 3162 q^{61} - 1010 q^{62} + 954 q^{63} + 8795 q^{64} + 370 q^{65} + 2424 q^{66} + 2699 q^{67} + 2799 q^{68} - 2967 q^{69} + 443 q^{70} + 2140 q^{71} + 243 q^{72} + 922 q^{73} + 2281 q^{74} + 4968 q^{75} + 2237 q^{76} + 879 q^{77} - 867 q^{78} + 5078 q^{79} + 5377 q^{80} + 3483 q^{81} + 1045 q^{82} + 2670 q^{83} + 5493 q^{84} - 1087 q^{85} + 3249 q^{86} + 3741 q^{87} + 8305 q^{88} + 1893 q^{89} + 288 q^{90} + 6847 q^{91} - 4830 q^{92} + 2082 q^{93} - 1128 q^{94} + 6973 q^{95} + 264 q^{96} + 3040 q^{97} + 2581 q^{98} + 981 q^{99}+O(q^{100}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9 + 32 * q^10 + 109 * q^11 + 630 * q^12 + 235 * q^13 + 205 * q^14 + 75 * q^15 + 1190 * q^16 + 228 * q^17 + 18 * q^18 + 291 * q^19 + 407 * q^20 + 318 * q^21 + 808 * q^22 - 989 * q^23 + 81 * q^24 + 1656 * q^25 - 289 * q^26 + 1161 * q^27 + 1831 * q^28 + 1247 * q^29 + 96 * q^30 + 694 * q^31 + 88 * q^32 + 327 * q^33 + 1158 * q^34 - 43 * q^35 + 1890 * q^36 + 1167 * q^37 + 35 * q^38 + 705 * q^39 + 1117 * q^40 + 977 * q^41 + 615 * q^42 + 1361 * q^43 + 798 * q^44 + 225 * q^45 - 46 * q^46 + 684 * q^47 + 3570 * q^48 + 3417 * q^49 + 267 * q^50 + 684 * q^51 + 3054 * q^52 + 1344 * q^53 + 54 * q^54 + 1072 * q^55 + 1741 * q^56 + 873 * q^57 + 58 * q^58 - 313 * q^59 + 1221 * q^60 + 3162 * q^61 - 1010 * q^62 + 954 * q^63 + 8795 * q^64 + 370 * q^65 + 2424 * q^66 + 2699 * q^67 + 2799 * q^68 - 2967 * q^69 + 443 * q^70 + 2140 * q^71 + 243 * q^72 + 922 * q^73 + 2281 * q^74 + 4968 * q^75 + 2237 * q^76 + 879 * q^77 - 867 * q^78 + 5078 * q^79 + 5377 * q^80 + 3483 * q^81 + 1045 * q^82 + 2670 * q^83 + 5493 * q^84 - 1087 * q^85 + 3249 * q^86 + 3741 * q^87 + 8305 * q^88 + 1893 * q^89 + 288 * q^90 + 6847 * q^91 - 4830 * q^92 + 2082 * q^93 - 1128 * q^94 + 6973 * q^95 + 264 * q^96 + 3040 * q^97 + 2581 * 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 $

$2$	5.28814	1.86964	0.934820	−	0.355121i	$-0.115560\pi$
$2$	5.28814	1.86964	0.934820	+	0.355121i	$0.115560\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	19.9645	2.49556
$5$	4.18300	0.374139	0.187070	−	0.982347i	$-0.440101\pi$
$5$	4.18300	0.374139	0.187070	+	0.982347i	$0.440101\pi$
$6$	15.8644	1.07944
$7$	−2.80401	−0.151402	−0.0757011	−	0.997131i	$-0.524119\pi$
$7$	−2.80401	−0.151402	−0.0757011	+	0.997131i	$0.524119\pi$
$8$	63.2698	2.79615
$9$	9.00000	0.333333
$10$	22.1203	0.699506
$11$	3.76713	0.103257	0.0516287	−	0.998666i	$-0.483559\pi$
$11$	3.76713	0.103257	0.0516287	+	0.998666i	$0.483559\pi$
$12$	59.8934	1.44081
$13$	43.6724	0.931735	0.465867	−	0.884855i	$-0.345742\pi$
$13$	43.6724	0.931735	0.465867	+	0.884855i	$0.345742\pi$
$14$	−14.8280	−0.283068
$15$	12.5490	0.216009
$16$	174.864	2.73225
$17$	33.0896	0.472083	0.236042	−	0.971743i	$-0.424150\pi$
$17$	33.0896	0.472083	0.236042	+	0.971743i	$0.424150\pi$
$18$	47.5933	0.623214
$19$	82.9357	1.00141	0.500704	−	0.865618i	$-0.333074\pi$
$19$	82.9357	1.00141	0.500704	+	0.865618i	$0.333074\pi$
$20$	83.5114	0.933686
$21$	−8.41203	−0.0874121
$22$	19.9211	0.193054
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	189.809	1.61436
$25$	−107.502	−0.860020
$26$	230.946	1.74201
$27$	27.0000	0.192450
$28$	−55.9805	−0.377833
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	66.3610	0.403860
$31$	185.018	1.07194	0.535970	−	0.844237i	$-0.319946\pi$
$31$	185.018	1.07194	0.535970	+	0.844237i	$0.319946\pi$
$32$	418.547	2.31217
$33$	11.3014	0.0596157
$34$	174.983	0.882626
$35$	−11.7292	−0.0566455
$36$	179.680	0.831852
$37$	−239.983	−1.06630	−0.533149	−	0.846021i	$-0.678991\pi$
$37$	−239.983	−1.06630	−0.533149	+	0.846021i	$0.678991\pi$
$38$	438.576	1.87227
$39$	131.017	0.537937
$40$	264.658	1.04615
$41$	−344.479	−1.31216	−0.656081	−	0.754691i	$-0.727787\pi$
$41$	−344.479	−1.31216	−0.656081	+	0.754691i	$0.727787\pi$
$42$	−44.4840	−0.163429
$43$	−40.3736	−0.143184	−0.0715921	−	0.997434i	$-0.522808\pi$
$43$	−40.3736	−0.143184	−0.0715921	+	0.997434i	$0.522808\pi$
$44$	75.2086	0.257685
$45$	37.6470	0.124713
$46$	−121.627	−0.389847
$47$	−337.164	−1.04639	−0.523196	−	0.852212i	$-0.675261\pi$
$47$	−337.164	−1.04639	−0.523196	+	0.852212i	$0.675261\pi$
$48$	524.592	1.57746
$49$	−335.138	−0.977077
$50$	−568.489	−1.60793
$51$	99.2689	0.272557
$52$	871.896	2.32520
$53$	430.576	1.11593	0.557964	−	0.829865i	$-0.311583\pi$
$53$	430.576	1.11593	0.557964	+	0.829865i	$0.311583\pi$
$54$	142.780	0.359813
$55$	15.7579	0.0386326
$56$	−177.409	−0.423344
$57$	248.807	0.578163
$58$	153.356	0.347184
$59$	528.991	1.16727	0.583634	−	0.812017i	$-0.301630\pi$
$59$	528.991	1.16727	0.583634	+	0.812017i	$0.301630\pi$
$60$	250.534	0.539064
$61$	−30.2410	−0.0634748	−0.0317374	−	0.999496i	$-0.510104\pi$
$61$	−30.2410	−0.0634748	−0.0317374	+	0.999496i	$0.510104\pi$
$62$	978.399	2.00414
$63$	−25.2361	−0.0504674
$64$	814.427	1.59068
$65$	182.682	0.348599
$66$	59.7633	0.111460
$67$	85.5260	0.155950	0.0779751	−	0.996955i	$-0.475155\pi$
$67$	85.5260	0.155950	0.0779751	+	0.996955i	$0.475155\pi$
$68$	660.616	1.17811
$69$	−69.0000	−0.120386
$70$	−62.0256	−0.105907
$71$	−463.619	−0.774950	−0.387475	−	0.921880i	$-0.626653\pi$
$71$	−463.619	−0.774950	−0.387475	+	0.921880i	$0.626653\pi$
$72$	569.428	0.932052
$73$	810.128	1.29888	0.649441	−	0.760412i	$-0.275003\pi$
$73$	810.128	1.29888	0.649441	+	0.760412i	$0.275003\pi$
$74$	−1269.07	−1.99359
$75$	−322.507	−0.496533
$76$	1655.77	2.49907
$77$	−10.5631	−0.0156334
$78$	692.838	1.00575
$79$	343.607	0.489352	0.244676	−	0.969605i	$-0.421318\pi$
$79$	343.607	0.489352	0.244676	+	0.969605i	$0.421318\pi$
$80$	731.456	1.02224
$81$	81.0000	0.111111
$82$	−1821.65	−2.45327
$83$	−904.210	−1.19578	−0.597891	−	0.801577i	$-0.703995\pi$
$83$	−904.210	−1.19578	−0.597891	+	0.801577i	$0.703995\pi$
$84$	−167.942	−0.218142
$85$	138.414	0.176625
$86$	−213.501	−0.267703
$87$	87.0000	0.107211
$88$	238.345	0.288724
$89$	375.401	0.447106	0.223553	−	0.974692i	$-0.428234\pi$
$89$	375.401	0.447106	0.223553	+	0.974692i	$0.428234\pi$
$90$	199.083	0.233169
$91$	−122.458	−0.141067
$92$	−459.183	−0.520360
$93$	555.053	0.618885
$94$	−1782.97	−1.95638
$95$	346.920	0.374666
$96$	1255.64	1.33493
$97$	1665.21	1.74306	0.871530	−	0.490341i	$-0.163128\pi$
$97$	1665.21	1.74306	0.871530	+	0.490341i	$0.163128\pi$
$98$	−1772.26	−1.82678
$99$	33.9041	0.0344191
$100$	−2146.23	−2.14623
$101$	−25.4378	−0.0250609	−0.0125305	−	0.999921i	$-0.503989\pi$
$101$	−25.4378	−0.0250609	−0.0125305	+	0.999921i	$0.503989\pi$
$102$	524.948	0.509584
$103$	1781.38	1.70412	0.852062	−	0.523441i	$-0.175352\pi$
$103$	1781.38	1.70412	0.852062	+	0.523441i	$0.175352\pi$
$104$	2763.14	2.60527
$105$	−35.1875	−0.0327043
$106$	2276.95	2.08639
$107$	−274.621	−0.248118	−0.124059	−	0.992275i	$-0.539591\pi$
$107$	−274.621	−0.248118	−0.124059	+	0.992275i	$0.539591\pi$
$108$	539.040	0.480270
$109$	−1305.43	−1.14714	−0.573569	−	0.819158i	$-0.694441\pi$
$109$	−1305.43	−1.14714	−0.573569	+	0.819158i	$0.694441\pi$
$110$	83.3300	0.0722291
$111$	−719.950	−0.615627
$112$	−490.320	−0.413669
$113$	1237.22	1.02999	0.514993	−	0.857195i	$-0.327795\pi$
$113$	1237.22	1.02999	0.514993	+	0.857195i	$0.327795\pi$
$114$	1315.73	1.08096
$115$	−96.2091	−0.0780134
$116$	578.969	0.463413
$117$	393.052	0.310578
$118$	2797.38	2.18237
$119$	−92.7836	−0.0714745
$120$	793.973	0.603996
$121$	−1316.81	−0.989338
$122$	−159.919	−0.118675
$123$	−1033.44	−0.757577
$124$	3693.78	2.67509
$125$	−972.559	−0.695906
$126$	−133.452	−0.0943560
$127$	1499.60	1.04778	0.523890	−	0.851786i	$-0.324480\pi$
$127$	1499.60	1.04778	0.523890	+	0.851786i	$0.324480\pi$
$128$	958.426	0.661826
$129$	−121.121	−0.0826674
$130$	966.048	0.651754
$131$	−432.956	−0.288760	−0.144380	−	0.989522i	$-0.546119\pi$
$131$	−432.956	−0.288760	−0.144380	+	0.989522i	$0.546119\pi$
$132$	225.626	0.148774
$133$	−232.553	−0.151615
$134$	452.274	0.291571
$135$	112.941	0.0720031
$136$	2093.57	1.32002
$137$	3015.50	1.88052	0.940262	−	0.340452i	$-0.110580\pi$
$137$	3015.50	1.88052	0.940262	+	0.340452i	$0.110580\pi$
$138$	−364.882	−0.225078
$139$	−2387.95	−1.45715	−0.728573	−	0.684968i	$-0.759816\pi$
$139$	−2387.95	−1.45715	−0.728573	+	0.684968i	$0.759816\pi$
$140$	−234.167	−0.141362
$141$	−1011.49	−0.604135
$142$	−2451.68	−1.44888
$143$	164.519	0.0962085
$144$	1573.78	0.910750
$145$	121.307	0.0694759
$146$	4284.07	2.42844
$147$	−1005.41	−0.564116
$148$	−4791.14	−2.66101
$149$	−2179.27	−1.19821	−0.599104	−	0.800671i	$-0.704476\pi$
$149$	−2179.27	−1.19821	−0.599104	+	0.800671i	$0.704476\pi$
$150$	−1705.47	−0.928338
$151$	−1322.52	−0.712752	−0.356376	−	0.934343i	$-0.615988\pi$
$151$	−1322.52	−0.712752	−0.356376	+	0.934343i	$0.615988\pi$
$152$	5247.32	2.80009
$153$	297.807	0.157361
$154$	−55.8589	−0.0292288
$155$	773.929	0.401055
$156$	2615.69	1.34245
$157$	−1350.77	−0.686642	−0.343321	−	0.939218i	$-0.611552\pi$
$157$	−1350.77	−0.686642	−0.343321	+	0.939218i	$0.611552\pi$
$158$	1817.04	0.914913
$159$	1291.73	0.644282
$160$	1750.78	0.865073
$161$	64.4922	0.0315696
$162$	428.340	0.207738
$163$	−109.314	−0.0525285	−0.0262643	−	0.999655i	$-0.508361\pi$
$163$	−109.314	−0.0525285	−0.0262643	+	0.999655i	$0.508361\pi$
$164$	−6877.34	−3.27457
$165$	47.2737	0.0223046
$166$	−4781.59	−2.23568
$167$	−1186.42	−0.549747	−0.274873	−	0.961480i	$-0.588636\pi$
$167$	−1186.42	−0.549747	−0.274873	+	0.961480i	$0.588636\pi$
$168$	−532.227	−0.244418
$169$	−289.719	−0.131870
$170$	731.953	0.330225
$171$	746.421	0.333803
$172$	−806.037	−0.357324
$173$	1936.37	0.850981	0.425490	−	0.904963i	$-0.360102\pi$
$173$	1936.37	0.850981	0.425490	+	0.904963i	$0.360102\pi$
$174$	460.068	0.200447
$175$	301.438	0.130209
$176$	658.734	0.282125
$177$	1586.97	0.673922
$178$	1985.17	0.835927
$179$	−2714.15	−1.13332	−0.566662	−	0.823950i	$-0.691766\pi$
$179$	−2714.15	−1.13332	−0.566662	+	0.823950i	$0.691766\pi$
$180$	751.603	0.311229
$181$	1146.57	0.470850	0.235425	−	0.971892i	$-0.424352\pi$
$181$	1146.57	0.470850	0.235425	+	0.971892i	$0.424352\pi$
$182$	−647.575	−0.263744
$183$	−90.7230	−0.0366472
$184$	−1455.20	−0.583039
$185$	−1003.85	−0.398944
$186$	2935.20	1.15709
$187$	124.653	0.0487461
$188$	−6731.30	−2.61133
$189$	−75.7083	−0.0291374
$190$	1834.56	0.700491
$191$	−506.242	−0.191782	−0.0958911	−	0.995392i	$-0.530570\pi$
$191$	−506.242	−0.191782	−0.0958911	+	0.995392i	$0.530570\pi$
$192$	2443.28	0.918378
$193$	922.546	0.344074	0.172037	−	0.985090i	$-0.444965\pi$
$193$	922.546	0.344074	0.172037	+	0.985090i	$0.444965\pi$
$194$	8805.89	3.25890
$195$	548.046	0.201263
$196$	−6690.84	−2.43835
$197$	1711.69	0.619050	0.309525	−	0.950891i	$-0.399830\pi$
$197$	1711.69	0.619050	0.309525	+	0.950891i	$0.399830\pi$
$198$	179.290	0.0643514
$199$	−1673.71	−0.596210	−0.298105	−	0.954533i	$-0.596355\pi$
$199$	−1673.71	−0.596210	−0.298105	+	0.954533i	$0.596355\pi$
$200$	−6801.66	−2.40475
$201$	256.578	0.0900379
$202$	−134.519	−0.0468549
$203$	−81.3163	−0.0281147
$204$	1981.85	0.680182
$205$	−1440.96	−0.490931
$206$	9420.20	3.18610
$207$	−207.000	−0.0695048
$208$	7636.73	2.54573
$209$	312.429	0.103403
$210$	−186.077	−0.0611453
$211$	−5471.99	−1.78534	−0.892672	−	0.450708i	$-0.851172\pi$
$211$	−5471.99	−1.78534	−0.892672	+	0.450708i	$0.851172\pi$
$212$	8596.22	2.78486
$213$	−1390.86	−0.447418
$214$	−1452.24	−0.463891
$215$	−168.883	−0.0535708
$216$	1708.28	0.538120
$217$	−518.791	−0.162294
$218$	−6903.32	−2.14473
$219$	2430.39	0.749910
$220$	314.598	0.0964099
$221$	1445.10	0.439856
$222$	−3807.20	−1.15100
$223$	1076.36	0.323220	0.161610	−	0.986855i	$-0.448331\pi$
$223$	1076.36	0.323220	0.161610	+	0.986855i	$0.448331\pi$
$224$	−1173.61	−0.350068
$225$	−967.522	−0.286673
$226$	6542.62	1.92570
$227$	−4636.08	−1.35554	−0.677770	−	0.735274i	$-0.737053\pi$
$227$	−4636.08	−1.35554	−0.677770	+	0.735274i	$0.737053\pi$
$228$	4967.30	1.44284
$229$	3388.48	0.977804	0.488902	−	0.872339i	$-0.337398\pi$
$229$	3388.48	0.977804	0.488902	+	0.872339i	$0.337398\pi$
$230$	−508.767	−0.145857
$231$	−31.6892	−0.00902595
$232$	1834.82	0.519233
$233$	4486.13	1.26136	0.630679	−	0.776044i	$-0.282777\pi$
$233$	4486.13	1.26136	0.630679	+	0.776044i	$0.282777\pi$
$234$	2078.51	0.580670
$235$	−1410.36	−0.391496
$236$	10561.0	2.91298
$237$	1030.82	0.282528
$238$	−490.653	−0.133632
$239$	−5151.58	−1.39426	−0.697129	−	0.716946i	$-0.745540\pi$
$239$	−5151.58	−1.39426	−0.697129	+	0.716946i	$0.745540\pi$
$240$	2194.37	0.590191
$241$	−1288.85	−0.344490	−0.172245	−	0.985054i	$-0.555102\pi$
$241$	−1288.85	−0.344490	−0.172245	+	0.985054i	$0.555102\pi$
$242$	−6963.47	−1.84971
$243$	243.000	0.0641500
$244$	−603.745	−0.158405
$245$	−1401.88	−0.365563
$246$	−5464.96	−1.41640
$247$	3622.00	0.933047
$248$	11706.0	2.99731
$249$	−2712.63	−0.690386
$250$	−5143.03	−1.30110
$251$	−6564.52	−1.65079	−0.825395	−	0.564555i	$-0.809048\pi$
$251$	−6564.52	−1.65079	−0.825395	+	0.564555i	$0.809048\pi$
$252$	−503.825	−0.125944
$253$	−86.6439	−0.0215306
$254$	7930.11	1.95897
$255$	415.242	0.101974
$256$	−1447.12	−0.353300
$257$	−5038.50	−1.22293	−0.611464	−	0.791272i	$-0.709419\pi$
$257$	−5038.50	−1.22293	−0.611464	+	0.791272i	$0.709419\pi$
$258$	−640.504	−0.154558
$259$	672.915	0.161440
$260$	3647.15	0.869948
$261$	261.000	0.0618984
$262$	−2289.53	−0.539877
$263$	−2372.17	−0.556177	−0.278088	−	0.960555i	$-0.589701\pi$
$263$	−2372.17	−0.556177	−0.278088	+	0.960555i	$0.589701\pi$
$264$	715.035	0.166695
$265$	1801.10	0.417513
$266$	−1229.77	−0.283467
$267$	1126.20	0.258136
$268$	1707.48	0.389183
$269$	2474.04	0.560762	0.280381	−	0.959889i	$-0.409539\pi$
$269$	2474.04	0.560762	0.280381	+	0.959889i	$0.409539\pi$
$270$	597.249	0.134620
$271$	−6595.22	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$271$	−6595.22	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$272$	5786.18	1.28985
$273$	−367.374	−0.0814449
$274$	15946.4	3.51590
$275$	−404.975	−0.0888034
$276$	−1377.55	−0.300430
$277$	−4363.10	−0.946401	−0.473201	−	0.880955i	$-0.656901\pi$
$277$	−4363.10	−0.946401	−0.473201	+	0.880955i	$0.656901\pi$
$278$	−12627.8	−2.72434
$279$	1665.16	0.357313
$280$	−742.103	−0.158390
$281$	−8065.87	−1.71235	−0.856174	−	0.516688i	$-0.827165\pi$
$281$	−8065.87	−1.71235	−0.856174	+	0.516688i	$0.827165\pi$
$282$	−5348.92	−1.12952
$283$	8200.44	1.72249	0.861246	−	0.508188i	$-0.169684\pi$
$283$	8200.44	1.72249	0.861246	+	0.508188i	$0.169684\pi$
$284$	−9255.90	−1.93393
$285$	1040.76	0.216314
$286$	870.003	0.179875
$287$	965.923	0.198664
$288$	3766.93	0.770723
$289$	−3818.08	−0.777138
$290$	641.489	0.129895
$291$	4995.64	1.00636
$292$	16173.8	3.24143
$293$	−3938.58	−0.785304	−0.392652	−	0.919687i	$-0.628442\pi$
$293$	−3938.58	−0.785304	−0.392652	+	0.919687i	$0.628442\pi$
$294$	−5316.77	−1.05469
$295$	2212.77	0.436721
$296$	−15183.7	−2.98153
$297$	101.712	0.0198719
$298$	−11524.3	−2.24022
$299$	−1004.47	−0.194280
$300$	−6438.69	−1.23913
$301$	113.208	0.0216784
$302$	−6993.70	−1.33259
$303$	−76.3133	−0.0144689
$304$	14502.5	2.73610
$305$	−126.498	−0.0237484
$306$	1574.84	0.294209
$307$	5185.04	0.963928	0.481964	−	0.876191i	$-0.339924\pi$
$307$	5185.04	0.963928	0.481964	+	0.876191i	$0.339924\pi$
$308$	−210.886	−0.0390140
$309$	5344.15	0.983877
$310$	4092.65	0.749828
$311$	9807.58	1.78822	0.894111	−	0.447846i	$-0.147809\pi$
$311$	9807.58	1.78822	0.894111	+	0.447846i	$0.147809\pi$
$312$	8289.43	1.50416
$313$	2738.92	0.494610	0.247305	−	0.968938i	$-0.420455\pi$
$313$	2738.92	0.494610	0.247305	+	0.968938i	$0.420455\pi$
$314$	−7143.04	−1.28377
$315$	−105.563	−0.0188818
$316$	6859.93	1.22121
$317$	−7173.62	−1.27101	−0.635506	−	0.772096i	$-0.719208\pi$
$317$	−7173.62	−1.27101	−0.635506	+	0.772096i	$0.719208\pi$
$318$	6830.85	1.20458
$319$	109.247	0.0191744
$320$	3406.75	0.595135
$321$	−823.863	−0.143251
$322$	341.044	0.0590237
$323$	2744.31	0.472748
$324$	1617.12	0.277284
$325$	−4694.89	−0.801310
$326$	−578.069	−0.0982095
$327$	−3916.30	−0.662300
$328$	−21795.1	−3.66901
$329$	945.412	0.158426
$330$	249.990	0.0417015
$331$	7682.87	1.27580	0.637898	−	0.770121i	$-0.279804\pi$
$331$	7682.87	1.27580	0.637898	+	0.770121i	$0.279804\pi$
$332$	−18052.1	−2.98414
$333$	−2159.85	−0.355433
$334$	−6273.94	−1.02783
$335$	357.756	0.0583471
$336$	−1470.96	−0.238832
$337$	−5975.47	−0.965888	−0.482944	−	0.875651i	$-0.660433\pi$
$337$	−5975.47	−0.965888	−0.482944	+	0.875651i	$0.660433\pi$
$338$	−1532.08	−0.246550
$339$	3711.67	0.594662
$340$	2763.36	0.440777
$341$	696.984	0.110686
$342$	3947.18	0.624091
$343$	1901.50	0.299334
$344$	−2554.43	−0.400365
$345$	−288.627	−0.0450411
$346$	10239.8	1.59103
$347$	−8449.50	−1.30718	−0.653592	−	0.756847i	$-0.726739\pi$
$347$	−8449.50	−1.30718	−0.653592	+	0.756847i	$0.726739\pi$
$348$	1736.91	0.267552
$349$	−2593.33	−0.397759	−0.198879	−	0.980024i	$-0.563730\pi$
$349$	−2593.33	−0.397759	−0.198879	+	0.980024i	$0.563730\pi$
$350$	1594.05	0.243444
$351$	1179.16	0.179312
$352$	1576.72	0.238748
$353$	−872.009	−0.131480	−0.0657399	−	0.997837i	$-0.520941\pi$
$353$	−872.009	−0.131480	−0.0657399	+	0.997837i	$0.520941\pi$
$354$	8392.15	1.25999
$355$	−1939.32	−0.289939
$356$	7494.67	1.11578
$357$	−278.351	−0.0412658
$358$	−14352.8	−2.11891
$359$	3651.35	0.536798	0.268399	−	0.963308i	$-0.413505\pi$
$359$	3651.35	0.536798	0.268399	+	0.963308i	$0.413505\pi$
$360$	2381.92	0.348717
$361$	19.3319	0.00281847
$362$	6063.23	0.880321
$363$	−3950.43	−0.571195
$364$	−2444.81	−0.352040
$365$	3388.77	0.485963
$366$	−479.756	−0.0685171
$367$	−5872.58	−0.835276	−0.417638	−	0.908613i	$-0.637142\pi$
$367$	−5872.58	−0.835276	−0.417638	+	0.908613i	$0.637142\pi$
$368$	−4021.87	−0.569713
$369$	−3100.31	−0.437387
$370$	−5308.51	−0.745882
$371$	−1207.34	−0.168954
$372$	11081.3	1.54446
$373$	−185.350	−0.0257294	−0.0128647	−	0.999917i	$-0.504095\pi$
$373$	−185.350	−0.0257294	−0.0128647	+	0.999917i	$0.504095\pi$
$374$	659.182	0.0911376
$375$	−2917.68	−0.401782
$376$	−21332.3	−2.92588
$377$	1266.50	0.173019
$378$	−400.356	−0.0544764
$379$	−3190.93	−0.432473	−0.216236	−	0.976341i	$-0.569378\pi$
$379$	−3190.93	−0.432473	−0.216236	+	0.976341i	$0.569378\pi$
$380$	6926.08	0.935001
$381$	4498.80	0.604936
$382$	−2677.08	−0.358564
$383$	7340.54	0.979331	0.489666	−	0.871910i	$-0.337119\pi$
$383$	7340.54	0.979331	0.489666	+	0.871910i	$0.337119\pi$
$384$	2875.28	0.382105
$385$	−44.1853	−0.00584907
$386$	4878.56	0.643295
$387$	−363.363	−0.0477281
$388$	33245.1	4.34991
$389$	−2018.37	−0.263073	−0.131536	−	0.991311i	$-0.541991\pi$
$389$	−2018.37	−0.263073	−0.131536	+	0.991311i	$0.541991\pi$
$390$	2898.14	0.376290
$391$	−761.061	−0.0984361
$392$	−21204.1	−2.73206
$393$	−1298.87	−0.166716
$394$	9051.66	1.15740
$395$	1437.31	0.183086
$396$	676.877	0.0858949
$397$	−11524.0	−1.45686	−0.728430	−	0.685121i	$-0.759749\pi$
$397$	−11524.0	−1.45686	−0.728430	+	0.685121i	$0.759749\pi$
$398$	−8850.80	−1.11470
$399$	−697.658	−0.0875352
$400$	−18798.3	−2.34979
$401$	9527.53	1.18649	0.593244	−	0.805022i	$-0.297847\pi$
$401$	9527.53	1.18649	0.593244	+	0.805022i	$0.297847\pi$
$402$	1356.82	0.168339
$403$	8080.17	0.998764
$404$	−507.851	−0.0625410
$405$	338.823	0.0415710
$406$	−430.012	−0.0525644
$407$	−904.047	−0.110103
$408$	6280.72	0.762113
$409$	−7916.22	−0.957047	−0.478523	−	0.878075i	$-0.658828\pi$
$409$	−7916.22	−0.957047	−0.478523	+	0.878075i	$0.658828\pi$
$410$	−7619.99	−0.917865
$411$	9046.51	1.08572
$412$	35564.3	4.25274
$413$	−1483.30	−0.176727
$414$	−1094.65	−0.129949
$415$	−3782.32	−0.447389
$416$	18279.0	2.15433
$417$	−7163.86	−0.841284
$418$	1652.17	0.193326
$419$	6122.25	0.713822	0.356911	−	0.934138i	$-0.383830\pi$
$419$	6122.25	0.713822	0.356911	+	0.934138i	$0.383830\pi$
$420$	−702.500	−0.0816155
$421$	9164.57	1.06094	0.530468	−	0.847705i	$-0.322016\pi$
$421$	9164.57	1.06094	0.530468	+	0.847705i	$0.322016\pi$
$422$	−28936.7	−3.33795
$423$	−3034.48	−0.348798
$424$	27242.5	3.12031
$425$	−3557.22	−0.406001
$426$	−7355.05	−0.836511
$427$	84.7960	0.00961023
$428$	−5482.66	−0.619192
$429$	493.558	0.0555460
$430$	−893.077	−0.100158
$431$	−15353.3	−1.71587	−0.857937	−	0.513755i	$-0.828254\pi$
$431$	−15353.3	−1.71587	−0.857937	+	0.513755i	$0.828254\pi$
$432$	4721.33	0.525821
$433$	−10164.3	−1.12809	−0.564046	−	0.825743i	$-0.690756\pi$
$433$	−10164.3	−1.12809	−0.564046	+	0.825743i	$0.690756\pi$
$434$	−2743.44	−0.303432
$435$	363.921	0.0401119
$436$	−26062.3	−2.86275
$437$	−1907.52	−0.208808
$438$	12852.2	1.40206
$439$	7636.75	0.830256	0.415128	−	0.909763i	$-0.363737\pi$
$439$	7636.75	0.830256	0.415128	+	0.909763i	$0.363737\pi$
$440$	996.999	0.108023
$441$	−3016.24	−0.325692
$442$	7641.92	0.822373
$443$	6132.50	0.657706	0.328853	−	0.944381i	$-0.393338\pi$
$443$	6132.50	0.657706	0.328853	+	0.944381i	$0.393338\pi$
$444$	−14373.4	−1.53633
$445$	1570.30	0.167280
$446$	5691.92	0.604306
$447$	−6537.82	−0.691786
$448$	−2283.66	−0.240832
$449$	−21.9414	−0.00230618	−0.00115309	−	0.999999i	$-0.500367\pi$
$449$	−21.9414	−0.00230618	−0.00115309	+	0.999999i	$0.500367\pi$
$450$	−5116.40	−0.535976
$451$	−1297.70	−0.135490
$452$	24700.5	2.57039
$453$	−3967.57	−0.411507
$454$	−24516.2	−2.53437
$455$	−512.242	−0.0527786
$456$	15742.0	1.61663
$457$	1417.97	0.145142	0.0725709	−	0.997363i	$-0.476880\pi$
$457$	1417.97	0.145142	0.0725709	+	0.997363i	$0.476880\pi$
$458$	17918.8	1.82814
$459$	893.420	0.0908524
$460$	−1920.76	−0.194687
$461$	6585.49	0.665329	0.332665	−	0.943045i	$-0.392052\pi$
$461$	6585.49	0.665329	0.332665	+	0.943045i	$0.392052\pi$
$462$	−167.577	−0.0168753
$463$	−1727.63	−0.173412	−0.0867058	−	0.996234i	$-0.527634\pi$
$463$	−1727.63	−0.173412	−0.0867058	+	0.996234i	$0.527634\pi$
$464$	5071.05	0.507366
$465$	2321.79	0.231549
$466$	23723.3	2.35829
$467$	12986.1	1.28678	0.643389	−	0.765540i	$-0.277528\pi$
$467$	12986.1	1.28678	0.643389	+	0.765540i	$0.277528\pi$
$468$	7847.07	0.775066
$469$	−239.816	−0.0236112
$470$	−7458.18	−0.731958
$471$	−4052.30	−0.396433
$472$	33469.2	3.26386
$473$	−152.092	−0.0147848
$474$	5451.13	0.528225
$475$	−8915.79	−0.861231
$476$	−1852.37	−0.178369
$477$	3875.19	0.371976
$478$	−27242.3	−2.60676
$479$	13850.6	1.32119	0.660594	−	0.750744i	$-0.270305\pi$
$479$	13850.6	1.32119	0.660594	+	0.750744i	$0.270305\pi$
$480$	5252.35	0.499450
$481$	−10480.7	−0.993507
$482$	−6815.62	−0.644073
$483$	193.477	0.0182267
$484$	−26289.4	−2.46895
$485$	6965.60	0.652147
$486$	1285.02	0.119938
$487$	−8059.96	−0.749962	−0.374981	−	0.927033i	$-0.622351\pi$
$487$	−8059.96	−0.749962	−0.374981	+	0.927033i	$0.622351\pi$
$488$	−1913.34	−0.177485
$489$	−327.943	−0.0303274
$490$	−7413.35	−0.683471
$491$	8281.86	0.761212	0.380606	−	0.924737i	$-0.375715\pi$
$491$	8281.86	0.761212	0.380606	+	0.924737i	$0.375715\pi$
$492$	−20632.0	−1.89058
$493$	959.599	0.0876636
$494$	19153.7	1.74446
$495$	141.821	0.0128775
$496$	32352.9	2.92881
$497$	1299.99	0.117329
$498$	−14344.8	−1.29077
$499$	14797.6	1.32752	0.663760	−	0.747945i	$-0.268959\pi$
$499$	14797.6	1.32752	0.663760	+	0.747945i	$0.268959\pi$
$500$	−19416.6	−1.73667
$501$	−3559.25	−0.317396
$502$	−34714.1	−3.08639
$503$	−13939.8	−1.23567	−0.617837	−	0.786306i	$-0.711991\pi$
$503$	−13939.8	−1.23567	−0.617837	+	0.786306i	$0.711991\pi$
$504$	−1596.68	−0.141115
$505$	−106.406	−0.00937627
$506$	−458.185	−0.0402546
$507$	−869.158	−0.0761354
$508$	29938.7	2.61480
$509$	17210.6	1.49872	0.749359	−	0.662164i	$-0.230362\pi$
$509$	17210.6	1.49872	0.749359	+	0.662164i	$0.230362\pi$
$510$	2195.86	0.190655
$511$	−2271.61	−0.196654
$512$	−15320.0	−1.32237
$513$	2239.26	0.192721
$514$	−26644.3	−2.28644
$515$	7451.53	0.637580
$516$	−2418.11	−0.206301
$517$	−1270.14	−0.108048
$518$	3558.47	0.301835
$519$	5809.12	0.491314
$520$	11558.2	0.974735
$521$	8201.22	0.689639	0.344819	−	0.938669i	$-0.387940\pi$
$521$	8201.22	0.689639	0.344819	+	0.938669i	$0.387940\pi$
$522$	1380.21	0.115728
$523$	23377.8	1.95457	0.977285	−	0.211929i	$-0.0679746\pi$
$523$	23377.8	1.95457	0.977285	+	0.211929i	$0.0679746\pi$
$524$	−8643.73	−0.720617
$525$	904.314	0.0751762
$526$	−12544.4	−1.03985
$527$	6122.16	0.506045
$528$	1976.20	0.162885
$529$	529.000	0.0434783
$530$	9524.49	0.780599
$531$	4760.92	0.389089
$532$	−4642.78	−0.378365
$533$	−15044.2	−1.22259
$534$	5955.52	0.482623
$535$	−1148.74	−0.0928306
$536$	5411.21	0.436061
$537$	−8142.45	−0.654325
$538$	13083.1	1.04842
$539$	−1262.50	−0.100890
$540$	2254.81	0.179688
$541$	617.811	0.0490975	0.0245488	−	0.999699i	$-0.492185\pi$
$541$	617.811	0.0490975	0.0245488	+	0.999699i	$0.492185\pi$
$542$	−34876.5	−2.76397
$543$	3439.71	0.271846
$544$	13849.6	1.09154
$545$	−5460.64	−0.429189
$546$	−1942.72	−0.152273
$547$	13992.5	1.09374	0.546868	−	0.837219i	$-0.315820\pi$
$547$	13992.5	1.09374	0.546868	+	0.837219i	$0.315820\pi$
$548$	60202.9	4.69295
$549$	−272.169	−0.0211583
$550$	−2141.57	−0.166030
$551$	2405.14	0.185957
$552$	−4365.61	−0.336618
$553$	−963.478	−0.0740890
$554$	−23072.7	−1.76943
$555$	−3011.55	−0.230330
$556$	−47674.2	−3.63639
$557$	10571.1	0.804154	0.402077	−	0.915606i	$-0.368288\pi$
$557$	10571.1	0.804154	0.402077	+	0.915606i	$0.368288\pi$
$558$	8805.59	0.668048
$559$	−1763.21	−0.133410
$560$	−2051.01	−0.154770
$561$	373.958	0.0281435
$562$	−42653.5	−3.20148
$563$	5881.82	0.440300	0.220150	−	0.975466i	$-0.429345\pi$
$563$	5881.82	0.440300	0.220150	+	0.975466i	$0.429345\pi$
$564$	−20193.9	−1.50765
$565$	5175.32	0.385358
$566$	43365.1	3.22044
$567$	−227.125	−0.0168225
$568$	−29333.1	−2.16688
$569$	−5457.19	−0.402069	−0.201035	−	0.979584i	$-0.564430\pi$
$569$	−5457.19	−0.402069	−0.201035	+	0.979584i	$0.564430\pi$
$570$	5503.69	0.404429
$571$	−563.496	−0.0412987	−0.0206494	−	0.999787i	$-0.506573\pi$
$571$	−563.496	−0.0412987	−0.0206494	+	0.999787i	$0.506573\pi$
$572$	3284.54	0.240094
$573$	−1518.73	−0.110726
$574$	5107.94	0.371431
$575$	2472.56	0.179327
$576$	7329.84	0.530226
$577$	17.9541	0.00129539	0.000647694	−	1.00000i	$-0.499794\pi$
$577$	17.9541	0.00129539	0.000647694		1.00000i	$0.499794\pi$
$578$	−20190.5	−1.45297
$579$	2767.64	0.198651
$580$	2421.83	0.173381
$581$	2535.41	0.181044
$582$	26417.7	1.88153
$583$	1622.04	0.115228
$584$	51256.6	3.63187
$585$	1644.14	0.116200
$586$	−20827.8	−1.46824
$587$	−26474.2	−1.86151	−0.930757	−	0.365638i	$-0.880851\pi$
$587$	−26474.2	−1.86151	−0.930757	+	0.365638i	$0.880851\pi$
$588$	−20072.5	−1.40778
$589$	15344.6	1.07345
$590$	11701.5	0.816511
$591$	5135.07	0.357409
$592$	−41964.4	−2.91339
$593$	−15549.7	−1.07681	−0.538406	−	0.842685i	$-0.680973\pi$
$593$	−15549.7	−1.07681	−0.538406	+	0.842685i	$0.680973\pi$
$594$	537.870	0.0371533
$595$	−388.114	−0.0267414
$596$	−43508.0	−2.99020
$597$	−5021.12	−0.344222
$598$	−5311.76	−0.363234
$599$	−49.3800	−0.00336830	−0.00168415	−	0.999999i	$-0.500536\pi$
$599$	−49.3800	−0.00336830	−0.00168415	+	0.999999i	$0.500536\pi$
$600$	−20405.0	−1.38838
$601$	−15653.6	−1.06244	−0.531218	−	0.847235i	$-0.678265\pi$
$601$	−15653.6	−1.06244	−0.531218	+	0.847235i	$0.678265\pi$
$602$	598.660	0.0405308
$603$	769.734	0.0519834
$604$	−26403.5	−1.77871
$605$	−5508.22	−0.370150
$606$	−403.556	−0.0270517
$607$	−24036.6	−1.60728	−0.803638	−	0.595119i	$-0.797105\pi$
$607$	−24036.6	−1.60728	−0.803638	+	0.595119i	$0.797105\pi$
$608$	34712.5	2.31542
$609$	−243.949	−0.0162320
$610$	−668.941	−0.0444010
$611$	−14724.8	−0.974960
$612$	5945.55	0.392703
$613$	4987.63	0.328627	0.164314	−	0.986408i	$-0.447459\pi$
$613$	4987.63	0.328627	0.164314	+	0.986408i	$0.447459\pi$
$614$	27419.2	1.80220
$615$	−4322.87	−0.283439
$616$	−668.322	−0.0437134
$617$	19881.7	1.29726	0.648629	−	0.761105i	$-0.275343\pi$
$617$	19881.7	1.29726	0.648629	+	0.761105i	$0.275343\pi$
$618$	28260.6	1.83950
$619$	8704.39	0.565200	0.282600	−	0.959238i	$-0.408803\pi$
$619$	8704.39	0.565200	0.282600	+	0.959238i	$0.408803\pi$
$620$	15451.1	1.00086
$621$	−621.000	−0.0401286
$622$	51863.9	3.34333
$623$	−1052.63	−0.0676928
$624$	22910.2	1.46978
$625$	9369.59	0.599654
$626$	14483.8	0.924744
$627$	937.288	0.0596996
$628$	−26967.3	−1.71355
$629$	−7940.96	−0.503381
$630$	−558.230	−0.0353023
$631$	−7477.69	−0.471762	−0.235881	−	0.971782i	$-0.575798\pi$
$631$	−7477.69	−0.471762	−0.235881	+	0.971782i	$0.575798\pi$
$632$	21739.9	1.36830
$633$	−16416.0	−1.03077
$634$	−37935.1	−2.37634
$635$	6272.84	0.392016
$636$	25788.7	1.60784
$637$	−14636.3	−0.910377
$638$	577.712	0.0358493
$639$	−4172.57	−0.258317
$640$	4009.10	0.247615
$641$	−3625.16	−0.223378	−0.111689	−	0.993743i	$-0.535626\pi$
$641$	−3625.16	−0.223378	−0.111689	+	0.993743i	$0.535626\pi$
$642$	−4356.71	−0.267828
$643$	−15769.0	−0.967136	−0.483568	−	0.875307i	$-0.660659\pi$
$643$	−15769.0	−0.967136	−0.483568	+	0.875307i	$0.660659\pi$
$644$	1287.55	0.0787836
$645$	−506.649	−0.0309291
$646$	14512.3	0.883869
$647$	−10013.4	−0.608452	−0.304226	−	0.952600i	$-0.598398\pi$
$647$	−10013.4	−0.608452	−0.304226	+	0.952600i	$0.598398\pi$
$648$	5124.85	0.310684
$649$	1992.78	0.120529
$650$	−24827.3	−1.49816
$651$	−1556.37	−0.0937006
$652$	−2182.40	−0.131088
$653$	7924.47	0.474898	0.237449	−	0.971400i	$-0.423689\pi$
$653$	7924.47	0.474898	0.237449	+	0.971400i	$0.423689\pi$
$654$	−20710.0	−1.23826
$655$	−1811.06	−0.108036
$656$	−60237.0	−3.58515
$657$	7291.16	0.432961
$658$	4999.47	0.296200
$659$	1685.01	0.0996035	0.0498017	−	0.998759i	$-0.484141\pi$
$659$	1685.01	0.0996035	0.0498017	+	0.998759i	$0.484141\pi$
$660$	943.794	0.0556623
$661$	−25529.5	−1.50224	−0.751121	−	0.660165i	$-0.770486\pi$
$661$	−25529.5	−1.50224	−0.751121	+	0.660165i	$0.770486\pi$
$662$	40628.1	2.38528
$663$	4335.31	0.253951
$664$	−57209.2	−3.34359
$665$	−972.768	−0.0567253
$666$	−11421.6	−0.664531
$667$	−667.000	−0.0387202
$668$	−23686.2	−1.37192
$669$	3229.07	0.186611
$670$	1891.86	0.109088
$671$	−113.922	−0.00655424
$672$	−3520.83	−0.202112
$673$	26990.8	1.54594	0.772970	−	0.634443i	$-0.218770\pi$
$673$	26990.8	1.54594	0.772970	+	0.634443i	$0.218770\pi$
$674$	−31599.1	−1.80586
$675$	−2902.57	−0.165511
$676$	−5784.09	−0.329090
$677$	23638.3	1.34194	0.670971	−	0.741483i	$-0.265877\pi$
$677$	23638.3	1.34194	0.670971	+	0.741483i	$0.265877\pi$
$678$	19627.9	1.11180
$679$	−4669.28	−0.263903
$680$	8757.42	0.493870
$681$	−13908.2	−0.782621
$682$	3685.75	0.206942
$683$	−14648.3	−0.820649	−0.410324	−	0.911940i	$-0.634585\pi$
$683$	−14648.3	−0.820649	−0.410324	+	0.911940i	$0.634585\pi$
$684$	14901.9	0.833024
$685$	12613.9	0.703578
$686$	10055.4	0.559647
$687$	10165.4	0.564536
$688$	−7059.89	−0.391215
$689$	18804.3	1.03975
$690$	−1526.30	−0.0842106
$691$	10162.7	0.559490	0.279745	−	0.960074i	$-0.409750\pi$
$691$	10162.7	0.559490	0.279745	+	0.960074i	$0.409750\pi$
$692$	38658.6	2.12367
$693$	−95.0675	−0.00521113
$694$	−44682.2	−2.44397
$695$	−9988.81	−0.545176
$696$	5504.47	0.299779
$697$	−11398.7	−0.619449
$698$	−13713.9	−0.743666
$699$	13458.4	0.728245
$700$	6018.05	0.324944
$701$	−16938.0	−0.912610	−0.456305	−	0.889823i	$-0.650827\pi$
$701$	−16938.0	−0.912610	−0.456305	+	0.889823i	$0.650827\pi$
$702$	6235.54	0.335250
$703$	−19903.2	−1.06780
$704$	3068.05	0.164249
$705$	−4231.08	−0.226031
$706$	−4611.31	−0.245820
$707$	71.3278	0.00379428
$708$	31683.1	1.68181
$709$	−765.465	−0.0405468	−0.0202734	−	0.999794i	$-0.506454\pi$
$709$	−765.465	−0.0405468	−0.0202734	+	0.999794i	$0.506454\pi$
$710$	−10255.4	−0.542082
$711$	3092.46	0.163117
$712$	23751.5	1.25018
$713$	−4255.40	−0.223515
$714$	−1471.96	−0.0771522
$715$	688.186	0.0359954
$716$	−54186.5	−2.82828
$717$	−15454.7	−0.804975
$718$	19308.8	1.00362
$719$	−9610.11	−0.498465	−0.249233	−	0.968444i	$-0.580178\pi$
$719$	−9610.11	−0.498465	−0.249233	+	0.968444i	$0.580178\pi$
$720$	6583.11	0.340747
$721$	−4995.01	−0.258008
$722$	102.230	0.00526952
$723$	−3866.55	−0.198891
$724$	22890.7	1.17503
$725$	−3117.57	−0.159702
$726$	−20890.4	−1.06793
$727$	−18504.2	−0.943991	−0.471996	−	0.881601i	$-0.656466\pi$
$727$	−18504.2	−0.943991	−0.471996	+	0.881601i	$0.656466\pi$
$728$	−7747.88	−0.394445
$729$	729.000	0.0370370
$730$	17920.3	0.908575
$731$	−1335.95	−0.0675948
$732$	−1811.24	−0.0914552
$733$	26614.8	1.34112	0.670560	−	0.741856i	$-0.266054\pi$
$733$	26614.8	1.34112	0.670560	+	0.741856i	$0.266054\pi$
$734$	−31055.1	−1.56167
$735$	−4205.64	−0.211058
$736$	−9626.59	−0.482121
$737$	322.187	0.0161030
$738$	−16394.9	−0.817757
$739$	−9015.67	−0.448778	−0.224389	−	0.974500i	$-0.572039\pi$
$739$	−9015.67	−0.448778	−0.224389	+	0.974500i	$0.572039\pi$
$740$	−20041.3	−0.995587
$741$	10866.0	0.538695
$742$	−6384.59	−0.315884
$743$	37843.2	1.86855	0.934276	−	0.356551i	$-0.116047\pi$
$743$	37843.2	1.86855	0.934276	+	0.356551i	$0.116047\pi$
$744$	35118.1	1.73050
$745$	−9115.91	−0.448297
$746$	−980.158	−0.0481047
$747$	−8137.89	−0.398594
$748$	2488.62	0.121649
$749$	770.040	0.0375656
$750$	−15429.1	−0.751188
$751$	34577.3	1.68009	0.840043	−	0.542519i	$-0.182529\pi$
$751$	34577.3	1.68009	0.840043	+	0.542519i	$0.182529\pi$
$752$	−58957.8	−2.85900
$753$	−19693.5	−0.953085
$754$	6697.44	0.323483
$755$	−5532.12	−0.266668
$756$	−1511.47	−0.0727140
$757$	−34865.1	−1.67397	−0.836984	−	0.547228i	$-0.815683\pi$
$757$	−34865.1	−1.67397	−0.836984	+	0.547228i	$0.815683\pi$
$758$	−16874.1	−0.808568
$759$	−259.932	−0.0124307
$760$	21949.6	1.04762
$761$	34641.9	1.65015	0.825077	−	0.565021i	$-0.191132\pi$
$761$	34641.9	1.65015	0.825077	+	0.565021i	$0.191132\pi$
$762$	23790.3	1.13101
$763$	3660.45	0.173679
$764$	−10106.9	−0.478603
$765$	1245.73	0.0588749
$766$	38817.8	1.83100
$767$	23102.3	1.08758
$768$	−4341.35	−0.203978
$769$	−13862.6	−0.650062	−0.325031	−	0.945703i	$-0.605375\pi$
$769$	−13862.6	−0.650062	−0.325031	+	0.945703i	$0.605375\pi$
$770$	−233.658	−0.0109357
$771$	−15115.5	−0.706058
$772$	18418.1	0.858657
$773$	10851.5	0.504919	0.252460	−	0.967607i	$-0.418760\pi$
$773$	10851.5	0.504919	0.252460	+	0.967607i	$0.418760\pi$
$774$	−1921.51	−0.0892343
$775$	−19889.8	−0.921890
$776$	105358.	4.87387
$777$	2018.75	0.0932074
$778$	−10673.4	−0.491852
$779$	−28569.6	−1.31401
$780$	10941.4	0.502264
$781$	−1746.51	−0.0800193
$782$	−4024.60	−0.184040
$783$	783.000	0.0357371
$784$	−58603.5	−2.66962
$785$	−5650.26	−0.256900
$786$	−6868.60	−0.311698
$787$	29778.2	1.34877	0.674383	−	0.738382i	$-0.264410\pi$
$787$	29778.2	1.34877	0.674383	+	0.738382i	$0.264410\pi$
$788$	34172.9	1.54487
$789$	−7116.52	−0.321109
$790$	7600.70	0.342305
$791$	−3469.19	−0.155942
$792$	2145.11	0.0962412
$793$	−1320.70	−0.0591417
$794$	−60940.6	−2.72380
$795$	5403.31	0.241051
$796$	−33414.6	−1.48788
$797$	5411.37	0.240503	0.120251	−	0.992743i	$-0.461630\pi$
$797$	5411.37	0.240503	0.120251	+	0.992743i	$0.461630\pi$
$798$	−3689.31	−0.163659
$799$	−11156.6	−0.493984
$800$	−44994.9	−1.98851
$801$	3378.61	0.149035
$802$	50382.9	2.21831
$803$	3051.85	0.134119
$804$	5122.44	0.224695
$805$	269.771	0.0118114
$806$	42729.1	1.86733
$807$	7422.12	0.323756
$808$	−1609.44	−0.0700742
$809$	−14450.6	−0.628004	−0.314002	−	0.949422i	$-0.601670\pi$
$809$	−14450.6	−0.628004	−0.314002	+	0.949422i	$0.601670\pi$
$810$	1791.75	0.0777229
$811$	19309.5	0.836064	0.418032	−	0.908432i	$-0.362720\pi$
$811$	19309.5	0.836064	0.418032	+	0.908432i	$0.362720\pi$
$812$	−1623.44	−0.0701618
$813$	−19785.7	−0.853522
$814$	−4780.73	−0.205853
$815$	−457.262	−0.0196530
$816$	17358.5	0.744694
$817$	−3348.41	−0.143386
$818$	−41862.1	−1.78933
$819$	−1102.12	−0.0470223
$820$	−28767.9	−1.22515
$821$	−17556.9	−0.746335	−0.373168	−	0.927764i	$-0.621728\pi$
$821$	−17556.9	−0.746335	−0.373168	+	0.927764i	$0.621728\pi$
$822$	47839.2	2.02991
$823$	29414.2	1.24583	0.622913	−	0.782291i	$-0.285949\pi$
$823$	29414.2	1.24583	0.622913	+	0.782291i	$0.285949\pi$
$824$	112708.	4.76500
$825$	−1214.93	−0.0512707
$826$	−7843.88	−0.330416
$827$	−14018.5	−0.589447	−0.294723	−	0.955583i	$-0.595228\pi$
$827$	−14018.5	−0.589447	−0.294723	+	0.955583i	$0.595228\pi$
$828$	−4132.64	−0.173453
$829$	−30894.0	−1.29432	−0.647161	−	0.762353i	$-0.724044\pi$
$829$	−30894.0	−1.29432	−0.647161	+	0.762353i	$0.724044\pi$
$830$	−20001.4	−0.836457
$831$	−13089.3	−0.546405
$832$	35568.0	1.48209
$833$	−11089.6	−0.461262
$834$	−37883.5	−1.57290
$835$	−4962.79	−0.205682
$836$	6237.48	0.258048
$837$	4995.47	0.206295
$838$	32375.3	1.33459
$839$	−35520.3	−1.46162	−0.730809	−	0.682582i	$-0.760857\pi$
$839$	−35520.3	−1.46162	−0.730809	+	0.682582i	$0.760857\pi$
$840$	−2226.31	−0.0914463
$841$	841.000	0.0344828
$842$	48463.6	1.98357
$843$	−24197.6	−0.988624
$844$	−109245.	−4.45543
$845$	−1211.90	−0.0493379
$846$	−16046.8	−0.652126
$847$	3692.34	0.149788
$848$	75292.3	3.04899
$849$	24601.3	0.994481
$850$	−18811.1	−0.759076
$851$	5519.62	0.222338
$852$	−27767.7	−1.11656
$853$	−11533.4	−0.462948	−0.231474	−	0.972841i	$-0.574355\pi$
$853$	−11533.4	−0.462948	−0.231474	+	0.972841i	$0.574355\pi$
$854$	448.414	0.0179677
$855$	3122.28	0.124889
$856$	−17375.2	−0.693776
$857$	−41845.1	−1.66791	−0.833956	−	0.551831i	$-0.813929\pi$
$857$	−41845.1	−1.66791	−0.833956	+	0.551831i	$0.813929\pi$
$858$	2610.01	0.103851
$859$	−32102.0	−1.27509	−0.637547	−	0.770411i	$-0.720051\pi$
$859$	−32102.0	−1.27509	−0.637547	+	0.770411i	$0.720051\pi$
$860$	−3371.66	−0.133689
$861$	2897.77	0.114699
$862$	−81190.4	−3.20807
$863$	16195.0	0.638800	0.319400	−	0.947620i	$-0.396519\pi$
$863$	16195.0	0.638800	0.319400	+	0.947620i	$0.396519\pi$
$864$	11300.8	0.444977
$865$	8099.85	0.318385
$866$	−53750.2	−2.10913
$867$	−11454.2	−0.448681
$868$	−10357.4	−0.405014
$869$	1294.41	0.0505292
$870$	1924.47	0.0749949
$871$	3735.13	0.145304
$872$	−82594.5	−3.20757
$873$	14986.9	0.581020
$874$	−10087.2	−0.390396
$875$	2727.06	0.105362
$876$	48521.3	1.87144
$877$	−12380.9	−0.476708	−0.238354	−	0.971178i	$-0.576608\pi$
$877$	−12380.9	−0.476708	−0.238354	+	0.971178i	$0.576608\pi$
$878$	40384.2	1.55228
$879$	−11815.7	−0.453395
$880$	2755.49	0.105554
$881$	17354.4	0.663659	0.331830	−	0.943339i	$-0.392334\pi$
$881$	17354.4	0.663659	0.331830	+	0.943339i	$0.392334\pi$
$882$	−15950.3	−0.608928
$883$	27464.8	1.04673	0.523366	−	0.852108i	$-0.324676\pi$
$883$	27464.8	1.04673	0.523366	+	0.852108i	$0.324676\pi$
$884$	28850.7	1.09769
$885$	6638.32	0.252141
$886$	32429.5	1.22967
$887$	13612.5	0.515290	0.257645	−	0.966240i	$-0.417053\pi$
$887$	13612.5	0.515290	0.257645	+	0.966240i	$0.417053\pi$
$888$	−45551.1	−1.72139
$889$	−4204.90	−0.158636
$890$	8303.98	0.312753
$891$	305.137	0.0114730
$892$	21488.9	0.806614
$893$	−27962.9	−1.04787
$894$	−34572.9	−1.29339
$895$	−11353.3	−0.424021
$896$	−2687.44	−0.100202
$897$	−3013.40	−0.112168
$898$	−116.029	−0.00431174
$899$	5365.51	0.199054
$900$	−19316.1	−0.715410
$901$	14247.6	0.526811
$902$	−6862.40	−0.253318
$903$	339.624	0.0125160
$904$	78278.9	2.88000
$905$	4796.11	0.176164
$906$	−20981.1	−0.769371
$907$	22116.0	0.809646	0.404823	−	0.914395i	$-0.367333\pi$
$907$	22116.0	0.809646	0.404823	+	0.914395i	$0.367333\pi$
$908$	−92556.8	−3.38283
$909$	−228.940	−0.00835364
$910$	−2708.81	−0.0986770
$911$	32258.4	1.17318	0.586591	−	0.809883i	$-0.300470\pi$
$911$	32258.4	1.17318	0.586591	+	0.809883i	$0.300470\pi$
$912$	43507.4	1.57969
$913$	−3406.27	−0.123473
$914$	7498.42	0.271363
$915$	−379.495	−0.0137112
$916$	67649.2	2.44017
$917$	1214.01	0.0437189
$918$	4724.53	0.169861
$919$	−14830.1	−0.532317	−0.266158	−	0.963929i	$-0.585754\pi$
$919$	−14830.1	−0.532317	−0.266158	+	0.963929i	$0.585754\pi$
$920$	−6087.13	−0.218138
$921$	15555.1	0.556524
$922$	34825.0	1.24393
$923$	−20247.4	−0.722048
$924$	−632.657	−0.0225248
$925$	25798.8	0.917037
$926$	−9135.93	−0.324217
$927$	16032.4	0.568041
$928$	12137.9	0.429359
$929$	34202.7	1.20792	0.603958	−	0.797016i	$-0.293589\pi$
$929$	34202.7	1.20792	0.603958	+	0.797016i	$0.293589\pi$
$930$	12277.9	0.432914
$931$	−27794.9	−0.978453
$932$	89563.2	3.14779
$933$	29422.7	1.03243
$934$	68672.3	2.40581
$935$	521.423	0.0182378
$936$	24868.3	0.868425
$937$	43662.4	1.52229	0.761146	−	0.648581i	$-0.224637\pi$
$937$	43662.4	1.52229	0.761146	+	0.648581i	$0.224637\pi$
$938$	−1268.18	−0.0441445
$939$	8216.77	0.285563
$940$	−28157.1	−0.977002
$941$	35964.8	1.24593	0.622965	−	0.782250i	$-0.285928\pi$
$941$	35964.8	1.24593	0.622965	+	0.782250i	$0.285928\pi$
$942$	−21429.1	−0.741187
$943$	7923.02	0.273604
$944$	92501.5	3.18927
$945$	−316.688	−0.0109014
$946$	−804.287	−0.0276423
$947$	27799.7	0.953926	0.476963	−	0.878923i	$-0.341738\pi$
$947$	27799.7	0.953926	0.476963	+	0.878923i	$0.341738\pi$
$948$	20579.8	0.705064
$949$	35380.3	1.21021
$950$	−47148.0	−1.61019
$951$	−21520.9	−0.733819
$952$	−5870.40	−0.199854
$953$	21449.8	0.729095	0.364548	−	0.931185i	$-0.381224\pi$
$953$	21449.8	0.729095	0.364548	+	0.931185i	$0.381224\pi$
$954$	20492.5	0.695462
$955$	−2117.61	−0.0717532
$956$	−102848.	−3.47945
$957$	327.740	0.0110704
$958$	73243.8	2.47015
$959$	−8455.50	−0.284716
$960$	10220.2	0.343601
$961$	4440.50	0.149055
$962$	−55423.2	−1.85750
$963$	−2471.59	−0.0827060
$964$	−25731.2	−0.859695
$965$	3859.01	0.128732
$966$	1023.13	0.0340774
$967$	43875.6	1.45909	0.729547	−	0.683930i	$-0.239731\pi$
$967$	43875.6	1.45909	0.729547	+	0.683930i	$0.239731\pi$
$968$	−83314.2	−2.76634
$969$	8232.94	0.272941
$970$	36835.1	1.21928
$971$	16704.5	0.552084	0.276042	−	0.961146i	$-0.410977\pi$
$971$	16704.5	0.552084	0.276042	+	0.961146i	$0.410977\pi$
$972$	4851.36	0.160090
$973$	6695.84	0.220615
$974$	−42622.2	−1.40216
$975$	−14084.7	−0.462637
$976$	−5288.06	−0.173429
$977$	−38714.6	−1.26775	−0.633875	−	0.773436i	$-0.718537\pi$
$977$	−38714.6	−1.26775	−0.633875	+	0.773436i	$0.718537\pi$
$978$	−1734.21	−0.0567013
$979$	1414.18	0.0461669
$980$	−27987.8	−0.912283
$981$	−11748.9	−0.382379
$982$	43795.7	1.42319
$983$	8085.25	0.262339	0.131170	−	0.991360i	$-0.458127\pi$
$983$	8085.25	0.262339	0.131170	+	0.991360i	$0.458127\pi$
$984$	−65385.3	−2.11830
$985$	7160.00	0.231611
$986$	5074.50	0.163900
$987$	2836.23	0.0914674
$988$	72311.3	2.32847
$989$	928.593	0.0298560
$990$	749.970	0.0240764
$991$	18890.4	0.605522	0.302761	−	0.953066i	$-0.402092\pi$
$991$	18890.4	0.605522	0.302761	+	0.953066i	$0.402092\pi$
$992$	77438.6	2.47851
$993$	23048.6	0.736582
$994$	6874.55	0.219364
$995$	−7001.12	−0.223066
$996$	−54156.2	−1.72290
$997$	21387.7	0.679395	0.339697	−	0.940535i	$-0.389675\pi$
$997$	21387.7	0.679395	0.339697	+	0.940535i	$0.389675\pi$
$998$	78252.0	2.48199
$999$	−6479.55	−0.205209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.g.1.41	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.g.1.41	✓	43	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)

\(f(q)\)	\(=\)	\(q+5.28814 q^{2} +3.00000 q^{3} +19.9645 q^{4} +4.18300 q^{5} +15.8644 q^{6} -2.80401 q^{7} +63.2698 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.28814 q^{2} +3.00000 q^{3} +19.9645 q^{4} +4.18300 q^{5} +15.8644 q^{6} -2.80401 q^{7} +63.2698 q^{8} +9.00000 q^{9} +22.1203 q^{10} +3.76713 q^{11} +59.8934 q^{12} +43.6724 q^{13} -14.8280 q^{14} +12.5490 q^{15} +174.864 q^{16} +33.0896 q^{17} +47.5933 q^{18} +82.9357 q^{19} +83.5114 q^{20} -8.41203 q^{21} +19.9211 q^{22} -23.0000 q^{23} +189.809 q^{24} -107.502 q^{25} +230.946 q^{26} +27.0000 q^{27} -55.9805 q^{28} +29.0000 q^{29} +66.3610 q^{30} +185.018 q^{31} +418.547 q^{32} +11.3014 q^{33} +174.983 q^{34} -11.7292 q^{35} +179.680 q^{36} -239.983 q^{37} +438.576 q^{38} +131.017 q^{39} +264.658 q^{40} -344.479 q^{41} -44.4840 q^{42} -40.3736 q^{43} +75.2086 q^{44} +37.6470 q^{45} -121.627 q^{46} -337.164 q^{47} +524.592 q^{48} -335.138 q^{49} -568.489 q^{50} +99.2689 q^{51} +871.896 q^{52} +430.576 q^{53} +142.780 q^{54} +15.7579 q^{55} -177.409 q^{56} +248.807 q^{57} +153.356 q^{58} +528.991 q^{59} +250.534 q^{60} -30.2410 q^{61} +978.399 q^{62} -25.2361 q^{63} +814.427 q^{64} +182.682 q^{65} +59.7633 q^{66} +85.5260 q^{67} +660.616 q^{68} -69.0000 q^{69} -62.0256 q^{70} -463.619 q^{71} +569.428 q^{72} +810.128 q^{73} -1269.07 q^{74} -322.507 q^{75} +1655.77 q^{76} -10.5631 q^{77} +692.838 q^{78} +343.607 q^{79} +731.456 q^{80} +81.0000 q^{81} -1821.65 q^{82} -904.210 q^{83} -167.942 q^{84} +138.414 q^{85} -213.501 q^{86} +87.0000 q^{87} +238.345 q^{88} +375.401 q^{89} +199.083 q^{90} -122.458 q^{91} -459.183 q^{92} +555.053 q^{93} -1782.97 q^{94} +346.920 q^{95} +1255.64 q^{96} +1665.21 q^{97} -1772.26 q^{98} +33.9041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9}+O(q^{10}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9	\( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9} + 32 q^{10} + 109 q^{11} + 630 q^{12} + 235 q^{13} + 205 q^{14} + 75 q^{15} + 1190 q^{16} + 228 q^{17} + 18 q^{18} + 291 q^{19} + 407 q^{20} + 318 q^{21} + 808 q^{22} - 989 q^{23} + 81 q^{24} + 1656 q^{25} - 289 q^{26} + 1161 q^{27} + 1831 q^{28} + 1247 q^{29} + 96 q^{30} + 694 q^{31} + 88 q^{32} + 327 q^{33} + 1158 q^{34} - 43 q^{35} + 1890 q^{36} + 1167 q^{37} + 35 q^{38} + 705 q^{39} + 1117 q^{40} + 977 q^{41} + 615 q^{42} + 1361 q^{43} + 798 q^{44} + 225 q^{45} - 46 q^{46} + 684 q^{47} + 3570 q^{48} + 3417 q^{49} + 267 q^{50} + 684 q^{51} + 3054 q^{52} + 1344 q^{53} + 54 q^{54} + 1072 q^{55} + 1741 q^{56} + 873 q^{57} + 58 q^{58} - 313 q^{59} + 1221 q^{60} + 3162 q^{61} - 1010 q^{62} + 954 q^{63} + 8795 q^{64} + 370 q^{65} + 2424 q^{66} + 2699 q^{67} + 2799 q^{68} - 2967 q^{69} + 443 q^{70} + 2140 q^{71} + 243 q^{72} + 922 q^{73} + 2281 q^{74} + 4968 q^{75} + 2237 q^{76} + 879 q^{77} - 867 q^{78} + 5078 q^{79} + 5377 q^{80} + 3483 q^{81} + 1045 q^{82} + 2670 q^{83} + 5493 q^{84} - 1087 q^{85} + 3249 q^{86} + 3741 q^{87} + 8305 q^{88} + 1893 q^{89} + 288 q^{90} + 6847 q^{91} - 4830 q^{92} + 2082 q^{93} - 1128 q^{94} + 6973 q^{95} + 264 q^{96} + 3040 q^{97} + 2581 q^{98} + 981 q^{99}+O(q^{100}) \) 43 * q + 2 * q^2 + 129 * q^3 + 210 * q^4 + 25 * q^5 + 6 * q^6 + 106 * q^7 + 27 * q^8 + 387 * q^9 + 32 * q^10 + 109 * q^11 + 630 * q^12 + 235 * q^13 + 205 * q^14 + 75 * q^15 + 1190 * q^16 + 228 * q^17 + 18 * q^18 + 291 * q^19 + 407 * q^20 + 318 * q^21 + 808 * q^22 - 989 * q^23 + 81 * q^24 + 1656 * q^25 - 289 * q^26 + 1161 * q^27 + 1831 * q^28 + 1247 * q^29 + 96 * q^30 + 694 * q^31 + 88 * q^32 + 327 * q^33 + 1158 * q^34 - 43 * q^35 + 1890 * q^36 + 1167 * q^37 + 35 * q^38 + 705 * q^39 + 1117 * q^40 + 977 * q^41 + 615 * q^42 + 1361 * q^43 + 798 * q^44 + 225 * q^45 - 46 * q^46 + 684 * q^47 + 3570 * q^48 + 3417 * q^49 + 267 * q^50 + 684 * q^51 + 3054 * q^52 + 1344 * q^53 + 54 * q^54 + 1072 * q^55 + 1741 * q^56 + 873 * q^57 + 58 * q^58 - 313 * q^59 + 1221 * q^60 + 3162 * q^61 - 1010 * q^62 + 954 * q^63 + 8795 * q^64 + 370 * q^65 + 2424 * q^66 + 2699 * q^67 + 2799 * q^68 - 2967 * q^69 + 443 * q^70 + 2140 * q^71 + 243 * q^72 + 922 * q^73 + 2281 * q^74 + 4968 * q^75 + 2237 * q^76 + 879 * q^77 - 867 * q^78 + 5078 * q^79 + 5377 * q^80 + 3483 * q^81 + 1045 * q^82 + 2670 * q^83 + 5493 * q^84 - 1087 * q^85 + 3249 * q^86 + 3741 * q^87 + 8305 * q^88 + 1893 * q^89 + 288 * q^90 + 6847 * q^91 - 4830 * q^92 + 2082 * q^93 - 1128 * q^94 + 6973 * q^95 + 264 * q^96 + 3040 * q^97 + 2581 * q^98 + 981 * q^99

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