LMFDB - Embedded newform 2001.4.a.c.1.10

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

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-3.05952 q^{2} -3.00000 q^{3} +1.36067 q^{4} -2.38782 q^{5} +9.17856 q^{6} -16.8938 q^{7} +20.3132 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.05952 q^{2} -3.00000 q^{3} +1.36067 q^{4} -2.38782 q^{5} +9.17856 q^{6} -16.8938 q^{7} +20.3132 q^{8} +9.00000 q^{9} +7.30559 q^{10} +7.51747 q^{11} -4.08200 q^{12} +68.8213 q^{13} +51.6869 q^{14} +7.16347 q^{15} -73.0339 q^{16} -114.206 q^{17} -27.5357 q^{18} +58.8902 q^{19} -3.24903 q^{20} +50.6814 q^{21} -22.9998 q^{22} +23.0000 q^{23} -60.9395 q^{24} -119.298 q^{25} -210.560 q^{26} -27.0000 q^{27} -22.9868 q^{28} -29.0000 q^{29} -21.9168 q^{30} +112.461 q^{31} +60.9434 q^{32} -22.5524 q^{33} +349.415 q^{34} +40.3394 q^{35} +12.2460 q^{36} -158.605 q^{37} -180.176 q^{38} -206.464 q^{39} -48.5042 q^{40} +17.0282 q^{41} -155.061 q^{42} -318.461 q^{43} +10.2288 q^{44} -21.4904 q^{45} -70.3690 q^{46} -20.7555 q^{47} +219.102 q^{48} -57.6000 q^{49} +364.996 q^{50} +342.617 q^{51} +93.6429 q^{52} +553.486 q^{53} +82.6071 q^{54} -17.9504 q^{55} -343.166 q^{56} -176.671 q^{57} +88.7261 q^{58} -280.429 q^{59} +9.74710 q^{60} +152.988 q^{61} -344.078 q^{62} -152.044 q^{63} +397.814 q^{64} -164.333 q^{65} +68.9995 q^{66} -150.140 q^{67} -155.396 q^{68} -69.0000 q^{69} -123.419 q^{70} +207.768 q^{71} +182.819 q^{72} +1028.67 q^{73} +485.254 q^{74} +357.895 q^{75} +80.1301 q^{76} -126.998 q^{77} +631.680 q^{78} +423.836 q^{79} +174.392 q^{80} +81.0000 q^{81} -52.0982 q^{82} +1415.69 q^{83} +68.9605 q^{84} +272.703 q^{85} +974.337 q^{86} +87.0000 q^{87} +152.704 q^{88} -988.230 q^{89} +65.7503 q^{90} -1162.65 q^{91} +31.2954 q^{92} -337.384 q^{93} +63.5019 q^{94} -140.619 q^{95} -182.830 q^{96} +16.7639 q^{97} +176.228 q^{98} +67.6572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9} + 26 q^{10} - 109 q^{11} - 414 q^{12} + 115 q^{13} - 243 q^{14} + 45 q^{15} + 406 q^{16} - 228 q^{17} - 72 q^{18} - 135 q^{19} - 73 q^{20} + 18 q^{21} - 40 q^{22} + 851 q^{23} + 423 q^{24} + 942 q^{25} - 543 q^{26} - 999 q^{27} + 853 q^{28} - 1073 q^{29} - 78 q^{30} - 518 q^{31} - 1596 q^{32} + 327 q^{33} + 312 q^{34} - 37 q^{35} + 1242 q^{36} + 245 q^{37} - 59 q^{38} - 345 q^{39} + 293 q^{40} - 915 q^{41} + 729 q^{42} - 389 q^{43} - 832 q^{44} - 135 q^{45} - 184 q^{46} - 926 q^{47} - 1218 q^{48} + 1655 q^{49} - 439 q^{50} + 684 q^{51} + 1290 q^{52} - 1134 q^{53} + 216 q^{54} - 404 q^{55} - 1141 q^{56} + 405 q^{57} + 232 q^{58} - 179 q^{59} + 219 q^{60} + 10 q^{61} + 1378 q^{62} - 54 q^{63} + 1359 q^{64} + 110 q^{65} + 120 q^{66} + 1385 q^{67} - 3375 q^{68} - 2553 q^{69} - 637 q^{70} - 2432 q^{71} - 1269 q^{72} - 1638 q^{73} - 2193 q^{74} - 2826 q^{75} - 1319 q^{76} - 3703 q^{77} + 1629 q^{78} - 4728 q^{79} - 1567 q^{80} + 2997 q^{81} + 537 q^{82} - 1416 q^{83} - 2559 q^{84} - 2093 q^{85} - 1187 q^{86} + 3219 q^{87} + 1497 q^{88} - 4019 q^{89} + 234 q^{90} - 545 q^{91} + 3174 q^{92} + 1554 q^{93} + 108 q^{94} - 807 q^{95} + 4788 q^{96} - 754 q^{97} - 5561 q^{98} - 981 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9 + 26 * q^10 - 109 * q^11 - 414 * q^12 + 115 * q^13 - 243 * q^14 + 45 * q^15 + 406 * q^16 - 228 * q^17 - 72 * q^18 - 135 * q^19 - 73 * q^20 + 18 * q^21 - 40 * q^22 + 851 * q^23 + 423 * q^24 + 942 * q^25 - 543 * q^26 - 999 * q^27 + 853 * q^28 - 1073 * q^29 - 78 * q^30 - 518 * q^31 - 1596 * q^32 + 327 * q^33 + 312 * q^34 - 37 * q^35 + 1242 * q^36 + 245 * q^37 - 59 * q^38 - 345 * q^39 + 293 * q^40 - 915 * q^41 + 729 * q^42 - 389 * q^43 - 832 * q^44 - 135 * q^45 - 184 * q^46 - 926 * q^47 - 1218 * q^48 + 1655 * q^49 - 439 * q^50 + 684 * q^51 + 1290 * q^52 - 1134 * q^53 + 216 * q^54 - 404 * q^55 - 1141 * q^56 + 405 * q^57 + 232 * q^58 - 179 * q^59 + 219 * q^60 + 10 * q^61 + 1378 * q^62 - 54 * q^63 + 1359 * q^64 + 110 * q^65 + 120 * q^66 + 1385 * q^67 - 3375 * q^68 - 2553 * q^69 - 637 * q^70 - 2432 * q^71 - 1269 * q^72 - 1638 * q^73 - 2193 * q^74 - 2826 * q^75 - 1319 * q^76 - 3703 * q^77 + 1629 * q^78 - 4728 * q^79 - 1567 * q^80 + 2997 * q^81 + 537 * q^82 - 1416 * q^83 - 2559 * q^84 - 2093 * q^85 - 1187 * q^86 + 3219 * q^87 + 1497 * q^88 - 4019 * q^89 + 234 * q^90 - 545 * q^91 + 3174 * q^92 + 1554 * q^93 + 108 * q^94 - 807 * q^95 + 4788 * q^96 - 754 * q^97 - 5561 * 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 $

$2$	−3.05952	−1.08170	−0.540852	−	0.841118i	$-0.681898\pi$
$2$	−3.05952	−1.08170	−0.540852	+	0.841118i	$0.681898\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	1.36067	0.170084
$5$	−2.38782	−0.213573	−0.106787	−	0.994282i	$-0.534056\pi$
$5$	−2.38782	−0.213573	−0.106787	+	0.994282i	$0.534056\pi$
$6$	9.17856	0.624522
$7$	−16.8938	−0.912179	−0.456089	−	0.889934i	$-0.650750\pi$
$7$	−16.8938	−0.912179	−0.456089	+	0.889934i	$0.650750\pi$
$8$	20.3132	0.897724
$9$	9.00000	0.333333
$10$	7.30559	0.231023
$11$	7.51747	0.206055	0.103027	−	0.994679i	$-0.467147\pi$
$11$	7.51747	0.206055	0.103027	+	0.994679i	$0.467147\pi$
$12$	−4.08200	−0.0981978
$13$	68.8213	1.46828	0.734138	−	0.679000i	$-0.237586\pi$
$13$	68.8213	1.46828	0.734138	+	0.679000i	$0.237586\pi$
$14$	51.6869	0.986707
$15$	7.16347	0.123307
$16$	−73.0339	−1.14116
$17$	−114.206	−1.62935	−0.814675	−	0.579918i	$-0.803084\pi$
$17$	−114.206	−1.62935	−0.814675	+	0.579918i	$0.803084\pi$
$18$	−27.5357	−0.360568
$19$	58.8902	0.711071	0.355536	−	0.934663i	$-0.384299\pi$
$19$	58.8902	0.711071	0.355536	+	0.934663i	$0.384299\pi$
$20$	−3.24903	−0.0363253
$21$	50.6814	0.526647
$22$	−22.9998	−0.222890
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−60.9395	−0.518301
$25$	−119.298	−0.954386
$26$	−210.560	−1.58824
$27$	−27.0000	−0.192450
$28$	−22.9868	−0.155147
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−21.9168	−0.133381
$31$	112.461	0.651570	0.325785	−	0.945444i	$-0.394371\pi$
$31$	112.461	0.651570	0.325785	+	0.945444i	$0.394371\pi$
$32$	60.9434	0.336668
$33$	−22.5524	−0.118966
$34$	349.415	1.76247
$35$	40.3394	0.194817
$36$	12.2460	0.0566945
$37$	−158.605	−0.704714	−0.352357	−	0.935866i	$-0.614620\pi$
$37$	−158.605	−0.704714	−0.352357	+	0.935866i	$0.614620\pi$
$38$	−180.176	−0.769168
$39$	−206.464	−0.847710
$40$	−48.5042	−0.191730
$41$	17.0282	0.0648625	0.0324313	−	0.999474i	$-0.489675\pi$
$41$	17.0282	0.0648625	0.0324313	+	0.999474i	$0.489675\pi$
$42$	−155.061	−0.569676
$43$	−318.461	−1.12941	−0.564707	−	0.825291i	$-0.691011\pi$
$43$	−318.461	−1.12941	−0.564707	+	0.825291i	$0.691011\pi$
$44$	10.2288	0.0350465
$45$	−21.4904	−0.0711911
$46$	−70.3690	−0.225551
$47$	−20.7555	−0.0644149	−0.0322075	−	0.999481i	$-0.510254\pi$
$47$	−20.7555	−0.0644149	−0.0322075	+	0.999481i	$0.510254\pi$
$48$	219.102	0.658846
$49$	−57.6000	−0.167930
$50$	364.996	1.03236
$51$	342.617	0.940705
$52$	93.6429	0.249730
$53$	553.486	1.43447	0.717237	−	0.696829i	$-0.245406\pi$
$53$	553.486	1.43447	0.717237	+	0.696829i	$0.245406\pi$
$54$	82.6071	0.208174
$55$	−17.9504	−0.0440078
$56$	−343.166	−0.818885
$57$	−176.671	−0.410537
$58$	88.7261	0.200867
$59$	−280.429	−0.618792	−0.309396	−	0.950933i	$-0.600127\pi$
$59$	−280.429	−0.618792	−0.309396	+	0.950933i	$0.600127\pi$
$60$	9.74710	0.0209724
$61$	152.988	0.321117	0.160559	−	0.987026i	$-0.448670\pi$
$61$	152.988	0.321117	0.160559	+	0.987026i	$0.448670\pi$
$62$	−344.078	−0.704806
$63$	−152.044	−0.304060
$64$	397.814	0.776980
$65$	−164.333	−0.313585
$66$	68.9995	0.128686
$67$	−150.140	−0.273769	−0.136884	−	0.990587i	$-0.543709\pi$
$67$	−150.140	−0.273769	−0.136884	+	0.990587i	$0.543709\pi$
$68$	−155.396	−0.277125
$69$	−69.0000	−0.120386
$70$	−123.419	−0.210734
$71$	207.768	0.347290	0.173645	−	0.984808i	$-0.444446\pi$
$71$	207.768	0.347290	0.173645	+	0.984808i	$0.444446\pi$
$72$	182.819	0.299241
$73$	1028.67	1.64926	0.824632	−	0.565670i	$-0.191382\pi$
$73$	1028.67	1.64926	0.824632	+	0.565670i	$0.191382\pi$
$74$	485.254	0.762292
$75$	357.895	0.551015
$76$	80.1301	0.120941
$77$	−126.998	−0.187959
$78$	631.680	0.916971
$79$	423.836	0.603612	0.301806	−	0.953369i	$-0.402411\pi$
$79$	423.836	0.603612	0.301806	+	0.953369i	$0.402411\pi$
$80$	174.392	0.243720
$81$	81.0000	0.111111
$82$	−52.0982	−0.0701620
$83$	1415.69	1.87219	0.936097	−	0.351742i	$-0.114411\pi$
$83$	1415.69	1.87219	0.936097	+	0.351742i	$0.114411\pi$
$84$	68.9605	0.0895739
$85$	272.703	0.347986
$86$	974.337	1.22169
$87$	87.0000	0.107211
$88$	152.704	0.184980
$89$	−988.230	−1.17699	−0.588496	−	0.808500i	$-0.700280\pi$
$89$	−988.230	−1.17699	−0.588496	+	0.808500i	$0.700280\pi$
$90$	65.7503	0.0770077
$91$	−1162.65	−1.33933
$92$	31.2954	0.0354649
$93$	−337.384	−0.376184
$94$	63.5019	0.0696779
$95$	−140.619	−0.151866
$96$	−182.830	−0.194375
$97$	16.7639	0.0175476	0.00877379	−	0.999962i	$-0.497207\pi$
$97$	16.7639	0.0175476	0.00877379	+	0.999962i	$0.497207\pi$
$98$	176.228	0.181650
$99$	67.6572	0.0686849
$100$	−162.325	−0.162325
$101$	−114.808	−0.113107	−0.0565535	−	0.998400i	$-0.518011\pi$
$101$	−114.808	−0.113107	−0.0565535	+	0.998400i	$0.518011\pi$
$102$	−1048.24	−1.01756
$103$	35.4817	0.0339428	0.0169714	−	0.999856i	$-0.494598\pi$
$103$	35.4817	0.0339428	0.0169714	+	0.999856i	$0.494598\pi$
$104$	1397.98	1.31811
$105$	−121.018	−0.112478
$106$	−1693.40	−1.55168
$107$	1389.42	1.25533	0.627666	−	0.778483i	$-0.284010\pi$
$107$	1389.42	1.25533	0.627666	+	0.778483i	$0.284010\pi$
$108$	−36.7380	−0.0327326
$109$	1712.63	1.50495	0.752477	−	0.658619i	$-0.228859\pi$
$109$	1712.63	1.50495	0.752477	+	0.658619i	$0.228859\pi$
$110$	54.9195	0.0476034
$111$	475.814	0.406867
$112$	1233.82	1.04094
$113$	−1978.42	−1.64703	−0.823513	−	0.567297i	$-0.807989\pi$
$113$	−1978.42	−1.64703	−0.823513	+	0.567297i	$0.807989\pi$
$114$	540.528	0.444080
$115$	−54.9199	−0.0445331
$116$	−39.4594	−0.0315837
$117$	619.392	0.489425
$118$	857.979	0.669350
$119$	1929.37	1.48626
$120$	145.513	0.110695
$121$	−1274.49	−0.957541
$122$	−468.071	−0.347354
$123$	−51.0847	−0.0374484
$124$	153.023	0.110821
$125$	583.341	0.417405
$126$	465.182	0.328902
$127$	−551.867	−0.385593	−0.192796	−	0.981239i	$-0.561756\pi$
$127$	−551.867	−0.385593	−0.192796	+	0.981239i	$0.561756\pi$
$128$	−1704.67	−1.17713
$129$	955.382	0.652068
$130$	502.780	0.339206
$131$	−214.365	−0.142970	−0.0714852	−	0.997442i	$-0.522774\pi$
$131$	−214.365	−0.142970	−0.0714852	+	0.997442i	$0.522774\pi$
$132$	−30.6863	−0.0202341
$133$	−994.879	−0.648624
$134$	459.356	0.296137
$135$	64.4712	0.0411022
$136$	−2319.88	−1.46271
$137$	2791.69	1.74095	0.870475	−	0.492213i	$-0.163812\pi$
$137$	2791.69	1.74095	0.870475	+	0.492213i	$0.163812\pi$
$138$	211.107	0.130222
$139$	−2329.52	−1.42149	−0.710745	−	0.703450i	$-0.751642\pi$
$139$	−2329.52	−1.42149	−0.710745	+	0.703450i	$0.751642\pi$
$140$	54.8885	0.0331352
$141$	62.2665	0.0371900
$142$	−635.671	−0.375664
$143$	517.362	0.302545
$144$	−657.305	−0.380385
$145$	69.2468	0.0396596
$146$	−3147.23	−1.78402
$147$	172.800	0.0969544
$148$	−215.808	−0.119860
$149$	−2218.44	−1.21974	−0.609871	−	0.792501i	$-0.708779\pi$
$149$	−2218.44	−1.21974	−0.609871	+	0.792501i	$0.708779\pi$
$150$	−1094.99	−0.596035
$151$	−278.166	−0.149913	−0.0749564	−	0.997187i	$-0.523882\pi$
$151$	−278.166	−0.149913	−0.0749564	+	0.997187i	$0.523882\pi$
$152$	1196.25	0.638346
$153$	−1027.85	−0.543116
$154$	388.554	0.203316
$155$	−268.538	−0.139158
$156$	−280.929	−0.144181
$157$	3299.62	1.67732	0.838658	−	0.544658i	$-0.183341\pi$
$157$	3299.62	1.67732	0.838658	+	0.544658i	$0.183341\pi$
$158$	−1296.74	−0.652929
$159$	−1660.46	−0.828194
$160$	−145.522	−0.0719033
$161$	−388.557	−0.190202
$162$	−247.821	−0.120189
$163$	106.322	0.0510906	0.0255453	−	0.999674i	$-0.491868\pi$
$163$	106.322	0.0510906	0.0255453	+	0.999674i	$0.491868\pi$
$164$	23.1698	0.0110320
$165$	53.8511	0.0254079
$166$	−4331.33	−2.02516
$167$	−239.888	−0.111156	−0.0555782	−	0.998454i	$-0.517700\pi$
$167$	−239.888	−0.111156	−0.0555782	+	0.998454i	$0.517700\pi$
$168$	1029.50	0.472783
$169$	2539.37	1.15583
$170$	−834.340	−0.376417
$171$	530.012	0.237024
$172$	−433.319	−0.192095
$173$	−1051.14	−0.461948	−0.230974	−	0.972960i	$-0.574191\pi$
$173$	−1051.14	−0.461948	−0.230974	+	0.972960i	$0.574191\pi$
$174$	−266.178	−0.115971
$175$	2015.40	0.870571
$176$	−549.030	−0.235140
$177$	841.287	0.357260
$178$	3023.51	1.27316
$179$	1947.68	0.813276	0.406638	−	0.913589i	$-0.366701\pi$
$179$	1947.68	0.813276	0.406638	+	0.913589i	$0.366701\pi$
$180$	−29.2413	−0.0121084
$181$	3104.11	1.27473	0.637366	−	0.770562i	$-0.280024\pi$
$181$	3104.11	1.27473	0.637366	+	0.770562i	$0.280024\pi$
$182$	3557.16	1.44876
$183$	−458.965	−0.185397
$184$	467.203	0.187188
$185$	378.719	0.150508
$186$	1032.23	0.406920
$187$	−858.537	−0.335735
$188$	−28.2414	−0.0109559
$189$	456.132	0.175549
$190$	430.228	0.164274
$191$	−790.986	−0.299653	−0.149827	−	0.988712i	$-0.547872\pi$
$191$	−790.986	−0.299653	−0.149827	+	0.988712i	$0.547872\pi$
$192$	−1193.44	−0.448590
$193$	2683.23	1.00074	0.500371	−	0.865811i	$-0.333197\pi$
$193$	2683.23	1.00074	0.500371	+	0.865811i	$0.333197\pi$
$194$	−51.2895	−0.0189813
$195$	492.999	0.181048
$196$	−78.3744	−0.0285621
$197$	211.929	0.0766464	0.0383232	−	0.999265i	$-0.487798\pi$
$197$	211.929	0.0766464	0.0383232	+	0.999265i	$0.487798\pi$
$198$	−206.999	−0.0742967
$199$	2987.58	1.06424	0.532121	−	0.846668i	$-0.321395\pi$
$199$	2987.58	1.06424	0.532121	+	0.846668i	$0.321395\pi$
$200$	−2423.33	−0.856776
$201$	450.419	0.158060
$202$	351.257	0.122348
$203$	489.920	0.169387
$204$	466.188	0.159998
$205$	−40.6604	−0.0138529
$206$	−108.557	−0.0367161
$207$	207.000	0.0695048
$208$	−5026.29	−1.67553
$209$	442.705	0.146519
$210$	370.257	0.121668
$211$	2788.07	0.909661	0.454831	−	0.890578i	$-0.349700\pi$
$211$	2788.07	0.909661	0.454831	+	0.890578i	$0.349700\pi$
$212$	753.111	0.243980
$213$	−623.305	−0.200508
$214$	−4250.97	−1.35790
$215$	760.428	0.241213
$216$	−548.456	−0.172767
$217$	−1899.90	−0.594348
$218$	−5239.82	−1.62791
$219$	−3086.00	−0.952203
$220$	−24.4245	−0.00748500
$221$	−7859.78	−2.39233
$222$	−1455.76	−0.440110
$223$	3581.04	1.07536	0.537678	−	0.843150i	$-0.319302\pi$
$223$	3581.04	1.07536	0.537678	+	0.843150i	$0.319302\pi$
$224$	−1029.57	−0.307101
$225$	−1073.68	−0.318129
$226$	6053.02	1.78160
$227$	−6707.47	−1.96119	−0.980595	−	0.196043i	$-0.937191\pi$
$227$	−6707.47	−1.96119	−0.980595	+	0.196043i	$0.937191\pi$
$228$	−240.390	−0.0698256
$229$	−2020.43	−0.583028	−0.291514	−	0.956567i	$-0.594159\pi$
$229$	−2020.43	−0.583028	−0.291514	+	0.956567i	$0.594159\pi$
$230$	168.029	0.0481716
$231$	380.995	0.108518
$232$	−589.082	−0.166703
$233$	3282.22	0.922854	0.461427	−	0.887178i	$-0.347338\pi$
$233$	3282.22	0.922854	0.461427	+	0.887178i	$0.347338\pi$
$234$	−1895.04	−0.529413
$235$	49.5605	0.0137573
$236$	−381.571	−0.105246
$237$	−1271.51	−0.348495
$238$	−5902.94	−1.60769
$239$	2115.97	0.572680	0.286340	−	0.958128i	$-0.407561\pi$
$239$	2115.97	0.572680	0.286340	+	0.958128i	$0.407561\pi$
$240$	−523.176	−0.140712
$241$	−755.591	−0.201958	−0.100979	−	0.994889i	$-0.532198\pi$
$241$	−755.591	−0.201958	−0.100979	+	0.994889i	$0.532198\pi$
$242$	3899.32	1.03578
$243$	−243.000	−0.0641500
$244$	208.166	0.0546167
$245$	137.538	0.0358653
$246$	156.295	0.0405081
$247$	4052.90	1.04405
$248$	2284.45	0.584930
$249$	−4247.07	−1.08091
$250$	−1784.74	−0.451508
$251$	−6630.24	−1.66732	−0.833659	−	0.552280i	$-0.813758\pi$
$251$	−6630.24	−1.66732	−0.833659	+	0.552280i	$0.813758\pi$
$252$	−206.882	−0.0517155
$253$	172.902	0.0429654
$254$	1688.45	0.417097
$255$	−818.108	−0.200910
$256$	2032.95	0.496327
$257$	−4881.48	−1.18482	−0.592409	−	0.805637i	$-0.701823\pi$
$257$	−4881.48	−1.18482	−0.592409	+	0.805637i	$0.701823\pi$
$258$	−2923.01	−0.705344
$259$	2679.43	0.642825
$260$	−223.603	−0.0533356
$261$	−261.000	−0.0618984
$262$	655.853	0.154652
$263$	6753.37	1.58339	0.791693	−	0.610919i	$-0.209200\pi$
$263$	6753.37	1.58339	0.791693	+	0.610919i	$0.209200\pi$
$264$	−458.111	−0.106798
$265$	−1321.63	−0.306365
$266$	3043.85	0.701619
$267$	2964.69	0.679536
$268$	−204.290	−0.0465635
$269$	7313.78	1.65773	0.828864	−	0.559450i	$-0.188988\pi$
$269$	7313.78	1.65773	0.828864	+	0.559450i	$0.188988\pi$
$270$	−197.251	−0.0444604
$271$	−208.263	−0.0466829	−0.0233415	−	0.999728i	$-0.507430\pi$
$271$	−208.263	−0.0466829	−0.0233415	+	0.999728i	$0.507430\pi$
$272$	8340.89	1.85934
$273$	3487.96	0.773263
$274$	−8541.23	−1.88319
$275$	−896.821	−0.196656
$276$	−93.8861	−0.0204756
$277$	−3169.09	−0.687408	−0.343704	−	0.939078i	$-0.611682\pi$
$277$	−3169.09	−0.687408	−0.343704	+	0.939078i	$0.611682\pi$
$278$	7127.21	1.53763
$279$	1012.15	0.217190
$280$	819.420	0.174892
$281$	−8371.54	−1.77724	−0.888620	−	0.458645i	$-0.848335\pi$
$281$	−8371.54	−1.77724	−0.888620	+	0.458645i	$0.848335\pi$
$282$	−190.506	−0.0402286
$283$	−527.780	−0.110860	−0.0554298	−	0.998463i	$-0.517653\pi$
$283$	−527.780	−0.110860	−0.0554298	+	0.998463i	$0.517653\pi$
$284$	282.704	0.0590682
$285$	421.858	0.0876798
$286$	−1582.88	−0.327264
$287$	−287.671	−0.0591662
$288$	548.491	0.112223
$289$	8129.93	1.65478
$290$	−211.862	−0.0428999
$291$	−50.2917	−0.0101311
$292$	1399.67	0.280513
$293$	−7932.29	−1.58160	−0.790801	−	0.612073i	$-0.790336\pi$
$293$	−7932.29	−1.58160	−0.790801	+	0.612073i	$0.790336\pi$
$294$	−528.685	−0.104876
$295$	669.615	0.132158
$296$	−3221.76	−0.632639
$297$	−202.972	−0.0396552
$298$	6787.35	1.31940
$299$	1582.89	0.306157
$300$	486.976	0.0937186
$301$	5380.01	1.03023
$302$	851.054	0.162161
$303$	344.424	0.0653024
$304$	−4300.99	−0.811442
$305$	−365.309	−0.0685821
$306$	3144.73	0.587491
$307$	191.015	0.0355107	0.0177554	−	0.999842i	$-0.494348\pi$
$307$	191.015	0.0355107	0.0177554	+	0.999842i	$0.494348\pi$
$308$	−172.803	−0.0319687
$309$	−106.445	−0.0195969
$310$	821.597	0.150528
$311$	−7881.94	−1.43712	−0.718559	−	0.695466i	$-0.755198\pi$
$311$	−7881.94	−1.43712	−0.718559	+	0.695466i	$0.755198\pi$
$312$	−4193.94	−0.761009
$313$	10206.1	1.84307	0.921536	−	0.388293i	$-0.126935\pi$
$313$	10206.1	1.84307	0.921536	+	0.388293i	$0.126935\pi$
$314$	−10095.3	−1.81436
$315$	363.054	0.0649390
$316$	576.701	0.102664
$317$	−7154.61	−1.26764	−0.633821	−	0.773479i	$-0.718515\pi$
$317$	−7154.61	−1.26764	−0.633821	+	0.773479i	$0.718515\pi$
$318$	5080.20	0.895861
$319$	−218.006	−0.0382634
$320$	−949.908	−0.165942
$321$	−4168.27	−0.724766
$322$	1188.80	0.205743
$323$	−6725.60	−1.15858
$324$	110.214	0.0188982
$325$	−8210.26	−1.40130
$326$	−325.294	−0.0552649
$327$	−5137.88	−0.868885
$328$	345.897	0.0582286
$329$	350.639	0.0587579
$330$	−164.759	−0.0274838
$331$	1927.88	0.320138	0.160069	−	0.987106i	$-0.448828\pi$
$331$	1927.88	0.320138	0.160069	+	0.987106i	$0.448828\pi$
$332$	1926.28	0.318429
$333$	−1427.44	−0.234905
$334$	733.944	0.120238
$335$	358.507	0.0584697
$336$	−3701.46	−0.600986
$337$	−11372.7	−1.83832	−0.919159	−	0.393887i	$-0.871130\pi$
$337$	−11372.7	−1.83832	−0.919159	+	0.393887i	$0.871130\pi$
$338$	−7769.25	−1.25027
$339$	5935.26	0.950911
$340$	371.058	0.0591866
$341$	845.425	0.134259
$342$	−1621.58	−0.256389
$343$	6767.65	1.06536
$344$	−6468.95	−1.01390
$345$	164.760	0.0257112
$346$	3216.00	0.499691
$347$	−9635.06	−1.49060	−0.745298	−	0.666731i	$-0.767693\pi$
$347$	−9635.06	−1.49060	−0.745298	+	0.666731i	$0.767693\pi$
$348$	118.378	0.0182349
$349$	−3545.25	−0.543763	−0.271881	−	0.962331i	$-0.587646\pi$
$349$	−3545.25	−0.543763	−0.271881	+	0.962331i	$0.587646\pi$
$350$	−6166.16	−0.941700
$351$	−1858.17	−0.282570
$352$	458.140	0.0693720
$353$	−6899.87	−1.04035	−0.520174	−	0.854060i	$-0.674133\pi$
$353$	−6899.87	−1.04035	−0.520174	+	0.854060i	$0.674133\pi$
$354$	−2573.94	−0.386450
$355$	−496.114	−0.0741718
$356$	−1344.65	−0.200187
$357$	−5788.10	−0.858091
$358$	−5958.97	−0.879724
$359$	−4630.22	−0.680706	−0.340353	−	0.940298i	$-0.610547\pi$
$359$	−4630.22	−0.680706	−0.340353	+	0.940298i	$0.610547\pi$
$360$	−436.538	−0.0639100
$361$	−3390.94	−0.494378
$362$	−9497.07	−1.37888
$363$	3823.46	0.552837
$364$	−1581.98	−0.227798
$365$	−2456.27	−0.352239
$366$	1404.21	0.200545
$367$	−4879.55	−0.694034	−0.347017	−	0.937859i	$-0.612805\pi$
$367$	−4879.55	−0.694034	−0.347017	+	0.937859i	$0.612805\pi$
$368$	−1679.78	−0.237947
$369$	153.254	0.0216208
$370$	−1158.70	−0.162805
$371$	−9350.47	−1.30850
$372$	−459.068	−0.0639827
$373$	−75.0979	−0.0104247	−0.00521236	−	0.999986i	$-0.501659\pi$
$373$	−75.0979	−0.0104247	−0.00521236	+	0.999986i	$0.501659\pi$
$374$	2626.71	0.363166
$375$	−1750.02	−0.240989
$376$	−421.610	−0.0578268
$377$	−1995.82	−0.272652
$378$	−1395.55	−0.189892
$379$	−4331.39	−0.587041	−0.293521	−	0.955953i	$-0.594827\pi$
$379$	−4331.39	−0.587041	−0.293521	+	0.955953i	$0.594827\pi$
$380$	−191.336	−0.0258299
$381$	1655.60	0.222622
$382$	2420.04	0.324136
$383$	−7794.24	−1.03986	−0.519931	−	0.854209i	$-0.674042\pi$
$383$	−7794.24	−1.03986	−0.519931	+	0.854209i	$0.674042\pi$
$384$	5114.00	0.679617
$385$	303.250	0.0401430
$386$	−8209.39	−1.08251
$387$	−2866.15	−0.376471
$388$	22.8101	0.00298456
$389$	9928.30	1.29405	0.647024	−	0.762470i	$-0.276013\pi$
$389$	9928.30	1.29405	0.647024	+	0.762470i	$0.276013\pi$
$390$	−1508.34	−0.195840
$391$	−2626.73	−0.339743
$392$	−1170.04	−0.150755
$393$	643.094	0.0825440
$394$	−648.403	−0.0829088
$395$	−1012.05	−0.128915
$396$	92.0590	0.0116822
$397$	2401.73	0.303626	0.151813	−	0.988409i	$-0.451489\pi$
$397$	2401.73	0.303626	0.151813	+	0.988409i	$0.451489\pi$
$398$	−9140.57	−1.15119
$399$	2984.64	0.374483
$400$	8712.82	1.08910
$401$	−4999.77	−0.622635	−0.311317	−	0.950306i	$-0.600770\pi$
$401$	−4999.77	−0.622635	−0.311317	+	0.950306i	$0.600770\pi$
$402$	−1378.07	−0.170975
$403$	7739.74	0.956684
$404$	−156.215	−0.0192376
$405$	−193.414	−0.0237304
$406$	−1498.92	−0.183227
$407$	−1192.30	−0.145210
$408$	6959.64	0.844494
$409$	3566.46	0.431174	0.215587	−	0.976485i	$-0.430833\pi$
$409$	3566.46	0.431174	0.215587	+	0.976485i	$0.430833\pi$
$410$	124.401	0.0149847
$411$	−8375.07	−1.00514
$412$	48.2788	0.00577312
$413$	4737.51	0.564449
$414$	−633.321	−0.0751836
$415$	−3380.41	−0.399851
$416$	4194.20	0.494322
$417$	6988.55	0.820698
$418$	−1354.47	−0.158491
$419$	−16108.6	−1.87817	−0.939087	−	0.343681i	$-0.888326\pi$
$419$	−16108.6	−1.87817	−0.939087	+	0.343681i	$0.888326\pi$
$420$	−164.665	−0.0191306
$421$	−5021.03	−0.581260	−0.290630	−	0.956836i	$-0.593865\pi$
$421$	−5021.03	−0.581260	−0.290630	+	0.956836i	$0.593865\pi$
$422$	−8530.15	−0.983984
$423$	−186.800	−0.0214716
$424$	11243.1	1.28776
$425$	13624.5	1.55503
$426$	1907.01	0.216890
$427$	−2584.55	−0.292916
$428$	1890.54	0.213511
$429$	−1552.08	−0.174674
$430$	−2326.54	−0.260921
$431$	8931.38	0.998166	0.499083	−	0.866554i	$-0.333670\pi$
$431$	8931.38	0.998166	0.499083	+	0.866554i	$0.333670\pi$
$432$	1971.92	0.219615
$433$	16831.2	1.86803	0.934014	−	0.357236i	$-0.116281\pi$
$433$	16831.2	1.86803	0.934014	+	0.357236i	$0.116281\pi$
$434$	5812.78	0.642909
$435$	−207.741	−0.0228975
$436$	2330.32	0.255968
$437$	1354.48	0.148269
$438$	9441.68	1.03000
$439$	−12257.3	−1.33259	−0.666297	−	0.745686i	$-0.732122\pi$
$439$	−12257.3	−1.33259	−0.666297	+	0.745686i	$0.732122\pi$
$440$	−364.629	−0.0395068
$441$	−518.400	−0.0559766
$442$	24047.2	2.58780
$443$	42.6747	0.00457683	0.00228842	−	0.999997i	$-0.499272\pi$
$443$	42.6747	0.00457683	0.00228842	+	0.999997i	$0.499272\pi$
$444$	647.424	0.0692013
$445$	2359.72	0.251374
$446$	−10956.3	−1.16322
$447$	6655.31	0.704218
$448$	−6720.58	−0.708745
$449$	−7197.08	−0.756462	−0.378231	−	0.925711i	$-0.623467\pi$
$449$	−7197.08	−0.756462	−0.378231	+	0.925711i	$0.623467\pi$
$450$	3284.96	0.344121
$451$	128.009	0.0133652
$452$	−2691.97	−0.280132
$453$	834.498	0.0865522
$454$	20521.6	2.12143
$455$	2776.21	0.286045
$456$	−3588.74	−0.368549
$457$	−7654.99	−0.783557	−0.391778	−	0.920060i	$-0.628140\pi$
$457$	−7654.99	−0.783557	−0.391778	+	0.920060i	$0.628140\pi$
$458$	6181.54	0.630664
$459$	3083.55	0.313568
$460$	−74.7278	−0.00757435
$461$	8846.14	0.893722	0.446861	−	0.894603i	$-0.352542\pi$
$461$	8846.14	0.893722	0.446861	+	0.894603i	$0.352542\pi$
$462$	−1165.66	−0.117384
$463$	−8297.13	−0.832830	−0.416415	−	0.909175i	$-0.636714\pi$
$463$	−8297.13	−0.832830	−0.416415	+	0.909175i	$0.636714\pi$
$464$	2117.98	0.211907
$465$	805.613	0.0803429
$466$	−10042.0	−0.998255
$467$	−17209.9	−1.70531	−0.852657	−	0.522472i	$-0.825010\pi$
$467$	−17209.9	−1.70531	−0.852657	+	0.522472i	$0.825010\pi$
$468$	842.786	0.0832432
$469$	2536.43	0.249726
$470$	−151.631	−0.0148813
$471$	−9898.87	−0.968399
$472$	−5696.40	−0.555505
$473$	−2394.02	−0.232721
$474$	3890.21	0.376969
$475$	−7025.51	−0.678637
$476$	2625.23	0.252788
$477$	4981.37	0.478158
$478$	−6473.85	−0.619470
$479$	10948.7	1.04438	0.522190	−	0.852829i	$-0.325115\pi$
$479$	10948.7	1.04438	0.522190	+	0.852829i	$0.325115\pi$
$480$	436.566	0.0415134
$481$	−10915.4	−1.03471
$482$	2311.75	0.218459
$483$	1165.67	0.109813
$484$	−1734.15	−0.162862
$485$	−40.0292	−0.00374770
$486$	743.464	0.0693913
$487$	19943.0	1.85565	0.927825	−	0.373015i	$-0.121676\pi$
$487$	19943.0	1.85565	0.927825	+	0.373015i	$0.121676\pi$
$488$	3107.68	0.288275
$489$	−318.965	−0.0294972
$490$	−420.802	−0.0387957
$491$	−16997.3	−1.56227	−0.781136	−	0.624360i	$-0.785360\pi$
$491$	−16997.3	−1.56227	−0.781136	+	0.624360i	$0.785360\pi$
$492$	−69.5093	−0.00636935
$493$	3311.96	0.302563
$494$	−12399.9	−1.12935
$495$	−161.553	−0.0146693
$496$	−8213.50	−0.743542
$497$	−3509.99	−0.316790
$498$	12994.0	1.16923
$499$	19392.7	1.73975	0.869876	−	0.493270i	$-0.164198\pi$
$499$	19392.7	1.73975	0.869876	+	0.493270i	$0.164198\pi$
$500$	793.733	0.0709937
$501$	719.665	0.0641762
$502$	20285.3	1.80354
$503$	−7561.81	−0.670307	−0.335153	−	0.942164i	$-0.608788\pi$
$503$	−7561.81	−0.670307	−0.335153	+	0.942164i	$0.608788\pi$
$504$	−3088.50	−0.272962
$505$	274.141	0.0241566
$506$	−528.996	−0.0464758
$507$	−7618.11	−0.667321
$508$	−750.908	−0.0655830
$509$	−1137.24	−0.0990321	−0.0495160	−	0.998773i	$-0.515768\pi$
$509$	−1137.24	−0.0990321	−0.0495160	+	0.998773i	$0.515768\pi$
$510$	2503.02	0.217325
$511$	−17378.1	−1.50442
$512$	7417.47	0.640252
$513$	−1590.04	−0.136846
$514$	14935.0	1.28162
$515$	−84.7239	−0.00724928
$516$	1299.96	0.110906
$517$	−156.029	−0.0132730
$518$	−8197.77	−0.695347
$519$	3153.43	0.266706
$520$	−3338.12	−0.281512
$521$	23013.0	1.93516	0.967579	−	0.252570i	$-0.0812759\pi$
$521$	23013.0	1.93516	0.967579	+	0.252570i	$0.0812759\pi$
$522$	798.535	0.0669558
$523$	−13111.9	−1.09626	−0.548130	−	0.836393i	$-0.684660\pi$
$523$	−13111.9	−1.09626	−0.548130	+	0.836393i	$0.684660\pi$
$524$	−291.679	−0.0243169
$525$	−6046.20	−0.502624
$526$	−20662.1	−1.71275
$527$	−12843.7	−1.06163
$528$	1647.09	0.135758
$529$	529.000	0.0434783
$530$	4043.54	0.331397
$531$	−2523.86	−0.206264
$532$	−1353.70	−0.110320
$533$	1171.90	0.0952361
$534$	−9070.53	−0.735057
$535$	−3317.69	−0.268105
$536$	−3049.82	−0.245769
$537$	−5843.04	−0.469545
$538$	−22376.7	−1.79317
$539$	−433.006	−0.0346027
$540$	87.7239	0.00699081
$541$	−5695.94	−0.452658	−0.226329	−	0.974051i	$-0.572672\pi$
$541$	−5695.94	−0.452658	−0.226329	+	0.974051i	$0.572672\pi$
$542$	637.185	0.0504971
$543$	−9312.32	−0.735966
$544$	−6960.08	−0.548550
$545$	−4089.45	−0.321418
$546$	−10671.5	−0.836441
$547$	13474.7	1.05326	0.526632	−	0.850094i	$-0.323455\pi$
$547$	13474.7	1.05326	0.526632	+	0.850094i	$0.323455\pi$
$548$	3798.56	0.296107
$549$	1376.89	0.107039
$550$	2743.84	0.212723
$551$	−1707.82	−0.132043
$552$	−1401.61	−0.108073
$553$	−7160.20	−0.550602
$554$	9695.89	0.743572
$555$	−1136.16	−0.0868959
$556$	−3169.70	−0.241772
$557$	916.032	0.0696832	0.0348416	−	0.999393i	$-0.488907\pi$
$557$	916.032	0.0696832	0.0348416	+	0.999393i	$0.488907\pi$
$558$	−3096.70	−0.234935
$559$	−21916.9	−1.65829
$560$	−2946.14	−0.222316
$561$	2575.61	0.193837
$562$	25612.9	1.92245
$563$	8577.58	0.642099	0.321050	−	0.947062i	$-0.395964\pi$
$563$	8577.58	0.642099	0.321050	+	0.947062i	$0.395964\pi$
$564$	84.7241	0.00632540
$565$	4724.11	0.351761
$566$	1614.75	0.119917
$567$	−1368.40	−0.101353
$568$	4220.43	0.311770
$569$	−4051.13	−0.298475	−0.149238	−	0.988801i	$-0.547682\pi$
$569$	−4051.13	−0.298475	−0.149238	+	0.988801i	$0.547682\pi$
$570$	−1290.68	−0.0948435
$571$	13.1256	0.000961977 0	0.000480988	−	1.00000i	$-0.499847\pi$
$571$	13.1256	0.000961977 0	0.000480988		1.00000i	$0.499847\pi$
$572$	703.957	0.0514579
$573$	2372.96	0.173005
$574$	880.136	0.0640003
$575$	−2743.86	−0.199003
$576$	3580.32	0.258993
$577$	21279.3	1.53530	0.767649	−	0.640870i	$-0.221426\pi$
$577$	21279.3	1.53530	0.767649	+	0.640870i	$0.221426\pi$
$578$	−24873.7	−1.78998
$579$	−8049.69	−0.577778
$580$	94.2220	0.00674544
$581$	−23916.4	−1.70778
$582$	153.868	0.0109589
$583$	4160.81	0.295580
$584$	20895.5	1.48058
$585$	−1479.00	−0.104528
$586$	24269.0	1.71083
$587$	−13410.1	−0.942922	−0.471461	−	0.881887i	$-0.656273\pi$
$587$	−13410.1	−0.942922	−0.471461	+	0.881887i	$0.656273\pi$
$588$	235.123	0.0164903
$589$	6622.88	0.463312
$590$	−2048.70	−0.142955
$591$	−635.788	−0.0442518
$592$	11583.5	0.804188
$593$	−27022.4	−1.87129	−0.935645	−	0.352941i	$-0.885181\pi$
$593$	−27022.4	−1.87129	−0.935645	+	0.352941i	$0.885181\pi$
$594$	620.996	0.0428952
$595$	−4606.98	−0.317425
$596$	−3018.56	−0.207458
$597$	−8962.75	−0.614440
$598$	−4842.88	−0.331171
$599$	10037.3	0.684660	0.342330	−	0.939580i	$-0.388784\pi$
$599$	10037.3	0.684660	0.342330	+	0.939580i	$0.388784\pi$
$600$	7269.98	0.494660
$601$	−26038.9	−1.76730	−0.883651	−	0.468146i	$-0.844922\pi$
$601$	−26038.9	−1.76730	−0.883651	+	0.468146i	$0.844922\pi$
$602$	−16460.2	−1.11440
$603$	−1351.26	−0.0912562
$604$	−378.492	−0.0254977
$605$	3043.25	0.204505
$606$	−1053.77	−0.0706378
$607$	−18117.8	−1.21150	−0.605748	−	0.795657i	$-0.707126\pi$
$607$	−18117.8	−1.21150	−0.605748	+	0.795657i	$0.707126\pi$
$608$	3588.97	0.239395
$609$	−1469.76	−0.0977958
$610$	1117.67	0.0741855
$611$	−1428.42	−0.0945789
$612$	−1398.56	−0.0923752
$613$	8425.59	0.555149	0.277574	−	0.960704i	$-0.410470\pi$
$613$	8425.59	0.555149	0.277574	+	0.960704i	$0.410470\pi$
$614$	−584.414	−0.0384121
$615$	121.981	0.00799798
$616$	−2579.74	−0.168735
$617$	−5488.02	−0.358086	−0.179043	−	0.983841i	$-0.557300\pi$
$617$	−5488.02	−0.358086	−0.179043	+	0.983841i	$0.557300\pi$
$618$	325.671	0.0211980
$619$	−23047.3	−1.49653	−0.748263	−	0.663403i	$-0.769112\pi$
$619$	−23047.3	−1.49653	−0.748263	+	0.663403i	$0.769112\pi$
$620$	−365.391	−0.0236685
$621$	−621.000	−0.0401286
$622$	24115.0	1.55454
$623$	16695.0	1.07363
$624$	15078.9	0.967368
$625$	13519.4	0.865240
$626$	−31225.7	−1.99366
$627$	−1328.12	−0.0845931
$628$	4489.69	0.285284
$629$	18113.5	1.14823
$630$	−1110.77	−0.0702448
$631$	−4019.59	−0.253594	−0.126797	−	0.991929i	$-0.540470\pi$
$631$	−4019.59	−0.253594	−0.126797	+	0.991929i	$0.540470\pi$
$632$	8609.46	0.541877
$633$	−8364.20	−0.525193
$634$	21889.7	1.37121
$635$	1317.76	0.0823523
$636$	−2259.33	−0.140862
$637$	−3964.10	−0.246567
$638$	666.995	0.0413897
$639$	1869.91	0.115763
$640$	4070.44	0.251404
$641$	−720.731	−0.0444105	−0.0222053	−	0.999753i	$-0.507069\pi$
$641$	−720.731	−0.0444105	−0.0222053	+	0.999753i	$0.507069\pi$
$642$	12752.9	0.783983
$643$	−18114.4	−1.11098	−0.555491	−	0.831523i	$-0.687470\pi$
$643$	−18114.4	−1.11098	−0.555491	+	0.831523i	$0.687470\pi$
$644$	−528.697	−0.0323503
$645$	−2281.28	−0.139264
$646$	20577.1	1.25324
$647$	−9397.26	−0.571012	−0.285506	−	0.958377i	$-0.592162\pi$
$647$	−9397.26	−0.571012	−0.285506	+	0.958377i	$0.592162\pi$
$648$	1645.37	0.0997471
$649$	−2108.12	−0.127505
$650$	25119.5	1.51579
$651$	5699.70	0.343147
$652$	144.669	0.00868966
$653$	−12810.7	−0.767722	−0.383861	−	0.923391i	$-0.625406\pi$
$653$	−12810.7	−0.767722	−0.383861	+	0.923391i	$0.625406\pi$
$654$	15719.5	0.939877
$655$	511.865	0.0305347
$656$	−1243.64	−0.0740182
$657$	9257.99	0.549755
$658$	−1072.79	−0.0635587
$659$	2881.21	0.170312	0.0851562	−	0.996368i	$-0.472861\pi$
$659$	2881.21	0.170312	0.0851562	+	0.996368i	$0.472861\pi$
$660$	73.2735	0.00432147
$661$	9153.38	0.538616	0.269308	−	0.963054i	$-0.413205\pi$
$661$	9153.38	0.538616	0.269308	+	0.963054i	$0.413205\pi$
$662$	−5898.38	−0.346295
$663$	23579.3	1.38121
$664$	28757.1	1.68071
$665$	2375.60	0.138529
$666$	4367.28	0.254097
$667$	−667.000	−0.0387202
$668$	−326.409	−0.0189059
$669$	−10743.1	−0.620857
$670$	−1096.86	−0.0632469
$671$	1150.08	0.0661677
$672$	3088.70	0.177305
$673$	7673.20	0.439495	0.219747	−	0.975557i	$-0.429477\pi$
$673$	7673.20	0.439495	0.219747	+	0.975557i	$0.429477\pi$
$674$	34795.2	1.98852
$675$	3221.05	0.183672
$676$	3455.24	0.196588
$677$	24517.3	1.39184	0.695921	−	0.718118i	$-0.254996\pi$
$677$	24517.3	1.39184	0.695921	+	0.718118i	$0.254996\pi$
$678$	−18159.0	−1.02860
$679$	−283.206	−0.0160065
$680$	5539.46	0.312395
$681$	20122.4	1.13229
$682$	−2586.59	−0.145228
$683$	−21783.0	−1.22036	−0.610178	−	0.792265i	$-0.708902\pi$
$683$	−21783.0	−1.22036	−0.610178	+	0.792265i	$0.708902\pi$
$684$	721.171	0.0403138
$685$	−6666.06	−0.371820
$686$	−20705.8	−1.15241
$687$	6061.28	0.336612
$688$	23258.4	1.28884
$689$	38091.6	2.10620
$690$	−504.086	−0.0278119
$691$	−28059.5	−1.54477	−0.772383	−	0.635157i	$-0.780936\pi$
$691$	−28059.5	−1.54477	−0.772383	+	0.635157i	$0.780936\pi$
$692$	−1430.26	−0.0785697
$693$	−1142.99	−0.0626529
$694$	29478.7	1.61238
$695$	5562.47	0.303592
$696$	1767.25	0.0962461
$697$	−1944.72	−0.105684
$698$	10846.8	0.588190
$699$	−9846.65	−0.532810
$700$	2742.29	0.148070
$701$	13034.3	0.702278	0.351139	−	0.936323i	$-0.385794\pi$
$701$	13034.3	0.702278	0.351139	+	0.936323i	$0.385794\pi$
$702$	5685.12	0.305657
$703$	−9340.26	−0.501102
$704$	2990.55	0.160100
$705$	−148.681	−0.00794279
$706$	21110.3	1.12535
$707$	1939.54	0.103174
$708$	1144.71	0.0607640
$709$	5703.87	0.302134	0.151067	−	0.988523i	$-0.451729\pi$
$709$	5703.87	0.302134	0.151067	+	0.988523i	$0.451729\pi$
$710$	1517.87	0.0802319
$711$	3814.53	0.201204
$712$	−20074.1	−1.05661
$713$	2586.61	0.135862
$714$	17708.8	0.928201
$715$	−1235.37	−0.0646156
$716$	2650.15	0.138325
$717$	−6347.90	−0.330637
$718$	14166.2	0.736323
$719$	−13716.1	−0.711437	−0.355719	−	0.934593i	$-0.615764\pi$
$719$	−13716.1	−0.711437	−0.355719	+	0.934593i	$0.615764\pi$
$720$	1569.53	0.0812401
$721$	−599.419	−0.0309619
$722$	10374.6	0.534771
$723$	2266.77	0.116601
$724$	4223.66	0.216811
$725$	3459.65	0.177225
$726$	−11698.0	−0.598006
$727$	−29885.8	−1.52462	−0.762312	−	0.647210i	$-0.775936\pi$
$727$	−29885.8	−1.52462	−0.762312	+	0.647210i	$0.775936\pi$
$728$	−23617.2	−1.20235
$729$	729.000	0.0370370
$730$	7515.01	0.381018
$731$	36370.0	1.84021
$732$	−624.499	−0.0315330
$733$	17662.7	0.890022	0.445011	−	0.895525i	$-0.353200\pi$
$733$	17662.7	0.890022	0.445011	+	0.895525i	$0.353200\pi$
$734$	14929.1	0.750740
$735$	−412.615	−0.0207069
$736$	1401.70	0.0702001
$737$	−1128.67	−0.0564113
$738$	−468.884	−0.0233873
$739$	6311.96	0.314194	0.157097	−	0.987583i	$-0.449786\pi$
$739$	6311.96	0.314194	0.157097	+	0.987583i	$0.449786\pi$
$740$	515.311	0.0255990
$741$	−12158.7	−0.602782
$742$	28608.0	1.41541
$743$	14949.5	0.738149	0.369074	−	0.929400i	$-0.379675\pi$
$743$	14949.5	0.738149	0.369074	+	0.929400i	$0.379675\pi$
$744$	−6853.34	−0.337709
$745$	5297.23	0.260504
$746$	229.764	0.0112765
$747$	12741.2	0.624065
$748$	−1168.18	−0.0571030
$749$	−23472.6	−1.14509
$750$	5354.23	0.260679
$751$	18945.0	0.920521	0.460261	−	0.887784i	$-0.347756\pi$
$751$	18945.0	0.920521	0.460261	+	0.887784i	$0.347756\pi$
$752$	1515.86	0.0735074
$753$	19890.7	0.962626
$754$	6106.24	0.294929
$755$	664.211	0.0320174
$756$	620.645	0.0298580
$757$	24018.2	1.15318	0.576589	−	0.817034i	$-0.304383\pi$
$757$	24018.2	1.15318	0.576589	+	0.817034i	$0.304383\pi$
$758$	13252.0	0.635005
$759$	−518.705	−0.0248061
$760$	−2856.43	−0.136334
$761$	26290.3	1.25233	0.626164	−	0.779692i	$-0.284624\pi$
$761$	26290.3	1.25233	0.626164	+	0.779692i	$0.284624\pi$
$762$	−5065.35	−0.240811
$763$	−28932.8	−1.37279
$764$	−1076.27	−0.0509661
$765$	2454.33	0.115995
$766$	23846.6	1.12482
$767$	−19299.5	−0.908558
$768$	−6098.86	−0.286554
$769$	−9043.62	−0.424085	−0.212042	−	0.977260i	$-0.568011\pi$
$769$	−9043.62	−0.424085	−0.212042	+	0.977260i	$0.568011\pi$
$770$	−927.799	−0.0434228
$771$	14644.4	0.684055
$772$	3650.98	0.170210
$773$	−18581.0	−0.864572	−0.432286	−	0.901737i	$-0.642293\pi$
$773$	−18581.0	−0.864572	−0.432286	+	0.901737i	$0.642293\pi$
$774$	8769.04	0.407231
$775$	−13416.5	−0.621849
$776$	340.528	0.0157529
$777$	−8038.29	−0.371135
$778$	−30375.8	−1.39978
$779$	1002.80	0.0461219
$780$	670.808	0.0307933
$781$	1561.89	0.0715606
$782$	8036.53	0.367501
$783$	783.000	0.0357371
$784$	4206.75	0.191634
$785$	−7878.92	−0.358230
$786$	−1967.56	−0.0892882
$787$	36728.3	1.66356	0.831780	−	0.555106i	$-0.187322\pi$
$787$	36728.3	1.66356	0.831780	+	0.555106i	$0.187322\pi$
$788$	288.366	0.0130363
$789$	−20260.1	−0.914168
$790$	3096.38	0.139448
$791$	33423.0	1.50238
$792$	1374.33	0.0616601
$793$	10528.9	0.471489
$794$	−7348.15	−0.328433
$795$	3964.88	0.176880
$796$	4065.11	0.181010
$797$	21649.2	0.962175	0.481087	−	0.876673i	$-0.340242\pi$
$797$	21649.2	0.962175	0.481087	+	0.876673i	$0.340242\pi$
$798$	−9131.56	−0.405080
$799$	2370.40	0.104954
$800$	−7270.45	−0.321311
$801$	−8894.07	−0.392330
$802$	15296.9	0.673506
$803$	7732.96	0.339838
$804$	612.871	0.0268835
$805$	927.805	0.0406222
$806$	−23679.9	−1.03485
$807$	−21941.3	−0.957090
$808$	−2332.11	−0.101539
$809$	−11175.3	−0.485666	−0.242833	−	0.970068i	$-0.578077\pi$
$809$	−11175.3	−0.485666	−0.242833	+	0.970068i	$0.578077\pi$
$810$	591.753	0.0256692
$811$	−44360.9	−1.92074	−0.960371	−	0.278724i	$-0.910089\pi$
$811$	−44360.9	−1.92074	−0.960371	+	0.278724i	$0.910089\pi$
$812$	666.618	0.0288100
$813$	624.789	0.0269524
$814$	3647.88	0.157074
$815$	−253.877	−0.0109116
$816$	−25022.7	−1.07349
$817$	−18754.2	−0.803094
$818$	−10911.7	−0.466403
$819$	−10463.9	−0.446443
$820$	−55.3253	−0.00235615
$821$	−32467.6	−1.38018	−0.690089	−	0.723725i	$-0.742429\pi$
$821$	−32467.6	−1.38018	−0.690089	+	0.723725i	$0.742429\pi$
$822$	25623.7	1.08726
$823$	30901.1	1.30880	0.654402	−	0.756147i	$-0.272920\pi$
$823$	30901.1	1.30880	0.654402	+	0.756147i	$0.272920\pi$
$824$	720.745	0.0304713
$825$	2690.46	0.113539
$826$	−14494.5	−0.610567
$827$	−13818.8	−0.581050	−0.290525	−	0.956867i	$-0.593830\pi$
$827$	−13818.8	−0.581050	−0.290525	+	0.956867i	$0.593830\pi$
$828$	281.658	0.0118216
$829$	−798.114	−0.0334374	−0.0167187	−	0.999860i	$-0.505322\pi$
$829$	−798.114	−0.0334374	−0.0167187	+	0.999860i	$0.505322\pi$
$830$	10342.4	0.432520
$831$	9507.27	0.396875
$832$	27378.0	1.14082
$833$	6578.24	0.273616
$834$	−21381.6	−0.887752
$835$	572.811	0.0237401
$836$	602.375	0.0249206
$837$	−3036.46	−0.125395
$838$	49284.5	2.03163
$839$	−12216.3	−0.502687	−0.251343	−	0.967898i	$-0.580872\pi$
$839$	−12216.3	−0.502687	−0.251343	+	0.967898i	$0.580872\pi$
$840$	−2458.26	−0.100974
$841$	841.000	0.0344828
$842$	15362.0	0.628751
$843$	25114.6	1.02609
$844$	3793.64	0.154718
$845$	−6063.56	−0.246855
$846$	571.517	0.0232260
$847$	21530.9	0.873449
$848$	−40423.2	−1.63696
$849$	1583.34	0.0640048
$850$	−41684.6	−1.68208
$851$	−3647.90	−0.146943
$852$	−848.111	−0.0341031
$853$	23320.9	0.936100	0.468050	−	0.883702i	$-0.344957\pi$
$853$	23320.9	0.936100	0.468050	+	0.883702i	$0.344957\pi$
$854$	7907.49	0.316849
$855$	−1265.58	−0.0506219
$856$	28223.6	1.12694
$857$	27624.9	1.10111	0.550553	−	0.834800i	$-0.314417\pi$
$857$	27624.9	1.10111	0.550553	+	0.834800i	$0.314417\pi$
$858$	4748.64	0.188946
$859$	−23892.0	−0.948991	−0.474495	−	0.880258i	$-0.657369\pi$
$859$	−23892.0	−0.948991	−0.474495	+	0.880258i	$0.657369\pi$
$860$	1034.69	0.0410263
$861$	863.014	0.0341596
$862$	−27325.8	−1.07972
$863$	13708.6	0.540726	0.270363	−	0.962758i	$-0.412856\pi$
$863$	13708.6	0.540726	0.270363	+	0.962758i	$0.412856\pi$
$864$	−1645.47	−0.0647918
$865$	2509.94	0.0986598
$866$	−51495.4	−2.02065
$867$	−24389.8	−0.955387
$868$	−2585.13	−0.101089
$869$	3186.17	0.124377
$870$	635.587	0.0247683
$871$	−10332.8	−0.401968
$872$	34788.9	1.35103
$873$	150.875	0.00584920
$874$	−4144.05	−0.160383
$875$	−9854.84	−0.380748
$876$	−4199.02	−0.161954
$877$	7746.28	0.298259	0.149130	−	0.988818i	$-0.452353\pi$
$877$	7746.28	0.298259	0.149130	+	0.988818i	$0.452353\pi$
$878$	37501.5	1.44147
$879$	23796.9	0.913139
$880$	1310.99	0.0502197
$881$	21969.3	0.840141	0.420071	−	0.907491i	$-0.362005\pi$
$881$	21969.3	0.840141	0.420071	+	0.907491i	$0.362005\pi$
$882$	1586.05	0.0605501
$883$	−22439.0	−0.855190	−0.427595	−	0.903970i	$-0.640639\pi$
$883$	−22439.0	−0.855190	−0.427595	+	0.903970i	$0.640639\pi$
$884$	−10694.6	−0.406897
$885$	−2008.84	−0.0763012
$886$	−130.564	−0.00495078
$887$	43545.2	1.64837	0.824185	−	0.566321i	$-0.191634\pi$
$887$	43545.2	1.64837	0.824185	+	0.566321i	$0.191634\pi$
$888$	9665.28	0.365254
$889$	9323.12	0.351729
$890$	−7219.61	−0.271912
$891$	608.915	0.0228950
$892$	4872.61	0.182900
$893$	−1222.30	−0.0458036
$894$	−20362.1	−0.761755
$895$	−4650.71	−0.173694
$896$	28798.3	1.07375
$897$	−4748.67	−0.176760
$898$	22019.6	0.818267
$899$	−3261.38	−0.120993
$900$	−1460.93	−0.0541085
$901$	−63211.2	−2.33726
$902$	−391.647	−0.0144572
$903$	−16140.0	−0.594802
$904$	−40188.0	−1.47858
$905$	−7412.05	−0.272249
$906$	−2553.16	−0.0936238
$907$	−44887.8	−1.64330	−0.821651	−	0.569991i	$-0.806946\pi$
$907$	−44887.8	−1.64330	−0.821651	+	0.569991i	$0.806946\pi$
$908$	−9126.64	−0.333566
$909$	−1033.27	−0.0377023
$910$	−8493.86	−0.309416
$911$	2328.29	0.0846759	0.0423379	−	0.999103i	$-0.486519\pi$
$911$	2328.29	0.0846759	0.0423379	+	0.999103i	$0.486519\pi$
$912$	12903.0	0.468486
$913$	10642.4	0.385774
$914$	23420.6	0.847576
$915$	1095.93	0.0395959
$916$	−2749.13	−0.0991635
$917$	3621.43	0.130415
$918$	−9434.19	−0.339188
$919$	21995.6	0.789518	0.394759	−	0.918785i	$-0.370828\pi$
$919$	21995.6	0.789518	0.394759	+	0.918785i	$0.370828\pi$
$920$	−1115.60	−0.0399784
$921$	−573.045	−0.0205021
$922$	−27064.9	−0.966742
$923$	14298.9	0.509917
$924$	518.408	0.0184571
$925$	18921.2	0.672570
$926$	25385.2	0.900876
$927$	319.335	0.0113143
$928$	−1767.36	−0.0625177
$929$	−45924.2	−1.62188	−0.810939	−	0.585131i	$-0.801043\pi$
$929$	−45924.2	−1.62188	−0.810939	+	0.585131i	$0.801043\pi$
$930$	−2464.79	−0.0869072
$931$	−3392.08	−0.119410
$932$	4466.01	0.156962
$933$	23645.8	0.829720
$934$	52654.2	1.84464
$935$	2050.03	0.0717040
$936$	12581.8	0.439369
$937$	528.797	0.0184365	0.00921827	−	0.999958i	$-0.497066\pi$
$937$	528.797	0.0184365	0.00921827	+	0.999958i	$0.497066\pi$
$938$	−7760.26	−0.270129
$939$	−30618.2	−1.06410
$940$	67.4353	0.00233989
$941$	−47380.3	−1.64140	−0.820698	−	0.571362i	$-0.806415\pi$
$941$	−47380.3	−1.64140	−0.820698	+	0.571362i	$0.806415\pi$
$942$	30285.8	1.04752
$943$	391.649	0.0135248
$944$	20480.8	0.706138
$945$	−1089.16	−0.0374926
$946$	7324.55	0.251735
$947$	−51199.3	−1.75687	−0.878433	−	0.477865i	$-0.841411\pi$
$947$	−51199.3	−1.75687	−0.878433	+	0.477865i	$0.841411\pi$
$948$	−1730.10	−0.0592733
$949$	70794.1	2.42157
$950$	21494.7	0.734084
$951$	21463.8	0.731874
$952$	39191.5	1.33425
$953$	−21417.5	−0.727996	−0.363998	−	0.931400i	$-0.618589\pi$
$953$	−21417.5	−0.727996	−0.363998	+	0.931400i	$0.618589\pi$
$954$	−15240.6	−0.517225
$955$	1888.73	0.0639979
$956$	2879.13	0.0974034
$957$	654.019	0.0220914
$958$	−33497.7	−1.12971
$959$	−47162.2	−1.58806
$960$	2849.73	0.0958068
$961$	−17143.4	−0.575457
$962$	33395.8	1.11926
$963$	12504.8	0.418444
$964$	−1028.11	−0.0343497
$965$	−6407.07	−0.213732
$966$	−3566.40	−0.118786
$967$	−33501.0	−1.11409	−0.557043	−	0.830484i	$-0.688064\pi$
$967$	−33501.0	−1.11409	−0.557043	+	0.830484i	$0.688064\pi$
$968$	−25888.9	−0.859608
$969$	20176.8	0.668908
$970$	122.470	0.00405390
$971$	−39514.5	−1.30595	−0.652977	−	0.757378i	$-0.726480\pi$
$971$	−39514.5	−1.30595	−0.652977	+	0.757378i	$0.726480\pi$
$972$	−330.642	−0.0109109
$973$	39354.4	1.29665
$974$	−61015.9	−2.00726
$975$	24630.8	0.809043
$976$	−11173.3	−0.366444
$977$	38661.9	1.26602	0.633012	−	0.774142i	$-0.281819\pi$
$977$	38661.9	1.26602	0.633012	+	0.774142i	$0.281819\pi$
$978$	975.881	0.0319072
$979$	−7428.99	−0.242524
$980$	187.144	0.00610010
$981$	15413.6	0.501651
$982$	52003.5	1.68992
$983$	40157.4	1.30297	0.651487	−	0.758660i	$-0.274146\pi$
$983$	40157.4	1.30297	0.651487	+	0.758660i	$0.274146\pi$
$984$	−1037.69	−0.0336183
$985$	−506.050	−0.0163696
$986$	−10133.0	−0.327283
$987$	−1051.92	−0.0339239
$988$	5514.66	0.177575
$989$	−7324.60	−0.235499
$990$	494.276	0.0158678
$991$	−51040.9	−1.63609	−0.818045	−	0.575154i	$-0.804942\pi$
$991$	−51040.9	−1.63609	−0.818045	+	0.575154i	$0.804942\pi$
$992$	6853.78	0.219363
$993$	−5783.63	−0.184832
$994$	10738.9	0.342673
$995$	−7133.81	−0.227294
$996$	−5778.85	−0.183845
$997$	−31657.4	−1.00562	−0.502808	−	0.864398i	$-0.667700\pi$
$997$	−31657.4	−1.00562	−0.502808	+	0.864398i	$0.667700\pi$
$998$	−59332.4	−1.88190
$999$	4282.32	0.135622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.c.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.c.1.10	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-3.05952 q^{2} -3.00000 q^{3} +1.36067 q^{4} -2.38782 q^{5} +9.17856 q^{6} -16.8938 q^{7} +20.3132 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.05952 q^{2} -3.00000 q^{3} +1.36067 q^{4} -2.38782 q^{5} +9.17856 q^{6} -16.8938 q^{7} +20.3132 q^{8} +9.00000 q^{9} +7.30559 q^{10} +7.51747 q^{11} -4.08200 q^{12} +68.8213 q^{13} +51.6869 q^{14} +7.16347 q^{15} -73.0339 q^{16} -114.206 q^{17} -27.5357 q^{18} +58.8902 q^{19} -3.24903 q^{20} +50.6814 q^{21} -22.9998 q^{22} +23.0000 q^{23} -60.9395 q^{24} -119.298 q^{25} -210.560 q^{26} -27.0000 q^{27} -22.9868 q^{28} -29.0000 q^{29} -21.9168 q^{30} +112.461 q^{31} +60.9434 q^{32} -22.5524 q^{33} +349.415 q^{34} +40.3394 q^{35} +12.2460 q^{36} -158.605 q^{37} -180.176 q^{38} -206.464 q^{39} -48.5042 q^{40} +17.0282 q^{41} -155.061 q^{42} -318.461 q^{43} +10.2288 q^{44} -21.4904 q^{45} -70.3690 q^{46} -20.7555 q^{47} +219.102 q^{48} -57.6000 q^{49} +364.996 q^{50} +342.617 q^{51} +93.6429 q^{52} +553.486 q^{53} +82.6071 q^{54} -17.9504 q^{55} -343.166 q^{56} -176.671 q^{57} +88.7261 q^{58} -280.429 q^{59} +9.74710 q^{60} +152.988 q^{61} -344.078 q^{62} -152.044 q^{63} +397.814 q^{64} -164.333 q^{65} +68.9995 q^{66} -150.140 q^{67} -155.396 q^{68} -69.0000 q^{69} -123.419 q^{70} +207.768 q^{71} +182.819 q^{72} +1028.67 q^{73} +485.254 q^{74} +357.895 q^{75} +80.1301 q^{76} -126.998 q^{77} +631.680 q^{78} +423.836 q^{79} +174.392 q^{80} +81.0000 q^{81} -52.0982 q^{82} +1415.69 q^{83} +68.9605 q^{84} +272.703 q^{85} +974.337 q^{86} +87.0000 q^{87} +152.704 q^{88} -988.230 q^{89} +65.7503 q^{90} -1162.65 q^{91} +31.2954 q^{92} -337.384 q^{93} +63.5019 q^{94} -140.619 q^{95} -182.830 q^{96} +16.7639 q^{97} +176.228 q^{98} +67.6572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} - 111 q^{3} + 138 q^{4} - 15 q^{5} + 24 q^{6} - 6 q^{7} - 141 q^{8} + 333 q^{9} + 26 q^{10} - 109 q^{11} - 414 q^{12} + 115 q^{13} - 243 q^{14} + 45 q^{15} + 406 q^{16} - 228 q^{17} - 72 q^{18} - 135 q^{19} - 73 q^{20} + 18 q^{21} - 40 q^{22} + 851 q^{23} + 423 q^{24} + 942 q^{25} - 543 q^{26} - 999 q^{27} + 853 q^{28} - 1073 q^{29} - 78 q^{30} - 518 q^{31} - 1596 q^{32} + 327 q^{33} + 312 q^{34} - 37 q^{35} + 1242 q^{36} + 245 q^{37} - 59 q^{38} - 345 q^{39} + 293 q^{40} - 915 q^{41} + 729 q^{42} - 389 q^{43} - 832 q^{44} - 135 q^{45} - 184 q^{46} - 926 q^{47} - 1218 q^{48} + 1655 q^{49} - 439 q^{50} + 684 q^{51} + 1290 q^{52} - 1134 q^{53} + 216 q^{54} - 404 q^{55} - 1141 q^{56} + 405 q^{57} + 232 q^{58} - 179 q^{59} + 219 q^{60} + 10 q^{61} + 1378 q^{62} - 54 q^{63} + 1359 q^{64} + 110 q^{65} + 120 q^{66} + 1385 q^{67} - 3375 q^{68} - 2553 q^{69} - 637 q^{70} - 2432 q^{71} - 1269 q^{72} - 1638 q^{73} - 2193 q^{74} - 2826 q^{75} - 1319 q^{76} - 3703 q^{77} + 1629 q^{78} - 4728 q^{79} - 1567 q^{80} + 2997 q^{81} + 537 q^{82} - 1416 q^{83} - 2559 q^{84} - 2093 q^{85} - 1187 q^{86} + 3219 q^{87} + 1497 q^{88} - 4019 q^{89} + 234 q^{90} - 545 q^{91} + 3174 q^{92} + 1554 q^{93} + 108 q^{94} - 807 q^{95} + 4788 q^{96} - 754 q^{97} - 5561 q^{98} - 981 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 - 111 * q^3 + 138 * q^4 - 15 * q^5 + 24 * q^6 - 6 * q^7 - 141 * q^8 + 333 * q^9 + 26 * q^10 - 109 * q^11 - 414 * q^12 + 115 * q^13 - 243 * q^14 + 45 * q^15 + 406 * q^16 - 228 * q^17 - 72 * q^18 - 135 * q^19 - 73 * q^20 + 18 * q^21 - 40 * q^22 + 851 * q^23 + 423 * q^24 + 942 * q^25 - 543 * q^26 - 999 * q^27 + 853 * q^28 - 1073 * q^29 - 78 * q^30 - 518 * q^31 - 1596 * q^32 + 327 * q^33 + 312 * q^34 - 37 * q^35 + 1242 * q^36 + 245 * q^37 - 59 * q^38 - 345 * q^39 + 293 * q^40 - 915 * q^41 + 729 * q^42 - 389 * q^43 - 832 * q^44 - 135 * q^45 - 184 * q^46 - 926 * q^47 - 1218 * q^48 + 1655 * q^49 - 439 * q^50 + 684 * q^51 + 1290 * q^52 - 1134 * q^53 + 216 * q^54 - 404 * q^55 - 1141 * q^56 + 405 * q^57 + 232 * q^58 - 179 * q^59 + 219 * q^60 + 10 * q^61 + 1378 * q^62 - 54 * q^63 + 1359 * q^64 + 110 * q^65 + 120 * q^66 + 1385 * q^67 - 3375 * q^68 - 2553 * q^69 - 637 * q^70 - 2432 * q^71 - 1269 * q^72 - 1638 * q^73 - 2193 * q^74 - 2826 * q^75 - 1319 * q^76 - 3703 * q^77 + 1629 * q^78 - 4728 * q^79 - 1567 * q^80 + 2997 * q^81 + 537 * q^82 - 1416 * q^83 - 2559 * q^84 - 2093 * q^85 - 1187 * q^86 + 3219 * q^87 + 1497 * q^88 - 4019 * q^89 + 234 * q^90 - 545 * q^91 + 3174 * q^92 + 1554 * q^93 + 108 * q^94 - 807 * q^95 + 4788 * q^96 - 754 * q^97 - 5561 * q^98 - 981 * q^99

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