LMFDB - Embedded newform 6029.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79474 q^{2} -0.330575 q^{3} +5.81059 q^{4} -0.623259 q^{5} +0.923873 q^{6} -2.39329 q^{7} -10.6496 q^{8} -2.89072 q^{9} +O(q^{10})$	\(q-2.79474 q^{2} -0.330575 q^{3} +5.81059 q^{4} -0.623259 q^{5} +0.923873 q^{6} -2.39329 q^{7} -10.6496 q^{8} -2.89072 q^{9} +1.74185 q^{10} +2.20941 q^{11} -1.92084 q^{12} +4.48105 q^{13} +6.68863 q^{14} +0.206034 q^{15} +18.1417 q^{16} -6.29018 q^{17} +8.07882 q^{18} -2.03311 q^{19} -3.62150 q^{20} +0.791162 q^{21} -6.17474 q^{22} -4.01100 q^{23} +3.52050 q^{24} -4.61155 q^{25} -12.5234 q^{26} +1.94733 q^{27} -13.9064 q^{28} +3.79512 q^{29} -0.575812 q^{30} +3.19051 q^{31} -29.4023 q^{32} -0.730377 q^{33} +17.5794 q^{34} +1.49164 q^{35} -16.7968 q^{36} +5.24582 q^{37} +5.68203 q^{38} -1.48133 q^{39} +6.63746 q^{40} -1.26588 q^{41} -2.21109 q^{42} +0.478550 q^{43} +12.8380 q^{44} +1.80167 q^{45} +11.2097 q^{46} +0.0438981 q^{47} -5.99721 q^{48} -1.27217 q^{49} +12.8881 q^{50} +2.07938 q^{51} +26.0375 q^{52} -3.96897 q^{53} -5.44228 q^{54} -1.37704 q^{55} +25.4876 q^{56} +0.672097 q^{57} -10.6064 q^{58} -3.03123 q^{59} +1.19718 q^{60} -1.42330 q^{61} -8.91666 q^{62} +6.91833 q^{63} +45.8883 q^{64} -2.79286 q^{65} +2.04122 q^{66} -2.77620 q^{67} -36.5496 q^{68} +1.32594 q^{69} -4.16874 q^{70} -8.74363 q^{71} +30.7850 q^{72} -4.64295 q^{73} -14.6607 q^{74} +1.52446 q^{75} -11.8136 q^{76} -5.28776 q^{77} +4.13992 q^{78} -6.67943 q^{79} -11.3070 q^{80} +8.02842 q^{81} +3.53782 q^{82} -3.41406 q^{83} +4.59711 q^{84} +3.92041 q^{85} -1.33742 q^{86} -1.25457 q^{87} -23.5294 q^{88} -2.49945 q^{89} -5.03519 q^{90} -10.7245 q^{91} -23.3063 q^{92} -1.05470 q^{93} -0.122684 q^{94} +1.26716 q^{95} +9.71966 q^{96} -9.04616 q^{97} +3.55539 q^{98} -6.38679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * 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 $

$2$	−2.79474	−1.97618	−0.988091	−	0.153873i	$-0.950825\pi$
$2$	−2.79474	−1.97618	−0.988091	+	0.153873i	$0.950825\pi$
$3$	−0.330575	−0.190858	−0.0954289	−	0.995436i	$-0.530422\pi$
$3$	−0.330575	−0.190858	−0.0954289	+	0.995436i	$0.530422\pi$
$4$	5.81059	2.90529
$5$	−0.623259	−0.278730	−0.139365	−	0.990241i	$-0.544506\pi$
$5$	−0.623259	−0.278730	−0.139365	+	0.990241i	$0.544506\pi$
$6$	0.923873	0.377169
$7$	−2.39329	−0.904578	−0.452289	−	0.891871i	$-0.649392\pi$
$7$	−2.39329	−0.904578	−0.452289	+	0.891871i	$0.649392\pi$
$8$	−10.6496	−3.76520
$9$	−2.89072	−0.963573
$10$	1.74185	0.550821
$11$	2.20941	0.666163	0.333082	−	0.942898i	$-0.391912\pi$
$11$	2.20941	0.666163	0.333082	+	0.942898i	$0.391912\pi$
$12$	−1.92084	−0.554498
$13$	4.48105	1.24282	0.621410	−	0.783485i	$-0.286560\pi$
$13$	4.48105	1.24282	0.621410	+	0.783485i	$0.286560\pi$
$14$	6.68863	1.78761
$15$	0.206034	0.0531977
$16$	18.1417	4.53543
$17$	−6.29018	−1.52559	−0.762797	−	0.646639i	$-0.776174\pi$
$17$	−6.29018	−1.52559	−0.762797	+	0.646639i	$0.776174\pi$
$18$	8.07882	1.90420
$19$	−2.03311	−0.466428	−0.233214	−	0.972425i	$-0.574924\pi$
$19$	−2.03311	−0.466428	−0.233214	+	0.972425i	$0.574924\pi$
$20$	−3.62150	−0.809792
$21$	0.791162	0.172646
$22$	−6.17474	−1.31646
$23$	−4.01100	−0.836352	−0.418176	−	0.908366i	$-0.637330\pi$
$23$	−4.01100	−0.836352	−0.418176	+	0.908366i	$0.637330\pi$
$24$	3.52050	0.718618
$25$	−4.61155	−0.922310
$26$	−12.5234	−2.45604
$27$	1.94733	0.374763
$28$	−13.9064	−2.62806
$29$	3.79512	0.704736	0.352368	−	0.935862i	$-0.385377\pi$
$29$	3.79512	0.704736	0.352368	+	0.935862i	$0.385377\pi$
$30$	−0.575812	−0.105128
$31$	3.19051	0.573033	0.286517	−	0.958075i	$-0.407503\pi$
$31$	3.19051	0.573033	0.286517	+	0.958075i	$0.407503\pi$
$32$	−29.4023	−5.19763
$33$	−0.730377	−0.127142
$34$	17.5794	3.01485
$35$	1.49164	0.252133
$36$	−16.7968	−2.79946
$37$	5.24582	0.862408	0.431204	−	0.902255i	$-0.358089\pi$
$37$	5.24582	0.862408	0.431204	+	0.902255i	$0.358089\pi$
$38$	5.68203	0.921747
$39$	−1.48133	−0.237202
$40$	6.63746	1.04947
$41$	−1.26588	−0.197698	−0.0988490	−	0.995102i	$-0.531516\pi$
$41$	−1.26588	−0.197698	−0.0988490	+	0.995102i	$0.531516\pi$
$42$	−2.21109	−0.341179
$43$	0.478550	0.0729782	0.0364891	−	0.999334i	$-0.488383\pi$
$43$	0.478550	0.0729782	0.0364891	+	0.999334i	$0.488383\pi$
$44$	12.8380	1.93540
$45$	1.80167	0.268577
$46$	11.2097	1.65278
$47$	0.0438981	0.00640319	0.00320160	−	0.999995i	$-0.498981\pi$
$47$	0.0438981	0.00640319	0.00320160	+	0.999995i	$0.498981\pi$
$48$	−5.99721	−0.865623
$49$	−1.27217	−0.181738
$50$	12.8881	1.82265
$51$	2.07938	0.291171
$52$	26.0375	3.61076
$53$	−3.96897	−0.545180	−0.272590	−	0.962130i	$-0.587880\pi$
$53$	−3.96897	−0.545180	−0.272590	+	0.962130i	$0.587880\pi$
$54$	−5.44228	−0.740600
$55$	−1.37704	−0.185679
$56$	25.4876	3.40592
$57$	0.672097	0.0890215
$58$	−10.6064	−1.39269
$59$	−3.03123	−0.394633	−0.197317	−	0.980340i	$-0.563223\pi$
$59$	−3.03123	−0.394633	−0.197317	+	0.980340i	$0.563223\pi$
$60$	1.19718	0.154555
$61$	−1.42330	−0.182235	−0.0911175	−	0.995840i	$-0.529044\pi$
$61$	−1.42330	−0.182235	−0.0911175	+	0.995840i	$0.529044\pi$
$62$	−8.91666	−1.13242
$63$	6.91833	0.871627
$64$	45.8883	5.73604
$65$	−2.79286	−0.346411
$66$	2.04122	0.251256
$67$	−2.77620	−0.339167	−0.169583	−	0.985516i	$-0.554242\pi$
$67$	−2.77620	−0.339167	−0.169583	+	0.985516i	$0.554242\pi$
$68$	−36.5496	−4.43229
$69$	1.32594	0.159624
$70$	−4.16874	−0.498260
$71$	−8.74363	−1.03768	−0.518839	−	0.854872i	$-0.673636\pi$
$71$	−8.74363	−1.03768	−0.518839	+	0.854872i	$0.673636\pi$
$72$	30.7850	3.62805
$73$	−4.64295	−0.543416	−0.271708	−	0.962380i	$-0.587589\pi$
$73$	−4.64295	−0.543416	−0.271708	+	0.962380i	$0.587589\pi$
$74$	−14.6607	−1.70427
$75$	1.52446	0.176030
$76$	−11.8136	−1.35511
$77$	−5.28776	−0.602596
$78$	4.13992	0.468754
$79$	−6.67943	−0.751494	−0.375747	−	0.926722i	$-0.622614\pi$
$79$	−6.67943	−0.751494	−0.375747	+	0.926722i	$0.622614\pi$
$80$	−11.3070	−1.26416
$81$	8.02842	0.892047
$82$	3.53782	0.390687
$83$	−3.41406	−0.374741	−0.187371	−	0.982289i	$-0.559997\pi$
$83$	−3.41406	−0.374741	−0.187371	+	0.982289i	$0.559997\pi$
$84$	4.59711	0.501586
$85$	3.92041	0.425228
$86$	−1.33742	−0.144218
$87$	−1.25457	−0.134504
$88$	−23.5294	−2.50824
$89$	−2.49945	−0.264941	−0.132471	−	0.991187i	$-0.542291\pi$
$89$	−2.49945	−0.264941	−0.132471	+	0.991187i	$0.542291\pi$
$90$	−5.03519	−0.530756
$91$	−10.7245	−1.12423
$92$	−23.3063	−2.42985
$93$	−1.05470	−0.109368
$94$	−0.122684	−0.0126539
$95$	1.26716	0.130008
$96$	9.71966	0.992009
$97$	−9.04616	−0.918498	−0.459249	−	0.888308i	$-0.651881\pi$
$97$	−9.04616	−0.918498	−0.459249	+	0.888308i	$0.651881\pi$
$98$	3.55539	0.359148
$99$	−6.38679	−0.641897
$100$	−26.7958	−2.67958
$101$	10.5155	1.04633	0.523164	−	0.852232i	$-0.324751\pi$
$101$	10.5155	1.04633	0.523164	+	0.852232i	$0.324751\pi$
$102$	−5.81133	−0.575407
$103$	6.56190	0.646564	0.323282	−	0.946303i	$-0.395214\pi$
$103$	6.56190	0.646564	0.323282	+	0.946303i	$0.395214\pi$
$104$	−47.7215	−4.67947
$105$	−0.493099	−0.0481215
$106$	11.0922	1.07737
$107$	−11.2370	−1.08632	−0.543159	−	0.839630i	$-0.682772\pi$
$107$	−11.2370	−1.08632	−0.543159	+	0.839630i	$0.682772\pi$
$108$	11.3151	1.08880
$109$	7.93060	0.759613	0.379807	−	0.925066i	$-0.375990\pi$
$109$	7.93060	0.759613	0.379807	+	0.925066i	$0.375990\pi$
$110$	3.84846	0.366936
$111$	−1.73414	−0.164597
$112$	−43.4184	−4.10265
$113$	0.437106	0.0411194	0.0205597	−	0.999789i	$-0.493455\pi$
$113$	0.437106	0.0411194	0.0205597	+	0.999789i	$0.493455\pi$
$114$	−1.87834	−0.175923
$115$	2.49989	0.233116
$116$	22.0519	2.04746
$117$	−12.9535	−1.19755
$118$	8.47152	0.779866
$119$	15.0542	1.38002
$120$	−2.19418	−0.200300
$121$	−6.11849	−0.556227
$122$	3.97776	0.360129
$123$	0.418470	0.0377322
$124$	18.5387	1.66483
$125$	5.99048	0.535805
$126$	−19.3349	−1.72249
$127$	5.89684	0.523260	0.261630	−	0.965168i	$-0.415740\pi$
$127$	5.89684	0.523260	0.261630	+	0.965168i	$0.415740\pi$
$128$	−69.4414	−6.13781
$129$	−0.158197	−0.0139284
$130$	7.80531	0.684571
$131$	−3.46236	−0.302508	−0.151254	−	0.988495i	$-0.548331\pi$
$131$	−3.46236	−0.302508	−0.151254	+	0.988495i	$0.548331\pi$
$132$	−4.24392	−0.369386
$133$	4.86583	0.421921
$134$	7.75876	0.670255
$135$	−1.21369	−0.104458
$136$	66.9880	5.74417
$137$	−10.6457	−0.909526	−0.454763	−	0.890612i	$-0.650276\pi$
$137$	−10.6457	−0.909526	−0.454763	+	0.890612i	$0.650276\pi$
$138$	−3.70566	−0.315446
$139$	12.5122	1.06127	0.530635	−	0.847601i	$-0.321954\pi$
$139$	12.5122	1.06127	0.530635	+	0.847601i	$0.321954\pi$
$140$	8.66729	0.732520
$141$	−0.0145116	−0.00122210
$142$	24.4362	2.05064
$143$	9.90050	0.827921
$144$	−52.4427	−4.37022
$145$	−2.36534	−0.196431
$146$	12.9759	1.07389
$147$	0.420548	0.0346862
$148$	30.4813	2.50555
$149$	−8.83357	−0.723674	−0.361837	−	0.932241i	$-0.617850\pi$
$149$	−8.83357	−0.723674	−0.361837	+	0.932241i	$0.617850\pi$
$150$	−4.26048	−0.347867
$151$	2.38584	0.194157	0.0970786	−	0.995277i	$-0.469050\pi$
$151$	2.38584	0.194157	0.0970786	+	0.995277i	$0.469050\pi$
$152$	21.6519	1.75620
$153$	18.1832	1.47002
$154$	14.7779	1.19084
$155$	−1.98852	−0.159721
$156$	−8.60737	−0.689141
$157$	−13.1898	−1.05266	−0.526329	−	0.850281i	$-0.676432\pi$
$157$	−13.1898	−1.05266	−0.526329	+	0.850281i	$0.676432\pi$
$158$	18.6673	1.48509
$159$	1.31204	0.104052
$160$	18.3252	1.44874
$161$	9.59949	0.756545
$162$	−22.4374	−1.76285
$163$	11.7047	0.916785	0.458392	−	0.888750i	$-0.348425\pi$
$163$	11.7047	0.916785	0.458392	+	0.888750i	$0.348425\pi$
$164$	−7.35553	−0.574371
$165$	0.455214	0.0354384
$166$	9.54141	0.740557
$167$	−1.31711	−0.101921	−0.0509605	−	0.998701i	$-0.516228\pi$
$167$	−1.31711	−0.101921	−0.0509605	+	0.998701i	$0.516228\pi$
$168$	−8.42556	−0.650046
$169$	7.07984	0.544603
$170$	−10.9565	−0.840328
$171$	5.87717	0.449438
$172$	2.78065	0.212023
$173$	1.29453	0.0984211	0.0492106	−	0.998788i	$-0.484329\pi$
$173$	1.29453	0.0984211	0.0492106	+	0.998788i	$0.484329\pi$
$174$	3.50621	0.265805
$175$	11.0368	0.834301
$176$	40.0826	3.02134
$177$	1.00205	0.0753188
$178$	6.98533	0.523572
$179$	−9.24013	−0.690640	−0.345320	−	0.938485i	$-0.612230\pi$
$179$	−9.24013	−0.690640	−0.345320	+	0.938485i	$0.612230\pi$
$180$	10.4687	0.780294
$181$	8.17566	0.607692	0.303846	−	0.952721i	$-0.401729\pi$
$181$	8.17566	0.607692	0.303846	+	0.952721i	$0.401729\pi$
$182$	29.9721	2.22168
$183$	0.470508	0.0347809
$184$	42.7156	3.14903
$185$	−3.26950	−0.240379
$186$	2.94763	0.216131
$187$	−13.8976	−1.01629
$188$	0.255074	0.0186032
$189$	−4.66051	−0.339003
$190$	−3.54138	−0.256918
$191$	11.8183	0.855139	0.427570	−	0.903982i	$-0.359370\pi$
$191$	11.8183	0.855139	0.427570	+	0.903982i	$0.359370\pi$
$192$	−15.1695	−1.09477
$193$	−23.3865	−1.68340	−0.841699	−	0.539946i	$-0.818444\pi$
$193$	−23.3865	−1.68340	−0.841699	+	0.539946i	$0.818444\pi$
$194$	25.2817	1.81512
$195$	0.923249	0.0661152
$196$	−7.39205	−0.528004
$197$	19.1053	1.36119	0.680597	−	0.732658i	$-0.261721\pi$
$197$	19.1053	1.36119	0.680597	+	0.732658i	$0.261721\pi$
$198$	17.8494	1.26850
$199$	−4.99487	−0.354077	−0.177039	−	0.984204i	$-0.556652\pi$
$199$	−4.99487	−0.354077	−0.177039	+	0.984204i	$0.556652\pi$
$200$	49.1112	3.47268
$201$	0.917742	0.0647325
$202$	−29.3880	−2.06774
$203$	−9.08282	−0.637489
$204$	12.0824	0.845938
$205$	0.788974	0.0551043
$206$	−18.3388	−1.27773
$207$	11.5947	0.805886
$208$	81.2941	5.63673
$209$	−4.49199	−0.310717
$210$	1.37808	0.0950968
$211$	15.1423	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$211$	15.1423	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$212$	−23.0620	−1.58391
$213$	2.89043	0.198049
$214$	31.4044	2.14676
$215$	−0.298260	−0.0203412
$216$	−20.7383	−1.41106
$217$	−7.63582	−0.518353
$218$	−22.1640	−1.50113
$219$	1.53484	0.103715
$220$	−8.00139	−0.539453
$221$	−28.1866	−1.89604
$222$	4.84647	0.325274
$223$	−10.0286	−0.671567	−0.335783	−	0.941939i	$-0.609001\pi$
$223$	−10.0286	−0.671567	−0.335783	+	0.941939i	$0.609001\pi$
$224$	70.3681	4.70167
$225$	13.3307	0.888713
$226$	−1.22160	−0.0812595
$227$	0.494592	0.0328273	0.0164136	−	0.999865i	$-0.494775\pi$
$227$	0.494592	0.0328273	0.0164136	+	0.999865i	$0.494775\pi$
$228$	3.90528	0.258633
$229$	22.5145	1.48780	0.743901	−	0.668290i	$-0.232973\pi$
$229$	22.5145	1.48780	0.743901	+	0.668290i	$0.232973\pi$
$230$	−6.98655	−0.460680
$231$	1.74800	0.115010
$232$	−40.4165	−2.65347
$233$	3.34484	0.219128	0.109564	−	0.993980i	$-0.465055\pi$
$233$	3.34484	0.219128	0.109564	+	0.993980i	$0.465055\pi$
$234$	36.2016	2.36657
$235$	−0.0273599	−0.00178476
$236$	−17.6132	−1.14652
$237$	2.20805	0.143428
$238$	−42.0727	−2.72717
$239$	25.6901	1.66176	0.830878	−	0.556454i	$-0.187838\pi$
$239$	25.6901	1.66176	0.830878	+	0.556454i	$0.187838\pi$
$240$	3.73781	0.241275
$241$	5.92415	0.381608	0.190804	−	0.981628i	$-0.438891\pi$
$241$	5.92415	0.381608	0.190804	+	0.981628i	$0.438891\pi$
$242$	17.0996	1.09921
$243$	−8.49598	−0.545017
$244$	−8.27021	−0.529446
$245$	0.792891	0.0506559
$246$	−1.16952	−0.0745656
$247$	−9.11050	−0.579687
$248$	−33.9777	−2.15759
$249$	1.12860	0.0715223
$250$	−16.7419	−1.05885
$251$	−30.2815	−1.91135	−0.955675	−	0.294423i	$-0.904872\pi$
$251$	−30.2815	−1.91135	−0.955675	+	0.294423i	$0.904872\pi$
$252$	40.1995	2.53233
$253$	−8.86196	−0.557147
$254$	−16.4802	−1.03406
$255$	−1.29599	−0.0811581
$256$	102.294	6.39339
$257$	−12.4908	−0.779152	−0.389576	−	0.920994i	$-0.627378\pi$
$257$	−12.4908	−0.779152	−0.389576	+	0.920994i	$0.627378\pi$
$258$	0.442119	0.0275251
$259$	−12.5548	−0.780115
$260$	−16.2281	−1.00643
$261$	−10.9706	−0.679065
$262$	9.67642	0.597811
$263$	2.41437	0.148877	0.0744384	−	0.997226i	$-0.476284\pi$
$263$	2.41437	0.148877	0.0744384	+	0.997226i	$0.476284\pi$
$264$	7.77823	0.478717
$265$	2.47369	0.151958
$266$	−13.5987	−0.833792
$267$	0.826257	0.0505661
$268$	−16.1313	−0.985378
$269$	19.2431	1.17327	0.586636	−	0.809851i	$-0.300452\pi$
$269$	19.2431	1.17327	0.586636	+	0.809851i	$0.300452\pi$
$270$	3.39195	0.206427
$271$	18.2178	1.10665	0.553327	−	0.832964i	$-0.313358\pi$
$271$	18.2178	1.10665	0.553327	+	0.832964i	$0.313358\pi$
$272$	−114.115	−6.91923
$273$	3.54524	0.214568
$274$	29.7521	1.79739
$275$	−10.1888	−0.614409
$276$	7.70448	0.463755
$277$	4.27004	0.256562	0.128281	−	0.991738i	$-0.459054\pi$
$277$	4.27004	0.256562	0.128281	+	0.991738i	$0.459054\pi$
$278$	−34.9683	−2.09726
$279$	−9.22288	−0.552159
$280$	−15.8854	−0.949332
$281$	11.4399	0.682448	0.341224	−	0.939982i	$-0.389159\pi$
$281$	11.4399	0.682448	0.341224	+	0.939982i	$0.389159\pi$
$282$	0.0405563	0.00241509
$283$	−30.8061	−1.83123	−0.915617	−	0.402052i	$-0.868297\pi$
$283$	−30.8061	−1.83123	−0.915617	+	0.402052i	$0.868297\pi$
$284$	−50.8056	−3.01476
$285$	−0.418891	−0.0248129
$286$	−27.6693	−1.63612
$287$	3.02963	0.178833
$288$	84.9937	5.00830
$289$	22.5664	1.32743
$290$	6.61052	0.388183
$291$	2.99044	0.175302
$292$	−26.9783	−1.57878
$293$	−3.93979	−0.230165	−0.115082	−	0.993356i	$-0.536713\pi$
$293$	−3.93979	−0.230165	−0.115082	+	0.993356i	$0.536713\pi$
$294$	−1.17532	−0.0685462
$295$	1.88924	0.109996
$296$	−55.8659	−3.24714
$297$	4.30245	0.249653
$298$	24.6876	1.43011
$299$	−17.9735	−1.03944
$300$	8.85803	0.511418
$301$	−1.14531	−0.0660144
$302$	−6.66782	−0.383690
$303$	−3.47616	−0.199700
$304$	−36.8842	−2.11546
$305$	0.887084	0.0507943
$306$	−50.8172	−2.90503
$307$	−2.13230	−0.121697	−0.0608483	−	0.998147i	$-0.519381\pi$
$307$	−2.13230	−0.121697	−0.0608483	+	0.998147i	$0.519381\pi$
$308$	−30.7250	−1.75072
$309$	−2.16920	−0.123402
$310$	5.55739	0.315638
$311$	−13.5338	−0.767434	−0.383717	−	0.923451i	$-0.625356\pi$
$311$	−13.5338	−0.767434	−0.383717	+	0.923451i	$0.625356\pi$
$312$	15.7755	0.893114
$313$	30.7227	1.73655	0.868275	−	0.496083i	$-0.165229\pi$
$313$	30.7227	1.73655	0.868275	+	0.496083i	$0.165229\pi$
$314$	36.8620	2.08024
$315$	−4.31191	−0.242948
$316$	−38.8114	−2.18331
$317$	−15.9498	−0.895828	−0.447914	−	0.894077i	$-0.647833\pi$
$317$	−15.9498	−0.895828	−0.447914	+	0.894077i	$0.647833\pi$
$318$	−3.66682	−0.205625
$319$	8.38498	0.469469
$320$	−28.6003	−1.59880
$321$	3.71466	0.207332
$322$	−26.8281	−1.49507
$323$	12.7887	0.711580
$324$	46.6498	2.59166
$325$	−20.6646	−1.14627
$326$	−32.7117	−1.81173
$327$	−2.62166	−0.144978
$328$	13.4812	0.744373
$329$	−0.105061	−0.00579219
$330$	−1.27221	−0.0700326
$331$	−7.28800	−0.400585	−0.200292	−	0.979736i	$-0.564189\pi$
$331$	−7.28800	−0.400585	−0.200292	+	0.979736i	$0.564189\pi$
$332$	−19.8377	−1.08873
$333$	−15.1642	−0.830993
$334$	3.68098	0.201414
$335$	1.73029	0.0945358
$336$	14.3531	0.783023
$337$	16.2291	0.884057	0.442028	−	0.897001i	$-0.354259\pi$
$337$	16.2291	0.884057	0.442028	+	0.897001i	$0.354259\pi$
$338$	−19.7863	−1.07624
$339$	−0.144496	−0.00784796
$340$	22.7799	1.23541
$341$	7.04916	0.381733
$342$	−16.4252	−0.888171
$343$	19.7977	1.06897
$344$	−5.09637	−0.274778
$345$	−0.826403	−0.0444920
$346$	−3.61787	−0.194498
$347$	−3.77404	−0.202601	−0.101301	−	0.994856i	$-0.532300\pi$
$347$	−3.77404	−0.202601	−0.101301	+	0.994856i	$0.532300\pi$
$348$	−7.28980	−0.390774
$349$	−20.9869	−1.12341	−0.561703	−	0.827339i	$-0.689853\pi$
$349$	−20.9869	−1.12341	−0.561703	+	0.827339i	$0.689853\pi$
$350$	−30.8449	−1.64873
$351$	8.72607	0.465763
$352$	−64.9617	−3.46247
$353$	0.755157	0.0401929	0.0200965	−	0.999798i	$-0.493603\pi$
$353$	0.755157	0.0401929	0.0200965	+	0.999798i	$0.493603\pi$
$354$	−2.80047	−0.148844
$355$	5.44954	0.289232
$356$	−14.5233	−0.769733
$357$	−4.97655	−0.263387
$358$	25.8238	1.36483
$359$	35.6784	1.88303	0.941516	−	0.336968i	$-0.109401\pi$
$359$	35.6784	1.88303	0.941516	+	0.336968i	$0.109401\pi$
$360$	−19.1870	−1.01125
$361$	−14.8664	−0.782444
$362$	−22.8489	−1.20091
$363$	2.02262	0.106160
$364$	−62.3154	−3.26621
$365$	2.89376	0.151466
$366$	−1.31495	−0.0687335
$367$	−36.6431	−1.91275	−0.956376	−	0.292139i	$-0.905633\pi$
$367$	−36.6431	−1.91275	−0.956376	+	0.292139i	$0.905633\pi$
$368$	−72.7665	−3.79322
$369$	3.65932	0.190496
$370$	9.13742	0.475032
$371$	9.49888	0.493157
$372$	−6.12845	−0.317745
$373$	−2.52955	−0.130975	−0.0654876	−	0.997853i	$-0.520860\pi$
$373$	−2.52955	−0.130975	−0.0654876	+	0.997853i	$0.520860\pi$
$374$	38.8402	2.00838
$375$	−1.98031	−0.102263
$376$	−0.467497	−0.0241093
$377$	17.0061	0.875860
$378$	13.0249	0.669930
$379$	−24.7157	−1.26956	−0.634780	−	0.772693i	$-0.718909\pi$
$379$	−24.7157	−1.26956	−0.634780	+	0.772693i	$0.718909\pi$
$380$	7.36292	0.377710
$381$	−1.94935	−0.0998683
$382$	−33.0290	−1.68991
$383$	−12.3446	−0.630778	−0.315389	−	0.948963i	$-0.602135\pi$
$383$	−12.3446	−0.630778	−0.315389	+	0.948963i	$0.602135\pi$
$384$	22.9556	1.17145
$385$	3.29564	0.167962
$386$	65.3593	3.32670
$387$	−1.38335	−0.0703198
$388$	−52.5635	−2.66851
$389$	25.9399	1.31521	0.657603	−	0.753365i	$-0.271570\pi$
$389$	25.9399	1.31521	0.657603	+	0.753365i	$0.271570\pi$
$390$	−2.58024	−0.130656
$391$	25.2299	1.27593
$392$	13.5481	0.684283
$393$	1.14457	0.0577360
$394$	−53.3943	−2.68997
$395$	4.16301	0.209464
$396$	−37.1110	−1.86490
$397$	14.4471	0.725079	0.362540	−	0.931968i	$-0.381910\pi$
$397$	14.4471	0.725079	0.362540	+	0.931968i	$0.381910\pi$
$398$	13.9594	0.699721
$399$	−1.60852	−0.0805269
$400$	−83.6615	−4.18307
$401$	−36.1366	−1.80457	−0.902287	−	0.431136i	$-0.858113\pi$
$401$	−36.1366	−1.80457	−0.902287	+	0.431136i	$0.858113\pi$
$402$	−2.56485	−0.127923
$403$	14.2969	0.712177
$404$	61.1011	3.03989
$405$	−5.00378	−0.248640
$406$	25.3841	1.25979
$407$	11.5902	0.574504
$408$	−22.1446	−1.09632
$409$	20.5863	1.01793	0.508964	−	0.860788i	$-0.330029\pi$
$409$	20.5863	1.01793	0.508964	+	0.860788i	$0.330029\pi$
$410$	−2.20498	−0.108896
$411$	3.51922	0.173590
$412$	38.1285	1.87846
$413$	7.25462	0.356976
$414$	−32.4042	−1.59258
$415$	2.12784	0.104452
$416$	−131.753	−6.45973
$417$	−4.13622	−0.202551
$418$	12.5540	0.614034
$419$	12.2823	0.600029	0.300015	−	0.953935i	$-0.403008\pi$
$419$	12.2823	0.600029	0.300015	+	0.953935i	$0.403008\pi$
$420$	−2.86519	−0.139807
$421$	−7.08369	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$421$	−7.08369	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$422$	−42.3189	−2.06005
$423$	−0.126897	−0.00616995
$424$	42.2679	2.05271
$425$	29.0075	1.40707
$426$	−8.07800	−0.391380
$427$	3.40637	0.164846
$428$	−65.2933	−3.15607
$429$	−3.27286	−0.158015
$430$	0.833561	0.0401979
$431$	−9.17324	−0.441859	−0.220930	−	0.975290i	$-0.570909\pi$
$431$	−9.17324	−0.441859	−0.220930	+	0.975290i	$0.570909\pi$
$432$	35.3279	1.69971
$433$	20.5359	0.986893	0.493447	−	0.869776i	$-0.335737\pi$
$433$	20.5359	0.986893	0.493447	+	0.869776i	$0.335737\pi$
$434$	21.3401	1.02436
$435$	0.781923	0.0374904
$436$	46.0814	2.20690
$437$	8.15483	0.390098
$438$	−4.28950	−0.204960
$439$	36.9682	1.76440	0.882198	−	0.470879i	$-0.156063\pi$
$439$	36.9682	1.76440	0.882198	+	0.470879i	$0.156063\pi$
$440$	14.6649	0.699121
$441$	3.67749	0.175118
$442$	78.7744	3.74692
$443$	2.34048	0.111200	0.0555999	−	0.998453i	$-0.482293\pi$
$443$	2.34048	0.111200	0.0555999	+	0.998453i	$0.482293\pi$
$444$	−10.0764	−0.478203
$445$	1.55781	0.0738471
$446$	28.0274	1.32714
$447$	2.92016	0.138119
$448$	−109.824	−5.18869
$449$	−20.5274	−0.968746	−0.484373	−	0.874862i	$-0.660952\pi$
$449$	−20.5274	−0.968746	−0.484373	+	0.874862i	$0.660952\pi$
$450$	−37.2559	−1.75626
$451$	−2.79686	−0.131699
$452$	2.53984	0.119464
$453$	−0.788701	−0.0370564
$454$	−1.38226	−0.0648726
$455$	6.68411	0.313356
$456$	−7.15757	−0.335184
$457$	−11.5588	−0.540699	−0.270350	−	0.962762i	$-0.587139\pi$
$457$	−11.5588	−0.540699	−0.270350	+	0.962762i	$0.587139\pi$
$458$	−62.9223	−2.94017
$459$	−12.2490	−0.571736
$460$	14.5258	0.677271
$461$	4.94895	0.230496	0.115248	−	0.993337i	$-0.463234\pi$
$461$	4.94895	0.230496	0.115248	+	0.993337i	$0.463234\pi$
$462$	−4.88522	−0.227281
$463$	15.1701	0.705016	0.352508	−	0.935809i	$-0.385329\pi$
$463$	15.1701	0.705016	0.352508	+	0.935809i	$0.385329\pi$
$464$	68.8500	3.19628
$465$	0.657354	0.0304841
$466$	−9.34797	−0.433037
$467$	−13.5756	−0.628206	−0.314103	−	0.949389i	$-0.601704\pi$
$467$	−13.5756	−0.628206	−0.314103	+	0.949389i	$0.601704\pi$
$468$	−75.2673	−3.47923
$469$	6.64424	0.306803
$470$	0.0764638	0.00352701
$471$	4.36021	0.200908
$472$	32.2814	1.48587
$473$	1.05731	0.0486153
$474$	−6.17094	−0.283441
$475$	9.37581	0.430192
$476$	87.4738	4.00936
$477$	11.4732	0.525320
$478$	−71.7973	−3.28393
$479$	−3.57824	−0.163494	−0.0817471	−	0.996653i	$-0.526050\pi$
$479$	−3.57824	−0.163494	−0.0817471	+	0.996653i	$0.526050\pi$
$480$	−6.05786	−0.276502
$481$	23.5068	1.07182
$482$	−16.5565	−0.754126
$483$	−3.17335	−0.144393
$484$	−35.5520	−1.61600
$485$	5.63810	0.256013
$486$	23.7441	1.07705
$487$	26.4700	1.19947	0.599735	−	0.800199i	$-0.295273\pi$
$487$	26.4700	1.19947	0.599735	+	0.800199i	$0.295273\pi$
$488$	15.1576	0.686152
$489$	−3.86929	−0.174975
$490$	−2.21593	−0.100105
$491$	−9.22312	−0.416233	−0.208117	−	0.978104i	$-0.566733\pi$
$491$	−9.22312	−0.416233	−0.208117	+	0.978104i	$0.566733\pi$
$492$	2.43156	0.109623
$493$	−23.8720	−1.07514
$494$	25.4615	1.14557
$495$	3.98063	0.178916
$496$	57.8814	2.59895
$497$	20.9260	0.938661
$498$	−3.15415	−0.141341
$499$	17.3038	0.774624	0.387312	−	0.921949i	$-0.373404\pi$
$499$	17.3038	0.774624	0.387312	+	0.921949i	$0.373404\pi$
$500$	34.8082	1.55667
$501$	0.435404	0.0194524
$502$	84.6289	3.77717
$503$	29.3781	1.30990	0.654952	−	0.755671i	$-0.272689\pi$
$503$	29.3781	1.30990	0.654952	+	0.755671i	$0.272689\pi$
$504$	−73.6775	−3.28185
$505$	−6.55386	−0.291643
$506$	24.7669	1.10102
$507$	−2.34042	−0.103942
$508$	34.2641	1.52022
$509$	−17.7447	−0.786521	−0.393260	−	0.919427i	$-0.628653\pi$
$509$	−17.7447	−0.786521	−0.393260	+	0.919427i	$0.628653\pi$
$510$	3.62196	0.160383
$511$	11.1119	0.491563
$512$	−147.003	−6.49669
$513$	−3.95914	−0.174800
$514$	34.9085	1.53975
$515$	−4.08976	−0.180217
$516$	−0.919216	−0.0404662
$517$	0.0969890	0.00426557
$518$	35.0873	1.54165
$519$	−0.427939	−0.0187844
$520$	29.7428	1.30431
$521$	42.8047	1.87531	0.937655	−	0.347568i	$-0.112992\pi$
$521$	42.8047	1.87531	0.937655	+	0.347568i	$0.112992\pi$
$522$	30.6601	1.34196
$523$	0.869846	0.0380357	0.0190179	−	0.999819i	$-0.493946\pi$
$523$	0.869846	0.0380357	0.0190179	+	0.999819i	$0.493946\pi$
$524$	−20.1184	−0.878875
$525$	−3.64848	−0.159233
$526$	−6.74756	−0.294207
$527$	−20.0689	−0.874215
$528$	−13.2503	−0.576646
$529$	−6.91186	−0.300516
$530$	−6.91334	−0.300296
$531$	8.76245	0.380258
$532$	28.2733	1.22580
$533$	−5.67250	−0.245703
$534$	−2.30918	−0.0999278
$535$	7.00353	0.302789
$536$	29.5654	1.27703
$537$	3.05456	0.131814
$538$	−53.7795	−2.31860
$539$	−2.81075	−0.121067
$540$	−7.05224	−0.303480
$541$	32.1976	1.38428	0.692142	−	0.721762i	$-0.256667\pi$
$541$	32.1976	1.38428	0.692142	+	0.721762i	$0.256667\pi$
$542$	−50.9141	−2.18695
$543$	−2.70267	−0.115983
$544$	184.946	7.92948
$545$	−4.94281	−0.211727
$546$	−9.90803	−0.424025
$547$	43.7615	1.87110	0.935552	−	0.353188i	$-0.114902\pi$
$547$	43.7615	1.87110	0.935552	+	0.353188i	$0.114902\pi$
$548$	−61.8579	−2.64244
$549$	4.11436	0.175597
$550$	28.4751	1.21418
$551$	−7.71591	−0.328709
$552$	−14.1207	−0.601018
$553$	15.9858	0.679785
$554$	−11.9337	−0.507013
$555$	1.08082	0.0458781
$556$	72.7031	3.08330
$557$	0.655201	0.0277617	0.0138809	−	0.999904i	$-0.495581\pi$
$557$	0.655201	0.0277617	0.0138809	+	0.999904i	$0.495581\pi$
$558$	25.7756	1.09117
$559$	2.14441	0.0906988
$560$	27.0609	1.14353
$561$	4.59421	0.193968
$562$	−31.9716	−1.34864
$563$	35.7392	1.50623	0.753113	−	0.657891i	$-0.228551\pi$
$563$	35.7392	1.50623	0.753113	+	0.657891i	$0.228551\pi$
$564$	−0.0843210	−0.00355056
$565$	−0.272430	−0.0114612
$566$	86.0952	3.61885
$567$	−19.2143	−0.806926
$568$	93.1162	3.90707
$569$	−41.2438	−1.72903	−0.864514	−	0.502608i	$-0.832374\pi$
$569$	−41.2438	−1.72903	−0.864514	+	0.502608i	$0.832374\pi$
$570$	1.17069	0.0490349
$571$	26.3962	1.10465	0.552324	−	0.833630i	$-0.313741\pi$
$571$	26.3962	1.10465	0.552324	+	0.833630i	$0.313741\pi$
$572$	57.5277	2.40535
$573$	−3.90682	−0.163210
$574$	−8.46703	−0.353407
$575$	18.4969	0.771375
$576$	−132.650	−5.52709
$577$	−13.1789	−0.548644	−0.274322	−	0.961638i	$-0.588453\pi$
$577$	−13.1789	−0.548644	−0.274322	+	0.961638i	$0.588453\pi$
$578$	−63.0672	−2.62325
$579$	7.73101	0.321290
$580$	−13.7440	−0.570689
$581$	8.17082	0.338983
$582$	−8.35750	−0.346429
$583$	−8.76909	−0.363178
$584$	49.4456	2.04607
$585$	8.07337	0.333793
$586$	11.0107	0.454847
$587$	20.5331	0.847493	0.423746	−	0.905781i	$-0.360715\pi$
$587$	20.5331	0.847493	0.423746	+	0.905781i	$0.360715\pi$
$588$	2.44363	0.100774
$589$	−6.48668	−0.267279
$590$	−5.27995	−0.217372
$591$	−6.31573	−0.259794
$592$	95.1683	3.91139
$593$	8.34657	0.342753	0.171376	−	0.985206i	$-0.445179\pi$
$593$	8.34657	0.342753	0.171376	+	0.985206i	$0.445179\pi$
$594$	−12.0242	−0.493360
$595$	−9.38267	−0.384652
$596$	−51.3282	−2.10249
$597$	1.65118	0.0675784
$598$	50.2313	2.05411
$599$	33.9023	1.38521	0.692606	−	0.721316i	$-0.256462\pi$
$599$	33.9023	1.38521	0.692606	+	0.721316i	$0.256462\pi$
$600$	−16.2349	−0.662789
$601$	−25.3508	−1.03408	−0.517041	−	0.855961i	$-0.672966\pi$
$601$	−25.3508	−1.03408	−0.517041	+	0.855961i	$0.672966\pi$
$602$	3.20084	0.130457
$603$	8.02521	0.326812
$604$	13.8632	0.564084
$605$	3.81341	0.155037
$606$	9.71496	0.394643
$607$	0.902994	0.0366514	0.0183257	−	0.999832i	$-0.494166\pi$
$607$	0.902994	0.0366514	0.0183257	+	0.999832i	$0.494166\pi$
$608$	59.7782	2.42432
$609$	3.00255	0.121670
$610$	−2.47917	−0.100379
$611$	0.196710	0.00795802
$612$	105.655	4.27084
$613$	−13.9241	−0.562388	−0.281194	−	0.959651i	$-0.590730\pi$
$613$	−13.9241	−0.562388	−0.281194	+	0.959651i	$0.590730\pi$
$614$	5.95922	0.240494
$615$	−0.260815	−0.0105171
$616$	56.3126	2.26890
$617$	41.4968	1.67060	0.835300	−	0.549795i	$-0.185294\pi$
$617$	41.4968	1.67060	0.835300	+	0.549795i	$0.185294\pi$
$618$	6.06236	0.243864
$619$	−7.56592	−0.304100	−0.152050	−	0.988373i	$-0.548587\pi$
$619$	−7.56592	−0.304100	−0.152050	+	0.988373i	$0.548587\pi$
$620$	−11.5544	−0.464037
$621$	−7.81073	−0.313434
$622$	37.8236	1.51659
$623$	5.98191	0.239660
$624$	−26.8738	−1.07581
$625$	19.3241	0.772965
$626$	−85.8621	−3.43174
$627$	1.48494	0.0593028
$628$	−76.6403	−3.05828
$629$	−32.9972	−1.31568
$630$	12.0507	0.480110
$631$	3.41538	0.135964	0.0679820	−	0.997687i	$-0.478344\pi$
$631$	3.41538	0.135964	0.0679820	+	0.997687i	$0.478344\pi$
$632$	71.1333	2.82953
$633$	−5.00567	−0.198958
$634$	44.5755	1.77032
$635$	−3.67526	−0.145848
$636$	7.62373	0.302301
$637$	−5.70066	−0.225868
$638$	−23.4339	−0.927756
$639$	25.2754	0.999879
$640$	43.2800	1.71079
$641$	−27.6102	−1.09054	−0.545268	−	0.838262i	$-0.683572\pi$
$641$	−27.6102	−1.09054	−0.545268	+	0.838262i	$0.683572\pi$
$642$	−10.3815	−0.409726
$643$	−4.72415	−0.186302	−0.0931512	−	0.995652i	$-0.529694\pi$
$643$	−4.72415	−0.186302	−0.0931512	+	0.995652i	$0.529694\pi$
$644$	55.7786	2.19799
$645$	0.0985975	0.00388227
$646$	−35.7410	−1.40621
$647$	36.4799	1.43417	0.717086	−	0.696984i	$-0.245475\pi$
$647$	36.4799	1.43417	0.717086	+	0.696984i	$0.245475\pi$
$648$	−85.4995	−3.35874
$649$	−6.69725	−0.262890
$650$	57.7522	2.26523
$651$	2.52421	0.0989317
$652$	68.0113	2.66353
$653$	3.84452	0.150448	0.0752238	−	0.997167i	$-0.476033\pi$
$653$	3.84452	0.150448	0.0752238	+	0.997167i	$0.476033\pi$
$654$	7.32686	0.286503
$655$	2.15795	0.0843180
$656$	−22.9653	−0.896646
$657$	13.4215	0.523622
$658$	0.293618	0.0114464
$659$	0.00723341	0.000281774 0	0.000140887	−	1.00000i	$-0.499955\pi$
$659$	0.00723341	0.000281774 0	0.000140887		1.00000i	$0.499955\pi$
$660$	2.64506	0.102959
$661$	−38.0081	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$661$	−38.0081	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$662$	20.3681	0.791628
$663$	9.31781	0.361874
$664$	36.3584	1.41098
$665$	−3.03267	−0.117602
$666$	42.3800	1.64219
$667$	−15.2222	−0.589407
$668$	−7.65318	−0.296110
$669$	3.31522	0.128174
$670$	−4.83571	−0.186820
$671$	−3.14466	−0.121398
$672$	−23.2620	−0.897349
$673$	18.3536	0.707478	0.353739	−	0.935344i	$-0.384910\pi$
$673$	18.3536	0.707478	0.353739	+	0.935344i	$0.384910\pi$
$674$	−45.3562	−1.74706
$675$	−8.98019	−0.345648
$676$	41.1380	1.58223
$677$	−46.1492	−1.77366	−0.886829	−	0.462098i	$-0.847097\pi$
$677$	−46.1492	−1.77366	−0.886829	+	0.462098i	$0.847097\pi$
$678$	0.403830	0.0155090
$679$	21.6501	0.830853
$680$	−41.7508	−1.60107
$681$	−0.163500	−0.00626534
$682$	−19.7006	−0.754375
$683$	37.6989	1.44251	0.721255	−	0.692670i	$-0.243566\pi$
$683$	37.6989	1.44251	0.721255	+	0.692670i	$0.243566\pi$
$684$	34.1498	1.30575
$685$	6.63504	0.253512
$686$	−55.3294	−2.11249
$687$	−7.44275	−0.283958
$688$	8.68172	0.330988
$689$	−17.7852	−0.677560
$690$	2.30958	0.0879243
$691$	8.27959	0.314970	0.157485	−	0.987521i	$-0.449661\pi$
$691$	8.27959	0.314970	0.157485	+	0.987521i	$0.449661\pi$
$692$	7.52196	0.285942
$693$	15.2854	0.580646
$694$	10.5475	0.400377
$695$	−7.79833	−0.295807
$696$	13.3607	0.506436
$697$	7.96264	0.301607
$698$	58.6531	2.22005
$699$	−1.10572	−0.0418223
$700$	64.1301	2.42389
$701$	49.7219	1.87797	0.938986	−	0.343956i	$-0.111767\pi$
$701$	49.7219	1.87797	0.938986	+	0.343956i	$0.111767\pi$
$702$	−24.3871	−0.920433
$703$	−10.6654	−0.402252
$704$	101.386	3.82114
$705$	0.00904450	0.000340635 0
$706$	−2.11047	−0.0794285
$707$	−25.1666	−0.946486
$708$	5.82250	0.218823
$709$	39.4685	1.48227	0.741134	−	0.671357i	$-0.234288\pi$
$709$	39.4685	1.48227	0.741134	+	0.671357i	$0.234288\pi$
$710$	−15.2301	−0.571574
$711$	19.3084	0.724120
$712$	26.6182	0.997559
$713$	−12.7972	−0.479257
$714$	13.9082	0.520501
$715$	−6.17057	−0.230766
$716$	−53.6906	−2.00651
$717$	−8.49252	−0.317159
$718$	−99.7119	−3.72121
$719$	−28.2869	−1.05492	−0.527461	−	0.849579i	$-0.676856\pi$
$719$	−28.2869	−1.05492	−0.527461	+	0.849579i	$0.676856\pi$
$720$	32.6854	1.21811
$721$	−15.7045	−0.584867
$722$	41.5479	1.54625
$723$	−1.95838	−0.0728328
$724$	47.5054	1.76552
$725$	−17.5014	−0.649985
$726$	−5.65271	−0.209792
$727$	25.2554	0.936672	0.468336	−	0.883550i	$-0.344854\pi$
$727$	25.2554	0.936672	0.468336	+	0.883550i	$0.344854\pi$
$728$	114.211	4.23295
$729$	−21.2767	−0.788026
$730$	−8.08731	−0.299325
$731$	−3.01016	−0.111335
$732$	2.73393	0.101049
$733$	28.1004	1.03791	0.518956	−	0.854801i	$-0.326321\pi$
$733$	28.1004	1.03791	0.518956	+	0.854801i	$0.326321\pi$
$734$	102.408	3.77994
$735$	−0.262110	−0.00966808
$736$	117.933	4.34705
$737$	−6.13377	−0.225940
$738$	−10.2269	−0.376456
$739$	−13.8948	−0.511130	−0.255565	−	0.966792i	$-0.582261\pi$
$739$	−13.8948	−0.511130	−0.255565	+	0.966792i	$0.582261\pi$
$740$	−18.9977	−0.698371
$741$	3.01170	0.110638
$742$	−26.5469	−0.974569
$743$	−23.0052	−0.843978	−0.421989	−	0.906601i	$-0.638668\pi$
$743$	−23.0052	−0.843978	−0.421989	+	0.906601i	$0.638668\pi$
$744$	11.2322	0.411792
$745$	5.50560	0.201710
$746$	7.06944	0.258831
$747$	9.86908	0.361091
$748$	−80.7532	−2.95263
$749$	26.8933	0.982659
$750$	5.53444	0.202089
$751$	35.1121	1.28126	0.640630	−	0.767850i	$-0.278673\pi$
$751$	35.1121	1.28126	0.640630	+	0.767850i	$0.278673\pi$
$752$	0.796387	0.0290413
$753$	10.0103	0.364796
$754$	−47.5278	−1.73086
$755$	−1.48700	−0.0541174
$756$	−27.0803	−0.984902
$757$	34.0605	1.23795	0.618975	−	0.785411i	$-0.287548\pi$
$757$	34.0605	1.23795	0.618975	+	0.785411i	$0.287548\pi$
$758$	69.0740	2.50888
$759$	2.92954	0.106336
$760$	−13.4947	−0.489505
$761$	35.3699	1.28216	0.641079	−	0.767475i	$-0.278487\pi$
$761$	35.3699	1.28216	0.641079	+	0.767475i	$0.278487\pi$
$762$	5.44793	0.197358
$763$	−18.9802	−0.687130
$764$	68.6710	2.48443
$765$	−11.3328	−0.409739
$766$	34.4999	1.24653
$767$	−13.5831	−0.490458
$768$	−33.8160	−1.22023
$769$	5.63382	0.203161	0.101580	−	0.994827i	$-0.467610\pi$
$769$	5.63382	0.203161	0.101580	+	0.994827i	$0.467610\pi$
$770$	−9.21048	−0.331923
$771$	4.12914	0.148707
$772$	−135.889	−4.89077
$773$	24.7903	0.891645	0.445823	−	0.895121i	$-0.352911\pi$
$773$	24.7903	0.891645	0.445823	+	0.895121i	$0.352911\pi$
$774$	3.86612	0.138965
$775$	−14.7132	−0.528514
$776$	96.3380	3.45833
$777$	4.15029	0.148891
$778$	−72.4954	−2.59909
$779$	2.57369	0.0922120
$780$	5.36462	0.192084
$781$	−19.3183	−0.691263
$782$	−70.5112	−2.52147
$783$	7.39034	0.264109
$784$	−23.0794	−0.824263
$785$	8.22064	0.293407
$786$	−3.19878	−0.114097
$787$	−40.5353	−1.44493	−0.722463	−	0.691409i	$-0.756990\pi$
$787$	−40.5353	−1.44493	−0.722463	+	0.691409i	$0.756990\pi$
$788$	111.013	3.95467
$789$	−0.798133	−0.0284143
$790$	−11.6345	−0.413939
$791$	−1.04612	−0.0371957
$792$	68.0168	2.41687
$793$	−6.37789	−0.226485
$794$	−40.3759	−1.43289
$795$	−0.817742	−0.0290023
$796$	−29.0231	−1.02870
$797$	45.9602	1.62799	0.813997	−	0.580869i	$-0.197287\pi$
$797$	45.9602	1.62799	0.813997	+	0.580869i	$0.197287\pi$
$798$	4.49541	0.159136
$799$	−0.276127	−0.00976867
$800$	135.590	4.79383
$801$	7.22522	0.255291
$802$	100.992	3.56617
$803$	−10.2582	−0.362004
$804$	5.33262	0.188067
$805$	−5.98296	−0.210872
$806$	−39.9560	−1.40739
$807$	−6.36129	−0.223928
$808$	−111.986	−3.93964
$809$	9.87673	0.347247	0.173624	−	0.984812i	$-0.444452\pi$
$809$	9.87673	0.347247	0.173624	+	0.984812i	$0.444452\pi$
$810$	13.9843	0.491358
$811$	−36.5860	−1.28471	−0.642354	−	0.766408i	$-0.722042\pi$
$811$	−36.5860	−1.28471	−0.642354	+	0.766408i	$0.722042\pi$
$812$	−52.7765	−1.85209
$813$	−6.02236	−0.211213
$814$	−32.3916	−1.13532
$815$	−7.29507	−0.255535
$816$	37.7235	1.32059
$817$	−0.972947	−0.0340391
$818$	−57.5335	−2.01161
$819$	31.0014	1.08328
$820$	4.58440	0.160094
$821$	−37.0901	−1.29445	−0.647227	−	0.762298i	$-0.724071\pi$
$821$	−37.0901	−1.29445	−0.647227	+	0.762298i	$0.724071\pi$
$822$	−9.83530	−0.343045
$823$	−11.7090	−0.408149	−0.204074	−	0.978955i	$-0.565418\pi$
$823$	−11.7090	−0.408149	−0.204074	+	0.978955i	$0.565418\pi$
$824$	−69.8817	−2.43444
$825$	3.36817	0.117265
$826$	−20.2748	−0.705450
$827$	11.7577	0.408854	0.204427	−	0.978882i	$-0.434467\pi$
$827$	11.7577	0.408854	0.204427	+	0.978882i	$0.434467\pi$
$828$	67.3719	2.34134
$829$	−5.81284	−0.201888	−0.100944	−	0.994892i	$-0.532186\pi$
$829$	−5.81284	−0.201888	−0.100944	+	0.994892i	$0.532186\pi$
$830$	−5.94677	−0.206415
$831$	−1.41157	−0.0489668
$832$	205.628	7.12886
$833$	8.00218	0.277259
$834$	11.5597	0.400278
$835$	0.820900	0.0284084
$836$	−26.1011	−0.902725
$837$	6.21297	0.214752
$838$	−34.3258	−1.18577
$839$	11.5725	0.399527	0.199764	−	0.979844i	$-0.435983\pi$
$839$	11.5725	0.399527	0.199764	+	0.979844i	$0.435983\pi$
$840$	5.25131	0.181187
$841$	−14.5971	−0.503347
$842$	19.7971	0.682253
$843$	−3.78175	−0.130250
$844$	87.9857	3.02859
$845$	−4.41258	−0.151797
$846$	0.354645	0.0121929
$847$	14.6433	0.503151
$848$	−72.0039	−2.47263
$849$	10.1837	0.349505
$850$	−81.0684	−2.78062
$851$	−21.0410	−0.721276
$852$	16.7951	0.575390
$853$	−8.68302	−0.297301	−0.148650	−	0.988890i	$-0.547493\pi$
$853$	−8.68302	−0.297301	−0.148650	+	0.988890i	$0.547493\pi$
$854$	−9.51992	−0.325765
$855$	−3.66299	−0.125272
$856$	119.669	4.09021
$857$	−37.0237	−1.26471	−0.632353	−	0.774680i	$-0.717911\pi$
$857$	−37.0237	−1.26471	−0.632353	+	0.774680i	$0.717911\pi$
$858$	9.14680	0.312267
$859$	−1.68428	−0.0574671	−0.0287335	−	0.999587i	$-0.509147\pi$
$859$	−1.68428	−0.0574671	−0.0287335	+	0.999587i	$0.509147\pi$
$860$	−1.73307	−0.0590971
$861$	−1.00152	−0.0341317
$862$	25.6368	0.873194
$863$	−24.1536	−0.822197	−0.411098	−	0.911591i	$-0.634855\pi$
$863$	−24.1536	−0.822197	−0.411098	+	0.911591i	$0.634855\pi$
$864$	−57.2558	−1.94788
$865$	−0.806826	−0.0274329
$866$	−57.3926	−1.95028
$867$	−7.45989	−0.253351
$868$	−44.3686	−1.50597
$869$	−14.7576	−0.500618
$870$	−2.18527	−0.0740877
$871$	−12.4403	−0.421523
$872$	−84.4577	−2.86010
$873$	26.1499	0.885040
$874$	−22.7906	−0.770905
$875$	−14.3370	−0.484677
$876$	8.91835	0.301323
$877$	−33.3341	−1.12561	−0.562805	−	0.826589i	$-0.690278\pi$
$877$	−33.3341	−1.12561	−0.562805	+	0.826589i	$0.690278\pi$
$878$	−103.317	−3.48677
$879$	1.30240	0.0439287
$880$	−24.9818	−0.842137
$881$	−24.1179	−0.812551	−0.406276	−	0.913751i	$-0.633173\pi$
$881$	−24.1179	−0.812551	−0.406276	+	0.913751i	$0.633173\pi$
$882$	−10.2776	−0.346066
$883$	−7.24027	−0.243654	−0.121827	−	0.992551i	$-0.538875\pi$
$883$	−7.24027	−0.243654	−0.121827	+	0.992551i	$0.538875\pi$
$884$	−163.781	−5.50855
$885$	−0.624537	−0.0209936
$886$	−6.54105	−0.219751
$887$	22.2778	0.748015	0.374007	−	0.927426i	$-0.377983\pi$
$887$	22.2778	0.748015	0.374007	+	0.927426i	$0.377983\pi$
$888$	18.4679	0.619742
$889$	−14.1129	−0.473330
$890$	−4.35367	−0.145935
$891$	17.7381	0.594249
$892$	−58.2722	−1.95110
$893$	−0.0892499	−0.00298663
$894$	−8.16109	−0.272948
$895$	5.75899	0.192502
$896$	166.193	5.55213
$897$	5.94160	0.198384
$898$	57.3687	1.91442
$899$	12.1084	0.403837
$900$	77.4591	2.58197
$901$	24.9655	0.831722
$902$	7.81651	0.260261
$903$	0.378610	0.0125994
$904$	−4.65500	−0.154823
$905$	−5.09555	−0.169382
$906$	2.20422	0.0732302
$907$	29.7323	0.987246	0.493623	−	0.869676i	$-0.335672\pi$
$907$	29.7323	0.987246	0.493623	+	0.869676i	$0.335672\pi$
$908$	2.87387	0.0953728
$909$	−30.3973	−1.00821
$910$	−18.6804	−0.619248
$911$	49.7698	1.64895	0.824474	−	0.565900i	$-0.191471\pi$
$911$	49.7698	1.64895	0.824474	+	0.565900i	$0.191471\pi$
$912$	12.1930	0.403751
$913$	−7.54306	−0.249639
$914$	32.3039	1.06852
$915$	−0.293248	−0.00969449
$916$	130.823	4.32250
$917$	8.28644	0.273642
$918$	34.2329	1.12985
$919$	40.4139	1.33313	0.666566	−	0.745446i	$-0.267764\pi$
$919$	40.4139	1.33313	0.666566	+	0.745446i	$0.267764\pi$
$920$	−26.6229	−0.877730
$921$	0.704884	0.0232267
$922$	−13.8311	−0.455501
$923$	−39.1807	−1.28965
$924$	10.1569	0.334138
$925$	−24.1914	−0.795407
$926$	−42.3966	−1.39324
$927$	−18.9686	−0.623011
$928$	−111.585	−3.66296
$929$	5.87454	0.192737	0.0963686	−	0.995346i	$-0.469277\pi$
$929$	5.87454	0.192737	0.0963686	+	0.995346i	$0.469277\pi$
$930$	−1.83714	−0.0602420
$931$	2.58647	0.0847680
$932$	19.4355	0.636631
$933$	4.47396	0.146471
$934$	37.9404	1.24145
$935$	8.66181	0.283271
$936$	137.949	4.50902
$937$	57.5276	1.87935	0.939673	−	0.342075i	$-0.111130\pi$
$937$	57.5276	1.87935	0.939673	+	0.342075i	$0.111130\pi$
$938$	−18.5689	−0.606298
$939$	−10.1562	−0.331434
$940$	−0.158977	−0.00518525
$941$	−0.596455	−0.0194439	−0.00972194	−	0.999953i	$-0.503095\pi$
$941$	−0.596455	−0.0194439	−0.00972194	+	0.999953i	$0.503095\pi$
$942$	−12.1857	−0.397030
$943$	5.07747	0.165345
$944$	−54.9918	−1.78983
$945$	2.90471	0.0944901
$946$	−2.95492	−0.0960727
$947$	−45.3623	−1.47408	−0.737038	−	0.675851i	$-0.763776\pi$
$947$	−45.3623	−1.47408	−0.737038	+	0.675851i	$0.763776\pi$
$948$	12.8301	0.416702
$949$	−20.8053	−0.675369
$950$	−26.2030	−0.850136
$951$	5.27260	0.170976
$952$	−160.322	−5.19605
$953$	41.8079	1.35429	0.677145	−	0.735849i	$-0.263217\pi$
$953$	41.8079	1.35429	0.677145	+	0.735849i	$0.263217\pi$
$954$	−32.0646	−1.03813
$955$	−7.36583	−0.238353
$956$	149.275	4.82789
$957$	−2.77187	−0.0896018
$958$	10.0003	0.323094
$959$	25.4783	0.822737
$960$	9.45454	0.305144
$961$	−20.8206	−0.671633
$962$	−65.6955	−2.11811
$963$	32.4829	1.04675
$964$	34.4228	1.10868
$965$	14.5759	0.469213
$966$	8.86870	0.285346
$967$	45.4896	1.46285	0.731424	−	0.681923i	$-0.238856\pi$
$967$	45.4896	1.46285	0.731424	+	0.681923i	$0.238856\pi$
$968$	65.1596	2.09431
$969$	−4.22761	−0.135811
$970$	−15.7570	−0.505928
$971$	−25.3124	−0.812313	−0.406156	−	0.913804i	$-0.633131\pi$
$971$	−25.3124	−0.812313	−0.406156	+	0.913804i	$0.633131\pi$
$972$	−49.3666	−1.58343
$973$	−29.9453	−0.960001
$974$	−73.9769	−2.37037
$975$	6.83121	0.218774
$976$	−25.8211	−0.826514
$977$	11.0938	0.354923	0.177462	−	0.984128i	$-0.443211\pi$
$977$	11.0938	0.354923	0.177462	+	0.984128i	$0.443211\pi$
$978$	10.8137	0.345783
$979$	−5.52232	−0.176494
$980$	4.60716	0.147170
$981$	−22.9251	−0.731943
$982$	25.7762	0.822553
$983$	22.1141	0.705331	0.352666	−	0.935749i	$-0.385275\pi$
$983$	22.1141	0.705331	0.352666	+	0.935749i	$0.385275\pi$
$984$	−4.45654	−0.142069
$985$	−11.9075	−0.379405
$986$	66.7161	2.12467
$987$	0.0347305	0.00110548
$988$	−52.9373	−1.68416
$989$	−1.91946	−0.0610354
$990$	−11.1248	−0.353570
$991$	−5.36024	−0.170274	−0.0851369	−	0.996369i	$-0.527133\pi$
$991$	−5.36024	−0.170274	−0.0851369	+	0.996369i	$0.527133\pi$
$992$	−93.8083	−2.97842
$993$	2.40923	0.0764547
$994$	−58.4829	−1.85496
$995$	3.11310	0.0986919
$996$	6.55784	0.207793
$997$	−53.9683	−1.70919	−0.854597	−	0.519293i	$-0.826195\pi$
$997$	−53.9683	−1.70919	−0.854597	+	0.519293i	$0.826195\pi$
$998$	−48.3596	−1.53080
$999$	10.2153	0.323199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.2	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.2	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79474 q^{2} -0.330575 q^{3} +5.81059 q^{4} -0.623259 q^{5} +0.923873 q^{6} -2.39329 q^{7} -10.6496 q^{8} -2.89072 q^{9} +O(q^{10})\)	\(q-2.79474 q^{2} -0.330575 q^{3} +5.81059 q^{4} -0.623259 q^{5} +0.923873 q^{6} -2.39329 q^{7} -10.6496 q^{8} -2.89072 q^{9} +1.74185 q^{10} +2.20941 q^{11} -1.92084 q^{12} +4.48105 q^{13} +6.68863 q^{14} +0.206034 q^{15} +18.1417 q^{16} -6.29018 q^{17} +8.07882 q^{18} -2.03311 q^{19} -3.62150 q^{20} +0.791162 q^{21} -6.17474 q^{22} -4.01100 q^{23} +3.52050 q^{24} -4.61155 q^{25} -12.5234 q^{26} +1.94733 q^{27} -13.9064 q^{28} +3.79512 q^{29} -0.575812 q^{30} +3.19051 q^{31} -29.4023 q^{32} -0.730377 q^{33} +17.5794 q^{34} +1.49164 q^{35} -16.7968 q^{36} +5.24582 q^{37} +5.68203 q^{38} -1.48133 q^{39} +6.63746 q^{40} -1.26588 q^{41} -2.21109 q^{42} +0.478550 q^{43} +12.8380 q^{44} +1.80167 q^{45} +11.2097 q^{46} +0.0438981 q^{47} -5.99721 q^{48} -1.27217 q^{49} +12.8881 q^{50} +2.07938 q^{51} +26.0375 q^{52} -3.96897 q^{53} -5.44228 q^{54} -1.37704 q^{55} +25.4876 q^{56} +0.672097 q^{57} -10.6064 q^{58} -3.03123 q^{59} +1.19718 q^{60} -1.42330 q^{61} -8.91666 q^{62} +6.91833 q^{63} +45.8883 q^{64} -2.79286 q^{65} +2.04122 q^{66} -2.77620 q^{67} -36.5496 q^{68} +1.32594 q^{69} -4.16874 q^{70} -8.74363 q^{71} +30.7850 q^{72} -4.64295 q^{73} -14.6607 q^{74} +1.52446 q^{75} -11.8136 q^{76} -5.28776 q^{77} +4.13992 q^{78} -6.67943 q^{79} -11.3070 q^{80} +8.02842 q^{81} +3.53782 q^{82} -3.41406 q^{83} +4.59711 q^{84} +3.92041 q^{85} -1.33742 q^{86} -1.25457 q^{87} -23.5294 q^{88} -2.49945 q^{89} -5.03519 q^{90} -10.7245 q^{91} -23.3063 q^{92} -1.05470 q^{93} -0.122684 q^{94} +1.26716 q^{95} +9.71966 q^{96} -9.04616 q^{97} +3.55539 q^{98} -6.38679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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