LMFDB - Embedded newform 6033.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.48355 q^{2} -1.00000 q^{3} +0.200920 q^{4} +1.86269 q^{5} +1.48355 q^{6} -2.05902 q^{7} +2.66903 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.48355 q^{2} -1.00000 q^{3} +0.200920 q^{4} +1.86269 q^{5} +1.48355 q^{6} -2.05902 q^{7} +2.66903 q^{8} +1.00000 q^{9} -2.76340 q^{10} +2.13537 q^{11} -0.200920 q^{12} +1.06144 q^{13} +3.05466 q^{14} -1.86269 q^{15} -4.36147 q^{16} -4.40666 q^{17} -1.48355 q^{18} -3.83475 q^{19} +0.374251 q^{20} +2.05902 q^{21} -3.16793 q^{22} +1.77020 q^{23} -2.66903 q^{24} -1.53038 q^{25} -1.57469 q^{26} -1.00000 q^{27} -0.413698 q^{28} -6.47567 q^{29} +2.76340 q^{30} +3.49590 q^{31} +1.13241 q^{32} -2.13537 q^{33} +6.53750 q^{34} -3.83532 q^{35} +0.200920 q^{36} +7.18455 q^{37} +5.68904 q^{38} -1.06144 q^{39} +4.97157 q^{40} -5.10482 q^{41} -3.05466 q^{42} +10.8686 q^{43} +0.429038 q^{44} +1.86269 q^{45} -2.62617 q^{46} -12.8751 q^{47} +4.36147 q^{48} -2.76043 q^{49} +2.27039 q^{50} +4.40666 q^{51} +0.213263 q^{52} +10.4544 q^{53} +1.48355 q^{54} +3.97754 q^{55} -5.49558 q^{56} +3.83475 q^{57} +9.60698 q^{58} +3.15602 q^{59} -0.374251 q^{60} +4.38928 q^{61} -5.18634 q^{62} -2.05902 q^{63} +7.04296 q^{64} +1.97713 q^{65} +3.16793 q^{66} -10.7911 q^{67} -0.885384 q^{68} -1.77020 q^{69} +5.68989 q^{70} +4.46846 q^{71} +2.66903 q^{72} +0.465562 q^{73} -10.6586 q^{74} +1.53038 q^{75} -0.770477 q^{76} -4.39677 q^{77} +1.57469 q^{78} +6.81869 q^{79} -8.12408 q^{80} +1.00000 q^{81} +7.57325 q^{82} +1.87272 q^{83} +0.413698 q^{84} -8.20825 q^{85} -16.1241 q^{86} +6.47567 q^{87} +5.69936 q^{88} +11.0240 q^{89} -2.76340 q^{90} -2.18552 q^{91} +0.355667 q^{92} -3.49590 q^{93} +19.1008 q^{94} -7.14296 q^{95} -1.13241 q^{96} +11.1131 q^{97} +4.09524 q^{98} +2.13537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.48355	−1.04903	−0.524514	−	0.851402i	$-0.675753\pi$
$2$	−1.48355	−1.04903	−0.524514	+	0.851402i	$0.675753\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.200920	0.100460
$5$	1.86269	0.833021	0.416511	−	0.909131i	$-0.363253\pi$
$5$	1.86269	0.833021	0.416511	+	0.909131i	$0.363253\pi$
$6$	1.48355	0.605657
$7$	−2.05902	−0.778237	−0.389118	−	0.921188i	$-0.627220\pi$
$7$	−2.05902	−0.778237	−0.389118	+	0.921188i	$0.627220\pi$
$8$	2.66903	0.943643
$9$	1.00000	0.333333
$10$	−2.76340	−0.873862
$11$	2.13537	0.643838	0.321919	−	0.946767i	$-0.395672\pi$
$11$	2.13537	0.643838	0.321919	+	0.946767i	$0.395672\pi$
$12$	−0.200920	−0.0580005
$13$	1.06144	0.294390	0.147195	−	0.989108i	$-0.452976\pi$
$13$	1.06144	0.294390	0.147195	+	0.989108i	$0.452976\pi$
$14$	3.05466	0.816392
$15$	−1.86269	−0.480945
$16$	−4.36147	−1.09037
$17$	−4.40666	−1.06877	−0.534386	−	0.845241i	$-0.679457\pi$
$17$	−4.40666	−1.06877	−0.534386	+	0.845241i	$0.679457\pi$
$18$	−1.48355	−0.349676
$19$	−3.83475	−0.879752	−0.439876	−	0.898059i	$-0.644978\pi$
$19$	−3.83475	−0.879752	−0.439876	+	0.898059i	$0.644978\pi$
$20$	0.374251	0.0836851
$21$	2.05902	0.449315
$22$	−3.16793	−0.675404
$23$	1.77020	0.369111	0.184556	−	0.982822i	$-0.440915\pi$
$23$	1.77020	0.369111	0.184556	+	0.982822i	$0.440915\pi$
$24$	−2.66903	−0.544812
$25$	−1.53038	−0.306076
$26$	−1.57469	−0.308823
$27$	−1.00000	−0.192450
$28$	−0.413698	−0.0781815
$29$	−6.47567	−1.20250	−0.601251	−	0.799060i	$-0.705331\pi$
$29$	−6.47567	−1.20250	−0.601251	+	0.799060i	$0.705331\pi$
$30$	2.76340	0.504525
$31$	3.49590	0.627882	0.313941	−	0.949443i	$-0.398351\pi$
$31$	3.49590	0.627882	0.313941	+	0.949443i	$0.398351\pi$
$32$	1.13241	0.200183
$33$	−2.13537	−0.371720
$34$	6.53750	1.12117
$35$	−3.83532	−0.648288
$36$	0.200920	0.0334866
$37$	7.18455	1.18113	0.590566	−	0.806989i	$-0.298904\pi$
$37$	7.18455	1.18113	0.590566	+	0.806989i	$0.298904\pi$
$38$	5.68904	0.922885
$39$	−1.06144	−0.169966
$40$	4.97157	0.786074
$41$	−5.10482	−0.797239	−0.398619	−	0.917116i	$-0.630511\pi$
$41$	−5.10482	−0.797239	−0.398619	+	0.917116i	$0.630511\pi$
$42$	−3.05466	−0.471344
$43$	10.8686	1.65745	0.828723	−	0.559660i	$-0.189068\pi$
$43$	10.8686	1.65745	0.828723	+	0.559660i	$0.189068\pi$
$44$	0.429038	0.0646799
$45$	1.86269	0.277674
$46$	−2.62617	−0.387208
$47$	−12.8751	−1.87802	−0.939011	−	0.343887i	$-0.888256\pi$
$47$	−12.8751	−1.87802	−0.939011	+	0.343887i	$0.888256\pi$
$48$	4.36147	0.629524
$49$	−2.76043	−0.394347
$50$	2.27039	0.321082
$51$	4.40666	0.617056
$52$	0.213263	0.0295743
$53$	10.4544	1.43603	0.718014	−	0.696029i	$-0.245052\pi$
$53$	10.4544	1.43603	0.718014	+	0.696029i	$0.245052\pi$
$54$	1.48355	0.201886
$55$	3.97754	0.536331
$56$	−5.49558	−0.734378
$57$	3.83475	0.507925
$58$	9.60698	1.26146
$59$	3.15602	0.410879	0.205440	−	0.978670i	$-0.434138\pi$
$59$	3.15602	0.410879	0.205440	+	0.978670i	$0.434138\pi$
$60$	−0.374251	−0.0483156
$61$	4.38928	0.561989	0.280995	−	0.959709i	$-0.409336\pi$
$61$	4.38928	0.561989	0.280995	+	0.959709i	$0.409336\pi$
$62$	−5.18634	−0.658665
$63$	−2.05902	−0.259412
$64$	7.04296	0.880370
$65$	1.97713	0.245233
$66$	3.16793	0.389945
$67$	−10.7911	−1.31834	−0.659170	−	0.751994i	$-0.729092\pi$
$67$	−10.7911	−1.31834	−0.659170	+	0.751994i	$0.729092\pi$
$68$	−0.885384	−0.107369
$69$	−1.77020	−0.213107
$70$	5.68989	0.680072
$71$	4.46846	0.530309	0.265154	−	0.964206i	$-0.414577\pi$
$71$	4.46846	0.530309	0.265154	+	0.964206i	$0.414577\pi$
$72$	2.66903	0.314548
$73$	0.465562	0.0544899	0.0272450	−	0.999629i	$-0.491327\pi$
$73$	0.465562	0.0544899	0.0272450	+	0.999629i	$0.491327\pi$
$74$	−10.6586	−1.23904
$75$	1.53038	0.176713
$76$	−0.770477	−0.0883797
$77$	−4.39677	−0.501059
$78$	1.57469	0.178299
$79$	6.81869	0.767163	0.383581	−	0.923507i	$-0.374691\pi$
$79$	6.81869	0.767163	0.383581	+	0.923507i	$0.374691\pi$
$80$	−8.12408	−0.908299
$81$	1.00000	0.111111
$82$	7.57325	0.836326
$83$	1.87272	0.205558	0.102779	−	0.994704i	$-0.467227\pi$
$83$	1.87272	0.205558	0.102779	+	0.994704i	$0.467227\pi$
$84$	0.413698	0.0451381
$85$	−8.20825	−0.890310
$86$	−16.1241	−1.73871
$87$	6.47567	0.694264
$88$	5.69936	0.607553
$89$	11.0240	1.16854	0.584269	−	0.811560i	$-0.301381\pi$
$89$	11.0240	1.16854	0.584269	+	0.811560i	$0.301381\pi$
$90$	−2.76340	−0.291287
$91$	−2.18552	−0.229105
$92$	0.355667	0.0370809
$93$	−3.49590	−0.362508
$94$	19.1008	1.97010
$95$	−7.14296	−0.732852
$96$	−1.13241	−0.115576
$97$	11.1131	1.12837	0.564183	−	0.825649i	$-0.309191\pi$
$97$	11.1131	1.12837	0.564183	+	0.825649i	$0.309191\pi$
$98$	4.09524	0.413681
$99$	2.13537	0.214613
$100$	−0.307483	−0.0307483
$101$	15.1199	1.50448	0.752242	−	0.658886i	$-0.228972\pi$
$101$	15.1199	1.50448	0.752242	+	0.658886i	$0.228972\pi$
$102$	−6.53750	−0.647309
$103$	−0.577178	−0.0568711	−0.0284355	−	0.999596i	$-0.509053\pi$
$103$	−0.577178	−0.0568711	−0.0284355	+	0.999596i	$0.509053\pi$
$104$	2.83300	0.277799
$105$	3.83532	0.374289
$106$	−15.5097	−1.50643
$107$	−3.24580	−0.313783	−0.156892	−	0.987616i	$-0.550147\pi$
$107$	−3.24580	−0.313783	−0.156892	+	0.987616i	$0.550147\pi$
$108$	−0.200920	−0.0193335
$109$	−19.6937	−1.88631	−0.943156	−	0.332350i	$-0.892159\pi$
$109$	−19.6937	−1.88631	−0.943156	+	0.332350i	$0.892159\pi$
$110$	−5.90087	−0.562626
$111$	−7.18455	−0.681927
$112$	8.98036	0.848564
$113$	−4.35181	−0.409384	−0.204692	−	0.978826i	$-0.565619\pi$
$113$	−4.35181	−0.409384	−0.204692	+	0.978826i	$0.565619\pi$
$114$	−5.68904	−0.532828
$115$	3.29733	0.307478
$116$	−1.30109	−0.120803
$117$	1.06144	0.0981299
$118$	−4.68212	−0.431024
$119$	9.07341	0.831758
$120$	−4.97157	−0.453840
$121$	−6.44020	−0.585472
$122$	−6.51171	−0.589542
$123$	5.10482	0.460286
$124$	0.702394	0.0630769
$125$	−12.1641	−1.08799
$126$	3.05466	0.272131
$127$	1.32941	0.117966	0.0589832	−	0.998259i	$-0.481214\pi$
$127$	1.32941	0.117966	0.0589832	+	0.998259i	$0.481214\pi$
$128$	−12.7134	−1.12372
$129$	−10.8686	−0.956926
$130$	−2.93317	−0.257256
$131$	0.286316	0.0250155	0.0125078	−	0.999922i	$-0.496019\pi$
$131$	0.286316	0.0250155	0.0125078	+	0.999922i	$0.496019\pi$
$132$	−0.429038	−0.0373429
$133$	7.89583	0.684656
$134$	16.0091	1.38297
$135$	−1.86269	−0.160315
$136$	−11.7615	−1.00854
$137$	−22.0466	−1.88357	−0.941786	−	0.336213i	$-0.890854\pi$
$137$	−22.0466	−1.88357	−0.941786	+	0.336213i	$0.890854\pi$
$138$	2.62617	0.223555
$139$	21.9017	1.85768	0.928838	−	0.370486i	$-0.120809\pi$
$139$	21.9017	1.85768	0.928838	+	0.370486i	$0.120809\pi$
$140$	−0.770592	−0.0651269
$141$	12.8751	1.08428
$142$	−6.62919	−0.556309
$143$	2.26656	0.189539
$144$	−4.36147	−0.363456
$145$	−12.0622	−1.00171
$146$	−0.690684	−0.0571615
$147$	2.76043	0.227676
$148$	1.44352	0.118656
$149$	−4.01438	−0.328871	−0.164435	−	0.986388i	$-0.552580\pi$
$149$	−4.01438	−0.328871	−0.164435	+	0.986388i	$0.552580\pi$
$150$	−2.27039	−0.185377
$151$	−5.20629	−0.423681	−0.211841	−	0.977304i	$-0.567946\pi$
$151$	−5.20629	−0.423681	−0.211841	+	0.977304i	$0.567946\pi$
$152$	−10.2350	−0.830172
$153$	−4.40666	−0.356257
$154$	6.52283	0.525625
$155$	6.51178	0.523039
$156$	−0.213263	−0.0170747
$157$	−20.3881	−1.62715	−0.813573	−	0.581463i	$-0.802480\pi$
$157$	−20.3881	−1.62715	−0.813573	+	0.581463i	$0.802480\pi$
$158$	−10.1159	−0.804775
$159$	−10.4544	−0.829091
$160$	2.10933	0.166757
$161$	−3.64487	−0.287256
$162$	−1.48355	−0.116559
$163$	−1.66745	−0.130605	−0.0653025	−	0.997866i	$-0.520801\pi$
$163$	−1.66745	−0.130605	−0.0653025	+	0.997866i	$0.520801\pi$
$164$	−1.02566	−0.0800905
$165$	−3.97754	−0.309651
$166$	−2.77828	−0.215636
$167$	11.5585	0.894427	0.447213	−	0.894427i	$-0.352417\pi$
$167$	11.5585	0.894427	0.447213	+	0.894427i	$0.352417\pi$
$168$	5.49558	0.423993
$169$	−11.8734	−0.913335
$170$	12.1773	0.933960
$171$	−3.83475	−0.293251
$172$	2.18371	0.166507
$173$	21.0987	1.60411	0.802054	−	0.597252i	$-0.203741\pi$
$173$	21.0987	1.60411	0.802054	+	0.597252i	$0.203741\pi$
$174$	−9.60698	−0.728303
$175$	3.15108	0.238200
$176$	−9.31335	−0.702020
$177$	−3.15602	−0.237221
$178$	−16.3546	−1.22583
$179$	20.5822	1.53839	0.769194	−	0.639016i	$-0.220658\pi$
$179$	20.5822	1.53839	0.769194	+	0.639016i	$0.220658\pi$
$180$	0.374251	0.0278950
$181$	22.5924	1.67928	0.839641	−	0.543142i	$-0.182766\pi$
$181$	22.5924	1.67928	0.839641	+	0.543142i	$0.182766\pi$
$182$	3.24233	0.240337
$183$	−4.38928	−0.324465
$184$	4.72470	0.348309
$185$	13.3826	0.983908
$186$	5.18634	0.380281
$187$	−9.40985	−0.688116
$188$	−2.58685	−0.188666
$189$	2.05902	0.149772
$190$	10.5969	0.768782
$191$	6.56369	0.474932	0.237466	−	0.971396i	$-0.423683\pi$
$191$	6.56369	0.474932	0.237466	+	0.971396i	$0.423683\pi$
$192$	−7.04296	−0.508282
$193$	−5.48314	−0.394685	−0.197343	−	0.980335i	$-0.563231\pi$
$193$	−5.48314	−0.394685	−0.197343	+	0.980335i	$0.563231\pi$
$194$	−16.4869	−1.18369
$195$	−1.97713	−0.141585
$196$	−0.554625	−0.0396160
$197$	−19.0427	−1.35674	−0.678368	−	0.734722i	$-0.737313\pi$
$197$	−19.0427	−1.35674	−0.678368	+	0.734722i	$0.737313\pi$
$198$	−3.16793	−0.225135
$199$	1.61712	0.114635	0.0573173	−	0.998356i	$-0.481745\pi$
$199$	1.61712	0.114635	0.0573173	+	0.998356i	$0.481745\pi$
$200$	−4.08462	−0.288826
$201$	10.7911	0.761143
$202$	−22.4311	−1.57825
$203$	13.3335	0.935831
$204$	0.885384	0.0619893
$205$	−9.50871	−0.664117
$206$	0.856273	0.0596593
$207$	1.77020	0.123037
$208$	−4.62943	−0.320993
$209$	−8.18861	−0.566418
$210$	−5.68989	−0.392640
$211$	5.17007	0.355922	0.177961	−	0.984038i	$-0.443050\pi$
$211$	5.17007	0.355922	0.177961	+	0.984038i	$0.443050\pi$
$212$	2.10050	0.144263
$213$	−4.46846	−0.306174
$214$	4.81530	0.329167
$215$	20.2448	1.38069
$216$	−2.66903	−0.181604
$217$	−7.19813	−0.488641
$218$	29.2166	1.97879
$219$	−0.465562	−0.0314598
$220$	0.799165	0.0538797
$221$	−4.67739	−0.314635
$222$	10.6586	0.715361
$223$	−4.57579	−0.306417	−0.153209	−	0.988194i	$-0.548961\pi$
$223$	−4.57579	−0.306417	−0.153209	+	0.988194i	$0.548961\pi$
$224$	−2.33165	−0.155790
$225$	−1.53038	−0.102025
$226$	6.45612	0.429455
$227$	21.7544	1.44389	0.721945	−	0.691951i	$-0.243249\pi$
$227$	21.7544	1.44389	0.721945	+	0.691951i	$0.243249\pi$
$228$	0.770477	0.0510261
$229$	0.531819	0.0351436	0.0175718	−	0.999846i	$-0.494406\pi$
$229$	0.531819	0.0351436	0.0175718	+	0.999846i	$0.494406\pi$
$230$	−4.89175	−0.322553
$231$	4.39677	0.289286
$232$	−17.2837	−1.13473
$233$	15.6231	1.02350	0.511752	−	0.859133i	$-0.328997\pi$
$233$	15.6231	1.02350	0.511752	+	0.859133i	$0.328997\pi$
$234$	−1.57469	−0.102941
$235$	−23.9823	−1.56443
$236$	0.634107	0.0412769
$237$	−6.81869	−0.442922
$238$	−13.4609	−0.872537
$239$	−16.6422	−1.07650	−0.538248	−	0.842787i	$-0.680914\pi$
$239$	−16.6422	−1.07650	−0.538248	+	0.842787i	$0.680914\pi$
$240$	8.12408	0.524407
$241$	−0.938245	−0.0604376	−0.0302188	−	0.999543i	$-0.509620\pi$
$241$	−0.938245	−0.0604376	−0.0302188	+	0.999543i	$0.509620\pi$
$242$	9.55435	0.614177
$243$	−1.00000	−0.0641500
$244$	0.881892	0.0564573
$245$	−5.14183	−0.328500
$246$	−7.57325	−0.482853
$247$	−4.07034	−0.258990
$248$	9.33063	0.592496
$249$	−1.87272	−0.118679
$250$	18.0460	1.14133
$251$	1.15201	0.0727140	0.0363570	−	0.999339i	$-0.488425\pi$
$251$	1.15201	0.0727140	0.0363570	+	0.999339i	$0.488425\pi$
$252$	−0.413698	−0.0260605
$253$	3.78002	0.237648
$254$	−1.97225	−0.123750
$255$	8.20825	0.514020
$256$	4.77504	0.298440
$257$	1.71866	0.107207	0.0536036	−	0.998562i	$-0.482929\pi$
$257$	1.71866	0.107207	0.0536036	+	0.998562i	$0.482929\pi$
$258$	16.1241	1.00384
$259$	−14.7931	−0.919201
$260$	0.397244	0.0246360
$261$	−6.47567	−0.400834
$262$	−0.424764	−0.0262420
$263$	19.9280	1.22881	0.614406	−	0.788990i	$-0.289396\pi$
$263$	19.9280	1.22881	0.614406	+	0.788990i	$0.289396\pi$
$264$	−5.69936	−0.350771
$265$	19.4734	1.19624
$266$	−11.7139	−0.718223
$267$	−11.0240	−0.674656
$268$	−2.16814	−0.132440
$269$	12.4263	0.757645	0.378822	−	0.925469i	$-0.376329\pi$
$269$	12.4263	0.757645	0.378822	+	0.925469i	$0.376329\pi$
$270$	2.76340	0.168175
$271$	−28.1905	−1.71245	−0.856226	−	0.516602i	$-0.827197\pi$
$271$	−28.1905	−1.71245	−0.856226	+	0.516602i	$0.827197\pi$
$272$	19.2195	1.16535
$273$	2.18552	0.132274
$274$	32.7073	1.97592
$275$	−3.26793	−0.197063
$276$	−0.355667	−0.0214086
$277$	20.6159	1.23869	0.619345	−	0.785119i	$-0.287398\pi$
$277$	20.6159	1.23869	0.619345	+	0.785119i	$0.287398\pi$
$278$	−32.4922	−1.94875
$279$	3.49590	0.209294
$280$	−10.2366	−0.611752
$281$	19.8514	1.18424	0.592118	−	0.805851i	$-0.298292\pi$
$281$	19.8514	1.18424	0.592118	+	0.805851i	$0.298292\pi$
$282$	−19.1008	−1.13744
$283$	10.9818	0.652799	0.326400	−	0.945232i	$-0.394164\pi$
$283$	10.9818	0.652799	0.326400	+	0.945232i	$0.394164\pi$
$284$	0.897802	0.0532747
$285$	7.14296	0.423112
$286$	−3.36255	−0.198832
$287$	10.5109	0.620441
$288$	1.13241	0.0667278
$289$	2.41865	0.142274
$290$	17.8948	1.05082
$291$	−11.1131	−0.651463
$292$	0.0935406	0.00547405
$293$	−3.47326	−0.202910	−0.101455	−	0.994840i	$-0.532350\pi$
$293$	−3.47326	−0.202910	−0.101455	+	0.994840i	$0.532350\pi$
$294$	−4.09524	−0.238839
$295$	5.87870	0.342271
$296$	19.1757	1.11457
$297$	−2.13537	−0.123907
$298$	5.95553	0.344995
$299$	1.87895	0.108663
$300$	0.307483	0.0177526
$301$	−22.3787	−1.28989
$302$	7.72378	0.444454
$303$	−15.1199	−0.868615
$304$	16.7252	0.959253
$305$	8.17587	0.468149
$306$	6.53750	0.373724
$307$	−18.6697	−1.06554	−0.532769	−	0.846261i	$-0.678849\pi$
$307$	−18.6697	−1.06554	−0.532769	+	0.846261i	$0.678849\pi$
$308$	−0.883398	−0.0503363
$309$	0.577178	0.0328345
$310$	−9.66054	−0.548682
$311$	−26.8813	−1.52430	−0.762151	−	0.647400i	$-0.775856\pi$
$311$	−26.8813	−1.52430	−0.762151	+	0.647400i	$0.775856\pi$
$312$	−2.83300	−0.160387
$313$	4.27659	0.241727	0.120864	−	0.992669i	$-0.461434\pi$
$313$	4.27659	0.241727	0.120864	+	0.992669i	$0.461434\pi$
$314$	30.2467	1.70692
$315$	−3.83532	−0.216096
$316$	1.37001	0.0770690
$317$	29.8137	1.67450	0.837252	−	0.546817i	$-0.184160\pi$
$317$	29.8137	1.67450	0.837252	+	0.546817i	$0.184160\pi$
$318$	15.5097	0.869739
$319$	−13.8279	−0.774216
$320$	13.1189	0.733366
$321$	3.24580	0.181163
$322$	5.40735	0.301340
$323$	16.8984	0.940254
$324$	0.200920	0.0111622
$325$	−1.62440	−0.0901056
$326$	2.47375	0.137008
$327$	19.6937	1.08906
$328$	−13.6249	−0.752309
$329$	26.5100	1.46155
$330$	5.90087	0.324832
$331$	7.18879	0.395132	0.197566	−	0.980290i	$-0.436696\pi$
$331$	7.18879	0.395132	0.197566	+	0.980290i	$0.436696\pi$
$332$	0.376267	0.0206503
$333$	7.18455	0.393711
$334$	−17.1477	−0.938278
$335$	−20.1004	−1.09820
$336$	−8.98036	−0.489919
$337$	4.33525	0.236156	0.118078	−	0.993004i	$-0.462327\pi$
$337$	4.33525	0.236156	0.118078	+	0.993004i	$0.462327\pi$
$338$	17.6147	0.958114
$339$	4.35181	0.236358
$340$	−1.64920	−0.0894403
$341$	7.46503	0.404254
$342$	5.68904	0.307628
$343$	20.0969	1.08513
$344$	29.0086	1.56404
$345$	−3.29733	−0.177522
$346$	−31.3010	−1.68275
$347$	35.0725	1.88279	0.941396	−	0.337302i	$-0.109514\pi$
$347$	35.0725	1.88279	0.941396	+	0.337302i	$0.109514\pi$
$348$	1.30109	0.0697457
$349$	22.5249	1.20573	0.602864	−	0.797844i	$-0.294026\pi$
$349$	22.5249	1.20573	0.602864	+	0.797844i	$0.294026\pi$
$350$	−4.67479	−0.249878
$351$	−1.06144	−0.0566553
$352$	2.41811	0.128886
$353$	7.97887	0.424672	0.212336	−	0.977197i	$-0.431893\pi$
$353$	7.97887	0.424672	0.212336	+	0.977197i	$0.431893\pi$
$354$	4.68212	0.248852
$355$	8.32337	0.441759
$356$	2.21493	0.117391
$357$	−9.07341	−0.480216
$358$	−30.5347	−1.61381
$359$	−25.6715	−1.35489	−0.677444	−	0.735575i	$-0.736912\pi$
$359$	−25.6715	−1.35489	−0.677444	+	0.735575i	$0.736912\pi$
$360$	4.97157	0.262025
$361$	−4.29469	−0.226036
$362$	−33.5170	−1.76161
$363$	6.44020	0.338023
$364$	−0.439114	−0.0230158
$365$	0.867199	0.0453913
$366$	6.51171	0.340372
$367$	6.58602	0.343787	0.171894	−	0.985116i	$-0.445011\pi$
$367$	6.58602	0.343787	0.171894	+	0.985116i	$0.445011\pi$
$368$	−7.72066	−0.402467
$369$	−5.10482	−0.265746
$370$	−19.8538	−1.03215
$371$	−21.5259	−1.11757
$372$	−0.702394	−0.0364174
$373$	−35.3275	−1.82919	−0.914593	−	0.404375i	$-0.867489\pi$
$373$	−35.3275	−1.82919	−0.914593	+	0.404375i	$0.867489\pi$
$374$	13.9600	0.721853
$375$	12.1641	0.628151
$376$	−34.3639	−1.77218
$377$	−6.87351	−0.354004
$378$	−3.05466	−0.157115
$379$	24.4058	1.25364	0.626822	−	0.779163i	$-0.284355\pi$
$379$	24.4058	1.25364	0.626822	+	0.779163i	$0.284355\pi$
$380$	−1.43516	−0.0736222
$381$	−1.32941	−0.0681080
$382$	−9.73757	−0.498217
$383$	−6.92034	−0.353613	−0.176806	−	0.984246i	$-0.556577\pi$
$383$	−6.92034	−0.353613	−0.176806	+	0.984246i	$0.556577\pi$
$384$	12.7134	0.648778
$385$	−8.18983	−0.417392
$386$	8.13451	0.414036
$387$	10.8686	0.552482
$388$	2.23285	0.113356
$389$	−1.95811	−0.0992800	−0.0496400	−	0.998767i	$-0.515807\pi$
$389$	−1.95811	−0.0992800	−0.0496400	+	0.998767i	$0.515807\pi$
$390$	2.93317	0.148527
$391$	−7.80065	−0.394496
$392$	−7.36766	−0.372123
$393$	−0.286316	−0.0144427
$394$	28.2508	1.42326
$395$	12.7011	0.639063
$396$	0.429038	0.0215600
$397$	24.4326	1.22624	0.613119	−	0.789991i	$-0.289915\pi$
$397$	24.4326	1.22624	0.613119	+	0.789991i	$0.289915\pi$
$398$	−2.39908	−0.120255
$399$	−7.89583	−0.395286
$400$	6.67471	0.333735
$401$	2.43140	0.121418	0.0607091	−	0.998156i	$-0.480664\pi$
$401$	2.43140	0.121418	0.0607091	+	0.998156i	$0.480664\pi$
$402$	−16.0091	−0.798461
$403$	3.71067	0.184842
$404$	3.03788	0.151140
$405$	1.86269	0.0925579
$406$	−19.7810	−0.981713
$407$	15.3417	0.760458
$408$	11.7615	0.582280
$409$	−25.1189	−1.24205	−0.621025	−	0.783791i	$-0.713284\pi$
$409$	−25.1189	−1.24205	−0.621025	+	0.783791i	$0.713284\pi$
$410$	14.1066	0.696677
$411$	22.0466	1.08748
$412$	−0.115966	−0.00571326
$413$	−6.49832	−0.319762
$414$	−2.62617	−0.129069
$415$	3.48831	0.171234
$416$	1.20198	0.0589319
$417$	−21.9017	−1.07253
$418$	12.1482	0.594188
$419$	−25.0871	−1.22559	−0.612793	−	0.790243i	$-0.709954\pi$
$419$	−25.0871	−1.22559	−0.612793	+	0.790243i	$0.709954\pi$
$420$	0.770592	0.0376010
$421$	−13.6622	−0.665854	−0.332927	−	0.942953i	$-0.608036\pi$
$421$	−13.6622	−0.665854	−0.332927	+	0.942953i	$0.608036\pi$
$422$	−7.67005	−0.373372
$423$	−12.8751	−0.626007
$424$	27.9032	1.35510
$425$	6.74386	0.327125
$426$	6.62919	0.321185
$427$	−9.03761	−0.437361
$428$	−0.652144	−0.0315226
$429$	−2.26656	−0.109431
$430$	−30.0342	−1.44838
$431$	−17.4778	−0.841878	−0.420939	−	0.907089i	$-0.638299\pi$
$431$	−17.4778	−0.841878	−0.420939	+	0.907089i	$0.638299\pi$
$432$	4.36147	0.209841
$433$	11.3562	0.545742	0.272871	−	0.962051i	$-0.412027\pi$
$433$	11.3562	0.545742	0.272871	+	0.962051i	$0.412027\pi$
$434$	10.6788	0.512598
$435$	12.0622	0.578337
$436$	−3.95685	−0.189499
$437$	−6.78826	−0.324726
$438$	0.690684	0.0330022
$439$	21.1770	1.01072	0.505362	−	0.862908i	$-0.331359\pi$
$439$	21.1770	1.01072	0.505362	+	0.862908i	$0.331359\pi$
$440$	10.6161	0.506105
$441$	−2.76043	−0.131449
$442$	6.93914	0.330061
$443$	16.1045	0.765147	0.382573	−	0.923925i	$-0.375038\pi$
$443$	16.1045	0.765147	0.382573	+	0.923925i	$0.375038\pi$
$444$	−1.44352	−0.0685063
$445$	20.5343	0.973417
$446$	6.78840	0.321440
$447$	4.01438	0.189874
$448$	−14.5016	−0.685136
$449$	−24.5117	−1.15678	−0.578389	−	0.815761i	$-0.696318\pi$
$449$	−24.5117	−1.15678	−0.578389	+	0.815761i	$0.696318\pi$
$450$	2.27039	0.107027
$451$	−10.9007	−0.513293
$452$	−0.874364	−0.0411266
$453$	5.20629	0.244613
$454$	−32.2737	−1.51468
$455$	−4.07095	−0.190849
$456$	10.2350	0.479300
$457$	0.257793	0.0120591	0.00602953	−	0.999982i	$-0.498081\pi$
$457$	0.257793	0.0120591	0.00602953	+	0.999982i	$0.498081\pi$
$458$	−0.788980	−0.0368666
$459$	4.40666	0.205685
$460$	0.662498	0.0308891
$461$	−5.52301	−0.257232	−0.128616	−	0.991694i	$-0.541054\pi$
$461$	−5.52301	−0.257232	−0.128616	+	0.991694i	$0.541054\pi$
$462$	−6.52283	−0.303470
$463$	2.83650	0.131823	0.0659117	−	0.997825i	$-0.479004\pi$
$463$	2.83650	0.131823	0.0659117	+	0.997825i	$0.479004\pi$
$464$	28.2434	1.31117
$465$	−6.51178	−0.301976
$466$	−23.1777	−1.07369
$467$	3.11599	0.144191	0.0720953	−	0.997398i	$-0.477031\pi$
$467$	3.11599	0.144191	0.0720953	+	0.997398i	$0.477031\pi$
$468$	0.213263	0.00985811
$469$	22.2190	1.02598
$470$	35.5789	1.64113
$471$	20.3881	0.939433
$472$	8.42351	0.387723
$473$	23.2085	1.06713
$474$	10.1159	0.464637
$475$	5.86862	0.269271
$476$	1.82303	0.0835582
$477$	10.4544	0.478676
$478$	24.6896	1.12927
$479$	10.5947	0.484083	0.242042	−	0.970266i	$-0.422183\pi$
$479$	10.5947	0.484083	0.242042	+	0.970266i	$0.422183\pi$
$480$	−2.10933	−0.0962772
$481$	7.62594	0.347713
$482$	1.39193	0.0634008
$483$	3.64487	0.165847
$484$	−1.29396	−0.0588165
$485$	20.7003	0.939953
$486$	1.48355	0.0672952
$487$	34.8340	1.57848	0.789239	−	0.614086i	$-0.210475\pi$
$487$	34.8340	1.57848	0.789239	+	0.614086i	$0.210475\pi$
$488$	11.7151	0.530317
$489$	1.66745	0.0754048
$490$	7.62816	0.344605
$491$	7.35619	0.331980	0.165990	−	0.986127i	$-0.446918\pi$
$491$	7.35619	0.331980	0.165990	+	0.986127i	$0.446918\pi$
$492$	1.02566	0.0462403
$493$	28.5361	1.28520
$494$	6.03856	0.271688
$495$	3.97754	0.178777
$496$	−15.2472	−0.684622
$497$	−9.20066	−0.412706
$498$	2.77828	0.124498
$499$	8.60829	0.385360	0.192680	−	0.981262i	$-0.438282\pi$
$499$	8.60829	0.385360	0.192680	+	0.981262i	$0.438282\pi$
$500$	−2.44400	−0.109299
$501$	−11.5585	−0.516397
$502$	−1.70906	−0.0762791
$503$	42.1173	1.87792	0.938959	−	0.344030i	$-0.111792\pi$
$503$	42.1173	1.87792	0.938959	+	0.344030i	$0.111792\pi$
$504$	−5.49558	−0.244793
$505$	28.1637	1.25327
$506$	−5.60785	−0.249299
$507$	11.8734	0.527314
$508$	0.267105	0.0118509
$509$	−30.0112	−1.33022	−0.665112	−	0.746743i	$-0.731616\pi$
$509$	−30.0112	−1.33022	−0.665112	+	0.746743i	$0.731616\pi$
$510$	−12.1773	−0.539222
$511$	−0.958602	−0.0424061
$512$	18.3428	0.810644
$513$	3.83475	0.169308
$514$	−2.54972	−0.112463
$515$	−1.07511	−0.0473748
$516$	−2.18371	−0.0961327
$517$	−27.4930	−1.20914
$518$	21.9464	0.964268
$519$	−21.0987	−0.926132
$520$	5.27701	0.231412
$521$	−22.9318	−1.00466	−0.502330	−	0.864676i	$-0.667524\pi$
$521$	−22.9318	−1.00466	−0.502330	+	0.864676i	$0.667524\pi$
$522$	9.60698	0.420486
$523$	12.6370	0.552579	0.276290	−	0.961074i	$-0.410895\pi$
$523$	12.6370	0.552579	0.276290	+	0.961074i	$0.410895\pi$
$524$	0.0575265	0.00251305
$525$	−3.15108	−0.137525
$526$	−29.5641	−1.28906
$527$	−15.4052	−0.671062
$528$	9.31335	0.405312
$529$	−19.8664	−0.863757
$530$	−28.8897	−1.25489
$531$	3.15602	0.136960
$532$	1.58643	0.0687804
$533$	−5.41844	−0.234699
$534$	16.3546	0.707733
$535$	−6.04592	−0.261388
$536$	−28.8016	−1.24404
$537$	−20.5822	−0.888188
$538$	−18.4350	−0.794791
$539$	−5.89454	−0.253896
$540$	−0.374251	−0.0161052
$541$	4.62573	0.198876	0.0994378	−	0.995044i	$-0.468296\pi$
$541$	4.62573	0.198876	0.0994378	+	0.995044i	$0.468296\pi$
$542$	41.8220	1.79641
$543$	−22.5924	−0.969534
$544$	−4.99014	−0.213950
$545$	−36.6833	−1.57134
$546$	−3.24233	−0.138759
$547$	39.5766	1.69217	0.846086	−	0.533046i	$-0.178953\pi$
$547$	39.5766	1.69217	0.846086	+	0.533046i	$0.178953\pi$
$548$	−4.42960	−0.189223
$549$	4.38928	0.187330
$550$	4.84813	0.206725
$551$	24.8326	1.05790
$552$	−4.72470	−0.201096
$553$	−14.0398	−0.597035
$554$	−30.5847	−1.29942
$555$	−13.3826	−0.568060
$556$	4.40048	0.186622
$557$	42.8240	1.81451	0.907255	−	0.420582i	$-0.138174\pi$
$557$	42.8240	1.81451	0.907255	+	0.420582i	$0.138174\pi$
$558$	−5.18634	−0.219555
$559$	11.5363	0.487935
$560$	16.7276	0.706872
$561$	9.40985	0.397284
$562$	−29.4505	−1.24230
$563$	37.7848	1.59244	0.796221	−	0.605006i	$-0.206829\pi$
$563$	37.7848	1.59244	0.796221	+	0.605006i	$0.206829\pi$
$564$	2.58685	0.108926
$565$	−8.10608	−0.341025
$566$	−16.2920	−0.684805
$567$	−2.05902	−0.0864708
$568$	11.9264	0.500422
$569$	−7.58563	−0.318006	−0.159003	−	0.987278i	$-0.550828\pi$
$569$	−7.58563	−0.318006	−0.159003	+	0.987278i	$0.550828\pi$
$570$	−10.5969	−0.443857
$571$	36.9148	1.54484	0.772419	−	0.635113i	$-0.219047\pi$
$571$	36.9148	1.54484	0.772419	+	0.635113i	$0.219047\pi$
$572$	0.455396	0.0190411
$573$	−6.56369	−0.274202
$574$	−15.5935	−0.650860
$575$	−2.70907	−0.112976
$576$	7.04296	0.293457
$577$	−41.9709	−1.74727	−0.873636	−	0.486580i	$-0.838244\pi$
$577$	−41.9709	−1.74727	−0.873636	+	0.486580i	$0.838244\pi$
$578$	−3.58819	−0.149249
$579$	5.48314	0.227872
$580$	−2.42353	−0.100632
$581$	−3.85598	−0.159973
$582$	16.4869	0.683403
$583$	22.3241	0.924569
$584$	1.24260	0.0514190
$585$	1.97713	0.0817442
$586$	5.15275	0.212858
$587$	−2.42098	−0.0999246	−0.0499623	−	0.998751i	$-0.515910\pi$
$587$	−2.42098	−0.0999246	−0.0499623	+	0.998751i	$0.515910\pi$
$588$	0.554625	0.0228723
$589$	−13.4059	−0.552380
$590$	−8.72134	−0.359052
$591$	19.0427	0.783312
$592$	−31.3352	−1.28787
$593$	24.5645	1.00874	0.504372	−	0.863486i	$-0.331724\pi$
$593$	24.5645	1.00874	0.504372	+	0.863486i	$0.331724\pi$
$594$	3.16793	0.129982
$595$	16.9010	0.692872
$596$	−0.806568	−0.0330383
$597$	−1.61712	−0.0661844
$598$	−2.78752	−0.113990
$599$	−0.355559	−0.0145278	−0.00726388	−	0.999974i	$-0.502312\pi$
$599$	−0.355559	−0.0145278	−0.00726388	+	0.999974i	$0.502312\pi$
$600$	4.08462	0.166754
$601$	48.3796	1.97344	0.986722	−	0.162418i	$-0.0519292\pi$
$601$	48.3796	1.97344	0.986722	+	0.162418i	$0.0519292\pi$
$602$	33.1999	1.35313
$603$	−10.7911	−0.439446
$604$	−1.04604	−0.0425630
$605$	−11.9961	−0.487711
$606$	22.4311	0.911201
$607$	36.5629	1.48404	0.742021	−	0.670376i	$-0.233867\pi$
$607$	36.5629	1.48404	0.742021	+	0.670376i	$0.233867\pi$
$608$	−4.34250	−0.176112
$609$	−13.3335	−0.540302
$610$	−12.1293	−0.491101
$611$	−13.6661	−0.552870
$612$	−0.885384	−0.0357895
$613$	5.98468	0.241719	0.120859	−	0.992670i	$-0.461435\pi$
$613$	5.98468	0.241719	0.120859	+	0.992670i	$0.461435\pi$
$614$	27.6975	1.11778
$615$	9.50871	0.383428
$616$	−11.7351	−0.472820
$617$	37.9562	1.52806	0.764029	−	0.645182i	$-0.223219\pi$
$617$	37.9562	1.52806	0.764029	+	0.645182i	$0.223219\pi$
$618$	−0.856273	−0.0344443
$619$	−28.4062	−1.14174	−0.570871	−	0.821039i	$-0.693395\pi$
$619$	−28.4062	−1.14174	−0.570871	+	0.821039i	$0.693395\pi$
$620$	1.30834	0.0525444
$621$	−1.77020	−0.0710355
$622$	39.8798	1.59903
$623$	−22.6986	−0.909400
$624$	4.62943	0.185325
$625$	−15.0060	−0.600242
$626$	−6.34453	−0.253579
$627$	8.18861	0.327022
$628$	−4.09636	−0.163463
$629$	−31.6599	−1.26236
$630$	5.68989	0.226691
$631$	−14.0815	−0.560577	−0.280288	−	0.959916i	$-0.590430\pi$
$631$	−14.0815	−0.560577	−0.280288	+	0.959916i	$0.590430\pi$
$632$	18.1993	0.723928
$633$	−5.17007	−0.205492
$634$	−44.2301	−1.75660
$635$	2.47629	0.0982685
$636$	−2.10050	−0.0832903
$637$	−2.93002	−0.116092
$638$	20.5144	0.812175
$639$	4.46846	0.176770
$640$	−23.6811	−0.936079
$641$	43.1861	1.70575	0.852874	−	0.522116i	$-0.174857\pi$
$641$	43.1861	1.70575	0.852874	+	0.522116i	$0.174857\pi$
$642$	−4.81530	−0.190045
$643$	20.7808	0.819513	0.409757	−	0.912195i	$-0.365614\pi$
$643$	20.7808	0.819513	0.409757	+	0.912195i	$0.365614\pi$
$644$	−0.732326	−0.0288577
$645$	−20.2448	−0.797140
$646$	−25.0697	−0.986353
$647$	−26.8739	−1.05652	−0.528260	−	0.849082i	$-0.677156\pi$
$647$	−26.8739	−1.05652	−0.528260	+	0.849082i	$0.677156\pi$
$648$	2.66903	0.104849
$649$	6.73928	0.264540
$650$	2.40988	0.0945233
$651$	7.19813	0.282117
$652$	−0.335024	−0.0131206
$653$	42.5181	1.66386	0.831931	−	0.554880i	$-0.187236\pi$
$653$	42.5181	1.66386	0.831931	+	0.554880i	$0.187236\pi$
$654$	−29.2166	−1.14246
$655$	0.533318	0.0208385
$656$	22.2645	0.869284
$657$	0.465562	0.0181633
$658$	−39.3290	−1.53320
$659$	48.7308	1.89828	0.949141	−	0.314852i	$-0.101955\pi$
$659$	48.7308	1.89828	0.949141	+	0.314852i	$0.101955\pi$
$660$	−0.799165	−0.0311075
$661$	−12.9907	−0.505280	−0.252640	−	0.967560i	$-0.581299\pi$
$661$	−12.9907	−0.505280	−0.252640	+	0.967560i	$0.581299\pi$
$662$	−10.6649	−0.414504
$663$	4.67739	0.181655
$664$	4.99835	0.193974
$665$	14.7075	0.570333
$666$	−10.6586	−0.413014
$667$	−11.4632	−0.443857
$668$	2.32234	0.0898539
$669$	4.57579	0.176910
$670$	29.8200	1.15205
$671$	9.37272	0.361830
$672$	2.33165	0.0899455
$673$	−24.1336	−0.930283	−0.465142	−	0.885236i	$-0.653997\pi$
$673$	−24.1336	−0.930283	−0.465142	+	0.885236i	$0.653997\pi$
$674$	−6.43156	−0.247734
$675$	1.53038	0.0589043
$676$	−2.38559	−0.0917534
$677$	22.6833	0.871789	0.435894	−	0.899998i	$-0.356432\pi$
$677$	22.6833	0.871789	0.435894	+	0.899998i	$0.356432\pi$
$678$	−6.45612	−0.247946
$679$	−22.8822	−0.878137
$680$	−21.9080	−0.840134
$681$	−21.7544	−0.833630
$682$	−11.0747	−0.424074
$683$	40.3591	1.54430	0.772149	−	0.635441i	$-0.219182\pi$
$683$	40.3591	1.54430	0.772149	+	0.635441i	$0.219182\pi$
$684$	−0.770477	−0.0294599
$685$	−41.0661	−1.56906
$686$	−29.8148	−1.13833
$687$	−0.531819	−0.0202902
$688$	−47.4031	−1.80722
$689$	11.0967	0.422751
$690$	4.89175	0.186226
$691$	47.7362	1.81597	0.907985	−	0.419003i	$-0.137620\pi$
$691$	47.7362	1.81597	0.907985	+	0.419003i	$0.137620\pi$
$692$	4.23915	0.161148
$693$	−4.39677	−0.167020
$694$	−52.0319	−1.97510
$695$	40.7961	1.54748
$696$	17.2837	0.655138
$697$	22.4952	0.852067
$698$	−33.4167	−1.26484
$699$	−15.6231	−0.590921
$700$	0.633115	0.0239295
$701$	45.3198	1.71170	0.855852	−	0.517221i	$-0.173034\pi$
$701$	45.3198	1.71170	0.855852	+	0.517221i	$0.173034\pi$
$702$	1.57469	0.0594330
$703$	−27.5510	−1.03910
$704$	15.0393	0.566816
$705$	23.9823	0.903225
$706$	−11.8370	−0.445493
$707$	−31.1322	−1.17085
$708$	−0.634107	−0.0238312
$709$	−27.7681	−1.04285	−0.521427	−	0.853296i	$-0.674600\pi$
$709$	−27.7681	−1.04285	−0.521427	+	0.853296i	$0.674600\pi$
$710$	−12.3481	−0.463417
$711$	6.81869	0.255721
$712$	29.4232	1.10268
$713$	6.18842	0.231758
$714$	13.4609	0.503760
$715$	4.22190	0.157890
$716$	4.13537	0.154546
$717$	16.6422	0.621515
$718$	38.0849	1.42131
$719$	24.6934	0.920909	0.460455	−	0.887683i	$-0.347686\pi$
$719$	24.6934	0.920909	0.460455	+	0.887683i	$0.347686\pi$
$720$	−8.12408	−0.302766
$721$	1.18842	0.0442592
$722$	6.37139	0.237118
$723$	0.938245	0.0348937
$724$	4.53926	0.168700
$725$	9.91023	0.368057
$726$	−9.55435	−0.354595
$727$	37.6055	1.39471	0.697355	−	0.716726i	$-0.254360\pi$
$727$	37.6055	1.39471	0.697355	+	0.716726i	$0.254360\pi$
$728$	−5.83321	−0.216193
$729$	1.00000	0.0370370
$730$	−1.28653	−0.0476167
$731$	−47.8942	−1.77143
$732$	−0.881892	−0.0325957
$733$	−50.4311	−1.86272	−0.931358	−	0.364104i	$-0.881375\pi$
$733$	−50.4311	−1.86272	−0.931358	+	0.364104i	$0.881375\pi$
$734$	−9.77068	−0.360642
$735$	5.14183	0.189659
$736$	2.00458	0.0738900
$737$	−23.0429	−0.848797
$738$	7.57325	0.278775
$739$	6.46770	0.237918	0.118959	−	0.992899i	$-0.462044\pi$
$739$	6.46770	0.237918	0.118959	+	0.992899i	$0.462044\pi$
$740$	2.68883	0.0988433
$741$	4.07034	0.149528
$742$	31.9348	1.17236
$743$	28.0493	1.02903	0.514515	−	0.857481i	$-0.327972\pi$
$743$	28.0493	1.02903	0.514515	+	0.857481i	$0.327972\pi$
$744$	−9.33063	−0.342078
$745$	−7.47755	−0.273956
$746$	52.4100	1.91887
$747$	1.87272	0.0685194
$748$	−1.89062	−0.0691280
$749$	6.68317	0.244198
$750$	−18.0460	−0.658948
$751$	16.4446	0.600071	0.300036	−	0.953928i	$-0.403001\pi$
$751$	16.4446	0.600071	0.300036	+	0.953928i	$0.403001\pi$
$752$	56.1542	2.04773
$753$	−1.15201	−0.0419815
$754$	10.1972	0.371360
$755$	−9.69770	−0.352936
$756$	0.413698	0.0150460
$757$	3.02915	0.110096	0.0550481	−	0.998484i	$-0.482469\pi$
$757$	3.02915	0.110096	0.0550481	+	0.998484i	$0.482469\pi$
$758$	−36.2073	−1.31511
$759$	−3.78002	−0.137206
$760$	−19.0647	−0.691551
$761$	−19.0544	−0.690722	−0.345361	−	0.938470i	$-0.612244\pi$
$761$	−19.0544	−0.690722	−0.345361	+	0.938470i	$0.612244\pi$
$762$	1.97225	0.0714472
$763$	40.5497	1.46800
$764$	1.31877	0.0477116
$765$	−8.20825	−0.296770
$766$	10.2667	0.370950
$767$	3.34992	0.120959
$768$	−4.77504	−0.172304
$769$	22.6835	0.817989	0.408995	−	0.912537i	$-0.365880\pi$
$769$	22.6835	0.817989	0.408995	+	0.912537i	$0.365880\pi$
$770$	12.1500	0.437856
$771$	−1.71866	−0.0618962
$772$	−1.10167	−0.0396500
$773$	24.6903	0.888050	0.444025	−	0.896015i	$-0.353550\pi$
$773$	24.6903	0.888050	0.444025	+	0.896015i	$0.353550\pi$
$774$	−16.1241	−0.579569
$775$	−5.35005	−0.192179
$776$	29.6612	1.06478
$777$	14.7931	0.530701
$778$	2.90495	0.104148
$779$	19.5757	0.701373
$780$	−0.397244	−0.0142236
$781$	9.54182	0.341433
$782$	11.5727	0.413837
$783$	6.47567	0.231421
$784$	12.0395	0.429983
$785$	−37.9767	−1.35545
$786$	0.424764	0.0151508
$787$	−0.154755	−0.00551642	−0.00275821	−	0.999996i	$-0.500878\pi$
$787$	−0.154755	−0.00551642	−0.00275821	+	0.999996i	$0.500878\pi$
$788$	−3.82605	−0.136298
$789$	−19.9280	−0.709454
$790$	−18.8427	−0.670395
$791$	8.96047	0.318598
$792$	5.69936	0.202518
$793$	4.65894	0.165444
$794$	−36.2470	−1.28636
$795$	−19.4734	−0.690650
$796$	0.324911	0.0115162
$797$	10.3576	0.366884	0.183442	−	0.983031i	$-0.441276\pi$
$797$	10.3576	0.366884	0.183442	+	0.983031i	$0.441276\pi$
$798$	11.7139	0.414666
$799$	56.7361	2.00718
$800$	−1.73301	−0.0612713
$801$	11.0240	0.389513
$802$	−3.60710	−0.127371
$803$	0.994147	0.0350827
$804$	2.16814	0.0764643
$805$	−6.78927	−0.239290
$806$	−5.50497	−0.193904
$807$	−12.4263	−0.437427
$808$	40.3554	1.41970
$809$	14.5422	0.511276	0.255638	−	0.966773i	$-0.417714\pi$
$809$	14.5422	0.511276	0.255638	+	0.966773i	$0.417714\pi$
$810$	−2.76340	−0.0970958
$811$	−0.186476	−0.00654806	−0.00327403	−	0.999995i	$-0.501042\pi$
$811$	−0.186476	−0.00654806	−0.00327403	+	0.999995i	$0.501042\pi$
$812$	2.67897	0.0940134
$813$	28.1905	0.988685
$814$	−22.7601	−0.797742
$815$	−3.10595	−0.108797
$816$	−19.2195	−0.672818
$817$	−41.6783	−1.45814
$818$	37.2652	1.30295
$819$	−2.18552	−0.0763683
$820$	−1.91049	−0.0667171
$821$	22.8734	0.798288	0.399144	−	0.916888i	$-0.369307\pi$
$821$	22.8734	0.798288	0.399144	+	0.916888i	$0.369307\pi$
$822$	−32.7073	−1.14080
$823$	−20.7854	−0.724533	−0.362266	−	0.932075i	$-0.617997\pi$
$823$	−20.7854	−0.724533	−0.362266	+	0.932075i	$0.617997\pi$
$824$	−1.54050	−0.0536660
$825$	3.26793	0.113775
$826$	9.64058	0.335439
$827$	−33.5480	−1.16658	−0.583289	−	0.812265i	$-0.698235\pi$
$827$	−33.5480	−1.16658	−0.583289	+	0.812265i	$0.698235\pi$
$828$	0.355667	0.0123603
$829$	−28.5671	−0.992175	−0.496088	−	0.868272i	$-0.665231\pi$
$829$	−28.5671	−0.992175	−0.496088	+	0.868272i	$0.665231\pi$
$830$	−5.17508	−0.179630
$831$	−20.6159	−0.715158
$832$	7.47565	0.259172
$833$	12.1643	0.421467
$834$	32.4922	1.12511
$835$	21.5300	0.745076
$836$	−1.64525	−0.0569022
$837$	−3.49590	−0.120836
$838$	37.2180	1.28567
$839$	2.27372	0.0784977	0.0392488	−	0.999229i	$-0.487503\pi$
$839$	2.27372	0.0784977	0.0392488	+	0.999229i	$0.487503\pi$
$840$	10.2366	0.353195
$841$	12.9343	0.446010
$842$	20.2685	0.698499
$843$	−19.8514	−0.683719
$844$	1.03877	0.0357559
$845$	−22.1164	−0.760827
$846$	19.1008	0.656699
$847$	13.2605	0.455636
$848$	−45.5967	−1.56580
$849$	−10.9818	−0.376894
$850$	−10.0049	−0.343164
$851$	12.7181	0.435969
$852$	−0.897802	−0.0307582
$853$	−14.7837	−0.506185	−0.253093	−	0.967442i	$-0.581448\pi$
$853$	−14.7837	−0.506185	−0.253093	+	0.967442i	$0.581448\pi$
$854$	13.4077	0.458804
$855$	−7.14296	−0.244284
$856$	−8.66311	−0.296099
$857$	−10.5001	−0.358677	−0.179338	−	0.983787i	$-0.557396\pi$
$857$	−10.5001	−0.358677	−0.179338	+	0.983787i	$0.557396\pi$
$858$	3.36255	0.114796
$859$	10.9221	0.372656	0.186328	−	0.982488i	$-0.440341\pi$
$859$	10.9221	0.372656	0.186328	+	0.982488i	$0.440341\pi$
$860$	4.06759	0.138704
$861$	−10.5109	−0.358212
$862$	25.9293	0.883154
$863$	−23.0053	−0.783110	−0.391555	−	0.920155i	$-0.628063\pi$
$863$	−23.0053	−0.783110	−0.391555	+	0.920155i	$0.628063\pi$
$864$	−1.13241	−0.0385253
$865$	39.3005	1.33626
$866$	−16.8474	−0.572498
$867$	−2.41865	−0.0821417
$868$	−1.44624	−0.0490887
$869$	14.5604	0.493929
$870$	−17.8948	−0.606692
$871$	−11.4540	−0.388105
$872$	−52.5629	−1.78001
$873$	11.1131	0.376122
$874$	10.0707	0.340647
$875$	25.0461	0.846713
$876$	−0.0935406	−0.00316044
$877$	−32.4502	−1.09577	−0.547883	−	0.836555i	$-0.684566\pi$
$877$	−32.4502	−1.09577	−0.547883	+	0.836555i	$0.684566\pi$
$878$	−31.4171	−1.06028
$879$	3.47326	0.117150
$880$	−17.3479	−0.584798
$881$	−26.4346	−0.890605	−0.445303	−	0.895380i	$-0.646904\pi$
$881$	−26.4346	−0.890605	−0.445303	+	0.895380i	$0.646904\pi$
$882$	4.09524	0.137894
$883$	13.2757	0.446764	0.223382	−	0.974731i	$-0.428290\pi$
$883$	13.2757	0.446764	0.223382	+	0.974731i	$0.428290\pi$
$884$	−0.939780	−0.0316082
$885$	−5.87870	−0.197610
$886$	−23.8918	−0.802660
$887$	5.15836	0.173201	0.0866004	−	0.996243i	$-0.472400\pi$
$887$	5.15836	0.173201	0.0866004	+	0.996243i	$0.472400\pi$
$888$	−19.1757	−0.643496
$889$	−2.73729	−0.0918059
$890$	−30.4636	−1.02114
$891$	2.13537	0.0715376
$892$	−0.919365	−0.0307826
$893$	49.3727	1.65219
$894$	−5.95553	−0.199183
$895$	38.3383	1.28151
$896$	26.1772	0.874517
$897$	−1.87895	−0.0627363
$898$	36.3643	1.21349
$899$	−22.6383	−0.755028
$900$	−0.307483	−0.0102494
$901$	−46.0691	−1.53479
$902$	16.1717	0.538459
$903$	22.3787	0.744716
$904$	−11.6151	−0.386312
$905$	42.0827	1.39888
$906$	−7.72378	−0.256605
$907$	−3.28409	−0.109046	−0.0545232	−	0.998513i	$-0.517364\pi$
$907$	−3.28409	−0.109046	−0.0545232	+	0.998513i	$0.517364\pi$
$908$	4.37088	0.145053
$909$	15.1199	0.501495
$910$	6.03946	0.200206
$911$	50.3187	1.66713	0.833567	−	0.552418i	$-0.186295\pi$
$911$	50.3187	1.66713	0.833567	+	0.552418i	$0.186295\pi$
$912$	−16.7252	−0.553825
$913$	3.99896	0.132346
$914$	−0.382449	−0.0126503
$915$	−8.17587	−0.270286
$916$	0.106853	0.00353052
$917$	−0.589530	−0.0194680
$918$	−6.53750	−0.215770
$919$	−5.94731	−0.196184	−0.0980918	−	0.995177i	$-0.531274\pi$
$919$	−5.94731	−0.196184	−0.0980918	+	0.995177i	$0.531274\pi$
$920$	8.80065	0.290149
$921$	18.6697	0.615189
$922$	8.19367	0.269844
$923$	4.74299	0.156117
$924$	0.883398	0.0290617
$925$	−10.9951	−0.361516
$926$	−4.20809	−0.138287
$927$	−0.577178	−0.0189570
$928$	−7.33310	−0.240721
$929$	−23.2642	−0.763274	−0.381637	−	0.924312i	$-0.624640\pi$
$929$	−23.2642	−0.763274	−0.381637	+	0.924312i	$0.624640\pi$
$930$	9.66054	0.316782
$931$	10.5856	0.346928
$932$	3.13899	0.102821
$933$	26.8813	0.880056
$934$	−4.62272	−0.151260
$935$	−17.5276	−0.573215
$936$	2.83300	0.0925995
$937$	−51.0450	−1.66757	−0.833784	−	0.552092i	$-0.813830\pi$
$937$	−51.0450	−1.66757	−0.833784	+	0.552092i	$0.813830\pi$
$938$	−32.9631	−1.07628
$939$	−4.27659	−0.139561
$940$	−4.81851	−0.157163
$941$	15.7437	0.513230	0.256615	−	0.966514i	$-0.417393\pi$
$941$	15.7437	0.513230	0.256615	+	0.966514i	$0.417393\pi$
$942$	−30.2467	−0.985491
$943$	−9.03653	−0.294270
$944$	−13.7649	−0.448010
$945$	3.83532	0.124763
$946$	−34.4309	−1.11945
$947$	33.1072	1.07584	0.537919	−	0.842996i	$-0.319211\pi$
$947$	33.1072	1.07584	0.537919	+	0.842996i	$0.319211\pi$
$948$	−1.37001	−0.0444958
$949$	0.494165	0.0160413
$950$	−8.70639	−0.282473
$951$	−29.8137	−0.966776
$952$	24.2172	0.784882
$953$	−1.34810	−0.0436692	−0.0218346	−	0.999762i	$-0.506951\pi$
$953$	−1.34810	−0.0436692	−0.0218346	+	0.999762i	$0.506951\pi$
$954$	−15.5097	−0.502144
$955$	12.2261	0.395629
$956$	−3.34375	−0.108145
$957$	13.8279	0.446994
$958$	−15.7177	−0.507817
$959$	45.3945	1.46587
$960$	−13.1189	−0.423409
$961$	−18.7787	−0.605765
$962$	−11.3135	−0.364761
$963$	−3.24580	−0.104594
$964$	−0.188512	−0.00607156
$965$	−10.2134	−0.328781
$966$	−5.40735	−0.173979
$967$	16.7557	0.538827	0.269414	−	0.963025i	$-0.413170\pi$
$967$	16.7557	0.538827	0.269414	+	0.963025i	$0.413170\pi$
$968$	−17.1890	−0.552477
$969$	−16.8984	−0.542856
$970$	−30.7100	−0.986038
$971$	40.5909	1.30262	0.651311	−	0.758810i	$-0.274219\pi$
$971$	40.5909	1.30262	0.651311	+	0.758810i	$0.274219\pi$
$972$	−0.200920	−0.00644450
$973$	−45.0960	−1.44571
$974$	−51.6780	−1.65587
$975$	1.62440	0.0520225
$976$	−19.1437	−0.612775
$977$	−12.3154	−0.394005	−0.197002	−	0.980403i	$-0.563121\pi$
$977$	−12.3154	−0.394005	−0.197002	+	0.980403i	$0.563121\pi$
$978$	−2.47375	−0.0791018
$979$	23.5402	0.752350
$980$	−1.03309	−0.0330010
$981$	−19.6937	−0.628771
$982$	−10.9133	−0.348257
$983$	−52.0764	−1.66098	−0.830489	−	0.557035i	$-0.811939\pi$
$983$	−52.0764	−1.66098	−0.830489	+	0.557035i	$0.811939\pi$
$984$	13.6249	0.434346
$985$	−35.4707	−1.13019
$986$	−42.3347	−1.34821
$987$	−26.5100	−0.843824
$988$	−0.817812	−0.0260181
$989$	19.2395	0.611782
$990$	−5.90087	−0.187542
$991$	−59.6306	−1.89423	−0.947114	−	0.320897i	$-0.896016\pi$
$991$	−59.6306	−1.89423	−0.947114	+	0.320897i	$0.896016\pi$
$992$	3.95878	0.125691
$993$	−7.18879	−0.228129
$994$	13.6496	0.432940
$995$	3.01220	0.0954931
$996$	−0.376267	−0.0119225
$997$	−56.4578	−1.78804	−0.894018	−	0.448031i	$-0.852125\pi$
$997$	−56.4578	−1.78804	−0.894018	+	0.448031i	$0.852125\pi$
$998$	−12.7708	−0.404254
$999$	−7.18455	−0.227309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.20	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.20	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.48355 q^{2} -1.00000 q^{3} +0.200920 q^{4} +1.86269 q^{5} +1.48355 q^{6} -2.05902 q^{7} +2.66903 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.48355 q^{2} -1.00000 q^{3} +0.200920 q^{4} +1.86269 q^{5} +1.48355 q^{6} -2.05902 q^{7} +2.66903 q^{8} +1.00000 q^{9} -2.76340 q^{10} +2.13537 q^{11} -0.200920 q^{12} +1.06144 q^{13} +3.05466 q^{14} -1.86269 q^{15} -4.36147 q^{16} -4.40666 q^{17} -1.48355 q^{18} -3.83475 q^{19} +0.374251 q^{20} +2.05902 q^{21} -3.16793 q^{22} +1.77020 q^{23} -2.66903 q^{24} -1.53038 q^{25} -1.57469 q^{26} -1.00000 q^{27} -0.413698 q^{28} -6.47567 q^{29} +2.76340 q^{30} +3.49590 q^{31} +1.13241 q^{32} -2.13537 q^{33} +6.53750 q^{34} -3.83532 q^{35} +0.200920 q^{36} +7.18455 q^{37} +5.68904 q^{38} -1.06144 q^{39} +4.97157 q^{40} -5.10482 q^{41} -3.05466 q^{42} +10.8686 q^{43} +0.429038 q^{44} +1.86269 q^{45} -2.62617 q^{46} -12.8751 q^{47} +4.36147 q^{48} -2.76043 q^{49} +2.27039 q^{50} +4.40666 q^{51} +0.213263 q^{52} +10.4544 q^{53} +1.48355 q^{54} +3.97754 q^{55} -5.49558 q^{56} +3.83475 q^{57} +9.60698 q^{58} +3.15602 q^{59} -0.374251 q^{60} +4.38928 q^{61} -5.18634 q^{62} -2.05902 q^{63} +7.04296 q^{64} +1.97713 q^{65} +3.16793 q^{66} -10.7911 q^{67} -0.885384 q^{68} -1.77020 q^{69} +5.68989 q^{70} +4.46846 q^{71} +2.66903 q^{72} +0.465562 q^{73} -10.6586 q^{74} +1.53038 q^{75} -0.770477 q^{76} -4.39677 q^{77} +1.57469 q^{78} +6.81869 q^{79} -8.12408 q^{80} +1.00000 q^{81} +7.57325 q^{82} +1.87272 q^{83} +0.413698 q^{84} -8.20825 q^{85} -16.1241 q^{86} +6.47567 q^{87} +5.69936 q^{88} +11.0240 q^{89} -2.76340 q^{90} -2.18552 q^{91} +0.355667 q^{92} -3.49590 q^{93} +19.1008 q^{94} -7.14296 q^{95} -1.13241 q^{96} +11.1131 q^{97} +4.09524 q^{98} +2.13537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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