LMFDB - Embedded newform 8026.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.70684 q^{3} +1.00000 q^{4} -2.82175 q^{5} -1.70684 q^{6} +3.08724 q^{7} +1.00000 q^{8} -0.0867059 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.70684 q^{3} +1.00000 q^{4} -2.82175 q^{5} -1.70684 q^{6} +3.08724 q^{7} +1.00000 q^{8} -0.0867059 q^{9} -2.82175 q^{10} -4.90438 q^{11} -1.70684 q^{12} +4.27139 q^{13} +3.08724 q^{14} +4.81627 q^{15} +1.00000 q^{16} -1.86202 q^{17} -0.0867059 q^{18} +2.06959 q^{19} -2.82175 q^{20} -5.26942 q^{21} -4.90438 q^{22} +2.71479 q^{23} -1.70684 q^{24} +2.96229 q^{25} +4.27139 q^{26} +5.26851 q^{27} +3.08724 q^{28} -6.82587 q^{29} +4.81627 q^{30} -3.46894 q^{31} +1.00000 q^{32} +8.37097 q^{33} -1.86202 q^{34} -8.71144 q^{35} -0.0867059 q^{36} +7.04587 q^{37} +2.06959 q^{38} -7.29056 q^{39} -2.82175 q^{40} +2.46434 q^{41} -5.26942 q^{42} +4.50056 q^{43} -4.90438 q^{44} +0.244663 q^{45} +2.71479 q^{46} -12.4312 q^{47} -1.70684 q^{48} +2.53108 q^{49} +2.96229 q^{50} +3.17816 q^{51} +4.27139 q^{52} -4.92975 q^{53} +5.26851 q^{54} +13.8389 q^{55} +3.08724 q^{56} -3.53246 q^{57} -6.82587 q^{58} +3.42311 q^{59} +4.81627 q^{60} +3.82089 q^{61} -3.46894 q^{62} -0.267682 q^{63} +1.00000 q^{64} -12.0528 q^{65} +8.37097 q^{66} +4.78132 q^{67} -1.86202 q^{68} -4.63371 q^{69} -8.71144 q^{70} +12.8785 q^{71} -0.0867059 q^{72} +2.86681 q^{73} +7.04587 q^{74} -5.05615 q^{75} +2.06959 q^{76} -15.1410 q^{77} -7.29056 q^{78} -10.2935 q^{79} -2.82175 q^{80} -8.73236 q^{81} +2.46434 q^{82} +0.795079 q^{83} -5.26942 q^{84} +5.25416 q^{85} +4.50056 q^{86} +11.6506 q^{87} -4.90438 q^{88} +15.8941 q^{89} +0.244663 q^{90} +13.1868 q^{91} +2.71479 q^{92} +5.92092 q^{93} -12.4312 q^{94} -5.83988 q^{95} -1.70684 q^{96} +11.0382 q^{97} +2.53108 q^{98} +0.425238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.70684	−0.985443	−0.492722	−	0.870187i	$-0.663998\pi$
$3$	−1.70684	−0.985443	−0.492722	+	0.870187i	$0.663998\pi$
$4$	1.00000	0.500000
$5$	−2.82175	−1.26193	−0.630963	−	0.775813i	$-0.717340\pi$
$5$	−2.82175	−1.26193	−0.630963	+	0.775813i	$0.717340\pi$
$6$	−1.70684	−0.696813
$7$	3.08724	1.16687	0.583434	−	0.812160i	$-0.301709\pi$
$7$	3.08724	1.16687	0.583434	+	0.812160i	$0.301709\pi$
$8$	1.00000	0.353553
$9$	−0.0867059	−0.0289020
$10$	−2.82175	−0.892317
$11$	−4.90438	−1.47873	−0.739363	−	0.673308i	$-0.764873\pi$
$11$	−4.90438	−1.47873	−0.739363	+	0.673308i	$0.764873\pi$
$12$	−1.70684	−0.492722
$13$	4.27139	1.18467	0.592335	−	0.805692i	$-0.298206\pi$
$13$	4.27139	1.18467	0.592335	+	0.805692i	$0.298206\pi$
$14$	3.08724	0.825101
$15$	4.81627	1.24356
$16$	1.00000	0.250000
$17$	−1.86202	−0.451606	−0.225803	−	0.974173i	$-0.572501\pi$
$17$	−1.86202	−0.451606	−0.225803	+	0.974173i	$0.572501\pi$
$18$	−0.0867059	−0.0204368
$19$	2.06959	0.474797	0.237399	−	0.971412i	$-0.423705\pi$
$19$	2.06959	0.474797	0.237399	+	0.971412i	$0.423705\pi$
$20$	−2.82175	−0.630963
$21$	−5.26942	−1.14988
$22$	−4.90438	−1.04562
$23$	2.71479	0.566073	0.283037	−	0.959109i	$-0.408658\pi$
$23$	2.71479	0.566073	0.283037	+	0.959109i	$0.408658\pi$
$24$	−1.70684	−0.348407
$25$	2.96229	0.592458
$26$	4.27139	0.837688
$27$	5.26851	1.01392
$28$	3.08724	0.583434
$29$	−6.82587	−1.26753	−0.633766	−	0.773525i	$-0.718492\pi$
$29$	−6.82587	−1.26753	−0.633766	+	0.773525i	$0.718492\pi$
$30$	4.81627	0.879327
$31$	−3.46894	−0.623040	−0.311520	−	0.950240i	$-0.600838\pi$
$31$	−3.46894	−0.623040	−0.311520	+	0.950240i	$0.600838\pi$
$32$	1.00000	0.176777
$33$	8.37097	1.45720
$34$	−1.86202	−0.319334
$35$	−8.71144	−1.47250
$36$	−0.0867059	−0.0144510
$37$	7.04587	1.15833	0.579167	−	0.815209i	$-0.303378\pi$
$37$	7.04587	1.15833	0.579167	+	0.815209i	$0.303378\pi$
$38$	2.06959	0.335732
$39$	−7.29056	−1.16742
$40$	−2.82175	−0.446158
$41$	2.46434	0.384865	0.192433	−	0.981310i	$-0.438362\pi$
$41$	2.46434	0.384865	0.192433	+	0.981310i	$0.438362\pi$
$42$	−5.26942	−0.813090
$43$	4.50056	0.686329	0.343165	−	0.939275i	$-0.388501\pi$
$43$	4.50056	0.686329	0.343165	+	0.939275i	$0.388501\pi$
$44$	−4.90438	−0.739363
$45$	0.244663	0.0364721
$46$	2.71479	0.400274
$47$	−12.4312	−1.81328	−0.906638	−	0.421910i	$-0.861360\pi$
$47$	−12.4312	−1.81328	−0.906638	+	0.421910i	$0.861360\pi$
$48$	−1.70684	−0.246361
$49$	2.53108	0.361582
$50$	2.96229	0.418931
$51$	3.17816	0.445032
$52$	4.27139	0.592335
$53$	−4.92975	−0.677153	−0.338576	−	0.940939i	$-0.609945\pi$
$53$	−4.92975	−0.677153	−0.338576	+	0.940939i	$0.609945\pi$
$54$	5.26851	0.716953
$55$	13.8389	1.86604
$56$	3.08724	0.412550
$57$	−3.53246	−0.467886
$58$	−6.82587	−0.896280
$59$	3.42311	0.445652	0.222826	−	0.974858i	$-0.428472\pi$
$59$	3.42311	0.445652	0.222826	+	0.974858i	$0.428472\pi$
$60$	4.81627	0.621778
$61$	3.82089	0.489215	0.244607	−	0.969622i	$-0.421341\pi$
$61$	3.82089	0.489215	0.244607	+	0.969622i	$0.421341\pi$
$62$	−3.46894	−0.440556
$63$	−0.267682	−0.0337248
$64$	1.00000	0.125000
$65$	−12.0528	−1.49497
$66$	8.37097	1.03040
$67$	4.78132	0.584131	0.292065	−	0.956398i	$-0.405657\pi$
$67$	4.78132	0.584131	0.292065	+	0.956398i	$0.405657\pi$
$68$	−1.86202	−0.225803
$69$	−4.63371	−0.557833
$70$	−8.71144	−1.04122
$71$	12.8785	1.52839	0.764197	−	0.644983i	$-0.223136\pi$
$71$	12.8785	1.52839	0.764197	+	0.644983i	$0.223136\pi$
$72$	−0.0867059	−0.0102184
$73$	2.86681	0.335534	0.167767	−	0.985827i	$-0.446344\pi$
$73$	2.86681	0.335534	0.167767	+	0.985827i	$0.446344\pi$
$74$	7.04587	0.819066
$75$	−5.05615	−0.583833
$76$	2.06959	0.237399
$77$	−15.1410	−1.72548
$78$	−7.29056	−0.825494
$79$	−10.2935	−1.15811	−0.579053	−	0.815290i	$-0.696578\pi$
$79$	−10.2935	−1.15811	−0.579053	+	0.815290i	$0.696578\pi$
$80$	−2.82175	−0.315482
$81$	−8.73236	−0.970263
$82$	2.46434	0.272141
$83$	0.795079	0.0872713	0.0436356	−	0.999048i	$-0.486106\pi$
$83$	0.795079	0.0872713	0.0436356	+	0.999048i	$0.486106\pi$
$84$	−5.26942	−0.574941
$85$	5.25416	0.569893
$86$	4.50056	0.485308
$87$	11.6506	1.24908
$88$	−4.90438	−0.522808
$89$	15.8941	1.68477	0.842384	−	0.538878i	$-0.181152\pi$
$89$	15.8941	1.68477	0.842384	+	0.538878i	$0.181152\pi$
$90$	0.244663	0.0257897
$91$	13.1868	1.38235
$92$	2.71479	0.283037
$93$	5.92092	0.613971
$94$	−12.4312	−1.28218
$95$	−5.83988	−0.599159
$96$	−1.70684	−0.174203
$97$	11.0382	1.12076	0.560381	−	0.828235i	$-0.310655\pi$
$97$	11.0382	1.12076	0.560381	+	0.828235i	$0.310655\pi$
$98$	2.53108	0.255677
$99$	0.425238	0.0427380
$100$	2.96229	0.296229
$101$	−15.3300	−1.52540	−0.762698	−	0.646755i	$-0.776126\pi$
$101$	−15.3300	−1.52540	−0.762698	+	0.646755i	$0.776126\pi$
$102$	3.17816	0.314685
$103$	−10.6269	−1.04710	−0.523548	−	0.851996i	$-0.675392\pi$
$103$	−10.6269	−1.04710	−0.523548	+	0.851996i	$0.675392\pi$
$104$	4.27139	0.418844
$105$	14.8690	1.45107
$106$	−4.92975	−0.478819
$107$	−5.25181	−0.507711	−0.253856	−	0.967242i	$-0.581699\pi$
$107$	−5.25181	−0.507711	−0.253856	+	0.967242i	$0.581699\pi$
$108$	5.26851	0.506962
$109$	−6.98503	−0.669044	−0.334522	−	0.942388i	$-0.608575\pi$
$109$	−6.98503	−0.669044	−0.334522	+	0.942388i	$0.608575\pi$
$110$	13.8389	1.31949
$111$	−12.0262	−1.14147
$112$	3.08724	0.291717
$113$	−1.61175	−0.151621	−0.0758103	−	0.997122i	$-0.524154\pi$
$113$	−1.61175	−0.151621	−0.0758103	+	0.997122i	$0.524154\pi$
$114$	−3.53246	−0.330845
$115$	−7.66047	−0.714342
$116$	−6.82587	−0.633766
$117$	−0.370354	−0.0342393
$118$	3.42311	0.315123
$119$	−5.74851	−0.526965
$120$	4.81627	0.439664
$121$	13.0529	1.18663
$122$	3.82089	0.345927
$123$	−4.20623	−0.379263
$124$	−3.46894	−0.311520
$125$	5.74992	0.514288
$126$	−0.267682	−0.0238470
$127$	−4.27704	−0.379526	−0.189763	−	0.981830i	$-0.560772\pi$
$127$	−4.27704	−0.379526	−0.189763	+	0.981830i	$0.560772\pi$
$128$	1.00000	0.0883883
$129$	−7.68173	−0.676338
$130$	−12.0528	−1.05710
$131$	−11.3467	−0.991369	−0.495684	−	0.868503i	$-0.665083\pi$
$131$	−11.3467	−0.991369	−0.495684	+	0.868503i	$0.665083\pi$
$132$	8.37097	0.728600
$133$	6.38934	0.554026
$134$	4.78132	0.413043
$135$	−14.8664	−1.27950
$136$	−1.86202	−0.159667
$137$	−12.3410	−1.05436	−0.527179	−	0.849754i	$-0.676750\pi$
$137$	−12.3410	−1.05436	−0.527179	+	0.849754i	$0.676750\pi$
$138$	−4.63371	−0.394447
$139$	14.9438	1.26752	0.633760	−	0.773530i	$-0.281511\pi$
$139$	14.9438	1.26752	0.633760	+	0.773530i	$0.281511\pi$
$140$	−8.71144	−0.736251
$141$	21.2180	1.78688
$142$	12.8785	1.08074
$143$	−20.9485	−1.75180
$144$	−0.0867059	−0.00722549
$145$	19.2609	1.59953
$146$	2.86681	0.237259
$147$	−4.32014	−0.356319
$148$	7.04587	0.579167
$149$	5.25295	0.430339	0.215169	−	0.976577i	$-0.430970\pi$
$149$	5.25295	0.430339	0.215169	+	0.976577i	$0.430970\pi$
$150$	−5.05615	−0.412833
$151$	−19.4477	−1.58263	−0.791316	−	0.611407i	$-0.790604\pi$
$151$	−19.4477	−1.58263	−0.791316	+	0.611407i	$0.790604\pi$
$152$	2.06959	0.167866
$153$	0.161448	0.0130523
$154$	−15.1410	−1.22010
$155$	9.78849	0.786231
$156$	−7.29056	−0.583712
$157$	−1.41664	−0.113060	−0.0565300	−	0.998401i	$-0.518004\pi$
$157$	−1.41664	−0.113060	−0.0565300	+	0.998401i	$0.518004\pi$
$158$	−10.2935	−0.818905
$159$	8.41428	0.667296
$160$	−2.82175	−0.223079
$161$	8.38122	0.660533
$162$	−8.73236	−0.686079
$163$	18.9578	1.48489	0.742445	−	0.669907i	$-0.233666\pi$
$163$	18.9578	1.48489	0.742445	+	0.669907i	$0.233666\pi$
$164$	2.46434	0.192433
$165$	−23.6208	−1.83888
$166$	0.795079	0.0617101
$167$	−24.0862	−1.86385	−0.931924	−	0.362655i	$-0.881870\pi$
$167$	−24.0862	−1.86385	−0.931924	+	0.362655i	$0.881870\pi$
$168$	−5.26942	−0.406545
$169$	5.24474	0.403442
$170$	5.25416	0.402975
$171$	−0.179446	−0.0137226
$172$	4.50056	0.343165
$173$	−17.6195	−1.33959	−0.669794	−	0.742547i	$-0.733618\pi$
$173$	−17.6195	−1.33959	−0.669794	+	0.742547i	$0.733618\pi$
$174$	11.6506	0.883233
$175$	9.14531	0.691320
$176$	−4.90438	−0.369681
$177$	−5.84270	−0.439164
$178$	15.8941	1.19131
$179$	14.9754	1.11931	0.559657	−	0.828725i	$-0.310933\pi$
$179$	14.9754	1.11931	0.559657	+	0.828725i	$0.310933\pi$
$180$	0.244663	0.0182361
$181$	−15.6659	−1.16444	−0.582219	−	0.813032i	$-0.697815\pi$
$181$	−15.6659	−1.16444	−0.582219	+	0.813032i	$0.697815\pi$
$182$	13.1868	0.977472
$183$	−6.52164	−0.482093
$184$	2.71479	0.200137
$185$	−19.8817	−1.46173
$186$	5.92092	0.434143
$187$	9.13204	0.667801
$188$	−12.4312	−0.906638
$189$	16.2652	1.18312
$190$	−5.83988	−0.423670
$191$	−12.9141	−0.934430	−0.467215	−	0.884144i	$-0.654743\pi$
$191$	−12.9141	−0.934430	−0.467215	+	0.884144i	$0.654743\pi$
$192$	−1.70684	−0.123180
$193$	−5.68924	−0.409521	−0.204760	−	0.978812i	$-0.565642\pi$
$193$	−5.68924	−0.409521	−0.204760	+	0.978812i	$0.565642\pi$
$194$	11.0382	0.792499
$195$	20.5722	1.47320
$196$	2.53108	0.180791
$197$	17.1411	1.22125	0.610626	−	0.791919i	$-0.290918\pi$
$197$	17.1411	1.22125	0.610626	+	0.791919i	$0.290918\pi$
$198$	0.425238	0.0302204
$199$	6.80696	0.482532	0.241266	−	0.970459i	$-0.422437\pi$
$199$	6.80696	0.482532	0.241266	+	0.970459i	$0.422437\pi$
$200$	2.96229	0.209465
$201$	−8.16093	−0.575628
$202$	−15.3300	−1.07862
$203$	−21.0731	−1.47904
$204$	3.17816	0.222516
$205$	−6.95376	−0.485672
$206$	−10.6269	−0.740408
$207$	−0.235388	−0.0163606
$208$	4.27139	0.296167
$209$	−10.1501	−0.702095
$210$	14.8690	1.02606
$211$	−16.0737	−1.10656	−0.553279	−	0.832996i	$-0.686624\pi$
$211$	−16.0737	−1.10656	−0.553279	+	0.832996i	$0.686624\pi$
$212$	−4.92975	−0.338576
$213$	−21.9815	−1.50614
$214$	−5.25181	−0.359006
$215$	−12.6995	−0.866097
$216$	5.26851	0.358476
$217$	−10.7095	−0.727006
$218$	−6.98503	−0.473086
$219$	−4.89317	−0.330650
$220$	13.8389	0.933021
$221$	−7.95340	−0.535004
$222$	−12.0262	−0.807143
$223$	−27.7619	−1.85907	−0.929536	−	0.368732i	$-0.879792\pi$
$223$	−27.7619	−1.85907	−0.929536	+	0.368732i	$0.879792\pi$
$224$	3.08724	0.206275
$225$	−0.256848	−0.0171232
$226$	−1.61175	−0.107212
$227$	15.6189	1.03666	0.518332	−	0.855179i	$-0.326553\pi$
$227$	15.6189	1.03666	0.518332	+	0.855179i	$0.326553\pi$
$228$	−3.53246	−0.233943
$229$	−23.9025	−1.57952	−0.789761	−	0.613415i	$-0.789795\pi$
$229$	−23.9025	−1.57952	−0.789761	+	0.613415i	$0.789795\pi$
$230$	−7.66047	−0.505116
$231$	25.8432	1.70036
$232$	−6.82587	−0.448140
$233$	−25.1744	−1.64923	−0.824615	−	0.565694i	$-0.808608\pi$
$233$	−25.1744	−1.64923	−0.824615	+	0.565694i	$0.808608\pi$
$234$	−0.370354	−0.0242108
$235$	35.0778	2.28822
$236$	3.42311	0.222826
$237$	17.5693	1.14125
$238$	−5.74851	−0.372620
$239$	8.48723	0.548993	0.274497	−	0.961588i	$-0.411489\pi$
$239$	8.48723	0.548993	0.274497	+	0.961588i	$0.411489\pi$
$240$	4.81627	0.310889
$241$	−15.9876	−1.02985	−0.514924	−	0.857236i	$-0.672180\pi$
$241$	−15.9876	−1.02985	−0.514924	+	0.857236i	$0.672180\pi$
$242$	13.0529	0.839073
$243$	−0.900789	−0.0577856
$244$	3.82089	0.244607
$245$	−7.14207	−0.456290
$246$	−4.20623	−0.268179
$247$	8.84003	0.562478
$248$	−3.46894	−0.220278
$249$	−1.35707	−0.0860009
$250$	5.74992	0.363657
$251$	−5.52678	−0.348847	−0.174424	−	0.984671i	$-0.555806\pi$
$251$	−5.52678	−0.348847	−0.174424	+	0.984671i	$0.555806\pi$
$252$	−0.267682	−0.0168624
$253$	−13.3144	−0.837066
$254$	−4.27704	−0.268365
$255$	−8.96799	−0.561597
$256$	1.00000	0.0625000
$257$	17.0469	1.06335	0.531677	−	0.846947i	$-0.321562\pi$
$257$	17.0469	1.06335	0.531677	+	0.846947i	$0.321562\pi$
$258$	−7.68173	−0.478243
$259$	21.7523	1.35162
$260$	−12.0528	−0.747483
$261$	0.591843	0.0366342
$262$	−11.3467	−0.701003
$263$	−13.9641	−0.861061	−0.430531	−	0.902576i	$-0.641674\pi$
$263$	−13.9641	−0.861061	−0.430531	+	0.902576i	$0.641674\pi$
$264$	8.37097	0.515198
$265$	13.9105	0.854517
$266$	6.38934	0.391756
$267$	−27.1286	−1.66024
$268$	4.78132	0.292065
$269$	4.58325	0.279446	0.139723	−	0.990191i	$-0.455379\pi$
$269$	4.58325	0.279446	0.139723	+	0.990191i	$0.455379\pi$
$270$	−14.8664	−0.904741
$271$	19.4977	1.18440	0.592202	−	0.805790i	$-0.298259\pi$
$271$	19.4977	1.18440	0.592202	+	0.805790i	$0.298259\pi$
$272$	−1.86202	−0.112901
$273$	−22.5077	−1.36223
$274$	−12.3410	−0.745544
$275$	−14.5282	−0.876082
$276$	−4.63371	−0.278916
$277$	16.4752	0.989897	0.494948	−	0.868922i	$-0.335187\pi$
$277$	16.4752	0.989897	0.494948	+	0.868922i	$0.335187\pi$
$278$	14.9438	0.896272
$279$	0.300778	0.0180071
$280$	−8.71144	−0.520608
$281$	−12.5757	−0.750205	−0.375103	−	0.926983i	$-0.622393\pi$
$281$	−12.5757	−0.750205	−0.375103	+	0.926983i	$0.622393\pi$
$282$	21.2180	1.26352
$283$	−25.0183	−1.48718	−0.743591	−	0.668634i	$-0.766879\pi$
$283$	−25.0183	−1.48718	−0.743591	+	0.668634i	$0.766879\pi$
$284$	12.8785	0.764197
$285$	9.96773	0.590437
$286$	−20.9485	−1.23871
$287$	7.60802	0.449087
$288$	−0.0867059	−0.00510919
$289$	−13.5329	−0.796052
$290$	19.2609	1.13104
$291$	−18.8405	−1.10445
$292$	2.86681	0.167767
$293$	3.09061	0.180555	0.0902776	−	0.995917i	$-0.471225\pi$
$293$	3.09061	0.180555	0.0902776	+	0.995917i	$0.471225\pi$
$294$	−4.32014	−0.251955
$295$	−9.65918	−0.562379
$296$	7.04587	0.409533
$297$	−25.8387	−1.49932
$298$	5.25295	0.304295
$299$	11.5959	0.670610
$300$	−5.05615	−0.291917
$301$	13.8943	0.800856
$302$	−19.4477	−1.11909
$303$	26.1659	1.50319
$304$	2.06959	0.118699
$305$	−10.7816	−0.617353
$306$	0.161448	0.00922937
$307$	29.1634	1.66445	0.832223	−	0.554442i	$-0.187068\pi$
$307$	29.1634	1.66445	0.832223	+	0.554442i	$0.187068\pi$
$308$	−15.1410	−0.862739
$309$	18.1383	1.03185
$310$	9.78849	0.555949
$311$	−5.57897	−0.316354	−0.158177	−	0.987411i	$-0.550562\pi$
$311$	−5.57897	−0.316354	−0.158177	+	0.987411i	$0.550562\pi$
$312$	−7.29056	−0.412747
$313$	2.04723	0.115716	0.0578581	−	0.998325i	$-0.481573\pi$
$313$	2.04723	0.115716	0.0578581	+	0.998325i	$0.481573\pi$
$314$	−1.41664	−0.0799456
$315$	0.755333	0.0425582
$316$	−10.2935	−0.579053
$317$	20.9604	1.17725	0.588627	−	0.808405i	$-0.299669\pi$
$317$	20.9604	1.17725	0.588627	+	0.808405i	$0.299669\pi$
$318$	8.41428	0.471849
$319$	33.4766	1.87433
$320$	−2.82175	−0.157741
$321$	8.96398	0.500321
$322$	8.38122	0.467067
$323$	−3.85362	−0.214421
$324$	−8.73236	−0.485131
$325$	12.6531	0.701867
$326$	18.9578	1.04998
$327$	11.9223	0.659305
$328$	2.46434	0.136070
$329$	−38.3781	−2.11585
$330$	−23.6208	−1.30028
$331$	−1.44693	−0.0795303	−0.0397652	−	0.999209i	$-0.512661\pi$
$331$	−1.44693	−0.0795303	−0.0397652	+	0.999209i	$0.512661\pi$
$332$	0.795079	0.0436356
$333$	−0.610918	−0.0334781
$334$	−24.0862	−1.31794
$335$	−13.4917	−0.737130
$336$	−5.26942	−0.287471
$337$	−18.7472	−1.02123	−0.510613	−	0.859811i	$-0.670581\pi$
$337$	−18.7472	−1.02123	−0.510613	+	0.859811i	$0.670581\pi$
$338$	5.24474	0.285276
$339$	2.75100	0.149414
$340$	5.25416	0.284947
$341$	17.0130	0.921305
$342$	−0.179446	−0.00970332
$343$	−13.7967	−0.744950
$344$	4.50056	0.242654
$345$	13.0752	0.703944
$346$	−17.6195	−0.947231
$347$	−31.6900	−1.70121	−0.850605	−	0.525805i	$-0.823764\pi$
$347$	−31.6900	−1.70121	−0.850605	+	0.525805i	$0.823764\pi$
$348$	11.6506	0.624540
$349$	−21.1615	−1.13275	−0.566373	−	0.824149i	$-0.691654\pi$
$349$	−21.1615	−1.13275	−0.566373	+	0.824149i	$0.691654\pi$
$350$	9.14531	0.488837
$351$	22.5038	1.20117
$352$	−4.90438	−0.261404
$353$	1.21473	0.0646537	0.0323269	−	0.999477i	$-0.489708\pi$
$353$	1.21473	0.0646537	0.0323269	+	0.999477i	$0.489708\pi$
$354$	−5.84270	−0.310536
$355$	−36.3399	−1.92872
$356$	15.8941	0.842384
$357$	9.81177	0.519294
$358$	14.9754	0.791474
$359$	−21.2652	−1.12233	−0.561166	−	0.827703i	$-0.689647\pi$
$359$	−21.2652	−1.12233	−0.561166	+	0.827703i	$0.689647\pi$
$360$	0.244663	0.0128948
$361$	−14.7168	−0.774568
$362$	−15.6659	−0.823382
$363$	−22.2792	−1.16935
$364$	13.1868	0.691177
$365$	−8.08942	−0.423420
$366$	−6.52164	−0.340891
$367$	−26.6271	−1.38992	−0.694961	−	0.719048i	$-0.744578\pi$
$367$	−26.6271	−1.38992	−0.694961	+	0.719048i	$0.744578\pi$
$368$	2.71479	0.141518
$369$	−0.213673	−0.0111234
$370$	−19.8817	−1.03360
$371$	−15.2193	−0.790148
$372$	5.92092	0.306985
$373$	−25.0452	−1.29679	−0.648396	−	0.761303i	$-0.724560\pi$
$373$	−25.0452	−1.29679	−0.648396	+	0.761303i	$0.724560\pi$
$374$	9.13204	0.472207
$375$	−9.81417	−0.506802
$376$	−12.4312	−0.641090
$377$	−29.1559	−1.50161
$378$	16.2652	0.836590
$379$	34.2529	1.75945	0.879727	−	0.475479i	$-0.157725\pi$
$379$	34.2529	1.75945	0.879727	+	0.475479i	$0.157725\pi$
$380$	−5.83988	−0.299580
$381$	7.30021	0.374001
$382$	−12.9141	−0.660742
$383$	12.5747	0.642539	0.321269	−	0.946988i	$-0.395890\pi$
$383$	12.5747	0.642539	0.321269	+	0.946988i	$0.395890\pi$
$384$	−1.70684	−0.0871017
$385$	42.7242	2.17743
$386$	−5.68924	−0.289575
$387$	−0.390225	−0.0198363
$388$	11.0382	0.560381
$389$	11.7727	0.596900	0.298450	−	0.954425i	$-0.403530\pi$
$389$	11.7727	0.596900	0.298450	+	0.954425i	$0.403530\pi$
$390$	20.5722	1.04171
$391$	−5.05499	−0.255642
$392$	2.53108	0.127839
$393$	19.3670	0.976937
$394$	17.1411	0.863555
$395$	29.0456	1.46144
$396$	0.425238	0.0213690
$397$	−9.59148	−0.481382	−0.240691	−	0.970602i	$-0.577374\pi$
$397$	−9.59148	−0.481382	−0.240691	+	0.970602i	$0.577374\pi$
$398$	6.80696	0.341202
$399$	−10.9056	−0.545961
$400$	2.96229	0.148114
$401$	12.9004	0.644216	0.322108	−	0.946703i	$-0.395609\pi$
$401$	12.9004	0.644216	0.322108	+	0.946703i	$0.395609\pi$
$402$	−8.16093	−0.407030
$403$	−14.8172	−0.738097
$404$	−15.3300	−0.762698
$405$	24.6406	1.22440
$406$	−21.0731	−1.04584
$407$	−34.5556	−1.71286
$408$	3.17816	0.157343
$409$	−33.3682	−1.64995	−0.824975	−	0.565169i	$-0.808811\pi$
$409$	−33.3682	−1.64995	−0.824975	+	0.565169i	$0.808811\pi$
$410$	−6.95376	−0.343422
$411$	21.0640	1.03901
$412$	−10.6269	−0.523548
$413$	10.5680	0.520017
$414$	−0.235388	−0.0115687
$415$	−2.24352	−0.110130
$416$	4.27139	0.209422
$417$	−25.5067	−1.24907
$418$	−10.1501	−0.496456
$419$	−37.9374	−1.85336	−0.926682	−	0.375847i	$-0.877352\pi$
$419$	−37.9374	−1.85336	−0.926682	+	0.375847i	$0.877352\pi$
$420$	14.8690	0.725533
$421$	−20.4084	−0.994643	−0.497321	−	0.867566i	$-0.665683\pi$
$421$	−20.4084	−0.994643	−0.497321	+	0.867566i	$0.665683\pi$
$422$	−16.0737	−0.782455
$423$	1.07786	0.0524072
$424$	−4.92975	−0.239410
$425$	−5.51584	−0.267557
$426$	−21.9815	−1.06501
$427$	11.7960	0.570849
$428$	−5.25181	−0.253856
$429$	35.7557	1.72630
$430$	−12.6995	−0.612423
$431$	0.480525	0.0231461	0.0115730	−	0.999933i	$-0.496316\pi$
$431$	0.480525	0.0231461	0.0115730	+	0.999933i	$0.496316\pi$
$432$	5.26851	0.253481
$433$	31.0825	1.49373	0.746865	−	0.664976i	$-0.231558\pi$
$433$	31.0825	1.49373	0.746865	+	0.664976i	$0.231558\pi$
$434$	−10.7095	−0.514071
$435$	−32.8752	−1.57625
$436$	−6.98503	−0.334522
$437$	5.61851	0.268770
$438$	−4.89317	−0.233805
$439$	−26.0470	−1.24315	−0.621577	−	0.783353i	$-0.713508\pi$
$439$	−26.0470	−1.24315	−0.621577	+	0.783353i	$0.713508\pi$
$440$	13.8389	0.659745
$441$	−0.219459	−0.0104504
$442$	−7.95340	−0.378305
$443$	0.328188	0.0155927	0.00779634	−	0.999970i	$-0.497518\pi$
$443$	0.328188	0.0155927	0.00779634	+	0.999970i	$0.497518\pi$
$444$	−12.0262	−0.570736
$445$	−44.8491	−2.12605
$446$	−27.7619	−1.31456
$447$	−8.96593	−0.424074
$448$	3.08724	0.145859
$449$	4.53151	0.213855	0.106928	−	0.994267i	$-0.465899\pi$
$449$	4.53151	0.213855	0.106928	+	0.994267i	$0.465899\pi$
$450$	−0.256848	−0.0121079
$451$	−12.0860	−0.569110
$452$	−1.61175	−0.0758103
$453$	33.1941	1.55959
$454$	15.6189	0.733032
$455$	−37.2099	−1.74443
$456$	−3.53246	−0.165423
$457$	−10.6555	−0.498444	−0.249222	−	0.968446i	$-0.580175\pi$
$457$	−10.6555	−0.498444	−0.249222	+	0.968446i	$0.580175\pi$
$458$	−23.9025	−1.11689
$459$	−9.81005	−0.457894
$460$	−7.66047	−0.357171
$461$	29.2492	1.36227	0.681136	−	0.732157i	$-0.261486\pi$
$461$	29.2492	1.36227	0.681136	+	0.732157i	$0.261486\pi$
$462$	25.8432	1.20234
$463$	−17.0576	−0.792732	−0.396366	−	0.918093i	$-0.629729\pi$
$463$	−17.0576	−0.792732	−0.396366	+	0.918093i	$0.629729\pi$
$464$	−6.82587	−0.316883
$465$	−16.7074	−0.774786
$466$	−25.1744	−1.16618
$467$	−25.3357	−1.17240	−0.586199	−	0.810167i	$-0.699376\pi$
$467$	−25.3357	−1.17240	−0.586199	+	0.810167i	$0.699376\pi$
$468$	−0.370354	−0.0171196
$469$	14.7611	0.681604
$470$	35.0778	1.61802
$471$	2.41797	0.111414
$472$	3.42311	0.157562
$473$	−22.0724	−1.01489
$474$	17.5693	0.806984
$475$	6.13073	0.281297
$476$	−5.74851	−0.263482
$477$	0.427438	0.0195710
$478$	8.48723	0.388197
$479$	19.1424	0.874638	0.437319	−	0.899306i	$-0.355928\pi$
$479$	19.1424	0.874638	0.437319	+	0.899306i	$0.355928\pi$
$480$	4.81627	0.219832
$481$	30.0956	1.37224
$482$	−15.9876	−0.728213
$483$	−14.3054	−0.650918
$484$	13.0529	0.593314
$485$	−31.1472	−1.41432
$486$	−0.900789	−0.0408606
$487$	−1.20359	−0.0545398	−0.0272699	−	0.999628i	$-0.508681\pi$
$487$	−1.20359	−0.0545398	−0.0272699	+	0.999628i	$0.508681\pi$
$488$	3.82089	0.172964
$489$	−32.3579	−1.46328
$490$	−7.14207	−0.322646
$491$	32.5980	1.47113	0.735565	−	0.677455i	$-0.236917\pi$
$491$	32.5980	1.47113	0.735565	+	0.677455i	$0.236917\pi$
$492$	−4.20623	−0.189631
$493$	12.7099	0.572425
$494$	8.84003	0.397732
$495$	−1.19992	−0.0539323
$496$	−3.46894	−0.155760
$497$	39.7590	1.78343
$498$	−1.35707	−0.0608118
$499$	10.0147	0.448320	0.224160	−	0.974552i	$-0.428036\pi$
$499$	10.0147	0.448320	0.224160	+	0.974552i	$0.428036\pi$
$500$	5.74992	0.257144
$501$	41.1112	1.83672
$502$	−5.52678	−0.246672
$503$	9.21479	0.410867	0.205434	−	0.978671i	$-0.434140\pi$
$503$	9.21479	0.410867	0.205434	+	0.978671i	$0.434140\pi$
$504$	−0.267682	−0.0119235
$505$	43.2576	1.92494
$506$	−13.3144	−0.591895
$507$	−8.95192	−0.397569
$508$	−4.27704	−0.189763
$509$	27.8474	1.23431	0.617157	−	0.786840i	$-0.288284\pi$
$509$	27.8474	1.23431	0.617157	+	0.786840i	$0.288284\pi$
$510$	−8.96799	−0.397109
$511$	8.85053	0.391524
$512$	1.00000	0.0441942
$513$	10.9037	0.481409
$514$	17.0469	0.751905
$515$	29.9864	1.32136
$516$	−7.68173	−0.338169
$517$	60.9672	2.68134
$518$	21.7523	0.955742
$519$	30.0737	1.32009
$520$	−12.0528	−0.528550
$521$	19.2339	0.842652	0.421326	−	0.906909i	$-0.361565\pi$
$521$	19.2339	0.842652	0.421326	+	0.906909i	$0.361565\pi$
$522$	0.591843	0.0259043
$523$	12.9035	0.564232	0.282116	−	0.959380i	$-0.408964\pi$
$523$	12.9035	0.564232	0.282116	+	0.959380i	$0.408964\pi$
$524$	−11.3467	−0.495684
$525$	−15.6096	−0.681257
$526$	−13.9641	−0.608862
$527$	6.45923	0.281369
$528$	8.37097	0.364300
$529$	−15.6299	−0.679561
$530$	13.9105	0.604235
$531$	−0.296804	−0.0128802
$532$	6.38934	0.277013
$533$	10.5261	0.455938
$534$	−27.1286	−1.17397
$535$	14.8193	0.640694
$536$	4.78132	0.206521
$537$	−25.5606	−1.10302
$538$	4.58325	0.197598
$539$	−12.4133	−0.534681
$540$	−14.8664	−0.639749
$541$	12.6438	0.543598	0.271799	−	0.962354i	$-0.412381\pi$
$541$	12.6438	0.543598	0.271799	+	0.962354i	$0.412381\pi$
$542$	19.4977	0.837500
$543$	26.7392	1.14749
$544$	−1.86202	−0.0798334
$545$	19.7100	0.844284
$546$	−22.5077	−0.963243
$547$	−12.6650	−0.541517	−0.270759	−	0.962647i	$-0.587275\pi$
$547$	−12.6650	−0.541517	−0.270759	+	0.962647i	$0.587275\pi$
$548$	−12.3410	−0.527179
$549$	−0.331294	−0.0141393
$550$	−14.5282	−0.619484
$551$	−14.1268	−0.601821
$552$	−4.63371	−0.197224
$553$	−31.7785	−1.35136
$554$	16.4752	0.699963
$555$	33.9348	1.44045
$556$	14.9438	0.633760
$557$	−37.9663	−1.60868	−0.804341	−	0.594167i	$-0.797482\pi$
$557$	−37.9663	−1.60868	−0.804341	+	0.594167i	$0.797482\pi$
$558$	0.300778	0.0127329
$559$	19.2236	0.813073
$560$	−8.71144	−0.368126
$561$	−15.5869	−0.658080
$562$	−12.5757	−0.530475
$563$	−36.9059	−1.55540	−0.777698	−	0.628638i	$-0.783613\pi$
$563$	−36.9059	−1.55540	−0.777698	+	0.628638i	$0.783613\pi$
$564$	21.2180	0.893440
$565$	4.54796	0.191334
$566$	−25.0183	−1.05160
$567$	−26.9589	−1.13217
$568$	12.8785	0.540369
$569$	34.9042	1.46326	0.731630	−	0.681702i	$-0.238760\pi$
$569$	34.9042	1.46326	0.731630	+	0.681702i	$0.238760\pi$
$570$	9.96773	0.417502
$571$	41.5873	1.74037	0.870187	−	0.492722i	$-0.163998\pi$
$571$	41.5873	1.74037	0.870187	+	0.492722i	$0.163998\pi$
$572$	−20.9485	−0.875900
$573$	22.0422	0.920828
$574$	7.60802	0.317553
$575$	8.04200	0.335374
$576$	−0.0867059	−0.00361274
$577$	13.8486	0.576524	0.288262	−	0.957552i	$-0.406923\pi$
$577$	13.8486	0.576524	0.288262	+	0.957552i	$0.406923\pi$
$578$	−13.5329	−0.562894
$579$	9.71061	0.403559
$580$	19.2609	0.799766
$581$	2.45460	0.101834
$582$	−18.8405	−0.780962
$583$	24.1773	1.00132
$584$	2.86681	0.118629
$585$	1.04505	0.0432074
$586$	3.09061	0.127672
$587$	−4.36473	−0.180152	−0.0900759	−	0.995935i	$-0.528711\pi$
$587$	−4.36473	−0.180152	−0.0900759	+	0.995935i	$0.528711\pi$
$588$	−4.32014	−0.178159
$589$	−7.17930	−0.295818
$590$	−9.65918	−0.397662
$591$	−29.2570	−1.20347
$592$	7.04587	0.289583
$593$	−39.7743	−1.63333	−0.816667	−	0.577109i	$-0.804181\pi$
$593$	−39.7743	−1.63333	−0.816667	+	0.577109i	$0.804181\pi$
$594$	−25.8387	−1.06018
$595$	16.2209	0.664991
$596$	5.25295	0.215169
$597$	−11.6184	−0.475508
$598$	11.5959	0.474193
$599$	22.1781	0.906171	0.453085	−	0.891467i	$-0.350323\pi$
$599$	22.1781	0.906171	0.453085	+	0.891467i	$0.350323\pi$
$600$	−5.05615	−0.206416
$601$	−4.96324	−0.202455	−0.101227	−	0.994863i	$-0.532277\pi$
$601$	−4.96324	−0.202455	−0.101227	+	0.994863i	$0.532277\pi$
$602$	13.8943	0.566291
$603$	−0.414568	−0.0168825
$604$	−19.4477	−0.791316
$605$	−36.8321	−1.49744
$606$	26.1659	1.06292
$607$	−42.1484	−1.71075	−0.855376	−	0.518007i	$-0.826674\pi$
$607$	−42.1484	−1.71075	−0.855376	+	0.518007i	$0.826674\pi$
$608$	2.06959	0.0839331
$609$	35.9684	1.45751
$610$	−10.7816	−0.436535
$611$	−53.0984	−2.14813
$612$	0.161448	0.00652615
$613$	31.5622	1.27478	0.637392	−	0.770540i	$-0.280013\pi$
$613$	31.5622	1.27478	0.637392	+	0.770540i	$0.280013\pi$
$614$	29.1634	1.17694
$615$	11.8689	0.478602
$616$	−15.1410	−0.610049
$617$	−45.7995	−1.84382	−0.921910	−	0.387405i	$-0.873372\pi$
$617$	−45.7995	−1.84382	−0.921910	+	0.387405i	$0.873372\pi$
$618$	18.1383	0.729630
$619$	−39.2693	−1.57837	−0.789184	−	0.614157i	$-0.789496\pi$
$619$	−39.2693	−1.57837	−0.789184	+	0.614157i	$0.789496\pi$
$620$	9.78849	0.393115
$621$	14.3029	0.573955
$622$	−5.57897	−0.223696
$623$	49.0688	1.96590
$624$	−7.29056	−0.291856
$625$	−31.0363	−1.24145
$626$	2.04723	0.0818238
$627$	17.3245	0.691874
$628$	−1.41664	−0.0565300
$629$	−13.1195	−0.523110
$630$	0.755333	0.0300932
$631$	−31.5596	−1.25637	−0.628185	−	0.778064i	$-0.716202\pi$
$631$	−31.5596	−1.25637	−0.628185	+	0.778064i	$0.716202\pi$
$632$	−10.2935	−0.409452
$633$	27.4352	1.09045
$634$	20.9604	0.832445
$635$	12.0687	0.478934
$636$	8.41428	0.333648
$637$	10.8112	0.428356
$638$	33.4766	1.32535
$639$	−1.11664	−0.0441736
$640$	−2.82175	−0.111540
$641$	8.93197	0.352791	0.176396	−	0.984319i	$-0.443556\pi$
$641$	8.93197	0.352791	0.176396	+	0.984319i	$0.443556\pi$
$642$	8.96398	0.353780
$643$	7.75384	0.305782	0.152891	−	0.988243i	$-0.451142\pi$
$643$	7.75384	0.305782	0.152891	+	0.988243i	$0.451142\pi$
$644$	8.38122	0.330266
$645$	21.6759	0.853489
$646$	−3.85362	−0.151619
$647$	−38.3324	−1.50700	−0.753500	−	0.657447i	$-0.771636\pi$
$647$	−38.3324	−1.50700	−0.753500	+	0.657447i	$0.771636\pi$
$648$	−8.73236	−0.343040
$649$	−16.7882	−0.658996
$650$	12.6531	0.496295
$651$	18.2793	0.716423
$652$	18.9578	0.742445
$653$	2.42412	0.0948631	0.0474315	−	0.998874i	$-0.484896\pi$
$653$	2.42412	0.0948631	0.0474315	+	0.998874i	$0.484896\pi$
$654$	11.9223	0.466199
$655$	32.0177	1.25103
$656$	2.46434	0.0962163
$657$	−0.248569	−0.00969760
$658$	−38.3781	−1.49614
$659$	−38.5775	−1.50277	−0.751383	−	0.659867i	$-0.770613\pi$
$659$	−38.5775	−1.50277	−0.751383	+	0.659867i	$0.770613\pi$
$660$	−23.6208	−0.919439
$661$	−9.75974	−0.379610	−0.189805	−	0.981822i	$-0.560786\pi$
$661$	−9.75974	−0.379610	−0.189805	+	0.981822i	$0.560786\pi$
$662$	−1.44693	−0.0562364
$663$	13.5752	0.527216
$664$	0.795079	0.0308550
$665$	−18.0291	−0.699140
$666$	−0.610918	−0.0236726
$667$	−18.5308	−0.717516
$668$	−24.0862	−0.931924
$669$	47.3850	1.83201
$670$	−13.4917	−0.521230
$671$	−18.7391	−0.723414
$672$	−5.26942	−0.203272
$673$	−13.3783	−0.515694	−0.257847	−	0.966186i	$-0.583013\pi$
$673$	−13.3783	−0.515694	−0.257847	+	0.966186i	$0.583013\pi$
$674$	−18.7472	−0.722115
$675$	15.6068	0.600707
$676$	5.24474	0.201721
$677$	−36.4979	−1.40273	−0.701365	−	0.712803i	$-0.747426\pi$
$677$	−36.4979	−1.40273	−0.701365	+	0.712803i	$0.747426\pi$
$678$	2.75100	0.105651
$679$	34.0777	1.30778
$680$	5.25416	0.201488
$681$	−26.6590	−1.02157
$682$	17.0130	0.651461
$683$	−13.8067	−0.528300	−0.264150	−	0.964482i	$-0.585091\pi$
$683$	−13.8067	−0.528300	−0.264150	+	0.964482i	$0.585091\pi$
$684$	−0.179446	−0.00686129
$685$	34.8231	1.33052
$686$	−13.7967	−0.526759
$687$	40.7977	1.55653
$688$	4.50056	0.171582
$689$	−21.0569	−0.802202
$690$	13.0752	0.497763
$691$	40.2612	1.53161	0.765804	−	0.643075i	$-0.222341\pi$
$691$	40.2612	1.53161	0.765804	+	0.643075i	$0.222341\pi$
$692$	−17.6195	−0.669794
$693$	1.31281	0.0498697
$694$	−31.6900	−1.20294
$695$	−42.1678	−1.59952
$696$	11.6506	0.441617
$697$	−4.58865	−0.173807
$698$	−21.1615	−0.800973
$699$	42.9686	1.62522
$700$	9.14531	0.345660
$701$	4.17150	0.157556	0.0787778	−	0.996892i	$-0.474898\pi$
$701$	4.17150	0.157556	0.0787778	+	0.996892i	$0.474898\pi$
$702$	22.5038	0.849352
$703$	14.5821	0.549974
$704$	−4.90438	−0.184841
$705$	−59.8720	−2.25491
$706$	1.21473	0.0457171
$707$	−47.3276	−1.77994
$708$	−5.84270	−0.219582
$709$	−26.6999	−1.00274	−0.501368	−	0.865234i	$-0.667170\pi$
$709$	−26.6999	−1.00274	−0.501368	+	0.865234i	$0.667170\pi$
$710$	−36.3399	−1.36381
$711$	0.892505	0.0334715
$712$	15.8941	0.595655
$713$	−9.41745	−0.352686
$714$	9.81177	0.367196
$715$	59.1114	2.21064
$716$	14.9754	0.559657
$717$	−14.4863	−0.541002
$718$	−21.2652	−0.793609
$719$	38.2674	1.42713	0.713567	−	0.700587i	$-0.247079\pi$
$719$	38.2674	1.42713	0.713567	+	0.700587i	$0.247079\pi$
$720$	0.244663	0.00911803
$721$	−32.8077	−1.22182
$722$	−14.7168	−0.547702
$723$	27.2882	1.01486
$724$	−15.6659	−0.582219
$725$	−20.2202	−0.750959
$726$	−22.2792	−0.826858
$727$	5.20464	0.193029	0.0965147	−	0.995332i	$-0.469231\pi$
$727$	5.20464	0.193029	0.0965147	+	0.995332i	$0.469231\pi$
$728$	13.1868	0.488736
$729$	27.7346	1.02721
$730$	−8.08942	−0.299403
$731$	−8.38013	−0.309950
$732$	−6.52164	−0.241047
$733$	−46.1205	−1.70350	−0.851749	−	0.523949i	$-0.824458\pi$
$733$	−46.1205	−1.70350	−0.851749	+	0.523949i	$0.824458\pi$
$734$	−26.6271	−0.982823
$735$	12.1904	0.449648
$736$	2.71479	0.100069
$737$	−23.4494	−0.863769
$738$	−0.213673	−0.00786540
$739$	25.0390	0.921074	0.460537	−	0.887641i	$-0.347657\pi$
$739$	25.0390	0.921074	0.460537	+	0.887641i	$0.347657\pi$
$740$	−19.8817	−0.730866
$741$	−15.0885	−0.554290
$742$	−15.2193	−0.558719
$743$	12.9154	0.473819	0.236909	−	0.971532i	$-0.423866\pi$
$743$	12.9154	0.473819	0.236909	+	0.971532i	$0.423866\pi$
$744$	5.92092	0.217071
$745$	−14.8225	−0.543055
$746$	−25.0452	−0.916970
$747$	−0.0689380	−0.00252231
$748$	9.13204	0.333900
$749$	−16.2136	−0.592432
$750$	−9.81417	−0.358363
$751$	22.1175	0.807078	0.403539	−	0.914962i	$-0.367780\pi$
$751$	22.1175	0.807078	0.403539	+	0.914962i	$0.367780\pi$
$752$	−12.4312	−0.453319
$753$	9.43331	0.343769
$754$	−29.1559	−1.06180
$755$	54.8766	1.99716
$756$	16.2652	0.591558
$757$	−11.0278	−0.400812	−0.200406	−	0.979713i	$-0.564226\pi$
$757$	−11.0278	−0.400812	−0.200406	+	0.979713i	$0.564226\pi$
$758$	34.2529	1.24412
$759$	22.7254	0.824881
$760$	−5.83988	−0.211835
$761$	−12.4649	−0.451854	−0.225927	−	0.974144i	$-0.572541\pi$
$761$	−12.4649	−0.451854	−0.225927	+	0.974144i	$0.572541\pi$
$762$	7.30021	0.264459
$763$	−21.5645	−0.780687
$764$	−12.9141	−0.467215
$765$	−0.455566	−0.0164710
$766$	12.5747	0.454344
$767$	14.6214	0.527950
$768$	−1.70684	−0.0615902
$769$	49.1734	1.77324	0.886619	−	0.462500i	$-0.153047\pi$
$769$	49.1734	1.77324	0.886619	+	0.462500i	$0.153047\pi$
$770$	42.7242	1.53967
$771$	−29.0962	−1.04787
$772$	−5.68924	−0.204760
$773$	−39.6495	−1.42610	−0.713048	−	0.701116i	$-0.752686\pi$
$773$	−39.6495	−1.42610	−0.713048	+	0.701116i	$0.752686\pi$
$774$	−0.390225	−0.0140264
$775$	−10.2760	−0.369125
$776$	11.0382	0.396249
$777$	−37.1277	−1.33195
$778$	11.7727	0.422072
$779$	5.10018	0.182733
$780$	20.5722	0.736602
$781$	−63.1609	−2.26007
$782$	−5.05499	−0.180766
$783$	−35.9621	−1.28518
$784$	2.53108	0.0903956
$785$	3.99740	0.142673
$786$	19.3670	0.690799
$787$	22.2282	0.792348	0.396174	−	0.918175i	$-0.370338\pi$
$787$	22.2282	0.792348	0.396174	+	0.918175i	$0.370338\pi$
$788$	17.1411	0.610626
$789$	23.8344	0.848527
$790$	29.0456	1.03340
$791$	−4.97587	−0.176921
$792$	0.425238	0.0151102
$793$	16.3205	0.579558
$794$	−9.59148	−0.340389
$795$	−23.7430	−0.842078
$796$	6.80696	0.241266
$797$	−20.8894	−0.739940	−0.369970	−	0.929044i	$-0.620632\pi$
$797$	−20.8894	−0.739940	−0.369970	+	0.929044i	$0.620632\pi$
$798$	−10.9056	−0.386053
$799$	23.1471	0.818886
$800$	2.96229	0.104733
$801$	−1.37811	−0.0486931
$802$	12.9004	0.455530
$803$	−14.0599	−0.496163
$804$	−8.16093	−0.287814
$805$	−23.6497	−0.833544
$806$	−14.8172	−0.521913
$807$	−7.82287	−0.275378
$808$	−15.3300	−0.539309
$809$	6.45324	0.226884	0.113442	−	0.993545i	$-0.463812\pi$
$809$	6.45324	0.226884	0.113442	+	0.993545i	$0.463812\pi$
$810$	24.6406	0.865782
$811$	25.5681	0.897819	0.448909	−	0.893577i	$-0.351813\pi$
$811$	25.5681	0.897819	0.448909	+	0.893577i	$0.351813\pi$
$812$	−21.0731	−0.739522
$813$	−33.2795	−1.16716
$814$	−34.5556	−1.21117
$815$	−53.4943	−1.87382
$816$	3.17816	0.111258
$817$	9.31433	0.325867
$818$	−33.3682	−1.16669
$819$	−1.14337	−0.0399527
$820$	−6.95376	−0.242836
$821$	22.3784	0.781011	0.390506	−	0.920601i	$-0.372300\pi$
$821$	22.3784	0.781011	0.390506	+	0.920601i	$0.372300\pi$
$822$	21.0640	0.734691
$823$	−1.18403	−0.0412726	−0.0206363	−	0.999787i	$-0.506569\pi$
$823$	−1.18403	−0.0412726	−0.0206363	+	0.999787i	$0.506569\pi$
$824$	−10.6269	−0.370204
$825$	24.7972	0.863329
$826$	10.5680	0.367707
$827$	9.64076	0.335242	0.167621	−	0.985851i	$-0.446391\pi$
$827$	9.64076	0.335242	0.167621	+	0.985851i	$0.446391\pi$
$828$	−0.235388	−0.00818031
$829$	9.86036	0.342465	0.171232	−	0.985231i	$-0.445225\pi$
$829$	9.86036	0.342465	0.171232	+	0.985231i	$0.445225\pi$
$830$	−2.24352	−0.0778736
$831$	−28.1204	−0.975487
$832$	4.27139	0.148084
$833$	−4.71291	−0.163293
$834$	−25.5067	−0.883225
$835$	67.9653	2.35204
$836$	−10.1501	−0.351047
$837$	−18.2761	−0.631716
$838$	−37.9374	−1.31053
$839$	50.3599	1.73862	0.869308	−	0.494271i	$-0.164565\pi$
$839$	50.3599	1.73862	0.869308	+	0.494271i	$0.164565\pi$
$840$	14.8690	0.513030
$841$	17.5925	0.606637
$842$	−20.4084	−0.703318
$843$	21.4647	0.739285
$844$	−16.0737	−0.553279
$845$	−14.7994	−0.509114
$846$	1.07786	0.0370575
$847$	40.2975	1.38464
$848$	−4.92975	−0.169288
$849$	42.7022	1.46553
$850$	−5.51584	−0.189192
$851$	19.1281	0.655702
$852$	−21.9815	−0.753072
$853$	−27.8290	−0.952846	−0.476423	−	0.879216i	$-0.658067\pi$
$853$	−27.8290	−0.952846	−0.476423	+	0.879216i	$0.658067\pi$
$854$	11.7960	0.403652
$855$	0.506352	0.0173169
$856$	−5.25181	−0.179503
$857$	13.3452	0.455865	0.227932	−	0.973677i	$-0.426803\pi$
$857$	13.3452	0.455865	0.227932	+	0.973677i	$0.426803\pi$
$858$	35.7557	1.22068
$859$	−36.0157	−1.22884	−0.614420	−	0.788979i	$-0.710610\pi$
$859$	−36.0157	−1.22884	−0.614420	+	0.788979i	$0.710610\pi$
$860$	−12.6995	−0.433048
$861$	−12.9857	−0.442550
$862$	0.480525	0.0163668
$863$	41.5617	1.41478	0.707389	−	0.706824i	$-0.249873\pi$
$863$	41.5617	1.41478	0.707389	+	0.706824i	$0.249873\pi$
$864$	5.26851	0.179238
$865$	49.7179	1.69046
$866$	31.0825	1.05623
$867$	23.0984	0.784464
$868$	−10.7095	−0.363503
$869$	50.4831	1.71252
$870$	−32.8752	−1.11458
$871$	20.4229	0.692002
$872$	−6.98503	−0.236543
$873$	−0.957079	−0.0323922
$874$	5.61851	0.190049
$875$	17.7514	0.600107
$876$	−4.89317	−0.165325
$877$	6.46760	0.218395	0.109198	−	0.994020i	$-0.465172\pi$
$877$	6.46760	0.218395	0.109198	+	0.994020i	$0.465172\pi$
$878$	−26.0470	−0.879043
$879$	−5.27517	−0.177927
$880$	13.8389	0.466510
$881$	−19.1361	−0.644711	−0.322355	−	0.946619i	$-0.604475\pi$
$881$	−19.1361	−0.644711	−0.322355	+	0.946619i	$0.604475\pi$
$882$	−0.219459	−0.00738958
$883$	15.0470	0.506372	0.253186	−	0.967418i	$-0.418522\pi$
$883$	15.0470	0.506372	0.253186	+	0.967418i	$0.418522\pi$
$884$	−7.95340	−0.267502
$885$	16.4867	0.554193
$886$	0.328188	0.0110257
$887$	−48.1976	−1.61832	−0.809159	−	0.587590i	$-0.800077\pi$
$887$	−48.1976	−1.61832	−0.809159	+	0.587590i	$0.800077\pi$
$888$	−12.0262	−0.403571
$889$	−13.2043	−0.442857
$890$	−44.8491	−1.50335
$891$	42.8268	1.43475
$892$	−27.7619	−0.929536
$893$	−25.7275	−0.860938
$894$	−8.96593	−0.299866
$895$	−42.2568	−1.41249
$896$	3.08724	0.103138
$897$	−19.7924	−0.660847
$898$	4.53151	0.151218
$899$	23.6785	0.789723
$900$	−0.256848	−0.00856159
$901$	9.17928	0.305806
$902$	−12.0860	−0.402421
$903$	−23.7154	−0.789198
$904$	−1.61175	−0.0536060
$905$	44.2053	1.46943
$906$	33.1941	1.10280
$907$	−5.11398	−0.169807	−0.0849035	−	0.996389i	$-0.527058\pi$
$907$	−5.11398	−0.169807	−0.0849035	+	0.996389i	$0.527058\pi$
$908$	15.6189	0.518332
$909$	1.32920	0.0440869
$910$	−37.2099	−1.23350
$911$	23.3633	0.774060	0.387030	−	0.922067i	$-0.373501\pi$
$911$	23.3633	0.774060	0.387030	+	0.922067i	$0.373501\pi$
$912$	−3.53246	−0.116971
$913$	−3.89937	−0.129050
$914$	−10.6555	−0.352453
$915$	18.4025	0.608366
$916$	−23.9025	−0.789761
$917$	−35.0301	−1.15680
$918$	−9.81005	−0.323780
$919$	19.1538	0.631827	0.315914	−	0.948788i	$-0.397689\pi$
$919$	19.1538	0.631827	0.315914	+	0.948788i	$0.397689\pi$
$920$	−7.66047	−0.252558
$921$	−49.7773	−1.64022
$922$	29.2492	0.963272
$923$	55.0089	1.81064
$924$	25.8432	0.850180
$925$	20.8719	0.686264
$926$	−17.0576	−0.560546
$927$	0.921411	0.0302631
$928$	−6.82587	−0.224070
$929$	14.4439	0.473890	0.236945	−	0.971523i	$-0.423854\pi$
$929$	14.4439	0.473890	0.236945	+	0.971523i	$0.423854\pi$
$930$	−16.7074	−0.547856
$931$	5.23830	0.171678
$932$	−25.1744	−0.824615
$933$	9.52239	0.311749
$934$	−25.3357	−0.829010
$935$	−25.7684	−0.842715
$936$	−0.370354	−0.0121054
$937$	7.51504	0.245506	0.122753	−	0.992437i	$-0.460828\pi$
$937$	7.51504	0.245506	0.122753	+	0.992437i	$0.460828\pi$
$938$	14.7611	0.481967
$939$	−3.49429	−0.114032
$940$	35.0778	1.14411
$941$	8.05139	0.262468	0.131234	−	0.991351i	$-0.458106\pi$
$941$	8.05139	0.262468	0.131234	+	0.991351i	$0.458106\pi$
$942$	2.41797	0.0787818
$943$	6.69017	0.217862
$944$	3.42311	0.111413
$945$	−45.8963	−1.49301
$946$	−22.0724	−0.717637
$947$	−0.885851	−0.0287863	−0.0143932	−	0.999896i	$-0.504582\pi$
$947$	−0.885851	−0.0287863	−0.0143932	+	0.999896i	$0.504582\pi$
$948$	17.5693	0.570624
$949$	12.2452	0.397497
$950$	6.13073	0.198907
$951$	−35.7760	−1.16012
$952$	−5.74851	−0.186310
$953$	10.9699	0.355349	0.177674	−	0.984089i	$-0.443143\pi$
$953$	10.9699	0.355349	0.177674	+	0.984089i	$0.443143\pi$
$954$	0.427438	0.0138388
$955$	36.4403	1.17918
$956$	8.48723	0.274497
$957$	−57.1392	−1.84705
$958$	19.1424	0.618463
$959$	−38.0995	−1.23030
$960$	4.81627	0.155445
$961$	−18.9665	−0.611821
$962$	30.0956	0.970322
$963$	0.455362	0.0146739
$964$	−15.9876	−0.514924
$965$	16.0536	0.516785
$966$	−14.3054	−0.460268
$967$	−27.1806	−0.874069	−0.437034	−	0.899445i	$-0.643971\pi$
$967$	−27.1806	−0.874069	−0.437034	+	0.899445i	$0.643971\pi$
$968$	13.0529	0.419536
$969$	6.57751	0.211300
$970$	−31.1472	−1.00007
$971$	29.9932	0.962528	0.481264	−	0.876576i	$-0.340178\pi$
$971$	29.9932	0.962528	0.481264	+	0.876576i	$0.340178\pi$
$972$	−0.900789	−0.0288928
$973$	46.1353	1.47903
$974$	−1.20359	−0.0385654
$975$	−21.5967	−0.691650
$976$	3.82089	0.122304
$977$	57.8715	1.85147	0.925737	−	0.378168i	$-0.123446\pi$
$977$	57.8715	1.85147	0.925737	+	0.378168i	$0.123446\pi$
$978$	−32.3579	−1.03469
$979$	−77.9505	−2.49131
$980$	−7.14207	−0.228145
$981$	0.605643	0.0193367
$982$	32.5980	1.04025
$983$	27.7521	0.885155	0.442578	−	0.896730i	$-0.354064\pi$
$983$	27.7521	0.885155	0.442578	+	0.896730i	$0.354064\pi$
$984$	−4.20623	−0.134090
$985$	−48.3679	−1.54113
$986$	12.7099	0.404765
$987$	65.5052	2.08505
$988$	8.84003	0.281239
$989$	12.2181	0.388513
$990$	−1.19992	−0.0381359
$991$	18.4073	0.584727	0.292364	−	0.956307i	$-0.405558\pi$
$991$	18.4073	0.584727	0.292364	+	0.956307i	$0.405558\pi$
$992$	−3.46894	−0.110139
$993$	2.46967	0.0783726
$994$	39.7590	1.26108
$995$	−19.2076	−0.608920
$996$	−1.35707	−0.0430004
$997$	6.67212	0.211308	0.105654	−	0.994403i	$-0.466306\pi$
$997$	6.67212	0.211308	0.105654	+	0.994403i	$0.466306\pi$
$998$	10.0147	0.317010
$999$	37.1212	1.17446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.20	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.20	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.70684 q^{3} +1.00000 q^{4} -2.82175 q^{5} -1.70684 q^{6} +3.08724 q^{7} +1.00000 q^{8} -0.0867059 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.70684 q^{3} +1.00000 q^{4} -2.82175 q^{5} -1.70684 q^{6} +3.08724 q^{7} +1.00000 q^{8} -0.0867059 q^{9} -2.82175 q^{10} -4.90438 q^{11} -1.70684 q^{12} +4.27139 q^{13} +3.08724 q^{14} +4.81627 q^{15} +1.00000 q^{16} -1.86202 q^{17} -0.0867059 q^{18} +2.06959 q^{19} -2.82175 q^{20} -5.26942 q^{21} -4.90438 q^{22} +2.71479 q^{23} -1.70684 q^{24} +2.96229 q^{25} +4.27139 q^{26} +5.26851 q^{27} +3.08724 q^{28} -6.82587 q^{29} +4.81627 q^{30} -3.46894 q^{31} +1.00000 q^{32} +8.37097 q^{33} -1.86202 q^{34} -8.71144 q^{35} -0.0867059 q^{36} +7.04587 q^{37} +2.06959 q^{38} -7.29056 q^{39} -2.82175 q^{40} +2.46434 q^{41} -5.26942 q^{42} +4.50056 q^{43} -4.90438 q^{44} +0.244663 q^{45} +2.71479 q^{46} -12.4312 q^{47} -1.70684 q^{48} +2.53108 q^{49} +2.96229 q^{50} +3.17816 q^{51} +4.27139 q^{52} -4.92975 q^{53} +5.26851 q^{54} +13.8389 q^{55} +3.08724 q^{56} -3.53246 q^{57} -6.82587 q^{58} +3.42311 q^{59} +4.81627 q^{60} +3.82089 q^{61} -3.46894 q^{62} -0.267682 q^{63} +1.00000 q^{64} -12.0528 q^{65} +8.37097 q^{66} +4.78132 q^{67} -1.86202 q^{68} -4.63371 q^{69} -8.71144 q^{70} +12.8785 q^{71} -0.0867059 q^{72} +2.86681 q^{73} +7.04587 q^{74} -5.05615 q^{75} +2.06959 q^{76} -15.1410 q^{77} -7.29056 q^{78} -10.2935 q^{79} -2.82175 q^{80} -8.73236 q^{81} +2.46434 q^{82} +0.795079 q^{83} -5.26942 q^{84} +5.25416 q^{85} +4.50056 q^{86} +11.6506 q^{87} -4.90438 q^{88} +15.8941 q^{89} +0.244663 q^{90} +13.1868 q^{91} +2.71479 q^{92} +5.92092 q^{93} -12.4312 q^{94} -5.83988 q^{95} -1.70684 q^{96} +11.0382 q^{97} +2.53108 q^{98} +0.425238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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