LMFDB - Embedded newform 4022.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.41980 q^{3} +1.00000 q^{4} +2.76587 q^{5} -1.41980 q^{6} -4.92374 q^{7} +1.00000 q^{8} -0.984179 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.41980 q^{3} +1.00000 q^{4} +2.76587 q^{5} -1.41980 q^{6} -4.92374 q^{7} +1.00000 q^{8} -0.984179 q^{9} +2.76587 q^{10} +2.50379 q^{11} -1.41980 q^{12} -1.97665 q^{13} -4.92374 q^{14} -3.92696 q^{15} +1.00000 q^{16} -4.79804 q^{17} -0.984179 q^{18} -3.03116 q^{19} +2.76587 q^{20} +6.99071 q^{21} +2.50379 q^{22} +1.77097 q^{23} -1.41980 q^{24} +2.65001 q^{25} -1.97665 q^{26} +5.65672 q^{27} -4.92374 q^{28} +0.104614 q^{29} -3.92696 q^{30} +7.96893 q^{31} +1.00000 q^{32} -3.55487 q^{33} -4.79804 q^{34} -13.6184 q^{35} -0.984179 q^{36} +7.75679 q^{37} -3.03116 q^{38} +2.80644 q^{39} +2.76587 q^{40} -1.20461 q^{41} +6.99071 q^{42} +5.72882 q^{43} +2.50379 q^{44} -2.72211 q^{45} +1.77097 q^{46} +10.5374 q^{47} -1.41980 q^{48} +17.2432 q^{49} +2.65001 q^{50} +6.81224 q^{51} -1.97665 q^{52} +0.555185 q^{53} +5.65672 q^{54} +6.92514 q^{55} -4.92374 q^{56} +4.30363 q^{57} +0.104614 q^{58} +12.3515 q^{59} -3.92696 q^{60} -10.7239 q^{61} +7.96893 q^{62} +4.84584 q^{63} +1.00000 q^{64} -5.46715 q^{65} -3.55487 q^{66} +4.59614 q^{67} -4.79804 q^{68} -2.51442 q^{69} -13.6184 q^{70} -2.55194 q^{71} -0.984179 q^{72} +5.62254 q^{73} +7.75679 q^{74} -3.76247 q^{75} -3.03116 q^{76} -12.3280 q^{77} +2.80644 q^{78} -11.4697 q^{79} +2.76587 q^{80} -5.07885 q^{81} -1.20461 q^{82} +10.5323 q^{83} +6.99071 q^{84} -13.2707 q^{85} +5.72882 q^{86} -0.148531 q^{87} +2.50379 q^{88} -3.63481 q^{89} -2.72211 q^{90} +9.73253 q^{91} +1.77097 q^{92} -11.3143 q^{93} +10.5374 q^{94} -8.38379 q^{95} -1.41980 q^{96} +0.573374 q^{97} +17.2432 q^{98} -2.46418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−1.41980	−0.819720	−0.409860	−	0.912149i	$-0.634422\pi$
$3$	−1.41980	−0.819720	−0.409860	+	0.912149i	$0.634422\pi$
$4$	1.00000	0.500000
$5$	2.76587	1.23693	0.618466	−	0.785811i	$-0.287754\pi$
$5$	2.76587	1.23693	0.618466	+	0.785811i	$0.287754\pi$
$6$	−1.41980	−0.579629
$7$	−4.92374	−1.86100	−0.930500	−	0.366293i	$-0.880627\pi$
$7$	−4.92374	−1.86100	−0.930500	+	0.366293i	$0.880627\pi$
$8$	1.00000	0.353553
$9$	−0.984179	−0.328060
$10$	2.76587	0.874643
$11$	2.50379	0.754920	0.377460	−	0.926026i	$-0.376798\pi$
$11$	2.50379	0.754920	0.377460	+	0.926026i	$0.376798\pi$
$12$	−1.41980	−0.409860
$13$	−1.97665	−0.548225	−0.274112	−	0.961698i	$-0.588384\pi$
$13$	−1.97665	−0.548225	−0.274112	+	0.961698i	$0.588384\pi$
$14$	−4.92374	−1.31593
$15$	−3.92696	−1.01394
$16$	1.00000	0.250000
$17$	−4.79804	−1.16370	−0.581848	−	0.813298i	$-0.697670\pi$
$17$	−4.79804	−1.16370	−0.581848	+	0.813298i	$0.697670\pi$
$18$	−0.984179	−0.231973
$19$	−3.03116	−0.695397	−0.347698	−	0.937606i	$-0.613037\pi$
$19$	−3.03116	−0.695397	−0.347698	+	0.937606i	$0.613037\pi$
$20$	2.76587	0.618466
$21$	6.99071	1.52550
$22$	2.50379	0.533809
$23$	1.77097	0.369273	0.184637	−	0.982807i	$-0.440889\pi$
$23$	1.77097	0.369273	0.184637	+	0.982807i	$0.440889\pi$
$24$	−1.41980	−0.289815
$25$	2.65001	0.530002
$26$	−1.97665	−0.387653
$27$	5.65672	1.08864
$28$	−4.92374	−0.930500
$29$	0.104614	0.0194264	0.00971319	−	0.999953i	$-0.496908\pi$
$29$	0.104614	0.0194264	0.00971319	+	0.999953i	$0.496908\pi$
$30$	−3.92696	−0.716962
$31$	7.96893	1.43126	0.715631	−	0.698478i	$-0.246139\pi$
$31$	7.96893	1.43126	0.715631	+	0.698478i	$0.246139\pi$
$32$	1.00000	0.176777
$33$	−3.55487	−0.618823
$34$	−4.79804	−0.822857
$35$	−13.6184	−2.30193
$36$	−0.984179	−0.164030
$37$	7.75679	1.27521	0.637604	−	0.770364i	$-0.279926\pi$
$37$	7.75679	1.27521	0.637604	+	0.770364i	$0.279926\pi$
$38$	−3.03116	−0.491720
$39$	2.80644	0.449391
$40$	2.76587	0.437322
$41$	−1.20461	−0.188128	−0.0940640	−	0.995566i	$-0.529986\pi$
$41$	−1.20461	−0.188128	−0.0940640	+	0.995566i	$0.529986\pi$
$42$	6.99071	1.07869
$43$	5.72882	0.873636	0.436818	−	0.899550i	$-0.356105\pi$
$43$	5.72882	0.873636	0.436818	+	0.899550i	$0.356105\pi$
$44$	2.50379	0.377460
$45$	−2.72211	−0.405788
$46$	1.77097	0.261115
$47$	10.5374	1.53704	0.768522	−	0.639823i	$-0.220992\pi$
$47$	10.5374	1.53704	0.768522	+	0.639823i	$0.220992\pi$
$48$	−1.41980	−0.204930
$49$	17.2432	2.46332
$50$	2.65001	0.374768
$51$	6.81224	0.953904
$52$	−1.97665	−0.274112
$53$	0.555185	0.0762605	0.0381303	−	0.999273i	$-0.487860\pi$
$53$	0.555185	0.0762605	0.0381303	+	0.999273i	$0.487860\pi$
$54$	5.65672	0.769782
$55$	6.92514	0.933785
$56$	−4.92374	−0.657963
$57$	4.30363	0.570030
$58$	0.104614	0.0137365
$59$	12.3515	1.60803	0.804016	−	0.594608i	$-0.202693\pi$
$59$	12.3515	1.60803	0.804016	+	0.594608i	$0.202693\pi$
$60$	−3.92696	−0.506969
$61$	−10.7239	−1.37305	−0.686527	−	0.727104i	$-0.740866\pi$
$61$	−10.7239	−1.37305	−0.686527	+	0.727104i	$0.740866\pi$
$62$	7.96893	1.01206
$63$	4.84584	0.610519
$64$	1.00000	0.125000
$65$	−5.46715	−0.678117
$66$	−3.55487	−0.437574
$67$	4.59614	0.561508	0.280754	−	0.959780i	$-0.409415\pi$
$67$	4.59614	0.561508	0.280754	+	0.959780i	$0.409415\pi$
$68$	−4.79804	−0.581848
$69$	−2.51442	−0.302700
$70$	−13.6184	−1.62771
$71$	−2.55194	−0.302859	−0.151430	−	0.988468i	$-0.548388\pi$
$71$	−2.55194	−0.302859	−0.151430	+	0.988468i	$0.548388\pi$
$72$	−0.984179	−0.115987
$73$	5.62254	0.658069	0.329034	−	0.944318i	$-0.393277\pi$
$73$	5.62254	0.658069	0.329034	+	0.944318i	$0.393277\pi$
$74$	7.75679	0.901709
$75$	−3.76247	−0.434453
$76$	−3.03116	−0.347698
$77$	−12.3280	−1.40491
$78$	2.80644	0.317767
$79$	−11.4697	−1.29044	−0.645219	−	0.763998i	$-0.723234\pi$
$79$	−11.4697	−1.29044	−0.645219	+	0.763998i	$0.723234\pi$
$80$	2.76587	0.309233
$81$	−5.07885	−0.564317
$82$	−1.20461	−0.133027
$83$	10.5323	1.15607	0.578037	−	0.816011i	$-0.303819\pi$
$83$	10.5323	1.15607	0.578037	+	0.816011i	$0.303819\pi$
$84$	6.99071	0.762749
$85$	−13.2707	−1.43941
$86$	5.72882	0.617754
$87$	−0.148531	−0.0159242
$88$	2.50379	0.266905
$89$	−3.63481	−0.385289	−0.192644	−	0.981269i	$-0.561706\pi$
$89$	−3.63481	−0.385289	−0.192644	+	0.981269i	$0.561706\pi$
$90$	−2.72211	−0.286935
$91$	9.73253	1.02025
$92$	1.77097	0.184637
$93$	−11.3143	−1.17323
$94$	10.5374	1.08685
$95$	−8.38379	−0.860159
$96$	−1.41980	−0.144907
$97$	0.573374	0.0582173	0.0291086	−	0.999576i	$-0.490733\pi$
$97$	0.573374	0.0582173	0.0291086	+	0.999576i	$0.490733\pi$
$98$	17.2432	1.74183
$99$	−2.46418	−0.247659
$100$	2.65001	0.265001
$101$	−6.02981	−0.599989	−0.299994	−	0.953941i	$-0.596985\pi$
$101$	−6.02981	−0.599989	−0.299994	+	0.953941i	$0.596985\pi$
$102$	6.81224	0.674512
$103$	11.3834	1.12164	0.560822	−	0.827937i	$-0.310485\pi$
$103$	11.3834	1.12164	0.560822	+	0.827937i	$0.310485\pi$
$104$	−1.97665	−0.193827
$105$	19.3354	1.88694
$106$	0.555185	0.0539244
$107$	14.4395	1.39592	0.697960	−	0.716137i	$-0.254091\pi$
$107$	14.4395	1.39592	0.697960	+	0.716137i	$0.254091\pi$
$108$	5.65672	0.544318
$109$	11.0385	1.05729	0.528647	−	0.848842i	$-0.322699\pi$
$109$	11.0385	1.05729	0.528647	+	0.848842i	$0.322699\pi$
$110$	6.92514	0.660286
$111$	−11.0131	−1.04531
$112$	−4.92374	−0.465250
$113$	10.1257	0.952543	0.476271	−	0.879298i	$-0.341988\pi$
$113$	10.1257	0.952543	0.476271	+	0.879298i	$0.341988\pi$
$114$	4.30363	0.403072
$115$	4.89827	0.456766
$116$	0.104614	0.00971319
$117$	1.94538	0.179851
$118$	12.3515	1.13705
$119$	23.6243	2.16564
$120$	−3.92696	−0.358481
$121$	−4.73105	−0.430095
$122$	−10.7239	−0.970896
$123$	1.71030	0.154212
$124$	7.96893	0.715631
$125$	−6.49975	−0.581356
$126$	4.84584	0.431702
$127$	−4.69089	−0.416249	−0.208124	−	0.978102i	$-0.566736\pi$
$127$	−4.69089	−0.416249	−0.208124	+	0.978102i	$0.566736\pi$
$128$	1.00000	0.0883883
$129$	−8.13375	−0.716137
$130$	−5.46715	−0.479501
$131$	17.7999	1.55519	0.777593	−	0.628768i	$-0.216440\pi$
$131$	17.7999	1.55519	0.777593	+	0.628768i	$0.216440\pi$
$132$	−3.55487	−0.309411
$133$	14.9247	1.29413
$134$	4.59614	0.397046
$135$	15.6457	1.34657
$136$	−4.79804	−0.411428
$137$	−18.0615	−1.54310	−0.771550	−	0.636169i	$-0.780518\pi$
$137$	−18.0615	−1.54310	−0.771550	+	0.636169i	$0.780518\pi$
$138$	−2.51442	−0.214041
$139$	−10.9976	−0.932806	−0.466403	−	0.884572i	$-0.654450\pi$
$139$	−10.9976	−0.932806	−0.466403	+	0.884572i	$0.654450\pi$
$140$	−13.6184	−1.15097
$141$	−14.9610	−1.25995
$142$	−2.55194	−0.214154
$143$	−4.94912	−0.413866
$144$	−0.984179	−0.0820149
$145$	0.289349	0.0240291
$146$	5.62254	0.465325
$147$	−24.4819	−2.01923
$148$	7.75679	0.637604
$149$	−5.69228	−0.466330	−0.233165	−	0.972437i	$-0.574908\pi$
$149$	−5.69228	−0.466330	−0.233165	+	0.972437i	$0.574908\pi$
$150$	−3.76247	−0.307205
$151$	−5.53590	−0.450505	−0.225253	−	0.974300i	$-0.572321\pi$
$151$	−5.53590	−0.450505	−0.225253	+	0.974300i	$0.572321\pi$
$152$	−3.03116	−0.245860
$153$	4.72213	0.381762
$154$	−12.3280	−0.993419
$155$	22.0410	1.77038
$156$	2.80644	0.224695
$157$	−4.55748	−0.363726	−0.181863	−	0.983324i	$-0.558213\pi$
$157$	−4.55748	−0.363726	−0.181863	+	0.983324i	$0.558213\pi$
$158$	−11.4697	−0.912477
$159$	−0.788250	−0.0625123
$160$	2.76587	0.218661
$161$	−8.71980	−0.687217
$162$	−5.07885	−0.399032
$163$	4.78967	0.375156	0.187578	−	0.982250i	$-0.439936\pi$
$163$	4.78967	0.375156	0.187578	+	0.982250i	$0.439936\pi$
$164$	−1.20461	−0.0940640
$165$	−9.83228	−0.765442
$166$	10.5323	0.817468
$167$	−6.29987	−0.487498	−0.243749	−	0.969838i	$-0.578377\pi$
$167$	−6.29987	−0.487498	−0.243749	+	0.969838i	$0.578377\pi$
$168$	6.99071	0.539345
$169$	−9.09284	−0.699450
$170$	−13.2707	−1.01782
$171$	2.98321	0.228132
$172$	5.72882	0.436818
$173$	15.6508	1.18991	0.594954	−	0.803760i	$-0.297170\pi$
$173$	15.6508	1.18991	0.594954	+	0.803760i	$0.297170\pi$
$174$	−0.148531	−0.0112601
$175$	−13.0480	−0.986334
$176$	2.50379	0.188730
$177$	−17.5366	−1.31813
$178$	−3.63481	−0.272440
$179$	−2.91516	−0.217889	−0.108945	−	0.994048i	$-0.534747\pi$
$179$	−2.91516	−0.217889	−0.108945	+	0.994048i	$0.534747\pi$
$180$	−2.72211	−0.202894
$181$	22.3624	1.66219	0.831094	−	0.556132i	$-0.187715\pi$
$181$	22.3624	1.66219	0.831094	+	0.556132i	$0.187715\pi$
$182$	9.73253	0.721423
$183$	15.2257	1.12552
$184$	1.77097	0.130558
$185$	21.4542	1.57735
$186$	−11.3143	−0.829602
$187$	−12.0133	−0.878497
$188$	10.5374	0.768522
$189$	−27.8522	−2.02595
$190$	−8.38379	−0.608224
$191$	2.49471	0.180511	0.0902555	−	0.995919i	$-0.471232\pi$
$191$	2.49471	0.180511	0.0902555	+	0.995919i	$0.471232\pi$
$192$	−1.41980	−0.102465
$193$	−8.19446	−0.589850	−0.294925	−	0.955520i	$-0.595295\pi$
$193$	−8.19446	−0.589850	−0.294925	+	0.955520i	$0.595295\pi$
$194$	0.573374	0.0411658
$195$	7.76224	0.555866
$196$	17.2432	1.23166
$197$	9.68429	0.689977	0.344989	−	0.938607i	$-0.387883\pi$
$197$	9.68429	0.689977	0.344989	+	0.938607i	$0.387883\pi$
$198$	−2.46418	−0.175121
$199$	−13.2994	−0.942766	−0.471383	−	0.881929i	$-0.656245\pi$
$199$	−13.2994	−0.942766	−0.471383	+	0.881929i	$0.656245\pi$
$200$	2.65001	0.187384
$201$	−6.52559	−0.460279
$202$	−6.02981	−0.424256
$203$	−0.515094	−0.0361525
$204$	6.81224	0.476952
$205$	−3.33178	−0.232702
$206$	11.3834	0.793122
$207$	−1.74295	−0.121144
$208$	−1.97665	−0.137056
$209$	−7.58939	−0.524969
$210$	19.3354	1.33427
$211$	−21.0200	−1.44708	−0.723538	−	0.690284i	$-0.757486\pi$
$211$	−21.0200	−1.44708	−0.723538	+	0.690284i	$0.757486\pi$
$212$	0.555185	0.0381303
$213$	3.62323	0.248260
$214$	14.4395	0.987064
$215$	15.8451	1.08063
$216$	5.65672	0.384891
$217$	−39.2370	−2.66358
$218$	11.0385	0.747620
$219$	−7.98286	−0.539432
$220$	6.92514	0.466893
$221$	9.48406	0.637967
$222$	−11.0131	−0.739148
$223$	−2.22932	−0.149286	−0.0746432	−	0.997210i	$-0.523782\pi$
$223$	−2.22932	−0.149286	−0.0746432	+	0.997210i	$0.523782\pi$
$224$	−4.92374	−0.328981
$225$	−2.60809	−0.173872
$226$	10.1257	0.673549
$227$	14.3535	0.952673	0.476336	−	0.879263i	$-0.341964\pi$
$227$	14.3535	0.952673	0.476336	+	0.879263i	$0.341964\pi$
$228$	4.30363	0.285015
$229$	−8.22830	−0.543741	−0.271871	−	0.962334i	$-0.587642\pi$
$229$	−8.22830	−0.543741	−0.271871	+	0.962334i	$0.587642\pi$
$230$	4.89827	0.322982
$231$	17.5032	1.15163
$232$	0.104614	0.00686826
$233$	0.864336	0.0566246	0.0283123	−	0.999599i	$-0.490987\pi$
$233$	0.864336	0.0566246	0.0283123	+	0.999599i	$0.490987\pi$
$234$	1.94538	0.127174
$235$	29.1452	1.90122
$236$	12.3515	0.804016
$237$	16.2846	1.05780
$238$	23.6243	1.53134
$239$	24.8169	1.60527	0.802635	−	0.596471i	$-0.203431\pi$
$239$	24.8169	1.60527	0.802635	+	0.596471i	$0.203431\pi$
$240$	−3.92696	−0.253484
$241$	−0.498490	−0.0321106	−0.0160553	−	0.999871i	$-0.505111\pi$
$241$	−0.498490	−0.0321106	−0.0160553	+	0.999871i	$0.505111\pi$
$242$	−4.73105	−0.304123
$243$	−9.75923	−0.626055
$244$	−10.7239	−0.686527
$245$	47.6924	3.04696
$246$	1.71030	0.109044
$247$	5.99156	0.381234
$248$	7.96893	0.506028
$249$	−14.9538	−0.947656
$250$	−6.49975	−0.411081
$251$	−7.57709	−0.478261	−0.239131	−	0.970987i	$-0.576862\pi$
$251$	−7.57709	−0.478261	−0.239131	+	0.970987i	$0.576862\pi$
$252$	4.84584	0.305259
$253$	4.43414	0.278772
$254$	−4.69089	−0.294332
$255$	18.8417	1.17991
$256$	1.00000	0.0625000
$257$	23.4689	1.46395	0.731976	−	0.681331i	$-0.238598\pi$
$257$	23.4689	1.46395	0.731976	+	0.681331i	$0.238598\pi$
$258$	−8.13375	−0.506385
$259$	−38.1924	−2.37316
$260$	−5.46715	−0.339059
$261$	−0.102959	−0.00637301
$262$	17.7999	1.09968
$263$	3.09491	0.190841	0.0954203	−	0.995437i	$-0.469580\pi$
$263$	3.09491	0.190841	0.0954203	+	0.995437i	$0.469580\pi$
$264$	−3.55487	−0.218787
$265$	1.53557	0.0943292
$266$	14.9247	0.915090
$267$	5.16068	0.315829
$268$	4.59614	0.280754
$269$	−9.93605	−0.605812	−0.302906	−	0.953021i	$-0.597957\pi$
$269$	−9.93605	−0.605812	−0.302906	+	0.953021i	$0.597957\pi$
$270$	15.6457	0.952169
$271$	8.86916	0.538763	0.269381	−	0.963034i	$-0.413181\pi$
$271$	8.86916	0.538763	0.269381	+	0.963034i	$0.413181\pi$
$272$	−4.79804	−0.290924
$273$	−13.8182	−0.836316
$274$	−18.0615	−1.09114
$275$	6.63506	0.400109
$276$	−2.51442	−0.151350
$277$	5.46838	0.328563	0.164281	−	0.986414i	$-0.447469\pi$
$277$	5.46838	0.328563	0.164281	+	0.986414i	$0.447469\pi$
$278$	−10.9976	−0.659594
$279$	−7.84286	−0.469540
$280$	−13.6184	−0.813855
$281$	10.9438	0.652852	0.326426	−	0.945223i	$-0.394156\pi$
$281$	10.9438	0.652852	0.326426	+	0.945223i	$0.394156\pi$
$282$	−14.9610	−0.890916
$283$	2.00833	0.119383	0.0596913	−	0.998217i	$-0.480988\pi$
$283$	2.00833	0.119383	0.0596913	+	0.998217i	$0.480988\pi$
$284$	−2.55194	−0.151430
$285$	11.9033	0.705089
$286$	−4.94912	−0.292647
$287$	5.93117	0.350106
$288$	−0.984179	−0.0579933
$289$	6.02118	0.354187
$290$	0.289349	0.0169912
$291$	−0.814074	−0.0477219
$292$	5.62254	0.329034
$293$	19.9032	1.16276	0.581380	−	0.813632i	$-0.302513\pi$
$293$	19.9032	1.16276	0.581380	+	0.813632i	$0.302513\pi$
$294$	−24.4819	−1.42781
$295$	34.1627	1.98903
$296$	7.75679	0.450854
$297$	14.1632	0.821834
$298$	−5.69228	−0.329745
$299$	−3.50059	−0.202445
$300$	−3.76247	−0.217227
$301$	−28.2072	−1.62584
$302$	−5.53590	−0.318555
$303$	8.56110	0.491823
$304$	−3.03116	−0.173849
$305$	−29.6609	−1.69838
$306$	4.72213	0.269946
$307$	24.4752	1.39688	0.698438	−	0.715671i	$-0.253879\pi$
$307$	24.4752	1.39688	0.698438	+	0.715671i	$0.253879\pi$
$308$	−12.3280	−0.702453
$309$	−16.1622	−0.919433
$310$	22.0410	1.25184
$311$	7.95660	0.451177	0.225589	−	0.974223i	$-0.427569\pi$
$311$	7.95660	0.451177	0.225589	+	0.974223i	$0.427569\pi$
$312$	2.80644	0.158884
$313$	3.81687	0.215742	0.107871	−	0.994165i	$-0.465597\pi$
$313$	3.81687	0.215742	0.107871	+	0.994165i	$0.465597\pi$
$314$	−4.55748	−0.257193
$315$	13.4030	0.755171
$316$	−11.4697	−0.645219
$317$	−1.71738	−0.0964577	−0.0482289	−	0.998836i	$-0.515358\pi$
$317$	−1.71738	−0.0964577	−0.0482289	+	0.998836i	$0.515358\pi$
$318$	−0.788250	−0.0442028
$319$	0.261932	0.0146654
$320$	2.76587	0.154617
$321$	−20.5012	−1.14426
$322$	−8.71980	−0.485936
$323$	14.5436	0.809230
$324$	−5.07885	−0.282159
$325$	−5.23815	−0.290560
$326$	4.78967	0.265275
$327$	−15.6724	−0.866685
$328$	−1.20461	−0.0665133
$329$	−51.8837	−2.86044
$330$	−9.83228	−0.541249
$331$	−22.3451	−1.22820	−0.614099	−	0.789229i	$-0.710481\pi$
$331$	−22.3451	−1.22820	−0.614099	+	0.789229i	$0.710481\pi$
$332$	10.5323	0.578037
$333$	−7.63407	−0.418345
$334$	−6.29987	−0.344713
$335$	12.7123	0.694548
$336$	6.99071	0.381374
$337$	−25.4591	−1.38685	−0.693423	−	0.720531i	$-0.743898\pi$
$337$	−25.4591	−1.38685	−0.693423	+	0.720531i	$0.743898\pi$
$338$	−9.09284	−0.494586
$339$	−14.3764	−0.780818
$340$	−13.2707	−0.719706
$341$	19.9525	1.08049
$342$	2.98321	0.161313
$343$	−50.4350	−2.72323
$344$	5.72882	0.308877
$345$	−6.95454	−0.374420
$346$	15.6508	0.841392
$347$	14.5074	0.778798	0.389399	−	0.921069i	$-0.372683\pi$
$347$	14.5074	0.778798	0.389399	+	0.921069i	$0.372683\pi$
$348$	−0.148531	−0.00796209
$349$	36.1653	1.93588	0.967942	−	0.251174i	$-0.0808165\pi$
$349$	36.1653	1.93588	0.967942	+	0.251174i	$0.0808165\pi$
$350$	−13.0480	−0.697443
$351$	−11.1814	−0.596818
$352$	2.50379	0.133452
$353$	27.9529	1.48778	0.743891	−	0.668301i	$-0.232978\pi$
$353$	27.9529	1.48778	0.743891	+	0.668301i	$0.232978\pi$
$354$	−17.5366	−0.932062
$355$	−7.05831	−0.374616
$356$	−3.63481	−0.192644
$357$	−33.5417	−1.77521
$358$	−2.91516	−0.154071
$359$	−30.2159	−1.59474	−0.797368	−	0.603493i	$-0.793775\pi$
$359$	−30.2159	−1.59474	−0.797368	+	0.603493i	$0.793775\pi$
$360$	−2.72211	−0.143468
$361$	−9.81204	−0.516423
$362$	22.3624	1.17534
$363$	6.71712	0.352558
$364$	9.73253	0.510123
$365$	15.5512	0.813987
$366$	15.2257	0.795863
$367$	−20.5895	−1.07476	−0.537382	−	0.843339i	$-0.680587\pi$
$367$	−20.5895	−1.07476	−0.537382	+	0.843339i	$0.680587\pi$
$368$	1.77097	0.0923183
$369$	1.18555	0.0617172
$370$	21.4542	1.11535
$371$	−2.73359	−0.141921
$372$	−11.3143	−0.586617
$373$	33.1378	1.71581	0.857904	−	0.513810i	$-0.171766\pi$
$373$	33.1378	1.71581	0.857904	+	0.513810i	$0.171766\pi$
$374$	−12.0133	−0.621191
$375$	9.22832	0.476549
$376$	10.5374	0.543427
$377$	−0.206786	−0.0106500
$378$	−27.8522	−1.43256
$379$	12.7696	0.655932	0.327966	−	0.944690i	$-0.393637\pi$
$379$	12.7696	0.655932	0.327966	+	0.944690i	$0.393637\pi$
$380$	−8.38379	−0.430079
$381$	6.66010	0.341207
$382$	2.49471	0.127640
$383$	20.2482	1.03464	0.517318	−	0.855793i	$-0.326930\pi$
$383$	20.2482	1.03464	0.517318	+	0.855793i	$0.326930\pi$
$384$	−1.41980	−0.0724537
$385$	−34.0976	−1.73777
$386$	−8.19446	−0.417087
$387$	−5.63818	−0.286605
$388$	0.573374	0.0291086
$389$	−7.80259	−0.395607	−0.197804	−	0.980242i	$-0.563381\pi$
$389$	−7.80259	−0.395607	−0.197804	+	0.980242i	$0.563381\pi$
$390$	7.76224	0.393057
$391$	−8.49719	−0.429721
$392$	17.2432	0.870914
$393$	−25.2723	−1.27482
$394$	9.68429	0.487888
$395$	−31.7235	−1.59618
$396$	−2.46418	−0.123829
$397$	2.32755	0.116817	0.0584083	−	0.998293i	$-0.481397\pi$
$397$	2.32755	0.116817	0.0584083	+	0.998293i	$0.481397\pi$
$398$	−13.2994	−0.666636
$399$	−21.1900	−1.06083
$400$	2.65001	0.132501
$401$	−14.2718	−0.712702	−0.356351	−	0.934352i	$-0.615979\pi$
$401$	−14.2718	−0.712702	−0.356351	+	0.934352i	$0.615979\pi$
$402$	−6.52559	−0.325467
$403$	−15.7518	−0.784654
$404$	−6.02981	−0.299994
$405$	−14.0474	−0.698022
$406$	−0.515094	−0.0255637
$407$	19.4214	0.962681
$408$	6.81224	0.337256
$409$	1.89790	0.0938449	0.0469224	−	0.998899i	$-0.485059\pi$
$409$	1.89790	0.0938449	0.0469224	+	0.998899i	$0.485059\pi$
$410$	−3.33178	−0.164545
$411$	25.6437	1.26491
$412$	11.3834	0.560822
$413$	−60.8157	−2.99255
$414$	−1.74295	−0.0856615
$415$	29.1310	1.42999
$416$	−1.97665	−0.0969134
$417$	15.6144	0.764640
$418$	−7.58939	−0.371209
$419$	7.67186	0.374795	0.187397	−	0.982284i	$-0.439995\pi$
$419$	7.67186	0.374795	0.187397	+	0.982284i	$0.439995\pi$
$420$	19.3354	0.943469
$421$	17.3190	0.844076	0.422038	−	0.906578i	$-0.361315\pi$
$421$	17.3190	0.844076	0.422038	+	0.906578i	$0.361315\pi$
$422$	−21.0200	−1.02324
$423$	−10.3707	−0.504242
$424$	0.555185	0.0269622
$425$	−12.7149	−0.616761
$426$	3.62323	0.175546
$427$	52.8017	2.55525
$428$	14.4395	0.697960
$429$	7.02674	0.339254
$430$	15.8451	0.764120
$431$	4.77263	0.229890	0.114945	−	0.993372i	$-0.463331\pi$
$431$	4.77263	0.229890	0.114945	+	0.993372i	$0.463331\pi$
$432$	5.65672	0.272159
$433$	−28.6089	−1.37486	−0.687429	−	0.726252i	$-0.741261\pi$
$433$	−28.6089	−1.37486	−0.687429	+	0.726252i	$0.741261\pi$
$434$	−39.2370	−1.88343
$435$	−0.410817	−0.0196971
$436$	11.0385	0.528647
$437$	−5.36810	−0.256791
$438$	−7.98286	−0.381436
$439$	0.421893	0.0201358	0.0100679	−	0.999949i	$-0.496795\pi$
$439$	0.421893	0.0201358	0.0100679	+	0.999949i	$0.496795\pi$
$440$	6.92514	0.330143
$441$	−16.9704	−0.808116
$442$	9.48406	0.451111
$443$	31.4728	1.49532	0.747658	−	0.664084i	$-0.231178\pi$
$443$	31.4728	1.49532	0.747658	+	0.664084i	$0.231178\pi$
$444$	−11.0131	−0.522657
$445$	−10.0534	−0.476576
$446$	−2.22932	−0.105561
$447$	8.08188	0.382260
$448$	−4.92374	−0.232625
$449$	−0.746007	−0.0352063	−0.0176031	−	0.999845i	$-0.505604\pi$
$449$	−0.746007	−0.0352063	−0.0176031	+	0.999845i	$0.505604\pi$
$450$	−2.60809	−0.122946
$451$	−3.01608	−0.142022
$452$	10.1257	0.476271
$453$	7.85985	0.369288
$454$	14.3535	0.673641
$455$	26.9189	1.26198
$456$	4.30363	0.201536
$457$	−9.45978	−0.442510	−0.221255	−	0.975216i	$-0.571015\pi$
$457$	−9.45978	−0.442510	−0.221255	+	0.975216i	$0.571015\pi$
$458$	−8.22830	−0.384483
$459$	−27.1412	−1.26684
$460$	4.89827	0.228383
$461$	−4.49796	−0.209491	−0.104745	−	0.994499i	$-0.533403\pi$
$461$	−4.49796	−0.209491	−0.104745	+	0.994499i	$0.533403\pi$
$462$	17.5032	0.814325
$463$	−1.77142	−0.0823247	−0.0411623	−	0.999152i	$-0.513106\pi$
$463$	−1.77142	−0.0823247	−0.0411623	+	0.999152i	$0.513106\pi$
$464$	0.104614	0.00485660
$465$	−31.2937	−1.45121
$466$	0.864336	0.0400396
$467$	−22.9522	−1.06210	−0.531050	−	0.847341i	$-0.678202\pi$
$467$	−22.9522	−1.06210	−0.531050	+	0.847341i	$0.678202\pi$
$468$	1.94538	0.0899253
$469$	−22.6302	−1.04497
$470$	29.1452	1.34437
$471$	6.47069	0.298153
$472$	12.3515	0.568525
$473$	14.3437	0.659526
$474$	16.2846	0.747975
$475$	−8.03262	−0.368562
$476$	23.6243	1.08282
$477$	−0.546402	−0.0250180
$478$	24.8169	1.13510
$479$	−12.1642	−0.555797	−0.277899	−	0.960610i	$-0.589638\pi$
$479$	−12.1642	−0.555797	−0.277899	+	0.960610i	$0.589638\pi$
$480$	−3.92696	−0.179241
$481$	−15.3325	−0.699101
$482$	−0.498490	−0.0227056
$483$	12.3803	0.563325
$484$	−4.73105	−0.215048
$485$	1.58587	0.0720109
$486$	−9.75923	−0.442688
$487$	−2.72647	−0.123548	−0.0617740	−	0.998090i	$-0.519676\pi$
$487$	−2.72647	−0.123548	−0.0617740	+	0.998090i	$0.519676\pi$
$488$	−10.7239	−0.485448
$489$	−6.80035	−0.307522
$490$	47.6924	2.15452
$491$	35.1614	1.58681	0.793405	−	0.608694i	$-0.208306\pi$
$491$	35.1614	1.58681	0.793405	+	0.608694i	$0.208306\pi$
$492$	1.71030	0.0771061
$493$	−0.501943	−0.0226064
$494$	5.99156	0.269573
$495$	−6.81558	−0.306337
$496$	7.96893	0.357816
$497$	12.5651	0.563621
$498$	−14.9538	−0.670094
$499$	−10.4909	−0.469637	−0.234818	−	0.972039i	$-0.575449\pi$
$499$	−10.4909	−0.469637	−0.234818	+	0.972039i	$0.575449\pi$
$500$	−6.49975	−0.290678
$501$	8.94453	0.399612
$502$	−7.57709	−0.338182
$503$	15.5447	0.693105	0.346553	−	0.938031i	$-0.387352\pi$
$503$	15.5447	0.693105	0.346553	+	0.938031i	$0.387352\pi$
$504$	4.84584	0.215851
$505$	−16.6777	−0.742146
$506$	4.43414	0.197121
$507$	12.9100	0.573353
$508$	−4.69089	−0.208124
$509$	8.77428	0.388913	0.194456	−	0.980911i	$-0.437706\pi$
$509$	8.77428	0.388913	0.194456	+	0.980911i	$0.437706\pi$
$510$	18.8417	0.834326
$511$	−27.6839	−1.22467
$512$	1.00000	0.0441942
$513$	−17.1465	−0.757034
$514$	23.4689	1.03517
$515$	31.4850	1.38740
$516$	−8.13375	−0.358068
$517$	26.3835	1.16035
$518$	−38.1924	−1.67808
$519$	−22.2209	−0.975391
$520$	−5.46715	−0.239751
$521$	15.9038	0.696760	0.348380	−	0.937353i	$-0.386732\pi$
$521$	15.9038	0.696760	0.348380	+	0.937353i	$0.386732\pi$
$522$	−0.102959	−0.00450640
$523$	7.10239	0.310566	0.155283	−	0.987870i	$-0.450371\pi$
$523$	7.10239	0.310566	0.155283	+	0.987870i	$0.450371\pi$
$524$	17.7999	0.777593
$525$	18.5255	0.808517
$526$	3.09491	0.134945
$527$	−38.2353	−1.66555
$528$	−3.55487	−0.154706
$529$	−19.8637	−0.863637
$530$	1.53557	0.0667008
$531$	−12.1561	−0.527530
$532$	14.9247	0.647066
$533$	2.38109	0.103136
$534$	5.16068	0.223325
$535$	39.9377	1.72666
$536$	4.59614	0.198523
$537$	4.13893	0.178608
$538$	−9.93605	−0.428373
$539$	43.1734	1.85961
$540$	15.6457	0.673285
$541$	−37.0064	−1.59103	−0.795514	−	0.605935i	$-0.792799\pi$
$541$	−37.0064	−1.59103	−0.795514	+	0.605935i	$0.792799\pi$
$542$	8.86916	0.380963
$543$	−31.7501	−1.36253
$544$	−4.79804	−0.205714
$545$	30.5309	1.30780
$546$	−13.8182	−0.591364
$547$	4.21904	0.180393	0.0901967	−	0.995924i	$-0.471250\pi$
$547$	4.21904	0.180393	0.0901967	+	0.995924i	$0.471250\pi$
$548$	−18.0615	−0.771550
$549$	10.5542	0.450444
$550$	6.63506	0.282920
$551$	−0.317103	−0.0135090
$552$	−2.51442	−0.107021
$553$	56.4736	2.40150
$554$	5.46838	0.232329
$555$	−30.4606	−1.29298
$556$	−10.9976	−0.466403
$557$	7.23993	0.306766	0.153383	−	0.988167i	$-0.450983\pi$
$557$	7.23993	0.306766	0.153383	+	0.988167i	$0.450983\pi$
$558$	−7.84286	−0.332015
$559$	−11.3239	−0.478949
$560$	−13.6184	−0.575483
$561$	17.0564	0.720121
$562$	10.9438	0.461636
$563$	9.00373	0.379462	0.189731	−	0.981836i	$-0.439238\pi$
$563$	9.00373	0.379462	0.189731	+	0.981836i	$0.439238\pi$
$564$	−14.9610	−0.629973
$565$	28.0062	1.17823
$566$	2.00833	0.0844162
$567$	25.0070	1.05019
$568$	−2.55194	−0.107077
$569$	4.01922	0.168494	0.0842472	−	0.996445i	$-0.473151\pi$
$569$	4.01922	0.168494	0.0842472	+	0.996445i	$0.473151\pi$
$570$	11.9033	0.498573
$571$	31.4954	1.31804	0.659021	−	0.752125i	$-0.270971\pi$
$571$	31.4954	1.31804	0.659021	+	0.752125i	$0.270971\pi$
$572$	−4.94912	−0.206933
$573$	−3.54198	−0.147968
$574$	5.93117	0.247562
$575$	4.69309	0.195715
$576$	−0.984179	−0.0410075
$577$	−27.5199	−1.14567	−0.572834	−	0.819671i	$-0.694156\pi$
$577$	−27.5199	−1.14567	−0.572834	+	0.819671i	$0.694156\pi$
$578$	6.02118	0.250448
$579$	11.6345	0.483512
$580$	0.289349	0.0120146
$581$	−51.8585	−2.15145
$582$	−0.814074	−0.0337444
$583$	1.39007	0.0575706
$584$	5.62254	0.232663
$585$	5.38066	0.222463
$586$	19.9032	0.822195
$587$	−2.44401	−0.100875	−0.0504375	−	0.998727i	$-0.516062\pi$
$587$	−2.44401	−0.100875	−0.0504375	+	0.998727i	$0.516062\pi$
$588$	−24.4819	−1.00962
$589$	−24.1551	−0.995295
$590$	34.1627	1.40645
$591$	−13.7497	−0.565588
$592$	7.75679	0.318802
$593$	−44.8746	−1.84278	−0.921389	−	0.388642i	$-0.872944\pi$
$593$	−44.8746	−1.84278	−0.921389	+	0.388642i	$0.872944\pi$
$594$	14.1632	0.581124
$595$	65.3416	2.67875
$596$	−5.69228	−0.233165
$597$	18.8824	0.772804
$598$	−3.50059	−0.143150
$599$	−8.49757	−0.347201	−0.173601	−	0.984816i	$-0.555540\pi$
$599$	−8.49757	−0.347201	−0.173601	+	0.984816i	$0.555540\pi$
$600$	−3.76247	−0.153602
$601$	−18.8168	−0.767553	−0.383777	−	0.923426i	$-0.625377\pi$
$601$	−18.8168	−0.767553	−0.383777	+	0.923426i	$0.625377\pi$
$602$	−28.2072	−1.14964
$603$	−4.52343	−0.184208
$604$	−5.53590	−0.225253
$605$	−13.0854	−0.531999
$606$	8.56110	0.347771
$607$	−17.3578	−0.704530	−0.352265	−	0.935900i	$-0.614588\pi$
$607$	−17.3578	−0.704530	−0.352265	+	0.935900i	$0.614588\pi$
$608$	−3.03116	−0.122930
$609$	0.731328	0.0296349
$610$	−29.6609	−1.20093
$611$	−20.8289	−0.842646
$612$	4.72213	0.190881
$613$	7.06740	0.285450	0.142725	−	0.989762i	$-0.454414\pi$
$613$	7.06740	0.285450	0.142725	+	0.989762i	$0.454414\pi$
$614$	24.4752	0.987740
$615$	4.73045	0.190750
$616$	−12.3280	−0.496709
$617$	−21.2387	−0.855037	−0.427518	−	0.904007i	$-0.640612\pi$
$617$	−21.2387	−0.855037	−0.427518	+	0.904007i	$0.640612\pi$
$618$	−16.1622	−0.650137
$619$	39.8893	1.60328	0.801642	−	0.597804i	$-0.203960\pi$
$619$	39.8893	1.60328	0.801642	+	0.597804i	$0.203960\pi$
$620$	22.0410	0.885188
$621$	10.0179	0.402004
$622$	7.95660	0.319031
$623$	17.8968	0.717022
$624$	2.80644	0.112348
$625$	−31.2275	−1.24910
$626$	3.81687	0.152553
$627$	10.7754	0.430327
$628$	−4.55748	−0.181863
$629$	−37.2174	−1.48395
$630$	13.4030	0.533986
$631$	−36.7001	−1.46101	−0.730504	−	0.682909i	$-0.760715\pi$
$631$	−36.7001	−1.46101	−0.730504	+	0.682909i	$0.760715\pi$
$632$	−11.4697	−0.456238
$633$	29.8441	1.18620
$634$	−1.71738	−0.0682059
$635$	−12.9744	−0.514872
$636$	−0.788250	−0.0312561
$637$	−34.0839	−1.35045
$638$	0.261932	0.0103700
$639$	2.51156	0.0993559
$640$	2.76587	0.109330
$641$	23.0999	0.912392	0.456196	−	0.889879i	$-0.349212\pi$
$641$	23.0999	0.912392	0.456196	+	0.889879i	$0.349212\pi$
$642$	−20.5012	−0.809116
$643$	3.02172	0.119165	0.0595826	−	0.998223i	$-0.481023\pi$
$643$	3.02172	0.119165	0.0595826	+	0.998223i	$0.481023\pi$
$644$	−8.71980	−0.343608
$645$	−22.4969	−0.885813
$646$	14.5436	0.572212
$647$	6.63874	0.260996	0.130498	−	0.991449i	$-0.458342\pi$
$647$	6.63874	0.260996	0.130498	+	0.991449i	$0.458342\pi$
$648$	−5.07885	−0.199516
$649$	30.9256	1.21394
$650$	−5.23815	−0.205457
$651$	55.7085	2.18339
$652$	4.78967	0.187578
$653$	49.3981	1.93310	0.966548	−	0.256487i	$-0.0825652\pi$
$653$	49.3981	1.93310	0.966548	+	0.256487i	$0.0825652\pi$
$654$	−15.6724	−0.612839
$655$	49.2322	1.92366
$656$	−1.20461	−0.0470320
$657$	−5.53359	−0.215886
$658$	−51.8837	−2.02264
$659$	−27.1450	−1.05742	−0.528710	−	0.848802i	$-0.677324\pi$
$659$	−27.1450	−1.05742	−0.528710	+	0.848802i	$0.677324\pi$
$660$	−9.83228	−0.382721
$661$	29.3305	1.14083	0.570413	−	0.821358i	$-0.306783\pi$
$661$	29.3305	1.14083	0.570413	+	0.821358i	$0.306783\pi$
$662$	−22.3451	−0.868468
$663$	−13.4654	−0.522954
$664$	10.5323	0.408734
$665$	41.2796	1.60075
$666$	−7.63407	−0.295814
$667$	0.185269	0.00717364
$668$	−6.29987	−0.243749
$669$	3.16518	0.122373
$670$	12.7123	0.491119
$671$	−26.8504	−1.03655
$672$	6.99071	0.269672
$673$	11.5839	0.446527	0.223263	−	0.974758i	$-0.428329\pi$
$673$	11.5839	0.446527	0.223263	+	0.974758i	$0.428329\pi$
$674$	−25.4591	−0.980648
$675$	14.9904	0.576980
$676$	−9.09284	−0.349725
$677$	−7.42867	−0.285507	−0.142753	−	0.989758i	$-0.545596\pi$
$677$	−7.42867	−0.285507	−0.142753	+	0.989758i	$0.545596\pi$
$678$	−14.3764	−0.552122
$679$	−2.82314	−0.108342
$680$	−13.2707	−0.508909
$681$	−20.3790	−0.780924
$682$	19.9525	0.764021
$683$	−15.6148	−0.597484	−0.298742	−	0.954334i	$-0.596567\pi$
$683$	−15.6148	−0.597484	−0.298742	+	0.954334i	$0.596567\pi$
$684$	2.98321	0.114066
$685$	−49.9557	−1.90871
$686$	−50.4350	−1.92562
$687$	11.6825	0.445715
$688$	5.72882	0.218409
$689$	−1.09741	−0.0418079
$690$	−6.95454	−0.264755
$691$	39.3973	1.49874	0.749372	−	0.662149i	$-0.230356\pi$
$691$	39.3973	1.49874	0.749372	+	0.662149i	$0.230356\pi$
$692$	15.6508	0.594954
$693$	12.1330	0.460893
$694$	14.5074	0.550693
$695$	−30.4179	−1.15382
$696$	−0.148531	−0.00563005
$697$	5.77975	0.218924
$698$	36.1653	1.36888
$699$	−1.22718	−0.0464163
$700$	−13.0480	−0.493167
$701$	17.3108	0.653821	0.326911	−	0.945055i	$-0.393992\pi$
$701$	17.3108	0.653821	0.326911	+	0.945055i	$0.393992\pi$
$702$	−11.1814	−0.422014
$703$	−23.5121	−0.886776
$704$	2.50379	0.0943650
$705$	−41.3802	−1.55847
$706$	27.9529	1.05202
$707$	29.6892	1.11658
$708$	−17.5366	−0.659067
$709$	−1.24939	−0.0469218	−0.0234609	−	0.999725i	$-0.507469\pi$
$709$	−1.24939	−0.0469218	−0.0234609	+	0.999725i	$0.507469\pi$
$710$	−7.05831	−0.264894
$711$	11.2882	0.423340
$712$	−3.63481	−0.136220
$713$	14.1128	0.528527
$714$	−33.5417	−1.25527
$715$	−13.6886	−0.511924
$716$	−2.91516	−0.108945
$717$	−35.2349	−1.31587
$718$	−30.2159	−1.12765
$719$	1.13885	0.0424721	0.0212361	−	0.999774i	$-0.493240\pi$
$719$	1.13885	0.0424721	0.0212361	+	0.999774i	$0.493240\pi$
$720$	−2.72211	−0.101447
$721$	−56.0491	−2.08738
$722$	−9.81204	−0.365166
$723$	0.707754	0.0263217
$724$	22.3624	0.831094
$725$	0.277229	0.0102960
$726$	6.71712	0.249296
$727$	12.9747	0.481206	0.240603	−	0.970624i	$-0.422655\pi$
$727$	12.9747	0.481206	0.240603	+	0.970624i	$0.422655\pi$
$728$	9.73253	0.360711
$729$	29.0927	1.07751
$730$	15.5512	0.575576
$731$	−27.4871	−1.01665
$732$	15.2257	0.562760
$733$	41.4976	1.53275	0.766375	−	0.642393i	$-0.222058\pi$
$733$	41.4976	1.53275	0.766375	+	0.642393i	$0.222058\pi$
$734$	−20.5895	−0.759973
$735$	−67.7135	−2.49765
$736$	1.77097	0.0652789
$737$	11.5078	0.423894
$738$	1.18555	0.0436407
$739$	−44.8684	−1.65051	−0.825256	−	0.564759i	$-0.808969\pi$
$739$	−44.8684	−1.65051	−0.825256	+	0.564759i	$0.808969\pi$
$740$	21.4542	0.788673
$741$	−8.50679	−0.312505
$742$	−2.73359	−0.100353
$743$	−24.4480	−0.896909	−0.448454	−	0.893806i	$-0.648025\pi$
$743$	−24.4480	−0.896909	−0.448454	+	0.893806i	$0.648025\pi$
$744$	−11.3143	−0.414801
$745$	−15.7441	−0.576819
$746$	33.1378	1.21326
$747$	−10.3657	−0.379261
$748$	−12.0133	−0.439249
$749$	−71.0964	−2.59781
$750$	9.22832	0.336971
$751$	−25.0127	−0.912728	−0.456364	−	0.889793i	$-0.650848\pi$
$751$	−25.0127	−0.912728	−0.456364	+	0.889793i	$0.650848\pi$
$752$	10.5374	0.384261
$753$	10.7579	0.392040
$754$	−0.206786	−0.00753070
$755$	−15.3116	−0.557245
$756$	−27.8522	−1.01298
$757$	−26.6906	−0.970085	−0.485042	−	0.874491i	$-0.661196\pi$
$757$	−26.6906	−0.970085	−0.485042	+	0.874491i	$0.661196\pi$
$758$	12.7696	0.463814
$759$	−6.29557	−0.228515
$760$	−8.38379	−0.304112
$761$	37.5909	1.36267	0.681335	−	0.731972i	$-0.261400\pi$
$761$	37.5909	1.36267	0.681335	+	0.731972i	$0.261400\pi$
$762$	6.66010	0.241270
$763$	−54.3506	−1.96762
$764$	2.49471	0.0902555
$765$	13.0608	0.472213
$766$	20.2482	0.731599
$767$	−24.4147	−0.881563
$768$	−1.41980	−0.0512325
$769$	−46.2411	−1.66750	−0.833748	−	0.552145i	$-0.813810\pi$
$769$	−46.2411	−1.66750	−0.833748	+	0.552145i	$0.813810\pi$
$770$	−34.0976	−1.22879
$771$	−33.3211	−1.20003
$772$	−8.19446	−0.294925
$773$	1.56330	0.0562280	0.0281140	−	0.999605i	$-0.491050\pi$
$773$	1.56330	0.0562280	0.0281140	+	0.999605i	$0.491050\pi$
$774$	−5.63818	−0.202660
$775$	21.1178	0.758572
$776$	0.573374	0.0205829
$777$	54.2255	1.94533
$778$	−7.80259	−0.279736
$779$	3.65136	0.130824
$780$	7.76224	0.277933
$781$	−6.38950	−0.228634
$782$	−8.49719	−0.303859
$783$	0.591774	0.0211483
$784$	17.2432	0.615830
$785$	−12.6054	−0.449905
$786$	−25.2723	−0.901432
$787$	−16.4672	−0.586992	−0.293496	−	0.955960i	$-0.594819\pi$
$787$	−16.4672	−0.586992	−0.293496	+	0.955960i	$0.594819\pi$
$788$	9.68429	0.344989
$789$	−4.39415	−0.156436
$790$	−31.7235	−1.12867
$791$	−49.8562	−1.77268
$792$	−2.46418	−0.0875607
$793$	21.1974	0.752742
$794$	2.32755	0.0826018
$795$	−2.18019	−0.0773235
$796$	−13.2994	−0.471383
$797$	37.1320	1.31528	0.657642	−	0.753331i	$-0.271554\pi$
$797$	37.1320	1.31528	0.657642	+	0.753331i	$0.271554\pi$
$798$	−21.1900	−0.750117
$799$	−50.5591	−1.78865
$800$	2.65001	0.0936920
$801$	3.57730	0.126398
$802$	−14.2718	−0.503956
$803$	14.0777	0.496790
$804$	−6.52559	−0.230140
$805$	−24.1178	−0.850041
$806$	−15.7518	−0.554834
$807$	14.1072	0.496596
$808$	−6.02981	−0.212128
$809$	5.32830	0.187333	0.0936665	−	0.995604i	$-0.470141\pi$
$809$	5.32830	0.187333	0.0936665	+	0.995604i	$0.470141\pi$
$810$	−14.0474	−0.493576
$811$	−23.1264	−0.812078	−0.406039	−	0.913856i	$-0.633090\pi$
$811$	−23.1264	−0.812078	−0.406039	+	0.913856i	$0.633090\pi$
$812$	−0.515094	−0.0180762
$813$	−12.5924	−0.441634
$814$	19.4214	0.680718
$815$	13.2476	0.464042
$816$	6.81224	0.238476
$817$	−17.3650	−0.607524
$818$	1.89790	0.0663583
$819$	−9.57855	−0.334702
$820$	−3.33178	−0.116351
$821$	−40.9784	−1.43016	−0.715078	−	0.699044i	$-0.753609\pi$
$821$	−40.9784	−1.43016	−0.715078	+	0.699044i	$0.753609\pi$
$822$	25.6437	0.894426
$823$	12.3934	0.432008	0.216004	−	0.976393i	$-0.430698\pi$
$823$	12.3934	0.432008	0.216004	+	0.976393i	$0.430698\pi$
$824$	11.3834	0.396561
$825$	−9.42044	−0.327977
$826$	−60.8157	−2.11605
$827$	14.4984	0.504159	0.252080	−	0.967706i	$-0.418886\pi$
$827$	14.4984	0.504159	0.252080	+	0.967706i	$0.418886\pi$
$828$	−1.74295	−0.0605718
$829$	−1.82976	−0.0635503	−0.0317751	−	0.999495i	$-0.510116\pi$
$829$	−1.82976	−0.0635503	−0.0317751	+	0.999495i	$0.510116\pi$
$830$	29.1310	1.01115
$831$	−7.76398	−0.269329
$832$	−1.97665	−0.0685281
$833$	−82.7337	−2.86655
$834$	15.6144	0.540682
$835$	−17.4246	−0.603003
$836$	−7.58939	−0.262485
$837$	45.0780	1.55812
$838$	7.67186	0.265020
$839$	26.6622	0.920482	0.460241	−	0.887794i	$-0.347763\pi$
$839$	26.6622	0.920482	0.460241	+	0.887794i	$0.347763\pi$
$840$	19.3354	0.667133
$841$	−28.9891	−0.999623
$842$	17.3190	0.596852
$843$	−15.5380	−0.535156
$844$	−21.0200	−0.723538
$845$	−25.1496	−0.865172
$846$	−10.3707	−0.356553
$847$	23.2945	0.800407
$848$	0.555185	0.0190651
$849$	−2.85141	−0.0978602
$850$	−12.7149	−0.436116
$851$	13.7371	0.470900
$852$	3.62323	0.124130
$853$	−43.7876	−1.49926	−0.749629	−	0.661858i	$-0.769768\pi$
$853$	−43.7876	−1.49926	−0.749629	+	0.661858i	$0.769768\pi$
$854$	52.8017	1.80684
$855$	8.25115	0.282184
$856$	14.4395	0.493532
$857$	−31.0467	−1.06054	−0.530268	−	0.847830i	$-0.677909\pi$
$857$	−31.0467	−1.06054	−0.530268	+	0.847830i	$0.677909\pi$
$858$	7.02674	0.239889
$859$	32.0864	1.09478	0.547388	−	0.836879i	$-0.315622\pi$
$859$	32.0864	1.09478	0.547388	+	0.836879i	$0.315622\pi$
$860$	15.8451	0.540315
$861$	−8.42105	−0.286989
$862$	4.77263	0.162557
$863$	−39.5281	−1.34555	−0.672776	−	0.739847i	$-0.734898\pi$
$863$	−39.5281	−1.34555	−0.672776	+	0.739847i	$0.734898\pi$
$864$	5.65672	0.192446
$865$	43.2880	1.47184
$866$	−28.6089	−0.972171
$867$	−8.54884	−0.290334
$868$	−39.2370	−1.33179
$869$	−28.7176	−0.974177
$870$	−0.410817	−0.0139280
$871$	−9.08498	−0.307833
$872$	11.0385	0.373810
$873$	−0.564303	−0.0190988
$874$	−5.36810	−0.181579
$875$	32.0031	1.08190
$876$	−7.98286	−0.269716
$877$	37.7361	1.27426	0.637129	−	0.770757i	$-0.280122\pi$
$877$	37.7361	1.27426	0.637129	+	0.770757i	$0.280122\pi$
$878$	0.421893	0.0142382
$879$	−28.2585	−0.953137
$880$	6.92514	0.233446
$881$	−56.8670	−1.91590	−0.957950	−	0.286936i	$-0.907363\pi$
$881$	−56.8670	−1.91590	−0.957950	+	0.286936i	$0.907363\pi$
$882$	−16.9704	−0.571424
$883$	34.1673	1.14982	0.574911	−	0.818216i	$-0.305037\pi$
$883$	34.1673	1.14982	0.574911	+	0.818216i	$0.305037\pi$
$884$	9.48406	0.318983
$885$	−48.5040	−1.63044
$886$	31.4728	1.05735
$887$	−55.6416	−1.86826	−0.934132	−	0.356929i	$-0.883824\pi$
$887$	−55.6416	−1.86826	−0.934132	+	0.356929i	$0.883824\pi$
$888$	−11.0131	−0.369574
$889$	23.0967	0.774639
$890$	−10.0534	−0.336990
$891$	−12.7164	−0.426014
$892$	−2.22932	−0.0746432
$893$	−31.9407	−1.06886
$894$	8.08188	0.270298
$895$	−8.06294	−0.269514
$896$	−4.92374	−0.164491
$897$	4.97013	0.165948
$898$	−0.746007	−0.0248946
$899$	0.833664	0.0278043
$900$	−2.60809	−0.0869362
$901$	−2.66380	−0.0887440
$902$	−3.01608	−0.100424
$903$	40.0485	1.33273
$904$	10.1257	0.336775
$905$	61.8515	2.05601
$906$	7.85985	0.261126
$907$	30.4338	1.01054	0.505269	−	0.862962i	$-0.331393\pi$
$907$	30.4338	1.01054	0.505269	+	0.862962i	$0.331393\pi$
$908$	14.3535	0.476336
$909$	5.93442	0.196832
$910$	26.9189	0.892351
$911$	33.5168	1.11046	0.555231	−	0.831696i	$-0.312630\pi$
$911$	33.5168	1.11046	0.555231	+	0.831696i	$0.312630\pi$
$912$	4.30363	0.142508
$913$	26.3707	0.872743
$914$	−9.45978	−0.312902
$915$	42.1124	1.39219
$916$	−8.22830	−0.271871
$917$	−87.6422	−2.89420
$918$	−27.1412	−0.895792
$919$	−32.6087	−1.07566	−0.537830	−	0.843053i	$-0.680756\pi$
$919$	−32.6087	−1.07566	−0.537830	+	0.843053i	$0.680756\pi$
$920$	4.89827	0.161491
$921$	−34.7499	−1.14505
$922$	−4.49796	−0.148132
$923$	5.04429	0.166035
$924$	17.5032	0.575815
$925$	20.5556	0.675863
$926$	−1.77142	−0.0582123
$927$	−11.2033	−0.367966
$928$	0.104614	0.00343413
$929$	−52.5053	−1.72264	−0.861321	−	0.508062i	$-0.830362\pi$
$929$	−52.5053	−1.72264	−0.861321	+	0.508062i	$0.830362\pi$
$930$	−31.2937	−1.02616
$931$	−52.2671	−1.71298
$932$	0.864336	0.0283123
$933$	−11.2967	−0.369839
$934$	−22.9522	−0.751017
$935$	−33.2271	−1.08664
$936$	1.94538	0.0635868
$937$	−16.7949	−0.548665	−0.274333	−	0.961635i	$-0.588457\pi$
$937$	−16.7949	−0.548665	−0.274333	+	0.961635i	$0.588457\pi$
$938$	−22.6302	−0.738903
$939$	−5.41918	−0.176848
$940$	29.1452	0.950610
$941$	−16.1392	−0.526122	−0.263061	−	0.964779i	$-0.584732\pi$
$941$	−16.1392	−0.526122	−0.263061	+	0.964779i	$0.584732\pi$
$942$	6.47069	0.210826
$943$	−2.13332	−0.0694706
$944$	12.3515	0.402008
$945$	−77.0355	−2.50597
$946$	14.3437	0.466355
$947$	−7.07925	−0.230045	−0.115022	−	0.993363i	$-0.536694\pi$
$947$	−7.07925	−0.230045	−0.115022	+	0.993363i	$0.536694\pi$
$948$	16.2846	0.528898
$949$	−11.1138	−0.360770
$950$	−8.03262	−0.260613
$951$	2.43833	0.0790683
$952$	23.6243	0.765668
$953$	40.8855	1.32441	0.662206	−	0.749322i	$-0.269621\pi$
$953$	40.8855	1.32441	0.662206	+	0.749322i	$0.269621\pi$
$954$	−0.546402	−0.0176904
$955$	6.90003	0.223280
$956$	24.8169	0.802635
$957$	−0.371890	−0.0120215
$958$	−12.1642	−0.393008
$959$	88.9302	2.87171
$960$	−3.92696	−0.126742
$961$	32.5039	1.04851
$962$	−15.3325	−0.494339
$963$	−14.2111	−0.457945
$964$	−0.498490	−0.0160553
$965$	−22.6648	−0.729605
$966$	12.3803	0.398331
$967$	−49.3075	−1.58562	−0.792812	−	0.609467i	$-0.791384\pi$
$967$	−49.3075	−1.58562	−0.792812	+	0.609467i	$0.791384\pi$
$968$	−4.73105	−0.152062
$969$	−20.6490	−0.663342
$970$	1.58587	0.0509194
$971$	−11.2590	−0.361319	−0.180660	−	0.983546i	$-0.557823\pi$
$971$	−11.2590	−0.361319	−0.180660	+	0.983546i	$0.557823\pi$
$972$	−9.75923	−0.313027
$973$	54.1495	1.73595
$974$	−2.72647	−0.0873617
$975$	7.43711	0.238178
$976$	−10.7239	−0.343264
$977$	−13.8339	−0.442585	−0.221293	−	0.975207i	$-0.571028\pi$
$977$	−13.8339	−0.442585	−0.221293	+	0.975207i	$0.571028\pi$
$978$	−6.80035	−0.217451
$979$	−9.10078	−0.290862
$980$	47.6924	1.52348
$981$	−10.8638	−0.346856
$982$	35.1614	1.12204
$983$	−20.7044	−0.660366	−0.330183	−	0.943917i	$-0.607111\pi$
$983$	−20.7044	−0.660366	−0.330183	+	0.943917i	$0.607111\pi$
$984$	1.71030	0.0545222
$985$	26.7855	0.853456
$986$	−0.501943	−0.0159851
$987$	73.6642	2.34476
$988$	5.99156	0.190617
$989$	10.1456	0.322610
$990$	−6.81558	−0.216613
$991$	2.91869	0.0927151	0.0463576	−	0.998925i	$-0.485239\pi$
$991$	2.91869	0.0927151	0.0463576	+	0.998925i	$0.485239\pi$
$992$	7.96893	0.253014
$993$	31.7255	1.00678
$994$	12.5651	0.398540
$995$	−36.7842	−1.16614
$996$	−14.9538	−0.473828
$997$	−49.8947	−1.58018	−0.790091	−	0.612990i	$-0.789967\pi$
$997$	−49.8947	−1.58018	−0.790091	+	0.612990i	$0.789967\pi$
$998$	−10.4909	−0.332083
$999$	43.8780	1.38824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.15	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.15	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.41980 q^{3} +1.00000 q^{4} +2.76587 q^{5} -1.41980 q^{6} -4.92374 q^{7} +1.00000 q^{8} -0.984179 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.41980 q^{3} +1.00000 q^{4} +2.76587 q^{5} -1.41980 q^{6} -4.92374 q^{7} +1.00000 q^{8} -0.984179 q^{9} +2.76587 q^{10} +2.50379 q^{11} -1.41980 q^{12} -1.97665 q^{13} -4.92374 q^{14} -3.92696 q^{15} +1.00000 q^{16} -4.79804 q^{17} -0.984179 q^{18} -3.03116 q^{19} +2.76587 q^{20} +6.99071 q^{21} +2.50379 q^{22} +1.77097 q^{23} -1.41980 q^{24} +2.65001 q^{25} -1.97665 q^{26} +5.65672 q^{27} -4.92374 q^{28} +0.104614 q^{29} -3.92696 q^{30} +7.96893 q^{31} +1.00000 q^{32} -3.55487 q^{33} -4.79804 q^{34} -13.6184 q^{35} -0.984179 q^{36} +7.75679 q^{37} -3.03116 q^{38} +2.80644 q^{39} +2.76587 q^{40} -1.20461 q^{41} +6.99071 q^{42} +5.72882 q^{43} +2.50379 q^{44} -2.72211 q^{45} +1.77097 q^{46} +10.5374 q^{47} -1.41980 q^{48} +17.2432 q^{49} +2.65001 q^{50} +6.81224 q^{51} -1.97665 q^{52} +0.555185 q^{53} +5.65672 q^{54} +6.92514 q^{55} -4.92374 q^{56} +4.30363 q^{57} +0.104614 q^{58} +12.3515 q^{59} -3.92696 q^{60} -10.7239 q^{61} +7.96893 q^{62} +4.84584 q^{63} +1.00000 q^{64} -5.46715 q^{65} -3.55487 q^{66} +4.59614 q^{67} -4.79804 q^{68} -2.51442 q^{69} -13.6184 q^{70} -2.55194 q^{71} -0.984179 q^{72} +5.62254 q^{73} +7.75679 q^{74} -3.76247 q^{75} -3.03116 q^{76} -12.3280 q^{77} +2.80644 q^{78} -11.4697 q^{79} +2.76587 q^{80} -5.07885 q^{81} -1.20461 q^{82} +10.5323 q^{83} +6.99071 q^{84} -13.2707 q^{85} +5.72882 q^{86} -0.148531 q^{87} +2.50379 q^{88} -3.63481 q^{89} -2.72211 q^{90} +9.73253 q^{91} +1.77097 q^{92} -11.3143 q^{93} +10.5374 q^{94} -8.38379 q^{95} -1.41980 q^{96} +0.573374 q^{97} +17.2432 q^{98} -2.46418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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