LMFDB - Embedded newform 4022.2.a.f.1.8

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			1.8
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.46190 q^{3} +1.00000 q^{4} +2.99591 q^{5} -2.46190 q^{6} +1.50567 q^{7} +1.00000 q^{8} +3.06093 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.46190 q^{3} +1.00000 q^{4} +2.99591 q^{5} -2.46190 q^{6} +1.50567 q^{7} +1.00000 q^{8} +3.06093 q^{9} +2.99591 q^{10} +5.08824 q^{11} -2.46190 q^{12} +2.98655 q^{13} +1.50567 q^{14} -7.37563 q^{15} +1.00000 q^{16} +2.94825 q^{17} +3.06093 q^{18} +6.04409 q^{19} +2.99591 q^{20} -3.70681 q^{21} +5.08824 q^{22} -4.72973 q^{23} -2.46190 q^{24} +3.97549 q^{25} +2.98655 q^{26} -0.150012 q^{27} +1.50567 q^{28} -3.65835 q^{29} -7.37563 q^{30} +6.39024 q^{31} +1.00000 q^{32} -12.5267 q^{33} +2.94825 q^{34} +4.51087 q^{35} +3.06093 q^{36} +7.83760 q^{37} +6.04409 q^{38} -7.35258 q^{39} +2.99591 q^{40} -7.97956 q^{41} -3.70681 q^{42} +6.69773 q^{43} +5.08824 q^{44} +9.17029 q^{45} -4.72973 q^{46} -9.45111 q^{47} -2.46190 q^{48} -4.73294 q^{49} +3.97549 q^{50} -7.25828 q^{51} +2.98655 q^{52} -0.721698 q^{53} -0.150012 q^{54} +15.2439 q^{55} +1.50567 q^{56} -14.8799 q^{57} -3.65835 q^{58} +3.68957 q^{59} -7.37563 q^{60} -8.85295 q^{61} +6.39024 q^{62} +4.60877 q^{63} +1.00000 q^{64} +8.94745 q^{65} -12.5267 q^{66} -3.85242 q^{67} +2.94825 q^{68} +11.6441 q^{69} +4.51087 q^{70} -11.5071 q^{71} +3.06093 q^{72} -11.0351 q^{73} +7.83760 q^{74} -9.78724 q^{75} +6.04409 q^{76} +7.66124 q^{77} -7.35258 q^{78} +10.8396 q^{79} +2.99591 q^{80} -8.81349 q^{81} -7.97956 q^{82} -4.50222 q^{83} -3.70681 q^{84} +8.83269 q^{85} +6.69773 q^{86} +9.00648 q^{87} +5.08824 q^{88} -11.7478 q^{89} +9.17029 q^{90} +4.49678 q^{91} -4.72973 q^{92} -15.7321 q^{93} -9.45111 q^{94} +18.1076 q^{95} -2.46190 q^{96} +3.71720 q^{97} -4.73294 q^{98} +15.5748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.46190	−1.42138	−0.710688	−	0.703507i	$-0.751616\pi$
$3$	−2.46190	−1.42138	−0.710688	+	0.703507i	$0.751616\pi$
$4$	1.00000	0.500000
$5$	2.99591	1.33981	0.669906	−	0.742446i	$-0.266334\pi$
$5$	2.99591	1.33981	0.669906	+	0.742446i	$0.266334\pi$
$6$	−2.46190	−1.00506
$7$	1.50567	0.569092	0.284546	−	0.958662i	$-0.408157\pi$
$7$	1.50567	0.569092	0.284546	+	0.958662i	$0.408157\pi$
$8$	1.00000	0.353553
$9$	3.06093	1.02031
$10$	2.99591	0.947391
$11$	5.08824	1.53416	0.767082	−	0.641550i	$-0.221708\pi$
$11$	5.08824	1.53416	0.767082	+	0.641550i	$0.221708\pi$
$12$	−2.46190	−0.710688
$13$	2.98655	0.828321	0.414160	−	0.910204i	$-0.364075\pi$
$13$	2.98655	0.828321	0.414160	+	0.910204i	$0.364075\pi$
$14$	1.50567	0.402408
$15$	−7.37563	−1.90438
$16$	1.00000	0.250000
$17$	2.94825	0.715055	0.357528	−	0.933903i	$-0.383620\pi$
$17$	2.94825	0.715055	0.357528	+	0.933903i	$0.383620\pi$
$18$	3.06093	0.721469
$19$	6.04409	1.38661	0.693305	−	0.720644i	$-0.256154\pi$
$19$	6.04409	1.38661	0.693305	+	0.720644i	$0.256154\pi$
$20$	2.99591	0.669906
$21$	−3.70681	−0.808893
$22$	5.08824	1.08482
$23$	−4.72973	−0.986216	−0.493108	−	0.869968i	$-0.664139\pi$
$23$	−4.72973	−0.986216	−0.493108	+	0.869968i	$0.664139\pi$
$24$	−2.46190	−0.502532
$25$	3.97549	0.795098
$26$	2.98655	0.585711
$27$	−0.150012	−0.0288698
$28$	1.50567	0.284546
$29$	−3.65835	−0.679339	−0.339669	−	0.940545i	$-0.610315\pi$
$29$	−3.65835	−0.679339	−0.339669	+	0.940545i	$0.610315\pi$
$30$	−7.37563	−1.34660
$31$	6.39024	1.14772	0.573860	−	0.818953i	$-0.305445\pi$
$31$	6.39024	1.14772	0.573860	+	0.818953i	$0.305445\pi$
$32$	1.00000	0.176777
$33$	−12.5267	−2.18062
$34$	2.94825	0.505620
$35$	4.51087	0.762476
$36$	3.06093	0.510156
$37$	7.83760	1.28849	0.644247	−	0.764818i	$-0.277171\pi$
$37$	7.83760	1.28849	0.644247	+	0.764818i	$0.277171\pi$
$38$	6.04409	0.980482
$39$	−7.35258	−1.17736
$40$	2.99591	0.473695
$41$	−7.97956	−1.24620	−0.623099	−	0.782143i	$-0.714127\pi$
$41$	−7.97956	−1.24620	−0.623099	+	0.782143i	$0.714127\pi$
$42$	−3.70681	−0.571974
$43$	6.69773	1.02139	0.510697	−	0.859761i	$-0.329387\pi$
$43$	6.69773	1.02139	0.510697	+	0.859761i	$0.329387\pi$
$44$	5.08824	0.767082
$45$	9.17029	1.36703
$46$	−4.72973	−0.697360
$47$	−9.45111	−1.37859	−0.689293	−	0.724483i	$-0.742079\pi$
$47$	−9.45111	−1.37859	−0.689293	+	0.724483i	$0.742079\pi$
$48$	−2.46190	−0.355344
$49$	−4.73294	−0.676135
$50$	3.97549	0.562219
$51$	−7.25828	−1.01636
$52$	2.98655	0.414160
$53$	−0.721698	−0.0991328	−0.0495664	−	0.998771i	$-0.515784\pi$
$53$	−0.721698	−0.0991328	−0.0495664	+	0.998771i	$0.515784\pi$
$54$	−0.150012	−0.0204140
$55$	15.2439	2.05549
$56$	1.50567	0.201204
$57$	−14.8799	−1.97090
$58$	−3.65835	−0.480365
$59$	3.68957	0.480342	0.240171	−	0.970731i	$-0.422797\pi$
$59$	3.68957	0.480342	0.240171	+	0.970731i	$0.422797\pi$
$60$	−7.37563	−0.952189
$61$	−8.85295	−1.13350	−0.566752	−	0.823888i	$-0.691800\pi$
$61$	−8.85295	−1.13350	−0.566752	+	0.823888i	$0.691800\pi$
$62$	6.39024	0.811561
$63$	4.60877	0.580650
$64$	1.00000	0.125000
$65$	8.94745	1.10979
$66$	−12.5267	−1.54193
$67$	−3.85242	−0.470648	−0.235324	−	0.971917i	$-0.575615\pi$
$67$	−3.85242	−0.470648	−0.235324	+	0.971917i	$0.575615\pi$
$68$	2.94825	0.357528
$69$	11.6441	1.40178
$70$	4.51087	0.539152
$71$	−11.5071	−1.36565	−0.682823	−	0.730584i	$-0.739248\pi$
$71$	−11.5071	−1.36565	−0.682823	+	0.730584i	$0.739248\pi$
$72$	3.06093	0.360734
$73$	−11.0351	−1.29156	−0.645778	−	0.763526i	$-0.723467\pi$
$73$	−11.0351	−1.29156	−0.645778	+	0.763526i	$0.723467\pi$
$74$	7.83760	0.911103
$75$	−9.78724	−1.13013
$76$	6.04409	0.693305
$77$	7.66124	0.873079
$78$	−7.35258	−0.832516
$79$	10.8396	1.21955	0.609773	−	0.792576i	$-0.291260\pi$
$79$	10.8396	1.21955	0.609773	+	0.792576i	$0.291260\pi$
$80$	2.99591	0.334953
$81$	−8.81349	−0.979276
$82$	−7.97956	−0.881195
$83$	−4.50222	−0.494183	−0.247091	−	0.968992i	$-0.579475\pi$
$83$	−4.50222	−0.494183	−0.247091	+	0.968992i	$0.579475\pi$
$84$	−3.70681	−0.404447
$85$	8.83269	0.958040
$86$	6.69773	0.722235
$87$	9.00648	0.965596
$88$	5.08824	0.542409
$89$	−11.7478	−1.24526	−0.622630	−	0.782517i	$-0.713936\pi$
$89$	−11.7478	−1.24526	−0.622630	+	0.782517i	$0.713936\pi$
$90$	9.17029	0.966633
$91$	4.49678	0.471390
$92$	−4.72973	−0.493108
$93$	−15.7321	−1.63134
$94$	−9.45111	−0.974808
$95$	18.1076	1.85780
$96$	−2.46190	−0.251266
$97$	3.71720	0.377425	0.188712	−	0.982032i	$-0.439569\pi$
$97$	3.71720	0.377425	0.188712	+	0.982032i	$0.439569\pi$
$98$	−4.73294	−0.478100
$99$	15.5748	1.56532
$100$	3.97549	0.397549
$101$	−2.09495	−0.208456	−0.104228	−	0.994553i	$-0.533237\pi$
$101$	−2.09495	−0.208456	−0.104228	+	0.994553i	$0.533237\pi$
$102$	−7.25828	−0.718677
$103$	−1.96986	−0.194097	−0.0970483	−	0.995280i	$-0.530940\pi$
$103$	−1.96986	−0.194097	−0.0970483	+	0.995280i	$0.530940\pi$
$104$	2.98655	0.292856
$105$	−11.1053	−1.08377
$106$	−0.721698	−0.0700975
$107$	−7.93645	−0.767245	−0.383623	−	0.923490i	$-0.625324\pi$
$107$	−7.93645	−0.767245	−0.383623	+	0.923490i	$0.625324\pi$
$108$	−0.150012	−0.0144349
$109$	−0.579514	−0.0555074	−0.0277537	−	0.999615i	$-0.508835\pi$
$109$	−0.579514	−0.0555074	−0.0277537	+	0.999615i	$0.508835\pi$
$110$	15.2439	1.45345
$111$	−19.2954	−1.83143
$112$	1.50567	0.142273
$113$	−2.41317	−0.227012	−0.113506	−	0.993537i	$-0.536208\pi$
$113$	−2.41317	−0.227012	−0.113506	+	0.993537i	$0.536208\pi$
$114$	−14.8799	−1.39363
$115$	−14.1698	−1.32135
$116$	−3.65835	−0.339669
$117$	9.14164	0.845145
$118$	3.68957	0.339653
$119$	4.43910	0.406932
$120$	−7.37563	−0.673299
$121$	14.8902	1.35366
$122$	−8.85295	−0.801508
$123$	19.6448	1.77132
$124$	6.39024	0.573860
$125$	−3.06934	−0.274530
$126$	4.60877	0.410582
$127$	8.77902	0.779012	0.389506	−	0.921024i	$-0.372646\pi$
$127$	8.77902	0.779012	0.389506	+	0.921024i	$0.372646\pi$
$128$	1.00000	0.0883883
$129$	−16.4891	−1.45179
$130$	8.94745	0.784743
$131$	2.19488	0.191767	0.0958837	−	0.995393i	$-0.469432\pi$
$131$	2.19488	0.191767	0.0958837	+	0.995393i	$0.469432\pi$
$132$	−12.5267	−1.09031
$133$	9.10044	0.789108
$134$	−3.85242	−0.332798
$135$	−0.449422	−0.0386801
$136$	2.94825	0.252810
$137$	−3.58032	−0.305887	−0.152944	−	0.988235i	$-0.548875\pi$
$137$	−3.58032	−0.305887	−0.152944	+	0.988235i	$0.548875\pi$
$138$	11.6441	0.991212
$139$	13.4578	1.14148	0.570740	−	0.821131i	$-0.306657\pi$
$139$	13.4578	1.14148	0.570740	+	0.821131i	$0.306657\pi$
$140$	4.51087	0.381238
$141$	23.2677	1.95949
$142$	−11.5071	−0.965657
$143$	15.1963	1.27078
$144$	3.06093	0.255078
$145$	−10.9601	−0.910187
$146$	−11.0351	−0.913268
$147$	11.6520	0.961042
$148$	7.83760	0.644247
$149$	−9.26869	−0.759321	−0.379661	−	0.925126i	$-0.623959\pi$
$149$	−9.26869	−0.759321	−0.379661	+	0.925126i	$0.623959\pi$
$150$	−9.78724	−0.799125
$151$	−7.05179	−0.573867	−0.286933	−	0.957951i	$-0.592636\pi$
$151$	−7.05179	−0.573867	−0.286933	+	0.957951i	$0.592636\pi$
$152$	6.04409	0.490241
$153$	9.02439	0.729579
$154$	7.66124	0.617360
$155$	19.1446	1.53773
$156$	−7.35258	−0.588678
$157$	21.3895	1.70707	0.853534	−	0.521037i	$-0.174454\pi$
$157$	21.3895	1.70707	0.853534	+	0.521037i	$0.174454\pi$
$158$	10.8396	0.862350
$159$	1.77675	0.140905
$160$	2.99591	0.236848
$161$	−7.12143	−0.561247
$162$	−8.81349	−0.692453
$163$	14.9418	1.17033	0.585167	−	0.810913i	$-0.301029\pi$
$163$	14.9418	1.17033	0.585167	+	0.810913i	$0.301029\pi$
$164$	−7.97956	−0.623099
$165$	−37.5290	−2.92163
$166$	−4.50222	−0.349440
$167$	−22.6384	−1.75181	−0.875905	−	0.482484i	$-0.839735\pi$
$167$	−22.6384	−1.75181	−0.875905	+	0.482484i	$0.839735\pi$
$168$	−3.70681	−0.285987
$169$	−4.08050	−0.313885
$170$	8.83269	0.677437
$171$	18.5006	1.41477
$172$	6.69773	0.510697
$173$	7.39447	0.562191	0.281096	−	0.959680i	$-0.409302\pi$
$173$	7.39447	0.562191	0.281096	+	0.959680i	$0.409302\pi$
$174$	9.00648	0.682780
$175$	5.98579	0.452484
$176$	5.08824	0.383541
$177$	−9.08335	−0.682746
$178$	−11.7478	−0.880531
$179$	−16.9766	−1.26889	−0.634445	−	0.772968i	$-0.718771\pi$
$179$	−16.9766	−1.26889	−0.634445	+	0.772968i	$0.718771\pi$
$180$	9.17029	0.683513
$181$	−19.7536	−1.46827	−0.734136	−	0.679003i	$-0.762412\pi$
$181$	−19.7536	−1.46827	−0.734136	+	0.679003i	$0.762412\pi$
$182$	4.49678	0.333323
$183$	21.7950	1.61114
$184$	−4.72973	−0.348680
$185$	23.4808	1.72634
$186$	−15.7321	−1.15353
$187$	15.0014	1.09701
$188$	−9.45111	−0.689293
$189$	−0.225869	−0.0164295
$190$	18.1076	1.31366
$191$	−2.11592	−0.153102	−0.0765512	−	0.997066i	$-0.524391\pi$
$191$	−2.11592	−0.153102	−0.0765512	+	0.997066i	$0.524391\pi$
$192$	−2.46190	−0.177672
$193$	−17.9326	−1.29082	−0.645410	−	0.763837i	$-0.723313\pi$
$193$	−17.9326	−1.29082	−0.645410	+	0.763837i	$0.723313\pi$
$194$	3.71720	0.266880
$195$	−22.0277	−1.57744
$196$	−4.73294	−0.338067
$197$	21.2606	1.51476	0.757378	−	0.652976i	$-0.226480\pi$
$197$	21.2606	1.51476	0.757378	+	0.652976i	$0.226480\pi$
$198$	15.5748	1.10685
$199$	−6.06525	−0.429954	−0.214977	−	0.976619i	$-0.568968\pi$
$199$	−6.06525	−0.429954	−0.214977	+	0.976619i	$0.568968\pi$
$200$	3.97549	0.281110
$201$	9.48426	0.668968
$202$	−2.09495	−0.147400
$203$	−5.50829	−0.386606
$204$	−7.25828	−0.508181
$205$	−23.9061	−1.66967
$206$	−1.96986	−0.137247
$207$	−14.4774	−1.00625
$208$	2.98655	0.207080
$209$	30.7538	2.12729
$210$	−11.1053	−0.766338
$211$	24.1755	1.66431	0.832154	−	0.554545i	$-0.187108\pi$
$211$	24.1755	1.66431	0.832154	+	0.554545i	$0.187108\pi$
$212$	−0.721698	−0.0495664
$213$	28.3294	1.94110
$214$	−7.93645	−0.542524
$215$	20.0658	1.36848
$216$	−0.150012	−0.0102070
$217$	9.62162	0.653158
$218$	−0.579514	−0.0392496
$219$	27.1672	1.83579
$220$	15.2439	1.02775
$221$	8.80510	0.592295
$222$	−19.2954	−1.29502
$223$	−6.58760	−0.441138	−0.220569	−	0.975371i	$-0.570791\pi$
$223$	−6.58760	−0.441138	−0.220569	+	0.975371i	$0.570791\pi$
$224$	1.50567	0.100602
$225$	12.1687	0.811247
$226$	−2.41317	−0.160522
$227$	20.9466	1.39028	0.695138	−	0.718876i	$-0.255343\pi$
$227$	20.9466	1.39028	0.695138	+	0.718876i	$0.255343\pi$
$228$	−14.8799	−0.985448
$229$	−7.97847	−0.527232	−0.263616	−	0.964628i	$-0.584915\pi$
$229$	−7.97847	−0.527232	−0.263616	+	0.964628i	$0.584915\pi$
$230$	−14.1698	−0.934332
$231$	−18.8612	−1.24097
$232$	−3.65835	−0.240183
$233$	−5.92944	−0.388450	−0.194225	−	0.980957i	$-0.562219\pi$
$233$	−5.92944	−0.388450	−0.194225	+	0.980957i	$0.562219\pi$
$234$	9.14164	0.597608
$235$	−28.3147	−1.84705
$236$	3.68957	0.240171
$237$	−26.6859	−1.73344
$238$	4.43910	0.287744
$239$	28.1527	1.82105	0.910524	−	0.413456i	$-0.135679\pi$
$239$	28.1527	1.82105	0.910524	+	0.413456i	$0.135679\pi$
$240$	−7.37563	−0.476095
$241$	−16.0293	−1.03254	−0.516271	−	0.856426i	$-0.672680\pi$
$241$	−16.0293	−1.03254	−0.516271	+	0.856426i	$0.672680\pi$
$242$	14.8902	0.957179
$243$	22.1479	1.42079
$244$	−8.85295	−0.566752
$245$	−14.1795	−0.905894
$246$	19.6448	1.25251
$247$	18.0510	1.14856
$248$	6.39024	0.405781
$249$	11.0840	0.702420
$250$	−3.06934	−0.194122
$251$	1.32124	0.0833961	0.0416981	−	0.999130i	$-0.486723\pi$
$251$	1.32124	0.0833961	0.0416981	+	0.999130i	$0.486723\pi$
$252$	4.60877	0.290325
$253$	−24.0660	−1.51302
$254$	8.77902	0.550845
$255$	−21.7452	−1.36174
$256$	1.00000	0.0625000
$257$	8.87659	0.553706	0.276853	−	0.960912i	$-0.410708\pi$
$257$	8.87659	0.553706	0.276853	+	0.960912i	$0.410708\pi$
$258$	−16.4891	−1.02657
$259$	11.8009	0.733271
$260$	8.94745	0.554897
$261$	−11.1980	−0.693137
$262$	2.19488	0.135600
$263$	20.4295	1.25974	0.629869	−	0.776701i	$-0.283108\pi$
$263$	20.4295	1.25974	0.629869	+	0.776701i	$0.283108\pi$
$264$	−12.5267	−0.770967
$265$	−2.16214	−0.132819
$266$	9.10044	0.557984
$267$	28.9218	1.76998
$268$	−3.85242	−0.235324
$269$	13.4594	0.820636	0.410318	−	0.911942i	$-0.365418\pi$
$269$	13.4594	0.820636	0.410318	+	0.911942i	$0.365418\pi$
$270$	−0.449422	−0.0273509
$271$	−0.00727702	−0.000442048 0	−0.000221024	−	1.00000i	$-0.500070\pi$
$271$	−0.00727702	−0.000442048 0	−0.000221024		1.00000i	$0.500070\pi$
$272$	2.94825	0.178764
$273$	−11.0706	−0.670023
$274$	−3.58032	−0.216295
$275$	20.2283	1.21981
$276$	11.6441	0.700892
$277$	2.41431	0.145062	0.0725310	−	0.997366i	$-0.476892\pi$
$277$	2.41431	0.145062	0.0725310	+	0.997366i	$0.476892\pi$
$278$	13.4578	0.807148
$279$	19.5601	1.17103
$280$	4.51087	0.269576
$281$	1.43354	0.0855179	0.0427589	−	0.999085i	$-0.486385\pi$
$281$	1.43354	0.0855179	0.0427589	+	0.999085i	$0.486385\pi$
$282$	23.2677	1.38557
$283$	−11.4343	−0.679699	−0.339850	−	0.940480i	$-0.610376\pi$
$283$	−11.4343	−0.679699	−0.339850	+	0.940480i	$0.610376\pi$
$284$	−11.5071	−0.682823
$285$	−44.5790	−2.64063
$286$	15.1963	0.898577
$287$	−12.0146	−0.709200
$288$	3.06093	0.180367
$289$	−8.30783	−0.488696
$290$	−10.9601	−0.643599
$291$	−9.15137	−0.536463
$292$	−11.0351	−0.645778
$293$	24.4903	1.43074	0.715370	−	0.698746i	$-0.246258\pi$
$293$	24.4903	1.43074	0.715370	+	0.698746i	$0.246258\pi$
$294$	11.6520	0.679559
$295$	11.0536	0.643568
$296$	7.83760	0.455551
$297$	−0.763296	−0.0442909
$298$	−9.26869	−0.536921
$299$	−14.1256	−0.816904
$300$	−9.78724	−0.565067
$301$	10.0846	0.581267
$302$	−7.05179	−0.405785
$303$	5.15756	0.296294
$304$	6.04409	0.346653
$305$	−26.5227	−1.51868
$306$	9.02439	0.515890
$307$	26.0471	1.48659	0.743294	−	0.668965i	$-0.233263\pi$
$307$	26.0471	1.48659	0.743294	+	0.668965i	$0.233263\pi$
$308$	7.66124	0.436540
$309$	4.84960	0.275884
$310$	19.1446	1.08734
$311$	−9.03142	−0.512125	−0.256062	−	0.966660i	$-0.582425\pi$
$311$	−9.03142	−0.512125	−0.256062	+	0.966660i	$0.582425\pi$
$312$	−7.35258	−0.416258
$313$	27.6629	1.56360	0.781799	−	0.623530i	$-0.214302\pi$
$313$	27.6629	1.56360	0.781799	+	0.623530i	$0.214302\pi$
$314$	21.3895	1.20708
$315$	13.8075	0.777963
$316$	10.8396	0.609773
$317$	−25.5369	−1.43430	−0.717148	−	0.696920i	$-0.754553\pi$
$317$	−25.5369	−1.43430	−0.717148	+	0.696920i	$0.754553\pi$
$318$	1.77675	0.0996349
$319$	−18.6146	−1.04222
$320$	2.99591	0.167477
$321$	19.5387	1.09054
$322$	−7.12143	−0.396862
$323$	17.8195	0.991503
$324$	−8.81349	−0.489638
$325$	11.8730	0.658596
$326$	14.9418	0.827550
$327$	1.42670	0.0788968
$328$	−7.97956	−0.440597
$329$	−14.2303	−0.784542
$330$	−37.5290	−2.06590
$331$	13.3136	0.731784	0.365892	−	0.930657i	$-0.380764\pi$
$331$	13.3136	0.731784	0.365892	+	0.930657i	$0.380764\pi$
$332$	−4.50222	−0.247091
$333$	23.9904	1.31466
$334$	−22.6384	−1.23872
$335$	−11.5415	−0.630580
$336$	−3.70681	−0.202223
$337$	−23.4953	−1.27987	−0.639934	−	0.768430i	$-0.721038\pi$
$337$	−23.4953	−1.27987	−0.639934	+	0.768430i	$0.721038\pi$
$338$	−4.08050	−0.221950
$339$	5.94097	0.322669
$340$	8.83269	0.479020
$341$	32.5151	1.76079
$342$	18.5006	1.00040
$343$	−17.6660	−0.953874
$344$	6.69773	0.361117
$345$	34.8847	1.87813
$346$	7.39447	0.397529
$347$	5.52495	0.296595	0.148297	−	0.988943i	$-0.452621\pi$
$347$	5.52495	0.296595	0.148297	+	0.988943i	$0.452621\pi$
$348$	9.00648	0.482798
$349$	18.4548	0.987863	0.493931	−	0.869501i	$-0.335559\pi$
$349$	18.4548	0.987863	0.493931	+	0.869501i	$0.335559\pi$
$350$	5.98579	0.319954
$351$	−0.448018	−0.0239134
$352$	5.08824	0.271204
$353$	6.11775	0.325615	0.162808	−	0.986658i	$-0.447945\pi$
$353$	6.11775	0.325615	0.162808	+	0.986658i	$0.447945\pi$
$354$	−9.08335	−0.482774
$355$	−34.4744	−1.82971
$356$	−11.7478	−0.622630
$357$	−10.9286	−0.578403
$358$	−16.9766	−0.897241
$359$	−2.12858	−0.112342	−0.0561710	−	0.998421i	$-0.517889\pi$
$359$	−2.12858	−0.112342	−0.0561710	+	0.998421i	$0.517889\pi$
$360$	9.17029	0.483317
$361$	17.5311	0.922688
$362$	−19.7536	−1.03822
$363$	−36.6582	−1.92405
$364$	4.49678	0.235695
$365$	−33.0601	−1.73044
$366$	21.7950	1.13925
$367$	−21.5588	−1.12536	−0.562679	−	0.826675i	$-0.690229\pi$
$367$	−21.5588	−1.12536	−0.562679	+	0.826675i	$0.690229\pi$
$368$	−4.72973	−0.246554
$369$	−24.4249	−1.27151
$370$	23.4808	1.22071
$371$	−1.08664	−0.0564157
$372$	−15.7321	−0.815672
$373$	−34.9505	−1.80967	−0.904834	−	0.425763i	$-0.860006\pi$
$373$	−34.9505	−1.80967	−0.904834	+	0.425763i	$0.860006\pi$
$374$	15.0014	0.775704
$375$	7.55640	0.390211
$376$	−9.45111	−0.487404
$377$	−10.9259	−0.562711
$378$	−0.225869	−0.0116174
$379$	12.0178	0.617314	0.308657	−	0.951173i	$-0.400120\pi$
$379$	12.0178	0.617314	0.308657	+	0.951173i	$0.400120\pi$
$380$	18.1076	0.928899
$381$	−21.6130	−1.10727
$382$	−2.11592	−0.108260
$383$	−34.5305	−1.76443	−0.882213	−	0.470851i	$-0.843947\pi$
$383$	−34.5305	−1.76443	−0.882213	+	0.470851i	$0.843947\pi$
$384$	−2.46190	−0.125633
$385$	22.9524	1.16976
$386$	−17.9326	−0.912747
$387$	20.5013	1.04214
$388$	3.71720	0.188712
$389$	−29.9357	−1.51780	−0.758901	−	0.651206i	$-0.774264\pi$
$389$	−29.9357	−1.51780	−0.758901	+	0.651206i	$0.774264\pi$
$390$	−22.0277	−1.11542
$391$	−13.9444	−0.705199
$392$	−4.73294	−0.239050
$393$	−5.40356	−0.272574
$394$	21.2606	1.07109
$395$	32.4744	1.63396
$396$	15.5748	0.782662
$397$	23.7686	1.19291	0.596455	−	0.802646i	$-0.296575\pi$
$397$	23.7686	1.19291	0.596455	+	0.802646i	$0.296575\pi$
$398$	−6.06525	−0.304024
$399$	−22.4043	−1.12162
$400$	3.97549	0.198775
$401$	12.4945	0.623946	0.311973	−	0.950091i	$-0.399010\pi$
$401$	12.4945	0.623946	0.311973	+	0.950091i	$0.399010\pi$
$402$	9.48426	0.473032
$403$	19.0848	0.950681
$404$	−2.09495	−0.104228
$405$	−26.4044	−1.31205
$406$	−5.50829	−0.273372
$407$	39.8796	1.97676
$408$	−7.25828	−0.359339
$409$	−31.5695	−1.56101	−0.780507	−	0.625147i	$-0.785039\pi$
$409$	−31.5695	−1.56101	−0.780507	+	0.625147i	$0.785039\pi$
$410$	−23.9061	−1.18064
$411$	8.81437	0.434781
$412$	−1.96986	−0.0970483
$413$	5.55530	0.273358
$414$	−14.4774	−0.711524
$415$	−13.4883	−0.662112
$416$	2.98655	0.146428
$417$	−33.1318	−1.62247
$418$	30.7538	1.50422
$419$	−23.3063	−1.13859	−0.569295	−	0.822133i	$-0.692784\pi$
$419$	−23.3063	−1.13859	−0.569295	+	0.822133i	$0.692784\pi$
$420$	−11.1053	−0.541883
$421$	−34.6522	−1.68885	−0.844423	−	0.535677i	$-0.820056\pi$
$421$	−34.6522	−1.68885	−0.844423	+	0.535677i	$0.820056\pi$
$422$	24.1755	1.17684
$423$	−28.9292	−1.40659
$424$	−0.721698	−0.0350487
$425$	11.7207	0.568539
$426$	28.3294	1.37256
$427$	−13.3297	−0.645067
$428$	−7.93645	−0.383623
$429$	−37.4117	−1.80626
$430$	20.0658	0.967659
$431$	−10.5413	−0.507755	−0.253878	−	0.967236i	$-0.581706\pi$
$431$	−10.5413	−0.507755	−0.253878	+	0.967236i	$0.581706\pi$
$432$	−0.150012	−0.00721744
$433$	36.2167	1.74046	0.870231	−	0.492644i	$-0.163969\pi$
$433$	36.2167	1.74046	0.870231	+	0.492644i	$0.163969\pi$
$434$	9.62162	0.461852
$435$	26.9826	1.29372
$436$	−0.579514	−0.0277537
$437$	−28.5869	−1.36750
$438$	27.1672	1.29810
$439$	1.23126	0.0587648	0.0293824	−	0.999568i	$-0.490646\pi$
$439$	1.23126	0.0587648	0.0293824	+	0.999568i	$0.490646\pi$
$440$	15.2439	0.726726
$441$	−14.4872	−0.689868
$442$	8.80510	0.418816
$443$	−7.25796	−0.344836	−0.172418	−	0.985024i	$-0.555158\pi$
$443$	−7.25796	−0.344836	−0.172418	+	0.985024i	$0.555158\pi$
$444$	−19.2954	−0.915717
$445$	−35.1952	−1.66841
$446$	−6.58760	−0.311932
$447$	22.8186	1.07928
$448$	1.50567	0.0711364
$449$	27.6245	1.30368	0.651840	−	0.758356i	$-0.273997\pi$
$449$	27.6245	1.30368	0.651840	+	0.758356i	$0.273997\pi$
$450$	12.1687	0.573638
$451$	−40.6019	−1.91187
$452$	−2.41317	−0.113506
$453$	17.3608	0.815681
$454$	20.9466	0.983074
$455$	13.4720	0.631575
$456$	−14.8799	−0.696817
$457$	−9.36755	−0.438196	−0.219098	−	0.975703i	$-0.570311\pi$
$457$	−9.36755	−0.438196	−0.219098	+	0.975703i	$0.570311\pi$
$458$	−7.97847	−0.372810
$459$	−0.442272	−0.0206435
$460$	−14.1698	−0.660673
$461$	21.7263	1.01189	0.505946	−	0.862565i	$-0.331143\pi$
$461$	21.7263	1.01189	0.505946	+	0.862565i	$0.331143\pi$
$462$	−18.8612	−0.877501
$463$	−24.8843	−1.15647	−0.578235	−	0.815870i	$-0.696258\pi$
$463$	−24.8843	−1.15647	−0.578235	+	0.815870i	$0.696258\pi$
$464$	−3.65835	−0.169835
$465$	−47.1320	−2.18569
$466$	−5.92944	−0.274676
$467$	13.1677	0.609327	0.304663	−	0.952460i	$-0.401456\pi$
$467$	13.1677	0.609327	0.304663	+	0.952460i	$0.401456\pi$
$468$	9.14164	0.422572
$469$	−5.80049	−0.267842
$470$	−28.3147	−1.30606
$471$	−52.6588	−2.42639
$472$	3.68957	0.169826
$473$	34.0797	1.56698
$474$	−26.6859	−1.22572
$475$	24.0282	1.10249
$476$	4.43910	0.203466
$477$	−2.20907	−0.101146
$478$	28.1527	1.28768
$479$	−2.64392	−0.120804	−0.0604019	−	0.998174i	$-0.519238\pi$
$479$	−2.64392	−0.120804	−0.0604019	+	0.998174i	$0.519238\pi$
$480$	−7.37563	−0.336650
$481$	23.4074	1.06729
$482$	−16.0293	−0.730117
$483$	17.5322	0.797744
$484$	14.8902	0.676828
$485$	11.1364	0.505679
$486$	22.1479	1.00465
$487$	−3.61405	−0.163768	−0.0818841	−	0.996642i	$-0.526094\pi$
$487$	−3.61405	−0.163768	−0.0818841	+	0.996642i	$0.526094\pi$
$488$	−8.85295	−0.400754
$489$	−36.7852	−1.66348
$490$	−14.1795	−0.640564
$491$	−19.6302	−0.885899	−0.442949	−	0.896547i	$-0.646068\pi$
$491$	−19.6302	−0.885899	−0.442949	+	0.896547i	$0.646068\pi$
$492$	19.6448	0.885658
$493$	−10.7857	−0.485765
$494$	18.0510	0.812153
$495$	46.6607	2.09724
$496$	6.39024	0.286930
$497$	−17.3260	−0.777177
$498$	11.0840	0.496686
$499$	32.5620	1.45768	0.728838	−	0.684686i	$-0.240061\pi$
$499$	32.5620	1.45768	0.728838	+	0.684686i	$0.240061\pi$
$500$	−3.06934	−0.137265
$501$	55.7333	2.48998
$502$	1.32124	0.0589700
$503$	23.5586	1.05043	0.525213	−	0.850971i	$-0.323986\pi$
$503$	23.5586	1.05043	0.525213	+	0.850971i	$0.323986\pi$
$504$	4.60877	0.205291
$505$	−6.27629	−0.279291
$506$	−24.0660	−1.06986
$507$	10.0458	0.446148
$508$	8.77902	0.389506
$509$	−26.6937	−1.18318	−0.591589	−	0.806240i	$-0.701499\pi$
$509$	−26.6937	−1.18318	−0.591589	+	0.806240i	$0.701499\pi$
$510$	−21.7452	−0.962893
$511$	−16.6152	−0.735013
$512$	1.00000	0.0441942
$513$	−0.906685	−0.0400311
$514$	8.87659	0.391529
$515$	−5.90154	−0.260053
$516$	−16.4891	−0.725893
$517$	−48.0895	−2.11498
$518$	11.8009	0.518501
$519$	−18.2044	−0.799086
$520$	8.94745	0.392372
$521$	−20.3781	−0.892780	−0.446390	−	0.894839i	$-0.647291\pi$
$521$	−20.3781	−0.892780	−0.446390	+	0.894839i	$0.647291\pi$
$522$	−11.1980	−0.490122
$523$	−0.0821073	−0.00359030	−0.00179515	−	0.999998i	$-0.500571\pi$
$523$	−0.0821073	−0.00359030	−0.00179515	+	0.999998i	$0.500571\pi$
$524$	2.19488	0.0958837
$525$	−14.7364	−0.643149
$526$	20.4295	0.890770
$527$	18.8400	0.820684
$528$	−12.5267	−0.545156
$529$	−0.629677	−0.0273773
$530$	−2.16214	−0.0939175
$531$	11.2935	0.490098
$532$	9.10044	0.394554
$533$	−23.8314	−1.03225
$534$	28.9218	1.25157
$535$	−23.7769	−1.02796
$536$	−3.85242	−0.166399
$537$	41.7946	1.80357
$538$	13.4594	0.580277
$539$	−24.0824	−1.03730
$540$	−0.449422	−0.0193400
$541$	10.9829	0.472193	0.236096	−	0.971730i	$-0.424132\pi$
$541$	10.9829	0.472193	0.236096	+	0.971730i	$0.424132\pi$
$542$	−0.00727702	−0.000312575 0
$543$	48.6313	2.08697
$544$	2.94825	0.126405
$545$	−1.73617	−0.0743695
$546$	−11.0706	−0.473778
$547$	3.44728	0.147395	0.0736976	−	0.997281i	$-0.476520\pi$
$547$	3.44728	0.147395	0.0736976	+	0.997281i	$0.476520\pi$
$548$	−3.58032	−0.152944
$549$	−27.0983	−1.15653
$550$	20.2283	0.862536
$551$	−22.1114	−0.941978
$552$	11.6441	0.495606
$553$	16.3209	0.694034
$554$	2.41431	0.102574
$555$	−57.8072	−2.45378
$556$	13.4578	0.570740
$557$	31.4558	1.33283	0.666413	−	0.745583i	$-0.267829\pi$
$557$	31.4558	1.33283	0.666413	+	0.745583i	$0.267829\pi$
$558$	19.5601	0.828045
$559$	20.0031	0.846042
$560$	4.51087	0.190619
$561$	−36.9319	−1.55927
$562$	1.43354	0.0604703
$563$	0.851130	0.0358708	0.0179354	−	0.999839i	$-0.494291\pi$
$563$	0.851130	0.0358708	0.0179354	+	0.999839i	$0.494291\pi$
$564$	23.2677	0.979745
$565$	−7.22964	−0.304153
$566$	−11.4343	−0.480620
$567$	−13.2702	−0.557298
$568$	−11.5071	−0.482828
$569$	26.5389	1.11257	0.556285	−	0.830991i	$-0.312226\pi$
$569$	26.5389	1.11257	0.556285	+	0.830991i	$0.312226\pi$
$570$	−44.5790	−1.86721
$571$	−20.8119	−0.870951	−0.435475	−	0.900201i	$-0.643420\pi$
$571$	−20.8119	−0.870951	−0.435475	+	0.900201i	$0.643420\pi$
$572$	15.1963	0.635390
$573$	5.20917	0.217616
$574$	−12.0146	−0.501480
$575$	−18.8030	−0.784139
$576$	3.06093	0.127539
$577$	14.8796	0.619445	0.309722	−	0.950827i	$-0.399764\pi$
$577$	14.8796	0.619445	0.309722	+	0.950827i	$0.399764\pi$
$578$	−8.30783	−0.345560
$579$	44.1483	1.83474
$580$	−10.9601	−0.455093
$581$	−6.77888	−0.281235
$582$	−9.15137	−0.379337
$583$	−3.67217	−0.152086
$584$	−11.0351	−0.456634
$585$	27.3876	1.13234
$586$	24.4903	1.01169
$587$	−17.8584	−0.737093	−0.368547	−	0.929609i	$-0.620145\pi$
$587$	−17.8584	−0.737093	−0.368547	+	0.929609i	$0.620145\pi$
$588$	11.6520	0.480521
$589$	38.6232	1.59144
$590$	11.0536	0.455071
$591$	−52.3415	−2.15304
$592$	7.83760	0.322123
$593$	2.93935	0.120705	0.0603523	−	0.998177i	$-0.480778\pi$
$593$	2.93935	0.120705	0.0603523	+	0.998177i	$0.480778\pi$
$594$	−0.763296	−0.0313184
$595$	13.2992	0.545213
$596$	−9.26869	−0.379661
$597$	14.9320	0.611127
$598$	−14.1256	−0.577638
$599$	24.2868	0.992333	0.496166	−	0.868227i	$-0.334741\pi$
$599$	24.2868	0.992333	0.496166	+	0.868227i	$0.334741\pi$
$600$	−9.78724	−0.399563
$601$	6.05826	0.247122	0.123561	−	0.992337i	$-0.460569\pi$
$601$	6.05826	0.247122	0.123561	+	0.992337i	$0.460569\pi$
$602$	10.0846	0.411018
$603$	−11.7920	−0.480207
$604$	−7.05179	−0.286933
$605$	44.6098	1.81365
$606$	5.15756	0.209511
$607$	20.0300	0.812992	0.406496	−	0.913653i	$-0.366751\pi$
$607$	20.0300	0.812992	0.406496	+	0.913653i	$0.366751\pi$
$608$	6.04409	0.245120
$609$	13.5608	0.549513
$610$	−26.5227	−1.07387
$611$	−28.2262	−1.14191
$612$	9.02439	0.364789
$613$	20.1782	0.814989	0.407494	−	0.913208i	$-0.366403\pi$
$613$	20.1782	0.814989	0.407494	+	0.913208i	$0.366403\pi$
$614$	26.0471	1.05118
$615$	58.8542	2.37323
$616$	7.66124	0.308680
$617$	−22.0614	−0.888160	−0.444080	−	0.895987i	$-0.646469\pi$
$617$	−22.0614	−0.888160	−0.444080	+	0.895987i	$0.646469\pi$
$618$	4.84960	0.195080
$619$	43.1656	1.73497	0.867486	−	0.497461i	$-0.165734\pi$
$619$	43.1656	1.73497	0.867486	+	0.497461i	$0.165734\pi$
$620$	19.1446	0.768865
$621$	0.709514	0.0284718
$622$	−9.03142	−0.362127
$623$	−17.6883	−0.708667
$624$	−7.35258	−0.294339
$625$	−29.0729	−1.16292
$626$	27.6629	1.10563
$627$	−75.7127	−3.02367
$628$	21.3895	0.853534
$629$	23.1072	0.921344
$630$	13.8075	0.550103
$631$	−24.1801	−0.962593	−0.481297	−	0.876558i	$-0.659834\pi$
$631$	−24.1801	−0.962593	−0.481297	+	0.876558i	$0.659834\pi$
$632$	10.8396	0.431175
$633$	−59.5175	−2.36561
$634$	−25.5369	−1.01420
$635$	26.3012	1.04373
$636$	1.77675	0.0704525
$637$	−14.1352	−0.560057
$638$	−18.6146	−0.736958
$639$	−35.2226	−1.39338
$640$	2.99591	0.118424
$641$	−22.1248	−0.873879	−0.436939	−	0.899491i	$-0.643938\pi$
$641$	−22.1248	−0.873879	−0.436939	+	0.899491i	$0.643938\pi$
$642$	19.5387	0.771131
$643$	7.99928	0.315461	0.157730	−	0.987482i	$-0.449582\pi$
$643$	7.99928	0.315461	0.157730	+	0.987482i	$0.449582\pi$
$644$	−7.12143	−0.280624
$645$	−49.3999	−1.94512
$646$	17.8195	0.701099
$647$	−21.2476	−0.835331	−0.417666	−	0.908601i	$-0.637152\pi$
$647$	−21.2476	−0.835331	−0.417666	+	0.908601i	$0.637152\pi$
$648$	−8.81349	−0.346226
$649$	18.7734	0.736922
$650$	11.8730	0.465698
$651$	−23.6874	−0.928384
$652$	14.9418	0.585167
$653$	1.49286	0.0584202	0.0292101	−	0.999573i	$-0.490701\pi$
$653$	1.49286	0.0584202	0.0292101	+	0.999573i	$0.490701\pi$
$654$	1.42670	0.0557885
$655$	6.57566	0.256932
$656$	−7.97956	−0.311549
$657$	−33.7776	−1.31779
$658$	−14.2303	−0.554755
$659$	−38.4039	−1.49600	−0.748001	−	0.663698i	$-0.768986\pi$
$659$	−38.4039	−1.49600	−0.748001	+	0.663698i	$0.768986\pi$
$660$	−37.5290	−1.46081
$661$	−12.0757	−0.469692	−0.234846	−	0.972033i	$-0.575459\pi$
$661$	−12.0757	−0.469692	−0.234846	+	0.972033i	$0.575459\pi$
$662$	13.3136	0.517449
$663$	−21.6772	−0.841874
$664$	−4.50222	−0.174720
$665$	27.2641	1.05726
$666$	23.9904	0.929608
$667$	17.3030	0.669975
$668$	−22.6384	−0.875905
$669$	16.2180	0.627023
$670$	−11.5415	−0.445888
$671$	−45.0460	−1.73898
$672$	−3.70681	−0.142993
$673$	−14.9487	−0.576230	−0.288115	−	0.957596i	$-0.593029\pi$
$673$	−14.9487	−0.576230	−0.288115	+	0.957596i	$0.593029\pi$
$674$	−23.4953	−0.905004
$675$	−0.596370	−0.0229543
$676$	−4.08050	−0.156942
$677$	7.67564	0.294999	0.147499	−	0.989062i	$-0.452878\pi$
$677$	7.67564	0.294999	0.147499	+	0.989062i	$0.452878\pi$
$678$	5.94097	0.228162
$679$	5.59690	0.214789
$680$	8.83269	0.338718
$681$	−51.5684	−1.97611
$682$	32.5151	1.24507
$683$	−0.148764	−0.00569231	−0.00284615	−	0.999996i	$-0.500906\pi$
$683$	−0.148764	−0.00569231	−0.00284615	+	0.999996i	$0.500906\pi$
$684$	18.5006	0.707387
$685$	−10.7263	−0.409832
$686$	−17.6660	−0.674491
$687$	19.6422	0.749396
$688$	6.69773	0.255349
$689$	−2.15539	−0.0821138
$690$	34.8847	1.32804
$691$	−31.8793	−1.21274	−0.606372	−	0.795181i	$-0.707376\pi$
$691$	−31.8793	−1.21274	−0.606372	+	0.795181i	$0.707376\pi$
$692$	7.39447	0.281096
$693$	23.4505	0.890812
$694$	5.52495	0.209724
$695$	40.3185	1.52937
$696$	9.00648	0.341390
$697$	−23.5257	−0.891100
$698$	18.4548	0.698524
$699$	14.5977	0.552134
$700$	5.98579	0.226242
$701$	−51.1437	−1.93167	−0.965836	−	0.259156i	$-0.916556\pi$
$701$	−51.1437	−1.93167	−0.965836	+	0.259156i	$0.916556\pi$
$702$	−0.448018	−0.0169093
$703$	47.3712	1.78664
$704$	5.08824	0.191770
$705$	69.7078	2.62535
$706$	6.11775	0.230245
$707$	−3.15432	−0.118630
$708$	−9.08335	−0.341373
$709$	−4.94843	−0.185842	−0.0929210	−	0.995673i	$-0.529620\pi$
$709$	−4.94843	−0.185842	−0.0929210	+	0.995673i	$0.529620\pi$
$710$	−34.4744	−1.29380
$711$	33.1792	1.24432
$712$	−11.7478	−0.440266
$713$	−30.2241	−1.13190
$714$	−10.9286	−0.408993
$715$	45.5268	1.70261
$716$	−16.9766	−0.634445
$717$	−69.3091	−2.58839
$718$	−2.12858	−0.0794378
$719$	−10.2334	−0.381642	−0.190821	−	0.981625i	$-0.561115\pi$
$719$	−10.2334	−0.381642	−0.190821	+	0.981625i	$0.561115\pi$
$720$	9.17029	0.341756
$721$	−2.96598	−0.110459
$722$	17.5311	0.652439
$723$	39.4626	1.46763
$724$	−19.7536	−0.734136
$725$	−14.5437	−0.540141
$726$	−36.6582	−1.36051
$727$	−10.8125	−0.401014	−0.200507	−	0.979692i	$-0.564259\pi$
$727$	−10.8125	−0.401014	−0.200507	+	0.979692i	$0.564259\pi$
$728$	4.49678	0.166662
$729$	−28.0854	−1.04020
$730$	−33.0601	−1.22361
$731$	19.7466	0.730353
$732$	21.7950	0.805568
$733$	−4.90020	−0.180993	−0.0904965	−	0.995897i	$-0.528845\pi$
$733$	−4.90020	−0.180993	−0.0904965	+	0.995897i	$0.528845\pi$
$734$	−21.5588	−0.795749
$735$	34.9084	1.28762
$736$	−4.72973	−0.174340
$737$	−19.6020	−0.722051
$738$	−24.4249	−0.899093
$739$	−8.74369	−0.321642	−0.160821	−	0.986984i	$-0.551414\pi$
$739$	−8.74369	−0.321642	−0.160821	+	0.986984i	$0.551414\pi$
$740$	23.4808	0.863170
$741$	−44.4397	−1.63253
$742$	−1.08664	−0.0398919
$743$	5.32704	0.195430	0.0977151	−	0.995214i	$-0.468847\pi$
$743$	5.32704	0.195430	0.0977151	+	0.995214i	$0.468847\pi$
$744$	−15.7321	−0.576767
$745$	−27.7682	−1.01735
$746$	−34.9505	−1.27963
$747$	−13.7810	−0.504220
$748$	15.0014	0.548506
$749$	−11.9497	−0.436633
$750$	7.55640	0.275921
$751$	33.2623	1.21376	0.606879	−	0.794794i	$-0.292421\pi$
$751$	33.2623	1.21376	0.606879	+	0.794794i	$0.292421\pi$
$752$	−9.45111	−0.344647
$753$	−3.25276	−0.118537
$754$	−10.9259	−0.397896
$755$	−21.1265	−0.768874
$756$	−0.225869	−0.00821477
$757$	16.8240	0.611479	0.305739	−	0.952115i	$-0.401096\pi$
$757$	16.8240	0.611479	0.305739	+	0.952115i	$0.401096\pi$
$758$	12.0178	0.436507
$759$	59.2480	2.15057
$760$	18.1076	0.656831
$761$	43.5028	1.57697	0.788487	−	0.615052i	$-0.210865\pi$
$761$	43.5028	1.57697	0.788487	+	0.615052i	$0.210865\pi$
$762$	−21.6130	−0.782958
$763$	−0.872559	−0.0315888
$764$	−2.11592	−0.0765512
$765$	27.0363	0.977499
$766$	−34.5305	−1.24764
$767$	11.0191	0.397877
$768$	−2.46190	−0.0888360
$769$	40.9654	1.47725	0.738624	−	0.674117i	$-0.235476\pi$
$769$	40.9654	1.47725	0.738624	+	0.674117i	$0.235476\pi$
$770$	22.9524	0.827147
$771$	−21.8532	−0.787025
$772$	−17.9326	−0.645410
$773$	10.8817	0.391387	0.195694	−	0.980665i	$-0.437304\pi$
$773$	10.8817	0.391387	0.195694	+	0.980665i	$0.437304\pi$
$774$	20.5013	0.736904
$775$	25.4043	0.912550
$776$	3.71720	0.133440
$777$	−29.0525	−1.04225
$778$	−29.9357	−1.07325
$779$	−48.2292	−1.72799
$780$	−22.0277	−0.788718
$781$	−58.5511	−2.09512
$782$	−13.9444	−0.498651
$783$	0.548796	0.0196124
$784$	−4.73294	−0.169034
$785$	64.0811	2.28715
$786$	−5.40356	−0.192739
$787$	−33.2746	−1.18611	−0.593056	−	0.805161i	$-0.702079\pi$
$787$	−33.2746	−1.18611	−0.593056	+	0.805161i	$0.702079\pi$
$788$	21.2606	0.757378
$789$	−50.2954	−1.79056
$790$	32.4744	1.15539
$791$	−3.63345	−0.129191
$792$	15.5748	0.553425
$793$	−26.4398	−0.938905
$794$	23.7686	0.843515
$795$	5.32297	0.188786
$796$	−6.06525	−0.214977
$797$	−31.0038	−1.09821	−0.549105	−	0.835754i	$-0.685031\pi$
$797$	−31.0038	−1.09821	−0.549105	+	0.835754i	$0.685031\pi$
$798$	−22.4043	−0.793105
$799$	−27.8642	−0.985765
$800$	3.97549	0.140555
$801$	−35.9591	−1.27055
$802$	12.4945	0.441197
$803$	−56.1490	−1.98146
$804$	9.48426	0.334484
$805$	−21.3352	−0.751966
$806$	19.0848	0.672233
$807$	−33.1357	−1.16643
$808$	−2.09495	−0.0737002
$809$	−32.1574	−1.13059	−0.565296	−	0.824888i	$-0.691238\pi$
$809$	−32.1574	−1.13059	−0.565296	+	0.824888i	$0.691238\pi$
$810$	−26.4044	−0.927757
$811$	0.924240	0.0324545	0.0162272	−	0.999868i	$-0.494834\pi$
$811$	0.924240	0.0324545	0.0162272	+	0.999868i	$0.494834\pi$
$812$	−5.50829	−0.193303
$813$	0.0179153	0.000628316 0
$814$	39.8796	1.39778
$815$	44.7644	1.56803
$816$	−7.25828	−0.254091
$817$	40.4817	1.41628
$818$	−31.5695	−1.10380
$819$	13.7643	0.480965
$820$	−23.9061	−0.834836
$821$	−20.9110	−0.729798	−0.364899	−	0.931047i	$-0.618897\pi$
$821$	−20.9110	−0.729798	−0.364899	+	0.931047i	$0.618897\pi$
$822$	8.81437	0.307437
$823$	10.8925	0.379690	0.189845	−	0.981814i	$-0.439201\pi$
$823$	10.8925	0.379690	0.189845	+	0.981814i	$0.439201\pi$
$824$	−1.96986	−0.0686235
$825$	−49.7999	−1.73381
$826$	5.55530	0.193294
$827$	−17.1419	−0.596082	−0.298041	−	0.954553i	$-0.596333\pi$
$827$	−17.1419	−0.596082	−0.298041	+	0.954553i	$0.596333\pi$
$828$	−14.4774	−0.503124
$829$	−43.6304	−1.51534	−0.757672	−	0.652635i	$-0.773663\pi$
$829$	−43.6304	−1.51534	−0.757672	+	0.652635i	$0.773663\pi$
$830$	−13.4883	−0.468184
$831$	−5.94379	−0.206188
$832$	2.98655	0.103540
$833$	−13.9539	−0.483474
$834$	−33.1318	−1.14726
$835$	−67.8226	−2.34710
$836$	30.7538	1.06364
$837$	−0.958610	−0.0331344
$838$	−23.3063	−0.805104
$839$	45.5853	1.57378	0.786890	−	0.617093i	$-0.211690\pi$
$839$	45.5853	1.57378	0.786890	+	0.617093i	$0.211690\pi$
$840$	−11.1053	−0.383169
$841$	−15.6165	−0.538499
$842$	−34.6522	−1.19419
$843$	−3.52923	−0.121553
$844$	24.1755	0.832154
$845$	−12.2248	−0.420547
$846$	−28.9292	−0.994607
$847$	22.4198	0.770354
$848$	−0.721698	−0.0247832
$849$	28.1501	0.966109
$850$	11.7207	0.402018
$851$	−37.0697	−1.27073
$852$	28.3294	0.970548
$853$	35.1004	1.20182	0.600908	−	0.799318i	$-0.294806\pi$
$853$	35.1004	1.20182	0.600908	+	0.799318i	$0.294806\pi$
$854$	−13.3297	−0.456132
$855$	55.4261	1.89553
$856$	−7.93645	−0.271262
$857$	48.5916	1.65986	0.829929	−	0.557869i	$-0.188381\pi$
$857$	48.5916	1.65986	0.829929	+	0.557869i	$0.188381\pi$
$858$	−37.4117	−1.27722
$859$	37.2811	1.27201	0.636007	−	0.771683i	$-0.280585\pi$
$859$	37.2811	1.27201	0.636007	+	0.771683i	$0.280585\pi$
$860$	20.0658	0.684238
$861$	29.5787	1.00804
$862$	−10.5413	−0.359037
$863$	2.93440	0.0998883	0.0499441	−	0.998752i	$-0.484096\pi$
$863$	2.93440	0.0998883	0.0499441	+	0.998752i	$0.484096\pi$
$864$	−0.150012	−0.00510350
$865$	22.1532	0.753231
$866$	36.2167	1.23069
$867$	20.4530	0.694621
$868$	9.62162	0.326579
$869$	55.1544	1.87098
$870$	26.9826	0.914797
$871$	−11.5055	−0.389848
$872$	−0.579514	−0.0196248
$873$	11.3781	0.385091
$874$	−28.5869	−0.966967
$875$	−4.62143	−0.156233
$876$	27.1672	0.917893
$877$	−48.7428	−1.64593	−0.822963	−	0.568094i	$-0.807681\pi$
$877$	−48.7428	−1.64593	−0.822963	+	0.568094i	$0.807681\pi$
$878$	1.23126	0.0415530
$879$	−60.2926	−2.03362
$880$	15.2439	0.513873
$881$	−30.7090	−1.03461	−0.517306	−	0.855801i	$-0.673065\pi$
$881$	−30.7090	−1.03461	−0.517306	+	0.855801i	$0.673065\pi$
$882$	−14.4872	−0.487810
$883$	12.7018	0.427450	0.213725	−	0.976894i	$-0.431440\pi$
$883$	12.7018	0.427450	0.213725	+	0.976894i	$0.431440\pi$
$884$	8.80510	0.296148
$885$	−27.2129	−0.914752
$886$	−7.25796	−0.243836
$887$	−7.52924	−0.252807	−0.126404	−	0.991979i	$-0.540343\pi$
$887$	−7.52924	−0.252807	−0.126404	+	0.991979i	$0.540343\pi$
$888$	−19.2954	−0.647510
$889$	13.2184	0.443329
$890$	−35.1952	−1.17975
$891$	−44.8452	−1.50237
$892$	−6.58760	−0.220569
$893$	−57.1234	−1.91156
$894$	22.8186	0.763167
$895$	−50.8604	−1.70007
$896$	1.50567	0.0503011
$897$	34.7757	1.16113
$898$	27.6245	0.921841
$899$	−23.3777	−0.779691
$900$	12.1687	0.405624
$901$	−2.12774	−0.0708855
$902$	−40.6019	−1.35190
$903$	−24.8272	−0.826199
$904$	−2.41317	−0.0802608
$905$	−59.1800	−1.96721
$906$	17.3608	0.576773
$907$	−20.9281	−0.694906	−0.347453	−	0.937697i	$-0.612953\pi$
$907$	−20.9281	−0.694906	−0.347453	+	0.937697i	$0.612953\pi$
$908$	20.9466	0.695138
$909$	−6.41251	−0.212690
$910$	13.4720	0.446591
$911$	−31.6883	−1.04988	−0.524941	−	0.851139i	$-0.675913\pi$
$911$	−31.6883	−1.04988	−0.524941	+	0.851139i	$0.675913\pi$
$912$	−14.8799	−0.492724
$913$	−22.9084	−0.758157
$914$	−9.36755	−0.309851
$915$	65.2960	2.15862
$916$	−7.97847	−0.263616
$917$	3.30477	0.109133
$918$	−0.442272	−0.0145971
$919$	−26.9762	−0.889863	−0.444932	−	0.895565i	$-0.646772\pi$
$919$	−26.9762	−0.889863	−0.444932	+	0.895565i	$0.646772\pi$
$920$	−14.1698	−0.467166
$921$	−64.1253	−2.11300
$922$	21.7263	0.715516
$923$	−34.3667	−1.13119
$924$	−18.8612	−0.620487
$925$	31.1583	1.02448
$926$	−24.8843	−0.817748
$927$	−6.02963	−0.198039
$928$	−3.65835	−0.120091
$929$	49.7392	1.63189	0.815945	−	0.578130i	$-0.196217\pi$
$929$	49.7392	1.63189	0.815945	+	0.578130i	$0.196217\pi$
$930$	−47.1320	−1.54552
$931$	−28.6064	−0.937536
$932$	−5.92944	−0.194225
$933$	22.2344	0.727922
$934$	13.1677	0.430859
$935$	44.9429	1.46979
$936$	9.14164	0.298804
$937$	36.3744	1.18830	0.594150	−	0.804354i	$-0.297489\pi$
$937$	36.3744	1.18830	0.594150	+	0.804354i	$0.297489\pi$
$938$	−5.80049	−0.189393
$939$	−68.1031	−2.22246
$940$	−28.3147	−0.923524
$941$	−43.4065	−1.41501	−0.707506	−	0.706707i	$-0.750180\pi$
$941$	−43.4065	−1.41501	−0.707506	+	0.706707i	$0.750180\pi$
$942$	−52.6588	−1.71571
$943$	37.7411	1.22902
$944$	3.68957	0.120085
$945$	−0.676683	−0.0220125
$946$	34.0797	1.10803
$947$	46.1409	1.49938	0.749689	−	0.661790i	$-0.230203\pi$
$947$	46.1409	1.49938	0.749689	+	0.661790i	$0.230203\pi$
$948$	−26.6859	−0.866718
$949$	−32.9568	−1.06982
$950$	24.0282	0.779579
$951$	62.8693	2.03868
$952$	4.43910	0.143872
$953$	−37.7516	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$953$	−37.7516	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$954$	−2.20907	−0.0715213
$955$	−6.33910	−0.205129
$956$	28.1527	0.910524
$957$	45.8272	1.48138
$958$	−2.64392	−0.0854212
$959$	−5.39079	−0.174078
$960$	−7.37563	−0.238047
$961$	9.83514	0.317263
$962$	23.4074	0.754685
$963$	−24.2929	−0.782829
$964$	−16.0293	−0.516271
$965$	−53.7246	−1.72946
$966$	17.5322	0.564090
$967$	−1.36334	−0.0438419	−0.0219210	−	0.999760i	$-0.506978\pi$
$967$	−1.36334	−0.0438419	−0.0219210	+	0.999760i	$0.506978\pi$
$968$	14.8902	0.478590
$969$	−43.8697	−1.40930
$970$	11.1364	0.357569
$971$	54.7913	1.75834	0.879169	−	0.476510i	$-0.158099\pi$
$971$	54.7913	1.75834	0.879169	+	0.476510i	$0.158099\pi$
$972$	22.1479	0.710395
$973$	20.2631	0.649606
$974$	−3.61405	−0.115802
$975$	−29.2301	−0.936113
$976$	−8.85295	−0.283376
$977$	−20.2871	−0.649041	−0.324521	−	0.945879i	$-0.605203\pi$
$977$	−20.2871	−0.649041	−0.324521	+	0.945879i	$0.605203\pi$
$978$	−36.7852	−1.17626
$979$	−59.7754	−1.91043
$980$	−14.1795	−0.452947
$981$	−1.77385	−0.0566348
$982$	−19.6302	−0.626425
$983$	25.5664	0.815443	0.407721	−	0.913106i	$-0.366323\pi$
$983$	25.5664	0.815443	0.407721	+	0.913106i	$0.366323\pi$
$984$	19.6448	0.626255
$985$	63.6950	2.02949
$986$	−10.7857	−0.343488
$987$	35.0335	1.11513
$988$	18.0510	0.574279
$989$	−31.6784	−1.00732
$990$	46.6607	1.48297
$991$	11.2443	0.357186	0.178593	−	0.983923i	$-0.442845\pi$
$991$	11.2443	0.357186	0.178593	+	0.983923i	$0.442845\pi$
$992$	6.39024	0.202890
$993$	−32.7768	−1.04014
$994$	−17.3260	−0.549547
$995$	−18.1710	−0.576058
$996$	11.0840	0.351210
$997$	48.4132	1.53326	0.766631	−	0.642088i	$-0.221931\pi$
$997$	48.4132	1.53326	0.766631	+	0.642088i	$0.221931\pi$
$998$	32.5620	1.03073
$999$	−1.17573	−0.0371985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.8	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.46190 q^{3} +1.00000 q^{4} +2.99591 q^{5} -2.46190 q^{6} +1.50567 q^{7} +1.00000 q^{8} +3.06093 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.46190 q^{3} +1.00000 q^{4} +2.99591 q^{5} -2.46190 q^{6} +1.50567 q^{7} +1.00000 q^{8} +3.06093 q^{9} +2.99591 q^{10} +5.08824 q^{11} -2.46190 q^{12} +2.98655 q^{13} +1.50567 q^{14} -7.37563 q^{15} +1.00000 q^{16} +2.94825 q^{17} +3.06093 q^{18} +6.04409 q^{19} +2.99591 q^{20} -3.70681 q^{21} +5.08824 q^{22} -4.72973 q^{23} -2.46190 q^{24} +3.97549 q^{25} +2.98655 q^{26} -0.150012 q^{27} +1.50567 q^{28} -3.65835 q^{29} -7.37563 q^{30} +6.39024 q^{31} +1.00000 q^{32} -12.5267 q^{33} +2.94825 q^{34} +4.51087 q^{35} +3.06093 q^{36} +7.83760 q^{37} +6.04409 q^{38} -7.35258 q^{39} +2.99591 q^{40} -7.97956 q^{41} -3.70681 q^{42} +6.69773 q^{43} +5.08824 q^{44} +9.17029 q^{45} -4.72973 q^{46} -9.45111 q^{47} -2.46190 q^{48} -4.73294 q^{49} +3.97549 q^{50} -7.25828 q^{51} +2.98655 q^{52} -0.721698 q^{53} -0.150012 q^{54} +15.2439 q^{55} +1.50567 q^{56} -14.8799 q^{57} -3.65835 q^{58} +3.68957 q^{59} -7.37563 q^{60} -8.85295 q^{61} +6.39024 q^{62} +4.60877 q^{63} +1.00000 q^{64} +8.94745 q^{65} -12.5267 q^{66} -3.85242 q^{67} +2.94825 q^{68} +11.6441 q^{69} +4.51087 q^{70} -11.5071 q^{71} +3.06093 q^{72} -11.0351 q^{73} +7.83760 q^{74} -9.78724 q^{75} +6.04409 q^{76} +7.66124 q^{77} -7.35258 q^{78} +10.8396 q^{79} +2.99591 q^{80} -8.81349 q^{81} -7.97956 q^{82} -4.50222 q^{83} -3.70681 q^{84} +8.83269 q^{85} +6.69773 q^{86} +9.00648 q^{87} +5.08824 q^{88} -11.7478 q^{89} +9.17029 q^{90} +4.49678 q^{91} -4.72973 q^{92} -15.7321 q^{93} -9.45111 q^{94} +18.1076 q^{95} -2.46190 q^{96} +3.71720 q^{97} -4.73294 q^{98} +15.5748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 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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