LMFDB - Embedded newform 8023.2.a.e.1.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57473 q^{2} -2.20195 q^{3} +0.479767 q^{4} +3.05179 q^{5} +3.46748 q^{6} -0.157888 q^{7} +2.39395 q^{8} +1.84860 q^{9} +O(q^{10})$	\(q-1.57473 q^{2} -2.20195 q^{3} +0.479767 q^{4} +3.05179 q^{5} +3.46748 q^{6} -0.157888 q^{7} +2.39395 q^{8} +1.84860 q^{9} -4.80574 q^{10} +4.18716 q^{11} -1.05643 q^{12} -4.86143 q^{13} +0.248631 q^{14} -6.71990 q^{15} -4.72936 q^{16} -2.33826 q^{17} -2.91105 q^{18} +3.05363 q^{19} +1.46415 q^{20} +0.347663 q^{21} -6.59363 q^{22} +4.14936 q^{23} -5.27137 q^{24} +4.31343 q^{25} +7.65542 q^{26} +2.53533 q^{27} -0.0757497 q^{28} -6.70178 q^{29} +10.5820 q^{30} -4.39542 q^{31} +2.65954 q^{32} -9.21992 q^{33} +3.68212 q^{34} -0.481843 q^{35} +0.886898 q^{36} -1.56554 q^{37} -4.80863 q^{38} +10.7046 q^{39} +7.30584 q^{40} -0.0693174 q^{41} -0.547475 q^{42} -6.65278 q^{43} +2.00886 q^{44} +5.64155 q^{45} -6.53411 q^{46} -1.65291 q^{47} +10.4138 q^{48} -6.97507 q^{49} -6.79248 q^{50} +5.14874 q^{51} -2.33235 q^{52} +0.129710 q^{53} -3.99245 q^{54} +12.7783 q^{55} -0.377978 q^{56} -6.72394 q^{57} +10.5535 q^{58} -2.75208 q^{59} -3.22399 q^{60} -7.95287 q^{61} +6.92159 q^{62} -0.291873 q^{63} +5.27066 q^{64} -14.8361 q^{65} +14.5189 q^{66} +8.84706 q^{67} -1.12182 q^{68} -9.13670 q^{69} +0.758771 q^{70} -1.00000 q^{71} +4.42547 q^{72} +5.71510 q^{73} +2.46529 q^{74} -9.49797 q^{75} +1.46503 q^{76} -0.661104 q^{77} -16.8569 q^{78} +8.02025 q^{79} -14.4330 q^{80} -11.1285 q^{81} +0.109156 q^{82} +1.09000 q^{83} +0.166797 q^{84} -7.13588 q^{85} +10.4763 q^{86} +14.7570 q^{87} +10.0239 q^{88} +6.86944 q^{89} -8.88390 q^{90} +0.767563 q^{91} +1.99073 q^{92} +9.67852 q^{93} +2.60288 q^{94} +9.31903 q^{95} -5.85620 q^{96} +13.8811 q^{97} +10.9838 q^{98} +7.74038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−1.57473	−1.11350	−0.556750	−	0.830680i	$-0.687952\pi$
$2$	−1.57473	−1.11350	−0.556750	+	0.830680i	$0.687952\pi$
$3$	−2.20195	−1.27130	−0.635649	−	0.771978i	$-0.719268\pi$
$3$	−2.20195	−1.27130	−0.635649	+	0.771978i	$0.719268\pi$
$4$	0.479767	0.239884
$5$	3.05179	1.36480	0.682401	−	0.730978i	$-0.260936\pi$
$5$	3.05179	1.36480	0.682401	+	0.730978i	$0.260936\pi$
$6$	3.46748	1.41559
$7$	−0.157888	−0.0596762	−0.0298381	−	0.999555i	$-0.509499\pi$
$7$	−0.157888	−0.0596762	−0.0298381	+	0.999555i	$0.509499\pi$
$8$	2.39395	0.846390
$9$	1.84860	0.616201
$10$	−4.80574	−1.51971
$11$	4.18716	1.26247	0.631237	−	0.775590i	$-0.282547\pi$
$11$	4.18716	1.26247	0.631237	+	0.775590i	$0.282547\pi$
$12$	−1.05643	−0.304964
$13$	−4.86143	−1.34832	−0.674158	−	0.738587i	$-0.735493\pi$
$13$	−4.86143	−1.34832	−0.674158	+	0.738587i	$0.735493\pi$
$14$	0.248631	0.0664495
$15$	−6.71990	−1.73507
$16$	−4.72936	−1.18234
$17$	−2.33826	−0.567111	−0.283556	−	0.958956i	$-0.591514\pi$
$17$	−2.33826	−0.567111	−0.283556	+	0.958956i	$0.591514\pi$
$18$	−2.91105	−0.686140
$19$	3.05363	0.700550	0.350275	−	0.936647i	$-0.386088\pi$
$19$	3.05363	0.700550	0.350275	+	0.936647i	$0.386088\pi$
$20$	1.46415	0.327394
$21$	0.347663	0.0758663
$22$	−6.59363	−1.40577
$23$	4.14936	0.865201	0.432601	−	0.901586i	$-0.357596\pi$
$23$	4.14936	0.865201	0.432601	+	0.901586i	$0.357596\pi$
$24$	−5.27137	−1.07601
$25$	4.31343	0.862686
$26$	7.65542	1.50135
$27$	2.53533	0.487924
$28$	−0.0757497	−0.0143153
$29$	−6.70178	−1.24449	−0.622245	−	0.782823i	$-0.713779\pi$
$29$	−6.70178	−1.24449	−0.622245	+	0.782823i	$0.713779\pi$
$30$	10.5820	1.93200
$31$	−4.39542	−0.789441	−0.394721	−	0.918801i	$-0.629159\pi$
$31$	−4.39542	−0.789441	−0.394721	+	0.918801i	$0.629159\pi$
$32$	2.65954	0.470145
$33$	−9.21992	−1.60498
$34$	3.68212	0.631479
$35$	−0.481843	−0.0814463
$36$	0.886898	0.147816
$37$	−1.56554	−0.257372	−0.128686	−	0.991685i	$-0.541076\pi$
$37$	−1.56554	−0.257372	−0.128686	+	0.991685i	$0.541076\pi$
$38$	−4.80863	−0.780063
$39$	10.7046	1.71411
$40$	7.30584	1.15516
$41$	−0.0693174	−0.0108256	−0.00541278	−	0.999985i	$-0.501723\pi$
$41$	−0.0693174	−0.0108256	−0.00541278	+	0.999985i	$0.501723\pi$
$42$	−0.547475	−0.0844772
$43$	−6.65278	−1.01454	−0.507269	−	0.861788i	$-0.669345\pi$
$43$	−6.65278	−1.01454	−0.507269	+	0.861788i	$0.669345\pi$
$44$	2.00886	0.302847
$45$	5.64155	0.840992
$46$	−6.53411	−0.963402
$47$	−1.65291	−0.241101	−0.120550	−	0.992707i	$-0.538466\pi$
$47$	−1.65291	−0.241101	−0.120550	+	0.992707i	$0.538466\pi$
$48$	10.4138	1.50311
$49$	−6.97507	−0.996439
$50$	−6.79248	−0.960601
$51$	5.14874	0.720968
$52$	−2.33235	−0.323439
$53$	0.129710	0.0178170	0.00890849	−	0.999960i	$-0.497164\pi$
$53$	0.129710	0.0178170	0.00890849	+	0.999960i	$0.497164\pi$
$54$	−3.99245	−0.543303
$55$	12.7783	1.72303
$56$	−0.377978	−0.0505094
$57$	−6.72394	−0.890608
$58$	10.5535	1.38574
$59$	−2.75208	−0.358290	−0.179145	−	0.983823i	$-0.557333\pi$
$59$	−2.75208	−0.358290	−0.179145	+	0.983823i	$0.557333\pi$
$60$	−3.22399	−0.416215
$61$	−7.95287	−1.01826	−0.509130	−	0.860689i	$-0.670033\pi$
$61$	−7.95287	−1.01826	−0.509130	+	0.860689i	$0.670033\pi$
$62$	6.92159	0.879043
$63$	−0.291873	−0.0367725
$64$	5.27066	0.658832
$65$	−14.8361	−1.84019
$66$	14.5189	1.78715
$67$	8.84706	1.08084	0.540420	−	0.841395i	$-0.318265\pi$
$67$	8.84706	1.08084	0.540420	+	0.841395i	$0.318265\pi$
$68$	−1.12182	−0.136041
$69$	−9.13670	−1.09993
$70$	0.758771	0.0906905
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	4.42547	0.521546
$73$	5.71510	0.668902	0.334451	−	0.942413i	$-0.391449\pi$
$73$	5.71510	0.668902	0.334451	+	0.942413i	$0.391449\pi$
$74$	2.46529	0.286584
$75$	−9.49797	−1.09673
$76$	1.46503	0.168050
$77$	−0.661104	−0.0753397
$78$	−16.8569	−1.90867
$79$	8.02025	0.902349	0.451174	−	0.892436i	$-0.351005\pi$
$79$	8.02025	0.902349	0.451174	+	0.892436i	$0.351005\pi$
$80$	−14.4330	−1.61366
$81$	−11.1285	−1.23650
$82$	0.109156	0.0120543
$83$	1.09000	0.119643	0.0598213	−	0.998209i	$-0.480947\pi$
$83$	1.09000	0.119643	0.0598213	+	0.998209i	$0.480947\pi$
$84$	0.166797	0.0181991
$85$	−7.13588	−0.773995
$86$	10.4763	1.12969
$87$	14.7570	1.58212
$88$	10.0239	1.06855
$89$	6.86944	0.728159	0.364080	−	0.931368i	$-0.381384\pi$
$89$	6.86944	0.728159	0.364080	+	0.931368i	$0.381384\pi$
$90$	−8.88390	−0.936445
$91$	0.767563	0.0804625
$92$	1.99073	0.207548
$93$	9.67852	1.00362
$94$	2.60288	0.268466
$95$	9.31903	0.956112
$96$	−5.85620	−0.597695
$97$	13.8811	1.40941	0.704705	−	0.709501i	$-0.251079\pi$
$97$	13.8811	1.40941	0.704705	+	0.709501i	$0.251079\pi$
$98$	10.9838	1.10954
$99$	7.74038	0.777938
$100$	2.06944	0.206944
$101$	15.0106	1.49361	0.746804	−	0.665045i	$-0.231588\pi$
$101$	15.0106	1.49361	0.746804	+	0.665045i	$0.231588\pi$
$102$	−8.10786	−0.802798
$103$	10.5553	1.04004	0.520022	−	0.854153i	$-0.325924\pi$
$103$	10.5553	1.04004	0.520022	+	0.854153i	$0.325924\pi$
$104$	−11.6380	−1.14120
$105$	1.06100	0.103543
$106$	−0.204257	−0.0198392
$107$	3.07844	0.297604	0.148802	−	0.988867i	$-0.452458\pi$
$107$	3.07844	0.297604	0.148802	+	0.988867i	$0.452458\pi$
$108$	1.21637	0.117045
$109$	10.2359	0.980419	0.490210	−	0.871605i	$-0.336920\pi$
$109$	10.2359	0.980419	0.490210	+	0.871605i	$0.336920\pi$
$110$	−20.1224	−1.91859
$111$	3.44724	0.327197
$112$	0.746711	0.0705576
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	10.5884	0.991693
$115$	12.6630	1.18083
$116$	−3.21529	−0.298532
$117$	−8.98684	−0.830834
$118$	4.33378	0.398956
$119$	0.369184	0.0338431
$120$	−16.0871	−1.46855
$121$	6.53227	0.593843
$122$	12.5236	1.13383
$123$	0.152634	0.0137625
$124$	−2.10878	−0.189374
$125$	−2.09527	−0.187407
$126$	0.459621	0.0409462
$127$	−4.82671	−0.428301	−0.214151	−	0.976801i	$-0.568698\pi$
$127$	−4.82671	−0.428301	−0.214151	+	0.976801i	$0.568698\pi$
$128$	−13.6189	−1.20376
$129$	14.6491	1.28978
$130$	23.3627	2.04905
$131$	−12.1610	−1.06251	−0.531257	−	0.847211i	$-0.678280\pi$
$131$	−12.1610	−1.06251	−0.531257	+	0.847211i	$0.678280\pi$
$132$	−4.42342	−0.385009
$133$	−0.482132	−0.0418062
$134$	−13.9317	−1.20352
$135$	7.73728	0.665919
$136$	−5.59768	−0.479997
$137$	11.9285	1.01912	0.509562	−	0.860434i	$-0.329807\pi$
$137$	11.9285	1.01912	0.509562	+	0.860434i	$0.329807\pi$
$138$	14.3878	1.22477
$139$	17.9238	1.52028	0.760138	−	0.649762i	$-0.225131\pi$
$139$	17.9238	1.52028	0.760138	+	0.649762i	$0.225131\pi$
$140$	−0.231172	−0.0195376
$141$	3.63962	0.306511
$142$	1.57473	0.132148
$143$	−20.3555	−1.70222
$144$	−8.74270	−0.728558
$145$	−20.4524	−1.69848
$146$	−8.99973	−0.744823
$147$	15.3588	1.26677
$148$	−0.751092	−0.0617394
$149$	−20.7936	−1.70347	−0.851737	−	0.523969i	$-0.824451\pi$
$149$	−20.7936	−1.70347	−0.851737	+	0.523969i	$0.824451\pi$
$150$	14.9567	1.22121
$151$	13.0980	1.06590	0.532951	−	0.846146i	$-0.321083\pi$
$151$	13.0980	1.06590	0.532951	+	0.846146i	$0.321083\pi$
$152$	7.31024	0.592939
$153$	−4.32251	−0.349454
$154$	1.04106	0.0838909
$155$	−13.4139	−1.07743
$156$	5.13573	0.411188
$157$	0.852711	0.0680537	0.0340269	−	0.999421i	$-0.489167\pi$
$157$	0.852711	0.0680537	0.0340269	+	0.999421i	$0.489167\pi$
$158$	−12.6297	−1.00477
$159$	−0.285615	−0.0226507
$160$	8.11637	0.641656
$161$	−0.655136	−0.0516320
$162$	17.5243	1.37684
$163$	0.265237	0.0207749	0.0103875	−	0.999946i	$-0.496694\pi$
$163$	0.265237	0.0207749	0.0103875	+	0.999946i	$0.496694\pi$
$164$	−0.0332562	−0.00259687
$165$	−28.1373	−2.19048
$166$	−1.71645	−0.133222
$167$	2.23547	0.172986	0.0864930	−	0.996252i	$-0.472434\pi$
$167$	2.23547	0.172986	0.0864930	+	0.996252i	$0.472434\pi$
$168$	0.832289	0.0642125
$169$	10.6335	0.817958
$170$	11.2371	0.861844
$171$	5.64494	0.431679
$172$	−3.19178	−0.243371
$173$	6.79386	0.516527	0.258264	−	0.966074i	$-0.416850\pi$
$173$	6.79386	0.516527	0.258264	+	0.966074i	$0.416850\pi$
$174$	−23.2383	−1.76169
$175$	−0.681041	−0.0514818
$176$	−19.8026	−1.49267
$177$	6.05995	0.455494
$178$	−10.8175	−0.810806
$179$	−6.96918	−0.520901	−0.260450	−	0.965487i	$-0.583871\pi$
$179$	−6.96918	−0.520901	−0.260450	+	0.965487i	$0.583871\pi$
$180$	2.70663	0.201740
$181$	−5.15764	−0.383364	−0.191682	−	0.981457i	$-0.561394\pi$
$181$	−5.15764	−0.383364	−0.191682	+	0.981457i	$0.561394\pi$
$182$	−1.20870	−0.0895950
$183$	17.5119	1.29451
$184$	9.93337	0.732298
$185$	−4.77769	−0.351263
$186$	−15.2410	−1.11753
$187$	−9.79066	−0.715964
$188$	−0.793009	−0.0578362
$189$	−0.400299	−0.0291174
$190$	−14.6749	−1.06463
$191$	−13.6331	−0.986454	−0.493227	−	0.869901i	$-0.664183\pi$
$191$	−13.6331	−0.986454	−0.493227	+	0.869901i	$0.664183\pi$
$192$	−11.6057	−0.837573
$193$	9.72473	0.700001	0.350001	−	0.936749i	$-0.386181\pi$
$193$	9.72473	0.700001	0.350001	+	0.936749i	$0.386181\pi$
$194$	−21.8589	−1.56938
$195$	32.6683	2.33943
$196$	−3.34641	−0.239029
$197$	10.9899	0.783001	0.391501	−	0.920178i	$-0.371956\pi$
$197$	10.9899	0.783001	0.391501	+	0.920178i	$0.371956\pi$
$198$	−12.1890	−0.866234
$199$	−7.98766	−0.566231	−0.283115	−	0.959086i	$-0.591368\pi$
$199$	−7.98766	−0.566231	−0.283115	+	0.959086i	$0.591368\pi$
$200$	10.3261	0.730169
$201$	−19.4808	−1.37407
$202$	−23.6376	−1.66313
$203$	1.05813	0.0742664
$204$	2.47020	0.172948
$205$	−0.211542	−0.0147747
$206$	−16.6217	−1.15809
$207$	7.67051	0.533138
$208$	22.9914	1.59417
$209$	12.7860	0.884427
$210$	−1.67078	−0.115295
$211$	−10.0726	−0.693424	−0.346712	−	0.937972i	$-0.612702\pi$
$211$	−10.0726	−0.693424	−0.346712	+	0.937972i	$0.612702\pi$
$212$	0.0622304	0.00427400
$213$	2.20195	0.150875
$214$	−4.84770	−0.331382
$215$	−20.3029	−1.38464
$216$	6.06945	0.412974
$217$	0.693987	0.0471109
$218$	−16.1187	−1.09170
$219$	−12.5844	−0.850375
$220$	6.13062	0.413326
$221$	11.3673	0.764646
$222$	−5.42846	−0.364334
$223$	1.44699	0.0968973	0.0484487	−	0.998826i	$-0.484572\pi$
$223$	1.44699	0.0968973	0.0484487	+	0.998826i	$0.484572\pi$
$224$	−0.419911	−0.0280565
$225$	7.97382	0.531588
$226$	−1.57473	−0.104749
$227$	−1.69247	−0.112333	−0.0561665	−	0.998421i	$-0.517888\pi$
$227$	−1.69247	−0.112333	−0.0561665	+	0.998421i	$0.517888\pi$
$228$	−3.22593	−0.213642
$229$	−0.828447	−0.0547453	−0.0273727	−	0.999625i	$-0.508714\pi$
$229$	−0.828447	−0.0547453	−0.0273727	+	0.999625i	$0.508714\pi$
$230$	−19.9407	−1.31485
$231$	1.45572	0.0957793
$232$	−16.0437	−1.05332
$233$	20.6618	1.35360	0.676800	−	0.736167i	$-0.263366\pi$
$233$	20.6618	1.35360	0.676800	+	0.736167i	$0.263366\pi$
$234$	14.1518	0.925134
$235$	−5.04432	−0.329055
$236$	−1.32036	−0.0859479
$237$	−17.6602	−1.14716
$238$	−0.581365	−0.0376843
$239$	−14.5634	−0.942027	−0.471014	−	0.882126i	$-0.656112\pi$
$239$	−14.5634	−0.942027	−0.471014	+	0.882126i	$0.656112\pi$
$240$	31.7808	2.05144
$241$	8.06514	0.519522	0.259761	−	0.965673i	$-0.416356\pi$
$241$	8.06514	0.519522	0.259761	+	0.965673i	$0.416356\pi$
$242$	−10.2865	−0.661244
$243$	16.8984	1.08403
$244$	−3.81552	−0.244264
$245$	−21.2865	−1.35994
$246$	−0.240357	−0.0153246
$247$	−14.8450	−0.944563
$248$	−10.5224	−0.668175
$249$	−2.40012	−0.152101
$250$	3.29948	0.208677
$251$	2.01339	0.127084	0.0635421	−	0.997979i	$-0.479760\pi$
$251$	2.01339	0.127084	0.0635421	+	0.997979i	$0.479760\pi$
$252$	−0.140031	−0.00882113
$253$	17.3740	1.09229
$254$	7.60075	0.476914
$255$	15.7129	0.983979
$256$	10.9048	0.681550
$257$	−13.9196	−0.868280	−0.434140	−	0.900845i	$-0.642948\pi$
$257$	−13.9196	−0.868280	−0.434140	+	0.900845i	$0.642948\pi$
$258$	−23.0684	−1.43617
$259$	0.247180	0.0153590
$260$	−7.11785	−0.441430
$261$	−12.3889	−0.766855
$262$	19.1503	1.18311
$263$	−1.64075	−0.101173	−0.0505865	−	0.998720i	$-0.516109\pi$
$263$	−1.64075	−0.101173	−0.0505865	+	0.998720i	$0.516109\pi$
$264$	−22.0721	−1.35844
$265$	0.395847	0.0243167
$266$	0.759227	0.0465512
$267$	−15.1262	−0.925708
$268$	4.24453	0.259276
$269$	14.1061	0.860064	0.430032	−	0.902814i	$-0.358502\pi$
$269$	14.1061	0.860064	0.430032	+	0.902814i	$0.358502\pi$
$270$	−12.1841	−0.741501
$271$	−9.65968	−0.586784	−0.293392	−	0.955992i	$-0.594784\pi$
$271$	−9.65968	−0.586784	−0.293392	+	0.955992i	$0.594784\pi$
$272$	11.0585	0.670518
$273$	−1.69014	−0.102292
$274$	−18.7842	−1.13480
$275$	18.0610	1.08912
$276$	−4.38349	−0.263855
$277$	13.1214	0.788388	0.394194	−	0.919027i	$-0.371024\pi$
$277$	13.1214	0.788388	0.394194	+	0.919027i	$0.371024\pi$
$278$	−28.2251	−1.69283
$279$	−8.12539	−0.486454
$280$	−1.15351	−0.0689353
$281$	−19.8619	−1.18486	−0.592431	−	0.805621i	$-0.701832\pi$
$281$	−19.8619	−1.18486	−0.592431	+	0.805621i	$0.701832\pi$
$282$	−5.73141	−0.341301
$283$	−21.8417	−1.29835	−0.649177	−	0.760637i	$-0.724887\pi$
$283$	−21.8417	−1.29835	−0.649177	+	0.760637i	$0.724887\pi$
$284$	−0.479767	−0.0284689
$285$	−20.5201	−1.21550
$286$	32.0544	1.89542
$287$	0.0109444	0.000646029 0
$288$	4.91644	0.289704
$289$	−11.5325	−0.678385
$290$	32.2070	1.89126
$291$	−30.5655	−1.79178
$292$	2.74192	0.160459
$293$	1.57660	0.0921060	0.0460530	−	0.998939i	$-0.485336\pi$
$293$	1.57660	0.0921060	0.0460530	+	0.998939i	$0.485336\pi$
$294$	−24.1859	−1.41055
$295$	−8.39877	−0.488995
$296$	−3.74782	−0.217837
$297$	10.6158	0.615991
$298$	32.7442	1.89682
$299$	−20.1718	−1.16657
$300$	−4.55681	−0.263088
$301$	1.05040	0.0605439
$302$	−20.6258	−1.18688
$303$	−33.0526	−1.89882
$304$	−14.4417	−0.828288
$305$	−24.2705	−1.38972
$306$	6.80678	0.389118
$307$	−7.59450	−0.433441	−0.216720	−	0.976234i	$-0.569536\pi$
$307$	−7.59450	−0.433441	−0.216720	+	0.976234i	$0.569536\pi$
$308$	−0.317176	−0.0180728
$309$	−23.2423	−1.32221
$310$	21.1233	1.19972
$311$	1.58270	0.0897469	0.0448735	−	0.998993i	$-0.485712\pi$
$311$	1.58270	0.0897469	0.0448735	+	0.998993i	$0.485712\pi$
$312$	25.6264	1.45081
$313$	7.63017	0.431283	0.215641	−	0.976473i	$-0.430816\pi$
$313$	7.63017	0.431283	0.215641	+	0.976473i	$0.430816\pi$
$314$	−1.34279	−0.0757779
$315$	−0.890735	−0.0501873
$316$	3.84785	0.216459
$317$	9.67940	0.543649	0.271825	−	0.962347i	$-0.412373\pi$
$317$	9.67940	0.543649	0.271825	+	0.962347i	$0.412373\pi$
$318$	0.449765	0.0252216
$319$	−28.0614	−1.57114
$320$	16.0849	0.899176
$321$	−6.77857	−0.378343
$322$	1.03166	0.0574922
$323$	−7.14017	−0.397290
$324$	−5.33908	−0.296615
$325$	−20.9694	−1.16317
$326$	−0.417676	−0.0231329
$327$	−22.5389	−1.24641
$328$	−0.165943	−0.00916264
$329$	0.260975	0.0143880
$330$	44.3086	2.43911
$331$	−18.8652	−1.03693	−0.518463	−	0.855100i	$-0.673496\pi$
$331$	−18.8652	−1.03693	−0.518463	+	0.855100i	$0.673496\pi$
$332$	0.522944	0.0287003
$333$	−2.89405	−0.158593
$334$	−3.52026	−0.192620
$335$	26.9994	1.47513
$336$	−1.64422	−0.0896998
$337$	18.7768	1.02284	0.511420	−	0.859331i	$-0.329120\pi$
$337$	18.7768	1.02284	0.511420	+	0.859331i	$0.329120\pi$
$338$	−16.7448	−0.910797
$339$	−2.20195	−0.119594
$340$	−3.42356	−0.185669
$341$	−18.4043	−0.996649
$342$	−8.88924	−0.480675
$343$	2.20650	0.119140
$344$	−15.9264	−0.858696
$345$	−27.8833	−1.50119
$346$	−10.6985	−0.575154
$347$	14.5888	0.783166	0.391583	−	0.920143i	$-0.371928\pi$
$347$	14.5888	0.783166	0.391583	+	0.920143i	$0.371928\pi$
$348$	7.07993	0.379524
$349$	29.6403	1.58661	0.793304	−	0.608826i	$-0.208359\pi$
$349$	29.6403	1.58661	0.793304	+	0.608826i	$0.208359\pi$
$350$	1.07245	0.0573251
$351$	−12.3253	−0.657875
$352$	11.1359	0.593547
$353$	−21.3195	−1.13472	−0.567360	−	0.823470i	$-0.692035\pi$
$353$	−21.3195	−1.13472	−0.567360	+	0.823470i	$0.692035\pi$
$354$	−9.54278	−0.507193
$355$	−3.05179	−0.161972
$356$	3.29573	0.174673
$357$	−0.812927	−0.0430247
$358$	10.9746	0.580023
$359$	21.8310	1.15220	0.576099	−	0.817380i	$-0.304574\pi$
$359$	21.8310	1.15220	0.576099	+	0.817380i	$0.304574\pi$
$360$	13.5056	0.711808
$361$	−9.67537	−0.509230
$362$	8.12188	0.426876
$363$	−14.3838	−0.754951
$364$	0.368251	0.0193016
$365$	17.4413	0.912920
$366$	−27.5764	−1.44144
$367$	1.51732	0.0792033	0.0396017	−	0.999216i	$-0.487391\pi$
$367$	1.51732	0.0792033	0.0396017	+	0.999216i	$0.487391\pi$
$368$	−19.6238	−1.02296
$369$	−0.128140	−0.00667072
$370$	7.52356	0.391131
$371$	−0.0204797	−0.00106325
$372$	4.64343	0.240751
$373$	20.3209	1.05217	0.526087	−	0.850431i	$-0.323659\pi$
$373$	20.3209	1.05217	0.526087	+	0.850431i	$0.323659\pi$
$374$	15.4176	0.797226
$375$	4.61369	0.238250
$376$	−3.95698	−0.204065
$377$	32.5802	1.67797
$378$	0.630361	0.0324223
$379$	13.5757	0.697338	0.348669	−	0.937246i	$-0.386634\pi$
$379$	13.5757	0.697338	0.348669	+	0.937246i	$0.386634\pi$
$380$	4.47096	0.229356
$381$	10.6282	0.544499
$382$	21.4684	1.09842
$383$	22.2757	1.13823	0.569117	−	0.822257i	$-0.307285\pi$
$383$	22.2757	1.13823	0.569117	+	0.822257i	$0.307285\pi$
$384$	29.9883	1.53033
$385$	−2.01755	−0.102824
$386$	−15.3138	−0.779452
$387$	−12.2983	−0.625160
$388$	6.65968	0.338094
$389$	6.72426	0.340933	0.170467	−	0.985363i	$-0.445472\pi$
$389$	6.72426	0.340933	0.170467	+	0.985363i	$0.445472\pi$
$390$	−51.4437	−2.60495
$391$	−9.70228	−0.490665
$392$	−16.6980	−0.843376
$393$	26.7780	1.35077
$394$	−17.3062	−0.871873
$395$	24.4761	1.23153
$396$	3.71358	0.186614
$397$	28.7366	1.44225	0.721124	−	0.692806i	$-0.243626\pi$
$397$	28.7366	1.44225	0.721124	+	0.692806i	$0.243626\pi$
$398$	12.5784	0.630498
$399$	1.06163	0.0531482
$400$	−20.3997	−1.01999
$401$	26.1038	1.30356	0.651780	−	0.758408i	$-0.274023\pi$
$401$	26.1038	1.30356	0.651780	+	0.758408i	$0.274023\pi$
$402$	30.6770	1.53003
$403$	21.3680	1.06442
$404$	7.20157	0.358292
$405$	−33.9618	−1.68757
$406$	−1.66627	−0.0826957
$407$	−6.55514	−0.324926
$408$	12.3258	0.610220
$409$	20.6900	1.02306	0.511528	−	0.859267i	$-0.329080\pi$
$409$	20.6900	1.02306	0.511528	+	0.859267i	$0.329080\pi$
$410$	0.333121	0.0164517
$411$	−26.2661	−1.29561
$412$	5.06408	0.249489
$413$	0.434522	0.0213814
$414$	−12.0790	−0.593649
$415$	3.32644	0.163288
$416$	−12.9292	−0.633905
$417$	−39.4674	−1.93272
$418$	−20.1345	−0.984810
$419$	4.75524	0.232309	0.116154	−	0.993231i	$-0.462943\pi$
$419$	4.75524	0.232309	0.116154	+	0.993231i	$0.462943\pi$
$420$	0.509031	0.0248382
$421$	22.5310	1.09810	0.549048	−	0.835791i	$-0.314990\pi$
$421$	22.5310	1.09810	0.549048	+	0.835791i	$0.314990\pi$
$422$	15.8616	0.772128
$423$	−3.05556	−0.148567
$424$	0.310519	0.0150801
$425$	−10.0859	−0.489239
$426$	−3.46748	−0.168000
$427$	1.25567	0.0607660
$428$	1.47693	0.0713902
$429$	44.8220	2.16403
$430$	31.9715	1.54180
$431$	9.97725	0.480587	0.240294	−	0.970700i	$-0.422756\pi$
$431$	9.97725	0.480587	0.240294	+	0.970700i	$0.422756\pi$
$432$	−11.9905	−0.576891
$433$	10.2907	0.494538	0.247269	−	0.968947i	$-0.420467\pi$
$433$	10.2907	0.494538	0.247269	+	0.968947i	$0.420467\pi$
$434$	−1.09284	−0.0524580
$435$	45.0353	2.15928
$436$	4.91084	0.235186
$437$	12.6706	0.606117
$438$	19.8170	0.946893
$439$	3.60012	0.171824	0.0859122	−	0.996303i	$-0.472620\pi$
$439$	3.60012	0.171824	0.0859122	+	0.996303i	$0.472620\pi$
$440$	30.5907	1.45835
$441$	−12.8941	−0.614006
$442$	−17.9004	−0.851433
$443$	−18.1720	−0.863377	−0.431688	−	0.902023i	$-0.642082\pi$
$443$	−18.1720	−0.863377	−0.431688	+	0.902023i	$0.642082\pi$
$444$	1.65387	0.0784892
$445$	20.9641	0.993794
$446$	−2.27861	−0.107895
$447$	45.7865	2.16563
$448$	−0.832176	−0.0393166
$449$	19.0599	0.899495	0.449747	−	0.893156i	$-0.351514\pi$
$449$	19.0599	0.899495	0.449747	+	0.893156i	$0.351514\pi$
$450$	−12.5566	−0.591923
$451$	−0.290243	−0.0136670
$452$	0.479767	0.0225663
$453$	−28.8413	−1.35508
$454$	2.66517	0.125083
$455$	2.34244	0.109815
$456$	−16.0968	−0.753802
$457$	13.5343	0.633108	0.316554	−	0.948575i	$-0.397474\pi$
$457$	13.5343	0.633108	0.316554	+	0.948575i	$0.397474\pi$
$458$	1.30458	0.0609589
$459$	−5.92825	−0.276707
$460$	6.07528	0.283261
$461$	−12.8404	−0.598039	−0.299020	−	0.954247i	$-0.596660\pi$
$461$	−12.8404	−0.598039	−0.299020	+	0.954247i	$0.596660\pi$
$462$	−2.29236	−0.106650
$463$	8.36047	0.388544	0.194272	−	0.980948i	$-0.437766\pi$
$463$	8.36047	0.388544	0.194272	+	0.980948i	$0.437766\pi$
$464$	31.6951	1.47141
$465$	29.5368	1.36974
$466$	−32.5367	−1.50723
$467$	−3.18224	−0.147257	−0.0736283	−	0.997286i	$-0.523458\pi$
$467$	−3.18224	−0.147257	−0.0736283	+	0.997286i	$0.523458\pi$
$468$	−4.31159	−0.199303
$469$	−1.39685	−0.0645005
$470$	7.94343	0.366403
$471$	−1.87763	−0.0865166
$472$	−6.58835	−0.303253
$473$	−27.8562	−1.28083
$474$	27.8101	1.27736
$475$	13.1716	0.604354
$476$	0.177122	0.00811840
$477$	0.239782	0.0109788
$478$	22.9334	1.04895
$479$	−17.8726	−0.816618	−0.408309	−	0.912844i	$-0.633881\pi$
$479$	−17.8726	−0.816618	−0.408309	+	0.912844i	$0.633881\pi$
$480$	−17.8719	−0.815736
$481$	7.61073	0.347020
$482$	−12.7004	−0.578488
$483$	1.44258	0.0656396
$484$	3.13397	0.142453
$485$	42.3621	1.92357
$486$	−26.6104	−1.20707
$487$	−15.8914	−0.720106	−0.360053	−	0.932932i	$-0.617241\pi$
$487$	−15.8914	−0.720106	−0.360053	+	0.932932i	$0.617241\pi$
$488$	−19.0388	−0.861846
$489$	−0.584039	−0.0264112
$490$	33.5204	1.51430
$491$	−23.6946	−1.06932	−0.534661	−	0.845067i	$-0.679561\pi$
$491$	−23.6946	−1.06932	−0.534661	+	0.845067i	$0.679561\pi$
$492$	0.0732286	0.00330140
$493$	15.6705	0.705764
$494$	23.3768	1.05177
$495$	23.6220	1.06173
$496$	20.7875	0.933387
$497$	0.157888	0.00708227
$498$	3.77954	0.169365
$499$	−0.735730	−0.0329358	−0.0164679	−	0.999864i	$-0.505242\pi$
$499$	−0.735730	−0.0329358	−0.0164679	+	0.999864i	$0.505242\pi$
$500$	−1.00524	−0.0449558
$501$	−4.92241	−0.219917
$502$	−3.17055	−0.141508
$503$	33.7908	1.50666	0.753328	−	0.657644i	$-0.228447\pi$
$503$	33.7908	1.50666	0.753328	+	0.657644i	$0.228447\pi$
$504$	−0.698730	−0.0311239
$505$	45.8091	2.03848
$506$	−27.3593	−1.21627
$507$	−23.4144	−1.03987
$508$	−2.31570	−0.102742
$509$	15.3866	0.681997	0.340999	−	0.940064i	$-0.389235\pi$
$509$	15.3866	0.681997	0.340999	+	0.940064i	$0.389235\pi$
$510$	−24.7435	−1.09566
$511$	−0.902349	−0.0399176
$512$	10.0658	0.444849
$513$	7.74193	0.341815
$514$	21.9196	0.966831
$515$	32.2125	1.41945
$516$	7.02816	0.309397
$517$	−6.92097	−0.304384
$518$	−0.389241	−0.0171023
$519$	−14.9598	−0.656661
$520$	−35.5168	−1.55752
$521$	−27.6649	−1.21202	−0.606010	−	0.795457i	$-0.707231\pi$
$521$	−27.6649	−1.21202	−0.606010	+	0.795457i	$0.707231\pi$
$522$	19.5092	0.853894
$523$	−33.1318	−1.44875	−0.724377	−	0.689404i	$-0.757872\pi$
$523$	−33.1318	−1.44875	−0.724377	+	0.689404i	$0.757872\pi$
$524$	−5.83446	−0.254880
$525$	1.49962	0.0654488
$526$	2.58373	0.112656
$527$	10.2776	0.447701
$528$	43.6043	1.89763
$529$	−5.78282	−0.251427
$530$	−0.623351	−0.0270766
$531$	−5.08750	−0.220779
$532$	−0.231311	−0.0100286
$533$	0.336981	0.0145963
$534$	23.8196	1.03078
$535$	9.39474	0.406170
$536$	21.1794	0.914812
$537$	15.3458	0.662220
$538$	−22.2133	−0.957682
$539$	−29.2057	−1.25798
$540$	3.71209	0.159743
$541$	28.1958	1.21223	0.606116	−	0.795376i	$-0.292727\pi$
$541$	28.1958	1.21223	0.606116	+	0.795376i	$0.292727\pi$
$542$	15.2114	0.653384
$543$	11.3569	0.487371
$544$	−6.21871	−0.266625
$545$	31.2378	1.33808
$546$	2.66151	0.113902
$547$	−5.05855	−0.216288	−0.108144	−	0.994135i	$-0.534491\pi$
$547$	−5.05855	−0.216288	−0.108144	+	0.994135i	$0.534491\pi$
$548$	5.72292	0.244471
$549$	−14.7017	−0.627453
$550$	−28.4412	−1.21273
$551$	−20.4647	−0.871827
$552$	−21.8728	−0.930969
$553$	−1.26631	−0.0538488
$554$	−20.6626	−0.877870
$555$	10.5202	0.446560
$556$	8.59924	0.364689
$557$	−34.8775	−1.47781	−0.738904	−	0.673810i	$-0.764656\pi$
$557$	−34.8775	−1.47781	−0.738904	+	0.673810i	$0.764656\pi$
$558$	12.7953	0.541667
$559$	32.3420	1.36792
$560$	2.27881	0.0962971
$561$	21.5586	0.910204
$562$	31.2771	1.31934
$563$	−3.74495	−0.157831	−0.0789153	−	0.996881i	$-0.525146\pi$
$563$	−3.74495	−0.157831	−0.0789153	+	0.996881i	$0.525146\pi$
$564$	1.74617	0.0735270
$565$	3.05179	0.128390
$566$	34.3947	1.44572
$567$	1.75706	0.0737895
$568$	−2.39395	−0.100448
$569$	12.8440	0.538450	0.269225	−	0.963077i	$-0.413233\pi$
$569$	12.8440	0.538450	0.269225	+	0.963077i	$0.413233\pi$
$570$	32.3135	1.35346
$571$	9.90870	0.414666	0.207333	−	0.978270i	$-0.433522\pi$
$571$	9.90870	0.414666	0.207333	+	0.978270i	$0.433522\pi$
$572$	−9.76592	−0.408334
$573$	30.0194	1.25408
$574$	−0.0172345	−0.000719353 0
$575$	17.8980	0.746397
$576$	9.74335	0.405973
$577$	−5.62945	−0.234357	−0.117179	−	0.993111i	$-0.537385\pi$
$577$	−5.62945	−0.234357	−0.117179	+	0.993111i	$0.537385\pi$
$578$	18.1606	0.755382
$579$	−21.4134	−0.889911
$580$	−9.81240	−0.407438
$581$	−0.172098	−0.00713982
$582$	48.1323	1.99515
$583$	0.543114	0.0224935
$584$	13.6817	0.566152
$585$	−27.4260	−1.13392
$586$	−2.48272	−0.102560
$587$	−11.3443	−0.468231	−0.234115	−	0.972209i	$-0.575219\pi$
$587$	−11.3443	−0.468231	−0.234115	+	0.972209i	$0.575219\pi$
$588$	7.36864	0.303878
$589$	−13.4220	−0.553043
$590$	13.2258	0.544497
$591$	−24.1994	−0.995429
$592$	7.40398	0.304302
$593$	43.7886	1.79818	0.899091	−	0.437761i	$-0.144228\pi$
$593$	43.7886	1.79818	0.899091	+	0.437761i	$0.144228\pi$
$594$	−16.7170	−0.685907
$595$	1.12667	0.0461891
$596$	−9.97606	−0.408636
$597$	17.5885	0.719848
$598$	31.7651	1.29897
$599$	−7.38540	−0.301759	−0.150880	−	0.988552i	$-0.548211\pi$
$599$	−7.38540	−0.301759	−0.150880	+	0.988552i	$0.548211\pi$
$600$	−22.7377	−0.928263
$601$	−19.8407	−0.809320	−0.404660	−	0.914467i	$-0.632610\pi$
$601$	−19.8407	−0.809320	−0.404660	+	0.914467i	$0.632610\pi$
$602$	−1.65409	−0.0674156
$603$	16.3547	0.666014
$604$	6.28400	0.255693
$605$	19.9351	0.810478
$606$	52.0488	2.11434
$607$	9.82816	0.398913	0.199456	−	0.979907i	$-0.436082\pi$
$607$	9.82816	0.398913	0.199456	+	0.979907i	$0.436082\pi$
$608$	8.12125	0.329360
$609$	−2.32996	−0.0944148
$610$	38.2194	1.54746
$611$	8.03547	0.325080
$612$	−2.07380	−0.0838284
$613$	32.0827	1.29581	0.647904	−	0.761722i	$-0.275646\pi$
$613$	32.0827	1.29581	0.647904	+	0.761722i	$0.275646\pi$
$614$	11.9593	0.482637
$615$	0.465806	0.0187831
$616$	−1.58265	−0.0637668
$617$	−5.64491	−0.227256	−0.113628	−	0.993523i	$-0.536247\pi$
$617$	−5.64491	−0.227256	−0.113628	+	0.993523i	$0.536247\pi$
$618$	36.6002	1.47228
$619$	−0.0198462	−0.000797687 0	−0.000398844	−	1.00000i	$-0.500127\pi$
$619$	−0.0198462	−0.000797687 0	−0.000398844		1.00000i	$0.500127\pi$
$620$	−6.43555	−0.258458
$621$	10.5200	0.422152
$622$	−2.49233	−0.0999333
$623$	−1.08461	−0.0434538
$624$	−50.6260	−2.02666
$625$	−27.9615	−1.11846
$626$	−12.0154	−0.480234
$627$	−28.1542	−1.12437
$628$	0.409103	0.0163250
$629$	3.66063	0.145959
$630$	1.40267	0.0558835
$631$	18.8293	0.749583	0.374792	−	0.927109i	$-0.377714\pi$
$631$	18.8293	0.749583	0.374792	+	0.927109i	$0.377714\pi$
$632$	19.2001	0.763739
$633$	22.1793	0.881549
$634$	−15.2424	−0.605354
$635$	−14.7301	−0.584547
$636$	−0.137029	−0.00543353
$637$	33.9088	1.34352
$638$	44.1890	1.74946
$639$	−1.84860	−0.0731296
$640$	−41.5622	−1.64289
$641$	−21.9447	−0.866765	−0.433383	−	0.901210i	$-0.642680\pi$
$641$	−21.9447	−0.866765	−0.433383	+	0.901210i	$0.642680\pi$
$642$	10.6744	0.421285
$643$	20.3937	0.804251	0.402125	−	0.915585i	$-0.368272\pi$
$643$	20.3937	0.804251	0.402125	+	0.915585i	$0.368272\pi$
$644$	−0.314313	−0.0123857
$645$	44.7060	1.76030
$646$	11.2438	0.442382
$647$	46.1437	1.81410	0.907048	−	0.421028i	$-0.138331\pi$
$647$	46.1437	1.81410	0.907048	+	0.421028i	$0.138331\pi$
$648$	−26.6410	−1.04656
$649$	−11.5234	−0.452332
$650$	33.0211	1.29519
$651$	−1.52813	−0.0598920
$652$	0.127252	0.00498357
$653$	−16.0427	−0.627799	−0.313900	−	0.949456i	$-0.601636\pi$
$653$	−16.0427	−0.627799	−0.313900	+	0.949456i	$0.601636\pi$
$654$	35.4927	1.38787
$655$	−37.1129	−1.45012
$656$	0.327827	0.0127995
$657$	10.5650	0.412178
$658$	−0.410964	−0.0160210
$659$	15.2510	0.594097	0.297048	−	0.954862i	$-0.403998\pi$
$659$	15.2510	0.594097	0.297048	+	0.954862i	$0.403998\pi$
$660$	−13.4993	−0.525461
$661$	4.98662	0.193957	0.0969785	−	0.995286i	$-0.469082\pi$
$661$	4.98662	0.193957	0.0969785	+	0.995286i	$0.469082\pi$
$662$	29.7076	1.15462
$663$	−25.0302	−0.972093
$664$	2.60940	0.101264
$665$	−1.47137	−0.0570572
$666$	4.55734	0.176593
$667$	−27.8081	−1.07673
$668$	1.07251	0.0414965
$669$	−3.18620	−0.123185
$670$	−42.5166	−1.64256
$671$	−33.2999	−1.28553
$672$	0.924626	0.0356682
$673$	38.4466	1.48201	0.741003	−	0.671502i	$-0.234350\pi$
$673$	38.4466	1.48201	0.741003	+	0.671502i	$0.234350\pi$
$674$	−29.5684	−1.13893
$675$	10.9359	0.420925
$676$	5.10158	0.196215
$677$	0.740451	0.0284578	0.0142289	−	0.999899i	$-0.495471\pi$
$677$	0.740451	0.0284578	0.0142289	+	0.999899i	$0.495471\pi$
$678$	3.46748	0.133168
$679$	−2.19166	−0.0841083
$680$	−17.0830	−0.655102
$681$	3.72673	0.142809
$682$	28.9818	1.10977
$683$	1.89031	0.0723309	0.0361654	−	0.999346i	$-0.488486\pi$
$683$	1.89031	0.0723309	0.0361654	+	0.999346i	$0.488486\pi$
$684$	2.70826	0.103553
$685$	36.4034	1.39090
$686$	−3.47464	−0.132662
$687$	1.82420	0.0695976
$688$	31.4634	1.19953
$689$	−0.630574	−0.0240229
$690$	43.9086	1.67157
$691$	−13.0519	−0.496516	−0.248258	−	0.968694i	$-0.579858\pi$
$691$	−13.0519	−0.496516	−0.248258	+	0.968694i	$0.579858\pi$
$692$	3.25947	0.123906
$693$	−1.22212	−0.0464244
$694$	−22.9733	−0.872056
$695$	54.6997	2.07488
$696$	35.3276	1.33909
$697$	0.162082	0.00613930
$698$	−46.6754	−1.76669
$699$	−45.4963	−1.72083
$700$	−0.326741	−0.0123496
$701$	25.3052	0.955763	0.477882	−	0.878424i	$-0.341405\pi$
$701$	25.3052	0.955763	0.477882	+	0.878424i	$0.341405\pi$
$702$	19.4090	0.732545
$703$	−4.78056	−0.180302
$704$	22.0691	0.831759
$705$	11.1074	0.418328
$706$	33.5723	1.26351
$707$	−2.37000	−0.0891329
$708$	2.90737	0.109266
$709$	−30.9393	−1.16195	−0.580976	−	0.813921i	$-0.697329\pi$
$709$	−30.9393	−1.16195	−0.580976	+	0.813921i	$0.697329\pi$
$710$	4.80574	0.180356
$711$	14.8263	0.556028
$712$	16.4451	0.616307
$713$	−18.2382	−0.683025
$714$	1.28014	0.0479080
$715$	−62.1209	−2.32319
$716$	−3.34358	−0.124955
$717$	32.0679	1.19760
$718$	−34.3779	−1.28297
$719$	−41.5161	−1.54829	−0.774145	−	0.633008i	$-0.781820\pi$
$719$	−41.5161	−1.54829	−0.774145	+	0.633008i	$0.781820\pi$
$720$	−26.6809	−0.994338
$721$	−1.66656	−0.0620659
$722$	15.2361	0.567028
$723$	−17.7591	−0.660467
$724$	−2.47446	−0.0919628
$725$	−28.9077	−1.07360
$726$	22.6505	0.840639
$727$	−26.3604	−0.977653	−0.488827	−	0.872381i	$-0.662575\pi$
$727$	−26.3604	−0.977653	−0.488827	+	0.872381i	$0.662575\pi$
$728$	1.83751	0.0681026
$729$	−3.82412	−0.141634
$730$	−27.4653	−1.01654
$731$	15.5559	0.575356
$732$	8.40161	0.310532
$733$	3.90893	0.144380	0.0721898	−	0.997391i	$-0.477001\pi$
$733$	3.90893	0.144380	0.0721898	+	0.997391i	$0.477001\pi$
$734$	−2.38936	−0.0881929
$735$	46.8718	1.72889
$736$	11.0354	0.406770
$737$	37.0440	1.36453
$738$	0.201786	0.00742785
$739$	−21.4772	−0.790053	−0.395026	−	0.918670i	$-0.629265\pi$
$739$	−21.4772	−0.790053	−0.395026	+	0.918670i	$0.629265\pi$
$740$	−2.29218	−0.0842621
$741$	32.6880	1.20082
$742$	0.0322499	0.00118393
$743$	7.82324	0.287007	0.143503	−	0.989650i	$-0.454163\pi$
$743$	7.82324	0.287007	0.143503	+	0.989650i	$0.454163\pi$
$744$	23.1699	0.849450
$745$	−63.4576	−2.32491
$746$	−31.9998	−1.17160
$747$	2.01497	0.0737238
$748$	−4.69723	−0.171748
$749$	−0.486050	−0.0177599
$750$	−7.26530	−0.265291
$751$	−15.3838	−0.561364	−0.280682	−	0.959801i	$-0.590561\pi$
$751$	−15.3838	−0.561364	−0.280682	+	0.959801i	$0.590561\pi$
$752$	7.81718	0.285063
$753$	−4.43340	−0.161562
$754$	−51.3049	−1.86842
$755$	39.9725	1.45475
$756$	−0.192050	−0.00698479
$757$	−48.0617	−1.74683	−0.873416	−	0.486974i	$-0.838100\pi$
$757$	−48.0617	−1.74683	−0.873416	+	0.486974i	$0.838100\pi$
$758$	−21.3781	−0.776486
$759$	−38.2568	−1.38863
$760$	22.3093	0.809244
$761$	−18.1016	−0.656183	−0.328091	−	0.944646i	$-0.606405\pi$
$761$	−18.1016	−0.656183	−0.328091	+	0.944646i	$0.606405\pi$
$762$	−16.7365	−0.606300
$763$	−1.61613	−0.0585077
$764$	−6.54070	−0.236634
$765$	−13.1914	−0.476936
$766$	−35.0781	−1.26742
$767$	13.3790	0.483089
$768$	−24.0119	−0.866454
$769$	−15.0271	−0.541891	−0.270946	−	0.962595i	$-0.587336\pi$
$769$	−15.0271	−0.541891	−0.270946	+	0.962595i	$0.587336\pi$
$770$	3.17709	0.114494
$771$	30.6503	1.10384
$772$	4.66561	0.167919
$773$	−3.85837	−0.138776	−0.0693880	−	0.997590i	$-0.522105\pi$
$773$	−3.85837	−0.138776	−0.0693880	+	0.997590i	$0.522105\pi$
$774$	19.3665	0.696115
$775$	−18.9593	−0.681040
$776$	33.2306	1.19291
$777$	−0.544279	−0.0195259
$778$	−10.5889	−0.379630
$779$	−0.211669	−0.00758384
$780$	15.6732	0.561190
$781$	−4.18716	−0.149828
$782$	15.2784	0.546356
$783$	−16.9912	−0.607216
$784$	32.9876	1.17813
$785$	2.60230	0.0928799
$786$	−42.1681	−1.50409
$787$	1.58610	0.0565383	0.0282691	−	0.999600i	$-0.491000\pi$
$787$	1.58610	0.0565383	0.0282691	+	0.999600i	$0.491000\pi$
$788$	5.27262	0.187829
$789$	3.61285	0.128621
$790$	−38.5433	−1.37131
$791$	−0.157888	−0.00561387
$792$	18.5301	0.658439
$793$	38.6623	1.37294
$794$	−45.2523	−1.60594
$795$	−0.871636	−0.0309138
$796$	−3.83222	−0.135829
$797$	17.2392	0.610645	0.305323	−	0.952249i	$-0.401236\pi$
$797$	17.2392	0.610645	0.305323	+	0.952249i	$0.401236\pi$
$798$	−1.67178	−0.0591805
$799$	3.86492	0.136731
$800$	11.4718	0.405588
$801$	12.6989	0.448692
$802$	−41.1063	−1.45152
$803$	23.9300	0.844472
$804$	−9.34625	−0.329617
$805$	−1.99934	−0.0704674
$806$	−33.6488	−1.18523
$807$	−31.0610	−1.09340
$808$	35.9346	1.26417
$809$	35.6355	1.25288	0.626439	−	0.779471i	$-0.284512\pi$
$809$	35.6355	1.25288	0.626439	+	0.779471i	$0.284512\pi$
$810$	53.4806	1.87912
$811$	38.2914	1.34459	0.672296	−	0.740282i	$-0.265308\pi$
$811$	38.2914	1.34459	0.672296	+	0.740282i	$0.265308\pi$
$812$	0.507658	0.0178153
$813$	21.2702	0.745977
$814$	10.3226	0.361806
$815$	0.809447	0.0283537
$816$	−24.3502	−0.852429
$817$	−20.3151	−0.710735
$818$	−32.5811	−1.13917
$819$	1.41892	0.0495810
$820$	−0.101491	−0.00354422
$821$	−20.9487	−0.731114	−0.365557	−	0.930789i	$-0.619121\pi$
$821$	−20.9487	−0.731114	−0.365557	+	0.930789i	$0.619121\pi$
$822$	41.3620	1.44266
$823$	−48.1690	−1.67907	−0.839533	−	0.543309i	$-0.817171\pi$
$823$	−48.1690	−1.67907	−0.839533	+	0.543309i	$0.817171\pi$
$824$	25.2689	0.880282
$825$	−39.7695	−1.38460
$826$	−0.684253	−0.0238082
$827$	54.1538	1.88311	0.941556	−	0.336856i	$-0.109363\pi$
$827$	54.1538	1.88311	0.941556	+	0.336856i	$0.109363\pi$
$828$	3.68006	0.127891
$829$	30.4667	1.05815	0.529075	−	0.848575i	$-0.322539\pi$
$829$	30.4667	1.05815	0.529075	+	0.848575i	$0.322539\pi$
$830$	−5.23824	−0.181822
$831$	−28.8927	−1.00228
$832$	−25.6229	−0.888314
$833$	16.3095	0.565092
$834$	62.1503	2.15209
$835$	6.82220	0.236092
$836$	6.13430	0.212159
$837$	−11.1438	−0.385187
$838$	−7.48821	−0.258676
$839$	−6.12394	−0.211422	−0.105711	−	0.994397i	$-0.533712\pi$
$839$	−6.12394	−0.211422	−0.105711	+	0.994397i	$0.533712\pi$
$840$	2.53997	0.0876374
$841$	15.9138	0.548753
$842$	−35.4803	−1.22273
$843$	43.7350	1.50631
$844$	−4.83249	−0.166341
$845$	32.4511	1.11635
$846$	4.81168	0.165429
$847$	−1.03137	−0.0354383
$848$	−0.613443	−0.0210657
$849$	48.0944	1.65060
$850$	15.8826	0.544768
$851$	−6.49597	−0.222679
$852$	1.05643	0.0361925
$853$	31.1108	1.06521	0.532606	−	0.846363i	$-0.321213\pi$
$853$	31.1108	1.06521	0.532606	+	0.846363i	$0.321213\pi$
$854$	−1.97733	−0.0676629
$855$	17.2272	0.589157
$856$	7.36963	0.251889
$857$	47.6218	1.62673	0.813365	−	0.581754i	$-0.197633\pi$
$857$	47.6218	1.62673	0.813365	+	0.581754i	$0.197633\pi$
$858$	−70.5824	−2.40964
$859$	51.6147	1.76107	0.880535	−	0.473981i	$-0.157183\pi$
$859$	51.6147	1.76107	0.880535	+	0.473981i	$0.157183\pi$
$860$	−9.74065	−0.332154
$861$	−0.0240991	−0.000821295 0
$862$	−15.7114	−0.535134
$863$	30.4315	1.03590	0.517950	−	0.855411i	$-0.326695\pi$
$863$	30.4315	1.03590	0.517950	+	0.855411i	$0.326695\pi$
$864$	6.74281	0.229395
$865$	20.7334	0.704958
$866$	−16.2050	−0.550669
$867$	25.3941	0.862430
$868$	0.332952	0.0113011
$869$	33.5820	1.13919
$870$	−70.9184	−2.40436
$871$	−43.0093	−1.45731
$872$	24.5042	0.829817
$873$	25.6606	0.868479
$874$	−19.9527	−0.674911
$875$	0.330819	0.0111837
$876$	−6.03758	−0.203991
$877$	−15.9796	−0.539592	−0.269796	−	0.962918i	$-0.586956\pi$
$877$	−15.9796	−0.539592	−0.269796	+	0.962918i	$0.586956\pi$
$878$	−5.66921	−0.191327
$879$	−3.47160	−0.117094
$880$	−60.4333	−2.03720
$881$	33.4910	1.12834	0.564170	−	0.825658i	$-0.309196\pi$
$881$	33.4910	1.12834	0.564170	+	0.825658i	$0.309196\pi$
$882$	20.3047	0.683696
$883$	0.683363	0.0229970	0.0114985	−	0.999934i	$-0.496340\pi$
$883$	0.683363	0.0229970	0.0114985	+	0.999934i	$0.496340\pi$
$884$	5.45364	0.183426
$885$	18.4937	0.621659
$886$	28.6159	0.961370
$887$	−0.434295	−0.0145822	−0.00729110	−	0.999973i	$-0.502321\pi$
$887$	−0.434295	−0.0145822	−0.00729110	+	0.999973i	$0.502321\pi$
$888$	8.25252	0.276937
$889$	0.762082	0.0255594
$890$	−33.0128	−1.10659
$891$	−46.5967	−1.56105
$892$	0.694216	0.0232441
$893$	−5.04735	−0.168903
$894$	−72.1012	−2.41143
$895$	−21.2685	−0.710926
$896$	2.15027	0.0718356
$897$	44.4174	1.48305
$898$	−30.0142	−1.00159
$899$	29.4571	0.982451
$900$	3.82557	0.127519
$901$	−0.303295	−0.0101042
$902$	0.457053	0.0152182
$903$	−2.31293	−0.0769693
$904$	2.39395	0.0796217
$905$	−15.7400	−0.523216
$906$	45.4171	1.50888
$907$	22.3164	0.741005	0.370502	−	0.928832i	$-0.379186\pi$
$907$	22.3164	0.741005	0.370502	+	0.928832i	$0.379186\pi$
$908$	−0.811990	−0.0269468
$909$	27.7486	0.920362
$910$	−3.68871	−0.122279
$911$	1.44392	0.0478391	0.0239195	−	0.999714i	$-0.492385\pi$
$911$	1.44392	0.0478391	0.0239195	+	0.999714i	$0.492385\pi$
$912$	31.7999	1.05300
$913$	4.56398	0.151046
$914$	−21.3128	−0.704966
$915$	53.4425	1.76676
$916$	−0.397461	−0.0131325
$917$	1.92009	0.0634068
$918$	9.33538	0.308113
$919$	33.2345	1.09631	0.548153	−	0.836378i	$-0.315331\pi$
$919$	33.2345	1.09631	0.548153	+	0.836378i	$0.315331\pi$
$920$	30.3146	0.999442
$921$	16.7227	0.551033
$922$	20.2202	0.665917
$923$	4.86143	0.160016
$924$	0.698406	0.0229759
$925$	−6.75283	−0.222032
$926$	−13.1655	−0.432644
$927$	19.5125	0.640876
$928$	−17.8237	−0.585091
$929$	25.8957	0.849609	0.424805	−	0.905285i	$-0.360343\pi$
$929$	25.8957	0.849609	0.424805	+	0.905285i	$0.360343\pi$
$930$	−46.5124	−1.52520
$931$	−21.2993	−0.698055
$932$	9.91285	0.324706
$933$	−3.48504	−0.114095
$934$	5.01117	0.163970
$935$	−29.8790	−0.977149
$936$	−21.5141	−0.703210
$937$	−26.1675	−0.854854	−0.427427	−	0.904050i	$-0.640580\pi$
$937$	−26.1675	−0.854854	−0.427427	+	0.904050i	$0.640580\pi$
$938$	2.19966	0.0718213
$939$	−16.8013	−0.548289
$940$	−2.42010	−0.0789349
$941$	18.8416	0.614219	0.307110	−	0.951674i	$-0.400638\pi$
$941$	18.8416	0.614219	0.307110	+	0.951674i	$0.400638\pi$
$942$	2.95676	0.0963363
$943$	−0.287623	−0.00936629
$944$	13.0156	0.423621
$945$	−1.22163	−0.0397396
$946$	43.8659	1.42620
$947$	34.6801	1.12695	0.563476	−	0.826133i	$-0.309464\pi$
$947$	34.6801	1.12695	0.563476	+	0.826133i	$0.309464\pi$
$948$	−8.47280	−0.275184
$949$	−27.7836	−0.901892
$950$	−20.7417	−0.672949
$951$	−21.3136	−0.691141
$952$	0.883810	0.0286444
$953$	−25.0260	−0.810671	−0.405335	−	0.914168i	$-0.632845\pi$
$953$	−25.0260	−0.810671	−0.405335	+	0.914168i	$0.632845\pi$
$954$	−0.377591	−0.0122249
$955$	−41.6053	−1.34631
$956$	−6.98703	−0.225977
$957$	61.7899	1.99738
$958$	28.1444	0.909304
$959$	−1.88338	−0.0608175
$960$	−35.4183	−1.14312
$961$	−11.6803	−0.376783
$962$	−11.9848	−0.386406
$963$	5.69080	0.183384
$964$	3.86939	0.124625
$965$	29.6778	0.955364
$966$	−2.27167	−0.0730898
$967$	38.1106	1.22556	0.612778	−	0.790255i	$-0.290052\pi$
$967$	38.1106	1.22556	0.612778	+	0.790255i	$0.290052\pi$
$968$	15.6379	0.502623
$969$	15.7223	0.505074
$970$	−66.7088	−2.14189
$971$	30.5246	0.979580	0.489790	−	0.871840i	$-0.337073\pi$
$971$	30.5246	0.979580	0.489790	+	0.871840i	$0.337073\pi$
$972$	8.10731	0.260042
$973$	−2.82996	−0.0907243
$974$	25.0246	0.801839
$975$	46.1737	1.47874
$976$	37.6120	1.20393
$977$	−42.2934	−1.35309	−0.676544	−	0.736403i	$-0.736523\pi$
$977$	−42.2934	−1.35309	−0.676544	+	0.736403i	$0.736523\pi$
$978$	0.919702	0.0294088
$979$	28.7634	0.919283
$980$	−10.2125	−0.326228
$981$	18.9221	0.604135
$982$	37.3125	1.19069
$983$	−20.5712	−0.656121	−0.328060	−	0.944657i	$-0.606395\pi$
$983$	−20.5712	−0.656121	−0.328060	+	0.944657i	$0.606395\pi$
$984$	0.365398	0.0116485
$985$	33.5390	1.06864
$986$	−24.6768	−0.785869
$987$	−0.574654	−0.0182914
$988$	−7.12213	−0.226585
$989$	−27.6048	−0.877780
$990$	−37.1983	−1.18224
$991$	56.4876	1.79439	0.897194	−	0.441637i	$-0.145602\pi$
$991$	56.4876	1.79439	0.897194	+	0.441637i	$0.145602\pi$
$992$	−11.6898	−0.371152
$993$	41.5403	1.31824
$994$	−0.248631	−0.00788611
$995$	−24.3767	−0.772793
$996$	−1.15150	−0.0364866
$997$	−19.0127	−0.602139	−0.301070	−	0.953602i	$-0.597344\pi$
$997$	−19.0127	−0.602139	−0.301070	+	0.953602i	$0.597344\pi$
$998$	1.15857	0.0366740
$999$	−3.96914	−0.125578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.37	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.37	✓	172	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57473 q^{2} -2.20195 q^{3} +0.479767 q^{4} +3.05179 q^{5} +3.46748 q^{6} -0.157888 q^{7} +2.39395 q^{8} +1.84860 q^{9} +O(q^{10})\)	\(q-1.57473 q^{2} -2.20195 q^{3} +0.479767 q^{4} +3.05179 q^{5} +3.46748 q^{6} -0.157888 q^{7} +2.39395 q^{8} +1.84860 q^{9} -4.80574 q^{10} +4.18716 q^{11} -1.05643 q^{12} -4.86143 q^{13} +0.248631 q^{14} -6.71990 q^{15} -4.72936 q^{16} -2.33826 q^{17} -2.91105 q^{18} +3.05363 q^{19} +1.46415 q^{20} +0.347663 q^{21} -6.59363 q^{22} +4.14936 q^{23} -5.27137 q^{24} +4.31343 q^{25} +7.65542 q^{26} +2.53533 q^{27} -0.0757497 q^{28} -6.70178 q^{29} +10.5820 q^{30} -4.39542 q^{31} +2.65954 q^{32} -9.21992 q^{33} +3.68212 q^{34} -0.481843 q^{35} +0.886898 q^{36} -1.56554 q^{37} -4.80863 q^{38} +10.7046 q^{39} +7.30584 q^{40} -0.0693174 q^{41} -0.547475 q^{42} -6.65278 q^{43} +2.00886 q^{44} +5.64155 q^{45} -6.53411 q^{46} -1.65291 q^{47} +10.4138 q^{48} -6.97507 q^{49} -6.79248 q^{50} +5.14874 q^{51} -2.33235 q^{52} +0.129710 q^{53} -3.99245 q^{54} +12.7783 q^{55} -0.377978 q^{56} -6.72394 q^{57} +10.5535 q^{58} -2.75208 q^{59} -3.22399 q^{60} -7.95287 q^{61} +6.92159 q^{62} -0.291873 q^{63} +5.27066 q^{64} -14.8361 q^{65} +14.5189 q^{66} +8.84706 q^{67} -1.12182 q^{68} -9.13670 q^{69} +0.758771 q^{70} -1.00000 q^{71} +4.42547 q^{72} +5.71510 q^{73} +2.46529 q^{74} -9.49797 q^{75} +1.46503 q^{76} -0.661104 q^{77} -16.8569 q^{78} +8.02025 q^{79} -14.4330 q^{80} -11.1285 q^{81} +0.109156 q^{82} +1.09000 q^{83} +0.166797 q^{84} -7.13588 q^{85} +10.4763 q^{86} +14.7570 q^{87} +10.0239 q^{88} +6.86944 q^{89} -8.88390 q^{90} +0.767563 q^{91} +1.99073 q^{92} +9.67852 q^{93} +2.60288 q^{94} +9.31903 q^{95} -5.85620 q^{96} +13.8811 q^{97} +10.9838 q^{98} +7.74038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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