LMFDB - Embedded newform 8023.2.a.e.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.60904 q^{2} -1.86481 q^{3} +4.80711 q^{4} +2.29669 q^{5} +4.86538 q^{6} +1.81523 q^{7} -7.32387 q^{8} +0.477530 q^{9} +O(q^{10})$	\(q-2.60904 q^{2} -1.86481 q^{3} +4.80711 q^{4} +2.29669 q^{5} +4.86538 q^{6} +1.81523 q^{7} -7.32387 q^{8} +0.477530 q^{9} -5.99216 q^{10} +2.62092 q^{11} -8.96436 q^{12} +0.661466 q^{13} -4.73602 q^{14} -4.28289 q^{15} +9.49409 q^{16} -2.14602 q^{17} -1.24590 q^{18} +3.06611 q^{19} +11.0404 q^{20} -3.38507 q^{21} -6.83811 q^{22} +5.50652 q^{23} +13.6577 q^{24} +0.274770 q^{25} -1.72579 q^{26} +4.70394 q^{27} +8.72602 q^{28} +9.18600 q^{29} +11.1743 q^{30} +6.94750 q^{31} -10.1227 q^{32} -4.88754 q^{33} +5.59907 q^{34} +4.16902 q^{35} +2.29554 q^{36} -0.664780 q^{37} -7.99962 q^{38} -1.23351 q^{39} -16.8206 q^{40} -9.22716 q^{41} +8.83179 q^{42} +7.35190 q^{43} +12.5991 q^{44} +1.09674 q^{45} -14.3668 q^{46} +4.04700 q^{47} -17.7047 q^{48} -3.70493 q^{49} -0.716886 q^{50} +4.00193 q^{51} +3.17974 q^{52} +12.1183 q^{53} -12.2728 q^{54} +6.01944 q^{55} -13.2945 q^{56} -5.71772 q^{57} -23.9667 q^{58} -3.98736 q^{59} -20.5883 q^{60} -3.66010 q^{61} -18.1263 q^{62} +0.866827 q^{63} +7.42250 q^{64} +1.51918 q^{65} +12.7518 q^{66} +1.27873 q^{67} -10.3162 q^{68} -10.2686 q^{69} -10.8772 q^{70} -1.00000 q^{71} -3.49737 q^{72} +5.93665 q^{73} +1.73444 q^{74} -0.512394 q^{75} +14.7391 q^{76} +4.75759 q^{77} +3.21828 q^{78} -9.62774 q^{79} +21.8049 q^{80} -10.2046 q^{81} +24.0741 q^{82} +9.22360 q^{83} -16.2724 q^{84} -4.92874 q^{85} -19.1814 q^{86} -17.1302 q^{87} -19.1953 q^{88} +8.36579 q^{89} -2.86143 q^{90} +1.20071 q^{91} +26.4704 q^{92} -12.9558 q^{93} -10.5588 q^{94} +7.04189 q^{95} +18.8770 q^{96} -4.47524 q^{97} +9.66634 q^{98} +1.25157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60904	−1.84487	−0.922436	−	0.386149i	$-0.873805\pi$
$2$	−2.60904	−1.84487	−0.922436	+	0.386149i	$0.873805\pi$
$3$	−1.86481	−1.07665	−0.538325	−	0.842737i	$-0.680943\pi$
$3$	−1.86481	−1.07665	−0.538325	+	0.842737i	$0.680943\pi$
$4$	4.80711	2.40355
$5$	2.29669	1.02711	0.513555	−	0.858057i	$-0.328328\pi$
$5$	2.29669	1.02711	0.513555	+	0.858057i	$0.328328\pi$
$6$	4.86538	1.98628
$7$	1.81523	0.686093	0.343047	−	0.939318i	$-0.388541\pi$
$7$	1.81523	0.686093	0.343047	+	0.939318i	$0.388541\pi$
$8$	−7.32387	−2.58938
$9$	0.477530	0.159177
$10$	−5.99216	−1.89489
$11$	2.62092	0.790239	0.395119	−	0.918630i	$-0.370703\pi$
$11$	2.62092	0.790239	0.395119	+	0.918630i	$0.370703\pi$
$12$	−8.96436	−2.58779
$13$	0.661466	0.183458	0.0917288	−	0.995784i	$-0.470761\pi$
$13$	0.661466	0.183458	0.0917288	+	0.995784i	$0.470761\pi$
$14$	−4.73602	−1.26575
$15$	−4.28289	−1.10584
$16$	9.49409	2.37352
$17$	−2.14602	−0.520487	−0.260244	−	0.965543i	$-0.583803\pi$
$17$	−2.14602	−0.520487	−0.260244	+	0.965543i	$0.583803\pi$
$18$	−1.24590	−0.293661
$19$	3.06611	0.703414	0.351707	−	0.936110i	$-0.385601\pi$
$19$	3.06611	0.703414	0.351707	+	0.936110i	$0.385601\pi$
$20$	11.0404	2.46871
$21$	−3.38507	−0.738682
$22$	−6.83811	−1.45789
$23$	5.50652	1.14819	0.574094	−	0.818789i	$-0.305354\pi$
$23$	5.50652	1.14819	0.574094	+	0.818789i	$0.305354\pi$
$24$	13.6577	2.78786
$25$	0.274770	0.0549539
$26$	−1.72579	−0.338456
$27$	4.70394	0.905273
$28$	8.72602	1.64906
$29$	9.18600	1.70580	0.852899	−	0.522076i	$-0.174842\pi$
$29$	9.18600	1.70580	0.852899	+	0.522076i	$0.174842\pi$
$30$	11.1743	2.04013
$31$	6.94750	1.24781	0.623904	−	0.781501i	$-0.285546\pi$
$31$	6.94750	1.24781	0.623904	+	0.781501i	$0.285546\pi$
$32$	−10.1227	−1.78946
$33$	−4.88754	−0.850811
$34$	5.59907	0.960232
$35$	4.16902	0.704693
$36$	2.29554	0.382590
$37$	−0.664780	−0.109289	−0.0546446	−	0.998506i	$-0.517403\pi$
$37$	−0.664780	−0.109289	−0.0546446	+	0.998506i	$0.517403\pi$
$38$	−7.99962	−1.29771
$39$	−1.23351	−0.197520
$40$	−16.8206	−2.65958
$41$	−9.22716	−1.44104	−0.720520	−	0.693434i	$-0.756097\pi$
$41$	−9.22716	−1.44104	−0.720520	+	0.693434i	$0.756097\pi$
$42$	8.83179	1.36278
$43$	7.35190	1.12115	0.560577	−	0.828102i	$-0.310579\pi$
$43$	7.35190	1.12115	0.560577	+	0.828102i	$0.310579\pi$
$44$	12.5991	1.89938
$45$	1.09674	0.163492
$46$	−14.3668	−2.11826
$47$	4.04700	0.590315	0.295158	−	0.955449i	$-0.404628\pi$
$47$	4.04700	0.590315	0.295158	+	0.955449i	$0.404628\pi$
$48$	−17.7047	−2.55545
$49$	−3.70493	−0.529276
$50$	−0.716886	−0.101383
$51$	4.00193	0.560383
$52$	3.17974	0.440951
$53$	12.1183	1.66458	0.832291	−	0.554338i	$-0.187029\pi$
$53$	12.1183	1.66458	0.832291	+	0.554338i	$0.187029\pi$
$54$	−12.2728	−1.67011
$55$	6.01944	0.811662
$56$	−13.2945	−1.77656
$57$	−5.71772	−0.757331
$58$	−23.9667	−3.14698
$59$	−3.98736	−0.519110	−0.259555	−	0.965728i	$-0.583576\pi$
$59$	−3.98736	−0.519110	−0.259555	+	0.965728i	$0.583576\pi$
$60$	−20.5883	−2.65794
$61$	−3.66010	−0.468628	−0.234314	−	0.972161i	$-0.575284\pi$
$61$	−3.66010	−0.468628	−0.234314	+	0.972161i	$0.575284\pi$
$62$	−18.1263	−2.30205
$63$	0.866827	0.109210
$64$	7.42250	0.927813
$65$	1.51918	0.188431
$66$	12.7518	1.56964
$67$	1.27873	0.156222	0.0781110	−	0.996945i	$-0.475111\pi$
$67$	1.27873	0.156222	0.0781110	+	0.996945i	$0.475111\pi$
$68$	−10.3162	−1.25102
$69$	−10.2686	−1.23620
$70$	−10.8772	−1.30007
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−3.49737	−0.412169
$73$	5.93665	0.694833	0.347416	−	0.937711i	$-0.387059\pi$
$73$	5.93665	0.694833	0.347416	+	0.937711i	$0.387059\pi$
$74$	1.73444	0.201625
$75$	−0.512394	−0.0591662
$76$	14.7391	1.69069
$77$	4.75759	0.542177
$78$	3.21828	0.364399
$79$	−9.62774	−1.08321	−0.541603	−	0.840635i	$-0.682182\pi$
$79$	−9.62774	−1.08321	−0.541603	+	0.840635i	$0.682182\pi$
$80$	21.8049	2.43787
$81$	−10.2046	−1.13384
$82$	24.0741	2.65854
$83$	9.22360	1.01242	0.506211	−	0.862410i	$-0.331046\pi$
$83$	9.22360	1.01242	0.506211	+	0.862410i	$0.331046\pi$
$84$	−16.2724	−1.77546
$85$	−4.92874	−0.534597
$86$	−19.1814	−2.06839
$87$	−17.1302	−1.83655
$88$	−19.1953	−2.04623
$89$	8.36579	0.886772	0.443386	−	0.896331i	$-0.353777\pi$
$89$	8.36579	0.886772	0.443386	+	0.896331i	$0.353777\pi$
$90$	−2.86143	−0.301622
$91$	1.20071	0.125869
$92$	26.4704	2.75973
$93$	−12.9558	−1.34345
$94$	−10.5588	−1.08906
$95$	7.04189	0.722483
$96$	18.8770	1.92663
$97$	−4.47524	−0.454392	−0.227196	−	0.973849i	$-0.572956\pi$
$97$	−4.47524	−0.454392	−0.227196	+	0.973849i	$0.572956\pi$
$98$	9.66634	0.976447
$99$	1.25157	0.125788
$100$	1.32085	0.132085
$101$	−3.80394	−0.378506	−0.189253	−	0.981928i	$-0.560607\pi$
$101$	−3.80394	−0.378506	−0.189253	+	0.981928i	$0.560607\pi$
$102$	−10.4412	−1.03383
$103$	8.60387	0.847764	0.423882	−	0.905717i	$-0.360667\pi$
$103$	8.60387	0.847764	0.423882	+	0.905717i	$0.360667\pi$
$104$	−4.84449	−0.475042
$105$	−7.77444	−0.758708
$106$	−31.6173	−3.07094
$107$	11.9450	1.15476	0.577382	−	0.816474i	$-0.304074\pi$
$107$	11.9450	1.15476	0.577382	+	0.816474i	$0.304074\pi$
$108$	22.6123	2.17587
$109$	4.30630	0.412469	0.206235	−	0.978503i	$-0.433879\pi$
$109$	4.30630	0.412469	0.206235	+	0.978503i	$0.433879\pi$
$110$	−15.7050	−1.49741
$111$	1.23969	0.117666
$112$	17.2340	1.62846
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	14.9178	1.39718
$115$	12.6468	1.17932
$116$	44.1581	4.09998
$117$	0.315870	0.0292022
$118$	10.4032	0.957691
$119$	−3.89553	−0.357103
$120$	31.3674	2.86344
$121$	−4.13075	−0.375523
$122$	9.54937	0.864559
$123$	17.2069	1.55150
$124$	33.3974	2.99917
$125$	−10.8524	−0.970666
$126$	−2.26159	−0.201478
$127$	0.505777	0.0448804	0.0224402	−	0.999748i	$-0.492856\pi$
$127$	0.505777	0.0448804	0.0224402	+	0.999748i	$0.492856\pi$
$128$	0.879843	0.0777679
$129$	−13.7099	−1.20709
$130$	−3.96361	−0.347631
$131$	7.99659	0.698665	0.349332	−	0.936999i	$-0.386408\pi$
$131$	7.99659	0.698665	0.349332	+	0.936999i	$0.386408\pi$
$132$	−23.4949	−2.04497
$133$	5.56570	0.482607
$134$	−3.33627	−0.288210
$135$	10.8035	0.929815
$136$	15.7172	1.34774
$137$	14.2156	1.21452	0.607261	−	0.794503i	$-0.292268\pi$
$137$	14.2156	1.21452	0.607261	+	0.794503i	$0.292268\pi$
$138$	26.7913	2.28063
$139$	−6.05093	−0.513233	−0.256617	−	0.966513i	$-0.582608\pi$
$139$	−6.05093	−0.513233	−0.256617	+	0.966513i	$0.582608\pi$
$140$	20.0409	1.69377
$141$	−7.54690	−0.635563
$142$	2.60904	0.218946
$143$	1.73365	0.144975
$144$	4.53371	0.377809
$145$	21.0974	1.75204
$146$	−15.4890	−1.28188
$147$	6.90901	0.569846
$148$	−3.19567	−0.262683
$149$	−15.9120	−1.30356	−0.651782	−	0.758406i	$-0.725978\pi$
$149$	−15.9120	−1.30356	−0.651782	+	0.758406i	$0.725978\pi$
$150$	1.33686	0.109154
$151$	−9.05969	−0.737267	−0.368634	−	0.929575i	$-0.620174\pi$
$151$	−9.05969	−0.737267	−0.368634	+	0.929575i	$0.620174\pi$
$152$	−22.4558	−1.82141
$153$	−1.02479	−0.0828494
$154$	−12.4127	−1.00025
$155$	15.9562	1.28163
$156$	−5.92962	−0.474750
$157$	6.79245	0.542097	0.271048	−	0.962566i	$-0.412630\pi$
$157$	6.79245	0.542097	0.271048	+	0.962566i	$0.412630\pi$
$158$	25.1192	1.99838
$159$	−22.5985	−1.79217
$160$	−23.2488	−1.83798
$161$	9.99561	0.787764
$162$	26.6241	2.09179
$163$	−0.370020	−0.0289822	−0.0144911	−	0.999895i	$-0.504613\pi$
$163$	−0.370020	−0.0289822	−0.0144911	+	0.999895i	$0.504613\pi$
$164$	−44.3560	−3.46362
$165$	−11.2251	−0.873876
$166$	−24.0648	−1.86779
$167$	−2.36308	−0.182860	−0.0914302	−	0.995811i	$-0.529144\pi$
$167$	−2.36308	−0.182860	−0.0914302	+	0.995811i	$0.529144\pi$
$168$	24.7918	1.91273
$169$	−12.5625	−0.966343
$170$	12.8593	0.986264
$171$	1.46416	0.111967
$172$	35.3414	2.69476
$173$	5.55427	0.422283	0.211142	−	0.977455i	$-0.432282\pi$
$173$	5.55427	0.422283	0.211142	+	0.977455i	$0.432282\pi$
$174$	44.6934	3.38820
$175$	0.498770	0.0377035
$176$	24.8833	1.87565
$177$	7.43568	0.558900
$178$	−21.8267	−1.63598
$179$	9.84834	0.736099	0.368050	−	0.929806i	$-0.380026\pi$
$179$	9.84834	0.736099	0.368050	+	0.929806i	$0.380026\pi$
$180$	5.27213	0.392962
$181$	20.0112	1.48742	0.743711	−	0.668501i	$-0.233064\pi$
$181$	20.0112	1.48742	0.743711	+	0.668501i	$0.233064\pi$
$182$	−3.13272	−0.232212
$183$	6.82541	0.504549
$184$	−40.3291	−2.97310
$185$	−1.52679	−0.112252
$186$	33.8022	2.47850
$187$	−5.62457	−0.411309
$188$	19.4544	1.41886
$189$	8.53873	0.621102
$190$	−18.3726	−1.33289
$191$	2.92040	0.211312	0.105656	−	0.994403i	$-0.466306\pi$
$191$	2.92040	0.211312	0.105656	+	0.994403i	$0.466306\pi$
$192$	−13.8416	−0.998931
$193$	−0.0408839	−0.00294289	−0.00147144	−	0.999999i	$-0.500468\pi$
$193$	−0.0408839	−0.00294289	−0.00147144	+	0.999999i	$0.500468\pi$
$194$	11.6761	0.838296
$195$	−2.83299	−0.202874
$196$	−17.8100	−1.27214
$197$	16.9739	1.20934	0.604670	−	0.796476i	$-0.293305\pi$
$197$	16.9739	1.20934	0.604670	+	0.796476i	$0.293305\pi$
$198$	−3.26540	−0.232062
$199$	−9.54488	−0.676618	−0.338309	−	0.941035i	$-0.609855\pi$
$199$	−9.54488	−0.676618	−0.338309	+	0.941035i	$0.609855\pi$
$200$	−2.01238	−0.142297
$201$	−2.38460	−0.168197
$202$	9.92464	0.698295
$203$	16.6747	1.17034
$204$	19.2377	1.34691
$205$	−21.1919	−1.48011
$206$	−22.4479	−1.56402
$207$	2.62953	0.182765
$208$	6.28001	0.435441
$209$	8.03604	0.555865
$210$	20.2839	1.39972
$211$	25.4232	1.75021	0.875103	−	0.483937i	$-0.160793\pi$
$211$	25.4232	1.75021	0.875103	+	0.483937i	$0.160793\pi$
$212$	58.2542	4.00092
$213$	1.86481	0.127775
$214$	−31.1649	−2.13039
$215$	16.8850	1.15155
$216$	−34.4510	−2.34410
$217$	12.6113	0.856112
$218$	−11.2353	−0.760953
$219$	−11.0708	−0.748092
$220$	28.9361	1.95087
$221$	−1.41952	−0.0954873
$222$	−3.23441	−0.217079
$223$	−20.2225	−1.35420	−0.677098	−	0.735892i	$-0.736763\pi$
$223$	−20.2225	−1.35420	−0.677098	+	0.735892i	$0.736763\pi$
$224$	−18.3751	−1.22774
$225$	0.131211	0.00874738
$226$	−2.60904	−0.173551
$227$	4.88301	0.324097	0.162048	−	0.986783i	$-0.448190\pi$
$227$	4.88301	0.324097	0.162048	+	0.986783i	$0.448190\pi$
$228$	−27.4857	−1.82029
$229$	−14.0413	−0.927872	−0.463936	−	0.885869i	$-0.653563\pi$
$229$	−14.0413	−0.927872	−0.463936	+	0.885869i	$0.653563\pi$
$230$	−32.9959	−2.17569
$231$	−8.87201	−0.583735
$232$	−67.2771	−4.41696
$233$	3.60412	0.236114	0.118057	−	0.993007i	$-0.462333\pi$
$233$	3.60412	0.236114	0.118057	+	0.993007i	$0.462333\pi$
$234$	−0.824118	−0.0538743
$235$	9.29468	0.606318
$236$	−19.1677	−1.24771
$237$	17.9539	1.16623
$238$	10.1636	0.658809
$239$	−18.2683	−1.18168	−0.590840	−	0.806789i	$-0.701203\pi$
$239$	−18.2683	−1.18168	−0.590840	+	0.806789i	$0.701203\pi$
$240$	−40.6622	−2.62473
$241$	20.2967	1.30743	0.653713	−	0.756743i	$-0.273211\pi$
$241$	20.2967	1.30743	0.653713	+	0.756743i	$0.273211\pi$
$242$	10.7773	0.692792
$243$	4.91778	0.315476
$244$	−17.5945	−1.12637
$245$	−8.50907	−0.543625
$246$	−44.8937	−2.86231
$247$	2.02813	0.129047
$248$	−50.8826	−3.23105
$249$	−17.2003	−1.09002
$250$	28.3143	1.79075
$251$	−22.3851	−1.41294	−0.706468	−	0.707745i	$-0.749713\pi$
$251$	−22.3851	−1.41294	−0.706468	+	0.707745i	$0.749713\pi$
$252$	4.16693	0.262492
$253$	14.4322	0.907343
$254$	−1.31959	−0.0827987
$255$	9.19119	0.575575
$256$	−17.1406	−1.07128
$257$	−5.19472	−0.324038	−0.162019	−	0.986788i	$-0.551801\pi$
$257$	−5.19472	−0.324038	−0.162019	+	0.986788i	$0.551801\pi$
$258$	35.7698	2.22693
$259$	−1.20673	−0.0749826
$260$	7.30287	0.452904
$261$	4.38659	0.271523
$262$	−20.8634	−1.28895
$263$	−25.1047	−1.54802	−0.774010	−	0.633173i	$-0.781752\pi$
$263$	−25.1047	−1.54802	−0.774010	+	0.633173i	$0.781752\pi$
$264$	35.7957	2.20307
$265$	27.8320	1.70971
$266$	−14.5212	−0.890349
$267$	−15.6006	−0.954743
$268$	6.14701	0.375488
$269$	−2.07197	−0.126330	−0.0631651	−	0.998003i	$-0.520119\pi$
$269$	−2.07197	−0.126330	−0.0631651	+	0.998003i	$0.520119\pi$
$270$	−28.1867	−1.71539
$271$	6.34180	0.385237	0.192618	−	0.981274i	$-0.438302\pi$
$271$	6.34180	0.385237	0.192618	+	0.981274i	$0.438302\pi$
$272$	−20.3745	−1.23539
$273$	−2.23911	−0.135517
$274$	−37.0892	−2.24064
$275$	0.720150	0.0434267
$276$	−49.3625	−2.97127
$277$	−25.1262	−1.50969	−0.754843	−	0.655905i	$-0.772287\pi$
$277$	−25.1262	−1.50969	−0.754843	+	0.655905i	$0.772287\pi$
$278$	15.7871	0.946850
$279$	3.31764	0.198622
$280$	−30.5334	−1.82472
$281$	17.9791	1.07254	0.536272	−	0.844045i	$-0.319832\pi$
$281$	17.9791	1.07254	0.536272	+	0.844045i	$0.319832\pi$
$282$	19.6902	1.17253
$283$	−4.15489	−0.246982	−0.123491	−	0.992346i	$-0.539409\pi$
$283$	−4.15489	−0.246982	−0.123491	+	0.992346i	$0.539409\pi$
$284$	−4.80711	−0.285249
$285$	−13.1318	−0.777862
$286$	−4.52318	−0.267461
$287$	−16.7494	−0.988688
$288$	−4.83391	−0.284841
$289$	−12.3946	−0.729093
$290$	−55.0439	−3.23229
$291$	8.34550	0.489222
$292$	28.5381	1.67007
$293$	18.3900	1.07435	0.537177	−	0.843470i	$-0.319491\pi$
$293$	18.3900	1.07435	0.537177	+	0.843470i	$0.319491\pi$
$294$	−18.0259	−1.05129
$295$	−9.15771	−0.533183
$296$	4.86877	0.282991
$297$	12.3287	0.715382
$298$	41.5152	2.40491
$299$	3.64238	0.210644
$300$	−2.46313	−0.142209
$301$	13.3454	0.769216
$302$	23.6371	1.36016
$303$	7.09364	0.407519
$304$	29.1099	1.66957
$305$	−8.40611	−0.481332
$306$	2.67372	0.152847
$307$	13.2939	0.758723	0.379361	−	0.925249i	$-0.376144\pi$
$307$	13.2939	0.758723	0.379361	+	0.925249i	$0.376144\pi$
$308$	22.8702	1.30315
$309$	−16.0446	−0.912746
$310$	−41.6305	−2.36445
$311$	−24.1291	−1.36824	−0.684119	−	0.729371i	$-0.739813\pi$
$311$	−24.1291	−1.36824	−0.684119	+	0.729371i	$0.739813\pi$
$312$	9.03408	0.511454
$313$	2.43537	0.137655	0.0688276	−	0.997629i	$-0.478074\pi$
$313$	2.43537	0.137655	0.0688276	+	0.997629i	$0.478074\pi$
$314$	−17.7218	−1.00010
$315$	1.99083	0.112171
$316$	−46.2816	−2.60354
$317$	1.26779	0.0712061	0.0356030	−	0.999366i	$-0.488665\pi$
$317$	1.26779	0.0712061	0.0356030	+	0.999366i	$0.488665\pi$
$318$	58.9604	3.30633
$319$	24.0758	1.34799
$320$	17.0472	0.952966
$321$	−22.2751	−1.24328
$322$	−26.0790	−1.45332
$323$	−6.57994	−0.366118
$324$	−49.0544	−2.72525
$325$	0.181751	0.0100817
$326$	0.965399	0.0534685
$327$	−8.03046	−0.444085
$328$	67.5786	3.73140
$329$	7.34624	0.405011
$330$	29.2869	1.61219
$331$	−3.87397	−0.212933	−0.106466	−	0.994316i	$-0.533954\pi$
$331$	−3.87397	−0.212933	−0.106466	+	0.994316i	$0.533954\pi$
$332$	44.3388	2.43341
$333$	−0.317452	−0.0173963
$334$	6.16537	0.337354
$335$	2.93685	0.160457
$336$	−32.1381	−1.75328
$337$	−22.7113	−1.23717	−0.618583	−	0.785720i	$-0.712293\pi$
$337$	−22.7113	−1.23717	−0.618583	+	0.785720i	$0.712293\pi$
$338$	32.7760	1.78278
$339$	−1.86481	−0.101283
$340$	−23.6930	−1.28493
$341$	18.2089	0.986065
$342$	−3.82006	−0.206565
$343$	−19.4319	−1.04923
$344$	−53.8444	−2.90310
$345$	−23.5838	−1.26971
$346$	−14.4913	−0.779059
$347$	−10.6462	−0.571518	−0.285759	−	0.958302i	$-0.592246\pi$
$347$	−10.6462	−0.571518	−0.285759	+	0.958302i	$0.592246\pi$
$348$	−82.3467	−4.41424
$349$	19.9383	1.06727	0.533636	−	0.845714i	$-0.320825\pi$
$349$	19.9383	1.06727	0.533636	+	0.845714i	$0.320825\pi$
$350$	−1.30131	−0.0695581
$351$	3.11149	0.166079
$352$	−26.5309	−1.41410
$353$	−0.638509	−0.0339844	−0.0169922	−	0.999856i	$-0.505409\pi$
$353$	−0.638509	−0.0339844	−0.0169922	+	0.999856i	$0.505409\pi$
$354$	−19.4000	−1.03110
$355$	−2.29669	−0.121895
$356$	40.2153	2.13140
$357$	7.26444	0.384475
$358$	−25.6947	−1.35801
$359$	28.7788	1.51889	0.759445	−	0.650572i	$-0.225471\pi$
$359$	28.7788	1.51889	0.759445	+	0.650572i	$0.225471\pi$
$360$	−8.03236	−0.423343
$361$	−9.59897	−0.505209
$362$	−52.2102	−2.74410
$363$	7.70309	0.404307
$364$	5.77196	0.302533
$365$	13.6346	0.713669
$366$	−17.8078	−0.930828
$367$	−15.3803	−0.802845	−0.401422	−	0.915893i	$-0.631484\pi$
$367$	−15.3803	−0.802845	−0.401422	+	0.915893i	$0.631484\pi$
$368$	52.2794	2.72525
$369$	−4.40625	−0.229380
$370$	3.98347	0.207091
$371$	21.9976	1.14206
$372$	−62.2799	−3.22906
$373$	−3.60530	−0.186675	−0.0933377	−	0.995635i	$-0.529754\pi$
$373$	−3.60530	−0.186675	−0.0933377	+	0.995635i	$0.529754\pi$
$374$	14.6747	0.758813
$375$	20.2377	1.04507
$376$	−29.6397	−1.52855
$377$	6.07623	0.312942
$378$	−22.2779	−1.14585
$379$	−25.1992	−1.29439	−0.647197	−	0.762322i	$-0.724059\pi$
$379$	−25.1992	−1.29439	−0.647197	+	0.762322i	$0.724059\pi$
$380$	33.8512	1.73653
$381$	−0.943179	−0.0483205
$382$	−7.61944	−0.389845
$383$	−16.4893	−0.842566	−0.421283	−	0.906929i	$-0.638420\pi$
$383$	−16.4893	−0.842566	−0.421283	+	0.906929i	$0.638420\pi$
$384$	−1.64074	−0.0837288
$385$	10.9267	0.556875
$386$	0.106668	0.00542926
$387$	3.51075	0.178462
$388$	−21.5130	−1.09216
$389$	3.49107	0.177004	0.0885021	−	0.996076i	$-0.471792\pi$
$389$	3.49107	0.177004	0.0885021	+	0.996076i	$0.471792\pi$
$390$	7.39139	0.374278
$391$	−11.8171	−0.597618
$392$	27.1345	1.37050
$393$	−14.9121	−0.752218
$394$	−44.2857	−2.23108
$395$	−22.1119	−1.11257
$396$	6.01643	0.302337
$397$	−1.73003	−0.0868276	−0.0434138	−	0.999057i	$-0.513823\pi$
$397$	−1.73003	−0.0868276	−0.0434138	+	0.999057i	$0.513823\pi$
$398$	24.9030	1.24827
$399$	−10.3790	−0.519600
$400$	2.60869	0.130434
$401$	−4.17793	−0.208636	−0.104318	−	0.994544i	$-0.533266\pi$
$401$	−4.17793	−0.208636	−0.104318	+	0.994544i	$0.533266\pi$
$402$	6.22152	0.310301
$403$	4.59553	0.228920
$404$	−18.2860	−0.909760
$405$	−23.4367	−1.16458
$406$	−43.5051	−2.15912
$407$	−1.74234	−0.0863645
$408$	−29.3097	−1.45104
$409$	−5.26370	−0.260273	−0.130137	−	0.991496i	$-0.541542\pi$
$409$	−5.26370	−0.260273	−0.130137	+	0.991496i	$0.541542\pi$
$410$	55.2906	2.73061
$411$	−26.5095	−1.30762
$412$	41.3597	2.03765
$413$	−7.23798	−0.356158
$414$	−6.86055	−0.337178
$415$	21.1837	1.03987
$416$	−6.69585	−0.328291
$417$	11.2839	0.552573
$418$	−20.9664	−1.02550
$419$	15.4376	0.754176	0.377088	−	0.926177i	$-0.376925\pi$
$419$	15.4376	0.754176	0.377088	+	0.926177i	$0.376925\pi$
$420$	−37.3726	−1.82360
$421$	2.98235	0.145351	0.0726755	−	0.997356i	$-0.476846\pi$
$421$	2.98235	0.145351	0.0726755	+	0.997356i	$0.476846\pi$
$422$	−66.3303	−3.22891
$423$	1.93256	0.0939644
$424$	−88.7532	−4.31024
$425$	−0.589662	−0.0286028
$426$	−4.86538	−0.235728
$427$	−6.64393	−0.321523
$428$	57.4208	2.77554
$429$	−3.23294	−0.156088
$430$	−44.0537	−2.12446
$431$	20.4696	0.985987	0.492993	−	0.870033i	$-0.335903\pi$
$431$	20.4696	0.985987	0.492993	+	0.870033i	$0.335903\pi$
$432$	44.6596	2.14869
$433$	−9.81578	−0.471716	−0.235858	−	0.971787i	$-0.575790\pi$
$433$	−9.81578	−0.471716	−0.235858	+	0.971787i	$0.575790\pi$
$434$	−32.9035	−1.57942
$435$	−39.3427	−1.88634
$436$	20.7009	0.991392
$437$	16.8836	0.807652
$438$	28.8841	1.38013
$439$	12.0404	0.574656	0.287328	−	0.957832i	$-0.407233\pi$
$439$	12.0404	0.574656	0.287328	+	0.957832i	$0.407233\pi$
$440$	−44.0856	−2.10170
$441$	−1.76922	−0.0842484
$442$	3.70359	0.176162
$443$	2.99420	0.142259	0.0711293	−	0.997467i	$-0.477340\pi$
$443$	2.99420	0.142259	0.0711293	+	0.997467i	$0.477340\pi$
$444$	5.95933	0.282817
$445$	19.2136	0.910812
$446$	52.7613	2.49832
$447$	29.6730	1.40348
$448$	13.4736	0.636566
$449$	−39.3135	−1.85532	−0.927660	−	0.373425i	$-0.878183\pi$
$449$	−39.3135	−1.85532	−0.927660	+	0.373425i	$0.878183\pi$
$450$	−0.342334	−0.0161378
$451$	−24.1837	−1.13877
$452$	4.80711	0.226107
$453$	16.8946	0.793779
$454$	−12.7400	−0.597917
$455$	2.75766	0.129281
$456$	41.8759	1.96102
$457$	−1.80768	−0.0845598	−0.0422799	−	0.999106i	$-0.513462\pi$
$457$	−1.80768	−0.0845598	−0.0422799	+	0.999106i	$0.513462\pi$
$458$	36.6343	1.71181
$459$	−10.0948	−0.471183
$460$	60.7943	2.83455
$461$	25.9692	1.20951	0.604753	−	0.796413i	$-0.293272\pi$
$461$	25.9692	1.20951	0.604753	+	0.796413i	$0.293272\pi$
$462$	23.1475	1.07692
$463$	−6.29842	−0.292712	−0.146356	−	0.989232i	$-0.546755\pi$
$463$	−6.29842	−0.292712	−0.146356	+	0.989232i	$0.546755\pi$
$464$	87.2127	4.04875
$465$	−29.7554	−1.37987
$466$	−9.40332	−0.435600
$467$	10.4019	0.481343	0.240672	−	0.970607i	$-0.422632\pi$
$467$	10.4019	0.481343	0.240672	+	0.970607i	$0.422632\pi$
$468$	1.51842	0.0701890
$469$	2.32119	0.107183
$470$	−24.2502	−1.11858
$471$	−12.6667	−0.583649
$472$	29.2029	1.34417
$473$	19.2688	0.885980
$474$	−46.8426	−2.15155
$475$	0.842473	0.0386553
$476$	−18.7262	−0.858316
$477$	5.78687	0.264963
$478$	47.6629	2.18005
$479$	−7.21890	−0.329840	−0.164920	−	0.986307i	$-0.552737\pi$
$479$	−7.21890	−0.329840	−0.164920	+	0.986307i	$0.552737\pi$
$480$	43.3546	1.97886
$481$	−0.439730	−0.0200499
$482$	−52.9550	−2.41203
$483$	−18.6399	−0.848147
$484$	−19.8570	−0.902590
$485$	−10.2782	−0.466711
$486$	−12.8307	−0.582013
$487$	−25.9965	−1.17801	−0.589007	−	0.808128i	$-0.700481\pi$
$487$	−25.9965	−1.17801	−0.589007	+	0.808128i	$0.700481\pi$
$488$	26.8061	1.21346
$489$	0.690019	0.0312037
$490$	22.2005	1.00292
$491$	30.7327	1.38695	0.693473	−	0.720482i	$-0.256079\pi$
$491$	30.7327	1.38695	0.693473	+	0.720482i	$0.256079\pi$
$492$	82.7156	3.72911
$493$	−19.7134	−0.887846
$494$	−5.29147	−0.238075
$495$	2.87446	0.129198
$496$	65.9601	2.96170
$497$	−1.81523	−0.0814243
$498$	44.8763	2.01096
$499$	−10.0580	−0.450260	−0.225130	−	0.974329i	$-0.572281\pi$
$499$	−10.0580	−0.450260	−0.225130	+	0.974329i	$0.572281\pi$
$500$	−52.1686	−2.33305
$501$	4.40670	0.196877
$502$	58.4038	2.60669
$503$	−19.4811	−0.868617	−0.434309	−	0.900764i	$-0.643007\pi$
$503$	−19.4811	−0.868617	−0.434309	+	0.900764i	$0.643007\pi$
$504$	−6.34853	−0.282786
$505$	−8.73646	−0.388767
$506$	−37.6542	−1.67393
$507$	23.4267	1.04041
$508$	2.43132	0.107873
$509$	5.92088	0.262438	0.131219	−	0.991353i	$-0.458111\pi$
$509$	5.92088	0.262438	0.131219	+	0.991353i	$0.458111\pi$
$510$	−23.9802	−1.06186
$511$	10.7764	0.476720
$512$	42.9608	1.89862
$513$	14.4228	0.636782
$514$	13.5532	0.597808
$515$	19.7604	0.870747
$516$	−65.9051	−2.90131
$517$	10.6069	0.466490
$518$	3.14841	0.138333
$519$	−10.3577	−0.454651
$520$	−11.1263	−0.487920
$521$	−34.7154	−1.52091	−0.760454	−	0.649392i	$-0.775024\pi$
$521$	−34.7154	−1.52091	−0.760454	+	0.649392i	$0.775024\pi$
$522$	−11.4448	−0.500926
$523$	5.60248	0.244979	0.122490	−	0.992470i	$-0.460912\pi$
$523$	5.60248	0.244979	0.122490	+	0.992470i	$0.460912\pi$
$524$	38.4405	1.67928
$525$	−0.930114	−0.0405935
$526$	65.4992	2.85590
$527$	−14.9095	−0.649468
$528$	−46.4027	−2.01942
$529$	7.32176	0.318338
$530$	−72.6150	−3.15420
$531$	−1.90408	−0.0826301
$532$	26.7549	1.15997
$533$	−6.10345	−0.264370
$534$	40.7027	1.76138
$535$	27.4338	1.18607
$536$	−9.36527	−0.404518
$537$	−18.3653	−0.792522
$538$	5.40586	0.233063
$539$	−9.71035	−0.418255
$540$	51.9335	2.23486
$541$	9.92615	0.426759	0.213379	−	0.976969i	$-0.431553\pi$
$541$	9.92615	0.426759	0.213379	+	0.976969i	$0.431553\pi$
$542$	−16.5460	−0.710713
$543$	−37.3172	−1.60143
$544$	21.7236	0.931393
$545$	9.89023	0.423651
$546$	5.84193	0.250012
$547$	−32.4485	−1.38740	−0.693700	−	0.720264i	$-0.744021\pi$
$547$	−32.4485	−1.38740	−0.693700	+	0.720264i	$0.744021\pi$
$548$	68.3360	2.91917
$549$	−1.74781	−0.0745947
$550$	−1.87890	−0.0801167
$551$	28.1653	1.19988
$552$	75.2062	3.20099
$553$	−17.4766	−0.743180
$554$	65.5553	2.78518
$555$	2.84718	0.120856
$556$	−29.0875	−1.23358
$557$	9.90917	0.419865	0.209933	−	0.977716i	$-0.432676\pi$
$557$	9.90917	0.419865	0.209933	+	0.977716i	$0.432676\pi$
$558$	−8.65586	−0.366432
$559$	4.86303	0.205684
$560$	39.5810	1.67260
$561$	10.4888	0.442836
$562$	−46.9083	−1.97871
$563$	−21.7348	−0.916013	−0.458007	−	0.888949i	$-0.651436\pi$
$563$	−21.7348	−0.916013	−0.458007	+	0.888949i	$0.651436\pi$
$564$	−36.2788	−1.52761
$565$	2.29669	0.0966223
$566$	10.8403	0.455651
$567$	−18.5236	−0.777919
$568$	7.32387	0.307303
$569$	33.7478	1.41478	0.707391	−	0.706823i	$-0.249872\pi$
$569$	33.7478	1.41478	0.707391	+	0.706823i	$0.249872\pi$
$570$	34.2615	1.43506
$571$	−19.5677	−0.818882	−0.409441	−	0.912337i	$-0.634276\pi$
$571$	−19.5677	−0.818882	−0.409441	+	0.912337i	$0.634276\pi$
$572$	8.33386	0.348456
$573$	−5.44600	−0.227510
$574$	43.7000	1.82400
$575$	1.51302	0.0630975
$576$	3.54447	0.147686
$577$	−13.9097	−0.579067	−0.289534	−	0.957168i	$-0.593500\pi$
$577$	−13.9097	−0.579067	−0.289534	+	0.957168i	$0.593500\pi$
$578$	32.3380	1.34508
$579$	0.0762409	0.00316846
$580$	101.417	4.21113
$581$	16.7430	0.694615
$582$	−21.7738	−0.902552
$583$	31.7613	1.31542
$584$	−43.4793	−1.79919
$585$	0.725454	0.0299938
$586$	−47.9803	−1.98205
$587$	4.41542	0.182244	0.0911219	−	0.995840i	$-0.470955\pi$
$587$	4.41542	0.182244	0.0911219	+	0.995840i	$0.470955\pi$
$588$	33.2124	1.36966
$589$	21.3018	0.877725
$590$	23.8929	0.983654
$591$	−31.6532	−1.30204
$592$	−6.31148	−0.259400
$593$	−33.6749	−1.38286	−0.691432	−	0.722441i	$-0.743020\pi$
$593$	−33.6749	−1.38286	−0.691432	+	0.722441i	$0.743020\pi$
$594$	−32.1660	−1.31979
$595$	−8.94681	−0.366783
$596$	−76.4909	−3.13319
$597$	17.7994	0.728482
$598$	−9.50312	−0.388611
$599$	12.6127	0.515342	0.257671	−	0.966233i	$-0.417045\pi$
$599$	12.6127	0.515342	0.257671	+	0.966233i	$0.417045\pi$
$600$	3.75271	0.153204
$601$	18.3835	0.749877	0.374938	−	0.927050i	$-0.377664\pi$
$601$	18.3835	0.749877	0.374938	+	0.927050i	$0.377664\pi$
$602$	−34.8187	−1.41911
$603$	0.610633	0.0248669
$604$	−43.5509	−1.77206
$605$	−9.48705	−0.385703
$606$	−18.5076	−0.751820
$607$	−23.8358	−0.967464	−0.483732	−	0.875216i	$-0.660719\pi$
$607$	−23.8358	−0.967464	−0.483732	+	0.875216i	$0.660719\pi$
$608$	−31.0374	−1.25873
$609$	−31.0952	−1.26004
$610$	21.9319	0.887997
$611$	2.67695	0.108298
$612$	−4.92628	−0.199133
$613$	−2.21157	−0.0893247	−0.0446623	−	0.999002i	$-0.514221\pi$
$613$	−2.21157	−0.0893247	−0.0446623	+	0.999002i	$0.514221\pi$
$614$	−34.6844	−1.39975
$615$	39.5189	1.59356
$616$	−34.8439	−1.40390
$617$	−40.9489	−1.64854	−0.824270	−	0.566196i	$-0.808414\pi$
$617$	−40.9489	−1.64854	−0.824270	+	0.566196i	$0.808414\pi$
$618$	41.8611	1.68390
$619$	−0.935412	−0.0375974	−0.0187987	−	0.999823i	$-0.505984\pi$
$619$	−0.935412	−0.0375974	−0.0187987	+	0.999823i	$0.505984\pi$
$620$	76.7033	3.08048
$621$	25.9023	1.03942
$622$	62.9539	2.52422
$623$	15.1858	0.608408
$624$	−11.7111	−0.468817
$625$	−26.2983	−1.05193
$626$	−6.35399	−0.253956
$627$	−14.9857	−0.598472
$628$	32.6521	1.30296
$629$	1.42663	0.0568836
$630$	−5.19416	−0.206940
$631$	−38.0509	−1.51478	−0.757390	−	0.652962i	$-0.773526\pi$
$631$	−38.0509	−1.51478	−0.757390	+	0.652962i	$0.773526\pi$
$632$	70.5124	2.80483
$633$	−47.4096	−1.88436
$634$	−3.30772	−0.131366
$635$	1.16161	0.0460971
$636$	−108.633	−4.30759
$637$	−2.45069	−0.0970998
$638$	−62.8149	−2.48686
$639$	−0.477530	−0.0188908
$640$	2.02072	0.0798761
$641$	20.1030	0.794019	0.397009	−	0.917815i	$-0.370048\pi$
$641$	20.1030	0.794019	0.397009	+	0.917815i	$0.370048\pi$
$642$	58.1168	2.29369
$643$	35.2976	1.39200	0.696000	−	0.718042i	$-0.254961\pi$
$643$	35.2976	1.39200	0.696000	+	0.718042i	$0.254961\pi$
$644$	48.0500	1.89343
$645$	−31.4874	−1.23982
$646$	17.1674	0.675441
$647$	26.1983	1.02996	0.514980	−	0.857202i	$-0.327799\pi$
$647$	26.1983	1.02996	0.514980	+	0.857202i	$0.327799\pi$
$648$	74.7369	2.93594
$649$	−10.4506	−0.410221
$650$	−0.474195	−0.0185995
$651$	−23.5178	−0.921733
$652$	−1.77873	−0.0696603
$653$	27.3981	1.07217	0.536086	−	0.844164i	$-0.319902\pi$
$653$	27.3981	1.07217	0.536086	+	0.844164i	$0.319902\pi$
$654$	20.9518	0.819281
$655$	18.3657	0.717605
$656$	−87.6035	−3.42034
$657$	2.83493	0.110601
$658$	−19.1667	−0.747194
$659$	−2.31264	−0.0900877	−0.0450438	−	0.998985i	$-0.514343\pi$
$659$	−2.31264	−0.0900877	−0.0450438	+	0.998985i	$0.514343\pi$
$660$	−53.9605	−2.10041
$661$	23.2809	0.905523	0.452762	−	0.891632i	$-0.350439\pi$
$661$	23.2809	0.905523	0.452762	+	0.891632i	$0.350439\pi$
$662$	10.1074	0.392834
$663$	2.64714	0.102807
$664$	−67.5525	−2.62154
$665$	12.7827	0.495691
$666$	0.828247	0.0320939
$667$	50.5829	1.95858
$668$	−11.3596	−0.439515
$669$	37.7111	1.45800
$670$	−7.66236	−0.296023
$671$	−9.59285	−0.370328
$672$	34.2662	1.32185
$673$	−11.1989	−0.431686	−0.215843	−	0.976428i	$-0.569250\pi$
$673$	−11.1989	−0.431686	−0.215843	+	0.976428i	$0.569250\pi$
$674$	59.2549	2.28241
$675$	1.29250	0.0497483
$676$	−60.3891	−2.32266
$677$	−13.3487	−0.513033	−0.256517	−	0.966540i	$-0.582575\pi$
$677$	−13.3487	−0.513033	−0.256517	+	0.966540i	$0.582575\pi$
$678$	4.86538	0.186854
$679$	−8.12360	−0.311755
$680$	36.0975	1.38428
$681$	−9.10590	−0.348939
$682$	−47.5077	−1.81917
$683$	47.9799	1.83590	0.917951	−	0.396694i	$-0.129843\pi$
$683$	47.9799	1.83590	0.917951	+	0.396694i	$0.129843\pi$
$684$	7.03837	0.269119
$685$	32.6488	1.24745
$686$	50.6988	1.93569
$687$	26.1843	0.998995
$688$	69.7996	2.66108
$689$	8.01587	0.305380
$690$	61.5313	2.34245
$691$	−50.3680	−1.91609	−0.958044	−	0.286622i	$-0.907468\pi$
$691$	−50.3680	−1.91609	−0.958044	+	0.286622i	$0.907468\pi$
$692$	26.7000	1.01498
$693$	2.27189	0.0863019
$694$	27.7764	1.05438
$695$	−13.8971	−0.527147
$696$	125.459	4.75552
$697$	19.8017	0.750043
$698$	−52.0199	−1.96898
$699$	−6.72102	−0.254212
$700$	2.39764	0.0906224
$701$	−33.0676	−1.24894	−0.624472	−	0.781047i	$-0.714686\pi$
$701$	−33.0676	−1.24894	−0.624472	+	0.781047i	$0.714686\pi$
$702$	−8.11802	−0.306395
$703$	−2.03829	−0.0768755
$704$	19.4538	0.733194
$705$	−17.3329	−0.652793
$706$	1.66590	0.0626969
$707$	−6.90503	−0.259690
$708$	35.7441	1.34335
$709$	35.6343	1.33828	0.669138	−	0.743138i	$-0.266663\pi$
$709$	35.6343	1.33828	0.669138	+	0.743138i	$0.266663\pi$
$710$	5.99216	0.224882
$711$	−4.59753	−0.172421
$712$	−61.2700	−2.29619
$713$	38.2565	1.43272
$714$	−18.9532	−0.709307
$715$	3.98166	0.148906
$716$	47.3420	1.76926
$717$	34.0670	1.27226
$718$	−75.0853	−2.80216
$719$	23.2858	0.868416	0.434208	−	0.900813i	$-0.357028\pi$
$719$	23.2858	0.868416	0.434208	+	0.900813i	$0.357028\pi$
$720$	10.4125	0.388051
$721$	15.6180	0.581645
$722$	25.0441	0.932046
$723$	−37.8496	−1.40764
$724$	96.1961	3.57510
$725$	2.52403	0.0937402
$726$	−20.0977	−0.745895
$727$	4.60173	0.170669	0.0853344	−	0.996352i	$-0.472804\pi$
$727$	4.60173	0.170669	0.0853344	+	0.996352i	$0.472804\pi$
$728$	−8.79388	−0.325923
$729$	21.4429	0.794182
$730$	−35.5733	−1.31663
$731$	−15.7774	−0.583547
$732$	32.8105	1.21271
$733$	−49.0530	−1.81181	−0.905906	−	0.423479i	$-0.860809\pi$
$733$	−49.0530	−1.81181	−0.905906	+	0.423479i	$0.860809\pi$
$734$	40.1279	1.48115
$735$	15.8678	0.585294
$736$	−55.7411	−2.05464
$737$	3.35146	0.123453
$738$	11.4961	0.423177
$739$	2.80882	0.103324	0.0516620	−	0.998665i	$-0.483548\pi$
$739$	2.80882	0.103324	0.0516620	+	0.998665i	$0.483548\pi$
$740$	−7.33946	−0.269804
$741$	−3.78208	−0.138938
$742$	−57.3927	−2.10695
$743$	2.93916	0.107827	0.0539137	−	0.998546i	$-0.482830\pi$
$743$	2.93916	0.107827	0.0539137	+	0.998546i	$0.482830\pi$
$744$	94.8865	3.47871
$745$	−36.5449	−1.33890
$746$	9.40639	0.344392
$747$	4.40454	0.161154
$748$	−27.0379	−0.988604
$749$	21.6829	0.792275
$750$	−52.8009	−1.92802
$751$	−28.3764	−1.03547	−0.517734	−	0.855542i	$-0.673224\pi$
$751$	−28.3764	−1.03547	−0.517734	+	0.855542i	$0.673224\pi$
$752$	38.4225	1.40113
$753$	41.7441	1.52124
$754$	−15.8531	−0.577337
$755$	−20.8073	−0.757254
$756$	41.0466	1.49285
$757$	24.2559	0.881595	0.440798	−	0.897607i	$-0.354696\pi$
$757$	24.2559	0.881595	0.440798	+	0.897607i	$0.354696\pi$
$758$	65.7458	2.38799
$759$	−26.9133	−0.976892
$760$	−51.5739	−1.87078
$761$	9.44116	0.342242	0.171121	−	0.985250i	$-0.445261\pi$
$761$	9.44116	0.342242	0.171121	+	0.985250i	$0.445261\pi$
$762$	2.46080	0.0891453
$763$	7.81694	0.282992
$764$	14.0387	0.507901
$765$	−2.35362	−0.0850954
$766$	43.0214	1.55443
$767$	−2.63750	−0.0952347
$768$	31.9639	1.15340
$769$	9.54126	0.344067	0.172033	−	0.985091i	$-0.444966\pi$
$769$	9.54126	0.344067	0.172033	+	0.985091i	$0.444966\pi$
$770$	−28.5082	−1.02736
$771$	9.68718	0.348875
$772$	−0.196534	−0.00707340
$773$	38.1403	1.37181	0.685905	−	0.727691i	$-0.259407\pi$
$773$	38.1403	1.37181	0.685905	+	0.727691i	$0.259407\pi$
$774$	−9.15971	−0.329239
$775$	1.90896	0.0685719
$776$	32.7761	1.17659
$777$	2.25033	0.0807300
$778$	−9.10835	−0.326550
$779$	−28.2915	−1.01365
$780$	−13.6185	−0.487620
$781$	−2.62092	−0.0937841
$782$	30.8314	1.10253
$783$	43.2104	1.54421
$784$	−35.1750	−1.25625
$785$	15.6001	0.556793
$786$	38.9064	1.38775
$787$	−9.28863	−0.331104	−0.165552	−	0.986201i	$-0.552941\pi$
$787$	−9.28863	−0.331104	−0.165552	+	0.986201i	$0.552941\pi$
$788$	81.5954	2.90672
$789$	46.8155	1.66668
$790$	57.6909	2.05255
$791$	1.81523	0.0645422
$792$	−9.16634	−0.325712
$793$	−2.42103	−0.0859734
$794$	4.51372	0.160186
$795$	−51.9016	−1.84076
$796$	−45.8833	−1.62629
$797$	43.0406	1.52458	0.762289	−	0.647237i	$-0.224076\pi$
$797$	43.0406	1.52458	0.762289	+	0.647237i	$0.224076\pi$
$798$	27.0792	0.958595
$799$	−8.68495	−0.307251
$800$	−2.78142	−0.0983381
$801$	3.99491	0.141153
$802$	10.9004	0.384907
$803$	15.5595	0.549083
$804$	−11.4630	−0.404270
$805$	22.9568	0.809120
$806$	−11.9899	−0.422328
$807$	3.86384	0.136014
$808$	27.8596	0.980096
$809$	48.3817	1.70101	0.850506	−	0.525966i	$-0.176296\pi$
$809$	48.3817	1.70101	0.850506	+	0.525966i	$0.176296\pi$
$810$	61.1473	2.14850
$811$	36.7564	1.29069	0.645346	−	0.763891i	$-0.276713\pi$
$811$	36.7564	1.29069	0.645346	+	0.763891i	$0.276713\pi$
$812$	80.1572	2.81297
$813$	−11.8263	−0.414766
$814$	4.54584	0.159332
$815$	−0.849820	−0.0297679
$816$	37.9947	1.33008
$817$	22.5417	0.788636
$818$	13.7332	0.480171
$819$	0.573377	0.0200354
$820$	−101.872	−3.55752
$821$	−33.9972	−1.18651	−0.593255	−	0.805015i	$-0.702157\pi$
$821$	−33.9972	−1.18651	−0.593255	+	0.805015i	$0.702157\pi$
$822$	69.1644	2.41238
$823$	2.74218	0.0955863	0.0477931	−	0.998857i	$-0.484781\pi$
$823$	2.74218	0.0955863	0.0477931	+	0.998857i	$0.484781\pi$
$824$	−63.0136	−2.19518
$825$	−1.34295	−0.0467554
$826$	18.8842	0.657065
$827$	−43.9653	−1.52882	−0.764411	−	0.644729i	$-0.776970\pi$
$827$	−43.9653	−1.52882	−0.764411	+	0.644729i	$0.776970\pi$
$828$	12.6404	0.439285
$829$	36.0738	1.25290	0.626448	−	0.779463i	$-0.284508\pi$
$829$	36.0738	1.25290	0.626448	+	0.779463i	$0.284508\pi$
$830$	−55.2692	−1.91842
$831$	46.8557	1.62541
$832$	4.90973	0.170214
$833$	7.95088	0.275482
$834$	−29.4401	−1.01943
$835$	−5.42724	−0.187818
$836$	38.6301	1.33605
$837$	32.6806	1.12961
$838$	−40.2774	−1.39136
$839$	53.5821	1.84986	0.924930	−	0.380137i	$-0.124123\pi$
$839$	53.5821	1.84986	0.924930	+	0.380137i	$0.124123\pi$
$840$	56.9390	1.96458
$841$	55.3826	1.90974
$842$	−7.78109	−0.268154
$843$	−33.5277	−1.15476
$844$	122.212	4.20672
$845$	−28.8520	−0.992540
$846$	−5.04214	−0.173352
$847$	−7.49827	−0.257644
$848$	115.053	3.95092
$849$	7.74809	0.265914
$850$	1.53845	0.0527685
$851$	−3.66063	−0.125485
$852$	8.96436	0.307114
$853$	13.5315	0.463311	0.231655	−	0.972798i	$-0.425586\pi$
$853$	13.5315	0.463311	0.231655	+	0.972798i	$0.425586\pi$
$854$	17.3343	0.593168
$855$	3.36271	0.115002
$856$	−87.4834	−2.99012
$857$	24.7302	0.844766	0.422383	−	0.906417i	$-0.361194\pi$
$857$	24.7302	0.844766	0.422383	+	0.906417i	$0.361194\pi$
$858$	8.43488	0.287962
$859$	44.0205	1.50196	0.750980	−	0.660325i	$-0.229581\pi$
$859$	44.0205	1.50196	0.750980	+	0.660325i	$0.229581\pi$
$860$	81.1681	2.76781
$861$	31.2346	1.06447
$862$	−53.4061	−1.81902
$863$	−4.92804	−0.167753	−0.0838763	−	0.996476i	$-0.526730\pi$
$863$	−4.92804	−0.167753	−0.0838763	+	0.996476i	$0.526730\pi$
$864$	−47.6167	−1.61995
$865$	12.7564	0.433731
$866$	25.6098	0.870257
$867$	23.1136	0.784979
$868$	60.6240	2.05771
$869$	−25.2336	−0.855991
$870$	102.647	3.48005
$871$	0.845838	0.0286601
$872$	−31.5388	−1.06804
$873$	−2.13706	−0.0723286
$874$	−44.0500	−1.49001
$875$	−19.6996	−0.665967
$876$	−53.2183	−1.79808
$877$	49.5758	1.67406	0.837028	−	0.547160i	$-0.184291\pi$
$877$	49.5758	1.67406	0.837028	+	0.547160i	$0.184291\pi$
$878$	−31.4139	−1.06017
$879$	−34.2939	−1.15670
$880$	57.1491	1.92650
$881$	−0.792035	−0.0266843	−0.0133422	−	0.999911i	$-0.504247\pi$
$881$	−0.792035	−0.0266843	−0.0133422	+	0.999911i	$0.504247\pi$
$882$	4.61596	0.155428
$883$	−2.81236	−0.0946434	−0.0473217	−	0.998880i	$-0.515069\pi$
$883$	−2.81236	−0.0946434	−0.0473217	+	0.998880i	$0.515069\pi$
$884$	−6.82380	−0.229509
$885$	17.0774	0.574051
$886$	−7.81199	−0.262449
$887$	17.5174	0.588178	0.294089	−	0.955778i	$-0.404984\pi$
$887$	17.5174	0.588178	0.294089	+	0.955778i	$0.404984\pi$
$888$	−9.07934	−0.304683
$889$	0.918102	0.0307922
$890$	−50.1291	−1.68033
$891$	−26.7454	−0.896004
$892$	−97.2116	−3.25489
$893$	12.4085	0.415236
$894$	−77.4181	−2.58925
$895$	22.6185	0.756055
$896$	1.59712	0.0533560
$897$	−6.79235	−0.226790
$898$	102.571	3.42283
$899$	63.8197	2.12851
$900$	0.630744	0.0210248
$901$	−26.0063	−0.866394
$902$	63.0963	2.10088
$903$	−24.8867	−0.828177
$904$	−7.32387	−0.243588
$905$	45.9595	1.52775
$906$	−44.0788	−1.46442
$907$	31.6662	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$907$	31.6662	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$908$	23.4732	0.778984
$909$	−1.81649	−0.0602493
$910$	−7.19486	−0.238507
$911$	−28.9997	−0.960801	−0.480401	−	0.877049i	$-0.659509\pi$
$911$	−28.9997	−0.960801	−0.480401	+	0.877049i	$0.659509\pi$
$912$	−54.2846	−1.79754
$913$	24.1744	0.800054
$914$	4.71632	0.156002
$915$	15.6758	0.518227
$916$	−67.4979	−2.23019
$917$	14.5157	0.479349
$918$	26.3377	0.869273
$919$	−36.0825	−1.19025	−0.595126	−	0.803633i	$-0.702898\pi$
$919$	−36.0825	−1.19025	−0.595126	+	0.803633i	$0.702898\pi$
$920$	−92.6232	−3.05370
$921$	−24.7906	−0.816879
$922$	−67.7548	−2.23138
$923$	−0.661466	−0.0217724
$924$	−42.6487	−1.40304
$925$	−0.182661	−0.00600587
$926$	16.4328	0.540017
$927$	4.10860	0.134944
$928$	−92.9875	−3.05246
$929$	−46.7573	−1.53406	−0.767029	−	0.641612i	$-0.778266\pi$
$929$	−46.7573	−1.53406	−0.767029	+	0.641612i	$0.778266\pi$
$930$	77.6331	2.54569
$931$	−11.3597	−0.372300
$932$	17.3254	0.567513
$933$	44.9963	1.47311
$934$	−27.1390	−0.888017
$935$	−12.9179	−0.422459
$936$	−2.31339	−0.0756155
$937$	−24.3634	−0.795918	−0.397959	−	0.917403i	$-0.630281\pi$
$937$	−24.3634	−0.795918	−0.397959	+	0.917403i	$0.630281\pi$
$938$	−6.05610	−0.197739
$939$	−4.54151	−0.148207
$940$	44.6806	1.45732
$941$	−24.0766	−0.784876	−0.392438	−	0.919778i	$-0.628368\pi$
$941$	−24.0766	−0.784876	−0.392438	+	0.919778i	$0.628368\pi$
$942$	33.0479	1.07676
$943$	−50.8096	−1.65459
$944$	−37.8563	−1.23212
$945$	19.6108	0.637939
$946$	−50.2731	−1.63452
$947$	10.2589	0.333370	0.166685	−	0.986010i	$-0.446694\pi$
$947$	10.2589	0.333370	0.166685	+	0.986010i	$0.446694\pi$
$948$	86.3066	2.80311
$949$	3.92689	0.127472
$950$	−2.19805	−0.0713142
$951$	−2.36419	−0.0766641
$952$	28.5304	0.924674
$953$	8.29723	0.268774	0.134387	−	0.990929i	$-0.457094\pi$
$953$	8.29723	0.268774	0.134387	+	0.990929i	$0.457094\pi$
$954$	−15.0982	−0.488822
$955$	6.70724	0.217041
$956$	−87.8178	−2.84023
$957$	−44.8969	−1.45131
$958$	18.8344	0.608513
$959$	25.8046	0.833275
$960$	−31.7898	−1.02601
$961$	17.2677	0.557023
$962$	1.14727	0.0369896
$963$	5.70408	0.183811
$964$	97.5685	3.14247
$965$	−0.0938976	−0.00302267
$966$	48.6324	1.56472
$967$	30.3780	0.976891	0.488446	−	0.872594i	$-0.337564\pi$
$967$	30.3780	0.976891	0.488446	+	0.872594i	$0.337564\pi$
$968$	30.2531	0.972372
$969$	12.2704	0.394181
$970$	26.8164	0.861021
$971$	−5.84645	−0.187622	−0.0938108	−	0.995590i	$-0.529905\pi$
$971$	−5.84645	−0.187622	−0.0938108	+	0.995590i	$0.529905\pi$
$972$	23.6403	0.758264
$973$	−10.9838	−0.352126
$974$	67.8260	2.17328
$975$	−0.338931	−0.0108545
$976$	−34.7493	−1.11230
$977$	9.55694	0.305754	0.152877	−	0.988245i	$-0.451146\pi$
$977$	9.55694	0.305754	0.152877	+	0.988245i	$0.451146\pi$
$978$	−1.80029	−0.0575669
$979$	21.9261	0.700761
$980$	−40.9041	−1.30663
$981$	2.05639	0.0656555
$982$	−80.1829	−2.55874
$983$	57.3568	1.82940	0.914700	−	0.404134i	$-0.132427\pi$
$983$	57.3568	1.82940	0.914700	+	0.404134i	$0.132427\pi$
$984$	−126.021	−4.01742
$985$	38.9838	1.24213
$986$	51.4331	1.63796
$987$	−13.6994	−0.436056
$988$	9.74943	0.310171
$989$	40.4834	1.28730
$990$	−7.49960	−0.238353
$991$	−56.3895	−1.79127	−0.895636	−	0.444788i	$-0.853279\pi$
$991$	−56.3895	−1.79127	−0.895636	+	0.444788i	$0.853279\pi$
$992$	−70.3277	−2.23291
$993$	7.22423	0.229254
$994$	4.73602	0.150217
$995$	−21.9216	−0.694961
$996$	−82.6837	−2.61993
$997$	−7.11066	−0.225197	−0.112598	−	0.993641i	$-0.535917\pi$
$997$	−7.11066	−0.225197	−0.112598	+	0.993641i	$0.535917\pi$
$998$	26.2419	0.830672
$999$	−3.12708	−0.0989366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.6	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.60904 q^{2} -1.86481 q^{3} +4.80711 q^{4} +2.29669 q^{5} +4.86538 q^{6} +1.81523 q^{7} -7.32387 q^{8} +0.477530 q^{9} +O(q^{10})\)	\(q-2.60904 q^{2} -1.86481 q^{3} +4.80711 q^{4} +2.29669 q^{5} +4.86538 q^{6} +1.81523 q^{7} -7.32387 q^{8} +0.477530 q^{9} -5.99216 q^{10} +2.62092 q^{11} -8.96436 q^{12} +0.661466 q^{13} -4.73602 q^{14} -4.28289 q^{15} +9.49409 q^{16} -2.14602 q^{17} -1.24590 q^{18} +3.06611 q^{19} +11.0404 q^{20} -3.38507 q^{21} -6.83811 q^{22} +5.50652 q^{23} +13.6577 q^{24} +0.274770 q^{25} -1.72579 q^{26} +4.70394 q^{27} +8.72602 q^{28} +9.18600 q^{29} +11.1743 q^{30} +6.94750 q^{31} -10.1227 q^{32} -4.88754 q^{33} +5.59907 q^{34} +4.16902 q^{35} +2.29554 q^{36} -0.664780 q^{37} -7.99962 q^{38} -1.23351 q^{39} -16.8206 q^{40} -9.22716 q^{41} +8.83179 q^{42} +7.35190 q^{43} +12.5991 q^{44} +1.09674 q^{45} -14.3668 q^{46} +4.04700 q^{47} -17.7047 q^{48} -3.70493 q^{49} -0.716886 q^{50} +4.00193 q^{51} +3.17974 q^{52} +12.1183 q^{53} -12.2728 q^{54} +6.01944 q^{55} -13.2945 q^{56} -5.71772 q^{57} -23.9667 q^{58} -3.98736 q^{59} -20.5883 q^{60} -3.66010 q^{61} -18.1263 q^{62} +0.866827 q^{63} +7.42250 q^{64} +1.51918 q^{65} +12.7518 q^{66} +1.27873 q^{67} -10.3162 q^{68} -10.2686 q^{69} -10.8772 q^{70} -1.00000 q^{71} -3.49737 q^{72} +5.93665 q^{73} +1.73444 q^{74} -0.512394 q^{75} +14.7391 q^{76} +4.75759 q^{77} +3.21828 q^{78} -9.62774 q^{79} +21.8049 q^{80} -10.2046 q^{81} +24.0741 q^{82} +9.22360 q^{83} -16.2724 q^{84} -4.92874 q^{85} -19.1814 q^{86} -17.1302 q^{87} -19.1953 q^{88} +8.36579 q^{89} -2.86143 q^{90} +1.20071 q^{91} +26.4704 q^{92} -12.9558 q^{93} -10.5588 q^{94} +7.04189 q^{95} +18.8770 q^{96} -4.47524 q^{97} +9.66634 q^{98} +1.25157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 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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