LMFDB - Embedded newform 8029.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19859 q^{2} +1.85317 q^{3} +2.83381 q^{4} -0.955285 q^{5} -4.07436 q^{6} +1.00000 q^{7} -1.83320 q^{8} +0.434225 q^{9} +O(q^{10})$	\(q-2.19859 q^{2} +1.85317 q^{3} +2.83381 q^{4} -0.955285 q^{5} -4.07436 q^{6} +1.00000 q^{7} -1.83320 q^{8} +0.434225 q^{9} +2.10028 q^{10} -2.49420 q^{11} +5.25152 q^{12} +2.80187 q^{13} -2.19859 q^{14} -1.77030 q^{15} -1.63715 q^{16} -1.96972 q^{17} -0.954684 q^{18} +4.59598 q^{19} -2.70709 q^{20} +1.85317 q^{21} +5.48373 q^{22} +2.07051 q^{23} -3.39723 q^{24} -4.08743 q^{25} -6.16017 q^{26} -4.75481 q^{27} +2.83381 q^{28} +6.01329 q^{29} +3.89217 q^{30} +1.00000 q^{31} +7.26583 q^{32} -4.62217 q^{33} +4.33061 q^{34} -0.955285 q^{35} +1.23051 q^{36} +1.00000 q^{37} -10.1047 q^{38} +5.19233 q^{39} +1.75123 q^{40} +11.5944 q^{41} -4.07436 q^{42} -12.9703 q^{43} -7.06809 q^{44} -0.414809 q^{45} -4.55221 q^{46} -7.24856 q^{47} -3.03392 q^{48} +1.00000 q^{49} +8.98659 q^{50} -3.65021 q^{51} +7.93996 q^{52} +7.71285 q^{53} +10.4539 q^{54} +2.38267 q^{55} -1.83320 q^{56} +8.51712 q^{57} -13.2208 q^{58} +4.95210 q^{59} -5.01669 q^{60} +5.30201 q^{61} -2.19859 q^{62} +0.434225 q^{63} -12.7003 q^{64} -2.67658 q^{65} +10.1623 q^{66} -2.90641 q^{67} -5.58180 q^{68} +3.83701 q^{69} +2.10028 q^{70} +9.73376 q^{71} -0.796022 q^{72} -7.47694 q^{73} -2.19859 q^{74} -7.57469 q^{75} +13.0241 q^{76} -2.49420 q^{77} -11.4158 q^{78} +1.83243 q^{79} +1.56395 q^{80} -10.1141 q^{81} -25.4915 q^{82} -9.79963 q^{83} +5.25152 q^{84} +1.88164 q^{85} +28.5165 q^{86} +11.1436 q^{87} +4.57237 q^{88} +1.93059 q^{89} +0.911995 q^{90} +2.80187 q^{91} +5.86743 q^{92} +1.85317 q^{93} +15.9366 q^{94} -4.39047 q^{95} +13.4648 q^{96} -15.1426 q^{97} -2.19859 q^{98} -1.08304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) $ 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * 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 $

$2$	−2.19859	−1.55464	−0.777320	−	0.629106i	$-0.783421\pi$
$2$	−2.19859	−1.55464	−0.777320	+	0.629106i	$0.783421\pi$
$3$	1.85317	1.06993	0.534963	−	0.844875i	$-0.320326\pi$
$3$	1.85317	1.06993	0.534963	+	0.844875i	$0.320326\pi$
$4$	2.83381	1.41690
$5$	−0.955285	−0.427216	−0.213608	−	0.976919i	$-0.568522\pi$
$5$	−0.955285	−0.427216	−0.213608	+	0.976919i	$0.568522\pi$
$6$	−4.07436	−1.66335
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.83320	−0.648134
$9$	0.434225	0.144742
$10$	2.10028	0.664167
$11$	−2.49420	−0.752030	−0.376015	−	0.926614i	$-0.622706\pi$
$11$	−2.49420	−0.752030	−0.376015	+	0.926614i	$0.622706\pi$
$12$	5.25152	1.51598
$13$	2.80187	0.777099	0.388549	−	0.921428i	$-0.372976\pi$
$13$	2.80187	0.777099	0.388549	+	0.921428i	$0.372976\pi$
$14$	−2.19859	−0.587598
$15$	−1.77030	−0.457090
$16$	−1.63715	−0.409288
$17$	−1.96972	−0.477727	−0.238863	−	0.971053i	$-0.576775\pi$
$17$	−1.96972	−0.477727	−0.238863	+	0.971053i	$0.576775\pi$
$18$	−0.954684	−0.225021
$19$	4.59598	1.05439	0.527196	−	0.849744i	$-0.323244\pi$
$19$	4.59598	1.05439	0.527196	+	0.849744i	$0.323244\pi$
$20$	−2.70709	−0.605324
$21$	1.85317	0.404394
$22$	5.48373	1.16914
$23$	2.07051	0.431732	0.215866	−	0.976423i	$-0.430743\pi$
$23$	2.07051	0.431732	0.215866	+	0.976423i	$0.430743\pi$
$24$	−3.39723	−0.693456
$25$	−4.08743	−0.817486
$26$	−6.16017	−1.20811
$27$	−4.75481	−0.915063
$28$	2.83381	0.535539
$29$	6.01329	1.11664	0.558320	−	0.829625i	$-0.311446\pi$
$29$	6.01329	1.11664	0.558320	+	0.829625i	$0.311446\pi$
$30$	3.89217	0.710610
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.26583	1.28443
$33$	−4.62217	−0.804617
$34$	4.33061	0.742693
$35$	−0.955285	−0.161473
$36$	1.23051	0.205085
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−10.1047	−1.63920
$39$	5.19233	0.831438
$40$	1.75123	0.276894
$41$	11.5944	1.81075	0.905374	−	0.424615i	$-0.139590\pi$
$41$	11.5944	1.81075	0.905374	+	0.424615i	$0.139590\pi$
$42$	−4.07436	−0.628687
$43$	−12.9703	−1.97796	−0.988979	−	0.148055i	$-0.952699\pi$
$43$	−12.9703	−1.97796	−0.988979	+	0.148055i	$0.952699\pi$
$44$	−7.06809	−1.06555
$45$	−0.414809	−0.0618360
$46$	−4.55221	−0.671187
$47$	−7.24856	−1.05731	−0.528655	−	0.848837i	$-0.677304\pi$
$47$	−7.24856	−1.05731	−0.528655	+	0.848837i	$0.677304\pi$
$48$	−3.03392	−0.437908
$49$	1.00000	0.142857
$50$	8.98659	1.27090
$51$	−3.65021	−0.511132
$52$	7.93996	1.10107
$53$	7.71285	1.05944	0.529721	−	0.848172i	$-0.322297\pi$
$53$	7.71285	1.05944	0.529721	+	0.848172i	$0.322297\pi$
$54$	10.4539	1.42259
$55$	2.38267	0.321280
$56$	−1.83320	−0.244972
$57$	8.51712	1.12812
$58$	−13.2208	−1.73597
$59$	4.95210	0.644709	0.322354	−	0.946619i	$-0.395526\pi$
$59$	4.95210	0.644709	0.322354	+	0.946619i	$0.395526\pi$
$60$	−5.01669	−0.647652
$61$	5.30201	0.678853	0.339427	−	0.940633i	$-0.389767\pi$
$61$	5.30201	0.678853	0.339427	+	0.940633i	$0.389767\pi$
$62$	−2.19859	−0.279221
$63$	0.434225	0.0547072
$64$	−12.7003	−1.58754
$65$	−2.67658	−0.331989
$66$	10.1623	1.25089
$67$	−2.90641	−0.355075	−0.177537	−	0.984114i	$-0.556813\pi$
$67$	−2.90641	−0.355075	−0.177537	+	0.984114i	$0.556813\pi$
$68$	−5.58180	−0.676893
$69$	3.83701	0.461921
$70$	2.10028	0.251032
$71$	9.73376	1.15518	0.577592	−	0.816325i	$-0.303992\pi$
$71$	9.73376	1.15518	0.577592	+	0.816325i	$0.303992\pi$
$72$	−0.796022	−0.0938121
$73$	−7.47694	−0.875109	−0.437555	−	0.899192i	$-0.644155\pi$
$73$	−7.47694	−0.875109	−0.437555	+	0.899192i	$0.644155\pi$
$74$	−2.19859	−0.255581
$75$	−7.57469	−0.874650
$76$	13.0241	1.49397
$77$	−2.49420	−0.284241
$78$	−11.4158	−1.29259
$79$	1.83243	0.206165	0.103082	−	0.994673i	$-0.467129\pi$
$79$	1.83243	0.206165	0.103082	+	0.994673i	$0.467129\pi$
$80$	1.56395	0.174855
$81$	−10.1141	−1.12379
$82$	−25.4915	−2.81506
$83$	−9.79963	−1.07565	−0.537825	−	0.843057i	$-0.680754\pi$
$83$	−9.79963	−1.07565	−0.537825	+	0.843057i	$0.680754\pi$
$84$	5.25152	0.572987
$85$	1.88164	0.204093
$86$	28.5165	3.07501
$87$	11.1436	1.19472
$88$	4.57237	0.487417
$89$	1.93059	0.204642	0.102321	−	0.994751i	$-0.467373\pi$
$89$	1.93059	0.204642	0.102321	+	0.994751i	$0.467373\pi$
$90$	0.911995	0.0961327
$91$	2.80187	0.293716
$92$	5.86743	0.611722
$93$	1.85317	0.192164
$94$	15.9366	1.64374
$95$	−4.39047	−0.450453
$96$	13.4648	1.37424
$97$	−15.1426	−1.53749	−0.768747	−	0.639554i	$-0.779119\pi$
$97$	−15.1426	−1.53749	−0.768747	+	0.639554i	$0.779119\pi$
$98$	−2.19859	−0.222091
$99$	−1.08304	−0.108850
$100$	−11.5830	−1.15830
$101$	5.16341	0.513779	0.256889	−	0.966441i	$-0.417302\pi$
$101$	5.16341	0.513779	0.256889	+	0.966441i	$0.417302\pi$
$102$	8.02533	0.794626
$103$	3.75727	0.370215	0.185107	−	0.982718i	$-0.440737\pi$
$103$	3.75727	0.370215	0.185107	+	0.982718i	$0.440737\pi$
$104$	−5.13639	−0.503665
$105$	−1.77030	−0.172764
$106$	−16.9574	−1.64705
$107$	15.2724	1.47644	0.738218	−	0.674562i	$-0.235667\pi$
$107$	15.2724	1.47644	0.738218	+	0.674562i	$0.235667\pi$
$108$	−13.4742	−1.29656
$109$	−13.4663	−1.28984	−0.644921	−	0.764249i	$-0.723110\pi$
$109$	−13.4663	−1.28984	−0.644921	+	0.764249i	$0.723110\pi$
$110$	−5.23853	−0.499474
$111$	1.85317	0.175895
$112$	−1.63715	−0.154696
$113$	17.0148	1.60062	0.800310	−	0.599586i	$-0.204668\pi$
$113$	17.0148	1.60062	0.800310	+	0.599586i	$0.204668\pi$
$114$	−18.7257	−1.75382
$115$	−1.97793	−0.184443
$116$	17.0405	1.58217
$117$	1.21664	0.112479
$118$	−10.8877	−1.00229
$119$	−1.96972	−0.180564
$120$	3.24532	0.296256
$121$	−4.77896	−0.434451
$122$	−11.6570	−1.05537
$123$	21.4864	1.93737
$124$	2.83381	0.254483
$125$	8.68109	0.776460
$126$	−0.954684	−0.0850500
$127$	7.71745	0.684813	0.342406	−	0.939552i	$-0.388758\pi$
$127$	7.71745	0.684813	0.342406	+	0.939552i	$0.388758\pi$
$128$	13.3911	1.18362
$129$	−24.0362	−2.11627
$130$	5.88472	0.516124
$131$	22.4384	1.96046	0.980228	−	0.197870i	$-0.0634025\pi$
$131$	22.4384	1.96046	0.980228	+	0.197870i	$0.0634025\pi$
$132$	−13.0983	−1.14006
$133$	4.59598	0.398522
$134$	6.39002	0.552013
$135$	4.54220	0.390930
$136$	3.61089	0.309631
$137$	−9.48857	−0.810663	−0.405332	−	0.914170i	$-0.632844\pi$
$137$	−9.48857	−0.810663	−0.405332	+	0.914170i	$0.632844\pi$
$138$	−8.43601	−0.718121
$139$	5.00351	0.424392	0.212196	−	0.977227i	$-0.431938\pi$
$139$	5.00351	0.424392	0.212196	+	0.977227i	$0.431938\pi$
$140$	−2.70709	−0.228791
$141$	−13.4328	−1.13124
$142$	−21.4006	−1.79589
$143$	−6.98843	−0.584402
$144$	−0.710892	−0.0592410
$145$	−5.74441	−0.477047
$146$	16.4387	1.36048
$147$	1.85317	0.152847
$148$	2.83381	0.232937
$149$	−2.41172	−0.197576	−0.0987879	−	0.995109i	$-0.531497\pi$
$149$	−2.41172	−0.197576	−0.0987879	+	0.995109i	$0.531497\pi$
$150$	16.6537	1.35976
$151$	1.52530	0.124127	0.0620635	−	0.998072i	$-0.480232\pi$
$151$	1.52530	0.124127	0.0620635	+	0.998072i	$0.480232\pi$
$152$	−8.42536	−0.683387
$153$	−0.855301	−0.0691470
$154$	5.48373	0.441892
$155$	−0.955285	−0.0767303
$156$	14.7141	1.17807
$157$	−3.15123	−0.251496	−0.125748	−	0.992062i	$-0.540133\pi$
$157$	−3.15123	−0.251496	−0.125748	+	0.992062i	$0.540133\pi$
$158$	−4.02877	−0.320512
$159$	14.2932	1.13352
$160$	−6.94094	−0.548729
$161$	2.07051	0.163179
$162$	22.2368	1.74709
$163$	−15.4167	−1.20753	−0.603765	−	0.797163i	$-0.706333\pi$
$163$	−15.4167	−1.20753	−0.603765	+	0.797163i	$0.706333\pi$
$164$	32.8564	2.56566
$165$	4.41549	0.343745
$166$	21.5454	1.67225
$167$	12.5797	0.973447	0.486723	−	0.873556i	$-0.338192\pi$
$167$	12.5797	0.973447	0.486723	+	0.873556i	$0.338192\pi$
$168$	−3.39723	−0.262102
$169$	−5.14953	−0.396117
$170$	−4.13696	−0.317291
$171$	1.99569	0.152614
$172$	−36.7554	−2.80258
$173$	12.2124	0.928490	0.464245	−	0.885707i	$-0.346326\pi$
$173$	12.2124	0.928490	0.464245	+	0.885707i	$0.346326\pi$
$174$	−24.5003	−1.85736
$175$	−4.08743	−0.308981
$176$	4.08339	0.307797
$177$	9.17707	0.689791
$178$	−4.24458	−0.318144
$179$	−23.5882	−1.76306	−0.881531	−	0.472126i	$-0.843487\pi$
$179$	−23.5882	−1.76306	−0.881531	+	0.472126i	$0.843487\pi$
$180$	−1.17549	−0.0876157
$181$	−7.24636	−0.538617	−0.269309	−	0.963054i	$-0.586795\pi$
$181$	−7.24636	−0.538617	−0.269309	+	0.963054i	$0.586795\pi$
$182$	−6.16017	−0.456622
$183$	9.82551	0.726323
$184$	−3.79567	−0.279820
$185$	−0.955285	−0.0702339
$186$	−4.07436	−0.298746
$187$	4.91287	0.359265
$188$	−20.5410	−1.49811
$189$	−4.75481	−0.345861
$190$	9.65286	0.700292
$191$	17.5985	1.27338	0.636692	−	0.771118i	$-0.280302\pi$
$191$	17.5985	1.27338	0.636692	+	0.771118i	$0.280302\pi$
$192$	−23.5358	−1.69855
$193$	2.80581	0.201966	0.100983	−	0.994888i	$-0.467801\pi$
$193$	2.80581	0.201966	0.100983	+	0.994888i	$0.467801\pi$
$194$	33.2923	2.39025
$195$	−4.96015	−0.355204
$196$	2.83381	0.202415
$197$	5.90534	0.420738	0.210369	−	0.977622i	$-0.432533\pi$
$197$	5.90534	0.420738	0.210369	+	0.977622i	$0.432533\pi$
$198$	2.38117	0.169223
$199$	4.12179	0.292186	0.146093	−	0.989271i	$-0.453330\pi$
$199$	4.12179	0.292186	0.146093	+	0.989271i	$0.453330\pi$
$200$	7.49308	0.529841
$201$	−5.38607	−0.379904
$202$	−11.3522	−0.798741
$203$	6.01329	0.422050
$204$	−10.3440	−0.724225
$205$	−11.0760	−0.773581
$206$	−8.26071	−0.575551
$207$	0.899069	0.0624896
$208$	−4.58709	−0.318057
$209$	−11.4633	−0.792934
$210$	3.89217	0.268585
$211$	24.5050	1.68699	0.843496	−	0.537135i	$-0.180494\pi$
$211$	24.5050	1.68699	0.843496	+	0.537135i	$0.180494\pi$
$212$	21.8567	1.50113
$213$	18.0383	1.23596
$214$	−33.5777	−2.29533
$215$	12.3904	0.845016
$216$	8.71652	0.593084
$217$	1.00000	0.0678844
$218$	29.6070	2.00524
$219$	−13.8560	−0.936302
$220$	6.75204	0.455222
$221$	−5.51889	−0.371241
$222$	−4.07436	−0.273453
$223$	8.51780	0.570394	0.285197	−	0.958469i	$-0.407941\pi$
$223$	8.51780	0.570394	0.285197	+	0.958469i	$0.407941\pi$
$224$	7.26583	0.485469
$225$	−1.77486	−0.118324
$226$	−37.4087	−2.48839
$227$	−19.7301	−1.30953	−0.654767	−	0.755831i	$-0.727233\pi$
$227$	−19.7301	−1.30953	−0.654767	+	0.755831i	$0.727233\pi$
$228$	24.1359	1.59844
$229$	18.6657	1.23346	0.616732	−	0.787173i	$-0.288456\pi$
$229$	18.6657	1.23346	0.616732	+	0.787173i	$0.288456\pi$
$230$	4.34866	0.286742
$231$	−4.62217	−0.304117
$232$	−11.0236	−0.723733
$233$	3.47288	0.227516	0.113758	−	0.993508i	$-0.463711\pi$
$233$	3.47288	0.227516	0.113758	+	0.993508i	$0.463711\pi$
$234$	−2.67490	−0.174864
$235$	6.92444	0.451700
$236$	14.0333	0.913490
$237$	3.39580	0.220581
$238$	4.33061	0.280711
$239$	12.3931	0.801643	0.400821	−	0.916156i	$-0.368725\pi$
$239$	12.3931	0.801643	0.400821	+	0.916156i	$0.368725\pi$
$240$	2.89825	0.187081
$241$	13.6180	0.877209	0.438605	−	0.898680i	$-0.355473\pi$
$241$	13.6180	0.877209	0.438605	+	0.898680i	$0.355473\pi$
$242$	10.5070	0.675414
$243$	−4.47873	−0.287311
$244$	15.0249	0.961869
$245$	−0.955285	−0.0610309
$246$	−47.2399	−3.01191
$247$	12.8773	0.819366
$248$	−1.83320	−0.116408
$249$	−18.1604	−1.15087
$250$	−19.0862	−1.20712
$251$	−20.2771	−1.27988	−0.639939	−	0.768426i	$-0.721040\pi$
$251$	−20.2771	−1.27988	−0.639939	+	0.768426i	$0.721040\pi$
$252$	1.23051	0.0775148
$253$	−5.16428	−0.324675
$254$	−16.9675	−1.06464
$255$	3.48699	0.218364
$256$	−4.04098	−0.252562
$257$	−26.3158	−1.64153	−0.820767	−	0.571264i	$-0.806453\pi$
$257$	−26.3158	−1.64153	−0.820767	+	0.571264i	$0.806453\pi$
$258$	52.8458	3.29004
$259$	1.00000	0.0621370
$260$	−7.58492	−0.470397
$261$	2.61112	0.161624
$262$	−49.3330	−3.04780
$263$	21.5477	1.32869	0.664344	−	0.747427i	$-0.268711\pi$
$263$	21.5477	1.32869	0.664344	+	0.747427i	$0.268711\pi$
$264$	8.47337	0.521500
$265$	−7.36797	−0.452611
$266$	−10.1047	−0.619559
$267$	3.57770	0.218952
$268$	−8.23622	−0.503107
$269$	14.1235	0.861124	0.430562	−	0.902561i	$-0.358315\pi$
$269$	14.1235	0.861124	0.430562	+	0.902561i	$0.358315\pi$
$270$	−9.98644	−0.607755
$271$	17.6776	1.07384	0.536918	−	0.843634i	$-0.319588\pi$
$271$	17.6776	1.07384	0.536918	+	0.843634i	$0.319588\pi$
$272$	3.22473	0.195528
$273$	5.19233	0.314254
$274$	20.8615	1.26029
$275$	10.1949	0.614774
$276$	10.8733	0.654498
$277$	−0.851079	−0.0511364	−0.0255682	−	0.999673i	$-0.508139\pi$
$277$	−0.851079	−0.0511364	−0.0255682	+	0.999673i	$0.508139\pi$
$278$	−11.0007	−0.659777
$279$	0.434225	0.0259964
$280$	1.75123	0.104656
$281$	26.6197	1.58800	0.793999	−	0.607919i	$-0.207995\pi$
$281$	26.6197	1.58800	0.793999	+	0.607919i	$0.207995\pi$
$282$	29.5332	1.75868
$283$	20.1065	1.19520	0.597602	−	0.801793i	$-0.296120\pi$
$283$	20.1065	1.19520	0.597602	+	0.801793i	$0.296120\pi$
$284$	27.5836	1.63678
$285$	−8.13628	−0.481952
$286$	15.3647	0.908534
$287$	11.5944	0.684398
$288$	3.15501	0.185911
$289$	−13.1202	−0.771777
$290$	12.6296	0.741636
$291$	−28.0617	−1.64500
$292$	−21.1882	−1.23995
$293$	11.0586	0.646050	0.323025	−	0.946390i	$-0.395300\pi$
$293$	11.0586	0.646050	0.323025	+	0.946390i	$0.395300\pi$
$294$	−4.07436	−0.237621
$295$	−4.73067	−0.275430
$296$	−1.83320	−0.106553
$297$	11.8595	0.688155
$298$	5.30239	0.307159
$299$	5.80131	0.335498
$300$	−21.4652	−1.23929
$301$	−12.9703	−0.747598
$302$	−3.35351	−0.192973
$303$	9.56866	0.549705
$304$	−7.52433	−0.431550
$305$	−5.06493	−0.290017
$306$	1.88046	0.107499
$307$	25.4022	1.44978	0.724891	−	0.688863i	$-0.241890\pi$
$307$	25.4022	1.44978	0.724891	+	0.688863i	$0.241890\pi$
$308$	−7.06809	−0.402742
$309$	6.96285	0.396103
$310$	2.10028	0.119288
$311$	−33.3328	−1.89013	−0.945066	−	0.326880i	$-0.894003\pi$
$311$	−33.3328	−1.89013	−0.945066	+	0.326880i	$0.894003\pi$
$312$	−9.51859	−0.538884
$313$	2.26593	0.128078	0.0640390	−	0.997947i	$-0.479602\pi$
$313$	2.26593	0.128078	0.0640390	+	0.997947i	$0.479602\pi$
$314$	6.92828	0.390985
$315$	−0.414809	−0.0233718
$316$	5.19276	0.292115
$317$	1.56466	0.0878802	0.0439401	−	0.999034i	$-0.486009\pi$
$317$	1.56466	0.0878802	0.0439401	+	0.999034i	$0.486009\pi$
$318$	−31.4249	−1.76222
$319$	−14.9984	−0.839747
$320$	12.1324	0.678222
$321$	28.3023	1.57968
$322$	−4.55221	−0.253685
$323$	−9.05279	−0.503711
$324$	−28.6615	−1.59230
$325$	−11.4524	−0.635268
$326$	33.8950	1.87727
$327$	−24.9554	−1.38003
$328$	−21.2549	−1.17361
$329$	−7.24856	−0.399626
$330$	−9.70786	−0.534400
$331$	2.87851	0.158217	0.0791086	−	0.996866i	$-0.474793\pi$
$331$	2.87851	0.158217	0.0791086	+	0.996866i	$0.474793\pi$
$332$	−27.7703	−1.52409
$333$	0.434225	0.0237954
$334$	−27.6576	−1.51336
$335$	2.77645	0.151694
$336$	−3.03392	−0.165514
$337$	−10.9335	−0.595585	−0.297792	−	0.954631i	$-0.596250\pi$
$337$	−10.9335	−0.595585	−0.297792	+	0.954631i	$0.596250\pi$
$338$	11.3217	0.615820
$339$	31.5313	1.71255
$340$	5.33221	0.289180
$341$	−2.49420	−0.135069
$342$	−4.38771	−0.237260
$343$	1.00000	0.0539949
$344$	23.7772	1.28198
$345$	−3.66543	−0.197340
$346$	−26.8500	−1.44347
$347$	−7.17422	−0.385132	−0.192566	−	0.981284i	$-0.561681\pi$
$347$	−7.17422	−0.385132	−0.192566	+	0.981284i	$0.561681\pi$
$348$	31.5789	1.69281
$349$	7.21846	0.386395	0.193198	−	0.981160i	$-0.438114\pi$
$349$	7.21846	0.386395	0.193198	+	0.981160i	$0.438114\pi$
$350$	8.98659	0.480354
$351$	−13.3224	−0.711094
$352$	−18.1225	−0.965930
$353$	−10.2185	−0.543878	−0.271939	−	0.962315i	$-0.587665\pi$
$353$	−10.2185	−0.543878	−0.271939	+	0.962315i	$0.587665\pi$
$354$	−20.1766	−1.07238
$355$	−9.29851	−0.493514
$356$	5.47092	0.289958
$357$	−3.65021	−0.193190
$358$	51.8607	2.74093
$359$	9.53195	0.503077	0.251539	−	0.967847i	$-0.419063\pi$
$359$	9.53195	0.503077	0.251539	+	0.967847i	$0.419063\pi$
$360$	0.760427	0.0400780
$361$	2.12307	0.111741
$362$	15.9318	0.837356
$363$	−8.85620	−0.464830
$364$	7.93996	0.416167
$365$	7.14260	0.373861
$366$	−21.6023	−1.12917
$367$	22.3848	1.16848	0.584239	−	0.811582i	$-0.301393\pi$
$367$	22.3848	1.16848	0.584239	+	0.811582i	$0.301393\pi$
$368$	−3.38975	−0.176703
$369$	5.03460	0.262091
$370$	2.10028	0.109188
$371$	7.71285	0.400431
$372$	5.25152	0.272278
$373$	20.5137	1.06216	0.531080	−	0.847321i	$-0.321786\pi$
$373$	20.5137	1.06216	0.531080	+	0.847321i	$0.321786\pi$
$374$	−10.8014	−0.558527
$375$	16.0875	0.830755
$376$	13.2881	0.685279
$377$	16.8485	0.867740
$378$	10.4539	0.537690
$379$	19.2641	0.989532	0.494766	−	0.869026i	$-0.335254\pi$
$379$	19.2641	0.989532	0.494766	+	0.869026i	$0.335254\pi$
$380$	−12.4418	−0.638249
$381$	14.3017	0.732699
$382$	−38.6920	−1.97965
$383$	−2.26182	−0.115574	−0.0577869	−	0.998329i	$-0.518404\pi$
$383$	−2.26182	−0.115574	−0.0577869	+	0.998329i	$0.518404\pi$
$384$	24.8159	1.26638
$385$	2.38267	0.121432
$386$	−6.16883	−0.313985
$387$	−5.63205	−0.286293
$388$	−42.9111	−2.17848
$389$	29.1270	1.47680	0.738398	−	0.674365i	$-0.235583\pi$
$389$	29.1270	1.47680	0.738398	+	0.674365i	$0.235583\pi$
$390$	10.9054	0.552214
$391$	−4.07833	−0.206250
$392$	−1.83320	−0.0925906
$393$	41.5822	2.09754
$394$	−12.9834	−0.654096
$395$	−1.75049	−0.0880769
$396$	−3.06914	−0.154230
$397$	−13.2975	−0.667380	−0.333690	−	0.942683i	$-0.608294\pi$
$397$	−13.2975	−0.667380	−0.333690	+	0.942683i	$0.608294\pi$
$398$	−9.06214	−0.454244
$399$	8.51712	0.426389
$400$	6.69175	0.334587
$401$	28.4911	1.42278	0.711388	−	0.702800i	$-0.248067\pi$
$401$	28.4911	1.42278	0.711388	+	0.702800i	$0.248067\pi$
$402$	11.8418	0.590614
$403$	2.80187	0.139571
$404$	14.6321	0.727975
$405$	9.66187	0.480102
$406$	−13.2208	−0.656136
$407$	−2.49420	−0.123633
$408$	6.69158	0.331282
$409$	6.87511	0.339952	0.169976	−	0.985448i	$-0.445631\pi$
$409$	6.87511	0.339952	0.169976	+	0.985448i	$0.445631\pi$
$410$	24.3516	1.20264
$411$	−17.5839	−0.867350
$412$	10.6474	0.524559
$413$	4.95210	0.243677
$414$	−1.97668	−0.0971488
$415$	9.36144	0.459535
$416$	20.3579	0.998129
$417$	9.27233	0.454068
$418$	25.2031	1.23273
$419$	−16.8820	−0.824741	−0.412370	−	0.911016i	$-0.635299\pi$
$419$	−16.8820	−0.824741	−0.412370	+	0.911016i	$0.635299\pi$
$420$	−5.01669	−0.244790
$421$	23.8728	1.16349	0.581744	−	0.813372i	$-0.302371\pi$
$421$	23.8728	1.16349	0.581744	+	0.813372i	$0.302371\pi$
$422$	−53.8764	−2.62266
$423$	−3.14750	−0.153037
$424$	−14.1392	−0.686661
$425$	8.05108	0.390535
$426$	−39.6588	−1.92147
$427$	5.30201	0.256582
$428$	43.2790	2.09197
$429$	−12.9507	−0.625267
$430$	−27.2414	−1.31370
$431$	1.86378	0.0897749	0.0448874	−	0.998992i	$-0.485707\pi$
$431$	1.86378	0.0897749	0.0448874	+	0.998992i	$0.485707\pi$
$432$	7.78434	0.374524
$433$	−1.30293	−0.0626150	−0.0313075	−	0.999510i	$-0.509967\pi$
$433$	−1.30293	−0.0626150	−0.0313075	+	0.999510i	$0.509967\pi$
$434$	−2.19859	−0.105536
$435$	−10.6453	−0.510405
$436$	−38.1610	−1.82758
$437$	9.51605	0.455214
$438$	30.4637	1.45561
$439$	−8.99193	−0.429162	−0.214581	−	0.976706i	$-0.568839\pi$
$439$	−8.99193	−0.429162	−0.214581	+	0.976706i	$0.568839\pi$
$440$	−4.36792	−0.208232
$441$	0.434225	0.0206774
$442$	12.1338	0.577146
$443$	24.7224	1.17460	0.587298	−	0.809371i	$-0.300192\pi$
$443$	24.7224	1.17460	0.587298	+	0.809371i	$0.300192\pi$
$444$	5.25152	0.249226
$445$	−1.84426	−0.0874264
$446$	−18.7272	−0.886757
$447$	−4.46932	−0.211391
$448$	−12.7003	−0.600033
$449$	13.3189	0.628556	0.314278	−	0.949331i	$-0.398238\pi$
$449$	13.3189	0.628556	0.314278	+	0.949331i	$0.398238\pi$
$450$	3.90220	0.183952
$451$	−28.9189	−1.36174
$452$	48.2167	2.26792
$453$	2.82663	0.132807
$454$	43.3785	2.03585
$455$	−2.67658	−0.125480
$456$	−15.6136	−0.731174
$457$	−10.9991	−0.514515	−0.257258	−	0.966343i	$-0.582819\pi$
$457$	−10.9991	−0.514515	−0.257258	+	0.966343i	$0.582819\pi$
$458$	−41.0383	−1.91759
$459$	9.36563	0.437150
$460$	−5.60507	−0.261338
$461$	−30.6682	−1.42836	−0.714181	−	0.699961i	$-0.753201\pi$
$461$	−30.6682	−1.42836	−0.714181	+	0.699961i	$0.753201\pi$
$462$	10.1623	0.472791
$463$	29.1366	1.35409	0.677047	−	0.735940i	$-0.263260\pi$
$463$	29.1366	1.35409	0.677047	+	0.735940i	$0.263260\pi$
$464$	−9.84468	−0.457028
$465$	−1.77030	−0.0820958
$466$	−7.63545	−0.353705
$467$	0.618808	0.0286350	0.0143175	−	0.999897i	$-0.495442\pi$
$467$	0.618808	0.0286350	0.0143175	+	0.999897i	$0.495442\pi$
$468$	3.44773	0.159371
$469$	−2.90641	−0.134206
$470$	−15.2240	−0.702231
$471$	−5.83976	−0.269082
$472$	−9.07820	−0.417858
$473$	32.3506	1.48748
$474$	−7.46598	−0.342924
$475$	−18.7858	−0.861950
$476$	−5.58180	−0.255841
$477$	3.34911	0.153345
$478$	−27.2474	−1.24627
$479$	−23.6043	−1.07851	−0.539254	−	0.842143i	$-0.681294\pi$
$479$	−23.6043	−1.07851	−0.539254	+	0.842143i	$0.681294\pi$
$480$	−12.8627	−0.587100
$481$	2.80187	0.127754
$482$	−29.9403	−1.36374
$483$	3.83701	0.174590
$484$	−13.5426	−0.615575
$485$	14.4654	0.656842
$486$	9.84690	0.446664
$487$	18.7706	0.850576	0.425288	−	0.905058i	$-0.360173\pi$
$487$	18.7706	0.850576	0.425288	+	0.905058i	$0.360173\pi$
$488$	−9.71966	−0.439988
$489$	−28.5697	−1.29197
$490$	2.10028	0.0948811
$491$	10.6085	0.478754	0.239377	−	0.970927i	$-0.423057\pi$
$491$	10.6085	0.478754	0.239377	+	0.970927i	$0.423057\pi$
$492$	60.8884	2.74506
$493$	−11.8445	−0.533449
$494$	−28.3120	−1.27382
$495$	1.03462	0.0465025
$496$	−1.63715	−0.0735103
$497$	9.73376	0.436619
$498$	39.9272	1.78918
$499$	−8.39414	−0.375773	−0.187887	−	0.982191i	$-0.560164\pi$
$499$	−8.39414	−0.375773	−0.187887	+	0.982191i	$0.560164\pi$
$500$	24.6005	1.10017
$501$	23.3123	1.04152
$502$	44.5810	1.98975
$503$	6.99951	0.312093	0.156046	−	0.987750i	$-0.450125\pi$
$503$	6.99951	0.312093	0.156046	+	0.987750i	$0.450125\pi$
$504$	−0.796022	−0.0354576
$505$	−4.93253	−0.219495
$506$	11.3541	0.504753
$507$	−9.54293	−0.423816
$508$	21.8698	0.970314
$509$	−12.9940	−0.575948	−0.287974	−	0.957638i	$-0.592982\pi$
$509$	−12.9940	−0.575948	−0.287974	+	0.957638i	$0.592982\pi$
$510$	−7.66648	−0.339477
$511$	−7.47694	−0.330760
$512$	−17.8977	−0.790976
$513$	−21.8530	−0.964835
$514$	57.8577	2.55199
$515$	−3.58926	−0.158162
$516$	−68.1139	−2.99855
$517$	18.0794	0.795129
$518$	−2.19859	−0.0966006
$519$	22.6316	0.993416
$520$	4.90672	0.215174
$521$	−20.2192	−0.885821	−0.442911	−	0.896566i	$-0.646054\pi$
$521$	−20.2192	−0.885821	−0.442911	+	0.896566i	$0.646054\pi$
$522$	−5.74079	−0.251268
$523$	−32.6323	−1.42691	−0.713455	−	0.700701i	$-0.752870\pi$
$523$	−32.6323	−1.42691	−0.713455	+	0.700701i	$0.752870\pi$
$524$	63.5862	2.77778
$525$	−7.57469	−0.330587
$526$	−47.3746	−2.06563
$527$	−1.96972	−0.0858023
$528$	7.56720	0.329320
$529$	−18.7130	−0.813608
$530$	16.1992	0.703646
$531$	2.15033	0.0933162
$532$	13.0241	0.564668
$533$	32.4861	1.40713
$534$	−7.86591	−0.340391
$535$	−14.5895	−0.630758
$536$	5.32804	0.230136
$537$	−43.7128	−1.88635
$538$	−31.0518	−1.33874
$539$	−2.49420	−0.107433
$540$	12.8717	0.553910
$541$	−16.4890	−0.708917	−0.354459	−	0.935072i	$-0.615335\pi$
$541$	−16.4890	−0.708917	−0.354459	+	0.935072i	$0.615335\pi$
$542$	−38.8658	−1.66943
$543$	−13.4287	−0.576281
$544$	−14.3116	−0.613606
$545$	12.8642	0.551041
$546$	−11.4158	−0.488552
$547$	−13.5799	−0.580633	−0.290317	−	0.956931i	$-0.593761\pi$
$547$	−13.5799	−0.580633	−0.290317	+	0.956931i	$0.593761\pi$
$548$	−26.8888	−1.14863
$549$	2.30227	0.0982583
$550$	−22.4144	−0.955752
$551$	27.6370	1.17738
$552$	−7.03400	−0.299387
$553$	1.83243	0.0779229
$554$	1.87117	0.0794986
$555$	−1.77030	−0.0751451
$556$	14.1790	0.601323
$557$	−22.4371	−0.950690	−0.475345	−	0.879799i	$-0.657677\pi$
$557$	−22.4371	−0.950690	−0.475345	+	0.879799i	$0.657677\pi$
$558$	−0.954684	−0.0404150
$559$	−36.3412	−1.53707
$560$	1.56395	0.0660888
$561$	9.10437	0.384387
$562$	−58.5259	−2.46877
$563$	11.0123	0.464112	0.232056	−	0.972702i	$-0.425455\pi$
$563$	11.0123	0.464112	0.232056	+	0.972702i	$0.425455\pi$
$564$	−38.0659	−1.60286
$565$	−16.2540	−0.683811
$566$	−44.2059	−1.85811
$567$	−10.1141	−0.424753
$568$	−17.8439	−0.748715
$569$	0.00711389	0.000298230 0	0.000149115	−	1.00000i	$-0.499953\pi$
$569$	0.00711389	0.000298230 0	0.000149115		1.00000i	$0.499953\pi$
$570$	17.8884	0.749261
$571$	−18.4964	−0.774050	−0.387025	−	0.922069i	$-0.626497\pi$
$571$	−18.4964	−0.774050	−0.387025	+	0.922069i	$0.626497\pi$
$572$	−19.8039	−0.828041
$573$	32.6130	1.36243
$574$	−25.4915	−1.06399
$575$	−8.46308	−0.352935
$576$	−5.51479	−0.229783
$577$	−21.4461	−0.892811	−0.446406	−	0.894831i	$-0.647296\pi$
$577$	−21.4461	−0.892811	−0.446406	+	0.894831i	$0.647296\pi$
$578$	28.8460	1.19984
$579$	5.19963	0.216089
$580$	−16.2785	−0.675930
$581$	−9.79963	−0.406557
$582$	61.6961	2.55739
$583$	−19.2374	−0.796732
$584$	13.7067	0.567188
$585$	−1.16224	−0.0480527
$586$	−24.3133	−1.00437
$587$	−17.7924	−0.734373	−0.367186	−	0.930147i	$-0.619679\pi$
$587$	−17.7924	−0.734373	−0.367186	+	0.930147i	$0.619679\pi$
$588$	5.25152	0.216569
$589$	4.59598	0.189374
$590$	10.4008	0.428195
$591$	10.9436	0.450159
$592$	−1.63715	−0.0672865
$593$	−31.1575	−1.27949	−0.639743	−	0.768589i	$-0.720959\pi$
$593$	−31.1575	−1.27949	−0.639743	+	0.768589i	$0.720959\pi$
$594$	−26.0741	−1.06983
$595$	1.88164	0.0771398
$596$	−6.83435	−0.279946
$597$	7.63836	0.312617
$598$	−12.7547	−0.521579
$599$	−30.2632	−1.23652	−0.618261	−	0.785973i	$-0.712163\pi$
$599$	−30.2632	−1.23652	−0.618261	+	0.785973i	$0.712163\pi$
$600$	13.8859	0.566891
$601$	24.6288	1.00463	0.502314	−	0.864685i	$-0.332482\pi$
$601$	24.6288	1.00463	0.502314	+	0.864685i	$0.332482\pi$
$602$	28.5165	1.16225
$603$	−1.26204	−0.0513941
$604$	4.32240	0.175876
$605$	4.56527	0.185604
$606$	−21.0376	−0.854594
$607$	16.1346	0.654882	0.327441	−	0.944872i	$-0.393814\pi$
$607$	16.1346	0.654882	0.327441	+	0.944872i	$0.393814\pi$
$608$	33.3937	1.35429
$609$	11.1436	0.451563
$610$	11.1357	0.450872
$611$	−20.3095	−0.821635
$612$	−2.42376	−0.0979746
$613$	23.7330	0.958567	0.479283	−	0.877660i	$-0.340897\pi$
$613$	23.7330	0.958567	0.479283	+	0.877660i	$0.340897\pi$
$614$	−55.8492	−2.25389
$615$	−20.5257	−0.827675
$616$	4.57237	0.184226
$617$	39.4088	1.58654	0.793268	−	0.608872i	$-0.208378\pi$
$617$	39.4088	1.58654	0.793268	+	0.608872i	$0.208378\pi$
$618$	−15.3085	−0.615797
$619$	−0.433089	−0.0174073	−0.00870365	−	0.999962i	$-0.502770\pi$
$619$	−0.433089	−0.0174073	−0.00870365	+	0.999962i	$0.502770\pi$
$620$	−2.70709	−0.108719
$621$	−9.84489	−0.395062
$622$	73.2853	2.93847
$623$	1.93059	0.0773474
$624$	−8.50064	−0.340298
$625$	12.1442	0.485770
$626$	−4.98186	−0.199115
$627$	−21.2434	−0.848381
$628$	−8.92999	−0.356345
$629$	−1.96972	−0.0785378
$630$	0.911995	0.0363347
$631$	−11.3647	−0.452421	−0.226210	−	0.974078i	$-0.572634\pi$
$631$	−11.3647	−0.452421	−0.226210	+	0.974078i	$0.572634\pi$
$632$	−3.35922	−0.133622
$633$	45.4118	1.80496
$634$	−3.44006	−0.136622
$635$	−7.37236	−0.292563
$636$	40.5041	1.60609
$637$	2.80187	0.111014
$638$	32.9753	1.30550
$639$	4.22664	0.167203
$640$	−12.7923	−0.505661
$641$	14.6813	0.579876	0.289938	−	0.957045i	$-0.406365\pi$
$641$	14.6813	0.579876	0.289938	+	0.957045i	$0.406365\pi$
$642$	−62.2251	−2.45583
$643$	3.72681	0.146971	0.0734854	−	0.997296i	$-0.476588\pi$
$643$	3.72681	0.146971	0.0734854	+	0.997296i	$0.476588\pi$
$644$	5.86743	0.231209
$645$	22.9614	0.904105
$646$	19.9034	0.783089
$647$	35.2122	1.38434	0.692168	−	0.721737i	$-0.256656\pi$
$647$	35.2122	1.38434	0.692168	+	0.721737i	$0.256656\pi$
$648$	18.5412	0.728368
$649$	−12.3515	−0.484841
$650$	25.1793	0.987612
$651$	1.85317	0.0726313
$652$	−43.6880	−1.71095
$653$	−26.8133	−1.04929	−0.524643	−	0.851322i	$-0.675801\pi$
$653$	−26.8133	−1.04929	−0.524643	+	0.851322i	$0.675801\pi$
$654$	54.8667	2.14546
$655$	−21.4351	−0.837539
$656$	−18.9819	−0.741118
$657$	−3.24667	−0.126665
$658$	15.9366	0.621274
$659$	−32.0899	−1.25004	−0.625022	−	0.780607i	$-0.714910\pi$
$659$	−32.0899	−1.25004	−0.625022	+	0.780607i	$0.714910\pi$
$660$	12.5126	0.487054
$661$	35.1302	1.36641	0.683203	−	0.730229i	$-0.260587\pi$
$661$	35.1302	1.36641	0.683203	+	0.730229i	$0.260587\pi$
$662$	−6.32867	−0.245971
$663$	−10.2274	−0.397200
$664$	17.9647	0.697166
$665$	−4.39047	−0.170255
$666$	−0.954684	−0.0369932
$667$	12.4506	0.482089
$668$	35.6485	1.37928
$669$	15.7849	0.610280
$670$	−6.10429	−0.235829
$671$	−13.2243	−0.510518
$672$	13.4648	0.519416
$673$	50.8665	1.96076	0.980379	−	0.197121i	$-0.0631593\pi$
$673$	50.8665	1.96076	0.980379	+	0.197121i	$0.0631593\pi$
$674$	24.0383	0.925919
$675$	19.4349	0.748051
$676$	−14.5928	−0.561260
$677$	3.14562	0.120896	0.0604479	−	0.998171i	$-0.480747\pi$
$677$	3.14562	0.120896	0.0604479	+	0.998171i	$0.480747\pi$
$678$	−69.3245	−2.66239
$679$	−15.1426	−0.581118
$680$	−3.44943	−0.132279
$681$	−36.5632	−1.40110
$682$	5.48373	0.209983
$683$	−18.0902	−0.692202	−0.346101	−	0.938197i	$-0.612495\pi$
$683$	−18.0902	−0.692202	−0.346101	+	0.938197i	$0.612495\pi$
$684$	5.65540	0.216240
$685$	9.06429	0.346329
$686$	−2.19859	−0.0839426
$687$	34.5907	1.31972
$688$	21.2344	0.809555
$689$	21.6104	0.823291
$690$	8.05879	0.306793
$691$	14.9065	0.567071	0.283536	−	0.958962i	$-0.408493\pi$
$691$	14.9065	0.567071	0.283536	+	0.958962i	$0.408493\pi$
$692$	34.6075	1.31558
$693$	−1.08304	−0.0411415
$694$	15.7732	0.598742
$695$	−4.77978	−0.181307
$696$	−20.4285	−0.774341
$697$	−22.8378	−0.865043
$698$	−15.8704	−0.600705
$699$	6.43583	0.243425
$700$	−11.5830	−0.437796
$701$	11.4781	0.433520	0.216760	−	0.976225i	$-0.430451\pi$
$701$	11.4781	0.433520	0.216760	+	0.976225i	$0.430451\pi$
$702$	29.2904	1.10550
$703$	4.59598	0.173341
$704$	31.6771	1.19388
$705$	12.8321	0.483286
$706$	22.4664	0.845534
$707$	5.16341	0.194190
$708$	26.0060	0.977367
$709$	−48.9123	−1.83694	−0.918470	−	0.395490i	$-0.870575\pi$
$709$	−48.9123	−1.83694	−0.918470	+	0.395490i	$0.870575\pi$
$710$	20.4436	0.767236
$711$	0.795688	0.0298406
$712$	−3.53916	−0.132636
$713$	2.07051	0.0775413
$714$	8.02533	0.300341
$715$	6.67594	0.249666
$716$	−66.8443	−2.49809
$717$	22.9665	0.857699
$718$	−20.9569	−0.782104
$719$	2.76192	0.103002	0.0515011	−	0.998673i	$-0.483599\pi$
$719$	2.76192	0.103002	0.0515011	+	0.998673i	$0.483599\pi$
$720$	0.679105	0.0253087
$721$	3.75727	0.139928
$722$	−4.66777	−0.173717
$723$	25.2363	0.938549
$724$	−20.5348	−0.763169
$725$	−24.5789	−0.912838
$726$	19.4712	0.722643
$727$	−15.6408	−0.580084	−0.290042	−	0.957014i	$-0.593669\pi$
$727$	−15.6408	−0.580084	−0.290042	+	0.957014i	$0.593669\pi$
$728$	−5.13639	−0.190367
$729$	22.0425	0.816390
$730$	−15.7037	−0.581219
$731$	25.5479	0.944924
$732$	27.8436	1.02913
$733$	41.3953	1.52897	0.764485	−	0.644641i	$-0.222993\pi$
$733$	41.3953	1.52897	0.764485	+	0.644641i	$0.222993\pi$
$734$	−49.2151	−1.81656
$735$	−1.77030	−0.0652986
$736$	15.0440	0.554529
$737$	7.24918	0.267027
$738$	−11.0690	−0.407456
$739$	33.5368	1.23367	0.616835	−	0.787093i	$-0.288415\pi$
$739$	33.5368	1.23367	0.616835	+	0.787093i	$0.288415\pi$
$740$	−2.70709	−0.0995147
$741$	23.8639	0.876661
$742$	−16.9574	−0.622526
$743$	43.0576	1.57963	0.789815	−	0.613345i	$-0.210176\pi$
$743$	43.0576	1.57963	0.789815	+	0.613345i	$0.210176\pi$
$744$	−3.39723	−0.124548
$745$	2.30388	0.0844076
$746$	−45.1013	−1.65128
$747$	−4.25525	−0.155691
$748$	13.9221	0.509044
$749$	15.2724	0.558041
$750$	−35.3698	−1.29152
$751$	−4.65828	−0.169983	−0.0849916	−	0.996382i	$-0.527086\pi$
$751$	−4.65828	−0.169983	−0.0849916	+	0.996382i	$0.527086\pi$
$752$	11.8670	0.432745
$753$	−37.5768	−1.36937
$754$	−37.0429	−1.34902
$755$	−1.45709	−0.0530291
$756$	−13.4742	−0.490052
$757$	−22.7127	−0.825506	−0.412753	−	0.910843i	$-0.635433\pi$
$757$	−22.7127	−0.825506	−0.412753	+	0.910843i	$0.635433\pi$
$758$	−42.3540	−1.53837
$759$	−9.57027	−0.347379
$760$	8.04862	0.291954
$761$	24.4353	0.885778	0.442889	−	0.896576i	$-0.353954\pi$
$761$	24.4353	0.885778	0.442889	+	0.896576i	$0.353954\pi$
$762$	−31.4436	−1.13908
$763$	−13.4663	−0.487514
$764$	49.8708	1.80426
$765$	0.817056	0.0295407
$766$	4.97283	0.179675
$767$	13.8751	0.501002
$768$	−7.48862	−0.270222
$769$	28.3689	1.02301	0.511505	−	0.859280i	$-0.329088\pi$
$769$	28.3689	1.02301	0.511505	+	0.859280i	$0.329088\pi$
$770$	−5.23853	−0.188783
$771$	−48.7675	−1.75632
$772$	7.95112	0.286167
$773$	23.8822	0.858982	0.429491	−	0.903071i	$-0.358693\pi$
$773$	23.8822	0.858982	0.429491	+	0.903071i	$0.358693\pi$
$774$	12.3826	0.445082
$775$	−4.08743	−0.146825
$776$	27.7593	0.996502
$777$	1.85317	0.0664820
$778$	−64.0383	−2.29589
$779$	53.2879	1.90924
$780$	−14.0561	−0.503290
$781$	−24.2780	−0.868733
$782$	8.96658	0.320644
$783$	−28.5921	−1.02180
$784$	−1.63715	−0.0584697
$785$	3.01033	0.107443
$786$	−91.4222	−3.26092
$787$	−28.9143	−1.03068	−0.515341	−	0.856985i	$-0.672335\pi$
$787$	−28.9143	−1.03068	−0.515341	+	0.856985i	$0.672335\pi$
$788$	16.7346	0.596146
$789$	39.9315	1.42160
$790$	3.84862	0.136928
$791$	17.0148	0.604978
$792$	1.98544	0.0705495
$793$	14.8555	0.527536
$794$	29.2357	1.03754
$795$	−13.6541	−0.484260
$796$	11.6804	0.413999
$797$	40.2463	1.42560	0.712798	−	0.701369i	$-0.247427\pi$
$797$	40.2463	1.42560	0.712798	+	0.701369i	$0.247427\pi$
$798$	−18.7257	−0.662882
$799$	14.2776	0.505105
$800$	−29.6986	−1.05000
$801$	0.838310	0.0296202
$802$	−62.6402	−2.21190
$803$	18.6490	0.658108
$804$	−15.2631	−0.538287
$805$	−1.97793	−0.0697129
$806$	−6.16017	−0.216983
$807$	26.1732	0.921339
$808$	−9.46558	−0.332998
$809$	−30.4580	−1.07085	−0.535424	−	0.844583i	$-0.679848\pi$
$809$	−30.4580	−1.07085	−0.535424	+	0.844583i	$0.679848\pi$
$810$	−21.2425	−0.746386
$811$	30.0477	1.05512	0.527559	−	0.849519i	$-0.323108\pi$
$811$	30.0477	1.05512	0.527559	+	0.849519i	$0.323108\pi$
$812$	17.0405	0.598005
$813$	32.7595	1.14893
$814$	5.48373	0.192205
$815$	14.7273	0.515876
$816$	5.97596	0.209200
$817$	−59.6115	−2.08554
$818$	−15.1156	−0.528503
$819$	1.21664	0.0425129
$820$	−31.3872	−1.09609
$821$	4.47390	0.156140	0.0780700	−	0.996948i	$-0.475124\pi$
$821$	4.47390	0.156140	0.0780700	+	0.996948i	$0.475124\pi$
$822$	38.6598	1.34842
$823$	−40.8024	−1.42228	−0.711141	−	0.703050i	$-0.751821\pi$
$823$	−40.8024	−1.42228	−0.711141	+	0.703050i	$0.751821\pi$
$824$	−6.88783	−0.239949
$825$	18.8928	0.657763
$826$	−10.8877	−0.378830
$827$	6.00055	0.208660	0.104330	−	0.994543i	$-0.466730\pi$
$827$	6.00055	0.208660	0.104330	+	0.994543i	$0.466730\pi$
$828$	2.54779	0.0885417
$829$	33.9750	1.18000	0.590000	−	0.807403i	$-0.299128\pi$
$829$	33.9750	1.18000	0.590000	+	0.807403i	$0.299128\pi$
$830$	−20.5820	−0.714411
$831$	−1.57719	−0.0547121
$832$	−35.5846	−1.23367
$833$	−1.96972	−0.0682467
$834$	−20.3861	−0.705912
$835$	−12.0172	−0.415872
$836$	−32.4848	−1.12351
$837$	−4.75481	−0.164350
$838$	37.1167	1.28217
$839$	−47.7629	−1.64896	−0.824479	−	0.565892i	$-0.808532\pi$
$839$	−47.7629	−1.64896	−0.824479	+	0.565892i	$0.808532\pi$
$840$	3.24532	0.111974
$841$	7.15970	0.246886
$842$	−52.4865	−1.80880
$843$	49.3307	1.69904
$844$	69.4424	2.39030
$845$	4.91927	0.169228
$846$	6.92008	0.237917
$847$	−4.77896	−0.164207
$848$	−12.6271	−0.433617
$849$	37.2606	1.27878
$850$	−17.7011	−0.607141
$851$	2.07051	0.0709763
$852$	51.1170	1.75124
$853$	28.2353	0.966758	0.483379	−	0.875411i	$-0.339409\pi$
$853$	28.2353	0.966758	0.483379	+	0.875411i	$0.339409\pi$
$854$	−11.6570	−0.398893
$855$	−1.90645	−0.0651993
$856$	−27.9973	−0.956930
$857$	−48.6481	−1.66179	−0.830893	−	0.556432i	$-0.812170\pi$
$857$	−48.6481	−1.66179	−0.830893	+	0.556432i	$0.812170\pi$
$858$	28.4733	0.972064
$859$	24.7667	0.845029	0.422515	−	0.906356i	$-0.361148\pi$
$859$	24.7667	0.845029	0.422515	+	0.906356i	$0.361148\pi$
$860$	35.1119	1.19731
$861$	21.4864	0.732256
$862$	−4.09768	−0.139568
$863$	−41.2006	−1.40249	−0.701243	−	0.712922i	$-0.747371\pi$
$863$	−41.2006	−1.40249	−0.701243	+	0.712922i	$0.747371\pi$
$864$	−34.5476	−1.17533
$865$	−11.6663	−0.396666
$866$	2.86462	0.0973438
$867$	−24.3139	−0.825744
$868$	2.83381	0.0961857
$869$	−4.57046	−0.155042
$870$	23.4048	0.793496
$871$	−8.14339	−0.275928
$872$	24.6865	0.835991
$873$	−6.57527	−0.222539
$874$	−20.9219	−0.707694
$875$	8.68109	0.293474
$876$	−39.2652	−1.32665
$877$	2.72219	0.0919218	0.0459609	−	0.998943i	$-0.485365\pi$
$877$	2.72219	0.0919218	0.0459609	+	0.998943i	$0.485365\pi$
$878$	19.7696	0.667192
$879$	20.4934	0.691225
$880$	−3.90080	−0.131496
$881$	49.4139	1.66480	0.832399	−	0.554177i	$-0.186967\pi$
$881$	49.4139	1.66480	0.832399	+	0.554177i	$0.186967\pi$
$882$	−0.954684	−0.0321459
$883$	47.8115	1.60898	0.804492	−	0.593964i	$-0.202438\pi$
$883$	47.8115	1.60898	0.804492	+	0.593964i	$0.202438\pi$
$884$	−15.6395	−0.526012
$885$	−8.76672	−0.294690
$886$	−54.3544	−1.82607
$887$	36.8807	1.23833	0.619166	−	0.785260i	$-0.287471\pi$
$887$	36.8807	1.23833	0.619166	+	0.785260i	$0.287471\pi$
$888$	−3.39723	−0.114003
$889$	7.71745	0.258835
$890$	4.05478	0.135917
$891$	25.2267	0.845125
$892$	24.1378	0.808194
$893$	−33.3142	−1.11482
$894$	9.82621	0.328637
$895$	22.5334	0.753209
$896$	13.3911	0.447365
$897$	10.7508	0.358958
$898$	−29.2827	−0.977178
$899$	6.01329	0.200555
$900$	−5.02962	−0.167654
$901$	−15.1921	−0.506123
$902$	63.5808	2.11701
$903$	−24.0362	−0.799875
$904$	−31.1916	−1.03742
$905$	6.92233	0.230106
$906$	−6.21461	−0.206467
$907$	−2.62052	−0.0870128	−0.0435064	−	0.999053i	$-0.513853\pi$
$907$	−2.62052	−0.0870128	−0.0435064	+	0.999053i	$0.513853\pi$
$908$	−55.9114	−1.85548
$909$	2.24208	0.0743652
$910$	5.88472	0.195076
$911$	45.5923	1.51054	0.755270	−	0.655414i	$-0.227506\pi$
$911$	45.5923	1.51054	0.755270	+	0.655414i	$0.227506\pi$
$912$	−13.9438	−0.461726
$913$	24.4423	0.808921
$914$	24.1825	0.799886
$915$	−9.38616	−0.310297
$916$	52.8950	1.74770
$917$	22.4384	0.740983
$918$	−20.5912	−0.679611
$919$	35.1019	1.15790	0.578952	−	0.815362i	$-0.303462\pi$
$919$	35.1019	1.15790	0.578952	+	0.815362i	$0.303462\pi$
$920$	3.62594	0.119544
$921$	47.0746	1.55116
$922$	67.4269	2.22059
$923$	27.2727	0.897692
$924$	−13.0983	−0.430904
$925$	−4.08743	−0.134394
$926$	−64.0595	−2.10513
$927$	1.63150	0.0535855
$928$	43.6916	1.43425
$929$	13.3281	0.437282	0.218641	−	0.975805i	$-0.429838\pi$
$929$	13.3281	0.437282	0.218641	+	0.975805i	$0.429838\pi$
$930$	3.89217	0.127629
$931$	4.59598	0.150627
$932$	9.84147	0.322368
$933$	−61.7713	−2.02230
$934$	−1.36051	−0.0445171
$935$	−4.69319	−0.153484
$936$	−2.23035	−0.0729012
$937$	14.3348	0.468299	0.234149	−	0.972201i	$-0.424769\pi$
$937$	14.3348	0.468299	0.234149	+	0.972201i	$0.424769\pi$
$938$	6.39002	0.208641
$939$	4.19915	0.137034
$940$	19.6225	0.640016
$941$	37.9448	1.23697	0.618483	−	0.785798i	$-0.287748\pi$
$941$	37.9448	1.23697	0.618483	+	0.785798i	$0.287748\pi$
$942$	12.8393	0.418325
$943$	24.0065	0.781758
$944$	−8.10735	−0.263872
$945$	4.54220	0.147758
$946$	−71.1259	−2.31250
$947$	−15.0161	−0.487959	−0.243979	−	0.969780i	$-0.578453\pi$
$947$	−15.0161	−0.487959	−0.243979	+	0.969780i	$0.578453\pi$
$948$	9.62304	0.312542
$949$	−20.9494	−0.680046
$950$	41.3022	1.34002
$951$	2.89958	0.0940253
$952$	3.61089	0.117030
$953$	−54.0075	−1.74947	−0.874736	−	0.484599i	$-0.838966\pi$
$953$	−54.0075	−1.74947	−0.874736	+	0.484599i	$0.838966\pi$
$954$	−7.36333	−0.238397
$955$	−16.8116	−0.544010
$956$	35.1196	1.13585
$957$	−27.7945	−0.898468
$958$	51.8962	1.67669
$959$	−9.48857	−0.306402
$960$	22.4834	0.725647
$961$	1.00000	0.0322581
$962$	−6.16017	−0.198612
$963$	6.63165	0.213702
$964$	38.5906	1.24292
$965$	−2.68035	−0.0862834
$966$	−8.43601	−0.271424
$967$	51.7196	1.66319	0.831595	−	0.555383i	$-0.187428\pi$
$967$	51.7196	1.66319	0.831595	+	0.555383i	$0.187428\pi$
$968$	8.76079	0.281582
$969$	−16.7763	−0.538933
$970$	−31.8036	−1.02115
$971$	9.66179	0.310061	0.155031	−	0.987910i	$-0.450452\pi$
$971$	9.66179	0.310061	0.155031	+	0.987910i	$0.450452\pi$
$972$	−12.6919	−0.407091
$973$	5.00351	0.160405
$974$	−41.2688	−1.32234
$975$	−21.2233	−0.679689
$976$	−8.68020	−0.277847
$977$	−5.44003	−0.174042	−0.0870210	−	0.996206i	$-0.527735\pi$
$977$	−5.44003	−0.174042	−0.0870210	+	0.996206i	$0.527735\pi$
$978$	62.8132	2.00854
$979$	−4.81528	−0.153897
$980$	−2.70709	−0.0864749
$981$	−5.84742	−0.186694
$982$	−23.3237	−0.744290
$983$	−21.6558	−0.690714	−0.345357	−	0.938471i	$-0.612242\pi$
$983$	−21.6558	−0.690714	−0.345357	+	0.938471i	$0.612242\pi$
$984$	−39.3890	−1.25567
$985$	−5.64129	−0.179746
$986$	26.0412	0.829321
$987$	−13.4328	−0.427570
$988$	36.4919	1.16096
$989$	−26.8553	−0.853948
$990$	−2.27470	−0.0722947
$991$	53.1501	1.68837	0.844184	−	0.536054i	$-0.180086\pi$
$991$	53.1501	1.68837	0.844184	+	0.536054i	$0.180086\pi$
$992$	7.26583	0.230690
$993$	5.33436	0.169281
$994$	−21.4006	−0.678784
$995$	−3.93748	−0.124827
$996$	−51.4629	−1.63067
$997$	−43.6898	−1.38367	−0.691835	−	0.722056i	$-0.743197\pi$
$997$	−43.6898	−1.38367	−0.691835	+	0.722056i	$0.743197\pi$
$998$	18.4553	0.584192
$999$	−4.75481	−0.150435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.g.1.9	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.g.1.9	✓	70	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19859 q^{2} +1.85317 q^{3} +2.83381 q^{4} -0.955285 q^{5} -4.07436 q^{6} +1.00000 q^{7} -1.83320 q^{8} +0.434225 q^{9} +O(q^{10})\)	\(q-2.19859 q^{2} +1.85317 q^{3} +2.83381 q^{4} -0.955285 q^{5} -4.07436 q^{6} +1.00000 q^{7} -1.83320 q^{8} +0.434225 q^{9} +2.10028 q^{10} -2.49420 q^{11} +5.25152 q^{12} +2.80187 q^{13} -2.19859 q^{14} -1.77030 q^{15} -1.63715 q^{16} -1.96972 q^{17} -0.954684 q^{18} +4.59598 q^{19} -2.70709 q^{20} +1.85317 q^{21} +5.48373 q^{22} +2.07051 q^{23} -3.39723 q^{24} -4.08743 q^{25} -6.16017 q^{26} -4.75481 q^{27} +2.83381 q^{28} +6.01329 q^{29} +3.89217 q^{30} +1.00000 q^{31} +7.26583 q^{32} -4.62217 q^{33} +4.33061 q^{34} -0.955285 q^{35} +1.23051 q^{36} +1.00000 q^{37} -10.1047 q^{38} +5.19233 q^{39} +1.75123 q^{40} +11.5944 q^{41} -4.07436 q^{42} -12.9703 q^{43} -7.06809 q^{44} -0.414809 q^{45} -4.55221 q^{46} -7.24856 q^{47} -3.03392 q^{48} +1.00000 q^{49} +8.98659 q^{50} -3.65021 q^{51} +7.93996 q^{52} +7.71285 q^{53} +10.4539 q^{54} +2.38267 q^{55} -1.83320 q^{56} +8.51712 q^{57} -13.2208 q^{58} +4.95210 q^{59} -5.01669 q^{60} +5.30201 q^{61} -2.19859 q^{62} +0.434225 q^{63} -12.7003 q^{64} -2.67658 q^{65} +10.1623 q^{66} -2.90641 q^{67} -5.58180 q^{68} +3.83701 q^{69} +2.10028 q^{70} +9.73376 q^{71} -0.796022 q^{72} -7.47694 q^{73} -2.19859 q^{74} -7.57469 q^{75} +13.0241 q^{76} -2.49420 q^{77} -11.4158 q^{78} +1.83243 q^{79} +1.56395 q^{80} -10.1141 q^{81} -25.4915 q^{82} -9.79963 q^{83} +5.25152 q^{84} +1.88164 q^{85} +28.5165 q^{86} +11.1436 q^{87} +4.57237 q^{88} +1.93059 q^{89} +0.911995 q^{90} +2.80187 q^{91} +5.86743 q^{92} +1.85317 q^{93} +15.9366 q^{94} -4.39047 q^{95} +13.4648 q^{96} -15.1426 q^{97} -2.19859 q^{98} -1.08304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9}+O(q^{10}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9	\( 70 q + 5 q^{2} + 22 q^{3} + 71 q^{4} + 24 q^{5} + 9 q^{6} + 70 q^{7} + 9 q^{8} + 78 q^{9} + 4 q^{10} + 61 q^{11} + 49 q^{12} + 28 q^{13} + 5 q^{14} + 22 q^{15} + 73 q^{16} + 37 q^{17} + 8 q^{18} + 23 q^{19} + 45 q^{20} + 22 q^{21} - 10 q^{22} + 26 q^{23} + 3 q^{24} + 66 q^{25} + 57 q^{26} + 76 q^{27} + 71 q^{28} + 38 q^{29} - 14 q^{30} + 70 q^{31} - 2 q^{32} + 44 q^{33} + 34 q^{34} + 24 q^{35} + 46 q^{36} + 70 q^{37} + 21 q^{38} + 10 q^{39} + 13 q^{40} + 71 q^{41} + 9 q^{42} + 30 q^{43} + 108 q^{44} + 13 q^{45} - 14 q^{46} + 78 q^{47} + 85 q^{48} + 70 q^{49} - 12 q^{50} + 21 q^{51} + 23 q^{52} + 47 q^{53} + 17 q^{54} + 5 q^{55} + 9 q^{56} + 9 q^{57} + 8 q^{58} + 109 q^{59} - q^{60} + 41 q^{61} + 5 q^{62} + 78 q^{63} + 29 q^{64} + 36 q^{65} + 5 q^{66} + 23 q^{67} + 47 q^{68} + 8 q^{69} + 4 q^{70} + 99 q^{71} + 8 q^{72} + 33 q^{73} + 5 q^{74} + 94 q^{75} - 19 q^{76} + 61 q^{77} + 37 q^{78} + 52 q^{79} + 78 q^{80} + 102 q^{81} + 118 q^{83} + 49 q^{84} - 21 q^{85} + 74 q^{86} + 11 q^{87} - 21 q^{88} + 86 q^{89} - 7 q^{90} + 28 q^{91} + 14 q^{92} + 22 q^{93} + 35 q^{94} + 24 q^{95} - 40 q^{96} + 9 q^{97} + 5 q^{98} + 92 q^{99}+O(q^{100}) \) 70 * q + 5 * q^2 + 22 * q^3 + 71 * q^4 + 24 * q^5 + 9 * q^6 + 70 * q^7 + 9 * q^8 + 78 * q^9 + 4 * q^10 + 61 * q^11 + 49 * q^12 + 28 * q^13 + 5 * q^14 + 22 * q^15 + 73 * q^16 + 37 * q^17 + 8 * q^18 + 23 * q^19 + 45 * q^20 + 22 * q^21 - 10 * q^22 + 26 * q^23 + 3 * q^24 + 66 * q^25 + 57 * q^26 + 76 * q^27 + 71 * q^28 + 38 * q^29 - 14 * q^30 + 70 * q^31 - 2 * q^32 + 44 * q^33 + 34 * q^34 + 24 * q^35 + 46 * q^36 + 70 * q^37 + 21 * q^38 + 10 * q^39 + 13 * q^40 + 71 * q^41 + 9 * q^42 + 30 * q^43 + 108 * q^44 + 13 * q^45 - 14 * q^46 + 78 * q^47 + 85 * q^48 + 70 * q^49 - 12 * q^50 + 21 * q^51 + 23 * q^52 + 47 * q^53 + 17 * q^54 + 5 * q^55 + 9 * q^56 + 9 * q^57 + 8 * q^58 + 109 * q^59 - q^60 + 41 * q^61 + 5 * q^62 + 78 * q^63 + 29 * q^64 + 36 * q^65 + 5 * q^66 + 23 * q^67 + 47 * q^68 + 8 * q^69 + 4 * q^70 + 99 * q^71 + 8 * q^72 + 33 * q^73 + 5 * q^74 + 94 * q^75 - 19 * q^76 + 61 * q^77 + 37 * q^78 + 52 * q^79 + 78 * q^80 + 102 * q^81 + 118 * q^83 + 49 * q^84 - 21 * q^85 + 74 * q^86 + 11 * q^87 - 21 * q^88 + 86 * q^89 - 7 * q^90 + 28 * q^91 + 14 * q^92 + 22 * q^93 + 35 * q^94 + 24 * q^95 - 40 * q^96 + 9 * q^97 + 5 * q^98 + 92 * q^99

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