LMFDB - Embedded newform 8029.2.a.h.1.3

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:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.64917 q^{2} -3.09220 q^{3} +5.01811 q^{4} +0.332247 q^{5} +8.19178 q^{6} -1.00000 q^{7} -7.99549 q^{8} +6.56173 q^{9} +O(q^{10})$	\(q-2.64917 q^{2} -3.09220 q^{3} +5.01811 q^{4} +0.332247 q^{5} +8.19178 q^{6} -1.00000 q^{7} -7.99549 q^{8} +6.56173 q^{9} -0.880180 q^{10} +3.51676 q^{11} -15.5170 q^{12} -2.03365 q^{13} +2.64917 q^{14} -1.02738 q^{15} +11.1452 q^{16} +1.37911 q^{17} -17.3831 q^{18} -1.32531 q^{19} +1.66725 q^{20} +3.09220 q^{21} -9.31650 q^{22} -6.95898 q^{23} +24.7237 q^{24} -4.88961 q^{25} +5.38750 q^{26} -11.0136 q^{27} -5.01811 q^{28} -8.34849 q^{29} +2.72170 q^{30} -1.00000 q^{31} -13.5346 q^{32} -10.8745 q^{33} -3.65351 q^{34} -0.332247 q^{35} +32.9275 q^{36} +1.00000 q^{37} +3.51098 q^{38} +6.28847 q^{39} -2.65648 q^{40} +0.404567 q^{41} -8.19178 q^{42} -10.8628 q^{43} +17.6475 q^{44} +2.18012 q^{45} +18.4355 q^{46} -12.2788 q^{47} -34.4633 q^{48} +1.00000 q^{49} +12.9534 q^{50} -4.26450 q^{51} -10.2051 q^{52} -7.96572 q^{53} +29.1769 q^{54} +1.16843 q^{55} +7.99549 q^{56} +4.09813 q^{57} +22.1166 q^{58} +5.24437 q^{59} -5.15549 q^{60} -11.3502 q^{61} +2.64917 q^{62} -6.56173 q^{63} +13.5650 q^{64} -0.675676 q^{65} +28.8085 q^{66} +1.37546 q^{67} +6.92054 q^{68} +21.5186 q^{69} +0.880180 q^{70} +8.23059 q^{71} -52.4642 q^{72} -5.79846 q^{73} -2.64917 q^{74} +15.1197 q^{75} -6.65056 q^{76} -3.51676 q^{77} -16.6592 q^{78} -6.95533 q^{79} +3.70297 q^{80} +14.3711 q^{81} -1.07177 q^{82} -7.77384 q^{83} +15.5170 q^{84} +0.458207 q^{85} +28.7773 q^{86} +25.8152 q^{87} -28.1182 q^{88} -16.3150 q^{89} -5.77550 q^{90} +2.03365 q^{91} -34.9209 q^{92} +3.09220 q^{93} +32.5286 q^{94} -0.440331 q^{95} +41.8517 q^{96} -0.101583 q^{97} -2.64917 q^{98} +23.0760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−2.64917	−1.87325	−0.936624	−	0.350337i	$-0.886067\pi$
$2$	−2.64917	−1.87325	−0.936624	+	0.350337i	$0.886067\pi$
$3$	−3.09220	−1.78528	−0.892642	−	0.450766i	$-0.851151\pi$
$3$	−3.09220	−1.78528	−0.892642	+	0.450766i	$0.851151\pi$
$4$	5.01811	2.50906
$5$	0.332247	0.148586	0.0742928	−	0.997236i	$-0.476330\pi$
$5$	0.332247	0.148586	0.0742928	+	0.997236i	$0.476330\pi$
$6$	8.19178	3.34428
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.99549	−2.82683
$9$	6.56173	2.18724
$10$	−0.880180	−0.278337
$11$	3.51676	1.06034	0.530172	−	0.847890i	$-0.322128\pi$
$11$	3.51676	1.06034	0.530172	+	0.847890i	$0.322128\pi$
$12$	−15.5170	−4.47938
$13$	−2.03365	−0.564034	−0.282017	−	0.959409i	$-0.591004\pi$
$13$	−2.03365	−0.564034	−0.282017	+	0.959409i	$0.591004\pi$
$14$	2.64917	0.708021
$15$	−1.02738	−0.265267
$16$	11.1452	2.78630
$17$	1.37911	0.334484	0.167242	−	0.985916i	$-0.446514\pi$
$17$	1.37911	0.334484	0.167242	+	0.985916i	$0.446514\pi$
$18$	−17.3831	−4.09724
$19$	−1.32531	−0.304047	−0.152024	−	0.988377i	$-0.548579\pi$
$19$	−1.32531	−0.304047	−0.152024	+	0.988377i	$0.548579\pi$
$20$	1.66725	0.372809
$21$	3.09220	0.674774
$22$	−9.31650	−1.98628
$23$	−6.95898	−1.45105	−0.725524	−	0.688197i	$-0.758403\pi$
$23$	−6.95898	−1.45105	−0.725524	+	0.688197i	$0.758403\pi$
$24$	24.7237	5.04670
$25$	−4.88961	−0.977922
$26$	5.38750	1.05658
$27$	−11.0136	−2.11956
$28$	−5.01811	−0.948334
$29$	−8.34849	−1.55028	−0.775138	−	0.631792i	$-0.782320\pi$
$29$	−8.34849	−1.55028	−0.775138	+	0.631792i	$0.782320\pi$
$30$	2.72170	0.496912
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−13.5346	−2.39260
$33$	−10.8745	−1.89301
$34$	−3.65351	−0.626571
$35$	−0.332247	−0.0561600
$36$	32.9275	5.48791
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	3.51098	0.569556
$39$	6.28847	1.00696
$40$	−2.65648	−0.420027
$41$	0.404567	0.0631828	0.0315914	−	0.999501i	$-0.489942\pi$
$41$	0.404567	0.0631828	0.0315914	+	0.999501i	$0.489942\pi$
$42$	−8.19178	−1.26402
$43$	−10.8628	−1.65656	−0.828279	−	0.560316i	$-0.810680\pi$
$43$	−10.8628	−1.65656	−0.828279	+	0.560316i	$0.810680\pi$
$44$	17.6475	2.66046
$45$	2.18012	0.324992
$46$	18.4355	2.71817
$47$	−12.2788	−1.79105	−0.895523	−	0.445016i	$-0.853198\pi$
$47$	−12.2788	−1.79105	−0.895523	+	0.445016i	$0.853198\pi$
$48$	−34.4633	−4.97434
$49$	1.00000	0.142857
$50$	12.9534	1.83189
$51$	−4.26450	−0.597149
$52$	−10.2051	−1.41519
$53$	−7.96572	−1.09418	−0.547088	−	0.837075i	$-0.684264\pi$
$53$	−7.96572	−1.09418	−0.547088	+	0.837075i	$0.684264\pi$
$54$	29.1769	3.97047
$55$	1.16843	0.157552
$56$	7.99549	1.06844
$57$	4.09813	0.542811
$58$	22.1166	2.90405
$59$	5.24437	0.682759	0.341380	−	0.939925i	$-0.389106\pi$
$59$	5.24437	0.682759	0.341380	+	0.939925i	$0.389106\pi$
$60$	−5.15549	−0.665571
$61$	−11.3502	−1.45325	−0.726623	−	0.687036i	$-0.758911\pi$
$61$	−11.3502	−1.45325	−0.726623	+	0.687036i	$0.758911\pi$
$62$	2.64917	0.336445
$63$	−6.56173	−0.826700
$64$	13.5650	1.69563
$65$	−0.675676	−0.0838073
$66$	28.8085	3.54608
$67$	1.37546	0.168039	0.0840193	−	0.996464i	$-0.473224\pi$
$67$	1.37546	0.168039	0.0840193	+	0.996464i	$0.473224\pi$
$68$	6.92054	0.839239
$69$	21.5186	2.59053
$70$	0.880180	0.105202
$71$	8.23059	0.976791	0.488396	−	0.872622i	$-0.337582\pi$
$71$	8.23059	0.976791	0.488396	+	0.872622i	$0.337582\pi$
$72$	−52.4642	−6.18297
$73$	−5.79846	−0.678659	−0.339329	−	0.940668i	$-0.610200\pi$
$73$	−5.79846	−0.678659	−0.339329	+	0.940668i	$0.610200\pi$
$74$	−2.64917	−0.307960
$75$	15.1197	1.74587
$76$	−6.65056	−0.762871
$77$	−3.51676	−0.400772
$78$	−16.6592	−1.88629
$79$	−6.95533	−0.782536	−0.391268	−	0.920277i	$-0.627963\pi$
$79$	−6.95533	−0.782536	−0.391268	+	0.920277i	$0.627963\pi$
$80$	3.70297	0.414004
$81$	14.3711	1.59678
$82$	−1.07177	−0.118357
$83$	−7.77384	−0.853290	−0.426645	−	0.904419i	$-0.640305\pi$
$83$	−7.77384	−0.853290	−0.426645	+	0.904419i	$0.640305\pi$
$84$	15.5170	1.69305
$85$	0.458207	0.0496995
$86$	28.7773	3.10314
$87$	25.8152	2.76768
$88$	−28.1182	−2.99741
$89$	−16.3150	−1.72939	−0.864693	−	0.502301i	$-0.832487\pi$
$89$	−16.3150	−1.72939	−0.864693	+	0.502301i	$0.832487\pi$
$90$	−5.77550	−0.608791
$91$	2.03365	0.213185
$92$	−34.9209	−3.64076
$93$	3.09220	0.320647
$94$	32.5286	3.35507
$95$	−0.440331	−0.0451770
$96$	41.8517	4.27147
$97$	−0.101583	−0.0103142	−0.00515711	−	0.999987i	$-0.501642\pi$
$97$	−0.101583	−0.0103142	−0.00515711	+	0.999987i	$0.501642\pi$
$98$	−2.64917	−0.267607
$99$	23.0760	2.31923
$100$	−24.5366	−2.45366
$101$	−9.66687	−0.961890	−0.480945	−	0.876751i	$-0.659706\pi$
$101$	−9.66687	−0.961890	−0.480945	+	0.876751i	$0.659706\pi$
$102$	11.2974	1.11861
$103$	14.2680	1.40587	0.702936	−	0.711253i	$-0.251872\pi$
$103$	14.2680	1.40587	0.702936	+	0.711253i	$0.251872\pi$
$104$	16.2601	1.59443
$105$	1.02738	0.100262
$106$	21.1026	2.04966
$107$	18.9331	1.83033	0.915164	−	0.403082i	$-0.132061\pi$
$107$	18.9331	1.83033	0.915164	+	0.403082i	$0.132061\pi$
$108$	−55.2674	−5.31810
$109$	−9.07124	−0.868867	−0.434434	−	0.900704i	$-0.643051\pi$
$109$	−9.07124	−0.868867	−0.434434	+	0.900704i	$0.643051\pi$
$110$	−3.09538	−0.295133
$111$	−3.09220	−0.293499
$112$	−11.1452	−1.05312
$113$	8.31154	0.781884	0.390942	−	0.920415i	$-0.372149\pi$
$113$	8.31154	0.781884	0.390942	+	0.920415i	$0.372149\pi$
$114$	−10.8567	−1.01682
$115$	−2.31210	−0.215605
$116$	−41.8936	−3.88973
$117$	−13.3443	−1.23368
$118$	−13.8932	−1.27898
$119$	−1.37911	−0.126423
$120$	8.21438	0.749867
$121$	1.36760	0.124328
$122$	30.0687	2.72229
$123$	−1.25101	−0.112799
$124$	−5.01811	−0.450640
$125$	−3.28580	−0.293891
$126$	17.3831	1.54861
$127$	6.88031	0.610529	0.305265	−	0.952268i	$-0.401255\pi$
$127$	6.88031	0.610529	0.305265	+	0.952268i	$0.401255\pi$
$128$	−8.86693	−0.783733
$129$	33.5899	2.95743
$130$	1.78998	0.156992
$131$	14.9257	1.30407	0.652034	−	0.758190i	$-0.273916\pi$
$131$	14.9257	1.30407	0.652034	+	0.758190i	$0.273916\pi$
$132$	−54.5696	−4.74968
$133$	1.32531	0.114919
$134$	−3.64382	−0.314778
$135$	−3.65923	−0.314937
$136$	−11.0267	−0.945531
$137$	−4.68190	−0.400001	−0.200001	−	0.979796i	$-0.564094\pi$
$137$	−4.68190	−0.400001	−0.200001	+	0.979796i	$0.564094\pi$
$138$	−57.0065	−4.85271
$139$	−5.43750	−0.461203	−0.230601	−	0.973048i	$-0.574069\pi$
$139$	−5.43750	−0.461203	−0.230601	+	0.973048i	$0.574069\pi$
$140$	−1.66725	−0.140909
$141$	37.9685	3.19753
$142$	−21.8042	−1.82977
$143$	−7.15188	−0.598070
$144$	73.1318	6.09432
$145$	−2.77376	−0.230348
$146$	15.3611	1.27130
$147$	−3.09220	−0.255041
$148$	5.01811	0.412486
$149$	−0.692364	−0.0567207	−0.0283604	−	0.999598i	$-0.509029\pi$
$149$	−0.692364	−0.0567207	−0.0283604	+	0.999598i	$0.509029\pi$
$150$	−40.0546	−3.27045
$151$	7.31898	0.595611	0.297805	−	0.954627i	$-0.403745\pi$
$151$	7.31898	0.595611	0.297805	+	0.954627i	$0.403745\pi$
$152$	10.5965	0.859491
$153$	9.04936	0.731597
$154$	9.31650	0.750745
$155$	−0.332247	−0.0266867
$156$	31.5563	2.52652
$157$	12.8788	1.02784	0.513920	−	0.857838i	$-0.328193\pi$
$157$	12.8788	1.02784	0.513920	+	0.857838i	$0.328193\pi$
$158$	18.4259	1.46588
$159$	24.6316	1.95342
$160$	−4.49683	−0.355506
$161$	6.95898	0.548445
$162$	−38.0714	−2.99117
$163$	−3.62978	−0.284307	−0.142153	−	0.989845i	$-0.545403\pi$
$163$	−3.62978	−0.284307	−0.142153	+	0.989845i	$0.545403\pi$
$164$	2.03016	0.158529
$165$	−3.61304	−0.281275
$166$	20.5942	1.59842
$167$	−15.9155	−1.23158	−0.615790	−	0.787910i	$-0.711163\pi$
$167$	−15.9155	−1.23158	−0.615790	+	0.787910i	$0.711163\pi$
$168$	−24.7237	−1.90747
$169$	−8.86425	−0.681865
$170$	−1.21387	−0.0930994
$171$	−8.69633	−0.665025
$172$	−54.5106	−4.15639
$173$	−0.977548	−0.0743216	−0.0371608	−	0.999309i	$-0.511831\pi$
$173$	−0.977548	−0.0743216	−0.0371608	+	0.999309i	$0.511831\pi$
$174$	−68.3890	−5.18455
$175$	4.88961	0.369620
$176$	39.1950	2.95444
$177$	−16.2167	−1.21892
$178$	43.2212	3.23957
$179$	13.4008	1.00162	0.500811	−	0.865557i	$-0.333035\pi$
$179$	13.4008	1.00162	0.500811	+	0.865557i	$0.333035\pi$
$180$	10.9401	0.815424
$181$	−12.7553	−0.948094	−0.474047	−	0.880500i	$-0.657207\pi$
$181$	−12.7553	−0.948094	−0.474047	+	0.880500i	$0.657207\pi$
$182$	−5.38750	−0.399348
$183$	35.0972	2.59446
$184$	55.6405	4.10187
$185$	0.332247	0.0244273
$186$	−8.19178	−0.600650
$187$	4.85001	0.354668
$188$	−61.6163	−4.49383
$189$	11.0136	0.801120
$190$	1.16651	0.0846277
$191$	24.9451	1.80496	0.902482	−	0.430728i	$-0.141743\pi$
$191$	24.9451	1.80496	0.902482	+	0.430728i	$0.141743\pi$
$192$	−41.9459	−3.02718
$193$	1.12564	0.0810253	0.0405127	−	0.999179i	$-0.487101\pi$
$193$	1.12564	0.0810253	0.0405127	+	0.999179i	$0.487101\pi$
$194$	0.269112	0.0193211
$195$	2.08933	0.149620
$196$	5.01811	0.358436
$197$	22.4403	1.59881	0.799403	−	0.600795i	$-0.205149\pi$
$197$	22.4403	1.59881	0.799403	+	0.600795i	$0.205149\pi$
$198$	−61.1323	−4.34449
$199$	−25.7216	−1.82335	−0.911676	−	0.410909i	$-0.865211\pi$
$199$	−25.7216	−1.82335	−0.911676	+	0.410909i	$0.865211\pi$
$200$	39.0949	2.76442
$201$	−4.25319	−0.299997
$202$	25.6092	1.80186
$203$	8.34849	0.585949
$204$	−21.3997	−1.49828
$205$	0.134416	0.00938805
$206$	−37.7985	−2.63355
$207$	−45.6629	−3.17379
$208$	−22.6655	−1.57157
$209$	−4.66080	−0.322394
$210$	−2.72170	−0.187815
$211$	−6.28721	−0.432830	−0.216415	−	0.976302i	$-0.569436\pi$
$211$	−6.28721	−0.432830	−0.216415	+	0.976302i	$0.569436\pi$
$212$	−39.9729	−2.74535
$213$	−25.4507	−1.74385
$214$	−50.1569	−3.42866
$215$	−3.60913	−0.246140
$216$	88.0590	5.99166
$217$	1.00000	0.0678844
$218$	24.0313	1.62760
$219$	17.9300	1.21160
$220$	5.86333	0.395306
$221$	−2.80464	−0.188660
$222$	8.19178	0.549796
$223$	−3.86684	−0.258943	−0.129471	−	0.991583i	$-0.541328\pi$
$223$	−3.86684	−0.258943	−0.129471	+	0.991583i	$0.541328\pi$
$224$	13.5346	0.904318
$225$	−32.0843	−2.13895
$226$	−22.0187	−1.46466
$227$	−14.4626	−0.959916	−0.479958	−	0.877291i	$-0.659348\pi$
$227$	−14.4626	−0.959916	−0.479958	+	0.877291i	$0.659348\pi$
$228$	20.5649	1.36194
$229$	14.3280	0.946819	0.473410	−	0.880842i	$-0.343023\pi$
$229$	14.3280	0.946819	0.473410	+	0.880842i	$0.343023\pi$
$230$	6.12516	0.403881
$231$	10.8745	0.715492
$232$	66.7503	4.38237
$233$	−1.00605	−0.0659084	−0.0329542	−	0.999457i	$-0.510492\pi$
$233$	−1.00605	−0.0659084	−0.0329542	+	0.999457i	$0.510492\pi$
$234$	35.3513	2.31099
$235$	−4.07959	−0.266123
$236$	26.3168	1.71308
$237$	21.5073	1.39705
$238$	3.65351	0.236822
$239$	−8.16593	−0.528210	−0.264105	−	0.964494i	$-0.585077\pi$
$239$	−8.16593	−0.528210	−0.264105	+	0.964494i	$0.585077\pi$
$240$	−11.4503	−0.739115
$241$	13.6055	0.876409	0.438205	−	0.898875i	$-0.355615\pi$
$241$	13.6055	0.876409	0.438205	+	0.898875i	$0.355615\pi$
$242$	−3.62302	−0.232896
$243$	−11.3975	−0.731151
$244$	−56.9566	−3.64627
$245$	0.332247	0.0212265
$246$	3.31413	0.211301
$247$	2.69523	0.171493
$248$	7.99549	0.507714
$249$	24.0383	1.52337
$250$	8.70464	0.550530
$251$	19.9402	1.25862	0.629308	−	0.777156i	$-0.283338\pi$
$251$	19.9402	1.25862	0.629308	+	0.777156i	$0.283338\pi$
$252$	−32.9275	−2.07424
$253$	−24.4731	−1.53861
$254$	−18.2271	−1.14367
$255$	−1.41687	−0.0887277
$256$	−3.64006	−0.227504
$257$	22.7182	1.41712	0.708560	−	0.705650i	$-0.249345\pi$
$257$	22.7182	1.41712	0.708560	+	0.705650i	$0.249345\pi$
$258$	−88.9854	−5.53999
$259$	−1.00000	−0.0621370
$260$	−3.39062	−0.210277
$261$	−54.7805	−3.39083
$262$	−39.5408	−2.44284
$263$	22.8586	1.40952	0.704761	−	0.709445i	$-0.251054\pi$
$263$	22.8586	1.40952	0.704761	+	0.709445i	$0.251054\pi$
$264$	86.9473	5.35124
$265$	−2.64659	−0.162579
$266$	−3.51098	−0.215272
$267$	50.4493	3.08745
$268$	6.90219	0.421618
$269$	25.0382	1.52660	0.763302	−	0.646041i	$-0.223577\pi$
$269$	25.0382	1.52660	0.763302	+	0.646041i	$0.223577\pi$
$270$	9.69394	0.589954
$271$	−17.4542	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$271$	−17.4542	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$272$	15.3705	0.931974
$273$	−6.28847	−0.380596
$274$	12.4031	0.749301
$275$	−17.1956	−1.03693
$276$	107.983	6.49979
$277$	−28.9181	−1.73752	−0.868761	−	0.495231i	$-0.835083\pi$
$277$	−28.9181	−1.73752	−0.868761	+	0.495231i	$0.835083\pi$
$278$	14.4049	0.863947
$279$	−6.56173	−0.392840
$280$	2.65648	0.158755
$281$	−11.7737	−0.702359	−0.351179	−	0.936308i	$-0.614219\pi$
$281$	−11.7737	−0.702359	−0.351179	+	0.936308i	$0.614219\pi$
$282$	−100.585	−5.98976
$283$	−24.9817	−1.48501	−0.742504	−	0.669841i	$-0.766362\pi$
$283$	−24.9817	−1.48501	−0.742504	+	0.669841i	$0.766362\pi$
$284$	41.3020	2.45082
$285$	1.36159	0.0806539
$286$	18.9465	1.12033
$287$	−0.404567	−0.0238809
$288$	−88.8103	−5.23320
$289$	−15.0980	−0.888120
$290$	7.34817	0.431500
$291$	0.314116	0.0184138
$292$	−29.0973	−1.70279
$293$	−28.9594	−1.69183	−0.845914	−	0.533319i	$-0.820944\pi$
$293$	−28.9594	−1.69183	−0.845914	+	0.533319i	$0.820944\pi$
$294$	8.19178	0.477754
$295$	1.74243	0.101448
$296$	−7.99549	−0.464729
$297$	−38.7321	−2.24747
$298$	1.83419	0.106252
$299$	14.1522	0.818441
$300$	75.8722	4.38048
$301$	10.8628	0.626120
$302$	−19.3892	−1.11573
$303$	29.8919	1.71725
$304$	−14.7709	−0.847168
$305$	−3.77108	−0.215931
$306$	−23.9733	−1.37046
$307$	29.4250	1.67937	0.839687	−	0.543071i	$-0.182739\pi$
$307$	29.4250	1.67937	0.839687	+	0.543071i	$0.182739\pi$
$308$	−17.6475	−1.00556
$309$	−44.1197	−2.50988
$310$	0.880180	0.0499909
$311$	−18.2674	−1.03585	−0.517925	−	0.855426i	$-0.673295\pi$
$311$	−18.2674	−1.03585	−0.517925	+	0.855426i	$0.673295\pi$
$312$	−50.2795	−2.84651
$313$	−26.9553	−1.52360	−0.761801	−	0.647811i	$-0.775684\pi$
$313$	−26.9553	−1.52360	−0.761801	+	0.647811i	$0.775684\pi$
$314$	−34.1181	−1.92540
$315$	−2.18012	−0.122836
$316$	−34.9026	−1.96342
$317$	6.42876	0.361075	0.180538	−	0.983568i	$-0.442216\pi$
$317$	6.42876	0.361075	0.180538	+	0.983568i	$0.442216\pi$
$318$	−65.2534	−3.65923
$319$	−29.3596	−1.64382
$320$	4.50695	0.251946
$321$	−58.5449	−3.26766
$322$	−18.4355	−1.02737
$323$	−1.82775	−0.101699
$324$	72.1156	4.00642
$325$	9.94378	0.551582
$326$	9.61592	0.532577
$327$	28.0501	1.55118
$328$	−3.23472	−0.178607
$329$	12.2788	0.676951
$330$	9.57155	0.526897
$331$	5.52628	0.303752	0.151876	−	0.988400i	$-0.451469\pi$
$331$	5.52628	0.303752	0.151876	+	0.988400i	$0.451469\pi$
$332$	−39.0100	−2.14095
$333$	6.56173	0.359580
$334$	42.1629	2.30705
$335$	0.456991	0.0249681
$336$	34.4633	1.88013
$337$	−17.2463	−0.939467	−0.469734	−	0.882808i	$-0.655650\pi$
$337$	−17.2463	−0.939467	−0.469734	+	0.882808i	$0.655650\pi$
$338$	23.4829	1.27730
$339$	−25.7010	−1.39589
$340$	2.29933	0.124699
$341$	−3.51676	−0.190443
$342$	23.0381	1.24576
$343$	−1.00000	−0.0539949
$344$	86.8532	4.68281
$345$	7.14950	0.384916
$346$	2.58969	0.139223
$347$	12.5908	0.675912	0.337956	−	0.941162i	$-0.390264\pi$
$347$	12.5908	0.675912	0.337956	+	0.941162i	$0.390264\pi$
$348$	129.544	6.94427
$349$	−8.22964	−0.440522	−0.220261	−	0.975441i	$-0.570691\pi$
$349$	−8.22964	−0.440522	−0.220261	+	0.975441i	$0.570691\pi$
$350$	−12.9534	−0.692389
$351$	22.3978	1.19551
$352$	−47.5979	−2.53698
$353$	−12.5323	−0.667029	−0.333515	−	0.942745i	$-0.608235\pi$
$353$	−12.5323	−0.667029	−0.333515	+	0.942745i	$0.608235\pi$
$354$	42.9608	2.28334
$355$	2.73459	0.145137
$356$	−81.8704	−4.33912
$357$	4.26450	0.225701
$358$	−35.5010	−1.87629
$359$	−26.6723	−1.40771	−0.703854	−	0.710344i	$-0.748539\pi$
$359$	−26.6723	−1.40771	−0.703854	+	0.710344i	$0.748539\pi$
$360$	−17.4311	−0.918700
$361$	−17.2435	−0.907555
$362$	33.7910	1.77601
$363$	−4.22891	−0.221960
$364$	10.2051	0.534893
$365$	−1.92652	−0.100839
$366$	−92.9784	−4.86006
$367$	−2.09603	−0.109412	−0.0547058	−	0.998503i	$-0.517422\pi$
$367$	−2.09603	−0.109412	−0.0547058	+	0.998503i	$0.517422\pi$
$368$	−77.5593	−4.04306
$369$	2.65466	0.138196
$370$	−0.880180	−0.0457584
$371$	7.96572	0.413560
$372$	15.5170	0.804520
$373$	31.2100	1.61599	0.807996	−	0.589187i	$-0.200552\pi$
$373$	31.2100	1.61599	0.807996	+	0.589187i	$0.200552\pi$
$374$	−12.8485	−0.664381
$375$	10.1604	0.524678
$376$	98.1750	5.06299
$377$	16.9779	0.874408
$378$	−29.1769	−1.50070
$379$	−12.6463	−0.649596	−0.324798	−	0.945783i	$-0.605296\pi$
$379$	−12.6463	−0.649596	−0.324798	+	0.945783i	$0.605296\pi$
$380$	−2.20963	−0.113352
$381$	−21.2753	−1.08997
$382$	−66.0838	−3.38114
$383$	22.5854	1.15406	0.577029	−	0.816724i	$-0.304212\pi$
$383$	22.5854	1.15406	0.577029	+	0.816724i	$0.304212\pi$
$384$	27.4183	1.39919
$385$	−1.16843	−0.0595489
$386$	−2.98201	−0.151780
$387$	−71.2785	−3.62329
$388$	−0.509756	−0.0258789
$389$	−33.0025	−1.67330	−0.836648	−	0.547741i	$-0.815488\pi$
$389$	−33.0025	−1.67330	−0.836648	+	0.547741i	$0.815488\pi$
$390$	−5.53499	−0.280275
$391$	−9.59723	−0.485353
$392$	−7.99549	−0.403833
$393$	−46.1534	−2.32813
$394$	−59.4482	−2.99496
$395$	−2.31089	−0.116273
$396$	115.798	5.81907
$397$	25.0007	1.25475	0.627374	−	0.778718i	$-0.284130\pi$
$397$	25.0007	1.25475	0.627374	+	0.778718i	$0.284130\pi$
$398$	68.1408	3.41559
$399$	−4.09813	−0.205163
$400$	−54.4958	−2.72479
$401$	23.1419	1.15565	0.577826	−	0.816160i	$-0.303901\pi$
$401$	23.1419	1.15565	0.577826	+	0.816160i	$0.303901\pi$
$402$	11.2674	0.561968
$403$	2.03365	0.101304
$404$	−48.5094	−2.41343
$405$	4.77475	0.237259
$406$	−22.1166	−1.09763
$407$	3.51676	0.174319
$408$	34.0968	1.68804
$409$	−32.7096	−1.61738	−0.808692	−	0.588233i	$-0.799824\pi$
$409$	−32.7096	−1.61738	−0.808692	+	0.588233i	$0.799824\pi$
$410$	−0.356092	−0.0175861
$411$	14.4774	0.714116
$412$	71.5986	3.52741
$413$	−5.24437	−0.258059
$414$	120.969	5.94530
$415$	−2.58284	−0.126787
$416$	27.5247	1.34951
$417$	16.8139	0.823378
$418$	12.3473	0.603925
$419$	13.4571	0.657424	0.328712	−	0.944430i	$-0.393385\pi$
$419$	13.4571	0.657424	0.328712	+	0.944430i	$0.393385\pi$
$420$	5.15549	0.251562
$421$	−15.1314	−0.737460	−0.368730	−	0.929537i	$-0.620207\pi$
$421$	−15.1314	−0.737460	−0.368730	+	0.929537i	$0.620207\pi$
$422$	16.6559	0.810797
$423$	−80.5700	−3.91745
$424$	63.6899	3.09305
$425$	−6.74333	−0.327099
$426$	67.4232	3.26666
$427$	11.3502	0.549275
$428$	95.0082	4.59239
$429$	22.1151	1.06773
$430$	9.56120	0.461082
$431$	20.2591	0.975848	0.487924	−	0.872886i	$-0.337754\pi$
$431$	20.2591	0.975848	0.487924	+	0.872886i	$0.337754\pi$
$432$	−122.749	−5.90575
$433$	−21.0884	−1.01344	−0.506722	−	0.862110i	$-0.669143\pi$
$433$	−21.0884	−1.01344	−0.506722	+	0.862110i	$0.669143\pi$
$434$	−2.64917	−0.127164
$435$	8.57704	0.411238
$436$	−45.5205	−2.18004
$437$	9.22282	0.441187
$438$	−47.4997	−2.26962
$439$	0.647846	0.0309200	0.0154600	−	0.999880i	$-0.495079\pi$
$439$	0.647846	0.0309200	0.0154600	+	0.999880i	$0.495079\pi$
$440$	−9.34221	−0.445372
$441$	6.56173	0.312463
$442$	7.42997	0.353408
$443$	6.78675	0.322448	0.161224	−	0.986918i	$-0.448456\pi$
$443$	6.78675	0.322448	0.161224	+	0.986918i	$0.448456\pi$
$444$	−15.5170	−0.736405
$445$	−5.42061	−0.256962
$446$	10.2439	0.485064
$447$	2.14093	0.101263
$448$	−13.5650	−0.640888
$449$	−2.65595	−0.125342	−0.0626710	−	0.998034i	$-0.519962\pi$
$449$	−2.65595	−0.125342	−0.0626710	+	0.998034i	$0.519962\pi$
$450$	84.9968	4.00679
$451$	1.42277	0.0669955
$452$	41.7083	1.96179
$453$	−22.6318	−1.06333
$454$	38.3139	1.79816
$455$	0.675676	0.0316762
$456$	−32.7666	−1.53444
$457$	23.4156	1.09534	0.547668	−	0.836696i	$-0.315516\pi$
$457$	23.4156	1.09534	0.547668	+	0.836696i	$0.315516\pi$
$458$	−37.9573	−1.77363
$459$	−15.1890	−0.708961
$460$	−11.6024	−0.540964
$461$	−29.0280	−1.35197	−0.675986	−	0.736915i	$-0.736282\pi$
$461$	−29.0280	−1.35197	−0.675986	+	0.736915i	$0.736282\pi$
$462$	−28.8085	−1.34029
$463$	2.01081	0.0934501	0.0467251	−	0.998908i	$-0.485122\pi$
$463$	2.01081	0.0934501	0.0467251	+	0.998908i	$0.485122\pi$
$464$	−93.0457	−4.31954
$465$	1.02738	0.0476434
$466$	2.66519	0.123463
$467$	−11.2867	−0.522285	−0.261142	−	0.965300i	$-0.584099\pi$
$467$	−11.2867	−0.522285	−0.261142	+	0.965300i	$0.584099\pi$
$468$	−66.9631	−3.09537
$469$	−1.37546	−0.0635126
$470$	10.8075	0.498515
$471$	−39.8238	−1.83499
$472$	−41.9314	−1.93005
$473$	−38.2018	−1.75652
$474$	−56.9765	−2.61702
$475$	6.48026	0.297335
$476$	−6.92054	−0.317203
$477$	−52.2689	−2.39323
$478$	21.6330	0.989468
$479$	−13.3321	−0.609157	−0.304579	−	0.952487i	$-0.598516\pi$
$479$	−13.3321	−0.609157	−0.304579	+	0.952487i	$0.598516\pi$
$480$	13.9051	0.634679
$481$	−2.03365	−0.0927267
$482$	−36.0434	−1.64173
$483$	−21.5186	−0.979130
$484$	6.86279	0.311945
$485$	−0.0337508	−0.00153254
$486$	30.1940	1.36963
$487$	2.98509	0.135267	0.0676337	−	0.997710i	$-0.478455\pi$
$487$	2.98509	0.135267	0.0676337	+	0.997710i	$0.478455\pi$
$488$	90.7506	4.10808
$489$	11.2240	0.507568
$490$	−0.880180	−0.0397625
$491$	35.1033	1.58419	0.792094	−	0.610399i	$-0.208991\pi$
$491$	35.1033	1.58419	0.792094	+	0.610399i	$0.208991\pi$
$492$	−6.27768	−0.283020
$493$	−11.5135	−0.518542
$494$	−7.14011	−0.321249
$495$	7.66694	0.344604
$496$	−11.1452	−0.500435
$497$	−8.23059	−0.369192
$498$	−63.6816	−2.85364
$499$	15.3434	0.686866	0.343433	−	0.939177i	$-0.388410\pi$
$499$	15.3434	0.686866	0.343433	+	0.939177i	$0.388410\pi$
$500$	−16.4885	−0.737388
$501$	49.2140	2.19872
$502$	−52.8251	−2.35770
$503$	2.40954	0.107436	0.0537181	−	0.998556i	$-0.482893\pi$
$503$	2.40954	0.107436	0.0537181	+	0.998556i	$0.482893\pi$
$504$	52.4642	2.33694
$505$	−3.21179	−0.142923
$506$	64.8334	2.88220
$507$	27.4101	1.21732
$508$	34.5262	1.53185
$509$	−1.46724	−0.0650342	−0.0325171	−	0.999471i	$-0.510352\pi$
$509$	−1.46724	−0.0650342	−0.0325171	+	0.999471i	$0.510352\pi$
$510$	3.75353	0.166209
$511$	5.79846	0.256509
$512$	27.3770	1.20990
$513$	14.5964	0.644448
$514$	−60.1843	−2.65462
$515$	4.74052	0.208892
$516$	168.558	7.42035
$517$	−43.1816	−1.89912
$518$	2.64917	0.116398
$519$	3.02278	0.132685
$520$	5.40236	0.236909
$521$	−20.3572	−0.891864	−0.445932	−	0.895067i	$-0.647128\pi$
$521$	−20.3572	−0.891864	−0.445932	+	0.895067i	$0.647128\pi$
$522$	145.123	6.35186
$523$	−1.66192	−0.0726707	−0.0363353	−	0.999340i	$-0.511568\pi$
$523$	−1.66192	−0.0726707	−0.0363353	+	0.999340i	$0.511568\pi$
$524$	74.8990	3.27198
$525$	−15.1197	−0.659877
$526$	−60.5564	−2.64038
$527$	−1.37911	−0.0600751
$528$	−121.199	−5.27451
$529$	25.4275	1.10554
$530$	7.01127	0.304550
$531$	34.4121	1.49336
$532$	6.65056	0.288338
$533$	−0.822750	−0.0356373
$534$	−133.649	−5.78355
$535$	6.29046	0.271960
$536$	−10.9974	−0.475017
$537$	−41.4380	−1.78818
$538$	−66.3304	−2.85971
$539$	3.51676	0.151478
$540$	−18.3624	−0.790193
$541$	−0.0543392	−0.00233623	−0.00116811	−	0.999999i	$-0.500372\pi$
$541$	−0.0543392	−0.00233623	−0.00116811	+	0.999999i	$0.500372\pi$
$542$	46.2390	1.98614
$543$	39.4420	1.69262
$544$	−18.6657	−0.800287
$545$	−3.01390	−0.129101
$546$	16.6592	0.712950
$547$	27.9643	1.19567	0.597834	−	0.801620i	$-0.296028\pi$
$547$	27.9643	1.19567	0.597834	+	0.801620i	$0.296028\pi$
$548$	−23.4943	−1.00363
$549$	−74.4770	−3.17860
$550$	45.5541	1.94243
$551$	11.0643	0.471357
$552$	−172.052	−7.32301
$553$	6.95533	0.295771
$554$	76.6091	3.25481
$555$	−1.02738	−0.0436097
$556$	−27.2860	−1.15718
$557$	38.3042	1.62300	0.811500	−	0.584353i	$-0.198652\pi$
$557$	38.3042	1.62300	0.811500	+	0.584353i	$0.198652\pi$
$558$	17.3831	0.735887
$559$	22.0911	0.934355
$560$	−3.70297	−0.156479
$561$	−14.9972	−0.633183
$562$	31.1905	1.31569
$563$	−31.6516	−1.33395	−0.666977	−	0.745078i	$-0.732412\pi$
$563$	−31.6516	−1.33395	−0.666977	+	0.745078i	$0.732412\pi$
$564$	190.530	8.02277
$565$	2.76149	0.116177
$566$	66.1808	2.78179
$567$	−14.3711	−0.603528
$568$	−65.8076	−2.76123
$569$	11.0779	0.464408	0.232204	−	0.972667i	$-0.425406\pi$
$569$	11.0779	0.464408	0.232204	+	0.972667i	$0.425406\pi$
$570$	−3.60710	−0.151085
$571$	7.95818	0.333039	0.166520	−	0.986038i	$-0.446747\pi$
$571$	7.95818	0.333039	0.166520	+	0.986038i	$0.446747\pi$
$572$	−35.8889	−1.50059
$573$	−77.1353	−3.22237
$574$	1.07177	0.0447348
$575$	34.0267	1.41901
$576$	89.0100	3.70875
$577$	−8.13416	−0.338630	−0.169315	−	0.985562i	$-0.554155\pi$
$577$	−8.13416	−0.338630	−0.169315	+	0.985562i	$0.554155\pi$
$578$	39.9973	1.66367
$579$	−3.48071	−0.144653
$580$	−13.9190	−0.577957
$581$	7.77384	0.322513
$582$	−0.832148	−0.0344936
$583$	−28.0135	−1.16020
$584$	46.3616	1.91845
$585$	−4.43360	−0.183307
$586$	76.7185	3.16921
$587$	−30.9032	−1.27551	−0.637757	−	0.770238i	$-0.720137\pi$
$587$	−30.9032	−1.27551	−0.637757	+	0.770238i	$0.720137\pi$
$588$	−15.5170	−0.639911
$589$	1.32531	0.0546085
$590$	−4.61599	−0.190037
$591$	−69.3900	−2.85432
$592$	11.1452	0.458065
$593$	13.1710	0.540869	0.270434	−	0.962738i	$-0.412833\pi$
$593$	13.1710	0.540869	0.270434	+	0.962738i	$0.412833\pi$
$594$	102.608	4.21006
$595$	−0.458207	−0.0187846
$596$	−3.47436	−0.142315
$597$	79.5363	3.25520
$598$	−37.4915	−1.53314
$599$	25.3900	1.03741	0.518703	−	0.854954i	$-0.326415\pi$
$599$	25.3900	1.03741	0.518703	+	0.854954i	$0.326415\pi$
$600$	−120.889	−4.93528
$601$	35.9483	1.46636	0.733181	−	0.680033i	$-0.238035\pi$
$601$	35.9483	1.46636	0.733181	+	0.680033i	$0.238035\pi$
$602$	−28.7773	−1.17288
$603$	9.02536	0.367541
$604$	36.7275	1.49442
$605$	0.454383	0.0184733
$606$	−79.1889	−3.21683
$607$	−24.0500	−0.976158	−0.488079	−	0.872799i	$-0.662302\pi$
$607$	−24.0500	−0.976158	−0.488079	+	0.872799i	$0.662302\pi$
$608$	17.9376	0.727464
$609$	−25.8152	−1.04609
$610$	9.99023	0.404493
$611$	24.9708	1.01021
$612$	45.4107	1.83562
$613$	10.9867	0.443751	0.221875	−	0.975075i	$-0.428782\pi$
$613$	10.9867	0.443751	0.221875	+	0.975075i	$0.428782\pi$
$614$	−77.9519	−3.14588
$615$	−0.415643	−0.0167603
$616$	28.1182	1.13292
$617$	30.2388	1.21737	0.608684	−	0.793413i	$-0.291698\pi$
$617$	30.2388	1.21737	0.608684	+	0.793413i	$0.291698\pi$
$618$	116.881	4.70163
$619$	25.2696	1.01567	0.507835	−	0.861454i	$-0.330446\pi$
$619$	25.2696	1.01567	0.507835	+	0.861454i	$0.330446\pi$
$620$	−1.66725	−0.0669585
$621$	76.6433	3.07559
$622$	48.3935	1.94040
$623$	16.3150	0.653646
$624$	70.0864	2.80570
$625$	23.3564	0.934254
$626$	71.4091	2.85408
$627$	14.4122	0.575566
$628$	64.6272	2.57891
$629$	1.37911	0.0549888
$630$	5.77550	0.230101
$631$	−2.10078	−0.0836309	−0.0418154	−	0.999125i	$-0.513314\pi$
$631$	−2.10078	−0.0836309	−0.0418154	+	0.999125i	$0.513314\pi$
$632$	55.6113	2.21210
$633$	19.4413	0.772724
$634$	−17.0309	−0.676383
$635$	2.28597	0.0907158
$636$	123.604	4.90123
$637$	−2.03365	−0.0805763
$638$	77.7787	3.07929
$639$	54.0069	2.13648
$640$	−2.94601	−0.116451
$641$	24.5178	0.968393	0.484197	−	0.874959i	$-0.339112\pi$
$641$	24.5178	0.968393	0.484197	+	0.874959i	$0.339112\pi$
$642$	155.095	6.12113
$643$	−47.4250	−1.87026	−0.935129	−	0.354307i	$-0.884717\pi$
$643$	−47.4250	−1.87026	−0.935129	+	0.354307i	$0.884717\pi$
$644$	34.9209	1.37608
$645$	11.1602	0.439431
$646$	4.84203	0.190507
$647$	38.0251	1.49492	0.747460	−	0.664307i	$-0.231273\pi$
$647$	38.0251	1.49492	0.747460	+	0.664307i	$0.231273\pi$
$648$	−114.904	−4.51384
$649$	18.4432	0.723959
$650$	−26.3428	−1.03325
$651$	−3.09220	−0.121193
$652$	−18.2147	−0.713341
$653$	28.7804	1.12626	0.563131	−	0.826367i	$-0.309597\pi$
$653$	28.7804	1.12626	0.563131	+	0.826367i	$0.309597\pi$
$654$	−74.3096	−2.90574
$655$	4.95904	0.193766
$656$	4.50899	0.176046
$657$	−38.0479	−1.48439
$658$	−32.5286	−1.26810
$659$	−29.6045	−1.15323	−0.576613	−	0.817017i	$-0.695626\pi$
$659$	−29.6045	−1.15323	−0.576613	+	0.817017i	$0.695626\pi$
$660$	−18.1306	−0.705733
$661$	19.0567	0.741219	0.370609	−	0.928789i	$-0.379149\pi$
$661$	19.0567	0.741219	0.370609	+	0.928789i	$0.379149\pi$
$662$	−14.6401	−0.569002
$663$	8.67252	0.336813
$664$	62.1557	2.41211
$665$	0.440331	0.0170753
$666$	−17.3831	−0.673583
$667$	58.0970	2.24952
$668$	−79.8658	−3.09010
$669$	11.9571	0.462287
$670$	−1.21065	−0.0467714
$671$	−39.9160	−1.54094
$672$	−41.8517	−1.61447
$673$	25.0942	0.967312	0.483656	−	0.875258i	$-0.339309\pi$
$673$	25.0942	0.967312	0.483656	+	0.875258i	$0.339309\pi$
$674$	45.6885	1.75985
$675$	53.8521	2.07277
$676$	−44.4818	−1.71084
$677$	−6.68962	−0.257103	−0.128551	−	0.991703i	$-0.541033\pi$
$677$	−6.68962	−0.257103	−0.128551	+	0.991703i	$0.541033\pi$
$678$	68.0863	2.61484
$679$	0.101583	0.00389841
$680$	−3.66359	−0.140492
$681$	44.7213	1.71372
$682$	9.31650	0.356747
$683$	3.88222	0.148549	0.0742745	−	0.997238i	$-0.476336\pi$
$683$	3.88222	0.148549	0.0742745	+	0.997238i	$0.476336\pi$
$684$	−43.6391	−1.66858
$685$	−1.55555	−0.0594344
$686$	2.64917	0.101146
$687$	−44.3050	−1.69034
$688$	−121.068	−4.61567
$689$	16.1995	0.617153
$690$	−18.9402	−0.721043
$691$	17.3395	0.659626	0.329813	−	0.944046i	$-0.393014\pi$
$691$	17.3395	0.659626	0.329813	+	0.944046i	$0.393014\pi$
$692$	−4.90544	−0.186477
$693$	−23.0760	−0.876585
$694$	−33.3553	−1.26615
$695$	−1.80659	−0.0685281
$696$	−206.405	−7.82378
$697$	0.557944	0.0211336
$698$	21.8017	0.825207
$699$	3.11090	0.117665
$700$	24.5366	0.927397
$701$	15.2104	0.574488	0.287244	−	0.957857i	$-0.407261\pi$
$701$	15.2104	0.574488	0.287244	+	0.957857i	$0.407261\pi$
$702$	−59.3357	−2.23948
$703$	−1.32531	−0.0499851
$704$	47.7050	1.79795
$705$	12.6149	0.475106
$706$	33.2003	1.24951
$707$	9.66687	0.363560
$708$	−81.3771	−3.05834
$709$	34.1748	1.28346	0.641730	−	0.766930i	$-0.278217\pi$
$709$	34.1748	1.28346	0.641730	+	0.766930i	$0.278217\pi$
$710$	−7.24440	−0.271878
$711$	−45.6389	−1.71159
$712$	130.446	4.88869
$713$	6.95898	0.260616
$714$	−11.2974	−0.422794
$715$	−2.37619	−0.0888645
$716$	67.2467	2.51313
$717$	25.2507	0.943006
$718$	70.6594	2.63699
$719$	−7.15244	−0.266741	−0.133370	−	0.991066i	$-0.542580\pi$
$719$	−7.15244	−0.266741	−0.133370	+	0.991066i	$0.542580\pi$
$720$	24.2978	0.905527
$721$	−14.2680	−0.531370
$722$	45.6811	1.70008
$723$	−42.0711	−1.56464
$724$	−64.0075	−2.37882
$725$	40.8209	1.51605
$726$	11.2031	0.415786
$727$	−30.9354	−1.14733	−0.573665	−	0.819090i	$-0.694479\pi$
$727$	−30.9354	−1.14733	−0.573665	+	0.819090i	$0.694479\pi$
$728$	−16.2601	−0.602638
$729$	−7.86976	−0.291473
$730$	5.10369	0.188896
$731$	−14.9810	−0.554092
$732$	176.122	6.50964
$733$	0.382900	0.0141427	0.00707137	−	0.999975i	$-0.497749\pi$
$733$	0.382900	0.0141427	0.00707137	+	0.999975i	$0.497749\pi$
$734$	5.55273	0.204955
$735$	−1.02738	−0.0378954
$736$	94.1870	3.47178
$737$	4.83715	0.178179
$738$	−7.03265	−0.258875
$739$	−25.2668	−0.929456	−0.464728	−	0.885454i	$-0.653848\pi$
$739$	−25.2668	−0.929456	−0.464728	+	0.885454i	$0.653848\pi$
$740$	1.66725	0.0612895
$741$	−8.33419	−0.306164
$742$	−21.1026	−0.774700
$743$	6.12144	0.224574	0.112287	−	0.993676i	$-0.464182\pi$
$743$	6.12144	0.224574	0.112287	+	0.993676i	$0.464182\pi$
$744$	−24.7237	−0.906415
$745$	−0.230036	−0.00842787
$746$	−82.6807	−3.02715
$747$	−51.0098	−1.86635
$748$	24.3379	0.889881
$749$	−18.9331	−0.691799
$750$	−26.9165	−0.982852
$751$	−4.93306	−0.180010	−0.0900049	−	0.995941i	$-0.528688\pi$
$751$	−4.93306	−0.180010	−0.0900049	+	0.995941i	$0.528688\pi$
$752$	−136.850	−4.99039
$753$	−61.6593	−2.24699
$754$	−44.9775	−1.63798
$755$	2.43171	0.0884991
$756$	55.2674	2.01005
$757$	−25.5972	−0.930347	−0.465173	−	0.885220i	$-0.654008\pi$
$757$	−25.5972	−0.930347	−0.465173	+	0.885220i	$0.654008\pi$
$758$	33.5022	1.21685
$759$	75.6757	2.74686
$760$	3.52066	0.127708
$761$	3.92406	0.142247	0.0711235	−	0.997468i	$-0.477342\pi$
$761$	3.92406	0.142247	0.0711235	+	0.997468i	$0.477342\pi$
$762$	56.3620	2.04178
$763$	9.07124	0.328401
$764$	125.177	4.52875
$765$	3.00663	0.108705
$766$	−59.8325	−2.16184
$767$	−10.6652	−0.385100
$768$	11.2558	0.406159
$769$	32.8817	1.18575	0.592873	−	0.805296i	$-0.297994\pi$
$769$	32.8817	1.18575	0.592873	+	0.805296i	$0.297994\pi$
$770$	3.09538	0.111550
$771$	−70.2492	−2.52996
$772$	5.64858	0.203297
$773$	6.51112	0.234189	0.117094	−	0.993121i	$-0.462642\pi$
$773$	6.51112	0.234189	0.117094	+	0.993121i	$0.462642\pi$
$774$	188.829	6.78732
$775$	4.88961	0.175640
$776$	0.812208	0.0291566
$777$	3.09220	0.110932
$778$	87.4294	3.13450
$779$	−0.536178	−0.0192106
$780$	10.4845	0.375405
$781$	28.9450	1.03573
$782$	25.4247	0.909185
$783$	91.9467	3.28591
$784$	11.1452	0.398043
$785$	4.27894	0.152722
$786$	122.268	4.36117
$787$	−42.8800	−1.52851	−0.764253	−	0.644917i	$-0.776892\pi$
$787$	−42.8800	−1.52851	−0.764253	+	0.644917i	$0.776892\pi$
$788$	112.608	4.01149
$789$	−70.6835	−2.51640
$790$	6.12194	0.217809
$791$	−8.31154	−0.295525
$792$	−184.504	−6.55607
$793$	23.0824	0.819681
$794$	−66.2311	−2.35045
$795$	8.18380	0.290249
$796$	−129.074	−4.57489
$797$	−9.50389	−0.336645	−0.168323	−	0.985732i	$-0.553835\pi$
$797$	−9.50389	−0.336645	−0.168323	+	0.985732i	$0.553835\pi$
$798$	10.8567	0.384322
$799$	−16.9338	−0.599076
$800$	66.1789	2.33978
$801$	−107.055	−3.78258
$802$	−61.3068	−2.16482
$803$	−20.3918	−0.719611
$804$	−21.3430	−0.752708
$805$	2.31210	0.0814909
$806$	−5.38750	−0.189767
$807$	−77.4232	−2.72542
$808$	77.2914	2.71910
$809$	−47.0866	−1.65548	−0.827738	−	0.561115i	$-0.810373\pi$
$809$	−47.0866	−1.65548	−0.827738	+	0.561115i	$0.810373\pi$
$810$	−12.6491	−0.444445
$811$	0.423793	0.0148814	0.00744069	−	0.999972i	$-0.497632\pi$
$811$	0.423793	0.0148814	0.00744069	+	0.999972i	$0.497632\pi$
$812$	41.8936	1.47018
$813$	53.9718	1.89287
$814$	−9.31650	−0.326543
$815$	−1.20599	−0.0422438
$816$	−47.5287	−1.66384
$817$	14.3966	0.503672
$818$	86.6532	3.02976
$819$	13.3443	0.466287
$820$	0.674517	0.0235551
$821$	17.3185	0.604420	0.302210	−	0.953241i	$-0.402276\pi$
$821$	17.3185	0.604420	0.302210	+	0.953241i	$0.402276\pi$
$822$	−38.3531	−1.33772
$823$	−23.0195	−0.802410	−0.401205	−	0.915988i	$-0.631408\pi$
$823$	−23.0195	−0.802410	−0.401205	+	0.915988i	$0.631408\pi$
$824$	−114.080	−3.97417
$825$	53.1723	1.85122
$826$	13.8932	0.483408
$827$	40.5271	1.40927	0.704633	−	0.709571i	$-0.251111\pi$
$827$	40.5271	1.40927	0.704633	+	0.709571i	$0.251111\pi$
$828$	−229.142	−7.96322
$829$	1.70525	0.0592258	0.0296129	−	0.999561i	$-0.490573\pi$
$829$	1.70525	0.0592258	0.0296129	+	0.999561i	$0.490573\pi$
$830$	6.84238	0.237503
$831$	89.4208	3.10197
$832$	−27.5866	−0.956393
$833$	1.37911	0.0477834
$834$	−44.5428	−1.54239
$835$	−5.28789	−0.182995
$836$	−23.3884	−0.808906
$837$	11.0136	0.380685
$838$	−35.6503	−1.23152
$839$	−7.46362	−0.257673	−0.128836	−	0.991666i	$-0.541124\pi$
$839$	−7.46362	−0.257673	−0.128836	+	0.991666i	$0.541124\pi$
$840$	−8.21438	−0.283423
$841$	40.6973	1.40335
$842$	40.0857	1.38144
$843$	36.4066	1.25391
$844$	−31.5499	−1.08599
$845$	−2.94512	−0.101315
$846$	213.444	7.33835
$847$	−1.36760	−0.0469914
$848$	−88.7797	−3.04871
$849$	77.2485	2.65116
$850$	17.8642	0.612738
$851$	−6.95898	−0.238551
$852$	−127.714	−4.37542
$853$	−46.3568	−1.58723	−0.793613	−	0.608422i	$-0.791803\pi$
$853$	−46.3568	−1.58723	−0.793613	+	0.608422i	$0.791803\pi$
$854$	−30.0687	−1.02893
$855$	−2.88933	−0.0988131
$856$	−151.379	−5.17403
$857$	24.5388	0.838230	0.419115	−	0.907933i	$-0.362340\pi$
$857$	24.5388	0.838230	0.419115	+	0.907933i	$0.362340\pi$
$858$	−58.5866	−2.00011
$859$	34.3019	1.17037	0.585184	−	0.810901i	$-0.301022\pi$
$859$	34.3019	1.17037	0.585184	+	0.810901i	$0.301022\pi$
$860$	−18.1110	−0.617580
$861$	1.25101	0.0426341
$862$	−53.6699	−1.82800
$863$	−20.2657	−0.689853	−0.344927	−	0.938630i	$-0.612096\pi$
$863$	−20.2657	−0.689853	−0.344927	+	0.938630i	$0.612096\pi$
$864$	149.064	5.07127
$865$	−0.324788	−0.0110431
$866$	55.8668	1.89843
$867$	46.6862	1.58555
$868$	5.01811	0.170326
$869$	−24.4602	−0.829756
$870$	−22.7221	−0.770350
$871$	−2.79720	−0.0947795
$872$	72.5290	2.45614
$873$	−0.666562	−0.0225597
$874$	−24.4328	−0.826453
$875$	3.28580	0.111080
$876$	89.9749	3.03997
$877$	−19.4254	−0.655950	−0.327975	−	0.944686i	$-0.606366\pi$
$877$	−19.4254	−0.655950	−0.327975	+	0.944686i	$0.606366\pi$
$878$	−1.71626	−0.0579208
$879$	89.5485	3.02039
$880$	13.0224	0.438987
$881$	−25.4575	−0.857684	−0.428842	−	0.903379i	$-0.641078\pi$
$881$	−25.4575	−0.857684	−0.428842	+	0.903379i	$0.641078\pi$
$882$	−17.3831	−0.585321
$883$	32.5643	1.09587	0.547937	−	0.836520i	$-0.315413\pi$
$883$	32.5643	1.09587	0.547937	+	0.836520i	$0.315413\pi$
$884$	−14.0740	−0.473360
$885$	−5.38795	−0.181114
$886$	−17.9793	−0.604025
$887$	45.8845	1.54065	0.770326	−	0.637650i	$-0.220093\pi$
$887$	45.8845	1.54065	0.770326	+	0.637650i	$0.220093\pi$
$888$	24.7237	0.829673
$889$	−6.88031	−0.230758
$890$	14.3601	0.481353
$891$	50.5396	1.69314
$892$	−19.4042	−0.649702
$893$	16.2732	0.544562
$894$	−5.67170	−0.189690
$895$	4.45238	0.148827
$896$	8.86693	0.296223
$897$	−43.7614	−1.46115
$898$	7.03607	0.234797
$899$	8.34849	0.278438
$900$	−161.003	−5.36675
$901$	−10.9856	−0.365985
$902$	−3.76915	−0.125499
$903$	−33.5899	−1.11780
$904$	−66.4549	−2.21026
$905$	−4.23791	−0.140873
$906$	59.9555	1.99189
$907$	−48.9220	−1.62443	−0.812214	−	0.583360i	$-0.801738\pi$
$907$	−48.9220	−1.62443	−0.812214	+	0.583360i	$0.801738\pi$
$908$	−72.5749	−2.40848
$909$	−63.4314	−2.10389
$910$	−1.78998	−0.0593373
$911$	40.0699	1.32758	0.663788	−	0.747921i	$-0.268948\pi$
$911$	40.0699	1.32758	0.663788	+	0.747921i	$0.268948\pi$
$912$	45.6746	1.51244
$913$	−27.3388	−0.904781
$914$	−62.0320	−2.05184
$915$	11.6609	0.385499
$916$	71.8994	2.37562
$917$	−14.9257	−0.492891
$918$	40.2382	1.32806
$919$	35.5443	1.17250	0.586248	−	0.810131i	$-0.300604\pi$
$919$	35.5443	1.17250	0.586248	+	0.810131i	$0.300604\pi$
$920$	18.4864	0.609479
$921$	−90.9881	−2.99816
$922$	76.9003	2.53258
$923$	−16.7382	−0.550944
$924$	54.5696	1.79521
$925$	−4.88961	−0.160769
$926$	−5.32697	−0.175055
$927$	93.6230	3.07498
$928$	112.993	3.70919
$929$	1.29435	0.0424661	0.0212331	−	0.999775i	$-0.493241\pi$
$929$	1.29435	0.0424661	0.0212331	+	0.999775i	$0.493241\pi$
$930$	−2.72170	−0.0892479
$931$	−1.32531	−0.0434353
$932$	−5.04846	−0.165368
$933$	56.4866	1.84929
$934$	29.9003	0.978369
$935$	1.61140	0.0526985
$936$	106.694	3.48741
$937$	−2.35212	−0.0768403	−0.0384202	−	0.999262i	$-0.512233\pi$
$937$	−2.35212	−0.0768403	−0.0384202	+	0.999262i	$0.512233\pi$
$938$	3.64382	0.118975
$939$	83.3512	2.72006
$940$	−20.4719	−0.667718
$941$	−17.3044	−0.564108	−0.282054	−	0.959399i	$-0.591016\pi$
$941$	−17.3044	−0.564108	−0.282054	+	0.959399i	$0.591016\pi$
$942$	105.500	3.43738
$943$	−2.81538	−0.0916813
$944$	58.4497	1.90237
$945$	3.65923	0.119035
$946$	101.203	3.29039
$947$	−50.2437	−1.63270	−0.816350	−	0.577557i	$-0.804006\pi$
$947$	−50.2437	−1.63270	−0.816350	+	0.577557i	$0.804006\pi$
$948$	107.926	3.50527
$949$	11.7921	0.382787
$950$	−17.1673	−0.556981
$951$	−19.8790	−0.644622
$952$	11.0267	0.357377
$953$	19.3478	0.626736	0.313368	−	0.949632i	$-0.398543\pi$
$953$	19.3478	0.626736	0.313368	+	0.949632i	$0.398543\pi$
$954$	138.469	4.48311
$955$	8.28794	0.268192
$956$	−40.9775	−1.32531
$957$	90.7860	2.93469
$958$	35.3189	1.14110
$959$	4.68190	0.151186
$960$	−13.9364	−0.449795
$961$	1.00000	0.0322581
$962$	5.38750	0.173700
$963$	124.234	4.00337
$964$	68.2741	2.19896
$965$	0.373991	0.0120392
$966$	57.0065	1.83415
$967$	17.0616	0.548664	0.274332	−	0.961635i	$-0.411543\pi$
$967$	17.0616	0.548664	0.274332	+	0.961635i	$0.411543\pi$
$968$	−10.9347	−0.351454
$969$	5.65179	0.181562
$970$	0.0894116	0.00287083
$971$	48.0337	1.54148	0.770738	−	0.637152i	$-0.219888\pi$
$971$	48.0337	1.54148	0.770738	+	0.637152i	$0.219888\pi$
$972$	−57.1940	−1.83450
$973$	5.43750	0.174318
$974$	−7.90802	−0.253389
$975$	−30.7482	−0.984730
$976$	−126.501	−4.04918
$977$	−42.9359	−1.37364	−0.686821	−	0.726827i	$-0.740994\pi$
$977$	−42.9359	−1.37364	−0.686821	+	0.726827i	$0.740994\pi$
$978$	−29.7344	−0.950801
$979$	−57.3759	−1.83374
$980$	1.66725	0.0532585
$981$	−59.5230	−1.90042
$982$	−92.9945	−2.96758
$983$	23.7289	0.756835	0.378418	−	0.925635i	$-0.376468\pi$
$983$	23.7289	0.756835	0.378418	+	0.925635i	$0.376468\pi$
$984$	10.0024	0.318865
$985$	7.45573	0.237559
$986$	30.5013	0.971358
$987$	−37.9685	−1.20855
$988$	13.5249	0.430286
$989$	75.5939	2.40374
$990$	−20.3111	−0.645528
$991$	48.0636	1.52679	0.763396	−	0.645931i	$-0.223531\pi$
$991$	48.0636	1.52679	0.763396	+	0.645931i	$0.223531\pi$
$992$	13.5346	0.429724
$993$	−17.0884	−0.542283
$994$	21.8042	0.691589
$995$	−8.54592	−0.270924
$996$	120.627	3.82221
$997$	25.4630	0.806421	0.403210	−	0.915107i	$-0.367894\pi$
$997$	25.4630	0.806421	0.403210	+	0.915107i	$0.367894\pi$
$998$	−40.6474	−1.28667
$999$	−11.0136	−0.348454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.3	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.3	✓	71	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)

\(f(q)\)	\(=\)	\(q-2.64917 q^{2} -3.09220 q^{3} +5.01811 q^{4} +0.332247 q^{5} +8.19178 q^{6} -1.00000 q^{7} -7.99549 q^{8} +6.56173 q^{9} +O(q^{10})\)	\(q-2.64917 q^{2} -3.09220 q^{3} +5.01811 q^{4} +0.332247 q^{5} +8.19178 q^{6} -1.00000 q^{7} -7.99549 q^{8} +6.56173 q^{9} -0.880180 q^{10} +3.51676 q^{11} -15.5170 q^{12} -2.03365 q^{13} +2.64917 q^{14} -1.02738 q^{15} +11.1452 q^{16} +1.37911 q^{17} -17.3831 q^{18} -1.32531 q^{19} +1.66725 q^{20} +3.09220 q^{21} -9.31650 q^{22} -6.95898 q^{23} +24.7237 q^{24} -4.88961 q^{25} +5.38750 q^{26} -11.0136 q^{27} -5.01811 q^{28} -8.34849 q^{29} +2.72170 q^{30} -1.00000 q^{31} -13.5346 q^{32} -10.8745 q^{33} -3.65351 q^{34} -0.332247 q^{35} +32.9275 q^{36} +1.00000 q^{37} +3.51098 q^{38} +6.28847 q^{39} -2.65648 q^{40} +0.404567 q^{41} -8.19178 q^{42} -10.8628 q^{43} +17.6475 q^{44} +2.18012 q^{45} +18.4355 q^{46} -12.2788 q^{47} -34.4633 q^{48} +1.00000 q^{49} +12.9534 q^{50} -4.26450 q^{51} -10.2051 q^{52} -7.96572 q^{53} +29.1769 q^{54} +1.16843 q^{55} +7.99549 q^{56} +4.09813 q^{57} +22.1166 q^{58} +5.24437 q^{59} -5.15549 q^{60} -11.3502 q^{61} +2.64917 q^{62} -6.56173 q^{63} +13.5650 q^{64} -0.675676 q^{65} +28.8085 q^{66} +1.37546 q^{67} +6.92054 q^{68} +21.5186 q^{69} +0.880180 q^{70} +8.23059 q^{71} -52.4642 q^{72} -5.79846 q^{73} -2.64917 q^{74} +15.1197 q^{75} -6.65056 q^{76} -3.51676 q^{77} -16.6592 q^{78} -6.95533 q^{79} +3.70297 q^{80} +14.3711 q^{81} -1.07177 q^{82} -7.77384 q^{83} +15.5170 q^{84} +0.458207 q^{85} +28.7773 q^{86} +25.8152 q^{87} -28.1182 q^{88} -16.3150 q^{89} -5.77550 q^{90} +2.03365 q^{91} -34.9209 q^{92} +3.09220 q^{93} +32.5286 q^{94} -0.440331 q^{95} +41.8517 q^{96} -0.101583 q^{97} -2.64917 q^{98} +23.0760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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