LMFDB - Embedded newform 8007.2.a.h.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70764 q^{2} +1.00000 q^{3} +0.916030 q^{4} -1.21926 q^{5} +1.70764 q^{6} -2.14028 q^{7} -1.85103 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.70764 q^{2} +1.00000 q^{3} +0.916030 q^{4} -1.21926 q^{5} +1.70764 q^{6} -2.14028 q^{7} -1.85103 q^{8} +1.00000 q^{9} -2.08205 q^{10} +0.285683 q^{11} +0.916030 q^{12} +3.50963 q^{13} -3.65483 q^{14} -1.21926 q^{15} -4.99295 q^{16} -1.00000 q^{17} +1.70764 q^{18} +5.93903 q^{19} -1.11688 q^{20} -2.14028 q^{21} +0.487844 q^{22} +6.24152 q^{23} -1.85103 q^{24} -3.51341 q^{25} +5.99318 q^{26} +1.00000 q^{27} -1.96056 q^{28} -8.30374 q^{29} -2.08205 q^{30} +2.65307 q^{31} -4.82409 q^{32} +0.285683 q^{33} -1.70764 q^{34} +2.60956 q^{35} +0.916030 q^{36} -1.92200 q^{37} +10.1417 q^{38} +3.50963 q^{39} +2.25688 q^{40} -5.06269 q^{41} -3.65483 q^{42} -7.18058 q^{43} +0.261695 q^{44} -1.21926 q^{45} +10.6583 q^{46} +2.90935 q^{47} -4.99295 q^{48} -2.41919 q^{49} -5.99963 q^{50} -1.00000 q^{51} +3.21493 q^{52} +8.52120 q^{53} +1.70764 q^{54} -0.348322 q^{55} +3.96173 q^{56} +5.93903 q^{57} -14.1798 q^{58} +8.76294 q^{59} -1.11688 q^{60} +15.4535 q^{61} +4.53049 q^{62} -2.14028 q^{63} +1.74809 q^{64} -4.27915 q^{65} +0.487844 q^{66} +5.65625 q^{67} -0.916030 q^{68} +6.24152 q^{69} +4.45618 q^{70} +13.0257 q^{71} -1.85103 q^{72} +9.27570 q^{73} -3.28208 q^{74} -3.51341 q^{75} +5.44033 q^{76} -0.611443 q^{77} +5.99318 q^{78} +13.1129 q^{79} +6.08770 q^{80} +1.00000 q^{81} -8.64524 q^{82} +7.35023 q^{83} -1.96056 q^{84} +1.21926 q^{85} -12.2618 q^{86} -8.30374 q^{87} -0.528808 q^{88} +4.13745 q^{89} -2.08205 q^{90} -7.51160 q^{91} +5.71742 q^{92} +2.65307 q^{93} +4.96812 q^{94} -7.24121 q^{95} -4.82409 q^{96} +13.7666 q^{97} -4.13110 q^{98} +0.285683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.70764	1.20748	0.603741	−	0.797180i	$-0.293676\pi$
$2$	1.70764	1.20748	0.603741	+	0.797180i	$0.293676\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.916030	0.458015
$5$	−1.21926	−0.545269	−0.272634	−	0.962118i	$-0.587895\pi$
$5$	−1.21926	−0.545269	−0.272634	+	0.962118i	$0.587895\pi$
$6$	1.70764	0.697141
$7$	−2.14028	−0.808951	−0.404476	−	0.914549i	$-0.632546\pi$
$7$	−2.14028	−0.808951	−0.404476	+	0.914549i	$0.632546\pi$
$8$	−1.85103	−0.654438
$9$	1.00000	0.333333
$10$	−2.08205	−0.658403
$11$	0.285683	0.0861368	0.0430684	−	0.999072i	$-0.486287\pi$
$11$	0.285683	0.0861368	0.0430684	+	0.999072i	$0.486287\pi$
$12$	0.916030	0.264435
$13$	3.50963	0.973396	0.486698	−	0.873570i	$-0.338201\pi$
$13$	3.50963	0.973396	0.486698	+	0.873570i	$0.338201\pi$
$14$	−3.65483	−0.976795
$15$	−1.21926	−0.314811
$16$	−4.99295	−1.24824
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.70764	0.402494
$19$	5.93903	1.36251	0.681253	−	0.732048i	$-0.261435\pi$
$19$	5.93903	1.36251	0.681253	+	0.732048i	$0.261435\pi$
$20$	−1.11688	−0.249741
$21$	−2.14028	−0.467048
$22$	0.487844	0.104009
$23$	6.24152	1.30145	0.650724	−	0.759315i	$-0.274466\pi$
$23$	6.24152	1.30145	0.650724	+	0.759315i	$0.274466\pi$
$24$	−1.85103	−0.377840
$25$	−3.51341	−0.702682
$26$	5.99318	1.17536
$27$	1.00000	0.192450
$28$	−1.96056	−0.370512
$29$	−8.30374	−1.54197	−0.770983	−	0.636856i	$-0.780234\pi$
$29$	−8.30374	−1.54197	−0.770983	+	0.636856i	$0.780234\pi$
$30$	−2.08205	−0.380129
$31$	2.65307	0.476506	0.238253	−	0.971203i	$-0.423425\pi$
$31$	2.65307	0.476506	0.238253	+	0.971203i	$0.423425\pi$
$32$	−4.82409	−0.852787
$33$	0.285683	0.0497311
$34$	−1.70764	−0.292858
$35$	2.60956	0.441096
$36$	0.916030	0.152672
$37$	−1.92200	−0.315974	−0.157987	−	0.987441i	$-0.550500\pi$
$37$	−1.92200	−0.315974	−0.157987	+	0.987441i	$0.550500\pi$
$38$	10.1417	1.64520
$39$	3.50963	0.561991
$40$	2.25688	0.356845
$41$	−5.06269	−0.790659	−0.395330	−	0.918539i	$-0.629370\pi$
$41$	−5.06269	−0.790659	−0.395330	+	0.918539i	$0.629370\pi$
$42$	−3.65483	−0.563953
$43$	−7.18058	−1.09503	−0.547514	−	0.836796i	$-0.684426\pi$
$43$	−7.18058	−1.09503	−0.547514	+	0.836796i	$0.684426\pi$
$44$	0.261695	0.0394519
$45$	−1.21926	−0.181756
$46$	10.6583	1.57148
$47$	2.90935	0.424372	0.212186	−	0.977229i	$-0.431942\pi$
$47$	2.90935	0.424372	0.212186	+	0.977229i	$0.431942\pi$
$48$	−4.99295	−0.720670
$49$	−2.41919	−0.345598
$50$	−5.99963	−0.848476
$51$	−1.00000	−0.140028
$52$	3.21493	0.445830
$53$	8.52120	1.17048	0.585238	−	0.810861i	$-0.301001\pi$
$53$	8.52120	1.17048	0.585238	+	0.810861i	$0.301001\pi$
$54$	1.70764	0.232380
$55$	−0.348322	−0.0469677
$56$	3.96173	0.529408
$57$	5.93903	0.786643
$58$	−14.1798	−1.86190
$59$	8.76294	1.14084	0.570419	−	0.821354i	$-0.306781\pi$
$59$	8.76294	1.14084	0.570419	+	0.821354i	$0.306781\pi$
$60$	−1.11688	−0.144188
$61$	15.4535	1.97862	0.989310	−	0.145830i	$-0.0465852\pi$
$61$	15.4535	1.97862	0.989310	+	0.145830i	$0.0465852\pi$
$62$	4.53049	0.575373
$63$	−2.14028	−0.269650
$64$	1.74809	0.218511
$65$	−4.27915	−0.530763
$66$	0.487844	0.0600495
$67$	5.65625	0.691021	0.345510	−	0.938415i	$-0.387706\pi$
$67$	5.65625	0.691021	0.345510	+	0.938415i	$0.387706\pi$
$68$	−0.916030	−0.111085
$69$	6.24152	0.751391
$70$	4.45618	0.532616
$71$	13.0257	1.54587	0.772933	−	0.634488i	$-0.218789\pi$
$71$	13.0257	1.54587	0.772933	+	0.634488i	$0.218789\pi$
$72$	−1.85103	−0.218146
$73$	9.27570	1.08564	0.542819	−	0.839849i	$-0.317357\pi$
$73$	9.27570	1.08564	0.542819	+	0.839849i	$0.317357\pi$
$74$	−3.28208	−0.381534
$75$	−3.51341	−0.405694
$76$	5.44033	0.624048
$77$	−0.611443	−0.0696804
$78$	5.99318	0.678594
$79$	13.1129	1.47531	0.737656	−	0.675176i	$-0.235932\pi$
$79$	13.1129	1.47531	0.737656	+	0.675176i	$0.235932\pi$
$80$	6.08770	0.680625
$81$	1.00000	0.111111
$82$	−8.64524	−0.954707
$83$	7.35023	0.806793	0.403396	−	0.915025i	$-0.367830\pi$
$83$	7.35023	0.806793	0.403396	+	0.915025i	$0.367830\pi$
$84$	−1.96056	−0.213915
$85$	1.21926	0.132247
$86$	−12.2618	−1.32223
$87$	−8.30374	−0.890254
$88$	−0.528808	−0.0563712
$89$	4.13745	0.438569	0.219285	−	0.975661i	$-0.429628\pi$
$89$	4.13745	0.438569	0.219285	+	0.975661i	$0.429628\pi$
$90$	−2.08205	−0.219468
$91$	−7.51160	−0.787430
$92$	5.71742	0.596082
$93$	2.65307	0.275111
$94$	4.96812	0.512422
$95$	−7.24121	−0.742932
$96$	−4.82409	−0.492357
$97$	13.7666	1.39779	0.698893	−	0.715227i	$-0.253676\pi$
$97$	13.7666	1.39779	0.698893	+	0.715227i	$0.253676\pi$
$98$	−4.13110	−0.417304
$99$	0.285683	0.0287123
$100$	−3.21839	−0.321839
$101$	5.61949	0.559160	0.279580	−	0.960122i	$-0.409805\pi$
$101$	5.61949	0.559160	0.279580	+	0.960122i	$0.409805\pi$
$102$	−1.70764	−0.169081
$103$	−12.4864	−1.23032	−0.615161	−	0.788402i	$-0.710909\pi$
$103$	−12.4864	−1.23032	−0.615161	+	0.788402i	$0.710909\pi$
$104$	−6.49643	−0.637027
$105$	2.60956	0.254667
$106$	14.5511	1.41333
$107$	−1.88700	−0.182423	−0.0912115	−	0.995832i	$-0.529074\pi$
$107$	−1.88700	−0.182423	−0.0912115	+	0.995832i	$0.529074\pi$
$108$	0.916030	0.0881450
$109$	−16.7501	−1.60437	−0.802185	−	0.597075i	$-0.796329\pi$
$109$	−16.7501	−1.60437	−0.802185	+	0.597075i	$0.796329\pi$
$110$	−0.594808	−0.0567127
$111$	−1.92200	−0.182428
$112$	10.6863	1.00976
$113$	−10.2971	−0.968666	−0.484333	−	0.874884i	$-0.660938\pi$
$113$	−10.2971	−0.968666	−0.484333	+	0.874884i	$0.660938\pi$
$114$	10.1417	0.949858
$115$	−7.61003	−0.709639
$116$	−7.60647	−0.706243
$117$	3.50963	0.324465
$118$	14.9639	1.37754
$119$	2.14028	0.196199
$120$	2.25688	0.206024
$121$	−10.9184	−0.992580
$122$	26.3890	2.38915
$123$	−5.06269	−0.456487
$124$	2.43029	0.218247
$125$	10.3800	0.928420
$126$	−3.65483	−0.325598
$127$	−6.28995	−0.558143	−0.279071	−	0.960270i	$-0.590027\pi$
$127$	−6.28995	−0.558143	−0.279071	+	0.960270i	$0.590027\pi$
$128$	12.6333	1.11664
$129$	−7.18058	−0.632215
$130$	−7.30724	−0.640887
$131$	15.9238	1.39127	0.695636	−	0.718394i	$-0.255123\pi$
$131$	15.9238	1.39127	0.695636	+	0.718394i	$0.255123\pi$
$132$	0.261695	0.0227776
$133$	−12.7112	−1.10220
$134$	9.65883	0.834396
$135$	−1.21926	−0.104937
$136$	1.85103	0.158724
$137$	−15.4844	−1.32292	−0.661460	−	0.749981i	$-0.730063\pi$
$137$	−15.4844	−1.32292	−0.661460	+	0.749981i	$0.730063\pi$
$138$	10.6583	0.907292
$139$	−16.7022	−1.41666	−0.708330	−	0.705881i	$-0.750551\pi$
$139$	−16.7022	−1.41666	−0.708330	+	0.705881i	$0.750551\pi$
$140$	2.39043	0.202029
$141$	2.90935	0.245012
$142$	22.2432	1.86661
$143$	1.00264	0.0838452
$144$	−4.99295	−0.416079
$145$	10.1244	0.840786
$146$	15.8395	1.31089
$147$	−2.41919	−0.199531
$148$	−1.76061	−0.144721
$149$	3.21284	0.263206	0.131603	−	0.991302i	$-0.457988\pi$
$149$	3.21284	0.263206	0.131603	+	0.991302i	$0.457988\pi$
$150$	−5.99963	−0.489868
$151$	12.4103	1.00993	0.504967	−	0.863139i	$-0.331505\pi$
$151$	12.4103	1.00993	0.504967	+	0.863139i	$0.331505\pi$
$152$	−10.9933	−0.891675
$153$	−1.00000	−0.0808452
$154$	−1.04412	−0.0841380
$155$	−3.23478	−0.259824
$156$	3.21493	0.257400
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	22.3920	1.78141
$159$	8.52120	0.675775
$160$	5.88182	0.464999
$161$	−13.3586	−1.05281
$162$	1.70764	0.134165
$163$	6.26827	0.490969	0.245484	−	0.969401i	$-0.421053\pi$
$163$	6.26827	0.490969	0.245484	+	0.969401i	$0.421053\pi$
$164$	−4.63757	−0.362134
$165$	−0.348322	−0.0271168
$166$	12.5515	0.974189
$167$	17.1101	1.32402	0.662011	−	0.749494i	$-0.269703\pi$
$167$	17.1101	1.32402	0.662011	+	0.749494i	$0.269703\pi$
$168$	3.96173	0.305654
$169$	−0.682495	−0.0524996
$170$	2.08205	0.159686
$171$	5.93903	0.454169
$172$	−6.57763	−0.501540
$173$	15.8793	1.20728	0.603639	−	0.797258i	$-0.293717\pi$
$173$	15.8793	1.20728	0.603639	+	0.797258i	$0.293717\pi$
$174$	−14.1798	−1.07497
$175$	7.51969	0.568435
$176$	−1.42640	−0.107519
$177$	8.76294	0.658663
$178$	7.06528	0.529565
$179$	13.6460	1.01995	0.509974	−	0.860190i	$-0.329655\pi$
$179$	13.6460	1.01995	0.509974	+	0.860190i	$0.329655\pi$
$180$	−1.11688	−0.0832471
$181$	12.8676	0.956440	0.478220	−	0.878240i	$-0.341282\pi$
$181$	12.8676	0.956440	0.478220	+	0.878240i	$0.341282\pi$
$182$	−12.8271	−0.950808
$183$	15.4535	1.14236
$184$	−11.5532	−0.851716
$185$	2.34341	0.172291
$186$	4.53049	0.332192
$187$	−0.285683	−0.0208912
$188$	2.66505	0.194369
$189$	−2.14028	−0.155683
$190$	−12.3654	−0.897078
$191$	0.407772	0.0295054	0.0147527	−	0.999891i	$-0.495304\pi$
$191$	0.407772	0.0295054	0.0147527	+	0.999891i	$0.495304\pi$
$192$	1.74809	0.126157
$193$	16.1463	1.16224	0.581120	−	0.813818i	$-0.302615\pi$
$193$	16.1463	1.16224	0.581120	+	0.813818i	$0.302615\pi$
$194$	23.5084	1.68780
$195$	−4.27915	−0.306436
$196$	−2.21605	−0.158289
$197$	−1.50736	−0.107395	−0.0536974	−	0.998557i	$-0.517101\pi$
$197$	−1.50736	−0.107395	−0.0536974	+	0.998557i	$0.517101\pi$
$198$	0.487844	0.0346696
$199$	11.7934	0.836014	0.418007	−	0.908444i	$-0.362729\pi$
$199$	11.7934	0.836014	0.418007	+	0.908444i	$0.362729\pi$
$200$	6.50342	0.459861
$201$	5.65625	0.398961
$202$	9.59605	0.675176
$203$	17.7723	1.24737
$204$	−0.916030	−0.0641349
$205$	6.17273	0.431122
$206$	−21.3223	−1.48559
$207$	6.24152	0.433816
$208$	−17.5234	−1.21503
$209$	1.69668	0.117362
$210$	4.45618	0.307506
$211$	−22.0031	−1.51475	−0.757377	−	0.652978i	$-0.773519\pi$
$211$	−22.0031	−1.51475	−0.757377	+	0.652978i	$0.773519\pi$
$212$	7.80567	0.536096
$213$	13.0257	0.892506
$214$	−3.22231	−0.220273
$215$	8.75499	0.597085
$216$	−1.85103	−0.125947
$217$	−5.67833	−0.385470
$218$	−28.6032	−1.93725
$219$	9.27570	0.626794
$220$	−0.319073	−0.0215119
$221$	−3.50963	−0.236083
$222$	−3.28208	−0.220279
$223$	24.8758	1.66581	0.832904	−	0.553418i	$-0.186677\pi$
$223$	24.8758	1.66581	0.832904	+	0.553418i	$0.186677\pi$
$224$	10.3249	0.689863
$225$	−3.51341	−0.234227
$226$	−17.5837	−1.16965
$227$	8.55825	0.568031	0.284016	−	0.958820i	$-0.408333\pi$
$227$	8.55825	0.568031	0.284016	+	0.958820i	$0.408333\pi$
$228$	5.44033	0.360294
$229$	−17.5911	−1.16245	−0.581225	−	0.813743i	$-0.697426\pi$
$229$	−17.5911	−1.16245	−0.581225	+	0.813743i	$0.697426\pi$
$230$	−12.9952	−0.856877
$231$	−0.611443	−0.0402300
$232$	15.3705	1.00912
$233$	−13.7555	−0.901153	−0.450576	−	0.892738i	$-0.648781\pi$
$233$	−13.7555	−0.901153	−0.450576	+	0.892738i	$0.648781\pi$
$234$	5.99318	0.391786
$235$	−3.54725	−0.231397
$236$	8.02711	0.522520
$237$	13.1129	0.851772
$238$	3.65483	0.236907
$239$	7.68556	0.497138	0.248569	−	0.968614i	$-0.420040\pi$
$239$	7.68556	0.497138	0.248569	+	0.968614i	$0.420040\pi$
$240$	6.08770	0.392959
$241$	4.19732	0.270373	0.135187	−	0.990820i	$-0.456837\pi$
$241$	4.19732	0.270373	0.135187	+	0.990820i	$0.456837\pi$
$242$	−18.6447	−1.19852
$243$	1.00000	0.0641500
$244$	14.1559	0.906237
$245$	2.94961	0.188444
$246$	−8.64524	−0.551201
$247$	20.8438	1.32626
$248$	−4.91092	−0.311843
$249$	7.35023	0.465802
$250$	17.7254	1.12105
$251$	14.9578	0.944127	0.472064	−	0.881564i	$-0.343509\pi$
$251$	14.9578	0.944127	0.472064	+	0.881564i	$0.343509\pi$
$252$	−1.96056	−0.123504
$253$	1.78310	0.112102
$254$	−10.7410	−0.673948
$255$	1.21926	0.0763529
$256$	18.0769	1.12981
$257$	−13.4080	−0.836367	−0.418183	−	0.908363i	$-0.637333\pi$
$257$	−13.4080	−0.836367	−0.418183	+	0.908363i	$0.637333\pi$
$258$	−12.2618	−0.763389
$259$	4.11362	0.255608
$260$	−3.91983	−0.243097
$261$	−8.30374	−0.513988
$262$	27.1922	1.67994
$263$	−7.96688	−0.491259	−0.245629	−	0.969364i	$-0.578995\pi$
$263$	−7.96688	−0.491259	−0.245629	+	0.969364i	$0.578995\pi$
$264$	−0.528808	−0.0325459
$265$	−10.3895	−0.638225
$266$	−21.7061	−1.33089
$267$	4.13745	0.253208
$268$	5.18129	0.316498
$269$	−6.90789	−0.421182	−0.210591	−	0.977574i	$-0.567539\pi$
$269$	−6.90789	−0.421182	−0.210591	+	0.977574i	$0.567539\pi$
$270$	−2.08205	−0.126710
$271$	−15.7694	−0.957926	−0.478963	−	0.877835i	$-0.658987\pi$
$271$	−15.7694	−0.957926	−0.478963	+	0.877835i	$0.658987\pi$
$272$	4.99295	0.302742
$273$	−7.51160	−0.454623
$274$	−26.4417	−1.59740
$275$	−1.00372	−0.0605268
$276$	5.71742	0.344148
$277$	−7.40189	−0.444737	−0.222368	−	0.974963i	$-0.571379\pi$
$277$	−7.40189	−0.444737	−0.222368	+	0.974963i	$0.571379\pi$
$278$	−28.5213	−1.71059
$279$	2.65307	0.158835
$280$	−4.83037	−0.288670
$281$	23.7510	1.41687	0.708434	−	0.705777i	$-0.249402\pi$
$281$	23.7510	1.41687	0.708434	+	0.705777i	$0.249402\pi$
$282$	4.96812	0.295847
$283$	−0.887872	−0.0527785	−0.0263892	−	0.999652i	$-0.508401\pi$
$283$	−0.887872	−0.0527785	−0.0263892	+	0.999652i	$0.508401\pi$
$284$	11.9319	0.708030
$285$	−7.24121	−0.428932
$286$	1.71215	0.101242
$287$	10.8356	0.639605
$288$	−4.82409	−0.284262
$289$	1.00000	0.0588235
$290$	17.2888	1.01523
$291$	13.7666	0.807012
$292$	8.49682	0.497239
$293$	−8.79148	−0.513604	−0.256802	−	0.966464i	$-0.582669\pi$
$293$	−8.79148	−0.513604	−0.256802	+	0.966464i	$0.582669\pi$
$294$	−4.13110	−0.240930
$295$	−10.6843	−0.622063
$296$	3.55767	0.206786
$297$	0.285683	0.0165770
$298$	5.48637	0.317817
$299$	21.9054	1.26682
$300$	−3.21839	−0.185814
$301$	15.3685	0.885825
$302$	21.1923	1.21948
$303$	5.61949	0.322831
$304$	−29.6533	−1.70073
$305$	−18.8418	−1.07888
$306$	−1.70764	−0.0976192
$307$	3.14939	0.179745	0.0898725	−	0.995953i	$-0.471354\pi$
$307$	3.14939	0.179745	0.0898725	+	0.995953i	$0.471354\pi$
$308$	−0.560100	−0.0319147
$309$	−12.4864	−0.710326
$310$	−5.52384	−0.313733
$311$	10.5942	0.600742	0.300371	−	0.953822i	$-0.402890\pi$
$311$	10.5942	0.600742	0.300371	+	0.953822i	$0.402890\pi$
$312$	−6.49643	−0.367788
$313$	33.5215	1.89475	0.947373	−	0.320133i	$-0.103728\pi$
$313$	33.5215	1.89475	0.947373	+	0.320133i	$0.103728\pi$
$314$	−1.70764	−0.0963676
$315$	2.60956	0.147032
$316$	12.0118	0.675715
$317$	9.84711	0.553069	0.276534	−	0.961004i	$-0.410814\pi$
$317$	9.84711	0.553069	0.276534	+	0.961004i	$0.410814\pi$
$318$	14.5511	0.815987
$319$	−2.37224	−0.132820
$320$	−2.13137	−0.119147
$321$	−1.88700	−0.105322
$322$	−22.8117	−1.27125
$323$	−5.93903	−0.330456
$324$	0.916030	0.0508906
$325$	−12.3308	−0.683988
$326$	10.7039	0.592837
$327$	−16.7501	−0.926284
$328$	9.37118	0.517437
$329$	−6.22683	−0.343297
$330$	−0.594808	−0.0327431
$331$	11.5929	0.637202	0.318601	−	0.947889i	$-0.396787\pi$
$331$	11.5929	0.637202	0.318601	+	0.947889i	$0.396787\pi$
$332$	6.73303	0.369523
$333$	−1.92200	−0.105325
$334$	29.2179	1.59873
$335$	−6.89643	−0.376792
$336$	10.6863	0.582987
$337$	−26.1461	−1.42427	−0.712135	−	0.702043i	$-0.752272\pi$
$337$	−26.1461	−1.42427	−0.712135	+	0.702043i	$0.752272\pi$
$338$	−1.16546	−0.0633924
$339$	−10.2971	−0.559259
$340$	1.11688	0.0605712
$341$	0.757939	0.0410447
$342$	10.1417	0.548401
$343$	20.1597	1.08852
$344$	13.2915	0.716628
$345$	−7.61003	−0.409710
$346$	27.1160	1.45777
$347$	24.9774	1.34086	0.670429	−	0.741974i	$-0.266110\pi$
$347$	24.9774	1.34086	0.670429	+	0.741974i	$0.266110\pi$
$348$	−7.60647	−0.407750
$349$	−9.60164	−0.513964	−0.256982	−	0.966416i	$-0.582728\pi$
$349$	−9.60164	−0.513964	−0.256982	+	0.966416i	$0.582728\pi$
$350$	12.8409	0.686376
$351$	3.50963	0.187330
$352$	−1.37816	−0.0734564
$353$	−0.856514	−0.0455876	−0.0227938	−	0.999740i	$-0.507256\pi$
$353$	−0.856514	−0.0455876	−0.0227938	+	0.999740i	$0.507256\pi$
$354$	14.9639	0.795324
$355$	−15.8817	−0.842913
$356$	3.79003	0.200871
$357$	2.14028	0.113276
$358$	23.3024	1.23157
$359$	−27.1984	−1.43547	−0.717737	−	0.696314i	$-0.754822\pi$
$359$	−27.1984	−1.43547	−0.717737	+	0.696314i	$0.754822\pi$
$360$	2.25688	0.118948
$361$	16.2720	0.856423
$362$	21.9732	1.15489
$363$	−10.9184	−0.573067
$364$	−6.88085	−0.360655
$365$	−11.3095	−0.591965
$366$	26.3890	1.37938
$367$	13.9911	0.730328	0.365164	−	0.930943i	$-0.381013\pi$
$367$	13.9911	0.730328	0.365164	+	0.930943i	$0.381013\pi$
$368$	−31.1636	−1.62451
$369$	−5.06269	−0.263553
$370$	4.00170	0.208039
$371$	−18.2378	−0.946858
$372$	2.43029	0.126005
$373$	−23.2055	−1.20154	−0.600769	−	0.799423i	$-0.705139\pi$
$373$	−23.2055	−1.20154	−0.600769	+	0.799423i	$0.705139\pi$
$374$	−0.487844	−0.0252258
$375$	10.3800	0.536023
$376$	−5.38529	−0.277725
$377$	−29.1430	−1.50094
$378$	−3.65483	−0.187984
$379$	−30.1046	−1.54637	−0.773185	−	0.634181i	$-0.781337\pi$
$379$	−30.1046	−1.54637	−0.773185	+	0.634181i	$0.781337\pi$
$380$	−6.63316	−0.340274
$381$	−6.28995	−0.322244
$382$	0.696328	0.0356272
$383$	−26.8982	−1.37443	−0.687216	−	0.726453i	$-0.741167\pi$
$383$	−26.8982	−1.37443	−0.687216	+	0.726453i	$0.741167\pi$
$384$	12.6333	0.644690
$385$	0.745508	0.0379946
$386$	27.5721	1.40338
$387$	−7.18058	−0.365010
$388$	12.6106	0.640207
$389$	−12.3243	−0.624869	−0.312434	−	0.949939i	$-0.601144\pi$
$389$	−12.3243	−0.624869	−0.312434	+	0.949939i	$0.601144\pi$
$390$	−7.30724	−0.370016
$391$	−6.24152	−0.315647
$392$	4.47799	0.226172
$393$	15.9238	0.803251
$394$	−2.57402	−0.129677
$395$	−15.9880	−0.804442
$396$	0.261695	0.0131506
$397$	−3.96929	−0.199213	−0.0996066	−	0.995027i	$-0.531758\pi$
$397$	−3.96929	−0.199213	−0.0996066	+	0.995027i	$0.531758\pi$
$398$	20.1389	1.00947
$399$	−12.7112	−0.636356
$400$	17.5423	0.877114
$401$	−5.75956	−0.287619	−0.143809	−	0.989605i	$-0.545935\pi$
$401$	−5.75956	−0.287619	−0.143809	+	0.989605i	$0.545935\pi$
$402$	9.65883	0.481739
$403$	9.31130	0.463829
$404$	5.14762	0.256104
$405$	−1.21926	−0.0605854
$406$	30.3487	1.50618
$407$	−0.549083	−0.0272170
$408$	1.85103	0.0916396
$409$	−33.5333	−1.65811	−0.829057	−	0.559164i	$-0.811122\pi$
$409$	−33.5333	−1.65811	−0.829057	+	0.559164i	$0.811122\pi$
$410$	10.5408	0.520572
$411$	−15.4844	−0.763788
$412$	−11.4379	−0.563506
$413$	−18.7552	−0.922881
$414$	10.6583	0.523825
$415$	−8.96183	−0.439919
$416$	−16.9308	−0.830100
$417$	−16.7022	−0.817909
$418$	2.89732	0.141713
$419$	40.6569	1.98622	0.993110	−	0.117189i	$-0.0373884\pi$
$419$	40.6569	1.98622	0.993110	+	0.117189i	$0.0373884\pi$
$420$	2.39043	0.116641
$421$	−32.1527	−1.56702	−0.783512	−	0.621376i	$-0.786574\pi$
$421$	−32.1527	−1.56702	−0.783512	+	0.621376i	$0.786574\pi$
$422$	−37.5733	−1.82904
$423$	2.90935	0.141457
$424$	−15.7730	−0.766004
$425$	3.51341	0.170425
$426$	22.2432	1.07769
$427$	−33.0749	−1.60061
$428$	−1.72855	−0.0835525
$429$	1.00264	0.0484081
$430$	14.9504	0.720970
$431$	−6.78590	−0.326865	−0.163433	−	0.986555i	$-0.552257\pi$
$431$	−6.78590	−0.326865	−0.163433	+	0.986555i	$0.552257\pi$
$432$	−4.99295	−0.240223
$433$	16.2903	0.782862	0.391431	−	0.920208i	$-0.371980\pi$
$433$	16.2903	0.782862	0.391431	+	0.920208i	$0.371980\pi$
$434$	−9.69653	−0.465448
$435$	10.1244	0.485428
$436$	−15.3436	−0.734826
$437$	37.0686	1.77323
$438$	15.8395	0.756843
$439$	−11.4621	−0.547055	−0.273528	−	0.961864i	$-0.588191\pi$
$439$	−11.4621	−0.547055	−0.273528	+	0.961864i	$0.588191\pi$
$440$	0.644754	0.0307374
$441$	−2.41919	−0.115199
$442$	−5.99318	−0.285067
$443$	11.7702	0.559220	0.279610	−	0.960114i	$-0.409795\pi$
$443$	11.7702	0.559220	0.279610	+	0.960114i	$0.409795\pi$
$444$	−1.76061	−0.0835547
$445$	−5.04463	−0.239138
$446$	42.4789	2.01143
$447$	3.21284	0.151962
$448$	−3.74140	−0.176765
$449$	−20.7610	−0.979771	−0.489886	−	0.871787i	$-0.662961\pi$
$449$	−20.7610	−0.979771	−0.489886	+	0.871787i	$0.662961\pi$
$450$	−5.99963	−0.282825
$451$	−1.44633	−0.0681048
$452$	−9.43241	−0.443663
$453$	12.4103	0.583086
$454$	14.6144	0.685888
$455$	9.15859	0.429361
$456$	−10.9933	−0.514809
$457$	23.8571	1.11599	0.557995	−	0.829845i	$-0.311571\pi$
$457$	23.8571	1.11599	0.557995	+	0.829845i	$0.311571\pi$
$458$	−30.0392	−1.40364
$459$	−1.00000	−0.0466760
$460$	−6.97101	−0.325025
$461$	−6.09333	−0.283795	−0.141897	−	0.989881i	$-0.545320\pi$
$461$	−6.09333	−0.283795	−0.141897	+	0.989881i	$0.545320\pi$
$462$	−1.04412	−0.0485771
$463$	−5.89195	−0.273822	−0.136911	−	0.990583i	$-0.543717\pi$
$463$	−5.89195	−0.273822	−0.136911	+	0.990583i	$0.543717\pi$
$464$	41.4601	1.92474
$465$	−3.23478	−0.150009
$466$	−23.4894	−1.08813
$467$	8.93518	0.413471	0.206735	−	0.978397i	$-0.433716\pi$
$467$	8.93518	0.413471	0.206735	+	0.978397i	$0.433716\pi$
$468$	3.21493	0.148610
$469$	−12.1060	−0.559002
$470$	−6.05742	−0.279408
$471$	−1.00000	−0.0460776
$472$	−16.2205	−0.746607
$473$	−2.05137	−0.0943223
$474$	22.3920	1.02850
$475$	−20.8662	−0.957408
$476$	1.96056	0.0898623
$477$	8.52120	0.390159
$478$	13.1242	0.600285
$479$	6.61877	0.302419	0.151210	−	0.988502i	$-0.451683\pi$
$479$	6.61877	0.302419	0.151210	+	0.988502i	$0.451683\pi$
$480$	5.88182	0.268467
$481$	−6.74550	−0.307568
$482$	7.16751	0.326471
$483$	−13.3586	−0.607838
$484$	−10.0016	−0.454617
$485$	−16.7850	−0.762169
$486$	1.70764	0.0774601
$487$	−9.30915	−0.421838	−0.210919	−	0.977504i	$-0.567646\pi$
$487$	−9.30915	−0.421838	−0.210919	+	0.977504i	$0.567646\pi$
$488$	−28.6049	−1.29488
$489$	6.26827	0.283461
$490$	5.03688	0.227543
$491$	−31.6120	−1.42663	−0.713314	−	0.700844i	$-0.752807\pi$
$491$	−31.6120	−1.42663	−0.713314	+	0.700844i	$0.752807\pi$
$492$	−4.63757	−0.209078
$493$	8.30374	0.373981
$494$	35.5937	1.60143
$495$	−0.348322	−0.0156559
$496$	−13.2467	−0.594792
$497$	−27.8787	−1.25053
$498$	12.5515	0.562448
$499$	19.8285	0.887647	0.443823	−	0.896114i	$-0.353622\pi$
$499$	19.8285	0.887647	0.443823	+	0.896114i	$0.353622\pi$
$500$	9.50843	0.425230
$501$	17.1101	0.764424
$502$	25.5425	1.14002
$503$	−32.5441	−1.45107	−0.725536	−	0.688184i	$-0.758408\pi$
$503$	−32.5441	−1.45107	−0.725536	+	0.688184i	$0.758408\pi$
$504$	3.96173	0.176469
$505$	−6.85161	−0.304892
$506$	3.04489	0.135362
$507$	−0.682495	−0.0303107
$508$	−5.76178	−0.255638
$509$	38.0789	1.68782	0.843909	−	0.536486i	$-0.180248\pi$
$509$	38.0789	1.68782	0.843909	+	0.536486i	$0.180248\pi$
$510$	2.08205	0.0921949
$511$	−19.8526	−0.878229
$512$	5.60227	0.247588
$513$	5.93903	0.262214
$514$	−22.8960	−1.00990
$515$	15.2241	0.670856
$516$	−6.57763	−0.289564
$517$	0.831153	0.0365541
$518$	7.02458	0.308642
$519$	15.8793	0.697022
$520$	7.92083	0.347351
$521$	9.64425	0.422522	0.211261	−	0.977430i	$-0.432243\pi$
$521$	9.64425	0.422522	0.211261	+	0.977430i	$0.432243\pi$
$522$	−14.1798	−0.620632
$523$	22.2330	0.972182	0.486091	−	0.873908i	$-0.338422\pi$
$523$	22.2330	0.972182	0.486091	+	0.873908i	$0.338422\pi$
$524$	14.5867	0.637224
$525$	7.51969	0.328186
$526$	−13.6046	−0.593187
$527$	−2.65307	−0.115570
$528$	−1.42640	−0.0620762
$529$	15.9566	0.693765
$530$	−17.7416	−0.770645
$531$	8.76294	0.380279
$532$	−11.6438	−0.504825
$533$	−17.7682	−0.769625
$534$	7.06528	0.305744
$535$	2.30074	0.0994696
$536$	−10.4699	−0.452230
$537$	13.6460	0.588867
$538$	−11.7962	−0.508570
$539$	−0.691122	−0.0297687
$540$	−1.11688	−0.0480627
$541$	33.0581	1.42128	0.710640	−	0.703556i	$-0.248406\pi$
$541$	33.0581	1.42128	0.710640	+	0.703556i	$0.248406\pi$
$542$	−26.9285	−1.15668
$543$	12.8676	0.552201
$544$	4.82409	0.206831
$545$	20.4227	0.874814
$546$	−12.8271	−0.548949
$547$	−5.68450	−0.243052	−0.121526	−	0.992588i	$-0.538779\pi$
$547$	−5.68450	−0.243052	−0.121526	+	0.992588i	$0.538779\pi$
$548$	−14.1842	−0.605917
$549$	15.4535	0.659540
$550$	−1.71400	−0.0730850
$551$	−49.3161	−2.10094
$552$	−11.5532	−0.491738
$553$	−28.0653	−1.19346
$554$	−12.6398	−0.537012
$555$	2.34341	0.0994723
$556$	−15.2997	−0.648852
$557$	29.3162	1.24217	0.621083	−	0.783745i	$-0.286693\pi$
$557$	29.3162	1.24217	0.621083	+	0.783745i	$0.286693\pi$
$558$	4.53049	0.191791
$559$	−25.2012	−1.06590
$560$	−13.0294	−0.550592
$561$	−0.285683	−0.0120616
$562$	40.5582	1.71084
$563$	−10.6491	−0.448805	−0.224403	−	0.974497i	$-0.572043\pi$
$563$	−10.6491	−0.448805	−0.224403	+	0.974497i	$0.572043\pi$
$564$	2.66505	0.112219
$565$	12.5548	0.528183
$566$	−1.51616	−0.0637291
$567$	−2.14028	−0.0898835
$568$	−24.1109	−1.01167
$569$	−31.0813	−1.30299	−0.651497	−	0.758651i	$-0.725859\pi$
$569$	−31.0813	−1.30299	−0.651497	+	0.758651i	$0.725859\pi$
$570$	−12.3654	−0.517928
$571$	47.4371	1.98518	0.992590	−	0.121510i	$-0.0387735\pi$
$571$	47.4371	1.98518	0.992590	+	0.121510i	$0.0387735\pi$
$572$	0.918451	0.0384024
$573$	0.407772	0.0170349
$574$	18.5033	0.772312
$575$	−21.9290	−0.914503
$576$	1.74809	0.0728370
$577$	25.4663	1.06018	0.530089	−	0.847942i	$-0.322159\pi$
$577$	25.4663	1.06018	0.530089	+	0.847942i	$0.322159\pi$
$578$	1.70764	0.0710284
$579$	16.1463	0.671019
$580$	9.27425	0.385092
$581$	−15.7316	−0.652656
$582$	23.5084	0.974453
$583$	2.43437	0.100821
$584$	−17.1696	−0.710483
$585$	−4.27915	−0.176921
$586$	−15.0127	−0.620168
$587$	30.7165	1.26780	0.633902	−	0.773413i	$-0.281452\pi$
$587$	30.7165	1.26780	0.633902	+	0.773413i	$0.281452\pi$
$588$	−2.21605	−0.0913883
$589$	15.7567	0.649242
$590$	−18.2449	−0.751130
$591$	−1.50736	−0.0620044
$592$	9.59644	0.394411
$593$	−6.10647	−0.250763	−0.125381	−	0.992109i	$-0.540015\pi$
$593$	−6.10647	−0.250763	−0.125381	+	0.992109i	$0.540015\pi$
$594$	0.487844	0.0200165
$595$	−2.60956	−0.106981
$596$	2.94306	0.120552
$597$	11.7934	0.482673
$598$	37.4066	1.52967
$599$	4.53644	0.185354	0.0926770	−	0.995696i	$-0.470458\pi$
$599$	4.53644	0.185354	0.0926770	+	0.995696i	$0.470458\pi$
$600$	6.50342	0.265501
$601$	−12.9387	−0.527782	−0.263891	−	0.964552i	$-0.585006\pi$
$601$	−12.9387	−0.527782	−0.263891	+	0.964552i	$0.585006\pi$
$602$	26.2438	1.06962
$603$	5.65625	0.230340
$604$	11.3682	0.462565
$605$	13.3123	0.541223
$606$	9.59605	0.389813
$607$	32.2920	1.31069	0.655346	−	0.755329i	$-0.272523\pi$
$607$	32.2920	1.31069	0.655346	+	0.755329i	$0.272523\pi$
$608$	−28.6504	−1.16193
$609$	17.7723	0.720172
$610$	−32.1750	−1.30273
$611$	10.2107	0.413083
$612$	−0.916030	−0.0370283
$613$	−41.8718	−1.69119	−0.845593	−	0.533829i	$-0.820753\pi$
$613$	−41.8718	−1.69119	−0.845593	+	0.533829i	$0.820753\pi$
$614$	5.37802	0.217039
$615$	6.17273	0.248908
$616$	1.13180	0.0456015
$617$	−38.0365	−1.53129	−0.765646	−	0.643263i	$-0.777580\pi$
$617$	−38.0365	−1.53129	−0.765646	+	0.643263i	$0.777580\pi$
$618$	−21.3223	−0.857707
$619$	0.419626	0.0168662	0.00843310	−	0.999964i	$-0.497316\pi$
$619$	0.419626	0.0168662	0.00843310	+	0.999964i	$0.497316\pi$
$620$	−2.96316	−0.119003
$621$	6.24152	0.250464
$622$	18.0911	0.725386
$623$	−8.85533	−0.354781
$624$	−17.5234	−0.701498
$625$	4.91109	0.196443
$626$	57.2426	2.28787
$627$	1.69668	0.0677589
$628$	−0.916030	−0.0365536
$629$	1.92200	0.0766351
$630$	4.45618	0.177539
$631$	−4.87702	−0.194151	−0.0970755	−	0.995277i	$-0.530949\pi$
$631$	−4.87702	−0.194151	−0.0970755	+	0.995277i	$0.530949\pi$
$632$	−24.2723	−0.965500
$633$	−22.0031	−0.874544
$634$	16.8153	0.667821
$635$	7.66907	0.304338
$636$	7.80567	0.309515
$637$	−8.49045	−0.336404
$638$	−4.05093	−0.160378
$639$	13.0257	0.515289
$640$	−15.4032	−0.608867
$641$	11.7226	0.463014	0.231507	−	0.972833i	$-0.425634\pi$
$641$	11.7226	0.463014	0.231507	+	0.972833i	$0.425634\pi$
$642$	−3.22231	−0.127175
$643$	−49.0872	−1.93581	−0.967905	−	0.251315i	$-0.919137\pi$
$643$	−49.0872	−1.93581	−0.967905	+	0.251315i	$0.919137\pi$
$644$	−12.2369	−0.482201
$645$	8.75499	0.344727
$646$	−10.1417	−0.399020
$647$	−18.6831	−0.734508	−0.367254	−	0.930121i	$-0.619702\pi$
$647$	−18.6831	−0.734508	−0.367254	+	0.930121i	$0.619702\pi$
$648$	−1.85103	−0.0727153
$649$	2.50343	0.0982680
$650$	−21.0565	−0.825904
$651$	−5.67833	−0.222551
$652$	5.74192	0.224871
$653$	−39.8359	−1.55890	−0.779449	−	0.626466i	$-0.784501\pi$
$653$	−39.8359	−1.55890	−0.779449	+	0.626466i	$0.784501\pi$
$654$	−28.6032	−1.11847
$655$	−19.4153	−0.758618
$656$	25.2777	0.986930
$657$	9.27570	0.361880
$658$	−10.6332	−0.414525
$659$	12.7032	0.494848	0.247424	−	0.968907i	$-0.420416\pi$
$659$	12.7032	0.494848	0.247424	+	0.968907i	$0.420416\pi$
$660$	−0.319073	−0.0124199
$661$	25.9695	1.01010	0.505048	−	0.863091i	$-0.331475\pi$
$661$	25.9695	1.01010	0.505048	+	0.863091i	$0.331475\pi$
$662$	19.7964	0.769411
$663$	−3.50963	−0.136303
$664$	−13.6055	−0.527996
$665$	15.4982	0.600996
$666$	−3.28208	−0.127178
$667$	−51.8279	−2.00679
$668$	15.6734	0.606422
$669$	24.8758	0.961755
$670$	−11.7766	−0.454970
$671$	4.41481	0.170432
$672$	10.3249	0.398293
$673$	−41.2201	−1.58892	−0.794458	−	0.607319i	$-0.792245\pi$
$673$	−41.2201	−1.58892	−0.794458	+	0.607319i	$0.792245\pi$
$674$	−44.6481	−1.71978
$675$	−3.51341	−0.135231
$676$	−0.625186	−0.0240456
$677$	−31.6499	−1.21640	−0.608201	−	0.793783i	$-0.708109\pi$
$677$	−31.6499	−1.21640	−0.608201	+	0.793783i	$0.708109\pi$
$678$	−17.5837	−0.675296
$679$	−29.4644	−1.13074
$680$	−2.25688	−0.0865475
$681$	8.55825	0.327953
$682$	1.29429	0.0495608
$683$	−7.54056	−0.288531	−0.144266	−	0.989539i	$-0.546082\pi$
$683$	−7.54056	−0.288531	−0.144266	+	0.989539i	$0.546082\pi$
$684$	5.44033	0.208016
$685$	18.8795	0.721347
$686$	34.4255	1.31437
$687$	−17.5911	−0.671141
$688$	35.8523	1.36686
$689$	29.9063	1.13934
$690$	−12.9952	−0.494718
$691$	14.7815	0.562316	0.281158	−	0.959662i	$-0.409282\pi$
$691$	14.7815	0.562316	0.281158	+	0.959662i	$0.409282\pi$
$692$	14.5459	0.552951
$693$	−0.611443	−0.0232268
$694$	42.6524	1.61906
$695$	20.3643	0.772461
$696$	15.3705	0.582616
$697$	5.06269	0.191763
$698$	−16.3961	−0.620603
$699$	−13.7555	−0.520281
$700$	6.88826	0.260352
$701$	−6.28165	−0.237255	−0.118627	−	0.992939i	$-0.537849\pi$
$701$	−6.28165	−0.237255	−0.118627	+	0.992939i	$0.537849\pi$
$702$	5.99318	0.226198
$703$	−11.4148	−0.430517
$704$	0.499400	0.0188218
$705$	−3.54725	−0.133597
$706$	−1.46262	−0.0550463
$707$	−12.0273	−0.452333
$708$	8.02711	0.301677
$709$	−32.5999	−1.22432	−0.612158	−	0.790735i	$-0.709698\pi$
$709$	−32.5999	−1.22432	−0.612158	+	0.790735i	$0.709698\pi$
$710$	−27.1202	−1.01780
$711$	13.1129	0.491771
$712$	−7.65855	−0.287016
$713$	16.5592	0.620147
$714$	3.65483	0.136779
$715$	−1.22248	−0.0457182
$716$	12.5001	0.467152
$717$	7.68556	0.287022
$718$	−46.4450	−1.73331
$719$	−46.3013	−1.72675	−0.863373	−	0.504566i	$-0.831653\pi$
$719$	−46.3013	−1.72675	−0.863373	+	0.504566i	$0.831653\pi$
$720$	6.08770	0.226875
$721$	26.7244	0.995270
$722$	27.7868	1.03412
$723$	4.19732	0.156100
$724$	11.7871	0.438064
$725$	29.1744	1.08351
$726$	−18.6447	−0.691968
$727$	−25.5186	−0.946431	−0.473215	−	0.880947i	$-0.656907\pi$
$727$	−25.5186	−0.946431	−0.473215	+	0.880947i	$0.656907\pi$
$728$	13.9042	0.515324
$729$	1.00000	0.0370370
$730$	−19.3125	−0.714788
$731$	7.18058	0.265583
$732$	14.1559	0.523216
$733$	−5.00905	−0.185013	−0.0925067	−	0.995712i	$-0.529488\pi$
$733$	−5.00905	−0.185013	−0.0925067	+	0.995712i	$0.529488\pi$
$734$	23.8917	0.881859
$735$	2.94961	0.108798
$736$	−30.1097	−1.10986
$737$	1.61590	0.0595223
$738$	−8.64524	−0.318236
$739$	−23.7455	−0.873493	−0.436746	−	0.899585i	$-0.643869\pi$
$739$	−23.7455	−0.873493	−0.436746	+	0.899585i	$0.643869\pi$
$740$	2.14664	0.0789119
$741$	20.8438	0.765716
$742$	−31.1435	−1.14332
$743$	42.4818	1.55851	0.779253	−	0.626709i	$-0.215599\pi$
$743$	42.4818	1.55851	0.779253	+	0.626709i	$0.215599\pi$
$744$	−4.91092	−0.180043
$745$	−3.91729	−0.143518
$746$	−39.6267	−1.45084
$747$	7.35023	0.268931
$748$	−0.261695	−0.00956850
$749$	4.03871	0.147571
$750$	17.7254	0.647239
$751$	−33.7587	−1.23187	−0.615935	−	0.787797i	$-0.711222\pi$
$751$	−33.7587	−1.23187	−0.615935	+	0.787797i	$0.711222\pi$
$752$	−14.5262	−0.529717
$753$	14.9578	0.545092
$754$	−49.7658	−1.81236
$755$	−15.1313	−0.550686
$756$	−1.96056	−0.0713050
$757$	7.04363	0.256005	0.128002	−	0.991774i	$-0.459143\pi$
$757$	7.04363	0.256005	0.128002	+	0.991774i	$0.459143\pi$
$758$	−51.4078	−1.86721
$759$	1.78310	0.0647224
$760$	13.4037	0.486203
$761$	48.2714	1.74984	0.874918	−	0.484270i	$-0.160915\pi$
$761$	48.2714	1.74984	0.874918	+	0.484270i	$0.160915\pi$
$762$	−10.7410	−0.389104
$763$	35.8500	1.29786
$764$	0.373532	0.0135139
$765$	1.21926	0.0440824
$766$	−45.9323	−1.65960
$767$	30.7547	1.11049
$768$	18.0769	0.652295
$769$	−0.103344	−0.00372666	−0.00186333	−	0.999998i	$-0.500593\pi$
$769$	−0.103344	−0.00372666	−0.00186333	+	0.999998i	$0.500593\pi$
$770$	1.27306	0.0458778
$771$	−13.4080	−0.482877
$772$	14.7905	0.532323
$773$	−13.9139	−0.500448	−0.250224	−	0.968188i	$-0.580504\pi$
$773$	−13.9139	−0.500448	−0.250224	+	0.968188i	$0.580504\pi$
$774$	−12.2618	−0.440743
$775$	−9.32133	−0.334832
$776$	−25.4824	−0.914763
$777$	4.11362	0.147575
$778$	−21.0455	−0.754519
$779$	−30.0674	−1.07728
$780$	−3.91983	−0.140352
$781$	3.72122	0.133156
$782$	−10.6583	−0.381139
$783$	−8.30374	−0.296751
$784$	12.0789	0.431388
$785$	1.21926	0.0435172
$786$	27.1922	0.969912
$787$	33.5144	1.19466	0.597330	−	0.801995i	$-0.296228\pi$
$787$	33.5144	1.19466	0.597330	+	0.801995i	$0.296228\pi$
$788$	−1.38078	−0.0491884
$789$	−7.96688	−0.283628
$790$	−27.3017	−0.971350
$791$	22.0386	0.783603
$792$	−0.528808	−0.0187904
$793$	54.2361	1.92598
$794$	−6.77812	−0.240547
$795$	−10.3895	−0.368479
$796$	10.8031	0.382907
$797$	−46.7733	−1.65680	−0.828398	−	0.560140i	$-0.810747\pi$
$797$	−46.7733	−1.65680	−0.828398	+	0.560140i	$0.810747\pi$
$798$	−21.7061	−0.768389
$799$	−2.90935	−0.102925
$800$	16.9490	0.599238
$801$	4.13745	0.146190
$802$	−9.83524	−0.347294
$803$	2.64991	0.0935134
$804$	5.18129	0.182730
$805$	16.2876	0.574063
$806$	15.9003	0.560066
$807$	−6.90789	−0.243169
$808$	−10.4018	−0.365935
$809$	13.2925	0.467339	0.233670	−	0.972316i	$-0.424927\pi$
$809$	13.2925	0.467339	0.233670	+	0.972316i	$0.424927\pi$
$810$	−2.08205	−0.0731559
$811$	−20.0906	−0.705475	−0.352738	−	0.935722i	$-0.614749\pi$
$811$	−20.0906	−0.705475	−0.352738	+	0.935722i	$0.614749\pi$
$812$	16.2800	0.571316
$813$	−15.7694	−0.553059
$814$	−0.937635	−0.0328641
$815$	−7.64264	−0.267710
$816$	4.99295	0.174788
$817$	−42.6457	−1.49198
$818$	−57.2627	−2.00214
$819$	−7.51160	−0.262477
$820$	5.65440	0.197460
$821$	−1.15055	−0.0401544	−0.0200772	−	0.999798i	$-0.506391\pi$
$821$	−1.15055	−0.0401544	−0.0200772	+	0.999798i	$0.506391\pi$
$822$	−26.4417	−0.922261
$823$	−34.7166	−1.21015	−0.605073	−	0.796170i	$-0.706856\pi$
$823$	−34.7166	−1.21015	−0.605073	+	0.796170i	$0.706856\pi$
$824$	23.1127	0.805169
$825$	−1.00372	−0.0349451
$826$	−32.0270	−1.11436
$827$	−42.2519	−1.46924	−0.734621	−	0.678478i	$-0.762640\pi$
$827$	−42.2519	−1.46924	−0.734621	+	0.678478i	$0.762640\pi$
$828$	5.71742	0.198694
$829$	−38.5252	−1.33803	−0.669017	−	0.743247i	$-0.733285\pi$
$829$	−38.5252	−1.33803	−0.669017	+	0.743247i	$0.733285\pi$
$830$	−15.3036	−0.531195
$831$	−7.40189	−0.256769
$832$	6.13514	0.212698
$833$	2.41919	0.0838199
$834$	−28.5213	−0.987611
$835$	−20.8617	−0.721948
$836$	1.55421	0.0537535
$837$	2.65307	0.0917036
$838$	69.4273	2.39833
$839$	−33.2313	−1.14727	−0.573637	−	0.819110i	$-0.694468\pi$
$839$	−33.2313	−1.14727	−0.573637	+	0.819110i	$0.694468\pi$
$840$	−4.83037	−0.166664
$841$	39.9520	1.37766
$842$	−54.9051	−1.89216
$843$	23.7510	0.818029
$844$	−20.1555	−0.693780
$845$	0.832138	0.0286264
$846$	4.96812	0.170807
$847$	23.3684	0.802949
$848$	−42.5459	−1.46103
$849$	−0.887872	−0.0304717
$850$	5.99963	0.205786
$851$	−11.9962	−0.411224
$852$	11.9319	0.408781
$853$	16.2397	0.556038	0.278019	−	0.960576i	$-0.410322\pi$
$853$	16.2397	0.556038	0.278019	+	0.960576i	$0.410322\pi$
$854$	−56.4800	−1.93270
$855$	−7.24121	−0.247644
$856$	3.49289	0.119385
$857$	40.8447	1.39523	0.697614	−	0.716474i	$-0.254245\pi$
$857$	40.8447	1.39523	0.697614	+	0.716474i	$0.254245\pi$
$858$	1.71215	0.0584519
$859$	−35.3043	−1.20457	−0.602284	−	0.798282i	$-0.705743\pi$
$859$	−35.3043	−1.20457	−0.602284	+	0.798282i	$0.705743\pi$
$860$	8.01983	0.273474
$861$	10.8356	0.369276
$862$	−11.5879	−0.394684
$863$	57.2548	1.94898	0.974488	−	0.224438i	$-0.0720545\pi$
$863$	57.2548	1.94898	0.974488	+	0.224438i	$0.0720545\pi$
$864$	−4.82409	−0.164119
$865$	−19.3609	−0.658291
$866$	27.8179	0.945292
$867$	1.00000	0.0339618
$868$	−5.20152	−0.176551
$869$	3.74613	0.127079
$870$	17.2888	0.586146
$871$	19.8513	0.672637
$872$	31.0050	1.04996
$873$	13.7666	0.465928
$874$	63.2997	2.14114
$875$	−22.2162	−0.751046
$876$	8.49682	0.287081
$877$	−29.5833	−0.998958	−0.499479	−	0.866326i	$-0.666475\pi$
$877$	−29.5833	−0.998958	−0.499479	+	0.866326i	$0.666475\pi$
$878$	−19.5731	−0.660560
$879$	−8.79148	−0.296529
$880$	1.73915	0.0586269
$881$	55.3730	1.86556	0.932781	−	0.360443i	$-0.117374\pi$
$881$	55.3730	1.86556	0.932781	+	0.360443i	$0.117374\pi$
$882$	−4.13110	−0.139101
$883$	−23.3955	−0.787322	−0.393661	−	0.919256i	$-0.628792\pi$
$883$	−23.3955	−0.787322	−0.393661	+	0.919256i	$0.628792\pi$
$884$	−3.21493	−0.108130
$885$	−10.6843	−0.359148
$886$	20.0993	0.675249
$887$	−1.04899	−0.0352217	−0.0176108	−	0.999845i	$-0.505606\pi$
$887$	−1.04899	−0.0352217	−0.0176108	+	0.999845i	$0.505606\pi$
$888$	3.55767	0.119388
$889$	13.4623	0.451510
$890$	−8.61440	−0.288755
$891$	0.285683	0.00957075
$892$	22.7870	0.762965
$893$	17.2787	0.578210
$894$	5.48637	0.183492
$895$	−16.6380	−0.556146
$896$	−27.0388	−0.903304
$897$	21.9054	0.731401
$898$	−35.4523	−1.18306
$899$	−22.0304	−0.734756
$900$	−3.21839	−0.107280
$901$	−8.52120	−0.283882
$902$	−2.46980	−0.0822354
$903$	15.3685	0.511431
$904$	19.0602	0.633931
$905$	−15.6889	−0.521517
$906$	21.1923	0.704066
$907$	41.1589	1.36666	0.683329	−	0.730110i	$-0.260531\pi$
$907$	41.1589	1.36666	0.683329	+	0.730110i	$0.260531\pi$
$908$	7.83962	0.260167
$909$	5.61949	0.186387
$910$	15.6396	0.518446
$911$	−8.95510	−0.296696	−0.148348	−	0.988935i	$-0.547396\pi$
$911$	−8.95510	−0.296696	−0.148348	+	0.988935i	$0.547396\pi$
$912$	−29.6533	−0.981918
$913$	2.09984	0.0694946
$914$	40.7394	1.34754
$915$	−18.8418	−0.622891
$916$	−16.1139	−0.532420
$917$	−34.0815	−1.12547
$918$	−1.70764	−0.0563605
$919$	−11.3604	−0.374746	−0.187373	−	0.982289i	$-0.559997\pi$
$919$	−11.3604	−0.374746	−0.187373	+	0.982289i	$0.559997\pi$
$920$	14.0864	0.464414
$921$	3.14939	0.103776
$922$	−10.4052	−0.342677
$923$	45.7154	1.50474
$924$	−0.560100	−0.0184260
$925$	6.75276	0.222029
$926$	−10.0613	−0.330636
$927$	−12.4864	−0.410107
$928$	40.0580	1.31497
$929$	31.1385	1.02162	0.510811	−	0.859693i	$-0.329345\pi$
$929$	31.1385	1.02162	0.510811	+	0.859693i	$0.329345\pi$
$930$	−5.52384	−0.181134
$931$	−14.3676	−0.470880
$932$	−12.6004	−0.412741
$933$	10.5942	0.346839
$934$	15.2581	0.499259
$935$	0.348322	0.0113913
$936$	−6.49643	−0.212342
$937$	−41.3305	−1.35021	−0.675104	−	0.737722i	$-0.735901\pi$
$937$	−41.3305	−1.35021	−0.675104	+	0.737722i	$0.735901\pi$
$938$	−20.6726	−0.674986
$939$	33.5215	1.09393
$940$	−3.24939	−0.105983
$941$	26.7062	0.870598	0.435299	−	0.900286i	$-0.356643\pi$
$941$	26.7062	0.870598	0.435299	+	0.900286i	$0.356643\pi$
$942$	−1.70764	−0.0556379
$943$	−31.5989	−1.02900
$944$	−43.7529	−1.42404
$945$	2.60956	0.0848889
$946$	−3.50300	−0.113893
$947$	31.4429	1.02176	0.510879	−	0.859653i	$-0.329320\pi$
$947$	31.4429	1.02176	0.510879	+	0.859653i	$0.329320\pi$
$948$	12.0118	0.390124
$949$	32.5543	1.05676
$950$	−35.6320	−1.15605
$951$	9.84711	0.319314
$952$	−3.96173	−0.128400
$953$	−17.7993	−0.576576	−0.288288	−	0.957544i	$-0.593086\pi$
$953$	−17.7993	−0.576576	−0.288288	+	0.957544i	$0.593086\pi$
$954$	14.5511	0.471110
$955$	−0.497180	−0.0160884
$956$	7.04020	0.227696
$957$	−2.37224	−0.0766836
$958$	11.3025	0.365166
$959$	33.1410	1.07018
$960$	−2.13137	−0.0687897
$961$	−23.9612	−0.772942
$962$	−11.5189	−0.371384
$963$	−1.88700	−0.0608077
$964$	3.84487	0.123835
$965$	−19.6866	−0.633733
$966$	−22.8117	−0.733955
$967$	−42.2413	−1.35839	−0.679194	−	0.733959i	$-0.737671\pi$
$967$	−42.2413	−1.35839	−0.679194	+	0.733959i	$0.737671\pi$
$968$	20.2103	0.649582
$969$	−5.93903	−0.190789
$970$	−28.6628	−0.920306
$971$	26.0975	0.837508	0.418754	−	0.908100i	$-0.362467\pi$
$971$	26.0975	0.837508	0.418754	+	0.908100i	$0.362467\pi$
$972$	0.916030	0.0293817
$973$	35.7474	1.14601
$974$	−15.8967	−0.509362
$975$	−12.3308	−0.394901
$976$	−77.1586	−2.46979
$977$	1.74061	0.0556870	0.0278435	−	0.999612i	$-0.491136\pi$
$977$	1.74061	0.0556870	0.0278435	+	0.999612i	$0.491136\pi$
$978$	10.7039	0.342274
$979$	1.18200	0.0377770
$980$	2.70193	0.0863101
$981$	−16.7501	−0.534790
$982$	−53.9818	−1.72263
$983$	−8.71965	−0.278114	−0.139057	−	0.990284i	$-0.544407\pi$
$983$	−8.71965	−0.278114	−0.139057	+	0.990284i	$0.544407\pi$
$984$	9.37118	0.298742
$985$	1.83786	0.0585590
$986$	14.1798	0.451576
$987$	−6.22683	−0.198202
$988$	19.0935	0.607446
$989$	−44.8178	−1.42512
$990$	−0.594808	−0.0189042
$991$	−3.75747	−0.119360	−0.0596799	−	0.998218i	$-0.519008\pi$
$991$	−3.75747	−0.119360	−0.0596799	+	0.998218i	$0.519008\pi$
$992$	−12.7987	−0.406358
$993$	11.5929	0.367889
$994$	−47.6067	−1.50999
$995$	−14.3792	−0.455852
$996$	6.73303	0.213344
$997$	51.9709	1.64594	0.822968	−	0.568088i	$-0.192317\pi$
$997$	51.9709	1.64594	0.822968	+	0.568088i	$0.192317\pi$
$998$	33.8600	1.07182
$999$	−1.92200	−0.0608093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.41	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.41	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70764 q^{2} +1.00000 q^{3} +0.916030 q^{4} -1.21926 q^{5} +1.70764 q^{6} -2.14028 q^{7} -1.85103 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.70764 q^{2} +1.00000 q^{3} +0.916030 q^{4} -1.21926 q^{5} +1.70764 q^{6} -2.14028 q^{7} -1.85103 q^{8} +1.00000 q^{9} -2.08205 q^{10} +0.285683 q^{11} +0.916030 q^{12} +3.50963 q^{13} -3.65483 q^{14} -1.21926 q^{15} -4.99295 q^{16} -1.00000 q^{17} +1.70764 q^{18} +5.93903 q^{19} -1.11688 q^{20} -2.14028 q^{21} +0.487844 q^{22} +6.24152 q^{23} -1.85103 q^{24} -3.51341 q^{25} +5.99318 q^{26} +1.00000 q^{27} -1.96056 q^{28} -8.30374 q^{29} -2.08205 q^{30} +2.65307 q^{31} -4.82409 q^{32} +0.285683 q^{33} -1.70764 q^{34} +2.60956 q^{35} +0.916030 q^{36} -1.92200 q^{37} +10.1417 q^{38} +3.50963 q^{39} +2.25688 q^{40} -5.06269 q^{41} -3.65483 q^{42} -7.18058 q^{43} +0.261695 q^{44} -1.21926 q^{45} +10.6583 q^{46} +2.90935 q^{47} -4.99295 q^{48} -2.41919 q^{49} -5.99963 q^{50} -1.00000 q^{51} +3.21493 q^{52} +8.52120 q^{53} +1.70764 q^{54} -0.348322 q^{55} +3.96173 q^{56} +5.93903 q^{57} -14.1798 q^{58} +8.76294 q^{59} -1.11688 q^{60} +15.4535 q^{61} +4.53049 q^{62} -2.14028 q^{63} +1.74809 q^{64} -4.27915 q^{65} +0.487844 q^{66} +5.65625 q^{67} -0.916030 q^{68} +6.24152 q^{69} +4.45618 q^{70} +13.0257 q^{71} -1.85103 q^{72} +9.27570 q^{73} -3.28208 q^{74} -3.51341 q^{75} +5.44033 q^{76} -0.611443 q^{77} +5.99318 q^{78} +13.1129 q^{79} +6.08770 q^{80} +1.00000 q^{81} -8.64524 q^{82} +7.35023 q^{83} -1.96056 q^{84} +1.21926 q^{85} -12.2618 q^{86} -8.30374 q^{87} -0.528808 q^{88} +4.13745 q^{89} -2.08205 q^{90} -7.51160 q^{91} +5.71742 q^{92} +2.65307 q^{93} +4.96812 q^{94} -7.24121 q^{95} -4.82409 q^{96} +13.7666 q^{97} -4.13110 q^{98} +0.285683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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