LMFDB - Embedded newform 4334.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.683877 q^{3} +1.00000 q^{4} +2.76760 q^{5} +0.683877 q^{6} +4.51462 q^{7} +1.00000 q^{8} -2.53231 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.683877 q^{3} +1.00000 q^{4} +2.76760 q^{5} +0.683877 q^{6} +4.51462 q^{7} +1.00000 q^{8} -2.53231 q^{9} +2.76760 q^{10} +1.00000 q^{11} +0.683877 q^{12} -1.02623 q^{13} +4.51462 q^{14} +1.89270 q^{15} +1.00000 q^{16} +6.06071 q^{17} -2.53231 q^{18} +7.69643 q^{19} +2.76760 q^{20} +3.08744 q^{21} +1.00000 q^{22} -2.16709 q^{23} +0.683877 q^{24} +2.65961 q^{25} -1.02623 q^{26} -3.78342 q^{27} +4.51462 q^{28} -4.15501 q^{29} +1.89270 q^{30} +0.166048 q^{31} +1.00000 q^{32} +0.683877 q^{33} +6.06071 q^{34} +12.4947 q^{35} -2.53231 q^{36} -6.72954 q^{37} +7.69643 q^{38} -0.701815 q^{39} +2.76760 q^{40} -8.89676 q^{41} +3.08744 q^{42} -1.19188 q^{43} +1.00000 q^{44} -7.00843 q^{45} -2.16709 q^{46} -11.4869 q^{47} +0.683877 q^{48} +13.3818 q^{49} +2.65961 q^{50} +4.14478 q^{51} -1.02623 q^{52} -3.17738 q^{53} -3.78342 q^{54} +2.76760 q^{55} +4.51462 q^{56} +5.26341 q^{57} -4.15501 q^{58} -5.79089 q^{59} +1.89270 q^{60} +10.1741 q^{61} +0.166048 q^{62} -11.4324 q^{63} +1.00000 q^{64} -2.84020 q^{65} +0.683877 q^{66} -6.82726 q^{67} +6.06071 q^{68} -1.48202 q^{69} +12.4947 q^{70} -0.971613 q^{71} -2.53231 q^{72} +9.52771 q^{73} -6.72954 q^{74} +1.81885 q^{75} +7.69643 q^{76} +4.51462 q^{77} -0.701815 q^{78} +5.17725 q^{79} +2.76760 q^{80} +5.00955 q^{81} -8.89676 q^{82} -8.08657 q^{83} +3.08744 q^{84} +16.7736 q^{85} -1.19188 q^{86} -2.84152 q^{87} +1.00000 q^{88} -2.84199 q^{89} -7.00843 q^{90} -4.63304 q^{91} -2.16709 q^{92} +0.113557 q^{93} -11.4869 q^{94} +21.3006 q^{95} +0.683877 q^{96} +3.07564 q^{97} +13.3818 q^{98} -2.53231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.683877	0.394836	0.197418	−	0.980319i	$-0.436744\pi$
$3$	0.683877	0.394836	0.197418	+	0.980319i	$0.436744\pi$
$4$	1.00000	0.500000
$5$	2.76760	1.23771	0.618854	−	0.785506i	$-0.287597\pi$
$5$	2.76760	1.23771	0.618854	+	0.785506i	$0.287597\pi$
$6$	0.683877	0.279191
$7$	4.51462	1.70637	0.853183	−	0.521611i	$-0.174669\pi$
$7$	4.51462	1.70637	0.853183	+	0.521611i	$0.174669\pi$
$8$	1.00000	0.353553
$9$	−2.53231	−0.844104
$10$	2.76760	0.875192
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.683877	0.197418
$13$	−1.02623	−0.284625	−0.142313	−	0.989822i	$-0.545454\pi$
$13$	−1.02623	−0.284625	−0.142313	+	0.989822i	$0.545454\pi$
$14$	4.51462	1.20658
$15$	1.89270	0.488692
$16$	1.00000	0.250000
$17$	6.06071	1.46994	0.734969	−	0.678101i	$-0.237197\pi$
$17$	6.06071	1.46994	0.734969	+	0.678101i	$0.237197\pi$
$18$	−2.53231	−0.596872
$19$	7.69643	1.76568	0.882841	−	0.469671i	$-0.155628\pi$
$19$	7.69643	1.76568	0.882841	+	0.469671i	$0.155628\pi$
$20$	2.76760	0.618854
$21$	3.08744	0.673736
$22$	1.00000	0.213201
$23$	−2.16709	−0.451870	−0.225935	−	0.974142i	$-0.572544\pi$
$23$	−2.16709	−0.451870	−0.225935	+	0.974142i	$0.572544\pi$
$24$	0.683877	0.139596
$25$	2.65961	0.531922
$26$	−1.02623	−0.201260
$27$	−3.78342	−0.728119
$28$	4.51462	0.853183
$29$	−4.15501	−0.771567	−0.385783	−	0.922589i	$-0.626069\pi$
$29$	−4.15501	−0.771567	−0.385783	+	0.922589i	$0.626069\pi$
$30$	1.89270	0.345558
$31$	0.166048	0.0298231	0.0149116	−	0.999889i	$-0.495253\pi$
$31$	0.166048	0.0298231	0.0149116	+	0.999889i	$0.495253\pi$
$32$	1.00000	0.176777
$33$	0.683877	0.119048
$34$	6.06071	1.03940
$35$	12.4947	2.11198
$36$	−2.53231	−0.422052
$37$	−6.72954	−1.10633	−0.553165	−	0.833072i	$-0.686580\pi$
$37$	−6.72954	−1.10633	−0.553165	+	0.833072i	$0.686580\pi$
$38$	7.69643	1.24853
$39$	−0.701815	−0.112380
$40$	2.76760	0.437596
$41$	−8.89676	−1.38944	−0.694721	−	0.719280i	$-0.744472\pi$
$41$	−8.89676	−1.38944	−0.694721	+	0.719280i	$0.744472\pi$
$42$	3.08744	0.476403
$43$	−1.19188	−0.181761	−0.0908803	−	0.995862i	$-0.528968\pi$
$43$	−1.19188	−0.181761	−0.0908803	+	0.995862i	$0.528968\pi$
$44$	1.00000	0.150756
$45$	−7.00843	−1.04475
$46$	−2.16709	−0.319521
$47$	−11.4869	−1.67554	−0.837770	−	0.546024i	$-0.816141\pi$
$47$	−11.4869	−1.67554	−0.837770	+	0.546024i	$0.816141\pi$
$48$	0.683877	0.0987091
$49$	13.3818	1.91169
$50$	2.65961	0.376126
$51$	4.14478	0.580385
$52$	−1.02623	−0.142313
$53$	−3.17738	−0.436446	−0.218223	−	0.975899i	$-0.570026\pi$
$53$	−3.17738	−0.436446	−0.218223	+	0.975899i	$0.570026\pi$
$54$	−3.78342	−0.514858
$55$	2.76760	0.373183
$56$	4.51462	0.603292
$57$	5.26341	0.697156
$58$	−4.15501	−0.545580
$59$	−5.79089	−0.753910	−0.376955	−	0.926232i	$-0.623029\pi$
$59$	−5.79089	−0.753910	−0.376955	+	0.926232i	$0.623029\pi$
$60$	1.89270	0.244346
$61$	10.1741	1.30266	0.651332	−	0.758793i	$-0.274210\pi$
$61$	10.1741	1.30266	0.651332	+	0.758793i	$0.274210\pi$
$62$	0.166048	0.0210881
$63$	−11.4324	−1.44035
$64$	1.00000	0.125000
$65$	−2.84020	−0.352283
$66$	0.683877	0.0841794
$67$	−6.82726	−0.834083	−0.417041	−	0.908888i	$-0.636933\pi$
$67$	−6.82726	−0.834083	−0.417041	+	0.908888i	$0.636933\pi$
$68$	6.06071	0.734969
$69$	−1.48202	−0.178415
$70$	12.4947	1.49340
$71$	−0.971613	−0.115309	−0.0576546	−	0.998337i	$-0.518362\pi$
$71$	−0.971613	−0.115309	−0.0576546	+	0.998337i	$0.518362\pi$
$72$	−2.53231	−0.298436
$73$	9.52771	1.11513	0.557567	−	0.830132i	$-0.311735\pi$
$73$	9.52771	1.11513	0.557567	+	0.830132i	$0.311735\pi$
$74$	−6.72954	−0.782293
$75$	1.81885	0.210022
$76$	7.69643	0.882841
$77$	4.51462	0.514489
$78$	−0.701815	−0.0794649
$79$	5.17725	0.582486	0.291243	−	0.956649i	$-0.405931\pi$
$79$	5.17725	0.582486	0.291243	+	0.956649i	$0.405931\pi$
$80$	2.76760	0.309427
$81$	5.00955	0.556616
$82$	−8.89676	−0.982483
$83$	−8.08657	−0.887616	−0.443808	−	0.896122i	$-0.646373\pi$
$83$	−8.08657	−0.887616	−0.443808	+	0.896122i	$0.646373\pi$
$84$	3.08744	0.336868
$85$	16.7736	1.81936
$86$	−1.19188	−0.128524
$87$	−2.84152	−0.304643
$88$	1.00000	0.106600
$89$	−2.84199	−0.301250	−0.150625	−	0.988591i	$-0.548129\pi$
$89$	−2.84199	−0.301250	−0.150625	+	0.988591i	$0.548129\pi$
$90$	−7.00843	−0.738753
$91$	−4.63304	−0.485675
$92$	−2.16709	−0.225935
$93$	0.113557	0.0117753
$94$	−11.4869	−1.18479
$95$	21.3006	2.18540
$96$	0.683877	0.0697979
$97$	3.07564	0.312284	0.156142	−	0.987735i	$-0.450094\pi$
$97$	3.07564	0.312284	0.156142	+	0.987735i	$0.450094\pi$
$98$	13.3818	1.35177
$99$	−2.53231	−0.254507
$100$	2.65961	0.265961
$101$	10.6979	1.06448	0.532238	−	0.846595i	$-0.321351\pi$
$101$	10.6979	1.06448	0.532238	+	0.846595i	$0.321351\pi$
$102$	4.14478	0.410394
$103$	−12.5652	−1.23809	−0.619043	−	0.785357i	$-0.712479\pi$
$103$	−12.5652	−1.23809	−0.619043	+	0.785357i	$0.712479\pi$
$104$	−1.02623	−0.100630
$105$	8.54481	0.833888
$106$	−3.17738	−0.308614
$107$	−16.8782	−1.63168	−0.815840	−	0.578278i	$-0.803725\pi$
$107$	−16.8782	−1.63168	−0.815840	+	0.578278i	$0.803725\pi$
$108$	−3.78342	−0.364060
$109$	8.00845	0.767070	0.383535	−	0.923526i	$-0.374706\pi$
$109$	8.00845	0.767070	0.383535	+	0.923526i	$0.374706\pi$
$110$	2.76760	0.263880
$111$	−4.60218	−0.436819
$112$	4.51462	0.426592
$113$	−5.14654	−0.484146	−0.242073	−	0.970258i	$-0.577827\pi$
$113$	−5.14654	−0.484146	−0.242073	+	0.970258i	$0.577827\pi$
$114$	5.26341	0.492964
$115$	−5.99765	−0.559284
$116$	−4.15501	−0.385783
$117$	2.59874	0.240253
$118$	−5.79089	−0.533095
$119$	27.3618	2.50825
$120$	1.89270	0.172779
$121$	1.00000	0.0909091
$122$	10.1741	0.921123
$123$	−6.08429	−0.548602
$124$	0.166048	0.0149116
$125$	−6.47726	−0.579344
$126$	−11.4324	−1.01848
$127$	−18.5027	−1.64185	−0.820925	−	0.571036i	$-0.806542\pi$
$127$	−18.5027	−1.64185	−0.820925	+	0.571036i	$0.806542\pi$
$128$	1.00000	0.0883883
$129$	−0.815102	−0.0717657
$130$	−2.84020	−0.249102
$131$	13.6108	1.18918	0.594590	−	0.804029i	$-0.297314\pi$
$131$	13.6108	1.18918	0.594590	+	0.804029i	$0.297314\pi$
$132$	0.683877	0.0595238
$133$	34.7465	3.01290
$134$	−6.82726	−0.589786
$135$	−10.4710	−0.901200
$136$	6.06071	0.519702
$137$	−5.02259	−0.429109	−0.214555	−	0.976712i	$-0.568830\pi$
$137$	−5.02259	−0.429109	−0.214555	+	0.976712i	$0.568830\pi$
$138$	−1.48202	−0.126158
$139$	−15.6019	−1.32334	−0.661670	−	0.749795i	$-0.730152\pi$
$139$	−15.6019	−1.32334	−0.661670	+	0.749795i	$0.730152\pi$
$140$	12.4947	1.05599
$141$	−7.85564	−0.661564
$142$	−0.971613	−0.0815360
$143$	−1.02623	−0.0858177
$144$	−2.53231	−0.211026
$145$	−11.4994	−0.954975
$146$	9.52771	0.788519
$147$	9.15151	0.754804
$148$	−6.72954	−0.553165
$149$	16.9992	1.39263	0.696313	−	0.717738i	$-0.254822\pi$
$149$	16.9992	1.39263	0.696313	+	0.717738i	$0.254822\pi$
$150$	1.81885	0.148508
$151$	9.16508	0.745844	0.372922	−	0.927863i	$-0.378356\pi$
$151$	9.16508	0.745844	0.372922	+	0.927863i	$0.378356\pi$
$152$	7.69643	0.624263
$153$	−15.3476	−1.24078
$154$	4.51462	0.363799
$155$	0.459555	0.0369124
$156$	−0.701815	−0.0561902
$157$	−12.5275	−0.999799	−0.499900	−	0.866083i	$-0.666630\pi$
$157$	−12.5275	−0.999799	−0.499900	+	0.866083i	$0.666630\pi$
$158$	5.17725	0.411880
$159$	−2.17293	−0.172325
$160$	2.76760	0.218798
$161$	−9.78361	−0.771056
$162$	5.00955	0.393587
$163$	15.5530	1.21821	0.609103	−	0.793091i	$-0.291530\pi$
$163$	15.5530	1.21821	0.609103	+	0.793091i	$0.291530\pi$
$164$	−8.89676	−0.694721
$165$	1.89270	0.147346
$166$	−8.08657	−0.627639
$167$	13.2557	1.02575	0.512877	−	0.858462i	$-0.328580\pi$
$167$	13.2557	1.02575	0.512877	+	0.858462i	$0.328580\pi$
$168$	3.08744	0.238202
$169$	−11.9469	−0.918989
$170$	16.7736	1.28648
$171$	−19.4898	−1.49042
$172$	−1.19188	−0.0908803
$173$	11.7774	0.895422	0.447711	−	0.894178i	$-0.352239\pi$
$173$	11.7774	0.895422	0.447711	+	0.894178i	$0.352239\pi$
$174$	−2.84152	−0.215415
$175$	12.0071	0.907654
$176$	1.00000	0.0753778
$177$	−3.96025	−0.297671
$178$	−2.84199	−0.213016
$179$	4.11180	0.307330	0.153665	−	0.988123i	$-0.450892\pi$
$179$	4.11180	0.307330	0.153665	+	0.988123i	$0.450892\pi$
$180$	−7.00843	−0.522377
$181$	−11.5079	−0.855373	−0.427687	−	0.903927i	$-0.640671\pi$
$181$	−11.5079	−0.855373	−0.427687	+	0.903927i	$0.640671\pi$
$182$	−4.63304	−0.343424
$183$	6.95785	0.514339
$184$	−2.16709	−0.159760
$185$	−18.6247	−1.36931
$186$	0.113557	0.00832637
$187$	6.06071	0.443203
$188$	−11.4869	−0.837770
$189$	−17.0807	−1.24244
$190$	21.3006	1.54531
$191$	15.0229	1.08702	0.543508	−	0.839404i	$-0.317096\pi$
$191$	15.0229	1.08702	0.543508	+	0.839404i	$0.317096\pi$
$192$	0.683877	0.0493545
$193$	−7.57418	−0.545201	−0.272601	−	0.962127i	$-0.587884\pi$
$193$	−7.57418	−0.545201	−0.272601	+	0.962127i	$0.587884\pi$
$194$	3.07564	0.220818
$195$	−1.94234	−0.139094
$196$	13.3818	0.955844
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−2.53231	−0.179964
$199$	17.6974	1.25454	0.627268	−	0.778804i	$-0.284173\pi$
$199$	17.6974	1.25454	0.627268	+	0.778804i	$0.284173\pi$
$200$	2.65961	0.188063
$201$	−4.66900	−0.329326
$202$	10.6979	0.752698
$203$	−18.7583	−1.31658
$204$	4.14478	0.290193
$205$	−24.6227	−1.71972
$206$	−12.5652	−0.875459
$207$	5.48776	0.381426
$208$	−1.02623	−0.0711563
$209$	7.69643	0.532373
$210$	8.54481	0.589648
$211$	20.9464	1.44201	0.721006	−	0.692929i	$-0.243680\pi$
$211$	20.9464	1.44201	0.721006	+	0.692929i	$0.243680\pi$
$212$	−3.17738	−0.218223
$213$	−0.664464	−0.0455283
$214$	−16.8782	−1.15377
$215$	−3.29866	−0.224967
$216$	−3.78342	−0.257429
$217$	0.749645	0.0508892
$218$	8.00845	0.542401
$219$	6.51578	0.440295
$220$	2.76760	0.186592
$221$	−6.21968	−0.418381
$222$	−4.60218	−0.308878
$223$	−8.77257	−0.587455	−0.293727	−	0.955889i	$-0.594896\pi$
$223$	−8.77257	−0.587455	−0.293727	+	0.955889i	$0.594896\pi$
$224$	4.51462	0.301646
$225$	−6.73497	−0.448998
$226$	−5.14654	−0.342343
$227$	−14.2236	−0.944051	−0.472026	−	0.881585i	$-0.656477\pi$
$227$	−14.2236	−0.944051	−0.472026	+	0.881585i	$0.656477\pi$
$228$	5.26341	0.348578
$229$	−8.28622	−0.547569	−0.273784	−	0.961791i	$-0.588276\pi$
$229$	−8.28622	−0.547569	−0.273784	+	0.961791i	$0.588276\pi$
$230$	−5.99765	−0.395473
$231$	3.08744	0.203139
$232$	−4.15501	−0.272790
$233$	−7.03034	−0.460573	−0.230286	−	0.973123i	$-0.573966\pi$
$233$	−7.03034	−0.460573	−0.230286	+	0.973123i	$0.573966\pi$
$234$	2.59874	0.169885
$235$	−31.7912	−2.07383
$236$	−5.79089	−0.376955
$237$	3.54060	0.229987
$238$	27.3618	1.77360
$239$	6.27243	0.405730	0.202865	−	0.979207i	$-0.434975\pi$
$239$	6.27243	0.405730	0.202865	+	0.979207i	$0.434975\pi$
$240$	1.89270	0.122173
$241$	0.464683	0.0299329	0.0149664	−	0.999888i	$-0.495236\pi$
$241$	0.464683	0.0299329	0.0149664	+	0.999888i	$0.495236\pi$
$242$	1.00000	0.0642824
$243$	14.7762	0.947892
$244$	10.1741	0.651332
$245$	37.0355	2.36611
$246$	−6.08429	−0.387920
$247$	−7.89831	−0.502558
$248$	0.166048	0.0105441
$249$	−5.53021	−0.350463
$250$	−6.47726	−0.409658
$251$	−20.5139	−1.29483	−0.647413	−	0.762139i	$-0.724149\pi$
$251$	−20.5139	−1.29483	−0.647413	+	0.762139i	$0.724149\pi$
$252$	−11.4324	−0.720176
$253$	−2.16709	−0.136244
$254$	−18.5027	−1.16096
$255$	11.4711	0.718347
$256$	1.00000	0.0625000
$257$	−12.3801	−0.772247	−0.386123	−	0.922447i	$-0.626186\pi$
$257$	−12.3801	−0.772247	−0.386123	+	0.922447i	$0.626186\pi$
$258$	−0.815102	−0.0507460
$259$	−30.3813	−1.88780
$260$	−2.84020	−0.176141
$261$	10.5218	0.651283
$262$	13.6108	0.840877
$263$	−7.69701	−0.474618	−0.237309	−	0.971434i	$-0.576265\pi$
$263$	−7.69701	−0.474618	−0.237309	+	0.971434i	$0.576265\pi$
$264$	0.683877	0.0420897
$265$	−8.79371	−0.540193
$266$	34.7465	2.13044
$267$	−1.94357	−0.118945
$268$	−6.82726	−0.417041
$269$	−10.1729	−0.620250	−0.310125	−	0.950696i	$-0.600371\pi$
$269$	−10.1729	−0.620250	−0.310125	+	0.950696i	$0.600371\pi$
$270$	−10.4710	−0.637244
$271$	17.7473	1.07807	0.539037	−	0.842282i	$-0.318788\pi$
$271$	17.7473	1.07807	0.539037	+	0.842282i	$0.318788\pi$
$272$	6.06071	0.367485
$273$	−3.16843	−0.191762
$274$	−5.02259	−0.303426
$275$	2.65961	0.160381
$276$	−1.48202	−0.0892074
$277$	13.1898	0.792496	0.396248	−	0.918143i	$-0.370312\pi$
$277$	13.1898	0.792496	0.396248	+	0.918143i	$0.370312\pi$
$278$	−15.6019	−0.935743
$279$	−0.420486	−0.0251738
$280$	12.4947	0.746699
$281$	−13.4345	−0.801433	−0.400716	−	0.916202i	$-0.631239\pi$
$281$	−13.4345	−0.801433	−0.400716	+	0.916202i	$0.631239\pi$
$282$	−7.85564	−0.467796
$283$	2.33439	0.138765	0.0693827	−	0.997590i	$-0.477897\pi$
$283$	2.33439	0.138765	0.0693827	+	0.997590i	$0.477897\pi$
$284$	−0.971613	−0.0576546
$285$	14.5670	0.862875
$286$	−1.02623	−0.0606823
$287$	−40.1655	−2.37090
$288$	−2.53231	−0.149218
$289$	19.7322	1.16072
$290$	−11.4994	−0.675269
$291$	2.10336	0.123301
$292$	9.52771	0.557567
$293$	23.4965	1.37268	0.686339	−	0.727281i	$-0.259216\pi$
$293$	23.4965	1.37268	0.686339	+	0.727281i	$0.259216\pi$
$294$	9.15151	0.533727
$295$	−16.0269	−0.933120
$296$	−6.72954	−0.391147
$297$	−3.78342	−0.219536
$298$	16.9992	0.984736
$299$	2.22394	0.128614
$300$	1.81885	0.105011
$301$	−5.38091	−0.310150
$302$	9.16508	0.527391
$303$	7.31601	0.420294
$304$	7.69643	0.441421
$305$	28.1579	1.61232
$306$	−15.3476	−0.877365
$307$	−3.39471	−0.193746	−0.0968731	−	0.995297i	$-0.530884\pi$
$307$	−3.39471	−0.193746	−0.0968731	+	0.995297i	$0.530884\pi$
$308$	4.51462	0.257244
$309$	−8.59305	−0.488841
$310$	0.459555	0.0261010
$311$	31.4450	1.78308	0.891540	−	0.452942i	$-0.149625\pi$
$311$	31.4450	1.78308	0.891540	+	0.452942i	$0.149625\pi$
$312$	−0.701815	−0.0397324
$313$	15.6618	0.885257	0.442629	−	0.896705i	$-0.354046\pi$
$313$	15.6618	0.885257	0.442629	+	0.896705i	$0.354046\pi$
$314$	−12.5275	−0.706965
$315$	−31.6404	−1.78274
$316$	5.17725	0.291243
$317$	−25.2786	−1.41979	−0.709895	−	0.704307i	$-0.751258\pi$
$317$	−25.2786	−1.41979	−0.709895	+	0.704307i	$0.751258\pi$
$318$	−2.17293	−0.121852
$319$	−4.15501	−0.232636
$320$	2.76760	0.154714
$321$	−11.5426	−0.644247
$322$	−9.78361	−0.545219
$323$	46.6458	2.59544
$324$	5.00955	0.278308
$325$	−2.72937	−0.151398
$326$	15.5530	0.861401
$327$	5.47679	0.302867
$328$	−8.89676	−0.491242
$329$	−51.8591	−2.85909
$330$	1.89270	0.104190
$331$	32.7192	1.79841	0.899206	−	0.437525i	$-0.144145\pi$
$331$	32.7192	1.79841	0.899206	+	0.437525i	$0.144145\pi$
$332$	−8.08657	−0.443808
$333$	17.0413	0.933858
$334$	13.2557	0.725318
$335$	−18.8951	−1.03235
$336$	3.08744	0.168434
$337$	32.5905	1.77532	0.887659	−	0.460501i	$-0.152330\pi$
$337$	32.5905	1.77532	0.887659	+	0.460501i	$0.152330\pi$
$338$	−11.9469	−0.649823
$339$	−3.51960	−0.191159
$340$	16.7736	0.909678
$341$	0.166048	0.00899202
$342$	−19.4898	−1.05389
$343$	28.8115	1.55567
$344$	−1.19188	−0.0642621
$345$	−4.10165	−0.220826
$346$	11.7774	0.633159
$347$	27.1647	1.45828	0.729138	−	0.684366i	$-0.239921\pi$
$347$	27.1647	1.45828	0.729138	+	0.684366i	$0.239921\pi$
$348$	−2.84152	−0.152321
$349$	−33.2822	−1.78156	−0.890778	−	0.454439i	$-0.849840\pi$
$349$	−33.2822	−1.78156	−0.890778	+	0.454439i	$0.849840\pi$
$350$	12.0071	0.641809
$351$	3.88266	0.207241
$352$	1.00000	0.0533002
$353$	−3.98383	−0.212038	−0.106019	−	0.994364i	$-0.533810\pi$
$353$	−3.98383	−0.212038	−0.106019	+	0.994364i	$0.533810\pi$
$354$	−3.96025	−0.210485
$355$	−2.68904	−0.142719
$356$	−2.84199	−0.150625
$357$	18.7121	0.990350
$358$	4.11180	0.217315
$359$	−26.4224	−1.39452	−0.697260	−	0.716819i	$-0.745598\pi$
$359$	−26.4224	−1.39452	−0.697260	+	0.716819i	$0.745598\pi$
$360$	−7.00843	−0.369377
$361$	40.2351	2.11763
$362$	−11.5079	−0.604840
$363$	0.683877	0.0358942
$364$	−4.63304	−0.242837
$365$	26.3689	1.38021
$366$	6.95785	0.363693
$367$	−15.1085	−0.788656	−0.394328	−	0.918970i	$-0.629023\pi$
$367$	−15.1085	−0.788656	−0.394328	+	0.918970i	$0.629023\pi$
$368$	−2.16709	−0.112968
$369$	22.5294	1.17283
$370$	−18.6247	−0.968251
$371$	−14.3446	−0.744737
$372$	0.113557	0.00588763
$373$	9.68461	0.501450	0.250725	−	0.968058i	$-0.419331\pi$
$373$	9.68461	0.501450	0.250725	+	0.968058i	$0.419331\pi$
$374$	6.06071	0.313392
$375$	−4.42965	−0.228746
$376$	−11.4869	−0.592393
$377$	4.26400	0.219607
$378$	−17.0807	−0.878537
$379$	29.9618	1.53903	0.769517	−	0.638626i	$-0.220497\pi$
$379$	29.9618	1.53903	0.769517	+	0.638626i	$0.220497\pi$
$380$	21.3006	1.09270
$381$	−12.6536	−0.648262
$382$	15.0229	0.768636
$383$	31.8406	1.62698	0.813489	−	0.581580i	$-0.197565\pi$
$383$	31.8406	1.62698	0.813489	+	0.581580i	$0.197565\pi$
$384$	0.683877	0.0348989
$385$	12.4947	0.636787
$386$	−7.57418	−0.385515
$387$	3.01822	0.153425
$388$	3.07564	0.156142
$389$	2.23631	0.113385	0.0566926	−	0.998392i	$-0.481944\pi$
$389$	2.23631	0.113385	0.0566926	+	0.998392i	$0.481944\pi$
$390$	−1.94234	−0.0983544
$391$	−13.1341	−0.664221
$392$	13.3818	0.675884
$393$	9.30810	0.469532
$394$	1.00000	0.0503793
$395$	14.3286	0.720948
$396$	−2.53231	−0.127254
$397$	−7.35698	−0.369236	−0.184618	−	0.982810i	$-0.559105\pi$
$397$	−7.35698	−0.369236	−0.184618	+	0.982810i	$0.559105\pi$
$398$	17.6974	0.887090
$399$	23.7623	1.18960
$400$	2.65961	0.132981
$401$	24.2814	1.21256	0.606278	−	0.795253i	$-0.292662\pi$
$401$	24.2814	1.21256	0.606278	+	0.795253i	$0.292662\pi$
$402$	−4.66900	−0.232869
$403$	−0.170404	−0.00848841
$404$	10.6979	0.532238
$405$	13.8644	0.688929
$406$	−18.7583	−0.930960
$407$	−6.72954	−0.333571
$408$	4.14478	0.205197
$409$	11.3016	0.558830	0.279415	−	0.960170i	$-0.409859\pi$
$409$	11.3016	0.558830	0.279415	+	0.960170i	$0.409859\pi$
$410$	−24.6227	−1.21603
$411$	−3.43483	−0.169428
$412$	−12.5652	−0.619043
$413$	−26.1437	−1.28645
$414$	5.48776	0.269709
$415$	−22.3804	−1.09861
$416$	−1.02623	−0.0503151
$417$	−10.6698	−0.522503
$418$	7.69643	0.376445
$419$	−10.6451	−0.520047	−0.260024	−	0.965602i	$-0.583730\pi$
$419$	−10.6451	−0.520047	−0.260024	+	0.965602i	$0.583730\pi$
$420$	8.54481	0.416944
$421$	−20.9530	−1.02119	−0.510593	−	0.859823i	$-0.670574\pi$
$421$	−20.9530	−1.02119	−0.510593	+	0.859823i	$0.670574\pi$
$422$	20.9464	1.01966
$423$	29.0885	1.41433
$424$	−3.17738	−0.154307
$425$	16.1191	0.781893
$426$	−0.664464	−0.0321934
$427$	45.9324	2.22282
$428$	−16.8782	−0.815840
$429$	−0.701815	−0.0338839
$430$	−3.29866	−0.159075
$431$	4.54569	0.218958	0.109479	−	0.993989i	$-0.465082\pi$
$431$	4.54569	0.218958	0.109479	+	0.993989i	$0.465082\pi$
$432$	−3.78342	−0.182030
$433$	−1.27547	−0.0612951	−0.0306476	−	0.999530i	$-0.509757\pi$
$433$	−1.27547	−0.0612951	−0.0306476	+	0.999530i	$0.509757\pi$
$434$	0.749645	0.0359841
$435$	−7.86418	−0.377059
$436$	8.00845	0.383535
$437$	−16.6789	−0.797860
$438$	6.51578	0.311336
$439$	12.6217	0.602399	0.301200	−	0.953561i	$-0.402613\pi$
$439$	12.6217	0.602399	0.301200	+	0.953561i	$0.402613\pi$
$440$	2.76760	0.131940
$441$	−33.8869	−1.61366
$442$	−6.21968	−0.295840
$443$	33.9360	1.61235	0.806175	−	0.591677i	$-0.201534\pi$
$443$	33.9360	1.61235	0.806175	+	0.591677i	$0.201534\pi$
$444$	−4.60218	−0.218410
$445$	−7.86549	−0.372860
$446$	−8.77257	−0.415393
$447$	11.6253	0.549860
$448$	4.51462	0.213296
$449$	7.47472	0.352754	0.176377	−	0.984323i	$-0.443562\pi$
$449$	7.47472	0.352754	0.176377	+	0.984323i	$0.443562\pi$
$450$	−6.73497	−0.317489
$451$	−8.89676	−0.418932
$452$	−5.14654	−0.242073
$453$	6.26779	0.294486
$454$	−14.2236	−0.667545
$455$	−12.8224	−0.601124
$456$	5.26341	0.246482
$457$	−26.1726	−1.22430	−0.612152	−	0.790740i	$-0.709696\pi$
$457$	−26.1726	−1.22430	−0.612152	+	0.790740i	$0.709696\pi$
$458$	−8.28622	−0.387190
$459$	−22.9302	−1.07029
$460$	−5.99765	−0.279642
$461$	21.7144	1.01134	0.505671	−	0.862726i	$-0.331245\pi$
$461$	21.7144	1.01134	0.505671	+	0.862726i	$0.331245\pi$
$462$	3.08744	0.143641
$463$	−22.6623	−1.05321	−0.526603	−	0.850111i	$-0.676535\pi$
$463$	−22.6623	−1.05321	−0.526603	+	0.850111i	$0.676535\pi$
$464$	−4.15501	−0.192892
$465$	0.314279	0.0145743
$466$	−7.03034	−0.325674
$467$	8.61541	0.398674	0.199337	−	0.979931i	$-0.436121\pi$
$467$	8.61541	0.398674	0.199337	+	0.979931i	$0.436121\pi$
$468$	2.59874	0.120127
$469$	−30.8225	−1.42325
$470$	−31.7912	−1.46642
$471$	−8.56723	−0.394757
$472$	−5.79089	−0.266547
$473$	−1.19188	−0.0548029
$474$	3.54060	0.162625
$475$	20.4695	0.939206
$476$	27.3618	1.25413
$477$	8.04611	0.368406
$478$	6.27243	0.286894
$479$	−2.53757	−0.115945	−0.0579723	−	0.998318i	$-0.518464\pi$
$479$	−2.53757	−0.115945	−0.0579723	+	0.998318i	$0.518464\pi$
$480$	1.89270	0.0863894
$481$	6.90606	0.314889
$482$	0.464683	0.0211657
$483$	−6.69078	−0.304441
$484$	1.00000	0.0454545
$485$	8.51215	0.386517
$486$	14.7762	0.670261
$487$	−8.16015	−0.369772	−0.184886	−	0.982760i	$-0.559192\pi$
$487$	−8.16015	−0.369772	−0.184886	+	0.982760i	$0.559192\pi$
$488$	10.1741	0.460562
$489$	10.6363	0.480992
$490$	37.0355	1.67309
$491$	−8.16181	−0.368337	−0.184169	−	0.982895i	$-0.558959\pi$
$491$	−8.16181	−0.368337	−0.184169	+	0.982895i	$0.558959\pi$
$492$	−6.08429	−0.274301
$493$	−25.1823	−1.13416
$494$	−7.89831	−0.355362
$495$	−7.00843	−0.315005
$496$	0.166048	0.00745579
$497$	−4.38647	−0.196760
$498$	−5.53021	−0.247815
$499$	−41.9591	−1.87835	−0.939174	−	0.343441i	$-0.888408\pi$
$499$	−41.9591	−1.87835	−0.939174	+	0.343441i	$0.888408\pi$
$500$	−6.47726	−0.289672
$501$	9.06524	0.405005
$502$	−20.5139	−0.915581
$503$	−31.0989	−1.38663	−0.693315	−	0.720635i	$-0.743850\pi$
$503$	−31.0989	−1.38663	−0.693315	+	0.720635i	$0.743850\pi$
$504$	−11.4324	−0.509241
$505$	29.6074	1.31751
$506$	−2.16709	−0.0963391
$507$	−8.17017	−0.362850
$508$	−18.5027	−0.820925
$509$	−19.1318	−0.848003	−0.424001	−	0.905662i	$-0.639375\pi$
$509$	−19.1318	−0.848003	−0.424001	+	0.905662i	$0.639375\pi$
$510$	11.4711	0.507948
$511$	43.0140	1.90283
$512$	1.00000	0.0441942
$513$	−29.1188	−1.28563
$514$	−12.3801	−0.546061
$515$	−34.7755	−1.53239
$516$	−0.815102	−0.0358828
$517$	−11.4869	−0.505194
$518$	−30.3813	−1.33488
$519$	8.05432	0.353545
$520$	−2.84020	−0.124551
$521$	−21.4085	−0.937922	−0.468961	−	0.883219i	$-0.655372\pi$
$521$	−21.4085	−0.937922	−0.468961	+	0.883219i	$0.655372\pi$
$522$	10.5218	0.460527
$523$	−36.2710	−1.58602	−0.793010	−	0.609208i	$-0.791487\pi$
$523$	−36.2710	−1.58602	−0.793010	+	0.609208i	$0.791487\pi$
$524$	13.6108	0.594590
$525$	8.21140	0.358375
$526$	−7.69701	−0.335606
$527$	1.00637	0.0438382
$528$	0.683877	0.0297619
$529$	−18.3037	−0.795813
$530$	−8.79371	−0.381974
$531$	14.6643	0.636378
$532$	34.7465	1.50645
$533$	9.13013	0.395470
$534$	−1.94357	−0.0841065
$535$	−46.7122	−2.01954
$536$	−6.82726	−0.294893
$537$	2.81196	0.121345
$538$	−10.1729	−0.438583
$539$	13.3818	0.576395
$540$	−10.4710	−0.450600
$541$	19.8512	0.853470	0.426735	−	0.904377i	$-0.359664\pi$
$541$	19.8512	0.853470	0.426735	+	0.904377i	$0.359664\pi$
$542$	17.7473	0.762313
$543$	−7.86996	−0.337732
$544$	6.06071	0.259851
$545$	22.1642	0.949409
$546$	−3.16843	−0.135596
$547$	−29.1777	−1.24755	−0.623775	−	0.781604i	$-0.714402\pi$
$547$	−29.1777	−1.24755	−0.623775	+	0.781604i	$0.714402\pi$
$548$	−5.02259	−0.214555
$549$	−25.7641	−1.09958
$550$	2.65961	0.113406
$551$	−31.9788	−1.36234
$552$	−1.48202	−0.0630792
$553$	23.3733	0.993935
$554$	13.1898	0.560380
$555$	−12.7370	−0.540655
$556$	−15.6019	−0.661670
$557$	43.9037	1.86026	0.930131	−	0.367228i	$-0.119693\pi$
$557$	43.9037	1.86026	0.930131	+	0.367228i	$0.119693\pi$
$558$	−0.420486	−0.0178006
$559$	1.22315	0.0517336
$560$	12.4947	0.527996
$561$	4.14478	0.174993
$562$	−13.4345	−0.566699
$563$	−17.0739	−0.719577	−0.359789	−	0.933034i	$-0.617151\pi$
$563$	−17.0739	−0.719577	−0.359789	+	0.933034i	$0.617151\pi$
$564$	−7.85564	−0.330782
$565$	−14.2436	−0.599232
$566$	2.33439	0.0981219
$567$	22.6162	0.949791
$568$	−0.971613	−0.0407680
$569$	−2.46741	−0.103439	−0.0517196	−	0.998662i	$-0.516470\pi$
$569$	−2.46741	−0.103439	−0.0517196	+	0.998662i	$0.516470\pi$
$570$	14.5670	0.610145
$571$	31.0816	1.30072	0.650362	−	0.759624i	$-0.274617\pi$
$571$	31.0816	1.30072	0.650362	+	0.759624i	$0.274617\pi$
$572$	−1.02623	−0.0429088
$573$	10.2738	0.429193
$574$	−40.1655	−1.67648
$575$	−5.76363	−0.240360
$576$	−2.53231	−0.105513
$577$	−4.09684	−0.170554	−0.0852769	−	0.996357i	$-0.527177\pi$
$577$	−4.09684	−0.170554	−0.0852769	+	0.996357i	$0.527177\pi$
$578$	19.7322	0.820752
$579$	−5.17980	−0.215265
$580$	−11.4994	−0.477487
$581$	−36.5078	−1.51460
$582$	2.10336	0.0871871
$583$	−3.17738	−0.131593
$584$	9.52771	0.394259
$585$	7.19226	0.297363
$586$	23.4965	0.970630
$587$	−37.2822	−1.53880	−0.769400	−	0.638768i	$-0.779444\pi$
$587$	−37.2822	−1.53880	−0.769400	+	0.638768i	$0.779444\pi$
$588$	9.15151	0.377402
$589$	1.27798	0.0526582
$590$	−16.0269	−0.659816
$591$	0.683877	0.0281309
$592$	−6.72954	−0.276582
$593$	45.6992	1.87664	0.938321	−	0.345767i	$-0.112381\pi$
$593$	45.6992	1.87664	0.938321	+	0.345767i	$0.112381\pi$
$594$	−3.78342	−0.155236
$595$	75.7266	3.10449
$596$	16.9992	0.696313
$597$	12.1028	0.495336
$598$	2.22394	0.0909436
$599$	5.10678	0.208657	0.104329	−	0.994543i	$-0.466731\pi$
$599$	5.10678	0.208657	0.104329	+	0.994543i	$0.466731\pi$
$600$	1.81885	0.0742541
$601$	−12.2505	−0.499710	−0.249855	−	0.968283i	$-0.580383\pi$
$601$	−12.2505	−0.499710	−0.249855	+	0.968283i	$0.580383\pi$
$602$	−5.38091	−0.219309
$603$	17.2888	0.704053
$604$	9.16508	0.372922
$605$	2.76760	0.112519
$606$	7.31601	0.297193
$607$	16.8036	0.682037	0.341019	−	0.940057i	$-0.389228\pi$
$607$	16.8036	0.682037	0.341019	+	0.940057i	$0.389228\pi$
$608$	7.69643	0.312132
$609$	−12.8284	−0.519832
$610$	28.1579	1.14008
$611$	11.7882	0.476901
$612$	−15.3476	−0.620391
$613$	0.940345	0.0379802	0.0189901	−	0.999820i	$-0.493955\pi$
$613$	0.940345	0.0379802	0.0189901	+	0.999820i	$0.493955\pi$
$614$	−3.39471	−0.136999
$615$	−16.8389	−0.679009
$616$	4.51462	0.181899
$617$	15.0964	0.607758	0.303879	−	0.952711i	$-0.401718\pi$
$617$	15.0964	0.607758	0.303879	+	0.952711i	$0.401718\pi$
$618$	−8.59305	−0.345663
$619$	30.8143	1.23853	0.619266	−	0.785181i	$-0.287430\pi$
$619$	30.8143	1.23853	0.619266	+	0.785181i	$0.287430\pi$
$620$	0.459555	0.0184562
$621$	8.19903	0.329016
$622$	31.4450	1.26083
$623$	−12.8305	−0.514043
$624$	−0.701815	−0.0280951
$625$	−31.2245	−1.24898
$626$	15.6618	0.625971
$627$	5.26341	0.210200
$628$	−12.5275	−0.499900
$629$	−40.7858	−1.62624
$630$	−31.6404	−1.26058
$631$	31.8209	1.26677	0.633385	−	0.773837i	$-0.281665\pi$
$631$	31.8209	1.26677	0.633385	+	0.773837i	$0.281665\pi$
$632$	5.17725	0.205940
$633$	14.3248	0.569359
$634$	−25.2786	−1.00394
$635$	−51.2081	−2.03213
$636$	−2.17293	−0.0861624
$637$	−13.7328	−0.544114
$638$	−4.15501	−0.164499
$639$	2.46043	0.0973331
$640$	2.76760	0.109399
$641$	−25.4561	−1.00546	−0.502728	−	0.864445i	$-0.667670\pi$
$641$	−25.4561	−1.00546	−0.502728	+	0.864445i	$0.667670\pi$
$642$	−11.5426	−0.455551
$643$	−6.07547	−0.239593	−0.119797	−	0.992798i	$-0.538224\pi$
$643$	−6.07547	−0.239593	−0.119797	+	0.992798i	$0.538224\pi$
$644$	−9.78361	−0.385528
$645$	−2.25588	−0.0888250
$646$	46.6458	1.83526
$647$	−25.9208	−1.01905	−0.509525	−	0.860456i	$-0.670179\pi$
$647$	−25.9208	−1.01905	−0.509525	+	0.860456i	$0.670179\pi$
$648$	5.00955	0.196794
$649$	−5.79089	−0.227312
$650$	−2.72937	−0.107055
$651$	0.512665	0.0200929
$652$	15.5530	0.609103
$653$	−35.3269	−1.38245	−0.691224	−	0.722640i	$-0.742928\pi$
$653$	−35.3269	−1.38245	−0.691224	+	0.722640i	$0.742928\pi$
$654$	5.47679	0.214159
$655$	37.6692	1.47186
$656$	−8.89676	−0.347360
$657$	−24.1271	−0.941289
$658$	−51.8591	−2.02168
$659$	0.657945	0.0256299	0.0128149	−	0.999918i	$-0.495921\pi$
$659$	0.657945	0.0256299	0.0128149	+	0.999918i	$0.495921\pi$
$660$	1.89270	0.0736731
$661$	−2.79727	−0.108801	−0.0544007	−	0.998519i	$-0.517325\pi$
$661$	−2.79727	−0.108801	−0.0544007	+	0.998519i	$0.517325\pi$
$662$	32.7192	1.27167
$663$	−4.25350	−0.165192
$664$	−8.08657	−0.313820
$665$	96.1644	3.72909
$666$	17.0413	0.660337
$667$	9.00431	0.348648
$668$	13.2557	0.512877
$669$	−5.99936	−0.231949
$670$	−18.8951	−0.729983
$671$	10.1741	0.392768
$672$	3.08744	0.119101
$673$	−17.1058	−0.659381	−0.329690	−	0.944089i	$-0.606944\pi$
$673$	−17.1058	−0.659381	−0.329690	+	0.944089i	$0.606944\pi$
$674$	32.5905	1.25534
$675$	−10.0624	−0.387303
$676$	−11.9469	−0.459494
$677$	−33.6627	−1.29376	−0.646882	−	0.762590i	$-0.723927\pi$
$677$	−33.6627	−1.29376	−0.646882	+	0.762590i	$0.723927\pi$
$678$	−3.51960	−0.135169
$679$	13.8854	0.532872
$680$	16.7736	0.643239
$681$	−9.72716	−0.372746
$682$	0.166048	0.00635832
$683$	11.7852	0.450948	0.225474	−	0.974249i	$-0.427607\pi$
$683$	11.7852	0.450948	0.225474	+	0.974249i	$0.427607\pi$
$684$	−19.4898	−0.745210
$685$	−13.9005	−0.531112
$686$	28.8115	1.10003
$687$	−5.66675	−0.216200
$688$	−1.19188	−0.0454402
$689$	3.26072	0.124224
$690$	−4.10165	−0.156147
$691$	37.0978	1.41127	0.705633	−	0.708578i	$-0.250663\pi$
$691$	37.0978	1.41127	0.705633	+	0.708578i	$0.250663\pi$
$692$	11.7774	0.447711
$693$	−11.4324	−0.434282
$694$	27.1647	1.03116
$695$	−43.1800	−1.63791
$696$	−2.84152	−0.107707
$697$	−53.9207	−2.04239
$698$	−33.2822	−1.25975
$699$	−4.80789	−0.181851
$700$	12.0071	0.453827
$701$	−52.2628	−1.97394	−0.986969	−	0.160909i	$-0.948557\pi$
$701$	−52.2628	−1.97394	−0.986969	+	0.160909i	$0.948557\pi$
$702$	3.88266	0.146542
$703$	−51.7935	−1.95343
$704$	1.00000	0.0376889
$705$	−21.7413	−0.818823
$706$	−3.98383	−0.149933
$707$	48.2968	1.81639
$708$	−3.96025	−0.148835
$709$	−19.6331	−0.737337	−0.368668	−	0.929561i	$-0.620186\pi$
$709$	−19.6331	−0.737337	−0.368668	+	0.929561i	$0.620186\pi$
$710$	−2.68904	−0.100918
$711$	−13.1104	−0.491679
$712$	−2.84199	−0.106508
$713$	−0.359842	−0.0134762
$714$	18.7121	0.700283
$715$	−2.84020	−0.106217
$716$	4.11180	0.153665
$717$	4.28957	0.160197
$718$	−26.4224	−0.986074
$719$	−38.7240	−1.44416	−0.722081	−	0.691808i	$-0.756814\pi$
$719$	−38.7240	−1.44416	−0.722081	+	0.691808i	$0.756814\pi$
$720$	−7.00843	−0.261189
$721$	−56.7271	−2.11263
$722$	40.2351	1.49739
$723$	0.317786	0.0118186
$724$	−11.5079	−0.427687
$725$	−11.0507	−0.410414
$726$	0.683877	0.0253810
$727$	−36.4786	−1.35292	−0.676458	−	0.736482i	$-0.736486\pi$
$727$	−36.4786	−1.35292	−0.676458	+	0.736482i	$0.736486\pi$
$728$	−4.63304	−0.171712
$729$	−4.92356	−0.182354
$730$	26.3689	0.975956
$731$	−7.22366	−0.267177
$732$	6.95785	0.257170
$733$	−20.3228	−0.750640	−0.375320	−	0.926895i	$-0.622467\pi$
$733$	−20.3228	−0.750640	−0.375320	+	0.926895i	$0.622467\pi$
$734$	−15.1085	−0.557664
$735$	25.3277	0.934227
$736$	−2.16709	−0.0798801
$737$	−6.82726	−0.251485
$738$	22.5294	0.829318
$739$	27.5068	1.01185	0.505926	−	0.862577i	$-0.331151\pi$
$739$	27.5068	1.01185	0.505926	+	0.862577i	$0.331151\pi$
$740$	−18.6247	−0.684657
$741$	−5.40147	−0.198428
$742$	−14.3446	−0.526609
$743$	−12.0058	−0.440452	−0.220226	−	0.975449i	$-0.570679\pi$
$743$	−12.0058	−0.440452	−0.220226	+	0.975449i	$0.570679\pi$
$744$	0.113557	0.00416318
$745$	47.0469	1.72367
$746$	9.68461	0.354579
$747$	20.4777	0.749240
$748$	6.06071	0.221602
$749$	−76.1988	−2.78424
$750$	−4.42965	−0.161748
$751$	48.5848	1.77289	0.886443	−	0.462838i	$-0.153169\pi$
$751$	48.5848	1.77289	0.886443	+	0.462838i	$0.153169\pi$
$752$	−11.4869	−0.418885
$753$	−14.0290	−0.511245
$754$	4.26400	0.155286
$755$	25.3653	0.923137
$756$	−17.0807	−0.621219
$757$	−39.3085	−1.42869	−0.714345	−	0.699794i	$-0.753275\pi$
$757$	−39.3085	−1.42869	−0.714345	+	0.699794i	$0.753275\pi$
$758$	29.9618	1.08826
$759$	−1.48202	−0.0537941
$760$	21.3006	0.772656
$761$	4.18844	0.151831	0.0759154	−	0.997114i	$-0.475812\pi$
$761$	4.18844	0.151831	0.0759154	+	0.997114i	$0.475812\pi$
$762$	−12.6536	−0.458391
$763$	36.1551	1.30890
$764$	15.0229	0.543508
$765$	−42.4761	−1.53573
$766$	31.8406	1.15045
$767$	5.94279	0.214582
$768$	0.683877	0.0246773
$769$	−6.47082	−0.233344	−0.116672	−	0.993171i	$-0.537223\pi$
$769$	−6.47082	−0.233344	−0.116672	+	0.993171i	$0.537223\pi$
$770$	12.4947	0.450277
$771$	−8.46643	−0.304911
$772$	−7.57418	−0.272601
$773$	1.84223	0.0662605	0.0331302	−	0.999451i	$-0.489452\pi$
$773$	1.84223	0.0662605	0.0331302	+	0.999451i	$0.489452\pi$
$774$	3.01822	0.108488
$775$	0.441624	0.0158636
$776$	3.07564	0.110409
$777$	−20.7771	−0.745374
$778$	2.23631	0.0801755
$779$	−68.4733	−2.45331
$780$	−1.94234	−0.0695470
$781$	−0.971613	−0.0347671
$782$	−13.1341	−0.469676
$783$	15.7202	0.561793
$784$	13.3818	0.477922
$785$	−34.6710	−1.23746
$786$	9.30810	0.332009
$787$	−17.1751	−0.612225	−0.306113	−	0.951995i	$-0.599028\pi$
$787$	−17.1751	−0.612225	−0.306113	+	0.951995i	$0.599028\pi$
$788$	1.00000	0.0356235
$789$	−5.26381	−0.187396
$790$	14.3286	0.509787
$791$	−23.2347	−0.826131
$792$	−2.53231	−0.0899818
$793$	−10.4410	−0.370771
$794$	−7.35698	−0.261089
$795$	−6.01381	−0.213288
$796$	17.6974	0.627268
$797$	36.8259	1.30444	0.652220	−	0.758030i	$-0.273838\pi$
$797$	36.8259	1.30444	0.652220	+	0.758030i	$0.273838\pi$
$798$	23.7623	0.841176
$799$	−69.6189	−2.46294
$800$	2.65961	0.0940315
$801$	7.19681	0.254287
$802$	24.2814	0.857407
$803$	9.52771	0.336225
$804$	−4.66900	−0.164663
$805$	−27.0771	−0.954343
$806$	−0.170404	−0.00600222
$807$	−6.95698	−0.244897
$808$	10.6979	0.376349
$809$	3.87853	0.136362	0.0681809	−	0.997673i	$-0.478280\pi$
$809$	3.87853	0.136362	0.0681809	+	0.997673i	$0.478280\pi$
$810$	13.8644	0.487146
$811$	−32.6145	−1.14525	−0.572625	−	0.819818i	$-0.694075\pi$
$811$	−32.6145	−1.14525	−0.572625	+	0.819818i	$0.694075\pi$
$812$	−18.7583	−0.658288
$813$	12.1370	0.425662
$814$	−6.72954	−0.235870
$815$	43.0445	1.50778
$816$	4.14478	0.145096
$817$	−9.17325	−0.320932
$818$	11.3016	0.395152
$819$	11.7323	0.409960
$820$	−24.6227	−0.859862
$821$	24.2927	0.847821	0.423911	−	0.905704i	$-0.360657\pi$
$821$	24.2927	0.847821	0.423911	+	0.905704i	$0.360657\pi$
$822$	−3.43483	−0.119804
$823$	28.1457	0.981097	0.490549	−	0.871414i	$-0.336796\pi$
$823$	28.1457	0.981097	0.490549	+	0.871414i	$0.336796\pi$
$824$	−12.5652	−0.437730
$825$	1.81885	0.0633241
$826$	−26.1437	−0.909655
$827$	16.6503	0.578988	0.289494	−	0.957180i	$-0.406513\pi$
$827$	16.6503	0.578988	0.289494	+	0.957180i	$0.406513\pi$
$828$	5.48776	0.190713
$829$	26.5819	0.923228	0.461614	−	0.887081i	$-0.347270\pi$
$829$	26.5819	0.923228	0.461614	+	0.887081i	$0.347270\pi$
$830$	−22.3804	−0.776834
$831$	9.02017	0.312906
$832$	−1.02623	−0.0355781
$833$	81.1033	2.81006
$834$	−10.6698	−0.369465
$835$	36.6864	1.26958
$836$	7.69643	0.266187
$837$	−0.628230	−0.0217148
$838$	−10.6451	−0.367729
$839$	−29.5929	−1.02166	−0.510831	−	0.859681i	$-0.670662\pi$
$839$	−29.5929	−1.02166	−0.510831	+	0.859681i	$0.670662\pi$
$840$	8.54481	0.294824
$841$	−11.7359	−0.404685
$842$	−20.9530	−0.722087
$843$	−9.18752	−0.316435
$844$	20.9464	0.721006
$845$	−33.0641	−1.13744
$846$	29.0885	1.00008
$847$	4.51462	0.155124
$848$	−3.17738	−0.109112
$849$	1.59644	0.0547896
$850$	16.1191	0.552882
$851$	14.5835	0.499918
$852$	−0.664464	−0.0227642
$853$	−30.4339	−1.04204	−0.521019	−	0.853545i	$-0.674448\pi$
$853$	−30.4339	−1.04204	−0.521019	+	0.853545i	$0.674448\pi$
$854$	45.9324	1.57177
$855$	−53.9399	−1.84471
$856$	−16.8782	−0.576886
$857$	−1.09702	−0.0374734	−0.0187367	−	0.999824i	$-0.505964\pi$
$857$	−1.09702	−0.0374734	−0.0187367	+	0.999824i	$0.505964\pi$
$858$	−0.701815	−0.0239596
$859$	47.6157	1.62463	0.812313	−	0.583222i	$-0.198208\pi$
$859$	47.6157	1.62463	0.812313	+	0.583222i	$0.198208\pi$
$860$	−3.29866	−0.112483
$861$	−27.4683	−0.936116
$862$	4.54569	0.154827
$863$	−45.1367	−1.53647	−0.768236	−	0.640167i	$-0.778865\pi$
$863$	−45.1367	−1.53647	−0.768236	+	0.640167i	$0.778865\pi$
$864$	−3.78342	−0.128715
$865$	32.5953	1.10827
$866$	−1.27547	−0.0433422
$867$	13.4944	0.458294
$868$	0.749645	0.0254446
$869$	5.17725	0.175626
$870$	−7.86418	−0.266621
$871$	7.00634	0.237401
$872$	8.00845	0.271200
$873$	−7.78849	−0.263601
$874$	−16.6789	−0.564172
$875$	−29.2424	−0.988573
$876$	6.51578	0.220148
$877$	47.4476	1.60219	0.801095	−	0.598537i	$-0.204251\pi$
$877$	47.4476	1.60219	0.801095	+	0.598537i	$0.204251\pi$
$878$	12.6217	0.425960
$879$	16.0687	0.541983
$880$	2.76760	0.0932958
$881$	−25.2687	−0.851325	−0.425663	−	0.904882i	$-0.639959\pi$
$881$	−25.2687	−0.851325	−0.425663	+	0.904882i	$0.639959\pi$
$882$	−33.8869	−1.14103
$883$	36.7656	1.23726	0.618631	−	0.785682i	$-0.287688\pi$
$883$	36.7656	1.23726	0.618631	+	0.785682i	$0.287688\pi$
$884$	−6.21968	−0.209191
$885$	−10.9604	−0.368430
$886$	33.9360	1.14010
$887$	4.59827	0.154395	0.0771974	−	0.997016i	$-0.475403\pi$
$887$	4.59827	0.154395	0.0771974	+	0.997016i	$0.475403\pi$
$888$	−4.60218	−0.154439
$889$	−83.5328	−2.80160
$890$	−7.86549	−0.263652
$891$	5.00955	0.167826
$892$	−8.77257	−0.293727
$893$	−88.4083	−2.95847
$894$	11.6253	0.388809
$895$	11.3798	0.380385
$896$	4.51462	0.150823
$897$	1.52090	0.0507813
$898$	7.47472	0.249435
$899$	−0.689933	−0.0230106
$900$	−6.73497	−0.224499
$901$	−19.2572	−0.641549
$902$	−8.89676	−0.296230
$903$	−3.67988	−0.122459
$904$	−5.14654	−0.171172
$905$	−31.8492	−1.05870
$906$	6.26779	0.208233
$907$	40.3885	1.34108	0.670539	−	0.741874i	$-0.266063\pi$
$907$	40.3885	1.34108	0.670539	+	0.741874i	$0.266063\pi$
$908$	−14.2236	−0.472026
$909$	−27.0903	−0.898529
$910$	−12.8224	−0.425059
$911$	−11.3771	−0.376939	−0.188469	−	0.982079i	$-0.560353\pi$
$911$	−11.3771	−0.376939	−0.188469	+	0.982079i	$0.560353\pi$
$912$	5.26341	0.174289
$913$	−8.08657	−0.267626
$914$	−26.1726	−0.865714
$915$	19.2566	0.636602
$916$	−8.28622	−0.273784
$917$	61.4476	2.02918
$918$	−22.9302	−0.756810
$919$	−5.87376	−0.193757	−0.0968787	−	0.995296i	$-0.530886\pi$
$919$	−5.87376	−0.193757	−0.0968787	+	0.995296i	$0.530886\pi$
$920$	−5.99765	−0.197737
$921$	−2.32156	−0.0764980
$922$	21.7144	0.715127
$923$	0.997099	0.0328199
$924$	3.08744	0.101569
$925$	−17.8980	−0.588481
$926$	−22.6623	−0.744729
$927$	31.8190	1.04507
$928$	−4.15501	−0.136395
$929$	42.2136	1.38498	0.692491	−	0.721426i	$-0.256513\pi$
$929$	42.2136	1.38498	0.692491	+	0.721426i	$0.256513\pi$
$930$	0.314279	0.0103056
$931$	102.992	3.37543
$932$	−7.03034	−0.230286
$933$	21.5045	0.704025
$934$	8.61541	0.281905
$935$	16.7736	0.548556
$936$	2.59874	0.0849423
$937$	−19.0506	−0.622354	−0.311177	−	0.950352i	$-0.600723\pi$
$937$	−19.0506	−0.622354	−0.311177	+	0.950352i	$0.600723\pi$
$938$	−30.8225	−1.00639
$939$	10.7107	0.349532
$940$	−31.7912	−1.03691
$941$	35.5795	1.15986	0.579930	−	0.814667i	$-0.303080\pi$
$941$	35.5795	1.15986	0.579930	+	0.814667i	$0.303080\pi$
$942$	−8.56723	−0.279135
$943$	19.2801	0.627847
$944$	−5.79089	−0.188477
$945$	−47.2726	−1.53778
$946$	−1.19188	−0.0387515
$947$	−21.1880	−0.688519	−0.344259	−	0.938875i	$-0.611870\pi$
$947$	−21.1880	−0.688519	−0.344259	+	0.938875i	$0.611870\pi$
$948$	3.54060	0.114993
$949$	−9.77762	−0.317395
$950$	20.4695	0.664119
$951$	−17.2875	−0.560585
$952$	27.3618	0.886802
$953$	18.9958	0.615336	0.307668	−	0.951494i	$-0.400451\pi$
$953$	18.9958	0.615336	0.307668	+	0.951494i	$0.400451\pi$
$954$	8.04611	0.260502
$955$	41.5773	1.34541
$956$	6.27243	0.202865
$957$	−2.84152	−0.0918532
$958$	−2.53757	−0.0819853
$959$	−22.6751	−0.732217
$960$	1.89270	0.0610865
$961$	−30.9724	−0.999111
$962$	6.90606	0.222660
$963$	42.7410	1.37731
$964$	0.464683	0.0149664
$965$	−20.9623	−0.674800
$966$	−6.69078	−0.215272
$967$	51.8537	1.66750	0.833751	−	0.552141i	$-0.186189\pi$
$967$	51.8537	1.66750	0.833751	+	0.552141i	$0.186189\pi$
$968$	1.00000	0.0321412
$969$	31.9000	1.02478
$970$	8.51215	0.273309
$971$	32.8527	1.05429	0.527147	−	0.849774i	$-0.323262\pi$
$971$	32.8527	1.05429	0.527147	+	0.849774i	$0.323262\pi$
$972$	14.7762	0.473946
$973$	−70.4369	−2.25810
$974$	−8.16015	−0.261468
$975$	−1.86655	−0.0597776
$976$	10.1741	0.325666
$977$	5.38821	0.172384	0.0861921	−	0.996279i	$-0.472530\pi$
$977$	5.38821	0.172384	0.0861921	+	0.996279i	$0.472530\pi$
$978$	10.6363	0.340113
$979$	−2.84199	−0.0908304
$980$	37.0355	1.18306
$981$	−20.2799	−0.647487
$982$	−8.16181	−0.260454
$983$	−27.4906	−0.876815	−0.438407	−	0.898776i	$-0.644457\pi$
$983$	−27.4906	−0.876815	−0.438407	+	0.898776i	$0.644457\pi$
$984$	−6.08429	−0.193960
$985$	2.76760	0.0881831
$986$	−25.1823	−0.801969
$987$	−35.4652	−1.12887
$988$	−7.89831	−0.251279
$989$	2.58292	0.0821322
$990$	−7.00843	−0.222743
$991$	42.3435	1.34509	0.672543	−	0.740058i	$-0.265202\pi$
$991$	42.3435	1.34509	0.672543	+	0.740058i	$0.265202\pi$
$992$	0.166048	0.00527204
$993$	22.3759	0.710078
$994$	−4.38647	−0.139130
$995$	48.9793	1.55275
$996$	−5.53021	−0.175232
$997$	36.2457	1.14791	0.573956	−	0.818886i	$-0.305408\pi$
$997$	36.2457	1.14791	0.573956	+	0.818886i	$0.305408\pi$
$998$	−41.9591	−1.32819
$999$	25.4607	0.805540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.15	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.15	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.683877 q^{3} +1.00000 q^{4} +2.76760 q^{5} +0.683877 q^{6} +4.51462 q^{7} +1.00000 q^{8} -2.53231 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.683877 q^{3} +1.00000 q^{4} +2.76760 q^{5} +0.683877 q^{6} +4.51462 q^{7} +1.00000 q^{8} -2.53231 q^{9} +2.76760 q^{10} +1.00000 q^{11} +0.683877 q^{12} -1.02623 q^{13} +4.51462 q^{14} +1.89270 q^{15} +1.00000 q^{16} +6.06071 q^{17} -2.53231 q^{18} +7.69643 q^{19} +2.76760 q^{20} +3.08744 q^{21} +1.00000 q^{22} -2.16709 q^{23} +0.683877 q^{24} +2.65961 q^{25} -1.02623 q^{26} -3.78342 q^{27} +4.51462 q^{28} -4.15501 q^{29} +1.89270 q^{30} +0.166048 q^{31} +1.00000 q^{32} +0.683877 q^{33} +6.06071 q^{34} +12.4947 q^{35} -2.53231 q^{36} -6.72954 q^{37} +7.69643 q^{38} -0.701815 q^{39} +2.76760 q^{40} -8.89676 q^{41} +3.08744 q^{42} -1.19188 q^{43} +1.00000 q^{44} -7.00843 q^{45} -2.16709 q^{46} -11.4869 q^{47} +0.683877 q^{48} +13.3818 q^{49} +2.65961 q^{50} +4.14478 q^{51} -1.02623 q^{52} -3.17738 q^{53} -3.78342 q^{54} +2.76760 q^{55} +4.51462 q^{56} +5.26341 q^{57} -4.15501 q^{58} -5.79089 q^{59} +1.89270 q^{60} +10.1741 q^{61} +0.166048 q^{62} -11.4324 q^{63} +1.00000 q^{64} -2.84020 q^{65} +0.683877 q^{66} -6.82726 q^{67} +6.06071 q^{68} -1.48202 q^{69} +12.4947 q^{70} -0.971613 q^{71} -2.53231 q^{72} +9.52771 q^{73} -6.72954 q^{74} +1.81885 q^{75} +7.69643 q^{76} +4.51462 q^{77} -0.701815 q^{78} +5.17725 q^{79} +2.76760 q^{80} +5.00955 q^{81} -8.89676 q^{82} -8.08657 q^{83} +3.08744 q^{84} +16.7736 q^{85} -1.19188 q^{86} -2.84152 q^{87} +1.00000 q^{88} -2.84199 q^{89} -7.00843 q^{90} -4.63304 q^{91} -2.16709 q^{92} +0.113557 q^{93} -11.4869 q^{94} +21.3006 q^{95} +0.683877 q^{96} +3.07564 q^{97} +13.3818 q^{98} -2.53231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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