LMFDB - Embedded newform 8026.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41544 q^{3} +1.00000 q^{4} +3.01333 q^{5} -2.41544 q^{6} -2.26454 q^{7} +1.00000 q^{8} +2.83435 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41544 q^{3} +1.00000 q^{4} +3.01333 q^{5} -2.41544 q^{6} -2.26454 q^{7} +1.00000 q^{8} +2.83435 q^{9} +3.01333 q^{10} -5.39023 q^{11} -2.41544 q^{12} +5.88831 q^{13} -2.26454 q^{14} -7.27852 q^{15} +1.00000 q^{16} +7.95834 q^{17} +2.83435 q^{18} +4.49145 q^{19} +3.01333 q^{20} +5.46986 q^{21} -5.39023 q^{22} -1.76283 q^{23} -2.41544 q^{24} +4.08015 q^{25} +5.88831 q^{26} +0.400111 q^{27} -2.26454 q^{28} +1.13026 q^{29} -7.27852 q^{30} -1.63413 q^{31} +1.00000 q^{32} +13.0198 q^{33} +7.95834 q^{34} -6.82380 q^{35} +2.83435 q^{36} +7.71885 q^{37} +4.49145 q^{38} -14.2229 q^{39} +3.01333 q^{40} -7.81314 q^{41} +5.46986 q^{42} +3.64786 q^{43} -5.39023 q^{44} +8.54084 q^{45} -1.76283 q^{46} -1.21077 q^{47} -2.41544 q^{48} -1.87186 q^{49} +4.08015 q^{50} -19.2229 q^{51} +5.88831 q^{52} -0.0872916 q^{53} +0.400111 q^{54} -16.2425 q^{55} -2.26454 q^{56} -10.8488 q^{57} +1.13026 q^{58} +1.78241 q^{59} -7.27852 q^{60} -3.26218 q^{61} -1.63413 q^{62} -6.41850 q^{63} +1.00000 q^{64} +17.7434 q^{65} +13.0198 q^{66} -1.83138 q^{67} +7.95834 q^{68} +4.25800 q^{69} -6.82380 q^{70} -0.645077 q^{71} +2.83435 q^{72} -4.00514 q^{73} +7.71885 q^{74} -9.85537 q^{75} +4.49145 q^{76} +12.2064 q^{77} -14.2229 q^{78} -17.5036 q^{79} +3.01333 q^{80} -9.46950 q^{81} -7.81314 q^{82} +11.9923 q^{83} +5.46986 q^{84} +23.9811 q^{85} +3.64786 q^{86} -2.73008 q^{87} -5.39023 q^{88} -13.2988 q^{89} +8.54084 q^{90} -13.3343 q^{91} -1.76283 q^{92} +3.94715 q^{93} -1.21077 q^{94} +13.5342 q^{95} -2.41544 q^{96} +3.74825 q^{97} -1.87186 q^{98} -15.2778 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−2.41544	−1.39456	−0.697278	−	0.716801i	$-0.745606\pi$
$3$	−2.41544	−1.39456	−0.697278	+	0.716801i	$0.745606\pi$
$4$	1.00000	0.500000
$5$	3.01333	1.34760	0.673801	−	0.738913i	$-0.264661\pi$
$5$	3.01333	1.34760	0.673801	+	0.738913i	$0.264661\pi$
$6$	−2.41544	−0.986099
$7$	−2.26454	−0.855916	−0.427958	−	0.903799i	$-0.640767\pi$
$7$	−2.26454	−0.855916	−0.427958	+	0.903799i	$0.640767\pi$
$8$	1.00000	0.353553
$9$	2.83435	0.944784
$10$	3.01333	0.952898
$11$	−5.39023	−1.62521	−0.812607	−	0.582812i	$-0.801953\pi$
$11$	−5.39023	−1.62521	−0.812607	+	0.582812i	$0.801953\pi$
$12$	−2.41544	−0.697278
$13$	5.88831	1.63312	0.816562	−	0.577257i	$-0.195877\pi$
$13$	5.88831	1.63312	0.816562	+	0.577257i	$0.195877\pi$
$14$	−2.26454	−0.605224
$15$	−7.27852	−1.87931
$16$	1.00000	0.250000
$17$	7.95834	1.93018	0.965091	−	0.261916i	$-0.0843544\pi$
$17$	7.95834	1.93018	0.965091	+	0.261916i	$0.0843544\pi$
$18$	2.83435	0.668063
$19$	4.49145	1.03041	0.515205	−	0.857067i	$-0.327716\pi$
$19$	4.49145	1.03041	0.515205	+	0.857067i	$0.327716\pi$
$20$	3.01333	0.673801
$21$	5.46986	1.19362
$22$	−5.39023	−1.14920
$23$	−1.76283	−0.367575	−0.183787	−	0.982966i	$-0.558836\pi$
$23$	−1.76283	−0.367575	−0.183787	+	0.982966i	$0.558836\pi$
$24$	−2.41544	−0.493050
$25$	4.08015	0.816031
$26$	5.88831	1.15479
$27$	0.400111	0.0770015
$28$	−2.26454	−0.427958
$29$	1.13026	0.209884	0.104942	−	0.994478i	$-0.466534\pi$
$29$	1.13026	0.209884	0.104942	+	0.994478i	$0.466534\pi$
$30$	−7.27852	−1.32887
$31$	−1.63413	−0.293499	−0.146749	−	0.989174i	$-0.546881\pi$
$31$	−1.63413	−0.293499	−0.146749	+	0.989174i	$0.546881\pi$
$32$	1.00000	0.176777
$33$	13.0198	2.26645
$34$	7.95834	1.36484
$35$	−6.82380	−1.15343
$36$	2.83435	0.472392
$37$	7.71885	1.26897	0.634485	−	0.772935i	$-0.281212\pi$
$37$	7.71885	1.26897	0.634485	+	0.772935i	$0.281212\pi$
$38$	4.49145	0.728610
$39$	−14.2229	−2.27748
$40$	3.01333	0.476449
$41$	−7.81314	−1.22021	−0.610104	−	0.792322i	$-0.708872\pi$
$41$	−7.81314	−1.22021	−0.610104	+	0.792322i	$0.708872\pi$
$42$	5.46986	0.844018
$43$	3.64786	0.556293	0.278146	−	0.960539i	$-0.410280\pi$
$43$	3.64786	0.556293	0.278146	+	0.960539i	$0.410280\pi$
$44$	−5.39023	−0.812607
$45$	8.54084	1.27319
$46$	−1.76283	−0.259914
$47$	−1.21077	−0.176609	−0.0883046	−	0.996094i	$-0.528145\pi$
$47$	−1.21077	−0.176609	−0.0883046	+	0.996094i	$0.528145\pi$
$48$	−2.41544	−0.348639
$49$	−1.87186	−0.267408
$50$	4.08015	0.577021
$51$	−19.2229	−2.69174
$52$	5.88831	0.816562
$53$	−0.0872916	−0.0119904	−0.00599521	−	0.999982i	$-0.501908\pi$
$53$	−0.0872916	−0.0119904	−0.00599521	+	0.999982i	$0.501908\pi$
$54$	0.400111	0.0544482
$55$	−16.2425	−2.19014
$56$	−2.26454	−0.302612
$57$	−10.8488	−1.43696
$58$	1.13026	0.148411
$59$	1.78241	0.232050	0.116025	−	0.993246i	$-0.462985\pi$
$59$	1.78241	0.232050	0.116025	+	0.993246i	$0.462985\pi$
$60$	−7.27852	−0.939653
$61$	−3.26218	−0.417679	−0.208840	−	0.977950i	$-0.566969\pi$
$61$	−3.26218	−0.417679	−0.208840	+	0.977950i	$0.566969\pi$
$62$	−1.63413	−0.207535
$63$	−6.41850	−0.808656
$64$	1.00000	0.125000
$65$	17.7434	2.20080
$66$	13.0198	1.60262
$67$	−1.83138	−0.223738	−0.111869	−	0.993723i	$-0.535684\pi$
$67$	−1.83138	−0.223738	−0.111869	+	0.993723i	$0.535684\pi$
$68$	7.95834	0.965091
$69$	4.25800	0.512603
$70$	−6.82380	−0.815601
$71$	−0.645077	−0.0765565	−0.0382783	−	0.999267i	$-0.512187\pi$
$71$	−0.645077	−0.0765565	−0.0382783	+	0.999267i	$0.512187\pi$
$72$	2.83435	0.334032
$73$	−4.00514	−0.468766	−0.234383	−	0.972144i	$-0.575307\pi$
$73$	−4.00514	−0.468766	−0.234383	+	0.972144i	$0.575307\pi$
$74$	7.71885	0.897298
$75$	−9.85537	−1.13800
$76$	4.49145	0.515205
$77$	12.2064	1.39105
$78$	−14.2229	−1.61042
$79$	−17.5036	−1.96931	−0.984657	−	0.174503i	$-0.944168\pi$
$79$	−17.5036	−1.96931	−0.984657	+	0.174503i	$0.944168\pi$
$80$	3.01333	0.336900
$81$	−9.46950	−1.05217
$82$	−7.81314	−0.862817
$83$	11.9923	1.31633	0.658164	−	0.752874i	$-0.271333\pi$
$83$	11.9923	1.31633	0.658164	+	0.752874i	$0.271333\pi$
$84$	5.46986	0.596811
$85$	23.9811	2.60112
$86$	3.64786	0.393358
$87$	−2.73008	−0.292695
$88$	−5.39023	−0.574600
$89$	−13.2988	−1.40967	−0.704833	−	0.709373i	$-0.748978\pi$
$89$	−13.2988	−1.40967	−0.704833	+	0.709373i	$0.748978\pi$
$90$	8.54084	0.900283
$91$	−13.3343	−1.39782
$92$	−1.76283	−0.183787
$93$	3.94715	0.409300
$94$	−1.21077	−0.124882
$95$	13.5342	1.38858
$96$	−2.41544	−0.246525
$97$	3.74825	0.380577	0.190289	−	0.981728i	$-0.439058\pi$
$97$	3.74825	0.380577	0.190289	+	0.981728i	$0.439058\pi$
$98$	−1.87186	−0.189086
$99$	−15.2778	−1.53548
$100$	4.08015	0.408015
$101$	−7.62289	−0.758506	−0.379253	−	0.925293i	$-0.623819\pi$
$101$	−7.62289	−0.758506	−0.379253	+	0.925293i	$0.623819\pi$
$102$	−19.2229	−1.90335
$103$	10.7240	1.05667	0.528333	−	0.849037i	$-0.322817\pi$
$103$	10.7240	1.05667	0.528333	+	0.849037i	$0.322817\pi$
$104$	5.88831	0.577397
$105$	16.4825	1.60853
$106$	−0.0872916	−0.00847851
$107$	13.9527	1.34885	0.674427	−	0.738342i	$-0.264391\pi$
$107$	13.9527	1.34885	0.674427	+	0.738342i	$0.264391\pi$
$108$	0.400111	0.0385007
$109$	3.20308	0.306799	0.153400	−	0.988164i	$-0.450978\pi$
$109$	3.20308	0.306799	0.153400	+	0.988164i	$0.450978\pi$
$110$	−16.2425	−1.54866
$111$	−18.6444	−1.76965
$112$	−2.26454	−0.213979
$113$	−4.41958	−0.415759	−0.207880	−	0.978154i	$-0.566656\pi$
$113$	−4.41958	−0.415759	−0.207880	+	0.978154i	$0.566656\pi$
$114$	−10.8488	−1.01609
$115$	−5.31197	−0.495344
$116$	1.13026	0.104942
$117$	16.6896	1.54295
$118$	1.78241	0.164084
$119$	−18.0220	−1.65207
$120$	−7.27852	−0.664435
$121$	18.0546	1.64132
$122$	−3.26218	−0.295344
$123$	18.8722	1.70165
$124$	−1.63413	−0.146749
$125$	−2.77180	−0.247917
$126$	−6.41850	−0.571806
$127$	19.5239	1.73247	0.866233	−	0.499640i	$-0.166535\pi$
$127$	19.5239	1.73247	0.866233	+	0.499640i	$0.166535\pi$
$128$	1.00000	0.0883883
$129$	−8.81118	−0.775781
$130$	17.7434	1.55620
$131$	17.4120	1.52130	0.760649	−	0.649164i	$-0.224881\pi$
$131$	17.4120	1.52130	0.760649	+	0.649164i	$0.224881\pi$
$132$	13.0198	1.13323
$133$	−10.1711	−0.881944
$134$	−1.83138	−0.158207
$135$	1.20567	0.103767
$136$	7.95834	0.682422
$137$	−0.848963	−0.0725318	−0.0362659	−	0.999342i	$-0.511546\pi$
$137$	−0.848963	−0.0725318	−0.0362659	+	0.999342i	$0.511546\pi$
$138$	4.25800	0.362465
$139$	11.7433	0.996052	0.498026	−	0.867162i	$-0.334058\pi$
$139$	11.7433	0.996052	0.498026	+	0.867162i	$0.334058\pi$
$140$	−6.82380	−0.576717
$141$	2.92455	0.246291
$142$	−0.645077	−0.0541336
$143$	−31.7394	−2.65418
$144$	2.83435	0.236196
$145$	3.40585	0.282841
$146$	−4.00514	−0.331468
$147$	4.52136	0.372916
$148$	7.71885	0.634485
$149$	15.7698	1.29191	0.645956	−	0.763375i	$-0.276459\pi$
$149$	15.7698	1.29191	0.645956	+	0.763375i	$0.276459\pi$
$150$	−9.85537	−0.804687
$151$	5.48785	0.446595	0.223297	−	0.974750i	$-0.428318\pi$
$151$	5.48785	0.446595	0.223297	+	0.974750i	$0.428318\pi$
$152$	4.49145	0.364305
$153$	22.5567	1.82360
$154$	12.2064	0.983619
$155$	−4.92417	−0.395519
$156$	−14.2229	−1.13874
$157$	17.5923	1.40402	0.702010	−	0.712167i	$-0.252286\pi$
$157$	17.5923	1.40402	0.702010	+	0.712167i	$0.252286\pi$
$158$	−17.5036	−1.39251
$159$	0.210848	0.0167213
$160$	3.01333	0.238225
$161$	3.99199	0.314613
$162$	−9.46950	−0.743994
$163$	−12.4854	−0.977930	−0.488965	−	0.872304i	$-0.662625\pi$
$163$	−12.4854	−0.977930	−0.488965	+	0.872304i	$0.662625\pi$
$164$	−7.81314	−0.610104
$165$	39.2329	3.05427
$166$	11.9923	0.930785
$167$	−14.7814	−1.14382	−0.571908	−	0.820318i	$-0.693797\pi$
$167$	−14.7814	−1.14382	−0.571908	+	0.820318i	$0.693797\pi$
$168$	5.46986	0.422009
$169$	21.6723	1.66710
$170$	23.9811	1.83927
$171$	12.7304	0.973515
$172$	3.64786	0.278146
$173$	21.7565	1.65412	0.827059	−	0.562115i	$-0.190012\pi$
$173$	21.7565	1.65412	0.827059	+	0.562115i	$0.190012\pi$
$174$	−2.73008	−0.206967
$175$	−9.23967	−0.698453
$176$	−5.39023	−0.406304
$177$	−4.30531	−0.323607
$178$	−13.2988	−0.996785
$179$	19.5702	1.46274	0.731371	−	0.681979i	$-0.238881\pi$
$179$	19.5702	1.46274	0.731371	+	0.681979i	$0.238881\pi$
$180$	8.54084	0.636596
$181$	6.54843	0.486741	0.243370	−	0.969933i	$-0.421747\pi$
$181$	6.54843	0.486741	0.243370	+	0.969933i	$0.421747\pi$
$182$	−13.3343	−0.988406
$183$	7.87960	0.582476
$184$	−1.76283	−0.129957
$185$	23.2594	1.71007
$186$	3.94715	0.289419
$187$	−42.8973	−3.13696
$188$	−1.21077	−0.0883046
$189$	−0.906068	−0.0659067
$190$	13.5342	0.981876
$191$	9.86034	0.713469	0.356735	−	0.934206i	$-0.383890\pi$
$191$	9.86034	0.713469	0.356735	+	0.934206i	$0.383890\pi$
$192$	−2.41544	−0.174319
$193$	7.16670	0.515870	0.257935	−	0.966162i	$-0.416958\pi$
$193$	7.16670	0.515870	0.257935	+	0.966162i	$0.416958\pi$
$194$	3.74825	0.269109
$195$	−42.8582	−3.06914
$196$	−1.87186	−0.133704
$197$	6.51712	0.464325	0.232163	−	0.972677i	$-0.425420\pi$
$197$	6.51712	0.464325	0.232163	+	0.972677i	$0.425420\pi$
$198$	−15.2778	−1.08575
$199$	−24.8811	−1.76377	−0.881887	−	0.471461i	$-0.843727\pi$
$199$	−24.8811	−1.76377	−0.881887	+	0.471461i	$0.843727\pi$
$200$	4.08015	0.288510
$201$	4.42358	0.312015
$202$	−7.62289	−0.536344
$203$	−2.55952	−0.179643
$204$	−19.2229	−1.34587
$205$	−23.5436	−1.64435
$206$	10.7240	0.747176
$207$	−4.99647	−0.347279
$208$	5.88831	0.408281
$209$	−24.2099	−1.67464
$210$	16.4825	1.13740
$211$	−5.44043	−0.374535	−0.187267	−	0.982309i	$-0.559963\pi$
$211$	−5.44043	−0.374535	−0.187267	+	0.982309i	$0.559963\pi$
$212$	−0.0872916	−0.00599521
$213$	1.55814	0.106762
$214$	13.9527	0.953784
$215$	10.9922	0.749661
$216$	0.400111	0.0272241
$217$	3.70055	0.251210
$218$	3.20308	0.216940
$219$	9.67417	0.653720
$220$	−16.2425	−1.09507
$221$	46.8612	3.15223
$222$	−18.6444	−1.25133
$223$	−3.20118	−0.214367	−0.107184	−	0.994239i	$-0.534183\pi$
$223$	−3.20118	−0.214367	−0.107184	+	0.994239i	$0.534183\pi$
$224$	−2.26454	−0.151306
$225$	11.5646	0.770973
$226$	−4.41958	−0.293986
$227$	1.55908	0.103480	0.0517400	−	0.998661i	$-0.483523\pi$
$227$	1.55908	0.103480	0.0517400	+	0.998661i	$0.483523\pi$
$228$	−10.8488	−0.718482
$229$	−28.3567	−1.87387	−0.936933	−	0.349508i	$-0.886349\pi$
$229$	−28.3567	−1.87387	−0.936933	+	0.349508i	$0.886349\pi$
$230$	−5.31197	−0.350261
$231$	−29.4838	−1.93989
$232$	1.13026	0.0742054
$233$	−6.90769	−0.452538	−0.226269	−	0.974065i	$-0.572653\pi$
$233$	−6.90769	−0.452538	−0.226269	+	0.974065i	$0.572653\pi$
$234$	16.6896	1.09103
$235$	−3.64845	−0.237999
$236$	1.78241	0.116025
$237$	42.2790	2.74632
$238$	−18.0220	−1.16819
$239$	21.4645	1.38842	0.694212	−	0.719771i	$-0.255753\pi$
$239$	21.4645	1.38842	0.694212	+	0.719771i	$0.255753\pi$
$240$	−7.27852	−0.469826
$241$	3.66715	0.236222	0.118111	−	0.993000i	$-0.462316\pi$
$241$	3.66715	0.236222	0.118111	+	0.993000i	$0.462316\pi$
$242$	18.0546	1.16059
$243$	21.6727	1.39030
$244$	−3.26218	−0.208840
$245$	−5.64053	−0.360360
$246$	18.8722	1.20325
$247$	26.4471	1.68279
$248$	−1.63413	−0.103767
$249$	−28.9667	−1.83569
$250$	−2.77180	−0.175304
$251$	26.9898	1.70358	0.851790	−	0.523884i	$-0.175517\pi$
$251$	26.9898	1.70358	0.851790	+	0.523884i	$0.175517\pi$
$252$	−6.41850	−0.404328
$253$	9.50203	0.597388
$254$	19.5239	1.22504
$255$	−57.9249	−3.62740
$256$	1.00000	0.0625000
$257$	5.44187	0.339455	0.169727	−	0.985491i	$-0.445711\pi$
$257$	5.44187	0.339455	0.169727	+	0.985491i	$0.445711\pi$
$258$	−8.81118	−0.548560
$259$	−17.4796	−1.08613
$260$	17.7434	1.10040
$261$	3.20356	0.198296
$262$	17.4120	1.07572
$263$	20.9059	1.28911	0.644556	−	0.764557i	$-0.277042\pi$
$263$	20.9059	1.28911	0.644556	+	0.764557i	$0.277042\pi$
$264$	13.0198	0.801312
$265$	−0.263038	−0.0161583
$266$	−10.1711	−0.623628
$267$	32.1224	1.96586
$268$	−1.83138	−0.111869
$269$	−21.0014	−1.28048	−0.640238	−	0.768177i	$-0.721164\pi$
$269$	−21.0014	−1.28048	−0.640238	+	0.768177i	$0.721164\pi$
$270$	1.20567	0.0733746
$271$	−28.3552	−1.72246	−0.861228	−	0.508218i	$-0.830304\pi$
$271$	−28.3552	−1.72246	−0.861228	+	0.508218i	$0.830304\pi$
$272$	7.95834	0.482545
$273$	32.2083	1.94933
$274$	−0.848963	−0.0512877
$275$	−21.9930	−1.32623
$276$	4.25800	0.256301
$277$	−17.2799	−1.03825	−0.519125	−	0.854698i	$-0.673742\pi$
$277$	−17.2799	−1.03825	−0.519125	+	0.854698i	$0.673742\pi$
$278$	11.7433	0.704315
$279$	−4.63170	−0.277293
$280$	−6.82380	−0.407800
$281$	−25.6380	−1.52943	−0.764717	−	0.644366i	$-0.777121\pi$
$281$	−25.6380	−1.52943	−0.764717	+	0.644366i	$0.777121\pi$
$282$	2.92455	0.174154
$283$	−23.9463	−1.42346	−0.711730	−	0.702453i	$-0.752088\pi$
$283$	−23.9463	−1.42346	−0.711730	+	0.702453i	$0.752088\pi$
$284$	−0.645077	−0.0382783
$285$	−32.6911	−1.93645
$286$	−31.7394	−1.87679
$287$	17.6932	1.04439
$288$	2.83435	0.167016
$289$	46.3352	2.72560
$290$	3.40585	0.199999
$291$	−9.05368	−0.530736
$292$	−4.00514	−0.234383
$293$	2.94681	0.172155	0.0860774	−	0.996288i	$-0.472567\pi$
$293$	2.94681	0.172155	0.0860774	+	0.996288i	$0.472567\pi$
$294$	4.52136	0.263691
$295$	5.37100	0.312711
$296$	7.71885	0.448649
$297$	−2.15669	−0.125144
$298$	15.7698	0.913519
$299$	−10.3801	−0.600295
$300$	−9.85537	−0.569000
$301$	−8.26072	−0.476140
$302$	5.48785	0.315790
$303$	18.4126	1.05778
$304$	4.49145	0.257602
$305$	−9.83001	−0.562865
$306$	22.5567	1.28948
$307$	34.3222	1.95887	0.979436	−	0.201756i	$-0.0646647\pi$
$307$	34.3222	1.95887	0.979436	+	0.201756i	$0.0646647\pi$
$308$	12.2064	0.695523
$309$	−25.9032	−1.47358
$310$	−4.92417	−0.279674
$311$	20.9398	1.18738	0.593692	−	0.804692i	$-0.297670\pi$
$311$	20.9398	1.18738	0.593692	+	0.804692i	$0.297670\pi$
$312$	−14.2229	−0.805212
$313$	−23.7075	−1.34003	−0.670013	−	0.742349i	$-0.733712\pi$
$313$	−23.7075	−1.34003	−0.670013	+	0.742349i	$0.733712\pi$
$314$	17.5923	0.992791
$315$	−19.3411	−1.08975
$316$	−17.5036	−0.984657
$317$	17.1469	0.963066	0.481533	−	0.876428i	$-0.340080\pi$
$317$	17.1469	0.963066	0.481533	+	0.876428i	$0.340080\pi$
$318$	0.210848	0.0118238
$319$	−6.09237	−0.341107
$320$	3.01333	0.168450
$321$	−33.7018	−1.88105
$322$	3.99199	0.222465
$323$	35.7445	1.98888
$324$	−9.46950	−0.526083
$325$	24.0252	1.33268
$326$	−12.4854	−0.691501
$327$	−7.73684	−0.427848
$328$	−7.81314	−0.431408
$329$	2.74184	0.151163
$330$	39.2329	2.15970
$331$	8.47642	0.465906	0.232953	−	0.972488i	$-0.425161\pi$
$331$	8.47642	0.465906	0.232953	+	0.972488i	$0.425161\pi$
$332$	11.9923	0.658164
$333$	21.8779	1.19890
$334$	−14.7814	−0.808800
$335$	−5.51854	−0.301510
$336$	5.46986	0.298405
$337$	3.83530	0.208922	0.104461	−	0.994529i	$-0.466688\pi$
$337$	3.83530	0.208922	0.104461	+	0.994529i	$0.466688\pi$
$338$	21.6723	1.17882
$339$	10.6752	0.579799
$340$	23.9811	1.30056
$341$	8.80834	0.476998
$342$	12.7304	0.688379
$343$	20.0907	1.08479
$344$	3.64786	0.196679
$345$	12.8308	0.690785
$346$	21.7565	1.16964
$347$	−8.23961	−0.442325	−0.221163	−	0.975237i	$-0.570985\pi$
$347$	−8.23961	−0.442325	−0.221163	+	0.975237i	$0.570985\pi$
$348$	−2.73008	−0.146348
$349$	−31.9226	−1.70878	−0.854390	−	0.519632i	$-0.826069\pi$
$349$	−31.9226	−1.70878	−0.854390	+	0.519632i	$0.826069\pi$
$350$	−9.23967	−0.493881
$351$	2.35598	0.125753
$352$	−5.39023	−0.287300
$353$	18.4721	0.983173	0.491587	−	0.870829i	$-0.336417\pi$
$353$	18.4721	0.983173	0.491587	+	0.870829i	$0.336417\pi$
$354$	−4.30531	−0.228825
$355$	−1.94383	−0.103168
$356$	−13.2988	−0.704833
$357$	43.5310	2.30391
$358$	19.5702	1.03432
$359$	−17.7049	−0.934429	−0.467215	−	0.884144i	$-0.654742\pi$
$359$	−17.7049	−0.934429	−0.467215	+	0.884144i	$0.654742\pi$
$360$	8.54084	0.450142
$361$	1.17313	0.0617439
$362$	6.54843	0.344178
$363$	−43.6097	−2.28892
$364$	−13.3343	−0.698908
$365$	−12.0688	−0.631710
$366$	7.87960	0.411873
$367$	5.81037	0.303299	0.151649	−	0.988434i	$-0.451542\pi$
$367$	5.81037	0.303299	0.151649	+	0.988434i	$0.451542\pi$
$368$	−1.76283	−0.0918936
$369$	−22.1452	−1.15283
$370$	23.2594	1.20920
$371$	0.197675	0.0102628
$372$	3.94715	0.204650
$373$	27.5707	1.42756	0.713778	−	0.700372i	$-0.246983\pi$
$373$	27.5707	1.42756	0.713778	+	0.700372i	$0.246983\pi$
$374$	−42.8973	−2.21816
$375$	6.69512	0.345734
$376$	−1.21077	−0.0624408
$377$	6.65534	0.342767
$378$	−0.906068	−0.0466031
$379$	−36.1375	−1.85626	−0.928129	−	0.372259i	$-0.878583\pi$
$379$	−36.1375	−1.85626	−0.928129	+	0.372259i	$0.878583\pi$
$380$	13.5342	0.694291
$381$	−47.1588	−2.41602
$382$	9.86034	0.504499
$383$	29.0143	1.48256	0.741280	−	0.671195i	$-0.234219\pi$
$383$	29.0143	1.48256	0.741280	+	0.671195i	$0.234219\pi$
$384$	−2.41544	−0.123262
$385$	36.7819	1.87458
$386$	7.16670	0.364775
$387$	10.3393	0.525577
$388$	3.74825	0.190289
$389$	5.16875	0.262066	0.131033	−	0.991378i	$-0.458171\pi$
$389$	5.16875	0.262066	0.131033	+	0.991378i	$0.458171\pi$
$390$	−42.8582	−2.17021
$391$	−14.0292	−0.709485
$392$	−1.87186	−0.0945432
$393$	−42.0577	−2.12153
$394$	6.51712	0.328328
$395$	−52.7442	−2.65385
$396$	−15.2778	−0.767739
$397$	7.57921	0.380390	0.190195	−	0.981746i	$-0.439088\pi$
$397$	7.57921	0.380390	0.190195	+	0.981746i	$0.439088\pi$
$398$	−24.8811	−1.24718
$399$	24.5676	1.22992
$400$	4.08015	0.204008
$401$	16.3519	0.816573	0.408287	−	0.912854i	$-0.366126\pi$
$401$	16.3519	0.816573	0.408287	+	0.912854i	$0.366126\pi$
$402$	4.42358	0.220628
$403$	−9.62228	−0.479320
$404$	−7.62289	−0.379253
$405$	−28.5347	−1.41790
$406$	−2.55952	−0.127027
$407$	−41.6063	−2.06235
$408$	−19.2229	−0.951675
$409$	19.7882	0.978462	0.489231	−	0.872154i	$-0.337277\pi$
$409$	19.7882	0.978462	0.489231	+	0.872154i	$0.337277\pi$
$410$	−23.5436	−1.16273
$411$	2.05062	0.101150
$412$	10.7240	0.528333
$413$	−4.03634	−0.198616
$414$	−4.99647	−0.245563
$415$	36.1368	1.77389
$416$	5.88831	0.288698
$417$	−28.3652	−1.38905
$418$	−24.2099	−1.18415
$419$	4.84204	0.236549	0.118275	−	0.992981i	$-0.462264\pi$
$419$	4.84204	0.236549	0.118275	+	0.992981i	$0.462264\pi$
$420$	16.4825	0.804263
$421$	15.3494	0.748085	0.374042	−	0.927412i	$-0.377971\pi$
$421$	15.3494	0.748085	0.374042	+	0.927412i	$0.377971\pi$
$422$	−5.44043	−0.264836
$423$	−3.43175	−0.166858
$424$	−0.0872916	−0.00423926
$425$	32.4713	1.57509
$426$	1.55814	0.0754923
$427$	7.38733	0.357498
$428$	13.9527	0.674427
$429$	76.6645	3.70140
$430$	10.9922	0.530091
$431$	34.3372	1.65396	0.826981	−	0.562229i	$-0.190056\pi$
$431$	34.3372	1.65396	0.826981	+	0.562229i	$0.190056\pi$
$432$	0.400111	0.0192504
$433$	−24.6468	−1.18445	−0.592225	−	0.805773i	$-0.701750\pi$
$433$	−24.6468	−1.18445	−0.592225	+	0.805773i	$0.701750\pi$
$434$	3.70055	0.177632
$435$	−8.22663	−0.394437
$436$	3.20308	0.153400
$437$	−7.91764	−0.378752
$438$	9.67417	0.462250
$439$	−9.03184	−0.431066	−0.215533	−	0.976497i	$-0.569149\pi$
$439$	−9.03184	−0.431066	−0.215533	+	0.976497i	$0.569149\pi$
$440$	−16.2425	−0.774332
$441$	−5.30551	−0.252643
$442$	46.8612	2.22896
$443$	−6.73602	−0.320038	−0.160019	−	0.987114i	$-0.551156\pi$
$443$	−6.73602	−0.320038	−0.160019	+	0.987114i	$0.551156\pi$
$444$	−18.6444	−0.884825
$445$	−40.0736	−1.89967
$446$	−3.20118	−0.151580
$447$	−38.0910	−1.80164
$448$	−2.26454	−0.106989
$449$	9.91919	0.468115	0.234058	−	0.972223i	$-0.424800\pi$
$449$	9.91919	0.468115	0.234058	+	0.972223i	$0.424800\pi$
$450$	11.5646	0.545160
$451$	42.1146	1.98310
$452$	−4.41958	−0.207880
$453$	−13.2556	−0.622801
$454$	1.55908	0.0731714
$455$	−40.1807	−1.88370
$456$	−10.8488	−0.508043
$457$	−3.68799	−0.172517	−0.0862583	−	0.996273i	$-0.527491\pi$
$457$	−3.68799	−0.172517	−0.0862583	+	0.996273i	$0.527491\pi$
$458$	−28.3567	−1.32502
$459$	3.18422	0.148627
$460$	−5.31197	−0.247672
$461$	−0.175786	−0.00818718	−0.00409359	−	0.999992i	$-0.501303\pi$
$461$	−0.175786	−0.00818718	−0.00409359	+	0.999992i	$0.501303\pi$
$462$	−29.4838	−1.37171
$463$	4.41642	0.205249	0.102624	−	0.994720i	$-0.467276\pi$
$463$	4.41642	0.205249	0.102624	+	0.994720i	$0.467276\pi$
$464$	1.13026	0.0524711
$465$	11.8941	0.551573
$466$	−6.90769	−0.319992
$467$	−26.9393	−1.24660	−0.623301	−	0.781982i	$-0.714209\pi$
$467$	−26.9393	−1.24660	−0.623301	+	0.781982i	$0.714209\pi$
$468$	16.6896	0.771475
$469$	4.14722	0.191501
$470$	−3.64845	−0.168291
$471$	−42.4932	−1.95798
$472$	1.78241	0.0820422
$473$	−19.6628	−0.904095
$474$	42.2790	1.94194
$475$	18.3258	0.840846
$476$	−18.0220	−0.826036
$477$	−0.247415	−0.0113284
$478$	21.4645	0.981764
$479$	−40.2437	−1.83878	−0.919390	−	0.393347i	$-0.871317\pi$
$479$	−40.2437	−1.83878	−0.919390	+	0.393347i	$0.871317\pi$
$480$	−7.27852	−0.332217
$481$	45.4510	2.07239
$482$	3.66715	0.167034
$483$	−9.64241	−0.438745
$484$	18.0546	0.820661
$485$	11.2947	0.512866
$486$	21.6727	0.983093
$487$	12.6162	0.571697	0.285848	−	0.958275i	$-0.407725\pi$
$487$	12.6162	0.571697	0.285848	+	0.958275i	$0.407725\pi$
$488$	−3.26218	−0.147672
$489$	30.1577	1.36378
$490$	−5.64053	−0.254813
$491$	15.1333	0.682954	0.341477	−	0.939890i	$-0.389073\pi$
$491$	15.1333	0.682954	0.341477	+	0.939890i	$0.389073\pi$
$492$	18.8722	0.850823
$493$	8.99501	0.405115
$494$	26.4471	1.18991
$495$	−46.0371	−2.06921
$496$	−1.63413	−0.0733746
$497$	1.46080	0.0655259
$498$	−28.9667	−1.29803
$499$	30.6679	1.37288	0.686442	−	0.727185i	$-0.259172\pi$
$499$	30.6679	1.37288	0.686442	+	0.727185i	$0.259172\pi$
$500$	−2.77180	−0.123959
$501$	35.7035	1.59512
$502$	26.9898	1.20461
$503$	34.9265	1.55730	0.778648	−	0.627462i	$-0.215906\pi$
$503$	34.9265	1.55730	0.778648	+	0.627462i	$0.215906\pi$
$504$	−6.41850	−0.285903
$505$	−22.9703	−1.02216
$506$	9.50203	0.422417
$507$	−52.3480	−2.32486
$508$	19.5239	0.866233
$509$	−12.6978	−0.562820	−0.281410	−	0.959588i	$-0.590802\pi$
$509$	−12.6978	−0.562820	−0.281410	+	0.959588i	$0.590802\pi$
$510$	−57.9249	−2.56496
$511$	9.06980	0.401224
$512$	1.00000	0.0441942
$513$	1.79708	0.0793430
$514$	5.44187	0.240031
$515$	32.3149	1.42397
$516$	−8.81118	−0.387891
$517$	6.52634	0.287028
$518$	−17.4796	−0.768011
$519$	−52.5516	−2.30676
$520$	17.7434	0.778101
$521$	8.34720	0.365697	0.182849	−	0.983141i	$-0.441468\pi$
$521$	8.34720	0.365697	0.182849	+	0.983141i	$0.441468\pi$
$522$	3.20356	0.140216
$523$	23.6926	1.03601	0.518003	−	0.855379i	$-0.326676\pi$
$523$	23.6926	1.03601	0.518003	+	0.855379i	$0.326676\pi$
$524$	17.4120	0.760649
$525$	22.3179	0.974032
$526$	20.9059	0.911540
$527$	−13.0050	−0.566505
$528$	13.0198	0.566613
$529$	−19.8924	−0.864889
$530$	−0.263038	−0.0114257
$531$	5.05199	0.219238
$532$	−10.1711	−0.440972
$533$	−46.0062	−1.99275
$534$	32.1224	1.39007
$535$	42.0439	1.81772
$536$	−1.83138	−0.0791034
$537$	−47.2706	−2.03988
$538$	−21.0014	−0.905433
$539$	10.0897	0.434596
$540$	1.20567	0.0518836
$541$	36.4442	1.56686	0.783429	−	0.621481i	$-0.213469\pi$
$541$	36.4442	1.56686	0.783429	+	0.621481i	$0.213469\pi$
$542$	−28.3552	−1.21796
$543$	−15.8173	−0.678787
$544$	7.95834	0.341211
$545$	9.65193	0.413443
$546$	32.2083	1.37839
$547$	−20.6656	−0.883597	−0.441798	−	0.897114i	$-0.645659\pi$
$547$	−20.6656	−0.883597	−0.441798	+	0.897114i	$0.645659\pi$
$548$	−0.848963	−0.0362659
$549$	−9.24616	−0.394617
$550$	−21.9930	−0.937783
$551$	5.07652	0.216267
$552$	4.25800	0.181233
$553$	39.6377	1.68557
$554$	−17.2799	−0.734154
$555$	−56.1818	−2.38478
$556$	11.7433	0.498026
$557$	20.5729	0.871704	0.435852	−	0.900018i	$-0.356447\pi$
$557$	20.5729	0.871704	0.435852	+	0.900018i	$0.356447\pi$
$558$	−4.63170	−0.196076
$559$	21.4797	0.908496
$560$	−6.82380	−0.288358
$561$	103.616	4.37466
$562$	−25.6380	−1.08147
$563$	18.2014	0.767098	0.383549	−	0.923520i	$-0.374702\pi$
$563$	18.2014	0.767098	0.383549	+	0.923520i	$0.374702\pi$
$564$	2.92455	0.123146
$565$	−13.3177	−0.560278
$566$	−23.9463	−1.00654
$567$	21.4441	0.900566
$568$	−0.645077	−0.0270668
$569$	15.6546	0.656276	0.328138	−	0.944630i	$-0.393579\pi$
$569$	15.6546	0.656276	0.328138	+	0.944630i	$0.393579\pi$
$570$	−32.6911	−1.36928
$571$	−15.0778	−0.630985	−0.315492	−	0.948928i	$-0.602170\pi$
$571$	−15.0778	−0.630985	−0.315492	+	0.948928i	$0.602170\pi$
$572$	−31.7394	−1.32709
$573$	−23.8171	−0.994972
$574$	17.6932	0.738498
$575$	−7.19260	−0.299952
$576$	2.83435	0.118098
$577$	7.31906	0.304696	0.152348	−	0.988327i	$-0.451317\pi$
$577$	7.31906	0.304696	0.152348	+	0.988327i	$0.451317\pi$
$578$	46.3352	1.92729
$579$	−17.3107	−0.719409
$580$	3.40585	0.141420
$581$	−27.1571	−1.12667
$582$	−9.05368	−0.375287
$583$	0.470522	0.0194870
$584$	−4.00514	−0.165734
$585$	50.2911	2.07928
$586$	2.94681	0.121732
$587$	−45.2582	−1.86801	−0.934004	−	0.357264i	$-0.883710\pi$
$587$	−45.2582	−1.86801	−0.934004	+	0.357264i	$0.883710\pi$
$588$	4.52136	0.186458
$589$	−7.33962	−0.302424
$590$	5.37100	0.221120
$591$	−15.7417	−0.647527
$592$	7.71885	0.317243
$593$	36.0797	1.48162	0.740809	−	0.671716i	$-0.234442\pi$
$593$	36.0797	1.48162	0.740809	+	0.671716i	$0.234442\pi$
$594$	−2.15669	−0.0884901
$595$	−54.3062	−2.22634
$596$	15.7698	0.645956
$597$	60.0988	2.45968
$598$	−10.3801	−0.424473
$599$	−17.3672	−0.709603	−0.354802	−	0.934942i	$-0.615452\pi$
$599$	−17.3672	−0.709603	−0.354802	+	0.934942i	$0.615452\pi$
$600$	−9.85537	−0.402344
$601$	23.3609	0.952910	0.476455	−	0.879199i	$-0.341922\pi$
$601$	23.3609	0.952910	0.476455	+	0.879199i	$0.341922\pi$
$602$	−8.26072	−0.336682
$603$	−5.19076	−0.211384
$604$	5.48785	0.223297
$605$	54.4043	2.21185
$606$	18.4126	0.747962
$607$	9.56355	0.388173	0.194086	−	0.980984i	$-0.437826\pi$
$607$	9.56355	0.388173	0.194086	+	0.980984i	$0.437826\pi$
$608$	4.49145	0.182152
$609$	6.18238	0.250523
$610$	−9.83001	−0.398006
$611$	−7.12941	−0.288425
$612$	22.5567	0.911802
$613$	41.9258	1.69337	0.846683	−	0.532097i	$-0.178596\pi$
$613$	41.9258	1.69337	0.846683	+	0.532097i	$0.178596\pi$
$614$	34.3222	1.38513
$615$	56.8681	2.29314
$616$	12.2064	0.491809
$617$	−4.36089	−0.175563	−0.0877815	−	0.996140i	$-0.527978\pi$
$617$	−4.36089	−0.175563	−0.0877815	+	0.996140i	$0.527978\pi$
$618$	−25.9032	−1.04198
$619$	7.61863	0.306219	0.153109	−	0.988209i	$-0.451071\pi$
$619$	7.61863	0.306219	0.153109	+	0.988209i	$0.451071\pi$
$620$	−4.92417	−0.197760
$621$	−0.705326	−0.0283038
$622$	20.9398	0.839608
$623$	30.1156	1.20656
$624$	−14.2229	−0.569371
$625$	−28.7531	−1.15012
$626$	−23.7075	−0.947542
$627$	58.4777	2.33537
$628$	17.5923	0.702010
$629$	61.4292	2.44934
$630$	−19.3411	−0.770567
$631$	33.2930	1.32537	0.662687	−	0.748897i	$-0.269416\pi$
$631$	33.2930	1.32537	0.662687	+	0.748897i	$0.269416\pi$
$632$	−17.5036	−0.696257
$633$	13.1410	0.522309
$634$	17.1469	0.680990
$635$	58.8319	2.33467
$636$	0.210848	0.00836066
$637$	−11.0221	−0.436711
$638$	−6.09237	−0.241199
$639$	−1.82837	−0.0723294
$640$	3.01333	0.119112
$641$	−30.0299	−1.18611	−0.593055	−	0.805162i	$-0.702078\pi$
$641$	−30.0299	−1.18611	−0.593055	+	0.805162i	$0.702078\pi$
$642$	−33.7018	−1.33010
$643$	32.4377	1.27922	0.639608	−	0.768701i	$-0.279097\pi$
$643$	32.4377	1.27922	0.639608	+	0.768701i	$0.279097\pi$
$644$	3.99199	0.157306
$645$	−26.5510	−1.04544
$646$	35.7445	1.40635
$647$	−4.63828	−0.182350	−0.0911748	−	0.995835i	$-0.529062\pi$
$647$	−4.63828	−0.182350	−0.0911748	+	0.995835i	$0.529062\pi$
$648$	−9.46950	−0.371997
$649$	−9.60761	−0.377132
$650$	24.0252	0.942347
$651$	−8.93847	−0.350326
$652$	−12.4854	−0.488965
$653$	−3.55588	−0.139152	−0.0695761	−	0.997577i	$-0.522165\pi$
$653$	−3.55588	−0.139152	−0.0695761	+	0.997577i	$0.522165\pi$
$654$	−7.73684	−0.302535
$655$	52.4682	2.05010
$656$	−7.81314	−0.305052
$657$	−11.3520	−0.442883
$658$	2.74184	0.106888
$659$	−16.2261	−0.632080	−0.316040	−	0.948746i	$-0.602353\pi$
$659$	−16.2261	−0.632080	−0.316040	+	0.948746i	$0.602353\pi$
$660$	39.2329	1.52714
$661$	−3.66814	−0.142674	−0.0713371	−	0.997452i	$-0.522727\pi$
$661$	−3.66814	−0.142674	−0.0713371	+	0.997452i	$0.522727\pi$
$662$	8.47642	0.329445
$663$	−113.190	−4.39595
$664$	11.9923	0.465392
$665$	−30.6488	−1.18851
$666$	21.8779	0.847753
$667$	−1.99246	−0.0771482
$668$	−14.7814	−0.571908
$669$	7.73227	0.298947
$670$	−5.51854	−0.213200
$671$	17.5839	0.678818
$672$	5.46986	0.211004
$673$	−43.8464	−1.69015	−0.845077	−	0.534645i	$-0.820445\pi$
$673$	−43.8464	−1.69015	−0.845077	+	0.534645i	$0.820445\pi$
$674$	3.83530	0.147730
$675$	1.63252	0.0628356
$676$	21.6723	0.833548
$677$	−46.7720	−1.79760	−0.898798	−	0.438364i	$-0.855558\pi$
$677$	−46.7720	−1.79760	−0.898798	+	0.438364i	$0.855558\pi$
$678$	10.6752	0.409980
$679$	−8.48806	−0.325742
$680$	23.9811	0.919633
$681$	−3.76587	−0.144309
$682$	8.80834	0.337289
$683$	−30.4195	−1.16397	−0.581985	−	0.813199i	$-0.697724\pi$
$683$	−30.4195	−1.16397	−0.581985	+	0.813199i	$0.697724\pi$
$684$	12.7304	0.486757
$685$	−2.55821	−0.0977440
$686$	20.0907	0.767066
$687$	68.4940	2.61321
$688$	3.64786	0.139073
$689$	−0.514001	−0.0195819
$690$	12.8308	0.488459
$691$	5.22942	0.198937	0.0994683	−	0.995041i	$-0.468286\pi$
$691$	5.22942	0.198937	0.0994683	+	0.995041i	$0.468286\pi$
$692$	21.7565	0.827059
$693$	34.5972	1.31424
$694$	−8.23961	−0.312771
$695$	35.3864	1.34228
$696$	−2.73008	−0.103483
$697$	−62.1796	−2.35522
$698$	−31.9226	−1.20829
$699$	16.6851	0.631089
$700$	−9.23967	−0.349227
$701$	−22.0119	−0.831378	−0.415689	−	0.909507i	$-0.636460\pi$
$701$	−22.0119	−0.831378	−0.415689	+	0.909507i	$0.636460\pi$
$702$	2.35598	0.0889208
$703$	34.6688	1.30756
$704$	−5.39023	−0.203152
$705$	8.81262	0.331903
$706$	18.4721	0.695208
$707$	17.2623	0.649217
$708$	−4.30531	−0.161804
$709$	1.13182	0.0425064	0.0212532	−	0.999774i	$-0.493234\pi$
$709$	1.13182	0.0425064	0.0212532	+	0.999774i	$0.493234\pi$
$710$	−1.94383	−0.0729506
$711$	−49.6115	−1.86058
$712$	−13.2988	−0.498392
$713$	2.88069	0.107883
$714$	43.5310	1.62911
$715$	−95.6411	−3.57678
$716$	19.5702	0.731371
$717$	−51.8462	−1.93623
$718$	−17.7049	−0.660741
$719$	47.4548	1.76977	0.884883	−	0.465813i	$-0.154238\pi$
$719$	47.4548	1.76977	0.884883	+	0.465813i	$0.154238\pi$
$720$	8.54084	0.318298
$721$	−24.2849	−0.904417
$722$	1.17313	0.0436596
$723$	−8.85777	−0.329424
$724$	6.54843	0.243370
$725$	4.61164	0.171272
$726$	−43.6097	−1.61851
$727$	−30.2718	−1.12272	−0.561359	−	0.827572i	$-0.689721\pi$
$727$	−30.2718	−1.12272	−0.561359	+	0.827572i	$0.689721\pi$
$728$	−13.3343	−0.494203
$729$	−23.9406	−0.886688
$730$	−12.0688	−0.446686
$731$	29.0309	1.07375
$732$	7.87960	0.291238
$733$	−7.59305	−0.280456	−0.140228	−	0.990119i	$-0.544783\pi$
$733$	−7.59305	−0.280456	−0.140228	+	0.990119i	$0.544783\pi$
$734$	5.81037	0.214465
$735$	13.6244	0.502542
$736$	−1.76283	−0.0649786
$737$	9.87153	0.363622
$738$	−22.1452	−0.815176
$739$	−11.4426	−0.420921	−0.210461	−	0.977602i	$-0.567496\pi$
$739$	−11.4426	−0.420921	−0.210461	+	0.977602i	$0.567496\pi$
$740$	23.2594	0.855033
$741$	−63.8813	−2.34674
$742$	0.197675	0.00725689
$743$	−40.5797	−1.48873	−0.744363	−	0.667775i	$-0.767247\pi$
$743$	−40.5797	−1.48873	−0.744363	+	0.667775i	$0.767247\pi$
$744$	3.94715	0.144709
$745$	47.5196	1.74098
$746$	27.5707	1.00943
$747$	33.9905	1.24365
$748$	−42.8973	−1.56848
$749$	−31.5963	−1.15450
$750$	6.69512	0.244471
$751$	20.0384	0.731212	0.365606	−	0.930770i	$-0.380862\pi$
$751$	20.0384	0.731212	0.365606	+	0.930770i	$0.380862\pi$
$752$	−1.21077	−0.0441523
$753$	−65.1922	−2.37574
$754$	6.65534	0.242373
$755$	16.5367	0.601832
$756$	−0.906068	−0.0329534
$757$	11.8946	0.432316	0.216158	−	0.976358i	$-0.430647\pi$
$757$	11.8946	0.432316	0.216158	+	0.976358i	$0.430647\pi$
$758$	−36.1375	−1.31257
$759$	−22.9516	−0.833090
$760$	13.5342	0.490938
$761$	25.8625	0.937515	0.468758	−	0.883327i	$-0.344702\pi$
$761$	25.8625	0.937515	0.468758	+	0.883327i	$0.344702\pi$
$762$	−47.1588	−1.70838
$763$	−7.25350	−0.262594
$764$	9.86034	0.356735
$765$	67.9709	2.45749
$766$	29.0143	1.04833
$767$	10.4954	0.378967
$768$	−2.41544	−0.0871597
$769$	−51.5472	−1.85884	−0.929420	−	0.369023i	$-0.879692\pi$
$769$	−51.5472	−1.85884	−0.929420	+	0.369023i	$0.879692\pi$
$770$	36.7819	1.32553
$771$	−13.1445	−0.473388
$772$	7.16670	0.257935
$773$	2.36750	0.0851530	0.0425765	−	0.999093i	$-0.486443\pi$
$773$	2.36750	0.0851530	0.0425765	+	0.999093i	$0.486443\pi$
$774$	10.3393	0.371639
$775$	−6.66751	−0.239504
$776$	3.74825	0.134554
$777$	42.2210	1.51467
$778$	5.16875	0.185309
$779$	−35.0923	−1.25731
$780$	−42.8582	−1.53457
$781$	3.47711	0.124421
$782$	−14.0292	−0.501682
$783$	0.452231	0.0161614
$784$	−1.87186	−0.0668521
$785$	53.0114	1.89206
$786$	−42.0577	−1.50015
$787$	−12.1807	−0.434194	−0.217097	−	0.976150i	$-0.569659\pi$
$787$	−12.1807	−0.434194	−0.217097	+	0.976150i	$0.569659\pi$
$788$	6.51712	0.232163
$789$	−50.4969	−1.79774
$790$	−52.7442	−1.87656
$791$	10.0083	0.355855
$792$	−15.2778	−0.542873
$793$	−19.2087	−0.682122
$794$	7.57921	0.268976
$795$	0.635354	0.0225337
$796$	−24.8811	−0.881887
$797$	−13.8840	−0.491798	−0.245899	−	0.969296i	$-0.579083\pi$
$797$	−13.8840	−0.491798	−0.245899	+	0.969296i	$0.579083\pi$
$798$	24.5676	0.869684
$799$	−9.63574	−0.340888
$800$	4.08015	0.144255
$801$	−37.6934	−1.33183
$802$	16.3519	0.577405
$803$	21.5886	0.761845
$804$	4.42358	0.156008
$805$	12.0292	0.423973
$806$	−9.62228	−0.338930
$807$	50.7276	1.78569
$808$	−7.62289	−0.268172
$809$	−11.8609	−0.417007	−0.208503	−	0.978022i	$-0.566859\pi$
$809$	−11.8609	−0.417007	−0.208503	+	0.978022i	$0.566859\pi$
$810$	−28.5347	−1.00261
$811$	13.4696	0.472982	0.236491	−	0.971634i	$-0.424003\pi$
$811$	13.4696	0.472982	0.236491	+	0.971634i	$0.424003\pi$
$812$	−2.55952	−0.0898217
$813$	68.4903	2.40206
$814$	−41.6063	−1.45830
$815$	−37.6225	−1.31786
$816$	−19.2229	−0.672936
$817$	16.3842	0.573209
$818$	19.7882	0.691877
$819$	−37.7942	−1.32064
$820$	−23.5436	−0.822177
$821$	22.4277	0.782732	0.391366	−	0.920235i	$-0.372003\pi$
$821$	22.4277	0.782732	0.391366	+	0.920235i	$0.372003\pi$
$822$	2.05062	0.0715236
$823$	−34.2333	−1.19330	−0.596648	−	0.802503i	$-0.703501\pi$
$823$	−34.2333	−1.19330	−0.596648	+	0.802503i	$0.703501\pi$
$824$	10.7240	0.373588
$825$	53.1227	1.84949
$826$	−4.03634	−0.140442
$827$	−12.7160	−0.442178	−0.221089	−	0.975254i	$-0.570961\pi$
$827$	−12.7160	−0.442178	−0.221089	+	0.975254i	$0.570961\pi$
$828$	−4.99647	−0.173639
$829$	−16.2018	−0.562711	−0.281356	−	0.959604i	$-0.590784\pi$
$829$	−16.2018	−0.562711	−0.281356	+	0.959604i	$0.590784\pi$
$830$	36.1368	1.25433
$831$	41.7386	1.44790
$832$	5.88831	0.204141
$833$	−14.8969	−0.516147
$834$	−28.3652	−0.982206
$835$	−44.5411	−1.54141
$836$	−24.2099	−0.837318
$837$	−0.653834	−0.0225998
$838$	4.84204	0.167265
$839$	19.0876	0.658976	0.329488	−	0.944160i	$-0.393124\pi$
$839$	19.0876	0.658976	0.329488	+	0.944160i	$0.393124\pi$
$840$	16.4825	0.568700
$841$	−27.7225	−0.955949
$842$	15.3494	0.528976
$843$	61.9270	2.13288
$844$	−5.44043	−0.187267
$845$	65.3056	2.24658
$846$	−3.43175	−0.117986
$847$	−40.8853	−1.40483
$848$	−0.0872916	−0.00299761
$849$	57.8409	1.98509
$850$	32.4713	1.11375
$851$	−13.6070	−0.466441
$852$	1.55814	0.0533811
$853$	8.20866	0.281059	0.140530	−	0.990076i	$-0.455119\pi$
$853$	8.20866	0.281059	0.140530	+	0.990076i	$0.455119\pi$
$854$	7.38733	0.252789
$855$	38.3608	1.31191
$856$	13.9527	0.476892
$857$	−24.7498	−0.845437	−0.422719	−	0.906261i	$-0.638924\pi$
$857$	−24.7498	−0.845437	−0.422719	+	0.906261i	$0.638924\pi$
$858$	76.6645	2.61728
$859$	21.8174	0.744400	0.372200	−	0.928153i	$-0.378604\pi$
$859$	21.8174	0.744400	0.372200	+	0.928153i	$0.378604\pi$
$860$	10.9922	0.374831
$861$	−42.7368	−1.45647
$862$	34.3372	1.16953
$863$	−35.1803	−1.19755	−0.598775	−	0.800917i	$-0.704346\pi$
$863$	−35.1803	−1.19755	−0.598775	+	0.800917i	$0.704346\pi$
$864$	0.400111	0.0136121
$865$	65.5596	2.22909
$866$	−24.6468	−0.837533
$867$	−111.920	−3.80100
$868$	3.70055	0.125605
$869$	94.3486	3.20056
$870$	−8.22663	−0.278909
$871$	−10.7837	−0.365392
$872$	3.20308	0.108470
$873$	10.6239	0.359563
$874$	−7.91764	−0.267818
$875$	6.27685	0.212196
$876$	9.67417	0.326860
$877$	−2.41266	−0.0814697	−0.0407349	−	0.999170i	$-0.512970\pi$
$877$	−2.41266	−0.0814697	−0.0407349	+	0.999170i	$0.512970\pi$
$878$	−9.03184	−0.304810
$879$	−7.11785	−0.240079
$880$	−16.2425	−0.547536
$881$	−30.4378	−1.02548	−0.512738	−	0.858545i	$-0.671369\pi$
$881$	−30.4378	−1.02548	−0.512738	+	0.858545i	$0.671369\pi$
$882$	−5.30551	−0.178646
$883$	−31.6326	−1.06452	−0.532261	−	0.846580i	$-0.678658\pi$
$883$	−31.6326	−1.06452	−0.532261	+	0.846580i	$0.678658\pi$
$884$	46.8612	1.57611
$885$	−12.9733	−0.436093
$886$	−6.73602	−0.226301
$887$	42.8411	1.43846	0.719232	−	0.694769i	$-0.244494\pi$
$887$	42.8411	1.43846	0.719232	+	0.694769i	$0.244494\pi$
$888$	−18.6444	−0.625665
$889$	−44.2126	−1.48284
$890$	−40.0736	−1.34327
$891$	51.0428	1.71000
$892$	−3.20118	−0.107184
$893$	−5.43812	−0.181980
$894$	−38.0910	−1.27395
$895$	58.9714	1.97120
$896$	−2.26454	−0.0756530
$897$	25.0724	0.837145
$898$	9.91919	0.331008
$899$	−1.84700	−0.0616008
$900$	11.5646	0.385486
$901$	−0.694697	−0.0231437
$902$	42.1146	1.40226
$903$	19.9533	0.664003
$904$	−4.41958	−0.146993
$905$	19.7326	0.655933
$906$	−13.2556	−0.440387
$907$	46.4651	1.54285	0.771424	−	0.636321i	$-0.219545\pi$
$907$	46.4651	1.54285	0.771424	+	0.636321i	$0.219545\pi$
$908$	1.55908	0.0517400
$909$	−21.6059	−0.716624
$910$	−40.1807	−1.33198
$911$	−1.50783	−0.0499565	−0.0249783	−	0.999688i	$-0.507952\pi$
$911$	−1.50783	−0.0499565	−0.0249783	+	0.999688i	$0.507952\pi$
$912$	−10.8488	−0.359241
$913$	−64.6413	−2.13932
$914$	−3.68799	−0.121988
$915$	23.7438	0.784946
$916$	−28.3567	−0.936933
$917$	−39.4303	−1.30210
$918$	3.18422	0.105095
$919$	−46.6948	−1.54032	−0.770160	−	0.637850i	$-0.779824\pi$
$919$	−46.6948	−1.54032	−0.770160	+	0.637850i	$0.779824\pi$
$920$	−5.31197	−0.175131
$921$	−82.9032	−2.73175
$922$	−0.175786	−0.00578921
$923$	−3.79841	−0.125026
$924$	−29.4838	−0.969946
$925$	31.4941	1.03552
$926$	4.41642	0.145133
$927$	30.3956	0.998322
$928$	1.13026	0.0371027
$929$	−32.1862	−1.05599	−0.527997	−	0.849246i	$-0.677057\pi$
$929$	−32.1862	−1.05599	−0.527997	+	0.849246i	$0.677057\pi$
$930$	11.8941	0.390021
$931$	−8.40736	−0.275540
$932$	−6.90769	−0.226269
$933$	−50.5787	−1.65587
$934$	−26.9393	−0.881481
$935$	−129.264	−4.22737
$936$	16.6896	0.545515
$937$	−2.02493	−0.0661517	−0.0330759	−	0.999453i	$-0.510530\pi$
$937$	−2.02493	−0.0661517	−0.0330759	+	0.999453i	$0.510530\pi$
$938$	4.14722	0.135412
$939$	57.2640	1.86874
$940$	−3.64845	−0.118999
$941$	−15.0584	−0.490890	−0.245445	−	0.969410i	$-0.578934\pi$
$941$	−15.0584	−0.490890	−0.245445	+	0.969410i	$0.578934\pi$
$942$	−42.4932	−1.38450
$943$	13.7732	0.448517
$944$	1.78241	0.0580126
$945$	−2.73028	−0.0888161
$946$	−19.6628	−0.639292
$947$	19.1934	0.623701	0.311851	−	0.950131i	$-0.399051\pi$
$947$	19.1934	0.623701	0.311851	+	0.950131i	$0.399051\pi$
$948$	42.2790	1.37316
$949$	−23.5835	−0.765553
$950$	18.3258	0.594568
$951$	−41.4173	−1.34305
$952$	−18.0220	−0.584096
$953$	−10.3486	−0.335225	−0.167612	−	0.985853i	$-0.553606\pi$
$953$	−10.3486	−0.335225	−0.167612	+	0.985853i	$0.553606\pi$
$954$	−0.247415	−0.00801037
$955$	29.7125	0.961473
$956$	21.4645	0.694212
$957$	14.7158	0.475693
$958$	−40.2437	−1.30021
$959$	1.92251	0.0620811
$960$	−7.27852	−0.234913
$961$	−28.3296	−0.913859
$962$	45.4510	1.46540
$963$	39.5467	1.27438
$964$	3.66715	0.118111
$965$	21.5956	0.695188
$966$	−9.64241	−0.310239
$967$	12.1154	0.389604	0.194802	−	0.980843i	$-0.437594\pi$
$967$	12.1154	0.389604	0.194802	+	0.980843i	$0.437594\pi$
$968$	18.0546	0.580295
$969$	−86.3387	−2.77360
$970$	11.2947	0.362651
$971$	−19.4779	−0.625075	−0.312538	−	0.949905i	$-0.601179\pi$
$971$	−19.4779	−0.625075	−0.312538	+	0.949905i	$0.601179\pi$
$972$	21.6727	0.695152
$973$	−26.5931	−0.852537
$974$	12.6162	0.404251
$975$	−58.0315	−1.85850
$976$	−3.26218	−0.104420
$977$	−2.66489	−0.0852573	−0.0426287	−	0.999091i	$-0.513573\pi$
$977$	−2.66489	−0.0852573	−0.0426287	+	0.999091i	$0.513573\pi$
$978$	30.1577	0.964336
$979$	71.6834	2.29101
$980$	−5.64053	−0.180180
$981$	9.07865	0.289859
$982$	15.1333	0.482921
$983$	−52.1865	−1.66449	−0.832245	−	0.554407i	$-0.812945\pi$
$983$	−52.1865	−1.66449	−0.832245	+	0.554407i	$0.812945\pi$
$984$	18.8722	0.601623
$985$	19.6382	0.625726
$986$	8.99501	0.286460
$987$	−6.62275	−0.210805
$988$	26.4471	0.841394
$989$	−6.43053	−0.204479
$990$	−46.0371	−1.46315
$991$	−1.76056	−0.0559261	−0.0279630	−	0.999609i	$-0.508902\pi$
$991$	−1.76056	−0.0559261	−0.0279630	+	0.999609i	$0.508902\pi$
$992$	−1.63413	−0.0518837
$993$	−20.4743	−0.649732
$994$	1.46080	0.0463338
$995$	−74.9749	−2.37686
$996$	−28.9667	−0.917846
$997$	41.9868	1.32973	0.664867	−	0.746962i	$-0.268488\pi$
$997$	41.9868	1.32973	0.664867	+	0.746962i	$0.268488\pi$
$998$	30.6679	0.970775
$999$	3.08840	0.0977126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.15	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.15	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41544 q^{3} +1.00000 q^{4} +3.01333 q^{5} -2.41544 q^{6} -2.26454 q^{7} +1.00000 q^{8} +2.83435 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41544 q^{3} +1.00000 q^{4} +3.01333 q^{5} -2.41544 q^{6} -2.26454 q^{7} +1.00000 q^{8} +2.83435 q^{9} +3.01333 q^{10} -5.39023 q^{11} -2.41544 q^{12} +5.88831 q^{13} -2.26454 q^{14} -7.27852 q^{15} +1.00000 q^{16} +7.95834 q^{17} +2.83435 q^{18} +4.49145 q^{19} +3.01333 q^{20} +5.46986 q^{21} -5.39023 q^{22} -1.76283 q^{23} -2.41544 q^{24} +4.08015 q^{25} +5.88831 q^{26} +0.400111 q^{27} -2.26454 q^{28} +1.13026 q^{29} -7.27852 q^{30} -1.63413 q^{31} +1.00000 q^{32} +13.0198 q^{33} +7.95834 q^{34} -6.82380 q^{35} +2.83435 q^{36} +7.71885 q^{37} +4.49145 q^{38} -14.2229 q^{39} +3.01333 q^{40} -7.81314 q^{41} +5.46986 q^{42} +3.64786 q^{43} -5.39023 q^{44} +8.54084 q^{45} -1.76283 q^{46} -1.21077 q^{47} -2.41544 q^{48} -1.87186 q^{49} +4.08015 q^{50} -19.2229 q^{51} +5.88831 q^{52} -0.0872916 q^{53} +0.400111 q^{54} -16.2425 q^{55} -2.26454 q^{56} -10.8488 q^{57} +1.13026 q^{58} +1.78241 q^{59} -7.27852 q^{60} -3.26218 q^{61} -1.63413 q^{62} -6.41850 q^{63} +1.00000 q^{64} +17.7434 q^{65} +13.0198 q^{66} -1.83138 q^{67} +7.95834 q^{68} +4.25800 q^{69} -6.82380 q^{70} -0.645077 q^{71} +2.83435 q^{72} -4.00514 q^{73} +7.71885 q^{74} -9.85537 q^{75} +4.49145 q^{76} +12.2064 q^{77} -14.2229 q^{78} -17.5036 q^{79} +3.01333 q^{80} -9.46950 q^{81} -7.81314 q^{82} +11.9923 q^{83} +5.46986 q^{84} +23.9811 q^{85} +3.64786 q^{86} -2.73008 q^{87} -5.39023 q^{88} -13.2988 q^{89} +8.54084 q^{90} -13.3343 q^{91} -1.76283 q^{92} +3.94715 q^{93} -1.21077 q^{94} +13.5342 q^{95} -2.41544 q^{96} +3.74825 q^{97} -1.87186 q^{98} -15.2778 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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