LMFDB - Embedded newform 8026.2.a.a.1.18

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

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.89918 q^{3} +1.00000 q^{4} -0.474376 q^{5} -1.89918 q^{6} +1.52174 q^{7} +1.00000 q^{8} +0.606869 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.89918 q^{3} +1.00000 q^{4} -0.474376 q^{5} -1.89918 q^{6} +1.52174 q^{7} +1.00000 q^{8} +0.606869 q^{9} -0.474376 q^{10} -0.920528 q^{11} -1.89918 q^{12} -5.29639 q^{13} +1.52174 q^{14} +0.900923 q^{15} +1.00000 q^{16} +2.24387 q^{17} +0.606869 q^{18} -2.84670 q^{19} -0.474376 q^{20} -2.89006 q^{21} -0.920528 q^{22} +4.03610 q^{23} -1.89918 q^{24} -4.77497 q^{25} -5.29639 q^{26} +4.54498 q^{27} +1.52174 q^{28} +9.52537 q^{29} +0.900923 q^{30} +2.17587 q^{31} +1.00000 q^{32} +1.74824 q^{33} +2.24387 q^{34} -0.721877 q^{35} +0.606869 q^{36} +6.07135 q^{37} -2.84670 q^{38} +10.0588 q^{39} -0.474376 q^{40} -4.64986 q^{41} -2.89006 q^{42} -9.33090 q^{43} -0.920528 q^{44} -0.287884 q^{45} +4.03610 q^{46} +7.45874 q^{47} -1.89918 q^{48} -4.68430 q^{49} -4.77497 q^{50} -4.26151 q^{51} -5.29639 q^{52} +9.82477 q^{53} +4.54498 q^{54} +0.436676 q^{55} +1.52174 q^{56} +5.40638 q^{57} +9.52537 q^{58} +10.3268 q^{59} +0.900923 q^{60} -12.4248 q^{61} +2.17587 q^{62} +0.923497 q^{63} +1.00000 q^{64} +2.51248 q^{65} +1.74824 q^{66} -8.01654 q^{67} +2.24387 q^{68} -7.66527 q^{69} -0.721877 q^{70} -14.7261 q^{71} +0.606869 q^{72} +7.17654 q^{73} +6.07135 q^{74} +9.06850 q^{75} -2.84670 q^{76} -1.40081 q^{77} +10.0588 q^{78} -6.02606 q^{79} -0.474376 q^{80} -10.4523 q^{81} -4.64986 q^{82} -1.45656 q^{83} -2.89006 q^{84} -1.06444 q^{85} -9.33090 q^{86} -18.0903 q^{87} -0.920528 q^{88} +11.3979 q^{89} -0.287884 q^{90} -8.05973 q^{91} +4.03610 q^{92} -4.13237 q^{93} +7.45874 q^{94} +1.35040 q^{95} -1.89918 q^{96} -18.6021 q^{97} -4.68430 q^{98} -0.558639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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
$3$	−1.89918	−1.09649	−0.548245	−	0.836318i	$-0.684704\pi$
$3$	−1.89918	−1.09649	−0.548245	+	0.836318i	$0.684704\pi$
$4$	1.00000	0.500000
$5$	−0.474376	−0.212147	−0.106074	−	0.994358i	$-0.533828\pi$
$5$	−0.474376	−0.212147	−0.106074	+	0.994358i	$0.533828\pi$
$6$	−1.89918	−0.775335
$7$	1.52174	0.575164	0.287582	−	0.957756i	$-0.407149\pi$
$7$	1.52174	0.575164	0.287582	+	0.957756i	$0.407149\pi$
$8$	1.00000	0.353553
$9$	0.606869	0.202290
$10$	−0.474376	−0.150011
$11$	−0.920528	−0.277550	−0.138775	−	0.990324i	$-0.544316\pi$
$11$	−0.920528	−0.277550	−0.138775	+	0.990324i	$0.544316\pi$
$12$	−1.89918	−0.548245
$13$	−5.29639	−1.46895	−0.734477	−	0.678634i	$-0.762572\pi$
$13$	−5.29639	−1.46895	−0.734477	+	0.678634i	$0.762572\pi$
$14$	1.52174	0.406703
$15$	0.900923	0.232617
$16$	1.00000	0.250000
$17$	2.24387	0.544219	0.272110	−	0.962266i	$-0.412279\pi$
$17$	2.24387	0.544219	0.272110	+	0.962266i	$0.412279\pi$
$18$	0.606869	0.143040
$19$	−2.84670	−0.653078	−0.326539	−	0.945184i	$-0.605882\pi$
$19$	−2.84670	−0.653078	−0.326539	+	0.945184i	$0.605882\pi$
$20$	−0.474376	−0.106074
$21$	−2.89006	−0.630662
$22$	−0.920528	−0.196257
$23$	4.03610	0.841586	0.420793	−	0.907157i	$-0.361752\pi$
$23$	4.03610	0.841586	0.420793	+	0.907157i	$0.361752\pi$
$24$	−1.89918	−0.387668
$25$	−4.77497	−0.954994
$26$	−5.29639	−1.03871
$27$	4.54498	0.874681
$28$	1.52174	0.287582
$29$	9.52537	1.76882	0.884408	−	0.466715i	$-0.154562\pi$
$29$	9.52537	1.76882	0.884408	+	0.466715i	$0.154562\pi$
$30$	0.900923	0.164485
$31$	2.17587	0.390798	0.195399	−	0.980724i	$-0.437400\pi$
$31$	2.17587	0.390798	0.195399	+	0.980724i	$0.437400\pi$
$32$	1.00000	0.176777
$33$	1.74824	0.304330
$34$	2.24387	0.384821
$35$	−0.721877	−0.122020
$36$	0.606869	0.101145
$37$	6.07135	0.998124	0.499062	−	0.866566i	$-0.333678\pi$
$37$	6.07135	0.998124	0.499062	+	0.866566i	$0.333678\pi$
$38$	−2.84670	−0.461796
$39$	10.0588	1.61069
$40$	−0.474376	−0.0750054
$41$	−4.64986	−0.726186	−0.363093	−	0.931753i	$-0.618279\pi$
$41$	−4.64986	−0.726186	−0.363093	+	0.931753i	$0.618279\pi$
$42$	−2.89006	−0.445945
$43$	−9.33090	−1.42295	−0.711475	−	0.702712i	$-0.751972\pi$
$43$	−9.33090	−1.42295	−0.711475	+	0.702712i	$0.751972\pi$
$44$	−0.920528	−0.138775
$45$	−0.287884	−0.0429152
$46$	4.03610	0.595091
$47$	7.45874	1.08797	0.543984	−	0.839095i	$-0.316915\pi$
$47$	7.45874	1.08797	0.543984	+	0.839095i	$0.316915\pi$
$48$	−1.89918	−0.274122
$49$	−4.68430	−0.669186
$50$	−4.77497	−0.675282
$51$	−4.26151	−0.596731
$52$	−5.29639	−0.734477
$53$	9.82477	1.34954	0.674768	−	0.738030i	$-0.264244\pi$
$53$	9.82477	1.34954	0.674768	+	0.738030i	$0.264244\pi$
$54$	4.54498	0.618493
$55$	0.436676	0.0588814
$56$	1.52174	0.203351
$57$	5.40638	0.716093
$58$	9.52537	1.25074
$59$	10.3268	1.34443	0.672217	−	0.740354i	$-0.265342\pi$
$59$	10.3268	1.34443	0.672217	+	0.740354i	$0.265342\pi$
$60$	0.900923	0.116309
$61$	−12.4248	−1.59083	−0.795417	−	0.606062i	$-0.792748\pi$
$61$	−12.4248	−1.59083	−0.795417	+	0.606062i	$0.792748\pi$
$62$	2.17587	0.276336
$63$	0.923497	0.116350
$64$	1.00000	0.125000
$65$	2.51248	0.311634
$66$	1.74824	0.215194
$67$	−8.01654	−0.979376	−0.489688	−	0.871898i	$-0.662889\pi$
$67$	−8.01654	−0.979376	−0.489688	+	0.871898i	$0.662889\pi$
$68$	2.24387	0.272110
$69$	−7.66527	−0.922790
$70$	−0.721877	−0.0862808
$71$	−14.7261	−1.74767	−0.873836	−	0.486221i	$-0.838375\pi$
$71$	−14.7261	−1.74767	−0.873836	+	0.486221i	$0.838375\pi$
$72$	0.606869	0.0715201
$73$	7.17654	0.839950	0.419975	−	0.907536i	$-0.362039\pi$
$73$	7.17654	0.839950	0.419975	+	0.907536i	$0.362039\pi$
$74$	6.07135	0.705780
$75$	9.06850	1.04714
$76$	−2.84670	−0.326539
$77$	−1.40081	−0.159637
$78$	10.0588	1.13893
$79$	−6.02606	−0.677985	−0.338992	−	0.940789i	$-0.610086\pi$
$79$	−6.02606	−0.677985	−0.338992	+	0.940789i	$0.610086\pi$
$80$	−0.474376	−0.0530368
$81$	−10.4523	−1.16137
$82$	−4.64986	−0.513491
$83$	−1.45656	−0.159879	−0.0799393	−	0.996800i	$-0.525473\pi$
$83$	−1.45656	−0.159879	−0.0799393	+	0.996800i	$0.525473\pi$
$84$	−2.89006	−0.315331
$85$	−1.06444	−0.115455
$86$	−9.33090	−1.00618
$87$	−18.0903	−1.93949
$88$	−0.920528	−0.0981286
$89$	11.3979	1.20817	0.604086	−	0.796919i	$-0.293538\pi$
$89$	11.3979	1.20817	0.604086	+	0.796919i	$0.293538\pi$
$90$	−0.287884	−0.0303456
$91$	−8.05973	−0.844889
$92$	4.03610	0.420793
$93$	−4.13237	−0.428506
$94$	7.45874	0.769310
$95$	1.35040	0.138549
$96$	−1.89918	−0.193834
$97$	−18.6021	−1.88875	−0.944377	−	0.328863i	$-0.893334\pi$
$97$	−18.6021	−1.88875	−0.944377	+	0.328863i	$0.893334\pi$
$98$	−4.68430	−0.473186
$99$	−0.558639	−0.0561454
$100$	−4.77497	−0.477497
$101$	−14.3948	−1.43234	−0.716170	−	0.697926i	$-0.754106\pi$
$101$	−14.3948	−1.43234	−0.716170	+	0.697926i	$0.754106\pi$
$102$	−4.26151	−0.421952
$103$	−12.9300	−1.27403	−0.637013	−	0.770853i	$-0.719830\pi$
$103$	−12.9300	−1.27403	−0.637013	+	0.770853i	$0.719830\pi$
$104$	−5.29639	−0.519353
$105$	1.37097	0.133793
$106$	9.82477	0.954266
$107$	−7.64255	−0.738833	−0.369416	−	0.929264i	$-0.620442\pi$
$107$	−7.64255	−0.738833	−0.369416	+	0.929264i	$0.620442\pi$
$108$	4.54498	0.437341
$109$	16.4025	1.57108	0.785539	−	0.618812i	$-0.212386\pi$
$109$	16.4025	1.57108	0.785539	+	0.618812i	$0.212386\pi$
$110$	0.436676	0.0416354
$111$	−11.5306	−1.09443
$112$	1.52174	0.143791
$113$	18.8505	1.77330	0.886652	−	0.462436i	$-0.153025\pi$
$113$	18.8505	1.77330	0.886652	+	0.462436i	$0.153025\pi$
$114$	5.40638	0.506354
$115$	−1.91463	−0.178540
$116$	9.52537	0.884408
$117$	−3.21421	−0.297154
$118$	10.3268	0.950659
$119$	3.41459	0.313015
$120$	0.900923	0.0822426
$121$	−10.1526	−0.922966
$122$	−12.4248	−1.12489
$123$	8.83090	0.796256
$124$	2.17587	0.195399
$125$	4.63701	0.414747
$126$	0.923497	0.0822717
$127$	−11.7836	−1.04563	−0.522814	−	0.852446i	$-0.675118\pi$
$127$	−11.7836	−1.04563	−0.522814	+	0.852446i	$0.675118\pi$
$128$	1.00000	0.0883883
$129$	17.7210	1.56025
$130$	2.51248	0.220359
$131$	0.659888	0.0576547	0.0288274	−	0.999584i	$-0.490823\pi$
$131$	0.659888	0.0576547	0.0288274	+	0.999584i	$0.490823\pi$
$132$	1.74824	0.152165
$133$	−4.33194	−0.375627
$134$	−8.01654	−0.692523
$135$	−2.15603	−0.185561
$136$	2.24387	0.192410
$137$	−18.0708	−1.54389	−0.771946	−	0.635688i	$-0.780716\pi$
$137$	−18.0708	−1.54389	−0.771946	+	0.635688i	$0.780716\pi$
$138$	−7.66527	−0.652511
$139$	2.51333	0.213178	0.106589	−	0.994303i	$-0.466007\pi$
$139$	2.51333	0.213178	0.106589	+	0.994303i	$0.466007\pi$
$140$	−0.721877	−0.0610098
$141$	−14.1655	−1.19295
$142$	−14.7261	−1.23579
$143$	4.87547	0.407707
$144$	0.606869	0.0505724
$145$	−4.51860	−0.375249
$146$	7.17654	0.593935
$147$	8.89631	0.733756
$148$	6.07135	0.499062
$149$	20.0509	1.64263	0.821317	−	0.570472i	$-0.193240\pi$
$149$	20.0509	1.64263	0.821317	+	0.570472i	$0.193240\pi$
$150$	9.06850	0.740440
$151$	20.5697	1.67394	0.836969	−	0.547250i	$-0.184325\pi$
$151$	20.5697	1.67394	0.836969	+	0.547250i	$0.184325\pi$
$152$	−2.84670	−0.230898
$153$	1.36174	0.110090
$154$	−1.40081	−0.112880
$155$	−1.03218	−0.0829068
$156$	10.0588	0.805346
$157$	8.12818	0.648699	0.324350	−	0.945937i	$-0.394855\pi$
$157$	8.12818	0.648699	0.324350	+	0.945937i	$0.394855\pi$
$158$	−6.02606	−0.479408
$159$	−18.6590	−1.47975
$160$	−0.474376	−0.0375027
$161$	6.14191	0.484050
$162$	−10.4523	−0.821212
$163$	−11.6495	−0.912458	−0.456229	−	0.889863i	$-0.650800\pi$
$163$	−11.6495	−0.912458	−0.456229	+	0.889863i	$0.650800\pi$
$164$	−4.64986	−0.363093
$165$	−0.829325	−0.0645628
$166$	−1.45656	−0.113051
$167$	−23.4540	−1.81492	−0.907462	−	0.420133i	$-0.861983\pi$
$167$	−23.4540	−1.81492	−0.907462	+	0.420133i	$0.861983\pi$
$168$	−2.89006	−0.222973
$169$	15.0517	1.15782
$170$	−1.06444	−0.0816387
$171$	−1.72757	−0.132111
$172$	−9.33090	−0.711475
$173$	−5.12807	−0.389880	−0.194940	−	0.980815i	$-0.562451\pi$
$173$	−5.12807	−0.389880	−0.194940	+	0.980815i	$0.562451\pi$
$174$	−18.0903	−1.37143
$175$	−7.26627	−0.549278
$176$	−0.920528	−0.0693874
$177$	−19.6124	−1.47416
$178$	11.3979	0.854306
$179$	1.94733	0.145550	0.0727752	−	0.997348i	$-0.476814\pi$
$179$	1.94733	0.145550	0.0727752	+	0.997348i	$0.476814\pi$
$180$	−0.287884	−0.0214576
$181$	−13.8758	−1.03138	−0.515690	−	0.856775i	$-0.672464\pi$
$181$	−13.8758	−1.03138	−0.515690	+	0.856775i	$0.672464\pi$
$182$	−8.05973	−0.597427
$183$	23.5969	1.74433
$184$	4.03610	0.297545
$185$	−2.88010	−0.211749
$186$	−4.13237	−0.303000
$187$	−2.06555	−0.151048
$188$	7.45874	0.543984
$189$	6.91628	0.503085
$190$	1.35040	0.0979687
$191$	−4.73723	−0.342774	−0.171387	−	0.985204i	$-0.554825\pi$
$191$	−4.73723	−0.342774	−0.171387	+	0.985204i	$0.554825\pi$
$192$	−1.89918	−0.137061
$193$	−19.1266	−1.37676	−0.688380	−	0.725350i	$-0.741678\pi$
$193$	−19.1266	−1.37676	−0.688380	+	0.725350i	$0.741678\pi$
$194$	−18.6021	−1.33555
$195$	−4.77163	−0.341704
$196$	−4.68430	−0.334593
$197$	−0.0255767	−0.00182226	−0.000911131	−	1.00000i	$-0.500290\pi$
$197$	−0.0255767	−0.00182226	−0.000911131		1.00000i	$0.500290\pi$
$198$	−0.558639	−0.0397008
$199$	−8.54620	−0.605824	−0.302912	−	0.953019i	$-0.597959\pi$
$199$	−8.54620	−0.605824	−0.302912	+	0.953019i	$0.597959\pi$
$200$	−4.77497	−0.337641
$201$	15.2248	1.07388
$202$	−14.3948	−1.01282
$203$	14.4951	1.01736
$204$	−4.26151	−0.298365
$205$	2.20578	0.154058
$206$	−12.9300	−0.900872
$207$	2.44938	0.170244
$208$	−5.29639	−0.367238
$209$	2.62047	0.181261
$210$	1.37097	0.0946060
$211$	−2.14849	−0.147908	−0.0739540	−	0.997262i	$-0.523562\pi$
$211$	−2.14849	−0.147908	−0.0739540	+	0.997262i	$0.523562\pi$
$212$	9.82477	0.674768
$213$	27.9675	1.91630
$214$	−7.64255	−0.522434
$215$	4.42635	0.301875
$216$	4.54498	0.309247
$217$	3.31112	0.224773
$218$	16.4025	1.11092
$219$	−13.6295	−0.920997
$220$	0.436676	0.0294407
$221$	−11.8844	−0.799432
$222$	−11.5306	−0.773881
$223$	−4.66411	−0.312332	−0.156166	−	0.987731i	$-0.549913\pi$
$223$	−4.66411	−0.312332	−0.156166	+	0.987731i	$0.549913\pi$
$224$	1.52174	0.101676
$225$	−2.89778	−0.193185
$226$	18.8505	1.25392
$227$	24.7358	1.64177	0.820886	−	0.571093i	$-0.193480\pi$
$227$	24.7358	1.64177	0.820886	+	0.571093i	$0.193480\pi$
$228$	5.40638	0.358046
$229$	6.41733	0.424069	0.212034	−	0.977262i	$-0.431991\pi$
$229$	6.41733	0.424069	0.212034	+	0.977262i	$0.431991\pi$
$230$	−1.91463	−0.126247
$231$	2.66038	0.175040
$232$	9.52537	0.625371
$233$	−17.8204	−1.16745	−0.583727	−	0.811950i	$-0.698406\pi$
$233$	−17.8204	−1.16745	−0.583727	+	0.811950i	$0.698406\pi$
$234$	−3.21421	−0.210119
$235$	−3.53824	−0.230810
$236$	10.3268	0.672217
$237$	11.4445	0.743403
$238$	3.41459	0.221335
$239$	15.7396	1.01811	0.509055	−	0.860734i	$-0.329995\pi$
$239$	15.7396	1.01811	0.509055	+	0.860734i	$0.329995\pi$
$240$	0.900923	0.0581543
$241$	−15.7900	−1.01712	−0.508561	−	0.861026i	$-0.669822\pi$
$241$	−15.7900	−1.01712	−0.508561	+	0.861026i	$0.669822\pi$
$242$	−10.1526	−0.652636
$243$	6.21585	0.398747
$244$	−12.4248	−0.795417
$245$	2.22212	0.141966
$246$	8.83090	0.563038
$247$	15.0772	0.959340
$248$	2.17587	0.138168
$249$	2.76627	0.175305
$250$	4.63701	0.293270
$251$	−13.9282	−0.879141	−0.439571	−	0.898208i	$-0.644869\pi$
$251$	−13.9282	−0.879141	−0.439571	+	0.898208i	$0.644869\pi$
$252$	0.923497	0.0581749
$253$	−3.71535	−0.233582
$254$	−11.7836	−0.739371
$255$	2.02156	0.126595
$256$	1.00000	0.0625000
$257$	−3.20714	−0.200056	−0.100028	−	0.994985i	$-0.531893\pi$
$257$	−3.20714	−0.200056	−0.100028	+	0.994985i	$0.531893\pi$
$258$	17.7210	1.10326
$259$	9.23903	0.574085
$260$	2.51248	0.155817
$261$	5.78064	0.357813
$262$	0.659888	0.0407680
$263$	−9.37254	−0.577935	−0.288968	−	0.957339i	$-0.593312\pi$
$263$	−9.37254	−0.577935	−0.288968	+	0.957339i	$0.593312\pi$
$264$	1.74824	0.107597
$265$	−4.66063	−0.286300
$266$	−4.33194	−0.265608
$267$	−21.6466	−1.32475
$268$	−8.01654	−0.489688
$269$	−9.23306	−0.562950	−0.281475	−	0.959569i	$-0.590824\pi$
$269$	−9.23306	−0.562950	−0.281475	+	0.959569i	$0.590824\pi$
$270$	−2.15603	−0.131212
$271$	20.2899	1.23253	0.616263	−	0.787540i	$-0.288646\pi$
$271$	20.2899	1.23253	0.616263	+	0.787540i	$0.288646\pi$
$272$	2.24387	0.136055
$273$	15.3068	0.926413
$274$	−18.0708	−1.09170
$275$	4.39549	0.265058
$276$	−7.66527	−0.461395
$277$	28.0563	1.68574	0.842869	−	0.538119i	$-0.180865\pi$
$277$	28.0563	1.68574	0.842869	+	0.538119i	$0.180865\pi$
$278$	2.51333	0.150739
$279$	1.32047	0.0790544
$280$	−0.721877	−0.0431404
$281$	−23.9635	−1.42954	−0.714770	−	0.699359i	$-0.753469\pi$
$281$	−23.9635	−1.42954	−0.714770	+	0.699359i	$0.753469\pi$
$282$	−14.1655	−0.843540
$283$	−19.3437	−1.14987	−0.574933	−	0.818200i	$-0.694972\pi$
$283$	−19.3437	−1.14987	−0.574933	+	0.818200i	$0.694972\pi$
$284$	−14.7261	−0.873836
$285$	−2.56466	−0.151917
$286$	4.87547	0.288293
$287$	−7.07589	−0.417676
$288$	0.606869	0.0357601
$289$	−11.9650	−0.703826
$290$	−4.51860	−0.265341
$291$	35.3286	2.07100
$292$	7.17654	0.419975
$293$	−31.5039	−1.84048	−0.920238	−	0.391359i	$-0.872005\pi$
$293$	−31.5039	−1.84048	−0.920238	+	0.391359i	$0.872005\pi$
$294$	8.89631	0.518844
$295$	−4.89878	−0.285218
$296$	6.07135	0.352890
$297$	−4.18378	−0.242767
$298$	20.0509	1.16152
$299$	−21.3768	−1.23625
$300$	9.06850	0.523570
$301$	−14.1992	−0.818430
$302$	20.5697	1.18365
$303$	27.3383	1.57055
$304$	−2.84670	−0.163269
$305$	5.89403	0.337491
$306$	1.36174	0.0778452
$307$	2.54648	0.145335	0.0726676	−	0.997356i	$-0.476849\pi$
$307$	2.54648	0.145335	0.0726676	+	0.997356i	$0.476849\pi$
$308$	−1.40081	−0.0798183
$309$	24.5563	1.39696
$310$	−1.03218	−0.0586240
$311$	28.1482	1.59614	0.798070	−	0.602565i	$-0.205854\pi$
$311$	28.1482	1.59614	0.798070	+	0.602565i	$0.205854\pi$
$312$	10.0588	0.569466
$313$	−7.25457	−0.410052	−0.205026	−	0.978756i	$-0.565728\pi$
$313$	−7.25457	−0.410052	−0.205026	+	0.978756i	$0.565728\pi$
$314$	8.12818	0.458700
$315$	−0.438085	−0.0246833
$316$	−6.02606	−0.338992
$317$	−2.99240	−0.168070	−0.0840348	−	0.996463i	$-0.526781\pi$
$317$	−2.99240	−0.168070	−0.0840348	+	0.996463i	$0.526781\pi$
$318$	−18.6590	−1.04634
$319$	−8.76836	−0.490934
$320$	−0.474376	−0.0265184
$321$	14.5145	0.810123
$322$	6.14191	0.342275
$323$	−6.38763	−0.355417
$324$	−10.4523	−0.580684
$325$	25.2901	1.40284
$326$	−11.6495	−0.645205
$327$	−31.1513	−1.72267
$328$	−4.64986	−0.256746
$329$	11.3503	0.625761
$330$	−0.829325	−0.0456528
$331$	28.5966	1.57181	0.785905	−	0.618347i	$-0.212198\pi$
$331$	28.5966	1.57181	0.785905	+	0.618347i	$0.212198\pi$
$332$	−1.45656	−0.0799393
$333$	3.68451	0.201910
$334$	−23.4540	−1.28335
$335$	3.80285	0.207772
$336$	−2.89006	−0.157665
$337$	−20.0551	−1.09247	−0.546235	−	0.837632i	$-0.683939\pi$
$337$	−20.0551	−1.09247	−0.546235	+	0.837632i	$0.683939\pi$
$338$	15.0517	0.818705
$339$	−35.8004	−1.94441
$340$	−1.06444	−0.0577273
$341$	−2.00295	−0.108466
$342$	−1.72757	−0.0934164
$343$	−17.7805	−0.960056
$344$	−9.33090	−0.503088
$345$	3.63622	0.195767
$346$	−5.12807	−0.275687
$347$	−8.76935	−0.470763	−0.235382	−	0.971903i	$-0.575634\pi$
$347$	−8.76935	−0.470763	−0.235382	+	0.971903i	$0.575634\pi$
$348$	−18.0903	−0.969744
$349$	−17.1231	−0.916578	−0.458289	−	0.888803i	$-0.651538\pi$
$349$	−17.1231	−0.916578	−0.458289	+	0.888803i	$0.651538\pi$
$350$	−7.26627	−0.388398
$351$	−24.0720	−1.28487
$352$	−0.920528	−0.0490643
$353$	−26.2634	−1.39786	−0.698930	−	0.715190i	$-0.746340\pi$
$353$	−26.2634	−1.39786	−0.698930	+	0.715190i	$0.746340\pi$
$354$	−19.6124	−1.04239
$355$	6.98572	0.370764
$356$	11.3979	0.604086
$357$	−6.48491	−0.343218
$358$	1.94733	0.102920
$359$	7.73992	0.408497	0.204249	−	0.978919i	$-0.434525\pi$
$359$	7.73992	0.408497	0.204249	+	0.978919i	$0.434525\pi$
$360$	−0.287884	−0.0151728
$361$	−10.8963	−0.573490
$362$	−13.8758	−0.729296
$363$	19.2816	1.01202
$364$	−8.05973	−0.422445
$365$	−3.40438	−0.178193
$366$	23.5969	1.23343
$367$	−4.34000	−0.226546	−0.113273	−	0.993564i	$-0.536133\pi$
$367$	−4.34000	−0.226546	−0.113273	+	0.993564i	$0.536133\pi$
$368$	4.03610	0.210396
$369$	−2.82185	−0.146900
$370$	−2.88010	−0.149729
$371$	14.9508	0.776205
$372$	−4.13237	−0.214253
$373$	−33.7980	−1.74999	−0.874996	−	0.484129i	$-0.839136\pi$
$373$	−33.7980	−1.74999	−0.874996	+	0.484129i	$0.839136\pi$
$374$	−2.06555	−0.106807
$375$	−8.80649	−0.454765
$376$	7.45874	0.384655
$377$	−50.4500	−2.59831
$378$	6.91628	0.355735
$379$	−2.45982	−0.126353	−0.0631763	−	0.998002i	$-0.520123\pi$
$379$	−2.45982	−0.126353	−0.0631763	+	0.998002i	$0.520123\pi$
$380$	1.35040	0.0692743
$381$	22.3792	1.14652
$382$	−4.73723	−0.242378
$383$	−10.5007	−0.536561	−0.268281	−	0.963341i	$-0.586455\pi$
$383$	−10.5007	−0.536561	−0.268281	+	0.963341i	$0.586455\pi$
$384$	−1.89918	−0.0969169
$385$	0.664508	0.0338665
$386$	−19.1266	−0.973517
$387$	−5.66263	−0.287848
$388$	−18.6021	−0.944377
$389$	4.21812	0.213867	0.106934	−	0.994266i	$-0.465897\pi$
$389$	4.21812	0.213867	0.106934	+	0.994266i	$0.465897\pi$
$390$	−4.77163	−0.241621
$391$	9.05650	0.458007
$392$	−4.68430	−0.236593
$393$	−1.25324	−0.0632178
$394$	−0.0255767	−0.00128853
$395$	2.85862	0.143833
$396$	−0.558639	−0.0280727
$397$	20.2137	1.01450	0.507248	−	0.861800i	$-0.330663\pi$
$397$	20.2137	1.01450	0.507248	+	0.861800i	$0.330663\pi$
$398$	−8.54620	−0.428382
$399$	8.22712	0.411871
$400$	−4.77497	−0.238748
$401$	16.1519	0.806589	0.403294	−	0.915070i	$-0.367865\pi$
$401$	16.1519	0.806589	0.403294	+	0.915070i	$0.367865\pi$
$402$	15.2248	0.759345
$403$	−11.5243	−0.574065
$404$	−14.3948	−0.716170
$405$	4.95832	0.246381
$406$	14.4951	0.719382
$407$	−5.58885	−0.277029
$408$	−4.26151	−0.210976
$409$	−19.9455	−0.986241	−0.493120	−	0.869961i	$-0.664144\pi$
$409$	−19.9455	−0.986241	−0.493120	+	0.869961i	$0.664144\pi$
$410$	2.20578	0.108936
$411$	34.3196	1.69286
$412$	−12.9300	−0.637013
$413$	15.7147	0.773271
$414$	2.44938	0.120381
$415$	0.690958	0.0339178
$416$	−5.29639	−0.259677
$417$	−4.77325	−0.233747
$418$	2.62047	0.128171
$419$	−12.7155	−0.621192	−0.310596	−	0.950542i	$-0.600529\pi$
$419$	−12.7155	−0.621192	−0.310596	+	0.950542i	$0.600529\pi$
$420$	1.37097	0.0668966
$421$	17.9514	0.874897	0.437448	−	0.899244i	$-0.355882\pi$
$421$	17.9514	0.874897	0.437448	+	0.899244i	$0.355882\pi$
$422$	−2.14849	−0.104587
$423$	4.52647	0.220085
$424$	9.82477	0.477133
$425$	−10.7144	−0.519726
$426$	27.9675	1.35503
$427$	−18.9074	−0.914991
$428$	−7.64255	−0.369416
$429$	−9.25938	−0.447047
$430$	4.42635	0.213458
$431$	9.75020	0.469650	0.234825	−	0.972038i	$-0.424548\pi$
$431$	9.75020	0.469650	0.234825	+	0.972038i	$0.424548\pi$
$432$	4.54498	0.218670
$433$	−7.39580	−0.355420	−0.177710	−	0.984083i	$-0.556869\pi$
$433$	−7.39580	−0.355420	−0.177710	+	0.984083i	$0.556869\pi$
$434$	3.31112	0.158939
$435$	8.58162	0.411457
$436$	16.4025	0.785539
$437$	−11.4896	−0.549621
$438$	−13.6295	−0.651243
$439$	−15.6623	−0.747520	−0.373760	−	0.927525i	$-0.621932\pi$
$439$	−15.6623	−0.747520	−0.373760	+	0.927525i	$0.621932\pi$
$440$	0.436676	0.0208177
$441$	−2.84276	−0.135369
$442$	−11.8844	−0.565284
$443$	12.1603	0.577752	0.288876	−	0.957367i	$-0.406719\pi$
$443$	12.1603	0.577752	0.288876	+	0.957367i	$0.406719\pi$
$444$	−11.5306	−0.547216
$445$	−5.40687	−0.256310
$446$	−4.66411	−0.220852
$447$	−38.0802	−1.80113
$448$	1.52174	0.0718955
$449$	11.8787	0.560592	0.280296	−	0.959914i	$-0.409567\pi$
$449$	11.8787	0.560592	0.280296	+	0.959914i	$0.409567\pi$
$450$	−2.89778	−0.136603
$451$	4.28033	0.201553
$452$	18.8505	0.886652
$453$	−39.0655	−1.83546
$454$	24.7358	1.16091
$455$	3.82334	0.179241
$456$	5.40638	0.253177
$457$	6.95416	0.325302	0.162651	−	0.986684i	$-0.447996\pi$
$457$	6.95416	0.325302	0.162651	+	0.986684i	$0.447996\pi$
$458$	6.41733	0.299862
$459$	10.1983	0.476018
$460$	−1.91463	−0.0892700
$461$	−14.6145	−0.680664	−0.340332	−	0.940305i	$-0.610539\pi$
$461$	−14.6145	−0.680664	−0.340332	+	0.940305i	$0.610539\pi$
$462$	2.66038	0.123772
$463$	30.1481	1.40110	0.700550	−	0.713603i	$-0.252938\pi$
$463$	30.1481	1.40110	0.700550	+	0.713603i	$0.252938\pi$
$464$	9.52537	0.442204
$465$	1.96029	0.0909065
$466$	−17.8204	−0.825515
$467$	−5.27435	−0.244068	−0.122034	−	0.992526i	$-0.538942\pi$
$467$	−5.27435	−0.244068	−0.122034	+	0.992526i	$0.538942\pi$
$468$	−3.21421	−0.148577
$469$	−12.1991	−0.563302
$470$	−3.53824	−0.163207
$471$	−15.4368	−0.711292
$472$	10.3268	0.475329
$473$	8.58935	0.394939
$474$	11.4445	0.525666
$475$	13.5929	0.623685
$476$	3.41459	0.156508
$477$	5.96234	0.272997
$478$	15.7396	0.719913
$479$	−38.2459	−1.74750	−0.873750	−	0.486376i	$-0.838319\pi$
$479$	−38.2459	−1.74750	−0.873750	+	0.486376i	$0.838319\pi$
$480$	0.900923	0.0411213
$481$	−32.1562	−1.46620
$482$	−15.7900	−0.719214
$483$	−11.6646	−0.530756
$484$	−10.1526	−0.461483
$485$	8.82437	0.400694
$486$	6.21585	0.281957
$487$	9.37103	0.424642	0.212321	−	0.977200i	$-0.431898\pi$
$487$	9.37103	0.424642	0.212321	+	0.977200i	$0.431898\pi$
$488$	−12.4248	−0.562445
$489$	22.1244	1.00050
$490$	2.22212	0.100385
$491$	5.28585	0.238547	0.119274	−	0.992861i	$-0.461943\pi$
$491$	5.28585	0.238547	0.119274	+	0.992861i	$0.461943\pi$
$492$	8.83090	0.398128
$493$	21.3737	0.962623
$494$	15.0772	0.678356
$495$	0.265005	0.0119111
$496$	2.17587	0.0976996
$497$	−22.4094	−1.00520
$498$	2.76627	0.123959
$499$	−30.1969	−1.35180	−0.675899	−	0.736994i	$-0.736245\pi$
$499$	−30.1969	−1.35180	−0.675899	+	0.736994i	$0.736245\pi$
$500$	4.63701	0.207373
$501$	44.5433	1.99005
$502$	−13.9282	−0.621647
$503$	39.8715	1.77778	0.888890	−	0.458121i	$-0.151477\pi$
$503$	39.8715	1.77778	0.888890	+	0.458121i	$0.151477\pi$
$504$	0.923497	0.0411358
$505$	6.82856	0.303867
$506$	−3.71535	−0.165167
$507$	−28.5858	−1.26954
$508$	−11.7836	−0.522814
$509$	−31.7944	−1.40926	−0.704632	−	0.709573i	$-0.748888\pi$
$509$	−31.7944	−1.40926	−0.704632	+	0.709573i	$0.748888\pi$
$510$	2.02156	0.0895160
$511$	10.9208	0.483109
$512$	1.00000	0.0441942
$513$	−12.9382	−0.571235
$514$	−3.20714	−0.141461
$515$	6.13365	0.270281
$516$	17.7210	0.780124
$517$	−6.86598	−0.301965
$518$	9.23903	0.405940
$519$	9.73911	0.427499
$520$	2.51248	0.110179
$521$	−36.2342	−1.58745	−0.793724	−	0.608278i	$-0.791861\pi$
$521$	−36.2342	−1.58745	−0.793724	+	0.608278i	$0.791861\pi$
$522$	5.78064	0.253012
$523$	−14.7148	−0.643433	−0.321716	−	0.946836i	$-0.604260\pi$
$523$	−14.7148	−0.643433	−0.321716	+	0.946836i	$0.604260\pi$
$524$	0.659888	0.0288274
$525$	13.7999	0.602278
$526$	−9.37254	−0.408662
$527$	4.88238	0.212680
$528$	1.74824	0.0760826
$529$	−6.70987	−0.291734
$530$	−4.66063	−0.202445
$531$	6.26701	0.271965
$532$	−4.33194	−0.187813
$533$	24.6275	1.06673
$534$	−21.6466	−0.936738
$535$	3.62544	0.156741
$536$	−8.01654	−0.346262
$537$	−3.69832	−0.159594
$538$	−9.23306	−0.398066
$539$	4.31203	0.185732
$540$	−2.15603	−0.0927806
$541$	17.6741	0.759871	0.379935	−	0.925013i	$-0.375946\pi$
$541$	17.6741	0.759871	0.379935	+	0.925013i	$0.375946\pi$
$542$	20.2899	0.871527
$543$	26.3526	1.13090
$544$	2.24387	0.0962052
$545$	−7.78097	−0.333300
$546$	15.3068	0.655073
$547$	−10.7725	−0.460600	−0.230300	−	0.973120i	$-0.573971\pi$
$547$	−10.7725	−0.460600	−0.230300	+	0.973120i	$0.573971\pi$
$548$	−18.0708	−0.771946
$549$	−7.54023	−0.321809
$550$	4.39549	0.187424
$551$	−27.1158	−1.15517
$552$	−7.66527	−0.326256
$553$	−9.17011	−0.389953
$554$	28.0563	1.19200
$555$	5.46982	0.232181
$556$	2.51333	0.106589
$557$	35.3909	1.49956	0.749779	−	0.661688i	$-0.230160\pi$
$557$	35.3909	1.49956	0.749779	+	0.661688i	$0.230160\pi$
$558$	1.32047	0.0558999
$559$	49.4201	2.09025
$560$	−0.721877	−0.0305049
$561$	3.92284	0.165622
$562$	−23.9635	−1.01084
$563$	1.61038	0.0678693	0.0339347	−	0.999424i	$-0.489196\pi$
$563$	1.61038	0.0678693	0.0339347	+	0.999424i	$0.489196\pi$
$564$	−14.1655	−0.596473
$565$	−8.94221	−0.376202
$566$	−19.3437	−0.813078
$567$	−15.9057	−0.667978
$568$	−14.7261	−0.617895
$569$	−36.5776	−1.53341	−0.766707	−	0.641997i	$-0.778106\pi$
$569$	−36.5776	−1.53341	−0.766707	+	0.641997i	$0.778106\pi$
$570$	−2.56466	−0.107422
$571$	−8.69536	−0.363889	−0.181945	−	0.983309i	$-0.558239\pi$
$571$	−8.69536	−0.363889	−0.181945	+	0.983309i	$0.558239\pi$
$572$	4.87547	0.203854
$573$	8.99682	0.375848
$574$	−7.07589	−0.295342
$575$	−19.2723	−0.803709
$576$	0.606869	0.0252862
$577$	−34.2694	−1.42665	−0.713327	−	0.700831i	$-0.752813\pi$
$577$	−34.2694	−1.42665	−0.713327	+	0.700831i	$0.752813\pi$
$578$	−11.9650	−0.497680
$579$	36.3247	1.50960
$580$	−4.51860	−0.187625
$581$	−2.21651	−0.0919564
$582$	35.3286	1.46442
$583$	−9.04397	−0.374563
$584$	7.17654	0.296967
$585$	1.52474	0.0630404
$586$	−31.5039	−1.30141
$587$	40.2372	1.66077	0.830384	−	0.557191i	$-0.188121\pi$
$587$	40.2372	1.66077	0.830384	+	0.557191i	$0.188121\pi$
$588$	8.89631	0.366878
$589$	−6.19406	−0.255222
$590$	−4.89878	−0.201680
$591$	0.0485746	0.00199809
$592$	6.07135	0.249531
$593$	16.3111	0.669818	0.334909	−	0.942250i	$-0.391294\pi$
$593$	16.3111	0.669818	0.334909	+	0.942250i	$0.391294\pi$
$594$	−4.18378	−0.171662
$595$	−1.61980	−0.0664053
$596$	20.0509	0.821317
$597$	16.2307	0.664280
$598$	−21.3768	−0.874161
$599$	2.31888	0.0947468	0.0473734	−	0.998877i	$-0.484915\pi$
$599$	2.31888	0.0947468	0.0473734	+	0.998877i	$0.484915\pi$
$600$	9.06850	0.370220
$601$	−33.7925	−1.37842	−0.689211	−	0.724560i	$-0.742043\pi$
$601$	−33.7925	−1.37842	−0.689211	+	0.724560i	$0.742043\pi$
$602$	−14.1992	−0.578717
$603$	−4.86499	−0.198118
$604$	20.5697	0.836969
$605$	4.81616	0.195805
$606$	27.3383	1.11054
$607$	3.46623	0.140690	0.0703450	−	0.997523i	$-0.477590\pi$
$607$	3.46623	0.140690	0.0703450	+	0.997523i	$0.477590\pi$
$608$	−2.84670	−0.115449
$609$	−27.5288	−1.11552
$610$	5.89403	0.238642
$611$	−39.5044	−1.59818
$612$	1.36174	0.0550449
$613$	30.6317	1.23720	0.618602	−	0.785705i	$-0.287699\pi$
$613$	30.6317	1.23720	0.618602	+	0.785705i	$0.287699\pi$
$614$	2.54648	0.102767
$615$	−4.18916	−0.168923
$616$	−1.40081	−0.0564401
$617$	3.26656	0.131507	0.0657535	−	0.997836i	$-0.479055\pi$
$617$	3.26656	0.131507	0.0657535	+	0.997836i	$0.479055\pi$
$618$	24.5563	0.987797
$619$	−5.78702	−0.232600	−0.116300	−	0.993214i	$-0.537103\pi$
$619$	−5.78702	−0.232600	−0.116300	+	0.993214i	$0.537103\pi$
$620$	−1.03218	−0.0414534
$621$	18.3440	0.736119
$622$	28.1482	1.12864
$623$	17.3446	0.694897
$624$	10.0588	0.402673
$625$	21.6752	0.867006
$626$	−7.25457	−0.289951
$627$	−4.97672	−0.198751
$628$	8.12818	0.324350
$629$	13.6233	0.543198
$630$	−0.438085	−0.0174537
$631$	38.3426	1.52640	0.763198	−	0.646165i	$-0.223628\pi$
$631$	38.3426	1.52640	0.763198	+	0.646165i	$0.223628\pi$
$632$	−6.02606	−0.239704
$633$	4.08036	0.162180
$634$	−2.99240	−0.118843
$635$	5.58987	0.221827
$636$	−18.6590	−0.739876
$637$	24.8099	0.983003
$638$	−8.76836	−0.347143
$639$	−8.93683	−0.353536
$640$	−0.474376	−0.0187513
$641$	−14.2006	−0.560889	−0.280445	−	0.959870i	$-0.590482\pi$
$641$	−14.2006	−0.560889	−0.280445	+	0.959870i	$0.590482\pi$
$642$	14.5145	0.572843
$643$	−44.2889	−1.74658	−0.873291	−	0.487198i	$-0.838019\pi$
$643$	−44.2889	−1.74658	−0.873291	+	0.487198i	$0.838019\pi$
$644$	6.14191	0.242025
$645$	−8.40642	−0.331003
$646$	−6.38763	−0.251318
$647$	16.0642	0.631548	0.315774	−	0.948834i	$-0.397736\pi$
$647$	16.0642	0.631548	0.315774	+	0.948834i	$0.397736\pi$
$648$	−10.4523	−0.410606
$649$	−9.50610	−0.373147
$650$	25.2901	0.991958
$651$	−6.28839	−0.246462
$652$	−11.6495	−0.456229
$653$	−40.4822	−1.58419	−0.792095	−	0.610397i	$-0.791010\pi$
$653$	−40.4822	−1.58419	−0.792095	+	0.610397i	$0.791010\pi$
$654$	−31.1513	−1.21811
$655$	−0.313035	−0.0122313
$656$	−4.64986	−0.181547
$657$	4.35522	0.169913
$658$	11.3503	0.442480
$659$	−26.7398	−1.04163	−0.520816	−	0.853669i	$-0.674372\pi$
$659$	−26.7398	−1.04163	−0.520816	+	0.853669i	$0.674372\pi$
$660$	−0.829325	−0.0322814
$661$	−4.94207	−0.192224	−0.0961120	−	0.995371i	$-0.530641\pi$
$661$	−4.94207	−0.192224	−0.0961120	+	0.995371i	$0.530641\pi$
$662$	28.5966	1.11144
$663$	22.5706	0.876569
$664$	−1.45656	−0.0565256
$665$	2.05497	0.0796882
$666$	3.68451	0.142772
$667$	38.4454	1.48861
$668$	−23.4540	−0.907462
$669$	8.85796	0.342469
$670$	3.80285	0.146917
$671$	11.4374	0.441535
$672$	−2.89006	−0.111486
$673$	−0.284419	−0.0109635	−0.00548177	−	0.999985i	$-0.501745\pi$
$673$	−0.284419	−0.0109635	−0.00548177	+	0.999985i	$0.501745\pi$
$674$	−20.0551	−0.772493
$675$	−21.7021	−0.835315
$676$	15.0517	0.578912
$677$	33.5291	1.28863	0.644314	−	0.764761i	$-0.277143\pi$
$677$	33.5291	1.28863	0.644314	+	0.764761i	$0.277143\pi$
$678$	−35.8004	−1.37491
$679$	−28.3076	−1.08634
$680$	−1.06444	−0.0408194
$681$	−46.9776	−1.80019
$682$	−2.00295	−0.0766970
$683$	−3.12801	−0.119690	−0.0598450	−	0.998208i	$-0.519061\pi$
$683$	−3.12801	−0.119690	−0.0598450	+	0.998208i	$0.519061\pi$
$684$	−1.72757	−0.0660554
$685$	8.57234	0.327532
$686$	−17.7805	−0.678862
$687$	−12.1876	−0.464987
$688$	−9.33090	−0.355737
$689$	−52.0358	−1.98240
$690$	3.63622	0.138428
$691$	25.7481	0.979503	0.489752	−	0.871862i	$-0.337087\pi$
$691$	25.7481	0.979503	0.489752	+	0.871862i	$0.337087\pi$
$692$	−5.12807	−0.194940
$693$	−0.850105	−0.0322928
$694$	−8.76935	−0.332880
$695$	−1.19226	−0.0452251
$696$	−18.0903	−0.685713
$697$	−10.4337	−0.395204
$698$	−17.1231	−0.648119
$699$	33.8441	1.28010
$700$	−7.26627	−0.274639
$701$	−8.79899	−0.332333	−0.166167	−	0.986098i	$-0.553139\pi$
$701$	−8.79899	−0.332333	−0.166167	+	0.986098i	$0.553139\pi$
$702$	−24.0720	−0.908537
$703$	−17.2833	−0.651853
$704$	−0.920528	−0.0346937
$705$	6.71975	0.253080
$706$	−26.2634	−0.988436
$707$	−21.9052	−0.823831
$708$	−19.6124	−0.737079
$709$	14.2766	0.536168	0.268084	−	0.963396i	$-0.413609\pi$
$709$	14.2766	0.536168	0.268084	+	0.963396i	$0.413609\pi$
$710$	6.98572	0.262169
$711$	−3.65703	−0.137149
$712$	11.3979	0.427153
$713$	8.78205	0.328890
$714$	−6.48491	−0.242692
$715$	−2.31280	−0.0864940
$716$	1.94733	0.0727752
$717$	−29.8923	−1.11635
$718$	7.73992	0.288851
$719$	−18.6516	−0.695586	−0.347793	−	0.937571i	$-0.613069\pi$
$719$	−18.6516	−0.695586	−0.347793	+	0.937571i	$0.613069\pi$
$720$	−0.287884	−0.0107288
$721$	−19.6760	−0.732774
$722$	−10.8963	−0.405519
$723$	29.9880	1.11526
$724$	−13.8758	−0.515690
$725$	−45.4833	−1.68921
$726$	19.2816	0.715608
$727$	10.6762	0.395960	0.197980	−	0.980206i	$-0.436562\pi$
$727$	10.6762	0.395960	0.197980	+	0.980206i	$0.436562\pi$
$728$	−8.05973	−0.298714
$729$	19.5519	0.724146
$730$	−3.40438	−0.126002
$731$	−20.9374	−0.774396
$732$	23.5969	0.872167
$733$	19.2600	0.711383	0.355691	−	0.934603i	$-0.384245\pi$
$733$	19.2600	0.711383	0.355691	+	0.934603i	$0.384245\pi$
$734$	−4.34000	−0.160192
$735$	−4.22019	−0.155664
$736$	4.03610	0.148773
$737$	7.37945	0.271825
$738$	−2.82185	−0.103874
$739$	−51.2192	−1.88413	−0.942064	−	0.335433i	$-0.891117\pi$
$739$	−51.2192	−1.88413	−0.942064	+	0.335433i	$0.891117\pi$
$740$	−2.88010	−0.105875
$741$	−28.6343	−1.05191
$742$	14.9508	0.548860
$743$	38.7815	1.42276	0.711378	−	0.702809i	$-0.248071\pi$
$743$	38.7815	1.42276	0.711378	+	0.702809i	$0.248071\pi$
$744$	−4.13237	−0.151500
$745$	−9.51166	−0.348480
$746$	−33.7980	−1.23743
$747$	−0.883942	−0.0323418
$748$	−2.06555	−0.0755239
$749$	−11.6300	−0.424950
$750$	−8.80649	−0.321568
$751$	−30.7413	−1.12177	−0.560883	−	0.827895i	$-0.689538\pi$
$751$	−30.7413	−1.12177	−0.560883	+	0.827895i	$0.689538\pi$
$752$	7.45874	0.271992
$753$	26.4521	0.963969
$754$	−50.4500	−1.83728
$755$	−9.75777	−0.355122
$756$	6.91628	0.251543
$757$	−18.6652	−0.678396	−0.339198	−	0.940715i	$-0.610156\pi$
$757$	−18.6652	−0.678396	−0.339198	+	0.940715i	$0.610156\pi$
$758$	−2.45982	−0.0893448
$759$	7.05609	0.256120
$760$	1.35040	0.0489843
$761$	0.783478	0.0284010	0.0142005	−	0.999899i	$-0.495480\pi$
$761$	0.783478	0.0284010	0.0142005	+	0.999899i	$0.495480\pi$
$762$	22.3792	0.810713
$763$	24.9604	0.903628
$764$	−4.73723	−0.171387
$765$	−0.645974	−0.0233552
$766$	−10.5007	−0.379406
$767$	−54.6947	−1.97491
$768$	−1.89918	−0.0685306
$769$	−2.27967	−0.0822069	−0.0411034	−	0.999155i	$-0.513087\pi$
$769$	−2.27967	−0.0822069	−0.0411034	+	0.999155i	$0.513087\pi$
$770$	0.664508	0.0239472
$771$	6.09092	0.219359
$772$	−19.1266	−0.688380
$773$	−2.18767	−0.0786851	−0.0393426	−	0.999226i	$-0.512526\pi$
$773$	−2.18767	−0.0786851	−0.0393426	+	0.999226i	$0.512526\pi$
$774$	−5.66263	−0.203539
$775$	−10.3897	−0.373210
$776$	−18.6021	−0.667776
$777$	−17.5465	−0.629479
$778$	4.21812	0.151227
$779$	13.2368	0.474256
$780$	−4.77163	−0.170852
$781$	13.5558	0.485065
$782$	9.05650	0.323860
$783$	43.2926	1.54715
$784$	−4.68430	−0.167297
$785$	−3.85581	−0.137620
$786$	−1.25324	−0.0447017
$787$	40.5911	1.44692	0.723459	−	0.690368i	$-0.242551\pi$
$787$	40.5911	1.44692	0.723459	+	0.690368i	$0.242551\pi$
$788$	−0.0255767	−0.000911131 0
$789$	17.8001	0.633700
$790$	2.85862	0.101705
$791$	28.6856	1.01994
$792$	−0.558639	−0.0198504
$793$	65.8066	2.33686
$794$	20.2137	0.717357
$795$	8.85136	0.313925
$796$	−8.54620	−0.302912
$797$	13.7155	0.485829	0.242915	−	0.970048i	$-0.421897\pi$
$797$	13.7155	0.485829	0.242915	+	0.970048i	$0.421897\pi$
$798$	8.22712	0.291237
$799$	16.7365	0.592093
$800$	−4.77497	−0.168821
$801$	6.91701	0.244400
$802$	16.1519	0.570344
$803$	−6.60620	−0.233128
$804$	15.2248	0.536938
$805$	−2.91357	−0.102690
$806$	−11.5243	−0.405925
$807$	17.5352	0.617269
$808$	−14.3948	−0.506409
$809$	−35.5717	−1.25064	−0.625318	−	0.780370i	$-0.715031\pi$
$809$	−35.5717	−1.25064	−0.625318	+	0.780370i	$0.715031\pi$
$810$	4.95832	0.174218
$811$	−25.6664	−0.901271	−0.450635	−	0.892708i	$-0.648803\pi$
$811$	−25.6664	−0.901271	−0.450635	+	0.892708i	$0.648803\pi$
$812$	14.4951	0.508680
$813$	−38.5342	−1.35145
$814$	−5.58885	−0.195889
$815$	5.52623	0.193575
$816$	−4.26151	−0.149183
$817$	26.5623	0.929296
$818$	−19.9455	−0.697378
$819$	−4.89120	−0.170912
$820$	2.20578	0.0770292
$821$	7.97458	0.278315	0.139157	−	0.990270i	$-0.455561\pi$
$821$	7.97458	0.278315	0.139157	+	0.990270i	$0.455561\pi$
$822$	34.3196	1.19703
$823$	11.7074	0.408093	0.204046	−	0.978961i	$-0.434591\pi$
$823$	11.7074	0.408093	0.204046	+	0.978961i	$0.434591\pi$
$824$	−12.9300	−0.450436
$825$	−8.34781	−0.290633
$826$	15.7147	0.546785
$827$	34.2234	1.19006	0.595032	−	0.803702i	$-0.297139\pi$
$827$	34.2234	1.19006	0.595032	+	0.803702i	$0.297139\pi$
$828$	2.44938	0.0851220
$829$	32.2798	1.12112	0.560562	−	0.828113i	$-0.310585\pi$
$829$	32.2798	1.12112	0.560562	+	0.828113i	$0.310585\pi$
$830$	0.690958	0.0239835
$831$	−53.2838	−1.84839
$832$	−5.29639	−0.183619
$833$	−10.5110	−0.364184
$834$	−4.77325	−0.165284
$835$	11.1260	0.385031
$836$	2.62047	0.0906307
$837$	9.88930	0.341824
$838$	−12.7155	−0.439249
$839$	−1.18515	−0.0409159	−0.0204579	−	0.999791i	$-0.506512\pi$
$839$	−1.18515	−0.0409159	−0.0204579	+	0.999791i	$0.506512\pi$
$840$	1.37097	0.0473030
$841$	61.7326	2.12871
$842$	17.9514	0.618645
$843$	45.5108	1.56748
$844$	−2.14849	−0.0739540
$845$	−7.14016	−0.245629
$846$	4.52647	0.155623
$847$	−15.4497	−0.530857
$848$	9.82477	0.337384
$849$	36.7372	1.26082
$850$	−10.7144	−0.367502
$851$	24.5046	0.840007
$852$	27.9675	0.958152
$853$	56.5662	1.93679	0.968396	−	0.249419i	$-0.0802396\pi$
$853$	56.5662	1.93679	0.968396	+	0.249419i	$0.0802396\pi$
$854$	−18.9074	−0.646996
$855$	0.819518	0.0280269
$856$	−7.64255	−0.261217
$857$	−40.3408	−1.37801	−0.689007	−	0.724754i	$-0.741953\pi$
$857$	−40.3408	−1.37801	−0.689007	+	0.724754i	$0.741953\pi$
$858$	−9.25938	−0.316110
$859$	27.1631	0.926793	0.463396	−	0.886151i	$-0.346631\pi$
$859$	27.1631	0.926793	0.463396	+	0.886151i	$0.346631\pi$
$860$	4.42635	0.150937
$861$	13.4384	0.457978
$862$	9.75020	0.332093
$863$	−37.4665	−1.27538	−0.637688	−	0.770295i	$-0.720109\pi$
$863$	−37.4665	−1.27538	−0.637688	+	0.770295i	$0.720109\pi$
$864$	4.54498	0.154623
$865$	2.43263	0.0827120
$866$	−7.39580	−0.251320
$867$	22.7237	0.771738
$868$	3.31112	0.112387
$869$	5.54716	0.188174
$870$	8.58162	0.290944
$871$	42.4587	1.43866
$872$	16.4025	0.555460
$873$	−11.2890	−0.382075
$874$	−11.4896	−0.388641
$875$	7.05633	0.238547
$876$	−13.6295	−0.460498
$877$	0.0813141	0.00274578	0.00137289	−	0.999999i	$-0.499563\pi$
$877$	0.0813141	0.00274578	0.00137289	+	0.999999i	$0.499563\pi$
$878$	−15.6623	−0.528577
$879$	59.8314	2.01806
$880$	0.436676	0.0147203
$881$	−28.1510	−0.948433	−0.474216	−	0.880408i	$-0.657269\pi$
$881$	−28.1510	−0.948433	−0.474216	+	0.880408i	$0.657269\pi$
$882$	−2.84276	−0.0957206
$883$	13.9093	0.468085	0.234043	−	0.972226i	$-0.424805\pi$
$883$	13.9093	0.468085	0.234043	+	0.972226i	$0.424805\pi$
$884$	−11.8844	−0.399716
$885$	9.30365	0.312739
$886$	12.1603	0.408532
$887$	−46.9381	−1.57603	−0.788014	−	0.615658i	$-0.788890\pi$
$887$	−46.9381	−1.57603	−0.788014	+	0.615658i	$0.788890\pi$
$888$	−11.5306	−0.386940
$889$	−17.9317	−0.601408
$890$	−5.40687	−0.181239
$891$	9.62165	0.322337
$892$	−4.66411	−0.156166
$893$	−21.2328	−0.710528
$894$	−38.0802	−1.27359
$895$	−0.923766	−0.0308781
$896$	1.52174	0.0508378
$897$	40.5982	1.35554
$898$	11.8787	0.396399
$899$	20.7260	0.691250
$900$	−2.89778	−0.0965926
$901$	22.0455	0.734443
$902$	4.28033	0.142519
$903$	26.9668	0.897400
$904$	18.8505	0.626958
$905$	6.58234	0.218804
$906$	−39.0655	−1.29786
$907$	37.2000	1.23521	0.617604	−	0.786489i	$-0.288104\pi$
$907$	37.2000	1.23521	0.617604	+	0.786489i	$0.288104\pi$
$908$	24.7358	0.820886
$909$	−8.73577	−0.289747
$910$	3.82334	0.126743
$911$	35.3473	1.17111	0.585554	−	0.810634i	$-0.300877\pi$
$911$	35.3473	1.17111	0.585554	+	0.810634i	$0.300877\pi$
$912$	5.40638	0.179023
$913$	1.34081	0.0443742
$914$	6.95416	0.230023
$915$	−11.1938	−0.370055
$916$	6.41733	0.212034
$917$	1.00418	0.0331609
$918$	10.1983	0.336596
$919$	44.2972	1.46123	0.730615	−	0.682789i	$-0.239233\pi$
$919$	44.2972	1.46123	0.730615	+	0.682789i	$0.239233\pi$
$920$	−1.91463	−0.0631235
$921$	−4.83621	−0.159358
$922$	−14.6145	−0.481302
$923$	77.9953	2.56725
$924$	2.66038	0.0875199
$925$	−28.9905	−0.953202
$926$	30.1481	0.990727
$927$	−7.84678	−0.257722
$928$	9.52537	0.312685
$929$	14.3448	0.470639	0.235320	−	0.971918i	$-0.424386\pi$
$929$	14.3448	0.470639	0.235320	+	0.971918i	$0.424386\pi$
$930$	1.96029	0.0642806
$931$	13.3348	0.437030
$932$	−17.8204	−0.583727
$933$	−53.4584	−1.75015
$934$	−5.27435	−0.172582
$935$	0.979845	0.0320444
$936$	−3.21421	−0.105060
$937$	−5.53039	−0.180670	−0.0903350	−	0.995911i	$-0.528794\pi$
$937$	−5.53039	−0.180670	−0.0903350	+	0.995911i	$0.528794\pi$
$938$	−12.1991	−0.398315
$939$	13.7777	0.449618
$940$	−3.53824	−0.115405
$941$	37.9124	1.23591	0.617954	−	0.786215i	$-0.287962\pi$
$941$	37.9124	1.23591	0.617954	+	0.786215i	$0.287962\pi$
$942$	−15.4368	−0.502960
$943$	−18.7673	−0.611148
$944$	10.3268	0.336109
$945$	−3.28092	−0.106728
$946$	8.58935	0.279264
$947$	20.9172	0.679716	0.339858	−	0.940477i	$-0.389621\pi$
$947$	20.9172	0.679716	0.339858	+	0.940477i	$0.389621\pi$
$948$	11.4445	0.371702
$949$	−38.0097	−1.23385
$950$	13.5929	0.441012
$951$	5.68309	0.184287
$952$	3.41459	0.110668
$953$	61.4597	1.99087	0.995437	−	0.0954211i	$-0.0304198\pi$
$953$	61.4597	1.99087	0.995437	+	0.0954211i	$0.0304198\pi$
$954$	5.96234	0.193038
$955$	2.24722	0.0727185
$956$	15.7396	0.509055
$957$	16.6527	0.538304
$958$	−38.2459	−1.23567
$959$	−27.4991	−0.887992
$960$	0.900923	0.0290772
$961$	−26.2656	−0.847277
$962$	−32.1562	−1.03676
$963$	−4.63802	−0.149458
$964$	−15.7900	−0.508561
$965$	9.07318	0.292076
$966$	−11.6646	−0.375301
$967$	7.31619	0.235273	0.117636	−	0.993057i	$-0.462468\pi$
$967$	7.31619	0.235273	0.117636	+	0.993057i	$0.462468\pi$
$968$	−10.1526	−0.326318
$969$	12.1312	0.389711
$970$	8.82437	0.283334
$971$	−22.3676	−0.717809	−0.358904	−	0.933374i	$-0.616850\pi$
$971$	−22.3676	−0.717809	−0.358904	+	0.933374i	$0.616850\pi$
$972$	6.21585	0.199374
$973$	3.82464	0.122612
$974$	9.37103	0.300267
$975$	−48.0303	−1.53820
$976$	−12.4248	−0.397709
$977$	−20.3700	−0.651693	−0.325847	−	0.945423i	$-0.605649\pi$
$977$	−20.3700	−0.651693	−0.325847	+	0.945423i	$0.605649\pi$
$978$	22.1244	0.707461
$979$	−10.4921	−0.335327
$980$	2.22212	0.0709830
$981$	9.95419	0.317813
$982$	5.28585	0.168678
$983$	11.9196	0.380177	0.190088	−	0.981767i	$-0.439123\pi$
$983$	11.9196	0.380177	0.190088	+	0.981767i	$0.439123\pi$
$984$	8.83090	0.281519
$985$	0.0121330	0.000386588 0
$986$	21.3737	0.680677
$987$	−21.5562	−0.686140
$988$	15.0772	0.479670
$989$	−37.6605	−1.19753
$990$	0.265005	0.00842241
$991$	33.2396	1.05589	0.527946	−	0.849278i	$-0.322962\pi$
$991$	33.2396	1.05589	0.527946	+	0.849278i	$0.322962\pi$
$992$	2.17587	0.0690841
$993$	−54.3099	−1.72347
$994$	−22.4094	−0.710782
$995$	4.05411	0.128524
$996$	2.76627	0.0876526
$997$	−34.9324	−1.10632	−0.553160	−	0.833075i	$-0.686578\pi$
$997$	−34.9324	−1.10632	−0.553160	+	0.833075i	$0.686578\pi$
$998$	−30.1969	−0.955866
$999$	27.5942	0.873041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.18	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.18	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.89918 q^{3} +1.00000 q^{4} -0.474376 q^{5} -1.89918 q^{6} +1.52174 q^{7} +1.00000 q^{8} +0.606869 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.89918 q^{3} +1.00000 q^{4} -0.474376 q^{5} -1.89918 q^{6} +1.52174 q^{7} +1.00000 q^{8} +0.606869 q^{9} -0.474376 q^{10} -0.920528 q^{11} -1.89918 q^{12} -5.29639 q^{13} +1.52174 q^{14} +0.900923 q^{15} +1.00000 q^{16} +2.24387 q^{17} +0.606869 q^{18} -2.84670 q^{19} -0.474376 q^{20} -2.89006 q^{21} -0.920528 q^{22} +4.03610 q^{23} -1.89918 q^{24} -4.77497 q^{25} -5.29639 q^{26} +4.54498 q^{27} +1.52174 q^{28} +9.52537 q^{29} +0.900923 q^{30} +2.17587 q^{31} +1.00000 q^{32} +1.74824 q^{33} +2.24387 q^{34} -0.721877 q^{35} +0.606869 q^{36} +6.07135 q^{37} -2.84670 q^{38} +10.0588 q^{39} -0.474376 q^{40} -4.64986 q^{41} -2.89006 q^{42} -9.33090 q^{43} -0.920528 q^{44} -0.287884 q^{45} +4.03610 q^{46} +7.45874 q^{47} -1.89918 q^{48} -4.68430 q^{49} -4.77497 q^{50} -4.26151 q^{51} -5.29639 q^{52} +9.82477 q^{53} +4.54498 q^{54} +0.436676 q^{55} +1.52174 q^{56} +5.40638 q^{57} +9.52537 q^{58} +10.3268 q^{59} +0.900923 q^{60} -12.4248 q^{61} +2.17587 q^{62} +0.923497 q^{63} +1.00000 q^{64} +2.51248 q^{65} +1.74824 q^{66} -8.01654 q^{67} +2.24387 q^{68} -7.66527 q^{69} -0.721877 q^{70} -14.7261 q^{71} +0.606869 q^{72} +7.17654 q^{73} +6.07135 q^{74} +9.06850 q^{75} -2.84670 q^{76} -1.40081 q^{77} +10.0588 q^{78} -6.02606 q^{79} -0.474376 q^{80} -10.4523 q^{81} -4.64986 q^{82} -1.45656 q^{83} -2.89006 q^{84} -1.06444 q^{85} -9.33090 q^{86} -18.0903 q^{87} -0.920528 q^{88} +11.3979 q^{89} -0.287884 q^{90} -8.05973 q^{91} +4.03610 q^{92} -4.13237 q^{93} +7.45874 q^{94} +1.35040 q^{95} -1.89918 q^{96} -18.6021 q^{97} -4.68430 q^{98} -0.558639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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