LMFDB - Embedded newform 10.18.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10,18,Mod(1,10)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10.1"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	10.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,512,17628] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$18.3222087345$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2941}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 735 $ x^2 - x - 735
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$27.6155$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000 q^{2} -4201.44 q^{3} +65536.0 q^{4} -390625. q^{5} -1.07557e6 q^{6} +1.23193e7 q^{7} +1.67772e7 q^{8} -1.11488e8 q^{9} -1.00000e8 q^{10} +1.21513e9 q^{11} -2.75345e8 q^{12} +2.42392e9 q^{13} +3.15374e9 q^{14} +1.64119e9 q^{15} +4.29497e9 q^{16} -1.73631e10 q^{17} -2.85410e10 q^{18} +1.15322e11 q^{19} -2.56000e10 q^{20} -5.17587e10 q^{21} +3.11072e11 q^{22} +5.47905e11 q^{23} -7.04884e10 q^{24} +1.52588e11 q^{25} +6.20524e11 q^{26} +1.01098e12 q^{27} +8.07357e11 q^{28} +2.02736e12 q^{29} +4.20144e11 q^{30} -3.37643e12 q^{31} +1.09951e12 q^{32} -5.10528e12 q^{33} -4.44497e12 q^{34} -4.81222e12 q^{35} -7.30648e12 q^{36} -2.48073e13 q^{37} +2.95225e13 q^{38} -1.01840e13 q^{39} -6.55360e12 q^{40} -5.37038e13 q^{41} -1.32502e13 q^{42} -2.49397e13 q^{43} +7.96345e13 q^{44} +4.35500e13 q^{45} +1.40264e14 q^{46} -1.57049e14 q^{47} -1.80450e13 q^{48} -8.08656e13 q^{49} +3.90625e13 q^{50} +7.29502e13 q^{51} +1.58854e14 q^{52} +5.06856e14 q^{53} +2.58812e14 q^{54} -4.74659e14 q^{55} +2.06683e14 q^{56} -4.84519e14 q^{57} +5.19005e14 q^{58} +1.29796e15 q^{59} +1.07557e14 q^{60} +4.35989e14 q^{61} -8.64366e14 q^{62} -1.37345e15 q^{63} +2.81475e14 q^{64} -9.46844e14 q^{65} -1.30695e15 q^{66} -2.50888e15 q^{67} -1.13791e15 q^{68} -2.30199e15 q^{69} -1.23193e15 q^{70} -3.06603e15 q^{71} -1.87046e15 q^{72} +4.56009e15 q^{73} -6.35068e15 q^{74} -6.41088e14 q^{75} +7.55776e15 q^{76} +1.49695e16 q^{77} -2.60709e15 q^{78} +1.40515e16 q^{79} -1.67772e15 q^{80} +1.01500e16 q^{81} -1.37482e16 q^{82} +2.52434e16 q^{83} -3.39206e15 q^{84} +6.78248e15 q^{85} -6.38456e15 q^{86} -8.51784e15 q^{87} +2.03864e16 q^{88} -6.68155e16 q^{89} +1.11488e16 q^{90} +2.98610e16 q^{91} +3.59075e16 q^{92} +1.41859e16 q^{93} -4.02045e16 q^{94} -4.50478e16 q^{95} -4.61953e15 q^{96} +6.24209e16 q^{97} -2.07016e16 q^{98} -1.35472e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 512 q^{2} + 17628 q^{3} + 131072 q^{4} - 781250 q^{5} + 4512768 q^{6} + 27684196 q^{7} + 33554432 q^{8} + 235896066 q^{9} - 200000000 q^{10} + 64515264 q^{11} + 1155268608 q^{12} + 2895838468 q^{13}+ \cdots - 53\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 512 * q^2 + 17628 * q^3 + 131072 * q^4 - 781250 * q^5 + 4512768 * q^6 + 27684196 * q^7 + 33554432 * q^8 + 235896066 * q^9 - 200000000 * q^10 + 64515264 * q^11 + 1155268608 * q^12 + 2895838468 * q^13 + 7087154176 * q^14 - 6885937500 * q^15 + 8589934592 * q^16 + 1580212596 * q^17 + 60389392896 * q^18 + 44213712760 * q^19 - 51200000000 * q^20 + 283648477944 * q^21 + 16515907584 * q^22 + 487549782828 * q^23 + 295748763648 * q^24 + 305175781250 * q^25 + 741334647808 * q^26 + 5775127941960 * q^27 + 1814311469056 * q^28 + 3987314863500 * q^29 - 1762800000000 * q^30 - 5492261339336 * q^31 + 2199023255552 * q^32 - 30222474885504 * q^33 + 404534424576 * q^34 - 10814139062500 * q^35 + 15459684581376 * q^36 - 62715287637884 * q^37 + 11318710466560 * q^38 + 117745895352 * q^39 - 13107200000000 * q^40 + 23411477277324 * q^41 + 72614010353664 * q^42 - 124856923191092 * q^43 + 4228072341504 * q^44 - 92146900781250 * q^45 + 124812744403968 * q^46 - 185946612123564 * q^47 + 75711683493888 * q^48 - 77415796886406 * q^49 + 78125000000000 * q^50 + 486473079414744 * q^51 + 189781669838848 * q^52 + 359339780647668 * q^53 + 1478432753141760 * q^54 - 25201275000000 * q^55 + 464463736078336 * q^56 - 2036779039451760 * q^57 + 1020752605056000 * q^58 + 902179170360600 * q^59 - 451276800000000 * q^60 - 1564422918967676 * q^61 - 1406018902870016 * q^62 + 3964069932109668 * q^63 + 562949953421312 * q^64 - 1131186901562500 * q^65 - 7736953570689024 * q^66 - 5839738931054684 * q^67 + 103560812691456 * q^68 - 3619512981398808 * q^69 - 2768419600000000 * q^70 - 67588560434136 * q^71 + 3957679252832256 * q^72 + 3533390699585668 * q^73 - 16055113635298304 * q^74 + 2689819335937500 * q^75 + 2897589879439360 * q^76 - 2709533546636928 * q^77 + 30142949210112 * q^78 + 19002656396552080 * q^79 - 3355443200000000 * q^80 + 69287326451135082 * q^81 + 5993338182994944 * q^82 + 21675087975118188 * q^83 + 18589186650537984 * q^84 - 617270545312500 * q^85 - 31963372336919552 * q^86 + 34266820308892200 * q^87 + 1082386519425024 * q^88 - 97499522192222220 * q^89 - 23589606600000000 * q^90 + 37111957465918664 * q^91 + 31952062567415808 * q^92 - 32001580397816304 * q^93 - 47602332703632384 * q^94 - 17270981546875000 * q^95 + 19382190974435328 * q^96 + 99889937855386756 * q^97 - 19818444002919936 * q^98 - 535176281294791488 * q^99

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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	−4201.44	−0.369715	−0.184858	−	0.982765i	$-0.559182\pi$
$3$	−4201.44	−0.369715	−0.184858	+	0.982765i	$0.559182\pi$
$4$	65536.0	0.500000
$5$	−390625.	−0.447214
$5$	−390625.	−0.447214
$6$	−1.07557e6	−0.261428
$7$	1.23193e7	0.807704	0.403852	−	0.914824i	$-0.367671\pi$
$7$	1.23193e7	0.807704	0.403852	+	0.914824i	$0.367671\pi$
$8$	1.67772e7	0.353553
$9$	−1.11488e8	−0.863311
$10$	−1.00000e8	−0.316228
$11$	1.21513e9	1.70916	0.854582	−	0.519317i	$-0.173813\pi$
$11$	1.21513e9	1.70916	0.854582	+	0.519317i	$0.173813\pi$
$12$	−2.75345e8	−0.184858
$13$	2.42392e9	0.824138	0.412069	−	0.911153i	$-0.364806\pi$
$13$	2.42392e9	0.824138	0.412069	+	0.911153i	$0.364806\pi$
$14$	3.15374e9	0.571133
$15$	1.64119e9	0.165342
$16$	4.29497e9	0.250000
$17$	−1.73631e10	−0.603688	−0.301844	−	0.953357i	$-0.597602\pi$
$17$	−1.73631e10	−0.603688	−0.301844	+	0.953357i	$0.597602\pi$
$18$	−2.85410e10	−0.610453
$19$	1.15322e11	1.55779	0.778893	−	0.627157i	$-0.215782\pi$
$19$	1.15322e11	1.55779	0.778893	+	0.627157i	$0.215782\pi$
$20$	−2.56000e10	−0.223607
$21$	−5.17587e10	−0.298620
$22$	3.11072e11	1.20856
$23$	5.47905e11	1.45888	0.729439	−	0.684046i	$-0.239781\pi$
$23$	5.47905e11	1.45888	0.729439	+	0.684046i	$0.239781\pi$
$24$	−7.04884e10	−0.130714
$25$	1.52588e11	0.200000
$26$	6.20524e11	0.582754
$27$	1.01098e12	0.688894
$28$	8.07357e11	0.403852
$29$	2.02736e12	0.752573	0.376286	−	0.926503i	$-0.377201\pi$
$29$	2.02736e12	0.752573	0.376286	+	0.926503i	$0.377201\pi$
$30$	4.20144e11	0.116914
$31$	−3.37643e12	−0.711022	−0.355511	−	0.934672i	$-0.615693\pi$
$31$	−3.37643e12	−0.711022	−0.355511	+	0.934672i	$0.615693\pi$
$32$	1.09951e12	0.176777
$33$	−5.10528e12	−0.631904
$34$	−4.44497e12	−0.426872
$35$	−4.81222e12	−0.361216
$36$	−7.30648e12	−0.431655
$37$	−2.48073e13	−1.16109	−0.580545	−	0.814228i	$-0.697160\pi$
$37$	−2.48073e13	−1.16109	−0.580545	+	0.814228i	$0.697160\pi$
$38$	2.95225e13	1.10152
$39$	−1.01840e13	−0.304696
$40$	−6.55360e12	−0.158114
$41$	−5.37038e13	−1.05037	−0.525185	−	0.850988i	$-0.676004\pi$
$41$	−5.37038e13	−1.05037	−0.525185	+	0.850988i	$0.676004\pi$
$42$	−1.32502e13	−0.211157
$43$	−2.49397e13	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$43$	−2.49397e13	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$44$	7.96345e13	0.854582
$45$	4.35500e13	0.386084
$46$	1.40264e14	1.03158
$47$	−1.57049e14	−0.962062	−0.481031	−	0.876704i	$-0.659738\pi$
$47$	−1.57049e14	−0.962062	−0.481031	+	0.876704i	$0.659738\pi$
$48$	−1.80450e13	−0.0924288
$49$	−8.08656e13	−0.347614
$50$	3.90625e13	0.141421
$51$	7.29502e13	0.223193
$52$	1.58854e14	0.412069
$53$	5.06856e14	1.11825	0.559126	−	0.829083i	$-0.311137\pi$
$53$	5.06856e14	1.11825	0.559126	+	0.829083i	$0.311137\pi$
$54$	2.58812e14	0.487122
$55$	−4.74659e14	−0.764361
$56$	2.06683e14	0.285567
$57$	−4.84519e14	−0.575937
$58$	5.19005e14	0.532149
$59$	1.29796e15	1.15085	0.575424	−	0.817856i	$-0.304837\pi$
$59$	1.29796e15	1.15085	0.575424	+	0.817856i	$0.304837\pi$
$60$	1.07557e14	0.0826708
$61$	4.35989e14	0.291187	0.145593	−	0.989344i	$-0.453491\pi$
$61$	4.35989e14	0.291187	0.145593	+	0.989344i	$0.453491\pi$
$62$	−8.64366e14	−0.502769
$63$	−1.37345e15	−0.697300
$64$	2.81475e14	0.125000
$65$	−9.46844e14	−0.368566
$66$	−1.30695e15	−0.446823
$67$	−2.50888e15	−0.754820	−0.377410	−	0.926046i	$-0.623185\pi$
$67$	−2.50888e15	−0.754820	−0.377410	+	0.926046i	$0.623185\pi$
$68$	−1.13791e15	−0.301844
$69$	−2.30199e15	−0.539369
$70$	−1.23193e15	−0.255419
$71$	−3.06603e15	−0.563483	−0.281742	−	0.959490i	$-0.590912\pi$
$71$	−3.06603e15	−0.563483	−0.281742	+	0.959490i	$0.590912\pi$
$72$	−1.87046e15	−0.305226
$73$	4.56009e15	0.661804	0.330902	−	0.943665i	$-0.392647\pi$
$73$	4.56009e15	0.661804	0.330902	+	0.943665i	$0.392647\pi$
$74$	−6.35068e15	−0.821014
$75$	−6.41088e14	−0.0739430
$76$	7.55776e15	0.778893
$77$	1.49695e16	1.38050
$78$	−2.60709e15	−0.215453
$79$	1.40515e16	1.04206	0.521031	−	0.853538i	$-0.325548\pi$
$79$	1.40515e16	1.04206	0.521031	+	0.853538i	$0.325548\pi$
$80$	−1.67772e15	−0.111803
$81$	1.01500e16	0.608616
$82$	−1.37482e16	−0.742724
$83$	2.52434e16	1.23023	0.615113	−	0.788439i	$-0.289111\pi$
$83$	2.52434e16	1.23023	0.615113	+	0.788439i	$0.289111\pi$
$84$	−3.39206e15	−0.149310
$85$	6.78248e15	0.269978
$86$	−6.38456e15	−0.230088
$87$	−8.51784e15	−0.278237
$88$	2.03864e16	0.604281
$89$	−6.68155e16	−1.79913	−0.899564	−	0.436790i	$-0.856115\pi$
$89$	−6.68155e16	−1.79913	−0.899564	+	0.436790i	$0.856115\pi$
$90$	1.11488e16	0.273003
$91$	2.98610e16	0.665660
$92$	3.59075e16	0.729439
$93$	1.41859e16	0.262876
$94$	−4.02045e16	−0.680281
$95$	−4.50478e16	−0.696663
$96$	−4.61953e15	−0.0653570
$97$	6.24209e16	0.808667	0.404334	−	0.914612i	$-0.367503\pi$
$97$	6.24209e16	0.808667	0.404334	+	0.914612i	$0.367503\pi$
$98$	−2.07016e16	−0.245800
$99$	−1.35472e17	−1.47554
$100$	1.00000e16	0.100000
$101$	−1.29437e17	−1.18940	−0.594701	−	0.803947i	$-0.702729\pi$
$101$	−1.29437e17	−1.18940	−0.594701	+	0.803947i	$0.702729\pi$
$102$	1.86752e16	0.157821
$103$	−1.62161e16	−0.126134	−0.0630668	−	0.998009i	$-0.520088\pi$
$103$	−1.62161e16	−0.126134	−0.0630668	+	0.998009i	$0.520088\pi$
$104$	4.06666e16	0.291377
$105$	2.02183e16	0.133547
$106$	1.29755e17	0.790724
$107$	7.54294e16	0.424403	0.212201	−	0.977226i	$-0.431937\pi$
$107$	7.54294e16	0.424403	0.212201	+	0.977226i	$0.431937\pi$
$108$	6.62559e16	0.344447
$109$	−3.29149e17	−1.58222	−0.791112	−	0.611672i	$-0.790497\pi$
$109$	−3.29149e17	−1.58222	−0.791112	+	0.611672i	$0.790497\pi$
$110$	−1.21513e17	−0.540485
$111$	1.04227e17	0.429272
$112$	5.29110e16	0.201926
$113$	4.37906e17	1.54958	0.774791	−	0.632217i	$-0.217855\pi$
$113$	4.37906e17	1.54958	0.774791	+	0.632217i	$0.217855\pi$
$114$	−1.24037e17	−0.407249
$115$	−2.14025e17	−0.652430
$116$	1.32865e17	0.376286
$117$	−2.70238e17	−0.711487
$118$	3.32277e17	0.813772
$119$	−2.13902e17	−0.487602
$120$	2.75345e16	0.0584571
$121$	9.71086e17	1.92124
$122$	1.11613e17	0.205900
$123$	2.25633e17	0.388338
$124$	−2.21278e17	−0.355511
$125$	−5.96046e16	−0.0894427
$126$	−3.51604e17	−0.493065
$127$	4.26464e17	0.559179	0.279590	−	0.960120i	$-0.409802\pi$
$127$	4.26464e17	0.559179	0.279590	+	0.960120i	$0.409802\pi$
$128$	7.20576e16	0.0883883
$129$	1.04783e17	0.120303
$130$	−2.42392e17	−0.260615
$131$	−1.99048e17	−0.200517	−0.100259	−	0.994961i	$-0.531967\pi$
$131$	−1.99048e17	−0.200517	−0.100259	+	0.994961i	$0.531967\pi$
$132$	−3.34579e17	−0.315952
$133$	1.42069e18	1.25823
$134$	−6.42272e17	−0.533738
$135$	−3.94916e17	−0.308083
$136$	−2.91305e17	−0.213436
$137$	−2.15800e18	−1.48569	−0.742844	−	0.669465i	$-0.766524\pi$
$137$	−2.15800e18	−1.48569	−0.742844	+	0.669465i	$0.766524\pi$
$138$	−5.89309e17	−0.381391
$139$	−2.69991e18	−1.64332	−0.821662	−	0.569975i	$-0.806953\pi$
$139$	−2.69991e18	−1.64332	−0.821662	+	0.569975i	$0.806953\pi$
$140$	−3.15374e17	−0.180608
$141$	6.59831e17	0.355689
$142$	−7.84905e17	−0.398443
$143$	2.94537e18	1.40859
$144$	−4.78838e17	−0.215828
$145$	−7.91938e17	−0.336561
$146$	1.16738e18	0.467966
$147$	3.39752e17	0.128518
$148$	−1.62577e18	−0.580545
$149$	1.38331e18	0.466484	0.233242	−	0.972419i	$-0.425066\pi$
$149$	1.38331e18	0.466484	0.233242	+	0.972419i	$0.425066\pi$
$150$	−1.64119e17	−0.0522856
$151$	−3.60449e18	−1.08528	−0.542638	−	0.839967i	$-0.682574\pi$
$151$	−3.60449e18	−1.08528	−0.542638	+	0.839967i	$0.682574\pi$
$152$	1.93479e18	0.550760
$153$	1.93578e18	0.521170
$154$	3.83219e18	0.976160
$155$	1.31892e18	0.317979
$156$	−6.67415e17	−0.152348
$157$	6.76512e18	1.46261	0.731305	−	0.682051i	$-0.238912\pi$
$157$	6.76512e18	1.46261	0.731305	+	0.682051i	$0.238912\pi$
$158$	3.59719e18	0.736849
$159$	−2.12952e18	−0.413435
$160$	−4.29497e17	−0.0790569
$161$	6.74980e18	1.17834
$162$	2.59840e18	0.430357
$163$	−1.06804e19	−1.67877	−0.839386	−	0.543536i	$-0.817085\pi$
$163$	−1.06804e19	−1.67877	−0.839386	+	0.543536i	$0.817085\pi$
$164$	−3.51953e18	−0.525185
$165$	1.99425e18	0.282596
$166$	6.46232e18	0.869900
$167$	−2.93736e18	−0.375722	−0.187861	−	0.982196i	$-0.560155\pi$
$167$	−2.93736e18	−0.375722	−0.187861	+	0.982196i	$0.560155\pi$
$168$	−8.68367e17	−0.105578
$169$	−2.77502e18	−0.320797
$170$	1.73631e18	0.190903
$171$	−1.28571e19	−1.34485
$172$	−1.63445e18	−0.162697
$173$	−3.04250e18	−0.288296	−0.144148	−	0.989556i	$-0.546044\pi$
$173$	−3.04250e18	−0.288296	−0.144148	+	0.989556i	$0.546044\pi$
$174$	−2.18057e18	−0.196744
$175$	1.87977e18	0.161541
$176$	5.21893e18	0.427291
$177$	−5.45328e18	−0.425486
$178$	−1.71048e19	−1.27218
$179$	1.82741e19	1.29594	0.647970	−	0.761666i	$-0.275618\pi$
$179$	1.82741e19	1.29594	0.647970	+	0.761666i	$0.275618\pi$
$180$	2.85410e18	0.193042
$181$	−1.73562e19	−1.11992	−0.559959	−	0.828520i	$-0.689183\pi$
$181$	−1.73562e19	−1.11992	−0.559959	+	0.828520i	$0.689183\pi$
$182$	7.64441e18	0.470693
$183$	−1.83178e18	−0.107656
$184$	9.19232e18	0.515791
$185$	9.69037e18	0.519255
$186$	3.63158e18	0.185881
$187$	−2.10984e19	−1.03180
$188$	−1.02924e19	−0.481031
$189$	1.24546e19	0.556423
$190$	−1.15322e19	−0.492615
$191$	−1.78696e19	−0.730015	−0.365007	−	0.931005i	$-0.618934\pi$
$191$	−1.78696e19	−0.730015	−0.365007	+	0.931005i	$0.618934\pi$
$192$	−1.18260e18	−0.0462144
$193$	9.94962e18	0.372023	0.186011	−	0.982548i	$-0.440444\pi$
$193$	9.94962e18	0.372023	0.186011	+	0.982548i	$0.440444\pi$
$194$	1.59797e19	0.571814
$195$	3.97811e18	0.136264
$196$	−5.29961e18	−0.173807
$197$	5.27173e19	1.65573	0.827866	−	0.560925i	$-0.189554\pi$
$197$	5.27173e19	1.65573	0.827866	+	0.560925i	$0.189554\pi$
$198$	−3.46809e19	−1.04336
$199$	2.02822e18	0.0584606	0.0292303	−	0.999573i	$-0.490694\pi$
$199$	2.02822e18	0.0584606	0.0292303	+	0.999573i	$0.490694\pi$
$200$	2.56000e18	0.0707107
$201$	1.05409e19	0.279068
$202$	−3.31360e19	−0.841034
$203$	2.49757e19	0.607856
$204$	4.78086e18	0.111596
$205$	2.09781e19	0.469740
$206$	−4.15133e18	−0.0891899
$207$	−6.10849e19	−1.25946
$208$	1.04107e19	0.206034
$209$	1.40131e20	2.66251
$210$	5.17587e18	0.0944321
$211$	−2.55219e19	−0.447211	−0.223606	−	0.974680i	$-0.571783\pi$
$211$	−2.55219e19	−0.447211	−0.223606	+	0.974680i	$0.571783\pi$
$212$	3.32173e19	0.559126
$213$	1.28817e19	0.208328
$214$	1.93099e19	0.300098
$215$	9.74207e18	0.145521
$216$	1.69615e19	0.243561
$217$	−4.15952e19	−0.574296
$218$	−8.42622e19	−1.11880
$219$	−1.91589e19	−0.244679
$220$	−3.11072e19	−0.382181
$221$	−4.20869e19	−0.497522
$222$	2.66820e19	0.303541
$223$	−3.50141e19	−0.383399	−0.191700	−	0.981454i	$-0.561400\pi$
$223$	−3.50141e19	−0.383399	−0.191700	+	0.981454i	$0.561400\pi$
$224$	1.35452e19	0.142783
$225$	−1.70117e19	−0.172662
$226$	1.12104e20	1.09572
$227$	−1.19657e20	−1.12647	−0.563233	−	0.826298i	$-0.690443\pi$
$227$	−1.19657e20	−1.12647	−0.563233	+	0.826298i	$0.690443\pi$
$228$	−3.17535e19	−0.287968
$229$	−1.50518e20	−1.31518	−0.657591	−	0.753375i	$-0.728424\pi$
$229$	−1.50518e20	−1.31518	−0.657591	+	0.753375i	$0.728424\pi$
$230$	−5.47905e19	−0.461338
$231$	−6.28934e19	−0.510391
$232$	3.40135e19	0.266075
$233$	1.80295e20	1.35975	0.679875	−	0.733328i	$-0.262034\pi$
$233$	1.80295e20	1.35975	0.679875	+	0.733328i	$0.262034\pi$
$234$	−6.91810e19	−0.503097
$235$	6.13472e19	0.430247
$236$	8.50628e19	0.575424
$237$	−5.90367e19	−0.385266
$238$	−5.47588e19	−0.344786
$239$	−1.50864e20	−0.916650	−0.458325	−	0.888785i	$-0.651550\pi$
$239$	−1.50864e20	−0.916650	−0.458325	+	0.888785i	$0.651550\pi$
$240$	7.04884e18	0.0413354
$241$	−1.11959e20	−0.633747	−0.316874	−	0.948468i	$-0.602633\pi$
$241$	−1.11959e20	−0.633747	−0.316874	+	0.948468i	$0.602633\pi$
$242$	2.48598e20	1.35852
$243$	−1.73203e20	−0.913909
$244$	2.85730e19	0.145593
$245$	3.15881e19	0.155458
$246$	5.77621e19	0.274596
$247$	2.79532e20	1.28383
$248$	−5.66471e19	−0.251384
$249$	−1.06059e20	−0.454833
$250$	−1.52588e19	−0.0632456
$251$	2.00695e20	0.804098	0.402049	−	0.915618i	$-0.368298\pi$
$251$	2.00695e20	0.804098	0.402049	+	0.915618i	$0.368298\pi$
$252$	−9.00107e19	−0.348650
$253$	6.65774e20	2.49346
$254$	1.09175e20	0.395400
$255$	−2.84962e19	−0.0998148
$256$	1.84467e19	0.0625000
$257$	1.70143e20	0.557678	0.278839	−	0.960338i	$-0.410050\pi$
$257$	1.70143e20	0.557678	0.278839	+	0.960338i	$0.410050\pi$
$258$	2.68243e19	0.0850671
$259$	−3.05609e20	−0.937817
$260$	−6.20524e19	−0.184283
$261$	−2.26027e20	−0.649704
$262$	−5.09563e19	−0.141787
$263$	5.78686e20	1.55890	0.779452	−	0.626462i	$-0.215498\pi$
$263$	5.78686e20	1.55890	0.779452	+	0.626462i	$0.215498\pi$
$264$	−8.56523e19	−0.223412
$265$	−1.97991e20	−0.500098
$266$	3.63696e20	0.889703
$267$	2.80721e20	0.665165
$268$	−1.64422e20	−0.377410
$269$	−5.13106e20	−1.14107	−0.570536	−	0.821273i	$-0.693264\pi$
$269$	−5.13106e20	−1.14107	−0.570536	+	0.821273i	$0.693264\pi$
$270$	−1.01098e20	−0.217847
$271$	−4.64533e20	−0.970013	−0.485006	−	0.874511i	$-0.661183\pi$
$271$	−4.64533e20	−0.970013	−0.485006	+	0.874511i	$0.661183\pi$
$272$	−7.45742e19	−0.150922
$273$	−1.25459e20	−0.246104
$274$	−5.52449e20	−1.05054
$275$	1.85414e20	0.341833
$276$	−1.50863e20	−0.269684
$277$	−9.72733e20	−1.68623	−0.843113	−	0.537737i	$-0.819279\pi$
$277$	−9.72733e20	−1.68623	−0.843113	+	0.537737i	$0.819279\pi$
$278$	−6.91177e20	−1.16201
$279$	3.76432e20	0.613833
$280$	−8.07357e19	−0.127709
$281$	6.76588e20	1.03830	0.519148	−	0.854685i	$-0.326249\pi$
$281$	6.76588e20	1.03830	0.519148	+	0.854685i	$0.326249\pi$
$282$	1.68917e20	0.251510
$283$	1.12202e21	1.62112	0.810560	−	0.585656i	$-0.199163\pi$
$283$	1.12202e21	1.62112	0.810560	+	0.585656i	$0.199163\pi$
$284$	−2.00936e20	−0.281742
$285$	1.89265e20	0.257567
$286$	7.54015e20	0.996021
$287$	−6.61593e20	−0.848389
$288$	−1.22582e20	−0.152613
$289$	−5.25761e20	−0.635561
$290$	−2.02736e20	−0.237984
$291$	−2.62257e20	−0.298977
$292$	2.98850e20	0.330902
$293$	−3.05309e20	−0.328371	−0.164185	−	0.986429i	$-0.552500\pi$
$293$	−3.05309e20	−0.328371	−0.164185	+	0.986429i	$0.552500\pi$
$294$	8.69764e19	0.0908760
$295$	−5.07014e20	−0.514674
$296$	−4.16198e20	−0.410507
$297$	1.22847e21	1.17743
$298$	3.54128e20	0.329854
$299$	1.32808e21	1.20232
$300$	−4.20144e19	−0.0369715
$301$	−3.07239e20	−0.262822
$302$	−9.22750e20	−0.767406
$303$	5.43823e20	0.439740
$304$	4.95305e20	0.389446
$305$	−1.70308e20	−0.130223
$306$	4.95561e20	0.368523
$307$	−3.66561e20	−0.265137	−0.132569	−	0.991174i	$-0.542322\pi$
$307$	−3.66561e20	−0.265137	−0.132569	+	0.991174i	$0.542322\pi$
$308$	9.81041e20	0.690250
$309$	6.81310e19	0.0466335
$310$	3.37643e20	0.224845
$311$	−3.12925e19	−0.0202758	−0.0101379	−	0.999949i	$-0.503227\pi$
$311$	−3.12925e19	−0.0202758	−0.0101379	+	0.999949i	$0.503227\pi$
$312$	−1.70858e20	−0.107726
$313$	−2.54969e21	−1.56444	−0.782222	−	0.623000i	$-0.785914\pi$
$313$	−2.54969e21	−1.56444	−0.782222	+	0.623000i	$0.785914\pi$
$314$	1.73187e21	1.03422
$315$	5.36506e20	0.311842
$316$	9.20882e20	0.521031
$317$	−1.42704e21	−0.786018	−0.393009	−	0.919535i	$-0.628566\pi$
$317$	−1.42704e21	−0.786018	−0.393009	+	0.919535i	$0.628566\pi$
$318$	−5.45158e20	−0.292343
$319$	2.46350e21	1.28627
$320$	−1.09951e20	−0.0559017
$321$	−3.16912e20	−0.156908
$322$	1.72795e21	0.833213
$323$	−2.00236e21	−0.940416
$324$	6.65191e20	0.304308
$325$	3.69861e20	0.164828
$326$	−2.73417e21	−1.18707
$327$	1.38290e21	0.584972
$328$	−9.01001e20	−0.371362
$329$	−1.93473e21	−0.777062
$330$	5.10528e20	0.199825
$331$	−1.65282e20	−0.0630503	−0.0315251	−	0.999503i	$-0.510036\pi$
$331$	−1.65282e20	−0.0630503	−0.0315251	+	0.999503i	$0.510036\pi$
$332$	1.65435e21	0.615113
$333$	2.76572e21	1.00238
$334$	−7.51963e20	−0.265676
$335$	9.80029e20	0.337566
$336$	−2.22302e20	−0.0746551
$337$	−1.56766e21	−0.513332	−0.256666	−	0.966500i	$-0.582624\pi$
$337$	−1.56766e21	−0.513332	−0.256666	+	0.966500i	$0.582624\pi$
$338$	−7.10406e20	−0.226837
$339$	−1.83984e21	−0.572904
$340$	4.44497e20	0.134989
$341$	−4.10279e21	−1.21525
$342$	−3.29141e21	−0.950954
$343$	−3.86205e21	−1.08847
$344$	−4.18419e20	−0.115044
$345$	8.99214e20	0.241213
$346$	−7.78881e20	−0.203856
$347$	1.62532e21	0.415086	0.207543	−	0.978226i	$-0.433453\pi$
$347$	1.62532e21	0.415086	0.207543	+	0.978226i	$0.433453\pi$
$348$	−5.58225e20	−0.139119
$349$	3.60380e21	0.876486	0.438243	−	0.898857i	$-0.355601\pi$
$349$	3.60380e21	0.876486	0.438243	+	0.898857i	$0.355601\pi$
$350$	4.81222e20	0.114227
$351$	2.45055e21	0.567744
$352$	1.33605e21	0.302140
$353$	−7.99561e21	−1.76509	−0.882544	−	0.470230i	$-0.844171\pi$
$353$	−7.99561e21	−1.76509	−0.882544	+	0.470230i	$0.844171\pi$
$354$	−1.39604e21	−0.300864
$355$	1.19767e21	0.251997
$356$	−4.37882e21	−0.899564
$357$	8.98694e20	0.180274
$358$	4.67817e21	0.916368
$359$	7.69221e21	1.47146	0.735730	−	0.677275i	$-0.236839\pi$
$359$	7.69221e21	1.47146	0.735730	+	0.677275i	$0.236839\pi$
$360$	7.30648e20	0.136501
$361$	7.81884e21	1.42669
$362$	−4.44318e21	−0.791902
$363$	−4.07995e21	−0.710312
$364$	1.95697e21	0.332830
$365$	−1.78128e21	−0.295968
$366$	−4.68936e20	−0.0761244
$367$	4.40761e21	0.699104	0.349552	−	0.936917i	$-0.386334\pi$
$367$	4.40761e21	0.699104	0.349552	+	0.936917i	$0.386334\pi$
$368$	2.35323e21	0.364719
$369$	5.98734e21	0.906796
$370$	2.48073e21	0.367169
$371$	6.24411e21	0.903217
$372$	9.29684e20	0.131438
$373$	7.73260e21	1.06856	0.534282	−	0.845306i	$-0.320582\pi$
$373$	7.73260e21	1.06856	0.534282	+	0.845306i	$0.320582\pi$
$374$	−5.40120e21	−0.729594
$375$	2.50425e20	0.0330683
$376$	−2.63484e21	−0.340140
$377$	4.91417e21	0.620224
$378$	3.18838e21	0.393450
$379$	−6.86035e21	−0.827776	−0.413888	−	0.910328i	$-0.635829\pi$
$379$	−6.86035e21	−0.827776	−0.413888	+	0.910328i	$0.635829\pi$
$380$	−2.95225e21	−0.348331
$381$	−1.79176e21	−0.206737
$382$	−4.57462e21	−0.516198
$383$	−4.86654e21	−0.537070	−0.268535	−	0.963270i	$-0.586539\pi$
$383$	−4.86654e21	−0.537070	−0.268535	+	0.963270i	$0.586539\pi$
$384$	−3.02745e20	−0.0326785
$385$	−5.84746e21	−0.617378
$386$	2.54710e21	0.263060
$387$	2.78048e21	0.280916
$388$	4.09081e21	0.404334
$389$	−9.98351e21	−0.965410	−0.482705	−	0.875783i	$-0.660346\pi$
$389$	−9.98351e21	−0.965410	−0.482705	+	0.875783i	$0.660346\pi$
$390$	1.01840e21	0.0963534
$391$	−9.51336e21	−0.880707
$392$	−1.35670e21	−0.122900
$393$	8.36288e20	0.0741343
$394$	1.34956e22	1.17078
$395$	−5.48888e21	−0.466024
$396$	−8.87830e21	−0.737770
$397$	−5.08435e21	−0.413539	−0.206769	−	0.978390i	$-0.566295\pi$
$397$	−5.08435e21	−0.413539	−0.206769	+	0.978390i	$0.566295\pi$
$398$	5.19224e20	0.0413379
$399$	−5.96893e21	−0.465187
$400$	6.55360e20	0.0500000
$401$	1.05661e22	0.789198	0.394599	−	0.918853i	$-0.370883\pi$
$401$	1.05661e22	0.789198	0.394599	+	0.918853i	$0.370883\pi$
$402$	2.69847e21	0.197331
$403$	−8.18420e21	−0.585980
$404$	−8.48281e21	−0.594701
$405$	−3.96484e21	−0.272181
$406$	6.39377e21	0.429819
$407$	−3.01441e22	−1.98449
$408$	1.22390e21	0.0789105
$409$	1.73559e21	0.109597	0.0547985	−	0.998497i	$-0.482548\pi$
$409$	1.73559e21	0.109597	0.0547985	+	0.998497i	$0.482548\pi$
$410$	5.37038e21	0.332156
$411$	9.06672e21	0.549281
$412$	−1.06274e21	−0.0630668
$413$	1.59899e22	0.929544
$414$	−1.56377e22	−0.890576
$415$	−9.86071e21	−0.550173
$416$	2.66513e21	0.145688
$417$	1.13435e22	0.607562
$418$	3.58736e22	1.88268
$419$	−1.13030e22	−0.581264	−0.290632	−	0.956835i	$-0.593866\pi$
$419$	−1.13030e22	−0.581264	−0.290632	+	0.956835i	$0.593866\pi$
$420$	1.32502e21	0.0667736
$421$	−1.06234e21	−0.0524643	−0.0262321	−	0.999656i	$-0.508351\pi$
$421$	−1.06234e21	−0.0524643	−0.0262321	+	0.999656i	$0.508351\pi$
$422$	−6.53361e21	−0.316226
$423$	1.75091e22	0.830559
$424$	8.50363e21	0.395362
$425$	−2.64941e21	−0.120738
$426$	3.29773e21	0.147310
$427$	5.37108e21	0.235193
$428$	4.94334e21	0.212201
$429$	−1.23748e22	−0.520776
$430$	2.49397e21	0.102899
$431$	3.61567e22	1.46262	0.731310	−	0.682045i	$-0.238909\pi$
$431$	3.61567e22	1.46262	0.731310	+	0.682045i	$0.238909\pi$
$432$	4.34215e21	0.172224
$433$	−2.15292e22	−0.837298	−0.418649	−	0.908148i	$-0.637496\pi$
$433$	−2.15292e22	−0.837298	−0.418649	+	0.908148i	$0.637496\pi$
$434$	−1.06484e22	−0.406088
$435$	3.32728e21	0.124432
$436$	−2.15711e22	−0.791112
$437$	6.31857e22	2.27262
$438$	−4.90469e21	−0.173014
$439$	−2.88882e22	−0.999476	−0.499738	−	0.866177i	$-0.666570\pi$
$439$	−2.88882e22	−0.999476	−0.499738	+	0.866177i	$0.666570\pi$
$440$	−7.96345e21	−0.270243
$441$	9.01555e21	0.300099
$442$	−1.07742e22	−0.351801
$443$	3.43476e21	0.110018	0.0550091	−	0.998486i	$-0.482481\pi$
$443$	3.43476e21	0.110018	0.0550091	+	0.998486i	$0.482481\pi$
$444$	6.83059e21	0.214636
$445$	2.60998e22	0.804594
$446$	−8.96360e21	−0.271104
$447$	−5.81190e21	−0.172466
$448$	3.46757e21	0.100963
$449$	3.08875e22	0.882447	0.441223	−	0.897397i	$-0.354545\pi$
$449$	3.08875e22	0.882447	0.441223	+	0.897397i	$0.354545\pi$
$450$	−4.35500e21	−0.122091
$451$	−6.52570e22	−1.79526
$452$	2.86986e22	0.774791
$453$	1.51440e22	0.401243
$454$	−3.06322e22	−0.796532
$455$	−1.16644e22	−0.297692
$456$	−8.12888e21	−0.203624
$457$	−3.83285e22	−0.942398	−0.471199	−	0.882027i	$-0.656179\pi$
$457$	−3.83285e22	−0.942398	−0.471199	+	0.882027i	$0.656179\pi$
$458$	−3.85325e22	−0.929974
$459$	−1.75539e22	−0.415877
$460$	−1.40264e22	−0.326215
$461$	6.80144e22	1.55290	0.776449	−	0.630180i	$-0.217019\pi$
$461$	6.80144e22	1.55290	0.776449	+	0.630180i	$0.217019\pi$
$462$	−1.61007e22	−0.360901
$463$	4.57341e21	0.100647	0.0503236	−	0.998733i	$-0.483975\pi$
$463$	4.57341e21	0.100647	0.0503236	+	0.998733i	$0.483975\pi$
$464$	8.70746e21	0.188143
$465$	−5.54135e21	−0.117562
$466$	4.61556e22	0.961489
$467$	4.97766e22	1.01820	0.509099	−	0.860708i	$-0.329979\pi$
$467$	4.97766e22	1.01820	0.509099	+	0.860708i	$0.329979\pi$
$468$	−1.77103e22	−0.355744
$469$	−3.09076e22	−0.609671
$470$	1.57049e22	0.304231
$471$	−2.84232e22	−0.540749
$472$	2.17761e22	0.406886
$473$	−3.03049e22	−0.556151
$474$	−1.51134e22	−0.272424
$475$	1.75968e22	0.311557
$476$	−1.40183e22	−0.243801
$477$	−5.65084e22	−0.965399
$478$	−3.86212e22	−0.648169
$479$	9.35494e22	1.54237	0.771186	−	0.636610i	$-0.219664\pi$
$479$	9.35494e22	1.54237	0.771186	+	0.636610i	$0.219664\pi$
$480$	1.80450e21	0.0292285
$481$	−6.01310e22	−0.956898
$482$	−2.86616e22	−0.448127
$483$	−2.83589e22	−0.435651
$484$	6.36411e22	0.960621
$485$	−2.43831e22	−0.361647
$486$	−4.43400e22	−0.646231
$487$	−1.63934e22	−0.234786	−0.117393	−	0.993086i	$-0.537454\pi$
$487$	−1.63934e22	−0.234786	−0.117393	+	0.993086i	$0.537454\pi$
$488$	7.31468e21	0.102950
$489$	4.48729e22	0.620667
$490$	8.08656e21	0.109925
$491$	−2.62500e22	−0.350700	−0.175350	−	0.984506i	$-0.556106\pi$
$491$	−2.62500e22	−0.350700	−0.175350	+	0.984506i	$0.556106\pi$
$492$	1.47871e22	0.194169
$493$	−3.52014e22	−0.454319
$494$	7.15602e22	0.907805
$495$	5.29188e22	0.659881
$496$	−1.45017e22	−0.177756
$497$	−3.77714e22	−0.455128
$498$	−2.71510e22	−0.321615
$499$	1.91458e22	0.222956	0.111478	−	0.993767i	$-0.464442\pi$
$499$	1.91458e22	0.222956	0.111478	+	0.993767i	$0.464442\pi$
$500$	−3.90625e21	−0.0447214
$501$	1.23411e22	0.138910
$502$	5.13778e22	0.568583
$503$	3.67210e22	0.399564	0.199782	−	0.979840i	$-0.435977\pi$
$503$	3.67210e22	0.399564	0.199782	+	0.979840i	$0.435977\pi$
$504$	−2.30427e22	−0.246533
$505$	5.05615e22	0.531916
$506$	1.70438e23	1.76314
$507$	1.16591e22	0.118603
$508$	2.79488e22	0.279590
$509$	6.75737e22	0.664778	0.332389	−	0.943142i	$-0.392145\pi$
$509$	6.75737e22	0.664778	0.332389	+	0.943142i	$0.392145\pi$
$510$	−7.29502e21	−0.0705797
$511$	5.61771e22	0.534542
$512$	4.72237e21	0.0441942
$513$	1.16589e23	1.07315
$514$	4.35567e22	0.394338
$515$	6.33442e21	0.0564086
$516$	6.86703e21	0.0601515
$517$	−1.90834e23	−1.64432
$518$	−7.82359e22	−0.663137
$519$	1.27829e22	0.106588
$520$	−1.58854e22	−0.130308
$521$	−2.39219e23	−1.93052	−0.965262	−	0.261284i	$-0.915854\pi$
$521$	−2.39219e23	−1.93052	−0.965262	+	0.261284i	$0.915854\pi$
$522$	−5.78629e22	−0.459410
$523$	−1.23467e22	−0.0964465	−0.0482233	−	0.998837i	$-0.515356\pi$
$523$	−1.23467e22	−0.0964465	−0.0482233	+	0.998837i	$0.515356\pi$
$524$	−1.30448e22	−0.100259
$525$	−7.89776e21	−0.0597241
$526$	1.48144e23	1.10231
$527$	5.86254e22	0.429236
$528$	−2.19270e22	−0.157976
$529$	1.59150e23	1.12832
$530$	−5.06856e22	−0.353622
$531$	−1.44707e23	−0.993539
$532$	9.31063e22	0.629115
$533$	−1.30174e23	−0.865650
$534$	7.18646e22	0.470342
$535$	−2.94646e22	−0.189799
$536$	−4.20919e22	−0.266869
$537$	−7.67774e22	−0.479128
$538$	−1.31355e23	−0.806859
$539$	−9.82619e22	−0.594129
$540$	−2.58812e22	−0.154041
$541$	−2.47773e23	−1.45170	−0.725851	−	0.687851i	$-0.758554\pi$
$541$	−2.47773e23	−1.45170	−0.725851	+	0.687851i	$0.758554\pi$
$542$	−1.18920e23	−0.685903
$543$	7.29209e22	0.414051
$544$	−1.90910e22	−0.106718
$545$	1.28574e23	0.707592
$546$	−3.21175e22	−0.174022
$547$	5.48101e22	0.292394	0.146197	−	0.989256i	$-0.453297\pi$
$547$	5.48101e22	0.292394	0.146197	+	0.989256i	$0.453297\pi$
$548$	−1.41427e23	−0.742844
$549$	−4.86076e22	−0.251385
$550$	4.74659e22	0.241712
$551$	2.33800e23	1.17235
$552$	−3.86210e22	−0.190696
$553$	1.73105e23	0.841678
$554$	−2.49020e23	−1.19234
$555$	−4.07135e22	−0.191976
$556$	−1.76941e23	−0.821662
$557$	2.57560e23	1.17790	0.588952	−	0.808168i	$-0.299541\pi$
$557$	2.57560e23	1.17790	0.588952	+	0.808168i	$0.299541\pi$
$558$	9.63665e22	0.434046
$559$	−6.04519e22	−0.268169
$560$	−2.06683e22	−0.0903041
$561$	8.86437e22	0.381473
$562$	1.73207e23	0.734186
$563$	6.37462e22	0.266154	0.133077	−	0.991106i	$-0.457514\pi$
$563$	6.37462e22	0.266154	0.133077	+	0.991106i	$0.457514\pi$
$564$	4.32427e22	0.177844
$565$	−1.71057e23	−0.692994
$566$	2.87237e23	1.14630
$567$	1.25041e23	0.491582
$568$	−5.14395e22	−0.199221
$569$	−2.97128e23	−1.13368	−0.566839	−	0.823829i	$-0.691834\pi$
$569$	−2.97128e23	−1.13368	−0.566839	+	0.823829i	$0.691834\pi$
$570$	4.84519e22	0.182127
$571$	3.65472e23	1.35347	0.676733	−	0.736228i	$-0.263395\pi$
$571$	3.65472e23	1.35347	0.676733	+	0.736228i	$0.263395\pi$
$572$	1.93028e23	0.704293
$573$	7.50781e22	0.269898
$574$	−1.69368e23	−0.599901
$575$	8.36037e22	0.291775
$576$	−3.13811e22	−0.107914
$577$	1.73713e23	0.588623	0.294312	−	0.955710i	$-0.404910\pi$
$577$	1.73713e23	0.588623	0.294312	+	0.955710i	$0.404910\pi$
$578$	−1.34595e23	−0.449409
$579$	−4.18027e22	−0.137542
$580$	−5.19005e22	−0.168280
$581$	3.10981e23	0.993658
$582$	−6.71379e22	−0.211408
$583$	6.15894e23	1.91128
$584$	7.65056e22	0.233983
$585$	1.05562e23	0.318187
$586$	−7.81590e22	−0.232193
$587$	−4.20741e23	−1.23194	−0.615972	−	0.787768i	$-0.711237\pi$
$587$	−4.20741e23	−1.23194	−0.615972	+	0.787768i	$0.711237\pi$
$588$	2.22660e22	0.0642590
$589$	−3.89377e23	−1.10762
$590$	−1.29796e23	−0.363930
$591$	−2.21488e23	−0.612149
$592$	−1.06547e23	−0.290272
$593$	−4.26727e23	−1.14600	−0.573000	−	0.819555i	$-0.694221\pi$
$593$	−4.26727e23	−1.14600	−0.573000	+	0.819555i	$0.694221\pi$
$594$	3.14489e23	0.832571
$595$	8.35553e22	0.218062
$596$	9.06568e22	0.233242
$597$	−8.52143e21	−0.0216138
$598$	3.39988e23	0.850166
$599$	−1.66085e23	−0.409451	−0.204726	−	0.978819i	$-0.565630\pi$
$599$	−1.66085e23	−0.409451	−0.204726	+	0.978819i	$0.565630\pi$
$600$	−1.07557e22	−0.0261428
$601$	−3.30613e23	−0.792294	−0.396147	−	0.918187i	$-0.629653\pi$
$601$	−3.30613e23	−0.792294	−0.396147	+	0.918187i	$0.629653\pi$
$602$	−7.86533e22	−0.185843
$603$	2.79710e23	0.651644
$604$	−2.36224e23	−0.542638
$605$	−3.79330e23	−0.859205
$606$	1.39219e23	0.310943
$607$	3.28253e23	0.722944	0.361472	−	0.932383i	$-0.382274\pi$
$607$	3.28253e23	0.722944	0.361472	+	0.932383i	$0.382274\pi$
$608$	1.26798e23	0.275380
$609$	−1.04934e23	−0.224734
$610$	−4.35989e22	−0.0920814
$611$	−3.80674e23	−0.792872
$612$	1.26864e23	0.260585
$613$	4.83476e23	0.979401	0.489701	−	0.871891i	$-0.337106\pi$
$613$	4.83476e23	0.979401	0.489701	+	0.871891i	$0.337106\pi$
$614$	−9.38397e22	−0.187480
$615$	−8.81380e22	−0.173670
$616$	2.51147e23	0.488080
$617$	−4.09399e23	−0.784736	−0.392368	−	0.919808i	$-0.628344\pi$
$617$	−4.09399e23	−0.784736	−0.392368	+	0.919808i	$0.628344\pi$
$618$	1.74415e22	0.0329748
$619$	−5.33004e23	−0.993940	−0.496970	−	0.867768i	$-0.665554\pi$
$619$	−5.33004e23	−0.993940	−0.496970	+	0.867768i	$0.665554\pi$
$620$	8.64366e22	0.158989
$621$	5.53924e23	1.00501
$622$	−8.01089e21	−0.0143371
$623$	−8.23119e23	−1.45316
$624$	−4.37397e22	−0.0761741
$625$	2.32831e22	0.0400000
$626$	−6.52720e23	−1.10623
$627$	−5.88752e23	−0.984370
$628$	4.43359e23	0.731305
$629$	4.30734e23	0.700936
$630$	1.37345e23	0.220506
$631$	−2.81823e22	−0.0446402	−0.0223201	−	0.999751i	$-0.507105\pi$
$631$	−2.81823e22	−0.0446402	−0.0223201	+	0.999751i	$0.507105\pi$
$632$	2.35746e23	0.368425
$633$	1.07229e23	0.165341
$634$	−3.65322e23	−0.555799
$635$	−1.66588e23	−0.250073
$636$	−1.39560e23	−0.206717
$637$	−1.96012e23	−0.286482
$638$	6.30657e23	0.909530
$639$	3.41826e23	0.486461
$640$	−2.81475e22	−0.0395285
$641$	5.47552e23	0.758809	0.379404	−	0.925231i	$-0.376129\pi$
$641$	5.47552e23	0.758809	0.379404	+	0.925231i	$0.376129\pi$
$642$	−8.11294e22	−0.110951
$643$	−1.13082e24	−1.52616	−0.763079	−	0.646305i	$-0.776313\pi$
$643$	−1.13082e24	−1.52616	−0.763079	+	0.646305i	$0.776313\pi$
$644$	4.42355e23	0.589171
$645$	−4.09307e22	−0.0538011
$646$	−5.12604e23	−0.664975
$647$	9.71467e23	1.24377	0.621887	−	0.783107i	$-0.286366\pi$
$647$	9.71467e23	1.24377	0.621887	+	0.783107i	$0.286366\pi$
$648$	1.70289e23	0.215178
$649$	1.57718e24	1.96699
$650$	9.46844e22	0.116551
$651$	1.74760e23	0.212326
$652$	−6.99949e23	−0.839386
$653$	8.71125e22	0.103114	0.0515571	−	0.998670i	$-0.483582\pi$
$653$	8.71125e22	0.103114	0.0515571	+	0.998670i	$0.483582\pi$
$654$	3.54023e23	0.413638
$655$	7.77532e22	0.0896741
$656$	−2.30656e23	−0.262593
$657$	−5.08396e23	−0.571342
$658$	−4.95291e23	−0.549466
$659$	−5.51481e23	−0.603955	−0.301978	−	0.953315i	$-0.597647\pi$
$659$	−5.51481e23	−0.603955	−0.301978	+	0.953315i	$0.597647\pi$
$660$	1.30695e23	0.141298
$661$	1.72983e23	0.184626	0.0923128	−	0.995730i	$-0.470574\pi$
$661$	1.72983e23	0.184626	0.0923128	+	0.995730i	$0.470574\pi$
$662$	−4.23121e22	−0.0445833
$663$	1.76825e23	0.183942
$664$	4.23514e23	0.434950
$665$	−5.54957e23	−0.562697
$666$	7.08025e23	0.708790
$667$	1.11080e24	1.09791
$668$	−1.92503e23	−0.187861
$669$	1.47109e23	0.141748
$670$	2.50888e23	0.238695
$671$	5.29782e23	0.497686
$672$	−5.69093e22	−0.0527891
$673$	9.31240e23	0.852970	0.426485	−	0.904495i	$-0.359752\pi$
$673$	9.31240e23	0.852970	0.426485	+	0.904495i	$0.359752\pi$
$674$	−4.01321e23	−0.362981
$675$	1.54264e23	0.137779
$676$	−1.81864e23	−0.160398
$677$	−8.38487e21	−0.00730286	−0.00365143	−	0.999993i	$-0.501162\pi$
$677$	−8.38487e21	−0.00730286	−0.00365143	+	0.999993i	$0.501162\pi$
$678$	−4.70998e23	−0.405104
$679$	7.68981e23	0.653164
$680$	1.13791e23	0.0954515
$681$	5.02732e23	0.416472
$682$	−1.05031e24	−0.859314
$683$	−2.03510e24	−1.64440	−0.822202	−	0.569195i	$-0.807255\pi$
$683$	−2.03510e24	−1.64440	−0.822202	+	0.569195i	$0.807255\pi$
$684$	−8.42600e23	−0.672426
$685$	8.42971e23	0.664420
$686$	−9.88685e23	−0.769667
$687$	6.32390e23	0.486243
$688$	−1.07115e23	−0.0813485
$689$	1.22858e24	0.921594
$690$	2.30199e23	0.170563
$691$	−1.51213e24	−1.10669	−0.553343	−	0.832953i	$-0.686648\pi$
$691$	−1.51213e24	−1.10669	−0.553343	+	0.832953i	$0.686648\pi$
$692$	−1.99393e23	−0.144148
$693$	−1.66892e24	−1.19180
$694$	4.16082e23	0.293510
$695$	1.05465e24	0.734917
$696$	−1.42906e23	−0.0983718
$697$	9.32468e23	0.634096
$698$	9.22574e23	0.619769
$699$	−7.57500e23	−0.502720
$700$	1.23193e23	0.0807704
$701$	8.28511e23	0.536655	0.268328	−	0.963328i	$-0.413529\pi$
$701$	8.28511e23	0.536655	0.268328	+	0.963328i	$0.413529\pi$
$702$	6.27340e23	0.401456
$703$	−2.86084e24	−1.80873
$704$	3.42028e23	0.213645
$705$	−2.57747e23	−0.159069
$706$	−2.04688e24	−1.24811
$707$	−1.59458e24	−0.960684
$708$	−3.57386e23	−0.212743
$709$	−3.32788e22	−0.0195738	−0.00978689	−	0.999952i	$-0.503115\pi$
$709$	−3.32788e22	−0.0195738	−0.00978689	+	0.999952i	$0.503115\pi$
$710$	3.06603e23	0.178189
$711$	−1.56658e24	−0.899623
$712$	−1.12098e24	−0.636088
$713$	−1.84996e24	−1.03729
$714$	2.30066e23	0.127473
$715$	−1.15054e24	−0.629939
$716$	1.19761e24	0.647970
$717$	6.33846e23	0.338899
$718$	1.96921e24	1.04048
$719$	2.74357e23	0.143258	0.0716292	−	0.997431i	$-0.477180\pi$
$719$	2.74357e23	0.143258	0.0716292	+	0.997431i	$0.477180\pi$
$720$	1.87046e23	0.0965211
$721$	−1.99771e23	−0.101879
$722$	2.00162e24	1.00883
$723$	4.70391e23	0.234306
$724$	−1.13745e24	−0.559959
$725$	3.09351e23	0.150515
$726$	−1.04447e24	−0.502266
$727$	3.38639e24	1.60951	0.804756	−	0.593606i	$-0.202296\pi$
$727$	3.38639e24	1.60951	0.804756	+	0.593606i	$0.202296\pi$
$728$	5.00984e23	0.235346
$729$	−5.83070e23	−0.270730
$730$	−4.56009e23	−0.209281
$731$	4.33032e23	0.196436
$732$	−1.20048e23	−0.0538281
$733$	2.34817e24	1.04075	0.520375	−	0.853938i	$-0.325792\pi$
$733$	2.34817e24	1.04075	0.520375	+	0.853938i	$0.325792\pi$
$734$	1.12835e24	0.494341
$735$	−1.32715e23	−0.0574750
$736$	6.02428e23	0.257896
$737$	−3.04860e24	−1.29011
$738$	1.53276e24	0.641202
$739$	2.65236e24	1.09687	0.548434	−	0.836194i	$-0.315224\pi$
$739$	2.65236e24	1.09687	0.548434	+	0.836194i	$0.315224\pi$
$740$	6.35068e23	0.259627
$741$	−1.17444e24	−0.474651
$742$	1.59849e24	0.638671
$743$	4.48213e24	1.77043	0.885217	−	0.465178i	$-0.154010\pi$
$743$	4.48213e24	1.77043	0.885217	+	0.465178i	$0.154010\pi$
$744$	2.37999e23	0.0929406
$745$	−5.40357e23	−0.208618
$746$	1.97955e24	0.755589
$747$	−2.81434e24	−1.06207
$748$	−1.38271e24	−0.515901
$749$	9.29236e23	0.342792
$750$	6.41088e22	0.0233828
$751$	3.89653e24	1.40520	0.702600	−	0.711585i	$-0.252022\pi$
$751$	3.89653e24	1.40520	0.702600	+	0.711585i	$0.252022\pi$
$752$	−6.74520e23	−0.240516
$753$	−8.43206e23	−0.297287
$754$	1.25803e24	0.438564
$755$	1.40800e24	0.485350
$756$	8.16225e23	0.278211
$757$	−2.72183e24	−0.917373	−0.458687	−	0.888598i	$-0.651680\pi$
$757$	−2.72183e24	−0.917373	−0.458687	+	0.888598i	$0.651680\pi$
$758$	−1.75625e24	−0.585326
$759$	−2.79721e24	−0.921870
$760$	−7.55776e23	−0.246307
$761$	3.88834e23	0.125312	0.0626562	−	0.998035i	$-0.480043\pi$
$761$	3.88834e23	0.125312	0.0626562	+	0.998035i	$0.480043\pi$
$762$	−4.58691e23	−0.146185
$763$	−4.05489e24	−1.27797
$764$	−1.17110e24	−0.365007
$765$	−7.56166e23	−0.233075
$766$	−1.24583e24	−0.379766
$767$	3.14614e24	0.948457
$768$	−7.75028e22	−0.0231072
$769$	−2.20996e24	−0.651645	−0.325823	−	0.945431i	$-0.605641\pi$
$769$	−2.20996e24	−0.651645	−0.325823	+	0.945431i	$0.605641\pi$
$770$	−1.49695e24	−0.436552
$771$	−7.14847e23	−0.206182
$772$	6.52058e23	0.186011
$773$	5.39261e24	1.52151	0.760753	−	0.649042i	$-0.224830\pi$
$773$	5.39261e24	1.52151	0.760753	+	0.649042i	$0.224830\pi$
$774$	7.11803e23	0.198638
$775$	−5.15202e23	−0.142204
$776$	1.04725e24	0.285907
$777$	1.28400e24	0.346725
$778$	−2.55578e24	−0.682648
$779$	−6.19325e24	−1.63625
$780$	2.60709e23	0.0681322
$781$	−3.72562e24	−0.963085
$782$	−2.43542e24	−0.622754
$783$	2.04963e24	0.518443
$784$	−3.47315e23	−0.0869034
$785$	−2.64262e24	−0.654099
$786$	2.14090e23	0.0524209
$787$	−1.11664e24	−0.270475	−0.135238	−	0.990813i	$-0.543180\pi$
$787$	−1.11664e24	−0.270475	−0.135238	+	0.990813i	$0.543180\pi$
$788$	3.45488e24	0.827866
$789$	−2.43131e24	−0.576350
$790$	−1.40515e24	−0.329529
$791$	5.39470e24	1.25160
$792$	−2.27285e24	−0.521682
$793$	1.05680e24	0.239978
$794$	−1.30159e24	−0.292416
$795$	8.31845e23	0.184894
$796$	1.32921e23	0.0292303
$797$	−4.11242e24	−0.894751	−0.447375	−	0.894346i	$-0.647641\pi$
$797$	−4.11242e24	−0.894751	−0.447375	+	0.894346i	$0.647641\pi$
$798$	−1.52805e24	−0.328937
$799$	2.72686e24	0.580786
$800$	1.67772e23	0.0353553
$801$	7.44913e24	1.55321
$802$	2.70491e24	0.558047
$803$	5.54109e24	1.13113
$804$	6.90807e23	0.139534
$805$	−2.63664e24	−0.526970
$806$	−2.09515e24	−0.414351
$807$	2.15578e24	0.421871
$808$	−2.17160e24	−0.420517
$809$	1.99425e24	0.382135	0.191068	−	0.981577i	$-0.438805\pi$
$809$	1.99425e24	0.382135	0.191068	+	0.981577i	$0.438805\pi$
$810$	−1.01500e24	−0.192461
$811$	−6.54121e24	−1.22739	−0.613693	−	0.789545i	$-0.710317\pi$
$811$	−6.54121e24	−1.22739	−0.613693	+	0.789545i	$0.710317\pi$
$812$	1.63681e24	0.303928
$813$	1.95171e24	0.358628
$814$	−7.71688e24	−1.40325
$815$	4.17202e24	0.750769
$816$	3.13319e23	0.0557982
$817$	−2.87610e24	−0.506894
$818$	4.44311e23	0.0774968
$819$	−3.32914e24	−0.574671
$820$	1.37482e24	0.234870
$821$	−8.88770e24	−1.50270	−0.751351	−	0.659903i	$-0.770597\pi$
$821$	−8.88770e24	−1.50270	−0.751351	+	0.659903i	$0.770597\pi$
$822$	2.32108e24	0.388400
$823$	6.84928e24	1.13435	0.567174	−	0.823598i	$-0.308037\pi$
$823$	6.84928e24	1.13435	0.567174	+	0.823598i	$0.308037\pi$
$824$	−2.72061e23	−0.0445949
$825$	−7.79004e23	−0.126381
$826$	4.09341e24	0.657287
$827$	9.77573e24	1.55365	0.776824	−	0.629718i	$-0.216830\pi$
$827$	9.77573e24	1.55365	0.776824	+	0.629718i	$0.216830\pi$
$828$	−4.00326e24	−0.629732
$829$	7.90775e24	1.23123	0.615615	−	0.788047i	$-0.288908\pi$
$829$	7.90775e24	1.23123	0.615615	+	0.788047i	$0.288908\pi$
$830$	−2.52434e24	−0.389031
$831$	4.08688e24	0.623423
$832$	6.82273e23	0.103017
$833$	1.40408e24	0.209850
$834$	2.90394e24	0.429611
$835$	1.14740e24	0.168028
$836$	9.18364e24	1.33126
$837$	−3.41352e24	−0.489819
$838$	−2.89356e24	−0.411016
$839$	−7.46885e24	−1.05021	−0.525106	−	0.851037i	$-0.675974\pi$
$839$	−7.46885e24	−1.05021	−0.525106	+	0.851037i	$0.675974\pi$
$840$	3.39206e23	0.0472160
$841$	−3.14695e24	−0.433634
$842$	−2.71958e23	−0.0370978
$843$	−2.84264e24	−0.383873
$844$	−1.67260e24	−0.223606
$845$	1.08399e24	0.143465
$846$	4.48233e24	0.587294
$847$	1.19631e25	1.55179
$848$	2.17693e24	0.279563
$849$	−4.71409e24	−0.599352
$850$	−6.78248e23	−0.0853744
$851$	−1.35921e25	−1.69389
$852$	8.44218e23	0.104164
$853$	4.59203e24	0.560967	0.280484	−	0.959859i	$-0.409505\pi$
$853$	4.59203e24	0.560967	0.280484	+	0.959859i	$0.409505\pi$
$854$	1.37500e24	0.166307
$855$	5.02229e24	0.601436
$856$	1.26549e24	0.150049
$857$	−8.74464e24	−1.02661	−0.513304	−	0.858207i	$-0.671579\pi$
$857$	−8.74464e24	−1.02661	−0.513304	+	0.858207i	$0.671579\pi$
$858$	−3.16795e24	−0.368244
$859$	−1.25157e25	−1.44050	−0.720251	−	0.693714i	$-0.755973\pi$
$859$	−1.25157e25	−1.44050	−0.720251	+	0.693714i	$0.755973\pi$
$860$	6.38456e23	0.0727603
$861$	2.77964e24	0.313662
$862$	9.25611e24	1.03423
$863$	4.23769e22	0.00468854	0.00234427	−	0.999997i	$-0.499254\pi$
$863$	4.23769e22	0.00468854	0.00234427	+	0.999997i	$0.499254\pi$
$864$	1.11159e24	0.121780
$865$	1.18848e24	0.128930
$866$	−5.51147e24	−0.592059
$867$	2.20895e24	0.234976
$868$	−2.72598e24	−0.287148
$869$	1.70744e25	1.78105
$870$	8.51784e23	0.0879864
$871$	−6.08132e24	−0.622076
$872$	−5.52221e24	−0.559401
$873$	−6.95918e24	−0.698131
$874$	1.61755e25	1.60698
$875$	−7.34287e23	−0.0722433
$876$	−1.25560e24	−0.122339
$877$	−1.33197e25	−1.28528	−0.642638	−	0.766170i	$-0.722160\pi$
$877$	−1.33197e25	−1.28528	−0.642638	+	0.766170i	$0.722160\pi$
$878$	−7.39538e24	−0.706736
$879$	1.28274e24	0.121404
$880$	−2.03864e24	−0.191090
$881$	3.37699e23	0.0313498	0.0156749	−	0.999877i	$-0.495010\pi$
$881$	3.37699e23	0.0313498	0.0156749	+	0.999877i	$0.495010\pi$
$882$	2.30798e24	0.212202
$883$	−1.43309e25	−1.30499	−0.652495	−	0.757793i	$-0.726278\pi$
$883$	−1.43309e25	−1.30499	−0.652495	+	0.757793i	$0.726278\pi$
$884$	−2.75821e24	−0.248761
$885$	2.13019e24	0.190283
$886$	8.79298e23	0.0777946
$887$	−1.41818e25	−1.24274	−0.621369	−	0.783518i	$-0.713423\pi$
$887$	−1.41818e25	−1.24274	−0.621369	+	0.783518i	$0.713423\pi$
$888$	1.74863e24	0.151771
$889$	5.25374e24	0.451652
$890$	6.68155e24	0.568934
$891$	1.23335e25	1.04022
$892$	−2.29468e24	−0.191700
$893$	−1.81112e25	−1.49869
$894$	−1.48785e24	−0.121952
$895$	−7.13831e24	−0.579562
$896$	8.87699e23	0.0713917
$897$	−5.57984e24	−0.444514
$898$	7.90719e24	0.623984
$899$	−6.84525e24	−0.535096
$900$	−1.11488e24	−0.0863311
$901$	−8.80062e24	−0.675076
$902$	−1.67058e25	−1.26944
$903$	1.29085e24	0.0971693
$904$	7.34685e24	0.547860
$905$	6.77976e24	0.500843
$906$	3.87688e24	0.283721
$907$	2.50957e25	1.81944	0.909720	−	0.415222i	$-0.136296\pi$
$907$	2.50957e25	1.81944	0.909720	+	0.415222i	$0.136296\pi$
$908$	−7.84184e24	−0.563233
$909$	1.44307e25	1.02682
$910$	−2.98610e24	−0.210500
$911$	−2.35966e24	−0.164794	−0.0823972	−	0.996600i	$-0.526258\pi$
$911$	−2.35966e24	−0.164794	−0.0823972	+	0.996600i	$0.526258\pi$
$912$	−2.08099e24	−0.143984
$913$	3.06740e25	2.10266
$914$	−9.81210e24	−0.666376
$915$	7.15539e23	0.0481453
$916$	−9.86433e24	−0.657591
$917$	−2.45213e24	−0.161959
$918$	−4.49379e24	−0.294070
$919$	2.94936e25	1.91226	0.956129	−	0.292946i	$-0.0946357\pi$
$919$	2.94936e25	1.91226	0.956129	+	0.292946i	$0.0946357\pi$
$920$	−3.59075e24	−0.230669
$921$	1.54008e24	0.0980252
$922$	1.74117e25	1.09807
$923$	−7.43182e24	−0.464388
$924$	−4.12178e24	−0.255196
$925$	−3.78530e24	−0.232218
$926$	1.17079e24	0.0711684
$927$	1.80790e24	0.108892
$928$	2.22911e24	0.133037
$929$	1.27862e25	0.756150	0.378075	−	0.925775i	$-0.376586\pi$
$929$	1.27862e25	0.756150	0.378075	+	0.925775i	$0.376586\pi$
$930$	−1.41859e24	−0.0831286
$931$	−9.32560e24	−0.541508
$932$	1.18158e25	0.679875
$933$	1.31474e23	0.00749626
$934$	1.27428e25	0.719975
$935$	8.24157e24	0.461436
$936$	−4.53385e24	−0.251549
$937$	5.20286e24	0.286059	0.143029	−	0.989718i	$-0.454316\pi$
$937$	5.20286e24	0.286059	0.143029	+	0.989718i	$0.454316\pi$
$938$	−7.91234e24	−0.431103
$939$	1.07123e25	0.578398
$940$	4.02045e24	0.215124
$941$	2.51815e25	1.33527	0.667635	−	0.744488i	$-0.267306\pi$
$941$	2.51815e25	1.33527	0.667635	+	0.744488i	$0.267306\pi$
$942$	−7.27635e24	−0.382367
$943$	−2.94246e25	−1.53236
$944$	5.57467e24	0.287712
$945$	−4.86508e24	−0.248840
$946$	−7.75805e24	−0.393258
$947$	−2.26103e25	−1.13588	−0.567939	−	0.823071i	$-0.692259\pi$
$947$	−2.26103e25	−1.13588	−0.567939	+	0.823071i	$0.692259\pi$
$948$	−3.86903e24	−0.192633
$949$	1.10533e25	0.545417
$950$	4.50478e24	0.220304
$951$	5.99562e24	0.290603
$952$	−3.58867e24	−0.172393
$953$	2.71240e25	1.29141	0.645706	−	0.763586i	$-0.276563\pi$
$953$	2.71240e25	1.29141	0.645706	+	0.763586i	$0.276563\pi$
$954$	−1.44662e25	−0.682640
$955$	6.98032e24	0.326473
$956$	−9.88702e24	−0.458325
$957$	−1.03502e25	−0.475553
$958$	2.39486e25	1.09062
$959$	−2.65851e25	−1.20000
$960$	4.61953e23	0.0206677
$961$	−1.11498e25	−0.494447
$962$	−1.53935e25	−0.676629
$963$	−8.40947e24	−0.366392
$964$	−7.33738e24	−0.316874
$965$	−3.88657e24	−0.166374
$966$	−7.25987e24	−0.308052
$967$	2.72568e25	1.14644	0.573218	−	0.819403i	$-0.305695\pi$
$967$	2.72568e25	1.14644	0.573218	+	0.819403i	$0.305695\pi$
$968$	1.62921e25	0.679261
$969$	8.41278e24	0.347686
$970$	−6.24209e24	−0.255723
$971$	−5.68052e24	−0.230688	−0.115344	−	0.993326i	$-0.536797\pi$
$971$	−5.68052e24	−0.230688	−0.115344	+	0.993326i	$0.536797\pi$
$972$	−1.13511e25	−0.456954
$973$	−3.32610e25	−1.32732
$974$	−4.19670e24	−0.166019
$975$	−1.55395e24	−0.0609393
$976$	1.87256e24	0.0727967
$977$	−2.19879e25	−0.847383	−0.423691	−	0.905807i	$-0.639266\pi$
$977$	−2.19879e25	−0.847383	−0.423691	+	0.905807i	$0.639266\pi$
$978$	1.14875e25	0.438878
$979$	−8.11892e25	−3.07500
$980$	2.07016e24	0.0777288
$981$	3.66962e25	1.36595
$982$	−6.71999e24	−0.247983
$983$	1.62023e25	0.592748	0.296374	−	0.955072i	$-0.404222\pi$
$983$	1.62023e25	0.592748	0.296374	+	0.955072i	$0.404222\pi$
$984$	3.78550e24	0.137298
$985$	−2.05927e25	−0.740466
$986$	−9.01156e24	−0.321252
$987$	8.12865e24	0.287291
$988$	1.83194e25	0.641915
$989$	−1.36646e25	−0.474710
$990$	1.35472e25	0.466607
$991$	−1.63414e25	−0.558036	−0.279018	−	0.960286i	$-0.590009\pi$
$991$	−1.63414e25	−0.558036	−0.279018	+	0.960286i	$0.590009\pi$
$992$	−3.71242e24	−0.125692
$993$	6.94421e23	0.0233106
$994$	−9.66947e24	−0.321824
$995$	−7.92273e23	−0.0261444
$996$	−6.95066e24	−0.227416
$997$	3.96008e25	1.28468	0.642340	−	0.766420i	$-0.277964\pi$
$997$	3.96008e25	1.28468	0.642340	+	0.766420i	$0.277964\pi$
$998$	4.90132e24	0.157653
$999$	−2.50798e25	−0.799868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.a.d.1.1	✓	2
3.2	odd	2		90.18.a.j.1.1		2
4.3	odd	2		80.18.a.b.1.2		2
5.2	odd	4		50.18.b.f.49.4		4
5.3	odd	4		50.18.b.f.49.1		4
5.4	even	2		50.18.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.d.1.1	✓	2	1.1	even	1	trivial
50.18.a.c.1.2		2	5.4	even	2
50.18.b.f.49.1		4	5.3	odd	4
50.18.b.f.49.4		4	5.2	odd	4
80.18.a.b.1.2		2	4.3	odd	2
90.18.a.j.1.1		2	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+256.000 q^{2} -4201.44 q^{3} +65536.0 q^{4} -390625. q^{5} -1.07557e6 q^{6} +1.23193e7 q^{7} +1.67772e7 q^{8} -1.11488e8 q^{9} -1.00000e8 q^{10} +1.21513e9 q^{11} -2.75345e8 q^{12} +2.42392e9 q^{13} +3.15374e9 q^{14} +1.64119e9 q^{15} +4.29497e9 q^{16} -1.73631e10 q^{17} -2.85410e10 q^{18} +1.15322e11 q^{19} -2.56000e10 q^{20} -5.17587e10 q^{21} +3.11072e11 q^{22} +5.47905e11 q^{23} -7.04884e10 q^{24} +1.52588e11 q^{25} +6.20524e11 q^{26} +1.01098e12 q^{27} +8.07357e11 q^{28} +2.02736e12 q^{29} +4.20144e11 q^{30} -3.37643e12 q^{31} +1.09951e12 q^{32} -5.10528e12 q^{33} -4.44497e12 q^{34} -4.81222e12 q^{35} -7.30648e12 q^{36} -2.48073e13 q^{37} +2.95225e13 q^{38} -1.01840e13 q^{39} -6.55360e12 q^{40} -5.37038e13 q^{41} -1.32502e13 q^{42} -2.49397e13 q^{43} +7.96345e13 q^{44} +4.35500e13 q^{45} +1.40264e14 q^{46} -1.57049e14 q^{47} -1.80450e13 q^{48} -8.08656e13 q^{49} +3.90625e13 q^{50} +7.29502e13 q^{51} +1.58854e14 q^{52} +5.06856e14 q^{53} +2.58812e14 q^{54} -4.74659e14 q^{55} +2.06683e14 q^{56} -4.84519e14 q^{57} +5.19005e14 q^{58} +1.29796e15 q^{59} +1.07557e14 q^{60} +4.35989e14 q^{61} -8.64366e14 q^{62} -1.37345e15 q^{63} +2.81475e14 q^{64} -9.46844e14 q^{65} -1.30695e15 q^{66} -2.50888e15 q^{67} -1.13791e15 q^{68} -2.30199e15 q^{69} -1.23193e15 q^{70} -3.06603e15 q^{71} -1.87046e15 q^{72} +4.56009e15 q^{73} -6.35068e15 q^{74} -6.41088e14 q^{75} +7.55776e15 q^{76} +1.49695e16 q^{77} -2.60709e15 q^{78} +1.40515e16 q^{79} -1.67772e15 q^{80} +1.01500e16 q^{81} -1.37482e16 q^{82} +2.52434e16 q^{83} -3.39206e15 q^{84} +6.78248e15 q^{85} -6.38456e15 q^{86} -8.51784e15 q^{87} +2.03864e16 q^{88} -6.68155e16 q^{89} +1.11488e16 q^{90} +2.98610e16 q^{91} +3.59075e16 q^{92} +1.41859e16 q^{93} -4.02045e16 q^{94} -4.50478e16 q^{95} -4.61953e15 q^{96} +6.24209e16 q^{97} -2.07016e16 q^{98} -1.35472e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 512 q^{2} + 17628 q^{3} + 131072 q^{4} - 781250 q^{5} + 4512768 q^{6} + 27684196 q^{7} + 33554432 q^{8} + 235896066 q^{9} - 200000000 q^{10} + 64515264 q^{11} + 1155268608 q^{12} + 2895838468 q^{13}+ \cdots - 53\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 512 * q^2 + 17628 * q^3 + 131072 * q^4 - 781250 * q^5 + 4512768 * q^6 + 27684196 * q^7 + 33554432 * q^8 + 235896066 * q^9 - 200000000 * q^10 + 64515264 * q^11 + 1155268608 * q^12 + 2895838468 * q^13 + 7087154176 * q^14 - 6885937500 * q^15 + 8589934592 * q^16 + 1580212596 * q^17 + 60389392896 * q^18 + 44213712760 * q^19 - 51200000000 * q^20 + 283648477944 * q^21 + 16515907584 * q^22 + 487549782828 * q^23 + 295748763648 * q^24 + 305175781250 * q^25 + 741334647808 * q^26 + 5775127941960 * q^27 + 1814311469056 * q^28 + 3987314863500 * q^29 - 1762800000000 * q^30 - 5492261339336 * q^31 + 2199023255552 * q^32 - 30222474885504 * q^33 + 404534424576 * q^34 - 10814139062500 * q^35 + 15459684581376 * q^36 - 62715287637884 * q^37 + 11318710466560 * q^38 + 117745895352 * q^39 - 13107200000000 * q^40 + 23411477277324 * q^41 + 72614010353664 * q^42 - 124856923191092 * q^43 + 4228072341504 * q^44 - 92146900781250 * q^45 + 124812744403968 * q^46 - 185946612123564 * q^47 + 75711683493888 * q^48 - 77415796886406 * q^49 + 78125000000000 * q^50 + 486473079414744 * q^51 + 189781669838848 * q^52 + 359339780647668 * q^53 + 1478432753141760 * q^54 - 25201275000000 * q^55 + 464463736078336 * q^56 - 2036779039451760 * q^57 + 1020752605056000 * q^58 + 902179170360600 * q^59 - 451276800000000 * q^60 - 1564422918967676 * q^61 - 1406018902870016 * q^62 + 3964069932109668 * q^63 + 562949953421312 * q^64 - 1131186901562500 * q^65 - 7736953570689024 * q^66 - 5839738931054684 * q^67 + 103560812691456 * q^68 - 3619512981398808 * q^69 - 2768419600000000 * q^70 - 67588560434136 * q^71 + 3957679252832256 * q^72 + 3533390699585668 * q^73 - 16055113635298304 * q^74 + 2689819335937500 * q^75 + 2897589879439360 * q^76 - 2709533546636928 * q^77 + 30142949210112 * q^78 + 19002656396552080 * q^79 - 3355443200000000 * q^80 + 69287326451135082 * q^81 + 5993338182994944 * q^82 + 21675087975118188 * q^83 + 18589186650537984 * q^84 - 617270545312500 * q^85 - 31963372336919552 * q^86 + 34266820308892200 * q^87 + 1082386519425024 * q^88 - 97499522192222220 * q^89 - 23589606600000000 * q^90 + 37111957465918664 * q^91 + 31952062567415808 * q^92 - 32001580397816304 * q^93 - 47602332703632384 * q^94 - 17270981546875000 * q^95 + 19382190974435328 * q^96 + 99889937855386756 * q^97 - 19818444002919936 * q^98 - 535176281294791488 * q^99

Introduction

L-functions

Modular forms

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