LMFDB - Embedded newform 81.9.f.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

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:	no
Analytic conductor:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-26.8100 - 4.72733i) q^{2} +(455.867 + 165.922i) q^{4} +(418.443 + 498.682i) q^{5} +(2557.31 - 930.784i) q^{7} +(-5401.88 - 3118.78i) q^{8} +(-8861.04 - 15347.8i) q^{10} +(16649.6 - 19842.2i) q^{11} +(-2324.40 - 13182.3i) q^{13} +(-72961.5 + 12865.1i) q^{14} +(34944.7 + 29322.1i) q^{16} +(114990. - 66389.2i) q^{17} +(-10147.5 + 17576.0i) q^{19} +(108012. + 296761. i) q^{20} +(-540176. + 453262. i) q^{22} +(-93974.9 + 258194. i) q^{23} +(-5756.99 + 32649.5i) q^{25} +364407. i q^{26} +1.32023e6 q^{28} +(-373034. - 65776.0i) q^{29} +(23963.9 + 8722.16i) q^{31} +(228160. + 271911. i) q^{32} +(-3.39671e6 + 1.23630e6i) q^{34} +(1.53425e6 + 885801. i) q^{35} +(-1.41658e6 - 2.45359e6i) q^{37} +(355142. - 423242. i) q^{38} +(-705106. - 3.99885e6i) q^{40} +(1.23941e6 - 218542. i) q^{41} +(390374. + 327563. i) q^{43} +(1.08823e7 - 6.28287e6i) q^{44} +(3.74003e6 - 6.47792e6i) q^{46} +(-2.99482e6 - 8.22820e6i) q^{47} +(1.25737e6 - 1.05506e6i) q^{49} +(308690. - 848118. i) q^{50} +(1.12762e6 - 6.39506e6i) q^{52} +6.12277e6i q^{53} +1.68619e7 q^{55} +(-1.67172e7 - 2.94769e6i) q^{56} +(9.69011e6 + 3.52691e6i) q^{58} +(-1.30891e7 - 1.55989e7i) q^{59} +(3.01877e6 - 1.09874e6i) q^{61} +(-601240. - 347126. i) q^{62} +(-1.06706e7 - 1.84819e7i) q^{64} +(5.60116e6 - 6.67520e6i) q^{65} +(2.53228e6 + 1.43613e7i) q^{67} +(6.34353e7 - 1.11854e7i) q^{68} +(-3.69458e7 - 3.10012e7i) q^{70} +(-1.90737e7 + 1.10122e7i) q^{71} +(-6.96726e6 + 1.20676e7i) q^{73} +(2.63796e7 + 7.24775e7i) q^{74} +(-7.54215e6 + 6.32862e6i) q^{76} +(2.41093e7 - 6.62398e7i) q^{77} +(5.26432e6 - 2.98554e7i) q^{79} +2.96959e7i q^{80} -3.42618e7 q^{82} +(-6.05555e7 - 1.06776e7i) q^{83} +(8.12237e7 + 2.95630e7i) q^{85} +(-8.91743e6 - 1.06274e7i) q^{86} +(-1.51823e8 + 5.52589e7i) q^{88} +(9.16372e7 + 5.29067e7i) q^{89} +(-1.82141e7 - 3.15478e7i) q^{91} +(-8.56800e7 + 1.02110e8i) q^{92} +(4.13937e7 + 2.34755e8i) q^{94} +(-1.30110e7 + 2.29419e6i) q^{95} +(2.45606e7 + 2.06088e7i) q^{97} +(-3.86976e7 + 2.23421e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−26.8100	−	4.72733i	−1.67562	−	0.295458i	−0.746544	−	0.665336i	$-0.768288\pi$
$2$	−26.8100	−	4.72733i	−1.67562	−	0.295458i	−0.929080	+	0.369878i	$0.879399\pi$
$3$		0			0
$3$		0			0
$4$	455.867	+	165.922i	1.78073	+	0.648133i
$5$	418.443	+	498.682i	0.669510	+	0.797890i	0.988717	−	0.149794i	$-0.0478612\pi$
$5$	418.443	+	498.682i	0.669510	+	0.797890i	−0.319208	+	0.947685i	$0.603417\pi$
$6$		0			0
$7$	2557.31	−	930.784i	1.06510	−	0.387665i	0.250758	−	0.968050i	$-0.419320\pi$
$7$	2557.31	−	930.784i	1.06510	−	0.387665i	0.814342	+	0.580385i	$0.197098\pi$
$8$	−5401.88	−	3118.78i	−1.31882	−	0.761421i
$9$		0			0
$10$	−8861.04	−	15347.8i	−0.886104	−	1.53478i
$11$	16649.6	−	19842.2i	1.13719	−	1.35525i	0.211316	−	0.977418i	$-0.432225\pi$
$11$	16649.6	−	19842.2i	1.13719	−	1.35525i	0.925874	−	0.377832i	$-0.123330\pi$
$12$		0			0
$13$	−2324.40	−	13182.3i	−0.0813838	−	0.461550i	−0.998079	−	0.0619620i	$-0.980264\pi$
$13$	−2324.40	−	13182.3i	−0.0813838	−	0.461550i	0.916695	−	0.399588i	$-0.130847\pi$
$14$	−72961.5	+	12865.1i	−1.89925	+	0.334889i
$15$		0			0
$16$	34944.7	+	29322.1i	0.533214	+	0.447420i
$17$	114990.	−	66389.2i	1.37677	−	0.794881i	0.385004	−	0.922915i	$-0.374200\pi$
$17$	114990.	−	66389.2i	1.37677	−	0.794881i	0.991770	+	0.128034i	$0.0408667\pi$
$18$		0			0
$19$	−10147.5	+	17576.0i	−0.0778654	+	0.134867i	−0.902329	−	0.431048i	$-0.858144\pi$
$19$	−10147.5	+	17576.0i	−0.0778654	+	0.134867i	0.824463	+	0.565915i	$0.191477\pi$
$20$	108012.	+	296761.i	0.675077	+	1.85476i
$21$		0			0
$22$	−540176.	+	453262.i	−2.30592	+	1.93490i
$23$	−93974.9	+	258194.i	−0.335815	+	0.922645i	0.650752	+	0.759290i	$0.274454\pi$
$23$	−93974.9	+	258194.i	−0.335815	+	0.922645i	−0.986567	+	0.163355i	$0.947769\pi$
$24$		0			0
$25$	−5756.99	+	32649.5i	−0.0147379	+	0.0835828i
$26$			364407.i			0.797430i
$27$		0			0
$28$	1.32023e6			2.14792
$29$	−373034.	−	65776.0i	−0.527420	−	0.0929985i	−0.0964036	−	0.995342i	$-0.530734\pi$
$29$	−373034.	−	65776.0i	−0.527420	−	0.0929985i	−0.431017	+	0.902344i	$0.641845\pi$
$30$		0			0
$31$	23963.9	+	8722.16i	0.0259484	+	0.00944446i	0.354962	−	0.934881i	$-0.384494\pi$
$31$	23963.9	+	8722.16i	0.0259484	+	0.00944446i	−0.329013	+	0.944325i	$0.606716\pi$
$32$	228160.	+	271911.i	0.217591	+	0.259314i
$33$		0			0
$34$	−3.39671e6	+	1.23630e6i	−2.54181	+	0.925143i
$35$	1.53425e6	+	885801.i	1.02241	+	0.590288i
$36$		0			0
$37$	−1.41658e6	−	2.45359e6i	−0.755849	−	1.30917i	−0.944951	−	0.327211i	$-0.893891\pi$
$37$	−1.41658e6	−	2.45359e6i	−0.755849	−	1.30917i	0.189102	−	0.981957i	$-0.439442\pi$
$38$	355142.	−	423242.i	0.170321	−	0.202980i
$39$		0			0
$40$	−705106.	−	3.99885e6i	−0.275432	−	1.56205i
$41$	1.23941e6	−	218542.i	0.438613	−	0.0773393i	0.0500186	−	0.998748i	$-0.484072\pi$
$41$	1.23941e6	−	218542.i	0.438613	−	0.0773393i	0.388594	+	0.921409i	$0.372961\pi$
$42$		0			0
$43$	390374.	+	327563.i	0.114185	+	0.0958122i	0.698092	−	0.716008i	$-0.254033\pi$
$43$	390374.	+	327563.i	0.114185	+	0.0958122i	−0.583908	+	0.811820i	$0.698477\pi$
$44$	1.08823e7	−	6.28287e6i	2.90341	−	1.67628i
$45$		0			0
$46$	3.74003e6	−	6.47792e6i	0.835303	−	1.44679i
$47$	−2.99482e6	−	8.22820e6i	−0.613733	−	1.68622i	−0.721825	−	0.692076i	$-0.756696\pi$
$47$	−2.99482e6	−	8.22820e6i	−0.613733	−	1.68622i	0.108092	−	0.994141i	$-0.465526\pi$
$48$		0			0
$49$	1.25737e6	−	1.05506e6i	0.218111	−	0.183017i
$50$	308690.	−	848118.i	0.0493904	−	0.135699i
$51$		0			0
$52$	1.12762e6	−	6.39506e6i	0.154223	−	0.874644i
$53$			6.12277e6i			0.775970i	0.921666	+	0.387985i	$0.126829\pi$
$53$			6.12277e6i			0.775970i	−0.921666	+	0.387985i	$0.873171\pi$
$54$		0			0
$55$	1.68619e7			1.84270
$56$	−1.67172e7	−	2.94769e6i	−1.69985	−	0.299730i
$57$		0			0
$58$	9.69011e6	+	3.52691e6i	0.856282	+	0.311661i
$59$	−1.30891e7	−	1.55989e7i	−1.08019	−	1.28732i	−0.955457	−	0.295130i	$-0.904637\pi$
$59$	−1.30891e7	−	1.55989e7i	−1.08019	−	1.28732i	−0.124733	−	0.992190i	$-0.539807\pi$
$60$		0			0
$61$	3.01877e6	−	1.09874e6i	0.218027	−	0.0793554i	−0.230697	−	0.973026i	$-0.574101\pi$
$61$	3.01877e6	−	1.09874e6i	0.218027	−	0.0793554i	0.448724	+	0.893670i	$0.351878\pi$
$62$	−601240.	−	347126.i	−0.0406894	−	0.0234920i
$63$		0			0
$64$	−1.06706e7	−	1.84819e7i	−0.636014	−	1.10161i
$65$	5.60116e6	−	6.67520e6i	0.313779	−	0.373948i
$66$		0			0
$67$	2.53228e6	+	1.43613e7i	0.125665	+	0.712680i	0.980911	+	0.194458i	$0.0622947\pi$
$67$	2.53228e6	+	1.43613e7i	0.125665	+	0.712680i	−0.855246	+	0.518222i	$0.826594\pi$
$68$	6.34353e7	−	1.11854e7i	2.96685	−	0.523136i
$69$		0			0
$70$	−3.69458e7	−	3.10012e7i	−1.53877	−	1.29118i
$71$	−1.90737e7	+	1.10122e7i	−0.750586	+	0.433351i	−0.825906	−	0.563808i	$-0.809336\pi$
$71$	−1.90737e7	+	1.10122e7i	−0.750586	+	0.433351i	0.0753193	+	0.997159i	$0.476002\pi$
$72$		0			0
$73$	−6.96726e6	+	1.20676e7i	−0.245341	+	0.424943i	−0.962227	−	0.272247i	$-0.912233\pi$
$73$	−6.96726e6	+	1.20676e7i	−0.245341	+	0.424943i	0.716886	+	0.697190i	$0.245567\pi$
$74$	2.63796e7	+	7.24775e7i	0.879715	+	2.41700i
$75$		0			0
$76$	−7.54215e6	+	6.32862e6i	−0.226069	+	0.189694i
$77$	2.41093e7	−	6.62398e7i	0.685839	−	1.88433i
$78$		0			0
$79$	5.26432e6	−	2.98554e7i	0.135155	−	0.766505i	−0.839596	−	0.543212i	$-0.817208\pi$
$79$	5.26432e6	−	2.98554e7i	0.135155	−	0.766505i	0.974751	−	0.223293i	$-0.0716807\pi$
$80$			2.96959e7i			0.724998i
$81$		0			0
$82$	−3.42618e7			−0.757801
$83$	−6.05555e7	−	1.06776e7i	−1.27597	−	0.224988i	−0.505703	−	0.862708i	$-0.668767\pi$
$83$	−6.05555e7	−	1.06776e7i	−1.27597	−	0.224988i	−0.770269	+	0.637720i	$0.779878\pi$
$84$		0			0
$85$	8.12237e7	+	2.95630e7i	1.55599	+	0.566334i
$86$	−8.91743e6	−	1.06274e7i	−0.163022	−	0.194282i
$87$		0			0
$88$	−1.51823e8	+	5.52589e7i	−2.53166	+	0.921450i
$89$	9.16372e7	+	5.29067e7i	1.46053	+	0.843240i	0.999036	−	0.0439015i	$-0.0139788\pi$
$89$	9.16372e7	+	5.29067e7i	1.46053	+	0.843240i	0.461498	+	0.887141i	$0.347312\pi$
$90$		0			0
$91$	−1.82141e7	−	3.15478e7i	−0.265609	−	0.460048i
$92$	−8.56800e7	+	1.02110e8i	−1.19599	+	1.42533i
$93$		0			0
$94$	4.13937e7	+	2.34755e8i	0.530180	+	3.00680i
$95$	−1.30110e7	+	2.29419e6i	−0.159741	+	0.0281666i
$96$		0			0
$97$	2.45606e7	+	2.06088e7i	0.277429	+	0.232790i	0.770876	−	0.636986i	$-0.219819\pi$
$97$	2.45606e7	+	2.06088e7i	0.277429	+	0.232790i	−0.493447	+	0.869776i	$0.664263\pi$
$98$	−3.86976e7	+	2.23421e7i	−0.419547	+	0.242225i
$99$		0			0
$100$	−8.04169e6	+	1.39286e7i	−0.0804169	+	0.139286i
$101$	2.08552e7	+	5.72991e7i	0.200414	+	0.550633i	0.998663	−	0.0516944i	$-0.0164622\pi$
$101$	2.08552e7	+	5.72991e7i	0.200414	+	0.550633i	−0.798249	+	0.602328i	$0.794240\pi$
$102$		0			0
$103$	4.44654e7	−	3.73109e7i	0.395069	−	0.331502i	−0.423515	−	0.905889i	$-0.639204\pi$
$103$	4.44654e7	−	3.73109e7i	0.395069	−	0.331502i	0.818584	+	0.574387i	$0.194759\pi$
$104$	−2.85566e7	+	7.84587e7i	−0.244103	+	0.670669i
$105$		0			0
$106$	2.89443e7	−	1.64152e8i	0.229266	−	1.30023i
$107$		−	1.37917e8i		−	1.05216i	−0.850434	−	0.526082i	$-0.823660\pi$
$107$		−	1.37917e8i		−	1.05216i	0.850434	−	0.526082i	$-0.176340\pi$
$108$		0			0
$109$	1.64934e8			1.16843			0.584217	−	0.811597i	$-0.301402\pi$
$109$	1.64934e8			1.16843			0.584217	+	0.811597i	$0.301402\pi$
$110$	−4.52066e8	−	7.97115e7i	−3.08767	−	0.544440i
$111$		0			0
$112$	1.16657e8	+	4.24596e7i	0.741376	+	0.269839i
$113$	2.32407e7	+	2.76972e7i	0.142539	+	0.169872i	0.832591	−	0.553888i	$-0.186857\pi$
$113$	2.32407e7	+	2.76972e7i	0.142539	+	0.169872i	−0.690052	+	0.723760i	$0.742412\pi$
$114$		0			0
$115$	−1.68080e8	+	6.11760e7i	−0.961001	+	0.349776i
$116$	−1.59140e8	−	9.18797e7i	−0.878918	−	0.507444i
$117$		0			0
$118$	2.77176e8	+	4.80083e8i	1.42964	+	2.47622i
$119$	2.32270e8	−	2.76808e8i	1.15826	−	1.38036i
$120$		0			0
$121$	−7.92815e7	−	4.49627e8i	−0.369854	−	2.09755i
$122$	−8.61273e7	+	1.51866e7i	−0.388778	+	0.0685520i
$123$		0			0
$124$	9.47716e6	+	7.95228e6i	0.0400859	+	0.0336361i
$125$	2.01531e8	−	1.16354e8i	0.825471	−	0.476586i
$126$		0			0
$127$	1.67249e8	−	2.89684e8i	0.642908	−	1.11355i	−0.341873	−	0.939746i	$-0.611061\pi$
$127$	1.67249e8	−	2.89684e8i	0.642908	−	1.11355i	0.984780	−	0.173803i	$-0.0556055\pi$
$128$	1.67628e8	+	4.60556e8i	0.624465	+	1.71570i
$129$		0			0
$130$	−1.81723e8	+	1.52484e8i	−0.636262	+	0.533887i
$131$	3.77995e7	−	1.03853e8i	0.128352	−	0.352643i	−0.858826	−	0.512267i	$-0.828806\pi$
$131$	3.77995e7	−	1.03853e8i	0.128352	−	0.352643i	0.987178	+	0.159624i	$0.0510281\pi$
$132$		0			0
$133$	−9.59084e6	+	5.43923e7i	−0.0306514	+	0.173833i
$134$		−	3.96997e8i		−	1.23131i
$135$		0			0
$136$	−8.28213e8			−2.42095
$137$	−3.14533e8	−	5.54606e7i	−0.892861	−	0.157435i	−0.291649	−	0.956525i	$-0.594204\pi$
$137$	−3.14533e8	−	5.54606e7i	−0.892861	−	0.157435i	−0.601212	+	0.799090i	$0.705315\pi$
$138$		0			0
$139$	2.90327e8	+	1.05670e8i	0.777729	+	0.283070i	0.700225	−	0.713922i	$-0.253083\pi$
$139$	2.90327e8	+	1.05670e8i	0.777729	+	0.283070i	0.0775035	+	0.996992i	$0.475305\pi$
$140$	5.52441e8	+	6.58374e8i	1.43805	+	1.71380i
$141$		0			0
$142$	5.63423e8	−	2.05069e8i	1.38574	−	0.504367i
$143$	−3.00267e8	−	1.73359e8i	−0.718065	−	0.414575i
$144$		0			0
$145$	−1.23293e8	−	2.13549e8i	−0.278910	−	0.483087i
$146$	2.43840e8	−	2.90597e8i	0.536653	−	0.639558i
$147$		0			0
$148$	−2.38668e8	−	1.35355e9i	−0.497448	−	2.82117i
$149$	2.53267e8	−	4.46578e7i	0.513846	−	0.0906050i	0.0892886	−	0.996006i	$-0.471541\pi$
$149$	2.53267e8	−	4.46578e7i	0.513846	−	0.0906050i	0.424558	+	0.905401i	$0.360430\pi$
$150$		0			0
$151$	1.18622e8	+	9.95359e7i	0.228170	+	0.191457i	0.749704	−	0.661773i	$-0.230196\pi$
$151$	1.18622e8	+	9.95359e7i	0.228170	+	0.191457i	−0.521534	+	0.853230i	$0.674640\pi$
$152$	1.09631e8	−	6.32956e7i	0.205381	−	0.118577i
$153$		0			0
$154$	−9.59508e8	+	1.66192e9i	−1.70595	+	2.95479i
$155$	5.67797e6	+	1.56001e7i	0.00983708	+	0.0270272i
$156$		0			0
$157$	−2.30152e8	+	1.93120e8i	−0.378805	+	0.317855i	−0.812233	−	0.583333i	$-0.801748\pi$
$157$	−2.30152e8	+	1.93120e8i	−0.378805	+	0.317855i	0.433428	+	0.901188i	$0.357304\pi$
$158$	−2.82273e8	+	7.75537e8i	−0.452940	+	1.24444i
$159$		0			0
$160$	−4.01247e7	+	2.27559e8i	−0.0612255	+	0.347227i
$161$			7.47751e8i			1.11289i
$162$		0			0
$163$	−1.43882e8			−0.203825			−0.101913	−	0.994793i	$-0.532496\pi$
$163$	−1.43882e8			−0.203825			−0.101913	+	0.994793i	$0.532496\pi$
$164$	6.01269e8	+	1.06020e8i	0.831177	+	0.146559i
$165$		0			0
$166$	1.57302e9	+	5.72531e8i	2.07157	+	0.753992i
$167$	6.24363e8	+	7.44087e8i	0.802734	+	0.956661i	0.999718	−	0.0237457i	$-0.00755920\pi$
$167$	6.24363e8	+	7.44087e8i	0.802734	+	0.956661i	−0.196984	+	0.980407i	$0.563115\pi$
$168$		0			0
$169$	5.98165e8	−	2.17714e8i	0.733287	−	0.266895i
$170$	−2.03785e9	−	1.17655e9i	−2.43993	−	1.40869i
$171$		0			0
$172$	1.23609e8	+	2.14097e8i	0.141233	+	0.244622i
$173$	−6.43878e8	+	7.67343e8i	−0.718818	+	0.856654i	−0.994515	−	0.104591i	$-0.966647\pi$
$173$	−6.43878e8	+	7.67343e8i	−0.718818	+	0.856654i	0.275698	+	0.961244i	$0.411091\pi$
$174$		0			0
$175$	1.56672e7	+	8.88534e7i	0.0167048	+	0.0947375i
$176$	1.16363e9	−	2.05180e8i	1.21273	−	0.213837i
$177$		0			0
$178$	−2.20668e9	−	1.85163e9i	−2.19816	−	1.84448i
$179$	7.59344e8	−	4.38408e8i	0.739651	−	0.427038i	−0.0822916	−	0.996608i	$-0.526224\pi$
$179$	7.59344e8	−	4.38408e8i	0.739651	−	0.427038i	0.821942	+	0.569571i	$0.192891\pi$
$180$		0			0
$181$	−8.53185e8	+	1.47776e9i	−0.794930	+	1.37686i	0.127953	+	0.991780i	$0.459159\pi$
$181$	−8.53185e8	+	1.47776e9i	−0.794930	+	1.37686i	−0.922883	+	0.385080i	$0.874174\pi$
$182$	3.39184e8	+	9.31900e8i	0.309136	+	0.849344i
$183$		0			0
$184$	1.31289e9	−	1.10165e9i	1.14540	−	0.961105i
$185$	6.30802e8	−	1.73311e9i	0.538525	−	1.47959i
$186$		0			0
$187$	5.97220e8	−	3.38700e9i	0.488391	−	2.76980i
$188$		−	4.24787e9i		−	3.40048i
$189$		0			0
$190$	3.59670e8			0.275987
$191$	2.32863e9	+	4.10601e8i	1.74972	+	0.308522i	0.954590	−	0.297922i	$-0.0962937\pi$
$191$	2.32863e9	+	4.10601e8i	1.74972	+	0.308522i	0.795126	+	0.606445i	$0.207405\pi$
$192$		0			0
$193$	−8.05483e8	−	2.93172e8i	−0.580533	−	0.211297i	0.0350274	−	0.999386i	$-0.488848\pi$
$193$	−8.05483e8	−	2.93172e8i	−0.580533	−	0.211297i	−0.615561	+	0.788090i	$0.711070\pi$
$194$	−5.61044e8	−	6.68626e8i	−0.396087	−	0.472038i
$195$		0			0
$196$	7.48250e8	−	2.72341e8i	0.507017	−	0.184539i
$197$	6.61387e8	+	3.81852e8i	0.439127	+	0.253530i	0.703227	−	0.710965i	$-0.251742\pi$
$197$	6.61387e8	+	3.81852e8i	0.439127	+	0.253530i	−0.264100	+	0.964495i	$0.585075\pi$
$198$		0			0
$199$	−1.68090e8	−	2.91140e8i	−0.107184	−	0.185648i	0.807445	−	0.589943i	$-0.200850\pi$
$199$	−1.68090e8	−	2.91140e8i	−0.107184	−	0.185648i	−0.914628	+	0.404296i	$0.867517\pi$
$200$	1.32925e8	−	1.58414e8i	0.0830783	−	0.0990088i
$201$		0			0
$202$	−2.88256e8	−	1.63478e9i	−0.173130	−	0.981869i
$203$	−1.01519e9	+	1.79005e8i	−0.597808	+	0.105410i
$204$		0			0
$205$	6.27608e8	+	5.26626e8i	0.355364	+	0.298186i
$206$	−1.36850e9	+	7.90102e8i	−0.759932	+	0.438747i
$207$		0			0
$208$	3.05308e8	−	5.28809e8i	0.163112	−	0.282518i
$209$	1.79795e8	+	4.93982e8i	0.0942306	+	0.258896i
$210$		0			0
$211$	−2.12174e9	+	1.78035e9i	−1.07044	+	0.898204i	−0.995092	−	0.0989531i	$-0.968451\pi$
$211$	−2.12174e9	+	1.78035e9i	−1.07044	+	0.898204i	−0.0753462	+	0.997157i	$0.524006\pi$
$212$	−1.01590e9	+	2.79117e9i	−0.502931	+	1.38179i
$213$		0			0
$214$	−6.51980e8	+	3.69756e9i	−0.310870	+	1.76303i
$215$			3.31739e8i			0.155254i
$216$		0			0
$217$	6.94016e7			0.0312990
$218$	−4.42188e9	−	7.79697e8i	−1.95786	−	0.345223i
$219$		0			0
$220$	7.68676e9	+	2.79775e9i	3.28135	+	1.19431i
$221$	−1.14245e9	−	1.36152e9i	−0.478924	−	0.570760i
$222$		0			0
$223$	−1.19208e9	+	4.33882e8i	−0.482044	+	0.175450i	−0.571601	−	0.820532i	$-0.693677\pi$
$223$	−1.19208e9	+	4.33882e8i	−0.482044	+	0.175450i	0.0895565	+	0.995982i	$0.471455\pi$
$224$	8.36566e8	+	4.82992e8i	0.332283	+	0.191844i
$225$		0			0
$226$	−4.92149e8	−	8.52427e8i	−0.188653	−	0.326756i
$227$	−2.76684e9	+	3.29739e9i	−1.04203	+	1.24184i	−0.0723737	+	0.997378i	$0.523057\pi$
$227$	−2.76684e9	+	3.29739e9i	−1.04203	+	1.24184i	−0.969658	+	0.244467i	$0.921387\pi$
$228$		0			0
$229$	−1.77367e8	−	1.00590e9i	−0.0644958	−	0.365774i	−0.999925	−	0.0122592i	$-0.996098\pi$
$229$	−1.77367e8	−	1.00590e9i	−0.0644958	−	0.365774i	0.935429	−	0.353514i	$-0.115013\pi$
$230$	4.79541e9	−	8.45561e8i	1.71362	−	0.302158i
$231$		0			0
$232$	1.80995e9	+	1.51873e9i	0.624761	+	0.524237i
$233$	7.06563e8	−	4.07935e8i	0.239733	−	0.138410i	−0.375321	−	0.926895i	$-0.622468\pi$
$233$	7.06563e8	−	4.07935e8i	0.239733	−	0.138410i	0.615054	+	0.788485i	$0.289134\pi$
$234$		0			0
$235$	2.85009e9	−	4.93650e9i	0.934516	−	1.61863i
$236$	−3.37866e9	−	9.28280e9i	−1.08917	−	2.99248i
$237$		0			0
$238$	−7.53571e9	+	6.32321e9i	−2.34864	+	1.97074i
$239$	9.48835e7	−	2.60690e8i	0.0290803	−	0.0798975i	−0.924303	−	0.381660i	$-0.875353\pi$
$239$	9.48835e7	−	2.60690e8i	0.0290803	−	0.0798975i	0.953383	+	0.301762i	$0.0975749\pi$
$240$		0			0
$241$	−4.20007e8	+	2.38198e9i	−0.124505	+	0.706105i	0.857095	+	0.515158i	$0.172267\pi$
$241$	−4.20007e8	+	2.38198e9i	−0.124505	+	0.706105i	−0.981600	+	0.190947i	$0.938844\pi$
$242$			1.24293e10i			3.62397i
$243$		0			0
$244$	1.55846e9			0.439680
$245$	1.05228e9	+	1.85545e8i	0.292055	+	0.0514972i
$246$		0			0
$247$	2.55279e8	+	9.29141e7i	0.0685848	+	0.0249628i
$248$	−1.02248e8	−	1.21854e8i	−0.0270301	−	0.0322132i
$249$		0			0
$250$	−5.95309e9	+	2.16675e9i	−1.52399	+	0.554687i
$251$	5.20696e9	+	3.00624e9i	1.31187	+	0.757406i	0.982405	−	0.186763i	$-0.0597998\pi$
$251$	5.20696e9	+	3.00624e9i	1.31187	+	0.757406i	0.329461	+	0.944169i	$0.393133\pi$
$252$		0			0
$253$	3.55849e9	+	6.16349e9i	0.868529	+	1.50434i
$254$	−5.85337e9	+	6.97578e9i	−1.40628	+	1.67594i
$255$		0			0
$256$	−1.36823e9	−	7.75960e9i	−0.318565	−	1.80667i
$257$	−3.38337e9	+	5.96580e8i	−0.775564	+	0.136753i	−0.547401	−	0.836870i	$-0.684383\pi$
$257$	−3.38337e9	+	5.96580e8i	−0.775564	+	0.136753i	−0.228163	+	0.973623i	$0.573272\pi$
$258$		0			0
$259$	−5.90640e9	−	4.95606e9i	−1.31257	−	1.10138i
$260$	3.66094e9	−	2.11365e9i	0.801124	−	0.462529i
$261$		0			0
$262$	−1.50435e9	+	2.60562e9i	−0.319260	+	0.552975i
$263$	−1.00304e9	−	2.75584e9i	−0.209651	−	0.576011i	0.789644	−	0.613566i	$-0.210265\pi$
$263$	−1.00304e9	−	2.75584e9i	−0.209651	−	0.576011i	−0.999295	+	0.0375547i	$0.988043\pi$
$264$		0			0
$265$	−3.05331e9	+	2.56203e9i	−0.619139	+	0.519519i
$266$	5.14261e8	−	1.41292e9i	0.102720	−	0.282222i
$267$		0			0
$268$	−1.22847e9	+	6.96700e9i	−0.238136	+	1.35054i
$269$		−	4.43522e9i		−	0.847043i	−0.905886	−	0.423522i	$-0.860794\pi$
$269$		−	4.43522e9i		−	0.847043i	0.905886	−	0.423522i	$-0.139206\pi$
$270$		0			0
$271$	3.50202e9			0.649294			0.324647	−	0.945835i	$-0.394754\pi$
$271$	3.50202e9			0.649294			0.324647	+	0.945835i	$0.394754\pi$
$272$	5.96495e9	+	1.05178e9i	1.08976	+	0.192154i
$273$		0			0
$274$	8.17045e9	+	2.97380e9i	1.44958	+	0.527606i
$275$	5.51987e8	+	6.57833e8i	0.0965158	+	0.115023i
$276$		0			0
$277$	2.04456e9	−	7.44159e8i	0.347281	−	0.126400i	−0.162490	−	0.986710i	$-0.551952\pi$
$277$	2.04456e9	−	7.44159e8i	0.347281	−	0.126400i	0.509771	+	0.860310i	$0.329730\pi$
$278$	−7.28413e9	−	4.20549e9i	−1.21955	−	0.704105i
$279$		0			0
$280$	−5.52524e9	−	9.56999e9i	−0.898916	−	1.55697i
$281$	−2.18780e9	+	2.60731e9i	−0.350899	+	0.418185i	−0.912406	−	0.409287i	$-0.865777\pi$
$281$	−2.18780e9	+	2.60731e9i	−0.350899	+	0.418185i	0.561507	+	0.827472i	$0.310222\pi$
$282$		0			0
$283$	4.84520e8	+	2.74785e9i	0.0755381	+	0.428398i	0.999000	+	0.0447078i	$0.0142357\pi$
$283$	4.84520e8	+	2.74785e9i	0.0755381	+	0.428398i	−0.923462	+	0.383690i	$0.874653\pi$
$284$	−1.05222e10	+	1.85535e9i	−1.61746	+	0.285202i
$285$		0			0
$286$	7.23063e9	+	6.06722e9i	1.08072	+	0.906830i
$287$	2.96615e9	−	1.71251e9i	0.437185	−	0.252409i
$288$		0			0
$289$	5.32718e9	−	9.22695e9i	0.763671	−	1.32272i
$290$	2.29596e9	+	6.30809e9i	0.324617	+	0.891879i
$291$		0			0
$292$	−5.17843e9	+	4.34522e9i	−0.712306	+	0.597696i
$293$	2.69099e9	−	7.39343e9i	0.365125	−	1.00317i	−0.612065	−	0.790807i	$-0.709661\pi$
$293$	2.69099e9	−	7.39343e9i	0.365125	−	1.00317i	0.977190	−	0.212365i	$-0.0681167\pi$
$294$		0			0
$295$	2.30187e9	−	1.30545e10i	0.303943	−	1.72375i
$296$			1.76720e10i			2.30208i
$297$		0			0
$298$	−7.00120e9			−0.887784
$299$	3.62203e9	+	6.38662e8i	0.453177	+	0.0799073i
$300$		0			0
$301$	1.30320e9	+	4.74325e8i	0.158761	+	0.0577843i
$302$	−2.70972e9	−	3.22932e9i	−0.325759	−	0.388225i
$303$		0			0
$304$	−8.69967e8	+	3.16642e8i	−0.101861	+	0.0370744i
$305$	1.81111e9	+	1.04564e9i	0.209288	+	0.120833i
$306$		0			0
$307$	3.43939e9	+	5.95719e9i	0.387193	+	0.670638i	0.992071	−	0.125680i	$-0.0401113\pi$
$307$	3.43939e9	+	5.95719e9i	0.387193	+	0.670638i	−0.604878	+	0.796318i	$0.706778\pi$
$308$	2.19813e10	−	2.61963e10i	2.44259	−	2.91096i
$309$		0			0
$310$	−7.84796e7	−	4.45080e8i	−0.00849787	−	0.0481938i
$311$	1.02348e10	−	1.80468e9i	1.09406	−	0.192911i	0.402633	−	0.915362i	$-0.368095\pi$
$311$	1.02348e10	−	1.80468e9i	1.09406	−	0.192911i	0.691423	+	0.722450i	$0.256984\pi$
$312$		0			0
$313$	−2.97076e9	−	2.49276e9i	−0.309521	−	0.259719i	0.474773	−	0.880108i	$-0.342530\pi$
$313$	−2.97076e9	−	2.49276e9i	−0.309521	−	0.259719i	−0.784294	+	0.620389i	$0.786975\pi$
$314$	7.08331e9	−	4.08955e9i	0.728647	−	0.420685i
$315$		0			0
$316$	7.35350e9	−	1.27366e10i	0.737472	−	1.27734i
$317$	9.16844e8	+	2.51901e9i	0.0907943	+	0.249455i	0.976775	−	0.214266i	$-0.0687360\pi$
$317$	9.16844e8	+	2.51901e9i	0.0907943	+	0.249455i	−0.885981	+	0.463722i	$0.846514\pi$
$318$		0			0
$319$	−7.51602e9	+	6.30669e9i	−0.725813	+	0.609030i
$320$	4.75158e9	−	1.30549e10i	0.453146	−	1.24501i
$321$		0			0
$322$	3.53486e9	−	2.00472e10i	0.328813	−	1.86479i
$323$			2.69474e9i			0.247575i
$324$		0			0
$325$	4.43779e8			0.0397771
$326$	3.85749e9	+	6.80179e8i	0.341534	+	0.0602217i
$327$		0			0
$328$	−7.37676e9	−	2.68492e9i	−0.637339	−	0.231972i
$329$	−1.53173e10	−	1.82545e10i	−1.30737	−	1.55807i
$330$		0			0
$331$	1.18674e10	−	4.31938e9i	0.988653	−	0.359840i	0.203454	−	0.979084i	$-0.434783\pi$
$331$	1.18674e10	−	4.31938e9i	0.988653	−	0.359840i	0.785198	+	0.619244i	$0.212561\pi$
$332$	−2.58336e10	−	1.49150e10i	−2.12634	−	1.22764i
$333$		0			0
$334$	−1.32216e10	−	2.29005e10i	−1.06243	−	1.84018i
$335$	−6.10209e9	+	7.27219e9i	−0.484507	+	0.577412i
$336$		0			0
$337$	−3.62748e9	−	2.05725e10i	−0.281246	−	1.59502i	−0.718395	−	0.695635i	$-0.755123\pi$
$337$	−3.62748e9	−	2.05725e10i	−0.281246	−	1.59502i	0.437150	−	0.899389i	$-0.355988\pi$
$338$	−1.70660e10	+	3.00920e9i	−1.30757	+	0.230560i
$339$		0			0
$340$	3.21220e10	+	2.69536e10i	2.40374	+	2.01698i
$341$	5.72057e8	−	3.30277e8i	0.0423079	−	0.0244265i
$342$		0			0
$343$	−5.61080e9	+	9.71820e9i	−0.405367	+	0.702116i
$344$	−1.08716e9	−	2.98695e9i	−0.0776354	−	0.213301i
$345$		0			0
$346$	2.08898e10	−	1.75287e10i	1.45757	−	1.22305i
$347$	−2.51787e8	+	6.91779e8i	−0.0173666	+	0.0477144i	−0.948073	−	0.318053i	$-0.896971\pi$
$347$	−2.51787e8	+	6.91779e8i	−0.0173666	+	0.0477144i	0.930706	+	0.365767i	$0.119193\pi$
$348$		0			0
$349$	−2.30358e9	+	1.30643e10i	−0.155275	+	0.880609i	0.803259	+	0.595630i	$0.203098\pi$
$349$	−2.30358e9	+	1.30643e10i	−0.155275	+	0.880609i	−0.958534	+	0.284979i	$0.908014\pi$
$350$		−	2.45622e9i		−	0.163680i
$351$		0			0
$352$	9.19409e9			0.598878
$353$	8.76631e9	+	1.54574e9i	0.564571	+	0.0995490i	0.448647	−	0.893709i	$-0.351906\pi$
$353$	8.76631e9	+	1.54574e9i	0.564571	+	0.0995490i	0.115924	+	0.993258i	$0.463017\pi$
$354$		0			0
$355$	−1.34728e10	−	4.90371e9i	−0.848292	−	0.308753i
$356$	3.29960e10	+	3.93231e10i	2.05429	+	2.44820i
$357$		0			0
$358$	−2.24305e10	+	8.16404e9i	−1.36555	+	0.497019i
$359$	1.08215e10	+	6.24779e9i	0.651492	+	0.376139i	0.789028	−	0.614358i	$-0.210585\pi$
$359$	1.08215e10	+	6.24779e9i	0.651492	+	0.376139i	−0.137535	+	0.990497i	$0.543918\pi$
$360$		0			0
$361$	8.28584e9	+	1.43515e10i	0.487874	+	0.845022i
$362$	2.98597e10	−	3.55855e10i	1.73881	−	2.07223i
$363$		0			0
$364$	−3.06874e9	−	1.74037e10i	−0.174805	−	0.991371i
$365$	−8.93331e9	+	1.57518e9i	−0.503316	+	0.0887483i
$366$		0			0
$367$	4.76568e9	+	3.99888e9i	0.262700	+	0.220432i	0.764618	−	0.644483i	$-0.222928\pi$
$367$	4.76568e9	+	3.99888e9i	0.262700	+	0.220432i	−0.501918	+	0.864915i	$0.667372\pi$
$368$	−1.08547e10	+	6.26697e9i	−0.591871	+	0.341717i
$369$		0			0
$370$	−2.51048e10	+	4.34828e10i	−1.33952	+	2.32012i
$371$	5.69898e9	+	1.56578e10i	0.300816	+	0.826486i
$372$		0			0
$373$	−1.58533e10	+	1.33025e10i	−0.819002	+	0.687225i	−0.952738	−	0.303792i	$-0.901747\pi$
$373$	−1.58533e10	+	1.33025e10i	−0.819002	+	0.687225i	0.133736	+	0.991017i	$0.457303\pi$
$374$	−3.20229e10	+	8.79822e10i	−1.63672	+	4.49685i
$375$		0			0
$376$	−9.48427e9	+	5.37880e10i	−0.474518	+	2.69112i
$377$			5.07036e9i			0.251000i
$378$		0			0
$379$	−3.69202e9			−0.178940			−0.0894700	−	0.995990i	$-0.528517\pi$
$379$	−3.69202e9			−0.178940			−0.0894700	+	0.995990i	$0.528517\pi$
$380$	−6.31193e9	−	1.11296e9i	−0.302711	−	0.0533761i
$381$		0			0
$382$	−6.04896e10	−	2.20164e10i	−2.84071	−	1.03393i
$383$	−1.25353e10	−	1.49390e10i	−0.582558	−	0.694266i	0.391599	−	0.920136i	$-0.371922\pi$
$383$	−1.25353e10	−	1.49390e10i	−0.582558	−	0.694266i	−0.974157	+	0.225870i	$0.927478\pi$
$384$		0			0
$385$	4.31210e10	−	1.56947e10i	1.96266	−	0.714351i
$386$	2.02091e10	+	1.16677e10i	0.910326	+	0.525577i
$387$		0			0
$388$	7.77690e9	+	1.34700e10i	0.343147	+	0.594347i
$389$	9.38477e9	−	1.11843e10i	0.409850	−	0.488441i	−0.521147	−	0.853467i	$-0.674496\pi$
$389$	9.38477e9	−	1.11843e10i	0.409850	−	0.488441i	0.930997	+	0.365026i	$0.118940\pi$
$390$		0			0
$391$	6.33516e9	+	3.59285e10i	0.271051	+	1.53721i
$392$	−1.00826e10	+	1.77784e9i	−0.427002	+	0.0752921i
$393$		0			0
$394$	−1.59266e10	−	1.33640e10i	−0.660905	−	0.554565i
$395$	1.70912e10	−	9.86759e9i	0.702075	−	0.405343i
$396$		0			0
$397$	5.33817e9	−	9.24598e9i	0.214897	−	0.372213i	−0.738344	−	0.674425i	$-0.764392\pi$
$397$	5.33817e9	−	9.24598e9i	0.214897	−	0.372213i	0.953241	+	0.302212i	$0.0977251\pi$
$398$	3.13017e9	+	8.60007e9i	0.124749	+	0.342744i
$399$		0			0
$400$	−1.15853e9	+	9.72121e8i	−0.0452550	+	0.0379735i
$401$	2.37143e9	−	6.51546e9i	0.0917136	−	0.251981i	−0.885351	−	0.464923i	$-0.846082\pi$
$401$	2.37143e9	−	6.51546e9i	0.0917136	−	0.251981i	0.977065	+	0.212942i	$0.0683044\pi$
$402$		0			0
$403$	5.92766e7	−	3.36174e8i	0.00224731	−	0.0127451i
$404$			2.95811e10i			1.11042i
$405$		0			0
$406$	2.80634e10			1.03285
$407$	−7.22703e10	−	1.27432e10i	−2.63379	−	0.464409i
$408$		0			0
$409$	6.91538e9	+	2.51699e9i	0.247129	+	0.0899475i	0.462615	−	0.886559i	$-0.346911\pi$
$409$	6.91538e9	+	2.51699e9i	0.247129	+	0.0899475i	−0.215486	+	0.976507i	$0.569134\pi$
$410$	−1.43366e10	−	1.70857e10i	−0.507355	−	0.604642i
$411$		0			0
$412$	2.64610e10	−	9.63101e9i	0.918369	−	0.334259i
$413$	−4.79920e10	−	2.77082e10i	−1.64956	−	0.952374i
$414$		0			0
$415$	−2.00143e10	−	3.46658e10i	−0.674759	−	1.16872i
$416$	3.05408e9	−	3.63972e9i	0.101978	−	0.121533i
$417$		0			0
$418$	−2.48508e9	−	1.40936e10i	−0.0814021	−	0.461654i
$419$	1.43437e10	−	2.52917e9i	0.465376	−	0.0820583i	0.0639566	−	0.997953i	$-0.479628\pi$
$419$	1.43437e10	−	2.52917e9i	0.465376	−	0.0820583i	0.401419	+	0.915894i	$0.368517\pi$
$420$		0			0
$421$	−6.47420e9	−	5.43250e9i	−0.206090	−	0.172930i	0.533900	−	0.845547i	$-0.320726\pi$
$421$	−6.47420e9	−	5.43250e9i	−0.206090	−	0.172930i	−0.739991	+	0.672617i	$0.765170\pi$
$422$	6.53000e10	−	3.77010e10i	2.05903	−	1.18878i
$423$		0			0
$424$	1.90956e10	−	3.30745e10i	0.590839	−	1.02336i
$425$	1.50558e9	+	4.13656e9i	0.0461476	+	0.126789i
$426$		0			0
$427$	6.69723e9	−	5.61964e9i	0.201458	−	0.169043i
$428$	2.28835e10	−	6.28719e10i	0.681942	−	1.87362i
$429$		0			0
$430$	1.56824e9	−	8.89392e9i	0.0458710	−	0.260147i
$431$			3.49935e10i			1.01409i	0.861919	+	0.507047i	$0.169263\pi$
$431$			3.49935e10i			1.01409i	−0.861919	+	0.507047i	$0.830737\pi$
$432$		0			0
$433$	−5.36565e9			−0.152641			−0.0763205	−	0.997083i	$-0.524317\pi$
$433$	−5.36565e9			−0.152641			−0.0763205	+	0.997083i	$0.524317\pi$
$434$	−1.86066e9	−	3.28084e8i	−0.0524454	−	0.00924753i
$435$		0			0
$436$	7.51880e10	+	2.73662e10i	2.08067	+	0.757301i
$437$	−3.58440e9	−	4.27172e9i	−0.0982858	−	0.117133i
$438$		0			0
$439$	−4.02878e10	+	1.46636e10i	−1.08472	+	0.394804i	−0.821661	−	0.569977i	$-0.806952\pi$
$439$	−4.02878e10	+	1.46636e10i	−1.08472	+	0.394804i	−0.263055	+	0.964781i	$0.584730\pi$
$440$	−9.10858e10	−	5.25884e10i	−2.43019	−	1.40307i
$441$		0			0
$442$	2.41927e10	+	4.19029e10i	0.633862	+	1.09788i
$443$	−1.28620e10	+	1.53284e10i	−0.333960	+	0.397998i	−0.906726	−	0.421721i	$-0.861426\pi$
$443$	−1.28620e10	+	1.53284e10i	−0.333960	+	0.397998i	0.572766	+	0.819719i	$0.305871\pi$
$444$		0			0
$445$	1.19614e10	+	6.78363e10i	0.305029	+	1.72990i
$446$	3.40108e10	−	5.99702e9i	0.859563	−	0.151564i
$447$		0			0
$448$	−4.44906e10	−	3.73320e10i	−1.10448	−	0.926765i
$449$	−6.61592e10	+	3.81970e10i	−1.62781	+	0.939819i	−0.643070	+	0.765807i	$0.722340\pi$
$449$	−6.61592e10	+	3.81970e10i	−1.62781	+	0.939819i	−0.984744	+	0.174012i	$0.944327\pi$
$450$		0			0
$451$	1.62994e10	−	2.82314e10i	0.393972	−	0.682379i
$452$	5.99908e9	+	1.64823e10i	0.143725	+	0.394880i
$453$		0			0
$454$	8.97668e10	−	7.53233e10i	2.11297	−	1.77299i
$455$	8.11071e9	−	2.22840e10i	0.189240	−	0.519933i
$456$		0			0
$457$	−6.39906e9	+	3.62909e10i	−0.146707	+	0.832017i	0.819274	+	0.573403i	$0.194377\pi$
$457$	−6.39906e9	+	3.62909e10i	−0.146707	+	0.832017i	−0.965981	+	0.258614i	$0.916734\pi$
$458$			2.78066e10i			0.631955i
$459$		0			0
$460$	−8.67724e10			−1.93798
$461$	4.70462e10	+	8.29552e9i	1.04165	+	0.183671i	0.668201	−	0.743981i	$-0.267065\pi$
$461$	4.70462e10	+	8.29552e9i	1.04165	+	0.183671i	0.373447	+	0.927651i	$0.378176\pi$
$462$		0			0
$463$	1.13056e10	+	4.11492e9i	0.246021	+	0.0895442i	0.462087	−	0.886834i	$-0.347101\pi$
$463$	1.13056e10	+	4.11492e9i	0.246021	+	0.0895442i	−0.216067	+	0.976379i	$0.569323\pi$
$464$	−1.11069e10	−	1.32367e10i	−0.239619	−	0.285566i
$465$		0			0
$466$	−2.08714e10	+	7.59657e9i	−0.442596	+	0.161092i
$467$	7.32776e9	+	4.23068e9i	0.154065	+	0.0889494i	0.575051	−	0.818118i	$-0.304982\pi$
$467$	7.32776e9	+	4.23068e9i	0.154065	+	0.0889494i	−0.420986	+	0.907067i	$0.638316\pi$
$468$		0			0
$469$	1.98431e10	+	3.43692e10i	0.410127	+	0.710360i
$470$	−9.97473e10	+	1.18874e11i	−2.04414	+	2.43611i
$471$		0			0
$472$	2.20559e10	+	1.25085e11i	0.444383	+	2.52022i
$473$	1.29991e10	−	2.29210e9i	0.259699	−	0.0457919i
$474$		0			0
$475$	−5.15429e8	−	4.32496e8i	−0.0101250	−	0.00849587i
$476$	1.51813e11	−	8.76490e10i	2.95719	−	1.70734i
$477$		0			0
$478$	−3.77619e9	+	6.54056e9i	−0.0723341	+	0.125286i
$479$	2.41520e10	+	6.63571e10i	0.458787	+	1.26051i	0.926389	+	0.376568i	$0.122896\pi$
$479$	2.41520e10	+	6.63571e10i	0.458787	+	1.26051i	−0.467602	+	0.883939i	$0.654882\pi$
$480$		0			0
$481$	−2.90514e10	+	2.43770e10i	−0.542733	+	0.455407i
$482$	2.25208e10	−	6.18753e10i	0.417248	−	1.14638i
$483$		0			0
$484$	3.84613e10	−	2.18125e11i	0.700878	−	3.97488i
$485$			2.08715e10i			0.377213i
$486$		0			0
$487$	−1.28405e10			−0.228279			−0.114139	−	0.993465i	$-0.536411\pi$
$487$	−1.28405e10			−0.228279			−0.114139	+	0.993465i	$0.536411\pi$
$488$	−1.97338e10	−	3.47960e9i	−0.347961	−	0.0613549i
$489$		0			0
$490$	−2.73344e10	−	9.94889e9i	−0.474160	−	0.172580i
$491$	−2.22966e10	−	2.65720e10i	−0.383630	−	0.457192i	0.539327	−	0.842097i	$-0.318679\pi$
$491$	−2.22966e10	−	2.65720e10i	−0.383630	−	0.457192i	−0.922956	+	0.384905i	$0.874234\pi$
$492$		0			0
$493$	−4.72619e10	+	1.72019e10i	−0.800061	+	0.291199i
$494$	−6.40481e9	−	3.69782e9i	−0.107547	−	0.0620923i
$495$		0			0
$496$	5.81661e8	+	1.00747e9i	0.00961043	+	0.0166458i
$497$	−3.85273e10	+	4.59150e10i	−0.631455	+	0.752539i
$498$		0			0
$499$	9.51614e9	+	5.39687e10i	0.153482	+	0.870442i	0.960160	+	0.279450i	$0.0901522\pi$
$499$	9.51614e9	+	5.39687e10i	0.153482	+	0.870442i	−0.806678	+	0.590992i	$0.798737\pi$
$500$	1.11177e11	−	1.96035e10i	1.77883	−	0.313656i
$501$		0			0
$502$	−1.25387e11	−	1.05212e11i	−1.97441	−	1.65673i
$503$	1.70347e10	−	9.83496e9i	0.266110	−	0.153639i	−0.361009	−	0.932563i	$-0.617567\pi$
$503$	1.70347e10	−	9.83496e9i	0.266110	−	0.153639i	0.627119	+	0.778924i	$0.284234\pi$
$504$		0			0
$505$	−1.98473e10	+	3.43765e10i	−0.305166	+	0.528563i
$506$	−6.62664e10	−	1.82065e11i	−1.01086	−	2.77732i
$507$		0			0
$508$	1.24308e11	−	1.04307e11i	1.86657	−	1.56624i
$509$	−2.37969e10	+	6.53814e10i	−0.354527	+	0.974055i	0.626370	+	0.779526i	$0.284540\pi$
$509$	−2.37969e10	+	6.53814e10i	−0.354527	+	0.974055i	−0.980897	+	0.194529i	$0.937682\pi$
$510$		0			0
$511$	−6.58505e9	+	3.73457e10i	−0.0965774	+	0.547718i
$512$			8.90340e10i			1.29562i
$513$		0			0
$514$	9.35285e10			1.33996
$515$	3.72125e10	+	6.56157e9i	0.529005	+	0.0932779i
$516$		0			0
$517$	−2.13128e11	−	7.75723e10i	−2.98318	−	1.08579i
$518$	1.34922e11	+	1.60793e11i	1.87397	+	2.23331i
$519$		0			0
$520$	−5.10753e10	+	1.85899e10i	−0.698550	+	0.254251i
$521$	4.30417e10	+	2.48501e10i	0.584169	+	0.337270i	0.762788	−	0.646648i	$-0.223830\pi$
$521$	4.30417e10	+	2.48501e10i	0.584169	+	0.337270i	−0.178620	+	0.983918i	$0.557163\pi$
$522$		0			0
$523$	−3.84435e10	−	6.65861e10i	−0.513826	−	0.889973i	−0.999871	−	0.0160395i	$-0.994894\pi$
$523$	−3.84435e10	−	6.65861e10i	−0.513826	−	0.889973i	0.486045	−	0.873934i	$-0.338439\pi$
$524$	3.44631e10	−	4.10715e10i	0.457119	−	0.544773i
$525$		0			0
$526$	1.38638e10	+	7.86257e10i	0.181109	+	1.02712i
$527$	3.33466e9	−	5.87990e8i	0.0432323	−	0.00762303i
$528$		0			0
$529$	2.15692e9	+	1.80987e9i	0.0275431	+	0.0231114i
$530$	9.39709e10	−	5.42541e10i	1.19094	−	0.687590i
$531$		0			0
$532$	−1.33970e10	+	2.32043e10i	−0.167248	+	0.289683i
$533$	−5.76179e9	−	1.58304e10i	−0.0713919	−	0.196148i
$534$		0			0
$535$	6.87768e10	−	5.77106e10i	0.839512	−	0.704434i
$536$	3.11106e10	−	8.54757e10i	0.376920	−	1.03558i
$537$		0			0
$538$	−2.09667e10	+	1.18908e11i	−0.250266	+	1.41933i
$539$		−	4.25153e10i		−	0.503721i
$540$		0			0
$541$	−1.02774e11			−1.19976			−0.599879	−	0.800091i	$-0.704785\pi$
$541$	−1.02774e11			−1.19976			−0.599879	+	0.800091i	$0.704785\pi$
$542$	−9.38891e10	−	1.65552e10i	−1.08797	−	0.191839i
$543$		0			0
$544$	4.42880e10	+	1.61195e10i	0.505697	+	0.184059i
$545$	6.90156e10	+	8.22496e10i	0.782278	+	0.932283i
$546$		0			0
$547$	9.52616e10	−	3.46724e10i	1.06407	−	0.387288i	0.250112	−	0.968217i	$-0.419533\pi$
$547$	9.52616e10	−	3.46724e10i	1.06407	−	0.387288i	0.813954	+	0.580929i	$0.197310\pi$
$548$	−1.34183e11	−	7.74706e10i	−1.48791	−	0.859042i
$549$		0			0
$550$	−1.16890e10	−	2.02459e10i	−0.127740	−	0.221252i
$551$	4.94145e9	−	5.88899e9i	0.0536102	−	0.0638902i
$552$		0			0
$553$	−1.43265e10	−	8.12494e10i	−0.153193	−	0.868800i
$554$	−5.83325e10	+	1.02856e10i	−0.619258	+	0.109192i
$555$		0			0
$556$	1.14817e11	+	9.63432e10i	1.20146	+	1.00814i
$557$	−7.89315e10	+	4.55712e10i	−0.820030	+	0.473445i	−0.850427	−	0.526093i	$-0.823656\pi$
$557$	−7.89315e10	+	4.55712e10i	−0.820030	+	0.473445i	0.0303967	+	0.999538i	$0.490323\pi$
$558$		0			0
$559$	3.41066e9	−	5.90743e9i	0.0349294	−	0.0604994i
$560$	2.76405e10	+	7.59416e10i	0.281056	+	0.772196i
$561$		0			0
$562$	7.09804e10	−	5.95597e10i	0.711530	−	0.597045i
$563$	4.02419e10	−	1.10564e11i	0.400539	−	1.10047i	−0.561481	−	0.827490i	$-0.689768\pi$
$563$	4.02419e10	−	1.10564e11i	0.400539	−	1.10047i	0.962019	−	0.272981i	$-0.0880096\pi$
$564$		0			0
$565$	−4.08715e9	+	2.31794e10i	−0.0401076	+	0.227462i
$566$		−	7.59603e10i		−	0.740152i
$567$		0			0
$568$	1.37378e11			1.31985
$569$	7.37095e10	+	1.29970e10i	0.703193	+	0.123992i	0.513801	−	0.857910i	$-0.328237\pi$
$569$	7.37095e10	+	1.29970e10i	0.703193	+	0.123992i	0.189392	+	0.981901i	$0.439348\pi$
$570$		0			0
$571$	8.18831e10	+	2.98030e10i	0.770282	+	0.280360i	0.697115	−	0.716960i	$-0.254467\pi$
$571$	8.18831e10	+	2.98030e10i	0.770282	+	0.280360i	0.0731679	+	0.997320i	$0.476689\pi$
$572$	−1.08118e11	−	1.28850e11i	−1.00998	−	1.20365i
$573$		0			0
$574$	−8.76180e10	+	3.18903e10i	−0.807134	+	0.293773i
$575$	−7.88889e9	−	4.55465e9i	−0.0721680	−	0.0416662i
$576$		0			0
$577$	1.29325e10	+	2.23998e10i	0.116675	+	0.202088i	0.918448	−	0.395541i	$-0.129443\pi$
$577$	1.29325e10	+	2.23998e10i	0.116675	+	0.202088i	−0.801773	+	0.597629i	$0.796110\pi$
$578$	−1.86440e11	+	2.22191e11i	−1.67043	+	1.99074i
$579$		0			0
$580$	−2.07725e10	−	1.17807e11i	−0.183560	−	1.04102i
$581$	−1.64797e11	+	2.90582e10i	−1.44626	+	0.255014i
$582$		0			0
$583$	1.21489e11	+	1.01942e11i	1.05163	+	0.882425i
$584$	7.52726e10	−	4.34587e10i	0.647121	−	0.373616i
$585$		0			0
$586$	−1.07097e11	+	1.85497e11i	−0.908207	+	1.57306i
$587$	−6.12900e10	−	1.68393e11i	−0.516222	−	1.41831i	−0.874651	−	0.484753i	$-0.838910\pi$
$587$	−6.12900e10	−	1.68393e11i	−0.516222	−	1.41831i	0.358429	−	0.933557i	$-0.383313\pi$
$588$		0			0
$589$	−3.96475e8	+	3.32682e8i	−0.00329423	+	0.00276419i
$590$	−1.23426e11	+	3.39110e11i	−1.01859	+	2.79855i
$591$		0			0
$592$	2.24424e10	−	1.27277e11i	0.182719	−	1.03625i
$593$		−	8.12831e10i		−	0.657327i	−0.944447	−	0.328663i	$-0.893402\pi$
$593$		−	8.12831e10i		−	0.657327i	0.944447	−	0.328663i	$-0.106598\pi$
$594$		0			0
$595$	2.35231e11			1.87684
$596$	1.22866e11	+	2.16645e10i	0.973746	+	0.171698i
$597$		0			0
$598$	−9.40875e10	−	3.42451e10i	−0.735745	−	0.267789i
$599$	−2.84492e10	−	3.39045e10i	−0.220985	−	0.263360i	0.644149	−	0.764900i	$-0.277212\pi$
$599$	−2.84492e10	−	3.39045e10i	−0.220985	−	0.263360i	−0.865135	+	0.501540i	$0.832767\pi$
$600$		0			0
$601$	1.75916e11	−	6.40282e10i	1.34837	−	0.490765i	0.435928	−	0.899981i	$-0.356420\pi$
$601$	1.75916e11	−	6.40282e10i	1.34837	−	0.490765i	0.912437	+	0.409217i	$0.134198\pi$
$602$	−3.26964e10	−	1.88773e10i	−0.248951	−	0.143732i
$603$		0			0
$604$	3.75608e10	+	6.50571e10i	0.282219	+	0.488818i
$605$	1.91046e11	−	2.27680e11i	1.42599	−	1.69943i
$606$		0			0
$607$	−1.06371e10	−	6.03260e10i	−0.0783553	−	0.444375i	−0.998594	−	0.0530166i	$-0.983116\pi$
$607$	−1.06371e10	−	6.03260e10i	−0.0783553	−	0.444375i	0.920238	−	0.391358i	$-0.127995\pi$
$608$	−7.09436e9	+	1.25093e9i	−0.0519157	+	0.00915414i
$609$		0			0
$610$	−4.36127e10	−	3.65954e10i	−0.314987	−	0.264306i
$611$	−1.01506e11	+	5.86044e10i	−0.728326	+	0.420499i
$612$		0			0
$613$	8.37687e10	−	1.45092e11i	0.593253	−	1.02754i	−0.400538	−	0.916280i	$-0.631177\pi$
$613$	8.37687e10	−	1.45092e11i	0.593253	−	1.02754i	0.993791	−	0.111264i	$-0.0354900\pi$
$614$	−6.40484e10	−	1.75971e11i	−0.450645	−	1.23814i
$615$		0			0
$616$	−3.36823e11	+	2.82628e11i	−2.33926	+	1.96287i
$617$	1.30585e10	−	3.58779e10i	0.0901058	−	0.247564i	−0.886451	−	0.462822i	$-0.846837\pi$
$617$	1.30585e10	−	3.58779e10i	0.0901058	−	0.247564i	0.976557	+	0.215258i	$0.0690593\pi$
$618$		0			0
$619$	2.06765e10	−	1.17262e11i	0.140836	−	0.798723i	−0.829780	−	0.558091i	$-0.811534\pi$
$619$	2.06765e10	−	1.17262e11i	0.140836	−	0.798723i	0.970616	−	0.240632i	$-0.0773548\pi$
$620$			8.05367e9i			0.0545038i
$621$		0			0
$622$	−2.82927e11			−1.89022
$623$	2.83589e11	+	5.00044e10i	1.88251	+	0.331937i
$624$		0			0
$625$	1.54522e11	+	5.62415e10i	1.01268	+	0.368584i
$626$	6.78619e10	+	8.08747e10i	0.441905	+	0.526642i
$627$		0			0
$628$	−1.36961e11	+	4.98499e10i	−0.880561	+	0.320498i
$629$	−3.25784e11	−	1.88092e11i	−2.08127	−	1.20162i
$630$		0			0
$631$	−8.71629e10	−	1.50971e11i	−0.549812	−	0.952302i	−0.998287	−	0.0585068i	$-0.981366\pi$
$631$	−8.71629e10	−	1.50971e11i	−0.549812	−	0.952302i	0.448475	−	0.893795i	$-0.351967\pi$
$632$	−1.21550e11	+	1.44857e11i	−0.761878	+	0.907971i
$633$		0			0
$634$	−1.26724e10	−	7.18688e10i	−0.0784336	−	0.444819i
$635$	2.14444e11	−	3.78123e10i	1.31892	−	0.232562i
$636$		0			0
$637$	−1.68308e10	−	1.41227e10i	−0.102222	−	0.0857747i
$638$	2.31318e11	−	1.33552e11i	1.39613	−	0.806058i
$639$		0			0
$640$	−1.59527e11	+	2.76310e11i	−0.950858	+	1.64693i
$641$	1.11255e11	+	3.05669e11i	0.659001	+	1.81059i	0.581421	+	0.813603i	$0.302497\pi$
$641$	1.11255e11	+	3.05669e11i	0.659001	+	1.81059i	0.0775801	+	0.996986i	$0.475281\pi$
$642$		0			0
$643$	−8.32132e10	+	6.98242e10i	−0.486798	+	0.408472i	−0.852877	−	0.522112i	$-0.825144\pi$
$643$	−8.32132e10	+	6.98242e10i	−0.486798	+	0.408472i	0.366079	+	0.930584i	$0.380700\pi$
$644$	−1.24068e11	+	3.40875e11i	−0.721303	+	1.98176i
$645$		0			0
$646$	1.27389e10	−	7.22460e10i	0.0731480	−	0.414843i
$647$			2.13682e11i			1.21941i	0.792628	+	0.609705i	$0.208712\pi$
$647$			2.13682e11i			1.21941i	−0.792628	+	0.609705i	$0.791288\pi$
$648$		0			0
$649$	−5.27445e11			−2.97302
$650$	−1.18977e10	−	2.09789e9i	−0.0666515	−	0.0117524i
$651$		0			0
$652$	−6.55913e10	−	2.38733e10i	−0.362957	−	0.132106i
$653$	4.43881e10	+	5.28997e10i	0.244126	+	0.290938i	0.874169	−	0.485623i	$-0.161407\pi$
$653$	4.43881e10	+	5.28997e10i	0.244126	+	0.290938i	−0.630043	+	0.776560i	$0.716963\pi$
$654$		0			0
$655$	6.76067e10	−	2.46068e10i	0.367303	−	0.133687i
$656$	4.97191e10	+	2.87053e10i	0.268478	+	0.155006i
$657$		0			0
$658$	3.24363e11	+	5.61813e11i	1.73033	+	2.99701i
$659$	2.14251e11	−	2.55335e11i	1.13601	−	1.35384i	0.209395	−	0.977831i	$-0.432851\pi$
$659$	2.14251e11	−	2.55335e11i	1.13601	−	1.35384i	0.926615	−	0.376012i	$-0.122705\pi$
$660$		0			0
$661$	1.26287e10	+	7.16211e10i	0.0661537	+	0.375176i	0.999853	+	0.0171192i	$0.00544949\pi$
$661$	1.26287e10	+	7.16211e10i	0.0661537	+	0.375176i	−0.933700	+	0.358057i	$0.883439\pi$
$662$	−3.38584e11	+	5.97015e10i	−1.76293	+	0.310852i
$663$		0			0
$664$	2.93813e11	+	2.46538e11i	1.51147	+	1.26827i
$665$	−3.11377e10	+	1.79773e10i	−0.159221	+	0.0919261i
$666$		0			0
$667$	5.20388e10	−	9.01339e10i	0.262920	−	0.455391i
$668$	1.61166e11	+	4.42800e11i	0.809409	+	2.22383i
$669$		0			0
$670$	1.97975e11	−	1.66121e11i	0.982452	−	0.824375i
$671$	2.84598e10	−	7.81927e10i	0.140392	−	0.385723i
$672$		0			0
$673$	−5.91593e10	+	3.35509e11i	−0.288378	+	1.63548i	0.404584	+	0.914501i	$0.367416\pi$
$673$	−5.91593e10	+	3.35509e11i	−0.288378	+	1.63548i	−0.692962	+	0.720974i	$0.743695\pi$
$674$			5.68696e11i			2.75576i
$675$		0			0
$676$	3.08807e11			1.47877
$677$	−2.21182e11	−	3.90003e10i	−1.05292	−	0.185658i	−0.379706	−	0.925107i	$-0.623975\pi$
$677$	−2.21182e11	−	3.90003e10i	−1.05292	−	0.185658i	−0.673212	+	0.739449i	$0.735086\pi$
$678$		0			0
$679$	8.19912e10	+	2.98424e10i	0.385734	+	0.140396i
$680$	−3.46560e11	−	4.13015e11i	−1.62085	−	1.93166i
$681$		0			0
$682$	−1.68982e10	+	6.15043e9i	−0.0781092	+	0.0284294i
$683$	−2.40997e11	−	1.39140e11i	−1.10746	−	0.639393i	−0.169290	−	0.985566i	$-0.554148\pi$
$683$	−2.40997e11	−	1.39140e11i	−1.10746	−	0.639393i	−0.938171	+	0.346173i	$0.887481\pi$
$684$		0			0
$685$	−1.03957e11	−	1.80059e11i	−0.472163	−	0.817810i
$686$	1.96367e11	−	2.34021e11i	0.886689	−	1.05671i
$687$		0			0
$688$	4.03668e9	+	2.28932e10i	0.0180165	+	0.102177i
$689$	8.07125e10	−	1.42318e10i	0.358149	−	0.0631513i
$690$		0			0
$691$	−5.47166e9	−	4.59127e9i	−0.0239998	−	0.0201382i	0.630709	−	0.776020i	$-0.282764\pi$
$691$	−5.47166e9	−	4.59127e9i	−0.0239998	−	0.0201382i	−0.654709	+	0.755881i	$0.727209\pi$
$692$	−4.20842e11	+	2.42973e11i	−1.83525	+	1.05958i
$693$		0			0
$694$	1.00207e10	−	1.73563e10i	0.0431975	−	0.0748203i
$695$	6.87896e10	+	1.88998e11i	0.294838	+	0.810061i
$696$		0			0
$697$	1.28011e11	−	1.07414e11i	0.542395	−	0.455123i
$698$	1.23518e11	−	3.39363e11i	0.520365	−	1.42969i
$699$		0			0
$700$	−7.60055e9	+	4.31049e10i	−0.0316558	+	0.179529i
$701$		−	2.37125e11i		−	0.981988i	−0.871163	−	0.490994i	$-0.836634\pi$
$701$		−	2.37125e11i		−	0.981988i	0.871163	−	0.490994i	$-0.163366\pi$
$702$		0			0
$703$	5.74991e10			0.235418
$704$	−5.44383e11	−	9.59894e10i	−2.21623	−	0.390780i
$705$		0			0
$706$	−2.27718e11	−	8.28824e10i	−0.916596	−	0.333614i
$707$	1.06666e11	+	1.27120e11i	0.426923	+	0.508787i
$708$		0			0
$709$	2.44758e11	−	8.90848e10i	0.968619	−	0.352548i	0.191213	−	0.981548i	$-0.438758\pi$
$709$	2.44758e11	−	8.90848e10i	0.968619	−	0.352548i	0.777405	+	0.629000i	$0.216536\pi$
$710$	3.38025e11	+	1.95159e11i	1.33019	+	0.767988i
$711$		0			0
$712$	−3.30009e11	−	5.71592e11i	−1.28412	−	2.22416i
$713$	−4.50401e9	+	5.36767e9i	−0.0174278	+	0.0207696i
$714$		0			0
$715$	−3.91937e10	−	2.22279e11i	−0.149966	−	0.850499i
$716$	4.18901e11	−	7.38636e10i	1.59390	−	0.281047i
$717$		0			0
$718$	−2.60589e11	−	2.18660e11i	−0.980523	−	0.822757i
$719$	1.56748e11	−	9.04986e10i	0.586526	−	0.338631i	−0.177197	−	0.984175i	$-0.556703\pi$
$719$	1.56748e11	−	9.04986e10i	0.586526	−	0.338631i	0.763723	+	0.645545i	$0.223370\pi$
$720$		0			0
$721$	7.89833e10	−	1.36803e11i	0.292277	−	0.506238i
$722$	−1.54299e11	−	4.23933e11i	−0.567825	−	1.56009i
$723$		0			0
$724$	−6.34132e11	+	5.32100e11i	−2.30794	+	1.93659i
$725$	4.29511e9	−	1.18007e10i	0.0155461	−	0.0427127i
$726$		0			0
$727$	−5.51965e10	+	3.13035e11i	−0.197594	+	1.12061i	0.711082	+	0.703109i	$0.248206\pi$
$727$	−5.51965e10	+	3.13035e11i	−0.197594	+	1.12061i	−0.908676	+	0.417502i	$0.862906\pi$
$728$			2.27223e11i			0.808960i
$729$		0			0
$730$	2.46949e11			0.869591
$731$	6.66356e10	+	1.17496e10i	0.233365	+	0.0411486i
$732$		0			0
$733$	3.61219e11	+	1.31473e11i	1.25128	+	0.455429i	0.880834	−	0.473425i	$-0.156983\pi$
$733$	3.61219e11	+	1.31473e11i	1.25128	+	0.455429i	0.370446	+	0.928854i	$0.379205\pi$
$734$	−1.08864e11	−	1.29739e11i	−0.375059	−	0.446978i
$735$		0			0
$736$	−9.16470e10	+	3.33568e10i	−0.312325	+	0.113677i
$737$	3.27121e11	+	1.88864e11i	1.10876	+	0.640145i
$738$		0			0
$739$	−1.69671e11	−	2.93878e11i	−0.568891	−	0.985349i	−0.996676	−	0.0814679i	$-0.974039\pi$
$739$	−1.69671e11	−	2.93878e11i	−0.568891	−	0.985349i	0.427785	−	0.903881i	$-0.359294\pi$
$740$	5.75123e11	−	6.85405e11i	1.91794	−	2.28571i
$741$		0			0
$742$	−7.87700e10	−	4.46727e11i	−0.259863	−	1.47376i
$743$	1.09007e11	−	1.92209e10i	0.357685	−	0.0630695i	0.00808165	−	0.999967i	$-0.497428\pi$
$743$	1.09007e11	−	1.92209e10i	0.357685	−	0.0630695i	0.349603	+	0.936898i	$0.386316\pi$
$744$		0			0
$745$	1.28248e11	+	1.07613e11i	0.416318	+	0.349332i
$746$	4.87913e11	−	2.81697e11i	1.57539	−	0.909550i
$747$		0			0
$748$	8.34230e11	−	1.44493e12i	2.66489	−	4.61573i
$749$	−1.28371e11	−	3.52697e11i	−0.407887	−	1.12066i
$750$		0			0
$751$	−1.68463e11	+	1.41357e11i	−0.529596	+	0.444384i	−0.867962	−	0.496631i	$-0.834570\pi$
$751$	−1.68463e11	+	1.41357e11i	−0.529596	+	0.444384i	0.338366	+	0.941015i	$0.390126\pi$
$752$	1.36615e11	−	3.75347e11i	0.427196	−	1.17371i
$753$		0			0
$754$	2.39692e10	−	1.35936e11i	0.0741598	−	0.420581i
$755$			1.00805e11i			0.310237i
$756$		0			0
$757$	1.98033e11			0.603053			0.301526	−	0.953458i	$-0.402504\pi$
$757$	1.98033e11			0.603053			0.301526	+	0.953458i	$0.402504\pi$
$758$	9.89831e10	+	1.74534e10i	0.299836	+	0.0528692i
$759$		0			0
$760$	7.74389e10	+	2.81854e10i	0.232116	+	0.0844832i
$761$	−1.48821e11	−	1.77358e11i	−0.443737	−	0.528826i	0.497096	−	0.867696i	$-0.334400\pi$
$761$	−1.48821e11	−	1.77358e11i	−0.443737	−	0.528826i	−0.940833	+	0.338870i	$0.889955\pi$
$762$		0			0
$763$	4.21787e11	−	1.53518e11i	1.24450	−	0.452961i
$764$	9.93419e11	+	5.73551e11i	2.91581	+	1.68344i
$765$		0			0
$766$	2.65450e11	+	4.59772e11i	0.771023	+	1.33545i
$767$	−1.75206e11	+	2.08802e11i	−0.506253	+	0.603329i
$768$		0			0
$769$	−2.93676e10	−	1.66552e11i	−0.0839774	−	0.476260i	−0.997573	−	0.0696346i	$-0.977817\pi$
$769$	−2.93676e10	−	1.66552e11i	−0.0839774	−	0.476260i	0.913595	−	0.406625i	$-0.133294\pi$
$770$	−1.23027e12	+	2.16929e11i	−3.49975	+	0.617099i
$771$		0			0
$772$	−3.18549e11	−	2.67295e11i	−0.896824	−	0.752525i
$773$	−1.87386e11	+	1.08187e11i	−0.524829	+	0.303010i	−0.738908	−	0.673806i	$-0.764658\pi$
$773$	−1.87386e11	+	1.08187e11i	−0.524829	+	0.303010i	0.214079	+	0.976816i	$0.431325\pi$
$774$		0			0
$775$	−4.22734e8	+	7.32197e8i	−0.00117182	+	0.00202965i
$776$	−6.83991e10	−	1.87925e11i	−0.188627	−	0.518248i
$777$		0			0
$778$	−3.04478e11	+	2.55487e11i	−0.831069	+	0.697350i
$779$	−8.73587e9	+	2.40016e10i	−0.0237223	+	0.0651764i
$780$		0			0
$781$	−9.90627e10	+	5.61812e11i	−0.266260	+	1.51004i
$782$		−	9.93191e11i		−	2.65586i
$783$		0			0
$784$	7.48749e10			0.198186
$785$	−1.92611e11	−	3.39625e10i	−0.507227	−	0.0894378i
$786$		0			0
$787$	−4.22636e11	−	1.53827e11i	−1.10171	−	0.400990i	−0.273765	−	0.961797i	$-0.588269\pi$
$787$	−4.22636e11	−	1.53827e11i	−1.10171	−	0.400990i	−0.827947	+	0.560807i	$0.810491\pi$
$788$	2.38147e11	+	2.83812e11i	0.617646	+	0.736082i
$789$		0			0
$790$	−5.04861e11	+	1.83754e11i	−1.29618	+	0.471769i
$791$	8.52136e10	+	4.91981e10i	0.217672	+	0.125673i
$792$		0			0
$793$	−2.15008e10	−	3.72405e10i	−0.0543704	−	0.0941722i
$794$	−1.86825e11	+	2.22649e11i	−0.470060	+	0.560196i
$795$		0			0
$796$	−2.83200e10	−	1.60611e11i	−0.0705409	−	0.400058i
$797$	2.22560e11	−	3.92432e10i	0.551586	−	0.0972594i	0.109093	−	0.994032i	$-0.465205\pi$
$797$	2.22560e11	−	3.92432e10i	0.551586	−	0.0972594i	0.442493	+	0.896772i	$0.354094\pi$
$798$		0			0
$799$	−8.90637e11	−	7.47333e11i	−2.18531	−	1.83369i
$800$	−1.01913e10	+	5.88394e9i	−0.0248810	+	0.0143651i
$801$		0			0
$802$	−9.43789e10	+	1.63469e11i	−0.228127	+	0.395128i
$803$	1.23447e11	+	3.39167e11i	0.296905	+	0.815740i
$804$		0			0
$805$	−3.72890e11	+	3.12892e11i	−0.887967	+	0.745093i
$806$	−3.17841e9	+	8.73261e9i	−0.00753130	+	0.0206921i
$807$		0			0
$808$	6.60461e10	−	3.74566e11i	0.154954	−	0.878786i
$809$			1.85538e11i			0.433151i	0.976266	+	0.216576i	$0.0694888\pi$
$809$			1.85538e11i			0.433151i	−0.976266	+	0.216576i	$0.930511\pi$
$810$		0			0
$811$	8.26069e11			1.90956			0.954779	−	0.297318i	$-0.0960920\pi$
$811$	8.26069e11			1.90956			0.954779	+	0.297318i	$0.0960920\pi$
$812$	−4.92491e11	−	8.68394e10i	−1.13285	−	0.199753i
$813$		0			0
$814$	1.87732e12	+	6.83290e11i	4.27604	+	1.55635i
$815$	−6.02067e10	−	7.17515e10i	−0.136463	−	0.162630i
$816$		0			0
$817$	−9.71856e9	+	3.53727e9i	−0.0218129	+	0.00793925i
$818$	−1.73503e11	−	1.00172e11i	−0.387519	−	0.223734i
$819$		0			0
$820$	1.98727e11	+	3.44205e11i	0.439543	+	0.761311i
$821$	−4.30696e11	+	5.13284e11i	−0.947978	+	1.12976i	0.0434434	+	0.999056i	$0.486167\pi$
$821$	−4.30696e11	+	5.13284e11i	−0.947978	+	1.12976i	−0.991422	+	0.130701i	$0.958277\pi$
$822$		0			0
$823$	2.06496e10	+	1.17110e11i	0.0450104	+	0.255267i	0.999007	−	0.0445503i	$-0.0141855\pi$
$823$	2.06496e10	+	1.17110e11i	0.0450104	+	0.255267i	−0.953997	+	0.299817i	$0.903074\pi$
$824$	−3.56561e11	+	6.28713e10i	−0.773437	+	0.136378i
$825$		0			0
$826$	1.15568e12	+	9.69730e11i	2.48266	+	2.08320i
$827$	−6.41755e11	+	3.70518e11i	−1.37198	+	0.792112i	−0.991177	−	0.132544i	$-0.957685\pi$
$827$	−6.41755e11	+	3.70518e11i	−1.37198	+	0.792112i	−0.380802	+	0.924657i	$0.624352\pi$
$828$		0			0
$829$	−4.31016e11	+	7.46541e11i	−0.912588	+	1.58065i	−0.102194	+	0.994764i	$0.532586\pi$
$829$	−4.31016e11	+	7.46541e11i	−0.912588	+	1.58065i	−0.810394	+	0.585885i	$0.800747\pi$
$830$	3.72707e11	+	1.02401e12i	0.785336	+	2.15769i
$831$		0			0
$832$	−2.18832e11	+	1.83622e11i	−0.456687	+	0.383206i
$833$	7.45397e10	−	2.04796e11i	0.154813	−	0.425346i
$834$		0			0
$835$	−1.09802e11	+	6.22717e11i	−0.225873	+	1.28099i
$836$			2.55022e11i			0.522099i
$837$		0			0
$838$	−3.96510e11			−0.804040
$839$	5.92625e11	+	1.04496e11i	1.19600	+	0.210888i	0.735970	−	0.677014i	$-0.236726\pi$
$839$	5.92625e11	+	1.04496e11i	1.19600	+	0.210888i	0.460033	+	0.887902i	$0.347838\pi$
$840$		0			0
$841$	−3.35250e11	−	1.22021e11i	−0.670169	−	0.243922i
$842$	1.47892e11	+	1.76251e11i	0.294236	+	0.350657i
$843$		0			0
$844$	−1.26263e12	+	4.59559e11i	−2.48832	+	0.905673i
$845$	3.58868e11	+	2.07193e11i	0.703896	+	0.406394i
$846$		0			0
$847$	−6.21253e11	−	1.07604e12i	−1.20708	−	2.09072i
$848$	−1.79533e11	+	2.13959e11i	−0.347184	+	0.413758i
$849$		0			0
$850$	−2.08098e10	−	1.18018e11i	−0.0398651	−	0.226086i
$851$	7.66626e11	−	1.35177e11i	1.46172	−	0.257741i
$852$		0			0
$853$	−1.72828e11	−	1.45020e11i	−0.326450	−	0.273924i	0.464801	−	0.885415i	$-0.346126\pi$
$853$	−1.72828e11	−	1.45020e11i	−0.326450	−	0.273924i	−0.791252	+	0.611491i	$0.790570\pi$
$854$	−2.06119e11	+	1.19003e11i	−0.387512	+	0.223730i
$855$		0			0
$856$	−4.30134e11	+	7.45013e11i	−0.801140	+	1.38761i
$857$	−1.98117e11	−	5.44321e11i	−0.367280	−	1.00909i	−0.976391	−	0.216009i	$-0.930696\pi$
$857$	−1.98117e11	−	5.44321e11i	−0.367280	−	1.00909i	0.609111	−	0.793085i	$-0.291526\pi$
$858$		0			0
$859$	3.31406e11	−	2.78083e11i	0.608679	−	0.510742i	−0.285543	−	0.958366i	$-0.592174\pi$
$859$	3.31406e11	−	2.78083e11i	0.608679	−	0.510742i	0.894222	+	0.447624i	$0.147730\pi$
$860$	−5.50428e10	+	1.51229e11i	−0.100625	+	0.276465i
$861$		0			0
$862$	1.65426e11	−	9.38175e11i	0.299622	−	1.69924i
$863$			7.04378e11i			1.26988i	0.772562	+	0.634940i	$0.218975\pi$
$863$			7.04378e11i			1.26988i	−0.772562	+	0.634940i	$0.781025\pi$
$864$		0			0
$865$	−6.52086e11			−1.16477
$866$	1.43853e11	+	2.53652e10i	0.255769	+	0.0450990i
$867$		0			0
$868$	3.16379e10	+	1.15152e10i	0.0557350	+	0.0202859i
$869$	−5.04749e11	−	6.01536e11i	−0.885108	−	1.05483i
$870$		0			0
$871$	1.83429e11	−	6.67628e10i	0.318710	−	0.116001i
$872$	−8.90955e11	−	5.14393e11i	−1.54095	−	0.889670i
$873$		0			0
$874$	7.59040e10	+	1.31470e11i	0.130082	+	0.225309i
$875$	4.07076e11	−	4.85135e11i	0.694454	−	0.827618i
$876$		0			0
$877$	7.82513e10	+	4.43785e11i	0.132280	+	0.750196i	0.976715	+	0.214539i	$0.0688249\pi$
$877$	7.82513e10	+	4.43785e11i	0.132280	+	0.750196i	−0.844436	+	0.535657i	$0.820064\pi$
$878$	1.14944e12	−	2.02677e11i	1.93422	−	0.341056i
$879$		0			0
$880$	5.89233e11	+	4.94425e11i	0.982554	+	0.824461i
$881$	−6.29461e11	+	3.63419e11i	−1.04488	+	0.603260i	−0.921211	−	0.389064i	$-0.872798\pi$
$881$	−6.29461e11	+	3.63419e11i	−1.04488	+	0.603260i	−0.123666	+	0.992324i	$0.539465\pi$
$882$		0			0
$883$	−3.47680e11	+	6.02200e11i	−0.571922	+	0.990599i	0.424446	+	0.905453i	$0.360469\pi$
$883$	−3.47680e11	+	6.02200e11i	−0.571922	+	0.990599i	−0.996369	+	0.0851454i	$0.972865\pi$
$884$	−2.94898e11	−	8.10227e11i	−0.482907	−	1.32678i
$885$		0			0
$886$	4.17293e11	−	3.50150e11i	0.677183	−	0.568224i
$887$	−2.63284e11	+	7.23367e11i	−0.425334	+	1.16860i	0.523280	+	0.852161i	$0.324708\pi$
$887$	−2.63284e11	+	7.23367e11i	−0.425334	+	1.16860i	−0.948614	+	0.316435i	$0.897514\pi$
$888$		0			0
$889$	1.58074e11	−	8.96483e11i	0.253078	−	1.43527i
$890$		−	1.87523e12i		−	2.98879i
$891$		0			0
$892$	−6.15421e11			−0.972105
$893$	1.75009e11	+	3.08588e10i	0.275203	+	0.0485258i
$894$		0			0
$895$	5.36369e11	+	1.95222e11i	0.835932	+	0.304255i
$896$	8.57355e11	+	1.02176e12i	1.33024	+	1.58531i
$897$		0			0
$898$	1.95430e12	−	7.11306e11i	3.00528	−	1.09383i
$899$	−8.36566e9	−	4.82992e9i	−0.0128074	−	0.00739436i
$900$		0			0
$901$	4.06486e11	+	7.04055e11i	0.616803	+	1.06833i
$902$	−5.70445e11	+	6.79830e11i	−0.861763	+	1.02701i
$903$		0			0
$904$	−3.91621e10	−	2.22099e11i	−0.0586398	−	0.332563i
$905$	−1.09394e12	+	1.92891e11i	−1.63080	+	0.287553i
$906$		0			0
$907$	3.19173e11	+	2.67818e11i	0.471626	+	0.395741i	0.847387	−	0.530975i	$-0.178174\pi$
$907$	3.19173e11	+	2.67818e11i	0.471626	+	0.395741i	−0.375761	+	0.926716i	$0.622619\pi$
$908$	−1.80842e12	+	1.04409e12i	−2.66046	+	1.53602i
$909$		0			0
$910$	−3.22792e11	+	5.59092e11i	−0.470714	+	0.815300i
$911$	2.07672e11	+	5.70574e11i	0.301512	+	0.828398i	0.994238	+	0.107197i	$0.0341874\pi$
$911$	2.07672e11	+	5.70574e11i	0.301512	+	0.828398i	−0.692726	+	0.721201i	$0.743590\pi$
$912$		0			0
$913$	−1.22009e12	+	1.02378e12i	−1.75594	+	1.47341i
$914$	3.43117e11	−	9.42707e11i	0.491652	−	1.35080i
$915$		0			0
$916$	8.60449e10	−	4.87985e11i	0.122220	−	0.693146i
$917$		−	3.00768e11i		−	0.425358i
$918$		0			0
$919$	−1.01276e11			−0.141986			−0.0709931	−	0.997477i	$-0.522617\pi$
$919$	−1.01276e11			−0.141986			−0.0709931	+	0.997477i	$0.522617\pi$
$920$	1.09874e12	+	1.93738e11i	1.53371	+	0.270435i
$921$		0			0
$922$	−1.22209e12	−	4.44806e11i	−1.69115	−	0.615527i
$923$	1.89501e11	+	2.25839e11i	0.261099	+	0.311166i
$924$		0			0
$925$	8.82639e10	−	3.21254e10i	0.120564	−	0.0438816i
$926$	−2.83652e11	−	1.63766e11i	−0.385782	−	0.222731i
$927$		0			0
$928$	−6.72264e10	−	1.16440e11i	−0.0906459	−	0.157003i
$929$	−6.01206e11	+	7.16490e11i	−0.807162	+	0.961938i	−0.999813	−	0.0193293i	$-0.993847\pi$
$929$	−6.01206e11	+	7.16490e11i	−0.807162	+	0.961938i	0.192651	+	0.981267i	$0.438291\pi$
$930$		0			0
$931$	5.78453e9	+	3.28057e10i	0.00769962	+	0.0436667i
$932$	3.89784e11	−	6.87295e10i	0.516607	−	0.0910918i
$933$		0			0
$934$	−1.76457e11	−	1.48065e11i	−0.231874	−	0.194565i
$935$	1.93894e12	−	1.11945e12i	2.53698	−	1.46473i
$936$		0			0
$937$	2.03258e11	−	3.52053e11i	0.263687	−	0.456720i	−0.703532	−	0.710664i	$-0.748395\pi$
$937$	2.03258e11	−	3.52053e11i	0.263687	−	0.456720i	0.967219	+	0.253944i	$0.0817279\pi$
$938$	−3.69518e11	−	1.01524e12i	−0.477337	−	1.31147i
$939$		0			0
$940$	2.11833e12	−	1.77749e12i	2.71321	−	2.27665i
$941$	−1.53426e11	+	4.21534e11i	−0.195677	+	0.537618i	−0.998263	−	0.0589185i	$-0.981235\pi$
$941$	−1.53426e11	+	4.21534e11i	−0.195677	+	0.537618i	0.802586	+	0.596537i	$0.203457\pi$
$942$		0			0
$943$	−6.00476e10	+	3.40547e11i	−0.0759362	+	0.430655i
$944$		−	9.28899e11i		−	1.16972i
$945$		0			0
$946$	−3.59342e11			−0.448687
$947$	9.85987e11	+	1.73856e11i	1.22595	+	0.216167i	0.748883	−	0.662702i	$-0.230590\pi$
$947$	9.85987e11	+	1.73856e11i	1.22595	+	0.216167i	0.477062	+	0.878869i	$0.341702\pi$
$948$		0			0
$949$	1.75274e11	+	6.37947e10i	0.216099	+	0.0786538i
$950$	1.17741e10	+	1.40318e10i	0.0144555	+	0.0172274i
$951$		0			0
$952$	−2.11800e12	+	7.70888e11i	−2.57856	+	0.938519i
$953$	−1.01661e12	−	5.86941e11i	−1.23249	−	0.711579i	−0.264942	−	0.964264i	$-0.585353\pi$
$953$	−1.01661e12	−	5.86941e11i	−1.23249	−	0.711579i	−0.967548	+	0.252686i	$0.918686\pi$
$954$		0			0
$955$	7.69642e11	+	1.33306e12i	0.925285	+	1.60264i
$956$	8.65085e10	−	1.03097e11i	0.103568	−	0.123428i
$957$		0			0
$958$	−3.33824e11	−	1.89321e12i	−0.396328	−	2.24769i
$959$	−8.55979e11	+	1.50932e11i	−1.01202	+	0.178446i
$960$		0			0
$961$	−6.52854e11	−	5.47810e11i	−0.765460	−	0.642297i
$962$	8.94105e11	−	5.16212e11i	1.04397	−	0.602737i
$963$		0			0
$964$	−5.86689e11	+	1.01618e12i	−0.679360	+	1.17669i
$965$	−1.90850e11	−	5.24355e11i	−0.220081	−	0.604667i
$966$		0			0
$967$	9.51734e11	−	7.98600e11i	1.08845	−	0.913321i	0.0918585	−	0.995772i	$-0.470719\pi$
$967$	9.51734e11	−	7.98600e11i	1.08845	−	0.913321i	0.996595	+	0.0824511i	$0.0262748\pi$
$968$	−9.74020e11	+	2.67610e12i	−1.10934	+	3.04790i
$969$		0			0
$970$	9.86664e10	−	5.59565e11i	0.111451	−	0.632067i
$971$		−	1.27913e12i		−	1.43892i	−0.694533	−	0.719461i	$-0.744389\pi$
$971$		−	1.27913e12i		−	1.43892i	0.694533	−	0.719461i	$-0.255611\pi$
$972$		0			0
$973$	8.40812e11			0.938096
$974$	3.44253e11	+	6.07012e10i	0.382510	+	0.0674468i
$975$		0			0
$976$	1.37707e11	+	5.01214e10i	0.151760	+	0.0552362i
$977$	−9.07388e11	−	1.08138e12i	−0.995898	−	1.18686i	−0.982368	−	0.186956i	$-0.940138\pi$
$977$	−9.07388e11	−	1.08138e12i	−0.995898	−	1.18686i	−0.0135293	−	0.999908i	$-0.504307\pi$
$978$		0			0
$979$	2.57551e12	−	9.37409e11i	2.80371	−	1.02047i
$980$	4.48911e11	+	2.59179e11i	0.486694	+	0.280993i
$981$		0			0
$982$	4.72157e11	+	8.17799e11i	0.507738	+	0.879429i
$983$	−5.68095e11	+	6.77029e11i	−0.608425	+	0.725092i	−0.979034	−	0.203697i	$-0.934704\pi$
$983$	−5.68095e11	+	6.77029e11i	−0.608425	+	0.725092i	0.370610	+	0.928789i	$0.379149\pi$
$984$		0			0
$985$	8.63305e10	+	4.89605e11i	0.0917106	+	0.520117i
$986$	1.34841e12	−	2.37761e11i	1.42664	−	0.251555i
$987$		0			0
$988$	1.00957e11	+	8.47129e10i	0.105952	+	0.0889041i
$989$	−1.21260e11	+	7.00095e10i	−0.126745	+	0.0731765i
$990$		0			0
$991$	8.15770e11	−	1.41296e12i	0.845811	−	1.46499i	−0.0391049	−	0.999235i	$-0.512451\pi$
$991$	8.15770e11	−	1.41296e12i	0.845811	−	1.46499i	0.884915	−	0.465752i	$-0.154216\pi$
$992$	3.09597e9	+	8.50610e9i	0.00319705	+	0.00878383i
$993$		0			0
$994$	1.24997e12	−	1.04885e12i	1.28043	−	1.07440i
$995$	7.48501e10	−	2.05649e11i	0.0763660	−	0.209814i
$996$		0			0
$997$	−3.05755e11	+	1.73402e12i	−0.309452	+	1.75499i	0.292319	+	0.956321i	$0.405573\pi$
$997$	−3.05755e11	+	1.73402e12i	−0.309452	+	1.75499i	−0.601771	+	0.798669i	$0.705538\pi$
$998$		−	1.49189e12i		−	1.50388i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.3		138
3.2	odd	2		27.9.f.a.2.21	✓	138
27.13	even	9		27.9.f.a.14.21	yes	138
27.14	odd	18	inner	81.9.f.a.71.3		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.21	✓	138	3.2	odd	2
27.9.f.a.14.21	yes	138	27.13	even	9
81.9.f.a.8.3		138	1.1	even	1	trivial
81.9.f.a.71.3		138	27.14	odd	18	inner

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-26.8100 - 4.72733i) q^{2} +(455.867 + 165.922i) q^{4} +(418.443 + 498.682i) q^{5} +(2557.31 - 930.784i) q^{7} +(-5401.88 - 3118.78i) q^{8} +(-8861.04 - 15347.8i) q^{10} +(16649.6 - 19842.2i) q^{11} +(-2324.40 - 13182.3i) q^{13} +(-72961.5 + 12865.1i) q^{14} +(34944.7 + 29322.1i) q^{16} +(114990. - 66389.2i) q^{17} +(-10147.5 + 17576.0i) q^{19} +(108012. + 296761. i) q^{20} +(-540176. + 453262. i) q^{22} +(-93974.9 + 258194. i) q^{23} +(-5756.99 + 32649.5i) q^{25} +364407. i q^{26} +1.32023e6 q^{28} +(-373034. - 65776.0i) q^{29} +(23963.9 + 8722.16i) q^{31} +(228160. + 271911. i) q^{32} +(-3.39671e6 + 1.23630e6i) q^{34} +(1.53425e6 + 885801. i) q^{35} +(-1.41658e6 - 2.45359e6i) q^{37} +(355142. - 423242. i) q^{38} +(-705106. - 3.99885e6i) q^{40} +(1.23941e6 - 218542. i) q^{41} +(390374. + 327563. i) q^{43} +(1.08823e7 - 6.28287e6i) q^{44} +(3.74003e6 - 6.47792e6i) q^{46} +(-2.99482e6 - 8.22820e6i) q^{47} +(1.25737e6 - 1.05506e6i) q^{49} +(308690. - 848118. i) q^{50} +(1.12762e6 - 6.39506e6i) q^{52} +6.12277e6i q^{53} +1.68619e7 q^{55} +(-1.67172e7 - 2.94769e6i) q^{56} +(9.69011e6 + 3.52691e6i) q^{58} +(-1.30891e7 - 1.55989e7i) q^{59} +(3.01877e6 - 1.09874e6i) q^{61} +(-601240. - 347126. i) q^{62} +(-1.06706e7 - 1.84819e7i) q^{64} +(5.60116e6 - 6.67520e6i) q^{65} +(2.53228e6 + 1.43613e7i) q^{67} +(6.34353e7 - 1.11854e7i) q^{68} +(-3.69458e7 - 3.10012e7i) q^{70} +(-1.90737e7 + 1.10122e7i) q^{71} +(-6.96726e6 + 1.20676e7i) q^{73} +(2.63796e7 + 7.24775e7i) q^{74} +(-7.54215e6 + 6.32862e6i) q^{76} +(2.41093e7 - 6.62398e7i) q^{77} +(5.26432e6 - 2.98554e7i) q^{79} +2.96959e7i q^{80} -3.42618e7 q^{82} +(-6.05555e7 - 1.06776e7i) q^{83} +(8.12237e7 + 2.95630e7i) q^{85} +(-8.91743e6 - 1.06274e7i) q^{86} +(-1.51823e8 + 5.52589e7i) q^{88} +(9.16372e7 + 5.29067e7i) q^{89} +(-1.82141e7 - 3.15478e7i) q^{91} +(-8.56800e7 + 1.02110e8i) q^{92} +(4.13937e7 + 2.34755e8i) q^{94} +(-1.30110e7 + 2.29419e6i) q^{95} +(2.45606e7 + 2.06088e7i) q^{97} +(-3.86976e7 + 2.23421e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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