LMFDB - Embedded newform 81.9.f.a.35.22

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			35.22
Character	$\chi$	$=$	81.35
Dual form			81.9.f.a.44.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(18.6956 - 22.2805i) q^{2} +(-102.443 - 580.983i) q^{4} +(-117.116 + 321.773i) q^{5} +(-297.164 + 1685.30i) q^{7} +(-8411.56 - 4856.42i) q^{8} +(4979.72 + 8625.13i) q^{10} +(-5183.40 - 14241.3i) q^{11} +(-40531.4 + 34009.8i) q^{13} +(31993.8 + 38128.7i) q^{14} +(-123544. + 44966.5i) q^{16} +(-90546.3 + 52276.9i) q^{17} +(-55941.4 + 96893.4i) q^{19} +(198942. + 35078.9i) q^{20} +(-414209. - 150760. i) q^{22} +(114580. - 20203.6i) q^{23} +(209414. + 175719. i) q^{25} +1.53889e6i q^{26} +1.00957e6 q^{28} +(351769. - 419222. i) q^{29} +(-10686.3 - 60605.0i) q^{31} +(-457428. + 1.25677e6i) q^{32} +(-528058. + 2.99476e6i) q^{34} +(-507483. - 292995. i) q^{35} +(-473893. - 820807. i) q^{37} +(1.11298e6 + 3.05788e6i) q^{38} +(2.54779e6 - 2.13785e6i) q^{40} +(-3.23864e6 - 3.85967e6i) q^{41} +(-5.10427e6 + 1.85780e6i) q^{43} +(-7.74293e6 + 4.47038e6i) q^{44} +(1.69200e6 - 2.93063e6i) q^{46} +(2.46632e6 + 434879. i) q^{47} +(2.66520e6 + 970053. i) q^{49} +(7.83023e6 - 1.38068e6i) q^{50} +(2.39113e7 + 2.00639e7i) q^{52} -2.43779e6i q^{53} +5.18952e6 q^{55} +(1.06842e7 - 1.27329e7i) q^{56} +(-2.76396e6 - 1.56752e7i) q^{58} +(-4.49168e6 + 1.23408e7i) q^{59} +(3.69007e6 - 2.09274e7i) q^{61} +(-1.55010e6 - 894948. i) q^{62} +(2.62111e6 + 4.53989e6i) q^{64} +(-6.19659e6 - 1.70250e7i) q^{65} +(9.26949e6 - 7.77802e6i) q^{67} +(3.96478e7 + 4.72504e7i) q^{68} +(-1.60158e7 + 5.82926e6i) q^{70} +(-3.15050e7 + 1.81894e7i) q^{71} +(-2.25002e7 + 3.89715e7i) q^{73} +(-2.71477e7 - 4.78687e6i) q^{74} +(6.20241e7 + 2.25749e7i) q^{76} +(2.55412e7 - 4.50360e6i) q^{77} +(1.20481e7 + 1.01095e7i) q^{79} -4.50196e7i q^{80} -1.46544e8 q^{82} +(-3.05000e7 + 3.63485e7i) q^{83} +(-6.21691e6 - 3.52578e7i) q^{85} +(-5.40345e7 + 1.48458e8i) q^{86} +(-2.55611e7 + 1.44964e8i) q^{88} +(-5.83596e7 - 3.36939e7i) q^{89} +(-4.52724e7 - 7.84141e7i) q^{91} +(-2.34759e7 - 6.44995e7i) q^{92} +(5.57986e7 - 4.68206e7i) q^{94} +(-2.46261e7 - 2.93482e7i) q^{95} +(-4.83680e6 + 1.76045e6i) q^{97} +(7.14407e7 - 4.12463e7i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	18.6956	−	22.2805i	1.16847	−	1.39253i	0.264803	−	0.964303i	$-0.414693\pi$
$2$	18.6956	−	22.2805i	1.16847	−	1.39253i	0.903670	−	0.428229i	$-0.140862\pi$
$3$		0			0
$3$		0			0
$4$	−102.443	−	580.983i	−0.400168	−	2.26946i
$5$	−117.116	+	321.773i	−0.187385	+	0.514837i	−0.997439	−	0.0715182i	$-0.977216\pi$
$5$	−117.116	+	321.773i	−0.187385	+	0.514837i	0.810054	+	0.586355i	$0.199438\pi$
$6$		0			0
$7$	−297.164	+	1685.30i	−0.123767	+	0.701917i	0.858266	+	0.513206i	$0.171542\pi$
$7$	−297.164	+	1685.30i	−0.123767	+	0.701917i	−0.982033	+	0.188712i	$0.939569\pi$
$8$	−8411.56	−	4856.42i	−2.05360	−	1.18565i
$9$		0			0
$10$	4979.72	+	8625.13i	0.497972	+	0.862513i
$11$	−5183.40	−	14241.3i	−0.354033	−	0.972698i	−0.981061	−	0.193701i	$-0.937951\pi$
$11$	−5183.40	−	14241.3i	−0.354033	−	0.972698i	0.627027	−	0.778997i	$-0.284271\pi$
$12$		0			0
$13$	−40531.4	+	34009.8i	−1.41912	+	1.19078i	−0.467303	+	0.884097i	$0.654774\pi$
$13$	−40531.4	+	34009.8i	−1.41912	+	1.19078i	−0.951812	+	0.306682i	$0.900781\pi$
$14$	31993.8	+	38128.7i	0.832824	+	0.992521i
$15$		0			0
$16$	−123544.	+	44966.5i	−1.88514	+	0.686134i
$17$	−90546.3	+	52276.9i	−1.08411	+	0.625914i	−0.932003	−	0.362450i	$-0.881940\pi$
$17$	−90546.3	+	52276.9i	−1.08411	+	0.625914i	−0.152111	+	0.988363i	$0.548607\pi$
$18$		0			0
$19$	−55941.4	+	96893.4i	−0.429259	+	0.743498i	−0.996808	−	0.0798420i	$-0.974558\pi$
$19$	−55941.4	+	96893.4i	−0.429259	+	0.743498i	0.567549	+	0.823340i	$0.307892\pi$
$20$	198942.	+	35078.9i	1.24339	+	0.219243i
$21$		0			0
$22$	−414209.	−	150760.i	−1.76819	−	0.643569i
$23$	114580.	−	20203.6i	0.409448	−	0.0721967i	0.0348694	−	0.999392i	$-0.488898\pi$
$23$	114580.	−	20203.6i	0.409448	−	0.0721967i	0.374579	+	0.927195i	$0.377787\pi$
$24$		0			0
$25$	209414.	+	175719.i	0.536100	+	0.449842i
$26$			1.53889e6i			3.36756i
$27$		0			0
$28$	1.00957e6			1.64250
$29$	351769.	−	419222.i	0.497354	−	0.592723i	−0.457718	−	0.889097i	$-0.651333\pi$
$29$	351769.	−	419222.i	0.497354	−	0.592723i	0.955072	+	0.296374i	$0.0957776\pi$
$30$		0			0
$31$	−10686.3	−	60605.0i	−0.0115713	−	0.0656238i	0.978475	−	0.206364i	$-0.0661630\pi$
$31$	−10686.3	−	60605.0i	−0.0115713	−	0.0656238i	−0.990047	+	0.140740i	$0.955052\pi$
$32$	−457428.	+	1.25677e6i	−0.436238	+	1.19855i
$33$		0			0
$34$	−528058.	+	2.99476e6i	−0.395153	+	2.24103i
$35$	−507483.	−	292995.i	−0.338181	−	0.195249i
$36$		0			0
$37$	−473893.	−	820807.i	−0.252856	−	0.437960i	0.711455	−	0.702732i	$-0.248037\pi$
$37$	−473893.	−	820807.i	−0.252856	−	0.437960i	−0.964311	+	0.264772i	$0.914703\pi$
$38$	1.11298e6	+	3.05788e6i	0.533767	+	1.46651i
$39$		0			0
$40$	2.54779e6	−	2.13785e6i	0.995232	−	0.835099i
$41$	−3.23864e6	−	3.85967e6i	−1.14611	−	1.36589i	−0.920063	−	0.391770i	$-0.871863\pi$
$41$	−3.23864e6	−	3.85967e6i	−1.14611	−	1.36589i	−0.226051	−	0.974116i	$-0.572581\pi$
$42$		0			0
$43$	−5.10427e6	+	1.85780e6i	−1.49300	+	0.543408i	−0.954238	−	0.299049i	$-0.903331\pi$
$43$	−5.10427e6	+	1.85780e6i	−1.49300	+	0.543408i	−0.538763	+	0.842457i	$0.681108\pi$
$44$	−7.74293e6	+	4.47038e6i	−2.06583	+	1.19271i
$45$		0			0
$46$	1.69200e6	−	2.93063e6i	0.377893	−	0.654529i
$47$	2.46632e6	+	434879.i	0.505427	+	0.0891204i	0.420547	−	0.907271i	$-0.361838\pi$
$47$	2.46632e6	+	434879.i	0.505427	+	0.0891204i	0.0848801	+	0.996391i	$0.472949\pi$
$48$		0			0
$49$	2.66520e6	+	970053.i	0.462323	+	0.168272i
$50$	7.83023e6	−	1.38068e6i	1.25284	−	0.220909i
$51$		0			0
$52$	2.39113e7	+	2.00639e7i	3.27031	+	2.74412i
$53$		−	2.43779e6i		−	0.308954i	−0.987996	−	0.154477i	$-0.950631\pi$
$53$		−	2.43779e6i		−	0.308954i	0.987996	−	0.154477i	$-0.0493692\pi$
$54$		0			0
$55$	5.18952e6			0.567122
$56$	1.06842e7	−	1.27329e7i	1.08640	−	1.29472i
$57$		0			0
$58$	−2.76396e6	−	1.56752e7i	−0.244241	−	1.38516i
$59$	−4.49168e6	+	1.23408e7i	−0.370681	+	1.01844i	0.604417	+	0.796668i	$0.293406\pi$
$59$	−4.49168e6	+	1.23408e7i	−0.370681	+	1.01844i	−0.975099	+	0.221771i	$0.928816\pi$
$60$		0			0
$61$	3.69007e6	−	2.09274e7i	0.266511	−	1.51146i	−0.498186	−	0.867070i	$-0.666000\pi$
$61$	3.69007e6	−	2.09274e7i	0.266511	−	1.51146i	0.764697	−	0.644389i	$-0.222888\pi$
$62$	−1.55010e6	−	894948.i	−0.104904	−	0.0605663i
$63$		0			0
$64$	2.62111e6	+	4.53989e6i	0.156230	+	0.270599i
$65$	−6.19659e6	−	1.70250e7i	−0.347136	−	0.953748i
$66$		0			0
$67$	9.26949e6	−	7.77802e6i	0.459999	−	0.385985i	−0.383132	−	0.923694i	$-0.625155\pi$
$67$	9.26949e6	−	7.77802e6i	0.459999	−	0.385985i	0.843131	+	0.537709i	$0.180710\pi$
$68$	3.96478e7	+	4.72504e7i	1.85432	+	2.20989i
$69$		0			0
$70$	−1.60158e7	+	5.82926e6i	−0.667046	+	0.242785i
$71$	−3.15050e7	+	1.81894e7i	−1.23978	+	0.715790i	−0.969050	−	0.246865i	$-0.920600\pi$
$71$	−3.15050e7	+	1.81894e7i	−1.23978	+	0.715790i	−0.270734	+	0.962654i	$0.587266\pi$
$72$		0			0
$73$	−2.25002e7	+	3.89715e7i	−0.792309	+	1.37232i	0.132224	+	0.991220i	$0.457788\pi$
$73$	−2.25002e7	+	3.89715e7i	−0.792309	+	1.37232i	−0.924534	+	0.381100i	$0.875545\pi$
$74$	−2.71477e7	−	4.78687e6i	−0.905328	−	0.159634i
$75$		0			0
$76$	6.20241e7	+	2.25749e7i	1.85912	+	0.676663i
$77$	2.55412e7	−	4.50360e6i	0.726571	−	0.128114i
$78$		0			0
$79$	1.20481e7	+	1.01095e7i	0.309320	+	0.259551i	0.784211	−	0.620494i	$-0.213068\pi$
$79$	1.20481e7	+	1.01095e7i	0.309320	+	0.259551i	−0.474891	+	0.880045i	$0.657512\pi$
$80$		−	4.50196e7i		−	1.09911i
$81$		0			0
$82$	−1.46544e8			−3.24124
$83$	−3.05000e7	+	3.63485e7i	−0.642669	+	0.765903i	−0.984789	−	0.173753i	$-0.944411\pi$
$83$	−3.05000e7	+	3.63485e7i	−0.642669	+	0.765903i	0.342120	+	0.939656i	$0.388855\pi$
$84$		0			0
$85$	−6.21691e6	−	3.52578e7i	−0.119096	−	0.675430i
$86$	−5.40345e7	+	1.48458e8i	−0.987818	+	2.71401i
$87$		0			0
$88$	−2.55611e7	+	1.44964e8i	−0.426235	+	2.41730i
$89$	−5.83596e7	−	3.36939e7i	−0.930148	−	0.537021i	−0.0432895	−	0.999063i	$-0.513784\pi$
$89$	−5.83596e7	−	3.36939e7i	−0.930148	−	0.537021i	−0.886858	+	0.462042i	$0.847117\pi$
$90$		0			0
$91$	−4.52724e7	−	7.84141e7i	−0.660189	−	1.14348i
$92$	−2.34759e7	−	6.44995e7i	−0.327696	−	0.900336i
$93$		0			0
$94$	5.57986e7	−	4.68206e7i	0.714681	−	0.599689i
$95$	−2.46261e7	−	2.93482e7i	−0.302343	−	0.360319i
$96$		0			0
$97$	−4.83680e6	+	1.76045e6i	−0.0546350	+	0.0198855i	−0.369193	−	0.929353i	$-0.620366\pi$
$97$	−4.83680e6	+	1.76045e6i	−0.0546350	+	0.0198855i	0.314558	+	0.949238i	$0.398144\pi$
$98$	7.14407e7	−	4.12463e7i	0.774536	−	0.447178i
$99$		0			0
$100$	8.06369e7	−	1.39667e8i	0.806369	−	1.39667i
$101$	6.50334e7	+	1.14671e7i	0.624958	+	0.110197i	0.477154	−	0.878820i	$-0.341668\pi$
$101$	6.50334e7	+	1.14671e7i	0.624958	+	0.110197i	0.147804	+	0.989017i	$0.452779\pi$
$102$		0			0
$103$	−9.19846e7	−	3.34796e7i	−0.817271	−	0.297462i	−0.100647	−	0.994922i	$-0.532091\pi$
$103$	−9.19846e7	−	3.34796e7i	−0.817271	−	0.297462i	−0.716624	+	0.697460i	$0.754314\pi$
$104$	5.06098e8	−	8.92388e7i	4.32615	−	0.762817i
$105$		0			0
$106$	−5.43153e7	−	4.55759e7i	−0.430228	−	0.361004i
$107$		−	1.29460e7i		−	0.0987644i	−0.998780	−	0.0493822i	$-0.984275\pi$
$107$		−	1.29460e7i		−	0.0987644i	0.998780	−	0.0493822i	$-0.0157252\pi$
$108$		0			0
$109$	8.54794e6			0.0605557			0.0302779	−	0.999542i	$-0.490361\pi$
$109$	8.54794e6			0.0605557			0.0302779	+	0.999542i	$0.490361\pi$
$110$	9.70210e7	−	1.15625e8i	0.662667	−	0.789735i
$111$		0			0
$112$	−3.90692e7	−	2.21572e8i	−0.248292	−	1.40813i
$113$	−2.11163e7	+	5.80164e7i	−0.129510	+	0.355826i	−0.987452	−	0.157921i	$-0.949521\pi$
$113$	−2.11163e7	+	5.80164e7i	−0.129510	+	0.355826i	0.857942	+	0.513747i	$0.171743\pi$
$114$		0			0
$115$	−6.91820e6	+	3.92351e7i	−0.0395550	+	0.224328i
$116$	−2.79597e8	−	1.61425e8i	−1.54419	−	0.891537i
$117$		0			0
$118$	1.90985e8	+	3.30795e8i	0.985077	+	1.70620i
$119$	−6.11954e7	−	1.68133e8i	−0.305162	−	0.838426i
$120$		0			0
$121$	−1.17379e7	+	9.84926e6i	−0.0547582	+	0.0459475i
$122$	−3.97286e8	−	4.73467e8i	−1.79334	−	2.13722i
$123$		0			0
$124$	−3.41157e7	+	1.24171e7i	−0.144300	+	0.0525211i
$125$	−1.96907e8	+	1.13684e8i	−0.806529	+	0.465650i
$126$		0			0
$127$	1.33274e8	−	2.30837e8i	0.512307	−	0.887342i	−0.487591	−	0.873072i	$-0.662124\pi$
$127$	1.33274e8	−	2.30837e8i	0.512307	−	0.887342i	0.999898	−	0.0142696i	$-0.00454230\pi$
$128$	−1.87027e8	−	3.29779e7i	−0.696729	−	0.122852i
$129$		0			0
$130$	−4.95174e8	−	1.80229e8i	−1.73374	−	0.631031i
$131$	5.14499e7	−	9.07201e6i	0.174703	−	0.0308048i	−0.0856124	−	0.996329i	$-0.527285\pi$
$131$	5.14499e7	−	9.07201e6i	0.174703	−	0.0308048i	0.260315	+	0.965524i	$0.416174\pi$
$132$		0			0
$133$	−1.46671e8	−	1.23072e8i	−0.468746	−	0.393324i
$134$		−	3.51943e8i		−	1.09158i
$135$		0			0
$136$	1.01551e9			2.96846
$137$	−1.72635e8	+	2.05738e8i	−0.490056	+	0.584026i	−0.953232	−	0.302240i	$-0.902266\pi$
$137$	−1.72635e8	+	2.05738e8i	−0.490056	+	0.584026i	0.463175	+	0.886267i	$0.346710\pi$
$138$		0			0
$139$	−9.87783e7	−	5.60199e8i	−0.264607	−	1.50066i	−0.770150	−	0.637862i	$-0.779819\pi$
$139$	−9.87783e7	−	5.60199e8i	−0.264607	−	1.50066i	0.505543	−	0.862801i	$-0.331292\pi$
$140$	−1.18237e8	+	3.24854e8i	−0.307781	+	0.845622i
$141$		0			0
$142$	−1.83734e8	+	1.04201e9i	−0.451894	+	2.56282i
$143$	6.94434e8	+	4.00932e8i	1.66068	+	0.958796i
$144$		0			0
$145$	9.36966e7	+	1.62287e8i	0.211959	+	0.367124i
$146$	4.47650e8	+	1.22991e9i	0.985207	+	2.70683i
$147$		0			0
$148$	−4.28328e8	+	3.59409e8i	−0.892748	+	0.749105i
$149$	−2.02149e8	−	2.40912e8i	−0.410135	−	0.488780i	0.520947	−	0.853589i	$-0.325579\pi$
$149$	−2.02149e8	−	2.40912e8i	−0.410135	−	0.488780i	−0.931082	+	0.364809i	$0.881134\pi$
$150$		0			0
$151$	−3.93927e6	+	1.43378e6i	−0.00757719	+	0.00275787i	−0.345806	−	0.938306i	$-0.612394\pi$
$151$	−3.93927e6	+	1.43378e6i	−0.00757719	+	0.00275787i	0.338229	+	0.941064i	$0.390172\pi$
$152$	9.41110e8	−	5.43350e8i	1.76305	−	1.01790i
$153$		0			0
$154$	3.77165e8	−	6.53268e8i	0.670576	−	1.16147i
$155$	2.07526e7	+	3.65924e6i	0.0359539	+	0.00633964i
$156$		0			0
$157$	3.50588e8	+	1.27604e8i	0.577030	+	0.210022i	0.614016	−	0.789294i	$-0.289553\pi$
$157$	3.50588e8	+	1.27604e8i	0.577030	+	0.210022i	−0.0369852	+	0.999316i	$0.511775\pi$
$158$	4.50490e8	−	7.94336e7i	0.722865	−	0.127461i
$159$		0			0
$160$	−3.50824e8	−	2.94377e8i	−0.535315	−	0.449183i
$161$			1.99106e8i			0.296334i
$162$		0			0
$163$	−8.20265e8			−1.16199			−0.580997	−	0.813906i	$-0.697337\pi$
$163$	−8.20265e8			−1.16199			−0.580997	+	0.813906i	$0.697337\pi$
$164$	−1.91062e9	+	2.27699e9i	−2.64119	+	3.14765i
$165$		0			0
$166$	2.39648e8	+	1.35911e9i	0.315603	+	1.78987i
$167$	−4.50751e7	+	1.23843e8i	−0.0579523	+	0.159223i	−0.965290	−	0.261179i	$-0.915889\pi$
$167$	−4.50751e7	+	1.23843e8i	−0.0579523	+	0.159223i	0.907338	+	0.420402i	$0.138111\pi$
$168$		0			0
$169$	3.44471e8	−	1.95359e9i	0.422285	−	2.39490i
$170$	−9.01791e8	−	5.20649e8i	−1.07972	−	0.623375i
$171$		0			0
$172$	1.60225e9	+	2.77518e9i	1.83069	+	3.17086i
$173$	1.46812e8	+	4.03362e8i	0.163899	+	0.450309i	0.994269	−	0.106903i	$-0.0340933\pi$
$173$	1.46812e8	+	4.03362e8i	0.163899	+	0.450309i	−0.830370	+	0.557212i	$0.811871\pi$
$174$		0			0
$175$	−3.58371e8	+	3.00709e8i	−0.382103	+	0.320623i
$176$	1.28076e9	+	1.52635e9i	1.33480	+	1.59076i
$177$		0			0
$178$	−1.84178e9	+	6.70354e8i	−1.83467	+	0.667766i
$179$	1.52658e9	−	8.81371e8i	1.48699	−	0.858512i	0.487097	−	0.873348i	$-0.338056\pi$
$179$	1.52658e9	−	8.81371e8i	1.48699	−	0.858512i	0.999890	+	0.0148355i	$0.00472247\pi$
$180$		0			0
$181$	1.48283e8	−	2.56833e8i	0.138158	−	0.239297i	−0.788641	−	0.614853i	$-0.789215\pi$
$181$	1.48283e8	−	2.56833e8i	0.138158	−	0.239297i	0.926799	+	0.375557i	$0.122548\pi$
$182$	−2.59350e9	−	4.57304e8i	−2.36375	−	0.416792i
$183$		0			0
$184$	−1.06192e9	−	3.86506e8i	−0.926444	−	0.337198i
$185$	3.19614e8	−	5.63566e7i	0.272860	−	0.0481125i
$186$		0			0
$187$	1.21383e9	+	1.01852e9i	0.992638	+	0.832922i
$188$		−	1.47744e9i		−	1.18271i
$189$		0			0
$190$	−1.11429e9			−0.855036
$191$	4.80251e8	−	5.72340e8i	0.360856	−	0.430052i	−0.554819	−	0.831971i	$-0.687212\pi$
$191$	4.80251e8	−	5.72340e8i	0.360856	−	0.430052i	0.915675	+	0.401919i	$0.131657\pi$
$192$		0			0
$193$	8.42946e7	+	4.78058e8i	0.0607534	+	0.344549i	0.999999	+	0.00130414i	$0.000415122\pi$
$193$	8.42946e7	+	4.78058e8i	0.0607534	+	0.344549i	−0.939246	+	0.343245i	$0.888474\pi$
$194$	−5.12029e7	+	1.40679e8i	−0.0361483	+	0.0993167i
$195$		0			0
$196$	2.90553e8	−	1.64781e9i	0.196880	−	1.11656i
$197$	7.53162e8	+	4.34838e8i	0.500062	+	0.288711i	0.728739	−	0.684792i	$-0.240107\pi$
$197$	7.53162e8	+	4.34838e8i	0.500062	+	0.288711i	−0.228677	+	0.973502i	$0.573440\pi$
$198$		0			0
$199$	7.09537e8	+	1.22895e9i	0.452442	+	0.783652i	0.998537	−	0.0540709i	$-0.0172197\pi$
$199$	7.09537e8	+	1.22895e9i	0.452442	+	0.783652i	−0.546095	+	0.837723i	$0.683886\pi$
$200$	−9.08134e8	−	2.49508e9i	−0.567584	−	1.55942i
$201$		0			0
$202$	1.47133e9	−	1.23459e9i	0.883700	−	0.741512i
$203$	6.01983e8	+	7.17415e8i	0.354487	+	0.422461i
$204$		0			0
$205$	1.62123e9	−	5.90081e8i	0.917974	−	0.334115i
$206$	−2.46565e9	+	1.42354e9i	−1.36918	+	0.790499i
$207$		0			0
$208$	3.47812e9	−	6.02428e9i	1.85820	−	3.21849i
$209$	1.66985e9	+	2.94440e8i	0.875171	+	0.154316i
$210$		0			0
$211$	6.41754e8	+	2.33579e8i	0.323772	+	0.117843i	0.498792	−	0.866721i	$-0.333777\pi$
$211$	6.41754e8	+	2.33579e8i	0.323772	+	0.117843i	−0.175021	+	0.984565i	$0.555999\pi$
$212$	−1.41632e9	+	2.49735e8i	−0.701159	+	0.123633i
$213$		0			0
$214$	−2.88443e8	−	2.42033e8i	−0.137533	−	0.115403i
$215$		−	1.86000e9i		−	0.870479i
$216$		0			0
$217$	1.05313e8			0.0474946
$218$	1.59808e8	−	1.90452e8i	0.0707577	−	0.0843258i
$219$		0			0
$220$	−5.31630e8	−	3.01502e9i	−0.226944	−	1.28706i
$221$	1.89203e9	−	5.19832e9i	0.793158	−	2.17918i
$222$		0			0
$223$	−8.19134e8	+	4.64554e9i	−0.331235	+	1.87852i	0.130411	+	0.991460i	$0.458370\pi$
$223$	−8.19134e8	+	4.64554e9i	−0.331235	+	1.87852i	−0.461646	+	0.887064i	$0.652741\pi$
$224$	−1.98211e9	−	1.14437e9i	−0.787294	−	0.454544i
$225$		0			0
$226$	8.97855e8	+	1.55513e9i	0.344170	+	0.596119i
$227$	2.03965e8	+	5.60389e8i	0.0768161	+	0.211050i	0.972157	−	0.234332i	$-0.0752901\pi$
$227$	2.03965e8	+	5.60389e8i	0.0768161	+	0.211050i	−0.895341	+	0.445382i	$0.853068\pi$
$228$		0			0
$229$	3.16622e9	−	2.65678e9i	1.15133	−	0.966080i	0.151579	−	0.988445i	$-0.451564\pi$
$229$	3.16622e9	−	2.65678e9i	1.15133	−	0.966080i	0.999750	+	0.0223655i	$0.00711975\pi$
$230$	7.44837e8	+	8.87663e8i	0.266164	+	0.317202i
$231$		0			0
$232$	−4.99484e9	+	1.81797e9i	−1.72413	+	0.627532i
$233$	−2.32864e8	+	1.34444e8i	−0.0790094	+	0.0456161i	−0.538984	−	0.842316i	$-0.681192\pi$
$233$	−2.32864e8	+	1.34444e8i	−0.0790094	+	0.0456161i	0.459975	+	0.887932i	$0.347858\pi$
$234$		0			0
$235$	−4.28778e8	+	7.42666e8i	−0.140592	+	0.243513i
$236$	7.62993e9	+	1.34536e9i	2.45964	+	0.433702i
$237$		0			0
$238$	−4.89017e9	−	1.77988e9i	−1.52411	−	0.554730i
$239$	−1.62330e9	+	2.86231e8i	−0.497515	+	0.0877253i	−0.416775	−	0.909010i	$-0.636840\pi$
$239$	−1.62330e9	+	2.86231e8i	−0.497515	+	0.0877253i	−0.0807403	+	0.996735i	$0.525728\pi$
$240$		0			0
$241$	3.07650e9	+	2.58149e9i	0.911987	+	0.765248i	0.972496	−	0.232920i	$-0.0748279\pi$
$241$	3.07650e9	+	2.58149e9i	0.911987	+	0.765248i	−0.0605089	+	0.998168i	$0.519272\pi$
$242$			4.45664e8i			0.129941i
$243$		0			0
$244$	−1.25365e10			−3.53685
$245$	−6.24275e8	+	7.43981e8i	−0.173265	+	0.206489i
$246$		0			0
$247$	−1.02795e9	−	5.82978e9i	−0.276174	−	1.56626i
$248$	−2.04435e8	+	5.61680e8i	−0.0540441	+	0.148485i
$249$		0			0
$250$	−1.14834e9	+	6.51256e9i	−0.293975	+	1.66722i
$251$	4.63407e9	+	2.67548e9i	1.16753	+	0.674073i	0.953097	−	0.302666i	$-0.0978768\pi$
$251$	4.63407e9	+	2.67548e9i	1.16753	+	0.674073i	0.214432	+	0.976739i	$0.431210\pi$
$252$		0			0
$253$	−8.81641e8	−	1.52705e9i	−0.215184	−	0.372709i
$254$	−2.65154e9	−	7.28504e9i	−0.637035	−	1.75024i
$255$		0			0
$256$	−5.25937e9	+	4.41314e9i	−1.22454	+	1.02751i
$257$	7.20093e8	+	8.58174e8i	0.165066	+	0.196717i	0.842236	−	0.539108i	$-0.181239\pi$
$257$	7.20093e8	+	8.58174e8i	0.165066	+	0.196717i	−0.677171	+	0.735826i	$0.736794\pi$
$258$		0			0
$259$	1.52413e9	−	5.54739e8i	0.338707	−	0.123279i
$260$	−9.25643e9	+	5.34420e9i	−2.02558	+	1.16947i
$261$		0			0
$262$	7.59756e8	−	1.31594e9i	0.161239	−	0.279274i
$263$	−1.96364e9	−	3.46243e8i	−0.410431	−	0.0723700i	−0.0353791	−	0.999374i	$-0.511264\pi$
$263$	−1.96364e9	−	3.46243e8i	−0.410431	−	0.0723700i	−0.375052	+	0.927004i	$0.622375\pi$
$264$		0			0
$265$	7.84417e8	+	2.85504e8i	0.159061	+	0.0578934i
$266$	−5.48419e9	+	9.67011e8i	−1.09543	+	0.193154i
$267$		0			0
$268$	−5.46849e9	−	4.58861e9i	−1.06005	−	0.889491i
$269$			6.66631e9i			1.27314i	0.771219	+	0.636570i	$0.219647\pi$
$269$			6.66631e9i			1.27314i	−0.771219	+	0.636570i	$0.780353\pi$
$270$		0			0
$271$	−5.48803e9			−1.01751			−0.508755	−	0.860911i	$-0.669894\pi$
$271$	−5.48803e9			−1.01751			−0.508755	+	0.860911i	$0.669894\pi$
$272$	8.83578e9	−	1.05301e10i	1.61425	−	1.92378i
$273$		0			0
$274$	1.35644e9	+	7.69278e9i	0.240658	+	1.36484i
$275$	1.41699e9	−	3.89315e9i	0.247763	−	0.680723i
$276$		0			0
$277$	−2.20492e8	+	1.25047e9i	−0.0374518	+	0.212400i	−0.997791	−	0.0664357i	$-0.978837\pi$
$277$	−2.20492e8	+	1.25047e9i	−0.0374518	+	0.212400i	0.960339	+	0.278835i	$0.0899484\pi$
$278$	−1.43282e10	−	8.27241e9i	−2.39891	−	1.38501i
$279$		0			0
$280$	2.84582e9	+	4.92910e9i	0.462993	+	0.801928i
$281$	1.42767e9	+	3.92248e9i	0.228982	+	0.629123i	0.999970	−	0.00772678i	$-0.00245953\pi$
$281$	1.42767e9	+	3.92248e9i	0.228982	+	0.629123i	−0.770988	+	0.636849i	$0.780237\pi$
$282$		0			0
$283$	3.22228e9	−	2.70382e9i	0.502363	−	0.421533i	−0.356069	−	0.934460i	$-0.615883\pi$
$283$	3.22228e9	−	2.70382e9i	0.502363	−	0.421533i	0.858432	+	0.512927i	$0.171439\pi$
$284$	1.37952e10	+	1.64405e10i	2.12058	+	2.52721i
$285$		0			0
$286$	2.19158e10	−	7.97670e9i	3.27562	−	1.19223i
$287$	7.46712e9	−	4.31114e9i	1.10059	−	0.635426i
$288$		0			0
$289$	1.97788e9	−	3.42579e9i	0.283536	−	0.491099i
$290$	5.36755e9	+	9.46445e8i	0.758900	+	0.133815i
$291$		0			0
$292$	2.49467e10	+	9.07987e9i	3.43149	+	1.24896i
$293$	−4.67188e9	+	8.23779e8i	−0.633901	+	0.111774i	−0.481359	−	0.876523i	$-0.659857\pi$
$293$	−4.67188e9	+	8.23779e8i	−0.633901	+	0.111774i	−0.152541	+	0.988297i	$0.548746\pi$
$294$		0			0
$295$	−3.44489e9	−	2.89061e9i	−0.454870	−	0.381681i
$296$			9.20570e9i			1.19919i
$297$		0			0
$298$	−9.14693e9			−1.15987
$299$	−3.95698e9	+	4.71574e9i	−0.495084	+	0.590018i
$300$		0			0
$301$	−1.61415e9	−	9.15432e9i	−0.196643	−	1.11522i
$302$	−4.17016e7	+	1.14574e8i	−0.00501332	+	0.0137740i
$303$		0			0
$304$	2.55430e9	−	1.44861e10i	0.299073	−	1.69613i
$305$	6.30172e9	+	3.63830e9i	0.728215	+	0.420435i
$306$		0			0
$307$	2.72565e9	+	4.72096e9i	0.306843	+	0.531468i	0.977670	−	0.210146i	$-0.0673940\pi$
$307$	2.72565e9	+	4.72096e9i	0.306843	+	0.531468i	−0.670827	+	0.741614i	$0.734061\pi$
$308$	−5.23303e9	−	1.43776e10i	−0.581501	−	1.59766i
$309$		0			0
$310$	4.69511e8	−	3.93967e8i	0.0508393	−	0.0426592i
$311$	−5.15247e9	−	6.14047e9i	−0.550774	−	0.656387i	0.416793	−	0.909002i	$-0.363154\pi$
$311$	−5.15247e9	−	6.14047e9i	−0.550774	−	0.656387i	−0.967567	+	0.252614i	$0.918710\pi$
$312$		0			0
$313$	−5.18267e8	+	1.88634e8i	−0.0539978	+	0.0196536i	−0.368878	−	0.929478i	$-0.620258\pi$
$313$	−5.18267e8	+	1.88634e8i	−0.0539978	+	0.0196536i	0.314880	+	0.949131i	$0.398036\pi$
$314$	9.39752e9	−	5.42566e9i	0.966706	−	0.558128i
$315$		0			0
$316$	4.63922e9	−	8.03536e9i	0.465261	−	0.805855i
$317$	−1.75400e10	−	3.09277e9i	−1.73697	−	0.306275i	−0.786616	−	0.617443i	$-0.788169\pi$
$317$	−1.75400e10	−	3.09277e9i	−1.73697	−	0.306275i	−0.950355	+	0.311168i	$0.899280\pi$
$318$		0			0
$319$	−7.79361e9	−	2.83664e9i	−0.752620	−	0.273931i
$320$	−1.76779e9	+	3.11709e8i	−0.168589	+	0.0297269i
$321$		0			0
$322$	4.43619e9	+	3.72241e9i	0.412655	+	0.346259i
$323$		−	1.16978e10i		−	1.07472i
$324$		0			0
$325$	−1.44640e10			−1.29645
$326$	−1.53353e10	+	1.82759e10i	−1.35776	+	1.61811i
$327$		0			0
$328$	8.49791e9	+	4.81940e10i	0.734204	+	4.16388i
$329$	−1.46581e9	+	4.02727e9i	−0.125110	+	0.343738i
$330$		0			0
$331$	9.84318e8	−	5.58235e9i	0.0820018	−	0.465056i	−0.915962	−	0.401266i	$-0.868570\pi$
$331$	9.84318e8	−	5.58235e9i	0.0820018	−	0.465056i	0.997963	−	0.0637895i	$-0.0203186\pi$
$332$	2.42423e10	+	1.39963e10i	1.99536	+	1.15202i
$333$		0			0
$334$	1.91658e9	+	3.31961e9i	0.154007	+	0.266748i
$335$	1.41716e9	+	3.89360e9i	0.112522	+	0.309152i
$336$		0			0
$337$	4.83874e9	−	4.06018e9i	0.375156	−	0.314794i	−0.435641	−	0.900121i	$-0.643478\pi$
$337$	4.83874e9	−	4.06018e9i	0.375156	−	0.314794i	0.810797	+	0.585327i	$0.199034\pi$
$338$	−3.70869e10	−	4.41985e10i	−2.84154	−	3.38642i
$339$		0			0
$340$	−1.98473e10	+	7.22383e9i	−1.48520	+	0.540570i
$341$	−8.07701e8	+	4.66326e8i	−0.0597356	+	0.0344884i
$342$		0			0
$343$	−7.35949e9	+	1.27470e10i	−0.531706	+	0.920942i
$344$	5.19572e10	+	9.16146e9i	3.71033	+	0.654231i
$345$		0			0
$346$	1.17318e10	+	4.27004e9i	0.818582	+	0.297939i
$347$	−1.80957e9	+	3.19076e8i	−0.124813	+	0.0220078i	−0.235705	−	0.971825i	$-0.575740\pi$
$347$	−1.80957e9	+	3.19076e8i	−0.124813	+	0.0220078i	0.110893	+	0.993832i	$0.464629\pi$
$348$		0			0
$349$	1.35676e10	+	1.13845e10i	0.914535	+	0.767386i	0.972976	−	0.230905i	$-0.0741686\pi$
$349$	1.35676e10	+	1.13845e10i	0.914535	+	0.767386i	−0.0584413	+	0.998291i	$0.518613\pi$
$350$			1.36066e10i			0.906729i
$351$		0			0
$352$	2.02691e10			1.32027
$353$	−1.24790e9	+	1.48719e9i	−0.0803677	+	0.0957785i	−0.804730	−	0.593641i	$-0.797690\pi$
$353$	−1.24790e9	+	1.48719e9i	−0.0803677	+	0.0957785i	0.724362	+	0.689420i	$0.242134\pi$
$354$		0			0
$355$	−2.16313e9	−	1.22677e10i	−0.136198	−	0.772415i
$356$	−1.35970e10	+	3.73576e10i	−0.846534	+	2.32583i
$357$		0			0
$358$	8.90287e9	−	5.04907e10i	0.541998	−	3.07382i
$359$	2.26258e9	+	1.30630e9i	0.136215	+	0.0786440i	0.566559	−	0.824021i	$-0.308274\pi$
$359$	2.26258e9	+	1.30630e9i	0.136215	+	0.0786440i	−0.430344	+	0.902665i	$0.641608\pi$
$360$		0			0
$361$	2.23290e9	+	3.86750e9i	0.131474	+	0.227720i
$362$	−2.95014e9	−	8.10546e9i	−0.171794	−	0.472001i
$363$		0			0
$364$	−4.09194e10	+	3.43355e10i	−2.33090	+	1.95586i
$365$	−9.90485e9	−	1.18041e10i	−0.558054	−	0.665063i
$366$		0			0
$367$	−1.05553e10	+	3.84183e9i	−0.581846	+	0.211775i	−0.616139	−	0.787637i	$-0.711304\pi$
$367$	−1.05553e10	+	3.84183e9i	−0.581846	+	0.211775i	0.0342933	+	0.999412i	$0.489082\pi$
$368$	−1.32473e10	+	7.64832e9i	−0.722330	+	0.417037i
$369$		0			0
$370$	4.71971e9	−	8.17478e9i	0.251831	−	0.436184i
$371$	4.10842e9	+	7.24426e8i	0.216860	+	0.0382383i
$372$		0			0
$373$	−2.89879e10	−	1.05507e10i	−1.49755	−	0.545064i	−0.542126	−	0.840297i	$-0.682381\pi$
$373$	−2.89879e10	−	1.05507e10i	−1.49755	−	0.545064i	−0.955425	+	0.295233i	$0.904603\pi$
$374$	4.53864e10	−	8.00285e9i	2.31974	−	0.409033i
$375$		0			0
$376$	−1.86337e10	−	1.56355e10i	−0.932282	−	0.782277i
$377$			2.89552e10i			1.43338i
$378$		0			0
$379$	1.77157e10			0.858622			0.429311	−	0.903157i	$-0.358756\pi$
$379$	1.77157e10			0.858622			0.429311	+	0.903157i	$0.358756\pi$
$380$	−1.45280e10	+	1.73138e10i	−0.696742	+	0.830345i
$381$		0			0
$382$	−3.77348e9	−	2.14005e10i	−0.177210	−	1.00501i
$383$	1.40103e9	−	3.84929e9i	0.0651105	−	0.178890i	−0.902871	−	0.429912i	$-0.858545\pi$
$383$	1.40103e9	−	3.84929e9i	0.0651105	−	0.178890i	0.967981	+	0.251022i	$0.0807668\pi$
$384$		0			0
$385$	−1.54214e9	+	8.74592e9i	−0.0701910	+	0.398073i
$386$	1.22273e10	+	7.05944e9i	0.550785	+	0.317996i
$387$		0			0
$388$	1.51829e9	+	2.62975e9i	0.0669926	+	0.116035i
$389$	7.14910e9	+	1.96420e10i	0.312214	+	0.857802i	0.992209	+	0.124585i	$0.0397598\pi$
$389$	7.14910e9	+	1.96420e10i	0.312214	+	0.857802i	−0.679995	+	0.733217i	$0.738018\pi$
$390$		0			0
$391$	−9.31865e9	+	7.81927e9i	−0.398700	+	0.334549i
$392$	−1.77075e10	−	2.11030e10i	−0.749917	−	0.893717i
$393$		0			0
$394$	2.37692e10	−	8.65128e9i	0.986347	−	0.359001i
$395$	−4.66399e9	+	2.69276e9i	−0.191588	+	0.110614i
$396$		0			0
$397$	−1.55874e9	+	2.69982e9i	−0.0627498	+	0.108686i	−0.895694	−	0.444672i	$-0.853320\pi$
$397$	−1.55874e9	+	2.69982e9i	−0.0627498	+	0.108686i	0.832944	+	0.553358i	$0.186654\pi$
$398$	4.06469e10	+	7.16715e9i	1.61993	+	0.285637i
$399$		0			0
$400$	−3.37735e10	−	1.22925e10i	−1.31928	−	0.480177i
$401$	−2.16825e10	+	3.82321e9i	−0.838556	+	0.147860i	−0.576402	−	0.817166i	$-0.695544\pi$
$401$	−2.16825e10	+	3.82321e9i	−0.838556	+	0.147860i	−0.262154	+	0.965026i	$0.584433\pi$
$402$		0			0
$403$	2.49430e9	+	2.09296e9i	0.0945644	+	0.0793490i
$404$		−	3.89580e10i		−	1.46242i
$405$		0			0
$406$	2.72388e10			1.00250
$407$	−9.23296e9	+	1.10034e10i	−0.336483	+	0.401005i
$408$		0			0
$409$	8.64567e8	+	4.90320e9i	0.0308962	+	0.175221i	0.996351	−	0.0853491i	$-0.0272005\pi$
$409$	8.64567e8	+	4.90320e9i	0.0308962	+	0.175221i	−0.965455	+	0.260570i	$0.916089\pi$
$410$	1.71626e10	−	4.71538e10i	0.607361	−	1.66871i
$411$		0			0
$412$	−1.00279e10	+	5.68712e10i	−0.348034	+	1.97380i
$413$	−1.94632e10	−	1.12371e10i	−0.668982	−	0.386237i
$414$		0			0
$415$	−8.12394e9	−	1.40711e10i	−0.273889	−	0.474389i
$416$	−2.42025e10	−	6.64958e10i	−0.808141	−	2.22035i
$417$		0			0
$418$	3.77791e10	−	3.17004e10i	1.23750	−	1.03839i
$419$	−3.66213e10	−	4.36436e10i	−1.18817	−	1.41600i	−0.886586	−	0.462563i	$-0.846930\pi$
$419$	−3.66213e10	−	4.36436e10i	−1.18817	−	1.41600i	−0.301581	−	0.953440i	$-0.597515\pi$
$420$		0			0
$421$	−3.87019e9	+	1.40863e9i	−0.123198	+	0.0448404i	−0.402884	−	0.915251i	$-0.631992\pi$
$421$	−3.87019e9	+	1.40863e9i	−0.123198	+	0.0448404i	0.279685	+	0.960092i	$0.409770\pi$
$422$	1.72022e10	−	9.93171e9i	0.542419	−	0.313166i
$423$		0			0
$424$	−1.18389e10	+	2.05057e10i	−0.366311	+	0.634469i
$425$	−2.81478e10	−	4.96321e9i	−0.862756	−	0.152127i
$426$		0			0
$427$	3.41725e10	+	1.24378e10i	1.02793	+	0.374137i
$428$	−7.52140e9	+	1.32623e9i	−0.224142	+	0.0395223i
$429$		0			0
$430$	−4.14417e10	−	3.47737e10i	−1.21217	−	1.01713i
$431$			1.81563e10i			0.526161i	0.964774	+	0.263081i	$0.0847385\pi$
$431$			1.81563e10i			0.526161i	−0.964774	+	0.263081i	$0.915261\pi$
$432$		0			0
$433$	1.39834e10			0.397798			0.198899	−	0.980020i	$-0.436263\pi$
$433$	1.39834e10			0.397798			0.198899	+	0.980020i	$0.436263\pi$
$434$	1.96889e9	−	2.34644e9i	0.0554962	−	0.0661378i
$435$		0			0
$436$	−8.75675e8	−	4.96620e9i	−0.0242324	−	0.137429i
$437$	−4.45219e9	+	1.22323e10i	−0.122081	+	0.335415i
$438$		0			0
$439$	1.36672e8	−	7.75106e8i	0.00367978	−	0.0208691i	−0.982913	−	0.184073i	$-0.941072\pi$
$439$	1.36672e8	−	7.75106e8i	0.00367978	−	0.0208691i	0.986592	+	0.163204i	$0.0521828\pi$
$440$	−4.36520e10	−	2.52025e10i	−1.16464	−	0.672408i
$441$		0			0
$442$	−8.04486e10	−	1.39341e11i	−2.10780	−	3.65082i
$443$	−2.40685e10	−	6.61276e10i	−0.624933	−	1.71699i	−0.694577	−	0.719418i	$-0.744408\pi$
$443$	−2.40685e10	−	6.61276e10i	−0.624933	−	1.71699i	0.0696435	−	0.997572i	$-0.477814\pi$
$444$		0			0
$445$	1.76766e10	−	1.48325e10i	0.450775	−	0.378245i
$446$	8.81908e10	+	1.05102e11i	2.22887	+	2.65626i
$447$		0			0
$448$	−8.42999e9	+	3.06827e9i	−0.209274	+	0.0761695i
$449$	5.13070e10	−	2.96221e10i	1.26238	−	0.728837i	0.288848	−	0.957375i	$-0.406728\pi$
$449$	5.13070e10	−	2.96221e10i	1.26238	−	0.728837i	0.973535	+	0.228538i	$0.0733944\pi$
$450$		0			0
$451$	−3.81794e10	+	6.61286e10i	−0.922832	+	1.59839i
$452$	3.58698e10	+	6.32480e9i	0.859359	+	0.151528i
$453$		0			0
$454$	1.62990e10	+	5.93235e9i	0.383652	+	0.139638i
$455$	3.05337e10	−	5.38391e9i	0.712416	−	0.125618i
$456$		0			0
$457$	5.53699e10	+	4.64609e10i	1.26943	+	1.06518i	0.994610	+	0.103683i	$0.0330628\pi$
$457$	5.53699e10	+	4.64609e10i	1.26943	+	1.06518i	0.274820	+	0.961496i	$0.411382\pi$
$458$		−	1.20215e11i		−	2.73210i
$459$		0			0
$460$	2.35036e10			0.524932
$461$	2.25930e10	−	2.69253e10i	0.500231	−	0.596152i	−0.455558	−	0.890206i	$-0.650560\pi$
$461$	2.25930e10	−	2.69253e10i	0.500231	−	0.596152i	0.955789	+	0.294054i	$0.0950045\pi$
$462$		0			0
$463$	−3.31286e9	−	1.87882e10i	−0.0720908	−	0.408847i	−0.999403	−	0.0345576i	$-0.988998\pi$
$463$	−3.31286e9	−	1.87882e10i	−0.0720908	−	0.408847i	0.927312	−	0.374289i	$-0.122113\pi$
$464$	−2.46081e10	+	6.76103e10i	−0.530893	+	1.45862i
$465$		0			0
$466$	−1.35804e9	+	7.70184e9i	−0.0287985	+	0.163324i
$467$	7.65051e10	+	4.41702e10i	1.60851	+	0.928671i	0.989705	+	0.143124i	$0.0457147\pi$
$467$	7.65051e10	+	4.41702e10i	1.60851	+	0.928671i	0.618801	+	0.785548i	$0.287619\pi$
$468$		0			0
$469$	1.03538e10	+	1.79333e10i	0.213997	+	0.370653i
$470$	8.53072e9	+	2.34379e10i	0.174821	+	0.480317i
$471$		0			0
$472$	9.77141e10	−	8.19919e10i	1.96874	−	1.65197i
$473$	5.29150e10	+	6.30616e10i	1.05714	+	1.25986i
$474$		0			0
$475$	−2.87410e10	+	1.04609e10i	−0.564582	+	0.205491i
$476$	−9.14132e10	+	5.27774e10i	−1.78066	+	1.02807i
$477$		0			0
$478$	−2.39711e10	+	4.15191e10i	−0.459172	+	0.795310i
$479$	−2.99876e10	−	5.28762e9i	−0.569639	−	0.100443i	−0.118592	−	0.992943i	$-0.537838\pi$
$479$	−2.99876e10	−	5.28762e9i	−0.569639	−	0.100443i	−0.451047	+	0.892500i	$0.648949\pi$
$480$		0			0
$481$	4.71230e10	+	1.71514e10i	0.880345	+	0.320420i
$482$	1.15034e11	−	2.02836e10i	2.13126	−	0.375799i
$483$		0			0
$484$	6.92471e9	+	5.81053e9i	0.126189	+	0.105885i
$485$		−	1.76253e9i		−	0.0318544i
$486$		0			0
$487$	1.67793e10			0.298304			0.149152	−	0.988814i	$-0.452346\pi$
$487$	1.67793e10			0.298304			0.149152	+	0.988814i	$0.452346\pi$
$488$	−1.32672e11	+	1.58112e11i	−2.33937	+	2.78795i
$489$		0			0
$490$	4.90512e9	+	2.78183e10i	0.0850874	+	0.482554i
$491$	−1.00866e10	+	2.77127e10i	−0.173547	+	0.476818i	−0.995720	−	0.0924205i	$-0.970540\pi$
$491$	−1.00866e10	+	2.77127e10i	−0.173547	+	0.476818i	0.822173	+	0.569238i	$0.192762\pi$
$492$		0			0
$493$	−9.93574e9	+	5.63484e10i	−0.168195	+	0.953880i
$494$	−1.49108e11	−	8.60878e10i	−2.50377	−	1.44555i
$495$		0			0
$496$	4.04543e9	+	7.00689e9i	0.0668402	+	0.115771i
$497$	−2.12925e10	−	5.85007e10i	−0.348981	−	0.958817i
$498$		0			0
$499$	−5.03462e10	+	4.22455e10i	−0.812016	+	0.681362i	−0.951088	−	0.308920i	$-0.900033\pi$
$499$	−5.03462e10	+	4.22455e10i	−0.812016	+	0.681362i	0.139072	+	0.990282i	$0.455588\pi$
$500$	8.62201e10	+	1.02753e11i	1.37952	+	1.64405i
$501$		0			0
$502$	1.46248e11	−	5.32297e10i	2.30289	−	0.838184i
$503$	−4.10135e10	+	2.36792e10i	−0.640700	+	0.369909i	−0.784884	−	0.619642i	$-0.787278\pi$
$503$	−4.10135e10	+	2.36792e10i	−0.640700	+	0.369909i	0.144184	+	0.989551i	$0.453944\pi$
$504$		0			0
$505$	−1.13063e10	+	1.95830e10i	−0.173842	+	0.301103i
$506$	−5.05062e10	−	8.90560e9i	−0.770446	−	0.135850i
$507$		0			0
$508$	−1.47765e11	−	5.37822e10i	−2.21880	−	0.807576i
$509$	−6.60982e10	+	1.16549e10i	−0.984733	+	0.173635i	−0.642754	−	0.766073i	$-0.722208\pi$
$509$	−6.60982e10	+	1.16549e10i	−0.984733	+	0.173635i	−0.341979	+	0.939708i	$0.611097\pi$
$510$		0			0
$511$	−5.89925e10	−	4.95006e10i	−0.865193	−	0.725983i
$512$			1.51070e11i			2.19836i
$513$		0			0
$514$	3.25831e10			0.466810
$515$	2.15457e10	−	2.56772e10i	0.306289	−	0.365021i
$516$		0			0
$517$	−6.59071e9	−	3.73777e10i	−0.0922507	−	0.523180i
$518$	1.61347e10	−	4.43296e10i	0.224099	−	0.615708i
$519$		0			0
$520$	−3.05575e10	+	1.73300e11i	−0.417931	+	2.37020i
$521$	−5.02218e10	−	2.89956e10i	−0.681618	−	0.393533i	0.118846	−	0.992913i	$-0.462080\pi$
$521$	−5.02218e10	−	2.89956e10i	−0.681618	−	0.393533i	−0.800465	+	0.599380i	$0.795414\pi$
$522$		0			0
$523$	3.17202e10	+	5.49410e10i	0.423964	+	0.734328i	0.996323	−	0.0856755i	$-0.0273048\pi$
$523$	3.17202e10	+	5.49410e10i	0.423964	+	0.734328i	−0.572359	+	0.820003i	$0.693971\pi$
$524$	−1.05414e10	−	2.89621e10i	−0.139821	−	0.384154i
$525$		0			0
$526$	−4.44259e10	+	3.72778e10i	−0.580355	+	0.486975i
$527$	4.13585e9	+	4.92891e9i	0.0536194	+	0.0639011i
$528$		0			0
$529$	−6.08678e10	+	2.21541e10i	−0.777257	+	0.282899i
$530$	2.10263e10	−	1.21395e10i	0.266477	−	0.153850i
$531$		0			0
$532$	−5.64770e10	+	9.78210e10i	−0.705058	+	1.22120i
$533$	2.62533e11	+	4.62917e10i	3.25294	+	0.573580i
$534$		0			0
$535$	4.16568e9	+	1.51618e9i	0.0508476	+	0.0185070i
$536$	−1.15744e11	+	2.04088e10i	−1.40230	+	0.247263i
$537$		0			0
$538$	1.48529e11	+	1.24630e11i	1.77289	+	1.48763i
$539$		−	4.29840e10i		−	0.509275i
$540$		0			0
$541$	6.34800e10			0.741051			0.370525	−	0.928822i	$-0.379178\pi$
$541$	6.34800e10			0.741051			0.370525	+	0.928822i	$0.379178\pi$
$542$	−1.02602e11	+	1.22276e11i	−1.18893	+	1.41692i
$543$		0			0
$544$	−2.42819e10	−	1.37709e11i	−0.277259	−	1.57242i
$545$	−1.00110e9	+	2.75050e9i	−0.0113473	+	0.0311763i
$546$		0			0
$547$	−8.95748e9	+	5.08004e10i	−0.100054	+	0.567437i	0.893026	+	0.450004i	$0.148578\pi$
$547$	−8.95748e9	+	5.08004e10i	−0.100054	+	0.567437i	−0.993081	+	0.117433i	$0.962534\pi$
$548$	1.37215e11	+	7.92214e10i	1.52153	+	0.878456i
$549$		0			0
$550$	−6.02499e10	−	1.04356e11i	−0.658424	−	1.14042i
$551$	2.09414e10	+	5.75359e10i	0.227195	+	0.624213i
$552$		0			0
$553$	−2.06179e10	+	1.73004e10i	−0.220467	+	0.184994i
$554$	2.37389e10	+	2.82909e10i	0.252012	+	0.300336i
$555$		0			0
$556$	−3.15347e11	+	1.14777e11i	−3.29981	+	1.20103i
$557$	−3.24890e10	+	1.87576e10i	−0.337533	+	0.194875i	−0.659180	−	0.751985i	$-0.729097\pi$
$557$	−3.24890e10	+	1.87576e10i	−0.337533	+	0.194875i	0.321648	+	0.946859i	$0.395763\pi$
$558$		0			0
$559$	1.43700e11	−	2.48895e11i	1.47166	−	2.54899i
$560$	7.58717e10	+	1.33782e10i	0.771485	+	0.136034i
$561$		0			0
$562$	1.14086e11	+	4.15238e10i	1.14363	+	0.416248i
$563$	−9.97636e10	+	1.75910e10i	−0.992975	+	0.175088i	−0.646453	−	0.762954i	$-0.723748\pi$
$563$	−9.97636e10	+	1.75910e10i	−0.992975	+	0.175088i	−0.346522	+	0.938042i	$0.612637\pi$
$564$		0			0
$565$	−1.61951e10	−	1.35893e10i	−0.158924	−	0.133353i
$566$		−	1.22343e11i		−	1.19211i
$567$		0			0
$568$	3.53342e11			3.39470
$569$	3.40776e10	−	4.06121e10i	0.325102	−	0.387442i	−0.578594	−	0.815616i	$-0.696398\pi$
$569$	3.40776e10	−	4.06121e10i	0.325102	−	0.387442i	0.903696	+	0.428174i	$0.140843\pi$
$570$		0			0
$571$	−2.90038e10	−	1.64489e11i	−0.272841	−	1.54736i	−0.745736	−	0.666241i	$-0.767902\pi$
$571$	−2.90038e10	−	1.64489e11i	−0.272841	−	1.54736i	0.472895	−	0.881119i	$-0.343209\pi$
$572$	1.61794e11	−	4.44527e11i	1.51140	−	4.15254i
$573$		0			0
$574$	4.35475e10	−	2.46970e11i	0.401159	−	2.27508i
$575$	2.75449e10	+	1.59031e10i	0.251982	+	0.145482i
$576$		0			0
$577$	−5.16324e9	−	8.94300e9i	−0.0465821	−	0.0806826i	0.841794	−	0.539799i	$-0.181500\pi$
$577$	−5.16324e9	−	8.94300e9i	−0.0465821	−	0.0806826i	−0.888376	+	0.459116i	$0.848166\pi$
$578$	−3.93507e10	−	1.08115e11i	−0.352566	−	0.968668i
$579$		0			0
$580$	8.46875e10	−	7.10613e10i	0.748355	−	0.627944i
$581$	−5.21947e10	−	6.22032e10i	−0.458060	−	0.545894i
$582$		0			0
$583$	−3.47173e10	+	1.26361e10i	−0.300519	+	0.109380i
$584$	3.78524e11	−	2.18541e11i	3.25418	−	1.87880i
$585$		0			0
$586$	−6.89892e10	+	1.19493e11i	−0.585047	+	1.01333i
$587$	−1.25797e11	−	2.21814e10i	−1.05954	−	0.186825i	−0.383388	−	0.923588i	$-0.625243\pi$
$587$	−1.25797e11	−	2.21814e10i	−1.05954	−	0.186825i	−0.676152	+	0.736762i	$0.736354\pi$
$588$		0			0
$589$	6.47003e9	+	2.35490e9i	0.0537582	+	0.0195664i
$590$	−1.28808e11	+	2.27124e10i	−1.06301	+	0.187437i
$591$		0			0
$592$	9.54557e10	+	8.00968e10i	0.777168	+	0.652122i
$593$			1.50149e11i			1.21424i	0.794610	+	0.607121i	$0.207676\pi$
$593$			1.50149e11i			1.21424i	−0.794610	+	0.607121i	$0.792324\pi$
$594$		0			0
$595$	6.12676e10			0.488836
$596$	−1.19257e11	+	1.42125e11i	−0.945145	+	1.12638i
$597$		0			0
$598$	3.10912e10	+	1.76327e11i	0.243127	+	1.37884i
$599$	−1.73084e10	+	4.75544e10i	−0.134446	+	0.369388i	−0.988586	−	0.150655i	$-0.951862\pi$
$599$	−1.73084e10	+	4.75544e10i	−0.134446	+	0.369388i	0.854140	+	0.520043i	$0.174084\pi$
$600$		0			0
$601$	3.29413e10	−	1.86819e11i	0.252489	−	1.43194i	−0.549948	−	0.835199i	$-0.685352\pi$
$601$	3.29413e10	−	1.86819e11i	0.252489	−	1.43194i	0.802437	−	0.596737i	$-0.203537\pi$
$602$	−2.34140e11	−	1.35181e11i	−1.78275	−	1.02927i
$603$		0			0
$604$	1.23655e9	+	2.14177e9i	0.00929103	+	0.0160925i
$605$	−1.79454e9	−	4.93045e9i	−0.0133946	−	0.0368014i
$606$		0			0
$607$	−7.51967e10	+	6.30975e10i	−0.553916	+	0.464791i	−0.876264	−	0.481830i	$-0.839972\pi$
$607$	−7.51967e10	+	6.30975e10i	−0.553916	+	0.464791i	0.322349	+	0.946621i	$0.395528\pi$
$608$	−9.61839e10	−	1.14628e11i	−0.703863	−	0.838831i
$609$		0			0
$610$	1.98877e11	−	7.23855e10i	1.43637	−	0.522796i
$611$	−1.14754e11	+	6.62530e10i	−0.823382	+	0.475380i
$612$		0			0
$613$	−4.14147e10	+	7.17324e10i	−0.293300	+	0.508011i	−0.974588	−	0.224005i	$-0.928087\pi$
$613$	−4.14147e10	+	7.17324e10i	−0.293300	+	0.508011i	0.681288	+	0.732016i	$0.261420\pi$
$614$	1.56143e11	+	2.75322e10i	1.09862	+	0.193717i
$615$		0			0
$616$	−2.36713e11	−	8.61564e10i	−1.64399	−	0.598363i
$617$	1.59756e11	−	2.81693e10i	1.10234	−	0.194373i	0.407266	−	0.913309i	$-0.366482\pi$
$617$	1.59756e11	−	2.81693e10i	1.10234	−	0.194373i	0.695075	+	0.718937i	$0.255371\pi$
$618$		0			0
$619$	−1.60477e11	−	1.34657e11i	−1.09308	−	0.917202i	−0.0961381	−	0.995368i	$-0.530649\pi$
$619$	−1.60477e11	−	1.34657e11i	−1.09308	−	0.917202i	−0.996940	+	0.0781663i	$0.975094\pi$
$620$		−	1.24318e10i		−	0.0841329i
$621$		0			0
$622$	−2.33141e11			−1.55761
$623$	7.41268e10	−	8.83409e10i	0.492066	−	0.586421i
$624$		0			0
$625$	5.02350e9	+	2.84897e10i	0.0329220	+	0.186710i
$626$	−5.48644e9	+	1.50739e10i	−0.0357267	+	0.0981584i
$627$		0			0
$628$	3.82202e10	−	2.16758e11i	0.245728	−	1.39359i
$629$	8.58186e10	+	4.95474e10i	0.548250	+	0.316532i
$630$		0			0
$631$	2.53569e10	+	4.39195e10i	0.159948	+	0.277038i	0.934850	−	0.355044i	$-0.115534\pi$
$631$	2.53569e10	+	4.39195e10i	0.159948	+	0.277038i	−0.774902	+	0.632082i	$0.782201\pi$
$632$	−5.22469e10	−	1.43547e11i	−0.327486	−	0.899760i
$633$		0			0
$634$	−3.96829e11	+	3.32979e11i	−2.45610	+	2.06091i
$635$	5.86687e10	+	6.99187e10i	0.360838	+	0.430030i
$636$		0			0
$637$	−1.41016e11	+	5.13255e10i	−0.856464	+	0.311727i
$638$	−2.08908e11	+	1.20613e11i	−1.26087	+	0.727966i
$639$		0			0
$640$	3.25152e10	−	5.63180e10i	0.193806	−	0.335681i
$641$	−2.83399e11	−	4.99709e10i	−1.67867	−	0.295996i	−0.748506	−	0.663128i	$-0.769228\pi$
$641$	−2.83399e11	−	4.99709e10i	−1.67867	−	0.295996i	−0.930169	+	0.367133i	$0.880339\pi$
$642$		0			0
$643$	2.17650e9	+	7.92180e8i	0.0127325	+	0.00463426i	0.348379	−	0.937354i	$-0.386732\pi$
$643$	2.17650e9	+	7.92180e8i	0.0127325	+	0.00463426i	−0.335646	+	0.941988i	$0.608955\pi$
$644$	1.15677e11	−	2.03970e10i	0.672520	−	0.118583i
$645$		0			0
$646$	−2.60632e11	−	2.18697e11i	−1.49658	−	1.25578i
$647$		−	3.21533e11i		−	1.83488i	−0.397873	−	0.917440i	$-0.630252\pi$
$647$		−	3.21533e11i		−	1.83488i	0.397873	−	0.917440i	$-0.369748\pi$
$648$		0			0
$649$	1.99031e11			1.12187
$650$	−2.70413e11	+	3.22266e11i	−1.51487	+	1.80535i
$651$		0			0
$652$	8.40304e10	+	4.76560e11i	0.464992	+	2.63710i
$653$	−6.71116e10	+	1.84388e11i	−0.369101	+	1.01410i	0.606603	+	0.795005i	$0.292532\pi$
$653$	−6.71116e10	+	1.84388e11i	−0.369101	+	1.01410i	−0.975704	+	0.219092i	$0.929691\pi$
$654$		0			0
$655$	−3.10647e9	+	1.76177e10i	−0.0168773	+	0.0957158i
$656$	5.73672e11	+	3.31210e11i	3.09776	+	1.78850i
$657$		0			0
$658$	6.23256e10	+	1.07951e11i	0.332478	+	0.575869i
$659$	−1.84964e10	−	5.08185e10i	−0.0980722	−	0.269451i	0.880948	−	0.473212i	$-0.156906\pi$
$659$	−1.84964e10	−	5.08185e10i	−0.0980722	−	0.269451i	−0.979021	+	0.203761i	$0.934683\pi$
$660$		0			0
$661$	4.30383e10	−	3.61134e10i	0.225449	−	0.189174i	−0.523065	−	0.852292i	$-0.675212\pi$
$661$	4.30383e10	−	3.61134e10i	0.225449	−	0.189174i	0.748515	+	0.663118i	$0.230767\pi$
$662$	−1.05975e11	−	1.26296e11i	−0.551788	−	0.657595i
$663$		0			0
$664$	4.33076e11	−	1.57627e11i	2.22788	−	0.810882i
$665$	5.67786e10	−	3.27811e10i	0.290334	−	0.167625i
$666$		0			0
$667$	3.18360e10	−	5.51416e10i	0.160848	−	0.278597i
$668$	7.65681e10	+	1.35010e10i	0.384541	+	0.0678049i
$669$		0			0
$670$	1.13246e11	+	4.12182e10i	0.561984	+	0.204545i
$671$	−3.17160e11	+	5.59239e10i	−1.56455	+	0.275872i
$672$		0			0
$673$	−2.10541e11	−	1.76664e11i	−1.02630	−	0.861170i	−0.0358962	−	0.999356i	$-0.511429\pi$
$673$	−2.10541e11	−	1.76664e11i	−1.02630	−	0.861170i	−0.990406	+	0.138185i	$0.955873\pi$
$674$		−	1.83717e11i		−	0.890245i
$675$		0			0
$676$	−1.17029e12			−5.60412
$677$	1.79260e11	−	2.13634e11i	0.853355	−	1.01699i	−0.146260	−	0.989246i	$-0.546724\pi$
$677$	1.79260e11	−	2.13634e11i	0.853355	−	1.01699i	0.999615	−	0.0277427i	$-0.00883191\pi$
$678$		0			0
$679$	−1.52957e9	−	8.67462e9i	−0.00719598	−	0.0408104i
$680$	−1.18933e11	+	3.26766e11i	−0.556245	+	1.52827i
$681$		0			0
$682$	−4.71044e9	+	2.67142e10i	−0.0217733	+	0.123482i
$683$	9.60015e10	+	5.54265e10i	0.441159	+	0.254703i	0.704089	−	0.710111i	$-0.251355\pi$
$683$	9.60015e10	+	5.54265e10i	0.441159	+	0.254703i	−0.262930	+	0.964815i	$0.584689\pi$
$684$		0			0
$685$	−4.59828e10	−	7.96445e10i	−0.208849	−	0.361737i
$686$	1.46420e11	+	4.02286e11i	0.661157	+	1.81651i
$687$		0			0
$688$	5.47066e11	−	4.59043e11i	2.44166	−	2.04880i
$689$	8.29090e10	+	9.88071e10i	0.367896	+	0.438441i
$690$		0			0
$691$	9.87087e10	−	3.59270e10i	0.432956	−	0.157583i	−0.116343	−	0.993209i	$-0.537117\pi$
$691$	9.87087e10	−	3.59270e10i	0.432956	−	0.157583i	0.549299	+	0.835626i	$0.314895\pi$
$692$	2.19307e11	−	1.26617e11i	0.956373	−	0.552162i
$693$		0			0
$694$	−2.67218e10	+	4.62835e10i	−0.115193	+	0.199521i
$695$	1.91826e11	+	3.38240e10i	0.822181	+	0.144973i
$696$		0			0
$697$	4.95019e11	+	1.80172e11i	2.09744	+	0.763407i
$698$	5.07307e11	−	8.94519e10i	2.13722	−	0.376849i
$699$		0			0
$700$	2.11419e11	+	1.77402e11i	0.880546	+	0.738866i
$701$			2.70180e11i			1.11887i	0.828874	+	0.559436i	$0.188982\pi$
$701$			2.70180e11i			1.11887i	−0.828874	+	0.559436i	$0.811018\pi$
$702$		0			0
$703$	1.06041e11			0.434163
$704$	5.10676e10	−	6.08600e10i	0.207900	−	0.247766i
$705$		0			0
$706$	9.80514e9	+	5.56077e10i	0.0394671	+	0.223829i
$707$	−3.86512e10	+	1.06193e11i	−0.154698	+	0.425030i
$708$		0			0
$709$	−7.29321e10	+	4.13619e11i	−0.288625	+	1.63687i	0.403416	+	0.915016i	$0.367823\pi$
$709$	−7.29321e10	+	4.13619e11i	−0.288625	+	1.63687i	−0.692042	+	0.721858i	$0.743289\pi$
$710$	−3.13772e11	−	1.81157e11i	−1.23476	−	0.712887i
$711$		0			0
$712$	3.27263e11	+	5.66837e11i	1.27344	+	2.20566i
$713$	−2.44888e9	−	6.72824e9i	−0.00947565	−	0.0260341i
$714$		0			0
$715$	−2.10338e11	+	1.76495e11i	−0.804812	+	0.675317i
$716$	−6.68448e11	−	7.96626e11i	−2.54341	−	3.03111i
$717$		0			0
$718$	7.14053e10	−	2.59894e10i	0.268678	−	0.0977909i
$719$	5.39880e10	−	3.11700e10i	0.202014	−	0.116633i	−0.395580	−	0.918431i	$-0.629457\pi$
$719$	5.39880e10	−	3.11700e10i	0.202014	−	0.116633i	0.597595	+	0.801798i	$0.296123\pi$
$720$		0			0
$721$	8.37579e10	−	1.45073e11i	0.309945	−	0.536841i
$722$	1.27915e11	+	2.25549e10i	0.470731	+	0.0830026i
$723$		0			0
$724$	−1.64406e11	−	5.98389e10i	−0.598362	−	0.217786i
$725$	1.47331e11	−	2.59784e10i	0.533263	−	0.0940286i
$726$		0			0
$727$	−1.10498e11	−	9.27187e10i	−0.395563	−	0.331917i	0.423212	−	0.906030i	$-0.360902\pi$
$727$	−1.10498e11	−	9.27187e10i	−0.395563	−	0.331917i	−0.818776	+	0.574113i	$0.805347\pi$
$728$			8.79448e11i			3.13101i
$729$		0			0
$730$	−4.48179e11			−1.57819
$731$	3.65053e11	−	4.35053e11i	1.27846	−	1.52361i
$732$		0			0
$733$	−7.04889e10	−	3.99763e11i	−0.244177	−	1.38480i	−0.822396	−	0.568915i	$-0.807363\pi$
$733$	−7.04889e10	−	3.99763e11i	−0.244177	−	1.38480i	0.578219	−	0.815882i	$-0.303748\pi$
$734$	−1.11740e11	+	3.07004e11i	−0.384968	+	1.05769i
$735$		0			0
$736$	−2.70209e10	+	1.53243e11i	−0.0920851	+	0.522240i
$737$	−1.58816e11	−	9.16927e10i	−0.538302	−	0.310789i
$738$		0			0
$739$	−1.14018e11	−	1.97484e11i	−0.382291	−	0.662148i	0.609098	−	0.793095i	$-0.291532\pi$
$739$	−1.14018e11	−	1.97484e11i	−0.382291	−	0.662148i	−0.991389	+	0.130947i	$0.958198\pi$
$740$	−6.54844e10	−	1.79917e11i	−0.218379	−	0.599991i
$741$		0			0
$742$	9.29498e10	−	7.79942e10i	0.306643	−	0.257304i
$743$	−1.78400e11	−	2.12609e11i	−0.585382	−	0.697631i	0.389330	−	0.921099i	$-0.372707\pi$
$743$	−1.78400e11	−	2.12609e11i	−0.585382	−	0.697631i	−0.974711	+	0.223468i	$0.928262\pi$
$744$		0			0
$745$	1.01194e11	−	3.68316e10i	0.328495	−	0.119563i
$746$	−7.77021e11	+	4.48614e11i	−2.50887	+	1.44850i
$747$		0			0
$748$	4.67396e11	−	8.09553e11i	1.49306	−	2.58606i
$749$	2.18179e10	+	3.84709e9i	0.0693244	+	0.0122238i
$750$		0			0
$751$	−3.38584e11	−	1.23234e11i	−1.06440	−	0.387411i	−0.250322	−	0.968163i	$-0.580537\pi$
$751$	−3.38584e11	−	1.23234e11i	−1.06440	−	0.387411i	−0.814081	+	0.580752i	$0.802759\pi$
$752$	−3.24256e11	+	5.71750e10i	−1.01395	+	0.178787i
$753$		0			0
$754$	6.45137e11	+	5.41334e11i	1.99603	+	1.67487i
$755$		−	1.43547e9i		−	0.00441780i
$756$		0			0
$757$	4.15300e11			1.26467			0.632336	−	0.774694i	$-0.282096\pi$
$757$	4.15300e11			1.26467			0.632336	+	0.774694i	$0.282096\pi$
$758$	3.31206e11	−	3.94715e11i	1.00328	−	1.19566i
$759$		0			0
$760$	6.46166e10	+	3.66459e11i	0.193682	+	1.09843i
$761$	−1.61344e11	+	4.43288e11i	−0.481075	+	1.32174i	0.427498	+	0.904016i	$0.359395\pi$
$761$	−1.61344e11	+	4.43288e11i	−0.481075	+	1.32174i	−0.908573	+	0.417727i	$0.862827\pi$
$762$		0			0
$763$	−2.54014e9	+	1.44059e10i	−0.00749480	+	0.0425051i
$764$	−3.81718e11	−	2.20385e11i	−1.12039	−	0.646857i
$765$		0			0
$766$	−5.95711e10	−	1.03180e11i	−0.173030	−	0.299696i
$767$	−2.37655e11	−	6.52950e11i	−0.686696	−	1.88668i
$768$		0			0
$769$	−9.60197e10	+	8.05701e10i	−0.274571	+	0.230393i	−0.769667	−	0.638446i	$-0.779578\pi$
$769$	−9.60197e10	+	8.05701e10i	−0.274571	+	0.230393i	0.495095	+	0.868839i	$0.335133\pi$
$770$	1.66032e11	+	1.97870e11i	0.472313	+	0.562880i
$771$		0			0
$772$	2.69108e11	−	9.79473e10i	0.757631	−	0.275755i
$773$	−1.88263e11	+	1.08694e11i	−0.527287	+	0.304429i	−0.739911	−	0.672705i	$-0.765132\pi$
$773$	−1.88263e11	+	1.08694e11i	−0.527287	+	0.304429i	0.212624	+	0.977134i	$0.431799\pi$
$774$		0			0
$775$	8.41161e9	−	1.45693e10i	0.0233170	−	0.0403862i
$776$	4.92345e10	+	8.68138e9i	0.135776	+	0.0239410i
$777$		0			0
$778$	5.71290e11	+	2.07932e11i	1.55933	+	0.567550i
$779$	5.55150e11	−	9.78880e10i	1.50751	−	0.265815i
$780$		0			0
$781$	4.22343e11	+	3.54388e11i	1.13517	+	0.952522i
$782$			3.53810e11i			0.946113i
$783$		0			0
$784$	−3.72891e11			−0.987000
$785$	−8.21189e10	+	9.78655e10i	−0.216254	+	0.257722i
$786$		0			0
$787$	−1.04940e11	−	5.95142e11i	−0.273553	−	1.55139i	−0.743522	−	0.668711i	$-0.766846\pi$
$787$	−1.04940e11	−	5.95142e11i	−0.273553	−	1.55139i	0.469970	−	0.882682i	$-0.344265\pi$
$788$	1.75477e11	−	4.82120e11i	0.455110	−	1.25040i
$789$		0			0
$790$	−2.72000e10	+	1.54259e11i	−0.0698329	+	0.396042i
$791$	−9.15003e10	−	5.28277e10i	−0.233731	−	0.134945i
$792$		0			0
$793$	5.62175e11	+	9.73716e11i	1.42160	+	2.46229i
$794$	3.10118e10	+	8.52043e10i	0.0780271	+	0.214378i
$795$		0			0
$796$	6.41314e11	−	5.38126e11i	1.59742	−	1.34039i
$797$	3.05559e11	+	3.64151e11i	0.757290	+	0.902503i	0.997673	−	0.0681748i	$-0.0217176\pi$
$797$	3.05559e11	+	3.64151e11i	0.757290	+	0.902503i	−0.240383	+	0.970678i	$0.577273\pi$
$798$		0			0
$799$	−2.46051e11	+	8.95551e10i	−0.603723	+	0.219737i
$800$	−3.16632e11	+	1.82807e11i	−0.773026	+	0.446307i
$801$		0			0
$802$	−3.20184e11	+	5.54574e11i	−0.773930	+	1.34049i
$803$	6.71631e11	+	1.18427e11i	1.61536	+	0.284831i
$804$		0			0
$805$	−6.40671e10	−	2.33185e10i	−0.152564	−	0.0555287i
$806$	9.32646e10	−	1.64451e10i	0.220992	−	0.0389668i
$807$		0			0
$808$	−4.91344e11	−	4.12286e11i	−1.15276	−	0.967283i
$809$			2.48092e11i			0.579186i	0.957150	+	0.289593i	$0.0935199\pi$
$809$			2.48092e11i			0.579186i	−0.957150	+	0.289593i	$0.906480\pi$
$810$		0			0
$811$	−4.35627e11			−1.00700			−0.503502	−	0.863994i	$-0.667955\pi$
$811$	−4.35627e11			−1.00700			−0.503502	+	0.863994i	$0.667955\pi$
$812$	3.55137e11	−	4.23235e11i	0.816905	−	0.973549i
$813$		0			0
$814$	7.25462e10	+	4.11430e11i	0.165241	+	0.937127i
$815$	9.60661e10	−	2.63939e11i	0.217741	−	0.598238i
$816$		0			0
$817$	1.05531e11	−	5.98498e11i	0.236861	−	1.34331i
$818$	1.25409e11	+	7.24052e10i	0.280102	+	0.161717i
$819$		0			0
$820$	−5.08911e11	−	8.81459e11i	−1.12561	−	1.94961i
$821$	2.06171e11	+	5.66450e11i	0.453790	+	1.24678i	0.930037	+	0.367465i	$0.119774\pi$
$821$	2.06171e11	+	5.66450e11i	0.453790	+	1.24678i	−0.476248	+	0.879311i	$0.658003\pi$
$822$		0			0
$823$	2.70947e10	−	2.27352e10i	0.0590589	−	0.0495563i	−0.612780	−	0.790253i	$-0.709949\pi$
$823$	2.70947e10	−	2.27352e10i	0.0590589	−	0.0495563i	0.671839	+	0.740697i	$0.265505\pi$
$824$	6.11143e11	+	7.28332e11i	1.32567	+	1.57987i
$825$		0			0
$826$	−6.14244e11	+	2.23566e11i	−1.31953	+	0.480271i
$827$	1.39326e11	−	8.04397e10i	0.297858	−	0.171968i	−0.343622	−	0.939108i	$-0.611654\pi$
$827$	1.39326e11	−	8.04397e10i	0.297858	−	0.171968i	0.641480	+	0.767140i	$0.278321\pi$
$828$		0			0
$829$	3.40888e11	−	5.90435e11i	0.721761	−	1.25013i	−0.238532	−	0.971135i	$-0.576666\pi$
$829$	3.40888e11	−	5.90435e11i	0.721761	−	1.25013i	0.960293	−	0.278993i	$-0.0900005\pi$
$830$	−4.65392e11	−	8.20612e10i	−0.980633	−	0.172912i
$831$		0			0
$832$	−2.60638e11	−	9.48645e10i	−0.543932	−	0.197975i
$833$	−2.92035e11	+	5.14937e10i	−0.606535	+	0.106948i
$834$		0			0
$835$	−3.45703e10	−	2.90079e10i	−0.0711144	−	0.0596720i
$836$		−	1.00032e12i		−	2.04792i
$837$		0			0
$838$	−1.65706e12			−3.36017
$839$	−4.63519e11	+	5.52400e11i	−0.935448	+	1.11482i	0.0577439	+	0.998331i	$0.481609\pi$
$839$	−4.63519e11	+	5.52400e11i	−0.935448	+	1.11482i	−0.993192	+	0.116492i	$0.962835\pi$
$840$		0			0
$841$	3.48613e10	+	1.97708e11i	0.0696883	+	0.395222i
$842$	−4.09703e10	+	1.12565e11i	−0.0815118	+	0.223952i
$843$		0			0
$844$	6.99624e10	−	3.96776e11i	0.137878	−	0.781945i
$845$	5.88271e11	+	3.39638e11i	1.15385	+	0.666177i
$846$		0			0
$847$	−1.31109e10	−	2.27088e10i	−0.0254741	−	0.0441225i
$848$	1.09619e11	+	3.01176e11i	0.211984	+	0.582421i
$849$		0			0
$850$	−6.36821e11	+	5.34356e11i	−1.21995	+	1.02366i
$851$	−7.08821e10	−	8.44740e10i	−0.135151	−	0.161066i
$852$		0			0
$853$	−6.87875e11	+	2.50366e11i	−1.29931	+	0.472911i	−0.896773	−	0.442492i	$-0.854095\pi$
$853$	−6.87875e11	+	2.50366e11i	−1.29931	+	0.472911i	−0.402539	+	0.915403i	$0.631872\pi$
$854$	9.15994e11	−	5.28850e11i	1.72211	−	0.994262i
$855$		0			0
$856$	−6.28712e10	+	1.08896e11i	−0.117100	+	0.202823i
$857$	−1.83544e11	−	3.23638e10i	−0.340265	−	0.0599979i	0.000904747	−	1.00000i	$-0.499712\pi$
$857$	−1.83544e11	−	3.23638e10i	−0.340265	−	0.0599979i	−0.341170	+	0.940002i	$0.610823\pi$
$858$		0			0
$859$	7.71986e11	+	2.80980e11i	1.41787	+	0.516063i	0.933429	−	0.358761i	$-0.116801\pi$
$859$	7.71986e11	+	2.80980e11i	1.41787	+	0.516063i	0.484441	+	0.874824i	$0.339023\pi$
$860$	−1.08063e12	+	1.90543e11i	−1.97552	+	0.348338i
$861$		0			0
$862$	4.04532e11	+	3.39443e11i	0.732696	+	0.614805i
$863$		−	3.32474e11i		−	0.599397i	−0.954034	−	0.299699i	$-0.903114\pi$
$863$		−	3.32474e11i		−	0.599397i	0.954034	−	0.299699i	$-0.0968861\pi$
$864$		0			0
$865$	−1.46985e11			−0.262548
$866$	2.61428e11	−	3.11558e11i	0.464816	−	0.553946i
$867$		0			0
$868$	−1.07886e10	−	6.11852e10i	−0.0190058	−	0.107787i
$869$	8.15225e10	−	2.23981e11i	0.142955	−	0.392765i
$870$		0			0
$871$	−1.11176e11	+	6.30508e11i	−0.193169	+	1.09551i
$872$	−7.19015e10	−	4.15124e10i	−0.124358	−	0.0717979i
$873$		0			0
$874$	1.89305e11	+	3.27887e11i	0.324427	+	0.561925i
$875$	−1.33078e11	−	3.65630e11i	−0.227026	−	0.623749i
$876$		0			0
$877$	−3.69136e11	+	3.09742e11i	−0.624005	+	0.523602i	−0.899060	−	0.437826i	$-0.855748\pi$
$877$	−3.69136e11	+	3.09742e11i	−0.624005	+	0.523602i	0.275055	+	0.961429i	$0.411304\pi$
$878$	−1.47146e10	−	1.75362e10i	−0.0247611	−	0.0295091i
$879$		0			0
$880$	−6.41137e11	+	2.33355e11i	−1.06910	+	0.389122i
$881$	6.48703e11	−	3.74529e11i	1.07682	−	0.621701i	0.146781	−	0.989169i	$-0.453109\pi$
$881$	6.48703e11	−	3.74529e11i	1.07682	−	0.621701i	0.930036	+	0.367468i	$0.119775\pi$
$882$		0			0
$883$	−2.75384e11	+	4.76979e11i	−0.452997	+	0.784614i	−0.998571	−	0.0534488i	$-0.982979\pi$
$883$	−2.75384e11	+	4.76979e11i	−0.452997	+	0.784614i	0.545573	+	0.838063i	$0.316312\pi$
$884$	−3.21396e12	−	5.66708e11i	−5.26297	−	0.928004i
$885$		0			0
$886$	−1.92333e12	−	7.00035e11i	−3.12118	−	1.13602i
$887$	−7.94655e11	+	1.40119e11i	−1.28376	+	0.226362i	−0.773576	−	0.633704i	$-0.781534\pi$
$887$	−7.94655e11	+	1.40119e11i	−1.28376	+	0.226362i	−0.510184	+	0.860065i	$0.670423\pi$
$888$		0			0
$889$	3.49426e11	+	2.93204e11i	0.559434	+	0.469421i
$890$		−	6.71145e11i		−	1.06969i
$891$		0			0
$892$	2.78289e12			4.39579
$893$	−1.80107e11	+	2.14643e11i	−0.283220	+	0.337528i
$894$		0			0
$895$	1.04815e11	+	5.94435e11i	0.163354	+	0.926429i
$896$	1.11155e11	−	3.05397e11i	0.172464	−	0.473841i
$897$		0			0
$898$	2.99218e11	−	1.69695e12i	0.460131	−	2.60953i
$899$	−2.91660e10	−	1.68390e10i	−0.0446518	−	0.0257797i
$900$		0			0
$901$	1.27440e11	+	2.20733e11i	0.193378	+	0.334941i
$902$	7.59594e11	+	2.08697e12i	1.14751	+	3.15275i
$903$		0			0
$904$	4.59373e11	−	3.85460e11i	0.687847	−	0.577172i
$905$	6.52758e10	+	7.77927e10i	0.0973101	+	0.115970i
$906$		0			0
$907$	4.96262e11	−	1.80625e11i	0.733300	−	0.266899i	0.0517391	−	0.998661i	$-0.483524\pi$
$907$	4.96262e11	−	1.80625e11i	0.733300	−	0.266899i	0.681561	+	0.731761i	$0.261301\pi$
$908$	3.04681e11	−	1.75908e11i	0.448232	−	0.258787i
$909$		0			0
$910$	4.50888e11	−	7.80962e11i	0.657512	−	1.13884i
$911$	6.94494e10	+	1.22458e10i	0.100831	+	0.0177793i	0.223836	−	0.974627i	$-0.428142\pi$
$911$	6.94494e10	+	1.22458e10i	0.100831	+	0.0177793i	−0.123005	+	0.992406i	$0.539253\pi$
$912$		0			0
$913$	6.75743e11	+	2.45950e11i	0.972519	+	0.353968i
$914$	2.07034e12	−	3.65057e11i	2.96659	−	0.523090i
$915$		0			0
$916$	−1.86790e12	−	1.56735e12i	−2.65321	−	2.22630i
$917$			8.94046e10i			0.126439i
$918$		0			0
$919$	−1.12965e12			−1.58373			−0.791863	−	0.610698i	$-0.790889\pi$
$919$	−1.12965e12			−1.58373			−0.791863	+	0.610698i	$0.790889\pi$
$920$	2.48735e11	−	2.96431e11i	0.347204	−	0.413782i
$921$		0			0
$922$	−1.77520e11	−	1.00677e12i	−0.245654	−	1.39318i
$923$	6.58321e11	−	1.80872e12i	0.907049	−	2.49210i
$924$		0			0
$925$	4.49917e10	−	2.55161e11i	0.0614562	−	0.348536i
$926$	−4.80546e11	−	2.77443e11i	−0.653569	−	0.377338i
$927$		0			0
$928$	3.65958e11	+	6.33858e11i	0.493446	+	0.854673i
$929$	−1.27673e11	−	3.50779e11i	−0.171410	−	0.470946i	0.824006	−	0.566581i	$-0.191734\pi$
$929$	−1.27673e11	−	3.50779e11i	−0.171410	−	0.470946i	−0.995416	+	0.0956349i	$0.969512\pi$
$930$		0			0
$931$	−2.43087e11	+	2.03974e11i	−0.323566	+	0.271504i
$932$	1.01965e11	+	1.21517e11i	0.135141	+	0.161055i
$933$		0			0
$934$	2.41444e12	−	8.78784e11i	3.17270	−	1.15477i
$935$	−4.69892e11	+	2.71292e11i	−0.614825	+	0.354969i
$936$		0			0
$937$	−4.28605e11	+	7.42365e11i	−0.556030	+	0.963073i	0.441792	+	0.897117i	$0.354343\pi$
$937$	−4.28605e11	+	7.42365e11i	−0.556030	+	0.963073i	−0.997823	+	0.0659554i	$0.978990\pi$
$938$	5.93132e11	+	1.04585e11i	0.766196	+	0.135101i
$939$		0			0
$940$	4.75401e11	+	1.73032e11i	0.608904	+	0.221623i
$941$	−9.99686e11	+	1.76272e11i	−1.27499	+	0.224814i	−0.769849	−	0.638226i	$-0.779669\pi$
$941$	−9.99686e11	+	1.76272e11i	−1.27499	+	0.224814i	−0.505136	+	0.863040i	$0.668558\pi$
$942$		0			0
$943$	−4.49064e11	−	3.76810e11i	−0.567887	−	0.476513i
$944$		−	1.72661e12i		−	2.17424i
$945$		0			0
$946$	2.39432e12			2.98963
$947$	−1.33452e11	+	1.59042e11i	−0.165930	+	0.197748i	−0.842602	−	0.538537i	$-0.818977\pi$
$947$	−1.33452e11	+	1.59042e11i	−0.165930	+	0.197748i	0.676672	+	0.736285i	$0.263422\pi$
$948$		0			0
$949$	−4.13451e11	−	2.34479e12i	−0.509752	−	2.89095i
$950$	−3.04255e11	+	8.35935e11i	−0.373546	+	1.02631i
$951$		0			0
$952$	−3.01775e11	+	1.71145e12i	−0.367397	+	2.08361i
$953$	6.67557e10	+	3.85414e10i	0.0809314	+	0.0467257i	0.539920	−	0.841717i	$-0.318455\pi$
$953$	6.67557e10	+	3.85414e10i	0.0809314	+	0.0467257i	−0.458988	+	0.888442i	$0.651788\pi$
$954$		0			0
$955$	1.27919e11	+	2.21562e11i	0.153788	+	0.266368i
$956$	3.32590e11	+	9.13784e11i	0.398179	+	1.09399i
$957$		0			0
$958$	−6.78446e11	+	5.69284e11i	−0.805477	+	0.675876i
$959$	−2.95430e11	−	3.52080e11i	−0.349285	−	0.416262i
$960$		0			0
$961$	7.97897e11	−	2.90411e11i	0.935520	−	0.340501i
$962$	1.26313e12	−	7.29271e11i	1.47485	−	0.851507i
$963$		0			0
$964$	1.18463e12	−	2.05185e12i	1.37175	−	2.37595i
$965$	−1.63699e11	−	2.88645e10i	−0.188771	−	0.0332855i
$966$		0			0
$967$	−1.60364e11	−	5.83679e10i	−0.183401	−	0.0667526i	0.248687	−	0.968584i	$-0.420001\pi$
$967$	−1.60364e11	−	5.83679e10i	−0.183401	−	0.0667526i	−0.432088	+	0.901831i	$0.642223\pi$
$968$	1.46566e11	−	2.58436e10i	0.166929	−	0.0294341i
$969$		0			0
$970$	−3.92700e10	−	3.29515e10i	−0.0443583	−	0.0372210i
$971$			1.10689e12i			1.24516i	0.782556	+	0.622581i	$0.213916\pi$
$971$			1.10689e12i			1.24516i	−0.782556	+	0.622581i	$0.786084\pi$
$972$		0			0
$973$	9.73459e11			1.08609
$974$	3.13699e11	−	3.73852e11i	0.348560	−	0.415397i
$975$		0			0
$976$	4.85146e11	+	2.75140e12i	0.534654	+	3.03217i
$977$	−1.06866e11	+	2.93612e11i	−0.117290	+	0.322252i	−0.984421	−	0.175829i	$-0.943740\pi$
$977$	−1.06866e11	+	2.93612e11i	−0.117290	+	0.322252i	0.867131	+	0.498081i	$0.165962\pi$
$978$		0			0
$979$	−1.77343e11	+	1.00576e12i	−0.193056	+	1.09488i
$980$	4.96193e11	+	2.86477e11i	0.537955	+	0.310589i
$981$		0			0
$982$	4.28878e11	+	7.42838e11i	0.461198	+	0.798819i
$983$	−1.37248e10	−	3.77085e10i	−0.0146991	−	0.0403855i	0.932126	−	0.362134i	$-0.117952\pi$
$983$	−1.37248e10	−	3.77085e10i	−0.0146991	−	0.0403855i	−0.946825	+	0.321748i	$0.895729\pi$
$984$		0			0
$985$	−2.28127e11	+	1.91421e11i	−0.242343	+	0.203350i
$986$	1.06972e12	+	1.27484e12i	1.13178	+	1.34880i
$987$		0			0
$988$	−3.28169e12	+	1.19444e12i	−3.44406	+	1.25353i
$989$	−5.47315e11	+	3.15993e11i	−0.572074	+	0.330287i
$990$		0			0
$991$	−3.79443e11	+	6.57215e11i	−0.393416	+	0.681416i	−0.992898	−	0.118972i	$-0.962040\pi$
$991$	−3.79443e11	+	6.57215e11i	−0.393416	+	0.681416i	0.599482	+	0.800388i	$0.295373\pi$
$992$	8.10550e10	+	1.42922e10i	0.0837015	+	0.0147588i
$993$		0			0
$994$	−1.70150e12	−	6.19296e11i	−1.74296	−	0.634385i
$995$	−4.78543e11	+	8.43800e10i	−0.488234	+	0.0860889i
$996$		0			0
$997$	1.30003e11	+	1.09085e11i	0.131575	+	0.110404i	0.706200	−	0.708012i	$-0.250408\pi$
$997$	1.30003e11	+	1.09085e11i	0.131575	+	0.110404i	−0.574626	+	0.818416i	$0.694852\pi$
$998$			1.91154e12i			1.92691i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.35.22		138
3.2	odd	2		27.9.f.a.11.2	yes	138
27.5	odd	18	inner	81.9.f.a.44.22		138
27.22	even	9		27.9.f.a.5.2	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.5.2	✓	138	27.22	even	9
27.9.f.a.11.2	yes	138	3.2	odd	2
81.9.f.a.35.22		138	1.1	even	1	trivial
81.9.f.a.44.22		138	27.5	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+(18.6956 - 22.2805i) q^{2} +(-102.443 - 580.983i) q^{4} +(-117.116 + 321.773i) q^{5} +(-297.164 + 1685.30i) q^{7} +(-8411.56 - 4856.42i) q^{8} +(4979.72 + 8625.13i) q^{10} +(-5183.40 - 14241.3i) q^{11} +(-40531.4 + 34009.8i) q^{13} +(31993.8 + 38128.7i) q^{14} +(-123544. + 44966.5i) q^{16} +(-90546.3 + 52276.9i) q^{17} +(-55941.4 + 96893.4i) q^{19} +(198942. + 35078.9i) q^{20} +(-414209. - 150760. i) q^{22} +(114580. - 20203.6i) q^{23} +(209414. + 175719. i) q^{25} +1.53889e6i q^{26} +1.00957e6 q^{28} +(351769. - 419222. i) q^{29} +(-10686.3 - 60605.0i) q^{31} +(-457428. + 1.25677e6i) q^{32} +(-528058. + 2.99476e6i) q^{34} +(-507483. - 292995. i) q^{35} +(-473893. - 820807. i) q^{37} +(1.11298e6 + 3.05788e6i) q^{38} +(2.54779e6 - 2.13785e6i) q^{40} +(-3.23864e6 - 3.85967e6i) q^{41} +(-5.10427e6 + 1.85780e6i) q^{43} +(-7.74293e6 + 4.47038e6i) q^{44} +(1.69200e6 - 2.93063e6i) q^{46} +(2.46632e6 + 434879. i) q^{47} +(2.66520e6 + 970053. i) q^{49} +(7.83023e6 - 1.38068e6i) q^{50} +(2.39113e7 + 2.00639e7i) q^{52} -2.43779e6i q^{53} +5.18952e6 q^{55} +(1.06842e7 - 1.27329e7i) q^{56} +(-2.76396e6 - 1.56752e7i) q^{58} +(-4.49168e6 + 1.23408e7i) q^{59} +(3.69007e6 - 2.09274e7i) q^{61} +(-1.55010e6 - 894948. i) q^{62} +(2.62111e6 + 4.53989e6i) q^{64} +(-6.19659e6 - 1.70250e7i) q^{65} +(9.26949e6 - 7.77802e6i) q^{67} +(3.96478e7 + 4.72504e7i) q^{68} +(-1.60158e7 + 5.82926e6i) q^{70} +(-3.15050e7 + 1.81894e7i) q^{71} +(-2.25002e7 + 3.89715e7i) q^{73} +(-2.71477e7 - 4.78687e6i) q^{74} +(6.20241e7 + 2.25749e7i) q^{76} +(2.55412e7 - 4.50360e6i) q^{77} +(1.20481e7 + 1.01095e7i) q^{79} -4.50196e7i q^{80} -1.46544e8 q^{82} +(-3.05000e7 + 3.63485e7i) q^{83} +(-6.21691e6 - 3.52578e7i) q^{85} +(-5.40345e7 + 1.48458e8i) q^{86} +(-2.55611e7 + 1.44964e8i) q^{88} +(-5.83596e7 - 3.36939e7i) q^{89} +(-4.52724e7 - 7.84141e7i) q^{91} +(-2.34759e7 - 6.44995e7i) q^{92} +(5.57986e7 - 4.68206e7i) q^{94} +(-2.46261e7 - 2.93482e7i) q^{95} +(-4.83680e6 + 1.76045e6i) q^{97} +(7.14407e7 - 4.12463e7i) 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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