LMFDB - Embedded newform 81.9.f.a.8.13

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			8.13
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.24198 + 0.571649i) q^{2} +(-230.378 - 83.8506i) q^{4} +(-387.667 - 462.003i) q^{5} +(-3862.15 + 1405.71i) q^{7} +(-1428.79 - 824.913i) q^{8} +(-992.706 - 1719.42i) q^{10} +(-11423.3 + 13613.8i) q^{11} +(-882.859 - 5006.94i) q^{13} +(-13324.6 + 2349.49i) q^{14} +(43917.7 + 36851.3i) q^{16} +(-23746.9 + 13710.3i) q^{17} +(92857.3 - 160834. i) q^{19} +(50570.5 + 138941. i) q^{20} +(-44816.5 + 37605.5i) q^{22} +(88410.2 - 242905. i) q^{23} +(4669.78 - 26483.6i) q^{25} -16737.1i q^{26} +1.00762e6 q^{28} +(234351. + 41322.5i) q^{29} +(-618503. - 225117. i) q^{31} +(392799. + 468120. i) q^{32} +(-84824.4 + 30873.6i) q^{34} +(2.14667e6 + 1.23938e6i) q^{35} +(779022. + 1.34931e6i) q^{37} +(392982. - 468338. i) q^{38} +(172782. + 979898. i) q^{40} +(-3.82274e6 + 674052. i) q^{41} +(-1.19676e6 - 1.00420e6i) q^{43} +(3.77320e6 - 2.17846e6i) q^{44} +(425481. - 736954. i) q^{46} +(-407155. - 1.11865e6i) q^{47} +(8.52411e6 - 7.15258e6i) q^{49} +(30278.7 - 83190.0i) q^{50} +(-216444. + 1.22752e6i) q^{52} +1.29944e7i q^{53} +1.07180e7 q^{55} +(6.67780e6 + 1.17748e6i) q^{56} +(736141. + 267934. i) q^{58} +(1.38268e7 + 1.64782e7i) q^{59} +(1.39731e7 - 5.08578e6i) q^{61} +(-1.87649e6 - 1.08339e6i) q^{62} +(-6.33245e6 - 1.09681e7i) q^{64} +(-1.97097e6 + 2.34891e6i) q^{65} +(-1.06177e6 - 6.02157e6i) q^{67} +(6.62036e6 - 1.16735e6i) q^{68} +(6.25098e6 + 5.24520e6i) q^{70} +(-3.07395e7 + 1.77475e7i) q^{71} +(6.89919e6 - 1.19498e7i) q^{73} +(1.75425e6 + 4.81975e6i) q^{74} +(-3.48782e7 + 2.92663e7i) q^{76} +(2.49816e7 - 6.86363e7i) q^{77} +(-7.76297e6 + 4.40260e7i) q^{79} -3.45761e7i q^{80} -1.27786e7 q^{82} +(4.57442e7 + 8.06593e6i) q^{83} +(1.55401e7 + 5.65612e6i) q^{85} +(-3.30581e6 - 3.93971e6i) q^{86} +(2.75517e7 - 1.00280e7i) q^{88} +(3.60126e6 + 2.07919e6i) q^{89} +(1.04480e7 + 1.80965e7i) q^{91} +(-4.07355e7 + 4.85466e7i) q^{92} +(-680516. - 3.85940e6i) q^{94} +(-1.10303e8 + 1.94495e7i) q^{95} +(-1.08572e8 - 9.11031e7i) q^{97} +(3.17238e7 - 1.83157e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.24198	+	0.571649i	0.202624	+	0.0357281i	0.274039	−	0.961719i	$-0.411640\pi$
$2$	3.24198	+	0.571649i	0.202624	+	0.0357281i	−0.0714149	+	0.997447i	$0.522751\pi$
$3$		0			0
$3$		0			0
$4$	−230.378	−	83.8506i	−0.899913	−	0.327541i
$5$	−387.667	−	462.003i	−0.620267	−	0.739206i	0.360849	−	0.932624i	$-0.382487\pi$
$5$	−387.667	−	462.003i	−0.620267	−	0.739206i	−0.981116	+	0.193419i	$0.938042\pi$
$6$		0			0
$7$	−3862.15	+	1405.71i	−1.60856	+	0.585468i	−0.981155	−	0.193225i	$-0.938105\pi$
$7$	−3862.15	+	1405.71i	−1.60856	+	0.585468i	−0.627405	+	0.778693i	$0.715883\pi$
$8$	−1428.79	−	824.913i	−0.348826	−	0.201395i
$9$		0			0
$10$	−992.706	−	1719.42i	−0.0992706	−	0.171942i
$11$	−11423.3	+	13613.8i	−0.780227	+	0.929839i	−0.998944	−	0.0459497i	$-0.985369\pi$
$11$	−11423.3	+	13613.8i	−0.780227	+	0.929839i	0.218716	+	0.975788i	$0.429813\pi$
$12$		0			0
$13$	−882.859	−	5006.94i	−0.0309113	−	0.175307i	0.965443	−	0.260612i	$-0.0839245\pi$
$13$	−882.859	−	5006.94i	−0.0309113	−	0.175307i	−0.996355	+	0.0853055i	$0.972813\pi$
$14$	−13324.6	+	2349.49i	−0.346850	+	0.0611591i
$15$		0			0
$16$	43917.7	+	36851.3i	0.670130	+	0.562306i
$17$	−23746.9	+	13710.3i	−0.284322	+	0.164153i	−0.635378	−	0.772201i	$-0.719156\pi$
$17$	−23746.9	+	13710.3i	−0.284322	+	0.164153i	0.351056	+	0.936354i	$0.385823\pi$
$18$		0			0
$19$	92857.3	−	160834.i	0.712528	−	1.23413i	−0.251378	−	0.967889i	$-0.580884\pi$
$19$	92857.3	−	160834.i	0.712528	−	1.23413i	0.963905	−	0.266245i	$-0.0857831\pi$
$20$	50570.5	+	138941.i	0.316066	+	0.868384i
$21$		0			0
$22$	−44816.5	+	37605.5i	−0.191314	+	0.160532i
$23$	88410.2	−	242905.i	0.315930	−	0.868011i	−0.675498	−	0.737361i	$-0.736072\pi$
$23$	88410.2	−	242905.i	0.315930	−	0.868011i	0.991429	−	0.130650i	$-0.0417063\pi$
$24$		0			0
$25$	4669.78	−	26483.6i	0.0119546	−	0.0677981i
$26$		−	16737.1i		−	0.0366258i
$27$		0			0
$28$	1.00762e6			1.63933
$29$	234351.	+	41322.5i	0.331341	+	0.0584244i	0.336844	−	0.941560i	$-0.390640\pi$
$29$	234351.	+	41322.5i	0.331341	+	0.0584244i	−0.00550273	+	0.999985i	$0.501752\pi$
$30$		0			0
$31$	−618503.	−	225117.i	−0.669723	−	0.243759i	−0.0152945	−	0.999883i	$-0.504869\pi$
$31$	−618503.	−	225117.i	−0.669723	−	0.243759i	−0.654429	+	0.756124i	$0.727091\pi$
$32$	392799.	+	468120.i	0.374602	+	0.446434i
$33$		0			0
$34$	−84824.4	+	30873.6i	−0.0634754	+	0.0231031i
$35$	2.14667e6	+	1.23938e6i	1.43052	+	0.825910i
$36$		0			0
$37$	779022.	+	1.34931e6i	0.415664	+	0.719952i	0.995498	−	0.0947831i	$-0.0302158\pi$
$37$	779022.	+	1.34931e6i	0.415664	+	0.719952i	−0.579834	+	0.814735i	$0.696882\pi$
$38$	392982.	−	468338.i	0.188468	−	0.224608i
$39$		0			0
$40$	172782.	+	979898.i	0.0674931	+	0.382773i
$41$	−3.82274e6	+	674052.i	−1.35282	+	0.238538i	−0.802617	−	0.596494i	$-0.796560\pi$
$41$	−3.82274e6	+	674052.i	−1.35282	+	0.238538i	−0.550201	+	0.835033i	$0.685449\pi$
$42$		0			0
$43$	−1.19676e6	−	1.00420e6i	−0.350051	−	0.293728i	0.450759	−	0.892645i	$-0.351153\pi$
$43$	−1.19676e6	−	1.00420e6i	−0.350051	−	0.293728i	−0.800811	+	0.598918i	$0.795598\pi$
$44$	3.77320e6	−	2.17846e6i	1.00670	−	0.581217i
$45$		0			0
$46$	425481.	−	736954.i	0.0950274	−	0.164592i
$47$	−407155.	−	1.11865e6i	−0.0834390	−	0.229247i	0.890956	−	0.454089i	$-0.150035\pi$
$47$	−407155.	−	1.11865e6i	−0.0834390	−	0.229247i	−0.974395	+	0.224843i	$0.927813\pi$
$48$		0			0
$49$	8.52411e6	−	7.15258e6i	1.47865	−	1.24073i
$50$	30278.7	−	83190.0i	0.00484459	−	0.0133104i
$51$		0			0
$52$	−216444.	+	1.22752e6i	−0.0296028	+	0.167886i
$53$			1.29944e7i			1.64684i	0.567432	+	0.823420i	$0.307937\pi$
$53$			1.29944e7i			1.64684i	−0.567432	+	0.823420i	$0.692063\pi$
$54$		0			0
$55$	1.07180e7			1.17129
$56$	6.67780e6	+	1.17748e6i	0.679018	+	0.119729i
$57$		0			0
$58$	736141.	+	267934.i	0.0650503	+	0.0236764i
$59$	1.38268e7	+	1.64782e7i	1.14107	+	1.35988i	0.923391	+	0.383861i	$0.125406\pi$
$59$	1.38268e7	+	1.64782e7i	1.14107	+	1.35988i	0.217684	+	0.976019i	$0.430150\pi$
$60$		0			0
$61$	1.39731e7	−	5.08578e6i	1.00919	−	0.367315i	0.216068	−	0.976378i	$-0.430677\pi$
$61$	1.39731e7	−	5.08578e6i	1.00919	−	0.367315i	0.793121	+	0.609064i	$0.208455\pi$
$62$	−1.87649e6	−	1.08339e6i	−0.126993	−	0.0733194i
$63$		0			0
$64$	−6.33245e6	−	1.09681e7i	−0.377443	−	0.653751i
$65$	−1.97097e6	+	2.34891e6i	−0.110415	+	0.131587i
$66$		0			0
$67$	−1.06177e6	−	6.02157e6i	−0.0526901	−	0.298821i	0.947063	−	0.321048i	$-0.104035\pi$
$67$	−1.06177e6	−	6.02157e6i	−0.0526901	−	0.298821i	−0.999753	+	0.0222278i	$0.992924\pi$
$68$	6.62036e6	−	1.16735e6i	0.309632	−	0.0545965i
$69$		0			0
$70$	6.25098e6	+	5.24520e6i	0.260349	+	0.218459i
$71$	−3.07395e7	+	1.77475e7i	−1.20966	+	0.698398i	−0.962685	−	0.270624i	$-0.912770\pi$
$71$	−3.07395e7	+	1.77475e7i	−1.20966	+	0.698398i	−0.246975	+	0.969022i	$0.579437\pi$
$72$		0			0
$73$	6.89919e6	−	1.19498e7i	0.242944	−	0.420792i	−0.718607	−	0.695416i	$-0.755220\pi$
$73$	6.89919e6	−	1.19498e7i	0.242944	−	0.420792i	0.961552	+	0.274624i	$0.0885534\pi$
$74$	1.75425e6	+	4.81975e6i	0.0585011	+	0.160730i
$75$		0			0
$76$	−3.48782e7	+	2.92663e7i	−1.04544	+	0.877231i
$77$	2.49816e7	−	6.86363e7i	0.710652	−	1.95250i
$78$		0			0
$79$	−7.76297e6	+	4.40260e7i	−0.199306	+	1.13032i	0.706846	+	0.707367i	$0.250117\pi$
$79$	−7.76297e6	+	4.40260e7i	−0.199306	+	1.13032i	−0.906152	+	0.422952i	$0.860994\pi$
$80$		−	3.45761e7i		−	0.844144i
$81$		0			0
$82$	−1.27786e7			−0.282636
$83$	4.57442e7	+	8.06593e6i	0.963881	+	0.169958i	0.633374	−	0.773846i	$-0.281669\pi$
$83$	4.57442e7	+	8.06593e6i	0.963881	+	0.169958i	0.330506	+	0.943804i	$0.392780\pi$
$84$		0			0
$85$	1.55401e7	+	5.65612e6i	0.297699	+	0.108354i
$86$	−3.30581e6	−	3.93971e6i	−0.0604344	−	0.0720230i
$87$		0			0
$88$	2.75517e7	−	1.00280e7i	0.459428	−	0.167218i
$89$	3.60126e6	+	2.07919e6i	0.0573977	+	0.0331386i	0.528424	−	0.848980i	$-0.322783\pi$
$89$	3.60126e6	+	2.07919e6i	0.0573977	+	0.0331386i	−0.471027	+	0.882119i	$0.656116\pi$
$90$		0			0
$91$	1.04480e7	+	1.80965e7i	0.152359	+	0.263894i
$92$	−4.07355e7	+	4.85466e7i	−0.568619	+	0.677654i
$93$		0			0
$94$	−680516.	−	3.85940e6i	−0.00871619	−	0.0494320i
$95$	−1.10303e8	+	1.94495e7i	−1.35424	+	0.238788i
$96$		0			0
$97$	−1.08572e8	−	9.11031e7i	−1.22640	−	1.02907i	−0.998464	−	0.0553970i	$-0.982358\pi$
$97$	−1.08572e8	−	9.11031e7i	−1.22640	−	1.02907i	−0.227937	−	0.973676i	$-0.573198\pi$
$98$	3.17238e7	−	1.83157e7i	0.343938	−	0.198573i
$99$		0			0
$100$	−3.29648e6	+	5.70967e6i	−0.0329648	+	0.0570967i
$101$	−4.07022e7	−	1.11828e8i	−0.391140	−	1.07465i	−0.966482	−	0.256735i	$-0.917353\pi$
$101$	−4.07022e7	−	1.11828e8i	−0.391140	−	1.07465i	0.575342	−	0.817913i	$-0.304869\pi$
$102$		0			0
$103$	−2.77608e7	+	2.32941e7i	−0.246651	+	0.206965i	−0.757729	−	0.652570i	$-0.773691\pi$
$103$	−2.77608e7	+	2.32941e7i	−0.246651	+	0.206965i	0.511077	+	0.859535i	$0.329247\pi$
$104$	−2.86887e6	+	7.88216e6i	−0.0245232	+	0.0673770i
$105$		0			0
$106$	−7.42821e6	+	4.21275e7i	−0.0588384	+	0.333689i
$107$			1.86649e8i			1.42394i	0.702212	+	0.711968i	$0.252196\pi$
$107$			1.86649e8i			1.42394i	−0.702212	+	0.711968i	$0.747804\pi$
$108$		0			0
$109$	1.05606e8			0.748138			0.374069	−	0.927401i	$-0.377962\pi$
$109$	1.05606e8			0.748138			0.374069	+	0.927401i	$0.377962\pi$
$110$	3.47477e7	+	6.12696e6i	0.237332	+	0.0418480i
$111$		0			0
$112$	−2.21419e8	−	8.05899e7i	−1.40716	−	0.512163i
$113$	−1.87685e8	−	2.23674e8i	−1.15110	−	1.37183i	−0.916643	−	0.399708i	$-0.869112\pi$
$113$	−1.87685e8	−	2.23674e8i	−1.15110	−	1.37183i	−0.234462	−	0.972125i	$-0.575333\pi$
$114$		0			0
$115$	−1.46497e8	+	5.33204e7i	−0.837599	+	0.304861i
$116$	−5.05244e7	−	2.91703e7i	−0.279042	−	0.161105i
$117$		0			0
$118$	3.54066e7	+	6.13260e7i	0.182623	+	0.316313i
$119$	7.24414e7	−	8.63323e7i	0.361243	−	0.430512i
$120$		0			0
$121$	−1.76197e7	−	9.99263e7i	−0.0821972	−	0.466164i
$122$	4.82078e7	−	8.50033e6i	0.217609	−	0.0383704i
$123$		0			0
$124$	1.23613e8	+	1.03724e8i	0.522851	+	0.438724i
$125$	−2.18070e8	+	1.25903e8i	−0.893215	+	0.515698i
$126$		0			0
$127$	1.44951e8	−	2.51062e8i	0.557192	−	0.965085i	−0.440537	−	0.897734i	$-0.645212\pi$
$127$	1.44951e8	−	2.51062e8i	0.557192	−	0.965085i	0.997729	−	0.0673506i	$-0.0214546\pi$
$128$	−6.77648e7	−	1.86182e8i	−0.252444	−	0.693583i
$129$		0			0
$130$	−7.73260e6	+	6.48842e6i	−0.0270740	+	0.0227178i
$131$	−5.14222e7	+	1.41281e8i	−0.174609	+	0.479733i	−0.995867	−	0.0908232i	$-0.971050\pi$
$131$	−5.14222e7	+	1.41281e8i	−0.174609	+	0.479733i	0.821258	+	0.570556i	$0.193272\pi$
$132$		0			0
$133$	−1.32544e8	+	7.51694e8i	−0.423598	+	2.40234i
$134$		−	2.01288e7i		−	0.0624307i
$135$		0			0
$136$	4.52391e7			0.132239
$137$	6.49465e8	+	1.14518e8i	1.84363	+	0.325082i	0.982923	−	0.184020i	$-0.0589110\pi$
$137$	6.49465e8	+	1.14518e8i	1.84363	+	0.325082i	0.860707	+	0.509101i	$0.170022\pi$
$138$		0			0
$139$	−4.91164e8	−	1.78769e8i	−1.31573	−	0.478887i	−0.413643	−	0.910439i	$-0.635744\pi$
$139$	−4.91164e8	−	1.78769e8i	−1.31573	−	0.478887i	−0.902088	+	0.431552i	$0.857966\pi$
$140$	−3.90622e8	−	4.65525e8i	−1.01682	−	1.21180i
$141$		0			0
$142$	−1.09802e8	+	3.99648e7i	−0.270059	+	0.0982933i
$143$	7.82485e7	+	4.51768e7i	0.187125	+	0.108037i
$144$		0			0
$145$	−7.17592e7	−	1.24291e8i	−0.162332	−	0.281168i
$146$	2.91981e7	−	3.47970e7i	0.0642604	−	0.0765826i
$147$		0			0
$148$	−6.63292e7	−	3.76171e8i	−0.138248	−	0.784041i
$149$	5.15210e8	−	9.08454e7i	1.04530	−	0.184314i	0.375472	−	0.926834i	$-0.377481\pi$
$149$	5.15210e8	−	9.08454e7i	1.04530	−	0.184314i	0.669824	+	0.742520i	$0.266370\pi$
$150$		0			0
$151$	5.15851e8	+	4.32850e8i	0.992239	+	0.832588i	0.985890	−	0.167392i	$-0.0535346\pi$
$151$	5.15851e8	+	4.32850e8i	0.992239	+	0.832588i	0.00634899	+	0.999980i	$0.497979\pi$
$152$	−2.65347e8	+	1.53198e8i	−0.497096	+	0.286999i
$153$		0			0
$154$	1.20226e8	−	2.08237e8i	0.213754	−	0.370233i
$155$	1.35769e8	+	3.73021e8i	0.235219	+	0.646259i
$156$		0			0
$157$	4.46343e8	−	3.74526e8i	0.734633	−	0.616430i	−0.196758	−	0.980452i	$-0.563041\pi$
$157$	4.46343e8	−	3.74526e8i	0.734633	−	0.616430i	0.931390	+	0.364022i	$0.118597\pi$
$158$	−5.03349e7	+	1.38294e8i	−0.0807682	+	0.221909i
$159$		0			0
$160$	6.39977e7	−	3.62949e8i	0.0976528	−	0.553816i
$161$			1.06242e9i			1.58121i
$162$		0			0
$163$	1.04960e9			1.48687			0.743437	−	0.668806i	$-0.233194\pi$
$163$	1.04960e9			1.48687			0.743437	+	0.668806i	$0.233194\pi$
$164$	9.37194e8	+	1.65253e8i	1.29555	+	0.228440i
$165$		0			0
$166$	1.43691e8	+	5.22992e7i	0.189233	+	0.0688752i
$167$	1.58207e8	+	1.88544e8i	0.203404	+	0.242407i	0.858097	−	0.513487i	$-0.171647\pi$
$167$	1.58207e8	+	1.88544e8i	0.203404	+	0.242407i	−0.654693	+	0.755895i	$0.727202\pi$
$168$		0			0
$169$	7.42246e8	−	2.70155e8i	0.909916	−	0.331182i
$170$	4.71473e7	+	2.72205e7i	0.0564496	+	0.0325912i
$171$		0			0
$172$	1.91503e8	+	3.31693e8i	0.218808	+	0.378986i
$173$	2.45942e8	−	2.93102e8i	0.274567	−	0.327216i	−0.611086	−	0.791564i	$-0.709267\pi$
$173$	2.45942e8	−	2.93102e8i	0.274567	−	0.327216i	0.885653	+	0.464348i	$0.153711\pi$
$174$		0			0
$175$	1.91929e7	+	1.08848e8i	0.0204639	+	0.116056i
$176$	−1.00337e9	+	1.76921e8i	−1.04571	+	0.184387i
$177$		0			0
$178$	1.04867e7	+	8.79935e6i	0.0104462	+	0.00876538i
$179$	1.76049e8	−	1.01642e8i	0.171483	−	0.0990057i	−0.411802	−	0.911273i	$-0.635100\pi$
$179$	1.76049e8	−	1.01642e8i	0.171483	−	0.0990057i	0.583285	+	0.812268i	$0.301767\pi$
$180$		0			0
$181$	3.05406e8	−	5.28979e8i	0.284553	−	0.492861i	−0.687948	−	0.725760i	$-0.741488\pi$
$181$	3.05406e8	−	5.28979e8i	0.284553	−	0.492861i	0.972501	+	0.232900i	$0.0748214\pi$
$182$	2.35275e7	+	6.46413e7i	0.0214432	+	0.0589148i
$183$		0			0
$184$	−3.26695e8	+	2.74130e8i	−0.285017	+	0.239158i
$185$	3.21383e8	−	8.82992e8i	0.274369	−	0.753824i
$186$		0			0
$187$	8.46195e7	−	4.79901e8i	0.0691997	−	0.392451i
$188$			2.91852e8i			0.233632i
$189$		0			0
$190$	−3.68720e8			−0.282932
$191$	−1.58410e8	−	2.79319e7i	−0.119028	−	0.0209878i	0.113817	−	0.993502i	$-0.463692\pi$
$191$	−1.58410e8	−	2.79319e7i	−0.119028	−	0.0209878i	−0.232845	+	0.972514i	$0.574803\pi$
$192$		0			0
$193$	−1.24511e8	−	4.53181e7i	−0.0897381	−	0.0326620i	0.296761	−	0.954952i	$-0.404094\pi$
$193$	−1.24511e8	−	4.53181e7i	−0.0897381	−	0.0326620i	−0.386499	+	0.922290i	$0.626316\pi$
$194$	−2.99911e8	−	3.57420e8i	−0.211731	−	0.252332i
$195$		0			0
$196$	−2.56351e9	+	9.33042e8i	−1.73705	+	0.632233i
$197$	5.26529e7	+	3.03991e7i	0.0349588	+	0.0201835i	0.517378	−	0.855757i	$-0.326908\pi$
$197$	5.26529e7	+	3.03991e7i	0.0349588	+	0.0201835i	−0.482419	+	0.875941i	$0.660242\pi$
$198$		0			0
$199$	−3.16579e8	−	5.48332e8i	−0.201869	−	0.349648i	0.747261	−	0.664530i	$-0.231368\pi$
$199$	−3.16579e8	−	5.48332e8i	−0.201869	−	0.349648i	−0.949131	+	0.314882i	$0.898035\pi$
$200$	−2.85188e7	+	3.39874e7i	−0.0178243	+	0.0212421i
$201$		0			0
$202$	−6.80292e7	−	3.85813e8i	−0.0408592	−	0.231724i
$203$	−9.63188e8	+	1.69836e8i	−0.567188	+	0.100011i
$204$		0			0
$205$	1.79336e9	+	1.50481e9i	1.01544	+	0.852053i
$206$	−1.03316e8	+	5.96496e7i	−0.0573719	+	0.0331237i
$207$		0			0
$208$	1.45739e8	−	2.52428e8i	0.0778616	−	0.134860i
$209$	1.12881e9	+	3.10139e9i	0.591612	+	1.62544i
$210$		0			0
$211$	−1.27463e9	+	1.06955e9i	−0.643067	+	0.539597i	−0.904958	−	0.425500i	$-0.860098\pi$
$211$	−1.27463e9	+	1.06955e9i	−0.643067	+	0.539597i	0.261892	+	0.965097i	$0.415654\pi$
$212$	1.08958e9	−	2.99361e9i	0.539408	−	1.48201i
$213$		0			0
$214$	−1.06698e8	+	6.05112e8i	−0.0508745	+	0.288523i
$215$			9.42199e8i			0.440950i
$216$		0			0
$217$	2.70520e9			1.22000
$218$	3.42372e8	+	6.03695e7i	0.151591	+	0.0267295i
$219$		0			0
$220$	−2.46920e9	−	8.98715e8i	−1.05406	−	0.383646i
$221$	8.96116e7	+	1.06795e8i	0.0375660	+	0.0447695i
$222$		0			0
$223$	−9.28099e7	+	3.37800e7i	−0.0375297	+	0.0136597i	−0.360717	−	0.932675i	$-0.617468\pi$
$223$	−9.28099e7	+	3.37800e7i	−0.0375297	+	0.0136597i	0.323187	+	0.946335i	$0.395246\pi$
$224$	−2.17509e9	−	1.25579e9i	−0.863943	−	0.498798i
$225$		0			0
$226$	−4.80607e8	−	8.32436e8i	−0.184228	−	0.319093i
$227$	2.09551e9	−	2.49733e9i	0.789198	−	0.940529i	−0.210112	−	0.977677i	$-0.567383\pi$
$227$	2.09551e9	−	2.49733e9i	0.789198	−	0.940529i	0.999310	+	0.0371480i	$0.0118273\pi$
$228$		0			0
$229$	−2.35578e8	−	1.33603e9i	−0.0856630	−	0.485819i	−0.997212	−	0.0746264i	$-0.976224\pi$
$229$	−2.35578e8	−	1.33603e9i	−0.0856630	−	0.485819i	0.911549	−	0.411192i	$-0.134888\pi$
$230$	−5.05420e8	+	8.91192e7i	−0.180610	+	0.0318464i
$231$		0			0
$232$	−3.00752e8	−	2.52361e8i	−0.103814	−	0.0871104i
$233$	−6.27753e8	+	3.62433e8i	−0.212993	+	0.122972i	−0.602702	−	0.797967i	$-0.705909\pi$
$233$	−6.27753e8	+	3.62433e8i	−0.212993	+	0.122972i	0.389709	+	0.920938i	$0.372576\pi$
$234$		0			0
$235$	−3.58980e8	+	6.21771e8i	−0.117706	+	0.203873i
$236$	−1.80369e9	−	4.95559e9i	−0.581451	−	1.59752i
$237$		0			0
$238$	2.84206e8	−	2.38477e8i	0.0885778	−	0.0743256i
$239$	−7.45604e8	+	2.04853e9i	−0.228516	+	0.627842i	−0.999964	−	0.00844956i	$-0.997310\pi$
$239$	−7.45604e8	+	2.04853e9i	−0.228516	+	0.627842i	0.771448	+	0.636292i	$0.219533\pi$
$240$		0			0
$241$	−2.83147e8	+	1.60581e9i	−0.0839352	+	0.476020i	0.913646	+	0.406511i	$0.133255\pi$
$241$	−2.83147e8	+	1.60581e9i	−0.0839352	+	0.476020i	−0.997581	+	0.0695097i	$0.977857\pi$
$242$		−	3.34032e8i		−	0.0973927i
$243$		0			0
$244$	−3.64553e9			−1.02849
$245$	−6.60903e9	−	1.16535e9i	−1.83431	−	0.323439i
$246$		0			0
$247$	−8.87265e8	−	3.22938e8i	−0.238378	−	0.0867623i
$248$	6.98010e8	+	8.31856e8i	0.184525	+	0.219908i
$249$		0			0
$250$	−7.78952e8	+	2.83515e8i	−0.199412	+	0.0725799i
$251$	5.80211e8	+	3.34985e8i	0.146181	+	0.0843977i	0.571307	−	0.820737i	$-0.306437\pi$
$251$	5.80211e8	+	3.34985e8i	0.146181	+	0.0843977i	−0.425126	+	0.905134i	$0.639770\pi$
$252$		0			0
$253$	2.29692e9	+	3.97838e9i	0.560613	+	0.971010i
$254$	6.13446e8	−	7.31077e8i	0.147381	−	0.175642i
$255$		0			0
$256$	4.49743e8	+	2.55062e9i	0.104714	+	0.593862i
$257$	−3.70746e9	+	6.53725e8i	−0.849853	+	0.149852i	−0.581578	−	0.813491i	$-0.697565\pi$
$257$	−3.70746e9	+	6.53725e8i	−0.849853	+	0.149852i	−0.268275	+	0.963343i	$0.586453\pi$
$258$		0			0
$259$	−4.90543e9	−	4.11615e9i	−1.09013	−	0.914728i
$260$	6.51025e8	−	3.75869e8i	0.142464	−	0.0822514i
$261$		0			0
$262$	−2.47473e8	+	4.28636e8i	−0.0525198	+	0.0909670i
$263$	8.27508e8	+	2.27356e9i	0.172961	+	0.475207i	0.995638	−	0.0933024i	$-0.0297423\pi$
$263$	8.27508e8	+	2.27356e9i	0.172961	+	0.475207i	−0.822676	+	0.568510i	$0.807520\pi$
$264$		0			0
$265$	6.00344e9	−	5.03748e9i	1.21735	−	1.02148i
$266$	−8.59411e8	+	2.36121e9i	−0.171662	+	0.471638i
$267$		0			0
$268$	−2.60305e8	+	1.47626e9i	−0.0504596	+	0.286171i
$269$			2.83899e9i			0.542195i	0.962552	+	0.271097i	$0.0873865\pi$
$269$			2.83899e9i			0.542195i	−0.962552	+	0.271097i	$0.912613\pi$
$270$		0			0
$271$	−4.82586e9			−0.894741			−0.447370	−	0.894349i	$-0.647639\pi$
$271$	−4.82586e9			−0.894741			−0.447370	+	0.894349i	$0.647639\pi$
$272$	−1.54815e9	−	2.72980e8i	−0.282837	−	0.0498719i
$273$		0			0
$274$	2.04009e9	+	7.42532e8i	0.361949	+	0.131739i
$275$	3.07198e8	+	3.66104e8i	0.0537139	+	0.0640138i
$276$		0			0
$277$	1.86396e9	−	6.78426e8i	0.316605	−	0.115235i	−0.178830	−	0.983880i	$-0.557231\pi$
$277$	1.86396e9	−	6.78426e8i	0.316605	−	0.115235i	0.495434	+	0.868645i	$0.335009\pi$
$278$	−1.49015e9	−	8.60339e8i	−0.249489	−	0.144043i
$279$		0			0
$280$	−2.04476e9	−	3.54163e9i	−0.332668	−	0.576198i
$281$	7.81636e8	−	9.31518e8i	0.125366	−	0.149405i	−0.699710	−	0.714427i	$-0.746688\pi$
$281$	7.81636e8	−	9.31518e8i	0.125366	−	0.149405i	0.825076	+	0.565021i	$0.191132\pi$
$282$		0			0
$283$	1.67891e9	+	9.52155e9i	0.261746	+	1.48444i	0.778143	+	0.628087i	$0.216162\pi$
$283$	1.67891e9	+	9.52155e9i	0.261746	+	1.48444i	−0.516396	+	0.856350i	$0.672727\pi$
$284$	8.56983e9	−	1.51109e9i	1.31734	−	0.232283i
$285$		0			0
$286$	2.27855e8	+	1.91193e8i	0.0340561	+	0.0285764i
$287$	1.38165e10	−	7.97695e9i	2.03643	−	1.17573i
$288$		0			0
$289$	−3.11194e9	+	5.39003e9i	−0.446107	+	0.772680i
$290$	−1.61591e8	−	4.43969e8i	−0.0228469	−	0.0627712i
$291$		0			0
$292$	−2.59141e9	+	2.17445e9i	−0.356456	+	0.299102i
$293$	−1.75048e8	+	4.80940e8i	−0.0237512	+	0.0652560i	−0.951002	−	0.309186i	$-0.899943\pi$
$293$	−1.75048e8	+	4.80940e8i	−0.0237512	+	0.0652560i	0.927250	+	0.374442i	$0.122166\pi$
$294$		0			0
$295$	2.25277e9	−	1.27761e10i	0.297460	−	1.68698i
$296$		−	2.57050e9i		−	0.334850i
$297$		0			0
$298$	1.72223e9			0.218387
$299$	−1.29427e9	−	2.28214e8i	−0.161934	−	0.0285534i
$300$		0			0
$301$	6.03366e9	+	2.19607e9i	0.735047	+	0.267535i
$302$	1.42494e9	+	1.69818e9i	0.171305	+	0.204153i
$303$		0			0
$304$	1.00050e10	−	3.64152e9i	1.17145	−	0.426372i
$305$	−7.76655e9	−	4.48402e9i	−0.897488	−	0.518165i
$306$		0			0
$307$	3.72843e8	+	6.45783e8i	0.0419733	+	0.0726998i	0.886249	−	0.463209i	$-0.153302\pi$
$307$	3.72843e8	+	6.45783e8i	0.0419733	+	0.0726998i	−0.844276	+	0.535909i	$0.819969\pi$
$308$	−1.15104e10	+	1.37175e10i	−1.27905	+	1.52431i
$309$		0			0
$310$	2.26922e8	+	1.28694e9i	0.0245714	+	0.139351i
$311$	1.43070e10	−	2.52271e9i	1.52935	−	0.269666i	0.655252	−	0.755411i	$-0.272563\pi$
$311$	1.43070e10	−	2.52271e9i	1.52935	−	0.269666i	0.874101	+	0.485745i	$0.161452\pi$
$312$		0			0
$313$	−4.83723e9	−	4.05892e9i	−0.503988	−	0.422896i	0.355020	−	0.934859i	$-0.384474\pi$
$313$	−4.83723e9	−	4.05892e9i	−0.503988	−	0.422896i	−0.859008	+	0.511963i	$0.828919\pi$
$314$	1.66113e9	−	9.59056e8i	0.170878	−	0.0986565i
$315$		0			0
$316$	5.48002e9	−	9.49168e9i	0.549584	−	0.951907i
$317$	3.91673e9	+	1.07611e10i	0.387870	+	1.06566i	0.967958	+	0.251110i	$0.0807957\pi$
$317$	3.91673e9	+	1.07611e10i	0.387870	+	1.06566i	−0.580089	+	0.814553i	$0.696982\pi$
$318$		0			0
$319$	−3.23962e9	+	2.71837e9i	−0.312847	+	0.262510i
$320$	−2.61243e9	+	7.17759e9i	−0.249141	+	0.684509i
$321$		0			0
$322$	−6.07329e8	+	3.44433e9i	−0.0564937	+	0.320392i
$323$			5.09239e9i			0.467856i
$324$		0			0
$325$	−1.36725e8			−0.0122550
$326$	3.40279e9	+	6.00004e8i	0.301276	+	0.0531232i
$327$		0			0
$328$	6.01793e9	+	2.19035e9i	0.519938	+	0.189242i
$329$	3.14499e9	+	3.74806e9i	0.268433	+	0.319906i
$330$		0			0
$331$	1.41536e10	−	5.15148e9i	1.17911	−	0.429161i	0.323223	−	0.946323i	$-0.395234\pi$
$331$	1.41536e10	−	5.15148e9i	1.17911	−	0.429161i	0.855888	+	0.517162i	$0.173011\pi$
$332$	−9.86210e9	−	5.69389e9i	−0.811740	−	0.468658i
$333$		0			0
$334$	4.05123e8	+	7.01694e8i	0.0325538	+	0.0563848i
$335$	−2.37038e9	+	2.82490e9i	−0.188208	+	0.224297i
$336$		0			0
$337$	−9.05604e8	−	5.13594e9i	−0.0702132	−	0.398199i	−0.999578	−	0.0290371i	$-0.990756\pi$
$337$	−9.05604e8	−	5.13594e9i	−0.0702132	−	0.398199i	0.929365	−	0.369162i	$-0.120355\pi$
$338$	2.56078e9	−	4.51535e8i	0.196203	−	0.0345959i
$339$		0			0
$340$	−3.10581e9	−	2.60609e9i	−0.232413	−	0.195017i
$341$	1.01300e10	−	5.84858e9i	0.749193	−	0.432547i
$342$		0			0
$343$	−1.10203e10	+	1.90877e10i	−0.796188	+	1.37904i
$344$	8.81538e8	+	2.42201e9i	0.0629517	+	0.172958i
$345$		0			0
$346$	9.64890e8	−	8.09639e8i	0.0673246	−	0.0564920i
$347$	−5.88556e9	+	1.61705e10i	−0.405948	+	1.11533i	0.553353	+	0.832947i	$0.313348\pi$
$347$	−5.88556e9	+	1.61705e10i	−0.405948	+	1.11533i	−0.959301	+	0.282386i	$0.908874\pi$
$348$		0			0
$349$	1.33644e9	−	7.57932e9i	0.0900840	−	0.510891i	−0.906059	−	0.423151i	$-0.860924\pi$
$349$	1.33644e9	−	7.57932e9i	0.0900840	−	0.510891i	0.996143	−	0.0877409i	$-0.0279648\pi$
$350$			3.63855e8i			0.0242469i
$351$		0			0
$352$	−1.08599e10			−0.707387
$353$	−1.16353e10	−	2.05161e9i	−0.749337	−	0.132128i	−0.214078	−	0.976817i	$-0.568675\pi$
$353$	−1.16353e10	−	2.05161e9i	−0.749337	−	0.132128i	−0.535259	+	0.844688i	$0.679786\pi$
$354$		0			0
$355$	2.01161e10	+	7.32165e9i	1.26657	+	0.460995i
$356$	−6.55309e8	−	7.80966e8i	−0.0407987	−	0.0486219i
$357$		0			0
$358$	6.28850e8	−	2.28883e8i	0.0382838	−	0.0139342i
$359$	7.89075e9	+	4.55572e9i	0.475051	+	0.274271i	0.718352	−	0.695680i	$-0.244897\pi$
$359$	7.89075e9	+	4.55572e9i	0.475051	+	0.274271i	−0.243301	+	0.969951i	$0.578230\pi$
$360$		0			0
$361$	−8.75319e9	−	1.51610e10i	−0.515392	−	0.892684i
$362$	1.29251e9	−	1.54036e9i	0.0752662	−	0.0896988i
$363$		0			0
$364$	−8.89589e8	−	5.04511e9i	−0.0506739	−	0.287386i
$365$	−8.19542e9	+	1.44507e9i	−0.461742	+	0.0814176i
$366$		0			0
$367$	4.80686e9	+	4.03344e9i	0.264971	+	0.222337i	0.765587	−	0.643333i	$-0.222449\pi$
$367$	4.80686e9	+	4.03344e9i	0.264971	+	0.222337i	−0.500616	+	0.865669i	$0.666893\pi$
$368$	1.28341e10	−	7.40979e9i	0.699802	−	0.404031i
$369$		0			0
$370$	1.54668e9	−	2.67893e9i	0.0825265	−	0.142940i
$371$	−1.82663e10	−	5.01862e10i	−0.964172	−	2.64904i
$372$		0			0
$373$	1.92922e10	−	1.61881e10i	0.996660	−	0.836297i	0.0101421	−	0.999949i	$-0.496772\pi$
$373$	1.92922e10	−	1.61881e10i	0.996660	−	0.836297i	0.986518	+	0.163651i	$0.0523272\pi$
$374$	5.48670e8	−	1.50746e9i	0.0280430	−	0.0770476i
$375$		0			0
$376$	−3.41049e8	+	1.93419e9i	−0.0170634	+	0.0967713i
$377$		−	1.20987e9i		−	0.0598924i
$378$		0			0
$379$	−4.03794e9			−0.195705			−0.0978527	−	0.995201i	$-0.531197\pi$
$379$	−4.03794e9			−0.195705			−0.0978527	+	0.995201i	$0.531197\pi$
$380$	2.70423e10	+	4.76828e9i	1.29691	+	0.228680i
$381$		0			0
$382$	−4.97594e8	−	1.81109e8i	−0.0233680	−	0.00850526i
$383$	1.68071e10	+	2.00299e10i	0.781082	+	0.930857i	0.998982	−	0.0451138i	$-0.0143650\pi$
$383$	1.68071e10	+	2.00299e10i	0.781082	+	0.930857i	−0.217900	+	0.975971i	$0.569921\pi$
$384$		0			0
$385$	−4.13947e10	+	1.50665e10i	−1.88409	+	0.685754i
$386$	−3.77755e8	−	2.18097e8i	−0.0170161	−	0.00982427i
$387$		0			0
$388$	1.73736e10	+	3.00920e10i	0.766590	+	1.32777i
$389$	−5.81049e8	+	6.92467e8i	−0.0253755	+	0.0302413i	−0.778583	−	0.627542i	$-0.784061\pi$
$389$	−5.81049e8	+	6.92467e8i	−0.0253755	+	0.0302413i	0.753207	+	0.657783i	$0.228506\pi$
$390$		0			0
$391$	1.23083e9	+	6.98036e9i	0.0526611	+	0.298656i
$392$	−1.80794e10	+	3.18789e9i	−0.765668	+	0.135008i
$393$		0			0
$394$	1.53322e8	+	1.28652e8i	0.00636238	+	0.00533867i
$395$	2.33496e10	−	1.34809e10i	0.959161	−	0.553772i
$396$		0			0
$397$	−1.45975e10	+	2.52837e10i	−0.587648	+	1.01784i	0.406892	+	0.913476i	$0.366613\pi$
$397$	−1.45975e10	+	2.52837e10i	−0.587648	+	1.01784i	−0.994540	+	0.104360i	$0.966721\pi$
$398$	−7.12892e8	−	1.95865e9i	−0.0284113	−	0.0780594i
$399$		0			0
$400$	1.18104e9	−	9.91012e8i	0.0461344	−	0.0387114i
$401$	7.29919e9	−	2.00544e10i	0.282291	−	0.775589i	−0.714797	−	0.699332i	$-0.753481\pi$
$401$	7.29919e9	−	2.00544e10i	0.282291	−	0.775589i	0.997088	−	0.0762567i	$-0.0242968\pi$
$402$		0			0
$403$	−5.81096e8	+	3.29556e9i	−0.0220307	+	0.124942i
$404$			2.91756e10i			1.09520i
$405$		0			0
$406$	−3.21973e9			−0.118499
$407$	−2.72681e10	−	4.80811e9i	−0.993752	−	0.175225i
$408$		0			0
$409$	−4.86243e10	−	1.76978e10i	−1.73764	−	0.632450i	−0.738516	−	0.674236i	$-0.764473\pi$
$409$	−4.86243e10	−	1.76978e10i	−1.73764	−	0.632450i	−0.999127	+	0.0417856i	$0.986695\pi$
$410$	4.95383e9	+	5.90375e9i	0.175310	+	0.208926i
$411$		0			0
$412$	8.34869e9	−	3.03868e9i	0.289754	−	0.105462i
$413$	−7.65648e10	−	4.42047e10i	−2.63165	−	1.51939i
$414$		0			0
$415$	−1.40070e10	−	2.42609e10i	−0.472229	−	0.817925i
$416$	1.99706e9	−	2.38001e9i	0.0666835	−	0.0794703i
$417$		0			0
$418$	1.88669e9	+	1.06999e10i	0.0618009	+	0.350490i
$419$	−3.61100e10	+	6.36717e9i	−1.17158	+	0.206581i	−0.725378	−	0.688351i	$-0.758335\pi$
$419$	−3.61100e10	+	6.36717e9i	−1.17158	+	0.206581i	−0.446202	+	0.894932i	$0.647224\pi$
$420$		0			0
$421$	−6.06361e9	−	5.08797e9i	−0.193020	−	0.161963i	0.541156	−	0.840922i	$-0.317987\pi$
$421$	−6.06361e9	−	5.08797e9i	−0.193020	−	0.161963i	−0.734176	+	0.678959i	$0.762431\pi$
$422$	−4.74375e9	+	2.73881e9i	−0.149579	+	0.0863597i
$423$		0			0
$424$	1.07192e10	−	1.85662e10i	0.331665	−	0.574460i
$425$	2.52205e8	+	6.92927e8i	0.00773032	+	0.0212389i
$426$		0			0
$427$	−4.68170e10	+	3.92841e10i	−1.40829	+	1.18170i
$428$	1.56506e10	−	4.29997e10i	0.466398	−	1.28142i
$429$		0			0
$430$	−5.38607e8	+	3.05459e9i	−0.0157543	+	0.0893469i
$431$			5.13707e10i			1.48870i	0.667791	+	0.744349i	$0.267240\pi$
$431$			5.13707e10i			1.48870i	−0.667791	+	0.744349i	$0.732760\pi$
$432$		0			0
$433$	−1.87525e9			−0.0533468			−0.0266734	−	0.999644i	$-0.508491\pi$
$433$	−1.87525e9			−0.0533468			−0.0266734	+	0.999644i	$0.508491\pi$
$434$	8.77022e9	+	1.54643e9i	0.247202	+	0.0435884i
$435$		0			0
$436$	−2.43292e10	−	8.85511e9i	−0.673259	−	0.245046i
$437$	−3.08578e10	−	3.67748e10i	−0.846133	−	1.00838i
$438$		0			0
$439$	−1.43069e10	+	5.20730e9i	−0.385202	+	0.140202i	−0.527360	−	0.849642i	$-0.676818\pi$
$439$	−1.43069e10	+	5.20730e9i	−0.385202	+	0.140202i	0.142158	+	0.989844i	$0.454596\pi$
$440$	−1.53139e10	−	8.84146e9i	−0.408577	−	0.235892i
$441$		0			0
$442$	2.29470e8	+	3.97454e8i	0.00601225	+	0.0104135i
$443$	−2.80078e10	+	3.33784e10i	−0.727217	+	0.866663i	−0.995311	−	0.0967298i	$-0.969162\pi$
$443$	−2.80078e10	+	3.33784e10i	−0.727217	+	0.866663i	0.268094	+	0.963393i	$0.413606\pi$
$444$		0			0
$445$	−4.35497e8	−	2.46983e9i	−0.0111057	−	0.0629835i
$446$	−3.20198e8	+	5.64596e7i	−0.00809245	+	0.00142692i
$447$		0			0
$448$	3.98749e10	+	3.34590e10i	0.989891	+	0.830617i
$449$	4.37682e10	−	2.52696e10i	1.07690	−	0.621746i	0.146838	−	0.989161i	$-0.453090\pi$
$449$	4.37682e10	−	2.52696e10i	1.07690	−	0.621746i	0.930057	+	0.367415i	$0.119757\pi$
$450$		0			0
$451$	3.44920e10	−	5.97418e10i	0.833703	−	1.44402i
$452$	2.44832e10	+	6.72669e10i	0.586562	+	1.61156i
$453$		0			0
$454$	8.22120e9	−	6.89840e9i	0.193514	−	0.162377i
$455$	4.31030e9	−	1.18425e10i	0.100569	−	0.276310i
$456$		0			0
$457$	6.63960e9	−	3.76550e10i	0.152222	−	0.863293i	−0.809060	−	0.587726i	$-0.800023\pi$
$457$	6.63960e9	−	3.76550e10i	0.152222	−	0.863293i	0.961282	−	0.275567i	$-0.0888656\pi$
$458$		−	4.46605e9i		−	0.101499i
$459$		0			0
$460$	3.82205e10			0.853621
$461$	5.77035e10	+	1.01747e10i	1.27761	+	0.225277i	0.770965	−	0.636877i	$-0.219774\pi$
$461$	5.77035e10	+	1.01747e10i	1.27761	+	0.225277i	0.506646	+	0.862154i	$0.330885\pi$
$462$		0			0
$463$	6.30183e10	+	2.29368e10i	1.37133	+	0.499124i	0.919539	−	0.392999i	$-0.128562\pi$
$463$	6.30183e10	+	2.29368e10i	1.37133	+	0.499124i	0.451793	+	0.892123i	$0.350785\pi$
$464$	8.76938e9	+	1.04509e10i	0.189190	+	0.225467i
$465$		0			0
$466$	−2.24235e9	+	8.16148e8i	−0.0475510	+	0.0173071i
$467$	7.50725e9	+	4.33431e9i	0.157839	+	0.0911281i	0.576839	−	0.816858i	$-0.304286\pi$
$467$	7.50725e9	+	4.33431e9i	0.157839	+	0.0911281i	−0.419000	+	0.907986i	$0.637619\pi$
$468$		0			0
$469$	1.25653e10	+	2.17637e10i	0.259705	+	0.449823i
$470$	−1.51924e9	+	1.81056e9i	−0.0311340	+	0.0371041i
$471$		0			0
$472$	−6.16259e9	−	3.49498e10i	−0.124164	−	0.704168i
$473$	2.73418e10	−	4.82110e9i	0.546239	−	0.0963167i
$474$		0			0
$475$	−3.82583e9	−	3.21026e9i	−0.0751539	−	0.0630616i
$476$	−2.39279e10	+	1.38148e10i	−0.466097	+	0.269101i
$477$		0			0
$478$	−3.58827e9	+	6.21507e9i	−0.0687344	+	0.119051i
$479$	−1.03071e10	−	2.83185e10i	−0.195792	−	0.537933i	0.802482	−	0.596677i	$-0.203513\pi$
$479$	−1.03071e10	−	2.83185e10i	−0.195792	−	0.537933i	−0.998273	+	0.0587442i	$0.981290\pi$
$480$		0			0
$481$	6.06813e9	−	5.09176e9i	0.113364	−	0.0951235i
$482$	−1.83592e9	+	5.04414e9i	−0.0340146	+	0.0934543i
$483$		0			0
$484$	−4.31970e9	+	2.44982e10i	−0.0787176	+	0.446429i
$485$			8.54785e10i			1.54486i
$486$		0			0
$487$	2.41067e10			0.428570			0.214285	−	0.976771i	$-0.431258\pi$
$487$	2.41067e10			0.428570			0.214285	+	0.976771i	$0.431258\pi$
$488$	−2.41599e10	−	4.26005e9i	−0.426007	−	0.0751165i
$489$		0			0
$490$	−2.07602e10	−	7.55609e9i	−0.360120	−	0.131073i
$491$	−3.30867e10	−	3.94312e10i	−0.569282	−	0.678444i	0.402202	−	0.915551i	$-0.368245\pi$
$491$	−3.30867e10	−	3.94312e10i	−0.569282	−	0.678444i	−0.971483	+	0.237108i	$0.923801\pi$
$492$		0			0
$493$	−6.13166e9	+	2.23174e9i	−0.103798	+	0.0377795i
$494$	−2.69189e9	−	1.55416e9i	−0.0452011	−	0.0260969i
$495$		0			0
$496$	−1.88674e10	−	3.26793e10i	−0.311735	−	0.539940i
$497$	9.37729e10	−	1.11754e11i	1.53692	−	1.83163i
$498$		0			0
$499$	−5.22963e9	−	2.96587e10i	−0.0843468	−	0.478355i	−0.997496	−	0.0707282i	$-0.977468\pi$
$499$	−5.22963e9	−	2.96587e10i	−0.0843468	−	0.478355i	0.913149	−	0.407626i	$-0.133643\pi$
$500$	6.07955e10	−	1.07199e10i	0.972728	−	0.171518i
$501$		0			0
$502$	1.68954e9	+	1.41769e9i	0.0266044	+	0.0223238i
$503$	1.24574e10	−	7.19230e9i	0.194606	−	0.112356i	−0.399531	−	0.916720i	$-0.630827\pi$
$503$	1.24574e10	−	7.19230e9i	0.194606	−	0.112356i	0.594137	+	0.804364i	$0.297494\pi$
$504$		0			0
$505$	−3.58862e10	+	6.21567e10i	−0.551774	+	0.955701i
$506$	5.17233e9	+	1.42109e10i	0.0789013	+	0.216779i
$507$		0			0
$508$	−5.44450e10	+	4.56848e10i	−0.817529	+	0.685989i
$509$	−2.93880e10	+	8.07429e10i	−0.437824	+	1.20291i	0.503081	+	0.864239i	$0.332200\pi$
$509$	−2.93880e10	+	8.07429e10i	−0.437824	+	1.20291i	−0.940905	+	0.338671i	$0.890023\pi$
$510$		0			0
$511$	−9.84787e9	+	5.58500e10i	−0.144430	+	0.819105i
$512$			5.92477e10i			0.862168i
$513$		0			0
$514$	−1.23932e10			−0.177554
$515$	2.15239e10	+	3.79524e9i	0.305979	+	0.0539524i
$516$		0			0
$517$	1.98801e10	+	7.23577e9i	0.278264	+	0.101280i
$518$	−1.35503e10	−	1.61487e10i	−0.188205	−	0.224294i
$519$		0			0
$520$	4.75375e9	−	1.73022e9i	0.0650164	−	0.0236640i
$521$	−3.91268e8	−	2.25899e8i	−0.00531036	−	0.00306594i	0.497342	−	0.867554i	$-0.334309\pi$
$521$	−3.91268e8	−	2.25899e8i	−0.00531036	−	0.00306594i	−0.502653	+	0.864488i	$0.667643\pi$
$522$		0			0
$523$	3.63173e10	+	6.29034e10i	0.485408	+	0.840751i	0.999859	−	0.0167684i	$-0.00533780\pi$
$523$	3.63173e10	+	6.29034e10i	0.485408	+	0.840751i	−0.514452	+	0.857519i	$0.672004\pi$
$524$	2.36931e10	−	2.82363e10i	0.314265	−	0.374526i
$525$		0			0
$526$	1.38309e9	+	7.84388e9i	0.0180679	+	0.102468i
$527$	1.77739e10	−	3.13402e9i	0.230431	−	0.0406312i
$528$		0			0
$529$	8.80320e9	+	7.38676e9i	0.112413	+	0.0943260i
$530$	2.23427e10	−	1.28996e10i	0.283160	−	0.163483i
$531$		0			0
$532$	9.35652e10	−	1.62060e11i	1.16807	−	2.02315i
$533$	6.74988e9	+	1.85451e10i	0.0836349	+	0.229785i
$534$		0			0
$535$	8.62324e10	−	7.23576e10i	1.05258	−	0.883220i
$536$	−3.45023e9	+	9.47943e9i	−0.0418012	+	0.114848i
$537$		0			0
$538$	−1.62291e9	+	9.20397e9i	−0.0193716	+	0.109862i
$539$			1.97751e11i			2.34296i
$540$		0			0
$541$	1.03907e11			1.21298			0.606491	−	0.795091i	$-0.292577\pi$
$541$	1.03907e11			1.21298			0.606491	+	0.795091i	$0.292577\pi$
$542$	−1.56453e10	−	2.75870e9i	−0.181296	−	0.0319674i
$543$		0			0
$544$	−1.57458e10	−	5.73100e9i	−0.179791	−	0.0654387i
$545$	−4.09399e10	−	4.87902e10i	−0.464045	−	0.553028i
$546$		0			0
$547$	2.07308e10	−	7.54538e9i	0.231561	−	0.0842814i	−0.223633	−	0.974673i	$-0.571792\pi$
$547$	2.07308e10	−	7.54538e9i	0.231561	−	0.0842814i	0.455195	+	0.890392i	$0.349570\pi$
$548$	−1.40020e11	−	8.08405e10i	−1.55263	−	0.896410i
$549$		0			0
$550$	7.86646e8	+	1.36251e9i	0.00859664	+	0.0148898i
$551$	2.84073e10	−	3.38545e10i	0.308193	−	0.367291i
$552$		0			0
$553$	−3.19060e10	−	1.80948e11i	−0.341170	−	1.93487i
$554$	6.43075e9	−	1.13391e9i	0.0682688	−	0.0120376i
$555$		0			0
$556$	9.81633e10	+	8.23688e10i	1.02719	+	0.861913i
$557$	1.00807e11	−	5.82008e10i	1.04729	−	0.604656i	0.125404	−	0.992106i	$-0.459977\pi$
$557$	1.00807e11	−	5.82008e10i	1.04729	−	0.604656i	0.921891	+	0.387450i	$0.126644\pi$
$558$		0			0
$559$	−3.97139e9	+	6.87865e9i	−0.0406720	+	0.0704459i
$560$	4.86040e10	+	1.33538e11i	0.494219	+	1.35786i
$561$		0			0
$562$	3.06655e9	−	2.57314e9i	0.0307401	−	0.0257940i
$563$	1.04359e10	−	2.86725e10i	0.103872	−	0.285386i	−0.876860	−	0.480747i	$-0.840366\pi$
$563$	1.04359e10	−	2.86725e10i	0.103872	−	0.285386i	0.980731	+	0.195361i	$0.0625879\pi$
$564$		0			0
$565$	−3.05790e10	+	1.73422e11i	−0.300074	+	1.70181i
$566$			3.18284e10i			0.310134i
$567$		0			0
$568$	5.85604e10			0.562615
$569$	7.50849e10	+	1.32395e10i	0.716314	+	0.126305i	0.519914	−	0.854219i	$-0.325964\pi$
$569$	7.50849e10	+	1.32395e10i	0.716314	+	0.126305i	0.196400	+	0.980524i	$0.437075\pi$
$570$		0			0
$571$	−1.53807e11	−	5.59810e10i	−1.44687	−	0.526619i	−0.505157	−	0.863027i	$-0.668566\pi$
$571$	−1.53807e11	−	5.59810e10i	−1.44687	−	0.526619i	−0.941716	+	0.336408i	$0.890788\pi$
$572$	−1.42386e10	−	1.69689e10i	−0.133010	−	0.158515i
$573$		0			0
$574$	4.93528e10	−	1.79630e10i	0.454637	−	0.165474i
$575$	−6.02015e9	−	3.47573e9i	−0.0550726	−	0.0317962i
$576$		0			0
$577$	−3.03217e10	−	5.25187e10i	−0.273559	−	0.473818i	0.696212	−	0.717836i	$-0.254867\pi$
$577$	−3.03217e10	−	5.25187e10i	−0.273559	−	0.473818i	−0.969770	+	0.244019i	$0.921534\pi$
$578$	−1.31701e10	+	1.56955e10i	−0.117998	+	0.140625i
$579$		0			0
$580$	6.10987e9	+	3.46508e10i	0.0539909	+	0.306197i
$581$	−1.88009e11	+	3.31511e10i	−1.64996	+	0.290933i
$582$		0			0
$583$	−1.76902e11	−	1.48439e11i	−1.53130	−	1.28491i
$584$	−1.97150e10	+	1.13825e10i	−0.169491	+	0.0978554i
$585$		0			0
$586$	−8.42431e8	+	1.45913e9i	−0.00714404	+	0.0123738i
$587$	−2.20481e10	−	6.05765e10i	−0.185703	−	0.510214i	0.811551	−	0.584282i	$-0.198624\pi$
$587$	−2.20481e10	−	6.05765e10i	−0.185703	−	0.510214i	−0.997253	+	0.0740686i	$0.976402\pi$
$588$		0			0
$589$	−9.36389e10	+	7.85724e10i	−0.778028	+	0.652843i
$590$	1.46069e10	−	4.01320e10i	0.120545	−	0.331194i
$591$		0			0
$592$	−1.55108e10	+	8.79663e10i	−0.126284	+	0.716192i
$593$		−	8.45828e10i		−	0.684011i	−0.939698	−	0.342006i	$-0.888894\pi$
$593$		−	8.45828e10i		−	0.684011i	0.939698	−	0.342006i	$-0.111106\pi$
$594$		0			0
$595$	−6.79690e10			−0.542304
$596$	−1.26310e11	−	2.22719e10i	−1.00105	−	0.176511i
$597$		0			0
$598$	−4.06553e9	−	1.47973e9i	−0.0317916	−	0.0115712i
$599$	−1.36255e10	−	1.62383e10i	−0.105839	−	0.126134i	0.710524	−	0.703673i	$-0.248458\pi$
$599$	−1.36255e10	−	1.62383e10i	−0.105839	−	0.126134i	−0.816364	+	0.577538i	$0.804013\pi$
$600$		0			0
$601$	8.36696e9	−	3.04533e9i	0.0641313	−	0.0233419i	−0.309755	−	0.950816i	$-0.600247\pi$
$601$	8.36696e9	−	3.04533e9i	0.0641313	−	0.0233419i	0.373887	+	0.927474i	$0.378025\pi$
$602$	1.83056e10	+	1.05688e10i	0.139380	+	0.0804708i
$603$		0			0
$604$	−8.25458e10	−	1.42973e11i	−0.620222	−	1.07426i
$605$	−3.93357e10	+	4.68785e10i	−0.293606	+	0.349907i
$606$		0			0
$607$	3.13171e10	+	1.77608e11i	0.230689	+	1.30830i	0.851506	+	0.524345i	$0.175690\pi$
$607$	3.13171e10	+	1.77608e11i	0.230689	+	1.30830i	−0.620817	+	0.783955i	$0.713199\pi$
$608$	1.11764e11	−	1.97070e10i	0.817874	−	0.144213i
$609$		0			0
$610$	−2.26157e10	−	1.89769e10i	−0.163340	−	0.137058i
$611$	−5.24156e9	+	3.02621e9i	−0.0376093	+	0.0217138i
$612$		0			0
$613$	−9.37926e10	+	1.62454e11i	−0.664243	+	1.15050i	0.315248	+	0.949009i	$0.397912\pi$
$613$	−9.37926e10	+	1.62454e11i	−0.664243	+	1.15050i	−0.979490	+	0.201492i	$0.935421\pi$
$614$	8.39590e8	+	2.30675e9i	0.00590736	+	0.0162303i
$615$		0			0
$616$	−9.23124e10	+	7.74593e10i	−0.641117	+	0.537961i
$617$	−6.58893e9	+	1.81029e10i	−0.0454647	+	0.124913i	−0.960347	−	0.278807i	$-0.910061\pi$
$617$	−6.58893e9	+	1.81029e10i	−0.0454647	+	0.124913i	0.914882	+	0.403720i	$0.132283\pi$
$618$		0			0
$619$	3.75319e10	−	2.12854e11i	0.255646	−	1.44984i	−0.538764	−	0.842457i	$-0.681109\pi$
$619$	3.75319e10	−	2.12854e11i	0.255646	−	1.44984i	0.794410	−	0.607382i	$-0.207780\pi$
$620$		−	9.73200e10i		−	0.658621i
$621$		0			0
$622$	4.78252e10			0.319518
$623$	−1.68313e10	−	2.96782e9i	−0.111729	−	0.0197009i
$624$		0			0
$625$	1.32835e11	+	4.83479e10i	0.870547	+	0.316853i
$626$	−1.33620e10	−	1.59242e10i	−0.0870107	−	0.103695i
$627$		0			0
$628$	−1.34232e11	+	4.88563e10i	−0.863011	+	0.314110i
$629$	−3.69987e10	−	2.13612e10i	−0.236365	−	0.136466i
$630$		0			0
$631$	1.52109e11	+	2.63460e11i	0.959482	+	1.66187i	0.723760	+	0.690052i	$0.242412\pi$
$631$	1.52109e11	+	2.63460e11i	0.959482	+	1.66187i	0.235722	+	0.971820i	$0.424254\pi$
$632$	4.74093e10	−	5.65002e10i	0.297163	−	0.354145i
$633$		0			0
$634$	6.54638e9	+	3.71263e10i	0.0405176	+	0.229787i
$635$	−1.72184e11	+	3.03607e10i	−1.05900	+	0.186731i
$636$		0			0
$637$	−4.33381e10	−	3.63650e10i	−0.263216	−	0.220865i
$638$	−1.20568e10	+	6.96097e9i	−0.0727692	+	0.0420133i
$639$		0			0
$640$	−5.97467e10	+	1.03484e11i	−0.356118	+	0.616814i
$641$	−7.60783e10	−	2.09023e11i	−0.450639	−	1.23812i	−0.932276	−	0.361749i	$-0.882180\pi$
$641$	−7.60783e10	−	2.09023e11i	−0.450639	−	1.23812i	0.481637	−	0.876371i	$-0.340042\pi$
$642$		0			0
$643$	2.07474e11	−	1.74091e11i	1.21372	−	1.01844i	0.214595	−	0.976703i	$-0.431157\pi$
$643$	2.07474e11	−	1.74091e11i	1.21372	−	1.01844i	0.999129	−	0.0417321i	$-0.0132876\pi$
$644$	8.90842e10	−	2.44757e11i	0.517913	−	1.42295i
$645$		0			0
$646$	−2.91106e9	+	1.65095e10i	−0.0167156	+	0.0947988i
$647$			2.00279e9i			0.0114293i	0.999984	+	0.00571463i	$0.00181903\pi$
$647$			2.00279e9i			0.0114293i	−0.999984	+	0.00571463i	$0.998181\pi$
$648$		0			0
$649$	−3.82278e11			−2.15477
$650$	−4.43259e8	−	7.81586e7i	−0.00248316	−	0.000437848i
$651$		0			0
$652$	−2.41805e11	−	8.80098e10i	−1.33806	−	0.487013i
$653$	1.92647e11	+	2.29588e11i	1.05952	+	1.26269i	0.963614	+	0.267299i	$0.0861311\pi$
$653$	1.92647e11	+	2.29588e11i	1.05952	+	1.26269i	0.0959083	+	0.995390i	$0.469424\pi$
$654$		0			0
$655$	8.52072e10	−	3.10129e10i	0.462925	−	0.168491i
$656$	−1.92726e11	−	1.11270e11i	−1.04070	−	0.600846i
$657$		0			0
$658$	8.05344e9	+	1.39490e10i	0.0429614	+	0.0744112i
$659$	−1.37639e11	+	1.64032e11i	−0.729794	+	0.869734i	−0.995543	−	0.0943079i	$-0.969936\pi$
$659$	−1.37639e11	+	1.64032e11i	−0.729794	+	0.869734i	0.265749	+	0.964042i	$0.414381\pi$
$660$		0			0
$661$	3.06780e10	+	1.73984e11i	0.160702	+	0.911386i	0.953386	+	0.301753i	$0.0975719\pi$
$661$	3.06780e10	+	1.73984e11i	0.160702	+	0.911386i	−0.792684	+	0.609633i	$0.791317\pi$
$662$	4.88305e10	−	8.61014e9i	0.254249	−	0.0448310i
$663$		0			0
$664$	−5.87052e10	−	4.92595e10i	−0.301998	−	0.253406i
$665$	3.98668e11	−	2.30171e11i	2.03857	−	1.17697i
$666$		0			0
$667$	3.07565e10	−	5.32718e10i	0.155394	−	0.269150i
$668$	−2.06378e10	−	5.67020e10i	−0.103647	−	0.284769i
$669$		0			0
$670$	−9.29957e9	+	7.80327e9i	−0.0461491	+	0.0387237i
$671$	−9.03821e10	+	2.48323e11i	−0.445853	+	1.22497i
$672$		0			0
$673$	5.10778e10	−	2.89676e11i	0.248984	−	1.41206i	−0.562071	−	0.827089i	$-0.689995\pi$
$673$	5.10778e10	−	2.89676e11i	0.248984	−	1.41206i	0.811055	−	0.584970i	$-0.198894\pi$
$674$		−	1.71683e10i		−	0.0831932i
$675$		0			0
$676$	−1.93650e11			−0.927320
$677$	−1.66165e11	−	2.92994e10i	−0.791015	−	0.139477i	−0.236479	−	0.971637i	$-0.575993\pi$
$677$	−1.66165e11	−	2.92994e10i	−0.791015	−	0.139477i	−0.554537	+	0.832159i	$0.687104\pi$
$678$		0			0
$679$	5.47388e11	+	1.99233e11i	2.57523	+	0.937307i
$680$	−1.75377e10	−	2.09006e10i	−0.0820232	−	0.0977515i
$681$		0			0
$682$	3.61848e10	−	1.31702e10i	0.167259	−	0.0608771i
$683$	−5.30164e10	−	3.06090e10i	−0.243628	−	0.140659i	0.373215	−	0.927745i	$-0.378255\pi$
$683$	−5.30164e10	−	3.06090e10i	−0.243628	−	0.140659i	−0.616843	+	0.787086i	$0.711589\pi$
$684$		0			0
$685$	−1.98868e11	−	3.44450e11i	−0.903240	−	1.56446i
$686$	−4.66389e10	+	5.55821e10i	−0.210597	+	0.250980i
$687$		0			0
$688$	−1.55527e10	−	8.82040e10i	−0.0694150	−	0.393672i
$689$	6.50620e10	−	1.14722e10i	0.288703	−	0.0509060i
$690$		0			0
$691$	2.97075e11	+	2.49275e11i	1.30303	+	1.09337i	0.989613	+	0.143754i	$0.0459173\pi$
$691$	2.97075e11	+	2.49275e11i	1.30303	+	1.09337i	0.313414	+	0.949616i	$0.398527\pi$
$692$	−8.12362e10	+	4.69018e10i	−0.354263	+	0.204534i
$693$		0			0
$694$	−2.83247e10	+	4.90599e10i	−0.122103	+	0.211489i
$695$	1.07816e11	+	2.96222e11i	0.462109	+	1.26963i
$696$		0			0
$697$	8.15367e10	−	6.84174e10i	0.345479	−	0.289892i
$698$	8.66543e9	−	2.38081e10i	0.0365063	−	0.100300i
$699$		0			0
$700$	4.70537e9	−	2.66855e10i	0.0195976	−	0.111143i
$701$			5.50796e10i			0.228096i	0.993475	+	0.114048i	$0.0363818\pi$
$701$			5.50796e10i			0.228096i	−0.993475	+	0.114048i	$0.963618\pi$
$702$		0			0
$703$	2.89352e11			1.18469
$704$	2.21655e11	+	3.90838e10i	0.902375	+	0.159113i
$705$		0			0
$706$	−3.65485e10	−	1.33026e10i	−0.147113	−	0.0535447i
$707$	3.14396e11	+	3.74682e11i	1.25834	+	1.49964i
$708$		0			0
$709$	9.30404e10	−	3.38639e10i	0.368202	−	0.134015i	−0.151291	−	0.988489i	$-0.548343\pi$
$709$	9.30404e10	−	3.38639e10i	0.368202	−	0.134015i	0.519493	+	0.854475i	$0.326121\pi$
$710$	6.10306e10	+	3.52360e10i	0.240167	+	0.138661i
$711$		0			0
$712$	−3.43030e9	−	5.94145e9i	−0.0133479	−	0.0231192i
$713$	−1.09364e11	+	1.30335e11i	−0.423171	+	0.504316i
$714$		0			0
$715$	−9.46253e9	−	5.36646e10i	−0.0362062	−	0.205336i
$716$	−4.90804e10	+	8.65420e9i	−0.186748	+	0.0329287i
$717$		0			0
$718$	2.29774e10	+	1.92803e10i	0.0864576	+	0.0725465i
$719$	−2.21541e11	+	1.27907e11i	−0.828968	+	0.478605i	−0.853499	−	0.521094i	$-0.825524\pi$
$719$	−2.21541e11	+	1.27907e11i	−0.828968	+	0.478605i	0.0245313	+	0.999699i	$0.492191\pi$
$720$		0			0
$721$	7.44718e10	−	1.28989e11i	0.275582	−	0.477322i
$722$	−1.97109e10	−	5.41553e10i	−0.0725368	−	0.199293i
$723$		0			0
$724$	−1.14714e11	+	9.62564e10i	−0.417505	+	0.350329i
$725$	2.18874e9	−	6.01351e9i	0.00792213	−	0.0217659i
$726$		0			0
$727$	1.05428e10	−	5.97912e10i	0.0377414	−	0.214042i	−0.960105	−	0.279641i	$-0.909785\pi$
$727$	1.05428e10	−	5.97912e10i	0.0377414	−	0.214042i	0.997846	+	0.0655987i	$0.0208957\pi$
$728$		−	3.44749e10i		−	0.122738i
$729$		0			0
$730$	−2.73955e10			−0.0964689
$731$	4.21870e10	+	7.43871e9i	0.147744	+	0.0260512i
$732$		0			0
$733$	−4.73428e10	−	1.72314e10i	−0.163998	−	0.0596903i	0.258717	−	0.965953i	$-0.416700\pi$
$733$	−4.73428e10	−	1.72314e10i	−0.163998	−	0.0596903i	−0.422714	+	0.906263i	$0.638923\pi$
$734$	1.32781e10	+	1.58242e10i	0.0457457	+	0.0545176i
$735$		0			0
$736$	1.48436e11	−	5.40263e10i	0.505858	−	0.184117i
$737$	9.41051e10	+	5.43316e10i	0.318965	+	0.184155i
$738$		0			0
$739$	2.34907e11	+	4.06871e11i	0.787624	+	1.36420i	0.927419	+	0.374024i	$0.122022\pi$
$739$	2.34907e11	+	4.06871e11i	0.787624	+	1.36420i	−0.139796	+	0.990180i	$0.544645\pi$
$740$	−1.48079e11	+	1.76473e11i	−0.493817	+	0.588508i
$741$		0			0
$742$	−3.05301e10	−	1.73145e11i	−0.100719	−	0.571207i
$743$	5.04740e11	−	8.89993e10i	1.65620	−	0.292033i	0.734116	−	0.679024i	$-0.237597\pi$
$743$	5.04740e11	−	8.89993e10i	1.65620	−	0.292033i	0.922083	+	0.386991i	$0.126486\pi$
$744$		0			0
$745$	−2.41701e11	−	2.02811e11i	−0.784608	−	0.658364i
$746$	7.17990e10	−	4.14532e10i	0.231827	−	0.133845i
$747$		0			0
$748$	−5.97344e10	+	1.03463e11i	−0.190818	+	0.330506i
$749$	−2.62374e11	−	7.20866e11i	−0.833668	−	2.29049i
$750$		0			0
$751$	2.12965e10	−	1.78699e10i	0.0669498	−	0.0561776i	−0.608699	−	0.793401i	$-0.708308\pi$
$751$	2.12965e10	−	1.78699e10i	0.0669498	−	0.0561776i	0.675649	+	0.737224i	$0.263864\pi$
$752$	2.33424e10	−	6.41327e10i	0.0729918	−	0.200543i
$753$		0			0
$754$	6.91619e8	−	3.92237e9i	0.00213984	−	0.0121356i
$755$		−	4.06127e11i		−	1.24990i
$756$		0			0
$757$	−3.59044e11			−1.09336			−0.546681	−	0.837341i	$-0.684109\pi$
$757$	−3.59044e11			−1.09336			−0.546681	+	0.837341i	$0.684109\pi$
$758$	−1.30909e10	−	2.30828e9i	−0.0396546	−	0.00699218i
$759$		0			0
$760$	1.73645e11	+	6.32015e10i	0.520484	+	0.189441i
$761$	−4.75589e10	−	5.66785e10i	−0.141806	−	0.168997i	0.690467	−	0.723364i	$-0.257405\pi$
$761$	−4.75589e10	−	5.66785e10i	−0.141806	−	0.168997i	−0.832273	+	0.554367i	$0.812961\pi$
$762$		0			0
$763$	−4.07866e11	+	1.48451e11i	−1.20343	+	0.438011i
$764$	3.41519e10	+	1.97176e10i	0.100240	+	0.0578737i
$765$		0			0
$766$	4.30381e10	+	7.45443e10i	0.125008	+	0.216521i
$767$	7.02981e10	−	8.37780e10i	0.203124	−	0.242074i
$768$		0			0
$769$	6.71441e10	+	3.80793e11i	0.192000	+	1.08889i	0.916626	+	0.399746i	$0.130902\pi$
$769$	6.71441e10	+	3.80793e11i	0.192000	+	1.08889i	−0.724626	+	0.689143i	$0.757987\pi$
$770$	−1.42814e11	+	2.51819e10i	−0.406263	+	0.0716351i
$771$		0			0
$772$	2.48845e10	+	2.08806e10i	0.0700583	+	0.0587859i
$773$	3.24557e11	−	1.87383e11i	0.909020	−	0.524823i	0.0289045	−	0.999582i	$-0.490798\pi$
$773$	3.24557e11	−	1.87383e11i	0.909020	−	0.524823i	0.880116	+	0.474759i	$0.157465\pi$
$774$		0			0
$775$	−8.85018e9	+	1.53290e10i	−0.0245327	+	0.0424919i
$776$	7.99752e10	+	2.19730e11i	0.220551	+	0.605958i
$777$		0			0
$778$	−2.27960e9	+	1.91281e9i	−0.00622214	+	0.00522100i
$779$	−2.46559e11	+	6.77416e11i	−0.669532	+	1.83952i
$780$		0			0
$781$	1.09537e11	−	6.21215e11i	0.294413	−	1.66970i
$782$			2.33338e10i			0.0623963i
$783$		0			0
$784$	6.37941e11			1.68856
$785$	−3.46065e11	−	6.10206e10i	−0.911337	−	0.160693i
$786$		0			0
$787$	1.64892e11	+	6.00158e10i	0.429834	+	0.156447i	0.547872	−	0.836562i	$-0.315438\pi$
$787$	1.64892e11	+	6.00158e10i	0.429834	+	0.156447i	−0.118038	+	0.993009i	$0.537660\pi$
$788$	−9.58105e9	−	1.14183e10i	−0.0248490	−	0.0296139i
$789$		0			0
$790$	8.34054e10	−	3.03571e10i	0.214134	−	0.0779384i
$791$	1.03929e12	+	6.00032e11i	2.65479	+	1.53274i
$792$		0			0
$793$	−3.78005e10	−	6.54723e10i	−0.0955883	−	0.165564i
$794$	−6.17783e10	+	7.36245e10i	−0.155437	+	0.185242i
$795$		0			0
$796$	2.69549e10	+	1.52869e11i	0.0671406	+	0.380773i
$797$	−1.75652e10	+	3.09722e9i	−0.0435331	+	0.00767606i	−0.195372	−	0.980729i	$-0.562592\pi$
$797$	−1.75652e10	+	3.09722e9i	−0.0435331	+	0.00767606i	0.151839	+	0.988405i	$0.451480\pi$
$798$		0			0
$799$	2.50057e10	+	2.09822e10i	0.0613552	+	0.0514831i
$800$	1.42318e10	−	8.21673e9i	0.0347456	−	0.0200604i
$801$		0			0
$802$	3.51279e10	−	6.08433e10i	0.0849092	−	0.147067i
$803$	8.38696e10	+	2.30430e11i	0.201717	+	0.554213i
$804$		0			0
$805$	4.90840e11	−	4.11863e11i	1.16884	−	0.980775i
$806$	−3.76781e9	+	1.03520e10i	−0.00892788	+	0.0245291i
$807$		0			0
$808$	−3.40937e10	+	1.93355e11i	−0.0799887	+	0.453638i
$809$			1.94607e11i			0.454323i	0.973857	+	0.227161i	$0.0729445\pi$
$809$			1.94607e11i			0.454323i	−0.973857	+	0.227161i	$0.927056\pi$
$810$		0			0
$811$	−8.64952e10			−0.199944			−0.0999720	−	0.994990i	$-0.531875\pi$
$811$	−8.64952e10			−0.199944			−0.0999720	+	0.994990i	$0.531875\pi$
$812$	2.36138e11	+	4.16375e10i	0.543177	+	0.0957768i
$813$		0			0
$814$	−8.56543e10	−	3.11756e10i	−0.195097	−	0.0710097i
$815$	−4.06896e11	−	4.84920e11i	−0.922259	−	1.09911i
$816$		0			0
$817$	−2.72636e11	+	9.92315e10i	−0.611921	+	0.222721i
$818$	−1.47522e11	−	8.51721e10i	−0.329492	−	0.190232i
$819$		0			0
$820$	−2.86972e11	−	4.97050e11i	−0.634722	−	1.09937i
$821$	1.63679e11	−	1.95065e11i	0.360264	−	0.429346i	−0.555218	−	0.831705i	$-0.687365\pi$
$821$	1.63679e11	−	1.95065e11i	0.360264	−	0.429346i	0.915482	+	0.402359i	$0.131810\pi$
$822$		0			0
$823$	4.26800e10	+	2.42050e11i	0.0930304	+	0.527602i	0.995333	+	0.0964986i	$0.0307643\pi$
$823$	4.26800e10	+	2.42050e11i	0.0930304	+	0.527602i	−0.902303	+	0.431103i	$0.858125\pi$
$824$	5.88800e10	−	1.03821e10i	0.127720	−	0.0225205i
$825$		0			0
$826$	−2.22952e11	−	1.87079e11i	−0.478951	−	0.401888i
$827$	−5.42919e11	+	3.13454e11i	−1.16068	+	0.670120i	−0.951467	−	0.307750i	$-0.900424\pi$
$827$	−5.42919e11	+	3.13454e11i	−1.16068	+	0.670120i	−0.209214	+	0.977870i	$0.567091\pi$
$828$		0			0
$829$	−3.00938e11	+	5.21239e11i	−0.637174	+	1.10362i	0.348876	+	0.937169i	$0.386564\pi$
$829$	−3.00938e11	+	5.21239e11i	−0.637174	+	1.10362i	−0.986050	+	0.166449i	$0.946770\pi$
$830$	−3.15418e10	−	8.66604e10i	−0.0664621	−	0.182603i
$831$		0			0
$832$	−4.93261e10	+	4.13895e10i	−0.102940	+	0.0863768i
$833$	−1.04357e11	+	2.86719e11i	−0.216742	+	0.595493i
$834$		0			0
$835$	2.57762e10	−	1.46184e11i	0.0530241	−	0.300715i
$836$		−	8.09143e11i		−	1.65653i
$837$		0			0
$838$	−1.20708e11			−0.244771
$839$	−2.19890e11	−	3.87726e10i	−0.443770	−	0.0782486i	−0.0527018	−	0.998610i	$-0.516783\pi$
$839$	−2.19890e11	−	3.87726e10i	−0.443770	−	0.0782486i	−0.391068	+	0.920362i	$0.627894\pi$
$840$		0			0
$841$	−4.16865e11	−	1.51726e11i	−0.833319	−	0.303303i
$842$	−1.67496e10	−	1.99614e10i	−0.0333239	−	0.0397138i
$843$		0			0
$844$	3.83329e11	−	1.39520e11i	0.755444	−	0.274959i
$845$	−4.12557e11	−	2.38190e11i	−0.809202	−	0.467193i
$846$		0			0
$847$	2.08517e11	+	3.61162e11i	0.405143	+	0.701728i
$848$	−4.78859e11	+	5.70682e11i	−0.926028	+	1.10360i
$849$		0			0
$850$	4.21533e8	+	2.39063e9i	0.000807524	+	0.00457970i
$851$	3.96627e11	−	6.99360e10i	0.756247	−	0.133347i
$852$		0			0
$853$	1.07390e10	+	9.01105e9i	0.0202846	+	0.0170208i	0.652874	−	0.757467i	$-0.273563\pi$
$853$	1.07390e10	+	9.01105e9i	0.0202846	+	0.0170208i	−0.632589	+	0.774488i	$0.718008\pi$
$854$	−1.74237e11	+	1.00596e11i	−0.327573	+	0.189124i
$855$		0			0
$856$	1.53969e11	−	2.66682e11i	0.286773	−	0.496706i
$857$	3.56164e10	+	9.78554e10i	0.0660279	+	0.181410i	0.968319	−	0.249718i	$-0.0803379\pi$
$857$	3.56164e10	+	9.78554e10i	0.0660279	+	0.181410i	−0.902291	+	0.431128i	$0.858116\pi$
$858$		0			0
$859$	−2.94212e11	+	2.46873e11i	−0.540365	+	0.453420i	−0.871663	−	0.490106i	$-0.836958\pi$
$859$	−2.94212e11	+	2.46873e11i	−0.540365	+	0.453420i	0.331298	+	0.943526i	$0.392514\pi$
$860$	7.90040e10	−	2.17062e11i	0.144429	−	0.396816i
$861$		0			0
$862$	−2.93660e10	+	1.66543e11i	−0.0531883	+	0.301646i
$863$		−	2.17241e11i		−	0.391650i	−0.980639	−	0.195825i	$-0.937262\pi$
$863$		−	2.17241e11i		−	0.391650i	0.980639	−	0.195825i	$-0.0627384\pi$
$864$		0			0
$865$	−2.30758e11			−0.412184
$866$	−6.07954e9	−	1.07199e9i	−0.0108093	−	0.00190598i
$867$		0			0
$868$	−6.23218e11	−	2.26833e11i	−1.09790	−	0.399602i
$869$	−5.10681e11	−	6.08606e11i	−0.895511	−	1.06723i
$870$		0			0
$871$	−2.92123e10	+	1.06324e10i	−0.0507566	+	0.0184739i
$872$	−1.50889e11	−	8.71156e10i	−0.260970	−	0.150671i
$873$		0			0
$874$	−7.90180e10	−	1.36863e11i	−0.135419	−	0.234553i
$875$	6.65237e11	−	7.92799e11i	1.13487	−	1.35248i
$876$		0			0
$877$	−2.14413e10	−	1.21600e11i	−0.0362454	−	0.205558i	0.961307	−	0.275479i	$-0.0888364\pi$
$877$	−2.14413e10	−	1.21600e11i	−0.0362454	−	0.205558i	−0.997553	+	0.0699210i	$0.977725\pi$
$878$	−4.93596e10	+	8.70343e9i	−0.0830603	+	0.0146458i
$879$		0			0
$880$	4.70712e11	+	3.94974e11i	0.784918	+	0.658624i
$881$	−7.64992e11	+	4.41668e11i	−1.26985	+	0.733150i	−0.974960	−	0.222381i	$-0.928617\pi$
$881$	−7.64992e11	+	4.41668e11i	−1.26985	+	0.733150i	−0.294893	+	0.955530i	$0.595284\pi$
$882$		0			0
$883$	8.16461e10	−	1.41415e11i	0.134305	−	0.232623i	−0.791027	−	0.611782i	$-0.790453\pi$
$883$	8.16461e10	−	1.41415e11i	0.134305	−	0.232623i	0.925332	+	0.379158i	$0.123786\pi$
$884$	−1.16897e10	−	3.21172e10i	−0.0191423	−	0.0525930i
$885$		0			0
$886$	−1.09881e11	+	9.22015e10i	−0.178316	+	0.149625i
$887$	3.73853e11	−	1.02715e12i	0.603957	−	1.65936i	−0.139218	−	0.990262i	$-0.544459\pi$
$887$	3.73853e11	−	1.02715e12i	0.603957	−	1.65936i	0.743175	−	0.669097i	$-0.233319\pi$
$888$		0			0
$889$	−2.06901e11	+	1.17340e12i	−0.331251	+	1.87862i
$890$		−	8.25609e9i		−	0.0131587i
$891$		0			0
$892$	2.42138e10			0.0382475
$893$	−2.17724e11	−	3.83906e10i	−0.342374	−	0.0603697i
$894$		0			0
$895$	−1.15207e11	−	4.19320e10i	−0.179551	−	0.0653511i
$896$	5.23436e11	+	6.23807e11i	0.812141	+	0.967872i
$897$		0			0
$898$	1.56341e11	−	5.69035e10i	0.240419	−	0.0875052i
$899$	−1.35645e11	−	7.83146e10i	−0.207665	−	0.119896i
$900$		0			0
$901$	−1.78156e11	−	3.08575e11i	−0.270334	−	0.468233i
$902$	1.45974e11	−	1.73965e11i	0.220520	−	0.262806i
$903$		0			0
$904$	8.36507e10	+	4.74407e11i	0.125255	+	0.710357i
$905$	−3.62786e11	+	6.39690e10i	−0.540824	+	0.0953619i
$906$		0			0
$907$	−2.36599e11	−	1.98531e11i	−0.349611	−	0.293358i	0.451023	−	0.892512i	$-0.351059\pi$
$907$	−2.36599e11	−	1.98531e11i	−0.349611	−	0.293358i	−0.800634	+	0.599154i	$0.795504\pi$
$908$	−6.92161e11	+	3.99619e11i	−1.01827	+	0.587899i
$909$		0			0
$910$	2.07437e10	−	3.59291e10i	0.0302496	−	0.0523939i
$911$	2.99551e11	+	8.23009e11i	0.434907	+	1.19490i	0.942765	+	0.333457i	$0.108215\pi$
$911$	2.99551e11	+	8.23009e11i	0.434907	+	1.19490i	−0.507858	+	0.861441i	$0.669563\pi$
$912$		0			0
$913$	−6.32357e11	+	5.30611e11i	−0.910080	+	0.763648i
$914$	4.30509e10	−	1.18282e11i	0.0616876	−	0.169485i
$915$		0			0
$916$	−5.77550e10	+	3.27545e11i	−0.0820366	+	0.465253i
$917$		−	6.17935e11i		−	0.873907i
$918$		0			0
$919$	−5.59623e11			−0.784574			−0.392287	−	0.919843i	$-0.628316\pi$
$919$	−5.59623e11			−0.784574			−0.392287	+	0.919843i	$0.628316\pi$
$920$	2.53298e11	+	4.46632e10i	0.353574	+	0.0623446i
$921$		0			0
$922$	1.81258e11	+	6.59723e10i	0.250826	+	0.0912932i
$923$	1.15999e11	+	1.38242e11i	0.159826	+	0.190474i
$924$		0			0
$925$	3.93724e10	−	1.43304e10i	0.0537805	−	0.0195745i
$926$	1.91192e11	+	1.10385e11i	0.260032	+	0.150130i
$927$		0			0
$928$	7.27092e10	+	1.25936e11i	0.0980386	+	0.169808i
$929$	4.11643e11	−	4.90577e11i	0.552660	−	0.658634i	−0.415316	−	0.909677i	$-0.636329\pi$
$929$	4.11643e11	−	4.90577e11i	0.552660	−	0.658634i	0.967976	+	0.251043i	$0.0807736\pi$
$930$		0			0
$931$	−3.58849e11	−	2.03513e12i	−0.477653	−	2.70891i
$932$	1.75011e11	−	3.08591e10i	0.231953	−	0.0408996i
$933$		0			0
$934$	2.18607e10	+	1.83433e10i	0.0287260	+	0.0241040i
$935$	−2.54520e11	+	1.46947e11i	−0.333024	+	0.192272i
$936$		0			0
$937$	1.69447e11	−	2.93491e11i	0.219824	−	0.380747i	−0.734930	−	0.678143i	$-0.762785\pi$
$937$	1.69447e11	−	2.93491e11i	0.219824	−	0.380747i	0.954754	+	0.297396i	$0.0961182\pi$
$938$	2.82952e10	+	7.77404e10i	0.0365512	+	0.100424i
$939$		0			0
$940$	1.34837e11	−	1.13141e11i	0.172702	−	0.144914i
$941$	2.45934e11	−	6.75699e11i	0.313661	−	0.861777i	−0.678249	−	0.734833i	$-0.737261\pi$
$941$	2.45934e11	−	6.75699e11i	0.313661	−	0.861777i	0.991910	−	0.126945i	$-0.0405170\pi$
$942$		0			0
$943$	−1.74239e11	+	9.88156e11i	−0.220342	+	1.24962i
$944$			1.23322e12i			1.55293i
$945$		0			0
$946$	9.13977e10			0.114122
$947$	4.79075e11	+	8.44739e10i	0.595667	+	0.105032i	0.463350	−	0.886175i	$-0.346647\pi$
$947$	4.79075e11	+	8.44739e10i	0.595667	+	0.105032i	0.132317	+	0.991207i	$0.457758\pi$
$948$		0			0
$949$	−6.59227e10	−	2.39939e10i	−0.0812775	−	0.0295826i
$950$	−1.05681e10	−	1.25946e10i	−0.0129749	−	0.0154629i
$951$		0			0
$952$	−1.74720e11	+	6.35930e10i	−0.212714	+	0.0774215i
$953$	7.27038e11	+	4.19755e11i	0.881425	+	0.508891i	0.871128	−	0.491056i	$-0.163389\pi$
$953$	7.27038e11	+	4.19755e11i	0.881425	+	0.508891i	0.0102969	+	0.999947i	$0.496722\pi$
$954$		0			0
$955$	4.85055e10	+	8.40140e10i	0.0583147	+	0.101004i
$956$	3.43541e11	−	4.09416e11i	0.411289	−	0.490155i
$957$		0			0
$958$	−1.72272e10	−	9.77001e10i	−0.0204527	−	0.115993i
$959$	−2.66931e12	+	4.70672e11i	−3.15591	+	0.556473i
$960$		0			0
$961$	−3.21484e11	−	2.69757e11i	−0.376934	−	0.316285i
$962$	2.25835e10	−	1.30386e10i	0.0263688	−	0.0152240i
$963$		0			0
$964$	1.99879e11	−	3.46200e11i	0.231451	−	0.400884i
$965$	2.73315e10	+	7.50926e10i	0.0315177	+	0.0865940i
$966$		0			0
$967$	3.58024e11	−	3.00417e11i	0.409455	−	0.343573i	−0.414680	−	0.909967i	$-0.636106\pi$
$967$	3.58024e11	−	3.00417e11i	0.409455	−	0.343573i	0.824135	+	0.566394i	$0.191662\pi$
$968$	−5.72556e10	+	1.57309e11i	−0.0652104	+	0.179164i
$969$		0			0
$970$	−4.88637e10	+	2.77120e11i	−0.0551950	+	0.313026i
$971$		−	9.07616e11i		−	1.02100i	−0.859878	−	0.510500i	$-0.829461\pi$
$971$		−	9.07616e11i		−	1.02100i	0.859878	−	0.510500i	$-0.170539\pi$
$972$		0			0
$973$	2.14825e12			2.39681
$974$	7.81535e10	+	1.37806e10i	0.0868386	+	0.0153120i
$975$		0			0
$976$	8.01083e11	+	2.91570e11i	0.882832	+	0.321325i
$977$	−1.09047e11	−	1.29957e11i	−0.119684	−	0.142634i	0.702876	−	0.711313i	$-0.251899\pi$
$977$	−1.09047e11	−	1.29957e11i	−0.119684	−	0.142634i	−0.822559	+	0.568679i	$0.807455\pi$
$978$		0			0
$979$	−6.94439e10	+	2.52755e10i	−0.0755968	+	0.0275150i
$980$	1.42486e12	+	8.22642e11i	1.54478	+	0.891880i
$981$		0			0
$982$	−8.47257e10	−	1.46749e11i	−0.0911106	−	0.157808i
$983$	2.30885e11	−	2.75158e11i	0.247276	−	0.294692i	−0.628102	−	0.778131i	$-0.716168\pi$
$983$	2.30885e11	−	2.75158e11i	0.247276	−	0.294692i	0.875378	+	0.483439i	$0.160613\pi$
$984$		0			0
$985$	−6.36726e9	−	3.61105e10i	−0.00676407	−	0.0383609i
$986$	−2.11545e10	+	3.73011e9i	−0.0223818	+	0.00394652i
$987$		0			0
$988$	1.77327e11	+	1.48795e11i	0.186101	+	0.156157i
$989$	−3.49730e11	+	2.01917e11i	−0.365551	+	0.211051i
$990$		0			0
$991$	1.75783e11	−	3.04465e11i	0.182256	−	0.315677i	−0.760392	−	0.649464i	$-0.774993\pi$
$991$	1.75783e11	−	3.04465e11i	0.182256	−	0.315677i	0.942648	+	0.333787i	$0.108327\pi$
$992$	−1.37566e11	−	3.77959e11i	−0.142058	−	0.390300i
$993$		0			0
$994$	3.67894e11	−	3.08700e11i	0.376858	−	0.316221i
$995$	−1.30604e11	+	3.58831e11i	−0.133249	+	0.366098i
$996$		0			0
$997$	2.09430e11	−	1.18774e12i	0.211962	−	1.20210i	−0.674139	−	0.738604i	$-0.735485\pi$
$997$	2.09430e11	−	1.18774e12i	0.211962	−	1.20210i	0.886101	−	0.463492i	$-0.153404\pi$
$998$		−	9.91425e10i		−	0.0999397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.13		138
3.2	odd	2		27.9.f.a.2.11	✓	138
27.13	even	9		27.9.f.a.14.11	yes	138
27.14	odd	18	inner	81.9.f.a.71.13		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.11	✓	138	3.2	odd	2
27.9.f.a.14.11	yes	138	27.13	even	9
81.9.f.a.8.13		138	1.1	even	1	trivial
81.9.f.a.71.13		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)

\(f(q)\)	\(=\)	\(q+(3.24198 + 0.571649i) q^{2} +(-230.378 - 83.8506i) q^{4} +(-387.667 - 462.003i) q^{5} +(-3862.15 + 1405.71i) q^{7} +(-1428.79 - 824.913i) q^{8} +(-992.706 - 1719.42i) q^{10} +(-11423.3 + 13613.8i) q^{11} +(-882.859 - 5006.94i) q^{13} +(-13324.6 + 2349.49i) q^{14} +(43917.7 + 36851.3i) q^{16} +(-23746.9 + 13710.3i) q^{17} +(92857.3 - 160834. i) q^{19} +(50570.5 + 138941. i) q^{20} +(-44816.5 + 37605.5i) q^{22} +(88410.2 - 242905. i) q^{23} +(4669.78 - 26483.6i) q^{25} -16737.1i q^{26} +1.00762e6 q^{28} +(234351. + 41322.5i) q^{29} +(-618503. - 225117. i) q^{31} +(392799. + 468120. i) q^{32} +(-84824.4 + 30873.6i) q^{34} +(2.14667e6 + 1.23938e6i) q^{35} +(779022. + 1.34931e6i) q^{37} +(392982. - 468338. i) q^{38} +(172782. + 979898. i) q^{40} +(-3.82274e6 + 674052. i) q^{41} +(-1.19676e6 - 1.00420e6i) q^{43} +(3.77320e6 - 2.17846e6i) q^{44} +(425481. - 736954. i) q^{46} +(-407155. - 1.11865e6i) q^{47} +(8.52411e6 - 7.15258e6i) q^{49} +(30278.7 - 83190.0i) q^{50} +(-216444. + 1.22752e6i) q^{52} +1.29944e7i q^{53} +1.07180e7 q^{55} +(6.67780e6 + 1.17748e6i) q^{56} +(736141. + 267934. i) q^{58} +(1.38268e7 + 1.64782e7i) q^{59} +(1.39731e7 - 5.08578e6i) q^{61} +(-1.87649e6 - 1.08339e6i) q^{62} +(-6.33245e6 - 1.09681e7i) q^{64} +(-1.97097e6 + 2.34891e6i) q^{65} +(-1.06177e6 - 6.02157e6i) q^{67} +(6.62036e6 - 1.16735e6i) q^{68} +(6.25098e6 + 5.24520e6i) q^{70} +(-3.07395e7 + 1.77475e7i) q^{71} +(6.89919e6 - 1.19498e7i) q^{73} +(1.75425e6 + 4.81975e6i) q^{74} +(-3.48782e7 + 2.92663e7i) q^{76} +(2.49816e7 - 6.86363e7i) q^{77} +(-7.76297e6 + 4.40260e7i) q^{79} -3.45761e7i q^{80} -1.27786e7 q^{82} +(4.57442e7 + 8.06593e6i) q^{83} +(1.55401e7 + 5.65612e6i) q^{85} +(-3.30581e6 - 3.93971e6i) q^{86} +(2.75517e7 - 1.00280e7i) q^{88} +(3.60126e6 + 2.07919e6i) q^{89} +(1.04480e7 + 1.80965e7i) q^{91} +(-4.07355e7 + 4.85466e7i) q^{92} +(-680516. - 3.85940e6i) q^{94} +(-1.10303e8 + 1.94495e7i) q^{95} +(-1.08572e8 - 9.11031e7i) q^{97} +(3.17238e7 - 1.83157e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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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