LMFDB - Embedded newform 81.10.e.a.10.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,10,Mod(10,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.10"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.81300 - 21.6246i) q^{2} +(28.0377 - 10.2049i) q^{4} +(-47.8760 - 40.1728i) q^{5} +(-9290.87 - 3381.60i) q^{7} +(-5948.89 - 10303.8i) q^{8} +(-686.169 + 1188.48i) q^{10} +(43242.5 - 36284.8i) q^{11} +(25533.6 - 144809. i) q^{13} +(-37699.7 + 213805. i) q^{14} +(-188429. + 158111. i) q^{16} +(-90726.3 + 157143. i) q^{17} +(230723. + 399623. i) q^{19} +(-1752.29 - 637.782i) q^{20} +(-949528. - 796749. i) q^{22} +(781538. - 284456. i) q^{23} +(-338478. - 1.91961e6i) q^{25} -3.22879e6 q^{26} -295003. q^{28} +(-130819. - 741913. i) q^{29} +(-6.96328e6 + 2.53442e6i) q^{31} +(-528909. - 443807. i) q^{32} +(3.74409e6 + 1.36274e6i) q^{34} +(308962. + 535137. i) q^{35} +(-8.69333e6 + 1.50573e7i) q^{37} +(7.76196e6 - 6.51305e6i) q^{38} +(-129122. + 732287. i) q^{40} +(-1.02028e6 + 5.78631e6i) q^{41} +(-2.27597e7 + 1.90977e7i) q^{43} +(842138. - 1.45863e6i) q^{44} +(-9.13127e6 - 1.58158e7i) q^{46} +(-3.09371e7 - 1.12602e7i) q^{47} +(4.39723e7 + 3.68972e7i) q^{49} +(-4.02201e7 + 1.46389e7i) q^{50} +(-761850. - 4.32066e6i) q^{52} +8.37558e7 q^{53} -3.52794e6 q^{55} +(2.04271e7 + 1.15848e8i) q^{56} +(-1.55448e7 + 5.65784e6i) q^{58} +(1.16955e8 + 9.81373e7i) q^{59} +(-5.56721e7 - 2.02630e7i) q^{61} +(8.13569e7 + 1.40914e8i) q^{62} +(-7.05506e7 + 1.22197e8i) q^{64} +(-7.03981e6 + 5.90710e6i) q^{65} +(4.95235e6 - 2.80862e7i) q^{67} +(-940134. + 5.33177e6i) q^{68} +(1.03941e7 - 8.72165e6i) q^{70} +(-8.31647e7 + 1.44046e8i) q^{71} +(8.24703e7 + 1.42843e8i) q^{73} +(3.58756e8 + 1.30576e8i) q^{74} +(1.05470e7 + 8.85002e6i) q^{76} +(-5.24461e8 + 1.90888e8i) q^{77} +(-4.64491e6 - 2.63426e7i) q^{79} +1.53730e7 q^{80} +1.29017e8 q^{82} +(-1.45000e8 - 8.22337e8i) q^{83} +(1.06565e7 - 3.87864e6i) q^{85} +(4.99762e8 + 4.19350e8i) q^{86} +(-6.31115e8 - 2.29707e8i) q^{88} +(-3.80324e7 - 6.58740e7i) q^{89} +(-7.26914e8 + 1.25905e9i) q^{91} +(1.90097e7 - 1.59510e7i) q^{92} +(-1.25534e8 + 7.11939e8i) q^{94} +(5.00789e6 - 2.84011e7i) q^{95} +(3.94882e8 - 3.31345e8i) q^{97} +(6.30220e8 - 1.09157e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−3.81300	−	21.6246i	−0.168513	−	0.955682i	−0.945369	−	0.326004i	$-0.894298\pi$
$2$	−3.81300	−	21.6246i	−0.168513	−	0.955682i	0.776856	−	0.629678i	$-0.216813\pi$
$3$		0			0
$3$		0			0
$4$	28.0377	−	10.2049i	0.0547611	−	0.0199314i
$5$	−47.8760	−	40.1728i	−0.0342573	−	0.0287453i	0.625498	−	0.780226i	$-0.284896\pi$
$5$	−47.8760	−	40.1728i	−0.0342573	−	0.0287453i	−0.659756	+	0.751480i	$0.729340\pi$
$6$		0			0
$7$	−9290.87	−	3381.60i	−1.46256	−	0.532330i	−0.516494	−	0.856291i	$-0.672763\pi$
$7$	−9290.87	−	3381.60i	−1.46256	−	0.532330i	−0.946071	+	0.323961i	$0.894985\pi$
$8$	−5948.89	−	10303.8i	−0.513488	−	0.889388i
$9$		0			0
$10$	−686.169	+	1188.48i	−0.0216986	+	0.0375830i
$11$	43242.5	−	36284.8i	0.890520	−	0.747235i	−0.0777942	−	0.996969i	$-0.524788\pi$
$11$	43242.5	−	36284.8i	0.890520	−	0.747235i	0.968314	+	0.249734i	$0.0803433\pi$
$12$		0			0
$13$	25533.6	−	144809.i	0.247952	−	1.40621i	−0.565583	−	0.824691i	$-0.691349\pi$
$13$	25533.6	−	144809.i	0.247952	−	1.40621i	0.813536	−	0.581515i	$-0.197540\pi$
$14$	−37699.7	+	213805.i	−0.262278	+	1.48745i
$15$		0			0
$16$	−188429.	+	158111.i	−0.718801	+	0.603146i
$17$	−90726.3	+	157143.i	−0.263459	+	0.456324i	−0.967159	−	0.254173i	$-0.918197\pi$
$17$	−90726.3	+	157143.i	−0.263459	+	0.456324i	0.703700	+	0.710498i	$0.251530\pi$
$18$		0			0
$19$	230723.	+	399623.i	0.406162	+	0.703493i	0.994456	−	0.105154i	$-0.0335336\pi$
$19$	230723.	+	399623.i	0.406162	+	0.703493i	−0.588294	+	0.808647i	$0.700200\pi$
$20$	−1752.29	−	637.782i	−0.00244890	−	0.000891327i
$21$		0			0
$22$	−949528.	−	796749.i	−0.864183	−	0.725136i
$23$	781538.	−	284456.i	0.582337	−	0.211953i	−0.0340185	−	0.999421i	$-0.510831\pi$
$23$	781538.	−	284456.i	0.582337	−	0.211953i	0.616356	+	0.787468i	$0.288608\pi$
$24$		0			0
$25$	−338478.	−	1.91961e6i	−0.173301	−	0.982838i
$26$	−3.22879e6			−1.38567
$27$		0			0
$28$	−295003.			−0.0907018
$29$	−130819.	−	741913.i	−0.0343464	−	0.194788i	0.962807	−	0.270191i	$-0.0870868\pi$
$29$	−130819.	−	741913.i	−0.0343464	−	0.194788i	−0.997153	+	0.0754029i	$0.975976\pi$
$30$		0			0
$31$	−6.96328e6	+	2.53442e6i	−1.35421	+	0.492892i	−0.914259	−	0.405130i	$-0.867226\pi$
$31$	−6.96328e6	+	2.53442e6i	−1.35421	+	0.492892i	−0.439951	+	0.898022i	$0.645004\pi$
$32$	−528909.	−	443807.i	−0.0891673	−	0.0748203i
$33$		0			0
$34$	3.74409e6	+	1.36274e6i	0.480497	+	0.174887i
$35$	308962.	+	535137.i	0.0348015	+	0.0602780i
$36$		0			0
$37$	−8.69333e6	+	1.50573e7i	−0.762568	+	1.32081i	0.178955	+	0.983857i	$0.442728\pi$
$37$	−8.69333e6	+	1.50573e7i	−0.762568	+	1.32081i	−0.941523	+	0.336949i	$0.890605\pi$
$38$	7.76196e6	−	6.51305e6i	0.603872	−	0.506709i
$39$		0			0
$40$	−129122.	+	732287.i	−0.00797499	+	0.0452284i
$41$	−1.02028e6	+	5.78631e6i	−0.0563888	+	0.319797i	−0.999934	−	0.0114456i	$-0.996357\pi$
$41$	−1.02028e6	+	5.78631e6i	−0.0563888	+	0.319797i	0.943546	+	0.331242i	$0.107468\pi$
$42$		0			0
$43$	−2.27597e7	+	1.90977e7i	−1.01522	+	0.851867i	−0.989019	−	0.147789i	$-0.952784\pi$
$43$	−2.27597e7	+	1.90977e7i	−1.01522	+	0.851867i	−0.0261973	+	0.999657i	$0.508340\pi$
$44$	842138.	−	1.45863e6i	0.0338724	−	0.0586688i
$45$		0			0
$46$	−9.13127e6	−	1.58158e7i	−0.300691	−	0.520813i
$47$	−3.09371e7	−	1.12602e7i	−0.924783	−	0.336593i	−0.164643	−	0.986353i	$-0.552647\pi$
$47$	−3.09371e7	−	1.12602e7i	−0.924783	−	0.336593i	−0.760140	+	0.649760i	$0.774870\pi$
$48$		0			0
$49$	4.39723e7	+	3.68972e7i	1.08968	+	0.914346i
$50$	−4.02201e7	+	1.46389e7i	−0.910077	+	0.331241i
$51$		0			0
$52$	−761850.	−	4.32066e6i	−0.0144495	−	0.0819475i
$53$	8.37558e7			1.45805			0.729027	−	0.684485i	$-0.239973\pi$
$53$	8.37558e7			1.45805			0.729027	+	0.684485i	$0.239973\pi$
$54$		0			0
$55$	−3.52794e6			−0.0519863
$56$	2.04271e7	+	1.15848e8i	0.277562	+	1.57413i
$57$		0			0
$58$	−1.55448e7	+	5.65784e6i	−0.180368	+	0.0656484i
$59$	1.16955e8	+	9.81373e7i	1.25657	+	1.05439i	0.996039	+	0.0889209i	$0.0283418\pi$
$59$	1.16955e8	+	9.81373e7i	1.25657	+	1.05439i	0.260530	+	0.965466i	$0.416103\pi$
$60$		0			0
$61$	−5.56721e7	−	2.02630e7i	−0.514818	−	0.187378i	0.0715291	−	0.997439i	$-0.477212\pi$
$61$	−5.56721e7	−	2.02630e7i	−0.514818	−	0.187378i	−0.586347	+	0.810060i	$0.699434\pi$
$62$	8.13569e7	+	1.40914e8i	0.699249	+	1.21114i
$63$		0			0
$64$	−7.05506e7	+	1.22197e8i	−0.525643	+	0.910440i
$65$	−7.03981e6	+	5.90710e6i	−0.0489160	+	0.0410454i
$66$		0			0
$67$	4.95235e6	−	2.80862e7i	0.0300244	−	0.170277i	−0.966108	−	0.258137i	$-0.916892\pi$
$67$	4.95235e6	−	2.80862e7i	0.0300244	−	0.170277i	0.996133	+	0.0878595i	$0.0280027\pi$
$68$	−940134.	+	5.33177e6i	−0.00533212	+	0.0302399i
$69$		0			0
$70$	1.03941e7	−	8.72165e6i	0.0517421	−	0.0434168i
$71$	−8.31647e7	+	1.44046e8i	−0.388398	+	0.672725i	−0.992234	−	0.124384i	$-0.960305\pi$
$71$	−8.31647e7	+	1.44046e8i	−0.388398	+	0.672725i	0.603836	+	0.797108i	$0.293638\pi$
$72$		0			0
$73$	8.24703e7	+	1.42843e8i	0.339895	+	0.588715i	0.984413	−	0.175874i	$-0.0562751\pi$
$73$	8.24703e7	+	1.42843e8i	0.339895	+	0.588715i	−0.644518	+	0.764589i	$0.722942\pi$
$74$	3.58756e8	+	1.30576e8i	1.39077	+	0.506200i
$75$		0			0
$76$	1.05470e7	+	8.85002e6i	0.0362635	+	0.0304287i
$77$	−5.24461e8	+	1.90888e8i	−1.70022	+	0.618829i
$78$		0			0
$79$	−4.64491e6	−	2.63426e7i	−0.0134170	−	0.0760916i	0.977364	−	0.211564i	$-0.0678558\pi$
$79$	−4.64491e6	−	2.63426e7i	−0.0134170	−	0.0760916i	−0.990781	+	0.135473i	$0.956745\pi$
$80$	1.53730e7			0.0419618
$81$		0			0
$82$	1.29017e8			0.315126
$83$	−1.45000e8	−	8.22337e8i	−0.335365	−	1.90195i	−0.423603	−	0.905848i	$-0.639235\pi$
$83$	−1.45000e8	−	8.22337e8i	−0.335365	−	1.90195i	0.0882380	−	0.996099i	$-0.471876\pi$
$84$		0			0
$85$	1.06565e7	−	3.87864e6i	0.0221426	−	0.00805924i
$86$	4.99762e8	+	4.19350e8i	0.985191	+	0.826673i
$87$		0			0
$88$	−6.31115e8	−	2.29707e8i	−1.12185	−	0.408321i
$89$	−3.80324e7	−	6.58740e7i	−0.0642537	−	0.111291i	0.832109	−	0.554612i	$-0.187133\pi$
$89$	−3.80324e7	−	6.58740e7i	−0.0642537	−	0.111291i	−0.896363	+	0.443321i	$0.853800\pi$
$90$		0			0
$91$	−7.26914e8	+	1.25905e9i	−1.11121	+	1.92468i
$92$	1.90097e7	−	1.59510e7i	0.0276649	−	0.0232136i
$93$		0			0
$94$	−1.25534e8	+	7.11939e8i	−0.165839	+	0.940519i
$95$	5.00789e6	−	2.84011e7i	0.00630810	−	0.0357750i
$96$		0			0
$97$	3.94882e8	−	3.31345e8i	0.452892	−	0.380021i	−0.387616	−	0.921821i	$-0.626701\pi$
$97$	3.94882e8	−	3.31345e8i	0.452892	−	0.380021i	0.840508	+	0.541800i	$0.182257\pi$
$98$	6.30220e8	−	1.09157e9i	0.690200	−	1.19546i
$99$		0			0
$100$	−2.90795e7	−	5.03672e7i	−0.0290795	−	0.0503672i
$101$	−1.20305e9	−	4.37876e8i	−1.15037	−	0.418702i	−0.304724	−	0.952441i	$-0.598564\pi$
$101$	−1.20305e9	−	4.37876e8i	−1.15037	−	0.418702i	−0.845649	+	0.533739i	$0.820787\pi$
$102$		0			0
$103$	−1.82405e8	−	1.53056e8i	−0.159687	−	0.133993i	0.559443	−	0.828869i	$-0.311015\pi$
$103$	−1.82405e8	−	1.53056e8i	−0.159687	−	0.133993i	−0.719130	+	0.694876i	$0.755459\pi$
$104$	−1.64397e9	+	5.98356e8i	−1.37798	+	0.501545i
$105$		0			0
$106$	−3.19361e8	−	1.81119e9i	−0.245700	−	1.39344i
$107$	1.09457e9			0.807266			0.403633	−	0.914921i	$-0.367747\pi$
$107$	1.09457e9			0.807266			0.403633	+	0.914921i	$0.367747\pi$
$108$		0			0
$109$	−1.30250e8			−0.0883807			−0.0441903	−	0.999023i	$-0.514071\pi$
$109$	−1.30250e8			−0.0883807			−0.0441903	+	0.999023i	$0.514071\pi$
$110$	1.34520e7	+	7.62903e7i	0.00876034	+	0.0496824i
$111$		0			0
$112$	2.28534e9	−	8.31796e8i	1.37237	−	0.499500i
$113$	−1.66285e9	−	1.39530e9i	−0.959401	−	0.805033i	0.0214546	−	0.999770i	$-0.493170\pi$
$113$	−1.66285e9	−	1.39530e9i	−0.959401	−	0.805033i	−0.980856	+	0.194737i	$0.937615\pi$
$114$		0			0
$115$	−4.88443e7	−	1.77779e7i	−0.0260420	−	0.00947850i
$116$	−1.12390e7	−	1.94665e7i	−0.00576325	−	0.00998224i
$117$		0			0
$118$	1.67623e9	−	2.90331e9i	0.795911	−	1.37856i
$119$	1.37432e9	−	1.15319e9i	0.628241	−	0.527157i
$120$		0			0
$121$	1.43876e8	−	8.15964e8i	0.0610176	−	0.346048i
$122$	−2.25901e8	+	1.28115e9i	−0.0923208	+	0.523577i
$123$		0			0
$124$	−1.69371e8	+	1.42119e8i	−0.0643340	+	0.0539826i
$125$	−1.21944e8	+	2.11213e8i	−0.0446750	+	0.0773794i
$126$		0			0
$127$	1.31247e9	+	2.27327e9i	0.447686	+	0.775415i	0.998235	−	0.0593877i	$-0.0189148\pi$
$127$	1.31247e9	+	2.27327e9i	0.447686	+	0.775415i	−0.550549	+	0.834803i	$0.685582\pi$
$128$	2.57929e9	+	9.38785e8i	0.849289	+	0.309116i
$129$		0			0
$130$	1.54582e8	+	1.29709e8i	0.0474693	+	0.0398314i
$131$	4.55403e8	−	1.65753e8i	0.135106	−	0.0491746i	−0.273582	−	0.961849i	$-0.588209\pi$
$131$	4.55403e8	−	1.65753e8i	0.135106	−	0.0491746i	0.408688	+	0.912674i	$0.365986\pi$
$132$		0			0
$133$	−7.92248e8	−	4.49306e9i	−0.219548	−	1.24512i
$134$	−6.26236e8			−0.167790
$135$		0			0
$136$	2.15888e9			0.541133
$137$	1.40483e8	+	7.96716e8i	0.0340706	+	0.193224i	0.997093	−	0.0761985i	$-0.0242783\pi$
$137$	1.40483e8	+	7.96716e8i	0.0340706	+	0.193224i	−0.963022	+	0.269423i	$0.913167\pi$
$138$		0			0
$139$	−2.15460e9	+	7.84209e8i	−0.489553	+	0.178183i	−0.574989	−	0.818161i	$-0.694994\pi$
$139$	−2.15460e9	+	7.84209e8i	−0.489553	+	0.178183i	0.0854364	+	0.996344i	$0.472772\pi$
$140$	1.41236e7	+	1.18511e7i	0.00310720	+	0.00260725i
$141$		0			0
$142$	3.43204e9	+	1.24916e9i	0.708361	+	0.257822i
$143$	−4.15020e9	−	7.18837e9i	−0.829960	−	1.43753i
$144$		0			0
$145$	−2.35416e7	+	4.07752e7i	−0.00442262	+	0.00766021i
$146$	2.77446e9	−	2.32805e9i	0.505348	−	0.424037i
$147$		0			0
$148$	−9.00830e7	+	5.10886e8i	−0.0154335	+	0.0875278i
$149$	−8.39767e8	+	4.76255e9i	−0.139579	+	0.791593i	0.831982	+	0.554803i	$0.187206\pi$
$149$	−8.39767e8	+	4.76255e9i	−0.139579	+	0.791593i	−0.971561	+	0.236790i	$0.923905\pi$
$150$		0			0
$151$	7.32282e9	−	6.14457e9i	1.14626	−	0.961824i	0.146631	−	0.989191i	$-0.453157\pi$
$151$	7.32282e9	−	6.14457e9i	1.14626	−	0.961824i	0.999625	+	0.0273677i	$0.00871249\pi$
$152$	2.74509e9	−	4.75463e9i	0.417119	−	0.722471i
$153$		0			0
$154$	6.12765e9	+	1.06134e10i	0.877912	+	1.52059i
$155$	4.35189e8	+	1.58396e8i	0.0605599	+	0.0220420i
$156$		0			0
$157$	−5.50427e9	−	4.61863e9i	−0.723022	−	0.606688i	0.205197	−	0.978721i	$-0.434216\pi$
$157$	−5.50427e9	−	4.61863e9i	−0.723022	−	0.606688i	−0.928219	+	0.372033i	$0.878661\pi$
$158$	−5.51937e8	+	2.00889e8i	−0.0704584	+	0.0256448i
$159$		0			0
$160$	7.49309e6	+	4.24954e7i	0.000903902	+	0.00512628i
$161$	−8.22308e9			−0.964535
$162$		0			0
$163$	4.81370e9			0.534115			0.267057	−	0.963681i	$-0.413949\pi$
$163$	4.81370e9			0.534115			0.267057	+	0.963681i	$0.413949\pi$
$164$	3.04422e7	+	1.72647e8i	0.00328609	+	0.0186363i
$165$		0			0
$166$	−1.72298e10	+	6.27115e9i	−1.76114	+	0.641004i
$167$	−3.43540e9	−	2.88265e9i	−0.341786	−	0.286792i	0.455696	−	0.890135i	$-0.349390\pi$
$167$	−3.43540e9	−	2.88265e9i	−0.341786	−	0.286792i	−0.797482	+	0.603343i	$0.793835\pi$
$168$		0			0
$169$	−1.03526e10	−	3.76803e9i	−0.976243	−	0.355323i
$170$	−1.24507e8	−	2.15653e8i	−0.0114334	−	0.0198032i
$171$		0			0
$172$	−4.43240e8	+	7.67714e8i	−0.0386154	+	0.0668839i
$173$	−3.83230e8	+	3.21568e8i	−0.0325276	+	0.0272939i	−0.658907	−	0.752225i	$-0.728981\pi$
$173$	−3.83230e8	+	3.21568e8i	−0.0325276	+	0.0272939i	0.626379	+	0.779519i	$0.284536\pi$
$174$		0			0
$175$	−3.34658e9	+	1.89794e10i	−0.269731	+	1.52972i
$176$	−2.41114e9	+	1.36742e10i	−0.189415	+	1.07423i
$177$		0			0
$178$	−1.27948e9	+	1.07361e9i	−0.0955309	+	0.0801600i
$179$	1.24116e9	−	2.14976e9i	0.0903629	−	0.156513i	−0.817301	−	0.576211i	$-0.804531\pi$
$179$	1.24116e9	−	2.14976e9i	0.0903629	−	0.156513i	0.907664	+	0.419698i	$0.137864\pi$
$180$		0			0
$181$	−9.01501e9	−	1.56145e10i	−0.624328	−	1.08137i	−0.988670	−	0.150103i	$-0.952040\pi$
$181$	−9.01501e9	−	1.56145e10i	−0.624328	−	1.08137i	0.364342	−	0.931265i	$-0.381294\pi$
$182$	2.99982e10	+	1.09185e10i	2.02663	+	0.737633i
$183$		0			0
$184$	−7.58025e9	−	6.36059e9i	−0.487532	−	0.409088i
$185$	1.02109e9	−	3.71648e8i	0.0640904	−	0.0233270i
$186$		0			0
$187$	1.77865e9	+	1.00872e10i	0.106366	+	0.603232i
$188$	−9.82315e8			−0.0573509
$189$		0			0
$190$	−6.33259e8			−0.0352525
$191$	6.11314e9	+	3.46694e10i	0.332364	+	1.88493i	0.451846	+	0.892096i	$0.350766\pi$
$191$	6.11314e9	+	3.46694e10i	0.332364	+	1.88493i	−0.119482	+	0.992836i	$0.538123\pi$
$192$		0			0
$193$	−7.21602e9	+	2.62642e9i	−0.374360	+	0.136256i	−0.522346	−	0.852733i	$-0.674943\pi$
$193$	−7.21602e9	+	2.62642e9i	−0.374360	+	0.136256i	0.147986	+	0.988989i	$0.452721\pi$
$194$	−8.67090e9	−	7.27575e9i	−0.439498	−	0.368782i
$195$		0			0
$196$	1.60941e9	+	5.85779e8i	0.0778961	+	0.0283518i
$197$	−1.64003e10	−	2.84062e10i	−0.775809	−	1.34374i	−0.934338	−	0.356387i	$-0.884008\pi$
$197$	−1.64003e10	−	2.84062e10i	−0.775809	−	1.34374i	0.158529	−	0.987354i	$-0.449325\pi$
$198$		0			0
$199$	4.34935e9	−	7.53329e9i	0.196601	−	0.340523i	−0.750823	−	0.660503i	$-0.770343\pi$
$199$	4.34935e9	−	7.53329e9i	0.196601	−	0.340523i	0.947424	+	0.319980i	$0.103676\pi$
$200$	−1.77656e10	+	1.49071e10i	−0.785137	+	0.658808i
$201$		0			0
$202$	−4.88165e9	+	2.76852e10i	−0.206293	+	1.16995i
$203$	−1.29343e9	+	7.33540e9i	−0.0534577	+	0.303174i
$204$		0			0
$205$	2.81299e8	−	2.36038e8i	0.0111244	−	0.00933446i
$206$	−2.61426e9	+	4.52804e9i	−0.101146	+	0.175189i
$207$		0			0
$208$	1.80845e10	+	3.13233e10i	0.669919	+	1.16033i
$209$	2.44773e10	+	8.90900e9i	0.887370	+	0.322976i
$210$		0			0
$211$	−3.77321e10	−	3.16610e10i	−1.31051	−	1.09965i	−0.988226	−	0.153003i	$-0.951106\pi$
$211$	−3.77321e10	−	3.16610e10i	−1.31051	−	1.09965i	−0.322282	−	0.946644i	$-0.604450\pi$
$212$	2.34832e9	−	8.54719e8i	0.0798447	−	0.0290611i
$213$		0			0
$214$	−4.17360e9	−	2.36697e10i	−0.136034	−	0.771490i
$215$	1.85685e9			0.0592657
$216$		0			0
$217$	7.32653e10			2.24300
$218$	4.96642e8	+	2.81660e9i	0.0148933	+	0.0844638i
$219$		0			0
$220$	−9.89152e7	+	3.60022e7i	−0.00284683	+	0.00103616i
$221$	2.04390e10	+	1.71504e10i	0.576361	+	0.483624i
$222$		0			0
$223$	2.64943e10	+	9.64313e9i	0.717431	+	0.261124i	0.674835	−	0.737969i	$-0.264215\pi$
$223$	2.64943e10	+	9.64313e9i	0.717431	+	0.261124i	0.0425963	+	0.999092i	$0.486437\pi$
$224$	3.41324e9	+	5.91191e9i	0.0905839	+	0.156896i
$225$		0			0
$226$	−2.38323e10	+	4.12788e10i	−0.607684	+	1.05254i
$227$	4.45874e10	−	3.74132e10i	1.11454	−	0.935210i	0.116223	−	0.993223i	$-0.462921\pi$
$227$	4.45874e10	−	3.74132e10i	1.11454	−	0.935210i	0.998316	+	0.0580136i	$0.0184767\pi$
$228$		0			0
$229$	−9.20753e9	+	5.22185e10i	−0.221250	+	1.25477i	0.648475	+	0.761236i	$0.275407\pi$
$229$	−9.20753e9	+	5.22185e10i	−0.221250	+	1.25477i	−0.869725	+	0.493536i	$0.835704\pi$
$230$	−1.98196e8	+	1.12403e9i	−0.00467003	+	0.0264851i
$231$		0			0
$232$	−6.86628e9	+	5.76149e9i	−0.155606	+	0.130569i
$233$	1.22517e10	−	2.12205e10i	0.272329	−	0.471688i	−0.697129	−	0.716946i	$-0.745539\pi$
$233$	1.22517e10	−	2.12205e10i	0.272329	−	0.471688i	0.969458	+	0.245258i	$0.0788727\pi$
$234$		0			0
$235$	1.02879e9	+	1.78192e9i	0.0220051	+	0.0381139i
$236$	4.28064e9	+	1.55803e9i	0.0898265	+	0.0326942i
$237$		0			0
$238$	−3.01776e10	−	2.53220e10i	−0.609661	−	0.511566i
$239$	−8.71749e10	+	3.17291e10i	−1.72823	+	0.629023i	−0.998502	−	0.0547177i	$-0.982574\pi$
$239$	−8.71749e10	+	3.17291e10i	−1.72823	+	0.629023i	−0.729725	+	0.683741i	$0.760352\pi$
$240$		0			0
$241$	−1.16966e10	−	6.63349e10i	−0.223349	−	1.26668i	−0.865816	−	0.500363i	$-0.833200\pi$
$241$	−1.16966e10	−	6.63349e10i	−0.223349	−	1.26668i	0.642467	−	0.766314i	$-0.277911\pi$
$242$	−1.81935e10			−0.340994
$243$		0			0
$244$	−1.76770e9			−0.0319267
$245$	−6.22960e8	−	3.53298e9i	−0.0110462	−	0.0626461i
$246$		0			0
$247$	6.37601e10	−	2.32068e10i	1.08996	−	0.396715i
$248$	6.75379e10	+	5.66710e10i	1.13374	+	0.951324i
$249$		0			0
$250$	5.03237e9	+	1.83163e9i	0.0814784	+	0.0296557i
$251$	−4.40948e10	−	7.63745e10i	−0.701223	−	1.21455i	−0.968037	−	0.250806i	$-0.919304\pi$
$251$	−4.40948e10	−	7.63745e10i	−0.701223	−	1.21455i	0.266815	−	0.963748i	$-0.414029\pi$
$252$		0			0
$253$	2.34742e10	−	4.06585e10i	0.360204	−	0.623892i
$254$	4.41541e10	−	3.70497e10i	0.665610	−	0.558513i
$255$		0			0
$256$	−2.07899e9	+	1.17905e10i	−0.0302532	+	0.171575i
$257$	9.63201e9	−	5.46259e10i	0.137727	−	0.781087i	−0.835195	−	0.549953i	$-0.814646\pi$
$257$	9.63201e9	−	5.46259e10i	0.137727	−	0.781087i	0.972922	−	0.231133i	$-0.0742434\pi$
$258$		0			0
$259$	1.31686e11	−	1.10498e11i	1.81841	−	1.52583i
$260$	−1.37099e8	+	2.37462e8i	−0.00186060	+	0.00322265i
$261$		0			0
$262$	−5.32080e9	−	9.21590e9i	−0.0697624	−	0.120832i
$263$	−8.12421e10	−	2.95697e10i	−1.04708	−	0.381106i	−0.239520	−	0.970891i	$-0.576990\pi$
$263$	−8.12421e10	−	2.95697e10i	−1.04708	−	0.381106i	−0.807560	+	0.589785i	$0.799212\pi$
$264$		0			0
$265$	−4.00990e9	−	3.36470e9i	−0.0499490	−	0.0419122i
$266$	−9.41398e10	+	3.42641e10i	−1.15294	+	0.419635i
$267$		0			0
$268$	−1.47764e8	−	8.38010e8i	−0.00174969	−	0.00992299i
$269$	2.46138e10			0.286612			0.143306	−	0.989678i	$-0.454227\pi$
$269$	2.46138e10			0.286612			0.143306	+	0.989678i	$0.454227\pi$
$270$		0			0
$271$	−1.10516e11			−1.24469			−0.622347	−	0.782741i	$-0.713821\pi$
$271$	−1.10516e11			−1.24469			−0.622347	+	0.782741i	$0.713821\pi$
$272$	−7.75047e9	−	4.39551e10i	−0.0858555	−	0.486911i
$273$		0			0
$274$	1.66930e10	−	6.07576e9i	0.178919	−	0.0651213i
$275$	−8.42891e10	−	7.07270e10i	−0.888739	−	0.745741i
$276$		0			0
$277$	−1.26961e11	−	4.62100e10i	−1.29572	−	0.471603i	−0.400119	−	0.916463i	$-0.631031\pi$
$277$	−1.26961e11	−	4.62100e10i	−1.29572	−	0.471603i	−0.895600	+	0.444860i	$0.853253\pi$
$278$	2.51737e10	+	4.36021e10i	0.252782	+	0.437831i
$279$		0			0
$280$	3.67595e9	−	6.36694e9i	0.0357404	−	0.0619041i
$281$	−5.33888e10	+	4.47985e10i	−0.510824	+	0.428632i	−0.861419	−	0.507895i	$-0.830424\pi$
$281$	−5.33888e10	+	4.47985e10i	−0.510824	+	0.428632i	0.350595	+	0.936527i	$0.385979\pi$
$282$		0			0
$283$	3.42188e9	−	1.94064e10i	0.0317122	−	0.179849i	−0.964838	−	0.262847i	$-0.915339\pi$
$283$	3.42188e9	−	1.94064e10i	0.0317122	−	0.179849i	0.996550	+	0.0829984i	$0.0264496\pi$
$284$	−8.61779e8	+	4.88739e9i	−0.00786074	+	0.0445805i
$285$		0			0
$286$	−1.39621e11	+	1.17156e11i	−1.23397	+	1.03542i
$287$	2.90463e10	−	5.03096e10i	0.252710	−	0.437706i
$288$		0			0
$289$	4.28314e10	+	7.41862e10i	0.361179	+	0.625580i
$290$	9.71513e8	+	3.53602e8i	0.00806599	+	0.00293578i
$291$		0			0
$292$	3.76997e9	+	3.16338e9i	0.0303470	+	0.0254641i
$293$	1.13270e11	−	4.12268e10i	0.897863	−	0.326795i	0.148467	−	0.988917i	$-0.452566\pi$
$293$	1.13270e11	−	4.12268e10i	0.897863	−	0.326795i	0.749396	+	0.662122i	$0.230344\pi$
$294$		0			0
$295$	−1.65692e9	−	9.39684e9i	−0.0127380	−	0.0722409i
$296$	2.06862e11			1.56628
$297$		0			0
$298$	1.06190e11			0.780032
$299$	−2.12362e10	−	1.20437e11i	−0.153659	−	0.871441i
$300$		0			0
$301$	2.76038e11	−	1.00470e11i	1.93829	−	0.705481i
$302$	−1.60796e11	−	1.34924e11i	−1.11236	−	0.933378i
$303$		0			0
$304$	−1.06660e11	−	3.88210e10i	−0.716258	−	0.260697i
$305$	1.85134e9	+	3.20661e9i	0.0122500	+	0.0212176i
$306$		0			0
$307$	−1.30046e10	+	2.25246e10i	−0.0835553	+	0.144722i	−0.904775	−	0.425891i	$-0.859961\pi$
$307$	−1.30046e10	+	2.25246e10i	−0.0835553	+	0.144722i	0.821219	+	0.570613i	$0.193294\pi$
$308$	−1.27567e10	+	1.07041e10i	−0.0807717	+	0.0677755i
$309$		0			0
$310$	1.76587e9	−	1.00148e10i	0.0108600	−	0.0615903i
$311$	−9.42724e9	+	5.34645e10i	−0.0571430	+	0.324074i	−0.999957	−	0.00924462i	$-0.997057\pi$
$311$	−9.42724e9	+	5.34645e10i	−0.0571430	+	0.324074i	0.942814	+	0.333318i	$0.108168\pi$
$312$		0			0
$313$	2.27595e10	−	1.90975e10i	0.134034	−	0.112468i	−0.573306	−	0.819341i	$-0.694339\pi$
$313$	2.27595e10	−	1.90975e10i	0.134034	−	0.112468i	0.707340	+	0.706874i	$0.249895\pi$
$314$	−7.88884e10	+	1.36639e11i	−0.457962	+	0.793214i
$315$		0			0
$316$	−3.99056e8	−	6.91185e8i	−0.00225134	−	0.00389944i
$317$	−8.31617e10	−	3.02684e10i	−0.462548	−	0.168354i	0.100226	−	0.994965i	$-0.468043\pi$
$317$	−8.31617e10	−	3.02684e10i	−0.462548	−	0.168354i	−0.562774	+	0.826611i	$0.690266\pi$
$318$		0			0
$319$	−3.25771e10	−	2.73354e10i	−0.176139	−	0.147798i
$320$	8.28668e9	−	3.01610e9i	0.0441780	−	0.0160795i
$321$		0			0
$322$	3.13546e10	+	1.77821e11i	0.162536	+	0.921789i
$323$	−8.37305e10			−0.428028
$324$		0			0
$325$	−2.86618e11			−1.42504
$326$	−1.83546e10	−	1.04094e11i	−0.0900050	−	0.510444i
$327$		0			0
$328$	6.56903e10	−	2.39093e10i	0.313378	−	0.114060i
$329$	2.49355e11	+	2.09234e11i	1.17338	+	0.984579i
$330$		0			0
$331$	3.69992e11	+	1.34666e11i	1.69421	+	0.616641i	0.995145	−	0.0984203i	$-0.0313790\pi$
$331$	3.69992e11	+	1.34666e11i	1.69421	+	0.616641i	0.699062	+	0.715061i	$0.253601\pi$
$332$	−1.24573e10	−	2.15767e10i	−0.0562734	−	0.0974685i
$333$		0			0
$334$	−4.92369e10	+	8.52808e10i	−0.216487	+	0.374966i
$335$	−1.36540e9	+	1.14571e9i	−0.00592322	+	0.00497017i
$336$		0			0
$337$	−5.74736e10	+	3.25949e11i	−0.242736	+	1.37662i	0.582957	+	0.812503i	$0.301896\pi$
$337$	−5.74736e10	+	3.25949e11i	−0.242736	+	1.37662i	−0.825692	+	0.564120i	$0.809215\pi$
$338$	−4.20078e10	+	2.38238e11i	−0.175067	+	0.992854i
$339$		0			0
$340$	2.59202e8	−	2.17496e8i	0.00105192	−	0.000882665i
$341$	−2.09148e11	+	3.62256e11i	−0.837645	+	1.45084i
$342$		0			0
$343$	−8.42789e10	−	1.45975e11i	−0.328773	−	0.569451i
$344$	3.32173e11	+	1.20901e11i	1.27894	+	0.465497i
$345$		0			0
$346$	8.41504e9	+	7.06105e9i	0.0315656	+	0.0264867i
$347$	4.29853e11	−	1.56454e11i	1.59161	−	0.579299i	0.613924	−	0.789365i	$-0.289590\pi$
$347$	4.29853e11	−	1.56454e11i	1.59161	−	0.579299i	0.977687	+	0.210066i	$0.0673677\pi$
$348$		0			0
$349$	−2.91387e10	−	1.65254e11i	−0.105137	−	0.596262i	−0.991165	−	0.132631i	$-0.957658\pi$
$349$	−2.91387e10	−	1.65254e11i	−0.105137	−	0.596262i	0.886028	−	0.463631i	$-0.153454\pi$
$350$	4.23183e11			1.50738
$351$		0			0
$352$	−3.89748e10			−0.135314
$353$	4.45513e10	+	2.52663e11i	0.152713	+	0.866076i	0.960847	+	0.277078i	$0.0893661\pi$
$353$	4.45513e10	+	2.52663e11i	0.152713	+	0.866076i	−0.808135	+	0.588997i	$0.799523\pi$
$354$		0			0
$355$	9.76830e9	−	3.55537e9i	0.0326431	−	0.0118811i
$356$	−1.73858e9	−	1.45884e9i	−0.00573678	−	0.00481373i
$357$		0			0
$358$	−5.12202e10	−	1.86426e10i	−0.164804	−	0.0599838i
$359$	1.58947e11	+	2.75304e11i	0.505041	+	0.874756i	0.999983	+	0.00583025i	$0.00185584\pi$
$359$	1.58947e11	+	2.75304e11i	0.505041	+	0.874756i	−0.494942	+	0.868926i	$0.664811\pi$
$360$		0			0
$361$	5.48779e10	−	9.50514e10i	0.170065	−	0.294561i
$362$	−3.03282e11	+	2.54484e11i	−0.928237	+	0.778883i
$363$		0			0
$364$	−7.53251e9	+	4.27190e10i	−0.0224897	+	0.127545i
$365$	1.79004e9	−	1.01518e10i	0.00527891	−	0.0299382i
$366$		0			0
$367$	−2.88550e11	+	2.42123e11i	−0.830280	+	0.696687i	−0.955355	−	0.295460i	$-0.904527\pi$
$367$	−2.88550e11	+	2.42123e11i	−0.830280	+	0.696687i	0.125076	+	0.992147i	$0.460083\pi$
$368$	−1.02289e11	+	1.77170e11i	−0.290746	+	0.503587i
$369$		0			0
$370$	−1.19302e10	−	2.06637e10i	−0.0330932	−	0.0573192i
$371$	−7.78164e11	−	2.83229e11i	−2.13250	−	0.776166i
$372$		0			0
$373$	−5.65704e11	−	4.74682e11i	−1.51321	−	1.26974i	−0.857197	−	0.514988i	$-0.827796\pi$
$373$	−5.65704e11	−	4.74682e11i	−1.51321	−	1.26974i	−0.656015	−	0.754748i	$-0.727759\pi$
$374$	2.11350e11	−	7.69252e10i	0.558574	−	0.203304i
$375$		0			0
$376$	6.80190e10	+	3.85755e11i	0.175503	+	0.995328i
$377$	−1.10776e11			−0.282428
$378$		0			0
$379$	−1.96200e11			−0.488452			−0.244226	−	0.969718i	$-0.578534\pi$
$379$	−1.96200e11			−0.488452			−0.244226	+	0.969718i	$0.578534\pi$
$380$	−1.49421e8	−	8.47407e8i	−0.000367608	−	0.00208481i
$381$		0			0
$382$	7.26402e11	−	2.64389e11i	1.74539	−	0.635269i
$383$	−2.28764e11	−	1.91956e11i	−0.543243	−	0.455835i	0.329402	−	0.944190i	$-0.393153\pi$
$383$	−2.28764e11	−	1.91956e11i	−0.543243	−	0.455835i	−0.872645	+	0.488355i	$0.837597\pi$
$384$		0			0
$385$	3.27776e10	+	1.19301e10i	0.0760333	+	0.0276739i
$386$	8.43099e10	+	1.46029e11i	0.193302	+	0.334809i
$387$		0			0
$388$	7.69024e9	−	1.33199e10i	0.0172265	−	0.0298372i
$389$	2.30204e11	−	1.93164e11i	0.509730	−	0.427714i	−0.351304	−	0.936261i	$-0.614262\pi$
$389$	2.30204e11	−	1.93164e11i	0.509730	−	0.427714i	0.861034	+	0.508547i	$0.169817\pi$
$390$		0			0
$391$	−2.62058e10	+	1.48621e11i	−0.0567025	+	0.321576i
$392$	1.18594e11	−	6.72578e11i	0.253673	−	1.43865i
$393$		0			0
$394$	−5.51739e11	+	4.62964e11i	−1.15346	+	0.967864i
$395$	−8.35875e8	+	1.44778e9i	−0.00172764	+	0.00299237i
$396$		0			0
$397$	−3.62020e11	−	6.27037e11i	−0.731434	−	1.26688i	−0.956270	−	0.292485i	$-0.905518\pi$
$397$	−3.62020e11	−	6.27037e11i	−0.731434	−	1.26688i	0.224836	−	0.974397i	$-0.427815\pi$
$398$	−1.79489e11	−	6.53285e10i	−0.358561	−	0.130506i
$399$		0			0
$400$	3.67290e11	+	3.08193e11i	0.717364	+	0.601940i
$401$	2.06903e11	−	7.53065e10i	0.399592	−	0.145440i	−0.134404	−	0.990927i	$-0.542912\pi$
$401$	2.06903e11	−	7.53065e10i	0.399592	−	0.145440i	0.533996	+	0.845487i	$0.320690\pi$
$402$		0			0
$403$	1.89208e11	+	1.07305e12i	0.357329	+	2.02651i
$404$	−3.81993e10			−0.0713411
$405$		0			0
$406$	1.63557e11			0.298746
$407$	1.70429e11	+	9.66550e11i	0.307871	+	1.74602i
$408$		0			0
$409$	−4.98189e11	+	1.81326e11i	−0.880317	+	0.320409i	−0.742338	−	0.670026i	$-0.766283\pi$
$409$	−4.98189e11	+	1.81326e11i	−0.880317	+	0.320409i	−0.137979	+	0.990435i	$0.544061\pi$
$410$	−6.17682e9	−	5.18297e9i	−0.0107954	−	0.00905839i
$411$		0			0
$412$	−6.67613e9	−	2.42991e9i	−0.0114153	−	0.00415483i
$413$	−7.54756e11	−	1.30728e12i	−1.27653	−	2.21102i
$414$		0			0
$415$	−2.60935e10	+	4.51953e10i	−0.0431833	+	0.0747957i
$416$	−7.77720e10	+	6.52585e10i	−0.127322	+	0.106836i
$417$		0			0
$418$	9.93217e10	−	5.63282e11i	0.159130	−	0.902469i
$419$	1.71211e11	−	9.70985e11i	0.271374	−	1.53904i	−0.478875	−	0.877883i	$-0.658955\pi$
$419$	1.71211e11	−	9.70985e11i	0.271374	−	1.53904i	0.750249	−	0.661155i	$-0.229934\pi$
$420$		0			0
$421$	1.76453e11	−	1.48061e11i	0.273753	−	0.229706i	−0.495567	−	0.868570i	$-0.665040\pi$
$421$	1.76453e11	−	1.48061e11i	0.273753	−	0.229706i	0.769320	+	0.638864i	$0.220595\pi$
$422$	−5.40784e11	+	9.36665e11i	−0.830075	+	1.43773i
$423$		0			0
$424$	−4.98254e11	−	8.63001e11i	−0.748694	−	1.29678i
$425$	3.32361e11	+	1.20969e11i	0.494151	+	0.179856i
$426$		0			0
$427$	4.48721e11	+	3.76521e11i	0.653207	+	0.548106i
$428$	3.06892e10	−	1.11700e10i	0.0442068	−	0.0160900i
$429$		0			0
$430$	−7.08017e9	−	4.01537e10i	−0.00998702	−	0.0566392i
$431$	3.63101e11			0.506850			0.253425	−	0.967355i	$-0.418443\pi$
$431$	3.63101e11			0.506850			0.253425	+	0.967355i	$0.418443\pi$
$432$		0			0
$433$	4.46965e11			0.611052			0.305526	−	0.952184i	$-0.401168\pi$
$433$	4.46965e11			0.611052			0.305526	+	0.952184i	$0.401168\pi$
$434$	−2.79361e11	−	1.58433e12i	−0.377974	−	2.14360i
$435$		0			0
$436$	−3.65190e9	+	1.32918e9i	−0.00483983	+	0.00176155i
$437$	2.93994e11	+	2.46690e11i	0.385631	+	0.323583i
$438$		0			0
$439$	5.78846e11	+	2.10683e11i	0.743829	+	0.270731i	0.686006	−	0.727595i	$-0.259362\pi$
$439$	5.78846e11	+	2.10683e11i	0.743829	+	0.270731i	0.0578221	+	0.998327i	$0.481584\pi$
$440$	2.09873e10	+	3.63511e10i	0.0266944	+	0.0462360i
$441$		0			0
$442$	2.92936e11	−	5.07380e11i	0.365067	−	0.632315i
$443$	−7.23024e11	+	6.06689e11i	−0.891941	+	0.748427i	−0.968599	−	0.248630i	$-0.920020\pi$
$443$	−7.23024e11	+	6.06689e11i	−0.891941	+	0.748427i	0.0766574	+	0.997057i	$0.475575\pi$
$444$		0			0
$445$	−8.25501e8	+	4.68165e9i	−0.000997924	+	0.00565951i
$446$	1.07506e11	−	6.09698e11i	0.128655	−	0.729639i
$447$		0			0
$448$	1.06870e12	−	8.96744e11i	1.25344	−	1.05176i
$449$	−2.59666e11	+	4.49754e11i	−0.301513	+	0.522236i	−0.976479	−	0.215613i	$-0.930825\pi$
$449$	−2.59666e11	+	4.49754e11i	−0.301513	+	0.522236i	0.674966	+	0.737849i	$0.264158\pi$
$450$		0			0
$451$	1.65835e11	+	2.87235e11i	0.188748	+	0.326921i
$452$	−6.08613e10	−	2.21517e10i	−0.0685833	−	0.0249623i
$453$		0			0
$454$	−9.79058e11	−	8.21528e11i	−1.08158	−	0.907551i
$455$	8.53813e10	−	3.10763e10i	0.0933924	−	0.0339921i
$456$		0			0
$457$	−1.52243e11	−	8.63411e11i	−0.163273	−	0.925965i	−0.950828	−	0.309721i	$-0.899764\pi$
$457$	−1.52243e11	−	8.63411e11i	−0.163273	−	0.925965i	0.787555	−	0.616245i	$-0.211347\pi$
$458$	1.16431e12			1.23645
$459$		0			0
$460$	−1.55090e9			−0.00161501
$461$	−1.34794e11	−	7.64456e11i	−0.139001	−	0.788313i	−0.971990	−	0.235023i	$-0.924483\pi$
$461$	−1.34794e11	−	7.64456e11i	−0.139001	−	0.788313i	0.832989	−	0.553290i	$-0.186628\pi$
$462$		0			0
$463$	−5.17365e10	+	1.88306e10i	−0.0523218	+	0.0190436i	−0.368048	−	0.929807i	$-0.619974\pi$
$463$	−5.17365e10	+	1.88306e10i	−0.0523218	+	0.0190436i	0.315727	+	0.948850i	$0.397752\pi$
$464$	1.41955e11	+	1.19114e11i	0.142174	+	0.119298i
$465$		0			0
$466$	−5.05602e11	−	1.84024e11i	−0.496675	−	0.180775i
$467$	−9.15905e10	−	1.58639e11i	−0.0891096	−	0.154342i	0.818025	−	0.575182i	$-0.195069\pi$
$467$	−9.15905e10	−	1.58639e11i	−0.0891096	−	0.154342i	−0.907135	+	0.420840i	$0.861735\pi$
$468$		0			0
$469$	−1.40988e11	+	2.44198e11i	−0.134556	+	0.233058i
$470$	3.46106e10	−	2.90418e10i	0.0327167	−	0.0274525i
$471$		0			0
$472$	3.15429e11	−	1.78889e12i	0.292525	−	1.65899i
$473$	−2.91232e11	+	1.65166e12i	−0.267525	+	1.51721i
$474$		0			0
$475$	6.89025e11	−	5.78161e11i	0.621032	−	0.521107i
$476$	2.67646e10	−	4.63576e10i	0.0238962	−	0.0413894i
$477$		0			0
$478$	1.01853e12	+	1.76414e12i	0.892374	+	1.54564i
$479$	6.53190e11	+	2.37742e11i	0.566930	+	0.206346i	0.609553	−	0.792746i	$-0.291349\pi$
$479$	6.53190e11	+	2.37742e11i	0.566930	+	0.206346i	−0.0426226	+	0.999091i	$0.513571\pi$
$480$		0			0
$481$	1.95845e12	+	1.64334e12i	1.66825	+	1.39982i
$482$	−1.38987e12	+	5.05871e11i	−1.17290	+	0.426902i
$483$		0			0
$484$	−4.29285e9	−	2.43460e10i	−0.00355584	−	0.0201662i
$485$	−3.22164e10			−0.0264387
$486$		0			0
$487$	−4.92422e11			−0.396695			−0.198348	−	0.980132i	$-0.563558\pi$
$487$	−4.92422e11			−0.396695			−0.198348	+	0.980132i	$0.563558\pi$
$488$	1.22402e11	+	6.94175e11i	0.0977009	+	0.554089i
$489$		0			0
$490$	−7.40240e10	+	2.69425e10i	−0.0580083	+	0.0211133i
$491$	1.68718e12	+	1.41571e12i	1.31007	+	1.09928i	0.988310	+	0.152458i	$0.0487189\pi$
$491$	1.68718e12	+	1.41571e12i	1.31007	+	1.09928i	0.321760	+	0.946821i	$0.395726\pi$
$492$		0			0
$493$	1.28455e11	+	4.67538e10i	0.0979354	+	0.0356456i
$494$	−7.44955e11	−	1.29030e12i	−0.562806	−	0.974808i
$495$		0			0
$496$	9.11365e11	−	1.57853e12i	0.676122	−	1.17108i
$497$	1.25978e12	−	1.05708e12i	0.926168	−	0.777147i
$498$		0			0
$499$	3.46666e10	−	1.96604e11i	0.0250299	−	0.141952i	−0.969732	−	0.244172i	$-0.921484\pi$
$499$	3.46666e10	−	1.96604e11i	0.0250299	−	0.141952i	0.994762	+	0.102221i	$0.0325948\pi$
$500$	−1.26362e9	+	7.16634e9i	−0.000904172	+	0.00512782i
$501$		0			0
$502$	−1.48344e12	+	1.24475e12i	−1.04256	+	0.874814i
$503$	−3.05547e11	+	5.29223e11i	−0.212825	+	0.368624i	−0.952598	−	0.304233i	$-0.901600\pi$
$503$	−3.05547e11	+	5.29223e11i	−0.212825	+	0.368624i	0.739773	+	0.672857i	$0.234933\pi$
$504$		0			0
$505$	4.00068e10	+	6.92937e10i	0.0273730	+	0.0474114i
$506$	−9.68732e11	−	3.52590e11i	−0.656941	−	0.239107i
$507$		0			0
$508$	5.99972e10	+	5.03436e10i	0.0399709	+	0.0335396i
$509$	−6.56669e11	+	2.39008e11i	−0.433627	+	0.157827i	−0.549605	−	0.835424i	$-0.685222\pi$
$509$	−6.56669e11	+	2.39008e11i	−0.433627	+	0.157827i	0.115978	+	0.993252i	$0.463000\pi$
$510$		0			0
$511$	−2.83184e11	−	1.60601e12i	−0.183728	−	1.04197i
$512$	1.66824e12			1.07286
$513$		0			0
$514$	−1.21799e12			−0.769679
$515$	2.58414e9	+	1.46554e10i	0.00161877	+	0.00918048i
$516$		0			0
$517$	−1.74637e12	+	6.35628e11i	−1.07505	+	0.391287i
$518$	−2.89159e12	−	2.42634e12i	−1.76463	−	1.48070i
$519$		0			0
$520$	1.02744e11	+	3.73959e10i	0.0616230	+	0.0224290i
$521$	−8.20450e11	−	1.42106e12i	−0.487845	−	0.844973i	0.512057	−	0.858951i	$-0.328884\pi$
$521$	−8.20450e11	−	1.42106e12i	−0.487845	−	0.844973i	−0.999902	+	0.0139787i	$0.995550\pi$
$522$		0			0
$523$	−1.09287e12	+	1.89290e12i	−0.638720	+	1.10630i	0.346994	+	0.937867i	$0.387202\pi$
$523$	−1.09287e12	+	1.89290e12i	−0.638720	+	1.10630i	−0.985714	+	0.168428i	$0.946131\pi$
$524$	1.10770e10	−	9.29467e9i	0.00641844	−	0.00538571i
$525$		0			0
$526$	−3.29657e11	+	1.86958e12i	−0.187770	+	1.06490i
$527$	2.33486e11	−	1.32417e12i	0.131860	−	0.747816i
$528$		0			0
$529$	−8.49877e11	+	7.13132e11i	−0.471852	+	0.395931i
$530$	−5.74707e10	+	9.95421e10i	−0.0316377	+	0.0547981i
$531$		0			0
$532$	−6.80639e10	−	1.17890e11i	−0.0368396	−	0.0638080i
$533$	8.11855e11	+	2.95491e11i	0.435719	+	0.158589i
$534$		0			0
$535$	−5.24037e10	−	4.39719e10i	−0.0276548	−	0.0232051i
$536$	−3.18855e11	+	1.16054e11i	−0.166860	+	0.0607319i
$537$		0			0
$538$	−9.38527e10	−	5.32265e11i	−0.0482977	−	0.273910i
$539$	3.24028e12			1.65361
$540$		0			0
$541$	6.60279e11			0.331390			0.165695	−	0.986177i	$-0.447013\pi$
$541$	6.60279e11			0.331390			0.165695	+	0.986177i	$0.447013\pi$
$542$	4.21397e11	+	2.38986e12i	0.209747	+	1.18953i
$543$		0			0
$544$	1.17727e11	−	4.28491e10i	0.0576343	−	0.0209772i
$545$	6.23584e9	+	5.23249e9i	0.00302768	+	0.00254053i
$546$		0			0
$547$	−2.43130e12	−	8.84922e11i	−1.16117	−	0.422632i	−0.311655	−	0.950195i	$-0.600883\pi$
$547$	−2.43130e12	−	8.84922e11i	−1.16117	−	0.422632i	−0.849515	+	0.527564i	$0.823106\pi$
$548$	1.20692e10	+	2.09045e10i	0.00571697	+	0.00990209i
$549$		0			0
$550$	−1.20805e12	+	2.09240e12i	−0.562927	+	0.975019i
$551$	2.66303e11	−	2.23455e11i	0.123082	−	0.103278i
$552$		0			0
$553$	−4.59248e10	+	2.60453e11i	−0.0208826	+	0.118431i
$554$	−5.15171e11	+	2.92168e12i	−0.232358	+	1.31777i
$555$		0			0
$556$	−5.24072e10	+	4.39748e10i	−0.0232570	+	0.0195150i
$557$	−1.51656e12	+	2.62676e12i	−0.667593	+	1.15631i	0.310982	+	0.950416i	$0.399342\pi$
$557$	−1.51656e12	+	2.62676e12i	−0.667593	+	1.15631i	−0.978575	+	0.205890i	$0.933991\pi$
$558$		0			0
$559$	2.18437e12	+	3.78343e12i	0.946176	+	1.63883i
$560$	−1.42829e11	−	5.19853e10i	−0.0613718	−	0.0223375i
$561$		0			0
$562$	1.17232e12	+	9.83695e11i	0.495716	+	0.415955i
$563$	−1.52139e12	+	5.53741e11i	−0.638194	+	0.232284i	−0.640794	−	0.767713i	$-0.721395\pi$
$563$	−1.52139e12	+	5.53741e11i	−0.638194	+	0.232284i	0.00259974	+	0.999997i	$0.499172\pi$
$564$		0			0
$565$	2.35577e10	+	1.33603e11i	0.00972558	+	0.0551565i
$566$	−4.32705e11			−0.177222
$567$		0			0
$568$	1.97895e12			0.797751
$569$	−2.61329e11	−	1.48207e12i	−0.104516	−	0.592740i	−0.991413	−	0.130772i	$-0.958255\pi$
$569$	−2.61329e11	−	1.48207e12i	−0.104516	−	0.592740i	0.886896	−	0.461968i	$-0.152857\pi$
$570$		0			0
$571$	−2.95914e12	+	1.07704e12i	−1.16494	+	0.424002i	−0.850859	−	0.525395i	$-0.823918\pi$
$571$	−2.95914e12	+	1.07704e12i	−1.16494	+	0.424002i	−0.314078	+	0.949397i	$0.601695\pi$
$572$	−1.89719e11	−	1.59193e11i	−0.0741016	−	0.0621787i
$573$		0			0
$574$	−1.19868e12	−	4.36284e11i	−0.460892	−	0.167751i
$575$	−8.10578e11	−	1.40396e12i	−0.309236	−	0.535612i
$576$		0			0
$577$	−3.80226e11	+	6.58570e11i	−0.142807	+	0.247349i	−0.928553	−	0.371201i	$-0.878946\pi$
$577$	−3.80226e11	+	6.58570e11i	−0.142807	+	0.247349i	0.785745	+	0.618550i	$0.212280\pi$
$578$	1.44093e12	−	1.20908e12i	0.536992	−	0.450590i
$579$		0			0
$580$	−2.43945e8	+	1.38348e9i	−8.95090e−5	+	0.000507631i
$581$	−1.43364e12	+	8.13056e12i	−0.521971	+	2.96025i
$582$		0			0
$583$	3.62181e12	−	3.03906e12i	1.29843	−	1.08951i
$584$	9.81213e11	−	1.69951e12i	0.349064	−	0.604597i
$585$		0			0
$586$	−1.32341e12	−	2.29222e12i	−0.463613	−	0.803002i
$587$	3.39270e12	+	1.23484e12i	1.17944	+	0.429280i	0.856003	−	0.516971i	$-0.172941\pi$
$587$	3.39270e12	+	1.23484e12i	1.17944	+	0.429280i	0.323434	+	0.946251i	$0.395163\pi$
$588$		0			0
$589$	−2.61940e12	−	2.19794e12i	−0.896774	−	0.752483i
$590$	−1.96885e11	+	7.16604e10i	−0.0668928	+	0.0243470i
$591$		0			0
$592$	−7.42645e11	−	4.21175e12i	−0.248504	−	1.40934i
$593$	3.92221e12			1.30252			0.651261	−	0.758854i	$-0.274240\pi$
$593$	3.92221e12			1.30252			0.651261	+	0.758854i	$0.274240\pi$
$594$		0			0
$595$	−1.12124e11			−0.0366751
$596$	2.50562e10	+	1.42101e11i	0.00813405	+	0.0461305i
$597$		0			0
$598$	−2.52342e12	+	9.18450e11i	−0.806927	+	0.293697i
$599$	2.00073e12	+	1.67881e12i	0.634992	+	0.532821i	0.902476	−	0.430741i	$-0.141748\pi$
$599$	2.00073e12	+	1.67881e12i	0.634992	+	0.532821i	−0.267484	+	0.963562i	$0.586192\pi$
$600$		0			0
$601$	1.72587e12	+	6.28166e11i	0.539602	+	0.196399i	0.597420	−	0.801928i	$-0.296192\pi$
$601$	1.72587e12	+	6.28166e11i	0.539602	+	0.196399i	−0.0578189	+	0.998327i	$0.518415\pi$
$602$	−3.22515e12	−	5.58612e12i	−1.00084	−	1.73351i
$603$		0			0
$604$	1.42610e11	−	2.47008e11i	0.0435998	−	0.0755170i
$605$	−3.96677e10	+	3.32852e10i	−0.0120376	+	0.0101007i
$606$		0			0
$607$	7.66638e11	−	4.34782e12i	0.229214	−	1.29994i	−0.625249	−	0.780426i	$-0.715002\pi$
$607$	7.66638e11	−	4.34782e12i	0.229214	−	1.29994i	0.854463	−	0.519512i	$-0.173886\pi$
$608$	5.53245e10	−	3.13761e11i	0.0164192	−	0.0931177i
$609$		0			0
$610$	6.22826e10	−	5.22613e10i	0.0182130	−	0.0152826i
$611$	−2.42051e12	+	4.19245e12i	−0.702622	+	1.21698i
$612$		0			0
$613$	8.94099e11	+	1.54862e12i	0.255749	+	0.442970i	0.965099	−	0.261887i	$-0.0843447\pi$
$613$	8.94099e11	+	1.54862e12i	0.255749	+	0.442970i	−0.709350	+	0.704856i	$0.751011\pi$
$614$	5.36672e11	+	1.95333e11i	0.152388	+	0.0554648i
$615$		0			0
$616$	5.08683e12	+	4.26835e12i	1.42342	+	1.19439i
$617$	4.38887e12	−	1.59742e12i	1.21919	−	0.443747i	0.349305	−	0.937009i	$-0.386418\pi$
$617$	4.38887e12	−	1.59742e12i	1.21919	−	0.443747i	0.869881	+	0.493262i	$0.164196\pi$
$618$		0			0
$619$	5.82096e11	+	3.30123e12i	0.159363	+	0.903791i	0.954688	+	0.297608i	$0.0961889\pi$
$619$	5.82096e11	+	3.30123e12i	0.159363	+	0.903791i	−0.795325	+	0.606183i	$0.792700\pi$
$620$	1.38181e10			0.00375565
$621$		0			0
$622$	1.19210e12			0.319341
$623$	1.30594e11	+	7.40636e11i	0.0347318	+	0.196974i
$624$		0			0
$625$	−3.56315e12	+	1.29688e12i	−0.934059	+	0.339970i
$626$	−4.99759e11	−	4.19347e11i	−0.130070	−	0.109141i
$627$		0			0
$628$	−2.01460e11	−	7.33253e10i	−0.0516856	−	0.0188120i
$629$	−1.57743e12	−	2.73218e12i	−0.401811	−	0.695956i
$630$		0			0
$631$	−1.10248e11	+	1.90954e11i	−0.0276845	+	0.0479510i	−0.879536	−	0.475833i	$-0.842147\pi$
$631$	−1.10248e11	+	1.90954e11i	−0.0276845	+	0.0479510i	0.851851	+	0.523784i	$0.175480\pi$
$632$	−2.43796e11	+	2.04569e11i	−0.0607855	+	0.0510051i
$633$		0			0
$634$	−3.37446e11	+	1.91375e12i	−0.0829474	+	0.470418i
$635$	2.84875e10	−	1.61561e11i	0.00695301	−	0.0394325i
$636$		0			0
$637$	6.46580e12	−	5.42545e12i	1.55595	−	1.30559i
$638$	−4.66902e11	+	8.08698e11i	−0.111566	+	0.193238i
$639$		0			0
$640$	−8.57726e10	−	1.48562e11i	−0.0202087	−	0.0350025i
$641$	1.76707e12	+	6.43163e11i	0.413422	+	0.150473i	0.540353	−	0.841438i	$-0.318291\pi$
$641$	1.76707e12	+	6.43163e11i	0.413422	+	0.150473i	−0.126931	+	0.991912i	$0.540513\pi$
$642$		0			0
$643$	−1.60030e12	−	1.34281e12i	−0.369193	−	0.309789i	0.439250	−	0.898365i	$-0.355244\pi$
$643$	−1.60030e12	−	1.34281e12i	−0.369193	−	0.309789i	−0.808442	+	0.588576i	$0.799689\pi$
$644$	−2.30556e11	+	8.39156e10i	−0.0528190	+	0.0192246i
$645$		0			0
$646$	3.19265e11	+	1.81064e12i	0.0721281	+	0.409059i
$647$	−2.53376e12			−0.568455			−0.284228	−	0.958757i	$-0.591737\pi$
$647$	−2.53376e12			−0.568455			−0.284228	+	0.958757i	$0.591737\pi$
$648$		0			0
$649$	8.61833e12			1.90687
$650$	1.09287e12	+	6.19800e12i	0.240138	+	1.36189i
$651$		0			0
$652$	1.34965e11	−	4.91232e10i	0.0292487	−	0.0106457i
$653$	−6.18388e12	−	5.18889e12i	−1.33092	−	1.11677i	−0.983862	−	0.178930i	$-0.942736\pi$
$653$	−6.18388e12	−	5.18889e12i	−1.33092	−	1.11677i	−0.347058	−	0.937844i	$-0.612819\pi$
$654$		0			0
$655$	−2.84617e10	−	1.03592e10i	−0.00604191	−	0.00219908i
$656$	−7.22628e11	−	1.25163e12i	−0.152352	−	0.263881i
$657$		0			0
$658$	3.57381e12	−	6.19002e12i	0.743216	−	1.28729i
$659$	7.75793e11	−	6.50968e11i	0.160236	−	0.134454i	−0.559144	−	0.829070i	$-0.688870\pi$
$659$	7.75793e11	−	6.50968e11i	0.160236	−	0.134454i	0.719381	+	0.694616i	$0.244426\pi$
$660$		0			0
$661$	2.19948e11	−	1.24739e12i	0.0448139	−	0.254152i	−0.954168	−	0.299273i	$-0.903256\pi$
$661$	2.19948e11	−	1.24739e12i	0.0448139	−	0.254152i	0.998982	+	0.0451202i	$0.0143671\pi$
$662$	1.50132e12	−	8.51442e12i	0.303817	−	1.72303i
$663$		0			0
$664$	−7.61059e12	+	6.38604e12i	−1.51936	+	1.27490i
$665$	−1.42569e11	+	2.46937e11i	−0.0282701	+	0.0489653i
$666$		0			0
$667$	−3.13282e11	−	5.42621e11i	−0.0612872	−	0.106153i
$668$	−1.25738e11	−	4.57648e10i	−0.0244327	−	0.00889279i
$669$		0			0
$670$	2.99817e10	+	2.51576e10i	0.00574804	+	0.00482318i
$671$	−3.14264e12	+	1.14383e12i	−0.598471	+	0.217826i
$672$		0			0
$673$	−6.28951e11	−	3.56696e12i	−0.118181	−	0.670240i	−0.985126	−	0.171835i	$-0.945030\pi$
$673$	−6.28951e11	−	3.56696e12i	−0.118181	−	0.670240i	0.866944	−	0.498405i	$-0.166081\pi$
$674$	7.26767e12			1.35652
$675$		0			0
$676$	−3.28714e11			−0.0605423
$677$	−1.88171e12	−	1.06717e13i	−0.344273	−	1.95247i	−0.301795	−	0.953373i	$-0.597586\pi$
$677$	−1.88171e12	−	1.06717e13i	−0.344273	−	1.95247i	−0.0424780	−	0.999097i	$-0.513525\pi$
$678$		0			0
$679$	−4.78927e12	+	1.74315e12i	−0.864680	+	0.314718i
$680$	−1.03359e11	−	8.67282e10i	−0.0185377	−	0.0155550i
$681$		0			0
$682$	8.63112e12	+	3.14147e12i	1.52770	+	0.556037i
$683$	−4.48117e12	−	7.76162e12i	−0.787950	−	1.36477i	−0.927221	−	0.374515i	$-0.877809\pi$
$683$	−4.48117e12	−	7.76162e12i	−0.787950	−	1.36477i	0.139271	−	0.990254i	$-0.455524\pi$
$684$		0			0
$685$	2.52805e10	−	4.37872e10i	0.00438711	−	0.00759870i
$686$	−2.83531e12	+	2.37910e12i	−0.488811	+	0.410162i
$687$		0			0
$688$	1.26905e12	−	7.19712e12i	0.215938	−	1.22465i
$689$	2.13859e12	−	1.21286e13i	0.361528	−	2.05033i
$690$		0			0
$691$	−5.91842e12	+	4.96614e12i	−0.987539	+	0.828644i	−0.985210	−	0.171354i	$-0.945186\pi$
$691$	−5.91842e12	+	4.96614e12i	−0.987539	+	0.828644i	−0.00232960	+	0.999997i	$0.500742\pi$
$692$	−7.46331e9	+	1.29268e10i	−0.00123724	+	0.00214296i
$693$		0			0
$694$	−5.02228e12	−	8.69884e12i	−0.821832	−	1.42346i
$695$	1.34657e11	+	4.90113e10i	0.0218927	+	0.00796828i
$696$		0			0
$697$	−8.16709e11	−	6.85300e11i	−0.131075	−	0.109985i
$698$	−3.46244e12	+	1.26023e12i	−0.552120	+	0.200955i
$699$		0			0
$700$	9.98522e10	+	5.66290e11i	0.0157187	+	0.0891452i
$701$	−1.15920e13			−1.81313			−0.906565	−	0.422066i	$-0.861305\pi$
$701$	−1.15920e13			−1.81313			−0.906565	+	0.422066i	$0.861305\pi$
$702$		0			0
$703$	−8.02299e12			−1.23890
$704$	1.38311e12	+	7.84402e12i	0.212217	+	1.20354i
$705$		0			0
$706$	5.29387e12	−	1.92681e12i	0.801959	−	0.291889i
$707$	9.69669e12	+	8.13649e12i	1.45961	+	1.22476i
$708$		0			0
$709$	−3.50199e12	−	1.27462e12i	−0.520484	−	0.189441i	0.0684004	−	0.997658i	$-0.478210\pi$
$709$	−3.50199e12	−	1.27462e12i	−0.520484	−	0.189441i	−0.588884	+	0.808217i	$0.700433\pi$
$710$	−1.14130e11	−	1.97679e11i	−0.0168553	−	0.0291943i
$711$		0			0
$712$	−4.52500e11	+	7.83753e11i	−0.0659871	+	0.114293i
$713$	−4.72113e12	+	3.96150e12i	−0.684137	+	0.574059i
$714$		0			0
$715$	−9.00811e10	+	5.10876e11i	−0.0128901	+	0.0731035i
$716$	1.28613e10	−	7.29402e10i	0.00182884	−	0.0103719i
$717$		0			0
$718$	5.34727e12	−	4.48689e12i	0.750883	−	0.630066i
$719$	−6.40281e11	+	1.10900e12i	−0.0893492	+	0.154757i	−0.907236	−	0.420621i	$-0.861812\pi$
$719$	−6.40281e11	+	1.10900e12i	−0.0893492	+	0.154757i	0.817887	+	0.575379i	$0.195145\pi$
$720$		0			0
$721$	1.17713e12	+	2.03884e12i	0.162224	+	0.280980i
$722$	−2.26470e12	−	8.24283e11i	−0.310165	−	0.112891i
$723$		0			0
$724$	−4.12104e11	−	3.45796e11i	−0.0557421	−	0.0467732i
$725$	−1.37990e12	+	5.02243e11i	−0.185493	+	0.0675139i
$726$		0			0
$727$	2.27316e11	+	1.28917e12i	0.0301804	+	0.171162i	0.996172	−	0.0874104i	$-0.0278591\pi$
$727$	2.27316e11	+	1.28917e12i	0.0301804	+	0.171162i	−0.965992	+	0.258572i	$0.916748\pi$
$728$	1.72973e13			2.28238
$729$		0			0
$730$	−2.26354e11			−0.0295009
$731$	−9.36151e11	−	5.30918e12i	−0.121260	−	0.687700i
$732$		0			0
$733$	5.58899e12	−	2.03422e12i	0.715097	−	0.260274i	0.0412544	−	0.999149i	$-0.486865\pi$
$733$	5.58899e12	−	2.03422e12i	0.715097	−	0.260274i	0.673843	+	0.738874i	$0.264642\pi$
$734$	6.33605e12	+	5.31658e12i	0.805724	+	0.676083i
$735$		0			0
$736$	−5.39606e11	−	1.96401e11i	−0.0677839	−	0.0246713i
$737$	−8.04949e11	−	1.39421e12i	−0.100500	−	0.174070i
$738$		0			0
$739$	4.23364e12	−	7.33288e12i	0.522172	−	0.904429i	−0.477495	−	0.878634i	$-0.658455\pi$
$739$	4.23364e12	−	7.33288e12i	0.522172	−	0.904429i	0.999667	−	0.0257944i	$-0.00821154\pi$
$740$	2.48365e10	−	2.08403e10i	0.00304472	−	0.00255483i
$741$		0			0
$742$	−3.15757e12	+	1.79075e13i	−0.382415	+	2.16878i
$743$	−9.88086e11	+	5.60371e12i	−0.118945	+	0.674569i	0.865777	+	0.500431i	$0.166825\pi$
$743$	−9.88086e11	+	5.60371e12i	−0.118945	+	0.674569i	−0.984721	+	0.174138i	$0.944286\pi$
$744$		0			0
$745$	2.31530e11	−	1.94276e11i	0.0275362	−	0.0231056i
$746$	−8.10779e12	+	1.40431e13i	−0.958468	+	1.66012i
$747$		0			0
$748$	1.52808e11	+	2.64671e11i	0.0178480	+	0.0309136i
$749$	−1.01695e13	−	3.70140e12i	−1.18068	−	0.429732i
$750$		0			0
$751$	−2.98564e12	−	2.50525e12i	−0.342498	−	0.287390i	0.455271	−	0.890353i	$-0.349542\pi$
$751$	−2.98564e12	−	2.50525e12i	−0.342498	−	0.287390i	−0.797769	+	0.602963i	$0.793987\pi$
$752$	7.60983e12	−	2.76975e12i	0.867750	−	0.315835i
$753$		0			0
$754$	4.22388e11	+	2.39548e12i	0.0475927	+	0.269912i
$755$	−5.97432e11			−0.0669155
$756$		0			0
$757$	−6.71271e12			−0.742961			−0.371481	−	0.928441i	$-0.621150\pi$
$757$	−6.71271e12			−0.742961			−0.371481	+	0.928441i	$0.621150\pi$
$758$	7.48110e11	+	4.24274e12i	0.0823102	+	0.466805i
$759$		0			0
$760$	−3.22430e11	+	1.17355e11i	−0.0350570	+	0.0127597i
$761$	−5.34871e12	−	4.48810e12i	−0.578120	−	0.485100i	0.306209	−	0.951964i	$-0.400939\pi$
$761$	−5.34871e12	−	4.48810e12i	−0.578120	−	0.485100i	−0.884329	+	0.466864i	$0.845384\pi$
$762$		0			0
$763$	1.21013e12	+	4.40452e11i	0.129262	+	0.0470477i
$764$	5.25195e11	+	9.09665e11i	0.0557700	+	0.0965965i
$765$		0			0
$766$	−3.27870e12	+	5.67887e12i	−0.344090	+	0.595981i
$767$	1.71974e13	−	1.44303e13i	1.79425	−	1.50556i
$768$		0			0
$769$	1.67906e12	−	9.52243e12i	0.173140	−	0.981927i	−0.767129	−	0.641493i	$-0.778315\pi$
$769$	1.67906e12	−	9.52243e12i	0.173140	−	0.981927i	0.940269	−	0.340433i	$-0.110574\pi$
$770$	1.33002e11	−	7.54292e11i	0.0136348	−	0.0773271i
$771$		0			0
$772$	−1.75518e11	+	1.47277e11i	−0.0177846	+	0.0149231i
$773$	−3.86430e12	+	6.69317e12i	−0.389281	+	0.674255i	−0.992353	−	0.123432i	$-0.960610\pi$
$773$	−3.86430e12	+	6.69317e12i	−0.389281	+	0.674255i	0.603072	+	0.797687i	$0.293943\pi$
$774$		0			0
$775$	7.22202e12	+	1.25089e13i	0.719119	+	1.24555i
$776$	−5.76321e12	−	2.09764e12i	−0.570541	−	0.207660i
$777$		0			0
$778$	−5.05487e12	−	4.24154e12i	−0.494654	−	0.415064i
$779$	−2.54775e12	+	9.27304e11i	−0.247878	+	0.0902201i
$780$		0			0
$781$	1.63041e12	+	9.24650e12i	0.156807	+	0.889299i
$782$	3.31378e12			0.316879
$783$		0			0
$784$	−1.41195e13			−1.33474
$785$	7.79795e10	+	4.42244e11i	0.00732937	+	0.0415669i
$786$		0			0
$787$	1.19366e13	−	4.34456e12i	1.10916	−	0.403700i	0.278473	−	0.960444i	$-0.410172\pi$
$787$	1.19366e13	−	4.34456e12i	1.10916	−	0.403700i	0.830684	+	0.556744i	$0.187949\pi$
$788$	−7.49710e11	−	6.29082e11i	−0.0692668	−	0.0581218i
$789$		0			0
$790$	3.44948e10	+	1.25551e10i	0.00315088	+	0.00114683i
$791$	1.07310e13	+	1.85866e13i	0.974643	+	1.68813i
$792$		0			0
$793$	−4.35576e12	+	7.54441e12i	−0.391143	+	0.677479i
$794$	−1.21790e13	+	1.02194e13i	−1.08748	+	0.912504i
$795$		0			0
$796$	4.50693e10	−	2.55601e11i	0.00397898	−	0.0225659i
$797$	−3.22546e11	+	1.82925e12i	−0.0283158	+	0.160587i	−0.995687	−	0.0927766i	$-0.970426\pi$
$797$	−3.22546e11	+	1.82925e12i	−0.0283158	+	0.160587i	0.967371	+	0.253364i	$0.0815369\pi$
$798$		0			0
$799$	4.57627e12	−	3.83995e12i	0.397238	−	0.333322i
$800$	−6.72911e11	+	1.16552e12i	−0.0580835	+	0.100604i
$801$		0			0
$802$	−2.41740e12	−	4.18705e12i	−0.206330	−	0.357375i
$803$	8.74924e12	+	3.18446e12i	0.742592	+	0.270281i
$804$		0			0
$805$	3.93688e11	+	3.30344e11i	0.0330424	+	0.0277258i
$806$	2.24829e13	−	8.18312e12i	1.87649	−	0.682985i
$807$		0			0
$808$	2.64506e12	+	1.50009e13i	0.218315	+	1.23813i
$809$	9.54858e12			0.783737			0.391869	−	0.920021i	$-0.371829\pi$
$809$	9.54858e12			0.783737			0.391869	+	0.920021i	$0.371829\pi$
$810$		0			0
$811$	1.48597e13			1.20619			0.603097	−	0.797668i	$-0.293933\pi$
$811$	1.48597e13			1.20619			0.603097	+	0.797668i	$0.293933\pi$
$812$	3.85921e10	+	2.18867e11i	0.00311528	+	0.0176676i
$813$		0			0
$814$	2.02514e13	−	7.37092e12i	1.61676	−	0.588453i
$815$	−2.30461e11	−	1.93379e11i	−0.0182973	−	0.0153533i
$816$		0			0
$817$	−1.28831e13	−	4.68905e12i	−1.01162	−	0.368201i
$818$	5.82070e12	+	1.00817e13i	0.454554	+	0.787310i
$819$		0			0
$820$	5.47823e9	−	9.48858e9i	0.000423134	−	0.000732890i
$821$	−4.65992e12	+	3.91014e12i	−0.357960	+	0.300364i	−0.803977	−	0.594660i	$-0.797286\pi$
$821$	−4.65992e12	+	3.91014e12i	−0.357960	+	0.300364i	0.446017	+	0.895024i	$0.352842\pi$
$822$		0			0
$823$	−3.75246e12	+	2.12813e13i	−0.285113	+	1.61696i	0.419768	+	0.907631i	$0.362111\pi$
$823$	−3.75246e12	+	2.12813e13i	−0.285113	+	1.61696i	−0.704881	+	0.709325i	$0.749000\pi$
$824$	−4.91947e11	+	2.78997e12i	−0.0371746	+	0.210827i
$825$		0			0
$826$	−2.53915e13	+	2.13060e13i	−1.89792	+	1.59254i
$827$	9.85373e11	−	1.70672e12i	0.0732531	−	0.126878i	−0.827072	−	0.562096i	$-0.809995\pi$
$827$	9.85373e11	−	1.70672e12i	0.0732531	−	0.126878i	0.900325	+	0.435218i	$0.143329\pi$
$828$		0			0
$829$	−7.89520e12	−	1.36749e13i	−0.580588	−	1.00561i	−0.995410	−	0.0957049i	$-0.969489\pi$
$829$	−7.89520e12	−	1.36749e13i	−0.580588	−	1.00561i	0.414822	−	0.909903i	$-0.363844\pi$
$830$	1.07683e12	+	3.91932e11i	0.0787579	+	0.0286655i
$831$		0			0
$832$	1.58938e13	+	1.33365e13i	1.14993	+	0.964908i
$833$	−9.78756e12	+	3.56238e12i	−0.704323	+	0.256353i
$834$		0			0
$835$	4.86696e10	+	2.76019e11i	0.00346473	+	0.0196494i
$836$	7.77201e11			0.0550307
$837$		0			0
$838$	−2.16500e13			−1.51656
$839$	−2.54915e12	−	1.44570e13i	−0.177610	−	1.00727i	−0.935088	−	0.354415i	$-0.884680\pi$
$839$	−2.54915e12	−	1.44570e13i	−0.177610	−	1.00727i	0.757479	−	0.652860i	$-0.226431\pi$
$840$		0			0
$841$	1.30989e13	−	4.76762e12i	0.902930	−	0.328640i
$842$	−3.87458e12	−	3.25116e12i	−0.265657	−	0.222912i
$843$		0			0
$844$	−1.38102e12	−	5.02649e11i	−0.0936824	−	0.0340976i
$845$	3.44268e11	+	5.96289e11i	0.0232296	+	0.0402348i
$846$		0			0
$847$	−4.09600e12	+	7.09448e12i	−0.273454	+	0.473636i
$848$	−1.57821e13	+	1.32427e13i	−1.04805	+	0.879419i
$849$		0			0
$850$	1.34862e12	−	7.64843e12i	0.0886147	−	0.502559i
$851$	−2.51102e12	+	1.42407e13i	−0.164122	+	0.930784i
$852$		0			0
$853$	1.27112e12	−	1.06660e12i	0.0822086	−	0.0689812i	−0.600757	−	0.799431i	$-0.705134\pi$
$853$	1.27112e12	−	1.06660e12i	0.0822086	−	0.0689812i	0.682966	+	0.730450i	$0.260690\pi$
$854$	6.43116e12	−	1.11391e13i	0.413741	−	0.716621i
$855$		0			0
$856$	−6.51148e12	−	1.12782e13i	−0.414522	−	0.717973i
$857$	−1.82758e13	−	6.65183e12i	−1.15734	−	0.421238i	−0.309195	−	0.950999i	$-0.600059\pi$
$857$	−1.82758e13	−	6.65183e12i	−1.15734	−	0.421238i	−0.848147	+	0.529761i	$0.822282\pi$
$858$		0			0
$859$	−1.27391e13	−	1.06894e13i	−0.798305	−	0.669858i	0.149481	−	0.988765i	$-0.452240\pi$
$859$	−1.27391e13	−	1.06894e13i	−0.798305	−	0.669858i	−0.947786	+	0.318907i	$0.896684\pi$
$860$	5.20618e10	−	1.89489e10i	0.00324546	−	0.00118125i
$861$		0			0
$862$	−1.38450e12	−	7.85191e12i	−0.0854106	−	0.484387i
$863$	4.88611e12			0.299857			0.149929	−	0.988697i	$-0.452096\pi$
$863$	4.88611e12			0.299857			0.149929	+	0.988697i	$0.452096\pi$
$864$		0			0
$865$	3.12658e10			0.00189888
$866$	−1.70428e12	−	9.66545e12i	−0.102970	−	0.583971i
$867$		0			0
$868$	2.05419e12	−	7.47664e11i	0.122829	−	0.0447062i
$869$	−1.15669e12	−	9.70580e11i	−0.0688064	−	0.0577354i
$870$		0			0
$871$	−3.94067e12	−	1.43429e12i	−0.232000	−	0.0844411i
$872$	7.74840e11	+	1.34206e12i	0.0453825	+	0.0786047i
$873$		0			0
$874$	4.21358e12	−	7.29814e12i	0.244259	−	0.423068i
$875$	1.84720e12	−	1.54999e12i	0.106531	−	0.0893905i
$876$		0			0
$877$	5.50299e12	−	3.12090e13i	0.314123	−	1.78148i	−0.262969	−	0.964804i	$-0.584702\pi$
$877$	5.50299e12	−	3.12090e13i	0.314123	−	1.78148i	0.577093	−	0.816679i	$-0.304187\pi$
$878$	2.34879e12	−	1.33207e13i	0.133389	−	0.756485i
$879$		0			0
$880$	6.64767e11	−	5.57806e11i	0.0373678	−	0.0313553i
$881$	−4.79066e12	+	8.29767e12i	−0.267919	+	0.464050i	−0.968324	−	0.249696i	$-0.919669\pi$
$881$	−4.79066e12	+	8.29767e12i	−0.267919	+	0.464050i	0.700405	+	0.713746i	$0.253003\pi$
$882$		0			0
$883$	4.23988e12	+	7.34369e12i	0.234709	+	0.406529i	0.959188	−	0.282768i	$-0.0912528\pi$
$883$	4.23988e12	+	7.34369e12i	0.234709	+	0.406529i	−0.724479	+	0.689297i	$0.757919\pi$
$884$	7.48080e11	+	2.72279e11i	0.0412015	+	0.0149961i
$885$		0			0
$886$	1.58763e13	+	1.33218e13i	0.865562	+	0.726293i
$887$	8.43638e12	−	3.07059e12i	0.457615	−	0.166558i	−0.102919	−	0.994690i	$-0.532818\pi$
$887$	8.43638e12	−	3.07059e12i	0.457615	−	0.166558i	0.560534	+	0.828132i	$0.310596\pi$
$888$		0			0
$889$	−4.50673e12	−	2.55589e13i	−0.241993	−	1.37241i
$890$	1.04386e11			0.00557685
$891$		0			0
$892$	8.41245e11			0.0444919
$893$	−2.63806e12	−	1.49612e13i	−0.138820	−	0.787290i
$894$		0			0
$895$	−1.45784e11	+	5.30609e10i	−0.00759460	+	0.00276421i
$896$	−2.07892e13	−	1.74442e13i	−1.07759	−	0.904203i
$897$		0			0
$898$	1.07159e13	+	3.90025e12i	0.549900	+	0.200147i
$899$	2.79126e12	+	4.83460e12i	0.142522	+	0.246855i
$900$		0			0
$901$	−7.59886e12	+	1.31616e13i	−0.384138	+	0.665346i
$902$	5.57902e12	−	4.68135e12i	0.280626	−	0.235473i
$903$		0			0
$904$	−4.48472e12	+	2.54341e13i	−0.223345	+	1.26665i
$905$	−1.95673e11	+	1.10972e12i	−0.00969644	+	0.0549912i
$906$		0			0
$907$	1.21803e13	−	1.02205e13i	0.597621	−	0.501463i	−0.293059	−	0.956094i	$-0.594673\pi$
$907$	1.21803e13	−	1.02205e13i	0.597621	−	0.501463i	0.890680	+	0.454631i	$0.150229\pi$
$908$	8.68329e11	−	1.50399e12i	0.0423934	−	0.0734275i
$909$		0			0
$910$	−9.97572e11	−	1.72784e12i	−0.0482234	−	0.0835254i
$911$	−6.41396e12	−	2.33449e12i	−0.308527	−	0.112295i	0.183116	−	0.983091i	$-0.441381\pi$
$911$	−6.41396e12	−	2.33449e12i	−0.308527	−	0.112295i	−0.491644	+	0.870797i	$0.663604\pi$
$912$		0			0
$913$	−3.61085e13	−	3.02986e13i	−1.71985	−	1.44313i
$914$	−1.80904e13	+	6.58438e12i	−0.857415	+	0.312074i
$915$		0			0
$916$	2.74726e11	+	1.55805e12i	0.0128935	+	0.0731225i
$917$	−4.79160e12			−0.223779
$918$		0			0
$919$	8.89475e11			0.0411352			0.0205676	−	0.999788i	$-0.493453\pi$
$919$	8.89475e11			0.0411352			0.0205676	+	0.999788i	$0.493453\pi$
$920$	1.07390e11	+	6.09039e11i	0.00494218	+	0.0280285i
$921$		0			0
$922$	−1.60171e13	+	5.82975e12i	−0.729953	+	0.265681i
$923$	1.87355e13	+	1.57210e13i	0.849685	+	0.712971i
$924$		0			0
$925$	3.18466e13	+	1.15912e13i	1.43029	+	0.520584i
$926$	6.04475e11	+	1.04698e12i	0.0270165	+	0.0467939i
$927$		0			0
$928$	−2.60075e11	+	4.50463e11i	−0.0115115	+	0.0199385i
$929$	2.16115e13	−	1.81342e13i	0.951950	−	0.798781i	−0.0276752	−	0.999617i	$-0.508810\pi$
$929$	2.16115e13	−	1.81342e13i	0.951950	−	0.798781i	0.979625	+	0.200836i	$0.0643660\pi$
$930$		0			0
$931$	−4.59956e12	+	2.60854e13i	−0.200652	+	1.13795i
$932$	1.26956e11	−	7.20002e11i	0.00551164	−	0.0312581i
$933$		0			0
$934$	−3.08128e12	+	2.58550e12i	−0.132486	+	0.111169i
$935$	3.20077e11	−	5.54389e11i	0.0136963	−	0.0237226i
$936$		0			0
$937$	−4.44155e12	−	7.69300e12i	−0.188238	−	0.326037i	0.756425	−	0.654080i	$-0.226944\pi$
$937$	−4.44155e12	−	7.69300e12i	−0.188238	−	0.326037i	−0.944663	+	0.328043i	$0.893611\pi$
$938$	5.81828e12	+	2.11768e12i	0.245404	+	0.0893198i
$939$		0			0
$940$	4.70293e10	+	3.94623e10i	0.00196469	+	0.00164857i
$941$	3.15984e13	−	1.15009e13i	1.31375	−	0.478165i	0.412297	−	0.911049i	$-0.364727\pi$
$941$	3.15984e13	−	1.15009e13i	1.31375	−	0.478165i	0.901449	+	0.432885i	$0.142504\pi$
$942$		0			0
$943$	8.48564e11	+	4.81244e12i	0.0349447	+	0.198181i
$944$	−3.75544e13			−1.53917
$945$		0			0
$946$	3.68270e13			1.49505
$947$	1.14447e12	+	6.49059e12i	0.0462411	+	0.262246i	0.999160	−	0.0409790i	$-0.0130477\pi$
$947$	1.14447e12	+	6.49059e12i	0.0462411	+	0.262246i	−0.952919	+	0.303225i	$0.901937\pi$
$948$		0			0
$949$	2.27906e13	−	8.29511e12i	0.912133	−	0.331989i
$950$	−1.51298e13	−	1.26954e13i	−0.602664	−	0.505696i
$951$		0			0
$952$	−2.00579e13	−	7.30047e12i	−0.791442	−	0.288061i
$953$	−2.12833e13	−	3.68638e13i	−0.835837	−	1.44771i	−0.893347	−	0.449367i	$-0.851650\pi$
$953$	−2.12833e13	−	3.68638e13i	−0.835837	−	1.44771i	0.0575108	−	0.998345i	$-0.481684\pi$
$954$		0			0
$955$	1.10009e12	−	1.90541e12i	0.0427970	−	0.0741266i
$956$	−2.12039e12	+	1.77922e12i	−0.0821023	+	0.0688920i
$957$		0			0
$958$	2.65046e12	−	1.50315e13i	0.101666	−	0.576577i
$959$	1.38897e12	−	7.87724e12i	0.0530285	−	0.300739i
$960$		0			0
$961$	2.18100e13	−	1.83007e13i	0.824897	−	0.692171i
$962$	2.80689e13	−	4.86168e13i	1.05667	−	1.83020i
$963$		0			0
$964$	−1.00489e12	−	1.74052e12i	−0.0374775	−	0.0649129i
$965$	4.50985e11	+	1.64145e11i	0.0167413	+	0.00609333i
$966$		0			0
$967$	1.42651e13	+	1.19698e13i	0.524633	+	0.440219i	0.866243	−	0.499622i	$-0.166528\pi$
$967$	1.42651e13	+	1.19698e13i	0.524633	+	0.440219i	−0.341610	+	0.939842i	$0.610972\pi$
$968$	−9.26341e12	+	3.37161e12i	−0.339103	+	0.123423i
$969$		0			0
$970$	1.22841e11	+	6.96668e11i	0.00445525	+	0.0252670i
$971$	−3.48883e13			−1.25949			−0.629743	−	0.776803i	$-0.716840\pi$
$971$	−3.48883e13			−1.25949			−0.629743	+	0.776803i	$0.716840\pi$
$972$		0			0
$973$	2.26700e13			0.810855
$974$	1.87761e12	+	1.06484e13i	0.0668481	+	0.379115i
$975$		0			0
$976$	1.36941e13	−	4.98423e12i	0.483068	−	0.175822i
$977$	1.51067e13	+	1.26760e13i	0.530450	+	0.445100i	0.868257	−	0.496115i	$-0.165241\pi$
$977$	1.51067e13	+	1.26760e13i	0.530450	+	0.445100i	−0.337807	+	0.941215i	$0.609685\pi$
$978$		0			0
$979$	−4.03484e12	−	1.46856e12i	−0.140380	−	0.0510940i
$980$	−5.35200e10	−	9.26994e10i	−0.00185353	−	0.00321040i
$981$		0			0
$982$	2.41810e13	−	4.18827e13i	0.829798	−	1.43725i
$983$	3.74861e12	−	3.14546e12i	0.128050	−	0.107447i	−0.576514	−	0.817088i	$-0.695587\pi$
$983$	3.74861e12	−	3.14546e12i	0.128050	−	0.107447i	0.704564	+	0.709641i	$0.251143\pi$
$984$		0			0
$985$	−3.55973e11	+	2.01882e12i	−0.0120491	+	0.0683338i
$986$	5.21233e11	−	2.95606e12i	0.0175625	−	0.0996018i
$987$		0			0
$988$	1.55086e12	−	1.30133e12i	0.0517806	−	0.0434491i
$989$	−1.23551e13	+	2.13997e13i	−0.410642	+	0.711253i
$990$		0			0
$991$	1.17997e13	+	2.04377e13i	0.388634	+	0.673134i	0.992266	−	0.124129i	$-0.0396138\pi$
$991$	1.17997e13	+	2.04377e13i	0.388634	+	0.673134i	−0.603632	+	0.797263i	$0.706280\pi$
$992$	4.80773e12	+	1.74987e12i	0.157630	+	0.0573725i
$993$		0			0
$994$	−2.76624e13	−	2.32115e13i	−0.898777	−	0.754163i
$995$	−5.10863e11	+	1.85939e11i	−0.0165234	+	0.00601404i
$996$		0			0
$997$	4.76886e12	+	2.70456e13i	0.152857	+	0.866898i	0.960718	+	0.277525i	$0.0895140\pi$
$997$	4.76886e12	+	2.70456e13i	0.152857	+	0.866898i	−0.807861	+	0.589373i	$0.799375\pi$
$998$	−4.38368e12			−0.139879
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.7		156
3.2	odd	2		27.10.e.a.13.20	✓	156
27.2	odd	18		27.10.e.a.25.20	yes	156
27.25	even	9	inner	81.10.e.a.73.7		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.20	✓	156	3.2	odd	2
27.10.e.a.25.20	yes	156	27.2	odd	18
81.10.e.a.10.7		156	1.1	even	1	trivial
81.10.e.a.73.7		156	27.25	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.81300 - 21.6246i) q^{2} +(28.0377 - 10.2049i) q^{4} +(-47.8760 - 40.1728i) q^{5} +(-9290.87 - 3381.60i) q^{7} +(-5948.89 - 10303.8i) q^{8} +(-686.169 + 1188.48i) q^{10} +(43242.5 - 36284.8i) q^{11} +(25533.6 - 144809. i) q^{13} +(-37699.7 + 213805. i) q^{14} +(-188429. + 158111. i) q^{16} +(-90726.3 + 157143. i) q^{17} +(230723. + 399623. i) q^{19} +(-1752.29 - 637.782i) q^{20} +(-949528. - 796749. i) q^{22} +(781538. - 284456. i) q^{23} +(-338478. - 1.91961e6i) q^{25} -3.22879e6 q^{26} -295003. q^{28} +(-130819. - 741913. i) q^{29} +(-6.96328e6 + 2.53442e6i) q^{31} +(-528909. - 443807. i) q^{32} +(3.74409e6 + 1.36274e6i) q^{34} +(308962. + 535137. i) q^{35} +(-8.69333e6 + 1.50573e7i) q^{37} +(7.76196e6 - 6.51305e6i) q^{38} +(-129122. + 732287. i) q^{40} +(-1.02028e6 + 5.78631e6i) q^{41} +(-2.27597e7 + 1.90977e7i) q^{43} +(842138. - 1.45863e6i) q^{44} +(-9.13127e6 - 1.58158e7i) q^{46} +(-3.09371e7 - 1.12602e7i) q^{47} +(4.39723e7 + 3.68972e7i) q^{49} +(-4.02201e7 + 1.46389e7i) q^{50} +(-761850. - 4.32066e6i) q^{52} +8.37558e7 q^{53} -3.52794e6 q^{55} +(2.04271e7 + 1.15848e8i) q^{56} +(-1.55448e7 + 5.65784e6i) q^{58} +(1.16955e8 + 9.81373e7i) q^{59} +(-5.56721e7 - 2.02630e7i) q^{61} +(8.13569e7 + 1.40914e8i) q^{62} +(-7.05506e7 + 1.22197e8i) q^{64} +(-7.03981e6 + 5.90710e6i) q^{65} +(4.95235e6 - 2.80862e7i) q^{67} +(-940134. + 5.33177e6i) q^{68} +(1.03941e7 - 8.72165e6i) q^{70} +(-8.31647e7 + 1.44046e8i) q^{71} +(8.24703e7 + 1.42843e8i) q^{73} +(3.58756e8 + 1.30576e8i) q^{74} +(1.05470e7 + 8.85002e6i) q^{76} +(-5.24461e8 + 1.90888e8i) q^{77} +(-4.64491e6 - 2.63426e7i) q^{79} +1.53730e7 q^{80} +1.29017e8 q^{82} +(-1.45000e8 - 8.22337e8i) q^{83} +(1.06565e7 - 3.87864e6i) q^{85} +(4.99762e8 + 4.19350e8i) q^{86} +(-6.31115e8 - 2.29707e8i) q^{88} +(-3.80324e7 - 6.58740e7i) q^{89} +(-7.26914e8 + 1.25905e9i) q^{91} +(1.90097e7 - 1.59510e7i) q^{92} +(-1.25534e8 + 7.11939e8i) q^{94} +(5.00789e6 - 2.84011e7i) q^{95} +(3.94882e8 - 3.31345e8i) q^{97} +(6.30220e8 - 1.09157e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

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