LMFDB - Embedded newform 81.10.e.a.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,Mod(10,81)]

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([8]))

N = Newforms(chi, 10, names="a")

//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: f = N[0] # Warning: the index may be different

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			19.7
Character	$\chi$	$=$	81.19
Dual form			81.10.e.a.64.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.7357 + 8.63908i) q^{2} +(96.5341 - 81.0017i) q^{4} +(237.448 + 1346.63i) q^{5} +(-5786.38 - 4855.35i) q^{7} +(4874.78 - 8443.36i) q^{8} +O(q^{10})$	\(q+(-23.7357 + 8.63908i) q^{2} +(96.5341 - 81.0017i) q^{4} +(237.448 + 1346.63i) q^{5} +(-5786.38 - 4855.35i) q^{7} +(4874.78 - 8443.36i) q^{8} +(-17269.7 - 29911.9i) q^{10} +(-7489.73 + 42476.4i) q^{11} +(84515.8 + 30761.2i) q^{13} +(179290. + 65256.1i) q^{14} +(-53967.1 + 306063. i) q^{16} +(-97939.0 - 169635. i) q^{17} +(254414. - 440658. i) q^{19} +(132001. + 110762. i) q^{20} +(-189183. - 1.07291e6i) q^{22} +(82173.4 - 68951.6i) q^{23} +(78298.2 - 28498.2i) q^{25} -2.27179e6 q^{26} -951876. q^{28} +(3.92260e6 - 1.42771e6i) q^{29} +(6.00051e6 - 5.03503e6i) q^{31} +(-496342. - 2.81490e6i) q^{32} +(3.79014e6 + 3.18031e6i) q^{34} +(5.16441e6 - 8.94503e6i) q^{35} +(5.90946e6 + 1.02355e7i) q^{37} +(-2.23181e6 + 1.26572e7i) q^{38} +(1.25276e7 + 4.55968e6i) q^{40} +(-2.01033e7 - 7.31699e6i) q^{41} +(-5.67694e6 + 3.21955e7i) q^{43} +(2.71765e6 + 4.70710e6i) q^{44} +(-1.35476e6 + 2.34652e6i) q^{46} +(-2.96618e7 - 2.48892e7i) q^{47} +(2.90046e6 + 1.64493e7i) q^{49} +(-1.61226e6 + 1.35285e6i) q^{50} +(1.06504e7 - 3.87642e6i) q^{52} -1.00849e7 q^{53} -5.89785e7 q^{55} +(-6.92028e7 + 2.51878e7i) q^{56} +(-8.07715e7 + 6.77753e7i) q^{58} +(2.96301e7 + 1.68041e8i) q^{59} +(-2.42940e7 - 2.03851e7i) q^{61} +(-9.89282e7 + 1.71349e8i) q^{62} +(-4.34616e7 - 7.52777e7i) q^{64} +(-2.13560e7 + 1.21116e8i) q^{65} +(2.06054e8 + 7.49977e7i) q^{67} +(-2.31952e7 - 8.44237e6i) q^{68} +(-4.53041e7 + 2.56932e8i) q^{70} +(1.20690e8 + 2.09042e8i) q^{71} +(-1.68439e8 + 2.91745e8i) q^{73} +(-2.28690e8 - 1.91894e8i) q^{74} +(-1.11344e7 - 6.31466e7i) q^{76} +(2.49576e8 - 2.09419e8i) q^{77} +(-4.25803e8 + 1.54980e8i) q^{79} -4.24969e8 q^{80} +5.40377e8 q^{82} +(5.94638e7 - 2.16430e7i) q^{83} +(2.05181e8 - 1.72167e8i) q^{85} +(-1.43394e8 - 8.13226e8i) q^{86} +(3.22133e8 + 2.70301e8i) q^{88} +(-4.61593e8 + 7.99503e8i) q^{89} +(-3.39684e8 - 5.88350e8i) q^{91} +(2.34733e6 - 1.33124e7i) q^{92} +(9.19062e8 + 3.34511e8i) q^{94} +(6.53815e8 + 2.37969e8i) q^{95} +(6.12907e7 - 3.47597e8i) q^{97} +(-2.10952e8 - 3.65379e8i) 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}+O(q^{10}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23} + 2192178 q^{25} + 33129678 q^{26} - 12 q^{28} - 19657236 q^{29} - 4633692 q^{31} + 37550952 q^{32} + 14341770 q^{34} - 34449663 q^{35} - 3 q^{37} + 92022060 q^{38} + 6645801 q^{40} + 33127221 q^{41} + 2356203 q^{43} - 1001541 q^{44} - 3 q^{46} + 33488952 q^{47} - 93214644 q^{49} + 72027753 q^{50} + 160531713 q^{52} - 4841352 q^{53} - 12 q^{55} + 91770981 q^{56} - 320682489 q^{58} - 538090854 q^{59} + 36683436 q^{61} + 55862958 q^{62} - 956301315 q^{64} + 852347310 q^{65} - 109026897 q^{67} + 508886217 q^{68} - 815297649 q^{70} - 940878639 q^{71} - 221849931 q^{73} - 838884579 q^{74} + 908401146 q^{76} + 967811358 q^{77} - 1228059150 q^{79} + 2497115154 q^{80} - 12 q^{82} + 297703284 q^{83} + 1535949369 q^{85} - 2930201574 q^{86} + 2837227002 q^{88} - 1774997208 q^{89} + 551343507 q^{91} + 6896645517 q^{92} + 414852915 q^{94} + 9000269169 q^{95} + 3371772333 q^{97} - 6901039926 q^{98}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−23.7357	+	8.63908i	−1.04898	+	0.381797i	−0.808277	−	0.588802i	$-0.799600\pi$
$2$	−23.7357	+	8.63908i	−1.04898	+	0.381797i	−0.240702	+	0.970599i	$0.577378\pi$
$3$		0			0
$3$		0			0
$4$	96.5341	−	81.0017i	0.188543	−	0.158207i
$5$	237.448	+	1346.63i	0.169904	+	0.963572i	0.943863	+	0.330337i	$0.107162\pi$
$5$	237.448	+	1346.63i	0.169904	+	0.963572i	−0.773959	+	0.633235i	$0.781727\pi$
$6$		0			0
$7$	−5786.38	−	4855.35i	−0.910890	−	0.764328i	0.0613978	−	0.998113i	$-0.480444\pi$
$7$	−5786.38	−	4855.35i	−0.910890	−	0.764328i	−0.972288	+	0.233786i	$0.924889\pi$
$8$	4874.78	−	8443.36i	0.420775	−	0.728804i
$9$		0			0
$10$	−17269.7	−	29911.9i	−0.546114	−	0.945898i
$11$	−7489.73	+	42476.4i	−0.154241	+	0.874743i	0.805236	+	0.592955i	$0.202039\pi$
$11$	−7489.73	+	42476.4i	−0.154241	+	0.874743i	−0.959477	+	0.281788i	$0.909072\pi$
$12$		0			0
$13$	84515.8	+	30761.2i	0.820716	+	0.298716i	0.718043	−	0.695999i	$-0.245038\pi$
$13$	84515.8	+	30761.2i	0.820716	+	0.298716i	0.102673	+	0.994715i	$0.467260\pi$
$14$	179290.	+	65256.1i	1.24732	+	0.453988i
$15$		0			0
$16$	−53967.1	+	306063.i	−0.205868	+	1.16754i
$17$	−97939.0	−	169635.i	−0.284404	−	0.492602i	0.688061	−	0.725653i	$-0.258462\pi$
$17$	−97939.0	−	169635.i	−0.284404	−	0.492602i	−0.972464	+	0.233051i	$0.925129\pi$
$18$		0			0
$19$	254414.	−	440658.i	0.447868	−	0.775730i	−0.550379	−	0.834915i	$-0.685517\pi$
$19$	254414.	−	440658.i	0.447868	−	0.775730i	0.998247	+	0.0591845i	$0.0188500\pi$
$20$	132001.	+	110762.i	0.184478	+	0.154795i
$21$		0			0
$22$	−189183.	−	1.07291e6i	−0.172179	−	0.976475i
$23$	82173.4	−	68951.6i	0.0612288	−	0.0513771i	−0.611660	−	0.791121i	$-0.709498\pi$
$23$	82173.4	−	68951.6i	0.0612288	−	0.0513771i	0.672888	+	0.739744i	$0.265053\pi$
$24$		0			0
$25$	78298.2	−	28498.2i	0.0400887	−	0.0145911i
$26$	−2.27179e6			−0.974963
$27$		0			0
$28$	−951876.			−0.292664
$29$	3.92260e6	−	1.42771e6i	1.02987	−	0.374843i	0.228840	−	0.973464i	$-0.426507\pi$
$29$	3.92260e6	−	1.42771e6i	1.02987	−	0.374843i	0.801032	+	0.598622i	$0.204285\pi$
$30$		0			0
$31$	6.00051e6	−	5.03503e6i	1.16697	−	0.979206i	0.166995	−	0.985958i	$-0.446594\pi$
$31$	6.00051e6	−	5.03503e6i	1.16697	−	0.979206i	0.999977	+	0.00675186i	$0.00214920\pi$
$32$	−496342.	−	2.81490e6i	−0.0836771	−	0.474556i
$33$		0			0
$34$	3.79014e6	+	3.18031e6i	0.486408	+	0.408145i
$35$	5.16441e6	−	8.94503e6i	0.581721	−	1.00757i
$36$		0			0
$37$	5.90946e6	+	1.02355e7i	0.518371	+	0.897844i	0.999772	+	0.0213441i	$0.00679454\pi$
$37$	5.90946e6	+	1.02355e7i	0.518371	+	0.897844i	−0.481402	+	0.876500i	$0.659872\pi$
$38$	−2.23181e6	+	1.26572e7i	−0.173633	+	0.984720i
$39$		0			0
$40$	1.25276e7	+	4.55968e6i	0.773746	+	0.281621i
$41$	−2.01033e7	−	7.31699e6i	−1.11106	−	0.404394i	−0.279680	−	0.960093i	$-0.590229\pi$
$41$	−2.01033e7	−	7.31699e6i	−1.11106	−	0.404394i	−0.831384	+	0.555699i	$0.812451\pi$
$42$		0			0
$43$	−5.67694e6	+	3.21955e7i	−0.253225	+	1.43611i	0.547364	+	0.836895i	$0.315631\pi$
$43$	−5.67694e6	+	3.21955e7i	−0.253225	+	1.43611i	−0.800589	+	0.599214i	$0.795480\pi$
$44$	2.71765e6	+	4.70710e6i	0.109309	+	0.189329i
$45$		0			0
$46$	−1.35476e6	+	2.34652e6i	−0.0446121	+	0.0772704i
$47$	−2.96618e7	−	2.48892e7i	−0.886659	−	0.743995i	0.0808780	−	0.996724i	$-0.474228\pi$
$47$	−2.96618e7	−	2.48892e7i	−0.886659	−	0.743995i	−0.967537	+	0.252729i	$0.918672\pi$
$48$		0			0
$49$	2.90046e6	+	1.64493e7i	0.0718761	+	0.407630i
$50$	−1.61226e6	+	1.35285e6i	−0.0364813	+	0.0306115i
$51$		0			0
$52$	1.06504e7	−	3.87642e6i	0.201999	−	0.0735217i
$53$	−1.00849e7			−0.175561			−0.0877806	−	0.996140i	$-0.527977\pi$
$53$	−1.00849e7			−0.175561			−0.0877806	+	0.996140i	$0.527977\pi$
$54$		0			0
$55$	−5.89785e7			−0.869084
$56$	−6.92028e7	+	2.51878e7i	−0.940325	+	0.342250i
$57$		0			0
$58$	−8.07715e7	+	6.77753e7i	−0.937200	+	0.786404i
$59$	2.96301e7	+	1.68041e8i	0.318346	+	1.80543i	0.552814	+	0.833305i	$0.313554\pi$
$59$	2.96301e7	+	1.68041e8i	0.318346	+	1.80543i	−0.234468	+	0.972124i	$0.575335\pi$
$60$		0			0
$61$	−2.42940e7	−	2.03851e7i	−0.224654	−	0.188507i	0.523513	−	0.852018i	$-0.324621\pi$
$61$	−2.42940e7	−	2.03851e7i	−0.224654	−	0.188507i	−0.748167	+	0.663511i	$0.769066\pi$
$62$	−9.89282e7	+	1.71349e8i	−0.850271	+	1.47271i
$63$		0			0
$64$	−4.34616e7	−	7.52777e7i	−0.323814	−	0.560863i
$65$	−2.13560e7	+	1.21116e8i	−0.148392	+	0.841572i
$66$		0			0
$67$	2.06054e8	+	7.49977e7i	1.24924	+	0.454685i	0.880144	−	0.474707i	$-0.157446\pi$
$67$	2.06054e8	+	7.49977e7i	1.24924	+	0.454685i	0.369094	+	0.929392i	$0.379668\pi$
$68$	−2.31952e7	−	8.44237e6i	−0.131555	−	0.0478822i
$69$		0			0
$70$	−4.53041e7	+	2.56932e8i	−0.225526	+	1.27902i
$71$	1.20690e8	+	2.09042e8i	0.563650	+	0.976271i	0.997174	+	0.0751286i	$0.0239367\pi$
$71$	1.20690e8	+	2.09042e8i	0.563650	+	0.976271i	−0.433524	+	0.901142i	$0.642730\pi$
$72$		0			0
$73$	−1.68439e8	+	2.91745e8i	−0.694209	+	1.20241i	0.276238	+	0.961089i	$0.410912\pi$
$73$	−1.68439e8	+	2.91745e8i	−0.694209	+	1.20241i	−0.970447	+	0.241316i	$0.922421\pi$
$74$	−2.28690e8	−	1.91894e8i	−0.886554	−	0.743907i
$75$		0			0
$76$	−1.11344e7	−	6.31466e7i	−0.0382831	−	0.217114i
$77$	2.49576e8	−	2.09419e8i	0.809087	−	0.678904i
$78$		0			0
$79$	−4.25803e8	+	1.54980e8i	−1.22995	+	0.447665i	−0.873580	−	0.486681i	$-0.838207\pi$
$79$	−4.25803e8	+	1.54980e8i	−1.22995	+	0.447665i	−0.356368	+	0.934346i	$0.615985\pi$
$80$	−4.24969e8			−1.15998
$81$		0			0
$82$	5.40377e8			1.31988
$83$	5.94638e7	−	2.16430e7i	0.137531	−	0.0500572i	−0.272338	−	0.962202i	$-0.587797\pi$
$83$	5.94638e7	−	2.16430e7i	0.137531	−	0.0500572i	0.409869	+	0.912145i	$0.365575\pi$
$84$		0			0
$85$	2.05181e8	−	1.72167e8i	0.426336	−	0.357739i
$86$	−1.43394e8	−	8.13226e8i	−0.282675	−	1.60313i
$87$		0			0
$88$	3.22133e8	+	2.70301e8i	0.572615	+	0.480481i
$89$	−4.61593e8	+	7.99503e8i	−0.779838	+	1.35072i	0.152197	+	0.988350i	$0.451365\pi$
$89$	−4.61593e8	+	7.99503e8i	−0.779838	+	1.35072i	−0.932035	+	0.362369i	$0.881968\pi$
$90$		0			0
$91$	−3.39684e8	−	5.88350e8i	−0.519265	−	0.899394i
$92$	2.34733e6	−	1.33124e7i	0.00341609	−	0.0193736i
$93$		0			0
$94$	9.19062e8	+	3.34511e8i	1.21414	+	0.441912i
$95$	6.53815e8	+	2.37969e8i	0.823567	+	0.299754i
$96$		0			0
$97$	6.12907e7	−	3.47597e8i	0.0702946	−	0.398661i	−0.929277	−	0.369384i	$-0.879569\pi$
$97$	6.12907e7	−	3.47597e8i	0.0702946	−	0.398661i	0.999571	−	0.0292763i	$-0.00932027\pi$
$98$	−2.10952e8	−	3.65379e8i	−0.231028	−	0.400153i
$99$		0			0
$100$	5.25004e6	−	9.09334e6i	0.00525004	−	0.00909334i
$101$	−1.04520e9	−	8.77030e8i	−0.999435	−	0.838626i	−0.0125291	−	0.999922i	$-0.503988\pi$
$101$	−1.04520e9	−	8.77030e8i	−0.999435	−	0.838626i	−0.986906	+	0.161296i	$0.948433\pi$
$102$		0			0
$103$	1.03146e8	+	5.84970e8i	0.0902994	+	0.512113i	0.996087	+	0.0883808i	$0.0281692\pi$
$103$	1.03146e8	+	5.84970e8i	0.0902994	+	0.512113i	−0.905787	+	0.423733i	$0.860720\pi$
$104$	6.71724e8	−	5.63643e8i	0.563042	−	0.472448i
$105$		0			0
$106$	2.39371e8	−	8.71240e7i	0.184160	−	0.0670288i
$107$	1.99313e9			1.46997			0.734987	−	0.678081i	$-0.237188\pi$
$107$	1.99313e9			1.46997			0.734987	+	0.678081i	$0.237188\pi$
$108$		0			0
$109$	−1.64982e9			−1.11948			−0.559741	−	0.828668i	$-0.689099\pi$
$109$	−1.64982e9			−1.11948			−0.559741	+	0.828668i	$0.689099\pi$
$110$	1.39990e9	−	5.09520e8i	0.911651	−	0.331814i
$111$		0			0
$112$	1.79832e9	−	1.50897e9i	1.07990	−	0.906147i
$113$	−2.13411e8	−	1.21031e9i	−0.123130	−	0.698303i	−0.982401	−	0.186783i	$-0.940194\pi$
$113$	−2.13411e8	−	1.21031e9i	−0.123130	−	0.698303i	0.859271	−	0.511520i	$-0.170917\pi$
$114$		0			0
$115$	1.12364e8	+	9.42850e7i	0.0599085	+	0.0502692i
$116$	2.63018e8	−	4.55560e8i	0.134873	−	0.233606i
$117$		0			0
$118$	−2.15501e9	−	3.73258e9i	−1.02325	−	1.77231i
$119$	−2.56927e8	+	1.45710e9i	−0.117449	+	0.666084i
$120$		0			0
$121$	4.67600e8	+	1.70192e8i	0.198308	+	0.0721782i
$122$	7.52742e8	+	2.73976e8i	0.307629	+	0.111968i
$123$		0			0
$124$	1.71408e8	−	9.72103e8i	0.0651079	−	0.369245i
$125$	1.39233e9	+	2.41158e9i	0.510089	+	0.883500i
$126$		0			0
$127$	−9.02261e8	+	1.56276e9i	−0.307762	+	0.533060i	−0.977873	−	0.209202i	$-0.932913\pi$
$127$	−9.02261e8	+	1.56276e9i	−0.307762	+	0.533060i	0.670110	+	0.742262i	$0.266247\pi$
$128$	2.80300e9	+	2.35199e9i	0.922949	+	0.774446i
$129$		0			0
$130$	−5.39431e8	−	3.05927e9i	−0.165650	−	0.939447i
$131$	5.27743e8	−	4.42829e8i	0.156567	−	0.131376i	−0.561139	−	0.827722i	$-0.689637\pi$
$131$	5.27743e8	−	4.42829e8i	0.156567	−	0.131376i	0.717706	+	0.696346i	$0.245192\pi$
$132$		0			0
$133$	−3.61169e9	+	1.31455e9i	−1.00087	+	0.364287i
$134$	−5.53875e9			−1.48402
$135$		0			0
$136$	−1.90972e9			−0.478680
$137$	−4.06478e8	+	1.47946e8i	−0.0985813	+	0.0358807i	−0.390840	−	0.920459i	$-0.627815\pi$
$137$	−4.06478e8	+	1.47946e8i	−0.0985813	+	0.0358807i	0.292259	+	0.956339i	$0.405593\pi$
$138$		0			0
$139$	2.50343e9	−	2.10063e9i	0.568812	−	0.477290i	−0.312439	−	0.949938i	$-0.601146\pi$
$139$	2.50343e9	−	2.10063e9i	0.568812	−	0.477290i	0.881251	+	0.472648i	$0.156702\pi$
$140$	−2.26021e8	−	1.28183e9i	−0.0497247	−	0.282003i
$141$		0			0
$142$	−4.67059e9	−	3.91909e9i	−0.963995	−	0.808887i
$143$	−1.93963e9	+	3.35953e9i	−0.387888	+	0.671841i
$144$		0			0
$145$	2.85401e9	+	4.94330e9i	0.536167	+	0.928668i
$146$	1.47761e9	−	8.37993e9i	0.269136	−	1.52634i
$147$		0			0
$148$	1.39956e9	+	5.09397e8i	0.239780	+	0.0872728i
$149$	−1.43528e9	−	5.22400e8i	−0.238561	−	0.0868291i	0.219973	−	0.975506i	$-0.429403\pi$
$149$	−1.43528e9	−	5.22400e8i	−0.238561	−	0.0868291i	−0.458534	+	0.888677i	$0.651625\pi$
$150$		0			0
$151$	1.13085e9	−	6.41335e9i	0.177014	−	1.00390i	−0.758780	−	0.651347i	$-0.774204\pi$
$151$	1.13085e9	−	6.41335e9i	0.177014	−	1.00390i	0.935794	−	0.352549i	$-0.114685\pi$
$152$	−2.48043e9	−	4.29622e9i	−0.376903	−	0.652816i
$153$		0			0
$154$	−4.11467e9	+	7.12682e9i	−0.589511	+	1.02106i
$155$	8.20514e9	+	6.88493e9i	1.14181	+	0.958091i
$156$		0			0
$157$	2.05841e9	+	1.16739e10i	0.270386	+	1.53344i	0.753246	+	0.657739i	$0.228487\pi$
$157$	2.05841e9	+	1.16739e10i	0.270386	+	1.53344i	−0.482860	+	0.875698i	$0.660402\pi$
$158$	8.76784e9	−	7.35709e9i	1.11927	−	0.939181i
$159$		0			0
$160$	3.67278e9	−	1.33678e9i	0.443052	−	0.161258i
$161$	−8.10271e8			−0.0950417
$162$		0			0
$163$	1.30621e10			1.44934			0.724668	−	0.689098i	$-0.241993\pi$
$163$	1.30621e10			1.44934			0.724668	+	0.689098i	$0.241993\pi$
$164$	−2.53334e9	+	9.22060e8i	−0.273461	+	0.0995318i
$165$		0			0
$166$	−1.22444e9	+	1.02742e9i	−0.125156	+	0.105018i
$167$	−1.52734e9	−	8.66195e9i	−0.151953	−	0.861771i	−0.961518	−	0.274740i	$-0.911408\pi$
$167$	−1.52734e9	−	8.66195e9i	−0.151953	−	0.861771i	0.809565	−	0.587030i	$-0.199703\pi$
$168$		0			0
$169$	−1.92685e9	−	1.61682e9i	−0.181701	−	0.152465i
$170$	−3.38275e9	+	5.85909e9i	−0.310634	+	0.538034i
$171$		0			0
$172$	2.05988e9	+	3.56781e9i	0.179458	+	0.310830i
$173$	−2.37124e9	+	1.34480e10i	−0.201265	+	1.14143i	0.701946	+	0.712230i	$0.252315\pi$
$173$	−2.37124e9	+	1.34480e10i	−0.201265	+	1.14143i	−0.903210	+	0.429198i	$0.858796\pi$
$174$		0			0
$175$	−5.91432e8	−	2.15264e8i	−0.0476687	−	0.0173500i
$176$	−1.25962e10	−	4.58466e9i	−0.989541	−	0.360163i
$177$		0			0
$178$	4.04926e9	−	2.29645e10i	0.302333	−	1.71462i
$179$	−4.80430e9	−	8.32130e9i	−0.349777	−	0.605832i	0.636432	−	0.771333i	$-0.280409\pi$
$179$	−4.80430e9	−	8.32130e9i	−0.349777	−	0.605832i	−0.986210	+	0.165500i	$0.947076\pi$
$180$		0			0
$181$	−6.68095e9	+	1.15717e10i	−0.462684	+	0.801392i	−0.999094	−	0.0425655i	$-0.986447\pi$
$181$	−6.68095e9	+	1.15717e10i	−0.462684	+	0.801392i	0.536410	+	0.843958i	$0.319780\pi$
$182$	1.31454e10	+	1.10303e10i	0.888084	+	0.745191i
$183$		0			0
$184$	−1.81607e8	−	1.02994e9i	−0.0116802	−	0.0662420i
$185$	−1.23803e10	+	1.03883e10i	−0.777065	+	0.652035i
$186$		0			0
$187$	7.93903e9	−	2.88957e9i	0.474767	−	0.172801i
$188$	−4.87944e9			−0.284878
$189$		0			0
$190$	−1.75746e10			−0.978349
$191$	1.41398e10	−	5.14646e9i	0.768763	−	0.279807i	0.0722841	−	0.997384i	$-0.476971\pi$
$191$	1.41398e10	−	5.14646e9i	0.768763	−	0.279807i	0.696479	+	0.717577i	$0.254749\pi$
$192$		0			0
$193$	−4.42867e9	+	3.71609e9i	−0.229755	+	0.192787i	−0.750396	−	0.660988i	$-0.770137\pi$
$193$	−4.42867e9	+	3.71609e9i	−0.229755	+	0.192787i	0.520641	+	0.853776i	$0.325693\pi$
$194$	1.54814e9	+	8.77995e9i	0.0784699	+	0.445025i
$195$		0			0
$196$	1.61242e9	+	1.35298e9i	0.0780415	+	0.0654846i
$197$	−5.11236e9	+	8.85486e9i	−0.241837	+	0.418874i	−0.961238	−	0.275721i	$-0.911083\pi$
$197$	−5.11236e9	+	8.85486e9i	−0.241837	+	0.418874i	0.719400	+	0.694596i	$0.244417\pi$
$198$		0			0
$199$	1.61677e10	+	2.80033e10i	0.730818	+	1.26581i	0.956534	+	0.291621i	$0.0941946\pi$
$199$	1.61677e10	+	2.80033e10i	0.730818	+	1.26581i	−0.225716	+	0.974193i	$0.572472\pi$
$200$	1.41065e8	−	8.00022e8i	0.00623427	−	0.0353563i
$201$		0			0
$202$	3.23854e10	+	1.17873e10i	1.36857	+	0.498119i
$203$	−2.96297e10	−	1.07843e10i	−1.22460	−	0.445719i
$204$		0			0
$205$	5.07982e9	−	2.88091e10i	0.200889	−	1.13930i
$206$	−7.50184e9	−	1.29936e10i	−0.290246	−	0.502720i
$207$		0			0
$208$	−1.39759e10	+	2.42070e10i	−0.517721	+	0.896720i
$209$	1.68121e10	+	1.41070e10i	0.609485	+	0.511419i
$210$		0			0
$211$	2.98464e9	+	1.69267e10i	0.103662	+	0.587899i	0.991746	+	0.128217i	$0.0409254\pi$
$211$	2.98464e9	+	1.69267e10i	0.103662	+	0.587899i	−0.888084	+	0.459682i	$0.847963\pi$
$212$	−9.73534e8	+	8.16892e8i	−0.0331009	+	0.0277749i
$213$		0			0
$214$	−4.73084e10	+	1.72189e10i	−1.54197	+	0.561232i
$215$	−4.47035e10			−1.42682
$216$		0			0
$217$	−5.91681e10			−1.81142
$218$	3.91596e10	−	1.42529e10i	1.17431	−	0.427415i
$219$		0			0
$220$	−5.69344e9	+	4.77736e9i	−0.163860	+	0.137495i
$221$	−3.05920e9	−	1.73496e10i	−0.0862666	−	0.489242i
$222$		0			0
$223$	3.95219e10	+	3.31628e10i	1.07020	+	0.898006i	0.995071	−	0.0991679i	$-0.0316181\pi$
$223$	3.95219e10	+	3.31628e10i	1.07020	+	0.898006i	0.0751309	+	0.997174i	$0.476063\pi$
$224$	−1.07953e10	+	1.86980e10i	−0.286496	+	0.496225i
$225$		0			0
$226$	1.55214e10	+	2.68839e10i	0.395771	+	0.685495i
$227$	−1.30319e10	+	7.39073e10i	−0.325754	+	1.84744i	0.178568	+	0.983928i	$0.442854\pi$
$227$	−1.30319e10	+	7.39073e10i	−0.325754	+	1.84744i	−0.504322	+	0.863516i	$0.668258\pi$
$228$		0			0
$229$	1.89288e10	+	6.88954e9i	0.454846	+	0.165550i	0.559275	−	0.828982i	$-0.311079\pi$
$229$	1.89288e10	+	6.88954e9i	0.454846	+	0.165550i	−0.104429	+	0.994532i	$0.533302\pi$
$230$	−3.48158e9	−	1.26719e9i	−0.0820354	−	0.0298584i
$231$		0			0
$232$	7.06713e9	−	4.00797e10i	0.160158	−	0.908298i
$233$	1.37981e10	+	2.38990e10i	0.306702	+	0.531223i	0.977639	−	0.210291i	$-0.0674412\pi$
$233$	1.37981e10	+	2.38990e10i	0.306702	+	0.531223i	−0.670937	+	0.741514i	$0.734108\pi$
$234$		0			0
$235$	2.64735e10	−	4.58534e10i	0.566247	−	0.980768i
$236$	1.64719e10	+	1.38216e10i	0.345653	+	0.290037i
$237$		0			0
$238$	−6.48971e9	−	3.68050e10i	−0.131108	−	0.743550i
$239$	1.94913e10	−	1.63551e10i	0.386411	−	0.324237i	−0.428802	−	0.903398i	$-0.641064\pi$
$239$	1.94913e10	−	1.63551e10i	0.386411	−	0.324237i	0.815213	+	0.579161i	$0.196620\pi$
$240$		0			0
$241$	−5.12698e10	+	1.86607e10i	−0.979006	+	0.356329i	−0.781454	−	0.623963i	$-0.785521\pi$
$241$	−5.12698e10	+	1.86607e10i	−0.979006	+	0.356329i	−0.197552	+	0.980292i	$0.563299\pi$
$242$	−1.25691e10			−0.235578
$243$		0			0
$244$	−3.99642e9			−0.0721800
$245$	−2.14625e10	+	7.81171e9i	−0.380569	+	0.138516i
$246$		0			0
$247$	3.50572e10	−	2.94165e10i	0.599296	−	0.502869i
$248$	−1.32614e10	−	7.52091e10i	−0.222616	−	1.26252i
$249$		0			0
$250$	−5.38817e10	−	4.52121e10i	−0.872391	−	0.732023i
$251$	2.32348e10	−	4.02439e10i	0.369494	−	0.639983i	−0.619992	−	0.784608i	$-0.712864\pi$
$251$	2.32348e10	−	4.02439e10i	0.369494	−	0.639983i	0.989487	+	0.144625i	$0.0461975\pi$
$252$		0			0
$253$	2.31336e9	+	4.00686e9i	0.0354977	+	0.0614839i
$254$	7.91495e9	−	4.48879e10i	0.119315	−	0.676671i
$255$		0			0
$256$	−4.50294e10	−	1.63894e10i	−0.655264	−	0.238497i
$257$	8.77846e10	+	3.19510e10i	1.25522	+	0.456862i	0.882162	−	0.470946i	$-0.156087\pi$
$257$	8.77846e10	+	3.19510e10i	1.25522	+	0.456862i	0.373057	+	0.927808i	$0.378310\pi$
$258$		0			0
$259$	1.55025e10	−	8.79190e10i	0.214068	−	1.21404i
$260$	7.74902e9	+	1.34217e10i	0.105164	+	0.182149i
$261$		0			0
$262$	−8.70070e9	+	1.50701e10i	−0.114077	+	0.197587i
$263$	−4.65852e10	−	3.90896e10i	−0.600409	−	0.503803i	0.291168	−	0.956672i	$-0.405956\pi$
$263$	−4.65852e10	−	3.90896e10i	−0.600409	−	0.503803i	−0.891577	+	0.452869i	$0.850401\pi$
$264$		0			0
$265$	−2.39463e9	−	1.35806e10i	−0.0298285	−	0.169166i
$266$	7.43695e10	−	6.24034e10i	0.910809	−	0.764259i
$267$		0			0
$268$	2.59662e10	−	9.45093e9i	0.307470	−	0.111910i
$269$	1.74477e10			0.203167			0.101583	−	0.994827i	$-0.467609\pi$
$269$	1.74477e10			0.203167			0.101583	+	0.994827i	$0.467609\pi$
$270$		0			0
$271$	6.87617e9			0.0774434			0.0387217	−	0.999250i	$-0.487671\pi$
$271$	6.87617e9			0.0774434			0.0387217	+	0.999250i	$0.487671\pi$
$272$	5.72045e10	−	2.08208e10i	0.633681	−	0.230641i
$273$		0			0
$274$	8.36992e9	−	7.02319e9i	0.0897106	−	0.0752761i
$275$	6.24068e8	+	3.53927e9i	0.00658013	+	0.0373178i
$276$		0			0
$277$	7.74363e10	+	6.49767e10i	0.790288	+	0.663130i	0.945817	−	0.324701i	$-0.105264\pi$
$277$	7.74363e10	+	6.49767e10i	0.790288	+	0.663130i	−0.155529	+	0.987831i	$0.549708\pi$
$278$	−4.12731e10	+	7.14871e10i	−0.414444	+	0.717838i
$279$		0			0
$280$	−5.03507e10	−	8.72101e10i	−0.489547	−	0.847921i
$281$	1.88219e10	−	1.06744e11i	0.180088	−	1.02133i	−0.752017	−	0.659144i	$-0.770919\pi$
$281$	1.88219e10	−	1.06744e11i	0.180088	−	1.02133i	0.932105	−	0.362188i	$-0.117970\pi$
$282$		0			0
$283$	1.89357e11	+	6.89203e10i	1.75486	+	0.638716i	0.999855	−	0.0170042i	$-0.00541286\pi$
$283$	1.89357e11	+	6.89203e10i	1.75486	+	0.638716i	0.755004	+	0.655721i	$0.227635\pi$
$284$	2.85835e10	+	1.04035e10i	0.260725	+	0.0948961i
$285$		0			0
$286$	1.70151e10	−	9.64974e10i	0.150379	−	0.852841i
$287$	8.07986e10	+	1.39947e11i	0.702968	+	1.21758i
$288$		0			0
$289$	4.01098e10	−	6.94723e10i	0.338229	−	0.585829i
$290$	−1.10448e11	−	9.26765e10i	−0.916991	−	0.769447i
$291$		0			0
$292$	7.37174e9	+	4.18072e10i	0.0593400	+	0.336534i
$293$	8.69536e10	−	7.29627e10i	0.689260	−	0.578358i	−0.229436	−	0.973324i	$-0.573688\pi$
$293$	8.69536e10	−	7.29627e10i	0.689260	−	0.578358i	0.918696	+	0.394966i	$0.129244\pi$
$294$		0			0
$295$	−2.19253e11	+	7.98017e10i	−1.68557	+	0.613498i
$296$	1.15229e11			0.872469
$297$		0			0
$298$	3.85805e10			0.283396
$299$	9.06599e9	−	3.29975e9i	0.0655986	−	0.0238759i
$300$		0			0
$301$	1.89170e11	−	1.58732e11i	1.32832	−	1.11459i
$302$	2.85640e10	+	1.61995e11i	0.197601	+	1.12065i
$303$		0			0
$304$	1.21139e11	+	1.01648e11i	0.813492	+	0.682601i
$305$	2.16826e10	−	3.75554e10i	0.143471	−	0.248498i
$306$		0			0
$307$	−1.52083e11	−	2.63416e11i	−0.977144	−	1.69246i	−0.672669	−	0.739944i	$-0.734852\pi$
$307$	−1.52083e11	−	2.63416e11i	−0.977144	−	1.69246i	−0.304476	−	0.952520i	$-0.598481\pi$
$308$	7.12929e9	−	4.04322e10i	0.0451407	−	0.256006i
$309$		0			0
$310$	−2.54234e11	−	9.25336e10i	−1.56353	−	0.569078i
$311$	−2.45130e11	−	8.92200e10i	−1.48585	−	0.540805i	−0.533496	−	0.845803i	$-0.679122\pi$
$311$	−2.45130e11	−	8.92200e10i	−1.48585	−	0.540805i	−0.952353	+	0.304998i	$0.901344\pi$
$312$		0			0
$313$	−4.72104e10	+	2.67743e11i	−0.278028	+	1.57677i	0.451150	+	0.892448i	$0.351014\pi$
$313$	−4.72104e10	+	2.67743e11i	−0.278028	+	1.57677i	−0.729178	+	0.684324i	$0.760097\pi$
$314$	−1.49709e11	−	2.59304e11i	−0.869091	−	1.50531i
$315$		0			0
$316$	−2.85509e10	+	4.94516e10i	−0.161075	+	0.278990i
$317$	−6.29520e10	−	5.28230e10i	−0.350141	−	0.293803i	0.450706	−	0.892673i	$-0.351172\pi$
$317$	−6.29520e10	−	5.28230e10i	−0.350141	−	0.293803i	−0.800847	+	0.598869i	$0.795617\pi$
$318$		0			0
$319$	3.12647e10	+	1.77311e11i	0.169043	+	0.958689i
$320$	9.10516e10	−	7.64014e10i	0.485414	−	0.407311i
$321$		0			0
$322$	1.92323e10	−	7.00000e9i	0.0996967	−	0.0362866i
$323$	−9.96683e10			−0.509502
$324$		0			0
$325$	7.49407e9			0.0372600
$326$	−3.10038e11	+	1.12845e11i	−1.52032	+	0.553352i
$327$		0			0
$328$	−1.59779e11	+	1.34070e11i	−0.762232	+	0.639589i
$329$	5.07886e10	+	2.88037e11i	0.238993	+	1.35540i
$330$		0			0
$331$	2.31971e11	+	1.94647e11i	1.06220	+	0.891295i	0.994324	−	0.106399i	$-0.0339319\pi$
$331$	2.31971e11	+	1.94647e11i	1.06220	+	0.891295i	0.0678803	+	0.997693i	$0.478376\pi$
$332$	3.98716e9	−	6.90596e9i	0.0180112	−	0.0311963i
$333$		0			0
$334$	1.11084e11	+	1.92403e11i	0.488417	+	0.845964i
$335$	−5.20672e10	+	2.95288e11i	−0.225872	+	1.28098i
$336$		0			0
$337$	−8.08193e10	−	2.94158e10i	−0.341335	−	0.124236i	0.165665	−	0.986182i	$-0.447023\pi$
$337$	−8.08193e10	−	2.94158e10i	−0.341335	−	0.124236i	−0.506999	+	0.861946i	$0.669245\pi$
$338$	5.97029e10	+	2.17301e10i	0.248812	+	0.0905600i
$339$		0			0
$340$	5.86112e9	−	3.32401e10i	0.0237862	−	0.134898i
$341$	1.68927e11	+	2.92591e11i	0.676559	+	1.17183i
$342$		0			0
$343$	−8.93231e10	+	1.54712e11i	−0.348450	+	0.603533i
$344$	2.44165e11	+	2.04878e11i	0.940091	+	0.788830i
$345$		0			0
$346$	−5.98950e10	−	3.39682e11i	−0.224672	−	1.27418i
$347$	−2.35341e11	+	1.97475e11i	−0.871395	+	0.731187i	−0.964391	−	0.264479i	$-0.914800\pi$
$347$	−2.35341e11	+	1.97475e11i	−0.871395	+	0.731187i	0.0929965	+	0.995666i	$0.470355\pi$
$348$		0			0
$349$	−2.96003e11	+	1.07736e11i	−1.06803	+	0.388730i	−0.815439	−	0.578844i	$-0.803504\pi$
$349$	−2.96003e11	+	1.07736e11i	−1.06803	+	0.388730i	−0.252589	+	0.967574i	$0.581282\pi$
$350$	1.58977e10			0.0566277
$351$		0			0
$352$	1.23284e11			0.428021
$353$	−2.28613e11	+	8.32085e10i	−0.783638	+	0.285221i	−0.702689	−	0.711497i	$-0.748017\pi$
$353$	−2.28613e11	+	8.32085e10i	−0.783638	+	0.285221i	−0.0809493	+	0.996718i	$0.525795\pi$
$354$		0			0
$355$	−2.52845e11	+	2.12162e11i	−0.844941	+	0.708990i
$356$	2.02016e10	+	1.14569e11i	0.0666594	+	0.378044i
$357$		0			0
$358$	1.85922e11	+	1.56007e11i	0.598214	+	0.501961i
$359$	5.66187e10	−	9.80665e10i	0.179902	−	0.311599i	−0.761945	−	0.647642i	$-0.775755\pi$
$359$	5.66187e10	−	9.80665e10i	0.179902	−	0.311599i	0.941847	+	0.336043i	$0.109089\pi$
$360$		0			0
$361$	3.18906e10	+	5.52362e10i	0.0988281	+	0.171175i
$362$	5.86076e10	−	3.32380e11i	0.179377	−	1.01729i
$363$		0			0
$364$	−8.04485e10	−	2.92809e10i	−0.240194	−	0.0874234i
$365$	−4.32869e11	−	1.57551e11i	−1.27655	−	0.464627i
$366$		0			0
$367$	4.11165e10	−	2.33183e11i	0.118309	−	0.670965i	−0.866749	−	0.498745i	$-0.833795\pi$
$367$	4.11165e10	−	2.33183e11i	0.118309	−	0.670965i	0.985058	−	0.172221i	$-0.0550943\pi$
$368$	1.66689e10	+	2.88713e10i	0.0473795	+	0.0820638i
$369$		0			0
$370$	2.04109e11	−	3.53527e11i	0.566179	−	0.980651i
$371$	5.83549e10	+	4.89656e10i	0.159917	+	0.134186i
$372$		0			0
$373$	3.24676e9	+	1.84133e10i	0.00868482	+	0.0492541i	0.988842	−	0.148967i	$-0.0475948\pi$
$373$	3.24676e9	+	1.84133e10i	0.00868482	+	0.0492541i	−0.980157	+	0.198221i	$0.936484\pi$
$374$	−1.63475e11	+	1.37172e11i	−0.432045	+	0.362529i
$375$		0			0
$376$	−3.54743e11	+	1.29116e11i	−0.915311	+	0.333146i
$377$	3.75440e11			0.957204
$378$		0			0
$379$	3.73495e11			0.929840			0.464920	−	0.885353i	$-0.346083\pi$
$379$	3.73495e11			0.929840			0.464920	+	0.885353i	$0.346083\pi$
$380$	8.23914e10	−	2.99880e10i	0.202701	−	0.0737771i
$381$		0			0
$382$	−2.91157e11	+	2.44309e11i	−0.699587	+	0.587023i
$383$	7.09945e10	+	4.02630e11i	0.168589	+	0.956118i	0.945286	+	0.326243i	$0.105783\pi$
$383$	7.09945e10	+	4.02630e11i	0.168589	+	0.956118i	−0.776697	+	0.629875i	$0.783106\pi$
$384$		0			0
$385$	3.41272e11	+	2.86361e11i	0.791640	+	0.664265i
$386$	7.30138e10	−	1.26464e11i	0.167403	−	0.289950i
$387$		0			0
$388$	−2.22393e10	−	3.85196e10i	−0.0498171	−	0.0862858i
$389$	6.23249e10	−	3.53462e11i	0.138003	−	0.782654i	−0.834718	−	0.550677i	$-0.814370\pi$
$389$	6.23249e10	−	3.53462e11i	0.138003	−	0.782654i	0.972721	−	0.231977i	$-0.0745193\pi$
$390$		0			0
$391$	−1.97446e10	−	7.18645e9i	−0.0427222	−	0.0155496i
$392$	1.53027e11	+	5.56972e10i	0.327326	+	0.119137i
$393$		0			0
$394$	4.48474e10	−	2.54342e11i	0.0937571	−	0.531723i
$395$	−3.09807e11	−	5.36601e11i	−0.640330	−	1.10908i
$396$		0			0
$397$	2.48545e10	−	4.30493e10i	0.0502167	−	0.0869778i	−0.839824	−	0.542858i	$-0.817342\pi$
$397$	2.48545e10	−	4.30493e10i	0.0502167	−	0.0869778i	0.890041	+	0.455880i	$0.150675\pi$
$398$	−6.25674e11	−	5.25003e11i	−1.24990	−	1.04879i
$399$		0			0
$400$	4.49671e9	+	2.55021e10i	0.00878264	+	0.0498088i
$401$	−2.96822e10	+	2.49063e10i	−0.0573254	+	0.0481017i	−0.671000	−	0.741457i	$-0.734135\pi$
$401$	−2.96822e10	+	2.49063e10i	−0.0573254	+	0.0481017i	0.613675	+	0.789559i	$0.289691\pi$
$402$		0			0
$403$	6.62021e11	−	2.40956e11i	1.25026	−	0.455056i
$404$	−1.71939e11			−0.321113
$405$		0			0
$406$	7.96448e11			1.45476
$407$	−4.79027e11	+	1.74352e11i	−0.865337	+	0.314957i
$408$		0			0
$409$	−2.10879e11	+	1.76948e11i	−0.372630	+	0.312674i	−0.809801	−	0.586705i	$-0.800425\pi$
$409$	−2.10879e11	+	1.76948e11i	−0.372630	+	0.312674i	0.437171	+	0.899378i	$0.355980\pi$
$410$	1.28311e11	+	7.27689e11i	0.224252	+	1.27180i
$411$		0			0
$412$	5.73407e10	+	4.81146e10i	0.0980450	+	0.0822695i
$413$	6.44446e11	−	1.11621e12i	1.08996	−	1.88787i
$414$		0			0
$415$	4.32648e10	+	7.49368e10i	0.0716008	+	0.124016i
$416$	4.46410e10	−	2.53171e11i	0.0730825	−	0.414472i
$417$		0			0
$418$	−5.20918e11	−	1.89599e11i	−0.834595	−	0.303768i
$419$	3.21103e11	+	1.16872e11i	0.508957	+	0.185245i	0.583718	−	0.811956i	$-0.301597\pi$
$419$	3.21103e11	+	1.16872e11i	0.508957	+	0.185245i	−0.0747612	+	0.997201i	$0.523819\pi$
$420$		0			0
$421$	−1.22268e9	+	6.93416e9i	−0.00189690	+	0.0107578i	−0.985742	−	0.168267i	$-0.946183\pi$
$421$	−1.22268e9	+	6.93416e9i	−0.00189690	+	0.0107578i	0.983845	+	0.179025i	$0.0572941\pi$
$422$	−2.17074e11	−	3.75983e11i	−0.333198	−	0.577115i
$423$		0			0
$424$	−4.91615e10	+	8.51502e10i	−0.0738718	+	0.127950i
$425$	−1.25027e10	−	1.04910e10i	−0.0185890	−	0.0155980i
$426$		0			0
$427$	4.15976e10	+	2.35912e11i	0.0605540	+	0.343419i
$428$	1.92406e11	−	1.61447e11i	0.277154	−	0.232559i
$429$		0			0
$430$	1.06107e12	−	3.86197e11i	1.49670	−	0.544755i
$431$	1.15221e12			1.60836			0.804182	−	0.594384i	$-0.202604\pi$
$431$	1.15221e12			1.60836			0.804182	+	0.594384i	$0.202604\pi$
$432$		0			0
$433$	−3.13373e11			−0.428416			−0.214208	−	0.976788i	$-0.568717\pi$
$433$	−3.13373e11			−0.428416			−0.214208	+	0.976788i	$0.568717\pi$
$434$	1.40439e12	−	5.11158e11i	1.90014	−	0.691594i
$435$		0			0
$436$	−1.59264e11	+	1.33638e11i	−0.211071	+	0.177109i
$437$	−9.47805e9	−	5.37527e10i	−0.0124323	−	0.0705072i
$438$		0			0
$439$	−7.03029e11	−	5.89912e11i	−0.903406	−	0.758048i	0.0674467	−	0.997723i	$-0.478515\pi$
$439$	−7.03029e11	−	5.89912e11i	−0.903406	−	0.758048i	−0.970853	+	0.239675i	$0.922959\pi$
$440$	−2.87507e11	+	4.97977e11i	−0.365689	+	0.633391i
$441$		0			0
$442$	2.22497e11	+	3.85376e11i	0.277283	+	0.480269i
$443$	−2.00282e11	+	1.13586e12i	−0.247073	+	1.40122i	0.568555	+	0.822645i	$0.307503\pi$
$443$	−2.00282e11	+	1.13586e12i	−0.247073	+	1.40122i	−0.815628	+	0.578576i	$0.803609\pi$
$444$		0			0
$445$	−1.18624e12	−	4.31757e11i	−1.43401	−	0.521938i
$446$	−1.22457e12	−	4.45709e11i	−1.46547	−	0.533389i
$447$		0			0
$448$	−1.14014e11	+	6.46607e11i	−0.133724	+	0.758385i
$449$	3.17938e11	+	5.50685e11i	0.369176	+	0.639432i	0.989437	−	0.144964i	$-0.0463065\pi$
$449$	3.17938e11	+	5.50685e11i	0.369176	+	0.639432i	−0.620261	+	0.784396i	$0.712973\pi$
$450$		0			0
$451$	4.61367e11	−	7.99111e11i	0.525112	−	0.909521i
$452$	−1.18639e11	−	9.95497e10i	−0.133691	−	0.112180i
$453$		0			0
$454$	−3.29171e11	−	1.86682e12i	−0.363639	−	2.06230i
$455$	7.11635e11	−	5.97133e11i	0.778406	−	0.653160i
$456$		0			0
$457$	−1.35801e12	+	4.94276e11i	−1.45640	+	0.530087i	−0.944372	−	0.328881i	$-0.893329\pi$
$457$	−1.35801e12	+	4.94276e11i	−1.45640	+	0.530087i	−0.512030	+	0.858967i	$0.671106\pi$
$458$	−5.08808e11			−0.540331
$459$		0			0
$460$	1.84842e10			0.0192483
$461$	4.49559e11	−	1.63626e11i	0.463589	−	0.168732i	−0.0996572	−	0.995022i	$-0.531775\pi$
$461$	4.49559e11	−	1.63626e11i	0.463589	−	0.168732i	0.563246	+	0.826289i	$0.309552\pi$
$462$		0			0
$463$	5.11919e11	−	4.29551e11i	0.517710	−	0.434410i	−0.346123	−	0.938189i	$-0.612502\pi$
$463$	5.11919e11	−	4.29551e11i	0.517710	−	0.434410i	0.863833	+	0.503779i	$0.168057\pi$
$464$	2.25277e11	+	1.27761e12i	0.225625	+	1.27958i
$465$		0			0
$466$	−5.33971e11	−	4.48055e11i	−0.524543	−	0.440144i
$467$	3.80875e10	−	6.59694e10i	0.0370558	−	0.0641825i	−0.846903	−	0.531748i	$-0.821535\pi$
$467$	3.80875e10	−	6.59694e10i	0.0370558	−	0.0641825i	0.883959	+	0.467565i	$0.154869\pi$
$468$		0			0
$469$	−8.28170e11	−	1.43443e12i	−0.790390	−	1.36900i
$470$	−2.32235e11	+	1.31707e12i	−0.219526	+	1.24500i
$471$		0			0
$472$	1.56327e12	+	5.68983e11i	1.44975	+	0.527668i
$473$	−1.32503e12	−	4.82272e11i	−1.21717	−	0.443013i
$474$		0			0
$475$	7.36220e9	−	4.17531e10i	0.00663569	−	0.0376329i
$476$	9.32258e10	+	1.61472e11i	0.0832347	+	0.144167i
$477$		0			0
$478$	−3.21345e11	+	5.56586e11i	−0.281544	+	0.487649i
$479$	5.61011e11	+	4.70744e11i	0.486925	+	0.408578i	0.852923	−	0.522037i	$-0.174828\pi$
$479$	5.61011e11	+	4.70744e11i	0.486925	+	0.408578i	−0.365998	+	0.930616i	$0.619272\pi$
$480$		0			0
$481$	1.84587e11	+	1.04684e12i	0.157234	+	0.891721i
$482$	1.05571e12	−	8.85849e11i	0.890911	−	0.747563i
$483$		0			0
$484$	5.89252e10	−	2.14470e10i	0.0488087	−	0.0177649i
$485$	4.82639e11			0.396082
$486$		0			0
$487$	−1.82826e12			−1.47284			−0.736422	−	0.676523i	$-0.763486\pi$
$487$	−1.82826e12			−1.47284			−0.736422	+	0.676523i	$0.763486\pi$
$488$	−2.90546e11	+	1.05750e11i	−0.231913	+	0.0844096i
$489$		0			0
$490$	4.41941e11	−	3.70833e11i	0.346324	−	0.290600i
$491$	−3.39248e10	−	1.92397e11i	−0.0263421	−	0.149394i	0.968800	−	0.247845i	$-0.0797223\pi$
$491$	−3.39248e10	−	1.92397e11i	−0.0263421	−	0.149394i	−0.995142	+	0.0984512i	$0.968611\pi$
$492$		0			0
$493$	−6.26366e11	−	5.25583e11i	−0.477548	−	0.400710i
$494$	−5.77976e11	+	1.00108e12i	−0.436655	+	0.756308i
$495$		0			0
$496$	1.21720e12	+	2.10826e12i	0.903016	+	1.56407i
$497$	3.16611e11	−	1.79559e12i	0.232767	−	1.32009i
$498$		0			0
$499$	−4.29772e11	−	1.56424e11i	−0.310303	−	0.112941i	0.182174	−	0.983266i	$-0.441686\pi$
$499$	−4.29772e11	−	1.56424e11i	−0.310303	−	0.112941i	−0.492478	+	0.870325i	$0.663909\pi$
$500$	3.29749e11	+	1.20019e11i	0.235949	+	0.0858785i
$501$		0			0
$502$	−2.03824e11	+	1.15594e12i	−0.143248	+	0.812401i
$503$	−4.67457e11	−	8.09660e11i	−0.325601	−	0.563958i	0.656033	−	0.754733i	$-0.272233\pi$
$503$	−4.67457e11	−	8.09660e11i	−0.325601	−	0.563958i	−0.981634	+	0.190775i	$0.938900\pi$
$504$		0			0
$505$	9.32856e11	−	1.61575e12i	0.638269	−	1.10551i
$506$	−8.95247e10	−	7.51202e10i	−0.0607108	−	0.0509424i
$507$		0			0
$508$	3.94875e10	+	2.23945e11i	0.0263071	+	0.149195i
$509$	1.48264e12	−	1.24408e12i	0.979051	−	0.821522i	−0.00489455	−	0.999988i	$-0.501558\pi$
$509$	1.48264e12	−	1.24408e12i	0.979051	−	0.821522i	0.983946	+	0.178466i	$0.0571135\pi$
$510$		0			0
$511$	2.39118e12	−	8.70318e11i	1.55138	−	0.564656i
$512$	−6.63043e11			−0.426409
$513$		0			0
$514$	−2.35966e12			−1.49113
$515$	−7.63248e11	+	2.77800e11i	−0.478116	+	0.174020i
$516$		0			0
$517$	1.27936e12	−	1.07351e12i	0.787564	−	0.660844i
$518$	3.91577e11	+	2.22075e12i	0.238965	+	1.35524i
$519$		0			0
$520$	9.18520e11	+	7.70730e11i	0.550901	+	0.462261i
$521$	−8.23497e11	+	1.42634e12i	−0.489658	+	0.848112i	−0.999929	−	0.0119016i	$-0.996212\pi$
$521$	−8.23497e11	+	1.42634e12i	−0.489658	+	0.848112i	0.510272	+	0.860013i	$0.329545\pi$
$522$		0			0
$523$	−3.82015e11	−	6.61669e11i	−0.223266	−	0.386708i	0.732532	−	0.680733i	$-0.238338\pi$
$523$	−3.82015e11	−	6.61669e11i	−0.223266	−	0.386708i	−0.955798	+	0.294025i	$0.905005\pi$
$524$	1.50753e10	−	8.54962e10i	0.00873524	−	0.0495400i
$525$		0			0
$526$	1.44343e12	+	5.25366e11i	0.822167	+	0.299244i
$527$	−1.44180e12	−	5.24773e11i	−0.814250	−	0.296363i
$528$		0			0
$529$	−3.10769e11	+	1.76246e12i	−0.172539	+	0.978516i
$530$	1.74162e11	+	3.01658e11i	0.0958765	+	0.166063i
$531$		0			0
$532$	−2.42171e11	+	4.19452e11i	−0.131075	+	0.227028i
$533$	−1.47396e12	−	1.23680e12i	−0.791069	−	0.663786i
$534$		0			0
$535$	4.73265e11	+	2.68402e12i	0.249754	+	1.41643i
$536$	1.63770e12	−	1.37419e12i	0.857024	−	0.719129i
$537$		0			0
$538$	−4.14133e11	+	1.50732e11i	−0.213118	+	0.0775686i
$539$	−7.20432e11			−0.367657
$540$		0			0
$541$	4.89967e10			0.0245912			0.0122956	−	0.999924i	$-0.496086\pi$
$541$	4.89967e10			0.0245912			0.0122956	+	0.999924i	$0.496086\pi$
$542$	−1.63211e11	+	5.94038e10i	−0.0812365	+	0.0295677i
$543$		0			0
$544$	−4.28895e11	+	3.59886e11i	−0.209969	+	0.176185i
$545$	−3.91746e11	−	2.22170e12i	−0.190204	−	1.07870i
$546$		0			0
$547$	−5.71367e11	−	4.79434e11i	−0.272880	−	0.228974i	0.496070	−	0.868283i	$-0.334776\pi$
$547$	−5.71367e11	−	4.79434e11i	−0.272880	−	0.228974i	−0.768950	+	0.639309i	$0.779220\pi$
$548$	−2.72551e10	+	4.72073e10i	−0.0129103	+	0.0223613i
$549$		0			0
$550$	−4.53887e10	−	7.86155e10i	−0.0211502	−	0.0366333i
$551$	3.68833e11	−	2.09176e12i	0.170470	−	0.966783i
$552$		0			0
$553$	3.21634e12	+	1.17065e12i	1.46251	+	0.532310i
$554$	−2.39934e12	−	8.73289e11i	−1.08218	−	0.393880i
$555$		0			0
$556$	7.15119e10	−	4.05564e11i	0.0317353	−	0.179980i
$557$	1.48199e12	+	2.56689e12i	0.652375	+	1.12995i	0.982545	+	0.186025i	$0.0595607\pi$
$557$	1.48199e12	+	2.56689e12i	0.652375	+	1.12995i	−0.330170	+	0.943922i	$0.607106\pi$
$558$		0			0
$559$	−1.47017e12	+	2.54640e12i	−0.636815	+	1.10300i
$560$	2.45903e12	+	2.06337e12i	1.05662	+	0.886608i
$561$		0			0
$562$	4.75423e11	+	2.69626e12i	0.201033	+	1.14011i
$563$	9.81998e11	−	8.23994e11i	0.411929	−	0.345650i	−0.413154	−	0.910661i	$-0.635573\pi$
$563$	9.81998e11	−	8.23994e11i	0.411929	−	0.345650i	0.825083	+	0.565012i	$0.191128\pi$
$564$		0			0
$565$	1.57917e12	−	5.74771e11i	0.651946	−	0.237289i
$566$	−5.08992e12			−2.08467
$567$		0			0
$568$	2.35335e12			0.948680
$569$	−2.71614e12	+	9.88593e11i	−1.08629	+	0.395378i	−0.822246	−	0.569132i	$-0.807279\pi$
$569$	−2.71614e12	+	9.88593e11i	−1.08629	+	0.395378i	−0.264046	+	0.964510i	$0.585057\pi$
$570$		0			0
$571$	1.67182e12	−	1.40282e12i	0.658152	−	0.552255i	−0.251380	−	0.967888i	$-0.580884\pi$
$571$	1.67182e12	−	1.40282e12i	0.658152	−	0.552255i	0.909532	+	0.415633i	$0.136440\pi$
$572$	8.48878e10	+	4.81423e11i	0.0331561	+	0.188037i
$573$		0			0
$574$	−3.12683e12	−	2.62372e12i	−1.20227	−	1.00882i
$575$	4.46903e9	−	7.74058e9i	0.00170493	−	0.00295303i
$576$		0			0
$577$	2.84456e11	+	4.92693e11i	0.106838	+	0.185048i	0.914488	−	0.404614i	$-0.132594\pi$
$577$	2.84456e11	+	4.92693e11i	0.106838	+	0.185048i	−0.807650	+	0.589662i	$0.799261\pi$
$578$	−3.51858e11	+	1.99548e12i	−0.131127	+	0.743658i
$579$		0			0
$580$	6.75925e11	+	2.46017e11i	0.248012	+	0.0902690i
$581$	−4.49165e11	−	1.63483e11i	−0.163536	−	0.0595222i
$582$		0			0
$583$	7.55329e10	−	4.28369e11i	0.0270787	−	0.153571i
$584$	1.64221e12	+	2.84439e12i	0.584211	+	1.01188i
$585$		0			0
$586$	−1.43357e12	+	2.48302e12i	−0.502204	+	0.869843i
$587$	−6.17617e11	−	5.18243e11i	−0.214708	−	0.180161i	0.529090	−	0.848565i	$-0.322533\pi$
$587$	−6.17617e11	−	5.18243e11i	−0.214708	−	0.180161i	−0.743798	+	0.668404i	$0.766978\pi$
$588$		0			0
$589$	−6.92111e11	−	3.92516e12i	−0.236950	−	1.34381i
$590$	4.51472e12	−	3.78830e12i	1.53390	−	1.28709i
$591$		0			0
$592$	−3.45162e12	+	1.25629e12i	−1.15498	+	0.420379i
$593$	−9.58035e11			−0.318153			−0.159076	−	0.987266i	$-0.550852\pi$
$593$	−9.58035e11			−0.318153			−0.159076	+	0.987266i	$0.550852\pi$
$594$		0			0
$595$	−2.02319e12			−0.661775
$596$	−1.80869e11	+	6.58310e10i	−0.0587160	+	0.0213709i
$597$		0			0
$598$	−1.86681e11	+	1.56644e11i	−0.0596958	+	0.0500907i
$599$	9.02574e11	+	5.11875e12i	0.286459	+	1.62459i	0.700028	+	0.714115i	$0.253171\pi$
$599$	9.02574e11	+	5.11875e12i	0.286459	+	1.62459i	−0.413570	+	0.910473i	$0.635718\pi$
$600$		0			0
$601$	−4.65274e12	−	3.90412e12i	−1.45470	−	1.22064i	−0.929057	−	0.369936i	$-0.879380\pi$
$601$	−4.65274e12	−	3.90412e12i	−1.45470	−	1.22064i	−0.525645	−	0.850704i	$-0.676176\pi$
$602$	−3.11877e12	+	5.40187e12i	−0.967830	+	1.67633i
$603$		0			0
$604$	−4.10327e11	−	7.10708e11i	−0.125448	−	0.217283i
$605$	−1.18156e11	+	6.70097e11i	−0.0358556	+	0.203347i
$606$		0			0
$607$	−2.48311e12	−	9.03779e11i	−0.742416	−	0.270217i	−0.0570049	−	0.998374i	$-0.518155\pi$
$607$	−2.48311e12	−	9.03779e11i	−0.742416	−	0.270217i	−0.685411	+	0.728157i	$0.740377\pi$
$608$	−1.36669e12	−	4.97433e11i	−0.405604	−	0.147628i
$609$		0			0
$610$	−1.90208e11	+	1.07872e12i	−0.0556217	+	0.315446i
$611$	−1.74127e12	−	3.01596e12i	−0.505452	−	0.875468i
$612$		0			0
$613$	−7.39092e11	+	1.28014e12i	−0.211410	+	0.366173i	−0.952156	−	0.305612i	$-0.901139\pi$
$613$	−7.39092e11	+	1.28014e12i	−0.211410	+	0.366173i	0.740746	+	0.671785i	$0.234472\pi$
$614$	5.88547e12	+	4.93850e12i	1.67118	+	1.40229i
$615$		0			0
$616$	−5.51575e11	−	3.12814e12i	−0.154344	−	0.875331i
$617$	−2.09674e12	+	1.75938e12i	−0.582454	+	0.488737i	−0.885752	−	0.464159i	$-0.846357\pi$
$617$	−2.09674e12	+	1.75938e12i	−0.582454	+	0.488737i	0.303298	+	0.952896i	$0.401912\pi$
$618$		0			0
$619$	3.95764e12	−	1.44046e12i	1.08350	−	0.394361i	0.262290	−	0.964989i	$-0.415522\pi$
$619$	3.95764e12	−	1.44046e12i	1.08350	−	0.394361i	0.821209	+	0.570628i	$0.193300\pi$
$620$	1.34977e12			0.366856
$621$		0			0
$622$	6.58911e12			1.76510
$623$	6.55283e12	−	2.38503e12i	1.74274	−	0.634305i
$624$		0			0
$625$	−2.79224e12	+	2.34297e12i	−0.731970	+	0.614195i
$626$	−1.19249e12	−	6.76292e12i	−0.310362	−	1.76015i
$627$		0			0
$628$	1.14431e12	+	9.60190e11i	0.293579	+	0.246342i
$629$	1.15753e12	−	2.00491e12i	0.294853	−	0.510701i
$630$		0			0
$631$	1.08609e12	+	1.88117e12i	0.272732	+	0.472385i	0.969560	−	0.244852i	$-0.0787395\pi$
$631$	1.08609e12	+	1.88117e12i	0.272732	+	0.472385i	−0.696829	+	0.717238i	$0.745406\pi$
$632$	−7.67146e11	+	4.35070e12i	−0.191272	+	1.08476i
$633$		0			0
$634$	1.95055e12	+	7.09942e11i	0.479464	+	0.174510i
$635$	−2.31871e12	−	8.43940e11i	−0.565932	−	0.205982i
$636$		0			0
$637$	−2.60867e11	+	1.47945e12i	−0.0627757	+	0.356019i
$638$	−2.27389e12	−	3.93850e12i	−0.543347	−	0.941104i
$639$		0			0
$640$	−2.50171e12	+	4.33308e12i	−0.589422	+	1.02091i
$641$	−1.02973e12	−	8.64045e11i	−0.240914	−	0.202151i	0.514334	−	0.857590i	$-0.328039\pi$
$641$	−1.02973e12	−	8.64045e11i	−0.240914	−	0.202151i	−0.755248	+	0.655439i	$0.772484\pi$
$642$		0			0
$643$	8.02950e11	+	4.55376e12i	0.185242	+	1.05056i	0.925644	+	0.378395i	$0.123524\pi$
$643$	8.02950e11	+	4.55376e12i	0.185242	+	1.05056i	−0.740402	+	0.672164i	$0.765365\pi$
$644$	−7.82188e10	+	6.56334e10i	−0.0179195	+	0.0150362i
$645$		0			0
$646$	2.36570e12	−	8.61043e11i	0.534457	−	0.194526i
$647$	3.02505e12			0.678677			0.339338	−	0.940664i	$-0.389797\pi$
$647$	3.02505e12			0.678677			0.339338	+	0.940664i	$0.389797\pi$
$648$		0			0
$649$	−7.35968e12			−1.62839
$650$	−1.77877e11	+	6.47419e10i	−0.0390849	+	0.0142258i
$651$		0			0
$652$	1.26094e12	−	1.05805e12i	0.273262	−	0.229294i
$653$	1.58785e12	+	9.00513e12i	0.341743	+	1.93812i	0.346283	+	0.938130i	$0.387444\pi$
$653$	1.58785e12	+	9.00513e12i	0.341743	+	1.93812i	−0.00454019	+	0.999990i	$0.501445\pi$
$654$		0			0
$655$	7.21639e11	+	6.05527e11i	0.153191	+	0.128543i
$656$	3.32437e12	−	5.75798e12i	0.700878	−	1.21396i
$657$		0			0
$658$	−3.69388e12	−	6.39798e12i	−0.768185	−	1.33054i
$659$	3.75520e11	−	2.12968e12i	0.0775620	−	0.439876i	−0.921153	−	0.389200i	$-0.872751\pi$
$659$	3.75520e11	−	2.12968e12i	0.0775620	−	0.439876i	0.998715	−	0.0506756i	$-0.0161374\pi$
$660$		0			0
$661$	5.95254e12	+	2.16655e12i	1.21282	+	0.441430i	0.867680	−	0.497122i	$-0.165610\pi$
$661$	5.95254e12	+	2.16655e12i	1.21282	+	0.441430i	0.345138	+	0.938552i	$0.387832\pi$
$662$	−7.18756e12	−	2.61606e12i	−1.45452	−	0.529403i
$663$		0			0
$664$	1.07133e11	−	6.07579e11i	0.0213878	−	0.121296i
$665$	−2.62780e12	−	4.55149e12i	−0.521069	−	0.902518i
$666$		0			0
$667$	2.23890e11	−	3.87789e11i	0.0437995	−	0.0758630i
$668$	−8.49073e11	−	7.12457e11i	−0.164988	−	0.138441i
$669$		0			0
$670$	−1.31516e12	−	7.45867e12i	−0.252141	−	1.42996i
$671$	1.04784e12	−	8.79241e11i	0.199546	−	0.167439i
$672$		0			0
$673$	8.96171e12	−	3.26179e12i	1.68393	−	0.612899i	0.690086	−	0.723727i	$-0.257573\pi$
$673$	8.96171e12	−	3.26179e12i	1.68393	−	0.612899i	0.993840	+	0.110828i	$0.0353504\pi$
$674$	2.17243e12			0.405486
$675$		0			0
$676$	−3.16972e11			−0.0583795
$677$	1.72732e12	−	6.28693e11i	0.316027	−	0.115024i	−0.179137	−	0.983824i	$-0.557330\pi$
$677$	1.72732e12	−	6.28693e11i	0.316027	−	0.115024i	0.495163	+	0.868800i	$0.335108\pi$
$678$		0			0
$679$	−2.04236e12	+	1.71374e12i	−0.368738	+	0.309408i
$680$	−4.53460e11	−	2.57170e12i	−0.0813296	−	0.461243i
$681$		0			0
$682$	−6.53732e12	−	5.48547e12i	−1.15710	−	0.970921i
$683$	1.22063e12	−	2.11418e12i	0.214629	−	0.371749i	−0.738528	−	0.674222i	$-0.764479\pi$
$683$	1.22063e12	−	2.11418e12i	0.214629	−	0.371749i	0.953158	+	0.302473i	$0.0978123\pi$
$684$		0			0
$685$	−2.95746e11	−	5.12247e11i	−0.0513229	−	0.0888939i
$686$	7.83574e11	−	4.44387e12i	0.135089	−	0.766131i
$687$		0			0
$688$	−9.54748e12	−	3.47500e12i	−1.62458	−	0.591298i
$689$	−8.52330e11	−	3.10223e11i	−0.144086	−	0.0524430i
$690$		0			0
$691$	1.71217e12	−	9.71022e12i	0.285691	−	1.62023i	−0.417116	−	0.908853i	$-0.636959\pi$
$691$	1.71217e12	−	9.71022e12i	0.285691	−	1.62023i	0.702807	−	0.711380i	$-0.251930\pi$
$692$	8.60402e11	+	1.49026e12i	0.142634	+	0.247050i
$693$		0			0
$694$	3.87998e12	−	6.72032e12i	0.634910	−	1.09970i
$695$	3.42321e12	+	2.87241e12i	0.556547	+	0.466998i
$696$		0			0
$697$	7.27674e11	+	4.12684e12i	0.116786	+	0.662324i
$698$	6.09510e12	−	5.11440e12i	0.971922	−	0.815539i
$699$		0			0
$700$	−7.45301e10	+	2.71267e10i	−0.0117325	+	0.00427028i
$701$	1.94842e11			0.0304755			0.0152377	−	0.999884i	$-0.495149\pi$
$701$	1.94842e11			0.0304755			0.0152377	+	0.999884i	$0.495149\pi$
$702$		0			0
$703$	6.01381e12			0.928647
$704$	3.52304e12	−	1.28228e12i	0.540556	−	0.196746i
$705$		0			0
$706$	4.70745e12	−	3.95002e12i	0.713123	−	0.598381i
$707$	1.78966e12	+	1.01497e13i	0.269391	+	1.52779i
$708$		0			0
$709$	4.54812e12	+	3.81633e12i	0.675965	+	0.567202i	0.914824	−	0.403852i	$-0.132329\pi$
$709$	4.54812e12	+	3.81633e12i	0.675965	+	0.567202i	−0.238859	+	0.971054i	$0.576773\pi$
$710$	4.16856e12	−	7.22016e12i	0.615635	−	1.06631i
$711$		0			0
$712$	4.50033e12	+	7.79480e12i	0.656273	+	1.13670i
$713$	1.45909e11	−	8.27490e11i	0.0211436	−	0.119911i
$714$		0			0
$715$	−4.98462e12	−	1.81425e12i	−0.713271	−	0.259609i
$716$	−1.13782e12	−	4.14132e11i	−0.161795	−	0.0588885i
$717$		0			0
$718$	−4.96679e11	+	2.81681e12i	−0.0697455	+	0.395546i
$719$	4.49993e12	+	7.79411e12i	0.627951	+	1.08764i	0.987962	+	0.154695i	$0.0494395\pi$
$719$	4.49993e12	+	7.79411e12i	0.627951	+	1.08764i	−0.360011	+	0.932948i	$0.617227\pi$
$720$		0			0
$721$	2.24339e12	−	3.88567e12i	0.309170	−	0.535497i
$722$	−1.23414e12	−	1.03556e12i	−0.169023	−	0.141827i
$723$		0			0
$724$	2.92392e11	+	1.65824e12i	0.0395496	+	0.224297i
$725$	2.66445e11	−	2.23574e11i	0.0358168	−	0.0300539i
$726$		0			0
$727$	−4.83998e12	+	1.76161e12i	−0.642598	+	0.233886i	−0.642705	−	0.766114i	$-0.722188\pi$
$727$	−4.83998e12	+	1.76161e12i	−0.642598	+	0.233886i	0.000107583		1.00000i	$0.499966\pi$
$728$	−6.62354e12			−0.873975
$729$		0			0
$730$	1.16355e13			1.51647
$731$	6.01749e12	−	2.19019e12i	0.779448	−	0.283696i
$732$		0			0
$733$	−8.06359e12	+	6.76616e12i	−1.03172	+	0.865713i	−0.991054	−	0.133459i	$-0.957391\pi$
$733$	−8.06359e12	+	6.76616e12i	−1.03172	+	0.865713i	−0.0406629	+	0.999173i	$0.512947\pi$
$734$	1.03856e12	+	5.88997e12i	0.132069	+	0.748999i
$735$		0			0
$736$	−2.34878e11	−	1.97086e11i	−0.0295048	−	0.0247574i
$737$	−4.72892e12	+	8.19073e12i	−0.590416	+	1.02263i
$738$		0			0
$739$	4.72856e12	+	8.19011e12i	0.583216	+	1.01016i	0.995095	+	0.0989210i	$0.0315391\pi$
$739$	4.72856e12	+	8.19011e12i	0.583216	+	1.01016i	−0.411880	+	0.911238i	$0.635128\pi$
$740$	−3.53649e11	+	2.00565e12i	−0.0433541	+	0.245873i
$741$		0			0
$742$	−1.80811e12	−	6.58099e11i	−0.218982	−	0.0797028i
$743$	−3.05399e12	−	1.11156e12i	−0.367636	−	0.133808i	0.151595	−	0.988443i	$-0.451559\pi$
$743$	−3.05399e12	−	1.11156e12i	−0.367636	−	0.133808i	−0.519230	+	0.854634i	$0.673781\pi$
$744$		0			0
$745$	3.62677e11	−	2.05684e12i	0.0431337	−	0.244623i
$746$	−2.36138e11	−	4.09003e11i	−0.0279153	−	0.0483506i
$747$		0			0
$748$	5.32327e11	−	9.22018e11i	0.0621758	−	0.107692i
$749$	−1.15330e13	−	9.67737e12i	−1.33899	−	1.12354i
$750$		0			0
$751$	−4.29439e11	−	2.43547e12i	−0.0492631	−	0.279385i	0.950218	−	0.311585i	$-0.100860\pi$
$751$	−4.29439e11	−	2.43547e12i	−0.0492631	−	0.279385i	−0.999481	+	0.0321998i	$0.989749\pi$
$752$	9.21841e12	−	7.73517e12i	1.05118	−	0.882042i
$753$		0			0
$754$	−8.91132e12	+	3.24346e12i	−1.00409	+	0.365458i
$755$	8.90495e12			0.997402
$756$		0			0
$757$	−9.28008e12			−1.02712			−0.513559	−	0.858054i	$-0.671673\pi$
$757$	−9.28008e12			−1.02712			−0.513559	+	0.858054i	$0.671673\pi$
$758$	−8.86516e12	+	3.22665e12i	−0.975383	+	0.355010i
$759$		0			0
$760$	5.19647e12	−	4.36035e12i	0.564998	−	0.474090i
$761$	5.97625e11	+	3.38930e12i	0.0645949	+	0.366336i	0.999921	+	0.0125497i	$0.00399479\pi$
$761$	5.97625e11	+	3.38930e12i	0.0645949	+	0.366336i	−0.935326	+	0.353786i	$0.884894\pi$
$762$		0			0
$763$	9.54648e12	+	8.01045e12i	1.01972	+	0.855651i
$764$	9.48099e11	−	1.64216e12i	0.100678	−	0.174379i
$765$		0			0
$766$	−5.16345e12	−	8.94336e12i	−0.541890	−	0.938580i
$767$	−2.66493e12	+	1.51135e13i	−0.278039	+	1.57684i
$768$		0			0
$769$	−8.99530e12	−	3.27402e12i	−0.927571	−	0.337608i	−0.166325	−	0.986071i	$-0.553190\pi$
$769$	−8.99530e12	−	3.27402e12i	−0.927571	−	0.337608i	−0.761246	+	0.648463i	$0.775412\pi$
$770$	−1.05742e13	−	3.84871e12i	−1.08403	−	0.394554i
$771$		0			0
$772$	−1.26507e11	+	7.17459e11i	−0.0128185	+	0.0726975i
$773$	−3.47782e12	−	6.02376e12i	−0.350348	−	0.606820i	0.635963	−	0.771720i	$-0.280603\pi$
$773$	−3.47782e12	−	6.02376e12i	−0.350348	−	0.606820i	−0.986310	+	0.164900i	$0.947270\pi$
$774$		0			0
$775$	3.26340e11	−	5.65237e11i	0.0324947	−	0.0562824i
$776$	−2.63611e12	−	2.21196e12i	−0.260967	−	0.218977i
$777$		0			0
$778$	1.57426e12	+	8.92809e12i	0.154053	+	0.873676i
$779$	−8.33885e12	+	6.99712e12i	−0.811311	+	0.680771i
$780$		0			0
$781$	−9.78327e12	+	3.56082e12i	−0.940924	+	0.342468i
$782$	5.30736e11			0.0507514
$783$		0			0
$784$	−5.19106e12			−0.490720
$785$	−1.52316e13	+	5.54386e12i	−1.43164	+	0.521073i
$786$		0			0
$787$	−1.15045e13	+	9.65346e12i	−1.06901	+	0.897009i	−0.994963	−	0.100246i	$-0.968037\pi$
$787$	−1.15045e13	+	9.65346e12i	−1.06901	+	0.897009i	−0.0740506	+	0.997254i	$0.523593\pi$
$788$	2.23742e11	+	1.26891e12i	0.0206719	+	0.117236i
$789$		0			0
$790$	1.19892e13	+	1.00601e13i	1.09514	+	0.918930i
$791$	−4.64161e12	+	8.03951e12i	−0.421575	+	0.730189i
$792$		0			0
$793$	−1.42615e12	−	2.47017e12i	−0.128067	−	0.221819i
$794$	−2.18033e11	+	1.23652e12i	−0.0194683	+	0.110410i
$795$		0			0
$796$	3.82905e12	+	1.39366e12i	0.338051	+	0.123040i
$797$	1.67636e13	+	6.10146e12i	1.47165	+	0.535638i	0.948549	−	0.316631i	$-0.102552\pi$
$797$	1.67636e13	+	6.10146e12i	1.47165	+	0.535638i	0.523104	+	0.852269i	$0.324774\pi$
$798$		0			0
$799$	−1.31704e12	+	7.46931e12i	−0.114324	+	0.648365i
$800$	−1.19082e11	−	2.06256e11i	−0.0102788	−	0.0178034i
$801$		0			0
$802$	4.89360e11	−	8.47596e11i	0.0417680	−	0.0723443i
$803$	−1.11307e13	−	9.33978e12i	−0.944720	−	0.792714i
$804$		0			0
$805$	−1.92397e11	−	1.09114e12i	−0.0161479	−	0.0915795i
$806$	−1.36319e13	+	1.14385e13i	−1.13775	+	0.954689i
$807$		0			0
$808$	−1.25002e13	+	4.54971e12i	−1.03173	+	0.375519i
$809$	2.83506e12			0.232698			0.116349	−	0.993208i	$-0.462881\pi$
$809$	2.83506e12			0.232698			0.116349	+	0.993208i	$0.462881\pi$
$810$		0			0
$811$	8.41140e12			0.682770			0.341385	−	0.939924i	$-0.389104\pi$
$811$	8.41140e12			0.682770			0.341385	+	0.939924i	$0.389104\pi$
$812$	−3.73383e12	+	1.35900e12i	−0.301406	+	0.109703i
$813$		0			0
$814$	9.86379e12	−	8.27671e12i	0.787470	−	0.660766i
$815$	3.10157e12	+	1.75899e13i	0.246248	+	1.39654i
$816$		0			0
$817$	1.27429e13	+	1.06926e13i	1.00062	+	0.839622i
$818$	3.47668e12	−	6.02178e12i	0.271503	−	0.470257i
$819$		0			0
$820$	−1.84321e12	−	3.19254e12i	−0.142368	−	0.246589i
$821$	4.38315e12	−	2.48581e13i	0.336700	−	1.90952i	−0.0730651	−	0.997327i	$-0.523278\pi$
$821$	4.38315e12	−	2.48581e13i	0.336700	−	1.90952i	0.409765	−	0.912191i	$-0.365611\pi$
$822$		0			0
$823$	5.93216e12	+	2.15913e12i	0.450727	+	0.164051i	0.557402	−	0.830243i	$-0.311798\pi$
$823$	5.93216e12	+	2.15913e12i	0.450727	+	0.164051i	−0.106675	+	0.994294i	$0.534021\pi$
$824$	5.44193e12	+	1.98070e12i	0.411226	+	0.149674i
$825$		0			0
$826$	−5.65330e12	+	3.20615e13i	−0.422564	+	2.39648i
$827$	7.86028e12	+	1.36144e13i	0.584337	+	1.01210i	0.994958	+	0.100295i	$0.0319787\pi$
$827$	7.86028e12	+	1.36144e13i	0.584337	+	1.01210i	−0.410621	+	0.911806i	$0.634688\pi$
$828$		0			0
$829$	5.93246e11	−	1.02753e12i	0.0436254	−	0.0755614i	−0.843388	−	0.537305i	$-0.819443\pi$
$829$	5.93246e11	−	1.02753e12i	0.0436254	−	0.0755614i	0.887014	+	0.461743i	$0.152776\pi$
$830$	−1.67430e12	−	1.40491e12i	−0.122457	−	0.102753i
$831$		0			0
$832$	−1.35756e12	−	7.69909e12i	−0.0982207	−	0.557037i
$833$	2.50632e12	−	2.10305e12i	0.180357	−	0.151338i
$834$		0			0
$835$	1.13018e13	−	4.11352e12i	0.804561	−	0.292836i
$836$	2.76563e12			0.195824
$837$		0			0
$838$	−8.63126e12			−0.604611
$839$	−1.27093e13	+	4.62580e12i	−0.885507	+	0.322298i	−0.744430	−	0.667700i	$-0.767279\pi$
$839$	−1.27093e13	+	4.62580e12i	−0.885507	+	0.322298i	−0.141077	+	0.989999i	$0.545056\pi$
$840$		0			0
$841$	2.23532e12	−	1.87566e12i	0.154084	−	0.129292i
$842$	−3.08837e10	−	1.75150e11i	−0.00211750	−	0.0120090i
$843$		0			0
$844$	1.65922e12	+	1.39225e12i	0.112554	+	0.0944442i
$845$	1.71974e12	−	2.97867e12i	0.116040	−	0.200987i
$846$		0			0
$847$	−1.87937e12	−	3.25516e12i	−0.125469	−	0.217319i
$848$	5.44251e11	−	3.08660e12i	0.0361425	−	0.204974i
$849$		0			0
$850$	3.87394e11	+	1.41000e11i	0.0254547	+	0.00926475i
$851$	1.19135e12	+	4.33618e11i	0.0778678	+	0.0283416i
$852$		0			0
$853$	2.77611e12	−	1.57441e13i	0.179542	−	1.01823i	−0.753228	−	0.657759i	$-0.771504\pi$
$853$	2.77611e12	−	1.57441e13i	0.179542	−	1.01823i	0.932770	−	0.360472i	$-0.117385\pi$
$854$	−3.02541e12	−	5.24016e12i	−0.194636	−	0.337120i
$855$		0			0
$856$	9.71609e12	−	1.68288e13i	0.618528	−	1.07132i
$857$	7.83839e12	+	6.57719e12i	0.496379	+	0.416511i	0.856306	−	0.516469i	$-0.172754\pi$
$857$	7.83839e12	+	6.57719e12i	0.496379	+	0.416511i	−0.359927	+	0.932980i	$0.617198\pi$
$858$		0			0
$859$	1.28508e12	+	7.28804e12i	0.0805305	+	0.456711i	0.998232	+	0.0594403i	$0.0189316\pi$
$859$	1.28508e12	+	7.28804e12i	0.0805305	+	0.456711i	−0.917701	+	0.397271i	$0.869957\pi$
$860$	−4.31542e12	+	3.62106e12i	−0.269017	+	0.225732i
$861$		0			0
$862$	−2.73485e13	+	9.95404e12i	−1.68714	+	0.614068i
$863$	7.47108e12			0.458495			0.229247	−	0.973368i	$-0.426373\pi$
$863$	7.47108e12			0.458495			0.229247	+	0.973368i	$0.426373\pi$
$864$		0			0
$865$	−1.86725e13			−1.13404
$866$	7.43811e12	−	2.70725e12i	0.449399	−	0.163568i
$867$		0			0
$868$	−5.71174e12	+	4.79272e12i	−0.341531	+	0.286578i
$869$	−3.39382e12	−	1.92473e13i	−0.201883	−	1.14494i
$870$		0			0
$871$	1.51078e13	+	1.26770e13i	0.889448	+	0.746335i
$872$	−8.04250e12	+	1.39300e13i	−0.471050	+	0.815882i
$873$		0			0
$874$	6.89342e11	+	1.19397e12i	0.0399607	+	0.0692140i
$875$	3.65254e12	−	2.07146e13i	0.210649	−	1.19465i
$876$		0			0
$877$	1.10232e13	+	4.01212e12i	0.629230	+	0.229021i	0.636896	−	0.770950i	$-0.280218\pi$
$877$	1.10232e13	+	4.01212e12i	0.629230	+	0.229021i	−0.00766608	+	0.999971i	$0.502440\pi$
$878$	2.17832e13	+	7.92843e12i	1.23707	+	0.450258i
$879$		0			0
$880$	3.18290e12	−	1.80511e13i	0.178917	−	1.01469i
$881$	−4.75652e12	−	8.23853e12i	−0.266010	−	0.460742i	0.701818	−	0.712356i	$-0.252372\pi$
$881$	−4.75652e12	−	8.23853e12i	−0.266010	−	0.460742i	−0.967828	+	0.251614i	$0.919039\pi$
$882$		0			0
$883$	1.68872e13	−	2.92495e13i	0.934835	−	1.61918i	0.159907	−	0.987132i	$-0.448881\pi$
$883$	1.68872e13	−	2.92495e13i	0.934835	−	1.61918i	0.774928	−	0.632049i	$-0.217786\pi$
$884$	−1.70066e12	−	1.42703e12i	−0.0936663	−	0.0785954i
$885$		0			0
$886$	−5.05892e12	−	2.86906e13i	−0.275808	−	1.56418i
$887$	−7.93307e12	+	6.65664e12i	−0.430314	+	0.361076i	−0.832070	−	0.554670i	$-0.812844\pi$
$887$	−7.93307e12	+	6.65664e12i	−0.430314	+	0.361076i	0.401756	+	0.915747i	$0.368400\pi$
$888$		0			0
$889$	1.28086e13	−	4.66195e12i	0.687770	−	0.250328i
$890$	3.18862e13			1.70352
$891$		0			0
$892$	6.50145e12			0.343850
$893$	−1.85140e13	+	6.73855e12i	−0.974246	+	0.354597i
$894$		0			0
$895$	1.00650e13	−	8.44551e12i	0.524335	−	0.439969i
$896$	−4.79946e12	−	2.72191e13i	−0.248775	−	1.41087i
$897$		0			0
$898$	−1.23039e13	−	1.03242e13i	−0.631391	−	0.529800i
$899$	1.63490e13	−	2.83174e13i	0.834783	−	1.44589i
$900$		0			0
$901$	9.87702e11	+	1.71075e12i	0.0499303	+	0.0864818i
$902$	−4.04728e12	+	2.29532e13i	−0.203579	+	1.15455i
$903$		0			0
$904$	−1.12594e13	−	4.09810e12i	−0.560736	−	0.204091i
$905$	−1.71693e13	−	6.24910e12i	−0.850811	−	0.309670i
$906$		0			0
$907$	2.69113e12	−	1.52622e13i	0.132039	−	0.748830i	−0.844837	−	0.535023i	$-0.820303\pi$
$907$	2.69113e12	−	1.52622e13i	0.132039	−	0.748830i	0.976876	−	0.213806i	$-0.0685861\pi$
$908$	4.72860e12	+	8.19018e12i	0.230859	+	0.399859i
$909$		0			0
$910$	−1.17325e13	+	2.03212e13i	−0.567156	+	0.982344i
$911$	−5.85805e12	−	4.91548e12i	−0.281786	−	0.236447i	0.490929	−	0.871200i	$-0.336658\pi$
$911$	−5.85805e12	−	4.91548e12i	−0.281786	−	0.236447i	−0.772715	+	0.634753i	$0.781102\pi$
$912$		0			0
$913$	4.73950e11	+	2.68791e12i	0.0225743	+	0.128025i
$914$	2.79633e13	−	2.34640e13i	1.32535	−	1.11210i
$915$		0			0
$916$	2.38534e12	−	8.68194e11i	0.111949	−	0.0407462i
$917$	−5.20381e12			−0.243030
$918$		0			0
$919$	9.87726e12			0.456790			0.228395	−	0.973569i	$-0.426652\pi$
$919$	9.87726e12			0.456790			0.228395	+	0.973569i	$0.426652\pi$
$920$	1.34383e12	−	4.89115e11i	0.0618444	−	0.0225095i
$921$		0			0
$922$	−9.25702e12	+	7.76756e12i	−0.421873	+	0.353994i
$923$	3.76985e12	+	2.13799e13i	0.170969	+	0.969612i
$924$		0			0
$925$	7.54393e11	+	6.33011e11i	0.0338813	+	0.0284298i
$926$	−8.43981e12	+	1.46182e13i	−0.377210	+	0.653347i
$927$		0			0
$928$	−5.96581e12	−	1.03331e13i	−0.264061	−	0.457366i
$929$	4.29860e12	−	2.43786e13i	0.189346	−	1.07383i	−0.730897	−	0.682488i	$-0.760898\pi$
$929$	4.29860e12	−	2.43786e13i	0.189346	−	1.07383i	0.920243	−	0.391347i	$-0.127991\pi$
$930$		0			0
$931$	7.98646e12	+	2.90683e12i	0.348402	+	0.126808i
$932$	3.26784e12	+	1.18940e12i	0.141870	+	0.0516363i
$933$		0			0
$934$	−3.34117e11	+	1.89487e12i	−0.0143661	+	0.0814739i
$935$	5.77630e12	+	1.00048e13i	0.247171	+	0.428112i
$936$		0			0
$937$	−2.20971e12	+	3.82734e12i	−0.0936501	+	0.162207i	−0.909044	−	0.416699i	$-0.863187\pi$
$937$	−2.20971e12	+	3.82734e12i	−0.0936501	+	0.162207i	0.815394	+	0.578906i	$0.196520\pi$
$938$	3.20493e13	+	2.68926e13i	1.35178	+	1.13428i
$939$		0			0
$940$	−1.15861e12	−	6.57082e12i	−0.0484019	−	0.274501i
$941$	5.06657e12	−	4.25136e12i	0.210650	−	0.176756i	−0.531358	−	0.847147i	$-0.678318\pi$
$941$	5.06657e12	−	4.25136e12i	0.210650	−	0.176756i	0.742008	+	0.670391i	$0.233874\pi$
$942$		0			0
$943$	−2.15647e12	+	7.84891e11i	−0.0888057	+	0.0323226i
$944$	−5.30300e13			−2.17344
$945$		0			0
$946$	3.56169e13			1.44593
$947$	1.59591e13	−	5.80865e12i	0.644814	−	0.234693i	0.00114761	−	0.999999i	$-0.499635\pi$
$947$	1.59591e13	−	5.80865e12i	0.644814	−	0.234693i	0.643666	+	0.765306i	$0.277412\pi$
$948$		0			0
$949$	−2.32102e13	+	1.94757e13i	−0.928926	+	0.779462i
$950$	1.85962e11	+	1.05464e12i	0.00740742	+	0.0420096i
$951$		0			0
$952$	1.10504e13	+	9.27238e12i	0.436025	+	0.365869i
$953$	8.10874e12	−	1.40447e13i	0.318446	−	0.551564i	−0.661718	−	0.749753i	$-0.730173\pi$
$953$	8.10874e12	−	1.40447e13i	0.318446	−	0.551564i	0.980164	+	0.198189i	$0.0635058\pi$
$954$		0			0
$955$	1.02878e13	+	1.78191e13i	0.400230	+	0.693218i
$956$	5.56779e11	−	3.15765e12i	0.0215587	−	0.122265i
$957$		0			0
$958$	−1.73828e13	−	6.32681e12i	−0.666767	−	0.242684i
$959$	3.07037e12	+	1.11752e12i	0.117221	+	0.0426651i
$960$		0			0
$961$	6.06344e12	−	3.43875e13i	0.229332	−	1.30060i
$962$	−1.34251e13	−	2.32529e13i	−0.505392	−	0.875365i
$963$		0			0
$964$	−3.43774e12	+	5.95434e12i	−0.128211	+	0.222069i
$965$	−6.05579e12	−	5.08141e12i	−0.224801	−	0.188630i
$966$		0			0
$967$	2.60683e11	+	1.47840e12i	0.00958723	+	0.0543719i	0.989226	−	0.146396i	$-0.0467674\pi$
$967$	2.60683e11	+	1.47840e12i	0.00958723	+	0.0543719i	−0.979639	+	0.200768i	$0.935656\pi$
$968$	3.71644e12	−	3.11846e12i	0.136047	−	0.114157i
$969$		0			0
$970$	−1.14558e13	+	4.16956e12i	−0.415481	+	0.151223i
$971$	−9.65545e12			−0.348567			−0.174283	−	0.984696i	$-0.555761\pi$
$971$	−9.65545e12			−0.348567			−0.174283	+	0.984696i	$0.555761\pi$
$972$		0			0
$973$	−2.46851e13			−0.882931
$974$	4.33949e13	−	1.57944e13i	1.54498	−	0.562327i
$975$		0			0
$976$	7.55018e12	−	6.33536e12i	0.266338	−	0.223484i
$977$	−3.77976e12	−	2.14361e13i	−0.132721	−	0.752697i	−0.976420	−	0.215881i	$-0.930738\pi$
$977$	−3.77976e12	−	2.14361e13i	−0.132721	−	0.752697i	0.843699	−	0.536817i	$-0.180373\pi$
$978$		0			0
$979$	−3.05028e13	−	2.55949e13i	−1.06125	−	0.890494i
$980$	−1.43910e12	+	2.49260e12i	−0.0498396	+	0.0863246i
$981$		0			0
$982$	2.46736e12	+	4.27360e12i	0.0846704	+	0.146653i
$983$	−5.54433e12	+	3.14435e13i	−0.189391	+	1.07409i	0.730793	+	0.682600i	$0.239151\pi$
$983$	−5.54433e12	+	3.14435e13i	−0.189391	+	1.07409i	−0.920183	+	0.391488i	$0.871960\pi$
$984$		0			0
$985$	−1.31382e13	−	4.78190e12i	−0.444705	−	0.161859i
$986$	1.94078e13	+	7.06385e12i	0.653927	+	0.238010i
$987$		0			0
$988$	1.00143e12	−	5.67939e12i	0.0334360	−	0.189625i
$989$	1.75344e12	+	3.03705e12i	0.0582784	+	0.100941i
$990$		0			0
$991$	−1.60306e13	+	2.77657e13i	−0.527980	+	0.914488i	0.471488	+	0.881872i	$0.343717\pi$
$991$	−1.60306e13	+	2.77657e13i	−0.527980	+	0.914488i	−0.999468	+	0.0326155i	$0.989616\pi$
$992$	−1.71514e13	−	1.43917e13i	−0.562337	−	0.471857i
$993$		0			0
$994$	7.99727e12	+	4.53548e13i	0.259838	+	1.47362i
$995$	−3.38711e13	+	2.84213e13i	−1.09553	+	0.919263i
$996$		0			0
$997$	−3.02430e13	+	1.10075e13i	−0.969384	+	0.352827i	−0.777704	−	0.628630i	$-0.783616\pi$
$997$	−3.02430e13	+	1.10075e13i	−0.969384	+	0.352827i	−0.191680	+	0.981457i	$0.561394\pi$
$998$	1.15523e13			0.368622
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.19.7		156
3.2	odd	2		27.10.e.a.7.20	yes	156
27.4	even	9	inner	81.10.e.a.64.7		156
27.23	odd	18		27.10.e.a.4.20	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.20	✓	156	27.23	odd	18
27.10.e.a.7.20	yes	156	3.2	odd	2
81.10.e.a.19.7		156	1.1	even	1	trivial
81.10.e.a.64.7		156	27.4	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-23.7357 + 8.63908i) q^{2} +(96.5341 - 81.0017i) q^{4} +(237.448 + 1346.63i) q^{5} +(-5786.38 - 4855.35i) q^{7} +(4874.78 - 8443.36i) q^{8} +O(q^{10})\)	\(q+(-23.7357 + 8.63908i) q^{2} +(96.5341 - 81.0017i) q^{4} +(237.448 + 1346.63i) q^{5} +(-5786.38 - 4855.35i) q^{7} +(4874.78 - 8443.36i) q^{8} +(-17269.7 - 29911.9i) q^{10} +(-7489.73 + 42476.4i) q^{11} +(84515.8 + 30761.2i) q^{13} +(179290. + 65256.1i) q^{14} +(-53967.1 + 306063. i) q^{16} +(-97939.0 - 169635. i) q^{17} +(254414. - 440658. i) q^{19} +(132001. + 110762. i) q^{20} +(-189183. - 1.07291e6i) q^{22} +(82173.4 - 68951.6i) q^{23} +(78298.2 - 28498.2i) q^{25} -2.27179e6 q^{26} -951876. q^{28} +(3.92260e6 - 1.42771e6i) q^{29} +(6.00051e6 - 5.03503e6i) q^{31} +(-496342. - 2.81490e6i) q^{32} +(3.79014e6 + 3.18031e6i) q^{34} +(5.16441e6 - 8.94503e6i) q^{35} +(5.90946e6 + 1.02355e7i) q^{37} +(-2.23181e6 + 1.26572e7i) q^{38} +(1.25276e7 + 4.55968e6i) q^{40} +(-2.01033e7 - 7.31699e6i) q^{41} +(-5.67694e6 + 3.21955e7i) q^{43} +(2.71765e6 + 4.70710e6i) q^{44} +(-1.35476e6 + 2.34652e6i) q^{46} +(-2.96618e7 - 2.48892e7i) q^{47} +(2.90046e6 + 1.64493e7i) q^{49} +(-1.61226e6 + 1.35285e6i) q^{50} +(1.06504e7 - 3.87642e6i) q^{52} -1.00849e7 q^{53} -5.89785e7 q^{55} +(-6.92028e7 + 2.51878e7i) q^{56} +(-8.07715e7 + 6.77753e7i) q^{58} +(2.96301e7 + 1.68041e8i) q^{59} +(-2.42940e7 - 2.03851e7i) q^{61} +(-9.89282e7 + 1.71349e8i) q^{62} +(-4.34616e7 - 7.52777e7i) q^{64} +(-2.13560e7 + 1.21116e8i) q^{65} +(2.06054e8 + 7.49977e7i) q^{67} +(-2.31952e7 - 8.44237e6i) q^{68} +(-4.53041e7 + 2.56932e8i) q^{70} +(1.20690e8 + 2.09042e8i) q^{71} +(-1.68439e8 + 2.91745e8i) q^{73} +(-2.28690e8 - 1.91894e8i) q^{74} +(-1.11344e7 - 6.31466e7i) q^{76} +(2.49576e8 - 2.09419e8i) q^{77} +(-4.25803e8 + 1.54980e8i) q^{79} -4.24969e8 q^{80} +5.40377e8 q^{82} +(5.94638e7 - 2.16430e7i) q^{83} +(2.05181e8 - 1.72167e8i) q^{85} +(-1.43394e8 - 8.13226e8i) q^{86} +(3.22133e8 + 2.70301e8i) q^{88} +(-4.61593e8 + 7.99503e8i) q^{89} +(-3.39684e8 - 5.88350e8i) q^{91} +(2.34733e6 - 1.33124e7i) q^{92} +(9.19062e8 + 3.34511e8i) q^{94} +(6.53815e8 + 2.37969e8i) q^{95} +(6.12907e7 - 3.47597e8i) q^{97} +(-2.10952e8 - 3.65379e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8}+O(q^{10}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23} + 2192178 q^{25} + 33129678 q^{26} - 12 q^{28} - 19657236 q^{29} - 4633692 q^{31} + 37550952 q^{32} + 14341770 q^{34} - 34449663 q^{35} - 3 q^{37} + 92022060 q^{38} + 6645801 q^{40} + 33127221 q^{41} + 2356203 q^{43} - 1001541 q^{44} - 3 q^{46} + 33488952 q^{47} - 93214644 q^{49} + 72027753 q^{50} + 160531713 q^{52} - 4841352 q^{53} - 12 q^{55} + 91770981 q^{56} - 320682489 q^{58} - 538090854 q^{59} + 36683436 q^{61} + 55862958 q^{62} - 956301315 q^{64} + 852347310 q^{65} - 109026897 q^{67} + 508886217 q^{68} - 815297649 q^{70} - 940878639 q^{71} - 221849931 q^{73} - 838884579 q^{74} + 908401146 q^{76} + 967811358 q^{77} - 1228059150 q^{79} + 2497115154 q^{80} - 12 q^{82} + 297703284 q^{83} + 1535949369 q^{85} - 2930201574 q^{86} + 2837227002 q^{88} - 1774997208 q^{89} + 551343507 q^{91} + 6896645517 q^{92} + 414852915 q^{94} + 9000269169 q^{95} + 3371772333 q^{97} - 6901039926 q^{98}+O(q^{100}) \) 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

Modular forms

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Database

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