LMFDB - Embedded newform 81.9.f.a.8.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			8.16
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.24786 + 1.45432i) q^{2} +(-174.649 - 63.5671i) q^{4} +(-723.153 - 861.820i) q^{5} +(2191.55 - 797.660i) q^{7} +(-3204.82 - 1850.30i) q^{8} +(-4711.10 - 8159.87i) q^{10} +(-2798.09 + 3334.63i) q^{11} +(-6274.91 - 35586.8i) q^{13} +(19235.7 - 3391.77i) q^{14} +(12706.1 + 10661.7i) q^{16} +(-32378.2 + 18693.6i) q^{17} +(34340.1 - 59478.9i) q^{19} +(71514.6 + 196485. i) q^{20} +(-27927.9 + 23434.3i) q^{22} +(-148858. + 408984. i) q^{23} +(-151952. + 861764. i) q^{25} -302641. i q^{26} -433458. q^{28} +(-292777. - 51624.5i) q^{29} +(764612. + 278296. i) q^{31} +(698240. + 832130. i) q^{32} +(-294238. + 107094. i) q^{34} +(-2.27227e6 - 1.31189e6i) q^{35} +(-1.13655e6 - 1.96857e6i) q^{37} +(369734. - 440632. i) q^{38} +(722945. + 4.10002e6i) q^{40} +(-1.45417e6 + 256409. i) q^{41} +(1.39504e6 + 1.17057e6i) q^{43} +(700657. - 404524. i) q^{44} +(-1.82256e6 + 3.15676e6i) q^{46} +(647951. + 1.78023e6i) q^{47} +(-249448. + 209312. i) q^{49} +(-2.50656e6 + 6.88672e6i) q^{50} +(-1.16624e6 + 6.61408e6i) q^{52} +6.52907e6i q^{53} +4.89730e6 q^{55} +(-8.49944e6 - 1.49868e6i) q^{56} +(-2.33970e6 - 851583. i) q^{58} +(-1.53319e7 - 1.82719e7i) q^{59} +(1.95580e7 - 7.11851e6i) q^{61} +(5.90169e6 + 3.40734e6i) q^{62} +(2.42571e6 + 4.20146e6i) q^{64} +(-2.61317e7 + 3.11425e7i) q^{65} +(-370662. - 2.10213e6i) q^{67} +(6.84313e6 - 1.20663e6i) q^{68} +(-1.68334e7 - 1.41249e7i) q^{70} +(1.54472e7 - 8.91846e6i) q^{71} +(-1.66329e7 + 2.88091e7i) q^{73} +(-6.51120e6 - 1.78894e7i) q^{74} +(-9.77838e6 + 8.20503e6i) q^{76} +(-3.47226e6 + 9.53995e6i) q^{77} +(-9.65767e6 + 5.47714e7i) q^{79} -1.86604e7i q^{80} -1.23667e7 q^{82} +(5.73546e7 + 1.01132e7i) q^{83} +(3.95249e7 + 1.43859e7i) q^{85} +(9.80367e6 + 1.16836e7i) q^{86} +(1.51374e7 - 5.50958e6i) q^{88} +(4.54337e7 + 2.62311e7i) q^{89} +(-4.21380e7 - 7.29851e7i) q^{91} +(5.19959e7 - 6.19663e7i) q^{92} +(2.75518e6 + 1.56254e7i) q^{94} +(-7.60932e7 + 1.34173e7i) q^{95} +(-7.13382e7 - 5.98599e7i) q^{97} +(-2.36182e6 + 1.36360e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	8.24786	+	1.45432i	0.515491	+	0.0908950i	0.425341	−	0.905033i	$-0.360154\pi$
$2$	8.24786	+	1.45432i	0.515491	+	0.0908950i	0.0901503	+	0.995928i	$0.471265\pi$
$3$		0			0
$3$		0			0
$4$	−174.649	−	63.5671i	−0.682223	−	0.248309i
$5$	−723.153	−	861.820i	−1.15704	−	1.37891i	−0.912400	−	0.409299i	$-0.865773\pi$
$5$	−723.153	−	861.820i	−1.15704	−	1.37891i	−0.244644	−	0.969613i	$-0.578671\pi$
$6$		0			0
$7$	2191.55	−	797.660i	0.912767	−	0.332220i	0.157410	−	0.987533i	$-0.449686\pi$
$7$	2191.55	−	797.660i	0.912767	−	0.332220i	0.755357	+	0.655313i	$0.227463\pi$
$8$	−3204.82	−	1850.30i	−0.782426	−	0.451734i
$9$		0			0
$10$	−4711.10	−	8159.87i	−0.471110	−	0.815987i
$11$	−2798.09	+	3334.63i	−0.191113	+	0.227760i	−0.853089	−	0.521765i	$-0.825274\pi$
$11$	−2798.09	+	3334.63i	−0.191113	+	0.227760i	0.661976	+	0.749525i	$0.269718\pi$
$12$		0			0
$13$	−6274.91	−	35586.8i	−0.219702	−	1.24599i	−0.872558	−	0.488510i	$-0.837541\pi$
$13$	−6274.91	−	35586.8i	−0.219702	−	1.24599i	0.652856	−	0.757482i	$-0.273571\pi$
$14$	19235.7	−	3391.77i	0.500721	−	0.0882906i
$15$		0			0
$16$	12706.1	+	10661.7i	0.193880	+	0.162685i
$17$	−32378.2	+	18693.6i	−0.387666	+	0.223819i	−0.681148	−	0.732145i	$-0.738519\pi$
$17$	−32378.2	+	18693.6i	−0.387666	+	0.223819i	0.293482	+	0.955964i	$0.405186\pi$
$18$		0			0
$19$	34340.1	−	59478.9i	0.263504	−	0.456403i	−0.703666	−	0.710531i	$-0.748455\pi$
$19$	34340.1	−	59478.9i	0.263504	−	0.456403i	0.967171	+	0.254128i	$0.0817883\pi$
$20$	71514.6	+	196485.i	0.446966	+	1.22803i
$21$		0			0
$22$	−27927.9	+	23434.3i	−0.119219	+	0.100037i
$23$	−148858.	+	408984.i	−0.531938	+	1.46149i	0.324823	+	0.945775i	$0.394695\pi$
$23$	−148858.	+	408984.i	−0.531938	+	1.46149i	−0.856761	+	0.515713i	$0.827527\pi$
$24$		0			0
$25$	−151952.	+	861764.i	−0.388998	+	2.20612i
$26$		−	302641.i		−	0.662268i
$27$		0			0
$28$	−433458.			−0.705204
$29$	−292777.	−	51624.5i	−0.413947	−	0.0729900i	−0.0372036	−	0.999308i	$-0.511845\pi$
$29$	−292777.	−	51624.5i	−0.413947	−	0.0729900i	−0.376743	+	0.926318i	$0.622956\pi$
$30$		0			0
$31$	764612.	+	278296.i	0.827932	+	0.301342i	0.721010	−	0.692925i	$-0.243678\pi$
$31$	764612.	+	278296.i	0.827932	+	0.301342i	0.106922	+	0.994267i	$0.465901\pi$
$32$	698240.	+	832130.i	0.665894	+	0.793581i
$33$		0			0
$34$	−294238.	+	107094.i	−0.220182	+	0.0801399i
$35$	−2.27227e6	−	1.31189e6i	−1.51421	−	0.874232i
$36$		0			0
$37$	−1.13655e6	−	1.96857e6i	−0.606432	−	1.05037i	−0.991823	−	0.127618i	$-0.959267\pi$
$37$	−1.13655e6	−	1.96857e6i	−0.606432	−	1.05037i	0.385391	−	0.922753i	$-0.374067\pi$
$38$	369734.	−	440632.i	0.177319	−	0.211321i
$39$		0			0
$40$	722945.	+	4.10002e6i	0.282400	+	1.60157i
$41$	−1.45417e6	+	256409.i	−0.514612	+	0.0907400i	−0.424922	−	0.905230i	$-0.639699\pi$
$41$	−1.45417e6	+	256409.i	−0.514612	+	0.0907400i	−0.0896896	+	0.995970i	$0.528587\pi$
$42$		0			0
$43$	1.39504e6	+	1.17057e6i	0.408048	+	0.342393i	0.823595	−	0.567179i	$-0.191965\pi$
$43$	1.39504e6	+	1.17057e6i	0.408048	+	0.342393i	−0.415546	+	0.909572i	$0.636410\pi$
$44$	700657.	−	404524.i	0.186937	−	0.107928i
$45$		0			0
$46$	−1.82256e6	+	3.15676e6i	−0.407052	+	0.705034i
$47$	647951.	+	1.78023e6i	0.132786	+	0.364825i	0.988210	−	0.153102i	$-0.0489262\pi$
$47$	647951.	+	1.78023e6i	0.132786	+	0.364825i	−0.855425	+	0.517927i	$0.826704\pi$
$48$		0			0
$49$	−249448.	+	209312.i	−0.0432709	+	0.0363086i
$50$	−2.50656e6	+	6.88672e6i	−0.401050	+	1.10188i
$51$		0			0
$52$	−1.16624e6	+	6.61408e6i	−0.159505	+	0.904599i
$53$			6.52907e6i			0.827462i	0.910399	+	0.413731i	$0.135775\pi$
$53$			6.52907e6i			0.827462i	−0.910399	+	0.413731i	$0.864225\pi$
$54$		0			0
$55$	4.89730e6			0.535187
$56$	−8.49944e6	−	1.49868e6i	−0.864247	−	0.152390i
$57$		0			0
$58$	−2.33970e6	−	851583.i	−0.206752	−	0.0752515i
$59$	−1.53319e7	−	1.82719e7i	−1.26528	−	1.50791i	−0.768208	−	0.640200i	$-0.778851\pi$
$59$	−1.53319e7	−	1.82719e7i	−1.26528	−	1.50791i	−0.497076	−	0.867707i	$-0.665593\pi$
$60$		0			0
$61$	1.95580e7	−	7.11851e6i	1.41255	−	0.514126i	0.480673	−	0.876900i	$-0.340392\pi$
$61$	1.95580e7	−	7.11851e6i	1.41255	−	0.514126i	0.931877	+	0.362773i	$0.118170\pi$
$62$	5.90169e6	+	3.40734e6i	0.399401	+	0.230594i
$63$		0			0
$64$	2.42571e6	+	4.20146e6i	0.144584	+	0.250426i
$65$	−2.61317e7	+	3.11425e7i	−1.46391	+	1.74462i
$66$		0			0
$67$	−370662.	−	2.10213e6i	−0.0183941	−	0.104318i	0.974228	−	0.225564i	$-0.0724223\pi$
$67$	−370662.	−	2.10213e6i	−0.0183941	−	0.104318i	−0.992623	+	0.121245i	$0.961311\pi$
$68$	6.84313e6	−	1.20663e6i	0.320051	−	0.0564336i
$69$		0			0
$70$	−1.68334e7	−	1.41249e7i	−0.701101	−	0.588294i
$71$	1.54472e7	−	8.91846e6i	0.607879	−	0.350959i	−0.164256	−	0.986418i	$-0.552522\pi$
$71$	1.54472e7	−	8.91846e6i	0.607879	−	0.350959i	0.772135	+	0.635459i	$0.219189\pi$
$72$		0			0
$73$	−1.66329e7	+	2.88091e7i	−0.585703	+	1.01447i	0.409084	+	0.912497i	$0.365848\pi$
$73$	−1.66329e7	+	2.88091e7i	−0.585703	+	1.01447i	−0.994787	+	0.101971i	$0.967485\pi$
$74$	−6.51120e6	−	1.78894e7i	−0.217137	−	0.596579i
$75$		0			0
$76$	−9.77838e6	+	8.20503e6i	−0.293098	+	0.245938i
$77$	−3.47226e6	+	9.53995e6i	−0.0987755	+	0.271383i
$78$		0			0
$79$	−9.65767e6	+	5.47714e7i	−0.247950	+	1.40619i	0.565591	+	0.824686i	$0.308648\pi$
$79$	−9.65767e6	+	5.47714e7i	−0.247950	+	1.40619i	−0.813541	+	0.581508i	$0.802463\pi$
$80$		−	1.86604e7i		−	0.455577i
$81$		0			0
$82$	−1.23667e7			−0.273526
$83$	5.73546e7	+	1.01132e7i	1.20853	+	0.213096i	0.741381	−	0.671085i	$-0.234171\pi$
$83$	5.73546e7	+	1.01132e7i	1.20853	+	0.213096i	0.467145	+	0.884181i	$0.345283\pi$
$84$		0			0
$85$	3.95249e7	+	1.43859e7i	0.757173	+	0.275588i
$86$	9.80367e6	+	1.16836e7i	0.179223	+	0.213590i
$87$		0			0
$88$	1.51374e7	−	5.50958e6i	0.252419	−	0.0918729i
$89$	4.54337e7	+	2.62311e7i	0.724132	+	0.418078i	0.816272	−	0.577668i	$-0.196037\pi$
$89$	4.54337e7	+	2.62311e7i	0.724132	+	0.418078i	−0.0921395	+	0.995746i	$0.529371\pi$
$90$		0			0
$91$	−4.21380e7	−	7.29851e7i	−0.614480	−	1.06431i
$92$	5.19959e7	−	6.19663e7i	0.725801	−	0.864976i
$93$		0			0
$94$	2.75518e6	+	1.56254e7i	0.0352890	+	0.200134i
$95$	−7.60932e7	+	1.34173e7i	−0.934225	+	0.164729i
$96$		0			0
$97$	−7.13382e7	−	5.98599e7i	−0.805815	−	0.676159i	0.143790	−	0.989608i	$-0.454071\pi$
$97$	−7.13382e7	−	5.98599e7i	−0.805815	−	0.676159i	−0.949605	+	0.313449i	$0.898515\pi$
$98$	−2.36182e6	+	1.36360e6i	−0.0256061	+	0.0147837i
$99$		0			0
$100$	8.13181e7	−	1.40847e8i	0.813181	−	1.40847i
$101$	−2.69891e7	−	7.41520e7i	−0.259360	−	0.712586i	−0.999207	−	0.0398109i	$-0.987324\pi$
$101$	−2.69891e7	−	7.41520e7i	−0.259360	−	0.712586i	0.739847	−	0.672775i	$-0.234898\pi$
$102$		0			0
$103$	1.12352e8	−	9.42747e7i	0.998234	−	0.837618i	0.0114956	−	0.999934i	$-0.496341\pi$
$103$	1.12352e8	−	9.42747e7i	0.998234	−	0.837618i	0.986739	+	0.162316i	$0.0518963\pi$
$104$	−4.57363e7	+	1.25660e8i	−0.390956	+	1.07414i
$105$		0			0
$106$	−9.49536e6	+	5.38509e7i	−0.0752122	+	0.426549i
$107$		−	1.20604e8i		−	0.920086i	−0.887897	−	0.460043i	$-0.847834\pi$
$107$		−	1.20604e8i		−	0.920086i	0.887897	−	0.460043i	$-0.152166\pi$
$108$		0			0
$109$	−2.72284e8			−1.92893			−0.964465	−	0.264212i	$-0.914888\pi$
$109$	−2.72284e8			−1.92893			−0.964465	+	0.264212i	$0.914888\pi$
$110$	4.03922e7	+	7.12224e6i	0.275884	+	0.0486459i
$111$		0			0
$112$	3.63506e7	+	1.32305e7i	0.231014	+	0.0840824i
$113$	4.31308e7	+	5.14013e7i	0.264529	+	0.315254i	0.881917	−	0.471406i	$-0.156253\pi$
$113$	4.31308e7	+	5.14013e7i	0.264529	+	0.315254i	−0.617387	+	0.786659i	$0.711809\pi$
$114$		0			0
$115$	4.60118e8	−	1.67469e8i	2.63074	−	0.957511i
$116$	4.78516e7	+	2.76271e7i	0.264280	+	0.152582i
$117$		0			0
$118$	−9.98823e7	−	1.73001e8i	−0.515182	−	0.892321i
$119$	−5.60475e7	+	6.67948e7i	−0.279491	+	0.333085i
$120$		0			0
$121$	3.39326e7	+	1.92441e8i	0.158298	+	0.897752i
$122$	1.71664e8	−	3.02690e7i	0.774889	−	0.136634i
$123$		0			0
$124$	−1.15848e8	−	9.72083e7i	−0.490008	−	0.411166i
$125$	4.71984e8	−	2.72500e8i	1.93324	−	1.11616i
$126$		0			0
$127$	−2.33715e7	+	4.04807e7i	−0.0898405	+	0.155608i	−0.907444	−	0.420174i	$-0.861969\pi$
$127$	−2.33715e7	+	4.04807e7i	−0.0898405	+	0.155608i	0.817603	+	0.575782i	$0.195302\pi$
$128$	−8.12140e7	−	2.23134e8i	−0.302546	−	0.831237i
$129$		0			0
$130$	−2.60822e8	+	2.18855e8i	−0.913209	+	0.766273i
$131$	6.93121e7	−	1.90433e8i	0.235355	−	0.646633i	−0.764643	−	0.644455i	$-0.777084\pi$
$131$	6.93121e7	−	1.90433e8i	0.235355	−	0.646633i	0.999998	−	0.00217818i	$-0.000693337\pi$
$132$		0			0
$133$	2.78143e7	−	1.57743e8i	0.0888919	−	0.504131i
$134$		−	1.78771e7i		−	0.0554470i
$135$		0			0
$136$	1.38355e8			0.404426
$137$	−5.65911e8	−	9.97854e7i	−1.60645	−	0.283260i	−0.702751	−	0.711436i	$-0.748045\pi$
$137$	−5.65911e8	−	9.97854e7i	−1.60645	−	0.283260i	−0.903695	+	0.428176i	$0.859156\pi$
$138$		0			0
$139$	−3.84931e8	−	1.40103e8i	−1.03115	−	0.375309i	−0.229634	−	0.973277i	$-0.573753\pi$
$139$	−3.84931e8	−	1.40103e8i	−1.03115	−	0.375309i	−0.801520	+	0.597968i	$0.795975\pi$
$140$	3.13456e8	+	3.73563e8i	0.815952	+	0.972414i
$141$		0			0
$142$	1.40377e8	−	5.10930e7i	0.345257	−	0.125663i
$143$	1.36227e8	+	7.86505e7i	0.325775	+	0.188086i
$144$		0			0
$145$	1.67231e8	+	2.89653e8i	0.378308	+	0.655249i
$146$	−1.79084e8	+	2.13424e8i	−0.394135	+	0.469712i
$147$		0			0
$148$	7.33618e7	+	4.16056e8i	0.152906	+	0.867171i
$149$	−7.36420e8	+	1.29851e8i	−1.49410	+	0.263451i	−0.860198	−	0.509960i	$-0.829660\pi$
$149$	−7.36420e8	+	1.29851e8i	−1.49410	+	0.263451i	−0.633905	+	0.773411i	$0.718549\pi$
$150$		0			0
$151$	5.25046e8	+	4.40566e8i	1.00993	+	0.847428i	0.988328	−	0.152338i	$-0.0486804\pi$
$151$	5.25046e8	+	4.40566e8i	1.00993	+	0.847428i	0.0215973	+	0.999767i	$0.493125\pi$
$152$	−2.20108e8	+	1.27079e8i	−0.412345	+	0.238068i
$153$		0			0
$154$	−4.25129e7	+	7.36344e7i	−0.0755853	+	0.130918i
$155$	−3.13090e8	−	8.60209e8i	−0.542429	−	1.49031i
$156$		0			0
$157$	−6.35963e8	+	5.33636e8i	−1.04673	+	0.878308i	−0.992746	−	0.120234i	$-0.961635\pi$
$157$	−6.35963e8	+	5.33636e8i	−1.04673	+	0.878308i	−0.0539807	+	0.998542i	$0.517191\pi$
$158$	−1.59310e8	+	4.37702e8i	−0.255632	+	0.702344i
$159$		0			0
$160$	2.12212e8	−	1.20351e9i	0.323810	−	1.83642i
$161$			1.01505e9i			1.51072i
$162$		0			0
$163$	−5.47300e8			−0.775310			−0.387655	−	0.921805i	$-0.626715\pi$
$163$	−5.47300e8			−0.775310			−0.387655	+	0.921805i	$0.626715\pi$
$164$	2.70269e8	+	4.76557e7i	0.373612	+	0.0658778i
$165$		0			0
$166$	4.58345e8	+	1.66824e8i	0.603615	+	0.219698i
$167$	2.33736e8	+	2.78556e8i	0.300511	+	0.358134i	0.895077	−	0.445912i	$-0.147121\pi$
$167$	2.33736e8	+	2.78556e8i	0.300511	+	0.358134i	−0.594566	+	0.804047i	$0.702676\pi$
$168$		0			0
$169$	−4.60508e8	+	1.67611e8i	−0.564535	+	0.205474i
$170$	3.05074e8	+	1.76135e8i	0.365267	+	0.210887i
$171$		0			0
$172$	−1.69232e8	−	2.93118e8i	−0.193361	−	0.334910i
$173$	−3.34053e8	+	3.98109e8i	−0.372933	+	0.444445i	−0.919571	−	0.392925i	$-0.871463\pi$
$173$	−3.34053e8	+	3.98109e8i	−0.372933	+	0.444445i	0.546637	+	0.837370i	$0.315908\pi$
$174$		0			0
$175$	3.54383e8	+	2.00981e9i	0.377852	+	2.14290i
$176$	−7.11057e7	+	1.25379e7i	−0.0741061	+	0.0130669i
$177$		0			0
$178$	3.36582e8	+	2.82426e8i	0.335283	+	0.281336i
$179$	3.90561e8	−	2.25491e8i	0.380432	−	0.219642i	−0.297574	−	0.954699i	$-0.596178\pi$
$179$	3.90561e8	−	2.25491e8i	0.380432	−	0.219642i	0.678006	+	0.735056i	$0.262844\pi$
$180$		0			0
$181$	−5.83299e8	+	1.01030e9i	−0.543472	+	0.941320i	0.455230	+	0.890374i	$0.349557\pi$
$181$	−5.83299e8	+	1.01030e9i	−0.543472	+	0.941320i	−0.998701	+	0.0509464i	$0.983776\pi$
$182$	−2.41404e8	−	6.63253e8i	−0.220019	−	0.604496i
$183$		0			0
$184$	1.23381e9	−	1.03529e9i	1.07641	−	0.903212i
$185$	−8.74648e8	+	2.40308e9i	−0.746701	+	2.05154i
$186$		0			0
$187$	2.82610e7	−	1.60276e8i	0.0231111	−	0.131070i
$188$		−	3.52104e8i		−	0.281864i
$189$		0			0
$190$	−6.47120e8			−0.496558
$191$	−6.23017e8	−	1.09855e8i	−0.468130	−	0.0825439i	−0.0653926	−	0.997860i	$-0.520830\pi$
$191$	−6.23017e8	−	1.09855e8i	−0.468130	−	0.0825439i	−0.402737	+	0.915316i	$0.631941\pi$
$192$		0			0
$193$	4.83654e7	+	1.76036e7i	0.0348583	+	0.0126874i	0.359390	−	0.933187i	$-0.382985\pi$
$193$	4.83654e7	+	1.76036e7i	0.0348583	+	0.0126874i	−0.324532	+	0.945875i	$0.605207\pi$
$194$	−5.01332e8	−	5.97465e8i	−0.353931	−	0.421799i
$195$		0			0
$196$	5.68713e7	−	2.06994e7i	0.0385362	−	0.0140260i
$197$	−1.06838e9	−	6.16830e8i	−0.709351	−	0.409544i	0.101470	−	0.994839i	$-0.467646\pi$
$197$	−1.06838e9	−	6.16830e8i	−0.709351	−	0.409544i	−0.810821	+	0.585295i	$0.800979\pi$
$198$		0			0
$199$	−1.12322e9	−	1.94548e9i	−0.716231	−	1.24055i	−0.962483	−	0.271343i	$-0.912532\pi$
$199$	−1.12322e9	−	1.94548e9i	−0.716231	−	1.24055i	0.246251	−	0.969206i	$-0.420801\pi$
$200$	2.08150e9	−	2.48064e9i	1.30094	−	1.55040i
$201$		0			0
$202$	−1.14762e8	−	6.50846e8i	−0.0689274	−	0.390906i
$203$	−6.82815e8	+	1.20399e8i	−0.402086	+	0.0708986i
$204$		0			0
$205$	1.27257e9	+	1.06781e9i	0.720551	+	0.604614i
$206$	1.06377e9	−	6.14168e8i	0.590717	−	0.341050i
$207$		0			0
$208$	2.99686e8	−	5.19071e8i	0.160108	−	0.277315i
$209$	1.02253e8	+	2.80939e8i	0.0535911	+	0.147240i
$210$		0			0
$211$	−2.64889e8	+	2.22268e8i	−0.133639	+	0.112137i	−0.707157	−	0.707056i	$-0.750023\pi$
$211$	−2.64889e8	+	2.22268e8i	−0.133639	+	0.112137i	0.573518	+	0.819193i	$0.305578\pi$
$212$	4.15034e8	−	1.14030e9i	0.205466	−	0.564513i
$213$		0			0
$214$	1.75398e8	−	9.94729e8i	0.0836312	−	0.474296i
$215$		−	2.04877e9i		−	0.958826i
$216$		0			0
$217$	1.89767e9			0.855821
$218$	−2.24576e9	−	3.95988e8i	−0.994346	−	0.175330i
$219$		0			0
$220$	−8.55309e8	−	3.11307e8i	−0.365117	−	0.132892i
$221$	8.68415e8	+	1.03494e9i	0.364048	+	0.433855i
$222$		0			0
$223$	−1.74659e9	+	6.35708e8i	−0.706273	+	0.257062i	−0.670087	−	0.742283i	$-0.733743\pi$
$223$	−1.74659e9	+	6.35708e8i	−0.706273	+	0.257062i	−0.0361862	+	0.999345i	$0.511521\pi$
$224$	2.19399e9	+	1.26670e9i	0.871450	+	0.503132i
$225$		0			0
$226$	2.80983e8	+	4.86677e8i	0.107708	+	0.186555i
$227$	−7.82998e8	+	9.33140e8i	−0.294888	+	0.351434i	−0.893063	−	0.449932i	$-0.851448\pi$
$227$	−7.82998e8	+	9.33140e8i	−0.294888	+	0.351434i	0.598175	+	0.801365i	$0.295893\pi$
$228$		0			0
$229$	2.81289e8	+	1.59527e9i	0.102285	+	0.580086i	0.992270	+	0.124097i	$0.0396033\pi$
$229$	2.81289e8	+	1.59527e9i	0.102285	+	0.580086i	−0.889985	+	0.455989i	$0.849286\pi$
$230$	4.03854e9	−	7.12104e8i	1.44316	−	0.254467i
$231$		0			0
$232$	8.42775e8	+	7.07172e8i	0.290911	+	0.244103i
$233$	2.41883e8	−	1.39651e8i	0.0820695	−	0.0473828i	−0.458404	−	0.888744i	$-0.651579\pi$
$233$	2.41883e8	−	1.39651e8i	0.0820695	−	0.0473828i	0.540473	+	0.841361i	$0.318245\pi$
$234$		0			0
$235$	1.06567e9	−	1.84580e9i	0.349423	−	0.605218i
$236$	1.51622e9	+	4.16577e9i	0.488779	+	1.34291i
$237$		0			0
$238$	−5.59413e8	+	4.69404e8i	−0.174351	+	0.146298i
$239$	2.08449e8	−	5.72709e8i	0.0638864	−	0.175526i	−0.903642	−	0.428288i	$-0.859117\pi$
$239$	2.08449e8	−	5.72709e8i	0.0638864	−	0.175526i	0.967528	+	0.252762i	$0.0813390\pi$
$240$		0			0
$241$	5.19762e8	−	2.94772e9i	0.154076	−	0.873811i	−0.805549	−	0.592529i	$-0.798129\pi$
$241$	5.19762e8	−	2.94772e9i	0.154076	−	0.873811i	0.959625	−	0.281281i	$-0.0907594\pi$
$242$			1.63658e9i			0.477172i
$243$		0			0
$244$	−3.86828e9			−1.09134
$245$	3.60778e8	+	6.36150e7i	0.100133	+	0.0176561i
$246$		0			0
$247$	−2.33214e9	−	8.48831e8i	−0.626567	−	0.228052i
$248$	−1.93551e9	−	2.30665e9i	−0.511668	−	0.609783i
$249$		0			0
$250$	4.28916e9	−	1.56113e9i	1.09802	−	0.399648i
$251$	−8.66654e8	−	5.00363e8i	−0.218349	−	0.126064i	0.386837	−	0.922148i	$-0.373568\pi$
$251$	−8.66654e8	−	5.00363e8i	−0.218349	−	0.126064i	−0.605185	+	0.796085i	$0.706901\pi$
$252$		0			0
$253$	−9.47294e8	−	1.64076e9i	−0.231208	−	0.400464i
$254$	−2.51637e8	+	2.99889e8i	−0.0604560	+	0.0720487i
$255$		0			0
$256$	−5.60999e8	−	3.18158e9i	−0.130618	−	0.740770i
$257$	−5.28366e8	+	9.31651e7i	−0.121116	+	0.0213561i	−0.233878	−	0.972266i	$-0.575142\pi$
$257$	−5.28366e8	+	9.31651e7i	−0.121116	+	0.0213561i	0.112761	+	0.993622i	$0.464030\pi$
$258$		0			0
$259$	−4.06106e9	−	3.40764e9i	−0.902486	−	0.757276i
$260$	6.54351e9	−	3.77790e9i	1.43192	−	0.826717i
$261$		0			0
$262$	8.48627e8	−	1.46987e9i	0.180099	−	0.311941i
$263$	−4.02022e7	−	1.10455e8i	−0.00840286	−	0.0230867i	0.935420	−	0.353538i	$-0.115021\pi$
$263$	−4.02022e7	−	1.10455e8i	−0.00840286	−	0.0230867i	−0.943823	+	0.330451i	$0.892799\pi$
$264$		0			0
$265$	5.62688e9	−	4.72151e9i	1.14100	−	0.957410i
$266$	4.58818e8	−	1.26059e9i	0.0916460	−	0.251795i
$267$		0			0
$268$	−6.88903e7	+	3.90696e8i	−0.0133542	+	0.0757356i
$269$			3.54894e9i			0.677781i	0.940826	+	0.338890i	$0.110052\pi$
$269$			3.54894e9i			0.677781i	−0.940826	+	0.338890i	$0.889948\pi$
$270$		0			0
$271$	2.25698e9			0.418456			0.209228	−	0.977867i	$-0.432905\pi$
$271$	2.25698e9			0.418456			0.209228	+	0.977867i	$0.432905\pi$
$272$	−6.10707e8	−	1.07684e8i	−0.111573	−	0.0196733i
$273$		0			0
$274$	−4.52244e9	−	1.64603e9i	−0.802362	−	0.292036i
$275$	−2.44849e9	−	2.91800e9i	−0.428122	−	0.510216i
$276$		0			0
$277$	−3.66946e9	+	1.33557e9i	−0.623280	+	0.226855i	−0.634304	−	0.773084i	$-0.718713\pi$
$277$	−3.66946e9	+	1.33557e9i	−0.623280	+	0.226855i	0.0110239	+	0.999939i	$0.496491\pi$
$278$	−2.97110e9	−	1.71537e9i	−0.497437	−	0.287195i
$279$		0			0
$280$	4.85480e9	+	8.40876e9i	0.789840	+	1.36804i
$281$	−1.16091e8	+	1.38352e8i	−0.0186198	+	0.0221902i	−0.775274	−	0.631625i	$-0.782388\pi$
$281$	−1.16091e8	+	1.38352e8i	−0.0186198	+	0.0221902i	0.756654	+	0.653815i	$0.226833\pi$
$282$		0			0
$283$	1.07604e9	+	6.10253e9i	0.167758	+	0.951402i	0.946175	+	0.323655i	$0.104912\pi$
$283$	1.07604e9	+	6.10253e9i	0.167758	+	0.951402i	−0.778417	+	0.627747i	$0.783977\pi$
$284$	−3.26476e9	+	5.75666e8i	−0.501855	+	0.0884906i
$285$		0			0
$286$	1.00920e9	+	8.46815e8i	0.150838	+	0.126568i
$287$	−2.98236e9	+	1.72187e9i	−0.439575	+	0.253789i
$288$		0			0
$289$	−2.78898e9	+	4.83065e9i	−0.399810	+	0.692491i
$290$	9.58053e8	+	2.63223e9i	0.135456	+	0.372162i
$291$		0			0
$292$	4.73624e9	−	3.97418e9i	0.651482	−	0.546658i
$293$	2.18993e9	−	6.01679e9i	0.297139	−	0.816383i	−0.697836	−	0.716258i	$-0.745853\pi$
$293$	2.18993e9	−	6.01679e9i	0.297139	−	0.816383i	0.994975	−	0.100125i	$-0.0319244\pi$
$294$		0			0
$295$	−4.65974e9	+	2.64267e10i	−0.615281	+	3.48943i
$296$			8.41185e9i			1.09578i
$297$		0			0
$298$	−6.26274e9			−0.794144
$299$	1.54885e10	+	2.73104e9i	1.93787	+	0.341699i
$300$		0			0
$301$	3.99102e9	+	1.45261e9i	0.486203	+	0.176963i
$302$	3.68978e9	+	4.39731e9i	0.443581	+	0.528639i
$303$		0			0
$304$	1.07048e9	−	3.89622e8i	0.125338	−	0.0456193i
$305$	−2.02783e10	−	1.17077e10i	−2.34332	−	1.35292i
$306$		0			0
$307$	3.63881e8	+	6.30261e8i	0.0409644	+	0.0709524i	0.885781	−	0.464104i	$-0.153624\pi$
$307$	3.63881e8	+	6.30261e8i	0.0409644	+	0.0709524i	−0.844816	+	0.535056i	$0.820290\pi$
$308$	1.21285e9	−	1.44542e9i	0.134774	−	0.160617i
$309$		0			0
$310$	−1.33131e9	−	7.55022e9i	−0.144156	−	0.817547i
$311$	−5.69479e9	+	1.00414e9i	−0.608746	+	0.107338i	−0.469519	−	0.882922i	$-0.655573\pi$
$311$	−5.69479e9	+	1.00414e9i	−0.608746	+	0.107338i	−0.139227	+	0.990261i	$0.544462\pi$
$312$		0			0
$313$	−1.12798e10	−	9.46487e9i	−1.17523	−	0.986137i	−0.999999	−	0.00161011i	$-0.999487\pi$
$313$	−1.12798e10	−	9.46487e9i	−1.17523	−	0.986137i	−0.175234	−	0.984527i	$-0.556068\pi$
$314$	−6.02141e9	+	3.47646e9i	−0.619412	+	0.357618i
$315$		0			0
$316$	5.16836e9	−	8.95186e9i	0.518328	−	0.897770i
$317$	2.34590e9	+	6.44530e9i	0.232312	+	0.638272i	0.999997	−	0.00255559i	$-0.000813471\pi$
$317$	2.34590e9	+	6.44530e9i	0.232312	+	0.638272i	−0.767685	+	0.640828i	$0.778591\pi$
$318$		0			0
$319$	9.91364e8	−	8.31854e8i	0.0957350	−	0.0803312i
$320$	1.86674e9	−	5.12882e9i	0.178026	−	0.489123i
$321$		0			0
$322$	−1.47621e9	+	8.37199e9i	−0.137317	+	0.778763i
$323$			2.56776e9i			0.235909i
$324$		0			0
$325$	3.16209e10			2.83427
$326$	−4.51406e9	−	7.95950e8i	−0.399666	−	0.0704718i
$327$		0			0
$328$	5.13478e9	+	1.86891e9i	0.443636	+	0.161470i
$329$	2.84004e9	+	3.38463e9i	0.242405	+	0.288886i
$330$		0			0
$331$	−7.96602e9	+	2.89939e9i	−0.663635	+	0.241543i	−0.651805	−	0.758387i	$-0.725988\pi$
$331$	−7.96602e9	+	2.89939e9i	−0.663635	+	0.241543i	−0.0118300	+	0.999930i	$0.503766\pi$
$332$	−9.37407e9	−	5.41212e9i	−0.771571	−	0.445467i
$333$		0			0
$334$	1.52271e9	+	2.63742e9i	0.122358	+	0.211930i
$335$	−1.54361e9	+	1.83960e9i	−0.122563	+	0.146065i
$336$		0			0
$337$	−2.39583e9	−	1.35874e10i	−0.185753	−	1.05346i	−0.924984	−	0.380006i	$-0.875922\pi$
$337$	−2.39583e9	−	1.35874e10i	−0.185753	−	1.05346i	0.739231	−	0.673452i	$-0.235189\pi$
$338$	−4.04197e9	+	7.12708e8i	−0.309689	+	0.0546066i
$339$		0			0
$340$	−5.98852e9	−	5.02497e9i	−0.448130	−	0.376026i
$341$	−3.06747e9	+	1.77100e9i	−0.226862	+	0.130979i
$342$		0			0
$343$	−7.10206e9	+	1.23011e10i	−0.513107	+	0.888727i
$344$	−2.30492e9	−	6.33271e9i	−0.164597	−	0.452226i
$345$		0			0
$346$	−3.33420e9	+	2.79773e9i	−0.232642	+	0.195210i
$347$	1.10725e8	−	3.04213e8i	0.00763706	−	0.0209826i	−0.935816	−	0.352490i	$-0.885335\pi$
$347$	1.10725e8	−	3.04213e8i	0.00763706	−	0.0209826i	0.943453	+	0.331508i	$0.107557\pi$
$348$		0			0
$349$	2.48752e9	−	1.41074e10i	0.167673	−	0.950923i	−0.778592	−	0.627531i	$-0.784066\pi$
$349$	2.48752e9	−	1.41074e10i	0.167673	−	0.950923i	0.946265	−	0.323392i	$-0.104823\pi$
$350$			1.70920e10i			1.13899i
$351$		0			0
$352$	−4.72859e9			−0.308007
$353$	−7.08502e9	−	1.24928e9i	−0.456291	−	0.0804565i	−0.0592215	−	0.998245i	$-0.518862\pi$
$353$	−7.08502e9	−	1.24928e9i	−0.456291	−	0.0804565i	−0.397070	+	0.917788i	$0.629973\pi$
$354$		0			0
$355$	−1.88568e10	−	6.86331e9i	−1.18728	−	0.432136i
$356$	−6.26751e9	−	7.46933e9i	−0.390207	−	0.465031i
$357$		0			0
$358$	3.54923e9	−	1.29181e9i	0.216074	−	0.0786444i
$359$	7.51187e9	+	4.33698e9i	0.452242	+	0.261102i	0.708776	−	0.705433i	$-0.249247\pi$
$359$	7.51187e9	+	4.33698e9i	0.452242	+	0.261102i	−0.256535	+	0.966535i	$0.582581\pi$
$360$		0			0
$361$	6.13329e9	+	1.06232e10i	0.361131	+	0.625497i
$362$	−6.28027e9	+	7.48454e9i	−0.365716	+	0.435844i
$363$		0			0
$364$	2.71991e9	+	1.54254e10i	0.154935	+	0.878679i
$365$	3.68564e10	−	6.49878e9i	2.07655	−	0.366151i
$366$		0			0
$367$	1.47566e10	+	1.23822e10i	0.813432	+	0.682551i	0.951424	−	0.307883i	$-0.0996204\pi$
$367$	1.47566e10	+	1.23822e10i	0.813432	+	0.682551i	−0.137992	+	0.990433i	$0.544065\pi$
$368$	−6.25188e9	+	3.60952e9i	−0.340894	+	0.196815i
$369$		0			0
$370$	−1.07088e10	+	1.85482e10i	−0.571393	+	0.989682i
$371$	5.20798e9	+	1.43088e10i	0.274899	+	0.755280i
$372$		0			0
$373$	−8.42335e9	+	7.06803e9i	−0.435161	+	0.365143i	−0.833895	−	0.551923i	$-0.813894\pi$
$373$	−8.42335e9	+	7.06803e9i	−0.435161	+	0.365143i	0.398734	+	0.917067i	$0.369450\pi$
$374$	4.66185e8	−	1.28083e9i	0.0238271	−	0.0654645i
$375$		0			0
$376$	1.21740e9	−	6.90422e9i	0.0609090	−	0.345432i
$377$			1.07429e10i			0.531811i
$378$		0			0
$379$	3.72517e9			0.180546			0.0902732	−	0.995917i	$-0.471226\pi$
$379$	3.72517e9			0.180546			0.0902732	+	0.995917i	$0.471226\pi$
$380$	1.41425e10	+	2.49371e9i	0.678254	+	0.119594i
$381$		0			0
$382$	−4.97879e9	−	1.81213e9i	−0.233814	−	0.0851013i
$383$	−1.28156e10	−	1.52730e10i	−0.595586	−	0.709791i	0.381084	−	0.924541i	$-0.375551\pi$
$383$	−1.28156e10	−	1.52730e10i	−0.595586	−	0.709791i	−0.976669	+	0.214749i	$0.931107\pi$
$384$		0			0
$385$	1.07327e10	−	3.90638e9i	0.488501	−	0.177800i
$386$	3.73310e8	+	2.15531e8i	0.0168159	+	0.00970868i
$387$		0			0
$388$	8.65404e9	+	1.49892e10i	0.381849	+	0.661382i
$389$	−1.15508e10	+	1.37657e10i	−0.504446	+	0.601175i	−0.956830	−	0.290648i	$-0.906129\pi$
$389$	−1.15508e10	+	1.37657e10i	−0.504446	+	0.601175i	0.452384	+	0.891823i	$0.350573\pi$
$390$		0			0
$391$	−2.82562e9	−	1.60249e10i	−0.120895	−	0.685627i
$392$	1.18673e9	−	2.09252e8i	0.0502581	−	0.00886186i
$393$		0			0
$394$	−7.91479e9	−	6.64130e9i	−0.328439	−	0.275593i
$395$	5.41870e10	−	3.12849e10i	2.22591	−	1.28513i
$396$		0			0
$397$	1.47034e10	−	2.54670e10i	0.591909	−	1.02522i	−0.402066	−	0.915611i	$-0.631708\pi$
$397$	1.47034e10	−	2.54670e10i	0.591909	−	1.02522i	0.993975	−	0.109606i	$-0.0349590\pi$
$398$	−6.43483e9	−	1.76796e10i	−0.256451	−	0.704594i
$399$		0			0
$400$	−1.11186e10	+	9.32961e9i	−0.434320	+	0.364438i
$401$	9.86675e9	−	2.71087e10i	0.381590	−	1.04841i	−0.589097	−	0.808062i	$-0.700517\pi$
$401$	9.86675e9	−	2.71087e10i	0.381590	−	1.04841i	0.970687	−	0.240347i	$-0.0772613\pi$
$402$		0			0
$403$	5.10579e9	−	2.89564e10i	0.193572	−	1.09780i
$404$			1.46662e10i			0.550544i
$405$		0			0
$406$	−5.80686e9			−0.213716
$407$	9.74462e9	+	1.71824e9i	0.355130	+	0.0626190i
$408$		0			0
$409$	−1.33883e10	−	4.87296e9i	−0.478447	−	0.174140i	0.0915282	−	0.995802i	$-0.470825\pi$
$409$	−1.33883e10	−	4.87296e9i	−0.478447	−	0.174140i	−0.569975	+	0.821662i	$0.693047\pi$
$410$	8.94301e9	+	1.06579e10i	0.316482	+	0.377168i
$411$		0			0
$412$	−2.56150e10	+	9.32309e9i	−0.889007	+	0.323572i
$413$	−4.81754e10	−	2.78141e10i	−1.65587	−	0.956015i
$414$		0			0
$415$	−3.27604e10	−	5.67427e10i	−1.10448	−	1.91301i
$416$	2.52314e10	−	3.00697e10i	0.842498	−	1.00405i
$417$		0			0
$418$	4.34797e8	+	2.46586e9i	0.0142423	+	0.0807723i
$419$	3.80542e9	−	6.70998e8i	0.123466	−	0.0217703i	−0.111574	−	0.993756i	$-0.535589\pi$
$419$	3.80542e9	−	6.70998e8i	0.123466	−	0.0217703i	0.235040	+	0.971986i	$0.424478\pi$
$420$		0			0
$421$	2.36141e10	+	1.98145e10i	0.751696	+	0.630748i	0.935951	−	0.352131i	$-0.114543\pi$
$421$	2.36141e10	+	1.98145e10i	0.751696	+	0.630748i	−0.184255	+	0.982878i	$0.558987\pi$
$422$	−2.50802e9	+	1.44801e9i	−0.0790826	+	0.0456584i
$423$		0			0
$424$	1.20807e10	−	2.09245e10i	0.373792	−	0.647427i
$425$	−1.11895e10	−	3.07429e10i	−0.342969	−	0.942301i
$426$		0			0
$427$	3.71842e10	−	3.12012e10i	1.11853	−	0.938555i
$428$	−7.66647e9	+	2.10635e10i	−0.228465	+	0.627704i
$429$		0			0
$430$	2.97957e9	−	1.68980e10i	0.0871526	−	0.494267i
$431$			2.11816e9i			0.0613832i	0.999529	+	0.0306916i	$0.00977098\pi$
$431$			2.11816e9i			0.0613832i	−0.999529	+	0.0306916i	$0.990229\pi$
$432$		0			0
$433$	2.28664e10			0.650497			0.325249	−	0.945629i	$-0.394552\pi$
$433$	2.28664e10			0.650497			0.325249	+	0.945629i	$0.394552\pi$
$434$	1.56518e10	+	2.75983e9i	0.441168	+	0.0777899i
$435$		0			0
$436$	4.75542e10	+	1.73083e10i	1.31596	+	0.478970i
$437$	1.92141e10	+	2.28985e10i	0.526859	+	0.627887i
$438$		0			0
$439$	−3.91566e10	+	1.42518e10i	−1.05426	+	0.383718i	−0.810268	−	0.586060i	$-0.800678\pi$
$439$	−3.91566e10	+	1.42518e10i	−1.05426	+	0.383718i	−0.243989	+	0.969778i	$0.578456\pi$
$440$	−1.56949e10	−	9.06148e9i	−0.418744	−	0.241762i
$441$		0			0
$442$	5.65744e9	+	9.79897e9i	0.148228	+	0.256739i
$443$	−2.04217e10	+	2.43376e10i	−0.530245	+	0.631922i	−0.962971	−	0.269604i	$-0.913107\pi$
$443$	−2.04217e10	+	2.43376e10i	−0.530245	+	0.631922i	0.432726	+	0.901525i	$0.357552\pi$
$444$		0			0
$445$	−1.02490e10	−	5.81248e10i	−0.261360	−	1.48225i
$446$	−1.53302e10	+	2.70313e9i	−0.387443	+	0.0683167i
$447$		0			0
$448$	8.66741e9	+	7.27282e9i	0.215168	+	0.180547i
$449$	6.82298e10	−	3.93925e10i	1.67876	−	0.969233i	0.716309	−	0.697784i	$-0.245830\pi$
$449$	6.82298e10	−	3.93925e10i	1.67876	−	0.969233i	0.962453	−	0.271450i	$-0.0875030\pi$
$450$		0			0
$451$	3.21387e9	−	5.56658e9i	0.0776822	−	0.134550i
$452$	−4.26533e9	−	1.17189e10i	−0.102188	−	0.280759i
$453$		0			0
$454$	−7.81514e9	+	6.55768e9i	−0.183956	+	0.154357i
$455$	−3.24278e10	+	8.90947e10i	−0.756610	+	2.07877i
$456$		0			0
$457$	4.45048e8	−	2.52399e9i	0.0102033	−	0.0578660i	−0.979281	−	0.202506i	$-0.935091\pi$
$457$	4.45048e8	−	2.52399e9i	0.0102033	−	0.0578660i	0.989484	+	0.144640i	$0.0462025\pi$
$458$			1.35666e10i			0.308326i
$459$		0			0
$460$	−9.10047e10			−2.03251
$461$	2.71507e10	+	4.78740e9i	0.601142	+	0.105998i	0.465934	−	0.884820i	$-0.345719\pi$
$461$	2.71507e10	+	4.78740e9i	0.601142	+	0.105998i	0.135208	+	0.990817i	$0.456830\pi$
$462$		0			0
$463$	6.49788e10	+	2.36504e10i	1.41399	+	0.514652i	0.932300	−	0.361687i	$-0.117799\pi$
$463$	6.49788e10	+	2.36504e10i	1.41399	+	0.514652i	0.481695	+	0.876339i	$0.340021\pi$
$464$	−3.16965e9	−	3.77745e9i	−0.0683817	−	0.0814942i
$465$		0			0
$466$	2.19811e9	−	8.00048e8i	0.0466130	−	0.0169657i
$467$	−2.12274e10	−	1.22556e10i	−0.446302	−	0.257673i	0.259965	−	0.965618i	$-0.416289\pi$
$467$	−2.12274e10	−	1.22556e10i	−0.446302	−	0.257673i	−0.706267	+	0.707945i	$0.749622\pi$
$468$		0			0
$469$	−2.48911e9	−	4.31126e9i	−0.0514461	−	0.0891072i
$470$	1.14739e10	−	1.36740e10i	0.235136	−	0.280224i
$471$		0			0
$472$	1.53275e10	+	8.69266e10i	0.308818	+	1.75140i
$473$	−7.80687e9	+	1.37656e9i	−0.155967	+	0.0275012i
$474$		0			0
$475$	4.60387e10	+	3.86311e10i	0.904375	+	0.758861i
$476$	1.40346e10	−	8.10288e9i	0.273384	−	0.157838i
$477$		0			0
$478$	2.55216e9	−	4.42047e9i	0.0488874	−	0.0846754i
$479$	1.34160e10	+	3.68601e10i	0.254847	+	0.700187i	0.999465	+	0.0326963i	$0.0104094\pi$
$479$	1.34160e10	+	3.68601e10i	0.254847	+	0.700187i	−0.744618	+	0.667491i	$0.767368\pi$
$480$		0			0
$481$	−6.29232e10	+	5.27988e10i	−1.17552	+	0.986379i
$482$	8.57385e9	−	2.35564e10i	0.158850	−	0.436437i
$483$		0			0
$484$	6.30663e9	−	3.57667e10i	0.114925	−	0.651774i
$485$			1.04768e11i			1.89349i
$486$		0			0
$487$	−4.28638e10			−0.762036			−0.381018	−	0.924568i	$-0.624426\pi$
$487$	−4.28638e10			−0.762036			−0.381018	+	0.924568i	$0.624426\pi$
$488$	−7.58510e10	−	1.33746e10i	−1.33746	−	0.235831i
$489$		0			0
$490$	2.88313e9	+	1.04937e9i	0.0500127	+	0.0182031i
$491$	−3.85804e10	−	4.59783e10i	−0.663805	−	0.791092i	0.324121	−	0.946016i	$-0.394931\pi$
$491$	−3.85804e10	−	4.59783e10i	−0.663805	−	0.791092i	−0.987927	+	0.154923i	$0.950487\pi$
$492$		0			0
$493$	1.04446e10	−	3.80154e9i	0.176810	−	0.0643535i
$494$	−1.80007e10	−	1.03927e10i	−0.302261	−	0.174510i
$495$		0			0
$496$	6.74815e9	+	1.16881e10i	0.111496	+	0.193116i
$497$	2.67395e10	−	3.18669e10i	0.438256	−	0.522293i
$498$		0			0
$499$	−1.66640e8	−	9.45061e8i	−0.00268767	−	0.0152426i	0.983434	−	0.181264i	$-0.0580189\pi$
$499$	−1.66640e8	−	9.45061e8i	−0.00268767	−	0.0152426i	−0.986122	+	0.166022i	$0.946908\pi$
$500$	−9.97535e10	+	1.75892e10i	−1.59606	+	0.281428i
$501$		0			0
$502$	−6.42035e9	−	5.38731e9i	−0.101098	−	0.0848316i
$503$	1.04601e11	−	6.03911e10i	1.63404	−	0.943412i	0.651206	−	0.758901i	$-0.274263\pi$
$503$	1.04601e11	−	6.03911e10i	1.63404	−	0.943412i	0.982830	−	0.184511i	$-0.0590701\pi$
$504$		0			0
$505$	−4.43884e10	+	7.68829e10i	−0.682502	+	1.18213i
$506$	−5.42696e9	−	1.49104e10i	−0.0827855	−	0.227451i
$507$		0			0
$508$	6.65505e9	−	5.58425e9i	0.0999302	−	0.0838514i
$509$	1.07658e9	−	2.95787e9i	0.0160389	−	0.0440664i	−0.931415	−	0.363959i	$-0.881425\pi$
$509$	1.07658e9	−	2.95787e9i	0.0160389	−	0.0440664i	0.947454	+	0.319893i	$0.103647\pi$
$510$		0			0
$511$	−1.34721e10	+	7.64041e10i	−0.197584	+	1.12056i
$512$			3.37310e10i			0.490851i
$513$		0			0
$514$	−4.49338e9			−0.0643755
$515$	−1.62496e11	−	2.86523e10i	−2.31000	−	0.407316i
$516$		0			0
$517$	−7.74944e9	−	2.82057e9i	−0.108470	−	0.0394797i
$518$	−2.85393e10	−	3.40118e10i	−0.396391	−	0.472401i
$519$		0			0
$520$	1.41370e11	−	5.14546e10i	1.93350	−	0.703737i
$521$	3.84871e10	+	2.22205e10i	0.522354	+	0.301581i	0.737897	−	0.674913i	$-0.235819\pi$
$521$	3.84871e10	+	2.22205e10i	0.522354	+	0.301581i	−0.215544	+	0.976494i	$0.569152\pi$
$522$		0			0
$523$	−8.50074e9	−	1.47237e10i	−0.113619	−	0.196793i	0.803608	−	0.595159i	$-0.202911\pi$
$523$	−8.50074e9	−	1.47237e10i	−0.113619	−	0.196793i	−0.917227	+	0.398366i	$0.869578\pi$
$524$	−2.42106e10	+	2.88530e10i	−0.321129	+	0.382707i
$525$		0			0
$526$	−1.70946e8	−	9.69483e8i	−0.00223314	−	0.0126648i
$527$	−2.99592e10	+	5.28261e9i	−0.388407	+	0.0684866i
$528$		0			0
$529$	−8.51198e10	−	7.14240e10i	−1.08695	−	0.912055i
$530$	5.32763e10	−	3.07591e10i	0.675198	−	0.389826i
$531$		0			0
$532$	−1.48850e10	+	2.57816e10i	−0.185824	+	0.321857i
$533$	1.82496e10	+	5.01403e10i	0.226123	+	0.621267i
$534$		0			0
$535$	−1.03939e11	+	8.72154e10i	−1.26872	+	1.06458i
$536$	−2.70167e9	+	7.42276e9i	−0.0327320	+	0.0899304i
$537$		0			0
$538$	−5.16129e9	+	2.92711e10i	−0.0616069	+	0.349390i
$539$		−	1.41749e9i		−	0.0167944i
$540$		0			0
$541$	6.17429e10			0.720772			0.360386	−	0.932803i	$-0.382645\pi$
$541$	6.17429e10			0.720772			0.360386	+	0.932803i	$0.382645\pi$
$542$	1.86152e10	+	3.28237e9i	0.215711	+	0.0380356i
$543$		0			0
$544$	−3.81633e10	−	1.38903e10i	−0.435763	−	0.158605i
$545$	1.96903e11	+	2.34660e11i	2.23186	+	2.65982i
$546$		0			0
$547$	8.78250e10	−	3.19657e10i	0.980999	−	0.357054i	0.198771	−	0.980046i	$-0.436305\pi$
$547$	8.78250e10	−	3.19657e10i	0.980999	−	0.357054i	0.782229	+	0.622992i	$0.214083\pi$
$548$	9.24928e10	+	5.34008e10i	1.02562	+	0.592141i
$549$		0			0
$550$	−1.59511e10	−	2.76281e10i	−0.174317	−	0.301926i
$551$	−1.31246e10	+	1.56412e10i	−0.142390	+	0.169693i
$552$		0			0
$553$	2.25237e10	+	1.27738e11i	0.240845	+	1.36590i
$554$	−3.22076e10	+	5.67906e9i	−0.341915	+	0.0602889i
$555$		0			0
$556$	5.83219e10	+	4.89379e10i	0.610284	+	0.512089i
$557$	−6.24314e10	+	3.60448e10i	−0.648608	+	0.374474i	−0.787923	−	0.615774i	$-0.788843\pi$
$557$	−6.24314e10	+	3.60448e10i	−0.648608	+	0.374474i	0.139315	+	0.990248i	$0.455510\pi$
$558$		0			0
$559$	3.29032e10	−	5.69901e10i	0.336970	−	0.583649i
$560$	−1.48847e10	−	4.08953e10i	−0.151352	−	0.415836i
$561$		0			0
$562$	−1.15871e9	+	9.72277e8i	−0.0116153	+	0.00974641i
$563$	2.67337e10	−	7.34502e10i	0.266088	−	0.731071i	−0.732638	−	0.680618i	$-0.761711\pi$
$563$	2.67337e10	−	7.34502e10i	0.266088	−	0.731071i	0.998726	−	0.0504528i	$-0.0160664\pi$
$564$		0			0
$565$	1.31085e10	−	7.43420e10i	0.128635	−	0.729525i
$566$			5.18977e10i			0.505688i
$567$		0			0
$568$	−6.60073e10			−0.634160
$569$	−9.51210e10	−	1.67724e10i	−0.907460	−	0.160010i	−0.299610	−	0.954062i	$-0.596857\pi$
$569$	−9.51210e10	−	1.67724e10i	−0.907460	−	0.160010i	−0.607850	+	0.794052i	$0.707968\pi$
$570$		0			0
$571$	6.27444e10	+	2.28371e10i	0.590243	+	0.214831i	0.619836	−	0.784731i	$-0.287199\pi$
$571$	6.27444e10	+	2.28371e10i	0.590243	+	0.214831i	−0.0295935	+	0.999562i	$0.509421\pi$
$572$	−1.87923e10	−	2.23958e10i	−0.175548	−	0.209210i
$573$		0			0
$574$	−2.71023e10	+	9.86442e9i	−0.249665	+	0.0908708i
$575$	−3.29829e11	−	1.90427e11i	−3.01729	−	1.74203i
$576$		0			0
$577$	−2.51942e10	−	4.36376e10i	−0.227299	−	0.393693i	0.729708	−	0.683759i	$-0.239656\pi$
$577$	−2.51942e10	−	4.36376e10i	−0.227299	−	0.393693i	−0.957007	+	0.290066i	$0.906323\pi$
$578$	−3.00284e10	+	3.57865e10i	−0.269043	+	0.320633i
$579$		0			0
$580$	−1.07944e10	−	6.12181e10i	−0.0953864	−	0.540963i
$581$	1.33763e11	−	2.35859e10i	1.17390	−	0.206990i
$582$		0			0
$583$	−2.17721e10	−	1.82689e10i	−0.188463	−	0.158139i
$584$	1.06611e11	−	6.15519e10i	0.916539	−	0.529164i
$585$		0			0
$586$	2.68126e10	−	4.64408e10i	0.227378	−	0.393830i
$587$	−2.77982e10	−	7.63749e10i	−0.234134	−	0.643277i	−1.00000		0.000277290i	$-0.999912\pi$
$587$	−2.77982e10	−	7.63749e10i	−0.234134	−	0.643277i	0.765866	−	0.643000i	$-0.222310\pi$
$588$		0			0
$589$	4.28096e10	−	3.59216e10i	0.355697	−	0.298465i
$590$	−7.68657e10	+	2.11187e11i	−0.634344	+	1.74285i
$591$		0			0
$592$	6.54710e9	−	3.71304e10i	0.0533042	−	0.302303i
$593$		−	1.67268e11i		−	1.35268i	−0.736589	−	0.676340i	$-0.763565\pi$
$593$		−	1.67268e11i		−	1.35268i	0.736589	−	0.676340i	$-0.236435\pi$
$594$		0			0
$595$	9.80960e10			0.782679
$596$	1.36869e11	+	2.41338e10i	1.08473	+	0.191267i
$597$		0			0
$598$	1.23775e11	+	4.50505e10i	0.967897	+	0.352286i
$599$	−7.02335e10	−	8.37010e10i	−0.545553	−	0.650165i	0.420870	−	0.907121i	$-0.361725\pi$
$599$	−7.02335e10	−	8.37010e10i	−0.545553	−	0.650165i	−0.966423	+	0.256956i	$0.917280\pi$
$600$		0			0
$601$	3.89186e9	−	1.41652e9i	0.0298304	−	0.0108574i	−0.327062	−	0.945003i	$-0.606059\pi$
$601$	3.89186e9	−	1.41652e9i	0.0298304	−	0.0108574i	0.356892	+	0.934146i	$0.383836\pi$
$602$	3.08048e10	+	1.77852e10i	0.234548	+	0.135417i
$603$		0			0
$604$	−6.36933e10	−	1.10320e11i	−0.478571	−	0.828909i
$605$	1.41311e11	−	1.68408e11i	1.05476	−	1.25702i
$606$		0			0
$607$	−3.22230e10	−	1.82746e11i	−0.237362	−	1.34615i	−0.837582	−	0.546312i	$-0.816031\pi$
$607$	−3.22230e10	−	1.82746e11i	−0.237362	−	1.34615i	0.600220	−	0.799835i	$-0.295080\pi$
$608$	7.34719e10	−	1.29551e10i	0.537659	−	0.0948037i
$609$		0			0
$610$	−1.50226e11	−	1.26054e11i	−1.08499	−	0.910413i
$611$	5.92869e10	−	3.42293e10i	0.425396	−	0.245603i
$612$		0			0
$613$	3.54611e10	−	6.14205e10i	0.251137	−	0.434982i	−0.712702	−	0.701467i	$-0.752529\pi$
$613$	3.54611e10	−	6.14205e10i	0.251137	−	0.434982i	0.963839	+	0.266485i	$0.0858622\pi$
$614$	2.08464e9	+	5.72751e9i	0.0146676	+	0.0402988i
$615$		0			0
$616$	2.87797e10	−	2.41491e10i	0.199877	−	0.167717i
$617$	2.38334e10	−	6.54817e10i	0.164454	−	0.451834i	−0.829904	−	0.557906i	$-0.811605\pi$
$617$	2.38334e10	−	6.54817e10i	0.164454	−	0.451834i	0.994359	+	0.106072i	$0.0338273\pi$
$618$		0			0
$619$	−4.48234e10	+	2.54206e11i	−0.305311	+	1.73150i	0.316728	+	0.948516i	$0.397416\pi$
$619$	−4.48234e10	+	2.54206e11i	−0.305311	+	1.73150i	−0.622039	+	0.782986i	$0.713695\pi$
$620$			1.70137e11i			1.15141i
$621$		0			0
$622$	−4.84302e10			−0.323560
$623$	1.20494e11	+	2.12463e10i	0.799858	+	0.141037i
$624$		0			0
$625$	−2.54957e11	−	9.27966e10i	−1.67088	−	0.608152i
$626$	−7.92692e10	−	9.44694e10i	−0.516187	−	0.615168i
$627$		0			0
$628$	1.44992e11	−	5.27728e10i	0.932192	−	0.339290i
$629$	7.35991e10	+	4.24925e10i	0.470186	+	0.271462i
$630$		0			0
$631$	2.54957e10	+	4.41599e10i	0.160824	+	0.278555i	0.935164	−	0.354214i	$-0.115252\pi$
$631$	2.54957e10	+	4.41599e10i	0.160824	+	0.278555i	−0.774341	+	0.632769i	$0.781918\pi$
$632$	1.32295e11	−	1.57663e11i	0.829228	−	0.988235i
$633$		0			0
$634$	9.97510e9	+	5.65716e10i	0.0617391	+	0.350140i
$635$	5.17882e10	−	9.13166e9i	0.318519	−	0.0561636i
$636$		0			0
$637$	9.01400e9	+	7.56365e9i	0.0547470	+	0.0459381i
$638$	9.38642e9	−	5.41925e9i	0.0566523	−	0.0327082i
$639$		0			0
$640$	−1.33571e11	+	2.31351e11i	−0.796144	+	1.37896i
$641$	−1.59959e10	−	4.39484e10i	−0.0947495	−	0.260322i	0.883260	−	0.468884i	$-0.155344\pi$
$641$	−1.59959e10	−	4.39484e10i	−0.0947495	−	0.260322i	−0.978009	+	0.208562i	$0.933122\pi$
$642$		0			0
$643$	1.15582e11	−	9.69848e10i	0.676155	−	0.567362i	−0.238725	−	0.971087i	$-0.576729\pi$
$643$	1.15582e11	−	9.69848e10i	0.676155	−	0.567362i	0.914880	+	0.403726i	$0.132285\pi$
$644$	6.45237e10	−	1.77277e11i	0.375125	−	1.03065i
$645$		0			0
$646$	−3.73435e9	+	2.11785e10i	−0.0214430	+	0.121609i
$647$			2.93630e11i			1.67565i	0.545937	+	0.837826i	$0.316174\pi$
$647$			2.93630e11i			1.67565i	−0.545937	+	0.837826i	$0.683826\pi$
$648$		0			0
$649$	1.03830e11			0.585253
$650$	2.60805e11	+	4.59869e10i	1.46104	+	0.257621i
$651$		0			0
$652$	9.55855e10	+	3.47903e10i	0.528934	+	0.192516i
$653$	6.83847e10	+	8.14977e10i	0.376102	+	0.448221i	0.920580	−	0.390554i	$-0.127717\pi$
$653$	6.83847e10	+	8.14977e10i	0.376102	+	0.448221i	−0.544478	+	0.838775i	$0.683272\pi$
$654$		0			0
$655$	−2.14242e11	+	7.79779e10i	−1.16397	+	0.423649i
$656$	−2.12106e10	−	1.22460e10i	−0.114535	−	0.0661268i
$657$		0			0
$658$	1.85019e10	+	3.20463e10i	0.0986991	+	0.170952i
$659$	−1.69892e11	+	2.02470e11i	−0.900808	+	1.07354i	0.0961314	+	0.995369i	$0.469353\pi$
$659$	−1.69892e11	+	2.02470e11i	−0.900808	+	1.07354i	−0.996940	+	0.0781730i	$0.975091\pi$
$660$		0			0
$661$	−3.22461e9	−	1.82877e10i	−0.0168916	−	0.0957971i	0.975196	−	0.221341i	$-0.0710434\pi$
$661$	−3.22461e9	−	1.82877e10i	−0.0168916	−	0.0957971i	−0.992088	+	0.125544i	$0.959932\pi$
$662$	−6.99193e10	+	1.23287e10i	−0.364053	+	0.0641924i
$663$		0			0
$664$	−1.65099e11	−	1.38534e11i	−0.849319	−	0.712663i
$665$	−1.56060e11	+	9.01013e10i	−0.798004	+	0.460728i
$666$		0			0
$667$	6.46958e10	−	1.12056e11i	0.326868	−	0.566153i
$668$	−2.31148e10	−	6.35074e10i	−0.116087	−	0.318947i
$669$		0			0
$670$	−1.54069e10	+	1.29279e10i	−0.0764565	+	0.0641547i
$671$	−3.09873e10	+	8.51368e10i	−0.152860	+	0.419979i
$672$		0			0
$673$	2.78834e10	−	1.58135e11i	0.135921	−	0.770845i	−0.838293	−	0.545220i	$-0.816446\pi$
$673$	2.78834e10	−	1.58135e11i	0.135921	−	0.770845i	0.974214	−	0.225626i	$-0.0724426\pi$
$674$		−	1.15551e11i		−	0.559933i
$675$		0			0
$676$	9.10819e10			0.436160
$677$	−1.93835e11	−	3.41783e10i	−0.922735	−	0.162703i	−0.307954	−	0.951401i	$-0.599644\pi$
$677$	−1.93835e11	−	3.41783e10i	−0.922735	−	0.162703i	−0.614781	+	0.788698i	$0.710755\pi$
$678$		0			0
$679$	−2.04089e11	−	7.42824e10i	−0.960155	−	0.349468i
$680$	−1.00052e11	−	1.19237e11i	−0.467939	−	0.557668i
$681$		0			0
$682$	−2.78757e10	+	1.01459e10i	−0.128851	+	0.0468979i
$683$	−1.70433e11	−	9.83995e10i	−0.783196	−	0.452179i	0.0543656	−	0.998521i	$-0.482686\pi$
$683$	−1.70433e11	−	9.83995e10i	−0.783196	−	0.452179i	−0.837562	+	0.546343i	$0.816020\pi$
$684$		0			0
$685$	3.23243e11	+	5.59874e11i	1.46814	+	2.54289i
$686$	−7.64666e10	+	9.11294e10i	−0.345283	+	0.411492i
$687$		0			0
$688$	5.24518e9	+	2.97469e10i	0.0234103	+	0.132766i
$689$	2.32349e11	−	4.09693e10i	1.03101	−	0.181795i
$690$		0			0
$691$	1.49376e11	+	1.25341e11i	0.655191	+	0.549771i	0.908641	−	0.417578i	$-0.137121\pi$
$691$	1.49376e11	+	1.25341e11i	0.655191	+	0.549771i	−0.253450	+	0.967349i	$0.581565\pi$
$692$	8.36488e10	−	4.82946e10i	0.364783	−	0.210608i
$693$		0			0
$694$	1.35566e9	−	2.34808e9i	0.00584406	−	0.0101222i
$695$	1.57620e11	+	4.33057e11i	0.675572	+	1.85612i
$696$		0			0
$697$	4.22903e10	−	3.54857e10i	0.179188	−	0.150357i
$698$	4.10334e10	−	1.12738e11i	0.172868	−	0.474952i
$699$		0			0
$700$	6.58649e10	−	3.73538e11i	0.274323	−	1.55576i
$701$			1.28248e11i			0.531102i	0.964097	+	0.265551i	$0.0855539\pi$
$701$			1.28248e11i			0.531102i	−0.964097	+	0.265551i	$0.914446\pi$
$702$		0			0
$703$	−1.56117e11			−0.639190
$704$	−2.07977e10	−	3.66719e9i	−0.0846690	−	0.0149294i
$705$		0			0
$706$	−5.66194e10	−	2.06078e10i	−0.227901	−	0.0829492i
$707$	−1.18296e11	−	1.40980e11i	−0.473471	−	0.564260i
$708$		0			0
$709$	−2.19859e11	+	8.00221e10i	−0.870079	+	0.316683i	−0.738199	−	0.674583i	$-0.764324\pi$
$709$	−2.19859e11	+	8.00221e10i	−0.870079	+	0.316683i	−0.131880	+	0.991266i	$0.542101\pi$
$710$	−1.45547e11	−	8.40315e10i	−0.572756	−	0.330681i
$711$		0			0
$712$	−9.70710e10	−	1.68132e11i	−0.377720	−	0.654230i
$713$	−2.27638e11	+	2.71288e11i	−0.880817	+	1.04972i
$714$		0			0
$715$	−3.07301e10	−	1.74279e11i	−0.117582	−	0.666839i
$716$	−8.25449e10	+	1.45549e10i	−0.314079	+	0.0553805i
$717$		0			0
$718$	5.56495e10	+	4.66955e10i	0.209394	+	0.175702i
$719$	−2.15794e11	+	1.24589e11i	−0.807466	+	0.466191i	−0.846075	−	0.533064i	$-0.821041\pi$
$719$	−2.15794e11	+	1.24589e11i	−0.807466	+	0.466191i	0.0386092	+	0.999254i	$0.487707\pi$
$720$		0			0
$721$	1.71027e11	−	2.96227e11i	0.632882	−	1.09618i
$722$	3.51370e10	+	9.65382e10i	0.129305	+	0.355263i
$723$		0			0
$724$	1.66095e11	−	1.39370e11i	0.604507	−	0.507242i
$725$	8.89762e10	−	2.44460e11i	0.322049	−	0.884822i
$726$		0			0
$727$	−5.77710e10	+	3.27636e11i	−0.206811	+	1.17288i	0.687755	+	0.725943i	$0.258596\pi$
$727$	−5.77710e10	+	3.27636e11i	−0.206811	+	1.17288i	−0.894565	+	0.446937i	$0.852515\pi$
$728$			3.11872e11i			1.11033i
$729$		0			0
$730$	3.13438e11			1.10372
$731$	−6.70510e10	−	1.18229e10i	−0.234820	−	0.0414052i
$732$		0			0
$733$	−2.51734e11	−	9.16237e10i	−0.872019	−	0.317389i	−0.133035	−	0.991111i	$-0.542472\pi$
$733$	−2.51734e11	−	9.16237e10i	−0.872019	−	0.317389i	−0.738984	+	0.673722i	$0.764694\pi$
$734$	1.03702e11	+	1.23588e11i	0.357277	+	0.425786i
$735$		0			0
$736$	−4.44267e11	+	1.61700e11i	−1.51402	+	0.551060i
$737$	8.04697e9	+	4.64592e9i	0.0272748	+	0.0157471i
$738$		0			0
$739$	2.13852e11	+	3.70403e11i	0.717028	+	1.24193i	0.962172	+	0.272443i	$0.0878315\pi$
$739$	2.13852e11	+	3.70403e11i	0.717028	+	1.24193i	−0.245144	+	0.969487i	$0.578835\pi$
$740$	3.05513e11	−	3.64096e11i	1.01883	−	1.21420i
$741$		0			0
$742$	2.21451e10	+	1.25591e11i	0.0730571	+	0.414327i
$743$	−1.08760e10	+	1.91774e9i	−0.0356874	+	0.00629265i	−0.191463	−	0.981500i	$-0.561323\pi$
$743$	−1.08760e10	+	1.91774e9i	−0.0356874	+	0.00629265i	0.155776	+	0.987792i	$0.450212\pi$
$744$		0			0
$745$	6.44452e11	+	5.40760e11i	2.09202	+	1.75541i
$746$	−7.97538e10	+	4.60459e10i	−0.257511	+	0.148674i
$747$		0			0
$748$	−1.51240e10	+	2.61956e10i	−0.0483127	+	0.0836800i
$749$	−9.62014e10	−	2.64311e11i	−0.305671	−	0.839824i
$750$		0			0
$751$	−1.54799e11	+	1.29892e11i	−0.486641	+	0.408340i	−0.852821	−	0.522204i	$-0.825110\pi$
$751$	−1.54799e11	+	1.29892e11i	−0.486641	+	0.408340i	0.366180	+	0.930544i	$0.380666\pi$
$752$	−1.07473e10	+	2.95281e10i	−0.0336070	+	0.0923345i
$753$		0			0
$754$	−1.56237e10	+	8.86062e10i	−0.0483390	+	0.274144i
$755$		−	7.71091e11i		−	2.37311i
$756$		0			0
$757$	8.13103e9			0.0247607			0.0123803	−	0.999923i	$-0.496059\pi$
$757$	8.13103e9			0.0247607			0.0123803	+	0.999923i	$0.496059\pi$
$758$	3.07247e10	+	5.41759e9i	0.0930702	+	0.0164108i
$759$		0			0
$760$	2.68691e11	+	9.77955e10i	0.805376	+	0.293133i
$761$	−3.03699e11	−	3.61934e11i	−0.905533	−	1.07917i	−0.996523	−	0.0833201i	$-0.973448\pi$
$761$	−3.03699e11	−	3.61934e11i	−0.905533	−	1.07917i	0.0909901	−	0.995852i	$-0.470997\pi$
$762$		0			0
$763$	−5.96725e11	+	2.17190e11i	−1.76066	+	0.640829i
$764$	1.01826e11	+	5.87894e10i	0.298872	+	0.172554i
$765$		0			0
$766$	−8.34895e10	−	1.44608e11i	−0.242503	−	0.420027i
$767$	−5.54030e11	+	6.60267e11i	−1.60085	+	1.90782i
$768$		0			0
$769$	−4.67617e10	−	2.65199e11i	−0.133717	−	0.758344i	−0.975745	−	0.218911i	$-0.929750\pi$
$769$	−4.67617e10	−	2.65199e11i	−0.133717	−	0.758344i	0.842028	−	0.539433i	$-0.181362\pi$
$770$	9.42029e10	−	1.66105e10i	0.267979	−	0.0472520i
$771$		0			0
$772$	−7.32797e9	−	6.14890e9i	−0.0206307	−	0.0173112i
$773$	3.80987e10	−	2.19963e10i	0.106707	−	0.0616072i	−0.445697	−	0.895184i	$-0.647044\pi$
$773$	3.80987e10	−	2.19963e10i	0.106707	−	0.0616072i	0.552404	+	0.833577i	$0.313711\pi$
$774$		0			0
$775$	−3.56010e11	+	6.16628e11i	−0.986860	+	1.70929i
$776$	1.17867e11	+	3.23837e11i	0.325046	+	0.893058i
$777$		0			0
$778$	−1.15289e11	+	9.67392e10i	−0.314681	+	0.264049i
$779$	−3.46855e10	+	9.52976e10i	−0.0941885	+	0.258781i
$780$		0			0
$781$	−1.34829e10	+	7.64654e10i	−0.0362393	+	0.205523i
$782$		−	1.36280e11i		−	0.364424i
$783$		0			0
$784$	−5.40114e9			−0.0142962
$785$	9.19796e11	+	1.62185e11i	2.42222	+	0.427102i
$786$		0			0
$787$	1.72186e11	+	6.26704e10i	0.448847	+	0.163367i	0.556546	−	0.830817i	$-0.312126\pi$
$787$	1.72186e11	+	6.26704e10i	0.448847	+	0.163367i	−0.107700	+	0.994183i	$0.534348\pi$
$788$	1.47382e11	+	1.75643e11i	0.382242	+	0.455539i
$789$		0			0
$790$	4.92425e11	−	1.79228e11i	1.26425	−	0.460149i
$791$	1.35524e11	+	7.82450e10i	0.346187	+	0.199871i
$792$		0			0
$793$	−3.76049e11	−	6.51337e11i	−0.950938	−	1.64707i
$794$	1.58309e11	−	1.88665e11i	0.398311	−	0.474689i
$795$		0			0
$796$	7.25014e10	+	4.11176e11i	0.180590	+	1.02418i
$797$	−6.11243e11	+	1.07779e11i	−1.51489	+	0.267116i	−0.868422	−	0.495826i	$-0.834865\pi$
$797$	−6.11243e11	+	1.07779e11i	−1.51489	+	0.267116i	−0.646467	+	0.762942i	$0.723754\pi$
$798$		0			0
$799$	−5.42584e10	−	4.55282e10i	−0.133131	−	0.111710i
$800$	−8.23199e11	+	4.75274e11i	−2.00976	+	1.16034i
$801$		0			0
$802$	1.20804e11	−	2.09239e11i	0.292001	−	0.505761i
$803$	−4.95273e10	−	1.36075e11i	−0.119119	−	0.327278i
$804$		0			0
$805$	8.74790e11	−	7.34036e11i	2.08315	−	1.74797i
$806$	8.42237e10	−	2.31403e11i	0.199569	−	0.548313i
$807$		0			0
$808$	−5.07084e10	+	2.87581e11i	−0.118969	+	0.674707i
$809$		−	5.19353e11i		−	1.21246i	−0.795288	−	0.606231i	$-0.792681\pi$
$809$		−	5.19353e11i		−	1.21246i	0.795288	−	0.606231i	$-0.207319\pi$
$810$		0			0
$811$	−3.87789e11			−0.896422			−0.448211	−	0.893928i	$-0.647939\pi$
$811$	−3.87789e11			−0.896422			−0.448211	+	0.893928i	$0.647939\pi$
$812$	1.26906e11	+	2.23770e10i	0.291917	+	0.0514729i
$813$		0			0
$814$	7.78734e10	+	2.83436e10i	0.177375	+	0.0645591i
$815$	3.95782e11	+	4.71674e11i	0.897068	+	1.06908i
$816$		0			0
$817$	1.17530e11	−	4.27775e10i	0.263792	−	0.0960123i
$818$	−1.03338e11	−	5.96624e10i	−0.230807	−	0.133256i
$819$		0			0
$820$	−1.54375e11	−	2.67385e11i	−0.341446	−	0.591401i
$821$	9.20066e10	−	1.09649e11i	0.202510	−	0.241342i	−0.655225	−	0.755433i	$-0.727426\pi$
$821$	9.20066e10	−	1.09649e11i	0.202510	−	0.241342i	0.857735	+	0.514092i	$0.171871\pi$
$822$		0			0
$823$	5.72758e10	+	3.24827e11i	0.124845	+	0.708033i	0.981400	+	0.191976i	$0.0614895\pi$
$823$	5.72758e10	+	3.24827e11i	0.124845	+	0.708033i	−0.856554	+	0.516057i	$0.827399\pi$
$824$	−5.34504e11	+	9.42476e10i	−1.15942	+	0.204438i
$825$		0			0
$826$	−3.56894e11	−	2.99469e11i	−0.766688	−	0.643328i
$827$	−1.91636e10	+	1.10641e10i	−0.0409691	+	0.0236535i	−0.520345	−	0.853956i	$-0.674197\pi$
$827$	−1.91636e10	+	1.10641e10i	−0.0409691	+	0.0236535i	0.479376	+	0.877610i	$0.340863\pi$
$828$		0			0
$829$	1.96260e11	−	3.39932e11i	0.415540	−	0.719736i	−0.579945	−	0.814656i	$-0.696926\pi$
$829$	1.96260e11	−	3.39932e11i	0.415540	−	0.719736i	0.995485	+	0.0949194i	$0.0302593\pi$
$830$	−1.87681e11	−	5.15650e11i	−0.395465	−	1.08653i
$831$		0			0
$832$	1.34295e11	−	1.12687e11i	0.280264	−	0.235169i
$833$	4.16390e9	−	1.14402e10i	0.00864810	−	0.0237605i
$834$		0			0
$835$	7.10380e10	−	4.02877e11i	0.146132	−	0.828755i
$836$		−	5.55657e10i		−	0.113758i
$837$		0			0
$838$	3.23624e10			0.0656243
$839$	−8.15516e11	−	1.43797e11i	−1.64583	−	0.290204i	−0.727525	−	0.686081i	$-0.759330\pi$
$839$	−8.15516e11	−	1.43797e11i	−1.64583	−	0.290204i	−0.918303	+	0.395877i	$0.870441\pi$
$840$		0			0
$841$	−3.87025e11	−	1.40865e11i	−0.773668	−	0.281592i
$842$	1.65949e11	+	1.97770e11i	0.330161	+	0.393471i
$843$		0			0
$844$	6.03916e10	−	2.19807e10i	0.119016	−	0.0433184i
$845$	4.77469e11	+	2.75667e11i	0.936522	+	0.540701i
$846$		0			0
$847$	2.27868e11	+	3.94678e11i	0.442740	+	0.766849i
$848$	−6.96110e10	+	8.29592e10i	−0.134615	+	0.160428i
$849$		0			0
$850$	−4.75795e10	−	2.69837e11i	−0.0911473	−	0.516922i
$851$	9.74298e11	−	1.71795e11i	1.85769	−	0.327561i
$852$		0			0
$853$	−4.34350e11	−	3.64463e11i	−0.820434	−	0.688426i	0.132640	−	0.991164i	$-0.457655\pi$
$853$	−4.34350e11	−	3.64463e11i	−0.820434	−	0.688426i	−0.953074	+	0.302738i	$0.902099\pi$
$854$	3.52066e11	−	2.03266e11i	0.661901	−	0.382149i
$855$		0			0
$856$	−2.23155e11	+	3.86515e11i	−0.415634	+	0.719899i
$857$	3.15301e11	+	8.66281e11i	0.584523	+	1.60596i	0.780363	+	0.625327i	$0.215035\pi$
$857$	3.15301e11	+	8.66281e11i	0.584523	+	1.60596i	−0.195840	+	0.980636i	$0.562743\pi$
$858$		0			0
$859$	−4.09903e11	+	3.43949e11i	−0.752850	+	0.631716i	−0.936255	−	0.351321i	$-0.885732\pi$
$859$	−4.09903e11	+	3.43949e11i	−0.752850	+	0.631716i	0.183405	+	0.983037i	$0.441288\pi$
$860$	−1.30235e11	+	3.57816e11i	−0.238085	+	0.654134i
$861$		0			0
$862$	−3.08048e9	+	1.74703e10i	−0.00557943	+	0.0316425i
$863$			6.95049e11i			1.25306i	0.779397	+	0.626530i	$0.215525\pi$
$863$			6.95049e11i			1.25306i	−0.779397	+	0.626530i	$0.784475\pi$
$864$		0			0
$865$	5.84670e11			1.04435
$866$	1.88599e11	+	3.32550e10i	0.335326	+	0.0591270i
$867$		0			0
$868$	−3.31427e11	−	1.20630e11i	−0.583861	−	0.212508i
$869$	−1.55619e11	−	1.85460e11i	−0.272888	−	0.325215i
$870$		0			0
$871$	−7.24821e10	+	2.63813e10i	−0.125938	+	0.0458378i
$872$	8.72620e11	+	5.03808e11i	1.50924	+	0.871362i
$873$		0			0
$874$	1.25174e11	+	2.16807e11i	0.214520	+	0.371559i
$875$	8.17015e11	−	9.73681e11i	1.39379	−	1.66106i
$876$		0			0
$877$	1.09110e9	+	6.18796e9i	0.00184445	+	0.0104604i	0.985716	−	0.168416i	$-0.0538650\pi$
$877$	1.09110e9	+	6.18796e9i	0.00184445	+	0.0104604i	−0.983872	+	0.178876i	$0.942754\pi$
$878$	−3.43685e11	+	6.06009e10i	−0.578338	+	0.101977i
$879$		0			0
$880$	6.22257e10	+	5.22135e10i	0.103762	+	0.0870668i
$881$	1.32363e11	−	7.64201e10i	0.219717	−	0.126854i	−0.386102	−	0.922456i	$-0.626179\pi$
$881$	1.32363e11	−	7.64201e10i	0.219717	−	0.126854i	0.605819	+	0.795602i	$0.292845\pi$
$882$		0			0
$883$	2.95623e11	−	5.12034e11i	0.486290	−	0.842278i	−0.513586	−	0.858038i	$-0.671683\pi$
$883$	2.95623e11	−	5.12034e11i	0.486290	−	0.842278i	0.999876	+	0.0157597i	$0.00501669\pi$
$884$	−8.58800e10	−	2.35953e11i	−0.140632	−	0.386382i
$885$		0			0
$886$	−2.03830e11	+	1.71034e11i	−0.330775	+	0.277554i
$887$	1.89777e11	−	5.21408e11i	0.306584	−	0.842332i	−0.686733	−	0.726910i	$-0.740956\pi$
$887$	1.89777e11	−	5.21408e11i	0.306584	−	0.842332i	0.993317	−	0.115422i	$-0.0368220\pi$
$888$		0			0
$889$	−1.89301e10	+	1.07358e11i	−0.0303072	+	0.171881i
$890$		−	4.94310e11i		−	0.787843i
$891$		0			0
$892$	3.45451e11			0.545667
$893$	1.28137e11	+	2.25940e10i	0.201497	+	0.0355293i
$894$		0			0
$895$	−4.76767e11	−	1.73529e11i	−0.743044	−	0.270446i
$896$	−3.55970e11	−	4.24228e11i	−0.552307	−	0.658214i
$897$		0			0
$898$	6.20040e11	−	2.25676e11i	0.953485	−	0.347040i
$899$	−2.09494e11	−	1.20951e11i	−0.320725	−	0.185171i
$900$		0			0
$901$	−1.22052e11	−	2.11400e11i	−0.185202	−	0.320779i
$902$	3.46031e10	−	4.12384e10i	0.0522744	−	0.0622982i
$903$		0			0
$904$	−4.31184e10	−	2.44537e11i	−0.0645638	−	0.366160i
$905$	1.29251e12	−	2.27905e11i	1.92682	−	0.339750i
$906$		0			0
$907$	−3.64411e11	−	3.05777e11i	−0.538471	−	0.451831i	0.332543	−	0.943088i	$-0.392093\pi$
$907$	−3.64411e11	−	3.05777e11i	−0.538471	−	0.451831i	−0.871015	+	0.491257i	$0.836538\pi$
$908$	1.96067e11	−	1.13199e11i	0.288444	−	0.166533i
$909$		0			0
$910$	−3.97032e11	+	6.87680e11i	−0.578976	+	1.00282i
$911$	−2.57051e11	−	7.06242e11i	−0.373204	−	1.02537i	−0.974115	−	0.226053i	$-0.927418\pi$
$911$	−2.57051e11	−	7.06242e11i	−0.373204	−	1.02537i	0.600911	−	0.799316i	$-0.294805\pi$
$912$		0			0
$913$	−1.94207e11	+	1.62959e11i	−0.279500	+	0.234528i
$914$	7.34139e9	−	2.01703e10i	0.0105195	−	0.0289020i
$915$		0			0
$916$	5.22797e10	−	2.96493e11i	0.0742594	−	0.421146i
$917$		−	4.72632e11i		−	0.668415i
$918$		0			0
$919$	−7.46604e11			−1.04671			−0.523357	−	0.852113i	$-0.675321\pi$
$919$	−7.46604e11			−1.04671			−0.523357	+	0.852113i	$0.675321\pi$
$920$	−1.78446e12	−	3.14649e11i	−2.49090	−	0.439212i
$921$		0			0
$922$	2.16973e11	+	7.89716e10i	0.300249	+	0.109282i
$923$	−4.14309e11	−	4.93754e11i	−0.570844	−	0.680306i
$924$		0			0
$925$	1.86914e12	−	6.80312e11i	2.55314	−	0.929268i
$926$	5.01541e11	+	2.89565e11i	0.682123	+	0.393824i
$927$		0			0
$928$	−1.61470e11	−	2.79675e11i	−0.217721	−	0.377104i
$929$	−2.90198e11	+	3.45844e11i	−0.389611	+	0.464320i	−0.924823	−	0.380398i	$-0.875787\pi$
$929$	−2.90198e11	+	3.45844e11i	−0.389611	+	0.464320i	0.535212	+	0.844718i	$0.320232\pi$
$930$		0			0
$931$	3.88355e9	+	2.20247e10i	0.00516928	+	0.0293164i
$932$	−5.11219e10	+	9.01416e9i	−0.0677553	+	0.0119471i
$933$		0			0
$934$	−1.57257e11	−	1.31954e11i	−0.206644	−	0.173395i
$935$	−1.58566e11	+	9.15481e10i	−0.207474	+	0.119785i
$936$		0			0
$937$	3.20942e11	−	5.55887e11i	0.416359	−	0.721154i	−0.579211	−	0.815177i	$-0.696639\pi$
$937$	3.20942e11	−	5.55887e11i	0.416359	−	0.721154i	0.995570	+	0.0940230i	$0.0299727\pi$
$938$	−1.42599e10	−	3.91787e10i	−0.0184206	−	0.0506102i
$939$		0			0
$940$	−3.03450e11	+	2.54625e11i	−0.388666	+	0.326129i
$941$	−4.64465e11	+	1.27611e12i	−0.592372	+	1.62753i	0.173717	+	0.984796i	$0.444422\pi$
$941$	−4.64465e11	+	1.27611e12i	−0.592372	+	1.62753i	−0.766089	+	0.642734i	$0.777800\pi$
$942$		0			0
$943$	1.11598e11	−	6.32902e11i	0.141126	−	0.800367i
$944$		−	3.95629e11i		−	0.498195i
$945$		0			0
$946$	−6.63919e10			−0.0828993
$947$	−2.88970e11	−	5.09532e10i	−0.359296	−	0.0633536i	−0.00891360	−	0.999960i	$-0.502837\pi$
$947$	−2.88970e11	−	5.09532e10i	−0.359296	−	0.0633536i	−0.350383	+	0.936607i	$0.613948\pi$
$948$		0			0
$949$	1.12959e12	+	4.11138e11i	1.39270	+	0.506901i
$950$	3.23539e11	+	3.85579e11i	0.397221	+	0.473389i
$951$		0			0
$952$	3.03213e11	−	1.10360e11i	0.369147	−	0.134359i
$953$	9.42582e11	+	5.44200e11i	1.14274	+	0.659761i	0.947108	−	0.320916i	$-0.103991\pi$
$953$	9.42582e11	+	5.44200e11i	1.14274	+	0.659761i	0.195632	+	0.980677i	$0.437324\pi$
$954$		0			0
$955$	3.55861e11	+	6.16370e11i	0.427826	+	0.741016i
$956$	−7.28109e10	+	8.67726e10i	−0.0871695	+	0.103885i
$957$		0			0
$958$	5.70467e10	+	3.23528e11i	0.0677280	+	0.384105i
$959$	−1.31982e12	+	2.32720e11i	−1.56042	+	0.275143i
$960$		0			0
$961$	−1.46169e11	−	1.22651e11i	−0.171381	−	0.143806i
$962$	−5.95768e11	+	3.43967e11i	−0.695628	+	0.401621i
$963$		0			0
$964$	−2.78154e11	+	4.81776e11i	−0.322089	+	0.557875i
$965$	−1.98045e10	−	5.44124e10i	−0.0228378	−	0.0627463i
$966$		0			0
$967$	−1.16061e12	+	9.73866e11i	−1.32733	+	1.11376i	−0.342640	+	0.939467i	$0.611321\pi$
$967$	−1.16061e12	+	9.73866e11i	−1.32733	+	1.11376i	−0.984693	+	0.174297i	$0.944235\pi$
$968$	2.47326e11	−	6.79524e11i	0.281688	−	0.773933i
$969$		0			0
$970$	−1.52367e11	+	8.64116e11i	−0.172109	+	0.976079i
$971$		−	7.60219e11i		−	0.855188i	−0.903971	−	0.427594i	$-0.859361\pi$
$971$		−	7.60219e11i		−	0.855188i	0.903971	−	0.427594i	$-0.140639\pi$
$972$		0			0
$973$	−9.55351e11			−1.06589
$974$	−3.53535e11	−	6.23378e10i	−0.392823	−	0.0692653i
$975$		0			0
$976$	3.24401e11	+	1.18072e11i	0.357506	+	0.130122i
$977$	1.00716e12	+	1.20028e12i	1.10540	+	1.31736i	0.943804	+	0.330507i	$0.107220\pi$
$977$	1.00716e12	+	1.20028e12i	1.10540	+	1.31736i	0.161596	+	0.986857i	$0.448336\pi$
$978$		0			0
$979$	−2.14599e11	+	7.81076e10i	−0.233613	+	0.0850281i
$980$	−5.89658e10	−	3.40439e10i	−0.0639287	−	0.0369093i
$981$		0			0
$982$	−2.51339e11	−	4.35331e11i	−0.270280	−	0.468138i
$983$	9.63142e11	−	1.14783e12i	1.03152	−	1.22931i	0.0585695	−	0.998283i	$-0.481346\pi$
$983$	9.63142e11	−	1.14783e12i	1.03152	−	1.22931i	0.972947	−	0.231030i	$-0.0742095\pi$
$984$		0			0
$985$	2.41006e11	+	1.36681e12i	0.256026	+	1.45199i
$986$	9.16747e10	−	1.61647e10i	0.0969933	−	0.0171025i
$987$		0			0
$988$	3.53349e11	+	2.96495e11i	0.370831	+	0.311164i
$989$	−6.86409e11	+	3.96298e11i	−0.717460	+	0.414226i
$990$		0			0
$991$	3.29931e11	−	5.71457e11i	0.342081	−	0.592501i	−0.642738	−	0.766086i	$-0.722202\pi$
$991$	3.29931e11	−	5.71457e11i	0.342081	−	0.592501i	0.984819	+	0.173585i	$0.0555351\pi$
$992$	3.02304e11	+	8.30575e11i	0.312175	+	0.857693i
$993$		0			0
$994$	2.66889e11	−	2.23946e11i	0.273391	−	0.229402i
$995$	−8.64390e11	+	2.37489e12i	−0.881896	+	2.42299i
$996$		0			0
$997$	3.24379e10	−	1.83965e11i	0.0328301	−	0.186189i	−0.963983	−	0.265965i	$-0.914309\pi$
$997$	3.24379e10	−	1.83965e11i	0.0328301	−	0.186189i	0.996813	+	0.0797761i	$0.0254205\pi$
$998$		−	8.03708e9i		−	0.00810170i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.16		138
3.2	odd	2		27.9.f.a.2.8	✓	138
27.13	even	9		27.9.f.a.14.8	yes	138
27.14	odd	18	inner	81.9.f.a.71.16		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.8	✓	138	3.2	odd	2
27.9.f.a.14.8	yes	138	27.13	even	9
81.9.f.a.8.16		138	1.1	even	1	trivial
81.9.f.a.71.16		138	27.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(8.24786 + 1.45432i) q^{2} +(-174.649 - 63.5671i) q^{4} +(-723.153 - 861.820i) q^{5} +(2191.55 - 797.660i) q^{7} +(-3204.82 - 1850.30i) q^{8} +(-4711.10 - 8159.87i) q^{10} +(-2798.09 + 3334.63i) q^{11} +(-6274.91 - 35586.8i) q^{13} +(19235.7 - 3391.77i) q^{14} +(12706.1 + 10661.7i) q^{16} +(-32378.2 + 18693.6i) q^{17} +(34340.1 - 59478.9i) q^{19} +(71514.6 + 196485. i) q^{20} +(-27927.9 + 23434.3i) q^{22} +(-148858. + 408984. i) q^{23} +(-151952. + 861764. i) q^{25} -302641. i q^{26} -433458. q^{28} +(-292777. - 51624.5i) q^{29} +(764612. + 278296. i) q^{31} +(698240. + 832130. i) q^{32} +(-294238. + 107094. i) q^{34} +(-2.27227e6 - 1.31189e6i) q^{35} +(-1.13655e6 - 1.96857e6i) q^{37} +(369734. - 440632. i) q^{38} +(722945. + 4.10002e6i) q^{40} +(-1.45417e6 + 256409. i) q^{41} +(1.39504e6 + 1.17057e6i) q^{43} +(700657. - 404524. i) q^{44} +(-1.82256e6 + 3.15676e6i) q^{46} +(647951. + 1.78023e6i) q^{47} +(-249448. + 209312. i) q^{49} +(-2.50656e6 + 6.88672e6i) q^{50} +(-1.16624e6 + 6.61408e6i) q^{52} +6.52907e6i q^{53} +4.89730e6 q^{55} +(-8.49944e6 - 1.49868e6i) q^{56} +(-2.33970e6 - 851583. i) q^{58} +(-1.53319e7 - 1.82719e7i) q^{59} +(1.95580e7 - 7.11851e6i) q^{61} +(5.90169e6 + 3.40734e6i) q^{62} +(2.42571e6 + 4.20146e6i) q^{64} +(-2.61317e7 + 3.11425e7i) q^{65} +(-370662. - 2.10213e6i) q^{67} +(6.84313e6 - 1.20663e6i) q^{68} +(-1.68334e7 - 1.41249e7i) q^{70} +(1.54472e7 - 8.91846e6i) q^{71} +(-1.66329e7 + 2.88091e7i) q^{73} +(-6.51120e6 - 1.78894e7i) q^{74} +(-9.77838e6 + 8.20503e6i) q^{76} +(-3.47226e6 + 9.53995e6i) q^{77} +(-9.65767e6 + 5.47714e7i) q^{79} -1.86604e7i q^{80} -1.23667e7 q^{82} +(5.73546e7 + 1.01132e7i) q^{83} +(3.95249e7 + 1.43859e7i) q^{85} +(9.80367e6 + 1.16836e7i) q^{86} +(1.51374e7 - 5.50958e6i) q^{88} +(4.54337e7 + 2.62311e7i) q^{89} +(-4.21380e7 - 7.29851e7i) q^{91} +(5.19959e7 - 6.19663e7i) q^{92} +(2.75518e6 + 1.56254e7i) q^{94} +(-7.60932e7 + 1.34173e7i) q^{95} +(-7.13382e7 - 5.98599e7i) q^{97} +(-2.36182e6 + 1.36360e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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