LMFDB - Embedded newform 81.10.e.a.19.17

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			19.17
Character	$\chi$	$=$	81.19
Dual form			81.10.e.a.64.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.9570 - 4.71595i) q^{2} +(-246.572 + 206.898i) q^{4} +(222.415 + 1261.38i) q^{5} +(-4998.24 - 4194.02i) q^{7} +(-5748.96 + 9957.50i) q^{8} +(8830.42 + 15294.7i) q^{10} +(-4387.44 + 24882.4i) q^{11} +(14554.5 + 5297.40i) q^{13} +(-84540.9 - 30770.4i) q^{14} +(1087.25 - 6166.10i) q^{16} +(-187103. - 324072. i) q^{17} +(-331545. + 574253. i) q^{19} +(-315818. - 265003. i) q^{20} +(60496.3 + 343092. i) q^{22} +(1.82158e6 - 1.52849e6i) q^{23} +(293733. - 106910. i) q^{25} +213564. q^{26} +2.10016e6 q^{28} +(-2.27688e6 + 828718. i) q^{29} +(4.94152e6 - 4.14643e6i) q^{31} +(-1.03725e6 - 5.88253e6i) q^{32} +(-3.95260e6 - 3.31663e6i) q^{34} +(4.17856e6 - 7.23748e6i) q^{35} +(-8.89215e6 - 1.54017e7i) q^{37} +(-1.58767e6 + 9.00413e6i) q^{38} +(-1.38388e7 - 5.03692e6i) q^{40} +(-3.98972e6 - 1.45214e6i) q^{41} +(-2.25330e6 + 1.27791e7i) q^{43} +(-4.06631e6 - 7.04305e6i) q^{44} +(1.63939e7 - 2.83951e7i) q^{46} +(1.91163e6 + 1.60405e6i) q^{47} +(385257. + 2.18490e6i) q^{49} +(3.30171e6 - 2.77047e6i) q^{50} +(-4.68475e6 + 1.70511e6i) q^{52} +9.09978e6 q^{53} -3.23619e7 q^{55} +(7.04967e7 - 2.56587e7i) q^{56} +(-2.55933e7 + 2.14754e7i) q^{58} +(-2.51267e7 - 1.42501e8i) q^{59} +(-1.76413e6 - 1.48028e6i) q^{61} +(4.44728e7 - 7.70291e7i) q^{62} +(-3.95784e7 - 6.85519e7i) q^{64} +(-3.44489e6 + 1.95369e7i) q^{65} +(-2.75317e8 - 1.00207e8i) q^{67} +(1.13184e8 + 4.11957e7i) q^{68} +(2.00099e7 - 1.13482e8i) q^{70} +(-3.55199e7 - 6.15222e7i) q^{71} +(-2.15747e8 + 3.73685e8i) q^{73} +(-1.87849e8 - 1.57624e8i) q^{74} +(-3.70623e7 - 2.10191e8i) q^{76} +(1.26287e8 - 1.05967e8i) q^{77} +(3.19548e8 - 1.16306e8i) q^{79} +8.01960e6 q^{80} -5.85430e7 q^{82} +(1.63239e8 - 5.94141e7i) q^{83} +(3.67163e8 - 3.08086e8i) q^{85} +(3.10697e7 + 1.76205e8i) q^{86} +(-2.22543e8 - 1.86736e8i) q^{88} +(2.35605e8 - 4.08079e8i) q^{89} +(-5.05294e7 - 8.75195e7i) q^{91} +(-1.32909e8 + 7.53763e8i) q^{92} +(3.23336e7 + 1.17685e7i) q^{94} +(-7.98090e8 - 2.90481e8i) q^{95} +(1.26743e8 - 7.18794e8i) q^{97} +(1.52957e7 + 2.64928e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

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

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 $

$2$	12.9570	−	4.71595i	0.572623	−	0.208418i	−0.0394465	−	0.999222i	$-0.512559\pi$
$2$	12.9570	−	4.71595i	0.572623	−	0.208418i	0.612070	+	0.790804i	$0.290337\pi$
$3$		0			0
$3$		0			0
$4$	−246.572	+	206.898i	−0.481585	+	0.404098i
$5$	222.415	+	1261.38i	0.159147	+	0.902568i	0.954896	+	0.296941i	$0.0959665\pi$
$5$	222.415	+	1261.38i	0.159147	+	0.902568i	−0.795749	+	0.605627i	$0.792922\pi$
$6$		0			0
$7$	−4998.24	−	4194.02i	−0.786821	−	0.660221i	0.158135	−	0.987417i	$-0.449452\pi$
$7$	−4998.24	−	4194.02i	−0.786821	−	0.660221i	−0.944956	+	0.327196i	$0.893896\pi$
$8$	−5748.96	+	9957.50i	−0.496232	+	0.859499i
$9$		0			0
$10$	8830.42	+	15294.7i	0.279242	+	0.483662i
$11$	−4387.44	+	24882.4i	−0.0903533	+	0.512419i	0.905719	+	0.423878i	$0.139332\pi$
$11$	−4387.44	+	24882.4i	−0.0903533	+	0.512419i	−0.996073	+	0.0885409i	$0.971780\pi$
$12$		0			0
$13$	14554.5	+	5297.40i	0.141336	+	0.0514420i	0.411719	−	0.911311i	$-0.364928\pi$
$13$	14554.5	+	5297.40i	0.141336	+	0.0514420i	−0.270384	+	0.962753i	$0.587151\pi$
$14$	−84540.9	−	30770.4i	−0.588154	−	0.214070i
$15$		0			0
$16$	1087.25	−	6166.10i	0.00414753	−	0.0235218i
$17$	−187103.	−	324072.i	−0.543326	−	0.941069i	−0.998710	−	0.0507737i	$-0.983831\pi$
$17$	−187103.	−	324072.i	−0.543326	−	0.941069i	0.455384	−	0.890295i	$-0.349502\pi$
$18$		0			0
$19$	−331545.	+	574253.i	−0.583649	+	1.01091i	0.411394	+	0.911458i	$0.365042\pi$
$19$	−331545.	+	574253.i	−0.583649	+	1.01091i	−0.995042	+	0.0994513i	$0.968291\pi$
$20$	−315818.	−	265003.i	−0.441369	−	0.370352i
$21$		0			0
$22$	60496.3	+	343092.i	0.0550588	+	0.312254i
$23$	1.82158e6	−	1.52849e6i	1.35729	−	1.13890i	0.380483	−	0.924788i	$-0.375758\pi$
$23$	1.82158e6	−	1.52849e6i	1.35729	−	1.13890i	0.976809	−	0.214114i	$-0.0686865\pi$
$24$		0			0
$25$	293733.	−	106910.i	0.150391	−	0.0547380i
$26$	213564.			0.0916535
$27$		0			0
$28$	2.10016e6			0.645715
$29$	−2.27688e6	+	828718.i	−0.597792	+	0.217578i	−0.623153	−	0.782100i	$-0.714149\pi$
$29$	−2.27688e6	+	828718.i	−0.597792	+	0.217578i	0.0253612	+	0.999678i	$0.491926\pi$
$30$		0			0
$31$	4.94152e6	−	4.14643e6i	0.961021	−	0.806392i	−0.0200981	−	0.999798i	$-0.506398\pi$
$31$	4.94152e6	−	4.14643e6i	0.961021	−	0.806392i	0.981119	+	0.193406i	$0.0619534\pi$
$32$	−1.03725e6	−	5.88253e6i	−0.174867	−	0.991720i
$33$		0			0
$34$	−3.95260e6	−	3.31663e6i	−0.507257	−	0.425639i
$35$	4.17856e6	−	7.23748e6i	0.470674	−	0.815232i
$36$		0			0
$37$	−8.89215e6	−	1.54017e7i	−0.780008	−	1.35101i	−0.931936	−	0.362622i	$-0.881882\pi$
$37$	−8.89215e6	−	1.54017e7i	−0.780008	−	1.35101i	0.151928	−	0.988392i	$-0.451452\pi$
$38$	−1.58767e6	+	9.00413e6i	−0.123519	+	0.700512i
$39$		0			0
$40$	−1.38388e7	−	5.03692e6i	−0.854730	−	0.311096i
$41$	−3.98972e6	−	1.45214e6i	−0.220503	−	0.0802567i	0.229406	−	0.973331i	$-0.426322\pi$
$41$	−3.98972e6	−	1.45214e6i	−0.220503	−	0.0802567i	−0.449910	+	0.893074i	$0.648544\pi$
$42$		0			0
$43$	−2.25330e6	+	1.27791e7i	−0.100510	+	0.570023i	0.892408	+	0.451229i	$0.149014\pi$
$43$	−2.25330e6	+	1.27791e7i	−0.100510	+	0.570023i	−0.992919	+	0.118795i	$0.962097\pi$
$44$	−4.06631e6	−	7.04305e6i	−0.163555	−	0.283285i
$45$		0			0
$46$	1.63939e7	−	2.83951e7i	0.539849	−	0.935045i
$47$	1.91163e6	+	1.60405e6i	0.0571432	+	0.0479488i	0.670912	−	0.741537i	$-0.265903\pi$
$47$	1.91163e6	+	1.60405e6i	0.0571432	+	0.0479488i	−0.613769	+	0.789486i	$0.710347\pi$
$48$		0			0
$49$	385257.	+	2.18490e6i	0.00954702	+	0.0541439i
$50$	3.30171e6	−	2.77047e6i	0.0747092	−	0.0626885i
$51$		0			0
$52$	−4.68475e6	+	1.70511e6i	−0.0888528	+	0.0323398i
$53$	9.09978e6			0.158412			0.0792062	−	0.996858i	$-0.474761\pi$
$53$	9.09978e6			0.158412			0.0792062	+	0.996858i	$0.474761\pi$
$54$		0			0
$55$	−3.23619e7			−0.476872
$56$	7.04967e7	−	2.56587e7i	0.957905	−	0.348649i
$57$		0			0
$58$	−2.55933e7	+	2.14754e7i	−0.296962	+	0.249181i
$59$	−2.51267e7	−	1.42501e8i	−0.269961	−	1.53103i	−0.754525	−	0.656271i	$-0.772133\pi$
$59$	−2.51267e7	−	1.42501e8i	−0.269961	−	1.53103i	0.484564	−	0.874756i	$-0.338978\pi$
$60$		0			0
$61$	−1.76413e6	−	1.48028e6i	−0.0163135	−	0.0136886i	0.634594	−	0.772845i	$-0.281167\pi$
$61$	−1.76413e6	−	1.48028e6i	−0.0163135	−	0.0136886i	−0.650908	+	0.759157i	$0.725612\pi$
$62$	4.44728e7	−	7.70291e7i	0.382236	−	0.662052i
$63$		0			0
$64$	−3.95784e7	−	6.85519e7i	−0.294882	−	0.510751i
$65$	−3.44489e6	+	1.95369e7i	−0.0239367	+	0.135752i
$66$		0			0
$67$	−2.75317e8	−	1.00207e8i	−1.66916	−	0.607523i	−0.677394	−	0.735620i	$-0.736891\pi$
$67$	−2.75317e8	−	1.00207e8i	−1.66916	−	0.607523i	−0.991762	+	0.128097i	$0.959113\pi$
$68$	1.13184e8	+	4.11957e7i	0.641942	+	0.233648i
$69$		0			0
$70$	2.00099e7	−	1.13482e8i	0.0996101	−	0.564917i
$71$	−3.55199e7	−	6.15222e7i	−0.165886	−	0.287322i	0.771084	−	0.636734i	$-0.219715\pi$
$71$	−3.55199e7	−	6.15222e7i	−0.165886	−	0.287322i	−0.936969	+	0.349411i	$0.886382\pi$
$72$		0			0
$73$	−2.15747e8	+	3.73685e8i	−0.889186	+	1.54011i	−0.0483457	+	0.998831i	$0.515395\pi$
$73$	−2.15747e8	+	3.73685e8i	−0.889186	+	1.54011i	−0.840840	+	0.541284i	$0.817938\pi$
$74$	−1.87849e8	−	1.57624e8i	−0.728226	−	0.611054i
$75$		0			0
$76$	−3.70623e7	−	2.10191e8i	−0.127430	−	0.722690i
$77$	1.26287e8	−	1.05967e8i	0.409402	−	0.343529i
$78$		0			0
$79$	3.19548e8	−	1.16306e8i	0.923025	−	0.335954i	0.163584	−	0.986529i	$-0.447695\pi$
$79$	3.19548e8	−	1.16306e8i	0.923025	−	0.335954i	0.759441	+	0.650576i	$0.225472\pi$
$80$	8.01960e6			0.0218901
$81$		0			0
$82$	−5.85430e7			−0.142992
$83$	1.63239e8	−	5.94141e7i	0.377548	−	0.137416i	−0.146274	−	0.989244i	$-0.546728\pi$
$83$	1.63239e8	−	5.94141e7i	0.377548	−	0.137416i	0.523822	+	0.851828i	$0.324506\pi$
$84$		0			0
$85$	3.67163e8	−	3.08086e8i	0.762910	−	0.640157i
$86$	3.10697e7	+	1.76205e8i	0.0612483	+	0.347357i
$87$		0			0
$88$	−2.22543e8	−	1.86736e8i	−0.395587	−	0.331937i
$89$	2.35605e8	−	4.08079e8i	0.398042	−	0.689429i	−0.595443	−	0.803398i	$-0.703023\pi$
$89$	2.35605e8	−	4.08079e8i	0.398042	−	0.689429i	0.993484	+	0.113969i	$0.0363566\pi$
$90$		0			0
$91$	−5.05294e7	−	8.75195e7i	−0.0772428	−	0.133788i
$92$	−1.32909e8	+	7.53763e8i	−0.193423	+	1.09696i
$93$		0			0
$94$	3.23336e7	+	1.17685e7i	0.0427149	+	0.0155469i
$95$	−7.98090e8	−	2.90481e8i	−1.00530	−	0.365899i
$96$		0			0
$97$	1.26743e8	−	7.18794e8i	0.145362	−	0.824389i	−0.821714	−	0.569900i	$-0.806982\pi$
$97$	1.26743e8	−	7.18794e8i	0.145362	−	0.824389i	0.967076	−	0.254488i	$-0.0819070\pi$
$98$	1.52957e7	+	2.64928e7i	0.0167514	+	0.0290142i
$99$		0			0
$100$	−5.03068e7	+	8.71339e7i	−0.0503068	+	0.0871339i
$101$	9.00064e7	+	7.55243e7i	0.0860651	+	0.0722172i	0.684805	−	0.728726i	$-0.259887\pi$
$101$	9.00064e7	+	7.55243e7i	0.0860651	+	0.0722172i	−0.598740	+	0.800943i	$0.704332\pi$
$102$		0			0
$103$	2.01766e8	+	1.14427e9i	0.176637	+	1.00176i	0.936238	+	0.351367i	$0.114283\pi$
$103$	2.01766e8	+	1.14427e9i	0.176637	+	1.00176i	−0.759601	+	0.650389i	$0.774606\pi$
$104$	−1.36422e8	+	1.14472e8i	−0.114350	+	0.0959507i
$105$		0			0
$106$	1.17906e8	−	4.29141e7i	0.0907106	−	0.0330160i
$107$	1.71487e8			0.126475			0.0632373	−	0.997999i	$-0.479858\pi$
$107$	1.71487e8			0.126475			0.0632373	+	0.997999i	$0.479858\pi$
$108$		0			0
$109$	−1.54312e8			−0.104708			−0.0523539	−	0.998629i	$-0.516672\pi$
$109$	−1.54312e8			−0.104708			−0.0523539	+	0.998629i	$0.516672\pi$
$110$	−4.19313e8	+	1.52617e8i	−0.273068	+	0.0993887i
$111$		0			0
$112$	−3.12951e7	+	2.62597e7i	−0.0187930	+	0.0157692i
$113$	−1.57576e8	−	8.93656e8i	−0.0909151	−	0.515605i	−0.995923	−	0.0902099i	$-0.971246\pi$
$113$	−1.57576e8	−	8.93656e8i	−0.0909151	−	0.515605i	0.905008	−	0.425395i	$-0.139865\pi$
$114$		0			0
$115$	2.33315e9	+	1.95774e9i	1.24395	+	1.04379i
$116$	3.89955e8	−	6.75422e8i	0.199965	−	0.346349i
$117$		0			0
$118$	−9.97593e8	−	1.72788e9i	−0.473679	−	0.820436i
$119$	−4.23979e8	+	2.40450e9i	−0.193813	+	1.09917i
$120$		0			0
$121$	1.61586e9	+	5.88126e8i	0.685283	+	0.249423i
$122$	−2.98387e7	−	1.08604e7i	−0.0121944	−	0.00443841i
$123$		0			0
$124$	−3.60550e8	+	2.04478e9i	−0.136952	+	0.776693i
$125$	1.45100e9	+	2.51321e9i	0.531585	+	0.920732i
$126$		0			0
$127$	−2.53672e9	+	4.39373e9i	−0.865279	+	1.49871i	0.00148997	+	0.999999i	$0.499526\pi$
$127$	−2.53672e9	+	4.39373e9i	−0.865279	+	1.49871i	−0.866769	+	0.498709i	$0.833808\pi$
$128$	1.50670e9	+	1.26427e9i	0.496115	+	0.416290i
$129$		0			0
$130$	4.74999e7	+	2.69385e8i	0.0145864	+	0.0827235i
$131$	1.39004e9	−	1.16638e9i	0.412388	−	0.346035i	−0.412870	−	0.910790i	$-0.635474\pi$
$131$	1.39004e9	−	1.16638e9i	0.412388	−	0.346035i	0.825259	+	0.564755i	$0.191029\pi$
$132$		0			0
$133$	4.06557e9	−	1.47975e9i	1.12665	−	0.410067i
$134$	−4.03985e9			−1.08242
$135$		0			0
$136$	4.30260e9			1.07846
$137$	−5.71529e9	+	2.08019e9i	−1.38610	+	0.504500i	−0.924023	−	0.382338i	$-0.875119\pi$
$137$	−5.71529e9	+	2.08019e9i	−1.38610	+	0.504500i	−0.462080	+	0.886838i	$0.652897\pi$
$138$		0			0
$139$	−6.07364e9	+	5.09639e9i	−1.38001	+	1.15797i	−0.410802	+	0.911724i	$0.634751\pi$
$139$	−6.07364e9	+	5.09639e9i	−1.38001	+	1.15797i	−0.969208	+	0.246242i	$0.920804\pi$
$140$	4.67107e8	+	2.64909e9i	0.102764	+	0.582802i
$141$		0			0
$142$	−7.50366e8	−	6.29632e8i	−0.154873	−	0.129954i
$143$	−1.95669e8	+	3.38909e8i	−0.0391300	+	0.0677751i
$144$		0			0
$145$	−1.55174e9	−	2.68769e9i	−0.291516	−	0.504921i
$146$	−1.03315e9	+	5.85929e9i	−0.188181	+	1.06723i
$147$		0			0
$148$	5.37913e9	+	1.95784e9i	0.921582	+	0.335429i
$149$	9.88175e9	+	3.59666e9i	1.64246	+	0.597808i	0.987467	−	0.157824i	$-0.0504479\pi$
$149$	9.88175e9	+	3.59666e9i	1.64246	+	0.597808i	0.654996	+	0.755632i	$0.272670\pi$
$150$		0			0
$151$	6.60043e8	−	3.74329e9i	0.103318	−	0.585945i	−0.888561	−	0.458759i	$-0.848294\pi$
$151$	6.60043e8	−	3.74329e9i	0.103318	−	0.585945i	0.991879	−	0.127186i	$-0.0405947\pi$
$152$	−3.81208e9	−	6.60272e9i	−0.579250	−	1.00329i
$153$		0			0
$154$	1.13656e9	−	1.96858e9i	0.162835	−	0.282039i
$155$	6.32927e9	+	5.31089e9i	0.880767	+	0.739052i
$156$		0			0
$157$	8.69173e7	+	4.92933e8i	0.0114172	+	0.0647499i	0.989984	−	0.141179i	$-0.0450894\pi$
$157$	8.69173e7	+	4.92933e8i	0.0114172	+	0.0647499i	−0.978567	+	0.205929i	$0.933978\pi$
$158$	3.59188e9	−	3.01394e9i	0.458527	−	0.384750i
$159$		0			0
$160$	7.18938e9	−	2.61672e9i	0.867265	−	0.315659i
$161$	−1.55152e10			−1.81987
$162$		0			0
$163$	−1.47137e10			−1.63259			−0.816295	−	0.577635i	$-0.803976\pi$
$163$	−1.47137e10			−1.63259			−0.816295	+	0.577635i	$0.803976\pi$
$164$	1.28420e9	−	4.67410e8i	0.138623	−	0.0504545i
$165$		0			0
$166$	1.83489e9	−	1.53965e9i	0.187553	−	0.157375i
$167$	−9.07130e7	−	5.14459e8i	−0.00902496	−	0.0511831i	0.979963	−	0.199181i	$-0.0638282\pi$
$167$	−9.07130e7	−	5.14459e8i	−0.00902496	−	0.0511831i	−0.988988	+	0.147998i	$0.952717\pi$
$168$		0			0
$169$	−7.93975e9	−	6.66224e9i	−0.748715	−	0.628246i
$170$	3.30440e9	−	5.72339e9i	0.303440	−	0.525573i
$171$		0			0
$172$	−2.08837e9	−	3.61717e9i	−0.181941	−	0.315131i
$173$	2.60634e9	−	1.47813e10i	0.221219	−	1.25460i	−0.648563	−	0.761161i	$-0.724630\pi$
$173$	2.60634e9	−	1.47813e10i	0.221219	−	1.25460i	0.869782	−	0.493436i	$-0.164259\pi$
$174$		0			0
$175$	−1.91653e9	−	6.97561e8i	−0.154470	−	0.0562226i
$176$	1.48657e8	+	5.41068e7i	0.0116783	+	0.00425055i
$177$		0			0
$178$	1.12824e9	−	6.39857e9i	0.0842387	−	0.477742i
$179$	−7.83220e9	−	1.35658e10i	−0.570224	−	0.987656i	−0.996543	−	0.0830834i	$-0.973523\pi$
$179$	−7.83220e9	−	1.35658e10i	−0.570224	−	0.987656i	0.426319	−	0.904573i	$-0.359810\pi$
$180$		0			0
$181$	7.25470e9	−	1.25655e10i	0.502419	−	0.870215i	−0.497577	−	0.867420i	$-0.665777\pi$
$181$	7.25470e9	−	1.25655e10i	0.502419	−	0.870215i	0.999996	−	0.00279503i	$-0.000889686\pi$
$182$	−1.06745e9	−	8.95694e8i	−0.0721149	−	0.0605116i
$183$		0			0
$184$	4.74771e9	+	2.69256e10i	0.305354	+	1.73175i
$185$	1.74496e10	−	1.46419e10i	1.09525	−	0.919020i
$186$		0			0
$187$	8.88460e9	−	3.23373e9i	0.531313	−	0.193382i
$188$	−8.03230e8			−0.0468953
$189$		0			0
$190$	−1.17107e10			−0.651918
$191$	−5.33447e9	+	1.94159e9i	−0.290029	+	0.105562i	−0.482937	−	0.875655i	$-0.660430\pi$
$191$	−5.33447e9	+	1.94159e9i	−0.290029	+	0.105562i	0.192909	+	0.981217i	$0.438208\pi$
$192$		0			0
$193$	−6.22322e9	+	5.22191e9i	−0.322855	+	0.270908i	−0.789781	−	0.613389i	$-0.789806\pi$
$193$	−6.22322e9	+	5.22191e9i	−0.322855	+	0.270908i	0.466926	+	0.884296i	$0.345361\pi$
$194$	−1.74760e9	−	9.91112e9i	−0.0885796	−	0.502360i
$195$		0			0
$196$	−5.47045e8	−	4.59026e8i	−0.0264771	−	0.0222170i
$197$	9.16280e9	−	1.58704e10i	0.433441	−	0.750743i	−0.563726	−	0.825962i	$-0.690632\pi$
$197$	9.16280e9	−	1.58704e10i	0.433441	−	0.750743i	0.997167	+	0.0752196i	$0.0239658\pi$
$198$		0			0
$199$	−1.25288e10	−	2.17006e10i	−0.566333	−	0.980918i	−0.996924	−	0.0783710i	$-0.975028\pi$
$199$	−1.25288e10	−	2.17006e10i	−0.566333	−	0.980918i	0.430591	−	0.902547i	$-0.358305\pi$
$200$	−6.24105e8	+	3.53947e9i	−0.0275818	+	0.156424i
$201$		0			0
$202$	1.52238e9	+	5.54101e8i	0.0643342	+	0.0234157i
$203$	1.48561e10	+	5.40717e9i	0.614005	+	0.223480i
$204$		0			0
$205$	9.44323e8	−	5.35552e9i	0.0373446	−	0.211792i
$206$	8.01061e9	+	1.38748e10i	0.309930	+	0.536814i
$207$		0			0
$208$	4.84887e7	−	8.39849e7i	0.00179620	−	0.00311111i
$209$	−1.28342e10	−	1.07691e10i	−0.465274	−	0.390412i
$210$		0			0
$211$	2.99464e9	+	1.69835e10i	0.104010	+	0.589868i	0.991611	+	0.129256i	$0.0412589\pi$
$211$	2.99464e9	+	1.69835e10i	0.104010	+	0.589868i	−0.887602	+	0.460612i	$0.847630\pi$
$212$	−2.24375e9	+	1.88273e9i	−0.0762891	+	0.0640142i
$213$		0			0
$214$	2.22195e9	−	8.08723e8i	0.0724222	−	0.0263595i
$215$	−1.66204e10			−0.530481
$216$		0			0
$217$	−4.20891e10			−1.28855
$218$	−1.99941e9	+	7.27727e8i	−0.0599581	+	0.0218230i
$219$		0			0
$220$	7.97954e9	−	6.69562e9i	0.229655	−	0.192703i
$221$	−1.00645e9	−	5.70786e9i	−0.0283810	−	0.160956i
$222$		0			0
$223$	−3.04226e10	−	2.55276e10i	−0.823804	−	0.691254i	0.130056	−	0.991507i	$-0.458484\pi$
$223$	−3.04226e10	−	2.55276e10i	−0.823804	−	0.691254i	−0.953860	+	0.300253i	$0.902929\pi$
$224$	−1.94870e10	+	3.37525e10i	−0.517165	+	0.895757i
$225$		0			0
$226$	−6.25614e9	−	1.08360e10i	−0.159521	−	0.276299i
$227$	−1.16503e10	+	6.60722e10i	−0.291220	+	1.65159i	0.390961	+	0.920407i	$0.372143\pi$
$227$	−1.16503e10	+	6.60722e10i	−0.291220	+	1.65159i	−0.682181	+	0.731183i	$0.738968\pi$
$228$		0			0
$229$	8.92141e9	+	3.24713e9i	0.214375	+	0.0780261i	0.446975	−	0.894546i	$-0.352501\pi$
$229$	8.92141e9	+	3.24713e9i	0.214375	+	0.0780261i	−0.232600	+	0.972572i	$0.574723\pi$
$230$	3.94631e10	+	1.43634e10i	0.929857	+	0.338440i
$231$		0			0
$232$	4.83777e9	−	2.74363e10i	0.109635	−	0.621771i
$233$	−3.72517e10	−	6.45218e10i	−0.828027	−	1.43418i	−0.899584	−	0.436748i	$-0.856130\pi$
$233$	−3.72517e10	−	6.45218e10i	−0.828027	−	1.43418i	0.0715572	−	0.997437i	$-0.477203\pi$
$234$		0			0
$235$	−1.59814e9	+	2.76806e9i	−0.0341829	+	0.0592065i
$236$	3.56787e10	+	2.99380e10i	0.748694	+	0.628229i
$237$		0			0
$238$	5.84605e9	+	3.31546e10i	0.118104	+	0.669803i
$239$	4.24492e10	−	3.56191e10i	0.841548	−	0.706142i	−0.116364	−	0.993207i	$-0.537124\pi$
$239$	4.24492e10	−	3.56191e10i	0.841548	−	0.706142i	0.957911	+	0.287064i	$0.0926794\pi$
$240$		0			0
$241$	4.96719e10	−	1.80791e10i	0.948493	−	0.345223i	0.178979	−	0.983853i	$-0.442721\pi$
$241$	4.96719e10	−	1.80791e10i	0.948493	−	0.345223i	0.769514	+	0.638630i	$0.220498\pi$
$242$	2.37103e10			0.444393
$243$		0			0
$244$	7.41252e8			0.0133879
$245$	−2.67030e9	+	9.71908e8i	−0.0473491	+	0.0172337i
$246$		0			0
$247$	−7.86752e9	+	6.60163e9i	−0.134494	+	0.112853i
$248$	1.28794e10	+	7.30428e10i	0.216204	+	1.22615i
$249$		0			0
$250$	3.06528e10	+	2.57207e10i	0.496295	+	0.416441i
$251$	2.08476e10	−	3.61091e10i	0.331531	−	0.574229i	−0.651281	−	0.758837i	$-0.725768\pi$
$251$	2.08476e10	−	3.61091e10i	0.331531	−	0.574229i	0.982812	+	0.184607i	$0.0591014\pi$
$252$		0			0
$253$	3.00404e10	+	5.20314e10i	0.460960	+	0.798405i
$254$	−1.21476e10	+	6.88926e10i	−0.183122	+	1.03853i
$255$		0			0
$256$	6.35687e10	+	2.31371e10i	0.925047	+	0.336689i
$257$	−9.68995e10	−	3.52685e10i	−1.38555	−	0.504299i	−0.461694	−	0.887039i	$-0.652758\pi$
$257$	−9.68995e10	−	3.52685e10i	−1.38555	−	0.504299i	−0.923856	+	0.382740i	$0.874981\pi$
$258$		0			0
$259$	−2.01498e10	+	1.14275e11i	−0.278241	+	1.57798i
$260$	−3.19274e9	−	5.52999e9i	−0.0433295	−	0.0750489i
$261$		0			0
$262$	1.25101e10	−	2.16681e10i	0.164023	−	0.284097i
$263$	−2.32813e10	−	1.95354e10i	−0.300059	−	0.251780i	0.480310	−	0.877099i	$-0.340524\pi$
$263$	−2.32813e10	−	1.95354e10i	−0.300059	−	0.251780i	−0.780369	+	0.625319i	$0.784969\pi$
$264$		0			0
$265$	2.02393e9	+	1.14783e10i	0.0252109	+	0.142978i
$266$	4.56991e10	−	3.83461e10i	0.559681	−	0.469628i
$267$		0			0
$268$	8.86182e10	−	3.22544e10i	1.04934	−	0.381928i
$269$	−1.06100e11			−1.23546			−0.617732	−	0.786388i	$-0.711948\pi$
$269$	−1.06100e11			−1.23546			−0.617732	+	0.786388i	$0.711948\pi$
$270$		0			0
$271$	−5.16724e10			−0.581965			−0.290982	−	0.956728i	$-0.593982\pi$
$271$	−5.16724e10			−0.581965			−0.290982	+	0.956728i	$0.593982\pi$
$272$	−2.20169e9	+	8.01349e8i	−0.0243891	+	0.00887691i
$273$		0			0
$274$	−6.42427e10	+	5.39061e10i	−0.688568	+	0.577777i
$275$	1.37145e9	+	7.77785e9i	0.0144604	+	0.0820092i
$276$		0			0
$277$	1.47446e10	+	1.23722e10i	0.150478	+	0.126266i	0.714919	−	0.699207i	$-0.246464\pi$
$277$	1.47446e10	+	1.23722e10i	0.150478	+	0.126266i	−0.564441	+	0.825474i	$0.690908\pi$
$278$	−5.46617e10	+	9.46768e10i	−0.548885	+	0.950697i
$279$		0			0
$280$	4.80448e10	+	8.32160e10i	0.467127	+	0.809088i
$281$	4.53849e9	−	2.57391e10i	0.0434243	−	0.246271i	−0.955367	−	0.295421i	$-0.904540\pi$
$281$	4.53849e9	−	2.57391e10i	0.0434243	−	0.246271i	0.998791	+	0.0491497i	$0.0156511\pi$
$282$		0			0
$283$	−1.56995e11	−	5.71417e10i	−1.45495	−	0.529559i	−0.510981	−	0.859592i	$-0.670718\pi$
$283$	−1.56995e11	−	5.71417e10i	−1.45495	−	0.529559i	−0.943969	+	0.330033i	$0.892940\pi$
$284$	2.14870e10	+	7.82064e9i	0.195994	+	0.0713362i
$285$		0			0
$286$	−9.37001e8	+	5.31400e9i	−0.00828119	+	0.0469650i
$287$	1.38513e10	+	2.39911e10i	0.120510	+	0.208729i
$288$		0			0
$289$	−1.07212e10	+	1.85697e10i	−0.0904072	+	0.156590i
$290$	−3.27809e10	−	2.75064e10i	−0.272163	−	0.228372i
$291$		0			0
$292$	−2.41176e10	−	1.36778e11i	−0.194139	−	1.10101i
$293$	−1.34724e11	+	1.13047e11i	−1.06792	+	0.896094i	−0.994863	−	0.101234i	$-0.967721\pi$
$293$	−1.34724e11	+	1.13047e11i	−1.06792	+	0.896094i	−0.0730601	+	0.997328i	$0.523276\pi$
$294$		0			0
$295$	1.74158e11	−	6.33885e10i	1.33889	−	0.487317i
$296$	2.04483e11			1.54826
$297$		0			0
$298$	1.44999e11			1.06511
$299$	3.46092e10	−	1.25967e10i	0.250421	−	0.0911458i
$300$		0			0
$301$	6.48584e10	−	5.44227e10i	0.455425	−	0.382147i
$302$	−9.10102e9	−	5.16144e10i	−0.0629591	−	0.357059i
$303$		0			0
$304$	3.18043e9	+	2.66870e9i	0.0213577	+	0.0179212i
$305$	1.47482e9	−	2.55447e9i	0.00975868	−	0.0169025i
$306$		0			0
$307$	−6.84591e10	−	1.18575e11i	−0.439854	−	0.761850i	0.557824	−	0.829959i	$-0.311637\pi$
$307$	−6.84591e10	−	1.18575e11i	−0.439854	−	0.761850i	−0.997678	+	0.0681098i	$0.978303\pi$
$308$	−9.21432e9	+	5.22570e10i	−0.0583425	+	0.330877i
$309$		0			0
$310$	1.07054e11	+	3.89645e10i	0.658379	+	0.239630i
$311$	−8.66299e10	−	3.15307e10i	−0.525105	−	0.191123i	0.0658464	−	0.997830i	$-0.479025\pi$
$311$	−8.66299e10	−	3.15307e10i	−0.525105	−	0.191123i	−0.590951	+	0.806707i	$0.701247\pi$
$312$		0			0
$313$	−1.13520e10	+	6.43802e10i	−0.0668531	+	0.379143i	0.932963	+	0.359972i	$0.117214\pi$
$313$	−1.13520e10	+	6.43802e10i	−0.0668531	+	0.379143i	−0.999816	+	0.0191709i	$0.993897\pi$
$314$	3.45083e9	+	5.97702e9i	0.0200328	+	0.0346978i
$315$		0			0
$316$	−5.47279e10	+	9.47916e10i	−0.308757	+	0.534783i
$317$	1.34809e11	+	1.13118e11i	0.749810	+	0.629166i	0.935453	−	0.353452i	$-0.114992\pi$
$317$	1.34809e11	+	1.13118e11i	0.749810	+	0.629166i	−0.185642	+	0.982617i	$0.559437\pi$
$318$		0			0
$319$	−1.06308e10	−	6.02903e10i	−0.0574789	−	0.325979i
$320$	7.76669e10	−	6.51703e10i	0.414058	−	0.347436i
$321$		0			0
$322$	−2.01030e11	+	7.31690e10i	−1.04210	+	0.379294i
$323$	2.48132e11			1.26845
$324$		0			0
$325$	4.84148e9			0.0240715
$326$	−1.90645e11	+	6.93891e10i	−0.934859	+	0.340261i
$327$		0			0
$328$	3.73964e10	−	3.13793e10i	0.178401	−	0.149696i
$329$	−2.82738e9	−	1.60349e10i	−0.0133046	−	0.0754542i
$330$		0			0
$331$	−2.89334e11	−	2.42780e11i	−1.32487	−	1.11170i	−0.985247	−	0.171138i	$-0.945256\pi$
$331$	−2.89334e11	−	2.42780e11i	−1.32487	−	1.11170i	−0.339624	−	0.940561i	$-0.610300\pi$
$332$	−2.79574e10	+	4.84236e10i	−0.126292	+	0.218744i
$333$		0			0
$334$	−3.60153e9	−	6.23803e9i	−0.0158354	−	0.0274276i
$335$	6.51645e10	−	3.69567e11i	0.282690	−	1.60321i
$336$		0			0
$337$	4.53479e10	+	1.65053e10i	0.191524	+	0.0697090i	0.436002	−	0.899946i	$-0.356394\pi$
$337$	4.53479e10	+	1.65053e10i	0.191524	+	0.0697090i	−0.244478	+	0.969655i	$0.578616\pi$
$338$	−1.34294e11	−	4.88790e10i	−0.559669	−	0.203703i
$339$		0			0
$340$	−2.67895e10	+	1.51931e11i	−0.108720	+	0.616581i
$341$	8.14924e10	+	1.41149e11i	0.326379	+	0.565306i
$342$		0			0
$343$	−1.24410e11	+	2.15485e11i	−0.485326	+	0.840609i
$344$	−1.14294e11	−	9.59039e10i	−0.440058	−	0.369252i
$345$		0			0
$346$	−3.59375e10	−	2.03812e11i	−0.134805	−	0.764517i
$347$	−3.16547e10	+	2.65615e10i	−0.117208	+	0.0983489i	−0.699508	−	0.714625i	$-0.746597\pi$
$347$	−3.16547e10	+	2.65615e10i	−0.117208	+	0.0983489i	0.582300	+	0.812974i	$0.302153\pi$
$348$		0			0
$349$	−3.17062e11	+	1.15401e11i	−1.14401	+	0.416386i	−0.843360	−	0.537349i	$-0.819426\pi$
$349$	−3.17062e11	+	1.15401e11i	−1.14401	+	0.416386i	−0.300650	+	0.953735i	$0.597204\pi$
$350$	−2.81221e10			−0.100171
$351$		0			0
$352$	1.50922e11			0.523976
$353$	1.78882e11	−	6.51076e10i	0.613168	−	0.223175i	−0.0167207	−	0.999860i	$-0.505323\pi$
$353$	1.78882e11	−	6.51076e10i	0.613168	−	0.223175i	0.629889	+	0.776685i	$0.283100\pi$
$354$		0			0
$355$	6.97026e10	−	5.84874e10i	0.232928	−	0.195450i
$356$	2.63374e10	+	1.49367e11i	0.0869057	+	0.492867i
$357$		0			0
$358$	−1.65457e11	−	1.38835e11i	−0.532368	−	0.446710i
$359$	2.11214e11	−	3.65833e11i	0.671116	−	1.16241i	−0.306473	−	0.951880i	$-0.599149\pi$
$359$	2.11214e11	−	3.65833e11i	0.671116	−	1.16241i	0.977588	−	0.210527i	$-0.0675179\pi$
$360$		0			0
$361$	−5.85005e10	−	1.01326e11i	−0.181291	−	0.314006i
$362$	3.47406e10	−	1.97024e11i	0.106328	−	0.603018i
$363$		0			0
$364$	3.05667e10	+	1.11254e10i	0.0912626	+	0.0332169i
$365$	−5.19343e11	−	1.89026e11i	−1.53157	−	0.557446i
$366$		0			0
$367$	−4.99129e10	+	2.83070e11i	−0.143620	+	0.814511i	0.824844	+	0.565360i	$0.191263\pi$
$367$	−4.99129e10	+	2.83070e11i	−0.143620	+	0.814511i	−0.968465	+	0.249151i	$0.919848\pi$
$368$	−7.44430e9	−	1.28939e10i	−0.0211596	−	0.0366496i
$369$		0			0
$370$	1.57043e11	−	2.72006e11i	0.435623	−	0.754521i
$371$	−4.54829e10	−	3.81647e10i	−0.124642	−	0.104587i
$372$		0			0
$373$	−2.05333e10	−	1.16450e11i	−0.0549247	−	0.311494i	0.944952	−	0.327210i	$-0.106108\pi$
$373$	−2.05333e10	−	1.16450e11i	−0.0549247	−	0.311494i	−0.999876	+	0.0157160i	$0.994997\pi$
$374$	9.98674e10	−	8.37987e10i	0.263938	−	0.221470i
$375$		0			0
$376$	−2.69623e10	+	9.81346e9i	−0.0695682	+	0.0253208i
$377$	−3.75289e10			−0.0956820
$378$		0			0
$379$	4.22411e11			1.05162			0.525809	−	0.850602i	$-0.323763\pi$
$379$	4.22411e11			1.05162			0.525809	+	0.850602i	$0.323763\pi$
$380$	2.56886e11	−	9.34990e10i	0.631997	−	0.230028i
$381$		0			0
$382$	−5.99622e10	+	5.03142e10i	−0.144076	+	0.120894i
$383$	1.06688e11	+	6.05059e11i	0.253351	+	1.43682i	0.800271	+	0.599639i	$0.204689\pi$
$383$	1.06688e11	+	6.05059e11i	0.253351	+	1.43682i	−0.546920	+	0.837185i	$0.684200\pi$
$384$		0			0
$385$	1.61753e11	+	1.35727e11i	0.375213	+	0.314841i
$386$	−5.60079e10	+	9.70086e10i	−0.128412	+	0.222417i
$387$		0			0
$388$	1.17466e11	+	2.03457e11i	0.263130	+	0.455754i
$389$	1.41597e11	−	8.03037e11i	0.313532	−	1.77813i	−0.266806	−	0.963750i	$-0.585968\pi$
$389$	1.41597e11	−	8.03037e11i	0.313532	−	1.77813i	0.580338	−	0.814376i	$-0.302921\pi$
$390$		0			0
$391$	−8.36163e11	−	3.04339e11i	−1.80924	−	0.658509i
$392$	−2.39710e10	−	8.72472e9i	−0.0512741	−	0.0186623i
$393$		0			0
$394$	4.38780e10	−	2.48844e11i	0.0917305	−	0.520229i
$395$	2.17778e11	+	3.77202e11i	0.450118	+	0.779627i
$396$		0			0
$397$	1.49240e11	−	2.58492e11i	0.301529	−	0.522264i	−0.674953	−	0.737860i	$-0.735836\pi$
$397$	1.49240e11	−	2.58492e11i	0.301529	−	0.522264i	0.976482	+	0.215597i	$0.0691697\pi$
$398$	−2.64675e11	−	2.22089e11i	−0.528736	−	0.443662i
$399$		0			0
$400$	−3.39858e8	−	1.92743e9i	−0.000663784	−	0.00376451i
$401$	2.63089e11	−	2.20758e11i	0.508104	−	0.426350i	−0.352357	−	0.935866i	$-0.614620\pi$
$401$	2.63089e11	−	2.20758e11i	0.508104	−	0.426350i	0.860462	+	0.509515i	$0.170175\pi$
$402$		0			0
$403$	9.38865e10	−	3.41719e10i	0.177309	−	0.0645352i
$404$	−3.78189e10			−0.0706305
$405$		0			0
$406$	2.17990e11			0.398170
$407$	4.22244e11	−	1.53684e11i	0.762761	−	0.277622i
$408$		0			0
$409$	5.18351e11	−	4.34948e11i	0.915945	−	0.768569i	−0.0572959	−	0.998357i	$-0.518248\pi$
$409$	5.18351e11	−	4.34948e11i	0.915945	−	0.768569i	0.973241	+	0.229788i	$0.0738034\pi$
$410$	−1.30208e10	−	7.38447e10i	−0.0227568	−	0.129060i
$411$		0			0
$412$	−2.86498e11	−	2.40400e11i	−0.489873	−	0.411052i
$413$	−4.72061e11	+	8.17634e11i	−0.798405	+	1.38288i
$414$		0			0
$415$	1.11250e11	+	1.92691e11i	0.184113	+	0.318893i
$416$	1.60655e10	−	9.11119e10i	0.0263011	−	0.149161i
$417$		0			0
$418$	−2.17079e11	−	7.90102e10i	−0.347796	−	0.126587i
$419$	−3.78288e11	−	1.37685e11i	−0.599597	−	0.218235i	0.0243484	−	0.999704i	$-0.492249\pi$
$419$	−3.78288e11	−	1.37685e11i	−0.599597	−	0.218235i	−0.623945	+	0.781468i	$0.714471\pi$
$420$		0			0
$421$	−6.68416e10	+	3.79078e11i	−0.103700	+	0.588110i	0.888032	+	0.459782i	$0.152072\pi$
$421$	−6.68416e10	+	3.79078e11i	−0.103700	+	0.588110i	−0.991732	+	0.128328i	$0.959039\pi$
$422$	1.18895e11	+	2.05932e11i	0.182497	+	0.316095i
$423$		0			0
$424$	−5.23143e10	+	9.06110e10i	−0.0786093	+	0.136155i
$425$	−8.96050e10	−	7.51876e10i	−0.133224	−	0.111788i
$426$		0			0
$427$	2.60922e9	+	1.47976e10i	0.00379826	+	0.0215410i
$428$	−4.22837e10	+	3.54803e10i	−0.0609083	+	0.0511081i
$429$		0			0
$430$	−2.15351e11	+	7.83813e10i	−0.303765	+	0.110562i
$431$	−7.95097e11			−1.10987			−0.554935	−	0.831894i	$-0.687257\pi$
$431$	−7.95097e11			−1.10987			−0.554935	+	0.831894i	$0.687257\pi$
$432$		0			0
$433$	6.46577e11			0.883945			0.441972	−	0.897029i	$-0.354279\pi$
$433$	6.46577e11			0.883945			0.441972	+	0.897029i	$0.354279\pi$
$434$	−5.45347e11	+	1.98490e11i	−0.737852	+	0.268556i
$435$		0			0
$436$	3.80489e10	−	3.19268e10i	0.0504258	−	0.0423123i
$437$	2.73802e11	+	1.55281e12i	0.359146	+	2.03682i
$438$		0			0
$439$	8.41026e11	+	7.05704e11i	1.08073	+	0.906844i	0.995982	−	0.0895585i	$-0.0285456\pi$
$439$	8.41026e11	+	7.05704e11i	1.08073	+	0.906844i	0.0847525	+	0.996402i	$0.472990\pi$
$440$	1.86048e11	−	3.22244e11i	0.236639	−	0.409871i
$441$		0			0
$442$	−3.99586e10	−	6.92103e10i	−0.0497978	−	0.0862522i
$443$	−2.71358e11	+	1.53895e12i	−0.334754	+	1.89849i	0.0948913	+	0.995488i	$0.469750\pi$
$443$	−2.71358e11	+	1.53895e12i	−0.334754	+	1.89849i	−0.429645	+	0.902998i	$0.641361\pi$
$444$		0			0
$445$	5.67143e11	+	2.06423e11i	0.685603	+	0.249539i
$446$	−5.14571e11	−	1.87289e11i	−0.615799	−	0.224132i
$447$		0			0
$448$	−8.96855e10	+	5.08632e11i	−0.105189	+	0.596557i
$449$	3.60741e11	+	6.24821e11i	0.418877	+	0.725517i	0.995827	−	0.0912631i	$-0.0290904\pi$
$449$	3.60741e11	+	6.24821e11i	0.418877	+	0.725517i	−0.576950	+	0.816780i	$0.695757\pi$
$450$		0			0
$451$	5.36374e10	−	9.29027e10i	0.0610482	−	0.105739i
$452$	2.23749e11	+	1.87748e11i	0.252138	+	0.211569i
$453$		0			0
$454$	1.60641e11	+	9.11038e11i	0.177461	+	1.00643i
$455$	9.91566e10	−	8.32023e10i	0.108460	−	0.0910089i
$456$		0			0
$457$	−6.15961e11	+	2.24192e11i	−0.660588	+	0.240434i	−0.650490	−	0.759515i	$-0.725436\pi$
$457$	−6.15961e11	+	2.24192e11i	−0.660588	+	0.240434i	−0.0100976	+	0.999949i	$0.503214\pi$
$458$	1.30908e11			0.139018
$459$		0			0
$460$	−9.80341e11			−1.02086
$461$	6.52984e11	−	2.37667e11i	0.673361	−	0.245083i	0.0173669	−	0.999849i	$-0.494472\pi$
$461$	6.52984e11	−	2.37667e11i	0.673361	−	0.245083i	0.655994	+	0.754766i	$0.272249\pi$
$462$		0			0
$463$	−5.45783e11	+	4.57966e11i	−0.551957	+	0.463147i	−0.875603	−	0.483031i	$-0.839536\pi$
$463$	−5.45783e11	+	4.57966e11i	−0.551957	+	0.463147i	0.323646	+	0.946178i	$0.395091\pi$
$464$	2.63442e9	+	1.49405e10i	0.00263848	+	0.0149636i
$465$		0			0
$466$	−7.86951e11	−	6.60331e11i	−0.773057	−	0.648671i
$467$	5.02439e11	−	8.70251e11i	0.488830	−	0.846678i	−0.511088	−	0.859529i	$-0.670757\pi$
$467$	5.02439e11	−	8.70251e11i	0.488830	−	0.846678i	0.999917	+	0.0128505i	$0.00409055\pi$
$468$		0			0
$469$	9.55830e11	+	1.65555e12i	0.912227	+	1.58002i
$470$	−7.65301e9	+	4.34024e10i	−0.00723422	+	0.0410273i
$471$		0			0
$472$	1.56340e12	+	5.69032e11i	1.44988	+	0.527713i
$473$	−3.08089e11	−	1.12135e11i	−0.283009	−	0.103007i
$474$		0			0
$475$	−3.59924e10	+	2.04123e11i	−0.0324406	+	0.183980i
$476$	−3.92946e11	−	6.80603e11i	−0.350834	−	0.607663i
$477$		0			0
$478$	3.82035e11	−	6.61704e11i	0.334717	−	0.579747i
$479$	−5.42349e11	−	4.55085e11i	−0.470727	−	0.394987i	0.376333	−	0.926485i	$-0.377185\pi$
$479$	−5.42349e11	−	4.55085e11i	−0.470727	−	0.394987i	−0.847060	+	0.531498i	$0.821629\pi$
$480$		0			0
$481$	−4.78320e10	−	2.71268e11i	−0.0407442	−	0.231072i
$482$	5.58338e11	−	4.68501e11i	0.471178	−	0.395366i
$483$		0			0
$484$	−5.20108e11	+	1.89304e11i	−0.430813	+	0.156803i
$485$	9.34860e11			0.767201
$486$		0			0
$487$	−7.20835e11			−0.580705			−0.290352	−	0.956920i	$-0.593772\pi$
$487$	−7.20835e11			−0.580705			−0.290352	+	0.956920i	$0.593772\pi$
$488$	2.48818e10	−	9.05625e9i	0.0198606	−	0.00722868i
$489$		0			0
$490$	−3.00155e10	+	2.51860e10i	−0.0235214	+	0.0197368i
$491$	8.41069e9	+	4.76994e10i	0.00653078	+	0.0370379i	0.987899	−	0.155099i	$-0.0495695\pi$
$491$	8.41069e9	+	4.76994e10i	0.00653078	+	0.0370379i	−0.981368	+	0.192136i	$0.938458\pi$
$492$		0			0
$493$	6.94577e11	+	5.82819e11i	0.529552	+	0.444347i
$494$	−7.08063e10	+	1.22640e11i	−0.0534934	+	0.0926533i
$495$		0			0
$496$	−2.01946e10	−	3.49781e10i	−0.0149819	−	0.0259495i
$497$	−8.04887e10	+	4.56474e11i	−0.0591740	+	0.335592i
$498$		0			0
$499$	−1.77993e9	−	6.47841e8i	−0.00128514	−	0.000467752i	0.341377	−	0.939926i	$-0.389107\pi$
$499$	−1.77993e9	−	6.47841e8i	−0.00128514	−	0.000467752i	−0.342663	+	0.939459i	$0.611329\pi$
$500$	−8.77754e11	−	3.19476e11i	−0.628070	−	0.228599i
$501$		0			0
$502$	9.98331e10	−	5.66182e11i	0.0701630	−	0.397914i
$503$	3.06799e11	+	5.31392e11i	0.213697	+	0.370134i	0.952869	−	0.303383i	$-0.0981161\pi$
$503$	3.06799e11	+	5.31392e11i	0.213697	+	0.370134i	−0.739172	+	0.673517i	$0.764783\pi$
$504$		0			0
$505$	−7.52459e10	+	1.30330e11i	−0.0514839	+	0.0891728i
$506$	6.34610e11	+	5.32501e11i	0.430358	+	0.361113i
$507$		0			0
$508$	−2.83572e11	−	1.60821e12i	−0.188919	−	1.07141i
$509$	8.03082e11	−	6.73866e11i	0.530310	−	0.444983i	−0.337898	−	0.941183i	$-0.609716\pi$
$509$	8.03082e11	−	6.73866e11i	0.530310	−	0.444983i	0.868208	+	0.496200i	$0.165272\pi$
$510$		0			0
$511$	2.64560e12	−	9.62920e11i	1.71645	−	0.624735i
$512$	−7.42595e10			−0.0477570
$513$		0			0
$514$	−1.42185e12			−0.898503
$515$	−1.39848e12	+	5.09006e11i	−0.876041	+	0.318853i
$516$		0			0
$517$	−4.82998e10	+	4.05284e10i	−0.0297330	+	0.0249489i
$518$	2.77836e11	+	1.57568e12i	0.169552	+	0.961580i
$519$		0			0
$520$	−1.74734e11	−	1.46619e11i	−0.104800	−	0.0879380i
$521$	−4.58453e11	+	7.94065e11i	−0.272600	+	0.472157i	−0.969527	−	0.244985i	$-0.921217\pi$
$521$	−4.58453e11	+	7.94065e11i	−0.272600	+	0.472157i	0.696927	+	0.717142i	$0.254550\pi$
$522$		0			0
$523$	−1.39425e12	−	2.41491e12i	−0.814859	−	1.41138i	−0.909429	−	0.415859i	$-0.863481\pi$
$523$	−1.39425e12	−	2.41491e12i	−0.814859	−	1.41138i	0.0945696	−	0.995518i	$-0.469853\pi$
$524$	−1.01422e11	+	5.75193e11i	−0.0587681	+	0.333291i
$525$		0			0
$526$	−3.93784e11	−	1.43326e11i	−0.224296	−	0.0816372i
$527$	−2.26831e12	−	8.25599e11i	−1.28102	−	0.466253i
$528$		0			0
$529$	6.69114e11	−	3.79473e12i	0.371492	−	2.10684i
$530$	8.03549e10	+	1.39179e11i	0.0442355	+	0.0766181i
$531$		0			0
$532$	−6.96298e11	+	1.20602e12i	−0.376871	+	0.652760i
$533$	−5.03758e10	−	4.22703e10i	−0.0270364	−	0.0226863i
$534$		0			0
$535$	3.81411e10	+	2.16309e11i	0.0201280	+	0.114152i
$536$	2.58060e12	−	2.16538e12i	1.35045	−	1.13317i
$537$		0			0
$538$	−1.37474e12	+	5.00363e11i	−0.707455	+	0.257493i
$539$	−5.60559e10			−0.0286069
$540$		0			0
$541$	−7.18636e11			−0.360679			−0.180340	−	0.983604i	$-0.557720\pi$
$541$	−7.18636e11			−0.360679			−0.180340	+	0.983604i	$0.557720\pi$
$542$	−6.69518e11	+	2.43685e11i	−0.333246	+	0.121292i
$543$		0			0
$544$	−1.71229e12	+	1.43678e12i	−0.838267	+	0.703389i
$545$	−3.43212e10	−	1.94645e11i	−0.0166640	−	0.0945060i
$546$		0			0
$547$	2.56936e12	+	2.15595e12i	1.22711	+	1.02967i	0.998421	+	0.0561655i	$0.0178875\pi$
$547$	2.56936e12	+	2.15595e12i	1.22711	+	1.02967i	0.228686	+	0.973500i	$0.426557\pi$
$548$	9.78839e11	−	1.69540e12i	0.463659	−	0.803081i
$549$		0			0
$550$	5.44498e10	+	9.43098e10i	0.0253726	+	0.0439466i
$551$	2.78996e11	−	1.58227e12i	0.128948	−	0.731303i
$552$		0			0
$553$	−2.08496e12	−	7.58865e11i	−0.948059	−	0.345065i
$554$	2.49392e11	+	9.07712e10i	0.112483	+	0.0409406i
$555$		0			0
$556$	4.43154e11	−	2.51325e12i	0.196661	−	1.11532i
$557$	−1.76719e12	−	3.06086e12i	−0.777920	−	1.34740i	−0.933139	−	0.359517i	$-0.882942\pi$
$557$	−1.76719e12	−	3.06086e12i	−0.777920	−	1.34740i	0.155219	−	0.987880i	$-0.450392\pi$
$558$		0			0
$559$	−1.00492e11	+	1.74057e11i	−0.0435288	+	0.0753942i
$560$	−4.00839e10	−	3.36344e10i	−0.0172236	−	0.0144523i
$561$		0			0
$562$	−6.25791e10	−	3.54904e11i	−0.0264616	−	0.150071i
$563$	2.27381e12	−	1.90796e12i	0.953822	−	0.800351i	−0.0261154	−	0.999659i	$-0.508314\pi$
$563$	2.27381e12	−	1.90796e12i	0.953822	−	0.800351i	0.979937	+	0.199308i	$0.0638693\pi$
$564$		0			0
$565$	1.09219e12	−	3.97525e11i	0.450900	−	0.164114i
$566$	−2.30366e12			−0.943507
$567$		0			0
$568$	8.16810e11			0.329271
$569$	1.81230e12	−	6.59623e11i	0.724811	−	0.263809i	0.0468440	−	0.998902i	$-0.485084\pi$
$569$	1.81230e12	−	6.59623e11i	0.724811	−	0.263809i	0.677967	+	0.735093i	$0.262861\pi$
$570$		0			0
$571$	1.10008e12	−	9.23075e11i	0.433073	−	0.363391i	−0.400037	−	0.916499i	$-0.631003\pi$
$571$	1.10008e12	−	9.23075e11i	0.433073	−	0.363391i	0.833110	+	0.553108i	$0.186558\pi$
$572$	−2.18732e10	−	1.24049e11i	−0.00854337	−	0.0484519i
$573$		0			0
$574$	2.92612e11	+	2.45530e11i	0.112509	+	0.0944065i
$575$	3.71648e11	−	6.43713e11i	0.141784	−	0.245577i
$576$		0			0
$577$	−1.23593e12	−	2.14069e12i	−0.464196	−	0.804011i	0.534969	−	0.844872i	$-0.320323\pi$
$577$	−1.23593e12	−	2.14069e12i	−0.464196	−	0.804011i	−0.999165	+	0.0408609i	$0.986990\pi$
$578$	−5.13407e10	+	2.91167e11i	−0.0191331	+	0.108509i
$579$		0			0
$580$	9.38693e11	+	3.41656e11i	0.344427	+	0.125361i
$581$	−1.06509e12	−	3.87661e11i	−0.387788	−	0.141143i
$582$		0			0
$583$	−3.99247e10	+	2.26424e11i	−0.0143131	+	0.0811736i
$584$	−2.48065e12	−	4.29661e12i	−0.882485	−	1.52851i
$585$		0			0
$586$	−1.21249e12	+	2.10009e12i	−0.424755	+	0.735698i
$587$	4.16012e12	+	3.49076e12i	1.44622	+	1.21352i	0.935280	+	0.353909i	$0.115148\pi$
$587$	4.16012e12	+	3.49076e12i	1.44622	+	1.21352i	0.510942	+	0.859615i	$0.329297\pi$
$588$		0			0
$589$	7.42761e11	+	4.21241e12i	0.254291	+	1.44215i
$590$	1.95763e12	−	1.64265e12i	0.665115	−	0.558098i
$591$		0			0
$592$	−1.04636e11	+	3.80845e10i	−0.0350134	+	0.0127438i
$593$	1.89941e12			0.630771			0.315385	−	0.948964i	$-0.397866\pi$
$593$	1.89941e12			0.630771			0.315385	+	0.948964i	$0.397866\pi$
$594$		0			0
$595$	−3.12729e12			−1.02292
$596$	−3.18070e12	+	1.15768e12i	−1.03256	+	0.375821i
$597$		0			0
$598$	3.89025e11	−	3.26431e11i	0.124400	−	0.104384i
$599$	7.76877e11	+	4.40589e12i	0.246565	+	1.39834i	0.816830	+	0.576879i	$0.195729\pi$
$599$	7.76877e11	+	4.40589e12i	0.246565	+	1.39834i	−0.570265	+	0.821461i	$0.693159\pi$
$600$		0			0
$601$	−1.00690e12	−	8.44891e11i	−0.314813	−	0.264159i	0.471665	−	0.881778i	$-0.343653\pi$
$601$	−1.00690e12	−	8.44891e11i	−0.314813	−	0.264159i	−0.786478	+	0.617619i	$0.788098\pi$
$602$	5.83714e11	−	1.01102e12i	0.181141	−	0.313745i
$603$		0			0
$604$	6.11732e11	+	1.05955e12i	0.187023	+	0.323933i
$605$	−3.82456e11	+	2.16902e12i	−0.116060	+	0.658209i
$606$		0			0
$607$	−1.80181e12	−	6.55806e11i	−0.538717	−	0.196077i	0.0583095	−	0.998299i	$-0.481429\pi$
$607$	−1.80181e12	−	6.55806e11i	−0.538717	−	0.196077i	−0.597026	+	0.802222i	$0.703651\pi$
$608$	3.72195e12	+	1.35468e12i	1.10460	+	0.402041i
$609$		0			0
$610$	7.06250e9	−	4.00534e10i	0.00206526	−	0.0117127i
$611$	1.93255e10	+	3.34728e10i	0.00560979	+	0.00971643i
$612$		0			0
$613$	2.95639e12	−	5.12062e12i	0.845648	−	1.46470i	−0.0394096	−	0.999223i	$-0.512548\pi$
$613$	2.95639e12	−	5.12062e12i	0.845648	−	1.46470i	0.885057	−	0.465482i	$-0.154119\pi$
$614$	−1.44622e12	−	1.21352e12i	−0.410654	−	0.344579i
$615$		0			0
$616$	3.29150e11	+	1.86670e12i	0.0921045	+	0.522350i
$617$	2.81691e12	−	2.36367e12i	0.782509	−	0.656603i	−0.161370	−	0.986894i	$-0.551591\pi$
$617$	2.81691e12	−	2.36367e12i	0.782509	−	0.656603i	0.943879	+	0.330291i	$0.107147\pi$
$618$		0			0
$619$	−2.12668e12	+	7.74047e11i	−0.582228	+	0.211914i	−0.616308	−	0.787505i	$-0.711372\pi$
$619$	−2.12668e12	+	7.74047e11i	−0.582228	+	0.211914i	0.0340794	+	0.999419i	$0.489150\pi$
$620$	−2.65943e12			−0.722814
$621$		0			0
$622$	−1.27116e12			−0.340520
$623$	−2.88910e12	+	1.05155e12i	−0.768363	+	0.279661i
$624$		0			0
$625$	−2.37970e12	+	1.99680e12i	−0.623823	+	0.523450i
$626$	1.56527e11	+	8.87708e11i	0.0407385	+	0.231039i
$627$		0			0
$628$	−1.23418e11	−	1.03560e11i	−0.0316637	−	0.0265690i
$629$	−3.32750e12	+	5.76340e12i	−0.847598	+	1.46808i
$630$		0			0
$631$	−1.36584e12	−	2.36571e12i	−0.342980	−	0.594058i	0.642005	−	0.766700i	$-0.278103\pi$
$631$	−1.36584e12	−	2.36571e12i	−0.342980	−	0.594058i	−0.984985	+	0.172642i	$0.944769\pi$
$632$	−6.78953e11	+	3.85053e12i	−0.169283	+	0.960050i
$633$		0			0
$634$	2.28017e12	+	8.29915e11i	0.560488	+	0.204001i
$635$	−6.10636e12	−	2.22253e12i	−1.49039	−	0.542459i
$636$		0			0
$637$	−5.96707e9	+	3.38410e10i	−0.00143593	+	0.00814358i
$638$	−4.22070e11	−	7.31046e11i	−0.100853	−	0.174683i
$639$		0			0
$640$	−1.25961e12	+	2.18171e12i	−0.296775	+	0.514029i
$641$	1.28639e12	+	1.07941e12i	0.300962	+	0.252537i	0.780745	−	0.624850i	$-0.214840\pi$
$641$	1.28639e12	+	1.07941e12i	0.300962	+	0.252537i	−0.479782	+	0.877387i	$0.659284\pi$
$642$		0			0
$643$	9.77213e11	+	5.54205e12i	0.225444	+	1.27856i	0.861834	+	0.507191i	$0.169316\pi$
$643$	9.77213e11	+	5.54205e12i	0.225444	+	1.27856i	−0.636389	+	0.771368i	$0.719573\pi$
$644$	3.82561e12	−	3.21007e12i	0.876424	−	0.735407i
$645$		0			0
$646$	3.21505e12	−	1.17018e12i	0.726342	−	0.264367i
$647$	1.59682e12			0.358251			0.179125	−	0.983826i	$-0.442673\pi$
$647$	1.59682e12			0.358251			0.179125	+	0.983826i	$0.442673\pi$
$648$		0			0
$649$	3.65600e12			0.808919
$650$	6.27310e10	−	2.28322e10i	0.0137839	−	0.00501693i
$651$		0			0
$652$	3.62798e12	−	3.04424e12i	0.786232	−	0.659727i
$653$	1.01835e12	+	5.77536e12i	0.219174	+	1.24300i	0.873515	+	0.486797i	$0.161835\pi$
$653$	1.01835e12	+	5.77536e12i	0.219174	+	1.24300i	−0.654341	+	0.756199i	$0.727054\pi$
$654$		0			0
$655$	1.78041e12	+	1.49394e12i	0.377950	+	0.317138i
$656$	−1.32919e10	+	2.30222e10i	−0.00280233	+	0.00485377i
$657$		0			0
$658$	−1.12254e11	−	1.94430e11i	−0.0233445	−	0.0404339i
$659$	7.78837e10	−	4.41701e11i	0.0160865	−	0.0912313i	−0.975707	−	0.219077i	$-0.929695\pi$
$659$	7.78837e10	−	4.41701e11i	0.0160865	−	0.0912313i	0.991794	+	0.127846i	$0.0408064\pi$
$660$		0			0
$661$	5.62012e12	+	2.04556e12i	1.14509	+	0.416778i	0.843749	−	0.536738i	$-0.180344\pi$
$661$	5.62012e12	+	2.04556e12i	1.14509	+	0.416778i	0.301341	+	0.953517i	$0.402566\pi$
$662$	−4.89384e12	−	1.78121e12i	−0.990350	−	0.360458i
$663$		0			0
$664$	−3.46839e11	+	1.96702e12i	−0.0692422	+	0.392692i
$665$	2.77076e12	+	4.79910e12i	0.549417	+	0.951618i
$666$		0			0
$667$	−2.88084e12	+	4.98977e12i	−0.563577	+	0.976144i
$668$	1.28808e11	+	1.08083e11i	0.0250293	+	0.0210021i
$669$		0			0
$670$	−8.98523e11	−	5.09578e12i	−0.172263	−	0.976954i
$671$	4.45730e10	−	3.74012e10i	0.00848829	−	0.00712252i
$672$		0			0
$673$	−1.29754e12	+	4.72267e11i	−0.243811	+	0.0887400i	−0.461035	−	0.887382i	$-0.652522\pi$
$673$	−1.29754e12	+	4.72267e11i	−0.243811	+	0.0887400i	0.217224	+	0.976122i	$0.430300\pi$
$674$	6.65411e11			0.124200
$675$		0			0
$676$	3.33612e12			0.614443
$677$	3.95060e12	−	1.43790e12i	0.722794	−	0.263076i	0.0456826	−	0.998956i	$-0.485454\pi$
$677$	3.95060e12	−	1.43790e12i	0.722794	−	0.263076i	0.677111	+	0.735880i	$0.263231\pi$
$678$		0			0
$679$	−3.64813e12	+	3.06114e12i	−0.658653	+	0.552675i
$680$	9.56961e11	+	5.42720e12i	0.171634	+	0.973387i
$681$		0			0
$682$	1.72155e12	+	1.44455e12i	0.304712	+	0.255684i
$683$	−1.96679e12	+	3.40657e12i	−0.345831	+	0.598997i	−0.985504	−	0.169650i	$-0.945736\pi$
$683$	−1.96679e12	+	3.40657e12i	−0.345831	+	0.598997i	0.639674	+	0.768647i	$0.279070\pi$
$684$		0			0
$685$	−3.89507e12	−	6.74647e12i	−0.675940	−	1.17076i
$686$	−5.95765e11	+	3.37875e12i	−0.102711	+	0.582502i
$687$		0			0
$688$	7.63474e10	+	2.77882e10i	0.0129911	+	0.00472838i
$689$	1.32443e11	+	4.82052e10i	0.0223893	+	0.00814905i
$690$		0			0
$691$	1.28113e11	−	7.26566e11i	0.0213768	−	0.121234i	−0.972252	−	0.233936i	$-0.924839\pi$
$691$	1.28113e11	−	7.26566e11i	0.0213768	−	0.121234i	0.993629	+	0.112702i	$0.0359506\pi$
$692$	2.41557e12	+	4.18389e12i	0.400444	+	0.693589i
$693$		0			0
$694$	−2.84887e11	+	4.93439e11i	−0.0466181	+	0.0807450i
$695$	−7.77934e12	−	6.52764e12i	−1.26477	−	1.06127i
$696$		0			0
$697$	2.75891e11	+	1.56466e12i	0.0442782	+	0.251114i
$698$	−3.56394e12	+	2.99050e12i	−0.568304	+	0.476864i
$699$		0			0
$700$	6.16887e11	−	2.24529e11i	0.0971101	−	0.0353452i
$701$	−3.66781e12			−0.573688			−0.286844	−	0.957977i	$-0.592606\pi$
$701$	−3.66781e12			−0.573688			−0.286844	+	0.957977i	$0.592606\pi$
$702$		0			0
$703$	1.17926e13			1.82100
$704$	1.87938e12	−	6.84040e11i	0.288362	−	0.104955i
$705$		0			0
$706$	2.01072e12	−	1.68720e12i	0.304601	−	0.255590i
$707$	−1.33123e11	−	7.54977e11i	−0.0200385	−	0.113644i
$708$		0			0
$709$	1.18616e12	+	9.95307e11i	0.176293	+	0.147928i	0.726665	−	0.686992i	$-0.241069\pi$
$709$	1.18616e12	+	9.95307e11i	0.176293	+	0.147928i	−0.550371	+	0.834920i	$0.685514\pi$
$710$	6.27311e11	−	1.08653e12i	0.0926446	−	0.160465i
$711$		0			0
$712$	2.70896e12	+	4.69206e12i	0.395042	+	0.684233i
$713$	2.66361e12	−	1.51061e13i	0.385983	−	2.18902i
$714$		0			0
$715$	−4.71011e11	−	1.71434e11i	−0.0673991	−	0.0245313i
$716$	4.73793e12	+	1.72447e12i	0.673721	+	0.245215i
$717$		0			0
$718$	1.01144e12	−	5.73617e12i	0.142030	−	0.805493i
$719$	−3.82048e12	−	6.61726e12i	−0.533136	−	0.923418i	−0.999251	−	0.0386944i	$-0.987680\pi$
$719$	−3.82048e12	−	6.61726e12i	−0.533136	−	0.923418i	0.466115	−	0.884724i	$-0.345653\pi$
$720$		0			0
$721$	3.79063e12	−	6.56556e12i	0.522399	−	0.904822i
$722$	−1.23584e12	−	1.03699e12i	−0.169256	−	0.142023i
$723$		0			0
$724$	8.10977e11	+	4.59928e12i	0.109695	+	0.622109i
$725$	−5.80199e11	+	4.86844e11i	−0.0779930	+	0.0654439i
$726$		0			0
$727$	−7.54231e12	+	2.74518e12i	−1.00138	+	0.364473i	−0.790117	−	0.612956i	$-0.789980\pi$
$727$	−7.54231e12	+	2.74518e12i	−1.00138	+	0.364473i	−0.211265	+	0.977429i	$0.567758\pi$
$728$	1.16197e12			0.153321
$729$		0			0
$730$	−7.62056e12			−0.993193
$731$	4.56295e12	−	1.66078e12i	0.591041	−	0.215121i
$732$		0			0
$733$	−9.34072e11	+	7.83779e11i	−0.119512	+	0.100283i	−0.700585	−	0.713569i	$-0.747078\pi$
$733$	−9.34072e11	+	7.83779e11i	−0.119512	+	0.100283i	0.581073	+	0.813852i	$0.302633\pi$
$734$	6.88226e11	+	3.90312e12i	0.0875182	+	0.496341i
$735$		0			0
$736$	−1.08808e13	−	9.13007e12i	−1.36682	−	1.14690i
$737$	3.70134e12	−	6.41090e12i	0.462120	−	0.800416i
$738$		0			0
$739$	5.43105e12	+	9.40686e12i	0.669860	+	1.16023i	0.977943	+	0.208872i	$0.0669791\pi$
$739$	5.43105e12	+	9.40686e12i	0.669860	+	1.16023i	−0.308083	+	0.951359i	$0.599688\pi$
$740$	−1.27318e12	+	7.22056e12i	−0.156080	+	0.885173i
$741$		0			0
$742$	−7.69303e11	−	2.80004e11i	−0.0931709	−	0.0339114i
$743$	−1.39701e13	−	5.08470e12i	−1.68171	−	0.612091i	−0.688164	−	0.725555i	$-0.741583\pi$
$743$	−1.39701e13	−	5.08470e12i	−1.68171	−	0.612091i	−0.993542	+	0.113464i	$0.963805\pi$
$744$		0			0
$745$	−2.33890e12	+	1.32646e13i	−0.278169	+	1.57757i
$746$	−8.15221e11	−	1.41200e12i	−0.0963720	−	0.166921i
$747$		0			0
$748$	−1.52164e12	+	2.63555e12i	−0.177727	+	0.307833i
$749$	−8.57131e11	−	7.19218e11i	−0.0995128	−	0.0835011i
$750$		0			0
$751$	−1.87953e12	−	1.06593e13i	−0.215610	−	1.22279i	−0.879844	−	0.475262i	$-0.842353\pi$
$751$	−1.87953e12	−	1.06593e13i	−0.215610	−	1.22279i	0.664234	−	0.747525i	$-0.268758\pi$
$752$	1.19692e10	−	1.00433e10i	0.00136485	−	0.00114524i
$753$		0			0
$754$	−4.86262e11	+	1.76985e11i	−0.0547897	+	0.0199418i
$755$	4.86850e12			0.545298
$756$		0			0
$757$	−7.14231e12			−0.790509			−0.395255	−	0.918572i	$-0.629344\pi$
$757$	−7.14231e12			−0.790509			−0.395255	+	0.918572i	$0.629344\pi$
$758$	5.47316e12	−	1.99207e12i	0.602181	−	0.219176i
$759$		0			0
$760$	7.48066e12	−	6.27702e12i	0.813352	−	0.682483i
$761$	−1.46504e11	−	8.30866e11i	−0.0158350	−	0.0898050i	0.975866	−	0.218370i	$-0.0700740\pi$
$761$	−1.46504e11	−	8.30866e11i	−0.0158350	−	0.0898050i	−0.991701	+	0.128565i	$0.958963\pi$
$762$		0			0
$763$	7.71286e11	+	6.47186e11i	0.0823863	+	0.0691304i
$764$	9.13618e11	−	1.58243e12i	0.0970163	−	0.168037i
$765$		0			0
$766$	4.23579e12	+	7.33660e12i	0.444534	+	0.769955i
$767$	3.89177e11	−	2.20713e12i	0.0406039	−	0.230276i
$768$		0			0
$769$	−8.68614e12	−	3.16150e12i	−0.895692	−	0.326005i	−0.147167	−	0.989112i	$-0.547015\pi$
$769$	−8.68614e12	−	3.16150e12i	−0.895692	−	0.326005i	−0.748525	+	0.663107i	$0.769238\pi$
$770$	2.73591e12	+	9.95788e11i	0.280474	+	0.102084i
$771$		0			0
$772$	4.54068e11	−	2.57515e12i	0.0460090	−	0.260930i
$773$	8.26371e12	+	1.43132e13i	0.832467	+	1.44188i	0.896076	+	0.443901i	$0.146406\pi$
$773$	8.26371e12	+	1.43132e13i	0.832467	+	1.44188i	−0.0636087	+	0.997975i	$0.520261\pi$
$774$		0			0
$775$	1.00819e12	−	1.74624e12i	0.100389	−	0.173879i
$776$	6.42876e12	+	5.39437e12i	0.636428	+	0.534026i
$777$		0			0
$778$	−1.95242e12	−	1.10727e13i	−0.191058	−	1.08354i
$779$	2.15667e12	−	1.80966e12i	0.209829	−	0.176067i
$780$		0			0
$781$	1.68666e12	−	6.13895e11i	0.162218	−	0.0590424i
$782$	−1.22694e13			−1.17326
$783$		0			0
$784$	1.38912e10			0.00131316
$785$	−6.02442e11	+	2.19271e11i	−0.0566242	+	0.0206095i
$786$		0			0
$787$	−9.13055e12	+	7.66144e12i	−0.848419	+	0.711908i	−0.959441	−	0.281910i	$-0.909032\pi$
$787$	−9.13055e12	+	7.66144e12i	−0.848419	+	0.711908i	0.111022	+	0.993818i	$0.464588\pi$
$788$	1.02428e12	+	5.80897e12i	0.0946346	+	0.536699i
$789$		0			0
$790$	4.60061e12	+	3.86037e12i	0.420236	+	0.352620i
$791$	−2.96041e12	+	5.12758e12i	−0.268880	+	0.465713i
$792$		0			0
$793$	−1.78344e10	−	3.08900e10i	−0.00160151	−	0.00277389i
$794$	7.14668e11	−	4.05309e12i	0.0638135	−	0.361904i
$795$		0			0
$796$	7.57907e12	+	2.75856e12i	0.669125	+	0.243542i
$797$	2.81485e12	+	1.02452e12i	0.247111	+	0.0899412i	0.462606	−	0.886564i	$-0.346914\pi$
$797$	2.81485e12	+	1.02452e12i	0.247111	+	0.0899412i	−0.215495	+	0.976505i	$0.569137\pi$
$798$		0			0
$799$	1.62156e11	−	9.19630e11i	0.0140757	−	0.0798275i
$800$	−9.33576e11	−	1.61700e12i	−0.0805833	−	0.139574i
$801$		0			0
$802$	2.36775e12	−	4.10107e12i	0.202093	−	0.350036i
$803$	−8.35161e12	−	7.00783e12i	−0.708843	−	0.594790i
$804$		0			0
$805$	−3.45081e12	−	1.95705e13i	−0.289627	−	1.64256i
$806$	1.05533e12	−	8.85529e11i	0.0880809	−	0.0739086i
$807$		0			0
$808$	−1.26948e12	+	4.62052e11i	−0.104779	+	0.0381364i
$809$	1.91885e13			1.57497			0.787487	−	0.616332i	$-0.211382\pi$
$809$	1.91885e13			1.57497			0.787487	+	0.616332i	$0.211382\pi$
$810$		0			0
$811$	1.24781e12			0.101287			0.0506436	−	0.998717i	$-0.483873\pi$
$811$	1.24781e12			0.101287			0.0506436	+	0.998717i	$0.483873\pi$
$812$	−4.78182e12	+	1.74044e12i	−0.386003	+	0.140494i
$813$		0			0
$814$	4.74624e12	−	3.98257e12i	0.378913	−	0.317946i
$815$	−3.27254e12	−	1.85595e13i	−0.259822	−	1.47352i
$816$		0			0
$817$	−6.59137e12	−	5.53082e12i	−0.517579	−	0.434300i
$818$	4.66507e12	−	8.08014e12i	0.364308	−	0.630999i
$819$		0			0
$820$	8.75204e11	+	1.51590e12i	0.0676001	+	0.117087i
$821$	1.44793e12	−	8.21161e12i	0.111225	−	0.630789i	−0.877325	−	0.479897i	$-0.840674\pi$
$821$	1.44793e12	−	8.21161e12i	0.111225	−	0.630789i	0.988550	−	0.150893i	$-0.0482148\pi$
$822$		0			0
$823$	−2.33039e13	−	8.48193e12i	−1.77064	−	0.644460i	−0.999974	−	0.00721795i	$-0.997702\pi$
$823$	−2.33039e13	−	8.48193e12i	−1.77064	−	0.644460i	−0.770664	−	0.637242i	$-0.780075\pi$
$824$	−1.25540e13	−	4.56930e12i	−0.948661	−	0.345284i
$825$		0			0
$826$	−2.26056e12	+	1.28203e13i	−0.168969	+	0.958269i
$827$	1.00616e13	+	1.74272e13i	0.747983	+	1.29554i	0.948788	+	0.315913i	$0.102311\pi$
$827$	1.00616e13	+	1.74272e13i	0.747983	+	1.29554i	−0.200805	+	0.979631i	$0.564356\pi$
$828$		0			0
$829$	6.94330e12	−	1.20261e13i	0.510588	−	0.884364i	−0.489337	−	0.872095i	$-0.662761\pi$
$829$	6.94330e12	−	1.20261e13i	0.510588	−	0.884364i	0.999925	−	0.0122690i	$-0.00390544\pi$
$830$	2.35019e12	+	1.97204e12i	0.171890	+	0.144233i
$831$		0			0
$832$	−2.12897e11	−	1.20740e12i	−0.0154033	−	0.0873567i
$833$	6.35982e11	−	5.33652e11i	0.0457660	−	0.0384022i
$834$		0			0
$835$	6.28751e11	−	2.28846e11i	0.0447599	−	0.0162913i
$836$	5.39266e12			0.381834
$837$		0			0
$838$	−5.55079e12			−0.388827
$839$	−5.97583e12	+	2.17502e12i	−0.416360	+	0.151543i	−0.541701	−	0.840571i	$-0.682220\pi$
$839$	−5.97583e12	+	2.17502e12i	−0.416360	+	0.151543i	0.125341	+	0.992114i	$0.459997\pi$
$840$		0			0
$841$	−6.61569e12	+	5.55122e12i	−0.456030	+	0.382654i
$842$	9.21647e11	+	5.22692e12i	0.0631917	+	0.358378i
$843$		0			0
$844$	−4.25224e12	−	3.56805e12i	−0.288454	−	0.242042i
$845$	6.63768e12	−	1.14968e13i	0.447879	−	0.775750i
$846$		0			0
$847$	−5.60985e12	−	9.71655e12i	−0.374521	−	0.648689i
$848$	9.89374e9	−	5.61102e10i	0.000657021	−	0.00372615i
$849$		0			0
$850$	−1.51559e12	−	5.51630e11i	−0.0995857	−	0.0362462i
$851$	−3.97390e13	−	1.44638e13i	−2.59737	−	0.945366i
$852$		0			0
$853$	−3.54122e12	+	2.00833e13i	−0.229025	+	1.29886i	0.625815	+	0.779972i	$0.284767\pi$
$853$	−3.54122e12	+	2.00833e13i	−0.229025	+	1.29886i	−0.854840	+	0.518892i	$0.826345\pi$
$854$	1.03592e11	+	1.79427e11i	0.00666450	+	0.0115433i
$855$		0			0
$856$	−9.85870e11	+	1.70758e12i	−0.0627607	+	0.108705i
$857$	7.65823e12	+	6.42602e12i	0.484970	+	0.406938i	0.852220	−	0.523184i	$-0.175256\pi$
$857$	7.65823e12	+	6.42602e12i	0.484970	+	0.406938i	−0.367250	+	0.930122i	$0.619701\pi$
$858$		0			0
$859$	−3.02450e11	−	1.71528e12i	−0.0189533	−	0.107489i	0.973864	−	0.227134i	$-0.0729356\pi$
$859$	−3.02450e11	−	1.71528e12i	−0.0189533	−	0.107489i	−0.992817	+	0.119645i	$0.961824\pi$
$860$	4.09813e12	−	3.43874e12i	0.255472	−	0.214366i
$861$		0			0
$862$	−1.03021e13	+	3.74964e12i	−0.635537	+	0.231317i
$863$	1.83269e12			0.112471			0.0562355	−	0.998418i	$-0.482090\pi$
$863$	1.83269e12			0.112471			0.0562355	+	0.998418i	$0.482090\pi$
$864$		0			0
$865$	1.92244e13			1.16756
$866$	8.37769e12	−	3.04923e12i	0.506167	−	0.184230i
$867$		0			0
$868$	1.03780e13	−	8.70816e12i	0.620546	−	0.520700i
$869$	1.49197e12	+	8.46140e12i	0.0887507	+	0.503330i
$870$		0			0
$871$	−3.47626e12	−	2.91693e12i	−0.204659	−	0.171729i
$872$	8.87132e11	−	1.53656e12i	0.0519594	−	0.0899963i
$873$		0			0
$874$	1.08706e13	+	1.88285e13i	0.630164	+	1.09148i
$875$	3.28799e12	−	1.86471e13i	0.189625	−	1.07541i
$876$		0			0
$877$	6.43018e12	+	2.34039e12i	0.367050	+	0.133595i	0.518959	−	0.854799i	$-0.326320\pi$
$877$	6.43018e12	+	2.34039e12i	0.367050	+	0.133595i	−0.151909	+	0.988395i	$0.548542\pi$
$878$	1.42252e13	+	5.17756e12i	0.807855	+	0.294035i
$879$		0			0
$880$	−3.51855e10	+	1.99547e11i	−0.00197784	+	0.0112169i
$881$	−2.12745e10	−	3.68485e10i	−0.00118978	−	0.00206077i	0.865430	−	0.501030i	$-0.167045\pi$
$881$	−2.12745e10	−	3.68485e10i	−0.00118978	−	0.00206077i	−0.866620	+	0.498969i	$0.833712\pi$
$882$		0			0
$883$	−6.88601e12	+	1.19269e13i	−0.381193	+	0.660245i	−0.991233	−	0.132125i	$-0.957820\pi$
$883$	−6.88601e12	+	1.19269e13i	−0.381193	+	0.660245i	0.610040	+	0.792370i	$0.291153\pi$
$884$	1.42911e12	+	1.19916e12i	0.0787100	+	0.0660456i
$885$		0			0
$886$	3.74163e12	+	2.12198e13i	0.203990	+	1.15688i
$887$	−1.87682e13	+	1.57484e13i	−1.01804	+	0.854239i	−0.989380	−	0.145350i	$-0.953569\pi$
$887$	−1.87682e13	+	1.57484e13i	−1.01804	+	0.854239i	−0.0286618	+	0.999589i	$0.509125\pi$
$888$		0			0
$889$	3.11066e13	−	1.13219e13i	1.67030	−	0.607939i
$890$	8.32195e12			0.444601
$891$		0			0
$892$	1.27829e13			0.676066
$893$	−1.55492e12	+	5.65946e11i	−0.0818234	+	0.0297813i
$894$		0			0
$895$	1.53696e13	−	1.28966e13i	0.800677	−	0.671848i
$896$	−2.22847e12	−	1.26383e13i	−0.115510	−	0.655091i
$897$		0			0
$898$	7.62074e12	+	6.39456e12i	0.391069	+	0.328146i
$899$	−7.81505e12	+	1.35361e13i	−0.399037	+	0.691152i
$900$		0			0
$901$	−1.70260e12	−	2.94898e12i	−0.0860697	−	0.149077i
$902$	2.56854e11	−	1.45669e12i	0.0129198	−	0.0732719i
$903$		0			0
$904$	9.80447e12	+	3.56854e12i	0.488277	+	0.177718i
$905$	1.74634e13	+	6.35615e12i	0.865386	+	0.314975i
$906$		0			0
$907$	−1.56173e12	+	8.85699e12i	−0.0766253	+	0.434564i	0.922226	+	0.386651i	$0.126368\pi$
$907$	−1.56173e12	+	8.85699e12i	−0.0766253	+	0.434564i	−0.998852	+	0.0479128i	$0.984743\pi$
$908$	−1.07976e13	−	1.87020e13i	−0.527157	−	0.913063i
$909$		0			0
$910$	8.92392e11	−	1.54567e12i	0.0431389	−	0.0747188i
$911$	−9.82893e12	−	8.24745e12i	−0.472796	−	0.396723i	0.375017	−	0.927018i	$-0.377637\pi$
$911$	−9.82893e12	−	8.24745e12i	−0.472796	−	0.396723i	−0.847813	+	0.530295i	$0.822081\pi$
$912$		0			0
$913$	7.62164e11	+	4.32245e12i	0.0363020	+	0.205879i
$914$	−6.92372e12	+	5.80969e12i	−0.328157	+	0.275356i
$915$		0			0
$916$	−2.87159e12	+	1.04517e12i	−0.134770	+	0.0490523i
$917$	−1.18396e13			−0.552935
$918$		0			0
$919$	−2.60634e13			−1.20535			−0.602673	−	0.797988i	$-0.705898\pi$
$919$	−2.60634e13			−1.20535			−0.602673	+	0.797988i	$0.705898\pi$
$920$	−3.29074e13	+	1.19773e13i	−1.51443	+	0.551206i
$921$		0			0
$922$	7.33987e12	−	6.15888e12i	0.334502	−	0.280681i
$923$	−1.91066e11	−	1.08359e12i	−0.00866513	−	0.0491424i
$924$		0			0
$925$	−4.25852e12	−	3.57332e12i	−0.191258	−	0.160485i
$926$	−4.91195e12	+	8.50775e12i	−0.219535	+	0.380246i
$927$		0			0
$928$	7.23665e12	+	1.25342e13i	0.320311	+	0.554795i
$929$	−3.73400e12	+	2.11766e13i	−0.164477	+	0.932793i	0.785126	+	0.619336i	$0.212598\pi$
$929$	−3.73400e12	+	2.11766e13i	−0.164477	+	0.932793i	−0.949602	+	0.313457i	$0.898513\pi$
$930$		0			0
$931$	−1.38242e12	−	5.03158e11i	−0.0603066	−	0.0219498i
$932$	2.25347e13	+	8.20195e12i	0.978317	+	0.356078i
$933$		0			0
$934$	2.40603e12	−	1.36453e13i	0.103452	−	0.586708i
$935$	6.05502e12	+	1.04876e13i	0.259097	+	0.448770i
$936$		0			0
$937$	−7.93720e12	+	1.37476e13i	−0.336387	+	0.582639i	−0.983750	−	0.179542i	$-0.942538\pi$
$937$	−7.93720e12	+	1.37476e13i	−0.336387	+	0.582639i	0.647363	+	0.762181i	$0.275872\pi$
$938$	2.01922e13	+	1.69432e13i	0.851667	+	0.714634i
$939$		0			0
$940$	−1.78650e11	−	1.01318e12i	−0.00746325	−	0.0423262i
$941$	−2.31783e13	+	1.94489e13i	−0.963668	+	0.808614i	−0.981546	−	0.191226i	$-0.938754\pi$
$941$	−2.31783e13	+	1.94489e13i	−0.963668	+	0.808614i	0.0178776	+	0.999840i	$0.494309\pi$
$942$		0			0
$943$	−9.48717e12	+	3.45305e12i	−0.390692	+	0.142200i
$944$	−9.05993e11			−0.0371322
$945$		0			0
$946$	−4.52072e12			−0.183526
$947$	3.32281e13	−	1.20941e13i	1.34255	−	0.488649i	0.431937	−	0.901904i	$-0.357830\pi$
$947$	3.32281e13	−	1.20941e13i	1.34255	−	0.488649i	0.910615	+	0.413255i	$0.135608\pi$
$948$		0			0
$949$	−5.11965e12	+	4.29590e12i	−0.204900	+	0.171932i
$950$	4.96282e11	+	2.81455e12i	0.0197684	+	0.112112i
$951$		0			0
$952$	−2.15054e13	−	1.80452e13i	−0.848558	−	0.712025i
$953$	−1.03871e13	+	1.79911e13i	−0.407923	+	0.706543i	−0.994657	−	0.103236i	$-0.967080\pi$
$953$	−1.03871e13	+	1.79911e13i	−0.407923	+	0.706543i	0.586734	+	0.809780i	$0.300414\pi$
$954$		0			0
$955$	−3.63554e12	−	6.29694e12i	−0.141434	−	0.244971i
$956$	−3.09724e12	+	1.75653e13i	−0.119926	+	0.680135i
$957$		0			0
$958$	−9.17336e12	−	3.33883e12i	−0.351871	−	0.128071i
$959$	3.72908e13	+	1.35727e13i	1.42370	+	0.518183i
$960$		0			0
$961$	2.63456e12	−	1.49413e13i	0.0996444	−	0.565111i
$962$	−1.89905e12	−	3.28925e12i	−0.0714904	−	0.123825i
$963$		0			0
$964$	−8.50716e12	+	1.47348e13i	−0.317276	+	0.549539i
$965$	−7.97093e12	−	6.68840e12i	−0.295894	−	0.248284i
$966$		0			0
$967$	5.22949e12	+	2.96579e13i	0.192327	+	1.09074i	0.916174	+	0.400781i	$0.131261\pi$
$967$	5.22949e12	+	2.96579e13i	0.192327	+	1.09074i	−0.723847	+	0.689961i	$0.757628\pi$
$968$	−1.51458e13	+	1.27088e13i	−0.554438	+	0.465229i
$969$		0			0
$970$	1.21130e13	−	4.40876e12i	0.439317	−	0.159898i
$971$	−2.37260e13			−0.856519			−0.428260	−	0.903656i	$-0.640873\pi$
$971$	−2.37260e13			−0.856519			−0.428260	+	0.903656i	$0.640873\pi$
$972$		0			0
$973$	5.17319e13			1.85034
$974$	−9.33984e12	+	3.39942e12i	−0.332525	+	0.121029i
$975$		0			0
$976$	−1.10456e10	+	9.26838e9i	−0.000389642	+	0.000326949i
$977$	−1.62850e12	−	9.23568e12i	−0.0571824	−	0.324297i	0.942776	−	0.333427i	$-0.108205\pi$
$977$	−1.62850e12	−	9.23568e12i	−0.0571824	−	0.324297i	−0.999958	+	0.00912959i	$0.997094\pi$
$978$		0			0
$979$	9.12029e12	+	7.65283e12i	0.317312	+	0.266256i
$980$	4.57333e11	−	7.92124e11i	0.0158386	−	0.0274332i
$981$		0			0
$982$	3.33925e11	+	5.78376e11i	0.0114590	+	0.0198476i
$983$	5.48739e11	−	3.11206e12i	0.0187446	−	0.106306i	−0.974000	−	0.226548i	$-0.927256\pi$
$983$	5.48739e11	−	3.11206e12i	0.0187446	−	0.106306i	0.992745	+	0.120242i	$0.0383671\pi$
$984$		0			0
$985$	2.20566e13	+	8.02793e12i	0.746577	+	0.271732i
$986$	1.17482e13	+	4.27598e12i	0.395844	+	0.144075i
$987$		0			0
$988$	5.74041e11	−	3.25555e12i	0.0191662	−	0.108697i
$989$	1.54281e13	+	2.67223e13i	0.512779	+	0.888159i
$990$		0			0
$991$	1.11313e12	−	1.92800e12i	0.0366619	−	0.0635002i	−0.847112	−	0.531414i	$-0.821661\pi$
$991$	1.11313e12	−	1.92800e12i	0.0366619	−	0.0635002i	0.883774	+	0.467914i	$0.154994\pi$
$992$	−2.95170e13	−	2.47677e13i	−0.967766	−	0.812052i
$993$		0			0
$994$	1.10982e12	+	6.29410e12i	0.0360590	+	0.204501i
$995$	2.45860e13	−	2.06301e13i	0.795215	−	0.667265i
$996$		0			0
$997$	4.38513e13	−	1.59606e13i	1.40558	−	0.511588i	0.475748	−	0.879582i	$-0.342178\pi$
$997$	4.38513e13	−	1.59606e13i	1.40558	−	0.511588i	0.929828	+	0.367994i	$0.119955\pi$
$998$	−2.61177e10			−0.000833388
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.19.17		156
3.2	odd	2		27.10.e.a.7.10	yes	156
27.4	even	9	inner	81.10.e.a.64.17		156
27.23	odd	18		27.10.e.a.4.10	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.10	✓	156	27.23	odd	18
27.10.e.a.7.10	yes	156	3.2	odd	2
81.10.e.a.19.17		156	1.1	even	1	trivial
81.10.e.a.64.17		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+(12.9570 - 4.71595i) q^{2} +(-246.572 + 206.898i) q^{4} +(222.415 + 1261.38i) q^{5} +(-4998.24 - 4194.02i) q^{7} +(-5748.96 + 9957.50i) q^{8} +(8830.42 + 15294.7i) q^{10} +(-4387.44 + 24882.4i) q^{11} +(14554.5 + 5297.40i) q^{13} +(-84540.9 - 30770.4i) q^{14} +(1087.25 - 6166.10i) q^{16} +(-187103. - 324072. i) q^{17} +(-331545. + 574253. i) q^{19} +(-315818. - 265003. i) q^{20} +(60496.3 + 343092. i) q^{22} +(1.82158e6 - 1.52849e6i) q^{23} +(293733. - 106910. i) q^{25} +213564. q^{26} +2.10016e6 q^{28} +(-2.27688e6 + 828718. i) q^{29} +(4.94152e6 - 4.14643e6i) q^{31} +(-1.03725e6 - 5.88253e6i) q^{32} +(-3.95260e6 - 3.31663e6i) q^{34} +(4.17856e6 - 7.23748e6i) q^{35} +(-8.89215e6 - 1.54017e7i) q^{37} +(-1.58767e6 + 9.00413e6i) q^{38} +(-1.38388e7 - 5.03692e6i) q^{40} +(-3.98972e6 - 1.45214e6i) q^{41} +(-2.25330e6 + 1.27791e7i) q^{43} +(-4.06631e6 - 7.04305e6i) q^{44} +(1.63939e7 - 2.83951e7i) q^{46} +(1.91163e6 + 1.60405e6i) q^{47} +(385257. + 2.18490e6i) q^{49} +(3.30171e6 - 2.77047e6i) q^{50} +(-4.68475e6 + 1.70511e6i) q^{52} +9.09978e6 q^{53} -3.23619e7 q^{55} +(7.04967e7 - 2.56587e7i) q^{56} +(-2.55933e7 + 2.14754e7i) q^{58} +(-2.51267e7 - 1.42501e8i) q^{59} +(-1.76413e6 - 1.48028e6i) q^{61} +(4.44728e7 - 7.70291e7i) q^{62} +(-3.95784e7 - 6.85519e7i) q^{64} +(-3.44489e6 + 1.95369e7i) q^{65} +(-2.75317e8 - 1.00207e8i) q^{67} +(1.13184e8 + 4.11957e7i) q^{68} +(2.00099e7 - 1.13482e8i) q^{70} +(-3.55199e7 - 6.15222e7i) q^{71} +(-2.15747e8 + 3.73685e8i) q^{73} +(-1.87849e8 - 1.57624e8i) q^{74} +(-3.70623e7 - 2.10191e8i) q^{76} +(1.26287e8 - 1.05967e8i) q^{77} +(3.19548e8 - 1.16306e8i) q^{79} +8.01960e6 q^{80} -5.85430e7 q^{82} +(1.63239e8 - 5.94141e7i) q^{83} +(3.67163e8 - 3.08086e8i) q^{85} +(3.10697e7 + 1.76205e8i) q^{86} +(-2.22543e8 - 1.86736e8i) q^{88} +(2.35605e8 - 4.08079e8i) q^{89} +(-5.05294e7 - 8.75195e7i) q^{91} +(-1.32909e8 + 7.53763e8i) q^{92} +(3.23336e7 + 1.17685e7i) q^{94} +(-7.98090e8 - 2.90481e8i) q^{95} +(1.26743e8 - 7.18794e8i) q^{97} +(1.52957e7 + 2.64928e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

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