LMFDB - Embedded newform 81.10.e.a.10.9

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			10.9
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.47036 - 19.6814i) q^{2} +(105.808 - 38.5110i) q^{4} +(245.404 + 205.919i) q^{5} +(4352.22 + 1584.08i) q^{7} +(-6241.31 - 10810.3i) q^{8} +(3201.13 - 5544.51i) q^{10} +(-15391.2 + 12914.7i) q^{11} +(1492.45 - 8464.09i) q^{13} +(16073.1 - 91155.2i) q^{14} +(-146939. + 123296. i) q^{16} +(90872.5 - 157396. i) q^{17} +(91487.2 + 158461. i) q^{19} +(33895.9 + 12337.1i) q^{20} +(307593. + 258101. i) q^{22} +(2.02036e6 - 735350. i) q^{23} +(-321336. - 1.82239e6i) q^{25} -171765. q^{26} +521505. q^{28} +(174760. + 991116. i) q^{29} +(4.04575e6 - 1.47253e6i) q^{31} +(-1.95929e6 - 1.64404e6i) q^{32} +(-3.41313e6 - 1.24228e6i) q^{34} +(741862. + 1.28494e6i) q^{35} +(3.91332e6 - 6.77807e6i) q^{37} +(2.80123e6 - 2.35051e6i) q^{38} +(694391. - 3.93809e6i) q^{40} +(-1.14770e6 + 6.50891e6i) q^{41} +(2.33766e7 - 1.96153e7i) q^{43} +(-1.13115e6 + 1.95921e6i) q^{44} +(-2.14841e7 - 3.72115e7i) q^{46} +(-2.61315e6 - 951111. i) q^{47} +(-1.44801e7 - 1.21503e7i) q^{49} +(-3.47520e7 + 1.26487e7i) q^{50} +(-168048. - 953046. i) q^{52} -5.07132e7 q^{53} -6.43644e6 q^{55} +(-1.00392e7 - 5.69354e7i) q^{56} +(1.89001e7 - 6.87906e6i) q^{58} +(-1.21065e8 - 1.01585e8i) q^{59} +(-1.97095e7 - 7.17368e6i) q^{61} +(-4.30217e7 - 7.45158e7i) q^{62} +(-7.46622e7 + 1.29319e8i) q^{64} +(2.10917e6 - 1.76980e6i) q^{65} +(-801013. + 4.54277e6i) q^{67} +(3.55358e6 - 2.01534e7i) q^{68} +(2.27149e7 - 1.90601e7i) q^{70} +(-2.95764e7 + 5.12277e7i) q^{71} +(-1.49276e8 - 2.58554e8i) q^{73} +(-1.46982e8 - 5.34973e7i) q^{74} +(1.57826e7 + 1.32432e7i) q^{76} +(-8.74437e7 + 3.18269e7i) q^{77} +(-9.91742e7 - 5.62445e8i) q^{79} -6.14484e7 q^{80} +1.32087e8 q^{82} +(-1.22408e7 - 6.94213e7i) q^{83} +(5.47112e7 - 1.99133e7i) q^{85} +(-4.67181e8 - 3.92012e8i) q^{86} +(2.35673e8 + 8.57778e7i) q^{88} +(3.85185e8 + 6.67159e8i) q^{89} +(1.99032e7 - 3.44734e7i) q^{91} +(1.85451e8 - 1.55612e8i) q^{92} +(-9.65060e6 + 5.47313e7i) q^{94} +(-1.01786e7 + 5.77258e7i) q^{95} +(1.22147e9 - 1.02493e9i) q^{97} +(-1.88883e8 + 3.27155e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−3.47036	−	19.6814i	−0.153370	−	0.869804i	−0.960261	−	0.279103i	$-0.909963\pi$
$2$	−3.47036	−	19.6814i	−0.153370	−	0.869804i	0.806891	−	0.590700i	$-0.201148\pi$
$3$		0			0
$3$		0			0
$4$	105.808	−	38.5110i	0.206657	−	0.0752169i
$5$	245.404	+	205.919i	0.175597	+	0.147343i	0.726350	−	0.687325i	$-0.241215\pi$
$5$	245.404	+	205.919i	0.175597	+	0.147343i	−0.550753	+	0.834668i	$0.685660\pi$
$6$		0			0
$7$	4352.22	+	1584.08i	0.685125	+	0.249365i	0.661046	−	0.750345i	$-0.270113\pi$
$7$	4352.22	+	1584.08i	0.685125	+	0.249365i	0.0240785	+	0.999710i	$0.492335\pi$
$8$	−6241.31	−	10810.3i	−0.538730	−	0.933107i
$9$		0			0
$10$	3201.13	−	5544.51i	0.101228	−	0.175333i
$11$	−15391.2	+	12914.7i	−0.316960	+	0.265961i	−0.787362	−	0.616491i	$-0.788553\pi$
$11$	−15391.2	+	12914.7i	−0.316960	+	0.265961i	0.470402	+	0.882452i	$0.344109\pi$
$12$		0			0
$13$	1492.45	−	8464.09i	0.0144929	−	0.0821931i	−0.976703	−	0.214593i	$-0.931157\pi$
$13$	1492.45	−	8464.09i	0.0144929	−	0.0821931i	0.991196	+	0.132400i	$0.0422685\pi$
$14$	16073.1	−	91155.2i	0.111821	−	0.634169i
$15$		0			0
$16$	−146939.	+	123296.i	−0.560527	+	0.470338i
$17$	90872.5	−	157396.i	0.263884	−	0.457060i	−0.703387	−	0.710807i	$-0.748330\pi$
$17$	90872.5	−	157396.i	0.263884	−	0.457060i	0.967271	+	0.253747i	$0.0816632\pi$
$18$		0			0
$19$	91487.2	+	158461.i	0.161053	+	0.278952i	0.935247	−	0.353997i	$-0.115178\pi$
$19$	91487.2	+	158461.i	0.161053	+	0.278952i	−0.774193	+	0.632949i	$0.781844\pi$
$20$	33895.9	+	12337.1i	0.0473710	+	0.0172416i
$21$		0			0
$22$	307593.	+	258101.i	0.279946	+	0.234902i
$23$	2.02036e6	−	735350.i	1.50540	−	0.547922i	0.547950	−	0.836511i	$-0.315408\pi$
$23$	2.02036e6	−	735350.i	1.50540	−	0.547922i	0.957453	+	0.288589i	$0.0931862\pi$
$24$		0			0
$25$	−321336.	−	1.82239e6i	−0.164524	−	0.933062i
$26$	−171765.			−0.0737146
$27$		0			0
$28$	521505.			0.160342
$29$	174760.	+	991116.i	0.0458830	+	0.260216i	0.999117	−	0.0420182i	$-0.0133787\pi$
$29$	174760.	+	991116.i	0.0458830	+	0.260216i	−0.953234	+	0.302234i	$0.902268\pi$
$30$		0			0
$31$	4.04575e6	−	1.47253e6i	0.786813	−	0.286376i	0.0828023	−	0.996566i	$-0.473613\pi$
$31$	4.04575e6	−	1.47253e6i	0.786813	−	0.286376i	0.704010	+	0.710190i	$0.251391\pi$
$32$	−1.95929e6	−	1.64404e6i	−0.330312	−	0.277165i
$33$		0			0
$34$	−3.41313e6	−	1.24228e6i	−0.438024	−	0.159428i
$35$	741862.	+	1.28494e6i	0.0835635	+	0.144736i
$36$		0			0
$37$	3.91332e6	−	6.77807e6i	0.343271	−	0.594563i	−0.641767	−	0.766900i	$-0.721798\pi$
$37$	3.91332e6	−	6.77807e6i	0.343271	−	0.594563i	0.985038	+	0.172337i	$0.0551317\pi$
$38$	2.80123e6	−	2.35051e6i	0.217933	−	0.182868i
$39$		0			0
$40$	694391.	−	3.93809e6i	0.0428878	−	0.243229i
$41$	−1.14770e6	+	6.50891e6i	−0.0634307	+	0.359734i	0.936527	+	0.350594i	$0.114020\pi$
$41$	−1.14770e6	+	6.50891e6i	−0.0634307	+	0.359734i	−0.999958	+	0.00913945i	$0.997091\pi$
$42$		0			0
$43$	2.33766e7	−	1.96153e7i	1.04273	−	0.874956i	0.0504214	−	0.998728i	$-0.483944\pi$
$43$	2.33766e7	−	1.96153e7i	1.04273	−	0.874956i	0.992311	+	0.123772i	$0.0394991\pi$
$44$	−1.13115e6	+	1.95921e6i	−0.0454971	+	0.0788033i
$45$		0			0
$46$	−2.14841e7	−	3.72115e7i	−0.707468	−	1.22537i
$47$	−2.61315e6	−	951111.i	−0.0781133	−	0.0284309i	0.302668	−	0.953096i	$-0.402123\pi$
$47$	−2.61315e6	−	951111.i	−0.0781133	−	0.0284309i	−0.380781	+	0.924665i	$0.624345\pi$
$48$		0			0
$49$	−1.44801e7	−	1.21503e7i	−0.358831	−	0.301095i
$50$	−3.47520e7	+	1.26487e7i	−0.786347	+	0.286207i
$51$		0			0
$52$	−168048.	−	953046.i	−0.00318726	−	0.0180759i
$53$	−5.07132e7			−0.882834			−0.441417	−	0.897302i	$-0.645524\pi$
$53$	−5.07132e7			−0.882834			−0.441417	+	0.897302i	$0.645524\pi$
$54$		0			0
$55$	−6.43644e6			−0.0948447
$56$	−1.00392e7	−	5.69354e7i	−0.136413	−	0.773635i
$57$		0			0
$58$	1.89001e7	−	6.87906e6i	0.219299	−	0.0798185i
$59$	−1.21065e8	−	1.01585e8i	−1.30072	−	1.09143i	−0.990021	−	0.140923i	$-0.954993\pi$
$59$	−1.21065e8	−	1.01585e8i	−1.30072	−	1.09143i	−0.310697	−	0.950509i	$-0.600562\pi$
$60$		0			0
$61$	−1.97095e7	−	7.17368e6i	−0.182260	−	0.0663373i	0.249278	−	0.968432i	$-0.419807\pi$
$61$	−1.97095e7	−	7.17368e6i	−0.182260	−	0.0663373i	−0.431538	+	0.902095i	$0.642029\pi$
$62$	−4.30217e7	−	7.45158e7i	−0.369765	−	0.640451i
$63$		0			0
$64$	−7.46622e7	+	1.29319e8i	−0.556277	+	0.963500i
$65$	2.10917e6	−	1.76980e6i	0.0146555	−	0.0122974i
$66$		0			0
$67$	−801013.	+	4.54277e6i	−0.00485627	+	0.0275413i	−0.987140	−	0.159861i	$-0.948896\pi$
$67$	−801013.	+	4.54277e6i	−0.00485627	+	0.0275413i	0.982283	+	0.187402i	$0.0600067\pi$
$68$	3.55358e6	−	2.01534e7i	0.0201547	−	0.114303i
$69$		0			0
$70$	2.27149e7	−	1.90601e7i	0.113076	−	0.0948821i
$71$	−2.95764e7	+	5.12277e7i	−0.138128	+	0.239245i	−0.926788	−	0.375585i	$-0.877442\pi$
$71$	−2.95764e7	+	5.12277e7i	−0.138128	+	0.239245i	0.788660	+	0.614830i	$0.210775\pi$
$72$		0			0
$73$	−1.49276e8	−	2.58554e8i	−0.615231	−	1.06561i	−0.990344	−	0.138632i	$-0.955729\pi$
$73$	−1.49276e8	−	2.58554e8i	−0.615231	−	1.06561i	0.375113	−	0.926979i	$-0.377604\pi$
$74$	−1.46982e8	−	5.34973e7i	−0.569801	−	0.207390i
$75$		0			0
$76$	1.57826e7	+	1.32432e7i	0.0542646	+	0.0455334i
$77$	−8.74437e7	+	3.18269e7i	−0.283478	+	0.103178i
$78$		0			0
$79$	−9.91742e7	−	5.62445e8i	−0.286469	−	1.62464i	−0.699992	−	0.714151i	$-0.746813\pi$
$79$	−9.91742e7	−	5.62445e8i	−0.286469	−	1.62464i	0.413524	−	0.910493i	$-0.364298\pi$
$80$	−6.14484e7			−0.167728
$81$		0			0
$82$	1.32087e8			0.322626
$83$	−1.22408e7	−	6.94213e7i	−0.0283113	−	0.160561i	0.967374	−	0.253351i	$-0.0815327\pi$
$83$	−1.22408e7	−	6.94213e7i	−0.0283113	−	0.160561i	−0.995686	+	0.0927895i	$0.970422\pi$
$84$		0			0
$85$	5.47112e7	−	1.99133e7i	0.113682	−	0.0413768i
$86$	−4.67181e8	−	3.92012e8i	−0.920964	−	0.772780i
$87$		0			0
$88$	2.35673e8	+	8.57778e7i	0.418926	+	0.152477i
$89$	3.85185e8	+	6.67159e8i	0.650749	+	1.12713i	0.982941	+	0.183919i	$0.0588785\pi$
$89$	3.85185e8	+	6.67159e8i	0.650749	+	1.12713i	−0.332192	+	0.943212i	$0.607788\pi$
$90$		0			0
$91$	1.99032e7	−	3.44734e7i	0.0304255	−	0.0526985i
$92$	1.85451e8	−	1.55612e8i	0.269889	−	0.226463i
$93$		0			0
$94$	−9.65060e6	+	5.47313e7i	−0.0127491	+	0.0723036i
$95$	−1.01786e7	+	5.77258e7i	−0.0128213	+	0.0727133i
$96$		0			0
$97$	1.22147e9	−	1.02493e9i	1.40091	−	1.17550i	0.440212	−	0.897894i	$-0.354903\pi$
$97$	1.22147e9	−	1.02493e9i	1.40091	−	1.17550i	0.960695	−	0.277607i	$-0.0895413\pi$
$98$	−1.88883e8	+	3.27155e8i	−0.206860	+	0.358292i
$99$		0			0
$100$	−1.04182e8	−	1.80448e8i	−0.104182	−	0.180448i
$101$	1.43854e9	+	5.23588e8i	1.37555	+	0.500660i	0.920827	−	0.389971i	$-0.127515\pi$
$101$	1.43854e9	+	5.23588e8i	1.37555	+	0.500660i	0.454726	+	0.890632i	$0.349737\pi$
$102$		0			0
$103$	2.89639e8	+	2.43036e8i	0.253565	+	0.212766i	0.760706	−	0.649097i	$-0.224853\pi$
$103$	2.89639e8	+	2.43036e8i	0.253565	+	0.212766i	−0.507141	+	0.861863i	$0.669297\pi$
$104$	−1.00814e8	+	3.66933e7i	−0.0845027	+	0.0307565i
$105$		0			0
$106$	1.75993e8	+	9.98106e8i	0.135400	+	0.767892i
$107$	1.72565e9			1.27270			0.636348	−	0.771402i	$-0.280444\pi$
$107$	1.72565e9			1.27270			0.636348	+	0.771402i	$0.280444\pi$
$108$		0			0
$109$	−1.80263e9			−1.22317			−0.611585	−	0.791179i	$-0.709468\pi$
$109$	−1.80263e9			−1.22317			−0.611585	+	0.791179i	$0.709468\pi$
$110$	2.23368e7	+	1.26678e8i	0.0145463	+	0.0824963i
$111$		0			0
$112$	−8.34821e8	+	3.03850e8i	−0.501317	+	0.182464i
$113$	−1.01650e9	−	8.52941e8i	−0.586479	−	0.492114i	0.300589	−	0.953754i	$-0.402817\pi$
$113$	−1.01650e9	−	8.52941e8i	−0.586479	−	0.492114i	−0.887068	+	0.461640i	$0.847261\pi$
$114$		0			0
$115$	6.47226e8	+	2.35571e8i	0.345077	+	0.125598i
$116$	5.66600e7	+	9.81380e7i	0.0290546	+	0.0503241i
$117$		0			0
$118$	−1.57920e9	+	2.73526e9i	−0.749840	+	1.29876i
$119$	6.44825e8	−	5.41072e8i	0.294768	−	0.247340i
$120$		0			0
$121$	−3.39355e8	+	1.92458e9i	−0.143920	+	0.816210i
$122$	−7.27889e7	+	4.12806e8i	−0.0297472	+	0.168705i
$123$		0			0
$124$	3.71365e8	−	3.11612e8i	0.141060	−	0.118363i
$125$	6.09250e8	−	1.05525e9i	0.223203	−	0.386599i
$126$		0			0
$127$	2.38598e9	+	4.13264e9i	0.813861	+	1.40965i	0.910143	+	0.414295i	$0.135972\pi$
$127$	2.38598e9	+	4.13264e9i	0.813861	+	1.40965i	−0.0962817	+	0.995354i	$0.530695\pi$
$128$	1.57373e9	+	5.72789e8i	0.518184	+	0.188604i
$129$		0			0
$130$	−4.21517e7	−	3.53695e7i	−0.0129441	−	0.0108614i
$131$	−5.68996e8	+	2.07097e8i	−0.168806	+	0.0614404i	−0.425041	−	0.905174i	$-0.639740\pi$
$131$	−5.68996e8	+	2.07097e8i	−0.168806	+	0.0614404i	0.256235	+	0.966615i	$0.417518\pi$
$132$		0			0
$133$	1.47159e8	+	8.34578e8i	0.0407806	+	0.231278i
$134$	9.21880e7			0.0247003
$135$		0			0
$136$	−2.26866e9			−0.568648
$137$	8.37424e8	+	4.74927e9i	0.203097	+	1.15182i	0.900407	+	0.435049i	$0.143269\pi$
$137$	8.37424e8	+	4.74927e9i	0.203097	+	1.15182i	−0.697310	+	0.716770i	$0.745620\pi$
$138$		0			0
$139$	1.04982e9	−	3.82103e8i	0.238533	−	0.0868188i	−0.219988	−	0.975503i	$-0.570602\pi$
$139$	1.04982e9	−	3.82103e8i	0.238533	−	0.0868188i	0.458521	+	0.888684i	$0.348380\pi$
$140$	1.27980e8	+	1.07388e8i	0.0281556	+	0.0236253i
$141$		0			0
$142$	1.11087e9	+	4.04325e8i	0.229281	+	0.0834514i
$143$	8.63409e7	+	1.49547e8i	0.0172665	+	0.0299064i
$144$		0			0
$145$	−1.61202e8	+	2.79210e8i	−0.0302841	+	0.0524536i
$146$	−4.57067e9	+	3.83525e9i	−0.832515	+	0.698563i
$147$		0			0
$148$	1.53031e8	−	8.67881e8i	0.0262181	−	0.148690i
$149$	8.28387e8	−	4.69802e9i	0.137688	−	0.780866i	−0.835263	−	0.549851i	$-0.814684\pi$
$149$	8.28387e8	−	4.69802e9i	0.137688	−	0.780866i	0.972950	−	0.231015i	$-0.0742045\pi$
$150$		0			0
$151$	2.80492e7	−	2.35361e7i	0.00439061	−	0.00368416i	−0.640590	−	0.767883i	$-0.721310\pi$
$151$	2.80492e7	−	2.35361e7i	0.00439061	−	0.00368416i	0.644980	+	0.764199i	$0.276866\pi$
$152$	1.14200e9	−	1.97800e9i	0.173528	−	0.300560i
$153$		0			0
$154$	9.29859e8	+	1.61056e9i	0.133221	+	0.230746i
$155$	1.29607e9	+	4.71729e8i	0.180358	+	0.0656448i
$156$		0			0
$157$	−1.02379e10	−	8.59064e9i	−1.34482	−	1.12844i	−0.980360	−	0.197216i	$-0.936810\pi$
$157$	−1.02379e10	−	8.59064e9i	−1.34482	−	1.12844i	−0.364458	−	0.931220i	$-0.618746\pi$
$158$	−1.07255e10	+	3.90378e9i	−1.36919	+	0.498343i
$159$		0			0
$160$	−1.42280e8	−	8.06910e8i	−0.0171634	−	0.0973386i
$161$	9.95789e9			1.16802
$162$		0			0
$163$	3.18897e9			0.353840			0.176920	−	0.984225i	$-0.443387\pi$
$163$	3.18897e9			0.353840			0.176920	+	0.984225i	$0.443387\pi$
$164$	1.29229e8	+	7.32895e8i	0.0139497	+	0.0791124i
$165$		0			0
$166$	−1.32383e9	+	4.81834e8i	−0.135315	+	0.0492506i
$167$	2.36925e9	+	1.98804e9i	0.235715	+	0.197789i	0.752992	−	0.658030i	$-0.228610\pi$
$167$	2.36925e9	+	1.98804e9i	0.235715	+	0.197789i	−0.517277	+	0.855818i	$0.673054\pi$
$168$		0			0
$169$	9.89556e9	+	3.60169e9i	0.933147	+	0.339638i
$170$	−5.81789e8	−	1.00769e9i	−0.0534251	−	0.0925350i
$171$		0			0
$172$	1.71803e9	−	2.97571e9i	0.149676	−	0.259247i
$173$	−5.34677e9	+	4.48647e9i	−0.453820	+	0.380800i	−0.840851	−	0.541266i	$-0.817945\pi$
$173$	−5.34677e9	+	4.48647e9i	−0.453820	+	0.380800i	0.387031	+	0.922067i	$0.373501\pi$
$174$		0			0
$175$	1.48828e9	−	8.44045e9i	0.119954	−	0.680290i
$176$	6.69222e8	−	3.79535e9i	0.0525730	−	0.298157i
$177$		0			0
$178$	1.17939e10	−	9.89626e9i	0.880577	−	0.738892i
$179$	1.24806e10	−	2.16171e10i	0.908654	−	1.57383i	0.0927174	−	0.995692i	$-0.470445\pi$
$179$	1.24806e10	−	2.16171e10i	0.908654	−	1.57383i	0.815936	−	0.578142i	$-0.196222\pi$
$180$		0			0
$181$	5.17947e9	+	8.97110e9i	0.358700	+	0.621287i	0.987744	−	0.156083i	$-0.0498867\pi$
$181$	5.17947e9	+	8.97110e9i	0.358700	+	0.621287i	−0.629044	+	0.777370i	$0.716553\pi$
$182$	−7.47557e8	−	2.72089e8i	−0.0505037	−	0.0183818i
$183$		0			0
$184$	−2.05590e10	−	1.72511e10i	−1.32228	−	1.10952i
$185$	2.35607e9	−	8.57541e8i	0.147882	−	0.0538247i
$186$		0			0
$187$	6.34089e8	+	3.59610e9i	0.0379195	+	0.215052i
$188$	−3.13121e8			−0.0182811
$189$		0			0
$190$	1.17145e9			0.0652127
$191$	2.47186e9	+	1.40186e10i	0.134392	+	0.762176i	0.975281	+	0.220968i	$0.0709216\pi$
$191$	2.47186e9	+	1.40186e10i	0.134392	+	0.762176i	−0.840889	+	0.541208i	$0.817967\pi$
$192$		0			0
$193$	8.94285e9	−	3.25493e9i	0.463947	−	0.168863i	−0.0994617	−	0.995041i	$-0.531712\pi$
$193$	8.94285e9	−	3.25493e9i	0.463947	−	0.168863i	0.563408	+	0.826179i	$0.309490\pi$
$194$	−2.44111e10	−	2.04833e10i	−1.23731	−	1.03823i
$195$		0			0
$196$	−2.00004e9	−	7.27954e8i	−0.0968023	−	0.0352332i
$197$	−1.52971e10	−	2.64954e10i	−0.723622	−	1.25335i	−0.959539	−	0.281576i	$-0.909143\pi$
$197$	−1.52971e10	−	2.64954e10i	−0.723622	−	1.25335i	0.235917	−	0.971773i	$-0.424191\pi$
$198$		0			0
$199$	−1.42302e10	+	2.46475e10i	−0.643240	+	1.11412i	0.341466	+	0.939894i	$0.389077\pi$
$199$	−1.42302e10	+	2.46475e10i	−0.643240	+	1.11412i	−0.984705	+	0.174229i	$0.944257\pi$
$200$	−1.76949e10	+	1.48478e10i	−0.782013	+	0.656186i
$201$		0			0
$202$	5.31267e9	−	3.01296e10i	0.224508	−	1.27325i
$203$	−8.09410e8	+	4.59039e9i	−0.0334531	+	0.189722i
$204$		0			0
$205$	−1.62195e9	+	1.36098e9i	−0.0641426	+	0.0538220i
$206$	3.77814e9	−	6.54393e9i	0.146176	−	0.253184i
$207$		0			0
$208$	8.24292e8	+	1.42772e9i	0.0305349	+	0.0528880i
$209$	−3.45457e9	−	1.25736e9i	−0.125238	−	0.0455828i
$210$		0			0
$211$	−3.38931e10	−	2.84397e10i	−1.17717	−	0.987766i	−0.999994	−	0.00358737i	$-0.998858\pi$
$211$	−3.38931e10	−	2.84397e10i	−1.17717	−	0.987766i	−0.177180	−	0.984178i	$-0.556697\pi$
$212$	−5.36587e9	+	1.95302e9i	−0.182444	+	0.0664040i
$213$		0			0
$214$	−5.98862e9	−	3.39632e10i	−0.195193	−	1.10700i
$215$	9.77586e9			0.312019
$216$		0			0
$217$	1.99406e10			0.610477
$218$	6.25577e9	+	3.54782e10i	0.187597	+	1.06392i
$219$		0			0
$220$	−6.81028e8	+	2.47874e8i	−0.0196003	+	0.00713393i
$221$	−1.19659e9	−	1.00406e9i	−0.0337427	−	0.0283135i
$222$		0			0
$223$	3.70559e10	+	1.34872e10i	1.00343	+	0.365217i	0.790905	−	0.611939i	$-0.209610\pi$
$223$	3.70559e10	+	1.34872e10i	1.00343	+	0.365217i	0.212521	+	0.977156i	$0.431832\pi$
$224$	−5.92298e9	−	1.02589e10i	−0.157190	−	0.272261i
$225$		0			0
$226$	−1.32595e10	+	2.29661e10i	−0.338095	+	0.585597i
$227$	−3.32667e10	+	2.79141e10i	−0.831560	+	0.697762i	−0.955649	−	0.294509i	$-0.904844\pi$
$227$	−3.32667e10	+	2.79141e10i	−0.831560	+	0.697762i	0.124088	+	0.992271i	$0.460399\pi$
$228$		0			0
$229$	−8.40748e9	+	4.76812e10i	−0.202025	+	1.14574i	0.700027	+	0.714117i	$0.253171\pi$
$229$	−8.40748e9	+	4.76812e10i	−0.202025	+	1.14574i	−0.902052	+	0.431627i	$0.857940\pi$
$230$	2.39026e9	−	1.35558e10i	0.0563209	−	0.319412i
$231$		0			0
$232$	9.62349e9	−	8.07507e9i	0.218091	−	0.183000i
$233$	−1.91260e9	+	3.31272e9i	−0.0425130	+	0.0736347i	−0.886499	−	0.462731i	$-0.846870\pi$
$233$	−1.91260e9	+	3.31272e9i	−0.0425130	+	0.0736347i	0.843986	+	0.536365i	$0.180203\pi$
$234$		0			0
$235$	−4.45428e8	−	7.71503e8i	−0.00952734	−	0.0165018i
$236$	−1.67218e10	−	6.08623e9i	−0.350896	−	0.127716i
$237$		0			0
$238$	−1.28868e10	−	1.08133e10i	−0.260346	−	0.218456i
$239$	−2.31142e10	+	8.41288e9i	−0.458235	+	0.166784i	−0.560816	−	0.827941i	$-0.689512\pi$
$239$	−2.31142e10	+	8.41288e9i	−0.458235	+	0.166784i	0.102580	+	0.994725i	$0.467290\pi$
$240$		0			0
$241$	9.59917e9	+	5.44396e10i	0.183298	+	1.03953i	0.928123	+	0.372273i	$0.121422\pi$
$241$	9.59917e9	+	5.44396e10i	0.183298	+	1.03953i	−0.744825	+	0.667259i	$0.767467\pi$
$242$	3.90561e10			0.732015
$243$		0			0
$244$	−2.36169e9			−0.0426549
$245$	−1.05152e9	−	5.96346e9i	−0.0186453	−	0.105743i
$246$		0			0
$247$	1.47776e9	−	5.37862e8i	0.0252621	−	0.00919464i
$248$	−4.11693e10	−	3.45451e10i	−0.691099	−	0.579901i
$249$		0			0
$250$	−2.28832e10	−	8.32879e9i	−0.370498	−	0.134850i
$251$	3.40271e10	+	5.89367e10i	0.541120	+	0.937247i	0.998840	+	0.0481509i	$0.0153329\pi$
$251$	3.40271e10	+	5.89367e10i	0.541120	+	0.937247i	−0.457720	+	0.889096i	$0.651334\pi$
$252$		0			0
$253$	−2.15988e10	+	3.74102e10i	−0.331427	+	0.574048i
$254$	7.30560e10	−	6.13012e10i	1.10130	−	0.924097i
$255$		0			0
$256$	−7.46422e9	+	4.23317e10i	−0.108619	+	0.616007i
$257$	−4.61848e9	+	2.61927e10i	−0.0660389	+	0.374525i	0.933820	+	0.357742i	$0.116453\pi$
$257$	−4.61848e9	+	2.61927e10i	−0.0660389	+	0.374525i	−0.999859	+	0.0167826i	$0.994658\pi$
$258$		0			0
$259$	2.77686e10	−	2.33006e10i	0.383447	−	0.321750i
$260$	1.55010e8	−	2.68486e8i	0.00210368	−	0.00364369i
$261$		0			0
$262$	6.05059e9	+	1.04799e10i	0.0793308	+	0.137405i
$263$	1.04298e11	+	3.79613e10i	1.34423	+	0.489260i	0.911143	−	0.412091i	$-0.135202\pi$
$263$	1.04298e11	+	3.79613e10i	1.34423	+	0.489260i	0.433089	+	0.901351i	$0.357424\pi$
$264$		0			0
$265$	−1.24452e10	−	1.04428e10i	−0.155023	−	0.130080i
$266$	1.59150e10	−	5.79258e9i	0.194912	−	0.0709422i
$267$		0			0
$268$	9.01931e7	+	5.11511e8i	0.00106799	+	0.00605687i
$269$	1.15400e11			1.34375			0.671877	−	0.740663i	$-0.265488\pi$
$269$	1.15400e11			1.34375			0.671877	+	0.740663i	$0.265488\pi$
$270$		0			0
$271$	−7.26689e10			−0.818440			−0.409220	−	0.912436i	$-0.634199\pi$
$271$	−7.26689e10			−0.818440			−0.409220	+	0.912436i	$0.634199\pi$
$272$	6.05362e9	+	3.43318e10i	0.0670587	+	0.380309i
$273$		0			0
$274$	9.05661e10	−	3.29634e10i	0.970707	−	0.353309i
$275$	2.84813e10	+	2.38987e10i	0.300305	+	0.251986i
$276$		0			0
$277$	8.90994e10	+	3.24295e10i	0.909318	+	0.330965i	0.753980	−	0.656897i	$-0.228131\pi$
$277$	8.90994e10	+	3.24295e10i	0.909318	+	0.330965i	0.155337	+	0.987861i	$0.450354\pi$
$278$	−1.11636e10	−	1.93359e10i	−0.112099	−	0.194161i
$279$		0			0
$280$	9.26038e9	−	1.60395e10i	0.0900363	−	0.155947i
$281$	5.24844e10	−	4.40396e10i	0.502171	−	0.421372i	−0.356193	−	0.934412i	$-0.615925\pi$
$281$	5.24844e10	−	4.40396e10i	0.502171	−	0.421372i	0.858364	+	0.513041i	$0.171481\pi$
$282$		0			0
$283$	−3.13332e10	+	1.77700e11i	−0.290380	+	1.64683i	0.395030	+	0.918668i	$0.370734\pi$
$283$	−3.13332e10	+	1.77700e11i	−0.290380	+	1.64683i	−0.685410	+	0.728158i	$0.740377\pi$
$284$	−1.15659e9	+	6.55933e9i	−0.0105498	+	0.0598311i
$285$		0			0
$286$	2.64366e9	−	2.21829e9i	0.0233646	−	0.0196052i
$287$	−1.53057e10	+	2.65102e10i	−0.133163	+	0.230645i
$288$		0			0
$289$	4.27783e10	+	7.40942e10i	0.360731	+	0.624804i
$290$	6.05468e9	+	2.20372e9i	0.0502690	+	0.0182964i
$291$		0			0
$292$	−2.57519e10	−	2.16084e10i	−0.207294	−	0.173940i
$293$	3.69540e10	−	1.34502e10i	0.292926	−	0.106616i	−0.191377	−	0.981517i	$-0.561295\pi$
$293$	3.69540e10	−	1.34502e10i	0.292926	−	0.106616i	0.484303	+	0.874900i	$0.339073\pi$
$294$		0			0
$295$	−8.79146e9	−	4.98589e10i	−0.0675868	−	0.383304i
$296$	−9.76969e10			−0.739721
$297$		0			0
$298$	−9.53384e10			−0.700317
$299$	−3.20879e9	−	1.81980e10i	−0.0232178	−	0.131675i
$300$		0			0
$301$	1.32812e11	−	4.83397e10i	0.932585	−	0.339433i
$302$	−5.60565e8	−	4.70370e8i	−0.00387788	−	0.00325393i
$303$		0			0
$304$	−3.29806e10	−	1.20040e10i	−0.221477	−	0.0806109i
$305$	−3.35960e9	−	5.81900e9i	−0.0222300	−	0.0385034i
$306$		0			0
$307$	5.83914e10	−	1.01137e11i	0.375169	−	0.649811i	−0.615184	−	0.788384i	$-0.710918\pi$
$307$	5.83914e10	−	1.01137e11i	0.375169	−	0.649811i	0.990352	+	0.138573i	$0.0442515\pi$
$308$	−8.02657e9	+	6.73509e9i	−0.0508220	+	0.0426447i
$309$		0			0
$310$	4.78648e9	−	2.71455e10i	0.0294367	−	0.166944i
$311$	−8.69989e9	+	4.93396e10i	−0.0527342	+	0.299070i	−0.999756	−	0.0220995i	$-0.992965\pi$
$311$	−8.69989e9	+	4.93396e10i	−0.0527342	+	0.299070i	0.947022	+	0.321170i	$0.104076\pi$
$312$		0			0
$313$	−5.13524e10	+	4.30898e10i	−0.302420	+	0.253761i	−0.781351	−	0.624092i	$-0.785469\pi$
$313$	−5.13524e10	+	4.30898e10i	−0.302420	+	0.253761i	0.478930	+	0.877853i	$0.341025\pi$
$314$	−1.33547e11	+	2.31309e11i	−0.775263	+	1.34280i
$315$		0			0
$316$	−3.21538e10	−	5.56920e10i	−0.181401	−	0.314196i
$317$	−1.52494e10	−	5.55033e9i	−0.0848177	−	0.0308711i	0.299263	−	0.954171i	$-0.403259\pi$
$317$	−1.52494e10	−	5.55033e9i	−0.0848177	−	0.0308711i	−0.384081	+	0.923300i	$0.625481\pi$
$318$		0			0
$319$	−1.54898e10	−	1.29974e10i	−0.0837503	−	0.0702748i
$320$	−4.49516e10	+	1.63610e10i	−0.239646	+	0.0872239i
$321$		0			0
$322$	−3.45575e10	−	1.95985e11i	−0.179139	−	1.01595i
$323$	3.32547e10			0.169997
$324$		0			0
$325$	−1.59044e10			−0.0790756
$326$	−1.10669e10	−	6.27635e10i	−0.0542684	−	0.307771i
$327$		0			0
$328$	7.75262e10	−	2.82172e10i	0.369842	−	0.134611i
$329$	−9.86639e9	−	8.27889e9i	−0.0464277	−	0.0389574i
$330$		0			0
$331$	−1.08408e11	−	3.94572e10i	−0.496404	−	0.180676i	0.0816721	−	0.996659i	$-0.473974\pi$
$331$	−1.08408e11	−	3.94572e10i	−0.496404	−	0.180676i	−0.578076	+	0.815983i	$0.696196\pi$
$332$	−3.96867e9	−	6.87393e9i	−0.0179276	−	0.0310516i
$333$		0			0
$334$	3.09053e10	−	5.35295e10i	0.135886	−	0.235361i
$335$	−1.13201e9	+	9.49872e8i	−0.00491077	+	0.00412063i
$336$		0			0
$337$	−6.26852e10	+	3.55506e11i	−0.264747	+	1.50145i	0.505009	+	0.863114i	$0.331489\pi$
$337$	−6.26852e10	+	3.55506e11i	−0.264747	+	1.50145i	−0.769755	+	0.638339i	$0.779622\pi$
$338$	3.65451e10	−	2.07258e11i	0.152302	−	0.863745i
$339$		0			0
$340$	5.02202e9	−	4.21397e9i	0.0203809	−	0.0171016i
$341$	−4.32514e10	+	7.49137e10i	−0.173223	+	0.300031i
$342$		0			0
$343$	−1.37223e11	−	2.37678e11i	−0.535309	−	0.927182i
$344$	−3.57947e11	−	1.30282e11i	−1.37818	−	0.501616i
$345$		0			0
$346$	1.06855e11	+	8.96622e10i	0.400824	+	0.336331i
$347$	−8.66972e10	+	3.15552e10i	−0.321013	+	0.116839i	−0.497500	−	0.867464i	$-0.665749\pi$
$347$	−8.66972e10	+	3.15552e10i	−0.321013	+	0.116839i	0.176487	+	0.984303i	$0.443526\pi$
$348$		0			0
$349$	5.76627e10	+	3.27022e11i	0.208056	+	1.17995i	0.892557	+	0.450934i	$0.148909\pi$
$349$	5.76627e10	+	3.27022e11i	0.208056	+	1.17995i	−0.684501	+	0.729012i	$0.739980\pi$
$350$	−1.71285e11			−0.610116
$351$		0			0
$352$	5.13881e10			0.178411
$353$	−8.40751e10	−	4.76814e11i	−0.288192	−	1.63442i	−0.693657	−	0.720305i	$-0.744002\pi$
$353$	−8.40751e10	−	4.76814e11i	−0.288192	−	1.63442i	0.405466	−	0.914110i	$-0.367109\pi$
$354$		0			0
$355$	−1.78069e10	+	6.48118e9i	−0.0595060	+	0.0216584i
$356$	6.64487e10	+	5.57571e10i	0.219261	+	0.183982i
$357$		0			0
$358$	−4.68768e11	−	1.70617e11i	−1.50829	−	0.548971i
$359$	−2.10059e11	−	3.63834e11i	−0.667448	−	1.15605i	−0.978615	−	0.205698i	$-0.934054\pi$
$359$	−2.10059e11	−	3.63834e11i	−0.667448	−	1.15605i	0.311168	−	0.950355i	$-0.399280\pi$
$360$		0			0
$361$	1.44604e11	−	2.50462e11i	0.448124	−	0.776173i
$362$	1.58589e11	−	1.33072e11i	0.485384	−	0.407285i
$363$		0			0
$364$	7.78319e8	−	4.41407e9i	0.00232381	−	0.0131790i
$365$	1.66081e10	−	9.41891e10i	0.0489780	−	0.277768i
$366$		0			0
$367$	3.59527e10	−	3.01679e10i	0.103451	−	0.0868057i	−0.589595	−	0.807699i	$-0.700713\pi$
$367$	3.59527e10	−	3.01679e10i	0.103451	−	0.0868057i	0.693046	+	0.720893i	$0.256268\pi$
$368$	−2.06203e11	+	3.57154e11i	−0.586111	+	1.01517i
$369$		0			0
$370$	−2.50540e10	−	4.33949e10i	−0.0694976	−	0.120373i
$371$	−2.20715e11	−	8.03336e10i	−0.604852	−	0.220148i
$372$		0			0
$373$	−2.65307e11	−	2.22619e11i	−0.709675	−	0.595488i	0.214833	−	0.976651i	$-0.431079\pi$
$373$	−2.65307e11	−	2.22619e11i	−0.709675	−	0.595488i	−0.924508	+	0.381163i	$0.875524\pi$
$374$	6.85758e10	−	2.49595e10i	0.181238	−	0.0659651i
$375$		0			0
$376$	6.02775e9	+	3.41851e10i	0.0155529	+	0.0882046i
$377$	8.64972e9			0.0220529
$378$		0			0
$379$	6.32637e11			1.57499			0.787496	−	0.616320i	$-0.211377\pi$
$379$	6.32637e11			1.57499			0.787496	+	0.616320i	$0.211377\pi$
$380$	1.14610e9	+	6.49985e9i	0.00281966	+	0.0159911i
$381$		0			0
$382$	2.67328e11	−	9.72994e10i	0.642332	−	0.233790i
$383$	6.38415e11	+	5.35694e11i	1.51603	+	1.27210i	0.850831	+	0.525440i	$0.176099\pi$
$383$	6.38415e11	+	5.35694e11i	1.51603	+	1.27210i	0.665203	+	0.746663i	$0.268345\pi$
$384$		0			0
$385$	−2.80128e10	−	1.01958e10i	−0.0649805	−	0.0236510i
$386$	−9.50965e10	−	1.64712e11i	−0.218033	−	0.377644i
$387$		0			0
$388$	8.97701e10	−	1.55486e11i	0.201089	−	0.348297i
$389$	−2.36074e11	+	1.98090e11i	−0.522727	+	0.438620i	−0.865581	−	0.500768i	$-0.833051\pi$
$389$	−2.36074e11	+	1.98090e11i	−0.522727	+	0.438620i	0.342854	+	0.939389i	$0.388606\pi$
$390$		0			0
$391$	6.78540e10	−	3.84819e11i	0.146818	−	0.832647i
$392$	−4.09727e10	+	2.32368e11i	−0.0876410	+	0.497037i
$393$		0			0
$394$	−4.68380e11	+	3.93017e11i	−0.979186	+	0.821635i
$395$	9.14801e10	−	1.58448e11i	0.189077	−	0.327492i
$396$		0			0
$397$	−2.86481e11	−	4.96200e11i	−0.578813	−	1.00253i	−0.995616	−	0.0935371i	$-0.970183\pi$
$397$	−2.86481e11	−	4.96200e11i	−0.578813	−	1.00253i	0.416802	−	0.908997i	$-0.363151\pi$
$398$	5.34481e11	+	1.94535e11i	1.06772	+	0.388619i
$399$		0			0
$400$	2.71910e11	+	2.28160e11i	0.531074	+	0.445624i
$401$	7.15077e11	−	2.60267e11i	1.38103	−	0.502654i	0.458539	−	0.888674i	$-0.348373\pi$
$401$	7.15077e11	−	2.60267e11i	1.38103	−	0.502654i	0.922490	+	0.386021i	$0.126151\pi$
$402$		0			0
$403$	−6.42558e9	−	3.64413e10i	−0.0121350	−	0.0688210i
$404$	1.72374e11			0.321925
$405$		0			0
$406$	9.31543e10			0.170151
$407$	2.73063e10	+	1.54862e11i	0.0493274	+	0.279749i
$408$		0			0
$409$	4.70124e11	−	1.71111e11i	0.830725	−	0.302359i	0.108569	−	0.994089i	$-0.465373\pi$
$409$	4.70124e11	−	1.71111e11i	0.830725	−	0.302359i	0.722156	+	0.691730i	$0.243151\pi$
$410$	3.24148e10	+	2.71993e10i	0.0566521	+	0.0475368i
$411$		0			0
$412$	4.00058e10	+	1.45609e10i	0.0684046	+	0.0248972i
$413$	−3.65981e11	−	6.33897e11i	−0.618989	−	1.07212i
$414$		0			0
$415$	1.12912e10	−	1.95569e10i	0.0186863	−	0.0323656i
$416$	−1.68395e10	+	1.41300e10i	−0.0275682	+	0.0231325i
$417$		0			0
$418$	−1.27580e10	+	7.23543e10i	−0.0204404	+	0.115923i
$419$	−1.66310e11	+	9.43189e11i	−0.263605	+	1.49498i	0.509372	+	0.860547i	$0.329878\pi$
$419$	−1.66310e11	+	9.43189e11i	−0.263605	+	1.49498i	−0.772977	+	0.634434i	$0.781233\pi$
$420$		0			0
$421$	−3.95028e11	+	3.31468e11i	−0.612856	+	0.514248i	−0.895549	−	0.444963i	$-0.853217\pi$
$421$	−3.95028e11	+	3.31468e11i	−0.612856	+	0.514248i	0.282693	+	0.959211i	$0.408772\pi$
$422$	−4.42112e11	+	7.65760e11i	−0.678619	+	1.17540i
$423$		0			0
$424$	3.16517e11	+	5.48223e11i	0.475609	+	0.823779i
$425$	−3.16037e11	−	1.15028e11i	−0.469880	−	0.171022i
$426$		0			0
$427$	−7.44165e10	−	6.24428e10i	−0.108329	−	0.0908986i
$428$	1.82588e11	−	6.64564e10i	0.263011	−	0.0957283i
$429$		0			0
$430$	−3.39258e10	−	1.92403e11i	−0.0478544	−	0.271396i
$431$	4.87168e11			0.680035			0.340017	−	0.940419i	$-0.389567\pi$
$431$	4.87168e11			0.680035			0.340017	+	0.940419i	$0.389567\pi$
$432$		0			0
$433$	2.17825e11			0.297792			0.148896	−	0.988853i	$-0.452428\pi$
$433$	2.17825e11			0.297792			0.148896	+	0.988853i	$0.452428\pi$
$434$	−6.92011e10	−	3.92459e11i	−0.0936288	−	0.530995i
$435$		0			0
$436$	−1.90733e11	+	6.94210e10i	−0.252776	+	0.0920030i
$437$	3.01361e11	+	2.52872e11i	0.395294	+	0.331691i
$438$		0			0
$439$	3.59861e10	+	1.30979e10i	0.0462428	+	0.0168310i	0.365038	−	0.930993i	$-0.381056\pi$
$439$	3.59861e10	+	1.30979e10i	0.0462428	+	0.0168310i	−0.318795	+	0.947824i	$0.603278\pi$
$440$	4.01718e10	+	6.95796e10i	0.0510957	+	0.0885003i
$441$		0			0
$442$	−1.56087e10	+	2.70350e10i	−0.0194521	+	0.0336920i
$443$	2.35836e11	−	1.97890e11i	0.290933	−	0.244122i	−0.485626	−	0.874167i	$-0.661408\pi$
$443$	2.35836e11	−	1.97890e11i	0.290933	−	0.244122i	0.776558	+	0.630045i	$0.216964\pi$
$444$		0			0
$445$	−4.28546e10	+	2.43040e11i	−0.0518056	+	0.293804i
$446$	1.36851e11	−	7.76118e11i	0.163772	−	0.928797i
$447$		0			0
$448$	−5.29798e11	+	4.44553e11i	−0.621382	+	0.521402i
$449$	−3.56406e11	+	6.17314e11i	−0.413844	+	0.716799i	−0.995306	−	0.0967743i	$-0.969148\pi$
$449$	−3.56406e11	+	6.17314e11i	−0.413844	+	0.716799i	0.581462	+	0.813573i	$0.302481\pi$
$450$		0			0
$451$	−6.63964e10	−	1.15002e11i	−0.0755701	−	0.130891i
$452$	−1.40401e11	−	5.11019e10i	−0.158215	−	0.0575856i
$453$		0			0
$454$	6.64836e11	+	5.57864e11i	0.734452	+	0.616278i
$455$	1.19831e10	−	4.36148e9i	0.0131074	−	0.00477070i
$456$		0			0
$457$	1.73926e11	+	9.86382e11i	0.186527	+	1.05785i	0.923978	+	0.382445i	$0.124918\pi$
$457$	1.73926e11	+	9.86382e11i	0.186527	+	1.05785i	−0.737452	+	0.675400i	$0.763971\pi$
$458$	9.67610e11			1.02756
$459$		0			0
$460$	7.75539e10			0.0807595
$461$	1.21689e9	+	6.90135e9i	0.00125487	+	0.00711672i	0.985429	−	0.170089i	$-0.0544054\pi$
$461$	1.21689e9	+	6.90135e9i	0.00125487	+	0.00711672i	−0.984174	+	0.177205i	$0.943294\pi$
$462$		0			0
$463$	−1.24329e12	+	4.52520e11i	−1.25735	+	0.457639i	−0.882880	−	0.469599i	$-0.844398\pi$
$463$	−1.24329e12	+	4.52520e11i	−1.25735	+	0.457639i	−0.374473	+	0.927238i	$0.622176\pi$
$464$	−1.47880e11	−	1.24086e11i	−0.148108	−	0.124277i
$465$		0			0
$466$	7.18363e10	+	2.61463e10i	0.0705679	+	0.0256846i
$467$	−2.79444e11	−	4.84011e11i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$467$	−2.79444e11	−	4.84011e11i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$468$		0			0
$469$	−1.06823e10	+	1.85023e10i	−0.0101950	+	0.0176582i
$470$	−1.36385e10	+	1.14440e10i	−0.0128922	+	0.0108178i
$471$		0			0
$472$	−3.42562e11	+	1.94277e12i	−0.317688	+	1.80170i
$473$	−1.06467e11	+	6.03804e11i	−0.0978001	+	0.554652i
$474$		0			0
$475$	2.59378e11	−	2.17644e11i	0.233783	−	0.196167i
$476$	4.73905e10	−	8.20828e10i	0.0423117	−	0.0732860i
$477$		0			0
$478$	2.45792e11	+	4.25724e11i	0.215349	+	0.372995i
$479$	4.91701e11	+	1.78964e11i	0.426767	+	0.155331i	0.546469	−	0.837479i	$-0.315972\pi$
$479$	4.91701e11	+	1.78964e11i	0.426767	+	0.155331i	−0.119702	+	0.992810i	$0.538194\pi$
$480$		0			0
$481$	−5.15297e10	−	4.32386e10i	−0.0438940	−	0.0368314i
$482$	1.03814e12	−	3.77850e11i	0.876077	−	0.318866i
$483$		0			0
$484$	3.82110e10	+	2.16705e11i	0.0316508	+	0.179500i
$485$	5.10806e11			0.419197
$486$		0			0
$487$	−1.73423e12			−1.39710			−0.698548	−	0.715563i	$-0.746170\pi$
$487$	−1.73423e12			−1.39710			−0.698548	+	0.715563i	$0.746170\pi$
$488$	4.54638e10	+	2.57838e11i	0.0362892	+	0.205806i
$489$		0			0
$490$	−1.13720e11	+	4.13907e10i	−0.0891158	+	0.0324355i
$491$	−1.16225e12	−	9.75244e11i	−0.902471	−	0.757263i	0.0682008	−	0.997672i	$-0.478274\pi$
$491$	−1.16225e12	−	9.75244e11i	−0.902471	−	0.757263i	−0.970672	+	0.240409i	$0.922719\pi$
$492$		0			0
$493$	1.71878e11	+	6.25587e10i	0.131042	+	0.0476954i
$494$	−1.57143e10	−	2.72179e10i	−0.0118720	−	0.0205629i
$495$		0			0
$496$	−4.12920e11	+	7.15198e11i	−0.306336	+	0.530590i
$497$	−2.09872e11	+	1.76103e11i	−0.154294	+	0.129468i
$498$		0			0
$499$	4.05103e11	−	2.29745e12i	0.292491	−	1.65880i	−0.384737	−	0.923026i	$-0.625708\pi$
$499$	4.05103e11	−	2.29745e12i	0.292491	−	1.65880i	0.677228	−	0.735773i	$-0.263181\pi$
$500$	2.38248e10	−	1.35117e11i	0.0170476	−	0.0966820i
$501$		0			0
$502$	1.04187e12	−	8.74234e11i	0.732230	−	0.614414i
$503$	−9.78309e11	+	1.69448e12i	−0.681428	+	1.18027i	0.293117	+	0.956077i	$0.405308\pi$
$503$	−9.78309e11	+	1.69448e12i	−0.681428	+	1.18027i	−0.974545	+	0.224192i	$0.928026\pi$
$504$		0			0
$505$	2.45209e11	+	4.24714e11i	0.167774	+	0.290593i
$506$	8.11242e11	+	2.95268e11i	0.550140	+	0.200234i
$507$		0			0
$508$	4.11609e11	+	3.45381e11i	0.274219	+	0.230097i
$509$	−2.33768e12	+	8.50845e11i	−1.54367	+	0.561850i	−0.966922	−	0.255072i	$-0.917901\pi$
$509$	−2.33768e12	+	8.50845e11i	−1.54367	+	0.561850i	−0.576749	+	0.816922i	$0.695679\pi$
$510$		0			0
$511$	−2.40113e11	−	1.36175e12i	−0.155784	−	0.883494i
$512$	1.71651e12			1.10390
$513$		0			0
$514$	5.31537e11			0.335892
$515$	2.10330e10	+	1.19284e11i	0.0131756	+	0.0747223i
$516$		0			0
$517$	5.25028e10	−	1.91095e10i	0.0323203	−	0.0117636i
$518$	−5.54956e11	−	4.65664e11i	−0.338669	−	0.284177i
$519$		0			0
$520$	−3.22960e10	−	1.17548e10i	−0.0193702	−	0.00705016i
$521$	−1.03973e12	−	1.80086e12i	−0.618231	−	1.07081i	−0.989808	−	0.142405i	$-0.954516\pi$
$521$	−1.03973e12	−	1.80086e12i	−0.618231	−	1.07081i	0.371578	−	0.928402i	$-0.378817\pi$
$522$		0			0
$523$	1.47398e10	−	2.55301e10i	0.00861457	−	0.0149209i	−0.861686	−	0.507442i	$-0.830591\pi$
$523$	1.47398e10	−	2.55301e10i	0.00861457	−	0.0149209i	0.870301	+	0.492521i	$0.163925\pi$
$524$	−5.22289e10	+	4.38252e10i	−0.0302636	+	0.0253941i
$525$		0			0
$526$	3.85180e11	−	2.18447e12i	0.219396	−	1.24425i
$527$	1.35877e11	−	7.70597e11i	0.0767359	−	0.435191i
$528$		0			0
$529$	2.16134e12	−	1.81358e12i	1.19998	−	1.00690i
$530$	−1.62339e11	+	2.81180e11i	−0.0893680	+	0.154790i
$531$		0			0
$532$	4.77111e10	+	8.26380e10i	0.0258236	+	0.0447278i
$533$	5.33791e10	+	1.94284e10i	0.0286483	+	0.0104271i
$534$		0			0
$535$	4.23481e11	+	3.55343e11i	0.223482	+	0.187523i
$536$	5.41080e10	−	1.96937e10i	0.0283152	−	0.0103059i
$537$		0			0
$538$	−4.00479e11	−	2.27123e12i	−0.206091	−	1.16880i
$539$	3.79784e11			0.193815
$540$		0			0
$541$	−2.59028e12			−1.30005			−0.650023	−	0.759914i	$-0.725241\pi$
$541$	−2.59028e12			−1.30005			−0.650023	+	0.759914i	$0.725241\pi$
$542$	2.52187e11	+	1.43023e12i	0.125524	+	0.711882i
$543$		0			0
$544$	−4.36811e11	+	1.58986e11i	−0.213845	+	0.0778332i
$545$	−4.42372e11	−	3.71194e11i	−0.214785	−	0.180226i
$546$		0			0
$547$	2.29572e12	+	8.35572e11i	1.09642	+	0.399063i	0.825994	−	0.563679i	$-0.190615\pi$
$547$	2.29572e12	+	8.35572e11i	1.09642	+	0.399063i	0.270422	+	0.962742i	$0.412837\pi$
$548$	2.71506e11	+	4.70262e11i	0.128608	+	0.222755i
$549$		0			0
$550$	3.71519e11	−	6.43490e11i	0.173121	−	0.299854i
$551$	−1.41064e11	+	1.18367e11i	−0.0651982	+	0.0547078i
$552$		0			0
$553$	4.59329e11	−	2.60498e12i	0.208863	−	1.18452i
$554$	3.29051e11	−	1.86614e12i	0.148412	−	0.841688i
$555$		0			0
$556$	9.63643e10	−	8.08593e10i	0.0427641	−	0.0358834i
$557$	3.69543e11	−	6.40067e11i	0.162673	−	0.281758i	−0.773153	−	0.634219i	$-0.781322\pi$
$557$	3.69543e11	−	6.40067e11i	0.162673	−	0.281758i	0.935827	+	0.352461i	$0.114655\pi$
$558$		0			0
$559$	−1.31137e11	−	2.27136e11i	−0.0568032	−	0.0983860i
$560$	−2.67437e11	−	9.73391e10i	−0.114915	−	0.0418255i
$561$		0			0
$562$	−1.04890e12	−	8.80133e11i	−0.443528	−	0.372165i
$563$	−4.14841e12	+	1.50990e12i	−1.74018	+	0.633373i	−0.999269	−	0.0382313i	$-0.987828\pi$
$563$	−4.14841e12	+	1.50990e12i	−1.74018	+	0.633373i	−0.740910	+	0.671605i	$0.765605\pi$
$564$		0			0
$565$	−7.38158e10	−	4.18630e11i	−0.0304741	−	0.172827i
$566$	3.60612e12			1.47695
$567$		0			0
$568$	7.38381e11			0.297655
$569$	6.13062e10	+	3.47685e11i	0.0245188	+	0.139053i	0.994610	−	0.103688i	$-0.0330645\pi$
$569$	6.13062e10	+	3.47685e11i	0.0245188	+	0.139053i	−0.970091	+	0.242741i	$0.921953\pi$
$570$		0			0
$571$	−3.50994e12	+	1.27751e12i	−1.38177	+	0.502925i	−0.922716	−	0.385481i	$-0.874035\pi$
$571$	−3.50994e12	+	1.27751e12i	−1.38177	+	0.502925i	−0.459059	+	0.888406i	$0.651813\pi$
$572$	1.48948e10	+	1.24982e10i	0.00581771	+	0.00488163i
$573$		0			0
$574$	5.74874e11	+	2.09237e11i	0.221039	+	0.0804516i
$575$	−1.98930e12	−	3.44558e12i	−0.758920	−	1.31449i
$576$		0			0
$577$	−1.05763e12	+	1.83187e12i	−0.397230	+	0.688023i	−0.993383	−	0.114848i	$-0.963362\pi$
$577$	−1.05763e12	+	1.83187e12i	−0.397230	+	0.688023i	0.596153	+	0.802871i	$0.296695\pi$
$578$	1.30982e12	−	1.09907e12i	0.488132	−	0.409591i
$579$		0			0
$580$	−6.30383e9	+	3.57508e10i	−0.00231302	+	0.0131178i
$581$	5.66939e10	−	3.21527e11i	0.0206416	−	0.117064i
$582$		0			0
$583$	7.80534e11	−	6.54946e11i	0.279823	−	0.234799i
$584$	−1.86336e12	+	3.22743e12i	−0.662886	+	1.14815i
$585$		0			0
$586$	−3.92962e11	−	6.80630e11i	−0.137661	−	0.238436i
$587$	−2.55179e11	−	9.28776e10i	−0.0887102	−	0.0322879i	0.297284	−	0.954789i	$-0.403919\pi$
$587$	−2.55179e11	−	9.28776e10i	−0.0887102	−	0.0322879i	−0.385994	+	0.922501i	$0.626141\pi$
$588$		0			0
$589$	6.03473e11	+	5.06374e11i	0.206604	+	0.173361i
$590$	−9.50783e11	+	3.46057e11i	−0.323033	+	0.117575i
$591$		0			0
$592$	2.60692e11	+	1.47846e12i	0.0872329	+	0.494722i
$593$	4.53303e12			1.50537			0.752684	−	0.658382i	$-0.228759\pi$
$593$	4.53303e12			1.50537			0.752684	+	0.658382i	$0.228759\pi$
$594$		0			0
$595$	2.69660e11			0.0882042
$596$	−9.32754e10	−	5.28991e11i	−0.0302802	−	0.171728i
$597$		0			0
$598$	−3.47026e11	+	1.26307e11i	−0.110970	+	0.0403898i
$599$	−4.53366e12	−	3.80419e12i	−1.43889	−	1.20737i	−0.940212	−	0.340589i	$-0.889374\pi$
$599$	−4.53366e12	−	3.80419e12i	−1.43889	−	1.20737i	−0.498680	−	0.866786i	$-0.666182\pi$
$600$		0			0
$601$	5.01269e11	+	1.82447e11i	0.156724	+	0.0570429i	0.419191	−	0.907898i	$-0.362314\pi$
$601$	5.01269e11	+	1.82447e11i	0.156724	+	0.0570429i	−0.262467	+	0.964941i	$0.584536\pi$
$602$	−1.41230e12	−	2.44617e12i	−0.438271	−	0.759107i
$603$		0			0
$604$	2.06144e9	−	3.57052e9i	0.000630238	−	0.00109160i
$605$	−4.79586e11	+	4.02420e11i	−0.145535	+	0.122118i
$606$		0			0
$607$	3.27407e10	−	1.85682e11i	0.00978902	−	0.0555163i	−0.979522	−	0.201337i	$-0.935471\pi$
$607$	3.27407e10	−	1.85682e11i	0.00978902	−	0.0555163i	0.989311	+	0.145821i	$0.0465824\pi$
$608$	8.12655e10	−	4.60880e11i	0.0241179	−	0.136780i
$609$		0			0
$610$	−1.02867e11	+	8.63158e10i	−0.0300810	+	0.0252410i
$611$	−1.19503e10	+	2.06985e10i	−0.00346891	+	0.00600832i
$612$		0			0
$613$	6.23914e11	+	1.08065e12i	0.178465	+	0.309110i	0.941355	−	0.337418i	$-0.109554\pi$
$613$	6.23914e11	+	1.08065e12i	0.178465	+	0.309110i	−0.762890	+	0.646528i	$0.776220\pi$
$614$	−2.19316e12	−	7.98244e11i	−0.622747	−	0.226662i
$615$		0			0
$616$	8.89820e11	+	7.46648e11i	0.248994	+	0.208931i
$617$	2.09459e12	−	7.62369e11i	0.581856	−	0.211778i	−0.0342875	−	0.999412i	$-0.510916\pi$
$617$	2.09459e12	−	7.62369e11i	0.581856	−	0.211778i	0.616144	+	0.787634i	$0.288694\pi$
$618$		0			0
$619$	3.66524e11	+	2.07866e12i	0.100345	+	0.569083i	0.992978	+	0.118300i	$0.0377443\pi$
$619$	3.66524e11	+	2.07866e12i	0.100345	+	0.569083i	−0.892633	+	0.450784i	$0.851145\pi$
$620$	1.55301e11			0.0422097
$621$		0			0
$622$	1.00126e12			0.268220
$623$	6.19575e11	+	3.51379e12i	0.164778	+	0.934500i
$624$		0			0
$625$	−3.02948e12	+	1.10264e12i	−0.794160	+	0.289051i
$626$	1.02628e12	+	8.61150e11i	0.267104	+	0.224127i
$627$		0			0
$628$	−1.41409e12	−	5.14687e11i	−0.362793	−	0.132046i
$629$	−7.11226e11	−	1.23188e12i	−0.181167	−	0.313791i
$630$		0			0
$631$	−3.26317e12	+	5.65198e12i	−0.819422	+	1.41928i	0.0866865	+	0.996236i	$0.472372\pi$
$631$	−3.26317e12	+	5.65198e12i	−0.819422	+	1.41928i	−0.906109	+	0.423045i	$0.860961\pi$
$632$	−5.46120e12	+	4.58249e12i	−1.36164	+	1.14255i
$633$		0			0
$634$	−5.63174e10	+	3.19392e11i	−0.0138433	+	0.0785095i
$635$	−2.65458e11	+	1.50549e12i	−0.0647908	+	0.367447i
$636$		0			0
$637$	−1.24452e11	+	1.04428e11i	−0.0299484	+	0.0251297i
$638$	−2.02053e11	+	3.49966e11i	−0.0482805	+	0.0836244i
$639$		0			0
$640$	2.68251e11	+	4.64624e11i	0.0632021	+	0.109469i
$641$	4.19369e12	+	1.52638e12i	0.981150	+	0.357109i	0.782287	−	0.622918i	$-0.214053\pi$
$641$	4.19369e12	+	1.52638e12i	0.981150	+	0.357109i	0.198863	+	0.980027i	$0.436275\pi$
$642$		0			0
$643$	−2.62240e12	−	2.20045e12i	−0.604991	−	0.507648i	0.288054	−	0.957614i	$-0.406992\pi$
$643$	−2.62240e12	−	2.20045e12i	−0.604991	−	0.507648i	−0.893046	+	0.449966i	$0.851436\pi$
$644$	1.05363e12	−	3.83489e11i	0.241379	−	0.0878549i
$645$		0			0
$646$	−1.15406e11	−	6.54500e11i	−0.0260725	−	0.147864i
$647$	1.27565e12			0.286195			0.143098	−	0.989709i	$-0.454294\pi$
$647$	1.27565e12			0.286195			0.143098	+	0.989709i	$0.454294\pi$
$648$		0			0
$649$	3.17527e12			0.702553
$650$	5.51941e10	+	3.13021e11i	0.0121278	+	0.0687803i
$651$		0			0
$652$	3.37420e11	−	1.22811e11i	0.0731234	−	0.0266147i
$653$	5.15112e12	+	4.32230e12i	1.10864	+	0.930263i	0.997976	−	0.0635939i	$-0.0202562\pi$
$653$	5.15112e12	+	4.32230e12i	1.10864	+	0.930263i	0.110669	+	0.993857i	$0.464701\pi$
$654$		0			0
$655$	−1.82279e11	−	6.63442e10i	−0.0386947	−	0.0140837i
$656$	−6.33883e11	−	1.09792e12i	−0.133642	−	0.231474i
$657$		0			0
$658$	−1.28700e11	+	2.22915e11i	−0.0267647	+	0.0463578i
$659$	3.06111e12	−	2.56857e12i	0.632258	−	0.530527i	−0.269372	−	0.963036i	$-0.586816\pi$
$659$	3.06111e12	−	2.56857e12i	0.632258	−	0.530527i	0.901630	+	0.432509i	$0.142372\pi$
$660$		0			0
$661$	1.47780e12	−	8.38104e12i	0.301100	−	1.70762i	−0.340219	−	0.940346i	$-0.610501\pi$
$661$	1.47780e12	−	8.38104e12i	0.301100	−	1.70762i	0.641318	−	0.767275i	$-0.278388\pi$
$662$	−4.00359e11	+	2.27055e12i	−0.0810194	+	0.459484i
$663$		0			0
$664$	−6.74064e11	+	5.65607e11i	−0.134569	+	0.112917i
$665$	−1.35742e11	+	2.35112e11i	−0.0269164	+	0.0466205i
$666$		0			0
$667$	1.08190e12	+	1.87390e12i	0.211650	+	0.366589i
$668$	3.27248e11	+	1.19109e11i	0.0635891	+	0.0231446i
$669$		0			0
$670$	2.26233e10	+	1.89832e10i	0.00433730	+	0.00363943i
$671$	3.95998e11	−	1.44132e11i	0.0754123	−	0.0274478i
$672$		0			0
$673$	8.88543e11	+	5.03918e12i	0.166959	+	0.946873i	0.947021	+	0.321171i	$0.104076\pi$
$673$	8.88543e11	+	5.03918e12i	0.166959	+	0.946873i	−0.780062	+	0.625702i	$0.784813\pi$
$674$	7.21439e12			1.34657
$675$		0			0
$676$	1.18574e12			0.218388
$677$	1.23990e12	+	7.03183e12i	0.226850	+	1.28653i	0.859118	+	0.511778i	$0.171013\pi$
$677$	1.23990e12	+	7.03183e12i	0.226850	+	1.28653i	−0.632268	+	0.774750i	$0.717876\pi$
$678$		0			0
$679$	6.93967e12	−	2.52584e12i	1.25293	−	0.456027i
$680$	−5.56737e11	−	4.67158e11i	−0.0998528	−	0.0837865i
$681$		0			0
$682$	1.62451e12	+	5.91272e11i	0.287536	+	0.104654i
$683$	−3.48140e12	−	6.02996e12i	−0.612153	−	1.06028i	−0.990877	−	0.134771i	$-0.956970\pi$
$683$	−3.48140e12	−	6.02996e12i	−0.612153	−	1.06028i	0.378723	−	0.925510i	$-0.376363\pi$
$684$		0			0
$685$	−7.72455e11	+	1.33793e12i	−0.134050	+	0.232181i
$686$	−4.20162e12	+	3.52558e12i	−0.724366	+	0.607815i
$687$		0			0
$688$	−1.01643e12	+	5.76449e12i	−0.172954	+	0.980873i
$689$	−7.56867e10	+	4.29241e11i	−0.0127948	+	0.0725629i
$690$		0			0
$691$	1.53839e10	−	1.29086e10i	0.00256693	−	0.00215391i	−0.641503	−	0.767120i	$-0.721689\pi$
$691$	1.53839e10	−	1.29086e10i	0.00256693	−	0.00215391i	0.644070	+	0.764966i	$0.277244\pi$
$692$	−3.92953e11	+	6.80615e11i	−0.0651424	+	0.112830i
$693$		0			0
$694$	9.21922e11	+	1.59682e12i	0.150861	+	0.261299i
$695$	3.36312e11	+	1.22408e11i	0.0546778	+	0.0199011i
$696$		0			0
$697$	9.20182e11	+	7.72124e11i	0.147681	+	0.123919i
$698$	6.23613e12	−	2.26977e12i	0.994411	−	0.361936i
$699$		0			0
$700$	−1.67578e11	−	9.50384e11i	−0.0263801	−	0.149609i
$701$	3.08521e12			0.482562			0.241281	−	0.970455i	$-0.422432\pi$
$701$	3.08521e12			0.482562			0.241281	+	0.970455i	$0.422432\pi$
$702$		0			0
$703$	1.43207e12			0.221140
$704$	−5.20977e11	−	2.95461e12i	−0.0799359	−	0.453339i
$705$		0			0
$706$	−9.09259e12	+	3.30943e12i	−1.37742	+	0.501340i
$707$	5.43146e12	+	4.55754e12i	0.817578	+	0.686030i
$708$		0			0
$709$	1.93379e12	+	7.03841e11i	0.287409	+	0.104608i	0.481702	−	0.876335i	$-0.340019\pi$
$709$	1.93379e12	+	7.03841e11i	0.287409	+	0.104608i	−0.194293	+	0.980944i	$0.562241\pi$
$710$	1.89355e11	+	3.27973e11i	0.0279650	+	0.0484368i
$711$		0			0
$712$	4.80811e12	−	8.32790e12i	0.701156	−	1.21444i
$713$	7.09103e12	−	5.95008e12i	1.02756	−	0.862224i
$714$		0			0
$715$	−9.60604e9	+	5.44786e10i	−0.00137457	+	0.00779558i
$716$	4.88057e11	−	2.76791e12i	0.0694004	−	0.393589i
$717$		0			0
$718$	−6.43177e12	+	5.39690e12i	−0.903173	+	0.757852i
$719$	−2.06163e12	+	3.57084e12i	−0.287693	+	0.498300i	−0.973259	−	0.229711i	$-0.926222\pi$
$719$	−2.06163e12	+	3.57084e12i	−0.287693	+	0.498300i	0.685565	+	0.728011i	$0.259555\pi$
$720$		0			0
$721$	8.75585e11	+	1.51656e12i	0.120667	+	0.209002i
$722$	−5.43126e12	−	1.97682e12i	−0.743847	−	0.270738i
$723$		0			0
$724$	8.93517e11	+	7.49750e11i	0.120859	+	0.101413i
$725$	1.75004e12	−	6.36962e11i	0.235248	−	0.0856234i
$726$		0			0
$727$	2.53687e11	+	1.43873e12i	0.0336816	+	0.191018i	0.997006	−	0.0773207i	$-0.0246365\pi$
$727$	2.53687e11	+	1.43873e12i	0.0336816	+	0.191018i	−0.963325	+	0.268339i	$0.913525\pi$
$728$	−4.96889e11			−0.0655645
$729$		0			0
$730$	−1.91141e12			−0.249116
$731$	−9.63074e11	−	5.46187e12i	−0.124747	−	0.707478i
$732$		0			0
$733$	3.33582e12	−	1.21414e12i	0.426810	−	0.155346i	−0.119679	−	0.992813i	$-0.538186\pi$
$733$	3.33582e12	−	1.21414e12i	0.426810	−	0.155346i	0.546488	+	0.837467i	$0.315964\pi$
$734$	−7.18517e11	−	6.02907e11i	−0.0913702	−	0.0766687i
$735$		0			0
$736$	−5.16742e12	−	1.88079e12i	−0.649118	−	0.236259i
$737$	−4.63401e10	−	8.02634e10i	−0.00578567	−	0.0100211i
$738$		0			0
$739$	8.83848e11	−	1.53087e12i	0.109013	−	0.188816i	−0.806358	−	0.591428i	$-0.798564\pi$
$739$	8.83848e11	−	1.53087e12i	0.109013	−	0.188816i	0.915371	+	0.402612i	$0.131898\pi$
$740$	2.16267e11	−	1.81470e11i	0.0265123	−	0.0222465i
$741$		0			0
$742$	−8.15118e11	+	4.62277e12i	−0.0987195	+	0.559866i
$743$	−8.25056e11	+	4.67912e12i	−0.0993193	+	0.563268i	0.894019	+	0.448030i	$0.147874\pi$
$743$	−8.25056e11	+	4.67912e12i	−0.0993193	+	0.563268i	−0.993338	+	0.115238i	$0.963237\pi$
$744$		0			0
$745$	1.17070e12	−	9.82333e11i	0.139233	−	0.116830i
$746$	−3.46075e12	+	5.99419e12i	−0.409115	+	0.708608i
$747$		0			0
$748$	2.05581e11	+	3.56077e11i	0.0240119	+	0.0415898i
$749$	7.51039e12	+	2.73356e12i	0.871956	+	0.317366i
$750$		0			0
$751$	−1.44827e12	−	1.21524e12i	−0.166138	−	0.139406i	0.555928	−	0.831230i	$-0.312363\pi$
$751$	−1.44827e12	−	1.21524e12i	−0.166138	−	0.139406i	−0.722066	+	0.691824i	$0.756807\pi$
$752$	5.01242e11	−	1.82437e11i	0.0571567	−	0.0208033i
$753$		0			0
$754$	−3.00177e10	−	1.70239e11i	−0.00338225	−	0.0191817i
$755$	1.17299e10			0.00131381
$756$		0			0
$757$	−3.90031e12			−0.431686			−0.215843	−	0.976428i	$-0.569250\pi$
$757$	−3.90031e12			−0.431686			−0.215843	+	0.976428i	$0.569250\pi$
$758$	−2.19548e12	−	1.24512e13i	−0.241556	−	1.36993i
$759$		0			0
$760$	6.87559e11	−	2.50251e11i	0.0747565	−	0.0272091i
$761$	−4.97467e12	−	4.17424e12i	−0.537691	−	0.451177i	0.333056	−	0.942907i	$-0.391920\pi$
$761$	−4.97467e12	−	4.17424e12i	−0.537691	−	0.451177i	−0.870748	+	0.491730i	$0.836365\pi$
$762$		0			0
$763$	−7.84543e12	−	2.85550e12i	−0.838024	−	0.305016i
$764$	8.01415e11	+	1.38809e12i	0.0851015	+	0.147400i
$765$		0			0
$766$	8.32768e12	−	1.44240e13i	0.873966	−	1.51375i
$767$	−1.04051e12	+	8.73091e11i	−0.108559	+	0.0910920i
$768$		0			0
$769$	−6.97962e11	+	3.95834e12i	−0.0719720	+	0.408173i	0.927443	+	0.373965i	$0.122002\pi$
$769$	−6.97962e11	+	3.95834e12i	−0.0719720	+	0.408173i	−0.999415	+	0.0342082i	$0.989109\pi$
$770$	−1.03454e11	+	5.86714e11i	−0.0106056	+	0.0601476i
$771$		0			0
$772$	8.20876e11	−	6.88797e11i	0.0831763	−	0.0697932i
$773$	−3.67449e12	+	6.36440e12i	−0.370160	+	0.641135i	−0.989590	−	0.143916i	$-0.954030\pi$
$773$	−3.67449e12	+	6.36440e12i	−0.370160	+	0.641135i	0.619430	+	0.785052i	$0.287364\pi$
$774$		0			0
$775$	−3.98357e12	−	6.89974e12i	−0.396656	−	0.687029i
$776$	−1.87034e13	−	6.80747e12i	−1.85158	−	0.673919i
$777$		0			0
$778$	4.71795e12	+	3.95883e12i	0.461684	+	0.387399i
$779$	−1.13641e12	+	4.13618e11i	−0.110564	+	0.0402421i
$780$		0			0
$781$	−2.06377e11	−	1.17042e12i	−0.0198487	−	0.112568i
$782$	−7.80926e12			−0.746757
$783$		0			0
$784$	3.62578e12			0.342751
$785$	−7.43457e11	−	4.21636e12i	−0.0698783	−	0.396300i
$786$		0			0
$787$	1.41522e13	−	5.15098e12i	1.31504	−	0.478634i	0.413171	−	0.910653i	$-0.364421\pi$
$787$	1.41522e13	−	5.15098e12i	1.31504	−	0.478634i	0.901864	+	0.432019i	$0.142199\pi$
$788$	−2.63893e12	−	2.21432e12i	−0.243814	−	0.204584i
$789$		0			0
$790$	−3.43595e12	−	1.25058e12i	−0.313852	−	0.114233i
$791$	−3.07289e12	−	5.32240e12i	−0.279095	−	0.483407i
$792$		0			0
$793$	−9.01341e10	+	1.56117e11i	−0.00809393	+	0.0140191i
$794$	−8.77172e12	+	7.36034e12i	−0.783235	+	0.657212i
$795$		0			0
$796$	−5.56475e11	+	3.15592e12i	−0.0491288	+	0.278624i
$797$	−1.32140e12	+	7.49406e12i	−0.116004	+	0.657892i	0.870244	+	0.492621i	$0.163961\pi$
$797$	−1.32140e12	+	7.49406e12i	−0.116004	+	0.657892i	−0.986248	+	0.165271i	$0.947150\pi$
$798$		0			0
$799$	−3.87165e11	+	3.24870e11i	−0.0336074	+	0.0282000i
$800$	−2.36649e12	+	4.09888e12i	−0.204268	+	0.353802i
$801$		0			0
$802$	−7.60399e12	−	1.31705e13i	−0.649018	−	1.12413i
$803$	5.63669e12	+	2.05159e12i	0.478415	+	0.174129i
$804$		0			0
$805$	2.44371e12	+	2.05051e12i	0.205101	+	0.172100i
$806$	−6.94916e11	+	2.52929e11i	−0.0579996	+	0.0211101i
$807$		0			0
$808$	−3.31828e12	−	1.88189e13i	−0.273881	−	1.55326i
$809$	−1.55017e13			−1.27236			−0.636182	−	0.771539i	$-0.719487\pi$
$809$	−1.55017e13			−1.27236			−0.636182	+	0.771539i	$0.719487\pi$
$810$		0			0
$811$	−2.15441e13			−1.74878			−0.874389	−	0.485225i	$-0.838738\pi$
$811$	−2.15441e13			−1.74878			−0.874389	+	0.485225i	$0.838738\pi$
$812$	9.11385e10	+	5.16872e11i	0.00735698	+	0.0417235i
$813$		0			0
$814$	2.95313e12	−	1.07485e12i	0.235762	−	0.0858102i
$815$	7.82587e11	+	6.56669e11i	0.0621332	+	0.0521359i
$816$		0			0
$817$	5.24691e12	+	1.90972e12i	0.412006	+	0.149958i
$818$	−4.99921e12	−	8.65888e12i	−0.390401	−	0.676195i
$819$		0			0
$820$	−1.19203e11	+	2.06466e11i	−0.00920717	+	0.0159473i
$821$	1.60433e13	−	1.34620e13i	1.23240	−	1.03410i	0.234318	−	0.972160i	$-0.424714\pi$
$821$	1.60433e13	−	1.34620e13i	1.23240	−	1.03410i	0.998080	−	0.0619440i	$-0.0197300\pi$
$822$		0			0
$823$	−1.18996e12	+	6.74862e12i	−0.0904138	+	0.512762i	0.905643	+	0.424041i	$0.139389\pi$
$823$	−1.18996e12	+	6.74862e12i	−0.0904138	+	0.512762i	−0.996057	+	0.0887206i	$0.971722\pi$
$824$	8.19557e11	−	4.64794e12i	0.0619308	−	0.351227i
$825$		0			0
$826$	−1.12059e13	+	9.40287e12i	−0.837600	+	0.702830i
$827$	−9.39045e12	+	1.62647e13i	−0.698090	+	1.20913i	0.271037	+	0.962569i	$0.412633\pi$
$827$	−9.39045e12	+	1.62647e13i	−0.698090	+	1.20913i	−0.969128	+	0.246559i	$0.920700\pi$
$828$		0			0
$829$	5.37150e12	+	9.30372e12i	0.395003	+	0.684165i	0.993102	−	0.117257i	$-0.0374102\pi$
$829$	5.37150e12	+	9.30372e12i	0.395003	+	0.684165i	−0.598098	+	0.801423i	$0.704077\pi$
$830$	−4.24092e11	−	1.54357e11i	−0.0310176	−	0.0112895i
$831$		0			0
$832$	9.83136e11	+	8.24949e11i	0.0711310	+	0.0596860i
$833$	−3.22825e12	+	1.17499e12i	−0.232308	+	0.0845533i
$834$		0			0
$835$	1.72050e11	+	9.75747e11i	0.0122480	+	0.0694621i
$836$	−4.13944e11			−0.0293098
$837$		0			0
$838$	1.91404e13			1.34077
$839$	−1.85017e12	−	1.04928e13i	−0.128909	−	0.731079i	−0.978909	−	0.204297i	$-0.934509\pi$
$839$	−1.85017e12	−	1.04928e13i	−0.128909	−	0.731079i	0.850000	−	0.526783i	$-0.176602\pi$
$840$		0			0
$841$	1.26805e13	−	4.61532e12i	0.874086	−	0.318141i
$842$	7.89465e12	+	6.62440e12i	0.541288	+	0.454195i
$843$		0			0
$844$	−4.68141e12	−	1.70389e12i	−0.317567	−	0.115585i
$845$	1.68676e12	+	2.92155e12i	0.113814	+	0.197132i
$846$		0			0
$847$	−4.52564e12	+	7.83863e12i	−0.302137	+	0.523317i
$848$	7.45173e12	−	6.25274e12i	0.494852	−	0.415230i
$849$		0			0
$850$	−1.16715e12	+	6.61924e12i	−0.0766905	+	0.434933i
$851$	2.92205e12	−	1.65718e13i	0.190987	−	1.08314i
$852$		0			0
$853$	4.67333e12	−	3.92139e12i	0.302243	−	0.253612i	−0.479034	−	0.877796i	$-0.659013\pi$
$853$	4.67333e12	−	3.92139e12i	0.302243	−	0.253612i	0.781277	+	0.624184i	$0.214569\pi$
$854$	−9.70711e11	+	1.68132e12i	−0.0624496	+	0.108166i
$855$		0			0
$856$	−1.07703e13	−	1.86547e13i	−0.685639	−	1.18756i
$857$	1.48084e13	+	5.38983e12i	0.937768	+	0.341319i	0.765284	−	0.643693i	$-0.222599\pi$
$857$	1.48084e13	+	5.38983e12i	0.937768	+	0.341319i	0.172484	+	0.985012i	$0.444821\pi$
$858$		0			0
$859$	−1.64683e12	−	1.38186e12i	−0.103200	−	0.0865951i	0.589728	−	0.807602i	$-0.299235\pi$
$859$	−1.64683e12	−	1.38186e12i	−0.103200	−	0.0865951i	−0.692928	+	0.721007i	$0.743680\pi$
$860$	1.03437e12	−	3.76478e11i	0.0644809	−	0.0234691i
$861$		0			0
$862$	−1.69065e12	−	9.58815e12i	−0.104297	−	0.591497i
$863$	7.51767e11			0.0461354			0.0230677	−	0.999734i	$-0.492657\pi$
$863$	7.51767e11			0.0461354			0.0230677	+	0.999734i	$0.492657\pi$
$864$		0			0
$865$	−2.23597e12			−0.135798
$866$	−7.55933e11	−	4.28711e12i	−0.0456723	−	0.259021i
$867$		0			0
$868$	2.10988e12	−	7.67933e11i	0.126159	−	0.0459182i
$869$	8.79023e12	+	7.37588e12i	0.522891	+	0.438758i
$870$		0			0
$871$	3.72550e10	+	1.35597e10i	0.00219332	+	0.000798304i
$872$	1.12508e13	+	1.94869e13i	0.658958	+	1.14135i
$873$		0			0
$874$	3.93104e12	−	6.80876e12i	0.227880	−	0.394700i
$875$	4.32319e12	−	3.62759e12i	0.249326	−	0.209210i
$876$		0			0
$877$	−4.22948e12	+	2.39866e13i	−0.241429	+	1.36921i	0.587214	+	0.809431i	$0.300225\pi$
$877$	−4.22948e12	+	2.39866e13i	−0.241429	+	1.36921i	−0.828643	+	0.559778i	$0.810887\pi$
$878$	1.32900e11	−	7.53711e11i	0.00754741	−	0.0428035i
$879$		0			0
$880$	9.45762e11	−	7.93589e11i	0.0531630	−	0.0446091i
$881$	1.20102e13	−	2.08023e13i	0.671674	−	1.16337i	−0.305755	−	0.952110i	$-0.598909\pi$
$881$	1.20102e13	−	2.08023e13i	0.671674	−	1.16337i	0.977429	−	0.211264i	$-0.0677579\pi$
$882$		0			0
$883$	−6.14230e12	−	1.06388e13i	−0.340023	−	0.588937i	0.644414	−	0.764677i	$-0.277101\pi$
$883$	−6.14230e12	−	1.06388e13i	−0.340023	−	0.588937i	−0.984437	+	0.175740i	$0.943768\pi$
$884$	−1.65276e11	−	6.01557e10i	−0.00910282	−	0.00331315i
$885$		0			0
$886$	−4.71318e12	−	3.95483e12i	−0.256958	−	0.215614i
$887$	−1.62535e13	+	5.91578e12i	−0.881637	+	0.320890i	−0.742870	−	0.669435i	$-0.766536\pi$
$887$	−1.62535e13	+	5.91578e12i	−0.881637	+	0.320890i	−0.138767	+	0.990325i	$0.544314\pi$
$888$		0			0
$889$	3.83789e12	+	2.17657e13i	0.206079	+	1.16873i
$890$	4.93210e12			0.263497
$891$		0			0
$892$	4.44023e12			0.234835
$893$	−8.83568e10	−	5.01096e11i	−0.00464952	−	0.0263688i
$894$		0			0
$895$	7.51417e12	−	2.73493e12i	0.391451	−	0.142476i
$896$	5.94186e12	+	4.98581e12i	0.307990	+	0.258434i
$897$		0			0
$898$	1.33865e13	+	4.87228e12i	0.686946	+	0.250028i
$899$	2.16649e12	+	3.75247e12i	0.110621	+	0.191601i
$900$		0			0
$901$	−4.60843e12	+	7.98204e12i	−0.232966	+	0.403508i
$902$	−2.03298e12	+	1.70587e12i	−0.102259	+	0.0858059i
$903$		0			0
$904$	−2.87626e12	+	1.63121e13i	−0.143242	+	0.812364i
$905$	−5.76253e11	+	3.26809e12i	−0.0285558	+	0.161948i
$906$		0			0
$907$	1.24654e13	−	1.04597e13i	0.611609	−	0.513201i	−0.283544	−	0.958959i	$-0.591510\pi$
$907$	1.24654e13	−	1.04597e13i	0.611609	−	0.513201i	0.895154	+	0.445758i	$0.147066\pi$
$908$	−2.44489e12	+	4.23468e12i	−0.119364	+	0.206745i
$909$		0			0
$910$	−1.27426e11	−	2.20708e11i	−0.00615985	−	0.0106692i
$911$	−6.34240e12	−	2.30845e12i	−0.305085	−	0.111042i	0.184941	−	0.982750i	$-0.440791\pi$
$911$	−6.34240e12	−	2.30845e12i	−0.305085	−	0.111042i	−0.490026	+	0.871708i	$0.663013\pi$
$912$		0			0
$913$	1.08496e12	+	9.10387e11i	0.0516766	+	0.0433618i
$914$	1.88098e13	−	6.84620e12i	0.891510	−	0.324483i
$915$		0			0
$916$	9.46672e11	+	5.36884e12i	0.0444293	+	0.251971i
$917$	−2.80445e12			−0.130974
$918$		0			0
$919$	3.46415e12			0.160205			0.0801026	−	0.996787i	$-0.474475\pi$
$919$	3.46415e12			0.160205			0.0801026	+	0.996787i	$0.474475\pi$
$920$	−1.49295e12	−	8.46696e12i	−0.0687070	−	0.389657i
$921$		0			0
$922$	1.31605e11	−	4.79004e10i	0.00599769	−	0.00218298i
$923$	3.89455e11	+	3.26792e11i	0.0176624	+	0.0148205i
$924$		0			0
$925$	−1.36097e13	−	4.95354e12i	−0.611240	−	0.222473i
$926$	1.32209e13	+	2.28992e13i	0.590896	+	1.02346i
$927$		0			0
$928$	1.28703e12	−	2.22920e12i	0.0569669	−	0.0986696i
$929$	−2.03175e12	+	1.70484e12i	−0.0894950	+	0.0750952i	−0.686438	−	0.727189i	$-0.740826\pi$
$929$	−2.03175e12	+	1.70484e12i	−0.0894950	+	0.0750952i	0.596943	+	0.802284i	$0.296382\pi$
$930$		0			0
$931$	6.00592e11	−	3.40613e12i	0.0262003	−	0.148589i
$932$	−7.47924e10	+	4.24169e11i	−0.00324703	+	0.0184148i
$933$		0			0
$934$	−8.55625e12	+	7.17955e12i	−0.367894	+	0.308700i
$935$	−5.84895e11	+	1.01307e12i	−0.0250280	+	0.0433497i
$936$		0			0
$937$	2.01221e13	+	3.48526e13i	0.852797	+	1.47709i	0.878674	+	0.477423i	$0.158429\pi$
$937$	2.01221e13	+	3.48526e13i	0.852797	+	1.47709i	−0.0258764	+	0.999665i	$0.508238\pi$
$938$	4.01222e11	+	1.46033e11i	0.0169228	+	0.00615940i
$939$		0			0
$940$	−7.68413e10	−	6.44775e10i	−0.00321011	−	0.00269360i
$941$	2.28129e12	−	8.30320e11i	0.0948476	−	0.0345217i	−0.294161	−	0.955756i	$-0.595040\pi$
$941$	2.28129e12	−	8.30320e11i	0.0948476	−	0.0345217i	0.389008	+	0.921234i	$0.372818\pi$
$942$		0			0
$943$	2.46757e12	+	1.39943e13i	0.101617	+	0.576299i
$944$	3.03142e13			1.24243
$945$		0			0
$946$	1.22532e13			0.497438
$947$	5.16420e12	+	2.92876e13i	0.208655	+	1.18334i	0.891584	+	0.452855i	$0.149594\pi$
$947$	5.16420e12	+	2.92876e13i	0.208655	+	1.18334i	−0.682930	+	0.730484i	$0.739294\pi$
$948$		0			0
$949$	−2.41121e12	+	8.77610e11i	−0.0965023	+	0.0351240i
$950$	−5.18368e12	−	4.34962e12i	−0.206482	−	0.173259i
$951$		0			0
$952$	−9.87369e12	−	3.59373e12i	−0.389595	−	0.141801i
$953$	−2.80262e12	−	4.85429e12i	−0.110064	−	0.190637i	0.805732	−	0.592281i	$-0.201772\pi$
$953$	−2.80262e12	−	4.85429e12i	−0.110064	−	0.190637i	−0.915796	+	0.401644i	$0.868439\pi$
$954$		0			0
$955$	−2.28009e12	+	3.94923e12i	−0.0887027	+	0.153638i
$956$	−2.12168e12	+	1.78030e12i	−0.0821524	+	0.0689340i
$957$		0			0
$958$	1.81589e12	−	1.02984e13i	0.0696538	−	0.395027i
$959$	−3.87856e12	+	2.19964e13i	−0.148077	+	0.839785i
$960$		0			0
$961$	−6.05419e12	+	5.08007e12i	−0.228982	+	0.192138i
$962$	−6.72169e11	+	1.16423e12i	−0.0253041	+	0.0438280i
$963$		0			0
$964$	3.11220e12	+	5.39048e12i	0.116070	+	0.201039i
$965$	2.86486e12	+	1.04272e12i	0.106348	+	0.0387076i
$966$		0			0
$967$	−3.16313e13	−	2.65418e13i	−1.16332	−	0.976138i	−0.163370	−	0.986565i	$-0.552236\pi$
$967$	−3.16313e13	−	2.65418e13i	−1.16332	−	0.976138i	−0.999946	+	0.0104270i	$0.996681\pi$
$968$	2.29232e13	−	8.34338e12i	0.839145	−	0.305424i
$969$		0			0
$970$	−1.77268e12	−	1.00534e13i	−0.0642922	−	0.364619i
$971$	−3.56316e13			−1.28632			−0.643160	−	0.765732i	$-0.722377\pi$
$971$	−3.56316e13			−1.28632			−0.643160	+	0.765732i	$0.722377\pi$
$972$		0			0
$973$	5.17433e12			0.185074
$974$	6.01841e12	+	3.41321e13i	0.214272	+	1.21520i
$975$		0			0
$976$	3.78058e12	−	1.37602e12i	0.133363	−	0.0485400i
$977$	−5.90533e12	−	4.95516e12i	−0.207357	−	0.173993i	0.533195	−	0.845993i	$-0.320991\pi$
$977$	−5.90533e12	−	4.95516e12i	−0.207357	−	0.173993i	−0.740552	+	0.671999i	$0.765436\pi$
$978$		0			0
$979$	−1.45446e13	−	5.29381e12i	−0.506034	−	0.184181i
$980$	−3.40918e11	−	5.90488e11i	−0.0118068	−	0.0204500i
$981$		0			0
$982$	−1.51608e13	+	2.62592e13i	−0.520258	+	0.901114i
$983$	−3.64293e13	+	3.05678e13i	−1.24440	+	1.04418i	−0.247234	+	0.968956i	$0.579522\pi$
$983$	−3.64293e13	+	3.05678e13i	−1.24440	+	1.04418i	−0.997167	+	0.0752202i	$0.976034\pi$
$984$		0			0
$985$	1.70191e12	−	9.65204e12i	0.0576069	−	0.326705i
$986$	6.34762e11	−	3.59991e12i	0.0213877	−	0.121296i
$987$		0			0
$988$	1.35646e11	−	1.13820e11i	0.00452898	−	0.00380027i
$989$	3.28049e13	−	5.68198e13i	1.09032	−	1.88850i
$990$		0			0
$991$	−3.16007e12	−	5.47341e12i	−0.104080	−	0.180271i	0.809282	−	0.587420i	$-0.199856\pi$
$991$	−3.16007e12	−	5.47341e12i	−0.104080	−	0.180271i	−0.913362	+	0.407149i	$0.866523\pi$
$992$	−1.03477e13	−	3.76626e12i	−0.339267	−	0.123483i
$993$		0			0
$994$	4.19429e12	+	3.51943e12i	0.136276	+	0.114349i
$995$	−8.56752e12	+	3.11832e12i	−0.277110	+	0.100860i
$996$		0			0
$997$	4.99252e12	+	2.83140e13i	0.160026	+	0.907554i	0.954046	+	0.299662i	$0.0968738\pi$
$997$	4.99252e12	+	2.83140e13i	0.160026	+	0.907554i	−0.794019	+	0.607893i	$0.792015\pi$
$998$	−4.66229e13			−1.48769
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.9		156
3.2	odd	2		27.10.e.a.13.18	✓	156
27.2	odd	18		27.10.e.a.25.18	yes	156
27.25	even	9	inner	81.10.e.a.73.9		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.18	✓	156	3.2	odd	2
27.10.e.a.25.18	yes	156	27.2	odd	18
81.10.e.a.10.9		156	1.1	even	1	trivial
81.10.e.a.73.9		156	27.25	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.47036 - 19.6814i) q^{2} +(105.808 - 38.5110i) q^{4} +(245.404 + 205.919i) q^{5} +(4352.22 + 1584.08i) q^{7} +(-6241.31 - 10810.3i) q^{8} +(3201.13 - 5544.51i) q^{10} +(-15391.2 + 12914.7i) q^{11} +(1492.45 - 8464.09i) q^{13} +(16073.1 - 91155.2i) q^{14} +(-146939. + 123296. i) q^{16} +(90872.5 - 157396. i) q^{17} +(91487.2 + 158461. i) q^{19} +(33895.9 + 12337.1i) q^{20} +(307593. + 258101. i) q^{22} +(2.02036e6 - 735350. i) q^{23} +(-321336. - 1.82239e6i) q^{25} -171765. q^{26} +521505. q^{28} +(174760. + 991116. i) q^{29} +(4.04575e6 - 1.47253e6i) q^{31} +(-1.95929e6 - 1.64404e6i) q^{32} +(-3.41313e6 - 1.24228e6i) q^{34} +(741862. + 1.28494e6i) q^{35} +(3.91332e6 - 6.77807e6i) q^{37} +(2.80123e6 - 2.35051e6i) q^{38} +(694391. - 3.93809e6i) q^{40} +(-1.14770e6 + 6.50891e6i) q^{41} +(2.33766e7 - 1.96153e7i) q^{43} +(-1.13115e6 + 1.95921e6i) q^{44} +(-2.14841e7 - 3.72115e7i) q^{46} +(-2.61315e6 - 951111. i) q^{47} +(-1.44801e7 - 1.21503e7i) q^{49} +(-3.47520e7 + 1.26487e7i) q^{50} +(-168048. - 953046. i) q^{52} -5.07132e7 q^{53} -6.43644e6 q^{55} +(-1.00392e7 - 5.69354e7i) q^{56} +(1.89001e7 - 6.87906e6i) q^{58} +(-1.21065e8 - 1.01585e8i) q^{59} +(-1.97095e7 - 7.17368e6i) q^{61} +(-4.30217e7 - 7.45158e7i) q^{62} +(-7.46622e7 + 1.29319e8i) q^{64} +(2.10917e6 - 1.76980e6i) q^{65} +(-801013. + 4.54277e6i) q^{67} +(3.55358e6 - 2.01534e7i) q^{68} +(2.27149e7 - 1.90601e7i) q^{70} +(-2.95764e7 + 5.12277e7i) q^{71} +(-1.49276e8 - 2.58554e8i) q^{73} +(-1.46982e8 - 5.34973e7i) q^{74} +(1.57826e7 + 1.32432e7i) q^{76} +(-8.74437e7 + 3.18269e7i) q^{77} +(-9.91742e7 - 5.62445e8i) q^{79} -6.14484e7 q^{80} +1.32087e8 q^{82} +(-1.22408e7 - 6.94213e7i) q^{83} +(5.47112e7 - 1.99133e7i) q^{85} +(-4.67181e8 - 3.92012e8i) q^{86} +(2.35673e8 + 8.57778e7i) q^{88} +(3.85185e8 + 6.67159e8i) q^{89} +(1.99032e7 - 3.44734e7i) q^{91} +(1.85451e8 - 1.55612e8i) q^{92} +(-9.65060e6 + 5.47313e7i) q^{94} +(-1.01786e7 + 5.77258e7i) q^{95} +(1.22147e9 - 1.02493e9i) q^{97} +(-1.88883e8 + 3.27155e8i) 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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