LMFDB - Embedded newform 27.10.e.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	27.4
Dual form			27.10.e.a.7.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(23.5230 + 8.56168i) q^{2} +(-83.7573 + 112.551i) q^{3} +(87.8153 + 73.6858i) q^{4} +(-425.267 + 2411.81i) q^{5} +(-2933.85 + 1930.43i) q^{6} +(3548.49 - 2977.54i) q^{7} +(-4973.56 - 8614.45i) q^{8} +(-5652.42 - 18853.9i) q^{9} +(-30652.7 + 53092.0i) q^{10} +(-4933.64 - 27980.1i) q^{11} +(-15648.6 + 3711.97i) q^{12} +(-164231. + 59775.2i) q^{13} +(108964. - 39659.6i) q^{14} +(-235832. - 249871. i) q^{15} +(-53430.8 - 303021. i) q^{16} +(-136602. + 236602. i) q^{17} +(28459.2 - 491896. i) q^{18} +(292780. + 507109. i) q^{19} +(-215061. + 180458. i) q^{20} +(37912.5 + 648777. i) q^{21} +(123502. - 700416. i) q^{22} +(395850. + 332158. i) q^{23} +(1.38614e6 + 161745. i) q^{24} +(-3.80064e6 - 1.38332e6i) q^{25} -4.37499e6 q^{26} +(2.59546e6 + 942969. i) q^{27} +531014. q^{28} +(1.13009e6 + 411318. i) q^{29} +(-3.40817e6 - 7.89684e6i) q^{30} +(-3.31766e6 - 2.78385e6i) q^{31} +(453140. - 2.56988e6i) q^{32} +(3.56241e6 + 1.78825e6i) q^{33} +(-5.23902e6 + 4.39606e6i) q^{34} +(5.67220e6 + 9.82453e6i) q^{35} +(892897. - 2.07217e6i) q^{36} +(-1.02641e7 + 1.77780e7i) q^{37} +(2.54535e6 + 1.44354e7i) q^{38} +(7.02780e6 - 2.34910e7i) q^{39} +(2.28915e7 - 8.33183e6i) q^{40} +(1.41195e7 - 5.13909e6i) q^{41} +(-4.66280e6 + 1.55858e7i) q^{42} +(2.97399e6 + 1.68663e7i) q^{43} +(1.62849e6 - 2.82062e6i) q^{44} +(4.78759e7 - 5.61461e6i) q^{45} +(6.46776e6 + 1.12025e7i) q^{46} +(1.46906e7 - 1.23269e7i) q^{47} +(3.85805e7 + 1.93666e7i) q^{48} +(-3.28127e6 + 1.86090e7i) q^{49} +(-7.75589e7 - 6.50796e7i) q^{50} +(-1.51884e7 - 3.51919e7i) q^{51} +(-1.88266e7 - 6.85232e6i) q^{52} -7.19089e7 q^{53} +(5.29796e7 + 4.44030e7i) q^{54} +6.95807e7 q^{55} +(-4.32985e7 - 1.57594e7i) q^{56} +(-8.15980e7 - 9.52148e6i) q^{57} +(2.30615e7 + 1.93509e7i) q^{58} +(-2.81120e7 + 1.59431e8i) q^{59} +(-2.29774e6 - 3.93200e7i) q^{60} +(-4.30566e7 + 3.61288e7i) q^{61} +(-5.42070e7 - 9.38892e7i) q^{62} +(-7.61959e7 - 5.00727e7i) q^{63} +(-4.61084e7 + 7.98621e7i) q^{64} +(-7.43244e7 - 4.21515e8i) q^{65} +(6.84883e7 + 7.25653e7i) q^{66} +(-2.09545e7 + 7.62680e6i) q^{67} +(-2.94300e7 + 1.07117e7i) q^{68} +(-7.05400e7 + 1.67327e7i) q^{69} +(4.93127e7 + 2.79666e8i) q^{70} +(1.41806e8 - 2.45615e8i) q^{71} +(-1.34304e8 + 1.42464e8i) q^{72} +(4.43683e7 + 7.68481e7i) q^{73} +(-3.93652e8 + 3.30314e8i) q^{74} +(4.74025e8 - 3.11902e8i) q^{75} +(-1.16562e7 + 6.61056e7i) q^{76} +(-1.00819e8 - 8.45970e7i) q^{77} +(3.66437e8 - 4.92409e8i) q^{78} +(2.02624e8 + 7.37491e7i) q^{79} +7.53552e8 q^{80} +(-3.23521e8 + 2.13141e8i) q^{81} +3.76133e8 q^{82} +(-3.51637e8 - 1.27986e8i) q^{83} +(-4.44763e7 + 5.97661e7i) q^{84} +(-5.12547e8 - 4.30078e8i) q^{85} +(-7.44469e7 + 4.22209e8i) q^{86} +(-1.40947e8 + 9.27415e7i) q^{87} +(-2.16495e8 + 1.81661e8i) q^{88} +(1.28124e8 + 2.21917e8i) q^{89} +(1.17426e9 + 2.77825e8i) q^{90} +(-4.04790e8 + 7.01116e8i) q^{91} +(1.02864e7 + 5.83370e7i) q^{92} +(5.91203e8 - 1.40238e8i) q^{93} +(4.51106e8 - 1.64189e8i) q^{94} +(-1.34756e9 + 4.90472e8i) q^{95} +(2.51289e8 + 2.66248e8i) q^{96} +(-6.14418e7 - 3.48454e8i) q^{97} +(-2.36510e8 + 4.09647e8i) q^{98} +(-4.99647e8 + 2.51174e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) $ 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	23.5230	+	8.56168i	1.03958	+	0.378376i	0.804721	−	0.593653i	$-0.202315\pi$
$2$	23.5230	+	8.56168i	1.03958	+	0.378376i	0.234859	+	0.972029i	$0.424537\pi$
$3$	−83.7573	+	112.551i	−0.597004	+	0.802238i
$3$	−83.7573	+	112.551i	−0.597004	+	0.802238i
$4$	87.8153	+	73.6858i	0.171514	+	0.143918i
$5$	−425.267	+	2411.81i	−0.304296	+	1.72575i	0.322502	+	0.946569i	$0.395476\pi$
$5$	−425.267	+	2411.81i	−0.304296	+	1.72575i	−0.626798	+	0.779182i	$0.715635\pi$
$6$	−2933.85	+	1930.43i	−0.924181	+	0.608099i
$7$	3548.49	−	2977.54i	0.558602	−	0.468723i	−0.319239	−	0.947674i	$-0.603427\pi$
$7$	3548.49	−	2977.54i	0.558602	−	0.468723i	0.877841	+	0.478951i	$0.158983\pi$
$8$	−4973.56	−	8614.45i	−0.429301	−	0.743572i
$9$	−5652.42	−	18853.9i	−0.287173	−	0.957879i
$10$	−30652.7	+	53092.0i	−0.969324	+	1.67892i
$11$	−4933.64	−	27980.1i	−0.101602	−	0.576211i	−0.992523	−	0.122055i	$-0.961052\pi$
$11$	−4933.64	−	27980.1i	−0.101602	−	0.576211i	0.890922	−	0.454157i	$-0.150059\pi$
$12$	−15648.6	+	3711.97i	−0.217851	+	0.0516760i
$13$	−164231.	+	59775.2i	−1.59482	+	0.580465i	−0.978357	−	0.206923i	$-0.933655\pi$
$13$	−164231.	+	59775.2i	−1.59482	+	0.580465i	−0.616458	+	0.787388i	$0.711433\pi$
$14$	108964.	−	39659.6i	0.758065	−	0.275913i
$15$	−235832.	−	249871.i	−1.20280	−	1.27440i
$16$	−53430.8	−	303021.i	−0.203822	−	1.15593i
$17$	−136602.	+	236602.i	−0.396678	+	0.687067i	−0.993314	−	0.115445i	$-0.963170\pi$
$17$	−136602.	+	236602.i	−0.396678	+	0.687067i	0.596636	+	0.802512i	$0.296504\pi$
$18$	28459.2	−	491896.i	0.0638993	−	1.10445i
$19$	292780.	+	507109.i	0.515406	+	0.892710i	0.999840	+	0.0178819i	$0.00569228\pi$
$19$	292780.	+	507109.i	0.515406	+	0.892710i	−0.484434	+	0.874828i	$0.660974\pi$
$20$	−215061.	+	180458.i	−0.300557	+	0.252197i
$21$	37912.5	+	648777.i	0.0425399	+	0.727961i
$22$	123502.	−	700416.i	0.112402	−	0.637462i
$23$	395850.	+	332158.i	0.294955	+	0.247496i	0.778241	−	0.627966i	$-0.216112\pi$
$23$	395850.	+	332158.i	0.294955	+	0.247496i	−0.483286	+	0.875463i	$0.660557\pi$
$24$	1.38614e6	+	161745.i	0.852816	+	0.0995131i
$25$	−3.80064e6	−	1.38332e6i	−1.94593	−	0.708259i
$26$	−4.37499e6			−1.87757
$27$	2.59546e6	+	942969.i	0.939890	+	0.341476i
$28$	531014.			0.163266
$29$	1.13009e6	+	411318.i	0.296702	+	0.107991i	0.486082	−	0.873913i	$-0.338426\pi$
$29$	1.13009e6	+	411318.i	0.296702	+	0.107991i	−0.189380	+	0.981904i	$0.560648\pi$
$30$	−3.40817e6	−	7.89684e6i	−0.768202	−	1.77995i
$31$	−3.31766e6	−	2.78385e6i	−0.645214	−	0.541399i	0.260400	−	0.965501i	$-0.416146\pi$
$31$	−3.31766e6	−	2.78385e6i	−0.645214	−	0.541399i	−0.905615	+	0.424102i	$0.860590\pi$
$32$	453140.	−	2.56988e6i	0.0763936	−	0.433250i
$33$	3.56241e6	+	1.78825e6i	0.522915	+	0.262492i
$34$	−5.23902e6	+	4.39606e6i	−0.672349	+	0.564168i
$35$	5.67220e6	+	9.82453e6i	0.638918	+	1.10664i
$36$	892897.	−	2.07217e6i	0.0886013	−	0.205619i
$37$	−1.02641e7	+	1.77780e7i	−0.900355	+	1.55946i	−0.0733217	+	0.997308i	$0.523360\pi$
$37$	−1.02641e7	+	1.77780e7i	−0.900355	+	1.55946i	−0.827034	+	0.562153i	$0.809973\pi$
$38$	2.54535e6	+	1.44354e7i	0.198026	+	1.12306i
$39$	7.02780e6	−	2.34910e7i	0.486439	−	1.62596i
$40$	2.28915e7	−	8.33183e6i	1.41385	−	0.514601i
$41$	1.41195e7	−	5.13909e6i	0.780357	−	0.284027i	0.0790353	−	0.996872i	$-0.474816\pi$
$41$	1.41195e7	−	5.13909e6i	0.780357	−	0.284027i	0.701321	+	0.712845i	$0.252594\pi$
$42$	−4.66280e6	+	1.55858e7i	−0.231220	+	0.772870i
$43$	2.97399e6	+	1.68663e7i	0.132657	+	0.752337i	0.976462	+	0.215687i	$0.0691992\pi$
$43$	2.97399e6	+	1.68663e7i	0.132657	+	0.752337i	−0.843805	+	0.536650i	$0.819690\pi$
$44$	1.62849e6	−	2.82062e6i	0.0655008	−	0.113451i
$45$	4.78759e7	−	5.61461e6i	1.74045	−	0.204110i
$46$	6.46776e6	+	1.12025e7i	0.212982	+	0.368896i
$47$	1.46906e7	−	1.23269e7i	0.439136	−	0.368479i	−0.396250	−	0.918143i	$-0.629689\pi$
$47$	1.46906e7	−	1.23269e7i	0.439136	−	0.368479i	0.835386	+	0.549664i	$0.185244\pi$
$48$	3.85805e7	+	1.93666e7i	1.04902	+	0.526583i
$49$	−3.28127e6	+	1.86090e7i	−0.0813129	+	0.461149i
$50$	−7.75589e7	−	6.50796e7i	−1.75496	−	1.47258i
$51$	−1.51884e7	−	3.51919e7i	−0.314373	−	0.728412i
$52$	−1.88266e7	−	6.85232e6i	−0.357073	−	0.129964i
$53$	−7.19089e7			−1.25182			−0.625909	−	0.779896i	$-0.715272\pi$
$53$	−7.19089e7			−1.25182			−0.625909	+	0.779896i	$0.715272\pi$
$54$	5.29796e7	+	4.44030e7i	0.847885	+	0.710624i
$55$	6.95807e7			1.02531
$56$	−4.32985e7	−	1.57594e7i	−0.588338	−	0.214137i
$57$	−8.15980e7	−	9.52148e6i	−1.02387	−	0.119472i
$58$	2.30615e7	+	1.93509e7i	0.267585	+	0.224530i
$59$	−2.81120e7	+	1.59431e8i	−0.302035	+	1.71292i	0.335109	+	0.942179i	$0.391227\pi$
$59$	−2.81120e7	+	1.59431e8i	−0.302035	+	1.71292i	−0.637144	+	0.770745i	$0.719884\pi$
$60$	−2.29774e6	−	3.93200e7i	−0.0228887	−	0.391681i
$61$	−4.30566e7	+	3.61288e7i	−0.398158	+	0.334094i	−0.819781	−	0.572677i	$-0.805905\pi$
$61$	−4.30566e7	+	3.61288e7i	−0.398158	+	0.334094i	0.421623	+	0.906771i	$0.361461\pi$
$62$	−5.42070e7	−	9.38892e7i	−0.465900	−	0.806962i
$63$	−7.61959e7	−	5.00727e7i	−0.609395	−	0.400469i
$64$	−4.61084e7	+	7.98621e7i	−0.343534	+	0.595019i
$65$	−7.43244e7	−	4.21515e8i	−0.516442	−	2.92889i
$66$	6.84883e7	+	7.25653e7i	0.444292	+	0.470740i
$67$	−2.09545e7	+	7.62680e6i	−0.127040	+	0.0462387i	−0.404758	−	0.914424i	$-0.632644\pi$
$67$	−2.09545e7	+	7.62680e6i	−0.127040	+	0.0462387i	0.277718	+	0.960663i	$0.410422\pi$
$68$	−2.94300e7	+	1.07117e7i	−0.166917	+	0.0607528i
$69$	−7.05400e7	+	1.67327e7i	−0.374640	+	0.0888677i
$70$	4.93127e7	+	2.79666e8i	0.245481	+	1.39219i
$71$	1.41806e8	−	2.45615e8i	0.662264	−	1.14707i	−0.317756	−	0.948173i	$-0.602929\pi$
$71$	1.41806e8	−	2.45615e8i	0.662264	−	1.14707i	0.980019	−	0.198902i	$-0.0637375\pi$
$72$	−1.34304e8	+	1.42464e8i	−0.588968	+	0.624752i
$73$	4.43683e7	+	7.68481e7i	0.182860	+	0.316723i	0.942853	−	0.333208i	$-0.108131\pi$
$73$	4.43683e7	+	7.68481e7i	0.182860	+	0.316723i	−0.759993	+	0.649931i	$0.774798\pi$
$74$	−3.93652e8	+	3.30314e8i	−1.52605	+	1.28051i
$75$	4.74025e8	−	3.11902e8i	1.72992	−	1.13826i
$76$	−1.16562e7	+	6.61056e7i	−0.0400771	+	0.227288i
$77$	−1.00819e8	−	8.45970e7i	−0.326838	−	0.274250i
$78$	3.66437e8	−	4.92409e8i	1.12092	−	1.50626i
$79$	2.02624e8	+	7.37491e7i	0.585287	+	0.213027i	0.617655	−	0.786449i	$-0.288083\pi$
$79$	2.02624e8	+	7.37491e7i	0.585287	+	0.213027i	−0.0323683	+	0.999476i	$0.510305\pi$
$80$	7.53552e8			2.05688
$81$	−3.23521e8	+	2.13141e8i	−0.835063	+	0.550154i
$82$	3.76133e8			0.918712
$83$	−3.51637e8	−	1.27986e8i	−0.813287	−	0.296012i	−0.0983059	−	0.995156i	$-0.531342\pi$
$83$	−3.51637e8	−	1.27986e8i	−0.813287	−	0.296012i	−0.714981	+	0.699144i	$0.753565\pi$
$84$	−4.44763e7	+	5.97661e7i	−0.0974702	+	0.130978i
$85$	−5.12547e8	−	4.30078e8i	−1.06500	−	0.893640i
$86$	−7.44469e7	+	4.22209e8i	−0.146759	+	0.832309i
$87$	−1.40947e8	+	9.27415e7i	−0.263767	+	0.173555i
$88$	−2.16495e8	+	1.81661e8i	−0.384837	+	0.322916i
$89$	1.28124e8	+	2.21917e8i	0.216458	+	0.374917i	0.953723	−	0.300688i	$-0.0972162\pi$
$89$	1.28124e8	+	2.21917e8i	0.216458	+	0.374917i	−0.737264	+	0.675604i	$0.763883\pi$
$90$	1.17426e9	+	2.77825e8i	1.88656	+	0.446355i
$91$	−4.04790e8	+	7.01116e8i	−0.618790	+	1.07178i
$92$	1.02864e7	+	5.83370e7i	0.0149699	+	0.0848983i
$93$	5.91203e8	−	1.40238e8i	0.819527	−	0.194398i
$94$	4.51106e8	−	1.64189e8i	0.595941	−	0.216905i
$95$	−1.34756e9	+	4.90472e8i	−1.69743	+	0.617814i
$96$	2.51289e8	+	2.66248e8i	0.301962	+	0.319938i
$97$	−6.14418e7	−	3.48454e8i	−0.0704678	−	0.399643i	−0.999556	−	0.0297854i	$-0.990518\pi$
$97$	−6.14418e7	−	3.48454e8i	−0.0704678	−	0.399643i	0.929088	−	0.369858i	$-0.120593\pi$
$98$	−2.36510e8	+	4.09647e8i	−0.259019	+	0.448634i
$99$	−4.99647e8	+	2.51174e8i	−0.522763	+	0.262794i
$100$	−2.31823e8	−	4.01529e8i	−0.231823	−	0.401529i
$101$	1.19124e9	−	9.99572e8i	1.13908	−	0.955802i	0.139672	−	0.990198i	$-0.455395\pi$
$101$	1.19124e9	−	9.99572e8i	1.13908	−	0.955802i	0.999408	+	0.0343960i	$0.0109507\pi$
$102$	−5.59743e7	−	9.57858e8i	−0.0512021	−	0.876194i
$103$	1.49062e8	−	8.45372e8i	0.130497	−	0.740082i	−0.847394	−	0.530965i	$-0.821830\pi$
$103$	1.49062e8	−	8.45372e8i	0.130497	−	0.740082i	0.977890	−	0.209118i	$-0.0670592\pi$
$104$	1.33174e9	+	1.11747e9i	1.11627	+	0.936665i
$105$	−1.58085e9	−	1.84466e8i	−1.26922	−	0.148103i
$106$	−1.69151e9	−	6.15660e8i	−1.30136	−	0.473658i
$107$	4.95122e8			0.365162			0.182581	−	0.983191i	$-0.441555\pi$
$107$	4.95122e8			0.365162			0.182581	+	0.983191i	$0.441555\pi$
$108$	1.58438e8	+	2.74056e8i	0.112060	+	0.193835i
$109$	2.48542e9			1.68648			0.843240	−	0.537537i	$-0.180645\pi$
$109$	2.48542e9			1.68648			0.843240	+	0.537537i	$0.180645\pi$
$110$	1.63675e9	+	5.95728e8i	1.06590	+	0.387955i
$111$	−1.14123e9	−	2.64427e9i	−0.713544	−	1.65330i
$112$	−1.09186e9	−	9.16176e8i	−0.655669	−	0.550171i
$113$	1.61029e8	−	9.13243e8i	0.0929078	−	0.526906i	−0.902461	−	0.430772i	$-0.858241\pi$
$113$	1.61029e8	−	9.13243e8i	0.0929078	−	0.526906i	0.995368	−	0.0961339i	$-0.0306477\pi$
$114$	−1.83791e9	−	9.22590e8i	−1.01918	−	0.511608i
$115$	−9.69443e8	+	8.13459e8i	−0.516871	+	0.433706i
$116$	6.89307e7	+	1.19391e8i	0.0353469	+	0.0612227i
$117$	2.05530e9	+	2.75853e9i	1.01400	+	1.36095i
$118$	−2.02627e9	+	3.50961e9i	−0.962119	+	1.66644i
$119$	2.19760e8	+	1.24632e9i	0.100459	+	0.569729i
$120$	−9.79576e8	+	3.27431e9i	−0.431244	+	1.44147i
$121$	1.45720e9	−	5.30378e8i	0.617996	−	0.224932i
$122$	−1.32214e9	+	4.81221e8i	−0.540331	+	0.196664i
$123$	−6.04205e8	+	2.01960e9i	−0.238019	+	0.795597i
$124$	−8.62113e7	−	4.88929e8i	−0.0327466	−	0.185715i
$125$	2.56097e9	−	4.43573e9i	0.938230	−	1.62506i
$126$	−1.36365e9	−	1.83023e9i	−0.481987	−	0.646900i
$127$	−1.37367e9	−	2.37926e9i	−0.468560	−	0.811569i	0.530794	−	0.847501i	$-0.321894\pi$
$127$	−1.37367e9	−	2.37926e9i	−0.468560	−	0.811569i	−0.999354	+	0.0359311i	$0.988560\pi$
$128$	−2.79186e9	+	2.34265e9i	−0.919281	+	0.771369i
$129$	−2.14741e9	−	1.07795e9i	−0.682751	−	0.342725i
$130$	1.86054e9	−	1.05516e10i	0.571339	−	3.24022i
$131$	−2.88837e9	−	2.42363e9i	−0.856904	−	0.719028i	0.104395	−	0.994536i	$-0.466709\pi$
$131$	−2.88837e9	−	2.42363e9i	−0.856904	−	0.719028i	−0.961299	+	0.275508i	$0.911154\pi$
$132$	1.81066e8	+	4.19535e8i	0.0519103	+	0.120278i
$133$	2.54886e9	+	9.27710e8i	0.706340	+	0.257087i
$134$	−5.58211e8			−0.149564
$135$	−3.37802e9	+	5.85874e9i	−0.875308	+	1.51811i
$136$	2.71760e9			0.681178
$137$	9.86186e8	+	3.58942e8i	0.239175	+	0.0870527i	0.458827	−	0.888526i	$-0.348270\pi$
$137$	9.86186e8	+	3.58942e8i	0.239175	+	0.0870527i	−0.219652	+	0.975578i	$0.570492\pi$
$138$	−1.80257e9	−	2.10338e8i	−0.423094	−	0.0493699i
$139$	1.75559e9	+	1.47312e9i	0.398894	+	0.334712i	0.820066	−	0.572269i	$-0.193937\pi$
$139$	1.75559e9	+	1.47312e9i	0.398894	+	0.334712i	−0.421172	+	0.906981i	$0.638381\pi$
$140$	−2.25823e8	+	1.28070e9i	−0.0496812	+	0.281756i
$141$	1.56956e8	+	2.68591e9i	0.0334420	+	0.572275i
$142$	5.43857e9	−	4.56350e9i	1.12250	−	0.941891i
$143$	2.48277e9	+	4.30029e9i	0.496506	+	0.859974i
$144$	−5.41113e9	+	2.72019e9i	−1.04871	+	0.527190i
$145$	−1.47261e9	+	2.55064e9i	−0.276651	+	0.479173i
$146$	3.85727e8	+	2.18757e9i	0.0702574	+	0.398449i
$147$	−1.81963e9	−	1.92795e9i	−0.321407	−	0.340540i
$148$	−2.21133e9	+	8.04859e8i	−0.378858	+	0.137893i
$149$	1.13285e9	−	4.12324e8i	0.188293	−	0.0685330i	−0.246153	−	0.969231i	$-0.579167\pi$
$149$	1.13285e9	−	4.12324e8i	0.188293	−	0.0685330i	0.434446	+	0.900698i	$0.356944\pi$
$150$	1.38209e10	−	3.27843e9i	2.22908	−	0.528756i
$151$	1.54323e9	+	8.75212e9i	0.241566	+	1.36999i	0.828334	+	0.560234i	$0.189289\pi$
$151$	1.54323e9	+	8.75212e9i	0.241566	+	1.36999i	−0.586769	+	0.809755i	$0.699600\pi$
$152$	2.91231e9	−	5.04427e9i	0.442529	−	0.766483i
$153$	5.23302e9	+	1.23812e9i	0.772042	+	0.182663i
$154$	−1.64727e9	−	2.85315e9i	−0.236005	−	0.408773i
$155$	8.12500e9	−	6.81768e9i	1.13066	−	0.948733i
$156$	2.34810e9	−	1.54502e9i	0.317436	−	0.208869i
$157$	−2.22634e9	+	1.26262e10i	−0.292444	+	1.65853i	0.384967	+	0.922930i	$0.374213\pi$
$157$	−2.22634e9	+	1.26262e10i	−0.292444	+	1.65853i	−0.677412	+	0.735604i	$0.736898\pi$
$158$	4.13491e9	+	3.46960e9i	0.527848	+	0.442917i
$159$	6.02289e9	−	8.09341e9i	0.747340	−	1.00426i
$160$	6.00536e9	+	2.18577e9i	0.724435	+	0.263673i
$161$	2.39368e9			0.280770
$162$	−9.43503e9	+	2.24383e9i	−1.07628	+	0.255961i
$163$	−1.22424e10			−1.35838			−0.679191	−	0.733961i	$-0.737669\pi$
$163$	−1.22424e10			−1.35838			−0.679191	+	0.733961i	$0.737669\pi$
$164$	1.61859e9	+	5.89118e8i	0.174719	+	0.0635924i
$165$	−5.82790e9	+	7.83138e9i	−0.612116	+	0.822546i
$166$	−7.17580e9	−	6.02121e9i	−0.733473	−	0.615457i
$167$	−1.87799e9	+	1.06506e10i	−0.186840	+	1.05962i	0.736729	+	0.676188i	$0.236369\pi$
$167$	−1.87799e9	+	1.06506e10i	−0.186840	+	1.05962i	−0.923569	+	0.383433i	$0.874742\pi$
$168$	5.40030e9	−	3.55332e9i	0.523029	−	0.344146i
$169$	1.52753e10	−	1.28175e10i	1.44045	−	1.20868i
$170$	−8.37447e9	−	1.45050e10i	−0.769019	−	1.33198i
$171$	7.90609e9	−	8.38644e9i	0.707097	−	0.750059i
$172$	−9.81647e8	+	1.70026e9i	−0.0855219	+	0.148128i
$173$	2.54117e9	+	1.44117e10i	0.215688	+	1.22323i	0.879708	+	0.475514i	$0.157738\pi$
$173$	2.54117e9	+	1.44117e10i	0.215688	+	1.22323i	−0.664020	+	0.747715i	$0.731151\pi$
$174$	−4.10953e9	+	9.74814e8i	−0.339876	+	0.0806214i
$175$	−1.76054e10	+	6.40784e9i	−1.41898	+	0.516465i
$176$	−8.21495e9	+	2.99000e9i	−0.645354	+	0.234890i
$177$	−1.55895e10	−	1.65175e10i	−1.19386	−	1.26493i
$178$	1.11388e9	+	6.31710e9i	0.0831661	+	0.471659i
$179$	−3.22583e9	+	5.58729e9i	−0.234856	+	0.406783i	−0.959231	−	0.282624i	$-0.908795\pi$
$179$	−3.22583e9	+	5.58729e9i	−0.234856	+	0.406783i	0.724375	+	0.689407i	$0.242129\pi$
$180$	4.61795e9	+	3.03472e9i	0.327886	+	0.215473i
$181$	−2.48315e9	−	4.30094e9i	−0.171969	−	0.297859i	0.767139	−	0.641480i	$-0.221679\pi$
$181$	−2.48315e9	−	4.30094e9i	−0.171969	−	0.297859i	−0.939108	+	0.343622i	$0.888346\pi$
$182$	−1.55246e10	+	1.30267e10i	−1.04882	+	0.880061i
$183$	−4.60022e8	−	7.87211e9i	−0.0303214	−	0.518873i
$184$	8.92574e8	−	5.06204e9i	0.0574069	−	0.325571i
$185$	−3.85121e10	−	3.23155e10i	−2.41727	−	2.02833i
$186$	1.51075e10	+	1.76286e9i	0.925520	+	0.107997i
$187$	7.29410e9	+	2.65484e9i	0.436199	+	0.158763i
$188$	2.19838e9			0.128349
$189$	1.20177e10	−	4.38196e9i	0.685083	−	0.249799i
$190$	−3.58979e10			−1.99838
$191$	8.56982e9	+	3.11916e9i	0.465931	+	0.169585i	0.564308	−	0.825564i	$-0.309143\pi$
$191$	8.56982e9	+	3.11916e9i	0.465931	+	0.169585i	−0.0983772	+	0.995149i	$0.531365\pi$
$192$	−5.12664e9	−	1.18786e10i	−0.272256	−	0.630825i
$193$	−2.71070e9	−	2.27455e9i	−0.140629	−	0.118001i	0.569760	−	0.821811i	$-0.307036\pi$
$193$	−2.71070e9	−	2.27455e9i	−0.140629	−	0.118001i	−0.710388	+	0.703810i	$0.751481\pi$
$194$	1.53805e9	−	8.72272e9i	0.0779584	−	0.442124i
$195$	5.36671e10	+	2.69396e10i	2.65798	+	1.33425i
$196$	−1.65937e9	+	1.39237e9i	−0.0803137	+	0.0673912i
$197$	−1.33926e10	−	2.31966e10i	−0.633529	−	1.09730i	−0.986825	−	0.161792i	$-0.948273\pi$
$197$	−1.33926e10	−	2.31966e10i	−0.633529	−	1.09730i	0.353296	−	0.935511i	$-0.385061\pi$
$198$	−1.39037e10	+	1.63055e9i	−0.642890	+	0.0753945i
$199$	−1.24215e10	+	2.15146e10i	−0.561481	+	0.972513i	0.435887	+	0.900001i	$0.356435\pi$
$199$	−1.24215e10	+	2.15146e10i	−0.561481	+	0.972513i	−0.997368	+	0.0725114i	$0.976899\pi$
$200$	6.98615e9	+	3.96204e10i	0.308747	+	1.75099i
$201$	8.96686e8	−	2.99725e9i	0.0387488	−	0.129521i
$202$	3.65797e10	−	1.33139e10i	1.54582	−	0.562632i
$203$	5.23482e9	−	1.90532e9i	0.216356	−	0.0787473i
$204$	1.25937e9	−	4.20956e9i	0.0509118	−	0.170177i
$205$	6.38994e9	+	3.62391e10i	0.252699	+	1.43313i
$206$	1.07442e10	−	1.86095e10i	0.415691	−	0.719998i
$207$	4.02496e9	−	9.34082e9i	0.152369	−	0.353605i
$208$	2.68882e10	+	4.65717e10i	0.996039	+	1.72519i
$209$	1.27445e10	−	1.06939e10i	0.462023	−	0.387684i
$210$	−3.56070e10	−	1.78739e10i	−1.26342	−	0.634209i
$211$	2.27293e9	−	1.28905e10i	0.0789434	−	0.447710i	−0.919557	−	0.392958i	$-0.871452\pi$
$211$	2.27293e9	−	1.28905e10i	0.0789434	−	0.447710i	0.998500	−	0.0547526i	$-0.0174370\pi$
$212$	−6.31470e9	−	5.29866e9i	−0.214705	−	0.180158i
$213$	1.57669e10	+	3.65324e10i	0.524853	+	1.21610i
$214$	1.16468e10	+	4.23908e9i	0.379615	+	0.138169i
$215$	−4.19431e10			−1.33871
$216$	−4.78550e9	−	2.70484e10i	−0.149584	−	0.845472i
$217$	−2.00617e10			−0.614184
$218$	5.84647e10	+	2.12794e10i	1.75323	+	0.638124i
$219$	−1.23655e10	−	1.44290e9i	−0.363256	−	0.0423875i
$220$	6.11025e9	+	5.12711e9i	0.175856	+	0.147561i
$221$	8.29141e9	−	4.70229e10i	0.233810	−	1.32600i
$222$	−4.20583e9	−	7.19721e10i	−0.116215	−	1.98873i
$223$	3.25233e10	−	2.72903e10i	0.880690	−	0.738987i	−0.0856305	−	0.996327i	$-0.527290\pi$
$223$	3.25233e10	−	2.72903e10i	0.880690	−	0.738987i	0.966321	+	0.257340i	$0.0828460\pi$
$224$	−6.04396e9	−	1.04684e10i	−0.160400	−	0.277822i
$225$	−4.59818e9	+	7.94760e10i	−0.119609	+	2.06735i
$226$	1.16068e10	−	2.01036e10i	0.295954	−	0.512607i
$227$	−2.90201e7	−	1.64581e8i	−0.000725407	−	0.00411399i	0.984443	−	0.175705i	$-0.0562204\pi$
$227$	−2.90201e7	−	1.64581e8i	−0.000725407	−	0.00411399i	−0.985168	+	0.171591i	$0.945109\pi$
$228$	−6.46396e9	−	6.84875e9i	−0.158413	−	0.167843i
$229$	1.15909e10	−	4.21875e9i	0.278521	−	0.101373i	−0.198983	−	0.980003i	$-0.563764\pi$
$229$	1.15909e10	−	4.21875e9i	0.278521	−	0.101373i	0.477504	+	0.878630i	$0.341542\pi$
$230$	−2.97688e10	+	1.08350e10i	−0.701433	+	0.255301i
$231$	1.79658e10	−	4.26163e9i	0.415138	−	0.0984740i
$232$	−2.07727e9	−	1.17808e10i	−0.0470758	−	0.266980i
$233$	8.71148e9	−	1.50887e10i	0.193638	−	0.335391i	−0.752815	−	0.658232i	$-0.771305\pi$
$233$	8.71148e9	−	1.50887e10i	0.193638	−	0.335391i	0.946453	+	0.322841i	$0.104638\pi$
$234$	2.47293e10	+	8.24857e10i	0.539188	+	1.79849i
$235$	2.34827e10	+	4.06732e10i	0.502275	+	0.869967i
$236$	−1.42164e10	+	1.19290e10i	−0.298323	+	0.250323i
$237$	−2.52718e10	+	1.66285e10i	−0.520317	+	0.342362i
$238$	−5.50118e9	+	3.11987e10i	−0.111137	+	0.630291i
$239$	1.99933e10	+	1.67764e10i	0.396363	+	0.332588i	0.819086	−	0.573671i	$-0.194481\pi$
$239$	1.99933e10	+	1.67764e10i	0.396363	+	0.332588i	−0.422723	+	0.906259i	$0.638926\pi$
$240$	−6.31155e10	+	8.48130e10i	−1.22796	+	1.65011i
$241$	−3.76154e10	−	1.36909e10i	−0.718271	−	0.261429i	−0.0430796	−	0.999072i	$-0.513717\pi$
$241$	−3.76154e10	−	1.36909e10i	−0.718271	−	0.261429i	−0.675192	+	0.737642i	$0.735939\pi$
$242$	3.88187e10			0.727565
$243$	3.10803e9	−	5.42647e10i	0.0571817	−	0.998364i
$244$	−6.44321e9			−0.116372
$245$	−4.34860e10	−	1.58276e10i	−0.771084	−	0.280652i
$246$	−3.15039e10	+	4.23342e10i	−0.548475	+	0.737026i
$247$	−7.83961e10	−	6.57821e10i	−1.34016	−	1.12453i
$248$	−7.48075e9	+	4.24254e10i	−0.125578	+	0.712187i
$249$	4.38571e10	−	2.88574e10i	0.723008	−	0.475729i
$250$	9.82190e10	−	8.24155e10i	1.59025	−	1.33438i
$251$	3.32489e10	+	5.75888e10i	0.528745	+	0.915812i	0.999438	+	0.0335157i	$0.0106704\pi$
$251$	3.32489e10	+	5.75888e10i	0.528745	+	0.915812i	−0.470694	+	0.882297i	$0.655996\pi$
$252$	−3.00152e9	−	1.00117e10i	−0.0468855	−	0.156389i
$253$	7.34081e9	−	1.27147e10i	0.112642	−	0.195102i
$254$	−1.19423e10	−	6.77284e10i	−0.180027	−	1.02098i
$255$	9.13353e10	−	2.16655e10i	1.35272	−	0.320876i
$256$	−4.13623e10	+	1.50547e10i	−0.601901	+	0.219074i
$257$	−6.87520e10	+	2.50237e10i	−0.983074	+	0.357810i	−0.783035	−	0.621978i	$-0.786329\pi$
$257$	−6.87520e10	+	2.50237e10i	−0.983074	+	0.357810i	−0.200040	+	0.979788i	$0.564107\pi$
$258$	−4.12846e10	−	4.37422e10i	−0.580095	−	0.614627i
$259$	1.65125e10	+	9.36468e10i	0.228015	+	1.29314i
$260$	2.45328e10	−	4.24921e10i	0.332941	−	0.576671i
$261$	1.36723e9	−	2.36315e10i	0.0182372	−	0.315217i
$262$	−4.71928e10	−	8.17404e10i	−0.618757	−	1.07172i
$263$	−1.14309e10	+	9.59170e9i	−0.147327	+	0.123622i	−0.713472	−	0.700684i	$-0.752878\pi$
$263$	−1.14309e10	+	9.59170e9i	−0.147327	+	0.123622i	0.566146	+	0.824305i	$0.308434\pi$
$264$	−2.31306e9	−	3.95822e10i	−0.0293069	−	0.501513i
$265$	3.05805e10	−	1.73430e11i	0.380923	−	2.16032i
$266$	5.20142e10	+	4.36451e10i	0.637022	+	0.534525i
$267$	−3.57082e10	−	4.16671e9i	−0.429999	−	0.0501756i
$268$	−2.40211e9	−	8.74297e8i	−0.0284437	−	0.0103527i
$269$	9.80805e10			1.14208			0.571041	−	0.820921i	$-0.306540\pi$
$269$	9.80805e10			1.14208			0.571041	+	0.820921i	$0.306540\pi$
$270$	−1.29622e11	+	1.08894e11i	−1.48437	+	1.24700i
$271$	−8.46393e10			−0.953258			−0.476629	−	0.879105i	$-0.658141\pi$
$271$	−8.46393e10			−0.953258			−0.476629	+	0.879105i	$0.658141\pi$
$272$	7.89944e10	+	2.87516e10i	0.875056	+	0.318494i
$273$	−4.50072e10	−	1.04283e11i	−0.490399	−	1.13627i
$274$	2.01249e10	+	1.68868e10i	0.215703	+	0.180996i
$275$	−1.99544e10	+	1.13167e11i	−0.210398	+	1.19322i
$276$	−7.42745e9	−	3.72841e9i	−0.0770458	−	0.0386752i
$277$	−8.94392e10	+	7.50484e10i	−0.912786	+	0.765918i	−0.972647	−	0.232289i	$-0.925379\pi$
$277$	−8.94392e10	+	7.50484e10i	−0.912786	+	0.765918i	0.0598612	+	0.998207i	$0.480934\pi$
$278$	2.86845e10	+	4.96830e10i	0.288035	+	0.498891i
$279$	−3.37336e10	+	7.82864e10i	−0.333307	+	0.773512i
$280$	5.64220e10	−	9.77258e10i	0.548577	−	0.950163i
$281$	−4.97236e7	−	2.81996e8i	−0.000475755	−	0.00269814i	0.984569	−	0.174997i	$-0.0559916\pi$
$281$	−4.97236e7	−	2.81996e8i	−0.000475755	−	0.00269814i	−0.985045	+	0.172299i	$0.944880\pi$
$282$	−1.93038e10	+	6.45245e10i	−0.181770	+	0.607580i
$283$	−4.87407e10	+	1.77402e10i	−0.451703	+	0.164407i	−0.557846	−	0.829944i	$-0.688372\pi$
$283$	−4.87407e10	+	1.77402e10i	−0.451703	+	0.164407i	0.106143	+	0.994351i	$0.466150\pi$
$284$	3.05510e10	−	1.11197e10i	0.278672	−	0.101428i
$285$	5.76650e10	−	1.92750e11i	0.517738	−	1.73058i
$286$	2.15846e10	+	1.22413e11i	0.190764	+	1.08188i
$287$	3.48012e10	−	6.02775e10i	0.302779	−	0.524429i
$288$	−5.10137e10	+	5.98260e9i	−0.436939	+	0.0512418i
$289$	2.19735e10	+	3.80591e10i	0.185293	+	0.320936i
$290$	−5.64780e10	+	4.73906e10i	−0.468908	+	0.393461i
$291$	4.43650e10	+	2.22702e10i	0.362678	+	0.182056i
$292$	−1.76640e9	+	1.00177e10i	−0.0142189	+	0.0806394i
$293$	−1.10567e10	−	9.27767e9i	−0.0876438	−	0.0735419i	0.597913	−	0.801561i	$-0.295997\pi$
$293$	−1.10567e10	−	9.27767e9i	−0.0876438	−	0.0735419i	−0.685557	+	0.728019i	$0.740441\pi$
$294$	−2.62967e10	−	6.09303e10i	−0.205276	−	0.475631i
$295$	−3.72562e11	−	1.35601e11i	−2.86417	−	1.04247i
$296$	2.04197e11			1.54609
$297$	1.35793e10	−	7.72734e10i	0.101268	−	0.576270i
$298$	3.01782e10			0.221677
$299$	−8.48657e10	−	3.08886e10i	−0.614061	−	0.223500i
$300$	6.46094e10	+	7.53912e9i	0.460522	+	0.0537372i
$301$	6.07733e10	+	5.09949e10i	0.426740	+	0.358078i
$302$	−3.86313e10	+	2.19089e11i	−0.267244	+	1.51562i
$303$	1.27274e10	+	2.17797e11i	0.0867457	+	1.48443i
$304$	1.38021e11	−	1.15814e11i	0.926863	−	0.777730i
$305$	−6.88252e10	−	1.19209e11i	−0.455405	−	0.788785i
$306$	1.12496e11	+	7.39277e10i	0.733485	+	0.482015i
$307$	−5.27509e10	+	9.13673e10i	−0.338928	+	0.587041i	−0.984231	−	0.176886i	$-0.943398\pi$
$307$	−5.27509e10	+	9.13673e10i	−0.338928	+	0.587041i	0.645303	+	0.763926i	$0.276731\pi$
$308$	−2.61983e9	−	1.48578e10i	−0.0165881	−	0.0940756i
$309$	8.26623e10	+	8.75831e10i	0.515816	+	0.546521i
$310$	2.49495e11	−	9.08089e10i	1.53439	−	0.558471i
$311$	1.91694e11	−	6.97708e10i	1.16195	−	0.422914i	0.312154	−	0.950031i	$-0.398949\pi$
$311$	1.91694e11	−	6.97708e10i	1.16195	−	0.422914i	0.849793	+	0.527117i	$0.176727\pi$
$312$	−2.37315e11	+	5.62931e10i	−1.41785	+	0.336325i
$313$	4.44057e9	+	2.51837e10i	0.0261511	+	0.148310i	0.995087	−	0.0990001i	$-0.0315644\pi$
$313$	4.44057e9	+	2.51837e10i	0.0261511	+	0.148310i	−0.968936	+	0.247310i	$0.920453\pi$
$314$	−1.60472e11	+	2.77945e11i	−0.931570	+	1.61353i
$315$	1.53169e11	−	1.62476e11i	0.876546	−	0.929803i
$316$	1.23592e10	+	2.14068e10i	0.0697267	+	0.120770i
$317$	1.86671e11	−	1.56636e11i	1.03827	−	0.871213i	0.0464590	−	0.998920i	$-0.485206\pi$
$317$	1.86671e11	−	1.56636e11i	1.03827	−	0.871213i	0.991812	+	0.127707i	$0.0407619\pi$
$318$	2.10970e11	−	1.38815e11i	1.15691	−	0.761229i
$319$	5.93327e9	−	3.36492e10i	0.0320801	−	0.181935i
$320$	−1.73004e11	−	1.45167e11i	−0.922318	−	0.773917i
$321$	−4.14701e10	+	5.57265e10i	−0.218003	+	0.292947i
$322$	5.63066e10	+	2.04939e10i	0.291883	+	0.106237i
$323$	−1.59978e11			−0.817802
$324$	−4.41155e10	−	5.12185e9i	−0.222402	−	0.0258211i
$325$	7.06871e11			3.51451
$326$	−2.87978e11	−	1.04815e11i	−1.41215	−	0.513980i
$327$	−2.08172e11	+	2.79737e11i	−1.00684	+	1.35296i
$328$	−1.14495e11	−	9.60725e10i	−0.546202	−	0.458318i
$329$	1.54257e10	−	8.74837e10i	0.0725879	−	0.411666i
$330$	−2.04139e11	+	1.34321e11i	−0.947576	+	0.623493i
$331$	−2.94855e9	+	2.47413e9i	−0.0135015	+	0.0113291i	−0.649513	−	0.760350i	$-0.725027\pi$
$331$	−2.94855e9	+	2.47413e9i	−0.0135015	+	0.0113291i	0.636012	+	0.771679i	$0.280583\pi$
$332$	−2.14484e10	−	3.71498e10i	−0.0968889	−	0.167817i
$333$	3.93202e11	+	9.30303e10i	1.75233	+	0.414596i
$334$	−1.35363e11	+	2.34456e11i	−0.595170	+	1.03086i
$335$	−9.48315e9	−	5.37816e10i	−0.0411387	−	0.233309i
$336$	1.94567e11	−	4.61530e10i	0.832805	−	0.197548i
$337$	−2.42231e11	+	8.81650e10i	−1.02305	+	0.372359i	−0.798430	−	0.602088i	$-0.794336\pi$
$337$	−2.42231e11	+	8.81650e10i	−1.02305	+	0.372359i	−0.224618	+	0.974447i	$0.572113\pi$
$338$	4.69059e11	−	1.70724e11i	1.95480	−	0.711489i
$339$	8.92990e10	+	9.46148e10i	0.367238	+	0.389099i
$340$	−1.33188e10	−	7.55349e10i	−0.0540520	−	0.306544i
$341$	−6.15241e10	+	1.06563e11i	−0.246406	+	0.426787i
$342$	2.57777e11	−	1.29585e11i	1.01889	−	0.512198i
$343$	1.37229e11	+	2.37688e11i	0.535331	+	0.927220i
$344$	1.30503e11	−	1.09505e11i	0.502467	−	0.421619i
$345$	−1.03577e10	−	1.77245e11i	−0.0393618	−	0.673578i
$346$	−6.36123e10	+	3.60763e11i	−0.238616	+	1.35326i
$347$	−3.08455e11	−	2.58824e11i	−1.14211	−	0.958346i	−0.142606	−	0.989779i	$-0.545548\pi$
$347$	−3.08455e11	−	2.58824e11i	−1.14211	−	0.958346i	−0.999506	+	0.0314335i	$0.989993\pi$
$348$	−1.92111e10	−	2.24169e9i	−0.0702174	−	0.00819351i
$349$	−4.00876e11	−	1.45907e11i	−1.44643	−	0.526456i	−0.504835	−	0.863216i	$-0.668447\pi$
$349$	−4.00876e11	−	1.45907e11i	−1.44643	−	0.526456i	−0.941590	+	0.336760i	$0.890669\pi$
$350$	−4.68994e11			−1.67056
$351$	−4.82621e11	+	2.79360e8i	−1.69717	+	0.000982385i
$352$	−7.41412e10			−0.257405
$353$	−7.44330e10	−	2.70914e10i	−0.255140	−	0.0928635i	0.211284	−	0.977425i	$-0.432236\pi$
$353$	−7.44330e10	−	2.70914e10i	−0.255140	−	0.0928635i	−0.466424	+	0.884561i	$0.654458\pi$
$354$	−2.25294e11	−	5.22014e11i	−0.762493	−	1.76672i
$355$	5.32070e11	+	4.46460e11i	1.77804	+	1.49195i
$356$	−5.10088e9	+	2.89286e10i	−0.0168314	+	0.0954557i
$357$	−1.58681e11	−	7.96543e10i	−0.517033	−	0.259539i
$358$	−1.23718e11	+	1.03812e11i	−0.398069	+	0.334020i
$359$	1.23274e11	+	2.13518e11i	0.391695	+	0.678436i	0.992673	−	0.120830i	$-0.0385555\pi$
$359$	1.23274e11	+	2.13518e11i	0.391695	+	0.678436i	−0.600978	+	0.799265i	$0.705222\pi$
$360$	−2.86480e11	−	3.84500e11i	−0.898946	−	1.20652i
$361$	−1.00960e10	+	1.74867e10i	−0.0312871	+	0.0541909i
$362$	−2.15879e10	−	1.22431e11i	−0.0660727	−	0.374717i
$363$	−6.23568e10	+	2.08432e11i	−0.188497	+	0.630065i
$364$	−8.72090e10	+	3.17415e10i	−0.260379	+	0.0947701i
$365$	−2.04211e11	+	7.43268e10i	−0.602229	+	0.219194i
$366$	5.65774e10	−	1.89114e11i	0.164808	−	0.550883i
$367$	1.03981e11	+	5.89708e11i	0.299198	+	1.69684i	0.649633	+	0.760248i	$0.274923\pi$
$367$	1.03981e11	+	5.89708e11i	0.299198	+	1.69684i	−0.350435	+	0.936587i	$0.613966\pi$
$368$	7.95002e10	−	1.37698e11i	0.225971	−	0.391394i
$369$	−1.76702e11	−	2.37160e11i	−0.496160	−	0.665922i
$370$	−6.29246e11	−	1.08989e12i	−1.74547	−	3.02324i
$371$	−2.55168e11	+	2.14111e11i	−0.699268	+	0.586755i
$372$	6.22502e10	+	3.12482e10i	0.168538	+	0.0846022i
$373$	−5.72314e9	+	3.24575e10i	−0.0153089	+	0.0868212i	−0.991505	−	0.130069i	$-0.958480\pi$
$373$	−5.72314e9	+	3.24575e10i	−0.0153089	+	0.0868212i	0.976196	+	0.216890i	$0.0695913\pi$
$374$	1.48849e11	+	1.24900e11i	0.393392	+	0.330095i
$375$	2.84745e11	+	6.59764e11i	0.743560	+	1.72285i
$376$	−1.79254e11	−	6.52431e10i	−0.462512	−	0.168341i
$377$	−2.10182e11			−0.535870
$378$	3.20209e11	−	1.85349e8i	0.806716	−	0.000466958i
$379$	3.99459e9			0.00994478			0.00497239	−	0.999988i	$-0.498417\pi$
$379$	3.99459e9			0.00994478			0.00497239	+	0.999988i	$0.498417\pi$
$380$	−1.54477e11	−	5.62251e10i	−0.380048	−	0.138326i
$381$	3.82843e11	+	4.46731e10i	0.930804	+	0.108613i
$382$	1.74883e11	+	1.46744e11i	0.420206	+	0.352595i
$383$	1.05935e11	−	6.00785e11i	0.251561	−	1.42667i	−0.553188	−	0.833057i	$-0.686589\pi$
$383$	1.05935e11	−	6.00785e11i	0.251561	−	1.42667i	0.804748	−	0.593616i	$-0.202300\pi$
$384$	−2.98286e10	−	5.10440e11i	−0.0700071	−	1.19799i
$385$	2.46907e11	−	2.07179e11i	0.572743	−	0.480588i
$386$	−4.42899e10	−	7.67124e10i	−0.101546	−	0.175883i
$387$	3.01186e11	−	1.51407e11i	0.682552	−	0.343120i
$388$	2.02805e10	−	3.51269e10i	0.0454294	−	0.0786860i
$389$	−6.34824e10	−	3.60026e11i	−0.140566	−	0.797189i	−0.970821	−	0.239805i	$-0.922916\pi$
$389$	−6.34824e10	−	3.60026e11i	−0.140566	−	0.797189i	0.830255	−	0.557384i	$-0.188195\pi$
$390$	1.03176e12	+	1.09318e12i	2.25834	+	2.39277i
$391$	−1.32663e11	+	4.82855e10i	−0.287049	+	0.104477i
$392$	1.76626e11	−	6.42866e10i	0.377805	−	0.137510i
$393$	5.14704e11	−	1.22092e11i	1.08841	−	0.258179i
$394$	−1.16432e11	−	6.60318e11i	−0.243410	−	1.38045i
$395$	−2.64038e11	+	4.57327e11i	−0.545732	+	0.945236i
$396$	−6.23846e10	−	1.47600e10i	−0.127482	−	0.0301619i
$397$	−7.97135e10	−	1.38068e11i	−0.161055	−	0.278956i	0.774192	−	0.632951i	$-0.218156\pi$
$397$	−7.97135e10	−	1.38068e11i	−0.161055	−	0.278956i	−0.935247	+	0.353995i	$0.884823\pi$
$398$	−4.76392e11	+	3.99741e11i	−0.951680	+	0.798554i
$399$	−3.17901e11	+	2.09174e11i	−0.627933	+	0.413172i
$400$	−2.16104e11	+	1.22559e12i	−0.422078	+	2.39372i
$401$	7.03795e11	+	5.90554e11i	1.35924	+	1.14054i	0.976216	+	0.216801i	$0.0695621\pi$
$401$	7.03795e11	+	5.90554e11i	1.35924	+	1.14054i	0.383025	+	0.923738i	$0.374882\pi$
$402$	4.67542e10	−	6.28271e10i	0.0892902	−	0.119986i
$403$	7.11268e11	+	2.58880e11i	1.34326	+	0.488907i
$404$	1.78264e11			0.332925
$405$	−3.76472e11	−	8.70912e11i	−0.695321	−	1.60852i
$406$	1.39452e11			0.254716
$407$	5.48069e11	+	1.99481e11i	0.990057	+	0.360351i
$408$	−2.27619e11	+	3.05869e11i	−0.406666	+	0.546467i
$409$	−6.65433e11	−	5.58365e11i	−1.17584	−	0.986650i	−0.999998	−	0.00223273i	$-0.999289\pi$
$409$	−6.65433e11	−	5.58365e11i	−1.17584	−	0.986650i	−0.175847	−	0.984418i	$-0.556266\pi$
$410$	−1.59957e11	+	9.07162e11i	−0.279561	+	1.58547i
$411$	−1.23000e11	+	8.09321e10i	−0.212626	+	0.139905i
$412$	7.53818e10	−	6.32528e10i	0.128893	−	0.108154i
$413$	3.74956e11	+	6.49443e11i	0.634169	+	1.09841i
$414$	1.74652e11	−	1.85264e11i	0.292195	−	0.309948i
$415$	4.58217e11	−	7.93654e11i	0.758323	−	1.31345i
$416$	7.91957e10	+	4.49141e11i	0.129653	+	0.735297i
$417$	−3.12844e11	+	7.42092e10i	−0.506659	+	0.120184i
$418$	3.91346e11	−	1.42438e11i	0.627001	−	0.228210i
$419$	1.03141e12	−	3.75403e11i	1.63481	−	0.595024i	0.648693	−	0.761051i	$-0.275316\pi$
$419$	1.03141e12	−	3.75403e11i	1.63481	−	0.595024i	0.986121	+	0.166027i	$0.0530939\pi$
$420$	−1.25230e11	−	1.32685e11i	−0.196376	−	0.208065i
$421$	−2.18580e10	−	1.23963e11i	−0.0339110	−	0.192319i	0.963146	−	0.268978i	$-0.0866858\pi$
$421$	−2.18580e10	−	1.23963e11i	−0.0339110	−	0.192319i	−0.997057	+	0.0766590i	$0.975575\pi$
$422$	1.63830e11	−	2.83762e11i	0.251471	−	0.435561i
$423$	−3.15448e11	−	2.07299e11i	−0.479066	−	0.314822i
$424$	3.57643e11	+	6.19455e11i	0.537407	+	0.930816i
$425$	8.46473e11	−	7.10275e11i	1.25853	−	1.05603i
$426$	5.81064e10	+	9.94343e11i	0.0854832	+	1.46283i
$427$	−4.52112e10	+	2.56405e11i	−0.0658143	+	0.373252i
$428$	4.34793e10	+	3.64835e10i	0.0626305	+	0.0525532i
$429$	−6.91952e11	−	8.07423e10i	−0.986321	−	0.115091i
$430$	−9.86628e11	−	3.59103e11i	−1.39170	−	0.506537i
$431$	−6.62424e11			−0.924673			−0.462336	−	0.886705i	$-0.652989\pi$
$431$	−6.62424e11			−0.924673			−0.462336	+	0.886705i	$0.652989\pi$
$432$	1.47062e11	−	8.36863e11i	0.203153	−	1.15605i
$433$	−8.92082e11			−1.21958			−0.609788	−	0.792564i	$-0.708746\pi$
$433$	−8.92082e11			−1.21958			−0.609788	+	0.792564i	$0.708746\pi$
$434$	−4.71912e11	−	1.71762e11i	−0.638494	−	0.232393i
$435$	−1.63735e11	−	3.79378e11i	−0.219250	−	0.508008i
$436$	2.18258e11	+	1.83140e11i	0.289255	+	0.242714i
$437$	−5.25434e10	+	2.97988e11i	−0.0689210	+	0.390870i
$438$	−2.78520e11	−	1.39811e11i	−0.361595	−	0.181513i
$439$	−6.38548e10	+	5.35806e10i	−0.0820547	+	0.0688521i	−0.682892	−	0.730519i	$-0.739278\pi$
$439$	−6.38548e10	+	5.35806e10i	−0.0820547	+	0.0688521i	0.600838	+	0.799371i	$0.294834\pi$
$440$	−3.46064e11	−	5.99400e11i	−0.440169	−	0.762394i
$441$	3.69400e11	−	4.33212e10i	0.465075	−	0.0545414i
$442$	5.97634e11	−	1.03513e12i	0.744792	−	1.29002i
$443$	−9.04993e10	−	5.13247e11i	−0.111642	−	0.633155i	−0.988358	−	0.152146i	$-0.951382\pi$
$443$	−9.04993e10	−	5.13247e11i	−0.111642	−	0.633155i	0.876716	−	0.481009i	$-0.159729\pi$
$444$	9.46275e10	−	3.16300e11i	0.115556	−	0.386257i
$445$	−5.89707e11	+	2.14636e11i	−0.712880	+	0.259467i
$446$	9.98698e11	−	3.63496e11i	1.19516	−	0.435004i
$447$	−4.84770e10	+	1.62038e11i	−0.0574318	+	0.191970i
$448$	7.41772e10	+	4.20680e11i	0.0870000	+	0.493401i
$449$	−3.97860e11	+	6.89114e11i	−0.461979	+	0.800171i	−0.999060	−	0.0433600i	$-0.986194\pi$
$449$	−3.97860e11	+	6.89114e11i	−0.461979	+	0.800171i	0.537081	+	0.843531i	$0.319527\pi$
$450$	−7.88611e11	+	1.83015e12i	−0.906581	+	2.10392i
$451$	−2.13453e11	−	3.69711e11i	−0.242945	−	0.420793i
$452$	8.14339e10	−	6.83311e10i	0.0917661	−	0.0770009i
$453$	−1.11432e12	−	5.59361e11i	−1.24327	−	0.624095i
$454$	7.26450e8	−	4.11990e9i	0.000802517	−	0.00455130i
$455$	−1.51882e12	−	1.27444e12i	−1.66132	−	1.39401i
$456$	3.23810e11	+	7.50278e11i	0.350710	+	0.812607i
$457$	4.07664e11	+	1.48378e11i	0.437200	+	0.159128i	0.551237	−	0.834349i	$-0.314156\pi$
$457$	4.07664e11	+	1.48378e11i	0.437200	+	0.159128i	−0.114037	+	0.993476i	$0.536378\pi$
$458$	3.08773e11			0.327902
$459$	−5.77655e11	+	4.85280e11i	−0.607451	+	0.510312i
$460$	−1.45072e11			−0.151069
$461$	2.38231e11	+	8.67090e10i	0.245666	+	0.0894150i	0.461918	−	0.886922i	$-0.347161\pi$
$461$	2.38231e11	+	8.67090e10i	0.245666	+	0.0894150i	−0.216253	+	0.976337i	$0.569384\pi$
$462$	4.59096e11	+	5.35708e10i	0.468829	+	0.0547066i
$463$	9.55851e11	+	8.02055e11i	0.966665	+	0.811128i	0.982024	−	0.188754i	$-0.0604449\pi$
$463$	9.55851e11	+	8.02055e11i	0.966665	+	0.811128i	−0.0153596	+	0.999882i	$0.504889\pi$
$464$	6.42567e10	−	3.64418e11i	0.0643557	−	0.364979i
$465$	8.68085e10	+	1.48551e12i	0.0861041	+	1.47345i
$466$	3.34105e11	−	2.80347e11i	0.328206	−	0.275397i
$467$	5.86250e11	+	1.01542e12i	0.570371	+	0.987911i	0.996528	+	0.0832617i	$0.0265337\pi$
$467$	5.86250e11	+	1.01542e12i	0.570371	+	0.987911i	−0.426157	+	0.904649i	$0.640133\pi$
$468$	−2.27772e10	+	3.93687e11i	−0.0219480	+	0.379354i
$469$	−5.16477e10	+	8.94564e10i	−0.0492916	+	0.0853756i
$470$	2.04153e11	+	1.15781e12i	0.192981	+	1.09445i
$471$	−1.23462e12	−	1.30811e12i	−1.15595	−	1.22476i
$472$	1.51323e12	−	5.50769e11i	1.40335	−	0.510776i
$473$	4.57249e11	−	1.66425e11i	0.420027	−	0.152877i
$474$	−7.36836e11	+	1.74783e11i	−0.670453	+	0.159037i
$475$	−4.11255e11	−	2.33234e12i	−0.370672	−	2.10219i
$476$	−7.25379e10	+	1.25639e11i	−0.0647640	+	0.112174i
$477$	4.06459e11	+	1.35576e12i	0.359488	+	1.19909i
$478$	3.26668e11	+	5.65806e11i	0.286208	+	0.495727i
$479$	−6.45073e11	+	5.41280e11i	−0.559885	+	0.469799i	−0.878272	−	0.478162i	$-0.841303\pi$
$479$	−6.45073e11	+	5.41280e11i	−0.559885	+	0.469799i	0.318387	+	0.947961i	$0.396859\pi$
$480$	−7.49004e11	+	4.92835e11i	−0.644019	+	0.423756i
$481$	6.23005e11	−	3.53324e12i	0.530687	−	3.00968i
$482$	−7.67610e11	−	6.44101e11i	−0.647782	−	0.543554i
$483$	−2.00488e11	+	2.69411e11i	−0.167621	+	0.225244i
$484$	1.67046e11	+	6.07998e10i	0.138367	+	0.0503614i
$485$	8.66533e11			0.711127
$486$	5.37707e11	−	1.24986e12i	0.437202	−	1.01624i
$487$	1.83919e11			0.148166			0.0740828	−	0.997252i	$-0.476397\pi$
$487$	1.83919e11			0.148166			0.0740828	+	0.997252i	$0.476397\pi$
$488$	5.25374e11	+	1.91221e11i	0.419353	+	0.152632i
$489$	1.02539e12	−	1.37789e12i	0.810959	−	1.08975i
$490$	−8.87410e11	−	7.44626e11i	−0.695412	−	0.583520i
$491$	−2.81770e11	+	1.59800e12i	−0.218790	+	1.24082i	0.655417	+	0.755267i	$0.272493\pi$
$491$	−2.81770e11	+	1.59800e12i	−0.218790	+	1.24082i	−0.874207	+	0.485553i	$0.838618\pi$
$492$	−2.01875e11	+	1.32831e11i	−0.155324	+	0.102201i
$493$	−2.51692e11	+	2.11194e11i	−0.191892	+	0.161017i
$494$	−1.28091e12	−	2.21860e12i	−0.967713	−	1.67613i
$495$	−3.93300e11	−	1.31187e12i	−0.294442	−	0.982127i
$496$	−6.66299e11	+	1.15406e12i	−0.494313	+	0.856175i
$497$	−2.28131e11	−	1.29379e12i	−0.167718	−	0.951176i
$498$	1.27872e12	−	3.03323e11i	0.931629	−	0.220990i
$499$	−1.43722e12	+	5.23106e11i	−1.03770	+	0.377691i	−0.804007	−	0.594619i	$-0.797303\pi$
$499$	−1.43722e12	+	5.23106e11i	−1.03770	+	0.377691i	−0.233691	+	0.972311i	$0.575081\pi$
$500$	5.51742e11	−	2.00818e11i	0.394795	−	0.143694i
$501$	−1.04144e12	−	1.10344e12i	−0.738524	−	0.782487i
$502$	2.89058e11	+	1.63933e12i	0.203151	+	1.15213i
$503$	−2.63005e11	+	4.55537e11i	−0.183192	+	0.317298i	−0.942966	−	0.332889i	$-0.891976\pi$
$503$	−2.63005e11	+	4.55537e11i	−0.183192	+	0.317298i	0.759774	+	0.650188i	$0.225310\pi$
$504$	−5.23844e10	+	9.05425e11i	−0.0361630	+	0.625051i
$505$	1.90418e12	+	3.29814e12i	1.30286	+	2.25662i
$506$	2.81537e11	−	2.36238e11i	0.190923	−	0.160203i
$507$	1.63203e11	+	2.79280e12i	0.109696	+	1.87717i
$508$	5.46888e10	−	3.10156e11i	0.0364344	−	0.206630i
$509$	−2.03562e12	−	1.70809e12i	−1.34421	−	1.12792i	−0.980524	−	0.196402i	$-0.937074\pi$
$509$	−2.03562e12	−	1.70809e12i	−1.34421	−	1.12792i	−0.363684	−	0.931522i	$-0.618481\pi$
$510$	2.33398e12	+	2.72346e11i	1.52767	+	0.178261i
$511$	3.86258e11	+	1.40587e11i	0.250602	+	0.0912115i
$512$	7.64130e11			0.491420
$513$	2.81709e11	+	1.59226e12i	0.179586	+	1.01505i
$514$	−1.83150e12			−1.15737
$515$	1.97548e12	+	7.19017e11i	1.23749	+	0.450409i
$516$	−1.09146e11	−	2.52895e11i	−0.0677773	−	0.157042i
$517$	−4.17385e11	−	3.50228e11i	−0.256939	−	0.215597i
$518$	−4.13351e11	+	2.34423e12i	−0.252252	+	1.43059i
$519$	−1.83489e12	−	9.21074e11i	−1.11009	−	0.557239i
$520$	−3.26146e12	+	2.73669e12i	−1.95613	+	1.64139i
$521$	9.82672e11	+	1.70204e12i	0.584304	+	1.01204i	0.994962	+	0.100255i	$0.0319657\pi$
$521$	9.82672e11	+	1.70204e12i	0.584304	+	1.01204i	−0.410658	+	0.911790i	$0.634701\pi$
$522$	2.34487e11	−	5.44179e11i	0.138230	−	0.320793i
$523$	8.50867e11	−	1.47374e12i	0.497284	−	0.861320i	−0.502712	−	0.864454i	$-0.667664\pi$
$523$	8.50867e11	−	1.47374e12i	0.497284	−	0.861320i	0.999995	+	0.00313390i	$0.000997552\pi$
$524$	−7.50560e10	−	4.25664e11i	−0.0434905	−	0.246647i
$525$	7.53373e11	−	2.51821e12i	0.432806	−	1.44669i
$526$	−3.51011e11	+	1.27758e11i	−0.199933	+	0.0727698i
$527$	1.11187e12	−	4.04686e11i	0.627920	−	0.228544i
$528$	3.51535e11	−	1.17503e12i	0.196841	−	0.657958i
$529$	−2.66398e11	−	1.51082e12i	−0.147904	−	0.838807i
$530$	2.20420e12	−	3.81779e12i	1.21342	−	2.10170i
$531$	3.16480e12	−	3.71150e11i	1.72751	−	0.202593i
$532$	1.55470e11	+	2.69282e11i	0.0841482	+	0.145749i
$533$	−2.01168e12	+	1.68800e12i	−1.07966	+	0.905940i
$534$	−8.04291e11	−	4.03736e11i	−0.428033	−	0.214863i
$535$	−2.10559e11	+	1.19414e12i	−0.111117	+	0.630178i
$536$	1.69919e11	+	1.42579e11i	0.0889202	+	0.0746129i
$537$	−3.58669e11	−	8.31046e11i	−0.186127	−	0.431262i
$538$	2.30715e12	+	8.39734e11i	1.18729	+	0.432137i
$539$	5.36870e11			0.273981
$540$	−7.28348e11	+	2.65575e11i	−0.368610	+	0.134405i
$541$	2.76138e12			1.38592			0.692960	−	0.720976i	$-0.256306\pi$
$541$	2.76138e12			1.38592			0.692960	+	0.720976i	$0.256306\pi$
$542$	−1.99097e12	−	7.24655e11i	−0.990988	−	0.360690i
$543$	6.92057e11	+	8.07545e10i	0.341620	+	0.0398628i
$544$	5.46141e11	+	4.58266e11i	0.267368	+	0.224348i
$545$	−1.05697e12	+	5.99437e12i	−0.513190	+	2.91044i
$546$	−1.65867e11	−	2.83839e12i	−0.0798717	−	1.36680i
$547$	−7.75592e11	+	6.50799e11i	−0.370416	+	0.310816i	−0.808926	−	0.587910i	$-0.799951\pi$
$547$	−7.75592e11	+	6.50799e11i	−0.370416	+	0.310816i	0.438510	+	0.898726i	$0.355506\pi$
$548$	6.01533e10	+	1.04189e11i	0.0284936	+	0.0493523i
$549$	9.24544e11	+	6.07571e11i	0.434362	+	0.285444i
$550$	−1.43829e12	+	2.49118e12i	−0.670213	+	1.16084i
$551$	1.22283e11	+	6.93503e11i	0.0565178	+	0.320528i
$552$	4.94977e11	+	5.24443e11i	0.226913	+	0.240421i
$553$	9.38600e11	−	3.41622e11i	0.426793	−	0.155340i
$554$	−2.74642e12	+	9.99615e11i	−1.23872	+	0.450857i
$555$	6.86281e12	−	1.62791e12i	3.07032	−	0.728304i
$556$	4.56201e10	+	2.58724e11i	0.0202451	+	0.114816i
$557$	1.12873e12	−	1.95502e12i	0.496868	−	0.860601i	−0.503125	−	0.864213i	$-0.667817\pi$
$557$	1.12873e12	−	1.95502e12i	0.496868	−	0.860601i	0.999993	+	0.00361254i	$0.00114991\pi$
$558$	−1.46378e12	+	1.55272e12i	−0.639178	+	0.678013i
$559$	−1.49661e12	−	2.59220e12i	−0.648269	−	1.12284i
$560$	2.67397e12	−	2.24373e12i	1.14898	−	0.964105i
$561$	−9.09739e11	+	5.98596e11i	−0.387779	+	0.255153i
$562$	1.24471e9	−	7.05912e9i	0.000526328	−	0.00298495i
$563$	1.81019e11	+	1.51893e11i	0.0759339	+	0.0637161i	0.679965	−	0.733245i	$-0.261995\pi$
$563$	1.81019e11	+	1.51893e11i	0.0759339	+	0.0637161i	−0.604031	+	0.796961i	$0.706440\pi$
$564$	−1.84130e11	+	2.47429e11i	−0.0766247	+	0.102966i
$565$	2.13409e12	+	7.76744e11i	0.881037	+	0.320671i
$566$	−1.29842e12			−0.531789
$567$	−5.13376e11	+	1.71962e12i	−0.208599	+	0.698730i
$568$	−2.82111e12			−1.13724
$569$	−4.08481e12	−	1.48675e12i	−1.63368	−	0.594610i	−0.647761	−	0.761843i	$-0.724295\pi$
$569$	−4.08481e12	−	1.48675e12i	−1.63368	−	0.594610i	−0.985917	+	0.167233i	$0.946517\pi$
$570$	3.00672e12	−	4.04035e12i	1.19304	−	1.60318i
$571$	−3.03936e12	−	2.55033e12i	−1.19652	−	1.00400i	−0.999723	−	0.0235563i	$-0.992501\pi$
$571$	−3.03936e12	−	2.55033e12i	−1.19652	−	1.00400i	−0.196798	−	0.980444i	$-0.563054\pi$
$572$	−9.88447e10	+	5.60576e11i	−0.0386075	+	0.218954i
$573$	−1.06885e12	+	7.03289e11i	−0.414210	+	0.272545i
$574$	1.33471e12	−	1.11995e12i	0.513195	−	0.430622i
$575$	−1.04500e12	−	1.81000e12i	−0.398668	−	0.690514i
$576$	1.76634e12	+	4.17910e11i	0.668610	+	0.158191i
$577$	−8.55077e11	+	1.48104e12i	−0.321154	+	0.556256i	−0.980727	−	0.195386i	$-0.937404\pi$
$577$	−8.55077e11	+	1.48104e12i	−0.321154	+	0.556256i	0.659572	+	0.751641i	$0.270738\pi$
$578$	1.91032e11	+	1.08340e12i	0.0711919	+	0.403749i
$579$	4.83044e11	−	1.14582e11i	0.178621	−	0.0423704i
$580$	−3.17263e11	+	1.15474e11i	−0.116411	+	0.0423701i
$581$	−1.62886e12	+	5.92858e11i	−0.593051	+	0.215853i
$582$	8.52928e11	+	9.03701e11i	0.308148	+	0.326491i
$583$	3.54773e11	+	2.01202e12i	0.127187	+	0.721311i
$584$	4.41336e11	−	7.64417e11i	0.157004	−	0.271940i
$585$	−7.52709e12	+	3.78389e12i	−2.65721	+	1.33579i
$586$	−1.80654e11	−	3.12903e11i	−0.0632862	−	0.109615i
$587$	6.67368e11	−	5.59988e11i	0.232003	−	0.194674i	−0.519373	−	0.854547i	$-0.673835\pi$
$587$	6.67368e11	−	5.59988e11i	0.232003	−	0.194674i	0.751377	+	0.659874i	$0.229390\pi$
$588$	−1.77289e10	−	3.03385e11i	−0.00611622	−	0.104664i
$589$	4.40371e11	−	2.49747e12i	0.150765	−	0.855030i
$590$	−7.60280e12	−	6.37951e12i	−2.58309	−	2.16747i
$591$	3.73253e12	+	4.35540e11i	1.25852	+	0.146854i
$592$	5.93552e12	+	2.16035e12i	1.98615	+	0.722898i
$593$	2.55764e12			0.849363			0.424682	−	0.905343i	$-0.360386\pi$
$593$	2.55764e12			0.849363			0.424682	+	0.905343i	$0.360386\pi$
$594$	9.81016e11	−	1.70144e12i	0.323323	−	0.560762i
$595$	−3.09935e12			−1.01378
$596$	1.29864e11	+	4.72666e10i	0.0421580	+	0.0153443i
$597$	−1.38110e12	−	3.20006e12i	−0.444981	−	1.03104i
$598$	−1.73184e12	−	1.45319e12i	−0.553799	−	0.464693i
$599$	8.73004e11	−	4.95105e12i	0.277074	−	1.57136i	−0.455223	−	0.890378i	$-0.650440\pi$
$599$	8.73004e11	−	4.95105e12i	0.277074	−	1.57136i	0.732296	−	0.680986i	$-0.238449\pi$
$600$	−5.04446e12	−	2.53220e12i	−1.58904	−	0.797660i
$601$	−1.46486e12	+	1.22916e12i	−0.457994	+	0.384303i	−0.842392	−	0.538865i	$-0.818853\pi$
$601$	−1.46486e12	+	1.22916e12i	−0.457994	+	0.384303i	0.384398	+	0.923167i	$0.374409\pi$
$602$	9.92970e11	+	1.71987e12i	0.308143	+	0.533719i
$603$	2.62239e11	+	3.51964e11i	0.0807735	+	0.108410i
$604$	−5.09387e11	+	8.82285e11i	−0.155733	+	0.269738i
$605$	6.59471e11	+	3.74005e12i	0.200123	+	1.13495i
$606$	−1.56532e12	+	5.23221e12i	−0.471495	+	1.57601i
$607$	−9.53009e11	+	3.46867e11i	−0.284936	+	0.103708i	−0.480535	−	0.876976i	$-0.659557\pi$
$607$	−9.53009e11	+	3.46867e11i	−0.284936	+	0.103708i	0.195598	+	0.980684i	$0.437335\pi$
$608$	1.43588e12	−	5.22618e11i	0.426140	−	0.155102i
$609$	−2.24009e11	+	7.48768e11i	−0.0659915	+	0.220582i
$610$	−5.98349e11	−	3.39341e12i	−0.174973	−	0.992320i
$611$	−1.67581e12	+	2.90259e12i	−0.486452	+	0.842559i
$612$	3.68308e11	+	4.94325e11i	0.106128	+	0.142440i
$613$	2.14833e12	+	3.72101e12i	0.614509	+	1.06436i	0.990470	+	0.137725i	$0.0439791\pi$
$613$	2.14833e12	+	3.72101e12i	0.614509	+	1.06436i	−0.375962	+	0.926635i	$0.622688\pi$
$614$	−2.02312e12	+	1.69760e12i	−0.574465	+	0.482034i
$615$	−4.61395e12	−	2.31610e12i	−1.30057	−	0.652858i
$616$	−2.27329e11	+	1.28925e12i	−0.0636124	+	0.360764i
$617$	1.47281e12	+	1.23583e12i	0.409132	+	0.343302i	0.824011	−	0.566574i	$-0.191732\pi$
$617$	1.47281e12	+	1.23583e12i	0.409132	+	0.343302i	−0.414879	+	0.909877i	$0.636176\pi$
$618$	1.19461e12	+	2.76795e12i	0.329441	+	0.763325i
$619$	1.13970e12	+	4.14818e11i	0.312021	+	0.113566i	0.493284	−	0.869868i	$-0.335796\pi$
$619$	1.13970e12	+	4.14818e11i	0.312021	+	0.113566i	−0.181263	+	0.983435i	$0.558018\pi$
$620$	1.21587e12			0.330463
$621$	7.14198e11	+	1.23538e12i	0.192711	+	0.333340i
$622$	5.10657e12			1.36796
$623$	1.11541e12	+	4.05976e11i	0.296646	+	0.107970i
$624$	−7.49377e12	−	8.74430e11i	−1.97865	−	0.230884i
$625$	3.55765e12	+	2.98523e12i	0.932618	+	0.782559i
$626$	−1.11159e11	+	6.30416e11i	−0.0289309	+	0.164075i
$627$	1.36164e11	+	2.33010e12i	0.0351850	+	0.602102i
$628$	−1.12588e12	+	9.44725e11i	−0.288851	+	0.242374i
$629$	−2.80421e12	−	4.85703e12i	−0.714303	−	1.23721i
$630$	4.99407e12	−	2.51053e12i	1.26305	−	0.634940i
$631$	−3.30730e12	+	5.72841e12i	−0.830503	+	1.43847i	0.0671375	+	0.997744i	$0.478613\pi$
$631$	−3.30730e12	+	5.72841e12i	−0.830503	+	1.43847i	−0.897640	+	0.440729i	$0.854720\pi$
$632$	−3.72454e11	−	2.11229e12i	−0.0928636	−	0.526656i
$633$	1.26046e12	+	1.33549e12i	0.312041	+	0.330616i
$634$	5.73214e12	−	2.08633e12i	1.40901	−	0.512839i
$635$	6.32250e12	−	2.30120e12i	1.54315	−	0.561660i
$636$	1.12527e12	−	2.66924e11i	0.272709	−	0.0646889i
$637$	−5.73471e11	−	3.25232e12i	−0.138002	−	0.782646i
$638$	4.27662e11	−	7.40733e11i	0.102190	−	0.176998i
$639$	−5.43234e12	−	1.28528e12i	−1.28894	−	0.304960i
$640$	−4.46273e12	−	7.72968e12i	−1.05146	−	1.82117i
$641$	2.68786e12	−	2.25539e12i	0.628849	−	0.527667i	−0.271722	−	0.962376i	$-0.587593\pi$
$641$	2.68786e12	−	2.25539e12i	0.628849	−	0.527667i	0.900571	+	0.434709i	$0.143149\pi$
$642$	−1.45261e12	+	9.55801e11i	−0.337476	+	0.222055i
$643$	2.76710e11	−	1.56930e12i	0.0638375	−	0.362040i	−0.936109	−	0.351710i	$-0.885600\pi$
$643$	2.76710e11	−	1.56930e12i	0.0638375	−	0.362040i	0.999947	−	0.0103307i	$-0.00328843\pi$
$644$	2.10202e11	+	1.76380e11i	0.0481560	+	0.0404077i
$645$	3.51304e12	−	4.72074e12i	0.799217	−	1.07397i
$646$	−3.76316e12	−	1.36968e12i	−0.850171	−	0.309437i
$647$	−9.04507e11			−0.202928			−0.101464	−	0.994839i	$-0.532353\pi$
$647$	−9.04507e11			−0.202928			−0.101464	+	0.994839i	$0.532353\pi$
$648$	3.44514e12	+	1.72689e12i	0.767572	+	0.384748i
$649$	4.59958e12			1.01769
$650$	1.66277e13	+	6.05200e12i	3.65362	+	1.32981i
$651$	1.68031e12	−	2.25796e12i	0.366670	−	0.492722i
$652$	−1.07507e12	−	9.02090e11i	−0.232982	−	0.195495i
$653$	−5.51766e11	+	3.12922e12i	−0.118753	+	0.673483i	0.866070	+	0.499923i	$0.166638\pi$
$653$	−5.51766e11	+	3.12922e12i	−0.118753	+	0.673483i	−0.984823	+	0.173561i	$0.944473\pi$
$654$	−7.29186e12	+	4.79795e12i	−1.55861	+	1.02555i
$655$	7.07366e12	−	5.93551e12i	1.50161	−	1.26000i
$656$	−2.31167e12	−	4.00393e12i	−0.487370	−	0.844150i
$657$	1.19810e12	−	1.27089e12i	0.250870	−	0.266112i
$658$	1.11187e12	−	1.92581e12i	0.231226	−	0.400495i
$659$	7.84632e11	+	4.44987e12i	0.162062	+	0.919101i	0.952042	+	0.305968i	$0.0989799\pi$
$659$	7.84632e11	+	4.44987e12i	0.162062	+	0.919101i	−0.789980	+	0.613133i	$0.789909\pi$
$660$	−1.08884e12	+	2.58282e11i	−0.223366	+	0.0529841i
$661$	−2.33170e12	+	8.48670e11i	−0.475080	+	0.172915i	−0.568452	−	0.822716i	$-0.692458\pi$
$661$	−2.33170e12	+	8.48670e11i	−0.475080	+	0.172915i	0.0933723	+	0.995631i	$0.470235\pi$
$662$	−9.05416e10	+	3.29544e10i	−0.0183226	+	0.00666888i
$663$	4.59801e12	+	4.87172e12i	0.924185	+	0.979200i
$664$	6.46363e11	+	3.66571e12i	0.129039	+	0.731815i
$665$	−3.32141e12	+	5.75285e12i	−0.658605	+	1.14074i
$666$	8.45280e12	+	5.55482e12i	1.66482	+	1.09405i
$667$	3.10723e11	+	5.38187e11i	0.0607864	+	0.105285i
$668$	−9.49715e11	+	7.96905e11i	−0.184544	+	0.154851i
$669$	3.47484e11	+	5.94630e12i	0.0670682	+	1.14770i
$670$	2.37389e11	−	1.34630e12i	0.0455117	−	0.258110i
$671$	1.22331e12	+	1.02648e12i	0.232962	+	0.195479i
$672$	1.68446e12	+	1.96556e11i	0.318639	+	0.0371812i
$673$	5.81409e11	+	2.11616e11i	0.109248	+	0.0397631i	0.396066	−	0.918222i	$-0.370375\pi$
$673$	5.81409e11	+	2.11616e11i	0.109248	+	0.0397631i	−0.286818	+	0.957985i	$0.592597\pi$
$674$	−6.45285e12			−1.20443
$675$	−8.55997e12	−	7.17423e12i	−1.58710	−	1.33017i
$676$	2.28587e12			0.421008
$677$	−5.17630e12	−	1.88402e12i	−0.947044	−	0.344696i	−0.178101	−	0.984012i	$-0.556995\pi$
$677$	−5.17630e12	−	1.88402e12i	−0.947044	−	0.344696i	−0.768944	+	0.639316i	$0.779217\pi$
$678$	1.29052e12	+	2.99017e12i	0.234548	+	0.543454i
$679$	−1.25556e12	−	1.05354e12i	−0.226685	−	0.190211i
$680$	−1.15571e12	+	6.55434e12i	−0.207280	+	1.17554i
$681$	2.09544e10	+	1.05186e10i	0.00373347	+	0.00187412i
$682$	−2.35959e12	+	1.97993e12i	−0.417644	+	0.350445i
$683$	−6.22659e11	−	1.07848e12i	−0.109486	−	0.189635i	0.806076	−	0.591812i	$-0.201587\pi$
$683$	−6.22659e11	−	1.07848e12i	−0.109486	−	0.189635i	−0.915562	+	0.402177i	$0.868254\pi$
$684$	1.31224e12	−	1.53892e11i	0.229224	−	0.0268821i
$685$	−1.28509e12	+	2.22585e12i	−0.223011	+	0.386267i
$686$	1.19304e12	+	6.76604e12i	0.205681	+	1.16648i
$687$	−4.96000e11	+	1.65792e12i	−0.0849525	+	0.283961i
$688$	4.95195e12	−	1.80236e12i	0.842614	−	0.306686i
$689$	1.18097e13	−	4.29837e12i	1.99642	−	0.726636i
$690$	1.27387e12	−	4.25801e12i	0.213946	−	0.715132i
$691$	−1.90904e12	−	1.08267e13i	−0.318540	−	1.80653i	−0.551643	−	0.834080i	$-0.685999\pi$
$691$	−1.90904e12	−	1.08267e13i	−0.318540	−	1.80653i	0.233102	−	0.972452i	$-0.425112\pi$
$692$	−8.38784e11	+	1.45282e12i	−0.139051	+	0.240843i
$693$	−1.02511e12	+	2.37901e12i	−0.168839	+	0.391829i
$694$	−5.03982e12	−	8.72922e12i	−0.824702	−	1.42843i
$695$	−4.29947e12	+	3.60769e12i	−0.699010	+	0.586539i
$696$	1.49993e12	+	7.52929e11i	0.242286	+	0.121622i
$697$	−7.12842e11	+	4.04273e12i	−0.114405	+	0.648825i
$698$	−8.18061e12	−	6.86435e12i	−1.30448	−	1.09459i
$699$	9.68600e11	+	2.24428e12i	0.153461	+	0.355573i
$700$	−2.01819e12	−	7.34562e11i	−0.317703	−	0.115634i
$701$	5.11019e12			0.799293			0.399646	−	0.916669i	$-0.369133\pi$
$701$	5.11019e12			0.799293			0.399646	+	0.916669i	$0.369133\pi$
$702$	−1.13551e13	−	4.12548e12i	−1.76471	−	0.641146i
$703$	−1.20205e13			−1.85619
$704$	2.46203e12	+	8.96106e11i	0.377761	+	0.137494i
$705$	−6.54465e12	−	7.63680e11i	−0.997781	−	0.116429i
$706$	−1.51894e12	−	1.27454e12i	−0.230102	−	0.193078i
$707$	1.25085e12	−	7.09395e12i	0.188287	−	1.06783i
$708$	−1.51890e11	−	2.59922e12i	−0.0227185	−	0.388770i
$709$	−1.75291e12	+	1.47086e12i	−0.260526	+	0.218607i	−0.763689	−	0.645584i	$-0.776614\pi$
$709$	−1.75291e12	+	1.47086e12i	−0.260526	+	0.218607i	0.503163	+	0.864191i	$0.332169\pi$
$710$	8.69345e12	+	1.50575e13i	1.28390	+	2.22377i
$711$	2.45143e11	−	4.23712e12i	0.0359755	−	0.621810i
$712$	1.27446e12	−	2.20743e12i	0.185852	−	0.321904i
$713$	−3.88620e11	−	2.20397e12i	−0.0563147	−	0.319377i
$714$	−3.05068e12	−	3.23229e12i	−0.439294	−	0.465444i
$715$	−1.14273e13	+	4.15920e12i	−1.63519	+	0.595159i
$716$	−6.94981e11	+	2.52952e11i	−0.0988244	+	0.0359692i
$717$	−3.56278e12	+	8.45120e11i	−0.503445	+	0.119421i
$718$	1.07172e12	+	6.07801e12i	0.150494	+	0.853497i
$719$	4.85103e12	−	8.40223e12i	0.676946	−	1.17250i	−0.298951	−	0.954269i	$-0.596637\pi$
$719$	4.85103e12	−	8.40223e12i	0.676946	−	1.17250i	0.975896	−	0.218235i	$-0.0700301\pi$
$720$	−4.25940e12	−	1.42074e13i	−0.590679	−	1.97024i
$721$	−1.98818e12	−	3.44363e12i	−0.273998	−	0.474578i
$722$	−3.87203e11	+	3.24902e11i	−0.0530300	+	0.0444975i
$723$	4.69148e12	−	3.08693e12i	0.638540	−	0.420151i
$724$	9.88597e10	−	5.60661e11i	0.0133720	−	0.0758363i
$725$	−3.72607e12	−	3.12654e12i	−0.500875	−	0.420284i
$726$	−3.25135e12	+	4.36908e12i	−0.434359	+	0.583681i
$727$	7.19276e12	+	2.61795e12i	0.954972	+	0.347581i	0.772061	−	0.635548i	$-0.219226\pi$
$727$	7.19276e12	+	2.61795e12i	0.954972	+	0.347581i	0.182911	+	0.983130i	$0.441448\pi$
$728$	8.05298e12			1.06259
$729$	5.84722e12	+	4.89487e12i	0.766788	+	0.641900i
$730$	−5.44003e12			−0.709003
$731$	−4.39687e12	−	1.60033e12i	−0.569528	−	0.207291i
$732$	5.39666e11	−	7.25189e11i	0.0694744	−	0.0933580i
$733$	2.34134e12	+	1.96462e12i	0.299569	+	0.251368i	0.780165	−	0.625574i	$-0.215135\pi$
$733$	2.34134e12	+	1.96462e12i	0.299569	+	0.251368i	−0.480596	+	0.876942i	$0.659580\pi$
$734$	−2.60293e12	+	1.47620e13i	−0.331002	+	1.87721i
$735$	5.42368e12	−	3.56871e12i	0.685490	−	0.451043i
$736$	1.03298e12	−	8.66774e11i	0.129760	−	0.108882i
$737$	3.16780e11	+	5.48680e11i	0.0395507	+	0.0685039i
$738$	−2.12607e12	−	7.09159e12i	−0.263829	−	0.880015i
$739$	2.65007e12	−	4.59005e12i	0.326856	−	0.566132i	−0.655030	−	0.755603i	$-0.727344\pi$
$739$	2.65007e12	−	4.59005e12i	0.326856	−	0.566132i	0.981886	+	0.189471i	$0.0606773\pi$
$740$	−1.00076e12	−	5.67559e12i	−0.122684	−	0.695774i
$741$	1.39701e13	−	3.31382e12i	1.70223	−	0.403782i
$742$	−7.83547e12	+	2.85188e12i	−0.948959	+	0.345393i
$743$	1.00811e13	−	3.66923e12i	1.21355	−	0.441698i	0.345619	−	0.938375i	$-0.387669\pi$
$743$	1.00811e13	−	3.66923e12i	1.21355	−	0.441698i	0.867935	+	0.496677i	$0.165447\pi$
$744$	−4.14846e12	−	4.39541e12i	−0.496373	−	0.525921i
$745$	5.12682e11	+	2.90756e12i	0.0609740	+	0.345801i
$746$	−4.12516e11	+	7.14499e11i	−0.0487659	+	0.0844651i
$747$	−4.25427e11	+	7.35317e12i	−0.0499899	+	0.864037i
$748$	4.44910e11	+	7.70607e11i	0.0519655	+	0.0900069i
$749$	1.75694e12	−	1.47425e12i	0.203980	−	0.171160i
$750$	1.04938e12	+	1.79575e13i	0.121104	+	2.07239i
$751$	−2.96038e12	+	1.67891e13i	−0.339600	+	1.92597i	0.0363807	+	0.999338i	$0.488417\pi$
$751$	−2.96038e12	+	1.67891e13i	−0.339600	+	1.92597i	−0.375980	+	0.926628i	$0.622694\pi$
$752$	−4.52024e12	−	3.79293e12i	−0.515444	−	0.432509i
$753$	−9.26652e12	−	1.08129e12i	−1.05036	−	0.122564i
$754$	−4.94412e12	−	1.79951e12i	−0.557080	−	0.202761i
$755$	−2.17647e13			−2.43777
$756$	1.37823e12	+	5.00730e11i	0.153452	+	0.0557513i
$757$	1.50509e13			1.66583			0.832913	−	0.553404i	$-0.186671\pi$
$757$	1.50509e13			1.66583			0.832913	+	0.553404i	$0.186671\pi$
$758$	9.39647e10	+	3.42004e10i	0.0103384	+	0.00376287i
$759$	8.16200e11	+	1.89116e12i	0.0892707	+	0.206843i
$760$	1.09273e13	+	9.16911e12i	1.18810	+	0.996933i
$761$	−2.45893e12	+	1.39453e13i	−0.265776	+	1.50729i	0.501040	+	0.865424i	$0.332951\pi$
$761$	−2.45893e12	+	1.39453e13i	−0.265776	+	1.50729i	−0.766816	+	0.641867i	$0.778160\pi$
$762$	8.62315e12	+	4.32862e12i	0.926549	+	0.465107i
$763$	8.81951e12	−	7.40044e12i	0.942071	−	0.790492i
$764$	5.22724e11	+	9.05384e11i	0.0555076	+	0.0961419i
$765$	−5.21153e12	+	1.20945e13i	−0.550160	+	1.27677i
$766$	7.63563e12	−	1.32253e13i	0.801337	−	1.38796i
$767$	−4.91316e12	−	2.78639e13i	−0.512603	−	2.90712i
$768$	1.76998e12	−	5.91630e12i	0.183588	−	0.613656i
$769$	3.88995e12	−	1.41583e12i	0.401121	−	0.145996i	−0.133579	−	0.991038i	$-0.542647\pi$
$769$	3.88995e12	−	1.41583e12i	0.401121	−	0.145996i	0.534700	+	0.845042i	$0.320425\pi$
$770$	7.58179e12	−	2.75955e12i	0.777255	−	0.282898i
$771$	2.94204e12	−	9.83402e12i	0.299850	−	1.00227i
$772$	−7.04392e10	−	3.99480e11i	−0.00713734	−	0.0404779i
$773$	−9.58201e11	+	1.65965e12i	−0.0965270	+	0.167190i	−0.910245	−	0.414070i	$-0.864107\pi$
$773$	−9.58201e11	+	1.65965e12i	−0.0965270	+	0.167190i	0.813718	+	0.581260i	$0.197440\pi$
$774$	8.38111e12	−	9.82890e11i	0.839396	−	0.0984397i
$775$	8.75827e12	+	1.51698e13i	0.872088	+	1.51050i
$776$	−2.69615e12	+	2.26234e12i	−0.266911	+	0.223965i
$777$	−1.19231e13	−	5.98511e12i	−1.17353	−	0.589085i
$778$	1.58913e12	−	9.01242e12i	0.155508	−	0.881929i
$779$	6.73999e12	+	5.65553e12i	0.655754	+	0.550243i
$780$	2.72772e12	+	6.32021e12i	0.263860	+	0.611373i
$781$	−7.57193e12	−	2.75596e12i	−0.728244	−	0.265059i
$782$	−3.53405e12			−0.337942
$783$	2.54524e12	+	2.13320e12i	0.241991	+	0.202816i
$784$	5.81425e12			0.549631
$785$	−2.95052e13	−	1.07390e13i	−2.77323	−	1.00937i
$786$	1.31527e13	+	1.53476e12i	1.22917	+	0.143430i
$787$	1.44352e11	+	1.21126e11i	0.0134134	+	0.0112552i	0.649470	−	0.760388i	$-0.274991\pi$
$787$	1.44352e11	+	1.21126e11i	0.0134134	+	0.0112552i	−0.636056	+	0.771643i	$0.719435\pi$
$788$	5.33188e11	−	3.02386e12i	0.0492621	−	0.279379i
$789$	−1.22130e11	−	2.08994e12i	−0.0112195	−	0.191994i
$790$	−1.01265e13	+	8.49711e12i	−0.924987	+	0.776156i
$791$	−2.14780e12	−	3.72011e12i	−0.195075	−	0.337879i
$792$	4.64875e12	+	3.05496e12i	0.419829	+	0.275894i
$793$	4.91163e12	−	8.50719e12i	0.441058	−	0.763936i
$794$	−6.93010e11	−	3.93025e12i	−0.0618795	−	0.350936i
$795$	1.69584e13	+	1.79679e13i	1.50568	+	1.59531i
$796$	−2.67612e12	+	9.74028e11i	−0.236264	+	0.0859929i
$797$	−6.72654e12	+	2.44826e12i	−0.590512	+	0.214929i	−0.619955	−	0.784638i	$-0.712849\pi$
$797$	−6.72654e12	+	2.44826e12i	−0.590512	+	0.214929i	0.0294424	+	0.999566i	$0.490627\pi$
$798$	−9.26886e12	+	2.19865e12i	−0.809121	+	0.191930i
$799$	9.09797e11	+	5.15972e12i	0.0789740	+	0.447884i
$800$	−5.27718e12	+	9.14035e12i	−0.455509	+	0.788965i
$801$	3.45979e12	−	3.67000e12i	0.296964	−	0.315007i
$802$	1.14992e13	+	1.99173e13i	0.981487	+	1.69999i
$803$	1.93132e12	−	1.62057e12i	0.163921	−	0.137546i
$804$	2.99597e11	−	1.97131e11i	0.0252863	−	0.0166381i
$805$	−1.01795e12	+	5.77311e12i	−0.0854372	+	0.484538i
$806$	1.45147e13	+	1.21793e13i	1.21144	+	1.01652i
$807$	−8.21496e12	+	1.10391e13i	−0.681828	+	0.916222i
$808$	−1.45355e13	−	5.29048e12i	−1.19972	−	0.436661i
$809$	5.02057e12			0.412083			0.206041	−	0.978543i	$-0.433942\pi$
$809$	5.02057e12			0.412083			0.206041	+	0.978543i	$0.433942\pi$
$810$	−1.39930e12	−	2.37097e13i	−0.114216	−	1.93528i
$811$	−1.82397e13			−1.48055			−0.740275	−	0.672304i	$-0.765305\pi$
$811$	−1.82397e13			−1.48055			−0.740275	+	0.672304i	$0.765305\pi$
$812$	6.00092e11	+	2.18416e11i	0.0484413	+	0.0176312i
$813$	7.08916e12	−	9.52623e12i	0.569098	−	0.764740i
$814$	1.11843e13	+	9.38477e12i	0.892895	+	0.749228i
$815$	5.20629e12	−	2.95263e13i	0.413351	−	2.34423i
$816$	−9.85237e12	+	6.48273e12i	−0.777920	+	0.511861i
$817$	−7.68235e12	+	6.44625e12i	−0.603246	+	0.506184i
$818$	−1.08725e13	−	1.88317e13i	−0.849059	−	1.47061i
$819$	1.55068e13	+	3.66887e12i	1.20433	+	0.284941i
$820$	−2.10917e12	+	3.65320e12i	−0.162911	+	0.282170i
$821$	1.31150e12	+	7.43790e12i	0.100745	+	0.571355i	0.992835	+	0.119496i	$0.0381279\pi$
$821$	1.31150e12	+	7.43790e12i	0.100745	+	0.571355i	−0.892089	+	0.451859i	$0.850761\pi$
$822$	−3.58624e12	+	8.50684e11i	−0.273978	+	0.0649898i
$823$	1.18898e13	−	4.32753e12i	0.903389	−	0.328807i	0.151779	−	0.988415i	$-0.451500\pi$
$823$	1.18898e13	−	4.32753e12i	0.903389	−	0.328807i	0.751610	+	0.659608i	$0.229278\pi$
$824$	−8.02378e12	+	2.92042e12i	−0.606327	+	0.220685i
$825$	−1.10657e13	−	1.17244e13i	−0.831642	−	0.881149i
$826$	3.25978e12	+	1.84871e13i	0.243656	+	1.38184i
$827$	−1.60366e11	+	2.77762e11i	−0.0119217	+	0.0206489i	−0.871925	−	0.489640i	$-0.837128\pi$
$827$	−1.60366e11	+	2.77762e11i	−0.0119217	+	0.0206489i	0.860003	+	0.510289i	$0.170462\pi$
$828$	1.04174e12	−	5.23685e11i	0.0770234	−	0.0387198i
$829$	7.16593e12	+	1.24118e13i	0.526960	+	0.912721i	0.999506	+	0.0314152i	$0.0100014\pi$
$829$	7.16593e12	+	1.24118e13i	0.526960	+	0.912721i	−0.472547	+	0.881306i	$0.656665\pi$
$830$	1.75737e13	−	1.47460e13i	1.28532	−	1.07851i
$831$	−9.55580e11	−	1.63523e13i	−0.0695124	−	1.18953i
$832$	2.79866e12	−	1.58720e13i	0.202486	−	1.14836i
$833$	−3.95471e12	−	3.31839e12i	−0.284585	−	0.238795i
$834$	−7.99440e12	−	9.32848e11i	−0.572188	−	0.0667673i
$835$	−2.48886e13	−	9.05871e12i	−1.77179	−	0.644877i
$836$	1.90715e12			0.135038
$837$	−5.98577e12	−	1.03538e13i	−0.421556	−	0.729181i
$838$	2.74760e13			1.92466
$839$	7.77705e12	+	2.83061e12i	0.541859	+	0.197220i	0.598426	−	0.801178i	$-0.295793\pi$
$839$	7.77705e12	+	2.83061e12i	0.541859	+	0.197220i	−0.0565670	+	0.998399i	$0.518015\pi$
$840$	6.27337e12	+	1.45356e13i	0.434755	+	1.00734i
$841$	−1.00052e13	−	8.39536e12i	−0.689674	−	0.578705i
$842$	5.47164e11	−	3.10312e12i	0.0375157	−	0.212762i
$843$	3.59037e10	+	1.80228e10i	0.00244858	+	0.00122913i
$844$	1.14944e12	−	9.64496e11i	0.0779733	−	0.0654274i
$845$	2.44172e13	+	4.22919e13i	1.64756	+	2.85366i
$846$	−5.64546e12	−	7.57706e12i	−0.378907	−	0.508550i
$847$	3.59165e12	−	6.22092e12i	0.239783	−	0.415316i
$848$	3.84215e12	+	2.17899e13i	0.255148	+	1.44702i
$849$	2.08572e12	−	6.97169e12i	0.137775	−	0.460525i
$850$	2.59927e13	−	9.46058e12i	1.70792	−	0.621631i
$851$	−9.96814e12	+	3.62811e12i	−0.651525	+	0.237136i
$852$	−1.30734e12	+	4.36990e12i	−0.0849985	+	0.284114i
$853$	1.75887e12	+	9.97505e12i	0.113753	+	0.645126i	0.987360	+	0.158494i	$0.0506637\pi$
$853$	1.75887e12	+	9.97505e12i	0.113753	+	0.645126i	−0.873607	+	0.486632i	$0.838225\pi$
$854$	−3.25876e12	+	5.64435e12i	−0.209649	+	0.363123i
$855$	1.68643e13	+	2.26344e13i	1.07925	+	1.44851i
$856$	−2.46252e12	−	4.26521e12i	−0.156764	−	0.271524i
$857$	−1.35337e13	+	1.13562e13i	−0.857046	+	0.719147i	−0.961330	−	0.275400i	$-0.911190\pi$
$857$	−1.35337e13	+	1.13562e13i	−0.857046	+	0.719147i	0.104283	+	0.994548i	$0.466745\pi$
$858$	−1.55855e13	−	7.82357e12i	−0.981812	−	0.492847i
$859$	−2.52702e12	+	1.43315e13i	−0.158358	+	0.898093i	0.797293	+	0.603592i	$0.206264\pi$
$859$	−2.52702e12	+	1.43315e13i	−0.158358	+	0.898093i	−0.955651	+	0.294501i	$0.904847\pi$
$860$	−3.68325e12	−	3.09061e12i	−0.229608	−	0.192664i
$861$	3.86943e12	+	8.96559e12i	0.239957	+	0.555987i
$862$	−1.55822e13	−	5.67146e12i	−0.961272	−	0.349874i
$863$	2.21890e13			1.36172			0.680862	−	0.732412i	$-0.261605\pi$
$863$	2.21890e13			1.36172			0.680862	+	0.732412i	$0.261605\pi$
$864$	3.59942e12	−	6.24273e12i	0.219746	−	0.381121i
$865$	−3.58390e13			−2.17662
$866$	−2.09845e13	−	7.63772e12i	−1.26785	−	0.461459i
$867$	−6.12403e12	−	7.14599e11i	−0.368088	−	0.0429513i
$868$	−1.76172e12	−	1.47826e12i	−0.105341	−	0.0883919i
$869$	1.06383e12	−	6.03329e12i	0.0632825	−	0.358893i
$870$	−6.03418e11	−	1.03260e13i	−0.0357093	−	0.611074i
$871$	2.98548e12	−	2.50512e12i	0.175765	−	0.147484i
$872$	−1.23614e13	−	2.14106e13i	−0.724008	−	1.25402i
$873$	−6.22242e12	+	3.12803e12i	−0.362573	+	0.182266i
$874$	−3.78726e12	+	6.55972e12i	−0.219545	+	0.380263i
$875$	−4.11997e12	−	2.33655e13i	−0.237606	−	1.34753i
$876$	−9.79558e11	−	1.03787e12i	−0.0562033	−	0.0595490i
$877$	−1.77882e13	+	6.47436e12i	−1.01539	+	0.369572i	−0.795500	−	0.605953i	$-0.792792\pi$
$877$	−1.77882e13	+	6.47436e12i	−1.01539	+	0.369572i	−0.219890	+	0.975525i	$0.570570\pi$
$878$	−1.96080e12	+	7.13672e11i	−0.111354	+	0.0405297i
$879$	1.97029e12	−	4.67369e11i	0.111322	−	0.0264064i
$880$	−3.71776e12	−	2.10844e13i	−0.208982	−	1.18520i
$881$	−5.02494e12	+	8.70344e12i	−0.281021	+	0.486743i	−0.971637	−	0.236479i	$-0.924006\pi$
$881$	−5.02494e12	+	8.70344e12i	−0.281021	+	0.486743i	0.690615	+	0.723222i	$0.257340\pi$
$882$	9.06031e12	+	2.14364e12i	0.504120	+	0.119273i
$883$	2.22773e11	+	3.85853e11i	0.0123321	+	0.0213599i	0.872126	−	0.489282i	$-0.162741\pi$
$883$	2.22773e11	+	3.85853e11i	0.0123321	+	0.0213599i	−0.859793	+	0.510642i	$0.829408\pi$
$884$	4.19303e12	−	3.51837e12i	0.230937	−	0.193779i
$885$	4.64668e13	−	3.05746e13i	2.54623	−	1.67539i
$886$	2.26544e12	−	1.28479e13i	0.123510	−	0.700458i
$887$	1.47666e13	+	1.23907e13i	0.800986	+	0.672107i	0.948438	−	0.316962i	$-0.102663\pi$
$887$	1.47666e13	+	1.23907e13i	0.800986	+	0.672107i	−0.147452	+	0.989069i	$0.547107\pi$
$888$	−1.71030e13	+	2.29825e13i	−0.923024	+	1.24034i
$889$	−1.19588e13	−	4.35265e12i	−0.642140	−	0.233720i
$890$	−1.57093e13			−0.839272
$891$	7.55983e12	+	8.00057e12i	0.401849	+	0.425277i
$892$	4.86696e12			0.257404
$893$	1.05522e13	+	3.84068e12i	0.555279	+	0.202105i
$894$	−2.52765e12	+	3.39659e12i	−0.132342	+	0.177838i
$895$	−1.21036e13	−	1.01562e13i	−0.630540	−	0.529086i
$896$	−2.93156e12	+	1.66257e13i	−0.151954	+	0.861776i
$897$	1.05847e13	−	6.96457e12i	0.545897	−	0.359193i
$898$	−1.52589e13	+	1.28037e13i	−0.783030	+	0.657040i
$899$	−2.60420e12	−	4.51060e12i	−0.132971	−	0.230312i
$900$	−6.26004e12	+	6.64039e12i	−0.318043	+	0.337367i
$901$	9.82293e12	−	1.70138e13i	0.496569	−	0.860082i
$902$	−1.85571e12	−	1.05242e13i	−0.0933427	−	0.529373i
$903$	−1.08297e13	+	2.56890e12i	−0.542029	+	0.128574i
$904$	−8.66798e12	+	3.15489e12i	−0.431678	+	0.157118i
$905$	1.14291e13	−	4.15984e12i	0.566359	−	0.206138i
$906$	−2.14230e13	−	2.26983e13i	−1.05634	−	1.11922i
$907$	3.07924e11	+	1.74632e12i	0.0151081	+	0.0856823i	0.991430	−	0.130643i	$-0.0417040\pi$
$907$	3.07924e11	+	1.74632e12i	0.0151081	+	0.0856823i	−0.976321	+	0.216325i	$0.930593\pi$
$908$	9.57887e9	−	1.65911e10i	0.000467658	−	0.000810007i
$909$	−2.55793e13	−	1.68096e13i	−1.24266	−	0.816620i
$910$	−2.48158e13	−	4.29822e13i	−1.19962	−	2.07779i
$911$	−8.88223e11	+	7.45308e11i	−0.0427257	+	0.0358511i	−0.663900	−	0.747821i	$-0.731100\pi$
$911$	−8.88223e11	+	7.45308e11i	−0.0427257	+	0.0358511i	0.621175	+	0.783672i	$0.286656\pi$
$912$	1.47464e12	+	2.52347e13i	0.0705844	+	1.20787i
$913$	−1.84619e12	+	1.04703e13i	−0.0879343	+	0.498700i
$914$	8.31914e12	+	6.98058e12i	0.394294	+	0.330852i
$915$	1.91817e13	+	2.23826e12i	0.904673	+	0.105564i
$916$	1.32872e12	+	4.83615e11i	0.0623598	+	0.0226971i
$917$	−1.74658e13			−0.815693
$918$	−1.77430e13	+	6.46956e12i	−0.824584	+	0.300665i
$919$	3.62996e13			1.67873			0.839367	−	0.543565i	$-0.182926\pi$
$919$	3.62996e13			1.67873			0.839367	+	0.543565i	$0.182926\pi$
$920$	1.18291e13	+	4.30543e12i	0.544385	+	0.198140i
$921$	−5.86520e12	−	1.35898e13i	−0.268605	−	0.622367i
$922$	4.86154e12	+	4.07932e12i	0.221557	+	0.185908i
$923$	−8.60723e12	+	4.88140e13i	−0.390351	+	2.21379i
$924$	1.89169e12	+	9.49586e11i	0.0853742	+	0.0428559i
$925$	6.36028e13	−	5.33691e13i	2.85653	−	2.39691i
$926$	1.56176e13	+	2.70504e13i	0.698014	+	1.20900i
$927$	−1.67811e13	+	1.96800e12i	−0.746384	+	0.0875318i
$928$	1.56913e12	−	2.71781e12i	0.0694532	−	0.120296i
$929$	1.96057e12	+	1.11189e13i	0.0863598	+	0.489771i	0.997055	+	0.0766914i	$0.0244356\pi$
$929$	1.96057e12	+	1.11189e13i	0.0863598	+	0.489771i	−0.910695	+	0.413079i	$0.864453\pi$
$930$	−1.06764e13	+	3.56868e13i	−0.468008	+	1.56435i
$931$	−1.03975e13	+	3.78438e12i	−0.453581	+	0.165090i
$932$	1.87683e12	−	6.83109e11i	0.0814802	−	0.0296564i
$933$	−8.20299e12	+	2.74191e13i	−0.354409	+	1.18464i
$934$	5.09672e12	+	2.89049e13i	0.219144	+	1.24283i
$935$	−9.50490e12	+	1.64630e13i	−0.406720	+	0.704459i
$936$	1.35410e13	−	3.14250e13i	0.576648	−	1.33824i
$937$	3.23571e12	+	5.60441e12i	0.137133	+	0.237521i	0.926410	−	0.376516i	$-0.122878\pi$
$937$	3.23571e12	+	5.60441e12i	0.137133	+	0.237521i	−0.789277	+	0.614037i	$0.789545\pi$
$938$	−1.98081e12	+	1.66209e12i	−0.0835467	+	0.0701040i
$939$	−3.20638e12	−	1.60953e12i	−0.134592	−	0.0675623i
$940$	−9.34897e11	+	5.30206e12i	−0.0390561	+	0.221498i
$941$	2.08008e13	+	1.74540e13i	0.864824	+	0.725673i	0.963002	−	0.269496i	$-0.0868570\pi$
$941$	2.08008e13	+	1.74540e13i	0.864824	+	0.725673i	−0.0981780	+	0.995169i	$0.531301\pi$
$942$	−1.78423e13	−	4.13412e13i	−0.738282	−	1.71062i
$943$	7.29621e12	+	2.65560e12i	0.300465	+	0.109360i
$944$	4.98130e13			2.04159
$945$	5.45773e12	+	3.08479e13i	0.222622	+	1.25829i
$946$	1.21807e13			0.494497
$947$	5.85954e12	+	2.13270e12i	0.236749	+	0.0861697i	0.457670	−	0.889122i	$-0.348684\pi$
$947$	5.85954e12	+	2.13270e12i	0.236749	+	0.0861697i	−0.220921	+	0.975292i	$0.570906\pi$
$948$	−3.44453e12	−	4.01934e11i	−0.138514	−	0.0161628i
$949$	−1.18803e13	−	9.96872e12i	−0.475475	−	0.398971i
$950$	1.02948e13	−	5.83848e13i	0.410074	−	2.32565i
$951$	1.99442e12	+	3.41294e13i	0.0790686	+	1.35306i
$952$	9.64339e12	−	8.09176e12i	0.380508	−	0.319284i
$953$	3.95886e11	+	6.85694e11i	0.0155472	+	0.0269285i	0.873694	−	0.486475i	$-0.161718\pi$
$953$	3.95886e11	+	6.85694e11i	0.0155472	+	0.0269285i	−0.858147	+	0.513404i	$0.828384\pi$
$954$	−2.04647e12	+	3.53716e13i	−0.0799903	+	1.38257i
$955$	−1.11673e13	+	1.93423e13i	−0.434443	+	0.752477i
$956$	5.19537e11	+	2.94644e12i	0.0201167	+	0.114087i
$957$	3.29030e12	+	3.48616e12i	0.126804	+	0.134352i
$958$	−1.98083e13	+	7.20964e12i	−0.759806	+	0.276547i
$959$	4.56824e12	−	1.66270e12i	0.174407	−	0.0634791i
$960$	3.08291e13	−	7.31291e12i	1.17149	−	0.277888i
$961$	−1.33413e12	−	7.56624e12i	−0.0504596	−	0.286171i
$962$	4.49054e13	−	7.77784e13i	1.69048	−	2.92800i
$963$	−2.79864e12	−	9.33500e12i	−0.104865	−	0.349781i
$964$	−2.29438e12	−	3.97399e12i	−0.0855695	−	0.148211i
$965$	6.63855e12	−	5.57040e12i	0.246434	−	0.206783i
$966$	−7.02270e12	+	4.62085e12i	−0.259482	+	0.170736i
$967$	−6.87921e12	+	3.90139e13i	−0.252999	+	1.43483i	0.548157	+	0.836375i	$0.315329\pi$
$967$	−6.87921e12	+	3.90139e13i	−0.252999	+	1.43483i	−0.801157	+	0.598455i	$0.795782\pi$
$968$	−1.18164e13	−	9.91513e12i	−0.432560	−	0.362961i
$969$	1.33993e13	−	1.80056e13i	0.488231	−	0.656072i
$970$	2.03835e13	+	7.41897e12i	0.739274	+	0.269074i
$971$	8.63679e12			0.311793			0.155896	−	0.987773i	$-0.450173\pi$
$971$	8.63679e12			0.311793			0.155896	+	0.987773i	$0.450173\pi$
$972$	4.27147e12	−	4.53625e12i	0.153490	−	0.163004i
$973$	1.06160e13			0.379710
$974$	4.32634e12	+	1.57466e12i	0.154030	+	0.0560624i
$975$	−5.92056e13	+	7.95590e13i	−2.09818	+	2.81948i
$976$	1.32483e13	+	1.11167e13i	0.467345	+	0.392149i
$977$	2.81418e11	−	1.59600e12i	0.00988157	−	0.0560412i	−0.979468	−	0.201598i	$-0.935386\pi$
$977$	2.81418e11	−	1.59600e12i	0.00988157	−	0.0560412i	0.989350	+	0.145557i	$0.0464975\pi$
$978$	3.59173e13	−	2.36331e13i	1.25539	−	0.826031i
$979$	5.57713e12	−	4.67976e12i	0.194039	−	0.162818i
$980$	−2.65246e12	−	4.59420e12i	−0.0918612	−	0.159108i
$981$	−1.40487e13	−	4.68600e13i	−0.484311	−	1.61544i
$982$	−2.03096e13	+	3.51773e13i	−0.696947	+	1.20715i
$983$	−5.43198e11	−	3.08063e12i	−0.0185553	−	0.105232i	0.974124	−	0.226016i	$-0.0725702\pi$
$983$	−5.43198e11	−	3.08063e12i	−0.0185553	−	0.105232i	−0.992679	+	0.120784i	$0.961459\pi$
$984$	2.04028e13	−	4.83972e12i	0.693765	−	0.164567i
$985$	6.16413e13	−	2.24356e13i	2.08645	−	0.759407i
$986$	−7.72873e12	+	2.81303e12i	−0.260412	+	0.0947824i
$987$	8.55435e12	+	9.06358e12i	0.286919	+	0.303999i
$988$	−2.03717e12	−	1.15534e13i	−0.0680175	−	0.385746i
$989$	−4.42503e12	+	7.66437e12i	−0.147073	+	0.254738i
$990$	1.98021e12	−	3.42265e13i	0.0655169	−	1.13241i
$991$	−8.39631e12	−	1.45428e13i	−0.276539	−	0.478980i	0.693983	−	0.719991i	$-0.255854\pi$
$991$	−8.39631e12	−	1.45428e13i	−0.276539	−	0.478980i	−0.970522	+	0.241011i	$0.922521\pi$
$992$	−8.65752e12	+	7.26452e12i	−0.283851	+	0.238180i
$993$	−3.15027e10	−	5.39089e11i	−0.00102820	−	0.0175950i
$994$	5.71072e12	−	3.23871e13i	0.185546	−	1.05228i
$995$	−4.66068e13	−	3.91077e13i	−1.50746	−	1.26491i
$996$	5.97770e12	+	6.97524e11i	0.192472	+	0.0224591i
$997$	3.83660e13	+	1.39641e13i	1.22975	+	0.447594i	0.873513	−	0.486800i	$-0.161836\pi$
$997$	3.83660e13	+	1.39641e13i	1.22975	+	0.447594i	0.356241	+	0.934394i	$0.384058\pi$
$998$	−3.82865e13			−1.22168
$999$	−4.34042e13	+	3.64633e13i	−1.37875	+	1.15827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.e.a.4.19	✓	156
3.2	odd	2		81.10.e.a.64.8		156
27.7	even	9	inner	27.10.e.a.7.19	yes	156
27.20	odd	18		81.10.e.a.19.8		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.19	✓	156	1.1	even	1	trivial
27.10.e.a.7.19	yes	156	27.7	even	9	inner
81.10.e.a.19.8		156	27.20	odd	18
81.10.e.a.64.8		156	3.2	odd	2

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(23.5230 + 8.56168i) q^{2} +(-83.7573 + 112.551i) q^{3} +(87.8153 + 73.6858i) q^{4} +(-425.267 + 2411.81i) q^{5} +(-2933.85 + 1930.43i) q^{6} +(3548.49 - 2977.54i) q^{7} +(-4973.56 - 8614.45i) q^{8} +(-5652.42 - 18853.9i) q^{9} +(-30652.7 + 53092.0i) q^{10} +(-4933.64 - 27980.1i) q^{11} +(-15648.6 + 3711.97i) q^{12} +(-164231. + 59775.2i) q^{13} +(108964. - 39659.6i) q^{14} +(-235832. - 249871. i) q^{15} +(-53430.8 - 303021. i) q^{16} +(-136602. + 236602. i) q^{17} +(28459.2 - 491896. i) q^{18} +(292780. + 507109. i) q^{19} +(-215061. + 180458. i) q^{20} +(37912.5 + 648777. i) q^{21} +(123502. - 700416. i) q^{22} +(395850. + 332158. i) q^{23} +(1.38614e6 + 161745. i) q^{24} +(-3.80064e6 - 1.38332e6i) q^{25} -4.37499e6 q^{26} +(2.59546e6 + 942969. i) q^{27} +531014. q^{28} +(1.13009e6 + 411318. i) q^{29} +(-3.40817e6 - 7.89684e6i) q^{30} +(-3.31766e6 - 2.78385e6i) q^{31} +(453140. - 2.56988e6i) q^{32} +(3.56241e6 + 1.78825e6i) q^{33} +(-5.23902e6 + 4.39606e6i) q^{34} +(5.67220e6 + 9.82453e6i) q^{35} +(892897. - 2.07217e6i) q^{36} +(-1.02641e7 + 1.77780e7i) q^{37} +(2.54535e6 + 1.44354e7i) q^{38} +(7.02780e6 - 2.34910e7i) q^{39} +(2.28915e7 - 8.33183e6i) q^{40} +(1.41195e7 - 5.13909e6i) q^{41} +(-4.66280e6 + 1.55858e7i) q^{42} +(2.97399e6 + 1.68663e7i) q^{43} +(1.62849e6 - 2.82062e6i) q^{44} +(4.78759e7 - 5.61461e6i) q^{45} +(6.46776e6 + 1.12025e7i) q^{46} +(1.46906e7 - 1.23269e7i) q^{47} +(3.85805e7 + 1.93666e7i) q^{48} +(-3.28127e6 + 1.86090e7i) q^{49} +(-7.75589e7 - 6.50796e7i) q^{50} +(-1.51884e7 - 3.51919e7i) q^{51} +(-1.88266e7 - 6.85232e6i) q^{52} -7.19089e7 q^{53} +(5.29796e7 + 4.44030e7i) q^{54} +6.95807e7 q^{55} +(-4.32985e7 - 1.57594e7i) q^{56} +(-8.15980e7 - 9.52148e6i) q^{57} +(2.30615e7 + 1.93509e7i) q^{58} +(-2.81120e7 + 1.59431e8i) q^{59} +(-2.29774e6 - 3.93200e7i) q^{60} +(-4.30566e7 + 3.61288e7i) q^{61} +(-5.42070e7 - 9.38892e7i) q^{62} +(-7.61959e7 - 5.00727e7i) q^{63} +(-4.61084e7 + 7.98621e7i) q^{64} +(-7.43244e7 - 4.21515e8i) q^{65} +(6.84883e7 + 7.25653e7i) q^{66} +(-2.09545e7 + 7.62680e6i) q^{67} +(-2.94300e7 + 1.07117e7i) q^{68} +(-7.05400e7 + 1.67327e7i) q^{69} +(4.93127e7 + 2.79666e8i) q^{70} +(1.41806e8 - 2.45615e8i) q^{71} +(-1.34304e8 + 1.42464e8i) q^{72} +(4.43683e7 + 7.68481e7i) q^{73} +(-3.93652e8 + 3.30314e8i) q^{74} +(4.74025e8 - 3.11902e8i) q^{75} +(-1.16562e7 + 6.61056e7i) q^{76} +(-1.00819e8 - 8.45970e7i) q^{77} +(3.66437e8 - 4.92409e8i) q^{78} +(2.02624e8 + 7.37491e7i) q^{79} +7.53552e8 q^{80} +(-3.23521e8 + 2.13141e8i) q^{81} +3.76133e8 q^{82} +(-3.51637e8 - 1.27986e8i) q^{83} +(-4.44763e7 + 5.97661e7i) q^{84} +(-5.12547e8 - 4.30078e8i) q^{85} +(-7.44469e7 + 4.22209e8i) q^{86} +(-1.40947e8 + 9.27415e7i) q^{87} +(-2.16495e8 + 1.81661e8i) q^{88} +(1.28124e8 + 2.21917e8i) q^{89} +(1.17426e9 + 2.77825e8i) q^{90} +(-4.04790e8 + 7.01116e8i) q^{91} +(1.02864e7 + 5.83370e7i) q^{92} +(5.91203e8 - 1.40238e8i) q^{93} +(4.51106e8 - 1.64189e8i) q^{94} +(-1.34756e9 + 4.90472e8i) q^{95} +(2.51289e8 + 2.66248e8i) q^{96} +(-6.14418e7 - 3.48454e8i) q^{97} +(-2.36510e8 + 4.09647e8i) q^{98} +(-4.99647e8 + 2.51174e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) 156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

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