LMFDB - Embedded newform 27.9.f.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(2,27)]

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([1]))

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

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

chi := DirichletCharacter("27.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, 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:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.66670 - 1.35185i) q^{2} +(72.7671 - 35.5802i) q^{3} +(-183.611 - 66.8288i) q^{4} +(-24.0534 - 28.6657i) q^{5} +(-605.982 + 174.413i) q^{6} +(-2598.90 + 945.921i) q^{7} +(3043.29 + 1757.05i) q^{8} +(4029.09 - 5178.14i) q^{9} +(145.659 + 252.288i) q^{10} +(-4786.80 + 5704.68i) q^{11} +(-15738.6 + 1669.97i) q^{12} +(2684.14 + 15222.5i) q^{13} +(21203.7 - 3738.78i) q^{14} +(-2770.23 - 1230.10i) q^{15} +(17361.5 + 14568.0i) q^{16} +(-124728. + 72011.7i) q^{17} +(-37889.9 + 34252.5i) q^{18} +(-101393. + 175618. i) q^{19} +(2500.76 + 6870.79i) q^{20} +(-155458. + 161301. i) q^{21} +(44410.8 - 37265.1i) q^{22} +(-39698.1 + 109070. i) q^{23} +(283967. + 19574.0i) q^{24} +(67588.2 - 383312. i) q^{25} -120335. i q^{26} +(108946. - 520154. i) q^{27} +540399. q^{28} +(-609347. - 107444. i) q^{29} +(19575.6 + 13175.7i) q^{30} +(1.01617e6 + 369854. i) q^{31} +(-691668. - 824298. i) q^{32} +(-145347. + 585428. i) q^{33} +(1.05360e6 - 383479. i) q^{34} +(89627.8 + 51746.6i) q^{35} +(-1.08583e6 + 681502. i) q^{36} +(-978631. - 1.69504e6i) q^{37} +(1.01476e6 - 1.20934e6i) q^{38} +(736937. + 1.01219e6i) q^{39} +(-22834.5 - 129501. i) q^{40} +(-1.39463e6 + 245911. i) q^{41} +(1.40990e6 - 1.02649e6i) q^{42} +(2.04961e6 + 1.71982e6i) q^{43} +(1.26014e6 - 727544. i) q^{44} +(-245349. + 9054.95i) q^{45} +(451799. - 782539. i) q^{46} +(-1.82238e6 - 5.00694e6i) q^{47} +(1.78168e6 + 442347. i) q^{48} +(1.44340e6 - 1.21116e6i) q^{49} +(-1.03636e6 + 2.84736e6i) q^{50} +(-6.51389e6 + 9.67792e6i) q^{51} +(524465. - 2.97439e6i) q^{52} +3.45452e6i q^{53} +(-1.53842e6 + 3.84059e6i) q^{54} +278668. q^{55} +(-9.57122e6 - 1.68767e6i) q^{56} +(-1.12955e6 + 1.63868e7i) q^{57} +(4.52643e6 + 1.64749e6i) q^{58} +(-1.16111e7 - 1.38375e7i) q^{59} +(426437. + 410989. i) q^{60} +(1.16719e7 - 4.24821e6i) q^{61} +(-7.29065e6 - 4.20926e6i) q^{62} +(-5.57309e6 + 1.72687e7i) q^{63} +(1.28751e6 + 2.23004e6i) q^{64} +(371801. - 443096. i) q^{65} +(1.90574e6 - 4.29181e6i) q^{66} +(-1.92937e6 - 1.09420e7i) q^{67} +(2.77138e7 - 4.88669e6i) q^{68} +(992009. + 9.34915e6i) q^{69} +(-617196. - 517889. i) q^{70} +(-2.34487e7 + 1.35381e7i) q^{71} +(2.13599e7 - 8.67929e6i) q^{72} +(-1.28556e7 + 2.22665e7i) q^{73} +(5.21144e6 + 1.43183e7i) q^{74} +(-8.72012e6 - 3.02973e7i) q^{75} +(3.03531e7 - 2.54693e7i) q^{76} +(7.04421e6 - 1.93538e7i) q^{77} +(-4.28154e6 - 8.75641e6i) q^{78} +(-981583. + 5.56684e6i) q^{79} -848091. i q^{80} +(-1.05795e7 - 4.17264e7i) q^{81} +1.10246e7 q^{82} +(5.90784e6 + 1.04171e6i) q^{83} +(3.93233e7 - 1.92275e7i) q^{84} +(5.06440e6 + 1.84329e6i) q^{85} +(-1.33888e7 - 1.59561e7i) q^{86} +(-4.81633e7 + 1.38623e7i) q^{87} +(-2.45910e7 + 8.95039e6i) q^{88} +(3.29258e7 + 1.90097e7i) q^{89} +(1.89325e6 + 262252. i) q^{90} +(-2.13751e7 - 3.70227e7i) q^{91} +(1.45780e7 - 1.73734e7i) q^{92} +(8.71029e7 - 9.24222e6i) q^{93} +(7.20300e6 + 4.08503e7i) q^{94} +(7.47305e6 - 1.31770e6i) q^{95} +(-7.96594e7 - 3.53720e7i) q^{96} +(9.92181e6 + 8.32538e6i) q^{97} +(-1.27034e7 + 7.33433e6i) q^{98} +(1.02532e7 + 4.77714e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) $ 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−7.66670	−	1.35185i	−0.479169	−	0.0844904i	−0.0711532	−	0.997465i	$-0.522668\pi$
$2$	−7.66670	−	1.35185i	−0.479169	−	0.0844904i	−0.408015	+	0.912975i	$0.633779\pi$
$3$	72.7671	−	35.5802i	0.898359	−	0.439262i
$3$	72.7671	−	35.5802i	0.898359	−	0.439262i
$4$	−183.611	−	66.8288i	−0.717229	−	0.261050i
$5$	−24.0534	−	28.6657i	−0.0384854	−	0.0458652i	0.746458	−	0.665432i	$-0.231753\pi$
$5$	−24.0534	−	28.6657i	−0.0384854	−	0.0458652i	−0.784944	+	0.619567i	$0.787308\pi$
$6$	−605.982	+	174.413i	−0.467579	+	0.134578i
$7$	−2598.90	+	945.921i	−1.08242	+	0.393970i	−0.820809	−	0.571203i	$-0.806477\pi$
$7$	−2598.90	+	945.921i	−1.08242	+	0.393970i	−0.261614	+	0.965173i	$0.584255\pi$
$8$	3043.29	+	1757.05i	0.742991	+	0.428966i
$9$	4029.09	−	5178.14i	0.614098	−	0.789230i
$10$	145.659	+	252.288i	0.0145659	+	0.0252288i
$11$	−4786.80	+	5704.68i	−0.326945	+	0.389637i	−0.904330	−	0.426835i	$-0.859629\pi$
$11$	−4786.80	+	5704.68i	−0.326945	+	0.389637i	0.577385	+	0.816472i	$0.304073\pi$
$12$	−15738.6	+	1669.97i	−0.758998	+	0.0805349i
$13$	2684.14	+	15222.5i	0.0939791	+	0.532982i	0.995055	+	0.0993213i	$0.0316672\pi$
$13$	2684.14	+	15222.5i	0.0939791	+	0.532982i	−0.901076	+	0.433661i	$0.857222\pi$
$14$	21203.7	−	3738.78i	0.551949	−	0.0973236i
$15$	−2770.23	−	1230.10i	−0.0547206	−	0.0242982i
$16$	17361.5	+	14568.0i	0.264916	+	0.222291i
$17$	−124728.	+	72011.7i	−1.49337	+	0.862198i	−0.999971	−	0.00760413i	$-0.997580\pi$
$17$	−124728.	+	72011.7i	−1.49337	+	0.862198i	−0.493400	+	0.869802i	$0.664246\pi$
$18$	−37889.9	+	34252.5i	−0.360939	+	0.326289i
$19$	−101393.	+	175618.i	−0.778024	+	1.34758i	0.155054	+	0.987906i	$0.450445\pi$
$19$	−101393.	+	175618.i	−0.778024	+	1.34758i	−0.933079	+	0.359672i	$0.882889\pi$
$20$	2500.76	+	6870.79i	0.0156298	+	0.0429424i
$21$	−155458.	+	161301.i	−0.799348	+	0.829393i
$22$	44410.8	−	37265.1i	0.189582	−	0.159078i
$23$	−39698.1	+	109070.i	−0.141860	+	0.389756i	−0.990193	−	0.139707i	$-0.955384\pi$
$23$	−39698.1	+	109070.i	−0.141860	+	0.389756i	0.848333	+	0.529462i	$0.177606\pi$
$24$	283967.	+	19574.0i	0.855901	+	0.0589977i
$25$	67588.2	−	383312.i	0.173026	−	0.981277i
$26$		−	120335.i		−	0.263329i
$27$	108946.	−	520154.i	0.205001	−	0.978762i
$28$	540399.			0.879190
$29$	−609347.	−	107444.i	−0.861534	−	0.151912i	−0.274612	−	0.961555i	$-0.588549\pi$
$29$	−609347.	−	107444.i	−0.861534	−	0.151912i	−0.586922	+	0.809643i	$0.699660\pi$
$30$	19575.6	+	13175.7i	0.0241674	+	0.0162663i
$31$	1.01617e6	+	369854.i	1.10032	+	0.400483i	0.827433	−	0.561564i	$-0.189800\pi$
$31$	1.01617e6	+	369854.i	1.10032	+	0.400483i	0.272884	+	0.962047i	$0.412022\pi$
$32$	−691668.	−	824298.i	−0.659626	−	0.786112i
$33$	−145347.	+	585428.i	−0.122561	+	0.493649i
$34$	1.05360e6	−	383479.i	0.788424	−	0.286963i
$35$	89627.8	+	51746.6i	0.0597270	+	0.0344834i
$36$	−1.08583e6	+	681502.i	−0.646477	+	0.405748i
$37$	−978631.	−	1.69504e6i	−0.522170	−	0.904426i	−0.999667	−	0.0257923i	$-0.991789\pi$
$37$	−978631.	−	1.69504e6i	−0.522170	−	0.904426i	0.477497	−	0.878633i	$-0.341544\pi$
$38$	1.01476e6	−	1.20934e6i	0.486662	−	0.579982i
$39$	736937.	+	1.01219e6i	0.318546	+	0.437528i
$40$	−22834.5	−	129501.i	−0.00891974	−	0.0505864i
$41$	−1.39463e6	+	245911.i	−0.493541	+	0.0870247i	−0.414879	−	0.909877i	$-0.636176\pi$
$41$	−1.39463e6	+	245911.i	−0.493541	+	0.0870247i	−0.0786625	+	0.996901i	$0.525065\pi$
$42$	1.40990e6	−	1.02649e6i	0.453098	−	0.329882i
$43$	2.04961e6	+	1.71982e6i	0.599510	+	0.503049i	0.891288	−	0.453437i	$-0.149802\pi$
$43$	2.04961e6	+	1.71982e6i	0.599510	+	0.503049i	−0.291778	+	0.956486i	$0.594247\pi$
$44$	1.26014e6	−	727544.i	0.336209	−	0.194110i
$45$	−245349.	+	9054.95i	−0.0598320	+	0.00220819i
$46$	451799.	−	782539.i	0.100905	−	0.174773i
$47$	−1.82238e6	−	5.00694e6i	−0.373462	−	1.02608i	−0.974013	−	0.226492i	$-0.927274\pi$
$47$	−1.82238e6	−	5.00694e6i	−0.373462	−	1.02608i	0.600551	−	0.799587i	$-0.294948\pi$
$48$	1.78168e6	+	442347.i	0.335633	+	0.0833293i
$49$	1.44340e6	−	1.21116e6i	0.250382	−	0.210095i
$50$	−1.03636e6	+	2.84736e6i	−0.165817	+	0.455578i
$51$	−6.51389e6	+	9.67792e6i	−0.962852	+	1.43055i
$52$	524465.	−	2.97439e6i	0.0717304	−	0.406803i
$53$			3.45452e6i			0.437809i	0.975746	+	0.218905i	$0.0702483\pi$
$53$			3.45452e6i			0.437809i	−0.975746	+	0.218905i	$0.929752\pi$
$54$	−1.53842e6	+	3.84059e6i	−0.180926	+	0.451671i
$55$	278668.			0.0304534
$56$	−9.57122e6	−	1.68767e6i	−0.973230	−	0.171607i
$57$	−1.12955e6	+	1.63868e7i	−0.107005	+	1.55237i
$58$	4.52643e6	+	1.64749e6i	0.399985	+	0.145583i
$59$	−1.16111e7	−	1.38375e7i	−0.958217	−	1.14196i	−0.989801	−	0.142458i	$-0.954499\pi$
$59$	−1.16111e7	−	1.38375e7i	−0.958217	−	1.14196i	0.0315836	−	0.999501i	$-0.489945\pi$
$60$	426437.	+	410989.i	0.0329041	+	0.0317122i
$61$	1.16719e7	−	4.24821e6i	0.842987	−	0.306822i	0.115810	−	0.993271i	$-0.463054\pi$
$61$	1.16719e7	−	4.24821e6i	0.842987	−	0.306822i	0.727178	+	0.686449i	$0.240832\pi$
$62$	−7.29065e6	−	4.20926e6i	−0.493401	−	0.284865i
$63$	−5.57309e6	+	1.72687e7i	−0.353780	+	1.09622i
$64$	1.28751e6	+	2.23004e6i	0.0767418	+	0.132921i
$65$	371801.	−	443096.i	0.0208285	−	0.0248224i
$66$	1.90574e6	−	4.29181e6i	0.100436	−	0.226186i
$67$	−1.92937e6	−	1.09420e7i	−0.0957452	−	0.542998i	−0.994516	−	0.104580i	$-0.966650\pi$
$67$	−1.92937e6	−	1.09420e7i	−0.0957452	−	0.542998i	0.898771	−	0.438418i	$-0.144461\pi$
$68$	2.77138e7	−	4.88669e6i	1.29617	−	0.228549i
$69$	992009.	+	9.34915e6i	0.0437642	+	0.412454i
$70$	−617196.	−	517889.i	−0.0257058	−	0.0215697i
$71$	−2.34487e7	+	1.35381e7i	−0.922752	+	0.532751i	−0.884512	−	0.466518i	$-0.845508\pi$
$71$	−2.34487e7	+	1.35381e7i	−0.922752	+	0.532751i	−0.0382397	+	0.999269i	$0.512175\pi$
$72$	2.13599e7	−	8.67929e6i	0.794822	−	0.322964i
$73$	−1.28556e7	+	2.22665e7i	−0.452690	+	0.784082i	−0.998552	−	0.0537933i	$-0.982869\pi$
$73$	−1.28556e7	+	2.22665e7i	−0.452690	+	0.784082i	0.545862	+	0.837875i	$0.316202\pi$
$74$	5.21144e6	+	1.43183e7i	0.173792	+	0.477491i
$75$	−8.72012e6	−	3.02973e7i	−0.275599	−	0.957543i
$76$	3.03531e7	−	2.54693e7i	0.909807	−	0.763418i
$77$	7.04421e6	−	1.93538e7i	0.200387	−	0.550558i
$78$	−4.28154e6	−	8.75641e6i	−0.115670	−	0.236564i
$79$	−981583.	+	5.56684e6i	−0.0252011	+	0.142922i	−0.994812	−	0.101729i	$-0.967562\pi$
$79$	−981583.	+	5.56684e6i	−0.0252011	+	0.142922i	0.969611	+	0.244652i	$0.0786736\pi$
$80$		−	848091.i		−	0.0207054i
$81$	−1.05795e7	−	4.17264e7i	−0.245768	−	0.969329i
$82$	1.10246e7			0.243842
$83$	5.90784e6	+	1.04171e6i	0.124485	+	0.0219500i	0.235543	−	0.971864i	$-0.424313\pi$
$83$	5.90784e6	+	1.04171e6i	0.124485	+	0.0219500i	−0.111059	+	0.993814i	$0.535424\pi$
$84$	3.93233e7	−	1.92275e7i	0.789828	−	0.386195i
$85$	5.06440e6	+	1.84329e6i	0.0970179	+	0.0353116i
$86$	−1.33888e7	−	1.59561e7i	−0.244764	−	0.291698i
$87$	−4.81633e7	+	1.38623e7i	−0.840696	+	0.241968i
$88$	−2.45910e7	+	8.95039e6i	−0.410058	+	0.149249i
$89$	3.29258e7	+	1.90097e7i	0.524779	+	0.302981i	0.738888	−	0.673829i	$-0.235351\pi$
$89$	3.29258e7	+	1.90097e7i	0.524779	+	0.302981i	−0.214109	+	0.976810i	$0.568685\pi$
$90$	1.89325e6	+	262252.i	0.0288562	+	0.00399713i
$91$	−2.13751e7	−	3.70227e7i	−0.311704	−	0.539887i
$92$	1.45780e7	−	1.73734e7i	0.203491	−	0.242512i
$93$	8.71029e7	−	9.24222e6i	1.16440	−	0.123551i
$94$	7.20300e6	+	4.08503e7i	0.0922576	+	0.523219i
$95$	7.47305e6	−	1.31770e6i	0.0917495	−	0.0161779i
$96$	−7.96594e7	−	3.53720e7i	−0.937890	−	0.416462i
$97$	9.92181e6	+	8.32538e6i	0.112074	+	0.0940410i	0.697102	−	0.716972i	$-0.254472\pi$
$97$	9.92181e6	+	8.32538e6i	0.112074	+	0.0940410i	−0.585029	+	0.811013i	$0.698917\pi$
$98$	−1.27034e7	+	7.33433e6i	−0.137726	+	0.0795162i
$99$	1.02532e7	+	4.77714e7i	0.106738	+	0.497310i
$100$	−3.80261e7	+	6.58632e7i	−0.380261	+	0.658632i
$101$	2.54486e7	+	6.99195e7i	0.244556	+	0.671912i	0.999863	+	0.0165413i	$0.00526549\pi$
$101$	2.54486e7	+	6.99195e7i	0.244556	+	0.671912i	−0.755307	+	0.655371i	$0.772512\pi$
$102$	6.30231e7	−	6.53920e7i	0.582236	−	0.604121i
$103$	−3.98778e7	+	3.34615e7i	−0.354309	+	0.297301i	−0.802518	−	0.596628i	$-0.796507\pi$
$103$	−3.98778e7	+	3.34615e7i	−0.354309	+	0.297301i	0.448209	+	0.893929i	$0.352062\pi$
$104$	−1.85780e7	+	5.10426e7i	−0.158806	+	0.436315i
$105$	8.36311e6	+	576473.i	0.0688035	+	0.00474266i
$106$	4.66998e6	−	2.64848e7i	0.0369906	−	0.209784i
$107$			2.19636e8i			1.67559i	0.545986	+	0.837795i	$0.316155\pi$
$107$			2.19636e8i			1.67559i	−0.545986	+	0.837795i	$0.683845\pi$
$108$	−5.47649e7	+	8.82251e7i	−0.402538	+	0.648480i
$109$	−2.65997e8			−1.88439			−0.942194	−	0.335067i	$-0.891241\pi$
$109$	−2.65997e8			−1.88439			−0.942194	+	0.335067i	$0.891241\pi$
$110$	−2.13646e6	−	376716.i	−0.0145923	−	0.00257302i
$111$	−1.31522e8	−	8.85231e7i	−0.866376	−	0.583129i
$112$	−5.89010e7	−	2.14382e7i	−0.374326	−	0.136244i
$113$	−7.63601e6	−	9.10024e6i	−0.0468331	−	0.0558135i	0.742119	−	0.670268i	$-0.233821\pi$
$113$	−7.63601e6	−	9.10024e6i	−0.0468331	−	0.0558135i	−0.788953	+	0.614454i	$0.789376\pi$
$114$	3.08123e7	−	1.24105e8i	0.182433	−	0.734804i
$115$	4.08144e6	−	1.48552e6i	0.0233357	−	0.00849352i
$116$	1.04702e8	+	6.04498e7i	0.578260	+	0.333859i
$117$	8.96388e7	+	4.74340e7i	0.478358	+	0.253132i
$118$	7.03123e7	+	1.21785e8i	0.362663	+	0.628151i
$119$	2.56037e8	−	3.05134e8i	1.27678	−	1.52161i
$120$	−6.26928e6	−	8.61096e6i	−0.0302338	−	0.0415266i
$121$	2.75931e7	+	1.56488e8i	0.128724	+	0.730028i
$122$	−9.52276e7	+	1.67912e7i	−0.429857	+	0.0757953i
$123$	−9.27336e7	+	6.75155e7i	−0.405151	+	0.294973i
$124$	−1.61862e8	−	1.35818e8i	−0.684633	−	0.574476i
$125$	−2.52726e7	+	1.45912e7i	−0.103517	+	0.0597654i
$126$	6.60717e7	−	1.24860e8i	0.262140	−	0.495381i
$127$	−1.66357e7	+	2.88139e7i	−0.0639479	+	0.110761i	−0.896227	−	0.443596i	$-0.853702\pi$
$127$	−1.66357e7	+	2.88139e7i	−0.0639479	+	0.110761i	0.832279	+	0.554357i	$0.187036\pi$
$128$	8.73591e7	+	2.40017e8i	0.325438	+	0.894133i
$129$	2.10336e8	+	5.22211e7i	0.759546	+	0.188576i
$130$	−3.44948e6	+	2.89446e6i	−0.0120776	+	0.0101343i
$131$	1.61936e8	−	4.44915e8i	0.549867	−	1.51075i	−0.284022	−	0.958818i	$-0.591669\pi$
$131$	1.61936e8	−	4.44915e8i	0.549867	−	1.51075i	0.833890	−	0.551931i	$-0.186109\pi$
$132$	6.58107e7	−	9.77774e7i	0.216771	−	0.322064i
$133$	9.73893e7	−	5.52322e8i	0.311246	−	1.76517i
$134$			8.64974e7i			0.268277i
$135$	−1.75311e7	+	9.38846e6i	−0.0527806	+	0.0282657i
$136$	−5.06111e8			−1.47942
$137$	2.76763e8	+	4.88007e7i	0.785643	+	0.138530i	0.552057	−	0.833806i	$-0.313843\pi$
$137$	2.76763e8	+	4.88007e7i	0.785643	+	0.138530i	0.233586	+	0.972336i	$0.424954\pi$
$138$	5.03317e6	−	7.30181e7i	0.0138780	−	0.201333i
$139$	6.76410e8	+	2.46193e8i	1.81197	+	0.659503i	0.996769	+	0.0803220i	$0.0255949\pi$
$139$	6.76410e8	+	2.46193e8i	1.81197	+	0.659503i	0.815199	+	0.579180i	$0.196627\pi$
$140$	−1.29984e7	−	1.54909e7i	−0.0338360	−	0.0403242i
$141$	−3.10757e8	−	2.99500e8i	−0.786221	−	0.757739i
$142$	1.98075e8	−	7.20935e7i	0.487166	−	0.177314i
$143$	−9.96879e7	−	5.75548e7i	−0.238396	−	0.137638i
$144$	1.45386e8	−	3.12043e7i	0.338123	−	0.0725713i
$145$	1.15769e7	+	2.00518e7i	0.0261891	+	0.0453608i
$146$	1.28661e8	−	1.53332e8i	0.283162	−	0.337459i
$147$	6.19388e7	−	1.39489e8i	0.132646	−	0.298724i
$148$	6.64097e7	+	3.76628e8i	0.138415	+	0.784993i
$149$	−8.91020e8	+	1.57111e8i	−1.80777	+	0.318758i	−0.972819	−	0.231569i	$-0.925614\pi$
$149$	−8.91020e8	+	1.57111e8i	−1.80777	+	0.318758i	−0.834949	+	0.550327i	$0.814503\pi$
$150$	2.58973e7	+	2.44068e8i	0.0511552	+	0.482110i
$151$	−2.47852e8	−	2.07973e8i	−0.476744	−	0.400036i	0.372503	−	0.928031i	$-0.378500\pi$
$151$	−2.47852e8	−	2.07973e8i	−0.476744	−	0.400036i	−0.849247	+	0.527995i	$0.822944\pi$
$152$	−6.17136e8	+	3.56304e8i	−1.15613	+	0.667492i
$153$	−1.29654e8	+	9.36000e8i	−0.236603	+	1.70809i
$154$	−8.01692e7	+	1.38857e8i	−0.142536	+	0.246880i
$155$	−1.38401e7	−	3.80254e7i	−0.0239780	−	0.0658790i
$156$	−6.76656e7	−	2.35098e8i	−0.114254	−	0.396964i
$157$	5.95886e8	−	5.00008e8i	0.980764	−	0.822959i	−0.00344009	−	0.999994i	$-0.501095\pi$
$157$	5.95886e8	−	5.00008e8i	0.980764	−	0.822959i	0.984205	+	0.177035i	$0.0566506\pi$
$158$	1.50510e7	−	4.13523e7i	0.0241511	−	0.0663546i
$159$	1.22913e8	+	2.51376e8i	0.192313	+	0.393310i
$160$	−6.99213e6	+	3.96543e7i	−0.0106691	+	0.0605077i
$161$		−	3.21012e8i		−	0.477769i
$162$	2.47024e7	+	3.34206e8i	0.0358656	+	0.485237i
$163$	1.09107e9			1.54561			0.772806	−	0.634642i	$-0.218852\pi$
$163$	1.09107e9			1.54561			0.772806	+	0.634642i	$0.218852\pi$
$164$	2.72503e8	+	4.80496e7i	0.376700	+	0.0664223i
$165$	2.02778e7	−	9.91506e6i	0.0273581	−	0.0133770i
$166$	−4.38854e7	−	1.59730e7i	−0.0577947	−	0.0210355i
$167$	−8.88832e8	−	1.05927e9i	−1.14276	−	1.36188i	−0.922294	−	0.386488i	$-0.873688\pi$
$167$	−8.88832e8	−	1.05927e9i	−1.14276	−	1.36188i	−0.220462	−	0.975396i	$-0.570757\pi$
$168$	−7.56518e8	+	2.17740e8i	−0.949690	+	0.273339i
$169$	5.42016e8	−	1.97278e8i	0.664455	−	0.241842i
$170$	−3.63354e7	−	2.09782e7i	−0.0435045	−	0.0251173i
$171$	5.00851e8	+	1.23261e9i	0.585766	+	1.44158i
$172$	−2.61396e8	−	4.52751e8i	−0.298665	−	0.517303i
$173$	2.53987e7	−	3.02690e7i	0.0283548	−	0.0337920i	−0.751681	−	0.659527i	$-0.770757\pi$
$173$	2.53987e7	−	3.02690e7i	0.0283548	−	0.0337920i	0.780035	+	0.625735i	$0.215201\pi$
$174$	3.87993e8	−	4.11687e7i	0.423279	−	0.0449128i
$175$	1.86928e8	+	1.06012e9i	0.199307	+	1.13032i
$176$	−1.66212e8	+	2.93077e7i	−0.173225	+	0.0305443i
$177$	−1.33725e9	−	5.93792e8i	−1.36244	−	0.604980i
$178$	−2.26734e8	−	1.90252e8i	−0.225858	−	0.189518i
$179$	−5.49026e8	+	3.16980e8i	−0.534787	+	0.308759i	−0.742963	−	0.669332i	$-0.766580\pi$
$179$	−5.49026e8	+	3.16980e8i	−0.534787	+	0.308759i	0.208177	+	0.978091i	$0.433247\pi$
$180$	4.56537e7	+	1.47338e7i	0.0434897	+	0.0140354i
$181$	−4.29163e8	+	7.43332e8i	−0.399860	+	0.692578i	−0.993708	−	0.111999i	$-0.964275\pi$
$181$	−4.29163e8	+	7.43332e8i	−0.399860	+	0.692578i	0.593848	+	0.804577i	$0.297608\pi$
$182$	1.13827e8	+	3.12738e8i	0.103743	+	0.285033i
$183$	6.98175e8	−	7.24418e8i	0.622530	−	0.645929i
$184$	−3.12453e8	+	2.62179e8i	−0.272592	+	0.228732i
$185$	−2.50501e7	+	6.88246e7i	−0.0213857	+	0.0587567i
$186$	−6.80286e8	−	4.68924e7i	−0.568381	−	0.0391788i
$187$	1.86243e8	−	1.05624e9i	0.152305	−	0.863764i
$188$			1.04111e9i			0.833425i
$189$	2.08885e8	+	1.45488e9i	0.163705	+	1.14020i
$190$	−5.90750e7			−0.0453304
$191$	6.61152e8	+	1.16579e8i	0.496784	+	0.0875965i	0.416426	−	0.909170i	$-0.363282\pi$
$191$	6.61152e8	+	1.16579e8i	0.496784	+	0.0875965i	0.0803582	+	0.996766i	$0.474394\pi$
$192$	1.73034e8	+	1.16463e8i	0.127329	+	0.0857008i
$193$	−2.97918e7	−	1.08433e7i	−0.0214718	−	0.00781508i	0.331262	−	0.943539i	$-0.392526\pi$
$193$	−2.97918e7	−	1.08433e7i	−0.0214718	−	0.00781508i	−0.352734	+	0.935724i	$0.614748\pi$
$194$	−6.48129e7	−	7.72410e7i	−0.0457567	−	0.0545307i
$195$	1.12894e7	−	4.54715e7i	0.00780790	−	0.0314486i
$196$	−3.45964e8	+	1.25921e8i	−0.234426	+	0.0853242i
$197$	−8.67018e8	−	5.00573e8i	−0.575656	−	0.332355i	0.183749	−	0.982973i	$-0.441177\pi$
$197$	−8.67018e8	−	5.00573e8i	−0.575656	−	0.332355i	−0.759405	+	0.650618i	$0.774510\pi$
$198$	−1.40285e7	−	3.80109e8i	−0.00912747	−	0.247314i
$199$	1.45511e8	+	2.52033e8i	0.0927865	+	0.160711i	0.908683	−	0.417488i	$-0.137089\pi$
$199$	1.45511e8	+	2.52033e8i	0.0927865	+	0.160711i	−0.815896	+	0.578198i	$0.803756\pi$
$200$	8.79186e8	−	1.04777e9i	0.549491	−	0.654858i
$201$	−5.29715e8	−	7.27571e8i	−0.324532	−	0.445750i
$202$	−1.00586e8	−	5.70454e8i	−0.0604135	−	0.342622i
$203$	1.68526e9	−	2.97157e8i	0.992392	−	0.174986i
$204$	1.84278e9	−	1.34165e9i	1.06403	−	0.774675i
$205$	4.05948e7	+	3.40631e7i	0.0229856	+	0.0192872i
$206$	3.50966e8	−	2.02630e8i	0.194893	−	0.112521i
$207$	4.04830e8	+	6.45014e8i	0.220491	+	0.351308i
$208$	−1.75161e8	+	3.03388e8i	−0.0935803	+	0.162086i
$209$	−5.16496e8	−	1.41906e9i	−0.270696	−	0.743731i
$210$	−6.33381e7	−	1.57253e7i	−0.0325678	−	0.00808577i
$211$	2.57792e9	−	2.16313e9i	1.30059	−	1.09132i	0.310543	−	0.950559i	$-0.399489\pi$
$211$	2.57792e9	−	2.16313e9i	1.30059	−	1.09132i	0.990043	−	0.140762i	$-0.0449553\pi$
$212$	2.30862e8	−	6.34287e8i	0.114290	−	0.314009i
$213$	−1.22460e9	+	1.81944e9i	−0.594945	+	0.883931i
$214$	2.96913e8	−	1.68388e9i	0.141571	−	0.802890i
$215$		−	1.00121e8i		−	0.0468567i
$216$	1.24549e9	−	1.39156e9i	0.572170	−	0.639273i
$217$	−2.99076e9			−1.34879
$218$	2.03932e9	+	3.59587e8i	0.902940	+	0.159213i
$219$	−1.43215e8	+	2.07768e9i	−0.0622605	+	0.903236i
$220$	−5.11663e7	−	1.86230e7i	−0.0218420	−	0.00794985i
$221$	−1.43098e9	−	1.70538e9i	−0.599882	−	0.714911i
$222$	8.88670e8	+	8.56478e8i	0.365872	+	0.352618i
$223$	−3.84150e8	+	1.39819e8i	−0.155339	+	0.0565388i	−0.418519	−	0.908208i	$-0.637451\pi$
$223$	−3.84150e8	+	1.39819e8i	−0.155339	+	0.0565388i	0.263180	+	0.964747i	$0.415229\pi$
$224$	2.57729e9	+	1.48800e9i	1.02370	+	0.591032i
$225$	−1.71252e9	−	1.89438e9i	−0.668199	−	0.739157i
$226$	4.62409e7	+	8.00915e7i	0.0177252	+	0.0307010i
$227$	−1.70797e9	+	2.03548e9i	−0.643246	+	0.766591i	−0.984879	−	0.173243i	$-0.944575\pi$
$227$	−1.70797e9	+	2.03548e9i	−0.643246	+	0.766591i	0.341633	+	0.939833i	$0.389020\pi$
$228$	1.30250e9	−	2.93330e9i	0.481992	−	1.08547i
$229$	7.47013e8	+	4.23652e9i	0.271635	+	1.54052i	0.749451	+	0.662060i	$0.230318\pi$
$229$	7.47013e8	+	4.23652e9i	0.271635	+	1.54052i	−0.477816	+	0.878460i	$0.658571\pi$
$230$	−3.32993e7	+	5.87157e6i	−0.0118994	+	0.00209818i
$231$	−1.76026e8	−	1.65895e9i	−0.0618201	−	0.582621i
$232$	−1.66563e9	−	1.39763e9i	−0.574947	−	0.482438i
$233$	−2.49677e9	+	1.44151e9i	−0.847138	+	0.489095i	−0.859684	−	0.510826i	$-0.829340\pi$
$233$	−2.49677e9	+	1.44151e9i	−0.847138	+	0.489095i	0.0125463	+	0.999921i	$0.496006\pi$
$234$	−6.23110e8	−	4.84840e8i	−0.207827	−	0.161709i
$235$	−9.96932e7	+	1.72674e8i	−0.0326884	+	0.0566180i
$236$	1.20717e9	+	3.31667e9i	0.389153	+	1.06919i
$237$	1.26642e8	+	4.40007e8i	0.0401408	+	0.139465i
$238$	−2.37546e9	+	1.99324e9i	−0.740353	+	0.621230i
$239$	−6.28233e8	+	1.72606e9i	−0.192544	+	0.529010i	−0.997970	−	0.0636865i	$-0.979714\pi$
$239$	−6.28233e8	+	1.72606e9i	−0.192544	+	0.529010i	0.805426	+	0.592696i	$0.201936\pi$
$240$	−3.01753e7	−	6.17131e7i	−0.00909508	−	0.0186008i
$241$	−7.37356e8	+	4.18175e9i	−0.218579	+	1.23962i	0.656007	+	0.754755i	$0.272244\pi$
$241$	−7.37356e8	+	4.18175e9i	−0.218579	+	1.23962i	−0.874586	+	0.484870i	$0.838867\pi$
$242$		−	1.23705e9i		−	0.360682i
$243$	−2.25448e9	−	2.65989e9i	−0.646578	−	0.762848i
$244$	−2.42698e9			−0.684711
$245$	−6.94374e7	−	1.22437e7i	−0.0192721	−	0.00339819i
$246$	8.02231e8	−	3.92259e8i	0.219058	−	0.107111i
$247$	−2.94549e9	−	1.07207e9i	−0.791353	−	0.288029i
$248$	2.44264e9	+	2.91102e9i	0.645733	+	0.769554i
$249$	4.66961e8	−	1.34400e8i	0.121474	−	0.0349625i
$250$	2.13483e8	−	7.77013e7i	0.0546516	−	0.0198915i
$251$	6.55995e9	+	3.78739e9i	1.65274	+	0.954212i	0.975937	+	0.218052i	$0.0699704\pi$
$251$	6.55995e9	+	3.78739e9i	1.65274	+	0.954212i	0.676807	+	0.736160i	$0.263363\pi$
$252$	2.17732e9	−	2.79826e9i	0.539908	−	0.693883i
$253$	−4.32181e8	−	7.48559e8i	−0.105483	−	0.182702i
$254$	1.66493e8	−	1.98419e8i	0.0400001	−	0.0476703i
$255$	4.34106e8	−	4.60616e7i	0.102668	−	0.0108938i
$256$	−4.59760e8	−	2.60743e9i	−0.107046	−	0.607089i
$257$	−1.33863e8	+	2.36037e7i	−0.0306852	+	0.00541062i	−0.188970	−	0.981983i	$-0.560515\pi$
$257$	−1.33863e8	+	2.36037e7i	−0.0306852	+	0.00541062i	0.158285	+	0.987394i	$0.449404\pi$
$258$	−1.54198e9	−	6.84705e8i	−0.348018	−	0.154534i
$259$	4.14673e9	+	3.47952e9i	0.921525	+	0.773251i
$260$	−9.78782e7	+	5.65100e7i	−0.0214187	+	0.0123661i
$261$	−3.01148e9	+	2.72238e9i	−0.648959	+	0.586660i
$262$	−1.84297e9	+	3.19212e9i	−0.391123	+	0.677445i
$263$	−3.23234e9	−	8.88079e9i	−0.675608	−	1.85622i	−0.484899	−	0.874570i	$-0.661144\pi$
$263$	−3.23234e9	−	8.88079e9i	−0.675608	−	1.85622i	−0.190709	−	0.981647i	$-0.561079\pi$
$264$	−1.47096e9	+	1.52625e9i	−0.302820	+	0.314202i
$265$	9.90265e7	−	8.30931e7i	0.0200802	−	0.0168493i
$266$	−1.49331e9	+	4.10283e9i	−0.298279	+	0.819515i
$267$	3.07228e9	+	2.11774e8i	0.604528	+	0.0416704i
$268$	−3.76989e8	+	2.13801e9i	−0.0730784	+	0.414448i
$269$			1.18549e8i			0.0226407i	0.999936	+	0.0113204i	$0.00360346\pi$
$269$			1.18549e8i			0.0226407i	−0.999936	+	0.0113204i	$0.996397\pi$
$270$	1.47098e8	−	4.82791e7i	0.0276790	−	0.00908457i
$271$	3.58270e9			0.664252			0.332126	−	0.943235i	$-0.392234\pi$
$271$	3.58270e9			0.664252			0.332126	+	0.943235i	$0.392234\pi$
$272$	−3.21453e9	−	5.66809e8i	−0.587276	−	0.103553i
$273$	−2.87268e9	−	1.93350e9i	−0.517174	−	0.348092i
$274$	−2.05589e9	−	7.48281e8i	−0.364751	−	0.132759i
$275$	1.86314e9	+	2.22040e9i	0.325773	+	0.388241i
$276$	4.42649e8	−	1.78290e9i	0.0762822	−	0.307249i
$277$	1.39013e9	−	5.05965e8i	0.236122	−	0.0859412i	−0.221249	−	0.975217i	$-0.571013\pi$
$277$	1.39013e9	−	5.05965e8i	0.236122	−	0.0859412i	0.457371	+	0.889276i	$0.348791\pi$
$278$	−4.85301e9	−	2.80189e9i	−0.812517	−	0.469107i
$279$	6.00939e9	−	3.77167e9i	0.991775	−	0.622468i
$280$	1.81842e8	+	3.14960e8i	0.0295844	+	0.0512417i
$281$	−3.91017e9	+	4.65996e9i	−0.627149	+	0.747407i	−0.982282	−	0.187409i	$-0.939991\pi$
$281$	−3.91017e9	+	4.65996e9i	−0.627149	+	0.747407i	0.355133	+	0.934816i	$0.384435\pi$
$282$	1.97760e9	+	2.71627e9i	0.312711	+	0.429513i
$283$	−8.05969e8	−	4.57088e9i	−0.125653	−	0.712613i	−0.980918	−	0.194422i	$-0.937717\pi$
$283$	−8.05969e8	−	4.57088e9i	−0.125653	−	0.712613i	0.855265	−	0.518191i	$-0.173394\pi$
$284$	5.21016e9	−	9.18691e8i	0.800898	−	0.141220i
$285$	4.96908e8	−	3.61778e8i	0.0753176	−	0.0548357i
$286$	6.86472e8	+	5.76018e8i	0.102603	+	0.0860938i
$287$	3.39189e9	−	1.95831e9i	0.499935	−	0.288638i
$288$	−7.05512e9	+	2.60380e8i	−1.02550	+	0.0378475i
$289$	6.88348e9	−	1.19225e10i	0.986772	−	1.70914i
$290$	−6.16496e7	−	1.69381e8i	−0.00871643	−	0.0239482i
$291$	1.01820e9	+	2.52794e8i	0.141991	+	0.0352528i
$292$	3.84847e9	−	3.22925e9i	0.529366	−	0.444191i
$293$	3.86218e9	−	1.06113e10i	0.524037	−	1.43978i	−0.341952	−	0.939717i	$-0.611088\pi$
$293$	3.86218e9	−	1.06113e10i	0.524037	−	1.43978i	0.865989	−	0.500063i	$-0.166690\pi$
$294$	−6.63434e8	+	9.85688e8i	−0.0887991	+	0.131932i
$295$	−1.17377e8	+	6.65679e8i	−0.0154987	+	0.0878976i
$296$		−	6.87800e9i		−	0.895974i
$297$	2.44581e9	+	3.11137e9i	0.314338	+	0.399877i
$298$	7.04357e9			0.893158
$299$	−1.76687e9	−	3.11546e8i	−0.221065	−	0.0389797i
$300$	−4.23623e8	+	6.14565e9i	−0.0522991	+	0.758722i
$301$	−6.95353e9	−	2.53088e9i	−0.847109	−	0.308323i
$302$	1.61906e9	+	1.92952e9i	0.194642	+	0.231965i
$303$	4.33957e9	+	4.18237e9i	0.514845	+	0.496194i
$304$	−4.31874e9	+	1.57189e9i	−0.505665	+	0.184047i
$305$	−4.02526e8	−	2.32399e8i	−0.0465152	−	0.0268556i
$306$	2.25934e9	−	7.00076e9i	0.257690	−	0.798471i
$307$	1.60427e9	+	2.77868e9i	0.180603	+	0.312813i	0.942086	−	0.335372i	$-0.108862\pi$
$307$	1.60427e9	+	2.77868e9i	0.180603	+	0.312813i	−0.761483	+	0.648185i	$0.775529\pi$
$308$	−2.58678e9	+	3.08281e9i	−0.287446	+	0.342565i
$309$	−1.71123e9	+	3.85375e9i	−0.187704	+	0.422717i
$310$	5.47035e7	+	3.10239e8i	0.00592336	+	0.0335931i
$311$	−5.93601e9	+	1.04668e9i	−0.634531	+	0.111885i	−0.481656	−	0.876361i	$-0.659964\pi$
$311$	−5.93601e9	+	1.04668e9i	−0.634531	+	0.111885i	−0.152875	+	0.988245i	$0.548853\pi$
$312$	4.64242e8	+	4.37523e9i	0.0489921	+	0.461724i
$313$	2.47074e9	+	2.07320e9i	0.257425	+	0.216005i	0.762362	−	0.647151i	$-0.224040\pi$
$313$	2.47074e9	+	2.07320e9i	0.257425	+	0.216005i	−0.504937	+	0.863156i	$0.668484\pi$
$314$	−5.24441e9	+	3.02786e9i	−0.539484	+	0.311471i
$315$	6.29070e8	−	2.55613e8i	0.0638935	−	0.0259622i
$316$	5.52254e8	−	9.56532e8i	0.0553848	−	0.0959292i
$317$	1.44241e9	+	3.96300e9i	0.142841	+	0.392452i	0.990397	−	0.138254i	$-0.0441490\pi$
$317$	1.44241e9	+	3.96300e9i	0.142841	+	0.392452i	−0.847556	+	0.530706i	$0.821927\pi$
$318$	−6.02514e8	−	2.09338e9i	−0.0589195	−	0.204710i
$319$	3.52975e9	−	2.96181e9i	0.340864	−	0.286019i
$320$	3.29566e7	−	9.05476e7i	0.00314299	−	0.00863529i
$321$	7.81468e9	+	1.59822e10i	0.736023	+	1.50528i
$322$	−4.33959e8	+	2.46110e9i	−0.0403669	+	0.228932i
$323$		−	2.92059e10i		−	2.68325i
$324$	−8.46013e8	+	8.36843e9i	−0.0767709	+	0.759388i
$325$	6.01637e9			0.539264
$326$	−8.36487e9	−	1.47495e9i	−0.740609	−	0.130589i
$327$	−1.93558e10	+	9.46423e9i	−1.69286	+	0.827741i
$328$	−4.67634e9	−	1.70205e9i	−0.404028	−	0.147054i
$329$	9.47233e9	+	1.12887e10i	0.808488	+	0.963518i
$330$	−1.68868e8	+	4.86033e7i	−0.0142394	+	0.00409836i
$331$	−5.24937e9	+	1.91061e9i	−0.437316	+	0.159170i	−0.551290	−	0.834314i	$-0.685864\pi$
$331$	−5.24937e9	+	1.91061e9i	−0.437316	+	0.159170i	0.113974	+	0.993484i	$0.463642\pi$
$332$	−1.01513e9	−	5.86083e8i	−0.0835541	−	0.0482400i
$333$	−1.27201e10	−	1.76198e9i	−1.03446	−	0.143293i
$334$	5.38244e9	+	9.32265e9i	0.432507	+	0.749124i
$335$	−2.67253e8	+	3.18500e8i	−0.0212199	+	0.0252889i
$336$	−5.04883e9	+	5.35715e8i	−0.396126	+	0.0420317i
$337$	−3.28023e8	−	1.86031e9i	−0.0254322	−	0.144233i	0.969448	−	0.245299i	$-0.0788860\pi$
$337$	−3.28023e8	−	1.86031e9i	−0.0254322	−	0.144233i	−0.994880	+	0.101065i	$0.967775\pi$
$338$	−4.42217e9	+	7.79747e8i	−0.338819	+	0.0597430i
$339$	−8.79439e8	−	3.90507e8i	−0.0665897	−	0.0295686i
$340$	−8.06692e8	−	6.76895e8i	−0.0603659	−	0.0506530i
$341$	−6.97408e9	+	4.02649e9i	−0.515786	+	0.297789i
$342$	−2.17358e9	−	1.01271e10i	−0.158881	−	0.740254i
$343$	5.36623e9	−	9.29458e9i	0.387697	−	0.671511i
$344$	3.21574e9	+	8.83518e9i	0.229640	+	0.630931i
$345$	2.44139e8	−	2.53315e8i	0.0172330	−	0.0178807i
$346$	−2.35643e8	+	1.97728e8i	−0.0164418	+	0.0137963i
$347$	−4.26463e9	+	1.17170e10i	−0.294146	+	0.808160i	0.701303	+	0.712864i	$0.252602\pi$
$347$	−4.26463e9	+	1.17170e10i	−0.294146	+	0.808160i	−0.995449	+	0.0952965i	$0.969620\pi$
$348$	9.76968e9	+	6.73429e8i	0.666137	+	0.0459171i
$349$	−2.62191e9	+	1.48696e10i	−0.176733	+	1.00230i	0.759392	+	0.650633i	$0.225496\pi$
$349$	−2.62191e9	+	1.48696e10i	−0.176733	+	1.00230i	−0.936125	+	0.351667i	$0.885615\pi$
$350$		−	8.38032e9i		−	0.558455i
$351$	8.21047e9	+	2.62265e8i	0.540928	+	0.0172787i
$352$	8.01323e9			0.521960
$353$	−1.77537e10	−	3.13045e9i	−1.14338	−	0.201608i	−0.430295	−	0.902688i	$-0.641591\pi$
$353$	−1.77537e10	−	3.13045e9i	−1.14338	−	0.201608i	−0.713083	+	0.701080i	$0.752702\pi$
$354$	9.44954e9	+	6.36017e9i	0.601725	+	0.405001i
$355$	9.52100e8	+	3.46536e8i	0.0599472	+	0.0218190i
$356$	−4.77513e9	−	5.69077e9i	−0.297293	−	0.354300i
$357$	7.77437e9	−	3.13135e10i	0.478622	−	1.92779i
$358$	4.63772e9	−	1.68799e9i	0.282340	−	0.102763i
$359$	2.52845e10	+	1.45980e10i	1.52222	+	0.878852i	0.999655	+	0.0262509i	$0.00835688\pi$
$359$	2.52845e10	+	1.45980e10i	1.52222	+	0.878852i	0.522562	+	0.852602i	$0.324976\pi$
$360$	−7.62577e8	−	4.03532e8i	−0.0454019	−	0.0240252i
$361$	−1.20693e10	−	2.09046e10i	−0.710644	−	1.23087i
$362$	4.29513e9	−	5.11874e9i	0.250117	−	0.298077i
$363$	7.57575e9	+	1.04054e10i	0.436314	+	0.599284i
$364$	1.45051e9	+	8.22623e9i	0.0826255	+	0.468592i
$365$	9.47507e8	−	1.67071e8i	0.0533840	−	0.00941304i
$366$	−6.33200e9	+	4.61007e9i	−0.352872	+	0.256911i
$367$	6.35266e9	+	5.33051e9i	0.350180	+	0.293836i	0.800862	−	0.598849i	$-0.204375\pi$
$367$	6.35266e9	+	5.33051e9i	0.350180	+	0.293836i	−0.450682	+	0.892684i	$0.648819\pi$
$368$	−2.27815e9	+	1.31529e9i	−0.124220	+	0.0717184i
$369$	−4.34573e9	+	8.21239e9i	−0.234400	+	0.442959i
$370$	2.85092e8	−	4.93794e8i	0.0152117	−	0.0263475i
$371$	−3.26771e9	−	8.97795e9i	−0.172483	−	0.473894i
$372$	−1.66107e10	−	4.12401e9i	−0.867392	−	0.215352i
$373$	−2.11366e10	+	1.77357e10i	−1.09194	+	0.916248i	−0.996857	−	0.0792207i	$-0.974757\pi$
$373$	−2.11366e10	+	1.77357e10i	−1.09194	+	0.916248i	−0.0950853	+	0.995469i	$0.530312\pi$
$374$	−2.85574e9	+	7.84608e9i	−0.145960	+	0.401020i
$375$	−1.31986e9	+	1.96096e9i	−0.0667425	+	0.0991618i
$376$	3.25139e9	−	1.84396e10i	0.162674	−	0.922570i
$377$		−	9.56417e9i		−	0.473458i
$378$	3.65313e8	−	1.14365e10i	0.0178936	−	0.560178i
$379$	2.32513e10			1.12691			0.563457	−	0.826145i	$-0.309471\pi$
$379$	2.32513e10			1.12691			0.563457	+	0.826145i	$0.309471\pi$
$380$	−1.46019e9	−	2.57471e8i	−0.0700286	−	0.0123479i
$381$	−1.85327e8	+	2.68861e9i	−0.00879505	+	0.127593i
$382$	−4.91126e9	−	1.78755e9i	−0.230642	−	0.0839470i
$383$	3.20145e9	+	3.81534e9i	0.148782	+	0.177312i	0.835288	−	0.549812i	$-0.185301\pi$
$383$	3.20145e9	+	3.81534e9i	0.148782	+	0.177312i	−0.686506	+	0.727124i	$0.740856\pi$
$384$	1.48967e10	+	1.43571e10i	0.685119	+	0.660300i
$385$	−7.24228e8	+	2.63597e8i	−0.0329634	+	0.0119977i
$386$	2.13746e8	+	1.23406e8i	0.00962829	+	0.00555890i
$387$	1.71635e10	−	3.68382e9i	0.765179	−	0.164231i
$388$	−1.26537e9	−	2.19169e9i	−0.0558331	−	0.0967057i
$389$	6.62163e9	−	7.89136e9i	0.289179	−	0.344630i	−0.601823	−	0.798630i	$-0.705559\pi$
$389$	6.62163e9	−	7.89136e9i	0.289179	−	0.344630i	0.891002	+	0.453999i	$0.150003\pi$
$390$	−1.48023e8	+	3.33355e8i	−0.00639840	+	0.0144095i
$391$	−2.90283e9	−	1.64628e10i	−0.124198	−	0.704361i
$392$	6.52075e9	−	1.14978e9i	0.276155	−	0.0486936i
$393$	−4.04659e9	−	3.81369e10i	−0.169636	−	1.59873i
$394$	5.97047e9	+	5.00982e9i	0.247756	+	0.207892i
$395$	1.83188e8	−	1.05764e8i	0.00752503	−	0.00434458i
$396$	1.30991e9	−	9.45654e9i	0.0532673	−	0.384549i
$397$	−1.12454e10	+	1.94777e10i	−0.452704	+	0.784107i	−0.998553	−	0.0537771i	$-0.982874\pi$
$397$	−1.12454e10	+	1.94777e10i	−0.452704	+	0.784107i	0.545849	+	0.837884i	$0.316207\pi$
$398$	−7.74882e8	−	2.12897e9i	−0.0308818	−	0.0848472i
$399$	−1.25650e10	−	4.36560e10i	−0.495760	−	1.72247i
$400$	6.75753e9	−	5.67024e9i	0.263966	−	0.221494i
$401$	−1.26623e10	+	3.47894e10i	−0.489705	+	1.34545i	0.411242	+	0.911526i	$0.365095\pi$
$401$	−1.26623e10	+	3.47894e10i	−0.489705	+	1.34545i	−0.900947	+	0.433928i	$0.857127\pi$
$402$	3.07760e9	+	6.29416e9i	0.117844	+	0.241009i
$403$	−2.90258e9	+	1.64613e10i	−0.110043	+	0.624086i
$404$		−	1.45386e10i		−	0.545756i
$405$	−9.41645e8	+	1.30693e9i	−0.0349999	+	0.0485772i
$406$	−1.33221e10			−0.490308
$407$	1.43542e10	+	2.53103e9i	0.523119	+	0.0922400i
$408$	−3.68282e10	+	1.80075e10i	−1.32905	+	0.649851i
$409$	−1.04727e10	−	3.81173e9i	−0.374251	−	0.136216i	0.148044	−	0.988981i	$-0.452702\pi$
$409$	−1.04727e10	−	3.81173e9i	−0.374251	−	0.136216i	−0.522296	+	0.852764i	$0.674924\pi$
$410$	−2.65180e8	−	3.16029e8i	−0.00938438	−	0.0111839i
$411$	2.18756e10	−	6.29620e9i	0.766641	−	0.220654i
$412$	9.55817e9	−	3.47889e9i	0.331731	−	0.120740i
$413$	4.32652e10	+	2.49792e10i	1.48709	+	0.858574i
$414$	−2.23175e9	−	5.49240e9i	−0.0759705	−	0.186965i
$415$	−1.12242e8	−	1.94409e8i	−0.00378411	−	0.00655428i
$416$	1.06913e10	−	1.27414e10i	0.356992	−	0.425447i
$417$	5.79800e10	−	6.15207e9i	1.91749	−	0.203459i
$418$	2.04147e9	+	1.15777e10i	0.0668709	+	0.379244i
$419$	2.88812e10	−	5.09254e9i	0.937044	−	0.165226i	0.315784	−	0.948831i	$-0.397732\pi$
$419$	2.88812e10	−	5.09254e9i	0.937044	−	0.165226i	0.621259	+	0.783605i	$0.286621\pi$
$420$	−1.49703e9	−	6.64743e8i	−0.0481098	−	0.0213627i
$421$	−3.97225e10	−	3.33311e10i	−1.26447	−	1.06102i	−0.995191	−	0.0979530i	$-0.968771\pi$
$421$	−3.97225e10	−	3.33311e10i	−1.26447	−	1.06102i	−0.269278	−	0.963062i	$-0.586785\pi$
$422$	−2.26883e10	+	1.30991e10i	−0.715406	+	0.413040i
$423$	−3.32691e10	−	1.07369e10i	−1.03915	−	0.335365i
$424$	−6.06976e9	+	1.05131e10i	−0.187805	+	0.325288i
$425$	1.91728e10	+	5.26768e10i	0.587664	+	1.61459i
$426$	1.18483e10	−	1.22936e10i	0.359763	−	0.373285i
$427$	−2.63155e10	+	2.20813e10i	−0.791590	+	0.664223i
$428$	1.46780e10	−	4.03274e10i	0.437412	−	1.20178i
$429$	−9.30181e9	−	6.41178e8i	−0.274624	−	0.0189299i
$430$	−1.35348e8	+	7.67598e8i	−0.00395894	+	0.0224523i
$431$			2.99834e9i			0.0868905i	0.999056	+	0.0434452i	$0.0138334\pi$
$431$			2.99834e9i			0.0868905i	−0.999056	+	0.0434452i	$0.986167\pi$
$432$	9.46909e9	−	7.44353e9i	0.271878	−	0.213719i
$433$	−6.72699e10			−1.91368			−0.956839	−	0.290617i	$-0.906139\pi$
$433$	−6.72699e10			−1.91368			−0.956839	+	0.290617i	$0.906139\pi$
$434$	2.29293e10	+	4.04305e9i	0.646296	+	0.113959i
$435$	1.55586e9	+	1.04720e9i	0.0434525	+	0.0292464i
$436$	4.88398e10	+	1.77762e10i	1.35154	+	0.491919i
$437$	−1.51295e10	−	1.80306e10i	−0.414856	−	0.494406i
$438$	3.90668e9	−	1.57353e10i	0.106148	−	0.427542i
$439$	−4.83773e10	+	1.76079e10i	−1.30252	+	0.474078i	−0.897816	−	0.440371i	$-0.854847\pi$
$439$	−4.83773e10	+	1.76079e10i	−1.30252	+	0.474078i	−0.404702	+	0.914449i	$0.632625\pi$
$440$	8.48067e8	+	4.89631e8i	0.0226266	+	0.0130635i
$441$	−4.55943e8	−	1.23540e10i	−0.0120547	−	0.326628i
$442$	8.66551e9	+	1.50091e10i	0.227041	+	0.393247i
$443$	−1.96213e10	+	2.33837e10i	−0.509463	+	0.607154i	−0.958056	−	0.286582i	$-0.907481\pi$
$443$	−1.96213e10	+	2.33837e10i	−0.509463	+	0.607154i	0.448593	+	0.893736i	$0.351925\pi$
$444$	1.82329e10	+	2.50432e10i	0.469164	+	0.644404i
$445$	−2.47050e8	−	1.40109e9i	−0.00630006	−	0.0357294i
$446$	3.13417e9	−	5.52639e8i	0.0792107	−	0.0139670i
$447$	−5.92469e10	+	4.31352e10i	−1.48401	+	1.08044i
$448$	−5.45556e9	−	4.57776e9i	−0.135434	−	0.113642i
$449$	−4.45495e10	+	2.57207e10i	−1.09612	+	0.632845i	−0.935199	−	0.354123i	$-0.884780\pi$
$449$	−4.45495e10	+	2.57207e10i	−1.09612	+	0.632845i	−0.160920	+	0.986967i	$0.551446\pi$
$450$	1.05685e10	+	1.68387e10i	0.257728	+	0.410637i
$451$	5.27297e9	−	9.13304e9i	0.127453	−	0.220754i
$452$	7.93894e8	+	2.18121e9i	0.0190199	+	0.0522568i
$453$	−2.54352e10	−	6.31493e9i	−0.604008	−	0.149960i
$454$	1.58462e10	−	1.32965e10i	0.372993	−	0.312978i
$455$	−5.47140e8	+	1.50325e9i	−0.0127659	+	0.0350741i
$456$	−3.22298e10	+	4.78851e10i	−0.745416	+	1.10749i
$457$	1.83947e9	−	1.04321e10i	0.0421723	−	0.239171i	−0.956434	−	0.291949i	$-0.905696\pi$
$457$	1.83947e9	−	1.04321e10i	0.0421723	−	0.239171i	0.998606	+	0.0527778i	$0.0168075\pi$
$458$		−	3.34900e10i		−	0.761120i
$459$	2.38686e10	+	7.27231e10i	0.537744	+	1.63841i
$460$	−8.48670e8			−0.0189543
$461$	−1.61670e10	−	2.85068e9i	−0.357953	−	0.0631168i	−0.00822026	−	0.999966i	$-0.502617\pi$
$461$	−1.61670e10	−	2.85068e9i	−0.357953	−	0.0631168i	−0.349733	+	0.936849i	$0.613728\pi$
$462$	−8.93109e8	+	1.29567e10i	−0.0196036	+	0.284397i
$463$	2.17181e10	+	7.90475e9i	0.472605	+	0.172014i	0.567332	−	0.823489i	$-0.307976\pi$
$463$	2.17181e10	+	7.90475e9i	0.472605	+	0.172014i	−0.0947270	+	0.995503i	$0.530198\pi$
$464$	−9.01393e9	−	1.07424e10i	−0.194465	−	0.231755i
$465$	−2.36006e9	−	2.27456e9i	−0.0504790	−	0.0486504i
$466$	2.10906e10	−	7.67637e9i	0.447246	−	0.162784i
$467$	3.17397e10	+	1.83249e10i	0.667322	+	0.385278i	0.795061	−	0.606529i	$-0.207439\pi$
$467$	3.17397e10	+	1.83249e10i	0.667322	+	0.385278i	−0.127739	+	0.991808i	$0.540772\pi$
$468$	−1.32887e10	−	1.46998e10i	−0.277012	−	0.306429i
$469$	1.53645e10	+	2.66121e10i	0.317562	+	0.550033i
$470$	9.97745e8	−	1.18907e9i	0.0204469	−	0.0243677i
$471$	2.55705e10	−	5.75859e10i	0.519584	−	1.17013i
$472$	−1.10227e10	−	6.25128e10i	−0.222085	−	1.25951i
$473$	−1.96221e10	+	3.45990e9i	−0.392013	+	0.0691225i
$474$	−3.76107e8	−	3.54460e9i	−0.00745071	−	0.0702189i
$475$	6.04633e10	+	5.07348e10i	1.18773	+	0.996624i
$476$	−6.74029e10	+	3.89151e10i	−1.31296	+	0.758036i
$477$	1.78880e10	+	1.39186e10i	0.345532	+	0.268858i
$478$	7.14984e9	−	1.23839e10i	0.136957	−	0.237217i
$479$	−3.04605e10	−	8.36895e10i	−0.578622	−	1.58975i	−0.790505	−	0.612456i	$-0.790182\pi$
$479$	−3.04605e10	−	8.36895e10i	−0.578622	−	1.58975i	0.211883	−	0.977295i	$-0.432040\pi$
$480$	9.02114e8	+	3.13431e9i	0.0169940	+	0.0590442i
$481$	2.31759e10	−	1.94469e10i	0.432969	−	0.363304i
$482$	1.13062e10	−	3.10634e10i	0.209473	−	0.575521i
$483$	−1.14217e10	−	2.33591e10i	−0.209866	−	0.429208i
$484$	5.39153e9	−	3.05769e10i	0.0982495	−	0.557200i
$485$		−	4.84670e8i		−	0.00875949i
$486$	1.36886e10	+	2.34403e10i	0.245366	+	0.420162i
$487$	−2.06487e10			−0.367093			−0.183547	−	0.983011i	$-0.558758\pi$
$487$	−2.06487e10			−0.367093			−0.183547	+	0.983011i	$0.558758\pi$
$488$	4.29852e10	+	7.57945e9i	0.757948	+	0.133647i
$489$	7.93937e10	−	3.88204e10i	1.38851	−	0.678929i
$490$	5.15804e8	+	1.87737e8i	0.00894748	+	0.00325662i
$491$	−1.51222e10	−	1.80220e10i	−0.260190	−	0.310082i	0.620096	−	0.784526i	$-0.287094\pi$
$491$	−1.51222e10	−	1.80220e10i	−0.260190	−	0.310082i	−0.880286	+	0.474444i	$0.842649\pi$
$492$	2.15388e10	−	6.19928e9i	0.367588	−	0.105799i
$493$	8.37397e10	−	3.04788e10i	1.41757	−	0.515953i
$494$	2.11329e10	+	1.22011e10i	0.354856	+	0.204876i
$495$	1.12278e9	−	1.44298e9i	0.0187013	−	0.0240347i
$496$	1.22541e10	+	2.12248e10i	0.202468	+	0.350684i
$497$	4.81347e10	−	5.73647e10i	0.788919	−	0.940198i
$498$	−3.76174e9	+	3.99146e8i	−0.0611605	+	0.00648955i
$499$	4.39743e9	+	2.49391e10i	0.0709246	+	0.402233i	0.999515	+	0.0311280i	$0.00990996\pi$
$499$	4.39743e9	+	2.49391e10i	0.0709246	+	0.402233i	−0.928591	+	0.371105i	$0.878979\pi$
$500$	5.61543e9	−	9.90152e8i	0.0898469	−	0.0158424i
$501$	−1.02367e11	−	4.54550e10i	−1.62483	−	0.721491i
$502$	−4.51732e10	−	3.79048e10i	−0.711322	−	0.596870i
$503$	−8.07649e10	+	4.66296e10i	−1.26168	+	0.728434i	−0.973400	−	0.229111i	$-0.926418\pi$
$503$	−8.07649e10	+	4.66296e10i	−1.26168	+	0.728434i	−0.288284	+	0.957545i	$0.593085\pi$
$504$	−4.73023e10	+	4.27614e10i	−0.733095	+	0.662719i
$505$	1.39217e9	−	2.41130e9i	0.0214055	−	0.0370754i
$506$	2.30146e9	+	6.32322e9i	0.0351077	+	0.0964575i
$507$	3.24218e10	−	3.36404e10i	0.490687	−	0.509131i
$508$	4.98009e9	−	4.17879e9i	0.0747795	−	0.0627474i
$509$	2.18961e10	−	6.01590e10i	0.326208	−	0.896250i	−0.662854	−	0.748749i	$-0.730655\pi$
$509$	2.18961e10	−	6.01590e10i	0.326208	−	0.896250i	0.989062	−	0.147501i	$-0.0471230\pi$
$510$	−3.39043e9	−	2.33704e8i	−0.0501157	−	0.00345450i
$511$	1.23480e10	−	7.00288e10i	0.181097	−	1.02705i
$512$		−	4.47759e10i		−	0.651575i
$513$	8.03019e10	+	7.18728e10i	1.15946	+	1.03776i
$514$	1.05820e9			0.0151605
$515$	1.91839e9	+	3.38265e8i	0.0272715	+	0.00480870i
$516$	−3.51300e10	−	2.36448e10i	−0.495540	−	0.333532i
$517$	3.72863e10	+	1.35711e10i	0.521900	+	0.189956i
$518$	−2.70880e10	−	3.22822e10i	−0.376234	−	0.448378i
$519$	7.71211e8	−	3.10628e9i	0.0106293	−	0.0428125i
$520$	1.91004e9	−	6.95197e8i	0.0261233	−	0.00950812i
$521$	9.62836e10	+	5.55894e10i	1.30678	+	0.754468i	0.981557	−	0.191170i	$-0.0612283\pi$
$521$	9.62836e10	+	5.55894e10i	1.30678	+	0.754468i	0.325220	+	0.945638i	$0.394562\pi$
$522$	2.67683e10	−	1.68006e10i	0.360528	−	0.226278i
$523$	−3.92357e10	−	6.79583e10i	−0.524415	−	0.908313i	−0.999596	−	0.0284250i	$-0.990951\pi$
$523$	−3.92357e10	−	6.79583e10i	−0.524415	−	0.908313i	0.475181	−	0.879888i	$-0.342383\pi$
$524$	−5.94663e10	+	7.08692e10i	−0.788761	+	0.940009i
$525$	5.13215e10	+	7.04909e10i	0.675557	+	0.927888i
$526$	1.27759e10	+	7.24560e10i	0.166898	+	0.946523i
$527$	−1.53378e11	+	2.70447e10i	−1.98848	+	0.350622i
$528$	−1.10520e10	+	8.04649e9i	−0.142202	+	0.103531i
$529$	4.96694e10	+	4.16776e10i	0.634259	+	0.532206i
$530$	−8.71535e8	+	5.03181e8i	−0.0110454	+	0.00637706i
$531$	−1.18435e11	+	4.37101e9i	−1.48971	+	0.0549798i
$532$	−5.47927e10	+	9.49037e10i	−0.684031	+	1.18478i
$533$	−7.48676e9	−	2.05697e10i	−0.0927651	−	0.254870i
$534$	−2.32680e10	−	5.77686e9i	−0.286150	−	0.0710439i
$535$	6.29601e9	−	5.28298e9i	0.0768512	−	0.0644858i
$536$	1.33540e10	−	3.66898e10i	0.161790	−	0.444514i
$537$	−2.86728e10	+	4.26002e10i	−0.344804	+	0.512288i
$538$	1.60261e8	−	9.08883e8i	0.00191292	−	0.0108487i
$539$			1.40317e10i			0.166248i
$540$	3.84632e9	−	5.52237e8i	0.0452345	−	0.00649457i
$541$	5.30837e10			0.619687			0.309844	−	0.950788i	$-0.399723\pi$
$541$	5.30837e10			0.619687			0.309844	+	0.950788i	$0.399723\pi$
$542$	−2.74675e10	−	4.84326e9i	−0.318289	−	0.0561229i
$543$	−4.78100e9	+	6.93598e10i	−0.0549946	+	0.797827i
$544$	1.45629e11	+	5.30047e10i	1.66285	+	0.605228i
$545$	6.39813e9	+	7.62499e9i	0.0725215	+	0.0864278i
$546$	1.94102e10	+	1.87070e10i	0.218403	+	0.210491i
$547$	2.28786e10	−	8.32712e9i	0.255552	−	0.0930134i	−0.211067	−	0.977472i	$-0.567694\pi$
$547$	2.28786e10	−	8.32712e9i	0.255552	−	0.0930134i	0.466620	+	0.884458i	$0.345472\pi$
$548$	−4.75553e10	−	2.74560e10i	−0.527323	−	0.304450i
$549$	2.50292e10	−	7.75550e10i	0.275523	−	0.853730i
$550$	−1.12825e10	−	1.95418e10i	−0.123297	−	0.213557i
$551$	8.06525e10	−	9.61180e10i	0.875007	−	1.04279i
$552$	−1.34079e10	+	3.01952e10i	−0.144412	+	0.325223i
$553$	−2.71475e9	−	1.53961e10i	−0.0290288	−	0.164631i
$554$	−1.13417e10	+	1.99984e9i	−0.120403	+	0.0212303i
$555$	6.25973e8	+	5.89946e9i	0.00659756	+	0.0621785i
$556$	−1.07743e11	−	9.04073e10i	−1.12743	−	0.946028i
$557$	−5.15104e10	+	2.97396e10i	−0.535149	+	0.308968i	−0.743111	−	0.669169i	$-0.766650\pi$
$557$	−5.15104e10	+	2.97396e10i	−0.535149	+	0.308968i	0.207962	+	0.978137i	$0.433317\pi$
$558$	−5.11709e10	+	2.07925e10i	−0.527820	+	0.214472i
$559$	−2.06786e10	+	3.58164e10i	−0.211775	+	0.366804i
$560$	8.02227e8	+	2.20410e9i	0.00815728	+	0.0224119i
$561$	−2.40288e10	−	8.34859e10i	−0.242594	−	0.842872i
$562$	3.62776e10	−	3.04406e10i	0.363659	−	0.305146i
$563$	−8.78895e9	+	2.41474e10i	−0.0874789	+	0.240346i	−0.975716	−	0.219039i	$-0.929708\pi$
$563$	−8.78895e9	+	2.41474e10i	−0.0874789	+	0.240346i	0.888237	+	0.459385i	$0.151930\pi$
$564$	3.70431e10	+	7.57588e10i	0.366092	+	0.748715i
$565$	−7.71931e7	+	4.37784e8i	−0.000757503	+	0.00429601i
$566$			3.61331e10i			0.352078i
$567$	6.69650e10	+	9.84352e10i	0.647911	+	0.952398i
$568$	−9.51482e10			−0.914128
$569$	1.36983e11	+	2.41538e10i	1.30683	+	0.230429i	0.783334	−	0.621601i	$-0.213517\pi$
$569$	1.36983e11	+	2.41538e10i	1.30683	+	0.230429i	0.523493	+	0.852030i	$0.324629\pi$
$570$	−4.29871e9	+	2.10190e9i	−0.0407229	+	0.0199119i
$571$	−3.21798e10	−	1.17125e10i	−0.302719	−	0.110181i	0.186195	−	0.982513i	$-0.440384\pi$
$571$	−3.21798e10	−	1.17125e10i	−0.302719	−	0.110181i	−0.488913	+	0.872332i	$0.662607\pi$
$572$	1.44574e10	+	1.72297e10i	0.135054	+	0.160951i
$573$	5.22580e10	−	1.50408e10i	0.484768	−	0.139525i
$574$	−2.86519e10	+	1.04284e10i	−0.263940	+	0.0960664i
$575$	3.91245e10	+	2.25886e10i	0.357913	+	0.206641i
$576$	1.67350e10	+	2.31811e9i	0.152032	+	0.0210593i
$577$	−4.06482e10	−	7.04048e10i	−0.366723	−	0.635183i	0.622328	−	0.782756i	$-0.286187\pi$
$577$	−4.06482e10	−	7.04048e10i	−0.366723	−	0.635183i	−0.989051	+	0.147574i	$0.952854\pi$
$578$	−6.88910e10	+	8.21011e10i	−0.617236	+	0.735593i
$579$	−2.55367e9	+	2.70962e8i	−0.0227222	+	0.00241098i
$580$	−7.85604e8	−	4.45538e9i	−0.00694212	−	0.0393707i
$581$	−1.63392e10	+	2.88105e9i	−0.143393	+	0.0252840i
$582$	−7.46449e9	−	3.31454e9i	−0.0650591	−	0.0288889i
$583$	−1.97070e10	−	1.65361e10i	−0.170587	−	0.143139i
$584$	−7.82466e10	+	4.51757e10i	−0.672689	+	0.388377i
$585$	−7.96388e8	−	3.71051e9i	−0.00679988	−	0.0316818i
$586$	−4.39549e10	+	7.61322e10i	−0.372750	+	0.645621i
$587$	1.12180e10	+	3.08212e10i	0.0944850	+	0.259595i	0.977928	−	0.208944i	$-0.0670026\pi$
$587$	1.12180e10	+	3.08212e10i	0.0944850	+	0.259595i	−0.883443	+	0.468539i	$0.844780\pi$
$588$	−2.06945e10	+	2.14724e10i	−0.173119	+	0.179626i
$589$	−1.67985e11	+	1.40956e11i	−1.39576	+	1.17118i
$590$	1.79979e9	−	4.94489e9i	0.0148530	−	0.0408083i
$591$	−8.09008e10	−	5.57653e9i	−0.663137	−	0.0457103i
$592$	7.70288e9	−	4.36852e10i	0.0627142	−	0.355670i
$593$		−	1.79096e11i		−	1.44833i	−0.689628	−	0.724164i	$-0.742226\pi$
$593$		−	1.79096e11i		−	1.44833i	0.689628	−	0.724164i	$-0.257774\pi$
$594$	−1.45452e10	−	2.71603e10i	−0.116835	−	0.218167i
$595$	−1.49054e10			−0.118926
$596$	1.74100e11	+	3.06986e10i	1.37979	+	0.243295i
$597$	1.95558e10	+	1.31624e10i	0.153950	+	0.103618i
$598$	1.31249e10	+	4.77706e9i	0.102634	+	0.0373557i
$599$	−3.31382e10	−	3.94926e10i	−0.257408	−	0.306767i	0.621828	−	0.783154i	$-0.286390\pi$
$599$	−3.31382e10	−	3.94926e10i	−0.257408	−	0.306767i	−0.879235	+	0.476387i	$0.841946\pi$
$600$	2.66958e10	−	1.07525e11i	0.205986	−	0.829669i
$601$	−1.52122e10	+	5.53680e9i	−0.116599	+	0.0424386i	−0.399661	−	0.916663i	$-0.630872\pi$
$601$	−1.52122e10	+	5.53680e9i	−0.116599	+	0.0424386i	0.283062	+	0.959102i	$0.408650\pi$
$602$	4.98893e10	+	2.88036e10i	0.379858	+	0.219311i
$603$	−6.44329e10	−	3.40959e10i	−0.487347	−	0.257889i
$604$	3.16097e10	+	5.47497e10i	0.237505	+	0.411371i
$605$	3.82214e9	−	4.55504e9i	0.0285289	−	0.0339994i
$606$	−2.76163e10	−	3.79314e10i	−0.204774	−	0.281260i
$607$	6.49937e9	+	3.68597e10i	0.0478758	+	0.271517i	0.999343	−	0.0362316i	$-0.0115354\pi$
$607$	6.49937e9	+	3.68597e10i	0.0478758	+	0.271517i	−0.951468	+	0.307749i	$0.900424\pi$
$608$	2.14892e11	−	3.78912e10i	1.57255	−	0.277283i
$609$	1.12059e11	−	8.15853e10i	0.814660	−	0.593120i
$610$	2.77188e9	+	2.32588e9i	0.0200196	+	0.0167984i
$611$	7.13266e10	−	4.11804e10i	0.511784	−	0.295479i
$612$	8.63575e10	−	1.63195e11i	0.615594	−	1.16332i
$613$	1.05930e11	−	1.83475e11i	0.750197	−	1.29938i	−0.197530	−	0.980297i	$-0.563292\pi$
$613$	1.05930e11	−	1.83475e11i	0.750197	−	1.29938i	0.947727	−	0.319083i	$-0.103375\pi$
$614$	−8.54311e9	−	2.34720e10i	−0.0601094	−	0.165149i
$615$	4.16594e9	+	1.03430e9i	0.0291214	+	0.00723012i
$616$	5.54431e10	−	4.65223e10i	0.385057	−	0.323101i
$617$	−5.33383e10	+	1.46546e11i	−0.368043	+	1.01119i	0.608062	+	0.793889i	$0.291947\pi$
$617$	−5.33383e10	+	1.46546e11i	−0.368043	+	1.01119i	−0.976105	+	0.217300i	$0.930275\pi$
$618$	1.83291e10	−	2.72323e10i	0.125657	−	0.186694i
$619$	7.73618e9	−	4.38741e10i	0.0526944	−	0.298845i	−0.947059	−	0.321060i	$-0.895961\pi$
$619$	7.73618e9	−	4.38741e10i	0.0526944	−	0.298845i	0.999753	+	0.0222154i	$0.00707198\pi$
$620$			7.90678e9i			0.0535098i
$621$	5.24081e10	+	3.25318e10i	0.352397	+	0.218747i
$622$	4.69245e10			0.313501
$623$	−1.03552e11	−	1.82591e10i	−0.687397	−	0.121207i
$624$	−1.95135e9	+	2.83089e10i	−0.0128705	+	0.186718i
$625$	−1.41846e11	−	5.16276e10i	−0.929599	−	0.338346i
$626$	−1.61398e10	−	1.92347e10i	−0.105100	−	0.125253i
$627$	−8.80744e10	−	8.48838e10i	−0.569875	−	0.549231i
$628$	−1.42826e11	+	5.19844e10i	−0.918266	+	0.334221i
$629$	2.44125e11	+	1.40946e11i	1.55959	+	0.900429i
$630$	−5.16844e9	+	1.10930e9i	−0.0328093	+	0.00704187i
$631$	9.52325e10	+	1.64948e11i	0.600714	+	1.04047i	0.992713	+	0.120502i	$0.0384503\pi$
$631$	9.52325e10	+	1.64948e11i	0.600714	+	1.04047i	−0.391999	+	0.919966i	$0.628216\pi$
$632$	−1.27684e10	+	1.52168e10i	−0.0800330	+	0.0953796i
$633$	1.10623e11	−	2.49128e11i	0.689017	−	1.55170i
$634$	−5.70119e9	−	3.23330e10i	−0.0352865	−	0.200120i
$635$	1.22612e9	−	2.16198e8i	0.00754114	−	0.00132971i
$636$	−5.76896e9	−	5.43693e10i	−0.0352589	−	0.332296i
$637$	2.23111e10	+	1.87213e10i	0.135508	+	0.113704i
$638$	−3.10655e10	+	1.79357e10i	−0.187497	+	0.108252i
$639$	−2.43747e10	+	1.75967e11i	−0.146196	+	1.05542i
$640$	4.77898e9	−	8.27744e9i	0.0284850	−	0.0493374i
$641$	−1.00079e10	−	2.74965e10i	−0.0592804	−	0.162871i	0.906517	−	0.422169i	$-0.138731\pi$
$641$	−1.00079e10	−	2.74965e10i	−0.0592804	−	0.162871i	−0.965797	+	0.259298i	$0.916509\pi$
$642$	−3.83073e10	−	1.33095e11i	−0.225497	−	0.783470i
$643$	−8.94608e10	+	7.50665e10i	−0.523346	+	0.439139i	−0.865796	−	0.500397i	$-0.833188\pi$
$643$	−8.94608e10	+	7.50665e10i	−0.523346	+	0.439139i	0.342450	+	0.939536i	$0.388743\pi$
$644$	−2.14528e10	+	5.89412e10i	−0.124721	+	0.342670i
$645$	−3.56233e9	−	7.28552e9i	−0.0205824	−	0.0420941i
$646$	−3.94819e10	+	2.23913e11i	−0.226708	+	1.28573i
$647$		−	2.25850e11i		−	1.28885i	−0.764667	−	0.644425i	$-0.777097\pi$
$647$		−	2.25850e11i		−	1.28885i	0.764667	−	0.644425i	$-0.222903\pi$
$648$	4.11186e10	−	1.45574e11i	0.233205	−	0.825629i
$649$	1.34518e11			0.758234
$650$	−4.61257e10	−	8.13321e9i	−0.258398	−	0.0455626i
$651$	−2.17629e11	+	1.06412e11i	−1.21169	+	0.592471i
$652$	−2.00331e11	−	7.29146e10i	−1.10856	−	0.403482i
$653$	1.81964e11	+	2.16856e11i	1.00077	+	1.19267i	0.981227	+	0.192858i	$0.0617757\pi$
$653$	1.81964e11	+	2.16856e11i	1.00077	+	1.19267i	0.0195398	+	0.999809i	$0.493780\pi$
$654$	1.61189e11	−	4.63933e10i	0.881100	−	0.253597i
$655$	−1.66489e10	+	6.05972e9i	−0.0904526	+	0.0329221i
$656$	−2.77953e10	−	1.60476e10i	−0.150092	−	0.0866554i
$657$	6.35028e10	+	1.56282e11i	0.340825	+	0.838779i
$658$	−5.73610e10	−	9.93521e10i	−0.305994	−	0.529997i
$659$	3.52316e10	−	4.19873e10i	0.186806	−	0.222626i	−0.664511	−	0.747278i	$-0.731360\pi$
$659$	3.52316e10	−	4.19873e10i	0.186806	−	0.222626i	0.851317	+	0.524652i	$0.175805\pi$
$660$	−4.38583e9	+	4.65367e8i	−0.0231141	+	0.00245256i
$661$	−1.81789e10	−	1.03098e11i	−0.0952276	−	0.540063i	−0.994677	−	0.103038i	$-0.967144\pi$
$661$	−1.81789e10	−	1.03098e11i	−0.0952276	−	0.540063i	0.899450	−	0.437024i	$-0.143968\pi$
$662$	4.28282e10	−	7.55176e9i	0.222996	−	0.0393202i
$663$	−1.64806e11	−	7.31808e10i	−0.852943	−	0.378742i
$664$	1.61490e10	+	1.35506e10i	0.0830753	+	0.0697085i
$665$	−1.81753e10	+	1.04935e10i	−0.0929381	+	0.0536578i
$666$	9.51396e10	+	3.07043e10i	0.483576	+	0.156064i
$667$	3.59088e10	−	6.21959e10i	0.181425	−	0.314238i
$668$	9.24093e10	+	2.53892e11i	0.464098	+	1.27510i
$669$	−2.29787e10	+	2.38424e10i	−0.114715	+	0.119027i
$670$	2.47951e9	−	2.08056e9i	0.0123046	−	0.0103248i
$671$	−3.16361e10	+	8.69196e10i	−0.156061	+	0.428773i
$672$	2.40486e11	+	1.65768e10i	1.17927	+	0.0812874i
$673$	−3.36410e10	+	1.90788e11i	−0.163987	+	0.930015i	0.786116	+	0.618079i	$0.212089\pi$
$673$	−3.36410e10	+	1.90788e11i	−0.163987	+	0.930015i	−0.950103	+	0.311936i	$0.899022\pi$
$674$			1.47059e10i			0.0712609i
$675$	−1.92018e11	−	7.69165e10i	−0.924966	−	0.370514i
$676$	−1.12704e11			−0.539699
$677$	−3.16004e11	−	5.57200e10i	−1.50431	−	0.265250i	−0.640065	−	0.768321i	$-0.721092\pi$
$677$	−3.16004e11	−	5.57200e10i	−1.50431	−	0.265250i	−0.864245	+	0.503071i	$0.832204\pi$
$678$	6.21449e9	+	4.18277e9i	0.0294094	+	0.0197945i
$679$	−3.36609e10	−	1.22516e10i	−0.158360	−	0.0576385i
$680$	1.21737e10	+	1.45080e10i	0.0569360	+	0.0678536i
$681$	−5.18612e10	+	2.08886e11i	−0.241131	+	0.971227i
$682$	5.89114e10	−	2.14420e10i	0.272309	−	0.0991123i
$683$	−3.37083e11	−	1.94615e11i	−1.54901	−	0.894321i	−0.998218	−	0.0596780i	$-0.980993\pi$
$683$	−3.37083e11	−	1.94615e11i	−1.54901	−	0.894321i	−0.550792	−	0.834643i	$-0.685674\pi$
$684$	−9.58796e9	−	2.59791e11i	−0.0438028	−	1.18686i
$685$	−5.25818e9	−	9.10743e9i	−0.0238821	−	0.0413650i
$686$	−5.37061e10	+	6.40044e10i	−0.242509	+	0.289010i
$687$	2.05094e11	+	2.81700e11i	0.920718	+	1.26462i
$688$	1.05298e10	+	5.97175e10i	0.0469966	+	0.266531i
$689$	−5.25865e10	+	9.27242e9i	−0.233344	+	0.0411449i
$690$	−2.21418e9	+	1.61206e9i	−0.00976826	+	0.00711187i
$691$	2.64622e11	+	2.22045e11i	1.16069	+	0.973930i	0.999915	−	0.0130614i	$-0.00415771\pi$
$691$	2.64622e11	+	2.22045e11i	1.16069	+	0.973930i	0.160770	+	0.986992i	$0.448602\pi$
$692$	−6.68630e9	+	3.86034e9i	−0.0291583	+	0.0168345i
$693$	−7.18349e10	−	1.14454e11i	−0.311460	−	0.496248i
$694$	4.85352e10	−	8.40654e10i	0.209227	−	0.362392i
$695$	−9.21265e9	−	2.53116e10i	−0.0394862	−	0.108487i
$696$	−1.70932e11	−	4.24380e10i	−0.728426	−	0.180850i
$697$	1.56241e11	−	1.31102e11i	0.662008	−	0.555491i
$698$	4.02028e10	−	1.10456e11i	0.169369	−	0.465339i
$699$	−1.30393e11	+	1.93730e11i	−0.546193	+	0.811499i
$700$	3.65246e10	−	2.07141e11i	0.152122	−	0.862729i
$701$		−	7.99935e9i		−	0.0331271i	−0.999863	−	0.0165635i	$-0.994727\pi$
$701$		−	7.99935e9i		−	0.0331271i	0.999863	−	0.0165635i	$-0.00527258\pi$
$702$	−6.25926e10	−	1.31100e10i	−0.257736	−	0.0539826i
$703$	3.96905e11			1.62505
$704$	−1.88847e10	−	3.32989e9i	−0.0768812	−	0.0135562i
$705$	−1.11061e9	+	1.61121e10i	−0.00449579	+	0.0652221i
$706$	1.31880e11	+	4.80005e10i	0.530837	+	0.193209i
$707$	−1.32277e11	−	1.57641e11i	−0.529426	−	0.630945i
$708$	2.05850e11	+	1.98393e11i	0.819253	+	0.789575i
$709$	−2.58748e11	+	9.41764e10i	−1.02398	+	0.372698i	−0.798786	−	0.601616i	$-0.794524\pi$
$709$	−2.58748e11	+	9.41764e10i	−1.02398	+	0.372698i	−0.225194	+	0.974314i	$0.572302\pi$
$710$	−6.83100e9	−	3.94388e9i	−0.0268813	−	0.0155199i
$711$	2.48710e10	+	2.75121e10i	0.0973227	+	0.107658i
$712$	6.68018e10	+	1.15704e11i	0.259937	+	0.450224i
$713$	−8.06798e10	+	9.61504e10i	−0.312181	+	0.372043i
$714$	−1.01935e11	+	2.29562e11i	−0.392220	+	0.883297i
$715$	7.47982e8	+	4.24201e9i	0.00286198	+	0.0162311i
$716$	1.21990e11	−	2.15102e10i	0.464166	−	0.0818450i
$717$	1.56988e10	+	1.47953e11i	0.0594005	+	0.559818i
$718$	−1.74114e11	−	1.46099e11i	−0.655144	−	0.549731i
$719$	2.56982e11	−	1.48369e11i	0.961585	−	0.555172i	0.0649248	−	0.997890i	$-0.479319\pi$
$719$	2.56982e11	−	1.48369e11i	0.961585	−	0.555172i	0.896661	+	0.442719i	$0.145986\pi$
$720$	−4.39153e9	−	3.41704e9i	−0.0163413	−	0.0127151i
$721$	7.19864e10	−	1.24684e11i	0.266385	−	0.461392i
$722$	6.42717e10	+	1.76585e11i	0.236522	+	0.649838i
$723$	9.51325e10	+	3.30529e11i	0.348157	+	1.20964i
$724$	1.28475e11	−	1.07803e11i	0.467588	−	0.392353i
$725$	−8.23692e10	+	2.26308e11i	−0.298135	+	0.819119i
$726$	−4.40145e10	−	9.00164e10i	−0.158434	−	0.324022i
$727$	−4.88255e10	+	2.76903e11i	−0.174787	+	0.991267i	0.763602	+	0.645687i	$0.223429\pi$
$727$	−4.88255e10	+	2.76903e11i	−0.174787	+	0.991267i	−0.938389	+	0.345580i	$0.887682\pi$
$728$		−	1.50228e11i		−	0.534841i
$729$	−2.58691e11	−	1.13337e11i	−0.915949	−	0.401294i
$730$	−7.49011e9			−0.0263752
$731$	−3.79490e11	−	6.69144e10i	−1.32902	−	0.234342i
$732$	−1.76604e11	+	8.63526e10i	−0.615116	+	0.300767i
$733$	−3.89034e11	−	1.41597e11i	−1.34763	−	0.490498i	−0.435424	−	0.900225i	$-0.643402\pi$
$733$	−3.89034e11	−	1.41597e11i	−1.34763	−	0.490498i	−0.912208	+	0.409728i	$0.865624\pi$
$734$	−4.14979e10	−	4.94552e10i	−0.142969	−	0.170384i
$735$	−5.48839e9	+	1.57966e9i	−0.0188060	+	0.00541271i
$736$	1.17364e11	−	4.27169e10i	0.399966	−	0.145576i
$737$	7.16562e10	+	4.13708e10i	0.242876	+	0.140224i
$738$	4.44193e10	−	5.70871e10i	0.149743	−	0.192448i
$739$	−7.10244e10	−	1.23018e11i	−0.238139	−	0.412468i	0.722042	−	0.691850i	$-0.243204\pi$
$739$	−7.10244e10	−	1.23018e11i	−0.238139	−	0.412468i	−0.960180	+	0.279382i	$0.909871\pi$
$740$	9.19893e9	−	1.09629e10i	0.0306768	−	0.0365592i
$741$	−2.52479e11	+	2.67898e10i	−0.837439	+	0.0888580i
$742$	1.29157e10	+	7.32487e10i	0.0426092	+	0.241649i
$743$	1.74447e11	−	3.07596e10i	0.572410	−	0.100931i	0.120052	−	0.992768i	$-0.461694\pi$
$743$	1.74447e11	−	3.07596e10i	0.572410	−	0.100931i	0.452358	+	0.891836i	$0.350583\pi$
$744$	2.81319e11	+	1.24917e11i	0.918136	+	0.407690i
$745$	2.59358e10	+	2.17627e10i	0.0841926	+	0.0706460i
$746$	1.86024e11	−	1.07401e11i	0.600639	−	0.346779i
$747$	2.91974e10	−	2.63945e10i	0.0937695	−	0.0847678i
$748$	−1.04783e11	+	1.81490e11i	−0.334723	+	0.579757i
$749$	−2.07758e11	−	5.70810e11i	−0.660131	−	1.81370i
$750$	1.27699e10	−	1.32499e10i	0.0403591	−	0.0418761i
$751$	1.35565e11	−	1.13753e11i	0.426175	−	0.357603i	−0.404331	−	0.914613i	$-0.632496\pi$
$751$	1.35565e11	−	1.13753e11i	0.426175	−	0.357603i	0.830506	+	0.557009i	$0.188051\pi$
$752$	4.13021e10	−	1.13476e11i	0.129152	−	0.354841i
$753$	6.12105e11	+	4.21927e10i	1.90391	+	0.131237i
$754$	−1.29293e10	+	7.33256e10i	−0.0400027	+	0.226866i
$755$			1.21073e10i			0.0372615i
$756$	5.88743e10	−	2.81091e11i	0.180235	−	0.860518i
$757$	−2.71823e11			−0.827755			−0.413878	−	0.910333i	$-0.635826\pi$
$757$	−2.71823e11			−0.827755			−0.413878	+	0.910333i	$0.635826\pi$
$758$	−1.78261e11	−	3.14322e10i	−0.539982	−	0.0952134i
$759$	−5.80825e10	−	3.90934e10i	−0.175016	−	0.117797i
$760$	2.50579e10	+	9.12035e9i	0.0751088	+	0.0273374i
$761$	2.67176e11	+	3.18408e11i	0.796634	+	0.949391i	0.999556	−	0.0298038i	$-0.00948826\pi$
$761$	2.67176e11	+	3.18408e11i	0.796634	+	0.949391i	−0.202922	+	0.979195i	$0.565044\pi$
$762$	5.05543e9	−	2.03622e10i	0.0149947	−	0.0603955i
$763$	6.91298e11	−	2.51612e11i	2.03970	−	0.742392i
$764$	−1.13604e11	−	6.55891e10i	−0.333441	−	0.192512i
$765$	2.99497e10	−	1.87974e10i	0.0874475	−	0.0548847i
$766$	−1.93868e10	−	3.35789e10i	−0.0563107	−	0.0975330i
$767$	1.79476e11	−	2.13891e11i	0.518591	−	0.618033i
$768$	−1.26228e11	−	1.73376e11i	−0.362837	−	0.498362i
$769$	−5.30732e10	−	3.00993e11i	−0.151765	−	0.860699i	−0.961684	−	0.274159i	$-0.911601\pi$
$769$	−5.30732e10	−	3.00993e11i	−0.151765	−	0.860699i	0.809920	−	0.586540i	$-0.199511\pi$
$770$	5.90878e9	−	1.04188e9i	0.0168087	−	0.00296383i
$771$	−8.90101e9	+	6.48045e9i	−0.0251896	+	0.0183395i
$772$	4.74544e9	+	3.98190e9i	0.0133600	+	0.0112104i
$773$	1.31306e11	−	7.58097e10i	0.367763	−	0.212328i	−0.304718	−	0.952443i	$-0.598562\pi$
$773$	1.31306e11	−	7.58097e10i	0.367763	−	0.212328i	0.672481	+	0.740115i	$0.265229\pi$
$774$	−1.36568e11	+	5.04023e9i	−0.380526	+	0.0140439i
$775$	2.10450e11	−	3.64510e11i	0.583368	−	1.01042i
$776$	1.55669e10	+	4.27696e10i	0.0429294	+	0.117947i
$777$	4.25548e11	+	1.05653e11i	1.16752	+	0.289866i
$778$	−6.14340e10	+	5.15492e10i	−0.167683	+	0.140703i
$779$	9.82193e10	−	2.69855e11i	0.266715	−	0.732793i
$780$	−5.11167e9	+	7.59459e9i	−0.0138097	+	0.0205176i
$781$	3.50135e10	−	1.98571e11i	0.0941090	−	0.533718i
$782$			1.30139e11i			0.348001i
$783$	−1.22273e11	+	3.05249e11i	−0.325301	+	0.812094i
$784$	4.27038e10			0.113032
$785$	−2.86662e10	−	5.05462e9i	−0.0754903	−	0.0133110i
$786$	−2.05312e10	+	2.97854e11i	−0.0537929	+	0.780394i
$787$	−1.69477e11	−	6.16845e10i	−0.441786	−	0.160797i	0.111543	−	0.993760i	$-0.464421\pi$
$787$	−1.69477e11	−	6.16845e10i	−0.441786	−	0.160797i	−0.553329	+	0.832963i	$0.686643\pi$
$788$	1.25741e11	+	1.49852e11i	0.326116	+	0.388650i
$789$	−5.51189e11	−	5.31222e11i	−1.42230	−	1.37078i
$790$	−1.54742e9	+	5.63215e8i	−0.00397283	+	0.00144599i
$791$	2.84533e10	+	1.64275e10i	0.0726820	+	0.0419630i
$792$	−5.27331e10	+	1.63398e11i	−0.134024	+	0.415284i
$793$	9.59973e10	+	1.66272e11i	0.242754	+	0.420462i
$794$	1.12546e11	−	1.34127e11i	0.283171	−	0.337470i
$795$	4.24940e9	−	9.56982e9i	0.0106380	−	0.0239572i
$796$	−9.87436e9	−	5.60003e10i	−0.0245956	−	0.139488i
$797$	−5.56877e11	+	9.81924e10i	−1.38015	+	0.243357i	−0.813961	−	0.580919i	$-0.802693\pi$
$797$	−5.56877e11	+	9.81924e10i	−1.38015	+	0.243357i	−0.566187	+	0.824277i	$0.691582\pi$
$798$	3.73160e10	+	3.51683e11i	0.0920203	+	0.867241i
$799$	5.87859e11	+	4.93272e11i	1.44240	+	1.21032i
$800$	−3.62711e11	+	2.09412e11i	−0.885526	+	0.511259i
$801$	2.31096e11	−	9.39024e10i	0.561387	−	0.228111i
$802$	1.44108e11	−	2.49602e11i	0.348329	−	0.603324i
$803$	−6.54864e10	−	1.79922e11i	−0.157503	−	0.432736i
$804$	4.86385e10	+	1.68990e11i	0.116401	+	0.404424i
$805$	−9.20204e9	+	7.72143e9i	−0.0219129	+	0.0183871i
$806$	4.45063e10	−	1.22280e11i	0.105459	−	0.289745i
$807$	4.21802e9	+	8.62650e9i	0.00994522	+	0.0203395i
$808$	−4.54041e10	+	2.57500e11i	−0.106525	+	0.604131i
$809$			5.05250e10i			0.117954i	0.998259	+	0.0589769i	$0.0187838\pi$
$809$			5.05250e10i			0.117954i	−0.998259	+	0.0589769i	$0.981216\pi$
$810$	8.98607e9	−	8.74690e9i	0.0208752	−	0.0203195i
$811$	3.28251e11			0.758791			0.379396	−	0.925235i	$-0.376132\pi$
$811$	3.28251e11			0.758791			0.379396	+	0.925235i	$0.376132\pi$
$812$	−3.29291e11	−	5.80628e10i	−0.757452	−	0.133559i
$813$	2.60703e11	−	1.27473e11i	0.596737	−	0.291781i
$814$	−1.06628e11	−	3.88092e10i	−0.242869	−	0.0883970i
$815$	−2.62439e10	−	3.12762e10i	−0.0594836	−	0.0708898i
$816$	−2.54079e11	+	7.31288e10i	−0.573071	+	0.164941i
$817$	−5.09847e11	+	1.85569e11i	−1.14433	+	0.416503i
$818$	7.51378e10	+	4.33808e10i	0.167821	+	0.0968913i
$819$	−2.77831e11	−	3.84849e10i	−0.617511	−	0.0855371i
$820$	−5.17724e9	−	8.96724e9i	−0.0114510	−	0.0198337i
$821$	−4.35639e11	+	5.19174e11i	−0.958857	+	1.14272i	0.0308373	+	0.999524i	$0.490183\pi$
$821$	−4.35639e11	+	5.19174e11i	−0.958857	+	1.14272i	−0.989694	+	0.143197i	$0.954262\pi$
$822$	−1.76225e11	+	1.86987e10i	−0.385993	+	0.0409565i
$823$	1.04516e11	+	5.92737e11i	0.227815	+	1.29200i	0.857231	+	0.514933i	$0.172183\pi$
$823$	1.04516e11	+	5.92737e11i	0.227815	+	1.29200i	−0.629416	+	0.777069i	$0.716706\pi$
$824$	−1.80153e11	+	3.17658e10i	−0.390780	+	0.0689051i
$825$	2.14578e11	+	9.52813e10i	0.463200	+	0.205680i
$826$	−2.97933e11	−	2.49995e11i	−0.640027	−	0.537047i
$827$	3.13017e11	−	1.80720e11i	0.669184	−	0.386353i	−0.126584	−	0.991956i	$-0.540401\pi$
$827$	3.13017e11	−	1.80720e11i	0.669184	−	0.386353i	0.795767	+	0.605603i	$0.207068\pi$
$828$	−3.12256e10	−	1.45486e11i	−0.0664339	−	0.309527i
$829$	−1.85216e11	+	3.20803e11i	−0.392157	+	0.679235i	−0.992734	−	0.120332i	$-0.961604\pi$
$829$	−1.85216e11	+	3.20803e11i	−0.392157	+	0.679235i	0.600577	+	0.799567i	$0.294938\pi$
$830$	5.97716e8	+	1.64221e9i	0.00125946	+	0.00346032i
$831$	8.31532e10	−	8.62787e10i	0.174371	−	0.180925i
$832$	−3.04909e10	+	2.55849e10i	−0.0636322	+	0.0533938i
$833$	−9.28149e10	+	2.55007e11i	−0.192769	+	0.529629i
$834$	−4.52831e11	−	3.12139e10i	−0.935993	−	0.0645184i
$835$	−8.98527e9	+	5.09580e10i	−0.0184835	+	0.104825i
$836$			2.95071e11i			0.604090i
$837$	3.03088e11	−	4.88269e11i	0.617544	−	0.994849i
$838$	−2.28308e11			−0.462962
$839$	4.93790e11	+	8.70685e10i	0.996539	+	0.175717i	0.648051	−	0.761597i	$-0.275584\pi$
$839$	4.93790e11	+	8.70685e10i	0.996539	+	0.175717i	0.348488	+	0.937313i	$0.386695\pi$
$840$	2.44385e10	+	1.64487e10i	0.0490860	+	0.0330381i
$841$	−1.10319e11	−	4.01528e10i	−0.220529	−	0.0802660i
$842$	2.59482e11	+	3.09238e11i	0.516248	+	0.615241i
$843$	−1.18729e11	+	4.78216e11i	−0.235097	+	0.946922i
$844$	−6.17892e11	+	2.24894e11i	−1.21771	+	0.443209i
$845$	−1.86925e10	−	1.07921e10i	−0.0366640	−	0.0211679i
$846$	2.40550e11	+	1.27291e11i	0.469595	+	0.248495i
$847$	−2.19737e11	−	3.80595e11i	−0.426942	−	0.739486i
$848$	−5.03256e10	+	5.99758e10i	−0.0973209	+	0.115982i
$849$	−2.21281e11	−	3.03933e11i	−0.425905	−	0.584988i
$850$	−7.57810e10	−	4.29775e11i	−0.145173	−	0.823315i
$851$	2.23727e11	−	3.94491e10i	0.426580	−	0.0752176i
$852$	3.46441e11	−	2.52229e11i	0.657462	−	0.478671i
$853$	−1.25556e11	−	1.05354e11i	−0.237160	−	0.199001i	0.516460	−	0.856312i	$-0.327250\pi$
$853$	−1.25556e11	−	1.05354e11i	−0.237160	−	0.199001i	−0.753620	+	0.657310i	$0.771694\pi$
$854$	2.31604e11	−	1.33716e11i	0.435425	−	0.251393i
$855$	2.32864e10	−	4.40057e10i	0.0435750	−	0.0823463i
$856$	−3.85910e11	+	6.68415e11i	−0.718771	+	1.24495i
$857$	2.24707e11	+	6.17377e11i	0.416575	+	1.14453i	0.953630	+	0.300982i	$0.0973145\pi$
$857$	2.24707e11	+	6.17377e11i	0.416575	+	1.14453i	−0.537055	+	0.843547i	$0.680463\pi$
$858$	7.04474e10	+	1.74903e10i	0.129992	+	0.0322737i
$859$	−2.05655e11	+	1.72565e11i	−0.377717	+	0.316943i	−0.811806	−	0.583928i	$-0.801515\pi$
$859$	−2.05655e11	+	1.72565e11i	−0.377717	+	0.316943i	0.434088	+	0.900870i	$0.357071\pi$
$860$	−6.69097e9	+	1.83833e10i	−0.0122319	+	0.0336070i
$861$	1.77141e11	−	2.63184e11i	0.322334	−	0.478903i
$862$	4.05330e9	−	2.29874e10i	0.00734141	−	0.0416352i
$863$			7.75412e11i			1.39794i	0.715150	+	0.698971i	$0.246358\pi$
$863$			7.75412e11i			1.39794i	−0.715150	+	0.698971i	$0.753642\pi$
$864$	−5.04116e11	+	2.69970e11i	−0.904640	+	0.484463i
$865$	−1.47861e9			−0.00264112
$866$	5.15738e11	+	9.09385e10i	0.916975	+	0.161687i
$867$	7.66840e10	−	1.11248e12i	0.135715	−	1.96887i
$868$	5.49136e11	+	1.99869e11i	0.967388	+	0.352101i
$869$	−2.70584e10	−	3.22469e10i	−0.0474485	−	0.0565469i
$870$	−1.05127e10	−	1.01318e10i	−0.0183500	−	0.0176853i
$871$	1.61386e11	−	5.87398e10i	0.280410	−	0.102061i
$872$	−8.09506e11	−	4.67368e11i	−1.40008	−	0.808339i
$873$	8.30859e10	−	1.78327e10i	0.143044	−	0.0307016i
$874$	9.16184e10	+	1.58688e11i	0.157014	+	0.271955i
$875$	5.18789e10	−	6.18268e10i	0.0885031	−	0.105474i
$876$	1.65144e11	−	3.71912e11i	0.280445	−	0.631574i
$877$	5.75848e10	+	3.26579e11i	0.0973440	+	0.552065i	0.994004	+	0.109345i	$0.0348754\pi$
$877$	5.75848e10	+	3.26579e11i	0.0973440	+	0.552065i	−0.896660	+	0.442720i	$0.854014\pi$
$878$	3.94698e11	−	6.95958e10i	0.664181	−	0.117113i
$879$	−9.65113e10	−	9.09567e11i	−0.161667	−	1.52363i
$880$	4.83809e9	+	4.05964e9i	0.00806758	+	0.00676950i
$881$	3.43576e11	−	1.98364e11i	0.570320	−	0.329275i	−0.186957	−	0.982368i	$-0.559862\pi$
$881$	3.43576e11	−	1.98364e11i	0.570320	−	0.329275i	0.757277	+	0.653094i	$0.226529\pi$
$882$	−1.32051e10	+	9.53308e10i	−0.0218207	+	0.157528i
$883$	−2.25631e11	+	3.90804e11i	−0.371155	+	0.642860i	−0.989744	−	0.142856i	$-0.954372\pi$
$883$	−2.25631e11	+	3.90804e11i	−0.371155	+	0.642860i	0.618588	+	0.785715i	$0.287705\pi$
$884$	1.48775e11	+	4.08757e11i	0.243625	+	0.669354i
$885$	1.51438e10	+	5.26158e10i	0.0246867	+	0.0857716i
$886$	1.82042e11	−	1.52751e11i	0.295417	−	0.247885i
$887$	1.74390e11	−	4.79133e11i	0.281726	−	0.774037i	−0.715431	−	0.698684i	$-0.753769\pi$
$887$	1.74390e11	−	4.79133e11i	0.281726	−	0.774037i	0.997157	−	0.0753529i	$-0.0240083\pi$
$888$	−2.44721e11	−	5.00492e11i	−0.393567	−	0.804906i
$889$	1.59788e10	−	9.06204e10i	0.0255822	−	0.145084i
$890$			1.10757e10i			0.0176527i
$891$	2.88678e11	+	1.39383e11i	0.458039	+	0.221156i
$892$	7.98779e10			0.126173
$893$	1.06408e12	+	1.87627e11i	1.67328	+	0.295045i
$894$	5.12540e11	−	2.50612e11i	0.802376	−	0.392330i
$895$	2.22924e10	+	8.11377e9i	0.0347428	+	0.0126453i
$896$	−4.54074e11	−	5.41145e11i	−0.704523	−	0.839617i
$897$	−1.39655e11	+	4.01952e10i	−0.215718	+	0.0620876i
$898$	3.76318e11	−	1.36969e11i	0.578695	−	0.210628i
$899$	−5.79459e11	−	3.34551e11i	−0.887123	−	0.512181i
$900$	1.87838e11	+	4.62274e11i	0.286295	+	0.704578i
$901$	−2.48766e11	−	4.30875e11i	−0.377478	−	0.653812i
$902$	−5.27727e10	+	6.28921e10i	−0.0797229	+	0.0950101i
$903$	−5.96037e11	+	6.32437e10i	−0.896443	+	0.0951187i
$904$	−7.24907e9	−	4.11115e10i	−0.0108545	−	0.0615587i
$905$	3.16310e10	−	5.57740e9i	0.0471540	−	0.00831452i
$906$	1.86467e11	+	8.27991e10i	0.276751	+	0.122889i
$907$	−8.86132e11	−	7.43553e11i	−1.30939	−	1.09871i	−0.988440	−	0.151614i	$-0.951553\pi$
$907$	−8.86132e11	−	7.43553e11i	−1.30939	−	1.09871i	−0.320952	−	0.947096i	$-0.604003\pi$
$908$	4.49630e11	−	2.59594e11i	0.661473	−	0.381901i
$909$	4.64587e11	+	1.49936e11i	0.680475	+	0.219609i
$910$	6.22692e9	−	1.07853e10i	0.00908046	−	0.0157278i
$911$	−1.13732e11	−	3.12476e11i	−0.165124	−	0.453673i	0.829341	−	0.558742i	$-0.188716\pi$
$911$	−1.13732e11	−	3.12476e11i	−0.165124	−	0.453673i	−0.994465	+	0.105069i	$0.966494\pi$
$912$	−2.58334e11	+	2.68044e11i	−0.373424	+	0.387460i
$913$	−3.42223e10	+	2.87159e10i	−0.0492522	+	0.0413275i
$914$	−2.82053e10	+	7.74933e10i	−0.0404153	+	0.111040i
$915$	−3.75595e10	−	2.58899e9i	−0.0535840	−	0.00369357i
$916$	1.45962e11	−	8.27792e11i	0.207328	−	1.17582i
$917$			1.30947e12i			1.85190i
$918$	−8.46827e10	−	5.89813e11i	−0.119241	−	0.830507i
$919$	−1.61529e11			−0.226459			−0.113229	−	0.993569i	$-0.536120\pi$
$919$	−1.61529e11			−0.226459			−0.113229	+	0.993569i	$0.536120\pi$
$920$	1.50311e10	+	2.65039e9i	0.0209817	+	0.00369964i
$921$	2.15604e11	+	1.45116e11i	0.299653	+	0.201686i
$922$	1.20094e11	+	4.37107e10i	0.166187	+	0.0604872i
$923$	−2.69023e11	−	3.20609e11i	−0.370666	−	0.441742i
$924$	−7.85456e10	+	3.16365e11i	−0.107754	+	0.434011i
$925$	−7.15872e11	+	2.60556e11i	−0.977842	+	0.355905i
$926$	−1.55820e11	−	8.99629e10i	−0.211924	−	0.122354i
$927$	1.25966e10	+	3.41312e11i	0.0170583	+	0.462203i
$928$	3.32899e11	+	5.76599e11i	0.448871	+	0.777467i
$929$	4.01736e11	−	4.78770e11i	0.539359	−	0.642783i	−0.425685	−	0.904872i	$-0.639967\pi$
$929$	4.01736e11	−	4.78770e11i	0.539359	−	0.642783i	0.965044	+	0.262088i	$0.0844112\pi$
$930$	1.50190e10	+	2.06288e10i	0.0200775	+	0.0275767i
$931$	6.63500e10	+	3.76290e11i	0.0883166	+	0.500868i
$932$	5.54767e11	−	9.78203e10i	0.735270	−	0.129648i
$933$	−3.94705e11	+	2.87368e11i	−0.520890	+	0.379238i
$934$	−2.18566e11	−	1.83399e11i	−0.287207	−	0.240996i
$935$	−3.47576e10	+	2.00673e10i	−0.0454782	+	0.0262569i
$936$	1.89453e11	+	3.01855e11i	0.246831	+	0.393274i
$937$	−2.07728e10	+	3.59796e10i	−0.0269487	+	0.0466765i	−0.879185	−	0.476480i	$-0.841912\pi$
$937$	−2.07728e10	+	3.59796e10i	−0.0269487	+	0.0466765i	0.852237	+	0.523157i	$0.175246\pi$
$938$	−8.18197e10	−	2.24798e11i	−0.105693	−	0.290389i
$939$	2.53554e11	+	6.29511e10i	0.326143	+	0.0809731i
$940$	2.98443e10	−	2.50423e10i	0.0382252	−	0.0320747i
$941$	−1.12104e11	+	3.08003e11i	−0.142976	+	0.392822i	−0.990425	−	0.138055i	$-0.955915\pi$
$941$	−1.12104e11	+	3.08003e11i	−0.142976	+	0.392822i	0.847449	+	0.530877i	$0.178137\pi$
$942$	−2.73889e11	+	4.06926e11i	−0.347833	+	0.516788i
$943$	2.85428e10	−	1.61874e11i	0.0360952	−	0.204706i
$944$		−	4.09391e11i		−	0.515526i
$945$	3.66808e10	−	4.09827e10i	0.0459951	−	0.0513894i
$946$	1.55114e11			0.193681
$947$	1.83765e11	+	3.24028e10i	0.228488	+	0.0402886i	0.286720	−	0.958014i	$-0.407435\pi$
$947$	1.83765e11	+	3.24028e10i	0.228488	+	0.0402886i	−0.0582317	+	0.998303i	$0.518546\pi$
$948$	6.15227e9	−	8.92533e10i	0.00761732	−	0.110507i
$949$	−3.73458e11	−	1.35928e11i	−0.460445	−	0.167588i
$950$	−3.94969e11	−	4.70705e11i	−0.484918	−	0.577902i
$951$	2.45965e11	+	2.37054e11i	0.300712	+	0.289819i
$952$	1.31533e12	−	4.78741e11i	1.60135	−	0.582845i
$953$	2.43325e11	+	1.40483e11i	0.294995	+	0.170315i	0.640192	−	0.768215i	$-0.278855\pi$
$953$	2.43325e11	+	1.40483e11i	0.294995	+	0.170315i	−0.345197	+	0.938530i	$0.612188\pi$
$954$	−1.18326e11	−	1.30892e11i	−0.142852	−	0.158022i
$955$	−1.25611e10	−	2.17565e10i	−0.0151013	−	0.0261563i
$956$	2.30701e11	−	2.74938e11i	0.276196	−	0.329157i
$957$	1.51468e11	−	3.41112e11i	0.180581	−	0.406677i
$958$	1.20396e11	+	6.82800e11i	0.142939	+	0.810647i
$959$	−7.65439e11	+	1.34968e11i	−0.904974	+	0.159571i
$960$	−8.23547e8	−	7.76149e9i	−0.000969624	−	0.00913819i
$961$	2.42449e11	+	2.03439e11i	0.284268	+	0.238529i
$962$	−2.03972e11	+	1.17763e11i	−0.238161	+	0.137502i
$963$	1.13730e12	+	8.84932e11i	1.32243	+	1.02898i
$964$	4.14848e11	−	7.18537e11i	0.480375	−	0.832034i
$965$	4.05762e8	+	1.11482e9i	0.000467910	+	0.00128557i
$966$	5.59887e10	+	1.94528e11i	0.0642972	+	0.223395i
$967$	3.59916e11	−	3.02005e11i	0.411619	−	0.345389i	−0.413345	−	0.910574i	$-0.635640\pi$
$967$	3.59916e11	−	3.02005e11i	0.411619	−	0.345389i	0.824964	+	0.565185i	$0.191195\pi$
$968$	−1.90983e11	+	5.24721e11i	−0.217517	+	0.597622i
$969$	−1.03915e12	−	2.12523e12i	−1.17865	−	2.41052i
$970$	−6.55198e8	+	3.71582e9i	−0.000740092	+	0.00419727i
$971$			1.13211e12i			1.27354i	0.771056	+	0.636768i	$0.219729\pi$
$971$			1.13211e12i			1.27354i	−0.771056	+	0.636768i	$0.780271\pi$
$972$	2.36189e11	+	6.39047e11i	0.264603	+	0.715926i
$973$	−1.99080e12			−2.22114
$974$	1.58307e11	+	2.79138e10i	0.175899	+	0.0310158i
$975$	4.37794e11	−	2.14064e11i	0.484453	−	0.236878i
$976$	2.64529e11	+	9.62808e10i	0.291524	+	0.106106i
$977$	−1.01318e11	−	1.20746e11i	−0.111201	−	0.132524i	0.707573	−	0.706640i	$-0.249790\pi$
$977$	−1.01318e11	−	1.20746e11i	−0.111201	−	0.132524i	−0.818774	+	0.574117i	$0.805346\pi$
$978$	−6.61167e11	+	1.90296e11i	−0.722696	+	0.208005i
$979$	−2.66053e11	+	9.68355e10i	−0.289626	+	0.105415i
$980$	1.19312e10	+	6.88849e9i	0.0129354	+	0.00746827i
$981$	−1.07173e12	+	1.37737e12i	−1.15720	+	1.48722i
$982$	9.15746e10	+	1.58612e11i	0.0984757	+	0.170565i
$983$	2.32916e11	−	2.77578e11i	0.249451	−	0.297284i	−0.626760	−	0.779213i	$-0.715619\pi$
$983$	2.32916e11	−	2.77578e11i	0.249451	−	0.297284i	0.876210	+	0.481929i	$0.160064\pi$
$984$	−4.00843e11	+	4.25322e10i	−0.427557	+	0.0453667i
$985$	6.50544e9	+	3.68942e10i	0.00691085	+	0.0391934i
$986$	−6.83210e11	+	1.20468e11i	−0.722847	+	0.127457i
$987$	1.09093e12	+	4.84417e11i	1.14955	+	0.510447i
$988$	4.69178e11	+	3.93687e11i	0.492391	+	0.413165i
$989$	−2.68946e11	+	1.55276e11i	−0.281113	+	0.162300i
$990$	−1.05587e10	+	9.54506e9i	−0.0109918	+	0.00993661i
$991$	2.02286e11	−	3.50370e11i	0.209735	−	0.363272i	−0.741896	−	0.670515i	$-0.766073\pi$
$991$	2.02286e11	−	3.50370e11i	0.209735	−	0.363272i	0.951631	+	0.307243i	$0.0994064\pi$
$992$	−3.97980e11	−	1.09344e12i	−0.410974	−	1.12914i
$993$	−3.14001e11	+	3.25803e11i	−0.322949	+	0.335088i
$994$	−4.46582e11	+	3.74727e11i	−0.457463	+	0.383857i
$995$	3.72467e9	−	1.02334e10i	0.00380010	−	0.0104407i
$996$	−9.47207e10	−	6.52914e9i	−0.0962515	−	0.00663466i
$997$	2.68798e11	−	1.52443e12i	0.272048	−	1.54286i	−0.476137	−	0.879371i	$-0.657963\pi$
$997$	2.68798e11	−	1.52443e12i	0.272048	−	1.54286i	0.748185	−	0.663490i	$-0.230926\pi$
$998$		−	1.97145e11i		−	0.198730i
$999$	−9.88300e11	+	3.24371e11i	−0.992263	+	0.325672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.2.10	✓	138
3.2	odd	2		81.9.f.a.8.14		138
27.13	even	9		81.9.f.a.71.14		138
27.14	odd	18	inner	27.9.f.a.14.10	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.10	✓	138	1.1	even	1	trivial
27.9.f.a.14.10	yes	138	27.14	odd	18	inner
81.9.f.a.8.14		138	3.2	odd	2
81.9.f.a.71.14		138	27.13	even	9

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.66670 - 1.35185i) q^{2} +(72.7671 - 35.5802i) q^{3} +(-183.611 - 66.8288i) q^{4} +(-24.0534 - 28.6657i) q^{5} +(-605.982 + 174.413i) q^{6} +(-2598.90 + 945.921i) q^{7} +(3043.29 + 1757.05i) q^{8} +(4029.09 - 5178.14i) q^{9} +(145.659 + 252.288i) q^{10} +(-4786.80 + 5704.68i) q^{11} +(-15738.6 + 1669.97i) q^{12} +(2684.14 + 15222.5i) q^{13} +(21203.7 - 3738.78i) q^{14} +(-2770.23 - 1230.10i) q^{15} +(17361.5 + 14568.0i) q^{16} +(-124728. + 72011.7i) q^{17} +(-37889.9 + 34252.5i) q^{18} +(-101393. + 175618. i) q^{19} +(2500.76 + 6870.79i) q^{20} +(-155458. + 161301. i) q^{21} +(44410.8 - 37265.1i) q^{22} +(-39698.1 + 109070. i) q^{23} +(283967. + 19574.0i) q^{24} +(67588.2 - 383312. i) q^{25} -120335. i q^{26} +(108946. - 520154. i) q^{27} +540399. q^{28} +(-609347. - 107444. i) q^{29} +(19575.6 + 13175.7i) q^{30} +(1.01617e6 + 369854. i) q^{31} +(-691668. - 824298. i) q^{32} +(-145347. + 585428. i) q^{33} +(1.05360e6 - 383479. i) q^{34} +(89627.8 + 51746.6i) q^{35} +(-1.08583e6 + 681502. i) q^{36} +(-978631. - 1.69504e6i) q^{37} +(1.01476e6 - 1.20934e6i) q^{38} +(736937. + 1.01219e6i) q^{39} +(-22834.5 - 129501. i) q^{40} +(-1.39463e6 + 245911. i) q^{41} +(1.40990e6 - 1.02649e6i) q^{42} +(2.04961e6 + 1.71982e6i) q^{43} +(1.26014e6 - 727544. i) q^{44} +(-245349. + 9054.95i) q^{45} +(451799. - 782539. i) q^{46} +(-1.82238e6 - 5.00694e6i) q^{47} +(1.78168e6 + 442347. i) q^{48} +(1.44340e6 - 1.21116e6i) q^{49} +(-1.03636e6 + 2.84736e6i) q^{50} +(-6.51389e6 + 9.67792e6i) q^{51} +(524465. - 2.97439e6i) q^{52} +3.45452e6i q^{53} +(-1.53842e6 + 3.84059e6i) q^{54} +278668. q^{55} +(-9.57122e6 - 1.68767e6i) q^{56} +(-1.12955e6 + 1.63868e7i) q^{57} +(4.52643e6 + 1.64749e6i) q^{58} +(-1.16111e7 - 1.38375e7i) q^{59} +(426437. + 410989. i) q^{60} +(1.16719e7 - 4.24821e6i) q^{61} +(-7.29065e6 - 4.20926e6i) q^{62} +(-5.57309e6 + 1.72687e7i) q^{63} +(1.28751e6 + 2.23004e6i) q^{64} +(371801. - 443096. i) q^{65} +(1.90574e6 - 4.29181e6i) q^{66} +(-1.92937e6 - 1.09420e7i) q^{67} +(2.77138e7 - 4.88669e6i) q^{68} +(992009. + 9.34915e6i) q^{69} +(-617196. - 517889. i) q^{70} +(-2.34487e7 + 1.35381e7i) q^{71} +(2.13599e7 - 8.67929e6i) q^{72} +(-1.28556e7 + 2.22665e7i) q^{73} +(5.21144e6 + 1.43183e7i) q^{74} +(-8.72012e6 - 3.02973e7i) q^{75} +(3.03531e7 - 2.54693e7i) q^{76} +(7.04421e6 - 1.93538e7i) q^{77} +(-4.28154e6 - 8.75641e6i) q^{78} +(-981583. + 5.56684e6i) q^{79} -848091. i q^{80} +(-1.05795e7 - 4.17264e7i) q^{81} +1.10246e7 q^{82} +(5.90784e6 + 1.04171e6i) q^{83} +(3.93233e7 - 1.92275e7i) q^{84} +(5.06440e6 + 1.84329e6i) q^{85} +(-1.33888e7 - 1.59561e7i) q^{86} +(-4.81633e7 + 1.38623e7i) q^{87} +(-2.45910e7 + 8.95039e6i) q^{88} +(3.29258e7 + 1.90097e7i) q^{89} +(1.89325e6 + 262252. i) q^{90} +(-2.13751e7 - 3.70227e7i) q^{91} +(1.45780e7 - 1.73734e7i) q^{92} +(8.71029e7 - 9.24222e6i) q^{93} +(7.20300e6 + 4.08503e7i) q^{94} +(7.47305e6 - 1.31770e6i) q^{95} +(-7.96594e7 - 3.53720e7i) q^{96} +(9.92181e6 + 8.32538e6i) q^{97} +(-1.27034e7 + 7.33433e6i) q^{98} +(1.02532e7 + 4.77714e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 447 q^{5} - 774 q^{6} - 6 q^{7} - 9 q^{8} - 12960 q^{9} - 3 q^{10} + 28668 q^{11} + 77421 q^{12} - 6 q^{13} - 120975 q^{14} + 105507 q^{15} - 774 q^{16} - 9 q^{17}+ \cdots + 228876057 q^{99}+O(q^{100}) \) 138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

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