LMFDB - Embedded newform 81.9.f.a.8.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			8.18
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(18.2801 + 3.22328i) q^{2} +(83.2125 + 30.2869i) q^{4} +(223.403 + 266.242i) q^{5} +(-1438.86 + 523.701i) q^{7} +(-2691.76 - 1554.09i) q^{8} +(3225.67 + 5587.03i) q^{10} +(-262.444 + 312.769i) q^{11} +(-7243.71 - 41081.1i) q^{13} +(-27990.6 + 4935.49i) q^{14} +(-61562.3 - 51656.9i) q^{16} +(-52651.8 + 30398.5i) q^{17} +(81686.6 - 141485. i) q^{19} +(10526.3 + 28920.8i) q^{20} +(-5805.66 + 4871.53i) q^{22} +(-88565.0 + 243330. i) q^{23} +(46855.7 - 265732. i) q^{25} -774316. i q^{26} -135592. q^{28} +(-833385. - 146948. i) q^{29} +(-733729. - 267056. i) q^{31} +(-447401. - 533192. i) q^{32} +(-1.06047e6 + 385978. i) q^{34} +(-460877. - 266087. i) q^{35} +(-858362. - 1.48673e6i) q^{37} +(1.94929e6 - 2.32307e6i) q^{38} +(-187585. - 1.06385e6i) q^{40} +(24637.0 - 4344.17i) q^{41} +(738972. + 620071. i) q^{43} +(-31311.4 + 18077.7i) q^{44} +(-2.40330e6 + 4.16264e6i) q^{46} +(-463987. - 1.27479e6i) q^{47} +(-2.62005e6 + 2.19848e6i) q^{49} +(1.71306e6 - 4.70659e6i) q^{50} +(641451. - 3.63785e6i) q^{52} -6.06703e6i q^{53} -141903. q^{55} +(4.68694e6 + 826433. i) q^{56} +(-1.47607e7 - 5.37247e6i) q^{58} +(1.23794e7 + 1.47532e7i) q^{59} +(7.35050e6 - 2.67536e6i) q^{61} +(-1.25519e7 - 7.24683e6i) q^{62} +(3.82665e6 + 6.62796e6i) q^{64} +(9.31923e6 - 1.11062e7i) q^{65} +(-3.57529e6 - 2.02765e7i) q^{67} +(-5.30197e6 + 934880. i) q^{68} +(-7.56721e6 - 6.34965e6i) q^{70} +(-1.86096e7 + 1.07443e7i) q^{71} +(-2.63704e7 + 4.56749e7i) q^{73} +(-1.08988e7 - 2.99443e7i) q^{74} +(1.10825e7 - 9.29932e6i) q^{76} +(213822. - 587472. i) q^{77} +(6.77127e6 - 3.84018e7i) q^{79} -2.79308e7i q^{80} +464371. q^{82} +(1.82582e7 + 3.21941e6i) q^{83} +(-1.98560e7 - 7.22697e6i) q^{85} +(1.15098e7 + 1.37169e7i) q^{86} +(1.19251e6 - 434037. i) q^{88} +(-7.85112e7 - 4.53284e7i) q^{89} +(3.19369e7 + 5.53163e7i) q^{91} +(-1.47394e7 + 1.75658e7i) q^{92} +(-4.37272e6 - 2.47989e7i) q^{94} +(5.59184e7 - 9.85992e6i) q^{95} +(5.90263e7 + 4.95290e7i) q^{97} +(-5.49811e7 + 3.17433e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	18.2801	+	3.22328i	1.14251	+	0.201455i	0.712703	−	0.701466i	$-0.247471\pi$
$2$	18.2801	+	3.22328i	1.14251	+	0.201455i	0.429806	+	0.902921i	$0.358582\pi$
$3$		0			0
$3$		0			0
$4$	83.2125	+	30.2869i	0.325049	+	0.118308i
$5$	223.403	+	266.242i	0.357445	+	0.425987i	0.914561	−	0.404448i	$-0.132536\pi$
$5$	223.403	+	266.242i	0.357445	+	0.425987i	−0.557116	+	0.830435i	$0.688092\pi$
$6$		0			0
$7$	−1438.86	+	523.701i	−0.599274	+	0.218118i	−0.623804	−	0.781581i	$-0.714414\pi$
$7$	−1438.86	+	523.701i	−0.599274	+	0.218118i	0.0245293	+	0.999699i	$0.492191\pi$
$8$	−2691.76	−	1554.09i	−0.657168	−	0.379416i
$9$		0			0
$10$	3225.67	+	5587.03i	0.322567	+	0.558703i
$11$	−262.444	+	312.769i	−0.0179253	+	0.0213625i	−0.774933	−	0.632044i	$-0.782216\pi$
$11$	−262.444	+	312.769i	−0.0179253	+	0.0213625i	0.757007	+	0.653406i	$0.226661\pi$
$12$		0			0
$13$	−7243.71	−	41081.1i	−0.253622	−	1.43836i	−0.799585	−	0.600554i	$-0.794947\pi$
$13$	−7243.71	−	41081.1i	−0.253622	−	1.43836i	0.545962	−	0.837810i	$-0.316164\pi$
$14$	−27990.6	+	4935.49i	−0.728617	+	0.128475i
$15$		0			0
$16$	−61562.3	−	51656.9i	−0.939367	−	0.788222i
$17$	−52651.8	+	30398.5i	−0.630402	+	0.363963i	−0.780908	−	0.624646i	$-0.785243\pi$
$17$	−52651.8	+	30398.5i	−0.630402	+	0.363963i	0.150506	+	0.988609i	$0.451910\pi$
$18$		0			0
$19$	81686.6	−	141485.i	0.626811	−	1.08567i	−0.361377	−	0.932420i	$-0.617693\pi$
$19$	81686.6	−	141485.i	0.626811	−	1.08567i	0.988188	−	0.153249i	$-0.0489735\pi$
$20$	10526.3	+	28920.8i	0.0657895	+	0.180755i
$21$		0			0
$22$	−5805.66	+	4871.53i	−0.0247834	+	0.0207957i
$23$	−88565.0	+	243330.i	−0.316483	+	0.869531i	0.674826	+	0.737977i	$0.264219\pi$
$23$	−88565.0	+	243330.i	−0.316483	+	0.869531i	−0.991309	+	0.131554i	$0.958003\pi$
$24$		0			0
$25$	46855.7	−	265732.i	0.119951	−	0.680274i
$26$		−	774316.i		−	1.69444i
$27$		0			0
$28$	−135592.			−0.220599
$29$	−833385.	−	146948.i	−1.17829	−	0.207765i	−0.449999	−	0.893029i	$-0.648576\pi$
$29$	−833385.	−	146948.i	−1.17829	−	0.207765i	−0.728295	+	0.685264i	$0.759687\pi$
$30$		0			0
$31$	−733729.	−	267056.i	−0.794491	−	0.289171i	−0.0872894	−	0.996183i	$-0.527820\pi$
$31$	−733729.	−	267056.i	−0.794491	−	0.289171i	−0.707202	+	0.707012i	$0.750043\pi$
$32$	−447401.	−	533192.i	−0.426675	−	0.508492i
$33$		0			0
$34$	−1.06047e6	+	385978.i	−0.793562	+	0.288833i
$35$	−460877.	−	266087.i	−0.307123	−	0.177318i
$36$		0			0
$37$	−858362.	−	1.48673e6i	−0.457998	−	0.793276i	0.540857	−	0.841115i	$-0.318100\pi$
$37$	−858362.	−	1.48673e6i	−0.457998	−	0.793276i	−0.998855	+	0.0478387i	$0.984767\pi$
$38$	1.94929e6	−	2.32307e6i	0.934850	−	1.11411i
$39$		0			0
$40$	−187585.	−	1.06385e6i	−0.0732754	−	0.415565i
$41$	24637.0	−	4344.17i	0.00871872	−	0.00153735i	−0.169287	−	0.985567i	$-0.554147\pi$
$41$	24637.0	−	4344.17i	0.00871872	−	0.00153735i	0.178006	+	0.984029i	$0.443035\pi$
$42$		0			0
$43$	738972.	+	620071.i	0.216150	+	0.181371i	0.744433	−	0.667697i	$-0.232720\pi$
$43$	738972.	+	620071.i	0.216150	+	0.181371i	−0.528284	+	0.849068i	$0.677164\pi$
$44$	−31311.4	+	18077.7i	−0.00835396	+	0.00482316i
$45$		0			0
$46$	−2.40330e6	+	4.16264e6i	−0.536756	+	0.929689i
$47$	−463987.	−	1.27479e6i	−0.0950854	−	0.261245i	0.883027	−	0.469322i	$-0.155502\pi$
$47$	−463987.	−	1.27479e6i	−0.0950854	−	0.261245i	−0.978112	+	0.208077i	$0.933279\pi$
$48$		0			0
$49$	−2.62005e6	+	2.19848e6i	−0.454490	+	0.381362i
$50$	1.71306e6	−	4.70659e6i	0.274089	−	0.753054i
$51$		0			0
$52$	641451.	−	3.63785e6i	0.0877304	−	0.497544i
$53$		−	6.06703e6i		−	0.768905i	−0.923145	−	0.384452i	$-0.874390\pi$
$53$		−	6.06703e6i		−	0.768905i	0.923145	−	0.384452i	$-0.125610\pi$
$54$		0			0
$55$	−141903.			−0.0155075
$56$	4.68694e6	+	826433.i	0.476581	+	0.0840341i
$57$		0			0
$58$	−1.47607e7	−	5.37247e6i	−1.30436	−	0.474747i
$59$	1.23794e7	+	1.47532e7i	1.02163	+	1.21753i	0.975820	+	0.218575i	$0.0701408\pi$
$59$	1.23794e7	+	1.47532e7i	1.02163	+	1.21753i	0.0458050	+	0.998950i	$0.485415\pi$
$60$		0			0
$61$	7.35050e6	−	2.67536e6i	0.530881	−	0.193225i	−0.0626504	−	0.998036i	$-0.519955\pi$
$61$	7.35050e6	−	2.67536e6i	0.530881	−	0.193225i	0.593532	+	0.804810i	$0.297733\pi$
$62$	−1.25519e7	−	7.24683e6i	−0.849458	−	0.490435i
$63$		0			0
$64$	3.82665e6	+	6.62796e6i	0.228086	+	0.395057i
$65$	9.31923e6	−	1.11062e7i	0.522068	−	0.622176i
$66$		0			0
$67$	−3.57529e6	−	2.02765e7i	−0.177424	−	1.00622i	−0.935309	−	0.353832i	$-0.884878\pi$
$67$	−3.57529e6	−	2.02765e7i	−0.177424	−	1.00622i	0.757885	−	0.652388i	$-0.226233\pi$
$68$	−5.30197e6	+	934880.i	−0.247971	+	0.0437240i
$69$		0			0
$70$	−7.56721e6	−	6.34965e6i	−0.315169	−	0.264458i
$71$	−1.86096e7	+	1.07443e7i	−0.732325	+	0.422808i	−0.819272	−	0.573405i	$-0.805622\pi$
$71$	−1.86096e7	+	1.07443e7i	−0.732325	+	0.422808i	0.0869473	+	0.996213i	$0.472289\pi$
$72$		0			0
$73$	−2.63704e7	+	4.56749e7i	−0.928593	+	1.60837i	−0.142914	+	0.989735i	$0.545647\pi$
$73$	−2.63704e7	+	4.56749e7i	−0.928593	+	1.60837i	−0.785678	+	0.618635i	$0.787686\pi$
$74$	−1.08988e7	−	2.99443e7i	−0.363457	−	0.998590i
$75$		0			0
$76$	1.10825e7	−	9.29932e6i	0.332188	−	0.278738i
$77$	213822.	−	587472.i	0.00608262	−	0.0167119i
$78$		0			0
$79$	6.77127e6	−	3.84018e7i	0.173845	−	0.985923i	−0.765624	−	0.643289i	$-0.777570\pi$
$79$	6.77127e6	−	3.84018e7i	0.173845	−	0.985923i	0.939469	−	0.342635i	$-0.111319\pi$
$80$		−	2.79308e7i		−	0.681904i
$81$		0			0
$82$	464371.			0.0102709
$83$	1.82582e7	+	3.21941e6i	0.384721	+	0.0678366i	0.362664	−	0.931920i	$-0.381867\pi$
$83$	1.82582e7	+	3.21941e6i	0.384721	+	0.0678366i	0.0220569	+	0.999757i	$0.492979\pi$
$84$		0			0
$85$	−1.98560e7	−	7.22697e6i	−0.380378	−	0.138446i
$86$	1.15098e7	+	1.37169e7i	0.210415	+	0.250762i
$87$		0			0
$88$	1.19251e6	−	434037.i	0.0198852	−	0.00723763i
$89$	−7.85112e7	−	4.53284e7i	−1.25133	−	0.722455i	−0.279955	−	0.960013i	$-0.590320\pi$
$89$	−7.85112e7	−	4.53284e7i	−1.25133	−	0.722455i	−0.971373	+	0.237558i	$0.923653\pi$
$90$		0			0
$91$	3.19369e7	+	5.53163e7i	0.465722	+	0.806655i
$92$	−1.47394e7	+	1.75658e7i	−0.205745	+	0.245197i
$93$		0			0
$94$	−4.37272e6	−	2.47989e7i	−0.0560068	−	0.317630i
$95$	5.59184e7	−	9.85992e6i	0.686531	−	0.121054i
$96$		0			0
$97$	5.90263e7	+	4.95290e7i	0.666744	+	0.559464i	0.912100	−	0.409969i	$-0.134460\pi$
$97$	5.90263e7	+	4.95290e7i	0.666744	+	0.559464i	−0.245356	+	0.969433i	$0.578905\pi$
$98$	−5.49811e7	+	3.17433e7i	−0.596086	+	0.344151i
$99$		0			0
$100$	1.19472e7	−	2.06931e7i	0.119472	−	0.206931i
$101$	6.70812e7	+	1.84304e8i	0.644637	+	1.77113i	0.636645	+	0.771157i	$0.280322\pi$
$101$	6.70812e7	+	1.84304e8i	0.644637	+	1.77113i	0.00799213	+	0.999968i	$0.497456\pi$
$102$		0			0
$103$	8.03334e7	−	6.74077e7i	0.713752	−	0.598909i	−0.211897	−	0.977292i	$-0.567964\pi$
$103$	8.03334e7	−	6.74077e7i	0.713752	−	0.598909i	0.925649	+	0.378383i	$0.123520\pi$
$104$	−4.43453e7	+	1.21838e8i	−0.379066	+	1.04147i
$105$		0			0
$106$	1.95557e7	−	1.10906e8i	0.154900	−	0.878480i
$107$			1.09060e8i			0.832017i	0.909361	+	0.416009i	$0.136571\pi$
$107$			1.09060e8i			0.832017i	−0.909361	+	0.416009i	$0.863429\pi$
$108$		0			0
$109$	7.61337e6			0.0539350			0.0269675	−	0.999636i	$-0.491415\pi$
$109$	7.61337e6			0.0539350			0.0269675	+	0.999636i	$0.491415\pi$
$110$	−2.59401e6	−	457393.i	−0.0177174	−	0.00312406i
$111$		0			0
$112$	1.15632e8	+	4.20867e7i	0.734864	+	0.267469i
$113$	1.13330e8	+	1.35062e8i	0.695076	+	0.828359i	0.991960	−	0.126555i	$-0.0403919\pi$
$113$	1.13330e8	+	1.35062e8i	0.695076	+	0.828359i	−0.296884	+	0.954914i	$0.595947\pi$
$114$		0			0
$115$	−8.45704e7	+	3.07811e7i	−0.483534	+	0.175992i
$116$	−6.48975e7	−	3.74686e7i	−0.358423	−	0.206936i
$117$		0			0
$118$	1.78743e8	+	3.09593e8i	0.921939	+	1.59684i
$119$	5.98387e7	−	7.13130e7i	0.298397	−	0.355616i
$120$		0			0
$121$	3.71941e7	+	2.10938e8i	0.173513	+	0.984042i
$122$	1.42992e8	−	2.52133e7i	0.645463	−	0.113812i
$123$		0			0
$124$	−5.29672e7	−	4.44447e7i	−0.224037	−	0.187989i
$125$	1.98791e8	−	1.14772e8i	0.814248	−	0.470106i
$126$		0			0
$127$	−9.87685e7	+	1.71072e8i	−0.379668	+	0.657604i	−0.991014	−	0.133759i	$-0.957295\pi$
$127$	−9.87685e7	+	1.71072e8i	−0.379668	+	0.657604i	0.611346	+	0.791363i	$0.290628\pi$
$128$	1.09531e8	+	3.00933e8i	0.408033	+	1.12106i
$129$		0			0
$130$	2.06155e8	−	1.72985e8i	0.721807	−	0.605668i
$131$	9.97225e7	−	2.73985e8i	0.338616	−	0.930341i	−0.647171	−	0.762345i	$-0.724048\pi$
$131$	9.97225e7	−	2.73985e8i	0.338616	−	0.930341i	0.985788	−	0.167996i	$-0.0537297\pi$
$132$		0			0
$133$	−4.34394e7	+	2.46357e8i	−0.138828	+	0.787332i
$134$		−	3.82180e8i		−	1.18536i
$135$		0			0
$136$	1.88968e8			0.552373
$137$	−4.29187e8	−	7.56772e7i	−1.21833	−	0.214824i	−0.472722	−	0.881212i	$-0.656728\pi$
$137$	−4.29187e8	−	7.56772e7i	−1.21833	−	0.214824i	−0.745605	+	0.666388i	$0.767840\pi$
$138$		0			0
$139$	−1.12303e8	−	4.08750e7i	−0.300838	−	0.109496i	0.187191	−	0.982324i	$-0.440062\pi$
$139$	−1.12303e8	−	4.08750e7i	−0.300838	−	0.109496i	−0.488029	+	0.872827i	$0.662284\pi$
$140$	−3.02918e7	−	3.61003e7i	−0.0788519	−	0.0939721i
$141$		0			0
$142$	−3.74818e8	+	1.36423e8i	−0.921864	+	0.335531i
$143$	1.47500e7	+	8.51589e6i	0.0352733	+	0.0203651i
$144$		0			0
$145$	−1.47057e8	−	2.54711e8i	−0.332671	−	0.576202i
$146$	−6.29278e8	+	7.49944e8i	−1.38494	+	1.65051i
$147$		0			0
$148$	−2.63981e7	−	1.49711e8i	−0.0550208	−	0.312038i
$149$	6.60425e8	−	1.16451e8i	1.33992	−	0.236264i	0.542686	−	0.839936i	$-0.317407\pi$
$149$	6.60425e8	−	1.16451e8i	1.33992	−	0.236264i	0.797233	+	0.603672i	$0.206296\pi$
$150$		0			0
$151$	−6.82796e8	−	5.72934e8i	−1.31336	−	1.10204i	−0.987668	−	0.156562i	$-0.949959\pi$
$151$	−6.82796e8	−	5.72934e8i	−1.31336	−	1.10204i	−0.325691	−	0.945476i	$-0.605597\pi$
$152$	−4.39762e8	+	2.53896e8i	−0.823840	+	0.475644i
$153$		0			0
$154$	5.80229e6	−	1.00499e7i	0.0103161	−	0.0178681i
$155$	−9.28162e7	−	2.55010e8i	−0.160804	−	0.441805i
$156$		0			0
$157$	9.14157e8	−	7.67068e8i	1.50460	−	1.26251i	0.631092	−	0.775708i	$-0.282607\pi$
$157$	9.14157e8	−	7.67068e8i	1.50460	−	1.26251i	0.873511	−	0.486804i	$-0.161837\pi$
$158$	2.47560e8	−	6.80164e8i	0.397239	−	1.09140i
$159$		0			0
$160$	4.20071e7	−	2.38234e8i	0.0640977	−	0.363516i
$161$		−	3.96499e8i		−	0.590118i
$162$		0			0
$163$	−8.51414e8			−1.20612			−0.603060	−	0.797696i	$-0.706052\pi$
$163$	−8.51414e8			−1.20612			−0.603060	+	0.797696i	$0.706052\pi$
$164$	2.18168e6	+	384689.i	0.00301589	+	0.000531783i
$165$		0			0
$166$	3.23385e8	+	1.17703e8i	0.425880	+	0.155008i
$167$	−9.10357e8	−	1.08492e9i	−1.17043	−	1.39487i	−0.902093	−	0.431541i	$-0.857970\pi$
$167$	−9.10357e8	−	1.08492e9i	−1.17043	−	1.39487i	−0.268338	−	0.963325i	$-0.586474\pi$
$168$		0			0
$169$	−8.68649e8	+	3.16162e8i	−1.06487	+	0.387582i
$170$	−3.39675e8	−	1.96111e8i	−0.406694	−	0.234805i
$171$		0			0
$172$	4.27117e7	+	7.39789e7i	0.0488015	+	0.0845267i
$173$	−2.97039e8	+	3.53997e8i	−0.331611	+	0.395199i	−0.905926	−	0.423436i	$-0.860824\pi$
$173$	−2.97039e8	+	3.53997e8i	−0.331611	+	0.395199i	0.574315	+	0.818634i	$0.305268\pi$
$174$		0			0
$175$	7.17455e7	+	4.06889e8i	0.0764967	+	0.433834i
$176$	3.23134e7	−	5.69772e6i	0.0336769	−	0.00593814i
$177$		0			0
$178$	−1.28909e9	−	1.08167e9i	−1.28411	−	1.07750i
$179$	6.54667e8	−	3.77972e8i	0.637688	−	0.368170i	−0.146035	−	0.989279i	$-0.546651\pi$
$179$	6.54667e8	−	3.77972e8i	0.637688	−	0.368170i	0.783723	+	0.621110i	$0.213318\pi$
$180$		0			0
$181$	1.30127e8	−	2.25387e8i	0.121242	−	0.209997i	−0.799016	−	0.601310i	$-0.794646\pi$
$181$	1.30127e8	−	2.25387e8i	0.121242	−	0.209997i	0.920258	+	0.391313i	$0.127979\pi$
$182$	4.05511e8	+	1.11413e9i	0.369587	+	1.01543i
$183$		0			0
$184$	6.16553e8	−	5.17349e8i	0.537897	−	0.451349i
$185$	2.04068e8	−	5.60671e8i	0.174216	−	0.478654i
$186$		0			0
$187$	4.31045e6	−	2.44458e7i	0.00352498	−	0.0199911i
$188$		−	1.20131e8i		−	0.0961668i
$189$		0			0
$190$	1.05398e9			0.808754
$191$	3.97575e8	+	7.01032e7i	0.298735	+	0.0526750i	0.321007	−	0.947077i	$-0.395979\pi$
$191$	3.97575e8	+	7.01032e7i	0.298735	+	0.0526750i	−0.0222719	+	0.999752i	$0.507090\pi$
$192$		0			0
$193$	−1.13999e9	−	4.14921e8i	−0.821619	−	0.299045i	−0.103204	−	0.994660i	$-0.532910\pi$
$193$	−1.13999e9	−	4.14921e8i	−0.821619	−	0.299045i	−0.718414	+	0.695615i	$0.755132\pi$
$194$	9.19364e8	+	1.09566e9i	0.649053	+	0.773512i
$195$		0			0
$196$	−2.84606e8	+	1.03588e8i	−0.192850	+	0.0701916i
$197$	−1.93591e9	−	1.11770e9i	−1.28535	−	0.742096i	−0.307527	−	0.951539i	$-0.599502\pi$
$197$	−1.93591e9	−	1.11770e9i	−1.28535	−	0.742096i	−0.977821	+	0.209443i	$0.932835\pi$
$198$		0			0
$199$	−1.14409e8	−	1.98163e8i	−0.0729540	−	0.126360i	0.827241	−	0.561848i	$-0.189909\pi$
$199$	−1.14409e8	−	1.98163e8i	−0.0729540	−	0.126360i	−0.900195	+	0.435488i	$0.856576\pi$
$200$	−5.39095e8	+	6.42469e8i	−0.336935	+	0.401543i
$201$		0			0
$202$	6.32189e8	+	3.58532e9i	0.379701	+	2.15339i
$203$	1.27608e9	−	2.25007e8i	0.751439	−	0.132499i
$204$		0			0
$205$	6.66059e6	+	5.58890e6i	0.00377135	+	0.00316454i
$206$	1.68578e9	−	9.73285e8i	0.936121	−	0.540470i
$207$		0			0
$208$	−1.67618e9	+	2.90324e9i	−0.895506	+	1.55106i
$209$	2.28140e7	+	6.26811e7i	0.0119569	+	0.0328512i
$210$		0			0
$211$	2.08099e9	−	1.74615e9i	1.04988	−	0.880953i	0.0567980	−	0.998386i	$-0.481911\pi$
$211$	2.08099e9	−	1.74615e9i	1.04988	−	0.880953i	0.993081	+	0.117433i	$0.0374665\pi$
$212$	1.83751e8	−	5.04853e8i	0.0909677	−	0.249932i
$213$		0			0
$214$	−3.51533e8	+	1.99364e9i	−0.167614	+	0.950587i
$215$			3.35271e8i			0.156907i
$216$		0			0
$217$	1.19559e9			0.539192
$218$	1.39173e8	+	2.45400e7i	0.0616212	+	0.0108655i
$219$		0			0
$220$	−1.18081e7	−	4.29780e6i	−0.00504068	−	0.00183466i
$221$	1.63020e9	+	1.94280e9i	0.683395	+	0.814438i
$222$		0			0
$223$	9.99762e8	−	3.63884e8i	0.404275	−	0.147144i	−0.131876	−	0.991266i	$-0.542100\pi$
$223$	9.99762e8	−	3.63884e8i	0.404275	−	0.147144i	0.536151	+	0.844122i	$0.319878\pi$
$224$	9.22981e8	+	5.32883e8i	0.366607	+	0.211661i
$225$		0			0
$226$	1.63635e9	+	2.83424e9i	0.627253	+	1.08643i
$227$	1.55800e9	−	1.85676e9i	0.586767	−	0.699281i	−0.388214	−	0.921569i	$-0.626908\pi$
$227$	1.55800e9	−	1.85676e9i	0.586767	−	0.699281i	0.974981	+	0.222288i	$0.0713525\pi$
$228$		0			0
$229$	−5.67440e8	−	3.21811e9i	−0.206337	−	1.17020i	−0.895321	−	0.445421i	$-0.853054\pi$
$229$	−5.67440e8	−	3.21811e9i	−0.206337	−	1.17020i	0.688984	−	0.724777i	$-0.258057\pi$
$230$	−1.64517e9	+	2.90089e8i	−0.587896	+	0.103662i
$231$		0			0
$232$	2.01490e9	+	1.69070e9i	0.695508	+	0.583600i
$233$	−3.12090e9	+	1.80185e9i	−1.05890	+	0.611358i	−0.925129	−	0.379653i	$-0.876043\pi$
$233$	−3.12090e9	+	1.80185e9i	−1.05890	+	0.611358i	−0.133775	+	0.991012i	$0.542710\pi$
$234$		0			0
$235$	2.35747e8	−	4.08325e8i	0.0772991	−	0.133886i
$236$	5.83293e8	+	1.60258e9i	0.188035	+	0.516622i
$237$		0			0
$238$	1.32372e9	−	1.11073e9i	0.412562	−	0.346180i
$239$	−7.81125e8	+	2.14612e9i	−0.239403	+	0.657754i	0.760561	+	0.649266i	$0.224924\pi$
$239$	−7.81125e8	+	2.14612e9i	−0.239403	+	0.657754i	−0.999964	+	0.00848739i	$0.997298\pi$
$240$		0			0
$241$	6.31882e8	−	3.58358e9i	0.187313	−	1.06230i	−0.735635	−	0.677379i	$-0.763116\pi$
$241$	6.31882e8	−	3.58358e9i	0.187313	−	1.06230i	0.922948	−	0.384926i	$-0.125773\pi$
$242$			3.97586e9i			1.15923i
$243$		0			0
$244$	6.92682e8			0.195422
$245$	−1.17065e9	−	2.06418e8i	−0.324911	−	0.0572905i
$246$		0			0
$247$	−6.40409e9	−	2.33090e9i	−1.72056	−	0.626232i
$248$	1.55999e9	+	1.85913e9i	0.412398	+	0.491477i
$249$		0			0
$250$	4.00387e9	−	1.45729e9i	1.02499	−	0.373066i
$251$	−3.02697e9	−	1.74762e9i	−0.762629	−	0.440304i	0.0676098	−	0.997712i	$-0.478463\pi$
$251$	−3.02697e9	−	1.74762e9i	−0.762629	−	0.440304i	−0.830239	+	0.557408i	$0.811796\pi$
$252$		0			0
$253$	−5.28628e7	−	9.15610e7i	−0.0129023	−	0.0223475i
$254$	−2.35692e9	+	2.80886e9i	−0.566251	+	0.674832i
$255$		0			0
$256$	6.92024e8	+	3.92466e9i	0.161124	+	0.913782i
$257$	−1.73307e9	+	3.05588e8i	−0.397269	+	0.0700493i	−0.368714	−	0.929543i	$-0.620202\pi$
$257$	−1.73307e9	+	3.05588e8i	−0.397269	+	0.0700493i	−0.0285553	+	0.999592i	$0.509091\pi$
$258$		0			0
$259$	2.01366e9	+	1.68966e9i	0.447494	+	0.375492i
$260$	1.11185e9	−	6.41927e8i	0.243306	−	0.140473i
$261$		0			0
$262$	2.70607e9	−	4.68706e9i	0.574294	−	0.994706i
$263$	−2.40551e9	−	6.60909e9i	−0.502787	−	1.38140i	−0.888542	−	0.458795i	$-0.848281\pi$
$263$	−2.40551e9	−	6.60909e9i	−0.502787	−	1.38140i	0.385755	−	0.922601i	$-0.373941\pi$
$264$		0			0
$265$	1.61530e9	−	1.35539e9i	0.327543	−	0.274841i
$266$	−1.58815e9	+	4.36342e9i	−0.317224	+	0.871566i
$267$		0			0
$268$	3.16602e8	−	1.79554e9i	0.0613726	−	0.348061i
$269$		−	4.63105e8i		−	0.0884445i	−0.999022	−	0.0442222i	$-0.985919\pi$
$269$		−	4.63105e8i		−	0.0884445i	0.999022	−	0.0442222i	$-0.0140810\pi$
$270$		0			0
$271$	−9.95879e9			−1.84642			−0.923208	−	0.384301i	$-0.874442\pi$
$271$	−9.95879e9			−1.84642			−0.923208	+	0.384301i	$0.874442\pi$
$272$	4.81167e9	+	8.48426e8i	0.879063	+	0.155002i
$273$		0			0
$274$	−7.60166e9	−	2.76678e9i	−1.34867	−	0.490876i
$275$	7.08157e7	+	8.43948e7i	0.0123822	+	0.0147566i
$276$		0			0
$277$	7.16936e9	−	2.60943e9i	1.21776	−	0.443228i	0.348370	−	0.937357i	$-0.386735\pi$
$277$	7.16936e9	−	2.60943e9i	1.21776	−	0.443228i	0.869388	+	0.494129i	$0.164513\pi$
$278$	−1.92117e9	−	1.10919e9i	−0.321652	−	0.185706i
$279$		0			0
$280$	8.27046e8	+	1.43249e9i	0.134554	+	0.233055i
$281$	6.16695e9	−	7.34949e9i	0.989112	−	1.17878i	0.00522454	−	0.999986i	$-0.498337\pi$
$281$	6.16695e9	−	7.34949e9i	0.989112	−	1.17878i	0.983887	−	0.178791i	$-0.0572186\pi$
$282$		0			0
$283$	1.71278e9	+	9.71364e9i	0.267027	+	1.51439i	0.763201	+	0.646162i	$0.223627\pi$
$283$	1.71278e9	+	9.71364e9i	0.267027	+	1.51439i	−0.496174	+	0.868223i	$0.665262\pi$
$284$	−1.87396e9	+	3.30430e8i	−0.288063	+	0.0507933i
$285$		0			0
$286$	2.42182e8	+	2.03215e8i	0.0361974	+	0.0303733i
$287$	−3.31741e7	+	1.91531e7i	−0.00488958	+	0.00282300i
$288$		0			0
$289$	−1.63974e9	+	2.84011e9i	−0.235062	+	0.407139i
$290$	−1.86722e9	−	5.13015e9i	−0.264000	−	0.725334i
$291$		0			0
$292$	−3.57770e9	+	3.00204e9i	−0.492121	+	0.412939i
$293$	−6.70230e8	+	1.84144e9i	−0.0909396	+	0.249855i	−0.976821	−	0.214057i	$-0.931332\pi$
$293$	−6.70230e8	+	1.84144e9i	−0.0909396	+	0.249855i	0.885882	+	0.463911i	$0.153554\pi$
$294$		0			0
$295$	−1.16232e9	+	6.59182e9i	−0.153475	+	0.870397i
$296$			5.33588e9i			0.695087i
$297$		0			0
$298$	1.24480e10			1.57846
$299$	1.06378e10	+	1.87573e9i	1.33097	+	0.234686i
$300$		0			0
$301$	−1.38801e9	−	5.05194e8i	−0.169093	−	0.0615449i
$302$	−1.06349e10	−	1.26742e10i	−1.27851	−	1.52367i
$303$		0			0
$304$	−1.23375e10	+	4.49049e9i	−1.44455	+	0.525775i
$305$	2.35442e9	+	1.35932e9i	0.272072	+	0.157081i
$306$		0			0
$307$	−2.48105e9	−	4.29730e9i	−0.279307	−	0.483773i	0.691906	−	0.721988i	$-0.256771\pi$
$307$	−2.48105e9	−	4.29730e9i	−0.279307	−	0.483773i	−0.971213	+	0.238214i	$0.923438\pi$
$308$	3.55854e7	−	4.24090e7i	0.00395429	−	0.00471254i
$309$		0			0
$310$	−8.74722e8	−	4.96080e9i	−0.0947160	−	0.537161i
$311$	6.42742e9	−	1.13333e9i	0.687060	−	0.121147i	0.180790	−	0.983522i	$-0.442135\pi$
$311$	6.42742e9	−	1.13333e9i	0.687060	−	0.121147i	0.506271	+	0.862375i	$0.331024\pi$
$312$		0			0
$313$	6.45751e9	+	5.41849e9i	0.672802	+	0.564548i	0.913893	−	0.405954i	$-0.133061\pi$
$313$	6.45751e9	+	5.41849e9i	0.672802	+	0.564548i	−0.241091	+	0.970502i	$0.577505\pi$
$314$	1.91834e10	−	1.10755e10i	1.97336	−	1.13932i
$315$		0			0
$316$	1.72652e9	−	2.99043e9i	0.173151	−	0.299906i
$317$	1.74715e8	+	4.80026e8i	0.0173019	+	0.0475366i	0.948043	−	0.318142i	$-0.103059\pi$
$317$	1.74715e8	+	4.80026e8i	0.0173019	+	0.0475366i	−0.930741	+	0.365679i	$0.880837\pi$
$318$		0			0
$319$	2.64678e8	−	2.22091e8i	0.0255597	−	0.0214471i
$320$	−9.09751e8	+	2.49952e9i	−0.0867607	+	0.238373i
$321$		0			0
$322$	1.27803e9	−	7.24806e9i	0.118882	−	0.674215i
$323$			9.93262e9i			0.912544i
$324$		0			0
$325$	−1.12560e10			−1.00890
$326$	−1.55640e10	−	2.74435e9i	−1.37800	−	0.242979i
$327$		0			0
$328$	−7.30682e7	−	2.65946e7i	−0.00631296	−	0.00229773i
$329$	1.33522e9	+	1.59125e9i	0.113965	+	0.135818i
$330$		0			0
$331$	−7.92073e9	+	2.88291e9i	−0.659862	+	0.240170i	−0.650177	−	0.759783i	$-0.725305\pi$
$331$	−7.92073e9	+	2.88291e9i	−0.659862	+	0.240170i	−0.00968542	+	0.999953i	$0.503083\pi$
$332$	1.42180e9	+	8.20879e8i	0.117027	+	0.0675658i
$333$		0			0
$334$	−1.31444e10	−	2.27668e10i	−1.05622	−	1.82944i
$335$	4.59971e9	−	5.48172e9i	0.365217	−	0.435249i
$336$		0			0
$337$	2.27225e9	+	1.28866e10i	0.176172	+	0.999120i	0.936783	+	0.349912i	$0.113788\pi$
$337$	2.27225e9	+	1.28866e10i	0.176172	+	0.999120i	−0.760611	+	0.649208i	$0.775101\pi$
$338$	−1.68981e10	+	2.97959e9i	−1.29471	+	0.228292i
$339$		0			0
$340$	−1.43338e9	−	1.20275e9i	−0.107262	−	0.0900035i
$341$	2.76090e8	−	1.59400e8i	0.0204189	−	0.0117889i
$342$		0			0
$343$	7.03206e9	−	1.21799e10i	0.508050	−	0.879968i
$344$	−1.02549e9	−	2.81751e9i	−0.0732315	−	0.201202i
$345$		0			0
$346$	−6.57095e9	+	5.51368e9i	−0.458483	+	0.384713i
$347$	5.29741e9	−	1.45545e10i	0.365381	−	1.00388i	−0.611715	−	0.791078i	$-0.709520\pi$
$347$	5.29741e9	−	1.45545e10i	0.365381	−	1.00388i	0.977096	−	0.212798i	$-0.0682576\pi$
$348$		0			0
$349$	−4.91194e8	+	2.78570e9i	−0.0331094	+	0.187773i	−0.996877	−	0.0789708i	$-0.974837\pi$
$349$	−4.91194e8	+	2.78570e9i	−0.0331094	+	0.187773i	0.963768	+	0.266744i	$0.0859477\pi$
$350$			7.66924e9i			0.511070i
$351$		0			0
$352$	2.84184e8			0.0185110
$353$	−1.90149e10	−	3.35285e9i	−1.22461	−	0.215931i	−0.476299	−	0.879284i	$-0.658022\pi$
$353$	−1.90149e10	−	3.35285e9i	−1.22461	−	0.215931i	−0.748307	+	0.663352i	$0.769133\pi$
$354$		0			0
$355$	−7.01802e9	−	2.55435e9i	−0.441877	−	0.160830i
$356$	−5.16025e9	−	6.14975e9i	−0.321271	−	0.382875i
$357$		0			0
$358$	1.31857e10	−	4.79921e9i	0.802734	−	0.292171i
$359$	7.35567e9	+	4.24680e9i	0.442838	+	0.255672i	0.704801	−	0.709405i	$-0.251036\pi$
$359$	7.35567e9	+	4.24680e9i	0.442838	+	0.255672i	−0.261963	+	0.965078i	$0.584370\pi$
$360$		0			0
$361$	−4.85363e9	−	8.40674e9i	−0.285784	−	0.494993i
$362$	3.10523e9	−	3.70066e9i	0.180825	−	0.215499i
$363$		0			0
$364$	9.82190e8	+	5.57028e9i	0.0559487	+	0.317301i
$365$	−1.80518e10	+	3.18302e9i	−1.01707	+	0.179336i
$366$		0			0
$367$	1.46247e10	+	1.22716e10i	0.806163	+	0.676451i	0.949689	−	0.313195i	$-0.101400\pi$
$367$	1.46247e10	+	1.22716e10i	0.806163	+	0.676451i	−0.143526	+	0.989647i	$0.545844\pi$
$368$	1.80220e10	−	1.04050e10i	0.982678	−	0.567349i
$369$		0			0
$370$	5.53759e9	−	9.59138e9i	0.295470	−	0.511769i
$371$	3.17731e9	+	8.72959e9i	0.167712	+	0.460785i
$372$		0			0
$373$	2.34539e9	−	1.96802e9i	0.121166	−	0.101670i	−0.580191	−	0.814480i	$-0.697022\pi$
$373$	2.34539e9	−	1.96802e9i	0.121166	−	0.101670i	0.701357	+	0.712810i	$0.252578\pi$
$374$	1.57591e8	−	4.32978e8i	0.00805463	−	0.0221299i
$375$		0			0
$376$	−7.32200e8	+	4.15251e9i	−0.0366335	+	0.207759i
$377$			3.53008e10i			1.74751i
$378$		0			0
$379$	9.45638e9			0.458319			0.229160	−	0.973389i	$-0.426402\pi$
$379$	9.45638e9			0.458319			0.229160	+	0.973389i	$0.426402\pi$
$380$	4.95173e9	+	8.73124e8i	0.237478	+	0.0418737i
$381$		0			0
$382$	7.04176e9	+	2.56299e9i	0.330695	+	0.120363i
$383$	−2.14845e9	−	2.56042e9i	−0.0998459	−	0.118992i	0.713808	−	0.700342i	$-0.246969\pi$
$383$	−2.14845e9	−	2.56042e9i	−0.0998459	−	0.118992i	−0.813653	+	0.581350i	$0.802525\pi$
$384$		0			0
$385$	2.04178e8	−	7.43148e7i	0.00929323	−	0.00338246i
$386$	−1.95017e10	−	1.12593e10i	−0.878462	−	0.507180i
$387$		0			0
$388$	3.41165e9	+	5.90915e9i	0.150535	+	0.260734i
$389$	−1.93823e9	+	2.30989e9i	−0.0846461	+	0.100877i	−0.806705	−	0.590954i	$-0.798751\pi$
$389$	−1.93823e9	+	2.30989e9i	−0.0846461	+	0.100877i	0.722059	+	0.691831i	$0.243196\pi$
$390$		0			0
$391$	−2.73378e9	−	1.55040e10i	−0.116965	−	0.663342i
$392$	1.04692e10	−	1.84600e9i	0.443371	−	0.0781783i
$393$		0			0
$394$	−3.17861e10	−	2.66717e10i	−1.31902	−	1.10679i
$395$	1.17369e10	−	6.77629e9i	0.482130	−	0.278358i
$396$		0			0
$397$	−4.50332e8	+	7.79998e8i	−0.0181289	+	0.0314001i	−0.874948	−	0.484218i	$-0.839104\pi$
$397$	−4.50332e8	+	7.79998e8i	−0.0181289	+	0.0314001i	0.856819	+	0.515618i	$0.172438\pi$
$398$	−1.45268e9	−	3.99121e9i	−0.0578947	−	0.159064i
$399$		0			0
$400$	−1.66114e10	+	1.39387e10i	−0.648885	+	0.544479i
$401$	−3.39206e9	+	9.31962e9i	−0.131186	+	0.360430i	−0.987843	−	0.155457i	$-0.950315\pi$
$401$	−3.39206e9	+	9.31962e9i	−0.131186	+	0.360430i	0.856657	+	0.515886i	$0.172537\pi$
$402$		0			0
$403$	−5.65602e9	+	3.20769e10i	−0.214432	+	1.21611i
$404$			1.73681e10i			0.651968i
$405$		0			0
$406$	2.40522e10			0.885218
$407$	6.90274e8	+	1.21714e8i	0.0251561	+	0.00443570i
$408$		0			0
$409$	4.63141e10	+	1.68570e10i	1.65508	+	0.602402i	0.989579	−	0.143991i	$-0.0459937\pi$
$409$	4.63141e10	+	1.68570e10i	1.65508	+	0.602402i	0.665506	+	0.746393i	$0.268216\pi$
$410$	1.03742e8	+	1.23635e8i	0.00367129	+	0.00437527i
$411$		0			0
$412$	8.72631e9	−	3.17612e9i	0.302860	−	0.110232i
$413$	−2.55385e10	−	1.47446e10i	−0.877798	−	0.506797i
$414$		0			0
$415$	3.22180e9	+	5.58032e9i	0.108619	+	0.188134i
$416$	−1.86633e10	+	2.22420e10i	−0.623182	+	0.742679i
$417$		0			0
$418$	2.15005e8	+	1.21935e9i	0.00704277	+	0.0399415i
$419$	9.07900e9	−	1.60087e9i	0.294565	−	0.0519398i	−0.0244125	−	0.999702i	$-0.507772\pi$
$419$	9.07900e9	−	1.60087e9i	0.294565	−	0.0519398i	0.318978	+	0.947762i	$0.396660\pi$
$420$		0			0
$421$	2.97544e10	+	2.49669e10i	0.947159	+	0.794761i	0.978817	−	0.204738i	$-0.0656343\pi$
$421$	2.97544e10	+	2.49669e10i	0.947159	+	0.794761i	−0.0316579	+	0.999499i	$0.510079\pi$
$422$	4.36690e10	−	2.52123e10i	1.37697	−	0.794993i
$423$		0			0
$424$	−9.42870e9	+	1.63310e10i	−0.291735	+	0.505300i
$425$	5.61083e9	+	1.54156e10i	0.171977	+	0.472504i
$426$		0			0
$427$	−9.17523e9	+	7.69893e9i	−0.275998	+	0.231590i
$428$	−3.30310e9	+	9.07519e9i	−0.0984344	+	0.270446i
$429$		0			0
$430$	−1.08067e9	+	6.12880e9i	−0.0316097	+	0.179268i
$431$			4.74289e10i			1.37447i	0.726436	+	0.687234i	$0.241175\pi$
$431$			4.74289e10i			1.37447i	−0.726436	+	0.687234i	$0.758825\pi$
$432$		0			0
$433$	−2.37974e10			−0.676984			−0.338492	−	0.940969i	$-0.609917\pi$
$433$	−2.37974e10			−0.676984			−0.338492	+	0.940969i	$0.609917\pi$
$434$	2.18555e10	+	3.85372e9i	0.616031	+	0.108623i
$435$		0			0
$436$	6.33527e8	+	2.30585e8i	0.0175315	+	0.00638095i
$437$	2.71931e10	+	3.24075e10i	0.745647	+	0.888628i
$438$		0			0
$439$	2.94082e10	−	1.07037e10i	0.791789	−	0.288188i	0.0857097	−	0.996320i	$-0.472684\pi$
$439$	2.94082e10	−	1.07037e10i	0.791789	−	0.288188i	0.706080	+	0.708132i	$0.250462\pi$
$440$	3.81969e8	+	2.20530e8i	0.0101910	+	0.00588378i
$441$		0			0
$442$	2.35381e10	+	4.07692e10i	0.616712	+	1.06818i
$443$	−9.78540e8	+	1.16618e9i	−0.0254076	+	0.0302796i	−0.778599	−	0.627522i	$-0.784069\pi$
$443$	−9.78540e8	+	1.16618e9i	−0.0254076	+	0.0302796i	0.753191	+	0.657802i	$0.228514\pi$
$444$		0			0
$445$	−5.47133e9	−	3.10295e10i	−0.139525	−	0.791287i
$446$	1.94487e10	−	3.42933e9i	0.491531	−	0.0866702i
$447$		0			0
$448$	−8.97708e9	−	7.53266e9i	−0.222855	−	0.186998i
$449$	−2.91593e10	+	1.68352e10i	−0.717451	+	0.414221i	−0.813814	−	0.581126i	$-0.802612\pi$
$449$	−2.91593e10	+	1.68352e10i	−0.717451	+	0.414221i	0.0963628	+	0.995346i	$0.469279\pi$
$450$		0			0
$451$	−5.10712e6	+	8.84580e6i	−0.000123444	+	0.000213811i
$452$	5.33990e9	+	1.46712e10i	0.127932	+	0.351490i
$453$		0			0
$454$	3.44654e10	−	2.89199e10i	0.811260	−	0.680728i
$455$	−7.59270e9	+	2.08608e10i	−0.177154	+	0.486726i
$456$		0			0
$457$	1.09556e10	−	6.21321e10i	0.251171	−	1.42446i	−0.554541	−	0.832156i	$-0.687106\pi$
$457$	1.09556e10	−	6.21321e10i	0.251171	−	1.42446i	0.805713	−	0.592307i	$-0.201783\pi$
$458$		−	6.06566e10i		−	1.37853i
$459$		0			0
$460$	−7.96958e9			−0.177993
$461$	3.07188e10	+	5.41656e9i	0.680145	+	0.119928i	0.503039	−	0.864264i	$-0.332215\pi$
$461$	3.07188e10	+	5.41656e9i	0.680145	+	0.119928i	0.177106	+	0.984192i	$0.443326\pi$
$462$		0			0
$463$	4.22751e10	+	1.53869e10i	0.919942	+	0.334831i	0.758215	−	0.652004i	$-0.226072\pi$
$463$	4.22751e10	+	1.53869e10i	0.919942	+	0.334831i	0.161726	+	0.986836i	$0.448294\pi$
$464$	4.37142e10	+	5.20966e10i	0.943085	+	1.12393i
$465$		0			0
$466$	−6.28584e10	+	2.28786e10i	−1.33297	+	0.485161i
$467$	−6.93681e10	−	4.00497e10i	−1.45845	−	0.842037i	−0.459516	−	0.888169i	$-0.651977\pi$
$467$	−6.93681e10	−	4.00497e10i	−1.45845	−	0.842037i	−0.998935	+	0.0461320i	$0.985310\pi$
$468$		0			0
$469$	1.57631e10	+	2.73026e10i	0.325800	+	0.564302i
$470$	5.62563e9	−	6.70437e9i	0.115287	−	0.137394i
$471$		0			0
$472$	−1.03946e10	−	5.89507e10i	−0.209431	−	1.18774i
$473$	−3.87878e8	+	6.83934e7i	−0.00774909	+	0.00136637i
$474$		0			0
$475$	−3.37697e10	−	2.83362e10i	−0.663366	−	0.556630i
$476$	7.13918e9	−	4.12181e9i	0.139066	−	0.0802897i
$477$		0			0
$478$	−2.11966e10	+	3.67137e10i	−0.406027	+	0.703260i
$479$	−5.05947e9	−	1.39008e10i	−0.0961088	−	0.264057i	0.882317	−	0.470656i	$-0.155983\pi$
$479$	−5.05947e9	−	1.39008e10i	−0.0961088	−	0.264057i	−0.978426	+	0.206599i	$0.933760\pi$
$480$		0			0
$481$	−5.48586e10	+	4.60319e10i	−1.02486	+	0.859960i
$482$	2.31018e10	−	6.34716e10i	0.428013	−	1.17596i
$483$		0			0
$484$	−3.29364e9	+	1.86792e10i	−0.0600199	+	0.340390i
$485$			2.67802e10i			0.484002i
$486$		0			0
$487$	−1.00517e10			−0.178699			−0.0893495	−	0.996000i	$-0.528479\pi$
$487$	−1.00517e10			−0.178699			−0.0893495	+	0.996000i	$0.528479\pi$
$488$	−2.39435e10	−	4.22189e9i	−0.422191	−	0.0744436i
$489$		0			0
$490$	−2.07344e10	−	7.54669e9i	−0.359672	−	0.130910i
$491$	−6.53311e10	−	7.78585e10i	−1.12407	−	1.33962i	−0.933763	−	0.357891i	$-0.883496\pi$
$491$	−6.53311e10	−	7.78585e10i	−1.12407	−	1.33962i	−0.190308	−	0.981724i	$-0.560949\pi$
$492$		0			0
$493$	4.83463e10	−	1.75966e10i	0.818418	−	0.297880i
$494$	−1.09554e11	−	6.32513e10i	−1.83960	−	1.06209i
$495$		0			0
$496$	3.13748e10	+	5.43428e10i	0.518387	+	0.897873i
$497$	2.11498e10	−	2.52053e10i	0.346641	−	0.413111i
$498$		0			0
$499$	−1.13923e10	−	6.46088e10i	−0.183742	−	1.04205i	−0.927561	−	0.373672i	$-0.878099\pi$
$499$	−1.13923e10	−	6.46088e10i	−0.183742	−	1.04205i	0.743819	−	0.668381i	$-0.233012\pi$
$500$	2.00180e10	−	3.52971e9i	0.320288	−	0.0564754i
$501$		0			0
$502$	−4.97004e10	−	4.17036e10i	−0.782609	−	0.656687i
$503$	9.70501e9	−	5.60319e9i	0.151609	−	0.0875313i	−0.422277	−	0.906467i	$-0.638769\pi$
$503$	9.70501e9	−	5.60319e9i	0.151609	−	0.0875313i	0.573885	+	0.818936i	$0.305436\pi$
$504$		0			0
$505$	−3.40833e10	+	5.90339e10i	−0.524053	+	0.907687i
$506$	−6.71212e8	−	1.84414e9i	−0.0102390	−	0.0281314i
$507$		0			0
$508$	−1.34000e10	+	1.12440e10i	−0.201210	+	0.168836i
$509$	9.23104e9	−	2.53621e10i	0.137524	−	0.377845i	−0.851743	−	0.523959i	$-0.824454\pi$
$509$	9.23104e9	−	2.53621e10i	0.137524	−	0.377845i	0.989268	+	0.146114i	$0.0466767\pi$
$510$		0			0
$511$	1.40233e10	−	7.95299e10i	0.205667	−	1.16640i
$512$		−	8.00907e9i		−	0.116547i
$513$		0			0
$514$	−3.26658e10			−0.467995
$515$	3.58935e10	+	6.32899e9i	0.510254	+	0.0899716i
$516$		0			0
$517$	5.20486e8	+	1.89441e8i	0.00728529	+	0.00265163i
$518$	3.13638e10	+	3.73779e10i	0.435621	+	0.519153i
$519$		0			0
$520$	−4.23452e10	+	1.54124e10i	−0.579149	+	0.210793i
$521$	−1.10388e11	−	6.37326e10i	−1.49820	−	0.864989i	−0.498207	−	0.867058i	$-0.666008\pi$
$521$	−1.10388e11	−	6.37326e10i	−1.49820	−	0.864989i	−0.999998	+	0.00206969i	$0.999341\pi$
$522$		0			0
$523$	−4.11516e10	−	7.12766e10i	−0.550022	−	0.952666i	−0.998272	−	0.0587576i	$-0.981286\pi$
$523$	−4.11516e10	−	7.12766e10i	−0.550022	−	0.952666i	0.448251	−	0.893908i	$-0.352047\pi$
$524$	1.65963e10	−	1.97787e10i	0.220134	−	0.262345i
$525$		0			0
$526$	−2.26701e10	−	1.28569e11i	−0.296149	−	1.67955i
$527$	4.67503e10	−	8.24334e9i	0.606096	−	0.106871i
$528$		0			0
$529$	8.62378e9	+	7.23621e9i	0.110122	+	0.0924035i
$530$	3.38966e10	−	1.95702e10i	0.429589	−	0.248023i
$531$		0			0
$532$	−1.10761e10	+	1.91843e10i	−0.138274	+	0.239497i
$533$	−3.56927e8	−	9.80648e8i	−0.00442252	−	0.0121508i
$534$		0			0
$535$	−2.90364e10	+	2.43645e10i	−0.354428	+	0.297401i
$536$	−2.18876e10	+	6.01356e10i	−0.265179	+	0.728573i
$537$		0			0
$538$	1.49272e9	−	8.46563e9i	0.0178176	−	0.101049i
$539$		−	1.39645e9i		−	0.0165451i
$540$		0			0
$541$	−2.87855e9			−0.0336035			−0.0168017	−	0.999859i	$-0.505348\pi$
$541$	−2.87855e9			−0.0336035			−0.0168017	+	0.999859i	$0.505348\pi$
$542$	−1.82048e11	−	3.21000e10i	−2.10955	−	0.371970i
$543$		0			0
$544$	3.97648e10	+	1.44732e10i	0.454049	+	0.165260i
$545$	1.70085e9	+	2.02700e9i	0.0192788	+	0.0229756i
$546$		0			0
$547$	−3.04941e10	+	1.10989e10i	−0.340617	+	0.123974i	−0.506665	−	0.862143i	$-0.669122\pi$
$547$	−3.04941e10	+	1.10989e10i	−0.340617	+	0.123974i	0.166047	+	0.986118i	$0.446899\pi$
$548$	−3.34217e10	−	1.92960e10i	−0.370600	−	0.213966i
$549$		0			0
$550$	1.02249e9	+	1.77101e9i	0.0111740	+	0.0193540i
$551$	−8.88675e10	+	1.05908e11i	−0.964132	+	1.14901i
$552$		0			0
$553$	1.03682e10	+	5.88009e10i	0.110867	+	0.628757i
$554$	1.39468e11	−	2.45919e10i	1.48059	−	0.261068i
$555$		0			0
$556$	−8.10706e9	−	6.80263e9i	−0.0848329	−	0.0711832i
$557$	1.21822e11	−	7.03341e10i	1.26563	−	0.730710i	0.291470	−	0.956580i	$-0.405856\pi$
$557$	1.21822e11	−	7.03341e10i	1.26563	−	0.730710i	0.974157	+	0.225870i	$0.0725225\pi$
$558$		0			0
$559$	2.01203e10	−	3.48494e10i	0.206057	−	0.356901i
$560$	1.46274e10	+	4.01884e10i	0.148736	+	0.408648i
$561$		0			0
$562$	1.36422e11	−	1.14472e11i	1.36754	−	1.14750i
$563$	1.95156e10	−	5.36186e10i	0.194244	−	0.533681i	−0.803888	−	0.594781i	$-0.797239\pi$
$563$	1.95156e10	−	5.36186e10i	0.194244	−	0.533681i	0.998132	+	0.0611000i	$0.0194609\pi$
$564$		0			0
$565$	−1.06407e10	+	6.03465e10i	−0.104418	+	0.592186i
$566$			1.83087e11i			1.78399i
$567$		0			0
$568$	6.67901e10			0.641680
$569$	1.32018e11	+	2.32784e10i	1.25946	+	0.222077i	0.763237	−	0.646118i	$-0.223609\pi$
$569$	1.32018e11	+	2.32784e10i	1.25946	+	0.222077i	0.496223	+	0.868195i	$0.334720\pi$
$570$		0			0
$571$	5.91665e10	+	2.15349e10i	0.556585	+	0.202580i	0.604970	−	0.796248i	$-0.293185\pi$
$571$	5.91665e10	+	2.15349e10i	0.556585	+	0.202580i	−0.0483848	+	0.998829i	$0.515407\pi$
$572$	9.69461e8	+	1.15536e9i	0.00905621	+	0.0107928i
$573$		0			0
$574$	−6.68163e8	+	2.43192e8i	−0.00615510	+	0.00224027i
$575$	6.05109e10	+	3.49360e10i	0.553557	+	0.319596i
$576$		0			0
$577$	6.37070e10	+	1.10344e11i	0.574756	+	0.995507i	0.996068	+	0.0885910i	$0.0282364\pi$
$577$	6.37070e10	+	1.10344e11i	0.574756	+	0.995507i	−0.421312	+	0.906916i	$0.638430\pi$
$578$	−3.91291e10	+	4.66322e10i	−0.350581	+	0.417806i
$579$		0			0
$580$	−4.52261e9	−	2.56490e10i	−0.0399648	−	0.226651i
$581$	−2.79570e10	+	4.92956e9i	−0.245350	+	0.0432617i
$582$		0			0
$583$	1.89758e9	+	1.59226e9i	0.0164258	+	0.0137828i
$584$	1.41966e11	−	8.19639e10i	1.22048	−	0.704646i
$585$		0			0
$586$	−1.81874e10	+	3.15015e10i	−0.154234	+	0.267141i
$587$	1.06263e10	+	2.91956e10i	0.0895015	+	0.245903i	0.976365	−	0.216128i	$-0.0693429\pi$
$587$	1.06263e10	+	2.91956e10i	0.0895015	+	0.245903i	−0.886863	+	0.462032i	$0.847121\pi$
$588$		0			0
$589$	−9.77203e10	+	8.19971e10i	−0.811940	+	0.681298i
$590$	−4.24946e10	+	1.16753e11i	−0.350692	+	0.963518i
$591$		0			0
$592$	−2.39570e10	+	1.35867e11i	−0.195050	+	1.10618i
$593$			7.72499e10i			0.624711i	0.949965	+	0.312356i	$0.101118\pi$
$593$			7.72499e10i			0.624711i	−0.949965	+	0.312356i	$0.898882\pi$
$594$		0			0
$595$	3.23547e10			0.258148
$596$	5.84825e10	+	1.03120e10i	0.463491	+	0.0817259i
$597$		0			0
$598$	1.88415e11	+	6.85774e10i	1.47336	+	0.536261i
$599$	−7.99461e10	−	9.52760e10i	−0.620998	−	0.740076i	0.360244	−	0.932858i	$-0.382693\pi$
$599$	−7.99461e10	−	9.52760e10i	−0.620998	−	0.740076i	−0.981242	+	0.192782i	$0.938249\pi$
$600$		0			0
$601$	−2.16119e11	+	7.86608e10i	−1.65651	+	0.602921i	−0.989809	−	0.142402i	$-0.954517\pi$
$601$	−2.16119e11	+	7.86608e10i	−1.65651	+	0.602921i	−0.666703	+	0.745323i	$0.732295\pi$
$602$	−2.37446e10	−	1.37090e10i	−0.180792	−	0.104380i
$603$		0			0
$604$	−3.94648e10	−	6.83550e10i	−0.296526	−	0.513597i
$605$	−4.78512e10	+	5.70269e10i	−0.357167	+	0.425655i
$606$		0			0
$607$	4.05256e10	+	2.29832e11i	0.298521	+	1.69300i	0.652537	+	0.757757i	$0.273705\pi$
$607$	4.05256e10	+	2.29832e11i	0.298521	+	1.69300i	−0.354016	+	0.935240i	$0.615184\pi$
$608$	−1.11986e11	+	1.97461e10i	−0.819498	+	0.144500i
$609$		0			0
$610$	3.86576e10	+	3.24376e10i	0.279200	+	0.234277i
$611$	−4.90089e10	+	2.82953e10i	−0.351650	+	0.203025i
$612$		0			0
$613$	7.90435e10	−	1.36907e11i	0.559789	−	0.969583i	−0.437725	−	0.899109i	$-0.644216\pi$
$613$	7.90435e10	−	1.36907e11i	0.559789	−	0.969583i	0.997514	−	0.0704739i	$-0.0224512\pi$
$614$	−3.15025e10	−	8.65523e10i	−0.221652	−	0.608983i
$615$		0			0
$616$	−1.48854e9	+	1.24904e9i	−0.0103380	+	0.00867465i
$617$	6.27486e10	−	1.72400e11i	0.432976	−	1.18959i	−0.511002	−	0.859580i	$-0.670725\pi$
$617$	6.27486e10	−	1.72400e11i	0.432976	−	1.18959i	0.943977	−	0.330011i	$-0.107052\pi$
$618$		0			0
$619$	3.91904e10	−	2.22260e11i	0.266942	−	1.51391i	−0.496504	−	0.868034i	$-0.665383\pi$
$619$	3.91904e10	−	2.22260e11i	0.266942	−	1.51391i	0.763447	−	0.645871i	$-0.223506\pi$
$620$		−	2.40312e10i		−	0.162633i
$621$		0			0
$622$	1.21147e11			0.809378
$623$	1.36705e11	+	2.41048e10i	0.907470	+	0.160011i
$624$		0			0
$625$	−2.40786e10	−	8.76390e9i	−0.157802	−	0.0574351i
$626$	1.00579e11	+	1.19865e11i	0.654951	+	0.780540i
$627$		0			0
$628$	9.93014e10	−	3.61427e10i	0.638435	−	0.232371i
$629$	9.03887e10	+	5.21859e10i	0.577446	+	0.333389i
$630$		0			0
$631$	−1.16579e11	−	2.01921e11i	−0.735368	−	1.27369i	−0.954562	−	0.298013i	$-0.903676\pi$
$631$	−1.16579e11	−	2.01921e11i	−0.735368	−	1.27369i	0.219194	−	0.975681i	$-0.429657\pi$
$632$	−7.79064e10	+	9.28452e10i	−0.488320	+	0.581958i
$633$		0			0
$634$	1.64656e9	+	9.33810e9i	0.0101911	+	0.0577965i
$635$	−6.76118e10	+	1.19218e10i	−0.415841	+	0.0733240i
$636$		0			0
$637$	1.09295e11	+	9.17092e10i	0.663807	+	0.557000i
$638$	5.55421e9	−	3.20673e9i	0.0335228	−	0.0193544i
$639$		0			0
$640$	−5.56514e10	+	9.63910e10i	−0.331708	+	0.574535i
$641$	7.15456e10	+	1.96570e11i	0.423790	+	1.16435i	0.949521	+	0.313703i	$0.101570\pi$
$641$	7.15456e10	+	1.96570e11i	0.423790	+	1.16435i	−0.525731	+	0.850651i	$0.676208\pi$
$642$		0			0
$643$	2.36854e9	−	1.98744e9i	0.0138560	−	0.0116265i	−0.635833	−	0.771826i	$-0.719343\pi$
$643$	2.36854e9	−	1.98744e9i	0.0138560	−	0.0116265i	0.649689	+	0.760200i	$0.274899\pi$
$644$	1.20087e10	−	3.29937e10i	0.0698158	−	0.191817i
$645$		0			0
$646$	−3.20156e10	+	1.81570e11i	−0.183837	+	1.04259i
$647$		−	3.30829e10i		−	0.188793i	−0.995535	−	0.0943966i	$-0.969908\pi$
$647$		−	3.30829e10i		−	0.188793i	0.995535	−	0.0943966i	$-0.0300922\pi$
$648$		0			0
$649$	−7.86324e9			−0.0443224
$650$	−2.05761e11	−	3.62812e10i	−1.15268	−	0.203249i
$651$		0			0
$652$	−7.08483e10	−	2.57867e10i	−0.392048	−	0.142694i
$653$	−7.83339e10	−	9.33547e10i	−0.430821	−	0.513433i	0.506338	−	0.862335i	$-0.330999\pi$
$653$	−7.83339e10	−	9.33547e10i	−0.430821	−	0.513433i	−0.937159	+	0.348903i	$0.886554\pi$
$654$		0			0
$655$	9.52247e10	−	3.46589e10i	0.517350	−	0.188300i
$656$	−1.74112e9	−	1.00524e9i	−0.00940185	−	0.00542816i
$657$		0			0
$658$	1.92790e10	+	3.33921e10i	0.102844	+	0.178132i
$659$	1.08052e11	−	1.28771e11i	0.572916	−	0.682775i	−0.399310	−	0.916816i	$-0.630750\pi$
$659$	1.08052e11	−	1.28771e11i	0.572916	−	0.682775i	0.972227	+	0.234041i	$0.0751949\pi$
$660$		0			0
$661$	3.13825e10	+	1.77979e11i	0.164392	+	0.932316i	0.949689	+	0.313196i	$0.101400\pi$
$661$	3.13825e10	+	1.77979e11i	0.164392	+	0.932316i	−0.785296	+	0.619120i	$0.787489\pi$
$662$	−1.54084e11	+	2.71693e10i	−0.802282	+	0.141464i
$663$		0			0
$664$	−4.41434e10	−	3.70407e10i	−0.227088	−	0.190549i
$665$	−7.52949e10	+	4.34716e10i	−0.385016	+	0.222289i
$666$		0			0
$667$	1.09566e11	−	1.89773e11i	0.553569	−	0.958809i
$668$	−4.28942e10	−	1.17851e11i	−0.215423	−	0.591871i
$669$		0			0
$670$	1.01752e11	−	8.53804e10i	0.504946	−	0.423700i
$671$	−1.09233e9	+	3.00114e9i	−0.00538843	+	0.0148046i
$672$		0			0
$673$	1.10197e10	−	6.24957e10i	0.0537166	−	0.304642i	−0.946098	−	0.323880i	$-0.895013\pi$
$673$	1.10197e10	−	6.24957e10i	0.0537166	−	0.304642i	0.999815	+	0.0192375i	$0.00612385\pi$
$674$			2.42892e11i			1.17699i
$675$		0			0
$676$	−8.18580e10			−0.391990
$677$	−1.72977e11	−	3.05005e10i	−0.823442	−	0.145195i	−0.253977	−	0.967210i	$-0.581739\pi$
$677$	−1.72977e11	−	3.05005e10i	−0.823442	−	0.145195i	−0.569465	+	0.822015i	$0.692850\pi$
$678$		0			0
$679$	−1.10869e11	−	4.03530e10i	−0.521592	−	0.189844i
$680$	4.22161e10	+	5.03112e10i	0.197443	+	0.235304i
$681$		0			0
$682$	5.56075e9	−	2.02395e9i	0.0257037	−	0.00935538i
$683$	2.25895e11	+	1.30420e11i	1.03806	+	0.599325i	0.919284	−	0.393596i	$-0.128769\pi$
$683$	2.25895e11	+	1.30420e11i	1.03806	+	0.599325i	0.118778	+	0.992921i	$0.462102\pi$
$684$		0			0
$685$	−7.57333e10	−	1.31174e11i	−0.343973	−	0.595779i
$686$	1.67806e11	−	1.99984e11i	0.757725	−	0.903021i
$687$		0			0
$688$	−1.34619e10	−	7.63461e10i	−0.0600830	−	0.340748i
$689$	−2.49240e11	+	4.39478e10i	−1.10596	+	0.195011i
$690$		0			0
$691$	−4.63160e10	−	3.88637e10i	−0.203151	−	0.170464i	0.535536	−	0.844512i	$-0.320109\pi$
$691$	−4.63160e10	−	3.88637e10i	−0.203151	−	0.170464i	−0.738687	+	0.674048i	$0.764554\pi$
$692$	−3.54388e10	+	2.04606e10i	−0.154545	+	0.0892266i
$693$		0			0
$694$	1.43751e11	−	2.48984e11i	0.619687	−	1.07333i
$695$	−1.42063e10	−	3.90314e10i	−0.0608893	−	0.167292i
$696$		0			0
$697$	−1.16513e9	+	9.77658e8i	−0.00493676	+	0.00414244i
$698$	−1.79582e10	+	4.93397e10i	−0.0756556	+	0.207862i
$699$		0			0
$700$	−6.35327e9	+	3.60312e10i	−0.0264609	+	0.150067i
$701$			2.34678e11i			0.971852i	0.874000	+	0.485926i	$0.161518\pi$
$701$			2.34678e11i			0.971852i	−0.874000	+	0.485926i	$0.838482\pi$
$702$		0			0
$703$	−2.80467e11			−1.14831
$704$	−3.07730e9	−	5.42611e8i	−0.0125279	−	0.00220901i
$705$		0			0
$706$	−3.36789e11	−	1.22581e11i	−1.35562	−	0.493406i
$707$	−1.93041e11	−	2.30057e11i	−0.772629	−	0.920783i
$708$		0			0
$709$	2.36805e11	−	8.61899e10i	0.937143	−	0.341092i	0.172106	−	0.985078i	$-0.444943\pi$
$709$	2.36805e11	−	8.61899e10i	0.937143	−	0.341092i	0.765037	+	0.643986i	$0.222721\pi$
$710$	−1.20057e11	−	6.93149e10i	−0.472448	−	0.272768i
$711$		0			0
$712$	1.40889e11	+	2.44026e11i	0.548222	+	0.949548i
$713$	1.29965e11	−	1.54887e11i	0.502886	−	0.599317i
$714$		0			0
$715$	1.02790e9	+	5.82953e9i	0.00393304	+	0.0223054i
$716$	6.59241e10	−	1.16242e10i	0.250837	−	0.0442294i
$717$		0			0
$718$	1.20774e11	+	1.01341e11i	0.454439	+	0.381320i
$719$	2.59305e11	−	1.49710e11i	0.970275	−	0.560189i	0.0709551	−	0.997480i	$-0.477395\pi$
$719$	2.59305e11	−	1.49710e11i	0.970275	−	0.560189i	0.899320	+	0.437291i	$0.144062\pi$
$720$		0			0
$721$	−8.02868e10	+	1.39061e11i	−0.297100	+	0.514593i
$722$	−6.16278e10	−	1.69321e11i	−0.226792	−	0.623106i
$723$		0			0
$724$	1.76545e10	−	1.48139e10i	0.0642540	−	0.0539155i
$725$	−7.80977e10	+	2.14572e11i	−0.282674	+	0.776641i
$726$		0			0
$727$	3.23715e10	−	1.83588e11i	0.115885	−	0.657214i	−0.870424	−	0.492303i	$-0.836155\pi$
$727$	3.23715e10	−	1.83588e11i	0.115885	−	0.657214i	0.986308	−	0.164911i	$-0.0527337\pi$
$728$		−	1.98531e11i		−	0.706810i
$729$		0			0
$730$	−3.40249e11			−1.19813
$731$	−5.77575e10	−	1.01842e10i	−0.202273	−	0.0356663i
$732$		0			0
$733$	−4.74456e11	−	1.72688e11i	−1.64354	−	0.598199i	−0.655886	−	0.754860i	$-0.727705\pi$
$733$	−4.74456e11	−	1.72688e11i	−1.64354	−	0.598199i	−0.987652	+	0.156661i	$0.949927\pi$
$734$	2.27787e11	+	2.71466e11i	0.784774	+	0.935257i
$735$		0			0
$736$	1.69366e11	−	6.16442e10i	0.577185	−	0.210078i
$737$	7.28016e9	+	4.20320e9i	0.0246758	+	0.0142466i
$738$		0			0
$739$	−3.06215e10	−	5.30379e10i	−0.102671	−	0.177832i	0.810113	−	0.586273i	$-0.199406\pi$
$739$	−3.06215e10	−	5.30379e10i	−0.102671	−	0.177832i	−0.912784	+	0.408442i	$0.866072\pi$
$740$	3.39620e10	−	4.04743e10i	0.113257	−	0.134975i
$741$		0			0
$742$	2.99438e10	+	1.69820e11i	0.0987849	+	0.560237i
$743$	3.40134e11	−	5.99748e10i	1.11608	−	0.196795i	0.414961	−	0.909839i	$-0.363795\pi$
$743$	3.40134e11	−	5.99748e10i	1.11608	−	0.196795i	0.701119	+	0.713044i	$0.252684\pi$
$744$		0			0
$745$	1.78545e11	+	1.49817e11i	0.579593	+	0.486336i
$746$	4.92176e10	−	2.84158e10i	0.158915	−	0.0917496i
$747$		0			0
$748$	1.09907e9	−	1.90364e9i	0.00351090	−	0.00608106i
$749$	−5.71151e10	−	1.56923e11i	−0.181478	−	0.498607i
$750$		0			0
$751$	−2.09990e11	+	1.76202e11i	−0.660143	+	0.553926i	−0.910130	−	0.414324i	$-0.864018\pi$
$751$	−2.09990e11	+	1.76202e11i	−0.660143	+	0.553926i	0.249987	+	0.968249i	$0.419574\pi$
$752$	−3.72878e10	+	1.02447e11i	−0.116599	+	0.320353i
$753$		0			0
$754$	−1.13784e11	+	6.45304e11i	−0.352045	+	1.99654i
$755$		−	3.09784e11i		−	0.953392i
$756$		0			0
$757$	4.12942e11			1.25749			0.628747	−	0.777610i	$-0.283568\pi$
$757$	4.12942e11			1.25749			0.628747	+	0.777610i	$0.283568\pi$
$758$	1.72864e11	+	3.04806e10i	0.523634	+	0.0923308i
$759$		0			0
$760$	−1.65842e11	−	6.03616e10i	−0.497096	−	0.180928i
$761$	−4.01928e10	−	4.78999e10i	−0.119842	−	0.142822i	0.702788	−	0.711400i	$-0.251938\pi$
$761$	−4.01928e10	−	4.78999e10i	−0.119842	−	0.142822i	−0.822630	+	0.568577i	$0.807494\pi$
$762$		0			0
$763$	−1.09546e10	+	3.98713e9i	−0.0323219	+	0.0117642i
$764$	3.09600e10	+	1.78748e10i	0.0908715	+	0.0524647i
$765$		0			0
$766$	−3.10210e10	−	5.37300e10i	−0.0901033	−	0.156064i
$767$	5.16405e11	−	6.15427e11i	1.49214	−	1.77826i
$768$		0			0
$769$	6.94082e10	+	3.93633e11i	0.198475	+	1.12561i	0.907383	+	0.420305i	$0.138077\pi$
$769$	6.94082e10	+	3.93633e11i	0.198475	+	1.12561i	−0.708908	+	0.705301i	$0.750812\pi$
$770$	3.97194e9	−	7.00361e8i	0.0112990	−	0.00199232i
$771$		0			0
$772$	−8.22944e10	−	6.90532e10i	−0.231687	−	0.194408i
$773$	−3.03906e11	+	1.75460e11i	−0.851179	+	0.491428i	−0.861048	−	0.508523i	$-0.830192\pi$
$773$	−3.03906e11	+	1.75460e11i	−0.851179	+	0.491428i	0.00986956	+	0.999951i	$0.496858\pi$
$774$		0			0
$775$	−1.05345e11	+	1.82462e11i	−0.292015	+	0.505785i
$776$	−8.19123e10	−	2.25052e11i	−0.225893	−	0.620635i
$777$		0			0
$778$	−4.28766e10	+	3.59777e10i	−0.117031	+	0.0982008i
$779$	1.39788e9	−	3.84064e9i	0.00379594	−	0.0104293i
$780$		0			0
$781$	1.52351e9	−	8.64027e9i	0.00409489	−	0.0232233i
$782$		−	2.92228e11i		−	0.781438i
$783$		0			0
$784$	2.74863e11			0.727531
$785$	4.08451e11	+	7.20210e10i	1.07563	+	0.189662i
$786$		0			0
$787$	−4.15833e11	−	1.51351e11i	−1.08398	−	0.394535i	−0.262590	−	0.964907i	$-0.584577\pi$
$787$	−4.15833e11	−	1.51351e11i	−1.08398	−	0.394535i	−0.821386	+	0.570372i	$0.806799\pi$
$788$	−1.27240e11	−	1.51639e11i	−0.330005	−	0.393285i
$789$		0			0
$790$	2.36394e11	−	8.60403e10i	0.606915	−	0.220899i
$791$	−2.33798e11	−	1.34983e11i	−0.597221	−	0.344806i
$792$		0			0
$793$	−1.63152e11	−	2.82587e11i	−0.412571	−	0.714594i
$794$	−1.07463e10	+	1.28069e10i	−0.0270381	+	0.0322228i
$795$		0			0
$796$	−3.51855e9	−	1.99547e10i	−0.00876419	−	0.0497042i
$797$	−4.61690e11	+	8.14084e10i	−1.14424	+	0.201760i	−0.713460	−	0.700696i	$-0.752873\pi$
$797$	−4.61690e11	+	8.14084e10i	−1.14424	+	0.201760i	−0.430781	+	0.902457i	$0.641762\pi$
$798$		0			0
$799$	6.31816e10	+	5.30156e10i	0.155026	+	0.130082i
$800$	−1.62650e11	+	9.39058e10i	−0.397094	+	0.229262i
$801$		0			0
$802$	−9.20472e10	+	1.59430e11i	−0.222491	+	0.385366i
$803$	−7.36492e9	−	2.02350e10i	−0.0177136	−	0.0486676i
$804$		0			0
$805$	1.05565e11	−	8.85793e10i	0.251383	−	0.210935i
$806$	−2.06786e11	+	5.68139e11i	−0.489982	+	1.34621i
$807$		0			0
$808$	1.05858e11	−	6.00352e11i	0.248359	−	1.40851i
$809$			2.16664e11i			0.505817i	0.967490	+	0.252908i	$0.0813871\pi$
$809$			2.16664e11i			0.505817i	−0.967490	+	0.252908i	$0.918613\pi$
$810$		0			0
$811$	−1.65427e11			−0.382405			−0.191203	−	0.981551i	$-0.561239\pi$
$811$	−1.65427e11			−0.382405			−0.191203	+	0.981551i	$0.561239\pi$
$812$	1.13001e11	+	1.99250e10i	0.259930	+	0.0458327i
$813$		0			0
$814$	1.22260e10	+	4.44989e9i	0.0278475	+	0.0101357i
$815$	−1.90209e11	−	2.26682e11i	−0.431122	−	0.513791i
$816$		0			0
$817$	1.48095e11	−	5.39023e10i	0.332394	−	0.120981i
$818$	7.92294e11	+	4.57431e11i	1.76959	+	1.02167i
$819$		0			0
$820$	3.84974e8	+	6.66795e8i	0.000851483	+	0.00147481i
$821$	−3.93958e11	+	4.69501e11i	−0.867116	+	1.03339i	0.131996	+	0.991250i	$0.457861\pi$
$821$	−3.93958e11	+	4.69501e11i	−0.867116	+	1.03339i	−0.999112	+	0.0421384i	$0.986583\pi$
$822$		0			0
$823$	−3.55321e10	−	2.01513e11i	−0.0774501	−	0.439241i	−0.998732	−	0.0503455i	$-0.983968\pi$
$823$	−3.55321e10	−	2.01513e11i	−0.0774501	−	0.439241i	0.921282	−	0.388896i	$-0.127143\pi$
$824$	−3.20996e11	+	5.66002e10i	−0.696290	+	0.122775i
$825$		0			0
$826$	−4.19321e11	−	3.51852e11i	−0.900795	−	0.755857i
$827$	−3.20967e11	+	1.85311e11i	−0.686181	+	0.396167i	−0.802180	−	0.597083i	$-0.796326\pi$
$827$	−3.20967e11	+	1.85311e11i	−0.686181	+	0.396167i	0.115999	+	0.993249i	$0.462993\pi$
$828$		0			0
$829$	1.52445e10	−	2.64043e10i	0.0322772	−	0.0559058i	−0.849436	−	0.527692i	$-0.823057\pi$
$829$	1.52445e10	−	2.64043e10i	0.0322772	−	0.0559058i	0.881713	+	0.471787i	$0.156391\pi$
$830$	4.09080e10	+	1.12394e11i	0.0861977	+	0.236826i
$831$		0			0
$832$	2.44565e11	−	2.05214e11i	0.510388	−	0.428266i
$833$	7.11196e10	−	1.95399e11i	0.147710	−	0.405829i
$834$		0			0
$835$	8.54745e10	−	4.84750e11i	0.175829	−	0.997176i
$836$			5.90681e9i			0.0120928i
$837$		0			0
$838$	1.71125e11			0.347007
$839$	−8.55531e10	−	1.50853e10i	−0.172658	−	0.0304443i	0.0866505	−	0.996239i	$-0.472384\pi$
$839$	−8.55531e10	−	1.50853e10i	−0.172658	−	0.0304443i	−0.259309	+	0.965794i	$0.583495\pi$
$840$		0			0
$841$	2.02859e11	+	7.38346e10i	0.405518	+	0.147597i
$842$	4.63439e11	+	5.52305e11i	0.922028	+	1.09883i
$843$		0			0
$844$	2.26050e11	−	8.22753e10i	0.445486	−	0.162144i
$845$	−2.78235e11	−	1.60639e11i	−0.545738	−	0.315082i
$846$		0			0
$847$	−1.63986e11	−	2.84031e11i	−0.318619	−	0.551865i
$848$	−3.13404e11	+	3.73501e11i	−0.606068	+	0.722284i
$849$		0			0
$850$	5.28778e10	+	2.99885e11i	0.101297	+	0.574485i
$851$	4.37787e11	−	7.71936e10i	0.834727	−	0.147185i
$852$		0			0
$853$	5.31783e11	+	4.46219e11i	1.00447	+	0.842853i	0.987598	−	0.157005i	$-0.0501838\pi$
$853$	5.31783e11	+	4.46219e11i	1.00447	+	0.842853i	0.0168750	+	0.999858i	$0.494628\pi$
$854$	−1.92540e11	+	1.11163e11i	−0.361985	+	0.208992i
$855$		0			0
$856$	1.69490e11	−	2.93565e11i	0.315681	−	0.546775i
$857$	1.56253e10	+	4.29300e10i	0.0289670	+	0.0795862i	0.953333	−	0.301920i	$-0.0976276\pi$
$857$	1.56253e10	+	4.29300e10i	0.0289670	+	0.0795862i	−0.924366	+	0.381506i	$0.875405\pi$
$858$		0			0
$859$	7.59299e11	−	6.37127e11i	1.39457	−	1.17018i	0.431119	−	0.902295i	$-0.358119\pi$
$859$	7.59299e11	−	6.37127e11i	1.39457	−	1.17018i	0.963450	−	0.267887i	$-0.0863255\pi$
$860$	−1.01543e10	+	2.78988e10i	−0.0185634	+	0.0510025i
$861$		0			0
$862$	−1.52877e11	+	8.67008e11i	−0.276893	+	1.57034i
$863$		−	2.70088e11i		−	0.486926i	−0.969910	−	0.243463i	$-0.921717\pi$
$863$		−	2.70088e11i		−	0.486926i	0.969910	−	0.243463i	$-0.0782834\pi$
$864$		0			0
$865$	−1.60608e11			−0.286882
$866$	−4.35020e11	−	7.67058e10i	−0.773460	−	0.136382i
$867$		0			0
$868$	9.94880e10	+	3.62107e10i	0.175264	+	0.0637907i
$869$	1.02338e10	+	1.21962e10i	0.0179456	+	0.0213867i
$870$		0			0
$871$	−8.07081e11	+	2.93753e11i	−1.40231	+	0.510399i
$872$	−2.04934e10	−	1.18318e10i	−0.0354444	−	0.0204638i
$873$		0			0
$874$	3.92635e11	+	6.80065e11i	0.672890	+	1.16548i
$875$	−2.25926e11	+	2.69248e11i	−0.385419	+	0.459325i
$876$		0			0
$877$	6.08459e10	+	3.45074e11i	0.102857	+	0.583330i	0.992055	+	0.125807i	$0.0401521\pi$
$877$	6.08459e10	+	3.45074e11i	0.102857	+	0.583330i	−0.889198	+	0.457523i	$0.848737\pi$
$878$	5.72086e11	−	1.00874e11i	0.962683	−	0.169747i
$879$		0			0
$880$	8.73588e9	+	7.33028e9i	0.0145672	+	0.0122233i
$881$	−4.63683e11	+	2.67708e11i	−0.769694	+	0.444383i	−0.832765	−	0.553626i	$-0.813244\pi$
$881$	−4.63683e11	+	2.67708e11i	−0.769694	+	0.444383i	0.0630716	+	0.998009i	$0.479910\pi$
$882$		0			0
$883$	−3.50386e10	+	6.06887e10i	−0.0576374	+	0.0998309i	−0.893404	−	0.449253i	$-0.851690\pi$
$883$	−3.50386e10	+	6.06887e10i	−0.0576374	+	0.0998309i	0.835767	+	0.549084i	$0.185023\pi$
$884$	7.68118e10	+	2.11039e11i	0.125782	+	0.345583i
$885$		0			0
$886$	−2.16468e10	+	1.81638e10i	−0.0351284	+	0.0294762i
$887$	2.07018e11	−	5.68777e11i	0.334436	−	0.918856i	−0.652506	−	0.757783i	$-0.726282\pi$
$887$	2.07018e11	−	5.68777e11i	0.334436	−	0.918856i	0.986943	−	0.161073i	$-0.0514954\pi$
$888$		0			0
$889$	5.25232e10	−	2.97874e11i	0.0840899	−	0.476898i
$890$		−	5.84858e11i		−	0.932161i
$891$		0			0
$892$	9.42136e10			0.148818
$893$	−2.18266e11	−	3.84862e10i	−0.343226	−	0.0605200i
$894$		0			0
$895$	2.46887e11	+	8.98594e10i	0.384774	+	0.140046i
$896$	−3.15198e11	−	3.75638e11i	−0.489048	−	0.582825i
$897$		0			0
$898$	−5.87301e11	+	2.13760e11i	−0.903141	+	0.328716i
$899$	5.72236e11	+	3.30380e11i	0.876064	+	0.505796i
$900$		0			0
$901$	1.84429e11	+	3.19440e11i	0.279853	+	0.484719i
$902$	−1.21871e8	+	1.45241e8i	−0.000184109	+	0.000219413i
$903$		0			0
$904$	−9.51599e10	−	5.39679e11i	−0.142489	−	0.808094i
$905$	8.90782e10	−	1.57069e10i	0.132794	−	0.0234151i
$906$		0			0
$907$	3.57812e11	+	3.00240e11i	0.528721	+	0.443649i	0.867659	−	0.497159i	$-0.165624\pi$
$907$	3.57812e11	+	3.00240e11i	0.528721	+	0.443649i	−0.338939	+	0.940808i	$0.610068\pi$
$908$	1.85881e11	−	1.07318e11i	0.273458	−	0.157881i
$909$		0			0
$910$	−2.06036e11	+	3.56864e11i	−0.300453	+	0.520401i
$911$	3.31123e11	+	9.09752e11i	0.480746	+	1.32084i	0.908855	+	0.417111i	$0.136958\pi$
$911$	3.31123e11	+	9.09752e11i	0.480746	+	1.32084i	−0.428110	+	0.903727i	$0.640820\pi$
$912$		0			0
$913$	−5.79869e9	+	4.86568e9i	−0.00834539	+	0.00700261i
$914$	4.00538e11	−	1.10047e12i	0.573930	−	1.57686i
$915$		0			0
$916$	5.02485e10	−	2.84973e11i	0.0713741	−	0.404783i
$917$			4.46451e11i			0.631388i
$918$		0			0
$919$	3.60571e11			0.505509			0.252755	−	0.967530i	$-0.418663\pi$
$919$	3.60571e11			0.505509			0.252755	+	0.967530i	$0.418663\pi$
$920$	2.75480e11	+	4.85745e10i	0.384537	+	0.0678043i
$921$		0			0
$922$	5.44086e11	+	1.98031e11i	0.752911	+	0.274037i
$923$	5.76188e11	+	6.86675e11i	0.793885	+	0.946116i
$924$		0			0
$925$	−4.35290e11	+	1.58433e11i	−0.594582	+	0.216410i
$926$	7.23198e11	+	4.17538e11i	0.983588	+	0.567875i
$927$		0			0
$928$	2.94506e11	+	5.10099e11i	0.397102	+	0.687801i
$929$	−2.68522e11	+	3.20012e11i	−0.360509	+	0.429638i	−0.915562	−	0.402177i	$-0.868254\pi$
$929$	−2.68522e11	+	3.20012e11i	−0.360509	+	0.429638i	0.555053	+	0.831815i	$0.312698\pi$
$930$		0			0
$931$	9.70300e10	+	5.50285e11i	0.129154	+	0.732468i
$932$	−3.14271e11	+	5.54144e10i	−0.416524	+	0.0734444i
$933$		0			0
$934$	−1.13897e12	−	9.55706e11i	−1.49666	−	1.25585i
$935$	7.47145e9	−	4.31365e9i	0.00977594	−	0.00564414i
$936$		0			0
$937$	−2.31539e11	+	4.01037e11i	−0.300376	+	0.520266i	−0.976221	−	0.216777i	$-0.930445\pi$
$937$	−2.31539e11	+	4.01037e11i	−0.300376	+	0.520266i	0.675845	+	0.737044i	$0.263779\pi$
$938$	2.00148e11	+	5.49903e11i	0.258548	+	0.710354i
$939$		0			0
$940$	3.19840e10	−	2.68377e10i	0.0409658	−	0.0343744i
$941$	−3.23231e11	+	8.88071e11i	−0.412245	+	1.13263i	0.543749	+	0.839248i	$0.317004\pi$
$941$	−3.23231e11	+	8.88071e11i	−0.412245	+	1.13263i	−0.955994	+	0.293386i	$0.905218\pi$
$942$		0			0
$943$	−1.12491e9	+	6.37968e9i	−0.00142256	+	0.00806774i
$944$		−	1.54772e12i		−	1.94897i
$945$		0			0
$946$	−7.31091e9			−0.00912866
$947$	−1.13441e11	−	2.00028e10i	−0.141049	−	0.0248708i	0.102678	−	0.994715i	$-0.467259\pi$
$947$	−1.13441e11	−	2.00028e10i	−0.141049	−	0.0248708i	−0.243727	+	0.969844i	$0.578370\pi$
$948$		0			0
$949$	2.06739e12	+	7.52470e11i	2.54893	+	0.927736i
$950$	−5.25980e11	−	6.26838e11i	−0.645765	−	0.769593i
$951$		0			0
$952$	−2.71898e11	+	9.89628e10i	−0.331023	+	0.120483i
$953$	7.23371e11	+	4.17638e11i	0.876980	+	0.506324i	0.869661	−	0.493649i	$-0.164337\pi$
$953$	7.23371e11	+	4.17638e11i	0.876980	+	0.506324i	0.00731829	+	0.999973i	$0.497670\pi$
$954$		0			0
$955$	7.01552e10	+	1.21512e11i	0.0843424	+	0.146085i
$956$	−1.29999e11	+	1.54927e11i	−0.155635	+	0.185479i
$957$		0			0
$958$	−4.76817e10	−	2.70416e11i	−0.0566096	−	0.321049i
$959$	6.57171e11	−	1.15877e11i	0.776969	−	0.137001i
$960$		0			0
$961$	−1.86313e11	−	1.56335e11i	−0.218448	−	0.183300i
$962$	−1.15120e12	+	6.64644e11i	−1.34415	+	0.776048i
$963$		0			0
$964$	1.61116e11	−	2.79061e11i	0.186565	−	0.323140i
$965$	−1.44207e11	−	3.96206e11i	−0.166295	−	0.456891i
$966$		0			0
$967$	−5.96657e11	+	5.00655e11i	−0.682369	+	0.572575i	−0.916697	−	0.399582i	$-0.869155\pi$
$967$	−5.96657e11	+	5.00655e11i	−0.682369	+	0.572575i	0.234329	+	0.972157i	$0.424711\pi$
$968$	2.27699e11	−	6.25598e11i	0.259334	−	0.712514i
$969$		0			0
$970$	−8.63202e10	+	4.89546e11i	−0.0975046	+	0.552976i
$971$		−	8.97129e11i		−	1.00920i	−0.863353	−	0.504601i	$-0.831640\pi$
$971$		−	8.97129e11i		−	1.00920i	0.863353	−	0.504601i	$-0.168360\pi$
$972$		0			0
$973$	1.82995e11			0.204168
$974$	−1.83746e11	−	3.23993e10i	−0.204165	−	0.0359998i
$975$		0			0
$976$	−5.90715e11	−	2.15003e11i	−0.650997	−	0.236943i
$977$	9.94842e10	+	1.18561e11i	0.109188	+	0.130125i	0.817871	−	0.575402i	$-0.195154\pi$
$977$	9.94842e10	+	1.18561e11i	0.109188	+	0.130125i	−0.708682	+	0.705528i	$0.750710\pi$
$978$		0			0
$979$	3.47821e10	−	1.26597e10i	0.0378639	−	0.0137813i
$980$	−9.11612e10	−	5.26320e10i	−0.0988339	−	0.0570618i
$981$		0			0
$982$	−9.43301e11	−	1.63384e12i	−1.01439	−	1.75697i
$983$	−1.17650e11	+	1.40210e11i	−0.126002	+	0.150163i	−0.825357	−	0.564611i	$-0.809026\pi$
$983$	−1.17650e11	+	1.40210e11i	−0.126002	+	0.150163i	0.699355	+	0.714774i	$0.253471\pi$
$984$		0			0
$985$	−1.34911e11	−	7.65118e11i	−0.143319	−	0.812800i
$986$	9.40495e11	−	1.65835e11i	0.995059	−	0.175456i
$987$		0			0
$988$	−4.62305e11	−	3.87920e11i	−0.485177	−	0.407112i
$989$	−2.16329e11	+	1.24898e11i	−0.226115	+	0.130548i
$990$		0			0
$991$	2.68198e11	−	4.64533e11i	0.278075	−	0.481640i	−0.692831	−	0.721100i	$-0.743637\pi$
$991$	2.68198e11	−	4.64533e11i	0.278075	−	0.481640i	0.970906	+	0.239460i	$0.0769703\pi$
$992$	1.85880e11	+	5.10700e11i	0.191949	+	0.527374i
$993$		0			0
$994$	4.67865e11	−	3.92585e11i	0.479264	−	0.402150i
$995$	2.71997e10	−	7.47307e10i	0.0277506	−	0.0762442i
$996$		0			0
$997$	−1.28567e11	+	7.29138e11i	−0.130121	+	0.737953i	0.848013	+	0.529976i	$0.177799\pi$
$997$	−1.28567e11	+	7.29138e11i	−0.130121	+	0.737953i	−0.978134	+	0.207977i	$0.933312\pi$
$998$		−	1.21778e12i		−	1.22757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.18		138
3.2	odd	2		27.9.f.a.2.6	✓	138
27.13	even	9		27.9.f.a.14.6	yes	138
27.14	odd	18	inner	81.9.f.a.71.18		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.6	✓	138	3.2	odd	2
27.9.f.a.14.6	yes	138	27.13	even	9
81.9.f.a.8.18		138	1.1	even	1	trivial
81.9.f.a.71.18		138	27.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(18.2801 + 3.22328i) q^{2} +(83.2125 + 30.2869i) q^{4} +(223.403 + 266.242i) q^{5} +(-1438.86 + 523.701i) q^{7} +(-2691.76 - 1554.09i) q^{8} +(3225.67 + 5587.03i) q^{10} +(-262.444 + 312.769i) q^{11} +(-7243.71 - 41081.1i) q^{13} +(-27990.6 + 4935.49i) q^{14} +(-61562.3 - 51656.9i) q^{16} +(-52651.8 + 30398.5i) q^{17} +(81686.6 - 141485. i) q^{19} +(10526.3 + 28920.8i) q^{20} +(-5805.66 + 4871.53i) q^{22} +(-88565.0 + 243330. i) q^{23} +(46855.7 - 265732. i) q^{25} -774316. i q^{26} -135592. q^{28} +(-833385. - 146948. i) q^{29} +(-733729. - 267056. i) q^{31} +(-447401. - 533192. i) q^{32} +(-1.06047e6 + 385978. i) q^{34} +(-460877. - 266087. i) q^{35} +(-858362. - 1.48673e6i) q^{37} +(1.94929e6 - 2.32307e6i) q^{38} +(-187585. - 1.06385e6i) q^{40} +(24637.0 - 4344.17i) q^{41} +(738972. + 620071. i) q^{43} +(-31311.4 + 18077.7i) q^{44} +(-2.40330e6 + 4.16264e6i) q^{46} +(-463987. - 1.27479e6i) q^{47} +(-2.62005e6 + 2.19848e6i) q^{49} +(1.71306e6 - 4.70659e6i) q^{50} +(641451. - 3.63785e6i) q^{52} -6.06703e6i q^{53} -141903. q^{55} +(4.68694e6 + 826433. i) q^{56} +(-1.47607e7 - 5.37247e6i) q^{58} +(1.23794e7 + 1.47532e7i) q^{59} +(7.35050e6 - 2.67536e6i) q^{61} +(-1.25519e7 - 7.24683e6i) q^{62} +(3.82665e6 + 6.62796e6i) q^{64} +(9.31923e6 - 1.11062e7i) q^{65} +(-3.57529e6 - 2.02765e7i) q^{67} +(-5.30197e6 + 934880. i) q^{68} +(-7.56721e6 - 6.34965e6i) q^{70} +(-1.86096e7 + 1.07443e7i) q^{71} +(-2.63704e7 + 4.56749e7i) q^{73} +(-1.08988e7 - 2.99443e7i) q^{74} +(1.10825e7 - 9.29932e6i) q^{76} +(213822. - 587472. i) q^{77} +(6.77127e6 - 3.84018e7i) q^{79} -2.79308e7i q^{80} +464371. q^{82} +(1.82582e7 + 3.21941e6i) q^{83} +(-1.98560e7 - 7.22697e6i) q^{85} +(1.15098e7 + 1.37169e7i) q^{86} +(1.19251e6 - 434037. i) q^{88} +(-7.85112e7 - 4.53284e7i) q^{89} +(3.19369e7 + 5.53163e7i) q^{91} +(-1.47394e7 + 1.75658e7i) q^{92} +(-4.37272e6 - 2.47989e7i) q^{94} +(5.59184e7 - 9.85992e6i) q^{95} +(5.90263e7 + 4.95290e7i) q^{97} +(-5.49811e7 + 3.17433e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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