LMFDB - Embedded newform 27.9.f.a.2.14

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			2.14
Character	$\chi$	$=$	27.2
Dual form			27.9.f.a.14.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.08460 + 1.24921i) q^{2} +(14.6630 + 79.6618i) q^{3} +(-191.930 - 69.8569i) q^{4} +(349.559 + 416.588i) q^{5} +(4.36750 + 582.689i) q^{6} +(22.4234 - 8.16143i) q^{7} +(-2867.39 - 1655.49i) q^{8} +(-6130.99 + 2336.16i) q^{9} +(1956.08 + 3388.03i) q^{10} +(-15469.2 + 18435.5i) q^{11} +(2750.65 - 16313.8i) q^{12} +(-8798.06 - 49896.3i) q^{13} +(169.056 - 29.8091i) q^{14} +(-28060.6 + 33954.9i) q^{15} +(21808.2 + 18299.3i) q^{16} +(-37540.0 + 21673.7i) q^{17} +(-46354.0 + 8891.89i) q^{18} +(-75167.3 + 130194. i) q^{19} +(-37989.4 - 104375. i) q^{20} +(978.948 + 1666.61i) q^{21} +(-132623. + 111284. i) q^{22} +(-108972. + 299398. i) q^{23} +(89834.6 - 252696. i) q^{24} +(16477.1 - 93446.3i) q^{25} -364486. i q^{26} +(-276001. - 454151. i) q^{27} -4873.85 q^{28} +(945594. + 166734. i) q^{29} +(-241215. + 205504. i) q^{30} +(736394. + 268025. i) q^{31} +(676476. + 806193. i) q^{32} +(-1.69543e6 - 961988. i) q^{33} +(-293031. + 106655. i) q^{34} +(11238.2 + 6488.40i) q^{35} +(1.33992e6 - 20087.6i) q^{36} +(1.21793e6 + 2.10952e6i) q^{37} +(-695170. + 828471. i) q^{38} +(3.84582e6 - 1.43250e6i) q^{39} +(-312665. - 1.77321e6i) q^{40} +(2.52414e6 - 445074. i) q^{41} +(4853.51 + 13030.2i) q^{42} +(-2.24939e6 - 1.88746e6i) q^{43} +(4.25687e6 - 2.45770e6i) q^{44} +(-3.11636e6 - 1.73747e6i) q^{45} +(-1.14603e6 + 1.98499e6i) q^{46} +(-569539. - 1.56479e6i) q^{47} +(-1.13798e6 + 2.00561e6i) q^{48} +(-4.41566e6 + 3.70518e6i) q^{49} +(233468. - 641447. i) q^{50} +(-2.27702e6 - 2.67270e6i) q^{51} +(-1.79699e6 + 1.01912e7i) q^{52} +3.88995e6i q^{53} +(-1.38803e6 - 3.56226e6i) q^{54} -1.30874e7 q^{55} +(-77807.6 - 13719.6i) q^{56} +(-1.14736e7 - 4.07893e6i) q^{57} +(6.49088e6 + 2.36249e6i) q^{58} +(6.87370e6 + 8.19175e6i) q^{59} +(7.75765e6 - 4.55675e6i) q^{60} +(-1.49222e7 + 5.43124e6i) q^{61} +(4.88224e6 + 2.81876e6i) q^{62} +(-118411. + 102422. i) q^{63} +(141478. + 245047. i) q^{64} +(1.77108e7 - 2.11069e7i) q^{65} +(-1.08097e7 - 8.93325e6i) q^{66} +(1.45408e6 + 8.24651e6i) q^{67} +(8.71913e6 - 1.53742e6i) q^{68} +(-2.54484e7 - 4.29083e6i) q^{69} +(71513.1 + 60006.6i) q^{70} +(-9.42132e6 + 5.43940e6i) q^{71} +(2.14474e7 + 3.45110e6i) q^{72} +(1.18791e7 - 2.05752e7i) q^{73} +(5.99334e6 + 1.64666e7i) q^{74} +(7.68570e6 - 57607.5i) q^{75} +(2.35218e7 - 1.97371e7i) q^{76} +(-196412. + 539638. i) q^{77} +(2.90356e7 - 5.34446e6i) q^{78} +(-7.07994e6 + 4.01523e7i) q^{79} +1.54817e7i q^{80} +(3.21314e7 - 2.86460e7i) q^{81} +1.84385e7 q^{82} +(-5.20151e7 - 9.17167e6i) q^{83} +(-71465.3 - 388260. i) q^{84} +(-2.21515e7 - 8.06248e6i) q^{85} +(-1.35782e7 - 1.61819e7i) q^{86} +(582937. + 7.77725e7i) q^{87} +(7.48761e7 - 2.72527e7i) q^{88} +(3.60266e7 + 2.07999e7i) q^{89} +(-1.99077e7 - 1.62023e7i) q^{90} +(-604507. - 1.04704e6i) q^{91} +(4.18301e7 - 4.98511e7i) q^{92} +(-1.05536e7 + 6.25925e7i) q^{93} +(-2.08020e6 - 1.17974e7i) q^{94} +(-8.05126e7 + 1.41965e7i) q^{95} +(-5.43036e7 + 6.57105e7i) q^{96} +(-7.44489e7 - 6.24700e7i) q^{97} +(-3.59117e7 + 2.07336e7i) q^{98} +(5.17735e7 - 1.49167e8i) 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 $

$2$	7.08460	+	1.24921i	0.442788	+	0.0780754i	0.390597	−	0.920562i	$-0.372269\pi$
$2$	7.08460	+	1.24921i	0.442788	+	0.0780754i	0.0521906	+	0.998637i	$0.483380\pi$
$3$	14.6630	+	79.6618i	0.181025	+	0.983479i
$3$	14.6630	+	79.6618i	0.181025	+	0.983479i
$4$	−191.930	−	69.8569i	−0.749727	−	0.272878i
$5$	349.559	+	416.588i	0.559294	+	0.666541i	0.969397	−	0.245498i	$-0.0789516\pi$
$5$	349.559	+	416.588i	0.559294	+	0.666541i	−0.410103	+	0.912039i	$0.634507\pi$
$6$	4.36750	+	582.689i	0.00336998	+	0.449606i
$7$	22.4234	−	8.16143i	0.00933917	−	0.00339918i	−0.337346	−	0.941381i	$-0.609529\pi$
$7$	22.4234	−	8.16143i	0.00933917	−	0.00339918i	0.346686	+	0.937981i	$0.387307\pi$
$8$	−2867.39	−	1655.49i	−0.700046	−	0.404172i
$9$	−6130.99	+	2336.16i	−0.934460	+	0.356068i
$10$	1956.08	+	3388.03i	0.195608	+	0.338803i
$11$	−15469.2	+	18435.5i	−1.05657	+	1.25917i	−0.0918844	+	0.995770i	$0.529289\pi$
$11$	−15469.2	+	18435.5i	−1.05657	+	1.25917i	−0.964686	+	0.263402i	$0.915155\pi$
$12$	2750.65	−	16313.8i	0.132651	−	0.786739i
$13$	−8798.06	−	49896.3i	−0.308045	−	1.74701i	−0.608815	−	0.793312i	$-0.708355\pi$
$13$	−8798.06	−	49896.3i	−0.308045	−	1.74701i	0.300771	−	0.953696i	$-0.402756\pi$
$14$	169.056	−	29.8091i	0.00440066	−	0.000775956i
$15$	−28060.6	+	33954.9i	−0.554283	+	0.670714i
$16$	21808.2	+	18299.3i	0.332767	+	0.279225i
$17$	−37540.0	+	21673.7i	−0.449468	+	0.259501i	−0.707606	−	0.706608i	$-0.750225\pi$
$17$	−37540.0	+	21673.7i	−0.449468	+	0.259501i	0.258137	+	0.966108i	$0.416891\pi$
$18$	−46354.0	+	8891.89i	−0.441568	+	0.0847040i
$19$	−75167.3	+	130194.i	−0.576786	+	0.999023i	0.419059	+	0.907959i	$0.362360\pi$
$19$	−75167.3	+	130194.i	−0.576786	+	0.999023i	−0.995845	+	0.0910639i	$0.970973\pi$
$20$	−37989.4	−	104375.i	−0.237434	−	0.652343i
$21$	978.948	+	1666.61i	0.00503364	+	0.00856954i
$22$	−132623.	+	111284.i	−0.566147	+	0.475054i
$23$	−108972.	+	299398.i	−0.389407	+	1.06989i	0.577862	+	0.816134i	$0.303887\pi$
$23$	−108972.	+	299398.i	−0.389407	+	1.06989i	−0.967269	+	0.253753i	$0.918335\pi$
$24$	89834.6	−	252696.i	0.270769	−	0.761645i
$25$	16477.1	−	93446.3i	0.0421814	−	0.239223i
$26$		−	364486.i		−	0.797605i
$27$	−276001.	−	454151.i	−0.519345	−	0.854565i
$28$	−4873.85			−0.00792940
$29$	945594.	+	166734.i	1.33694	+	0.235739i	0.795988	−	0.605312i	$-0.206952\pi$
$29$	945594.	+	166734.i	1.33694	+	0.235739i	0.540955	+	0.841052i	$0.318063\pi$
$30$	−241215.	+	205504.i	−0.297796	+	0.253708i
$31$	736394.	+	268025.i	0.797376	+	0.290221i	0.708399	−	0.705813i	$-0.249418\pi$
$31$	736394.	+	268025.i	0.797376	+	0.290221i	0.0889773	+	0.996034i	$0.471640\pi$
$32$	676476.	+	806193.i	0.645138	+	0.768845i
$33$	−1.69543e6	−	961988.i	−1.42963	−	0.811173i
$34$	−293031.	+	106655.i	−0.219280	+	0.0798113i
$35$	11238.2	+	6488.40i	0.00748904	+	0.00432380i
$36$	1.33992e6	−	20087.6i	0.797754	−	0.0119597i
$37$	1.21793e6	+	2.10952e6i	0.649855	+	1.12558i	0.983157	+	0.182761i	$0.0585035\pi$
$37$	1.21793e6	+	2.10952e6i	0.649855	+	1.12558i	−0.333303	+	0.942820i	$0.608163\pi$
$38$	−695170.	+	828471.i	−0.333393	+	0.397322i
$39$	3.84582e6	−	1.43250e6i	1.66238	−	0.619207i
$40$	−312665.	−	1.77321e6i	−0.122135	−	0.692660i
$41$	2.52414e6	−	445074.i	0.893261	−	0.157506i	0.291867	−	0.956459i	$-0.405723\pi$
$41$	2.52414e6	−	445074.i	0.893261	−	0.157506i	0.601394	+	0.798953i	$0.294612\pi$
$42$	4853.51	+	13030.2i	0.00155976	+	0.00418749i
$43$	−2.24939e6	−	1.88746e6i	−0.657948	−	0.552084i	0.251523	−	0.967851i	$-0.419068\pi$
$43$	−2.24939e6	−	1.88746e6i	−0.657948	−	0.552084i	−0.909471	+	0.415768i	$0.863513\pi$
$44$	4.25687e6	−	2.45770e6i	1.13574	−	0.655720i
$45$	−3.11636e6	−	1.73747e6i	−0.759972	−	0.423709i
$46$	−1.14603e6	+	1.98499e6i	−0.255957	+	0.443330i
$47$	−569539.	−	1.56479e6i	−0.116716	−	0.320676i	0.867554	−	0.497342i	$-0.165691\pi$
$47$	−569539.	−	1.56479e6i	−0.116716	−	0.320676i	−0.984271	+	0.176667i	$0.943468\pi$
$48$	−1.13798e6	+	2.00561e6i	−0.214373	+	0.377816i
$49$	−4.41566e6	+	3.70518e6i	−0.765969	+	0.642724i
$50$	233468.	−	641447.i	0.0373548	−	0.102631i
$51$	−2.27702e6	−	2.67270e6i	−0.336578	−	0.395066i
$52$	−1.79699e6	+	1.01912e7i	−0.245771	+	1.39384i
$53$			3.88995e6i			0.492993i	0.969144	+	0.246496i	$0.0792793\pi$
$53$			3.88995e6i			0.492993i	−0.969144	+	0.246496i	$0.920721\pi$
$54$	−1.38803e6	−	3.56226e6i	−0.163239	−	0.418939i
$55$	−1.30874e7			−1.43022
$56$	−77807.6	−	13719.6i	−0.00791170	−	0.00139505i
$57$	−1.14736e7	−	4.07893e6i	−1.08693	−	0.386409i
$58$	6.49088e6	+	2.36249e6i	0.573577	+	0.208765i
$59$	6.87370e6	+	8.19175e6i	0.567260	+	0.676034i	0.971066	−	0.238810i	$-0.0767574\pi$
$59$	6.87370e6	+	8.19175e6i	0.567260	+	0.676034i	−0.403806	+	0.914845i	$0.632313\pi$
$60$	7.75765e6	−	4.55675e6i	0.598584	−	0.351601i
$61$	−1.49222e7	+	5.43124e6i	−1.07774	+	0.392265i	−0.819065	−	0.573700i	$-0.805508\pi$
$61$	−1.49222e7	+	5.43124e6i	−1.07774	+	0.392265i	−0.258673	+	0.965965i	$0.583285\pi$
$62$	4.88224e6	+	2.81876e6i	0.330409	+	0.190762i
$63$	−118411.	+	102422.i	−0.00751675	+	0.00650178i
$64$	141478.	+	245047.i	0.00843275	+	0.0146060i
$65$	1.77108e7	−	2.11069e7i	0.992165	−	1.18242i
$66$	−1.08097e7	−	8.93325e6i	−0.569692	−	0.470797i
$67$	1.45408e6	+	8.24651e6i	0.0721588	+	0.409233i	0.999396	+	0.0347579i	$0.0110660\pi$
$67$	1.45408e6	+	8.24651e6i	0.0721588	+	0.409233i	−0.927237	+	0.374475i	$0.877823\pi$
$68$	8.71913e6	−	1.53742e6i	0.407791	−	0.0719045i
$69$	−2.54484e7	−	4.29083e6i	−1.12270	−	0.189298i
$70$	71513.1	+	60006.6i	0.00297847	+	0.00249924i
$71$	−9.42132e6	+	5.43940e6i	−0.370747	+	0.214051i	−0.673785	−	0.738927i	$-0.735333\pi$
$71$	−9.42132e6	+	5.43940e6i	−0.370747	+	0.214051i	0.303037	+	0.952979i	$0.401999\pi$
$72$	2.14474e7	+	3.45110e6i	0.798078	+	0.128419i
$73$	1.18791e7	−	2.05752e7i	0.418305	−	0.724525i	−0.577464	−	0.816416i	$-0.695958\pi$
$73$	1.18791e7	−	2.05752e7i	0.418305	−	0.724525i	0.995769	+	0.0918908i	$0.0292911\pi$
$74$	5.99334e6	+	1.64666e7i	0.199867	+	0.549131i
$75$	7.68570e6	−	57607.5i	0.242906	−	0.00182068i
$76$	2.35218e7	−	1.97371e7i	0.705044	−	0.591602i
$77$	−196412.	+	539638.i	−0.00558734	+	0.0153511i
$78$	2.90356e7	−	5.34446e6i	0.784427	−	0.144386i
$79$	−7.07994e6	+	4.01523e7i	−0.181770	+	1.03087i	0.748266	+	0.663398i	$0.230886\pi$
$79$	−7.07994e6	+	4.01523e7i	−0.181770	+	1.03087i	−0.930036	+	0.367468i	$0.880225\pi$
$80$			1.54817e7i			0.377972i
$81$	3.21314e7	−	2.86460e7i	0.746432	−	0.665462i
$82$	1.84385e7			0.407822
$83$	−5.20151e7	−	9.17167e6i	−1.09602	−	0.193257i	−0.403729	−	0.914879i	$-0.632286\pi$
$83$	−5.20151e7	−	9.17167e6i	−1.09602	−	0.193257i	−0.692288	+	0.721621i	$0.743397\pi$
$84$	−71465.3	−	388260.i	−0.00143542	−	0.00779839i
$85$	−2.21515e7	−	8.06248e6i	−0.424353	−	0.154452i
$86$	−1.35782e7	−	1.61819e7i	−0.248227	−	0.295825i
$87$	582937.	+	7.77725e7i	0.0101752	+	1.35753i
$88$	7.48761e7	−	2.72527e7i	1.24857	−	0.454442i
$89$	3.60266e7	+	2.07999e7i	0.574199	+	0.331514i	0.758825	−	0.651295i	$-0.225774\pi$
$89$	3.60266e7	+	2.07999e7i	0.574199	+	0.331514i	−0.184625	+	0.982809i	$0.559107\pi$
$90$	−1.99077e7	−	1.62023e7i	−0.303425	−	0.246948i
$91$	−604507.	−	1.04704e6i	−0.00881528	−	0.0152685i
$92$	4.18301e7	−	4.98511e7i	0.583898	−	0.695863i
$93$	−1.05536e7	+	6.25925e7i	−0.141082	+	0.836739i
$94$	−2.08020e6	−	1.17974e7i	−0.0266437	−	0.151104i
$95$	−8.05126e7	+	1.41965e7i	−0.988483	+	0.174296i
$96$	−5.43036e7	+	6.57105e7i	−0.639357	+	0.773659i
$97$	−7.44489e7	−	6.24700e7i	−0.840952	−	0.705642i	0.116826	−	0.993152i	$-0.462728\pi$
$97$	−7.44489e7	−	6.24700e7i	−0.840952	−	0.705642i	−0.957778	+	0.287510i	$0.907172\pi$
$98$	−3.59117e7	+	2.07336e7i	−0.389343	+	0.224787i
$99$	5.17735e7	−	1.49167e8i	0.538973	−	1.55286i
$100$	−9.69032e6	+	1.67841e7i	−0.0969032	+	0.167841i
$101$	−2.31756e7	−	6.36744e7i	−0.222713	−	0.611898i	0.777135	−	0.629334i	$-0.216672\pi$
$101$	−2.31756e7	−	6.36744e7i	−0.222713	−	0.611898i	−0.999848	+	0.0174353i	$0.994450\pi$
$102$	−1.27930e7	−	2.17795e7i	−0.118188	−	0.201209i
$103$	8.20157e7	−	6.88194e7i	0.728699	−	0.611451i	−0.201077	−	0.979575i	$-0.564444\pi$
$103$	8.20157e7	−	6.88194e7i	0.728699	−	0.611451i	0.929777	+	0.368124i	$0.120000\pi$
$104$	−5.73752e7	+	1.57637e8i	−0.490446	+	1.34749i
$105$	−352091.	+	990397.i	−0.00289666	+	0.00814802i
$106$	−4.85935e6	+	2.75588e7i	−0.0384906	+	0.218291i
$107$		−	6.59985e7i		−	0.503499i	−0.967792	−	0.251750i	$-0.918994\pi$
$107$		−	6.59985e7i		−	0.503499i	0.967792	−	0.251750i	$-0.0810060\pi$
$108$	2.12475e7	+	1.06446e8i	0.156175	+	0.782409i
$109$	1.44628e8			1.02458			0.512290	−	0.858813i	$-0.328797\pi$
$109$	1.44628e8			1.02458			0.512290	+	0.858813i	$0.328797\pi$
$110$	−9.27193e7	−	1.63489e7i	−0.633285	−	0.111665i
$111$	−1.50190e8	+	1.27954e8i	−0.989345	+	0.842876i
$112$	638362.	+	232345.i	0.00405691	+	0.00147659i
$113$	4.25133e7	+	5.06654e7i	0.260742	+	0.310740i	0.880494	−	0.474058i	$-0.157211\pi$
$113$	4.25133e7	+	5.06654e7i	0.260742	+	0.310740i	−0.619752	+	0.784798i	$0.712767\pi$
$114$	−7.61907e7	−	4.32306e7i	−0.451110	−	0.255960i
$115$	−1.62818e8	+	5.92609e7i	−0.930917	+	0.338826i
$116$	−1.69841e8	−	9.80575e7i	−0.938015	−	0.541563i
$117$	1.70507e8	+	2.85360e8i	0.909909	+	1.52282i
$118$	3.84642e7	+	6.66220e7i	0.198394	+	0.343629i
$119$	−664884.	+	792378.i	−0.00331557	+	0.00395134i
$120$	1.36672e8	−	5.09080e7i	0.659107	−	0.245505i
$121$	−6.33482e7	−	3.59265e8i	−0.295524	−	1.67600i
$122$	−1.12503e8	+	1.98372e7i	−0.507836	+	0.0895451i
$123$	7.24669e7	+	1.94551e8i	0.316606	+	0.849991i
$124$	−1.22613e8	−	1.02884e8i	−0.518620	−	0.435173i
$125$	2.28657e8	−	1.32015e8i	0.936579	−	0.540734i
$126$	−966842.	+	577701.i	−0.00383595	+	0.00229203i
$127$	−8.82421e7	+	1.52840e8i	−0.339204	+	0.587519i	−0.984283	−	0.176597i	$-0.943491\pi$
$127$	−8.82421e7	+	1.52840e8i	−0.339204	+	0.587519i	0.645079	+	0.764116i	$0.276824\pi$
$128$	−9.14498e7	−	2.51256e8i	−0.340677	−	0.936003i
$129$	1.17376e8	−	2.06866e8i	0.423858	−	0.747018i
$130$	1.51841e8	−	1.27409e8i	0.531636	−	0.446096i
$131$	−1.40625e7	+	3.86363e7i	−0.0477503	+	0.131193i	−0.961275	−	0.275589i	$-0.911127\pi$
$131$	−1.40625e7	+	3.86363e7i	−0.0477503	+	0.131193i	0.913525	+	0.406782i	$0.133349\pi$
$132$	2.58203e8	+	3.03072e8i	0.850484	+	0.998275i
$133$	−622937.	+	3.53285e6i	−0.00199085	+	0.0112906i
$134$			6.02397e7i			0.186837i
$135$	9.27150e7	−	2.73731e8i	0.279135	−	0.824118i
$136$	1.43522e8			0.419531
$137$	−3.79891e8	−	6.69850e7i	−1.07839	−	0.190150i	−0.393888	−	0.919159i	$-0.628870\pi$
$137$	−3.79891e8	−	6.69850e7i	−1.07839	−	0.190150i	−0.684504	+	0.729009i	$0.739981\pi$
$138$	−1.74932e8	−	6.21892e7i	−0.482340	−	0.171474i
$139$	4.70756e8	+	1.71341e8i	1.26106	+	0.458989i	0.884126	−	0.467249i	$-0.154755\pi$
$139$	4.70756e8	+	1.71341e8i	1.26106	+	0.458989i	0.376938	+	0.926239i	$0.376977\pi$
$140$	−1.70370e6	−	2.03039e6i	−0.00443487	−	0.00528527i
$141$	1.16303e8	−	6.83150e7i	0.294249	−	0.172838i
$142$	−7.35412e7	+	2.67668e7i	−0.180875	+	0.0658330i
$143$	1.05596e9	+	6.09661e8i	2.52525	+	1.45796i
$144$	−1.76456e8	−	6.12453e7i	−0.410381	−	0.142437i
$145$	2.61082e8	+	4.52207e8i	0.590615	+	1.02297i
$146$	1.09862e8	−	1.30928e8i	0.241788	−	0.288152i
$147$	−3.59908e8	−	2.97430e8i	−0.770765	−	0.636965i
$148$	−8.63934e7	−	4.89962e8i	−0.180067	−	1.02121i
$149$	−1.35585e8	+	2.39072e7i	−0.275084	+	0.0485048i	−0.309488	−	0.950903i	$-0.600158\pi$
$149$	−1.35585e8	+	2.39072e7i	−0.275084	+	0.0485048i	0.0344041	+	0.999408i	$0.489047\pi$
$150$	5.45221e7	+	9.19290e6i	0.107698	+	0.0181588i
$151$	−2.29217e8	−	1.92336e8i	−0.440900	−	0.369959i	0.395146	−	0.918618i	$-0.370694\pi$
$151$	−2.29217e8	−	1.92336e8i	−0.440900	−	0.369959i	−0.836046	+	0.548659i	$0.815138\pi$
$152$	4.31068e8	−	2.48877e8i	0.807554	−	0.466241i
$153$	1.79524e8	−	2.20581e8i	0.327610	−	0.402534i
$154$	−2.06562e6	+	3.57776e6i	−0.00367255	+	0.00636104i
$155$	1.45757e8	+	4.00463e8i	0.252524	+	0.693803i
$156$	−8.38199e8	+	6.28265e6i	−1.41530	+	0.0106083i
$157$	−6.09281e8	+	5.11248e8i	−1.00281	+	0.841459i	−0.987372	−	0.158422i	$-0.949359\pi$
$157$	−6.09281e8	+	5.11248e8i	−1.00281	+	0.841459i	−0.0154401	+	0.999881i	$0.504915\pi$
$158$	−1.00317e8	+	2.75619e8i	−0.160971	+	0.442263i
$159$	−3.09880e8	+	5.70383e7i	−0.484848	+	0.0892438i
$160$	−9.93821e7	+	5.63624e8i	−0.151645	+	0.860022i
$161$			7.60288e6i			0.0113155i
$162$	2.63423e8	−	1.62807e8i	0.382467	−	0.236381i
$163$	5.37083e8			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$163$	5.37083e8			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$164$	−5.15551e8	−	9.09055e7i	−0.712682	−	0.125665i
$165$	−1.91901e8	−	1.04257e9i	−0.258906	−	1.40659i
$166$	−3.57049e8	−	1.29955e8i	−0.470214	−	0.171144i
$167$	1.24169e8	+	1.47979e8i	0.159642	+	0.190254i	0.839936	−	0.542685i	$-0.182592\pi$
$167$	1.24169e8	+	1.47979e8i	0.159642	+	0.190254i	−0.680294	+	0.732939i	$0.738148\pi$
$168$	−47966.6	−	6.39946e6i	−6.02146e−5	−	0.00803353i
$169$	−1.64570e9	+	5.98985e8i	−2.01745	+	0.734293i
$170$	−1.46863e8	−	8.47913e7i	−0.175839	−	0.101521i
$171$	1.56697e8	−	9.73819e8i	0.183264	−	1.13892i
$172$	2.99874e8	+	5.19397e8i	0.342630	+	0.593452i
$173$	8.68042e8	−	1.03449e9i	0.969072	−	1.15490i	−0.0188306	−	0.999823i	$-0.505994\pi$
$173$	8.68042e8	−	1.03449e9i	0.969072	−	1.15490i	0.987903	−	0.155073i	$-0.0495612\pi$
$174$	−9.30241e7	+	5.51716e8i	−0.101484	+	0.601892i
$175$	−393184.	−	2.22986e6i	−0.000419221	−	0.00237752i
$176$	−6.74714e8	+	1.18970e8i	−0.703184	+	0.123990i
$177$	−5.51781e8	+	6.67686e8i	−0.562177	+	0.680267i
$178$	2.29250e8	+	1.92364e8i	0.228365	+	0.191621i
$179$	2.84475e8	−	1.64242e8i	0.277097	−	0.159982i	−0.355011	−	0.934862i	$-0.615523\pi$
$179$	2.84475e8	−	1.64242e8i	0.277097	−	0.159982i	0.632109	+	0.774880i	$0.282190\pi$
$180$	4.76749e8	+	5.51173e8i	0.454151	+	0.525047i
$181$	−4.80709e8	+	8.32613e8i	−0.447887	+	0.775762i	−0.998248	−	0.0591641i	$-0.981156\pi$
$181$	−4.80709e8	+	8.32613e8i	−0.447887	+	0.775762i	0.550362	+	0.834926i	$0.314490\pi$
$182$	−2.97473e6	−	8.17300e6i	−0.00271120	−	0.00744897i
$183$	−6.51466e8	−	1.10909e9i	−0.580881	−	0.988923i
$184$	8.08115e8	−	6.78089e8i	0.705021	−	0.591583i
$185$	−4.53062e8	+	1.24478e9i	−0.386786	+	1.06269i
$186$	−1.52959e8	+	4.30259e8i	−0.127798	+	0.359483i
$187$	1.81149e8	−	1.02735e9i	0.148139	−	0.840138i
$188$			3.40117e8i			0.272269i
$189$	−9.89540e6	−	7.93101e6i	−0.00775507	−	0.00621558i
$190$	−5.88134e8			−0.451296
$191$	1.19301e9	+	2.10360e8i	0.896419	+	0.158063i	0.602831	−	0.797869i	$-0.294039\pi$
$191$	1.19301e9	+	2.10360e8i	0.896419	+	0.158063i	0.293588	+	0.955932i	$0.405150\pi$
$192$	−1.74464e7	+	1.48635e7i	−0.0128381	+	0.0109375i
$193$	−1.71398e9	−	6.23836e8i	−1.23531	−	0.449615i	−0.359896	−	0.932992i	$-0.617188\pi$
$193$	−1.71398e9	−	6.23836e8i	−1.23531	−	0.449615i	−0.875412	+	0.483377i	$0.839410\pi$
$194$	−4.49403e8	−	5.35577e8i	−0.317270	−	0.378107i
$195$	1.94110e9	+	1.10138e9i	1.34249	+	0.761727i
$196$	1.10633e9	−	4.02671e8i	0.749653	−	0.272851i
$197$	1.52700e9	+	8.81617e8i	1.01385	+	0.585349i	0.912318	−	0.409483i	$-0.134291\pi$
$197$	1.52700e9	+	8.81617e8i	1.01385	+	0.585349i	0.101536	+	0.994832i	$0.467624\pi$
$198$	5.53135e8	−	9.92112e8i	0.359890	−	0.645505i
$199$	7.74048e8	+	1.34069e9i	0.493578	+	0.854902i	0.999973	−	0.00739959i	$-0.00235539\pi$
$199$	7.74048e8	+	1.34069e9i	0.493578	+	0.854902i	−0.506395	+	0.862302i	$0.669022\pi$
$200$	−2.01945e8	+	2.40669e8i	−0.126216	+	0.150418i
$201$	−6.35610e8	+	2.36753e8i	−0.389409	+	0.145048i
$202$	−8.46474e7	−	4.80059e8i	−0.0508403	−	0.288330i
$203$	2.25642e7	−	3.97867e6i	0.0132873	−	0.00234290i
$204$	2.50322e8	+	6.72038e8i	0.144537	+	0.388037i
$205$	1.06775e9	+	8.95948e8i	0.604580	+	0.507303i
$206$	6.67019e8	−	3.85103e8i	0.370398	−	0.213850i
$207$	−3.13354e7	−	2.09018e9i	−0.0170668	−	1.13842i
$208$	7.21197e8	−	1.24915e9i	0.385301	−	0.667361i
$209$	−1.23741e9	−	3.39975e9i	−0.648526	−	1.78181i
$210$	−3.73164e6	+	6.57674e6i	−0.00191877	+	0.00338169i
$211$	2.15590e8	−	1.80902e8i	0.108768	−	0.0912668i	−0.586782	−	0.809745i	$-0.699605\pi$
$211$	2.15590e8	−	1.80902e8i	0.108768	−	0.0912668i	0.695549	+	0.718478i	$0.255161\pi$
$212$	2.71740e8	−	7.46599e8i	0.134527	−	0.369610i
$213$	−5.71457e8	−	6.70761e8i	−0.277629	−	0.325874i
$214$	8.24458e7	−	4.67573e8i	0.0393109	−	0.222943i
$215$		−	1.59685e9i		−	0.747326i
$216$	3.95625e7	+	1.75914e9i	0.0181747	+	0.808139i
$217$	1.86999e7			0.00843335
$218$	1.02463e9	+	1.80670e8i	0.453671	+	0.0799945i
$219$	1.81324e9	+	6.44617e8i	0.788278	+	0.280237i
$220$	2.51187e9	+	9.14248e8i	1.07228	+	0.390277i
$221$	1.41172e9	+	1.68242e9i	0.591806	+	0.705287i
$222$	−1.22388e9	+	7.18889e8i	−0.503878	+	0.295972i
$223$	−3.57572e9	+	1.30146e9i	−1.44592	+	0.526272i	−0.941449	−	0.337156i	$-0.890535\pi$
$223$	−3.57572e9	+	1.30146e9i	−1.44592	+	0.526272i	−0.504472	+	0.863428i	$0.668313\pi$
$224$	2.17486e7	+	1.25565e7i	0.00863850	+	0.00498744i
$225$	1.17285e8	+	6.11412e8i	0.0457626	+	0.238563i
$226$	2.37898e8	+	4.12052e8i	0.0911922	+	0.157950i
$227$	−2.91521e9	+	3.47421e9i	−1.09791	+	1.30844i	−0.150431	+	0.988621i	$0.548066\pi$
$227$	−2.91521e9	+	3.47421e9i	−1.09791	+	1.30844i	−0.947479	+	0.319818i	$0.896378\pi$
$228$	1.91720e9	+	1.58438e9i	0.709459	+	0.586301i
$229$	−4.94015e8	−	2.80170e9i	−0.179638	−	1.01878i	−0.932653	−	0.360775i	$-0.882512\pi$
$229$	−4.94015e8	−	2.80170e9i	−0.179638	−	1.01878i	0.753015	−	0.658004i	$-0.228599\pi$
$230$	−1.22753e9	+	2.16447e8i	−0.438652	+	0.0773463i
$231$	−4.58685e7	−	7.73383e6i	−0.0161089	−	0.00271610i
$232$	−2.43536e9	−	2.04351e9i	−0.840643	−	0.705383i
$233$	−3.07386e9	+	1.77469e9i	−1.04294	+	0.602143i	−0.920665	−	0.390353i	$-0.872353\pi$
$233$	−3.07386e9	+	1.77469e9i	−1.04294	+	0.602143i	−0.122277	+	0.992496i	$0.539020\pi$
$234$	8.51498e8	+	2.23466e9i	0.284001	+	0.745330i
$235$	4.52787e8	−	7.84251e8i	0.148465	−	0.257148i
$236$	−7.47020e8	−	2.05242e9i	−0.240815	−	0.661635i
$237$	−3.30242e9	+	2.47530e7i	−1.04674	+	0.00784575i
$238$	−5.70029e6	+	4.78311e6i	−0.00177660	+	0.00149074i
$239$	−2.51801e8	+	6.91818e8i	−0.0771731	+	0.212031i	−0.972280	−	0.233821i	$-0.924877\pi$
$239$	−2.51801e8	+	6.91818e8i	−0.0771731	+	0.212031i	0.895107	+	0.445852i	$0.147099\pi$
$240$	−1.23330e9	+	2.27009e8i	−0.371727	+	0.0684223i
$241$	−2.07614e8	+	1.17744e9i	−0.0615445	+	0.349036i	0.938449	+	0.345418i	$0.112263\pi$
$241$	−2.07614e8	+	1.17744e9i	−0.0615445	+	0.349036i	−0.999993	+	0.00361833i	$0.998848\pi$
$242$		−	2.62439e9i		−	0.765185i
$243$	2.75313e9	+	2.13961e9i	0.789590	+	0.613634i
$244$	3.24343e9			0.915051
$245$	−3.08707e9	−	5.44333e8i	−0.856804	−	0.151078i
$246$	2.70364e8	+	1.46885e9i	0.0738259	+	0.401085i
$247$	7.15751e9	+	2.60512e9i	1.92298	+	0.699906i
$248$	−1.66781e9	−	1.98762e9i	−0.440901	−	0.525445i
$249$	−3.20661e7	−	4.27810e9i	−0.00834160	−	1.11289i
$250$	1.78486e9	−	6.49635e8i	0.456924	−	0.166307i
$251$	−1.64288e9	−	9.48514e8i	−0.413914	−	0.238973i	0.278556	−	0.960420i	$-0.410144\pi$
$251$	−1.64288e9	−	9.48514e8i	−0.413914	−	0.238973i	−0.692470	+	0.721447i	$0.743477\pi$
$252$	2.98815e7	−	1.13861e7i	0.00740971	−	0.00282340i
$253$	−3.83385e9	−	6.64042e9i	−0.935735	−	1.62074i
$254$	−8.16089e8	+	9.72577e8i	−0.196066	+	0.233663i
$255$	3.17464e8	−	1.88285e9i	0.0750817	−	0.445301i
$256$	−3.46593e8	−	1.96563e9i	−0.0806975	−	0.457658i
$257$	1.74694e9	−	3.08032e8i	0.400447	−	0.0706095i	0.0302019	−	0.999544i	$-0.490385\pi$
$257$	1.74694e9	−	3.08032e8i	0.400447	−	0.0706095i	0.370245	+	0.928934i	$0.379274\pi$
$258$	1.08998e9	−	1.31894e9i	0.246003	−	0.297678i
$259$	4.45268e7	+	3.73624e7i	0.00989516	+	0.00830302i
$260$	−4.87369e9	+	2.81383e9i	−1.06651	+	0.615749i
$261$	−6.18695e9	+	1.18682e9i	−1.33326	+	0.255753i
$262$	−1.47892e8	+	2.56156e8i	−0.0313862	+	0.0543624i
$263$	9.56007e8	+	2.62661e9i	0.199819	+	0.549000i	0.998616	−	0.0526024i	$-0.0167516\pi$
$263$	9.56007e8	+	2.62661e9i	0.199819	+	0.549000i	−0.798796	+	0.601602i	$0.794529\pi$
$264$	3.26891e9	+	5.56516e9i	0.672956	+	1.14568i
$265$	−1.62051e9	+	1.35977e9i	−0.328600	+	0.275728i
$266$	−8.82653e6	+	2.42507e7i	−0.00176304	+	0.00484392i
$267$	−1.12870e9	+	3.17493e9i	−0.222093	+	0.624725i
$268$	2.96993e8	−	1.68433e9i	0.0575714	−	0.326504i
$269$			3.73774e9i			0.713839i	0.934135	+	0.356919i	$0.116173\pi$
$269$			3.73774e9i			0.713839i	−0.934135	+	0.356919i	$0.883827\pi$
$270$	9.98796e8	−	1.82346e9i	0.187941	−	0.343116i
$271$	−4.23327e9			−0.784873			−0.392436	−	0.919779i	$-0.628368\pi$
$271$	−4.23327e9			−0.784873			−0.392436	+	0.919779i	$0.628368\pi$
$272$	−1.21530e9	−	2.14290e8i	−0.222027	−	0.0391494i
$273$	7.45450e7	−	6.35088e7i	0.0134205	−	0.0114336i
$274$	−2.60770e9	−	9.49124e8i	−0.462653	−	0.168392i
$275$	1.46784e9	+	1.74931e9i	0.256655	+	0.305869i
$276$	4.58458e9	+	2.60129e9i	0.790066	+	0.448283i
$277$	9.61877e9	−	3.50095e9i	1.63381	−	0.594657i	0.647866	−	0.761754i	$-0.275662\pi$
$277$	9.61877e9	−	3.50095e9i	1.63381	−	0.594657i	0.985940	+	0.167097i	$0.0534394\pi$
$278$	3.12108e9	+	1.80196e9i	0.522548	+	0.301693i
$279$	−5.14097e9	+	7.70718e7i	−0.848455	+	0.0127198i
$280$	−2.14829e7	−	3.72095e7i	−0.00349512	−	0.00605372i
$281$	3.70155e9	−	4.41134e9i	0.593688	−	0.707530i	−0.382622	−	0.923905i	$-0.624979\pi$
$281$	3.70155e9	−	4.41134e9i	0.593688	−	0.707530i	0.976310	+	0.216375i	$0.0694233\pi$
$282$	9.09301e8	−	3.38698e8i	0.143784	−	0.0535570i
$283$	5.45231e8	+	3.09216e9i	0.0850031	+	0.482077i	0.997356	+	0.0726717i	$0.0231525\pi$
$283$	5.45231e8	+	3.09216e9i	0.0850031	+	0.482077i	−0.912353	+	0.409405i	$0.865736\pi$
$284$	2.18821e9	−	3.85841e8i	0.336369	−	0.0593110i
$285$	−2.31148e9	−	6.20561e9i	−0.350356	−	0.940600i
$286$	6.71950e9	+	5.63833e9i	1.00432	+	0.842726i
$287$	5.29673e7	−	3.05807e7i	0.00780693	−	0.00450733i
$288$	−6.03087e9	−	3.36241e9i	−0.876617	−	0.488743i
$289$	−2.54838e9	+	4.41392e9i	−0.365319	+	0.632751i
$290$	1.28476e9	+	3.52985e9i	0.181648	+	0.499073i
$291$	3.88483e9	−	6.84672e9i	0.541751	−	0.954797i
$292$	−3.71728e9	+	3.11917e9i	−0.511322	+	0.429050i
$293$	2.74172e9	−	7.53280e9i	0.372008	−	1.02208i	−0.602576	−	0.798061i	$-0.705859\pi$
$293$	2.74172e9	−	7.53280e9i	0.372008	−	1.02208i	0.974584	−	0.224022i	$-0.0719186\pi$
$294$	−2.17825e9	−	2.55677e9i	−0.291554	−	0.342218i
$295$	−1.00982e9	+	5.72700e9i	−0.133339	+	0.756204i
$296$		−	8.06509e9i		−	1.05061i
$297$	1.26420e10	+	1.93714e9i	1.62477	+	0.248963i
$298$	−9.90429e8			−0.125591
$299$	1.58976e10	+	2.80318e9i	1.98906	+	0.350724i
$300$	−1.47914e9	−	5.25842e8i	−0.182610	−	0.0649188i
$301$	−6.58433e7	−	2.39650e7i	−0.00802132	−	0.00291952i
$302$	−1.38365e9	−	1.64897e9i	−0.166340	−	0.198237i
$303$	4.73259e9	−	2.77987e9i	0.561473	−	0.329802i
$304$	−4.02172e9	+	1.46379e9i	−0.470888	+	0.171389i
$305$	−7.47878e9	−	4.31787e9i	−0.864234	−	0.498966i
$306$	1.54741e9	−	1.33847e9i	0.176490	−	0.152659i
$307$	−2.44162e9	−	4.22901e9i	−0.274868	−	0.476086i	0.695234	−	0.718784i	$-0.255301\pi$
$307$	−2.44162e9	−	4.22901e9i	−0.274868	−	0.476086i	−0.970102	+	0.242698i	$0.921968\pi$
$308$	7.53948e7	−	8.98520e7i	0.00837797	−	0.00998447i
$309$	6.68487e9	+	5.52442e9i	0.733262	+	0.605972i
$310$	5.32367e8	+	3.01921e9i	0.0576454	+	0.326923i
$311$	1.23151e10	−	2.17148e9i	1.31643	−	0.232121i	0.529048	−	0.848592i	$-0.322549\pi$
$311$	1.23151e10	−	2.17148e9i	1.31643	−	0.232121i	0.787378	+	0.616471i	$0.211438\pi$
$312$	−1.33989e10	−	2.25918e9i	−1.41401	−	0.238414i
$313$	−7.17480e9	−	6.02037e9i	−0.747536	−	0.627258i	0.187314	−	0.982300i	$-0.440022\pi$
$313$	−7.17480e9	−	6.02037e9i	−0.747536	−	0.627258i	−0.934850	+	0.355043i	$0.884466\pi$
$314$	−4.95517e9	+	2.86087e9i	−0.509730	+	0.294293i
$315$	−8.40595e7	−	1.35260e7i	−0.00853777	−	0.00137381i
$316$	4.16377e9	−	7.21186e9i	0.417579	−	0.723268i
$317$	3.76140e9	+	1.03344e10i	0.372488	+	1.02340i	0.974396	+	0.224838i	$0.0721852\pi$
$317$	3.76140e9	+	1.03344e10i	0.372488	+	1.02340i	−0.601908	+	0.798565i	$0.705593\pi$
$318$	−2.26663e9	+	1.69893e7i	−0.221652	+	0.00166138i
$319$	−1.77015e10	+	1.48533e10i	−1.70941	+	1.43437i
$320$	−5.26288e7	+	1.44597e8i	−0.00501908	+	0.0137898i
$321$	5.25756e9	−	9.67736e8i	0.495181	−	0.0911458i
$322$	−9.49757e6	+	5.38634e7i	−0.000883464	+	0.00501038i
$323$		−	6.51663e9i		−	0.598705i
$324$	−8.16811e9	+	3.25342e9i	−0.741210	+	0.295230i
$325$	−4.80759e9			−0.430917
$326$	3.80502e9	+	6.70928e8i	0.336889	+	0.0594026i
$327$	2.12068e9	+	1.15213e10i	0.185474	+	1.00765i
$328$	−7.97451e9	−	2.90248e9i	−0.688983	−	0.250769i
$329$	−2.55419e7	−	3.04397e7i	−0.00218007	−	0.00259810i
$330$	−5.71594e7	−	7.62591e9i	−0.00481983	−	0.643037i
$331$	1.70860e10	−	6.21880e9i	1.42341	−	0.518077i	0.488371	−	0.872636i	$-0.337591\pi$
$331$	1.70860e10	−	6.21880e9i	1.42341	−	0.518077i	0.935034	+	0.354559i	$0.115369\pi$
$332$	9.34257e9	+	5.39393e9i	0.768978	+	0.443970i
$333$	−1.23953e10	−	1.00882e10i	−1.00805	−	0.820418i
$334$	6.94831e8	+	1.20348e9i	0.0558333	+	0.0967061i
$335$	−2.92711e9	+	3.48839e9i	−0.232413	+	0.276979i
$336$	−9.14870e6	+	5.42599e7i	−0.000717798	+	0.00425718i
$337$	3.85980e9	+	2.18900e10i	0.299257	+	1.69717i	0.649376	+	0.760468i	$0.275030\pi$
$337$	3.85980e9	+	2.18900e10i	0.299257	+	1.69717i	−0.350118	+	0.936705i	$0.613859\pi$
$338$	−1.24074e10	+	2.18776e9i	−0.950634	+	0.167622i
$339$	−3.41272e9	+	4.12959e9i	−0.258406	+	0.312686i
$340$	3.68832e9	+	3.09487e9i	0.276002	+	0.231593i
$341$	−1.63326e10	+	9.42966e9i	−1.20792	+	0.697394i
$342$	2.32664e9	−	6.70338e9i	0.170069	−	0.489992i
$343$	−1.37555e8	+	2.38253e8i	−0.00993805	+	0.0172132i
$344$	3.32521e9	+	9.13593e9i	0.237457	+	0.652408i
$345$	−7.10822e9	−	1.21014e10i	−0.501747	−	0.854201i
$346$	7.44203e9	−	6.24460e9i	0.519262	−	0.435713i
$347$	5.16122e9	−	1.41803e10i	0.355987	−	0.978067i	−0.624421	−	0.781088i	$-0.714665\pi$
$347$	5.16122e9	−	1.41803e10i	0.355987	−	0.978067i	0.980408	−	0.196979i	$-0.0631129\pi$
$348$	5.32106e9	−	1.49676e10i	0.362812	−	1.02055i
$349$	9.91134e8	−	5.62100e9i	0.0668083	−	0.378889i	−0.933010	−	0.359849i	$-0.882828\pi$
$349$	9.91134e8	−	5.62100e9i	0.0668083	−	0.378889i	0.999819	−	0.0190395i	$-0.00606082\pi$
$350$		−	1.62888e7i		−	0.00108547i
$351$	−2.02322e10	+	1.77671e10i	−1.33295	+	1.17054i
$352$	−2.53272e10			−1.64974
$353$	−1.45465e10	−	2.56494e9i	−0.936827	−	0.165188i	−0.315666	−	0.948870i	$-0.602228\pi$
$353$	−1.45465e10	−	2.56494e9i	−0.936827	−	0.165188i	−0.621162	+	0.783683i	$0.713339\pi$
$354$	−4.74323e9	+	4.04101e9i	−0.302037	+	0.257322i
$355$	−5.55930e9	−	2.02342e9i	−0.350031	−	0.127401i
$356$	−5.46157e9	−	6.50884e9i	−0.340030	−	0.405232i
$357$	−7.28715e7	−	4.13472e7i	−0.00448626	−	0.00254550i
$358$	2.22057e9	−	8.08220e8i	0.135186	−	0.0492037i
$359$	2.51153e10	+	1.45003e10i	1.51203	+	0.872972i	0.999901	+	0.0140646i	$0.00447704\pi$
$359$	2.51153e10	+	1.45003e10i	1.51203	+	0.872972i	0.512131	+	0.858907i	$0.328856\pi$
$360$	6.05945e9	+	1.01411e10i	0.360764	+	0.603775i
$361$	−2.80848e9	−	4.86443e9i	−0.165365	−	0.286420i
$362$	−4.44574e9	+	5.29823e9i	−0.258887	+	0.308529i
$363$	2.76908e10	−	1.03143e10i	1.59481	−	0.594039i
$364$	4.28805e7	+	2.43187e8i	0.00244261	+	0.0138527i
$365$	1.27239e10	−	2.24356e9i	0.716881	−	0.126405i
$366$	−3.22990e9	−	8.67128e9i	−0.179997	−	0.483236i
$367$	1.36601e9	+	1.14621e9i	0.0752988	+	0.0631832i	0.679660	−	0.733527i	$-0.262127\pi$
$367$	1.36601e9	+	1.14621e9i	0.0752988	+	0.0631832i	−0.604361	+	0.796710i	$0.706572\pi$
$368$	−7.85526e9	+	4.53524e9i	−0.428321	+	0.247291i
$369$	−1.44357e10	+	8.62555e9i	−0.778634	+	0.465244i
$370$	−4.76475e9	+	8.25279e9i	−0.254234	+	0.440346i
$371$	3.17476e7	+	8.72257e7i	0.00167577	+	0.00460414i
$372$	6.39808e9	−	1.12761e10i	0.334101	−	0.588828i
$373$	9.68547e9	−	8.12708e9i	0.500363	−	0.419855i	−0.357360	−	0.933967i	$-0.616323\pi$
$373$	9.68547e9	−	8.12708e9i	0.500363	−	0.419855i	0.857723	+	0.514112i	$0.171878\pi$
$374$	2.56674e9	−	7.05205e9i	0.131188	−	0.360437i
$375$	1.38694e10	+	1.62795e10i	0.701344	+	0.823219i
$376$	−9.57409e8	+	5.42974e9i	−0.0479012	+	0.271661i
$377$		−	4.86486e10i		−	2.40827i
$378$	−6.01975e7	−	6.85495e7i	−0.00294857	−	0.00335766i
$379$	2.90826e10			1.40954			0.704768	−	0.709438i	$-0.251051\pi$
$379$	2.90826e10			1.40954			0.704768	+	0.709438i	$0.251051\pi$
$380$	1.64445e10	+	2.89961e9i	0.788654	+	0.139061i
$381$	−1.34694e10	−	4.78843e9i	−0.639216	−	0.227245i
$382$	8.18923e9	+	2.98064e9i	0.384583	+	0.139977i
$383$	3.45256e9	+	4.11460e9i	0.160452	+	0.191220i	0.840281	−	0.542152i	$-0.182390\pi$
$383$	3.45256e9	+	4.11460e9i	0.160452	+	0.191220i	−0.679828	+	0.733371i	$0.737946\pi$
$384$	1.86746e10	−	1.09692e10i	0.858868	−	0.504488i
$385$	−2.93464e8	+	1.06812e8i	−0.0133571	+	0.00486159i
$386$	−1.13635e10	−	6.56074e9i	−0.511876	−	0.295531i
$387$	1.82004e10	+	6.31709e9i	0.811405	+	0.281626i
$388$	9.92502e9	+	1.71906e10i	0.437930	+	0.758517i
$389$	−1.48272e10	+	1.76703e10i	−0.647530	+	0.771697i	−0.985539	−	0.169446i	$-0.945802\pi$
$389$	−1.48272e10	+	1.76703e10i	−0.647530	+	0.771697i	0.338009	+	0.941143i	$0.390247\pi$
$390$	1.23761e10	+	1.02277e10i	0.534965	+	0.442099i
$391$	−2.39827e9	−	1.36013e10i	−0.102610	−	0.581931i
$392$	1.87953e10	−	3.31412e9i	0.795984	−	0.140354i
$393$	−3.28403e9	−	5.53716e8i	−0.137669	−	0.0232122i
$394$	9.71690e9	+	8.15345e9i	0.403221	+	0.338342i
$395$	−1.92018e10	+	1.10862e10i	−0.788778	+	0.455401i
$396$	−2.03572e10	+	2.50129e10i	−0.827824	+	1.01714i
$397$	1.33126e10	−	2.30581e10i	0.535921	−	0.928242i	−0.463198	−	0.886255i	$-0.653298\pi$
$397$	1.33126e10	−	2.30581e10i	0.535921	−	0.928242i	0.999118	−	0.0419866i	$-0.0133687\pi$
$398$	3.80903e9	+	1.04652e10i	0.151803	+	0.417077i
$399$	−2.90567e8	+	2.17792e6i	−0.0114645	+	8.59312e-5i
$400$	2.06934e9	−	1.73638e9i	0.0808335	−	0.0678274i
$401$	−6.68098e9	+	1.83559e10i	−0.258382	+	0.709900i	0.740885	+	0.671632i	$0.234406\pi$
$401$	−6.68098e9	+	1.83559e10i	−0.258382	+	0.709900i	−0.999268	+	0.0382681i	$0.987816\pi$
$402$	−4.79880e9	+	8.83294e8i	−0.183750	+	0.0338221i
$403$	6.89464e9	−	3.91014e10i	0.261391	−	1.48242i
$404$			1.38400e10i			0.519531i
$405$	2.31654e10	+	3.37212e9i	0.861033	+	0.125338i
$406$	1.64829e8			0.00606636
$407$	−5.77306e10	−	1.01795e10i	−2.10392	−	0.370977i
$408$	2.10447e9	+	1.14333e10i	0.0759455	+	0.412600i
$409$	2.91511e10	+	1.06101e10i	1.04174	+	0.379164i	0.805541	−	0.592539i	$-0.201875\pi$
$409$	2.91511e10	+	1.06101e10i	1.04174	+	0.379164i	0.236203	+	0.971704i	$0.424097\pi$
$410$	6.44536e9	+	7.68128e9i	0.228093	+	0.271830i
$411$	−2.34194e8	−	3.12450e10i	−0.00820745	−	1.09500i
$412$	−2.05488e10	+	7.47915e9i	−0.713178	+	0.259575i
$413$	2.20988e8	+	1.27587e8i	0.00759570	+	0.00438538i
$414$	2.38907e9	−	1.48473e10i	0.0813258	−	0.505412i
$415$	−1.43615e10	−	2.48749e10i	−0.484182	−	0.838628i
$416$	3.42744e10	−	4.08466e10i	1.14445	−	1.36390i
$417$	−6.74665e9	+	4.00136e10i	−0.223123	+	1.32332i
$418$	−4.51955e9	−	2.56317e10i	−0.148044	−	0.839598i
$419$	−5.06009e10	+	8.92230e9i	−1.64173	+	0.289481i	−0.916802	−	0.399342i	$-0.869239\pi$
$419$	−5.06009e10	+	8.92230e9i	−1.64173	+	0.289481i	−0.724929	+	0.688824i	$0.758127\pi$
$420$	1.36763e8	−	1.65491e8i	0.00439513	−	0.00531836i
$421$	−4.57824e9	−	3.84160e9i	−0.145737	−	0.122288i	0.567004	−	0.823715i	$-0.308102\pi$
$421$	−4.57824e9	−	3.84160e9i	−0.145737	−	0.122288i	−0.712741	+	0.701427i	$0.752547\pi$
$422$	1.75335e9	−	1.01230e9i	0.0552866	−	0.0319197i
$423$	7.14745e9	+	8.26321e9i	0.223249	+	0.258100i
$424$	6.43976e9	−	1.11540e10i	0.199254	−	0.345118i
$425$	1.40678e9	+	3.86510e9i	0.0431192	+	0.118469i
$426$	−3.21063e9	−	5.46594e9i	−0.0974881	−	0.165969i
$427$	−2.90279e8	+	2.43573e8i	−0.00873181	+	0.00732686i
$428$	−4.61045e9	+	1.26671e10i	−0.137394	+	0.377487i
$429$	−3.30831e10	+	9.30595e10i	−0.976736	+	2.74746i
$430$	1.99480e9	−	1.13130e10i	0.0583478	−	0.330907i
$431$		−	2.95889e10i		−	0.857473i	−0.903430	−	0.428736i	$-0.858959\pi$
$431$		−	2.95889e10i		−	0.857473i	0.903430	−	0.428736i	$-0.141041\pi$
$432$	2.29153e9	−	1.49549e10i	0.0657946	−	0.429385i
$433$	−6.02354e9			−0.171356			−0.0856782	−	0.996323i	$-0.527306\pi$
$433$	−6.02354e9			−0.171356			−0.0856782	+	0.996323i	$0.527306\pi$
$434$	1.32481e8	+	2.33600e7i	0.00373418	+	0.000658437i
$435$	−3.21953e10	+	2.74289e10i	−0.899158	+	0.766041i
$436$	−2.77584e10	−	1.01032e10i	−0.768155	−	0.279586i
$437$	−3.07886e10	−	3.66924e10i	−0.844237	−	1.00612i
$438$	1.20409e10	+	6.83197e9i	0.327160	+	0.185631i
$439$	3.27196e9	−	1.19090e9i	0.0880948	−	0.0320639i	−0.297597	−	0.954692i	$-0.596185\pi$
$439$	3.27196e9	−	1.19090e9i	0.0880948	−	0.0320639i	0.385692	+	0.922628i	$0.373963\pi$
$440$	3.75268e10	+	2.16661e10i	1.00122	+	0.578056i
$441$	1.84165e10	−	3.30321e10i	0.486914	−	0.873337i
$442$	7.89978e9	+	1.36828e10i	0.206979	+	0.358498i
$443$	9.32868e9	−	1.11175e10i	0.242217	−	0.288664i	−0.631216	−	0.775607i	$-0.717444\pi$
$443$	9.32868e9	−	1.11175e10i	0.242217	−	0.288664i	0.873433	+	0.486944i	$0.161888\pi$
$444$	3.77644e10	−	1.40666e10i	0.971742	−	0.361956i
$445$	3.92840e9	+	2.22790e10i	0.100179	+	0.568141i
$446$	−2.69584e10	+	4.75349e9i	−0.681325	+	0.120136i
$447$	−3.89257e9	−	1.04504e10i	−0.0975004	−	0.261759i
$448$	5.17235e6	+	4.34012e6i	0.000128403	+	0.000107743i
$449$	−5.23161e10	+	3.02047e10i	−1.28721	+	0.743171i	−0.978156	−	0.207873i	$-0.933346\pi$
$449$	−5.23161e10	+	3.02047e10i	−1.28721	+	0.743171i	−0.309055	+	0.951044i	$0.600013\pi$
$450$	6.71345e7	+	4.47812e9i	0.00163718	+	0.109206i
$451$	−3.08414e10	+	5.34189e10i	−0.745466	+	1.29119i
$452$	−4.62026e9	−	1.26941e10i	−0.110691	−	0.304121i
$453$	1.19608e10	−	2.10801e10i	0.284033	−	0.500587i
$454$	−2.49931e10	+	2.09717e10i	−0.588298	+	0.493641i
$455$	2.24872e8	−	6.17832e8i	0.00524675	−	0.0144153i
$456$	2.61467e10	+	3.06904e10i	0.604726	+	0.709811i
$457$	−2.85275e9	+	1.61788e10i	−0.0654033	+	0.370920i	0.934485	+	0.356001i	$0.115860\pi$
$457$	−2.85275e9	+	1.61788e10i	−0.0654033	+	0.370920i	−0.999889	+	0.0149190i	$0.995251\pi$
$458$		−	2.04661e10i		−	0.465128i
$459$	2.02042e10	+	1.10668e10i	0.455189	+	0.249329i
$460$	3.53895e10			0.790392
$461$	−1.19496e9	−	2.10704e8i	−0.0264576	−	0.00466519i	0.160404	−	0.987051i	$-0.448720\pi$
$461$	−1.19496e9	−	2.10704e8i	−0.0264576	−	0.00466519i	−0.186861	+	0.982386i	$0.559832\pi$
$462$	−3.15299e8	−	1.12090e8i	−0.00692077	−	0.00246037i
$463$	−3.29010e10	−	1.19750e10i	−0.715953	−	0.260586i	−0.0417465	−	0.999128i	$-0.513292\pi$
$463$	−3.29010e10	−	1.19750e10i	−0.715953	−	0.260586i	−0.674207	+	0.738543i	$0.735514\pi$
$464$	1.75706e10	+	2.09399e10i	0.379067	+	0.451754i
$465$	−2.97644e10	+	1.74832e10i	−0.636627	+	0.373947i
$466$	−2.39940e10	+	8.73312e9i	−0.508815	+	0.185193i
$467$	5.50338e10	+	3.17738e10i	1.15708	+	0.668039i	0.950602	−	0.310413i	$-0.100467\pi$
$467$	5.50338e10	+	3.17738e10i	1.15708	+	0.668039i	0.206475	+	0.978452i	$0.433801\pi$
$468$	−1.27910e10	−	6.66803e10i	−0.266637	−	1.39000i
$469$	9.99087e7	+	1.73047e8i	0.00206496	+	0.00357662i
$470$	4.18751e9	−	4.99048e9i	0.0858153	−	0.102271i
$471$	−4.96608e10	−	4.10400e10i	−1.00909	−	0.833919i
$472$	−6.14822e9	−	3.48683e10i	−0.123874	−	0.702526i
$473$	6.95928e10	−	1.22711e10i	1.39034	−	0.245154i
$474$	−2.34273e10	−	3.95004e9i	−0.464096	−	0.0782507i
$475$	1.09276e10	+	9.16932e9i	0.214659	+	0.180120i
$476$	1.82965e8	−	1.05635e8i	0.00356401	−	0.00205768i
$477$	−9.08755e9	−	2.38493e10i	−0.175539	−	0.460682i
$478$	−2.64814e9	+	4.58671e9i	−0.0507258	+	0.0878596i
$479$	−1.69332e10	−	4.65236e10i	−0.321660	−	0.883754i	−0.990147	−	0.140030i	$-0.955280\pi$
$479$	−1.69332e10	−	4.65236e10i	−0.321660	−	0.883754i	0.668487	−	0.743724i	$-0.266942\pi$
$480$	−4.63565e10	+	3.47461e8i	−0.873265	+	0.00654548i
$481$	9.45418e10	−	7.93300e10i	1.76622	−	1.48203i
$482$	−2.94173e9	+	8.08234e9i	−0.0545023	+	0.149744i
$483$	−6.05659e8	+	1.11481e8i	−0.0111286	+	0.00204839i
$484$	−1.29387e10	+	7.33792e10i	−0.235782	+	1.33719i
$485$		−	5.28515e10i		−	0.955191i
$486$	1.68320e10	+	1.85975e10i	0.301711	+	0.333357i
$487$	8.96707e9			0.159417			0.0797085	−	0.996818i	$-0.474601\pi$
$487$	8.96707e9			0.159417			0.0797085	+	0.996818i	$0.474601\pi$
$488$	5.17791e10	+	9.13005e9i	0.913009	+	0.160988i
$489$	7.87525e9	+	4.27850e10i	0.137730	+	0.748266i
$490$	−2.11907e10	−	7.71277e9i	−0.367587	−	0.133791i
$491$	4.41641e10	+	5.26328e10i	0.759878	+	0.905587i	0.997840	−	0.0656873i	$-0.0209240\pi$
$491$	4.41641e10	+	5.26328e10i	0.759878	+	0.905587i	−0.237962	+	0.971274i	$0.576480\pi$
$492$	−3.17825e8	−	4.24026e10i	−0.00542410	−	0.723656i
$493$	−3.91114e10	+	1.42354e10i	−0.662088	+	0.240980i
$494$	4.74538e10	+	2.73975e10i	0.796825	+	0.460047i
$495$	8.02390e10	−	3.05744e10i	1.33649	−	0.509256i
$496$	1.11548e10	+	1.93206e10i	0.184304	+	0.319223i
$497$	−1.66864e8	+	1.98861e8i	−0.00273488	+	0.00325930i
$498$	5.11706e9	−	3.03487e10i	0.0831961	−	0.493427i
$499$	1.11840e10	+	6.34274e10i	0.180382	+	1.02300i	0.931746	+	0.363110i	$0.118285\pi$
$499$	1.11840e10	+	6.34274e10i	0.180382	+	1.02300i	−0.751364	+	0.659888i	$0.770604\pi$
$500$	−5.31083e10	+	9.36443e9i	−0.849733	+	0.149831i
$501$	−9.96755e9	+	1.20613e10i	−0.158211	+	0.191445i
$502$	−1.04542e10	−	8.77214e9i	−0.164618	−	0.138131i
$503$	−1.39660e10	+	8.06327e9i	−0.218173	+	0.125962i	−0.605104	−	0.796147i	$-0.706868\pi$
$503$	−1.39660e10	+	8.06327e9i	−0.218173	+	0.125962i	0.386931	+	0.922109i	$0.373535\pi$
$504$	5.09089e8	−	9.76564e7i	0.00788990	−	0.00151349i
$505$	1.84248e10	−	3.19126e10i	0.283293	−	0.490679i
$506$	−1.88660e10	−	5.18340e10i	−0.287792	−	0.790702i
$507$	−7.18471e10	−	1.22316e11i	−1.08737	−	1.85120i
$508$	2.76132e10	−	2.31703e10i	0.414632	−	0.347917i
$509$	−2.93576e10	+	8.06594e10i	−0.437371	+	1.20167i	0.503825	+	0.863806i	$0.331926\pi$
$509$	−2.93576e10	+	8.06594e10i	−0.437371	+	1.20167i	−0.941196	+	0.337861i	$0.890297\pi$
$510$	4.60117e9	−	1.29426e10i	0.0680124	−	0.191312i
$511$	9.84463e7	−	5.58316e8i	0.00144383	−	0.00818836i
$512$			5.40910e10i			0.787127i
$513$	7.98738e10	−	1.79633e9i	1.15328	−	0.0259368i
$514$	1.27611e10			0.182826
$515$	5.73387e10	+	1.01104e10i	0.815115	+	0.143727i
$516$	−3.69790e10	+	3.15044e10i	−0.521623	+	0.444398i
$517$	3.76581e10	+	1.37064e10i	0.527105	+	0.191850i
$518$	2.68782e8	+	3.20321e8i	0.00373319	+	0.00444905i
$519$	9.51375e10	+	5.39810e10i	1.31124	+	0.743997i
$520$	−8.57258e10	+	3.12016e10i	−1.17246	+	0.426741i
$521$	1.02555e11	+	5.92104e10i	1.39190	+	0.803614i	0.993526	−	0.113609i	$-0.0362411\pi$
$521$	1.02555e11	+	5.92104e10i	1.39190	+	0.803614i	0.398374	+	0.917223i	$0.369574\pi$
$522$	−4.53147e10	+	6.79343e8i	−0.610319	+	0.00914970i
$523$	1.60296e10	+	2.77642e10i	0.214248	+	0.371089i	0.953040	−	0.302845i	$-0.0979365\pi$
$523$	1.60296e10	+	2.77642e10i	0.214248	+	0.371089i	−0.738792	+	0.673934i	$0.764603\pi$
$524$	5.39802e9	−	6.43311e9i	0.0715994	−	0.0853288i
$525$	1.71869e8	−	6.40181e7i	0.00226235	−	0.000842685i
$526$	3.49175e9	+	1.98027e10i	0.0456143	+	0.258691i
$527$	−3.34533e10	+	5.89873e9i	−0.433708	+	0.0764744i
$528$	−1.93707e10	−	5.20045e10i	−0.249236	−	0.669122i
$529$	−1.77747e10	−	1.49147e10i	−0.226976	−	0.190455i
$530$	−1.31793e10	+	7.60906e9i	−0.167028	+	0.0964334i
$531$	−6.12798e10	−	3.41655e10i	−0.770796	−	0.429744i
$532$	3.66354e8	−	6.34545e8i	0.00457357	−	0.00792165i
$533$	−4.44151e10	−	1.22030e11i	−0.550329	−	1.51202i
$534$	−1.19626e10	+	2.10831e10i	−0.147116	+	0.259281i
$535$	2.74942e10	−	2.30704e10i	0.335603	−	0.281604i
$536$	9.48257e9	−	2.60532e10i	0.114886	−	0.315647i
$537$	1.72551e10	+	2.02535e10i	0.207500	+	0.243559i
$538$	−4.66921e9	+	2.64804e10i	−0.0557333	+	0.316079i
$539$		−	1.38721e11i		−	1.64357i
$540$	−3.69168e10	+	4.60605e10i	−0.434160	+	0.541694i
$541$	−4.07582e10			−0.475801			−0.237901	−	0.971290i	$-0.576459\pi$
$541$	−4.07582e10			−0.475801			−0.237901	+	0.971290i	$0.576459\pi$
$542$	−2.99911e10	−	5.28824e9i	−0.347532	−	0.0612793i
$543$	−7.33760e10	−	2.60855e10i	−0.844024	−	0.300055i
$544$	−4.28682e10	−	1.56027e10i	−0.489485	−	0.178158i
$545$	5.05559e10	+	6.02502e10i	0.573041	+	0.682924i
$546$	6.07457e8	−	3.56813e8i	0.00683511	−	0.00401486i
$547$	−3.74514e8	+	1.36312e8i	−0.00418330	+	0.00152260i	−0.344111	−	0.938929i	$-0.611820\pi$
$547$	−3.74514e8	+	1.36312e8i	−0.00418330	+	0.00152260i	0.339928	+	0.940452i	$0.389597\pi$
$548$	6.82332e10	+	3.93944e10i	0.756612	+	0.436830i
$549$	7.87997e10	−	6.81595e10i	0.867431	−	0.750304i
$550$	8.21385e9	+	1.42268e10i	0.0897627	+	0.155473i
$551$	−9.27855e10	+	1.10577e11i	−1.00664	+	1.19967i
$552$	6.58672e10	+	5.44331e10i	0.709435	+	0.586282i
$553$	1.68945e8	+	9.58133e8i	0.00180652	+	0.0102453i
$554$	7.25186e10	−	1.27870e10i	0.769858	−	0.135747i
$555$	−1.05804e11	−	1.78396e10i	−1.11515	−	0.188023i
$556$	−7.83830e10	−	6.57711e10i	−0.820205	−	0.688234i
$557$	4.33094e10	−	2.50047e10i	0.449947	−	0.259777i	−0.257861	−	0.966182i	$-0.583018\pi$
$557$	4.33094e10	−	2.50047e10i	0.449947	−	0.259777i	0.707808	+	0.706405i	$0.249684\pi$
$558$	−3.65180e10	−	5.87612e9i	−0.376678	−	0.0606113i
$559$	−7.43872e10	+	1.28842e11i	−0.761817	+	1.31951i
$560$	1.26353e8	+	3.47152e8i	0.00128480	+	0.00352995i
$561$	8.44965e10	−	6.33336e8i	0.853075	−	0.00639415i
$562$	3.17347e10	−	2.66286e10i	0.318119	−	0.266933i
$563$	4.03175e9	−	1.10771e10i	0.0401292	−	0.110254i	−0.918010	−	0.396558i	$-0.870205\pi$
$563$	4.03175e9	−	1.10771e10i	0.0401292	−	0.110254i	0.958139	+	0.286304i	$0.0924268\pi$
$564$	−2.70944e10	+	4.98714e9i	−0.267770	+	0.0492873i
$565$	−6.24569e9	+	3.54211e10i	−0.0612896	+	0.347590i
$566$			2.25878e10i			0.220094i
$567$	4.86702e8	−	9.04577e8i	0.00470903	−	0.00875212i
$568$	3.60194e10			0.346054
$569$	−1.00783e11	−	1.77708e10i	−0.961476	−	0.169534i	−0.329185	−	0.944265i	$-0.606774\pi$
$569$	−1.00783e11	−	1.77708e10i	−0.961476	−	0.169534i	−0.632291	+	0.774731i	$0.717885\pi$
$570$	−8.62381e9	−	4.68518e10i	−0.0816958	−	0.443840i
$571$	−7.58711e10	−	2.76148e10i	−0.713726	−	0.259775i	−0.0404663	−	0.999181i	$-0.512884\pi$
$571$	−7.58711e10	−	2.76148e10i	−0.713726	−	0.259775i	−0.673260	+	0.739406i	$0.735107\pi$
$572$	−1.60082e11	−	1.90779e11i	−1.49541	−	1.78216i
$573$	7.35464e8	+	9.81219e10i	0.00682249	+	0.910222i
$574$	4.13454e8	−	1.50485e8i	0.00380872	−	0.00138626i
$575$	2.61821e10	+	1.51162e10i	0.239515	+	0.138284i
$576$	−1.43987e9	−	1.17187e9i	−0.0130808	−	0.0106460i
$577$	6.69536e10	+	1.15967e11i	0.604047	+	1.04624i	0.992201	+	0.124646i	$0.0397794\pi$
$577$	6.69536e10	+	1.15967e11i	0.604047	+	1.04624i	−0.388154	+	0.921594i	$0.626887\pi$
$578$	−2.35681e10	+	2.80874e10i	−0.211161	+	0.251652i
$579$	2.45639e10	−	1.45686e11i	0.218566	−	1.29629i
$580$	−1.85197e10	−	1.05030e11i	−0.163652	−	0.928118i
$581$	−1.24121e9	+	2.18858e8i	−0.0108928	+	0.00192070i
$582$	3.60754e10	−	4.36534e10i	0.314427	−	0.380475i
$583$	−7.17133e10	−	6.01746e10i	−0.620763	−	0.520882i
$584$	−6.81241e10	+	3.93315e10i	−0.585665	+	0.338134i
$585$	−5.92756e10	+	1.70781e11i	−0.506118	+	1.45820i
$586$	2.88340e10	−	4.99420e10i	0.244520	−	0.423521i
$587$	4.47539e10	+	1.22960e11i	0.376946	+	1.03565i	0.972615	+	0.232420i	$0.0746645\pi$
$587$	4.47539e10	+	1.22960e11i	0.376946	+	1.03565i	−0.595670	+	0.803229i	$0.703113\pi$
$588$	4.82996e10	+	8.22278e10i	0.404049	+	0.687875i
$589$	−9.02479e10	+	7.57270e10i	−0.749853	+	0.629201i
$590$	−1.43084e10	+	3.93121e10i	−0.118082	+	0.324428i
$591$	−4.78407e10	+	1.34571e11i	−0.392146	+	1.10307i
$592$	−1.20418e10	+	6.82922e10i	−0.0980400	+	0.556012i
$593$		−	1.64843e11i		−	1.33307i	−0.745474	−	0.666535i	$-0.767777\pi$
$593$		−	1.64843e11i		−	1.33307i	0.745474	−	0.666535i	$-0.232223\pi$
$594$	8.71440e10	+	2.95164e10i	0.699990	+	0.237092i
$595$	−5.62512e8			−0.00448811
$596$	2.76929e10	+	4.88300e9i	0.219474	+	0.0386992i
$597$	−9.54520e10	+	8.13206e10i	−0.751428	+	0.640182i
$598$	1.09127e11	+	3.97188e10i	0.853347	+	0.310593i
$599$	1.35576e11	+	1.61573e11i	1.05311	+	1.25505i	0.965914	+	0.258861i	$0.0833473\pi$
$599$	1.35576e11	+	1.61573e11i	1.05311	+	1.25505i	0.0871995	+	0.996191i	$0.472208\pi$
$600$	−2.21333e10	−	1.25584e10i	−0.170781	−	0.0969012i
$601$	2.01380e11	−	7.32965e10i	1.54355	−	0.561805i	0.576653	−	0.816989i	$-0.304358\pi$
$601$	2.01380e11	−	7.32965e10i	1.54355	−	0.561805i	0.966892	+	0.255185i	$0.0821363\pi$
$602$	−4.36537e8	−	2.52035e8i	−0.00332380	−	0.00191900i
$603$	−2.81801e10	−	4.71623e10i	−0.213144	−	0.356719i
$604$	3.05577e10	+	5.29275e10i	0.229601	+	0.397680i
$605$	1.27522e11	−	1.51975e11i	0.951838	−	1.13436i
$606$	3.70012e10	−	1.37823e10i	0.274363	−	0.102195i
$607$	−2.96670e10	−	1.68250e11i	−0.218534	−	1.23937i	−0.874668	−	0.484722i	$-0.838921\pi$
$607$	−2.96670e10	−	1.68250e11i	−0.218534	−	1.23937i	0.656135	−	0.754644i	$-0.272190\pi$
$608$	−1.55810e11	+	2.74735e10i	−1.14020	+	0.201048i
$609$	6.47807e8	+	1.73916e9i	0.00470952	+	0.0126436i
$610$	−4.75903e10	−	3.99330e10i	−0.343715	−	0.288411i
$611$	−7.30666e10	+	4.21850e10i	−0.524269	+	0.302687i
$612$	−4.98652e10	+	2.97952e10i	−0.355461	+	0.212393i
$613$	8.94848e10	−	1.54992e11i	0.633734	−	1.09766i	−0.353047	−	0.935605i	$-0.614855\pi$
$613$	8.94848e10	−	1.54992e11i	0.633734	−	1.09766i	0.986782	−	0.162055i	$-0.0518121\pi$
$614$	−1.20150e10	−	3.30109e10i	−0.0845377	−	0.232265i
$615$	−5.57164e10	+	9.81961e10i	−0.389478	+	0.686426i
$616$	1.45655e9	−	1.22219e9i	0.0101159	−	0.00848823i
$617$	−2.07969e10	+	5.71390e10i	−0.143502	+	0.394268i	−0.990533	−	0.137275i	$-0.956166\pi$
$617$	−2.07969e10	+	5.71390e10i	−0.143502	+	0.394268i	0.847031	+	0.531543i	$0.178388\pi$
$618$	4.04585e10	+	4.74891e10i	0.277368	+	0.325567i
$619$	3.90616e10	−	2.21529e11i	0.266065	−	1.50893i	−0.499921	−	0.866071i	$-0.666637\pi$
$619$	3.90616e10	−	2.21529e11i	0.266065	−	1.50893i	0.765985	−	0.642858i	$-0.222251\pi$
$620$		−	8.70431e10i		−	0.589071i
$621$	1.66048e11	−	3.31446e10i	1.11652	−	0.222867i
$622$	8.99602e10			0.601020
$623$	9.77593e8	+	1.72376e8i	0.00648942	+	0.00114426i
$624$	1.10084e11	+	3.91355e10i	0.726084	+	0.258127i
$625$	1.00095e11	+	3.64315e10i	0.655981	+	0.238758i
$626$	−4.33099e10	−	5.16148e10i	−0.282027	−	0.336106i
$627$	2.52686e11	−	1.48425e11i	1.63497	−	0.960363i
$628$	1.52654e11	−	5.55614e10i	0.981451	−	0.357219i
$629$	−9.14424e10	−	5.27943e10i	−0.584178	−	0.337275i
$630$	−5.78632e8	−	2.00834e8i	−0.00367316	−	0.00127490i
$631$	−1.08103e11	−	1.87240e11i	−0.681901	−	1.18109i	−0.974400	−	0.224821i	$-0.927820\pi$
$631$	−1.08103e11	−	1.87240e11i	−0.681901	−	1.18109i	0.292499	−	0.956266i	$-0.405513\pi$
$632$	8.67726e10	−	1.03412e11i	0.543894	−	0.648188i
$633$	1.75721e10	+	1.45217e10i	0.109449	+	0.0904490i
$634$	1.37383e10	+	7.79137e10i	0.0850306	+	0.482233i
$635$	−9.45171e10	+	1.66659e10i	−0.581320	+	0.102502i
$636$	6.34599e10	+	1.06999e10i	0.387856	+	0.0653960i
$637$	2.23724e11	+	1.87727e11i	1.35880	+	1.14017i
$638$	−1.43963e11	+	8.31169e10i	−0.868895	+	0.501657i
$639$	4.50547e10	−	5.53586e10i	0.270232	−	0.332033i
$640$	7.27033e10	−	1.25926e11i	0.433345	−	0.750576i
$641$	5.67063e10	+	1.55799e11i	0.335892	+	0.922854i	0.986547	+	0.163481i	$0.0522722\pi$
$641$	5.67063e10	+	1.55799e11i	0.335892	+	0.922854i	−0.650655	+	0.759373i	$0.725506\pi$
$642$	3.84566e10	−	2.88248e8i	0.226376	−	0.00169678i
$643$	−9.87208e10	+	8.28366e10i	−0.577517	+	0.484594i	−0.884131	−	0.467240i	$-0.845249\pi$
$643$	−9.87208e10	+	8.28366e10i	−0.577517	+	0.484594i	0.306614	+	0.951834i	$0.400804\pi$
$644$	5.31113e8	−	1.45922e9i	0.00308776	−	0.00848356i
$645$	1.27208e11	−	2.34146e10i	0.734979	−	0.135284i
$646$	8.14062e9	−	4.61678e10i	0.0467442	−	0.265099i
$647$		−	8.44054e8i		−	0.00481674i	−0.999997	−	0.00240837i	$-0.999233\pi$
$647$		−	8.44054e8i		−	0.00481674i	0.999997	−	0.00240837i	$-0.000766609\pi$
$648$	−1.39556e11	+	2.89459e10i	−0.791498	+	0.164168i
$649$	−2.57350e11			−1.45059
$650$	−3.40599e10	−	6.00568e9i	−0.190805	−	0.0336441i
$651$	2.74196e8	+	1.48967e9i	0.00152664	+	0.00829402i
$652$	−1.03083e11	−	3.75190e10i	−0.570420	−	0.207616i
$653$	−1.57212e11	−	1.87359e11i	−0.864638	−	1.03044i	−0.999218	−	0.0395325i	$-0.987413\pi$
$653$	−1.57212e11	−	1.87359e11i	−0.864638	−	1.03044i	0.134580	−	0.990903i	$-0.457031\pi$
$654$	6.31661e8	+	8.42730e10i	0.00345281	+	0.460657i
$655$	−2.10111e10	+	7.64740e9i	−0.114152	+	0.0415479i
$656$	6.31917e10	+	3.64837e10i	0.341228	+	0.197008i
$657$	−2.47637e10	+	1.53898e11i	−0.132909	+	0.825985i
$658$	−1.42929e8	−	2.47560e8i	−0.000762459	−	0.00132062i
$659$	−2.08795e11	+	2.48832e11i	−1.10708	+	1.31936i	−0.164122	+	0.986440i	$0.552479\pi$
$659$	−2.08795e11	+	2.48832e11i	−1.10708	+	1.31936i	−0.942954	+	0.332922i	$0.891965\pi$
$660$	−3.59990e10	+	2.13506e11i	−0.189721	+	1.12521i
$661$	2.43729e10	+	1.38226e11i	0.127674	+	0.724074i	0.979684	+	0.200548i	$0.0642724\pi$
$661$	2.43729e10	+	1.38226e11i	0.127674	+	0.724074i	−0.852010	+	0.523526i	$0.824616\pi$
$662$	1.28816e11	−	2.27138e10i	0.670715	−	0.118265i
$663$	−1.13325e11	+	1.37129e11i	−0.586503	+	0.709703i
$664$	1.33964e11	+	1.12409e11i	0.689153	+	0.578268i
$665$	−1.68950e9	+	9.75432e8i	−0.00863915	+	0.00498781i
$666$	−7.52137e10	−	8.69550e10i	−0.382296	−	0.441975i
$667$	−1.52963e11	+	2.64940e11i	−0.772829	+	1.33858i
$668$	−1.34944e10	−	3.70756e10i	−0.0677717	−	0.186201i
$669$	−1.56107e11	−	2.65765e11i	−0.779324	−	1.32676i
$670$	−2.50951e10	+	2.10573e10i	−0.124535	+	0.104497i
$671$	1.30707e11	−	3.59116e11i	0.644778	−	1.77151i
$672$	−6.81377e8	+	1.91664e9i	−0.00334126	+	0.00939863i
$673$	5.61098e9	−	3.18215e10i	0.0273513	−	0.155117i	−0.968073	−	0.250667i	$-0.919350\pi$
$673$	5.61098e9	−	3.18215e10i	0.0273513	−	0.155117i	0.995425	+	0.0955502i	$0.0304611\pi$
$674$			1.59904e11i			0.774852i
$675$	−4.69864e10	+	1.83082e10i	−0.226338	+	0.0881924i
$676$	3.57703e11			1.71291
$677$	9.66599e10	+	1.70437e10i	0.460142	+	0.0811354i	0.398914	−	0.916988i	$-0.369387\pi$
$677$	9.66599e10	+	1.70437e10i	0.460142	+	0.0811354i	0.0612279	+	0.998124i	$0.480498\pi$
$678$	−2.93365e10	+	2.49933e10i	−0.138832	+	0.118278i
$679$	−2.17924e9	−	7.93178e8i	−0.0102524	−	0.00373157i
$680$	5.01696e10	+	5.97898e10i	0.234641	+	0.279635i
$681$	−3.19508e11	−	1.81289e11i	−1.48557	−	0.842911i
$682$	−1.27490e11	+	4.64025e10i	−0.589303	+	0.214489i
$683$	−6.47335e10	−	3.73739e10i	−0.297472	−	0.171746i	0.343835	−	0.939030i	$-0.388274\pi$
$683$	−6.47335e10	−	3.73739e10i	−0.297472	−	0.171746i	−0.641307	+	0.767285i	$0.721607\pi$
$684$	−9.81029e10	+	1.75959e11i	−0.448185	+	0.803872i
$685$	−1.04889e11	−	1.81673e11i	−0.476396	−	0.825142i
$686$	−1.27215e9	+	1.51609e9i	−0.00574437	+	0.00684588i
$687$	2.15945e11	−	8.04354e10i	0.969428	−	0.361094i
$688$	−1.45160e10	−	8.23245e10i	−0.0647880	−	0.367431i
$689$	1.94094e11	−	3.42240e10i	0.861262	−	0.151864i
$690$	−3.52418e10	−	9.46134e10i	−0.155475	−	0.417404i
$691$	−1.56712e11	−	1.31497e11i	−0.687371	−	0.576772i	0.230779	−	0.973006i	$-0.425873\pi$
$691$	−1.56712e11	−	1.31497e11i	−0.687371	−	0.576772i	−0.918150	+	0.396234i	$0.870317\pi$
$692$	−2.38870e11	+	1.37912e11i	−1.04169	+	0.601418i
$693$	−5.64791e7	−	3.76737e9i	−0.000244881	−	0.0163345i
$694$	5.42794e10	−	9.40146e10i	0.233990	−	0.405282i
$695$	9.31783e10	+	2.56005e11i	0.399370	+	1.09726i
$696$	1.27080e11	−	2.23969e11i	0.541552	−	0.954446i
$697$	−8.51099e10	+	7.14157e10i	−0.360619	+	0.302596i
$698$	1.40436e10	−	3.85844e10i	0.0591638	−	0.162551i
$699$	−1.86447e11	−	2.18847e11i	−0.780993	−	0.916709i
$700$	−8.03069e7	+	4.55443e8i	−0.000334473	+	0.00189689i
$701$			1.17559e11i			0.486835i	0.969922	+	0.243418i	$0.0782686\pi$
$701$			1.17559e11i			0.486835i	−0.969922	+	0.243418i	$0.921731\pi$
$702$	−1.65532e11	+	1.00599e11i	−0.681605	+	0.414232i
$703$	−3.66195e11			−1.49931
$704$	−6.70613e9	−	1.18247e9i	−0.0273012	−	0.00481394i
$705$	6.91140e10	+	2.45704e10i	0.279776	+	0.0994616i
$706$	−9.98520e10	−	3.63432e10i	−0.401919	−	0.146286i
$707$	−1.03935e9	−	1.23865e9i	−0.00415991	−	0.00495758i
$708$	1.52546e11	−	8.96035e10i	0.607110	−	0.356609i
$709$	2.17824e11	−	7.92814e10i	0.862026	−	0.313752i	0.127092	−	0.991891i	$-0.459436\pi$
$709$	2.17824e11	−	7.92814e10i	0.862026	−	0.313752i	0.734934	+	0.678139i	$0.237213\pi$
$710$	−3.68577e10	−	2.12798e10i	−0.145043	−	0.0837403i
$711$	−5.03952e10	−	2.62714e11i	−0.197202	−	1.02803i
$712$	−6.88681e10	−	1.19283e11i	−0.267977	−	0.464150i
$713$	−1.60493e11	+	1.91268e11i	−0.621008	+	0.740088i
$714$	−4.64614e8	−	3.83960e8i	−0.00178772	−	0.00147738i
$715$	1.15144e11	+	6.53015e11i	0.440573	+	2.49861i
$716$	−6.60728e10	+	1.16504e10i	−0.251403	+	0.0443292i
$717$	−5.88036e10	−	9.91480e9i	−0.222499	−	0.0375152i
$718$	1.59818e11	+	1.34103e11i	0.601352	+	0.504594i
$719$	3.61669e11	−	2.08810e11i	1.35331	−	0.781332i	0.364595	−	0.931166i	$-0.381207\pi$
$719$	3.61669e11	−	2.08810e11i	1.35331	−	0.781332i	0.988711	+	0.149835i	$0.0478741\pi$
$720$	−3.61678e10	−	9.49184e10i	−0.134584	−	0.353200i
$721$	1.27740e9	−	2.21253e9i	0.00472701	−	0.00818743i
$722$	−1.38203e10	−	3.79709e10i	−0.0508590	−	0.139734i
$723$	−9.68412e10	+	7.25865e8i	−0.354411	+	0.00265646i
$724$	1.50426e11	−	1.26223e11i	0.547482	−	0.459392i
$725$	3.11613e10	−	8.56150e10i	0.112788	−	0.309883i
$726$	2.09063e11	−	3.84814e10i	0.752543	−	0.138517i
$727$	−5.38552e10	+	3.05428e11i	−0.192792	+	1.09338i	0.722735	+	0.691125i	$0.242885\pi$
$727$	−5.38552e10	+	3.05428e11i	−0.192792	+	1.09338i	−0.915528	+	0.402255i	$0.868226\pi$
$728$			4.00302e9i			0.0142515i
$729$	−1.30076e11	+	2.50692e11i	−0.460561	+	0.887628i
$730$	9.29461e10			0.327295
$731$	1.25351e11	+	2.21027e10i	0.438992	+	0.0774062i
$732$	4.75584e10	+	2.58377e11i	0.165647	+	0.899933i
$733$	9.20818e10	+	3.35150e10i	0.318976	+	0.116098i	0.496546	−	0.868010i	$-0.334601\pi$
$733$	9.20818e10	+	3.35150e10i	0.318976	+	0.116098i	−0.177570	+	0.984108i	$0.556824\pi$
$734$	8.24575e9	+	9.82690e9i	0.0284083	+	0.0338558i
$735$	−1.90311e9	−	2.53903e11i	−0.00652099	−	0.869997i
$736$	−3.15090e11	+	1.14683e11i	−1.07380	+	0.390831i
$737$	−1.74522e11	−	1.00760e11i	−0.591536	−	0.341523i
$738$	−1.13047e11	+	4.30754e10i	−0.381094	+	0.145212i
$739$	−1.88472e11	−	3.26443e11i	−0.631931	−	1.09454i	−0.987157	−	0.159755i	$-0.948929\pi$
$739$	−1.88472e11	−	3.26443e11i	−0.631931	−	1.09454i	0.355226	−	0.934780i	$-0.384404\pi$
$740$	1.73913e11	−	2.07261e11i	0.579968	−	0.691179i
$741$	−1.02578e11	+	6.08379e11i	−0.340237	+	2.01791i
$742$	1.15956e8	+	6.57619e8i	0.000382541	+	0.00216950i
$743$	5.58247e11	−	9.84340e10i	1.83177	−	0.322991i	0.852066	−	0.523434i	$-0.175349\pi$
$743$	5.58247e11	−	9.84340e10i	1.83177	−	0.322991i	0.979705	+	0.200443i	$0.0642382\pi$
$744$	1.33882e11	−	1.62005e11i	0.436950	−	0.528735i
$745$	−5.73543e10	−	4.81260e10i	−0.186183	−	0.156227i
$746$	7.87701e10	−	4.54780e10i	0.254335	−	0.146840i
$747$	3.40331e11	−	6.52842e10i	1.09300	−	0.209665i
$748$	−1.06535e11	+	1.84524e11i	−0.340320	+	0.589451i
$749$	−5.38642e8	−	1.47991e9i	−0.00171149	−	0.00470227i
$750$	7.79224e10	+	1.32659e11i	0.246273	+	0.419269i
$751$	−3.50924e11	+	2.94460e11i	−1.10320	+	0.925692i	−0.997636	−	0.0687214i	$-0.978108\pi$
$751$	−3.50924e11	+	2.94460e11i	−1.10320	+	0.925692i	−0.105560	+	0.994413i	$0.533664\pi$
$752$	1.62140e10	−	4.45476e10i	0.0507012	−	0.139300i
$753$	5.14709e10	−	1.44782e11i	0.160096	−	0.450335i
$754$	6.07722e10	−	3.44656e11i	0.188027	−	1.06635i
$755$		−	1.62722e11i		−	0.500794i
$756$	1.34519e9	+	2.21346e9i	0.00411809	+	0.00677618i
$757$	−2.66800e11			−0.812460			−0.406230	−	0.913771i	$-0.633157\pi$
$757$	−2.66800e11			−0.812460			−0.406230	+	0.913771i	$0.633157\pi$
$758$	2.06039e11	+	3.63302e10i	0.624125	+	0.110050i
$759$	4.72772e11	−	4.02780e11i	1.42457	−	1.21367i
$760$	2.54363e11	+	9.25806e10i	0.762429	+	0.277502i
$761$	3.48504e11	+	4.15330e11i	1.03913	+	1.23838i	0.970591	+	0.240735i	$0.0773884\pi$
$761$	3.48504e11	+	4.15330e11i	1.03913	+	1.23838i	0.0685361	+	0.997649i	$0.478167\pi$
$762$	−8.94435e10	−	5.07502e10i	−0.265295	−	0.150528i
$763$	3.24304e9	−	1.18037e9i	0.00956872	−	0.00348273i
$764$	−2.14280e11	−	1.23715e11i	−0.628938	−	0.363118i
$765$	1.54646e11	−	2.31840e9i	0.451536	−	0.00676928i
$766$	1.93200e10	+	3.34633e10i	0.0561167	+	0.0971971i
$767$	3.48263e11	−	4.15044e11i	1.00630	−	1.19926i
$768$	1.51503e11	−	5.64322e10i	0.435489	−	0.162212i
$769$	−5.95729e10	−	3.37855e11i	−0.170351	−	0.966106i	−0.943375	−	0.331729i	$-0.892368\pi$
$769$	−5.95729e10	−	3.37855e11i	−0.170351	−	0.966106i	0.773024	−	0.634377i	$-0.218743\pi$
$770$	−2.21251e9	+	3.90125e8i	−0.00629393	+	0.00110979i
$771$	5.01537e10	+	1.34647e11i	0.141934	+	0.381049i
$772$	2.85384e11	+	2.39466e11i	0.803454	+	0.674178i
$773$	−3.94669e11	+	2.27862e11i	−1.10539	+	0.638197i	−0.937631	−	0.347631i	$-0.886986\pi$
$773$	−3.94669e11	+	2.27862e11i	−1.10539	+	0.638197i	−0.167758	+	0.985828i	$0.553653\pi$
$774$	1.21051e11	+	6.74902e10i	0.337292	+	0.188051i
$775$	3.71796e10	−	6.43970e10i	0.103062	−	0.178508i
$776$	1.10055e11	+	3.02375e11i	0.303504	+	0.833871i
$777$	−2.32346e9	+	4.09493e9i	−0.00637458	+	0.0112347i
$778$	−1.27119e11	+	1.06665e11i	−0.346969	+	0.291142i
$779$	−1.31787e11	+	3.62082e11i	−0.357868	+	0.983235i
$780$	−2.95617e11	−	3.46988e11i	−0.798641	−	0.937423i
$781$	4.54625e10	−	2.57830e11i	0.122194	−	0.692995i
$782$		−	9.93554e10i		−	0.265683i
$783$	−1.85263e11	−	4.75461e11i	−0.492881	−	1.26493i
$784$	−1.64100e11			−0.434354
$785$	−4.25960e11	−	7.51082e10i	−1.12173	−	0.197792i
$786$	−2.25744e10	−	8.02530e9i	−0.0591460	−	0.0210267i
$787$	3.14201e11	+	1.14360e11i	0.819048	+	0.298109i	0.717356	−	0.696707i	$-0.245352\pi$
$787$	3.14201e11	+	1.14360e11i	0.819048	+	0.298109i	0.101692	+	0.994816i	$0.467574\pi$
$788$	−2.31491e11	−	2.75881e11i	−0.600385	−	0.715511i
$789$	−1.95222e11	+	1.14671e11i	−0.503757	+	0.295901i
$790$	−1.49886e11	+	5.45542e10i	−0.384817	+	0.140062i
$791$	1.36679e9	+	7.89118e8i	0.00349138	+	0.00201575i
$792$	−3.95398e11	+	3.42009e11i	−1.00493	+	0.869233i
$793$	4.02285e11	+	6.96778e11i	1.01728	+	1.76198i
$794$	1.23119e11	−	1.46727e11i	0.309772	−	0.369172i
$795$	−1.32083e11	−	1.09154e11i	−0.330657	−	0.273257i
$796$	−5.49068e10	−	3.11392e11i	−0.136765	−	0.775630i
$797$	2.18436e11	−	3.85161e10i	0.541365	−	0.0954573i	0.103722	−	0.994606i	$-0.466925\pi$
$797$	2.18436e11	−	3.85161e10i	0.541365	−	0.0954573i	0.437643	+	0.899149i	$0.355814\pi$
$798$	−2.06128e9	−	3.47549e8i	−0.00508305	−	0.000857047i
$799$	5.52954e10	+	4.63984e10i	0.135676	+	0.113845i
$800$	8.64821e10	−	4.99305e10i	0.211138	−	0.121901i
$801$	−2.69471e11	−	4.33605e10i	−0.654608	−	0.105333i
$802$	−7.02624e10	+	1.21698e11i	−0.169834	+	0.294162i
$803$	1.95554e11	+	5.37281e11i	0.470333	+	1.29223i
$804$	1.38532e11	−	1.03835e9i	0.331531	−	0.00248497i
$805$	−3.16727e9	+	2.65765e9i	−0.00754226	+	0.00632871i
$806$	9.76915e10	−	2.68405e11i	0.231482	−	0.635991i
$807$	−2.97755e11	+	5.48065e10i	−0.702045	+	0.129222i
$808$	−3.89588e10	+	2.20946e11i	−0.0914029	+	0.518371i
$809$		−	2.04827e11i		−	0.478181i	−0.970997	−	0.239091i	$-0.923151\pi$
$809$		−	2.04827e11i		−	0.478181i	0.970997	−	0.239091i	$-0.0768493\pi$
$810$	1.59905e11	+	5.28285e10i	0.371469	+	0.122724i
$811$	−5.70557e9			−0.0131891			−0.00659456	−	0.999978i	$-0.502099\pi$
$811$	−5.70557e9			−0.0131891			−0.00659456	+	0.999978i	$0.502099\pi$
$812$	−4.60869e9	−	8.12636e8i	−0.0106012	−	0.00186927i
$813$	−6.20725e10	−	3.37230e11i	−0.142081	−	0.771906i
$814$	−3.96282e11	−	1.44235e11i	−0.902625	−	0.328528i
$815$	1.87742e11	+	2.23743e11i	0.425532	+	0.507129i
$816$	−7.49203e8	−	9.99548e10i	−0.00168981	−	0.225446i
$817$	4.14817e11	−	1.50981e11i	0.931039	−	0.338871i
$818$	1.93270e11	+	1.11584e11i	0.431668	+	0.249224i
$819$	6.15228e9	+	5.00715e9i	0.0136742	+	0.0111290i
$820$	−1.42345e11	−	2.46549e11i	−0.314838	−	0.545316i
$821$	−3.53407e11	+	4.21174e11i	−0.777861	+	0.927019i	−0.998835	−	0.0482606i	$-0.984632\pi$
$821$	−3.53407e11	+	4.21174e11i	−0.777861	+	0.927019i	0.220973	+	0.975280i	$0.429077\pi$
$822$	3.73723e10	−	2.21651e11i	0.0818582	−	0.485492i
$823$	−3.62341e10	−	2.05494e11i	−0.0789802	−	0.447919i	−0.998494	−	0.0548611i	$-0.982528\pi$
$823$	−3.62341e10	−	2.05494e11i	−0.0789802	−	0.447919i	0.919514	−	0.393058i	$-0.128583\pi$
$824$	−3.49101e11	+	6.15559e10i	−0.757254	+	0.133524i
$825$	−1.17830e11	+	1.42581e11i	−0.254355	+	0.307784i
$826$	1.40623e9	+	1.17997e9i	0.00302089	+	0.00253483i
$827$	2.10222e11	−	1.21372e11i	0.449424	−	0.259475i	−0.258163	−	0.966101i	$-0.583117\pi$
$827$	2.10222e11	−	1.21372e11i	0.449424	−	0.259475i	0.707587	+	0.706626i	$0.249784\pi$
$828$	−1.40000e11	+	4.03359e11i	−0.297855	+	0.858163i
$829$	3.10954e11	−	5.38589e11i	0.658383	−	1.14035i	−0.322651	−	0.946518i	$-0.604574\pi$
$829$	3.10954e11	−	5.38589e11i	0.658383	−	1.14035i	0.981034	−	0.193835i	$-0.0620926\pi$
$830$	−7.06719e10	−	1.94169e11i	−0.148914	−	0.409137i
$831$	4.19932e11	+	7.14914e11i	0.880592	+	1.49917i
$832$	1.09822e10	−	9.21517e9i	0.0229191	−	0.0192314i
$833$	8.54589e10	−	2.34796e11i	0.177491	−	0.487653i
$834$	−9.77827e10	+	2.75053e11i	−0.202115	+	0.568528i
$835$	−1.82418e10	+	1.03455e11i	−0.0375251	+	0.212816i
$836$			7.38956e11i			1.51284i
$837$	−8.15217e10	−	4.08409e11i	−0.166101	−	0.832134i
$838$	−3.69633e11			−0.749540
$839$	−9.66564e10	−	1.70431e10i	−0.195066	−	0.0343955i	0.0752612	−	0.997164i	$-0.476021\pi$
$839$	−9.66564e10	−	1.70431e10i	−0.195066	−	0.0343955i	−0.270328	+	0.962768i	$0.587132\pi$
$840$	2.64917e9	−	2.25697e9i	0.00532100	−	0.00453324i
$841$	3.96271e11	+	1.44231e11i	0.792151	+	0.288319i
$842$	−2.76361e10	−	3.29354e10i	−0.0549829	−	0.0655261i
$843$	4.05691e11	+	2.30189e11i	0.803313	+	0.455799i
$844$	−5.40155e10	+	1.96600e10i	−0.106451	+	0.0387449i
$845$	−8.24799e11	−	4.76198e11i	−1.61779	−	0.934030i
$846$	4.03144e10	+	6.74702e10i	0.0787007	+	0.131714i
$847$	−4.35260e9	−	7.53892e9i	−0.00845698	−	0.0146479i
$848$	−7.11833e10	+	8.48330e10i	−0.137656	+	0.164052i
$849$	−2.38332e11	+	8.87744e10i	−0.458724	+	0.170866i
$850$	5.13818e9	+	2.91400e10i	0.00984313	+	0.0558232i
$851$	−7.64307e11	+	1.34768e11i	−1.45730	+	0.256962i
$852$	6.28226e10	+	1.68659e11i	0.119222	+	0.320075i
$853$	−2.23404e11	−	1.87458e11i	−0.421982	−	0.354085i	0.406934	−	0.913457i	$-0.366598\pi$
$853$	−2.23404e11	−	1.87458e11i	−0.421982	−	0.354085i	−0.828916	+	0.559372i	$0.811042\pi$
$854$	−2.36079e9	+	1.36300e9i	−0.00443839	+	0.00256250i
$855$	4.60457e11	−	2.75129e11i	0.861637	−	0.514840i
$856$	−1.09260e11	+	1.89243e11i	−0.203500	+	0.352473i
$857$	−2.91419e11	−	8.00668e11i	−0.540250	−	1.48433i	−0.846508	−	0.532377i	$-0.821299\pi$
$857$	−2.91419e11	−	8.00668e11i	−0.540250	−	1.48433i	0.306257	−	0.951949i	$-0.400923\pi$
$858$	−3.50631e11	+	6.17962e11i	−0.646996	+	1.14028i
$859$	−1.76996e11	+	1.48517e11i	−0.325081	+	0.272775i	−0.790692	−	0.612214i	$-0.790279\pi$
$859$	−1.76996e11	+	1.48517e11i	−0.325081	+	0.272775i	0.465611	+	0.884989i	$0.345835\pi$
$860$	−1.11551e11	+	3.06484e11i	−0.203929	+	0.560291i
$861$	3.21277e9	+	3.77106e9i	0.00584611	+	0.00686201i
$862$	3.69627e10	−	2.09626e11i	0.0669475	−	0.379678i
$863$			9.48191e11i			1.70944i	0.519093	+	0.854718i	$0.326270\pi$
$863$			9.48191e11i			1.70944i	−0.519093	+	0.854718i	$0.673730\pi$
$864$	1.79425e11	−	5.29732e11i	0.321979	−	0.950608i
$865$	7.34389e11			1.31178
$866$	−4.26744e10	−	7.52465e9i	−0.0758745	−	0.0133787i
$867$	−3.88987e11	−	1.38287e11i	−0.688429	−	0.244740i
$868$	−3.58907e9	−	1.30632e9i	−0.00632271	−	0.00230128i
$869$	−6.30708e11	−	7.51649e11i	−1.10599	−	1.31806i
$870$	−2.62356e11	+	1.54104e11i	−0.457945	+	0.268991i
$871$	3.98677e11	−	1.45107e11i	0.692706	−	0.252124i
$872$	−4.14704e11	−	2.39429e11i	−0.717253	−	0.414106i
$873$	6.02385e11	+	2.09079e11i	1.03709	+	0.359959i
$874$	−1.72289e11	−	2.98413e11i	−0.295264	−	0.511413i
$875$	4.04982e9	−	4.82639e9i	0.00690882	−	0.00823361i
$876$	−3.02985e11	−	2.50389e11i	−0.514523	−	0.425205i
$877$	3.40749e10	+	1.93249e11i	0.0576019	+	0.326677i	0.999969	−	0.00790482i	$-0.00251621\pi$
$877$	3.40749e10	+	1.93249e11i	0.0576019	+	0.326677i	−0.942367	+	0.334581i	$0.891405\pi$
$878$	2.46682e10	−	4.34968e9i	0.0415107	−	0.00731946i
$879$	6.40278e11	+	1.07956e11i	1.07254	+	0.180839i
$880$	−2.85414e11	−	2.39491e11i	−0.475932	−	0.399354i
$881$	5.35098e11	−	3.08939e11i	0.888238	−	0.512825i	0.0148725	−	0.999889i	$-0.495266\pi$
$881$	5.35098e11	−	3.08939e11i	0.888238	−	0.512825i	0.873366	+	0.487065i	$0.161932\pi$
$882$	1.71737e11	−	2.11013e11i	0.283786	−	0.348687i
$883$	4.02882e11	−	6.97813e11i	0.662728	−	1.14788i	−0.317168	−	0.948369i	$-0.602732\pi$
$883$	4.02882e11	−	6.97813e11i	0.662728	−	1.14788i	0.979896	−	0.199509i	$-0.0639348\pi$
$884$	−1.53423e11	−	4.21526e11i	−0.251236	−	0.690264i
$885$	−4.71030e11	+	3.53057e9i	−0.767849	+	0.00575534i
$886$	7.99781e10	−	6.71096e10i	0.129788	−	0.108905i
$887$	−1.44487e11	+	3.96974e11i	−0.233418	+	0.641310i	−1.00000		0.000836512i	$-0.999734\pi$
$887$	−1.44487e11	+	3.96974e11i	−0.233418	+	0.641310i	0.766582	+	0.642147i	$0.221956\pi$
$888$	6.42479e11	−	1.18258e11i	1.03325	−	0.190187i
$889$	−7.31292e8	+	4.14736e9i	−0.00117080	+	0.00663995i
$890$			1.62746e11i			0.259388i
$891$	3.10545e10	+	1.03549e12i	0.0492735	+	1.64299i
$892$	7.77205e11			1.22765
$893$	2.46537e11	+	4.34711e10i	0.387683	+	0.0683589i
$894$	−1.45227e10	−	7.88994e10i	−0.0227351	−	0.123516i
$895$	1.67862e11	+	6.10968e10i	0.261614	+	0.0952196i
$896$	−4.10122e9	−	4.88765e9i	−0.00636329	−	0.00758347i
$897$	9.80051e9	+	1.30753e12i	0.0151384	+	2.01968i
$898$	−4.08370e11	+	1.48635e11i	−0.627985	+	0.228568i
$899$	6.51641e11	+	3.76225e11i	0.997630	+	0.575982i
$900$	2.02009e10	−	1.25542e11i	0.0307893	−	0.191345i
$901$	−8.43098e10	−	1.46029e11i	−0.127932	−	0.221585i
$902$	−2.85230e11	+	3.39924e11i	−0.430893	+	0.513518i
$903$	9.43634e8	−	5.59659e9i	0.00141923	−	0.00841730i
$904$	−3.80262e10	−	2.15658e11i	−0.0569390	−	0.322917i
$905$	−5.14893e11	+	9.07895e10i	−0.767578	+	0.135345i
$906$	1.11071e11	−	1.34403e11i	0.164850	−	0.199478i
$907$	−4.22135e11	−	3.54213e11i	−0.623767	−	0.523402i	0.275218	−	0.961382i	$-0.411250\pi$
$907$	−4.22135e11	−	3.54213e11i	−0.623767	−	0.523402i	−0.898985	+	0.437979i	$0.855694\pi$
$908$	8.02215e11	−	4.63159e11i	1.18018	−	0.681376i
$909$	2.90843e11	+	3.36245e11i	0.425994	+	0.492494i
$910$	2.36493e9	−	4.09618e9i	0.00344868	−	0.00597329i
$911$	−1.83317e11	−	5.03660e11i	−0.266152	−	0.731247i	−0.998721	−	0.0505544i	$-0.983901\pi$
$911$	−1.83317e11	−	5.03660e11i	−0.266152	−	0.731247i	0.732569	−	0.680693i	$-0.238321\pi$
$912$	−1.75578e11	−	2.98914e11i	−0.253800	−	0.432082i
$913$	9.73719e11	−	8.17047e11i	1.40136	−	1.17588i
$914$	−4.04213e10	+	1.11057e11i	−0.0579195	+	0.159133i
$915$	2.34308e11	−	6.59086e11i	0.334274	−	0.940280i
$916$	−1.00902e11	+	5.72241e11i	−0.143323	+	0.812825i
$917$			9.81125e8i			0.00138754i
$918$	1.29314e11	+	1.03643e11i	0.182086	+	0.145939i
$919$	−4.66590e11			−0.654144			−0.327072	−	0.944999i	$-0.606062\pi$
$919$	−4.66590e11			−0.654144			−0.327072	+	0.944999i	$0.606062\pi$
$920$	5.64968e11	+	9.96191e10i	0.788628	+	0.139056i
$921$	3.01089e11	−	2.56514e11i	0.418462	−	0.356510i
$922$	−8.20262e9	−	2.98551e9i	−0.0113509	−	0.00413138i
$923$	3.54295e11	+	4.22233e11i	0.488156	+	0.581762i
$924$	8.26329e9	+	4.68858e9i	0.0113361	+	0.00643212i
$925$	2.17195e11	−	7.90525e10i	0.296676	−	0.107981i
$926$	−2.18131e11	−	1.25938e11i	−0.296670	−	0.171283i
$927$	−3.42065e11	+	6.13533e11i	−0.463222	+	0.830843i
$928$	5.05252e11	+	8.75123e11i	0.681266	+	1.17999i
$929$	−2.51335e11	+	2.99530e11i	−0.337435	+	0.402140i	−0.907903	−	0.419180i	$-0.862318\pi$
$929$	−2.51335e11	+	2.99530e11i	−0.337435	+	0.402140i	0.570468	+	0.821320i	$0.306762\pi$
$930$	−2.32709e11	+	8.66799e10i	−0.311087	+	0.115874i
$931$	−1.50477e11	−	8.53399e11i	−0.200296	−	1.13593i
$932$	7.13941e11	−	1.25887e11i	0.946235	−	0.166847i
$933$	3.53560e11	+	9.49202e11i	0.466592	+	1.25266i
$934$	3.50201e11	+	2.93853e11i	0.460182	+	0.386139i
$935$	4.91303e11	−	2.83654e11i	0.642840	−	0.371144i
$936$	−1.64985e10	−	1.10051e12i	−0.0214952	−	1.43381i
$937$	−6.00089e11	+	1.03938e12i	−0.778497	+	1.34840i	0.154311	+	0.988022i	$0.450684\pi$
$937$	−6.00089e11	+	1.03938e12i	−0.778497	+	1.34840i	−0.932808	+	0.360374i	$0.882649\pi$
$938$	4.91642e8	+	1.35078e9i	0.000635094	+	0.00174491i
$939$	3.74389e11	−	6.59834e11i	0.481572	−	0.848735i
$940$	−1.41689e11	+	1.18891e11i	−0.181478	+	0.152278i
$941$	2.70127e11	−	7.42169e11i	0.344517	−	0.946551i	−0.639550	−	0.768750i	$-0.720879\pi$
$941$	2.70127e11	−	7.42169e11i	0.344517	−	0.946551i	0.984066	−	0.177802i	$-0.0568986\pi$
$942$	−3.00560e11	−	3.52789e11i	−0.381704	−	0.448034i
$943$	−1.41806e11	+	8.04224e11i	−0.179328	+	1.01702i
$944$			3.04432e11i			0.383355i
$945$	−1.55058e8	−	6.89466e9i	−0.000194432	−	0.00864541i
$946$	5.08367e11			0.634764
$947$	−5.11065e11	−	9.01145e10i	−0.635442	−	0.112046i	−0.153358	−	0.988171i	$-0.549009\pi$
$947$	−5.11065e11	−	9.01145e10i	−0.635442	−	0.112046i	−0.482084	+	0.876125i	$0.660120\pi$
$948$	6.35563e11	+	2.25946e11i	0.786911	+	0.279751i
$949$	−1.13114e12	−	4.11702e11i	−1.39461	−	0.507596i
$950$	6.59632e10	+	7.86118e10i	0.0809855	+	0.0965147i
$951$	−7.68100e11	+	4.51173e11i	−0.939065	+	0.551595i
$952$	3.21825e9	−	1.17135e9i	0.00391807	−	0.00142606i
$953$	−3.61729e11	−	2.08844e11i	−0.438543	−	0.253193i	0.264437	−	0.964403i	$-0.414814\pi$
$953$	−3.61729e11	−	2.08844e11i	−0.438543	−	0.253193i	−0.702979	+	0.711210i	$0.748147\pi$
$954$	−3.45890e10	−	1.80315e11i	−0.0417585	−	0.217690i
$955$	3.29394e11	+	5.70528e11i	0.396007	+	0.685904i
$956$	9.66565e10	−	1.15191e11i	0.115718	−	0.137907i
$957$	−1.44280e12	−	1.19234e12i	−1.72011	−	1.42151i
$958$	−6.18474e10	−	3.50754e11i	−0.0734277	−	0.416429i
$959$	−9.06512e9	+	1.59842e9i	−0.0107176	+	0.00188981i
$960$	−1.22905e10	−	2.07229e9i	−0.0144705	−	0.00243986i
$961$	−1.82915e11	−	1.53484e11i	−0.214464	−	0.179957i
$962$	7.68891e11	−	4.43919e11i	0.897769	−	0.518327i
$963$	1.54183e11	+	4.04636e11i	0.179280	+	0.470500i
$964$	1.22100e11	−	2.11483e11i	0.141386	−	0.244888i
$965$	−3.39253e11	−	9.32089e11i	−0.391214	−	1.07485i
$966$	−4.43012e9	+	3.32056e7i	−0.00508753	+	3.81331e-5i
$967$	4.30878e11	−	3.61550e11i	0.492775	−	0.413487i	−0.362245	−	0.932083i	$-0.617990\pi$
$967$	4.30878e11	−	3.61550e11i	0.492775	−	0.413487i	0.855020	+	0.518596i	$0.173545\pi$
$968$	−4.13116e11	+	1.13503e12i	−0.470511	+	1.29272i
$969$	5.19126e11	−	9.55533e10i	0.588814	−	0.108380i
$970$	6.60224e10	−	3.74432e11i	0.0745769	−	0.422947i
$971$			4.33654e11i			0.487828i	0.969797	+	0.243914i	$0.0784315\pi$
$971$			4.33654e11i			0.487828i	−0.969797	+	0.243914i	$0.921569\pi$
$972$	−3.78942e11	−	6.02981e11i	−0.424530	−	0.675521i
$973$	1.19543e10			0.0133375
$974$	6.35282e10	+	1.12017e10i	0.0705879	+	0.0124466i
$975$	−7.04937e10	−	3.82981e11i	−0.0780067	−	0.423798i
$976$	−4.24815e11	−	1.54620e11i	−0.468166	−	0.170399i
$977$	−2.82117e11	−	3.36214e11i	−0.309636	−	0.369010i	0.588675	−	0.808370i	$-0.299650\pi$
$977$	−2.82117e11	−	3.36214e11i	−0.309636	−	0.369010i	−0.898311	+	0.439360i	$0.855205\pi$
$978$	2.34571e9	+	3.12953e11i	0.00256401	+	0.342077i
$979$	−9.40762e11	+	3.42409e11i	−1.02412	+	0.372748i
$980$	5.54476e11	+	3.20127e11i	0.601144	+	0.347070i
$981$	−8.86711e11	+	3.37873e11i	−0.957428	+	0.364820i
$982$	2.47136e11	+	4.28052e11i	0.265760	+	0.460311i
$983$	1.59758e11	−	1.90392e11i	0.171100	−	0.203909i	−0.673680	−	0.739023i	$-0.735287\pi$
$983$	1.59758e11	−	1.90392e11i	0.171100	−	0.203909i	0.844779	+	0.535115i	$0.179732\pi$
$984$	1.14287e11	−	6.77823e11i	0.121903	−	0.722996i
$985$	1.66507e11	+	9.44309e11i	0.176884	+	1.00316i
$986$	−2.94872e11	+	5.19938e10i	−0.311979	+	0.0550103i
$987$	2.05036e9	−	2.48105e9i	0.00216053	−	0.00261437i
$988$	−1.19176e12	−	1.00000e12i	−1.25072	−	1.04948i
$989$	8.10224e11	−	4.67783e11i	0.846876	−	0.488944i
$990$	6.06655e11	−	1.16372e11i	0.631540	−	0.121146i
$991$	−9.46761e11	+	1.63984e12i	−0.981625	+	1.70022i	−0.325557	+	0.945522i	$0.605552\pi$
$991$	−9.46761e11	+	1.63984e12i	−0.981625	+	1.70022i	−0.656068	+	0.754702i	$0.727782\pi$
$992$	2.82073e11	+	7.74988e11i	0.291282	+	0.800292i
$993$	7.45932e11	+	1.26991e12i	0.767189	+	1.30610i
$994$	−1.43059e9	+	1.20040e9i	−0.00146544	+	0.00122965i
$995$	−2.87941e11	+	7.91110e11i	−0.293772	+	0.807132i
$996$	−2.92700e11	+	8.23337e11i	−0.297431	+	0.836643i
$997$	1.58879e11	−	9.01049e11i	0.160800	−	0.911943i	−0.792489	−	0.609886i	$-0.791215\pi$
$997$	1.58879e11	−	9.01049e11i	0.160800	−	0.911943i	0.953290	−	0.302058i	$-0.0976735\pi$
$998$			4.63329e11i			0.467054i
$999$	6.21889e11	−	1.13536e12i	0.624383	−	1.13991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.f.a.2.14	✓	138
3.2	odd	2		81.9.f.a.8.10		138
27.13	even	9		81.9.f.a.71.10		138
27.14	odd	18	inner	27.9.f.a.14.14	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.14	✓	138	1.1	even	1	trivial
27.9.f.a.14.14	yes	138	27.14	odd	18	inner
81.9.f.a.8.10		138	3.2	odd	2
81.9.f.a.71.10		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+(7.08460 + 1.24921i) q^{2} +(14.6630 + 79.6618i) q^{3} +(-191.930 - 69.8569i) q^{4} +(349.559 + 416.588i) q^{5} +(4.36750 + 582.689i) q^{6} +(22.4234 - 8.16143i) q^{7} +(-2867.39 - 1655.49i) q^{8} +(-6130.99 + 2336.16i) q^{9} +(1956.08 + 3388.03i) q^{10} +(-15469.2 + 18435.5i) q^{11} +(2750.65 - 16313.8i) q^{12} +(-8798.06 - 49896.3i) q^{13} +(169.056 - 29.8091i) q^{14} +(-28060.6 + 33954.9i) q^{15} +(21808.2 + 18299.3i) q^{16} +(-37540.0 + 21673.7i) q^{17} +(-46354.0 + 8891.89i) q^{18} +(-75167.3 + 130194. i) q^{19} +(-37989.4 - 104375. i) q^{20} +(978.948 + 1666.61i) q^{21} +(-132623. + 111284. i) q^{22} +(-108972. + 299398. i) q^{23} +(89834.6 - 252696. i) q^{24} +(16477.1 - 93446.3i) q^{25} -364486. i q^{26} +(-276001. - 454151. i) q^{27} -4873.85 q^{28} +(945594. + 166734. i) q^{29} +(-241215. + 205504. i) q^{30} +(736394. + 268025. i) q^{31} +(676476. + 806193. i) q^{32} +(-1.69543e6 - 961988. i) q^{33} +(-293031. + 106655. i) q^{34} +(11238.2 + 6488.40i) q^{35} +(1.33992e6 - 20087.6i) q^{36} +(1.21793e6 + 2.10952e6i) q^{37} +(-695170. + 828471. i) q^{38} +(3.84582e6 - 1.43250e6i) q^{39} +(-312665. - 1.77321e6i) q^{40} +(2.52414e6 - 445074. i) q^{41} +(4853.51 + 13030.2i) q^{42} +(-2.24939e6 - 1.88746e6i) q^{43} +(4.25687e6 - 2.45770e6i) q^{44} +(-3.11636e6 - 1.73747e6i) q^{45} +(-1.14603e6 + 1.98499e6i) q^{46} +(-569539. - 1.56479e6i) q^{47} +(-1.13798e6 + 2.00561e6i) q^{48} +(-4.41566e6 + 3.70518e6i) q^{49} +(233468. - 641447. i) q^{50} +(-2.27702e6 - 2.67270e6i) q^{51} +(-1.79699e6 + 1.01912e7i) q^{52} +3.88995e6i q^{53} +(-1.38803e6 - 3.56226e6i) q^{54} -1.30874e7 q^{55} +(-77807.6 - 13719.6i) q^{56} +(-1.14736e7 - 4.07893e6i) q^{57} +(6.49088e6 + 2.36249e6i) q^{58} +(6.87370e6 + 8.19175e6i) q^{59} +(7.75765e6 - 4.55675e6i) q^{60} +(-1.49222e7 + 5.43124e6i) q^{61} +(4.88224e6 + 2.81876e6i) q^{62} +(-118411. + 102422. i) q^{63} +(141478. + 245047. i) q^{64} +(1.77108e7 - 2.11069e7i) q^{65} +(-1.08097e7 - 8.93325e6i) q^{66} +(1.45408e6 + 8.24651e6i) q^{67} +(8.71913e6 - 1.53742e6i) q^{68} +(-2.54484e7 - 4.29083e6i) q^{69} +(71513.1 + 60006.6i) q^{70} +(-9.42132e6 + 5.43940e6i) q^{71} +(2.14474e7 + 3.45110e6i) q^{72} +(1.18791e7 - 2.05752e7i) q^{73} +(5.99334e6 + 1.64666e7i) q^{74} +(7.68570e6 - 57607.5i) q^{75} +(2.35218e7 - 1.97371e7i) q^{76} +(-196412. + 539638. i) q^{77} +(2.90356e7 - 5.34446e6i) q^{78} +(-7.07994e6 + 4.01523e7i) q^{79} +1.54817e7i q^{80} +(3.21314e7 - 2.86460e7i) q^{81} +1.84385e7 q^{82} +(-5.20151e7 - 9.17167e6i) q^{83} +(-71465.3 - 388260. i) q^{84} +(-2.21515e7 - 8.06248e6i) q^{85} +(-1.35782e7 - 1.61819e7i) q^{86} +(582937. + 7.77725e7i) q^{87} +(7.48761e7 - 2.72527e7i) q^{88} +(3.60266e7 + 2.07999e7i) q^{89} +(-1.99077e7 - 1.62023e7i) q^{90} +(-604507. - 1.04704e6i) q^{91} +(4.18301e7 - 4.98511e7i) q^{92} +(-1.05536e7 + 6.25925e7i) q^{93} +(-2.08020e6 - 1.17974e7i) q^{94} +(-8.05126e7 + 1.41965e7i) q^{95} +(-5.43036e7 + 6.57105e7i) q^{96} +(-7.44489e7 - 6.24700e7i) q^{97} +(-3.59117e7 + 2.07336e7i) q^{98} +(5.17735e7 - 1.49167e8i) 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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