Properties

Label 54.9.f.a.5.11
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.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: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.11
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(73.1569 + 34.7717i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-324.095 - 890.442i) q^{5} +(-230.660 - 886.907i) q^{6} +(-575.632 - 3264.57i) q^{7} +(1254.14 - 724.077i) q^{8} +(4142.86 + 5087.58i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(73.1569 + 34.7717i) q^{3} +(-22.2270 + 126.055i) q^{4} +(-324.095 - 890.442i) q^{5} +(-230.660 - 886.907i) q^{6} +(-575.632 - 3264.57i) q^{7} +(1254.14 - 724.077i) q^{8} +(4142.86 + 5087.58i) q^{9} +(-5360.37 + 9284.44i) q^{10} +(-4408.18 + 12111.4i) q^{11} +(-6009.21 + 8448.95i) q^{12} +(3622.37 + 3039.53i) q^{13} +(-24107.2 + 28729.9i) q^{14} +(7252.43 - 76411.3i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-72590.8 - 41910.3i) q^{17} +(13964.8 - 72903.8i) q^{18} +(52894.2 + 91615.4i) q^{19} +(119449. - 21062.0i) q^{20} +(71403.2 - 258842. i) q^{21} +(137025. - 49872.9i) q^{22} +(-439599. - 77513.1i) q^{23} +(116926. - 9362.74i) q^{24} +(-388614. + 326086. i) q^{25} -53498.7i q^{26} +(126175. + 516245. i) q^{27} +424311. q^{28} +(-610092. - 727079. i) q^{29} +(-714984. + 492831. i) q^{30} +(41498.2 - 235348. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-743622. + 732751. i) q^{33} +(164674. + 933915. i) q^{34} +(-2.72035e6 + 1.57060e6i) q^{35} +(-733400. + 409149. i) q^{36} +(-563956. + 976800. i) q^{37} +(409350. - 1.12468e6i) q^{38} +(159312. + 348318. i) q^{39} +(-1.05121e6 - 882069. i) q^{40} +(-895786. + 1.06756e6i) q^{41} +(-2.76260e6 + 1.26354e6i) q^{42} +(-5.41819e6 - 1.97206e6i) q^{43} +(-1.42872e6 - 824874. i) q^{44} +(3.18751e6 - 5.33783e6i) q^{45} +(2.52511e6 + 4.37362e6i) q^{46} +(7.55349e6 - 1.33188e6i) q^{47} +(-931469. - 945288. i) q^{48} +(-4.90894e6 + 1.78671e6i) q^{49} +(5.65225e6 + 996644. i) q^{50} +(-3.85323e6 - 5.59013e6i) q^{51} +(-463663. + 389059. i) q^{52} +5.92050e6i q^{53} +(3.55661e6 - 4.84783e6i) q^{54} +1.22131e7 q^{55} +(-3.08573e6 - 3.67742e6i) q^{56} +(683952. + 8.54151e6i) q^{57} +(-1.86467e6 + 1.05751e7i) q^{58} +(-6.80853e6 - 1.87063e7i) q^{59} +(9.47086e6 + 2.61260e6i) q^{60} +(662289. + 3.75603e6i) q^{61} +(-2.34150e6 + 1.35187e6i) q^{62} +(1.42240e7 - 1.64532e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(1.53253e6 - 4.21060e6i) q^{65} +(1.17585e7 + 1.11603e6i) q^{66} +(9.00295e6 + 7.55437e6i) q^{67} +(6.89650e6 - 8.21893e6i) q^{68} +(-2.94644e7 - 2.09562e7i) q^{69} +(3.33953e7 + 1.21549e7i) q^{70} +(-4.11401e7 - 2.37522e7i) q^{71} +(8.87952e6 + 3.38077e6i) q^{72} +(1.46752e7 + 2.54183e7i) q^{73} +(1.25670e7 - 2.21590e6i) q^{74} +(-3.97684e7 + 1.03427e7i) q^{75} +(-1.27243e7 + 4.63126e6i) q^{76} +(4.20759e7 + 7.41912e6i) q^{77} +(1.86024e6 - 3.91380e6i) q^{78} +(1.46072e7 - 1.22569e7i) q^{79} +1.55253e7i q^{80} +(-8.72013e6 + 4.21542e7i) q^{81} +1.57667e7 q^{82} +(-6.82152e6 - 8.12958e6i) q^{83} +(3.10413e7 + 1.47540e7i) q^{84} +(-1.37924e7 + 7.82209e7i) q^{85} +(2.23113e7 + 6.12999e7i) q^{86} +(-1.93507e7 - 7.44048e7i) q^{87} +(3.24110e6 + 1.83812e7i) q^{88} +(8.66282e7 - 5.00148e7i) q^{89} +(-6.94426e7 + 1.11928e7i) q^{90} +(7.83760e6 - 1.35751e7i) q^{91} +(1.95419e7 - 5.36909e7i) q^{92} +(1.12193e7 - 1.57743e7i) q^{93} +(-6.64745e7 - 5.57787e7i) q^{94} +(6.44355e7 - 7.67912e7i) q^{95} +(-1.41869e6 + 1.49473e7i) q^{96} +(-6.74639e7 - 2.45549e7i) q^{97} +(5.11844e7 + 2.95513e7i) q^{98} +(-7.98800e7 + 2.77488e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) 73.1569 + 34.7717i 0.903171 + 0.429280i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) −324.095 890.442i −0.518551 1.42471i −0.872117 0.489298i \(-0.837253\pi\)
0.353565 0.935410i \(-0.384969\pi\)
\(6\) −230.660 886.907i −0.177979 0.684342i
\(7\) −575.632 3264.57i −0.239747 1.35967i −0.832383 0.554201i \(-0.813024\pi\)
0.592636 0.805471i \(-0.298087\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) 4142.86 + 5087.58i 0.631437 + 0.775427i
\(10\) −5360.37 + 9284.44i −0.536037 + 0.928444i
\(11\) −4408.18 + 12111.4i −0.301085 + 0.827223i 0.693228 + 0.720719i \(0.256188\pi\)
−0.994312 + 0.106504i \(0.966034\pi\)
\(12\) −6009.21 + 8448.95i −0.289796 + 0.407453i
\(13\) 3622.37 + 3039.53i 0.126829 + 0.106422i 0.703996 0.710204i \(-0.251397\pi\)
−0.577167 + 0.816626i \(0.695842\pi\)
\(14\) −24107.2 + 28729.9i −0.627531 + 0.747862i
\(15\) 7252.43 76411.3i 0.143258 1.50936i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −72590.8 41910.3i −0.869133 0.501794i −0.00207274 0.999998i \(-0.500660\pi\)
−0.867060 + 0.498204i \(0.833993\pi\)
\(18\) 13964.8 72903.8i 0.133029 0.694481i
\(19\) 52894.2 + 91615.4i 0.405876 + 0.702998i 0.994423 0.105465i \(-0.0336332\pi\)
−0.588547 + 0.808463i \(0.700300\pi\)
\(20\) 119449. 21062.0i 0.746554 0.131638i
\(21\) 71403.2 258842.i 0.367147 1.33094i
\(22\) 137025. 49872.9i 0.584935 0.212899i
\(23\) −439599. 77513.1i −1.57089 0.276990i −0.680692 0.732569i \(-0.738321\pi\)
−0.890195 + 0.455580i \(0.849432\pi\)
\(24\) 116926. 9362.74i 0.352425 0.0282201i
\(25\) −388614. + 326086.i −0.994852 + 0.834780i
\(26\) 53498.7i 0.117071i
\(27\) 126175. + 516245.i 0.237421 + 0.971407i
\(28\) 424311. 0.690323
\(29\) −610092. 727079.i −0.862588 1.02799i −0.999301 0.0373812i \(-0.988098\pi\)
0.136714 0.990611i \(-0.456346\pi\)
\(30\) −714984. + 492831.i −0.882696 + 0.608434i
\(31\) 41498.2 235348.i 0.0449347 0.254837i −0.954063 0.299607i \(-0.903144\pi\)
0.998997 + 0.0447698i \(0.0142554\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) −743622. + 732751.i −0.627041 + 0.617875i
\(34\) 164674. + 933915.i 0.123228 + 0.698863i
\(35\) −2.72035e6 + 1.57060e6i −1.81281 + 1.04663i
\(36\) −733400. + 409149.i −0.436647 + 0.243596i
\(37\) −563956. + 976800.i −0.300911 + 0.521193i −0.976343 0.216229i \(-0.930624\pi\)
0.675431 + 0.737423i \(0.263957\pi\)
\(38\) 409350. 1.12468e6i 0.196318 0.539379i
\(39\) 159312. + 348318.i 0.0688635 + 0.150563i
\(40\) −1.05121e6 882069.i −0.410628 0.344558i
\(41\) −895786. + 1.06756e6i −0.317007 + 0.377794i −0.900893 0.434042i \(-0.857087\pi\)
0.583886 + 0.811836i \(0.301532\pi\)
\(42\) −2.76260e6 + 1.26354e6i −0.887810 + 0.406061i
\(43\) −5.41819e6 1.97206e6i −1.58482 0.576828i −0.608577 0.793495i \(-0.708259\pi\)
−0.976246 + 0.216667i \(0.930482\pi\)
\(44\) −1.42872e6 824874.i −0.381186 0.220078i
\(45\) 3.18751e6 5.33783e6i 0.777324 1.30171i
\(46\) 2.52511e6 + 4.37362e6i 0.563960 + 0.976808i
\(47\) 7.55349e6 1.33188e6i 1.54795 0.272945i 0.666600 0.745415i \(-0.267749\pi\)
0.881346 + 0.472471i \(0.156638\pi\)
\(48\) −931469. 945288.i −0.175470 0.178074i
\(49\) −4.90894e6 + 1.78671e6i −0.851536 + 0.309934i
\(50\) 5.65225e6 + 996644.i 0.904360 + 0.159463i
\(51\) −3.85323e6 5.59013e6i −0.569566 0.826307i
\(52\) −463663. + 389059.i −0.0634145 + 0.0532111i
\(53\) 5.92050e6i 0.750335i 0.926957 + 0.375168i \(0.122415\pi\)
−0.926957 + 0.375168i \(0.877585\pi\)
\(54\) 3.55661e6 4.84783e6i 0.418275 0.570128i
\(55\) 1.22131e7 1.33468
\(56\) −3.08573e6 3.67742e6i −0.313765 0.373931i
\(57\) 683952. + 8.54151e6i 0.0647927 + 0.809162i
\(58\) −1.86467e6 + 1.05751e7i −0.164775 + 0.934485i
\(59\) −6.80853e6 1.87063e7i −0.561882 1.54376i −0.816874 0.576816i \(-0.804295\pi\)
0.254991 0.966943i \(-0.417927\pi\)
\(60\) 9.47086e6 + 2.61260e6i 0.730776 + 0.201589i
\(61\) 662289. + 3.75603e6i 0.0478330 + 0.271275i 0.999339 0.0363559i \(-0.0115750\pi\)
−0.951506 + 0.307631i \(0.900464\pi\)
\(62\) −2.34150e6 + 1.35187e6i −0.158463 + 0.0914886i
\(63\) 1.42240e7 1.64532e7i 0.902941 1.04445i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 1.53253e6 4.21060e6i 0.0858532 0.235880i
\(66\) 1.17585e7 + 1.11603e6i 0.619690 + 0.0588167i
\(67\) 9.00295e6 + 7.55437e6i 0.446772 + 0.374886i 0.838236 0.545307i \(-0.183587\pi\)
−0.391465 + 0.920193i \(0.628031\pi\)
\(68\) 6.89650e6 8.21893e6i 0.322547 0.384396i
\(69\) −2.94644e7 2.09562e7i −1.29987 0.924520i
\(70\) 3.33953e7 + 1.21549e7i 1.39089 + 0.506243i
\(71\) −4.11401e7 2.37522e7i −1.61894 0.934698i −0.987194 0.159525i \(-0.949004\pi\)
−0.631750 0.775172i \(-0.717663\pi\)
\(72\) 8.87952e6 + 3.38077e6i 0.330415 + 0.125802i
\(73\) 1.46752e7 + 2.54183e7i 0.516766 + 0.895065i 0.999810 + 0.0194693i \(0.00619766\pi\)
−0.483044 + 0.875596i \(0.660469\pi\)
\(74\) 1.25670e7 2.21590e6i 0.419088 0.0738964i
\(75\) −3.97684e7 + 1.03427e7i −1.25688 + 0.326880i
\(76\) −1.27243e7 + 4.63126e6i −0.381399 + 0.138818i
\(77\) 4.20759e7 + 7.41912e6i 1.19694 + 0.211052i
\(78\) 1.86024e6 3.91380e6i 0.0502563 0.105735i
\(79\) 1.46072e7 1.22569e7i 0.375024 0.314683i −0.435721 0.900082i \(-0.643507\pi\)
0.810745 + 0.585399i \(0.199062\pi\)
\(80\) 1.55253e7i 0.379036i
\(81\) −8.72013e6 + 4.21542e7i −0.202574 + 0.979267i
\(82\) 1.57667e7 0.348728
\(83\) −6.82152e6 8.12958e6i −0.143737 0.171299i 0.689373 0.724407i \(-0.257886\pi\)
−0.833110 + 0.553108i \(0.813442\pi\)
\(84\) 3.10413e7 + 1.47540e7i 0.623480 + 0.296342i
\(85\) −1.37924e7 + 7.82209e7i −0.264220 + 1.49847i
\(86\) 2.23113e7 + 6.12999e7i 0.407879 + 1.12064i
\(87\) −1.93507e7 7.44048e7i −0.337768 1.29874i
\(88\) 3.24110e6 + 1.83812e7i 0.0540458 + 0.306509i
\(89\) 8.66282e7 5.00148e7i 1.38070 0.797147i 0.388458 0.921467i \(-0.373008\pi\)
0.992242 + 0.124319i \(0.0396747\pi\)
\(90\) −6.94426e7 + 1.11928e7i −1.05841 + 0.170596i
\(91\) 7.83760e6 1.35751e7i 0.114292 0.197960i
\(92\) 1.95419e7 5.36909e7i 0.272782 0.749462i
\(93\) 1.12193e7 1.57743e7i 0.149980 0.210872i
\(94\) −6.64745e7 5.57787e7i −0.851419 0.714426i
\(95\) 6.44355e7 7.67912e7i 0.791099 0.942795i
\(96\) −1.41869e6 + 1.49473e7i −0.0167033 + 0.175986i
\(97\) −6.74639e7 2.45549e7i −0.762052 0.277364i −0.0683840 0.997659i \(-0.521784\pi\)
−0.693668 + 0.720295i \(0.744007\pi\)
\(98\) 5.11844e7 + 2.95513e7i 0.554923 + 0.320385i
\(99\) −7.98800e7 + 2.77488e7i −0.831567 + 0.288871i
\(100\) −3.24672e7 5.62348e7i −0.324672 0.562348i
\(101\) 5.68075e7 1.00167e7i 0.545909 0.0962584i 0.106109 0.994354i \(-0.466161\pi\)
0.439799 + 0.898096i \(0.355050\pi\)
\(102\) −2.04267e7 + 7.40484e7i −0.188711 + 0.684092i
\(103\) 1.66931e8 6.07579e7i 1.48316 0.539826i 0.531522 0.847045i \(-0.321620\pi\)
0.951639 + 0.307218i \(0.0993981\pi\)
\(104\) 6.74380e6 + 1.18911e6i 0.0576463 + 0.0101646i
\(105\) −2.53625e8 + 2.03087e7i −2.08658 + 0.167080i
\(106\) 5.13118e7 4.30558e7i 0.406438 0.341042i
\(107\) 7.21849e7i 0.550695i 0.961345 + 0.275348i \(0.0887930\pi\)
−0.961345 + 0.275348i \(0.911207\pi\)
\(108\) −6.78800e7 + 4.43050e6i −0.498938 + 0.0325655i
\(109\) −1.62618e8 −1.15203 −0.576013 0.817441i \(-0.695392\pi\)
−0.576013 + 0.817441i \(0.695392\pi\)
\(110\) −8.88178e7 1.05849e8i −0.606638 0.722963i
\(111\) −7.52223e7 + 5.18500e7i −0.495512 + 0.341552i
\(112\) −9.43116e6 + 5.34867e7i −0.0599367 + 0.339918i
\(113\) −8.32314e7 2.28676e8i −0.510474 1.40251i −0.880745 0.473591i \(-0.842957\pi\)
0.370271 0.928924i \(-0.379265\pi\)
\(114\) 6.90537e7 6.80442e7i 0.408853 0.402876i
\(115\) 7.34506e7 + 4.16559e8i 0.419956 + 2.38169i
\(116\) 1.05213e8 6.07446e7i 0.581081 0.335487i
\(117\) −456861. + 3.10214e7i −0.00243804 + 0.165546i
\(118\) −1.12610e8 + 1.95046e8i −0.580830 + 1.00603i
\(119\) −9.50337e7 + 2.61103e8i −0.473903 + 1.30204i
\(120\) −4.62321e7 1.01082e8i −0.222956 0.487470i
\(121\) 3.69551e7 + 3.10090e7i 0.172398 + 0.144659i
\(122\) 2.77364e7 3.30549e7i 0.125202 0.149210i
\(123\) −1.02654e8 + 4.69511e7i −0.448491 + 0.205128i
\(124\) 2.87445e7 + 1.04621e7i 0.121582 + 0.0442521i
\(125\) 9.57476e7 + 5.52799e7i 0.392182 + 0.226427i
\(126\) −2.46038e8 3.62347e6i −0.976159 0.0143762i
\(127\) 7.79502e7 + 1.35014e8i 0.299642 + 0.518995i 0.976054 0.217529i \(-0.0697995\pi\)
−0.676412 + 0.736523i \(0.736466\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −3.27806e8 3.32670e8i −1.18375 1.20131i
\(130\) −4.76375e7 + 1.73386e7i −0.166792 + 0.0607074i
\(131\) −2.72163e6 479896.i −0.00924151 0.00162953i 0.169026 0.985612i \(-0.445938\pi\)
−0.178267 + 0.983982i \(0.557049\pi\)
\(132\) −7.58387e7 1.10024e8i −0.249802 0.362404i
\(133\) 2.68637e8 2.25414e8i 0.858539 0.720400i
\(134\) 1.32965e8i 0.412398i
\(135\) 4.18794e8 2.79664e8i 1.26086 0.841980i
\(136\) −1.21385e8 −0.354822
\(137\) 2.65354e8 + 3.16237e8i 0.753258 + 0.897698i 0.997402 0.0720414i \(-0.0229514\pi\)
−0.244144 + 0.969739i \(0.578507\pi\)
\(138\) 3.26511e7 + 4.07762e8i 0.0900288 + 1.12432i
\(139\) 9.66695e7 5.48240e8i 0.258958 1.46863i −0.526745 0.850023i \(-0.676588\pi\)
0.785704 0.618603i \(-0.212301\pi\)
\(140\) −1.37517e8 3.77825e8i −0.357968 0.983509i
\(141\) 5.98901e8 + 1.65211e8i 1.51523 + 0.417987i
\(142\) 9.33275e7 + 5.29287e8i 0.229539 + 1.30178i
\(143\) −5.27809e7 + 3.04731e7i −0.126221 + 0.0728739i
\(144\) −3.52741e7 1.01543e8i −0.0820364 0.236157i
\(145\) −4.49695e8 + 7.78894e8i −1.01729 + 1.76200i
\(146\) 1.13572e8 3.12037e8i 0.249954 0.686744i
\(147\) −4.21249e8 3.99821e7i −0.902132 0.0856241i
\(148\) −1.10596e8 9.28010e7i −0.230511 0.193422i
\(149\) 3.53614e8 4.21421e8i 0.717439 0.855010i −0.276940 0.960887i \(-0.589320\pi\)
0.994379 + 0.105877i \(0.0337649\pi\)
\(150\) 3.78846e8 + 2.69450e8i 0.748338 + 0.532246i
\(151\) 3.13030e8 + 1.13934e8i 0.602114 + 0.219151i 0.625049 0.780586i \(-0.285079\pi\)
−0.0229354 + 0.999737i \(0.507301\pi\)
\(152\) 1.32673e8 + 7.65989e7i 0.248547 + 0.143499i
\(153\) −8.75117e7 5.42940e8i −0.159698 0.990800i
\(154\) −2.41689e8 4.18618e8i −0.429709 0.744278i
\(155\) −2.23013e8 + 3.93232e7i −0.386370 + 0.0681274i
\(156\) −4.74484e7 + 1.23400e7i −0.0801167 + 0.0208362i
\(157\) 4.98626e8 1.81485e8i 0.820684 0.298704i 0.102654 0.994717i \(-0.467266\pi\)
0.718030 + 0.696013i \(0.245044\pi\)
\(158\) −2.12457e8 3.74618e7i −0.340912 0.0601119i
\(159\) −2.05866e8 + 4.33126e8i −0.322104 + 0.677681i
\(160\) 1.34555e8 1.12905e8i 0.205314 0.172279i
\(161\) 1.47972e9i 2.20230i
\(162\) 4.28758e8 2.30983e8i 0.622518 0.335367i
\(163\) 2.18451e8 0.309459 0.154730 0.987957i \(-0.450549\pi\)
0.154730 + 0.987957i \(0.450549\pi\)
\(164\) −1.14661e8 1.36647e8i −0.158503 0.188897i
\(165\) 8.93476e8 + 4.24672e8i 1.20544 + 0.572951i
\(166\) −2.08492e7 + 1.18242e8i −0.0274572 + 0.155718i
\(167\) −1.20844e8 3.32015e8i −0.155367 0.426867i 0.837450 0.546515i \(-0.184046\pi\)
−0.992816 + 0.119648i \(0.961823\pi\)
\(168\) −9.78718e7 3.76325e8i −0.122863 0.472417i
\(169\) −1.37767e8 7.81317e8i −0.168888 0.957813i
\(170\) 7.78228e8 4.49310e8i 0.931775 0.537961i
\(171\) −2.46967e8 + 6.48653e8i −0.288838 + 0.758626i
\(172\) 3.69019e8 6.39160e8i 0.421633 0.730290i
\(173\) 1.19471e8 3.28243e8i 0.133376 0.366447i −0.854969 0.518679i \(-0.826424\pi\)
0.988345 + 0.152232i \(0.0486462\pi\)
\(174\) −5.04127e8 + 7.08803e8i −0.549975 + 0.773265i
\(175\) 1.28823e9 + 1.08095e9i 1.37354 + 1.15254i
\(176\) 1.35736e8 1.61764e8i 0.141463 0.168590i
\(177\) 1.52358e8 1.60524e9i 0.155229 1.63548i
\(178\) −1.06346e9 3.87066e8i −1.05935 0.385572i
\(179\) −1.49423e9 8.62691e8i −1.45547 0.840317i −0.456689 0.889626i \(-0.650965\pi\)
−0.998784 + 0.0493090i \(0.984298\pi\)
\(180\) 6.02014e8 + 5.20447e8i 0.573478 + 0.495777i
\(181\) 4.60998e7 + 7.98472e7i 0.0429521 + 0.0743953i 0.886702 0.462341i \(-0.152990\pi\)
−0.843750 + 0.536736i \(0.819657\pi\)
\(182\) −1.74650e8 + 3.07956e7i −0.159178 + 0.0280674i
\(183\) −8.21524e7 + 2.97808e8i −0.0732514 + 0.265541i
\(184\) −6.07443e8 + 2.21091e8i −0.529949 + 0.192886i
\(185\) 1.05256e9 + 1.85595e8i 0.898586 + 0.158445i
\(186\) −2.18304e8 + 1.74804e7i −0.182393 + 0.0146049i
\(187\) 8.27585e8 6.94426e8i 0.676778 0.567884i
\(188\) 9.81761e8i 0.785913i
\(189\) 1.61269e9 7.09076e8i 1.26387 0.555706i
\(190\) −1.13413e9 −0.870259
\(191\) −1.08299e9 1.29066e9i −0.813753 0.969793i 0.186166 0.982518i \(-0.440394\pi\)
−0.999919 + 0.0127255i \(0.995949\pi\)
\(192\) 1.39862e8 9.64058e7i 0.102919 0.0709412i
\(193\) 5.65772e7 3.20865e8i 0.0407767 0.231256i −0.957608 0.288075i \(-0.906985\pi\)
0.998385 + 0.0568189i \(0.0180958\pi\)
\(194\) 2.77807e8 + 7.63267e8i 0.196126 + 0.538852i
\(195\) 2.58525e8 2.54746e8i 0.178799 0.176185i
\(196\) −1.16113e8 6.58511e8i −0.0786788 0.446210i
\(197\) −7.71058e8 + 4.45170e8i −0.511944 + 0.295571i −0.733632 0.679547i \(-0.762176\pi\)
0.221689 + 0.975117i \(0.428843\pi\)
\(198\) 8.21406e8 + 4.90506e8i 0.534437 + 0.319142i
\(199\) −5.23978e8 + 9.07557e8i −0.334119 + 0.578711i −0.983315 0.181910i \(-0.941772\pi\)
0.649196 + 0.760621i \(0.275105\pi\)
\(200\) −2.51265e8 + 6.90344e8i −0.157040 + 0.431465i
\(201\) 3.95950e8 + 8.65702e8i 0.242580 + 0.530377i
\(202\) −4.99934e8 4.19495e8i −0.300267 0.251954i
\(203\) −2.02241e9 + 2.41022e9i −1.19093 + 1.41929i
\(204\) 7.90312e8 3.61468e8i 0.456329 0.208713i
\(205\) 1.24092e9 + 4.51657e8i 0.702631 + 0.255737i
\(206\) −1.74055e9 1.00491e9i −0.966536 0.558030i
\(207\) −1.42684e9 2.55762e9i −0.777132 1.39301i
\(208\) −3.87372e7 6.70948e7i −0.0206955 0.0358456i
\(209\) −1.34276e9 + 2.36764e8i −0.703739 + 0.124088i
\(210\) 2.02045e9 + 2.05043e9i 1.03889 + 1.05431i
\(211\) −2.73541e9 + 9.95607e8i −1.38004 + 0.502294i −0.922191 0.386735i \(-0.873603\pi\)
−0.457851 + 0.889029i \(0.651381\pi\)
\(212\) −7.46312e8 1.31595e8i −0.369468 0.0651472i
\(213\) −2.18378e9 3.16815e9i −1.06094 1.53917i
\(214\) 6.25613e8 5.24951e8i 0.298298 0.250302i
\(215\) 5.46372e9i 2.55702i
\(216\) 5.32043e8 + 5.56083e8i 0.244417 + 0.255461i
\(217\) −7.92197e8 −0.357268
\(218\) 1.18261e9 + 1.40938e9i 0.523618 + 0.624023i
\(219\) 1.89759e8 + 2.36981e9i 0.0824948 + 1.03023i
\(220\) −2.71461e8 + 1.53953e9i −0.115882 + 0.657201i
\(221\) −1.35563e8 3.72456e8i −0.0568293 0.156137i
\(222\) 9.96413e8 + 2.74867e8i 0.410230 + 0.113165i
\(223\) −6.61999e8 3.75438e9i −0.267694 1.51817i −0.761254 0.648454i \(-0.775416\pi\)
0.493560 0.869712i \(-0.335695\pi\)
\(224\) 5.32145e8 3.07234e8i 0.211368 0.122033i
\(225\) −3.26896e9 6.26175e8i −1.27550 0.244324i
\(226\) −1.37661e9 + 2.38436e9i −0.527687 + 0.913981i
\(227\) −5.24687e8 + 1.44157e9i −0.197605 + 0.542914i −0.998432 0.0559814i \(-0.982171\pi\)
0.800827 + 0.598895i \(0.204393\pi\)
\(228\) −1.09191e9 1.03636e8i −0.404060 0.0383506i
\(229\) −1.33192e9 1.11761e9i −0.484325 0.406397i 0.367663 0.929959i \(-0.380158\pi\)
−0.851987 + 0.523563i \(0.824603\pi\)
\(230\) 3.07608e9 3.66593e9i 1.09922 1.31000i
\(231\) 2.82017e9 + 2.00581e9i 0.990438 + 0.704437i
\(232\) −1.29160e9 4.70104e8i −0.445837 0.162272i
\(233\) −2.37768e9 1.37276e9i −0.806733 0.465768i 0.0390868 0.999236i \(-0.487555\pi\)
−0.845820 + 0.533468i \(0.820888\pi\)
\(234\) 2.72179e8 2.21638e8i 0.0907801 0.0739231i
\(235\) −3.63401e9 6.29429e9i −1.19156 2.06384i
\(236\) 2.50936e9 4.42468e8i 0.808938 0.142638i
\(237\) 1.49481e9 3.88760e8i 0.473798 0.123222i
\(238\) 2.95404e9 1.07518e9i 0.920680 0.335100i
\(239\) −1.35767e9 2.39394e8i −0.416105 0.0733705i −0.0383235 0.999265i \(-0.512202\pi\)
−0.377781 + 0.925895i \(0.623313\pi\)
\(240\) −5.39841e8 + 1.13578e9i −0.162712 + 0.342334i
\(241\) 2.96431e9 2.48736e9i 0.878731 0.737343i −0.0871865 0.996192i \(-0.527788\pi\)
0.965918 + 0.258849i \(0.0833431\pi\)
\(242\) 5.45790e8i 0.159134i
\(243\) −2.10371e9 + 2.78066e9i −0.603338 + 0.797485i
\(244\) −4.88188e8 −0.137730
\(245\) 3.18192e9 + 3.79206e9i 0.883130 + 1.05247i
\(246\) 1.15345e9 + 5.48236e8i 0.314961 + 0.149702i
\(247\) −8.68653e7 + 4.92638e8i −0.0233377 + 0.132355i
\(248\) −1.18366e8 3.25207e8i −0.0312909 0.0859711i
\(249\) −2.16362e8 8.31930e8i −0.0562839 0.216416i
\(250\) −2.17206e8 1.23184e9i −0.0556048 0.315351i
\(251\) −3.01582e9 + 1.74118e9i −0.759819 + 0.438682i −0.829231 0.558906i \(-0.811221\pi\)
0.0694115 + 0.997588i \(0.477888\pi\)
\(252\) 1.75786e9 + 2.15872e9i 0.435896 + 0.535295i
\(253\) 2.87662e9 4.98245e9i 0.702102 1.21608i
\(254\) 6.03259e8 1.65744e9i 0.144934 0.398202i
\(255\) −3.72888e9 + 5.24281e9i −0.881897 + 1.23995i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 1.99919e9 2.38254e9i 0.458270 0.546145i −0.486585 0.873633i \(-0.661758\pi\)
0.944855 + 0.327488i \(0.106202\pi\)
\(258\) −4.99272e8 + 5.26031e9i −0.112683 + 1.18722i
\(259\) 3.51347e9 + 1.27880e9i 0.780795 + 0.284186i
\(260\) 4.96705e8 + 2.86773e8i 0.108694 + 0.0627545i
\(261\) 1.17154e9 6.11608e9i 0.252462 1.31799i
\(262\) 1.56333e7 + 2.70777e7i 0.00331777 + 0.00574655i
\(263\) 8.12302e9 1.43231e9i 1.69783 0.299373i 0.760895 0.648875i \(-0.224760\pi\)
0.936936 + 0.349502i \(0.113649\pi\)
\(264\) −4.02036e8 + 1.45741e9i −0.0827656 + 0.300031i
\(265\) 5.27187e9 1.91880e9i 1.06901 0.389087i
\(266\) −3.90723e9 6.88950e8i −0.780445 0.137614i
\(267\) 8.07655e9 6.46720e8i 1.58921 0.127254i
\(268\) −1.15238e9 + 9.66960e8i −0.223386 + 0.187443i
\(269\) 1.14947e9i 0.219528i 0.993958 + 0.109764i \(0.0350094\pi\)
−0.993958 + 0.109764i \(0.964991\pi\)
\(270\) −5.46940e9 1.59580e9i −1.02916 0.300278i
\(271\) 1.72708e9 0.320211 0.160105 0.987100i \(-0.448817\pi\)
0.160105 + 0.987100i \(0.448817\pi\)
\(272\) 8.82752e8 + 1.05202e9i 0.161273 + 0.192198i
\(273\) 1.04540e9 7.20587e8i 0.188206 0.129729i
\(274\) 8.11024e8 4.59954e9i 0.143890 0.816042i
\(275\) −2.23627e9 6.14410e9i −0.391015 1.07430i
\(276\) 3.29655e9 3.24836e9i 0.568098 0.559793i
\(277\) −5.05473e8 2.86668e9i −0.0858576 0.486923i −0.997168 0.0752033i \(-0.976039\pi\)
0.911311 0.411720i \(-0.135072\pi\)
\(278\) −5.45450e9 + 3.14915e9i −0.913220 + 0.527248i
\(279\) 1.36927e9 7.63888e8i 0.225981 0.126070i
\(280\) −2.27447e9 + 3.93949e9i −0.370039 + 0.640927i
\(281\) −3.02251e9 + 8.30426e9i −0.484777 + 1.33191i 0.420578 + 0.907256i \(0.361827\pi\)
−0.905354 + 0.424657i \(0.860395\pi\)
\(282\) −2.92355e9 6.39203e9i −0.462289 1.01075i
\(283\) 8.11325e9 + 6.80782e9i 1.26488 + 1.06136i 0.995144 + 0.0984251i \(0.0313805\pi\)
0.269735 + 0.962935i \(0.413064\pi\)
\(284\) 3.90852e9 4.65799e9i 0.600812 0.716020i
\(285\) 7.38406e9 3.37728e9i 1.11922 0.511903i
\(286\) 6.47943e8 + 2.35832e8i 0.0968440 + 0.0352483i
\(287\) 4.00076e9 + 2.30984e9i 0.589678 + 0.340450i
\(288\) −6.23530e8 + 1.04417e9i −0.0906332 + 0.151775i
\(289\) 2.50735e7 + 4.34286e7i 0.00359438 + 0.00622565i
\(290\) 1.00208e10 1.76694e9i 1.41681 0.249822i
\(291\) −4.08164e9 4.14219e9i −0.569197 0.577641i
\(292\) −3.53030e9 + 1.28492e9i −0.485601 + 0.176744i
\(293\) −7.33657e9 1.29363e9i −0.995457 0.175526i −0.347891 0.937535i \(-0.613102\pi\)
−0.647566 + 0.762009i \(0.724213\pi\)
\(294\) 2.71694e9 + 3.94165e9i 0.363656 + 0.527580i
\(295\) −1.44503e10 + 1.21252e10i −1.90804 + 1.60104i
\(296\) 1.63339e9i 0.212776i
\(297\) −6.80864e9 7.47547e8i −0.875054 0.0960755i
\(298\) −6.22397e9 −0.789228
\(299\) −1.35678e9 1.61695e9i −0.169756 0.202308i
\(300\) −4.19819e8 5.24290e9i −0.0518296 0.647272i
\(301\) −3.31905e9 + 1.88233e10i −0.404341 + 2.29313i
\(302\) −1.28901e9 3.54153e9i −0.154963 0.425759i
\(303\) 4.50415e9 + 1.24250e9i 0.534371 + 0.147410i
\(304\) −3.00973e8 1.70690e9i −0.0352398 0.199855i
\(305\) 3.12988e9 1.80704e9i 0.361683 0.208818i
\(306\) −4.06914e9 + 4.70688e9i −0.464106 + 0.536843i
\(307\) −6.63405e9 + 1.14905e10i −0.746836 + 1.29356i 0.202496 + 0.979283i \(0.435095\pi\)
−0.949332 + 0.314275i \(0.898239\pi\)
\(308\) −1.87044e9 + 5.13899e9i −0.207846 + 0.571052i
\(309\) 1.43248e10 + 1.35961e9i 1.57129 + 0.149135i
\(310\) 1.96263e9 + 1.64684e9i 0.212516 + 0.178322i
\(311\) −6.06772e9 + 7.23123e9i −0.648610 + 0.772984i −0.985704 0.168487i \(-0.946112\pi\)
0.337093 + 0.941471i \(0.390556\pi\)
\(312\) 4.52008e8 + 3.21485e8i 0.0477010 + 0.0339268i
\(313\) 1.33962e10 + 4.87580e9i 1.39574 + 0.508006i 0.926910 0.375285i \(-0.122455\pi\)
0.468825 + 0.883291i \(0.344677\pi\)
\(314\) −5.19905e9 3.00168e9i −0.534818 0.308777i
\(315\) −1.92606e10 7.33324e9i −1.95626 0.744824i
\(316\) 1.22038e9 + 2.11375e9i 0.122390 + 0.211985i
\(317\) 1.36690e10 2.41022e9i 1.35363 0.238682i 0.550676 0.834719i \(-0.314370\pi\)
0.802957 + 0.596037i \(0.203259\pi\)
\(318\) 5.25094e9 1.36563e9i 0.513486 0.133544i
\(319\) 1.14953e10 4.18395e9i 1.11009 0.404040i
\(320\) −1.95705e9 3.45080e8i −0.186639 0.0329094i
\(321\) −2.50999e9 + 5.28082e9i −0.236402 + 0.497372i
\(322\) 1.28244e10 1.07610e10i 1.19293 1.00099i
\(323\) 8.86725e9i 0.814664i
\(324\) −5.11995e9 2.03618e9i −0.464607 0.184772i
\(325\) −2.39885e9 −0.215015
\(326\) −1.58864e9 1.89327e9i −0.140655 0.167626i
\(327\) −1.18966e10 5.65449e9i −1.04048 0.494541i
\(328\) −3.50447e8 + 1.98748e9i −0.0302780 + 0.171715i
\(329\) −8.69606e9 2.38922e10i −0.742231 2.03926i
\(330\) −2.81709e9 1.08319e10i −0.237544 0.913377i
\(331\) −2.96738e9 1.68288e10i −0.247207 1.40198i −0.815310 0.579024i \(-0.803434\pi\)
0.568103 0.822957i \(-0.307677\pi\)
\(332\) 1.17640e9 6.79194e8i 0.0968283 0.0559038i
\(333\) −7.30594e9 + 1.17758e9i −0.594154 + 0.0957664i
\(334\) −1.99870e9 + 3.46185e9i −0.160606 + 0.278178i
\(335\) 3.80893e9 1.04649e10i 0.302429 0.830917i
\(336\) −2.54978e9 + 3.58499e9i −0.200053 + 0.281275i
\(337\) 6.47691e9 + 5.43477e9i 0.502167 + 0.421368i 0.858363 0.513043i \(-0.171482\pi\)
−0.356196 + 0.934411i \(0.615926\pi\)
\(338\) −5.76964e9 + 6.87599e9i −0.442061 + 0.526827i
\(339\) 1.86251e9 1.96233e10i 0.141026 1.48585i
\(340\) −9.55360e9 3.47722e9i −0.714910 0.260206i
\(341\) 2.66745e9 + 1.54005e9i 0.197278 + 0.113899i
\(342\) 7.41777e9 2.57679e9i 0.542212 0.188354i
\(343\) −8.96389e8 1.55259e9i −0.0647620 0.112171i
\(344\) −8.22309e9 + 1.44995e9i −0.587221 + 0.103543i
\(345\) −9.11104e9 + 3.30282e10i −0.643119 + 2.33135i
\(346\) −3.71364e9 + 1.35166e9i −0.259117 + 0.0943108i
\(347\) 2.08670e10 + 3.67942e9i 1.43927 + 0.253782i 0.838178 0.545397i \(-0.183621\pi\)
0.601093 + 0.799179i \(0.294732\pi\)
\(348\) 9.80923e9 7.85463e8i 0.668833 0.0535560i
\(349\) 1.35101e10 1.13363e10i 0.910658 0.764133i −0.0615857 0.998102i \(-0.519616\pi\)
0.972244 + 0.233969i \(0.0751713\pi\)
\(350\) 1.90259e10i 1.26786i
\(351\) −1.11209e9 + 2.25354e9i −0.0732674 + 0.148470i
\(352\) −2.38909e9 −0.155619
\(353\) 4.41410e9 + 5.26052e9i 0.284278 + 0.338789i 0.889220 0.457480i \(-0.151248\pi\)
−0.604942 + 0.796270i \(0.706804\pi\)
\(354\) −1.50203e10 + 1.03533e10i −0.956456 + 0.659276i
\(355\) −7.81672e9 + 4.43308e10i −0.492166 + 2.79121i
\(356\) 4.37915e9 + 1.20316e10i 0.272640 + 0.749074i
\(357\) −1.60314e10 + 1.57970e10i −0.986955 + 0.972527i
\(358\) 3.38970e9 + 1.92239e10i 0.206361 + 1.17033i
\(359\) −2.53809e10 + 1.46537e10i −1.52802 + 0.882203i −0.528576 + 0.848886i \(0.677274\pi\)
−0.999445 + 0.0333176i \(0.989393\pi\)
\(360\) 1.32581e8 9.00239e9i 0.00789351 0.535979i
\(361\) 2.89620e9 5.01636e9i 0.170529 0.295366i
\(362\) 3.56768e8 9.80212e8i 0.0207755 0.0570802i
\(363\) 1.62528e9 + 3.55351e9i 0.0936058 + 0.204659i
\(364\) 1.53701e9 + 1.28971e9i 0.0875531 + 0.0734658i
\(365\) 1.78773e10 2.13054e10i 1.00724 1.20038i
\(366\) 3.17848e9 1.45375e9i 0.177131 0.0810153i
\(367\) −1.91704e10 6.97746e9i −1.05674 0.384621i −0.245536 0.969388i \(-0.578964\pi\)
−0.811202 + 0.584767i \(0.801186\pi\)
\(368\) 6.33367e9 + 3.65675e9i 0.345354 + 0.199390i
\(369\) −9.14239e9 1.34643e8i −0.493122 0.00726234i
\(370\) −6.04603e9 1.04720e10i −0.322599 0.558758i
\(371\) 1.93279e10 3.40803e9i 1.02021 0.179890i
\(372\) 1.73907e9 + 1.76487e9i 0.0908125 + 0.0921597i
\(373\) −1.28990e10 + 4.69486e9i −0.666380 + 0.242542i −0.652988 0.757368i \(-0.726485\pi\)
−0.0133914 + 0.999910i \(0.504263\pi\)
\(374\) −1.20369e10 2.12243e9i −0.615218 0.108479i
\(375\) 5.08242e9 + 7.37341e9i 0.257007 + 0.372858i
\(376\) 8.50873e9 7.13967e9i 0.425710 0.357213i
\(377\) 4.48814e9i 0.222178i
\(378\) −1.78734e10 8.82025e9i −0.875468 0.432030i
\(379\) −2.66606e10 −1.29215 −0.646075 0.763274i \(-0.723591\pi\)
−0.646075 + 0.763274i \(0.723591\pi\)
\(380\) 8.24774e9 + 9.82928e9i 0.395549 + 0.471398i
\(381\) 1.00794e9 + 1.25876e10i 0.0478338 + 0.597371i
\(382\) −3.31004e9 + 1.87722e10i −0.155446 + 0.881579i
\(383\) 9.12614e9 + 2.50739e10i 0.424123 + 1.16527i 0.949326 + 0.314292i \(0.101767\pi\)
−0.525203 + 0.850977i \(0.676011\pi\)
\(384\) −1.85265e9 5.11067e8i −0.0852058 0.0235046i
\(385\) −7.03028e9 3.98707e10i −0.319985 1.81473i
\(386\) −3.19233e9 + 1.84309e9i −0.143800 + 0.0830228i
\(387\) −1.24138e10 3.57354e10i −0.553428 1.59315i
\(388\) 4.59479e9 7.95841e9i 0.202740 0.351156i
\(389\) 6.15177e9 1.69018e10i 0.268659 0.738135i −0.729853 0.683604i \(-0.760412\pi\)
0.998512 0.0545305i \(-0.0173662\pi\)
\(390\) −4.08791e9 3.87996e8i −0.176702 0.0167714i
\(391\) 2.86622e10 + 2.40505e10i 1.22632 + 1.02900i
\(392\) −4.86277e9 + 5.79523e9i −0.205940 + 0.245429i
\(393\) −1.82419e8 1.29743e8i −0.00764715 0.00543894i
\(394\) 9.46558e9 + 3.44519e9i 0.392792 + 0.142964i
\(395\) −1.56482e10 9.03449e9i −0.642800 0.371121i
\(396\) −1.72239e9 1.06861e10i −0.0700409 0.434548i
\(397\) 7.26872e9 + 1.25898e10i 0.292615 + 0.506823i 0.974427 0.224703i \(-0.0721413\pi\)
−0.681813 + 0.731527i \(0.738808\pi\)
\(398\) 1.16762e10 2.05882e9i 0.465337 0.0820514i
\(399\) 2.74907e10 7.14958e9i 1.08466 0.282091i
\(400\) 7.81035e9 2.84274e9i 0.305092 0.111044i
\(401\) 1.48867e10 + 2.62492e9i 0.575732 + 0.101517i 0.453930 0.891037i \(-0.350022\pi\)
0.121802 + 0.992554i \(0.461133\pi\)
\(402\) 4.62340e9 9.72728e9i 0.177034 0.372466i
\(403\) 8.65667e8 7.26381e8i 0.0328194 0.0275388i
\(404\) 7.38353e9i 0.277165i
\(405\) 4.03621e10 5.89718e9i 1.50021 0.219192i
\(406\) 3.55965e10 1.31010
\(407\) −9.34438e9 1.11362e10i −0.340544 0.405844i
\(408\) −8.88017e9 4.22077e9i −0.320465 0.152318i
\(409\) 7.25117e9 4.11235e10i 0.259128 1.46959i −0.526120 0.850410i \(-0.676354\pi\)
0.785249 0.619180i \(-0.212535\pi\)
\(410\) −5.10991e9 1.40394e10i −0.180833 0.496835i
\(411\) 8.41640e9 + 3.23617e10i 0.294957 + 1.13413i
\(412\) 3.94850e9 + 2.23930e10i 0.137039 + 0.777184i
\(413\) −5.71488e10 + 3.29949e10i −1.96430 + 1.13409i
\(414\) −1.17899e10 + 3.09660e10i −0.401338 + 1.05410i
\(415\) −5.02810e9 + 8.70892e9i −0.169516 + 0.293611i
\(416\) −2.99788e8 + 8.23662e8i −0.0100102 + 0.0275027i
\(417\) 2.61353e10 3.67462e10i 0.864336 1.21526i
\(418\) 1.18169e10 + 9.91557e9i 0.387079 + 0.324798i
\(419\) 9.22075e9 1.09889e10i 0.299165 0.356530i −0.595432 0.803406i \(-0.703019\pi\)
0.894596 + 0.446876i \(0.147463\pi\)
\(420\) 3.07729e9 3.24222e10i 0.0988943 1.04195i
\(421\) −1.53666e10 5.59297e9i −0.489157 0.178039i 0.0856538 0.996325i \(-0.472702\pi\)
−0.574811 + 0.818286i \(0.694924\pi\)
\(422\) 2.85215e10 + 1.64669e10i 0.899336 + 0.519232i
\(423\) 3.80691e10 + 3.29111e10i 1.18908 + 1.02797i
\(424\) 4.28690e9 + 7.42513e9i 0.132642 + 0.229742i
\(425\) 4.18762e10 7.38391e9i 1.28355 0.226324i
\(426\) −1.15766e10 + 4.19661e10i −0.351515 + 1.27427i
\(427\) 1.18806e10 4.32418e9i 0.357377 0.130075i
\(428\) −9.09930e9 1.60445e9i −0.271165 0.0478136i
\(429\) −4.92088e9 + 3.94034e8i −0.145283 + 0.0116333i
\(430\) 4.73530e10 3.97339e10i 1.38508 1.16222i
\(431\) 4.41749e9i 0.128017i 0.997949 + 0.0640083i \(0.0203884\pi\)
−0.997949 + 0.0640083i \(0.979612\pi\)
\(432\) 9.50278e8 8.65512e9i 0.0272845 0.248507i
\(433\) −1.58198e9 −0.0450039 −0.0225020 0.999747i \(-0.507163\pi\)
−0.0225020 + 0.999747i \(0.507163\pi\)
\(434\) 5.76111e9 + 6.86582e9i 0.162385 + 0.193523i
\(435\) −5.99817e10 + 4.13448e10i −1.67518 + 1.15469i
\(436\) 3.61450e9 2.04988e10i 0.100024 0.567262i
\(437\) −1.61508e10 4.43740e10i −0.442862 1.21675i
\(438\) 1.91586e10 1.88786e10i 0.520557 0.512947i
\(439\) −2.69190e9 1.52665e10i −0.0724772 0.411039i −0.999363 0.0356945i \(-0.988636\pi\)
0.926886 0.375344i \(-0.122475\pi\)
\(440\) 1.53170e10 8.84326e9i 0.408660 0.235940i
\(441\) −2.94271e10 1.75725e10i −0.778023 0.464600i
\(442\) −2.24215e9 + 3.88352e9i −0.0587456 + 0.101750i
\(443\) −7.46721e9 + 2.05160e10i −0.193885 + 0.532694i −0.998098 0.0616470i \(-0.980365\pi\)
0.804213 + 0.594341i \(0.202587\pi\)
\(444\) −4.86401e9 1.06346e10i −0.125159 0.273647i
\(445\) −7.26110e10 6.09279e10i −1.85167 1.55373i
\(446\) −2.77242e10 + 3.30405e10i −0.700681 + 0.835039i
\(447\) 4.05229e10 1.85341e10i 1.01501 0.464239i
\(448\) −6.53267e9 2.37770e9i −0.162173 0.0590261i
\(449\) 4.22200e10 + 2.43757e10i 1.03880 + 0.599752i 0.919493 0.393105i \(-0.128599\pi\)
0.119308 + 0.992857i \(0.461933\pi\)
\(450\) 1.83460e10 + 3.28852e10i 0.447395 + 0.801956i
\(451\) −8.98079e9 1.55552e10i −0.217074 0.375984i
\(452\) 3.06759e10 5.40898e9i 0.734925 0.129587i
\(453\) 1.89387e10 + 1.92196e10i 0.449735 + 0.456407i
\(454\) 1.63095e10 5.93616e9i 0.383898 0.139728i
\(455\) −1.46280e10 2.57931e9i −0.341302 0.0601808i
\(456\) 7.04249e9 + 1.02170e10i 0.162880 + 0.236300i
\(457\) −4.66474e10 + 3.91418e10i −1.06945 + 0.897379i −0.995003 0.0998453i \(-0.968165\pi\)
−0.0744520 + 0.997225i \(0.523721\pi\)
\(458\) 1.96711e10i 0.447062i
\(459\) 1.24769e10 4.27627e10i 0.281096 0.963418i
\(460\) −5.41421e10 −1.20922
\(461\) −1.68516e10 2.00829e10i −0.373110 0.444656i 0.546517 0.837448i \(-0.315953\pi\)
−0.919627 + 0.392793i \(0.871509\pi\)
\(462\) −3.12518e9 3.90287e10i −0.0685973 0.856676i
\(463\) 5.09452e9 2.88924e10i 0.110861 0.628724i −0.877855 0.478926i \(-0.841026\pi\)
0.988717 0.149799i \(-0.0478625\pi\)
\(464\) 5.31862e9 + 1.46128e10i 0.114743 + 0.315255i
\(465\) −1.76823e10 4.87777e9i −0.378204 0.104330i
\(466\) 5.39384e9 + 3.05900e10i 0.114381 + 0.648688i
\(467\) 1.50287e10 8.67684e9i 0.315976 0.182429i −0.333621 0.942707i \(-0.608271\pi\)
0.649598 + 0.760278i \(0.274937\pi\)
\(468\) −3.90026e9 7.47101e8i −0.0813037 0.0155739i
\(469\) 1.94794e10 3.37393e10i 0.402610 0.697341i
\(470\) −2.81237e10 + 7.72693e10i −0.576343 + 1.58349i
\(471\) 4.27884e10 + 4.06118e9i 0.869446 + 0.0825218i
\(472\) −2.20836e10 1.85304e10i −0.444941 0.373350i
\(473\) 4.77687e10 5.69286e10i 0.954331 1.13733i
\(474\) −1.42400e10 1.01281e10i −0.282097 0.200638i
\(475\) −5.04299e10 1.83550e10i −0.990635 0.360562i
\(476\) −3.08011e10 1.77830e10i −0.599983 0.346400i
\(477\) −3.01210e10 + 2.45278e10i −0.581830 + 0.473790i
\(478\) 7.79862e9 + 1.35076e10i 0.149385 + 0.258742i
\(479\) −6.17842e10 + 1.08942e10i −1.17364 + 0.206945i −0.726274 0.687406i \(-0.758749\pi\)
−0.447367 + 0.894350i \(0.647638\pi\)
\(480\) 1.37695e10 3.58107e9i 0.259390 0.0674603i
\(481\) −5.01187e9 + 1.82417e9i −0.0936309 + 0.0340789i
\(482\) −4.31148e10 7.60231e9i −0.798801 0.140850i
\(483\) −5.14524e10 + 1.08252e11i −0.945403 + 1.98905i
\(484\) −4.73025e9 + 3.96915e9i −0.0861991 + 0.0723297i
\(485\) 6.80308e10i 1.22953i
\(486\) 3.93983e10 1.98937e9i 0.706207 0.0356591i
\(487\) −5.48911e10 −0.975856 −0.487928 0.872884i \(-0.662247\pi\)
−0.487928 + 0.872884i \(0.662247\pi\)
\(488\) 3.55026e9 + 4.23103e9i 0.0626009 + 0.0746048i
\(489\) 1.59812e10 + 7.59591e9i 0.279495 + 0.132845i
\(490\) 9.72516e9 5.51541e10i 0.168699 0.956740i
\(491\) −9.16161e9 2.51713e10i −0.157633 0.433092i 0.835585 0.549361i \(-0.185129\pi\)
−0.993218 + 0.116269i \(0.962907\pi\)
\(492\) −3.63676e9 1.39836e10i −0.0620661 0.238649i
\(493\) 1.38149e10 + 7.83484e10i 0.233863 + 1.32630i
\(494\) 4.90130e9 2.82977e9i 0.0823008 0.0475164i
\(495\) 5.05974e10 + 6.21353e10i 0.842766 + 1.03495i
\(496\) −1.95771e9 + 3.39085e9i −0.0323461 + 0.0560251i
\(497\) −5.38593e10 + 1.47977e11i −0.882745 + 2.42532i
\(498\) −5.63672e9 + 7.92523e9i −0.0916451 + 0.128853i
\(499\) 3.42570e10 + 2.87450e10i 0.552519 + 0.463618i 0.875793 0.482687i \(-0.160339\pi\)
−0.323274 + 0.946305i \(0.604784\pi\)
\(500\) −9.09651e9 + 1.08408e10i −0.145544 + 0.173453i
\(501\) 2.70418e9 2.84912e10i 0.0429225 0.452230i
\(502\) 3.70225e10 + 1.34751e10i 0.582976 + 0.212186i
\(503\) 4.87888e9 + 2.81682e9i 0.0762163 + 0.0440035i 0.537624 0.843185i \(-0.319322\pi\)
−0.461408 + 0.887188i \(0.652655\pi\)
\(504\) 5.92544e9 3.09339e10i 0.0918330 0.479416i
\(505\) −2.73303e10 4.73374e10i −0.420222 0.727845i
\(506\) −6.41016e10 + 1.13028e10i −0.977838 + 0.172419i
\(507\) 1.70891e10 6.19492e10i 0.258635 0.937570i
\(508\) −1.87518e10 + 6.82510e9i −0.281571 + 0.102483i
\(509\) −2.42351e10 4.27330e9i −0.361055 0.0636638i −0.00982196 0.999952i \(-0.503126\pi\)
−0.351233 + 0.936288i \(0.614238\pi\)
\(510\) 7.25560e10 5.80984e9i 1.07249 0.0858783i
\(511\) 7.45323e10 6.25400e10i 1.09310 0.917221i
\(512\) 3.03700e9i 0.0441942i
\(513\) −4.06221e10 + 3.88660e10i −0.586533 + 0.561177i
\(514\) −3.51877e10 −0.504126
\(515\) −1.08203e11 1.28951e11i −1.53819 1.83314i
\(516\) 4.92209e10 3.39275e10i 0.694306 0.478579i
\(517\) −1.71662e10 + 9.73543e10i −0.240277 + 1.36268i
\(518\) −1.44679e10 3.97503e10i −0.200950 0.552105i
\(519\) 2.01536e10 1.98590e10i 0.277769 0.273709i
\(520\) −1.12679e9 6.39035e9i −0.0154110 0.0874000i
\(521\) −1.23233e10 + 7.11489e9i −0.167254 + 0.0965644i −0.581291 0.813696i \(-0.697452\pi\)
0.414036 + 0.910260i \(0.364119\pi\)
\(522\) −6.15267e10 + 3.43245e10i −0.828669 + 0.462298i
\(523\) 6.23341e9 1.07966e10i 0.0833142 0.144304i −0.821357 0.570414i \(-0.806783\pi\)
0.904672 + 0.426109i \(0.140116\pi\)
\(524\) 1.20987e8 3.32409e8i 0.00160477 0.00440908i
\(525\) 5.66564e10 + 1.23873e11i 0.745781 + 1.63057i
\(526\) −7.14866e10 5.99844e10i −0.933860 0.783602i
\(527\) −1.28759e10 + 1.53449e10i −0.166930 + 0.198940i
\(528\) 1.55548e10 7.11437e9i 0.200138 0.0915379i
\(529\) 1.13650e11 + 4.13654e10i 1.45127 + 0.528220i
\(530\) −5.49686e10 3.17361e10i −0.696644 0.402208i
\(531\) 6.69629e10 1.12136e11i 0.842279 1.41049i
\(532\) 2.24436e10 + 3.88735e10i 0.280186 + 0.485296i
\(533\) −6.48973e9 + 1.14431e9i −0.0804114 + 0.0141787i
\(534\) −6.43402e10 6.52947e10i −0.791256 0.802995i
\(535\) 6.42765e10 2.33947e10i 0.784580 0.285564i
\(536\) 1.67609e10 + 2.95540e9i 0.203066 + 0.0358061i
\(537\) −7.93157e10 1.15069e11i −0.953810 1.38376i
\(538\) 9.96225e9 8.35932e9i 0.118913 0.0997796i
\(539\) 6.73301e10i 0.797727i
\(540\) 2.59446e10 + 5.90073e10i 0.305121 + 0.693954i
\(541\) 4.07466e10 0.475666 0.237833 0.971306i \(-0.423563\pi\)
0.237833 + 0.971306i \(0.423563\pi\)
\(542\) −1.25599e10 1.49683e10i −0.145542 0.173450i
\(543\) 5.96097e8 + 7.44434e9i 0.00685674 + 0.0856302i
\(544\) 2.69803e9 1.53013e10i 0.0308071 0.174716i
\(545\) 5.27035e10 + 1.44802e11i 0.597384 + 1.64130i
\(546\) −1.38477e10 3.81998e9i −0.155814 0.0429824i
\(547\) 1.05717e10 + 5.99554e10i 0.118086 + 0.669697i 0.985176 + 0.171546i \(0.0548764\pi\)
−0.867090 + 0.498151i \(0.834013\pi\)
\(548\) −4.57614e10 + 2.64203e10i −0.507431 + 0.292965i
\(549\) −1.63653e10 + 1.89301e10i −0.180150 + 0.208384i
\(550\) −3.69868e10 + 6.40631e10i −0.404200 + 0.700095i
\(551\) 3.43413e10 9.43520e10i 0.372572 1.02363i
\(552\) −5.21264e10 4.94747e9i −0.561437 0.0532877i
\(553\) −4.84220e10 4.06308e10i −0.517776 0.434466i
\(554\) −2.11690e10 + 2.52282e10i −0.224730 + 0.267823i
\(555\) 7.05485e10 + 5.01768e10i 0.743560 + 0.528848i
\(556\) 6.69599e10 + 2.43714e10i 0.700673 + 0.255024i
\(557\) 3.52293e10 + 2.03397e10i 0.366002 + 0.211312i 0.671711 0.740814i \(-0.265560\pi\)
−0.305708 + 0.952125i \(0.598893\pi\)
\(558\) −1.65782e10 6.31197e9i −0.171002 0.0651070i
\(559\) −1.36325e10 2.36123e10i −0.139614 0.241819i
\(560\) 5.06835e10 8.93686e9i 0.515364 0.0908726i
\(561\) 8.46899e10 2.20255e10i 0.855028 0.222370i
\(562\) 9.39520e10 3.41957e10i 0.941805 0.342789i
\(563\) 6.96009e10 + 1.22725e10i 0.692758 + 0.122152i 0.508932 0.860807i \(-0.330041\pi\)
0.183826 + 0.982959i \(0.441152\pi\)
\(564\) −3.41375e10 + 7.18226e10i −0.337377 + 0.709814i
\(565\) −1.76648e11 + 1.48226e11i −1.73347 + 1.45455i
\(566\) 1.19825e11i 1.16756i
\(567\) 1.42635e11 + 4.20217e9i 1.38005 + 0.0406575i
\(568\) −6.87938e10 −0.660931
\(569\) −1.74408e10 2.07852e10i −0.166387 0.198292i 0.676408 0.736527i \(-0.263536\pi\)
−0.842795 + 0.538235i \(0.819091\pi\)
\(570\) −8.29694e10 3.94356e10i −0.785993 0.373585i
\(571\) −1.06697e10 + 6.05109e10i −0.100371 + 0.569231i 0.892598 + 0.450854i \(0.148880\pi\)
−0.992969 + 0.118378i \(0.962231\pi\)
\(572\) −2.66813e9 7.33064e9i −0.0249243 0.0684790i
\(573\) −3.43500e10 1.32078e11i −0.318646 1.22522i
\(574\) −9.07584e9 5.14716e10i −0.0836063 0.474155i
\(575\) 1.96110e11 1.13224e11i 1.79403 1.03578i
\(576\) 1.35841e10 2.18950e9i 0.123407 0.0198909i
\(577\) 7.61788e10 1.31946e11i 0.687275 1.19040i −0.285441 0.958396i \(-0.592140\pi\)
0.972716 0.231999i \(-0.0745268\pi\)
\(578\) 1.94045e8 5.33134e8i 0.00173856 0.00477667i
\(579\) 1.52960e10 2.15062e10i 0.136102 0.191360i
\(580\) −8.81884e10 7.39989e10i −0.779291 0.653903i
\(581\) −2.26129e10 + 2.69490e10i −0.198450 + 0.236504i
\(582\) −6.21662e9 + 6.54981e10i −0.0541829 + 0.570869i
\(583\) −7.17054e10 2.60986e10i −0.620695 0.225914i
\(584\) 3.68096e10 + 2.12520e10i 0.316453 + 0.182704i
\(585\) 2.77708e10 9.64706e9i 0.237118 0.0823704i
\(586\) 4.21421e10 + 7.29923e10i 0.357376 + 0.618994i
\(587\) −5.69471e10 + 1.00413e10i −0.479644 + 0.0845742i −0.408243 0.912873i \(-0.633858\pi\)
−0.0714015 + 0.997448i \(0.522747\pi\)
\(588\) 1.44031e10 5.22121e10i 0.120488 0.436779i
\(589\) 2.37565e10 8.64665e9i 0.197388 0.0718434i
\(590\) 2.10174e11 + 3.70593e10i 1.73448 + 0.305836i
\(591\) −7.18875e10 + 5.75631e9i −0.589255 + 0.0471839i
\(592\) 1.41563e10 1.18785e10i 0.115256 0.0967110i
\(593\) 1.93247e11i 1.56277i 0.624052 + 0.781383i \(0.285485\pi\)
−0.624052 + 0.781383i \(0.714515\pi\)
\(594\) 4.30357e10 + 6.44456e10i 0.345687 + 0.517663i
\(595\) 2.63297e11 2.10077
\(596\) 4.52626e10 + 5.39419e10i 0.358719 + 0.427505i
\(597\) −6.98899e10 + 4.81744e10i −0.550196 + 0.379245i
\(598\) −4.14685e9 + 2.35180e10i −0.0324275 + 0.183906i
\(599\) 6.51126e10 + 1.78895e11i 0.505776 + 1.38961i 0.885557 + 0.464531i \(0.153777\pi\)
−0.379781 + 0.925076i \(0.624001\pi\)
\(600\) −4.23862e10 + 4.17665e10i −0.327054 + 0.322273i
\(601\) −3.25149e10 1.84401e11i −0.249221 1.41340i −0.810482 0.585764i \(-0.800795\pi\)
0.561261 0.827639i \(-0.310316\pi\)
\(602\) 1.87275e11 1.08123e11i 1.42591 0.823251i
\(603\) −1.13547e9 + 7.70999e10i −0.00858830 + 0.583156i
\(604\) −2.13197e10 + 3.69267e10i −0.160189 + 0.277455i
\(605\) 1.56348e10 4.29562e10i 0.116700 0.320630i
\(606\) −2.19871e10 4.80725e10i −0.163034 0.356456i
\(607\) −6.17735e10 5.18342e10i −0.455038 0.381822i 0.386263 0.922389i \(-0.373766\pi\)
−0.841301 + 0.540566i \(0.818210\pi\)
\(608\) −1.26046e10 + 1.50216e10i −0.0922393 + 0.109926i
\(609\) −2.31761e11 + 1.06001e11i −1.68489 + 0.770624i
\(610\) −3.84227e10 1.39847e10i −0.277504 0.101003i
\(611\) 3.14098e10 + 1.81344e10i 0.225372 + 0.130119i
\(612\) 7.03856e10 + 1.03659e9i 0.501740 + 0.00738926i
\(613\) 6.21449e10 + 1.07638e11i 0.440113 + 0.762298i 0.997697 0.0678225i \(-0.0216051\pi\)
−0.557585 + 0.830120i \(0.688272\pi\)
\(614\) 1.47831e11 2.60666e10i 1.04014 0.183405i
\(615\) 7.50767e10 + 7.61905e10i 0.524813 + 0.532599i
\(616\) 5.81411e10 2.11616e10i 0.403794 0.146969i
\(617\) 5.54761e10 + 9.78193e9i 0.382794 + 0.0674969i 0.361734 0.932281i \(-0.382185\pi\)
0.0210600 + 0.999778i \(0.493296\pi\)
\(618\) −9.23910e10 1.34038e11i −0.633397 0.918911i
\(619\) −1.22382e11 + 1.02691e11i −0.833595 + 0.699469i −0.956113 0.292997i \(-0.905347\pi\)
0.122518 + 0.992466i \(0.460903\pi\)
\(620\) 2.89860e10i 0.196165i
\(621\) −1.54507e10 2.36721e11i −0.103892 1.59173i
\(622\) 1.06798e11 0.713512
\(623\) −2.13143e11 2.54014e11i −1.41488 1.68619i
\(624\) −5.00894e8 6.25540e9i −0.00330375 0.0412588i
\(625\) −1.62185e10 + 9.19798e10i −0.106290 + 0.602799i
\(626\) −5.51634e10 1.51560e11i −0.359214 0.986934i
\(627\) −1.06464e11 2.93689e10i −0.688866 0.190028i
\(628\) 1.17942e10 + 6.68883e10i 0.0758281 + 0.430043i
\(629\) 8.18761e10 4.72712e10i 0.523063 0.301991i
\(630\) 7.65132e10 + 2.20257e11i 0.485707 + 1.39820i
\(631\) 2.29584e10 3.97651e10i 0.144818 0.250833i −0.784487 0.620146i \(-0.787074\pi\)
0.929305 + 0.369313i \(0.120407\pi\)
\(632\) 9.44453e9 2.59486e10i 0.0591987 0.162647i
\(633\) −2.34733e11 2.22792e10i −1.46204 0.138767i
\(634\) −1.20294e11 1.00939e11i −0.744541 0.624744i
\(635\) 9.49587e10 1.13167e11i 0.584036 0.696027i
\(636\) −5.00221e10 3.55776e10i −0.305726 0.217444i
\(637\) −2.32127e10 8.44874e9i −0.140983 0.0513138i
\(638\) −1.19859e11 6.92007e10i −0.723416 0.417664i
\(639\) −4.95963e10 3.07706e11i −0.297472 1.84558i
\(640\) 1.12415e10 + 1.94709e10i 0.0670047 + 0.116055i
\(641\) 9.70170e10 1.71067e10i 0.574667 0.101329i 0.121241 0.992623i \(-0.461313\pi\)
0.453426 + 0.891294i \(0.350202\pi\)
\(642\) 6.40213e10 1.66502e10i 0.376864 0.0980120i
\(643\) 7.48494e10 2.72430e10i 0.437869 0.159371i −0.113673 0.993518i \(-0.536262\pi\)
0.551542 + 0.834147i \(0.314039\pi\)
\(644\) −1.86527e11 3.28897e10i −1.08442 0.191213i
\(645\) −1.89983e11 + 3.99709e11i −1.09768 + 2.30943i
\(646\) −7.68507e10 + 6.44854e10i −0.441284 + 0.370281i
\(647\) 1.99611e11i 1.13912i 0.821951 + 0.569558i \(0.192885\pi\)
−0.821951 + 0.569558i \(0.807115\pi\)
\(648\) 1.95867e10 + 5.91813e10i 0.111086 + 0.335648i
\(649\) 2.56572e11 1.44621
\(650\) 1.74452e10 + 2.07904e10i 0.0977287 + 0.116469i
\(651\) −5.79547e10 2.75460e10i −0.322675 0.153368i
\(652\) −4.85550e9 + 2.75369e10i −0.0268685 + 0.152379i
\(653\) 9.21369e10 + 2.53144e11i 0.506735 + 1.39224i 0.884586 + 0.466377i \(0.154441\pi\)
−0.377851 + 0.925866i \(0.623337\pi\)
\(654\) 3.75095e10 + 1.44227e11i 0.205036 + 0.788379i
\(655\) 4.54744e8 + 2.57898e9i 0.00247060 + 0.0140115i
\(656\) 1.97737e10 1.14163e10i 0.106776 0.0616469i
\(657\) −6.85199e10 + 1.79966e11i −0.367752 + 0.965892i
\(658\) −1.43829e11 + 2.49119e11i −0.767259 + 1.32893i
\(659\) 3.86871e10 1.06292e11i 0.205128 0.563585i −0.793882 0.608072i \(-0.791943\pi\)
0.999010 + 0.0444873i \(0.0141654\pi\)
\(660\) −7.33914e10 + 1.03188e11i −0.386785 + 0.543819i
\(661\) −8.94986e10 7.50982e10i −0.468825 0.393391i 0.377541 0.925993i \(-0.376770\pi\)
−0.846366 + 0.532602i \(0.821214\pi\)
\(662\) −1.24273e11 + 1.48102e11i −0.647058 + 0.771134i
\(663\) 3.03356e9 3.19615e10i 0.0157000 0.165414i
\(664\) −1.44416e10 5.25630e9i −0.0742921 0.0270401i
\(665\) −2.87782e11 1.66151e11i −1.47156 0.849603i
\(666\) 6.33369e10 + 5.47554e10i 0.321929 + 0.278311i
\(667\) 2.11837e11 + 3.66913e11i 1.07028 + 1.85379i
\(668\) 4.45383e10 7.85331e9i 0.223680 0.0394409i
\(669\) 8.21164e10 2.97678e11i 0.409945 1.48608i
\(670\) −1.18397e11 + 4.30931e10i −0.587547 + 0.213850i
\(671\) −4.84101e10 8.53601e9i −0.238807 0.0421080i
\(672\) 4.96132e10 3.97272e9i 0.243287 0.0194810i
\(673\) −1.15841e11 + 9.72020e10i −0.564679 + 0.473822i −0.879875 0.475205i \(-0.842374\pi\)
0.315197 + 0.949026i \(0.397930\pi\)
\(674\) 9.56575e10i 0.463532i
\(675\) −2.17374e11 1.59476e11i −1.04711 0.768212i
\(676\) 1.01551e11 0.486294
\(677\) −7.17163e10 8.54682e10i −0.341400 0.406865i 0.567839 0.823140i \(-0.307780\pi\)
−0.909239 + 0.416275i \(0.863335\pi\)
\(678\) −1.83616e11 + 1.26565e11i −0.868946 + 0.598956i
\(679\) −4.13267e10 + 2.34375e11i −0.194425 + 1.10264i
\(680\) 3.93403e10 + 1.08087e11i 0.183993 + 0.505518i
\(681\) −8.85101e10 + 8.72162e10i −0.411533 + 0.405517i
\(682\) −6.05120e9 3.43181e10i −0.0279707 0.158630i
\(683\) 7.31022e10 4.22056e10i 0.335929 0.193949i −0.322541 0.946555i \(-0.604537\pi\)
0.658470 + 0.752607i \(0.271204\pi\)
\(684\) −7.62769e10 4.55491e10i −0.348472 0.208092i
\(685\) 1.95591e11 3.38773e11i 0.888354 1.53867i
\(686\) −6.93718e9 + 1.90598e10i −0.0313247 + 0.0860639i
\(687\) −5.85779e10 1.28074e11i −0.262970 0.574957i
\(688\) 7.23673e10 + 6.07234e10i 0.322990 + 0.271021i
\(689\) −1.79955e10 + 2.14462e10i −0.0798523 + 0.0951643i
\(690\) 3.52507e11 1.61227e11i 1.55515 0.711283i
\(691\) 4.92393e10 + 1.79216e10i 0.215973 + 0.0786078i 0.447741 0.894163i \(-0.352229\pi\)
−0.231768 + 0.972771i \(0.574451\pi\)
\(692\) 3.87213e10 + 2.23557e10i 0.168859 + 0.0974911i
\(693\) 1.36569e11 + 2.44801e11i 0.592135 + 1.06140i
\(694\) −1.19863e11 2.07608e11i −0.516709 0.894967i
\(695\) −5.19506e11 + 9.16029e10i −2.22665 + 0.392618i
\(696\) −7.81432e10 7.93025e10i −0.333008 0.337948i
\(697\) 1.09767e11 3.99521e10i 0.465096 0.169281i
\(698\) −1.96499e11 3.46480e10i −0.827824 0.145968i
\(699\) −1.26211e11 1.83102e11i −0.528674 0.766983i
\(700\) −1.64893e11 + 1.38362e11i −0.686770 + 0.576268i
\(701\) 2.75159e11i 1.13949i −0.821820 0.569747i \(-0.807041\pi\)
0.821820 0.569747i \(-0.192959\pi\)
\(702\) 2.76185e10 6.75021e9i 0.113724 0.0277952i
\(703\) −1.19320e11 −0.488530
\(704\) 1.73742e10 + 2.07058e10i 0.0707317 + 0.0842948i
\(705\) −4.69898e10 5.86831e11i −0.190216 2.37551i
\(706\) 1.34912e10 7.65123e10i 0.0543039 0.307973i
\(707\) −6.54004e10 1.79686e11i −0.261760 0.719179i
\(708\) 1.98962e11 + 5.48851e10i 0.791841 + 0.218435i
\(709\) 7.40731e10 + 4.20089e11i 0.293140 + 1.66248i 0.674666 + 0.738123i \(0.264287\pi\)
−0.381526 + 0.924358i \(0.624601\pi\)
\(710\) 4.41052e11 2.54642e11i 1.73563 1.00207i
\(711\) 1.22874e11 + 2.35367e10i 0.480818 + 0.0921014i
\(712\) 7.24292e10 1.25451e11i 0.281834 0.488151i
\(713\) −3.64851e10 + 1.00242e11i −0.141175 + 0.387875i
\(714\) 2.53494e11 + 2.40599e10i 0.975384 + 0.0925767i
\(715\) 4.42405e10 + 3.71222e10i 0.169276 + 0.142040i
\(716\) 1.41959e11 1.69180e11i 0.540146 0.643720i
\(717\) −9.09988e10 6.47218e10i −0.344317 0.244892i
\(718\) 3.11578e11 + 1.13405e11i 1.17238 + 0.426713i
\(719\) −1.10896e11 6.40257e10i −0.414953 0.239573i 0.277962 0.960592i \(-0.410341\pi\)
−0.692916 + 0.721018i \(0.743674\pi\)
\(720\) −7.89861e10 + 6.43191e10i −0.293914 + 0.239337i
\(721\) −2.94440e11 5.09984e11i −1.08957 1.88719i
\(722\) −6.45379e10 + 1.13798e10i −0.237501 + 0.0418779i
\(723\) 3.03350e11 7.88930e10i 1.11017 0.288726i
\(724\) −1.10898e10 + 4.03637e9i −0.0403618 + 0.0146905i
\(725\) 4.74181e11 + 8.36109e10i 1.71629 + 0.302629i
\(726\) 1.89780e10 3.99283e10i 0.0683132 0.143726i
\(727\) 9.78348e10 8.20931e10i 0.350232 0.293879i −0.450651 0.892700i \(-0.648808\pi\)
0.800883 + 0.598821i \(0.204364\pi\)
\(728\) 2.27001e10i 0.0808170i
\(729\) −2.50589e11 + 1.30275e11i −0.887263 + 0.461265i
\(730\) −3.14659e11 −1.10802
\(731\) 3.10661e11 + 3.70232e11i 1.08797 + 1.29659i
\(732\) −3.57143e10 1.69751e10i −0.124394 0.0591246i
\(733\) −5.08699e9 + 2.88498e10i −0.0176216 + 0.0999370i −0.992350 0.123456i \(-0.960602\pi\)
0.974728 + 0.223393i \(0.0717133\pi\)
\(734\) 7.89409e10 + 2.16888e11i 0.271968 + 0.747226i
\(735\) 1.00923e11 + 3.88056e11i 0.345812 + 1.32967i
\(736\) −1.43681e10 8.14857e10i −0.0489653 0.277696i
\(737\) −1.31180e11 + 7.57371e10i −0.444631 + 0.256708i
\(738\) 6.53194e10 + 8.02145e10i 0.220200 + 0.270413i
\(739\) −1.50049e11 + 2.59892e11i −0.503100 + 0.871395i 0.496893 + 0.867812i \(0.334474\pi\)
−0.999994 + 0.00358360i \(0.998859\pi\)
\(740\) −4.67904e10 + 1.28556e11i −0.156038 + 0.428711i
\(741\) −2.34846e10 + 3.30194e10i −0.0778952 + 0.109521i
\(742\) −1.70095e11 1.42727e11i −0.561147 0.470858i
\(743\) −3.18238e11 + 3.79262e11i −1.04423 + 1.24447i −0.0752947 + 0.997161i \(0.523990\pi\)
−0.968937 + 0.247306i \(0.920455\pi\)
\(744\) 2.64873e9 2.79069e10i 0.00864461 0.0910792i
\(745\) −4.89856e11 1.78293e11i −1.59017 0.578774i
\(746\) 1.34495e11 + 7.76509e10i 0.434262 + 0.250721i
\(747\) 1.30992e10 6.83847e10i 0.0420690 0.219622i
\(748\) 6.91415e10 + 1.19757e11i 0.220868 + 0.382554i
\(749\) 2.35653e11 4.15520e10i 0.748765 0.132027i
\(750\) 2.69430e10 9.76701e10i 0.0851530 0.308686i
\(751\) −3.97259e10 + 1.44590e10i −0.124886 + 0.0454548i −0.403707 0.914888i \(-0.632279\pi\)
0.278821 + 0.960343i \(0.410056\pi\)
\(752\) −1.23756e11 2.18216e10i −0.386987 0.0682362i
\(753\) −2.81172e11 + 2.25145e10i −0.874565 + 0.0700297i
\(754\) −3.88978e10 + 3.26391e10i −0.120348 + 0.100984i
\(755\) 3.15661e11i 0.971477i