Properties

Label 16.28.e.a.13.18
Level $16$
Weight $28$
Character 16.13
Analytic conductor $73.897$
Analytic rank $0$
Dimension $106$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,28,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 28, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 28);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), 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: \(73.8968919741\)
Analytic rank: \(0\)
Dimension: \(106\)
Relative dimension: \(53\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.18
Character \(\chi\) \(=\) 16.13
Dual form 16.28.e.a.5.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5041.21 + 10430.9i) q^{2} +(-329571. - 329571. i) q^{3} +(-8.33902e7 - 1.05169e8i) q^{4} +(-2.69387e8 + 2.69387e8i) q^{5} +(5.09916e9 - 1.77629e9i) q^{6} +2.71695e11i q^{7} +(1.51739e12 - 3.39659e11i) q^{8} -7.40836e12i q^{9} +O(q^{10})\) \(q+(-5041.21 + 10430.9i) q^{2} +(-329571. - 329571. i) q^{3} +(-8.33902e7 - 1.05169e8i) q^{4} +(-2.69387e8 + 2.69387e8i) q^{5} +(5.09916e9 - 1.77629e9i) q^{6} +2.71695e11i q^{7} +(1.51739e12 - 3.39659e11i) q^{8} -7.40836e12i q^{9} +(-1.45192e12 - 4.16799e12i) q^{10} +(2.66489e13 - 2.66489e13i) q^{11} +(-7.17757e12 + 6.21435e13i) q^{12} +(-4.16447e14 - 4.16447e14i) q^{13} +(-2.83402e15 - 1.36967e15i) q^{14} +1.77564e14 q^{15} +(-4.10654e15 + 1.75401e16i) q^{16} +2.48650e16 q^{17} +(7.72760e16 + 3.73471e16i) q^{18} +(3.21749e16 + 3.21749e16i) q^{19} +(5.07954e16 + 5.86686e15i) q^{20} +(8.95425e16 - 8.95425e16i) q^{21} +(1.43630e17 + 4.12316e17i) q^{22} +1.49823e18i q^{23} +(-6.12030e17 - 3.88147e17i) q^{24} +7.30544e18i q^{25} +(6.44332e18 - 2.24453e18i) q^{26} +(-4.95475e18 + 4.95475e18i) q^{27} +(2.85738e19 - 2.26567e19i) q^{28} +(8.47986e18 + 8.47986e18i) q^{29} +(-8.95138e17 + 1.85216e18i) q^{30} -1.32940e20 q^{31} +(-1.62257e20 - 1.31258e20i) q^{32} -1.75654e19 q^{33} +(-1.25350e20 + 2.59365e20i) q^{34} +(-7.31910e19 - 7.31910e19i) q^{35} +(-7.79128e20 + 6.17785e20i) q^{36} +(7.33132e20 - 7.33132e20i) q^{37} +(-4.97815e20 + 1.73414e20i) q^{38} +2.74498e20i q^{39} +(-3.17267e20 + 5.00266e20i) q^{40} -9.82451e20i q^{41} +(4.82608e20 + 1.38541e21i) q^{42} +(-1.30008e22 + 1.30008e22i) q^{43} +(-5.02490e21 - 5.80375e20i) q^{44} +(1.99572e21 + 1.99572e21i) q^{45} +(-1.56279e22 - 7.55286e21i) q^{46} -4.26559e22 q^{47} +(7.13409e21 - 4.42730e21i) q^{48} -8.10557e21 q^{49} +(-7.62024e22 - 3.68282e22i) q^{50} +(-8.19477e21 - 8.19477e21i) q^{51} +(-9.06962e21 + 7.85249e22i) q^{52} +(1.05894e23 - 1.05894e23i) q^{53} +(-2.67047e22 - 7.66605e22i) q^{54} +1.43578e22i q^{55} +(9.22835e22 + 4.12268e23i) q^{56} -2.12078e22i q^{57} +(-1.31201e23 + 4.57040e22i) q^{58} +(2.50600e23 - 2.50600e23i) q^{59} +(-1.48071e22 - 1.86742e22i) q^{60} +(2.69362e23 + 2.69362e23i) q^{61} +(6.70177e23 - 1.38668e24i) q^{62} +2.01281e24 q^{63} +(2.18712e24 - 1.03079e24i) q^{64} +2.24371e23 q^{65} +(8.85509e22 - 1.83223e23i) q^{66} +(-1.96312e24 - 1.96312e24i) q^{67} +(-2.07350e24 - 2.61502e24i) q^{68} +(4.93771e23 - 4.93771e23i) q^{69} +(1.13242e24 - 3.94478e23i) q^{70} -3.69903e24i q^{71} +(-2.51632e24 - 1.12414e25i) q^{72} -1.22287e25i q^{73} +(3.95137e24 + 1.13431e25i) q^{74} +(2.40766e24 - 2.40766e24i) q^{75} +(7.00724e23 - 6.06688e24i) q^{76} +(7.24037e24 + 7.24037e24i) q^{77} +(-2.86326e24 - 1.38380e24i) q^{78} +3.63425e25 q^{79} +(-3.61883e24 - 5.83133e24i) q^{80} -5.32273e25 q^{81} +(1.02479e25 + 4.95274e24i) q^{82} +(-8.16524e25 - 8.16524e25i) q^{83} +(-1.68840e25 - 1.95011e24i) q^{84} +(-6.69831e24 + 6.69831e24i) q^{85} +(-7.00708e25 - 2.01151e26i) q^{86} -5.58942e24i q^{87} +(3.13854e25 - 4.94885e25i) q^{88} -2.68126e26i q^{89} +(-3.08780e25 + 1.07563e25i) q^{90} +(1.13146e26 - 1.13146e26i) q^{91} +(1.57567e26 - 1.24937e26i) q^{92} +(4.38131e25 + 4.38131e25i) q^{93} +(2.15037e26 - 4.44940e26i) q^{94} -1.73350e25 q^{95} +(1.02164e25 + 9.67341e25i) q^{96} +1.84751e25 q^{97} +(4.08618e25 - 8.45485e25i) q^{98} +(-1.97425e26 - 1.97425e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5041.21 + 10430.9i −0.435140 + 0.900363i
\(3\) −329571. 329571.i −0.119347 0.119347i 0.644911 0.764258i \(-0.276894\pi\)
−0.764258 + 0.644911i \(0.776894\pi\)
\(4\) −8.33902e7 1.05169e8i −0.621306 0.783568i
\(5\) −2.69387e8 + 2.69387e8i −0.0986920 + 0.0986920i −0.754729 0.656037i \(-0.772232\pi\)
0.656037 + 0.754729i \(0.272232\pi\)
\(6\) 5.09916e9 1.77629e9i 0.159388 0.0555229i
\(7\) 2.71695e11i 1.05988i 0.848035 + 0.529941i \(0.177786\pi\)
−0.848035 + 0.529941i \(0.822214\pi\)
\(8\) 1.51739e12 3.39659e11i 0.975851 0.218438i
\(9\) 7.40836e12i 0.971513i
\(10\) −1.45192e12 4.16799e12i −0.0459137 0.131803i
\(11\) 2.66489e13 2.66489e13i 0.232744 0.232744i −0.581093 0.813837i \(-0.697375\pi\)
0.813837 + 0.581093i \(0.197375\pi\)
\(12\) −7.17757e12 + 6.21435e13i −0.0193656 + 0.167667i
\(13\) −4.16447e14 4.16447e14i −0.381351 0.381351i 0.490238 0.871589i \(-0.336910\pi\)
−0.871589 + 0.490238i \(0.836910\pi\)
\(14\) −2.83402e15 1.36967e15i −0.954278 0.461197i
\(15\) 1.77564e14 0.0235572
\(16\) −4.10654e15 + 1.75401e16i −0.227959 + 0.973671i
\(17\) 2.48650e16 0.608875 0.304437 0.952532i \(-0.401532\pi\)
0.304437 + 0.952532i \(0.401532\pi\)
\(18\) 7.72760e16 + 3.73471e16i 0.874714 + 0.422744i
\(19\) 3.21749e16 + 3.21749e16i 0.175527 + 0.175527i 0.789403 0.613876i \(-0.210390\pi\)
−0.613876 + 0.789403i \(0.710390\pi\)
\(20\) 5.07954e16 + 5.86686e15i 0.138650 + 0.0160140i
\(21\) 8.95425e16 8.95425e16i 0.126494 0.126494i
\(22\) 1.43630e17 + 4.12316e17i 0.108278 + 0.310830i
\(23\) 1.49823e18i 0.619800i 0.950769 + 0.309900i \(0.100296\pi\)
−0.950769 + 0.309900i \(0.899704\pi\)
\(24\) −6.12030e17 3.88147e17i −0.142535 0.0903949i
\(25\) 7.30544e18i 0.980520i
\(26\) 6.44332e18 2.24453e18i 0.509295 0.177413i
\(27\) −4.95475e18 + 4.95475e18i −0.235294 + 0.235294i
\(28\) 2.85738e19 2.26567e19i 0.830490 0.658510i
\(29\) 8.47986e18 + 8.47986e18i 0.153467 + 0.153467i 0.779665 0.626197i \(-0.215390\pi\)
−0.626197 + 0.779665i \(0.715390\pi\)
\(30\) −8.95138e17 + 1.85216e18i −0.0102507 + 0.0212100i
\(31\) −1.32940e20 −0.977851 −0.488925 0.872326i \(-0.662611\pi\)
−0.488925 + 0.872326i \(0.662611\pi\)
\(32\) −1.62257e20 1.31258e20i −0.777463 0.628929i
\(33\) −1.75654e19 −0.0555546
\(34\) −1.25350e20 + 2.59365e20i −0.264946 + 0.548208i
\(35\) −7.31910e19 7.31910e19i −0.104602 0.104602i
\(36\) −7.79128e20 + 6.17785e20i −0.761247 + 0.603606i
\(37\) 7.33132e20 7.33132e20i 0.494833 0.494833i −0.414992 0.909825i \(-0.636216\pi\)
0.909825 + 0.414992i \(0.136216\pi\)
\(38\) −4.97815e20 + 1.73414e20i −0.234417 + 0.0816591i
\(39\) 2.74498e20i 0.0910262i
\(40\) −3.17267e20 + 5.00266e20i −0.0747506 + 0.117867i
\(41\) 9.82451e20i 0.165855i −0.996556 0.0829276i \(-0.973573\pi\)
0.996556 0.0829276i \(-0.0264270\pi\)
\(42\) 4.82608e20 + 1.38541e21i 0.0588477 + 0.168933i
\(43\) −1.30008e22 + 1.30008e22i −1.15385 + 1.15385i −0.168070 + 0.985775i \(0.553753\pi\)
−0.985775 + 0.168070i \(0.946247\pi\)
\(44\) −5.02490e21 5.80375e20i −0.326976 0.0377657i
\(45\) 1.99572e21 + 1.99572e21i 0.0958805 + 0.0958805i
\(46\) −1.56279e22 7.55286e21i −0.558044 0.269700i
\(47\) −4.26559e22 −1.13935 −0.569676 0.821869i \(-0.692931\pi\)
−0.569676 + 0.821869i \(0.692931\pi\)
\(48\) 7.13409e21 4.42730e21i 0.143411 0.0889985i
\(49\) −8.10557e21 −0.123349
\(50\) −7.62024e22 3.68282e22i −0.882823 0.426664i
\(51\) −8.19477e21 8.19477e21i −0.0726674 0.0726674i
\(52\) −9.06962e21 + 7.85249e22i −0.0618791 + 0.535750i
\(53\) 1.05894e23 1.05894e23i 0.558658 0.558658i −0.370267 0.928925i \(-0.620734\pi\)
0.928925 + 0.370267i \(0.120734\pi\)
\(54\) −2.67047e22 7.66605e22i −0.109464 0.314236i
\(55\) 1.43578e22i 0.0459400i
\(56\) 9.22835e22 + 4.12268e23i 0.231518 + 1.03429i
\(57\) 2.12078e22i 0.0418973i
\(58\) −1.31201e23 + 4.57040e22i −0.204956 + 0.0713964i
\(59\) 2.50600e23 2.50600e23i 0.310799 0.310799i −0.534420 0.845219i \(-0.679470\pi\)
0.845219 + 0.534420i \(0.179470\pi\)
\(60\) −1.48071e22 1.86742e22i −0.0146362 0.0184587i
\(61\) 2.69362e23 + 2.69362e23i 0.213002 + 0.213002i 0.805541 0.592540i \(-0.201875\pi\)
−0.592540 + 0.805541i \(0.701875\pi\)
\(62\) 6.70177e23 1.38668e24i 0.425502 0.880420i
\(63\) 2.01281e24 1.02969
\(64\) 2.18712e24 1.03079e24i 0.904570 0.426326i
\(65\) 2.24371e23 0.0752726
\(66\) 8.85509e22 1.83223e23i 0.0241741 0.0500193i
\(67\) −1.96312e24 1.96312e24i −0.437458 0.437458i 0.453698 0.891156i \(-0.350105\pi\)
−0.891156 + 0.453698i \(0.850105\pi\)
\(68\) −2.07350e24 2.61502e24i −0.378297 0.477095i
\(69\) 4.93771e23 4.93771e23i 0.0739712 0.0739712i
\(70\) 1.13242e24 3.94478e23i 0.139696 0.0486631i
\(71\) 3.69903e24i 0.376791i −0.982093 0.188395i \(-0.939671\pi\)
0.982093 0.188395i \(-0.0603286\pi\)
\(72\) −2.51632e24 1.12414e25i −0.212215 0.948051i
\(73\) 1.22287e25i 0.856097i −0.903756 0.428049i \(-0.859201\pi\)
0.903756 0.428049i \(-0.140799\pi\)
\(74\) 3.95137e24 + 1.13431e25i 0.230207 + 0.660851i
\(75\) 2.40766e24 2.40766e24i 0.117022 0.117022i
\(76\) 7.00724e23 6.06688e24i 0.0284815 0.246593i
\(77\) 7.24037e24 + 7.24037e24i 0.246681 + 0.246681i
\(78\) −2.86326e24 1.38380e24i −0.0819566 0.0396092i
\(79\) 3.63425e25 0.875889 0.437944 0.899002i \(-0.355707\pi\)
0.437944 + 0.899002i \(0.355707\pi\)
\(80\) −3.61883e24 5.83133e24i −0.0735958 0.118591i
\(81\) −5.32273e25 −0.915349
\(82\) 1.02479e25 + 4.95274e24i 0.149330 + 0.0721703i
\(83\) −8.16524e25 8.16524e25i −1.01022 1.01022i −0.999947 0.0102696i \(-0.996731\pi\)
−0.0102696 0.999947i \(-0.503269\pi\)
\(84\) −1.68840e25 1.95011e24i −0.177708 0.0205252i
\(85\) −6.69831e24 + 6.69831e24i −0.0600911 + 0.0600911i
\(86\) −7.00708e25 2.01151e26i −0.536794 1.54096i
\(87\) 5.58942e24i 0.0366317i
\(88\) 3.13854e25 4.94885e25i 0.176283 0.277964i
\(89\) 2.68126e26i 1.29293i −0.762945 0.646463i \(-0.776247\pi\)
0.762945 0.646463i \(-0.223753\pi\)
\(90\) −3.08780e25 + 1.07563e25i −0.128049 + 0.0446057i
\(91\) 1.13146e26 1.13146e26i 0.404187 0.404187i
\(92\) 1.57567e26 1.24937e26i 0.485655 0.385085i
\(93\) 4.38131e25 + 4.38131e25i 0.116704 + 0.116704i
\(94\) 2.15037e26 4.44940e26i 0.495779 1.02583i
\(95\) −1.73350e25 −0.0346462
\(96\) 1.02164e25 + 9.67341e25i 0.0177270 + 0.167849i
\(97\) 1.84751e25 0.0278721 0.0139360 0.999903i \(-0.495564\pi\)
0.0139360 + 0.999903i \(0.495564\pi\)
\(98\) 4.08618e25 8.45485e25i 0.0536742 0.111059i
\(99\) −1.97425e26 1.97425e26i −0.226114 0.226114i
\(100\) 7.68304e26 6.09202e26i 0.768304 0.609202i
\(101\) 1.43550e27 1.43550e27i 1.25506 1.25506i 0.301637 0.953423i \(-0.402467\pi\)
0.953423 0.301637i \(-0.0975332\pi\)
\(102\) 1.26791e26 4.41674e25i 0.0970475 0.0338065i
\(103\) 4.16136e26i 0.279211i 0.990207 + 0.139606i \(0.0445835\pi\)
−0.990207 + 0.139606i \(0.955417\pi\)
\(104\) −7.73365e26 4.90465e26i −0.455443 0.288840i
\(105\) 4.82432e25i 0.0249678i
\(106\) 5.70736e26 + 1.63840e27i 0.259900 + 0.746089i
\(107\) 1.61351e27 1.61351e27i 0.647278 0.647278i −0.305056 0.952334i \(-0.598675\pi\)
0.952334 + 0.305056i \(0.0986753\pi\)
\(108\) 9.34263e26 + 1.07907e26i 0.330559 + 0.0381795i
\(109\) 8.78792e25 + 8.78792e25i 0.0274554 + 0.0274554i 0.720701 0.693246i \(-0.243820\pi\)
−0.693246 + 0.720701i \(0.743820\pi\)
\(110\) −1.49765e26 7.23805e25i −0.0413626 0.0199903i
\(111\) −4.83237e26 −0.118114
\(112\) −4.76555e27 1.11572e27i −1.03198 0.241609i
\(113\) −8.03820e27 −1.54383 −0.771916 0.635725i \(-0.780701\pi\)
−0.771916 + 0.635725i \(0.780701\pi\)
\(114\) 2.21217e26 + 1.06913e26i 0.0377227 + 0.0182312i
\(115\) −4.03603e26 4.03603e26i −0.0611693 0.0611693i
\(116\) 1.84679e26 1.59895e27i 0.0249020 0.215602i
\(117\) −3.08519e27 + 3.08519e27i −0.370487 + 0.370487i
\(118\) 1.35066e27 + 3.87732e27i 0.144590 + 0.415073i
\(119\) 6.75569e27i 0.645335i
\(120\) 2.69435e26 6.03113e25i 0.0229883 0.00514578i
\(121\) 1.16897e28i 0.891660i
\(122\) −4.16760e27 + 1.45178e27i −0.284465 + 0.0990931i
\(123\) −3.23787e26 + 3.23787e26i −0.0197943 + 0.0197943i
\(124\) 1.10859e28 + 1.39811e28i 0.607544 + 0.766213i
\(125\) −3.97508e27 3.97508e27i −0.195461 0.195461i
\(126\) −1.01470e28 + 2.09955e28i −0.448059 + 0.927093i
\(127\) −3.90825e27 −0.155107 −0.0775537 0.996988i \(-0.524711\pi\)
−0.0775537 + 0.996988i \(0.524711\pi\)
\(128\) −2.73589e26 + 2.80100e28i −0.00976706 + 0.999952i
\(129\) 8.56939e27 0.275416
\(130\) −1.13110e27 + 2.34040e27i −0.0327541 + 0.0677726i
\(131\) 9.69050e26 + 9.69050e26i 0.0253037 + 0.0253037i 0.719645 0.694342i \(-0.244304\pi\)
−0.694342 + 0.719645i \(0.744304\pi\)
\(132\) 1.46478e27 + 1.84733e27i 0.0345164 + 0.0435308i
\(133\) −8.74176e27 + 8.74176e27i −0.186038 + 0.186038i
\(134\) 3.03736e28 1.05806e28i 0.584227 0.203515i
\(135\) 2.66949e27i 0.0464433i
\(136\) 3.77300e28 8.44562e27i 0.594171 0.133001i
\(137\) 4.94336e28i 0.705172i −0.935779 0.352586i \(-0.885302\pi\)
0.935779 0.352586i \(-0.114698\pi\)
\(138\) 2.66128e27 + 7.63968e27i 0.0344131 + 0.0987888i
\(139\) −7.67653e28 + 7.67653e28i −0.900462 + 0.900462i −0.995476 0.0950144i \(-0.969710\pi\)
0.0950144 + 0.995476i \(0.469710\pi\)
\(140\) −1.59399e27 + 1.38008e28i −0.0169730 + 0.146952i
\(141\) 1.40581e28 + 1.40581e28i 0.135978 + 0.135978i
\(142\) 3.85843e28 + 1.86476e28i 0.339248 + 0.163957i
\(143\) −2.21958e28 −0.177514
\(144\) 1.29943e29 + 3.04227e28i 0.945933 + 0.221465i
\(145\) −4.56873e27 −0.0302920
\(146\) 1.27557e29 + 6.16476e28i 0.770798 + 0.372523i
\(147\) 2.67136e27 + 2.67136e27i 0.0147214 + 0.0147214i
\(148\) −1.38239e29 1.59665e28i −0.695178 0.0802930i
\(149\) −1.10859e29 + 1.10859e29i −0.509044 + 0.509044i −0.914233 0.405189i \(-0.867206\pi\)
0.405189 + 0.914233i \(0.367206\pi\)
\(150\) 1.29766e28 + 3.72516e28i 0.0544413 + 0.156283i
\(151\) 4.24881e29i 1.62959i −0.579750 0.814795i \(-0.696850\pi\)
0.579750 0.814795i \(-0.303150\pi\)
\(152\) 5.97506e28 + 3.78936e28i 0.209630 + 0.132946i
\(153\) 1.84209e29i 0.591530i
\(154\) −1.12024e29 + 3.90235e28i −0.329444 + 0.114762i
\(155\) 3.58123e28 3.58123e28i 0.0965060 0.0965060i
\(156\) 2.88686e28 2.28904e28i 0.0713252 0.0565551i
\(157\) −4.14338e29 4.14338e29i −0.939094 0.939094i 0.0591544 0.998249i \(-0.481160\pi\)
−0.998249 + 0.0591544i \(0.981160\pi\)
\(158\) −1.83210e29 + 3.79085e29i −0.381135 + 0.788617i
\(159\) −6.97989e28 −0.133348
\(160\) 7.90693e28 8.35077e27i 0.138800 0.0146591i
\(161\) −4.07060e29 −0.656914
\(162\) 2.68330e29 5.55210e29i 0.398306 0.824146i
\(163\) −5.13776e29 5.13776e29i −0.701845 0.701845i 0.262961 0.964806i \(-0.415301\pi\)
−0.964806 + 0.262961i \(0.915301\pi\)
\(164\) −1.03323e29 + 8.19268e28i −0.129959 + 0.103047i
\(165\) 4.73190e27 4.73190e27i 0.00548280 0.00548280i
\(166\) 1.26334e30 4.40083e29i 1.34915 0.469975i
\(167\) 8.93544e28i 0.0879921i −0.999032 0.0439960i \(-0.985991\pi\)
0.999032 0.0439960i \(-0.0140089\pi\)
\(168\) 1.05457e29 1.66285e29i 0.0958079 0.151070i
\(169\) 8.45676e29i 0.709143i
\(170\) −3.61020e28 1.03637e29i −0.0279557 0.0802518i
\(171\) 2.38364e29 2.38364e29i 0.170527 0.170527i
\(172\) 2.45143e30 + 2.83139e29i 1.62101 + 0.187226i
\(173\) −4.52209e29 4.52209e29i −0.276514 0.276514i 0.555202 0.831716i \(-0.312641\pi\)
−0.831716 + 0.555202i \(0.812641\pi\)
\(174\) 5.83028e28 + 2.81774e28i 0.0329818 + 0.0159399i
\(175\) −1.98485e30 −1.03923
\(176\) 3.57990e29 + 5.76860e29i 0.173560 + 0.279672i
\(177\) −1.65181e29 −0.0741858
\(178\) 2.79680e30 + 1.35168e30i 1.16410 + 0.562605i
\(179\) −1.97214e30 1.97214e30i −0.761064 0.761064i 0.215451 0.976515i \(-0.430878\pi\)
−0.976515 + 0.215451i \(0.930878\pi\)
\(180\) 4.34638e28 3.76311e29i 0.0155578 0.134700i
\(181\) 3.02766e30 3.02766e30i 1.00565 1.00565i 0.00566486 0.999984i \(-0.498197\pi\)
0.999984 0.00566486i \(-0.00180319\pi\)
\(182\) 6.09827e29 + 1.75062e30i 0.188037 + 0.539793i
\(183\) 1.77547e29i 0.0508422i
\(184\) 5.08886e29 + 2.27340e30i 0.135388 + 0.604832i
\(185\) 3.94993e29i 0.0976722i
\(186\) −6.77881e29 + 2.36140e29i −0.155858 + 0.0542931i
\(187\) 6.62626e29 6.62626e29i 0.141712 0.141712i
\(188\) 3.55709e30 + 4.48607e30i 0.707886 + 0.892761i
\(189\) −1.34618e30 1.34618e30i −0.249384 0.249384i
\(190\) 8.73895e28 1.80820e29i 0.0150760 0.0311942i
\(191\) −6.07002e30 −0.975528 −0.487764 0.872975i \(-0.662187\pi\)
−0.487764 + 0.872975i \(0.662187\pi\)
\(192\) −1.06053e30 3.81090e29i −0.158838 0.0570770i
\(193\) −1.28234e31 −1.79053 −0.895263 0.445538i \(-0.853012\pi\)
−0.895263 + 0.445538i \(0.853012\pi\)
\(194\) −9.31370e28 + 1.92713e29i −0.0121283 + 0.0250950i
\(195\) −7.39461e28 7.39461e28i −0.00898356 0.00898356i
\(196\) 6.75925e29 + 8.52452e29i 0.0766375 + 0.0966525i
\(197\) −9.66074e30 + 9.66074e30i −1.02262 + 1.02262i −0.0228865 + 0.999738i \(0.507286\pi\)
−0.999738 + 0.0228865i \(0.992714\pi\)
\(198\) 3.05458e30 1.06406e30i 0.301976 0.105193i
\(199\) 5.43325e30i 0.501814i 0.968011 + 0.250907i \(0.0807289\pi\)
−0.968011 + 0.250907i \(0.919271\pi\)
\(200\) 2.48136e30 + 1.10852e31i 0.214183 + 0.956841i
\(201\) 1.29397e30i 0.104419i
\(202\) 7.73692e30 + 2.22102e31i 0.583882 + 1.67614i
\(203\) −2.30393e30 + 2.30393e30i −0.162657 + 0.162657i
\(204\) −1.78470e29 + 1.54520e30i −0.0117912 + 0.102089i
\(205\) 2.64660e29 + 2.64660e29i 0.0163686 + 0.0163686i
\(206\) −4.34068e30 2.09783e30i −0.251391 0.121496i
\(207\) 1.10994e31 0.602143
\(208\) 9.01468e30 5.59437e30i 0.458243 0.284378i
\(209\) 1.71486e30 0.0817058
\(210\) −5.03221e29 2.43204e29i −0.0224801 0.0108645i
\(211\) −1.07638e31 1.07638e31i −0.450976 0.450976i 0.444702 0.895678i \(-0.353309\pi\)
−0.895678 + 0.444702i \(0.853309\pi\)
\(212\) −1.99672e31 2.30621e30i −0.784844 0.0906494i
\(213\) −1.21909e30 + 1.21909e30i −0.0449688 + 0.0449688i
\(214\) 8.69635e30 + 2.49644e31i 0.301128 + 0.864442i
\(215\) 7.00452e30i 0.227751i
\(216\) −5.83538e30 + 9.20123e30i −0.178215 + 0.281009i
\(217\) 3.61191e31i 1.03641i
\(218\) −1.35968e30 + 4.73643e29i −0.0366668 + 0.0127729i
\(219\) −4.03023e30 + 4.03023e30i −0.102173 + 0.102173i
\(220\) 1.50999e30 1.19730e30i 0.0359971 0.0285428i
\(221\) −1.03550e31 1.03550e31i −0.232195 0.232195i
\(222\) 2.43610e30 5.04061e30i 0.0513961 0.106345i
\(223\) −1.55403e31 −0.308563 −0.154281 0.988027i \(-0.549306\pi\)
−0.154281 + 0.988027i \(0.549306\pi\)
\(224\) 3.56621e31 4.40844e31i 0.666590 0.824018i
\(225\) 5.41214e31 0.952587
\(226\) 4.05222e31 8.38458e31i 0.671784 1.39001i
\(227\) 3.81035e31 + 3.81035e31i 0.595135 + 0.595135i 0.939014 0.343879i \(-0.111741\pi\)
−0.343879 + 0.939014i \(0.611741\pi\)
\(228\) −2.23040e30 + 1.76853e30i −0.0328294 + 0.0260310i
\(229\) 2.60208e31 2.60208e31i 0.361028 0.361028i −0.503163 0.864191i \(-0.667831\pi\)
0.864191 + 0.503163i \(0.167831\pi\)
\(230\) 6.24459e30 2.17530e30i 0.0816917 0.0284573i
\(231\) 4.77243e30i 0.0588813i
\(232\) 1.57475e31 + 9.98703e30i 0.183284 + 0.116238i
\(233\) 1.75984e31i 0.193272i 0.995320 + 0.0966358i \(0.0308082\pi\)
−0.995320 + 0.0966358i \(0.969192\pi\)
\(234\) −1.66283e31 4.77345e31i −0.172359 0.494787i
\(235\) 1.14910e31 1.14910e31i 0.112445 0.112445i
\(236\) −4.72529e31 5.45771e30i −0.436633 0.0504311i
\(237\) −1.19774e31 1.19774e31i −0.104535 0.104535i
\(238\) −7.04680e31 3.40568e31i −0.581036 0.280812i
\(239\) 4.27604e31 0.333173 0.166587 0.986027i \(-0.446725\pi\)
0.166587 + 0.986027i \(0.446725\pi\)
\(240\) −7.29174e29 + 3.11449e30i −0.00537007 + 0.0229369i
\(241\) −7.70917e31 −0.536757 −0.268379 0.963314i \(-0.586488\pi\)
−0.268379 + 0.963314i \(0.586488\pi\)
\(242\) −1.21934e32 5.89300e31i −0.802818 0.387997i
\(243\) 5.53251e31 + 5.53251e31i 0.344538 + 0.344538i
\(244\) 5.86631e30 5.07906e31i 0.0345623 0.299241i
\(245\) 2.18354e30 2.18354e30i 0.0121736 0.0121736i
\(246\) −1.74512e30 5.00967e30i −0.00920875 0.0264354i
\(247\) 2.67983e31i 0.133875i
\(248\) −2.01722e32 + 4.51542e31i −0.954236 + 0.213600i
\(249\) 5.38204e31i 0.241133i
\(250\) 6.15030e31 2.14245e31i 0.261039 0.0909330i
\(251\) 1.33650e32 1.33650e32i 0.537492 0.537492i −0.385299 0.922792i \(-0.625902\pi\)
0.922792 + 0.385299i \(0.125902\pi\)
\(252\) −1.67849e32 2.11685e32i −0.639751 0.806831i
\(253\) 3.99261e31 + 3.99261e31i 0.144255 + 0.144255i
\(254\) 1.97023e31 4.07667e31i 0.0674935 0.139653i
\(255\) 4.41513e30 0.0143434
\(256\) −2.90791e32 1.44058e32i −0.896070 0.443914i
\(257\) 1.37592e32 0.402249 0.201125 0.979566i \(-0.435540\pi\)
0.201125 + 0.979566i \(0.435540\pi\)
\(258\) −4.32001e31 + 8.93866e31i −0.119845 + 0.247974i
\(259\) 1.99188e32 + 1.99188e32i 0.524465 + 0.524465i
\(260\) −1.87104e31 2.35968e31i −0.0467673 0.0589812i
\(261\) 6.28219e31 6.28219e31i 0.149095 0.149095i
\(262\) −1.49933e31 + 5.22290e30i −0.0337931 + 0.0117718i
\(263\) 7.01364e32i 1.50155i 0.660556 + 0.750777i \(0.270321\pi\)
−0.660556 + 0.750777i \(0.729679\pi\)
\(264\) −2.66536e31 + 5.96625e30i −0.0542130 + 0.0121352i
\(265\) 5.70528e31i 0.110270i
\(266\) −4.71155e31 1.35254e32i −0.0865490 0.248454i
\(267\) −8.83664e31 + 8.83664e31i −0.154307 + 0.154307i
\(268\) −4.27538e31 + 3.70163e32i −0.0709832 + 0.614573i
\(269\) 6.36975e32 + 6.36975e32i 1.00570 + 1.00570i 0.999984 + 0.00571206i \(0.00181821\pi\)
0.00571206 + 0.999984i \(0.498182\pi\)
\(270\) 2.78453e31 + 1.34575e31i 0.0418158 + 0.0202094i
\(271\) 7.56447e32 1.08067 0.540335 0.841450i \(-0.318298\pi\)
0.540335 + 0.841450i \(0.318298\pi\)
\(272\) −1.02109e32 + 4.36135e32i −0.138798 + 0.592844i
\(273\) −7.45795e31 −0.0964770
\(274\) 5.15638e32 + 2.49205e32i 0.634910 + 0.306849i
\(275\) 1.94682e32 + 1.94682e32i 0.228210 + 0.228210i
\(276\) −9.31050e31 1.07536e31i −0.103920 0.0120028i
\(277\) 1.92129e32 1.92129e32i 0.204229 0.204229i −0.597580 0.801809i \(-0.703871\pi\)
0.801809 + 0.597580i \(0.203871\pi\)
\(278\) −4.13743e32 1.18772e33i −0.418915 1.20257i
\(279\) 9.84867e32i 0.949994i
\(280\) −1.35920e32 8.61996e31i −0.124925 0.0792268i
\(281\) 9.16183e32i 0.802503i −0.915968 0.401252i \(-0.868575\pi\)
0.915968 0.401252i \(-0.131425\pi\)
\(282\) −2.17509e32 + 7.57693e31i −0.181600 + 0.0632601i
\(283\) −6.94410e32 + 6.94410e32i −0.552712 + 0.552712i −0.927223 0.374511i \(-0.877811\pi\)
0.374511 + 0.927223i \(0.377811\pi\)
\(284\) −3.89022e32 + 3.08463e32i −0.295241 + 0.234102i
\(285\) 5.71312e30 + 5.71312e30i 0.00413492 + 0.00413492i
\(286\) 1.11893e32 2.31522e32i 0.0772437 0.159827i
\(287\) 2.66927e32 0.175787
\(288\) −9.72408e32 + 1.20206e33i −0.611013 + 0.755315i
\(289\) −1.04944e33 −0.629271
\(290\) 2.30319e31 4.76560e31i 0.0131813 0.0272738i
\(291\) −6.08886e30 6.08886e30i −0.00332645 0.00332645i
\(292\) −1.28608e33 + 1.01976e33i −0.670811 + 0.531898i
\(293\) −2.36830e32 + 2.36830e32i −0.117957 + 0.117957i −0.763621 0.645664i \(-0.776581\pi\)
0.645664 + 0.763621i \(0.276581\pi\)
\(294\) −4.13315e31 + 1.43978e31i −0.0196604 + 0.00684870i
\(295\) 1.35017e32i 0.0613467i
\(296\) 8.63435e32 1.36146e33i 0.374793 0.590974i
\(297\) 2.64078e32i 0.109527i
\(298\) −5.97497e32 1.71522e33i −0.236819 0.679830i
\(299\) 6.23932e32 6.23932e32i 0.236361 0.236361i
\(300\) −4.53986e32 5.24353e31i −0.164401 0.0189883i
\(301\) −3.53226e33 3.53226e33i −1.22294 1.22294i
\(302\) 4.43189e33 + 2.14191e33i 1.46722 + 0.709100i
\(303\) −9.46197e32 −0.299575
\(304\) −6.96479e32 + 4.32224e32i −0.210919 + 0.130893i
\(305\) −1.45125e32 −0.0420431
\(306\) 1.92147e33 + 9.28635e32i 0.532591 + 0.257399i
\(307\) 2.77134e33 + 2.77134e33i 0.735057 + 0.735057i 0.971617 0.236560i \(-0.0760198\pi\)
−0.236560 + 0.971617i \(0.576020\pi\)
\(308\) 1.57685e32 1.36524e33i 0.0400272 0.346556i
\(309\) 1.37146e32 1.37146e32i 0.0333230 0.0333230i
\(310\) 1.93018e32 + 5.54092e32i 0.0448967 + 0.128884i
\(311\) 2.46792e33i 0.549624i −0.961498 0.274812i \(-0.911384\pi\)
0.961498 0.274812i \(-0.0886156\pi\)
\(312\) 9.32356e31 + 4.16521e32i 0.0198836 + 0.0888280i
\(313\) 4.53667e33i 0.926592i −0.886204 0.463296i \(-0.846667\pi\)
0.886204 0.463296i \(-0.153333\pi\)
\(314\) 6.41068e33 2.23316e33i 1.25416 0.436888i
\(315\) −5.42226e32 + 5.42226e32i −0.101622 + 0.101622i
\(316\) −3.03061e33 3.82210e33i −0.544195 0.686319i
\(317\) −6.57166e33 6.57166e33i −1.13077 1.13077i −0.990049 0.140723i \(-0.955057\pi\)
−0.140723 0.990049i \(-0.544943\pi\)
\(318\) 3.51871e32 7.28067e32i 0.0580252 0.120062i
\(319\) 4.51959e32 0.0714372
\(320\) −3.11499e32 + 8.66863e32i −0.0471988 + 0.131349i
\(321\) −1.06353e33 −0.154501
\(322\) 2.05207e33 4.24600e33i 0.285850 0.591461i
\(323\) 8.00030e32 + 8.00030e32i 0.106874 + 0.106874i
\(324\) 4.43864e33 + 5.59785e33i 0.568712 + 0.717239i
\(325\) 3.04233e33 3.04233e33i 0.373922 0.373922i
\(326\) 7.94920e33 2.76910e33i 0.937316 0.326514i
\(327\) 5.79248e31i 0.00655345i
\(328\) −3.33698e32 1.49076e33i −0.0362291 0.161850i
\(329\) 1.15894e34i 1.20758i
\(330\) 2.55036e31 + 7.32125e31i 0.00255072 + 0.00732229i
\(331\) 1.65630e33 1.65630e33i 0.159023 0.159023i −0.623111 0.782134i \(-0.714131\pi\)
0.782134 + 0.623111i \(0.214131\pi\)
\(332\) −1.77827e33 + 1.53963e34i −0.163921 + 1.41923i
\(333\) −5.43131e33 5.43131e33i −0.480737 0.480737i
\(334\) 9.32048e32 + 4.50454e32i 0.0792248 + 0.0382889i
\(335\) 1.05768e33 0.0863472
\(336\) 1.20287e33 + 1.93829e33i 0.0943279 + 0.151999i
\(337\) −7.21385e33 −0.543455 −0.271727 0.962374i \(-0.587595\pi\)
−0.271727 + 0.962374i \(0.587595\pi\)
\(338\) 8.82118e33 + 4.26323e33i 0.638486 + 0.308577i
\(339\) 2.64915e33 + 2.64915e33i 0.184252 + 0.184252i
\(340\) 1.26303e33 + 1.45880e32i 0.0844204 + 0.00975055i
\(341\) −3.54271e33 + 3.54271e33i −0.227589 + 0.227589i
\(342\) 1.28471e33 + 3.68799e33i 0.0793328 + 0.227739i
\(343\) 1.56515e34i 0.929146i
\(344\) −1.53115e34 + 2.41433e34i −0.873937 + 1.37802i
\(345\) 2.66031e32i 0.0146007i
\(346\) 6.99664e33 2.43728e33i 0.369285 0.128640i
\(347\) −2.17247e34 + 2.17247e34i −1.10282 + 1.10282i −0.108756 + 0.994068i \(0.534687\pi\)
−0.994068 + 0.108756i \(0.965313\pi\)
\(348\) −5.87833e32 + 4.66103e32i −0.0287034 + 0.0227595i
\(349\) −1.27630e34 1.27630e34i −0.599526 0.599526i 0.340660 0.940186i \(-0.389349\pi\)
−0.940186 + 0.340660i \(0.889349\pi\)
\(350\) 1.00060e34 2.07038e34i 0.452213 0.935688i
\(351\) 4.12679e33 0.179459
\(352\) −7.82188e33 + 8.26094e32i −0.327329 + 0.0345703i
\(353\) −2.91455e34 −1.17385 −0.586925 0.809641i \(-0.699662\pi\)
−0.586925 + 0.809641i \(0.699662\pi\)
\(354\) 8.32711e32 1.72299e33i 0.0322812 0.0667941i
\(355\) 9.96471e32 + 9.96471e32i 0.0371862 + 0.0371862i
\(356\) −2.81985e34 + 2.23591e34i −1.01310 + 0.803303i
\(357\) 2.22648e33 2.22648e33i 0.0770188 0.0770188i
\(358\) 3.05131e34 1.06292e34i 1.01640 0.354064i
\(359\) 4.76762e34i 1.52942i 0.644375 + 0.764710i \(0.277118\pi\)
−0.644375 + 0.764710i \(0.722882\pi\)
\(360\) 3.70615e33 + 2.35043e33i 0.114509 + 0.0726211i
\(361\) 3.15302e34i 0.938380i
\(362\) 1.63182e34 + 4.68443e34i 0.467850 + 1.34305i
\(363\) 3.85257e33 3.85257e33i 0.106417 0.106417i
\(364\) −2.13348e34 2.46417e33i −0.567832 0.0655845i
\(365\) 3.29427e33 + 3.29427e33i 0.0844899 + 0.0844899i
\(366\) 1.85198e33 + 8.95053e32i 0.0457765 + 0.0221235i
\(367\) 3.17989e34 0.757566 0.378783 0.925486i \(-0.376343\pi\)
0.378783 + 0.925486i \(0.376343\pi\)
\(368\) −2.62790e34 6.15252e33i −0.603481 0.141289i
\(369\) −7.27835e33 −0.161130
\(370\) −4.12014e33 1.99124e33i −0.0879404 0.0425011i
\(371\) 2.87708e34 + 2.87708e34i 0.592111 + 0.592111i
\(372\) 9.54185e32 8.26135e33i 0.0189366 0.163954i
\(373\) 2.63701e34 2.63701e34i 0.504711 0.504711i −0.408187 0.912898i \(-0.633839\pi\)
0.912898 + 0.408187i \(0.133839\pi\)
\(374\) 3.57136e33 + 1.02522e34i 0.0659276 + 0.189257i
\(375\) 2.62014e33i 0.0466555i
\(376\) −6.47258e34 + 1.44885e34i −1.11184 + 0.248878i
\(377\) 7.06283e33i 0.117050i
\(378\) 2.08282e34 7.25551e33i 0.333053 0.116019i
\(379\) 1.01154e34 1.01154e34i 0.156082 0.156082i −0.624746 0.780828i \(-0.714797\pi\)
0.780828 + 0.624746i \(0.214797\pi\)
\(380\) 1.44557e33 + 1.82310e33i 0.0215259 + 0.0271477i
\(381\) 1.28805e33 + 1.28805e33i 0.0185116 + 0.0185116i
\(382\) 3.06002e34 6.33159e34i 0.424492 0.878329i
\(383\) 5.14162e34 0.688520 0.344260 0.938874i \(-0.388130\pi\)
0.344260 + 0.938874i \(0.388130\pi\)
\(384\) 9.32145e33 9.14112e33i 0.120507 0.118176i
\(385\) −3.90093e33 −0.0486909
\(386\) 6.46456e34 1.33760e35i 0.779130 1.61212i
\(387\) 9.63150e34 + 9.63150e34i 1.12097 + 1.12097i
\(388\) −1.54065e33 1.94301e33i −0.0173171 0.0218397i
\(389\) 1.04864e34 1.04864e34i 0.113843 0.113843i −0.647890 0.761734i \(-0.724348\pi\)
0.761734 + 0.647890i \(0.224348\pi\)
\(390\) 1.14410e33 3.98548e32i 0.0119976 0.00417935i
\(391\) 3.72534e34i 0.377381i
\(392\) −1.22993e34 + 2.75313e33i −0.120370 + 0.0269441i
\(393\) 6.38741e32i 0.00603984i
\(394\) −5.20686e34 1.49472e35i −0.475748 1.36572i
\(395\) −9.79020e33 + 9.79020e33i −0.0864432 + 0.0864432i
\(396\) −4.29963e33 + 3.72263e34i −0.0366899 + 0.317661i
\(397\) −1.24235e35 1.24235e35i −1.02464 1.02464i −0.999689 0.0249500i \(-0.992057\pi\)
−0.0249500 0.999689i \(-0.507943\pi\)
\(398\) −5.66738e34 2.73901e34i −0.451815 0.218360i
\(399\) 5.76205e33 0.0444061
\(400\) −1.28138e35 3.00001e34i −0.954703 0.223518i
\(401\) 1.20822e35 0.870359 0.435180 0.900344i \(-0.356685\pi\)
0.435180 + 0.900344i \(0.356685\pi\)
\(402\) −1.34973e34 6.52318e33i −0.0940146 0.0454368i
\(403\) 5.53625e34 + 5.53625e34i 0.372904 + 0.372904i
\(404\) −2.70676e35 3.12631e34i −1.76320 0.203650i
\(405\) 1.43388e34 1.43388e34i 0.0903376 0.0903376i
\(406\) −1.24175e34 3.56467e34i −0.0756717 0.217229i
\(407\) 3.90744e34i 0.230339i
\(408\) −1.52181e34 9.65127e33i −0.0867859 0.0550392i
\(409\) 2.18216e35i 1.20398i −0.798502 0.601992i \(-0.794374\pi\)
0.798502 0.601992i \(-0.205626\pi\)
\(410\) −4.09485e33 + 1.42644e33i −0.0218603 + 0.00761502i
\(411\) −1.62919e34 + 1.62919e34i −0.0841601 + 0.0841601i
\(412\) 4.37645e34 3.47017e34i 0.218781 0.173476i
\(413\) 6.80867e34 + 6.80867e34i 0.329410 + 0.329410i
\(414\) −5.59543e34 + 1.15777e35i −0.262017 + 0.542147i
\(415\) 4.39922e34 0.199401
\(416\) 1.29095e34 + 1.22234e35i 0.0566434 + 0.536329i
\(417\) 5.05992e34 0.214935
\(418\) −8.64494e33 + 1.78875e34i −0.0355535 + 0.0735649i
\(419\) 1.06185e35 + 1.06185e35i 0.422839 + 0.422839i 0.886180 0.463341i \(-0.153349\pi\)
−0.463341 + 0.886180i \(0.653349\pi\)
\(420\) 5.07368e33 4.02301e33i 0.0195640 0.0155127i
\(421\) 1.59527e34 1.59527e34i 0.0595699 0.0595699i −0.676694 0.736264i \(-0.736588\pi\)
0.736264 + 0.676694i \(0.236588\pi\)
\(422\) 1.66539e35 5.80139e34i 0.602280 0.209804i
\(423\) 3.16011e35i 1.10690i
\(424\) 1.24715e35 1.96650e35i 0.423135 0.667199i
\(425\) 1.81650e35i 0.597014i
\(426\) −6.57055e33 1.88619e34i −0.0209205 0.0600560i
\(427\) −7.31841e34 + 7.31841e34i −0.225757 + 0.225757i
\(428\) −3.04242e35 3.51399e34i −0.909344 0.105029i
\(429\) 7.31507e33 + 7.31507e33i 0.0211858 + 0.0211858i
\(430\) 7.30636e34 + 3.53112e34i 0.205058 + 0.0991035i
\(431\) 1.75558e35 0.477504 0.238752 0.971081i \(-0.423262\pi\)
0.238752 + 0.971081i \(0.423262\pi\)
\(432\) −6.65599e34 1.07254e35i −0.175462 0.282736i
\(433\) −5.02623e35 −1.28427 −0.642134 0.766592i \(-0.721951\pi\)
−0.642134 + 0.766592i \(0.721951\pi\)
\(434\) 3.76755e35 + 1.82084e35i 0.933141 + 0.450982i
\(435\) 1.50572e33 + 1.50572e33i 0.00361526 + 0.00361526i
\(436\) 1.91388e33 1.65704e34i 0.00445500 0.0385714i
\(437\) −4.82053e34 + 4.82053e34i −0.108792 + 0.108792i
\(438\) −2.17218e34 6.23562e34i −0.0475330 0.136452i
\(439\) 2.07452e35i 0.440196i −0.975478 0.220098i \(-0.929362\pi\)
0.975478 0.220098i \(-0.0706377\pi\)
\(440\) 4.87674e33 + 2.17864e34i 0.0100350 + 0.0448305i
\(441\) 6.00490e34i 0.119835i
\(442\) 1.60213e35 5.58103e34i 0.310097 0.108022i
\(443\) 1.45875e35 1.45875e35i 0.273861 0.273861i −0.556792 0.830652i \(-0.687968\pi\)
0.830652 + 0.556792i \(0.187968\pi\)
\(444\) 4.02973e34 + 5.08215e34i 0.0733847 + 0.0925502i
\(445\) 7.22297e34 + 7.22297e34i 0.127601 + 0.127601i
\(446\) 7.83418e34 1.62099e35i 0.134268 0.277818i
\(447\) 7.30716e34 0.121506
\(448\) 2.80061e35 + 5.94227e35i 0.451855 + 0.958737i
\(449\) −1.58886e35 −0.248749 −0.124374 0.992235i \(-0.539692\pi\)
−0.124374 + 0.992235i \(0.539692\pi\)
\(450\) −2.72837e35 + 5.64535e35i −0.414509 + 0.857674i
\(451\) −2.61813e34 2.61813e34i −0.0386018 0.0386018i
\(452\) 6.70307e35 + 8.45368e35i 0.959191 + 1.20970i
\(453\) −1.40028e35 + 1.40028e35i −0.194487 + 0.194487i
\(454\) −5.89542e35 + 2.05367e35i −0.794805 + 0.276870i
\(455\) 6.09604e34i 0.0797800i
\(456\) −7.20343e33 3.21806e34i −0.00915196 0.0408855i
\(457\) 4.37733e35i 0.539934i −0.962870 0.269967i \(-0.912987\pi\)
0.962870 0.269967i \(-0.0870129\pi\)
\(458\) 1.40244e35 + 4.02597e35i 0.167958 + 0.482154i
\(459\) −1.23200e35 + 1.23200e35i −0.143265 + 0.143265i
\(460\) −8.78988e33 + 7.61029e34i −0.00992550 + 0.0859351i
\(461\) 5.18659e35 + 5.18659e35i 0.568747 + 0.568747i 0.931777 0.363030i \(-0.118258\pi\)
−0.363030 + 0.931777i \(0.618258\pi\)
\(462\) 4.97808e34 + 2.40588e34i 0.0530145 + 0.0256216i
\(463\) −1.07568e36 −1.11260 −0.556300 0.830982i \(-0.687779\pi\)
−0.556300 + 0.830982i \(0.687779\pi\)
\(464\) −1.83560e35 + 1.13915e35i −0.184411 + 0.114442i
\(465\) −2.36054e34 −0.0230354
\(466\) −1.83567e35 8.87171e34i −0.174014 0.0841003i
\(467\) −1.42282e36 1.42282e36i −1.31030 1.31030i −0.921190 0.389113i \(-0.872782\pi\)
−0.389113 0.921190i \(-0.627218\pi\)
\(468\) 5.81741e35 + 6.71910e34i 0.520488 + 0.0601163i
\(469\) 5.33368e35 5.33368e35i 0.463654 0.463654i
\(470\) 6.19329e34 + 1.77790e35i 0.0523119 + 0.150171i
\(471\) 2.73107e35i 0.224156i
\(472\) 2.95140e35 4.65378e35i 0.235403 0.371183i
\(473\) 6.92918e35i 0.537101i
\(474\) 1.85316e35 6.45548e34i 0.139606 0.0486319i
\(475\) −2.35052e35 + 2.35052e35i −0.172108 + 0.172108i
\(476\) 7.10487e35 5.63358e35i 0.505664 0.400951i
\(477\) −7.84499e35 7.84499e35i −0.542743 0.542743i
\(478\) −2.15564e35 + 4.46030e35i −0.144977 + 0.299977i
\(479\) −1.77534e36 −1.16079 −0.580394 0.814336i \(-0.697101\pi\)
−0.580394 + 0.814336i \(0.697101\pi\)
\(480\) −2.88111e34 2.33068e34i −0.0183148 0.0148158i
\(481\) −6.10622e35 −0.377410
\(482\) 3.88635e35 8.04137e35i 0.233565 0.483276i
\(483\) 1.34155e35 + 1.34155e35i 0.0784008 + 0.0784008i
\(484\) 1.22939e36 9.74804e35i 0.698677 0.553994i
\(485\) −4.97697e33 + 4.97697e33i −0.00275075 + 0.00275075i
\(486\) −8.55997e35 + 2.98186e35i −0.460132 + 0.160287i
\(487\) 3.44720e36i 1.80229i −0.433515 0.901146i \(-0.642727\pi\)
0.433515 0.901146i \(-0.357273\pi\)
\(488\) 5.00219e35 + 3.17237e35i 0.254386 + 0.161330i
\(489\) 3.38651e35i 0.167526i
\(490\) 1.17686e34 + 3.37839e34i 0.00566342 + 0.0162578i
\(491\) 1.23849e36 1.23849e36i 0.579819 0.579819i −0.355034 0.934853i \(-0.615531\pi\)
0.934853 + 0.355034i \(0.115531\pi\)
\(492\) 6.10529e34 + 7.05161e33i 0.0278085 + 0.00321188i
\(493\) 2.10852e35 + 2.10852e35i 0.0934424 + 0.0934424i
\(494\) 2.79531e35 + 1.35096e35i 0.120536 + 0.0582544i
\(495\) 1.06368e35 0.0446313
\(496\) 5.45923e35 2.33178e36i 0.222910 0.952105i
\(497\) 1.00501e36 0.399354
\(498\) −5.61396e35 2.71320e35i −0.217107 0.104927i
\(499\) −1.72024e35 1.72024e35i −0.0647488 0.0647488i 0.673991 0.738740i \(-0.264579\pi\)
−0.738740 + 0.673991i \(0.764579\pi\)
\(500\) −8.65715e34 + 7.49538e35i −0.0317161 + 0.274599i
\(501\) −2.94486e34 + 2.94486e34i −0.0105016 + 0.0105016i
\(502\) 7.20332e35 + 2.06784e36i 0.250053 + 0.717823i
\(503\) 5.63157e36i 1.90310i −0.307494 0.951550i \(-0.599490\pi\)
0.307494 0.951550i \(-0.400510\pi\)
\(504\) 3.05423e36 6.83670e35i 1.00482 0.224923i
\(505\) 7.73410e35i 0.247729i
\(506\) −6.17742e35 + 2.15190e35i −0.192653 + 0.0671105i
\(507\) −2.78710e35 + 2.78710e35i −0.0846341 + 0.0846341i
\(508\) 3.25910e35 + 4.11026e35i 0.0963691 + 0.121537i
\(509\) 2.78787e36 + 2.78787e36i 0.802754 + 0.802754i 0.983525 0.180771i \(-0.0578593\pi\)
−0.180771 + 0.983525i \(0.557859\pi\)
\(510\) −2.22576e34 + 4.60539e34i −0.00624138 + 0.0129142i
\(511\) 3.32248e36 0.907362
\(512\) 2.96860e36 2.30699e36i 0.789599 0.613623i
\(513\) −3.18838e35 −0.0826010
\(514\) −6.93628e35 + 1.43521e36i −0.175035 + 0.362170i
\(515\) −1.12102e35 1.12102e35i −0.0275559 0.0275559i
\(516\) −7.14604e35 9.01232e35i −0.171117 0.215807i
\(517\) −1.13674e36 + 1.13674e36i −0.265178 + 0.265178i
\(518\) −3.08186e36 + 1.07357e36i −0.700424 + 0.243993i
\(519\) 2.98070e35i 0.0660022i
\(520\) 3.40459e35 7.62097e34i 0.0734548 0.0164424i
\(521\) 3.93661e36i 0.827586i 0.910371 + 0.413793i \(0.135796\pi\)
−0.910371 + 0.413793i \(0.864204\pi\)
\(522\) 3.38592e35 + 9.71988e35i 0.0693625 + 0.199117i
\(523\) −4.43031e36 + 4.43031e36i −0.884426 + 0.884426i −0.993981 0.109555i \(-0.965058\pi\)
0.109555 + 0.993981i \(0.465058\pi\)
\(524\) 2.11045e34 1.82723e35i 0.00410585 0.0355485i
\(525\) 6.54148e35 + 6.54148e35i 0.124030 + 0.124030i
\(526\) −7.31587e36 3.53572e36i −1.35194 0.653387i
\(527\) −3.30555e36 −0.595389
\(528\) 7.21331e34 3.08099e35i 0.0126642 0.0540919i
\(529\) 3.59853e36 0.615848
\(530\) −5.95113e35 2.87615e35i −0.0992831 0.0479830i
\(531\) −1.85654e36 1.85654e36i −0.301945 0.301945i
\(532\) 1.64834e36 + 1.90383e35i 0.261360 + 0.0301870i
\(533\) −4.09139e35 + 4.09139e35i −0.0632490 + 0.0632490i
\(534\) −4.76269e35 1.36722e36i −0.0717870 0.206077i
\(535\) 8.69318e35i 0.127762i
\(536\) −3.64561e36 2.31203e36i −0.522451 0.331336i
\(537\) 1.29992e36i 0.181661i
\(538\) −9.85535e36 + 3.43311e36i −1.34311 + 0.467872i
\(539\) −2.16005e35 + 2.16005e35i −0.0287088 + 0.0287088i
\(540\) −2.80747e35 + 2.22610e35i −0.0363915 + 0.0288555i
\(541\) 1.06990e37 + 1.06990e37i 1.35264 + 1.35264i 0.882701 + 0.469936i \(0.155723\pi\)
0.469936 + 0.882701i \(0.344277\pi\)
\(542\) −3.81340e36 + 7.89043e36i −0.470243 + 0.972994i
\(543\) −1.99566e36 −0.240042
\(544\) −4.03453e36 3.26374e36i −0.473378 0.382939i
\(545\) −4.73471e34 −0.00541926
\(546\) 3.75971e35 7.77932e35i 0.0419810 0.0868643i
\(547\) 3.51189e36 + 3.51189e36i 0.382571 + 0.382571i 0.872028 0.489456i \(-0.162805\pi\)
−0.489456 + 0.872028i \(0.662805\pi\)
\(548\) −5.19888e36 + 4.12228e36i −0.552550 + 0.438127i
\(549\) 1.99553e36 1.99553e36i 0.206934 0.206934i
\(550\) −3.01215e36 + 1.04928e36i −0.304775 + 0.106168i
\(551\) 5.45678e35i 0.0538753i
\(552\) 5.81531e35 9.16959e35i 0.0560268 0.0883430i
\(553\) 9.87406e36i 0.928338i
\(554\) 1.03552e36 + 2.97265e36i 0.0950118 + 0.272748i
\(555\) 1.30178e35 1.30178e35i 0.0116569 0.0116569i
\(556\) 1.44748e37 + 1.67184e36i 1.26503 + 0.146111i
\(557\) 5.37536e36 + 5.37536e36i 0.458525 + 0.458525i 0.898171 0.439646i \(-0.144896\pi\)
−0.439646 + 0.898171i \(0.644896\pi\)
\(558\) −1.02731e37 4.96492e36i −0.855339 0.413381i
\(559\) 1.08283e37 0.880040
\(560\) 1.58434e36 9.83216e35i 0.125693 0.0780028i
\(561\) −4.36764e35 −0.0338258
\(562\) 9.55662e36 + 4.61866e36i 0.722544 + 0.349202i
\(563\) 4.56503e36 + 4.56503e36i 0.336962 + 0.336962i 0.855223 0.518261i \(-0.173420\pi\)
−0.518261 + 0.855223i \(0.673420\pi\)
\(564\) 3.06166e35 2.65079e36i 0.0220642 0.191032i
\(565\) 2.16539e36 2.16539e36i 0.152364 0.152364i
\(566\) −3.74267e36 1.07440e37i −0.257134 0.738149i
\(567\) 1.44616e37i 0.970162i
\(568\) −1.25641e36 5.61289e36i −0.0823054 0.367692i
\(569\) 9.92659e36i 0.635016i 0.948256 + 0.317508i \(0.102846\pi\)
−0.948256 + 0.317508i \(0.897154\pi\)
\(570\) −8.83941e34 + 3.07920e34i −0.00552220 + 0.00192366i
\(571\) 1.08491e37 1.08491e37i 0.661921 0.661921i −0.293911 0.955833i \(-0.594957\pi\)
0.955833 + 0.293911i \(0.0949570\pi\)
\(572\) 1.85091e36 + 2.33430e36i 0.110291 + 0.139095i
\(573\) 2.00050e36 + 2.00050e36i 0.116426 + 0.116426i
\(574\) −1.34563e36 + 2.78429e36i −0.0764919 + 0.158272i
\(575\) −1.09452e37 −0.607726
\(576\) −7.63649e36 1.62029e37i −0.414181 0.878801i
\(577\) −2.35051e37 −1.24534 −0.622670 0.782485i \(-0.713952\pi\)
−0.622670 + 0.782485i \(0.713952\pi\)
\(578\) 5.29046e36 1.09466e37i 0.273821 0.566572i
\(579\) 4.22623e36 + 4.22623e36i 0.213694 + 0.213694i
\(580\) 3.80988e35 + 4.80488e35i 0.0188206 + 0.0237358i
\(581\) 2.21845e37 2.21845e37i 1.07071 1.07071i
\(582\) 9.42076e34 3.28172e34i 0.00444248 0.00154754i
\(583\) 5.64391e36i 0.260049i
\(584\) −4.15360e36 1.85558e37i −0.187004 0.835423i
\(585\) 1.66222e36i 0.0731283i
\(586\) −1.27645e36 3.66426e36i −0.0548763 0.157532i
\(587\) −5.43774e36 + 5.43774e36i −0.228457 + 0.228457i −0.812048 0.583591i \(-0.801647\pi\)
0.583591 + 0.812048i \(0.301647\pi\)
\(588\) 5.81782e34 5.03708e35i 0.00238873 0.0206816i
\(589\) −4.27734e36 4.27734e36i −0.171639 0.171639i
\(590\) −1.40835e36 6.80648e35i −0.0552342 0.0266944i
\(591\) 6.36779e36 0.244094
\(592\) 9.84857e36 + 1.58698e37i 0.369003 + 0.594606i
\(593\) −1.08949e37 −0.399012 −0.199506 0.979897i \(-0.563934\pi\)
−0.199506 + 0.979897i \(0.563934\pi\)
\(594\) −2.75457e36 1.33127e36i −0.0986137 0.0476595i
\(595\) −1.81990e36 1.81990e36i −0.0636894 0.0636894i
\(596\) 2.09034e37 + 2.41434e36i 0.715143 + 0.0825990i
\(597\) 1.79064e36 1.79064e36i 0.0598900 0.0598900i
\(598\) 3.36281e36 + 9.65355e36i 0.109960 + 0.315661i
\(599\) 2.67698e37i 0.855820i −0.903821 0.427910i \(-0.859250\pi\)
0.903821 0.427910i \(-0.140750\pi\)
\(600\) 2.83558e36 4.47115e36i 0.0886340 0.139758i
\(601\) 2.29702e37i 0.702037i −0.936368 0.351019i \(-0.885835\pi\)
0.936368 0.351019i \(-0.114165\pi\)
\(602\) 5.46515e37 1.90378e37i 1.63324 0.568938i
\(603\) −1.45435e37 + 1.45435e37i −0.424996 + 0.424996i
\(604\) −4.46842e37 + 3.54309e37i −1.27689 + 1.01247i
\(605\) −3.14905e36 3.14905e36i −0.0879997 0.0879997i
\(606\) 4.76997e36 9.86970e36i 0.130357 0.269726i
\(607\) −4.92115e37 −1.31528 −0.657642 0.753331i \(-0.728446\pi\)
−0.657642 + 0.753331i \(0.728446\pi\)
\(608\) −9.97395e35 9.44385e36i −0.0260717 0.246860i
\(609\) 1.51862e36 0.0388253
\(610\) 7.31606e35 1.51379e36i 0.0182947 0.0378541i
\(611\) 1.77639e37 + 1.77639e37i 0.434493 + 0.434493i
\(612\) −1.93730e37 + 1.53612e37i −0.463504 + 0.367521i
\(613\) −4.48554e36 + 4.48554e36i −0.104978 + 0.104978i −0.757645 0.652667i \(-0.773650\pi\)
0.652667 + 0.757645i \(0.273650\pi\)
\(614\) −4.28785e37 + 1.49367e37i −0.981671 + 0.341965i
\(615\) 1.74448e35i 0.00390708i
\(616\) 1.34458e37 + 8.52724e36i 0.294609 + 0.186840i
\(617\) 7.12796e37i 1.52797i −0.645232 0.763987i \(-0.723239\pi\)
0.645232 0.763987i \(-0.276761\pi\)
\(618\) 7.39178e35 + 2.12194e36i 0.0155026 + 0.0445030i
\(619\) −6.68210e37 + 6.68210e37i −1.37116 + 1.37116i −0.512439 + 0.858723i \(0.671258\pi\)
−0.858723 + 0.512439i \(0.828742\pi\)
\(620\) −6.75273e36 7.79940e35i −0.135579 0.0156593i
\(621\) −7.42333e36 7.42333e36i −0.145835 0.145835i
\(622\) 2.57426e37 + 1.24413e37i 0.494861 + 0.239164i
\(623\) 7.28484e37 1.37035
\(624\) −4.81471e36 1.12724e36i −0.0886295 0.0207502i
\(625\) −5.22881e37 −0.941939
\(626\) 4.73216e37 + 2.28703e37i 0.834269 + 0.403198i
\(627\) −5.65166e35 5.65166e35i −0.00975134 0.00975134i
\(628\) −9.02367e36 + 7.81271e37i −0.152380 + 1.31931i
\(629\) 1.82293e37 1.82293e37i 0.301292 0.301292i
\(630\) −2.92244e36 8.38938e36i −0.0472768 0.135716i
\(631\) 7.29155e37i 1.15458i −0.816540 0.577289i \(-0.804111\pi\)
0.816540 0.577289i \(-0.195889\pi\)
\(632\) 5.51459e37 1.23441e37i 0.854737 0.191327i
\(633\) 7.09488e36i 0.107645i
\(634\) 1.01677e38 3.54193e37i 1.51015 0.526060i
\(635\) 1.05283e36 1.05283e36i 0.0153079 0.0153079i
\(636\) 5.82055e36 + 7.34067e36i 0.0828500 + 0.104488i
\(637\) 3.37554e36 + 3.37554e36i 0.0470393 + 0.0470393i
\(638\) −2.27842e36 + 4.71434e36i −0.0310852 + 0.0643194i
\(639\) −2.74038e37 −0.366057
\(640\) −7.47185e36 7.61925e36i −0.0977233 0.0996512i
\(641\) −1.48409e38 −1.90054 −0.950272 0.311422i \(-0.899195\pi\)
−0.950272 + 0.311422i \(0.899195\pi\)
\(642\) 5.36148e36 1.10936e37i 0.0672298 0.139107i
\(643\) 9.72315e37 + 9.72315e37i 1.19387 + 1.19387i 0.975970 + 0.217905i \(0.0699223\pi\)
0.217905 + 0.975970i \(0.430078\pi\)
\(644\) 3.39448e37 + 4.28100e37i 0.408145 + 0.514737i
\(645\) −2.30848e36 + 2.30848e36i −0.0271813 + 0.0271813i
\(646\) −1.23782e37 + 4.31193e36i −0.142731 + 0.0497202i
\(647\) 1.26136e37i 0.142439i 0.997461 + 0.0712197i \(0.0226892\pi\)
−0.997461 + 0.0712197i \(0.977311\pi\)
\(648\) −8.07668e37 + 1.80791e37i −0.893244 + 0.199947i
\(649\) 1.33565e37i 0.144673i
\(650\) 1.63973e37 + 4.70713e37i 0.173957 + 0.499374i
\(651\) −1.19038e37 + 1.19038e37i −0.123692 + 0.123692i
\(652\) −1.11893e37 + 9.68771e37i −0.113883 + 0.986004i
\(653\) −3.28457e36 3.28457e36i −0.0327455 0.0327455i 0.690544 0.723290i \(-0.257371\pi\)
−0.723290 + 0.690544i \(0.757371\pi\)
\(654\) 6.04209e35 + 2.92011e35i 0.00590048 + 0.00285167i
\(655\) −5.22099e35 −0.00499454
\(656\) 1.72323e37 + 4.03447e36i 0.161488 + 0.0378081i
\(657\) −9.05949e37 −0.831709
\(658\) 1.20888e38 + 5.84245e37i 1.08726 + 0.525467i
\(659\) 1.21892e38 + 1.21892e38i 1.07404 + 1.07404i 0.997030 + 0.0770134i \(0.0245384\pi\)
0.0770134 + 0.997030i \(0.475462\pi\)
\(660\) −8.92242e35 1.03054e35i −0.00770264 0.000889654i
\(661\) 7.61509e37 7.61509e37i 0.644103 0.644103i −0.307459 0.951561i \(-0.599479\pi\)
0.951561 + 0.307459i \(0.0994785\pi\)
\(662\) 8.92696e36 + 2.56264e37i 0.0739811 + 0.212376i
\(663\) 6.82538e36i 0.0554236i
\(664\) −1.51633e38 9.61648e37i −1.20649 0.765151i
\(665\) 4.70984e36i 0.0367209i
\(666\) 8.40339e37 2.92732e37i 0.642025 0.223649i
\(667\) −1.27047e37 + 1.27047e37i −0.0951189 + 0.0951189i
\(668\) −9.39729e36 + 7.45128e36i −0.0689478 + 0.0546700i
\(669\) 5.12162e36 + 5.12162e36i 0.0368260 + 0.0368260i
\(670\) −5.33197e36 + 1.10325e37i −0.0375732 + 0.0777438i
\(671\) 1.43564e37 0.0991498
\(672\) −2.62821e37 + 2.77574e36i −0.177900 + 0.0187886i
\(673\) −1.93876e38 −1.28624 −0.643118 0.765767i \(-0.722360\pi\)
−0.643118 + 0.765767i \(0.722360\pi\)
\(674\) 3.63665e37 7.52470e37i 0.236479 0.489306i
\(675\) −3.61966e37 3.61966e37i −0.230711 0.230711i
\(676\) −8.89387e37 + 7.05211e37i −0.555662 + 0.440594i
\(677\) 1.81496e38 1.81496e38i 1.11153 1.11153i 0.118583 0.992944i \(-0.462165\pi\)
0.992944 0.118583i \(-0.0378353\pi\)
\(678\) −4.09880e37 + 1.42782e37i −0.246069 + 0.0857179i
\(679\) 5.01959e36i 0.0295411i
\(680\) −7.88884e36 + 1.24391e37i −0.0455138 + 0.0717661i
\(681\) 2.51156e37i 0.142055i
\(682\) −1.90942e37 5.48132e37i −0.105879 0.303946i
\(683\) −1.46467e38 + 1.46467e38i −0.796272 + 0.796272i −0.982506 0.186233i \(-0.940372\pi\)
0.186233 + 0.982506i \(0.440372\pi\)
\(684\) −4.49456e37 5.19121e36i −0.239569 0.0276702i
\(685\) 1.33168e37 + 1.33168e37i 0.0695948 + 0.0695948i
\(686\) −1.63259e38 7.89022e37i −0.836568 0.404309i
\(687\) −1.71514e37 −0.0861753
\(688\) −1.74648e38 2.81425e38i −0.860436 1.38649i
\(689\) −8.81983e37 −0.426090
\(690\) −2.77495e36 1.34112e36i −0.0131460 0.00635337i
\(691\) 8.84575e37 + 8.84575e37i 0.410943 + 0.410943i 0.882067 0.471124i \(-0.156152\pi\)
−0.471124 + 0.882067i \(0.656152\pi\)
\(692\) −9.84846e36 + 8.52681e37i −0.0448679 + 0.388467i
\(693\) 5.36393e37 5.36393e37i 0.239654 0.239654i
\(694\) −1.17090e38 3.36128e38i −0.513058 1.47283i
\(695\) 4.13592e37i 0.177737i
\(696\) −1.89850e36 8.48136e36i −0.00800176 0.0357471i
\(697\) 2.44287e37i 0.100985i
\(698\) 1.97470e38 6.87886e37i 0.800669 0.278913i
\(699\) 5.79991e36 5.79991e36i 0.0230664 0.0230664i
\(700\) 1.65517e38 + 2.08744e38i 0.645682 + 0.814312i
\(701\) 2.17436e38 + 2.17436e38i 0.832028 + 0.832028i 0.987794 0.155766i \(-0.0497847\pi\)
−0.155766 + 0.987794i \(0.549785\pi\)
\(702\) −2.08040e37 + 4.30462e37i −0.0780900 + 0.161578i
\(703\) 4.71770e37 0.173713
\(704\) 3.08148e37 8.57538e37i 0.111308 0.309758i
\(705\) −7.57416e36 −0.0268399
\(706\) 1.46928e38 3.04014e38i 0.510790 1.05689i
\(707\) 3.90017e38 + 3.90017e38i 1.33022 + 1.33022i
\(708\) 1.37745e37 + 1.73719e37i 0.0460920 + 0.0581296i
\(709\) 2.65902e38 2.65902e38i 0.872965 0.872965i −0.119830 0.992794i \(-0.538235\pi\)
0.992794 + 0.119830i \(0.0382349\pi\)
\(710\) −1.54175e37 + 5.37069e36i −0.0496623 + 0.0172999i
\(711\) 2.69238e38i 0.850937i
\(712\) −9.10714e37 4.06853e38i −0.282424 1.26170i
\(713\) 1.99174e38i 0.606072i
\(714\) 1.20001e37 + 3.44483e37i 0.0358309 + 0.102859i
\(715\) 5.97926e36 5.97926e36i 0.0175193 0.0175193i
\(716\) −4.29503e37 + 3.71864e38i −0.123492 + 1.06920i
\(717\) −1.40926e37 1.40926e37i −0.0397632 0.0397632i
\(718\) −4.97306e38 2.40346e38i −1.37703 0.665512i
\(719\) 5.65075e38 1.53556 0.767779 0.640715i \(-0.221362\pi\)
0.767779 + 0.640715i \(0.221362\pi\)
\(720\) −4.32006e37 + 2.68096e37i −0.115213 + 0.0714992i
\(721\) −1.13062e38 −0.295931
\(722\) 3.28888e38 + 1.58950e38i 0.844883 + 0.408327i
\(723\) 2.54072e37 + 2.54072e37i 0.0640603 + 0.0640603i
\(724\) −5.70893e38 6.59380e37i −1.41281 0.163179i
\(725\) −6.19491e37 + 6.19491e37i −0.150478 + 0.150478i
\(726\) 2.07642e37 + 5.96074e37i 0.0495075 + 0.142120i
\(727\) 6.96433e38i 1.62992i −0.579521 0.814958i \(-0.696760\pi\)
0.579521 0.814958i \(-0.303240\pi\)
\(728\) 1.33257e38 2.10119e38i 0.306136 0.482716i
\(729\) 3.69423e38i 0.833110i
\(730\) −5.09693e37 + 1.77551e37i −0.112837 + 0.0393066i
\(731\) −3.23266e38 + 3.23266e38i −0.702547 + 0.702547i
\(732\) −1.86724e37 + 1.48057e37i −0.0398384 + 0.0315886i
\(733\) 3.61307e38 + 3.61307e38i 0.756784 + 0.756784i 0.975736 0.218951i \(-0.0702636\pi\)
−0.218951 + 0.975736i \(0.570264\pi\)
\(734\) −1.60305e38 + 3.31692e38i −0.329648 + 0.682084i
\(735\) −1.43926e36 −0.00290576
\(736\) 1.96654e38 2.43098e38i 0.389810 0.481871i
\(737\) −1.04630e38 −0.203632
\(738\) 3.66917e37 7.59199e37i 0.0701143 0.145076i
\(739\) 3.43885e38 + 3.43885e38i 0.645229 + 0.645229i 0.951836 0.306607i \(-0.0991938\pi\)
−0.306607 + 0.951836i \(0.599194\pi\)
\(740\) 4.15409e37 3.29385e37i 0.0765328 0.0606843i
\(741\) −8.83195e36 + 8.83195e36i −0.0159776 + 0.0159776i
\(742\) −4.45145e38