Properties

Label 16.28.e.a.5.17
Level $16$
Weight $28$
Character 16.5
Analytic conductor $73.897$
Analytic rank $0$
Dimension $106$
Inner twists $2$

Related objects

Downloads

Learn more

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 5.17
Character \(\chi\) \(=\) 16.5
Dual form 16.28.e.a.13.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5798.80 - 10029.5i) q^{2} +(1.92086e6 - 1.92086e6i) q^{3} +(-6.69655e7 + 1.16319e8i) q^{4} +(4.80331e8 + 4.80331e8i) q^{5} +(-3.04040e10 - 8.12664e9i) q^{6} +4.11420e11i q^{7} +(1.55494e12 - 2.87564e9i) q^{8} +2.46204e11i q^{9} +O(q^{10})\) \(q+(-5798.80 - 10029.5i) q^{2} +(1.92086e6 - 1.92086e6i) q^{3} +(-6.69655e7 + 1.16319e8i) q^{4} +(4.80331e8 + 4.80331e8i) q^{5} +(-3.04040e10 - 8.12664e9i) q^{6} +4.11420e11i q^{7} +(1.55494e12 - 2.87564e9i) q^{8} +2.46204e11i q^{9} +(2.03215e12 - 7.60284e12i) q^{10} +(2.97858e13 + 2.97858e13i) q^{11} +(9.48003e13 + 3.52063e14i) q^{12} +(3.90244e14 - 3.90244e14i) q^{13} +(4.12636e15 - 2.38575e15i) q^{14} +1.84530e15 q^{15} +(-9.04564e15 - 1.55787e16i) q^{16} -1.80150e16 q^{17} +(2.46931e15 - 1.42769e15i) q^{18} +(3.44699e16 - 3.44699e16i) q^{19} +(-8.80370e16 + 2.37058e16i) q^{20} +(7.90280e17 + 7.90280e17i) q^{21} +(1.26016e17 - 4.71460e17i) q^{22} +2.55457e18i q^{23} +(2.98130e18 - 2.99235e18i) q^{24} -6.98915e18i q^{25} +(-6.17692e18 - 1.65102e18i) q^{26} +(1.51206e19 + 1.51206e19i) q^{27} +(-4.78558e19 - 2.75510e19i) q^{28} +(-7.52283e19 + 7.52283e19i) q^{29} +(-1.07005e19 - 1.85075e19i) q^{30} -1.10062e20 q^{31} +(-1.03793e20 + 1.81061e20i) q^{32} +1.14429e20 q^{33} +(1.04466e20 + 1.80682e20i) q^{34} +(-1.97618e20 + 1.97618e20i) q^{35} +(-2.86381e19 - 1.64872e19i) q^{36} +(-1.76426e21 - 1.76426e21i) q^{37} +(-5.45601e20 - 1.45833e20i) q^{38} -1.49921e21i q^{39} +(7.48268e20 + 7.45505e20i) q^{40} -3.54498e21i q^{41} +(3.34347e21 - 1.25088e22i) q^{42} +(5.32060e20 + 5.32060e20i) q^{43} +(-5.45926e21 + 1.47002e21i) q^{44} +(-1.18259e20 + 1.18259e20i) q^{45} +(2.56212e22 - 1.48135e22i) q^{46} +1.45259e22 q^{47} +(-4.72998e22 - 1.25490e22i) q^{48} -1.03554e23 q^{49} +(-7.00979e22 + 4.05287e22i) q^{50} +(-3.46043e22 + 3.46043e22i) q^{51} +(1.92598e22 + 7.15256e22i) q^{52} +(-2.22737e23 - 2.22737e23i) q^{53} +(6.39713e22 - 2.39334e23i) q^{54} +2.86141e22i q^{55} +(1.18310e21 + 6.39735e23i) q^{56} -1.32424e23i q^{57} +(1.19074e24 + 3.18271e23i) q^{58} +(-2.61506e22 - 2.61506e22i) q^{59} +(-1.23571e23 + 2.14642e23i) q^{60} +(-5.21421e23 + 5.21421e23i) q^{61} +(6.38230e23 + 1.10388e24i) q^{62} -1.01293e23 q^{63} +(2.41784e24 - 8.94290e21i) q^{64} +3.74893e23 q^{65} +(-6.63549e23 - 1.14767e24i) q^{66} +(-1.61528e24 + 1.61528e24i) q^{67} +(1.20639e24 - 2.09548e24i) q^{68} +(4.90697e24 + 4.90697e24i) q^{69} +(3.12796e24 + 8.36069e23i) q^{70} +6.23292e23i q^{71} +(7.07993e20 + 3.82833e23i) q^{72} +1.16831e25i q^{73} +(-7.46412e24 + 2.79253e25i) q^{74} +(-1.34252e25 - 1.34252e25i) q^{75} +(1.70120e24 + 6.31778e24i) q^{76} +(-1.22545e25 + 1.22545e25i) q^{77} +(-1.50364e25 + 8.69361e24i) q^{78} -2.79686e25 q^{79} +(3.13802e24 - 1.18278e25i) q^{80} +5.62117e25 q^{81} +(-3.55545e25 + 2.05566e25i) q^{82} +(1.86732e25 - 1.86732e25i) q^{83} +(-1.44846e26 + 3.90028e25i) q^{84} +(-8.65317e24 - 8.65317e24i) q^{85} +(2.25100e24 - 8.42162e24i) q^{86} +2.89006e26i q^{87} +(4.64008e25 + 4.62295e25i) q^{88} +1.37565e26i q^{89} +(1.87185e24 + 5.00324e23i) q^{90} +(1.60554e26 + 1.60554e26i) q^{91} +(-2.97144e26 - 1.71068e26i) q^{92} +(-2.11414e26 + 2.11414e26i) q^{93} +(-8.42326e25 - 1.45688e26i) q^{94} +3.31139e25 q^{95} +(1.48421e26 + 5.47165e26i) q^{96} +8.72016e26 q^{97} +(6.00491e26 + 1.03860e27i) q^{98} +(-7.33338e24 + 7.33338e24i) 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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5798.80 10029.5i −0.500534 0.865717i
\(3\) 1.92086e6 1.92086e6i 0.695598 0.695598i −0.267860 0.963458i \(-0.586316\pi\)
0.963458 + 0.267860i \(0.0863164\pi\)
\(4\) −6.69655e7 + 1.16319e8i −0.498932 + 0.866641i
\(5\) 4.80331e8 + 4.80331e8i 0.175973 + 0.175973i 0.789598 0.613625i \(-0.210289\pi\)
−0.613625 + 0.789598i \(0.710289\pi\)
\(6\) −3.04040e10 8.12664e9i −0.950361 0.254021i
\(7\) 4.11420e11i 1.60495i 0.596684 + 0.802476i \(0.296485\pi\)
−0.596684 + 0.802476i \(0.703515\pi\)
\(8\) 1.55494e12 2.87564e9i 0.999998 0.00184935i
\(9\) 2.46204e11i 0.0322865i
\(10\) 2.03215e12 7.60284e12i 0.0642623 0.240423i
\(11\) 2.97858e13 + 2.97858e13i 0.260140 + 0.260140i 0.825111 0.564971i \(-0.191112\pi\)
−0.564971 + 0.825111i \(0.691112\pi\)
\(12\) 9.48003e13 + 3.52063e14i 0.255778 + 0.949890i
\(13\) 3.90244e14 3.90244e14i 0.357356 0.357356i −0.505481 0.862838i \(-0.668685\pi\)
0.862838 + 0.505481i \(0.168685\pi\)
\(14\) 4.12636e15 2.38575e15i 1.38943 0.803333i
\(15\) 1.84530e15 0.244813
\(16\) −9.04564e15 1.55787e16i −0.502134 0.864790i
\(17\) −1.80150e16 −0.441138 −0.220569 0.975371i \(-0.570791\pi\)
−0.220569 + 0.975371i \(0.570791\pi\)
\(18\) 2.46931e15 1.42769e15i 0.0279510 0.0161605i
\(19\) 3.44699e16 3.44699e16i 0.188047 0.188047i −0.606804 0.794851i \(-0.707549\pi\)
0.794851 + 0.606804i \(0.207549\pi\)
\(20\) −8.80370e16 + 2.37058e16i −0.240304 + 0.0647068i
\(21\) 7.90280e17 + 7.90280e17i 1.11640 + 1.11640i
\(22\) 1.26016e17 4.71460e17i 0.0949990 0.355417i
\(23\) 2.55457e18i 1.05680i 0.848996 + 0.528399i \(0.177208\pi\)
−0.848996 + 0.528399i \(0.822792\pi\)
\(24\) 2.98130e18 2.99235e18i 0.694311 0.696883i
\(25\) 6.98915e18i 0.938067i
\(26\) −6.17692e18 1.65102e18i −0.488238 0.130500i
\(27\) 1.51206e19 + 1.51206e19i 0.718057 + 0.718057i
\(28\) −4.78558e19 2.75510e19i −1.39092 0.800762i
\(29\) −7.52283e19 + 7.52283e19i −1.36147 + 1.36147i −0.489424 + 0.872046i \(0.662793\pi\)
−0.872046 + 0.489424i \(0.837207\pi\)
\(30\) −1.07005e19 1.85075e19i −0.122537 0.211938i
\(31\) −1.10062e20 −0.809573 −0.404787 0.914411i \(-0.632654\pi\)
−0.404787 + 0.914411i \(0.632654\pi\)
\(32\) −1.03793e20 + 1.81061e20i −0.497328 + 0.867562i
\(33\) 1.14429e20 0.361906
\(34\) 1.04466e20 + 1.80682e20i 0.220804 + 0.381901i
\(35\) −1.97618e20 + 1.97618e20i −0.282428 + 0.282428i
\(36\) −2.86381e19 1.64872e19i −0.0279808 0.0161088i
\(37\) −1.76426e21 1.76426e21i −1.19080 1.19080i −0.976843 0.213959i \(-0.931364\pi\)
−0.213959 0.976843i \(-0.568636\pi\)
\(38\) −5.45601e20 1.45833e20i −0.256919 0.0686716i
\(39\) 1.49921e21i 0.497153i
\(40\) 7.48268e20 + 7.45505e20i 0.176298 + 0.175647i
\(41\) 3.54498e21i 0.598456i −0.954182 0.299228i \(-0.903271\pi\)
0.954182 0.299228i \(-0.0967290\pi\)
\(42\) 3.34347e21 1.25088e22i 0.407691 1.52529i
\(43\) 5.32060e20 + 5.32060e20i 0.0472211 + 0.0472211i 0.730323 0.683102i \(-0.239370\pi\)
−0.683102 + 0.730323i \(0.739370\pi\)
\(44\) −5.45926e21 + 1.47002e21i −0.355241 + 0.0956561i
\(45\) −1.18259e20 + 1.18259e20i −0.00568155 + 0.00568155i
\(46\) 2.56212e22 1.48135e22i 0.914888 0.528963i
\(47\) 1.45259e22 0.387990 0.193995 0.981003i \(-0.437855\pi\)
0.193995 + 0.981003i \(0.437855\pi\)
\(48\) −4.72998e22 1.25490e22i −0.950830 0.252263i
\(49\) −1.03554e23 −1.57587
\(50\) −7.00979e22 + 4.05287e22i −0.812101 + 0.469534i
\(51\) −3.46043e22 + 3.46043e22i −0.306855 + 0.306855i
\(52\) 1.92598e22 + 7.15256e22i 0.131403 + 0.487996i
\(53\) −2.22737e23 2.22737e23i −1.17508 1.17508i −0.980982 0.194098i \(-0.937822\pi\)
−0.194098 0.980982i \(-0.562178\pi\)
\(54\) 6.39713e22 2.39334e23i 0.262222 0.981045i
\(55\) 2.86141e22i 0.0915553i
\(56\) 1.18310e21 + 6.39735e23i 0.00296812 + 1.60495i
\(57\) 1.32424e23i 0.261610i
\(58\) 1.19074e24 + 3.18271e23i 1.86011 + 0.497186i
\(59\) −2.61506e22 2.61506e22i −0.0324324 0.0324324i 0.690705 0.723137i \(-0.257300\pi\)
−0.723137 + 0.690705i \(0.757300\pi\)
\(60\) −1.23571e23 + 2.14642e23i −0.122145 + 0.212165i
\(61\) −5.21421e23 + 5.21421e23i −0.412321 + 0.412321i −0.882546 0.470225i \(-0.844173\pi\)
0.470225 + 0.882546i \(0.344173\pi\)
\(62\) 6.38230e23 + 1.10388e24i 0.405219 + 0.700861i
\(63\) −1.01293e23 −0.0518183
\(64\) 2.41784e24 8.94290e21i 0.999993 0.00369870i
\(65\) 3.74893e23 0.125770
\(66\) −6.63549e23 1.14767e24i −0.181146 0.313309i
\(67\) −1.61528e24 + 1.61528e24i −0.359946 + 0.359946i −0.863793 0.503847i \(-0.831918\pi\)
0.503847 + 0.863793i \(0.331918\pi\)
\(68\) 1.20639e24 2.09548e24i 0.220098 0.382308i
\(69\) 4.90697e24 + 4.90697e24i 0.735107 + 0.735107i
\(70\) 3.12796e24 + 8.36069e23i 0.385867 + 0.103138i
\(71\) 6.23292e23i 0.0634898i 0.999496 + 0.0317449i \(0.0101064\pi\)
−0.999496 + 0.0317449i \(0.989894\pi\)
\(72\) 7.07993e20 + 3.82833e23i 5.97091e−5 + 0.0322864i
\(73\) 1.16831e25i 0.817900i 0.912557 + 0.408950i \(0.134105\pi\)
−0.912557 + 0.408950i \(0.865895\pi\)
\(74\) −7.46412e24 + 2.79253e25i −0.434861 + 1.62693i
\(75\) −1.34252e25 1.34252e25i −0.652518 0.652518i
\(76\) 1.70120e24 + 6.31778e24i 0.0691466 + 0.256792i
\(77\) −1.22545e25 + 1.22545e25i −0.417513 + 0.417513i
\(78\) −1.50364e25 + 8.69361e24i −0.430393 + 0.248842i
\(79\) −2.79686e25 −0.674069 −0.337035 0.941492i \(-0.609424\pi\)
−0.337035 + 0.941492i \(0.609424\pi\)
\(80\) 3.13802e24 1.18278e25i 0.0638176 0.240541i
\(81\) 5.62117e25 0.966671
\(82\) −3.55545e25 + 2.05566e25i −0.518093 + 0.299547i
\(83\) 1.86732e25 1.86732e25i 0.231028 0.231028i −0.582094 0.813122i \(-0.697766\pi\)
0.813122 + 0.582094i \(0.197766\pi\)
\(84\) −1.44846e26 + 3.90028e25i −1.52453 + 0.410511i
\(85\) −8.65317e24 8.65317e24i −0.0776283 0.0776283i
\(86\) 2.25100e24 8.42162e24i 0.0172444 0.0645159i
\(87\) 2.89006e26i 1.89407i
\(88\) 4.64008e25 + 4.62295e25i 0.260621 + 0.259659i
\(89\) 1.37565e26i 0.663349i 0.943394 + 0.331674i \(0.107614\pi\)
−0.943394 + 0.331674i \(0.892386\pi\)
\(90\) 1.87185e24 + 5.00324e23i 0.00776242 + 0.00207481i
\(91\) 1.60554e26 + 1.60554e26i 0.573540 + 0.573540i
\(92\) −2.97144e26 1.71068e26i −0.915865 0.527270i
\(93\) −2.11414e26 + 2.11414e26i −0.563138 + 0.563138i
\(94\) −8.42326e25 1.45688e26i −0.194202 0.335890i
\(95\) 3.31139e25 0.0661823
\(96\) 1.48421e26 + 5.47165e26i 0.257534 + 0.949415i
\(97\) 8.72016e26 1.31555 0.657773 0.753216i \(-0.271499\pi\)
0.657773 + 0.753216i \(0.271499\pi\)
\(98\) 6.00491e26 + 1.03860e27i 0.788778 + 1.36426i
\(99\) −7.33338e24 + 7.33338e24i −0.00839903 + 0.00839903i
\(100\) 8.12968e26 + 4.68032e26i 0.812968 + 0.468032i
\(101\) −6.47267e26 6.47267e26i −0.565907 0.565907i 0.365072 0.930979i \(-0.381044\pi\)
−0.930979 + 0.365072i \(0.881044\pi\)
\(102\) 5.47729e26 + 1.46402e26i 0.419241 + 0.112058i
\(103\) 2.56301e27i 1.71968i 0.510562 + 0.859841i \(0.329438\pi\)
−0.510562 + 0.859841i \(0.670562\pi\)
\(104\) 6.05685e26 6.07929e26i 0.356695 0.358016i
\(105\) 7.59192e26i 0.392913i
\(106\) −9.42339e26 + 3.52555e27i −0.429119 + 1.60545i
\(107\) −3.01990e27 3.01990e27i −1.21147 1.21147i −0.970544 0.240925i \(-0.922549\pi\)
−0.240925 0.970544i \(-0.577451\pi\)
\(108\) −2.77137e27 + 7.46249e26i −0.980559 + 0.264036i
\(109\) −7.85340e26 + 7.85340e26i −0.245358 + 0.245358i −0.819062 0.573704i \(-0.805506\pi\)
0.573704 + 0.819062i \(0.305506\pi\)
\(110\) 2.86986e26 1.65927e26i 0.0792610 0.0458265i
\(111\) −6.77779e27 −1.65664
\(112\) 6.40938e27 3.72156e27i 1.38795 0.805901i
\(113\) 7.96150e27 1.52910 0.764550 0.644565i \(-0.222961\pi\)
0.764550 + 0.644565i \(0.222961\pi\)
\(114\) −1.32815e27 + 7.67898e26i −0.226480 + 0.130945i
\(115\) −1.22704e27 + 1.22704e27i −0.185968 + 0.185968i
\(116\) −3.71275e27 1.37881e28i −0.500625 1.85919i
\(117\) 9.60797e25 + 9.60797e25i 0.0115378 + 0.0115378i
\(118\) −1.10636e26 + 4.13920e26i −0.0118438 + 0.0443108i
\(119\) 7.41175e27i 0.708006i
\(120\) 2.86933e27 5.30640e24i 0.244812 0.000452745i
\(121\) 1.13356e28i 0.864654i
\(122\) 8.25323e27 + 2.20599e27i 0.563334 + 0.150573i
\(123\) −6.80941e27 6.80941e27i −0.416285 0.416285i
\(124\) 7.37039e27 1.28023e28i 0.403922 0.701610i
\(125\) 6.93585e27 6.93585e27i 0.341047 0.341047i
\(126\) 5.87380e26 + 1.01592e27i 0.0259368 + 0.0448600i
\(127\) −1.22523e28 −0.486258 −0.243129 0.969994i \(-0.578174\pi\)
−0.243129 + 0.969994i \(0.578174\pi\)
\(128\) −1.41102e28 2.41979e28i −0.503732 0.863860i
\(129\) 2.04402e27 0.0656938
\(130\) −2.17393e27 3.76000e27i −0.0629521 0.108881i
\(131\) −2.63310e26 + 2.63310e26i −0.00687551 + 0.00687551i −0.710536 0.703661i \(-0.751548\pi\)
0.703661 + 0.710536i \(0.251548\pi\)
\(132\) −7.66277e27 + 1.33102e28i −0.180567 + 0.313643i
\(133\) 1.41816e28 + 1.41816e28i 0.301806 + 0.301806i
\(134\) 2.55672e28 + 6.83382e27i 0.491777 + 0.131446i
\(135\) 1.45258e28i 0.252717i
\(136\) −2.80123e28 + 5.18047e25i −0.441137 + 0.000815819i
\(137\) 1.10648e27i 0.0157839i 0.999969 + 0.00789195i \(0.00251211\pi\)
−0.999969 + 0.00789195i \(0.997488\pi\)
\(138\) 2.07601e28 7.76692e28i 0.268449 1.00434i
\(139\) 3.99650e28 + 3.99650e28i 0.468791 + 0.468791i 0.901523 0.432732i \(-0.142450\pi\)
−0.432732 + 0.901523i \(0.642450\pi\)
\(140\) −9.75306e27 3.62202e28i −0.103851 0.385676i
\(141\) 2.79021e28 2.79021e28i 0.269885 0.269885i
\(142\) 6.25133e27 3.61435e27i 0.0549642 0.0317788i
\(143\) 2.32475e28 0.185926
\(144\) 3.83553e27 2.22707e27i 0.0279210 0.0162121i
\(145\) −7.22689e28 −0.479163
\(146\) 1.17176e29 6.77481e28i 0.708070 0.409386i
\(147\) −1.98913e29 + 1.98913e29i −1.09617 + 1.09617i
\(148\) 3.23361e29 8.70717e28i 1.62613 0.437869i
\(149\) −3.60656e27 3.60656e27i −0.0165607 0.0165607i 0.698778 0.715339i \(-0.253728\pi\)
−0.715339 + 0.698778i \(0.753728\pi\)
\(150\) −5.67983e28 + 2.12498e29i −0.238289 + 0.891503i
\(151\) 4.10002e29i 1.57252i −0.617894 0.786261i \(-0.712014\pi\)
0.617894 0.786261i \(-0.287986\pi\)
\(152\) 5.34995e28 5.36978e28i 0.187699 0.188394i
\(153\) 4.43537e27i 0.0142428i
\(154\) 1.93968e29 + 5.18455e28i 0.570428 + 0.152469i
\(155\) −5.28664e28 5.28664e28i −0.142463 0.142463i
\(156\) 1.74386e29 + 1.00395e29i 0.430853 + 0.248045i
\(157\) −4.46652e29 + 4.46652e29i −1.01233 + 1.01233i −0.0124115 + 0.999923i \(0.503951\pi\)
−0.999923 + 0.0124115i \(0.996049\pi\)
\(158\) 1.62184e29 + 2.80512e29i 0.337394 + 0.583553i
\(159\) −8.55691e29 −1.63477
\(160\) −1.36824e29 + 3.71143e28i −0.240184 + 0.0651511i
\(161\) −1.05100e30 −1.69611
\(162\) −3.25960e29 5.63777e29i −0.483852 0.836864i
\(163\) −3.19372e29 + 3.19372e29i −0.436279 + 0.436279i −0.890758 0.454479i \(-0.849826\pi\)
0.454479 + 0.890758i \(0.349826\pi\)
\(164\) 4.12347e29 + 2.37391e29i 0.518646 + 0.298589i
\(165\) 5.49636e28 + 5.49636e28i 0.0636857 + 0.0636857i
\(166\) −2.95565e29 7.90013e28i −0.315642 0.0843674i
\(167\) 1.80078e30i 1.77333i 0.462413 + 0.886665i \(0.346984\pi\)
−0.462413 + 0.886665i \(0.653016\pi\)
\(168\) 1.23111e30 + 1.22657e30i 1.11846 + 1.11434i
\(169\) 8.87952e29i 0.744593i
\(170\) −3.66093e28 + 1.36965e29i −0.0283485 + 0.106060i
\(171\) 8.48662e27 + 8.48662e27i 0.00607138 + 0.00607138i
\(172\) −9.75181e28 + 2.62588e28i −0.0644839 + 0.0173636i
\(173\) −1.53158e30 + 1.53158e30i −0.936522 + 0.936522i −0.998102 0.0615805i \(-0.980386\pi\)
0.0615805 + 0.998102i \(0.480386\pi\)
\(174\) 2.89859e30 1.67589e30i 1.63973 0.948047i
\(175\) 2.87548e30 1.50555
\(176\) 1.94591e29 7.33455e29i 0.0943415 0.355592i
\(177\) −1.00463e29 −0.0451198
\(178\) 1.37971e30 7.97710e29i 0.574272 0.332028i
\(179\) 7.77018e29 7.77018e29i 0.299858 0.299858i −0.541100 0.840958i \(-0.681992\pi\)
0.840958 + 0.541100i \(0.181992\pi\)
\(180\) −5.83647e27 2.16751e28i −0.00208916 0.00775857i
\(181\) −2.70650e30 2.70650e30i −0.898974 0.898974i 0.0963716 0.995345i \(-0.469276\pi\)
−0.995345 + 0.0963716i \(0.969276\pi\)
\(182\) 6.79263e29 2.54131e30i 0.209447 0.783599i
\(183\) 2.00315e30i 0.573620i
\(184\) 7.34602e27 + 3.97221e30i 0.00195439 + 1.05680i
\(185\) 1.69486e30i 0.419097i
\(186\) 3.34634e30 + 8.94438e29i 0.769387 + 0.205648i
\(187\) −5.36592e29 5.36592e29i −0.114758 0.114758i
\(188\) −9.72731e29 + 1.68963e30i −0.193581 + 0.336248i
\(189\) −6.22093e30 + 6.22093e30i −1.15245 + 1.15245i
\(190\) −1.92021e29 3.32117e29i −0.0331265 0.0572951i
\(191\) −6.84092e30 −1.09942 −0.549710 0.835355i \(-0.685262\pi\)
−0.549710 + 0.835355i \(0.685262\pi\)
\(192\) 4.62714e30 4.66150e30i 0.693021 0.698166i
\(193\) 3.61438e30 0.504673 0.252337 0.967640i \(-0.418801\pi\)
0.252337 + 0.967640i \(0.418801\pi\)
\(194\) −5.05665e30 8.74592e30i −0.658475 1.13889i
\(195\) 7.20116e29 7.20116e29i 0.0874853 0.0874853i
\(196\) 6.93457e30 1.20453e31i 0.786253 1.36572i
\(197\) −3.90430e30 3.90430e30i −0.413285 0.413285i 0.469596 0.882881i \(-0.344399\pi\)
−0.882881 + 0.469596i \(0.844399\pi\)
\(198\) 1.16075e29 + 3.10256e28i 0.0114752 + 0.00306718i
\(199\) 7.25369e30i 0.669950i 0.942227 + 0.334975i \(0.108728\pi\)
−0.942227 + 0.334975i \(0.891272\pi\)
\(200\) −2.00983e28 1.08677e31i −0.00173482 0.938066i
\(201\) 6.20544e30i 0.500756i
\(202\) −2.73841e30 + 1.02452e31i −0.206660 + 0.773171i
\(203\) −3.09504e31 3.09504e31i −2.18509 2.18509i
\(204\) −1.70783e30 6.34242e30i −0.112833 0.419033i
\(205\) 1.70276e30 1.70276e30i 0.105312 0.105312i
\(206\) 2.57058e31 1.48624e31i 1.48876 0.860759i
\(207\) −6.28945e29 −0.0341203
\(208\) −9.60950e30 2.54948e30i −0.488479 0.129597i
\(209\) 2.05343e30 0.0978373
\(210\) 7.61434e30 4.40240e30i 0.340151 0.196666i
\(211\) −8.25043e30 + 8.25043e30i −0.345672 + 0.345672i −0.858494 0.512823i \(-0.828600\pi\)
0.512823 + 0.858494i \(0.328600\pi\)
\(212\) 4.08241e31 1.09927e31i 1.60466 0.432088i
\(213\) 1.19726e30 + 1.19726e30i 0.0441634 + 0.0441634i
\(214\) −1.27764e31 + 4.78001e31i −0.442408 + 1.65517i
\(215\) 5.11129e29i 0.0166193i
\(216\) 2.35552e31 + 2.34682e31i 0.719383 + 0.716727i
\(217\) 4.52819e31i 1.29933i
\(218\) 1.24306e31 + 3.32257e30i 0.335221 + 0.0896006i
\(219\) 2.24416e31 + 2.24416e31i 0.568930 + 0.568930i
\(220\) −3.32835e30 1.91616e30i −0.0793456 0.0456799i
\(221\) −7.03026e30 + 7.03026e30i −0.157643 + 0.157643i
\(222\) 3.93031e31 + 6.79781e31i 0.829204 + 1.43418i
\(223\) −1.75149e30 −0.0347771 −0.0173885 0.999849i \(-0.505535\pi\)
−0.0173885 + 0.999849i \(0.505535\pi\)
\(224\) −7.44923e31 4.27025e31i −1.39240 0.798188i
\(225\) 1.72075e30 0.0302869
\(226\) −4.61671e31 7.98501e31i −0.765366 1.32377i
\(227\) −2.57645e31 + 2.57645e31i −0.402414 + 0.402414i −0.879083 0.476669i \(-0.841844\pi\)
0.476669 + 0.879083i \(0.341844\pi\)
\(228\) 1.54033e31 + 8.86781e30i 0.226722 + 0.130526i
\(229\) 7.35315e31 + 7.35315e31i 1.02022 + 1.02022i 0.999791 + 0.0204302i \(0.00650360\pi\)
0.0204302 + 0.999791i \(0.493496\pi\)
\(230\) 1.94220e31 + 5.19128e30i 0.254079 + 0.0679123i
\(231\) 4.70783e31i 0.580843i
\(232\) −1.16759e32 + 1.17192e32i −1.35895 + 1.36399i
\(233\) 2.95940e31i 0.325012i 0.986708 + 0.162506i \(0.0519576\pi\)
−0.986708 + 0.162506i \(0.948042\pi\)
\(234\) 4.06488e29 1.52078e30i 0.00421340 0.0157635i
\(235\) 6.97722e30 + 6.97722e30i 0.0682757 + 0.0682757i
\(236\) 4.79298e30 1.29061e30i 0.0442888 0.0119257i
\(237\) −5.37236e31 + 5.37236e31i −0.468881 + 0.468881i
\(238\) −7.43364e31 + 4.29793e31i −0.612932 + 0.354381i
\(239\) 2.50948e32 1.95529 0.977645 0.210262i \(-0.0674316\pi\)
0.977645 + 0.210262i \(0.0674316\pi\)
\(240\) −1.66919e31 2.87472e31i −0.122929 0.211711i
\(241\) 1.32138e32 0.920019 0.460010 0.887914i \(-0.347846\pi\)
0.460010 + 0.887914i \(0.347846\pi\)
\(242\) −1.13691e32 + 6.57329e31i −0.748546 + 0.432788i
\(243\) −7.32907e30 + 7.32907e30i −0.0456420 + 0.0456420i
\(244\) −2.57337e31 9.55681e31i −0.151614 0.563055i
\(245\) −4.97403e31 4.97403e31i −0.277311 0.277311i
\(246\) −2.88088e31 + 1.07782e32i −0.152020 + 0.568749i
\(247\) 2.69034e31i 0.134399i
\(248\) −1.71141e32 + 3.16500e29i −0.809572 + 0.00149719i
\(249\) 7.17371e31i 0.321405i
\(250\) −1.09783e32 2.93437e31i −0.465956 0.124545i
\(251\) −2.83073e32 2.83073e32i −1.13842 1.13842i −0.988733 0.149690i \(-0.952172\pi\)
−0.149690 0.988733i \(-0.547828\pi\)
\(252\) 6.78316e30 1.17823e31i 0.0258538 0.0449079i
\(253\) −7.60899e31 + 7.60899e31i −0.274916 + 0.274916i
\(254\) 7.10486e31 + 1.22885e32i 0.243389 + 0.420962i
\(255\) −3.32430e31 −0.107996
\(256\) −1.60871e32 + 2.81838e32i −0.495723 + 0.868481i
\(257\) 3.07303e32 0.898401 0.449200 0.893431i \(-0.351709\pi\)
0.449200 + 0.893431i \(0.351709\pi\)
\(258\) −1.18529e31 2.05006e31i −0.0328820 0.0568723i
\(259\) 7.25853e32 7.25853e32i 1.91118 1.91118i
\(260\) −2.51049e31 + 4.36070e31i −0.0627506 + 0.108997i
\(261\) −1.85215e31 1.85215e31i −0.0439571 0.0439571i
\(262\) 4.16776e30 + 1.11400e30i 0.00939367 + 0.00251082i
\(263\) 9.92943e31i 0.212580i 0.994335 + 0.106290i \(0.0338971\pi\)
−0.994335 + 0.106290i \(0.966103\pi\)
\(264\) 1.77930e32 3.29055e29i 0.361906 0.000669292i
\(265\) 2.13975e32i 0.413564i
\(266\) 5.99986e31 2.24471e32i 0.110215 0.412343i
\(267\) 2.64242e32 + 2.64242e32i 0.461424 + 0.461424i
\(268\) −7.97190e31 2.96055e32i −0.132356 0.491533i
\(269\) −6.77329e32 + 6.77329e32i −1.06941 + 1.06941i −0.0720049 + 0.997404i \(0.522940\pi\)
−0.997404 + 0.0720049i \(0.977060\pi\)
\(270\) 1.45687e32 8.42322e31i 0.218781 0.126493i
\(271\) 9.89672e32 1.41386 0.706929 0.707285i \(-0.250080\pi\)
0.706929 + 0.707285i \(0.250080\pi\)
\(272\) 1.62957e32 + 2.80650e32i 0.221510 + 0.381492i
\(273\) 6.16805e32 0.797906
\(274\) 1.10974e31 6.41624e30i 0.0136644 0.00790038i
\(275\) 2.08177e32 2.08177e32i 0.244029 0.244029i
\(276\) −8.99369e32 + 2.42174e32i −1.00384 + 0.270306i
\(277\) −8.93560e32 8.93560e32i −0.949833 0.949833i 0.0489678 0.998800i \(-0.484407\pi\)
−0.998800 + 0.0489678i \(0.984407\pi\)
\(278\) 1.69081e32 6.32579e32i 0.171195 0.640487i
\(279\) 2.70978e31i 0.0261383i
\(280\) −3.06716e32 + 3.07853e32i −0.281905 + 0.282950i
\(281\) 4.24304e32i 0.371656i −0.982582 0.185828i \(-0.940503\pi\)
0.982582 0.185828i \(-0.0594968\pi\)
\(282\) −4.41644e32 1.18046e32i −0.368731 0.0985575i
\(283\) −8.55563e32 8.55563e32i −0.680981 0.680981i 0.279240 0.960221i \(-0.409918\pi\)
−0.960221 + 0.279240i \(0.909918\pi\)
\(284\) −7.25005e31 4.17391e31i −0.0550229 0.0316771i
\(285\) 6.36071e31 6.36071e31i 0.0460363 0.0460363i
\(286\) −1.34808e32 2.33161e32i −0.0930621 0.160959i
\(287\) 1.45848e33 0.960493
\(288\) −4.45780e31 2.55542e31i −0.0280106 0.0160570i
\(289\) −1.34317e33 −0.805397
\(290\) 4.19073e32 + 7.24824e32i 0.239837 + 0.414820i
\(291\) 1.67502e33 1.67502e33i 0.915091 0.915091i
\(292\) −1.35896e33 7.82366e32i −0.708826 0.408076i
\(293\) 7.75799e32 + 7.75799e32i 0.386399 + 0.386399i 0.873401 0.487002i \(-0.161909\pi\)
−0.487002 + 0.873401i \(0.661909\pi\)
\(294\) 3.14847e33 + 8.41549e32i 1.49765 + 0.400305i
\(295\) 2.51219e31i 0.0114144i
\(296\) −2.74840e33 2.73825e33i −1.19300 1.18860i
\(297\) 9.00759e32i 0.373591i
\(298\) −1.52584e31 + 5.70858e31i −0.00604768 + 0.0226260i
\(299\) 9.96907e32 + 9.96907e32i 0.377653 + 0.377653i
\(300\) 2.46062e33 6.62573e32i 0.891061 0.239937i
\(301\) −2.18900e32 + 2.18900e32i −0.0757876 + 0.0757876i
\(302\) −4.11213e33 + 2.37752e33i −1.36136 + 0.787100i
\(303\) −2.48662e33 −0.787287
\(304\) −8.48797e32 2.25193e32i −0.257046 0.0681963i
\(305\) −5.00909e32 −0.145115
\(306\) −4.44847e31 + 2.57198e31i −0.0123302 + 0.00712900i
\(307\) −4.78646e33 + 4.78646e33i −1.26954 + 1.26954i −0.323215 + 0.946326i \(0.604764\pi\)
−0.946326 + 0.323215i \(0.895236\pi\)
\(308\) −6.04797e32 2.24605e33i −0.153523 0.570145i
\(309\) 4.92318e33 + 4.92318e33i 1.19621 + 1.19621i
\(310\) −2.23664e32 + 8.36787e32i −0.0520251 + 0.194640i
\(311\) 8.17994e33i 1.82173i −0.412701 0.910867i \(-0.635415\pi\)
0.412701 0.910867i \(-0.364585\pi\)
\(312\) −4.31118e30 2.33118e33i −0.000919410 0.497152i
\(313\) 9.44940e33i 1.92999i 0.262261 + 0.964997i \(0.415532\pi\)
−0.262261 + 0.964997i \(0.584468\pi\)
\(314\) 7.06976e33 + 1.88967e33i 1.38310 + 0.369688i
\(315\) −4.86543e31 4.86543e31i −0.00911861 0.00911861i
\(316\) 1.87293e33 3.25326e33i 0.336315 0.584176i
\(317\) −2.40108e33 + 2.40108e33i −0.413150 + 0.413150i −0.882834 0.469685i \(-0.844368\pi\)
0.469685 + 0.882834i \(0.344368\pi\)
\(318\) 4.96198e33 + 8.58218e33i 0.818256 + 1.41525i
\(319\) −4.48147e33 −0.708347
\(320\) 1.16566e33 + 1.15707e33i 0.176622 + 0.175321i
\(321\) −1.16016e34 −1.68539
\(322\) 6.09455e33 + 1.05411e34i 0.848961 + 1.46835i
\(323\) −6.20976e32 + 6.20976e32i −0.0829546 + 0.0829546i
\(324\) −3.76424e33 + 6.53846e33i −0.482303 + 0.837757i
\(325\) −2.72747e33 2.72747e33i −0.335224 0.335224i
\(326\) 5.05513e33 + 1.35118e33i 0.596066 + 0.159322i
\(327\) 3.01706e33i 0.341341i
\(328\) −1.01941e31 5.51224e33i −0.00110675 0.598455i
\(329\) 5.97623e33i 0.622706i
\(330\) 2.32536e32 8.69982e32i 0.0232569 0.0870106i
\(331\) −4.34123e32 4.34123e32i −0.0416807 0.0416807i 0.685959 0.727640i \(-0.259383\pi\)
−0.727640 + 0.685959i \(0.759383\pi\)
\(332\) 9.21580e32 + 3.42250e33i 0.0849510 + 0.315485i
\(333\) 4.34368e32 4.34368e32i 0.0384468 0.0384468i
\(334\) 1.80610e34 1.04424e34i 1.53520 0.887611i
\(335\) −1.55174e33 −0.126681
\(336\) 5.16292e33 1.94601e34i 0.404870 1.52604i
\(337\) −2.00111e34 −1.50753 −0.753767 0.657142i \(-0.771765\pi\)
−0.753767 + 0.657142i \(0.771765\pi\)
\(338\) 8.90575e33 5.14906e33i 0.644607 0.372694i
\(339\) 1.52929e34 1.52929e34i 1.06364 1.06364i
\(340\) 1.58599e33 4.27061e32i 0.106007 0.0285446i
\(341\) −3.27830e33 3.27830e33i −0.210603 0.210603i
\(342\) 3.59046e31 1.34329e32i 0.00221717 0.00829503i
\(343\) 1.55690e34i 0.924249i
\(344\) 8.28852e32 + 8.25792e32i 0.0473084 + 0.0471337i
\(345\) 4.71394e33i 0.258718i
\(346\) 2.42424e34 + 6.47972e33i 1.27952 + 0.342002i
\(347\) 1.11424e34 + 1.11424e34i 0.565628 + 0.565628i 0.930901 0.365273i \(-0.119024\pi\)
−0.365273 + 0.930901i \(0.619024\pi\)
\(348\) −3.36167e34 1.93534e34i −1.64148 0.945013i
\(349\) −1.81949e34 + 1.81949e34i −0.854683 + 0.854683i −0.990706 0.136022i \(-0.956568\pi\)
0.136022 + 0.990706i \(0.456568\pi\)
\(350\) −1.66743e34 2.88397e34i −0.753580 1.30338i
\(351\) 1.18015e34 0.513204
\(352\) −8.48461e33 + 2.30150e33i −0.355063 + 0.0963129i
\(353\) −7.57777e33 −0.305199 −0.152599 0.988288i \(-0.548764\pi\)
−0.152599 + 0.988288i \(0.548764\pi\)
\(354\) 5.82566e32 + 1.00760e33i 0.0225840 + 0.0390610i
\(355\) −2.99386e32 + 2.99386e32i −0.0111725 + 0.0111725i
\(356\) −1.60013e34 9.21209e33i −0.574885 0.330966i
\(357\) −1.42369e34 1.42369e34i −0.492487 0.492487i
\(358\) −1.22989e34 3.28736e33i −0.409681 0.109503i
\(359\) 3.28159e34i 1.05271i −0.850264 0.526356i \(-0.823558\pi\)
0.850264 0.526356i \(-0.176442\pi\)
\(360\) −1.83546e32 + 1.84226e32i −0.00567103 + 0.00569204i
\(361\) 3.12243e34i 0.929277i
\(362\) −1.14505e34 + 4.28394e34i −0.328290 + 1.22822i
\(363\) −2.17741e34 2.17741e34i −0.601452 0.601452i
\(364\) −2.94271e34 + 7.92386e33i −0.783210 + 0.210896i
\(365\) −5.61176e33 + 5.61176e33i −0.143928 + 0.143928i
\(366\) 2.00907e34 1.16159e34i 0.496592 0.287116i
\(367\) 1.71102e34 0.407627 0.203814 0.979010i \(-0.434666\pi\)
0.203814 + 0.979010i \(0.434666\pi\)
\(368\) 3.97968e34 2.31077e34i 0.913908 0.530654i
\(369\) 8.72788e32 0.0193220
\(370\) −1.69986e34 + 9.82814e33i −0.362820 + 0.209772i
\(371\) 9.16384e34 9.16384e34i 1.88595 1.88595i
\(372\) −1.04340e34 3.87489e34i −0.207071 0.769006i
\(373\) 1.61906e34 + 1.61906e34i 0.309879 + 0.309879i 0.844863 0.534983i \(-0.179682\pi\)
−0.534983 + 0.844863i \(0.679682\pi\)
\(374\) −2.27018e33 + 8.49336e33i −0.0419076 + 0.156788i
\(375\) 2.66456e34i 0.474463i
\(376\) 2.25869e34 4.17711e31i 0.387989 0.000717530i
\(377\) 5.87148e34i 0.973059i
\(378\) 9.84670e34 + 2.63191e34i 1.57453 + 0.420854i
\(379\) 5.85197e34 + 5.85197e34i 0.902969 + 0.902969i 0.995692 0.0927227i \(-0.0295570\pi\)
−0.0927227 + 0.995692i \(0.529557\pi\)
\(380\) −2.21749e33 + 3.85176e33i −0.0330205 + 0.0573563i
\(381\) −2.35349e34 + 2.35349e34i −0.338240 + 0.338240i
\(382\) 3.96691e34 + 6.86112e34i 0.550297 + 0.951787i
\(383\) 6.29135e34 0.842481 0.421241 0.906949i \(-0.361595\pi\)
0.421241 + 0.906949i \(0.361595\pi\)
\(384\) −7.35845e34 1.93770e34i −0.951295 0.250504i
\(385\) −1.17724e34 −0.146942
\(386\) −2.09591e34 3.62506e34i −0.252606 0.436904i
\(387\) −1.30995e32 + 1.30995e32i −0.00152460 + 0.00152460i
\(388\) −5.83950e34 + 1.01432e35i −0.656368 + 1.14011i
\(389\) 2.91144e34 + 2.91144e34i 0.316073 + 0.316073i 0.847257 0.531184i \(-0.178253\pi\)
−0.531184 + 0.847257i \(0.678253\pi\)
\(390\) −1.13982e34 3.04662e33i −0.119527 0.0319482i
\(391\) 4.60207e34i 0.466194i
\(392\) −1.61021e35 + 2.97785e32i −1.57587 + 0.00291434i
\(393\) 1.01156e33i 0.00956519i
\(394\) −1.65181e34 + 6.17986e34i −0.150925 + 0.564651i
\(395\) −1.34342e34 1.34342e34i −0.118618 0.118618i
\(396\) −3.61925e32 1.34409e33i −0.00308840 0.0114695i
\(397\) −3.35154e34 + 3.35154e34i −0.276422 + 0.276422i −0.831679 0.555257i \(-0.812620\pi\)
0.555257 + 0.831679i \(0.312620\pi\)
\(398\) 7.27512e34 4.20627e34i 0.579987 0.335333i
\(399\) 5.44817e34 0.419872
\(400\) −1.08882e35 + 6.32213e34i −0.811231 + 0.471035i
\(401\) −1.58137e35 −1.13916 −0.569579 0.821937i \(-0.692894\pi\)
−0.569579 + 0.821937i \(0.692894\pi\)
\(402\) 6.22377e34 3.59841e34i 0.433513 0.250645i
\(403\) −4.29512e34 + 4.29512e34i −0.289306 + 0.289306i
\(404\) 1.18634e35 3.19446e34i 0.772787 0.208089i
\(405\) 2.70002e34 + 2.70002e34i 0.170108 + 0.170108i
\(406\) −1.30943e35 + 4.89894e35i −0.797960 + 2.98539i
\(407\) 1.05100e35i 0.619551i
\(408\) −5.37082e34 + 5.39072e34i −0.306287 + 0.307422i
\(409\) 1.01544e35i 0.560262i −0.959962 0.280131i \(-0.909622\pi\)
0.959962 0.280131i \(-0.0903778\pi\)
\(410\) −2.69519e34 7.20394e33i −0.143882 0.0384581i
\(411\) 2.12538e33 + 2.12538e33i 0.0109793 + 0.0109793i
\(412\) −2.98126e35 1.71633e35i −1.49035 0.858004i
\(413\) 1.07589e34 1.07589e34i 0.0520525 0.0520525i
\(414\) 3.64713e33 + 6.30803e33i 0.0170784 + 0.0295385i
\(415\) 1.79386e34 0.0813092
\(416\) 3.01535e34 + 1.11163e35i 0.132305 + 0.487752i
\(417\) 1.53534e35 0.652181
\(418\) −1.19074e34 2.05949e34i −0.0489708 0.0846994i
\(419\) 1.96727e35 1.96727e35i 0.783383 0.783383i −0.197017 0.980400i \(-0.563125\pi\)
0.980400 + 0.197017i \(0.0631253\pi\)
\(420\) −8.83082e34 5.08397e34i −0.340514 0.196037i
\(421\) 1.76535e35 + 1.76535e35i 0.659209 + 0.659209i 0.955193 0.295984i \(-0.0956474\pi\)
−0.295984 + 0.955193i \(0.595647\pi\)
\(422\) 1.30591e35 + 3.49054e34i 0.472274 + 0.126233i
\(423\) 3.57632e33i 0.0125268i
\(424\) −3.46983e35 3.45702e35i −1.17725 1.17290i
\(425\) 1.25910e35i 0.413817i
\(426\) 5.06527e33 1.89506e34i 0.0161277 0.0603382i
\(427\) −2.14523e35 2.14523e35i −0.661756 0.661756i
\(428\) 5.53501e35 1.49042e35i 1.65435 0.445468i
\(429\) 4.46551e34 4.46551e34i 0.129330 0.129330i
\(430\) 5.12639e33 2.96394e33i 0.0143876 0.00831850i
\(431\) 3.08951e35 0.840322 0.420161 0.907450i \(-0.361974\pi\)
0.420161 + 0.907450i \(0.361974\pi\)
\(432\) 9.87834e34 3.72335e35i 0.260407 0.981529i
\(433\) 6.37253e35 1.62827 0.814133 0.580678i \(-0.197213\pi\)
0.814133 + 0.580678i \(0.197213\pi\)
\(434\) −4.54157e35 + 2.62581e35i −1.12485 + 0.650357i
\(435\) −1.38818e35 + 1.38818e35i −0.333305 + 0.333305i
\(436\) −3.87590e34 1.43940e35i −0.0902204 0.335054i
\(437\) 8.80558e34 + 8.80558e34i 0.198728 + 0.198728i
\(438\) 9.49445e34 3.55213e35i 0.207764 0.777300i
\(439\) 5.41749e35i 1.14955i 0.818312 + 0.574774i \(0.194910\pi\)
−0.818312 + 0.574774i \(0.805090\pi\)
\(440\) 8.22838e31 + 4.44932e34i 0.000169318 + 0.0915551i
\(441\) 2.54955e34i 0.0508794i
\(442\) 1.11277e35 + 2.97432e34i 0.215380 + 0.0575687i
\(443\) −3.88681e35 3.88681e35i −0.729697 0.729697i 0.240862 0.970559i \(-0.422570\pi\)
−0.970559 + 0.240862i \(0.922570\pi\)
\(444\) 4.53878e35 7.88383e35i 0.826550 1.43571i
\(445\) −6.60766e34 + 6.60766e34i −0.116731 + 0.116731i
\(446\) 1.01566e34 + 1.75667e34i 0.0174071 + 0.0301071i
\(447\) −1.38554e34 −0.0230392
\(448\) 3.67929e33 + 9.94747e35i 0.00593623 + 1.60494i
\(449\) −3.77145e35 −0.590450 −0.295225 0.955428i \(-0.595395\pi\)
−0.295225 + 0.955428i \(0.595395\pi\)
\(450\) −9.97832e33 1.72584e34i −0.0151596 0.0262199i
\(451\) 1.05590e35 1.05590e35i 0.155683 0.155683i
\(452\) −5.33146e35 + 9.26070e35i −0.762916 + 1.32518i
\(453\) −7.87555e35 7.87555e35i −1.09384 1.09384i
\(454\) 4.07810e35 + 1.09003e35i 0.549799 + 0.146955i
\(455\) 1.54239e35i 0.201855i
\(456\) −3.80802e32 2.05911e35i −0.000483809 0.261610i
\(457\) 9.14618e35i 1.12816i −0.825720 0.564080i \(-0.809231\pi\)
0.825720 0.564080i \(-0.190769\pi\)
\(458\) 3.11092e35 1.16388e36i 0.372568 1.39388i
\(459\) −2.72398e35 2.72398e35i −0.316762 0.316762i
\(460\) −6.05582e34 2.24897e35i −0.0683821 0.253953i
\(461\) −1.11560e36 + 1.11560e36i −1.22333 + 1.22333i −0.256894 + 0.966440i \(0.582699\pi\)
−0.966440 + 0.256894i \(0.917301\pi\)
\(462\) 4.72173e35 2.72997e35i 0.502845 0.290731i
\(463\) −6.55011e35 −0.677494 −0.338747 0.940878i \(-0.610003\pi\)
−0.338747 + 0.940878i \(0.610003\pi\)
\(464\) 1.85244e36 + 4.91468e35i 1.86103 + 0.493745i
\(465\) −2.03098e35 −0.198194
\(466\) 2.96814e35 1.71610e35i 0.281368 0.162679i
\(467\) 8.69703e35 8.69703e35i 0.800927 0.800927i −0.182313 0.983240i \(-0.558359\pi\)
0.983240 + 0.182313i \(0.0583585\pi\)
\(468\) −1.76099e34 + 4.74183e33i −0.0157557 + 0.00424255i
\(469\) −6.64559e35 6.64559e35i −0.577697 0.577697i
\(470\) 2.95188e34 1.10438e35i 0.0249331 0.0932817i
\(471\) 1.71591e36i 1.40836i
\(472\) −4.07378e34 4.05874e34i −0.0324923 0.0323724i
\(473\) 3.16956e34i 0.0245682i
\(474\) 8.50356e35 + 2.27290e35i 0.640609 + 0.171228i
\(475\) −2.40915e35 2.40915e35i −0.176401 0.176401i
\(476\) 8.62124e35 + 4.96331e35i 0.613587 + 0.353247i
\(477\) 5.48386e34 5.48386e34i 0.0379392 0.0379392i
\(478\) −1.45520e36 2.51689e36i −0.978689 1.69273i
\(479\) −5.54869e35 −0.362795 −0.181398 0.983410i \(-0.558062\pi\)
−0.181398 + 0.983410i \(0.558062\pi\)
\(480\) −1.91529e35 + 3.34111e35i −0.121752 + 0.212390i
\(481\) −1.37698e36 −0.851081
\(482\) −7.66241e35 1.32528e36i −0.460501 0.796477i
\(483\) −2.01883e36 + 2.01883e36i −1.17981 + 1.17981i
\(484\) 1.31854e36 + 7.59095e35i 0.749345 + 0.431403i
\(485\) 4.18856e35 + 4.18856e35i 0.231500 + 0.231500i
\(486\) 1.16007e35 + 3.10074e34i 0.0623584 + 0.0166677i
\(487\) 1.84121e36i 0.962636i 0.876546 + 0.481318i \(0.159842\pi\)
−0.876546 + 0.481318i \(0.840158\pi\)
\(488\) −8.09279e35 + 8.12278e35i −0.411558 + 0.413083i
\(489\) 1.22694e36i 0.606949i
\(490\) −2.10438e35 + 7.87307e35i −0.101269 + 0.378876i
\(491\) 1.12746e36 + 1.12746e36i 0.527836 + 0.527836i 0.919927 0.392090i \(-0.128248\pi\)
−0.392090 + 0.919927i \(0.628248\pi\)
\(492\) 1.24806e36 3.36065e35i 0.568467 0.153072i
\(493\) 1.35524e36 1.35524e36i 0.600596 0.600596i
\(494\) −2.69828e35 + 1.56007e35i −0.116352 + 0.0672715i
\(495\) −7.04490e33 −0.00295600
\(496\) 9.95585e35 + 1.71463e36i 0.406514 + 0.700111i
\(497\) −2.56435e35 −0.101898
\(498\) −7.19490e35 + 4.15989e35i −0.278246 + 0.160874i
\(499\) −2.19578e36 + 2.19578e36i −0.826479 + 0.826479i −0.987028 0.160549i \(-0.948674\pi\)
0.160549 + 0.987028i \(0.448674\pi\)
\(500\) 3.42306e35 + 1.27123e36i 0.125406 + 0.465725i
\(501\) 3.45905e36 + 3.45905e36i 1.23352 + 1.23352i
\(502\) −1.19761e36 + 4.48058e36i −0.415733 + 1.55537i
\(503\) 4.88288e36i 1.65009i −0.565064 0.825047i \(-0.691149\pi\)
0.565064 0.825047i \(-0.308851\pi\)
\(504\) −1.57505e35 + 2.91283e32i −0.0518182 + 9.58303e-5i
\(505\) 6.21805e35i 0.199168i
\(506\) 1.20438e36 + 3.21916e35i 0.375604 + 0.100395i
\(507\) 1.70563e36 + 1.70563e36i 0.517938 + 0.517938i
\(508\) 8.20481e35 1.42517e36i 0.242610 0.421412i
\(509\) 3.60237e36 3.60237e36i 1.03729 1.03729i 0.0380079 0.999277i \(-0.487899\pi\)
0.999277 0.0380079i \(-0.0121012\pi\)
\(510\) 1.92770e35 + 3.33412e35i 0.0540557 + 0.0934941i
\(511\) −4.80667e36 −1.31269
\(512\) 3.75957e36 2.08585e34i 0.999985 0.00554803i
\(513\) 1.04241e36 0.270057
\(514\) −1.78199e36 3.08211e36i −0.449680 0.777761i
\(515\) −1.23109e36 + 1.23109e36i −0.302617 + 0.302617i
\(516\) −1.36879e35 + 2.37758e35i −0.0327767 + 0.0569330i
\(517\) 4.32664e35 + 4.32664e35i 0.100932 + 0.100932i
\(518\) −1.14890e37 3.07089e36i −2.61115 0.697931i
\(519\) 5.88390e36i 1.30289i
\(520\) 5.82936e35 1.07806e33i 0.125770 0.000232593i
\(521\) 4.71541e36i 0.991312i −0.868519 0.495656i \(-0.834928\pi\)
0.868519 0.495656i \(-0.165072\pi\)
\(522\) −7.83595e34 + 2.93164e35i −0.0160524 + 0.0600564i
\(523\) 1.91592e36 + 1.91592e36i 0.382477 + 0.382477i 0.871994 0.489517i \(-0.162827\pi\)
−0.489517 + 0.871994i \(0.662827\pi\)
\(524\) −1.29952e34 4.82606e34i −0.00252819 0.00938901i
\(525\) 5.52338e36 5.52338e36i 1.04726 1.04726i
\(526\) 9.95876e35 5.75788e35i 0.184034 0.106403i
\(527\) 1.98278e36 0.357134
\(528\) −1.03508e36 1.78265e36i −0.181726 0.312973i
\(529\) −6.82620e35 −0.116823
\(530\) −2.14607e36 + 1.24080e36i −0.358029 + 0.207003i
\(531\) 6.43837e33 6.43837e33i 0.00104713 0.00104713i
\(532\) −2.59926e36 + 6.99907e35i −0.412139 + 0.110977i
\(533\) −1.38341e36 1.38341e36i −0.213862 0.213862i
\(534\) 1.11794e36 4.18252e36i 0.168504 0.630421i
\(535\) 2.90111e36i 0.426371i
\(536\) −2.50702e36 + 2.51631e36i −0.359280 + 0.360611i
\(537\) 2.98508e36i 0.417161i
\(538\) 1.07210e37 + 2.86560e36i 1.46108 + 0.390530i
\(539\) −3.08445e36 3.08445e36i −0.409948 0.409948i
\(540\) −1.68962e36 9.72727e35i −0.219015 0.126088i
\(541\) 8.14549e36 8.14549e36i 1.02980 1.02980i 0.0302608 0.999542i \(-0.490366\pi\)
0.999542 0.0302608i \(-0.00963378\pi\)
\(542\) −5.73891e36 9.92595e36i −0.707684 1.22400i
\(543\) −1.03976e37 −1.25065
\(544\) 1.86983e36 3.26182e36i 0.219390 0.382715i
\(545\) −7.54447e35 −0.0863527
\(546\) −3.57673e36 6.18627e36i −0.399379 0.690761i
\(547\) 5.22456e36 5.22456e36i 0.569142 0.569142i −0.362746 0.931888i \(-0.618161\pi\)
0.931888 + 0.362746i \(0.118161\pi\)
\(548\) −1.28704e35 7.40957e34i −0.0136790 0.00787509i
\(549\) −1.28376e35 1.28376e35i −0.0133124 0.0133124i
\(550\) −3.29510e36 8.80743e35i −0.333405 0.0891154i
\(551\) 5.18622e36i 0.512041i
\(552\) 7.64416e36 + 7.61594e36i 0.736465 + 0.733746i
\(553\) 1.15068e37i 1.08185i
\(554\) −3.78042e36 + 1.41436e37i −0.346863 + 1.29771i
\(555\) −3.25558e36 3.25558e36i −0.291523 0.291523i
\(556\) −7.32494e36 + 1.97239e36i −0.640169 + 0.172379i
\(557\) 1.24729e37 1.24729e37i 1.06395 1.06395i 0.0661450 0.997810i \(-0.478930\pi\)
0.997810 0.0661450i \(-0.0210700\pi\)
\(558\) −2.71778e35 + 1.57135e35i −0.0226284 + 0.0130831i
\(559\) 4.15266e35 0.0337495
\(560\) 4.86620e36 + 1.29104e36i 0.386057 + 0.102424i
\(561\) −2.06143e36 −0.159651
\(562\) −4.25557e36 + 2.46045e36i −0.321749 + 0.186027i
\(563\) 6.46499e36 6.46499e36i 0.477204 0.477204i −0.427032 0.904236i \(-0.640441\pi\)
0.904236 + 0.427032i \(0.140441\pi\)
\(564\) 1.37706e36 + 5.11401e36i 0.0992393 + 0.368548i
\(565\) 3.82415e36 + 3.82415e36i 0.269080 + 0.269080i
\(566\) −3.61966e36 + 1.35421e37i −0.248683 + 0.930391i
\(567\) 2.31266e37i 1.55146i
\(568\) 1.79236e33 + 9.69183e35i 0.000117415 + 0.0634897i
\(569\) 2.49481e37i 1.59596i 0.602686 + 0.797978i \(0.294097\pi\)
−0.602686 + 0.797978i \(0.705903\pi\)
\(570\) −1.00680e36 2.69105e35i −0.0628971 0.0168117i
\(571\) −2.51848e35 2.51848e35i −0.0153656 0.0153656i 0.699382 0.714748i \(-0.253459\pi\)
−0.714748 + 0.699382i \(0.753459\pi\)
\(572\) −1.55678e36 + 2.70411e36i −0.0927642 + 0.161131i
\(573\) −1.31404e37 + 1.31404e37i −0.764755 + 0.764755i
\(574\) −8.45742e36 1.46279e37i −0.480759 0.831515i
\(575\) 1.78543e37 0.991348
\(576\) 2.20178e33 + 5.95280e35i 0.000119418 + 0.0322863i
\(577\) 2.93920e37 1.55724 0.778619 0.627497i \(-0.215921\pi\)
0.778619 + 0.627497i \(0.215921\pi\)
\(578\) 7.78878e36 + 1.34714e37i 0.403129 + 0.697246i
\(579\) 6.94271e36 6.94271e36i 0.351050 0.351050i
\(580\) 4.83952e36 8.40622e36i 0.239070 0.415263i
\(581\) 7.68253e36 + 7.68253e36i 0.370789 + 0.370789i
\(582\) −2.65128e37 7.08656e36i −1.25024 0.334176i
\(583\) 1.32688e37i 0.611372i
\(584\) 3.35964e34 + 1.81666e37i 0.00151258 + 0.817898i
\(585\) 9.23000e34i 0.00406067i
\(586\) 3.28220e36 1.22796e37i 0.141107 0.527918i
\(587\) −1.47989e35 1.47989e35i −0.00621747 0.00621747i 0.703991 0.710209i \(-0.251399\pi\)
−0.710209 + 0.703991i \(0.751399\pi\)
\(588\) −9.81699e36 3.64576e37i −0.403074 1.49691i
\(589\) −3.79384e36 + 3.79384e36i −0.152238 + 0.152238i
\(590\) −2.51961e35 + 1.45677e35i −0.00988167 + 0.00571331i
\(591\) −1.49992e37 −0.574960
\(592\) −1.15260e37 + 4.34437e37i −0.431851 + 1.62773i
\(593\) −4.23155e37 −1.54975 −0.774874 0.632116i \(-0.782187\pi\)
−0.774874 + 0.632116i \(0.782187\pi\)
\(594\) 9.03420e36 5.22332e36i 0.323424 0.186995i
\(595\) 3.56009e36 3.56009e36i 0.124590 0.124590i
\(596\) 6.61025e35 1.77995e35i 0.0226148 0.00608952i
\(597\) 1.39333e37 + 1.39333e37i 0.466016 + 0.466016i
\(598\) 4.21765e36 1.57794e37i 0.137913 0.515969i
\(599\) 5.49505e37i 1.75675i 0.477974 + 0.878374i \(0.341371\pi\)
−0.477974 + 0.878374i \(0.658629\pi\)
\(600\) −2.09139e37 2.08367e37i −0.653723 0.651310i
\(601\) 1.72453e37i 0.527066i −0.964650 0.263533i \(-0.915112\pi\)
0.964650 0.263533i \(-0.0848877\pi\)
\(602\) 3.46483e36 + 9.26109e35i 0.103545 + 0.0276764i
\(603\) −3.97688e35 3.97688e35i −0.0116214 0.0116214i
\(604\) 4.76908e37 + 2.74560e37i 1.36281 + 0.784581i
\(605\) 5.44484e36 5.44484e36i 0.152156 0.152156i
\(606\) 1.44194e37 + 2.49396e37i 0.394064 + 0.681568i
\(607\) 5.57558e37 1.49019 0.745096 0.666957i \(-0.232404\pi\)
0.745096 + 0.666957i \(0.232404\pi\)
\(608\) 2.66343e36 + 9.81889e36i 0.0696214 + 0.256664i
\(609\) −1.18903e38 −3.03990
\(610\) 2.90467e36 + 5.02389e36i 0.0726347 + 0.125628i
\(611\) 5.66863e36 5.66863e36i 0.138651 0.138651i
\(612\) 5.15916e35 + 2.97017e35i 0.0123434 + 0.00710619i
\(613\) −4.97190e36 4.97190e36i −0.116361 0.116361i 0.646529 0.762890i \(-0.276220\pi\)
−0.762890 + 0.646529i \(0.776220\pi\)
\(614\) 7.57618e37 + 2.02503e37i 1.73451 + 0.463615i
\(615\) 6.54154e36i 0.146509i
\(616\) −1.90198e37 + 1.90902e37i −0.416740 + 0.418285i
\(617\) 1.59253e37i 0.341379i −0.985325 0.170689i \(-0.945401\pi\)
0.985325 0.170689i \(-0.0545995\pi\)
\(618\) 2.08287e37 7.79258e37i 0.436835 1.63432i
\(619\) −5.19437e37 5.19437e37i −1.06588 1.06588i −0.997671 0.0682110i \(-0.978271\pi\)
−0.0682110 0.997671i \(-0.521729\pi\)
\(620\) 9.68957e36 2.60912e36i 0.194543 0.0523849i
\(621\) −3.86267e37 + 3.86267e37i −0.758841 + 0.758841i
\(622\) −8.20410e37 + 4.74338e37i −1.57711 + 0.911839i
\(623\) −5.65969e37 −1.06464
\(624\) −2.33557e37 + 1.35613e37i −0.429933 + 0.249637i
\(625\) −4.54102e37 −0.818037
\(626\) 9.47732e37 5.47952e37i 1.67083 0.966027i
\(627\) 3.94434e36 3.94434e36i 0.0680554 0.0680554i
\(628\) −2.20437e37 8.18642e37i −0.372245 1.38242i
\(629\) 3.17832e37 + 3.17832e37i 0.525308 + 0.525308i
\(630\) −2.05843e35 + 7.70117e35i −0.00332996 + 0.0124583i
\(631\) 1.50618e37i 0.238496i 0.992865 + 0.119248i \(0.0380483\pi\)
−0.992865 + 0.119248i \(0.961952\pi\)
\(632\) −4.34895e37 + 8.04275e34i −0.674068 + 0.00124659i
\(633\) 3.16958e37i 0.480897i
\(634\) 3.80052e37 + 1.01583e37i 0.564466 + 0.150875i
\(635\) −5.88515e36 5.88515e36i −0.0855682 0.0855682i
\(636\) 5.73018e37 9.95328e37i 0.815637 1.41676i
\(637\) −4.04115e37 + 4.04115e37i −0.563148 + 0.563148i
\(638\) 2.59871e37 + 4.49470e37i 0.354552 + 0.613228i
\(639\) −1.53457e35 −0.00204986
\(640\) 4.84542e36 1.84006e37i 0.0633726 0.240659i
\(641\) 8.00815e37 1.02553 0.512765 0.858529i \(-0.328621\pi\)
0.512765 + 0.858529i \(0.328621\pi\)
\(642\) 6.72755e37 + 1.16359e38i 0.843595 + 1.45907i
\(643\) 7.28689e37 7.28689e37i 0.894735 0.894735i −0.100230 0.994964i \(-0.531958\pi\)
0.994964 + 0.100230i \(0.0319578\pi\)
\(644\) 7.03809e37 1.22251e38i 0.846244 1.46992i
\(645\) 9.81807e35 + 9.81807e35i 0.0115603 + 0.0115603i
\(646\) 9.82902e36 + 2.62718e36i 0.113337 + 0.0302936i
\(647\) 8.15309e36i 0.0920692i 0.998940 + 0.0460346i \(0.0146584\pi\)
−0.998940 + 0.0460346i \(0.985342\pi\)
\(648\) 8.74059e37 1.61644e35i 0.966669 0.00178771i
\(649\) 1.55783e36i 0.0168740i
\(650\) −1.15392e37 + 4.31714e37i −0.122418 + 0.458000i
\(651\) −8.69802e37 8.69802e37i −0.903809 0.903809i
\(652\) −1.57620e37 5.85358e37i −0.160424 0.595770i
\(653\) 4.01892e37 4.01892e37i 0.400665 0.400665i −0.477802 0.878467i \(-0.658566\pi\)
0.878467 + 0.477802i \(0.158566\pi\)
\(654\) 3.02597e37 1.74953e37i 0.295505 0.170853i
\(655\) −2.52952e35 −0.00241981
\(656\) −5.52261e37 + 3.20666e37i −0.517538 + 0.300505i
\(657\) −2.87643e36 −0.0264071
\(658\) 5.99388e37 3.46550e37i 0.539087 0.311685i
\(659\) 9.00593e37 9.00593e37i 0.793552 0.793552i −0.188518 0.982070i \(-0.560368\pi\)
0.982070 + 0.188518i \(0.0603682\pi\)
\(660\) −1.00740e37 + 2.71262e36i −0.0869675 + 0.0234178i
\(661\) 1.26696e38 + 1.26696e38i 1.07163 + 1.07163i 0.997228 + 0.0744009i \(0.0237045\pi\)
0.0744009 + 0.997228i \(0.476296\pi\)
\(662\) −1.83666e36 + 6.87145e36i −0.0152211 + 0.0569463i
\(663\) 2.70083e37i 0.219313i
\(664\) 2.89820e37 2.90894e37i 0.230600 0.231455i
\(665\) 1.36237e37i 0.106219i
\(666\) −6.87532e36 1.83769e36i −0.0525280 0.0140401i
\(667\) −1.92176e38 1.92176e38i −1.43880 1.43880i
\(668\) −2.09465e38 1.20590e38i −1.53684 0.884771i
\(669\) −3.36437e36 + 3.36437e36i −0.0241909 + 0.0241909i
\(670\) 8.99821e36 + 1.55632e37i 0.0634084 + 0.109670i
\(671\) −3.10619e37 −0.214523
\(672\) −2.25115e38 + 6.10636e37i −1.52377 + 0.413330i
\(673\) −2.18110e38 −1.44701 −0.723506 0.690318i \(-0.757471\pi\)
−0.723506 + 0.690318i \(0.757471\pi\)
\(674\) 1.16040e38 + 2.00702e38i 0.754571 + 1.30510i
\(675\) 1.05680e38 1.05680e38i 0.673585 0.673585i
\(676\) −1.03285e38 5.94622e37i −0.645295 0.371501i
\(677\) 8.33269e36 + 8.33269e36i 0.0510315 + 0.0510315i 0.732162 0.681131i \(-0.238511\pi\)
−0.681131 + 0.732162i \(0.738511\pi\)
\(678\) −2.42061e38 6.47002e37i −1.45320 0.388423i
\(679\) 3.58765e38i 2.11139i
\(680\) −1.34801e37 1.34303e37i −0.0777717 0.0774846i
\(681\) 9.89801e37i 0.559837i
\(682\) −1.38696e37 + 5.18900e37i −0.0769086 + 0.287736i
\(683\) 1.18619e38 + 1.18619e38i 0.644876 + 0.644876i 0.951750 0.306874i \(-0.0992831\pi\)
−0.306874 + 0.951750i \(0.599283\pi\)
\(684\) −1.55546e36 + 4.18841e35i −0.00829091 + 0.00223250i
\(685\) −5.31475e35 + 5.31475e35i −0.00277754 + 0.00277754i
\(686\) −1.56149e38 + 9.02813e37i −0.800138 + 0.462618i
\(687\) 2.82487e38 1.41933
\(688\) 3.47596e36 1.31016e37i 0.0171250 0.0645477i
\(689\) −1.73843e38 −0.839844
\(690\) 4.72786e37 2.73352e37i 0.223976 0.129497i
\(691\) 1.42316e38 1.42316e38i 0.661151 0.661151i −0.294500 0.955651i \(-0.595153\pi\)
0.955651 + 0.294500i \(0.0951531\pi\)
\(692\) −7.55883e37 2.80715e38i −0.344368 1.27889i
\(693\) −3.01710e36 3.01710e36i −0.0134800 0.0134800i
\(694\) 4.71406e37 1.76366e38i 0.206558 0.772790i
\(695\) 3.83928e37i 0.164989i
\(696\) 8.31076e35 + 4.49387e38i 0.00350281 + 1.89407i
\(697\) 6.38629e37i 0.264001i
\(698\) 2.87994e38 + 7.69776e37i 1.16771 + 0.312116i
\(699\) 5.68459e37 + 5.68459e37i 0.226077 + 0.226077i
\(700\) −1.92558e38 + 3.34471e38i −0.751169 + 1.30477i
\(701\) 4.87512e36 4.87512e36i 0.0186548 0.0186548i −0.697718 0.716373i \(-0.745801\pi\)
0.716373 + 0.697718i \(0.245801\pi\)
\(702\) −6.84344e37 1.18363e38i −0.256876 0.444289i
\(703\) −1.21628e38 −0.447853
\(704\) 7.22835e37 + 7.17508e37i 0.261101 + 0.259177i
\(705\) 2.68045e37 0.0949849
\(706\) 4.39420e37 + 7.60015e37i 0.152762 + 0.264216i
\(707\) 2.66299e38 2.66299e38i 0.908254 0.908254i
\(708\) 6.72756e36 1.16857e37i 0.0225117 0.0391027i
\(709\) 1.72511e38 + 1.72511e38i 0.566362 + 0.566362i 0.931107 0.364746i \(-0.118844\pi\)
−0.364746 + 0.931107i \(0.618844\pi\)
\(710\) 4.73879e36 + 1.26662e36i 0.0152644 + 0.00408000i
\(711\) 6.88597e36i 0.0217633i
\(712\) 3.95586e35 + 2.13905e38i 0.00122677 + 0.663348i
\(713\) 2.81162e38i 0.855556i
\(714\) −6.02326e37 + 2.25347e38i −0.179848 + 0.672861i
\(715\) 1.11665e37 + 1.11665e37i 0.0327178 + 0.0327178i
\(716\) 3.83483e37 + 1.42415e38i 0.110260 + 0.409478i
\(717\) 4.82035e38 4.82035e38i 1.36010 1.36010i
\(718\) −3.29129e38 + 1.90293e38i −0.911351 + 0.526918i
\(719\) 1.03369e38 0.280899 0.140449 0.990088i \(-0.455145\pi\)
0.140449 + 0.990088i \(0.455145\pi\)
\(720\) 2.91205e36 + 7.72592e35i 0.00776624 + 0.00206045i
\(721\) −1.05448e39 −2.76001
\(722\) 3.13165e38 1.81063e38i 0.804491 0.465134i
\(723\) 2.53818e38 2.53818e38i 0.639964 0.639964i
\(724\) 4.96058e38 1.33574e38i 1.22761 0.330561i
\(725\) 5.25781e38 + 5.25781e38i 1.27715 + 1.27715i
\(726\) −9.21204e37 + 3.44648e38i −0.219640 + 0.821734i
\(727\) 7.47472e37i 0.174936i −0.996167 0.0874682i \(-0.972122\pi\)
0.996167 0.0874682i \(-0.0278776\pi\)
\(728\) 2.50114e38 + 2.49191e38i 0.574599 + 0.572478i
\(729\) 4.56804e38i 1.03017i
\(730\) 8.88249e37 + 2.37419e37i 0.196642 + 0.0525601i
\(731\) −9.58507e36 9.58507e36i −0.0208310 0.0208310i
\(732\) −2.33004e38 1.34142e38i −0.497122 0.286197i
\(733\) 8.00218e37 8.00218e37i 0.167612 0.167612i −0.618317 0.785929i \(-0.712185\pi\)
0.785929 + 0.618317i \(0.212185\pi\)
\(734\) −9.92187e37 1.71607e38i −0.204031 0.352890i
\(735\) −1.91088e38 −0.385794
\(736\) −4.62534e38 2.65146e38i −0.916839 0.525576i
\(737\) −9.62247e37 −0.187273
\(738\) −5.06113e36 8.75366e36i −0.00967133 0.0167274i
\(739\) −3.01672e38 + 3.01672e38i −0.566025 + 0.566025i −0.931012 0.364987i \(-0.881073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(740\) 1.97143e38 + 1.13497e38i 0.363207 + 0.209101i
\(741\) −5.16775e37 5.16775e37i −0.0934880 0.0934880i
\(742\) −1.45048e39 3.87698e38i −2.57668