Properties

Label 21.30.e.b.4.16
Level $21$
Weight $30$
Character 21.4
Analytic conductor $111.884$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,30,Mod(4,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 30, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.4");
 
S:= CuspForms(chi, 30);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.e (of order \(3\), 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: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.16
Character \(\chi\) \(=\) 21.4
Dual form 21.30.e.b.16.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(16123.2 + 27926.2i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.51480e8 + 4.35576e8i) q^{4} +(-4.30356e9 - 7.45399e9i) q^{5} -1.54234e11 q^{6} +(1.08632e12 + 1.42822e12i) q^{7} +1.09353e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\) \(q+(16123.2 + 27926.2i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.51480e8 + 4.35576e8i) q^{4} +(-4.30356e9 - 7.45399e9i) q^{5} -1.54234e11 q^{6} +(1.08632e12 + 1.42822e12i) q^{7} +1.09353e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(1.38774e14 - 2.40364e14i) q^{10} +(1.91128e14 - 3.31044e14i) q^{11} +(-1.20282e15 - 2.08334e15i) q^{12} -2.12386e16 q^{13} +(-2.23699e16 + 5.33642e16i) q^{14} +4.11676e16 q^{15} +(1.52643e17 + 2.64386e17i) q^{16} +(4.33194e17 - 7.50314e17i) q^{17} +(3.68847e17 - 6.38862e17i) q^{18} +(-1.45927e17 - 2.52753e17i) q^{19} +4.32904e18 q^{20} +(-8.51386e18 + 1.08414e18i) q^{21} +1.23264e19 q^{22} +(-3.34161e18 - 5.78784e18i) q^{23} +(-2.61515e18 + 4.52957e18i) q^{24} +(5.60909e19 - 9.71523e19i) q^{25} +(-3.42434e20 - 5.93114e20i) q^{26} +1.09419e20 q^{27} +(-8.95286e20 + 1.14005e20i) q^{28} +1.48379e21 q^{29} +(6.63754e20 + 1.14966e21i) q^{30} +(2.98473e21 - 5.16971e21i) q^{31} +(-4.62865e21 + 8.01706e21i) q^{32} +(9.14161e20 + 1.58337e21i) q^{33} +2.79379e22 q^{34} +(5.97092e21 - 1.42439e22i) q^{35} +1.15061e22 q^{36} +(9.54701e21 + 1.65359e22i) q^{37} +(4.70561e21 - 8.15036e21i) q^{38} +(5.07918e22 - 8.79740e22i) q^{39} +(-4.70606e21 - 8.15113e21i) q^{40} +3.44578e23 q^{41} +(-1.67547e23 - 2.20280e23i) q^{42} -2.00037e23 q^{43} +(9.61298e22 + 1.66502e23i) q^{44} +(-9.84517e22 + 1.70523e23i) q^{45} +(1.07755e23 - 1.86637e23i) q^{46} +(4.11782e23 + 7.13227e23i) q^{47} -1.46018e24 q^{48} +(-8.59733e23 + 3.10301e24i) q^{49} +3.61746e24 q^{50} +(2.07195e24 + 3.58873e24i) q^{51} +(5.34108e24 - 9.25102e24i) q^{52} +(-7.51479e23 + 1.30160e24i) q^{53} +(1.76418e24 + 3.05566e24i) q^{54} -3.29013e24 q^{55} +(1.18792e24 + 1.56180e24i) q^{56} +1.39593e24 q^{57} +(2.39234e25 + 4.14366e25i) q^{58} +(3.52055e25 - 6.09778e25i) q^{59} +(-1.03528e25 + 1.79316e25i) q^{60} +(6.09956e25 + 1.05647e26i) q^{61} +1.92494e26 q^{62} +(1.58700e25 - 3.78586e25i) q^{63} -1.34615e26 q^{64} +(9.14017e25 + 1.58312e26i) q^{65} +(-2.94784e25 + 5.10581e25i) q^{66} +(-1.37929e26 + 2.38901e26i) q^{67} +(2.17879e26 + 3.77378e26i) q^{68} +3.19656e25 q^{69} +(4.94047e26 - 6.29113e25i) q^{70} -1.41244e26 q^{71} +(-1.25082e25 - 2.16648e25i) q^{72} +(1.32787e26 - 2.29994e26i) q^{73} +(-3.07857e26 + 5.33223e26i) q^{74} +(2.68281e26 + 4.64677e26i) q^{75} +1.46790e26 q^{76} +(6.80431e26 - 8.66452e25i) q^{77} +3.27571e27 q^{78} +(2.34718e26 + 4.06543e26i) q^{79} +(1.31382e27 - 2.27560e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(5.55570e27 + 9.62275e27i) q^{82} +3.52927e27 q^{83} +(1.66884e27 - 3.98107e27i) q^{84} -7.45712e27 q^{85} +(-3.22524e27 - 5.58628e27i) q^{86} +(-3.54846e27 + 6.14611e27i) q^{87} +(2.09004e26 - 3.62005e26i) q^{88} +(-1.44289e28 - 2.49916e28i) q^{89} -6.34943e27 q^{90} +(-2.30719e28 - 3.03335e28i) q^{91} +3.36139e27 q^{92} +(1.42759e28 + 2.47266e28i) q^{93} +(-1.32785e28 + 2.29990e28i) q^{94} +(-1.25601e27 + 2.17547e27i) q^{95} +(-2.21387e28 - 3.83454e28i) q^{96} -1.14143e29 q^{97} +(-1.00517e29 + 2.60213e28i) q^{98} -8.74481e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16123.2 + 27926.2i 0.695851 + 1.20525i 0.969893 + 0.243532i \(0.0783060\pi\)
−0.274042 + 0.961718i \(0.588361\pi\)
\(3\) −2.39148e6 + 4.14217e6i −0.288675 + 0.500000i
\(4\) −2.51480e8 + 4.35576e8i −0.468417 + 0.811323i
\(5\) −4.30356e9 7.45399e9i −0.315328 0.546165i 0.664179 0.747574i \(-0.268781\pi\)
−0.979507 + 0.201409i \(0.935448\pi\)
\(6\) −1.54234e11 −0.803500
\(7\) 1.08632e12 + 1.42822e12i 0.605390 + 0.795929i
\(8\) 1.09353e12 0.0879072
\(9\) −1.14384e13 1.98119e13i −0.166667 0.288675i
\(10\) 1.38774e14 2.40364e14i 0.438843 0.760099i
\(11\) 1.91128e14 3.31044e14i 0.151751 0.262840i −0.780120 0.625630i \(-0.784842\pi\)
0.931871 + 0.362789i \(0.118176\pi\)
\(12\) −1.20282e15 2.08334e15i −0.270441 0.468417i
\(13\) −2.12386e16 −1.49606 −0.748028 0.663668i \(-0.768999\pi\)
−0.748028 + 0.663668i \(0.768999\pi\)
\(14\) −2.23699e16 + 5.33642e16i −0.538032 + 1.28349i
\(15\) 4.11676e16 0.364110
\(16\) 1.52643e17 + 2.64386e17i 0.529588 + 0.917273i
\(17\) 4.33194e17 7.50314e17i 0.623984 1.08077i −0.364753 0.931104i \(-0.618846\pi\)
0.988736 0.149667i \(-0.0478202\pi\)
\(18\) 3.68847e17 6.38862e17i 0.231950 0.401750i
\(19\) −1.45927e17 2.52753e17i −0.0418994 0.0725719i 0.844315 0.535847i \(-0.180008\pi\)
−0.886215 + 0.463275i \(0.846674\pi\)
\(20\) 4.32904e18 0.590821
\(21\) −8.51386e18 + 1.08414e18i −0.572726 + 0.0729301i
\(22\) 1.23264e19 0.422384
\(23\) −3.34161e18 5.78784e18i −0.0601038 0.104103i 0.834408 0.551148i \(-0.185810\pi\)
−0.894512 + 0.447045i \(0.852477\pi\)
\(24\) −2.61515e18 + 4.52957e18i −0.0253766 + 0.0439536i
\(25\) 5.60909e19 9.71523e19i 0.301136 0.521583i
\(26\) −3.42434e20 5.93114e20i −1.04103 1.80312i
\(27\) 1.09419e20 0.192450
\(28\) −8.95286e20 + 1.14005e20i −0.929330 + 0.118340i
\(29\) 1.48379e21 0.925979 0.462990 0.886364i \(-0.346777\pi\)
0.462990 + 0.886364i \(0.346777\pi\)
\(30\) 6.63754e20 + 1.14966e21i 0.253366 + 0.438843i
\(31\) 2.98473e21 5.16971e21i 0.708209 1.22665i −0.257313 0.966328i \(-0.582837\pi\)
0.965521 0.260325i \(-0.0838297\pi\)
\(32\) −4.62865e21 + 8.01706e21i −0.693075 + 1.20044i
\(33\) 9.14161e20 + 1.58337e21i 0.0876134 + 0.151751i
\(34\) 2.79379e22 1.73680
\(35\) 5.97092e21 1.42439e22i 0.243812 0.581622i
\(36\) 1.15061e22 0.312278
\(37\) 9.54701e21 + 1.65359e22i 0.174158 + 0.301650i 0.939869 0.341534i \(-0.110946\pi\)
−0.765712 + 0.643184i \(0.777613\pi\)
\(38\) 4.70561e21 8.15036e21i 0.0583115 0.100998i
\(39\) 5.07918e22 8.79740e22i 0.431874 0.748028i
\(40\) −4.70606e21 8.15113e21i −0.0277196 0.0480118i
\(41\) 3.44578e23 1.41880 0.709401 0.704805i \(-0.248966\pi\)
0.709401 + 0.704805i \(0.248966\pi\)
\(42\) −1.67547e23 2.20280e23i −0.486431 0.639529i
\(43\) −2.00037e23 −0.412874 −0.206437 0.978460i \(-0.566187\pi\)
−0.206437 + 0.978460i \(0.566187\pi\)
\(44\) 9.61298e22 + 1.66502e23i 0.142166 + 0.246238i
\(45\) −9.84517e22 + 1.70523e23i −0.105109 + 0.182055i
\(46\) 1.07755e23 1.86637e23i 0.0836467 0.144880i
\(47\) 4.11782e23 + 7.13227e23i 0.234017 + 0.405330i 0.958987 0.283451i \(-0.0914794\pi\)
−0.724969 + 0.688781i \(0.758146\pi\)
\(48\) −1.46018e24 −0.611515
\(49\) −8.59733e23 + 3.10301e24i −0.267006 + 0.963695i
\(50\) 3.61746e24 0.838183
\(51\) 2.07195e24 + 3.58873e24i 0.360257 + 0.623984i
\(52\) 5.34108e24 9.25102e24i 0.700778 1.21378i
\(53\) −7.51479e23 + 1.30160e24i −0.0748026 + 0.129562i −0.901000 0.433818i \(-0.857166\pi\)
0.826198 + 0.563380i \(0.190499\pi\)
\(54\) 1.76418e24 + 3.05566e24i 0.133917 + 0.231950i
\(55\) −3.29013e24 −0.191406
\(56\) 1.18792e24 + 1.56180e24i 0.0532181 + 0.0699679i
\(57\) 1.39593e24 0.0483812
\(58\) 2.39234e25 + 4.14366e25i 0.644344 + 1.11604i
\(59\) 3.52055e25 6.09778e25i 0.740043 1.28179i −0.212432 0.977176i \(-0.568139\pi\)
0.952475 0.304616i \(-0.0985281\pi\)
\(60\) −1.03528e25 + 1.79316e25i −0.170555 + 0.295411i
\(61\) 6.09956e25 + 1.05647e26i 0.790708 + 1.36955i 0.925529 + 0.378676i \(0.123620\pi\)
−0.134822 + 0.990870i \(0.543046\pi\)
\(62\) 1.92494e26 1.97123
\(63\) 1.58700e25 3.78586e25i 0.128867 0.307416i
\(64\) −1.34615e26 −0.869932
\(65\) 9.14017e25 + 1.58312e26i 0.471749 + 0.817093i
\(66\) −2.94784e25 + 5.10581e25i −0.121932 + 0.211192i
\(67\) −1.37929e26 + 2.38901e26i −0.458746 + 0.794571i −0.998895 0.0469981i \(-0.985035\pi\)
0.540149 + 0.841569i \(0.318368\pi\)
\(68\) 2.17879e26 + 3.77378e26i 0.584570 + 1.01250i
\(69\) 3.19656e25 0.0694019
\(70\) 4.94047e26 6.29113e25i 0.870656 0.110868i
\(71\) −1.41244e26 −0.202639 −0.101320 0.994854i \(-0.532306\pi\)
−0.101320 + 0.994854i \(0.532306\pi\)
\(72\) −1.25082e25 2.16648e25i −0.0146512 0.0253766i
\(73\) 1.32787e26 2.29994e26i 0.127343 0.220565i −0.795303 0.606212i \(-0.792688\pi\)
0.922646 + 0.385647i \(0.126022\pi\)
\(74\) −3.07857e26 + 5.33223e26i −0.242375 + 0.419807i
\(75\) 2.68281e26 + 4.64677e26i 0.173861 + 0.301136i
\(76\) 1.46790e26 0.0785056
\(77\) 6.80431e26 8.66452e25i 0.301071 0.0383380i
\(78\) 3.27571e27 1.20208
\(79\) 2.34718e26 + 4.06543e26i 0.0716067 + 0.124026i 0.899606 0.436703i \(-0.143854\pi\)
−0.827999 + 0.560730i \(0.810521\pi\)
\(80\) 1.31382e27 2.27560e27i 0.333988 0.578484i
\(81\) −2.61674e26 + 4.53232e26i −0.0555556 + 0.0962250i
\(82\) 5.55570e27 + 9.62275e27i 0.987274 + 1.71001i
\(83\) 3.52927e27 0.526081 0.263040 0.964785i \(-0.415275\pi\)
0.263040 + 0.964785i \(0.415275\pi\)
\(84\) 1.66884e27 3.98107e27i 0.209105 0.498827i
\(85\) −7.45712e27 −0.787039
\(86\) −3.22524e27 5.58628e27i −0.287299 0.497617i
\(87\) −3.54846e27 + 6.14611e27i −0.267307 + 0.462990i
\(88\) 2.09004e26 3.62005e26i 0.0133400 0.0231055i
\(89\) −1.44289e28 2.49916e28i −0.781767 1.35406i −0.930911 0.365245i \(-0.880985\pi\)
0.149144 0.988815i \(-0.452348\pi\)
\(90\) −6.34943e27 −0.292562
\(91\) −2.30719e28 3.03335e28i −0.905697 1.19075i
\(92\) 3.36139e27 0.112615
\(93\) 1.42759e28 + 2.47266e28i 0.408884 + 0.708209i
\(94\) −1.32785e28 + 2.29990e28i −0.325683 + 0.564099i
\(95\) −1.25601e27 + 2.17547e27i −0.0264241 + 0.0457680i
\(96\) −2.21387e28 3.83454e28i −0.400147 0.693075i
\(97\) −1.14143e29 −1.77524 −0.887622 0.460573i \(-0.847644\pi\)
−0.887622 + 0.460573i \(0.847644\pi\)
\(98\) −1.00517e29 + 2.60213e28i −1.34729 + 0.348780i
\(99\) −8.74481e27 −0.101167
\(100\) 2.82115e28 + 4.88637e28i 0.282115 + 0.488637i
\(101\) 6.36442e28 1.10235e29i 0.550934 0.954245i −0.447274 0.894397i \(-0.647605\pi\)
0.998208 0.0598479i \(-0.0190616\pi\)
\(102\) −6.68131e28 + 1.15724e29i −0.501371 + 0.868399i
\(103\) 1.05641e29 + 1.82976e29i 0.688166 + 1.19194i 0.972431 + 0.233193i \(0.0749172\pi\)
−0.284265 + 0.958746i \(0.591749\pi\)
\(104\) −2.32250e28 −0.131514
\(105\) 4.47211e28 + 5.87965e28i 0.220429 + 0.289806i
\(106\) −4.84650e28 −0.208206
\(107\) −1.92141e28 3.32797e28i −0.0720368 0.124771i 0.827757 0.561087i \(-0.189617\pi\)
−0.899794 + 0.436315i \(0.856283\pi\)
\(108\) −2.75167e28 + 4.76602e28i −0.0901470 + 0.156139i
\(109\) 1.31391e29 2.27577e29i 0.376602 0.652294i −0.613963 0.789334i \(-0.710426\pi\)
0.990565 + 0.137041i \(0.0437591\pi\)
\(110\) −5.30475e28 9.18809e28i −0.133190 0.230691i
\(111\) −9.13261e28 −0.201100
\(112\) −2.11783e29 + 5.05216e29i −0.409477 + 0.976822i
\(113\) 9.53492e29 1.62061 0.810307 0.586005i \(-0.199300\pi\)
0.810307 + 0.586005i \(0.199300\pi\)
\(114\) 2.25068e28 + 3.89829e28i 0.0336661 + 0.0583115i
\(115\) −2.87617e28 + 4.98167e28i −0.0379049 + 0.0656532i
\(116\) −3.73143e29 + 6.46302e29i −0.433745 + 0.751268i
\(117\) 2.42936e29 + 4.20777e29i 0.249343 + 0.431874i
\(118\) 2.27050e30 2.05984
\(119\) 1.54220e30 1.96382e29i 1.23797 0.157642i
\(120\) 4.50179e28 0.0320079
\(121\) 7.20095e29 + 1.24724e30i 0.453943 + 0.786253i
\(122\) −1.96689e30 + 3.40675e30i −1.10043 + 1.90600i
\(123\) −8.24053e29 + 1.42730e30i −0.409573 + 0.709401i
\(124\) 1.50120e30 + 2.60015e30i 0.663474 + 1.14917i
\(125\) −2.56877e30 −1.01048
\(126\) 1.31312e30 1.67211e29i 0.460185 0.0585993i
\(127\) −2.20226e30 −0.688199 −0.344099 0.938933i \(-0.611816\pi\)
−0.344099 + 0.938933i \(0.611816\pi\)
\(128\) 3.14559e29 + 5.44832e29i 0.0877318 + 0.151956i
\(129\) 4.78386e29 8.28588e29i 0.119187 0.206437i
\(130\) −2.94738e30 + 5.10501e30i −0.656534 + 1.13715i
\(131\) 4.70025e30 + 8.14107e30i 0.936887 + 1.62274i 0.771235 + 0.636551i \(0.219639\pi\)
0.165652 + 0.986184i \(0.447027\pi\)
\(132\) −9.19572e29 −0.164159
\(133\) 2.02464e29 4.82985e29i 0.0323966 0.0772832i
\(134\) −8.89545e30 −1.27688
\(135\) −4.70892e29 8.15608e29i −0.0606850 0.105109i
\(136\) 4.73709e29 8.20488e29i 0.0548526 0.0950076i
\(137\) −2.77604e30 + 4.80824e30i −0.289053 + 0.500654i −0.973584 0.228330i \(-0.926674\pi\)
0.684531 + 0.728983i \(0.260007\pi\)
\(138\) 5.15388e29 + 8.92679e29i 0.0482934 + 0.0836467i
\(139\) 4.29631e29 0.0362561 0.0181280 0.999836i \(-0.494229\pi\)
0.0181280 + 0.999836i \(0.494229\pi\)
\(140\) 4.70271e30 + 6.18283e30i 0.357677 + 0.470252i
\(141\) −3.93908e30 −0.270220
\(142\) −2.27730e30 3.94440e30i −0.141007 0.244231i
\(143\) −4.05930e30 + 7.03092e30i −0.227028 + 0.393224i
\(144\) 3.49199e30 6.04830e30i 0.176529 0.305758i
\(145\) −6.38558e30 1.10602e31i −0.291988 0.505738i
\(146\) 8.56382e30 0.354447
\(147\) −1.07972e31 1.09820e31i −0.404770 0.411698i
\(148\) −9.60351e30 −0.326314
\(149\) 1.35885e31 + 2.35360e31i 0.418766 + 0.725323i 0.995816 0.0913855i \(-0.0291295\pi\)
−0.577050 + 0.816709i \(0.695796\pi\)
\(150\) −8.65110e30 + 1.49841e31i −0.241963 + 0.419091i
\(151\) −3.31437e31 + 5.74066e31i −0.841852 + 1.45813i 0.0464761 + 0.998919i \(0.485201\pi\)
−0.888328 + 0.459210i \(0.848132\pi\)
\(152\) −1.59575e29 2.76391e29i −0.00368326 0.00637959i
\(153\) −1.98202e31 −0.415989
\(154\) 1.33904e31 + 1.76048e31i 0.255707 + 0.336188i
\(155\) −5.13800e31 −0.893273
\(156\) 2.55462e31 + 4.42474e31i 0.404594 + 0.700778i
\(157\) 4.64808e31 8.05071e31i 0.671009 1.16222i −0.306609 0.951835i \(-0.599194\pi\)
0.977618 0.210386i \(-0.0674722\pi\)
\(158\) −7.56881e30 + 1.31096e31i −0.0996552 + 0.172608i
\(159\) −3.59430e30 6.22551e30i −0.0431873 0.0748026i
\(160\) 7.96788e31 0.874185
\(161\) 4.63627e30 1.10600e31i 0.0464723 0.110861i
\(162\) −1.68761e31 −0.154634
\(163\) 4.82552e30 + 8.35805e30i 0.0404412 + 0.0700463i 0.885538 0.464568i \(-0.153790\pi\)
−0.845096 + 0.534614i \(0.820457\pi\)
\(164\) −8.66544e31 + 1.50090e32i −0.664591 + 1.15111i
\(165\) 7.86830e30 1.36283e31i 0.0552540 0.0957028i
\(166\) 5.69031e31 + 9.85591e31i 0.366074 + 0.634059i
\(167\) −5.43510e30 −0.0320493 −0.0160246 0.999872i \(-0.505101\pi\)
−0.0160246 + 0.999872i \(0.505101\pi\)
\(168\) −9.31012e30 + 1.18554e30i −0.0503467 + 0.00641108i
\(169\) 2.49541e32 1.23818
\(170\) −1.20233e32 2.08249e32i −0.547662 0.948579i
\(171\) −3.33834e30 + 5.78217e30i −0.0139665 + 0.0241906i
\(172\) 5.03053e31 8.71313e31i 0.193398 0.334974i
\(173\) 1.14057e32 + 1.97553e32i 0.403139 + 0.698257i 0.994103 0.108441i \(-0.0345858\pi\)
−0.590964 + 0.806698i \(0.701252\pi\)
\(174\) −2.28850e32 −0.744024
\(175\) 1.99688e32 2.54280e31i 0.597447 0.0760782i
\(176\) 1.16698e32 0.321462
\(177\) 1.68387e32 + 2.91655e32i 0.427264 + 0.740043i
\(178\) 4.65279e32 8.05888e32i 1.08799 1.88445i
\(179\) −2.64538e32 + 4.58194e32i −0.570321 + 0.987826i 0.426211 + 0.904624i \(0.359848\pi\)
−0.996533 + 0.0832021i \(0.973485\pi\)
\(180\) −4.95172e31 8.57663e31i −0.0984702 0.170555i
\(181\) 5.34778e32 0.981373 0.490686 0.871336i \(-0.336746\pi\)
0.490686 + 0.871336i \(0.336746\pi\)
\(182\) 4.75106e32 1.13338e33i 0.804925 1.92018i
\(183\) −5.83480e32 −0.913031
\(184\) −3.65414e30 6.32915e30i −0.00528356 0.00915139i
\(185\) 8.21723e31 1.42327e32i 0.109834 0.190238i
\(186\) −4.60346e32 + 7.97343e32i −0.569045 + 0.985615i
\(187\) −1.65591e32 2.86813e32i −0.189380 0.328016i
\(188\) −4.14219e32 −0.438471
\(189\) 1.18864e32 + 1.56275e32i 0.116507 + 0.153177i
\(190\) −8.10036e31 −0.0735491
\(191\) −7.65411e32 1.32573e33i −0.644037 1.11550i −0.984523 0.175255i \(-0.943925\pi\)
0.340486 0.940250i \(-0.389408\pi\)
\(192\) 3.21931e32 5.57600e32i 0.251128 0.434966i
\(193\) 5.93227e32 1.02750e33i 0.429181 0.743363i −0.567620 0.823291i \(-0.692136\pi\)
0.996801 + 0.0799280i \(0.0254690\pi\)
\(194\) −1.84035e33 3.18757e33i −1.23531 2.13961i
\(195\) −8.74343e32 −0.544729
\(196\) −1.13539e33 1.15482e33i −0.656797 0.668039i
\(197\) −5.31295e32 −0.285480 −0.142740 0.989760i \(-0.545591\pi\)
−0.142740 + 0.989760i \(0.545591\pi\)
\(198\) −1.40994e32 2.44209e32i −0.0703974 0.121932i
\(199\) 5.44121e32 9.42446e32i 0.252538 0.437408i −0.711686 0.702498i \(-0.752068\pi\)
0.964224 + 0.265090i \(0.0854015\pi\)
\(200\) 6.13369e31 1.06239e32i 0.0264720 0.0458509i
\(201\) −6.59712e32 1.14265e33i −0.264857 0.458746i
\(202\) 4.10460e33 1.53347
\(203\) 1.61187e33 + 2.11918e33i 0.560579 + 0.737014i
\(204\) −2.08422e33 −0.675003
\(205\) −1.48291e33 2.56848e33i −0.447388 0.774900i
\(206\) −3.40655e33 + 5.90031e33i −0.957722 + 1.65882i
\(207\) −7.64453e31 + 1.32407e32i −0.0200346 + 0.0347010i
\(208\) −3.24193e33 5.61519e33i −0.792292 1.37229i
\(209\) −1.11563e32 −0.0254331
\(210\) −9.20916e32 + 2.19688e33i −0.195903 + 0.467333i
\(211\) 7.86742e33 1.56220 0.781100 0.624406i \(-0.214659\pi\)
0.781100 + 0.624406i \(0.214659\pi\)
\(212\) −3.77963e32 6.54651e32i −0.0700777 0.121378i
\(213\) 3.37782e32 5.85056e32i 0.0584969 0.101320i
\(214\) 6.19584e32 1.07315e33i 0.100254 0.173645i
\(215\) 8.60872e32 + 1.49107e33i 0.130191 + 0.225498i
\(216\) 1.19653e32 0.0169177
\(217\) 1.06259e34 1.35308e33i 1.40507 0.178920i
\(218\) 8.47380e33 1.04824
\(219\) 6.35118e32 + 1.10006e33i 0.0735215 + 0.127343i
\(220\) 8.27402e32 1.43310e33i 0.0896577 0.155292i
\(221\) −9.20044e33 + 1.59356e34i −0.933514 + 1.61689i
\(222\) −1.47247e33 2.55039e33i −0.139936 0.242375i
\(223\) 4.59932e33 0.409519 0.204759 0.978812i \(-0.434359\pi\)
0.204759 + 0.978812i \(0.434359\pi\)
\(224\) −1.64783e34 + 2.09833e33i −1.37505 + 0.175097i
\(225\) −2.56636e33 −0.200757
\(226\) 1.53733e34 + 2.66274e34i 1.12771 + 1.95325i
\(227\) −1.59935e33 + 2.77015e33i −0.110044 + 0.190602i −0.915788 0.401662i \(-0.868433\pi\)
0.805744 + 0.592265i \(0.201766\pi\)
\(228\) −3.51047e32 + 6.08031e32i −0.0226626 + 0.0392528i
\(229\) −3.58104e33 6.20255e33i −0.216968 0.375799i 0.736912 0.675989i \(-0.236283\pi\)
−0.953879 + 0.300190i \(0.902950\pi\)
\(230\) −1.85492e33 −0.105505
\(231\) −1.26834e33 + 3.02567e33i −0.0677426 + 0.161603i
\(232\) 1.62256e33 0.0814002
\(233\) −6.83350e33 1.18360e34i −0.322094 0.557883i 0.658826 0.752295i \(-0.271053\pi\)
−0.980920 + 0.194412i \(0.937720\pi\)
\(234\) −7.83380e33 + 1.35685e34i −0.347011 + 0.601040i
\(235\) 3.54426e33 6.13884e33i 0.147585 0.255624i
\(236\) 1.77070e34 + 3.06693e34i 0.693298 + 1.20083i
\(237\) −2.24530e33 −0.0826843
\(238\) 3.03494e34 + 3.99015e34i 1.05144 + 1.38237i
\(239\) 5.30769e34 1.73036 0.865179 0.501463i \(-0.167205\pi\)
0.865179 + 0.501463i \(0.167205\pi\)
\(240\) 6.28396e33 + 1.08841e34i 0.192828 + 0.333988i
\(241\) 1.84213e34 3.19067e34i 0.532199 0.921795i −0.467094 0.884207i \(-0.654699\pi\)
0.999293 0.0375880i \(-0.0119675\pi\)
\(242\) −2.32205e34 + 4.02190e34i −0.631754 + 1.09423i
\(243\) −1.25158e33 2.16780e33i −0.0320750 0.0555556i
\(244\) −6.13566e34 −1.48152
\(245\) 2.68297e34 6.94554e33i 0.610531 0.158051i
\(246\) −5.31455e34 −1.14001
\(247\) 3.09928e33 + 5.36811e33i 0.0626838 + 0.108572i
\(248\) 3.26388e33 5.65321e33i 0.0622566 0.107832i
\(249\) −8.44019e33 + 1.46188e34i −0.151866 + 0.263040i
\(250\) −4.14167e34 7.17359e34i −0.703146 1.21789i
\(251\) −6.01123e34 −0.963152 −0.481576 0.876404i \(-0.659935\pi\)
−0.481576 + 0.876404i \(0.659935\pi\)
\(252\) 1.24993e34 + 1.64333e34i 0.189050 + 0.248551i
\(253\) −2.55471e33 −0.0364833
\(254\) −3.55074e34 6.15007e34i −0.478884 0.829451i
\(255\) 1.78336e34 3.08887e34i 0.227199 0.393520i
\(256\) −4.62789e34 + 8.01575e34i −0.557062 + 0.964860i
\(257\) −1.94791e34 3.37388e34i −0.221584 0.383795i 0.733705 0.679468i \(-0.237789\pi\)
−0.955289 + 0.295673i \(0.904456\pi\)
\(258\) 3.08524e34 0.331744
\(259\) −1.32459e34 + 3.15985e34i −0.134658 + 0.321233i
\(260\) −9.19427e34 −0.883901
\(261\) −1.69722e34 2.93967e34i −0.154330 0.267307i
\(262\) −1.51566e35 + 2.62520e35i −1.30387 + 2.25836i
\(263\) 4.60626e33 7.97827e33i 0.0374964 0.0649457i −0.846668 0.532121i \(-0.821395\pi\)
0.884165 + 0.467176i \(0.154728\pi\)
\(264\) 9.99659e32 + 1.73146e33i 0.00770185 + 0.0133400i
\(265\) 1.29361e34 0.0943495
\(266\) 1.67523e34 2.13322e33i 0.115689 0.0147317i
\(267\) 1.38026e35 0.902707
\(268\) −6.93729e34 1.20157e35i −0.429769 0.744382i
\(269\) 7.60184e34 1.31668e35i 0.446181 0.772808i −0.551953 0.833875i \(-0.686117\pi\)
0.998134 + 0.0610676i \(0.0194505\pi\)
\(270\) 1.51846e34 2.63004e34i 0.0844554 0.146281i
\(271\) 5.12603e34 + 8.87855e34i 0.270226 + 0.468045i 0.968920 0.247376i \(-0.0795684\pi\)
−0.698694 + 0.715421i \(0.746235\pi\)
\(272\) 2.64497e35 1.32182
\(273\) 1.80823e35 2.30257e34i 0.856829 0.109108i
\(274\) −1.79034e35 −0.804550
\(275\) −2.14411e34 3.71371e34i −0.0913953 0.158301i
\(276\) −8.03871e33 + 1.39235e34i −0.0325091 + 0.0563074i
\(277\) 1.86730e35 3.23426e35i 0.716567 1.24113i −0.245785 0.969324i \(-0.579046\pi\)
0.962352 0.271807i \(-0.0876211\pi\)
\(278\) 6.92702e33 + 1.19980e34i 0.0252288 + 0.0436976i
\(279\) −1.36562e35 −0.472139
\(280\) 6.52936e33 1.55760e34i 0.0214328 0.0511287i
\(281\) 5.83009e35 1.81733 0.908664 0.417528i \(-0.137103\pi\)
0.908664 + 0.417528i \(0.137103\pi\)
\(282\) −6.35106e34 1.10004e35i −0.188033 0.325683i
\(283\) 5.76295e34 9.98173e34i 0.162085 0.280739i −0.773532 0.633758i \(-0.781512\pi\)
0.935616 + 0.353019i \(0.114845\pi\)
\(284\) 3.55199e34 6.15224e34i 0.0949197 0.164406i
\(285\) −6.00746e33 1.04052e34i −0.0152560 0.0264241i
\(286\) −2.61796e35 −0.631910
\(287\) 3.74321e35 + 4.92134e35i 0.858928 + 1.12926i
\(288\) 2.11778e35 0.462050
\(289\) −1.34330e35 2.32667e35i −0.278711 0.482742i
\(290\) 2.05912e35 3.56650e35i 0.406360 0.703836i
\(291\) 2.72971e35 4.72799e35i 0.512469 0.887622i
\(292\) 6.67866e34 + 1.15678e35i 0.119299 + 0.206633i
\(293\) 4.21068e35 0.715767 0.357884 0.933766i \(-0.383498\pi\)
0.357884 + 0.933766i \(0.383498\pi\)
\(294\) 1.32600e35 4.78588e35i 0.214539 0.774328i
\(295\) −6.06037e35 −0.933426
\(296\) 1.04399e34 + 1.80824e34i 0.0153097 + 0.0265172i
\(297\) 2.09131e34 3.62225e34i 0.0292045 0.0505836i
\(298\) −4.38181e35 + 7.58951e35i −0.582797 + 1.00943i
\(299\) 7.09712e34 + 1.22926e35i 0.0899187 + 0.155744i
\(300\) −2.69869e35 −0.325758
\(301\) −2.17304e35 2.85697e35i −0.249950 0.328619i
\(302\) −2.13753e36 −2.34321
\(303\) 3.04408e35 + 5.27251e35i 0.318082 + 0.550934i
\(304\) 4.45495e34 7.71619e34i 0.0443788 0.0768663i
\(305\) 5.24997e35 9.09321e35i 0.498665 0.863714i
\(306\) −3.19565e35 5.53503e35i −0.289466 0.501371i
\(307\) −5.66193e35 −0.489168 −0.244584 0.969628i \(-0.578651\pi\)
−0.244584 + 0.969628i \(0.578651\pi\)
\(308\) −1.33374e35 + 3.18169e35i −0.109922 + 0.262224i
\(309\) −1.01056e36 −0.794626
\(310\) −8.28410e35 1.43485e36i −0.621585 1.07662i
\(311\) −1.40947e35 + 2.44127e35i −0.100932 + 0.174820i −0.912069 0.410037i \(-0.865516\pi\)
0.811137 + 0.584856i \(0.198849\pi\)
\(312\) 5.55422e34 9.62019e34i 0.0379648 0.0657570i
\(313\) −5.87285e35 1.01721e36i −0.383227 0.663769i 0.608294 0.793711i \(-0.291854\pi\)
−0.991521 + 0.129943i \(0.958521\pi\)
\(314\) 2.99768e36 1.86769
\(315\) −3.50495e35 + 4.46316e34i −0.208535 + 0.0265546i
\(316\) −2.36107e35 −0.134167
\(317\) −6.54402e35 1.13346e36i −0.355210 0.615242i 0.631944 0.775014i \(-0.282257\pi\)
−0.987154 + 0.159772i \(0.948924\pi\)
\(318\) 1.15903e35 2.00750e35i 0.0601038 0.104103i
\(319\) 2.83594e35 4.91200e35i 0.140518 0.243385i
\(320\) 5.79326e35 + 1.00342e36i 0.274314 + 0.475126i
\(321\) 1.83801e35 0.0831809
\(322\) 3.83615e35 4.88491e34i 0.165953 0.0211323i
\(323\) −2.52858e35 −0.104578
\(324\) −1.31611e35 2.27957e35i −0.0520464 0.0901470i
\(325\) −1.19129e36 + 2.06338e36i −0.450516 + 0.780316i
\(326\) −1.55606e35 + 2.69517e35i −0.0562821 + 0.0974835i
\(327\) 6.28441e35 + 1.08849e36i 0.217431 + 0.376602i
\(328\) 3.76805e35 0.124723
\(329\) −5.71321e35 + 1.36291e36i −0.180942 + 0.431644i
\(330\) 5.07449e35 0.153794
\(331\) 2.27125e36 + 3.93391e36i 0.658807 + 1.14109i 0.980925 + 0.194388i \(0.0622720\pi\)
−0.322118 + 0.946700i \(0.604395\pi\)
\(332\) −8.87539e35 + 1.53726e36i −0.246425 + 0.426821i
\(333\) 2.18405e35 3.78288e35i 0.0580525 0.100550i
\(334\) −8.76311e34 1.51782e35i −0.0223015 0.0386274i
\(335\) 2.37435e36 0.578623
\(336\) −1.58622e36 2.08546e36i −0.370205 0.486723i
\(337\) 2.83014e36 0.632665 0.316332 0.948648i \(-0.397549\pi\)
0.316332 + 0.948648i \(0.397549\pi\)
\(338\) 4.02339e36 + 6.96872e36i 0.861589 + 1.49232i
\(339\) −2.28026e36 + 3.94953e36i −0.467831 + 0.810307i
\(340\) 1.87531e36 3.24814e36i 0.368663 0.638543i
\(341\) −1.14094e36 1.97616e36i −0.214943 0.372291i
\(342\) −2.15299e35 −0.0388743
\(343\) −5.36573e36 + 2.14296e36i −0.928675 + 0.370894i
\(344\) −2.18746e35 −0.0362946
\(345\) −1.37566e35 2.38272e35i −0.0218844 0.0379049i
\(346\) −3.67794e36 + 6.37038e36i −0.561049 + 0.971766i
\(347\) −3.15076e34 + 5.45728e34i −0.00460933 + 0.00798360i −0.868321 0.496003i \(-0.834801\pi\)
0.863712 + 0.503986i \(0.168134\pi\)
\(348\) −1.78473e36 3.09124e36i −0.250423 0.433745i
\(349\) 1.00843e37 1.35730 0.678650 0.734462i \(-0.262566\pi\)
0.678650 + 0.734462i \(0.262566\pi\)
\(350\) 3.92971e36 + 5.16654e36i 0.507428 + 0.667134i
\(351\) −2.32391e36 −0.287916
\(352\) 1.76933e36 + 3.06458e36i 0.210349 + 0.364336i
\(353\) −4.79097e36 + 8.29821e36i −0.546626 + 0.946785i 0.451876 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547040i \(0.982578\pi\)
\(354\) −5.42987e36 + 9.40482e36i −0.594624 + 1.02992i
\(355\) 6.07852e35 + 1.05283e36i 0.0638979 + 0.110674i
\(356\) 1.45143e37 1.46477
\(357\) −2.87470e36 + 6.85771e36i −0.278551 + 0.664493i
\(358\) −1.70608e37 −1.58744
\(359\) 3.85800e36 + 6.68225e36i 0.344741 + 0.597109i 0.985307 0.170795i \(-0.0546335\pi\)
−0.640566 + 0.767903i \(0.721300\pi\)
\(360\) −1.07660e35 + 1.86472e35i −0.00923988 + 0.0160039i
\(361\) 6.02232e36 1.04310e37i 0.496489 0.859944i
\(362\) 8.62233e36 + 1.49343e37i 0.682889 + 1.18280i
\(363\) −6.88838e36 −0.524169
\(364\) 1.90146e37 2.42130e36i 1.39033 0.177043i
\(365\) −2.28583e36 −0.160620
\(366\) −9.40757e36 1.62944e37i −0.635333 1.10043i
\(367\) 1.25094e37 2.16669e37i 0.812043 1.40650i −0.0993885 0.995049i \(-0.531689\pi\)
0.911432 0.411451i \(-0.134978\pi\)
\(368\) 1.02015e36 1.76695e36i 0.0636605 0.110263i
\(369\) −3.94142e36 6.82674e36i −0.236467 0.409573i
\(370\) 5.29952e36 0.305712
\(371\) −2.67532e36 + 3.40672e35i −0.148407 + 0.0188979i
\(372\) −1.43604e37 −0.766114
\(373\) −6.94341e36 1.20263e37i −0.356283 0.617100i 0.631054 0.775739i \(-0.282623\pi\)
−0.987337 + 0.158639i \(0.949289\pi\)
\(374\) 5.33973e36 9.24868e36i 0.263561 0.456501i
\(375\) 6.14316e36 1.06403e37i 0.291702 0.505242i
\(376\) 4.50294e35 + 7.79932e35i 0.0205718 + 0.0356314i
\(377\) −3.15136e37 −1.38532
\(378\) −2.44769e36 + 5.83906e36i −0.103544 + 0.247009i
\(379\) −4.61970e37 −1.88081 −0.940406 0.340052i \(-0.889555\pi\)
−0.940406 + 0.340052i \(0.889555\pi\)
\(380\) −6.31722e35 1.09417e36i −0.0247551 0.0428770i
\(381\) 5.26666e36 9.12213e36i 0.198666 0.344099i
\(382\) 2.46817e37 4.27500e37i 0.896307 1.55245i
\(383\) −5.07466e36 8.78957e36i −0.177429 0.307316i 0.763570 0.645725i \(-0.223445\pi\)
−0.940999 + 0.338409i \(0.890111\pi\)
\(384\) −3.00905e36 −0.101304
\(385\) −3.57413e36 4.69904e36i −0.115875 0.152345i
\(386\) 3.82589e37 1.19458
\(387\) 2.28810e36 + 3.96311e36i 0.0688124 + 0.119187i
\(388\) 2.87046e37 4.97178e37i 0.831555 1.44030i
\(389\) −2.13347e37 + 3.69527e37i −0.595411 + 1.03128i 0.398078 + 0.917352i \(0.369677\pi\)
−0.993489 + 0.113930i \(0.963656\pi\)
\(390\) −1.40972e37 2.44171e37i −0.379050 0.656534i
\(391\) −5.79027e36 −0.150015
\(392\) −9.40141e35 + 3.39322e36i −0.0234717 + 0.0847157i
\(393\) −4.49623e37 −1.08182
\(394\) −8.56618e36 1.48371e37i −0.198651 0.344074i
\(395\) 2.02025e36 3.49917e36i 0.0451592 0.0782181i
\(396\) 2.19914e36 3.80903e36i 0.0473885 0.0820793i
\(397\) −4.03545e37 6.98961e37i −0.838359 1.45208i −0.891266 0.453480i \(-0.850182\pi\)
0.0529079 0.998599i \(-0.483151\pi\)
\(398\) 3.50919e37 0.702914
\(399\) 1.51642e36 + 1.99369e36i 0.0292895 + 0.0385080i
\(400\) 3.42476e37 0.637911
\(401\) 3.68279e37 + 6.37879e37i 0.661582 + 1.14589i 0.980200 + 0.198011i \(0.0634482\pi\)
−0.318617 + 0.947883i \(0.603218\pi\)
\(402\) 2.12733e37 3.68465e37i 0.368602 0.638438i
\(403\) −6.33916e37 + 1.09798e38i −1.05952 + 1.83514i
\(404\) 3.20105e37 + 5.54438e37i 0.516134 + 0.893970i
\(405\) 4.50452e36 0.0700730
\(406\) −3.31922e37 + 7.91813e37i −0.498206 + 1.18849i
\(407\) 7.29882e36 0.105714
\(408\) 2.26574e36 + 3.92437e36i 0.0316692 + 0.0548526i
\(409\) 2.91221e37 5.04410e37i 0.392857 0.680449i −0.599968 0.800024i \(-0.704820\pi\)
0.992825 + 0.119575i \(0.0381533\pi\)
\(410\) 4.78186e37 8.28243e37i 0.622631 1.07843i
\(411\) −1.32777e37 2.29976e37i −0.166885 0.289053i
\(412\) −1.06266e38 −1.28940
\(413\) 1.25334e38 1.59599e37i 1.46823 0.186963i
\(414\) −4.93017e36 −0.0557644
\(415\) −1.51884e37 2.63071e37i −0.165888 0.287327i
\(416\) 9.83062e37 1.70271e38i 1.03688 1.79593i
\(417\) −1.02745e36 + 1.77960e36i −0.0104662 + 0.0181280i
\(418\) −1.79875e36 3.11553e36i −0.0176976 0.0306532i
\(419\) 6.29261e37 0.598036 0.299018 0.954247i \(-0.403341\pi\)
0.299018 + 0.954247i \(0.403341\pi\)
\(420\) −3.68568e37 + 4.69330e36i −0.338378 + 0.0430887i
\(421\) −5.92759e37 −0.525760 −0.262880 0.964829i \(-0.584672\pi\)
−0.262880 + 0.964829i \(0.584672\pi\)
\(422\) 1.26848e38 + 2.19707e38i 1.08706 + 1.88284i
\(423\) 9.42025e36 1.63163e37i 0.0780058 0.135110i
\(424\) −8.21761e35 + 1.42333e36i −0.00657568 + 0.0113894i
\(425\) −4.85965e37 8.41717e37i −0.375808 0.650918i
\(426\) 2.17845e37 0.162820
\(427\) −8.46275e37 + 2.01882e38i −0.611375 + 1.45846i
\(428\) 1.93278e37 0.134973
\(429\) −1.94155e37 3.36287e37i −0.131075 0.227028i
\(430\) −2.77600e37 + 4.80818e37i −0.181187 + 0.313825i
\(431\) 6.99334e37 1.21128e38i 0.441331 0.764408i −0.556458 0.830876i \(-0.687840\pi\)
0.997789 + 0.0664684i \(0.0211732\pi\)
\(432\) 1.67021e37 + 2.89288e37i 0.101919 + 0.176529i
\(433\) 6.07223e37 0.358322 0.179161 0.983820i \(-0.442662\pi\)
0.179161 + 0.983820i \(0.442662\pi\)
\(434\) 2.09110e38 + 2.74924e38i 1.19336 + 1.56896i
\(435\) 6.10841e37 0.337158
\(436\) 6.60845e37 + 1.14462e38i 0.352814 + 0.611091i
\(437\) −9.75261e35 + 1.68920e36i −0.00503663 + 0.00872370i
\(438\) −2.04803e37 + 3.54728e37i −0.102320 + 0.177224i
\(439\) −4.89051e37 8.47061e37i −0.236384 0.409429i 0.723290 0.690545i \(-0.242629\pi\)
−0.959674 + 0.281115i \(0.909296\pi\)
\(440\) −3.59785e36 −0.0168259
\(441\) 7.13104e37 1.84605e37i 0.322696 0.0835379i
\(442\) −5.93362e38 −2.59835
\(443\) 4.01767e37 + 6.95882e37i 0.170263 + 0.294904i 0.938512 0.345247i \(-0.112205\pi\)
−0.768249 + 0.640152i \(0.778872\pi\)
\(444\) 2.29667e37 3.97794e37i 0.0941987 0.163157i
\(445\) −1.24191e38 + 2.15106e38i −0.493027 + 0.853948i
\(446\) 7.41558e37 + 1.28442e38i 0.284964 + 0.493572i
\(447\) −1.29987e38 −0.483549
\(448\) −1.46235e38 1.92261e38i −0.526648 0.692404i
\(449\) −3.36163e38 −1.17214 −0.586068 0.810262i \(-0.699325\pi\)
−0.586068 + 0.810262i \(0.699325\pi\)
\(450\) −4.13780e37 7.16687e37i −0.139697 0.241963i
\(451\) 6.58586e37 1.14071e38i 0.215304 0.372918i
\(452\) −2.39784e38 + 4.15318e38i −0.759124 + 1.31484i
\(453\) −1.58525e38 2.74574e38i −0.486043 0.841852i
\(454\) −1.03146e38 −0.306298
\(455\) −1.26814e38 + 3.02520e38i −0.364756 + 0.870138i
\(456\) 1.52648e36 0.00425306
\(457\) 2.98145e37 + 5.16402e37i 0.0804715 + 0.139381i 0.903453 0.428688i \(-0.141024\pi\)
−0.822981 + 0.568069i \(0.807691\pi\)
\(458\) 1.15476e38 2.00010e38i 0.301954 0.523000i
\(459\) 4.73997e37 8.20986e37i 0.120086 0.207995i
\(460\) −1.44660e37 2.50558e37i −0.0355106 0.0615062i
\(461\) 4.20694e38 1.00070 0.500349 0.865824i \(-0.333205\pi\)
0.500349 + 0.865824i \(0.333205\pi\)
\(462\) −1.04945e38 + 1.33636e37i −0.241910 + 0.0308045i
\(463\) 3.86844e37 0.0864195 0.0432097 0.999066i \(-0.486242\pi\)
0.0432097 + 0.999066i \(0.486242\pi\)
\(464\) 2.26490e38 + 3.92293e38i 0.490387 + 0.849376i
\(465\) 1.22874e38 2.12825e38i 0.257866 0.446637i
\(466\) 2.20356e38 3.81668e38i 0.448259 0.776407i
\(467\) −2.15967e38 3.74065e38i −0.425885 0.737654i 0.570618 0.821216i \(-0.306704\pi\)
−0.996503 + 0.0835618i \(0.973370\pi\)
\(468\) −2.44374e38 −0.467185
\(469\) −4.91039e38 + 6.25282e37i −0.910142 + 0.115896i
\(470\) 2.28579e38 0.410788
\(471\) 2.22316e38 + 3.85063e38i 0.387407 + 0.671009i
\(472\) 3.84982e37 6.66808e37i 0.0650551 0.112679i
\(473\) −3.82328e37 + 6.62211e37i −0.0626541 + 0.108520i
\(474\) −3.62014e37 6.27026e37i −0.0575359 0.0996552i
\(475\) −3.27407e37 −0.0504696
\(476\) −3.02293e38 + 7.21132e38i −0.451989 + 1.07824i
\(477\) 3.43828e37 0.0498684
\(478\) 8.55769e38 + 1.48224e39i 1.20407 + 2.08551i
\(479\) 4.77560e38 8.27159e38i 0.651874 1.12908i −0.330794 0.943703i \(-0.607317\pi\)
0.982668 0.185375i \(-0.0593501\pi\)
\(480\) −1.90551e38 + 3.30044e38i −0.252355 + 0.437092i
\(481\) −2.02765e38 3.51200e38i −0.260549 0.451285i
\(482\) 1.18804e39 1.48132
\(483\) 3.47248e37 + 4.56541e37i 0.0420152 + 0.0552390i
\(484\) −7.24357e38 −0.850540
\(485\) 4.91220e38 + 8.50819e38i 0.559785 + 0.969576i
\(486\) 4.03589e37 6.99036e37i 0.0446389 0.0773168i
\(487\) 7.64777e38 1.32463e39i 0.821041 1.42208i −0.0838670 0.996477i \(-0.526727\pi\)
0.904908 0.425608i \(-0.139940\pi\)
\(488\) 6.67003e37 + 1.15528e38i 0.0695089 + 0.120393i
\(489\) −4.61607e37 −0.0466975
\(490\) 6.26543e38 + 6.37267e38i 0.615330 + 0.625862i
\(491\) −1.72717e39 −1.64685 −0.823423 0.567428i \(-0.807938\pi\)
−0.823423 + 0.567428i \(0.807938\pi\)
\(492\) −4.14465e38 7.17875e38i −0.383702 0.664591i
\(493\) 6.42769e38 1.11331e39i 0.577796 1.00077i
\(494\) −9.99407e37 + 1.73102e38i −0.0872372 + 0.151099i
\(495\) 3.76338e37 + 6.51837e37i 0.0319009 + 0.0552540i
\(496\) 1.82240e39 1.50023
\(497\) −1.53436e38 2.01728e38i −0.122676 0.161286i
\(498\) −5.44332e38 −0.422706
\(499\) 1.27345e38 + 2.20568e38i 0.0960559 + 0.166374i 0.910049 0.414501i \(-0.136044\pi\)
−0.813993 + 0.580875i \(0.802711\pi\)
\(500\) 6.45992e38 1.11889e39i 0.473328 0.819829i
\(501\) 1.29979e37 2.25131e37i 0.00925183 0.0160246i
\(502\) −9.69203e38 1.67871e39i −0.670210 1.16084i
\(503\) 8.03161e38 0.539594 0.269797 0.962917i \(-0.413043\pi\)
0.269797 + 0.962917i \(0.413043\pi\)
\(504\) 1.73543e37 4.13993e37i 0.0113283 0.0270241i
\(505\) −1.09559e39 −0.694900
\(506\) −4.11901e37 7.13433e37i −0.0253869 0.0439714i
\(507\) −5.96773e38 + 1.03364e39i −0.357432 + 0.619090i
\(508\) 5.53823e38 9.59249e38i 0.322364 0.558351i
\(509\) −2.31944e38 4.01739e38i −0.131213 0.227267i 0.792932 0.609311i \(-0.208554\pi\)
−0.924144 + 0.382044i \(0.875220\pi\)
\(510\) 1.15014e39 0.632386
\(511\) 4.72732e38 6.01971e37i 0.252646 0.0321716i
\(512\) −2.64690e39 −1.37507
\(513\) −1.59672e37 2.76559e37i −0.00806354 0.0139665i
\(514\) 6.28132e38 1.08796e39i 0.308379 0.534129i
\(515\) 9.09267e38 1.57490e39i 0.433997 0.751704i
\(516\) 2.40608e38 + 4.16746e38i 0.111658 + 0.193398i
\(517\) 3.14813e38 0.142049
\(518\) −1.09599e39 + 1.39562e38i −0.480868 + 0.0612331i
\(519\) −1.09107e39 −0.465505
\(520\) 9.99502e37 + 1.73119e38i 0.0414701 + 0.0718283i
\(521\) 1.89877e39 3.28876e39i 0.766169 1.32704i −0.173458 0.984841i \(-0.555494\pi\)
0.939627 0.342202i \(-0.111173\pi\)
\(522\) 5.47291e38 9.47937e38i 0.214781 0.372012i
\(523\) 1.50481e39 + 2.60641e39i 0.574391 + 0.994875i 0.996107 + 0.0881471i \(0.0280945\pi\)
−0.421716 + 0.906728i \(0.638572\pi\)
\(524\) −4.72807e39 −1.75542
\(525\) −3.72223e38 + 8.87952e38i −0.134429 + 0.320686i
\(526\) 2.97070e38 0.104368
\(527\) −2.58594e39 4.47898e39i −0.883821 1.53082i
\(528\) −2.79081e38 + 4.83383e38i −0.0927980 + 0.160731i
\(529\) 1.52320e39 2.63825e39i 0.492775 0.853511i
\(530\) 2.08572e38 + 3.61257e38i 0.0656532 + 0.113715i
\(531\) −1.61078e39 −0.493362
\(532\) 1.59461e38 + 2.09649e38i 0.0475265 + 0.0624849i
\(533\) −7.31836e39 −2.12260
\(534\) 2.22542e39 + 3.85454e39i 0.628150 + 1.08799i
\(535\) −1.65378e38 + 2.86443e38i −0.0454305 + 0.0786880i
\(536\) −1.50829e38 + 2.61244e38i −0.0403271 + 0.0698485i
\(537\) −1.26528e39 2.19153e39i −0.329275 0.570321i
\(538\) 4.90264e39 1.24190
\(539\) 8.62913e38 + 8.77682e38i 0.212779 + 0.216421i
\(540\) 4.73679e38 0.113704
\(541\) −2.85667e39 4.94790e39i −0.667574 1.15627i −0.978580 0.205865i \(-0.933999\pi\)
0.311006 0.950408i \(-0.399334\pi\)
\(542\) −1.65296e39 + 2.86301e39i −0.376074 + 0.651379i
\(543\) −1.27891e39 + 2.21514e39i −0.283298 + 0.490686i
\(544\) 4.01021e39 + 6.94589e39i 0.864935 + 1.49811i
\(545\) −2.26180e39 −0.475013
\(546\) 3.55846e39 + 4.67844e39i 0.727727 + 0.956770i
\(547\) −7.16174e39 −1.42627 −0.713136 0.701026i \(-0.752726\pi\)
−0.713136 + 0.701026i \(0.752726\pi\)
\(548\) −1.39623e39 2.41835e39i −0.270795 0.469030i
\(549\) 1.39538e39 2.41688e39i 0.263569 0.456515i
\(550\) 6.91400e38 1.19754e39i 0.127195 0.220308i
\(551\) −2.16525e38 3.75032e38i −0.0387980 0.0672000i
\(552\) 3.49553e37 0.00610093
\(553\) −3.25656e38 + 7.76865e38i −0.0553662 + 0.132078i
\(554\) 1.20427e40 1.99450
\(555\) 3.93028e38 + 6.80744e38i 0.0634125 + 0.109834i
\(556\) −1.08043e38 + 1.87137e38i −0.0169830 + 0.0294154i
\(557\) −4.77365e39 + 8.26821e39i −0.731056 + 1.26623i 0.225376 + 0.974272i \(0.427639\pi\)
−0.956432 + 0.291954i \(0.905694\pi\)
\(558\) −2.20182e39 3.81367e39i −0.328538 0.569045i
\(559\) 4.24851e39 0.617683
\(560\) 4.67729e39 5.95601e38i 0.662626 0.0843779i
\(561\) 1.58404e39 0.218677
\(562\) 9.39997e39 + 1.62812e40i 1.26459 + 2.19033i
\(563\) −3.72919e39 + 6.45915e39i −0.488925 + 0.846844i −0.999919 0.0127409i \(-0.995944\pi\)
0.510993 + 0.859585i \(0.329278\pi\)
\(564\) 9.90598e38 1.71577e39i 0.126576 0.219236i
\(565\) −4.10342e39 7.10732e39i −0.511026 0.885123i
\(566\) 3.71669e39 0.451147
\(567\) −9.31578e38 + 1.18626e38i −0.110221 + 0.0140354i
\(568\) −1.54454e38 −0.0178134
\(569\) 2.18489e39 + 3.78435e39i 0.245642 + 0.425464i 0.962312 0.271948i \(-0.0876679\pi\)
−0.716670 + 0.697413i \(0.754335\pi\)
\(570\) 1.93719e38 3.35531e38i 0.0212318 0.0367745i
\(571\) −9.16407e38 + 1.58726e39i −0.0979185 + 0.169600i −0.910823 0.412797i \(-0.864552\pi\)
0.812904 + 0.582397i \(0.197885\pi\)
\(572\) −2.04166e39 3.53627e39i −0.212687 0.368385i
\(573\) 7.32187e39 0.743670
\(574\) −7.70818e39 + 1.83881e40i −0.763360 + 1.82102i
\(575\) −7.49736e38 −0.0723977
\(576\) 1.53978e39 + 2.66698e39i 0.144989 + 0.251128i
\(577\) −5.12095e39 + 8.86974e39i −0.470220 + 0.814445i −0.999420 0.0340522i \(-0.989159\pi\)
0.529200 + 0.848497i \(0.322492\pi\)
\(578\) 4.33166e39 7.50266e39i 0.387883 0.671834i
\(579\) 2.83739e39 + 4.91450e39i 0.247788 + 0.429181i
\(580\) 6.42338e39 0.547088
\(581\) 3.83391e39 + 5.04058e39i 0.318484 + 0.418723i
\(582\) 1.76046e40 1.42641
\(583\) 2.87258e38 + 4.97545e38i 0.0227027 + 0.0393223i
\(584\) 1.45206e38 2.51505e38i 0.0111944 0.0193892i
\(585\) 2.09098e39 3.62168e39i 0.157250 0.272364i
\(586\) 6.78896e39 + 1.17588e40i 0.498067 + 0.862678i
\(587\) −1.79584e40 −1.28534 −0.642668 0.766145i \(-0.722172\pi\)
−0.642668 + 0.766145i \(0.722172\pi\)
\(588\) 7.49874e39 1.94124e39i 0.523621 0.135552i
\(589\) −1.74221e39 −0.118694
\(590\) −9.77126e39 1.69243e40i −0.649526 1.12501i
\(591\) 1.27058e39 2.20072e39i 0.0824110 0.142740i
\(592\) −2.91457e39 + 5.04819e39i −0.184463 + 0.319500i
\(593\) −6.27552e39 1.08695e40i −0.387576 0.671301i 0.604547 0.796569i \(-0.293354\pi\)
−0.992123 + 0.125268i \(0.960021\pi\)
\(594\) 1.34874e39 0.0812879
\(595\) −8.10080e39 1.06504e40i −0.476466 0.626427i
\(596\) −1.36689e40 −0.784628
\(597\) 2.60252e39 + 4.50769e39i 0.145803 + 0.252538i
\(598\) −2.28857e39 + 3.96391e39i −0.125140 + 0.216749i
\(599\) −1.05998e40 + 1.83594e40i −0.565731 + 0.979874i 0.431251 + 0.902232i \(0.358072\pi\)
−0.996981 + 0.0776419i \(0.975261\pi\)
\(600\) 2.93372e38 + 5.08136e38i 0.0152836 + 0.0264720i
\(601\) −2.96740e40 −1.50902 −0.754512 0.656286i \(-0.772127\pi\)
−0.754512 + 0.656286i \(0.772127\pi\)
\(602\) 4.47481e39 1.06748e40i 0.222139 0.529922i
\(603\) 6.31076e39 0.305831
\(604\) −1.66699e40 2.88732e40i −0.788676 1.36603i
\(605\) 6.19795e39 1.07352e40i 0.286283 0.495856i
\(606\) −9.81608e39 + 1.70019e40i −0.442675 + 0.766735i
\(607\) −1.67492e40 2.90105e40i −0.737495 1.27738i −0.953620 0.301013i \(-0.902675\pi\)
0.216125 0.976366i \(-0.430658\pi\)
\(608\) 2.70178e39 0.116158
\(609\) −1.26328e40 + 1.60864e39i −0.530332 + 0.0675318i
\(610\) 3.38585e40 1.38799
\(611\) −8.74568e39 1.51480e40i −0.350103 0.606396i
\(612\) 4.98437e39 8.63319e39i 0.194857 0.337501i
\(613\) −1.38972e40 + 2.40706e40i −0.530579 + 0.918990i 0.468784 + 0.883313i \(0.344692\pi\)
−0.999363 + 0.0356773i \(0.988641\pi\)
\(614\) −9.12884e39 1.58116e40i −0.340388 0.589570i
\(615\) 1.41855e40 0.516600
\(616\) 7.44069e38 9.47488e37i 0.0264663 0.00337018i
\(617\) −2.90793e40 −1.01030 −0.505148 0.863033i \(-0.668562\pi\)
−0.505148 + 0.863033i \(0.668562\pi\)
\(618\) −1.62934e40 2.82210e40i −0.552941 0.957722i
\(619\) −1.20856e40 + 2.09329e40i −0.400639 + 0.693927i −0.993803 0.111154i \(-0.964545\pi\)
0.593164 + 0.805082i \(0.297879\pi\)
\(620\) 1.29210e40 2.23799e40i 0.418425 0.724733i
\(621\) −3.65636e38 6.33300e38i −0.0115670 0.0200346i
\(622\) −9.09005e39 −0.280935
\(623\) 2.00192e40 4.77564e40i 0.604462 1.44197i
\(624\) 3.10121e40 0.914860
\(625\) 6.07100e38 + 1.05153e39i 0.0174985 + 0.0303082i
\(626\) 1.89378e40 3.28013e40i 0.533338 0.923768i
\(627\) 2.66801e38 4.62113e38i 0.00734190 0.0127165i
\(628\) 2.33779e40 + 4.04918e40i 0.628625 + 1.08881i
\(629\) 1.65428e40 0.434686
\(630\) −6.89750e39 9.06840e39i −0.177114 0.232859i
\(631\) 4.23670e40 1.06317 0.531584 0.847005i \(-0.321597\pi\)
0.531584 + 0.847005i \(0.321597\pi\)
\(632\) 2.56670e38 + 4.44566e38i 0.00629474 + 0.0109028i
\(633\) −1.88148e40 + 3.25882e40i −0.450968 + 0.781100i
\(634\) 2.11021e40 3.65499e40i 0.494347 0.856234i
\(635\) 9.47755e39 + 1.64156e40i 0.217009 + 0.375870i
\(636\) 3.61557e39 0.0809187
\(637\) 1.82595e40 6.59036e40i 0.399455 1.44174i
\(638\) 1.82898e40 0.391119
\(639\) 1.61560e39 + 2.79831e39i 0.0337732 + 0.0584969i
\(640\) 2.70745e39 4.68944e39i 0.0553287 0.0958321i
\(641\) −6.33296e39 + 1.09690e40i −0.126522 + 0.219142i −0.922327 0.386411i \(-0.873715\pi\)
0.795805 + 0.605553i \(0.207048\pi\)
\(642\) 2.96345e39 + 5.13285e39i 0.0578815 + 0.100254i
\(643\) 8.10571e40 1.54786 0.773931 0.633270i \(-0.218288\pi\)
0.773931 + 0.633270i \(0.218288\pi\)
\(644\) 3.65154e39 + 4.80081e39i 0.0681759 + 0.0896333i
\(645\) −8.23505e39 −0.150332
\(646\) −4.07689e39 7.06138e39i −0.0727708 0.126043i
\(647\) −7.46353e39 + 1.29272e40i −0.130266 + 0.225628i −0.923779 0.382926i \(-0.874917\pi\)
0.793513 + 0.608553i \(0.208250\pi\)
\(648\) −2.86147e38 + 4.95621e38i −0.00488373 + 0.00845887i
\(649\) −1.34576e40 2.33092e40i −0.224604 0.389026i
\(650\) −7.68299e40 −1.25397
\(651\) −1.98069e40 + 4.72501e40i −0.316149 + 0.754185i
\(652\) −4.85409e39 −0.0757735
\(653\) −3.98271e40 6.89825e40i −0.608047 1.05317i −0.991562 0.129634i \(-0.958620\pi\)
0.383515 0.923535i \(-0.374714\pi\)
\(654\) −2.02650e40 + 3.50999e40i −0.302600 + 0.524118i
\(655\) 4.04556e40 7.00712e40i 0.590854 1.02339i
\(656\) 5.25975e40 + 9.11015e40i 0.751380 + 1.30143i
\(657\) −6.07549e39 −0.0848953
\(658\) −4.72723e40 + 6.01960e39i −0.646148 + 0.0822796i
\(659\) 6.09652e40 0.815161 0.407581 0.913169i \(-0.366373\pi\)
0.407581 + 0.913169i \(0.366373\pi\)
\(660\) 3.95744e39 + 6.85448e39i 0.0517639 + 0.0896577i
\(661\) −5.57921e40 + 9.66348e40i −0.713924 + 1.23655i 0.249450 + 0.968388i \(0.419750\pi\)
−0.963373 + 0.268164i \(0.913583\pi\)
\(662\) −7.32395e40 + 1.26855e41i −0.916863 + 1.58805i
\(663\) −4.40054e40 7.62197e40i −0.538965 0.933514i
\(664\) 3.85935e39 0.0462463
\(665\) −4.47149e39 + 5.69393e38i −0.0524249 + 0.00667573i
\(666\) 1.40855e40 0.161584
\(667\) −4.95825e39 8.58794e39i −0.0556549 0.0963972i
\(668\) 1.36682e39 2.36740e39i 0.0150124 0.0260023i
\(669\) −1.09992e40 + 1.90512e40i −0.118218 + 0.204759i
\(670\) 3.82822e40 + 6.63066e40i 0.402635 + 0.697385i
\(671\) 4.66320e40 0.479962
\(672\) 3.07160e40 7.32743e40i 0.309393 0.738069i
\(673\) 1.88107e41 1.85433 0.927163 0.374658i \(-0.122240\pi\)
0.927163 + 0.374658i \(0.122240\pi\)
\(674\) 4.56308e40 + 7.90349e40i 0.440240 + 0.762519i
\(675\) 6.13741e39 1.06303e40i 0.0579536 0.100379i
\(676\) −6.27544e40 + 1.08694e41i −0.579985 + 1.00456i
\(677\) 9.52801e40 + 1.65030e41i 0.861919 + 1.49289i 0.870074 + 0.492920i \(0.164071\pi\)
−0.00815560 + 0.999967i \(0.502596\pi\)
\(678\) −1.47060e41 −1.30216
\(679\) −1.23995e41 1.63021e41i −1.07472 1.41297i
\(680\) −8.15455e39 −0.0691864
\(681\) −7.64962e39 1.32495e40i −0.0635341 0.110044i
\(682\) 3.67910e40 6.37240e40i 0.299136 0.518119i
\(683\) −6.00093e40 + 1.03939e41i −0.477659 + 0.827330i −0.999672 0.0256076i \(-0.991848\pi\)
0.522013 + 0.852938i \(0.325181\pi\)
\(684\) −1.67905e39 2.90819e39i −0.0130843 0.0226626i
\(685\) 4.77874e40 0.364586
\(686\) −1.46357e41 1.15293e41i −1.09324 0.861199i
\(687\) 3.42560e40 0.250533
\(688\) −3.05343e40 5.28870e40i −0.218653 0.378718i
\(689\) 1.59604e40 2.76442e40i 0.111909 0.193832i
\(690\) 4.43601e39 7.68340e39i 0.0304566 0.0527523i
\(691\) 4.86401e40 + 8.42471e40i 0.327011 + 0.566400i 0.981917 0.189310i \(-0.0606252\pi\)
−0.654906 + 0.755710i \(0.727292\pi\)
\(692\) −1.14732e41 −0.755349
\(693\) −9.49964e39 1.24895e40i −0.0612457 0.0805220i
\(694\) −2.03201e39 −0.0128296
\(695\) −1.84894e39 3.20246e39i −0.0114326 0.0198018i
\(696\) −3.88033e39 + 6.72093e39i −0.0234982 + 0.0407001i
\(697\) 1.49269e41 2.58542e41i 0.885309 1.53340i
\(698\) 1.62591e41 + 2.81615e41i 0.944478 + 1.63588i
\(699\) 6.53689e40 0.371922
\(700\) −3.91416e40 + 9.33737e40i −0.218131 + 0.520359i
\(701\) 8.21684e39 0.0448532 0.0224266 0.999748i \(-0.492861\pi\)
0.0224266 + 0.999748i \(0.492861\pi\)
\(702\) −3.74688e40 6.48979e40i −0.200347 0.347011i
\(703\) 2.78633e39 4.82606e39i 0.0145942 0.0252779i
\(704\) −2.57288e40 + 4.45636e40i −0.132013 + 0.228653i
\(705\) 1.69521e40 + 2.93619e40i 0.0852081 + 0.147585i
\(706\) −3.08983e41 −1.52148
\(707\) 2.26578e41 2.88522e40i 1.09304 0.139186i
\(708\) −1.69384e41 −0.800551
\(709\) −1.20325e41 2.08408e41i −0.557165 0.965039i −0.997732 0.0673186i \(-0.978556\pi\)
0.440566 0.897720i \(-0.354778\pi\)
\(710\) −1.96010e40 + 3.39500e40i −0.0889268 + 0.154026i
\(711\) 5.36959e39 9.30041e39i 0.0238689 0.0413421i
\(712\) −1.57784e40 2.73289e40i −0.0687230 0.119032i
\(713\) −3.98953e40 −0.170264
\(714\) −2.37859e41 + 3.02887e40i −0.994709 + 0.126665i
\(715\) 6.98779e40 0.286353
\(716\) −1.33052e41 2.30453e41i −0.534297 0.925430i
\(717\) −1.26933e41 + 2.19854e41i −0.499511 + 0.865179i
\(718\) −1.24407e41 + 2.15479e41i −0.479776 + 0.830997i
\(719\) 1.29891e41 + 2.24977e41i 0.490918 + 0.850295i 0.999945 0.0104552i \(-0.00332806\pi\)
−0.509027 + 0.860750i \(0.669995\pi\)
\(720\) −6.01120e40 −0.222659
\(721\) −1.46570e41 + 3.49649e41i −0.532089 + 1.26932i
\(722\) 3.88396e41 1.38193
\(723\) 8.81087e40 + 1.52609e41i 0.307265 + 0.532199i
\(724\) −1.34486e41 + 2.32936e41i −0.459692 + 0.796210i
\(725\) 8.32271e40 1.44154e41i 0.278846 0.482975i
\(726\) −1.11063e41 1.92366e41i −0.364743 0.631754i
\(727\) 1.89639e41 0.610491 0.305245 0.952274i \(-0.401262\pi\)
0.305245 + 0.952274i \(0.401262\pi\)
\(728\) −2.52297e40 3.31704e40i −0.0796173 0.104676i
\(729\) 1.19725e40 0.0370370
\(730\) −3.68550e40 6.38347e40i −0.111767 0.193587i
\(731\) −8.66549e40 + 1.50091e41i −0.257627 + 0.446223i
\(732\) 1.46733e41 2.54150e41i 0.427679 0.740762i
\(733\) −8.34806e40 1.44593e41i −0.238549 0.413179i 0.721749 0.692155i \(-0.243338\pi\)
−0.960298 + 0.278976i \(0.910005\pi\)
\(734\) 8.06767e41 2.26024
\(735\) −3.53932e40 + 1.27743e41i −0.0972194 + 0.350891i
\(736\) 6.18686e40 0.166626
\(737\) 5.27245e40 + 9.13214e40i 0.139230 + 0.241154i
\(738\) 1.27097e41 2.20138e41i 0.329091 0.570003i
\(739\) −2.29554e41 + 3.97599e41i −0.582828 + 1.00949i 0.412314 + 0.911042i \(0.364721\pi\)
−0.995142 + 0.0984465i \(0.968613\pi\)
\(740\) 4.13293e40 + 7.15845e40i 0.102896 + 0.178221i
\(741\) −2.96475e40 −0.0723810
\(742\) −5.26483e40 6.92187e40i −0.126046 0.165717i
\(743\) −2.79202e40 −0.0655511 −0.0327756 0.999463i \(-0.510435\pi\)
−0.0327756 + 0.999463i \(0.510435\pi\)
\(744\) 1.56111e40 + 2.70391e40i 0.0359439 + 0.0622566i
\(745\) 1.16958e41 2.02577e41i 0.264097 0.457430i
\(746\) 2.23900e41 3.87806e41i 0.495840 0.858819i
\(747\) −4.03692e40 6.99215e40i −0.0876801 0.151866i
\(748\) 1.66572e41 0.354836
\(749\) 2.66583e40 6.35943e40i 0.0556988 0.132872i
\(750\) 3.96190e41 0.811923
\(751\) −7.64523e38 1.32419e39i −0.00153678 0.00266178i 0.865256 0.501330i \(-0.167156\pi\)
−0.866793 + 0.498669i \(0.833823\pi\)
\(752\) −1.25711e41 + 2.17739e41i −0.247866 + 0.429316i
\(753\) 1.43758e41 2.48996e41i 0.278038 0.481576i
\(754\) −5.08101e41 8.80056e41i −0.963974 1.66965i
\(755\) 5.70544e41 1.06184
\(756\) −9.79613e40 + 1.24743e40i −0.178850 + 0.0227745i
\(757\) 9.16996e40 0.164239 0.0821197 0.996622i \(-0.473831\pi\)
0.0821197 + 0.996622i \(0.473831\pi\)
\(758\) −7.44844e41 1.29011e42i −1.30877 2.26685i
\(759\) 6.10954e39 1.05820e40i 0.0105318 0.0182416i
\(760\) −1.37348e39 + 2.37894e39i −0.00232287 + 0.00402333i
\(761\) 2.95721e41 + 5.12204e41i 0.490688 + 0.849896i 0.999943 0.0107199i \(-0.00341233\pi\)
−0.509255 + 0.860616i \(0.670079\pi\)
\(762\) 3.39662e41 0.552968
\(763\) 4.67763e41 5.95643e40i 0.747171 0.0951438i
\(764\) 7.69941e41 1.20671
\(765\) 8.52974e40 + 1.47740e41i 0.131173 + 0.227199i
\(766\) 1.63640e41 2.83432e41i 0.246928 0.427693i
\(767\) −7.47717e41 + 1.29508e42i −1.10714 + 1.91763i
\(768\) −2.21351e41 3.83391e41i −0.321620 0.557062i
\(769\) −7.84015e41 −1.11787 −0.558937 0.829210i \(-0.688791\pi\)
−0.558937 + 0.829210i \(0.688791\pi\)
\(770\) 7.36000e40 1.75575e41i 0.102982 0.245668i
\(771\) 1.86336e41 0.255864
\(772\) 2.98369e41 + 5.16791e41i 0.402071 + 0.696408i
\(773\) 5.75959e41 9.97590e41i 0.761709 1.31932i −0.180260 0.983619i \(-0.557694\pi\)
0.941969 0.335699i \(-0.108973\pi\)
\(774\) −7.37831e40 + 1.27796e41i −0.0957664 + 0.165872i
\(775\) −3.34833e41 5.79948e41i −0.426534 0.738779i
\(776\) −1.24818e41 −0.156057
\(777\) −9.92092e40 1.30434e41i −0.121744 0.160061i
\(778\) −1.37593e42 −1.65727
\(779\) −5.02831e40 8.70929e40i −0.0594469 0.102965i
\(780\) 2.19880e41 3.80843e41i 0.255160 0.441951i
\(781\) −2.69957e40 + 4.67579e40i −0.0307507 + 0.0532617i
\(782\) −9.33576e40 1.61700e41i −0.104388 0.180806i
\(783\) 1.62355e41 0.178205
\(784\) −9.51624e41 + 2.46352e41i −1.02537 + 0.265444i
\(785\) −8.00132e41 −0.846353
\(786\) −7.24936e41 1.25563e42i −0.752788 1.30387i
\(787\) −4.07065e41 + 7.05058e41i −0.414983 + 0.718772i −0.995427 0.0955286i \(-0.969546\pi\)
0.580444 + 0.814300i \(0.302879\pi\)
\(788\) 1.33610e41 2.31419e41i 0.133724 0.231616i
\(789\) 2.20316e40 + 3.81598e40i 0.0216486 + 0.0374964i
\(790\) 1.30291e41 0.125696
\(791\) 1.03580e42 + 1.36180e42i 0.981104 + 1.28989i
\(792\) −9.56268e39 −0.00889333
\(793\) −1.29546e42 2.24381e42i −1.18294 2.04892i
\(794\) 1.30129e42 2.25390e42i 1.16675 2.02086i
\(795\) −3.09366e40 + 5.35838e40i −0.0272364 + 0.0471748i
\(796\) 2.73671e41 + 4.74012e41i 0.236586 + 0.409779i
\(797\) −2.19679e41 −0.186485 −0.0932424 0.995643i \(-0.529723\pi\)
−0.0932424 + 0.995643i \(0.529723\pi\)
\(798\) −3.12267e40 + 7.44925e40i −0.0260306 + 0.0620970i
\(799\) 7.13526e41 0.584092
\(800\) 5.19251e41 + 8.99369e41i 0.417419 + 0.722991i
\(801\) −3.30087e41 + 5.71727e41i −0.260589 + 0.451354i
\(802\) −1.18757e42 + 2.05693e42i −0.920726 + 1.59474i
\(803\) −5.07588e40 8.79169e40i −0.0386488 0.0669417i
\(804\) 6.63617e41 0.496255
\(805\) −1.02394e41 + 1.30387e40i −0.0752026 + 0.00957620i
\(806\) −4.08830e42 −2.94907
\(807\) 3.63594e41 + 6.29763e41i 0.257603 + 0.446181i
\(808\) 6.95966e40 1.20545e41i 0.0484310 0.0838850i
\(809\) −7.11426e41 + 1.23223e42i −0.486268 + 0.842242i −0.999875 0.0157839i \(-0.994976\pi\)
0.513607 + 0.858026i \(0.328309\pi\)
\(810\) 7.26273e40 + 1.25794e41i 0.0487604 + 0.0844554i
\(811\) 2.34428e42 1.54599 0.772994 0.634413i \(-0.218758\pi\)
0.772994 + 0.634413i \(0.218758\pi\)
\(812\) −1.32842e42 + 1.69159e41i −0.860541 + 0.109580i
\(813\) −4.90353e41 −0.312030
\(814\) 1.17680e41 + 2.03828e41i 0.0735614 + 0.127412i
\(815\) 4.15339e40 7.19388e40i 0.0255045 0.0441752i
\(816\) −6.32540e41 + 1.09559e42i −0.381576 + 0.660908i
\(817\) 2.91908e40 + 5.05599e40i 0.0172992 + 0.0299631i
\(818\) 1.87817e42 1.09348
\(819\) −3.37058e41 + 8.04064e41i −0.192791 + 0.459911i
\(820\) 1.49169e42 0.838258
\(821\) 1.35585e42 + 2.34839e42i 0.748573 + 1.29657i 0.948507 + 0.316758i \(0.102594\pi\)
−0.199933 + 0.979810i \(0.564073\pi\)
\(822\) 4.28158e41 7.41591e41i 0.232254 0.402275i
\(823\) 9.88108e41 1.71145e42i 0.526631 0.912152i −0.472887 0.881123i \(-0.656788\pi\)
0.999518 0.0310291i \(-0.00987847\pi\)
\(824\) 1.15521e41 + 2.00089e41i 0.0604947 + 0.104780i
\(825\) 2.05105e41 0.105534
\(826\) 2.46649e42 + 3.24278e42i 1.24701 + 1.63948i
\(827\) −2.63967e42 −1.31136 −0.655678 0.755041i \(-0.727617\pi\)
−0.655678 + 0.755041i \(0.727617\pi\)
\(828\) −3.84489e40 6.65954e40i −0.0187691 0.0325091i
\(829\) 1.05938e42 1.83490e42i 0.508172 0.880180i −0.491783 0.870718i \(-0.663655\pi\)
0.999955 0.00946239i \(-0.00301202\pi\)
\(830\) 4.89772e41 8.48311e41i 0.230867 0.399873i
\(831\) 8.93123e41 + 1.54693e42i 0.413710 + 0.716567i
\(832\) 2.85905e42 1.30147
\(833\) 1.95580e42 + 1.98927e42i 0.874927 + 0.889902i
\(834\) −6.62634e40 −0.0291317
\(835\) 2.33903e40 + 4.05132e40i 0.0101061 + 0.0175042i
\(836\) 2.80558e40 4.85941e40i 0.0119133 0.0206344i
\(837\) 3.26587e41 5.65665e41i 0.136295 0.236070i
\(838\) 1.01457e42 + 1.75729e42i 0.416144 + 0.720783i
\(839\) −1.12343e42 −0.452896 −0.226448 0.974023i \(-0.572711\pi\)
−0.226448 + 0.974023i \(0.572711\pi\)
\(840\) 4.89037e40 + 6.42955e40i 0.0193773 + 0.0254760i
\(841\) −3.66055e41 −0.142562
\(842\) −9.55717e41 1.65535e42i −0.365851 0.633672i
\(843\) −1.39426e42 + 2.41492e42i −0.524618 + 0.908664i
\(844\) −1.97850e42 + 3.42686e42i −0.731762 + 1.26745i
\(845\) −1.07391e42 1.86007e42i −0.390434 0.676251i
\(846\) 6.07538e41 0.217122
\(847\) −9.99085e41 + 2.38335e42i −0.350989 + 0.837296i
\(848\) −4.58833e41 −0.158458
\(849\) 2.75640e41 + 4.77423e41i 0.0935796 + 0.162085i
\(850\) 1.56706e42 2.71423e42i 0.523012 0.905884i
\(851\) 6.38048e40 1.10513e41i 0.0209351 0.0362606i
\(852\) 1.69891e41 + 2.94259e41i 0.0548019 + 0.0949197i
\(853\) 5.60597e42 1.77783 0.888915 0.458072i \(-0.151460\pi\)
0.888915 + 0.458072i \(0.151460\pi\)
\(854\) −7.00226e42 + 8.91659e41i −2.18323 + 0.278010i
\(855\) 5.74670e40 0.0176161
\(856\) −2.10111e40 3.63923e40i −0.00633255 0.0109683i
\(857\) −5.56322e41 + 9.63579e41i −0.164856 + 0.285539i −0.936604 0.350389i \(-0.886049\pi\)
0.771748 + 0.635928i \(0.219383\pi\)
\(858\) 6.26081e41 1.08440e42i 0.182417 0.315955i
\(859\) −8.97124e41 1.55386e42i −0.257011 0.445156i 0.708429 0.705782i \(-0.249404\pi\)
−0.965440 + 0.260626i \(0.916071\pi\)
\(860\) −8.65968e41 −0.243935
\(861\) −2.93369e42 + 3.73572e41i −0.812584 + 0.103473i
\(862\) 4.51020e42 1.22840
\(863\) −1.72536e42 2.98841e42i −0.462086 0.800357i 0.536978 0.843596i \(-0.319566\pi\)
−0.999065 + 0.0432388i \(0.986232\pi\)
\(864\) −5.06463e41 + 8.77219e41i −0.133382 + 0.231025i
\(865\) 9.81706e41 1.70036e42i 0.254242 0.440361i
\(866\) 9.79038e41 + 1.69574e42i 0.249339 + 0.431868i
\(867\) 1.28499e42 0.321828
\(868\) −2.08282e42 + 4.96864e42i −0.512998 + 1.22378i
\(869\) 1.79445e41 0.0434655
\(870\) 9.84871e41 + 1.70585e42i 0.234612 + 0.406360i
\(871\) 2.92943e42 5.07392e42i 0.686309 1.18872i
\(872\) 1.43680e41 2.48861e41i 0.0331060 0.0573413i
\(873\) 1.30561e42 + 2.26138e42i 0.295874 + 0.512469i
\(874\) −6.28973e40 −0.0140190
\(875\) −2.79050e42 3.66877e42i −0.611737 0.804273i
\(876\) −6.38877e41 −0.137755
\(877\) −9.76251e39 1.69092e40i −0.00207046 0.00358615i 0.864988 0.501792i \(-0.167326\pi\)
−0.867059 + 0.498206i \(0.833992\pi\)
\(878\) 1.57701e42 2.73147e42i 0.328976 0.569804i
\(879\) −1.00698e42 + 1.74414e42i −0.206624 + 0.357884i
\(880\) −5.02217e41 8.69865e41i −0.101366 0.175571i
\(881\) 9.61745e41 0.190945 0.0954727 0.995432i \(-0.469564\pi\)
0.0954727 + 0.995432i \(0.469564\pi\)
\(882\) 1.66528e42 + 1.69379e42i 0.325232 + 0.330799i
\(883\) −8.83239e42 −1.69687 −0.848433 0.529302i \(-0.822454\pi\)
−0.848433 + 0.529302i \(0.822454\pi\)
\(884\) −4.62745e42 8.01498e42i −0.874548 1.51476i
\(885\) 1.44933e42 2.51031e42i 0.269457 0.466713i
\(886\) −1.29556e42 + 2.24397e42i −0.236956 + 0.410419i
\(887\) −1.87602e42 3.24937e42i −0.337556 0.584664i 0.646416 0.762985i \(-0.276267\pi\)
−0.983972 + 0.178321i \(0.942934\pi\)
\(888\) −9.98675e40 −0.0176781
\(889\) −2.39235e42 3.14531e42i −0.416629 0.547757i
\(890\) −8.00944e42 −1.37229
\(891\) 1.00027e41 + 1.73251e41i 0.0168612 + 0.0292045i
\(892\) −1.15664e42 + 2.00335e42i −0.191826 + 0.332252i
\(893\) 1.20180e41 2.08158e41i 0.0196104 0.0339662i
\(894\) −2.09580e42 3.63004e42i −0.336478 0.582797i
\(895\) 4.55383e42 0.719354
\(896\) −4.36430e41 + 1.04112e42i −0.0678342 + 0.161821i
\(897\) −6.78906e41 −0.103829
\(898\) −5.42002e42 9.38775e42i −0.815632 1.41272i
\(899\) 4.42872e42 7.67076e42i 0.655786 1.13586i
\(900\) 6.45388e41 1.11784e42i 0.0940382 0.162879i
\(901\) 6.51072e41 + 1.12769e42i 0.0933512 + 0.161689i
\(902\) 4.24741e42 0.599279
\(903\) 1.70309e42 2.16869e41i 0.236464 0.0301110i
\(904\) 1.04267e42 0.142464
\(905\) −2.30145e42 3.98623e42i −0.309455 0.535991i
\(906\) 5.11187e42 8.85402e42i 0.676427 1.17161i
\(907\) 6.73345e42 1.16627e43i 0.876863 1.51877i 0.0220986 0.999756i \(-0.492965\pi\)
0.854765 0.519016i \(-0.173701\pi\)
\(908\) −8.04406e41 1.39327e42i −0.103093 0.178563i
\(909\) −2.91195e42 −0.367289
\(910\) −1.04929e43 + 1.33615e42i −1.30255 + 0.165865i
\(911\) 1.02274e43 1.24953 0.624767 0.780811i \(-0.285194\pi\)
0.624767 + 0.780811i \(0.285194\pi\)
\(912\) 2.13079e41 + 3.69063e41i 0.0256221 + 0.0443788i
\(913\) 6.74544e41 1.16834e42i 0.0798332 0.138275i
\(914\) −9.61409e41 + 1.66521e42i −0.111992 + 0.193977i
\(915\) 2.51104e42 + 4.34926e42i 0.287905 + 0.498665i
\(916\) 3.60224e42 0.406526
\(917\) −6.52129e42 + 1.55568e43i −0.724400 + 1.72808i
\(918\) 3.05694e42 0.334247
\(919\) 4.05933e42 + 7.03096e42i 0.436897 + 0.756728i 0.997448 0.0713919i \(-0.0227441\pi\)
−0.560551 + 0.828120i \(0.689411\pi\)
\(920\) −3.14516e40 + 5.44758e40i −0.00333211 + 0.00577139i
\(921\) 1.35404e42 2.34527e42i 0.141211 0.244584i
\(922\) 6.78294e42 + 1.17484e43i 0.696337 + 1.20609i
\(923\) 2.99982e42 0.303159
\(924\) −9.98947e41 1.31335e42i −0.0993800 0.130659i
\(925\) 2.14200e42 0.209780
\(926\) 6.23716e41 + 1.08031e42i 0.0601351 + 0.104157i
\(927\) 2.41673e42 4.18590e42i 0.229389 0.397313i
\(928\) −6.86795e42 + 1.18956e43i −0.641773 + 1.11158i
\(929\) 6.29384e42 + 1.09013e43i 0.579013 + 1.00288i 0.995593 + 0.0937805i \(0.0298952\pi\)
−0.416580 + 0.909099i \(0.636771\pi\)
\(930\) 7.92452e42 0.717745
\(931\) 9.09751e41 2.35512e41i 0.0811245 0.0210011i
\(932\) 6.87395e42 0.603498
\(933\) −6.74144e41 1.16765e42i −0.0582732 0.100932i
\(934\) 6.96415e42 1.20623e43i 0.592705 1.02659i
\(935\) −1.42527e42 + 2.46863e42i −0.119434 + 0.206866i
\(936\) 2.65657e41 + 4.60131e41i 0.0219190 + 0.0379648i
\(937\) −1.97732e43 −1.60640 −0.803198 0.595712i \(-0.796870\pi\)
−0.803198 + 0.595712i \(0.796870\pi\)
\(938\) −9.66329e42 1.27047e43i −0.773008 1.01630i
\(939\) 5.61793e42 0.442512
\(940\) 1.78262e42 + 3.08759e42i 0.138263 + 0.239478i
\(941\) −3.10870e42 + 5.38442e42i −0.237426 + 0.411235i −0.959975 0.280085i \(-0.909637\pi\)
0.722549 + 0.691320i \(0.242971\pi\)
\(942\) −7.16889e42 + 1.24169e43i −0.539156 + 0.933845i
\(943\) −1.15145e42 1.99436e42i −0.0852754 0.147701i
\(944\) 2.14956e43 1.56767
\(945\) 6.53332e41 1.55855e42i 0.0469216 0.111933i
\(946\) −2.46574e42 −0.174392
\(947\) −1.08764e43 1.88386e43i −0.757552 1.31212i −0.944096 0.329672i \(-0.893062\pi\)
0.186544 0.982447i \(-0.440271\pi\)
\(948\) 5.64647e41 9.77997e41i 0.0387307 0.0670836i
\(949\) −2.82022e42 + 4.88476e42i −0.190512 + 0.329977i
\(950\) −5.27884e41 9.14322e41i −0.0351193 0.0608285i
\(951\) 6.25997e42 0.410161
\(952\) 1.68644e42 2.14749e41i 0.108827 0.0138578i
\(953\) 2.26022e43 1.43649 0.718246 0.695789i \(-0.244945\pi\)
0.718246 + 0.695789i \(0.244945\pi\)
\(954\) 5.54361e41 + 9.60182e41i 0.0347010 + 0.0601038i
\(955\) −6.58799e42 + 1.14107e43i −0.406166 + 0.703501i
\(956\) −1.33478e43 + 2.31190e43i −0.810530 + 1.40388i
\(957\) 1.35642e42 + 2.34939e42i 0.0811282 + 0.140518i
\(958\) 3.07992e43 1.81443
\(959\) −9.88289e42 + 1.25847e42i −0.573474 + 0.0730255i
\(960\) −5.54180e42 −0.316751
\(961\) −8.93634e42 1.54782e43i −0.503119 0.871427i
\(962\) 6.53845e42 1.13249e43i 0.362607 0.628054i
\(963\) −4.39556e41 + 7.61334e41i −0.0240123 + 0.0415905i
\(964\) 9.26518e42 + 1.60478e43i 0.498582 + 0.863570i
\(965\) −1.02120e43 −0.541332
\(966\) −7.15069e41 + 1.70582e42i −0.0373404 + 0.0890770i
\(967\) −1.97067e43 −1.01375 −0.506873 0.862020i \(-0.669199\pi\)
−0.506873 + 0.862020i \(0.669199\pi\)
\(968\) 7.87442e41 + 1.36389e42i 0.0399049 + 0.0691173i
\(969\) 6.04707e41 1.04738e42i 0.0301891 0.0522891i
\(970\) −1.58401e43 + 2.74358e43i −0.779054 + 1.34936i
\(971\) −1.71338e43 2.96766e43i −0.830185 1.43792i −0.897892 0.440217i \(-0.854902\pi\)
0.0677069 0.997705i \(-0.478432\pi\)
\(972\) 1.25899e42 0.0600980
\(973\) 4.66715e41 + 6.13608e41i 0.0219491 + 0.0288572i
\(974\) 4.93226e43 2.28529
\(975\) −5.69792e42 9.86909e42i −0.260105 0.450516i
\(976\) −1.86211e43 + 3.22528e43i −0.837498 + 1.45059i
\(977\) −5.16850e42 + 8.95210e42i −0.229031 + 0.396692i −0.957521 0.288363i \(-0.906889\pi\)
0.728491 + 0.685056i \(0.240222\pi\)
\(978\) −7.44258e41 1.28909e42i −0.0324945 0.0562821i
\(979\) −1.10311e43 −0.474536
\(980\) −3.72182e42 + 1.34330e43i −0.157753 + 0.569372i
\(981\) −6.01163e42 −0.251068
\(982\) −2.78475e43 4.82332e43i −1.14596 1.98486i
\(983\) −1.58293e43 + 2.74172e43i −0.641855 + 1.11173i 0.343163 + 0.939276i \(0.388502\pi\)
−0.985018 + 0.172450i \(0.944832\pi\)
\(984\) −9.01123e41 + 1.56079e42i −0.0360044 + 0.0623614i
\(985\) 2.28646e42 + 3.96027e42i 0.0900199 + 0.155919i
\(986\) 4.14540e43 1.60824
\(987\) −4.27909e42 5.62588e42i −0.163589 0.215076i
\(988\) −3.11763e42 −0.117449
\(989\) 6.68446e41 + 1.15778e42i 0.0248153 + 0.0429814i
\(990\) −1.21356e42 + 2.10194e42i −0.0443966 + 0.0768971i
\(991\) −2.16589e43 + 3.75144e43i −0.780852 + 1.35248i 0.150593 + 0.988596i \(0.451882\pi\)
−0.931446 + 0.363880i \(0.881452\pi\)
\(992\) 2.76306e43 + 4.78576e43i 0.981683 + 1.70032i
\(993\) −2.17266e43 −0.760725
\(994\) 3.15961e42 7.53737e42i 0.109026 0.260086i
\(995\) −9.36664e42 −0.318529
\(996\) −4.24507e42 7.35268e42i −0.142274 0.246425i
\(997\) 3.97926e42 6.89229e42i 0.131439 0.227658i −0.792793 0.609491i \(-0.791374\pi\)
0.924231 + 0.381833i \(0.124707\pi\)
\(998\) −4.10642e42 + 7.11252e42i −0.133681 + 0.231543i
\(999\) 1.04462e42 + 1.80934e42i 0.0335166 + 0.0580525i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 21.30.e.b.4.16 40
7.2 even 3 inner 21.30.e.b.16.16 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.30.e.b.4.16 40 1.1 even 1 trivial
21.30.e.b.16.16 yes 40 7.2 even 3 inner