Properties

Label 12.20.b.a.11.9
Level 12
Weight 20
Character 12.11
Analytic conductor 27.458
Analytic rank 0
Dimension 36
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(27.4580035868\)
Analytic rank: \(0\)
Dimension: \(36\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.9
Character \(\chi\) = 12.11
Dual form 12.20.b.a.11.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +O(q^{10})\) \(q+(-519.517 - 504.371i) q^{2} +(-19784.5 - 27763.9i) q^{3} +(15507.7 + 524059. i) q^{4} -1.34492e6i q^{5} +(-3.72492e6 + 2.44026e7i) q^{6} -1.72563e8i q^{7} +(2.56263e8 - 2.80079e8i) q^{8} +(-3.79408e8 + 1.09859e9i) q^{9} +(-6.78338e8 + 6.98708e8i) q^{10} -1.32949e10 q^{11} +(1.42431e10 - 1.07988e10i) q^{12} -2.84987e10 q^{13} +(-8.70355e10 + 8.96492e10i) q^{14} +(-3.73402e10 + 2.66085e10i) q^{15} +(-2.74397e11 + 1.62539e10i) q^{16} +1.96504e11i q^{17} +(7.51206e11 - 3.79374e11i) q^{18} -2.26261e12i q^{19} +(7.04816e11 - 2.08566e10i) q^{20} +(-4.79101e12 + 3.41407e12i) q^{21} +(6.90691e12 + 6.70555e12i) q^{22} -9.34021e12 q^{23} +(-1.28461e13 - 1.57365e12i) q^{24} +1.72647e13 q^{25} +(1.48056e13 + 1.43739e13i) q^{26} +(3.80076e13 - 1.12012e13i) q^{27} +(9.04329e13 - 2.67605e12i) q^{28} -1.66276e13i q^{29} +(3.28194e13 + 5.00971e12i) q^{30} +4.90603e13i q^{31} +(1.50752e14 + 1.29954e14i) q^{32} +(2.63032e14 + 3.69117e14i) q^{33} +(9.91108e13 - 1.02087e14i) q^{34} -2.32082e14 q^{35} +(-5.81610e14 - 1.81795e14i) q^{36} +9.66977e14 q^{37} +(-1.14119e15 + 1.17546e15i) q^{38} +(5.63833e14 + 7.91235e14i) q^{39} +(-3.76683e14 - 3.44653e14i) q^{40} +1.16915e15i q^{41} +(4.21097e15 + 6.42782e14i) q^{42} -3.53338e14i q^{43} +(-2.06173e14 - 6.96729e15i) q^{44} +(1.47751e15 + 5.10272e14i) q^{45} +(4.85240e15 + 4.71093e15i) q^{46} +2.94330e15 q^{47} +(5.88008e15 + 7.29675e15i) q^{48} -1.83789e16 q^{49} +(-8.96930e15 - 8.70781e15i) q^{50} +(5.45571e15 - 3.88773e15i) q^{51} +(-4.41950e14 - 1.49350e16i) q^{52} -9.59360e15i q^{53} +(-2.53952e16 - 1.33507e16i) q^{54} +1.78805e16i q^{55} +(-4.83311e16 - 4.42215e16i) q^{56} +(-6.28188e16 + 4.47646e16i) q^{57} +(-8.38648e15 + 8.63832e15i) q^{58} -1.43314e15 q^{59} +(-1.45235e16 - 1.91558e16i) q^{60} -1.36745e16 q^{61} +(2.47446e16 - 2.54876e16i) q^{62} +(1.89576e17 + 6.54715e16i) q^{63} +(-1.27733e16 - 1.43548e17i) q^{64} +3.83284e16i q^{65} +(4.95223e16 - 3.24429e17i) q^{66} +3.13017e17i q^{67} +(-1.02980e17 + 3.04733e15i) q^{68} +(1.84791e17 + 2.59321e17i) q^{69} +(1.20571e17 + 1.17056e17i) q^{70} +4.79155e17 q^{71} +(2.10464e17 + 3.87793e17i) q^{72} -3.71378e17 q^{73} +(-5.02361e17 - 4.87715e17i) q^{74} +(-3.41573e17 - 4.79335e17i) q^{75} +(1.18574e18 - 3.50879e16i) q^{76} +2.29420e18i q^{77} +(1.06155e17 - 6.95441e17i) q^{78} +5.54718e17i q^{79} +(2.18602e16 + 3.69041e17i) q^{80} +(-1.06295e18 - 8.33627e17i) q^{81} +(5.89686e17 - 6.07394e17i) q^{82} +1.99175e18 q^{83} +(-1.86347e18 - 2.45783e18i) q^{84} +2.64282e17 q^{85} +(-1.78213e17 + 1.83565e17i) q^{86} +(-4.61647e17 + 3.28969e17i) q^{87} +(-3.40699e18 + 3.72361e18i) q^{88} -2.47725e18i q^{89} +(-5.10227e17 - 1.01031e18i) q^{90} +4.91781e18i q^{91} +(-1.44845e17 - 4.89482e18i) q^{92} +(1.36210e18 - 9.70633e17i) q^{93} +(-1.52910e18 - 1.48452e18i) q^{94} -3.04302e18 q^{95} +(6.25470e17 - 6.75653e18i) q^{96} -5.09428e18 q^{97} +(9.54817e18 + 9.26980e18i) q^{98} +(5.04417e18 - 1.46056e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} + O(q^{10}) \) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} - 4162950000q^{10} - 2268767880q^{12} - 25913431656q^{13} + 791689296672q^{16} + 2852271258192q^{18} - 1650825908424q^{21} + 7247870602416q^{22} + 23719435803936q^{24} - 118879690462380q^{25} - 7629081673968q^{28} + 37456727138640q^{30} + 529254701828640q^{33} - 248241675948480q^{34} - 1177548745309416q^{36} + 1847838600168120q^{37} - 40433256181440q^{40} - 2709671988768336q^{42} - 4365410114088000q^{45} + 17206125364795104q^{46} + 1561106052682272q^{48} - 49399737041580084q^{49} + 16558671470242896q^{52} + 40087412948587896q^{54} + 44803667812766472q^{57} - 34645536255764880q^{58} + 50260381053157440q^{60} + 174742350239997144q^{61} - 139766490424918656q^{64} - 87772097712685968q^{66} - 957190369821780672q^{69} + 244663962371376480q^{70} + 54134736422921280q^{72} - 1445122541399481432q^{73} + 2744130151937256048q^{76} + 1125465917961999024q^{78} + 1033298241353042436q^{81} + 1064985418859680800q^{82} + 1920709484261873424q^{84} - 1802899595088057600q^{85} - 9209792381828477760q^{88} - 5194944179528261040q^{90} + 6719944190337314136q^{93} - 3835186345170303552q^{94} - 11947184361208227456q^{96} + 12765226159947004488q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −519.517 504.371i −0.717488 0.696571i
\(3\) −19784.5 27763.9i −0.580328 0.814383i
\(4\) 15507.7 + 524059.i 0.0295787 + 0.999562i
\(5\) 1.34492e6i 0.307950i −0.988075 0.153975i \(-0.950792\pi\)
0.988075 0.153975i \(-0.0492076\pi\)
\(6\) −3.72492e6 + 2.44026e7i −0.150897 + 0.988550i
\(7\) 1.72563e8i 1.61627i −0.588994 0.808137i \(-0.700476\pi\)
0.588994 0.808137i \(-0.299524\pi\)
\(8\) 2.56263e8 2.80079e8i 0.675044 0.737778i
\(9\) −3.79408e8 + 1.09859e9i −0.326439 + 0.945218i
\(10\) −6.78338e8 + 6.98708e8i −0.214509 + 0.220951i
\(11\) −1.32949e10 −1.70002 −0.850009 0.526768i \(-0.823404\pi\)
−0.850009 + 0.526768i \(0.823404\pi\)
\(12\) 1.42431e10 1.07988e10i 0.796861 0.604162i
\(13\) −2.84987e10 −0.745355 −0.372678 0.927961i \(-0.621560\pi\)
−0.372678 + 0.927961i \(0.621560\pi\)
\(14\) −8.70355e10 + 8.96492e10i −1.12585 + 1.15966i
\(15\) −3.73402e10 + 2.66085e10i −0.250790 + 0.178712i
\(16\) −2.74397e11 + 1.62539e10i −0.998250 + 0.0591314i
\(17\) 1.96504e11i 0.401889i 0.979603 + 0.200945i \(0.0644011\pi\)
−0.979603 + 0.200945i \(0.935599\pi\)
\(18\) 7.51206e11 3.79374e11i 0.892627 0.450795i
\(19\) 2.26261e12i 1.60861i −0.594219 0.804304i \(-0.702539\pi\)
0.594219 0.804304i \(-0.297461\pi\)
\(20\) 7.04816e11 2.08566e10i 0.307816 0.00910876i
\(21\) −4.79101e12 + 3.41407e12i −1.31627 + 0.937969i
\(22\) 6.90691e12 + 6.70555e12i 1.21974 + 1.18418i
\(23\) −9.34021e12 −1.08129 −0.540645 0.841251i \(-0.681820\pi\)
−0.540645 + 0.841251i \(0.681820\pi\)
\(24\) −1.28461e13 1.57365e12i −0.992580 0.121591i
\(25\) 1.72647e13 0.905167
\(26\) 1.48056e13 + 1.43739e13i 0.534784 + 0.519192i
\(27\) 3.80076e13 1.12012e13i 0.959211 0.282690i
\(28\) 9.04329e13 2.67605e12i 1.61557 0.0478072i
\(29\) 1.66276e13i 0.212838i −0.994321 0.106419i \(-0.966062\pi\)
0.994321 0.106419i \(-0.0339384\pi\)
\(30\) 3.28194e13 + 5.00971e12i 0.304424 + 0.0464687i
\(31\) 4.90603e13i 0.333268i 0.986019 + 0.166634i \(0.0532899\pi\)
−0.986019 + 0.166634i \(0.946710\pi\)
\(32\) 1.50752e14 + 1.29954e14i 0.757422 + 0.652926i
\(33\) 2.63032e14 + 3.69117e14i 0.986568 + 1.38447i
\(34\) 9.91108e13 1.02087e14i 0.279944 0.288351i
\(35\) −2.32082e14 −0.497732
\(36\) −5.81610e14 1.81795e14i −0.954460 0.298338i
\(37\) 9.66977e14 1.22321 0.611603 0.791165i \(-0.290525\pi\)
0.611603 + 0.791165i \(0.290525\pi\)
\(38\) −1.14119e15 + 1.17546e15i −1.12051 + 1.15416i
\(39\) 5.63833e14 + 7.91235e14i 0.432550 + 0.607004i
\(40\) −3.76683e14 3.44653e14i −0.227199 0.207880i
\(41\) 1.16915e15i 0.557730i 0.960330 + 0.278865i \(0.0899582\pi\)
−0.960330 + 0.278865i \(0.910042\pi\)
\(42\) 4.21097e15 + 6.42782e14i 1.59777 + 0.243891i
\(43\) 3.53338e14i 0.107211i −0.998562 0.0536055i \(-0.982929\pi\)
0.998562 0.0536055i \(-0.0170714\pi\)
\(44\) −2.06173e14 6.96729e15i −0.0502842 1.69927i
\(45\) 1.47751e15 + 5.10272e14i 0.291080 + 0.100527i
\(46\) 4.85240e15 + 4.71093e15i 0.775813 + 0.753195i
\(47\) 2.94330e15 0.383624 0.191812 0.981432i \(-0.438564\pi\)
0.191812 + 0.981432i \(0.438564\pi\)
\(48\) 5.88008e15 + 7.29675e15i 0.627468 + 0.778642i
\(49\) −1.83789e16 −1.61234
\(50\) −8.96930e15 8.70781e15i −0.649446 0.630512i
\(51\) 5.45571e15 3.88773e15i 0.327292 0.233227i
\(52\) −4.41950e14 1.49350e16i −0.0220466 0.745029i
\(53\) 9.59360e15i 0.399357i −0.979861 0.199678i \(-0.936010\pi\)
0.979861 0.199678i \(-0.0639897\pi\)
\(54\) −2.53952e16 1.33507e16i −0.885136 0.465332i
\(55\) 1.78805e16i 0.523521i
\(56\) −4.83311e16 4.42215e16i −1.19245 1.09106i
\(57\) −6.28188e16 + 4.47646e16i −1.31002 + 0.933520i
\(58\) −8.38648e15 + 8.63832e15i −0.148256 + 0.152709i
\(59\) −1.43314e15 −0.0215374 −0.0107687 0.999942i \(-0.503428\pi\)
−0.0107687 + 0.999942i \(0.503428\pi\)
\(60\) −1.45235e16 1.91558e16i −0.186052 0.245394i
\(61\) −1.36745e16 −0.149719 −0.0748597 0.997194i \(-0.523851\pi\)
−0.0748597 + 0.997194i \(0.523851\pi\)
\(62\) 2.47446e16 2.54876e16i 0.232145 0.239116i
\(63\) 1.89576e17 + 6.54715e16i 1.52773 + 0.527615i
\(64\) −1.27733e16 1.43548e17i −0.0886324 0.996064i
\(65\) 3.83284e16i 0.229532i
\(66\) 4.95223e16 3.24429e17i 0.256527 1.68055i
\(67\) 3.13017e17i 1.40558i 0.711395 + 0.702792i \(0.248064\pi\)
−0.711395 + 0.702792i \(0.751936\pi\)
\(68\) −1.02980e17 + 3.04733e15i −0.401713 + 0.0118873i
\(69\) 1.84791e17 + 2.59321e17i 0.627503 + 0.880584i
\(70\) 1.20571e17 + 1.17056e17i 0.357117 + 0.346706i
\(71\) 4.79155e17 1.24029 0.620143 0.784489i \(-0.287075\pi\)
0.620143 + 0.784489i \(0.287075\pi\)
\(72\) 2.10464e17 + 3.87793e17i 0.477001 + 0.878903i
\(73\) −3.71378e17 −0.738327 −0.369163 0.929365i \(-0.620356\pi\)
−0.369163 + 0.929365i \(0.620356\pi\)
\(74\) −5.02361e17 4.87715e17i −0.877636 0.852050i
\(75\) −3.41573e17 4.79335e17i −0.525293 0.737152i
\(76\) 1.18574e18 3.50879e16i 1.60790 0.0475804i
\(77\) 2.29420e18i 2.74770i
\(78\) 1.06155e17 6.95441e17i 0.112472 0.736820i
\(79\) 5.54718e17i 0.520733i 0.965510 + 0.260367i \(0.0838434\pi\)
−0.965510 + 0.260367i \(0.916157\pi\)
\(80\) 2.18602e16 + 3.69041e17i 0.0182095 + 0.307412i
\(81\) −1.06295e18 8.33627e17i −0.786875 0.617112i
\(82\) 5.89686e17 6.07394e17i 0.388498 0.400165i
\(83\) 1.99175e18 1.16948 0.584741 0.811220i \(-0.301196\pi\)
0.584741 + 0.811220i \(0.301196\pi\)
\(84\) −1.86347e18 2.45783e18i −0.976492 1.28795i
\(85\) 2.64282e17 0.123762
\(86\) −1.78213e17 + 1.83565e17i −0.0746801 + 0.0769227i
\(87\) −4.61647e17 + 3.28969e17i −0.173331 + 0.123516i
\(88\) −3.40699e18 + 3.72361e18i −1.14759 + 1.25424i
\(89\) 2.47725e18i 0.749488i −0.927128 0.374744i \(-0.877731\pi\)
0.927128 0.374744i \(-0.122269\pi\)
\(90\) −5.10227e17 1.01031e18i −0.138823 0.274885i
\(91\) 4.91781e18i 1.20470i
\(92\) −1.44845e17 4.89482e18i −0.0319831 1.08082i
\(93\) 1.36210e18 9.70633e17i 0.271408 0.193405i
\(94\) −1.52910e18 1.48452e18i −0.275245 0.267221i
\(95\) −3.04302e18 −0.495371
\(96\) 6.25470e17 6.75653e18i 0.0921785 0.995743i
\(97\) −5.09428e18 −0.680380 −0.340190 0.940357i \(-0.610491\pi\)
−0.340190 + 0.940357i \(0.610491\pi\)
\(98\) 9.54817e18 + 9.26980e18i 1.15684 + 1.12311i
\(99\) 5.04417e18 1.46056e19i 0.554952 1.60689i
\(100\) 2.67736e17 + 9.04771e18i 0.0267736 + 0.904771i
\(101\) 1.23690e19i 1.12534i −0.826683 0.562668i \(-0.809775\pi\)
0.826683 0.562668i \(-0.190225\pi\)
\(102\) −4.79520e18 7.31961e17i −0.397287 0.0606438i
\(103\) 5.70221e17i 0.0430615i 0.999768 + 0.0215308i \(0.00685399\pi\)
−0.999768 + 0.0215308i \(0.993146\pi\)
\(104\) −7.30318e18 + 7.98189e18i −0.503147 + 0.549907i
\(105\) 4.59164e18 + 6.44352e18i 0.288848 + 0.405345i
\(106\) −4.83874e18 + 4.98404e18i −0.278180 + 0.286534i
\(107\) −3.38232e19 −1.77856 −0.889280 0.457363i \(-0.848794\pi\)
−0.889280 + 0.457363i \(0.848794\pi\)
\(108\) 6.45952e18 + 1.97445e19i 0.310939 + 0.950430i
\(109\) 1.77659e19 0.783494 0.391747 0.920073i \(-0.371871\pi\)
0.391747 + 0.920073i \(0.371871\pi\)
\(110\) 9.01841e18 9.28923e18i 0.364670 0.375620i
\(111\) −1.91312e19 2.68471e19i −0.709861 0.996159i
\(112\) 2.80482e18 + 4.73506e19i 0.0955726 + 1.61345i
\(113\) 6.36977e18i 0.199470i 0.995014 + 0.0997352i \(0.0317996\pi\)
−0.995014 + 0.0997352i \(0.968200\pi\)
\(114\) 5.52134e19 + 8.42803e18i 1.59019 + 0.242734i
\(115\) 1.25618e19i 0.332984i
\(116\) 8.71384e18 2.57856e17i 0.212745 0.00629545i
\(117\) 1.08126e19 3.13084e19i 0.243313 0.704523i
\(118\) 7.44540e17 + 7.22834e17i 0.0154529 + 0.0150024i
\(119\) 3.39092e19 0.649563
\(120\) −2.11643e18 + 1.72770e19i −0.0374439 + 0.305665i
\(121\) 1.15594e20 1.89006
\(122\) 7.10413e18 + 6.89702e18i 0.107422 + 0.104290i
\(123\) 3.24602e19 2.31311e19i 0.454206 0.323666i
\(124\) −2.57105e19 + 7.60814e17i −0.333122 + 0.00985762i
\(125\) 4.88719e19i 0.586697i
\(126\) −6.54658e19 1.29630e20i −0.728608 1.44273i
\(127\) 9.93306e19i 1.02553i 0.858530 + 0.512764i \(0.171378\pi\)
−0.858530 + 0.512764i \(0.828622\pi\)
\(128\) −6.57655e19 + 8.10181e19i −0.630236 + 0.776403i
\(129\) −9.81004e18 + 6.99061e18i −0.0873109 + 0.0622176i
\(130\) 1.93317e19 1.99123e19i 0.159886 0.164687i
\(131\) −1.27259e20 −0.978614 −0.489307 0.872111i \(-0.662750\pi\)
−0.489307 + 0.872111i \(0.662750\pi\)
\(132\) −1.89360e20 + 1.43569e20i −1.35468 + 1.02709i
\(133\) −3.90441e20 −2.59995
\(134\) 1.57877e20 1.62618e20i 0.979089 1.00849i
\(135\) −1.50648e19 5.11171e19i −0.0870545 0.295389i
\(136\) 5.50366e19 + 5.03567e19i 0.296505 + 0.271293i
\(137\) 2.01832e20i 1.01425i 0.861873 + 0.507124i \(0.169291\pi\)
−0.861873 + 0.507124i \(0.830709\pi\)
\(138\) 3.47915e19 2.27925e20i 0.163163 1.06891i
\(139\) 1.99551e20i 0.873802i −0.899510 0.436901i \(-0.856076\pi\)
0.899510 0.436901i \(-0.143924\pi\)
\(140\) −3.59907e18 1.21625e20i −0.0147223 0.497515i
\(141\) −5.82318e19 8.17176e19i −0.222628 0.312417i
\(142\) −2.48929e20 2.41672e20i −0.889890 0.863946i
\(143\) 3.78886e20 1.26712
\(144\) 8.62519e19 3.07617e20i 0.269976 0.962867i
\(145\) −2.23628e19 −0.0655434
\(146\) 1.92937e20 + 1.87312e20i 0.529741 + 0.514297i
\(147\) 3.63618e20 + 5.10271e20i 0.935688 + 1.31306i
\(148\) 1.49956e19 + 5.06753e20i 0.0361808 + 1.22267i
\(149\) 3.15970e20i 0.715117i 0.933891 + 0.357558i \(0.116391\pi\)
−0.933891 + 0.357558i \(0.883609\pi\)
\(150\) −6.43096e19 + 4.21302e20i −0.136587 + 0.894802i
\(151\) 2.46468e20i 0.491450i 0.969340 + 0.245725i \(0.0790261\pi\)
−0.969340 + 0.245725i \(0.920974\pi\)
\(152\) −6.33709e20 5.79824e20i −1.18679 1.08588i
\(153\) −2.15877e20 7.45550e19i −0.379873 0.131192i
\(154\) 1.15713e21 1.19187e21i 1.91396 1.97144i
\(155\) 6.59820e19 0.102630
\(156\) −4.05910e20 + 3.07752e20i −0.593945 + 0.450315i
\(157\) 8.77508e20 1.20838 0.604191 0.796839i \(-0.293496\pi\)
0.604191 + 0.796839i \(0.293496\pi\)
\(158\) 2.79784e20 2.88186e20i 0.362727 0.373620i
\(159\) −2.66356e20 + 1.89805e20i −0.325229 + 0.231758i
\(160\) 1.74777e20 2.02749e20i 0.201069 0.233248i
\(161\) 1.61177e21i 1.74766i
\(162\) 1.31764e20 + 9.69205e20i 0.134711 + 0.990885i
\(163\) 2.49747e20i 0.240834i −0.992723 0.120417i \(-0.961577\pi\)
0.992723 0.120417i \(-0.0384232\pi\)
\(164\) −6.12704e20 + 1.81309e19i −0.557486 + 0.0164969i
\(165\) 4.96433e20 3.53757e20i 0.426347 0.303814i
\(166\) −1.03475e21 1.00458e21i −0.839089 0.814627i
\(167\) −1.13644e21 −0.870440 −0.435220 0.900324i \(-0.643329\pi\)
−0.435220 + 0.900324i \(0.643329\pi\)
\(168\) −2.71553e20 + 2.21676e21i −0.196524 + 1.60428i
\(169\) −6.49744e20 −0.444446
\(170\) −1.37299e20 1.33296e20i −0.0887977 0.0862089i
\(171\) 2.48568e21 + 8.58450e20i 1.52048 + 0.525112i
\(172\) 1.85170e20 5.47947e18i 0.107164 0.00317116i
\(173\) 2.40894e21i 1.31944i −0.751514 0.659718i \(-0.770676\pi\)
0.751514 0.659718i \(-0.229324\pi\)
\(174\) 4.05756e20 + 6.19365e19i 0.210401 + 0.0321165i
\(175\) 2.97924e21i 1.46300i
\(176\) 3.64807e21 2.16094e20i 1.69704 0.100524i
\(177\) 2.83540e19 + 3.97895e19i 0.0124988 + 0.0175397i
\(178\) −1.24945e21 + 1.28697e21i −0.522071 + 0.537749i
\(179\) −4.71604e21 −1.86842 −0.934209 0.356727i \(-0.883893\pi\)
−0.934209 + 0.356727i \(0.883893\pi\)
\(180\) −2.44500e20 + 7.82217e20i −0.0918733 + 0.293926i
\(181\) −9.39386e20 −0.334887 −0.167443 0.985882i \(-0.553551\pi\)
−0.167443 + 0.985882i \(0.553551\pi\)
\(182\) 2.48040e21 2.55488e21i 0.839158 0.864357i
\(183\) 2.70543e20 + 3.79658e20i 0.0868863 + 0.121929i
\(184\) −2.39355e21 + 2.61600e21i −0.729918 + 0.797752i
\(185\) 1.30051e21i 0.376687i
\(186\) −1.19720e21 1.82746e20i −0.329452 0.0502891i
\(187\) 2.61249e21i 0.683219i
\(188\) 4.56440e19 + 1.54246e21i 0.0113471 + 0.383456i
\(189\) −1.93292e21 6.55868e21i −0.456905 1.55035i
\(190\) 1.58090e21 + 1.53481e21i 0.355423 + 0.345061i
\(191\) −2.28988e21 −0.489774 −0.244887 0.969552i \(-0.578751\pi\)
−0.244887 + 0.969552i \(0.578751\pi\)
\(192\) −3.73274e21 + 3.19466e21i −0.759742 + 0.650225i
\(193\) 3.21256e21 0.622381 0.311191 0.950348i \(-0.399272\pi\)
0.311191 + 0.950348i \(0.399272\pi\)
\(194\) 2.64656e21 + 2.56941e21i 0.488164 + 0.473932i
\(195\) 1.06415e21 7.58309e20i 0.186927 0.133204i
\(196\) −2.85016e20 9.63164e21i −0.0476909 1.61164i
\(197\) 3.88708e21i 0.619718i 0.950783 + 0.309859i \(0.100282\pi\)
−0.950783 + 0.309859i \(0.899718\pi\)
\(198\) −9.98719e21 + 5.04373e21i −1.51748 + 0.766360i
\(199\) 7.98638e21i 1.15677i 0.815765 + 0.578383i \(0.196316\pi\)
−0.815765 + 0.578383i \(0.803684\pi\)
\(200\) 4.42431e21 4.83547e21i 0.611027 0.667812i
\(201\) 8.69057e21 6.19288e21i 1.14468 0.815700i
\(202\) −6.23858e21 + 6.42592e21i −0.783876 + 0.807416i
\(203\) −2.86930e21 −0.344004
\(204\) 2.12201e21 + 2.79882e21i 0.242806 + 0.320250i
\(205\) 1.57241e21 0.171753
\(206\) 2.87603e20 2.96239e20i 0.0299954 0.0308961i
\(207\) 3.54375e21 1.02611e22i 0.352975 1.02205i
\(208\) 7.81996e21 4.63216e20i 0.744051 0.0440739i
\(209\) 3.00811e22i 2.73466i
\(210\) 8.64489e20 5.66340e21i 0.0751062 0.492033i
\(211\) 2.89424e21i 0.240354i −0.992752 0.120177i \(-0.961654\pi\)
0.992752 0.120177i \(-0.0383462\pi\)
\(212\) 5.02761e21 1.48775e20i 0.399182 0.0118124i
\(213\) −9.47985e21 1.33032e22i −0.719772 1.01007i
\(214\) 1.75717e22 + 1.70594e22i 1.27610 + 1.23889i
\(215\) −4.75210e20 −0.0330157
\(216\) 6.60272e21 1.35156e22i 0.438947 0.898513i
\(217\) 8.46596e21 0.538653
\(218\) −9.22970e21 8.96061e21i −0.562148 0.545759i
\(219\) 7.34752e21 + 1.03109e22i 0.428471 + 0.601281i
\(220\) −9.37043e21 + 2.77286e20i −0.523292 + 0.0154851i
\(221\) 5.60010e21i 0.299550i
\(222\) −3.60191e21 + 2.35967e22i −0.184578 + 1.20920i
\(223\) 3.31609e22i 1.62828i 0.580667 + 0.814141i \(0.302792\pi\)
−0.580667 + 0.814141i \(0.697208\pi\)
\(224\) 2.24251e22 2.60141e22i 1.05531 1.22420i
\(225\) −6.55035e21 + 1.89668e22i −0.295482 + 0.855580i
\(226\) 3.21273e21 3.30920e21i 0.138945 0.143118i
\(227\) −1.24463e21 −0.0516171 −0.0258085 0.999667i \(-0.508216\pi\)
−0.0258085 + 0.999667i \(0.508216\pi\)
\(228\) −2.44334e22 3.22265e22i −0.971860 1.28184i
\(229\) −4.26763e22 −1.62836 −0.814178 0.580615i \(-0.802812\pi\)
−0.814178 + 0.580615i \(0.802812\pi\)
\(230\) 6.33581e21 6.52607e21i 0.231947 0.238912i
\(231\) 6.36958e22 4.53895e22i 2.23768 1.59456i
\(232\) −4.65704e21 4.26105e21i −0.157027 0.143675i
\(233\) 1.68029e22i 0.543881i 0.962314 + 0.271941i \(0.0876654\pi\)
−0.962314 + 0.271941i \(0.912335\pi\)
\(234\) −2.14084e22 + 1.08117e22i −0.665324 + 0.336002i
\(235\) 3.95850e21i 0.118137i
\(236\) −2.22247e19 7.51049e20i −0.000637049 0.0215280i
\(237\) 1.54011e22 1.09748e22i 0.424076 0.302196i
\(238\) −1.76164e22 1.71028e22i −0.466054 0.452467i
\(239\) −7.18116e22 −1.82564 −0.912818 0.408366i \(-0.866099\pi\)
−0.912818 + 0.408366i \(0.866099\pi\)
\(240\) 9.81354e21 7.90823e21i 0.239783 0.193229i
\(241\) −3.21583e22 −0.755321 −0.377661 0.925944i \(-0.623271\pi\)
−0.377661 + 0.925944i \(0.623271\pi\)
\(242\) −6.00533e22 5.83025e22i −1.35610 1.31656i
\(243\) −2.11478e21 + 4.60046e22i −0.0459203 + 0.998945i
\(244\) −2.12061e20 7.16624e21i −0.00442850 0.149654i
\(245\) 2.47182e22i 0.496522i
\(246\) −2.85303e22 4.35500e21i −0.551344 0.0841597i
\(247\) 6.44814e22i 1.19898i
\(248\) 1.37407e22 + 1.25724e22i 0.245878 + 0.224971i
\(249\) −3.94058e22 5.52988e22i −0.678683 0.952406i
\(250\) −2.46495e22 + 2.53898e22i −0.408676 + 0.420948i
\(251\) 7.01962e22 1.12050 0.560252 0.828323i \(-0.310704\pi\)
0.560252 + 0.828323i \(0.310704\pi\)
\(252\) −3.13710e22 + 1.00364e23i −0.482196 + 1.54267i
\(253\) 1.24177e23 1.83821
\(254\) 5.00995e22 5.16039e22i 0.714353 0.735804i
\(255\) −5.22868e21 7.33749e21i −0.0718225 0.100790i
\(256\) 7.50295e22 8.92005e21i 0.993007 0.118056i
\(257\) 6.53328e22i 0.833233i −0.909082 0.416617i \(-0.863216\pi\)
0.909082 0.416617i \(-0.136784\pi\)
\(258\) 8.62234e21 + 1.31615e21i 0.105983 + 0.0161778i
\(259\) 1.66864e23i 1.97704i
\(260\) −2.00863e22 + 5.94387e20i −0.229432 + 0.00678926i
\(261\) 1.82669e22 + 6.30864e21i 0.201178 + 0.0694785i
\(262\) 6.61133e22 + 6.41858e22i 0.702144 + 0.681674i
\(263\) −3.76115e22 −0.385248 −0.192624 0.981273i \(-0.561700\pi\)
−0.192624 + 0.981273i \(0.561700\pi\)
\(264\) 1.70788e23 + 2.09214e22i 1.68740 + 0.206707i
\(265\) −1.29026e22 −0.122982
\(266\) 2.02841e23 + 1.96927e23i 1.86543 + 1.81105i
\(267\) −6.87781e22 + 4.90111e22i −0.610370 + 0.434949i
\(268\) −1.64039e23 + 4.85418e21i −1.40497 + 0.0415753i
\(269\) 1.99972e23i 1.65319i 0.562796 + 0.826596i \(0.309726\pi\)
−0.562796 + 0.826596i \(0.690274\pi\)
\(270\) −1.79556e22 + 3.41544e22i −0.143299 + 0.272578i
\(271\) 1.05713e23i 0.814557i −0.913304 0.407279i \(-0.866478\pi\)
0.913304 0.407279i \(-0.133522\pi\)
\(272\) −3.19396e21 5.39200e22i −0.0237643 0.401186i
\(273\) 1.36538e23 9.72964e22i 0.981086 0.699120i
\(274\) 1.01798e23 1.04855e23i 0.706496 0.727711i
\(275\) −2.29532e23 −1.53880
\(276\) −1.33034e23 + 1.00863e23i −0.861638 + 0.653275i
\(277\) −5.23245e22 −0.327452 −0.163726 0.986506i \(-0.552351\pi\)
−0.163726 + 0.986506i \(0.552351\pi\)
\(278\) −1.00648e23 + 1.03670e23i −0.608665 + 0.626942i
\(279\) −5.38972e22 1.86138e22i −0.315011 0.108792i
\(280\) −5.94742e22 + 6.50014e22i −0.335991 + 0.367216i
\(281\) 2.46223e23i 1.34468i −0.740244 0.672339i \(-0.765290\pi\)
0.740244 0.672339i \(-0.234710\pi\)
\(282\) −1.09636e22 + 7.18241e22i −0.0578876 + 0.379231i
\(283\) 2.13125e21i 0.0108809i −0.999985 0.00544043i \(-0.998268\pi\)
0.999985 0.00544043i \(-0.00173175\pi\)
\(284\) 7.43061e21 + 2.51105e23i 0.0366860 + 1.23974i
\(285\) 6.02047e22 + 8.44862e22i 0.287478 + 0.403422i
\(286\) −1.96838e23 1.91099e23i −0.909142 0.882637i
\(287\) 2.01752e23 0.901445
\(288\) −1.99962e23 + 1.16309e23i −0.864409 + 0.502789i
\(289\) 2.00459e23 0.838485
\(290\) 1.16178e22 + 1.12791e22i 0.0470267 + 0.0456556i
\(291\) 1.00788e23 + 1.41437e23i 0.394843 + 0.554090i
\(292\) −5.75922e21 1.94624e23i −0.0218387 0.738003i
\(293\) 3.06405e23i 1.12474i −0.826885 0.562371i \(-0.809889\pi\)
0.826885 0.562371i \(-0.190111\pi\)
\(294\) 6.84601e22 4.48493e23i 0.243297 1.59388i
\(295\) 1.92745e21i 0.00663246i
\(296\) 2.47801e23 2.70830e23i 0.825718 0.902455i
\(297\) −5.05306e23 + 1.48919e23i −1.63068 + 0.480578i
\(298\) 1.59366e23 1.64152e23i 0.498129 0.513088i
\(299\) 2.66184e23 0.805945
\(300\) 2.45903e23 1.86438e23i 0.721292 0.546868i
\(301\) −6.09728e22 −0.173283
\(302\) 1.24311e23 1.28044e23i 0.342330 0.352610i
\(303\) −3.43412e23 + 2.44715e23i −0.916455 + 0.653064i
\(304\) 3.67762e22 + 6.20853e23i 0.0951192 + 1.60579i
\(305\) 1.83911e22i 0.0461061i
\(306\) 7.45485e22 + 1.47615e23i 0.181170 + 0.358737i
\(307\) 5.86296e22i 0.138135i −0.997612 0.0690673i \(-0.977998\pi\)
0.997612 0.0690673i \(-0.0220023\pi\)
\(308\) −1.20229e24 + 3.55778e22i −2.74649 + 0.0812731i
\(309\) 1.58316e22 1.12815e22i 0.0350686 0.0249898i
\(310\) −3.42788e22 3.32794e22i −0.0736359 0.0714891i
\(311\) 2.84479e23 0.592689 0.296344 0.955081i \(-0.404232\pi\)
0.296344 + 0.955081i \(0.404232\pi\)
\(312\) 3.66098e23 + 4.48469e22i 0.739825 + 0.0906284i
\(313\) −5.93941e23 −1.16432 −0.582160 0.813075i \(-0.697792\pi\)
−0.582160 + 0.813075i \(0.697792\pi\)
\(314\) −4.55880e23 4.42590e23i −0.867000 0.841724i
\(315\) 8.80538e22 2.54964e23i 0.162479 0.470466i
\(316\) −2.90705e23 + 8.60242e21i −0.520505 + 0.0154026i
\(317\) 5.66222e23i 0.983839i 0.870641 + 0.491919i \(0.163705\pi\)
−0.870641 + 0.491919i \(0.836295\pi\)
\(318\) 2.34108e23 + 3.57354e22i 0.394784 + 0.0602617i
\(319\) 2.21062e23i 0.361828i
\(320\) −1.93060e23 + 1.71790e22i −0.306738 + 0.0272944i
\(321\) 6.69175e23 + 9.39064e23i 1.03215 + 1.44843i
\(322\) 8.12930e23 8.37342e23i 1.21737 1.25393i
\(323\) 4.44611e23 0.646482
\(324\) 4.20386e23 5.69977e23i 0.593568 0.804784i
\(325\) −4.92021e23 −0.674671
\(326\) −1.25965e23 + 1.29748e23i −0.167758 + 0.172796i
\(327\) −3.51490e23 4.93251e23i −0.454684 0.638064i
\(328\) 3.27455e23 + 2.99611e23i 0.411481 + 0.376492i
\(329\) 5.07904e23i 0.620041i
\(330\) −4.36330e23 6.66035e22i −0.517527 0.0789977i
\(331\) 8.00528e23i 0.922594i 0.887246 + 0.461297i \(0.152616\pi\)
−0.887246 + 0.461297i \(0.847384\pi\)
\(332\) 3.08876e22 + 1.04379e24i 0.0345917 + 1.16897i
\(333\) −3.66879e23 + 1.06231e24i −0.399303 + 1.15620i
\(334\) 5.90398e23 + 5.73186e23i 0.624530 + 0.606323i
\(335\) 4.20982e23 0.432850
\(336\) 1.25915e24 1.01468e24i 1.25850 1.01416i
\(337\) 1.11071e24 1.07924 0.539618 0.841910i \(-0.318569\pi\)
0.539618 + 0.841910i \(0.318569\pi\)
\(338\) 3.37553e23 + 3.27712e23i 0.318885 + 0.309588i
\(339\) 1.76850e23 1.26023e23i 0.162445 0.115758i
\(340\) 4.09841e21 + 1.38499e23i 0.00366071 + 0.123708i
\(341\) 6.52250e23i 0.566562i
\(342\) −8.58375e23 1.69968e24i −0.725152 1.43589i
\(343\) 1.20449e24i 0.989714i
\(344\) −9.89625e22 9.05475e22i −0.0790980 0.0723721i
\(345\) 3.48765e23 2.48529e23i 0.271176 0.193240i
\(346\) −1.21500e24 + 1.25149e24i −0.919080 + 0.946679i
\(347\) 6.08564e23 0.447895 0.223948 0.974601i \(-0.428106\pi\)
0.223948 + 0.974601i \(0.428106\pi\)
\(348\) −1.79558e23 2.36829e23i −0.128589 0.169602i
\(349\) 1.87965e24 1.30989 0.654945 0.755677i \(-0.272692\pi\)
0.654945 + 0.755677i \(0.272692\pi\)
\(350\) −1.50264e24 + 1.54776e24i −1.01908 + 1.04968i
\(351\) −1.08317e24 + 3.19221e23i −0.714953 + 0.210704i
\(352\) −2.00423e24 1.72772e24i −1.28763 1.10999i
\(353\) 1.85234e24i 1.15841i −0.815182 0.579205i \(-0.803363\pi\)
0.815182 0.579205i \(-0.196637\pi\)
\(354\) 5.33833e21 3.49723e22i 0.00324993 0.0212908i
\(355\) 6.44424e23i 0.381946i
\(356\) 1.29822e24 3.84165e22i 0.749160 0.0221688i
\(357\) −6.70877e23 9.41452e23i −0.376960 0.528993i
\(358\) 2.45006e24 + 2.37864e24i 1.34057 + 1.30148i
\(359\) 1.68585e23 0.0898299 0.0449149 0.998991i \(-0.485698\pi\)
0.0449149 + 0.998991i \(0.485698\pi\)
\(360\) 5.21549e23 2.83057e23i 0.270659 0.146892i
\(361\) −3.14097e24 −1.58762
\(362\) 4.88027e23 + 4.73799e23i 0.240277 + 0.233272i
\(363\) −2.28698e24 3.20935e24i −1.09686 1.53923i
\(364\) −2.57722e24 + 7.62641e22i −1.20417 + 0.0356334i
\(365\) 4.99472e23i 0.227368i
\(366\) 5.09364e22 3.33693e23i 0.0225922 0.148005i
\(367\) 2.15406e24i 0.930957i −0.885059 0.465478i \(-0.845882\pi\)
0.885059 0.465478i \(-0.154118\pi\)
\(368\) 2.56292e24 1.51815e23i 1.07940 0.0639382i
\(369\) −1.28442e24 4.43585e23i −0.527177 0.182065i
\(370\) −6.55937e23 + 6.75634e23i −0.262389 + 0.270268i
\(371\) −1.65550e24 −0.645470
\(372\) 5.29792e23 + 6.98770e23i 0.201348 + 0.265568i
\(373\) −3.67912e23 −0.136304 −0.0681522 0.997675i \(-0.521710\pi\)
−0.0681522 + 0.997675i \(0.521710\pi\)
\(374\) −1.31767e24 + 1.35723e24i −0.475910 + 0.490201i
\(375\) −1.35687e24 + 9.66906e23i −0.477796 + 0.340476i
\(376\) 7.54261e23 8.24357e23i 0.258963 0.283029i
\(377\) 4.73865e23i 0.158640i
\(378\) −2.30383e24 + 4.38225e24i −0.752104 + 1.43062i
\(379\) 7.64858e23i 0.243505i 0.992560 + 0.121753i \(0.0388514\pi\)
−0.992560 + 0.121753i \(0.961149\pi\)
\(380\) −4.71904e22 1.59472e24i −0.0146524 0.495154i
\(381\) 2.75781e24 1.96521e24i 0.835173 0.595143i
\(382\) 1.18963e24 + 1.15495e24i 0.351407 + 0.341162i
\(383\) 1.08282e24 0.312011 0.156005 0.987756i \(-0.450138\pi\)
0.156005 + 0.987756i \(0.450138\pi\)
\(384\) 3.55052e24 + 2.23004e23i 0.998033 + 0.0626854i
\(385\) 3.08551e24 0.846154
\(386\) −1.66898e24 1.62032e24i −0.446551 0.433532i
\(387\) 3.88174e23 + 1.34059e23i 0.101338 + 0.0349979i
\(388\) −7.90007e22 2.66970e24i −0.0201247 0.680082i
\(389\) 6.22083e24i 1.54642i −0.634151 0.773210i \(-0.718650\pi\)
0.634151 0.773210i \(-0.281350\pi\)
\(390\) −9.35311e23 1.42770e23i −0.226904 0.0346357i
\(391\) 1.83539e24i 0.434559i
\(392\) −4.70985e24 + 5.14755e24i −1.08840 + 1.18955i
\(393\) 2.51776e24 + 3.53321e24i 0.567917 + 0.796967i
\(394\) 1.96053e24 2.01940e24i 0.431677 0.444640i
\(395\) 7.46051e23 0.160360
\(396\) 7.73242e24 + 2.41694e24i 1.62260 + 0.507180i
\(397\) 5.85498e23 0.119954 0.0599771 0.998200i \(-0.480897\pi\)
0.0599771 + 0.998200i \(0.480897\pi\)
\(398\) 4.02810e24 4.14906e24i 0.805770 0.829967i
\(399\) 7.72469e24 + 1.08402e25i 1.50882 + 2.11736i
\(400\) −4.73738e24 + 2.80619e23i −0.903583 + 0.0535238i
\(401\) 9.89454e24i 1.84299i 0.388385 + 0.921497i \(0.373033\pi\)
−0.388385 + 0.921497i \(0.626967\pi\)
\(402\) −7.63841e24 1.16596e24i −1.38949 0.212098i
\(403\) 1.39815e24i 0.248403i
\(404\) 6.48209e24 1.91816e23i 1.12484 0.0332859i
\(405\) −1.12116e24 + 1.42958e24i −0.190040 + 0.242318i
\(406\) 1.49065e24 + 1.44719e24i 0.246819 + 0.239623i
\(407\) −1.28558e25 −2.07947
\(408\) 3.09228e23 2.52431e24i 0.0488660 0.398907i
\(409\) 5.98828e24 0.924551 0.462276 0.886736i \(-0.347033\pi\)
0.462276 + 0.886736i \(0.347033\pi\)
\(410\) −8.16895e23 7.93079e23i −0.123231 0.119638i
\(411\) 5.60364e24 3.99314e24i 0.825986 0.588597i
\(412\) −2.98829e23 + 8.84283e21i −0.0430427 + 0.00127370i
\(413\) 2.47306e23i 0.0348104i
\(414\) −7.01642e24 + 3.54343e24i −0.965189 + 0.487440i
\(415\) 2.67874e24i 0.360142i
\(416\) −4.29623e24 3.70351e24i −0.564548 0.486662i
\(417\) −5.54031e24 + 3.94801e24i −0.711609 + 0.507091i
\(418\) 1.51720e25 1.56276e25i 1.90488 1.96209i
\(419\) 1.45705e25 1.78830 0.894152 0.447764i \(-0.147780\pi\)
0.894152 + 0.447764i \(0.147780\pi\)
\(420\) −3.30557e24 + 2.50621e24i −0.396624 + 0.300711i
\(421\) −1.57623e25 −1.84901 −0.924505 0.381171i \(-0.875521\pi\)
−0.924505 + 0.381171i \(0.875521\pi\)
\(422\) −1.45977e24 + 1.50361e24i −0.167423 + 0.172451i
\(423\) −1.11671e24 + 3.23349e24i −0.125230 + 0.362608i
\(424\) −2.68697e24 2.45849e24i −0.294637 0.269583i
\(425\) 3.39258e24i 0.363777i
\(426\) −1.78481e24 + 1.16926e25i −0.187155 + 1.22608i
\(427\) 2.35971e24i 0.241988i
\(428\) −5.24521e23 1.77253e25i −0.0526074 1.77778i
\(429\) −7.49608e24 1.05194e25i −0.735343 1.03192i
\(430\) 2.46880e23 + 2.39682e23i 0.0236884 + 0.0229978i
\(431\) −9.19244e24 −0.862774 −0.431387 0.902167i \(-0.641976\pi\)
−0.431387 + 0.902167i \(0.641976\pi\)
\(432\) −1.02471e25 + 3.69136e24i −0.940817 + 0.338915i
\(433\) −3.24019e24 −0.291028 −0.145514 0.989356i \(-0.546484\pi\)
−0.145514 + 0.989356i \(0.546484\pi\)
\(434\) −4.39821e24 4.26999e24i −0.386477 0.375210i
\(435\) 4.42436e23 + 6.20877e23i 0.0380367 + 0.0533775i
\(436\) 2.75509e23 + 9.31038e24i 0.0231747 + 0.783152i
\(437\) 2.11332e25i 1.73937i
\(438\) 1.38335e24 9.06256e24i 0.111411 0.729872i
\(439\) 7.31359e24i 0.576391i 0.957572 + 0.288196i \(0.0930553\pi\)
−0.957572 + 0.288196i \(0.906945\pi\)
\(440\) 5.00795e24 + 4.58212e24i 0.386242 + 0.353400i
\(441\) 6.97311e24 2.01909e25i 0.526332 1.52402i
\(442\) −2.82453e24 + 2.90935e24i −0.208658 + 0.214924i
\(443\) 3.64224e24 0.263350 0.131675 0.991293i \(-0.457964\pi\)
0.131675 + 0.991293i \(0.457964\pi\)
\(444\) 1.37728e25 1.04422e25i 0.974726 0.739015i
\(445\) −3.33170e24 −0.230805
\(446\) 1.67254e25 1.72276e25i 1.13421 1.16827i
\(447\) 8.77257e24 6.25132e24i 0.582379 0.415002i
\(448\) −2.47710e25 + 2.20419e24i −1.60991 + 0.143254i
\(449\) 1.81510e24i 0.115494i −0.998331 0.0577471i \(-0.981608\pi\)
0.998331 0.0577471i \(-0.0183917\pi\)
\(450\) 1.29693e25 6.54978e24i 0.807977 0.408045i
\(451\) 1.55437e25i 0.948151i
\(452\) −3.33813e24 + 9.87807e22i −0.199383 + 0.00590006i
\(453\) 6.84292e24 4.87625e24i 0.400229 0.285202i
\(454\) 6.46605e23 + 6.27754e23i 0.0370347 + 0.0359549i
\(455\) 6.61405e24 0.370987
\(456\) −3.56055e24 + 2.90658e25i −0.195592 + 1.59667i
\(457\) 3.30144e24 0.177623 0.0888117 0.996048i \(-0.471693\pi\)
0.0888117 + 0.996048i \(0.471693\pi\)
\(458\) 2.21710e25 + 2.15247e25i 1.16833 + 1.13427i
\(459\) 2.20109e24 + 7.46863e24i 0.113610 + 0.385497i
\(460\) −6.58313e24 + 1.94805e23i −0.332838 + 0.00984921i
\(461\) 5.99006e24i 0.296669i −0.988937 0.148335i \(-0.952609\pi\)
0.988937 0.148335i \(-0.0473913\pi\)
\(462\) −5.59842e25 8.54570e24i −2.71623 0.414619i
\(463\) 3.87598e25i 1.84231i 0.389198 + 0.921154i \(0.372752\pi\)
−0.389198 + 0.921154i \(0.627248\pi\)
\(464\) 2.70264e23 + 4.56256e24i 0.0125854 + 0.212465i
\(465\) −1.30542e24 1.83192e24i −0.0595591 0.0835802i
\(466\) 8.47492e24 8.72941e24i 0.378852 0.390228i
\(467\) −3.39957e25 −1.48907 −0.744533 0.667586i \(-0.767328\pi\)
−0.744533 + 0.667586i \(0.767328\pi\)
\(468\) 1.65751e25 + 5.18093e24i 0.711412 + 0.222368i
\(469\) 5.40150e25 2.27181
\(470\) −1.99655e24 + 2.05651e24i −0.0822908 + 0.0847619i
\(471\) −1.73611e25 2.43630e25i −0.701258 0.984086i
\(472\) −3.67261e23 + 4.01392e23i −0.0145387 + 0.0158899i
\(473\) 4.69758e24i 0.182261i
\(474\) −1.35365e25 2.06628e24i −0.514770 0.0785770i
\(475\) 3.90632e25i 1.45606i
\(476\) 5.25855e23 + 1.77704e25i 0.0192132 + 0.649279i
\(477\) 1.05394e25 + 3.63989e24i 0.377479 + 0.130366i
\(478\) 3.73073e25 + 3.62197e25i 1.30987 + 1.27169i
\(479\) −5.21744e25 −1.79585 −0.897925 0.440149i \(-0.854926\pi\)
−0.897925 + 0.440149i \(0.854926\pi\)
\(480\) −9.08698e24 8.41205e23i −0.306639 0.0283864i
\(481\) −2.75576e25 −0.911723
\(482\) 1.67068e25 + 1.62197e25i 0.541934 + 0.526135i
\(483\) 4.47490e25 3.18881e25i 1.42327 1.01422i
\(484\) 1.79261e24 + 6.05783e25i 0.0559055 + 1.88923i
\(485\) 6.85139e24i 0.209523i
\(486\) 2.43020e25 2.28335e25i 0.728783 0.684745i
\(487\) 3.79996e25i 1.11752i 0.829331 + 0.558758i \(0.188722\pi\)
−0.829331 + 0.558758i \(0.811278\pi\)
\(488\) −3.50427e24 + 3.82994e24i −0.101067 + 0.110460i
\(489\) −6.93396e24 + 4.94113e24i −0.196131 + 0.139763i
\(490\) 1.24671e25 1.28415e25i 0.345862 0.356248i
\(491\) 6.00488e24 0.163392 0.0816959 0.996657i \(-0.473966\pi\)
0.0816959 + 0.996657i \(0.473966\pi\)
\(492\) 1.26254e25 + 1.66523e25i 0.336960 + 0.444434i
\(493\) 3.26739e24 0.0855372
\(494\) 3.25225e25 3.34992e25i 0.835177 0.860257i
\(495\) −1.96434e25 6.78400e24i −0.494842 0.170898i
\(496\) −7.97422e23 1.34620e25i −0.0197066 0.332685i
\(497\) 8.26842e25i 2.00464i
\(498\) −7.41912e24 + 4.86038e25i −0.176471 + 1.15609i
\(499\) 3.97513e25i 0.927675i −0.885920 0.463838i \(-0.846472\pi\)
0.885920 0.463838i \(-0.153528\pi\)
\(500\) 2.56117e25 7.57892e23i 0.586440 0.0173537i
\(501\) 2.24838e25 + 3.15519e25i 0.505141 + 0.708871i
\(502\) −3.64681e25 3.54049e25i −0.803948 0.780510i
\(503\) 5.75320e25 1.24455 0.622277 0.782797i \(-0.286208\pi\)
0.622277 + 0.782797i \(0.286208\pi\)
\(504\) 6.69185e25 3.63182e25i 1.42055 0.770964i
\(505\) −1.66353e25 −0.346548
\(506\) −6.45120e25 6.26312e25i −1.31890 1.28044i
\(507\) 1.28549e25 + 1.80394e25i 0.257924 + 0.361949i
\(508\) −5.20550e25 + 1.54039e24i −1.02508 + 0.0303337i
\(509\) 2.80394e25i 0.541938i 0.962588 + 0.270969i \(0.0873440\pi\)
−0.962588 + 0.270969i \(0.912656\pi\)
\(510\) −9.84428e23 + 6.44914e24i −0.0186753 + 0.122345i
\(511\) 6.40858e25i 1.19334i
\(512\) −4.34781e25 3.32086e25i −0.794705 0.606996i
\(513\) −2.53440e25 8.59962e25i −0.454737 1.54299i
\(514\) −3.29520e25 + 3.39415e25i −0.580406 + 0.597835i
\(515\) 7.66900e23 0.0132608
\(516\) −3.81562e24 5.03262e24i −0.0647729 0.0854324i
\(517\) −3.91308e25 −0.652167
\(518\) −8.41614e25 + 8.66887e25i −1.37715 + 1.41850i
\(519\) −6.68816e25 + 4.76597e25i −1.07453 + 0.765705i
\(520\) 1.07350e25 + 9.82217e24i 0.169344 + 0.154944i
\(521\) 6.80286e25i 1.05374i 0.849946 + 0.526870i \(0.176635\pi\)
−0.849946 + 0.526870i \(0.823365\pi\)
\(522\) −6.30808e24 1.24908e25i −0.0959462 0.189985i
\(523\) 4.08897e25i 0.610728i −0.952236 0.305364i \(-0.901222\pi\)
0.952236 0.305364i \(-0.0987781\pi\)
\(524\) −1.97350e24 6.66912e25i −0.0289461 0.978186i
\(525\) −8.27153e25 + 5.89428e25i −1.19144 + 0.849018i
\(526\) 1.95398e25 + 1.89701e25i 0.276411 + 0.268353i
\(527\) −9.64053e24 −0.133937
\(528\) −7.81749e25 9.70094e25i −1.06671 1.32371i
\(529\) 1.26240e25 0.169188
\(530\) 6.70312e24 + 6.50770e24i 0.0882382 + 0.0856657i
\(531\) 5.43744e23 1.57443e24i 0.00703066 0.0203576i
\(532\) −6.05486e24 2.04614e26i −0.0769030 2.59881i
\(533\) 3.33193e25i 0.415707i
\(534\) 6.04512e25 + 9.22755e24i 0.740906 + 0.113095i
\(535\) 4.54894e25i 0.547708i
\(536\) 8.76694e25 + 8.02148e25i 1.03701 + 0.948831i
\(537\) 9.33046e25 + 1.30936e26i 1.08429 + 1.52161i
\(538\) 1.00860e26 1.03889e26i 1.15156 1.18615i
\(539\) 2.44345e26 2.74101
\(540\) 2.65547e25 8.68752e24i 0.292685 0.0957536i
\(541\) −5.32934e25 −0.577164 −0.288582 0.957455i \(-0.593184\pi\)
−0.288582 + 0.957455i \(0.593184\pi\)
\(542\) −5.33188e25 + 5.49199e25i −0.567397 + 0.584435i
\(543\) 1.85853e25 + 2.60810e25i 0.194344 + 0.272726i
\(544\) −2.55364e25 + 2.96233e25i −0.262404 + 0.304400i
\(545\) 2.38937e25i 0.241277i
\(546\) −1.20007e26 1.83184e25i −1.19090 0.181785i
\(547\) 5.95545e25i 0.580811i −0.956904 0.290406i \(-0.906210\pi\)
0.956904 0.290406i \(-0.0937902\pi\)
\(548\) −1.05772e26 + 3.12995e24i −1.01380 + 0.0300001i
\(549\) 5.18821e24 1.50227e25i 0.0488743 0.141517i
\(550\) 1.19246e26 + 1.15769e26i 1.10407 + 1.07188i
\(551\) −3.76217e25 −0.342372
\(552\) 1.19986e26 + 1.46982e25i 1.07327 + 0.131475i
\(553\) 9.57236e25 0.841648
\(554\) 2.71835e25 + 2.63910e25i 0.234943 + 0.228093i
\(555\) −3.61071e25 + 2.57299e25i −0.306767 + 0.218602i
\(556\) 1.04576e26 3.09458e24i 0.873419 0.0258459i
\(557\) 6.57624e24i 0.0539950i 0.999636 + 0.0269975i \(0.00859461\pi\)
−0.999636 + 0.0269975i \(0.991405\pi\)
\(558\) 1.86122e25 + 3.68544e25i 0.150236 + 0.297484i
\(559\) 1.00697e25i 0.0799103i
\(560\) 6.36827e25 3.77225e24i 0.496861 0.0294316i
\(561\) −7.25330e25 + 5.16869e25i −0.556402 + 0.396491i
\(562\) −1.24188e26 + 1.27917e26i −0.936663 + 0.964790i
\(563\) 2.08374e25 0.154531 0.0772653 0.997011i \(-0.475381\pi\)
0.0772653 + 0.997011i \(0.475381\pi\)
\(564\) 4.19218e25 3.17841e25i 0.305695 0.231771i
\(565\) 8.56681e24 0.0614270
\(566\) −1.07494e24 + 1.10722e24i −0.00757928 + 0.00780688i
\(567\) −1.43853e26 + 1.83426e26i −0.997423 + 1.27181i
\(568\) 1.22790e26 1.34201e26i 0.837247 0.915055i
\(569\) 9.60683e25i 0.644189i 0.946707 + 0.322095i \(0.104387\pi\)
−0.946707 + 0.322095i \(0.895613\pi\)
\(570\) 1.13350e25 7.42575e25i 0.0747499 0.489699i
\(571\) 2.92701e26i 1.89837i −0.314714 0.949187i \(-0.601909\pi\)
0.314714 0.949187i \(-0.398091\pi\)
\(572\) 5.87567e24 + 1.98559e26i 0.0374796 + 1.26656i
\(573\) 4.53041e25 + 6.35760e25i 0.284229 + 0.398863i
\(574\) −1.04813e26 1.01758e26i −0.646776 0.627920i
\(575\) −1.61256e26 −0.978747
\(576\) 1.62547e26 + 4.04306e25i 0.970431 + 0.241377i
\(577\) −2.35505e25 −0.138302 −0.0691512 0.997606i \(-0.522029\pi\)
−0.0691512 + 0.997606i \(0.522029\pi\)
\(578\) −1.04142e26 1.01106e26i −0.601603 0.584064i
\(579\) −6.35589e25 8.91931e25i −0.361185 0.506857i
\(580\) −3.46796e23 1.17194e25i −0.00193869 0.0655148i
\(581\) 3.43702e26i 1.89020i
\(582\) 1.89758e25 1.24313e26i 0.102667 0.672589i
\(583\) 1.27546e26i 0.678914i
\(584\) −9.51705e25 + 1.04015e26i −0.498403 + 0.544721i
\(585\) −4.21072e25 1.45421e25i −0.216958 0.0749283i
\(586\) −1.54542e26 + 1.59182e26i −0.783462 + 0.806989i
\(587\) 2.73283e26 1.36317 0.681586 0.731738i \(-0.261290\pi\)
0.681586 + 0.731738i \(0.261290\pi\)
\(588\) −2.61773e26 + 1.98470e26i −1.28481 + 0.974117i
\(589\) 1.11004e26 0.536098
\(590\) 9.72152e23 1.00135e24i 0.00461998 0.00475871i
\(591\) 1.07920e26 7.69039e25i 0.504688 0.359640i
\(592\) −2.65336e26 + 1.57172e25i −1.22107 + 0.0723300i
\(593\) 1.58679e26i 0.718621i −0.933218 0.359310i \(-0.883012\pi\)
0.933218 0.359310i \(-0.116988\pi\)
\(594\) 3.37625e26 + 1.77496e26i 1.50475 + 0.791072i
\(595\) 4.56051e25i 0.200033i
\(596\) −1.65587e26 + 4.89999e24i −0.714804 + 0.0211522i
\(597\) 2.21733e26 1.58007e26i 0.942051 0.671304i
\(598\) −1.38287e26 1.34255e26i −0.578256 0.561398i
\(599\) −1.42414e26 −0.586137 −0.293069 0.956091i \(-0.594676\pi\)
−0.293069 + 0.956091i \(0.594676\pi\)
\(600\) −2.21784e26 2.71685e25i −0.898451 0.110060i
\(601\) −1.27474e26 −0.508293 −0.254146 0.967166i \(-0.581794\pi\)
−0.254146 + 0.967166i \(0.581794\pi\)
\(602\) 3.16764e25 + 3.07529e25i 0.124328 + 0.120704i
\(603\) −3.43877e26 1.18761e26i −1.32858 0.458838i
\(604\) −1.29164e26 + 3.82216e24i −0.491235 + 0.0145364i
\(605\) 1.55465e26i 0.582045i
\(606\) 3.01836e26 + 4.60736e25i 1.11245 + 0.169810i
\(607\) 3.23276e26i 1.17296i 0.809965 + 0.586478i \(0.199486\pi\)
−0.809965 + 0.586478i \(0.800514\pi\)
\(608\) 2.94034e26 3.41092e26i 1.05030 1.21839i
\(609\) 5.67677e25 + 7.96630e25i 0.199635 + 0.280151i
\(610\) 9.27593e24 9.55448e24i 0.0321162 0.0330806i
\(611\) −8.38803e25 −0.285936
\(612\) 3.57234e25 1.14289e26i 0.119899 0.383587i
\(613\) −1.95279e26 −0.645328 −0.322664 0.946514i \(-0.604578\pi\)
−0.322664 + 0.946514i \(0.604578\pi\)
\(614\) −2.95711e25 + 3.04591e25i −0.0962205 + 0.0991100i
\(615\) −3.11094e25 4.36563e25i −0.0996732 0.139873i
\(616\) 6.42556e26 + 5.87919e26i 2.02719 + 1.85481i
\(617\) 1.53509e26i 0.476898i −0.971155 0.238449i \(-0.923361\pi\)
0.971155 0.238449i \(-0.0766389\pi\)
\(618\) −1.39148e25 2.12403e24i −0.0425685 0.00649785i
\(619\) 9.80949e25i 0.295519i −0.989023 0.147759i \(-0.952794\pi\)
0.989023 0.147759i \(-0.0472061\pi\)
\(620\) 1.02323e24 + 3.45785e25i 0.00303566 + 0.102585i
\(621\) −3.54999e26 + 1.04622e26i −1.03719 + 0.305670i
\(622\) −1.47792e26 1.43483e26i −0.425247 0.412850i
\(623\) −4.27480e26 −1.21138
\(624\) −1.67575e26 2.07948e26i −0.467687 0.580365i
\(625\) 2.63569e26 0.724493
\(626\) 3.08562e26 + 2.99567e26i 0.835385 + 0.811031i
\(627\) 8.35168e26 5.95139e26i 2.22706 1.58700i
\(628\) 1.36082e25 + 4.59866e26i 0.0357423 + 1.20785i
\(629\) 1.90015e26i 0.491594i
\(630\) −1.74342e26 + 8.80461e25i −0.444290 + 0.224375i
\(631\) 1.66032e26i 0.416787i −0.978045 0.208393i \(-0.933177\pi\)
0.978045 0.208393i \(-0.0668235\pi\)
\(632\) 1.55365e26 + 1.42154e26i 0.384185 + 0.351518i
\(633\) −8.03553e25 + 5.72611e25i −0.195740 + 0.139484i
\(634\) 2.85586e26 2.94162e26i 0.685313 0.705893i
\(635\) 1.33591e26 0.315812
\(636\) −1.03599e26 1.36643e26i −0.241276 0.318232i
\(637\) 5.23776e26 1.20177
\(638\) 1.11497e26 1.14845e26i 0.252039 0.259607i
\(639\) −1.81795e26 + 5.26395e26i −0.404878 + 1.17234i
\(640\) 1.08963e26 + 8.84492e25i 0.239094 + 0.194082i
\(641\) 5.49273e26i 1.18751i 0.804647 + 0.593754i \(0.202355\pi\)
−0.804647 + 0.593754i \(0.797645\pi\)
\(642\) 1.25989e26 8.25372e26i 0.268379 1.75820i
\(643\) 5.99085e26i 1.25743i 0.777635 + 0.628716i \(0.216419\pi\)
−0.777635 + 0.628716i \(0.783581\pi\)
\(644\) −8.44662e26 + 2.49949e25i −1.74690 + 0.0516935i
\(645\) 9.40180e24 + 1.31937e25i 0.0191599 + 0.0268874i
\(646\) −2.30983e26 2.24249e26i −0.463843 0.450320i
\(647\) 1.22727e26 0.242855 0.121428 0.992600i \(-0.461253\pi\)
0.121428 + 0.992600i \(0.461253\pi\)
\(648\) −5.05877e26 + 8.40821e25i −0.986467 + 0.163961i
\(649\) 1.90534e25 0.0366140
\(650\) 2.55613e26 + 2.48161e26i 0.484068 + 0.469956i
\(651\) −1.67495e26 2.35048e26i −0.312595 0.438670i
\(652\) 1.30882e26 3.87301e24i 0.240729 0.00712355i
\(653\) 9.31026e26i 1.68767i 0.536606 + 0.843833i \(0.319706\pi\)
−0.536606 + 0.843833i \(0.680294\pi\)
\(654\) −6.61766e25 + 4.33534e26i −0.118227 + 0.774523i
\(655\) 1.71153e26i 0.301365i
\(656\) −1.90033e25 3.20812e26i −0.0329794 0.556754i
\(657\) 1.40903e26 4.07992e26i 0.241019 0.697880i
\(658\) −2.56172e26 + 2.63865e26i −0.431902 + 0.444872i
\(659\) 6.06156e26 1.00733 0.503666 0.863898i \(-0.331984\pi\)
0.503666 + 0.863898i \(0.331984\pi\)
\(660\) 1.93088e26 + 2.54674e26i 0.316292 + 0.417174i
\(661\) −1.19806e27 −1.93448 −0.967239 0.253869i \(-0.918297\pi\)
−0.967239 + 0.253869i \(0.918297\pi\)
\(662\) 4.03763e26 4.15888e26i 0.642652 0.661951i
\(663\) −1.55481e26 + 1.10795e26i −0.243948 + 0.173837i
\(664\) 5.10413e26 5.57848e26i 0.789451 0.862818i
\(665\) 5.25111e26i 0.800656i
\(666\) 7.26399e26 3.66846e26i 1.09187 0.551416i
\(667\) 1.55305e26i 0.230139i
\(668\) −1.76236e25 5.95559e26i −0.0257464 0.870059i
\(669\) 9.20675e26 6.56072e26i 1.32605 0.944938i
\(670\) −2.18707e26 2.12331e26i −0.310565 0.301511i
\(671\) 1.81801e26 0.254526
\(672\) −1.16592e27 1.07933e26i −1.60939 0.148986i
\(673\) −2.91934e26 −0.397321 −0.198661 0.980068i \(-0.563659\pi\)
−0.198661 + 0.980068i \(0.563659\pi\)
\(674\) −5.77032e26 5.60209e26i −0.774339 0.751764i
\(675\) 6.56189e26 1.93386e26i 0.868246 0.255882i
\(676\) −1.00761e25 3.40504e26i −0.0131461 0.444251i
\(677\) 4.63404e26i 0.596166i −0.954540 0.298083i \(-0.903653\pi\)
0.954540 0.298083i \(-0.0963473\pi\)
\(678\) −1.55439e26 2.37269e25i −0.197186 0.0300994i
\(679\) 8.79082e26i 1.09968i
\(680\) 6.77257e25 7.40197e25i 0.0835447 0.0913088i
\(681\) 2.46243e25 + 3.45557e25i 0.0299548 + 0.0420361i
\(682\) −3.28976e26 + 3.38855e26i −0.394650 + 0.406501i
\(683\) −5.52297e26 −0.653396 −0.326698 0.945129i \(-0.605936\pi\)
−0.326698 + 0.945129i \(0.605936\pi\)
\(684\) −4.11331e26 + 1.31595e27i −0.479909 + 1.53535i
\(685\) 2.71447e26 0.312338
\(686\) 6.07511e26 6.25754e26i 0.689406 0.710108i
\(687\) 8.44329e26 + 1.18486e27i 0.944980 + 1.32611i
\(688\) 5.74312e24 + 9.69548e25i 0.00633954 + 0.107023i
\(689\) 2.73405e26i 0.297663i
\(690\) −3.06540e26 4.67918e25i −0.329171 0.0502462i
\(691\) 1.21837e27i 1.29044i −0.763997 0.645219i \(-0.776766\pi\)
0.763997 0.645219i \(-0.223234\pi\)
\(692\) 1.26243e27 3.73572e25i 1.31886 0.0390271i
\(693\) −2.52038e27 8.70435e26i −2.59717 0.896955i
\(694\) −3.16159e26 3.06942e26i −0.321359 0.311991i
\(695\) −2.68379e26 −0.269088
\(696\) −2.61660e25 + 2.13600e26i −0.0258791 + 0.211259i
\(697\) −2.29743e26 −0.224146
\(698\) −9.76509e26 9.48040e26i −0.939831 0.912431i
\(699\) 4.66515e26 3.32438e26i 0.442928 0.315629i
\(700\) 1.56129e27 4.62012e25i 1.46236 0.0432735i
\(701\) 2.66734e25i 0.0246467i 0.999924 + 0.0123233i \(0.00392274\pi\)
−0.999924 + 0.0123233i \(0.996077\pi\)
\(702\) 7.23729e26 + 3.80477e26i 0.659741 + 0.346837i
\(703\) 2.18789e27i 1.96766i
\(704\) 1.69819e26 + 1.90845e27i 0.150677 + 1.69333i
\(705\) −1.09903e26 + 7.83170e25i −0.0962088 + 0.0685582i
\(706\) −9.34269e26 + 9.62324e26i −0.806914 + 0.831145i
\(707\) −2.13443e27 −1.81885
\(708\) −2.04123e25 + 1.54762e25i −0.0171624 + 0.0130121i
\(709\) 1.00195e27 0.831205 0.415603 0.909546i \(-0.363571\pi\)
0.415603 + 0.909546i \(0.363571\pi\)
\(710\) −3.25029e26 + 3.34789e26i −0.266053 + 0.274042i
\(711\) −6.09408e26 2.10464e26i −0.492206 0.169988i
\(712\) −6.93825e26 6.34828e26i −0.552955 0.505937i
\(713\) 4.58233e26i 0.360359i
\(714\) −1.26309e26 + 8.27471e26i −0.0980170 + 0.642125i
\(715\) 5.09571e26i 0.390209i
\(716\) −7.31351e25 2.47148e27i −0.0552653 1.86760i
\(717\) 1.42076e27 + 1.99377e27i 1.05947 + 1.48677i
\(718\) −8.75826e25 8.50292e25i −0.0644519 0.0625728i
\(719\) −1.66018e27 −1.20567 −0.602837 0.797865i \(-0.705963\pi\)
−0.602837 + 0.797865i \(0.705963\pi\)
\(720\) −4.13719e26 1.16002e26i −0.296515 0.0831392i
\(721\) 9.83988e25 0.0695993
\(722\) 1.63179e27 + 1.58422e27i 1.13910 + 1.10589i
\(723\) 6.36237e26 + 8.92841e26i 0.438334 + 0.615121i
\(724\) −1.45677e25 4.92293e26i −0.00990549 0.334740i
\(725\) 2.87070e26i 0.192654i
\(726\) −4.30580e26 + 2.82080e27i −0.285204 + 1.86842i
\(727\) 1.15179e27i 0.753001i 0.926416 + 0.376500i \(0.122873\pi\)
−0.926416 + 0.376500i \(0.877127\pi\)
\(728\) 1.37737e27 + 1.26025e27i 0.888800 + 0.813224i
\(729\) 1.31911e27 8.51464e26i 0.840173 0.542319i
\(730\) 2.51919e26 2.59484e26i 0.158378 0.163134i
\(731\) 6.94322e25 0.0430870
\(732\) −1.94767e26 + 1.47668e26i −0.119306 + 0.0904548i
\(733\) 1.45278e27 0.878441 0.439220 0.898379i \(-0.355255\pi\)
0.439220 + 0.898379i \(0.355255\pi\)
\(734\) −1.08644e27 + 1.11907e27i −0.648477 + 0.667950i
\(735\) 6.86272e26 4.89037e26i 0.404359 0.288145i
\(736\) −1.40805e27 1.21379e27i −0.818993 0.706002i
\(737\) 4.16152e27i 2.38952i
\(738\) 4.43546e26 + 8.78274e26i 0.251422 + 0.497845i
\(739\) 5.34107e25i 0.0298887i 0.999888 + 0.0149443i \(0.00475710\pi\)
−0.999888 + 0.0149443i \(0.995243\pi\)
\(740\) 6.81541e26 2.01679e25i 0.376522 0.0111419i
\(741\) 1.79025e27 1.27573e27i 0.976432 0.695804i
\(742\) 8.60058e26 + 8.34984e26i 0.463117 + 0.449616i
\(743\) 2.17557e27 1.15659 0.578294 0.815828i \(-0.303719\pi\)
0.578294 + 0.815828i \(0.303719\pi\)
\(744\) 7.72036e25 6.30235e26i 0.0405224 0.330795i
\(745\) 4.24954e26 0.220220
\(746\) 1.91137e26 + 1.85564e26i 0.0977969 + 0.0949457i
\(747\) −7.55686e26 + 2.18812e27i −0.381765 + 1.10542i
\(748\) 1.36910e27 4.05138e25i 0.682920 0.0202087i
\(749\) 5.83662e27i 2.87464i
\(750\) 1.19260e27 + 1.82044e26i 0.579979 + 0.0885307i
\(751\) 4.88121e26i 0.234395i 0.993109 + 0.117197i \(0.0373910\pi\)
−0.993109 + 0.117197i \(0.962609\pi\)
\(752\) −8.07633e26 + 4.78402e25i −0.382952 + 0.0226842i
\(753\) −1.38880e27 1.94892e27i −0.650259 0.912519i
\(754\) 2.39004e26 2.46181e26i 0.110504 0.113822i
\(755\) 3.31479e26 0.151342
\(756\) 3.40716e27 1.11467e27i 1.53616 0.502562i
\(757\) 4.50904e26 0.200758 0.100379 0.994949i \(-0.467994\pi\)
0.100379 + 0.994949i \(0.467994\pi\)
\(758\) 3.85772e26 3.97356e26i 0.169619 0.174712i
\(759\) −2.45678e27 3.44763e27i −1.06677 1.49701i
\(760\) −7.79815e26 + 8.52286e26i −0.334397 + 0.365474i
\(761\) 8.15361e26i 0.345299i 0.984983 + 0.172650i \(0.0552328\pi\)
−0.984983 + 0.172650i \(0.944767\pi\)
\(762\) −2.42392e27 3.69999e26i −1.01379 0.154749i
\(763\) 3.06573e27i