Properties

Label 17.10.d.a.15.13
Level $17$
Weight $10$
Character 17.15
Analytic conductor $8.756$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 15.13
Character \(\chi\) \(=\) 17.15
Dual form 17.10.d.a.8.13

$q$-expansion

\(f(q)\) \(=\) \(q+(28.7156 + 28.7156i) q^{2} +(39.4019 + 95.1246i) q^{3} +1137.17i q^{4} +(710.947 - 294.484i) q^{5} +(-1600.11 + 3863.01i) q^{6} +(-1447.96 - 599.766i) q^{7} +(-17952.2 + 17952.2i) q^{8} +(6421.80 - 6421.80i) q^{9} +O(q^{10})\) \(q+(28.7156 + 28.7156i) q^{2} +(39.4019 + 95.1246i) q^{3} +1137.17i q^{4} +(710.947 - 294.484i) q^{5} +(-1600.11 + 3863.01i) q^{6} +(-1447.96 - 599.766i) q^{7} +(-17952.2 + 17952.2i) q^{8} +(6421.80 - 6421.80i) q^{9} +(28871.6 + 11959.0i) q^{10} +(-6518.10 + 15736.1i) q^{11} +(-108173. + 44806.8i) q^{12} -141996. i q^{13} +(-24356.5 - 58801.9i) q^{14} +(56025.4 + 56025.4i) q^{15} -448786. q^{16} +(-213765. + 269986. i) q^{17} +368812. q^{18} +(525945. + 525945. i) q^{19} +(334879. + 808470. i) q^{20} -161369. i q^{21} +(-639042. + 264700. i) q^{22} +(595280. - 1.43713e6i) q^{23} +(-2.41505e6 - 1.00035e6i) q^{24} +(-962343. + 962343. i) q^{25} +(4.07751e6 - 4.07751e6i) q^{26} +(2.73624e6 + 1.13339e6i) q^{27} +(682038. - 1.64659e6i) q^{28} +(5.30192e6 - 2.19613e6i) q^{29} +3.21761e6i q^{30} +(-1.75648e6 - 4.24052e6i) q^{31} +(-3.69563e6 - 3.69563e6i) q^{32} -1.75371e6 q^{33} +(-1.38912e7 + 1.61441e6i) q^{34} -1.20605e6 q^{35} +(7.30269e6 + 7.30269e6i) q^{36} +(2.09832e6 + 5.06579e6i) q^{37} +3.02057e7i q^{38} +(1.35074e7 - 5.59493e6i) q^{39} +(-7.47645e6 + 1.80497e7i) q^{40} +(-1.67370e7 - 6.93270e6i) q^{41} +(4.63381e6 - 4.63381e6i) q^{42} +(-1.97878e7 + 1.97878e7i) q^{43} +(-1.78946e7 - 7.41221e6i) q^{44} +(2.67444e6 - 6.45667e6i) q^{45} +(5.83620e7 - 2.41743e7i) q^{46} -2.65154e7i q^{47} +(-1.76830e7 - 4.26906e7i) q^{48} +(-2.67974e7 - 2.67974e7i) q^{49} -5.52685e7 q^{50} +(-3.41051e7 - 9.69637e6i) q^{51} +1.61474e8 q^{52} +(-5.36103e7 - 5.36103e7i) q^{53} +(4.60269e7 + 1.11119e8i) q^{54} +1.31070e7i q^{55} +(3.67613e7 - 1.52270e7i) q^{56} +(-2.93071e7 + 7.07536e7i) q^{57} +(2.15311e8 + 8.91848e7i) q^{58} +(-3.36343e7 + 3.36343e7i) q^{59} +(-6.37106e7 + 6.37106e7i) q^{60} +(-1.29622e8 - 5.36913e7i) q^{61} +(7.13307e7 - 1.72207e8i) q^{62} +(-1.31501e7 + 5.44695e6i) q^{63} +1.75339e7i q^{64} +(-4.18157e7 - 1.00952e8i) q^{65} +(-5.03590e7 - 5.03590e7i) q^{66} +7.10319e7 q^{67} +(-3.07021e8 - 2.43088e8i) q^{68} +1.60162e8 q^{69} +(-3.46324e7 - 3.46324e7i) q^{70} +(2.73336e7 + 6.59891e7i) q^{71} +2.30571e8i q^{72} +(3.14349e8 - 1.30208e8i) q^{73} +(-8.52128e7 + 2.05722e8i) q^{74} +(-1.29461e8 - 5.36244e7i) q^{75} +(-5.98091e8 + 5.98091e8i) q^{76} +(1.88759e7 - 1.88759e7i) q^{77} +(5.48534e8 + 2.27210e8i) q^{78} +(1.22779e8 - 2.96415e8i) q^{79} +(-3.19063e8 + 1.32160e8i) q^{80} +1.26185e8i q^{81} +(-2.81537e8 - 6.79690e8i) q^{82} +(2.30965e8 + 2.30965e8i) q^{83} +1.83505e8 q^{84} +(-7.24692e7 + 2.54896e8i) q^{85} -1.13644e9 q^{86} +(4.17812e8 + 4.17812e8i) q^{87} +(-1.65483e8 - 3.99512e8i) q^{88} -2.75879e8i q^{89} +(2.62206e8 - 1.08609e8i) q^{90} +(-8.51646e7 + 2.05606e8i) q^{91} +(1.63427e9 + 6.76936e8i) q^{92} +(3.34169e8 - 3.34169e8i) q^{93} +(7.61407e8 - 7.61407e8i) q^{94} +(5.28802e8 + 2.19037e8i) q^{95} +(2.05931e8 - 4.97161e8i) q^{96} +(-6.15244e8 + 2.54842e8i) q^{97} -1.53901e9i q^{98} +(5.91960e7 + 1.42912e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} + O(q^{10}) \) \( 52q - 4q^{2} - 4q^{3} - 1140q^{5} + 12308q^{6} - 4q^{7} + 2044q^{8} - 83224q^{9} - 117636q^{10} - 115768q^{11} - 145528q^{12} + 463660q^{14} + 288244q^{15} - 3407880q^{16} - 271932q^{17} + 2193336q^{18} - 406700q^{19} + 493564q^{20} + 800964q^{22} - 4172180q^{23} + 15078440q^{24} + 11946576q^{25} - 14209012q^{26} - 7973656q^{27} + 13540804q^{28} + 7833752q^{29} + 5936252q^{31} - 26730116q^{32} - 1635208q^{33} - 53493988q^{34} + 46992776q^{35} - 12761764q^{36} + 74606796q^{37} + 74096776q^{39} - 69317672q^{40} - 71362288q^{41} - 308117664q^{42} - 3765712q^{43} + 163659820q^{44} + 14167408q^{45} + 72135428q^{46} + 164621412q^{48} - 284548508q^{49} + 226223888q^{50} - 406733132q^{51} + 103553016q^{52} - 244724728q^{53} + 971226260q^{54} + 470691652q^{56} - 440646580q^{57} - 308561768q^{58} - 481734984q^{59} + 379626176q^{60} + 507966228q^{61} + 358867236q^{62} + 1070586456q^{63} + 366263684q^{65} - 2244715148q^{66} - 311910088q^{67} - 1839196668q^{68} + 533688136q^{69} + 34867672q^{70} + 186006812q^{71} + 487115192q^{73} - 214149412q^{74} + 533015920q^{75} + 1104236912q^{76} - 237869092q^{77} - 2081523384q^{78} - 136338052q^{79} - 922534152q^{80} + 1951892384q^{82} + 1843663888q^{83} - 2630025952q^{84} - 395061976q^{85} + 1538547296q^{86} - 369395636q^{87} - 3388839640q^{88} + 874363684q^{90} + 2087197720q^{91} + 1061427500q^{92} + 576415420q^{93} + 6899365112q^{94} + 5031766876q^{95} + 490811364q^{96} - 3419996368q^{97} - 5630536112q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 28.7156 + 28.7156i 1.26906 + 1.26906i 0.946573 + 0.322490i \(0.104520\pi\)
0.322490 + 0.946573i \(0.395480\pi\)
\(3\) 39.4019 + 95.1246i 0.280848 + 0.678028i 0.999856 0.0169745i \(-0.00540340\pi\)
−0.719008 + 0.695002i \(0.755403\pi\)
\(4\) 1137.17i 2.22104i
\(5\) 710.947 294.484i 0.508713 0.210716i −0.113538 0.993534i \(-0.536218\pi\)
0.622251 + 0.782818i \(0.286218\pi\)
\(6\) −1600.11 + 3863.01i −0.504046 + 1.21687i
\(7\) −1447.96 599.766i −0.227938 0.0944150i 0.265792 0.964031i \(-0.414367\pi\)
−0.493730 + 0.869616i \(0.664367\pi\)
\(8\) −17952.2 + 17952.2i −1.54958 + 1.54958i
\(9\) 6421.80 6421.80i 0.326261 0.326261i
\(10\) 28871.6 + 11959.0i 0.913000 + 0.378177i
\(11\) −6518.10 + 15736.1i −0.134231 + 0.324063i −0.976676 0.214721i \(-0.931116\pi\)
0.842444 + 0.538784i \(0.181116\pi\)
\(12\) −108173. + 44806.8i −1.50593 + 0.623776i
\(13\) 141996.i 1.37890i −0.724334 0.689449i \(-0.757853\pi\)
0.724334 0.689449i \(-0.242147\pi\)
\(14\) −24356.5 58801.9i −0.169449 0.409086i
\(15\) 56025.4 + 56025.4i 0.285742 + 0.285742i
\(16\) −448786. −1.71198
\(17\) −213765. + 269986.i −0.620750 + 0.784009i
\(18\) 368812. 0.828091
\(19\) 525945. + 525945.i 0.925869 + 0.925869i 0.997436 0.0715668i \(-0.0227999\pi\)
−0.0715668 + 0.997436i \(0.522800\pi\)
\(20\) 334879. + 808470.i 0.468008 + 1.12987i
\(21\) 161369.i 0.181065i
\(22\) −639042. + 264700.i −0.581604 + 0.240908i
\(23\) 595280. 1.43713e6i 0.443553 1.07083i −0.531140 0.847284i \(-0.678236\pi\)
0.974693 0.223548i \(-0.0717640\pi\)
\(24\) −2.41505e6 1.00035e6i −1.48585 0.615461i
\(25\) −962343. + 962343.i −0.492719 + 0.492719i
\(26\) 4.07751e6 4.07751e6i 1.74991 1.74991i
\(27\) 2.73624e6 + 1.13339e6i 0.990871 + 0.410432i
\(28\) 682038. 1.64659e6i 0.209700 0.506260i
\(29\) 5.30192e6 2.19613e6i 1.39201 0.576589i 0.444345 0.895856i \(-0.353436\pi\)
0.947665 + 0.319266i \(0.103436\pi\)
\(30\) 3.21761e6i 0.725249i
\(31\) −1.75648e6 4.24052e6i −0.341598 0.824691i −0.997555 0.0698922i \(-0.977734\pi\)
0.655956 0.754799i \(-0.272266\pi\)
\(32\) −3.69563e6 3.69563e6i −0.623037 0.623037i
\(33\) −1.75371e6 −0.257422
\(34\) −1.38912e7 + 1.61441e6i −1.78273 + 0.207186i
\(35\) −1.20605e6 −0.135850
\(36\) 7.30269e6 + 7.30269e6i 0.724639 + 0.724639i
\(37\) 2.09832e6 + 5.06579e6i 0.184062 + 0.444365i 0.988796 0.149270i \(-0.0476924\pi\)
−0.804735 + 0.593635i \(0.797692\pi\)
\(38\) 3.02057e7i 2.34997i
\(39\) 1.35074e7 5.59493e6i 0.934931 0.387261i
\(40\) −7.47645e6 + 1.80497e7i −0.461770 + 1.11481i
\(41\) −1.67370e7 6.93270e6i −0.925019 0.383155i −0.131232 0.991352i \(-0.541893\pi\)
−0.793787 + 0.608196i \(0.791893\pi\)
\(42\) 4.63381e6 4.63381e6i 0.229782 0.229782i
\(43\) −1.97878e7 + 1.97878e7i −0.882650 + 0.882650i −0.993803 0.111153i \(-0.964546\pi\)
0.111153 + 0.993803i \(0.464546\pi\)
\(44\) −1.78946e7 7.41221e6i −0.719757 0.298133i
\(45\) 2.67444e6 6.45667e6i 0.0972248 0.234721i
\(46\) 5.83620e7 2.41743e7i 1.92185 0.796057i
\(47\) 2.65154e7i 0.792607i −0.918119 0.396304i \(-0.870293\pi\)
0.918119 0.396304i \(-0.129707\pi\)
\(48\) −1.76830e7 4.26906e7i −0.480808 1.16077i
\(49\) −2.67974e7 2.67974e7i −0.664065 0.664065i
\(50\) −5.52685e7 −1.25058
\(51\) −3.41051e7 9.69637e6i −0.705916 0.200698i
\(52\) 1.61474e8 3.06259
\(53\) −5.36103e7 5.36103e7i −0.933268 0.933268i 0.0646404 0.997909i \(-0.479410\pi\)
−0.997909 + 0.0646404i \(0.979410\pi\)
\(54\) 4.60269e7 + 1.11119e8i 0.736614 + 1.77834i
\(55\) 1.31070e7i 0.193140i
\(56\) 3.67613e7 1.52270e7i 0.499511 0.206904i
\(57\) −2.93071e7 + 7.07536e7i −0.367736 + 0.887793i
\(58\) 2.15311e8 + 8.91848e7i 2.49828 + 1.03482i
\(59\) −3.36343e7 + 3.36343e7i −0.361367 + 0.361367i −0.864316 0.502949i \(-0.832248\pi\)
0.502949 + 0.864316i \(0.332248\pi\)
\(60\) −6.37106e7 + 6.37106e7i −0.634645 + 0.634645i
\(61\) −1.29622e8 5.36913e7i −1.19866 0.496501i −0.308093 0.951356i \(-0.599691\pi\)
−0.890565 + 0.454855i \(0.849691\pi\)
\(62\) 7.13307e7 1.72207e8i 0.613075 1.48009i
\(63\) −1.31501e7 + 5.44695e6i −0.105171 + 0.0435633i
\(64\) 1.75339e7i 0.130638i
\(65\) −4.18157e7 1.00952e8i −0.290555 0.701463i
\(66\) −5.03590e7 5.03590e7i −0.326685 0.326685i
\(67\) 7.10319e7 0.430643 0.215321 0.976543i \(-0.430920\pi\)
0.215321 + 0.976543i \(0.430920\pi\)
\(68\) −3.07021e8 2.43088e8i −1.74132 1.37871i
\(69\) 1.60162e8 0.850625
\(70\) −3.46324e7 3.46324e7i −0.172402 0.172402i
\(71\) 2.73336e7 + 6.59891e7i 0.127654 + 0.308184i 0.974766 0.223231i \(-0.0716605\pi\)
−0.847112 + 0.531415i \(0.821661\pi\)
\(72\) 2.30571e8i 1.01113i
\(73\) 3.14349e8 1.30208e8i 1.29556 0.536640i 0.374925 0.927055i \(-0.377668\pi\)
0.920639 + 0.390415i \(0.127668\pi\)
\(74\) −8.52128e7 + 2.05722e8i −0.330341 + 0.797513i
\(75\) −1.29461e8 5.36244e7i −0.472457 0.195698i
\(76\) −5.98091e8 + 5.98091e8i −2.05639 + 2.05639i
\(77\) 1.88759e7 1.88759e7i 0.0611928 0.0611928i
\(78\) 5.48534e8 + 2.27210e8i 1.67794 + 0.695028i
\(79\) 1.22779e8 2.96415e8i 0.354652 0.856206i −0.641381 0.767222i \(-0.721638\pi\)
0.996033 0.0889832i \(-0.0283618\pi\)
\(80\) −3.19063e8 + 1.32160e8i −0.870908 + 0.360742i
\(81\) 1.26185e8i 0.325705i
\(82\) −2.81537e8 6.79690e8i −0.687659 1.66015i
\(83\) 2.30965e8 + 2.30965e8i 0.534190 + 0.534190i 0.921816 0.387627i \(-0.126705\pi\)
−0.387627 + 0.921816i \(0.626705\pi\)
\(84\) 1.83505e8 0.402152
\(85\) −7.24692e7 + 2.54896e8i −0.150580 + 0.529637i
\(86\) −1.13644e9 −2.24028
\(87\) 4.17812e8 + 4.17812e8i 0.781887 + 0.781887i
\(88\) −1.65483e8 3.99512e8i −0.294159 0.710163i
\(89\) 2.75879e8i 0.466084i −0.972467 0.233042i \(-0.925132\pi\)
0.972467 0.233042i \(-0.0748679\pi\)
\(90\) 2.62206e8 1.08609e8i 0.421261 0.174492i
\(91\) −8.51646e7 + 2.05606e8i −0.130189 + 0.314303i
\(92\) 1.63427e9 + 6.76936e8i 2.37836 + 0.985150i
\(93\) 3.34169e8 3.34169e8i 0.463226 0.463226i
\(94\) 7.61407e8 7.61407e8i 1.00587 1.00587i
\(95\) 5.28802e8 + 2.19037e8i 0.666096 + 0.275906i
\(96\) 2.05931e8 4.97161e8i 0.247457 0.597415i
\(97\) −6.15244e8 + 2.54842e8i −0.705625 + 0.292280i −0.706493 0.707720i \(-0.749724\pi\)
0.000867561 1.00000i \(0.499724\pi\)
\(98\) 1.53901e9i 1.68548i
\(99\) 5.91960e7 + 1.42912e8i 0.0619347 + 0.149524i
\(100\) −1.09435e9 1.09435e9i −1.09435 1.09435i
\(101\) −6.92506e8 −0.662182 −0.331091 0.943599i \(-0.607417\pi\)
−0.331091 + 0.943599i \(0.607417\pi\)
\(102\) −7.00911e8 1.25779e9i −0.641154 1.15055i
\(103\) −1.77196e9 −1.55127 −0.775633 0.631184i \(-0.782569\pi\)
−0.775633 + 0.631184i \(0.782569\pi\)
\(104\) 2.54915e9 + 2.54915e9i 2.13671 + 2.13671i
\(105\) −4.75206e7 1.14725e8i −0.0381531 0.0921098i
\(106\) 3.07890e9i 2.36875i
\(107\) 7.14189e8 2.95827e8i 0.526727 0.218178i −0.103442 0.994636i \(-0.532986\pi\)
0.630169 + 0.776458i \(0.282986\pi\)
\(108\) −1.28886e9 + 3.11158e9i −0.911587 + 2.20077i
\(109\) 1.95887e9 + 8.11389e8i 1.32919 + 0.550567i 0.930423 0.366488i \(-0.119440\pi\)
0.398762 + 0.917054i \(0.369440\pi\)
\(110\) −3.76376e8 + 3.76376e8i −0.245106 + 0.245106i
\(111\) −3.99204e8 + 3.99204e8i −0.249598 + 0.249598i
\(112\) 6.49827e8 + 2.69167e8i 0.390226 + 0.161637i
\(113\) −8.46924e8 + 2.04465e9i −0.488643 + 1.17969i 0.466761 + 0.884384i \(0.345421\pi\)
−0.955403 + 0.295304i \(0.904579\pi\)
\(114\) −2.87331e9 + 1.19016e9i −1.59335 + 0.659986i
\(115\) 1.19703e9i 0.638210i
\(116\) 2.49738e9 + 6.02920e9i 1.28063 + 3.09171i
\(117\) −9.11871e8 9.11871e8i −0.449881 0.449881i
\(118\) −1.93166e9 −0.917196
\(119\) 4.71453e8 2.62721e8i 0.215515 0.120097i
\(120\) −2.01156e9 −0.885560
\(121\) 1.46218e9 + 1.46218e9i 0.620108 + 0.620108i
\(122\) −2.18041e9 5.26396e9i −0.891083 2.15126i
\(123\) 1.86526e9i 0.734797i
\(124\) 4.82220e9 1.99742e9i 1.83167 0.758704i
\(125\) −9.75945e8 + 2.35614e9i −0.357545 + 0.863189i
\(126\) −5.34026e8 2.21201e8i −0.188753 0.0781843i
\(127\) 2.50403e8 2.50403e8i 0.0854129 0.0854129i −0.663110 0.748522i \(-0.730764\pi\)
0.748522 + 0.663110i \(0.230764\pi\)
\(128\) −2.39566e9 + 2.39566e9i −0.788825 + 0.788825i
\(129\) −2.66198e9 1.10263e9i −0.846352 0.350570i
\(130\) 1.69813e9 4.09966e9i 0.521467 1.25893i
\(131\) 2.42705e9 1.00532e9i 0.720042 0.298251i 0.00758938 0.999971i \(-0.497584\pi\)
0.712453 + 0.701720i \(0.247584\pi\)
\(132\) 1.99428e9i 0.571746i
\(133\) −4.46106e8 1.07699e9i −0.123625 0.298457i
\(134\) 2.03973e9 + 2.03973e9i 0.546512 + 0.546512i
\(135\) 2.27909e9 0.590553
\(136\) −1.00929e9 8.68441e9i −0.252983 2.17678i
\(137\) −3.91153e9 −0.948646 −0.474323 0.880351i \(-0.657307\pi\)
−0.474323 + 0.880351i \(0.657307\pi\)
\(138\) 4.59915e9 + 4.59915e9i 1.07950 + 1.07950i
\(139\) 1.41398e9 + 3.41366e9i 0.321276 + 0.775628i 0.999180 + 0.0404785i \(0.0128882\pi\)
−0.677905 + 0.735150i \(0.737112\pi\)
\(140\) 1.37149e9i 0.301728i
\(141\) 2.52227e9 1.04476e9i 0.537410 0.222602i
\(142\) −1.11002e9 + 2.67982e9i −0.229104 + 0.553105i
\(143\) 2.23447e9 + 9.25546e8i 0.446850 + 0.185091i
\(144\) −2.88201e9 + 2.88201e9i −0.558554 + 0.558554i
\(145\) 3.12266e9 3.12266e9i 0.586637 0.586637i
\(146\) 1.27657e10 + 5.28773e9i 2.32518 + 0.963122i
\(147\) 1.49323e9 3.60497e9i 0.263753 0.636756i
\(148\) −5.76069e9 + 2.38615e9i −0.986953 + 0.408809i
\(149\) 6.36801e9i 1.05844i 0.848485 + 0.529219i \(0.177515\pi\)
−0.848485 + 0.529219i \(0.822485\pi\)
\(150\) −2.17769e9 5.25740e9i −0.351224 0.847930i
\(151\) −6.30778e9 6.30778e9i −0.987370 0.987370i 0.0125508 0.999921i \(-0.496005\pi\)
−0.999921 + 0.0125508i \(0.996005\pi\)
\(152\) −1.88838e10 −2.86941
\(153\) 3.61038e8 + 3.10655e9i 0.0532650 + 0.458318i
\(154\) 1.08407e9 0.155315
\(155\) −2.49753e9 2.49753e9i −0.347551 0.347551i
\(156\) 6.36240e9 + 1.53602e10i 0.860123 + 2.07652i
\(157\) 4.57442e9i 0.600879i 0.953801 + 0.300440i \(0.0971334\pi\)
−0.953801 + 0.300440i \(0.902867\pi\)
\(158\) 1.20374e10 4.98606e9i 1.53665 0.636503i
\(159\) 2.98731e9 7.21200e9i 0.370675 0.894888i
\(160\) −3.71570e9 1.53909e9i −0.448230 0.185663i
\(161\) −1.72389e9 + 1.72389e9i −0.202205 + 0.202205i
\(162\) −3.62347e9 + 3.62347e9i −0.413340 + 0.413340i
\(163\) 6.10813e9 + 2.53007e9i 0.677741 + 0.280730i 0.694882 0.719123i \(-0.255456\pi\)
−0.0171410 + 0.999853i \(0.505456\pi\)
\(164\) 7.88368e9 1.90329e10i 0.851004 2.05450i
\(165\) −1.24680e9 + 5.16441e8i −0.130954 + 0.0542429i
\(166\) 1.32646e10i 1.35584i
\(167\) −4.97675e9 1.20149e10i −0.495133 1.19536i −0.952076 0.305861i \(-0.901056\pi\)
0.456943 0.889496i \(-0.348944\pi\)
\(168\) 2.89694e9 + 2.89694e9i 0.280574 + 0.280574i
\(169\) −9.55847e9 −0.901359
\(170\) −9.40050e9 + 5.23850e9i −0.863238 + 0.481046i
\(171\) 6.75503e9 0.604150
\(172\) −2.25021e10 2.25021e10i −1.96040 1.96040i
\(173\) −1.55862e9 3.76285e9i −0.132292 0.319381i 0.843828 0.536614i \(-0.180297\pi\)
−0.976120 + 0.217233i \(0.930297\pi\)
\(174\) 2.39954e10i 1.98453i
\(175\) 1.97062e9 8.16257e8i 0.158830 0.0657894i
\(176\) 2.92523e9 7.06214e9i 0.229802 0.554791i
\(177\) −4.52471e9 1.87420e9i −0.346506 0.143528i
\(178\) 7.92204e9 7.92204e9i 0.591489 0.591489i
\(179\) −1.74810e10 + 1.74810e10i −1.27271 + 1.27271i −0.328042 + 0.944663i \(0.606389\pi\)
−0.944663 + 0.328042i \(0.893611\pi\)
\(180\) 7.34236e9 + 3.04130e9i 0.521326 + 0.215940i
\(181\) −1.36886e9 + 3.30472e9i −0.0947992 + 0.228866i −0.964165 0.265304i \(-0.914528\pi\)
0.869366 + 0.494169i \(0.164528\pi\)
\(182\) −8.34965e9 + 3.45854e9i −0.564088 + 0.233653i
\(183\) 1.44458e10i 0.952165i
\(184\) 1.51131e10 + 3.64863e10i 0.972018 + 2.34666i
\(185\) 2.98359e9 + 2.98359e9i 0.187269 + 0.187269i
\(186\) 1.91917e10 1.17573
\(187\) −2.85518e9 5.12362e9i −0.170744 0.306401i
\(188\) 3.01526e10 1.76041
\(189\) −3.28221e9 3.28221e9i −0.187106 0.187106i
\(190\) 8.89510e9 + 2.14747e10i 0.495176 + 1.19546i
\(191\) 1.56335e10i 0.849975i 0.905199 + 0.424988i \(0.139722\pi\)
−0.905199 + 0.424988i \(0.860278\pi\)
\(192\) −1.66791e9 + 6.90871e8i −0.0885762 + 0.0366895i
\(193\) −3.03725e9 + 7.33258e9i −0.157570 + 0.380407i −0.982873 0.184282i \(-0.941004\pi\)
0.825304 + 0.564689i \(0.191004\pi\)
\(194\) −2.49850e10 1.03491e10i −1.26640 0.524562i
\(195\) 7.95540e9 7.95540e9i 0.394009 0.394009i
\(196\) 3.04733e10 3.04733e10i 1.47492 1.47492i
\(197\) −2.45077e10 1.01514e10i −1.15932 0.480207i −0.281673 0.959510i \(-0.590889\pi\)
−0.877649 + 0.479303i \(0.840889\pi\)
\(198\) −2.40395e9 + 5.80365e9i −0.111156 + 0.268354i
\(199\) 3.86785e10 1.60212e10i 1.74836 0.724195i 0.750358 0.661031i \(-0.229881\pi\)
0.998003 0.0631639i \(-0.0201191\pi\)
\(200\) 3.45524e10i 1.52701i
\(201\) 2.79879e9 + 6.75689e9i 0.120945 + 0.291988i
\(202\) −1.98857e10 1.98857e10i −0.840351 0.840351i
\(203\) −8.99416e9 −0.371731
\(204\) 1.10264e10 3.87834e10i 0.445759 1.56787i
\(205\) −1.39407e10 −0.551305
\(206\) −5.08829e10 5.08829e10i −1.96866 1.96866i
\(207\) −5.40621e9 1.30517e10i −0.204657 0.494085i
\(208\) 6.37260e10i 2.36065i
\(209\) −1.17045e10 + 4.84816e9i −0.424320 + 0.175759i
\(210\) 1.92981e9 4.65898e9i 0.0684744 0.165312i
\(211\) 2.32386e10 + 9.62576e9i 0.807123 + 0.334321i 0.747805 0.663918i \(-0.231108\pi\)
0.0593172 + 0.998239i \(0.481108\pi\)
\(212\) 6.09641e10 6.09641e10i 2.07283 2.07283i
\(213\) −5.20019e9 + 5.20019e9i −0.173106 + 0.173106i
\(214\) 2.90032e10 + 1.20135e10i 0.945331 + 0.391569i
\(215\) −8.24088e9 + 1.98952e10i −0.263027 + 0.635003i
\(216\) −6.94685e10 + 2.87748e10i −2.17143 + 0.899436i
\(217\) 7.19360e9i 0.220230i
\(218\) 3.29505e10 + 7.95496e10i 0.988116 + 2.38552i
\(219\) 2.47719e10 + 2.47719e10i 0.727714 + 0.727714i
\(220\) −1.49049e10 −0.428971
\(221\) 3.83370e10 + 3.03539e10i 1.08107 + 0.855951i
\(222\) −2.29268e10 −0.633512
\(223\) 2.42424e10 + 2.42424e10i 0.656453 + 0.656453i 0.954539 0.298086i \(-0.0963482\pi\)
−0.298086 + 0.954539i \(0.596348\pi\)
\(224\) 3.13463e9 + 7.56766e9i 0.0831897 + 0.200838i
\(225\) 1.23599e10i 0.321510i
\(226\) −8.30335e10 + 3.43936e10i −2.11722 + 0.876980i
\(227\) 1.50201e10 3.62617e10i 0.375453 0.906425i −0.617352 0.786687i \(-0.711795\pi\)
0.992806 0.119738i \(-0.0382054\pi\)
\(228\) −8.04592e10 3.33273e10i −1.97183 0.816757i
\(229\) 2.26058e10 2.26058e10i 0.543202 0.543202i −0.381264 0.924466i \(-0.624511\pi\)
0.924466 + 0.381264i \(0.124511\pi\)
\(230\) 3.43733e10 3.43733e10i 0.809928 0.809928i
\(231\) 2.53932e9 + 1.05182e9i 0.0586763 + 0.0243045i
\(232\) −5.57559e10 + 1.34607e11i −1.26356 + 3.05050i
\(233\) −7.94318e10 + 3.29017e10i −1.76560 + 0.731336i −0.769958 + 0.638094i \(0.779723\pi\)
−0.995644 + 0.0932417i \(0.970277\pi\)
\(234\) 5.23699e10i 1.14185i
\(235\) −7.80837e9 1.88511e10i −0.167015 0.403209i
\(236\) −3.82481e10 3.82481e10i −0.802612 0.802612i
\(237\) 3.30341e10 0.680135
\(238\) 2.10822e10 + 5.99386e9i 0.425913 + 0.121091i
\(239\) 3.27519e10 0.649300 0.324650 0.945834i \(-0.394753\pi\)
0.324650 + 0.945834i \(0.394753\pi\)
\(240\) −2.51434e10 2.51434e10i −0.489186 0.489186i
\(241\) −8.78857e8 2.12175e9i −0.0167819 0.0405151i 0.915266 0.402849i \(-0.131980\pi\)
−0.932048 + 0.362334i \(0.881980\pi\)
\(242\) 8.39749e10i 1.57391i
\(243\) 4.18541e10 1.73366e10i 0.770035 0.318959i
\(244\) 6.10563e10 1.47403e11i 1.10275 2.66227i
\(245\) −2.69430e10 1.11601e10i −0.477747 0.197889i
\(246\) 5.35622e10 5.35622e10i 0.932503 0.932503i
\(247\) 7.46823e10 7.46823e10i 1.27668 1.27668i
\(248\) 1.07660e11 + 4.45940e10i 1.80726 + 0.748590i
\(249\) −1.28700e10 + 3.10710e10i −0.212169 + 0.512222i
\(250\) −9.56828e10 + 3.96331e10i −1.54919 + 0.641694i
\(251\) 4.29930e10i 0.683700i 0.939755 + 0.341850i \(0.111053\pi\)
−0.939755 + 0.341850i \(0.888947\pi\)
\(252\) −6.19413e9 1.49540e10i −0.0967560 0.233590i
\(253\) 1.87347e10 + 1.87347e10i 0.287478 + 0.287478i
\(254\) 1.43810e10 0.216789
\(255\) −2.71023e10 + 3.14979e9i −0.401399 + 0.0466499i
\(256\) −1.28608e11 −1.87150
\(257\) 1.19346e10 + 1.19346e10i 0.170650 + 0.170650i 0.787265 0.616615i \(-0.211496\pi\)
−0.616615 + 0.787265i \(0.711496\pi\)
\(258\) −4.47777e10 1.08103e11i −0.629178 1.51897i
\(259\) 8.59359e9i 0.118666i
\(260\) 1.14800e11 4.75517e10i 1.55798 0.645336i
\(261\) 1.99448e10 4.81509e10i 0.266040 0.642277i
\(262\) 9.85626e10 + 4.08259e10i 1.29228 + 0.535279i
\(263\) −1.33222e10 + 1.33222e10i −0.171702 + 0.171702i −0.787727 0.616025i \(-0.788742\pi\)
0.616025 + 0.787727i \(0.288742\pi\)
\(264\) 3.14831e10 3.14831e10i 0.398896 0.398896i
\(265\) −5.39014e10 2.23267e10i −0.671419 0.278111i
\(266\) 1.81164e10 4.37368e10i 0.221873 0.535648i
\(267\) 2.62429e10 1.08702e10i 0.316018 0.130899i
\(268\) 8.07756e10i 0.956475i
\(269\) 3.54997e10 + 8.57039e10i 0.413370 + 0.997964i 0.984226 + 0.176914i \(0.0566115\pi\)
−0.570856 + 0.821050i \(0.693388\pi\)
\(270\) 6.54454e10 + 6.54454e10i 0.749449 + 0.749449i
\(271\) −1.11257e11 −1.25304 −0.626519 0.779406i \(-0.715521\pi\)
−0.626519 + 0.779406i \(0.715521\pi\)
\(272\) 9.59348e10 1.21166e11i 1.06271 1.34221i
\(273\) −2.29138e10 −0.249670
\(274\) −1.12322e11 1.12322e11i −1.20389 1.20389i
\(275\) −8.87086e9 2.14161e10i −0.0935338 0.225810i
\(276\) 1.82132e11i 1.88927i
\(277\) −1.15253e11 + 4.77393e10i −1.17623 + 0.487211i −0.883248 0.468906i \(-0.844648\pi\)
−0.292984 + 0.956117i \(0.594648\pi\)
\(278\) −5.74219e10 + 1.38629e11i −0.576602 + 1.39204i
\(279\) −3.85115e10 1.59520e10i −0.380515 0.157614i
\(280\) 2.16513e10 2.16513e10i 0.210510 0.210510i
\(281\) −6.11796e10 + 6.11796e10i −0.585367 + 0.585367i −0.936373 0.351006i \(-0.885840\pi\)
0.351006 + 0.936373i \(0.385840\pi\)
\(282\) 1.02429e11 + 4.24277e10i 0.964503 + 0.399510i
\(283\) 5.17938e10 1.25041e11i 0.479997 1.15882i −0.479613 0.877480i \(-0.659223\pi\)
0.959610 0.281335i \(-0.0907772\pi\)
\(284\) −7.50410e10 + 3.10830e10i −0.684489 + 0.283525i
\(285\) 5.89326e10i 0.529119i
\(286\) 3.75864e10 + 9.07417e10i 0.332188 + 0.801973i
\(287\) 2.00766e10 + 2.00766e10i 0.174671 + 0.174671i
\(288\) −4.74652e10 −0.406545
\(289\) −2.71969e10 1.15427e11i −0.229339 0.973347i
\(290\) 1.79338e11 1.48896
\(291\) −4.84836e10 4.84836e10i −0.396347 0.396347i
\(292\) 1.48068e11 + 3.57469e11i 1.19190 + 2.87750i
\(293\) 8.66175e10i 0.686596i −0.939227 0.343298i \(-0.888456\pi\)
0.939227 0.343298i \(-0.111544\pi\)
\(294\) 1.46398e11 6.06399e10i 1.14280 0.473364i
\(295\) −1.40075e10 + 3.38170e10i −0.107686 + 0.259978i
\(296\) −1.28612e11 5.32728e10i −0.973797 0.403360i
\(297\) −3.56702e10 + 3.56702e10i −0.266012 + 0.266012i
\(298\) −1.82861e11 + 1.82861e11i −1.34323 + 1.34323i
\(299\) −2.04068e11 8.45276e10i −1.47657 0.611615i
\(300\) 6.09802e10 1.47219e11i 0.434653 1.04935i
\(301\) 4.05200e10 1.67839e10i 0.284525 0.117854i
\(302\) 3.62263e11i 2.50607i
\(303\) −2.72861e10 6.58744e10i −0.185973 0.448978i
\(304\) −2.36037e11 2.36037e11i −1.58507 1.58507i
\(305\) −1.07966e11 −0.714393
\(306\) −7.88390e10 + 9.95739e10i −0.514038 + 0.649231i
\(307\) 1.77951e11 1.14335 0.571674 0.820481i \(-0.306294\pi\)
0.571674 + 0.820481i \(0.306294\pi\)
\(308\) 2.14652e10 + 2.14652e10i 0.135912 + 0.135912i
\(309\) −6.98186e10 1.68557e11i −0.435671 1.05180i
\(310\) 1.43436e11i 0.882127i
\(311\) 6.62952e10 2.74604e10i 0.401847 0.166450i −0.172601 0.984992i \(-0.555217\pi\)
0.574447 + 0.818542i \(0.305217\pi\)
\(312\) −1.42046e11 + 3.42929e11i −0.848657 + 2.04884i
\(313\) 2.45192e11 + 1.01562e11i 1.44397 + 0.598111i 0.960756 0.277394i \(-0.0894706\pi\)
0.483210 + 0.875504i \(0.339471\pi\)
\(314\) −1.31357e11 + 1.31357e11i −0.762554 + 0.762554i
\(315\) −7.74499e9 + 7.74499e9i −0.0443224 + 0.0443224i
\(316\) 3.37075e11 + 1.39621e11i 1.90167 + 0.787697i
\(317\) 2.88724e9 6.97041e9i 0.0160589 0.0387696i −0.915647 0.401984i \(-0.868321\pi\)
0.931706 + 0.363214i \(0.118321\pi\)
\(318\) 2.92880e11 1.21315e11i 1.60608 0.665260i
\(319\) 9.77460e10i 0.528495i
\(320\) 5.16347e9 + 1.24657e10i 0.0275275 + 0.0664572i
\(321\) 5.62808e10 + 5.62808e10i 0.295861 + 0.295861i
\(322\) −9.90050e10 −0.513222
\(323\) −2.54427e11 + 2.95691e10i −1.30062 + 0.151156i
\(324\) −1.43494e11 −0.723404
\(325\) 1.36649e11 + 1.36649e11i 0.679410 + 0.679410i
\(326\) 1.02746e11 + 2.48051e11i 0.503833 + 1.21636i
\(327\) 2.18307e11i 1.05585i
\(328\) 4.24924e11 1.76009e11i 2.02712 0.839660i
\(329\) −1.59031e10 + 3.83934e10i −0.0748340 + 0.180665i
\(330\) −5.06325e10 2.09727e10i −0.235026 0.0973512i
\(331\) 1.86346e11 1.86346e11i 0.853286 0.853286i −0.137250 0.990536i \(-0.543826\pi\)
0.990536 + 0.137250i \(0.0438264\pi\)
\(332\) −2.62648e11 + 2.62648e11i −1.18646 + 1.18646i
\(333\) 4.60065e10 + 1.90565e10i 0.205031 + 0.0849267i
\(334\) 2.02106e11 4.87927e11i 0.888628 2.14534i
\(335\) 5.05000e10 2.09178e10i 0.219073 0.0907431i
\(336\) 7.24202e10i 0.309980i
\(337\) −3.54672e10 8.56254e10i −0.149793 0.361633i 0.831116 0.556099i \(-0.187703\pi\)
−0.980909 + 0.194466i \(0.937703\pi\)
\(338\) −2.74477e11 2.74477e11i −1.14388 1.14388i
\(339\) −2.27867e11 −0.937095
\(340\) −2.89861e11 8.24100e10i −1.17635 0.334445i
\(341\) 7.81780e10 0.313105
\(342\) 1.93975e11 + 1.93975e11i 0.766704 + 0.766704i
\(343\) 4.69323e10 + 1.13305e11i 0.183083 + 0.442001i
\(344\) 7.10469e11i 2.73547i
\(345\) 1.13867e11 4.71651e10i 0.432724 0.179240i
\(346\) 6.32957e10 1.52809e11i 0.237428 0.573202i
\(347\) 1.53843e11 + 6.37240e10i 0.569635 + 0.235950i 0.648862 0.760906i \(-0.275245\pi\)
−0.0792272 + 0.996857i \(0.525245\pi\)
\(348\) −4.75124e11 + 4.75124e11i −1.73660 + 1.73660i
\(349\) 1.75870e11 1.75870e11i 0.634567 0.634567i −0.314643 0.949210i \(-0.601885\pi\)
0.949210 + 0.314643i \(0.101885\pi\)
\(350\) 8.00268e10 + 3.31482e10i 0.285056 + 0.118074i
\(351\) 1.60937e11 3.88536e11i 0.565944 1.36631i
\(352\) 8.22432e10 3.40663e10i 0.285534 0.118272i
\(353\) 2.22039e10i 0.0761102i 0.999276 + 0.0380551i \(0.0121162\pi\)
−0.999276 + 0.0380551i \(0.987884\pi\)
\(354\) −7.61112e10 1.83749e11i −0.257593 0.621884i
\(355\) 3.88655e10 + 3.88655e10i 0.129878 + 0.129878i
\(356\) 3.13722e11 1.03519
\(357\) 4.35674e10 + 3.44951e10i 0.141956 + 0.112396i
\(358\) −1.00396e12 −3.23029
\(359\) 2.27378e11 + 2.27378e11i 0.722477 + 0.722477i 0.969109 0.246632i \(-0.0793240\pi\)
−0.246632 + 0.969109i \(0.579324\pi\)
\(360\) 6.78995e10 + 1.63924e11i 0.213062 + 0.514377i
\(361\) 2.30550e11i 0.714467i
\(362\) −1.34205e11 + 5.55893e10i −0.410751 + 0.170139i
\(363\) −8.14768e10 + 1.96702e11i −0.246294 + 0.594607i
\(364\) −2.33809e11 9.68470e10i −0.698080 0.289154i
\(365\) 1.85141e11 1.85141e11i 0.545991 0.545991i
\(366\) 4.14821e11 4.14821e11i 1.20836 1.20836i
\(367\) 3.55069e10 + 1.47075e10i 0.102168 + 0.0423195i 0.433182 0.901306i \(-0.357391\pi\)
−0.331014 + 0.943626i \(0.607391\pi\)
\(368\) −2.67153e11 + 6.44965e11i −0.759356 + 1.83325i
\(369\) −1.52002e11 + 6.29613e10i −0.426806 + 0.176789i
\(370\) 1.71351e11i 0.475313i
\(371\) 4.54721e10 + 1.09779e11i 0.124613 + 0.300842i
\(372\) 3.80008e11 + 3.80008e11i 1.02884 + 1.02884i
\(373\) −2.79837e11 −0.748540 −0.374270 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(374\) 6.51397e10 2.29116e11i 0.172156 0.605527i
\(375\) −2.62581e11 −0.685682
\(376\) 4.76011e11 + 4.76011e11i 1.22821 + 1.22821i
\(377\) −3.11842e11 7.52854e11i −0.795058 1.91944i
\(378\) 1.88501e11i 0.474899i
\(379\) −2.03039e11 + 8.41013e10i −0.505478 + 0.209376i −0.620825 0.783949i \(-0.713202\pi\)
0.115347 + 0.993325i \(0.463202\pi\)
\(380\) −2.49083e11 + 6.01340e11i −0.612799 + 1.47943i
\(381\) 3.36859e10 + 1.39532e10i 0.0819003 + 0.0339242i
\(382\) −4.48926e11 + 4.48926e11i −1.07867 + 1.07867i
\(383\) −3.99755e11 + 3.99755e11i −0.949291 + 0.949291i −0.998775 0.0494839i \(-0.984242\pi\)
0.0494839 + 0.998775i \(0.484242\pi\)
\(384\) −3.22280e11 1.33493e11i −0.756385 0.313305i
\(385\) 7.86114e9 1.89785e10i 0.0182353 0.0440238i
\(386\) −2.97776e11 + 1.23343e11i −0.682727 + 0.282795i
\(387\) 2.54146e11i 0.575949i
\(388\) −2.89800e11 6.99639e11i −0.649165 1.56722i
\(389\) 3.65150e11 + 3.65150e11i 0.808533 + 0.808533i 0.984412 0.175879i \(-0.0562766\pi\)
−0.175879 + 0.984412i \(0.556277\pi\)
\(390\) 4.56888e11 1.00004
\(391\) 2.60755e11 + 4.67926e11i 0.564206 + 1.01247i
\(392\) 9.62148e11 2.05804
\(393\) 1.91261e11 + 1.91261e11i 0.404445 + 0.404445i
\(394\) −4.12249e11 9.95258e11i −0.861840 2.08067i
\(395\) 2.46892e11i 0.510293i
\(396\) −1.62515e11 + 6.73161e10i −0.332098 + 0.137559i
\(397\) 9.37139e10 2.26245e11i 0.189342 0.457112i −0.800491 0.599344i \(-0.795428\pi\)
0.989833 + 0.142233i \(0.0454281\pi\)
\(398\) 1.57074e12 + 6.50620e11i 3.13783 + 1.29973i
\(399\) 8.48713e10 8.48713e10i 0.167642 0.167642i
\(400\) 4.31886e11 4.31886e11i 0.843528 0.843528i
\(401\) −4.63444e11 1.91965e11i −0.895051 0.370742i −0.112736 0.993625i \(-0.535961\pi\)
−0.782315 + 0.622883i \(0.785961\pi\)
\(402\) −1.13659e11 + 2.74397e11i −0.217064 + 0.524038i
\(403\) −6.02138e11 + 2.49414e11i −1.13716 + 0.471029i
\(404\) 7.87499e11i 1.47073i
\(405\) 3.71594e10 + 8.97107e10i 0.0686311 + 0.165690i
\(406\) −2.58273e11 2.58273e11i −0.471750 0.471750i
\(407\) −9.33928e10 −0.168709
\(408\) 7.86334e11 4.38191e11i 1.40487 0.782875i
\(409\) 1.25612e11 0.221960 0.110980 0.993823i \(-0.464601\pi\)
0.110980 + 0.993823i \(0.464601\pi\)
\(410\) −4.00316e11 4.00316e11i −0.699641 0.699641i
\(411\) −1.54122e11 3.72083e11i −0.266425 0.643208i
\(412\) 2.01503e12i 3.44543i
\(413\) 6.88741e10 2.85286e10i 0.116488 0.0482508i
\(414\) 2.19546e11 5.30031e11i 0.367303 0.886747i
\(415\) 2.32220e11 + 9.61887e10i 0.384311 + 0.159187i
\(416\) −5.24766e11 + 5.24766e11i −0.859104 + 0.859104i
\(417\) −2.69010e11 + 2.69010e11i −0.435668 + 0.435668i
\(418\) −4.75319e11 1.96884e11i −0.761539 0.315440i
\(419\) −2.51859e11 + 6.08041e11i −0.399203 + 0.963761i 0.588652 + 0.808386i \(0.299659\pi\)
−0.987856 + 0.155375i \(0.950341\pi\)
\(420\) 1.30462e11 5.40392e10i 0.204580 0.0847397i
\(421\) 2.88370e11i 0.447384i −0.974660 0.223692i \(-0.928189\pi\)
0.974660 0.223692i \(-0.0718109\pi\)
\(422\) 3.90902e11 + 9.43721e11i 0.600015 + 1.44856i
\(423\) −1.70277e11 1.70277e11i −0.258597 0.258597i
\(424\) 1.92485e12 2.89234
\(425\) −5.41037e10 4.65534e11i −0.0804408 0.692152i
\(426\) −2.98654e11 −0.439364
\(427\) 1.55486e11 + 1.55486e11i 0.226343 + 0.226343i
\(428\) 3.36406e11 + 8.12156e11i 0.484582 + 1.16988i
\(429\) 2.49021e11i 0.354959i
\(430\) −8.07946e11 + 3.34662e11i −1.13966 + 0.472061i
\(431\) 1.22644e11 2.96089e11i 0.171198 0.413309i −0.814872 0.579642i \(-0.803193\pi\)
0.986070 + 0.166333i \(0.0531926\pi\)
\(432\) −1.22799e12 5.08649e11i −1.69636 0.702654i
\(433\) 8.01153e11 8.01153e11i 1.09527 1.09527i 0.100310 0.994956i \(-0.468016\pi\)
0.994956 0.100310i \(-0.0319836\pi\)
\(434\) −2.06569e11 + 2.06569e11i −0.279486 + 0.279486i
\(435\) 4.20081e11 + 1.74003e11i 0.562512 + 0.233000i
\(436\) −9.22690e11 + 2.22757e12i −1.22283 + 2.95218i
\(437\) 1.06894e12 4.42769e11i 1.40212 0.580778i
\(438\) 1.42268e12i 1.84703i
\(439\) −9.81558e10 2.36969e11i −0.126132 0.304510i 0.848181 0.529706i \(-0.177698\pi\)
−0.974313 + 0.225196i \(0.927698\pi\)
\(440\) −2.35300e11 2.35300e11i −0.299285 0.299285i
\(441\) −3.44175e11 −0.433317
\(442\) 2.29241e11 + 1.97250e12i 0.285688 + 2.45820i
\(443\) −3.11296e11 −0.384023 −0.192011 0.981393i \(-0.561501\pi\)
−0.192011 + 0.981393i \(0.561501\pi\)
\(444\) −4.53964e11 4.53964e11i −0.554368 0.554368i
\(445\) −8.12420e10 1.96136e11i −0.0982111 0.237103i
\(446\) 1.39227e12i 1.66616i
\(447\) −6.05755e11 + 2.50912e11i −0.717651 + 0.297261i
\(448\) 1.05163e10 2.53885e10i 0.0123342 0.0297774i
\(449\) 1.29563e12 + 5.36666e11i 1.50443 + 0.623154i 0.974399 0.224826i \(-0.0721812\pi\)
0.530028 + 0.847980i \(0.322181\pi\)
\(450\) −3.54923e11 + 3.54923e11i −0.408017 + 0.408017i
\(451\) 2.18187e11 2.18187e11i 0.248333 0.248333i
\(452\) −2.32513e12 9.63099e11i −2.62014 1.08530i
\(453\) 3.51487e11 8.48564e11i 0.392163 0.946766i
\(454\) 1.47259e12 6.09966e11i 1.62678 0.673836i
\(455\) 1.71254e11i 0.187323i
\(456\) −7.44058e11 1.79631e12i −0.805870 1.94554i
\(457\) 6.08257e11 + 6.08257e11i 0.652325 + 0.652325i 0.953552 0.301227i \(-0.0973963\pi\)
−0.301227 + 0.953552i \(0.597396\pi\)
\(458\) 1.29828e12 1.37871
\(459\) −8.90911e11 + 4.96468e11i −0.936866 + 0.522076i
\(460\) 1.36123e12 1.41749
\(461\) −1.01522e12 1.01522e12i −1.04690 1.04690i −0.998845 0.0480583i \(-0.984697\pi\)
−0.0480583 0.998845i \(-0.515303\pi\)
\(462\) 4.27144e10 + 1.03122e11i 0.0436200 + 0.105308i
\(463\) 1.35035e12i 1.36563i 0.730592 + 0.682814i \(0.239244\pi\)
−0.730592 + 0.682814i \(0.760756\pi\)
\(464\) −2.37943e12 + 9.85592e11i −2.38310 + 0.987112i
\(465\) 1.39169e11 3.35984e11i 0.138040 0.333258i
\(466\) −3.22573e12 1.33614e12i −3.16877 1.31255i
\(467\) 1.15975e12 1.15975e12i 1.12834 1.12834i 0.137893 0.990447i \(-0.455967\pi\)
0.990447 0.137893i \(-0.0440329\pi\)
\(468\) 1.03696e12 1.03696e12i 0.999203 0.999203i
\(469\) −1.02852e11 4.26026e10i −0.0981598 0.0406591i
\(470\) 3.17098e11 7.65542e11i 0.299746 0.723650i
\(471\) −4.35140e11 + 1.80241e11i −0.407413 + 0.168756i
\(472\) 1.20762e12i 1.11993i
\(473\) −1.82403e11 4.40360e11i −0.167555 0.404513i
\(474\) 9.48594e11 + 9.48594e11i 0.863134 + 0.863134i
\(475\) −1.01228e12 −0.912387
\(476\) 2.98759e11 + 5.36123e11i 0.266741 + 0.478667i
\(477\) −6.88548e11 −0.608978
\(478\) 9.40491e11 + 9.40491e11i 0.824003 + 0.824003i
\(479\) 1.05540e11 + 2.54795e11i 0.0916022 + 0.221147i 0.963040 0.269359i \(-0.0868118\pi\)
−0.871438 + 0.490506i \(0.836812\pi\)
\(480\) 4.14098e11i 0.356056i
\(481\) 7.19324e11 2.97954e11i 0.612734 0.253803i
\(482\) 3.56904e10 8.61643e10i 0.0301189 0.0727136i
\(483\) −2.31909e11 9.60597e10i −0.193890 0.0803118i
\(484\) −1.66275e12 + 1.66275e12i −1.37729 + 1.37729i
\(485\) −3.62359e11 + 3.62359e11i −0.297373 + 0.297373i
\(486\) 1.69970e12 + 7.04038e11i 1.38200 + 0.572444i
\(487\) 2.54556e11 6.14552e11i 0.205070 0.495084i −0.787564 0.616233i \(-0.788658\pi\)
0.992634 + 0.121149i \(0.0386580\pi\)
\(488\) 3.29089e12 1.36313e12i 2.62678 1.08805i
\(489\) 6.80723e11i 0.538370i
\(490\) −4.53214e11 1.09415e12i −0.355157 0.857425i
\(491\) 7.64555e10 + 7.64555e10i 0.0593666 + 0.0593666i 0.736167 0.676800i \(-0.236634\pi\)
−0.676800 + 0.736167i \(0.736634\pi\)
\(492\) 2.12113e12 1.63201
\(493\) −5.40442e11 + 1.90090e12i −0.412039 + 1.44927i
\(494\) 4.28910e12 3.24037
\(495\) 8.41705e10 + 8.41705e10i 0.0630139 + 0.0630139i
\(496\) 7.88284e11 + 1.90309e12i 0.584811 + 1.41186i
\(497\) 1.11944e11i 0.0822992i
\(498\) −1.26179e12 + 5.22652e11i −0.919298 + 0.380786i
\(499\) 4.55965e11 1.10080e12i 0.329215 0.794795i −0.669436 0.742870i \(-0.733464\pi\)
0.998651 0.0519254i \(-0.0165358\pi\)
\(500\) −2.67934e12 1.10982e12i −1.91718 0.794121i
\(501\) 9.46823e11 9.46823e11i 0.671428 0.671428i
\(502\) −1.23457e12 + 1.23457e12i −0.867658 + 0.867658i
\(503\) −2.43647e12 1.00922e12i −1.69709 0.702958i −0.697187 0.716890i \(-0.745565\pi\)
−0.999903 + 0.0139321i \(0.995565\pi\)
\(504\) 1.38289e11 3.33859e11i 0.0954662 0.230476i
\(505\) −4.92335e11 + 2.03932e11i −0.336860 + 0.139532i
\(506\) 1.07596e12i 0.729656i
\(507\) −3.76622e11 9.09246e11i −0.253145 0.611147i
\(508\) 2.84752e11 + 2.84752e11i 0.189705 + 0.189705i
\(509\) −1.59065e12 −1.05038 −0.525189 0.850986i \(-0.676005\pi\)
−0.525189 + 0.850986i \(0.676005\pi\)
\(510\) −8.68708e11 6.87812e11i −0.568602 0.450198i
\(511\) −5.33260e11 −0.345975
\(512\) −2.46649e12 2.46649e12i −1.58622 1.58622i
\(513\) 8.43013e11 + 2.03521e12i 0.537411 + 1.29742i
\(514\) 6.85416e11i 0.433132i
\(515\) −1.25977e12 + 5.21814e11i −0.789149 + 0.326876i
\(516\) 1.25388e12 3.02713e12i 0.778632 1.87978i
\(517\) 4.17249e11 + 1.72830e11i 0.256855 + 0.106393i
\(518\) 2.46770e11 2.46770e11i 0.150594 0.150594i
\(519\) 2.96527e11 2.96527e11i 0.179395 0.179395i
\(520\) 2.56300e12 + 1.06163e12i 1.53721 + 0.636733i
\(521\) 8.72066e11 2.10535e12i 0.518537 1.25186i −0.420265 0.907401i \(-0.638063\pi\)
0.938802 0.344457i \(-0.111937\pi\)
\(522\) 1.95541e12 8.09957e11i 1.15271 0.477469i
\(523\) 4.41293e11i 0.257910i 0.991650 + 0.128955i \(0.0411624\pi\)
−0.991650 + 0.128955i \(0.958838\pi\)
\(524\) 1.14322e12 + 2.75998e12i 0.662428 + 1.59924i
\(525\) 1.55292e11 + 1.55292e11i 0.0892140 + 0.0892140i
\(526\) −7.65110e11 −0.435801
\(527\) 1.52035e12 + 4.32250e11i 0.858612 + 0.244111i
\(528\) 7.87043e11 0.440703
\(529\) −4.37384e11 4.37384e11i −0.242836 0.242836i
\(530\) −9.06688e11 2.18894e12i −0.499133 1.20501i
\(531\) 4.31986e11i 0.235800i
\(532\) 1.22473e12 5.07300e11i 0.662885 0.274576i
\(533\) −9.84417e11 + 2.37659e12i −0.528332 + 1.27551i
\(534\) 1.06572e12 + 4.41438e11i 0.567165 + 0.234927i
\(535\) 4.20634e11 4.20634e11i 0.221979 0.221979i
\(536\) −1.27518e12 + 1.27518e12i −0.667314 + 0.667314i
\(537\) −2.35166e12 9.74089e11i −1.22037 0.505492i
\(538\) −1.44164e12 + 3.48043e12i −0.741887 + 1.79107i
\(539\) 5.96355e11 2.47018e11i 0.304337 0.126061i
\(540\) 2.59172e12i 1.31164i
\(541\) 3.92690e11 + 9.48037e11i 0.197089 + 0.475814i 0.991267 0.131871i \(-0.0420984\pi\)
−0.794178 + 0.607685i \(0.792098\pi\)
\(542\) −3.19480e12 3.19480e12i −1.59018 1.59018i
\(543\) −3.68296e11 −0.181801
\(544\) 1.78777e12 2.07771e11i 0.875216 0.101716i
\(545\) 1.63159e12 0.792186
\(546\) −6.57984e11 6.57984e11i −0.316846 0.316846i
\(547\) −1.16980e12 2.82415e12i −0.558687 1.34879i −0.910806 0.412835i \(-0.864539\pi\)
0.352119 0.935955i \(-0.385461\pi\)
\(548\) 4.44809e12i 2.10698i
\(549\) −1.17720e12 + 4.87613e11i −0.553064 + 0.229087i
\(550\) 3.60246e11 8.69710e11i 0.167867 0.405268i
\(551\) 3.94357e12 + 1.63348e12i 1.82267 + 0.754973i
\(552\) −2.87526e12 + 2.87526e12i −1.31811 + 1.31811i
\(553\) −3.55559e11 + 3.55559e11i −0.161677 + 0.161677i
\(554\) −4.68043e12 1.93870e12i −2.11102 0.874411i
\(555\) −1.66254e11 + 4.01372e11i −0.0743795 + 0.179568i
\(556\) −3.88192e12 + 1.60795e12i −1.72270 + 0.713567i
\(557\) 1.36756e12i 0.602002i −0.953624 0.301001i \(-0.902679\pi\)
0.953624 0.301001i \(-0.0973208\pi\)
\(558\) −6.47810e11 1.56395e12i −0.282875 0.682920i
\(559\) 2.80979e12 + 2.80979e12i 1.21708 + 1.21708i
\(560\) 5.41258e11 0.232572
\(561\) 3.74883e11 4.73478e11i 0.159795 0.201821i
\(562\) −3.51362e12 −1.48573
\(563\) −6.60574e11 6.60574e11i −0.277098 0.277098i 0.554851 0.831950i \(-0.312775\pi\)
−0.831950 + 0.554851i \(0.812775\pi\)
\(564\) 1.18807e12 + 2.86826e12i 0.494409 + 1.19361i
\(565\) 1.70305e12i 0.703087i
\(566\) 5.07793e12 2.10335e12i 2.07976 0.861463i
\(567\) 7.56814e10 1.82711e11i 0.0307514 0.0742405i
\(568\) −1.67535e12 6.93953e11i −0.675365 0.279745i
\(569\) −2.26163e11 + 2.26163e11i −0.0904516 + 0.0904516i −0.750885 0.660433i \(-0.770373\pi\)
0.660433 + 0.750885i \(0.270373\pi\)
\(570\) −1.69229e12 + 1.69229e12i −0.671486 + 0.671486i
\(571\) 3.88192e12 + 1.60795e12i 1.52822 + 0.633007i 0.979217 0.202816i \(-0.0650093\pi\)
0.548998 + 0.835823i \(0.315009\pi\)
\(572\) −1.05251e12 + 2.54097e12i −0.411095 + 0.992472i
\(573\) −1.48713e12 + 6.15990e11i −0.576307 + 0.238714i
\(574\) 1.15302e12i 0.443338i
\(575\) 8.10151e11 + 1.95588e12i 0.309073 + 0.746167i
\(576\) 1.12599e11 + 1.12599e11i 0.0426221 + 0.0426221i
\(577\) 2.55609e12 0.960029 0.480014 0.877261i \(-0.340631\pi\)
0.480014 + 0.877261i \(0.340631\pi\)
\(578\) 2.53359e12 4.09554e12i 0.944192 1.52628i
\(579\) −8.17183e11 −0.302180
\(580\) 3.55101e12 + 3.55101e12i 1.30294 + 1.30294i
\(581\) −1.95904e11 4.72955e11i −0.0713266 0.172198i
\(582\) 2.78447e12i 1.00598i
\(583\) 1.19305e12 4.94178e11i 0.427711 0.177164i
\(584\) −3.30575e12 + 7.98078e12i −1.17601 + 2.83914i
\(585\) −9.16824e11 3.79761e11i −0.323657 0.134063i
\(586\) 2.48728e12 2.48728e12i 0.871334 0.871334i
\(587\) −8.10598e11 + 8.10598e11i −0.281795 + 0.281795i −0.833825 0.552029i \(-0.813854\pi\)
0.552029 + 0.833825i \(0.313854\pi\)
\(588\) 4.09947e12 + 1.69806e12i 1.41426 + 0.585806i
\(589\) 1.30647e12 3.15409e12i 0.447281 1.07983i
\(590\) −1.37331e12 + 5.68844e11i −0.466589 + 0.193268i
\(591\) 2.73127e12i 0.920918i
\(592\) −9.41698e11 2.27346e12i −0.315111 0.760746i
\(593\) 2.15623e12 + 2.15623e12i 0.716060 + 0.716060i 0.967796 0.251736i \(-0.0810015\pi\)
−0.251736 + 0.967796i \(0.581002\pi\)
\(594\) −2.04858e12 −0.675172
\(595\) 2.57811e11 3.25616e11i 0.0843286 0.106507i
\(596\) −7.24154e12 −2.35084
\(597\) 3.04802e12 + 3.04802e12i 0.982049 + 0.982049i
\(598\) −3.43267e12 8.28719e12i −1.09768 2.65004i
\(599\) 3.29572e12i 1.04599i −0.852334 0.522997i \(-0.824814\pi\)
0.852334 0.522997i \(-0.175186\pi\)
\(600\) 3.28679e12 1.36143e12i 1.03536 0.428859i
\(601\) −2.94591e11 + 7.11206e11i −0.0921053 + 0.222362i −0.963218 0.268721i \(-0.913399\pi\)
0.871113 + 0.491083i \(0.163399\pi\)
\(602\) 1.64552e12 + 6.81596e11i 0.510644 + 0.211516i
\(603\) 4.56152e11 4.56152e11i 0.140502 0.140502i
\(604\) 7.17304e12 7.17304e12i 2.19299 2.19299i
\(605\) 1.47012e12 + 6.08945e11i 0.446123 + 0.184790i
\(606\) 1.10809e12 2.67516e12i 0.333770 0.805792i
\(607\) −1.48401e12 + 6.14696e11i −0.443698 + 0.183786i −0.593335 0.804955i \(-0.702189\pi\)
0.149638 + 0.988741i \(0.452189\pi\)
\(608\) 3.88740e12i 1.15370i
\(609\) −3.54387e11 8.55566e11i −0.104400 0.252044i
\(610\) −3.10031e12 3.10031e12i −0.906610 0.906610i
\(611\) −3.76509e12 −1.09292
\(612\) −3.53268e12 + 4.10563e11i −1.01794 + 0.118304i
\(613\) −4.16207e12 −1.19052 −0.595261 0.803533i \(-0.702951\pi\)
−0.595261 + 0.803533i \(0.702951\pi\)
\(614\) 5.10998e12 + 5.10998e12i 1.45098 + 1.45098i
\(615\) −5.49290e11 1.32610e12i −0.154833 0.373800i
\(616\) 6.77731e11i 0.189646i
\(617\) −3.62434e12 + 1.50125e12i −1.00680 + 0.417032i −0.824288 0.566171i \(-0.808424\pi\)
−0.182517 + 0.983203i \(0.558424\pi\)
\(618\) 2.83534e12 6.84511e12i 0.781909 1.88770i
\(619\) 9.58001e11 + 3.96817e11i 0.262276 + 0.108638i 0.509947 0.860206i \(-0.329665\pi\)
−0.247671 + 0.968844i \(0.579665\pi\)
\(620\) 2.84012e12 2.84012e12i 0.771924 0.771924i
\(621\) 3.25766e12 3.25766e12i 0.879009 0.879009i
\(622\) 2.69225e12 + 1.11517e12i 0.721205 + 0.298733i
\(623\) −1.65463e11 + 3.99463e11i −0.0440053 + 0.106238i
\(624\) −6.06192e12 + 2.51093e12i −1.60059 + 0.662985i
\(625\) 6.95630e11i 0.182355i
\(626\) 4.12443e12 + 9.95726e12i 1.07344 + 2.59152i
\(627\) −9.22358e11 9.22358e11i −0.238339 0.238339i
\(628\) −5.20190e12 −1.33458
\(629\) −1.81624e12 5.16373e11i −0.462642 0.131533i
\(630\) −4.44805e11 −0.112496
\(631\) 3.16412e12 + 3.16412e12i 0.794550 + 0.794550i 0.982230 0.187680i \(-0.0600968\pi\)
−0.187680 + 0.982230i \(0.560097\pi\)
\(632\) 3.11715e12 + 7.52547e12i 0.777197 + 1.87632i
\(633\) 2.58984e12i 0.641145i
\(634\) 2.83069e11 1.17251e11i 0.0695809 0.0288213i
\(635\) 1.04284e11 2.51763e11i 0.0254528 0.0614484i
\(636\) 8.20130e12 + 3.39709e12i 1.98758 + 0.823284i
\(637\) −3.80514e12 + 3.80514e12i −0.915678 + 0.915678i
\(638\) −2.80684e12 + 2.80684e12i −0.670694 + 0.670694i
\(639\) 5.99299e11 + 2.48238e11i 0.142197 + 0.0588998i
\(640\) −9.97705e11 + 2.40867e12i −0.235067 + 0.567503i
\(641\) −6.72575e10 + 2.78590e10i −0.0157355 + 0.00651784i −0.390537 0.920587i \(-0.627711\pi\)
0.374802 + 0.927105i \(0.377711\pi\)
\(642\) 3.23228e12i 0.750932i
\(643\) 7.12120e10 + 1.71921e11i 0.0164287 + 0.0396625i 0.931881 0.362764i \(-0.118167\pi\)
−0.915452 + 0.402426i \(0.868167\pi\)
\(644\) −1.96036e12 1.96036e12i −0.449106 0.449106i
\(645\) −2.21723e12 −0.504421
\(646\) −8.15511e12 6.45692e12i −1.84240 1.45874i
\(647\) 2.89537e12 0.649583 0.324791 0.945786i \(-0.394706\pi\)
0.324791 + 0.945786i \(0.394706\pi\)
\(648\) −2.26530e12 2.26530e12i −0.504705 0.504705i
\(649\) −3.10041e11 7.48505e11i −0.0685990 0.165613i
\(650\) 7.84793e12i 1.72443i
\(651\) −6.84288e11 + 2.83442e11i −0.149322 + 0.0618513i
\(652\) −2.87713e12 + 6.94600e12i −0.623512 + 1.50529i
\(653\) −4.12850e12 1.71008e12i −0.888551 0.368050i −0.108744 0.994070i \(-0.534683\pi\)
−0.779807 + 0.626020i \(0.784683\pi\)
\(654\) −6.26881e12 + 6.26881e12i −1.33994 + 1.33994i
\(655\) 1.42946e12 1.42946e12i 0.303448 0.303448i
\(656\) 7.51134e12 + 3.11130e12i 1.58362 + 0.655956i
\(657\) 1.18252e12 2.85485e12i 0.247607 0.597777i
\(658\) −1.55916e12 + 6.45823e11i −0.324245 + 0.134307i
\(659\) 4.32558e12i 0.893429i −0.894677 0.446714i \(-0.852594\pi\)
0.894677 0.446714i \(-0.147406\pi\)
\(660\) −5.87283e11 1.41783e12i −0.120476 0.290854i
\(661\) −2.46897e12 2.46897e12i −0.503048 0.503048i 0.409336 0.912384i \(-0.365760\pi\)
−0.912384 + 0.409336i \(0.865760\pi\)
\(662\) 1.07021e13 2.16575
\(663\) −1.37685e12 + 4.84279e12i −0.276742 + 0.973386i
\(664\) −8.29269e12 −1.65554
\(665\) −6.34316e11 6.34316e11i −0.125779 0.125779i
\(666\) 7.73885e11 + 1.86832e12i 0.152420 + 0.367975i
\(667\) 8.92687e12i 1.74636i
\(668\) 1.36631e13 5.65943e12i 2.65494 1.09971i
\(669\) −1.35085e12 + 3.26125e12i −0.260730 + 0.629457i
\(670\) 2.05080e12 + 8.49471e11i 0.393176 + 0.162859i
\(671\) 1.68978e12 1.68978e12i 0.321795 0.321795i
\(672\) −5.96360e11 + 5.96360e11i −0.112810 + 0.112810i
\(673\) −6.50255e12 2.69344e12i −1.22184 0.506104i −0.323849 0.946109i \(-0.604977\pi\)
−0.897996 + 0.440005i \(0.854977\pi\)
\(674\) 1.44032e12 3.47725e12i 0.268838 0.649032i
\(675\) −3.72391e12 + 1.54249e12i −0.690450 + 0.285994i
\(676\) 1.08696e13i 2.00196i
\(677\) −2.06108e12 4.97588e12i −0.377091 0.910377i −0.992508 0.122176i \(-0.961013\pi\)
0.615418 0.788201i \(-0.288987\pi\)
\(678\) −6.54336e12 6.54336e12i −1.18923 1.18923i
\(679\) 1.04370e12 0.188434
\(680\) −3.27497e12 5.87694e12i −0.587378 1.05405i
\(681\) 4.04120e12 0.720026
\(682\) 2.24493e12 + 2.24493e12i 0.397350 + 0.397350i
\(683\) 1.36929e12 + 3.30576e12i 0.240770 + 0.581269i 0.997360 0.0726201i \(-0.0231361\pi\)
−0.756590 + 0.653890i \(0.773136\pi\)
\(684\) 7.68164e12i 1.34184i
\(685\) −2.78089e12 + 1.15188e12i −0.482588 + 0.199894i
\(686\) −1.90592e12 + 4.60130e12i −0.328584 + 0.793271i
\(687\) 3.04109e12 + 1.25966e12i 0.520863 + 0.215749i
\(688\) 8.88048e12 8.88048e12i 1.51108 1.51108i
\(689\) −7.61246e12 + 7.61246e12i −1.28688 + 1.28688i
\(690\) 4.62413e12 + 1.91538e12i 0.776621 + 0.321687i
\(691\) 3.58248e12 8.64886e12i 0.597767 1.44314i −0.278084 0.960557i \(-0.589699\pi\)
0.875851 0.482581i \(-0.160301\pi\)
\(692\) 4.27901e12 1.77242e12i 0.709359 0.293826i
\(693\) 2.42435e11i 0.0399297i
\(694\) 2.58783e12 + 6.24759e12i 0.423466 + 1.02234i
\(695\) 2.01054e12 + 2.01054e12i 0.326874 + 0.326874i
\(696\) −1.50013e13 −2.42319
\(697\) 5.44952e12 3.03679e12i 0.874602 0.487379i
\(698\) 1.01004e13 1.61061
\(699\) −6.25953e12 6.25953e12i −0.991732 0.991732i
\(700\) 9.28226e11 + 2.24093e12i 0.146121 + 0.352767i
\(701\) 7.85905e12i 1.22925i 0.788821 + 0.614624i \(0.210692\pi\)
−0.788821 + 0.614624i \(0.789308\pi\)
\(702\) 1.57785e13 6.53565e12i 2.45215 1.01572i
\(703\) −1.56073e12 + 3.76793e12i −0.241006 + 0.581841i
\(704\) −2.75915e11 1.14288e11i −0.0423349 0.0175357i
\(705\) 1.48554e12 1.48554e12i 0.226481 0.226481i
\(706\) −6.37599e11 + 6.37599e11i −0.0965887 + 0.0965887i
\(707\) 1.00272e12 + 4.15342e11i 0.150936 + 0.0625199i
\(708\) 2.13129e12 5.14538e12i 0.318781 0.769605i
\(709\) 6.68205e12 2.76780e12i 0.993120 0.411364i 0.173850 0.984772i \(-0.444379\pi\)
0.819270 + 0.573408i \(0.194379\pi\)
\(710\) 2.23209e12i 0.329647i
\(711\) −1.11505e12 2.69198e12i −0.163637 0.395056i
\(712\) 4.95265e12 + 4.95265e12i 0.722233 + 0.722233i
\(713\) −7.13978e12 −1.03462
\(714\) 2.60517e11 + 2.24161e12i 0.0375140 + 0.322789i
\(715\) 1.86115e12 0.266320
\(716\) −1.98789e13 1.98789e13i −2.82673 2.82673i
\(717\) 1.29049e12 + 3.11551e12i 0.182355 + 0.440244i
\(718\) 1.30586e13i 1.83374i
\(719\) −3.17136e12 + 1.31362e12i −0.442553 + 0.183312i −0.592822 0.805334i \(-0.701986\pi\)
0.150269 + 0.988645i \(0.451986\pi\)
\(720\) −1.20025e12 + 2.89767e12i −0.166447 + 0.401839i
\(721\) 2.56574e12 + 1.06276e12i 0.353593 + 0.146463i
\(722\) −6.62037e12 + 6.62037e12i −0.906703 + 0.906703i
\(723\) 1.67202e11 1.67202e11i 0.0227572 0.0227572i
\(724\) −3.75803e12 1.55663e12i −0.508320 0.210553i
\(725\) −2.98884e12 + 7.21569e12i −0.401774 + 0.969967i
\(726\) −7.98809e12 + 3.30877e12i −1.06716 + 0.442030i
\(727\) 4.17490e12i 0.554295i 0.960827 + 0.277148i \(0.0893891\pi\)
−0.960827 + 0.277148i \(0.910611\pi\)
\(728\) −2.16219e12 5.21998e12i −0.285300 0.688775i
\(729\) 5.05450e12 + 5.05450e12i 0.662834 + 0.662834i
\(730\) 1.06329e13 1.38579
\(731\) −1.11248e12 9.57235e12i −0.144100 1.23991i
\(732\) 1.64274e13 2.11480
\(733\) −3.74549e11 3.74549e11i −0.0479227 0.0479227i 0.682739 0.730662i \(-0.260788\pi\)
−0.730662 + 0.682739i \(0.760788\pi\)
\(734\) 5.97270e11 + 1.44194e12i 0.0759519 + 0.183364i
\(735\) 3.00267e12i 0.379503i
\(736\) −7.51105e12 + 3.11118e12i −0.943518 + 0.390818i
\(737\) −4.62993e11 + 1.11776e12i −0.0578057 + 0.139555i
\(738\) −6.17280e12 2.55686e12i −0.766000 0.317288i
\(739\) 3.53280e12 3.53280e12i 0.435731 0.435731i −0.454841 0.890573i \(-0.650304\pi\)
0.890573 + 0.454841i \(0.150304\pi\)
\(740\) −3.39286e12 + 3.39286e12i −0.415933 + 0.415933i
\(741\) 1.00468e13 + 4.16150e12i 1.22418 + 0.507071i
\(742\) −1.84662e12 + 4.45814e12i −0.223646 + 0.539929i
\(743\) 3.92286e12 1.62490e12i 0.472230 0.195604i −0.133860 0.991000i \(-0.542737\pi\)
0.606090 + 0.795396i \(0.292737\pi\)
\(744\) 1.19982e13i 1.43561i
\(745\) 1.87528e12 + 4.52732e12i 0.223030 + 0.538441i
\(746\) −8.03568e12 8.03568e12i −0.949944 0.949944i
\(747\) 2.96643e12 0.348571
\(748\) 5.82644e12 3.24683e12i 0.680528 0.379230i
\(749\) −1.21155e12 −0.140660
\(750\) −7.54017e12 7.54017e12i −0.870173 0.870173i
\(751\) 6.18621e12 + 1.49348e13i 0.709651 + 1.71325i 0.700870 + 0.713289i \(0.252795\pi\)
0.00878097 + 0.999961i \(0.497205\pi\)
\(752\) 1.18998e13i 1.35693i
\(753\) −4.08969e12 + 1.69401e12i −0.463568 + 0.192016i
\(754\) 1.26639e13 3.05734e13i 1.42691 3.44487i
\(755\) −6.34204e12 2.62696e12i −0.710342 0.294233i
\(756\) 3.73244e12 3.73244e12i 0.415571 0.415571i
\(757\) 1.16982e13 1.16982e13i 1.29475 1.29475i 0.362939 0.931813i \(-0.381773\pi\)
0.931813 0.362939i \(-0.118227\pi\)
\(758\) −8.24540e12 3.41536e12i −0.907194 0.375772i
\(759\) −1.04395e12 + 2.52032e12i −0.114181 + 0.275656i
\(760\) −1.34254e13 + 5.56098e12i −1.45971 + 0.604630i
\(761\) 4.75009e12i 0.513418i −0.966489 0.256709i \(-0.917362\pi\)
0.966489 0.256709i \(-0.0826382\pi\)
\(762\)