Properties

Label 177.11.c.a.58.11
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.11
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.90

$q$-expansion

\(f(q)\) \(=\) \(q-53.2620i q^{2} -140.296 q^{3} -1812.84 q^{4} +3919.09 q^{5} +7472.46i q^{6} +33417.1 q^{7} +42015.4i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-53.2620i q^{2} -140.296 q^{3} -1812.84 q^{4} +3919.09 q^{5} +7472.46i q^{6} +33417.1 q^{7} +42015.4i q^{8} +19683.0 q^{9} -208739. i q^{10} -106418. i q^{11} +254335. q^{12} +359376. i q^{13} -1.77986e6i q^{14} -549833. q^{15} +381474. q^{16} +20865.6 q^{17} -1.04836e6i q^{18} +2.00076e6 q^{19} -7.10470e6 q^{20} -4.68829e6 q^{21} -5.66805e6 q^{22} +7.42032e6i q^{23} -5.89460e6i q^{24} +5.59365e6 q^{25} +1.91411e7 q^{26} -2.76145e6 q^{27} -6.05800e7 q^{28} -1.04434e7 q^{29} +2.92852e7i q^{30} -2.79714e7i q^{31} +2.27057e7i q^{32} +1.49301e7i q^{33} -1.11135e6i q^{34} +1.30965e8 q^{35} -3.56822e7 q^{36} -6.88027e7i q^{37} -1.06565e8i q^{38} -5.04190e7i q^{39} +1.64662e8i q^{40} +1.66483e8 q^{41} +2.49708e8i q^{42} +1.90640e8i q^{43} +1.92920e8i q^{44} +7.71395e7 q^{45} +3.95221e8 q^{46} -5.17915e7i q^{47} -5.35193e7 q^{48} +8.34228e8 q^{49} -2.97929e8i q^{50} -2.92737e6 q^{51} -6.51492e8i q^{52} +7.24197e7 q^{53} +1.47080e8i q^{54} -4.17063e8i q^{55} +1.40403e9i q^{56} -2.80699e8 q^{57} +5.56237e8i q^{58} +(4.01714e8 - 5.91390e8i) q^{59} +9.96762e8 q^{60} +8.18823e8i q^{61} -1.48981e9 q^{62} +6.57749e8 q^{63} +1.59998e9 q^{64} +1.40843e9i q^{65} +7.95205e8 q^{66} +7.49122e8i q^{67} -3.78261e7 q^{68} -1.04104e9i q^{69} -6.97545e9i q^{70} -1.37407e9 q^{71} +8.26989e8i q^{72} -2.48055e9i q^{73} -3.66457e9 q^{74} -7.84767e8 q^{75} -3.62706e9 q^{76} -3.55619e9i q^{77} -2.68542e9 q^{78} +5.64088e9 q^{79} +1.49503e9 q^{80} +3.87420e8 q^{81} -8.86723e9i q^{82} -1.03817e9i q^{83} +8.49914e9 q^{84} +8.17743e7 q^{85} +1.01539e10 q^{86} +1.46517e9 q^{87} +4.47120e9 q^{88} +4.10346e9i q^{89} -4.10860e9i q^{90} +1.20093e10i q^{91} -1.34519e10i q^{92} +3.92428e9i q^{93} -2.75852e9 q^{94} +7.84116e9 q^{95} -3.18552e9i q^{96} +1.42779e10i q^{97} -4.44327e10i q^{98} -2.09463e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 53.2620i 1.66444i −0.554447 0.832219i \(-0.687070\pi\)
0.554447 0.832219i \(-0.312930\pi\)
\(3\) −140.296 −0.577350
\(4\) −1812.84 −1.77035
\(5\) 3919.09 1.25411 0.627055 0.778975i \(-0.284260\pi\)
0.627055 + 0.778975i \(0.284260\pi\)
\(6\) 7472.46i 0.960964i
\(7\) 33417.1 1.98829 0.994143 0.108074i \(-0.0344684\pi\)
0.994143 + 0.108074i \(0.0344684\pi\)
\(8\) 42015.4i 1.28221i
\(9\) 19683.0 0.333333
\(10\) 208739.i 2.08739i
\(11\) 106418.i 0.660773i −0.943846 0.330387i \(-0.892821\pi\)
0.943846 0.330387i \(-0.107179\pi\)
\(12\) 254335. 1.02211
\(13\) 359376.i 0.967903i 0.875095 + 0.483951i \(0.160799\pi\)
−0.875095 + 0.483951i \(0.839201\pi\)
\(14\) 1.77986e6i 3.30938i
\(15\) −549833. −0.724060
\(16\) 381474. 0.363802
\(17\) 20865.6 0.0146956 0.00734780 0.999973i \(-0.497661\pi\)
0.00734780 + 0.999973i \(0.497661\pi\)
\(18\) 1.04836e6i 0.554813i
\(19\) 2.00076e6 0.808029 0.404015 0.914753i \(-0.367615\pi\)
0.404015 + 0.914753i \(0.367615\pi\)
\(20\) −7.10470e6 −2.22022
\(21\) −4.68829e6 −1.14794
\(22\) −5.66805e6 −1.09982
\(23\) 7.42032e6i 1.15288i 0.817140 + 0.576439i \(0.195558\pi\)
−0.817140 + 0.576439i \(0.804442\pi\)
\(24\) 5.89460e6i 0.740283i
\(25\) 5.59365e6 0.572790
\(26\) 1.91411e7 1.61101
\(27\) −2.76145e6 −0.192450
\(28\) −6.05800e7 −3.51997
\(29\) −1.04434e7 −0.509158 −0.254579 0.967052i \(-0.581937\pi\)
−0.254579 + 0.967052i \(0.581937\pi\)
\(30\) 2.92852e7i 1.20515i
\(31\) 2.79714e7i 0.977025i −0.872557 0.488512i \(-0.837540\pi\)
0.872557 0.488512i \(-0.162460\pi\)
\(32\) 2.27057e7i 0.676683i
\(33\) 1.49301e7i 0.381498i
\(34\) 1.11135e6i 0.0244599i
\(35\) 1.30965e8 2.49353
\(36\) −3.56822e7 −0.590118
\(37\) 6.88027e7i 0.992194i −0.868267 0.496097i \(-0.834766\pi\)
0.868267 0.496097i \(-0.165234\pi\)
\(38\) 1.06565e8i 1.34491i
\(39\) 5.04190e7i 0.558819i
\(40\) 1.64662e8i 1.60803i
\(41\) 1.66483e8 1.43698 0.718491 0.695536i \(-0.244833\pi\)
0.718491 + 0.695536i \(0.244833\pi\)
\(42\) 2.49708e8i 1.91067i
\(43\) 1.90640e8i 1.29680i 0.761302 + 0.648398i \(0.224561\pi\)
−0.761302 + 0.648398i \(0.775439\pi\)
\(44\) 1.92920e8i 1.16980i
\(45\) 7.71395e7 0.418036
\(46\) 3.95221e8 1.91889
\(47\) 5.17915e7i 0.225823i −0.993605 0.112912i \(-0.963982\pi\)
0.993605 0.112912i \(-0.0360177\pi\)
\(48\) −5.35193e7 −0.210041
\(49\) 8.34228e8 2.95328
\(50\) 2.97929e8i 0.953373i
\(51\) −2.92737e6 −0.00848450
\(52\) 6.51492e8i 1.71353i
\(53\) 7.24197e7 0.173172 0.0865860 0.996244i \(-0.472404\pi\)
0.0865860 + 0.996244i \(0.472404\pi\)
\(54\) 1.47080e8i 0.320321i
\(55\) 4.17063e8i 0.828682i
\(56\) 1.40403e9i 2.54940i
\(57\) −2.80699e8 −0.466516
\(58\) 5.56237e8i 0.847462i
\(59\) 4.01714e8 5.91390e8i 0.561897 0.827207i
\(60\) 9.96762e8 1.28184
\(61\) 8.18823e8i 0.969484i 0.874657 + 0.484742i \(0.161087\pi\)
−0.874657 + 0.484742i \(0.838913\pi\)
\(62\) −1.48981e9 −1.62620
\(63\) 6.57749e8 0.662762
\(64\) 1.59998e9 1.49010
\(65\) 1.40843e9i 1.21386i
\(66\) 7.95205e8 0.634979
\(67\) 7.49122e8i 0.554854i 0.960747 + 0.277427i \(0.0894816\pi\)
−0.960747 + 0.277427i \(0.910518\pi\)
\(68\) −3.78261e7 −0.0260164
\(69\) 1.04104e9i 0.665614i
\(70\) 6.97545e9i 4.15032i
\(71\) −1.37407e9 −0.761582 −0.380791 0.924661i \(-0.624348\pi\)
−0.380791 + 0.924661i \(0.624348\pi\)
\(72\) 8.26989e8i 0.427403i
\(73\) 2.48055e9i 1.19656i −0.801288 0.598279i \(-0.795851\pi\)
0.801288 0.598279i \(-0.204149\pi\)
\(74\) −3.66457e9 −1.65145
\(75\) −7.84767e8 −0.330700
\(76\) −3.62706e9 −1.43050
\(77\) 3.55619e9i 1.31381i
\(78\) −2.68542e9 −0.930120
\(79\) 5.64088e9 1.83321 0.916604 0.399797i \(-0.130919\pi\)
0.916604 + 0.399797i \(0.130919\pi\)
\(80\) 1.49503e9 0.456247
\(81\) 3.87420e8 0.111111
\(82\) 8.86723e9i 2.39177i
\(83\) 1.03817e9i 0.263558i −0.991279 0.131779i \(-0.957931\pi\)
0.991279 0.131779i \(-0.0420690\pi\)
\(84\) 8.49914e9 2.03226
\(85\) 8.17743e7 0.0184299
\(86\) 1.01539e10 2.15844
\(87\) 1.46517e9 0.293962
\(88\) 4.47120e9 0.847249
\(89\) 4.10346e9i 0.734853i 0.930053 + 0.367426i \(0.119761\pi\)
−0.930053 + 0.367426i \(0.880239\pi\)
\(90\) 4.10860e9i 0.695796i
\(91\) 1.20093e10i 1.92447i
\(92\) 1.34519e10i 2.04100i
\(93\) 3.92428e9i 0.564085i
\(94\) −2.75852e9 −0.375869
\(95\) 7.84116e9 1.01336
\(96\) 3.18552e9i 0.390683i
\(97\) 1.42779e10i 1.66267i 0.555769 + 0.831337i \(0.312424\pi\)
−0.555769 + 0.831337i \(0.687576\pi\)
\(98\) 4.44327e10i 4.91555i
\(99\) 2.09463e9i 0.220258i
\(100\) −1.01404e10 −1.01404
\(101\) 1.51177e10i 1.43840i −0.694802 0.719201i \(-0.744508\pi\)
0.694802 0.719201i \(-0.255492\pi\)
\(102\) 1.55918e8i 0.0141219i
\(103\) 1.02128e10i 0.880968i 0.897760 + 0.440484i \(0.145193\pi\)
−0.897760 + 0.440484i \(0.854807\pi\)
\(104\) −1.50993e10 −1.24105
\(105\) −1.83738e10 −1.43964
\(106\) 3.85722e9i 0.288234i
\(107\) 8.79307e9 0.626933 0.313467 0.949599i \(-0.398510\pi\)
0.313467 + 0.949599i \(0.398510\pi\)
\(108\) 5.00607e9 0.340705
\(109\) 5.87428e9i 0.381788i 0.981611 + 0.190894i \(0.0611387\pi\)
−0.981611 + 0.190894i \(0.938861\pi\)
\(110\) −2.22136e10 −1.37929
\(111\) 9.65275e9i 0.572844i
\(112\) 1.27477e10 0.723341
\(113\) 8.58791e9i 0.466117i −0.972463 0.233059i \(-0.925127\pi\)
0.972463 0.233059i \(-0.0748734\pi\)
\(114\) 1.49506e10i 0.776487i
\(115\) 2.90809e10i 1.44583i
\(116\) 1.89323e10 0.901390
\(117\) 7.07359e9i 0.322634i
\(118\) −3.14987e10 2.13961e10i −1.37684 0.935243i
\(119\) 6.97270e8 0.0292190
\(120\) 2.31015e10i 0.928396i
\(121\) 1.46126e10 0.563379
\(122\) 4.36122e10 1.61365
\(123\) −2.33570e10 −0.829642
\(124\) 5.07077e10i 1.72968i
\(125\) −1.63504e10 −0.535768
\(126\) 3.50331e10i 1.10313i
\(127\) 3.86487e8 0.0116981 0.00584907 0.999983i \(-0.498138\pi\)
0.00584907 + 0.999983i \(0.498138\pi\)
\(128\) 6.19676e10i 1.80349i
\(129\) 2.67460e10i 0.748705i
\(130\) 7.50156e10 2.02039
\(131\) 1.28381e10i 0.332769i 0.986061 + 0.166385i \(0.0532094\pi\)
−0.986061 + 0.166385i \(0.946791\pi\)
\(132\) 2.70659e10i 0.675386i
\(133\) 6.68596e10 1.60659
\(134\) 3.98997e10 0.923520
\(135\) −1.08224e10 −0.241353
\(136\) 8.76678e8i 0.0188428i
\(137\) 2.40665e10 0.498666 0.249333 0.968418i \(-0.419789\pi\)
0.249333 + 0.968418i \(0.419789\pi\)
\(138\) −5.54480e10 −1.10787
\(139\) 6.39766e10 1.23295 0.616477 0.787373i \(-0.288559\pi\)
0.616477 + 0.787373i \(0.288559\pi\)
\(140\) −2.37419e11 −4.41443
\(141\) 7.26614e9i 0.130379i
\(142\) 7.31856e10i 1.26761i
\(143\) 3.82441e10 0.639564
\(144\) 7.50855e9 0.121267
\(145\) −4.09287e10 −0.638539
\(146\) −1.32119e11 −1.99160
\(147\) −1.17039e11 −1.70508
\(148\) 1.24728e11i 1.75654i
\(149\) 1.48199e10i 0.201796i 0.994897 + 0.100898i \(0.0321716\pi\)
−0.994897 + 0.100898i \(0.967828\pi\)
\(150\) 4.17983e10i 0.550430i
\(151\) 9.56084e9i 0.121790i 0.998144 + 0.0608950i \(0.0193955\pi\)
−0.998144 + 0.0608950i \(0.980605\pi\)
\(152\) 8.40627e10i 1.03606i
\(153\) 4.10698e8 0.00489853
\(154\) −1.89410e11 −2.18675
\(155\) 1.09622e11i 1.22530i
\(156\) 9.14017e10i 0.989308i
\(157\) 1.61171e11i 1.68961i −0.535070 0.844807i \(-0.679715\pi\)
0.535070 0.844807i \(-0.320285\pi\)
\(158\) 3.00445e11i 3.05126i
\(159\) −1.01602e10 −0.0999809
\(160\) 8.89857e10i 0.848634i
\(161\) 2.47966e11i 2.29225i
\(162\) 2.06348e10i 0.184938i
\(163\) −2.19867e11 −1.91083 −0.955415 0.295266i \(-0.904592\pi\)
−0.955415 + 0.295266i \(0.904592\pi\)
\(164\) −3.01808e11 −2.54397
\(165\) 5.85123e10i 0.478440i
\(166\) −5.52949e10 −0.438676
\(167\) −1.07295e11 −0.826031 −0.413016 0.910724i \(-0.635525\pi\)
−0.413016 + 0.910724i \(0.635525\pi\)
\(168\) 1.96980e11i 1.47189i
\(169\) 8.70774e9 0.0631643
\(170\) 4.35547e9i 0.0306754i
\(171\) 3.93810e10 0.269343
\(172\) 3.45600e11i 2.29579i
\(173\) 7.34928e9i 0.0474258i −0.999719 0.0237129i \(-0.992451\pi\)
0.999719 0.0237129i \(-0.00754875\pi\)
\(174\) 7.80379e10i 0.489282i
\(175\) 1.86924e11 1.13887
\(176\) 4.05957e10i 0.240390i
\(177\) −5.63589e10 + 8.29698e10i −0.324411 + 0.477588i
\(178\) 2.18559e11 1.22312
\(179\) 2.35454e11i 1.28127i −0.767845 0.640636i \(-0.778671\pi\)
0.767845 0.640636i \(-0.221329\pi\)
\(180\) −1.39842e11 −0.740073
\(181\) −2.44056e11 −1.25631 −0.628156 0.778088i \(-0.716190\pi\)
−0.628156 + 0.778088i \(0.716190\pi\)
\(182\) 6.39639e11 3.20316
\(183\) 1.14878e11i 0.559732i
\(184\) −3.11768e11 −1.47823
\(185\) 2.69644e11i 1.24432i
\(186\) 2.09015e11 0.938885
\(187\) 2.22048e9i 0.00971046i
\(188\) 9.38898e10i 0.399787i
\(189\) −9.22796e10 −0.382646
\(190\) 4.17636e11i 1.68667i
\(191\) 4.10598e10i 0.161529i −0.996733 0.0807643i \(-0.974264\pi\)
0.996733 0.0807643i \(-0.0257361\pi\)
\(192\) −2.24471e11 −0.860309
\(193\) −2.03753e11 −0.760882 −0.380441 0.924805i \(-0.624228\pi\)
−0.380441 + 0.924805i \(0.624228\pi\)
\(194\) 7.60472e11 2.76742
\(195\) 1.97597e11i 0.700820i
\(196\) −1.51233e12 −5.22835
\(197\) 4.28827e11 1.44528 0.722639 0.691226i \(-0.242929\pi\)
0.722639 + 0.691226i \(0.242929\pi\)
\(198\) −1.11564e11 −0.366605
\(199\) 3.84437e11 1.23185 0.615927 0.787803i \(-0.288782\pi\)
0.615927 + 0.787803i \(0.288782\pi\)
\(200\) 2.35019e11i 0.734436i
\(201\) 1.05099e11i 0.320345i
\(202\) −8.05202e11 −2.39413
\(203\) −3.48989e11 −1.01235
\(204\) 5.30686e9 0.0150206
\(205\) 6.52463e11 1.80213
\(206\) 5.43956e11 1.46632
\(207\) 1.46054e11i 0.384293i
\(208\) 1.37092e11i 0.352125i
\(209\) 2.12917e11i 0.533924i
\(210\) 9.78628e11i 2.39619i
\(211\) 4.71673e11i 1.12779i 0.825846 + 0.563895i \(0.190698\pi\)
−0.825846 + 0.563895i \(0.809302\pi\)
\(212\) −1.31286e11 −0.306576
\(213\) 1.92776e11 0.439699
\(214\) 4.68337e11i 1.04349i
\(215\) 7.47135e11i 1.62632i
\(216\) 1.16023e11i 0.246761i
\(217\) 9.34723e11i 1.94260i
\(218\) 3.12876e11 0.635463
\(219\) 3.48012e11i 0.690834i
\(220\) 7.56069e11i 1.46706i
\(221\) 7.49860e9i 0.0142239i
\(222\) 5.14125e11 0.953463
\(223\) 1.68130e11 0.304874 0.152437 0.988313i \(-0.451288\pi\)
0.152437 + 0.988313i \(0.451288\pi\)
\(224\) 7.58759e11i 1.34544i
\(225\) 1.10100e11 0.190930
\(226\) −4.57409e11 −0.775823
\(227\) 9.48249e11i 1.57323i −0.617442 0.786616i \(-0.711831\pi\)
0.617442 0.786616i \(-0.288169\pi\)
\(228\) 5.08863e11 0.825898
\(229\) 1.07967e12i 1.71441i −0.514978 0.857203i \(-0.672200\pi\)
0.514978 0.857203i \(-0.327800\pi\)
\(230\) 1.54891e12 2.40650
\(231\) 4.98920e11i 0.758526i
\(232\) 4.38784e11i 0.652846i
\(233\) 9.34518e11i 1.36084i −0.732821 0.680421i \(-0.761797\pi\)
0.732821 0.680421i \(-0.238203\pi\)
\(234\) 3.76754e11 0.537005
\(235\) 2.02975e11i 0.283207i
\(236\) −7.28244e11 + 1.07210e12i −0.994757 + 1.46445i
\(237\) −7.91394e11 −1.05840
\(238\) 3.71380e10i 0.0486333i
\(239\) −3.82544e11 −0.490560 −0.245280 0.969452i \(-0.578880\pi\)
−0.245280 + 0.969452i \(0.578880\pi\)
\(240\) −2.09747e11 −0.263414
\(241\) 9.57291e11 1.17749 0.588747 0.808317i \(-0.299621\pi\)
0.588747 + 0.808317i \(0.299621\pi\)
\(242\) 7.78296e11i 0.937709i
\(243\) −5.43536e10 −0.0641500
\(244\) 1.48440e12i 1.71633i
\(245\) 3.26942e12 3.70374
\(246\) 1.24404e12i 1.38089i
\(247\) 7.19024e11i 0.782093i
\(248\) 1.17523e12 1.25275
\(249\) 1.45651e11i 0.152165i
\(250\) 8.70853e11i 0.891753i
\(251\) −4.55446e10 −0.0457160 −0.0228580 0.999739i \(-0.507277\pi\)
−0.0228580 + 0.999739i \(0.507277\pi\)
\(252\) −1.19240e12 −1.17332
\(253\) 7.89657e11 0.761791
\(254\) 2.05851e10i 0.0194708i
\(255\) −1.14726e10 −0.0106405
\(256\) −1.66214e12 −1.51171
\(257\) −1.22550e12 −1.09307 −0.546536 0.837436i \(-0.684054\pi\)
−0.546536 + 0.837436i \(0.684054\pi\)
\(258\) −1.42455e12 −1.24617
\(259\) 2.29919e12i 1.97277i
\(260\) 2.55325e12i 2.14896i
\(261\) −2.05558e11 −0.169719
\(262\) 6.83782e11 0.553874
\(263\) −6.51338e11 −0.517640 −0.258820 0.965926i \(-0.583334\pi\)
−0.258820 + 0.965926i \(0.583334\pi\)
\(264\) −6.27292e11 −0.489159
\(265\) 2.83820e11 0.217177
\(266\) 3.56108e12i 2.67407i
\(267\) 5.75700e11i 0.424268i
\(268\) 1.35804e12i 0.982288i
\(269\) 1.20428e11i 0.0855000i 0.999086 + 0.0427500i \(0.0136119\pi\)
−0.999086 + 0.0427500i \(0.986388\pi\)
\(270\) 5.76421e11i 0.401718i
\(271\) −1.19542e12 −0.817854 −0.408927 0.912567i \(-0.634097\pi\)
−0.408927 + 0.912567i \(0.634097\pi\)
\(272\) 7.95969e9 0.00534628
\(273\) 1.68486e12i 1.11109i
\(274\) 1.28183e12i 0.829998i
\(275\) 5.95266e11i 0.378484i
\(276\) 1.88725e12i 1.17837i
\(277\) 8.81594e11 0.540592 0.270296 0.962777i \(-0.412878\pi\)
0.270296 + 0.962777i \(0.412878\pi\)
\(278\) 3.40752e12i 2.05218i
\(279\) 5.50561e11i 0.325675i
\(280\) 5.50254e12i 3.19722i
\(281\) −1.00101e12 −0.571356 −0.285678 0.958326i \(-0.592219\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(282\) 3.87009e11 0.217008
\(283\) 2.60213e12i 1.43350i 0.697332 + 0.716748i \(0.254370\pi\)
−0.697332 + 0.716748i \(0.745630\pi\)
\(284\) 2.49097e12 1.34827
\(285\) −1.10008e12 −0.585062
\(286\) 2.03696e12i 1.06452i
\(287\) 5.56339e12 2.85713
\(288\) 4.46917e11i 0.225561i
\(289\) −2.01556e12 −0.999784
\(290\) 2.17994e12i 1.06281i
\(291\) 2.00314e12i 0.959945i
\(292\) 4.49685e12i 2.11833i
\(293\) 1.90454e12 0.881967 0.440984 0.897515i \(-0.354630\pi\)
0.440984 + 0.897515i \(0.354630\pi\)
\(294\) 6.23374e12i 2.83800i
\(295\) 1.57435e12 2.31771e12i 0.704680 1.03741i
\(296\) 2.89077e12 1.27220
\(297\) 2.93868e11i 0.127166i
\(298\) 7.89336e11 0.335877
\(299\) −2.66668e12 −1.11587
\(300\) 1.42266e12 0.585457
\(301\) 6.37063e12i 2.57840i
\(302\) 5.09230e11 0.202712
\(303\) 2.12096e12i 0.830462i
\(304\) 7.63237e11 0.293962
\(305\) 3.20904e12i 1.21584i
\(306\) 2.18746e10i 0.00815330i
\(307\) −3.59170e12 −1.31707 −0.658533 0.752552i \(-0.728823\pi\)
−0.658533 + 0.752552i \(0.728823\pi\)
\(308\) 6.44682e12i 2.32590i
\(309\) 1.43282e12i 0.508627i
\(310\) −5.83871e12 −2.03943
\(311\) −4.45288e12 −1.53052 −0.765261 0.643721i \(-0.777390\pi\)
−0.765261 + 0.643721i \(0.777390\pi\)
\(312\) 2.11837e12 0.716522
\(313\) 3.68117e12i 1.22536i 0.790330 + 0.612681i \(0.209909\pi\)
−0.790330 + 0.612681i \(0.790091\pi\)
\(314\) −8.58428e12 −2.81226
\(315\) 2.57778e12 0.831176
\(316\) −1.02260e13 −3.24543
\(317\) 2.44545e12 0.763947 0.381974 0.924173i \(-0.375245\pi\)
0.381974 + 0.924173i \(0.375245\pi\)
\(318\) 5.41153e11i 0.166412i
\(319\) 1.11137e12i 0.336438i
\(320\) 6.27047e12 1.86875
\(321\) −1.23363e12 −0.361960
\(322\) 1.32072e13 3.81531
\(323\) 4.17471e10 0.0118745
\(324\) −7.02333e11 −0.196706
\(325\) 2.01022e12i 0.554405i
\(326\) 1.17106e13i 3.18046i
\(327\) 8.24139e11i 0.220426i
\(328\) 6.99486e12i 1.84251i
\(329\) 1.73072e12i 0.449001i
\(330\) 3.11648e12 0.796333
\(331\) 5.22488e11 0.131503 0.0657517 0.997836i \(-0.479055\pi\)
0.0657517 + 0.997836i \(0.479055\pi\)
\(332\) 1.88203e12i 0.466592i
\(333\) 1.35424e12i 0.330731i
\(334\) 5.71474e12i 1.37488i
\(335\) 2.93588e12i 0.695847i
\(336\) −1.78846e12 −0.417621
\(337\) 1.68684e12i 0.388083i −0.980993 0.194041i \(-0.937840\pi\)
0.980993 0.194041i \(-0.0621596\pi\)
\(338\) 4.63792e11i 0.105133i
\(339\) 1.20485e12i 0.269113i
\(340\) −1.48244e11 −0.0326274
\(341\) −2.97666e12 −0.645592
\(342\) 2.09751e12i 0.448305i
\(343\) 1.84380e13 3.88368
\(344\) −8.00981e12 −1.66276
\(345\) 4.07994e12i 0.834753i
\(346\) −3.91438e11 −0.0789372
\(347\) 3.48479e12i 0.692674i 0.938110 + 0.346337i \(0.112575\pi\)
−0.938110 + 0.346337i \(0.887425\pi\)
\(348\) −2.65612e12 −0.520418
\(349\) 3.17418e12i 0.613062i −0.951861 0.306531i \(-0.900832\pi\)
0.951861 0.306531i \(-0.0991684\pi\)
\(350\) 9.95593e12i 1.89558i
\(351\) 9.92397e11i 0.186273i
\(352\) 2.41630e12 0.447134
\(353\) 7.96464e12i 1.45309i −0.687118 0.726545i \(-0.741125\pi\)
0.687118 0.726545i \(-0.258875\pi\)
\(354\) 4.41914e12 + 3.00179e12i 0.794916 + 0.539963i
\(355\) −5.38510e12 −0.955106
\(356\) 7.43893e12i 1.30095i
\(357\) −9.78242e10 −0.0168696
\(358\) −1.25408e13 −2.13260
\(359\) 1.00989e13 1.69357 0.846783 0.531939i \(-0.178536\pi\)
0.846783 + 0.531939i \(0.178536\pi\)
\(360\) 3.24105e12i 0.536010i
\(361\) −2.12803e12 −0.347089
\(362\) 1.29989e13i 2.09105i
\(363\) −2.05009e12 −0.325267
\(364\) 2.17710e13i 3.40699i
\(365\) 9.72151e12i 1.50062i
\(366\) −6.11862e12 −0.931639
\(367\) 2.77661e12i 0.417046i 0.978017 + 0.208523i \(0.0668657\pi\)
−0.978017 + 0.208523i \(0.933134\pi\)
\(368\) 2.83066e12i 0.419419i
\(369\) 3.27689e12 0.478994
\(370\) −1.43618e13 −2.07109
\(371\) 2.42006e12 0.344315
\(372\) 7.11410e12i 0.998631i
\(373\) −1.13795e13 −1.57608 −0.788042 0.615621i \(-0.788905\pi\)
−0.788042 + 0.615621i \(0.788905\pi\)
\(374\) −1.18267e11 −0.0161625
\(375\) 2.29389e12 0.309326
\(376\) 2.17604e12 0.289553
\(377\) 3.75311e12i 0.492815i
\(378\) 4.91500e12i 0.636890i
\(379\) 8.15104e12 1.04236 0.521179 0.853447i \(-0.325492\pi\)
0.521179 + 0.853447i \(0.325492\pi\)
\(380\) −1.42148e13 −1.79400
\(381\) −5.42227e10 −0.00675392
\(382\) −2.18693e12 −0.268854
\(383\) 7.96658e12 0.966670 0.483335 0.875435i \(-0.339425\pi\)
0.483335 + 0.875435i \(0.339425\pi\)
\(384\) 8.69381e12i 1.04125i
\(385\) 1.39370e13i 1.64766i
\(386\) 1.08523e13i 1.26644i
\(387\) 3.75236e12i 0.432265i
\(388\) 2.58837e13i 2.94352i
\(389\) 9.34395e12 1.04902 0.524509 0.851405i \(-0.324249\pi\)
0.524509 + 0.851405i \(0.324249\pi\)
\(390\) −1.05244e13 −1.16647
\(391\) 1.54830e11i 0.0169422i
\(392\) 3.50504e13i 3.78672i
\(393\) 1.80113e12i 0.192125i
\(394\) 2.28402e13i 2.40557i
\(395\) 2.21071e13 2.29904
\(396\) 3.79724e12i 0.389934i
\(397\) 9.32716e12i 0.945795i 0.881118 + 0.472897i \(0.156792\pi\)
−0.881118 + 0.472897i \(0.843208\pi\)
\(398\) 2.04759e13i 2.05035i
\(399\) −9.38015e12 −0.927567
\(400\) 2.13383e12 0.208382
\(401\) 1.61068e13i 1.55342i 0.629860 + 0.776709i \(0.283112\pi\)
−0.629860 + 0.776709i \(0.716888\pi\)
\(402\) −5.59778e12 −0.533194
\(403\) 1.00522e13 0.945665
\(404\) 2.74061e13i 2.54648i
\(405\) 1.51834e12 0.139345
\(406\) 1.85878e13i 1.68500i
\(407\) −7.32186e12 −0.655616
\(408\) 1.22995e11i 0.0108789i
\(409\) 2.87907e12i 0.251557i −0.992058 0.125778i \(-0.959857\pi\)
0.992058 0.125778i \(-0.0401429\pi\)
\(410\) 3.47515e13i 2.99954i
\(411\) −3.37643e12 −0.287905
\(412\) 1.85143e13i 1.55963i
\(413\) 1.34241e13 1.97626e13i 1.11721 1.64472i
\(414\) 7.77914e12 0.639631
\(415\) 4.06867e12i 0.330531i
\(416\) −8.15988e12 −0.654963
\(417\) −8.97567e12 −0.711847
\(418\) −1.13404e13 −0.888684
\(419\) 2.00459e13i 1.55223i −0.630593 0.776114i \(-0.717188\pi\)
0.630593 0.776114i \(-0.282812\pi\)
\(420\) 3.33089e13 2.54867
\(421\) 4.88487e12i 0.369354i 0.982799 + 0.184677i \(0.0591239\pi\)
−0.982799 + 0.184677i \(0.940876\pi\)
\(422\) 2.51223e13 1.87714
\(423\) 1.01941e12i 0.0752745i
\(424\) 3.04274e12i 0.222043i
\(425\) 1.16715e11 0.00841748
\(426\) 1.02677e13i 0.731852i
\(427\) 2.73627e13i 1.92761i
\(428\) −1.59405e13 −1.10989
\(429\) −5.36550e12 −0.369253
\(430\) 3.97939e13 2.70691
\(431\) 1.53241e13i 1.03036i 0.857083 + 0.515178i \(0.172274\pi\)
−0.857083 + 0.515178i \(0.827726\pi\)
\(432\) −1.05342e12 −0.0700136
\(433\) −5.71238e12 −0.375299 −0.187649 0.982236i \(-0.560087\pi\)
−0.187649 + 0.982236i \(0.560087\pi\)
\(434\) −4.97852e13 −3.23334
\(435\) 5.74213e12 0.368661
\(436\) 1.06492e13i 0.675901i
\(437\) 1.48463e13i 0.931559i
\(438\) 1.85358e13 1.14985
\(439\) 4.08315e11 0.0250422 0.0125211 0.999922i \(-0.496014\pi\)
0.0125211 + 0.999922i \(0.496014\pi\)
\(440\) 1.75231e13 1.06254
\(441\) 1.64201e13 0.984427
\(442\) 3.99391e11 0.0236748
\(443\) 2.05868e13i 1.20662i −0.797507 0.603309i \(-0.793849\pi\)
0.797507 0.603309i \(-0.206151\pi\)
\(444\) 1.74989e13i 1.01414i
\(445\) 1.60818e13i 0.921586i
\(446\) 8.95494e12i 0.507444i
\(447\) 2.07917e12i 0.116507i
\(448\) 5.34668e13 2.96274
\(449\) 2.14624e13 1.17611 0.588053 0.808823i \(-0.299895\pi\)
0.588053 + 0.808823i \(0.299895\pi\)
\(450\) 5.86414e12i 0.317791i
\(451\) 1.77168e13i 0.949519i
\(452\) 1.55685e13i 0.825193i
\(453\) 1.34135e12i 0.0703154i
\(454\) −5.05056e13 −2.61855
\(455\) 4.70655e13i 2.41349i
\(456\) 1.17937e13i 0.598170i
\(457\) 9.36974e12i 0.470053i −0.971989 0.235026i \(-0.924482\pi\)
0.971989 0.235026i \(-0.0755176\pi\)
\(458\) −5.75054e13 −2.85352
\(459\) −5.76194e10 −0.00282817
\(460\) 5.27191e13i 2.55964i
\(461\) −1.08135e13 −0.519352 −0.259676 0.965696i \(-0.583616\pi\)
−0.259676 + 0.965696i \(0.583616\pi\)
\(462\) 2.65735e13 1.26252
\(463\) 3.90979e13i 1.83759i −0.394736 0.918794i \(-0.629164\pi\)
0.394736 0.918794i \(-0.370836\pi\)
\(464\) −3.98389e12 −0.185232
\(465\) 1.53796e13i 0.707425i
\(466\) −4.97743e13 −2.26504
\(467\) 3.31716e13i 1.49342i 0.665150 + 0.746710i \(0.268367\pi\)
−0.665150 + 0.746710i \(0.731633\pi\)
\(468\) 1.28233e13i 0.571177i
\(469\) 2.50335e13i 1.10321i
\(470\) −1.08109e13 −0.471381
\(471\) 2.26116e13i 0.975500i
\(472\) 2.48475e13 + 1.68782e13i 1.06065 + 0.720469i
\(473\) 2.02875e13 0.856888
\(474\) 4.21512e13i 1.76165i
\(475\) 1.11915e13 0.462831
\(476\) −1.26404e12 −0.0517281
\(477\) 1.42544e12 0.0577240
\(478\) 2.03751e13i 0.816507i
\(479\) 1.19299e12 0.0473106 0.0236553 0.999720i \(-0.492470\pi\)
0.0236553 + 0.999720i \(0.492470\pi\)
\(480\) 1.24844e13i 0.489959i
\(481\) 2.47260e13 0.960348
\(482\) 5.09873e13i 1.95987i
\(483\) 3.47886e13i 1.32343i
\(484\) −2.64903e13 −0.997380
\(485\) 5.59565e13i 2.08517i
\(486\) 2.89498e12i 0.106774i
\(487\) −3.05250e13 −1.11432 −0.557162 0.830404i \(-0.688110\pi\)
−0.557162 + 0.830404i \(0.688110\pi\)
\(488\) −3.44032e13 −1.24308
\(489\) 3.08465e13 1.10322
\(490\) 1.74136e14i 6.16464i
\(491\) −1.04431e13 −0.365949 −0.182975 0.983118i \(-0.558573\pi\)
−0.182975 + 0.983118i \(0.558573\pi\)
\(492\) 4.23425e13 1.46876
\(493\) −2.17908e11 −0.00748238
\(494\) 3.82967e13 1.30175
\(495\) 8.20904e12i 0.276227i
\(496\) 1.06703e13i 0.355443i
\(497\) −4.59174e13 −1.51424
\(498\) 7.75765e12 0.253270
\(499\) −2.85799e13 −0.923759 −0.461880 0.886943i \(-0.652825\pi\)
−0.461880 + 0.886943i \(0.652825\pi\)
\(500\) 2.96406e13 0.948500
\(501\) 1.50531e13 0.476909
\(502\) 2.42580e12i 0.0760915i
\(503\) 3.67887e13i 1.14255i 0.820759 + 0.571275i \(0.193551\pi\)
−0.820759 + 0.571275i \(0.806449\pi\)
\(504\) 2.76356e13i 0.849799i
\(505\) 5.92478e13i 1.80391i
\(506\) 4.20587e13i 1.26795i
\(507\) −1.22166e12 −0.0364679
\(508\) −7.00641e11 −0.0207099
\(509\) 2.57696e13i 0.754257i −0.926161 0.377128i \(-0.876912\pi\)
0.926161 0.377128i \(-0.123088\pi\)
\(510\) 6.11055e11i 0.0177104i
\(511\) 8.28929e13i 2.37910i
\(512\) 2.50741e13i 0.712648i
\(513\) −5.52500e12 −0.155505
\(514\) 6.52727e13i 1.81935i
\(515\) 4.00250e13i 1.10483i
\(516\) 4.84864e13i 1.32547i
\(517\) −5.51155e12 −0.149218
\(518\) −1.22459e14 −3.28355
\(519\) 1.03108e12i 0.0273813i
\(520\) −5.91756e13 −1.55642
\(521\) −1.98770e13 −0.517801 −0.258900 0.965904i \(-0.583360\pi\)
−0.258900 + 0.965904i \(0.583360\pi\)
\(522\) 1.09484e13i 0.282487i
\(523\) −1.60013e13 −0.408927 −0.204463 0.978874i \(-0.565545\pi\)
−0.204463 + 0.978874i \(0.565545\pi\)
\(524\) 2.32734e13i 0.589120i
\(525\) −2.62247e13 −0.657527
\(526\) 3.46916e13i 0.861579i
\(527\) 5.83641e11i 0.0143580i
\(528\) 5.69542e12i 0.138789i
\(529\) −1.36346e13 −0.329127
\(530\) 1.51168e13i 0.361477i
\(531\) 7.90693e12 1.16403e13i 0.187299 0.275736i
\(532\) −1.21206e14 −2.84424
\(533\) 5.98300e13i 1.39086i
\(534\) −3.06629e13 −0.706167
\(535\) 3.44608e13 0.786243
\(536\) −3.14747e13 −0.711438
\(537\) 3.30333e13i 0.739743i
\(538\) 6.41424e12 0.142309
\(539\) 8.87771e13i 1.95145i
\(540\) 1.96193e13 0.427281
\(541\) 7.78574e13i 1.68002i 0.542573 + 0.840008i \(0.317450\pi\)
−0.542573 + 0.840008i \(0.682550\pi\)
\(542\) 6.36707e13i 1.36127i
\(543\) 3.42402e13 0.725332
\(544\) 4.73769e11i 0.00994426i
\(545\) 2.30219e13i 0.478804i
\(546\) −8.97389e13 −1.84934
\(547\) −3.95256e13 −0.807127 −0.403563 0.914952i \(-0.632229\pi\)
−0.403563 + 0.914952i \(0.632229\pi\)
\(548\) −4.36287e13 −0.882815
\(549\) 1.61169e13i 0.323161i
\(550\) −3.17051e13 −0.629964
\(551\) −2.08948e13 −0.411414
\(552\) 4.37398e13 0.853456
\(553\) 1.88502e14 3.64494
\(554\) 4.69555e13i 0.899782i
\(555\) 3.78300e13i 0.718408i
\(556\) −1.15980e14 −2.18277
\(557\) −5.66900e13 −1.05738 −0.528689 0.848815i \(-0.677316\pi\)
−0.528689 + 0.848815i \(0.677316\pi\)
\(558\) −2.93240e13 −0.542066
\(559\) −6.85113e13 −1.25517
\(560\) 4.99596e13 0.907149
\(561\) 3.11525e11i 0.00560633i
\(562\) 5.33158e13i 0.950987i
\(563\) 2.79964e13i 0.494949i −0.968894 0.247475i \(-0.920399\pi\)
0.968894 0.247475i \(-0.0796007\pi\)
\(564\) 1.31724e13i 0.230817i
\(565\) 3.36568e13i 0.584562i
\(566\) 1.38595e14 2.38597
\(567\) 1.29465e13 0.220921
\(568\) 5.77320e13i 0.976506i
\(569\) 8.11572e13i 1.36071i 0.732883 + 0.680355i \(0.238174\pi\)
−0.732883 + 0.680355i \(0.761826\pi\)
\(570\) 5.85927e13i 0.973799i
\(571\) 4.68005e13i 0.771027i −0.922702 0.385514i \(-0.874024\pi\)
0.922702 0.385514i \(-0.125976\pi\)
\(572\) −6.93306e13 −1.13226
\(573\) 5.76052e12i 0.0932586i
\(574\) 2.96317e14i 4.75552i
\(575\) 4.15066e13i 0.660356i
\(576\) 3.14924e13 0.496700
\(577\) −2.26889e13 −0.354759 −0.177380 0.984143i \(-0.556762\pi\)
−0.177380 + 0.984143i \(0.556762\pi\)
\(578\) 1.07353e14i 1.66408i
\(579\) 2.85857e13 0.439295
\(580\) 7.41973e13 1.13044
\(581\) 3.46925e13i 0.524029i
\(582\) −1.06691e14 −1.59777
\(583\) 7.70678e12i 0.114427i
\(584\) 1.04221e14 1.53424
\(585\) 2.77220e13i 0.404619i
\(586\) 1.01440e14i 1.46798i
\(587\) 6.53314e13i 0.937415i −0.883354 0.468707i \(-0.844720\pi\)
0.883354 0.468707i \(-0.155280\pi\)
\(588\) 2.12173e14 3.01859
\(589\) 5.59640e13i 0.789464i
\(590\) −1.23446e14 8.38532e13i −1.72670 1.17290i
\(591\) −6.01628e13 −0.834431
\(592\) 2.62464e13i 0.360962i
\(593\) −4.03338e13 −0.550042 −0.275021 0.961438i \(-0.588685\pi\)
−0.275021 + 0.961438i \(0.588685\pi\)
\(594\) 1.56520e13 0.211660
\(595\) 2.73266e12 0.0366439
\(596\) 2.68661e13i 0.357251i
\(597\) −5.39350e13 −0.711211
\(598\) 1.42033e14i 1.85730i
\(599\) 1.23104e13 0.159639 0.0798195 0.996809i \(-0.474566\pi\)
0.0798195 + 0.996809i \(0.474566\pi\)
\(600\) 3.29723e13i 0.424027i
\(601\) 1.21795e14i 1.55331i 0.629926 + 0.776655i \(0.283085\pi\)
−0.629926 + 0.776655i \(0.716915\pi\)
\(602\) 3.39313e14 4.29159
\(603\) 1.47450e13i 0.184951i
\(604\) 1.73323e13i 0.215611i
\(605\) 5.72681e13 0.706538
\(606\) 1.12967e14 1.38225
\(607\) −6.22812e13 −0.755811 −0.377906 0.925844i \(-0.623356\pi\)
−0.377906 + 0.925844i \(0.623356\pi\)
\(608\) 4.54287e13i 0.546779i
\(609\) 4.89618e13 0.584481
\(610\) 1.70920e14 2.02369
\(611\) 1.86126e13 0.218575
\(612\) −7.44532e11 −0.00867214
\(613\) 8.79024e13i 1.01554i 0.861492 + 0.507772i \(0.169531\pi\)
−0.861492 + 0.507772i \(0.830469\pi\)
\(614\) 1.91301e14i 2.19218i
\(615\) −9.15380e13 −1.04046
\(616\) 1.49415e14 1.68457
\(617\) 5.58242e12 0.0624304 0.0312152 0.999513i \(-0.490062\pi\)
0.0312152 + 0.999513i \(0.490062\pi\)
\(618\) −7.63149e13 −0.846578
\(619\) −5.46830e13 −0.601726 −0.300863 0.953667i \(-0.597275\pi\)
−0.300863 + 0.953667i \(0.597275\pi\)
\(620\) 1.98728e14i 2.16921i
\(621\) 2.04908e13i 0.221871i
\(622\) 2.37170e14i 2.54746i
\(623\) 1.37126e14i 1.46110i
\(624\) 1.92335e13i 0.203299i
\(625\) −1.18704e14 −1.24470
\(626\) 1.96067e14 2.03954
\(627\) 2.98715e13i 0.308261i
\(628\) 2.92177e14i 2.99122i
\(629\) 1.43561e12i 0.0145809i
\(630\) 1.37298e14i 1.38344i
\(631\) 3.18938e13 0.318830 0.159415 0.987212i \(-0.449039\pi\)
0.159415 + 0.987212i \(0.449039\pi\)
\(632\) 2.37004e14i 2.35055i
\(633\) 6.61739e13i 0.651130i
\(634\) 1.30250e14i 1.27154i
\(635\) 1.51468e12 0.0146707
\(636\) 1.84189e13 0.177002
\(637\) 2.99801e14i 2.85849i
\(638\) 5.91938e13 0.559980
\(639\) −2.70458e13 −0.253861
\(640\) 2.42857e14i 2.26178i
\(641\) −5.15106e13 −0.475999 −0.238000 0.971265i \(-0.576492\pi\)
−0.238000 + 0.971265i \(0.576492\pi\)
\(642\) 6.57058e13i 0.602460i
\(643\) −1.34620e14 −1.22477 −0.612387 0.790558i \(-0.709791\pi\)
−0.612387 + 0.790558i \(0.709791\pi\)
\(644\) 4.49523e14i 4.05810i
\(645\) 1.04820e14i 0.938958i
\(646\) 2.22354e12i 0.0197643i
\(647\) −1.82590e14 −1.61048 −0.805238 0.592951i \(-0.797963\pi\)
−0.805238 + 0.592951i \(0.797963\pi\)
\(648\) 1.62776e13i 0.142468i
\(649\) −6.29347e13 4.27497e13i −0.546596 0.371287i
\(650\) 1.07068e14 0.922772
\(651\) 1.31138e14i 1.12156i
\(652\) 3.98585e14 3.38285
\(653\) −1.37386e14 −1.15712 −0.578559 0.815640i \(-0.696385\pi\)
−0.578559 + 0.815640i \(0.696385\pi\)
\(654\) −4.38953e13 −0.366885
\(655\) 5.03136e13i 0.417329i
\(656\) 6.35090e13 0.522776
\(657\) 4.88247e13i 0.398853i
\(658\) −9.21817e13 −0.747335
\(659\) 8.92668e13i 0.718229i 0.933294 + 0.359114i \(0.116921\pi\)
−0.933294 + 0.359114i \(0.883079\pi\)
\(660\) 1.06074e14i 0.847008i
\(661\) 1.21953e14 0.966461 0.483230 0.875493i \(-0.339463\pi\)
0.483230 + 0.875493i \(0.339463\pi\)
\(662\) 2.78288e13i 0.218879i
\(663\) 1.05202e12i 0.00821217i
\(664\) 4.36190e13 0.337937
\(665\) 2.62029e14 2.01484
\(666\) −7.21297e13 −0.550482
\(667\) 7.74934e13i 0.586997i
\(668\) 1.94509e14 1.46237
\(669\) −2.35880e13 −0.176019
\(670\) 1.56371e14 1.15819
\(671\) 8.71377e13 0.640609
\(672\) 1.06451e14i 0.776790i
\(673\) 4.70316e12i 0.0340655i −0.999855 0.0170327i \(-0.994578\pi\)
0.999855 0.0170327i \(-0.00542195\pi\)
\(674\) −8.98445e13 −0.645940
\(675\) −1.54466e13 −0.110233
\(676\) −1.57858e13 −0.111823
\(677\) 2.28104e14 1.60395 0.801974 0.597359i \(-0.203783\pi\)
0.801974 + 0.597359i \(0.203783\pi\)
\(678\) 6.41728e13 0.447922
\(679\) 4.77128e14i 3.30587i
\(680\) 3.43578e12i 0.0236309i
\(681\) 1.33036e14i 0.908306i
\(682\) 1.58543e14i 1.07455i
\(683\) 2.29139e14i 1.54168i −0.637028 0.770841i \(-0.719836\pi\)
0.637028 0.770841i \(-0.280164\pi\)
\(684\) −7.13915e13 −0.476833
\(685\) 9.43187e13 0.625381
\(686\) 9.82045e14i 6.46414i
\(687\) 1.51474e14i 0.989813i
\(688\) 7.27241e13i 0.471776i
\(689\) 2.60259e13i 0.167614i
\(690\) −2.17306e14 −1.38939
\(691\) 2.46227e14i 1.56295i −0.623937 0.781474i \(-0.714468\pi\)
0.623937 0.781474i \(-0.285532\pi\)
\(692\) 1.33231e13i 0.0839604i
\(693\) 6.99965e13i 0.437935i
\(694\) 1.85607e14 1.15291
\(695\) 2.50730e14 1.54626
\(696\) 6.15597e13i 0.376921i
\(697\) 3.47378e12 0.0211173
\(698\) −1.69063e14 −1.02040
\(699\) 1.31109e14i 0.785683i
\(700\) −3.38863e14 −2.01620
\(701\) 1.24494e14i 0.735462i 0.929932 + 0.367731i \(0.119865\pi\)
−0.929932 + 0.367731i \(0.880135\pi\)
\(702\) −5.28571e13 −0.310040
\(703\) 1.37658e14i 0.801722i
\(704\) 1.70267e14i 0.984617i
\(705\) 2.84767e13i 0.163510i
\(706\) −4.24213e14 −2.41858
\(707\) 5.05192e14i 2.85995i
\(708\) 1.02170e14 1.50411e14i 0.574323 0.845501i
\(709\) 5.03176e13 0.280859 0.140430 0.990091i \(-0.455152\pi\)
0.140430 + 0.990091i \(0.455152\pi\)
\(710\) 2.86821e14i 1.58972i
\(711\) 1.11029e14 0.611069
\(712\) −1.72409e14 −0.942234
\(713\) 2.07557e14 1.12639
\(714\) 5.21032e12i 0.0280784i
\(715\) 1.49882e14 0.802083
\(716\) 4.26842e14i 2.26831i
\(717\) 5.36695e13 0.283225
\(718\) 5.37888e14i 2.81884i
\(719\) 2.68377e14i 1.39669i −0.715760 0.698346i \(-0.753920\pi\)
0.715760 0.698346i \(-0.246080\pi\)
\(720\) 2.94267e13 0.152082
\(721\) 3.41283e14i 1.75162i
\(722\) 1.13343e14i 0.577708i
\(723\) −1.34304e14 −0.679827
\(724\) 4.42436e14 2.22412
\(725\) −5.84168e13 −0.291640
\(726\) 1.09192e14i 0.541386i
\(727\) 4.13444e13 0.203585 0.101792 0.994806i \(-0.467542\pi\)
0.101792 + 0.994806i \(0.467542\pi\)
\(728\) −5.04575e14 −2.46757
\(729\) 7.62560e12 0.0370370
\(730\) −5.17787e14 −2.49768
\(731\) 3.97782e12i 0.0190572i
\(732\) 2.08255e14i 0.990924i
\(733\) −1.84839e14 −0.873522 −0.436761 0.899578i \(-0.643874\pi\)
−0.436761 + 0.899578i \(0.643874\pi\)
\(734\) 1.47888e14 0.694148
\(735\) −4.58687e14 −2.13835
\(736\) −1.68484e14 −0.780133
\(737\) 7.97202e13 0.366632
\(738\) 1.74534e14i 0.797256i
\(739\) 2.88722e14i 1.30996i 0.755648 + 0.654978i \(0.227322\pi\)
−0.755648 + 0.654978i \(0.772678\pi\)
\(740\) 4.88822e14i 2.20289i
\(741\) 1.00876e14i 0.451542i
\(742\) 1.28897e14i 0.573092i
\(743\) 1.09253e13 0.0482489 0.0241245 0.999709i \(-0.492320\pi\)
0.0241245 + 0.999709i \(0.492320\pi\)
\(744\) −1.64880e14 −0.723275
\(745\) 5.80804e13i 0.253074i
\(746\) 6.06096e14i 2.62330i
\(747\) 2.04342e13i 0.0878528i
\(748\) 4.02539e12i 0.0171910i
\(749\) 2.93839e14 1.24652
\(750\) 1.22177e14i 0.514854i
\(751\) 2.52489e14i 1.05692i −0.848957 0.528462i \(-0.822769\pi\)
0.848957 0.528462i \(-0.177231\pi\)
\(752\) 1.97571e13i 0.0821549i
\(753\) 6.38974e12 0.0263942
\(754\) −1.99898e14 −0.820261
\(755\) 3.74698e13i 0.152738i
\(756\) 1.67289e14 0.677419
\(757\) 2.01417e14 0.810245 0.405122 0.914262i \(-0.367229\pi\)
0.405122 + 0.914262i \(0.367229\pi\)
\(758\) 4.34141e14i 1.73494i
\(759\) −1.10786e14 −0.439820
\(760\) 3.29449e14i 1.29933i
\(761\) 2.30842e14 0.904464 0.452232 0.891900i \(-0.350628\pi\)
0.452232 + 0.891900i \(0.350628\pi\)
\(762\) 2.88801e12i 0.0112415i
\(763\) 1.96302e14i 0.759104i
\(764\) 7.44349e13i 0.285963i
\(765\) 1.60956e12 0.00614329
\(766\) 4.24316e14i 1.60896i
\(767\) 2.12531e14 + 1.44366e14i 0.800656 + 0.543862i
\(768\) 2.33192e14 0.872784
\(769\) 2.24358e14i 0.834274i 0.908844 + 0.417137i \(0.136967\pi\)
−0.908844 + 0.417137i \(0.863033\pi\)
\(770\) −7.42315e14 −2.74242
\(771\) 1.71933e14 0.631085
\(772\) 3.69372e14 1.34703
\(773\) 4.66834e14i 1.69147i 0.533601 + 0.845737i \(0.320839\pi\)
−0.533601 + 0.845737i \(0.679161\pi\)
\(774\) 1.99859e14 0.719479
\(775\) 1.56462e14i 0.559630i
\(776\) −5.99893e14 −2.13189
\(777\) 3.22567e14i 1.13898i
\(778\) 4.97678e14i 1.74602i
\(779\) 3.33093e14 1.16112