Properties

Label 43.11.b.b.42.12
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.12
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.23

$q$-expansion

\(f(q)\) \(=\) \(q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} +O(q^{10})\) \(q-24.5024i q^{2} -131.608i q^{3} +423.632 q^{4} -1067.29i q^{5} -3224.72 q^{6} +23187.4i q^{7} -35470.5i q^{8} +41728.3 q^{9} -26151.2 q^{10} +158882. q^{11} -55753.4i q^{12} +167670. q^{13} +568147. q^{14} -140464. q^{15} -435314. q^{16} +520761. q^{17} -1.02244e6i q^{18} +3.58799e6i q^{19} -452138. i q^{20} +3.05165e6 q^{21} -3.89300e6i q^{22} +5.91236e6 q^{23} -4.66820e6 q^{24} +8.62652e6 q^{25} -4.10833e6i q^{26} -1.32631e7i q^{27} +9.82290e6i q^{28} -2.07565e7i q^{29} +3.44171e6i q^{30} -5.10952e7 q^{31} -2.56555e7i q^{32} -2.09102e7i q^{33} -1.27599e7i q^{34} +2.47477e7 q^{35} +1.76774e7 q^{36} -2.80255e7i q^{37} +8.79145e7 q^{38} -2.20668e7i q^{39} -3.78573e7 q^{40} -3.53086e7 q^{41} -7.47727e7i q^{42} +(-2.73661e7 - 1.44439e8i) q^{43} +6.73076e7 q^{44} -4.45362e7i q^{45} -1.44867e8i q^{46} -1.53586e8 q^{47} +5.72908e7i q^{48} -2.55179e8 q^{49} -2.11370e8i q^{50} -6.85364e7i q^{51} +7.10305e7 q^{52} +6.12172e8 q^{53} -3.24978e8 q^{54} -1.69574e8i q^{55} +8.22467e8 q^{56} +4.72209e8 q^{57} -5.08585e8 q^{58} +1.45923e8 q^{59} -5.95051e7 q^{60} -2.72707e8i q^{61} +1.25196e9i q^{62} +9.67569e8i q^{63} -1.07438e9 q^{64} -1.78953e8i q^{65} -5.12351e8 q^{66} +1.22045e9 q^{67} +2.20611e8 q^{68} -7.78115e8i q^{69} -6.06377e8i q^{70} +1.66988e9i q^{71} -1.48012e9i q^{72} +3.53834e9i q^{73} -6.86692e8 q^{74} -1.13532e9i q^{75} +1.51999e9i q^{76} +3.68407e9i q^{77} -5.40690e8 q^{78} -5.02144e7 q^{79} +4.64606e8i q^{80} +7.18479e8 q^{81} +8.65147e8i q^{82} -7.32260e9 q^{83} +1.29277e9 q^{84} -5.55803e8i q^{85} +(-3.53910e9 + 6.70535e8i) q^{86} -2.73173e9 q^{87} -5.63563e9i q^{88} -5.46020e9i q^{89} -1.09124e9 q^{90} +3.88784e9i q^{91} +2.50466e9 q^{92} +6.72455e9i q^{93} +3.76324e9i q^{94} +3.82943e9 q^{95} -3.37648e9 q^{96} +1.01437e10 q^{97} +6.25250e9i q^{98} +6.62989e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.5024i 0.765701i −0.923810 0.382850i \(-0.874943\pi\)
0.923810 0.382850i \(-0.125057\pi\)
\(3\) 131.608i 0.541597i −0.962636 0.270799i \(-0.912712\pi\)
0.962636 0.270799i \(-0.0872878\pi\)
\(4\) 423.632 0.413703
\(5\) 1067.29i 0.341533i −0.985312 0.170766i \(-0.945376\pi\)
0.985312 0.170766i \(-0.0546244\pi\)
\(6\) −3224.72 −0.414701
\(7\) 23187.4i 1.37963i 0.723988 + 0.689813i \(0.242307\pi\)
−0.723988 + 0.689813i \(0.757693\pi\)
\(8\) 35470.5i 1.08247i
\(9\) 41728.3 0.706672
\(10\) −26151.2 −0.261512
\(11\) 158882. 0.986535 0.493267 0.869878i \(-0.335802\pi\)
0.493267 + 0.869878i \(0.335802\pi\)
\(12\) 55753.4i 0.224060i
\(13\) 167670. 0.451585 0.225793 0.974175i \(-0.427503\pi\)
0.225793 + 0.974175i \(0.427503\pi\)
\(14\) 568147. 1.05638
\(15\) −140464. −0.184973
\(16\) −435314. −0.415147
\(17\) 520761. 0.366770 0.183385 0.983041i \(-0.441294\pi\)
0.183385 + 0.983041i \(0.441294\pi\)
\(18\) 1.02244e6i 0.541099i
\(19\) 3.58799e6i 1.44905i 0.689248 + 0.724525i \(0.257941\pi\)
−0.689248 + 0.724525i \(0.742059\pi\)
\(20\) 452138.i 0.141293i
\(21\) 3.05165e6 0.747202
\(22\) 3.89300e6i 0.755390i
\(23\) 5.91236e6 0.918590 0.459295 0.888284i \(-0.348102\pi\)
0.459295 + 0.888284i \(0.348102\pi\)
\(24\) −4.66820e6 −0.586265
\(25\) 8.62652e6 0.883355
\(26\) 4.10833e6i 0.345779i
\(27\) 1.32631e7i 0.924329i
\(28\) 9.82290e6i 0.570755i
\(29\) 2.07565e7i 1.01196i −0.862544 0.505981i \(-0.831130\pi\)
0.862544 0.505981i \(-0.168870\pi\)
\(30\) 3.44171e6i 0.141634i
\(31\) −5.10952e7 −1.78473 −0.892363 0.451317i \(-0.850954\pi\)
−0.892363 + 0.451317i \(0.850954\pi\)
\(32\) 2.56555e7i 0.764594i
\(33\) 2.09102e7i 0.534305i
\(34\) 1.27599e7i 0.280836i
\(35\) 2.47477e7 0.471188
\(36\) 1.76774e7 0.292352
\(37\) 2.80255e7i 0.404152i −0.979370 0.202076i \(-0.935231\pi\)
0.979370 0.202076i \(-0.0647688\pi\)
\(38\) 8.79145e7 1.10954
\(39\) 2.20668e7i 0.244577i
\(40\) −3.78573e7 −0.369700
\(41\) −3.53086e7 −0.304762 −0.152381 0.988322i \(-0.548694\pi\)
−0.152381 + 0.988322i \(0.548694\pi\)
\(42\) 7.47727e7i 0.572133i
\(43\) −2.73661e7 1.44439e8i −0.186153 0.982521i
\(44\) 6.73076e7 0.408132
\(45\) 4.45362e7i 0.241352i
\(46\) 1.44867e8i 0.703365i
\(47\) −1.53586e8 −0.669674 −0.334837 0.942276i \(-0.608681\pi\)
−0.334837 + 0.942276i \(0.608681\pi\)
\(48\) 5.72908e7i 0.224843i
\(49\) −2.55179e8 −0.903367
\(50\) 2.11370e8i 0.676386i
\(51\) 6.85364e7i 0.198642i
\(52\) 7.10305e7 0.186822
\(53\) 6.12172e8 1.46384 0.731921 0.681389i \(-0.238624\pi\)
0.731921 + 0.681389i \(0.238624\pi\)
\(54\) −3.24978e8 −0.707759
\(55\) 1.69574e8i 0.336934i
\(56\) 8.22467e8 1.49341
\(57\) 4.72209e8 0.784802
\(58\) −5.08585e8 −0.774860
\(59\) 1.45923e8 0.204110 0.102055 0.994779i \(-0.467458\pi\)
0.102055 + 0.994779i \(0.467458\pi\)
\(60\) −5.95051e7 −0.0765240
\(61\) 2.72707e8i 0.322885i −0.986882 0.161442i \(-0.948385\pi\)
0.986882 0.161442i \(-0.0516146\pi\)
\(62\) 1.25196e9i 1.36657i
\(63\) 9.67569e8i 0.974943i
\(64\) −1.07438e9 −1.00060
\(65\) 1.78953e8i 0.154231i
\(66\) −5.12351e8 −0.409117
\(67\) 1.22045e9 0.903951 0.451975 0.892030i \(-0.350719\pi\)
0.451975 + 0.892030i \(0.350719\pi\)
\(68\) 2.20611e8 0.151734
\(69\) 7.78115e8i 0.497506i
\(70\) 6.06377e8i 0.360789i
\(71\) 1.66988e9i 0.925537i 0.886479 + 0.462768i \(0.153144\pi\)
−0.886479 + 0.462768i \(0.846856\pi\)
\(72\) 1.48012e9i 0.764953i
\(73\) 3.53834e9i 1.70681i 0.521247 + 0.853406i \(0.325467\pi\)
−0.521247 + 0.853406i \(0.674533\pi\)
\(74\) −6.86692e8 −0.309459
\(75\) 1.13532e9i 0.478423i
\(76\) 1.51999e9i 0.599476i
\(77\) 3.68407e9i 1.36105i
\(78\) −5.40690e8 −0.187273
\(79\) −5.02144e7 −0.0163190 −0.00815949 0.999967i \(-0.502597\pi\)
−0.00815949 + 0.999967i \(0.502597\pi\)
\(80\) 4.64606e8i 0.141786i
\(81\) 7.18479e8 0.206058
\(82\) 8.65147e8i 0.233357i
\(83\) −7.32260e9 −1.85898 −0.929490 0.368846i \(-0.879753\pi\)
−0.929490 + 0.368846i \(0.879753\pi\)
\(84\) 1.29277e9 0.309119
\(85\) 5.55803e8i 0.125264i
\(86\) −3.53910e9 + 6.70535e8i −0.752317 + 0.142538i
\(87\) −2.73173e9 −0.548076
\(88\) 5.63563e9i 1.06790i
\(89\) 5.46020e9i 0.977820i −0.872334 0.488910i \(-0.837395\pi\)
0.872334 0.488910i \(-0.162605\pi\)
\(90\) −1.09124e9 −0.184803
\(91\) 3.88784e9i 0.623019i
\(92\) 2.50466e9 0.380023
\(93\) 6.72455e9i 0.966604i
\(94\) 3.76324e9i 0.512770i
\(95\) 3.82943e9 0.494899
\(96\) −3.37648e9 −0.414102
\(97\) 1.01437e10 1.18124 0.590619 0.806951i \(-0.298884\pi\)
0.590619 + 0.806951i \(0.298884\pi\)
\(98\) 6.25250e9i 0.691709i
\(99\) 6.62989e9 0.697157
\(100\) 3.65446e9 0.365446
\(101\) 1.65056e10 1.57045 0.785225 0.619211i \(-0.212547\pi\)
0.785225 + 0.619211i \(0.212547\pi\)
\(102\) −1.67931e9 −0.152100
\(103\) −1.08367e10 −0.934785 −0.467393 0.884050i \(-0.654807\pi\)
−0.467393 + 0.884050i \(0.654807\pi\)
\(104\) 5.94735e9i 0.488829i
\(105\) 3.25699e9i 0.255194i
\(106\) 1.49997e10i 1.12087i
\(107\) −5.03613e9 −0.359069 −0.179535 0.983752i \(-0.557459\pi\)
−0.179535 + 0.983752i \(0.557459\pi\)
\(108\) 5.61867e9i 0.382398i
\(109\) 1.18460e10 0.769908 0.384954 0.922936i \(-0.374217\pi\)
0.384954 + 0.922936i \(0.374217\pi\)
\(110\) −4.15496e9 −0.257991
\(111\) −3.68838e9 −0.218888
\(112\) 1.00938e10i 0.572748i
\(113\) 9.85418e9i 0.534846i −0.963579 0.267423i \(-0.913828\pi\)
0.963579 0.267423i \(-0.0861720\pi\)
\(114\) 1.15703e10i 0.600923i
\(115\) 6.31020e9i 0.313729i
\(116\) 8.79312e9i 0.418652i
\(117\) 6.99660e9 0.319123
\(118\) 3.57546e9i 0.156287i
\(119\) 1.20751e10i 0.506006i
\(120\) 4.98233e9i 0.200229i
\(121\) −6.93801e8 −0.0267490
\(122\) −6.68199e9 −0.247233
\(123\) 4.64690e9i 0.165059i
\(124\) −2.16455e10 −0.738346
\(125\) 1.96298e10i 0.643228i
\(126\) 2.37078e10 0.746514
\(127\) 4.39995e10 1.33177 0.665885 0.746054i \(-0.268054\pi\)
0.665885 + 0.746054i \(0.268054\pi\)
\(128\) 5.37295e7i 0.00156373i
\(129\) −1.90093e10 + 3.60160e9i −0.532131 + 0.100820i
\(130\) −4.38478e9 −0.118095
\(131\) 9.22948e9i 0.239233i −0.992820 0.119616i \(-0.961834\pi\)
0.992820 0.119616i \(-0.0381665\pi\)
\(132\) 8.85823e9i 0.221043i
\(133\) −8.31961e10 −1.99915
\(134\) 2.99039e10i 0.692156i
\(135\) −1.41556e10 −0.315689
\(136\) 1.84716e10i 0.397019i
\(137\) 6.14452e10i 1.27317i 0.771208 + 0.636583i \(0.219653\pi\)
−0.771208 + 0.636583i \(0.780347\pi\)
\(138\) −1.90657e10 −0.380941
\(139\) −8.22126e10 −1.58440 −0.792199 0.610263i \(-0.791064\pi\)
−0.792199 + 0.610263i \(0.791064\pi\)
\(140\) 1.04839e10 0.194932
\(141\) 2.02132e10i 0.362694i
\(142\) 4.09161e10 0.708684
\(143\) 2.66399e10 0.445505
\(144\) −1.81649e10 −0.293373
\(145\) −2.21532e10 −0.345619
\(146\) 8.66980e10 1.30691
\(147\) 3.35836e10i 0.489261i
\(148\) 1.18725e10i 0.167199i
\(149\) 8.87329e10i 1.20824i 0.796893 + 0.604120i \(0.206475\pi\)
−0.796893 + 0.604120i \(0.793525\pi\)
\(150\) −2.78181e10 −0.366329
\(151\) 2.07161e10i 0.263890i 0.991257 + 0.131945i \(0.0421223\pi\)
−0.991257 + 0.131945i \(0.957878\pi\)
\(152\) 1.27268e11 1.56856
\(153\) 2.17305e10 0.259186
\(154\) 9.02685e10 1.04216
\(155\) 5.45334e10i 0.609543i
\(156\) 9.34820e9i 0.101182i
\(157\) 4.14184e10i 0.434205i −0.976149 0.217103i \(-0.930339\pi\)
0.976149 0.217103i \(-0.0696606\pi\)
\(158\) 1.23037e9i 0.0124954i
\(159\) 8.05669e10i 0.792814i
\(160\) −2.73819e10 −0.261134
\(161\) 1.37092e11i 1.26731i
\(162\) 1.76045e10i 0.157779i
\(163\) 8.98410e10i 0.780794i 0.920647 + 0.390397i \(0.127662\pi\)
−0.920647 + 0.390397i \(0.872338\pi\)
\(164\) −1.49578e10 −0.126081
\(165\) −2.23173e10 −0.182483
\(166\) 1.79421e11i 1.42342i
\(167\) 5.74168e10 0.442035 0.221017 0.975270i \(-0.429062\pi\)
0.221017 + 0.975270i \(0.429062\pi\)
\(168\) 1.08243e11i 0.808826i
\(169\) −1.09745e11 −0.796071
\(170\) −1.36185e10 −0.0959148
\(171\) 1.49721e11i 1.02400i
\(172\) −1.15931e10 6.11889e10i −0.0770121 0.406472i
\(173\) −1.67742e11 −1.08246 −0.541228 0.840876i \(-0.682041\pi\)
−0.541228 + 0.840876i \(0.682041\pi\)
\(174\) 6.69339e10i 0.419662i
\(175\) 2.00026e11i 1.21870i
\(176\) −6.91637e10 −0.409557
\(177\) 1.92047e10i 0.110545i
\(178\) −1.33788e11 −0.748717
\(179\) 3.46658e11i 1.88641i −0.332212 0.943205i \(-0.607795\pi\)
0.332212 0.943205i \(-0.392205\pi\)
\(180\) 1.88669e10i 0.0998479i
\(181\) 7.47797e10 0.384938 0.192469 0.981303i \(-0.438350\pi\)
0.192469 + 0.981303i \(0.438350\pi\)
\(182\) 9.52614e10 0.477046
\(183\) −3.58905e10 −0.174874
\(184\) 2.09714e11i 0.994349i
\(185\) −2.99113e10 −0.138031
\(186\) 1.64768e11 0.740129
\(187\) 8.27398e10 0.361832
\(188\) −6.50641e10 −0.277046
\(189\) 3.07537e11 1.27523
\(190\) 9.38303e10i 0.378944i
\(191\) 1.22579e11i 0.482223i 0.970497 + 0.241112i \(0.0775120\pi\)
−0.970497 + 0.241112i \(0.922488\pi\)
\(192\) 1.41398e11i 0.541921i
\(193\) −1.63773e11 −0.611582 −0.305791 0.952099i \(-0.598921\pi\)
−0.305791 + 0.952099i \(0.598921\pi\)
\(194\) 2.48545e11i 0.904474i
\(195\) −2.35517e10 −0.0835313
\(196\) −1.08102e11 −0.373725
\(197\) −5.73013e11 −1.93123 −0.965613 0.259985i \(-0.916283\pi\)
−0.965613 + 0.259985i \(0.916283\pi\)
\(198\) 1.62448e11i 0.533813i
\(199\) 2.02890e11i 0.650123i 0.945693 + 0.325062i \(0.105385\pi\)
−0.945693 + 0.325062i \(0.894615\pi\)
\(200\) 3.05987e11i 0.956208i
\(201\) 1.60621e11i 0.489577i
\(202\) 4.04427e11i 1.20249i
\(203\) 4.81289e11 1.39613
\(204\) 2.90342e10i 0.0821787i
\(205\) 3.76846e10i 0.104086i
\(206\) 2.65526e11i 0.715765i
\(207\) 2.46713e11 0.649142
\(208\) −7.29892e10 −0.187474
\(209\) 5.70069e11i 1.42954i
\(210\) −7.98042e10 −0.195402
\(211\) 7.00685e11i 1.67537i −0.546154 0.837685i \(-0.683909\pi\)
0.546154 0.837685i \(-0.316091\pi\)
\(212\) 2.59336e11 0.605596
\(213\) 2.19770e11 0.501268
\(214\) 1.23397e11i 0.274939i
\(215\) −1.54158e11 + 2.92076e10i −0.335563 + 0.0635774i
\(216\) −4.70449e11 −1.00056
\(217\) 1.18476e12i 2.46226i
\(218\) 2.90255e11i 0.589519i
\(219\) 4.65675e11 0.924405
\(220\) 7.18368e10i 0.139391i
\(221\) 8.73163e10 0.165628
\(222\) 9.03743e10i 0.167602i
\(223\) 9.10457e11i 1.65095i 0.564435 + 0.825477i \(0.309094\pi\)
−0.564435 + 0.825477i \(0.690906\pi\)
\(224\) 5.94884e11 1.05485
\(225\) 3.59970e11 0.624243
\(226\) −2.41451e11 −0.409532
\(227\) 6.74469e11i 1.11901i 0.828828 + 0.559503i \(0.189008\pi\)
−0.828828 + 0.559503i \(0.810992\pi\)
\(228\) 2.00043e11 0.324675
\(229\) −3.67497e11 −0.583549 −0.291774 0.956487i \(-0.594246\pi\)
−0.291774 + 0.956487i \(0.594246\pi\)
\(230\) −1.54615e11 −0.240222
\(231\) 4.84853e11 0.737141
\(232\) −7.36244e11 −1.09542
\(233\) 1.67787e11i 0.244332i −0.992510 0.122166i \(-0.961016\pi\)
0.992510 0.122166i \(-0.0389840\pi\)
\(234\) 1.71434e11i 0.244352i
\(235\) 1.63921e11i 0.228716i
\(236\) 6.18176e10 0.0844407
\(237\) 6.60863e9i 0.00883831i
\(238\) 2.95869e11 0.387449
\(239\) −1.00398e12 −1.28747 −0.643734 0.765250i \(-0.722616\pi\)
−0.643734 + 0.765250i \(0.722616\pi\)
\(240\) 6.11459e10 0.0767912
\(241\) 5.25994e11i 0.646987i −0.946230 0.323494i \(-0.895143\pi\)
0.946230 0.323494i \(-0.104857\pi\)
\(242\) 1.69998e10i 0.0204817i
\(243\) 8.77731e11i 1.03593i
\(244\) 1.15527e11i 0.133578i
\(245\) 2.72350e11i 0.308530i
\(246\) 1.13860e11 0.126385
\(247\) 6.01601e11i 0.654370i
\(248\) 1.81237e12i 1.93192i
\(249\) 9.63714e11i 1.00682i
\(250\) −4.80976e11 −0.492520
\(251\) 4.05965e11 0.407493 0.203746 0.979024i \(-0.434688\pi\)
0.203746 + 0.979024i \(0.434688\pi\)
\(252\) 4.09893e11i 0.403337i
\(253\) 9.39370e11 0.906221
\(254\) 1.07810e12i 1.01974i
\(255\) −7.31483e10 −0.0678427
\(256\) −1.09885e12 −0.999400
\(257\) 8.11867e11i 0.724135i 0.932152 + 0.362067i \(0.117929\pi\)
−0.932152 + 0.362067i \(0.882071\pi\)
\(258\) 8.82479e10 + 4.65775e11i 0.0771980 + 0.407453i
\(259\) 6.49837e11 0.557578
\(260\) 7.58102e10i 0.0638059i
\(261\) 8.66134e11i 0.715126i
\(262\) −2.26145e11 −0.183181
\(263\) 2.50633e11i 0.199186i −0.995028 0.0995931i \(-0.968246\pi\)
0.995028 0.0995931i \(-0.0317541\pi\)
\(264\) −7.41696e11 −0.578370
\(265\) 6.53366e11i 0.499951i
\(266\) 2.03851e12i 1.53075i
\(267\) −7.18608e11 −0.529585
\(268\) 5.17020e11 0.373967
\(269\) −4.25165e11 −0.301853 −0.150927 0.988545i \(-0.548226\pi\)
−0.150927 + 0.988545i \(0.548226\pi\)
\(270\) 3.46846e11i 0.241723i
\(271\) −2.73669e12 −1.87232 −0.936159 0.351576i \(-0.885646\pi\)
−0.936159 + 0.351576i \(0.885646\pi\)
\(272\) −2.26694e11 −0.152264
\(273\) 5.11671e11 0.337425
\(274\) 1.50556e12 0.974865
\(275\) 1.37060e12 0.871461
\(276\) 3.29634e11i 0.205820i
\(277\) 2.06235e12i 1.26463i 0.774711 + 0.632316i \(0.217896\pi\)
−0.774711 + 0.632316i \(0.782104\pi\)
\(278\) 2.01441e12i 1.21317i
\(279\) −2.13212e12 −1.26122
\(280\) 8.77811e11i 0.510048i
\(281\) −6.20030e11 −0.353901 −0.176950 0.984220i \(-0.556623\pi\)
−0.176950 + 0.984220i \(0.556623\pi\)
\(282\) 4.95273e11 0.277715
\(283\) 1.69904e12 0.935989 0.467995 0.883731i \(-0.344977\pi\)
0.467995 + 0.883731i \(0.344977\pi\)
\(284\) 7.07414e11i 0.382897i
\(285\) 5.03984e11i 0.268036i
\(286\) 6.52742e11i 0.341123i
\(287\) 8.18714e11i 0.420458i
\(288\) 1.07056e12i 0.540318i
\(289\) −1.74480e12 −0.865480
\(290\) 5.42808e11i 0.264640i
\(291\) 1.33499e12i 0.639755i
\(292\) 1.49895e12i 0.706113i
\(293\) −7.92366e11 −0.366934 −0.183467 0.983026i \(-0.558732\pi\)
−0.183467 + 0.983026i \(0.558732\pi\)
\(294\) 8.22880e11 0.374628
\(295\) 1.55742e11i 0.0697102i
\(296\) −9.94078e11 −0.437484
\(297\) 2.10728e12i 0.911883i
\(298\) 2.17417e12 0.925150
\(299\) 9.91328e11 0.414822
\(300\) 4.80957e11i 0.197925i
\(301\) 3.34916e12 6.34548e11i 1.35551 0.256822i
\(302\) 5.07595e11 0.202061
\(303\) 2.17227e12i 0.850551i
\(304\) 1.56190e12i 0.601570i
\(305\) −2.91058e11 −0.110276
\(306\) 5.32449e11i 0.198459i
\(307\) 1.21485e12 0.445482 0.222741 0.974878i \(-0.428499\pi\)
0.222741 + 0.974878i \(0.428499\pi\)
\(308\) 1.56069e12i 0.563070i
\(309\) 1.42620e12i 0.506277i
\(310\) 1.33620e12 0.466727
\(311\) −6.82248e11 −0.234499 −0.117249 0.993103i \(-0.537408\pi\)
−0.117249 + 0.993103i \(0.537408\pi\)
\(312\) −7.82720e11 −0.264749
\(313\) 3.52780e12i 1.17431i −0.809475 0.587154i \(-0.800248\pi\)
0.809475 0.587154i \(-0.199752\pi\)
\(314\) −1.01485e12 −0.332471
\(315\) 1.03268e12 0.332975
\(316\) −2.12724e10 −0.00675120
\(317\) −2.20482e12 −0.688775 −0.344388 0.938828i \(-0.611913\pi\)
−0.344388 + 0.938828i \(0.611913\pi\)
\(318\) −1.97408e12 −0.607058
\(319\) 3.29785e12i 0.998337i
\(320\) 1.14668e12i 0.341737i
\(321\) 6.62796e11i 0.194471i
\(322\) 3.35909e12 0.970380
\(323\) 1.86849e12i 0.531469i
\(324\) 3.04370e11 0.0852467
\(325\) 1.44641e12 0.398910
\(326\) 2.20132e12 0.597855
\(327\) 1.55903e12i 0.416980i
\(328\) 1.25241e12i 0.329897i
\(329\) 3.56127e12i 0.923900i
\(330\) 5.46827e11i 0.139727i
\(331\) 2.43102e12i 0.611855i −0.952055 0.305927i \(-0.901034\pi\)
0.952055 0.305927i \(-0.0989665\pi\)
\(332\) −3.10209e12 −0.769065
\(333\) 1.16946e12i 0.285603i
\(334\) 1.40685e12i 0.338466i
\(335\) 1.30257e12i 0.308729i
\(336\) −1.32842e12 −0.310199
\(337\) 5.39499e12 1.24120 0.620599 0.784128i \(-0.286889\pi\)
0.620599 + 0.784128i \(0.286889\pi\)
\(338\) 2.68902e12i 0.609552i
\(339\) −1.29689e12 −0.289671
\(340\) 2.35456e11i 0.0518221i
\(341\) −8.11813e12 −1.76070
\(342\) 3.66852e12 0.784080
\(343\) 6.32933e11i 0.133317i
\(344\) −5.12331e12 + 9.70688e11i −1.06355 + 0.201506i
\(345\) −8.30475e11 −0.169915
\(346\) 4.11008e12i 0.828838i
\(347\) 6.73837e12i 1.33939i 0.742636 + 0.669696i \(0.233575\pi\)
−0.742636 + 0.669696i \(0.766425\pi\)
\(348\) −1.15725e12 −0.226741
\(349\) 4.64781e12i 0.897680i −0.893612 0.448840i \(-0.851837\pi\)
0.893612 0.448840i \(-0.148163\pi\)
\(350\) 4.90113e12 0.933159
\(351\) 2.22383e12i 0.417414i
\(352\) 4.07621e12i 0.754299i
\(353\) 3.20848e12 0.585364 0.292682 0.956210i \(-0.405452\pi\)
0.292682 + 0.956210i \(0.405452\pi\)
\(354\) −4.70560e11 −0.0846446
\(355\) 1.78225e12 0.316101
\(356\) 2.31312e12i 0.404527i
\(357\) 1.58918e12 0.274051
\(358\) −8.49396e12 −1.44442
\(359\) 5.26470e11 0.0882879 0.0441440 0.999025i \(-0.485944\pi\)
0.0441440 + 0.999025i \(0.485944\pi\)
\(360\) −1.57972e12 −0.261257
\(361\) −6.74263e12 −1.09975
\(362\) 1.83228e12i 0.294747i
\(363\) 9.13099e10i 0.0144872i
\(364\) 1.64701e12i 0.257745i
\(365\) 3.77644e12 0.582933
\(366\) 8.79404e11i 0.133901i
\(367\) 1.17492e12 0.176473 0.0882363 0.996100i \(-0.471877\pi\)
0.0882363 + 0.996100i \(0.471877\pi\)
\(368\) −2.57373e12 −0.381350
\(369\) −1.47337e12 −0.215367
\(370\) 7.32900e11i 0.105691i
\(371\) 1.41947e13i 2.01956i
\(372\) 2.84873e12i 0.399887i
\(373\) 4.43290e12i 0.613965i 0.951715 + 0.306983i \(0.0993194\pi\)
−0.951715 + 0.306983i \(0.900681\pi\)
\(374\) 2.02733e12i 0.277055i
\(375\) −2.58344e12 −0.348371
\(376\) 5.44778e12i 0.724904i
\(377\) 3.48026e12i 0.456988i
\(378\) 7.53539e12i 0.976443i
\(379\) −4.00681e12 −0.512393 −0.256196 0.966625i \(-0.582469\pi\)
−0.256196 + 0.966625i \(0.582469\pi\)
\(380\) 1.62227e12 0.204741
\(381\) 5.79070e12i 0.721284i
\(382\) 3.00348e12 0.369239
\(383\) 1.39574e13i 1.69360i 0.531910 + 0.846801i \(0.321474\pi\)
−0.531910 + 0.846801i \(0.678526\pi\)
\(384\) 7.07124e9 0.000846914
\(385\) 3.93197e12 0.464843
\(386\) 4.01283e12i 0.468289i
\(387\) −1.14194e12 6.02719e12i −0.131549 0.694320i
\(388\) 4.29719e12 0.488681
\(389\) 2.31623e12i 0.260037i 0.991512 + 0.130018i \(0.0415036\pi\)
−0.991512 + 0.130018i \(0.958496\pi\)
\(390\) 5.77073e11i 0.0639599i
\(391\) 3.07893e12 0.336911
\(392\) 9.05131e12i 0.977870i
\(393\) −1.21468e12 −0.129568
\(394\) 1.40402e13i 1.47874i
\(395\) 5.35933e10i 0.00557347i
\(396\) 2.80863e12 0.288416
\(397\) 1.32705e13 1.34566 0.672828 0.739799i \(-0.265079\pi\)
0.672828 + 0.739799i \(0.265079\pi\)
\(398\) 4.97130e12 0.497800
\(399\) 1.09493e13i 1.08273i
\(400\) −3.75524e12 −0.366723
\(401\) 5.20703e12 0.502190 0.251095 0.967962i \(-0.419209\pi\)
0.251095 + 0.967962i \(0.419209\pi\)
\(402\) −3.93560e12 −0.374870
\(403\) −8.56716e12 −0.805957
\(404\) 6.99228e12 0.649699
\(405\) 7.66826e11i 0.0703755i
\(406\) 1.17927e13i 1.06902i
\(407\) 4.45276e12i 0.398710i
\(408\) −2.43102e12 −0.215024
\(409\) 9.54493e11i 0.0833981i 0.999130 + 0.0416991i \(0.0132771\pi\)
−0.999130 + 0.0416991i \(0.986723\pi\)
\(410\) 9.23363e11 0.0796990
\(411\) 8.08669e12 0.689544
\(412\) −4.59078e12 −0.386723
\(413\) 3.38357e12i 0.281595i
\(414\) 6.04506e12i 0.497048i
\(415\) 7.81534e12i 0.634903i
\(416\) 4.30168e12i 0.345280i
\(417\) 1.08199e13i 0.858106i
\(418\) 1.39681e13 1.09460
\(419\) 1.77962e12i 0.137803i −0.997623 0.0689015i \(-0.978051\pi\)
0.997623 0.0689015i \(-0.0219494\pi\)
\(420\) 1.37977e12i 0.105574i
\(421\) 1.87889e13i 1.42067i −0.703866 0.710333i \(-0.748544\pi\)
0.703866 0.710333i \(-0.251456\pi\)
\(422\) −1.71685e13 −1.28283
\(423\) −6.40890e12 −0.473240
\(424\) 2.17140e13i 1.58457i
\(425\) 4.49236e12 0.323988
\(426\) 5.38490e12i 0.383822i
\(427\) 6.32337e12 0.445460
\(428\) −2.13346e12 −0.148548
\(429\) 3.50603e12i 0.241284i
\(430\) 7.15656e11 + 3.77725e12i 0.0486813 + 0.256941i
\(431\) −1.99363e13 −1.34047 −0.670235 0.742149i \(-0.733807\pi\)
−0.670235 + 0.742149i \(0.733807\pi\)
\(432\) 5.77361e12i 0.383733i
\(433\) 1.49688e13i 0.983442i −0.870753 0.491721i \(-0.836368\pi\)
0.870753 0.491721i \(-0.163632\pi\)
\(434\) −2.90296e13 −1.88535
\(435\) 2.91555e12i 0.187186i
\(436\) 5.01834e12 0.318513
\(437\) 2.12135e13i 1.33108i
\(438\) 1.14102e13i 0.707818i
\(439\) −2.43384e13 −1.49269 −0.746345 0.665559i \(-0.768193\pi\)
−0.746345 + 0.665559i \(0.768193\pi\)
\(440\) −6.01486e12 −0.364722
\(441\) −1.06482e13 −0.638384
\(442\) 2.13946e12i 0.126821i
\(443\) 1.89341e13 1.10975 0.554877 0.831932i \(-0.312765\pi\)
0.554877 + 0.831932i \(0.312765\pi\)
\(444\) −1.56252e12 −0.0905544
\(445\) −5.82762e12 −0.333958
\(446\) 2.23084e13 1.26414
\(447\) 1.16780e13 0.654380
\(448\) 2.49121e13i 1.38045i
\(449\) 2.57193e13i 1.40938i 0.709516 + 0.704689i \(0.248914\pi\)
−0.709516 + 0.704689i \(0.751086\pi\)
\(450\) 8.82013e12i 0.477983i
\(451\) −5.60992e12 −0.300659
\(452\) 4.17454e12i 0.221267i
\(453\) 2.72641e12 0.142922
\(454\) 1.65261e13 0.856824
\(455\) 4.14945e12 0.212781
\(456\) 1.67495e13i 0.849527i
\(457\) 1.67762e13i 0.841612i −0.907151 0.420806i \(-0.861747\pi\)
0.907151 0.420806i \(-0.138253\pi\)
\(458\) 9.00458e12i 0.446823i
\(459\) 6.90692e12i 0.339016i
\(460\) 2.67320e12i 0.129790i
\(461\) 6.97906e12 0.335191 0.167595 0.985856i \(-0.446400\pi\)
0.167595 + 0.985856i \(0.446400\pi\)
\(462\) 1.18801e13i 0.564429i
\(463\) 2.32578e13i 1.09311i −0.837424 0.546554i \(-0.815939\pi\)
0.837424 0.546554i \(-0.184061\pi\)
\(464\) 9.03559e12i 0.420114i
\(465\) 7.17705e12 0.330127
\(466\) −4.11120e12 −0.187085
\(467\) 2.17367e13i 0.978610i −0.872113 0.489305i \(-0.837251\pi\)
0.872113 0.489305i \(-0.162749\pi\)
\(468\) 2.96398e12 0.132022
\(469\) 2.82989e13i 1.24711i
\(470\) 4.01647e12 0.175128
\(471\) −5.45100e12 −0.235164
\(472\) 5.17596e12i 0.220943i
\(473\) −4.34799e12 2.29488e13i −0.183647 0.969291i
\(474\) 1.61927e11 0.00676750
\(475\) 3.09519e13i 1.28003i
\(476\) 5.11539e12i 0.209336i
\(477\) 2.55449e13 1.03446
\(478\) 2.46000e13i 0.985815i
\(479\) −2.81669e10 −0.00111702 −0.000558510 1.00000i \(-0.500178\pi\)
−0.000558510 1.00000i \(0.500178\pi\)
\(480\) 3.60368e12i 0.141430i
\(481\) 4.69905e12i 0.182509i
\(482\) −1.28881e13 −0.495399
\(483\) 1.80424e13 0.686372
\(484\) −2.93916e11 −0.0110661
\(485\) 1.08263e13i 0.403432i
\(486\) −2.15065e13 −0.793212
\(487\) −1.20644e13 −0.440414 −0.220207 0.975453i \(-0.570673\pi\)
−0.220207 + 0.975453i \(0.570673\pi\)
\(488\) −9.67306e12 −0.349514
\(489\) 1.18238e13 0.422876
\(490\) 6.67323e12 0.236241
\(491\) 2.92117e13i 1.02365i 0.859091 + 0.511823i \(0.171030\pi\)
−0.859091 + 0.511823i \(0.828970\pi\)
\(492\) 1.96858e12i 0.0682852i
\(493\) 1.08092e13i 0.371158i
\(494\) 1.47407e13 0.501052
\(495\) 7.07602e12i 0.238102i
\(496\) 2.22424e13 0.740925
\(497\) −3.87201e13 −1.27689
\(498\) 2.36133e13 0.770922
\(499\) 2.16113e13i 0.698518i 0.937026 + 0.349259i \(0.113567\pi\)
−0.937026 + 0.349259i \(0.886433\pi\)
\(500\) 8.31578e12i 0.266105i
\(501\) 7.55652e12i 0.239405i
\(502\) 9.94712e12i 0.312017i
\(503\) 2.33146e13i 0.724081i 0.932162 + 0.362041i \(0.117920\pi\)
−0.932162 + 0.362041i \(0.882080\pi\)
\(504\) 3.43201e13 1.05535
\(505\) 1.76162e13i 0.536360i
\(506\) 2.30168e13i 0.693894i
\(507\) 1.44434e13i 0.431150i
\(508\) 1.86396e13 0.550957
\(509\) 2.70498e13 0.791725 0.395863 0.918310i \(-0.370446\pi\)
0.395863 + 0.918310i \(0.370446\pi\)
\(510\) 1.79231e12i 0.0519472i
\(511\) −8.20449e13 −2.35476
\(512\) 2.69796e13i 0.766805i
\(513\) 4.75880e13 1.33940
\(514\) 1.98927e13 0.554470
\(515\) 1.15659e13i 0.319260i
\(516\) −8.05295e12 + 1.52575e12i −0.220144 + 0.0417095i
\(517\) −2.44022e13 −0.660657
\(518\) 1.59226e13i 0.426938i
\(519\) 2.20762e13i 0.586256i
\(520\) −6.34755e12 −0.166951
\(521\) 3.62146e13i 0.943397i 0.881760 + 0.471699i \(0.156359\pi\)
−0.881760 + 0.471699i \(0.843641\pi\)
\(522\) −2.12224e13 −0.547572
\(523\) 6.31653e13i 1.61425i 0.590382 + 0.807124i \(0.298977\pi\)
−0.590382 + 0.807124i \(0.701023\pi\)
\(524\) 3.90990e12i 0.0989713i
\(525\) 2.63251e13 0.660045
\(526\) −6.14111e12 −0.152517
\(527\) −2.66084e13 −0.654585
\(528\) 9.10250e12i 0.221815i
\(529\) −6.47051e12 −0.156193
\(530\) −1.60090e13 −0.382812
\(531\) 6.08911e12 0.144239
\(532\) −3.52445e13 −0.827053
\(533\) −5.92021e12 −0.137626
\(534\) 1.76076e13i 0.405503i
\(535\) 5.37501e12i 0.122634i
\(536\) 4.32898e13i 0.978502i
\(537\) −4.56230e13 −1.02167
\(538\) 1.04176e13i 0.231129i
\(539\) −4.05434e13 −0.891203
\(540\) −5.99676e12 −0.130601
\(541\) −6.60110e13 −1.42439 −0.712197 0.701980i \(-0.752300\pi\)
−0.712197 + 0.701980i \(0.752300\pi\)
\(542\) 6.70556e13i 1.43364i
\(543\) 9.84163e12i 0.208482i
\(544\) 1.33604e13i 0.280430i
\(545\) 1.26431e13i 0.262949i
\(546\) 1.25372e13i 0.258367i
\(547\) 1.33250e13 0.272101 0.136051 0.990702i \(-0.456559\pi\)
0.136051 + 0.990702i \(0.456559\pi\)
\(548\) 2.60301e13i 0.526713i
\(549\) 1.13796e13i 0.228174i
\(550\) 3.35831e13i 0.667278i
\(551\) 7.44742e13 1.46639
\(552\) −2.76001e13 −0.538537
\(553\) 1.16434e12i 0.0225141i
\(554\) 5.05326e13 0.968329
\(555\) 3.93658e12i 0.0747574i
\(556\) −3.48279e13 −0.655470
\(557\) 3.39684e13 0.633576 0.316788 0.948496i \(-0.397396\pi\)
0.316788 + 0.948496i \(0.397396\pi\)
\(558\) 5.22420e13i 0.965714i
\(559\) −4.58849e12 2.42181e13i −0.0840641 0.443692i
\(560\) −1.07730e13 −0.195612
\(561\) 1.08892e13i 0.195967i
\(562\) 1.51922e13i 0.270982i
\(563\) 5.27802e13 0.933103 0.466551 0.884494i \(-0.345496\pi\)
0.466551 + 0.884494i \(0.345496\pi\)
\(564\) 8.56297e12i 0.150047i
\(565\) −1.05173e13 −0.182667
\(566\) 4.16305e13i 0.716687i
\(567\) 1.66596e13i 0.284283i
\(568\) 5.92315e13 1.00187
\(569\) −5.12927e13 −0.859991 −0.429995 0.902831i \(-0.641485\pi\)
−0.429995 + 0.902831i \(0.641485\pi\)
\(570\) −1.23488e13 −0.205235
\(571\) 5.33154e13i 0.878358i 0.898399 + 0.439179i \(0.144731\pi\)
−0.898399 + 0.439179i \(0.855269\pi\)
\(572\) 1.12855e13 0.184307
\(573\) 1.61324e13 0.261171
\(574\) −2.00605e13 −0.321945
\(575\) 5.10031e13 0.811441
\(576\) −4.48322e13 −0.707095
\(577\) 2.64948e13i 0.414268i −0.978313 0.207134i \(-0.933586\pi\)
0.978313 0.207134i \(-0.0664135\pi\)
\(578\) 4.27519e13i 0.662698i
\(579\) 2.15538e13i 0.331231i
\(580\) −9.38481e12 −0.142983
\(581\) 1.69792e14i 2.56470i
\(582\) −3.27105e13 −0.489861
\(583\) 9.72634e13 1.44413
\(584\) 1.25507e14 1.84758
\(585\) 7.46741e12i 0.108991i
\(586\) 1.94149e13i 0.280961i
\(587\) 5.20980e13i 0.747533i −0.927523 0.373767i \(-0.878066\pi\)
0.927523 0.373767i \(-0.121934\pi\)
\(588\) 1.42271e13i 0.202409i
\(589\) 1.83329e14i 2.58616i
\(590\) −3.81606e12 −0.0533771
\(591\) 7.54131e13i 1.04595i
\(592\) 1.21999e13i 0.167783i
\(593\) 3.57776e13i 0.487908i −0.969787 0.243954i \(-0.921555\pi\)
0.969787 0.243954i \(-0.0784446\pi\)
\(594\) −5.16334e13 −0.698229
\(595\) 1.28876e13 0.172818
\(596\) 3.75901e13i 0.499852i
\(597\) 2.67020e13 0.352105
\(598\) 2.42899e13i 0.317629i
\(599\) −1.26951e14 −1.64627 −0.823135 0.567846i \(-0.807777\pi\)
−0.823135 + 0.567846i \(0.807777\pi\)
\(600\) −4.02703e13 −0.517880
\(601\) 3.05716e13i 0.389894i 0.980814 + 0.194947i \(0.0624534\pi\)
−0.980814 + 0.194947i \(0.937547\pi\)
\(602\) −1.55479e13 8.20624e13i −0.196649 1.03792i
\(603\) 5.09271e13 0.638797
\(604\) 8.77600e12i 0.109172i
\(605\) 7.40487e11i 0.00913567i
\(606\) −5.32258e13 −0.651268
\(607\) 6.84395e13i 0.830545i 0.909697 + 0.415273i \(0.136314\pi\)
−0.909697 + 0.415273i \(0.863686\pi\)
\(608\) 9.20519e13 1.10794
\(609\) 6.33416e13i 0.756140i
\(610\) 7.13162e12i 0.0844382i
\(611\) −2.57519e13 −0.302415
\(612\) 9.20572e12 0.107226
\(613\) −8.53731e13 −0.986322 −0.493161 0.869938i \(-0.664159\pi\)
−0.493161 + 0.869938i \(0.664159\pi\)
\(614\) 2.97667e13i 0.341106i
\(615\) 4.95960e12 0.0563729
\(616\) 1.30676e14 1.47330
\(617\) 2.18524e13 0.244384 0.122192 0.992506i \(-0.461008\pi\)
0.122192 + 0.992506i \(0.461008\pi\)
\(618\) 3.49454e13 0.387657
\(619\) −2.04095e13 −0.224585 −0.112292 0.993675i \(-0.535819\pi\)
−0.112292 + 0.993675i \(0.535819\pi\)
\(620\) 2.31021e13i 0.252170i
\(621\) 7.84163e13i 0.849080i
\(622\) 1.67167e13i 0.179556i
\(623\) 1.26608e14 1.34903
\(624\) 9.60598e12i 0.101536i
\(625\) 6.32927e13 0.663672
\(626\) −8.64396e13 −0.899168
\(627\) 7.50258e13 0.774235
\(628\) 1.75461e13i 0.179632i
\(629\) 1.45946e13i 0.148231i
\(630\) 2.53031e13i 0.254959i
\(631\) 7.52469e13i 0.752215i 0.926576 + 0.376107i \(0.122738\pi\)
−0.926576 + 0.376107i \(0.877262\pi\)
\(632\) 1.78113e12i 0.0176648i
\(633\) −9.22159e13 −0.907376
\(634\) 5.40235e13i 0.527395i
\(635\) 4.69603e13i 0.454844i
\(636\) 3.41307e13i 0.327989i
\(637\) −4.27860e13 −0.407947
\(638\) −8.08052e13 −0.764427
\(639\) 6.96813e13i 0.654051i
\(640\) 5.73450e10 0.000534067
\(641\) 1.55867e14i 1.44034i −0.693797 0.720170i \(-0.744064\pi\)
0.693797 0.720170i \(-0.255936\pi\)
\(642\) 1.62401e13 0.148906
\(643\) −3.80391e13 −0.346079 −0.173040 0.984915i \(-0.555359\pi\)
−0.173040 + 0.984915i \(0.555359\pi\)
\(644\) 5.80765e13i 0.524290i
\(645\) 3.84395e12 + 2.02885e13i 0.0344334 + 0.181740i
\(646\) 4.57825e13 0.406946
\(647\) 1.74027e14i 1.53495i −0.641079 0.767475i \(-0.721513\pi\)
0.641079 0.767475i \(-0.278487\pi\)
\(648\) 2.54848e13i 0.223052i
\(649\) 2.31846e13 0.201361
\(650\) 3.54406e13i 0.305446i
\(651\) −1.55925e14 −1.33355
\(652\) 3.80595e13i 0.323017i
\(653\) 4.79001e12i 0.0403432i 0.999797 + 0.0201716i \(0.00642125\pi\)
−0.999797 + 0.0201716i \(0.993579\pi\)
\(654\) −3.82000e13 −0.319282
\(655\) −9.85054e12 −0.0817059
\(656\) 1.53703e13 0.126521
\(657\) 1.47649e14i 1.20616i
\(658\) −8.72596e13 −0.707431
\(659\) −7.60118e13 −0.611581 −0.305790 0.952099i \(-0.598921\pi\)
−0.305790 + 0.952099i \(0.598921\pi\)
\(660\) −9.45431e12 −0.0754936
\(661\) 8.15282e13 0.646101 0.323051 0.946382i \(-0.395292\pi\)
0.323051 + 0.946382i \(0.395292\pi\)
\(662\) −5.95658e13 −0.468498
\(663\) 1.14915e13i 0.0897037i
\(664\) 2.59736e14i 2.01230i
\(665\) 8.87944e13i 0.682775i
\(666\) −2.86545e13 −0.218686
\(667\) 1.22720e14i 0.929579i
\(668\) 2.43236e13 0.182871
\(669\) 1.19824e14 0.894153
\(670\) −3.19161e13 −0.236394
\(671\) 4.33284e13i 0.318537i
\(672\) 7.82916e13i 0.571306i
\(673\) 4.44217e13i 0.321751i −0.986975 0.160875i \(-0.948568\pi\)
0.986975 0.160875i \(-0.0514317\pi\)
\(674\) 1.32190e14i 0.950387i
\(675\) 1.14414e14i 0.816511i
\(676\) −4.64915e13 −0.329337
\(677\) 6.36171e13i 0.447332i 0.974666 + 0.223666i \(0.0718025\pi\)
−0.974666 + 0.223666i \(0.928197\pi\)
\(678\) 3.17770e13i 0.221801i
\(679\) 2.35206e14i 1.62967i
\(680\) −1.97146e13 −0.135595
\(681\) 8.87656e13 0.606051
\(682\) 1.98914e14i 1.34817i
\(683\) 6.12519e13 0.412113 0.206056 0.978540i \(-0.433937\pi\)
0.206056 + 0.978540i \(0.433937\pi\)
\(684\) 6.34265e13i 0.423633i
\(685\) 6.55799e13 0.434828
\(686\) 1.55084e13 0.102081
\(687\) 4.83657e13i 0.316048i
\(688\) 1.19128e13 + 6.28762e13i 0.0772810 + 0.407891i
\(689\) 1.02643e14 0.661050
\(690\) 2.03486e13i 0.130104i
\(691\) 1.50480e14i 0.955187i −0.878581 0.477594i \(-0.841509\pi\)
0.878581 0.477594i \(-0.158491\pi\)
\(692\) −7.10607e13 −0.447815
\(693\) 1.53730e14i 0.961815i
\(694\) 1.65106e14 1.02557
\(695\) 8.77447e13i 0.541124i
\(696\) 9.68957e13i 0.593278i
\(697\) −1.83874e13 −0.111778
\(698\) −1.13883e14 −0.687354
\(699\) −2.20822e13 −0.132329
\(700\) 8.47374e13i 0.504179i
\(701\) 1.47876e13 0.0873590 0.0436795 0.999046i \(-0.486092\pi\)
0.0436795 + 0.999046i \(0.486092\pi\)
\(702\) −5.44893e13 −0.319614
\(703\) 1.00555e14 0.585637
\(704\) −1.70701e14 −0.987124
\(705\) 2.15734e13 0.123872
\(706\) 7.86156e13i 0.448214i
\(707\) 3.82721e14i 2.16663i
\(708\) 8.13570e12i 0.0457329i
\(709\) 7.96554e13 0.444615 0.222307 0.974977i \(-0.428641\pi\)
0.222307 + 0.974977i \(0.428641\pi\)
\(710\) 4.36694e13i 0.242039i
\(711\) −2.09536e12 −0.0115322
\(712\) −1.93676e14 −1.05846
\(713\) −3.02093e14 −1.63943
\(714\) 3.89387e13i 0.209841i
\(715\) 2.84325e13i 0.152155i
\(716\) 1.46855e14i 0.780413i
\(717\) 1.32132e14i 0.697289i
\(718\) 1.28998e13i 0.0676021i
\(719\) 3.84020e13 0.199852 0.0999262 0.994995i \(-0.468139\pi\)
0.0999262 + 0.994995i \(0.468139\pi\)
\(720\) 1.93872e13i 0.100197i
\(721\) 2.51275e14i 1.28965i
\(722\) 1.65211e14i 0.842078i
\(723\) −6.92252e13 −0.350407
\(724\) 3.16791e13 0.159250
\(725\) 1.79056e14i 0.893923i
\(726\) 2.23731e12 0.0110929
\(727\) 2.21940e14i 1.09286i 0.837505 + 0.546430i \(0.184013\pi\)
−0.837505 + 0.546430i \(0.815987\pi\)
\(728\) 1.37903e14 0.674401
\(729\) −7.30912e13 −0.354999
\(730\) 9.25319e13i 0.446352i
\(731\) −1.42512e13 7.52182e13i −0.0682754 0.360359i
\(732\) −1.52044e13 −0.0723457
\(733\) 2.82237e14i 1.33381i −0.745142 0.666906i \(-0.767618\pi\)
0.745142 0.666906i \(-0.232382\pi\)
\(734\) 2.87883e13i 0.135125i
\(735\) 3.58435e13 0.167099
\(736\) 1.51685e14i 0.702349i
\(737\) 1.93908e14 0.891779
\(738\) 3.61011e13i 0.164907i
\(739\) 2.05686e14i 0.933217i 0.884464 + 0.466608i \(0.154524\pi\)
−0.884464 + 0.466608i \(0.845476\pi\)
\(740\) −1.26714e13 −0.0571039
\(741\) 7.91756e13 0.354405
\(742\) 3.47804e14 1.54637
\(743\) 5.47942e13i 0.241986i −0.992653 0.120993i \(-0.961392\pi\)
0.992653 0.120993i \(-0.0386079\pi\)
\(744\) 2.38523e14 1.04632
\(745\) 9.47038e13 0.412654
\(746\) 1.08617e14 0.470114
\(747\) −3.05560e14 −1.31369
\(748\) 3.50512e13 0.149691
\(749\) 1.16775e14i 0.495381i
\(750\) 6.33004e13i 0.266748i
\(751\) 3.24437e14i 1.35810i 0.734094 + 0.679048i \(0.237607\pi\)
−0.734094 + 0.679048i \(0.762393\pi\)
\(752\) 6.68583e13 0.278014
\(753\) 5.34283e13i 0.220697i
\(754\) −8.52747e13 −0.349916
\(755\) 2.21101e13 0.0901272
\(756\) 1.30282e14 0.527565
\(757\) 6.59659e13i 0.265363i 0.991159 + 0.132682i \(0.0423587\pi\)
−0.991159 + 0.132682i \(0.957641\pi\)
\(758\) 9.81766e13i 0.392339i
\(759\) 1.23629e14i 0.490807i
\(760\) 1.35832e14i 0.535714i
\(761\) 4.49280e14i 1.76033i −0.474668 0.880165i \(-0.657432\pi\)
0.474668 0.880165i \(-0.342568\pi\)
\(762\) −1.41886e14 −0.552287
\(763\) 2.74677e14i 1.06219i
\(764\) 5.19282e13i 0.199497i
\(765\) 2.31927e13i 0.0885207i
\(766\) 3.41991e14 1.29679
\(767\) 2.44670e13 0.0921729
\(768\) 1.44618e14i 0.541273i
\(769\) −7.97361e13 −0.296499 −0.148249 0.988950i \(-0.547364\pi\)
−0.148249 + 0.988950i \(0.547364\pi\)
\(770\) 9.63427e13i 0.355930i
\(771\) 1.06848e14 0.392189
\(772\) −6.93793e13 −0.253013
\(773\) 3.67163e14i 1.33033i −0.746694 0.665167i \(-0.768360\pi\)
0.746694 0.665167i \(-0.231640\pi\)
\(774\) −1.47681e14 + 2.79803e13i −0.531641 + 0.100727i
\(775\) −4.40774e14 −1.57655
\(776\) 3.59802e14i 1.27866i
\(777\) 8.55239e13i 0.301983i
\(778\) 5.67534e13 0.199110
\(779\) 1.26687e14i 0.441616i
\(780\)