Properties

Label 43.9.b.b.42.7
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.7
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.22

$q$-expansion

\(f(q)\) \(=\) \(q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} +O(q^{10})\) \(q-23.0076i q^{2} -78.5211i q^{3} -273.350 q^{4} -548.269i q^{5} -1806.58 q^{6} -2213.93i q^{7} +399.191i q^{8} +395.432 q^{9} -12614.4 q^{10} -22302.0 q^{11} +21463.8i q^{12} +25711.7 q^{13} -50937.3 q^{14} -43050.7 q^{15} -60793.3 q^{16} +94860.8 q^{17} -9097.95i q^{18} -13775.7i q^{19} +149870. i q^{20} -173841. q^{21} +513115. i q^{22} +444307. q^{23} +31345.0 q^{24} +90025.7 q^{25} -591564. i q^{26} -546227. i q^{27} +605180. i q^{28} +843909. i q^{29} +990495. i q^{30} +557250. q^{31} +1.50090e6i q^{32} +1.75117e6i q^{33} -2.18252e6i q^{34} -1.21383e6 q^{35} -108092. q^{36} +1.34789e6i q^{37} -316945. q^{38} -2.01891e6i q^{39} +218864. q^{40} -2.42209e6 q^{41} +3.99966e6i q^{42} +(-493656. - 3.38297e6i) q^{43} +6.09625e6 q^{44} -216803. i q^{45} -1.02224e7i q^{46} -4.12862e6 q^{47} +4.77356e6i q^{48} +863301. q^{49} -2.07128e6i q^{50} -7.44857e6i q^{51} -7.02829e6 q^{52} +717126. q^{53} -1.25674e7 q^{54} +1.22275e7i q^{55} +883783. q^{56} -1.08168e6 q^{57} +1.94163e7 q^{58} -1.58674e7 q^{59} +1.17679e7 q^{60} -1.76056e7i q^{61} -1.28210e7i q^{62} -875460. i q^{63} +1.89691e7 q^{64} -1.40969e7i q^{65} +4.02904e7 q^{66} +2.33402e7 q^{67} -2.59302e7 q^{68} -3.48875e7i q^{69} +2.79274e7i q^{70} +1.27010e7i q^{71} +157853. i q^{72} -4.05442e6i q^{73} +3.10116e7 q^{74} -7.06892e6i q^{75} +3.76559e6i q^{76} +4.93750e7i q^{77} -4.64503e7 q^{78} -6.41487e7 q^{79} +3.33311e7i q^{80} -4.02959e7 q^{81} +5.57265e7i q^{82} -4.42985e7 q^{83} +4.75194e7 q^{84} -5.20092e7i q^{85} +(-7.78341e7 + 1.13579e7i) q^{86} +6.62647e7 q^{87} -8.90275e6i q^{88} +8.42809e7i q^{89} -4.98813e6 q^{90} -5.69239e7i q^{91} -1.21451e8 q^{92} -4.37559e7i q^{93} +9.49898e7i q^{94} -7.55278e6 q^{95} +1.17852e8 q^{96} +6.90318e7 q^{97} -1.98625e7i q^{98} -8.81891e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.0076i 1.43798i −0.695022 0.718988i \(-0.744606\pi\)
0.695022 0.718988i \(-0.255394\pi\)
\(3\) 78.5211i 0.969397i −0.874681 0.484698i \(-0.838929\pi\)
0.874681 0.484698i \(-0.161071\pi\)
\(4\) −273.350 −1.06778
\(5\) 548.269i 0.877231i −0.898675 0.438616i \(-0.855469\pi\)
0.898675 0.438616i \(-0.144531\pi\)
\(6\) −1806.58 −1.39397
\(7\) 2213.93i 0.922088i −0.887377 0.461044i \(-0.847475\pi\)
0.887377 0.461044i \(-0.152525\pi\)
\(8\) 399.191i 0.0974589i
\(9\) 395.432 0.0602701
\(10\) −12614.4 −1.26144
\(11\) −22302.0 −1.52325 −0.761627 0.648016i \(-0.775599\pi\)
−0.761627 + 0.648016i \(0.775599\pi\)
\(12\) 21463.8i 1.03510i
\(13\) 25711.7 0.900237 0.450118 0.892969i \(-0.351382\pi\)
0.450118 + 0.892969i \(0.351382\pi\)
\(14\) −50937.3 −1.32594
\(15\) −43050.7 −0.850385
\(16\) −60793.3 −0.927632
\(17\) 94860.8 1.13577 0.567886 0.823107i \(-0.307762\pi\)
0.567886 + 0.823107i \(0.307762\pi\)
\(18\) 9097.95i 0.0866670i
\(19\) 13775.7i 0.105706i −0.998602 0.0528528i \(-0.983169\pi\)
0.998602 0.0528528i \(-0.0168314\pi\)
\(20\) 149870.i 0.936685i
\(21\) −173841. −0.893869
\(22\) 513115.i 2.19040i
\(23\) 444307. 1.58771 0.793856 0.608106i \(-0.208070\pi\)
0.793856 + 0.608106i \(0.208070\pi\)
\(24\) 31345.0 0.0944763
\(25\) 90025.7 0.230466
\(26\) 591564.i 1.29452i
\(27\) 546227.i 1.02782i
\(28\) 605180.i 0.984582i
\(29\) 843909.i 1.19317i 0.802549 + 0.596587i \(0.203477\pi\)
−0.802549 + 0.596587i \(0.796523\pi\)
\(30\) 990495.i 1.22283i
\(31\) 557250. 0.603398 0.301699 0.953403i \(-0.402446\pi\)
0.301699 + 0.953403i \(0.402446\pi\)
\(32\) 1.50090e6i 1.43137i
\(33\) 1.75117e6i 1.47664i
\(34\) 2.18252e6i 1.63321i
\(35\) −1.21383e6 −0.808884
\(36\) −108092. −0.0643549
\(37\) 1.34789e6i 0.719194i 0.933108 + 0.359597i \(0.117086\pi\)
−0.933108 + 0.359597i \(0.882914\pi\)
\(38\) −316945. −0.152002
\(39\) 2.01891e6i 0.872687i
\(40\) 218864. 0.0854939
\(41\) −2.42209e6 −0.857146 −0.428573 0.903507i \(-0.640984\pi\)
−0.428573 + 0.903507i \(0.640984\pi\)
\(42\) 3.99966e6i 1.28536i
\(43\) −493656. 3.38297e6i −0.144395 0.989520i
\(44\) 6.09625e6 1.62649
\(45\) 216803.i 0.0528708i
\(46\) 1.02224e7i 2.28309i
\(47\) −4.12862e6 −0.846084 −0.423042 0.906110i \(-0.639038\pi\)
−0.423042 + 0.906110i \(0.639038\pi\)
\(48\) 4.77356e6i 0.899243i
\(49\) 863301. 0.149754
\(50\) 2.07128e6i 0.331404i
\(51\) 7.44857e6i 1.10101i
\(52\) −7.02829e6 −0.961250
\(53\) 717126. 0.0908849 0.0454425 0.998967i \(-0.485530\pi\)
0.0454425 + 0.998967i \(0.485530\pi\)
\(54\) −1.25674e7 −1.47798
\(55\) 1.22275e7i 1.33625i
\(56\) 883783. 0.0898656
\(57\) −1.08168e6 −0.102471
\(58\) 1.94163e7 1.71575
\(59\) −1.58674e7 −1.30947 −0.654737 0.755856i \(-0.727221\pi\)
−0.654737 + 0.755856i \(0.727221\pi\)
\(60\) 1.17679e7 0.908020
\(61\) 1.76056e7i 1.27154i −0.771877 0.635772i \(-0.780682\pi\)
0.771877 0.635772i \(-0.219318\pi\)
\(62\) 1.28210e7i 0.867671i
\(63\) 875460.i 0.0555743i
\(64\) 1.89691e7 1.13065
\(65\) 1.40969e7i 0.789716i
\(66\) 4.02904e7 2.12337
\(67\) 2.33402e7 1.15826 0.579129 0.815236i \(-0.303393\pi\)
0.579129 + 0.815236i \(0.303393\pi\)
\(68\) −2.59302e7 −1.21275
\(69\) 3.48875e7i 1.53912i
\(70\) 2.79274e7i 1.16316i
\(71\) 1.27010e7i 0.499811i 0.968270 + 0.249905i \(0.0803995\pi\)
−0.968270 + 0.249905i \(0.919600\pi\)
\(72\) 157853.i 0.00587386i
\(73\) 4.05442e6i 0.142770i −0.997449 0.0713851i \(-0.977258\pi\)
0.997449 0.0713851i \(-0.0227419\pi\)
\(74\) 3.10116e7 1.03418
\(75\) 7.06892e6i 0.223413i
\(76\) 3.76559e6i 0.112870i
\(77\) 4.93750e7i 1.40457i
\(78\) −4.64503e7 −1.25490
\(79\) −6.41487e7 −1.64695 −0.823473 0.567356i \(-0.807966\pi\)
−0.823473 + 0.567356i \(0.807966\pi\)
\(80\) 3.33311e7i 0.813747i
\(81\) −4.02959e7 −0.936097
\(82\) 5.57265e7i 1.23256i
\(83\) −4.42985e7 −0.933420 −0.466710 0.884410i \(-0.654561\pi\)
−0.466710 + 0.884410i \(0.654561\pi\)
\(84\) 4.75194e7 0.954451
\(85\) 5.20092e7i 0.996334i
\(86\) −7.78341e7 + 1.13579e7i −1.42291 + 0.207636i
\(87\) 6.62647e7 1.15666
\(88\) 8.90275e6i 0.148455i
\(89\) 8.42809e7i 1.34329i 0.740874 + 0.671644i \(0.234412\pi\)
−0.740874 + 0.671644i \(0.765588\pi\)
\(90\) −4.98813e6 −0.0760270
\(91\) 5.69239e7i 0.830098i
\(92\) −1.21451e8 −1.69532
\(93\) 4.37559e7i 0.584932i
\(94\) 9.49898e7i 1.21665i
\(95\) −7.55278e6 −0.0927283
\(96\) 1.17852e8 1.38757
\(97\) 6.90318e7 0.779762 0.389881 0.920865i \(-0.372516\pi\)
0.389881 + 0.920865i \(0.372516\pi\)
\(98\) 1.98625e7i 0.215342i
\(99\) −8.81891e6 −0.0918067
\(100\) −2.46086e7 −0.246086
\(101\) 5.71873e6 0.0549558 0.0274779 0.999622i \(-0.491252\pi\)
0.0274779 + 0.999622i \(0.491252\pi\)
\(102\) −1.71374e8 −1.58323
\(103\) 4.67582e7 0.415441 0.207720 0.978188i \(-0.433396\pi\)
0.207720 + 0.978188i \(0.433396\pi\)
\(104\) 1.02639e7i 0.0877361i
\(105\) 9.53114e7i 0.784130i
\(106\) 1.64994e7i 0.130690i
\(107\) 1.33766e8 1.02050 0.510248 0.860027i \(-0.329554\pi\)
0.510248 + 0.860027i \(0.329554\pi\)
\(108\) 1.49311e8i 1.09748i
\(109\) 9.33602e7 0.661387 0.330694 0.943738i \(-0.392717\pi\)
0.330694 + 0.943738i \(0.392717\pi\)
\(110\) 2.81325e8 1.92149
\(111\) 1.05837e8 0.697184
\(112\) 1.34592e8i 0.855358i
\(113\) 2.60559e8i 1.59806i −0.601294 0.799028i \(-0.705348\pi\)
0.601294 0.799028i \(-0.294652\pi\)
\(114\) 2.48869e7i 0.147350i
\(115\) 2.43600e8i 1.39279i
\(116\) 2.30683e8i 1.27404i
\(117\) 1.01672e7 0.0542574
\(118\) 3.65071e8i 1.88299i
\(119\) 2.10015e8i 1.04728i
\(120\) 1.71855e7i 0.0828775i
\(121\) 2.83018e8 1.32030
\(122\) −4.05063e8 −1.82845
\(123\) 1.90185e8i 0.830914i
\(124\) −1.52325e8 −0.644293
\(125\) 2.63526e8i 1.07940i
\(126\) −2.01423e7 −0.0799146
\(127\) 2.42053e8 0.930457 0.465229 0.885191i \(-0.345972\pi\)
0.465229 + 0.885191i \(0.345972\pi\)
\(128\) 5.22027e7i 0.194470i
\(129\) −2.65635e8 + 3.87624e7i −0.959238 + 0.139976i
\(130\) −3.24337e8 −1.13559
\(131\) 3.17260e7i 0.107728i 0.998548 + 0.0538642i \(0.0171538\pi\)
−0.998548 + 0.0538642i \(0.982846\pi\)
\(132\) 4.78684e8i 1.57672i
\(133\) −3.04984e7 −0.0974700
\(134\) 5.37003e8i 1.66555i
\(135\) −2.99479e8 −0.901638
\(136\) 3.78676e7i 0.110691i
\(137\) 4.48682e7i 0.127367i −0.997970 0.0636834i \(-0.979715\pi\)
0.997970 0.0636834i \(-0.0202848\pi\)
\(138\) −8.02678e8 −2.21322
\(139\) 2.23751e8 0.599384 0.299692 0.954036i \(-0.403116\pi\)
0.299692 + 0.954036i \(0.403116\pi\)
\(140\) 3.31801e8 0.863706
\(141\) 3.24184e8i 0.820191i
\(142\) 2.92220e8 0.718716
\(143\) −5.73421e8 −1.37129
\(144\) −2.40396e7 −0.0559085
\(145\) 4.62689e8 1.04669
\(146\) −9.32826e7 −0.205300
\(147\) 6.77874e7i 0.145171i
\(148\) 3.68445e8i 0.767937i
\(149\) 5.16841e8i 1.04861i 0.851532 + 0.524303i \(0.175674\pi\)
−0.851532 + 0.524303i \(0.824326\pi\)
\(150\) −1.62639e8 −0.321262
\(151\) 2.26895e8i 0.436432i −0.975900 0.218216i \(-0.929976\pi\)
0.975900 0.218216i \(-0.0700238\pi\)
\(152\) 5.49913e6 0.0103020
\(153\) 3.75110e7 0.0684531
\(154\) 1.13600e9 2.01974
\(155\) 3.05523e8i 0.529319i
\(156\) 5.51870e8i 0.931833i
\(157\) 1.47899e8i 0.243426i 0.992565 + 0.121713i \(0.0388387\pi\)
−0.992565 + 0.121713i \(0.961161\pi\)
\(158\) 1.47591e9i 2.36827i
\(159\) 5.63095e7i 0.0881035i
\(160\) 8.22898e8 1.25564
\(161\) 9.83666e8i 1.46401i
\(162\) 9.27113e8i 1.34609i
\(163\) 5.39395e8i 0.764111i 0.924139 + 0.382056i \(0.124784\pi\)
−0.924139 + 0.382056i \(0.875216\pi\)
\(164\) 6.62079e8 0.915239
\(165\) 9.60116e8 1.29535
\(166\) 1.01920e9i 1.34224i
\(167\) −1.17007e9 −1.50434 −0.752171 0.658968i \(-0.770993\pi\)
−0.752171 + 0.658968i \(0.770993\pi\)
\(168\) 6.93957e7i 0.0871155i
\(169\) −1.54641e8 −0.189573
\(170\) −1.19661e9 −1.43270
\(171\) 5.44734e6i 0.00637089i
\(172\) 1.34941e8 + 9.24737e8i 0.154181 + 1.05658i
\(173\) −7.41901e7 −0.0828250 −0.0414125 0.999142i \(-0.513186\pi\)
−0.0414125 + 0.999142i \(0.513186\pi\)
\(174\) 1.52459e9i 1.66325i
\(175\) 1.99311e8i 0.212510i
\(176\) 1.35581e9 1.41302
\(177\) 1.24592e9i 1.26940i
\(178\) 1.93910e9 1.93162
\(179\) 1.95172e9i 1.90110i −0.310566 0.950552i \(-0.600519\pi\)
0.310566 0.950552i \(-0.399481\pi\)
\(180\) 5.92633e7i 0.0564541i
\(181\) −1.70935e9 −1.59264 −0.796319 0.604877i \(-0.793222\pi\)
−0.796319 + 0.604877i \(0.793222\pi\)
\(182\) −1.30968e9 −1.19366
\(183\) −1.38241e9 −1.23263
\(184\) 1.77363e8i 0.154737i
\(185\) 7.39004e8 0.630899
\(186\) −1.00672e9 −0.841118
\(187\) −2.11558e9 −1.73007
\(188\) 1.12856e9 0.903428
\(189\) −1.20931e9 −0.947743
\(190\) 1.73771e8i 0.133341i
\(191\) 2.52030e9i 1.89373i 0.321628 + 0.946866i \(0.395770\pi\)
−0.321628 + 0.946866i \(0.604230\pi\)
\(192\) 1.48947e9i 1.09604i
\(193\) 1.25620e9 0.905380 0.452690 0.891668i \(-0.350464\pi\)
0.452690 + 0.891668i \(0.350464\pi\)
\(194\) 1.58826e9i 1.12128i
\(195\) −1.10691e9 −0.765548
\(196\) −2.35984e8 −0.159903
\(197\) 7.03003e8 0.466758 0.233379 0.972386i \(-0.425022\pi\)
0.233379 + 0.972386i \(0.425022\pi\)
\(198\) 2.02902e8i 0.132016i
\(199\) 1.62062e9i 1.03340i 0.856166 + 0.516701i \(0.172840\pi\)
−0.856166 + 0.516701i \(0.827160\pi\)
\(200\) 3.59375e7i 0.0224609i
\(201\) 1.83270e9i 1.12281i
\(202\) 1.31574e8i 0.0790252i
\(203\) 1.86836e9 1.10021
\(204\) 2.03607e9i 1.17563i
\(205\) 1.32796e9i 0.751915i
\(206\) 1.07579e9i 0.597394i
\(207\) 1.75693e8 0.0956916
\(208\) −1.56310e9 −0.835088
\(209\) 3.07224e8i 0.161017i
\(210\) 2.19289e9 1.12756
\(211\) 2.02893e8i 0.102362i 0.998689 + 0.0511808i \(0.0162985\pi\)
−0.998689 + 0.0511808i \(0.983702\pi\)
\(212\) −1.96027e8 −0.0970446
\(213\) 9.97299e8 0.484515
\(214\) 3.07764e9i 1.46745i
\(215\) −1.85478e9 + 2.70657e8i −0.868038 + 0.126667i
\(216\) 2.18049e8 0.100170
\(217\) 1.23371e9i 0.556386i
\(218\) 2.14800e9i 0.951059i
\(219\) −3.18358e8 −0.138401
\(220\) 3.34239e9i 1.42681i
\(221\) 2.43903e9 1.02246
\(222\) 2.43507e9i 1.00253i
\(223\) 2.20052e9i 0.889827i −0.895573 0.444914i \(-0.853234\pi\)
0.895573 0.444914i \(-0.146766\pi\)
\(224\) 3.32289e9 1.31985
\(225\) 3.55990e7 0.0138902
\(226\) −5.99484e9 −2.29797
\(227\) 3.11333e9i 1.17252i −0.810122 0.586262i \(-0.800599\pi\)
0.810122 0.586262i \(-0.199401\pi\)
\(228\) 2.95678e8 0.109416
\(229\) 4.08434e9 1.48518 0.742592 0.669744i \(-0.233596\pi\)
0.742592 + 0.669744i \(0.233596\pi\)
\(230\) −5.60465e9 −2.00280
\(231\) 3.87698e9 1.36159
\(232\) −3.36881e8 −0.116285
\(233\) 3.98505e9i 1.35210i 0.736854 + 0.676052i \(0.236311\pi\)
−0.736854 + 0.676052i \(0.763689\pi\)
\(234\) 2.33924e8i 0.0780208i
\(235\) 2.26360e9i 0.742212i
\(236\) 4.33735e9 1.39822
\(237\) 5.03702e9i 1.59654i
\(238\) −4.83195e9 −1.50596
\(239\) 3.61698e9 1.10855 0.554274 0.832334i \(-0.312996\pi\)
0.554274 + 0.832334i \(0.312996\pi\)
\(240\) 2.61719e9 0.788844
\(241\) 5.13891e9i 1.52336i 0.647953 + 0.761680i \(0.275625\pi\)
−0.647953 + 0.761680i \(0.724375\pi\)
\(242\) 6.51158e9i 1.89856i
\(243\) 4.19713e8i 0.120373i
\(244\) 4.81250e9i 1.35772i
\(245\) 4.73321e8i 0.131369i
\(246\) 4.37571e9 1.19483
\(247\) 3.54195e8i 0.0951602i
\(248\) 2.22450e8i 0.0588064i
\(249\) 3.47837e9i 0.904854i
\(250\) −6.06311e9 −1.55216
\(251\) 3.59876e9 0.906688 0.453344 0.891336i \(-0.350231\pi\)
0.453344 + 0.891336i \(0.350231\pi\)
\(252\) 2.39307e8i 0.0593409i
\(253\) −9.90891e9 −2.41849
\(254\) 5.56907e9i 1.33798i
\(255\) −4.08382e9 −0.965843
\(256\) 3.65503e9 0.851002
\(257\) 3.58551e9i 0.821898i −0.911658 0.410949i \(-0.865197\pi\)
0.911658 0.410949i \(-0.134803\pi\)
\(258\) 8.91832e8 + 6.11162e9i 0.201282 + 1.37936i
\(259\) 2.98413e9 0.663160
\(260\) 3.85340e9i 0.843239i
\(261\) 3.33709e8i 0.0719127i
\(262\) 7.29939e8 0.154911
\(263\) 2.72133e9i 0.568799i −0.958706 0.284400i \(-0.908206\pi\)
0.958706 0.284400i \(-0.0917942\pi\)
\(264\) −6.99054e8 −0.143911
\(265\) 3.93178e8i 0.0797271i
\(266\) 7.01696e8i 0.140159i
\(267\) 6.61783e9 1.30218
\(268\) −6.38006e9 −1.23676
\(269\) −5.51586e9 −1.05343 −0.526713 0.850043i \(-0.676576\pi\)
−0.526713 + 0.850043i \(0.676576\pi\)
\(270\) 6.89031e9i 1.29653i
\(271\) −2.83300e9 −0.525255 −0.262627 0.964897i \(-0.584589\pi\)
−0.262627 + 0.964897i \(0.584589\pi\)
\(272\) −5.76689e9 −1.05358
\(273\) −4.46973e9 −0.804694
\(274\) −1.03231e9 −0.183150
\(275\) −2.00775e9 −0.351058
\(276\) 9.53650e9i 1.64344i
\(277\) 9.20304e9i 1.56319i −0.623785 0.781596i \(-0.714406\pi\)
0.623785 0.781596i \(-0.285594\pi\)
\(278\) 5.14797e9i 0.861900i
\(279\) 2.20355e8 0.0363668
\(280\) 4.84551e8i 0.0788329i
\(281\) 4.72092e9 0.757184 0.378592 0.925564i \(-0.376408\pi\)
0.378592 + 0.925564i \(0.376408\pi\)
\(282\) 7.45870e9 1.17942
\(283\) 1.11248e9 0.173439 0.0867194 0.996233i \(-0.472362\pi\)
0.0867194 + 0.996233i \(0.472362\pi\)
\(284\) 3.47183e9i 0.533685i
\(285\) 5.93053e8i 0.0898905i
\(286\) 1.31930e10i 1.97188i
\(287\) 5.36234e9i 0.790364i
\(288\) 5.93505e8i 0.0862689i
\(289\) 2.02281e9 0.289976
\(290\) 1.06454e10i 1.50511i
\(291\) 5.42045e9i 0.755899i
\(292\) 1.10828e9i 0.152446i
\(293\) −6.59517e9 −0.894860 −0.447430 0.894319i \(-0.647661\pi\)
−0.447430 + 0.894319i \(0.647661\pi\)
\(294\) −1.55963e9 −0.208752
\(295\) 8.69960e9i 1.14871i
\(296\) −5.38064e8 −0.0700918
\(297\) 1.21819e10i 1.56563i
\(298\) 1.18913e10 1.50787
\(299\) 1.14239e10 1.42932
\(300\) 1.93229e9i 0.238555i
\(301\) −7.48968e9 + 1.09292e9i −0.912425 + 0.133144i
\(302\) −5.22031e9 −0.627579
\(303\) 4.49041e8i 0.0532740i
\(304\) 8.37468e8i 0.0980559i
\(305\) −9.65261e9 −1.11544
\(306\) 8.63039e8i 0.0984339i
\(307\) 2.40305e9 0.270526 0.135263 0.990810i \(-0.456812\pi\)
0.135263 + 0.990810i \(0.456812\pi\)
\(308\) 1.34967e10i 1.49977i
\(309\) 3.67151e9i 0.402727i
\(310\) −7.02936e9 −0.761148
\(311\) 1.25145e10 1.33774 0.668870 0.743380i \(-0.266778\pi\)
0.668870 + 0.743380i \(0.266778\pi\)
\(312\) 8.05931e8 0.0850510
\(313\) 2.72482e9i 0.283897i 0.989874 + 0.141948i \(0.0453367\pi\)
−0.989874 + 0.141948i \(0.954663\pi\)
\(314\) 3.40280e9 0.350040
\(315\) −4.79988e8 −0.0487515
\(316\) 1.75351e10 1.75857
\(317\) 2.40399e9 0.238065 0.119033 0.992890i \(-0.462021\pi\)
0.119033 + 0.992890i \(0.462021\pi\)
\(318\) −1.29555e9 −0.126691
\(319\) 1.88208e10i 1.81751i
\(320\) 1.04002e10i 0.991837i
\(321\) 1.05035e10i 0.989265i
\(322\) −2.26318e10 −2.10521
\(323\) 1.30677e9i 0.120057i
\(324\) 1.10149e10 0.999541
\(325\) 2.31471e9 0.207474
\(326\) 1.24102e10 1.09877
\(327\) 7.33075e9i 0.641147i
\(328\) 9.66878e8i 0.0835365i
\(329\) 9.14049e9i 0.780164i
\(330\) 2.20900e10i 1.86268i
\(331\) 1.85040e10i 1.54153i 0.637118 + 0.770766i \(0.280126\pi\)
−0.637118 + 0.770766i \(0.719874\pi\)
\(332\) 1.21090e10 0.996683
\(333\) 5.32997e8i 0.0433459i
\(334\) 2.69206e10i 2.16321i
\(335\) 1.27967e10i 1.01606i
\(336\) 1.05683e10 0.829181
\(337\) 1.84917e10 1.43370 0.716849 0.697229i \(-0.245584\pi\)
0.716849 + 0.697229i \(0.245584\pi\)
\(338\) 3.55792e9i 0.272602i
\(339\) −2.04594e10 −1.54915
\(340\) 1.42167e10i 1.06386i
\(341\) −1.24278e10 −0.919128
\(342\) −1.25330e8 −0.00916119
\(343\) 1.46742e10i 1.06017i
\(344\) 1.35045e9 1.97063e8i 0.0964375 0.0140725i
\(345\) −1.91277e10 −1.35017
\(346\) 1.70694e9i 0.119100i
\(347\) 2.21431e9i 0.152729i 0.997080 + 0.0763643i \(0.0243312\pi\)
−0.997080 + 0.0763643i \(0.975669\pi\)
\(348\) −1.81135e10 −1.23505
\(349\) 1.01146e10i 0.681787i −0.940102 0.340893i \(-0.889270\pi\)
0.940102 0.340893i \(-0.110730\pi\)
\(350\) −4.58567e9 −0.305584
\(351\) 1.40444e10i 0.925284i
\(352\) 3.34730e10i 2.18034i
\(353\) −1.17769e10 −0.758461 −0.379230 0.925302i \(-0.623811\pi\)
−0.379230 + 0.925302i \(0.623811\pi\)
\(354\) 2.86658e10 1.82537
\(355\) 6.96359e9 0.438449
\(356\) 2.30382e10i 1.43433i
\(357\) −1.64906e10 −1.01523
\(358\) −4.49045e10 −2.73374
\(359\) −2.45068e9 −0.147540 −0.0737700 0.997275i \(-0.523503\pi\)
−0.0737700 + 0.997275i \(0.523503\pi\)
\(360\) 8.65461e7 0.00515273
\(361\) 1.67938e10 0.988826
\(362\) 3.93281e10i 2.29017i
\(363\) 2.22229e10i 1.27990i
\(364\) 1.55602e10i 0.886358i
\(365\) −2.22291e9 −0.125242
\(366\) 3.18060e10i 1.77249i
\(367\) 1.88958e10 1.04160 0.520800 0.853678i \(-0.325634\pi\)
0.520800 + 0.853678i \(0.325634\pi\)
\(368\) −2.70109e10 −1.47281
\(369\) −9.57772e8 −0.0516603
\(370\) 1.70027e10i 0.907218i
\(371\) 1.58767e9i 0.0838039i
\(372\) 1.19607e10i 0.624575i
\(373\) 6.77386e9i 0.349946i 0.984573 + 0.174973i \(0.0559838\pi\)
−0.984573 + 0.174973i \(0.944016\pi\)
\(374\) 4.86745e10i 2.48780i
\(375\) −2.06924e10 −1.04637
\(376\) 1.64811e9i 0.0824584i
\(377\) 2.16983e10i 1.07414i
\(378\) 2.78233e10i 1.36283i
\(379\) −3.86135e10 −1.87147 −0.935735 0.352704i \(-0.885262\pi\)
−0.935735 + 0.352704i \(0.885262\pi\)
\(380\) 2.06456e9 0.0990130
\(381\) 1.90063e10i 0.901982i
\(382\) 5.79861e10 2.72314
\(383\) 3.90536e10i 1.81495i −0.420101 0.907477i \(-0.638005\pi\)
0.420101 0.907477i \(-0.361995\pi\)
\(384\) −4.09901e9 −0.188519
\(385\) 2.70708e10 1.23214
\(386\) 2.89023e10i 1.30192i
\(387\) −1.95208e8 1.33774e9i −0.00870268 0.0596385i
\(388\) −1.88699e10 −0.832610
\(389\) 2.51473e10i 1.09823i 0.835747 + 0.549115i \(0.185035\pi\)
−0.835747 + 0.549115i \(0.814965\pi\)
\(390\) 2.54673e10i 1.10084i
\(391\) 4.21473e10 1.80328
\(392\) 3.44622e8i 0.0145948i
\(393\) 2.49116e9 0.104432
\(394\) 1.61744e10i 0.671187i
\(395\) 3.51707e10i 1.44475i
\(396\) 2.41065e9 0.0980289
\(397\) 3.45068e10 1.38913 0.694565 0.719430i \(-0.255597\pi\)
0.694565 + 0.719430i \(0.255597\pi\)
\(398\) 3.72866e10 1.48601
\(399\) 2.39477e9i 0.0944870i
\(400\) −5.47295e9 −0.213787
\(401\) 2.43097e10 0.940162 0.470081 0.882623i \(-0.344225\pi\)
0.470081 + 0.882623i \(0.344225\pi\)
\(402\) −4.21661e10 −1.61458
\(403\) 1.43278e10 0.543201
\(404\) −1.56322e9 −0.0586805
\(405\) 2.20930e10i 0.821174i
\(406\) 4.29865e10i 1.58208i
\(407\) 3.00605e10i 1.09552i
\(408\) 2.97341e9 0.107303
\(409\) 2.52284e10i 0.901564i 0.892634 + 0.450782i \(0.148855\pi\)
−0.892634 + 0.450782i \(0.851145\pi\)
\(410\) 3.05531e10 1.08124
\(411\) −3.52310e9 −0.123469
\(412\) −1.27814e10 −0.443597
\(413\) 3.51293e10i 1.20745i
\(414\) 4.04228e9i 0.137602i
\(415\) 2.42875e10i 0.818825i
\(416\) 3.85907e10i 1.28857i
\(417\) 1.75692e10i 0.581041i
\(418\) 7.06850e9 0.231538
\(419\) 4.21693e10i 1.36817i −0.729402 0.684085i \(-0.760202\pi\)
0.729402 0.684085i \(-0.239798\pi\)
\(420\) 2.60534e10i 0.837274i
\(421\) 2.56731e10i 0.817239i 0.912705 + 0.408620i \(0.133990\pi\)
−0.912705 + 0.408620i \(0.866010\pi\)
\(422\) 4.66808e9 0.147194
\(423\) −1.63259e9 −0.0509936
\(424\) 2.86270e8i 0.00885754i
\(425\) 8.53990e9 0.261756
\(426\) 2.29455e10i 0.696721i
\(427\) −3.89776e10 −1.17248
\(428\) −3.65650e10 −1.08966
\(429\) 4.50256e10i 1.32932i
\(430\) 6.22716e9 + 4.26741e10i 0.182145 + 1.24822i
\(431\) −4.50399e10 −1.30523 −0.652617 0.757688i \(-0.726329\pi\)
−0.652617 + 0.757688i \(0.726329\pi\)
\(432\) 3.32069e10i 0.953440i
\(433\) 3.23102e10i 0.919153i −0.888138 0.459577i \(-0.848001\pi\)
0.888138 0.459577i \(-0.151999\pi\)
\(434\) −2.83848e10 −0.800069
\(435\) 3.63309e10i 1.01466i
\(436\) −2.55201e10 −0.706213
\(437\) 6.12062e9i 0.167830i
\(438\) 7.32465e9i 0.199017i
\(439\) 2.51931e10 0.678303 0.339151 0.940732i \(-0.389860\pi\)
0.339151 + 0.940732i \(0.389860\pi\)
\(440\) −4.88111e9 −0.130229
\(441\) 3.41377e8 0.00902568
\(442\) 5.61162e10i 1.47028i
\(443\) −5.96388e10 −1.54851 −0.774255 0.632874i \(-0.781875\pi\)
−0.774255 + 0.632874i \(0.781875\pi\)
\(444\) −2.89307e10 −0.744436
\(445\) 4.62086e10 1.17837
\(446\) −5.06287e10 −1.27955
\(447\) 4.05830e10 1.01651
\(448\) 4.19963e10i 1.04255i
\(449\) 4.63343e10i 1.14003i −0.821633 0.570016i \(-0.806937\pi\)
0.821633 0.570016i \(-0.193063\pi\)
\(450\) 8.19049e8i 0.0199738i
\(451\) 5.40173e10 1.30565
\(452\) 7.12239e10i 1.70636i
\(453\) −1.78160e10 −0.423076
\(454\) −7.16303e10 −1.68606
\(455\) −3.12096e10 −0.728187
\(456\) 4.31798e8i 0.00998668i
\(457\) 2.64600e10i 0.606631i 0.952890 + 0.303316i \(0.0980937\pi\)
−0.952890 + 0.303316i \(0.901906\pi\)
\(458\) 9.39710e10i 2.13566i
\(459\) 5.18155e10i 1.16737i
\(460\) 6.65881e10i 1.48719i
\(461\) −4.70971e10 −1.04278 −0.521388 0.853320i \(-0.674585\pi\)
−0.521388 + 0.853320i \(0.674585\pi\)
\(462\) 8.92002e10i 1.95793i
\(463\) 4.28757e10i 0.933013i 0.884518 + 0.466507i \(0.154488\pi\)
−0.884518 + 0.466507i \(0.845512\pi\)
\(464\) 5.13040e10i 1.10683i
\(465\) −2.39900e10 −0.513120
\(466\) 9.16865e10 1.94429
\(467\) 5.17139e10i 1.08727i −0.839320 0.543637i \(-0.817047\pi\)
0.839320 0.543637i \(-0.182953\pi\)
\(468\) −2.77921e9 −0.0579347
\(469\) 5.16737e10i 1.06802i
\(470\) 5.20800e10 1.06728
\(471\) 1.16132e10 0.235976
\(472\) 6.33412e9i 0.127620i
\(473\) 1.10095e10 + 7.54469e10i 0.219950 + 1.50729i
\(474\) 1.15890e11 2.29579
\(475\) 1.24016e9i 0.0243615i
\(476\) 5.74078e10i 1.11826i
\(477\) 2.83575e8 0.00547764
\(478\) 8.32181e10i 1.59407i
\(479\) 5.36737e10 1.01958 0.509788 0.860300i \(-0.329724\pi\)
0.509788 + 0.860300i \(0.329724\pi\)
\(480\) 6.46149e10i 1.21722i
\(481\) 3.46564e10i 0.647445i
\(482\) 1.18234e11 2.19055
\(483\) −7.72385e10 −1.41921
\(484\) −7.73632e10 −1.40979
\(485\) 3.78480e10i 0.684031i
\(486\) −9.65660e9 −0.173093
\(487\) 3.86141e10 0.686483 0.343242 0.939247i \(-0.388475\pi\)
0.343242 + 0.939247i \(0.388475\pi\)
\(488\) 7.02800e9 0.123923
\(489\) 4.23539e10 0.740727
\(490\) −1.08900e10 −0.188905
\(491\) 8.61031e10i 1.48147i 0.671797 + 0.740735i \(0.265523\pi\)
−0.671797 + 0.740735i \(0.734477\pi\)
\(492\) 5.19872e10i 0.887230i
\(493\) 8.00538e10i 1.35517i
\(494\) −8.14919e9 −0.136838
\(495\) 4.83514e9i 0.0805357i
\(496\) −3.38771e10 −0.559731
\(497\) 2.81192e10 0.460869
\(498\) 8.00290e10 1.30116
\(499\) 7.90191e10i 1.27447i −0.770669 0.637235i \(-0.780078\pi\)
0.770669 0.637235i \(-0.219922\pi\)
\(500\) 7.20350e10i 1.15256i
\(501\) 9.18753e10i 1.45830i
\(502\) 8.27988e10i 1.30380i
\(503\) 9.92805e10i 1.55093i 0.631391 + 0.775464i \(0.282484\pi\)
−0.631391 + 0.775464i \(0.717516\pi\)
\(504\) 3.49476e8 0.00541621
\(505\) 3.13540e9i 0.0482090i
\(506\) 2.27980e11i 3.47773i
\(507\) 1.21426e10i 0.183772i
\(508\) −6.61654e10 −0.993519
\(509\) −8.82552e10 −1.31483 −0.657414 0.753529i \(-0.728350\pi\)
−0.657414 + 0.753529i \(0.728350\pi\)
\(510\) 9.39591e10i 1.38886i
\(511\) −8.97622e9 −0.131647
\(512\) 9.74573e10i 1.41819i
\(513\) −7.52464e9 −0.108647
\(514\) −8.24940e10 −1.18187
\(515\) 2.56361e10i 0.364437i
\(516\) 7.26114e10 1.05957e10i 1.02425 0.149462i
\(517\) 9.20764e10 1.28880
\(518\) 6.86577e10i 0.953608i
\(519\) 5.82549e9i 0.0802903i
\(520\) 5.62737e9 0.0769648
\(521\) 3.93047e10i 0.533450i 0.963773 + 0.266725i \(0.0859415\pi\)
−0.963773 + 0.266725i \(0.914059\pi\)
\(522\) 7.67784e9 0.103409
\(523\) 1.06896e11i 1.42875i −0.699763 0.714375i \(-0.746711\pi\)
0.699763 0.714375i \(-0.253289\pi\)
\(524\) 8.67231e9i 0.115030i
\(525\) −1.56501e10 −0.206006
\(526\) −6.26114e10 −0.817920
\(527\) 5.28612e10 0.685322
\(528\) 1.06460e11i 1.36978i
\(529\) 1.19098e11 1.52083
\(530\) −9.04609e9 −0.114646
\(531\) −6.27447e9 −0.0789222
\(532\) 8.33675e9 0.104076
\(533\) −6.22760e10 −0.771634
\(534\) 1.52261e11i 1.87250i
\(535\) 7.33399e10i 0.895211i
\(536\) 9.31721e9i 0.112883i
\(537\) −1.53251e11 −1.84292
\(538\) 1.26907e11i 1.51480i
\(539\) −1.92533e10 −0.228113
\(540\) 8.18628e10 0.962746
\(541\) −1.27179e11 −1.48466 −0.742331 0.670034i \(-0.766280\pi\)
−0.742331 + 0.670034i \(0.766280\pi\)
\(542\) 6.51807e10i 0.755304i
\(543\) 1.34220e11i 1.54390i
\(544\) 1.42377e11i 1.62571i
\(545\) 5.11866e10i 0.580190i
\(546\) 1.02838e11i 1.15713i
\(547\) −1.10966e11 −1.23949 −0.619744 0.784804i \(-0.712763\pi\)
−0.619744 + 0.784804i \(0.712763\pi\)
\(548\) 1.22647e10i 0.135999i
\(549\) 6.96182e9i 0.0766361i
\(550\) 4.61935e10i 0.504813i
\(551\) 1.16254e10 0.126125
\(552\) 1.39268e10 0.150001
\(553\) 1.42021e11i 1.51863i
\(554\) −2.11740e11 −2.24783
\(555\) 5.80275e10i 0.611592i
\(556\) −6.11624e10 −0.640007
\(557\) 1.70704e10 0.177347 0.0886734 0.996061i \(-0.471737\pi\)
0.0886734 + 0.996061i \(0.471737\pi\)
\(558\) 5.06984e9i 0.0522946i
\(559\) −1.26927e10 8.69819e10i −0.129989 0.890803i
\(560\) 7.37928e10 0.750346
\(561\) 1.66118e11i 1.67712i
\(562\) 1.08617e11i 1.08881i
\(563\) 6.49015e10 0.645983 0.322992 0.946402i \(-0.395311\pi\)
0.322992 + 0.946402i \(0.395311\pi\)
\(564\) 8.86159e10i 0.875780i
\(565\) −1.42856e11 −1.40186
\(566\) 2.55955e10i 0.249401i
\(567\) 8.92125e10i 0.863164i
\(568\) −5.07014e9 −0.0487110
\(569\) −9.81338e10 −0.936202 −0.468101 0.883675i \(-0.655062\pi\)
−0.468101 + 0.883675i \(0.655062\pi\)
\(570\) 1.36447e10 0.129260
\(571\) 1.38488e10i 0.130277i 0.997876 + 0.0651385i \(0.0207489\pi\)
−0.997876 + 0.0651385i \(0.979251\pi\)
\(572\) 1.56745e11 1.46423
\(573\) 1.97897e11 1.83578
\(574\) 1.23375e11 1.13652
\(575\) 3.99990e10 0.365913
\(576\) 7.50098e9 0.0681441
\(577\) 1.02819e11i 0.927621i −0.885934 0.463811i \(-0.846482\pi\)
0.885934 0.463811i \(-0.153518\pi\)
\(578\) 4.65399e10i 0.416979i
\(579\) 9.86386e10i 0.877673i
\(580\) −1.26476e11 −1.11763
\(581\) 9.80740e10i 0.860695i
\(582\) −1.24712e11 −1.08696
\(583\) −1.59933e10 −0.138441
\(584\) 1.61849e9 0.0139142
\(585\) 5.57438e9i 0.0475963i
\(586\) 1.51739e11i 1.28679i
\(587\) 2.83893e10i 0.239113i 0.992827 + 0.119556i \(0.0381472\pi\)
−0.992827 + 0.119556i \(0.961853\pi\)
\(588\) 1.85297e10i 0.155010i
\(589\) 7.67650e9i 0.0637826i
\(590\) 2.00157e11 1.65182
\(591\) 5.52006e10i 0.452474i
\(592\) 8.19424e10i 0.667147i
\(593\) 1.97060e11i 1.59360i 0.604242 + 0.796801i \(0.293476\pi\)
−0.604242 + 0.796801i \(0.706524\pi\)
\(594\) 2.80277e11 2.25134
\(595\) −1.15145e11 −0.918707
\(596\) 1.41279e11i 1.11968i
\(597\) 1.27253e11 1.00178
\(598\) 2.62836e11i 2.05532i
\(599\) 1.92220e11 1.49311 0.746553 0.665326i \(-0.231708\pi\)
0.746553 + 0.665326i \(0.231708\pi\)
\(600\) 2.82185e9 0.0217735
\(601\) 7.87414e10i 0.603539i −0.953381 0.301769i \(-0.902423\pi\)
0.953381 0.301769i \(-0.0975772\pi\)
\(602\) 2.51455e10 + 1.72320e11i 0.191459 + 1.31204i
\(603\) 9.22947e9 0.0698084
\(604\) 6.20218e10i 0.466012i
\(605\) 1.55170e11i 1.15821i
\(606\) −1.03314e10 −0.0766067
\(607\) 1.66376e11i 1.22556i −0.790252 0.612781i \(-0.790051\pi\)
0.790252 0.612781i \(-0.209949\pi\)
\(608\) 2.06759e10 0.151304
\(609\) 1.46706e11i 1.06654i
\(610\) 2.22084e11i 1.60397i
\(611\) −1.06154e11 −0.761676
\(612\) −1.02536e10 −0.0730925
\(613\) 1.70299e11 1.20606 0.603031 0.797718i \(-0.293960\pi\)
0.603031 + 0.797718i \(0.293960\pi\)
\(614\) 5.52885e10i 0.389011i
\(615\) 1.04273e11 0.728904
\(616\) −1.97101e10 −0.136888
\(617\) −2.65299e11 −1.83060 −0.915302 0.402767i \(-0.868048\pi\)
−0.915302 + 0.402767i \(0.868048\pi\)
\(618\) −8.44726e10 −0.579111
\(619\) −1.78200e11 −1.21379 −0.606896 0.794781i \(-0.707586\pi\)
−0.606896 + 0.794781i \(0.707586\pi\)
\(620\) 8.35149e10i 0.565194i
\(621\) 2.42692e11i 1.63189i
\(622\) 2.87929e11i 1.92364i
\(623\) 1.86592e11 1.23863
\(624\) 1.22736e11i 0.809532i
\(625\) −1.09317e11 −0.716420
\(626\) 6.26916e10 0.408236
\(627\) 2.41236e10 0.156089
\(628\) 4.04282e10i 0.259924i
\(629\) 1.27861e11i 0.816840i
\(630\) 1.10434e10i 0.0701035i
\(631\) 1.59654e11i 1.00708i −0.863973 0.503538i \(-0.832031\pi\)
0.863973 0.503538i \(-0.167969\pi\)
\(632\) 2.56076e10i 0.160509i
\(633\) 1.59314e10 0.0992290
\(634\) 5.53101e10i 0.342332i
\(635\) 1.32711e11i 0.816226i
\(636\) 1.53922e10i 0.0940747i
\(637\) 2.21969e10 0.134814
\(638\) −4.33022e11 −2.61353
\(639\) 5.02240e9i 0.0301236i
\(640\) −2.86211e10 −0.170595
\(641\) 2.14549e10i 0.127085i 0.997979 + 0.0635425i \(0.0202398\pi\)
−0.997979 + 0.0635425i \(0.979760\pi\)
\(642\) −2.41660e11 −1.42254
\(643\) 1.26797e11 0.741763 0.370882 0.928680i \(-0.379056\pi\)
0.370882 + 0.928680i \(0.379056\pi\)
\(644\) 2.68885e11i 1.56323i
\(645\) 2.12523e10 + 1.45639e11i 0.122791 + 0.841473i
\(646\) −3.00657e10 −0.172640
\(647\) 2.05924e11i 1.17514i 0.809173 + 0.587570i \(0.199916\pi\)
−0.809173 + 0.587570i \(0.800084\pi\)
\(648\) 1.60858e10i 0.0912310i
\(649\) 3.53874e11 1.99466
\(650\) 5.32560e10i 0.298342i
\(651\) −9.68727e10 −0.539358
\(652\) 1.47444e11i 0.815899i
\(653\) 9.69391e10i 0.533146i −0.963815 0.266573i \(-0.914109\pi\)
0.963815 0.266573i \(-0.0858913\pi\)
\(654\) −1.68663e11 −0.921954
\(655\) 1.73944e10 0.0945026
\(656\) 1.47247e11 0.795116
\(657\) 1.60325e9i 0.00860477i
\(658\) 2.10301e11 1.12186
\(659\) −2.33344e11 −1.23725 −0.618623 0.785688i \(-0.712309\pi\)
−0.618623 + 0.785688i \(0.712309\pi\)
\(660\) −2.62448e11 −1.38314
\(661\) 9.21767e10 0.482854 0.241427 0.970419i \(-0.422385\pi\)
0.241427 + 0.970419i \(0.422385\pi\)
\(662\) 4.25732e11 2.21669
\(663\) 1.91515e11i 0.991172i
\(664\) 1.76836e10i 0.0909700i
\(665\) 1.67213e10i 0.0855037i
\(666\) 1.22630e10 0.0623304
\(667\) 3.74954e11i 1.89442i
\(668\) 3.19839e11 1.60630
\(669\) −1.72787e11 −0.862596
\(670\) −2.94422e11 −1.46107
\(671\) 3.92639e11i 1.93688i
\(672\) 2.60917e11i 1.27946i
\(673\) 8.74582e10i 0.426324i 0.977017 + 0.213162i \(0.0683763\pi\)
−0.977017 + 0.213162i \(0.931624\pi\)
\(674\) 4.25450e11i 2.06162i
\(675\) 4.91744e10i 0.236878i
\(676\) 4.22712e10 0.202422
\(677\) 1.78736e11i 0.850861i −0.904991 0.425430i \(-0.860123\pi\)
0.904991 0.425430i \(-0.139877\pi\)
\(678\) 4.70721e11i 2.22764i
\(679\) 1.52832e11i 0.719009i
\(680\) 2.07616e10 0.0971016
\(681\) −2.44462e11 −1.13664
\(682\) 2.85933e11i 1.32168i
\(683\) 5.16028e10 0.237132 0.118566 0.992946i \(-0.462170\pi\)
0.118566 + 0.992946i \(0.462170\pi\)
\(684\) 1.48903e9i 0.00680268i
\(685\) −2.45998e10 −0.111730
\(686\) −3.37618e11 −1.52450
\(687\) 3.20707e11i 1.43973i
\(688\) 3.00110e10 + 2.05662e11i 0.133945 + 0.917910i
\(689\) 1.84385e10 0.0818180
\(690\) 4.40084e11i 1.94151i
\(691\) 1.07652e11i 0.472183i 0.971731 + 0.236091i \(0.0758665\pi\)
−0.971731 + 0.236091i \(0.924134\pi\)
\(692\) 2.02799e10 0.0884385
\(693\) 1.95245e10i 0.0846538i
\(694\) 5.09460e10 0.219620
\(695\) 1.22676e11i 0.525798i
\(696\) 2.64523e10i 0.112727i
\(697\) −2.29761e11 −0.973522
\(698\) −2.32714e11 −0.980393
\(699\) 3.12911e11 1.31073
\(700\) 5.44817e10i 0.226913i
\(701\) 2.84901e11 1.17984 0.589918 0.807463i \(-0.299160\pi\)
0.589918 + 0.807463i \(0.299160\pi\)
\(702\) −3.23128e11 −1.33054
\(703\) 1.85680e10 0.0760229
\(704\) −4.23048e11 −1.72226
\(705\) 1.77740e11 0.719497
\(706\) 2.70959e11i 1.09065i
\(707\) 1.26609e10i 0.0506741i
\(708\) 3.40574e11i 1.35543i
\(709\) 1.31805e11 0.521611 0.260805 0.965391i \(-0.416012\pi\)
0.260805 + 0.965391i \(0.416012\pi\)
\(710\) 1.60216e11i 0.630480i
\(711\) −2.53664e10 −0.0992616
\(712\) −3.36442e10 −0.130915
\(713\) 2.47590e11 0.958021
\(714\) 3.79410e11i 1.45988i
\(715\) 3.14389e11i 1.20294i
\(716\) 5.33504e11i 2.02995i
\(717\) 2.84010e11i 1.07462i
\(718\) 5.63844e10i 0.212159i
\(719\) 4.05208e11 1.51622 0.758110 0.652127i \(-0.226123\pi\)
0.758110 + 0.652127i \(0.226123\pi\)
\(720\) 1.31802e10i 0.0490446i
\(721\) 1.03520e11i 0.383073i
\(722\) 3.86385e11i 1.42191i
\(723\) 4.03513e11 1.47674
\(724\) 4.67252e11 1.70058
\(725\) 7.59735e10i 0.274986i
\(726\) −5.11297e11 −1.84046
\(727\) 5.30950e10i 0.190071i −0.995474 0.0950355i \(-0.969704\pi\)
0.995474 0.0950355i \(-0.0302965\pi\)
\(728\) 2.27235e10 0.0809004
\(729\) −2.97338e11 −1.05279
\(730\) 5.11440e10i 0.180096i
\(731\) −4.68286e10 3.20911e11i −0.163999 1.12387i
\(732\) 3.77883e11 1.31617
\(733\) 2.64810e11i 0.917314i −0.888613 0.458657i \(-0.848331\pi\)
0.888613 0.458657i \(-0.151669\pi\)
\(734\) 4.34748e11i 1.49780i
\(735\) −3.71657e10 −0.127348
\(736\) 6.66861e11i 2.27260i
\(737\) −5.20532e11 −1.76432
\(738\) 2.20361e10i 0.0742862i
\(739\) 3.49177e11i 1.17076i 0.810759 + 0.585381i \(0.199055\pi\)
−0.810759 + 0.585381i \(0.800945\pi\)
\(740\) −2.02007e11 −0.673659
\(741\) −2.78118e10 −0.0922480
\(742\) −3.65285e10 −0.120508
\(743\) 3.40681e11i 1.11787i −0.829210 0.558937i \(-0.811209\pi\)
0.829210 0.558937i \(-0.188791\pi\)
\(744\) 1.74670e10 0.0570068
\(745\) 2.83368e11 0.919869
\(746\) 1.55850e11 0.503214
\(747\) −1.75171e10 −0.0562573
\(748\) 5.78295e11 1.84732
\(749\) 2.96149e11i 0.940987i
\(750\) 4.76082e11i 1.50465i
\(751\) 1.73741e11i 0.546188i −0.961987 0.273094i \(-0.911953\pi\)
0.961987 0.273094i \(-0.0880470\pi\)
\(752\) 2.50992e11 0.784855
\(753\) 2.82579e11i 0.878940i
\(754\) 4.99226e11 1.54459
\(755\) −1.24400e11 −0.382852
\(756\) 3.30565e11 1.01198
\(757\) 5.97510e11i 1.81954i 0.415114 + 0.909769i \(0.363742\pi\)
−0.415114 + 0.909769i \(0.636258\pi\)
\(758\) 8.88406e11i 2.69113i
\(759\) 7.78059e11i 2.34447i
\(760\) 3.01501e9i 0.00903720i
\(761\) 3.40017e11i 1.01382i 0.861998 + 0.506912i \(0.169213\pi\)
−0.861998 + 0.506912i \(0.830787\pi\)
\(762\) −4.37290e11 −1.29703
\(763\) 2.06693e11i 0.609857i
\(764\) 6.88925e11i 2.02208i
\(765\) 2.05661e10i 0.0600491i
\(766\) −8.98530e11 −2.60986
\(767\) −4.07977e11 −1.17884
\(768\) 2.86997e11i 0.824959i
\(769\) 3.42285e11 0.978774 0.489387 0.872067i \(-0.337221\pi\)
0.489387 + 0.872067i \(0.337221\pi\)
\(770\) 6.22835e11i 1.77178i
\(771\) −2.81538e11 −0.796746
\(772\) −3.43384e11 −0.966742
\(773\) 3.41450e10i 0.0956332i 0.998856 + 0.0478166i \(0.0152263\pi\)
−0.998856 + 0.0478166i \(0.984774\pi\)
\(774\) −3.07781e10 + 4.49126e9i −0.0857587 + 0.0125142i
\(775\) 5.01668e10 0.139062
\(776\) 2.75569e10i 0.0759947i
\(777\) 2.34317e11i 0.642865i
\(778\) 5.78580e11 1.57923
\(779\) 3.33659e10i 0.0906052i
\(780\) 3.02573e11 0.817433
\(781\) 2.83258e11i 0.761339i
\(782\) 9.69708e11i