Properties

Label 43.9.b.b.42.18
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 42.18
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.11

$q$-expansion

\(f(q)\) \(=\) \(q+10.2230i q^{2} +141.129i q^{3} +151.490 q^{4} -508.524i q^{5} -1442.77 q^{6} -610.830i q^{7} +4165.77i q^{8} -13356.5 q^{9} +O(q^{10})\) \(q+10.2230i q^{2} +141.129i q^{3} +151.490 q^{4} -508.524i q^{5} -1442.77 q^{6} -610.830i q^{7} +4165.77i q^{8} -13356.5 q^{9} +5198.64 q^{10} -23389.3 q^{11} +21379.7i q^{12} -38247.2 q^{13} +6244.51 q^{14} +71767.6 q^{15} -3805.23 q^{16} +8276.38 q^{17} -136543. i q^{18} -43946.0i q^{19} -77036.4i q^{20} +86206.0 q^{21} -239109. i q^{22} -109327. q^{23} -587913. q^{24} +132028. q^{25} -391001. i q^{26} -959041. i q^{27} -92534.7i q^{28} +1.33800e6i q^{29} +733681. i q^{30} -624882. q^{31} +1.02754e6i q^{32} -3.30091e6i q^{33} +84609.5i q^{34} -310621. q^{35} -2.02338e6 q^{36} +12892.0i q^{37} +449260. q^{38} -5.39780e6i q^{39} +2.11840e6 q^{40} +4.22110e6 q^{41} +881284. i q^{42} +(-1.81225e6 + 2.89896e6i) q^{43} -3.54325e6 q^{44} +6.79209e6i q^{45} -1.11765e6i q^{46} +1.43455e6 q^{47} -537029. i q^{48} +5.39169e6 q^{49} +1.34973e6i q^{50} +1.16804e6i q^{51} -5.79407e6 q^{52} -1.03918e7 q^{53} +9.80428e6 q^{54} +1.18940e7i q^{55} +2.54458e6 q^{56} +6.20207e6 q^{57} -1.36784e7 q^{58} +8.60085e6 q^{59} +1.08721e7 q^{60} +1.46732e7i q^{61} -6.38818e6i q^{62} +8.15853e6i q^{63} -1.14787e7 q^{64} +1.94496e7i q^{65} +3.37453e7 q^{66} -9.05284e6 q^{67} +1.25379e6 q^{68} -1.54293e7i q^{69} -3.17548e6i q^{70} +1.39287e7i q^{71} -5.56401e7i q^{72} -4.77368e7i q^{73} -131795. q^{74} +1.86331e7i q^{75} -6.65739e6i q^{76} +1.42869e7i q^{77} +5.51817e7 q^{78} -2.98664e7 q^{79} +1.93505e6i q^{80} +4.77169e7 q^{81} +4.31523e7i q^{82} -3.68875e7 q^{83} +1.30594e7 q^{84} -4.20874e6i q^{85} +(-2.96361e7 - 1.85266e7i) q^{86} -1.88831e8 q^{87} -9.74345e7i q^{88} +9.08768e7i q^{89} -6.94355e7 q^{90} +2.33625e7i q^{91} -1.65620e7 q^{92} -8.81892e7i q^{93} +1.46654e7i q^{94} -2.23476e7 q^{95} -1.45016e8 q^{96} -4.00745e7 q^{97} +5.51192e7i q^{98} +3.12399e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.2230i 0.638938i 0.947597 + 0.319469i \(0.103504\pi\)
−0.947597 + 0.319469i \(0.896496\pi\)
\(3\) 141.129i 1.74234i 0.490984 + 0.871168i \(0.336637\pi\)
−0.490984 + 0.871168i \(0.663363\pi\)
\(4\) 151.490 0.591759
\(5\) 508.524i 0.813638i −0.913509 0.406819i \(-0.866638\pi\)
0.913509 0.406819i \(-0.133362\pi\)
\(6\) −1442.77 −1.11324
\(7\) 610.830i 0.254406i −0.991877 0.127203i \(-0.959400\pi\)
0.991877 0.127203i \(-0.0406000\pi\)
\(8\) 4165.77i 1.01703i
\(9\) −13356.5 −2.03574
\(10\) 5198.64 0.519864
\(11\) −23389.3 −1.59752 −0.798760 0.601650i \(-0.794510\pi\)
−0.798760 + 0.601650i \(0.794510\pi\)
\(12\) 21379.7i 1.03104i
\(13\) −38247.2 −1.33914 −0.669570 0.742749i \(-0.733522\pi\)
−0.669570 + 0.742749i \(0.733522\pi\)
\(14\) 6244.51 0.162550
\(15\) 71767.6 1.41763
\(16\) −3805.23 −0.0580631
\(17\) 8276.38 0.0990934 0.0495467 0.998772i \(-0.484222\pi\)
0.0495467 + 0.998772i \(0.484222\pi\)
\(18\) 136543.i 1.30071i
\(19\) 43946.0i 0.337214i −0.985683 0.168607i \(-0.946073\pi\)
0.985683 0.168607i \(-0.0539268\pi\)
\(20\) 77036.4i 0.481477i
\(21\) 86206.0 0.443262
\(22\) 239109.i 1.02072i
\(23\) −109327. −0.390676 −0.195338 0.980736i \(-0.562580\pi\)
−0.195338 + 0.980736i \(0.562580\pi\)
\(24\) −587913. −1.77202
\(25\) 132028. 0.337993
\(26\) 391001.i 0.855627i
\(27\) 959041.i 1.80460i
\(28\) 92534.7i 0.150547i
\(29\) 1.33800e6i 1.89175i 0.324534 + 0.945874i \(0.394792\pi\)
−0.324534 + 0.945874i \(0.605208\pi\)
\(30\) 733681.i 0.905778i
\(31\) −624882. −0.676630 −0.338315 0.941033i \(-0.609857\pi\)
−0.338315 + 0.941033i \(0.609857\pi\)
\(32\) 1.02754e6i 0.979936i
\(33\) 3.30091e6i 2.78342i
\(34\) 84609.5i 0.0633145i
\(35\) −310621. −0.206995
\(36\) −2.02338e6 −1.20467
\(37\) 12892.0i 0.00687879i 0.999994 + 0.00343939i \(0.00109480\pi\)
−0.999994 + 0.00343939i \(0.998905\pi\)
\(38\) 449260. 0.215459
\(39\) 5.39780e6i 2.33323i
\(40\) 2.11840e6 0.827498
\(41\) 4.22110e6 1.49379 0.746895 0.664941i \(-0.231544\pi\)
0.746895 + 0.664941i \(0.231544\pi\)
\(42\) 881284.i 0.283217i
\(43\) −1.81225e6 + 2.89896e6i −0.530082 + 0.847946i
\(44\) −3.54325e6 −0.945346
\(45\) 6.79209e6i 1.65635i
\(46\) 1.11765e6i 0.249618i
\(47\) 1.43455e6 0.293985 0.146992 0.989138i \(-0.453041\pi\)
0.146992 + 0.989138i \(0.453041\pi\)
\(48\) 537029.i 0.101166i
\(49\) 5.39169e6 0.935277
\(50\) 1.34973e6i 0.215956i
\(51\) 1.16804e6i 0.172654i
\(52\) −5.79407e6 −0.792448
\(53\) −1.03918e7 −1.31700 −0.658500 0.752581i \(-0.728809\pi\)
−0.658500 + 0.752581i \(0.728809\pi\)
\(54\) 9.80428e6 1.15303
\(55\) 1.18940e7i 1.29980i
\(56\) 2.54458e6 0.258740
\(57\) 6.20207e6 0.587540
\(58\) −1.36784e7 −1.20871
\(59\) 8.60085e6 0.709796 0.354898 0.934905i \(-0.384516\pi\)
0.354898 + 0.934905i \(0.384516\pi\)
\(60\) 1.08721e7 0.838896
\(61\) 1.46732e7i 1.05975i 0.848075 + 0.529877i \(0.177762\pi\)
−0.848075 + 0.529877i \(0.822238\pi\)
\(62\) 6.38818e6i 0.432325i
\(63\) 8.15853e6i 0.517905i
\(64\) −1.14787e7 −0.684181
\(65\) 1.94496e7i 1.08958i
\(66\) 3.37453e7 1.77843
\(67\) −9.05284e6 −0.449247 −0.224624 0.974446i \(-0.572115\pi\)
−0.224624 + 0.974446i \(0.572115\pi\)
\(68\) 1.25379e6 0.0586394
\(69\) 1.54293e7i 0.680690i
\(70\) 3.17548e6i 0.132257i
\(71\) 1.39287e7i 0.548123i 0.961712 + 0.274061i \(0.0883672\pi\)
−0.961712 + 0.274061i \(0.911633\pi\)
\(72\) 5.56401e7i 2.07042i
\(73\) 4.77368e7i 1.68098i −0.541828 0.840489i \(-0.682268\pi\)
0.541828 0.840489i \(-0.317732\pi\)
\(74\) −131795. −0.00439512
\(75\) 1.86331e7i 0.588897i
\(76\) 6.65739e6i 0.199549i
\(77\) 1.42869e7i 0.406419i
\(78\) 5.51817e7 1.49079
\(79\) −2.98664e7 −0.766788 −0.383394 0.923585i \(-0.625245\pi\)
−0.383394 + 0.923585i \(0.625245\pi\)
\(80\) 1.93505e6i 0.0472424i
\(81\) 4.77169e7 1.10849
\(82\) 4.31523e7i 0.954439i
\(83\) −3.68875e7 −0.777261 −0.388631 0.921394i \(-0.627052\pi\)
−0.388631 + 0.921394i \(0.627052\pi\)
\(84\) 1.30594e7 0.262304
\(85\) 4.20874e6i 0.0806262i
\(86\) −2.96361e7 1.85266e7i −0.541785 0.338689i
\(87\) −1.88831e8 −3.29606
\(88\) 9.74345e7i 1.62473i
\(89\) 9.08768e7i 1.44841i 0.689582 + 0.724207i \(0.257794\pi\)
−0.689582 + 0.724207i \(0.742206\pi\)
\(90\) −6.94355e7 −1.05831
\(91\) 2.33625e7i 0.340686i
\(92\) −1.65620e7 −0.231186
\(93\) 8.81892e7i 1.17892i
\(94\) 1.46654e7i 0.187838i
\(95\) −2.23476e7 −0.274370
\(96\) −1.45016e8 −1.70738
\(97\) −4.00745e7 −0.452670 −0.226335 0.974050i \(-0.572674\pi\)
−0.226335 + 0.974050i \(0.572674\pi\)
\(98\) 5.51192e7i 0.597584i
\(99\) 3.12399e8 3.25213
\(100\) 2.00010e7 0.200010
\(101\) 2.84924e7 0.273807 0.136903 0.990584i \(-0.456285\pi\)
0.136903 + 0.990584i \(0.456285\pi\)
\(102\) −1.19409e7 −0.110315
\(103\) 1.33245e8 1.18386 0.591932 0.805988i \(-0.298365\pi\)
0.591932 + 0.805988i \(0.298365\pi\)
\(104\) 1.59329e8i 1.36195i
\(105\) 4.38378e7i 0.360655i
\(106\) 1.06235e8i 0.841481i
\(107\) −1.39954e8 −1.06770 −0.533852 0.845578i \(-0.679256\pi\)
−0.533852 + 0.845578i \(0.679256\pi\)
\(108\) 1.45285e8i 1.06789i
\(109\) 2.11298e8 1.49689 0.748446 0.663196i \(-0.230800\pi\)
0.748446 + 0.663196i \(0.230800\pi\)
\(110\) −1.21593e8 −0.830494
\(111\) −1.81943e6 −0.0119852
\(112\) 2.32434e6i 0.0147716i
\(113\) 5.53627e7i 0.339550i −0.985483 0.169775i \(-0.945696\pi\)
0.985483 0.169775i \(-0.0543041\pi\)
\(114\) 6.34038e7i 0.375401i
\(115\) 5.55955e7i 0.317869i
\(116\) 2.02693e8i 1.11946i
\(117\) 5.10848e8 2.72614
\(118\) 8.79265e7i 0.453515i
\(119\) 5.05546e6i 0.0252100i
\(120\) 2.98968e8i 1.44178i
\(121\) 3.32700e8 1.55207
\(122\) −1.50004e8 −0.677117
\(123\) 5.95720e8i 2.60269i
\(124\) −9.46636e7 −0.400402
\(125\) 2.65782e8i 1.08864i
\(126\) −8.34047e7 −0.330909
\(127\) −8.40413e7 −0.323056 −0.161528 0.986868i \(-0.551642\pi\)
−0.161528 + 0.986868i \(0.551642\pi\)
\(128\) 1.45703e8i 0.542787i
\(129\) −4.09128e8 2.55761e8i −1.47741 0.923582i
\(130\) −1.98833e8 −0.696171
\(131\) 5.12788e8i 1.74122i 0.491978 + 0.870608i \(0.336274\pi\)
−0.491978 + 0.870608i \(0.663726\pi\)
\(132\) 5.00056e8i 1.64711i
\(133\) −2.68435e7 −0.0857893
\(134\) 9.25472e7i 0.287041i
\(135\) −4.87695e8 −1.46830
\(136\) 3.44775e7i 0.100781i
\(137\) 2.04952e8i 0.581794i 0.956754 + 0.290897i \(0.0939538\pi\)
−0.956754 + 0.290897i \(0.906046\pi\)
\(138\) 1.57734e8 0.434918
\(139\) −4.64854e8 −1.24525 −0.622626 0.782520i \(-0.713934\pi\)
−0.622626 + 0.782520i \(0.713934\pi\)
\(140\) −4.70561e7 −0.122491
\(141\) 2.02457e8i 0.512221i
\(142\) −1.42393e8 −0.350216
\(143\) 8.94575e8 2.13930
\(144\) 5.08244e7 0.118201
\(145\) 6.80404e8 1.53920
\(146\) 4.88014e8 1.07404
\(147\) 7.60925e8i 1.62957i
\(148\) 1.95301e6i 0.00407058i
\(149\) 7.12509e6i 0.0144559i −0.999974 0.00722795i \(-0.997699\pi\)
0.999974 0.00722795i \(-0.00230075\pi\)
\(150\) −1.90486e8 −0.376269
\(151\) 4.53627e8i 0.872552i −0.899813 0.436276i \(-0.856297\pi\)
0.899813 0.436276i \(-0.143703\pi\)
\(152\) 1.83069e8 0.342958
\(153\) −1.10543e8 −0.201728
\(154\) −1.46055e8 −0.259677
\(155\) 3.17768e8i 0.550532i
\(156\) 8.17714e8i 1.38071i
\(157\) 4.62842e8i 0.761789i −0.924619 0.380894i \(-0.875616\pi\)
0.924619 0.380894i \(-0.124384\pi\)
\(158\) 3.05325e8i 0.489930i
\(159\) 1.46658e9i 2.29466i
\(160\) 5.22527e8 0.797313
\(161\) 6.67803e7i 0.0993905i
\(162\) 4.87810e8i 0.708257i
\(163\) 3.93979e8i 0.558113i −0.960275 0.279057i \(-0.909978\pi\)
0.960275 0.279057i \(-0.0900217\pi\)
\(164\) 6.39455e8 0.883964
\(165\) −1.67859e9 −2.26470
\(166\) 3.77101e8i 0.496622i
\(167\) −1.50142e9 −1.93035 −0.965173 0.261614i \(-0.915745\pi\)
−0.965173 + 0.261614i \(0.915745\pi\)
\(168\) 3.59114e8i 0.450812i
\(169\) 6.47117e8 0.793297
\(170\) 4.30260e7 0.0515151
\(171\) 5.86964e8i 0.686479i
\(172\) −2.74537e8 + 4.39164e8i −0.313681 + 0.501780i
\(173\) 1.15836e9 1.29318 0.646591 0.762837i \(-0.276194\pi\)
0.646591 + 0.762837i \(0.276194\pi\)
\(174\) 1.93042e9i 2.10598i
\(175\) 8.06469e7i 0.0859875i
\(176\) 8.90015e7 0.0927570
\(177\) 1.21383e9i 1.23670i
\(178\) −9.29034e8 −0.925447
\(179\) 1.24575e9i 1.21344i −0.794916 0.606719i \(-0.792485\pi\)
0.794916 0.606719i \(-0.207515\pi\)
\(180\) 1.02893e9i 0.980162i
\(181\) −2.15685e8 −0.200958 −0.100479 0.994939i \(-0.532037\pi\)
−0.100479 + 0.994939i \(0.532037\pi\)
\(182\) −2.38835e8 −0.217677
\(183\) −2.07082e9 −1.84645
\(184\) 4.55433e8i 0.397331i
\(185\) 6.55587e6 0.00559685
\(186\) 9.01559e8 0.753255
\(187\) −1.93579e8 −0.158304
\(188\) 2.17321e8 0.173968
\(189\) −5.85811e8 −0.459103
\(190\) 2.28460e8i 0.175305i
\(191\) 1.65296e9i 1.24202i 0.783803 + 0.621009i \(0.213277\pi\)
−0.783803 + 0.621009i \(0.786723\pi\)
\(192\) 1.61997e9i 1.19207i
\(193\) 1.26825e9 0.914065 0.457033 0.889450i \(-0.348912\pi\)
0.457033 + 0.889450i \(0.348912\pi\)
\(194\) 4.09682e8i 0.289228i
\(195\) −2.74491e9 −1.89841
\(196\) 8.16788e8 0.553458
\(197\) 1.60703e9 1.06699 0.533494 0.845804i \(-0.320879\pi\)
0.533494 + 0.845804i \(0.320879\pi\)
\(198\) 3.19365e9i 2.07791i
\(199\) 1.63024e9i 1.03953i 0.854309 + 0.519766i \(0.173981\pi\)
−0.854309 + 0.519766i \(0.826019\pi\)
\(200\) 5.50001e8i 0.343750i
\(201\) 1.27762e9i 0.782740i
\(202\) 2.91278e8i 0.174945i
\(203\) 8.17288e8 0.481273
\(204\) 1.76947e8i 0.102170i
\(205\) 2.14653e9i 1.21541i
\(206\) 1.36216e9i 0.756415i
\(207\) 1.46023e9 0.795314
\(208\) 1.45539e8 0.0777547
\(209\) 1.02787e9i 0.538706i
\(210\) 4.48154e8 0.230436
\(211\) 2.53499e9i 1.27893i −0.768821 0.639464i \(-0.779156\pi\)
0.768821 0.639464i \(-0.220844\pi\)
\(212\) −1.57425e9 −0.779346
\(213\) −1.96575e9 −0.955015
\(214\) 1.43075e9i 0.682197i
\(215\) 1.47419e9 + 9.21570e8i 0.689922 + 0.431295i
\(216\) 3.99515e9 1.83535
\(217\) 3.81697e8i 0.172139i
\(218\) 2.16010e9i 0.956420i
\(219\) 6.73707e9 2.92883
\(220\) 1.80183e9i 0.769170i
\(221\) −3.16548e8 −0.132700
\(222\) 1.86001e7i 0.00765778i
\(223\) 3.90361e9i 1.57851i −0.614067 0.789254i \(-0.710468\pi\)
0.614067 0.789254i \(-0.289532\pi\)
\(224\) 6.27650e8 0.249302
\(225\) −1.76343e9 −0.688065
\(226\) 5.65974e8 0.216951
\(227\) 4.89808e9i 1.84469i 0.386373 + 0.922343i \(0.373728\pi\)
−0.386373 + 0.922343i \(0.626272\pi\)
\(228\) 9.39553e8 0.347682
\(229\) −4.85451e9 −1.76524 −0.882619 0.470089i \(-0.844222\pi\)
−0.882619 + 0.470089i \(0.844222\pi\)
\(230\) −5.68353e8 −0.203099
\(231\) −2.01630e9 −0.708119
\(232\) −5.57379e9 −1.92397
\(233\) 2.29736e8i 0.0779480i 0.999240 + 0.0389740i \(0.0124089\pi\)
−0.999240 + 0.0389740i \(0.987591\pi\)
\(234\) 5.22240e9i 1.74183i
\(235\) 7.29504e8i 0.239197i
\(236\) 1.30294e9 0.420028
\(237\) 4.21503e9i 1.33600i
\(238\) 5.16820e7 0.0161076
\(239\) 5.01758e9 1.53781 0.768905 0.639363i \(-0.220802\pi\)
0.768905 + 0.639363i \(0.220802\pi\)
\(240\) −2.73092e8 −0.0823122
\(241\) 8.41073e8i 0.249325i 0.992199 + 0.124662i \(0.0397848\pi\)
−0.992199 + 0.124662i \(0.960215\pi\)
\(242\) 3.40120e9i 0.991677i
\(243\) 4.41986e8i 0.126760i
\(244\) 2.22284e9i 0.627118i
\(245\) 2.74180e9i 0.760977i
\(246\) −6.09005e9 −1.66295
\(247\) 1.68081e9i 0.451577i
\(248\) 2.60312e9i 0.688157i
\(249\) 5.20591e9i 1.35425i
\(250\) 2.71709e9 0.695574
\(251\) 6.10592e8 0.153835 0.0769177 0.997037i \(-0.475492\pi\)
0.0769177 + 0.997037i \(0.475492\pi\)
\(252\) 1.23594e9i 0.306475i
\(253\) 2.55709e9 0.624113
\(254\) 8.59154e8i 0.206413i
\(255\) 5.93976e8 0.140478
\(256\) −4.42806e9 −1.03099
\(257\) 2.83448e9i 0.649743i 0.945758 + 0.324871i \(0.105321\pi\)
−0.945758 + 0.324871i \(0.894679\pi\)
\(258\) 2.61464e9 4.18252e9i 0.590111 0.943972i
\(259\) 7.87479e6 0.00175001
\(260\) 2.94643e9i 0.644766i
\(261\) 1.78709e10i 3.85110i
\(262\) −5.24223e9 −1.11253
\(263\) 3.92497e9i 0.820378i 0.912001 + 0.410189i \(0.134537\pi\)
−0.912001 + 0.410189i \(0.865463\pi\)
\(264\) 1.37509e10 2.83083
\(265\) 5.28446e9i 1.07156i
\(266\) 2.74422e8i 0.0548140i
\(267\) −1.28254e10 −2.52363
\(268\) −1.37142e9 −0.265846
\(269\) 5.01380e9 0.957543 0.478771 0.877940i \(-0.341082\pi\)
0.478771 + 0.877940i \(0.341082\pi\)
\(270\) 4.98571e9i 0.938149i
\(271\) 5.99686e9 1.11185 0.555926 0.831232i \(-0.312364\pi\)
0.555926 + 0.831232i \(0.312364\pi\)
\(272\) −3.14935e7 −0.00575368
\(273\) −3.29714e9 −0.593589
\(274\) −2.09522e9 −0.371730
\(275\) −3.08805e9 −0.539950
\(276\) 2.33738e9i 0.402804i
\(277\) 3.81516e9i 0.648027i 0.946052 + 0.324014i \(0.105032\pi\)
−0.946052 + 0.324014i \(0.894968\pi\)
\(278\) 4.75220e9i 0.795638i
\(279\) 8.34623e9 1.37744
\(280\) 1.29398e9i 0.210521i
\(281\) −9.65432e9 −1.54845 −0.774224 0.632912i \(-0.781859\pi\)
−0.774224 + 0.632912i \(0.781859\pi\)
\(282\) −2.06972e9 −0.327277
\(283\) −2.68907e9 −0.419234 −0.209617 0.977784i \(-0.567222\pi\)
−0.209617 + 0.977784i \(0.567222\pi\)
\(284\) 2.11006e9i 0.324356i
\(285\) 3.15390e9i 0.478045i
\(286\) 9.14524e9i 1.36688i
\(287\) 2.57837e9i 0.380030i
\(288\) 1.37243e10i 1.99489i
\(289\) −6.90726e9 −0.990180
\(290\) 6.95577e9i 0.983452i
\(291\) 5.65569e9i 0.788703i
\(292\) 7.23166e9i 0.994734i
\(293\) −8.49101e9 −1.15210 −0.576049 0.817415i \(-0.695406\pi\)
−0.576049 + 0.817415i \(0.695406\pi\)
\(294\) −7.77894e9 −1.04119
\(295\) 4.37374e9i 0.577517i
\(296\) −5.37050e7 −0.00699597
\(297\) 2.24313e10i 2.88289i
\(298\) 7.28398e7 0.00923642
\(299\) 4.18146e9 0.523170
\(300\) 2.82273e9i 0.348485i
\(301\) 1.77077e9 + 1.10697e9i 0.215723 + 0.134856i
\(302\) 4.63743e9 0.557507
\(303\) 4.02112e9i 0.477064i
\(304\) 1.67225e8i 0.0195797i
\(305\) 7.46166e9 0.862256
\(306\) 1.13008e9i 0.128892i
\(307\) −8.44085e9 −0.950239 −0.475120 0.879921i \(-0.657595\pi\)
−0.475120 + 0.879921i \(0.657595\pi\)
\(308\) 2.16432e9i 0.240502i
\(309\) 1.88048e10i 2.06269i
\(310\) −3.24854e9 −0.351756
\(311\) 6.75741e9 0.722335 0.361168 0.932501i \(-0.382378\pi\)
0.361168 + 0.932501i \(0.382378\pi\)
\(312\) 2.24860e10 2.37298
\(313\) 8.86708e9i 0.923854i 0.886918 + 0.461927i \(0.152842\pi\)
−0.886918 + 0.461927i \(0.847158\pi\)
\(314\) 4.73164e9 0.486735
\(315\) 4.14881e9 0.421387
\(316\) −4.52447e9 −0.453753
\(317\) −3.54232e9 −0.350793 −0.175397 0.984498i \(-0.556121\pi\)
−0.175397 + 0.984498i \(0.556121\pi\)
\(318\) 1.49929e10 1.46614
\(319\) 3.12948e10i 3.02211i
\(320\) 5.83717e9i 0.556676i
\(321\) 1.97516e10i 1.86030i
\(322\) −6.82695e8 −0.0635044
\(323\) 3.63714e8i 0.0334157i
\(324\) 7.22864e9 0.655959
\(325\) −5.04972e9 −0.452620
\(326\) 4.02765e9 0.356600
\(327\) 2.98204e10i 2.60809i
\(328\) 1.75841e10i 1.51924i
\(329\) 8.76267e8i 0.0747916i
\(330\) 1.71603e10i 1.44700i
\(331\) 8.57562e9i 0.714420i −0.934024 0.357210i \(-0.883728\pi\)
0.934024 0.357210i \(-0.116272\pi\)
\(332\) −5.58810e9 −0.459951
\(333\) 1.72191e8i 0.0140034i
\(334\) 1.53490e10i 1.23337i
\(335\) 4.60359e9i 0.365525i
\(336\) −3.28033e8 −0.0257372
\(337\) 1.16877e10 0.906166 0.453083 0.891468i \(-0.350324\pi\)
0.453083 + 0.891468i \(0.350324\pi\)
\(338\) 6.61548e9i 0.506867i
\(339\) 7.81331e9 0.591611
\(340\) 6.37583e8i 0.0477113i
\(341\) 1.46156e10 1.08093
\(342\) −6.00054e9 −0.438617
\(343\) 6.81471e9i 0.492347i
\(344\) −1.20764e10 7.54940e9i −0.862391 0.539112i
\(345\) −7.84616e9 −0.553835
\(346\) 1.18419e10i 0.826262i
\(347\) 1.00908e10i 0.695995i 0.937495 + 0.347998i \(0.113138\pi\)
−0.937495 + 0.347998i \(0.886862\pi\)
\(348\) −2.86060e10 −1.95047
\(349\) 1.53839e10i 1.03697i 0.855088 + 0.518483i \(0.173503\pi\)
−0.855088 + 0.518483i \(0.826497\pi\)
\(350\) 8.24453e8 0.0549407
\(351\) 3.66806e10i 2.41662i
\(352\) 2.40334e10i 1.56547i
\(353\) 8.54458e9 0.550290 0.275145 0.961403i \(-0.411274\pi\)
0.275145 + 0.961403i \(0.411274\pi\)
\(354\) −1.24090e10 −0.790177
\(355\) 7.08309e9 0.445974
\(356\) 1.37669e10i 0.857112i
\(357\) 7.13474e8 0.0439243
\(358\) 1.27353e10 0.775312
\(359\) 2.58791e10 1.55801 0.779006 0.627016i \(-0.215724\pi\)
0.779006 + 0.627016i \(0.215724\pi\)
\(360\) −2.82943e10 −1.68457
\(361\) 1.50523e10 0.886287
\(362\) 2.20494e9i 0.128400i
\(363\) 4.69538e10i 2.70423i
\(364\) 3.53919e9i 0.201604i
\(365\) −2.42753e10 −1.36771
\(366\) 2.11700e10i 1.17977i
\(367\) 2.44465e9 0.134757 0.0673786 0.997727i \(-0.478536\pi\)
0.0673786 + 0.997727i \(0.478536\pi\)
\(368\) 4.16015e8 0.0226839
\(369\) −5.63790e10 −3.04097
\(370\) 6.70207e7i 0.00357604i
\(371\) 6.34760e9i 0.335053i
\(372\) 1.33598e10i 0.697635i
\(373\) 7.22158e9i 0.373076i −0.982448 0.186538i \(-0.940273\pi\)
0.982448 0.186538i \(-0.0597267\pi\)
\(374\) 1.97896e9i 0.101146i
\(375\) 3.75096e10 1.89678
\(376\) 5.97602e9i 0.298993i
\(377\) 5.11746e10i 2.53332i
\(378\) 5.98874e9i 0.293338i
\(379\) 4.92413e9 0.238656 0.119328 0.992855i \(-0.461926\pi\)
0.119328 + 0.992855i \(0.461926\pi\)
\(380\) −3.38544e9 −0.162361
\(381\) 1.18607e10i 0.562872i
\(382\) −1.68982e10 −0.793572
\(383\) 2.26540e10i 1.05281i −0.850234 0.526404i \(-0.823540\pi\)
0.850234 0.526404i \(-0.176460\pi\)
\(384\) −2.05630e10 −0.945717
\(385\) 7.26522e9 0.330678
\(386\) 1.29654e10i 0.584031i
\(387\) 2.42052e10 3.87199e10i 1.07911 1.72620i
\(388\) −6.07090e9 −0.267871
\(389\) 4.06348e9i 0.177460i −0.996056 0.0887299i \(-0.971719\pi\)
0.996056 0.0887299i \(-0.0282808\pi\)
\(390\) 2.80612e10i 1.21296i
\(391\) −9.04834e8 −0.0387135
\(392\) 2.24606e10i 0.951209i
\(393\) −7.23694e10 −3.03378
\(394\) 1.64287e10i 0.681739i
\(395\) 1.51878e10i 0.623888i
\(396\) 4.73253e10 1.92448
\(397\) 3.30903e10 1.33211 0.666053 0.745905i \(-0.267983\pi\)
0.666053 + 0.745905i \(0.267983\pi\)
\(398\) −1.66659e10 −0.664196
\(399\) 3.78841e9i 0.149474i
\(400\) −5.02398e8 −0.0196249
\(401\) 8.53281e9 0.330001 0.165000 0.986294i \(-0.447237\pi\)
0.165000 + 0.986294i \(0.447237\pi\)
\(402\) 1.30611e10 0.500122
\(403\) 2.39000e10 0.906103
\(404\) 4.31633e9 0.162028
\(405\) 2.42652e10i 0.901911i
\(406\) 8.35514e9i 0.307503i
\(407\) 3.01534e8i 0.0109890i
\(408\) −4.86579e9 −0.175595
\(409\) 2.02511e10i 0.723694i −0.932237 0.361847i \(-0.882146\pi\)
0.932237 0.361847i \(-0.117854\pi\)
\(410\) 2.19440e10 0.776568
\(411\) −2.89247e10 −1.01368
\(412\) 2.01853e10 0.700562
\(413\) 5.25366e9i 0.180577i
\(414\) 1.49279e10i 0.508156i
\(415\) 1.87582e10i 0.632410i
\(416\) 3.93004e10i 1.31227i
\(417\) 6.56045e10i 2.16965i
\(418\) −1.05079e10 −0.344199
\(419\) 4.85618e10i 1.57557i 0.615948 + 0.787787i \(0.288773\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(420\) 6.64100e9i 0.213420i
\(421\) 5.23909e10i 1.66774i −0.551964 0.833868i \(-0.686121\pi\)
0.551964 0.833868i \(-0.313879\pi\)
\(422\) 2.59152e10 0.817155
\(423\) −1.91606e10 −0.598476
\(424\) 4.32897e10i 1.33943i
\(425\) 1.09272e9 0.0334929
\(426\) 2.00959e10i 0.610195i
\(427\) 8.96282e9 0.269608
\(428\) −2.12017e10 −0.631823
\(429\) 1.26251e11i 3.72739i
\(430\) −9.42121e9 + 1.50707e10i −0.275571 + 0.440817i
\(431\) −8.47294e9 −0.245542 −0.122771 0.992435i \(-0.539178\pi\)
−0.122771 + 0.992435i \(0.539178\pi\)
\(432\) 3.64937e9i 0.104781i
\(433\) 1.82972e10i 0.520516i −0.965539 0.260258i \(-0.916192\pi\)
0.965539 0.260258i \(-0.0838076\pi\)
\(434\) −3.90209e9 −0.109986
\(435\) 9.60249e10i 2.68180i
\(436\) 3.20096e10 0.885798
\(437\) 4.80450e9i 0.131741i
\(438\) 6.88731e10i 1.87134i
\(439\) 4.05234e10 1.09106 0.545529 0.838092i \(-0.316329\pi\)
0.545529 + 0.838092i \(0.316329\pi\)
\(440\) −4.95478e10 −1.32195
\(441\) −7.20140e10 −1.90398
\(442\) 3.23608e9i 0.0847871i
\(443\) −5.19815e10 −1.34969 −0.674845 0.737960i \(-0.735789\pi\)
−0.674845 + 0.737960i \(0.735789\pi\)
\(444\) −2.75626e8 −0.00709233
\(445\) 4.62130e10 1.17849
\(446\) 3.99066e10 1.00857
\(447\) 1.00556e9 0.0251870
\(448\) 7.01150e9i 0.174060i
\(449\) 1.28565e10i 0.316328i 0.987413 + 0.158164i \(0.0505575\pi\)
−0.987413 + 0.158164i \(0.949443\pi\)
\(450\) 1.80276e10i 0.439631i
\(451\) −9.87285e10 −2.38636
\(452\) 8.38691e9i 0.200932i
\(453\) 6.40201e10 1.52028
\(454\) −5.00731e10 −1.17864
\(455\) 1.18804e10 0.277195
\(456\) 2.58364e10i 0.597549i
\(457\) 5.62798e10i 1.29029i 0.764060 + 0.645146i \(0.223203\pi\)
−0.764060 + 0.645146i \(0.776797\pi\)
\(458\) 4.96277e10i 1.12788i
\(459\) 7.93739e9i 0.178824i
\(460\) 8.42218e9i 0.188102i
\(461\) −4.05469e10 −0.897746 −0.448873 0.893596i \(-0.648174\pi\)
−0.448873 + 0.893596i \(0.648174\pi\)
\(462\) 2.06126e10i 0.452444i
\(463\) 1.79105e9i 0.0389748i 0.999810 + 0.0194874i \(0.00620342\pi\)
−0.999810 + 0.0194874i \(0.993797\pi\)
\(464\) 5.09138e9i 0.109841i
\(465\) −4.48463e10 −0.959213
\(466\) −2.34859e9 −0.0498039
\(467\) 6.60966e9i 0.138967i 0.997583 + 0.0694835i \(0.0221351\pi\)
−0.997583 + 0.0694835i \(0.977865\pi\)
\(468\) 7.73884e10 1.61322
\(469\) 5.52974e9i 0.114291i
\(470\) 7.45773e9 0.152832
\(471\) 6.53206e10 1.32729
\(472\) 3.58292e10i 0.721887i
\(473\) 4.23871e10 6.78046e10i 0.846817 1.35461i
\(474\) 4.30903e10 0.853623
\(475\) 5.80213e9i 0.113976i
\(476\) 7.65853e8i 0.0149182i
\(477\) 1.38797e11 2.68107
\(478\) 5.12947e10i 0.982564i
\(479\) −5.75458e10 −1.09313 −0.546565 0.837417i \(-0.684065\pi\)
−0.546565 + 0.837417i \(0.684065\pi\)
\(480\) 7.37439e10i 1.38919i
\(481\) 4.93081e8i 0.00921166i
\(482\) −8.59829e9 −0.159303
\(483\) −9.42466e9 −0.173172
\(484\) 5.04008e10 0.918452
\(485\) 2.03789e10i 0.368309i
\(486\) −4.51842e9 −0.0809919
\(487\) 1.42045e10 0.252528 0.126264 0.991997i \(-0.459701\pi\)
0.126264 + 0.991997i \(0.459701\pi\)
\(488\) −6.11252e10 −1.07781
\(489\) 5.56019e10 0.972421
\(490\) 2.80295e10 0.486217
\(491\) 6.76583e10i 1.16411i −0.813149 0.582056i \(-0.802248\pi\)
0.813149 0.582056i \(-0.197752\pi\)
\(492\) 9.02458e10i 1.54016i
\(493\) 1.10738e10i 0.187460i
\(494\) −1.71829e10 −0.288529
\(495\) 1.58862e11i 2.64606i
\(496\) 2.37782e9 0.0392873
\(497\) 8.50808e9 0.139446
\(498\) 5.32200e10 0.865282
\(499\) 6.92061e10i 1.11620i 0.829773 + 0.558100i \(0.188470\pi\)
−0.829773 + 0.558100i \(0.811530\pi\)
\(500\) 4.02633e10i 0.644213i
\(501\) 2.11894e11i 3.36331i
\(502\) 6.24209e9i 0.0982913i
\(503\) 6.26497e10i 0.978695i −0.872089 0.489348i \(-0.837235\pi\)
0.872089 0.489348i \(-0.162765\pi\)
\(504\) −3.39866e10 −0.526727
\(505\) 1.44891e10i 0.222780i
\(506\) 2.61411e10i 0.398770i
\(507\) 9.13271e10i 1.38219i
\(508\) −1.27314e10 −0.191171
\(509\) 3.06030e10 0.455924 0.227962 0.973670i \(-0.426794\pi\)
0.227962 + 0.973670i \(0.426794\pi\)
\(510\) 6.07222e9i 0.0897567i
\(511\) −2.91591e10 −0.427652
\(512\) 7.96805e9i 0.115950i
\(513\) −4.21460e10 −0.608537
\(514\) −2.89769e10 −0.415145
\(515\) 6.77582e10i 0.963237i
\(516\) −6.19789e10 3.87453e10i −0.874269 0.546537i
\(517\) −3.35532e10 −0.469647
\(518\) 8.05040e7i 0.00111815i
\(519\) 1.63479e11i 2.25316i
\(520\) −8.10227e10 −1.10814
\(521\) 6.05568e10i 0.821886i −0.911661 0.410943i \(-0.865199\pi\)
0.911661 0.410943i \(-0.134801\pi\)
\(522\) 1.82695e11 2.46061
\(523\) 1.12688e11i 1.50616i 0.657931 + 0.753078i \(0.271432\pi\)
−0.657931 + 0.753078i \(0.728568\pi\)
\(524\) 7.76823e10i 1.03038i
\(525\) 1.13816e10 0.149819
\(526\) −4.01250e10 −0.524170
\(527\) −5.17177e9 −0.0670496
\(528\) 1.25607e10i 0.161614i
\(529\) −6.63585e10 −0.847372
\(530\) −5.40231e10 −0.684661
\(531\) −1.14877e11 −1.44496
\(532\) −4.06653e9 −0.0507666
\(533\) −1.61445e11 −2.00040
\(534\) 1.31114e11i 1.61244i
\(535\) 7.11701e10i 0.868725i
\(536\) 3.77121e10i 0.456900i
\(537\) 1.75811e11 2.11422
\(538\) 5.12561e10i 0.611810i
\(539\) −1.26108e11 −1.49412
\(540\) −7.38810e10 −0.868876
\(541\) −1.14693e9 −0.0133890 −0.00669451 0.999978i \(-0.502131\pi\)
−0.00669451 + 0.999978i \(0.502131\pi\)
\(542\) 6.13059e10i 0.710404i
\(543\) 3.04394e10i 0.350136i
\(544\) 8.50429e9i 0.0971052i
\(545\) 1.07450e11i 1.21793i
\(546\) 3.37066e10i 0.379267i
\(547\) −2.05760e10 −0.229833 −0.114916 0.993375i \(-0.536660\pi\)
−0.114916 + 0.993375i \(0.536660\pi\)
\(548\) 3.10482e10i 0.344282i
\(549\) 1.95982e11i 2.15738i
\(550\) 3.15692e10i 0.344995i
\(551\) 5.87997e10 0.637923
\(552\) 6.42749e10 0.692285
\(553\) 1.82433e10i 0.195076i
\(554\) −3.90024e10 −0.414049
\(555\) 9.25225e8i 0.00975159i
\(556\) −7.04208e10 −0.736888
\(557\) −5.52422e10 −0.573919 −0.286959 0.957943i \(-0.592644\pi\)
−0.286959 + 0.957943i \(0.592644\pi\)
\(558\) 8.53235e10i 0.880100i
\(559\) 6.93133e10 1.10877e11i 0.709854 1.13552i
\(560\) 1.18198e9 0.0120188
\(561\) 2.73196e10i 0.275819i
\(562\) 9.86962e10i 0.989361i
\(563\) 6.10219e10 0.607368 0.303684 0.952773i \(-0.401783\pi\)
0.303684 + 0.952773i \(0.401783\pi\)
\(564\) 3.06703e10i 0.303111i
\(565\) −2.81533e10 −0.276271
\(566\) 2.74904e10i 0.267865i
\(567\) 2.91469e10i 0.282007i
\(568\) −5.80239e10 −0.557460
\(569\) 1.19187e11 1.13705 0.568525 0.822666i \(-0.307514\pi\)
0.568525 + 0.822666i \(0.307514\pi\)
\(570\) 3.22424e10 0.305441
\(571\) 5.18835e10i 0.488073i −0.969766 0.244036i \(-0.921528\pi\)
0.969766 0.244036i \(-0.0784716\pi\)
\(572\) 1.35519e11 1.26595
\(573\) −2.33281e11 −2.16401
\(574\) 2.63587e10 0.242815
\(575\) −1.44343e10 −0.132046
\(576\) 1.53314e11 1.39281
\(577\) 1.07678e11i 0.971460i 0.874109 + 0.485730i \(0.161446\pi\)
−0.874109 + 0.485730i \(0.838554\pi\)
\(578\) 7.06129e10i 0.632664i
\(579\) 1.78988e11i 1.59261i
\(580\) 1.03074e11 0.910834
\(581\) 2.25320e10i 0.197740i
\(582\) 5.78181e10 0.503932
\(583\) 2.43056e11 2.10393
\(584\) 1.98861e11 1.70961
\(585\) 2.59778e11i 2.21809i
\(586\) 8.68037e10i 0.736118i
\(587\) 1.96919e11i 1.65858i 0.558819 + 0.829289i \(0.311254\pi\)
−0.558819 + 0.829289i \(0.688746\pi\)
\(588\) 1.15273e11i 0.964311i
\(589\) 2.74611e10i 0.228169i
\(590\) 4.47127e10 0.368997
\(591\) 2.26799e11i 1.85905i
\(592\) 4.90568e7i 0.000399404i
\(593\) 4.01305e10i 0.324530i 0.986747 + 0.162265i \(0.0518800\pi\)
−0.986747 + 0.162265i \(0.948120\pi\)
\(594\) −2.29315e11 −1.84199
\(595\) −2.57082e9 −0.0205118
\(596\) 1.07938e9i 0.00855440i
\(597\) −2.30074e11 −1.81122
\(598\) 4.27471e10i 0.334273i
\(599\) −1.50298e11 −1.16747 −0.583734 0.811945i \(-0.698409\pi\)
−0.583734 + 0.811945i \(0.698409\pi\)
\(600\) −7.76212e10 −0.598929
\(601\) 9.06889e10i 0.695114i 0.937659 + 0.347557i \(0.112989\pi\)
−0.937659 + 0.347557i \(0.887011\pi\)
\(602\) −1.13166e10 + 1.81026e10i −0.0861647 + 0.137834i
\(603\) 1.20914e11 0.914550
\(604\) 6.87201e10i 0.516340i
\(605\) 1.69186e11i 1.26282i
\(606\) −4.11079e10 −0.304814
\(607\) 5.62467e9i 0.0414326i 0.999785 + 0.0207163i \(0.00659468\pi\)
−0.999785 + 0.0207163i \(0.993405\pi\)
\(608\) 4.51562e10 0.330448
\(609\) 1.15343e11i 0.838539i
\(610\) 7.62806e10i 0.550928i
\(611\) −5.48676e10 −0.393687
\(612\) −1.67462e10 −0.119374
\(613\) 2.46512e11 1.74581 0.872905 0.487891i \(-0.162234\pi\)
0.872905 + 0.487891i \(0.162234\pi\)
\(614\) 8.62909e10i 0.607144i
\(615\) 3.02938e11 2.11765
\(616\) −5.95159e10 −0.413343
\(617\) −1.65485e11 −1.14187 −0.570936 0.820994i \(-0.693420\pi\)
−0.570936 + 0.820994i \(0.693420\pi\)
\(618\) −1.92241e11 −1.31793
\(619\) −1.66265e10 −0.113250 −0.0566250 0.998396i \(-0.518034\pi\)
−0.0566250 + 0.998396i \(0.518034\pi\)
\(620\) 4.81387e10i 0.325782i
\(621\) 1.04849e11i 0.705016i
\(622\) 6.90811e10i 0.461527i
\(623\) 5.55102e10 0.368486
\(624\) 2.05398e10i 0.135475i
\(625\) −8.35828e10 −0.547768
\(626\) −9.06482e10 −0.590285
\(627\) −1.45062e11 −0.938607
\(628\) 7.01161e10i 0.450795i
\(629\) 1.06699e8i 0.000681643i
\(630\) 4.24133e10i 0.269240i
\(631\) 7.50263e10i 0.473256i 0.971600 + 0.236628i \(0.0760423\pi\)
−0.971600 + 0.236628i \(0.923958\pi\)
\(632\) 1.24417e11i 0.779850i
\(633\) 3.57761e11 2.22832
\(634\) 3.62132e10i 0.224135i
\(635\) 4.27370e10i 0.262851i
\(636\) 2.22173e11i 1.35788i
\(637\) −2.06217e11 −1.25247
\(638\) 3.19927e11 1.93094
\(639\) 1.86039e11i 1.11583i
\(640\) 7.40936e10 0.441632
\(641\) 2.82104e11i 1.67100i 0.549489 + 0.835501i \(0.314822\pi\)
−0.549489 + 0.835501i \(0.685178\pi\)
\(642\) 2.01921e11 1.18862
\(643\) 1.95960e11 1.14637 0.573183 0.819427i \(-0.305708\pi\)
0.573183 + 0.819427i \(0.305708\pi\)
\(644\) 1.01166e10i 0.0588152i
\(645\) −1.30061e11 + 2.08051e11i −0.751461 + 1.20208i
\(646\) 3.71825e9 0.0213505
\(647\) 2.37614e9i 0.0135598i −0.999977 0.00677992i \(-0.997842\pi\)
0.999977 0.00677992i \(-0.00215813\pi\)
\(648\) 1.98778e11i 1.12737i
\(649\) −2.01168e11 −1.13391
\(650\) 5.16233e10i 0.289196i
\(651\) −5.38686e10 −0.299924
\(652\) 5.96839e10i 0.330268i
\(653\) 1.28525e11i 0.706862i −0.935461 0.353431i \(-0.885015\pi\)
0.935461 0.353431i \(-0.114985\pi\)
\(654\) −3.04854e11 −1.66641
\(655\) 2.60765e11 1.41672
\(656\) −1.60622e10 −0.0867342
\(657\) 6.37596e11i 3.42203i
\(658\) 8.95809e9 0.0477872
\(659\) 1.48704e11 0.788464 0.394232 0.919011i \(-0.371011\pi\)
0.394232 + 0.919011i \(0.371011\pi\)
\(660\) −2.54291e11 −1.34015
\(661\) −5.70041e10 −0.298607 −0.149304 0.988791i \(-0.547703\pi\)
−0.149304 + 0.988791i \(0.547703\pi\)
\(662\) 8.76686e10 0.456470
\(663\) 4.46743e10i 0.231208i
\(664\) 1.53665e11i 0.790502i
\(665\) 1.36506e10i 0.0698015i
\(666\) 1.76031e9 0.00894731
\(667\) 1.46280e11i 0.739061i
\(668\) −2.27450e11 −1.14230
\(669\) 5.50913e11 2.75029
\(670\) −4.70625e10 −0.233548
\(671\) 3.43195e11i 1.69298i
\(672\) 8.85798e10i 0.434368i
\(673\) 2.33498e11i 1.13821i −0.822264 0.569106i \(-0.807289\pi\)
0.822264 0.569106i \(-0.192711\pi\)
\(674\) 1.19483e11i 0.578983i
\(675\) 1.26621e11i 0.609943i
\(676\) 9.80318e10 0.469440
\(677\) 7.17939e10i 0.341769i −0.985291 0.170885i \(-0.945337\pi\)
0.985291 0.170885i \(-0.0546625\pi\)
\(678\) 7.98754e10i 0.378002i
\(679\) 2.44787e10i 0.115162i
\(680\) 1.75327e10 0.0819996
\(681\) −6.91262e11 −3.21406
\(682\) 1.49415e11i 0.690648i
\(683\) −3.60964e11 −1.65875 −0.829374 0.558694i \(-0.811303\pi\)
−0.829374 + 0.558694i \(0.811303\pi\)
\(684\) 8.89193e10i 0.406230i
\(685\) 1.04223e11 0.473370
\(686\) 6.96668e10 0.314579
\(687\) 6.85113e11i 3.07564i
\(688\) 6.89600e9 1.10312e10i 0.0307782 0.0492344i
\(689\) 3.97456e11 1.76365
\(690\) 8.02113e10i 0.353866i
\(691\) 2.51135e11i 1.10153i 0.834662 + 0.550763i \(0.185663\pi\)
−0.834662 + 0.550763i \(0.814337\pi\)
\(692\) 1.75480e11 0.765251
\(693\) 1.90822e11i 0.827363i
\(694\) −1.03158e11 −0.444697
\(695\) 2.36389e11i 1.01318i
\(696\) 7.86626e11i 3.35221i
\(697\) 3.49354e10 0.148025
\(698\) −1.57270e11 −0.662557
\(699\) −3.24224e10 −0.135812
\(700\) 1.22172e10i 0.0508839i
\(701\) −9.21164e10 −0.381474 −0.190737 0.981641i \(-0.561088\pi\)
−0.190737 + 0.981641i \(0.561088\pi\)
\(702\) −3.74986e11 −1.54407
\(703\) 5.66550e8 0.00231962
\(704\) 2.68478e11 1.09299
\(705\) 1.02954e11 0.416763
\(706\) 8.73513e10i 0.351601i
\(707\) 1.74040e10i 0.0696582i
\(708\) 1.83884e11i 0.731830i
\(709\) −4.42941e11 −1.75291 −0.876457 0.481480i \(-0.840100\pi\)
−0.876457 + 0.481480i \(0.840100\pi\)
\(710\) 7.24104e10i 0.284949i
\(711\) 3.98911e11 1.56098
\(712\) −3.78572e11 −1.47309
\(713\) 6.83167e10 0.264343
\(714\) 7.29384e9i 0.0280649i
\(715\) 4.54913e11i 1.74062i
\(716\) 1.88718e11i 0.718063i
\(717\) 7.08127e11i 2.67938i
\(718\) 2.64562e11i 0.995473i
\(719\) −5.11725e10 −0.191479 −0.0957395 0.995406i \(-0.530522\pi\)
−0.0957395 + 0.995406i \(0.530522\pi\)
\(720\) 2.58454e10i 0.0961731i
\(721\) 8.13900e10i 0.301183i
\(722\) 1.53880e11i 0.566282i
\(723\) −1.18700e11 −0.434408
\(724\) −3.26741e10 −0.118919
\(725\) 1.76654e11i 0.639397i
\(726\) −4.80008e11 −1.72784
\(727\) 1.66037e11i 0.594385i 0.954818 + 0.297192i \(0.0960502\pi\)
−0.954818 + 0.297192i \(0.903950\pi\)
\(728\) −9.73230e10 −0.346489
\(729\) 2.50693e11 0.887632
\(730\) 2.48167e11i 0.873881i
\(731\) −1.49988e10 + 2.39929e10i −0.0525277 + 0.0840259i
\(732\) −3.13708e11 −1.09265
\(733\) 2.79590e11i 0.968513i −0.874926 0.484257i \(-0.839090\pi\)
0.874926 0.484257i \(-0.160910\pi\)
\(734\) 2.49916e10i 0.0861014i
\(735\) 3.86949e11 1.32588
\(736\) 1.12338e11i 0.382838i
\(737\) 2.11740e11 0.717682
\(738\) 5.76362e11i 1.94299i
\(739\) 1.64286e11i 0.550837i 0.961324 + 0.275418i \(0.0888163\pi\)
−0.961324 + 0.275418i \(0.911184\pi\)
\(740\) 9.93150e8 0.00331198
\(741\) −2.37212e11 −0.786799
\(742\) −6.48915e10 −0.214078
\(743\) 4.46894e11i 1.46639i −0.680019 0.733195i \(-0.738028\pi\)
0.680019 0.733195i \(-0.261972\pi\)
\(744\) 3.67376e11 1.19900
\(745\) −3.62328e9 −0.0117619
\(746\) 7.38263e10 0.238372
\(747\) 4.92687e11 1.58230
\(748\) −2.93253e10 −0.0936776
\(749\) 8.54882e10i 0.271631i
\(750\) 3.83461e11i 1.21193i
\(751\) 1.65073e11i 0.518939i −0.965751 0.259469i \(-0.916452\pi\)
0.965751 0.259469i \(-0.0835477\pi\)
\(752\) −5.45880e9 −0.0170697
\(753\) 8.61725e10i 0.268033i
\(754\) 5.23158e11 1.61863
\(755\) −2.30680e11 −0.709942
\(756\) −8.87446e10 −0.271678
\(757\) 4.16379e11i 1.26796i 0.773350 + 0.633979i \(0.218580\pi\)
−0.773350 + 0.633979i \(0.781420\pi\)
\(758\) 5.03394e10i 0.152487i
\(759\) 3.60880e11i 1.08742i
\(760\) 9.30951e10i 0.279044i
\(761\) 5.59476e11i 1.66818i 0.551628 + 0.834090i \(0.314007\pi\)
−0.551628 + 0.834090i \(0.685993\pi\)
\(762\) 1.21252e11 0.359640
\(763\) 1.29067e11i 0.380819i
\(764\) 2.50407e11i 0.734975i
\(765\) 5.62139e10i 0.164134i
\(766\) 2.31592e11 0.672679
\(767\) −3.28958e11 −0.950516
\(768\) 6.24929e11i 1.79633i
\(769\) 3.83384e11 1.09630 0.548150 0.836380i \(-0.315332\pi\)
0.548150 + 0.836380i \(0.315332\pi\)
\(770\) 7.42723e10i 0.211283i
\(771\) −4.00029e11 −1.13207
\(772\) 1.92128e11 0.540906
\(773\) 1.08957e11i 0.305168i −0.988291 0.152584i \(-0.951241\pi\)
0.988291 0.152584i \(-0.0487594\pi\)
\(774\) 3.95834e11 + 2.47450e11i 1.10293 + 0.689483i
\(775\) −8.25023e10 −0.228696
\(776\) 1.66941e11i 0.460381i
\(777\) 1.11136e9i 0.00304910i
\(778\) 4.15410e10 0.113386
\(779\) 1.85500e11i 0.503727i
\(780\) −4.15827e11 −1.12340
\(781\) 3.25783e11i 0.875637i
\(782\)