Properties

Label 117.4.b.e.64.2
Level $117$
Weight $4$
Character 117.64
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1362828.1
Defining polynomial: \( x^{4} + 23x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 64.2
Root \(-1.52356i\) of defining polynomial
Character \(\chi\) \(=\) 117.64
Dual form 117.4.b.e.64.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.52356i q^{2} +5.67878 q^{4} +9.65841i q^{5} +22.3639i q^{7} -20.8404i q^{8} +O(q^{10})\) \(q-1.52356i q^{2} +5.67878 q^{4} +9.65841i q^{5} +22.3639i q^{7} -20.8404i q^{8} +14.7151 q^{10} +50.3050i q^{11} +(-39.7151 + 24.8940i) q^{13} +34.0727 q^{14} +13.6788 q^{16} +86.1454 q^{17} -116.880i q^{19} +54.8480i q^{20} +76.6424 q^{22} +72.0000 q^{23} +31.7151 q^{25} +(37.9273 + 60.5082i) q^{26} +127.000i q^{28} -14.1454 q^{29} +196.215i q^{31} -187.563i q^{32} -131.247i q^{34} -216.000 q^{35} -154.424i q^{37} -178.073 q^{38} +201.285 q^{40} -265.726i q^{41} -211.855 q^{43} +285.671i q^{44} -109.696i q^{46} -67.5535i q^{47} -157.145 q^{49} -48.3197i q^{50} +(-225.533 + 141.367i) q^{52} -686.581 q^{53} -485.866 q^{55} +466.073 q^{56} +21.5512i q^{58} +91.9304i q^{59} +329.006 q^{61} +298.945 q^{62} -176.333 q^{64} +(-240.436 - 383.585i) q^{65} -768.370i q^{67} +489.201 q^{68} +329.088i q^{70} +264.969i q^{71} +771.306i q^{73} -235.273 q^{74} -663.734i q^{76} -1125.02 q^{77} +1226.86 q^{79} +132.115i q^{80} -404.849 q^{82} -514.019i q^{83} +832.027i q^{85} +322.772i q^{86} +1048.38 q^{88} -527.889i q^{89} +(-556.727 - 888.186i) q^{91} +408.872 q^{92} -102.921 q^{94} +1128.87 q^{95} +74.2755i q^{97} +239.420i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 14 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 14 q^{4} - 88 q^{10} - 12 q^{13} - 84 q^{14} + 18 q^{16} - 96 q^{17} + 380 q^{22} + 288 q^{23} - 20 q^{25} + 372 q^{26} + 384 q^{29} - 864 q^{35} - 492 q^{38} + 952 q^{40} - 1288 q^{43} - 188 q^{49} - 1306 q^{52} - 984 q^{53} - 328 q^{55} + 1644 q^{56} + 288 q^{61} - 1668 q^{62} + 1314 q^{64} + 360 q^{65} + 4380 q^{68} - 3144 q^{74} - 1416 q^{77} + 4320 q^{79} - 3088 q^{82} + 1036 q^{88} - 24 q^{91} - 1008 q^{92} - 1660 q^{94} + 1872 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52356i 0.538658i −0.963048 0.269329i \(-0.913198\pi\)
0.963048 0.269329i \(-0.0868019\pi\)
\(3\) 0 0
\(4\) 5.67878 0.709847
\(5\) 9.65841i 0.863874i 0.901904 + 0.431937i \(0.142170\pi\)
−0.901904 + 0.431937i \(0.857830\pi\)
\(6\) 0 0
\(7\) 22.3639i 1.20754i 0.797159 + 0.603769i \(0.206335\pi\)
−0.797159 + 0.603769i \(0.793665\pi\)
\(8\) 20.8404i 0.921023i
\(9\) 0 0
\(10\) 14.7151 0.465333
\(11\) 50.3050i 1.37887i 0.724349 + 0.689433i \(0.242140\pi\)
−0.724349 + 0.689433i \(0.757860\pi\)
\(12\) 0 0
\(13\) −39.7151 + 24.8940i −0.847307 + 0.531103i
\(14\) 34.0727 0.650450
\(15\) 0 0
\(16\) 13.6788 0.213731
\(17\) 86.1454 1.22902 0.614509 0.788910i \(-0.289354\pi\)
0.614509 + 0.788910i \(0.289354\pi\)
\(18\) 0 0
\(19\) 116.880i 1.41127i −0.708578 0.705633i \(-0.750663\pi\)
0.708578 0.705633i \(-0.249337\pi\)
\(20\) 54.8480i 0.613219i
\(21\) 0 0
\(22\) 76.6424 0.742737
\(23\) 72.0000 0.652741 0.326370 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) 31.7151 0.253721
\(26\) 37.9273 + 60.5082i 0.286083 + 0.456409i
\(27\) 0 0
\(28\) 127.000i 0.857168i
\(29\) −14.1454 −0.0905768 −0.0452884 0.998974i \(-0.514421\pi\)
−0.0452884 + 0.998974i \(0.514421\pi\)
\(30\) 0 0
\(31\) 196.215i 1.13682i 0.822747 + 0.568408i \(0.192441\pi\)
−0.822747 + 0.568408i \(0.807559\pi\)
\(32\) 187.563i 1.03615i
\(33\) 0 0
\(34\) 131.247i 0.662021i
\(35\) −216.000 −1.04316
\(36\) 0 0
\(37\) 154.424i 0.686138i −0.939310 0.343069i \(-0.888533\pi\)
0.939310 0.343069i \(-0.111467\pi\)
\(38\) −178.073 −0.760190
\(39\) 0 0
\(40\) 201.285 0.795648
\(41\) 265.726i 1.01218i −0.862480 0.506091i \(-0.831090\pi\)
0.862480 0.506091i \(-0.168910\pi\)
\(42\) 0 0
\(43\) −211.855 −0.751338 −0.375669 0.926754i \(-0.622587\pi\)
−0.375669 + 0.926754i \(0.622587\pi\)
\(44\) 285.671i 0.978785i
\(45\) 0 0
\(46\) 109.696i 0.351604i
\(47\) 67.5535i 0.209653i −0.994491 0.104827i \(-0.966571\pi\)
0.994491 0.104827i \(-0.0334287\pi\)
\(48\) 0 0
\(49\) −157.145 −0.458150
\(50\) 48.3197i 0.136669i
\(51\) 0 0
\(52\) −225.533 + 141.367i −0.601459 + 0.377002i
\(53\) −686.581 −1.77942 −0.889710 0.456527i \(-0.849093\pi\)
−0.889710 + 0.456527i \(0.849093\pi\)
\(54\) 0 0
\(55\) −485.866 −1.19117
\(56\) 466.073 1.11217
\(57\) 0 0
\(58\) 21.5512i 0.0487899i
\(59\) 91.9304i 0.202853i 0.994843 + 0.101426i \(0.0323406\pi\)
−0.994843 + 0.101426i \(0.967659\pi\)
\(60\) 0 0
\(61\) 329.006 0.690572 0.345286 0.938498i \(-0.387782\pi\)
0.345286 + 0.938498i \(0.387782\pi\)
\(62\) 298.945 0.612355
\(63\) 0 0
\(64\) −176.333 −0.344400
\(65\) −240.436 383.585i −0.458807 0.731967i
\(66\) 0 0
\(67\) 768.370i 1.40106i −0.713621 0.700532i \(-0.752946\pi\)
0.713621 0.700532i \(-0.247054\pi\)
\(68\) 489.201 0.872416
\(69\) 0 0
\(70\) 329.088i 0.561908i
\(71\) 264.969i 0.442902i 0.975171 + 0.221451i \(0.0710793\pi\)
−0.975171 + 0.221451i \(0.928921\pi\)
\(72\) 0 0
\(73\) 771.306i 1.23664i 0.785927 + 0.618319i \(0.212186\pi\)
−0.785927 + 0.618319i \(0.787814\pi\)
\(74\) −235.273 −0.369594
\(75\) 0 0
\(76\) 663.734i 1.00178i
\(77\) −1125.02 −1.66503
\(78\) 0 0
\(79\) 1226.86 1.74725 0.873624 0.486602i \(-0.161764\pi\)
0.873624 + 0.486602i \(0.161764\pi\)
\(80\) 132.115i 0.184637i
\(81\) 0 0
\(82\) −404.849 −0.545220
\(83\) 514.019i 0.679771i −0.940467 0.339885i \(-0.889612\pi\)
0.940467 0.339885i \(-0.110388\pi\)
\(84\) 0 0
\(85\) 832.027i 1.06172i
\(86\) 322.772i 0.404714i
\(87\) 0 0
\(88\) 1048.38 1.26997
\(89\) 527.889i 0.628720i −0.949304 0.314360i \(-0.898210\pi\)
0.949304 0.314360i \(-0.101790\pi\)
\(90\) 0 0
\(91\) −556.727 888.186i −0.641328 1.02316i
\(92\) 408.872 0.463346
\(93\) 0 0
\(94\) −102.921 −0.112931
\(95\) 1128.87 1.21916
\(96\) 0 0
\(97\) 74.2755i 0.0777478i 0.999244 + 0.0388739i \(0.0123771\pi\)
−0.999244 + 0.0388739i \(0.987623\pi\)
\(98\) 239.420i 0.246786i
\(99\) 0 0
\(100\) 180.103 0.180103
\(101\) 609.419 0.600390 0.300195 0.953878i \(-0.402948\pi\)
0.300195 + 0.953878i \(0.402948\pi\)
\(102\) 0 0
\(103\) 32.4361 0.0310293 0.0155147 0.999880i \(-0.495061\pi\)
0.0155147 + 0.999880i \(0.495061\pi\)
\(104\) 518.799 + 827.678i 0.489158 + 0.780389i
\(105\) 0 0
\(106\) 1046.04i 0.958498i
\(107\) 1725.45 1.55893 0.779467 0.626444i \(-0.215490\pi\)
0.779467 + 0.626444i \(0.215490\pi\)
\(108\) 0 0
\(109\) 1273.43i 1.11902i −0.828825 0.559508i \(-0.810990\pi\)
0.828825 0.559508i \(-0.189010\pi\)
\(110\) 740.244i 0.641632i
\(111\) 0 0
\(112\) 305.911i 0.258088i
\(113\) −1114.73 −0.928006 −0.464003 0.885834i \(-0.653587\pi\)
−0.464003 + 0.885834i \(0.653587\pi\)
\(114\) 0 0
\(115\) 695.406i 0.563886i
\(116\) −80.3284 −0.0642957
\(117\) 0 0
\(118\) 140.061 0.109268
\(119\) 1926.55i 1.48409i
\(120\) 0 0
\(121\) −1199.59 −0.901272
\(122\) 501.259i 0.371982i
\(123\) 0 0
\(124\) 1114.26i 0.806966i
\(125\) 1513.62i 1.08306i
\(126\) 0 0
\(127\) −1174.01 −0.820289 −0.410144 0.912021i \(-0.634522\pi\)
−0.410144 + 0.912021i \(0.634522\pi\)
\(128\) 1231.85i 0.850637i
\(129\) 0 0
\(130\) −584.413 + 366.318i −0.394280 + 0.247140i
\(131\) 1445.16 0.963851 0.481925 0.876212i \(-0.339938\pi\)
0.481925 + 0.876212i \(0.339938\pi\)
\(132\) 0 0
\(133\) 2613.89 1.70416
\(134\) −1170.65 −0.754695
\(135\) 0 0
\(136\) 1795.30i 1.13195i
\(137\) 508.793i 0.317293i −0.987335 0.158646i \(-0.949287\pi\)
0.987335 0.158646i \(-0.0507130\pi\)
\(138\) 0 0
\(139\) −757.018 −0.461938 −0.230969 0.972961i \(-0.574190\pi\)
−0.230969 + 0.972961i \(0.574190\pi\)
\(140\) −1226.62 −0.740486
\(141\) 0 0
\(142\) 403.695 0.238573
\(143\) −1252.29 1997.87i −0.732320 1.16832i
\(144\) 0 0
\(145\) 136.622i 0.0782470i
\(146\) 1175.13 0.666125
\(147\) 0 0
\(148\) 876.939i 0.487054i
\(149\) 3247.79i 1.78570i −0.450352 0.892851i \(-0.648702\pi\)
0.450352 0.892851i \(-0.351298\pi\)
\(150\) 0 0
\(151\) 795.296i 0.428611i 0.976767 + 0.214305i \(0.0687488\pi\)
−0.976767 + 0.214305i \(0.931251\pi\)
\(152\) −2435.82 −1.29981
\(153\) 0 0
\(154\) 1714.03i 0.896884i
\(155\) −1895.13 −0.982067
\(156\) 0 0
\(157\) −65.2732 −0.0331807 −0.0165903 0.999862i \(-0.505281\pi\)
−0.0165903 + 0.999862i \(0.505281\pi\)
\(158\) 1869.19i 0.941169i
\(159\) 0 0
\(160\) 1811.56 0.895104
\(161\) 1610.20i 0.788210i
\(162\) 0 0
\(163\) 1855.39i 0.891568i −0.895140 0.445784i \(-0.852925\pi\)
0.895140 0.445784i \(-0.147075\pi\)
\(164\) 1509.00i 0.718495i
\(165\) 0 0
\(166\) −783.137 −0.366164
\(167\) 3532.54i 1.63686i 0.574604 + 0.818432i \(0.305156\pi\)
−0.574604 + 0.818432i \(0.694844\pi\)
\(168\) 0 0
\(169\) 957.581 1977.33i 0.435859 0.900015i
\(170\) 1267.64 0.571903
\(171\) 0 0
\(172\) −1203.08 −0.533335
\(173\) −3178.36 −1.39680 −0.698400 0.715708i \(-0.746104\pi\)
−0.698400 + 0.715708i \(0.746104\pi\)
\(174\) 0 0
\(175\) 709.275i 0.306378i
\(176\) 688.111i 0.294706i
\(177\) 0 0
\(178\) −804.267 −0.338665
\(179\) 2741.16 1.14460 0.572302 0.820043i \(-0.306050\pi\)
0.572302 + 0.820043i \(0.306050\pi\)
\(180\) 0 0
\(181\) −3871.09 −1.58970 −0.794850 0.606806i \(-0.792450\pi\)
−0.794850 + 0.606806i \(0.792450\pi\)
\(182\) −1353.20 + 848.204i −0.551131 + 0.345456i
\(183\) 0 0
\(184\) 1500.51i 0.601189i
\(185\) 1491.49 0.592737
\(186\) 0 0
\(187\) 4333.54i 1.69465i
\(188\) 383.621i 0.148822i
\(189\) 0 0
\(190\) 1719.90i 0.656708i
\(191\) 928.291 0.351669 0.175834 0.984420i \(-0.443738\pi\)
0.175834 + 0.984420i \(0.443738\pi\)
\(192\) 0 0
\(193\) 2261.51i 0.843456i −0.906722 0.421728i \(-0.861424\pi\)
0.906722 0.421728i \(-0.138576\pi\)
\(194\) 113.163 0.0418795
\(195\) 0 0
\(196\) −892.394 −0.325216
\(197\) 2265.59i 0.819374i −0.912226 0.409687i \(-0.865638\pi\)
0.912226 0.409687i \(-0.134362\pi\)
\(198\) 0 0
\(199\) 260.895 0.0929366 0.0464683 0.998920i \(-0.485203\pi\)
0.0464683 + 0.998920i \(0.485203\pi\)
\(200\) 660.955i 0.233683i
\(201\) 0 0
\(202\) 928.483i 0.323405i
\(203\) 316.346i 0.109375i
\(204\) 0 0
\(205\) 2566.49 0.874399
\(206\) 49.4181i 0.0167142i
\(207\) 0 0
\(208\) −543.254 + 340.519i −0.181096 + 0.113513i
\(209\) 5879.63 1.94595
\(210\) 0 0
\(211\) 5851.22 1.90907 0.954537 0.298092i \(-0.0963502\pi\)
0.954537 + 0.298092i \(0.0963502\pi\)
\(212\) −3898.94 −1.26312
\(213\) 0 0
\(214\) 2628.82i 0.839732i
\(215\) 2046.18i 0.649062i
\(216\) 0 0
\(217\) −4388.15 −1.37275
\(218\) −1940.15 −0.602767
\(219\) 0 0
\(220\) −2759.13 −0.845547
\(221\) −3421.27 + 2144.50i −1.04136 + 0.652736i
\(222\) 0 0
\(223\) 3463.60i 1.04009i 0.854139 + 0.520045i \(0.174085\pi\)
−0.854139 + 0.520045i \(0.825915\pi\)
\(224\) 4194.65 1.25119
\(225\) 0 0
\(226\) 1698.35i 0.499878i
\(227\) 5329.15i 1.55819i 0.626908 + 0.779093i \(0.284320\pi\)
−0.626908 + 0.779093i \(0.715680\pi\)
\(228\) 0 0
\(229\) 4773.95i 1.37761i 0.724949 + 0.688803i \(0.241863\pi\)
−0.724949 + 0.688803i \(0.758137\pi\)
\(230\) 1059.49 0.303742
\(231\) 0 0
\(232\) 294.795i 0.0834233i
\(233\) −4813.78 −1.35348 −0.676741 0.736221i \(-0.736608\pi\)
−0.676741 + 0.736221i \(0.736608\pi\)
\(234\) 0 0
\(235\) 652.459 0.181114
\(236\) 522.052i 0.143995i
\(237\) 0 0
\(238\) 2935.20 0.799416
\(239\) 1683.19i 0.455549i 0.973714 + 0.227775i \(0.0731449\pi\)
−0.973714 + 0.227775i \(0.926855\pi\)
\(240\) 0 0
\(241\) 664.861i 0.177707i −0.996045 0.0888537i \(-0.971680\pi\)
0.996045 0.0888537i \(-0.0283204\pi\)
\(242\) 1827.65i 0.485477i
\(243\) 0 0
\(244\) 1868.35 0.490201
\(245\) 1517.77i 0.395784i
\(246\) 0 0
\(247\) 2909.60 + 4641.89i 0.749528 + 1.19578i
\(248\) 4089.20 1.04703
\(249\) 0 0
\(250\) 2306.08 0.583398
\(251\) 2142.04 0.538662 0.269331 0.963048i \(-0.413198\pi\)
0.269331 + 0.963048i \(0.413198\pi\)
\(252\) 0 0
\(253\) 3621.96i 0.900042i
\(254\) 1788.67i 0.441855i
\(255\) 0 0
\(256\) −3287.46 −0.802603
\(257\) 3152.62 0.765194 0.382597 0.923915i \(-0.375030\pi\)
0.382597 + 0.923915i \(0.375030\pi\)
\(258\) 0 0
\(259\) 3453.52 0.828539
\(260\) −1365.38 2178.29i −0.325683 0.519585i
\(261\) 0 0
\(262\) 2201.79i 0.519186i
\(263\) 2167.71 0.508238 0.254119 0.967173i \(-0.418214\pi\)
0.254119 + 0.967173i \(0.418214\pi\)
\(264\) 0 0
\(265\) 6631.28i 1.53719i
\(266\) 3982.40i 0.917958i
\(267\) 0 0
\(268\) 4363.40i 0.994542i
\(269\) 3248.98 0.736409 0.368204 0.929745i \(-0.379973\pi\)
0.368204 + 0.929745i \(0.379973\pi\)
\(270\) 0 0
\(271\) 4897.70i 1.09784i −0.835876 0.548919i \(-0.815040\pi\)
0.835876 0.548919i \(-0.184960\pi\)
\(272\) 1178.36 0.262679
\(273\) 0 0
\(274\) −775.175 −0.170912
\(275\) 1595.43i 0.349847i
\(276\) 0 0
\(277\) −2900.33 −0.629111 −0.314555 0.949239i \(-0.601855\pi\)
−0.314555 + 0.949239i \(0.601855\pi\)
\(278\) 1153.36i 0.248827i
\(279\) 0 0
\(280\) 4501.52i 0.960776i
\(281\) 4396.53i 0.933364i −0.884425 0.466682i \(-0.845449\pi\)
0.884425 0.466682i \(-0.154551\pi\)
\(282\) 0 0
\(283\) 559.151 0.117449 0.0587245 0.998274i \(-0.481297\pi\)
0.0587245 + 0.998274i \(0.481297\pi\)
\(284\) 1504.70i 0.314393i
\(285\) 0 0
\(286\) −3043.86 + 1907.93i −0.629327 + 0.394470i
\(287\) 5942.69 1.22225
\(288\) 0 0
\(289\) 2508.02 0.510487
\(290\) −208.151 −0.0421484
\(291\) 0 0
\(292\) 4380.08i 0.877825i
\(293\) 6918.65i 1.37950i 0.724050 + 0.689748i \(0.242278\pi\)
−0.724050 + 0.689748i \(0.757722\pi\)
\(294\) 0 0
\(295\) −887.901 −0.175239
\(296\) −3218.25 −0.631949
\(297\) 0 0
\(298\) −4948.19 −0.961883
\(299\) −2859.49 + 1792.37i −0.553072 + 0.346673i
\(300\) 0 0
\(301\) 4737.90i 0.907270i
\(302\) 1211.68 0.230875
\(303\) 0 0
\(304\) 1598.77i 0.301631i
\(305\) 3177.67i 0.596567i
\(306\) 0 0
\(307\) 8980.94i 1.66961i −0.550548 0.834803i \(-0.685581\pi\)
0.550548 0.834803i \(-0.314419\pi\)
\(308\) −6388.73 −1.18192
\(309\) 0 0
\(310\) 2887.33i 0.528998i
\(311\) −7943.13 −1.44827 −0.724137 0.689656i \(-0.757762\pi\)
−0.724137 + 0.689656i \(0.757762\pi\)
\(312\) 0 0
\(313\) −5059.57 −0.913686 −0.456843 0.889547i \(-0.651020\pi\)
−0.456843 + 0.889547i \(0.651020\pi\)
\(314\) 99.4473i 0.0178730i
\(315\) 0 0
\(316\) 6967.07 1.24028
\(317\) 8702.12i 1.54183i −0.636939 0.770914i \(-0.719800\pi\)
0.636939 0.770914i \(-0.280200\pi\)
\(318\) 0 0
\(319\) 711.582i 0.124893i
\(320\) 1703.10i 0.297519i
\(321\) 0 0
\(322\) 2453.23 0.424576
\(323\) 10068.6i 1.73447i
\(324\) 0 0
\(325\) −1259.57 + 789.515i −0.214980 + 0.134752i
\(326\) −2826.79 −0.480250
\(327\) 0 0
\(328\) −5537.84 −0.932244
\(329\) 1510.76 0.253164
\(330\) 0 0
\(331\) 1737.65i 0.288549i 0.989538 + 0.144275i \(0.0460848\pi\)
−0.989538 + 0.144275i \(0.953915\pi\)
\(332\) 2919.00i 0.482533i
\(333\) 0 0
\(334\) 5382.02 0.881710
\(335\) 7421.23 1.21034
\(336\) 0 0
\(337\) −2917.47 −0.471586 −0.235793 0.971803i \(-0.575769\pi\)
−0.235793 + 0.971803i \(0.575769\pi\)
\(338\) −3012.58 1458.93i −0.484800 0.234779i
\(339\) 0 0
\(340\) 4724.90i 0.753658i
\(341\) −9870.61 −1.56752
\(342\) 0 0
\(343\) 4156.44i 0.654305i
\(344\) 4415.13i 0.692000i
\(345\) 0 0
\(346\) 4842.41i 0.752397i
\(347\) −5081.23 −0.786095 −0.393047 0.919518i \(-0.628579\pi\)
−0.393047 + 0.919518i \(0.628579\pi\)
\(348\) 0 0
\(349\) 4266.14i 0.654330i 0.944967 + 0.327165i \(0.106093\pi\)
−0.944967 + 0.327165i \(0.893907\pi\)
\(350\) 1080.62 0.165033
\(351\) 0 0
\(352\) 9435.38 1.42871
\(353\) 3264.49i 0.492213i 0.969243 + 0.246106i \(0.0791513\pi\)
−0.969243 + 0.246106i \(0.920849\pi\)
\(354\) 0 0
\(355\) −2559.18 −0.382612
\(356\) 2997.76i 0.446295i
\(357\) 0 0
\(358\) 4176.31i 0.616550i
\(359\) 4416.98i 0.649357i 0.945824 + 0.324679i \(0.105256\pi\)
−0.945824 + 0.324679i \(0.894744\pi\)
\(360\) 0 0
\(361\) −6801.87 −0.991670
\(362\) 5897.82i 0.856305i
\(363\) 0 0
\(364\) −3161.53 5043.81i −0.455245 0.726285i
\(365\) −7449.59 −1.06830
\(366\) 0 0
\(367\) −1740.22 −0.247516 −0.123758 0.992312i \(-0.539495\pi\)
−0.123758 + 0.992312i \(0.539495\pi\)
\(368\) 984.872 0.139511
\(369\) 0 0
\(370\) 2272.37i 0.319283i
\(371\) 15354.7i 2.14872i
\(372\) 0 0
\(373\) 1176.28 0.163285 0.0816427 0.996662i \(-0.473983\pi\)
0.0816427 + 0.996662i \(0.473983\pi\)
\(374\) 6602.39 0.912838
\(375\) 0 0
\(376\) −1407.84 −0.193095
\(377\) 561.785 352.134i 0.0767464 0.0481056i
\(378\) 0 0
\(379\) 7135.54i 0.967092i 0.875319 + 0.483546i \(0.160651\pi\)
−0.875319 + 0.483546i \(0.839349\pi\)
\(380\) 6410.62 0.865415
\(381\) 0 0
\(382\) 1414.30i 0.189429i
\(383\) 1942.87i 0.259207i 0.991566 + 0.129603i \(0.0413704\pi\)
−0.991566 + 0.129603i \(0.958630\pi\)
\(384\) 0 0
\(385\) 10865.9i 1.43838i
\(386\) −3445.53 −0.454334
\(387\) 0 0
\(388\) 421.794i 0.0551891i
\(389\) −7545.92 −0.983531 −0.491766 0.870728i \(-0.663648\pi\)
−0.491766 + 0.870728i \(0.663648\pi\)
\(390\) 0 0
\(391\) 6202.47 0.802231
\(392\) 3274.97i 0.421967i
\(393\) 0 0
\(394\) −3451.75 −0.441362
\(395\) 11849.5i 1.50940i
\(396\) 0 0
\(397\) 415.922i 0.0525806i −0.999654 0.0262903i \(-0.991631\pi\)
0.999654 0.0262903i \(-0.00836943\pi\)
\(398\) 397.489i 0.0500611i
\(399\) 0 0
\(400\) 433.824 0.0542280
\(401\) 958.178i 0.119324i −0.998219 0.0596622i \(-0.980998\pi\)
0.998219 0.0596622i \(-0.0190024\pi\)
\(402\) 0 0
\(403\) −4884.58 7792.71i −0.603767 0.963233i
\(404\) 3460.75 0.426185
\(405\) 0 0
\(406\) −481.970 −0.0589157
\(407\) 7768.29 0.946093
\(408\) 0 0
\(409\) 4284.83i 0.518022i 0.965874 + 0.259011i \(0.0833966\pi\)
−0.965874 + 0.259011i \(0.916603\pi\)
\(410\) 3910.20i 0.471002i
\(411\) 0 0
\(412\) 184.197 0.0220261
\(413\) −2055.92 −0.244953
\(414\) 0 0
\(415\) 4964.61 0.587236
\(416\) 4669.20 + 7449.10i 0.550303 + 0.877938i
\(417\) 0 0
\(418\) 8957.95i 1.04820i
\(419\) 9949.01 1.16000 0.580001 0.814616i \(-0.303052\pi\)
0.580001 + 0.814616i \(0.303052\pi\)
\(420\) 0 0
\(421\) 377.250i 0.0436724i −0.999762 0.0218362i \(-0.993049\pi\)
0.999762 0.0218362i \(-0.00695122\pi\)
\(422\) 8914.66i 1.02834i
\(423\) 0 0
\(424\) 14308.6i 1.63889i
\(425\) 2732.11 0.311828
\(426\) 0 0
\(427\) 7357.86i 0.833892i
\(428\) 9798.47 1.10661
\(429\) 0 0
\(430\) −3117.47 −0.349622
\(431\) 2437.13i 0.272373i −0.990683 0.136186i \(-0.956515\pi\)
0.990683 0.136186i \(-0.0434846\pi\)
\(432\) 0 0
\(433\) −11215.1 −1.24471 −0.622357 0.782733i \(-0.713825\pi\)
−0.622357 + 0.782733i \(0.713825\pi\)
\(434\) 6685.58i 0.739443i
\(435\) 0 0
\(436\) 7231.55i 0.794331i
\(437\) 8415.34i 0.921191i
\(438\) 0 0
\(439\) 1835.19 0.199519 0.0997596 0.995012i \(-0.468193\pi\)
0.0997596 + 0.995012i \(0.468193\pi\)
\(440\) 10125.6i 1.09709i
\(441\) 0 0
\(442\) 3267.26 + 5212.50i 0.351601 + 0.560935i
\(443\) −11610.1 −1.24518 −0.622588 0.782550i \(-0.713919\pi\)
−0.622588 + 0.782550i \(0.713919\pi\)
\(444\) 0 0
\(445\) 5098.56 0.543135
\(446\) 5276.99 0.560253
\(447\) 0 0
\(448\) 3943.50i 0.415877i
\(449\) 14087.0i 1.48064i 0.672255 + 0.740319i \(0.265326\pi\)
−0.672255 + 0.740319i \(0.734674\pi\)
\(450\) 0 0
\(451\) 13367.4 1.39566
\(452\) −6330.29 −0.658743
\(453\) 0 0
\(454\) 8119.26 0.839330
\(455\) 8578.47 5377.10i 0.883878 0.554027i
\(456\) 0 0
\(457\) 2375.01i 0.243103i −0.992585 0.121552i \(-0.961213\pi\)
0.992585 0.121552i \(-0.0387870\pi\)
\(458\) 7273.38 0.742058
\(459\) 0 0
\(460\) 3949.05i 0.400273i
\(461\) 6372.06i 0.643766i −0.946779 0.321883i \(-0.895684\pi\)
0.946779 0.321883i \(-0.104316\pi\)
\(462\) 0 0
\(463\) 63.4732i 0.00637117i −0.999995 0.00318558i \(-0.998986\pi\)
0.999995 0.00318558i \(-0.00101400\pi\)
\(464\) −193.491 −0.0193591
\(465\) 0 0
\(466\) 7334.06i 0.729064i
\(467\) −7855.78 −0.778420 −0.389210 0.921149i \(-0.627252\pi\)
−0.389210 + 0.921149i \(0.627252\pi\)
\(468\) 0 0
\(469\) 17183.8 1.69184
\(470\) 994.058i 0.0975584i
\(471\) 0 0
\(472\) 1915.86 0.186832
\(473\) 10657.3i 1.03599i
\(474\) 0 0
\(475\) 3706.85i 0.358068i
\(476\) 10940.4i 1.05348i
\(477\) 0 0
\(478\) 2564.43 0.245385
\(479\) 13033.3i 1.24323i 0.783324 + 0.621613i \(0.213523\pi\)
−0.783324 + 0.621613i \(0.786477\pi\)
\(480\) 0 0
\(481\) 3844.22 + 6132.96i 0.364410 + 0.581370i
\(482\) −1012.95 −0.0957235
\(483\) 0 0
\(484\) −6812.23 −0.639766
\(485\) −717.384 −0.0671643
\(486\) 0 0
\(487\) 69.8976i 0.00650383i 0.999995 + 0.00325191i \(0.00103512\pi\)
−0.999995 + 0.00325191i \(0.998965\pi\)
\(488\) 6856.60i 0.636033i
\(489\) 0 0
\(490\) −2312.41 −0.213192
\(491\) −2625.66 −0.241333 −0.120667 0.992693i \(-0.538503\pi\)
−0.120667 + 0.992693i \(0.538503\pi\)
\(492\) 0 0
\(493\) −1218.56 −0.111321
\(494\) 7072.18 4432.93i 0.644114 0.403739i
\(495\) 0 0
\(496\) 2683.99i 0.242973i
\(497\) −5925.75 −0.534821
\(498\) 0 0
\(499\) 7631.34i 0.684621i −0.939587 0.342310i \(-0.888791\pi\)
0.939587 0.342310i \(-0.111209\pi\)
\(500\) 8595.51i 0.768806i
\(501\) 0 0
\(502\) 3263.51i 0.290154i
\(503\) 4320.14 0.382953 0.191477 0.981497i \(-0.438672\pi\)
0.191477 + 0.981497i \(0.438672\pi\)
\(504\) 0 0
\(505\) 5886.01i 0.518662i
\(506\) 5518.26 0.484815
\(507\) 0 0
\(508\) −6666.95 −0.582280
\(509\) 12450.7i 1.08422i −0.840308 0.542109i \(-0.817626\pi\)
0.840308 0.542109i \(-0.182374\pi\)
\(510\) 0 0
\(511\) −17249.4 −1.49329
\(512\) 4846.21i 0.418309i
\(513\) 0 0
\(514\) 4803.18i 0.412178i
\(515\) 313.281i 0.0268054i
\(516\) 0 0
\(517\) 3398.28 0.289083
\(518\) 5261.63i 0.446299i
\(519\) 0 0
\(520\) −7994.05 + 5010.78i −0.674158 + 0.422571i
\(521\) −14373.1 −1.20863 −0.604314 0.796746i \(-0.706553\pi\)
−0.604314 + 0.796746i \(0.706553\pi\)
\(522\) 0 0
\(523\) −16946.7 −1.41688 −0.708439 0.705772i \(-0.750600\pi\)
−0.708439 + 0.705772i \(0.750600\pi\)
\(524\) 8206.76 0.684187
\(525\) 0 0
\(526\) 3302.62i 0.273767i
\(527\) 16903.0i 1.39717i
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) −10103.1 −0.828022
\(531\) 0 0
\(532\) 14843.7 1.20969
\(533\) 6614.98 + 10553.4i 0.537574 + 0.857630i
\(534\) 0 0
\(535\) 16665.1i 1.34672i
\(536\) −16013.1 −1.29041
\(537\) 0 0
\(538\) 4950.00i 0.396673i
\(539\) 7905.20i 0.631727i
\(540\) 0 0
\(541\) 815.667i 0.0648212i 0.999475 + 0.0324106i \(0.0103184\pi\)
−0.999475 + 0.0324106i \(0.989682\pi\)
\(542\) −7461.92 −0.591359
\(543\) 0 0
\(544\) 16157.7i 1.27345i
\(545\) 12299.3 0.966689
\(546\) 0 0
\(547\) −17971.4 −1.40476 −0.702378 0.711804i \(-0.747878\pi\)
−0.702378 + 0.711804i \(0.747878\pi\)
\(548\) 2889.32i 0.225230i
\(549\) 0 0
\(550\) 2430.72 0.188448
\(551\) 1653.31i 0.127828i
\(552\) 0 0
\(553\) 27437.4i 2.10987i
\(554\) 4418.81i 0.338876i
\(555\) 0 0
\(556\) −4298.94 −0.327906
\(557\) 6760.83i 0.514301i −0.966371 0.257151i \(-0.917216\pi\)
0.966371 0.257151i \(-0.0827836\pi\)
\(558\) 0 0
\(559\) 8413.83 5273.90i 0.636614 0.399038i
\(560\) −2954.62 −0.222956
\(561\) 0 0
\(562\) −6698.36 −0.502764
\(563\) −12962.7 −0.970359 −0.485179 0.874415i \(-0.661246\pi\)
−0.485179 + 0.874415i \(0.661246\pi\)
\(564\) 0 0
\(565\) 10766.5i 0.801681i
\(566\) 851.898i 0.0632649i
\(567\) 0 0
\(568\) 5522.05 0.407923
\(569\) −164.757 −0.0121388 −0.00606938 0.999982i \(-0.501932\pi\)
−0.00606938 + 0.999982i \(0.501932\pi\)
\(570\) 0 0
\(571\) −5216.55 −0.382322 −0.191161 0.981559i \(-0.561225\pi\)
−0.191161 + 0.981559i \(0.561225\pi\)
\(572\) −7111.48 11345.5i −0.519836 0.829331i
\(573\) 0 0
\(574\) 9054.01i 0.658375i
\(575\) 2283.49 0.165614
\(576\) 0 0
\(577\) 12753.3i 0.920151i −0.887880 0.460076i \(-0.847822\pi\)
0.887880 0.460076i \(-0.152178\pi\)
\(578\) 3821.11i 0.274978i
\(579\) 0 0
\(580\) 775.844i 0.0555434i
\(581\) 11495.5 0.820849
\(582\) 0 0
\(583\) 34538.5i 2.45358i
\(584\) 16074.3 1.13897
\(585\) 0 0
\(586\) 10540.9 0.743076
\(587\) 1575.38i 0.110771i 0.998465 + 0.0553857i \(0.0176388\pi\)
−0.998465 + 0.0553857i \(0.982361\pi\)
\(588\) 0 0
\(589\) 22933.6 1.60435
\(590\) 1352.77i 0.0943941i
\(591\) 0 0
\(592\) 2112.33i 0.146649i
\(593\) 3845.95i 0.266331i −0.991094 0.133165i \(-0.957486\pi\)
0.991094 0.133165i \(-0.0425142\pi\)
\(594\) 0 0
\(595\) −18607.4 −1.28207
\(596\) 18443.5i 1.26758i
\(597\) 0 0
\(598\) 2730.77 + 4356.59i 0.186738 + 0.297917i
\(599\) −6107.20 −0.416583 −0.208292 0.978067i \(-0.566790\pi\)
−0.208292 + 0.978067i \(0.566790\pi\)
\(600\) 0 0
\(601\) 9638.90 0.654208 0.327104 0.944988i \(-0.393927\pi\)
0.327104 + 0.944988i \(0.393927\pi\)
\(602\) −7218.46 −0.488708
\(603\) 0 0
\(604\) 4516.31i 0.304248i
\(605\) 11586.2i 0.778586i
\(606\) 0 0
\(607\) 11821.7 0.790489 0.395244 0.918576i \(-0.370660\pi\)
0.395244 + 0.918576i \(0.370660\pi\)
\(608\) −21922.4 −1.46228
\(609\) 0 0
\(610\) 4841.36 0.321346
\(611\) 1681.67 + 2682.90i 0.111347 + 0.177640i
\(612\) 0 0
\(613\) 8107.86i 0.534214i −0.963667 0.267107i \(-0.913932\pi\)
0.963667 0.267107i \(-0.0860677\pi\)
\(614\) −13683.0 −0.899347
\(615\) 0 0
\(616\) 23445.8i 1.53354i
\(617\) 27647.6i 1.80397i 0.431768 + 0.901985i \(0.357890\pi\)
−0.431768 + 0.901985i \(0.642110\pi\)
\(618\) 0 0
\(619\) 29181.9i 1.89486i 0.319956 + 0.947432i \(0.396332\pi\)
−0.319956 + 0.947432i \(0.603668\pi\)
\(620\) −10762.0 −0.697118
\(621\) 0 0
\(622\) 12101.8i 0.780125i
\(623\) 11805.7 0.759204
\(624\) 0 0
\(625\) −10654.8 −0.681905
\(626\) 7708.53i 0.492165i
\(627\) 0 0
\(628\) −370.672 −0.0235532
\(629\) 13302.9i 0.843277i
\(630\) 0 0
\(631\) 2209.34i 0.139386i −0.997569 0.0696928i \(-0.977798\pi\)
0.997569 0.0696928i \(-0.0222019\pi\)
\(632\) 25568.2i 1.60926i
\(633\) 0 0
\(634\) −13258.2 −0.830518
\(635\) 11339.1i 0.708627i
\(636\) 0 0
\(637\) 6241.05 3911.97i 0.388194 0.243325i
\(638\) −1084.13 −0.0672748
\(639\) 0 0
\(640\) 11897.8 0.734844
\(641\) −18256.0 −1.12491 −0.562455 0.826828i \(-0.690143\pi\)
−0.562455 + 0.826828i \(0.690143\pi\)
\(642\) 0 0
\(643\) 1281.61i 0.0786033i −0.999227 0.0393016i \(-0.987487\pi\)
0.999227 0.0393016i \(-0.0125133\pi\)
\(644\) 9143.99i 0.559509i
\(645\) 0 0
\(646\) −15340.1 −0.934287
\(647\) 16393.2 0.996107 0.498054 0.867146i \(-0.334048\pi\)
0.498054 + 0.867146i \(0.334048\pi\)
\(648\) 0 0
\(649\) −4624.56 −0.279707
\(650\) 1202.87 + 1919.02i 0.0725853 + 0.115800i
\(651\) 0 0
\(652\) 10536.4i 0.632878i
\(653\) −16759.2 −1.00434 −0.502172 0.864768i \(-0.667466\pi\)
−0.502172 + 0.864768i \(0.667466\pi\)
\(654\) 0 0
\(655\) 13958.0i 0.832646i
\(656\) 3634.81i 0.216335i
\(657\) 0 0
\(658\) 2301.73i 0.136369i
\(659\) 29659.3 1.75320 0.876601 0.481217i \(-0.159805\pi\)
0.876601 + 0.481217i \(0.159805\pi\)
\(660\) 0 0
\(661\) 10386.0i 0.611147i −0.952169 0.305573i \(-0.901152\pi\)
0.952169 0.305573i \(-0.0988481\pi\)
\(662\) 2647.40 0.155429
\(663\) 0 0
\(664\) −10712.4 −0.626084
\(665\) 25246.0i 1.47218i
\(666\) 0 0
\(667\) −1018.47 −0.0591232
\(668\) 20060.5i 1.16192i
\(669\) 0 0
\(670\) 11306.7i 0.651962i
\(671\) 16550.6i 0.952206i
\(672\) 0 0
\(673\) 19449.6 1.11400 0.557002 0.830511i \(-0.311951\pi\)
0.557002 + 0.830511i \(0.311951\pi\)
\(674\) 4444.92i 0.254024i
\(675\) 0 0
\(676\) 5437.89 11228.8i 0.309393 0.638873i
\(677\) 6629.48 0.376354 0.188177 0.982135i \(-0.439742\pi\)
0.188177 + 0.982135i \(0.439742\pi\)
\(678\) 0 0
\(679\) −1661.09 −0.0938835
\(680\) 17339.8 0.977867
\(681\) 0 0
\(682\) 15038.4i 0.844356i
\(683\) 2526.40i 0.141537i 0.997493 + 0.0707687i \(0.0225452\pi\)
−0.997493 + 0.0707687i \(0.977455\pi\)
\(684\) 0 0
\(685\) 4914.13 0.274101
\(686\) 6332.57 0.352447
\(687\) 0 0
\(688\) −2897.91 −0.160584
\(689\) 27267.7 17091.7i 1.50771 0.945055i
\(690\) 0 0
\(691\) 3808.76i 0.209685i −0.994489 0.104842i \(-0.966566\pi\)
0.994489 0.104842i \(-0.0334338\pi\)
\(692\) −18049.2 −0.991515
\(693\) 0 0
\(694\) 7741.54i 0.423436i
\(695\) 7311.59i 0.399056i
\(696\) 0 0
\(697\) 22891.1i 1.24399i
\(698\) 6499.69 0.352460
\(699\) 0 0
\(700\) 4027.81i 0.217482i
\(701\) 33617.8 1.81131 0.905655 0.424015i \(-0.139380\pi\)
0.905655 + 0.424015i \(0.139380\pi\)
\(702\) 0 0
\(703\) −18049.0 −0.968323
\(704\) 8870.43i 0.474882i
\(705\) 0 0
\(706\) 4973.63 0.265134
\(707\) 13629.0i 0.724994i
\(708\) 0 0
\(709\) 26606.5i 1.40935i 0.709530 + 0.704675i \(0.248907\pi\)
−0.709530 + 0.704675i \(0.751093\pi\)
\(710\) 3899.05i 0.206097i
\(711\) 0 0
\(712\) −11001.4 −0.579066
\(713\) 14127.5i 0.742046i
\(714\) 0 0
\(715\) 19296.2 12095.1i 1.00928 0.632633i
\(716\) 15566.5 0.812494
\(717\) 0 0
\(718\) 6729.51 0.349781
\(719\) −16539.3 −0.857877 −0.428939 0.903334i \(-0.641112\pi\)
−0.428939 + 0.903334i \(0.641112\pi\)
\(720\) 0 0
\(721\) 725.398i 0.0374691i
\(722\) 10363.0i 0.534171i
\(723\) 0 0
\(724\) −21983.1 −1.12844
\(725\) −448.622 −0.0229812
\(726\) 0 0
\(727\) 12757.5 0.650823 0.325411 0.945573i \(-0.394497\pi\)
0.325411 + 0.945573i \(0.394497\pi\)
\(728\) −18510.1 + 11602.4i −0.942350 + 0.590678i
\(729\) 0 0
\(730\) 11349.9i 0.575448i
\(731\) −18250.3 −0.923408
\(732\) 0 0
\(733\) 20523.4i 1.03417i 0.855933 + 0.517087i \(0.172984\pi\)
−0.855933 + 0.517087i \(0.827016\pi\)
\(734\) 2651.31i 0.133327i
\(735\) 0 0
\(736\) 13504.6i 0.676338i
\(737\) 38652.9 1.93188
\(738\) 0 0
\(739\) 7462.66i 0.371473i 0.982600 + 0.185736i \(0.0594670\pi\)
−0.982600 + 0.185736i \(0.940533\pi\)
\(740\) 8469.84 0.420753
\(741\) 0 0
\(742\) −23393.7 −1.15742
\(743\) 18847.8i 0.930632i −0.885145 0.465316i \(-0.845941\pi\)
0.885145 0.465316i \(-0.154059\pi\)
\(744\) 0 0
\(745\) 31368.5 1.54262
\(746\) 1792.13i 0.0879549i
\(747\) 0 0
\(748\) 24609.2i 1.20294i
\(749\) 38587.9i 1.88247i
\(750\) 0 0
\(751\) 20832.6 1.01224 0.506119 0.862464i \(-0.331080\pi\)
0.506119 + 0.862464i \(0.331080\pi\)
\(752\) 924.050i 0.0448093i
\(753\) 0 0
\(754\) −536.496 855.910i −0.0259125 0.0413400i
\(755\) −7681.29 −0.370266
\(756\) 0 0
\(757\) −20860.9 −1.00159 −0.500795 0.865566i \(-0.666959\pi\)
−0.500795 + 0.865566i \(0.666959\pi\)
\(758\) 10871.4 0.520932
\(759\) 0 0
\(760\) 23526.1i 1.12287i
\(761\) 4464.86i 0.212682i −0.994330 0.106341i \(-0.966086\pi\)
0.994330 0.106341i \(-0.0339135\pi\)
\(762\) 0 0
\(763\) 28479.0 1.35126
\(764\) 5271.56 0.249631
\(765\) 0 0
\(766\) 2960.08 0.139624
\(767\) −2288.51 3651.03i −0.107736 0.171879i
\(768\) 0 0
\(769\) 23797.7i 1.11595i 0.829857 + 0.557977i \(0.188422\pi\)
−0.829857 + 0.557977i \(0.811578\pi\)
\(770\) −16554.8 −0.774795
\(771\) 0 0
\(772\) 12842.6i 0.598725i
\(773\) 29418.7i 1.36885i −0.729085 0.684423i \(-0.760054\pi\)
0.729085 0.684423i \(-0.239946\pi\)
\(774\) 0 0
\(775\) 6222.99i 0.288434i
\(776\) 1547.93 0.0716075
\(777\) 0 0
\(778\) 11496.6i 0.529787i
\(779\) −31058.0 −1.42846
\(780\) 0 0
\(781\) −13329.3 −0.610703
\(782\) 9449.80i 0.432128i
\(783\) 0 0
\(784\) −2149.56 −0.0979208
\(785\) 630.435i 0.0286640i
\(786\) 0 0
\(787\) 23896.0i 1.08234i −0.840913 0.541170i \(-0.817982\pi\)
0.840913 0.541170i \(-0.182018\pi\)
\(788\) 12865.8i 0.581630i
\(789\) 0 0
\(790\) 18053.4 0.813052
\(791\) 24929.7i 1.12060i
\(792\) 0 0
\(793\) −13066.5 + 8190.26i −0.585126 + 0.366765i
\(794\) −633.680 −0.0283230