Properties

Label 128.4.g.a.81.10
Level $128$
Weight $4$
Character 128.81
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 81.10
Character \(\chi\) \(=\) 128.81
Dual form 128.4.g.a.49.10

$q$-expansion

\(f(q)\) \(=\) \(q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +O(q^{10})\) \(q+(6.06585 + 2.51256i) q^{3} +(-2.91165 - 7.02935i) q^{5} +(13.3899 - 13.3899i) q^{7} +(11.3897 + 11.3897i) q^{9} +(49.6279 - 20.5565i) q^{11} +(8.74801 - 21.1196i) q^{13} -49.9547i q^{15} +77.7412i q^{17} +(-53.3229 + 128.733i) q^{19} +(114.864 - 47.5784i) q^{21} +(35.5116 + 35.5116i) q^{23} +(47.4543 - 47.4543i) q^{25} +(-27.3680 - 66.0722i) q^{27} +(-245.435 - 101.662i) q^{29} +202.613 q^{31} +352.685 q^{33} +(-133.110 - 55.1358i) q^{35} +(36.3055 + 87.6493i) q^{37} +(106.128 - 106.128i) q^{39} +(-36.8088 - 36.8088i) q^{41} +(-185.642 + 76.8954i) q^{43} +(46.8995 - 113.225i) q^{45} -82.9731i q^{47} -15.5815i q^{49} +(-195.329 + 471.567i) q^{51} +(-534.758 + 221.504i) q^{53} +(-288.998 - 288.998i) q^{55} +(-646.898 + 646.898i) q^{57} +(-75.7461 - 182.867i) q^{59} +(-472.240 - 195.608i) q^{61} +305.016 q^{63} -173.928 q^{65} +(102.750 + 42.5604i) q^{67} +(126.183 + 304.633i) q^{69} +(-520.392 + 520.392i) q^{71} +(244.389 + 244.389i) q^{73} +(407.082 - 168.619i) q^{75} +(389.264 - 939.766i) q^{77} +774.758i q^{79} -904.451i q^{81} +(23.9166 - 57.7397i) q^{83} +(546.470 - 226.355i) q^{85} +(-1233.34 - 1233.34i) q^{87} +(-351.137 + 351.137i) q^{89} +(-165.654 - 399.925i) q^{91} +(1229.02 + 509.078i) q^{93} +1060.17 q^{95} +1302.03 q^{97} +(799.382 + 331.115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 6.06585 + 2.51256i 1.16737 + 0.483542i 0.880324 0.474373i \(-0.157325\pi\)
0.287050 + 0.957916i \(0.407325\pi\)
\(4\) 0 0
\(5\) −2.91165 7.02935i −0.260426 0.628724i 0.738539 0.674211i \(-0.235516\pi\)
−0.998965 + 0.0454866i \(0.985516\pi\)
\(6\) 0 0
\(7\) 13.3899 13.3899i 0.722989 0.722989i −0.246224 0.969213i \(-0.579190\pi\)
0.969213 + 0.246224i \(0.0791898\pi\)
\(8\) 0 0
\(9\) 11.3897 + 11.3897i 0.421842 + 0.421842i
\(10\) 0 0
\(11\) 49.6279 20.5565i 1.36031 0.563457i 0.421164 0.906985i \(-0.361622\pi\)
0.939143 + 0.343527i \(0.111622\pi\)
\(12\) 0 0
\(13\) 8.74801 21.1196i 0.186635 0.450578i −0.802672 0.596420i \(-0.796589\pi\)
0.989308 + 0.145842i \(0.0465892\pi\)
\(14\) 0 0
\(15\) 49.9547i 0.859884i
\(16\) 0 0
\(17\) 77.7412i 1.10912i 0.832144 + 0.554559i \(0.187113\pi\)
−0.832144 + 0.554559i \(0.812887\pi\)
\(18\) 0 0
\(19\) −53.3229 + 128.733i −0.643848 + 1.55439i 0.177599 + 0.984103i \(0.443167\pi\)
−0.821447 + 0.570284i \(0.806833\pi\)
\(20\) 0 0
\(21\) 114.864 47.5784i 1.19359 0.494403i
\(22\) 0 0
\(23\) 35.5116 + 35.5116i 0.321943 + 0.321943i 0.849512 0.527569i \(-0.176897\pi\)
−0.527569 + 0.849512i \(0.676897\pi\)
\(24\) 0 0
\(25\) 47.4543 47.4543i 0.379634 0.379634i
\(26\) 0 0
\(27\) −27.3680 66.0722i −0.195073 0.470948i
\(28\) 0 0
\(29\) −245.435 101.662i −1.57159 0.650973i −0.584535 0.811368i \(-0.698723\pi\)
−0.987053 + 0.160395i \(0.948723\pi\)
\(30\) 0 0
\(31\) 202.613 1.17389 0.586943 0.809629i \(-0.300331\pi\)
0.586943 + 0.809629i \(0.300331\pi\)
\(32\) 0 0
\(33\) 352.685 1.86044
\(34\) 0 0
\(35\) −133.110 55.1358i −0.642846 0.266276i
\(36\) 0 0
\(37\) 36.3055 + 87.6493i 0.161313 + 0.389445i 0.983783 0.179365i \(-0.0574042\pi\)
−0.822469 + 0.568809i \(0.807404\pi\)
\(38\) 0 0
\(39\) 106.128 106.128i 0.435747 0.435747i
\(40\) 0 0
\(41\) −36.8088 36.8088i −0.140209 0.140209i 0.633518 0.773728i \(-0.281610\pi\)
−0.773728 + 0.633518i \(0.781610\pi\)
\(42\) 0 0
\(43\) −185.642 + 76.8954i −0.658375 + 0.272708i −0.686754 0.726889i \(-0.740965\pi\)
0.0283797 + 0.999597i \(0.490965\pi\)
\(44\) 0 0
\(45\) 46.8995 113.225i 0.155364 0.375081i
\(46\) 0 0
\(47\) 82.9731i 0.257508i −0.991677 0.128754i \(-0.958902\pi\)
0.991677 0.128754i \(-0.0410977\pi\)
\(48\) 0 0
\(49\) 15.5815i 0.0454271i
\(50\) 0 0
\(51\) −195.329 + 471.567i −0.536305 + 1.29476i
\(52\) 0 0
\(53\) −534.758 + 221.504i −1.38594 + 0.574074i −0.946062 0.323984i \(-0.894978\pi\)
−0.439876 + 0.898059i \(0.644978\pi\)
\(54\) 0 0
\(55\) −288.998 288.998i −0.708519 0.708519i
\(56\) 0 0
\(57\) −646.898 + 646.898i −1.50322 + 1.50322i
\(58\) 0 0
\(59\) −75.7461 182.867i −0.167141 0.403513i 0.818010 0.575204i \(-0.195077\pi\)
−0.985151 + 0.171690i \(0.945077\pi\)
\(60\) 0 0
\(61\) −472.240 195.608i −0.991216 0.410575i −0.172647 0.984984i \(-0.555232\pi\)
−0.818569 + 0.574409i \(0.805232\pi\)
\(62\) 0 0
\(63\) 305.016 0.609975
\(64\) 0 0
\(65\) −173.928 −0.331894
\(66\) 0 0
\(67\) 102.750 + 42.5604i 0.187357 + 0.0776057i 0.474389 0.880315i \(-0.342669\pi\)
−0.287033 + 0.957921i \(0.592669\pi\)
\(68\) 0 0
\(69\) 126.183 + 304.633i 0.220155 + 0.531500i
\(70\) 0 0
\(71\) −520.392 + 520.392i −0.869847 + 0.869847i −0.992455 0.122608i \(-0.960874\pi\)
0.122608 + 0.992455i \(0.460874\pi\)
\(72\) 0 0
\(73\) 244.389 + 244.389i 0.391829 + 0.391829i 0.875339 0.483510i \(-0.160638\pi\)
−0.483510 + 0.875339i \(0.660638\pi\)
\(74\) 0 0
\(75\) 407.082 168.619i 0.626744 0.259606i
\(76\) 0 0
\(77\) 389.264 939.766i 0.576113 1.39086i
\(78\) 0 0
\(79\) 774.758i 1.10338i 0.834049 + 0.551690i \(0.186017\pi\)
−0.834049 + 0.551690i \(0.813983\pi\)
\(80\) 0 0
\(81\) 904.451i 1.24067i
\(82\) 0 0
\(83\) 23.9166 57.7397i 0.0316287 0.0763585i −0.907276 0.420536i \(-0.861842\pi\)
0.938905 + 0.344177i \(0.111842\pi\)
\(84\) 0 0
\(85\) 546.470 226.355i 0.697330 0.288843i
\(86\) 0 0
\(87\) −1233.34 1233.34i −1.51986 1.51986i
\(88\) 0 0
\(89\) −351.137 + 351.137i −0.418207 + 0.418207i −0.884585 0.466378i \(-0.845559\pi\)
0.466378 + 0.884585i \(0.345559\pi\)
\(90\) 0 0
\(91\) −165.654 399.925i −0.190827 0.460698i
\(92\) 0 0
\(93\) 1229.02 + 509.078i 1.37036 + 0.567623i
\(94\) 0 0
\(95\) 1060.17 1.14496
\(96\) 0 0
\(97\) 1302.03 1.36290 0.681452 0.731863i \(-0.261349\pi\)
0.681452 + 0.731863i \(0.261349\pi\)
\(98\) 0 0
\(99\) 799.382 + 331.115i 0.811525 + 0.336145i
\(100\) 0 0
\(101\) 255.210 + 616.132i 0.251429 + 0.607004i 0.998320 0.0579428i \(-0.0184541\pi\)
−0.746891 + 0.664947i \(0.768454\pi\)
\(102\) 0 0
\(103\) −119.916 + 119.916i −0.114715 + 0.114715i −0.762134 0.647419i \(-0.775848\pi\)
0.647419 + 0.762134i \(0.275848\pi\)
\(104\) 0 0
\(105\) −668.891 668.891i −0.621687 0.621687i
\(106\) 0 0
\(107\) 659.373 273.121i 0.595738 0.246763i −0.0643789 0.997926i \(-0.520507\pi\)
0.660117 + 0.751163i \(0.270507\pi\)
\(108\) 0 0
\(109\) −471.995 + 1139.50i −0.414761 + 1.00132i 0.569081 + 0.822281i \(0.307299\pi\)
−0.983842 + 0.179040i \(0.942701\pi\)
\(110\) 0 0
\(111\) 622.887i 0.532629i
\(112\) 0 0
\(113\) 832.434i 0.692998i −0.938050 0.346499i \(-0.887370\pi\)
0.938050 0.346499i \(-0.112630\pi\)
\(114\) 0 0
\(115\) 146.226 353.021i 0.118571 0.286255i
\(116\) 0 0
\(117\) 340.184 140.909i 0.268803 0.111342i
\(118\) 0 0
\(119\) 1040.95 + 1040.95i 0.801880 + 0.801880i
\(120\) 0 0
\(121\) 1099.20 1099.20i 0.825843 0.825843i
\(122\) 0 0
\(123\) −130.793 315.761i −0.0958795 0.231473i
\(124\) 0 0
\(125\) −1350.41 559.359i −0.966276 0.400245i
\(126\) 0 0
\(127\) −187.556 −0.131046 −0.0655232 0.997851i \(-0.520872\pi\)
−0.0655232 + 0.997851i \(0.520872\pi\)
\(128\) 0 0
\(129\) −1319.28 −0.900435
\(130\) 0 0
\(131\) −1001.26 414.737i −0.667793 0.276609i 0.0229207 0.999737i \(-0.492703\pi\)
−0.690714 + 0.723128i \(0.742703\pi\)
\(132\) 0 0
\(133\) 1009.74 + 2437.72i 0.658310 + 1.58930i
\(134\) 0 0
\(135\) −384.759 + 384.759i −0.245294 + 0.245294i
\(136\) 0 0
\(137\) −1273.38 1273.38i −0.794101 0.794101i 0.188057 0.982158i \(-0.439781\pi\)
−0.982158 + 0.188057i \(0.939781\pi\)
\(138\) 0 0
\(139\) 2129.20 881.945i 1.29926 0.538170i 0.377525 0.925999i \(-0.376775\pi\)
0.921731 + 0.387830i \(0.126775\pi\)
\(140\) 0 0
\(141\) 208.475 503.302i 0.124516 0.300608i
\(142\) 0 0
\(143\) 1227.95i 0.718085i
\(144\) 0 0
\(145\) 2021.25i 1.15763i
\(146\) 0 0
\(147\) 39.1494 94.5150i 0.0219659 0.0530304i
\(148\) 0 0
\(149\) 139.146 57.6361i 0.0765051 0.0316895i −0.344103 0.938932i \(-0.611817\pi\)
0.420608 + 0.907243i \(0.361817\pi\)
\(150\) 0 0
\(151\) 2027.42 + 2027.42i 1.09264 + 1.09264i 0.995245 + 0.0973988i \(0.0310522\pi\)
0.0973988 + 0.995245i \(0.468948\pi\)
\(152\) 0 0
\(153\) −885.452 + 885.452i −0.467873 + 0.467873i
\(154\) 0 0
\(155\) −589.940 1424.24i −0.305710 0.738050i
\(156\) 0 0
\(157\) 816.713 + 338.294i 0.415164 + 0.171967i 0.580481 0.814274i \(-0.302865\pi\)
−0.165317 + 0.986241i \(0.552865\pi\)
\(158\) 0 0
\(159\) −3800.31 −1.89550
\(160\) 0 0
\(161\) 950.997 0.465522
\(162\) 0 0
\(163\) 953.491 + 394.949i 0.458179 + 0.189784i 0.599821 0.800134i \(-0.295238\pi\)
−0.141642 + 0.989918i \(0.545238\pi\)
\(164\) 0 0
\(165\) −1026.90 2479.15i −0.484508 1.16971i
\(166\) 0 0
\(167\) 896.156 896.156i 0.415249 0.415249i −0.468313 0.883563i \(-0.655138\pi\)
0.883563 + 0.468313i \(0.155138\pi\)
\(168\) 0 0
\(169\) 1184.01 + 1184.01i 0.538919 + 0.538919i
\(170\) 0 0
\(171\) −2073.57 + 858.900i −0.927308 + 0.384104i
\(172\) 0 0
\(173\) −268.247 + 647.606i −0.117887 + 0.284604i −0.971798 0.235815i \(-0.924224\pi\)
0.853911 + 0.520419i \(0.174224\pi\)
\(174\) 0 0
\(175\) 1270.82i 0.548943i
\(176\) 0 0
\(177\) 1299.56i 0.551870i
\(178\) 0 0
\(179\) −842.440 + 2033.83i −0.351770 + 0.849249i 0.644631 + 0.764494i \(0.277011\pi\)
−0.996402 + 0.0847553i \(0.972989\pi\)
\(180\) 0 0
\(181\) 1394.35 577.557i 0.572602 0.237180i −0.0775438 0.996989i \(-0.524708\pi\)
0.650146 + 0.759809i \(0.274708\pi\)
\(182\) 0 0
\(183\) −2373.06 2373.06i −0.958589 0.958589i
\(184\) 0 0
\(185\) 510.408 510.408i 0.202843 0.202843i
\(186\) 0 0
\(187\) 1598.09 + 3858.13i 0.624941 + 1.50874i
\(188\) 0 0
\(189\) −1251.16 518.247i −0.481526 0.199455i
\(190\) 0 0
\(191\) −779.721 −0.295386 −0.147693 0.989033i \(-0.547185\pi\)
−0.147693 + 0.989033i \(0.547185\pi\)
\(192\) 0 0
\(193\) −4175.15 −1.55717 −0.778585 0.627539i \(-0.784062\pi\)
−0.778585 + 0.627539i \(0.784062\pi\)
\(194\) 0 0
\(195\) −1055.02 437.004i −0.387444 0.160485i
\(196\) 0 0
\(197\) −1793.41 4329.67i −0.648604 1.56587i −0.814778 0.579773i \(-0.803141\pi\)
0.166174 0.986096i \(-0.446859\pi\)
\(198\) 0 0
\(199\) −1333.84 + 1333.84i −0.475144 + 0.475144i −0.903575 0.428431i \(-0.859067\pi\)
0.428431 + 0.903575i \(0.359067\pi\)
\(200\) 0 0
\(201\) 516.330 + 516.330i 0.181190 + 0.181190i
\(202\) 0 0
\(203\) −4647.61 + 1925.10i −1.60689 + 0.665595i
\(204\) 0 0
\(205\) −151.568 + 365.917i −0.0516388 + 0.124667i
\(206\) 0 0
\(207\) 808.935i 0.271618i
\(208\) 0 0
\(209\) 7484.88i 2.47722i
\(210\) 0 0
\(211\) 1172.83 2831.46i 0.382658 0.923818i −0.608792 0.793330i \(-0.708346\pi\)
0.991450 0.130488i \(-0.0416544\pi\)
\(212\) 0 0
\(213\) −4464.13 + 1849.11i −1.43604 + 0.594829i
\(214\) 0 0
\(215\) 1081.05 + 1081.05i 0.342916 + 0.342916i
\(216\) 0 0
\(217\) 2712.98 2712.98i 0.848707 0.848707i
\(218\) 0 0
\(219\) 868.385 + 2096.47i 0.267945 + 0.646877i
\(220\) 0 0
\(221\) 1641.86 + 680.080i 0.499744 + 0.207001i
\(222\) 0 0
\(223\) 2462.13 0.739356 0.369678 0.929160i \(-0.379468\pi\)
0.369678 + 0.929160i \(0.379468\pi\)
\(224\) 0 0
\(225\) 1080.98 0.320291
\(226\) 0 0
\(227\) −2912.19 1206.27i −0.851494 0.352700i −0.0861187 0.996285i \(-0.527446\pi\)
−0.765375 + 0.643585i \(0.777446\pi\)
\(228\) 0 0
\(229\) −578.212 1395.93i −0.166853 0.402819i 0.818232 0.574889i \(-0.194955\pi\)
−0.985085 + 0.172070i \(0.944955\pi\)
\(230\) 0 0
\(231\) 4722.43 4722.43i 1.34508 1.34508i
\(232\) 0 0
\(233\) 3037.56 + 3037.56i 0.854065 + 0.854065i 0.990631 0.136566i \(-0.0436067\pi\)
−0.136566 + 0.990631i \(0.543607\pi\)
\(234\) 0 0
\(235\) −583.247 + 241.589i −0.161901 + 0.0670618i
\(236\) 0 0
\(237\) −1946.62 + 4699.57i −0.533531 + 1.28806i
\(238\) 0 0
\(239\) 68.1814i 0.0184531i −0.999957 0.00922654i \(-0.997063\pi\)
0.999957 0.00922654i \(-0.00293694\pi\)
\(240\) 0 0
\(241\) 6115.20i 1.63450i −0.576282 0.817251i \(-0.695497\pi\)
0.576282 0.817251i \(-0.304503\pi\)
\(242\) 0 0
\(243\) 1533.55 3702.32i 0.404845 0.977382i
\(244\) 0 0
\(245\) −109.528 + 45.3679i −0.0285611 + 0.0118304i
\(246\) 0 0
\(247\) 2252.31 + 2252.31i 0.580207 + 0.580207i
\(248\) 0 0
\(249\) 290.149 290.149i 0.0738451 0.0738451i
\(250\) 0 0
\(251\) −183.755 443.623i −0.0462092 0.111559i 0.899090 0.437765i \(-0.144230\pi\)
−0.945299 + 0.326206i \(0.894230\pi\)
\(252\) 0 0
\(253\) 2492.36 + 1032.37i 0.619341 + 0.256540i
\(254\) 0 0
\(255\) 3883.54 0.953712
\(256\) 0 0
\(257\) −26.1354 −0.00634350 −0.00317175 0.999995i \(-0.501010\pi\)
−0.00317175 + 0.999995i \(0.501010\pi\)
\(258\) 0 0
\(259\) 1659.75 + 687.490i 0.398192 + 0.164937i
\(260\) 0 0
\(261\) −1637.53 3953.34i −0.388354 0.937570i
\(262\) 0 0
\(263\) 2404.98 2404.98i 0.563869 0.563869i −0.366535 0.930404i \(-0.619456\pi\)
0.930404 + 0.366535i \(0.119456\pi\)
\(264\) 0 0
\(265\) 3114.06 + 3114.06i 0.721869 + 0.721869i
\(266\) 0 0
\(267\) −3012.20 + 1247.69i −0.690425 + 0.285983i
\(268\) 0 0
\(269\) 3217.65 7768.09i 0.729306 1.76070i 0.0844104 0.996431i \(-0.473099\pi\)
0.644896 0.764270i \(-0.276901\pi\)
\(270\) 0 0
\(271\) 4099.60i 0.918941i −0.888193 0.459471i \(-0.848039\pi\)
0.888193 0.459471i \(-0.151961\pi\)
\(272\) 0 0
\(273\) 2842.10i 0.630080i
\(274\) 0 0
\(275\) 1379.56 3330.55i 0.302511 0.730327i
\(276\) 0 0
\(277\) −62.6281 + 25.9414i −0.0135847 + 0.00562696i −0.389465 0.921041i \(-0.627340\pi\)
0.375881 + 0.926668i \(0.377340\pi\)
\(278\) 0 0
\(279\) 2307.71 + 2307.71i 0.495194 + 0.495194i
\(280\) 0 0
\(281\) 371.515 371.515i 0.0788709 0.0788709i −0.666571 0.745442i \(-0.732239\pi\)
0.745442 + 0.666571i \(0.232239\pi\)
\(282\) 0 0
\(283\) 1150.78 + 2778.24i 0.241721 + 0.583566i 0.997454 0.0713139i \(-0.0227192\pi\)
−0.755733 + 0.654880i \(0.772719\pi\)
\(284\) 0 0
\(285\) 6430.82 + 2663.73i 1.33659 + 0.553634i
\(286\) 0 0
\(287\) −985.737 −0.202739
\(288\) 0 0
\(289\) −1130.69 −0.230143
\(290\) 0 0
\(291\) 7897.95 + 3271.44i 1.59102 + 0.659021i
\(292\) 0 0
\(293\) 1547.04 + 3734.89i 0.308461 + 0.744691i 0.999755 + 0.0221175i \(0.00704081\pi\)
−0.691294 + 0.722573i \(0.742959\pi\)
\(294\) 0 0
\(295\) −1064.89 + 1064.89i −0.210171 + 0.210171i
\(296\) 0 0
\(297\) −2716.43 2716.43i −0.530718 0.530718i
\(298\) 0 0
\(299\) 1060.64 439.333i 0.205146 0.0849743i
\(300\) 0 0
\(301\) −1456.11 + 3515.36i −0.278833 + 0.673163i
\(302\) 0 0
\(303\) 4378.60i 0.830178i
\(304\) 0 0
\(305\) 3889.09i 0.730126i
\(306\) 0 0
\(307\) −2115.16 + 5106.46i −0.393221 + 0.949319i 0.596013 + 0.802975i \(0.296751\pi\)
−0.989234 + 0.146344i \(0.953249\pi\)
\(308\) 0 0
\(309\) −1028.69 + 426.097i −0.189386 + 0.0784461i
\(310\) 0 0
\(311\) −3571.19 3571.19i −0.651137 0.651137i 0.302130 0.953267i \(-0.402302\pi\)
−0.953267 + 0.302130i \(0.902302\pi\)
\(312\) 0 0
\(313\) −304.665 + 304.665i −0.0550182 + 0.0550182i −0.734081 0.679062i \(-0.762387\pi\)
0.679062 + 0.734081i \(0.262387\pi\)
\(314\) 0 0
\(315\) −888.101 2144.07i −0.158853 0.383506i
\(316\) 0 0
\(317\) −6782.93 2809.58i −1.20179 0.497798i −0.310213 0.950667i \(-0.600400\pi\)
−0.891577 + 0.452869i \(0.850400\pi\)
\(318\) 0 0
\(319\) −14270.2 −2.50464
\(320\) 0 0
\(321\) 4685.89 0.814770
\(322\) 0 0
\(323\) −10007.8 4145.39i −1.72400 0.714104i
\(324\) 0 0
\(325\) −587.083 1417.34i −0.100202 0.241908i
\(326\) 0 0
\(327\) −5726.10 + 5726.10i −0.968362 + 0.968362i
\(328\) 0 0
\(329\) −1111.01 1111.01i −0.186175 0.186175i
\(330\) 0 0
\(331\) 3670.23 1520.26i 0.609468 0.252450i −0.0565331 0.998401i \(-0.518005\pi\)
0.666001 + 0.745951i \(0.268005\pi\)
\(332\) 0 0
\(333\) −584.792 + 1411.81i −0.0962354 + 0.232333i
\(334\) 0 0
\(335\) 846.186i 0.138006i
\(336\) 0 0
\(337\) 5082.79i 0.821593i 0.911727 + 0.410797i \(0.134749\pi\)
−0.911727 + 0.410797i \(0.865251\pi\)
\(338\) 0 0
\(339\) 2091.54 5049.42i 0.335094 0.808988i
\(340\) 0 0
\(341\) 10055.3 4165.03i 1.59684 0.661434i
\(342\) 0 0
\(343\) 4384.12 + 4384.12i 0.690146 + 0.690146i
\(344\) 0 0
\(345\) 1773.97 1773.97i 0.276833 0.276833i
\(346\) 0 0
\(347\) 1154.04 + 2786.09i 0.178536 + 0.431023i 0.987660 0.156615i \(-0.0500580\pi\)
−0.809124 + 0.587638i \(0.800058\pi\)
\(348\) 0 0
\(349\) −2241.53 928.474i −0.343801 0.142407i 0.204100 0.978950i \(-0.434573\pi\)
−0.547901 + 0.836543i \(0.684573\pi\)
\(350\) 0 0
\(351\) −1634.83 −0.248606
\(352\) 0 0
\(353\) −8284.27 −1.24908 −0.624542 0.780991i \(-0.714715\pi\)
−0.624542 + 0.780991i \(0.714715\pi\)
\(354\) 0 0
\(355\) 5173.22 + 2142.82i 0.773425 + 0.320363i
\(356\) 0 0
\(357\) 3698.80 + 8929.70i 0.548351 + 1.32384i
\(358\) 0 0
\(359\) −1889.18 + 1889.18i −0.277736 + 0.277736i −0.832205 0.554469i \(-0.812922\pi\)
0.554469 + 0.832205i \(0.312922\pi\)
\(360\) 0 0
\(361\) −8878.78 8878.78i −1.29447 1.29447i
\(362\) 0 0
\(363\) 9429.36 3905.77i 1.36340 0.564738i
\(364\) 0 0
\(365\) 1006.32 2429.47i 0.144310 0.348395i
\(366\) 0 0
\(367\) 7429.67i 1.05675i −0.849012 0.528373i \(-0.822802\pi\)
0.849012 0.528373i \(-0.177198\pi\)
\(368\) 0 0
\(369\) 838.486i 0.118292i
\(370\) 0 0
\(371\) −4194.46 + 10126.3i −0.586969 + 1.41707i
\(372\) 0 0
\(373\) 1661.51 688.219i 0.230642 0.0955351i −0.264369 0.964421i \(-0.585164\pi\)
0.495012 + 0.868886i \(0.335164\pi\)
\(374\) 0 0
\(375\) −6785.98 6785.98i −0.934471 0.934471i
\(376\) 0 0
\(377\) −4294.13 + 4294.13i −0.586628 + 0.586628i
\(378\) 0 0
\(379\) −3773.37 9109.72i −0.511412 1.23466i −0.943062 0.332616i \(-0.892069\pi\)
0.431651 0.902041i \(-0.357931\pi\)
\(380\) 0 0
\(381\) −1137.69 471.245i −0.152980 0.0633664i
\(382\) 0 0
\(383\) 13137.5 1.75273 0.876366 0.481646i \(-0.159961\pi\)
0.876366 + 0.481646i \(0.159961\pi\)
\(384\) 0 0
\(385\) −7739.35 −1.02450
\(386\) 0 0
\(387\) −2990.23 1238.59i −0.392770 0.162691i
\(388\) 0 0
\(389\) 1767.36 + 4266.78i 0.230357 + 0.556130i 0.996219 0.0868742i \(-0.0276878\pi\)
−0.765863 + 0.643004i \(0.777688\pi\)
\(390\) 0 0
\(391\) −2760.71 + 2760.71i −0.357072 + 0.357072i
\(392\) 0 0
\(393\) −5031.47 5031.47i −0.645812 0.645812i
\(394\) 0 0
\(395\) 5446.04 2255.83i 0.693722 0.287349i
\(396\) 0 0
\(397\) −5649.54 + 13639.2i −0.714212 + 1.72426i −0.0250151 + 0.999687i \(0.507963\pi\)
−0.689197 + 0.724574i \(0.742037\pi\)
\(398\) 0 0
\(399\) 17323.9i 2.17363i
\(400\) 0 0
\(401\) 5422.25i 0.675247i −0.941281 0.337624i \(-0.890377\pi\)
0.941281 0.337624i \(-0.109623\pi\)
\(402\) 0 0
\(403\) 1772.46 4279.11i 0.219089 0.528927i
\(404\) 0 0
\(405\) −6357.70 + 2633.45i −0.780042 + 0.323104i
\(406\) 0 0
\(407\) 3603.53 + 3603.53i 0.438871 + 0.438871i
\(408\) 0 0
\(409\) −2622.89 + 2622.89i −0.317099 + 0.317099i −0.847652 0.530553i \(-0.821984\pi\)
0.530553 + 0.847652i \(0.321984\pi\)
\(410\) 0 0
\(411\) −4524.68 10923.5i −0.543031 1.31099i
\(412\) 0 0
\(413\) −3462.82 1434.35i −0.412577 0.170895i
\(414\) 0 0
\(415\) −475.509 −0.0562454
\(416\) 0 0
\(417\) 15131.4 1.77695
\(418\) 0 0
\(419\) 1293.33 + 535.717i 0.150796 + 0.0624617i 0.456805 0.889567i \(-0.348994\pi\)
−0.306009 + 0.952029i \(0.598994\pi\)
\(420\) 0 0
\(421\) −871.790 2104.69i −0.100923 0.243649i 0.865351 0.501166i \(-0.167096\pi\)
−0.966274 + 0.257517i \(0.917096\pi\)
\(422\) 0 0
\(423\) 945.041 945.041i 0.108628 0.108628i
\(424\) 0 0
\(425\) 3689.15 + 3689.15i 0.421059 + 0.421059i
\(426\) 0 0
\(427\) −8942.46 + 3704.09i −1.01348 + 0.419797i
\(428\) 0 0
\(429\) 3085.29 7448.55i 0.347224 0.838274i
\(430\) 0 0
\(431\) 5681.29i 0.634938i 0.948269 + 0.317469i \(0.102833\pi\)
−0.948269 + 0.317469i \(0.897167\pi\)
\(432\) 0 0
\(433\) 9616.41i 1.06729i −0.845710 0.533643i \(-0.820822\pi\)
0.845710 0.533643i \(-0.179178\pi\)
\(434\) 0 0
\(435\) −5078.51 + 12260.6i −0.559761 + 1.35138i
\(436\) 0 0
\(437\) −6465.09 + 2677.93i −0.707705 + 0.293141i
\(438\) 0 0
\(439\) −10175.7 10175.7i −1.10629 1.10629i −0.993634 0.112657i \(-0.964064\pi\)
−0.112657 0.993634i \(-0.535936\pi\)
\(440\) 0 0
\(441\) 177.469 177.469i 0.0191630 0.0191630i
\(442\) 0 0
\(443\) −925.474 2234.29i −0.0992564 0.239626i 0.866449 0.499265i \(-0.166397\pi\)
−0.965706 + 0.259639i \(0.916397\pi\)
\(444\) 0 0
\(445\) 3490.65 + 1445.88i 0.371849 + 0.154025i
\(446\) 0 0
\(447\) 988.852 0.104633
\(448\) 0 0
\(449\) 8501.56 0.893571 0.446785 0.894641i \(-0.352569\pi\)
0.446785 + 0.894641i \(0.352569\pi\)
\(450\) 0 0
\(451\) −2583.41 1070.08i −0.269729 0.111726i
\(452\) 0 0
\(453\) 7204.03 + 17392.1i 0.747185 + 1.80386i
\(454\) 0 0
\(455\) −2328.89 + 2328.89i −0.239956 + 0.239956i
\(456\) 0 0
\(457\) 7829.53 + 7829.53i 0.801422 + 0.801422i 0.983318 0.181895i \(-0.0582232\pi\)
−0.181895 + 0.983318i \(0.558223\pi\)
\(458\) 0 0
\(459\) 5136.53 2127.62i 0.522337 0.216359i
\(460\) 0 0
\(461\) 4138.96 9992.34i 0.418158 1.00952i −0.564723 0.825280i \(-0.691017\pi\)
0.982881 0.184241i \(-0.0589828\pi\)
\(462\) 0 0
\(463\) 13379.7i 1.34300i −0.741004 0.671501i \(-0.765650\pi\)
0.741004 0.671501i \(-0.234350\pi\)
\(464\) 0 0
\(465\) 10121.5i 1.00940i
\(466\) 0 0
\(467\) −2256.68 + 5448.12i −0.223612 + 0.539848i −0.995375 0.0960626i \(-0.969375\pi\)
0.771763 + 0.635910i \(0.219375\pi\)
\(468\) 0 0
\(469\) 1945.70 805.934i 0.191565 0.0793488i
\(470\) 0 0
\(471\) 4104.08 + 4104.08i 0.401499 + 0.401499i
\(472\) 0 0
\(473\) −7632.31 + 7632.31i −0.741932 + 0.741932i
\(474\) 0 0
\(475\) 3578.53 + 8639.33i 0.345672 + 0.834525i
\(476\) 0 0
\(477\) −8613.63 3567.88i −0.826816 0.342478i
\(478\) 0 0
\(479\) 15500.6 1.47858 0.739289 0.673389i \(-0.235162\pi\)
0.739289 + 0.673389i \(0.235162\pi\)
\(480\) 0 0
\(481\) 2168.71 0.205582
\(482\) 0 0
\(483\) 5768.61 + 2389.44i 0.543438 + 0.225100i
\(484\) 0 0
\(485\) −3791.07 9152.46i −0.354936 0.856891i
\(486\) 0 0
\(487\) 3384.07 3384.07i 0.314880 0.314880i −0.531917 0.846797i \(-0.678528\pi\)
0.846797 + 0.531917i \(0.178528\pi\)
\(488\) 0 0
\(489\) 4791.40 + 4791.40i 0.443098 + 0.443098i
\(490\) 0 0
\(491\) 5913.07 2449.27i 0.543489 0.225121i −0.0940105 0.995571i \(-0.529969\pi\)
0.637500 + 0.770451i \(0.279969\pi\)
\(492\) 0 0
\(493\) 7903.35 19080.4i 0.722006 1.74308i
\(494\) 0 0
\(495\) 6583.23i 0.597766i
\(496\) 0 0
\(497\) 13936.0i 1.25778i
\(498\) 0 0
\(499\) 5163.06 12464.7i 0.463187 1.11823i −0.503894 0.863765i \(-0.668100\pi\)
0.967081 0.254467i \(-0.0819001\pi\)
\(500\) 0 0
\(501\) 7687.60 3184.31i 0.685542 0.283961i
\(502\) 0 0
\(503\) −6921.39 6921.39i −0.613537 0.613537i 0.330329 0.943866i \(-0.392840\pi\)
−0.943866 + 0.330329i \(0.892840\pi\)
\(504\) 0 0
\(505\) 3587.93 3587.93i 0.316160 0.316160i
\(506\) 0 0
\(507\) 4207.12 + 10156.9i 0.368530 + 0.889710i
\(508\) 0 0
\(509\) 14532.1 + 6019.39i 1.26547 + 0.524174i 0.911584 0.411115i \(-0.134860\pi\)
0.353885 + 0.935289i \(0.384860\pi\)
\(510\) 0 0
\(511\) 6544.71 0.566577
\(512\) 0 0
\(513\) 9965.00 0.857633
\(514\) 0 0
\(515\) 1192.09 + 493.779i 0.101999 + 0.0422495i
\(516\) 0 0
\(517\) −1705.64 4117.78i −0.145095 0.350290i
\(518\) 0 0
\(519\) −3254.29 + 3254.29i −0.275236 + 0.275236i
\(520\) 0 0
\(521\) −6505.72 6505.72i −0.547065 0.547065i 0.378526 0.925591i \(-0.376431\pi\)
−0.925591 + 0.378526i \(0.876431\pi\)
\(522\) 0 0
\(523\) −18929.1 + 7840.67i −1.58262 + 0.655543i −0.988826 0.149075i \(-0.952370\pi\)
−0.593794 + 0.804617i \(0.702370\pi\)
\(524\) 0 0
\(525\) 3193.01 7708.61i 0.265437 0.640822i
\(526\) 0 0
\(527\) 15751.4i 1.30198i
\(528\) 0 0
\(529\) 9644.85i 0.792706i
\(530\) 0 0
\(531\) 1220.08 2945.54i 0.0997119 0.240726i
\(532\) 0 0
\(533\) −1099.39 + 455.382i −0.0893431 + 0.0370071i
\(534\) 0 0
\(535\) −3839.73 3839.73i −0.310292 0.310292i
\(536\) 0 0
\(537\) −10220.2 + 10220.2i −0.821295 + 0.821295i
\(538\) 0 0
\(539\) −320.301 773.276i −0.0255962 0.0617947i
\(540\) 0 0
\(541\) −14495.4 6004.19i −1.15195 0.477154i −0.276765 0.960938i \(-0.589262\pi\)
−0.875188 + 0.483783i \(0.839262\pi\)
\(542\) 0 0
\(543\) 9909.05 0.783127
\(544\) 0 0
\(545\) 9384.21 0.737569
\(546\) 0 0
\(547\) 17281.4 + 7158.21i 1.35082 + 0.559530i 0.936522 0.350609i \(-0.114025\pi\)
0.414303 + 0.910139i \(0.364025\pi\)
\(548\) 0 0
\(549\) −3150.76 7606.62i −0.244939 0.591334i
\(550\) 0 0
\(551\) 26174.6 26174.6i 2.02373 2.02373i
\(552\) 0 0
\(553\) 10374.0 + 10374.0i 0.797732 + 0.797732i
\(554\) 0 0
\(555\) 4378.49 1813.63i 0.334877 0.138711i
\(556\) 0 0
\(557\) −3341.04 + 8065.99i −0.254155 + 0.613585i −0.998531 0.0541753i \(-0.982747\pi\)
0.744376 + 0.667761i \(0.232747\pi\)
\(558\) 0 0
\(559\) 4593.35i 0.347546i
\(560\) 0 0
\(561\) 27418.1i 2.06345i
\(562\) 0 0
\(563\) −4945.85 + 11940.3i −0.370236 + 0.893828i 0.623474 + 0.781844i \(0.285721\pi\)
−0.993710 + 0.111984i \(0.964279\pi\)
\(564\) 0 0
\(565\) −5851.47 + 2423.76i −0.435705 + 0.180475i
\(566\) 0 0
\(567\) −12110.6 12110.6i −0.896994 0.896994i
\(568\) 0 0
\(569\) −8205.09 + 8205.09i −0.604526 + 0.604526i −0.941510 0.336984i \(-0.890593\pi\)
0.336984 + 0.941510i \(0.390593\pi\)
\(570\) 0 0
\(571\) −4078.90 9847.33i −0.298943 0.721712i −0.999963 0.00857103i \(-0.997272\pi\)
0.701020 0.713141i \(-0.252728\pi\)
\(572\) 0 0
\(573\) −4729.67 1959.09i −0.344825 0.142831i
\(574\) 0 0
\(575\) 3370.35 0.244441
\(576\) 0 0
\(577\) −4675.49 −0.337337 −0.168668 0.985673i \(-0.553947\pi\)
−0.168668 + 0.985673i \(0.553947\pi\)
\(578\) 0 0
\(579\) −25325.8 10490.3i −1.81780 0.752958i
\(580\) 0 0
\(581\) −452.890 1093.37i −0.0323391 0.0780736i
\(582\) 0 0
\(583\) −21985.6 + 21985.6i −1.56183 + 1.56183i
\(584\) 0 0
\(585\) −1980.99 1980.99i −0.140007 0.140007i
\(586\) 0 0
\(587\) −3400.03 + 1408.34i −0.239070 + 0.0990260i −0.499002 0.866601i \(-0.666300\pi\)
0.259932 + 0.965627i \(0.416300\pi\)
\(588\) 0 0
\(589\) −10803.9 + 26083.0i −0.755804 + 1.82467i
\(590\) 0 0
\(591\) 30769.2i 2.14158i
\(592\) 0 0
\(593\) 15975.1i 1.10627i −0.833090 0.553137i \(-0.813431\pi\)
0.833090 0.553137i \(-0.186569\pi\)
\(594\) 0 0
\(595\) 4286.32 10348.1i 0.295331 0.712993i
\(596\) 0 0
\(597\) −11442.3 + 4739.54i −0.784422 + 0.324918i
\(598\) 0 0
\(599\) 14655.9 + 14655.9i 0.999707 + 0.999707i 1.00000 0.000292806i \(-9.32030e-5\pi\)
−0.000292806 1.00000i \(0.500093\pi\)
\(600\) 0 0
\(601\) 12665.9 12665.9i 0.859656 0.859656i −0.131641 0.991297i \(-0.542025\pi\)
0.991297 + 0.131641i \(0.0420247\pi\)
\(602\) 0 0
\(603\) 685.542 + 1655.05i 0.0462976 + 0.111772i
\(604\) 0 0
\(605\) −10927.1 4526.16i −0.734299 0.304156i
\(606\) 0 0
\(607\) −18257.0 −1.22080 −0.610402 0.792092i \(-0.708992\pi\)
−0.610402 + 0.792092i \(0.708992\pi\)
\(608\) 0 0
\(609\) −33028.7 −2.19768
\(610\) 0 0
\(611\) −1752.35 725.849i −0.116027 0.0480601i
\(612\) 0 0
\(613\) −2056.78 4965.49i −0.135518 0.327169i 0.841523 0.540221i \(-0.181659\pi\)
−0.977041 + 0.213053i \(0.931659\pi\)
\(614\) 0 0
\(615\) −1838.77 + 1838.77i −0.120564 + 0.120564i
\(616\) 0 0
\(617\) 2198.69 + 2198.69i 0.143462 + 0.143462i 0.775190 0.631728i \(-0.217654\pi\)
−0.631728 + 0.775190i \(0.717654\pi\)
\(618\) 0 0
\(619\) −14373.8 + 5953.83i −0.933331 + 0.386598i −0.796941 0.604057i \(-0.793550\pi\)
−0.136390 + 0.990655i \(0.543550\pi\)
\(620\) 0 0
\(621\) 1374.45 3318.21i 0.0888159 0.214421i
\(622\) 0 0
\(623\) 9403.41i 0.604719i
\(624\) 0 0
\(625\) 2732.38i 0.174872i
\(626\) 0 0
\(627\) −18806.2 + 45402.2i −1.19784 + 2.89185i
\(628\) 0 0
\(629\) −6813.96 + 2822.43i −0.431940 + 0.178915i
\(630\) 0 0
\(631\) 21029.2 + 21029.2i 1.32672 + 1.32672i 0.908216 + 0.418502i \(0.137445\pi\)
0.418502 + 0.908216i \(0.362555\pi\)
\(632\) 0 0
\(633\) 14228.4 14228.4i 0.893410 0.893410i
\(634\) 0 0
\(635\) 546.098 + 1318.40i 0.0341279 + 0.0823921i
\(636\) 0 0
\(637\) −329.074 136.307i −0.0204684 0.00847830i
\(638\) 0 0
\(639\) −11854.3 −0.733876
\(640\) 0 0
\(641\) 22576.4 1.39113 0.695564 0.718464i \(-0.255155\pi\)
0.695564 + 0.718464i \(0.255155\pi\)
\(642\) 0 0
\(643\) −15365.6 6364.66i −0.942398 0.390354i −0.142029 0.989862i \(-0.545363\pi\)
−0.800368 + 0.599509i \(0.795363\pi\)
\(644\) 0 0
\(645\) 3841.29 + 9273.69i 0.234497 + 0.566126i
\(646\) 0 0
\(647\) 2866.06 2866.06i 0.174152 0.174152i −0.614649 0.788801i \(-0.710702\pi\)
0.788801 + 0.614649i \(0.210702\pi\)
\(648\) 0 0
\(649\) −7518.24 7518.24i −0.454725 0.454725i
\(650\) 0 0
\(651\) 23273.1 9640.03i 1.40114 0.580373i
\(652\) 0 0
\(653\) −1656.18 + 3998.36i −0.0992514 + 0.239614i −0.965704 0.259645i \(-0.916394\pi\)
0.866453 + 0.499259i \(0.166394\pi\)
\(654\) 0 0
\(655\) 8245.81i 0.491894i
\(656\) 0 0
\(657\) 5567.05i 0.330580i
\(658\) 0 0
\(659\) 7707.07 18606.5i 0.455576 1.09986i −0.514594 0.857434i \(-0.672057\pi\)
0.970170 0.242424i \(-0.0779426\pi\)
\(660\) 0 0
\(661\) 25591.1 10600.2i 1.50587 0.623751i 0.531168 0.847267i \(-0.321753\pi\)
0.974700 + 0.223515i \(0.0717533\pi\)
\(662\) 0 0
\(663\) 8250.53 + 8250.53i 0.483294 + 0.483294i
\(664\) 0 0
\(665\) 14195.6 14195.6i 0.827791 0.827791i
\(666\) 0 0
\(667\) −5105.58 12326.0i −0.296385 0.715537i
\(668\) 0 0
\(669\) 14934.9 + 6186.24i 0.863105 + 0.357510i
\(670\) 0 0
\(671\) −27457.3 −1.57970
\(672\) 0 0
\(673\) −32715.5 −1.87383 −0.936917 0.349553i \(-0.886333\pi\)
−0.936917 + 0.349553i \(0.886333\pi\)
\(674\) 0 0
\(675\) −4434.14 1836.68i −0.252844 0.104732i
\(676\) 0 0
\(677\) −249.757 602.967i −0.0141786 0.0342303i 0.916632 0.399733i \(-0.130897\pi\)
−0.930810 + 0.365503i \(0.880897\pi\)
\(678\) 0 0
\(679\) 17434.2 17434.2i 0.985365 0.985365i
\(680\) 0 0
\(681\) −14634.1 14634.1i −0.823466 0.823466i
\(682\) 0 0
\(683\) 1024.16 424.220i 0.0573767 0.0237662i −0.353811 0.935317i \(-0.615114\pi\)
0.411187 + 0.911551i \(0.365114\pi\)
\(684\) 0 0
\(685\) −5243.38 + 12658.6i −0.292466 + 0.706075i
\(686\) 0 0
\(687\) 9920.29i 0.550921i
\(688\) 0 0
\(689\) 13231.6i 0.731615i
\(690\) 0 0
\(691\) 6429.36 15521.9i 0.353957 0.854528i −0.642166 0.766565i \(-0.721964\pi\)
0.996124 0.0879632i \(-0.0280358\pi\)
\(692\) 0 0
\(693\) 15137.3 6270.08i 0.829753 0.343695i
\(694\) 0 0
\(695\) −12399.0 12399.0i −0.676721 0.676721i
\(696\) 0 0
\(697\) 2861.56 2861.56i 0.155508 0.155508i
\(698\) 0 0
\(699\) 10793.3 + 26057.4i 0.584037 + 1.40999i
\(700\) 0 0
\(701\) 20337.8 + 8424.21i 1.09579 + 0.453892i 0.856023 0.516938i \(-0.172928\pi\)
0.239769 + 0.970830i \(0.422928\pi\)
\(702\) 0 0
\(703\) −13219.3 −0.709209
\(704\) 0 0
\(705\) −4144.90 −0.221427
\(706\) 0 0
\(707\) 11667.2 + 4832.72i 0.620638 + 0.257077i
\(708\) 0 0
\(709\) −11697.5 28240.4i −0.619620 1.49589i −0.852146 0.523304i \(-0.824699\pi\)
0.232527 0.972590i \(-0.425301\pi\)
\(710\) 0 0
\(711\) −8824.29 + 8824.29i −0.465452 + 0.465452i
\(712\) 0 0
\(713\) 7195.13 + 7195.13i 0.377924 + 0.377924i
\(714\) 0 0
\(715\) −8631.68 + 3575.36i −0.451478 + 0.187008i
\(716\) 0 0
\(717\) 171.310 413.578i 0.00892284 0.0215416i
\(718\) 0 0
\(719\) 2930.75i 0.152015i −0.997107 0.0760074i \(-0.975783\pi\)
0.997107 0.0760074i \(-0.0242173\pi\)
\(720\) 0 0
\(721\) 3211.34i 0.165876i
\(722\) 0 0
\(723\) 15364.8 37093.9i 0.790350 1.90807i
\(724\) 0 0
\(725\) −16471.2 + 6822.61i −0.843760 + 0.349497i
\(726\) 0 0
\(727\) 11618.1 + 11618.1i 0.592696 + 0.592696i 0.938359 0.345663i \(-0.112346\pi\)
−0.345663 + 0.938359i \(0.612346\pi\)
\(728\) 0 0
\(729\) 1336.91 1336.91i 0.0679218 0.0679218i
\(730\) 0 0
\(731\) −5977.94 14432.0i −0.302465 0.730215i
\(732\) 0 0
\(733\) 8786.76 + 3639.59i 0.442764 + 0.183399i 0.592917 0.805264i \(-0.297976\pi\)
−0.150152 + 0.988663i \(0.547976\pi\)
\(734\) 0 0
\(735\) −778.369 −0.0390620
\(736\) 0 0
\(737\) 5974.15 0.298590
\(738\) 0 0
\(739\) 30367.3 + 12578.6i 1.51161 + 0.626130i 0.975890 0.218265i \(-0.0700397\pi\)
0.535721 + 0.844395i \(0.320040\pi\)
\(740\) 0 0
\(741\) 8003.13 + 19321.3i 0.396764 + 0.957874i
\(742\) 0 0
\(743\) −28118.1 + 28118.1i −1.38836 + 1.38836i −0.559596 + 0.828765i \(0.689044\pi\)
−0.828765 + 0.559596i \(0.810956\pi\)
\(744\) 0 0
\(745\) −810.288 810.288i −0.0398479 0.0398479i
\(746\) 0 0
\(747\) 930.043 385.236i 0.0455535 0.0188689i
\(748\) 0 0
\(749\) 5171.89 12486.1i 0.252305 0.609119i
\(750\) 0 0
\(751\) 2199.78i 0.106886i 0.998571 + 0.0534428i \(0.0170195\pi\)
−0.998571 + 0.0534428i \(0.982981\pi\)
\(752\) 0 0
\(753\) 3152.65i 0.152575i
\(754\) 0 0
\(755\) 8348.32 20154.6i 0.402419 0.971525i
\(756\) 0 0
\(757\) 1609.12 666.518i 0.0772581 0.0320013i −0.343720 0.939072i \(-0.611687\pi\)
0.420978 + 0.907071i \(0.361687\pi\)
\(758\) 0 0
\(759\) 12524.4 + 12524.4i 0.598955 + 0.598955i
\(760\) 0 0
\(761\) −13159.3 + 13159.3i −0.626837 + 0.626837i −0.947271 0.320434i \(-0.896171\pi\)
0.320434 + 0.947271i \(0.396171\pi\)
\(762\) 0 0
\(763\) 8937.81 + 21577.8i 0.424077 + 1.02381i
\(764\) 0 0
\(765\) 8802.28 + 3646.02i 0.416009 + 0.172317i
\(766\) 0 0
\(767\) −4524.70 −0.213008
\(768\) 0 0
\(769\) −13781.4 −0.646253 −0.323127 0.946356i \(-0.604734\pi\)
−0.323127 + 0.946356i \(0.604734\pi\)
\(770\) 0 0
\(771\) −158.533 65.6667i −0.00740524 0.00306735i
\(772\) 0 0
\(773\) −904.546 2183.77i −0.0420883 0.101610i 0.901437 0.432909i \(-0.142513\pi\)
−0.943526 + 0.331299i \(0.892513\pi\)
\(774\) 0 0
\(775\) 9614.87 9614.87i 0.445647 0.445647i
\(776\) 0 0
\(777\) 8340.43 + 8340.43i 0.385085 + 0.385085i
\(778\) 0 0
\(779\) 6701.26 2775.75i 0.308213 0.127666i
\(780\) 0 0
\(781\) −15128.5 + 36523.4i −0.693137 + 1.67338i
\(782\) 0 0
\(783\) 18998.7i 0.867124i
\(784\) 0 0
\(785\) 6725.96i 0.305809i
\(786\) 0 0
\(787\) 7363.51 17777.1i 0.333521 0.805190i −0.664787 0.747033i \(-0.731478\pi\)
0.998307 0.0581569i \(-0.0185224\pi\)
\(788\) 0 0
\(789\) 20630.9 8545.61i 0.930901 0.385592i
\(790\) 0 0
\(791\) −11146.2 11146.2i −0.501030 0.501030i
\(792\) 0 0
\(793\) −8262.32 + 8262.32i −0.369992 + 0.369992i
\(794\) 0 0
\(795\) 11065.2 + 26713.7i 0.493637 + 1.19175i
\(796\) 0 0
\(797\)