Properties

Label 128.4.g.a.49.10
Level $128$
Weight $4$
Character 128.49
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 49.10
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.10

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 0.287050 0.957916i \(-0.407325\pi\)
0.880324 + 0.474373i \(0.157325\pi\)
\(4\) 0 0
\(5\) −2.91165 + 7.02935i −0.260426 + 0.628724i −0.998965 0.0454866i \(-0.985516\pi\)
0.738539 + 0.674211i \(0.235516\pi\)
\(6\) 0 0
\(7\) 13.3899 + 13.3899i 0.722989 + 0.722989i 0.969213 0.246224i \(-0.0791898\pi\)
−0.246224 + 0.969213i \(0.579190\pi\)
\(8\) 0 0
\(9\) 11.3897 11.3897i 0.421842 0.421842i
\(10\) 0 0
\(11\) 49.6279 + 20.5565i 1.36031 + 0.563457i 0.939143 0.343527i \(-0.111622\pi\)
0.421164 + 0.906985i \(0.361622\pi\)
\(12\) 0 0
\(13\) 8.74801 + 21.1196i 0.186635 + 0.450578i 0.989308 0.145842i \(-0.0465892\pi\)
−0.802672 + 0.596420i \(0.796589\pi\)
\(14\) 0 0
\(15\) 49.9547i 0.859884i
\(16\) 0 0
\(17\) 77.7412i 1.10912i −0.832144 0.554559i \(-0.812887\pi\)
0.832144 0.554559i \(-0.187113\pi\)
\(18\) 0 0
\(19\) −53.3229 128.733i −0.643848 1.55439i −0.821447 0.570284i \(-0.806833\pi\)
0.177599 0.984103i \(-0.443167\pi\)
\(20\) 0 0
\(21\) 114.864 + 47.5784i 1.19359 + 0.494403i
\(22\) 0 0
\(23\) 35.5116 35.5116i 0.321943 0.321943i −0.527569 0.849512i \(-0.676897\pi\)
0.849512 + 0.527569i \(0.176897\pi\)
\(24\) 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 −0.987053 0.160395i \(-0.948723\pi\)
−0.584535 + 0.811368i \(0.698723\pi\)
\(30\) 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 −0.822469 0.568809i \(-0.807404\pi\)
0.983783 + 0.179365i \(0.0574042\pi\)
\(38\) 0 0
\(39\) 106.128 + 106.128i 0.435747 + 0.435747i
\(40\) 0 0
\(41\) −36.8088 + 36.8088i −0.140209 + 0.140209i −0.773728 0.633518i \(-0.781610\pi\)
0.633518 + 0.773728i \(0.281610\pi\)
\(42\) 0 0
\(43\) −185.642 76.8954i −0.658375 0.272708i 0.0283797 0.999597i \(-0.490965\pi\)
−0.686754 + 0.726889i \(0.740965\pi\)
\(44\) 0 0
\(45\) 46.8995 + 113.225i 0.155364 + 0.375081i
\(46\) 0 0
\(47\) 82.9731i 0.257508i 0.991677 + 0.128754i \(0.0410977\pi\)
−0.991677 + 0.128754i \(0.958902\pi\)
\(48\) 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 −0.439876 0.898059i \(-0.644978\pi\)
−0.946062 + 0.323984i \(0.894978\pi\)
\(54\) 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 −0.985151 0.171690i \(-0.945077\pi\)
0.818010 + 0.575204i \(0.195077\pi\)
\(60\) 0 0
\(61\) −472.240 + 195.608i −0.991216 + 0.410575i −0.818569 0.574409i \(-0.805232\pi\)
−0.172647 + 0.984984i \(0.555232\pi\)
\(62\) 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 −0.287033 0.957921i \(-0.592669\pi\)
0.474389 + 0.880315i \(0.342669\pi\)
\(68\) 0 0
\(69\) 126.183 304.633i 0.220155 0.531500i
\(70\) 0 0
\(71\) −520.392 520.392i −0.869847 0.869847i 0.122608 0.992455i \(-0.460874\pi\)
−0.992455 + 0.122608i \(0.960874\pi\)
\(72\) 0 0
\(73\) 244.389 244.389i 0.391829 0.391829i −0.483510 0.875339i \(-0.660638\pi\)
0.875339 + 0.483510i \(0.160638\pi\)
\(74\) 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 \(-0.813983\pi\)
0.834049 0.551690i \(-0.186017\pi\)
\(80\) 0 0
\(81\) 904.451i 1.24067i
\(82\) 0 0
\(83\) 23.9166 + 57.7397i 0.0316287 + 0.0763585i 0.938905 0.344177i \(-0.111842\pi\)
−0.907276 + 0.420536i \(0.861842\pi\)
\(84\) 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 0.466378 0.884585i \(-0.345559\pi\)
−0.884585 + 0.466378i \(0.845559\pi\)
\(90\) 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 −0.746891 0.664947i \(-0.768454\pi\)
0.998320 + 0.0579428i \(0.0184541\pi\)
\(102\) 0 0
\(103\) −119.916 119.916i −0.114715 0.114715i 0.647419 0.762134i \(-0.275848\pi\)
−0.762134 + 0.647419i \(0.775848\pi\)
\(104\) 0 0
\(105\) −668.891 + 668.891i −0.621687 + 0.621687i
\(106\) 0 0
\(107\) 659.373 + 273.121i 0.595738 + 0.246763i 0.660117 0.751163i \(-0.270507\pi\)
−0.0643789 + 0.997926i \(0.520507\pi\)
\(108\) 0 0
\(109\) −471.995 1139.50i −0.414761 1.00132i −0.983842 0.179040i \(-0.942701\pi\)
0.569081 0.822281i \(-0.307299\pi\)
\(110\) 0 0
\(111\) 622.887i 0.532629i
\(112\) 0 0
\(113\) 832.434i 0.692998i 0.938050 + 0.346499i \(0.112630\pi\)
−0.938050 + 0.346499i \(0.887370\pi\)
\(114\) 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 −0.690714 0.723128i \(-0.742703\pi\)
0.0229207 + 0.999737i \(0.492703\pi\)
\(132\) 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 −0.982158 0.188057i \(-0.939781\pi\)
0.188057 + 0.982158i \(0.439781\pi\)
\(138\) 0 0
\(139\) 2129.20 + 881.945i 1.29926 + 0.538170i 0.921731 0.387830i \(-0.126775\pi\)
0.377525 + 0.925999i \(0.376775\pi\)
\(140\) 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 0.420608 0.907243i \(-0.361817\pi\)
−0.344103 + 0.938932i \(0.611817\pi\)
\(150\) 0 0
\(151\) 2027.42 2027.42i 1.09264 1.09264i 0.0973988 0.995245i \(-0.468948\pi\)
0.995245 0.0973988i \(-0.0310522\pi\)
\(152\) 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 −0.165317 0.986241i \(-0.552865\pi\)
0.580481 + 0.814274i \(0.302865\pi\)
\(158\) 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 −0.141642 0.989918i \(-0.545238\pi\)
0.599821 + 0.800134i \(0.295238\pi\)
\(164\) 0 0
\(165\) −1026.90 + 2479.15i −0.484508 + 1.16971i
\(166\) 0 0
\(167\) 896.156 + 896.156i 0.415249 + 0.415249i 0.883563 0.468313i \(-0.155138\pi\)
−0.468313 + 0.883563i \(0.655138\pi\)
\(168\) 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 0.853911 0.520419i \(-0.174224\pi\)
−0.971798 + 0.235815i \(0.924224\pi\)
\(174\) 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 −0.996402 0.0847553i \(-0.972989\pi\)
0.644631 0.764494i \(-0.277011\pi\)
\(180\) 0 0
\(181\) 1394.35 + 577.557i 0.572602 + 0.237180i 0.650146 0.759809i \(-0.274708\pi\)
−0.0775438 + 0.996989i \(0.524708\pi\)
\(182\) 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 0.166174 + 0.986096i \(0.446859\pi\)
−0.814778 + 0.579773i \(0.803141\pi\)
\(198\) 0 0
\(199\) −1333.84 1333.84i −0.475144 0.475144i 0.428431 0.903575i \(-0.359067\pi\)
−0.903575 + 0.428431i \(0.859067\pi\)
\(200\) 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 0.991450 + 0.130488i \(0.0416544\pi\)
−0.608792 + 0.793330i \(0.708346\pi\)
\(212\) 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 −0.765375 0.643585i \(-0.777446\pi\)
−0.0861187 + 0.996285i \(0.527446\pi\)
\(228\) 0 0
\(229\) −578.212 + 1395.93i −0.166853 + 0.402819i −0.985085 0.172070i \(-0.944955\pi\)
0.818232 + 0.574889i \(0.194955\pi\)
\(230\) 0 0
\(231\) 4722.43 + 4722.43i 1.34508 + 1.34508i
\(232\) 0 0
\(233\) 3037.56 3037.56i 0.854065 0.854065i −0.136566 0.990631i \(-0.543607\pi\)
0.990631 + 0.136566i \(0.0436067\pi\)
\(234\) 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 \(0.00293694\pi\)
−0.999957 + 0.00922654i \(0.997063\pi\)
\(240\) 0 0
\(241\) 6115.20i 1.63450i 0.576282 + 0.817251i \(0.304503\pi\)
−0.576282 + 0.817251i \(0.695497\pi\)
\(242\) 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 −0.945299 0.326206i \(-0.894230\pi\)
0.899090 + 0.437765i \(0.144230\pi\)
\(252\) 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 0.930404 0.366535i \(-0.119456\pi\)
−0.366535 + 0.930404i \(0.619456\pi\)
\(264\) 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 0.644896 + 0.764270i \(0.276901\pi\)
0.0844104 + 0.996431i \(0.473099\pi\)
\(270\) 0 0
\(271\) 4099.60i 0.918941i 0.888193 + 0.459471i \(0.151961\pi\)
−0.888193 + 0.459471i \(0.848039\pi\)
\(272\) 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 0.375881 0.926668i \(-0.377340\pi\)
−0.389465 + 0.921041i \(0.627340\pi\)
\(278\) 0 0
\(279\) 2307.71 2307.71i 0.495194 0.495194i
\(280\) 0 0
\(281\) 371.515 + 371.515i 0.0788709 + 0.0788709i 0.745442 0.666571i \(-0.232239\pi\)
−0.666571 + 0.745442i \(0.732239\pi\)
\(282\) 0 0
\(283\) 1150.78 2778.24i 0.241721 0.583566i −0.755733 0.654880i \(-0.772719\pi\)
0.997454 + 0.0713139i \(0.0227192\pi\)
\(284\) 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 −0.691294 0.722573i \(-0.742959\pi\)
0.999755 0.0221175i \(-0.00704081\pi\)
\(294\) 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 −0.989234 0.146344i \(-0.953249\pi\)
0.596013 0.802975i \(-0.296751\pi\)
\(308\) 0 0
\(309\) −1028.69 426.097i −0.189386 0.0784461i
\(310\) 0 0
\(311\) −3571.19 + 3571.19i −0.651137 + 0.651137i −0.953267 0.302130i \(-0.902302\pi\)
0.302130 + 0.953267i \(0.402302\pi\)
\(312\) 0 0
\(313\) −304.665 304.665i −0.0550182 0.0550182i 0.679062 0.734081i \(-0.262387\pi\)
−0.734081 + 0.679062i \(0.762387\pi\)
\(314\) 0 0
\(315\) −888.101 + 2144.07i −0.158853 + 0.383506i
\(316\) 0 0
\(317\) −6782.93 + 2809.58i −1.20179 + 0.497798i −0.891577 0.452869i \(-0.850400\pi\)
−0.310213 + 0.950667i \(0.600400\pi\)
\(318\) 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 0.666001 0.745951i \(-0.268005\pi\)
−0.0565331 + 0.998401i \(0.518005\pi\)
\(332\) 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 \(-0.865251\pi\)
0.911727 0.410797i \(-0.134749\pi\)
\(338\) 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 −0.809124 0.587638i \(-0.800058\pi\)
0.987660 + 0.156615i \(0.0500580\pi\)
\(348\) 0 0
\(349\) −2241.53 + 928.474i −0.343801 + 0.142407i −0.547901 0.836543i \(-0.684573\pi\)
0.204100 + 0.978950i \(0.434573\pi\)
\(350\) 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 0.554469 0.832205i \(-0.312922\pi\)
−0.832205 + 0.554469i \(0.812922\pi\)
\(360\) 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 \(0.177198\pi\)
−0.849012 + 0.528373i \(0.822802\pi\)
\(368\) 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 0.495012 0.868886i \(-0.335164\pi\)
−0.264369 + 0.964421i \(0.585164\pi\)
\(374\) 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 0.431651 + 0.902041i \(0.357931\pi\)
−0.943062 + 0.332616i \(0.892069\pi\)
\(380\) 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 −0.765863 0.643004i \(-0.777688\pi\)
0.996219 + 0.0868742i \(0.0276878\pi\)
\(390\) 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 −0.689197 0.724574i \(-0.742037\pi\)
−0.0250151 0.999687i \(-0.507963\pi\)
\(398\) 0 0
\(399\) 17323.9i 2.17363i
\(400\) 0 0
\(401\) 5422.25i 0.675247i 0.941281 + 0.337624i \(0.109623\pi\)
−0.941281 + 0.337624i \(0.890377\pi\)
\(402\) 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 0.530553 0.847652i \(-0.321984\pi\)
−0.847652 + 0.530553i \(0.821984\pi\)
\(410\) 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 −0.306009 0.952029i \(-0.598994\pi\)
0.456805 + 0.889567i \(0.348994\pi\)
\(420\) 0 0
\(421\) −871.790 + 2104.69i −0.100923 + 0.243649i −0.966274 0.257517i \(-0.917096\pi\)
0.865351 + 0.501166i \(0.167096\pi\)
\(422\) 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 \(-0.897167\pi\)
0.948269 0.317469i \(-0.102833\pi\)
\(432\) 0 0
\(433\) 9616.41i 1.06729i 0.845710 + 0.533643i \(0.179178\pi\)
−0.845710 + 0.533643i \(0.820822\pi\)
\(434\) 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 −0.112657 + 0.993634i \(0.535936\pi\)
−0.993634 + 0.112657i \(0.964064\pi\)
\(440\) 0 0
\(441\) 177.469 + 177.469i 0.0191630 + 0.0191630i
\(442\) 0 0
\(443\) −925.474 + 2234.29i −0.0992564 + 0.239626i −0.965706 0.259639i \(-0.916397\pi\)
0.866449 + 0.499265i \(0.166397\pi\)
\(444\) 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 −0.181895 0.983318i \(-0.558223\pi\)
0.983318 + 0.181895i \(0.0582232\pi\)
\(458\) 0 0
\(459\) 5136.53 + 2127.62i 0.522337 + 0.216359i
\(460\) 0 0
\(461\) 4138.96 + 9992.34i 0.418158 + 1.00952i 0.982881 + 0.184241i \(0.0589828\pi\)
−0.564723 + 0.825280i \(0.691017\pi\)
\(462\) 0 0
\(463\) 13379.7i 1.34300i 0.741004 + 0.671501i \(0.234350\pi\)
−0.741004 + 0.671501i \(0.765650\pi\)
\(464\) 0 0
\(465\) 10121.5i 1.00940i
\(466\) 0 0
\(467\) −2256.68 5448.12i −0.223612 0.539848i 0.771763 0.635910i \(-0.219375\pi\)
−0.995375 + 0.0960626i \(0.969375\pi\)
\(468\) 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 0.846797 0.531917i \(-0.178528\pi\)
−0.531917 + 0.846797i \(0.678528\pi\)
\(488\) 0 0
\(489\) 4791.40 4791.40i 0.443098 0.443098i
\(490\) 0 0
\(491\) 5913.07 + 2449.27i 0.543489 + 0.225121i 0.637500 0.770451i \(-0.279969\pi\)
−0.0940105 + 0.995571i \(0.529969\pi\)
\(492\) 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 0.967081 + 0.254467i \(0.0819001\pi\)
−0.503894 + 0.863765i \(0.668100\pi\)
\(500\) 0 0
\(501\) 7687.60 + 3184.31i 0.685542 + 0.283961i
\(502\) 0 0
\(503\) −6921.39 + 6921.39i −0.613537 + 0.613537i −0.943866 0.330329i \(-0.892840\pi\)
0.330329 + 0.943866i \(0.392840\pi\)
\(504\) 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 0.353885 0.935289i \(-0.384860\pi\)
0.911584 + 0.411115i \(0.134860\pi\)
\(510\) 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 −0.925591 0.378526i \(-0.876431\pi\)
0.378526 + 0.925591i \(0.376431\pi\)
\(522\) 0 0
\(523\) −18929.1 7840.67i −1.58262 0.655543i −0.593794 0.804617i \(-0.702370\pi\)
−0.988826 + 0.149075i \(0.952370\pi\)
\(524\) 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 −0.875188 0.483783i \(-0.839262\pi\)
−0.276765 + 0.960938i \(0.589262\pi\)
\(542\) 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 0.414303 0.910139i \(-0.364025\pi\)
0.936522 + 0.350609i \(0.114025\pi\)
\(548\) 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 0.744376 0.667761i \(-0.232747\pi\)
−0.998531 + 0.0541753i \(0.982747\pi\)
\(558\) 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 −0.993710 0.111984i \(-0.964279\pi\)
0.623474 0.781844i \(-0.285721\pi\)
\(564\) 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 0.336984 0.941510i \(-0.390593\pi\)
−0.941510 + 0.336984i \(0.890593\pi\)
\(570\) 0 0
\(571\) −4078.90 + 9847.33i −0.298943 + 0.721712i 0.701020 + 0.713141i \(0.252728\pi\)
−0.999963 + 0.00857103i \(0.997272\pi\)
\(572\) 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 0.259932 0.965627i \(-0.416300\pi\)
−0.499002 + 0.866601i \(0.666300\pi\)
\(588\) 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 \(0.186569\pi\)
−0.833090 + 0.553137i \(0.813431\pi\)
\(594\) 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 −0.000292806 1.00000i \(-0.500093\pi\)
1.00000 0.000292806i \(9.32030e-5\pi\)
\(600\) 0 0
\(601\) 12665.9 + 12665.9i 0.859656 + 0.859656i 0.991297 0.131641i \(-0.0420247\pi\)
−0.131641 + 0.991297i \(0.542025\pi\)
\(602\) 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 −0.977041 0.213053i \(-0.931659\pi\)
0.841523 + 0.540221i \(0.181659\pi\)
\(614\) 0 0
\(615\) −1838.77 1838.77i −0.120564 0.120564i
\(616\) 0 0
\(617\) 2198.69 2198.69i 0.143462 0.143462i −0.631728 0.775190i \(-0.717654\pi\)
0.775190 + 0.631728i \(0.217654\pi\)
\(618\) 0 0
\(619\) −14373.8 5953.83i −0.933331 0.386598i −0.136390 0.990655i \(-0.543550\pi\)
−0.796941 + 0.604057i \(0.793550\pi\)
\(620\) 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 0.418502 0.908216i \(-0.362555\pi\)
0.908216 0.418502i \(-0.137445\pi\)
\(632\) 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 −0.800368 0.599509i \(-0.795363\pi\)
−0.142029 + 0.989862i \(0.545363\pi\)
\(644\) 0 0
\(645\) 3841.29 9273.69i 0.234497 0.566126i
\(646\) 0 0
\(647\) 2866.06 + 2866.06i 0.174152 + 0.174152i 0.788801 0.614649i \(-0.210702\pi\)
−0.614649 + 0.788801i \(0.710702\pi\)
\(648\) 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 0.866453 0.499259i \(-0.166394\pi\)
−0.965704 + 0.259645i \(0.916394\pi\)
\(654\) 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 0.970170 + 0.242424i \(0.0779426\pi\)
−0.514594 + 0.857434i \(0.672057\pi\)
\(660\) 0 0
\(661\) 25591.1 + 10600.2i 1.50587 + 0.623751i 0.974700 0.223515i \(-0.0717533\pi\)
0.531168 + 0.847267i \(0.321753\pi\)
\(662\) 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 −0.930810 0.365503i \(-0.880897\pi\)
0.916632 + 0.399733i \(0.130897\pi\)
\(678\) 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 0.411187 0.911551i \(-0.365114\pi\)
−0.353811 + 0.935317i \(0.615114\pi\)
\(684\) 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 0.996124 + 0.0879632i \(0.0280358\pi\)
−0.642166 + 0.766565i \(0.721964\pi\)
\(692\) 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 0.239769 0.970830i \(-0.422928\pi\)
0.856023 + 0.516938i \(0.172928\pi\)
\(702\) 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 0.232527 + 0.972590i \(0.425301\pi\)
−0.852146 + 0.523304i \(0.824699\pi\)
\(710\) 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 \(0.0242173\pi\)
−0.997107 + 0.0760074i \(0.975783\pi\)
\(720\) 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 −0.345663 0.938359i \(-0.612346\pi\)
0.938359 + 0.345663i \(0.112346\pi\)
\(728\) 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 −0.150152 0.988663i \(-0.547976\pi\)
0.592917 + 0.805264i \(0.297976\pi\)
\(734\) 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 0.535721 0.844395i \(-0.320040\pi\)
0.975890 + 0.218265i \(0.0700397\pi\)
\(740\) 0 0
\(741\) 8003.13 19321.3i 0.396764 0.957874i
\(742\) 0 0
\(743\) −28118.1 28118.1i −1.38836 1.38836i −0.828765 0.559596i \(-0.810956\pi\)
−0.559596 0.828765i \(-0.689044\pi\)
\(744\) 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 \(-0.982981\pi\)
0.998571 0.0534428i \(-0.0170195\pi\)
\(752\) 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 0.420978 0.907071i \(-0.361687\pi\)
−0.343720 + 0.939072i \(0.611687\pi\)
\(758\) 0 0
\(759\) 12524.4 12524.4i 0.598955 0.598955i
\(760\) 0 0
\(761\) −13159.3 13159.3i −0.626837 0.626837i 0.320434 0.947271i \(-0.396171\pi\)
−0.947271 + 0.320434i \(0.896171\pi\)
\(762\) 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 −0.943526 0.331299i \(-0.892513\pi\)
0.901437 + 0.432909i \(0.142513\pi\)
\(774\) 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 0.998307 + 0.0581569i \(0.0185224\pi\)
−0.664787 + 0.747033i \(0.731478\pi\)
\(788\) 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
\(797\) −2646.36 + 1096.16i &m