Properties

Label 405.4.b.f.244.8
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.8
Root \(-0.473990i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.f.244.9

$q$-expansion

\(f(q)\) \(=\) \(q-0.473990i q^{2} +7.77533 q^{4} +(-10.6248 + 3.48041i) q^{5} -8.20657i q^{7} -7.47735i q^{8} +O(q^{10})\) \(q-0.473990i q^{2} +7.77533 q^{4} +(-10.6248 + 3.48041i) q^{5} -8.20657i q^{7} -7.47735i q^{8} +(1.64968 + 5.03606i) q^{10} -5.26583 q^{11} +77.0342i q^{13} -3.88983 q^{14} +58.6585 q^{16} -88.9397i q^{17} +91.7358 q^{19} +(-82.6115 + 27.0613i) q^{20} +2.49595i q^{22} +154.441i q^{23} +(100.774 - 73.9574i) q^{25} +36.5135 q^{26} -63.8088i q^{28} +168.303 q^{29} +72.7885 q^{31} -87.6223i q^{32} -42.1565 q^{34} +(28.5622 + 87.1933i) q^{35} +154.836i q^{37} -43.4818i q^{38} +(26.0242 + 79.4455i) q^{40} -7.95157 q^{41} -23.2014i q^{43} -40.9436 q^{44} +73.2034 q^{46} +301.398i q^{47} +275.652 q^{49} +(-35.0551 - 47.7657i) q^{50} +598.967i q^{52} +344.542i q^{53} +(55.9485 - 18.3272i) q^{55} -61.3634 q^{56} -79.7741i q^{58} +251.558 q^{59} +272.902 q^{61} -34.5010i q^{62} +427.736 q^{64} +(-268.110 - 818.475i) q^{65} -835.467i q^{67} -691.535i q^{68} +(41.3288 - 13.5382i) q^{70} -351.152 q^{71} +522.749i q^{73} +73.3909 q^{74} +713.276 q^{76} +43.2144i q^{77} +700.107 q^{79} +(-623.236 + 204.155i) q^{80} +3.76897i q^{82} -241.303i q^{83} +(309.546 + 944.968i) q^{85} -10.9972 q^{86} +39.3744i q^{88} +1021.39 q^{89} +632.187 q^{91} +1200.83i q^{92} +142.860 q^{94} +(-974.676 + 319.278i) q^{95} +389.284i q^{97} -130.656i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} + 3 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 54 q^{4} + 3 q^{5} - 10 q^{10} + 90 q^{11} - 102 q^{14} + 146 q^{16} - 4 q^{19} - 6 q^{20} - 71 q^{25} + 468 q^{26} - 516 q^{29} + 38 q^{31} - 212 q^{34} + 267 q^{35} - 44 q^{40} + 576 q^{41} - 1644 q^{44} - 290 q^{46} + 4 q^{49} + 558 q^{50} + 15 q^{55} + 2430 q^{56} - 2202 q^{59} + 20 q^{61} + 322 q^{64} + 339 q^{65} - 636 q^{70} + 2952 q^{71} - 4080 q^{74} - 396 q^{76} + 218 q^{79} - 1266 q^{80} + 704 q^{85} + 6108 q^{86} - 4074 q^{89} - 942 q^{91} + 1078 q^{94} - 1692 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.473990i 0.167581i −0.996483 0.0837904i \(-0.973297\pi\)
0.996483 0.0837904i \(-0.0267026\pi\)
\(3\) 0 0
\(4\) 7.77533 0.971917
\(5\) −10.6248 + 3.48041i −0.950313 + 0.311297i
\(6\) 0 0
\(7\) 8.20657i 0.443113i −0.975148 0.221557i \(-0.928886\pi\)
0.975148 0.221557i \(-0.0711138\pi\)
\(8\) 7.47735i 0.330455i
\(9\) 0 0
\(10\) 1.64968 + 5.03606i 0.0521674 + 0.159254i
\(11\) −5.26583 −0.144337 −0.0721685 0.997392i \(-0.522992\pi\)
−0.0721685 + 0.997392i \(0.522992\pi\)
\(12\) 0 0
\(13\) 77.0342i 1.64350i 0.569851 + 0.821748i \(0.307001\pi\)
−0.569851 + 0.821748i \(0.692999\pi\)
\(14\) −3.88983 −0.0742573
\(15\) 0 0
\(16\) 58.6585 0.916539
\(17\) 88.9397i 1.26888i −0.772970 0.634442i \(-0.781230\pi\)
0.772970 0.634442i \(-0.218770\pi\)
\(18\) 0 0
\(19\) 91.7358 1.10766 0.553832 0.832628i \(-0.313165\pi\)
0.553832 + 0.832628i \(0.313165\pi\)
\(20\) −82.6115 + 27.0613i −0.923625 + 0.302555i
\(21\) 0 0
\(22\) 2.49595i 0.0241881i
\(23\) 154.441i 1.40014i 0.714076 + 0.700068i \(0.246847\pi\)
−0.714076 + 0.700068i \(0.753153\pi\)
\(24\) 0 0
\(25\) 100.774 73.9574i 0.806188 0.591659i
\(26\) 36.5135 0.275418
\(27\) 0 0
\(28\) 63.8088i 0.430669i
\(29\) 168.303 1.07769 0.538847 0.842403i \(-0.318860\pi\)
0.538847 + 0.842403i \(0.318860\pi\)
\(30\) 0 0
\(31\) 72.7885 0.421716 0.210858 0.977517i \(-0.432374\pi\)
0.210858 + 0.977517i \(0.432374\pi\)
\(32\) 87.6223i 0.484050i
\(33\) 0 0
\(34\) −42.1565 −0.212641
\(35\) 28.5622 + 87.1933i 0.137940 + 0.421096i
\(36\) 0 0
\(37\) 154.836i 0.687971i 0.938975 + 0.343986i \(0.111777\pi\)
−0.938975 + 0.343986i \(0.888223\pi\)
\(38\) 43.4818i 0.185623i
\(39\) 0 0
\(40\) 26.0242 + 79.4455i 0.102870 + 0.314036i
\(41\) −7.95157 −0.0302885 −0.0151442 0.999885i \(-0.504821\pi\)
−0.0151442 + 0.999885i \(0.504821\pi\)
\(42\) 0 0
\(43\) 23.2014i 0.0822833i −0.999153 0.0411416i \(-0.986901\pi\)
0.999153 0.0411416i \(-0.0130995\pi\)
\(44\) −40.9436 −0.140284
\(45\) 0 0
\(46\) 73.2034 0.234636
\(47\) 301.398i 0.935392i 0.883889 + 0.467696i \(0.154916\pi\)
−0.883889 + 0.467696i \(0.845084\pi\)
\(48\) 0 0
\(49\) 275.652 0.803651
\(50\) −35.0551 47.7657i −0.0991507 0.135102i
\(51\) 0 0
\(52\) 598.967i 1.59734i
\(53\) 344.542i 0.892952i 0.894796 + 0.446476i \(0.147321\pi\)
−0.894796 + 0.446476i \(0.852679\pi\)
\(54\) 0 0
\(55\) 55.9485 18.3272i 0.137165 0.0449317i
\(56\) −61.3634 −0.146429
\(57\) 0 0
\(58\) 79.7741i 0.180601i
\(59\) 251.558 0.555085 0.277542 0.960713i \(-0.410480\pi\)
0.277542 + 0.960713i \(0.410480\pi\)
\(60\) 0 0
\(61\) 272.902 0.572811 0.286406 0.958108i \(-0.407539\pi\)
0.286406 + 0.958108i \(0.407539\pi\)
\(62\) 34.5010i 0.0706715i
\(63\) 0 0
\(64\) 427.736 0.835421
\(65\) −268.110 818.475i −0.511616 1.56184i
\(66\) 0 0
\(67\) 835.467i 1.52341i −0.647923 0.761706i \(-0.724362\pi\)
0.647923 0.761706i \(-0.275638\pi\)
\(68\) 691.535i 1.23325i
\(69\) 0 0
\(70\) 41.3288 13.5382i 0.0705676 0.0231161i
\(71\) −351.152 −0.586959 −0.293479 0.955965i \(-0.594813\pi\)
−0.293479 + 0.955965i \(0.594813\pi\)
\(72\) 0 0
\(73\) 522.749i 0.838126i 0.907957 + 0.419063i \(0.137641\pi\)
−0.907957 + 0.419063i \(0.862359\pi\)
\(74\) 73.3909 0.115291
\(75\) 0 0
\(76\) 713.276 1.07656
\(77\) 43.2144i 0.0639576i
\(78\) 0 0
\(79\) 700.107 0.997065 0.498533 0.866871i \(-0.333872\pi\)
0.498533 + 0.866871i \(0.333872\pi\)
\(80\) −623.236 + 204.155i −0.870998 + 0.285316i
\(81\) 0 0
\(82\) 3.76897i 0.00507577i
\(83\) 241.303i 0.319113i −0.987189 0.159557i \(-0.948994\pi\)
0.987189 0.159557i \(-0.0510065\pi\)
\(84\) 0 0
\(85\) 309.546 + 944.968i 0.395000 + 1.20584i
\(86\) −10.9972 −0.0137891
\(87\) 0 0
\(88\) 39.3744i 0.0476969i
\(89\) 1021.39 1.21648 0.608242 0.793752i \(-0.291875\pi\)
0.608242 + 0.793752i \(0.291875\pi\)
\(90\) 0 0
\(91\) 632.187 0.728255
\(92\) 1200.83i 1.36082i
\(93\) 0 0
\(94\) 142.860 0.156754
\(95\) −974.676 + 319.278i −1.05263 + 0.344813i
\(96\) 0 0
\(97\) 389.284i 0.407483i 0.979025 + 0.203741i \(0.0653102\pi\)
−0.979025 + 0.203741i \(0.934690\pi\)
\(98\) 130.656i 0.134676i
\(99\) 0 0
\(100\) 783.548 575.043i 0.783548 0.575043i
\(101\) 864.519 0.851712 0.425856 0.904791i \(-0.359973\pi\)
0.425856 + 0.904791i \(0.359973\pi\)
\(102\) 0 0
\(103\) 1228.21i 1.17494i 0.809246 + 0.587470i \(0.199876\pi\)
−0.809246 + 0.587470i \(0.800124\pi\)
\(104\) 576.012 0.543102
\(105\) 0 0
\(106\) 163.309 0.149642
\(107\) 1860.34i 1.68080i −0.541963 0.840402i \(-0.682319\pi\)
0.541963 0.840402i \(-0.317681\pi\)
\(108\) 0 0
\(109\) −1037.31 −0.911524 −0.455762 0.890102i \(-0.650633\pi\)
−0.455762 + 0.890102i \(0.650633\pi\)
\(110\) −8.68692 26.5190i −0.00752969 0.0229863i
\(111\) 0 0
\(112\) 481.385i 0.406130i
\(113\) 1407.73i 1.17193i 0.810335 + 0.585967i \(0.199285\pi\)
−0.810335 + 0.585967i \(0.800715\pi\)
\(114\) 0 0
\(115\) −537.517 1640.90i −0.435858 1.33057i
\(116\) 1308.61 1.04743
\(117\) 0 0
\(118\) 119.236i 0.0930215i
\(119\) −729.890 −0.562259
\(120\) 0 0
\(121\) −1303.27 −0.979167
\(122\) 129.353i 0.0959922i
\(123\) 0 0
\(124\) 565.955 0.409873
\(125\) −813.299 + 1136.52i −0.581949 + 0.813225i
\(126\) 0 0
\(127\) 198.654i 0.138801i 0.997589 + 0.0694005i \(0.0221086\pi\)
−0.997589 + 0.0694005i \(0.977891\pi\)
\(128\) 903.721i 0.624050i
\(129\) 0 0
\(130\) −387.949 + 127.082i −0.261734 + 0.0857369i
\(131\) 1452.18 0.968532 0.484266 0.874921i \(-0.339087\pi\)
0.484266 + 0.874921i \(0.339087\pi\)
\(132\) 0 0
\(133\) 752.836i 0.490821i
\(134\) −396.003 −0.255295
\(135\) 0 0
\(136\) −665.033 −0.419310
\(137\) 636.656i 0.397030i 0.980098 + 0.198515i \(0.0636119\pi\)
−0.980098 + 0.198515i \(0.936388\pi\)
\(138\) 0 0
\(139\) −1523.24 −0.929494 −0.464747 0.885444i \(-0.653855\pi\)
−0.464747 + 0.885444i \(0.653855\pi\)
\(140\) 222.081 + 677.957i 0.134066 + 0.409270i
\(141\) 0 0
\(142\) 166.443i 0.0983630i
\(143\) 405.649i 0.237217i
\(144\) 0 0
\(145\) −1788.19 + 585.764i −1.02415 + 0.335483i
\(146\) 247.778 0.140454
\(147\) 0 0
\(148\) 1203.90i 0.668651i
\(149\) −2102.60 −1.15605 −0.578027 0.816018i \(-0.696177\pi\)
−0.578027 + 0.816018i \(0.696177\pi\)
\(150\) 0 0
\(151\) −2360.50 −1.27215 −0.636074 0.771628i \(-0.719443\pi\)
−0.636074 + 0.771628i \(0.719443\pi\)
\(152\) 685.940i 0.366034i
\(153\) 0 0
\(154\) 20.4832 0.0107181
\(155\) −773.365 + 253.334i −0.400762 + 0.131279i
\(156\) 0 0
\(157\) 2004.19i 1.01880i −0.860530 0.509400i \(-0.829868\pi\)
0.860530 0.509400i \(-0.170132\pi\)
\(158\) 331.844i 0.167089i
\(159\) 0 0
\(160\) 304.961 + 930.971i 0.150683 + 0.459998i
\(161\) 1267.43 0.620419
\(162\) 0 0
\(163\) 2772.38i 1.33220i −0.745861 0.666102i \(-0.767962\pi\)
0.745861 0.666102i \(-0.232038\pi\)
\(164\) −61.8261 −0.0294379
\(165\) 0 0
\(166\) −114.375 −0.0534773
\(167\) 1846.33i 0.855529i −0.903890 0.427764i \(-0.859301\pi\)
0.903890 0.427764i \(-0.140699\pi\)
\(168\) 0 0
\(169\) −3737.27 −1.70108
\(170\) 447.905 146.722i 0.202075 0.0661944i
\(171\) 0 0
\(172\) 180.399i 0.0799725i
\(173\) 193.172i 0.0848937i −0.999099 0.0424469i \(-0.986485\pi\)
0.999099 0.0424469i \(-0.0135153\pi\)
\(174\) 0 0
\(175\) −606.936 827.005i −0.262172 0.357233i
\(176\) −308.886 −0.132290
\(177\) 0 0
\(178\) 484.128i 0.203859i
\(179\) −3931.26 −1.64154 −0.820770 0.571258i \(-0.806456\pi\)
−0.820770 + 0.571258i \(0.806456\pi\)
\(180\) 0 0
\(181\) −1921.32 −0.789007 −0.394503 0.918894i \(-0.629083\pi\)
−0.394503 + 0.918894i \(0.629083\pi\)
\(182\) 299.650i 0.122042i
\(183\) 0 0
\(184\) 1154.81 0.462682
\(185\) −538.894 1645.11i −0.214163 0.653788i
\(186\) 0 0
\(187\) 468.341i 0.183147i
\(188\) 2343.47i 0.909123i
\(189\) 0 0
\(190\) 151.334 + 461.987i 0.0577840 + 0.176400i
\(191\) 1507.83 0.571219 0.285609 0.958346i \(-0.407804\pi\)
0.285609 + 0.958346i \(0.407804\pi\)
\(192\) 0 0
\(193\) 4065.65i 1.51633i −0.652061 0.758166i \(-0.726096\pi\)
0.652061 0.758166i \(-0.273904\pi\)
\(194\) 184.517 0.0682863
\(195\) 0 0
\(196\) 2143.29 0.781082
\(197\) 3916.67i 1.41650i 0.705960 + 0.708252i \(0.250516\pi\)
−0.705960 + 0.708252i \(0.749484\pi\)
\(198\) 0 0
\(199\) −615.676 −0.219317 −0.109659 0.993969i \(-0.534976\pi\)
−0.109659 + 0.993969i \(0.534976\pi\)
\(200\) −553.005 753.519i −0.195517 0.266409i
\(201\) 0 0
\(202\) 409.773i 0.142730i
\(203\) 1381.19i 0.477541i
\(204\) 0 0
\(205\) 84.4840 27.6747i 0.0287835 0.00942871i
\(206\) 582.157 0.196897
\(207\) 0 0
\(208\) 4518.71i 1.50633i
\(209\) −483.065 −0.159877
\(210\) 0 0
\(211\) −2233.49 −0.728719 −0.364360 0.931258i \(-0.618712\pi\)
−0.364360 + 0.931258i \(0.618712\pi\)
\(212\) 2678.93i 0.867875i
\(213\) 0 0
\(214\) −881.784 −0.281670
\(215\) 80.7503 + 246.511i 0.0256145 + 0.0781948i
\(216\) 0 0
\(217\) 597.344i 0.186868i
\(218\) 491.674i 0.152754i
\(219\) 0 0
\(220\) 435.018 142.500i 0.133313 0.0436698i
\(221\) 6851.40 2.08541
\(222\) 0 0
\(223\) 4630.44i 1.39048i 0.718778 + 0.695240i \(0.244702\pi\)
−0.718778 + 0.695240i \(0.755298\pi\)
\(224\) −719.079 −0.214489
\(225\) 0 0
\(226\) 667.252 0.196394
\(227\) 467.693i 0.136748i −0.997660 0.0683741i \(-0.978219\pi\)
0.997660 0.0683741i \(-0.0217812\pi\)
\(228\) 0 0
\(229\) −1457.15 −0.420485 −0.210242 0.977649i \(-0.567425\pi\)
−0.210242 + 0.977649i \(0.567425\pi\)
\(230\) −777.773 + 254.777i −0.222977 + 0.0730414i
\(231\) 0 0
\(232\) 1258.46i 0.356130i
\(233\) 2617.43i 0.735938i −0.929838 0.367969i \(-0.880053\pi\)
0.929838 0.367969i \(-0.119947\pi\)
\(234\) 0 0
\(235\) −1048.99 3202.30i −0.291185 0.888915i
\(236\) 1955.94 0.539496
\(237\) 0 0
\(238\) 345.960i 0.0942239i
\(239\) −3711.16 −1.00441 −0.502207 0.864748i \(-0.667478\pi\)
−0.502207 + 0.864748i \(0.667478\pi\)
\(240\) 0 0
\(241\) −1844.11 −0.492902 −0.246451 0.969155i \(-0.579264\pi\)
−0.246451 + 0.969155i \(0.579264\pi\)
\(242\) 617.737i 0.164090i
\(243\) 0 0
\(244\) 2121.90 0.556725
\(245\) −2928.75 + 959.382i −0.763719 + 0.250174i
\(246\) 0 0
\(247\) 7066.80i 1.82044i
\(248\) 544.265i 0.139358i
\(249\) 0 0
\(250\) 538.698 + 385.496i 0.136281 + 0.0975235i
\(251\) 7204.10 1.81163 0.905815 0.423674i \(-0.139260\pi\)
0.905815 + 0.423674i \(0.139260\pi\)
\(252\) 0 0
\(253\) 813.259i 0.202091i
\(254\) 94.1602 0.0232604
\(255\) 0 0
\(256\) 2993.53 0.730842
\(257\) 1757.15i 0.426489i 0.976999 + 0.213245i \(0.0684031\pi\)
−0.976999 + 0.213245i \(0.931597\pi\)
\(258\) 0 0
\(259\) 1270.68 0.304849
\(260\) −2084.65 6363.92i −0.497248 1.51797i
\(261\) 0 0
\(262\) 688.319i 0.162307i
\(263\) 5356.91i 1.25597i 0.778224 + 0.627987i \(0.216121\pi\)
−0.778224 + 0.627987i \(0.783879\pi\)
\(264\) 0 0
\(265\) −1199.15 3660.69i −0.277973 0.848584i
\(266\) −356.837 −0.0822521
\(267\) 0 0
\(268\) 6496.04i 1.48063i
\(269\) −1040.60 −0.235860 −0.117930 0.993022i \(-0.537626\pi\)
−0.117930 + 0.993022i \(0.537626\pi\)
\(270\) 0 0
\(271\) −1531.38 −0.343265 −0.171632 0.985161i \(-0.554904\pi\)
−0.171632 + 0.985161i \(0.554904\pi\)
\(272\) 5217.06i 1.16298i
\(273\) 0 0
\(274\) 301.768 0.0665347
\(275\) −530.656 + 389.447i −0.116363 + 0.0853983i
\(276\) 0 0
\(277\) 6231.09i 1.35159i −0.737090 0.675794i \(-0.763801\pi\)
0.737090 0.675794i \(-0.236199\pi\)
\(278\) 722.001i 0.155765i
\(279\) 0 0
\(280\) 651.975 213.570i 0.139153 0.0455829i
\(281\) 9113.95 1.93485 0.967425 0.253157i \(-0.0814690\pi\)
0.967425 + 0.253157i \(0.0814690\pi\)
\(282\) 0 0
\(283\) 1515.09i 0.318243i 0.987259 + 0.159122i \(0.0508662\pi\)
−0.987259 + 0.159122i \(0.949134\pi\)
\(284\) −2730.32 −0.570475
\(285\) 0 0
\(286\) −192.274 −0.0397531
\(287\) 65.2552i 0.0134212i
\(288\) 0 0
\(289\) −2997.26 −0.610067
\(290\) 277.646 + 847.586i 0.0562205 + 0.171627i
\(291\) 0 0
\(292\) 4064.55i 0.814588i
\(293\) 1384.30i 0.276013i 0.990431 + 0.138006i \(0.0440694\pi\)
−0.990431 + 0.138006i \(0.955931\pi\)
\(294\) 0 0
\(295\) −2672.75 + 875.522i −0.527504 + 0.172796i
\(296\) 1157.77 0.227344
\(297\) 0 0
\(298\) 996.613i 0.193732i
\(299\) −11897.2 −2.30112
\(300\) 0 0
\(301\) −190.404 −0.0364608
\(302\) 1118.85i 0.213188i
\(303\) 0 0
\(304\) 5381.08 1.01522
\(305\) −2899.53 + 949.809i −0.544350 + 0.178314i
\(306\) 0 0
\(307\) 1628.16i 0.302685i −0.988481 0.151342i \(-0.951640\pi\)
0.988481 0.151342i \(-0.0483596\pi\)
\(308\) 336.006i 0.0621615i
\(309\) 0 0
\(310\) 120.078 + 366.567i 0.0219998 + 0.0671600i
\(311\) 1406.63 0.256471 0.128236 0.991744i \(-0.459069\pi\)
0.128236 + 0.991744i \(0.459069\pi\)
\(312\) 0 0
\(313\) 5431.54i 0.980858i 0.871481 + 0.490429i \(0.163160\pi\)
−0.871481 + 0.490429i \(0.836840\pi\)
\(314\) −949.964 −0.170731
\(315\) 0 0
\(316\) 5443.56 0.969065
\(317\) 7681.60i 1.36101i −0.732741 0.680507i \(-0.761760\pi\)
0.732741 0.680507i \(-0.238240\pi\)
\(318\) 0 0
\(319\) −886.257 −0.155551
\(320\) −4544.61 + 1488.69i −0.793911 + 0.260064i
\(321\) 0 0
\(322\) 600.749i 0.103970i
\(323\) 8158.95i 1.40550i
\(324\) 0 0
\(325\) 5697.25 + 7763.01i 0.972389 + 1.32497i
\(326\) −1314.08 −0.223252
\(327\) 0 0
\(328\) 59.4567i 0.0100090i
\(329\) 2473.44 0.414485
\(330\) 0 0
\(331\) 4128.88 0.685630 0.342815 0.939403i \(-0.388620\pi\)
0.342815 + 0.939403i \(0.388620\pi\)
\(332\) 1876.21i 0.310152i
\(333\) 0 0
\(334\) −875.142 −0.143370
\(335\) 2907.77 + 8876.69i 0.474234 + 1.44772i
\(336\) 0 0
\(337\) 2624.15i 0.424174i 0.977251 + 0.212087i \(0.0680260\pi\)
−0.977251 + 0.212087i \(0.931974\pi\)
\(338\) 1771.43i 0.285068i
\(339\) 0 0
\(340\) 2406.82 + 7347.44i 0.383907 + 1.17197i
\(341\) −383.292 −0.0608693
\(342\) 0 0
\(343\) 5077.01i 0.799221i
\(344\) −173.485 −0.0271909
\(345\) 0 0
\(346\) −91.5617 −0.0142266
\(347\) 6914.81i 1.06976i −0.844928 0.534880i \(-0.820357\pi\)
0.844928 0.534880i \(-0.179643\pi\)
\(348\) 0 0
\(349\) 2660.41 0.408047 0.204024 0.978966i \(-0.434598\pi\)
0.204024 + 0.978966i \(0.434598\pi\)
\(350\) −391.992 + 287.682i −0.0598653 + 0.0439350i
\(351\) 0 0
\(352\) 461.404i 0.0698663i
\(353\) 4517.49i 0.681139i −0.940219 0.340569i \(-0.889380\pi\)
0.940219 0.340569i \(-0.110620\pi\)
\(354\) 0 0
\(355\) 3730.93 1222.15i 0.557794 0.182719i
\(356\) 7941.64 1.18232
\(357\) 0 0
\(358\) 1863.38i 0.275091i
\(359\) 2702.34 0.397281 0.198640 0.980072i \(-0.436347\pi\)
0.198640 + 0.980072i \(0.436347\pi\)
\(360\) 0 0
\(361\) 1556.45 0.226921
\(362\) 910.684i 0.132222i
\(363\) 0 0
\(364\) 4915.46 0.707803
\(365\) −1819.38 5554.12i −0.260906 0.796481i
\(366\) 0 0
\(367\) 3538.31i 0.503265i −0.967823 0.251632i \(-0.919033\pi\)
0.967823 0.251632i \(-0.0809674\pi\)
\(368\) 9059.26i 1.28328i
\(369\) 0 0
\(370\) −779.765 + 255.430i −0.109562 + 0.0358897i
\(371\) 2827.51 0.395679
\(372\) 0 0
\(373\) 5729.89i 0.795395i −0.917517 0.397697i \(-0.869809\pi\)
0.917517 0.397697i \(-0.130191\pi\)
\(374\) 221.989 0.0306919
\(375\) 0 0
\(376\) 2253.66 0.309105
\(377\) 12965.1i 1.77119i
\(378\) 0 0
\(379\) 8727.59 1.18287 0.591433 0.806354i \(-0.298563\pi\)
0.591433 + 0.806354i \(0.298563\pi\)
\(380\) −7578.43 + 2482.49i −1.02307 + 0.335129i
\(381\) 0 0
\(382\) 714.696i 0.0957252i
\(383\) 4562.80i 0.608742i 0.952554 + 0.304371i \(0.0984462\pi\)
−0.952554 + 0.304371i \(0.901554\pi\)
\(384\) 0 0
\(385\) −150.404 459.145i −0.0199098 0.0607797i
\(386\) −1927.08 −0.254108
\(387\) 0 0
\(388\) 3026.82i 0.396039i
\(389\) 12084.4 1.57507 0.787536 0.616269i \(-0.211357\pi\)
0.787536 + 0.616269i \(0.211357\pi\)
\(390\) 0 0
\(391\) 13735.9 1.77661
\(392\) 2061.15i 0.265571i
\(393\) 0 0
\(394\) 1856.46 0.237379
\(395\) −7438.51 + 2436.66i −0.947524 + 0.310383i
\(396\) 0 0
\(397\) 5880.63i 0.743426i 0.928348 + 0.371713i \(0.121230\pi\)
−0.928348 + 0.371713i \(0.878770\pi\)
\(398\) 291.824i 0.0367533i
\(399\) 0 0
\(400\) 5911.22 4338.23i 0.738903 0.542278i
\(401\) −3295.11 −0.410350 −0.205175 0.978725i \(-0.565776\pi\)
−0.205175 + 0.978725i \(0.565776\pi\)
\(402\) 0 0
\(403\) 5607.21i 0.693089i
\(404\) 6721.92 0.827793
\(405\) 0 0
\(406\) −654.672 −0.0800267
\(407\) 815.342i 0.0992997i
\(408\) 0 0
\(409\) 6217.42 0.751667 0.375834 0.926687i \(-0.377356\pi\)
0.375834 + 0.926687i \(0.377356\pi\)
\(410\) −13.1175 40.0446i −0.00158007 0.00482356i
\(411\) 0 0
\(412\) 9549.71i 1.14194i
\(413\) 2064.42i 0.245965i
\(414\) 0 0
\(415\) 839.831 + 2563.80i 0.0993390 + 0.303257i
\(416\) 6749.92 0.795534
\(417\) 0 0
\(418\) 228.968i 0.0267923i
\(419\) 1740.28 0.202908 0.101454 0.994840i \(-0.467651\pi\)
0.101454 + 0.994840i \(0.467651\pi\)
\(420\) 0 0
\(421\) −1284.58 −0.148709 −0.0743544 0.997232i \(-0.523690\pi\)
−0.0743544 + 0.997232i \(0.523690\pi\)
\(422\) 1058.65i 0.122119i
\(423\) 0 0
\(424\) 2576.26 0.295081
\(425\) −6577.74 8962.76i −0.750747 1.02296i
\(426\) 0 0
\(427\) 2239.59i 0.253820i
\(428\) 14464.8i 1.63360i
\(429\) 0 0
\(430\) 116.844 38.2748i 0.0131040 0.00429250i
\(431\) 11917.4 1.33189 0.665943 0.746003i \(-0.268030\pi\)
0.665943 + 0.746003i \(0.268030\pi\)
\(432\) 0 0
\(433\) 1603.61i 0.177978i 0.996033 + 0.0889889i \(0.0283636\pi\)
−0.996033 + 0.0889889i \(0.971636\pi\)
\(434\) −283.135 −0.0313155
\(435\) 0 0
\(436\) −8065.42 −0.885925
\(437\) 14167.7i 1.55088i
\(438\) 0 0
\(439\) −1816.45 −0.197482 −0.0987409 0.995113i \(-0.531482\pi\)
−0.0987409 + 0.995113i \(0.531482\pi\)
\(440\) −137.039 418.346i −0.0148479 0.0453270i
\(441\) 0 0
\(442\) 3247.49i 0.349474i
\(443\) 2265.28i 0.242950i 0.992594 + 0.121475i \(0.0387624\pi\)
−0.992594 + 0.121475i \(0.961238\pi\)
\(444\) 0 0
\(445\) −10852.1 + 3554.85i −1.15604 + 0.378688i
\(446\) 2194.78 0.233018
\(447\) 0 0
\(448\) 3510.24i 0.370186i
\(449\) −13259.9 −1.39371 −0.696854 0.717213i \(-0.745417\pi\)
−0.696854 + 0.717213i \(0.745417\pi\)
\(450\) 0 0
\(451\) 41.8716 0.00437175
\(452\) 10945.6i 1.13902i
\(453\) 0 0
\(454\) −221.682 −0.0229164
\(455\) −6716.87 + 2200.27i −0.692070 + 0.226704i
\(456\) 0 0
\(457\) 131.858i 0.0134968i −0.999977 0.00674840i \(-0.997852\pi\)
0.999977 0.00674840i \(-0.00214810\pi\)
\(458\) 690.673i 0.0704652i
\(459\) 0 0
\(460\) −4179.37 12758.6i −0.423618 1.29320i
\(461\) −12782.5 −1.29141 −0.645705 0.763587i \(-0.723436\pi\)
−0.645705 + 0.763587i \(0.723436\pi\)
\(462\) 0 0
\(463\) 4621.41i 0.463877i 0.972730 + 0.231939i \(0.0745069\pi\)
−0.972730 + 0.231939i \(0.925493\pi\)
\(464\) 9872.42 0.987749
\(465\) 0 0
\(466\) −1240.64 −0.123329
\(467\) 5550.68i 0.550010i −0.961443 0.275005i \(-0.911320\pi\)
0.961443 0.275005i \(-0.0886795\pi\)
\(468\) 0 0
\(469\) −6856.32 −0.675044
\(470\) −1517.86 + 497.210i −0.148965 + 0.0487970i
\(471\) 0 0
\(472\) 1880.98i 0.183431i
\(473\) 122.175i 0.0118765i
\(474\) 0 0
\(475\) 9244.54 6784.54i 0.892986 0.655360i
\(476\) −5675.13 −0.546469
\(477\) 0 0
\(478\) 1759.05i 0.168320i
\(479\) 1941.39 0.185186 0.0925932 0.995704i \(-0.470484\pi\)
0.0925932 + 0.995704i \(0.470484\pi\)
\(480\) 0 0
\(481\) −11927.7 −1.13068
\(482\) 874.088i 0.0826008i
\(483\) 0 0
\(484\) −10133.4 −0.951669
\(485\) −1354.87 4136.08i −0.126848 0.387236i
\(486\) 0 0
\(487\) 178.136i 0.0165752i −0.999966 0.00828761i \(-0.997362\pi\)
0.999966 0.00828761i \(-0.00263806\pi\)
\(488\) 2040.58i 0.189289i
\(489\) 0 0
\(490\) 454.737 + 1388.20i 0.0419244 + 0.127985i
\(491\) 5591.59 0.513941 0.256971 0.966419i \(-0.417276\pi\)
0.256971 + 0.966419i \(0.417276\pi\)
\(492\) 0 0
\(493\) 14968.8i 1.36747i
\(494\) 3349.59 0.305071
\(495\) 0 0
\(496\) 4269.66 0.386519
\(497\) 2881.75i 0.260089i
\(498\) 0 0
\(499\) −11367.0 −1.01976 −0.509879 0.860246i \(-0.670310\pi\)
−0.509879 + 0.860246i \(0.670310\pi\)
\(500\) −6323.67 + 8836.80i −0.565606 + 0.790387i
\(501\) 0 0
\(502\) 3414.67i 0.303594i
\(503\) 9225.98i 0.817825i −0.912574 0.408913i \(-0.865908\pi\)
0.912574 0.408913i \(-0.134092\pi\)
\(504\) 0 0
\(505\) −9185.36 + 3008.88i −0.809392 + 0.265135i
\(506\) −385.476 −0.0338666
\(507\) 0 0
\(508\) 1544.60i 0.134903i
\(509\) −18313.4 −1.59475 −0.797376 0.603483i \(-0.793779\pi\)
−0.797376 + 0.603483i \(0.793779\pi\)
\(510\) 0 0
\(511\) 4289.98 0.371384
\(512\) 8648.67i 0.746525i
\(513\) 0 0
\(514\) 832.870 0.0714714
\(515\) −4274.66 13049.5i −0.365755 1.11656i
\(516\) 0 0
\(517\) 1587.11i 0.135012i
\(518\) 602.288i 0.0510869i
\(519\) 0 0
\(520\) −6120.02 + 2004.76i −0.516117 + 0.169066i
\(521\) 11305.4 0.950670 0.475335 0.879805i \(-0.342327\pi\)
0.475335 + 0.879805i \(0.342327\pi\)
\(522\) 0 0
\(523\) 2825.92i 0.236269i −0.992998 0.118135i \(-0.962309\pi\)
0.992998 0.118135i \(-0.0376914\pi\)
\(524\) 11291.2 0.941332
\(525\) 0 0
\(526\) 2539.12 0.210477
\(527\) 6473.78i 0.535109i
\(528\) 0 0
\(529\) −11684.9 −0.960380
\(530\) −1735.13 + 568.383i −0.142206 + 0.0465830i
\(531\) 0 0
\(532\) 5853.55i 0.477037i
\(533\) 612.543i 0.0497790i
\(534\) 0 0
\(535\) 6474.75 + 19765.8i 0.523229 + 1.59729i
\(536\) −6247.08 −0.503420
\(537\) 0 0
\(538\) 493.233i 0.0395256i
\(539\) −1451.54 −0.115997
\(540\) 0 0
\(541\) −20588.2 −1.63615 −0.818075 0.575112i \(-0.804959\pi\)
−0.818075 + 0.575112i \(0.804959\pi\)
\(542\) 725.859i 0.0575246i
\(543\) 0 0
\(544\) −7793.10 −0.614203
\(545\) 11021.2 3610.25i 0.866233 0.283755i
\(546\) 0 0
\(547\) 4353.95i 0.340332i 0.985415 + 0.170166i \(0.0544303\pi\)
−0.985415 + 0.170166i \(0.945570\pi\)
\(548\) 4950.21i 0.385881i
\(549\) 0 0
\(550\) 184.594 + 251.526i 0.0143111 + 0.0195002i
\(551\) 15439.4 1.19372
\(552\) 0 0
\(553\) 5745.48i 0.441813i
\(554\) −2953.48 −0.226500
\(555\) 0 0
\(556\) −11843.7 −0.903391
\(557\) 22267.5i 1.69390i −0.531672 0.846951i \(-0.678436\pi\)
0.531672 0.846951i \(-0.321564\pi\)
\(558\) 0 0
\(559\) 1787.30 0.135232
\(560\) 1675.42 + 5114.63i 0.126427 + 0.385951i
\(561\) 0 0
\(562\) 4319.92i 0.324244i
\(563\) 23010.8i 1.72254i 0.508148 + 0.861270i \(0.330330\pi\)
−0.508148 + 0.861270i \(0.669670\pi\)
\(564\) 0 0
\(565\) −4899.49 14956.9i −0.364820 1.11370i
\(566\) 718.139 0.0533315
\(567\) 0 0
\(568\) 2625.69i 0.193964i
\(569\) −14244.0 −1.04945 −0.524726 0.851271i \(-0.675832\pi\)
−0.524726 + 0.851271i \(0.675832\pi\)
\(570\) 0 0
\(571\) −4793.42 −0.351310 −0.175655 0.984452i \(-0.556204\pi\)
−0.175655 + 0.984452i \(0.556204\pi\)
\(572\) 3154.06i 0.230556i
\(573\) 0 0
\(574\) 30.9303 0.00224914
\(575\) 11422.0 + 15563.5i 0.828403 + 1.12877i
\(576\) 0 0
\(577\) 6617.46i 0.477450i 0.971087 + 0.238725i \(0.0767294\pi\)
−0.971087 + 0.238725i \(0.923271\pi\)
\(578\) 1420.67i 0.102236i
\(579\) 0 0
\(580\) −13903.8 + 4554.51i −0.995386 + 0.326062i
\(581\) −1980.27 −0.141403
\(582\) 0 0
\(583\) 1814.30i 0.128886i
\(584\) 3908.78 0.276963
\(585\) 0 0
\(586\) 656.145 0.0462544
\(587\) 16455.4i 1.15705i 0.815665 + 0.578524i \(0.196371\pi\)
−0.815665 + 0.578524i \(0.803629\pi\)
\(588\) 0 0
\(589\) 6677.31 0.467120
\(590\) 414.989 + 1266.86i 0.0289573 + 0.0883996i
\(591\) 0 0
\(592\) 9082.47i 0.630552i
\(593\) 15990.1i 1.10731i 0.832746 + 0.553655i \(0.186767\pi\)
−0.832746 + 0.553655i \(0.813233\pi\)
\(594\) 0 0
\(595\) 7754.94 2540.31i 0.534322 0.175030i
\(596\) −16348.4 −1.12359
\(597\) 0 0
\(598\) 5639.17i 0.385623i
\(599\) 20460.9 1.39567 0.697836 0.716257i \(-0.254146\pi\)
0.697836 + 0.716257i \(0.254146\pi\)
\(600\) 0 0
\(601\) −641.739 −0.0435559 −0.0217779 0.999763i \(-0.506933\pi\)
−0.0217779 + 0.999763i \(0.506933\pi\)
\(602\) 90.2496i 0.00611013i
\(603\) 0 0
\(604\) −18353.6 −1.23642
\(605\) 13847.0 4535.91i 0.930515 0.304812i
\(606\) 0 0
\(607\) 18751.3i 1.25386i −0.779077 0.626928i \(-0.784312\pi\)
0.779077 0.626928i \(-0.215688\pi\)
\(608\) 8038.10i 0.536165i
\(609\) 0 0
\(610\) 450.200 + 1374.35i 0.0298821 + 0.0912226i
\(611\) −23218.0 −1.53731
\(612\) 0 0
\(613\) 24213.4i 1.59538i −0.603067 0.797690i \(-0.706055\pi\)
0.603067 0.797690i \(-0.293945\pi\)
\(614\) −771.733 −0.0507241
\(615\) 0 0
\(616\) 323.129 0.0211351
\(617\) 15870.9i 1.03556i −0.855515 0.517779i \(-0.826759\pi\)
0.855515 0.517779i \(-0.173241\pi\)
\(618\) 0 0
\(619\) 24434.2 1.58658 0.793289 0.608846i \(-0.208367\pi\)
0.793289 + 0.608846i \(0.208367\pi\)
\(620\) −6013.17 + 1969.75i −0.389508 + 0.127592i
\(621\) 0 0
\(622\) 666.727i 0.0429796i
\(623\) 8382.11i 0.539040i
\(624\) 0 0
\(625\) 4685.61 14905.9i 0.299879 0.953977i
\(626\) 2574.49 0.164373
\(627\) 0 0
\(628\) 15583.2i 0.990188i
\(629\) 13771.1 0.872956
\(630\) 0 0
\(631\) 22573.7 1.42416 0.712079 0.702099i \(-0.247754\pi\)
0.712079 + 0.702099i \(0.247754\pi\)
\(632\) 5234.94i 0.329486i
\(633\) 0 0
\(634\) −3641.00 −0.228080
\(635\) −691.398 2110.67i −0.0432083 0.131904i
\(636\) 0 0
\(637\) 21234.7i 1.32080i
\(638\) 420.077i 0.0260674i
\(639\) 0 0
\(640\) 3145.32 + 9601.87i 0.194265 + 0.593043i
\(641\) 3722.30 0.229364 0.114682 0.993402i \(-0.463415\pi\)
0.114682 + 0.993402i \(0.463415\pi\)
\(642\) 0 0
\(643\) 2998.76i 0.183919i 0.995763 + 0.0919593i \(0.0293130\pi\)
−0.995763 + 0.0919593i \(0.970687\pi\)
\(644\) 9854.68 0.602995
\(645\) 0 0
\(646\) −3867.26 −0.235535
\(647\) 4302.38i 0.261428i 0.991420 + 0.130714i \(0.0417270\pi\)
−0.991420 + 0.130714i \(0.958273\pi\)
\(648\) 0 0
\(649\) −1324.66 −0.0801193
\(650\) 3679.59 2700.44i 0.222039 0.162954i
\(651\) 0 0
\(652\) 21556.1i 1.29479i
\(653\) 801.281i 0.0480192i 0.999712 + 0.0240096i \(0.00764323\pi\)
−0.999712 + 0.0240096i \(0.992357\pi\)
\(654\) 0 0
\(655\) −15429.2 + 5054.18i −0.920408 + 0.301501i
\(656\) −466.427 −0.0277606
\(657\) 0 0
\(658\) 1172.39i 0.0694596i
\(659\) −7456.39 −0.440759 −0.220379 0.975414i \(-0.570730\pi\)
−0.220379 + 0.975414i \(0.570730\pi\)
\(660\) 0 0
\(661\) 2665.06 0.156821 0.0784106 0.996921i \(-0.475015\pi\)
0.0784106 + 0.996921i \(0.475015\pi\)
\(662\) 1957.05i 0.114898i
\(663\) 0 0
\(664\) −1804.30 −0.105453
\(665\) 2620.18 + 7998.75i 0.152791 + 0.466433i
\(666\) 0 0
\(667\) 25992.9i 1.50892i
\(668\) 14355.8i 0.831502i
\(669\) 0 0
\(670\) 4207.46 1378.25i 0.242610 0.0794724i
\(671\) −1437.05 −0.0826779
\(672\) 0 0
\(673\) 23549.8i 1.34885i 0.738342 + 0.674427i \(0.235609\pi\)
−0.738342 + 0.674427i \(0.764391\pi\)
\(674\) 1243.82 0.0710834
\(675\) 0 0
\(676\) −29058.6 −1.65331
\(677\) 9939.71i 0.564275i 0.959374 + 0.282138i \(0.0910434\pi\)
−0.959374 + 0.282138i \(0.908957\pi\)
\(678\) 0 0
\(679\) 3194.69 0.180561
\(680\) 7065.85 2314.58i 0.398475 0.130530i
\(681\) 0 0
\(682\) 181.676i 0.0102005i
\(683\) 11680.3i 0.654371i 0.944960 + 0.327185i \(0.106100\pi\)
−0.944960 + 0.327185i \(0.893900\pi\)
\(684\) 0 0
\(685\) −2215.82 6764.35i −0.123594 0.377303i
\(686\) −2406.45 −0.133934
\(687\) 0 0
\(688\) 1360.96i 0.0754158i
\(689\) −26541.5 −1.46756
\(690\) 0 0
\(691\) −12356.9 −0.680290 −0.340145 0.940373i \(-0.610476\pi\)
−0.340145 + 0.940373i \(0.610476\pi\)
\(692\) 1501.98i 0.0825096i
\(693\) 0 0
\(694\) −3277.55 −0.179271
\(695\) 16184.2 5301.50i 0.883310 0.289349i
\(696\) 0 0
\(697\) 707.210i 0.0384326i
\(698\) 1261.01i 0.0683808i
\(699\) 0 0
\(700\) −4719.13 6430.24i −0.254809 0.347200i
\(701\) −10659.6 −0.574333 −0.287167 0.957881i \(-0.592713\pi\)
−0.287167 + 0.957881i \(0.592713\pi\)
\(702\) 0 0
\(703\) 14204.0i 0.762042i
\(704\) −2252.38 −0.120582
\(705\) 0 0
\(706\) −2141.25 −0.114146
\(707\) 7094.74i 0.377405i
\(708\) 0 0
\(709\) −19338.6 −1.02437 −0.512183 0.858877i \(-0.671163\pi\)
−0.512183 + 0.858877i \(0.671163\pi\)
\(710\) −579.288 1768.42i −0.0306201 0.0934756i
\(711\) 0 0
\(712\) 7637.29i 0.401994i
\(713\) 11241.5i 0.590460i
\(714\) 0 0
\(715\) 1411.82 + 4309.95i 0.0738451 + 0.225431i
\(716\) −30566.8 −1.59544
\(717\) 0 0
\(718\) 1280.88i 0.0665766i
\(719\) −27300.1 −1.41603 −0.708013 0.706199i \(-0.750408\pi\)
−0.708013 + 0.706199i \(0.750408\pi\)
\(720\) 0 0
\(721\) 10079.4 0.520631
\(722\) 737.742i 0.0380276i
\(723\) 0 0
\(724\) −14938.9 −0.766849
\(725\) 16960.5 12447.3i 0.868825 0.637628i
\(726\) 0 0
\(727\) 1764.93i 0.0900381i −0.998986 0.0450191i \(-0.985665\pi\)
0.998986 0.0450191i \(-0.0143349\pi\)
\(728\) 4727.08i 0.240656i
\(729\) 0 0
\(730\) −2632.60 + 862.368i −0.133475 + 0.0437228i
\(731\) −2063.52 −0.104408
\(732\) 0 0
\(733\) 17305.5i 0.872024i 0.899941 + 0.436012i \(0.143609\pi\)
−0.899941 + 0.436012i \(0.856391\pi\)
\(734\) −1677.12 −0.0843375
\(735\) 0 0
\(736\) 13532.5 0.677735
\(737\) 4399.43i 0.219885i
\(738\) 0 0
\(739\) 1456.60 0.0725058 0.0362529 0.999343i \(-0.488458\pi\)
0.0362529 + 0.999343i \(0.488458\pi\)
\(740\) −4190.08 12791.3i −0.208149 0.635427i
\(741\) 0 0
\(742\) 1340.21i 0.0663082i
\(743\) 16937.1i 0.836288i −0.908381 0.418144i \(-0.862681\pi\)
0.908381 0.418144i \(-0.137319\pi\)
\(744\) 0 0
\(745\) 22339.8 7317.91i 1.09861 0.359876i
\(746\) −2715.91 −0.133293
\(747\) 0 0
\(748\) 3641.51i 0.178004i
\(749\) −15267.0 −0.744787
\(750\) 0 0
\(751\) 12935.6 0.628531 0.314265 0.949335i \(-0.398242\pi\)
0.314265 + 0.949335i \(0.398242\pi\)
\(752\) 17679.6i 0.857323i
\(753\) 0 0
\(754\) 6145.34 0.296817
\(755\) 25079.8 8215.48i 1.20894 0.396016i
\(756\) 0 0
\(757\) 37371.9i 1.79433i −0.441697 0.897164i \(-0.645623\pi\)
0.441697 0.897164i \(-0.354377\pi\)
\(758\) 4136.79i 0.198226i
\(759\) 0 0
\(760\) 2387.35 + 7287.99i 0.113945 + 0.347846i
\(761\) 13999.3 0.666854 0.333427 0.942776i \(-0.391795\pi\)
0.333427 + 0.942776i \(0.391795\pi\)
\(762\) 0 0
\(763\) 8512.74i 0.403908i
\(764\) 11723.9 0.555177
\(765\) 0 0
\(766\) 2162.72 0.102013
\(767\) 19378.5i 0.912280i
\(768\) 0 0
\(769\) 10442.5 0.489684 0.244842 0.969563i \(-0.421264\pi\)
0.244842 + 0.969563i \(0.421264\pi\)
\(770\) −217.630 + 71.2898i −0.0101855 + 0.00333650i
\(771\) 0 0
\(772\) 31611.8i 1.47375i
\(773\) 23092.7i 1.07450i −0.843424 0.537249i \(-0.819463\pi\)
0.843424 0.537249i \(-0.180537\pi\)
\(774\) 0 0
\(775\) 7335.16 5383.25i 0.339983 0.249512i
\(776\) 2910.82 0.134655
\(777\) 0 0
\(778\) 5727.88i 0.263952i
\(779\) −729.444 −0.0335495
\(780\) 0 0
\(781\) 1849.11 0.0847199
\(782\) 6510.68i 0.297726i
\(783\) 0 0
\(784\) 16169.3 0.736577
\(785\) 6975.38 + 21294.1i 0.317149 + 0.968178i
\(786\) 0 0
\(787\) 8516.24i 0.385732i 0.981225 + 0.192866i \(0.0617783\pi\)
−0.981225 + 0.192866i \(0.938222\pi\)
\(788\) 30453.4i 1.37672i
\(789\) 0 0
\(790\) 1154.95 + 3525.78i 0.0520143 + 0.158787i
\(791\) 11552.7 0.519299
\(792\) 0