Properties

Label 882.4.g.bg.667.2
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bg.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.53553 - 6.12372i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(3.53553 - 6.12372i) q^{5} -8.00000 q^{8} +(-7.07107 - 12.2474i) q^{10} +(-20.0000 - 34.6410i) q^{11} -63.6396 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(-5.65685 + 9.79796i) q^{19} -28.2843 q^{20} -80.0000 q^{22} +(-34.0000 + 58.8897i) q^{23} +(37.5000 + 64.9519i) q^{25} +(-63.6396 + 110.227i) q^{26} +110.000 q^{29} +(59.3970 + 102.879i) q^{31} +(16.0000 + 27.7128i) q^{32} -2.82843 q^{34} +(10.0000 - 17.3205i) q^{37} +(11.3137 + 19.5959i) q^{38} +(-28.2843 + 48.9898i) q^{40} -49.4975 q^{41} -340.000 q^{43} +(-80.0000 + 138.564i) q^{44} +(68.0000 + 117.779i) q^{46} +(-45.2548 + 78.3837i) q^{47} +150.000 q^{50} +(127.279 + 220.454i) q^{52} +(-314.000 - 543.864i) q^{53} -282.843 q^{55} +(110.000 - 190.526i) q^{58} +(438.406 + 759.342i) q^{59} +(-458.912 + 794.859i) q^{61} +237.588 q^{62} +64.0000 q^{64} +(-225.000 + 389.711i) q^{65} +(-270.000 - 467.654i) q^{67} +(-2.82843 + 4.89898i) q^{68} -420.000 q^{71} +(-144.957 - 251.073i) q^{73} +(-20.0000 - 34.6410i) q^{74} +45.2548 q^{76} +(380.000 - 658.179i) q^{79} +(56.5685 + 97.9796i) q^{80} +(-49.4975 + 85.7321i) q^{82} +944.695 q^{83} -10.0000 q^{85} +(-340.000 + 588.897i) q^{86} +(160.000 + 277.128i) q^{88} +(-576.292 + 998.167i) q^{89} +272.000 q^{92} +(90.5097 + 156.767i) q^{94} +(40.0000 + 69.2820i) q^{95} -502.046 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} - 80q^{11} - 32q^{16} - 320q^{22} - 136q^{23} + 150q^{25} + 440q^{29} + 64q^{32} + 40q^{37} - 1360q^{43} - 320q^{44} + 272q^{46} + 600q^{50} - 1256q^{53} + 440q^{58} + 256q^{64} - 900q^{65} - 1080q^{67} - 1680q^{71} - 80q^{74} + 1520q^{79} - 40q^{85} - 1360q^{86} + 640q^{88} + 1088q^{92} + 160q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 3.53553 6.12372i 0.316228 0.547723i −0.663470 0.748203i \(-0.730917\pi\)
0.979698 + 0.200480i \(0.0642503\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −7.07107 12.2474i −0.223607 0.387298i
\(11\) −20.0000 34.6410i −0.548202 0.949514i −0.998398 0.0565844i \(-0.981979\pi\)
0.450195 0.892930i \(-0.351354\pi\)
\(12\) 0 0
\(13\) −63.6396 −1.35773 −0.678864 0.734264i \(-0.737527\pi\)
−0.678864 + 0.734264i \(0.737527\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −0.707107 1.22474i −0.0100882 0.0174732i 0.860937 0.508711i \(-0.169878\pi\)
−0.871025 + 0.491238i \(0.836545\pi\)
\(18\) 0 0
\(19\) −5.65685 + 9.79796i −0.0683038 + 0.118306i −0.898155 0.439679i \(-0.855092\pi\)
0.829851 + 0.557985i \(0.188425\pi\)
\(20\) −28.2843 −0.316228
\(21\) 0 0
\(22\) −80.0000 −0.775275
\(23\) −34.0000 + 58.8897i −0.308239 + 0.533885i −0.977977 0.208712i \(-0.933073\pi\)
0.669738 + 0.742597i \(0.266406\pi\)
\(24\) 0 0
\(25\) 37.5000 + 64.9519i 0.300000 + 0.519615i
\(26\) −63.6396 + 110.227i −0.480029 + 0.831435i
\(27\) 0 0
\(28\) 0 0
\(29\) 110.000 0.704362 0.352181 0.935932i \(-0.385440\pi\)
0.352181 + 0.935932i \(0.385440\pi\)
\(30\) 0 0
\(31\) 59.3970 + 102.879i 0.344129 + 0.596050i 0.985195 0.171436i \(-0.0548408\pi\)
−0.641066 + 0.767486i \(0.721507\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.82843 −0.0142668
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 17.3205i 0.0444322 0.0769588i −0.842954 0.537986i \(-0.819185\pi\)
0.887386 + 0.461027i \(0.152519\pi\)
\(38\) 11.3137 + 19.5959i 0.0482980 + 0.0836547i
\(39\) 0 0
\(40\) −28.2843 + 48.9898i −0.111803 + 0.193649i
\(41\) −49.4975 −0.188542 −0.0942708 0.995547i \(-0.530052\pi\)
−0.0942708 + 0.995547i \(0.530052\pi\)
\(42\) 0 0
\(43\) −340.000 −1.20580 −0.602901 0.797816i \(-0.705989\pi\)
−0.602901 + 0.797816i \(0.705989\pi\)
\(44\) −80.0000 + 138.564i −0.274101 + 0.474757i
\(45\) 0 0
\(46\) 68.0000 + 117.779i 0.217958 + 0.377514i
\(47\) −45.2548 + 78.3837i −0.140449 + 0.243265i −0.927666 0.373412i \(-0.878188\pi\)
0.787217 + 0.616676i \(0.211521\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 150.000 0.424264
\(51\) 0 0
\(52\) 127.279 + 220.454i 0.339432 + 0.587913i
\(53\) −314.000 543.864i −0.813797 1.40954i −0.910189 0.414194i \(-0.864064\pi\)
0.0963923 0.995343i \(-0.469270\pi\)
\(54\) 0 0
\(55\) −282.843 −0.693427
\(56\) 0 0
\(57\) 0 0
\(58\) 110.000 190.526i 0.249029 0.431332i
\(59\) 438.406 + 759.342i 0.967383 + 1.67556i 0.703070 + 0.711121i \(0.251812\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(60\) 0 0
\(61\) −458.912 + 794.859i −0.963241 + 1.66838i −0.248972 + 0.968511i \(0.580093\pi\)
−0.714269 + 0.699872i \(0.753240\pi\)
\(62\) 237.588 0.486672
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −225.000 + 389.711i −0.429351 + 0.743658i
\(66\) 0 0
\(67\) −270.000 467.654i −0.492325 0.852731i 0.507636 0.861571i \(-0.330519\pi\)
−0.999961 + 0.00884020i \(0.997186\pi\)
\(68\) −2.82843 + 4.89898i −0.00504408 + 0.00873660i
\(69\) 0 0
\(70\) 0 0
\(71\) −420.000 −0.702040 −0.351020 0.936368i \(-0.614165\pi\)
−0.351020 + 0.936368i \(0.614165\pi\)
\(72\) 0 0
\(73\) −144.957 251.073i −0.232410 0.402546i 0.726107 0.687582i \(-0.241328\pi\)
−0.958517 + 0.285036i \(0.907994\pi\)
\(74\) −20.0000 34.6410i −0.0314183 0.0544181i
\(75\) 0 0
\(76\) 45.2548 0.0683038
\(77\) 0 0
\(78\) 0 0
\(79\) 380.000 658.179i 0.541182 0.937354i −0.457655 0.889130i \(-0.651311\pi\)
0.998837 0.0482240i \(-0.0153561\pi\)
\(80\) 56.5685 + 97.9796i 0.0790569 + 0.136931i
\(81\) 0 0
\(82\) −49.4975 + 85.7321i −0.0666595 + 0.115458i
\(83\) 944.695 1.24932 0.624661 0.780896i \(-0.285237\pi\)
0.624661 + 0.780896i \(0.285237\pi\)
\(84\) 0 0
\(85\) −10.0000 −0.0127606
\(86\) −340.000 + 588.897i −0.426316 + 0.738400i
\(87\) 0 0
\(88\) 160.000 + 277.128i 0.193819 + 0.335704i
\(89\) −576.292 + 998.167i −0.686369 + 1.18883i 0.286636 + 0.958040i \(0.407463\pi\)
−0.973005 + 0.230786i \(0.925870\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 272.000 0.308239
\(93\) 0 0
\(94\) 90.5097 + 156.767i 0.0993123 + 0.172014i
\(95\) 40.0000 + 69.2820i 0.0431991 + 0.0748230i
\(96\) 0 0
\(97\) −502.046 −0.525516 −0.262758 0.964862i \(-0.584632\pi\)
−0.262758 + 0.964862i \(0.584632\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 150.000 259.808i 0.150000 0.259808i
\(101\) 880.348 + 1524.81i 0.867306 + 1.50222i 0.864739 + 0.502221i \(0.167484\pi\)
0.00256667 + 0.999997i \(0.499183\pi\)
\(102\) 0 0
\(103\) −113.137 + 195.959i −0.108230 + 0.187461i −0.915053 0.403333i \(-0.867852\pi\)
0.806823 + 0.590793i \(0.201185\pi\)
\(104\) 509.117 0.480029
\(105\) 0 0
\(106\) −1256.00 −1.15088
\(107\) −1012.00 + 1752.84i −0.914334 + 1.58367i −0.106460 + 0.994317i \(0.533952\pi\)
−0.807874 + 0.589356i \(0.799382\pi\)
\(108\) 0 0
\(109\) 202.000 + 349.874i 0.177505 + 0.307448i 0.941025 0.338336i \(-0.109864\pi\)
−0.763520 + 0.645784i \(0.776531\pi\)
\(110\) −282.843 + 489.898i −0.245164 + 0.424636i
\(111\) 0 0
\(112\) 0 0
\(113\) 1008.00 0.839156 0.419578 0.907719i \(-0.362178\pi\)
0.419578 + 0.907719i \(0.362178\pi\)
\(114\) 0 0
\(115\) 240.416 + 416.413i 0.194947 + 0.337659i
\(116\) −220.000 381.051i −0.176090 0.304998i
\(117\) 0 0
\(118\) 1753.62 1.36809
\(119\) 0 0
\(120\) 0 0
\(121\) −134.500 + 232.961i −0.101052 + 0.175027i
\(122\) 917.825 + 1589.72i 0.681114 + 1.17972i
\(123\) 0 0
\(124\) 237.588 411.514i 0.172065 0.298025i
\(125\) 1414.21 1.01193
\(126\) 0 0
\(127\) 1000.00 0.698706 0.349353 0.936991i \(-0.386401\pi\)
0.349353 + 0.936991i \(0.386401\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 450.000 + 779.423i 0.303597 + 0.525845i
\(131\) −42.4264 + 73.4847i −0.0282963 + 0.0490106i −0.879827 0.475294i \(-0.842342\pi\)
0.851530 + 0.524305i \(0.175675\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1080.00 −0.696252
\(135\) 0 0
\(136\) 5.65685 + 9.79796i 0.00356670 + 0.00617771i
\(137\) −1017.00 1761.50i −0.634220 1.09850i −0.986680 0.162675i \(-0.947988\pi\)
0.352460 0.935827i \(-0.385345\pi\)
\(138\) 0 0
\(139\) −1736.65 −1.05972 −0.529860 0.848085i \(-0.677756\pi\)
−0.529860 + 0.848085i \(0.677756\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −420.000 + 727.461i −0.248209 + 0.429910i
\(143\) 1272.79 + 2204.54i 0.744309 + 1.28918i
\(144\) 0 0
\(145\) 388.909 673.610i 0.222739 0.385795i
\(146\) −579.828 −0.328677
\(147\) 0 0
\(148\) −80.0000 −0.0444322
\(149\) −1070.00 + 1853.29i −0.588307 + 1.01898i 0.406147 + 0.913808i \(0.366872\pi\)
−0.994454 + 0.105171i \(0.966461\pi\)
\(150\) 0 0
\(151\) −1060.00 1835.97i −0.571269 0.989466i −0.996436 0.0843517i \(-0.973118\pi\)
0.425167 0.905115i \(-0.360215\pi\)
\(152\) 45.2548 78.3837i 0.0241490 0.0418273i
\(153\) 0 0
\(154\) 0 0
\(155\) 840.000 0.435293
\(156\) 0 0
\(157\) −873.277 1512.56i −0.443918 0.768888i 0.554058 0.832478i \(-0.313078\pi\)
−0.997976 + 0.0635898i \(0.979745\pi\)
\(158\) −760.000 1316.36i −0.382673 0.662809i
\(159\) 0 0
\(160\) 226.274 0.111803
\(161\) 0 0
\(162\) 0 0
\(163\) −1670.00 + 2892.52i −0.802482 + 1.38994i 0.115497 + 0.993308i \(0.463154\pi\)
−0.917978 + 0.396631i \(0.870179\pi\)
\(164\) 98.9949 + 171.464i 0.0471354 + 0.0816409i
\(165\) 0 0
\(166\) 944.695 1636.26i 0.441702 0.765050i
\(167\) 367.696 0.170378 0.0851890 0.996365i \(-0.472851\pi\)
0.0851890 + 0.996365i \(0.472851\pi\)
\(168\) 0 0
\(169\) 1853.00 0.843423
\(170\) −10.0000 + 17.3205i −0.00451156 + 0.00781425i
\(171\) 0 0
\(172\) 680.000 + 1177.79i 0.301451 + 0.522128i
\(173\) −1694.93 + 2935.71i −0.744876 + 1.29016i 0.205377 + 0.978683i \(0.434158\pi\)
−0.950253 + 0.311480i \(0.899175\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 640.000 0.274101
\(177\) 0 0
\(178\) 1152.58 + 1996.33i 0.485336 + 0.840627i
\(179\) −360.000 623.538i −0.150322 0.260366i 0.781024 0.624501i \(-0.214698\pi\)
−0.931346 + 0.364136i \(0.881364\pi\)
\(180\) 0 0
\(181\) −1854.03 −0.761377 −0.380689 0.924703i \(-0.624313\pi\)
−0.380689 + 0.924703i \(0.624313\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 272.000 471.118i 0.108979 0.188757i
\(185\) −70.7107 122.474i −0.0281014 0.0486730i
\(186\) 0 0
\(187\) −28.2843 + 48.9898i −0.0110607 + 0.0191577i
\(188\) 362.039 0.140449
\(189\) 0 0
\(190\) 160.000 0.0610927
\(191\) −1990.00 + 3446.78i −0.753881 + 1.30576i 0.192047 + 0.981386i \(0.438487\pi\)
−0.945929 + 0.324375i \(0.894846\pi\)
\(192\) 0 0
\(193\) −1855.00 3212.95i −0.691844 1.19831i −0.971233 0.238130i \(-0.923465\pi\)
0.279390 0.960178i \(-0.409868\pi\)
\(194\) −502.046 + 869.569i −0.185798 + 0.321811i
\(195\) 0 0
\(196\) 0 0
\(197\) 956.000 0.345747 0.172874 0.984944i \(-0.444695\pi\)
0.172874 + 0.984944i \(0.444695\pi\)
\(198\) 0 0
\(199\) −2044.95 3541.96i −0.728457 1.26172i −0.957535 0.288316i \(-0.906905\pi\)
0.229079 0.973408i \(-0.426429\pi\)
\(200\) −300.000 519.615i −0.106066 0.183712i
\(201\) 0 0
\(202\) 3521.39 1.22656
\(203\) 0 0
\(204\) 0 0
\(205\) −175.000 + 303.109i −0.0596221 + 0.103269i
\(206\) 226.274 + 391.918i 0.0765304 + 0.132555i
\(207\) 0 0
\(208\) 509.117 881.816i 0.169716 0.293957i
\(209\) 452.548 0.149777
\(210\) 0 0
\(211\) 2868.00 0.935741 0.467870 0.883797i \(-0.345021\pi\)
0.467870 + 0.883797i \(0.345021\pi\)
\(212\) −1256.00 + 2175.46i −0.406898 + 0.704768i
\(213\) 0 0
\(214\) 2024.00 + 3505.67i 0.646532 + 1.11983i
\(215\) −1202.08 + 2082.07i −0.381308 + 0.660445i
\(216\) 0 0
\(217\) 0 0
\(218\) 808.000 0.251031
\(219\) 0 0
\(220\) 565.685 + 979.796i 0.173357 + 0.300263i
\(221\) 45.0000 + 77.9423i 0.0136970 + 0.0237238i
\(222\) 0 0
\(223\) 2630.44 0.789897 0.394949 0.918703i \(-0.370762\pi\)
0.394949 + 0.918703i \(0.370762\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1008.00 1745.91i 0.296687 0.513876i
\(227\) 84.8528 + 146.969i 0.0248100 + 0.0429722i 0.878164 0.478360i \(-0.158769\pi\)
−0.853354 + 0.521332i \(0.825435\pi\)
\(228\) 0 0
\(229\) 1571.90 2722.61i 0.453598 0.785655i −0.545008 0.838431i \(-0.683473\pi\)
0.998606 + 0.0527757i \(0.0168068\pi\)
\(230\) 961.665 0.275697
\(231\) 0 0
\(232\) −880.000 −0.249029
\(233\) 2241.00 3881.53i 0.630098 1.09136i −0.357433 0.933939i \(-0.616348\pi\)
0.987531 0.157423i \(-0.0503186\pi\)
\(234\) 0 0
\(235\) 320.000 + 554.256i 0.0888277 + 0.153854i
\(236\) 1753.62 3037.37i 0.483692 0.837779i
\(237\) 0 0
\(238\) 0 0
\(239\) −1740.00 −0.470926 −0.235463 0.971883i \(-0.575661\pi\)
−0.235463 + 0.971883i \(0.575661\pi\)
\(240\) 0 0
\(241\) −630.032 1091.25i −0.168398 0.291674i 0.769459 0.638697i \(-0.220526\pi\)
−0.937857 + 0.347023i \(0.887193\pi\)
\(242\) 269.000 + 465.922i 0.0714544 + 0.123763i
\(243\) 0 0
\(244\) 3671.30 0.963241
\(245\) 0 0
\(246\) 0 0
\(247\) 360.000 623.538i 0.0927379 0.160627i
\(248\) −475.176 823.029i −0.121668 0.210735i
\(249\) 0 0
\(250\) 1414.21 2449.49i 0.357771 0.619677i
\(251\) −5826.56 −1.46522 −0.732608 0.680651i \(-0.761697\pi\)
−0.732608 + 0.680651i \(0.761697\pi\)
\(252\) 0 0
\(253\) 2720.00 0.675909
\(254\) 1000.00 1732.05i 0.247030 0.427868i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2344.06 4060.03i 0.568943 0.985438i −0.427728 0.903908i \(-0.640686\pi\)
0.996671 0.0815308i \(-0.0259809\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1800.00 0.429351
\(261\) 0 0
\(262\) 84.8528 + 146.969i 0.0200085 + 0.0346557i
\(263\) −1086.00 1881.01i −0.254622 0.441019i 0.710171 0.704030i \(-0.248618\pi\)
−0.964793 + 0.263011i \(0.915284\pi\)
\(264\) 0 0
\(265\) −4440.63 −1.02938
\(266\) 0 0
\(267\) 0 0
\(268\) −1080.00 + 1870.61i −0.246162 + 0.426366i
\(269\) 1354.11 + 2345.39i 0.306920 + 0.531601i 0.977687 0.210067i \(-0.0673682\pi\)
−0.670767 + 0.741668i \(0.734035\pi\)
\(270\) 0 0
\(271\) −3094.30 + 5359.48i −0.693599 + 1.20135i 0.277052 + 0.960855i \(0.410643\pi\)
−0.970651 + 0.240494i \(0.922691\pi\)
\(272\) 22.6274 0.00504408
\(273\) 0 0
\(274\) −4068.00 −0.896923
\(275\) 1500.00 2598.08i 0.328921 0.569709i
\(276\) 0 0
\(277\) −3065.00 5308.74i −0.664830 1.15152i −0.979331 0.202263i \(-0.935170\pi\)
0.314501 0.949257i \(-0.398163\pi\)
\(278\) −1736.65 + 3007.97i −0.374668 + 0.648943i
\(279\) 0 0
\(280\) 0 0
\(281\) −1970.00 −0.418222 −0.209111 0.977892i \(-0.567057\pi\)
−0.209111 + 0.977892i \(0.567057\pi\)
\(282\) 0 0
\(283\) 777.817 + 1347.22i 0.163380 + 0.282982i 0.936079 0.351791i \(-0.114427\pi\)
−0.772699 + 0.634773i \(0.781094\pi\)
\(284\) 840.000 + 1454.92i 0.175510 + 0.303992i
\(285\) 0 0
\(286\) 5091.17 1.05261
\(287\) 0 0
\(288\) 0 0
\(289\) 2455.50 4253.05i 0.499796 0.865673i
\(290\) −777.817 1347.22i −0.157500 0.272798i
\(291\) 0 0
\(292\) −579.828 + 1004.29i −0.116205 + 0.201273i
\(293\) 7686.25 1.53254 0.766272 0.642516i \(-0.222109\pi\)
0.766272 + 0.642516i \(0.222109\pi\)
\(294\) 0 0
\(295\) 6200.00 1.22365
\(296\) −80.0000 + 138.564i −0.0157091 + 0.0272090i
\(297\) 0 0
\(298\) 2140.00 + 3706.59i 0.415996 + 0.720527i
\(299\) 2163.75 3747.72i 0.418504 0.724870i
\(300\) 0 0
\(301\) 0 0
\(302\) −4240.00 −0.807896
\(303\) 0 0
\(304\) −90.5097 156.767i −0.0170759 0.0295764i
\(305\) 3245.00 + 5620.50i 0.609207 + 1.05518i
\(306\) 0 0
\(307\) −8598.42 −1.59849 −0.799247 0.601003i \(-0.794768\pi\)
−0.799247 + 0.601003i \(0.794768\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 840.000 1454.92i 0.153899 0.266561i
\(311\) −3790.09 6564.63i −0.691050 1.19693i −0.971494 0.237063i \(-0.923815\pi\)
0.280445 0.959870i \(-0.409518\pi\)
\(312\) 0 0
\(313\) −1537.96 + 2663.82i −0.277733 + 0.481048i −0.970821 0.239805i \(-0.922916\pi\)
0.693088 + 0.720853i \(0.256250\pi\)
\(314\) −3493.11 −0.627794
\(315\) 0 0
\(316\) −3040.00 −0.541182
\(317\) 1162.00 2012.64i 0.205881 0.356597i −0.744532 0.667587i \(-0.767327\pi\)
0.950413 + 0.310990i \(0.100661\pi\)
\(318\) 0 0
\(319\) −2200.00 3810.51i −0.386133 0.668802i
\(320\) 226.274 391.918i 0.0395285 0.0684653i
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.00275623
\(324\) 0 0
\(325\) −2386.49 4133.51i −0.407318 0.705496i
\(326\) 3340.00 + 5785.05i 0.567440 + 0.982835i
\(327\) 0 0
\(328\) 395.980 0.0666595
\(329\) 0 0
\(330\) 0 0
\(331\) −4754.00 + 8234.17i −0.789436 + 1.36734i 0.136876 + 0.990588i \(0.456294\pi\)
−0.926313 + 0.376756i \(0.877040\pi\)
\(332\) −1889.39 3272.52i −0.312330 0.540972i
\(333\) 0 0
\(334\) 367.696 636.867i 0.0602377 0.104335i
\(335\) −3818.38 −0.622747
\(336\) 0 0
\(337\) −4720.00 −0.762952 −0.381476 0.924379i \(-0.624584\pi\)
−0.381476 + 0.924379i \(0.624584\pi\)
\(338\) 1853.00 3209.49i 0.298195 0.516489i
\(339\) 0 0
\(340\) 20.0000 + 34.6410i 0.00319015 + 0.00552551i
\(341\) 2375.88 4115.14i 0.377305 0.653512i
\(342\) 0 0
\(343\) 0 0
\(344\) 2720.00 0.426316
\(345\) 0 0
\(346\) 3389.87 + 5871.43i 0.526707 + 0.912283i
\(347\) 3252.00 + 5632.63i 0.503102 + 0.871399i 0.999994 + 0.00358597i \(0.00114145\pi\)
−0.496891 + 0.867813i \(0.665525\pi\)
\(348\) 0 0
\(349\) −5256.63 −0.806249 −0.403125 0.915145i \(-0.632076\pi\)
−0.403125 + 0.915145i \(0.632076\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 640.000 1108.51i 0.0969094 0.167852i
\(353\) −6105.87 10575.7i −0.920630 1.59458i −0.798442 0.602072i \(-0.794342\pi\)
−0.122188 0.992507i \(-0.538991\pi\)
\(354\) 0 0
\(355\) −1484.92 + 2571.96i −0.222004 + 0.384523i
\(356\) 4610.34 0.686369
\(357\) 0 0
\(358\) −1440.00 −0.212588
\(359\) 3670.00 6356.63i 0.539541 0.934512i −0.459388 0.888236i \(-0.651931\pi\)
0.998929 0.0462765i \(-0.0147355\pi\)
\(360\) 0 0
\(361\) 3365.50 + 5829.22i 0.490669 + 0.849864i
\(362\) −1854.03 + 3211.28i −0.269187 + 0.466246i
\(363\) 0 0
\(364\) 0 0
\(365\) −2050.00 −0.293978
\(366\) 0 0
\(367\) 3832.52 + 6638.12i 0.545111 + 0.944160i 0.998600 + 0.0528984i \(0.0168459\pi\)
−0.453489 + 0.891262i \(0.649821\pi\)
\(368\) −544.000 942.236i −0.0770597 0.133471i
\(369\) 0 0
\(370\) −282.843 −0.0397413
\(371\) 0 0
\(372\) 0 0
\(373\) 1495.00 2589.42i 0.207529 0.359450i −0.743407 0.668840i \(-0.766791\pi\)
0.950935 + 0.309389i \(0.100125\pi\)
\(374\) 56.5685 + 97.9796i 0.00782110 + 0.0135465i
\(375\) 0 0
\(376\) 362.039 627.069i 0.0496562 0.0860070i
\(377\) −7000.36 −0.956331
\(378\) 0 0
\(379\) −11900.0 −1.61283 −0.806414 0.591351i \(-0.798595\pi\)
−0.806414 + 0.591351i \(0.798595\pi\)
\(380\) 160.000 277.128i 0.0215995 0.0374115i
\(381\) 0 0
\(382\) 3980.00 + 6893.56i 0.533075 + 0.923312i
\(383\) 4856.41 8411.55i 0.647914 1.12222i −0.335707 0.941967i \(-0.608975\pi\)
0.983620 0.180253i \(-0.0576916\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7420.00 −0.978415
\(387\) 0 0
\(388\) 1004.09 + 1739.14i 0.131379 + 0.227555i
\(389\) −1075.00 1861.95i −0.140115 0.242686i 0.787425 0.616411i \(-0.211414\pi\)
−0.927540 + 0.373725i \(0.878081\pi\)
\(390\) 0 0
\(391\) 96.1665 0.0124382
\(392\) 0 0
\(393\) 0 0
\(394\) 956.000 1655.84i 0.122240 0.211726i
\(395\) −2687.01 4654.03i −0.342273 0.592835i
\(396\) 0 0
\(397\) −1700.59 + 2945.51i −0.214988 + 0.372370i −0.953269 0.302123i \(-0.902305\pi\)
0.738281 + 0.674493i \(0.235638\pi\)
\(398\) −8179.81 −1.03019
\(399\) 0 0
\(400\) −1200.00 −0.150000
\(401\) 6045.00 10470.2i 0.752800 1.30389i −0.193660 0.981069i \(-0.562036\pi\)
0.946461 0.322820i \(-0.104631\pi\)
\(402\) 0 0
\(403\) −3780.00 6547.15i −0.467234 0.809273i
\(404\) 3521.39 6099.23i 0.433653 0.751109i
\(405\) 0 0
\(406\) 0 0
\(407\) −800.000 −0.0974313
\(408\) 0 0
\(409\) −4096.27 7094.95i −0.495226 0.857757i 0.504759 0.863260i \(-0.331581\pi\)
−0.999985 + 0.00550362i \(0.998248\pi\)
\(410\) 350.000 + 606.218i 0.0421592 + 0.0730219i
\(411\) 0 0
\(412\) 905.097 0.108230
\(413\) 0 0
\(414\) 0 0
\(415\) 3340.00 5785.05i 0.395070 0.684282i
\(416\) −1018.23 1763.63i −0.120007 0.207859i
\(417\) 0 0
\(418\) 452.548 783.837i 0.0529542 0.0917194i
\(419\) −1046.52 −0.122019 −0.0610093 0.998137i \(-0.519432\pi\)
−0.0610093 + 0.998137i \(0.519432\pi\)
\(420\) 0 0
\(421\) −3870.00 −0.448010 −0.224005 0.974588i \(-0.571913\pi\)
−0.224005 + 0.974588i \(0.571913\pi\)
\(422\) 2868.00 4967.52i 0.330834 0.573022i
\(423\) 0 0
\(424\) 2512.00 + 4350.91i 0.287721 + 0.498347i
\(425\) 53.0330 91.8559i 0.00605289 0.0104839i
\(426\) 0 0
\(427\) 0 0
\(428\) 8096.00 0.914334
\(429\) 0 0
\(430\) 2404.16 + 4164.13i 0.269626 + 0.467005i
\(431\) 1350.00 + 2338.27i 0.150875 + 0.261324i 0.931549 0.363615i \(-0.118458\pi\)
−0.780674 + 0.624938i \(0.785124\pi\)
\(432\) 0 0
\(433\) −5876.06 −0.652160 −0.326080 0.945342i \(-0.605728\pi\)
−0.326080 + 0.945342i \(0.605728\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 808.000 1399.50i 0.0887527 0.153724i
\(437\) −384.666 666.261i −0.0421077 0.0729327i
\(438\) 0 0
\(439\) −3173.50 + 5496.65i −0.345017 + 0.597588i −0.985357 0.170504i \(-0.945460\pi\)
0.640339 + 0.768092i \(0.278794\pi\)
\(440\) 2262.74 0.245164
\(441\) 0 0
\(442\) 180.000 0.0193704
\(443\) 3464.00 5999.82i 0.371512 0.643477i −0.618287 0.785953i \(-0.712173\pi\)
0.989798 + 0.142476i \(0.0455063\pi\)
\(444\) 0 0
\(445\) 4075.00 + 7058.11i 0.434098 + 0.751879i
\(446\) 2630.44 4556.05i 0.279271 0.483711i
\(447\) 0 0
\(448\) 0 0
\(449\) −1320.00 −0.138741 −0.0693704 0.997591i \(-0.522099\pi\)
−0.0693704 + 0.997591i \(0.522099\pi\)
\(450\) 0 0
\(451\) 989.949 + 1714.64i 0.103359 + 0.179023i
\(452\) −2016.00 3491.81i −0.209789 0.363365i
\(453\) 0 0
\(454\) 339.411 0.0350867
\(455\) 0 0
\(456\) 0 0
\(457\) −645.000 + 1117.17i −0.0660215 + 0.114353i −0.897147 0.441733i \(-0.854364\pi\)
0.831125 + 0.556085i \(0.187697\pi\)
\(458\) −3143.80 5445.22i −0.320742 0.555542i
\(459\) 0 0
\(460\) 961.665 1665.65i 0.0974736 0.168829i
\(461\) −17642.3 −1.78240 −0.891198 0.453615i \(-0.850134\pi\)
−0.891198 + 0.453615i \(0.850134\pi\)
\(462\) 0 0
\(463\) 5680.00 0.570134 0.285067 0.958508i \(-0.407984\pi\)
0.285067 + 0.958508i \(0.407984\pi\)
\(464\) −880.000 + 1524.20i −0.0880452 + 0.152499i
\(465\) 0 0
\(466\) −4482.00 7763.05i −0.445546 0.771709i
\(467\) −3846.66 + 6662.61i −0.381161 + 0.660190i −0.991229 0.132159i \(-0.957809\pi\)
0.610067 + 0.792350i \(0.291142\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1280.00 0.125621
\(471\) 0 0
\(472\) −3507.25 6074.73i −0.342022 0.592399i
\(473\) 6800.00 + 11777.9i 0.661024 + 1.14493i
\(474\) 0 0
\(475\) −848.528 −0.0819645
\(476\) 0 0
\(477\) 0 0
\(478\) −1740.00 + 3013.77i −0.166497 + 0.288382i
\(479\) −8259.01 14305.0i −0.787816 1.36454i −0.927303 0.374313i \(-0.877879\pi\)
0.139487 0.990224i \(-0.455455\pi\)
\(480\) 0 0
\(481\) −636.396 + 1102.27i −0.0603267 + 0.104489i
\(482\) −2520.13 −0.238151
\(483\) 0 0
\(484\) 1076.00 0.101052
\(485\) −1775.00 + 3074.39i −0.166183 + 0.287837i
\(486\) 0 0
\(487\) −6840.00 11847.2i −0.636448 1.10236i −0.986206 0.165520i \(-0.947070\pi\)
0.349759 0.936840i \(-0.386264\pi\)
\(488\) 3671.30 6358.88i 0.340557 0.589862i
\(489\) 0 0
\(490\) 0 0
\(491\) 2280.00 0.209562 0.104781 0.994495i \(-0.466586\pi\)
0.104781 + 0.994495i \(0.466586\pi\)
\(492\) 0 0
\(493\) −77.7817 134.722i −0.00710571 0.0123074i
\(494\) −720.000 1247.08i −0.0655756 0.113580i
\(495\) 0 0
\(496\) −1900.70 −0.172065
\(497\) 0 0
\(498\) 0 0
\(499\) −430.000 + 744.782i −0.0385760 + 0.0668157i −0.884669 0.466220i \(-0.845616\pi\)
0.846093 + 0.533036i \(0.178949\pi\)
\(500\) −2828.43 4898.98i −0.252982 0.438178i
\(501\) 0 0
\(502\) −5826.56 + 10091.9i −0.518032 + 0.897258i
\(503\) 5730.39 0.507963 0.253982 0.967209i \(-0.418260\pi\)
0.253982 + 0.967209i \(0.418260\pi\)
\(504\) 0 0
\(505\) 12450.0 1.09706
\(506\) 2720.00 4711.18i 0.238970 0.413908i
\(507\) 0 0
\(508\) −2000.00 3464.10i −0.174676 0.302549i
\(509\) −2294.56 + 3974.30i −0.199813 + 0.346086i −0.948468 0.316874i \(-0.897367\pi\)
0.748655 + 0.662960i \(0.230700\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −4688.12 8120.06i −0.402304 0.696810i
\(515\) 800.000 + 1385.64i 0.0684509 + 0.118560i
\(516\) 0 0
\(517\) 3620.39 0.307978
\(518\) 0 0
\(519\) 0 0
\(520\) 1800.00 3117.69i 0.151799 0.262923i
\(521\) −7293.81 12633.2i −0.613335 1.06233i −0.990674 0.136252i \(-0.956494\pi\)
0.377339 0.926075i \(-0.376839\pi\)
\(522\) 0 0
\(523\) 3054.70 5290.90i 0.255397 0.442361i −0.709606 0.704599i \(-0.751127\pi\)
0.965003 + 0.262238i \(0.0844604\pi\)
\(524\) 339.411 0.0282963
\(525\) 0 0
\(526\) −4344.00 −0.360090
\(527\) 84.0000 145.492i 0.00694326 0.0120261i
\(528\) 0 0
\(529\) 3771.50 + 6532.43i 0.309978 + 0.536897i
\(530\) −4440.63 + 7691.40i −0.363941 + 0.630364i
\(531\) 0 0
\(532\) 0 0
\(533\) 3150.00 0.255988
\(534\) 0 0
\(535\) 7155.92 + 12394.4i 0.578276 + 1.00160i
\(536\) 2160.00 + 3741.23i 0.174063 + 0.301486i
\(537\) 0 0
\(538\) 5416.44 0.434051
\(539\) 0 0
\(540\) 0 0
\(541\) 8605.00 14904.3i 0.683841 1.18445i −0.289959 0.957039i \(-0.593642\pi\)
0.973800 0.227408i \(-0.0730250\pi\)
\(542\) 6188.60 + 10719.0i 0.490448 + 0.849482i
\(543\) 0 0
\(544\) 22.6274 39.1918i 0.00178335 0.00308885i
\(545\) 2856.71 0.224529
\(546\) 0 0
\(547\) 4060.00 0.317355 0.158677 0.987330i \(-0.449277\pi\)
0.158677 + 0.987330i \(0.449277\pi\)
\(548\) −4068.00 + 7045.98i −0.317110 + 0.549251i
\(549\) 0 0
\(550\) −3000.00 5196.15i −0.232583 0.402845i
\(551\) −622.254 + 1077.78i −0.0481105 + 0.0833299i
\(552\) 0 0
\(553\) 0 0
\(554\) −12260.0 −0.940212
\(555\) 0 0
\(556\) 3473.31 + 6015.95i 0.264930 + 0.458872i
\(557\) −5178.00 8968.56i −0.393894 0.682244i 0.599065 0.800700i \(-0.295539\pi\)
−0.992959 + 0.118456i \(0.962206\pi\)
\(558\) 0 0
\(559\) 21637.5 1.63715
\(560\) 0 0
\(561\) 0 0
\(562\) −1970.00 + 3412.14i −0.147864 + 0.256108i
\(563\) 11605.0 + 20100.5i 0.868728 + 1.50468i 0.863297 + 0.504696i \(0.168395\pi\)
0.00543113 + 0.999985i \(0.498271\pi\)
\(564\) 0 0
\(565\) 3563.82 6172.71i 0.265365 0.459625i
\(566\) 3111.27 0.231054
\(567\) 0 0
\(568\) 3360.00 0.248209
\(569\) −2945.00 + 5100.89i −0.216979 + 0.375818i −0.953883 0.300179i \(-0.902954\pi\)
0.736904 + 0.675997i \(0.236287\pi\)
\(570\) 0 0
\(571\) 2806.00 + 4860.13i 0.205652 + 0.356200i 0.950340 0.311212i \(-0.100735\pi\)
−0.744688 + 0.667413i \(0.767402\pi\)
\(572\) 5091.17 8818.16i 0.372155 0.644591i
\(573\) 0 0
\(574\) 0 0
\(575\) −5100.00 −0.369886
\(576\) 0 0
\(577\) −8898.94 15413.4i −0.642058 1.11208i −0.984973 0.172711i \(-0.944747\pi\)
0.342914 0.939367i \(-0.388586\pi\)
\(578\) −4911.00 8506.10i −0.353409 0.612123i
\(579\) 0 0
\(580\) −3111.27 −0.222739
\(581\) 0 0
\(582\) 0 0
\(583\) −12560.0 + 21754.6i −0.892251 + 1.54542i
\(584\) 1159.66 + 2008.58i 0.0821693 + 0.142321i
\(585\) 0 0
\(586\) 7686.25 13313.0i 0.541836 0.938488i
\(587\) 7942.22 0.558451 0.279225 0.960226i \(-0.409922\pi\)
0.279225 + 0.960226i \(0.409922\pi\)
\(588\) 0 0
\(589\) −1344.00 −0.0940213
\(590\) 6200.00 10738.7i 0.432627 0.749332i
\(591\) 0 0
\(592\) 160.000 + 277.128i 0.0111080 + 0.0192397i
\(593\) 7039.25 12192.3i 0.487466 0.844316i −0.512430 0.858729i \(-0.671255\pi\)
0.999896 + 0.0144132i \(0.00458802\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8560.00 0.588307
\(597\) 0 0
\(598\) −4327.49 7495.44i −0.295927 0.512561i
\(599\) 3650.00 + 6321.99i 0.248973 + 0.431234i 0.963241 0.268638i \(-0.0865736\pi\)
−0.714268 + 0.699872i \(0.753240\pi\)
\(600\) 0 0
\(601\) 8727.11 0.592323 0.296162 0.955138i \(-0.404293\pi\)
0.296162 + 0.955138i \(0.404293\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4240.00 + 7343.90i −0.285634 + 0.494733i
\(605\) 951.059 + 1647.28i 0.0639108 + 0.110697i
\(606\) 0 0
\(607\) 5303.30 9185.59i 0.354620 0.614220i −0.632433 0.774615i \(-0.717944\pi\)
0.987053 + 0.160395i \(0.0512769\pi\)
\(608\) −362.039 −0.0241490
\(609\) 0 0
\(610\) 12980.0 0.861549
\(611\) 2880.00 4988.31i 0.190691 0.330287i
\(612\) 0 0
\(613\) 6990.00 + 12107.0i 0.460560 + 0.797714i 0.998989 0.0449573i \(-0.0143152\pi\)
−0.538429 + 0.842671i \(0.680982\pi\)
\(614\) −8598.42 + 14892.9i −0.565153 + 0.978874i
\(615\) 0 0
\(616\) 0 0
\(617\) −2654.00 −0.173170 −0.0865851 0.996244i \(-0.527595\pi\)
−0.0865851 + 0.996244i \(0.527595\pi\)
\(618\) 0 0
\(619\) 11941.6 + 20683.5i 0.775403 + 1.34304i 0.934568 + 0.355785i \(0.115786\pi\)
−0.159165 + 0.987252i \(0.550880\pi\)
\(620\) −1680.00 2909.85i −0.108823 0.188487i
\(621\) 0 0
\(622\) −15160.4 −0.977292
\(623\) 0 0
\(624\) 0 0
\(625\) 312.500 541.266i 0.0200000 0.0346410i
\(626\) 3075.91 + 5327.64i 0.196387 + 0.340152i
\(627\) 0 0
\(628\) −3493.11 + 6050.24i −0.221959 + 0.384444i
\(629\) −28.2843 −0.00179295
\(630\) 0 0
\(631\) −6400.00 −0.403772 −0.201886 0.979409i \(-0.564707\pi\)
−0.201886 + 0.979409i \(0.564707\pi\)
\(632\) −3040.00 + 5265.43i −0.191337 + 0.331405i
\(633\) 0 0
\(634\) −2324.00 4025.29i −0.145580 0.252152i
\(635\) 3535.53 6123.72i 0.220950 0.382697i
\(636\) 0 0
\(637\) 0 0
\(638\) −8800.00 −0.546074
\(639\) 0 0
\(640\) −452.548 783.837i −0.0279508 0.0484123i
\(641\) −7675.00 13293.5i −0.472924 0.819128i 0.526596 0.850116i \(-0.323468\pi\)
−0.999520 + 0.0309874i \(0.990135\pi\)
\(642\) 0 0
\(643\) 17847.4 1.09461 0.547303 0.836934i \(-0.315655\pi\)
0.547303 + 0.836934i \(0.315655\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 16.0000 27.7128i 0.000974476 0.00168784i
\(647\) 7000.36 + 12125.0i 0.425367 + 0.736757i 0.996455 0.0841319i \(-0.0268117\pi\)
−0.571088 + 0.820889i \(0.693478\pi\)
\(648\) 0 0
\(649\) 17536.2 30373.7i 1.06064 1.83709i
\(650\) −9545.94 −0.576035
\(651\) 0 0
\(652\) 13360.0 0.802482
\(653\) −13191.0 + 22847.5i −0.790511 + 1.36921i 0.135140 + 0.990827i \(0.456852\pi\)
−0.925651 + 0.378379i \(0.876482\pi\)
\(654\) 0 0
\(655\) 300.000 + 519.615i 0.0178961 + 0.0309970i
\(656\) 395.980 685.857i 0.0235677 0.0408205i
\(657\) 0 0
\(658\) 0 0
\(659\) 14400.0 0.851205 0.425603 0.904910i \(-0.360062\pi\)
0.425603 + 0.904910i \(0.360062\pi\)
\(660\) 0 0
\(661\) −14291.3 24753.3i −0.840951 1.45657i −0.889092 0.457729i \(-0.848663\pi\)
0.0481409 0.998841i \(-0.484670\pi\)
\(662\) 9508.00 + 16468.3i 0.558216 + 0.966858i
\(663\) 0 0
\(664\) −7557.56 −0.441702
\(665\) 0 0
\(666\) 0 0
\(667\) −3740.00 + 6477.87i −0.217112 + 0.376048i
\(668\) −735.391 1273.73i −0.0425945 0.0737759i
\(669\) 0 0
\(670\) −3818.38 + 6613.62i −0.220174 + 0.381353i
\(671\) 36713.0 2.11220
\(672\) 0 0
\(673\) −18120.0 −1.03785 −0.518926 0.854819i \(-0.673668\pi\)
−0.518926 + 0.854819i \(0.673668\pi\)
\(674\) −4720.00 + 8175.28i −0.269744 + 0.467211i
\(675\) 0 0
\(676\) −3706.00 6418.98i −0.210856 0.365213i
\(677\) −8898.94 + 15413.4i −0.505191 + 0.875016i 0.494791 + 0.869012i \(0.335244\pi\)
−0.999982 + 0.00600394i \(0.998089\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 80.0000 0.00451156
\(681\) 0 0
\(682\) −4751.76 8230.29i −0.266795 0.462103i
\(683\) −864.000 1496.49i −0.0484042 0.0838385i 0.840808 0.541333i \(-0.182080\pi\)
−0.889212 + 0.457495i \(0.848747\pi\)
\(684\) 0 0
\(685\) −14382.6 −0.802232
\(686\) 0 0
\(687\) 0 0
\(688\) 2720.00 4711.18i 0.150725 0.261064i
\(689\) 19982.8 + 34611.3i 1.10491 + 1.91377i
\(690\) 0 0
\(691\) −8544.68 + 14799.8i −0.470412 + 0.814778i −0.999427 0.0338344i \(-0.989228\pi\)
0.529015 + 0.848612i \(0.322561\pi\)
\(692\) 13559.5 0.744876
\(693\) 0 0
\(694\) 13008.0 0.711494
\(695\) −6140.00 + 10634.8i −0.335113 + 0.580433i
\(696\) 0 0
\(697\) 35.0000 + 60.6218i 0.00190204 + 0.00329442i
\(698\) −5256.63 + 9104.75i −0.285052 + 0.493725i
\(699\) 0 0
\(700\) 0 0
\(701\) 13410.0 0.722523 0.361262 0.932465i \(-0.382346\pi\)
0.361262 + 0.932465i \(0.382346\pi\)
\(702\) 0 0
\(703\) 113.137 + 195.959i 0.00606977 + 0.0105131i
\(704\) −1280.00 2217.03i −0.0685253 0.118689i
\(705\) 0 0
\(706\) −24423.5 −1.30197
\(707\) 0 0
\(708\) 0 0
\(709\) 70.0000 121.244i 0.00370791 0.00642228i −0.864165 0.503208i \(-0.832153\pi\)
0.867873 + 0.496785i \(0.165486\pi\)
\(710\) 2969.85 + 5143.93i 0.156981 + 0.271899i
\(711\) 0 0
\(712\) 4610.34 7985.34i 0.242668 0.420313i
\(713\) −8077.99 −0.424296
\(714\) 0 0
\(715\) 18000.0 0.941485
\(716\) −1440.00 + 2494.15i −0.0751611 + 0.130183i
\(717\) 0 0
\(718\) −7340.00 12713.3i −0.381513 0.660800i
\(719\) −12968.3 + 22461.8i −0.672653 + 1.16507i 0.304496 + 0.952514i \(0.401512\pi\)
−0.977149 + 0.212555i \(0.931821\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13462.0 0.693911
\(723\) 0 0
\(724\) 3708.07 + 6422.56i 0.190344 + 0.329686i
\(725\) 4125.00 + 7144.71i 0.211308 + 0.365997i
\(726\) 0 0
\(727\) 9277.24 0.473279 0.236639 0.971598i \(-0.423954\pi\)
0.236639 + 0.971598i \(0.423954\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2050.00 + 3550.70i −0.103937 + 0.180024i
\(731\) 240.416 + 416.413i 0.0121643 + 0.0210692i
\(732\) 0 0
\(733\) 12738.5 22063.8i 0.641894 1.11179i −0.343116 0.939293i \(-0.611482\pi\)
0.985010 0.172500i \(-0.0551844\pi\)
\(734\) 15330.1 0.770904
\(735\) 0 0
\(736\) −2176.00 −0.108979
\(737\) −10800.0 + 18706.1i −0.539787 + 0.934939i
\(738\) 0 0
\(739\) 3462.00 + 5996.36i 0.172330 + 0.298484i 0.939234 0.343278i \(-0.111537\pi\)
−0.766904 + 0.641762i \(0.778204\pi\)
\(740\) −282.843 + 489.898i −0.0140507 + 0.0243365i
\(741\) 0 0
\(742\) 0 0
\(743\) −29108.0 −1.43724 −0.718620 0.695403i \(-0.755226\pi\)
−0.718620 + 0.695403i \(0.755226\pi\)
\(744\) 0 0
\(745\) 7566.04 + 13104.8i 0.372078 + 0.644459i
\(746\) −2990.00 5178.83i −0.146745 0.254170i
\(747\) 0 0
\(748\) 226.274 0.0110607
\(749\) 0 0
\(750\) 0 0
\(751\) −15724.0 + 27234.8i −0.764017 + 1.32332i 0.176747 + 0.984256i \(0.443442\pi\)
−0.940765 + 0.339060i \(0.889891\pi\)
\(752\) −724.077 1254.14i −0.0351122 0.0608161i
\(753\) 0 0
\(754\) −7000.36 + 12125.0i −0.338114 + 0.585631i
\(755\) −14990.7 −0.722604
\(756\) 0 0
\(757\) −13300.0 −0.638569 −0.319284 0.947659i \(-0.603443\pi\)
−0.319284 + 0.947659i \(0.603443\pi\)
\(758\) −11900.0 + 20611.4i −0.570221 + 0.987652i
\(759\) 0 0
\(760\) −320.000 554.256i −0.0152732 0.0264539i
\(761\) −2400.63 + 4158.01i −0.114353 + 0.198065i −0.917521 0.397687i \(-0.869813\pi\)
0.803168 + 0.595753i \(0.203146\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 15920.0 0.753881
\(765\) 0 0
\(766\) −9712.82 16823.1i −0.458144 0.793529i
\(767\) −27900.0 48324.2i −1.31344 2.27495i
\(768\) 0 0
\(769\) 16932.4 0.794015 0.397007 0.917815i \(-0.370049\pi\)
0.397007 + 0.917815i \(0.370049\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7420.00 + 12851.8i −0.345922 + 0.599154i
\(773\) 9720.60 + 16836.6i 0.452297 + 0.783401i 0.998528 0.0542330i \(-0.0172714\pi\)
−0.546231 + 0.837634i \(0.683938\pi\)
\(774\) 0 0
\(775\) −4454.77 + 7715.89i −0.206478 + 0.357630i
\(776\) 4016.37 0.185798
\(777\) 0 0
\(778\) −4300.00 −0.198152
\(779\) 280.000 484.974i 0.0128781 0.0223055i
\(780\) 0 0
\(781\) 8400.00 + 14549.2i 0.384860 + 0.666597i
\(782\) 96.1665 166.565i 0.00439758 0.00761683i
\(783\) 0 0
\(784\) 0 0
\(785\) −12350.0 −0.561516
\(786\) 0 0
\(787\) 10366.2 + 17954.8i 0.469523 + 0.813238i 0.999393 0.0348413i \(-0.0110926\pi\)
−0.529870 + 0.848079i \(0.677759\pi\)
\(788\) −1912.00 3311.68i −0.0864368 0.149713i
\(789\) 0 0
\(790\) −10748.0 −0.484047
\(791\) 0 0