Properties

Label 882.4.g.bc.361.1
Level $882$
Weight $4$
Character 882.361
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 361.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bc.667.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.269083\pi\)
−0.979698 + 0.200480i \(0.935750\pi\)
\(6\) 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 −0.450195 0.892930i \(-0.648646\pi\)
0.998398 0.0565844i \(-0.0180210\pi\)
\(12\) 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 \(-0.830122\pi\)
0.871025 + 0.491238i \(0.163455\pi\)
\(18\) 0 0
\(19\) −5.65685 9.79796i −0.0683038 0.118306i 0.829851 0.557985i \(-0.188425\pi\)
−0.898155 + 0.439679i \(0.855092\pi\)
\(20\) 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 \(-0.0669271\pi\)
−0.669738 + 0.742597i \(0.733594\pi\)
\(24\) 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 \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(30\) 0 0
\(31\) 59.3970 102.879i 0.344129 0.596050i −0.641066 0.767486i \(-0.721507\pi\)
0.985195 + 0.171436i \(0.0548408\pi\)
\(32\) −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 0.887386 0.461027i \(-0.152519\pi\)
−0.842954 + 0.537986i \(0.819185\pi\)
\(38\) −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 \(-0.469948\pi\)
0.0942708 + 0.995547i \(0.469948\pi\)
\(42\) 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 \(-0.121812\pi\)
−0.787217 + 0.616676i \(0.788479\pi\)
\(48\) 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 −0.0963923 0.995343i \(-0.530730\pi\)
0.910189 0.414194i \(-0.135936\pi\)
\(54\) 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 −0.264313 + 0.964437i \(0.585145\pi\)
−0.703070 + 0.711121i \(0.748188\pi\)
\(60\) 0 0
\(61\) −458.912 794.859i −0.963241 1.66838i −0.714269 0.699872i \(-0.753240\pi\)
−0.248972 0.968511i \(-0.580093\pi\)
\(62\) −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 −0.999961 0.00884020i \(-0.997186\pi\)
0.507636 + 0.861571i \(0.330519\pi\)
\(68\) 2.82843 + 4.89898i 0.00504408 + 0.00873660i
\(69\) 0 0
\(70\) 0 0
\(71\) 420.000 0.702040 0.351020 0.936368i \(-0.385835\pi\)
0.351020 + 0.936368i \(0.385835\pi\)
\(72\) 0 0
\(73\) −144.957 + 251.073i −0.232410 + 0.402546i −0.958517 0.285036i \(-0.907994\pi\)
0.726107 + 0.687582i \(0.241328\pi\)
\(74\) 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 0.998837 + 0.0482240i \(0.0153561\pi\)
−0.457655 + 0.889130i \(0.651311\pi\)
\(80\) −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 \(-0.714763\pi\)
−0.624661 + 0.780896i \(0.714763\pi\)
\(84\) 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 0.973005 + 0.230786i \(0.0741298\pi\)
−0.286636 + 0.958040i \(0.592537\pi\)
\(90\) 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 −0.00256667 + 0.999997i \(0.500817\pi\)
−0.864739 + 0.502221i \(0.832516\pi\)
\(102\) 0 0
\(103\) −113.137 195.959i −0.108230 0.187461i 0.806823 0.590793i \(-0.201185\pi\)
−0.915053 + 0.403333i \(0.867852\pi\)
\(104\) −509.117 −0.480029
\(105\) 0 0
\(106\) −1256.00 −1.15088
\(107\) 1012.00 + 1752.84i 0.914334 + 1.58367i 0.807874 + 0.589356i \(0.200618\pi\)
0.106460 + 0.994317i \(0.466048\pi\)
\(108\) 0 0
\(109\) 202.000 349.874i 0.177505 0.307448i −0.763520 0.645784i \(-0.776531\pi\)
0.941025 + 0.338336i \(0.109864\pi\)
\(110\) 282.843 + 489.898i 0.245164 + 0.424636i
\(111\) 0 0
\(112\) 0 0
\(113\) −1008.00 −0.839156 −0.419578 0.907719i \(-0.637822\pi\)
−0.419578 + 0.907719i \(0.637822\pi\)
\(114\) 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 \(-0.157658\pi\)
−0.851530 + 0.524305i \(0.824325\pi\)
\(132\) 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 −0.352460 0.935827i \(-0.614655\pi\)
0.986680 0.162675i \(-0.0520121\pi\)
\(138\) 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 0.994454 + 0.105171i \(0.0335389\pi\)
−0.406147 + 0.913808i \(0.633128\pi\)
\(150\) 0 0
\(151\) −1060.00 + 1835.97i −0.571269 + 0.989466i 0.425167 + 0.905115i \(0.360215\pi\)
−0.996436 + 0.0843517i \(0.973118\pi\)
\(152\) −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 −0.997976 0.0635898i \(-0.979745\pi\)
0.554058 + 0.832478i \(0.313078\pi\)
\(158\) 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 −0.917978 0.396631i \(-0.870179\pi\)
0.115497 0.993308i \(-0.463154\pi\)
\(164\) −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 \(-0.527149\pi\)
−0.0851890 + 0.996365i \(0.527149\pi\)
\(168\) 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 0.950253 + 0.311480i \(0.100825\pi\)
−0.205377 + 0.978683i \(0.565842\pi\)
\(174\) 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 \(-0.785302\pi\)
0.931346 + 0.364136i \(0.118636\pi\)
\(180\) 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 0.945929 + 0.324375i \(0.105154\pi\)
−0.192047 + 0.981386i \(0.561513\pi\)
\(192\) 0 0
\(193\) −1855.00 + 3212.95i −0.691844 + 1.19831i 0.279390 + 0.960178i \(0.409868\pi\)
−0.971233 + 0.238130i \(0.923465\pi\)
\(194\) 502.046 + 869.569i 0.185798 + 0.321811i
\(195\) 0 0
\(196\) 0 0
\(197\) −956.000 −0.345747 −0.172874 0.984944i \(-0.555305\pi\)
−0.172874 + 0.984944i \(0.555305\pi\)
\(198\) 0 0
\(199\) −2044.95 + 3541.96i −0.728457 + 1.26172i 0.229079 + 0.973408i \(0.426429\pi\)
−0.957535 + 0.288316i \(0.906905\pi\)
\(200\) 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 \(-0.841231\pi\)
0.853354 + 0.521332i \(0.174565\pi\)
\(228\) 0 0
\(229\) 1571.90 + 2722.61i 0.453598 + 0.785655i 0.998606 0.0527757i \(-0.0168068\pi\)
−0.545008 + 0.838431i \(0.683473\pi\)
\(230\) −961.665 −0.275697
\(231\) 0 0
\(232\) −880.000 −0.249029
\(233\) −2241.00 3881.53i −0.630098 1.09136i −0.987531 0.157423i \(-0.949681\pi\)
0.357433 0.933939i \(-0.383652\pi\)
\(234\) 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 \(-0.424339\pi\)
0.235463 + 0.971883i \(0.424339\pi\)
\(240\) 0 0
\(241\) −630.032 + 1091.25i −0.168398 + 0.291674i −0.937857 0.347023i \(-0.887193\pi\)
0.769459 + 0.638697i \(0.220526\pi\)
\(242\) −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 \(-0.238303\pi\)
0.732608 + 0.680651i \(0.238303\pi\)
\(252\) 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 −0.996671 0.0815308i \(-0.974019\pi\)
0.427728 0.903908i \(-0.359314\pi\)
\(258\) 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 \(-0.751382\pi\)
0.964793 + 0.263011i \(0.0847156\pi\)
\(264\) 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 \(-0.932632\pi\)
0.670767 + 0.741668i \(0.265965\pi\)
\(270\) 0 0
\(271\) −3094.30 5359.48i −0.693599 1.20135i −0.970651 0.240494i \(-0.922691\pi\)
0.277052 0.960855i \(-0.410643\pi\)
\(272\) −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 0.314501 + 0.949257i \(0.398163\pi\)
−0.979331 + 0.202263i \(0.935170\pi\)
\(278\) 1736.65 + 3007.97i 0.374668 + 0.648943i
\(279\) 0 0
\(280\) 0 0
\(281\) 1970.00 0.418222 0.209111 0.977892i \(-0.432943\pi\)
0.209111 + 0.977892i \(0.432943\pi\)
\(282\) 0 0
\(283\) 777.817 1347.22i 0.163380 0.282982i −0.772699 0.634773i \(-0.781094\pi\)
0.936079 + 0.351791i \(0.114427\pi\)
\(284\) −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 \(-0.777891\pi\)
−0.766272 + 0.642516i \(0.777891\pi\)
\(294\) 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 −0.280445 0.959870i \(-0.590482\pi\)
0.971494 0.237063i \(-0.0761847\pi\)
\(312\) 0 0
\(313\) −1537.96 2663.82i −0.277733 0.481048i 0.693088 0.720853i \(-0.256250\pi\)
−0.970821 + 0.239805i \(0.922916\pi\)
\(314\) 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 \(-0.232673\pi\)
−0.950413 + 0.310990i \(0.899339\pi\)
\(318\) 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 −0.926313 0.376756i \(-0.877040\pi\)
0.136876 0.990588i \(-0.456294\pi\)
\(332\) 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 0.496891 + 0.867813i \(0.334475\pi\)
−0.999994 + 0.00358597i \(0.998859\pi\)
\(348\) 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 0.122188 0.992507i \(-0.461009\pi\)
0.798442 0.602072i \(-0.205658\pi\)
\(354\) 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 −0.998929 0.0462765i \(-0.985264\pi\)
0.459388 0.888236i \(-0.348069\pi\)
\(360\) 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 −0.453489 0.891262i \(-0.649821\pi\)
0.998600 0.0528984i \(-0.0168459\pi\)
\(368\) 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 0.950935 0.309389i \(-0.100125\pi\)
−0.743407 + 0.668840i \(0.766791\pi\)
\(374\) −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 −0.983620 0.180253i \(-0.942308\pi\)
0.335707 0.941967i \(-0.391025\pi\)
\(384\) 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 \(-0.788586\pi\)
0.927540 + 0.373725i \(0.121919\pi\)
\(390\) 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 0.738281 0.674493i \(-0.235638\pi\)
−0.953269 + 0.302123i \(0.902305\pi\)
\(398\) 8179.81 1.03019
\(399\) 0 0
\(400\) −1200.00 −0.150000
\(401\) −6045.00 10470.2i −0.752800 1.30389i −0.946461 0.322820i \(-0.895369\pi\)
0.193660 0.981069i \(-0.437964\pi\)
\(402\) 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 −0.999985 0.00550362i \(-0.998248\pi\)
0.504759 + 0.863260i \(0.331581\pi\)
\(410\) −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 \(-0.480568\pi\)
0.0610093 + 0.998137i \(0.480568\pi\)
\(420\) 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 \(-0.881542\pi\)
0.780674 + 0.624938i \(0.214876\pi\)
\(432\) 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 0.640339 0.768092i \(-0.278794\pi\)
−0.985357 + 0.170504i \(0.945460\pi\)
\(440\) −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 \(-0.287827\pi\)
−0.989798 + 0.142476i \(0.954494\pi\)
\(444\) 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 \(-0.477901\pi\)
0.0693704 + 0.997591i \(0.477901\pi\)
\(450\) 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 0.831125 0.556085i \(-0.187697\pi\)
−0.897147 + 0.441733i \(0.854364\pi\)
\(458\) 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 \(-0.149866\pi\)
0.891198 + 0.453615i \(0.149866\pi\)
\(462\) 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 \(-0.0421910\pi\)
−0.610067 + 0.792350i \(0.708858\pi\)
\(468\) 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 −0.139487 0.990224i \(-0.544545\pi\)
0.927303 0.374313i \(-0.122121\pi\)
\(480\) 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 0.349759 + 0.936840i \(0.386264\pi\)
−0.986206 + 0.165520i \(0.947070\pi\)
\(488\) −3671.30 6358.88i −0.340557 0.589862i
\(489\) 0 0
\(490\) 0 0
\(491\) −2280.00 −0.209562 −0.104781 0.994495i \(-0.533414\pi\)
−0.104781 + 0.994495i \(0.533414\pi\)
\(492\) 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 0.846093 0.533036i \(-0.178949\pi\)
−0.884669 + 0.466220i \(0.845616\pi\)
\(500\) 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 \(-0.581740\pi\)
−0.253982 + 0.967209i \(0.581740\pi\)
\(504\) 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 \(-0.102633\pi\)
−0.748655 + 0.662960i \(0.769300\pi\)
\(510\) 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 −0.377339 0.926075i \(-0.623161\pi\)
0.990674 0.136252i \(-0.0435057\pi\)
\(522\) 0 0
\(523\) 3054.70 + 5290.90i 0.255397 + 0.442361i 0.965003 0.262238i \(-0.0844604\pi\)
−0.709606 + 0.704599i \(0.751127\pi\)
\(524\) −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 0.973800 + 0.227408i \(0.0730250\pi\)
−0.289959 + 0.957039i \(0.593642\pi\)
\(542\) −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 \(-0.704461\pi\)
0.992959 + 0.118456i \(0.0377944\pi\)
\(558\) 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 −0.00543113 + 0.999985i \(0.501729\pi\)
−0.863297 + 0.504696i \(0.831605\pi\)
\(564\) 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 \(-0.0970465\pi\)
−0.736904 + 0.675997i \(0.763713\pi\)
\(570\) 0 0
\(571\) 2806.00 4860.13i 0.205652 0.356200i −0.744688 0.667413i \(-0.767402\pi\)
0.950340 + 0.311212i \(0.100735\pi\)
\(572\) −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 0.342914 + 0.939367i \(0.388586\pi\)
−0.984973 + 0.172711i \(0.944747\pi\)
\(578\) 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 \(-0.590078\pi\)
−0.279225 + 0.960226i \(0.590078\pi\)
\(588\) 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 \(-0.328745\pi\)
−0.999896 + 0.0144132i \(0.995412\pi\)
\(594\) 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 \(-0.913426\pi\)
0.714268 + 0.699872i \(0.246760\pi\)
\(600\) 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 0.987053 0.160395i \(-0.0512769\pi\)
−0.632433 + 0.774615i \(0.717944\pi\)
\(608\) 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 −0.538429 0.842671i \(-0.680982\pi\)
0.998989 + 0.0449573i \(0.0143152\pi\)
\(614\) 8598.42 + 14892.9i 0.565153 + 0.978874i
\(615\) 0 0
\(616\) 0 0
\(617\) 2654.00 0.173170 0.0865851 0.996244i \(-0.472405\pi\)
0.0865851 + 0.996244i \(0.472405\pi\)
\(618\) 0 0
\(619\) 11941.6 20683.5i 0.775403 1.34304i −0.159165 0.987252i \(-0.550880\pi\)
0.934568 0.355785i \(-0.115786\pi\)
\(620\) 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 \(-0.676532\pi\)
0.999520 + 0.0309874i \(0.00986518\pi\)
\(642\) 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 \(-0.973188\pi\)
0.571088 + 0.820889i \(0.306522\pi\)
\(648\) 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 0.925651 + 0.378379i \(0.123518\pi\)
−0.135140 + 0.990827i \(0.543148\pi\)
\(654\) 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 \(-0.639938\pi\)
−0.425603 + 0.904910i \(0.639938\pi\)
\(660\) 0 0
\(661\) −14291.3 + 24753.3i −0.840951 + 1.45657i 0.0481409 + 0.998841i \(0.484670\pi\)
−0.889092 + 0.457729i \(0.848663\pi\)
\(662\) −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 0.999982 + 0.00600394i \(0.00191112\pi\)
−0.494791 + 0.869012i \(0.664756\pi\)
\(678\) 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 \(-0.817920\pi\)
0.889212 + 0.457495i \(0.151253\pi\)
\(684\) 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 0.529015 0.848612i \(-0.322561\pi\)
−0.999427 + 0.0338344i \(0.989228\pi\)
\(692\) −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 \(-0.617654\pi\)
−0.361262 + 0.932465i \(0.617654\pi\)
\(702\) 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 0.867873 0.496785i \(-0.165486\pi\)
−0.864165 + 0.503208i \(0.832153\pi\)
\(710\) −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 0.977149 + 0.212555i \(0.0681786\pi\)
−0.304496 + 0.952514i \(0.598488\pi\)
\(720\) 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 0.985010 + 0.172500i \(0.0551844\pi\)
−0.343116 + 0.939293i \(0.611482\pi\)
\(734\) −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 −0.766904 0.641762i \(-0.778204\pi\)
0.939234 + 0.343278i \(0.111537\pi\)
\(740\) 282.843 + 489.898i 0.0140507 + 0.0243365i
\(741\) 0 0
\(742\) 0 0
\(743\) 29108.0 1.43724 0.718620 0.695403i \(-0.244774\pi\)
0.718620 + 0.695403i \(0.244774\pi\)
\(744\) 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 −0.940765 0.339060i \(-0.889891\pi\)
0.176747 0.984256i \(-0.443442\pi\)
\(752\) 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 \(-0.130187\pi\)
−0.803168 + 0.595753i \(0.796854\pi\)
\(762\) 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 \(-0.982729\pi\)
0.546231 + 0.837634i \(0.316062\pi\)
\(774\) 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 −0.529870 0.848079i \(-0.677759\pi\)
0.999393 + 0.0348413i \(0.0110926\pi\)
\(788\) 1912.00 3311.68i 0.0864368 0.149713i
\(789\) 0 0
\(790\) −10748.0 −0.484047
\(791\) 0 0