Properties

Label 252.4.x.a.41.5
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.5
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +O(q^{10})\) \(q+(-4.37628 - 2.80147i) q^{3} +(-2.20656 + 3.82187i) q^{5} +(13.5618 - 12.6126i) q^{7} +(11.3036 + 24.5200i) q^{9} +(-59.1776 + 34.1662i) q^{11} +(29.9666 + 17.3012i) q^{13} +(20.3633 - 10.5440i) q^{15} +21.8129 q^{17} -124.247i q^{19} +(-94.6839 + 17.2036i) q^{21} +(61.3750 + 35.4349i) q^{23} +(52.7622 + 91.3868i) q^{25} +(19.2243 - 138.973i) q^{27} +(187.759 - 108.403i) q^{29} +(242.498 + 140.006i) q^{31} +(354.693 + 16.2633i) q^{33} +(18.2791 + 79.6618i) q^{35} +150.970 q^{37} +(-82.6734 - 159.665i) q^{39} +(136.432 - 236.307i) q^{41} +(-136.727 - 236.817i) q^{43} +(-118.654 - 10.9039i) q^{45} +(97.3555 + 168.625i) q^{47} +(24.8427 - 342.099i) q^{49} +(-95.4592 - 61.1081i) q^{51} +520.567i q^{53} -301.559i q^{55} +(-348.073 + 543.738i) q^{57} +(301.275 - 521.824i) q^{59} +(145.594 - 84.0586i) q^{61} +(462.558 + 189.966i) q^{63} +(-132.246 + 76.3523i) q^{65} +(371.461 - 643.390i) q^{67} +(-169.324 - 327.013i) q^{69} +758.080i q^{71} +1159.14i q^{73} +(25.1151 - 547.746i) q^{75} +(-371.626 + 1209.74i) q^{77} +(78.6173 + 136.169i) q^{79} +(-473.458 + 554.327i) q^{81} +(-137.159 - 237.567i) q^{83} +(-48.1314 + 83.3660i) q^{85} +(-1125.37 - 51.6003i) q^{87} -1047.80 q^{89} +(624.614 - 143.323i) q^{91} +(-669.015 - 1292.06i) q^{93} +(474.855 + 274.158i) q^{95} +(211.382 - 122.041i) q^{97} +(-1506.67 - 1064.83i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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 0
\(3\) −4.37628 2.80147i −0.842215 0.539142i
\(4\) 0 0
\(5\) −2.20656 + 3.82187i −0.197360 + 0.341838i −0.947672 0.319246i \(-0.896570\pi\)
0.750311 + 0.661085i \(0.229904\pi\)
\(6\) 0 0
\(7\) 13.5618 12.6126i 0.732266 0.681018i
\(8\) 0 0
\(9\) 11.3036 + 24.5200i 0.418651 + 0.908147i
\(10\) 0 0
\(11\) −59.1776 + 34.1662i −1.62207 + 0.936500i −0.635698 + 0.771938i \(0.719288\pi\)
−0.986367 + 0.164562i \(0.947379\pi\)
\(12\) 0 0
\(13\) 29.9666 + 17.3012i 0.639326 + 0.369115i 0.784355 0.620312i \(-0.212994\pi\)
−0.145029 + 0.989427i \(0.546327\pi\)
\(14\) 0 0
\(15\) 20.3633 10.5440i 0.350519 0.181496i
\(16\) 0 0
\(17\) 21.8129 0.311200 0.155600 0.987820i \(-0.450269\pi\)
0.155600 + 0.987820i \(0.450269\pi\)
\(18\) 0 0
\(19\) 124.247i 1.50022i −0.661313 0.750110i \(-0.730001\pi\)
0.661313 0.750110i \(-0.269999\pi\)
\(20\) 0 0
\(21\) −94.6839 + 17.2036i −0.983891 + 0.178768i
\(22\) 0 0
\(23\) 61.3750 + 35.4349i 0.556416 + 0.321247i 0.751706 0.659498i \(-0.229231\pi\)
−0.195289 + 0.980746i \(0.562565\pi\)
\(24\) 0 0
\(25\) 52.7622 + 91.3868i 0.422098 + 0.731095i
\(26\) 0 0
\(27\) 19.2243 138.973i 0.137027 0.990567i
\(28\) 0 0
\(29\) 187.759 108.403i 1.20228 0.694134i 0.241215 0.970472i \(-0.422454\pi\)
0.961061 + 0.276337i \(0.0891207\pi\)
\(30\) 0 0
\(31\) 242.498 + 140.006i 1.40497 + 0.811157i 0.994897 0.100897i \(-0.0321713\pi\)
0.410069 + 0.912055i \(0.365505\pi\)
\(32\) 0 0
\(33\) 354.693 + 16.2633i 1.87103 + 0.0857902i
\(34\) 0 0
\(35\) 18.2791 + 79.6618i 0.0882778 + 0.384723i
\(36\) 0 0
\(37\) 150.970 0.670793 0.335397 0.942077i \(-0.391130\pi\)
0.335397 + 0.942077i \(0.391130\pi\)
\(38\) 0 0
\(39\) −82.6734 159.665i −0.339444 0.655562i
\(40\) 0 0
\(41\) 136.432 236.307i 0.519685 0.900121i −0.480053 0.877239i \(-0.659383\pi\)
0.999738 0.0228815i \(-0.00728404\pi\)
\(42\) 0 0
\(43\) −136.727 236.817i −0.484898 0.839867i 0.514952 0.857219i \(-0.327810\pi\)
−0.999849 + 0.0173518i \(0.994476\pi\)
\(44\) 0 0
\(45\) −118.654 10.9039i −0.393065 0.0361214i
\(46\) 0 0
\(47\) 97.3555 + 168.625i 0.302144 + 0.523328i 0.976621 0.214967i \(-0.0689644\pi\)
−0.674478 + 0.738295i \(0.735631\pi\)
\(48\) 0 0
\(49\) 24.8427 342.099i 0.0724277 0.997374i
\(50\) 0 0
\(51\) −95.4592 61.1081i −0.262097 0.167781i
\(52\) 0 0
\(53\) 520.567i 1.34916i 0.738203 + 0.674579i \(0.235675\pi\)
−0.738203 + 0.674579i \(0.764325\pi\)
\(54\) 0 0
\(55\) 301.559i 0.739312i
\(56\) 0 0
\(57\) −348.073 + 543.738i −0.808832 + 1.26351i
\(58\) 0 0
\(59\) 301.275 521.824i 0.664792 1.15145i −0.314550 0.949241i \(-0.601854\pi\)
0.979342 0.202212i \(-0.0648130\pi\)
\(60\) 0 0
\(61\) 145.594 84.0586i 0.305596 0.176436i −0.339358 0.940657i \(-0.610210\pi\)
0.644954 + 0.764221i \(0.276876\pi\)
\(62\) 0 0
\(63\) 462.558 + 189.966i 0.925029 + 0.379896i
\(64\) 0 0
\(65\) −132.246 + 76.3523i −0.252355 + 0.145698i
\(66\) 0 0
\(67\) 371.461 643.390i 0.677332 1.17317i −0.298450 0.954425i \(-0.596470\pi\)
0.975782 0.218747i \(-0.0701970\pi\)
\(68\) 0 0
\(69\) −169.324 327.013i −0.295424 0.570547i
\(70\) 0 0
\(71\) 758.080i 1.26715i 0.773682 + 0.633574i \(0.218413\pi\)
−0.773682 + 0.633574i \(0.781587\pi\)
\(72\) 0 0
\(73\) 1159.14i 1.85845i 0.369520 + 0.929223i \(0.379522\pi\)
−0.369520 + 0.929223i \(0.620478\pi\)
\(74\) 0 0
\(75\) 25.1151 547.746i 0.0386672 0.843309i
\(76\) 0 0
\(77\) −371.626 + 1209.74i −0.550010 + 1.79042i
\(78\) 0 0
\(79\) 78.6173 + 136.169i 0.111964 + 0.193927i 0.916562 0.399893i \(-0.130953\pi\)
−0.804598 + 0.593820i \(0.797619\pi\)
\(80\) 0 0
\(81\) −473.458 + 554.327i −0.649463 + 0.760394i
\(82\) 0 0
\(83\) −137.159 237.567i −0.181388 0.314173i 0.760965 0.648792i \(-0.224726\pi\)
−0.942353 + 0.334619i \(0.891392\pi\)
\(84\) 0 0
\(85\) −48.1314 + 83.3660i −0.0614186 + 0.106380i
\(86\) 0 0
\(87\) −1125.37 51.6003i −1.38681 0.0635878i
\(88\) 0 0
\(89\) −1047.80 −1.24793 −0.623967 0.781451i \(-0.714480\pi\)
−0.623967 + 0.781451i \(0.714480\pi\)
\(90\) 0 0
\(91\) 624.614 143.323i 0.719531 0.165102i
\(92\) 0 0
\(93\) −669.015 1292.06i −0.745953 1.44065i
\(94\) 0 0
\(95\) 474.855 + 274.158i 0.512833 + 0.296084i
\(96\) 0 0
\(97\) 211.382 122.041i 0.221264 0.127747i −0.385272 0.922803i \(-0.625892\pi\)
0.606535 + 0.795057i \(0.292559\pi\)
\(98\) 0 0
\(99\) −1506.67 1064.83i −1.52956 1.08101i
\(100\) 0 0
\(101\) 525.022 + 909.365i 0.517244 + 0.895893i 0.999799 + 0.0200273i \(0.00637530\pi\)
−0.482556 + 0.875865i \(0.660291\pi\)
\(102\) 0 0
\(103\) −373.861 215.849i −0.357647 0.206488i 0.310401 0.950606i \(-0.399537\pi\)
−0.668048 + 0.744118i \(0.732870\pi\)
\(104\) 0 0
\(105\) 143.176 399.830i 0.133071 0.371613i
\(106\) 0 0
\(107\) 12.0965i 0.0109291i 0.999985 + 0.00546455i \(0.00173943\pi\)
−0.999985 + 0.00546455i \(0.998261\pi\)
\(108\) 0 0
\(109\) −877.008 −0.770662 −0.385331 0.922778i \(-0.625913\pi\)
−0.385331 + 0.922778i \(0.625913\pi\)
\(110\) 0 0
\(111\) −660.687 422.938i −0.564952 0.361653i
\(112\) 0 0
\(113\) 1041.65 + 601.395i 0.867167 + 0.500659i 0.866406 0.499340i \(-0.166424\pi\)
0.000761396 1.00000i \(0.499758\pi\)
\(114\) 0 0
\(115\) −270.855 + 156.378i −0.219629 + 0.126803i
\(116\) 0 0
\(117\) −85.4958 + 930.346i −0.0675563 + 0.735133i
\(118\) 0 0
\(119\) 295.821 275.118i 0.227881 0.211933i
\(120\) 0 0
\(121\) 1669.16 2891.07i 1.25406 2.17210i
\(122\) 0 0
\(123\) −1259.07 + 651.935i −0.922980 + 0.477911i
\(124\) 0 0
\(125\) −1017.33 −0.727942
\(126\) 0 0
\(127\) 2508.88 1.75297 0.876485 0.481429i \(-0.159882\pi\)
0.876485 + 0.481429i \(0.159882\pi\)
\(128\) 0 0
\(129\) −65.0826 + 1419.41i −0.0444202 + 0.968777i
\(130\) 0 0
\(131\) −203.928 + 353.215i −0.136010 + 0.235576i −0.925983 0.377566i \(-0.876761\pi\)
0.789973 + 0.613142i \(0.210095\pi\)
\(132\) 0 0
\(133\) −1567.08 1685.01i −1.02168 1.09856i
\(134\) 0 0
\(135\) 488.716 + 380.124i 0.311570 + 0.242340i
\(136\) 0 0
\(137\) −1998.46 + 1153.81i −1.24628 + 0.719540i −0.970365 0.241642i \(-0.922314\pi\)
−0.275914 + 0.961182i \(0.588981\pi\)
\(138\) 0 0
\(139\) 35.4504 + 20.4673i 0.0216321 + 0.0124893i 0.510777 0.859713i \(-0.329358\pi\)
−0.489145 + 0.872203i \(0.662691\pi\)
\(140\) 0 0
\(141\) 46.3417 1010.69i 0.0276786 0.603653i
\(142\) 0 0
\(143\) −2364.47 −1.38271
\(144\) 0 0
\(145\) 956.788i 0.547979i
\(146\) 0 0
\(147\) −1067.10 + 1427.52i −0.598726 + 0.800954i
\(148\) 0 0
\(149\) 2458.97 + 1419.69i 1.35199 + 0.780573i 0.988528 0.151035i \(-0.0482605\pi\)
0.363464 + 0.931608i \(0.381594\pi\)
\(150\) 0 0
\(151\) 383.904 + 664.941i 0.206898 + 0.358359i 0.950736 0.310002i \(-0.100330\pi\)
−0.743837 + 0.668361i \(0.766996\pi\)
\(152\) 0 0
\(153\) 246.564 + 534.851i 0.130284 + 0.282616i
\(154\) 0 0
\(155\) −1070.17 + 617.864i −0.554569 + 0.320181i
\(156\) 0 0
\(157\) −121.383 70.0804i −0.0617032 0.0356243i 0.468831 0.883288i \(-0.344675\pi\)
−0.530534 + 0.847664i \(0.678009\pi\)
\(158\) 0 0
\(159\) 1458.35 2278.15i 0.727388 1.13628i
\(160\) 0 0
\(161\) 1279.28 293.542i 0.626220 0.143691i
\(162\) 0 0
\(163\) −702.905 −0.337765 −0.168883 0.985636i \(-0.554016\pi\)
−0.168883 + 0.985636i \(0.554016\pi\)
\(164\) 0 0
\(165\) −844.806 + 1319.70i −0.398594 + 0.622659i
\(166\) 0 0
\(167\) 1094.61 1895.92i 0.507206 0.878506i −0.492759 0.870166i \(-0.664012\pi\)
0.999965 0.00834081i \(-0.00265499\pi\)
\(168\) 0 0
\(169\) −499.835 865.739i −0.227508 0.394055i
\(170\) 0 0
\(171\) 3046.53 1404.43i 1.36242 0.628068i
\(172\) 0 0
\(173\) −900.641 1559.96i −0.395806 0.685557i 0.597397 0.801945i \(-0.296202\pi\)
−0.993204 + 0.116389i \(0.962868\pi\)
\(174\) 0 0
\(175\) 1868.18 + 573.896i 0.806977 + 0.247900i
\(176\) 0 0
\(177\) −2780.34 + 1439.63i −1.18069 + 0.611353i
\(178\) 0 0
\(179\) 2708.76i 1.13107i 0.824723 + 0.565537i \(0.191331\pi\)
−0.824723 + 0.565537i \(0.808669\pi\)
\(180\) 0 0
\(181\) 466.672i 0.191644i −0.995399 0.0958218i \(-0.969452\pi\)
0.995399 0.0958218i \(-0.0305479\pi\)
\(182\) 0 0
\(183\) −872.646 40.0124i −0.352502 0.0161628i
\(184\) 0 0
\(185\) −333.124 + 576.988i −0.132388 + 0.229303i
\(186\) 0 0
\(187\) −1290.83 + 745.263i −0.504787 + 0.291439i
\(188\) 0 0
\(189\) −1492.10 2127.18i −0.574255 0.818677i
\(190\) 0 0
\(191\) 2131.65 1230.71i 0.807544 0.466236i −0.0385584 0.999256i \(-0.512277\pi\)
0.846102 + 0.533021i \(0.178943\pi\)
\(192\) 0 0
\(193\) −821.546 + 1422.96i −0.306405 + 0.530709i −0.977573 0.210596i \(-0.932460\pi\)
0.671168 + 0.741305i \(0.265793\pi\)
\(194\) 0 0
\(195\) 792.644 + 36.3441i 0.291089 + 0.0133470i
\(196\) 0 0
\(197\) 528.765i 0.191233i −0.995418 0.0956166i \(-0.969518\pi\)
0.995418 0.0956166i \(-0.0304823\pi\)
\(198\) 0 0
\(199\) 3314.80i 1.18080i −0.807109 0.590402i \(-0.798969\pi\)
0.807109 0.590402i \(-0.201031\pi\)
\(200\) 0 0
\(201\) −3428.05 + 1775.01i −1.20297 + 0.622885i
\(202\) 0 0
\(203\) 1179.10 3838.27i 0.407668 1.32706i
\(204\) 0 0
\(205\) 602.090 + 1042.85i 0.205131 + 0.355297i
\(206\) 0 0
\(207\) −175.105 + 1905.46i −0.0587954 + 0.639799i
\(208\) 0 0
\(209\) 4245.04 + 7352.63i 1.40496 + 2.43345i
\(210\) 0 0
\(211\) −2475.87 + 4288.34i −0.807801 + 1.39915i 0.106582 + 0.994304i \(0.466009\pi\)
−0.914384 + 0.404849i \(0.867324\pi\)
\(212\) 0 0
\(213\) 2123.73 3317.57i 0.683173 1.06721i
\(214\) 0 0
\(215\) 1206.78 0.382798
\(216\) 0 0
\(217\) 5054.55 1159.81i 1.58122 0.362824i
\(218\) 0 0
\(219\) 3247.28 5072.70i 1.00197 1.56521i
\(220\) 0 0
\(221\) 653.658 + 377.390i 0.198958 + 0.114869i
\(222\) 0 0
\(223\) 1349.02 778.858i 0.405100 0.233884i −0.283582 0.958948i \(-0.591523\pi\)
0.688682 + 0.725064i \(0.258190\pi\)
\(224\) 0 0
\(225\) −1644.40 + 2326.73i −0.487230 + 0.689400i
\(226\) 0 0
\(227\) 125.360 + 217.131i 0.0366540 + 0.0634866i 0.883770 0.467921i \(-0.154997\pi\)
−0.847116 + 0.531407i \(0.821663\pi\)
\(228\) 0 0
\(229\) 4341.47 + 2506.55i 1.25281 + 0.723308i 0.971666 0.236359i \(-0.0759542\pi\)
0.281140 + 0.959667i \(0.409288\pi\)
\(230\) 0 0
\(231\) 5015.38 4253.05i 1.42852 1.21139i
\(232\) 0 0
\(233\) 3160.66i 0.888676i −0.895859 0.444338i \(-0.853439\pi\)
0.895859 0.444338i \(-0.146561\pi\)
\(234\) 0 0
\(235\) −859.281 −0.238525
\(236\) 0 0
\(237\) 37.4223 816.157i 0.0102567 0.223692i
\(238\) 0 0
\(239\) −504.538 291.295i −0.136552 0.0788382i 0.430168 0.902749i \(-0.358454\pi\)
−0.566720 + 0.823911i \(0.691788\pi\)
\(240\) 0 0
\(241\) 2813.68 1624.48i 0.752054 0.434198i −0.0743818 0.997230i \(-0.523698\pi\)
0.826435 + 0.563031i \(0.190365\pi\)
\(242\) 0 0
\(243\) 3624.91 1099.51i 0.956947 0.290262i
\(244\) 0 0
\(245\) 1252.64 + 849.807i 0.326646 + 0.221601i
\(246\) 0 0
\(247\) 2149.62 3723.26i 0.553754 0.959130i
\(248\) 0 0
\(249\) −65.2887 + 1423.91i −0.0166165 + 0.362395i
\(250\) 0 0
\(251\) −4222.39 −1.06181 −0.530907 0.847430i \(-0.678148\pi\)
−0.530907 + 0.847430i \(0.678148\pi\)
\(252\) 0 0
\(253\) −4842.70 −1.20339
\(254\) 0 0
\(255\) 444.183 229.994i 0.109082 0.0564815i
\(256\) 0 0
\(257\) 3840.77 6652.41i 0.932220 1.61465i 0.152704 0.988272i \(-0.451202\pi\)
0.779517 0.626381i \(-0.215465\pi\)
\(258\) 0 0
\(259\) 2047.42 1904.13i 0.491199 0.456823i
\(260\) 0 0
\(261\) 4780.38 + 3378.51i 1.13371 + 0.801243i
\(262\) 0 0
\(263\) −5082.39 + 2934.32i −1.19161 + 0.687976i −0.958671 0.284515i \(-0.908167\pi\)
−0.232938 + 0.972492i \(0.574834\pi\)
\(264\) 0 0
\(265\) −1989.54 1148.66i −0.461194 0.266270i
\(266\) 0 0
\(267\) 4585.44 + 2935.36i 1.05103 + 0.672814i
\(268\) 0 0
\(269\) −810.599 −0.183729 −0.0918645 0.995772i \(-0.529283\pi\)
−0.0918645 + 0.995772i \(0.529283\pi\)
\(270\) 0 0
\(271\) 6222.78i 1.39486i 0.716653 + 0.697430i \(0.245673\pi\)
−0.716653 + 0.697430i \(0.754327\pi\)
\(272\) 0 0
\(273\) −3135.00 1122.62i −0.695014 0.248878i
\(274\) 0 0
\(275\) −6244.68 3605.37i −1.36934 0.790589i
\(276\) 0 0
\(277\) 285.059 + 493.737i 0.0618323 + 0.107097i 0.895284 0.445495i \(-0.146972\pi\)
−0.833452 + 0.552592i \(0.813639\pi\)
\(278\) 0 0
\(279\) −691.856 + 7528.62i −0.148460 + 1.61551i
\(280\) 0 0
\(281\) 2609.79 1506.76i 0.554047 0.319879i −0.196706 0.980463i \(-0.563024\pi\)
0.750753 + 0.660584i \(0.229691\pi\)
\(282\) 0 0
\(283\) −5937.64 3428.10i −1.24719 0.720068i −0.276646 0.960972i \(-0.589223\pi\)
−0.970549 + 0.240904i \(0.922556\pi\)
\(284\) 0 0
\(285\) −1310.05 2530.08i −0.272284 0.525856i
\(286\) 0 0
\(287\) −1130.20 4925.51i −0.232451 1.01304i
\(288\) 0 0
\(289\) −4437.20 −0.903154
\(290\) 0 0
\(291\) −1266.96 58.0924i −0.255225 0.0117025i
\(292\) 0 0
\(293\) 507.694 879.352i 0.101228 0.175332i −0.810963 0.585098i \(-0.801056\pi\)
0.912191 + 0.409766i \(0.134390\pi\)
\(294\) 0 0
\(295\) 1329.56 + 2302.87i 0.262407 + 0.454503i
\(296\) 0 0
\(297\) 3610.52 + 8880.89i 0.705400 + 1.73509i
\(298\) 0 0
\(299\) 1226.13 + 2123.73i 0.237155 + 0.410764i
\(300\) 0 0
\(301\) −4841.14 1487.18i −0.927039 0.284782i
\(302\) 0 0
\(303\) 249.913 5450.46i 0.0473833 1.03340i
\(304\) 0 0
\(305\) 741.920i 0.139286i
\(306\) 0 0
\(307\) 313.327i 0.0582493i −0.999576 0.0291246i \(-0.990728\pi\)
0.999576 0.0291246i \(-0.00927197\pi\)
\(308\) 0 0
\(309\) 1031.43 + 1991.98i 0.189889 + 0.366730i
\(310\) 0 0
\(311\) 2117.00 3666.76i 0.385994 0.668562i −0.605912 0.795531i \(-0.707192\pi\)
0.991907 + 0.126970i \(0.0405251\pi\)
\(312\) 0 0
\(313\) −2846.33 + 1643.33i −0.514007 + 0.296762i −0.734479 0.678631i \(-0.762573\pi\)
0.220472 + 0.975393i \(0.429240\pi\)
\(314\) 0 0
\(315\) −1746.69 + 1348.66i −0.312427 + 0.241234i
\(316\) 0 0
\(317\) 5320.94 3072.05i 0.942757 0.544301i 0.0519334 0.998651i \(-0.483462\pi\)
0.890823 + 0.454350i \(0.150128\pi\)
\(318\) 0 0
\(319\) −7407.42 + 12830.0i −1.30011 + 2.25186i
\(320\) 0 0
\(321\) 33.8880 52.9377i 0.00589234 0.00920465i
\(322\) 0 0
\(323\) 2710.18i 0.466869i
\(324\) 0 0
\(325\) 3651.41i 0.623211i
\(326\) 0 0
\(327\) 3838.03 + 2456.91i 0.649063 + 0.415497i
\(328\) 0 0
\(329\) 3447.11 + 1058.94i 0.577646 + 0.177450i
\(330\) 0 0
\(331\) 3009.90 + 5213.30i 0.499816 + 0.865707i 1.00000 0.000212000i \(-6.74816e-5\pi\)
−0.500184 + 0.865919i \(0.666734\pi\)
\(332\) 0 0
\(333\) 1706.50 + 3701.79i 0.280828 + 0.609179i
\(334\) 0 0
\(335\) 1639.30 + 2839.35i 0.267357 + 0.463076i
\(336\) 0 0
\(337\) −130.124 + 225.382i −0.0210336 + 0.0364313i −0.876351 0.481674i \(-0.840029\pi\)
0.855317 + 0.518105i \(0.173362\pi\)
\(338\) 0 0
\(339\) −2873.75 5550.01i −0.460414 0.889189i
\(340\) 0 0
\(341\) −19133.9 −3.03859
\(342\) 0 0
\(343\) −3977.86 4952.80i −0.626194 0.779668i
\(344\) 0 0
\(345\) 1623.42 + 74.4369i 0.253340 + 0.0116161i
\(346\) 0 0
\(347\) −7714.97 4454.24i −1.19355 0.689096i −0.234439 0.972131i \(-0.575325\pi\)
−0.959110 + 0.283035i \(0.908659\pi\)
\(348\) 0 0
\(349\) −2449.08 + 1413.98i −0.375635 + 0.216873i −0.675917 0.736978i \(-0.736252\pi\)
0.300283 + 0.953850i \(0.402919\pi\)
\(350\) 0 0
\(351\) 2980.49 3831.94i 0.453238 0.582717i
\(352\) 0 0
\(353\) −792.030 1371.84i −0.119421 0.206843i 0.800118 0.599843i \(-0.204770\pi\)
−0.919538 + 0.393001i \(0.871437\pi\)
\(354\) 0 0
\(355\) −2897.28 1672.75i −0.433160 0.250085i
\(356\) 0 0
\(357\) −2065.33 + 375.260i −0.306187 + 0.0556326i
\(358\) 0 0
\(359\) 7054.16i 1.03706i −0.855060 0.518529i \(-0.826480\pi\)
0.855060 0.518529i \(-0.173520\pi\)
\(360\) 0 0
\(361\) −8578.27 −1.25066
\(362\) 0 0
\(363\) −15403.9 + 7976.02i −2.22726 + 1.15326i
\(364\) 0 0
\(365\) −4430.06 2557.70i −0.635288 0.366784i
\(366\) 0 0
\(367\) −4786.15 + 2763.29i −0.680749 + 0.393031i −0.800137 0.599817i \(-0.795240\pi\)
0.119388 + 0.992848i \(0.461907\pi\)
\(368\) 0 0
\(369\) 7336.41 + 674.192i 1.03501 + 0.0951140i
\(370\) 0 0
\(371\) 6565.72 + 7059.81i 0.918802 + 0.987943i
\(372\) 0 0
\(373\) −117.016 + 202.678i −0.0162436 + 0.0281348i −0.874033 0.485867i \(-0.838504\pi\)
0.857789 + 0.514001i \(0.171837\pi\)
\(374\) 0 0
\(375\) 4452.12 + 2850.02i 0.613084 + 0.392465i
\(376\) 0 0
\(377\) 7502.01 1.02486
\(378\) 0 0
\(379\) 5344.34 0.724328 0.362164 0.932114i \(-0.382038\pi\)
0.362164 + 0.932114i \(0.382038\pi\)
\(380\) 0 0
\(381\) −10979.6 7028.55i −1.47638 0.945101i
\(382\) 0 0
\(383\) −1223.32 + 2118.85i −0.163208 + 0.282684i −0.936017 0.351954i \(-0.885517\pi\)
0.772810 + 0.634638i \(0.218851\pi\)
\(384\) 0 0
\(385\) −3803.45 4089.67i −0.503485 0.541373i
\(386\) 0 0
\(387\) 4261.25 6029.41i 0.559720 0.791970i
\(388\) 0 0
\(389\) 168.902 97.5154i 0.0220145 0.0127101i −0.488952 0.872310i \(-0.662621\pi\)
0.510967 + 0.859600i \(0.329287\pi\)
\(390\) 0 0
\(391\) 1338.77 + 772.937i 0.173157 + 0.0999722i
\(392\) 0 0
\(393\) 1881.97 974.465i 0.241559 0.125077i
\(394\) 0 0
\(395\) −693.894 −0.0883889
\(396\) 0 0
\(397\) 3572.40i 0.451621i −0.974171 0.225810i \(-0.927497\pi\)
0.974171 0.225810i \(-0.0725029\pi\)
\(398\) 0 0
\(399\) 2137.49 + 11764.2i 0.268191 + 1.47605i
\(400\) 0 0
\(401\) 1583.57 + 914.277i 0.197207 + 0.113857i 0.595352 0.803465i \(-0.297013\pi\)
−0.398145 + 0.917322i \(0.630346\pi\)
\(402\) 0 0
\(403\) 4844.56 + 8391.03i 0.598821 + 1.03719i
\(404\) 0 0
\(405\) −1073.85 3032.65i −0.131753 0.372083i
\(406\) 0 0
\(407\) −8934.05 + 5158.08i −1.08807 + 0.628198i
\(408\) 0 0
\(409\) 10364.8 + 5984.12i 1.25307 + 0.723461i 0.971718 0.236143i \(-0.0758833\pi\)
0.281353 + 0.959604i \(0.409217\pi\)
\(410\) 0 0
\(411\) 11978.2 + 549.222i 1.43757 + 0.0659151i
\(412\) 0 0
\(413\) −2495.76 10876.7i −0.297356 1.29591i
\(414\) 0 0
\(415\) 1210.60 0.143195
\(416\) 0 0
\(417\) −97.8023 188.884i −0.0114854 0.0221815i
\(418\) 0 0
\(419\) 895.525 1551.09i 0.104413 0.180849i −0.809085 0.587692i \(-0.800037\pi\)
0.913498 + 0.406842i \(0.133370\pi\)
\(420\) 0 0
\(421\) −3886.50 6731.62i −0.449920 0.779285i 0.548460 0.836177i \(-0.315214\pi\)
−0.998380 + 0.0568918i \(0.981881\pi\)
\(422\) 0 0
\(423\) −3034.21 + 4293.21i −0.348766 + 0.493483i
\(424\) 0 0
\(425\) 1150.90 + 1993.41i 0.131357 + 0.227517i
\(426\) 0 0
\(427\) 914.307 2976.30i 0.103622 0.337315i
\(428\) 0 0
\(429\) 10347.6 + 6623.98i 1.16453 + 0.745475i
\(430\) 0 0
\(431\) 11600.3i 1.29644i −0.761453 0.648221i \(-0.775513\pi\)
0.761453 0.648221i \(-0.224487\pi\)
\(432\) 0 0
\(433\) 12453.9i 1.38221i −0.722755 0.691105i \(-0.757124\pi\)
0.722755 0.691105i \(-0.242876\pi\)
\(434\) 0 0
\(435\) 2680.41 4187.17i 0.295438 0.461516i
\(436\) 0 0
\(437\) 4402.67 7625.65i 0.481941 0.834747i
\(438\) 0 0
\(439\) −10941.0 + 6316.81i −1.18949 + 0.686754i −0.958191 0.286128i \(-0.907632\pi\)
−0.231301 + 0.972882i \(0.574298\pi\)
\(440\) 0 0
\(441\) 8669.07 3257.80i 0.936084 0.351777i
\(442\) 0 0
\(443\) −11050.1 + 6379.76i −1.18511 + 0.684224i −0.957191 0.289456i \(-0.906526\pi\)
−0.227920 + 0.973680i \(0.573192\pi\)
\(444\) 0 0
\(445\) 2312.02 4004.54i 0.246293 0.426592i
\(446\) 0 0
\(447\) −6783.93 13101.7i −0.717828 1.38633i
\(448\) 0 0
\(449\) 3363.17i 0.353492i 0.984256 + 0.176746i \(0.0565571\pi\)
−0.984256 + 0.176746i \(0.943443\pi\)
\(450\) 0 0
\(451\) 18645.4i 1.94674i
\(452\) 0 0
\(453\) 182.740 3985.46i 0.0189534 0.413363i
\(454\) 0 0
\(455\) −830.486 + 2703.44i −0.0855687 + 0.278548i
\(456\) 0 0
\(457\) −1125.50 1949.43i −0.115205 0.199541i 0.802657 0.596441i \(-0.203419\pi\)
−0.917862 + 0.396900i \(0.870086\pi\)
\(458\) 0 0
\(459\) 419.337 3031.40i 0.0426427 0.308265i
\(460\) 0 0
\(461\) 907.079 + 1571.11i 0.0916418 + 0.158728i 0.908202 0.418532i \(-0.137455\pi\)
−0.816560 + 0.577260i \(0.804122\pi\)
\(462\) 0 0
\(463\) −4184.81 + 7248.31i −0.420053 + 0.727554i −0.995944 0.0899729i \(-0.971322\pi\)
0.575891 + 0.817527i \(0.304655\pi\)
\(464\) 0 0
\(465\) 6414.29 + 294.107i 0.639689 + 0.0293309i
\(466\) 0 0
\(467\) −8185.98 −0.811139 −0.405569 0.914064i \(-0.632927\pi\)
−0.405569 + 0.914064i \(0.632927\pi\)
\(468\) 0 0
\(469\) −3077.17 13410.6i −0.302965 1.32035i
\(470\) 0 0
\(471\) 334.877 + 646.741i 0.0327607 + 0.0632701i
\(472\) 0 0
\(473\) 16182.3 + 9342.85i 1.57307 + 0.908213i
\(474\) 0 0
\(475\) 11354.5 6555.54i 1.09680 0.633239i
\(476\) 0 0
\(477\) −12764.3 + 5884.27i −1.22523 + 0.564826i
\(478\) 0 0
\(479\) −576.208 998.022i −0.0549637 0.0952000i 0.837234 0.546844i \(-0.184171\pi\)
−0.892198 + 0.451644i \(0.850838\pi\)
\(480\) 0 0
\(481\) 4524.07 + 2611.97i 0.428856 + 0.247600i
\(482\) 0 0
\(483\) −6420.83 2299.24i −0.604882 0.216603i
\(484\) 0 0
\(485\) 1077.17i 0.100849i
\(486\) 0 0
\(487\) −336.704 −0.0313296 −0.0156648 0.999877i \(-0.504986\pi\)
−0.0156648 + 0.999877i \(0.504986\pi\)
\(488\) 0 0
\(489\) 3076.10 + 1969.16i 0.284471 + 0.182104i
\(490\) 0 0
\(491\) −2081.98 1202.03i −0.191361 0.110483i 0.401258 0.915965i \(-0.368573\pi\)
−0.592620 + 0.805482i \(0.701906\pi\)
\(492\) 0 0
\(493\) 4095.57 2364.58i 0.374148 0.216015i
\(494\) 0 0
\(495\) 7394.21 3408.69i 0.671404 0.309514i
\(496\) 0 0
\(497\) 9561.39 + 10280.9i 0.862951 + 0.927890i
\(498\) 0 0
\(499\) −3839.68 + 6650.52i −0.344464 + 0.596630i −0.985256 0.171085i \(-0.945273\pi\)
0.640792 + 0.767715i \(0.278606\pi\)
\(500\) 0 0
\(501\) −10101.7 + 5230.55i −0.900816 + 0.466435i
\(502\) 0 0
\(503\) 13936.7 1.23540 0.617699 0.786414i \(-0.288065\pi\)
0.617699 + 0.786414i \(0.288065\pi\)
\(504\) 0 0
\(505\) −4633.96 −0.408334
\(506\) 0 0
\(507\) −237.924 + 5188.98i −0.0208414 + 0.454538i
\(508\) 0 0
\(509\) 9073.41 15715.6i 0.790122 1.36853i −0.135770 0.990740i \(-0.543351\pi\)
0.925891 0.377790i \(-0.123316\pi\)
\(510\) 0 0
\(511\) 14619.8 + 15719.9i 1.26564 + 1.36088i
\(512\) 0 0
\(513\) −17266.9 2388.56i −1.48607 0.205570i
\(514\) 0 0
\(515\) 1649.89 952.566i 0.141171 0.0815050i
\(516\) 0 0
\(517\) −11522.5 6652.53i −0.980193 0.565915i
\(518\) 0 0
\(519\) −428.710 + 9349.92i −0.0362588 + 0.790782i
\(520\) 0 0
\(521\) −3194.77 −0.268648 −0.134324 0.990937i \(-0.542886\pi\)
−0.134324 + 0.990937i \(0.542886\pi\)
\(522\) 0 0
\(523\) 10093.3i 0.843884i 0.906623 + 0.421942i \(0.138651\pi\)
−0.906623 + 0.421942i \(0.861349\pi\)
\(524\) 0 0
\(525\) −6567.91 7745.16i −0.545995 0.643860i
\(526\) 0 0
\(527\) 5289.58 + 3053.94i 0.437226 + 0.252432i
\(528\) 0 0
\(529\) −3572.24 6187.30i −0.293600 0.508531i
\(530\) 0 0
\(531\) 16200.6 + 1488.78i 1.32400 + 0.121672i
\(532\) 0 0
\(533\) 8176.81 4720.88i 0.664497 0.383647i
\(534\) 0 0
\(535\) −46.2313 26.6916i −0.00373599 0.00215697i
\(536\) 0 0
\(537\) 7588.50 11854.3i 0.609810 0.952607i
\(538\) 0 0
\(539\) 10218.1 + 21093.4i 0.816558 + 1.68563i
\(540\) 0 0
\(541\) 13231.5 1.05151 0.525754 0.850636i \(-0.323783\pi\)
0.525754 + 0.850636i \(0.323783\pi\)
\(542\) 0 0
\(543\) −1307.37 + 2042.29i −0.103323 + 0.161405i
\(544\) 0 0
\(545\) 1935.17 3351.81i 0.152098 0.263442i
\(546\) 0 0
\(547\) 3714.66 + 6433.98i 0.290361 + 0.502920i 0.973895 0.226999i \(-0.0728913\pi\)
−0.683534 + 0.729918i \(0.739558\pi\)
\(548\) 0 0
\(549\) 3706.85 + 2619.79i 0.288168 + 0.203661i
\(550\) 0 0
\(551\) −13468.7 23328.5i −1.04135 1.80368i
\(552\) 0 0
\(553\) 2783.64 + 855.122i 0.214055 + 0.0657567i
\(554\) 0 0
\(555\) 3074.26 1591.82i 0.235126 0.121746i
\(556\) 0 0
\(557\) 9964.28i 0.757990i 0.925399 + 0.378995i \(0.123730\pi\)
−0.925399 + 0.378995i \(0.876270\pi\)
\(558\) 0 0
\(559\) 9462.15i 0.715933i
\(560\) 0 0
\(561\) 7736.88 + 354.750i 0.582266 + 0.0266979i
\(562\) 0 0
\(563\) −376.346 + 651.850i −0.0281724 + 0.0487961i −0.879768 0.475403i \(-0.842302\pi\)
0.851595 + 0.524200i \(0.175635\pi\)
\(564\) 0 0
\(565\) −4596.91 + 2654.03i −0.342289 + 0.197621i
\(566\) 0 0
\(567\) 570.597 + 13489.2i 0.0422625 + 0.999107i
\(568\) 0 0
\(569\) 4971.12 2870.08i 0.366257 0.211459i −0.305565 0.952171i \(-0.598845\pi\)
0.671822 + 0.740713i \(0.265512\pi\)
\(570\) 0 0
\(571\) 8003.90 13863.2i 0.586608 1.01603i −0.408065 0.912953i \(-0.633796\pi\)
0.994673 0.103081i \(-0.0328702\pi\)
\(572\) 0 0
\(573\) −12776.5 585.824i −0.931493 0.0427106i
\(574\) 0 0
\(575\) 7478.49i 0.542391i
\(576\) 0 0
\(577\) 970.474i 0.0700197i −0.999387 0.0350099i \(-0.988854\pi\)
0.999387 0.0350099i \(-0.0111463\pi\)
\(578\) 0 0
\(579\) 7581.69 3925.73i 0.544187 0.281775i
\(580\) 0 0
\(581\) −4856.47 1491.89i −0.346782 0.106530i
\(582\) 0 0
\(583\) −17785.8 30805.9i −1.26349 2.18842i
\(584\) 0 0
\(585\) −3367.01 2379.62i −0.237964 0.168180i
\(586\) 0 0
\(587\) 3363.90 + 5826.44i 0.236530 + 0.409681i 0.959716 0.280971i \(-0.0906566\pi\)
−0.723187 + 0.690653i \(0.757323\pi\)
\(588\) 0 0
\(589\) 17395.3 30129.6i 1.21691 2.10776i
\(590\) 0 0
\(591\) −1481.32 + 2314.02i −0.103102 + 0.161059i
\(592\) 0 0
\(593\) −20829.3 −1.44242 −0.721211 0.692716i \(-0.756414\pi\)
−0.721211 + 0.692716i \(0.756414\pi\)
\(594\) 0 0
\(595\) 398.719 + 1737.65i 0.0274721 + 0.119726i
\(596\) 0 0
\(597\) −9286.30 + 14506.5i −0.636622 + 0.994491i
\(598\) 0 0
\(599\) −3804.23 2196.37i −0.259494 0.149819i 0.364610 0.931160i \(-0.381202\pi\)
−0.624104 + 0.781342i \(0.714536\pi\)
\(600\) 0 0
\(601\) 24379.1 14075.3i 1.65465 0.955312i 0.679526 0.733652i \(-0.262186\pi\)
0.975124 0.221661i \(-0.0711477\pi\)
\(602\) 0 0
\(603\) 19974.7 + 1835.61i 1.34898 + 0.123967i
\(604\) 0 0
\(605\) 7366.19 + 12758.6i 0.495005 + 0.857374i
\(606\) 0 0
\(607\) 23547.8 + 13595.3i 1.57459 + 0.909091i 0.995595 + 0.0937614i \(0.0298891\pi\)
0.578997 + 0.815330i \(0.303444\pi\)
\(608\) 0 0
\(609\) −15912.8 + 13494.1i −1.05882 + 0.897881i
\(610\) 0 0
\(611\) 6737.48i 0.446103i
\(612\) 0 0
\(613\) 20898.3 1.37696 0.688478 0.725257i \(-0.258279\pi\)
0.688478 + 0.725257i \(0.258279\pi\)
\(614\) 0 0
\(615\) 286.598 6250.53i 0.0187915 0.409831i
\(616\) 0 0
\(617\) 4534.89 + 2618.22i 0.295896 + 0.170836i 0.640598 0.767877i \(-0.278687\pi\)
−0.344702 + 0.938712i \(0.612020\pi\)
\(618\) 0 0
\(619\) −1232.96 + 711.851i −0.0800596 + 0.0462224i −0.539495 0.841989i \(-0.681385\pi\)
0.459436 + 0.888211i \(0.348052\pi\)
\(620\) 0 0
\(621\) 6104.38 7848.25i 0.394461 0.507149i
\(622\) 0 0
\(623\) −14210.0 + 13215.5i −0.913820 + 0.849866i
\(624\) 0 0
\(625\) −4350.48 + 7535.25i −0.278431 + 0.482256i
\(626\) 0 0
\(627\) 2020.66 44069.5i 0.128704 2.80696i
\(628\) 0 0
\(629\) 3293.10 0.208751
\(630\) 0 0
\(631\) −1055.32 −0.0665793 −0.0332896 0.999446i \(-0.510598\pi\)
−0.0332896 + 0.999446i \(0.510598\pi\)
\(632\) 0 0
\(633\) 22848.7 11830.9i 1.43468 0.742867i
\(634\) 0 0
\(635\) −5535.99 + 9588.62i −0.345967 + 0.599232i
\(636\) 0 0
\(637\) 6663.19 9821.74i 0.414451 0.610913i
\(638\) 0 0
\(639\) −18588.1 + 8569.01i −1.15076 + 0.530493i
\(640\) 0 0
\(641\) −4293.85 + 2479.06i −0.264582 + 0.152756i −0.626423 0.779483i \(-0.715482\pi\)
0.361841 + 0.932240i \(0.382148\pi\)
\(642\) 0 0
\(643\) −10203.4 5890.91i −0.625787 0.361299i 0.153331 0.988175i \(-0.451000\pi\)
−0.779119 + 0.626876i \(0.784333\pi\)
\(644\) 0 0
\(645\) −5281.20 3380.75i −0.322398 0.206383i
\(646\) 0 0
\(647\) −23017.2 −1.39861 −0.699305 0.714824i \(-0.746507\pi\)
−0.699305 + 0.714824i \(0.746507\pi\)
\(648\) 0 0
\(649\) 41173.7i 2.49031i
\(650\) 0 0
\(651\) −25369.3 9084.51i −1.52734 0.546928i
\(652\) 0 0
\(653\) 13803.0 + 7969.16i 0.827187 + 0.477576i 0.852888 0.522093i \(-0.174849\pi\)
−0.0257018 + 0.999670i \(0.508182\pi\)
\(654\) 0 0
\(655\) −899.960 1558.78i −0.0536860 0.0929869i
\(656\) 0 0
\(657\) −28422.0 + 13102.4i −1.68774 + 0.778040i
\(658\) 0 0
\(659\) 9563.07 5521.24i 0.565287 0.326369i −0.189978 0.981788i \(-0.560842\pi\)
0.755265 + 0.655420i \(0.227508\pi\)
\(660\) 0 0
\(661\) −16985.4 9806.51i −0.999477 0.577048i −0.0913835 0.995816i \(-0.529129\pi\)
−0.908094 + 0.418767i \(0.862462\pi\)
\(662\) 0 0
\(663\) −1803.34 3482.76i −0.105635 0.204011i
\(664\) 0 0
\(665\) 9897.72 2271.11i 0.577169 0.132436i
\(666\) 0 0
\(667\) 15365.0 0.891955
\(668\) 0 0
\(669\) −8085.64 370.741i −0.467278 0.0214255i
\(670\) 0 0
\(671\) −5743.93 + 9948.77i −0.330465 + 0.572382i
\(672\) 0 0
\(673\) 3041.11 + 5267.35i 0.174184 + 0.301696i 0.939879 0.341508i \(-0.110938\pi\)
−0.765694 + 0.643205i \(0.777604\pi\)
\(674\) 0 0
\(675\) 13714.6 5575.66i 0.782037 0.317937i
\(676\) 0 0
\(677\) −8417.11 14578.9i −0.477837 0.827638i 0.521840 0.853043i \(-0.325246\pi\)
−0.999677 + 0.0254051i \(0.991912\pi\)
\(678\) 0 0
\(679\) 1327.45 4321.18i 0.0750261 0.244229i
\(680\) 0 0
\(681\) 59.6723 1301.42i 0.00335778 0.0732311i
\(682\) 0 0
\(683\) 6568.11i 0.367968i −0.982929 0.183984i \(-0.941101\pi\)
0.982929 0.183984i \(-0.0588994\pi\)
\(684\) 0 0
\(685\) 10183.8i 0.568035i
\(686\) 0 0
\(687\) −11977.5 23131.8i −0.665165 1.28462i
\(688\) 0 0
\(689\) −9006.45 + 15599.6i −0.497995 + 0.862553i
\(690\) 0 0
\(691\) −8934.79 + 5158.50i −0.491889 + 0.283992i −0.725358 0.688372i \(-0.758326\pi\)
0.233469 + 0.972364i \(0.424992\pi\)
\(692\) 0 0
\(693\) −33863.5 + 4562.11i −1.85623 + 0.250073i
\(694\) 0 0
\(695\) −156.447 + 90.3246i −0.00853865 + 0.00492979i
\(696\) 0 0
\(697\) 2975.97 5154.54i 0.161726 0.280118i
\(698\) 0 0
\(699\) −8854.47 + 13831.9i −0.479123 + 0.748456i
\(700\) 0 0
\(701\) 10545.7i 0.568195i 0.958795 + 0.284098i \(0.0916940\pi\)
−0.958795 + 0.284098i \(0.908306\pi\)
\(702\) 0 0
\(703\) 18757.6i 1.00634i
\(704\) 0 0
\(705\) 3760.45 + 2407.25i 0.200889 + 0.128599i
\(706\) 0 0
\(707\) 18589.7 + 5710.67i 0.988880 + 0.303779i
\(708\) 0 0
\(709\) 3965.20 + 6867.93i 0.210037 + 0.363795i 0.951726 0.306949i \(-0.0993082\pi\)
−0.741689 + 0.670744i \(0.765975\pi\)
\(710\) 0 0
\(711\) −2450.21 + 3466.89i −0.129240 + 0.182867i
\(712\) 0 0
\(713\) 9922.22 + 17185.8i 0.521164 + 0.902683i
\(714\) 0 0
\(715\) 5217.34 9036.69i 0.272891 0.472662i
\(716\) 0 0
\(717\) 1391.94 + 2688.23i 0.0725009 + 0.140019i
\(718\) 0 0
\(719\) 15064.3 0.781368 0.390684 0.920525i \(-0.372238\pi\)
0.390684 + 0.920525i \(0.372238\pi\)
\(720\) 0 0
\(721\) −7792.65 + 1788.09i −0.402515 + 0.0923604i
\(722\) 0 0
\(723\) −16864.4 773.260i −0.867485 0.0397757i
\(724\) 0 0
\(725\) 19813.2 + 11439.1i 1.01496 + 0.585985i
\(726\) 0 0
\(727\) −21471.0 + 12396.3i −1.09535 + 0.632398i −0.934995 0.354662i \(-0.884596\pi\)
−0.160351 + 0.987060i \(0.551263\pi\)
\(728\) 0 0
\(729\) −18943.9 5343.31i −0.962447 0.271468i
\(730\) 0 0
\(731\) −2982.40 5165.67i −0.150900 0.261367i
\(732\) 0 0
\(733\) −7401.55 4273.28i −0.372964 0.215331i 0.301789 0.953375i \(-0.402416\pi\)
−0.674752 + 0.738044i \(0.735750\pi\)
\(734\) 0 0
\(735\) −3101.20 7228.22i −0.155632 0.362744i
\(736\) 0 0
\(737\) 50765.7i 2.53728i
\(738\) 0 0
\(739\) 17244.9 0.858410 0.429205 0.903207i \(-0.358794\pi\)
0.429205 + 0.903207i \(0.358794\pi\)
\(740\) 0 0
\(741\) −19837.9 + 10271.9i −0.983487 + 0.509241i
\(742\) 0 0
\(743\) −10003.9 5775.74i −0.493952 0.285183i 0.232260 0.972654i \(-0.425388\pi\)
−0.726213 + 0.687470i \(0.758721\pi\)
\(744\) 0 0
\(745\) −10851.7 + 6265.25i −0.533660 + 0.308109i
\(746\) 0 0
\(747\) 4274.75 6048.51i 0.209377 0.296256i
\(748\) 0 0
\(749\) 152.569 + 164.050i 0.00744292 + 0.00800301i
\(750\) 0 0
\(751\) −7899.58 + 13682.5i −0.383835 + 0.664821i −0.991607 0.129290i \(-0.958730\pi\)
0.607772 + 0.794112i \(0.292063\pi\)
\(752\) 0 0
\(753\) 18478.4 + 11828.9i 0.894274 + 0.572468i
\(754\) 0 0
\(755\) −3388.42 −0.163334
\(756\) 0 0
\(757\) −15294.2 −0.734318 −0.367159 0.930158i \(-0.619669\pi\)
−0.367159 + 0.930158i \(0.619669\pi\)
\(758\) 0 0
\(759\) 21193.0 + 13566.7i 1.01351 + 0.648799i
\(760\) 0 0
\(761\) −8139.52 + 14098.1i −0.387723 + 0.671556i −0.992143 0.125110i \(-0.960072\pi\)
0.604420 + 0.796666i \(0.293405\pi\)
\(762\) 0 0
\(763\) −11893.8 + 11061.4i −0.564330 + 0.524835i
\(764\) 0 0
\(765\) −2588.19 237.846i −0.122322 0.0112410i
\(766\) 0 0
\(767\) 18056.4 10424.9i 0.850038 0.490770i
\(768\) 0 0
\(769\) 20947.3 + 12093.9i 0.982286 + 0.567123i 0.902960 0.429726i \(-0.141390\pi\)
0.0793265 + 0.996849i \(0.474723\pi\)
\(770\) 0 0
\(771\) −35444.8 + 18353.0i −1.65566 + 0.857285i
\(772\) 0 0
\(773\) −31168.4 −1.45026 −0.725128 0.688614i \(-0.758219\pi\)
−0.725128 + 0.688614i \(0.758219\pi\)
\(774\) 0 0
\(775\) 29548.2i 1.36955i
\(776\) 0 0
\(777\) −14294.4 + 2597.23i −0.659988 + 0.119916i
\(778\) 0 0
\(779\) −29360.4 16951.2i −1.35038 0.779642i
\(780\) 0 0
\(781\) −25900.7 44861.3i −1.18668 2.05540i
\(782\) 0 0
\(783\) −11455.5 28177.4i −0.522843 1.28605i
\(784\) 0 0
\(785\) 535.676 309.273i 0.0243555 0.0140617i
\(786\) 0 0
\(787\) 2609.54 + 1506.62i 0.118196 + 0.0682403i 0.557932 0.829886i \(-0.311595\pi\)
−0.439737 + 0.898127i \(0.644928\pi\)
\(788\) 0 0
\(789\) 30462.3 + 1396.75i 1.37451 + 0.0630236i
\(790\) 0 0
\(791\) 21711.7 4981.94i 0.975955 0.223941i
\(792\) 0 0
\(793\) 5817.27 0.260501
\(794\) 0 0
\(795\) 5488.84 + 10600.5i 0.244867 + 0.472906i