Properties

Label 624.4.q.i.529.1
Level $624$
Weight $4$
Character 624.529
Analytic conductor $36.817$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(2.66520 + 4.61626i\) of defining polynomial
Character \(\chi\) \(=\) 624.529
Dual form 624.4.q.i.289.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{3} -16.4131 q^{5} +(4.83984 + 8.38285i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{3} -16.4131 q^{5} +(4.83984 + 8.38285i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(13.7941 - 23.8921i) q^{11} +(-37.3033 + 28.3807i) q^{13} +(24.6196 - 42.6425i) q^{15} +(-53.9641 - 93.4685i) q^{17} +(-1.12362 - 1.94616i) q^{19} -29.0391 q^{21} +(20.9045 - 36.2077i) q^{23} +144.390 q^{25} +27.0000 q^{27} +(-30.8106 + 53.3656i) q^{29} -191.932 q^{31} +(41.3822 + 71.6762i) q^{33} +(-79.4368 - 137.589i) q^{35} +(-49.2118 + 85.2373i) q^{37} +(-17.7803 - 139.488i) q^{39} +(15.3726 - 26.6261i) q^{41} +(119.163 + 206.396i) q^{43} +(73.8589 + 127.927i) q^{45} +511.482 q^{47} +(124.652 - 215.903i) q^{49} +323.785 q^{51} +492.825 q^{53} +(-226.404 + 392.142i) q^{55} +6.74170 q^{57} +(242.089 + 419.311i) q^{59} +(222.011 + 384.534i) q^{61} +(43.5586 - 75.4457i) q^{63} +(612.262 - 465.815i) q^{65} +(95.0568 - 164.643i) q^{67} +(62.7135 + 108.623i) q^{69} +(242.392 + 419.836i) q^{71} -957.780 q^{73} +(-216.584 + 375.135i) q^{75} +267.045 q^{77} +375.216 q^{79} +(-40.5000 + 70.1481i) q^{81} +715.765 q^{83} +(885.717 + 1534.11i) q^{85} +(-92.4319 - 160.097i) q^{87} +(519.076 - 899.066i) q^{89} +(-418.453 - 175.350i) q^{91} +(287.898 - 498.654i) q^{93} +(18.4420 + 31.9425i) q^{95} +(-32.7818 - 56.7797i) q^{97} -248.293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{3} - 12 q^{5} - 14 q^{7} - 36 q^{9} + 40 q^{11} - 60 q^{13} + 18 q^{15} - 98 q^{17} + 124 q^{19} + 84 q^{21} + 104 q^{23} - 116 q^{25} + 216 q^{27} - 194 q^{29} - 52 q^{31} + 120 q^{33} + 88 q^{35} - 102 q^{37} - 342 q^{39} + 1054 q^{41} + 450 q^{43} + 54 q^{45} + 192 q^{47} - 1070 q^{49} + 588 q^{51} + 524 q^{53} + 204 q^{55} - 744 q^{57} + 308 q^{59} + 928 q^{61} - 126 q^{63} + 2346 q^{65} - 1134 q^{67} + 312 q^{69} + 1064 q^{71} + 1904 q^{73} + 174 q^{75} + 5016 q^{77} + 1492 q^{79} - 324 q^{81} + 808 q^{83} + 1394 q^{85} - 582 q^{87} - 1620 q^{89} - 3278 q^{91} + 78 q^{93} + 2204 q^{95} - 2166 q^{97} - 720 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −16.4131 −1.46803 −0.734016 0.679132i \(-0.762356\pi\)
−0.734016 + 0.679132i \(0.762356\pi\)
\(6\) 0 0
\(7\) 4.83984 + 8.38285i 0.261327 + 0.452631i 0.966595 0.256309i \(-0.0825066\pi\)
−0.705268 + 0.708941i \(0.749173\pi\)
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) 13.7941 23.8921i 0.378098 0.654884i −0.612688 0.790325i \(-0.709912\pi\)
0.990785 + 0.135441i \(0.0432451\pi\)
\(12\) 0 0
\(13\) −37.3033 + 28.3807i −0.795852 + 0.605491i
\(14\) 0 0
\(15\) 24.6196 42.6425i 0.423784 0.734016i
\(16\) 0 0
\(17\) −53.9641 93.4685i −0.769895 1.33350i −0.937619 0.347663i \(-0.886975\pi\)
0.167725 0.985834i \(-0.446358\pi\)
\(18\) 0 0
\(19\) −1.12362 1.94616i −0.0135671 0.0234989i 0.859162 0.511703i \(-0.170985\pi\)
−0.872729 + 0.488205i \(0.837652\pi\)
\(20\) 0 0
\(21\) −29.0391 −0.301754
\(22\) 0 0
\(23\) 20.9045 36.2077i 0.189517 0.328253i −0.755572 0.655065i \(-0.772641\pi\)
0.945089 + 0.326812i \(0.105974\pi\)
\(24\) 0 0
\(25\) 144.390 1.15512
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −30.8106 + 53.3656i −0.197289 + 0.341715i −0.947649 0.319315i \(-0.896547\pi\)
0.750359 + 0.661030i \(0.229881\pi\)
\(30\) 0 0
\(31\) −191.932 −1.11200 −0.556000 0.831182i \(-0.687665\pi\)
−0.556000 + 0.831182i \(0.687665\pi\)
\(32\) 0 0
\(33\) 41.3822 + 71.6762i 0.218295 + 0.378098i
\(34\) 0 0
\(35\) −79.4368 137.589i −0.383636 0.664477i
\(36\) 0 0
\(37\) −49.2118 + 85.2373i −0.218659 + 0.378728i −0.954398 0.298537i \(-0.903501\pi\)
0.735740 + 0.677265i \(0.236835\pi\)
\(38\) 0 0
\(39\) −17.7803 139.488i −0.0730031 0.572716i
\(40\) 0 0
\(41\) 15.3726 26.6261i 0.0585561 0.101422i −0.835261 0.549853i \(-0.814684\pi\)
0.893817 + 0.448431i \(0.148017\pi\)
\(42\) 0 0
\(43\) 119.163 + 206.396i 0.422608 + 0.731978i 0.996194 0.0871672i \(-0.0277814\pi\)
−0.573586 + 0.819145i \(0.694448\pi\)
\(44\) 0 0
\(45\) 73.8589 + 127.927i 0.244672 + 0.423784i
\(46\) 0 0
\(47\) 511.482 1.58739 0.793695 0.608316i \(-0.208155\pi\)
0.793695 + 0.608316i \(0.208155\pi\)
\(48\) 0 0
\(49\) 124.652 215.903i 0.363416 0.629456i
\(50\) 0 0
\(51\) 323.785 0.888998
\(52\) 0 0
\(53\) 492.825 1.27726 0.638630 0.769514i \(-0.279502\pi\)
0.638630 + 0.769514i \(0.279502\pi\)
\(54\) 0 0
\(55\) −226.404 + 392.142i −0.555059 + 0.961390i
\(56\) 0 0
\(57\) 6.74170 0.0156660
\(58\) 0 0
\(59\) 242.089 + 419.311i 0.534192 + 0.925248i 0.999202 + 0.0399427i \(0.0127175\pi\)
−0.465010 + 0.885306i \(0.653949\pi\)
\(60\) 0 0
\(61\) 222.011 + 384.534i 0.465993 + 0.807123i 0.999246 0.0388329i \(-0.0123640\pi\)
−0.533253 + 0.845956i \(0.679031\pi\)
\(62\) 0 0
\(63\) 43.5586 75.4457i 0.0871090 0.150877i
\(64\) 0 0
\(65\) 612.262 465.815i 1.16834 0.888880i
\(66\) 0 0
\(67\) 95.0568 164.643i 0.173329 0.300215i −0.766253 0.642539i \(-0.777881\pi\)
0.939582 + 0.342325i \(0.111214\pi\)
\(68\) 0 0
\(69\) 62.7135 + 108.623i 0.109418 + 0.189517i
\(70\) 0 0
\(71\) 242.392 + 419.836i 0.405164 + 0.701765i 0.994341 0.106239i \(-0.0338810\pi\)
−0.589176 + 0.808005i \(0.700548\pi\)
\(72\) 0 0
\(73\) −957.780 −1.53561 −0.767806 0.640683i \(-0.778651\pi\)
−0.767806 + 0.640683i \(0.778651\pi\)
\(74\) 0 0
\(75\) −216.584 + 375.135i −0.333453 + 0.577558i
\(76\) 0 0
\(77\) 267.045 0.395228
\(78\) 0 0
\(79\) 375.216 0.534368 0.267184 0.963646i \(-0.413907\pi\)
0.267184 + 0.963646i \(0.413907\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 715.765 0.946571 0.473286 0.880909i \(-0.343068\pi\)
0.473286 + 0.880909i \(0.343068\pi\)
\(84\) 0 0
\(85\) 885.717 + 1534.11i 1.13023 + 1.95762i
\(86\) 0 0
\(87\) −92.4319 160.097i −0.113905 0.197289i
\(88\) 0 0
\(89\) 519.076 899.066i 0.618224 1.07080i −0.371585 0.928399i \(-0.621186\pi\)
0.989810 0.142397i \(-0.0454810\pi\)
\(90\) 0 0
\(91\) −418.453 175.350i −0.482042 0.201996i
\(92\) 0 0
\(93\) 287.898 498.654i 0.321007 0.556000i
\(94\) 0 0
\(95\) 18.4420 + 31.9425i 0.0199169 + 0.0344972i
\(96\) 0 0
\(97\) −32.7818 56.7797i −0.0343143 0.0594341i 0.848358 0.529423i \(-0.177591\pi\)
−0.882673 + 0.469989i \(0.844258\pi\)
\(98\) 0 0
\(99\) −248.293 −0.252065
\(100\) 0 0
\(101\) −265.899 + 460.551i −0.261960 + 0.453728i −0.966763 0.255676i \(-0.917702\pi\)
0.704803 + 0.709403i \(0.251035\pi\)
\(102\) 0 0
\(103\) 735.984 0.704064 0.352032 0.935988i \(-0.385491\pi\)
0.352032 + 0.935988i \(0.385491\pi\)
\(104\) 0 0
\(105\) 476.621 0.442985
\(106\) 0 0
\(107\) −391.632 + 678.327i −0.353837 + 0.612863i −0.986918 0.161222i \(-0.948456\pi\)
0.633081 + 0.774085i \(0.281790\pi\)
\(108\) 0 0
\(109\) −532.339 −0.467788 −0.233894 0.972262i \(-0.575147\pi\)
−0.233894 + 0.972262i \(0.575147\pi\)
\(110\) 0 0
\(111\) −147.635 255.712i −0.126243 0.218659i
\(112\) 0 0
\(113\) 90.2946 + 156.395i 0.0751699 + 0.130198i 0.901160 0.433486i \(-0.142717\pi\)
−0.825990 + 0.563684i \(0.809383\pi\)
\(114\) 0 0
\(115\) −343.107 + 594.280i −0.278217 + 0.481886i
\(116\) 0 0
\(117\) 389.070 + 163.037i 0.307432 + 0.128827i
\(118\) 0 0
\(119\) 522.355 904.746i 0.402389 0.696957i
\(120\) 0 0
\(121\) 284.947 + 493.542i 0.214085 + 0.370805i
\(122\) 0 0
\(123\) 46.1178 + 79.8784i 0.0338074 + 0.0585561i
\(124\) 0 0
\(125\) −318.242 −0.227716
\(126\) 0 0
\(127\) 715.817 1239.83i 0.500146 0.866278i −0.499854 0.866110i \(-0.666613\pi\)
1.00000 0.000168331i \(-5.35814e-5\pi\)
\(128\) 0 0
\(129\) −714.976 −0.487986
\(130\) 0 0
\(131\) −2067.32 −1.37880 −0.689400 0.724381i \(-0.742126\pi\)
−0.689400 + 0.724381i \(0.742126\pi\)
\(132\) 0 0
\(133\) 10.8762 18.8382i 0.00709090 0.0122818i
\(134\) 0 0
\(135\) −443.153 −0.282523
\(136\) 0 0
\(137\) 193.756 + 335.595i 0.120830 + 0.209283i 0.920095 0.391695i \(-0.128111\pi\)
−0.799265 + 0.600978i \(0.794778\pi\)
\(138\) 0 0
\(139\) 376.284 + 651.743i 0.229611 + 0.397699i 0.957693 0.287792i \(-0.0929211\pi\)
−0.728082 + 0.685491i \(0.759588\pi\)
\(140\) 0 0
\(141\) −767.223 + 1328.87i −0.458240 + 0.793695i
\(142\) 0 0
\(143\) 163.508 + 1282.74i 0.0956171 + 0.750126i
\(144\) 0 0
\(145\) 505.698 875.894i 0.289627 0.501649i
\(146\) 0 0
\(147\) 373.956 + 647.710i 0.209819 + 0.363416i
\(148\) 0 0
\(149\) 1318.36 + 2283.47i 0.724862 + 1.25550i 0.959031 + 0.283301i \(0.0914296\pi\)
−0.234169 + 0.972196i \(0.575237\pi\)
\(150\) 0 0
\(151\) 3332.42 1.79595 0.897975 0.440046i \(-0.145038\pi\)
0.897975 + 0.440046i \(0.145038\pi\)
\(152\) 0 0
\(153\) −485.677 + 841.217i −0.256632 + 0.444499i
\(154\) 0 0
\(155\) 3150.20 1.63245
\(156\) 0 0
\(157\) −1625.26 −0.826179 −0.413089 0.910690i \(-0.635550\pi\)
−0.413089 + 0.910690i \(0.635550\pi\)
\(158\) 0 0
\(159\) −739.238 + 1280.40i −0.368713 + 0.638630i
\(160\) 0 0
\(161\) 404.698 0.198104
\(162\) 0 0
\(163\) −917.683 1589.47i −0.440972 0.763786i 0.556790 0.830653i \(-0.312033\pi\)
−0.997762 + 0.0668673i \(0.978700\pi\)
\(164\) 0 0
\(165\) −679.211 1176.43i −0.320463 0.555059i
\(166\) 0 0
\(167\) 972.498 1684.42i 0.450624 0.780503i −0.547801 0.836609i \(-0.684535\pi\)
0.998425 + 0.0561052i \(0.0178682\pi\)
\(168\) 0 0
\(169\) 586.072 2117.39i 0.266760 0.963763i
\(170\) 0 0
\(171\) −10.1125 + 17.5154i −0.00452237 + 0.00783298i
\(172\) 0 0
\(173\) −1265.81 2192.45i −0.556289 0.963522i −0.997802 0.0662666i \(-0.978891\pi\)
0.441512 0.897255i \(-0.354442\pi\)
\(174\) 0 0
\(175\) 698.823 + 1210.40i 0.301863 + 0.522842i
\(176\) 0 0
\(177\) −1452.54 −0.616832
\(178\) 0 0
\(179\) 2131.51 3691.88i 0.890035 1.54159i 0.0502037 0.998739i \(-0.484013\pi\)
0.839831 0.542847i \(-0.182654\pi\)
\(180\) 0 0
\(181\) 3944.61 1.61989 0.809946 0.586504i \(-0.199496\pi\)
0.809946 + 0.586504i \(0.199496\pi\)
\(182\) 0 0
\(183\) −1332.06 −0.538082
\(184\) 0 0
\(185\) 807.717 1399.01i 0.320998 0.555984i
\(186\) 0 0
\(187\) −2977.54 −1.16438
\(188\) 0 0
\(189\) 130.676 + 226.337i 0.0502924 + 0.0871090i
\(190\) 0 0
\(191\) −107.054 185.424i −0.0405559 0.0702449i 0.845035 0.534711i \(-0.179580\pi\)
−0.885591 + 0.464466i \(0.846246\pi\)
\(192\) 0 0
\(193\) 603.593 1045.45i 0.225117 0.389914i −0.731238 0.682123i \(-0.761057\pi\)
0.956355 + 0.292209i \(0.0943902\pi\)
\(194\) 0 0
\(195\) 291.829 + 2289.43i 0.107171 + 0.840765i
\(196\) 0 0
\(197\) 463.816 803.352i 0.167744 0.290541i −0.769883 0.638186i \(-0.779685\pi\)
0.937626 + 0.347645i \(0.113019\pi\)
\(198\) 0 0
\(199\) 239.476 + 414.784i 0.0853064 + 0.147755i 0.905522 0.424300i \(-0.139480\pi\)
−0.820215 + 0.572055i \(0.806146\pi\)
\(200\) 0 0
\(201\) 285.170 + 493.930i 0.100072 + 0.173329i
\(202\) 0 0
\(203\) −596.474 −0.206228
\(204\) 0 0
\(205\) −252.312 + 437.017i −0.0859621 + 0.148891i
\(206\) 0 0
\(207\) −376.281 −0.126345
\(208\) 0 0
\(209\) −61.9970 −0.0205188
\(210\) 0 0
\(211\) −725.477 + 1256.56i −0.236701 + 0.409978i −0.959766 0.280802i \(-0.909400\pi\)
0.723065 + 0.690780i \(0.242733\pi\)
\(212\) 0 0
\(213\) −1454.35 −0.467843
\(214\) 0 0
\(215\) −1955.83 3387.59i −0.620402 1.07457i
\(216\) 0 0
\(217\) −928.920 1608.94i −0.290595 0.503326i
\(218\) 0 0
\(219\) 1436.67 2488.38i 0.443293 0.767806i
\(220\) 0 0
\(221\) 4665.74 + 1955.15i 1.42014 + 0.595101i
\(222\) 0 0
\(223\) −1029.89 + 1783.83i −0.309268 + 0.535668i −0.978202 0.207654i \(-0.933417\pi\)
0.668935 + 0.743321i \(0.266751\pi\)
\(224\) 0 0
\(225\) −649.753 1125.41i −0.192519 0.333453i
\(226\) 0 0
\(227\) 2241.23 + 3881.93i 0.655311 + 1.13503i 0.981816 + 0.189837i \(0.0607959\pi\)
−0.326504 + 0.945196i \(0.605871\pi\)
\(228\) 0 0
\(229\) −1630.39 −0.470477 −0.235239 0.971938i \(-0.575587\pi\)
−0.235239 + 0.971938i \(0.575587\pi\)
\(230\) 0 0
\(231\) −400.567 + 693.803i −0.114093 + 0.197614i
\(232\) 0 0
\(233\) −1903.69 −0.535258 −0.267629 0.963522i \(-0.586240\pi\)
−0.267629 + 0.963522i \(0.586240\pi\)
\(234\) 0 0
\(235\) −8395.00 −2.33034
\(236\) 0 0
\(237\) −562.824 + 974.839i −0.154259 + 0.267184i
\(238\) 0 0
\(239\) −3763.79 −1.01866 −0.509328 0.860572i \(-0.670106\pi\)
−0.509328 + 0.860572i \(0.670106\pi\)
\(240\) 0 0
\(241\) 1807.37 + 3130.46i 0.483083 + 0.836724i 0.999811 0.0194250i \(-0.00618357\pi\)
−0.516728 + 0.856149i \(0.672850\pi\)
\(242\) 0 0
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) −2045.92 + 3543.64i −0.533507 + 0.924061i
\(246\) 0 0
\(247\) 97.1479 + 40.7092i 0.0250258 + 0.0104869i
\(248\) 0 0
\(249\) −1073.65 + 1859.61i −0.273252 + 0.473286i
\(250\) 0 0
\(251\) −2864.88 4962.12i −0.720438 1.24783i −0.960824 0.277158i \(-0.910608\pi\)
0.240387 0.970677i \(-0.422726\pi\)
\(252\) 0 0
\(253\) −576.717 998.903i −0.143312 0.248223i
\(254\) 0 0
\(255\) −5314.30 −1.30508
\(256\) 0 0
\(257\) 2762.89 4785.47i 0.670602 1.16152i −0.307132 0.951667i \(-0.599369\pi\)
0.977734 0.209849i \(-0.0672974\pi\)
\(258\) 0 0
\(259\) −952.709 −0.228565
\(260\) 0 0
\(261\) 554.591 0.131526
\(262\) 0 0
\(263\) 2611.60 4523.43i 0.612313 1.06056i −0.378536 0.925586i \(-0.623573\pi\)
0.990850 0.134971i \(-0.0430941\pi\)
\(264\) 0 0
\(265\) −8088.78 −1.87506
\(266\) 0 0
\(267\) 1557.23 + 2697.20i 0.356932 + 0.618224i
\(268\) 0 0
\(269\) −3601.94 6238.75i −0.816410 1.41406i −0.908311 0.418295i \(-0.862628\pi\)
0.0919010 0.995768i \(-0.470706\pi\)
\(270\) 0 0
\(271\) −4288.84 + 7428.49i −0.961360 + 1.66512i −0.242269 + 0.970209i \(0.577892\pi\)
−0.719091 + 0.694916i \(0.755442\pi\)
\(272\) 0 0
\(273\) 1083.25 824.148i 0.240152 0.182710i
\(274\) 0 0
\(275\) 1991.72 3449.76i 0.436747 0.756467i
\(276\) 0 0
\(277\) −3584.60 6208.70i −0.777536 1.34673i −0.933358 0.358947i \(-0.883136\pi\)
0.155822 0.987785i \(-0.450197\pi\)
\(278\) 0 0
\(279\) 863.694 + 1495.96i 0.185333 + 0.321007i
\(280\) 0 0
\(281\) 849.157 0.180272 0.0901360 0.995929i \(-0.471270\pi\)
0.0901360 + 0.995929i \(0.471270\pi\)
\(282\) 0 0
\(283\) 557.686 965.941i 0.117141 0.202895i −0.801492 0.598005i \(-0.795960\pi\)
0.918634 + 0.395110i \(0.129294\pi\)
\(284\) 0 0
\(285\) −110.652 −0.0229981
\(286\) 0 0
\(287\) 297.604 0.0612091
\(288\) 0 0
\(289\) −3367.75 + 5833.11i −0.685476 + 1.18728i
\(290\) 0 0
\(291\) 196.691 0.0396227
\(292\) 0 0
\(293\) 931.764 + 1613.86i 0.185782 + 0.321784i 0.943840 0.330403i \(-0.107185\pi\)
−0.758058 + 0.652188i \(0.773851\pi\)
\(294\) 0 0
\(295\) −3973.43 6882.19i −0.784211 1.35829i
\(296\) 0 0
\(297\) 372.440 645.085i 0.0727649 0.126033i
\(298\) 0 0
\(299\) 247.792 + 1943.95i 0.0479269 + 0.375992i
\(300\) 0 0
\(301\) −1153.46 + 1997.85i −0.220878 + 0.382571i
\(302\) 0 0
\(303\) −797.697 1381.65i −0.151243 0.261960i
\(304\) 0 0
\(305\) −3643.88 6311.39i −0.684092 1.18488i
\(306\) 0 0
\(307\) 6387.50 1.18747 0.593736 0.804660i \(-0.297652\pi\)
0.593736 + 0.804660i \(0.297652\pi\)
\(308\) 0 0
\(309\) −1103.98 + 1912.14i −0.203246 + 0.352032i
\(310\) 0 0
\(311\) 3492.59 0.636806 0.318403 0.947955i \(-0.396853\pi\)
0.318403 + 0.947955i \(0.396853\pi\)
\(312\) 0 0
\(313\) −5912.01 −1.06762 −0.533812 0.845603i \(-0.679241\pi\)
−0.533812 + 0.845603i \(0.679241\pi\)
\(314\) 0 0
\(315\) −714.931 + 1238.30i −0.127879 + 0.221492i
\(316\) 0 0
\(317\) −1677.54 −0.297224 −0.148612 0.988896i \(-0.547481\pi\)
−0.148612 + 0.988896i \(0.547481\pi\)
\(318\) 0 0
\(319\) 850.009 + 1472.26i 0.149189 + 0.258403i
\(320\) 0 0
\(321\) −1174.90 2034.98i −0.204288 0.353837i
\(322\) 0 0
\(323\) −121.270 + 210.045i −0.0208905 + 0.0361834i
\(324\) 0 0
\(325\) −5386.21 + 4097.88i −0.919301 + 0.699413i
\(326\) 0 0
\(327\) 798.509 1383.06i 0.135039 0.233894i
\(328\) 0 0
\(329\) 2475.49 + 4287.68i 0.414828 + 0.718503i
\(330\) 0 0
\(331\) 1005.15 + 1740.98i 0.166913 + 0.289102i 0.937333 0.348435i \(-0.113287\pi\)
−0.770420 + 0.637537i \(0.779953\pi\)
\(332\) 0 0
\(333\) 885.812 0.145772
\(334\) 0 0
\(335\) −1560.18 + 2702.30i −0.254452 + 0.440724i
\(336\) 0 0
\(337\) 7139.24 1.15400 0.577002 0.816743i \(-0.304222\pi\)
0.577002 + 0.816743i \(0.304222\pi\)
\(338\) 0 0
\(339\) −541.768 −0.0867988
\(340\) 0 0
\(341\) −2647.53 + 4585.65i −0.420444 + 0.728231i
\(342\) 0 0
\(343\) 5733.31 0.902536
\(344\) 0 0
\(345\) −1029.32 1782.84i −0.160629 0.278217i
\(346\) 0 0
\(347\) 0.569949 + 0.987181i 8.81743e−5 + 0.000152722i 0.866069 0.499924i \(-0.166639\pi\)
−0.865981 + 0.500076i \(0.833305\pi\)
\(348\) 0 0
\(349\) −6099.55 + 10564.7i −0.935535 + 1.62039i −0.161857 + 0.986814i \(0.551748\pi\)
−0.773678 + 0.633579i \(0.781585\pi\)
\(350\) 0 0
\(351\) −1007.19 + 766.279i −0.153162 + 0.116527i
\(352\) 0 0
\(353\) 5446.15 9433.01i 0.821160 1.42229i −0.0836595 0.996494i \(-0.526661\pi\)
0.904819 0.425796i \(-0.140006\pi\)
\(354\) 0 0
\(355\) −3978.41 6890.80i −0.594794 1.03021i
\(356\) 0 0
\(357\) 1567.07 + 2714.24i 0.232319 + 0.402389i
\(358\) 0 0
\(359\) 3525.78 0.518339 0.259169 0.965832i \(-0.416551\pi\)
0.259169 + 0.965832i \(0.416551\pi\)
\(360\) 0 0
\(361\) 3426.97 5935.69i 0.499632 0.865388i
\(362\) 0 0
\(363\) −1709.68 −0.247204
\(364\) 0 0
\(365\) 15720.1 2.25433
\(366\) 0 0
\(367\) 1191.88 2064.39i 0.169525 0.293625i −0.768728 0.639576i \(-0.779110\pi\)
0.938253 + 0.345950i \(0.112443\pi\)
\(368\) 0 0
\(369\) −276.707 −0.0390374
\(370\) 0 0
\(371\) 2385.20 + 4131.28i 0.333782 + 0.578128i
\(372\) 0 0
\(373\) 6641.10 + 11502.7i 0.921885 + 1.59675i 0.796495 + 0.604645i \(0.206685\pi\)
0.125390 + 0.992108i \(0.459982\pi\)
\(374\) 0 0
\(375\) 477.363 826.818i 0.0657358 0.113858i
\(376\) 0 0
\(377\) −365.214 2865.14i −0.0498925 0.391412i
\(378\) 0 0
\(379\) −2218.36 + 3842.32i −0.300659 + 0.520756i −0.976285 0.216488i \(-0.930540\pi\)
0.675627 + 0.737244i \(0.263873\pi\)
\(380\) 0 0
\(381\) 2147.45 + 3719.50i 0.288759 + 0.500146i
\(382\) 0 0
\(383\) −405.206 701.838i −0.0540602 0.0936351i 0.837729 0.546086i \(-0.183883\pi\)
−0.891789 + 0.452451i \(0.850550\pi\)
\(384\) 0 0
\(385\) −4383.03 −0.580207
\(386\) 0 0
\(387\) 1072.46 1857.56i 0.140869 0.243993i
\(388\) 0 0
\(389\) 3463.79 0.451469 0.225734 0.974189i \(-0.427522\pi\)
0.225734 + 0.974189i \(0.427522\pi\)
\(390\) 0 0
\(391\) −4512.37 −0.583633
\(392\) 0 0
\(393\) 3100.98 5371.06i 0.398025 0.689400i
\(394\) 0 0
\(395\) −6158.45 −0.784469
\(396\) 0 0
\(397\) −212.703 368.412i −0.0268898 0.0465745i 0.852267 0.523106i \(-0.175227\pi\)
−0.879157 + 0.476532i \(0.841894\pi\)
\(398\) 0 0
\(399\) 32.6287 + 56.5146i 0.00409394 + 0.00709090i
\(400\) 0 0
\(401\) 593.424 1027.84i 0.0739007 0.128000i −0.826707 0.562633i \(-0.809789\pi\)
0.900608 + 0.434633i \(0.143122\pi\)
\(402\) 0 0
\(403\) 7159.70 5447.16i 0.884987 0.673306i
\(404\) 0 0
\(405\) 664.730 1151.35i 0.0815573 0.141261i
\(406\) 0 0
\(407\) 1357.66 + 2351.54i 0.165349 + 0.286392i
\(408\) 0 0
\(409\) −4003.71 6934.63i −0.484036 0.838375i 0.515796 0.856711i \(-0.327496\pi\)
−0.999832 + 0.0183369i \(0.994163\pi\)
\(410\) 0 0
\(411\) −1162.54 −0.139522
\(412\) 0 0
\(413\) −2343.35 + 4058.80i −0.279198 + 0.483585i
\(414\) 0 0
\(415\) −11747.9 −1.38960
\(416\) 0 0
\(417\) −2257.70 −0.265132
\(418\) 0 0
\(419\) 3416.23 5917.08i 0.398314 0.689901i −0.595204 0.803575i \(-0.702929\pi\)
0.993518 + 0.113674i \(0.0362620\pi\)
\(420\) 0 0
\(421\) 10739.6 1.24326 0.621632 0.783309i \(-0.286470\pi\)
0.621632 + 0.783309i \(0.286470\pi\)
\(422\) 0 0
\(423\) −2301.67 3986.61i −0.264565 0.458240i
\(424\) 0 0
\(425\) −7791.85 13495.9i −0.889318 1.54034i
\(426\) 0 0
\(427\) −2148.99 + 3722.16i −0.243553 + 0.421846i
\(428\) 0 0
\(429\) −3577.91 1499.30i −0.402665 0.168734i
\(430\) 0 0
\(431\) 2607.22 4515.84i 0.291382 0.504688i −0.682755 0.730647i \(-0.739218\pi\)
0.974137 + 0.225959i \(0.0725517\pi\)
\(432\) 0 0
\(433\) −4321.12 7484.40i −0.479584 0.830664i 0.520142 0.854080i \(-0.325879\pi\)
−0.999726 + 0.0234161i \(0.992546\pi\)
\(434\) 0 0
\(435\) 1517.09 + 2627.68i 0.167216 + 0.289627i
\(436\) 0 0
\(437\) −93.9545 −0.0102848
\(438\) 0 0
\(439\) −6513.12 + 11281.1i −0.708097 + 1.22646i 0.257466 + 0.966287i \(0.417113\pi\)
−0.965562 + 0.260172i \(0.916221\pi\)
\(440\) 0 0
\(441\) −2243.73 −0.242278
\(442\) 0 0
\(443\) 11533.0 1.23690 0.618450 0.785824i \(-0.287761\pi\)
0.618450 + 0.785824i \(0.287761\pi\)
\(444\) 0 0
\(445\) −8519.64 + 14756.5i −0.907573 + 1.57196i
\(446\) 0 0
\(447\) −7910.17 −0.836998
\(448\) 0 0
\(449\) −4941.37 8558.71i −0.519372 0.899578i −0.999747 0.0225149i \(-0.992833\pi\)
0.480375 0.877063i \(-0.340501\pi\)
\(450\) 0 0
\(451\) −424.102 734.566i −0.0442798 0.0766949i
\(452\) 0 0
\(453\) −4998.63 + 8657.88i −0.518446 + 0.897975i
\(454\) 0 0
\(455\) 6868.11 + 2878.04i 0.707653 + 0.296537i
\(456\) 0 0
\(457\) 7814.04 13534.3i 0.799836 1.38536i −0.119886 0.992788i \(-0.538253\pi\)
0.919722 0.392569i \(-0.128414\pi\)
\(458\) 0 0
\(459\) −1457.03 2523.65i −0.148166 0.256632i
\(460\) 0 0
\(461\) 3873.73 + 6709.50i 0.391361 + 0.677858i 0.992629 0.121190i \(-0.0386709\pi\)
−0.601268 + 0.799047i \(0.705338\pi\)
\(462\) 0 0
\(463\) 333.422 0.0334675 0.0167337 0.999860i \(-0.494673\pi\)
0.0167337 + 0.999860i \(0.494673\pi\)
\(464\) 0 0
\(465\) −4725.29 + 8184.45i −0.471248 + 0.816225i
\(466\) 0 0
\(467\) −8198.33 −0.812363 −0.406182 0.913792i \(-0.633140\pi\)
−0.406182 + 0.913792i \(0.633140\pi\)
\(468\) 0 0
\(469\) 1840.24 0.181182
\(470\) 0 0
\(471\) 2437.89 4222.56i 0.238497 0.413089i
\(472\) 0 0
\(473\) 6574.96 0.639148
\(474\) 0 0
\(475\) −162.238 281.005i −0.0156716 0.0271440i
\(476\) 0 0
\(477\) −2217.71 3841.19i −0.212877 0.368713i
\(478\) 0 0
\(479\) −3217.94 + 5573.64i −0.306955 + 0.531662i −0.977695 0.210031i \(-0.932643\pi\)
0.670740 + 0.741693i \(0.265977\pi\)
\(480\) 0 0
\(481\) −583.332 4576.30i −0.0552966 0.433807i
\(482\) 0 0
\(483\) −607.047 + 1051.44i −0.0571876 + 0.0990518i
\(484\) 0 0
\(485\) 538.050 + 931.931i 0.0503745 + 0.0872511i
\(486\) 0 0
\(487\) 4047.69 + 7010.80i 0.376629 + 0.652340i 0.990569 0.137012i \(-0.0437500\pi\)
−0.613941 + 0.789352i \(0.710417\pi\)
\(488\) 0 0
\(489\) 5506.10 0.509191
\(490\) 0 0
\(491\) 2558.23 4430.99i 0.235135 0.407266i −0.724177 0.689614i \(-0.757780\pi\)
0.959312 + 0.282348i \(0.0911134\pi\)
\(492\) 0 0
\(493\) 6650.67 0.607568
\(494\) 0 0
\(495\) 4075.26 0.370039
\(496\) 0 0
\(497\) −2346.28 + 4063.88i −0.211761 + 0.366780i
\(498\) 0 0
\(499\) 18050.7 1.61936 0.809682 0.586870i \(-0.199640\pi\)
0.809682 + 0.586870i \(0.199640\pi\)
\(500\) 0 0
\(501\) 2917.50 + 5053.25i 0.260168 + 0.450624i
\(502\) 0 0
\(503\) 5265.53 + 9120.16i 0.466756 + 0.808445i 0.999279 0.0379705i \(-0.0120893\pi\)
−0.532523 + 0.846416i \(0.678756\pi\)
\(504\) 0 0
\(505\) 4364.22 7559.06i 0.384565 0.666087i
\(506\) 0 0
\(507\) 4622.02 + 4698.74i 0.404874 + 0.411595i
\(508\) 0 0
\(509\) 981.654 1700.27i 0.0854834 0.148062i −0.820114 0.572201i \(-0.806090\pi\)
0.905597 + 0.424139i \(0.139423\pi\)
\(510\) 0 0
\(511\) −4635.50 8028.93i −0.401297 0.695066i
\(512\) 0 0
\(513\) −30.3376 52.5463i −0.00261099 0.00452237i
\(514\) 0 0
\(515\) −12079.8 −1.03359
\(516\) 0 0
\(517\) 7055.43 12220.4i 0.600188 1.03956i
\(518\) 0 0
\(519\) 7594.89 0.642348
\(520\) 0 0
\(521\) −7044.93 −0.592407 −0.296203 0.955125i \(-0.595721\pi\)
−0.296203 + 0.955125i \(0.595721\pi\)
\(522\) 0 0
\(523\) −1606.65 + 2782.79i −0.134328 + 0.232664i −0.925341 0.379137i \(-0.876221\pi\)
0.791012 + 0.611800i \(0.209554\pi\)
\(524\) 0 0
\(525\) −4192.94 −0.348561
\(526\) 0 0
\(527\) 10357.4 + 17939.6i 0.856123 + 1.48285i
\(528\) 0 0
\(529\) 5209.50 + 9023.13i 0.428167 + 0.741606i
\(530\) 0 0
\(531\) 2178.80 3773.80i 0.178064 0.308416i
\(532\) 0 0
\(533\) 182.219 + 1429.53i 0.0148082 + 0.116172i
\(534\) 0 0
\(535\) 6427.90 11133.4i 0.519443 0.899702i
\(536\) 0 0
\(537\) 6394.52 + 11075.6i 0.513862 + 0.890035i
\(538\) 0 0
\(539\) −3438.92 5956.38i −0.274814 0.475991i
\(540\) 0 0
\(541\) 11251.4 0.894150 0.447075 0.894497i \(-0.352466\pi\)
0.447075 + 0.894497i \(0.352466\pi\)
\(542\) 0 0
\(543\) −5916.91 + 10248.4i −0.467623 + 0.809946i
\(544\) 0 0
\(545\) 8737.33 0.686727
\(546\) 0 0
\(547\) −1533.54 −0.119871 −0.0599353 0.998202i \(-0.519089\pi\)
−0.0599353 + 0.998202i \(0.519089\pi\)
\(548\) 0 0
\(549\) 1998.10 3460.80i 0.155331 0.269041i
\(550\) 0 0
\(551\) 138.477 0.0107066
\(552\) 0 0
\(553\) 1815.98 + 3145.38i 0.139645 + 0.241872i
\(554\) 0 0
\(555\) 2423.15 + 4197.02i 0.185328 + 0.320998i
\(556\) 0 0
\(557\) −8422.84 + 14588.8i −0.640731 + 1.10978i 0.344539 + 0.938772i \(0.388035\pi\)
−0.985270 + 0.171006i \(0.945298\pi\)
\(558\) 0 0
\(559\) −10302.8 4317.33i −0.779540 0.326661i
\(560\) 0 0
\(561\) 4466.31 7735.88i 0.336128 0.582191i
\(562\) 0 0
\(563\) −10410.0 18030.7i −0.779273 1.34974i −0.932361 0.361528i \(-0.882255\pi\)
0.153089 0.988212i \(-0.451078\pi\)
\(564\) 0 0
\(565\) −1482.01 2566.92i −0.110352 0.191135i
\(566\) 0 0
\(567\) −784.054 −0.0580726
\(568\) 0 0
\(569\) −11818.3 + 20469.9i −0.870735 + 1.50816i −0.00949803 + 0.999955i \(0.503023\pi\)
−0.861237 + 0.508203i \(0.830310\pi\)
\(570\) 0 0
\(571\) 26955.1 1.97554 0.987771 0.155913i \(-0.0498319\pi\)
0.987771 + 0.155913i \(0.0498319\pi\)
\(572\) 0 0
\(573\) 642.326 0.0468300
\(574\) 0 0
\(575\) 3018.39 5228.01i 0.218914 0.379170i
\(576\) 0 0
\(577\) 23499.8 1.69551 0.847755 0.530388i \(-0.177954\pi\)
0.847755 + 0.530388i \(0.177954\pi\)
\(578\) 0 0
\(579\) 1810.78 + 3136.36i 0.129971 + 0.225117i
\(580\) 0 0
\(581\) 3464.19 + 6000.15i 0.247365 + 0.428448i
\(582\) 0 0
\(583\) 6798.07 11774.6i 0.482929 0.836457i
\(584\) 0 0
\(585\) −6385.85 2675.95i −0.451320 0.189123i
\(586\) 0 0
\(587\) 2318.75 4016.19i 0.163041 0.282395i −0.772917 0.634507i \(-0.781203\pi\)
0.935958 + 0.352112i \(0.114536\pi\)
\(588\) 0 0
\(589\) 215.658 + 373.530i 0.0150866 + 0.0261308i
\(590\) 0 0
\(591\) 1391.45 + 2410.06i 0.0968468 + 0.167744i
\(592\) 0 0
\(593\) 12633.5 0.874869 0.437434 0.899250i \(-0.355887\pi\)
0.437434 + 0.899250i \(0.355887\pi\)
\(594\) 0 0
\(595\) −8573.47 + 14849.7i −0.590719 + 1.02316i
\(596\) 0 0
\(597\) −1436.85 −0.0985033
\(598\) 0 0
\(599\) 18757.1 1.27946 0.639730 0.768600i \(-0.279046\pi\)
0.639730 + 0.768600i \(0.279046\pi\)
\(600\) 0 0
\(601\) 1816.49 3146.25i 0.123288 0.213541i −0.797774 0.602956i \(-0.793989\pi\)
0.921062 + 0.389415i \(0.127323\pi\)
\(602\) 0 0
\(603\) −1711.02 −0.115553
\(604\) 0 0
\(605\) −4676.85 8100.55i −0.314283 0.544354i
\(606\) 0 0
\(607\) −6349.99 10998.5i −0.424610 0.735445i 0.571774 0.820411i \(-0.306255\pi\)
−0.996384 + 0.0849656i \(0.972922\pi\)
\(608\) 0 0
\(609\) 894.712 1549.69i 0.0595329 0.103114i
\(610\) 0 0
\(611\) −19080.0 + 14516.2i −1.26333 + 0.961151i
\(612\) 0 0
\(613\) −10820.1 + 18740.9i −0.712918 + 1.23481i 0.250839 + 0.968029i \(0.419293\pi\)
−0.963757 + 0.266781i \(0.914040\pi\)
\(614\) 0 0
\(615\) −756.936 1311.05i −0.0496303 0.0859621i
\(616\) 0 0
\(617\) 8270.85 + 14325.5i 0.539663 + 0.934723i 0.998922 + 0.0464208i \(0.0147815\pi\)
−0.459259 + 0.888302i \(0.651885\pi\)
\(618\) 0 0
\(619\) 21138.9 1.37261 0.686303 0.727316i \(-0.259233\pi\)
0.686303 + 0.727316i \(0.259233\pi\)
\(620\) 0 0
\(621\) 564.421 977.607i 0.0364726 0.0631723i
\(622\) 0 0
\(623\) 10049.0 0.646235
\(624\) 0 0
\(625\) −12825.4 −0.820823
\(626\) 0 0
\(627\) 92.9955 161.073i 0.00592326 0.0102594i
\(628\) 0 0
\(629\) 10622.7 0.673377
\(630\) 0 0
\(631\) 2744.90 + 4754.31i 0.173174 + 0.299946i 0.939528 0.342473i \(-0.111264\pi\)
−0.766354 + 0.642419i \(0.777931\pi\)
\(632\) 0 0
\(633\) −2176.43 3769.69i −0.136659 0.236701i
\(634\) 0 0
\(635\) −11748.8 + 20349.5i −0.734230 + 1.27172i
\(636\) 0 0
\(637\) 1477.56 + 11591.6i 0.0919044 + 0.720999i
\(638\) 0 0
\(639\) 2181.53 3778.52i 0.135055 0.233922i
\(640\) 0 0
\(641\) −2148.52 3721.35i −0.132389 0.229305i 0.792208 0.610251i \(-0.208932\pi\)
−0.924597 + 0.380946i \(0.875598\pi\)
\(642\) 0 0
\(643\) 12848.5 + 22254.2i 0.788016 + 1.36488i 0.927181 + 0.374615i \(0.122225\pi\)
−0.139164 + 0.990269i \(0.544442\pi\)
\(644\) 0 0
\(645\) 11735.0 0.716378
\(646\) 0 0
\(647\) 1087.49 1883.59i 0.0660798 0.114454i −0.831093 0.556134i \(-0.812284\pi\)
0.897172 + 0.441680i \(0.145617\pi\)
\(648\) 0 0
\(649\) 13357.6 0.807907
\(650\) 0 0
\(651\) 5573.52 0.335551
\(652\) 0 0
\(653\) 7727.27 13384.0i 0.463080 0.802078i −0.536032 0.844197i \(-0.680078\pi\)
0.999113 + 0.0421191i \(0.0134109\pi\)
\(654\) 0 0
\(655\) 33931.1 2.02412
\(656\) 0 0
\(657\) 4310.01 + 7465.15i 0.255935 + 0.443293i
\(658\) 0 0
\(659\) −1574.39 2726.92i −0.0930643 0.161192i 0.815735 0.578426i \(-0.196333\pi\)
−0.908799 + 0.417234i \(0.863000\pi\)
\(660\) 0 0
\(661\) 1049.85 1818.39i 0.0617767 0.107000i −0.833483 0.552545i \(-0.813657\pi\)
0.895260 + 0.445545i \(0.146990\pi\)
\(662\) 0 0
\(663\) −12078.2 + 9189.23i −0.707511 + 0.538281i
\(664\) 0 0
\(665\) −178.513 + 309.193i −0.0104097 + 0.0180301i
\(666\) 0 0
\(667\) 1288.16 + 2231.16i 0.0747794 + 0.129522i
\(668\) 0 0
\(669\) −3089.68 5351.48i −0.178556 0.309268i
\(670\) 0 0
\(671\) 12249.7 0.704763
\(672\) 0 0
\(673\) −15485.4 + 26821.5i −0.886950 + 1.53624i −0.0434884 + 0.999054i \(0.513847\pi\)
−0.843462 + 0.537189i \(0.819486\pi\)
\(674\) 0 0
\(675\) 3898.52 0.222302
\(676\) 0 0
\(677\) 14640.6 0.831141 0.415570 0.909561i \(-0.363582\pi\)
0.415570 + 0.909561i \(0.363582\pi\)
\(678\) 0 0
\(679\) 317.317 549.610i 0.0179345 0.0310635i
\(680\) 0 0
\(681\) −13447.4 −0.756688
\(682\) 0 0
\(683\) −3342.92 5790.10i −0.187281 0.324381i 0.757062 0.653343i \(-0.226634\pi\)
−0.944343 + 0.328963i \(0.893301\pi\)
\(684\) 0 0
\(685\) −3180.13 5508.15i −0.177382 0.307235i
\(686\) 0 0
\(687\) 2445.59 4235.88i 0.135815 0.235239i
\(688\) 0 0
\(689\) −18384.0 + 13986.7i −1.01651 + 0.773370i
\(690\) 0 0
\(691\) −15097.0 + 26148.8i −0.831141 + 1.43958i 0.0659934 + 0.997820i \(0.478978\pi\)
−0.897134 + 0.441758i \(0.854355\pi\)
\(692\) 0 0
\(693\) −1201.70 2081.41i −0.0658714 0.114093i
\(694\) 0 0
\(695\) −6175.98 10697.1i −0.337077 0.583834i
\(696\) 0 0
\(697\) −3318.28 −0.180328
\(698\) 0 0
\(699\) 2855.54 4945.94i 0.154516 0.267629i
\(700\) 0 0
\(701\) −30300.9 −1.63260 −0.816298 0.577631i \(-0.803977\pi\)
−0.816298 + 0.577631i \(0.803977\pi\)
\(702\) 0 0
\(703\) 221.181 0.0118663
\(704\) 0 0
\(705\) 12592.5 21810.9i 0.672711 1.16517i
\(706\) 0 0
\(707\) −5147.64 −0.273829
\(708\) 0 0
\(709\) −13061.6 22623.4i −0.691875 1.19836i −0.971223 0.238173i \(-0.923452\pi\)
0.279348 0.960190i \(-0.409882\pi\)
\(710\) 0 0
\(711\) −1688.47 2924.52i −0.0890613 0.154259i
\(712\) 0 0
\(713\) −4012.24 + 6949.41i −0.210743 + 0.365017i
\(714\) 0 0
\(715\) −2683.68 21053.7i −0.140369 1.10121i
\(716\) 0 0
\(717\) 5645.68 9778.60i 0.294061 0.509328i
\(718\) 0 0
\(719\) 9662.83 + 16736.5i 0.501200 + 0.868104i 0.999999 + 0.00138631i \(0.000441276\pi\)
−0.498799 + 0.866718i \(0.666225\pi\)
\(720\) 0 0
\(721\) 3562.05 + 6169.64i 0.183991 + 0.318682i
\(722\) 0 0
\(723\) −10844.2 −0.557816
\(724\) 0 0
\(725\) −4448.73 + 7705.43i −0.227892 + 0.394721i
\(726\) 0 0
\(727\) −26065.8 −1.32975 −0.664875 0.746954i \(-0.731515\pi\)
−0.664875 + 0.746954i \(0.731515\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 12861.0 22275.9i 0.650727 1.12709i
\(732\) 0 0
\(733\) 1055.45 0.0531843 0.0265921 0.999646i \(-0.491534\pi\)
0.0265921 + 0.999646i \(0.491534\pi\)
\(734\) 0 0
\(735\) −6137.77 10630.9i −0.308020 0.533507i
\(736\) 0 0
\(737\) −2622.44 4542.21i −0.131070 0.227021i
\(738\) 0 0
\(739\) 4705.20 8149.64i 0.234213 0.405669i −0.724831 0.688927i \(-0.758082\pi\)
0.959044 + 0.283258i \(0.0914153\pi\)
\(740\) 0 0
\(741\) −251.487 + 191.334i −0.0124678 + 0.00948560i
\(742\) 0 0
\(743\) −3761.85 + 6515.72i −0.185746 + 0.321721i −0.943827 0.330439i \(-0.892803\pi\)
0.758082 + 0.652159i \(0.226137\pi\)
\(744\) 0 0
\(745\) −21638.4 37478.8i −1.06412 1.84311i
\(746\) 0 0
\(747\) −3220.94 5578.84i −0.157762 0.273252i
\(748\) 0 0
\(749\) −7581.76 −0.369868
\(750\) 0 0
\(751\) −6492.03 + 11244.5i −0.315443 + 0.546363i −0.979532 0.201291i \(-0.935486\pi\)
0.664089 + 0.747654i \(0.268820\pi\)
\(752\) 0 0
\(753\) 17189.3 0.831890
\(754\) 0 0
\(755\) −54695.3 −2.63651
\(756\) 0 0
\(757\) 13967.3 24192.1i 0.670609 1.16153i −0.307123 0.951670i \(-0.599366\pi\)
0.977732 0.209859i \(-0.0673004\pi\)
\(758\) 0 0
\(759\) 3460.30 0.165482
\(760\) 0 0
\(761\) 7759.63 + 13440.1i 0.369627 + 0.640214i 0.989507 0.144483i \(-0.0461520\pi\)
−0.619880 + 0.784697i \(0.712819\pi\)
\(762\) 0 0
\(763\) −2576.44 4462.52i −0.122246 0.211735i
\(764\) 0 0
\(765\) 7971.46 13807.0i 0.376743 0.652539i
\(766\) 0 0
\(767\) −20931.1 8771.02i −0.985368 0.412912i
\(768\) 0 0
\(769\) −6442.59 + 11158.9i −0.302114 + 0.523277i −0.976615 0.214997i \(-0.931026\pi\)
0.674501 + 0.738274i \(0.264359\pi\)
\(770\) 0 0
\(771\) 8288.68 + 14356.4i 0.387172 + 0.670602i
\(772\) 0 0
\(773\) −2946.02 5102.66i −0.137078 0.237425i 0.789312 0.613993i \(-0.210438\pi\)
−0.926389 + 0.376567i \(0.877104\pi\)
\(774\) 0 0
\(775\) −27713.0 −1.28449
\(776\) 0 0
\(777\) 1429.06 2475.21i 0.0659812 0.114283i
\(778\) 0 0
\(779\) −69.0916 −0.00317775
\(780\) 0 0
\(781\) 13374.3 0.612766
\(782\) 0 0
\(783\) −831.887 + 1440.87i −0.0379684 + 0.0657631i
\(784\) 0 0
\(785\) 26675.6 1.21286
\(786\) 0 0
\(787\) −10510.2 18204.2i −0.476045 0.824535i 0.523578 0.851978i \(-0.324597\pi\)
−0.999623 + 0.0274430i \(0.991264\pi\)
\(788\) 0 0
\(789\) 7834.81 + 13570.3i 0.353519 + 0.612313i
\(790\) 0 0
\(791\) −874.023 +