Properties

Label 624.4.q.i.289.1
Level $624$
Weight $4$
Character 624.289
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 289.1
Root \(2.66520 - 4.61626i\) of defining polynomial
Character \(\chi\) \(=\) 624.289
Dual form 624.4.q.i.529.1

$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

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

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 −0.705268 0.708941i \(-0.749173\pi\)
0.966595 + 0.256309i \(0.0825066\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 13.7941 + 23.8921i 0.378098 + 0.654884i 0.990785 0.135441i \(-0.0432451\pi\)
−0.612688 + 0.790325i \(0.709912\pi\)
\(12\) 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 0.167725 + 0.985834i \(0.446358\pi\)
−0.937619 + 0.347663i \(0.886975\pi\)
\(18\) 0 0
\(19\) −1.12362 + 1.94616i −0.0135671 + 0.0234989i −0.872729 0.488205i \(-0.837652\pi\)
0.859162 + 0.511703i \(0.170985\pi\)
\(20\) 0 0
\(21\) −29.0391 −0.301754
\(22\) 0 0
\(23\) 20.9045 + 36.2077i 0.189517 + 0.328253i 0.945089 0.326812i \(-0.105974\pi\)
−0.755572 + 0.655065i \(0.772641\pi\)
\(24\) 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 0.750359 0.661030i \(-0.229881\pi\)
−0.947649 + 0.319315i \(0.896547\pi\)
\(30\) 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 0.735740 0.677265i \(-0.236835\pi\)
−0.954398 + 0.298537i \(0.903501\pi\)
\(38\) 0 0
\(39\) −17.7803 + 139.488i −0.0730031 + 0.572716i
\(40\) 0 0
\(41\) 15.3726 + 26.6261i 0.0585561 + 0.101422i 0.893817 0.448431i \(-0.148017\pi\)
−0.835261 + 0.549853i \(0.814684\pi\)
\(42\) 0 0
\(43\) 119.163 206.396i 0.422608 0.731978i −0.573586 0.819145i \(-0.694448\pi\)
0.996194 + 0.0871672i \(0.0277814\pi\)
\(44\) 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 −0.465010 0.885306i \(-0.653949\pi\)
0.999202 0.0399427i \(-0.0127175\pi\)
\(60\) 0 0
\(61\) 222.011 384.534i 0.465993 0.807123i −0.533253 0.845956i \(-0.679031\pi\)
0.999246 + 0.0388329i \(0.0123640\pi\)
\(62\) 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 0.939582 0.342325i \(-0.111214\pi\)
−0.766253 + 0.642539i \(0.777881\pi\)
\(68\) 0 0
\(69\) 62.7135 108.623i 0.109418 0.189517i
\(70\) 0 0
\(71\) 242.392 419.836i 0.405164 0.701765i −0.589176 0.808005i \(-0.700548\pi\)
0.994341 + 0.106239i \(0.0338810\pi\)
\(72\) 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 0.989810 + 0.142397i \(0.0454810\pi\)
−0.371585 + 0.928399i \(0.621186\pi\)
\(90\) 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 −0.882673 0.469989i \(-0.844258\pi\)
0.848358 + 0.529423i \(0.177591\pi\)
\(98\) 0 0
\(99\) −248.293 −0.252065
\(100\) 0 0
\(101\) −265.899 460.551i −0.261960 0.453728i 0.704803 0.709403i \(-0.251035\pi\)
−0.966763 + 0.255676i \(0.917702\pi\)
\(102\) 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 0.633081 0.774085i \(-0.281790\pi\)
−0.986918 + 0.161222i \(0.948456\pi\)
\(108\) 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 −0.825990 0.563684i \(-0.809383\pi\)
0.901160 + 0.433486i \(0.142717\pi\)
\(114\) 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 1.00000 0.000168331i \(5.35814e-5\pi\)
−0.499854 + 0.866110i \(0.666613\pi\)
\(128\) 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 −0.799265 0.600978i \(-0.794778\pi\)
0.920095 + 0.391695i \(0.128111\pi\)
\(138\) 0 0
\(139\) 376.284 651.743i 0.229611 0.397699i −0.728082 0.685491i \(-0.759588\pi\)
0.957693 + 0.287792i \(0.0929211\pi\)
\(140\) 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 −0.234169 0.972196i \(-0.575237\pi\)
0.959031 0.283301i \(-0.0914296\pi\)
\(150\) 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 −0.997762 0.0668673i \(-0.978700\pi\)
0.556790 + 0.830653i \(0.312033\pi\)
\(164\) 0 0
\(165\) −679.211 + 1176.43i −0.320463 + 0.555059i
\(166\) 0 0
\(167\) 972.498 + 1684.42i 0.450624 + 0.780503i 0.998425 0.0561052i \(-0.0178682\pi\)
−0.547801 + 0.836609i \(0.684535\pi\)
\(168\) 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 0.441512 + 0.897255i \(0.354442\pi\)
−0.997802 + 0.0662666i \(0.978891\pi\)
\(174\) 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 0.839831 + 0.542847i \(0.182654\pi\)
0.0502037 + 0.998739i \(0.484013\pi\)
\(180\) 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 −0.885591 0.464466i \(-0.846246\pi\)
0.845035 + 0.534711i \(0.179580\pi\)
\(192\) 0 0
\(193\) 603.593 + 1045.45i 0.225117 + 0.389914i 0.956355 0.292209i \(-0.0943902\pi\)
−0.731238 + 0.682123i \(0.761057\pi\)
\(194\) 0 0
\(195\) 291.829 2289.43i 0.107171 0.840765i
\(196\) 0 0
\(197\) 463.816 + 803.352i 0.167744 + 0.290541i 0.937626 0.347645i \(-0.113019\pi\)
−0.769883 + 0.638186i \(0.779685\pi\)
\(198\) 0 0
\(199\) 239.476 414.784i 0.0853064 0.147755i −0.820215 0.572055i \(-0.806146\pi\)
0.905522 + 0.424300i \(0.139480\pi\)
\(200\) 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 0.723065 0.690780i \(-0.242733\pi\)
−0.959766 + 0.280802i \(0.909400\pi\)
\(212\) 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 0.668935 0.743321i \(-0.266751\pi\)
−0.978202 + 0.207654i \(0.933417\pi\)
\(224\) 0 0
\(225\) −649.753 + 1125.41i −0.192519 + 0.333453i
\(226\) 0 0
\(227\) 2241.23 3881.93i 0.655311 1.13503i −0.326504 0.945196i \(-0.605871\pi\)
0.981816 0.189837i \(-0.0607959\pi\)
\(228\) 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 −0.516728 0.856149i \(-0.672850\pi\)
0.999811 + 0.0194250i \(0.00618357\pi\)
\(242\) 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 0.240387 + 0.970677i \(0.422726\pi\)
−0.960824 + 0.277158i \(0.910608\pi\)
\(252\) 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 0.977734 + 0.209849i \(0.0672974\pi\)
−0.307132 + 0.951667i \(0.599369\pi\)
\(258\) 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 0.990850 + 0.134971i \(0.0430941\pi\)
−0.378536 + 0.925586i \(0.623573\pi\)
\(264\) 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 0.0919010 + 0.995768i \(0.470706\pi\)
−0.908311 + 0.418295i \(0.862628\pi\)
\(270\) 0 0
\(271\) −4288.84 7428.49i −0.961360 1.66512i −0.719091 0.694916i \(-0.755442\pi\)
−0.242269 0.970209i \(-0.577892\pi\)
\(272\) 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 0.155822 + 0.987785i \(0.450197\pi\)
−0.933358 + 0.358947i \(0.883136\pi\)
\(278\) 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 0.918634 0.395110i \(-0.129294\pi\)
−0.801492 + 0.598005i \(0.795960\pi\)
\(284\) 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 −0.758058 0.652188i \(-0.773851\pi\)
0.943840 + 0.330403i \(0.107185\pi\)
\(294\) 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 −0.770420 0.637537i \(-0.779953\pi\)
0.937333 + 0.348435i \(0.113287\pi\)
\(332\) 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 −0.865981 0.500076i \(-0.833305\pi\)
0.866069 + 0.499924i \(0.166639\pi\)
\(348\) 0 0
\(349\) −6099.55 10564.7i −0.935535 1.62039i −0.773678 0.633579i \(-0.781585\pi\)
−0.161857 0.986814i \(-0.551748\pi\)
\(350\) 0 0
\(351\) −1007.19 766.279i −0.153162 0.116527i
\(352\) 0 0
\(353\) 5446.15 + 9433.01i 0.821160 + 1.42229i 0.904819 + 0.425796i \(0.140006\pi\)
−0.0836595 + 0.996494i \(0.526661\pi\)
\(354\) 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 0.938253 0.345950i \(-0.112443\pi\)
−0.768728 + 0.639576i \(0.779110\pi\)
\(368\) 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 0.125390 0.992108i \(-0.459982\pi\)
0.796495 0.604645i \(-0.206685\pi\)
\(374\) 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 0.675627 0.737244i \(-0.263873\pi\)
−0.976285 + 0.216488i \(0.930540\pi\)
\(380\) 0 0
\(381\) 2147.45 3719.50i 0.288759 0.500146i
\(382\) 0 0
\(383\) −405.206 + 701.838i −0.0540602 + 0.0936351i −0.891789 0.452451i \(-0.850550\pi\)
0.837729 + 0.546086i \(0.183883\pi\)
\(384\) 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 −0.879157 0.476532i \(-0.841894\pi\)
0.852267 + 0.523106i \(0.175227\pi\)
\(398\) 0 0
\(399\) 32.6287 56.5146i 0.00409394 0.00709090i
\(400\) 0 0
\(401\) 593.424 + 1027.84i 0.0739007 + 0.128000i 0.900608 0.434633i \(-0.143122\pi\)
−0.826707 + 0.562633i \(0.809789\pi\)
\(402\) 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 −0.999832 0.0183369i \(-0.994163\pi\)
0.515796 + 0.856711i \(0.327496\pi\)
\(410\) 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 0.993518 0.113674i \(-0.0362620\pi\)
−0.595204 + 0.803575i \(0.702929\pi\)
\(420\) 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 0.974137 0.225959i \(-0.0725517\pi\)
−0.682755 + 0.730647i \(0.739218\pi\)
\(432\) 0 0
\(433\) −4321.12 + 7484.40i −0.479584 + 0.830664i −0.999726 0.0234161i \(-0.992546\pi\)
0.520142 + 0.854080i \(0.325879\pi\)
\(434\) 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 −0.965562 0.260172i \(-0.916221\pi\)
0.257466 0.966287i \(-0.417113\pi\)
\(440\) 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 0.480375 + 0.877063i \(0.340501\pi\)
−0.999747 + 0.0225149i \(0.992833\pi\)
\(450\) 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 0.919722 + 0.392569i \(0.128414\pi\)
−0.119886 + 0.992788i \(0.538253\pi\)
\(458\) 0 0
\(459\) −1457.03 + 2523.65i −0.148166 + 0.256632i
\(460\) 0 0
\(461\) 3873.73 6709.50i 0.391361 0.677858i −0.601268 0.799047i \(-0.705338\pi\)
0.992629 + 0.121190i \(0.0386709\pi\)
\(462\) 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 0.670740 0.741693i \(-0.265977\pi\)
−0.977695 + 0.210031i \(0.932643\pi\)
\(480\) 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 −0.613941 0.789352i \(-0.710417\pi\)
0.990569 + 0.137012i \(0.0437500\pi\)
\(488\) 0 0
\(489\) 5506.10 0.509191
\(490\) 0 0
\(491\) 2558.23 + 4430.99i 0.235135 + 0.407266i 0.959312 0.282348i \(-0.0911134\pi\)
−0.724177 + 0.689614i \(0.757780\pi\)
\(492\) 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 −0.532523 0.846416i \(-0.678756\pi\)
0.999279 + 0.0379705i \(0.0120893\pi\)
\(504\) 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 0.905597 0.424139i \(-0.139423\pi\)
−0.820114 + 0.572201i \(0.806090\pi\)
\(510\) 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 0.791012 0.611800i \(-0.209554\pi\)
−0.925341 + 0.379137i \(0.876221\pi\)
\(524\) 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 −0.985270 0.171006i \(-0.945298\pi\)
0.344539 0.938772i \(-0.388035\pi\)
\(558\) 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 0.153089 + 0.988212i \(0.451078\pi\)
−0.932361 + 0.361528i \(0.882255\pi\)
\(564\) 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 −0.861237 0.508203i \(-0.830310\pi\)
−0.00949803 0.999955i \(-0.503023\pi\)
\(570\) 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 0.935958 0.352112i \(-0.114536\pi\)
−0.772917 + 0.634507i \(0.781203\pi\)
\(588\) 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 0.921062 0.389415i \(-0.127323\pi\)
−0.797774 + 0.602956i \(0.793989\pi\)
\(602\) 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 −0.996384 0.0849656i \(-0.972922\pi\)
0.571774 + 0.820411i \(0.306255\pi\)
\(608\) 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 −0.963757 0.266781i \(-0.914040\pi\)
0.250839 0.968029i \(-0.419293\pi\)
\(614\) 0 0
\(615\) −756.936 + 1311.05i −0.0496303 + 0.0859621i
\(616\) 0 0
\(617\) 8270.85 14325.5i 0.539663 0.934723i −0.459259 0.888302i \(-0.651885\pi\)
0.998922 0.0464208i \(-0.0147815\pi\)
\(618\) 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 −0.766354 0.642419i \(-0.777931\pi\)
0.939528 + 0.342473i \(0.111264\pi\)
\(632\) 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 −0.924597 0.380946i \(-0.875598\pi\)
0.792208 + 0.610251i \(0.208932\pi\)
\(642\) 0 0
\(643\) 12848.5 22254.2i 0.788016 1.36488i −0.139164 0.990269i \(-0.544442\pi\)
0.927181 0.374615i \(-0.122225\pi\)
\(644\) 0 0
\(645\) 11735.0 0.716378
\(646\) 0 0
\(647\) 1087.49 + 1883.59i 0.0660798 + 0.114454i 0.897172 0.441680i \(-0.145617\pi\)
−0.831093 + 0.556134i \(0.812284\pi\)
\(648\) 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 0.999113 0.0421191i \(-0.0134109\pi\)
−0.536032 + 0.844197i \(0.680078\pi\)
\(654\) 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 −0.908799 0.417234i \(-0.863000\pi\)
0.815735 + 0.578426i \(0.196333\pi\)
\(660\) 0 0
\(661\) 1049.85 + 1818.39i 0.0617767 + 0.107000i 0.895260 0.445545i \(-0.146990\pi\)
−0.833483 + 0.552545i \(0.813657\pi\)
\(662\) 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 −0.843462 0.537189i \(-0.819486\pi\)
−0.0434884 0.999054i \(-0.513847\pi\)
\(674\) 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 −0.944343 0.328963i \(-0.893301\pi\)
0.757062 + 0.653343i \(0.226634\pi\)
\(684\) 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 −0.897134 0.441758i \(-0.854355\pi\)
0.0659934 0.997820i \(-0.478978\pi\)
\(692\) 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 0.279348 + 0.960190i \(0.409882\pi\)
−0.971223 + 0.238173i \(0.923452\pi\)
\(710\) 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 −0.498799 0.866718i \(-0.666225\pi\)
0.999999 0.00138631i \(-0.000441276\pi\)
\(720\) 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 0.959044 0.283258i \(-0.0914153\pi\)
−0.724831 + 0.688927i \(0.758082\pi\)
\(740\) 0 0
\(741\) −251.487 191.334i −0.0124678 0.00948560i
\(742\) 0 0
\(743\) −3761.85 6515.72i −0.185746 0.321721i 0.758082 0.652159i \(-0.226137\pi\)
−0.943827 + 0.330439i \(0.892803\pi\)
\(744\) 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 0.664089 0.747654i \(-0.268820\pi\)
−0.979532 + 0.201291i \(0.935486\pi\)
\(752\) 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 0.977732 + 0.209859i \(0.0673004\pi\)
−0.307123 + 0.951670i \(0.599366\pi\)
\(758\) 0 0
\(759\) 3460.30 0.165482
\(760\) 0 0
\(761\) 7759.63 13440.1i 0.369627 0.640214i −0.619880 0.784697i \(-0.712819\pi\)
0.989507 + 0.144483i \(0.0461520\pi\)
\(762\) 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 0.674501 0.738274i \(-0.264359\pi\)
−0.976615 + 0.214997i \(0.931026\pi\)
\(770\) 0 0
\(771\) 8288.68 14356.4i 0.387172 0.670602i
\(772\) 0 0
\(773\) −2946.02 + 5102.66i −0.137078 + 0.237425i −0.926389 0.376567i \(-0.877104\pi\)
0.789312 + 0.613993i \(0.210438\pi\)
\(774\) 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 −0.999623 0.0274430i \(-0.991264\pi\)
0.523578 + 0.851978i \(0.324597\pi\)
\(788\) 0 0
\(789\) 7834.81 13570.3i 0.353519 0.612313i
\(790\) 0 0
\(791\) −874.023 1513.85i