Properties

Label 576.2.bb.e.49.16
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.16
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.64464 + 0.543291i) q^{3} +(-1.60558 + 0.430214i) q^{5} +(-3.62762 + 2.09441i) q^{7} +(2.40967 + 1.78703i) q^{9} +O(q^{10})\) \(q+(1.64464 + 0.543291i) q^{3} +(-1.60558 + 0.430214i) q^{5} +(-3.62762 + 2.09441i) q^{7} +(2.40967 + 1.78703i) q^{9} +(-1.24125 + 4.63241i) q^{11} +(-0.879738 - 3.28323i) q^{13} +(-2.87433 - 0.164751i) q^{15} -2.14142 q^{17} +(-1.03156 + 1.03156i) q^{19} +(-7.10399 + 1.47369i) q^{21} +(0.405884 + 0.234337i) q^{23} +(-1.93733 + 1.11852i) q^{25} +(2.99216 + 4.24818i) q^{27} +(6.55186 + 1.75557i) q^{29} +(-3.18054 + 5.50886i) q^{31} +(-4.55816 + 6.94428i) q^{33} +(4.92339 - 4.92339i) q^{35} +(-0.728237 - 0.728237i) q^{37} +(0.336896 - 5.87767i) q^{39} +(2.52351 + 1.45695i) q^{41} +(2.84802 - 10.6289i) q^{43} +(-4.63772 - 1.83255i) q^{45} +(4.61716 + 7.99715i) q^{47} +(5.27308 - 9.13324i) q^{49} +(-3.52186 - 1.16341i) q^{51} +(1.17892 + 1.17892i) q^{53} -7.97171i q^{55} +(-2.25698 + 1.13611i) q^{57} +(1.48185 - 0.397061i) q^{59} +(7.53224 + 2.01826i) q^{61} +(-12.4841 - 1.43585i) q^{63} +(2.82498 + 4.89300i) q^{65} +(-2.63252 - 9.82470i) q^{67} +(0.540220 + 0.605914i) q^{69} +8.27863i q^{71} +8.16641i q^{73} +(-3.79388 + 0.787022i) q^{75} +(-5.19937 - 19.4043i) q^{77} +(-3.63065 - 6.28847i) q^{79} +(2.61302 + 8.61232i) q^{81} +(7.59149 + 2.03413i) q^{83} +(3.43821 - 0.921267i) q^{85} +(9.82166 + 6.44684i) q^{87} +11.1968i q^{89} +(10.0678 + 10.0678i) q^{91} +(-8.22376 + 7.33213i) q^{93} +(1.21246 - 2.10004i) q^{95} +(-5.67759 - 9.83387i) q^{97} +(-11.2693 + 8.94443i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 1.64464 + 0.543291i 0.949532 + 0.313669i
\(4\) 0 0
\(5\) −1.60558 + 0.430214i −0.718037 + 0.192397i −0.599296 0.800528i \(-0.704553\pi\)
−0.118741 + 0.992925i \(0.537886\pi\)
\(6\) 0 0
\(7\) −3.62762 + 2.09441i −1.37111 + 0.791611i −0.991068 0.133358i \(-0.957424\pi\)
−0.380043 + 0.924969i \(0.624091\pi\)
\(8\) 0 0
\(9\) 2.40967 + 1.78703i 0.803223 + 0.595678i
\(10\) 0 0
\(11\) −1.24125 + 4.63241i −0.374251 + 1.39673i 0.480184 + 0.877168i \(0.340570\pi\)
−0.854436 + 0.519557i \(0.826097\pi\)
\(12\) 0 0
\(13\) −0.879738 3.28323i −0.243995 0.910603i −0.973886 0.227039i \(-0.927096\pi\)
0.729890 0.683564i \(-0.239571\pi\)
\(14\) 0 0
\(15\) −2.87433 0.164751i −0.742148 0.0425384i
\(16\) 0 0
\(17\) −2.14142 −0.519370 −0.259685 0.965693i \(-0.583619\pi\)
−0.259685 + 0.965693i \(0.583619\pi\)
\(18\) 0 0
\(19\) −1.03156 + 1.03156i −0.236656 + 0.236656i −0.815464 0.578808i \(-0.803518\pi\)
0.578808 + 0.815464i \(0.303518\pi\)
\(20\) 0 0
\(21\) −7.10399 + 1.47369i −1.55022 + 0.321585i
\(22\) 0 0
\(23\) 0.405884 + 0.234337i 0.0846327 + 0.0488627i 0.541719 0.840560i \(-0.317774\pi\)
−0.457086 + 0.889422i \(0.651107\pi\)
\(24\) 0 0
\(25\) −1.93733 + 1.11852i −0.387465 + 0.223703i
\(26\) 0 0
\(27\) 2.99216 + 4.24818i 0.575841 + 0.817562i
\(28\) 0 0
\(29\) 6.55186 + 1.75557i 1.21665 + 0.326000i 0.809368 0.587302i \(-0.199810\pi\)
0.407282 + 0.913302i \(0.366477\pi\)
\(30\) 0 0
\(31\) −3.18054 + 5.50886i −0.571242 + 0.989421i 0.425196 + 0.905101i \(0.360205\pi\)
−0.996439 + 0.0843198i \(0.973128\pi\)
\(32\) 0 0
\(33\) −4.55816 + 6.94428i −0.793473 + 1.20884i
\(34\) 0 0
\(35\) 4.92339 4.92339i 0.832204 0.832204i
\(36\) 0 0
\(37\) −0.728237 0.728237i −0.119721 0.119721i 0.644708 0.764429i \(-0.276979\pi\)
−0.764429 + 0.644708i \(0.776979\pi\)
\(38\) 0 0
\(39\) 0.336896 5.87767i 0.0539466 0.941181i
\(40\) 0 0
\(41\) 2.52351 + 1.45695i 0.394105 + 0.227537i 0.683937 0.729541i \(-0.260266\pi\)
−0.289832 + 0.957078i \(0.593599\pi\)
\(42\) 0 0
\(43\) 2.84802 10.6289i 0.434318 1.62090i −0.308374 0.951265i \(-0.599785\pi\)
0.742692 0.669633i \(-0.233549\pi\)
\(44\) 0 0
\(45\) −4.63772 1.83255i −0.691351 0.273181i
\(46\) 0 0
\(47\) 4.61716 + 7.99715i 0.673482 + 1.16650i 0.976910 + 0.213650i \(0.0685352\pi\)
−0.303429 + 0.952854i \(0.598131\pi\)
\(48\) 0 0
\(49\) 5.27308 9.13324i 0.753297 1.30475i
\(50\) 0 0
\(51\) −3.52186 1.16341i −0.493159 0.162910i
\(52\) 0 0
\(53\) 1.17892 + 1.17892i 0.161937 + 0.161937i 0.783424 0.621487i \(-0.213471\pi\)
−0.621487 + 0.783424i \(0.713471\pi\)
\(54\) 0 0
\(55\) 7.97171i 1.07491i
\(56\) 0 0
\(57\) −2.25698 + 1.13611i −0.298944 + 0.150481i
\(58\) 0 0
\(59\) 1.48185 0.397061i 0.192921 0.0516930i −0.161065 0.986944i \(-0.551493\pi\)
0.353986 + 0.935251i \(0.384826\pi\)
\(60\) 0 0
\(61\) 7.53224 + 2.01826i 0.964404 + 0.258411i 0.706464 0.707749i \(-0.250289\pi\)
0.257941 + 0.966161i \(0.416956\pi\)
\(62\) 0 0
\(63\) −12.4841 1.43585i −1.57285 0.180900i
\(64\) 0 0
\(65\) 2.82498 + 4.89300i 0.350395 + 0.606902i
\(66\) 0 0
\(67\) −2.63252 9.82470i −0.321614 1.20028i −0.917673 0.397338i \(-0.869934\pi\)
0.596059 0.802941i \(-0.296732\pi\)
\(68\) 0 0
\(69\) 0.540220 + 0.605914i 0.0650348 + 0.0729434i
\(70\) 0 0
\(71\) 8.27863i 0.982493i 0.871021 + 0.491246i \(0.163458\pi\)
−0.871021 + 0.491246i \(0.836542\pi\)
\(72\) 0 0
\(73\) 8.16641i 0.955806i 0.878413 + 0.477903i \(0.158603\pi\)
−0.878413 + 0.477903i \(0.841397\pi\)
\(74\) 0 0
\(75\) −3.79388 + 0.787022i −0.438079 + 0.0908775i
\(76\) 0 0
\(77\) −5.19937 19.4043i −0.592523 2.21133i
\(78\) 0 0
\(79\) −3.63065 6.28847i −0.408480 0.707508i 0.586240 0.810138i \(-0.300608\pi\)
−0.994720 + 0.102630i \(0.967274\pi\)
\(80\) 0 0
\(81\) 2.61302 + 8.61232i 0.290336 + 0.956925i
\(82\) 0 0
\(83\) 7.59149 + 2.03413i 0.833274 + 0.223275i 0.650142 0.759813i \(-0.274710\pi\)
0.183133 + 0.983088i \(0.441376\pi\)
\(84\) 0 0
\(85\) 3.43821 0.921267i 0.372927 0.0999254i
\(86\) 0 0
\(87\) 9.82166 + 6.44684i 1.05299 + 0.691174i
\(88\) 0 0
\(89\) 11.1968i 1.18686i 0.804886 + 0.593429i \(0.202226\pi\)
−0.804886 + 0.593429i \(0.797774\pi\)
\(90\) 0 0
\(91\) 10.0678 + 10.0678i 1.05539 + 1.05539i
\(92\) 0 0
\(93\) −8.22376 + 7.33213i −0.852764 + 0.760306i
\(94\) 0 0
\(95\) 1.21246 2.10004i 0.124396 0.215460i
\(96\) 0 0
\(97\) −5.67759 9.83387i −0.576472 0.998479i −0.995880 0.0906808i \(-0.971096\pi\)
0.419408 0.907798i \(-0.362238\pi\)
\(98\) 0 0
\(99\) −11.2693 + 8.94443i −1.13261 + 0.898949i
\(100\) 0 0
\(101\) 0.777558 2.90189i 0.0773699 0.288749i −0.916390 0.400286i \(-0.868911\pi\)
0.993760 + 0.111537i \(0.0355775\pi\)
\(102\) 0 0
\(103\) 1.24824 + 0.720669i 0.122992 + 0.0710096i 0.560234 0.828334i \(-0.310711\pi\)
−0.437242 + 0.899344i \(0.644045\pi\)
\(104\) 0 0
\(105\) 10.7720 5.42236i 1.05124 0.529168i
\(106\) 0 0
\(107\) −5.85602 5.85602i −0.566123 0.566123i 0.364917 0.931040i \(-0.381097\pi\)
−0.931040 + 0.364917i \(0.881097\pi\)
\(108\) 0 0
\(109\) −2.05249 + 2.05249i −0.196593 + 0.196593i −0.798538 0.601945i \(-0.794393\pi\)
0.601945 + 0.798538i \(0.294393\pi\)
\(110\) 0 0
\(111\) −0.802042 1.59333i −0.0761265 0.151232i
\(112\) 0 0
\(113\) −4.12726 + 7.14862i −0.388260 + 0.672486i −0.992216 0.124532i \(-0.960257\pi\)
0.603956 + 0.797018i \(0.293590\pi\)
\(114\) 0 0
\(115\) −0.752495 0.201630i −0.0701705 0.0188021i
\(116\) 0 0
\(117\) 3.74736 9.48361i 0.346443 0.876760i
\(118\) 0 0
\(119\) 7.76824 4.48500i 0.712114 0.411139i
\(120\) 0 0
\(121\) −10.3923 5.99998i −0.944752 0.545453i
\(122\) 0 0
\(123\) 3.35871 + 3.76715i 0.302845 + 0.339672i
\(124\) 0 0
\(125\) 8.50616 8.50616i 0.760814 0.760814i
\(126\) 0 0
\(127\) 1.68483 0.149504 0.0747521 0.997202i \(-0.476183\pi\)
0.0747521 + 0.997202i \(0.476183\pi\)
\(128\) 0 0
\(129\) 10.4586 15.9335i 0.920825 1.40286i
\(130\) 0 0
\(131\) −1.97334 7.36461i −0.172412 0.643449i −0.996978 0.0776838i \(-0.975248\pi\)
0.824566 0.565765i \(-0.191419\pi\)
\(132\) 0 0
\(133\) 1.58160 5.90261i 0.137142 0.511821i
\(134\) 0 0
\(135\) −6.63177 5.53352i −0.570772 0.476249i
\(136\) 0 0
\(137\) 8.26806 4.77357i 0.706388 0.407833i −0.103334 0.994647i \(-0.532951\pi\)
0.809722 + 0.586813i \(0.199618\pi\)
\(138\) 0 0
\(139\) 13.9684 3.74281i 1.18478 0.317461i 0.387960 0.921676i \(-0.373180\pi\)
0.796821 + 0.604215i \(0.206513\pi\)
\(140\) 0 0
\(141\) 3.24877 + 15.6609i 0.273596 + 1.31888i
\(142\) 0 0
\(143\) 16.3012 1.36318
\(144\) 0 0
\(145\) −11.2748 −0.936321
\(146\) 0 0
\(147\) 13.6343 12.1561i 1.12454 1.00261i
\(148\) 0 0
\(149\) −1.66249 + 0.445462i −0.136196 + 0.0364937i −0.326273 0.945276i \(-0.605793\pi\)
0.190077 + 0.981769i \(0.439126\pi\)
\(150\) 0 0
\(151\) −18.5071 + 10.6851i −1.50609 + 0.869542i −0.506115 + 0.862466i \(0.668919\pi\)
−0.999975 + 0.00707596i \(0.997748\pi\)
\(152\) 0 0
\(153\) −5.16011 3.82678i −0.417170 0.309377i
\(154\) 0 0
\(155\) 2.73663 10.2132i 0.219811 0.820346i
\(156\) 0 0
\(157\) 2.74550 + 10.2463i 0.219114 + 0.817746i 0.984677 + 0.174385i \(0.0557938\pi\)
−0.765563 + 0.643361i \(0.777539\pi\)
\(158\) 0 0
\(159\) 1.29840 + 2.57939i 0.102970 + 0.204559i
\(160\) 0 0
\(161\) −1.96319 −0.154721
\(162\) 0 0
\(163\) 3.47621 3.47621i 0.272278 0.272278i −0.557739 0.830017i \(-0.688331\pi\)
0.830017 + 0.557739i \(0.188331\pi\)
\(164\) 0 0
\(165\) 4.33096 13.1106i 0.337165 1.02066i
\(166\) 0 0
\(167\) −0.277442 0.160181i −0.0214691 0.0123952i 0.489227 0.872156i \(-0.337279\pi\)
−0.510696 + 0.859761i \(0.670612\pi\)
\(168\) 0 0
\(169\) 1.25270 0.723245i 0.0963613 0.0556342i
\(170\) 0 0
\(171\) −4.32915 + 0.642287i −0.331059 + 0.0491169i
\(172\) 0 0
\(173\) 11.6901 + 3.13236i 0.888784 + 0.238149i 0.674193 0.738555i \(-0.264491\pi\)
0.214591 + 0.976704i \(0.431158\pi\)
\(174\) 0 0
\(175\) 4.68525 8.11510i 0.354172 0.613444i
\(176\) 0 0
\(177\) 2.65283 + 0.152055i 0.199399 + 0.0114291i
\(178\) 0 0
\(179\) −18.6780 + 18.6780i −1.39606 + 1.39606i −0.585104 + 0.810958i \(0.698946\pi\)
−0.810958 + 0.585104i \(0.801054\pi\)
\(180\) 0 0
\(181\) 4.10527 + 4.10527i 0.305143 + 0.305143i 0.843022 0.537879i \(-0.180774\pi\)
−0.537879 + 0.843022i \(0.680774\pi\)
\(182\) 0 0
\(183\) 11.2913 + 7.41150i 0.834677 + 0.547874i
\(184\) 0 0
\(185\) 1.48254 + 0.855945i 0.108998 + 0.0629303i
\(186\) 0 0
\(187\) 2.65804 9.91993i 0.194375 0.725417i
\(188\) 0 0
\(189\) −19.7518 9.14397i −1.43673 0.665126i
\(190\) 0 0
\(191\) −8.60099 14.8974i −0.622346 1.07793i −0.989048 0.147596i \(-0.952846\pi\)
0.366702 0.930338i \(-0.380487\pi\)
\(192\) 0 0
\(193\) 9.17459 15.8909i 0.660402 1.14385i −0.320108 0.947381i \(-0.603719\pi\)
0.980510 0.196468i \(-0.0629473\pi\)
\(194\) 0 0
\(195\) 1.98774 + 9.58201i 0.142345 + 0.686182i
\(196\) 0 0
\(197\) 8.80431 + 8.80431i 0.627281 + 0.627281i 0.947383 0.320102i \(-0.103717\pi\)
−0.320102 + 0.947383i \(0.603717\pi\)
\(198\) 0 0
\(199\) 10.0277i 0.710847i −0.934705 0.355423i \(-0.884337\pi\)
0.934705 0.355423i \(-0.115663\pi\)
\(200\) 0 0
\(201\) 1.00813 17.5883i 0.0711077 1.24058i
\(202\) 0 0
\(203\) −27.4445 + 7.35374i −1.92623 + 0.516131i
\(204\) 0 0
\(205\) −4.67849 1.25360i −0.326760 0.0875550i
\(206\) 0 0
\(207\) 0.559278 + 1.29001i 0.0388725 + 0.0896616i
\(208\) 0 0
\(209\) −3.49819 6.05904i −0.241975 0.419112i
\(210\) 0 0
\(211\) 5.14678 + 19.2080i 0.354319 + 1.32234i 0.881340 + 0.472483i \(0.156642\pi\)
−0.527021 + 0.849852i \(0.676691\pi\)
\(212\) 0 0
\(213\) −4.49770 + 13.6154i −0.308178 + 0.932908i
\(214\) 0 0
\(215\) 18.2909i 1.24743i
\(216\) 0 0
\(217\) 26.6454i 1.80881i
\(218\) 0 0
\(219\) −4.43674 + 13.4308i −0.299807 + 0.907569i
\(220\) 0 0
\(221\) 1.88389 + 7.03076i 0.126724 + 0.472940i
\(222\) 0 0
\(223\) 6.96587 + 12.0652i 0.466469 + 0.807948i 0.999266 0.0382947i \(-0.0121926\pi\)
−0.532797 + 0.846243i \(0.678859\pi\)
\(224\) 0 0
\(225\) −6.66714 0.766813i −0.444476 0.0511209i
\(226\) 0 0
\(227\) 7.32092 + 1.96164i 0.485907 + 0.130198i 0.493452 0.869773i \(-0.335735\pi\)
−0.00754492 + 0.999972i \(0.502402\pi\)
\(228\) 0 0
\(229\) −18.4637 + 4.94734i −1.22012 + 0.326930i −0.810724 0.585428i \(-0.800926\pi\)
−0.409394 + 0.912358i \(0.634260\pi\)
\(230\) 0 0
\(231\) 1.99110 34.7378i 0.131005 2.28558i
\(232\) 0 0
\(233\) 10.7647i 0.705216i 0.935771 + 0.352608i \(0.114705\pi\)
−0.935771 + 0.352608i \(0.885295\pi\)
\(234\) 0 0
\(235\) −10.8537 10.8537i −0.708017 0.708017i
\(236\) 0 0
\(237\) −2.55464 12.3147i −0.165941 0.799929i
\(238\) 0 0
\(239\) 11.1429 19.3001i 0.720774 1.24842i −0.239916 0.970794i \(-0.577120\pi\)
0.960690 0.277624i \(-0.0895469\pi\)
\(240\) 0 0
\(241\) 13.7285 + 23.7785i 0.884332 + 1.53171i 0.846478 + 0.532424i \(0.178719\pi\)
0.0378540 + 0.999283i \(0.487948\pi\)
\(242\) 0 0
\(243\) −0.381525 + 15.5838i −0.0244748 + 0.999700i
\(244\) 0 0
\(245\) −4.53710 + 16.9327i −0.289865 + 1.08179i
\(246\) 0 0
\(247\) 4.29435 + 2.47934i 0.273243 + 0.157757i
\(248\) 0 0
\(249\) 11.3801 + 7.46980i 0.721186 + 0.473379i
\(250\) 0 0
\(251\) −11.4125 11.4125i −0.720350 0.720350i 0.248326 0.968676i \(-0.420119\pi\)
−0.968676 + 0.248326i \(0.920119\pi\)
\(252\) 0 0
\(253\) −1.58935 + 1.58935i −0.0999217 + 0.0999217i
\(254\) 0 0
\(255\) 6.15514 + 0.352800i 0.385450 + 0.0220932i
\(256\) 0 0
\(257\) −0.930384 + 1.61147i −0.0580357 + 0.100521i −0.893584 0.448897i \(-0.851817\pi\)
0.835548 + 0.549418i \(0.185150\pi\)
\(258\) 0 0
\(259\) 4.16699 + 1.11654i 0.258924 + 0.0693785i
\(260\) 0 0
\(261\) 12.6506 + 15.9387i 0.783051 + 0.986583i
\(262\) 0 0
\(263\) −0.0414842 + 0.0239509i −0.00255802 + 0.00147687i −0.501278 0.865286i \(-0.667137\pi\)
0.498720 + 0.866763i \(0.333803\pi\)
\(264\) 0 0
\(265\) −2.40003 1.38566i −0.147433 0.0851203i
\(266\) 0 0
\(267\) −6.08312 + 18.4147i −0.372281 + 1.12696i
\(268\) 0 0
\(269\) −14.5681 + 14.5681i −0.888235 + 0.888235i −0.994354 0.106118i \(-0.966158\pi\)
0.106118 + 0.994354i \(0.466158\pi\)
\(270\) 0 0
\(271\) 15.7807 0.958607 0.479304 0.877649i \(-0.340889\pi\)
0.479304 + 0.877649i \(0.340889\pi\)
\(272\) 0 0
\(273\) 11.0881 + 22.0275i 0.671083 + 1.33317i
\(274\) 0 0
\(275\) −2.77672 10.3629i −0.167442 0.624904i
\(276\) 0 0
\(277\) −1.93294 + 7.21383i −0.116139 + 0.433437i −0.999370 0.0355022i \(-0.988697\pi\)
0.883231 + 0.468939i \(0.155364\pi\)
\(278\) 0 0
\(279\) −17.5086 + 7.59080i −1.04821 + 0.454449i
\(280\) 0 0
\(281\) −5.84440 + 3.37427i −0.348648 + 0.201292i −0.664089 0.747653i \(-0.731181\pi\)
0.315442 + 0.948945i \(0.397847\pi\)
\(282\) 0 0
\(283\) −12.4414 + 3.33366i −0.739563 + 0.198165i −0.608884 0.793259i \(-0.708383\pi\)
−0.130679 + 0.991425i \(0.541716\pi\)
\(284\) 0 0
\(285\) 3.13499 2.79509i 0.185701 0.165567i
\(286\) 0 0
\(287\) −12.2058 −0.720483
\(288\) 0 0
\(289\) −12.4143 −0.730255
\(290\) 0 0
\(291\) −3.99493 19.2577i −0.234187 1.12891i
\(292\) 0 0
\(293\) 13.8785 3.71874i 0.810792 0.217251i 0.170475 0.985362i \(-0.445470\pi\)
0.640317 + 0.768111i \(0.278803\pi\)
\(294\) 0 0
\(295\) −2.20841 + 1.27503i −0.128579 + 0.0742349i
\(296\) 0 0
\(297\) −23.3933 + 8.58785i −1.35742 + 0.498318i
\(298\) 0 0
\(299\) 0.412311 1.53877i 0.0238446 0.0889891i
\(300\) 0 0
\(301\) 11.9298 + 44.5226i 0.687622 + 2.56624i
\(302\) 0 0
\(303\) 2.85537 4.35011i 0.164037 0.249907i
\(304\) 0 0
\(305\) −12.9619 −0.742196
\(306\) 0 0
\(307\) −12.2394 + 12.2394i −0.698539 + 0.698539i −0.964095 0.265556i \(-0.914444\pi\)
0.265556 + 0.964095i \(0.414444\pi\)
\(308\) 0 0
\(309\) 1.66136 + 1.86339i 0.0945116 + 0.106005i
\(310\) 0 0
\(311\) 0.742777 + 0.428842i 0.0421190 + 0.0243174i 0.520912 0.853611i \(-0.325592\pi\)
−0.478793 + 0.877928i \(0.658925\pi\)
\(312\) 0 0
\(313\) −15.8984 + 9.17895i −0.898631 + 0.518825i −0.876756 0.480936i \(-0.840297\pi\)
−0.0218755 + 0.999761i \(0.506964\pi\)
\(314\) 0 0
\(315\) 20.6620 3.06548i 1.16417 0.172720i
\(316\) 0 0
\(317\) −4.02641 1.07887i −0.226146 0.0605956i 0.143967 0.989583i \(-0.454014\pi\)
−0.370112 + 0.928987i \(0.620681\pi\)
\(318\) 0 0
\(319\) −16.2650 + 28.1718i −0.910666 + 1.57732i
\(320\) 0 0
\(321\) −6.44952 12.8126i −0.359977 0.715128i
\(322\) 0 0
\(323\) 2.20900 2.20900i 0.122912 0.122912i
\(324\) 0 0
\(325\) 5.37668 + 5.37668i 0.298244 + 0.298244i
\(326\) 0 0
\(327\) −4.49070 + 2.26050i −0.248336 + 0.125006i
\(328\) 0 0
\(329\) −33.4986 19.3404i −1.84684 1.06627i
\(330\) 0 0
\(331\) −1.33734 + 4.99103i −0.0735070 + 0.274332i −0.992891 0.119030i \(-0.962021\pi\)
0.919384 + 0.393362i \(0.128688\pi\)
\(332\) 0 0
\(333\) −0.453427 3.05620i −0.0248476 0.167478i
\(334\) 0 0
\(335\) 8.45344 + 14.6418i 0.461861 + 0.799966i
\(336\) 0 0
\(337\) 1.94762 3.37338i 0.106094 0.183760i −0.808091 0.589058i \(-0.799499\pi\)
0.914185 + 0.405298i \(0.132832\pi\)
\(338\) 0 0
\(339\) −10.6716 + 9.51459i −0.579603 + 0.516762i
\(340\) 0 0
\(341\) −21.5715 21.5715i −1.16816 1.16816i
\(342\) 0 0
\(343\) 14.8542i 0.802049i
\(344\) 0 0
\(345\) −1.12804 0.740433i −0.0607315 0.0398635i
\(346\) 0 0
\(347\) 3.04812 0.816741i 0.163632 0.0438449i −0.176073 0.984377i \(-0.556340\pi\)
0.339705 + 0.940532i \(0.389673\pi\)
\(348\) 0 0
\(349\) 1.39893 + 0.374843i 0.0748831 + 0.0200649i 0.296066 0.955167i \(-0.404325\pi\)
−0.221183 + 0.975232i \(0.570992\pi\)
\(350\) 0 0
\(351\) 11.3154 13.5612i 0.603972 0.723844i
\(352\) 0 0
\(353\) 7.73892 + 13.4042i 0.411901 + 0.713434i 0.995098 0.0988971i \(-0.0315315\pi\)
−0.583196 + 0.812331i \(0.698198\pi\)
\(354\) 0 0
\(355\) −3.56158 13.2920i −0.189029 0.705466i
\(356\) 0 0
\(357\) 15.2126 3.15578i 0.805137 0.167022i
\(358\) 0 0
\(359\) 4.78775i 0.252688i −0.991987 0.126344i \(-0.959676\pi\)
0.991987 0.126344i \(-0.0403242\pi\)
\(360\) 0 0
\(361\) 16.8718i 0.887988i
\(362\) 0 0
\(363\) −13.8318 15.5138i −0.725981 0.814264i
\(364\) 0 0
\(365\) −3.51330 13.1118i −0.183895 0.686304i
\(366\) 0 0
\(367\) 9.93807 + 17.2133i 0.518763 + 0.898524i 0.999762 + 0.0218032i \(0.00694073\pi\)
−0.480999 + 0.876721i \(0.659726\pi\)
\(368\) 0 0
\(369\) 3.47720 + 8.02035i 0.181016 + 0.417523i
\(370\) 0 0
\(371\) −6.74579 1.80753i −0.350224 0.0938422i
\(372\) 0 0
\(373\) −0.427591 + 0.114573i −0.0221398 + 0.00593235i −0.269872 0.962896i \(-0.586981\pi\)
0.247732 + 0.968829i \(0.420315\pi\)
\(374\) 0 0
\(375\) 18.6109 9.36823i 0.961061 0.483774i
\(376\) 0 0
\(377\) 23.0557i 1.18743i
\(378\) 0 0
\(379\) 6.18132 + 6.18132i 0.317513 + 0.317513i 0.847811 0.530298i \(-0.177920\pi\)
−0.530298 + 0.847811i \(0.677920\pi\)
\(380\) 0 0
\(381\) 2.77093 + 0.915351i 0.141959 + 0.0468949i
\(382\) 0 0
\(383\) −6.46708 + 11.2013i −0.330452 + 0.572360i −0.982601 0.185731i \(-0.940535\pi\)
0.652148 + 0.758091i \(0.273868\pi\)
\(384\) 0 0
\(385\) 16.6960 + 28.9183i 0.850907 + 1.47381i
\(386\) 0 0
\(387\) 25.8571 20.5227i 1.31439 1.04323i
\(388\) 0 0
\(389\) 7.08096 26.4265i 0.359019 1.33988i −0.516331 0.856389i \(-0.672703\pi\)
0.875351 0.483489i \(-0.160631\pi\)
\(390\) 0 0
\(391\) −0.869168 0.501814i −0.0439557 0.0253778i
\(392\) 0 0
\(393\) 0.755693 13.1842i 0.0381197 0.665056i
\(394\) 0 0
\(395\) 8.53468 + 8.53468i 0.429426 + 0.429426i
\(396\) 0 0
\(397\) 21.9741 21.9741i 1.10285 1.10285i 0.108781 0.994066i \(-0.465305\pi\)
0.994066 0.108781i \(-0.0346948\pi\)
\(398\) 0 0
\(399\) 5.80799 8.84839i 0.290763 0.442974i
\(400\) 0 0
\(401\) 13.4970 23.3775i 0.674009 1.16742i −0.302749 0.953070i \(-0.597904\pi\)
0.976758 0.214347i \(-0.0687624\pi\)
\(402\) 0 0
\(403\) 20.8849 + 5.59609i 1.04035 + 0.278761i
\(404\) 0 0
\(405\) −7.90055 12.7036i −0.392581 0.631248i
\(406\) 0 0
\(407\) 4.27742 2.46957i 0.212024 0.122412i
\(408\) 0 0
\(409\) 11.1537 + 6.43957i 0.551513 + 0.318416i 0.749732 0.661741i \(-0.230182\pi\)
−0.198219 + 0.980158i \(0.563516\pi\)
\(410\) 0 0
\(411\) 16.1914 3.35883i 0.798663 0.165679i
\(412\) 0 0
\(413\) −4.54399 + 4.54399i −0.223595 + 0.223595i
\(414\) 0 0
\(415\) −13.0638 −0.641279
\(416\) 0 0
\(417\) 25.0063 + 1.43331i 1.22457 + 0.0701896i
\(418\) 0 0
\(419\) 0.0545100 + 0.203434i 0.00266299 + 0.00993841i 0.967245 0.253846i \(-0.0816958\pi\)
−0.964582 + 0.263785i \(0.915029\pi\)
\(420\) 0 0
\(421\) 9.17194 34.2301i 0.447013 1.66827i −0.263554 0.964645i \(-0.584895\pi\)
0.710567 0.703630i \(-0.248439\pi\)
\(422\) 0 0
\(423\) −3.16535 + 27.5215i −0.153905 + 1.33814i
\(424\) 0 0
\(425\) 4.14862 2.39521i 0.201238 0.116185i
\(426\) 0 0
\(427\) −31.5511 + 8.45410i −1.52687 + 0.409123i
\(428\) 0 0
\(429\) 26.8096 + 8.85631i 1.29438 + 0.427587i
\(430\) 0 0
\(431\) −33.5339 −1.61527 −0.807635 0.589683i \(-0.799253\pi\)
−0.807635 + 0.589683i \(0.799253\pi\)
\(432\) 0 0
\(433\) −28.9691 −1.39217 −0.696083 0.717962i \(-0.745075\pi\)
−0.696083 + 0.717962i \(0.745075\pi\)
\(434\) 0 0
\(435\) −18.5430 6.12550i −0.889067 0.293695i
\(436\) 0 0
\(437\) −0.660427 + 0.176961i −0.0315925 + 0.00846519i
\(438\) 0 0
\(439\) 14.6656 8.46718i 0.699950 0.404116i −0.107379 0.994218i \(-0.534246\pi\)
0.807329 + 0.590102i \(0.200912\pi\)
\(440\) 0 0
\(441\) 29.0278 12.5849i 1.38227 0.599282i
\(442\) 0 0
\(443\) −0.826654 + 3.08511i −0.0392755 + 0.146578i −0.982779 0.184784i \(-0.940841\pi\)
0.943504 + 0.331362i \(0.107508\pi\)
\(444\) 0 0
\(445\) −4.81702 17.9773i −0.228348 0.852208i
\(446\) 0 0
\(447\) −2.97621 0.170590i −0.140770 0.00806863i
\(448\) 0 0
\(449\) −41.9192 −1.97829 −0.989145 0.146944i \(-0.953056\pi\)
−0.989145 + 0.146944i \(0.953056\pi\)
\(450\) 0 0
\(451\) −9.88149 + 9.88149i −0.465301 + 0.465301i
\(452\) 0 0
\(453\) −36.2427 + 7.51837i −1.70283 + 0.353244i
\(454\) 0 0
\(455\) −20.4959 11.8333i −0.960862 0.554754i
\(456\) 0 0
\(457\) 4.93980 2.85199i 0.231074 0.133411i −0.379993 0.924989i \(-0.624074\pi\)
0.611067 + 0.791579i \(0.290740\pi\)
\(458\) 0 0
\(459\) −6.40745 9.09712i −0.299074 0.424617i
\(460\) 0 0
\(461\) −38.3338 10.2715i −1.78538 0.478392i −0.793834 0.608135i \(-0.791918\pi\)
−0.991548 + 0.129743i \(0.958585\pi\)
\(462\) 0 0
\(463\) 6.28293 10.8824i 0.291992 0.505746i −0.682288 0.731083i \(-0.739015\pi\)
0.974281 + 0.225337i \(0.0723485\pi\)
\(464\) 0 0
\(465\) 10.0495 15.3103i 0.466035 0.709997i
\(466\) 0 0
\(467\) −12.1784 + 12.1784i −0.563550 + 0.563550i −0.930314 0.366764i \(-0.880466\pi\)
0.366764 + 0.930314i \(0.380466\pi\)
\(468\) 0 0
\(469\) 30.1267 + 30.1267i 1.39112 + 1.39112i
\(470\) 0 0
\(471\) −1.05139 + 18.3431i −0.0484455 + 0.845206i
\(472\) 0 0
\(473\) 45.7025 + 26.3864i 2.10140 + 1.21325i
\(474\) 0 0
\(475\) 0.844652 3.15228i 0.0387553 0.144637i
\(476\) 0 0
\(477\) 0.734036 + 4.94756i 0.0336092 + 0.226533i
\(478\) 0 0
\(479\) 10.6864 + 18.5094i 0.488275 + 0.845717i 0.999909 0.0134862i \(-0.00429292\pi\)
−0.511634 + 0.859204i \(0.670960\pi\)
\(480\) 0 0
\(481\) −1.75031 + 3.03162i −0.0798072 + 0.138230i
\(482\) 0 0
\(483\) −3.22874 1.06658i −0.146913 0.0485313i
\(484\) 0 0
\(485\) 13.3465 + 13.3465i 0.606033 + 0.606033i
\(486\) 0 0
\(487\) 39.3716i 1.78410i −0.451939 0.892049i \(-0.649268\pi\)
0.451939 0.892049i \(-0.350732\pi\)
\(488\) 0 0
\(489\) 7.60570 3.82851i 0.343942 0.173131i
\(490\) 0 0
\(491\) 33.8903 9.08087i 1.52945 0.409814i 0.606608 0.795001i \(-0.292530\pi\)
0.922839 + 0.385187i \(0.125863\pi\)
\(492\) 0 0
\(493\) −14.0303 3.75940i −0.631891 0.169315i
\(494\) 0 0
\(495\) 14.2457 19.2092i 0.640297 0.863389i
\(496\) 0 0
\(497\) −17.3388 30.0317i −0.777752 1.34711i
\(498\) 0 0
\(499\) −3.38889 12.6475i −0.151708 0.566181i −0.999365 0.0356364i \(-0.988654\pi\)
0.847657 0.530544i \(-0.178012\pi\)
\(500\) 0 0
\(501\) −0.369267 0.414172i −0.0164976 0.0185039i
\(502\) 0 0
\(503\) 2.93881i 0.131035i 0.997851 + 0.0655175i \(0.0208698\pi\)
−0.997851 + 0.0655175i \(0.979130\pi\)
\(504\) 0 0
\(505\) 4.99373i 0.222218i
\(506\) 0 0
\(507\) 2.45317 0.508897i 0.108949 0.0226009i
\(508\) 0 0
\(509\) 4.11461 + 15.3559i 0.182377 + 0.680640i 0.995177 + 0.0980972i \(0.0312756\pi\)
−0.812800 + 0.582543i \(0.802058\pi\)
\(510\) 0 0
\(511\) −17.1038 29.6246i −0.756627 1.31052i
\(512\) 0 0
\(513\) −7.46884 1.29566i −0.329757 0.0572048i
\(514\) 0 0
\(515\) −2.31418 0.620083i −0.101975 0.0273241i
\(516\) 0 0
\(517\) −42.7772 + 11.4621i −1.88134 + 0.504103i
\(518\) 0 0
\(519\) 17.5243 + 11.5027i 0.769230 + 0.504914i
\(520\) 0 0
\(521\) 19.2119i 0.841689i 0.907133 + 0.420844i \(0.138266\pi\)
−0.907133 + 0.420844i \(0.861734\pi\)
\(522\) 0 0
\(523\) 10.0495 + 10.0495i 0.439436 + 0.439436i 0.891822 0.452386i \(-0.149427\pi\)
−0.452386 + 0.891822i \(0.649427\pi\)
\(524\) 0 0
\(525\) 12.1144 10.8009i 0.528716 0.471392i
\(526\) 0 0
\(527\) 6.81087 11.7968i 0.296686 0.513875i
\(528\) 0 0
\(529\) −11.3902 19.7284i −0.495225 0.857755i
\(530\) 0 0
\(531\) 4.28034 + 1.69133i 0.185751 + 0.0733976i
\(532\) 0 0
\(533\) 2.56346 9.56697i 0.111036 0.414392i
\(534\) 0 0
\(535\) 11.9217 + 6.88297i 0.515418 + 0.297577i
\(536\) 0 0
\(537\) −40.8662 + 20.5710i −1.76351 + 0.887705i
\(538\) 0 0
\(539\) 35.7637 + 35.7637i 1.54045 + 1.54045i
\(540\) 0 0
\(541\) 15.3802 15.3802i 0.661246 0.661246i −0.294428 0.955674i \(-0.595129\pi\)
0.955674 + 0.294428i \(0.0951290\pi\)
\(542\) 0 0
\(543\) 4.52133 + 8.98205i 0.194029 + 0.385457i
\(544\) 0 0
\(545\) 2.41243 4.17844i 0.103337 0.178985i
\(546\) 0 0
\(547\) 23.1362 + 6.19933i 0.989233 + 0.265064i 0.716928 0.697147i \(-0.245548\pi\)
0.272304 + 0.962211i \(0.412214\pi\)
\(548\) 0 0
\(549\) 14.5435 + 18.3237i 0.620702 + 0.782036i
\(550\) 0 0
\(551\) −8.56961 + 4.94767i −0.365078 + 0.210778i
\(552\) 0 0
\(553\) 26.3412 + 15.2081i 1.12014 + 0.646714i
\(554\) 0 0
\(555\) 1.97321 + 2.21317i 0.0837583 + 0.0939438i
\(556\) 0 0
\(557\) 0.932077 0.932077i 0.0394934 0.0394934i −0.687084 0.726578i \(-0.741110\pi\)
0.726578 + 0.687084i \(0.241110\pi\)
\(558\) 0 0
\(559\) −37.4027 −1.58197
\(560\) 0 0
\(561\) 9.76092 14.8706i 0.412106 0.627838i
\(562\) 0 0
\(563\) 1.71390 + 6.39635i 0.0722321 + 0.269574i 0.992591 0.121500i \(-0.0387704\pi\)
−0.920359 + 0.391074i \(0.872104\pi\)
\(564\) 0 0
\(565\) 3.55121 13.2533i 0.149400 0.557570i
\(566\) 0 0
\(567\) −27.5167 25.7695i −1.15559 1.08222i
\(568\) 0 0
\(569\) 7.84553 4.52962i 0.328902 0.189892i −0.326452 0.945214i \(-0.605853\pi\)
0.655353 + 0.755322i \(0.272520\pi\)
\(570\) 0 0
\(571\) 17.9078 4.79838i 0.749417 0.200806i 0.136158 0.990687i \(-0.456525\pi\)
0.613260 + 0.789881i \(0.289858\pi\)
\(572\) 0 0
\(573\) −6.05192 29.1736i −0.252823 1.21874i
\(574\) 0 0
\(575\) −1.04844 −0.0437230
\(576\) 0 0
\(577\) 43.3455 1.80450 0.902248 0.431217i \(-0.141916\pi\)
0.902248 + 0.431217i \(0.141916\pi\)
\(578\) 0 0
\(579\) 23.7223 21.1502i 0.985863 0.878974i
\(580\) 0 0
\(581\) −31.7993 + 8.52060i −1.31926 + 0.353494i
\(582\) 0 0
\(583\) −6.92456 + 3.99790i −0.286786 + 0.165576i
\(584\) 0 0
\(585\) −1.93670 + 16.8389i −0.0800727 + 0.696201i
\(586\) 0 0
\(587\) 6.81553 25.4359i 0.281307 1.04985i −0.670189 0.742191i \(-0.733787\pi\)
0.951496 0.307662i \(-0.0995465\pi\)
\(588\) 0 0
\(589\) −2.40180 8.96364i −0.0989645 0.369341i
\(590\) 0 0
\(591\) 9.69660 + 19.2632i 0.398865 + 0.792382i
\(592\) 0 0
\(593\) 41.9274 1.72175 0.860876 0.508814i \(-0.169916\pi\)
0.860876 + 0.508814i \(0.169916\pi\)
\(594\) 0 0
\(595\) −10.5430 + 10.5430i −0.432222 + 0.432222i
\(596\) 0 0
\(597\) 5.44797 16.4920i 0.222971 0.674972i
\(598\) 0 0
\(599\) 21.1742 + 12.2249i 0.865154 + 0.499497i 0.865735 0.500503i \(-0.166852\pi\)
−0.000580933 1.00000i \(0.500185\pi\)
\(600\) 0 0
\(601\) 24.7521 14.2906i 1.00966 0.582928i 0.0985682 0.995130i \(-0.468574\pi\)
0.911092 + 0.412203i \(0.135240\pi\)
\(602\) 0 0
\(603\) 11.2136 28.3787i 0.456652 1.15567i
\(604\) 0 0
\(605\) 19.2669 + 5.16255i 0.783310 + 0.209887i
\(606\) 0 0
\(607\) 9.32245 16.1470i 0.378387 0.655385i −0.612441 0.790516i \(-0.709812\pi\)
0.990828 + 0.135131i \(0.0431456\pi\)
\(608\) 0 0
\(609\) −49.1315 2.81612i −1.99091 0.114115i
\(610\) 0 0
\(611\) 22.1946 22.1946i 0.897896 0.897896i
\(612\) 0 0
\(613\) −13.3177 13.3177i −0.537896 0.537896i 0.385014 0.922911i \(-0.374196\pi\)
−0.922911 + 0.385014i \(0.874196\pi\)
\(614\) 0 0
\(615\) −7.01335 4.60349i −0.282806 0.185631i
\(616\) 0 0
\(617\) −15.1035 8.72003i −0.608045 0.351055i 0.164155 0.986435i \(-0.447510\pi\)
−0.772200 + 0.635379i \(0.780844\pi\)
\(618\) 0 0
\(619\) −5.84959 + 21.8310i −0.235115 + 0.877461i 0.742982 + 0.669311i \(0.233411\pi\)
−0.978097 + 0.208150i \(0.933256\pi\)
\(620\) 0 0
\(621\) 0.218963 + 2.42544i 0.00878667 + 0.0973297i
\(622\) 0 0
\(623\) −23.4506 40.6177i −0.939530 1.62731i
\(624\) 0 0
\(625\) −4.40527 + 7.63015i −0.176211 + 0.305206i
\(626\) 0 0
\(627\) −2.46143 11.8655i −0.0983001 0.473861i
\(628\) 0 0
\(629\) 1.55946 + 1.55946i 0.0621797 + 0.0621797i
\(630\) 0 0
\(631\) 19.8510i 0.790254i 0.918627 + 0.395127i \(0.129299\pi\)
−0.918627 + 0.395127i \(0.870701\pi\)
\(632\) 0 0
\(633\) −1.97096 + 34.3865i −0.0783387 + 1.36674i
\(634\) 0 0
\(635\) −2.70512 + 0.724836i −0.107350 + 0.0287642i
\(636\) 0 0
\(637\) −34.6254 9.27785i −1.37191 0.367602i
\(638\) 0 0
\(639\) −14.7942 + 19.9488i −0.585249 + 0.789161i
\(640\) 0 0
\(641\) 20.5842 + 35.6529i 0.813026 + 1.40820i 0.910736 + 0.412988i \(0.135515\pi\)
−0.0977099 + 0.995215i \(0.531152\pi\)
\(642\) 0 0
\(643\) −6.73128 25.1215i −0.265456 0.990694i −0.961971 0.273152i \(-0.911934\pi\)
0.696515 0.717542i \(-0.254733\pi\)
\(644\) 0 0
\(645\) −9.93726 + 30.0818i −0.391279 + 1.18447i
\(646\) 0 0
\(647\) 40.3426i 1.58603i −0.609201 0.793016i \(-0.708510\pi\)
0.609201 0.793016i \(-0.291490\pi\)
\(648\) 0 0
\(649\) 7.35741i 0.288803i
\(650\) 0 0
\(651\) 14.4762 43.8220i 0.567367 1.71752i
\(652\) 0 0
\(653\) 1.68547 + 6.29024i 0.0659574 + 0.246156i 0.991031 0.133631i \(-0.0426638\pi\)
−0.925074 + 0.379787i \(0.875997\pi\)
\(654\) 0 0
\(655\) 6.33671 + 10.9755i 0.247596 + 0.428849i
\(656\) 0 0
\(657\) −14.5937 + 19.6784i −0.569353 + 0.767726i
\(658\) 0 0
\(659\) −0.0887093 0.0237696i −0.00345562 0.000925932i 0.257091 0.966387i \(-0.417236\pi\)
−0.260546 + 0.965461i \(0.583903\pi\)
\(660\) 0 0
\(661\) 27.0157 7.23883i 1.05079 0.281558i 0.308211 0.951318i \(-0.400270\pi\)
0.742578 + 0.669760i \(0.233603\pi\)
\(662\) 0 0
\(663\) −0.721435 + 12.5865i −0.0280182 + 0.488821i
\(664\) 0 0
\(665\) 10.1575i 0.393892i
\(666\) 0 0
\(667\) 2.24790 + 2.24790i 0.0870392 + 0.0870392i
\(668\) 0 0
\(669\) 4.90140 + 23.6274i 0.189499 + 0.913490i
\(670\) 0 0
\(671\) −18.6988 + 32.3873i −0.721859 + 1.25030i
\(672\) 0 0
\(673\) 2.48158 + 4.29822i 0.0956578 + 0.165684i 0.909883 0.414865i \(-0.136171\pi\)
−0.814225 + 0.580549i \(0.802838\pi\)
\(674\) 0 0
\(675\) −10.5484 4.88333i −0.406009 0.187959i
\(676\) 0 0
\(677\) 1.77876 6.63841i 0.0683632 0.255135i −0.923283 0.384119i \(-0.874505\pi\)
0.991647 + 0.128985i \(0.0411718\pi\)
\(678\) 0 0
\(679\) 41.1923 + 23.7824i 1.58081 + 0.912683i
\(680\) 0 0
\(681\) 10.9745 + 7.20357i 0.420545 + 0.276041i
\(682\) 0 0
\(683\) −20.7192 20.7192i −0.792797 0.792797i 0.189151 0.981948i \(-0.439426\pi\)
−0.981948 + 0.189151i \(0.939426\pi\)
\(684\) 0 0
\(685\) −11.2214 + 11.2214i −0.428747 + 0.428747i
\(686\) 0 0
\(687\) −33.0540 1.89459i −1.26109 0.0722831i
\(688\) 0 0
\(689\) 2.83351 4.90779i 0.107948 0.186972i
\(690\) 0 0
\(691\) 5.31450 + 1.42402i 0.202173 + 0.0541721i 0.358484 0.933536i \(-0.383294\pi\)
−0.156311 + 0.987708i \(0.549960\pi\)
\(692\) 0 0
\(693\) 22.1474 56.0494i 0.841310 2.12914i
\(694\) 0 0
\(695\) −20.8171 + 12.0188i −0.789638 + 0.455898i
\(696\) 0 0
\(697\) −5.40388 3.11993i −0.204687 0.118176i
\(698\) 0 0
\(699\) −5.84834 + 17.7040i −0.221205 + 0.669626i
\(700\) 0 0
\(701\) −1.06232 + 1.06232i −0.0401233 + 0.0401233i −0.726884 0.686760i \(-0.759032\pi\)
0.686760 + 0.726884i \(0.259032\pi\)
\(702\) 0 0
\(703\) 1.50244 0.0566656
\(704\) 0 0
\(705\) −11.9537 23.7471i −0.450202 0.894368i
\(706\) 0 0
\(707\) 3.25705 + 12.1555i 0.122494 + 0.457153i
\(708\) 0 0
\(709\) −9.50159 + 35.4604i −0.356840 + 1.33174i 0.521314 + 0.853365i \(0.325442\pi\)
−0.878153 + 0.478379i \(0.841224\pi\)
\(710\) 0 0
\(711\) 2.48904 21.6412i 0.0933463 0.811609i
\(712\) 0 0
\(713\) −2.58187 + 1.49064i −0.0966916 + 0.0558249i
\(714\) 0 0
\(715\) −26.1729 + 7.01301i −0.978812 + 0.262272i
\(716\) 0 0
\(717\) 28.8116 25.6878i 1.07599 0.959328i
\(718\) 0 0
\(719\) 7.37513 0.275046 0.137523 0.990499i \(-0.456086\pi\)
0.137523 + 0.990499i \(0.456086\pi\)
\(720\) 0 0
\(721\) −6.03749 −0.224848
\(722\) 0 0
\(723\) 9.65981 + 46.5656i 0.359252 + 1.73179i
\(724\) 0 0
\(725\) −14.6567 + 3.92726i −0.544337 + 0.145855i
\(726\) 0 0
\(727\) −5.80127 + 3.34936i −0.215157 + 0.124221i −0.603706 0.797207i \(-0.706310\pi\)
0.388549 + 0.921428i \(0.372977\pi\)
\(728\) 0 0
\(729\) −9.09400 + 25.4224i −0.336815 + 0.941571i
\(730\) 0 0
\(731\) −6.09879 + 22.7610i −0.225572 + 0.841846i
\(732\) 0 0
\(733\) −9.28281 34.6439i −0.342868 1.27960i −0.895083 0.445900i \(-0.852884\pi\)
0.552214 0.833702i \(-0.313783\pi\)
\(734\) 0 0
\(735\) −16.6613 + 25.3832i −0.614560 + 0.936272i
\(736\) 0 0
\(737\) 48.7797 1.79682
\(738\) 0 0
\(739\) −4.01107 + 4.01107i −0.147549 + 0.147549i −0.777022 0.629473i \(-0.783271\pi\)
0.629473 + 0.777022i \(0.283271\pi\)
\(740\) 0 0
\(741\) 5.71564 + 6.41070i 0.209969 + 0.235503i
\(742\) 0 0
\(743\) −19.1551 11.0592i −0.702734 0.405724i 0.105631 0.994405i \(-0.466314\pi\)
−0.808365 + 0.588682i \(0.799647\pi\)
\(744\) 0 0
\(745\) 2.47761 1.43045i 0.0907726 0.0524076i
\(746\) 0 0
\(747\) 14.6579 + 18.4678i 0.536305 + 0.675703i
\(748\) 0 0
\(749\) 33.5083 + 8.97853i 1.22437 + 0.328068i
\(750\) 0 0
\(751\) 6.05672 10.4905i 0.221013 0.382805i −0.734103 0.679038i \(-0.762397\pi\)
0.955116 + 0.296233i \(0.0957304\pi\)
\(752\) 0 0
\(753\) −12.5691 24.9697i −0.458044 0.909947i
\(754\) 0 0
\(755\) 25.1178 25.1178i 0.914131 0.914131i
\(756\) 0 0
\(757\) −19.9365 19.9365i −0.724604 0.724604i 0.244935 0.969539i \(-0.421233\pi\)
−0.969539 + 0.244935i \(0.921233\pi\)
\(758\) 0 0
\(759\) −3.47739 + 1.75043i −0.126221 + 0.0635366i
\(760\) 0 0
\(761\) −37.1681 21.4590i −1.34734 0.777889i −0.359471 0.933156i \(-0.617043\pi\)
−0.987873 + 0.155267i \(0.950376\pi\)
\(762\) 0 0
\(763\) 3.14690 11.7444i 0.113925 0.425176i
\(764\) 0 0
\(765\) 9.93130 + 3.92426i 0.359067 + 0.141882i
\(766\) 0 0
\(767\) −2.60728 4.51595i −0.0941435 0.163061i
\(768\) 0 0
\(769\) −13.7618 + 23.8361i −0.496263 + 0.859553i −0.999991 0.00430961i \(-0.998628\pi\)
0.503728 + 0.863863i \(0.331962\pi\)
\(770\) 0 0
\(771\) −2.40564 + 2.14482i −0.0866371 + 0.0772438i
\(772\) 0 0
\(773\) −11.4688 11.4688i −0.412504 0.412504i 0.470106 0.882610i \(-0.344216\pi\)
−0.882610 + 0.470106i \(0.844216\pi\)
\(774\) 0 0
\(775\) 14.2300i 0.511155i
\(776\) 0 0
\(777\) 6.24658 + 4.10019i 0.224095 + 0.147094i
\(778\) 0 0
\(779\) −4.10608 + 1.10022i −0.147115 + 0.0394195i
\(780\) 0 0
\(781\) −38.3500 10.2759i −1.37227 0.367699i
\(782\) 0 0
\(783\) 12.1462 + 33.0864i 0.434071 + 1.18241i
\(784\) 0 0
\(785\) −8.81622 15.2701i −0.314664 0.545015i
\(786\) 0 0
\(787\) −11.4753 42.8263i −0.409049 1.52659i −0.796463 0.604687i \(-0.793298\pi\)
0.387414 0.921906i \(-0.373368\pi\)
\(788\) 0 0
\(789\) −0.0812387 + 0.0168526i −0.00289217 + 0.000599968i
\(790\) 0 0
\(791\) 34.5766i 1.22940i
\(792\) 0 0
\(793\) 26.5056i 0.941241i
\(794\) 0 0
\(795\) −3.19437 3.58282i −0.113292 0.127070i
\(796\) 0 0
\(797\) 7.68647 + 28.6863i