Properties

Label 576.2.bb.e.49.4
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 49.4
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +O(q^{10})\) \(q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +(0.490535 - 1.83070i) q^{11} +(-1.35786 - 5.06759i) q^{13} +(0.0182197 + 0.00881653i) q^{15} -1.54238 q^{17} +(-4.06823 + 4.06823i) q^{19} +(2.07744 + 0.397131i) q^{21} +(-5.20660 - 3.00603i) q^{23} +(-4.33001 + 2.49993i) q^{25} +(2.78937 - 4.38400i) q^{27} +(-2.98082 - 0.798708i) q^{29} +(-2.92831 + 5.07198i) q^{31} +(-2.71580 + 1.84411i) q^{33} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-3.95811 + 8.17961i) q^{39} +(3.20829 + 1.85231i) q^{41} +(-1.29691 + 4.84015i) q^{43} +(-0.0138982 - 0.0321856i) q^{45} +(1.31218 + 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(2.02162 + 1.74639i) q^{51} +(-8.88508 - 8.88508i) q^{53} +0.0221483i q^{55} +(9.93862 - 0.725952i) q^{57} +(8.78724 - 2.35453i) q^{59} +(-12.1194 - 3.24737i) q^{61} +(-2.27326 - 2.87274i) q^{63} +(0.0306545 + 0.0530952i) q^{65} +(-3.18324 - 11.8800i) q^{67} +(3.42072 + 9.83532i) q^{69} -14.2363i q^{71} -4.32091i q^{73} +(8.50599 + 1.62604i) q^{75} +(0.599006 + 2.23552i) q^{77} +(0.261880 + 0.453589i) q^{79} +(-8.61992 + 2.58785i) q^{81} +(10.8824 + 2.91592i) q^{83} +(0.0174101 - 0.00466503i) q^{85} +(3.00264 + 4.42196i) q^{87} -10.7103i q^{89} +(4.53005 + 4.53005i) q^{91} +(9.58101 - 3.33227i) q^{93} +(0.0336169 - 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +(5.64765 + 0.657918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

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
\(3\) −1.31071 1.13227i −0.756740 0.653716i
\(4\) 0 0
\(5\) −0.0112878 + 0.00302457i −0.00504807 + 0.00135263i −0.261342 0.965246i \(-0.584165\pi\)
0.256294 + 0.966599i \(0.417498\pi\)
\(6\) 0 0
\(7\) −1.05753 + 0.610563i −0.399708 + 0.230771i −0.686358 0.727264i \(-0.740792\pi\)
0.286650 + 0.958035i \(0.407458\pi\)
\(8\) 0 0
\(9\) 0.435936 + 2.96816i 0.145312 + 0.989386i
\(10\) 0 0
\(11\) 0.490535 1.83070i 0.147902 0.551977i −0.851707 0.524018i \(-0.824432\pi\)
0.999609 0.0279594i \(-0.00890090\pi\)
\(12\) 0 0
\(13\) −1.35786 5.06759i −0.376602 1.40550i −0.850991 0.525181i \(-0.823998\pi\)
0.474389 0.880315i \(-0.342669\pi\)
\(14\) 0 0
\(15\) 0.0182197 + 0.00881653i 0.00470432 + 0.00227642i
\(16\) 0 0
\(17\) −1.54238 −0.374082 −0.187041 0.982352i \(-0.559890\pi\)
−0.187041 + 0.982352i \(0.559890\pi\)
\(18\) 0 0
\(19\) −4.06823 + 4.06823i −0.933317 + 0.933317i −0.997912 0.0645950i \(-0.979424\pi\)
0.0645950 + 0.997912i \(0.479424\pi\)
\(20\) 0 0
\(21\) 2.07744 + 0.397131i 0.453334 + 0.0866611i
\(22\) 0 0
\(23\) −5.20660 3.00603i −1.08565 0.626801i −0.153236 0.988190i \(-0.548970\pi\)
−0.932415 + 0.361388i \(0.882303\pi\)
\(24\) 0 0
\(25\) −4.33001 + 2.49993i −0.866002 + 0.499986i
\(26\) 0 0
\(27\) 2.78937 4.38400i 0.536814 0.843701i
\(28\) 0 0
\(29\) −2.98082 0.798708i −0.553524 0.148316i −0.0287946 0.999585i \(-0.509167\pi\)
−0.524730 + 0.851269i \(0.675834\pi\)
\(30\) 0 0
\(31\) −2.92831 + 5.07198i −0.525939 + 0.910954i 0.473604 + 0.880738i \(0.342953\pi\)
−0.999543 + 0.0302159i \(0.990381\pi\)
\(32\) 0 0
\(33\) −2.71580 + 1.84411i −0.472760 + 0.321018i
\(34\) 0 0
\(35\) 0.0100905 0.0100905i 0.00170561 0.00170561i
\(36\) 0 0
\(37\) 0.923082 + 0.923082i 0.151754 + 0.151754i 0.778901 0.627147i \(-0.215777\pi\)
−0.627147 + 0.778901i \(0.715777\pi\)
\(38\) 0 0
\(39\) −3.95811 + 8.17961i −0.633805 + 1.30979i
\(40\) 0 0
\(41\) 3.20829 + 1.85231i 0.501051 + 0.289282i 0.729147 0.684357i \(-0.239917\pi\)
−0.228096 + 0.973639i \(0.573250\pi\)
\(42\) 0 0
\(43\) −1.29691 + 4.84015i −0.197777 + 0.738115i 0.793753 + 0.608240i \(0.208124\pi\)
−0.991530 + 0.129875i \(0.958542\pi\)
\(44\) 0 0
\(45\) −0.0138982 0.0321856i −0.00207182 0.00479794i
\(46\) 0 0
\(47\) 1.31218 + 2.27277i 0.191402 + 0.331517i 0.945715 0.324997i \(-0.105363\pi\)
−0.754313 + 0.656515i \(0.772030\pi\)
\(48\) 0 0
\(49\) −2.75442 + 4.77080i −0.393489 + 0.681543i
\(50\) 0 0
\(51\) 2.02162 + 1.74639i 0.283083 + 0.244543i
\(52\) 0 0
\(53\) −8.88508 8.88508i −1.22046 1.22046i −0.967469 0.252991i \(-0.918586\pi\)
−0.252991 0.967469i \(-0.581414\pi\)
\(54\) 0 0
\(55\) 0.0221483i 0.00298648i
\(56\) 0 0
\(57\) 9.93862 0.725952i 1.31640 0.0961547i
\(58\) 0 0
\(59\) 8.78724 2.35453i 1.14400 0.306534i 0.363443 0.931617i \(-0.381601\pi\)
0.780559 + 0.625082i \(0.214935\pi\)
\(60\) 0 0
\(61\) −12.1194 3.24737i −1.55172 0.415783i −0.621692 0.783262i \(-0.713555\pi\)
−0.930032 + 0.367478i \(0.880221\pi\)
\(62\) 0 0
\(63\) −2.27326 2.87274i −0.286404 0.361931i
\(64\) 0 0
\(65\) 0.0306545 + 0.0530952i 0.00380223 + 0.00658565i
\(66\) 0 0
\(67\) −3.18324 11.8800i −0.388895 1.45137i −0.831935 0.554873i \(-0.812767\pi\)
0.443041 0.896501i \(-0.353900\pi\)
\(68\) 0 0
\(69\) 3.42072 + 9.83532i 0.411807 + 1.18403i
\(70\) 0 0
\(71\) 14.2363i 1.68954i −0.535129 0.844771i \(-0.679737\pi\)
0.535129 0.844771i \(-0.320263\pi\)
\(72\) 0 0
\(73\) 4.32091i 0.505724i −0.967502 0.252862i \(-0.918628\pi\)
0.967502 0.252862i \(-0.0813718\pi\)
\(74\) 0 0
\(75\) 8.50599 + 1.62604i 0.982187 + 0.187759i
\(76\) 0 0
\(77\) 0.599006 + 2.23552i 0.0682630 + 0.254761i
\(78\) 0 0
\(79\) 0.261880 + 0.453589i 0.0294638 + 0.0510328i 0.880381 0.474267i \(-0.157287\pi\)
−0.850918 + 0.525299i \(0.823953\pi\)
\(80\) 0 0
\(81\) −8.61992 + 2.58785i −0.957769 + 0.287539i
\(82\) 0 0
\(83\) 10.8824 + 2.91592i 1.19450 + 0.320064i 0.800661 0.599117i \(-0.204482\pi\)
0.393834 + 0.919181i \(0.371148\pi\)
\(84\) 0 0
\(85\) 0.0174101 0.00466503i 0.00188839 0.000505994i
\(86\) 0 0
\(87\) 3.00264 + 4.42196i 0.321917 + 0.474084i
\(88\) 0 0
\(89\) 10.7103i 1.13529i −0.823274 0.567644i \(-0.807855\pi\)
0.823274 0.567644i \(-0.192145\pi\)
\(90\) 0 0
\(91\) 4.53005 + 4.53005i 0.474879 + 0.474879i
\(92\) 0 0
\(93\) 9.58101 3.33227i 0.993504 0.345541i
\(94\) 0 0
\(95\) 0.0336169 0.0582262i 0.00344902 0.00597388i
\(96\) 0 0
\(97\) 8.78820 + 15.2216i 0.892306 + 1.54552i 0.837104 + 0.547044i \(0.184247\pi\)
0.0552025 + 0.998475i \(0.482420\pi\)
\(98\) 0 0
\(99\) 5.64765 + 0.657918i 0.567611 + 0.0661232i
\(100\) 0 0
\(101\) −1.80361 + 6.73117i −0.179466 + 0.669776i 0.816282 + 0.577654i \(0.196032\pi\)
−0.995748 + 0.0921222i \(0.970635\pi\)
\(102\) 0 0
\(103\) −2.20609 1.27369i −0.217373 0.125500i 0.387360 0.921928i \(-0.373387\pi\)
−0.604733 + 0.796428i \(0.706720\pi\)
\(104\) 0 0
\(105\) −0.0246509 + 0.00180059i −0.00240568 + 0.000175720i
\(106\) 0 0
\(107\) −3.52175 3.52175i −0.340460 0.340460i 0.516080 0.856540i \(-0.327391\pi\)
−0.856540 + 0.516080i \(0.827391\pi\)
\(108\) 0 0
\(109\) 3.14334 3.14334i 0.301077 0.301077i −0.540358 0.841435i \(-0.681711\pi\)
0.841435 + 0.540358i \(0.181711\pi\)
\(110\) 0 0
\(111\) −0.164719 2.25507i −0.0156344 0.214042i
\(112\) 0 0
\(113\) 7.90904 13.6989i 0.744020 1.28868i −0.206631 0.978419i \(-0.566250\pi\)
0.950651 0.310262i \(-0.100417\pi\)
\(114\) 0 0
\(115\) 0.0678632 + 0.0181839i 0.00632828 + 0.00169566i
\(116\) 0 0
\(117\) 14.4495 6.23947i 1.33585 0.576839i
\(118\) 0 0
\(119\) 1.63111 0.941721i 0.149523 0.0863274i
\(120\) 0 0
\(121\) 6.41543 + 3.70395i 0.583221 + 0.336723i
\(122\) 0 0
\(123\) −2.10784 6.06049i −0.190057 0.546456i
\(124\) 0 0
\(125\) 0.0826316 0.0826316i 0.00739079 0.00739079i
\(126\) 0 0
\(127\) 5.72603 0.508103 0.254052 0.967191i \(-0.418237\pi\)
0.254052 + 0.967191i \(0.418237\pi\)
\(128\) 0 0
\(129\) 7.18023 4.87559i 0.632184 0.429271i
\(130\) 0 0
\(131\) 1.75835 + 6.56224i 0.153628 + 0.573346i 0.999219 + 0.0395151i \(0.0125813\pi\)
−0.845591 + 0.533831i \(0.820752\pi\)
\(132\) 0 0
\(133\) 1.81835 6.78618i 0.157671 0.588436i
\(134\) 0 0
\(135\) −0.0182262 + 0.0579225i −0.00156866 + 0.00498517i
\(136\) 0 0
\(137\) 3.64923 2.10688i 0.311775 0.180003i −0.335946 0.941881i \(-0.609056\pi\)
0.647720 + 0.761878i \(0.275722\pi\)
\(138\) 0 0
\(139\) −15.6519 + 4.19392i −1.32758 + 0.355724i −0.851812 0.523847i \(-0.824496\pi\)
−0.475767 + 0.879571i \(0.657830\pi\)
\(140\) 0 0
\(141\) 0.853489 4.46469i 0.0718768 0.375995i
\(142\) 0 0
\(143\) −9.94332 −0.831502
\(144\) 0 0
\(145\) 0.0360627 0.00299485
\(146\) 0 0
\(147\) 9.01209 3.13440i 0.743305 0.258521i
\(148\) 0 0
\(149\) −3.76477 + 1.00877i −0.308422 + 0.0826415i −0.409710 0.912216i \(-0.634370\pi\)
0.101288 + 0.994857i \(0.467704\pi\)
\(150\) 0 0
\(151\) 13.0073 7.50979i 1.05852 0.611138i 0.133499 0.991049i \(-0.457379\pi\)
0.925023 + 0.379911i \(0.124045\pi\)
\(152\) 0 0
\(153\) −0.672378 4.57803i −0.0543586 0.370112i
\(154\) 0 0
\(155\) 0.0177137 0.0661085i 0.00142280 0.00530996i
\(156\) 0 0
\(157\) 2.53825 + 9.47288i 0.202574 + 0.756018i 0.990175 + 0.139832i \(0.0446564\pi\)
−0.787601 + 0.616186i \(0.788677\pi\)
\(158\) 0 0
\(159\) 1.58549 + 21.7061i 0.125738 + 1.72140i
\(160\) 0 0
\(161\) 7.34150 0.578591
\(162\) 0 0
\(163\) −5.22606 + 5.22606i −0.409336 + 0.409336i −0.881507 0.472171i \(-0.843471\pi\)
0.472171 + 0.881507i \(0.343471\pi\)
\(164\) 0 0
\(165\) 0.0250779 0.0290301i 0.00195231 0.00225999i
\(166\) 0 0
\(167\) −6.31476 3.64583i −0.488651 0.282123i 0.235364 0.971907i \(-0.424372\pi\)
−0.724015 + 0.689785i \(0.757705\pi\)
\(168\) 0 0
\(169\) −12.5783 + 7.26211i −0.967565 + 0.558624i
\(170\) 0 0
\(171\) −13.8486 10.3017i −1.05903 0.787788i
\(172\) 0 0
\(173\) 22.9394 + 6.14659i 1.74405 + 0.467317i 0.983340 0.181775i \(-0.0581842\pi\)
0.760710 + 0.649092i \(0.224851\pi\)
\(174\) 0 0
\(175\) 3.05273 5.28749i 0.230765 0.399697i
\(176\) 0 0
\(177\) −14.1835 6.86340i −1.06610 0.515885i
\(178\) 0 0
\(179\) −11.4489 + 11.4489i −0.855732 + 0.855732i −0.990832 0.135100i \(-0.956864\pi\)
0.135100 + 0.990832i \(0.456864\pi\)
\(180\) 0 0
\(181\) −3.01327 3.01327i −0.223974 0.223974i 0.586195 0.810170i \(-0.300625\pi\)
−0.810170 + 0.586195i \(0.800625\pi\)
\(182\) 0 0
\(183\) 12.2081 + 17.9787i 0.902448 + 1.32903i
\(184\) 0 0
\(185\) −0.0132115 0.00762768i −0.000971331 0.000560798i
\(186\) 0 0
\(187\) −0.756592 + 2.82364i −0.0553275 + 0.206485i
\(188\) 0 0
\(189\) −0.273120 + 6.33928i −0.0198666 + 0.461115i
\(190\) 0 0
\(191\) 2.25702 + 3.90928i 0.163313 + 0.282866i 0.936055 0.351854i \(-0.114449\pi\)
−0.772742 + 0.634720i \(0.781115\pi\)
\(192\) 0 0
\(193\) −1.75793 + 3.04482i −0.126539 + 0.219171i −0.922333 0.386395i \(-0.873720\pi\)
0.795795 + 0.605566i \(0.207053\pi\)
\(194\) 0 0
\(195\) 0.0199387 0.104302i 0.00142784 0.00746920i
\(196\) 0 0
\(197\) −4.81922 4.81922i −0.343355 0.343355i 0.514272 0.857627i \(-0.328062\pi\)
−0.857627 + 0.514272i \(0.828062\pi\)
\(198\) 0 0
\(199\) 4.66322i 0.330567i −0.986246 0.165284i \(-0.947146\pi\)
0.986246 0.165284i \(-0.0528539\pi\)
\(200\) 0 0
\(201\) −9.27905 + 19.1756i −0.654494 + 1.35254i
\(202\) 0 0
\(203\) 3.63996 0.975324i 0.255475 0.0684543i
\(204\) 0 0
\(205\) −0.0418171 0.0112049i −0.00292063 0.000782581i
\(206\) 0 0
\(207\) 6.65264 16.7645i 0.462390 1.16521i
\(208\) 0 0
\(209\) 5.45211 + 9.44333i 0.377130 + 0.653209i
\(210\) 0 0
\(211\) −4.67442 17.4452i −0.321800 1.20097i −0.917490 0.397760i \(-0.869788\pi\)
0.595689 0.803215i \(-0.296879\pi\)
\(212\) 0 0
\(213\) −16.1193 + 18.6597i −1.10448 + 1.27854i
\(214\) 0 0
\(215\) 0.0585574i 0.00399358i
\(216\) 0 0
\(217\) 7.15167i 0.485487i
\(218\) 0 0
\(219\) −4.89243 + 5.66347i −0.330599 + 0.382702i
\(220\) 0 0
\(221\) 2.09433 + 7.81615i 0.140880 + 0.525771i
\(222\) 0 0
\(223\) −2.85769 4.94966i −0.191365 0.331454i 0.754338 0.656486i \(-0.227958\pi\)
−0.945703 + 0.325032i \(0.894625\pi\)
\(224\) 0 0
\(225\) −9.30780 11.7623i −0.620520 0.784156i
\(226\) 0 0
\(227\) −19.6766 5.27233i −1.30598 0.349937i −0.462272 0.886738i \(-0.652966\pi\)
−0.843709 + 0.536802i \(0.819632\pi\)
\(228\) 0 0
\(229\) 3.70525 0.992819i 0.244850 0.0656073i −0.134307 0.990940i \(-0.542881\pi\)
0.379157 + 0.925332i \(0.376214\pi\)
\(230\) 0 0
\(231\) 1.74608 3.60836i 0.114884 0.237413i
\(232\) 0 0
\(233\) 5.33043i 0.349208i 0.984639 + 0.174604i \(0.0558645\pi\)
−0.984639 + 0.174604i \(0.944136\pi\)
\(234\) 0 0
\(235\) −0.0216859 0.0216859i −0.00141463 0.00141463i
\(236\) 0 0
\(237\) 0.170336 0.891043i 0.0110645 0.0578795i
\(238\) 0 0
\(239\) 13.8380 23.9681i 0.895104 1.55037i 0.0614282 0.998112i \(-0.480434\pi\)
0.833676 0.552254i \(-0.186232\pi\)
\(240\) 0 0
\(241\) 0.847203 + 1.46740i 0.0545731 + 0.0945234i 0.892021 0.451993i \(-0.149287\pi\)
−0.837448 + 0.546517i \(0.815954\pi\)
\(242\) 0 0
\(243\) 14.2284 + 6.36814i 0.912751 + 0.408516i
\(244\) 0 0
\(245\) 0.0166619 0.0621830i 0.00106449 0.00397273i
\(246\) 0 0
\(247\) 26.1402 + 15.0921i 1.66326 + 0.960284i
\(248\) 0 0
\(249\) −10.9621 16.1437i −0.694692 1.02307i
\(250\) 0 0
\(251\) −0.987980 0.987980i −0.0623607 0.0623607i 0.675239 0.737599i \(-0.264041\pi\)
−0.737599 + 0.675239i \(0.764041\pi\)
\(252\) 0 0
\(253\) −8.05717 + 8.05717i −0.506550 + 0.506550i
\(254\) 0 0
\(255\) −0.0281018 0.0135984i −0.00175980 0.000851567i
\(256\) 0 0
\(257\) 11.8214 20.4753i 0.737401 1.27722i −0.216260 0.976336i \(-0.569386\pi\)
0.953662 0.300881i \(-0.0972806\pi\)
\(258\) 0 0
\(259\) −1.53978 0.412584i −0.0956776 0.0256367i
\(260\) 0 0
\(261\) 1.07125 9.19572i 0.0663085 0.569201i
\(262\) 0 0
\(263\) −22.2619 + 12.8529i −1.37273 + 0.792545i −0.991271 0.131841i \(-0.957911\pi\)
−0.381458 + 0.924386i \(0.624578\pi\)
\(264\) 0 0
\(265\) 0.127167 + 0.0734198i 0.00781180 + 0.00451015i
\(266\) 0 0
\(267\) −12.1269 + 14.0381i −0.742156 + 0.859119i
\(268\) 0 0
\(269\) −13.6891 + 13.6891i −0.834637 + 0.834637i −0.988147 0.153510i \(-0.950942\pi\)
0.153510 + 0.988147i \(0.450942\pi\)
\(270\) 0 0
\(271\) 7.11000 0.431902 0.215951 0.976404i \(-0.430715\pi\)
0.215951 + 0.976404i \(0.430715\pi\)
\(272\) 0 0
\(273\) −0.808361 11.0668i −0.0489242 0.669795i
\(274\) 0 0
\(275\) 2.45261 + 9.15326i 0.147898 + 0.551962i
\(276\) 0 0
\(277\) 5.81917 21.7174i 0.349640 1.30487i −0.537457 0.843291i \(-0.680615\pi\)
0.887097 0.461583i \(-0.152718\pi\)
\(278\) 0 0
\(279\) −16.3310 6.48062i −0.977710 0.387985i
\(280\) 0 0
\(281\) −19.7952 + 11.4288i −1.18088 + 0.681783i −0.956218 0.292654i \(-0.905462\pi\)
−0.224664 + 0.974436i \(0.572128\pi\)
\(282\) 0 0
\(283\) 5.96971 1.59958i 0.354862 0.0950851i −0.0769838 0.997032i \(-0.524529\pi\)
0.431846 + 0.901947i \(0.357862\pi\)
\(284\) 0 0
\(285\) −0.109990 + 0.0382544i −0.00651523 + 0.00226600i
\(286\) 0 0
\(287\) −4.52381 −0.267032
\(288\) 0 0
\(289\) −14.6211 −0.860063
\(290\) 0 0
\(291\) 5.71614 29.9017i 0.335086 1.75287i
\(292\) 0 0
\(293\) −3.76752 + 1.00950i −0.220101 + 0.0589758i −0.367184 0.930148i \(-0.619678\pi\)
0.147083 + 0.989124i \(0.453011\pi\)
\(294\) 0 0
\(295\) −0.0920675 + 0.0531552i −0.00536038 + 0.00309482i
\(296\) 0 0
\(297\) −6.65751 7.25700i −0.386308 0.421094i
\(298\) 0 0
\(299\) −8.16352 + 30.4667i −0.472109 + 1.76193i
\(300\) 0 0
\(301\) −1.58370 5.91043i −0.0912827 0.340672i
\(302\) 0 0
\(303\) 9.98550 6.78045i 0.573652 0.389527i
\(304\) 0 0
\(305\) 0.146623 0.00839562
\(306\) 0 0
\(307\) −10.8111 + 10.8111i −0.617023 + 0.617023i −0.944767 0.327743i \(-0.893712\pi\)
0.327743 + 0.944767i \(0.393712\pi\)
\(308\) 0 0
\(309\) 1.44940 + 4.16733i 0.0824532 + 0.237071i
\(310\) 0 0
\(311\) 19.5372 + 11.2798i 1.10785 + 0.639619i 0.938273 0.345897i \(-0.112425\pi\)
0.169581 + 0.985516i \(0.445759\pi\)
\(312\) 0 0
\(313\) 5.17232 2.98624i 0.292357 0.168792i −0.346647 0.937996i \(-0.612680\pi\)
0.639004 + 0.769203i \(0.279347\pi\)
\(314\) 0 0
\(315\) 0.0343490 + 0.0255514i 0.00193535 + 0.00143966i
\(316\) 0 0
\(317\) −17.9792 4.81751i −1.00981 0.270579i −0.284262 0.958747i \(-0.591748\pi\)
−0.725551 + 0.688168i \(0.758415\pi\)
\(318\) 0 0
\(319\) −2.92439 + 5.06520i −0.163735 + 0.283597i
\(320\) 0 0
\(321\) 0.628435 + 8.60356i 0.0350758 + 0.480204i
\(322\) 0 0
\(323\) 6.27476 6.27476i 0.349137 0.349137i
\(324\) 0 0
\(325\) 18.5482 + 18.5482i 1.02887 + 1.02887i
\(326\) 0 0
\(327\) −7.67912 + 0.560910i −0.424656 + 0.0310184i
\(328\) 0 0
\(329\) −2.77534 1.60234i −0.153009 0.0883400i
\(330\) 0 0
\(331\) −2.72957 + 10.1869i −0.150031 + 0.559923i 0.849449 + 0.527671i \(0.176935\pi\)
−0.999480 + 0.0322521i \(0.989732\pi\)
\(332\) 0 0
\(333\) −2.33745 + 3.14226i −0.128091 + 0.172195i
\(334\) 0 0
\(335\) 0.0718638 + 0.124472i 0.00392634 + 0.00680062i
\(336\) 0 0
\(337\) 12.1222 20.9962i 0.660336 1.14374i −0.320192 0.947353i \(-0.603747\pi\)
0.980527 0.196382i \(-0.0629194\pi\)
\(338\) 0 0
\(339\) −25.8773 + 9.00011i −1.40546 + 0.488819i
\(340\) 0 0
\(341\) 7.84884 + 7.84884i 0.425038 + 0.425038i
\(342\) 0 0
\(343\) 15.2749i 0.824767i
\(344\) 0 0
\(345\) −0.0683602 0.100673i −0.00368039 0.00542007i
\(346\) 0 0
\(347\) 18.5696 4.97570i 0.996867 0.267110i 0.276735 0.960946i \(-0.410748\pi\)
0.720132 + 0.693837i \(0.244081\pi\)
\(348\) 0 0
\(349\) 15.6423 + 4.19134i 0.837313 + 0.224357i 0.651901 0.758304i \(-0.273972\pi\)
0.185411 + 0.982661i \(0.440638\pi\)
\(350\) 0 0
\(351\) −26.0039 8.18252i −1.38798 0.436750i
\(352\) 0 0
\(353\) −7.69391 13.3262i −0.409505 0.709284i 0.585329 0.810796i \(-0.300965\pi\)
−0.994834 + 0.101512i \(0.967632\pi\)
\(354\) 0 0
\(355\) 0.0430587 + 0.160697i 0.00228532 + 0.00852893i
\(356\) 0 0
\(357\) −3.20420 0.612527i −0.169584 0.0324184i
\(358\) 0 0
\(359\) 2.97883i 0.157217i 0.996906 + 0.0786083i \(0.0250476\pi\)
−0.996906 + 0.0786083i \(0.974952\pi\)
\(360\) 0 0
\(361\) 14.1010i 0.742159i
\(362\) 0 0
\(363\) −4.21492 12.1188i −0.221226 0.636073i
\(364\) 0 0
\(365\) 0.0130689 + 0.0487737i 0.000684056 + 0.00255293i
\(366\) 0 0
\(367\) −12.5585 21.7519i −0.655547 1.13544i −0.981756 0.190143i \(-0.939105\pi\)
0.326210 0.945297i \(-0.394228\pi\)
\(368\) 0 0
\(369\) −4.09933 + 10.3302i −0.213403 + 0.537769i
\(370\) 0 0
\(371\) 14.8211 + 3.97131i 0.769474 + 0.206180i
\(372\) 0 0
\(373\) −28.8046 + 7.71816i −1.49144 + 0.399631i −0.910224 0.414116i \(-0.864091\pi\)
−0.581220 + 0.813747i \(0.697424\pi\)
\(374\) 0 0
\(375\) −0.201867 + 0.0147451i −0.0104244 + 0.000761435i
\(376\) 0 0
\(377\) 16.1901i 0.833832i
\(378\) 0 0
\(379\) −10.1985 10.1985i −0.523864 0.523864i 0.394872 0.918736i \(-0.370789\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(380\) 0 0
\(381\) −7.50518 6.48341i −0.384502 0.332155i
\(382\) 0 0
\(383\) −10.5750 + 18.3164i −0.540356 + 0.935924i 0.458528 + 0.888680i \(0.348377\pi\)
−0.998883 + 0.0472436i \(0.984956\pi\)
\(384\) 0 0
\(385\) −0.0135230 0.0234224i −0.000689194 0.00119372i
\(386\) 0 0
\(387\) −14.9317 1.73945i −0.759020 0.0884213i
\(388\) 0 0
\(389\) −8.13193 + 30.3488i −0.412305 + 1.53874i 0.377867 + 0.925860i \(0.376658\pi\)
−0.790173 + 0.612884i \(0.790009\pi\)
\(390\) 0 0
\(391\) 8.03056 + 4.63645i 0.406123 + 0.234475i
\(392\) 0 0
\(393\) 5.12553 10.5921i 0.258549 0.534303i
\(394\) 0 0
\(395\) −0.00432797 0.00432797i −0.000217764 0.000217764i
\(396\) 0 0
\(397\) −3.24113 + 3.24113i −0.162668 + 0.162668i −0.783747 0.621080i \(-0.786694\pi\)
0.621080 + 0.783747i \(0.286694\pi\)
\(398\) 0 0
\(399\) −10.0671 + 6.83587i −0.503986 + 0.342221i
\(400\) 0 0
\(401\) −10.7429 + 18.6073i −0.536476 + 0.929203i 0.462614 + 0.886560i \(0.346911\pi\)
−0.999090 + 0.0426439i \(0.986422\pi\)
\(402\) 0 0
\(403\) 29.6789 + 7.95244i 1.47841 + 0.396139i
\(404\) 0 0
\(405\) 0.0894731 0.0552828i 0.00444596 0.00274702i
\(406\) 0 0
\(407\) 2.14269 1.23708i 0.106209 0.0613200i
\(408\) 0 0
\(409\) 23.1426 + 13.3614i 1.14433 + 0.660678i 0.947499 0.319760i \(-0.103602\pi\)
0.196829 + 0.980438i \(0.436936\pi\)
\(410\) 0 0
\(411\) −7.16865 1.37039i −0.353604 0.0675963i
\(412\) 0 0
\(413\) −7.85515 + 7.85515i −0.386527 + 0.386527i
\(414\) 0 0
\(415\) −0.131658 −0.00646283
\(416\) 0 0
\(417\) 25.2638 + 12.2252i 1.23718 + 0.598669i
\(418\) 0 0
\(419\) −2.36864 8.83989i −0.115716 0.431857i 0.883624 0.468198i \(-0.155097\pi\)
−0.999339 + 0.0363407i \(0.988430\pi\)
\(420\) 0 0
\(421\) 7.75295 28.9344i 0.377856 1.41018i −0.471272 0.881988i \(-0.656205\pi\)
0.849127 0.528188i \(-0.177128\pi\)
\(422\) 0 0
\(423\) −6.17391 + 4.88555i −0.300186 + 0.237544i
\(424\) 0 0
\(425\) 6.67852 3.85585i 0.323956 0.187036i
\(426\) 0 0
\(427\) 14.7993 3.96545i 0.716187 0.191902i
\(428\) 0 0
\(429\) 13.0328 + 11.2585i 0.629231 + 0.543566i
\(430\) 0 0
\(431\) 7.05544 0.339849 0.169924 0.985457i \(-0.445648\pi\)
0.169924 + 0.985457i \(0.445648\pi\)
\(432\) 0 0
\(433\) 13.1552 0.632201 0.316100 0.948726i \(-0.397626\pi\)
0.316100 + 0.948726i \(0.397626\pi\)
\(434\) 0 0
\(435\) −0.0472679 0.0408327i −0.00226632 0.00195778i
\(436\) 0 0
\(437\) 33.4109 8.95243i 1.59826 0.428253i
\(438\) 0 0
\(439\) −12.8757 + 7.43381i −0.614525 + 0.354796i −0.774734 0.632287i \(-0.782116\pi\)
0.160209 + 0.987083i \(0.448783\pi\)
\(440\) 0 0
\(441\) −15.3612 6.09580i −0.731488 0.290276i
\(442\) 0 0
\(443\) −0.797625 + 2.97678i −0.0378963 + 0.141431i −0.982282 0.187409i \(-0.939991\pi\)
0.944386 + 0.328840i \(0.106658\pi\)
\(444\) 0 0
\(445\) 0.0323940 + 0.120896i 0.00153562 + 0.00573102i
\(446\) 0 0
\(447\) 6.07673 + 2.94053i 0.287419 + 0.139082i
\(448\) 0 0
\(449\) −21.8550 −1.03140 −0.515701 0.856769i \(-0.672468\pi\)
−0.515701 + 0.856769i \(0.672468\pi\)
\(450\) 0 0
\(451\) 4.96480 4.96480i 0.233783 0.233783i
\(452\) 0 0
\(453\) −25.5520 4.88462i −1.20054 0.229500i
\(454\) 0 0
\(455\) −0.0648360 0.0374331i −0.00303956 0.00175489i
\(456\) 0 0
\(457\) 2.32261 1.34096i 0.108647 0.0627275i −0.444692 0.895684i \(-0.646687\pi\)
0.553339 + 0.832956i \(0.313353\pi\)
\(458\) 0 0
\(459\) −4.30226 + 6.76179i −0.200812 + 0.315613i
\(460\) 0 0
\(461\) −10.2573 2.74844i −0.477732 0.128008i 0.0119146 0.999929i \(-0.496207\pi\)
−0.489646 + 0.871921i \(0.662874\pi\)
\(462\) 0 0
\(463\) −11.8249 + 20.4814i −0.549550 + 0.951849i 0.448755 + 0.893655i \(0.351868\pi\)
−0.998305 + 0.0581943i \(0.981466\pi\)
\(464\) 0 0
\(465\) −0.0980702 + 0.0665926i −0.00454790 + 0.00308816i
\(466\) 0 0
\(467\) −2.22540 + 2.22540i −0.102979 + 0.102979i −0.756719 0.653740i \(-0.773199\pi\)
0.653740 + 0.756719i \(0.273199\pi\)
\(468\) 0 0
\(469\) 10.6199 + 10.6199i 0.490380 + 0.490380i
\(470\) 0 0
\(471\) 7.39893 15.2902i 0.340925 0.704536i
\(472\) 0 0
\(473\) 8.22468 + 4.74852i 0.378171 + 0.218337i
\(474\) 0 0
\(475\) 7.44518 27.7858i 0.341608 1.27490i
\(476\) 0 0
\(477\) 22.4990 30.2456i 1.03016 1.38485i
\(478\) 0 0
\(479\) 6.23896 + 10.8062i 0.285066 + 0.493748i 0.972625 0.232380i \(-0.0746513\pi\)
−0.687559 + 0.726128i \(0.741318\pi\)
\(480\) 0 0
\(481\) 3.42439 5.93121i 0.156139 0.270440i
\(482\) 0 0
\(483\) −9.62259 8.31255i −0.437843 0.378234i
\(484\) 0 0
\(485\) −0.145238 0.145238i −0.00659494 0.00659494i
\(486\) 0 0
\(487\) 12.5314i 0.567853i −0.958846 0.283927i \(-0.908363\pi\)
0.958846 0.283927i \(-0.0916372\pi\)
\(488\) 0 0
\(489\) 12.7672 0.932559i 0.577351 0.0421718i
\(490\) 0 0
\(491\) −14.6898 + 3.93613i −0.662942 + 0.177635i −0.574574 0.818453i \(-0.694832\pi\)
−0.0883688 + 0.996088i \(0.528165\pi\)
\(492\) 0 0
\(493\) 4.59756 + 1.23191i 0.207064 + 0.0554825i
\(494\) 0 0
\(495\) −0.0657397 + 0.00965524i −0.00295478 + 0.000433971i
\(496\) 0 0
\(497\) 8.69218 + 15.0553i 0.389898 + 0.675322i
\(498\) 0 0
\(499\) 7.88570 + 29.4298i 0.353012 + 1.31746i 0.882967 + 0.469434i \(0.155542\pi\)
−0.529955 + 0.848026i \(0.677791\pi\)
\(500\) 0 0
\(501\) 4.14878 + 11.9286i 0.185354 + 0.532933i
\(502\) 0 0
\(503\) 1.90106i 0.0847639i 0.999101 + 0.0423820i \(0.0134946\pi\)
−0.999101 + 0.0423820i \(0.986505\pi\)
\(504\) 0 0
\(505\) 0.0814355i 0.00362383i
\(506\) 0 0
\(507\) 24.7093 + 4.72352i 1.09738 + 0.209779i
\(508\) 0 0
\(509\) −3.34659 12.4896i −0.148335 0.553593i −0.999584 0.0288320i \(-0.990821\pi\)
0.851249 0.524761i \(-0.175845\pi\)
\(510\) 0 0
\(511\) 2.63819 + 4.56947i 0.116706 + 0.202142i
\(512\) 0 0
\(513\) 6.48734 + 29.1829i 0.286423 + 1.28846i
\(514\) 0 0
\(515\) 0.0287544 + 0.00770471i 0.00126707 + 0.000339510i
\(516\) 0 0
\(517\) 4.80444 1.28734i 0.211299 0.0566174i
\(518\) 0 0
\(519\) −23.1074 34.0300i −1.01430 1.49375i
\(520\) 0 0
\(521\) 1.24885i 0.0547130i −0.999626 0.0273565i \(-0.991291\pi\)
0.999626 0.0273565i \(-0.00870893\pi\)
\(522\) 0 0
\(523\) −9.58031 9.58031i −0.418918 0.418918i 0.465913 0.884831i \(-0.345726\pi\)
−0.884831 + 0.465913i \(0.845726\pi\)
\(524\) 0 0
\(525\) −9.98811 + 3.47387i −0.435917 + 0.151612i
\(526\) 0 0
\(527\) 4.51656 7.82292i 0.196745 0.340772i
\(528\) 0 0
\(529\) 6.57248 + 11.3839i 0.285760 + 0.494951i
\(530\) 0 0
\(531\) 10.8193 + 25.0555i 0.469518 + 1.08732i
\(532\) 0 0
\(533\) 5.03034 18.7735i 0.217888 0.813169i
\(534\) 0 0
\(535\) 0.0504047 + 0.0291012i 0.00217918 + 0.00125815i
\(536\) 0 0
\(537\) 27.9695 2.04299i 1.20697 0.0881616i
\(538\) 0 0
\(539\) 7.38278 + 7.38278i 0.317999 + 0.317999i
\(540\) 0 0
\(541\) 13.0165 13.0165i 0.559622 0.559622i −0.369578 0.929200i \(-0.620498\pi\)
0.929200 + 0.369578i \(0.120498\pi\)
\(542\) 0 0
\(543\) 0.537699 + 7.36135i 0.0230749 + 0.315906i
\(544\) 0 0
\(545\) −0.0259743 + 0.0449887i −0.00111262 + 0.00192711i
\(546\) 0 0
\(547\) 9.76080 + 2.61540i 0.417341 + 0.111826i 0.461378 0.887204i \(-0.347355\pi\)
−0.0440366 + 0.999030i \(0.514022\pi\)
\(548\) 0 0
\(549\) 4.35545 37.3878i 0.185886 1.59567i
\(550\) 0 0
\(551\) 15.3760 8.87733i 0.655039 0.378187i
\(552\) 0 0
\(553\) −0.553890 0.319788i −0.0235538 0.0135988i
\(554\) 0 0
\(555\) 0.00867994 + 0.0249567i 0.000368443 + 0.00105935i
\(556\) 0 0
\(557\) 26.6259 26.6259i 1.12818 1.12818i 0.137702 0.990474i \(-0.456029\pi\)
0.990474 0.137702i \(-0.0439715\pi\)
\(558\) 0 0
\(559\) 26.2889 1.11190
\(560\) 0 0
\(561\) 4.18879 2.84431i 0.176851 0.120087i
\(562\) 0 0
\(563\) −5.67141 21.1660i −0.239021 0.892039i −0.976295 0.216445i \(-0.930554\pi\)
0.737274 0.675594i \(-0.236113\pi\)
\(564\) 0 0
\(565\) −0.0478429 + 0.178552i −0.00201276 + 0.00751174i
\(566\) 0 0
\(567\) 7.53575 7.99973i 0.316472 0.335957i
\(568\) 0 0
\(569\) −8.15901 + 4.71061i −0.342044 + 0.197479i −0.661175 0.750231i \(-0.729942\pi\)
0.319132 + 0.947710i \(0.396609\pi\)
\(570\) 0 0
\(571\) 28.4258 7.61666i 1.18958 0.318747i 0.390861 0.920450i \(-0.372177\pi\)
0.798720 + 0.601702i \(0.205511\pi\)
\(572\) 0 0
\(573\) 1.46805 7.67950i 0.0613285 0.320816i
\(574\) 0 0
\(575\) 30.0595 1.25357
\(576\) 0 0
\(577\) −42.9309 −1.78724 −0.893618 0.448828i \(-0.851842\pi\)
−0.893618 + 0.448828i \(0.851842\pi\)
\(578\) 0 0
\(579\) 5.75170 2.00044i 0.239033 0.0831355i
\(580\) 0 0
\(581\) −13.2888 + 3.56071i −0.551310 + 0.147723i
\(582\) 0 0
\(583\) −20.6244 + 11.9075i −0.854175 + 0.493158i
\(584\) 0 0
\(585\) −0.144232 + 0.114134i −0.00596324 + 0.00471884i
\(586\) 0 0
\(587\) 8.13523 30.3611i 0.335777 1.25314i −0.567247 0.823548i \(-0.691992\pi\)
0.903024 0.429589i \(-0.141342\pi\)
\(588\) 0 0
\(589\) −8.72095 32.5470i −0.359340 1.34108i
\(590\) 0 0
\(591\) 0.859962 + 11.7733i 0.0353741 + 0.484288i
\(592\) 0 0
\(593\) 0.434128 0.0178275 0.00891374 0.999960i \(-0.497163\pi\)
0.00891374 + 0.999960i \(0.497163\pi\)
\(594\) 0 0
\(595\) −0.0155634 + 0.0155634i −0.000638037 + 0.000638037i
\(596\) 0 0
\(597\) −5.28002 + 6.11215i −0.216097 + 0.250154i
\(598\) 0 0
\(599\) 3.46143 + 1.99846i 0.141430 + 0.0816547i 0.569045 0.822306i \(-0.307313\pi\)
−0.427615 + 0.903961i \(0.640646\pi\)
\(600\) 0 0
\(601\) 3.54563 2.04707i 0.144629 0.0835019i −0.425939 0.904752i \(-0.640056\pi\)
0.570569 + 0.821250i \(0.306723\pi\)
\(602\) 0 0
\(603\) 33.8741 14.6273i 1.37946 0.595669i
\(604\) 0 0
\(605\) −0.0836192 0.0224057i −0.00339961 0.000910922i
\(606\) 0 0
\(607\) −16.8996 + 29.2709i −0.685932 + 1.18807i 0.287211 + 0.957867i \(0.407272\pi\)
−0.973143 + 0.230202i \(0.926061\pi\)
\(608\) 0 0
\(609\) −5.87527 2.84304i −0.238078 0.115206i
\(610\) 0 0
\(611\) 9.73570 9.73570i 0.393864 0.393864i
\(612\) 0 0
\(613\) 1.73094 + 1.73094i 0.0699119 + 0.0699119i 0.741198 0.671286i \(-0.234258\pi\)
−0.671286 + 0.741198i \(0.734258\pi\)
\(614\) 0 0
\(615\) 0.0421233 + 0.0620346i 0.00169858 + 0.00250147i
\(616\) 0 0
\(617\) 14.9093 + 8.60788i 0.600225 + 0.346540i 0.769130 0.639092i \(-0.220690\pi\)
−0.168905 + 0.985632i \(0.554023\pi\)
\(618\) 0 0
\(619\) 1.70053 6.34645i 0.0683499 0.255085i −0.923293 0.384095i \(-0.874513\pi\)
0.991643 + 0.129010i \(0.0411800\pi\)
\(620\) 0 0
\(621\) −27.7016 + 14.4408i −1.11163 + 0.579490i
\(622\) 0 0
\(623\) 6.53931 + 11.3264i 0.261992 + 0.453783i
\(624\) 0 0
\(625\) 12.4990 21.6489i 0.499959 0.865954i
\(626\) 0 0
\(627\) 3.54624 18.5507i 0.141623 0.740846i
\(628\) 0 0
\(629\) −1.42374 1.42374i −0.0567684 0.0567684i
\(630\) 0 0
\(631\) 13.3295i 0.530639i 0.964161 + 0.265319i \(0.0854774\pi\)
−0.964161 + 0.265319i \(0.914523\pi\)
\(632\) 0 0
\(633\) −13.6258 + 28.1583i −0.541577 + 1.11919i
\(634\) 0 0
\(635\) −0.0646345 + 0.0173188i −0.00256494 + 0.000687274i
\(636\) 0 0
\(637\) 27.9166 + 7.48023i 1.10610 + 0.296377i
\(638\) 0 0
\(639\) 42.2557 6.20612i 1.67161 0.245510i
\(640\) 0 0
\(641\) 8.26044 + 14.3075i 0.326268 + 0.565113i 0.981768 0.190082i \(-0.0608755\pi\)
−0.655500 + 0.755195i \(0.727542\pi\)
\(642\) 0 0
\(643\) −6.43213 24.0050i −0.253659 0.946667i −0.968832 0.247719i \(-0.920319\pi\)
0.715173 0.698947i \(-0.246348\pi\)
\(644\) 0 0
\(645\) −0.0663027 + 0.0767519i −0.00261067 + 0.00302210i
\(646\) 0 0
\(647\) 26.9660i 1.06014i 0.847954 + 0.530071i \(0.177835\pi\)
−0.847954 + 0.530071i \(0.822165\pi\)
\(648\) 0 0
\(649\) 17.2418i 0.676800i
\(650\) 0 0
\(651\) −8.09761 + 9.37378i −0.317370 + 0.367387i
\(652\) 0 0
\(653\) −1.41419 5.27782i −0.0553414 0.206537i 0.932719 0.360604i \(-0.117429\pi\)
−0.988060 + 0.154067i \(0.950763\pi\)
\(654\) 0 0
\(655\) −0.0396959 0.0687553i −0.00155105 0.00268649i
\(656\) 0 0
\(657\) 12.8251 1.88364i 0.500356 0.0734876i
\(658\) 0 0
\(659\) −0.689165 0.184661i −0.0268460 0.00719337i 0.245371 0.969429i \(-0.421090\pi\)
−0.272217 + 0.962236i \(0.587757\pi\)
\(660\) 0 0
\(661\) −36.9228 + 9.89344i −1.43613 + 0.384810i −0.891177 0.453656i \(-0.850120\pi\)
−0.544954 + 0.838466i \(0.683453\pi\)
\(662\) 0 0
\(663\) 6.10491 12.6161i 0.237095 0.489968i
\(664\) 0 0
\(665\) 0.0821010i 0.00318374i
\(666\) 0 0
\(667\) 13.1190 + 13.1190i 0.507970 + 0.507970i
\(668\) 0 0
\(669\) −1.85874 + 9.72326i −0.0718630 + 0.375923i
\(670\) 0 0
\(671\) −11.8899 + 20.5940i −0.459006 + 0.795022i
\(672\) 0 0
\(673\) −6.39173 11.0708i −0.246383 0.426748i 0.716137 0.697960i \(-0.245909\pi\)
−0.962520 + 0.271212i \(0.912575\pi\)
\(674\) 0 0
\(675\) −1.11828 + 25.9560i −0.0430427 + 0.999046i
\(676\) 0 0
\(677\) 6.82184 25.4595i 0.262185 0.978487i −0.701766 0.712407i \(-0.747605\pi\)
0.963951 0.266079i \(-0.0857284\pi\)
\(678\) 0 0
\(679\) −18.5875 10.7315i −0.713323 0.411837i
\(680\) 0 0
\(681\) 19.8207 + 29.1897i 0.759529 + 1.11855i
\(682\) 0 0
\(683\) −9.42670 9.42670i −0.360703 0.360703i 0.503369 0.864072i \(-0.332094\pi\)
−0.864072 + 0.503369i \(0.832094\pi\)
\(684\) 0 0
\(685\) −0.0348195 + 0.0348195i −0.00133039 + 0.00133039i
\(686\) 0 0
\(687\) −5.98065 2.89404i −0.228176 0.110414i
\(688\) 0 0
\(689\) −32.9613 + 57.0906i −1.25572 + 2.17498i
\(690\) 0 0
\(691\) 15.1910 + 4.07041i 0.577891 + 0.154846i 0.535913 0.844273i \(-0.319967\pi\)
0.0419780 + 0.999119i \(0.486634\pi\)
\(692\) 0 0
\(693\) −6.37425 + 2.75248i −0.242138 + 0.104558i
\(694\) 0 0
\(695\) 0.163992 0.0946807i 0.00622056 0.00359144i
\(696\) 0 0
\(697\) −4.94841 2.85696i −0.187434 0.108215i
\(698\) 0 0
\(699\) 6.03547 6.98666i 0.228283 0.264260i
\(700\) 0 0
\(701\) 9.62303 9.62303i 0.363457 0.363457i −0.501627 0.865084i \(-0.667265\pi\)
0.865084 + 0.501627i \(0.167265\pi\)
\(702\) 0 0
\(703\) −7.51063 −0.283269
\(704\) 0 0
\(705\) 0.00386971 + 0.0529782i 0.000145742 + 0.00199527i
\(706\) 0 0
\(707\) −2.20244 8.21961i −0.0828312 0.309130i
\(708\) 0 0
\(709\) −10.8223 + 40.3893i −0.406439 + 1.51685i 0.394947 + 0.918704i \(0.370763\pi\)
−0.801386 + 0.598148i \(0.795904\pi\)
\(710\) 0 0
\(711\) −1.23216 + 0.975036i −0.0462097 + 0.0365667i
\(712\) 0 0
\(713\) 30.4931 17.6052i 1.14197 0.659319i
\(714\) 0 0
\(715\) 0.112239 0.0300742i 0.00419749 0.00112471i
\(716\) 0 0
\(717\) −45.2759 + 15.7470i −1.69086 + 0.588081i
\(718\) 0 0
\(719\) −48.7757 −1.81903 −0.909514 0.415674i \(-0.863546\pi\)
−0.909514 + 0.415674i \(0.863546\pi\)
\(720\) 0 0
\(721\) 3.11067 0.115847
\(722\) 0 0
\(723\) 0.551050 2.88260i 0.0204938 0.107205i
\(724\) 0 0
\(725\) 14.9037 3.99343i 0.553509 0.148312i
\(726\) 0 0
\(727\) −34.9918 + 20.2025i −1.29777 + 0.749270i −0.980019 0.198902i \(-0.936262\pi\)
−0.317755 + 0.948173i \(0.602929\pi\)
\(728\) 0 0
\(729\) −11.4389 24.4571i −0.423662 0.905820i
\(730\) 0 0
\(731\) 2.00033 7.46535i 0.0739850 0.276116i
\(732\) 0 0
\(733\) 7.60991 + 28.4006i 0.281078 + 1.04900i 0.951658 + 0.307161i \(0.0993789\pi\)
−0.670579 + 0.741838i \(0.733954\pi\)
\(734\) 0 0
\(735\) −0.0922468 + 0.0626383i −0.00340257 + 0.00231045i
\(736\) 0 0
\(737\) −23.3102 −0.858644
\(738\) 0 0
\(739\) −15.4222 + 15.4222i −0.567316 + 0.567316i −0.931376 0.364060i \(-0.881390\pi\)
0.364060 + 0.931376i \(0.381390\pi\)
\(740\) 0 0
\(741\) −17.1740 49.3791i −0.630904 1.81399i
\(742\) 0 0
\(743\) −21.5896 12.4647i −0.792045 0.457287i 0.0486373 0.998817i \(-0.484512\pi\)
−0.840682 + 0.541529i \(0.817845\pi\)
\(744\) 0 0
\(745\) 0.0394451 0.0227736i 0.00144515 0.000834361i
\(746\) 0 0
\(747\) −3.91091 + 33.5718i −0.143093 + 1.22833i
\(748\) 0 0
\(749\) 5.87459 + 1.57409i 0.214653 + 0.0575161i
\(750\) 0 0
\(751\) 21.2809 36.8596i 0.776551 1.34503i −0.157368 0.987540i \(-0.550301\pi\)
0.933919 0.357486i \(-0.116366\pi\)
\(752\) 0 0
\(753\) 0.176299 + 2.41362i 0.00642470 + 0.0879571i
\(754\) 0 0
\(755\) −0.124111 + 0.124111i −0.00451686 + 0.00451686i
\(756\) 0 0
\(757\) 1.80855 + 1.80855i 0.0657328 + 0.0657328i 0.739209 0.673476i \(-0.235200\pi\)
−0.673476 + 0.739209i \(0.735200\pi\)
\(758\) 0 0
\(759\) 19.6835 1.43775i 0.714467 0.0521872i
\(760\) 0 0
\(761\) −18.5805 10.7275i −0.673543 0.388870i 0.123875 0.992298i \(-0.460468\pi\)
−0.797418 + 0.603428i \(0.793801\pi\)
\(762\) 0 0
\(763\) −1.40496 + 5.24337i −0.0508629 + 0.189823i
\(764\) 0 0
\(765\) 0.0214363 + 0.0496424i 0.000775029 + 0.00179482i
\(766\) 0 0
\(767\) −23.8636 41.3330i −0.861665 1.49245i
\(768\) 0 0
\(769\) −9.98382 + 17.2925i −0.360026 + 0.623583i −0.987965 0.154680i \(-0.950565\pi\)
0.627939 + 0.778263i \(0.283899\pi\)
\(770\) 0 0
\(771\) −38.6781 + 13.4522i −1.39296 + 0.484471i
\(772\) 0 0
\(773\) 24.8049 + 24.8049i 0.892171 + 0.892171i 0.994727 0.102557i \(-0.0327022\pi\)
−0.102557 + 0.994727i \(0.532702\pi\)
\(774\) 0 0
\(775\) 29.2823i 1.05185i
\(776\) 0 0
\(777\) 1.55106 + 2.28423i 0.0556439 + 0.0819463i
\(778\) 0 0
\(779\) −20.5877 + 5.51646i −0.737631 + 0.197648i
\(780\) 0 0
\(781\) −26.0625 6.98342i −0.932589 0.249886i
\(782\) 0 0
\(783\) −11.8161 + 10.8400i −0.422274 + 0.387391i
\(784\) 0 0
\(785\) −0.0573027 0.0992512i −0.00204522 0.00354243i
\(786\) 0 0
\(787\) 2.76911 + 10.3344i 0.0987080 + 0.368383i 0.997556 0.0698783i \(-0.0222611\pi\)
−0.898848 + 0.438261i \(0.855594\pi\)
\(788\) 0 0
\(789\) 43.7319 + 8.35998i 1.55690 + 0.297623i
\(790\) 0 0
\(791\) 19.3159i 0.686794i
\(792\) 0 0
\(793\) 65.8254i 2.33753i
\(794\) 0 0
\(795\) −0.0835483 0.240219i −0.00296315 0.00851971i
\(796\) 0 0