Properties

Label 1323.2.g.f.361.4
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.4
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.f.667.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +1.42494 q^{5} +2.38012 q^{8} +O(q^{10})\) \(q+(0.335166 - 0.580525i) q^{2} +(0.775327 + 1.34291i) q^{4} +1.42494 q^{5} +2.38012 q^{8} +(0.477591 - 0.827212i) q^{10} +4.93077 q^{11} +(1.37730 - 2.38556i) q^{13} +(-0.752918 + 1.30409i) q^{16} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(1.10479 + 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} -5.43661 q^{23} -2.96955 q^{25} +(-0.923251 - 1.59912i) q^{26} +(-3.40555 - 5.89858i) q^{29} +(1.25292 + 2.17012i) q^{31} +(2.88483 + 4.99666i) q^{32} +(-0.375279 - 0.650002i) q^{34} +(0.709787 + 1.22939i) q^{37} +2.69142 q^{38} +3.39152 q^{40} +(0.124384 - 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +(3.82296 + 6.62156i) q^{44} +(-1.82217 + 3.15609i) q^{46} +(4.73790 - 8.20628i) q^{47} +(-0.995294 + 1.72390i) q^{50} +4.27144 q^{52} +(0.410229 - 0.710537i) q^{53} +7.02604 q^{55} -4.56570 q^{58} +(3.29204 + 5.70197i) q^{59} +(0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +0.855913 q^{64} +(1.96257 - 3.39927i) q^{65} +(6.29385 + 10.9013i) q^{67} +1.73623 q^{68} -0.0804951 q^{71} +(-5.34551 + 9.25869i) q^{73} +0.951587 q^{74} +(-3.11297 + 5.39183i) q^{76} +(0.922457 - 1.59774i) q^{79} +(-1.07286 + 1.85825i) q^{80} +(-0.0833788 - 0.144416i) q^{82} +(-7.23583 - 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} -0.668072 q^{86} +11.7358 q^{88} +(6.76292 + 11.7137i) q^{89} +(-4.21515 - 7.30085i) q^{92} +(-3.17597 - 5.50094i) q^{94} +(2.86059 + 4.95469i) q^{95} +(-2.70160 - 4.67930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + 7q^{10} + 8q^{11} + 8q^{13} + 2q^{16} + 12q^{17} - q^{19} + 5q^{20} - q^{22} + 6q^{23} + 2q^{25} + 11q^{26} - 7q^{29} + 3q^{31} + 2q^{32} - 3q^{34} - 40q^{38} - 6q^{40} + 5q^{41} - 7q^{43} + 10q^{44} + 3q^{46} + 27q^{47} - 19q^{50} - 20q^{52} + 21q^{53} - 4q^{55} + 20q^{58} + 30q^{59} + 14q^{61} - 12q^{62} - 50q^{64} + 11q^{65} - 2q^{67} - 54q^{68} + 6q^{71} - 15q^{73} - 72q^{74} - 5q^{76} - 4q^{79} + 20q^{80} + 5q^{82} + 9q^{83} - 6q^{85} - 16q^{86} + 36q^{88} + 28q^{89} - 27q^{92} + 3q^{94} + 14q^{95} + 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.335166 0.580525i 0.236998 0.410493i −0.722853 0.691002i \(-0.757170\pi\)
0.959852 + 0.280508i \(0.0905031\pi\)
\(3\) 0 0
\(4\) 0.775327 + 1.34291i 0.387664 + 0.671453i
\(5\) 1.42494 0.637251 0.318626 0.947881i \(-0.396779\pi\)
0.318626 + 0.947881i \(0.396779\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.38012 0.841499
\(9\) 0 0
\(10\) 0.477591 0.827212i 0.151028 0.261587i
\(11\) 4.93077 1.48668 0.743342 0.668911i \(-0.233239\pi\)
0.743342 + 0.668911i \(0.233239\pi\)
\(12\) 0 0
\(13\) 1.37730 2.38556i 0.381995 0.661635i −0.609352 0.792900i \(-0.708571\pi\)
0.991347 + 0.131265i \(0.0419038\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.752918 + 1.30409i −0.188230 + 0.326023i
\(17\) 0.559839 0.969670i 0.135781 0.235180i −0.790115 0.612959i \(-0.789979\pi\)
0.925896 + 0.377780i \(0.123312\pi\)
\(18\) 0 0
\(19\) 2.00752 + 3.47713i 0.460557 + 0.797709i 0.998989 0.0449606i \(-0.0143162\pi\)
−0.538431 + 0.842669i \(0.680983\pi\)
\(20\) 1.10479 + 1.91356i 0.247039 + 0.427884i
\(21\) 0 0
\(22\) 1.65263 2.86244i 0.352342 0.610274i
\(23\) −5.43661 −1.13361 −0.566806 0.823851i \(-0.691821\pi\)
−0.566806 + 0.823851i \(0.691821\pi\)
\(24\) 0 0
\(25\) −2.96955 −0.593911
\(26\) −0.923251 1.59912i −0.181064 0.313613i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.40555 5.89858i −0.632394 1.09534i −0.987061 0.160346i \(-0.948739\pi\)
0.354667 0.934993i \(-0.384594\pi\)
\(30\) 0 0
\(31\) 1.25292 + 2.17012i 0.225031 + 0.389765i 0.956329 0.292294i \(-0.0944184\pi\)
−0.731298 + 0.682058i \(0.761085\pi\)
\(32\) 2.88483 + 4.99666i 0.509970 + 0.883294i
\(33\) 0 0
\(34\) −0.375279 0.650002i −0.0643597 0.111474i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.709787 + 1.22939i 0.116688 + 0.202110i 0.918453 0.395529i \(-0.129439\pi\)
−0.801765 + 0.597639i \(0.796106\pi\)
\(38\) 2.69142 0.436605
\(39\) 0 0
\(40\) 3.39152 0.536247
\(41\) 0.124384 0.215440i 0.0194256 0.0336460i −0.856149 0.516729i \(-0.827150\pi\)
0.875575 + 0.483083i \(0.160483\pi\)
\(42\) 0 0
\(43\) −0.498313 0.863104i −0.0759921 0.131622i 0.825525 0.564365i \(-0.190879\pi\)
−0.901517 + 0.432743i \(0.857546\pi\)
\(44\) 3.82296 + 6.62156i 0.576333 + 0.998238i
\(45\) 0 0
\(46\) −1.82217 + 3.15609i −0.268664 + 0.465340i
\(47\) 4.73790 8.20628i 0.691093 1.19701i −0.280387 0.959887i \(-0.590463\pi\)
0.971480 0.237122i \(-0.0762040\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.995294 + 1.72390i −0.140756 + 0.243796i
\(51\) 0 0
\(52\) 4.27144 0.592342
\(53\) 0.410229 0.710537i 0.0563493 0.0975998i −0.836475 0.548005i \(-0.815387\pi\)
0.892824 + 0.450406i \(0.148721\pi\)
\(54\) 0 0
\(55\) 7.02604 0.947392
\(56\) 0 0
\(57\) 0 0
\(58\) −4.56570 −0.599506
\(59\) 3.29204 + 5.70197i 0.428586 + 0.742334i 0.996748 0.0805836i \(-0.0256784\pi\)
−0.568161 + 0.822917i \(0.692345\pi\)
\(60\) 0 0
\(61\) 0.0376322 0.0651809i 0.00481831 0.00834556i −0.863606 0.504167i \(-0.831800\pi\)
0.868425 + 0.495821i \(0.165133\pi\)
\(62\) 1.67974 0.213328
\(63\) 0 0
\(64\) 0.855913 0.106989
\(65\) 1.96257 3.39927i 0.243427 0.421628i
\(66\) 0 0
\(67\) 6.29385 + 10.9013i 0.768916 + 1.33180i 0.938151 + 0.346226i \(0.112537\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(68\) 1.73623 0.210549
\(69\) 0 0
\(70\) 0 0
\(71\) −0.0804951 −0.00955301 −0.00477651 0.999989i \(-0.501520\pi\)
−0.00477651 + 0.999989i \(0.501520\pi\)
\(72\) 0 0
\(73\) −5.34551 + 9.25869i −0.625644 + 1.08365i 0.362772 + 0.931878i \(0.381830\pi\)
−0.988416 + 0.151769i \(0.951503\pi\)
\(74\) 0.951587 0.110620
\(75\) 0 0
\(76\) −3.11297 + 5.39183i −0.357083 + 0.618485i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.922457 1.59774i 0.103785 0.179760i −0.809456 0.587180i \(-0.800238\pi\)
0.913241 + 0.407420i \(0.133571\pi\)
\(80\) −1.07286 + 1.85825i −0.119950 + 0.207759i
\(81\) 0 0
\(82\) −0.0833788 0.144416i −0.00920765 0.0159481i
\(83\) −7.23583 12.5328i −0.794236 1.37566i −0.923323 0.384023i \(-0.874538\pi\)
0.129088 0.991633i \(-0.458795\pi\)
\(84\) 0 0
\(85\) 0.797736 1.38172i 0.0865266 0.149868i
\(86\) −0.668072 −0.0720400
\(87\) 0 0
\(88\) 11.7358 1.25104
\(89\) 6.76292 + 11.7137i 0.716868 + 1.24165i 0.962235 + 0.272222i \(0.0877584\pi\)
−0.245366 + 0.969430i \(0.578908\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.21515 7.30085i −0.439460 0.761167i
\(93\) 0 0
\(94\) −3.17597 5.50094i −0.327576 0.567378i
\(95\) 2.86059 + 4.95469i 0.293491 + 0.508341i
\(96\) 0 0
\(97\) −2.70160 4.67930i −0.274306 0.475111i 0.695654 0.718377i \(-0.255115\pi\)
−0.969960 + 0.243266i \(0.921781\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.30238 3.98783i −0.230238 0.398783i
\(101\) −5.13540 −0.510991 −0.255496 0.966810i \(-0.582239\pi\)
−0.255496 + 0.966810i \(0.582239\pi\)
\(102\) 0 0
\(103\) 14.2112 1.40027 0.700137 0.714009i \(-0.253122\pi\)
0.700137 + 0.714009i \(0.253122\pi\)
\(104\) 3.27814 5.67791i 0.321448 0.556765i
\(105\) 0 0
\(106\) −0.274990 0.476296i −0.0267094 0.0462620i
\(107\) −3.83015 6.63401i −0.370274 0.641334i 0.619333 0.785128i \(-0.287403\pi\)
−0.989608 + 0.143794i \(0.954070\pi\)
\(108\) 0 0
\(109\) −0.849394 + 1.47119i −0.0813572 + 0.140915i −0.903833 0.427885i \(-0.859259\pi\)
0.822476 + 0.568800i \(0.192592\pi\)
\(110\) 2.35489 4.07880i 0.224530 0.388898i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.300351 0.520224i 0.0282547 0.0489385i −0.851552 0.524270i \(-0.824338\pi\)
0.879807 + 0.475331i \(0.157672\pi\)
\(114\) 0 0
\(115\) −7.74683 −0.722395
\(116\) 5.28083 9.14666i 0.490312 0.849246i
\(117\) 0 0
\(118\) 4.41352 0.406297
\(119\) 0 0
\(120\) 0 0
\(121\) 13.3125 1.21023
\(122\) −0.0252261 0.0436929i −0.00228386 0.00395577i
\(123\) 0 0
\(124\) −1.94284 + 3.36510i −0.174472 + 0.302195i
\(125\) −11.3561 −1.01572
\(126\) 0 0
\(127\) 7.25977 0.644200 0.322100 0.946706i \(-0.395611\pi\)
0.322100 + 0.946706i \(0.395611\pi\)
\(128\) −5.48278 + 9.49645i −0.484614 + 0.839375i
\(129\) 0 0
\(130\) −1.31557 2.27864i −0.115384 0.199850i
\(131\) −20.4530 −1.78698 −0.893492 0.449079i \(-0.851752\pi\)
−0.893492 + 0.449079i \(0.851752\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.43794 0.728927
\(135\) 0 0
\(136\) 1.33248 2.30793i 0.114260 0.197903i
\(137\) −12.2116 −1.04331 −0.521655 0.853157i \(-0.674685\pi\)
−0.521655 + 0.853157i \(0.674685\pi\)
\(138\) 0 0
\(139\) 1.24092 2.14933i 0.105253 0.182304i −0.808588 0.588375i \(-0.799768\pi\)
0.913842 + 0.406071i \(0.133101\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.0269793 + 0.0467294i −0.00226405 + 0.00392145i
\(143\) 6.79117 11.7626i 0.567906 0.983642i
\(144\) 0 0
\(145\) −4.85269 8.40511i −0.402994 0.698006i
\(146\) 3.58327 + 6.20640i 0.296553 + 0.513645i
\(147\) 0 0
\(148\) −1.10063 + 1.90635i −0.0904715 + 0.156701i
\(149\) 8.55593 0.700929 0.350465 0.936576i \(-0.386024\pi\)
0.350465 + 0.936576i \(0.386024\pi\)
\(150\) 0 0
\(151\) −17.6592 −1.43709 −0.718544 0.695482i \(-0.755191\pi\)
−0.718544 + 0.695482i \(0.755191\pi\)
\(152\) 4.77814 + 8.27599i 0.387559 + 0.671271i
\(153\) 0 0
\(154\) 0 0
\(155\) 1.78533 + 3.09228i 0.143401 + 0.248378i
\(156\) 0 0
\(157\) 3.16074 + 5.47457i 0.252255 + 0.436918i 0.964146 0.265371i \(-0.0854946\pi\)
−0.711891 + 0.702289i \(0.752161\pi\)
\(158\) −0.618353 1.07102i −0.0491936 0.0852057i
\(159\) 0 0
\(160\) 4.11070 + 7.11993i 0.324979 + 0.562880i
\(161\) 0 0
\(162\) 0 0
\(163\) −4.01134 6.94784i −0.314192 0.544197i 0.665073 0.746778i \(-0.268400\pi\)
−0.979265 + 0.202581i \(0.935067\pi\)
\(164\) 0.385754 0.0301223
\(165\) 0 0
\(166\) −9.70083 −0.752930
\(167\) 1.06038 1.83663i 0.0820545 0.142123i −0.822078 0.569375i \(-0.807185\pi\)
0.904132 + 0.427253i \(0.140518\pi\)
\(168\) 0 0
\(169\) 2.70608 + 4.68706i 0.208160 + 0.360543i
\(170\) −0.534749 0.926212i −0.0410133 0.0710372i
\(171\) 0 0
\(172\) 0.772712 1.33838i 0.0589187 0.102050i
\(173\) 9.14404 15.8379i 0.695208 1.20414i −0.274902 0.961472i \(-0.588646\pi\)
0.970110 0.242664i \(-0.0780212\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.71247 + 6.43018i −0.279838 + 0.484693i
\(177\) 0 0
\(178\) 9.06681 0.679586
\(179\) −3.81276 + 6.60389i −0.284979 + 0.493598i −0.972604 0.232468i \(-0.925320\pi\)
0.687625 + 0.726066i \(0.258653\pi\)
\(180\) 0 0
\(181\) −15.5305 −1.15438 −0.577188 0.816611i \(-0.695850\pi\)
−0.577188 + 0.816611i \(0.695850\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −12.9398 −0.953933
\(185\) 1.01140 + 1.75180i 0.0743597 + 0.128795i
\(186\) 0 0
\(187\) 2.76044 4.78122i 0.201863 0.349638i
\(188\) 14.6937 1.07165
\(189\) 0 0
\(190\) 3.83510 0.278227
\(191\) 7.41624 12.8453i 0.536620 0.929454i −0.462463 0.886639i \(-0.653034\pi\)
0.999083 0.0428150i \(-0.0136326\pi\)
\(192\) 0 0
\(193\) −8.28387 14.3481i −0.596286 1.03280i −0.993364 0.115013i \(-0.963309\pi\)
0.397078 0.917785i \(-0.370024\pi\)
\(194\) −3.62194 −0.260040
\(195\) 0 0
\(196\) 0 0
\(197\) 4.03740 0.287653 0.143826 0.989603i \(-0.454059\pi\)
0.143826 + 0.989603i \(0.454059\pi\)
\(198\) 0 0
\(199\) 12.6407 21.8943i 0.896076 1.55205i 0.0636081 0.997975i \(-0.479739\pi\)
0.832468 0.554074i \(-0.186927\pi\)
\(200\) −7.06789 −0.499775
\(201\) 0 0
\(202\) −1.72121 + 2.98123i −0.121104 + 0.209758i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.177240 0.306988i 0.0123790 0.0214410i
\(206\) 4.76312 8.24997i 0.331862 0.574803i
\(207\) 0 0
\(208\) 2.07399 + 3.59226i 0.143805 + 0.249078i
\(209\) 9.89864 + 17.1449i 0.684703 + 1.18594i
\(210\) 0 0
\(211\) −3.76246 + 6.51678i −0.259019 + 0.448634i −0.965979 0.258619i \(-0.916732\pi\)
0.706961 + 0.707253i \(0.250066\pi\)
\(212\) 1.27225 0.0873782
\(213\) 0 0
\(214\) −5.13495 −0.351018
\(215\) −0.710065 1.22987i −0.0484261 0.0838764i
\(216\) 0 0
\(217\) 0 0
\(218\) 0.569377 + 0.986190i 0.0385631 + 0.0667932i
\(219\) 0 0
\(220\) 5.44748 + 9.43531i 0.367269 + 0.636129i
\(221\) −1.54214 2.67106i −0.103735 0.179675i
\(222\) 0 0
\(223\) −6.49230 11.2450i −0.434757 0.753020i 0.562519 0.826784i \(-0.309832\pi\)
−0.997276 + 0.0737638i \(0.976499\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.201335 0.348723i −0.0133926 0.0231967i
\(227\) −28.9665 −1.92257 −0.961286 0.275551i \(-0.911140\pi\)
−0.961286 + 0.275551i \(0.911140\pi\)
\(228\) 0 0
\(229\) −15.4358 −1.02003 −0.510013 0.860167i \(-0.670360\pi\)
−0.510013 + 0.860167i \(0.670360\pi\)
\(230\) −2.59648 + 4.49723i −0.171207 + 0.296538i
\(231\) 0 0
\(232\) −8.10561 14.0393i −0.532159 0.921727i
\(233\) 2.47324 + 4.28378i 0.162027 + 0.280640i 0.935596 0.353073i \(-0.114863\pi\)
−0.773568 + 0.633713i \(0.781530\pi\)
\(234\) 0 0
\(235\) 6.75121 11.6934i 0.440400 0.762795i
\(236\) −5.10481 + 8.84179i −0.332295 + 0.575551i
\(237\) 0 0
\(238\) 0 0
\(239\) −6.51732 + 11.2883i −0.421571 + 0.730182i −0.996093 0.0883069i \(-0.971854\pi\)
0.574523 + 0.818489i \(0.305188\pi\)
\(240\) 0 0
\(241\) −14.5825 −0.939339 −0.469670 0.882842i \(-0.655627\pi\)
−0.469670 + 0.882842i \(0.655627\pi\)
\(242\) 4.46191 7.72826i 0.286823 0.496791i
\(243\) 0 0
\(244\) 0.116709 0.00747154
\(245\) 0 0
\(246\) 0 0
\(247\) 11.0599 0.703722
\(248\) 2.98209 + 5.16514i 0.189363 + 0.327987i
\(249\) 0 0
\(250\) −3.80619 + 6.59251i −0.240724 + 0.416947i
\(251\) −14.0715 −0.888187 −0.444094 0.895980i \(-0.646474\pi\)
−0.444094 + 0.895980i \(0.646474\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) 2.43323 4.21448i 0.152674 0.264440i
\(255\) 0 0
\(256\) 4.53120 + 7.84826i 0.283200 + 0.490517i
\(257\) −8.36215 −0.521617 −0.260808 0.965391i \(-0.583989\pi\)
−0.260808 + 0.965391i \(0.583989\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.08653 0.377471
\(261\) 0 0
\(262\) −6.85515 + 11.8735i −0.423512 + 0.733545i
\(263\) −3.27066 −0.201678 −0.100839 0.994903i \(-0.532153\pi\)
−0.100839 + 0.994903i \(0.532153\pi\)
\(264\) 0 0
\(265\) 0.584551 1.01247i 0.0359087 0.0621956i
\(266\) 0 0
\(267\) 0 0
\(268\) −9.75958 + 16.9041i −0.596161 + 1.03258i
\(269\) −7.69349 + 13.3255i −0.469081 + 0.812471i −0.999375 0.0353420i \(-0.988748\pi\)
0.530295 + 0.847813i \(0.322081\pi\)
\(270\) 0 0
\(271\) −4.06308 7.03747i −0.246815 0.427496i 0.715825 0.698279i \(-0.246051\pi\)
−0.962640 + 0.270783i \(0.912717\pi\)
\(272\) 0.843026 + 1.46016i 0.0511160 + 0.0885355i
\(273\) 0 0
\(274\) −4.09293 + 7.08915i −0.247263 + 0.428271i
\(275\) −14.6422 −0.882958
\(276\) 0 0
\(277\) 12.8457 0.771826 0.385913 0.922535i \(-0.373887\pi\)
0.385913 + 0.922535i \(0.373887\pi\)
\(278\) −0.831826 1.44077i −0.0498896 0.0864114i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.724081 + 1.25415i 0.0431951 + 0.0748161i 0.886815 0.462125i \(-0.152913\pi\)
−0.843620 + 0.536941i \(0.819580\pi\)
\(282\) 0 0
\(283\) −8.71926 15.1022i −0.518306 0.897732i −0.999774 0.0212686i \(-0.993229\pi\)
0.481468 0.876464i \(-0.340104\pi\)
\(284\) −0.0624100 0.108097i −0.00370335 0.00641440i
\(285\) 0 0
\(286\) −4.55234 7.88489i −0.269186 0.466243i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.87316 + 13.6367i 0.463127 + 0.802160i
\(290\) −6.50584 −0.382036
\(291\) 0 0
\(292\) −16.5781 −0.970158
\(293\) −0.900048 + 1.55893i −0.0525814 + 0.0910736i −0.891118 0.453772i \(-0.850078\pi\)
0.838537 + 0.544845i \(0.183412\pi\)
\(294\) 0 0
\(295\) 4.69094 + 8.12495i 0.273117 + 0.473053i
\(296\) 1.68938 + 2.92609i 0.0981931 + 0.170075i
\(297\) 0 0
\(298\) 2.86766 4.96693i 0.166119 0.287727i
\(299\) −7.48786 + 12.9693i −0.433034 + 0.750037i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.91878 + 10.2516i −0.340588 + 0.589915i
\(303\) 0 0
\(304\) −6.04600 −0.346762
\(305\) 0.0536236 0.0928787i 0.00307048 0.00531822i
\(306\) 0 0
\(307\) −1.06478 −0.0607699 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.39353 0.135943
\(311\) 8.46463 + 14.6612i 0.479985 + 0.831359i 0.999736 0.0229591i \(-0.00730874\pi\)
−0.519751 + 0.854318i \(0.673975\pi\)
\(312\) 0 0
\(313\) −4.13928 + 7.16944i −0.233966 + 0.405241i −0.958972 0.283502i \(-0.908504\pi\)
0.725006 + 0.688743i \(0.241837\pi\)
\(314\) 4.23750 0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) 3.27371 5.67023i 0.183870 0.318472i −0.759325 0.650711i \(-0.774471\pi\)
0.943195 + 0.332239i \(0.107804\pi\)
\(318\) 0 0
\(319\) −16.7920 29.0846i −0.940171 1.62842i
\(320\) 1.21962 0.0681790
\(321\) 0 0
\(322\) 0 0
\(323\) 4.49556 0.250140
\(324\) 0 0
\(325\) −4.08997 + 7.08404i −0.226871 + 0.392952i
\(326\) −5.37786 −0.297852
\(327\) 0 0
\(328\) 0.296049 0.512773i 0.0163466 0.0283131i
\(329\) 0 0
\(330\) 0 0
\(331\) 13.3629 23.1453i 0.734493 1.27218i −0.220453 0.975398i \(-0.570754\pi\)
0.954946 0.296781i \(-0.0959131\pi\)
\(332\) 11.2203 19.4341i 0.615792 1.06658i
\(333\) 0 0
\(334\) −0.710806 1.23115i −0.0388936 0.0673657i
\(335\) 8.96834 + 15.5336i 0.489993 + 0.848692i
\(336\) 0 0
\(337\) −4.76164 + 8.24740i −0.259383 + 0.449264i −0.966077 0.258255i \(-0.916853\pi\)
0.706694 + 0.707520i \(0.250186\pi\)
\(338\) 3.62794 0.197334
\(339\) 0 0
\(340\) 2.47403 0.134173
\(341\) 6.17786 + 10.7004i 0.334550 + 0.579457i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.18605 2.05429i −0.0639473 0.110760i
\(345\) 0 0
\(346\) −6.12955 10.6167i −0.329526 0.570757i
\(347\) −9.35156 16.1974i −0.502018 0.869521i −0.999997 0.00233189i \(-0.999258\pi\)
0.497979 0.867189i \(-0.334076\pi\)
\(348\) 0 0
\(349\) 15.0542 + 26.0747i 0.805834 + 1.39574i 0.915727 + 0.401801i \(0.131616\pi\)
−0.109893 + 0.993943i \(0.535051\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 14.2244 + 24.6374i 0.758164 + 1.31318i
\(353\) 6.25933 0.333150 0.166575 0.986029i \(-0.446729\pi\)
0.166575 + 0.986029i \(0.446729\pi\)
\(354\) 0 0
\(355\) −0.114700 −0.00608767
\(356\) −10.4870 + 18.1639i −0.555807 + 0.962686i
\(357\) 0 0
\(358\) 2.55582 + 4.42680i 0.135079 + 0.233964i
\(359\) 5.09755 + 8.82921i 0.269038 + 0.465988i 0.968614 0.248571i \(-0.0799608\pi\)
−0.699575 + 0.714559i \(0.746628\pi\)
\(360\) 0 0
\(361\) 1.43970 2.49364i 0.0757739 0.131244i
\(362\) −5.20532 + 9.01587i −0.273585 + 0.473864i
\(363\) 0 0
\(364\) 0 0
\(365\) −7.61701 + 13.1931i −0.398693 + 0.690556i
\(366\) 0 0
\(367\) 28.6557 1.49581 0.747906 0.663804i \(-0.231059\pi\)
0.747906 + 0.663804i \(0.231059\pi\)
\(368\) 4.09332 7.08984i 0.213379 0.369584i
\(369\) 0 0
\(370\) 1.35595 0.0704926
\(371\) 0 0
\(372\) 0 0
\(373\) −16.0734 −0.832249 −0.416124 0.909308i \(-0.636612\pi\)
−0.416124 + 0.909308i \(0.636612\pi\)
\(374\) −1.85041 3.20501i −0.0956826 0.165727i
\(375\) 0 0
\(376\) 11.2768 19.5319i 0.581555 1.00728i
\(377\) −18.7619 −0.966286
\(378\) 0 0
\(379\) −1.01893 −0.0523388 −0.0261694 0.999658i \(-0.508331\pi\)
−0.0261694 + 0.999658i \(0.508331\pi\)
\(380\) −4.43579 + 7.68302i −0.227551 + 0.394130i
\(381\) 0 0
\(382\) −4.97135 8.61063i −0.254356 0.440558i
\(383\) −11.5865 −0.592044 −0.296022 0.955181i \(-0.595660\pi\)
−0.296022 + 0.955181i \(0.595660\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −11.1059 −0.565275
\(387\) 0 0
\(388\) 4.18924 7.25598i 0.212677 0.368367i
\(389\) −17.8135 −0.903181 −0.451590 0.892225i \(-0.649143\pi\)
−0.451590 + 0.892225i \(0.649143\pi\)
\(390\) 0 0
\(391\) −3.04363 + 5.27172i −0.153923 + 0.266602i
\(392\) 0 0
\(393\) 0 0
\(394\) 1.35320 2.34381i 0.0681732 0.118079i
\(395\) 1.31444 2.27668i 0.0661369 0.114552i
\(396\) 0 0
\(397\) 6.54229 + 11.3316i 0.328348 + 0.568715i 0.982184 0.187921i \(-0.0601748\pi\)
−0.653836 + 0.756636i \(0.726841\pi\)
\(398\) −8.47348 14.6765i −0.424737 0.735666i
\(399\) 0 0
\(400\) 2.23583 3.87257i 0.111792 0.193629i
\(401\) −14.1033 −0.704285 −0.352143 0.935946i \(-0.614547\pi\)
−0.352143 + 0.935946i \(0.614547\pi\)
\(402\) 0 0
\(403\) 6.90259 0.343842
\(404\) −3.98161 6.89636i −0.198093 0.343107i
\(405\) 0 0
\(406\) 0 0
\(407\) 3.49980 + 6.06183i 0.173479 + 0.300474i
\(408\) 0 0
\(409\) −1.32300 2.29150i −0.0654179 0.113307i 0.831461 0.555583i \(-0.187505\pi\)
−0.896879 + 0.442275i \(0.854171\pi\)
\(410\) −0.118810 0.205784i −0.00586759 0.0101630i
\(411\) 0 0
\(412\) 11.0183 + 19.0843i 0.542835 + 0.940217i
\(413\) 0 0
\(414\) 0 0
\(415\) −10.3106 17.8585i −0.506128 0.876639i
\(416\) 15.8931 0.779224
\(417\) 0 0
\(418\) 13.2708 0.649094
\(419\) 16.7567 29.0235i 0.818619 1.41789i −0.0880816 0.996113i \(-0.528074\pi\)
0.906700 0.421776i \(-0.138593\pi\)
\(420\) 0 0
\(421\) −2.41950 4.19071i −0.117919 0.204242i 0.801024 0.598633i \(-0.204289\pi\)
−0.918943 + 0.394390i \(0.870956\pi\)
\(422\) 2.52210 + 4.36841i 0.122774 + 0.212651i
\(423\) 0 0
\(424\) 0.976394 1.69116i 0.0474179 0.0821302i
\(425\) −1.66247 + 2.87949i −0.0806418 + 0.139676i
\(426\) 0 0
\(427\) 0 0
\(428\) 5.93923 10.2871i 0.287084 0.497244i
\(429\) 0 0
\(430\) −0.951960 −0.0459076
\(431\) −17.6643 + 30.5954i −0.850858 + 1.47373i 0.0295774 + 0.999562i \(0.490584\pi\)
−0.880435 + 0.474166i \(0.842749\pi\)
\(432\) 0 0
\(433\) −5.47404 −0.263066 −0.131533 0.991312i \(-0.541990\pi\)
−0.131533 + 0.991312i \(0.541990\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.63423 −0.126157
\(437\) −10.9141 18.9038i −0.522093 0.904292i
\(438\) 0 0
\(439\) 3.19906 5.54093i 0.152683 0.264454i −0.779530 0.626365i \(-0.784542\pi\)
0.932213 + 0.361911i \(0.117875\pi\)
\(440\) 16.7228 0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) −3.19341 + 5.53115i −0.151723 + 0.262793i −0.931861 0.362815i \(-0.881816\pi\)
0.780138 + 0.625608i \(0.215149\pi\)
\(444\) 0 0
\(445\) 9.63674 + 16.6913i 0.456825 + 0.791245i
\(446\) −8.70400 −0.412146
\(447\) 0 0
\(448\) 0 0
\(449\) 11.7460 0.554327 0.277163 0.960823i \(-0.410606\pi\)
0.277163 + 0.960823i \(0.410606\pi\)
\(450\) 0 0
\(451\) 0.613311 1.06229i 0.0288797 0.0500210i
\(452\) 0.931482 0.0438132
\(453\) 0 0
\(454\) −9.70859 + 16.8158i −0.455647 + 0.789203i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.26120 + 9.11266i −0.246108 + 0.426272i −0.962443 0.271485i \(-0.912485\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(458\) −5.17356 + 8.96087i −0.241745 + 0.418714i
\(459\) 0 0
\(460\) −6.00633 10.4033i −0.280046 0.485055i
\(461\) −3.54278 6.13627i −0.165004 0.285794i 0.771653 0.636044i \(-0.219430\pi\)
−0.936657 + 0.350249i \(0.886097\pi\)
\(462\) 0 0
\(463\) 16.3760 28.3641i 0.761059 1.31819i −0.181246 0.983438i \(-0.558013\pi\)
0.942305 0.334755i \(-0.108654\pi\)
\(464\) 10.2564 0.476141
\(465\) 0 0
\(466\) 3.31579 0.153601
\(467\) 1.96216 + 3.39856i 0.0907978 + 0.157266i 0.907847 0.419301i \(-0.137725\pi\)
−0.817049 + 0.576568i \(0.804392\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −4.52555 7.83849i −0.208748 0.361563i
\(471\) 0 0
\(472\) 7.83544 + 13.5714i 0.360655 + 0.624673i
\(473\) −2.45707 4.25577i −0.112976 0.195681i
\(474\) 0 0
\(475\) −5.96145 10.3255i −0.273530 0.473768i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.36878 + 7.56694i 0.199823 + 0.346104i
\(479\) 16.0865 0.735010 0.367505 0.930022i \(-0.380212\pi\)
0.367505 + 0.930022i \(0.380212\pi\)
\(480\) 0 0
\(481\) 3.91036 0.178297
\(482\) −4.88755 + 8.46549i −0.222622 + 0.385592i
\(483\) 0 0
\(484\) 10.3216 + 17.8775i 0.469162 + 0.812612i
\(485\) −3.84961 6.66771i −0.174802 0.302765i
\(486\) 0 0
\(487\) −1.75172 + 3.03407i −0.0793781 + 0.137487i −0.902982 0.429679i \(-0.858627\pi\)
0.823604 + 0.567166i \(0.191960\pi\)
\(488\) 0.0895692 0.155138i 0.00405461 0.00702279i
\(489\) 0 0
\(490\) 0 0
\(491\) 20.5546 35.6017i 0.927618 1.60668i 0.140321 0.990106i \(-0.455186\pi\)
0.787296 0.616575i \(-0.211480\pi\)
\(492\) 0 0
\(493\) −7.62624 −0.343468
\(494\) 3.70689 6.42053i 0.166781 0.288873i
\(495\) 0 0
\(496\) −3.77338 −0.169430
\(497\) 0 0
\(498\) 0 0
\(499\) 11.8297 0.529571 0.264785 0.964307i \(-0.414699\pi\)
0.264785 + 0.964307i \(0.414699\pi\)
\(500\) −8.80470 15.2502i −0.393758 0.682009i
\(501\) 0 0
\(502\) −4.71631 + 8.16888i −0.210499 + 0.364595i
\(503\) 21.8595 0.974665 0.487332 0.873217i \(-0.337970\pi\)
0.487332 + 0.873217i \(0.337970\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) −8.98470 + 15.5620i −0.399419 + 0.691813i
\(507\) 0 0
\(508\) 5.62869 + 9.74918i 0.249733 + 0.432550i
\(509\) 16.8966 0.748930 0.374465 0.927241i \(-0.377826\pi\)
0.374465 + 0.927241i \(0.377826\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −15.8563 −0.700756
\(513\) 0 0
\(514\) −2.80271 + 4.85444i −0.123622 + 0.214120i
\(515\) 20.2501 0.892326
\(516\) 0 0
\(517\) 23.3615 40.4633i 1.02744 1.77957i
\(518\) 0 0
\(519\) 0 0
\(520\) 4.67115 8.09067i 0.204843 0.354799i
\(521\) −17.2466 + 29.8720i −0.755587 + 1.30872i 0.189495 + 0.981882i \(0.439315\pi\)
−0.945082 + 0.326834i \(0.894018\pi\)
\(522\) 0 0
\(523\) −0.995615 1.72445i −0.0435352 0.0754051i 0.843437 0.537229i \(-0.180529\pi\)
−0.886972 + 0.461823i \(0.847195\pi\)
\(524\) −15.8577 27.4664i −0.692749 1.19988i
\(525\) 0 0
\(526\) −1.09622 + 1.89870i −0.0477972 + 0.0827873i
\(527\) 2.80573 0.122220
\(528\) 0 0
\(529\) 6.55673 0.285075
\(530\) −0.391843 0.678693i −0.0170206 0.0294805i
\(531\) 0 0
\(532\) 0 0
\(533\) −0.342629 0.593452i −0.0148409 0.0257052i
\(534\) 0 0
\(535\) −5.45772 9.45305i −0.235958 0.408691i
\(536\) 14.9801 + 25.9463i 0.647042 + 1.12071i
\(537\) 0 0
\(538\) 5.15720 + 8.93253i 0.222343 + 0.385109i
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0681 26.0988i −0.647830 1.12207i −0.983640 0.180145i \(-0.942343\pi\)
0.335810 0.941930i \(-0.390990\pi\)
\(542\) −5.44724 −0.233979
\(543\) 0 0
\(544\) 6.46015 0.276977
\(545\) −1.21033 + 2.09636i −0.0518450 + 0.0897982i
\(546\) 0 0
\(547\) 7.68070 + 13.3034i 0.328403 + 0.568810i 0.982195 0.187864i \(-0.0601563\pi\)
−0.653792 + 0.756674i \(0.726823\pi\)
\(548\) −9.46800 16.3991i −0.404453 0.700533i
\(549\) 0 0
\(550\) −4.90757 + 8.50016i −0.209260 + 0.362448i
\(551\) 13.6734 23.6831i 0.582508 1.00893i
\(552\) 0 0
\(553\) 0 0
\(554\) 4.30546 7.45728i 0.182921 0.316829i
\(555\) 0 0
\(556\) 3.84846 0.163211
\(557\) 11.6412 20.1631i 0.493252 0.854338i −0.506718 0.862112i \(-0.669141\pi\)
0.999970 + 0.00777438i \(0.00247469\pi\)
\(558\) 0 0
\(559\) −2.74531 −0.116114
\(560\) 0 0
\(561\) 0 0
\(562\) 0.970751 0.0409487
\(563\) −2.27942 3.94808i −0.0960663 0.166392i 0.813987 0.580883i \(-0.197293\pi\)
−0.910053 + 0.414492i \(0.863959\pi\)
\(564\) 0 0
\(565\) 0.427982 0.741286i 0.0180053 0.0311861i
\(566\) −11.6896 −0.491351
\(567\) 0 0
\(568\) −0.191588 −0.00803885
\(569\) 9.09976 15.7612i 0.381482 0.660746i −0.609793 0.792561i \(-0.708747\pi\)
0.991274 + 0.131815i \(0.0420806\pi\)
\(570\) 0 0
\(571\) 8.52275 + 14.7618i 0.356666 + 0.617763i 0.987402 0.158234i \(-0.0505801\pi\)
−0.630736 + 0.775998i \(0.717247\pi\)
\(572\) 21.0615 0.880625
\(573\) 0 0
\(574\) 0 0
\(575\) 16.1443 0.673264
\(576\) 0 0
\(577\) 5.70473 9.88088i 0.237491 0.411346i −0.722503 0.691368i \(-0.757008\pi\)
0.959994 + 0.280022i \(0.0903417\pi\)
\(578\) 10.5553 0.439041
\(579\) 0 0
\(580\) 7.52485 13.0334i 0.312452 0.541183i
\(581\) 0 0
\(582\) 0 0
\(583\) 2.02275 3.50350i 0.0837736 0.145100i
\(584\) −12.7229 + 22.0368i −0.526479 + 0.911889i
\(585\) 0 0
\(586\) 0.603332 + 1.04500i 0.0249234 + 0.0431686i
\(587\) 2.52544 + 4.37420i 0.104236 + 0.180543i 0.913426 0.407005i \(-0.133427\pi\)
−0.809190 + 0.587548i \(0.800094\pi\)
\(588\) 0 0
\(589\) −5.03052 + 8.71312i −0.207279 + 0.359018i
\(590\) 6.28899 0.258913
\(591\) 0 0
\(592\) −2.13765 −0.0878567
\(593\) −9.98892 17.3013i −0.410196 0.710480i 0.584715 0.811239i \(-0.301206\pi\)
−0.994911 + 0.100759i \(0.967873\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.63365 + 11.4898i 0.271725 + 0.470641i
\(597\) 0 0
\(598\) 5.01935 + 8.69378i 0.205257 + 0.355515i
\(599\) 2.19660 + 3.80463i 0.0897508 + 0.155453i 0.907406 0.420256i \(-0.138060\pi\)
−0.817655 + 0.575709i \(0.804726\pi\)
\(600\) 0 0
\(601\) −12.1778 21.0926i −0.496743 0.860385i 0.503250 0.864141i \(-0.332138\pi\)
−0.999993 + 0.00375637i \(0.998804\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −13.6917 23.7147i −0.557107 0.964937i
\(605\) 18.9695 0.771221
\(606\) 0 0
\(607\) −13.1256 −0.532752 −0.266376 0.963869i \(-0.585826\pi\)
−0.266376 + 0.963869i \(0.585826\pi\)
\(608\) −11.5827 + 20.0618i −0.469741 + 0.813615i
\(609\) 0 0
\(610\) −0.0359456 0.0622597i −0.00145540 0.00252082i
\(611\) −13.0510 22.6051i −0.527988 0.914502i
\(612\) 0 0
\(613\) −23.2403 + 40.2534i −0.938667 + 1.62582i −0.170707 + 0.985322i \(0.554605\pi\)
−0.767960 + 0.640497i \(0.778728\pi\)
\(614\) −0.356877 + 0.618129i −0.0144024 + 0.0249456i
\(615\) 0 0
\(616\) 0 0
\(617\) −14.1948 + 24.5862i −0.571463 + 0.989803i 0.424953 + 0.905215i \(0.360291\pi\)
−0.996416 + 0.0845873i \(0.973043\pi\)
\(618\) 0 0
\(619\) −31.9212 −1.28302 −0.641511 0.767114i \(-0.721692\pi\)
−0.641511 + 0.767114i \(0.721692\pi\)
\(620\) −2.76843 + 4.79506i −0.111183 + 0.192574i
\(621\) 0 0
\(622\) 11.3482 0.455023
\(623\) 0 0
\(624\) 0 0
\(625\) −1.33399 −0.0533594
\(626\) 2.77469 + 4.80591i 0.110899 + 0.192083i
\(627\) 0 0
\(628\) −4.90122 + 8.48916i −0.195580 + 0.338754i
\(629\) 1.58947 0.0633762
\(630\) 0 0
\(631\) 38.7184 1.54135 0.770677 0.637226i \(-0.219918\pi\)
0.770677 + 0.637226i \(0.219918\pi\)
\(632\) 2.19556 3.80282i 0.0873346 0.151268i
\(633\) 0 0
\(634\) −2.19447 3.80094i −0.0871537 0.150955i
\(635\) 10.3447 0.410517
\(636\) 0 0
\(637\) 0 0
\(638\) −22.5124 −0.891276
\(639\) 0 0
\(640\) −7.81261 + 13.5318i −0.308821 + 0.534893i
\(641\) 40.4001 1.59571 0.797854 0.602851i \(-0.205968\pi\)
0.797854 + 0.602851i \(0.205968\pi\)
\(642\) 0 0
\(643\) −6.27355 + 10.8661i −0.247405 + 0.428517i −0.962805 0.270198i \(-0.912911\pi\)
0.715400 + 0.698715i \(0.246244\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.50676 2.60979i 0.0592827 0.102681i
\(647\) 17.2774 29.9253i 0.679245 1.17649i −0.295964 0.955199i \(-0.595641\pi\)
0.975209 0.221287i \(-0.0710258\pi\)
\(648\) 0 0
\(649\) 16.2323 + 28.1151i 0.637173 + 1.10362i
\(650\) 2.74164 + 4.74866i 0.107536 + 0.186258i
\(651\) 0 0
\(652\) 6.22019 10.7737i 0.243602 0.421930i
\(653\) 22.2944 0.872446 0.436223 0.899839i \(-0.356316\pi\)
0.436223 + 0.899839i \(0.356316\pi\)
\(654\) 0 0
\(655\) −29.1442 −1.13876
\(656\) 0.187302 + 0.324417i 0.00731293 + 0.0126664i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.57493 6.19196i −0.139259 0.241204i 0.787957 0.615730i \(-0.211139\pi\)
−0.927217 + 0.374526i \(0.877806\pi\)
\(660\) 0 0
\(661\) 21.4530 + 37.1577i 0.834425 + 1.44527i 0.894498 + 0.447072i \(0.147533\pi\)
−0.0600736 + 0.998194i \(0.519134\pi\)
\(662\) −8.95760 15.5150i −0.348147 0.603008i
\(663\) 0 0
\(664\) −17.2221 29.8296i −0.668349 1.15761i
\(665\) 0 0
\(666\) 0 0
\(667\) 18.5146 + 32.0683i 0.716889 + 1.24169i
\(668\) 3.28856 0.127238
\(669\) 0 0
\(670\) 12.0235 0.464510
\(671\) 0.185556 0.321392i 0.00716331 0.0124072i
\(672\) 0 0
\(673\) −18.8270 32.6094i −0.725729 1.25700i −0.958673 0.284510i \(-0.908169\pi\)
0.232944 0.972490i \(-0.425164\pi\)
\(674\) 3.19188 + 5.52850i 0.122947 + 0.212950i
\(675\) 0 0
\(676\) −4.19619 + 7.26801i −0.161392 + 0.279539i
\(677\) 13.1808 22.8298i 0.506580 0.877422i −0.493391 0.869808i \(-0.664243\pi\)
0.999971 0.00761453i \(-0.00242380\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.89871 3.28866i 0.0728121 0.126114i
\(681\) 0 0
\(682\) 8.28244 0.317151
\(683\) −1.96588 + 3.40500i −0.0752222 + 0.130289i −0.901183 0.433439i \(-0.857300\pi\)
0.825961 + 0.563728i \(0.190633\pi\)
\(684\) 0 0
\(685\) −17.4008 −0.664850
\(686\) 0 0
\(687\) 0 0
\(688\) 1.50076 0.0572158
\(689\) −1.13002 1.95725i −0.0430503 0.0745653i
\(690\) 0 0
\(691\) 9.95052 17.2348i 0.378536 0.655643i −0.612314 0.790615i \(-0.709761\pi\)
0.990849 + 0.134972i \(0.0430944\pi\)
\(692\) 28.3585 1.07803
\(693\) 0 0
\(694\) −12.5373 −0.475910
\(695\) 1.76823 3.06266i 0.0670727 0.116173i
\(696\) 0 0
\(697\) −0.139270 0.241223i −0.00527524 0.00913699i
\(698\) 20.1827 0.763925
\(699\) 0 0
\(700\) 0 0
\(701\) −43.7908 −1.65396 −0.826979 0.562234i \(-0.809942\pi\)
−0.826979 + 0.562234i \(0.809942\pi\)
\(702\) 0 0
\(703\) −2.84983 + 4.93604i −0.107483 + 0.186166i
\(704\) 4.22031 0.159059
\(705\) 0 0
\(706\) 2.09792 3.63370i 0.0789561 0.136756i
\(707\) 0 0
\(708\) 0 0
\(709\) −22.3172 + 38.6545i −0.838139 + 1.45170i 0.0533097 + 0.998578i \(0.483023\pi\)
−0.891449 + 0.453121i \(0.850310\pi\)
\(710\) −0.0384437 + 0.0665865i −0.00144277 + 0.00249895i
\(711\) 0 0
\(712\) 16.0966 + 27.8801i 0.603244 + 1.04485i
\(713\) −6.81163 11.7981i −0.255097 0.441842i
\(714\) 0 0
\(715\) 9.67699 16.7610i 0.361899 0.626827i
\(716\) −11.8245 −0.441904
\(717\) 0 0
\(718\) 6.83411 0.255047
\(719\) −19.5096 33.7917i −0.727586 1.26022i −0.957901 0.287100i \(-0.907309\pi\)
0.230315 0.973116i \(-0.426024\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.965081 1.67157i −0.0359166 0.0622094i
\(723\) 0 0
\(724\) −12.0413 20.8561i −0.447510 0.775109i
\(725\) 10.1130 + 17.5162i 0.375586 + 0.650534i
\(726\) 0 0
\(727\) 11.2554 + 19.4949i 0.417439 + 0.723025i 0.995681 0.0928402i \(-0.0295946\pi\)
−0.578242 + 0.815865i \(0.696261\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 5.10593 + 8.84373i 0.188979 + 0.327321i
\(731\) −1.11590 −0.0412731
\(732\) 0 0
\(733\) 0.897039 0.0331329 0.0165664 0.999863i \(-0.494726\pi\)
0.0165664 + 0.999863i \(0.494726\pi\)
\(734\) 9.60441 16.6353i 0.354505 0.614021i
\(735\) 0 0
\(736\) −15.6837 27.1649i −0.578108 1.00131i
\(737\) 31.0335 + 53.7517i 1.14314 + 1.97997i
\(738\) 0 0
\(739\) 1.79032 3.10092i 0.0658578 0.114069i −0.831216 0.555949i \(-0.812355\pi\)
0.897074 + 0.441880i \(0.145688\pi\)
\(740\) −1.56833 + 2.71643i −0.0576531 + 0.0998581i
\(741\) 0 0
\(742\) 0 0
\(743\) 24.7964 42.9486i 0.909691 1.57563i 0.0951977 0.995458i \(-0.469652\pi\)
0.814493 0.580173i \(-0.197015\pi\)
\(744\) 0 0
\(745\) 12.1917 0.446668
\(746\) −5.38726 + 9.33101i −0.197242 + 0.341633i
\(747\) 0 0
\(748\) 8.56098 0.313020
\(749\) 0 0
\(750\) 0 0
\(751\) −42.9030 −1.56555 −0.782776 0.622304i \(-0.786197\pi\)
−0.782776 + 0.622304i \(0.786197\pi\)
\(752\) 7.13450 + 12.3573i 0.260168 + 0.450625i
\(753\) 0 0
\(754\) −6.28835 + 10.8917i −0.229008 + 0.396654i
\(755\) −25.1633 −0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) −0.341510 + 0.591513i −0.0124042 + 0.0214847i
\(759\) 0 0
\(760\) 6.80856 + 11.7928i 0.246972 + 0.427769i
\(761\) 40.7197 1.47609 0.738044 0.674752i \(-0.235749\pi\)
0.738044 + 0.674752i \(0.235749\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 23.0001 0.832113
\(765\) 0 0
\(766\) −3.88342 + 6.72627i −0.140313 + 0.243030i
\(767\) 18.1365 0.654871
\(768\) 0 0
\(769\) −5.57381 + 9.65413i −0.200997 + 0.348137i −0.948850 0.315728i \(-0.897751\pi\)
0.747853 + 0.663864i \(0.231085\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 12.8454 22.2489i 0.462317 0.800756i
\(773\) −0.462831 + 0.801647i −0.0166469 + 0.0288332i −0.874229 0.485514i \(-0.838632\pi\)
0.857582 + 0.514347i \(0.171966\pi\)
\(774\) 0 0
\(775\) −3.72061 6.44428i −0.133648 0.231485i
\(776\) −6.43012 11.1373i −0.230828 0.399806i
\(777\) 0 0
\(778\) −5.97049 + 10.3412i −0.214052 + 0.370750i
\(779\) 0.998817 0.0357863
\(780\) 0 0
\(781\) −0.396903 −0.0142023
\(782\) 2.04024 + 3.53381i 0.0729590 + 0.126369i
\(783\) 0 0
\(784\) 0 0
\(785\) 4.50386 + 7.80092i 0.160750 + 0.278427i
\(786\) 0 0
\(787\) 11.5120 + 19.9393i 0.410358 + 0.710761i 0.994929 0.100582i \(-0.0320704\pi\)
−0.584571 + 0.811343i \(0.698737\pi\)
\(788\) 3.13030 + 5.42184i 0.111512 + 0.193145i
\(789\) 0 0
\(790\) −0.881115 1.52614i −0.0313487 0.0542975i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.103662 0.179548i −0.00368114 0.00637593i
\(794\) 8.77102 0.311272
\(795\) 0 0