Properties

Label 1323.2.g.h.361.12
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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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: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.12
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.08816 - 1.88474i) q^{2} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} -1.60248 q^{8} +O(q^{10})\) \(q+(1.08816 - 1.88474i) q^{2} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} -1.60248 q^{8} +(1.38010 - 2.39040i) q^{10} +5.47733 q^{11} +(-2.37268 + 4.10960i) q^{13} +(0.992580 - 1.71920i) q^{16} +(2.40822 - 4.17116i) q^{17} +(2.69059 + 4.66025i) q^{19} +(-1.73523 - 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} +5.17631 q^{23} -3.39144 q^{25} +(5.16368 + 8.94376i) q^{26} +(-2.01656 - 3.49278i) q^{29} +(-0.732093 - 1.26802i) q^{31} +(-3.76264 - 6.51709i) q^{32} +(-5.24103 - 9.07773i) q^{34} +(-0.959170 - 1.66133i) q^{37} +11.7111 q^{38} -2.03241 q^{40} +(-1.94808 + 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} +(-7.49389 - 12.9798i) q^{44} +(5.63263 - 9.75600i) q^{46} +(-1.57773 + 2.73271i) q^{47} +(-3.69042 + 6.39199i) q^{50} +12.9849 q^{52} +(-3.57149 + 6.18601i) q^{53} +6.94684 q^{55} -8.77732 q^{58} +(-0.154341 - 0.267327i) q^{59} +(5.17143 - 8.95719i) q^{61} -3.18652 q^{62} -12.4070 q^{64} +(-3.00924 + 5.21216i) q^{65} +(-2.23655 - 3.87382i) q^{67} -13.1794 q^{68} +1.96688 q^{71} +(-5.27515 + 9.13683i) q^{73} -4.17491 q^{74} +(7.36235 - 12.7520i) q^{76} +(4.50822 - 7.80846i) q^{79} +(1.25888 - 2.18044i) q^{80} +(4.23963 + 7.34326i) q^{82} +(-5.08023 - 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} -7.22607 q^{86} -8.77732 q^{88} +(-2.59776 - 4.49945i) q^{89} +(-7.08205 - 12.2665i) q^{92} +(3.43363 + 5.94722i) q^{94} +(3.41245 + 5.91054i) q^{95} +(2.48521 + 4.30451i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08816 1.88474i 0.769442 1.33271i −0.168424 0.985715i \(-0.553868\pi\)
0.937866 0.346998i \(-0.112799\pi\)
\(3\) 0 0
\(4\) −1.36816 2.36973i −0.684082 1.18487i
\(5\) 1.26829 0.567196 0.283598 0.958943i \(-0.408472\pi\)
0.283598 + 0.958943i \(0.408472\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.60248 −0.566563
\(9\) 0 0
\(10\) 1.38010 2.39040i 0.436425 0.755910i
\(11\) 5.47733 1.65148 0.825739 0.564053i \(-0.190759\pi\)
0.825739 + 0.564053i \(0.190759\pi\)
\(12\) 0 0
\(13\) −2.37268 + 4.10960i −0.658062 + 1.13980i 0.323054 + 0.946380i \(0.395290\pi\)
−0.981117 + 0.193417i \(0.938043\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.992580 1.71920i 0.248145 0.429800i
\(17\) 2.40822 4.17116i 0.584079 1.01165i −0.410911 0.911676i \(-0.634789\pi\)
0.994990 0.0999785i \(-0.0318774\pi\)
\(18\) 0 0
\(19\) 2.69059 + 4.66025i 0.617265 + 1.06913i 0.989983 + 0.141189i \(0.0450925\pi\)
−0.372718 + 0.927945i \(0.621574\pi\)
\(20\) −1.73523 3.00550i −0.388009 0.672051i
\(21\) 0 0
\(22\) 5.96019 10.3233i 1.27072 2.20095i
\(23\) 5.17631 1.07934 0.539668 0.841878i \(-0.318550\pi\)
0.539668 + 0.841878i \(0.318550\pi\)
\(24\) 0 0
\(25\) −3.39144 −0.678288
\(26\) 5.16368 + 8.94376i 1.01268 + 1.75402i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.01656 3.49278i −0.374466 0.648594i 0.615781 0.787917i \(-0.288841\pi\)
−0.990247 + 0.139324i \(0.955507\pi\)
\(30\) 0 0
\(31\) −0.732093 1.26802i −0.131488 0.227744i 0.792763 0.609531i \(-0.208642\pi\)
−0.924250 + 0.381787i \(0.875309\pi\)
\(32\) −3.76264 6.51709i −0.665148 1.15207i
\(33\) 0 0
\(34\) −5.24103 9.07773i −0.898830 1.55682i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.959170 1.66133i −0.157687 0.273121i 0.776347 0.630305i \(-0.217070\pi\)
−0.934034 + 0.357184i \(0.883737\pi\)
\(38\) 11.7111 1.89980
\(39\) 0 0
\(40\) −2.03241 −0.321352
\(41\) −1.94808 + 3.37418i −0.304239 + 0.526958i −0.977092 0.212819i \(-0.931736\pi\)
0.672852 + 0.739777i \(0.265069\pi\)
\(42\) 0 0
\(43\) −1.66016 2.87549i −0.253173 0.438508i 0.711225 0.702964i \(-0.248141\pi\)
−0.964398 + 0.264457i \(0.914807\pi\)
\(44\) −7.49389 12.9798i −1.12975 1.95678i
\(45\) 0 0
\(46\) 5.63263 9.75600i 0.830486 1.43844i
\(47\) −1.57773 + 2.73271i −0.230135 + 0.398606i −0.957848 0.287276i \(-0.907250\pi\)
0.727712 + 0.685882i \(0.240584\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.69042 + 6.39199i −0.521904 + 0.903964i
\(51\) 0 0
\(52\) 12.9849 1.80068
\(53\) −3.57149 + 6.18601i −0.490582 + 0.849714i −0.999941 0.0108405i \(-0.996549\pi\)
0.509359 + 0.860554i \(0.329883\pi\)
\(54\) 0 0
\(55\) 6.94684 0.936712
\(56\) 0 0
\(57\) 0 0
\(58\) −8.77732 −1.15252
\(59\) −0.154341 0.267327i −0.0200935 0.0348030i 0.855804 0.517301i \(-0.173063\pi\)
−0.875897 + 0.482498i \(0.839730\pi\)
\(60\) 0 0
\(61\) 5.17143 8.95719i 0.662134 1.14685i −0.317920 0.948118i \(-0.602984\pi\)
0.980054 0.198732i \(-0.0636825\pi\)
\(62\) −3.18652 −0.404689
\(63\) 0 0
\(64\) −12.4070 −1.55088
\(65\) −3.00924 + 5.21216i −0.373250 + 0.646489i
\(66\) 0 0
\(67\) −2.23655 3.87382i −0.273238 0.473262i 0.696451 0.717604i \(-0.254761\pi\)
−0.969689 + 0.244342i \(0.921428\pi\)
\(68\) −13.1794 −1.59823
\(69\) 0 0
\(70\) 0 0
\(71\) 1.96688 0.233426 0.116713 0.993166i \(-0.462764\pi\)
0.116713 + 0.993166i \(0.462764\pi\)
\(72\) 0 0
\(73\) −5.27515 + 9.13683i −0.617409 + 1.06938i 0.372547 + 0.928013i \(0.378484\pi\)
−0.989957 + 0.141371i \(0.954849\pi\)
\(74\) −4.17491 −0.485323
\(75\) 0 0
\(76\) 7.36235 12.7520i 0.844520 1.46275i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.50822 7.80846i 0.507214 0.878520i −0.492751 0.870170i \(-0.664009\pi\)
0.999965 0.00835000i \(-0.00265792\pi\)
\(80\) 1.25888 2.18044i 0.140747 0.243781i
\(81\) 0 0
\(82\) 4.23963 + 7.34326i 0.468189 + 0.810927i
\(83\) −5.08023 8.79921i −0.557627 0.965839i −0.997694 0.0678739i \(-0.978378\pi\)
0.440066 0.897965i \(-0.354955\pi\)
\(84\) 0 0
\(85\) 3.05432 5.29023i 0.331287 0.573806i
\(86\) −7.22607 −0.779207
\(87\) 0 0
\(88\) −8.77732 −0.935666
\(89\) −2.59776 4.49945i −0.275362 0.476941i 0.694864 0.719141i \(-0.255464\pi\)
−0.970226 + 0.242200i \(0.922131\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.08205 12.2665i −0.738354 1.27887i
\(93\) 0 0
\(94\) 3.43363 + 5.94722i 0.354152 + 0.613409i
\(95\) 3.41245 + 5.91054i 0.350110 + 0.606409i
\(96\) 0 0
\(97\) 2.48521 + 4.30451i 0.252335 + 0.437057i 0.964168 0.265291i \(-0.0854682\pi\)
−0.711833 + 0.702348i \(0.752135\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.64005 + 8.03680i 0.464005 + 0.803680i
\(101\) 0.00533808 0.000531159 0.000265580 1.00000i \(-0.499915\pi\)
0.000265580 1.00000i \(0.499915\pi\)
\(102\) 0 0
\(103\) −13.0348 −1.28436 −0.642180 0.766554i \(-0.721970\pi\)
−0.642180 + 0.766554i \(0.721970\pi\)
\(104\) 3.80217 6.58555i 0.372834 0.645767i
\(105\) 0 0
\(106\) 7.77268 + 13.4627i 0.754950 + 1.30761i
\(107\) 4.71081 + 8.15936i 0.455411 + 0.788795i 0.998712 0.0507430i \(-0.0161589\pi\)
−0.543301 + 0.839538i \(0.682826\pi\)
\(108\) 0 0
\(109\) −8.44513 + 14.6274i −0.808896 + 1.40105i 0.104732 + 0.994500i \(0.466601\pi\)
−0.913629 + 0.406549i \(0.866732\pi\)
\(110\) 7.55924 13.0930i 0.720746 1.24837i
\(111\) 0 0
\(112\) 0 0
\(113\) 3.07313 5.32281i 0.289095 0.500728i −0.684499 0.729014i \(-0.739979\pi\)
0.973594 + 0.228286i \(0.0733122\pi\)
\(114\) 0 0
\(115\) 6.56506 0.612195
\(116\) −5.51797 + 9.55741i −0.512331 + 0.887383i
\(117\) 0 0
\(118\) −0.671790 −0.0618432
\(119\) 0 0
\(120\) 0 0
\(121\) 19.0012 1.72738
\(122\) −11.2546 19.4936i −1.01895 1.76487i
\(123\) 0 0
\(124\) −2.00325 + 3.46973i −0.179897 + 0.311591i
\(125\) −10.6428 −0.951919
\(126\) 0 0
\(127\) −13.9305 −1.23613 −0.618065 0.786127i \(-0.712083\pi\)
−0.618065 + 0.786127i \(0.712083\pi\)
\(128\) −5.97551 + 10.3499i −0.528165 + 0.914809i
\(129\) 0 0
\(130\) 6.54905 + 11.3433i 0.574389 + 0.994871i
\(131\) −0.179156 −0.0156529 −0.00782645 0.999969i \(-0.502491\pi\)
−0.00782645 + 0.999969i \(0.502491\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −9.73486 −0.840964
\(135\) 0 0
\(136\) −3.85913 + 6.68420i −0.330917 + 0.573166i
\(137\) −3.15206 −0.269299 −0.134649 0.990893i \(-0.542991\pi\)
−0.134649 + 0.990893i \(0.542991\pi\)
\(138\) 0 0
\(139\) −9.42857 + 16.3308i −0.799721 + 1.38516i 0.120077 + 0.992765i \(0.461686\pi\)
−0.919798 + 0.392392i \(0.871648\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.14027 3.70706i 0.179608 0.311090i
\(143\) −12.9959 + 22.5096i −1.08677 + 1.88235i
\(144\) 0 0
\(145\) −2.55758 4.42986i −0.212396 0.367880i
\(146\) 11.4804 + 19.8846i 0.950122 + 1.64566i
\(147\) 0 0
\(148\) −2.62461 + 4.54595i −0.215741 + 0.373675i
\(149\) 21.2740 1.74284 0.871418 0.490541i \(-0.163201\pi\)
0.871418 + 0.490541i \(0.163201\pi\)
\(150\) 0 0
\(151\) 6.36561 0.518026 0.259013 0.965874i \(-0.416603\pi\)
0.259013 + 0.965874i \(0.416603\pi\)
\(152\) −4.31163 7.46796i −0.349719 0.605731i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.928506 1.60822i −0.0745794 0.129175i
\(156\) 0 0
\(157\) 0.697976 + 1.20893i 0.0557045 + 0.0964830i 0.892533 0.450982i \(-0.148926\pi\)
−0.836828 + 0.547465i \(0.815593\pi\)
\(158\) −9.81128 16.9936i −0.780543 1.35194i
\(159\) 0 0
\(160\) −4.77212 8.26556i −0.377269 0.653450i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.53086 + 16.5079i 0.746515 + 1.29300i 0.949484 + 0.313816i \(0.101608\pi\)
−0.202969 + 0.979185i \(0.565059\pi\)
\(164\) 10.6612 0.832499
\(165\) 0 0
\(166\) −22.1123 −1.71625
\(167\) 0.872003 1.51035i 0.0674776 0.116875i −0.830313 0.557298i \(-0.811838\pi\)
0.897790 + 0.440423i \(0.145172\pi\)
\(168\) 0 0
\(169\) −4.75919 8.24317i −0.366092 0.634090i
\(170\) −6.64715 11.5132i −0.509813 0.883022i
\(171\) 0 0
\(172\) −4.54276 + 7.86828i −0.346382 + 0.599951i
\(173\) 5.03794 8.72598i 0.383028 0.663424i −0.608466 0.793580i \(-0.708215\pi\)
0.991493 + 0.130157i \(0.0415480\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.43669 9.41662i 0.409806 0.709805i
\(177\) 0 0
\(178\) −11.3071 −0.847500
\(179\) −9.27118 + 16.0582i −0.692961 + 1.20024i 0.277902 + 0.960609i \(0.410361\pi\)
−0.970863 + 0.239634i \(0.922973\pi\)
\(180\) 0 0
\(181\) 8.80982 0.654829 0.327414 0.944881i \(-0.393823\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −8.29494 −0.611511
\(185\) −1.21651 2.10705i −0.0894393 0.154913i
\(186\) 0 0
\(187\) 13.1906 22.8468i 0.964593 1.67072i
\(188\) 8.63437 0.629726
\(189\) 0 0
\(190\) 14.8531 1.07756
\(191\) 2.45469 4.25165i 0.177615 0.307639i −0.763448 0.645869i \(-0.776495\pi\)
0.941063 + 0.338231i \(0.109828\pi\)
\(192\) 0 0
\(193\) 4.88380 + 8.45899i 0.351544 + 0.608892i 0.986520 0.163640i \(-0.0523235\pi\)
−0.634976 + 0.772531i \(0.718990\pi\)
\(194\) 10.8172 0.776629
\(195\) 0 0
\(196\) 0 0
\(197\) −3.31445 −0.236145 −0.118073 0.993005i \(-0.537672\pi\)
−0.118073 + 0.993005i \(0.537672\pi\)
\(198\) 0 0
\(199\) 5.54432 9.60304i 0.393026 0.680742i −0.599821 0.800134i \(-0.704761\pi\)
0.992847 + 0.119393i \(0.0380948\pi\)
\(200\) 5.43472 0.384293
\(201\) 0 0
\(202\) 0.00580866 0.0100609i 0.000408696 0.000707883i
\(203\) 0 0
\(204\) 0 0
\(205\) −2.47073 + 4.27943i −0.172563 + 0.298889i
\(206\) −14.1839 + 24.5673i −0.988240 + 1.71168i
\(207\) 0 0
\(208\) 4.71014 + 8.15821i 0.326590 + 0.565670i
\(209\) 14.7373 + 25.5257i 1.01940 + 1.76565i
\(210\) 0 0
\(211\) −3.66118 + 6.34135i −0.252046 + 0.436557i −0.964089 0.265579i \(-0.914437\pi\)
0.712043 + 0.702136i \(0.247770\pi\)
\(212\) 19.5456 1.34240
\(213\) 0 0
\(214\) 20.5044 1.40165
\(215\) −2.10557 3.64695i −0.143599 0.248720i
\(216\) 0 0
\(217\) 0 0
\(218\) 18.3792 + 31.8337i 1.24480 + 2.15605i
\(219\) 0 0
\(220\) −9.50442 16.4621i −0.640788 1.10988i
\(221\) 11.4278 + 19.7936i 0.768720 + 1.33146i
\(222\) 0 0
\(223\) −2.02765 3.51199i −0.135782 0.235181i 0.790114 0.612960i \(-0.210021\pi\)
−0.925896 + 0.377779i \(0.876688\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.68808 11.5841i −0.444884 0.770562i
\(227\) 1.33417 0.0885522 0.0442761 0.999019i \(-0.485902\pi\)
0.0442761 + 0.999019i \(0.485902\pi\)
\(228\) 0 0
\(229\) 15.9966 1.05709 0.528544 0.848906i \(-0.322738\pi\)
0.528544 + 0.848906i \(0.322738\pi\)
\(230\) 7.14381 12.3734i 0.471049 0.815880i
\(231\) 0 0
\(232\) 3.23150 + 5.59712i 0.212158 + 0.367469i
\(233\) 4.06542 + 7.04151i 0.266334 + 0.461305i 0.967912 0.251288i \(-0.0808542\pi\)
−0.701578 + 0.712593i \(0.747521\pi\)
\(234\) 0 0
\(235\) −2.00102 + 3.46586i −0.130532 + 0.226088i
\(236\) −0.422329 + 0.731495i −0.0274913 + 0.0476163i
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0509 + 19.1407i −0.714823 + 1.23811i 0.248204 + 0.968708i \(0.420160\pi\)
−0.963028 + 0.269403i \(0.913174\pi\)
\(240\) 0 0
\(241\) −27.5947 −1.77753 −0.888765 0.458362i \(-0.848436\pi\)
−0.888765 + 0.458362i \(0.848436\pi\)
\(242\) 20.6762 35.8122i 1.32912 2.30210i
\(243\) 0 0
\(244\) −28.3015 −1.81182
\(245\) 0 0
\(246\) 0 0
\(247\) −25.5356 −1.62479
\(248\) 1.17317 + 2.03198i 0.0744961 + 0.129031i
\(249\) 0 0
\(250\) −11.5810 + 20.0589i −0.732447 + 1.26863i
\(251\) −16.5610 −1.04532 −0.522661 0.852541i \(-0.675061\pi\)
−0.522661 + 0.852541i \(0.675061\pi\)
\(252\) 0 0
\(253\) 28.3524 1.78250
\(254\) −15.1585 + 26.2553i −0.951130 + 1.64741i
\(255\) 0 0
\(256\) 0.597516 + 1.03493i 0.0373448 + 0.0646831i
\(257\) 2.06573 0.128857 0.0644285 0.997922i \(-0.479478\pi\)
0.0644285 + 0.997922i \(0.479478\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 16.4686 1.02134
\(261\) 0 0
\(262\) −0.194949 + 0.337662i −0.0120440 + 0.0208608i
\(263\) −10.1296 −0.624620 −0.312310 0.949980i \(-0.601103\pi\)
−0.312310 + 0.949980i \(0.601103\pi\)
\(264\) 0 0
\(265\) −4.52969 + 7.84565i −0.278257 + 0.481954i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.11994 + 10.6000i −0.373835 + 0.647501i
\(269\) 7.54972 13.0765i 0.460315 0.797289i −0.538662 0.842522i \(-0.681070\pi\)
0.998976 + 0.0452336i \(0.0144032\pi\)
\(270\) 0 0
\(271\) −14.4026 24.9459i −0.874893 1.51536i −0.856877 0.515521i \(-0.827598\pi\)
−0.0180156 0.999838i \(-0.505735\pi\)
\(272\) −4.78070 8.28041i −0.289872 0.502074i
\(273\) 0 0
\(274\) −3.42993 + 5.94082i −0.207210 + 0.358898i
\(275\) −18.5760 −1.12018
\(276\) 0 0
\(277\) −2.69963 −0.162205 −0.0811026 0.996706i \(-0.525844\pi\)
−0.0811026 + 0.996706i \(0.525844\pi\)
\(278\) 20.5195 + 35.5408i 1.23068 + 2.13160i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.46312 + 4.26626i 0.146938 + 0.254503i 0.930094 0.367321i \(-0.119725\pi\)
−0.783157 + 0.621825i \(0.786392\pi\)
\(282\) 0 0
\(283\) 1.79079 + 3.10173i 0.106451 + 0.184379i 0.914330 0.404969i \(-0.132718\pi\)
−0.807879 + 0.589348i \(0.799385\pi\)
\(284\) −2.69102 4.66098i −0.159682 0.276578i
\(285\) 0 0
\(286\) 28.2832 + 48.9879i 1.67242 + 2.89672i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.09903 5.36768i −0.182296 0.315746i
\(290\) −11.1322 −0.653704
\(291\) 0 0
\(292\) 28.8691 1.68944
\(293\) 12.1955 21.1232i 0.712469 1.23403i −0.251459 0.967868i \(-0.580910\pi\)
0.963928 0.266164i \(-0.0857563\pi\)
\(294\) 0 0
\(295\) −0.195750 0.339048i −0.0113970 0.0197401i
\(296\) 1.53705 + 2.66225i 0.0893394 + 0.154740i
\(297\) 0 0
\(298\) 23.1494 40.0960i 1.34101 2.32270i
\(299\) −12.2817 + 21.2726i −0.710270 + 1.23022i
\(300\) 0 0
\(301\) 0 0
\(302\) 6.92678 11.9975i 0.398591 0.690380i
\(303\) 0 0
\(304\) 10.6825 0.612685
\(305\) 6.55887 11.3603i 0.375560 0.650489i
\(306\) 0 0
\(307\) 23.9025 1.36419 0.682094 0.731265i \(-0.261070\pi\)
0.682094 + 0.731265i \(0.261070\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.04143 −0.229538
\(311\) 6.47082 + 11.2078i 0.366926 + 0.635535i 0.989083 0.147357i \(-0.0470768\pi\)
−0.622157 + 0.782893i \(0.713743\pi\)
\(312\) 0 0
\(313\) −13.4340 + 23.2684i −0.759336 + 1.31521i 0.183853 + 0.982954i \(0.441143\pi\)
−0.943189 + 0.332255i \(0.892190\pi\)
\(314\) 3.03802 0.171446
\(315\) 0 0
\(316\) −24.6719 −1.38790
\(317\) 4.15584 7.19813i 0.233415 0.404287i −0.725396 0.688332i \(-0.758343\pi\)
0.958811 + 0.284045i \(0.0916765\pi\)
\(318\) 0 0
\(319\) −11.0454 19.1311i −0.618422 1.07114i
\(320\) −15.7357 −0.879654
\(321\) 0 0
\(322\) 0 0
\(323\) 25.9182 1.44212
\(324\) 0 0
\(325\) 8.04680 13.9375i 0.446356 0.773111i
\(326\) 41.4842 2.29760
\(327\) 0 0
\(328\) 3.12177 5.40706i 0.172371 0.298555i
\(329\) 0 0
\(330\) 0 0
\(331\) −6.19889 + 10.7368i −0.340722 + 0.590147i −0.984567 0.175009i \(-0.944005\pi\)
0.643845 + 0.765156i \(0.277338\pi\)
\(332\) −13.9012 + 24.0775i −0.762926 + 1.32143i
\(333\) 0 0
\(334\) −1.89775 3.28700i −0.103840 0.179857i
\(335\) −2.83659 4.91312i −0.154980 0.268433i
\(336\) 0 0
\(337\) −12.9588 + 22.4454i −0.705913 + 1.22268i 0.260448 + 0.965488i \(0.416130\pi\)
−0.966361 + 0.257189i \(0.917204\pi\)
\(338\) −20.7150 −1.12675
\(339\) 0 0
\(340\) −16.7152 −0.906511
\(341\) −4.00992 6.94538i −0.217149 0.376113i
\(342\) 0 0
\(343\) 0 0
\(344\) 2.66038 + 4.60792i 0.143438 + 0.248442i
\(345\) 0 0
\(346\) −10.9641 18.9904i −0.589435 1.02093i
\(347\) −8.42415 14.5911i −0.452232 0.783289i 0.546292 0.837595i \(-0.316039\pi\)
−0.998524 + 0.0543058i \(0.982705\pi\)
\(348\) 0 0
\(349\) −15.5503 26.9340i −0.832390 1.44174i −0.896138 0.443776i \(-0.853639\pi\)
0.0637477 0.997966i \(-0.479695\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −20.6092 35.6963i −1.09848 1.90262i
\(353\) 2.65938 0.141544 0.0707722 0.997493i \(-0.477454\pi\)
0.0707722 + 0.997493i \(0.477454\pi\)
\(354\) 0 0
\(355\) 2.49457 0.132398
\(356\) −7.10833 + 12.3120i −0.376741 + 0.652534i
\(357\) 0 0
\(358\) 20.1770 + 34.9476i 1.06639 + 1.84704i
\(359\) −16.2715 28.1830i −0.858775 1.48744i −0.873098 0.487545i \(-0.837893\pi\)
0.0143230 0.999897i \(-0.495441\pi\)
\(360\) 0 0
\(361\) −4.97859 + 8.62318i −0.262031 + 0.453852i
\(362\) 9.58646 16.6042i 0.503853 0.872699i
\(363\) 0 0
\(364\) 0 0
\(365\) −6.69042 + 11.5881i −0.350192 + 0.606551i
\(366\) 0 0
\(367\) −14.1536 −0.738809 −0.369405 0.929269i \(-0.620438\pi\)
−0.369405 + 0.929269i \(0.620438\pi\)
\(368\) 5.13790 8.89911i 0.267832 0.463898i
\(369\) 0 0
\(370\) −5.29499 −0.275273
\(371\) 0 0
\(372\) 0 0
\(373\) 2.67628 0.138573 0.0692863 0.997597i \(-0.477928\pi\)
0.0692863 + 0.997597i \(0.477928\pi\)
\(374\) −28.7069 49.7217i −1.48440 2.57105i
\(375\) 0 0
\(376\) 2.52828 4.37911i 0.130386 0.225835i
\(377\) 19.1386 0.985687
\(378\) 0 0
\(379\) −0.312929 −0.0160741 −0.00803705 0.999968i \(-0.502558\pi\)
−0.00803705 + 0.999968i \(0.502558\pi\)
\(380\) 9.33759 16.1732i 0.479008 0.829667i
\(381\) 0 0
\(382\) −5.34218 9.25292i −0.273330 0.473421i
\(383\) −8.98880 −0.459306 −0.229653 0.973273i \(-0.573759\pi\)
−0.229653 + 0.973273i \(0.573759\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.2573 1.08197
\(387\) 0 0
\(388\) 6.80036 11.7786i 0.345236 0.597966i
\(389\) 26.9869 1.36829 0.684144 0.729347i \(-0.260176\pi\)
0.684144 + 0.729347i \(0.260176\pi\)
\(390\) 0 0
\(391\) 12.4657 21.5912i 0.630417 1.09191i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.60664 + 6.24689i −0.181700 + 0.314714i
\(395\) 5.71772 9.90339i 0.287690 0.498293i
\(396\) 0 0
\(397\) 14.7503 + 25.5482i 0.740295 + 1.28223i 0.952361 + 0.304973i \(0.0986475\pi\)
−0.212066 + 0.977255i \(0.568019\pi\)
\(398\) −12.0662 20.8992i −0.604822 1.04758i
\(399\) 0 0
\(400\) −3.36628 + 5.83056i −0.168314 + 0.291528i
\(401\) 34.2784 1.71178 0.855891 0.517156i \(-0.173009\pi\)
0.855891 + 0.517156i \(0.173009\pi\)
\(402\) 0 0
\(403\) 6.94808 0.346109
\(404\) −0.00730338 0.0126498i −0.000363357 0.000629352i
\(405\) 0 0
\(406\) 0 0
\(407\) −5.25369 9.09966i −0.260416 0.451054i
\(408\) 0 0
\(409\) 5.49225 + 9.51286i 0.271574 + 0.470381i 0.969265 0.246018i \(-0.0791224\pi\)
−0.697691 + 0.716399i \(0.745789\pi\)
\(410\) 5.37708 + 9.31338i 0.265555 + 0.459955i
\(411\) 0 0
\(412\) 17.8338 + 30.8890i 0.878608 + 1.52179i
\(413\) 0 0
\(414\) 0 0
\(415\) −6.44320 11.1599i −0.316284 0.547820i
\(416\) 35.7102 1.75083
\(417\) 0 0
\(418\) 64.1458 3.13747
\(419\) −3.33207 + 5.77132i −0.162782 + 0.281947i −0.935866 0.352357i \(-0.885380\pi\)
0.773083 + 0.634305i \(0.218714\pi\)
\(420\) 0 0
\(421\) −17.0430 29.5193i −0.830625 1.43868i −0.897543 0.440926i \(-0.854650\pi\)
0.0669186 0.997758i \(-0.478683\pi\)
\(422\) 7.96787 + 13.8008i 0.387870 + 0.671810i
\(423\) 0 0
\(424\) 5.72325 9.91297i 0.277946 0.481416i
\(425\) −8.16733 + 14.1462i −0.396174 + 0.686193i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.8903 22.3267i 0.623077 1.07920i
\(429\) 0 0
\(430\) −9.16474 −0.441963
\(431\) 1.12969 1.95669i 0.0544155 0.0942504i −0.837535 0.546384i \(-0.816004\pi\)
0.891950 + 0.452134i \(0.149337\pi\)
\(432\) 0 0
\(433\) −34.3904 −1.65270 −0.826348 0.563160i \(-0.809585\pi\)
−0.826348 + 0.563160i \(0.809585\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 46.2173 2.21341
\(437\) 13.9274 + 24.1229i 0.666236 + 1.15395i
\(438\) 0 0
\(439\) 2.99569 5.18869i 0.142977 0.247643i −0.785640 0.618684i \(-0.787666\pi\)
0.928616 + 0.371042i \(0.120999\pi\)
\(440\) −11.1322 −0.530706
\(441\) 0 0
\(442\) 49.7411 2.36594
\(443\) −19.7190 + 34.1543i −0.936879 + 1.62272i −0.165630 + 0.986188i \(0.552966\pi\)
−0.771249 + 0.636534i \(0.780368\pi\)
\(444\) 0 0
\(445\) −3.29471 5.70661i −0.156184 0.270519i
\(446\) −8.82560 −0.417904
\(447\) 0 0
\(448\) 0 0
\(449\) −2.45092 −0.115666 −0.0578330 0.998326i \(-0.518419\pi\)
−0.0578330 + 0.998326i \(0.518419\pi\)
\(450\) 0 0
\(451\) −10.6703 + 18.4815i −0.502444 + 0.870259i
\(452\) −16.8182 −0.791060
\(453\) 0 0
\(454\) 1.45179 2.51457i 0.0681358 0.118015i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.51058 + 9.54461i −0.257774 + 0.446478i −0.965645 0.259864i \(-0.916322\pi\)
0.707871 + 0.706342i \(0.249656\pi\)
\(458\) 17.4068 30.1495i 0.813368 1.40879i
\(459\) 0 0
\(460\) −8.98208 15.5574i −0.418792 0.725369i
\(461\) 14.6540 + 25.3814i 0.682503 + 1.18213i 0.974215 + 0.225624i \(0.0724420\pi\)
−0.291711 + 0.956506i \(0.594225\pi\)
\(462\) 0 0
\(463\) 0.593566 1.02809i 0.0275853 0.0477792i −0.851903 0.523699i \(-0.824552\pi\)
0.879489 + 0.475920i \(0.157885\pi\)
\(464\) −8.00639 −0.371687
\(465\) 0 0
\(466\) 17.6952 0.819715
\(467\) −11.0573 19.1519i −0.511673 0.886243i −0.999908 0.0135313i \(-0.995693\pi\)
0.488236 0.872712i \(-0.337641\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4.35483 + 7.54280i 0.200874 + 0.347923i
\(471\) 0 0
\(472\) 0.247329 + 0.428387i 0.0113842 + 0.0197181i
\(473\) −9.09327 15.7500i −0.418109 0.724186i
\(474\) 0 0
\(475\) −9.12499 15.8050i −0.418683 0.725181i
\(476\) 0 0
\(477\) 0 0
\(478\) 24.0502 + 41.6562i 1.10003 + 1.90531i
\(479\) −25.1428 −1.14880 −0.574402 0.818573i \(-0.694766\pi\)
−0.574402 + 0.818573i \(0.694766\pi\)
\(480\) 0 0
\(481\) 9.10321 0.415071
\(482\) −30.0273 + 52.0088i −1.36771 + 2.36894i
\(483\) 0 0
\(484\) −25.9967 45.0276i −1.18167 2.04671i
\(485\) 3.15197 + 5.45937i 0.143123 + 0.247897i
\(486\) 0 0
\(487\) −6.78904 + 11.7590i −0.307641 + 0.532849i −0.977846 0.209327i \(-0.932873\pi\)
0.670205 + 0.742176i \(0.266206\pi\)
\(488\) −8.28713 + 14.3537i −0.375141 + 0.649763i
\(489\) 0 0
\(490\) 0 0
\(491\) −7.25177 + 12.5604i −0.327268 + 0.566844i −0.981969 0.189044i \(-0.939461\pi\)
0.654701 + 0.755888i \(0.272795\pi\)
\(492\) 0 0
\(493\) −19.4253 −0.874870
\(494\) −27.7868 + 48.1281i −1.25019 + 2.16538i
\(495\) 0 0
\(496\) −2.90664 −0.130512
\(497\) 0 0
\(498\) 0 0
\(499\) 13.9915 0.626345 0.313172 0.949696i \(-0.398608\pi\)
0.313172 + 0.949696i \(0.398608\pi\)
\(500\) 14.5611 + 25.2205i 0.651191 + 1.12790i
\(501\) 0 0
\(502\) −18.0209 + 31.2132i −0.804314 + 1.39311i
\(503\) 28.4011 1.26634 0.633171 0.774012i \(-0.281753\pi\)
0.633171 + 0.774012i \(0.281753\pi\)
\(504\) 0 0
\(505\) 0.00677023 0.000301271
\(506\) 30.8518 53.4369i 1.37153 2.37556i
\(507\) 0 0
\(508\) 19.0592 + 33.0115i 0.845615 + 1.46465i
\(509\) −3.45993 −0.153359 −0.0766794 0.997056i \(-0.524432\pi\)
−0.0766794 + 0.997056i \(0.524432\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −21.3013 −0.941392
\(513\) 0 0
\(514\) 2.24784 3.89337i 0.0991480 0.171729i
\(515\) −16.5319 −0.728484
\(516\) 0 0
\(517\) −8.64174 + 14.9679i −0.380063 + 0.658289i
\(518\) 0 0
\(519\) 0 0
\(520\) 4.82225 8.35239i 0.211470 0.366276i
\(521\) −3.56797 + 6.17991i −0.156316 + 0.270747i −0.933537 0.358480i \(-0.883295\pi\)
0.777222 + 0.629227i \(0.216628\pi\)
\(522\) 0 0
\(523\) −6.53235 11.3144i −0.285640 0.494743i 0.687124 0.726540i \(-0.258873\pi\)
−0.972764 + 0.231797i \(0.925539\pi\)
\(524\) 0.245114 + 0.424551i 0.0107079 + 0.0185466i
\(525\) 0 0
\(526\) −11.0226 + 19.0917i −0.480609 + 0.832439i
\(527\) −7.05216 −0.307197
\(528\) 0 0
\(529\) 3.79420 0.164965
\(530\) 9.85801 + 17.0746i 0.428205 + 0.741672i
\(531\) 0 0
\(532\) 0 0
\(533\) −9.24434 16.0117i −0.400417 0.693542i
\(534\) 0 0
\(535\) 5.97467 + 10.3484i 0.258308 + 0.447402i
\(536\) 3.58403 + 6.20772i 0.154807 + 0.268133i
\(537\) 0 0
\(538\) −16.4305 28.4585i −0.708371 1.22693i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.46788 4.27450i −0.106103 0.183775i 0.808086 0.589065i \(-0.200504\pi\)
−0.914188 + 0.405290i \(0.867171\pi\)
\(542\) −62.6889 −2.69272
\(543\) 0 0
\(544\) −36.2451 −1.55399
\(545\) −10.7109 + 18.5518i −0.458803 + 0.794670i
\(546\) 0 0
\(547\) 0.559964 + 0.969887i 0.0239423 + 0.0414694i 0.877748 0.479122i \(-0.159045\pi\)
−0.853806 + 0.520591i \(0.825712\pi\)
\(548\) 4.31254 + 7.46954i 0.184223 + 0.319083i
\(549\) 0 0
\(550\) −20.2136 + 35.0110i −0.861912 + 1.49288i
\(551\) 10.8515 18.7953i 0.462289 0.800708i
\(552\) 0 0
\(553\) 0 0
\(554\) −2.93762 + 5.08811i −0.124808 + 0.216173i
\(555\) 0 0
\(556\) 51.5993 2.18830
\(557\) −5.47832 + 9.48873i −0.232124 + 0.402050i −0.958433 0.285318i \(-0.907901\pi\)
0.726309 + 0.687368i \(0.241234\pi\)
\(558\) 0 0
\(559\) 15.7561 0.666413
\(560\) 0 0
\(561\) 0 0
\(562\) 10.7210 0.452240
\(563\) 2.38048 + 4.12311i 0.100325 + 0.173768i 0.911819 0.410593i \(-0.134678\pi\)
−0.811493 + 0.584361i \(0.801345\pi\)
\(564\) 0 0
\(565\) 3.89761 6.75087i 0.163974 0.284011i
\(566\) 7.79462 0.327632
\(567\) 0 0
\(568\) −3.15189 −0.132250
\(569\) 1.74988 3.03088i 0.0733588 0.127061i −0.827013 0.562183i \(-0.809962\pi\)
0.900371 + 0.435122i \(0.143295\pi\)
\(570\) 0 0
\(571\) −3.53051 6.11501i −0.147747 0.255905i 0.782647 0.622465i \(-0.213869\pi\)
−0.930394 + 0.366560i \(0.880535\pi\)
\(572\) 71.1223 2.97377
\(573\) 0 0
\(574\) 0 0
\(575\) −17.5552 −0.732101
\(576\) 0 0
\(577\) 6.44149 11.1570i 0.268163 0.464472i −0.700225 0.713923i \(-0.746917\pi\)
0.968387 + 0.249451i \(0.0802502\pi\)
\(578\) −13.4889 −0.561064
\(579\) 0 0
\(580\) −6.99838 + 12.1216i −0.290592 + 0.503320i
\(581\) 0 0
\(582\) 0 0
\(583\) −19.5623 + 33.8828i −0.810186 + 1.40328i
\(584\) 8.45333 14.6416i 0.349801 0.605874i
\(585\) 0 0
\(586\) −26.5412 45.9707i −1.09641 1.89903i
\(587\) −19.5044 33.7826i −0.805034 1.39436i −0.916268 0.400565i \(-0.868814\pi\)
0.111235 0.993794i \(-0.464519\pi\)
\(588\) 0 0
\(589\) 3.93953 6.82347i 0.162326 0.281156i
\(590\) −0.852024 −0.0350773
\(591\) 0 0
\(592\) −3.80821 −0.156517
\(593\) −20.1513 34.9031i −0.827515 1.43330i −0.899982 0.435927i \(-0.856421\pi\)
0.0724676 0.997371i \(-0.476913\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −29.1064 50.4137i −1.19224 2.06503i
\(597\) 0 0
\(598\) 26.7288 + 46.2957i 1.09302 + 1.89317i
\(599\) −6.39103 11.0696i −0.261130 0.452291i 0.705412 0.708797i \(-0.250762\pi\)
−0.966543 + 0.256506i \(0.917429\pi\)
\(600\) 0 0
\(601\) 4.86311 + 8.42316i 0.198371 + 0.343588i 0.948000 0.318270i \(-0.103102\pi\)
−0.749630 + 0.661858i \(0.769768\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.70921 15.0848i −0.354373 0.613792i
\(605\) 24.0990 0.979762
\(606\) 0 0
\(607\) −41.4873 −1.68392 −0.841959 0.539541i \(-0.818598\pi\)
−0.841959 + 0.539541i \(0.818598\pi\)
\(608\) 20.2475 35.0697i 0.821145 1.42226i
\(609\) 0 0
\(610\) −14.2742 24.7236i −0.577943 1.00103i
\(611\) −7.48688 12.9677i −0.302887 0.524615i
\(612\) 0 0
\(613\) −7.64783 + 13.2464i −0.308893 + 0.535018i −0.978120 0.208039i \(-0.933292\pi\)
0.669228 + 0.743057i \(0.266625\pi\)
\(614\) 26.0096 45.0500i 1.04966 1.81807i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.66563 4.61700i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(618\) 0 0
\(619\) 12.6841 0.509817 0.254908 0.966965i \(-0.417955\pi\)
0.254908 + 0.966965i \(0.417955\pi\)
\(620\) −2.54070 + 4.40062i −0.102037 + 0.176733i
\(621\) 0 0
\(622\) 28.1650 1.12931
\(623\) 0 0
\(624\) 0 0
\(625\) 3.45909 0.138363
\(626\) 29.2366 + 50.6393i 1.16853 + 2.02395i
\(627\) 0 0
\(628\) 1.90989 3.30803i 0.0762129 0.132005i
\(629\) −9.23957 −0.368406
\(630\) 0 0
\(631\) 0.123764 0.00492698 0.00246349 0.999997i \(-0.499216\pi\)
0.00246349 + 0.999997i \(0.499216\pi\)
\(632\) −7.22433 + 12.5129i −0.287369 + 0.497737i
\(633\) 0 0
\(634\) −9.04441 15.6654i −0.359199 0.622151i
\(635\) −17.6679 −0.701128
\(636\) 0 0
\(637\) 0 0
\(638\) −48.0763 −1.90336
\(639\) 0 0
\(640\) −7.57868 + 13.1267i −0.299573 + 0.518876i
\(641\) −5.93177 −0.234291 −0.117145 0.993115i \(-0.537374\pi\)
−0.117145 + 0.993115i \(0.537374\pi\)
\(642\) 0 0
\(643\) 23.4140 40.5542i 0.923358 1.59930i 0.129178 0.991621i \(-0.458766\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 28.2030 48.8490i 1.10963 1.92194i
\(647\) 19.5701 33.8964i 0.769379 1.33260i −0.168521 0.985698i \(-0.553899\pi\)
0.937900 0.346905i \(-0.112767\pi\)
\(648\) 0 0
\(649\) −0.845379 1.46424i −0.0331840 0.0574764i
\(650\) −17.5123 30.3322i −0.686890 1.18973i
\(651\) 0 0
\(652\) 26.0796 45.1711i 1.02135 1.76904i
\(653\) −43.3281 −1.69556 −0.847779 0.530350i \(-0.822061\pi\)
−0.847779 + 0.530350i \(0.822061\pi\)
\(654\) 0 0
\(655\) −0.227221 −0.00887827
\(656\) 3.86726 + 6.69828i 0.150991 + 0.261524i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.43895 5.95643i −0.133962 0.232030i 0.791238 0.611508i \(-0.209437\pi\)
−0.925201 + 0.379478i \(0.876103\pi\)
\(660\) 0 0
\(661\) 19.3835 + 33.5733i 0.753932 + 1.30585i 0.945903 + 0.324449i \(0.105179\pi\)
−0.191971 + 0.981401i \(0.561488\pi\)
\(662\) 13.4907 + 23.3666i 0.524331 + 0.908168i
\(663\) 0 0
\(664\) 8.14097 + 14.1006i 0.315931 + 0.547209i
\(665\) 0 0
\(666\) 0 0
\(667\) −10.4383 18.0797i −0.404174 0.700050i
\(668\) −4.77217 −0.184641
\(669\) 0 0
\(670\) −12.3466 −0.476991
\(671\) 28.3257 49.0615i 1.09350 1.89400i
\(672\) 0 0
\(673\) 17.9897 + 31.1591i 0.693452 + 1.20109i 0.970700 + 0.240295i \(0.0772443\pi\)
−0.277248 + 0.960798i \(0.589422\pi\)
\(674\) 28.2025 + 48.8481i 1.08632 + 1.88156i
\(675\) 0 0
\(676\) −13.0227 + 22.5560i −0.500874 + 0.867539i
\(677\) −2.23329 + 3.86817i −0.0858322 + 0.148666i −0.905746 0.423822i \(-0.860688\pi\)
0.819913 + 0.572488i \(0.194022\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.89449 + 8.47750i −0.187695 + 0.325097i
\(681\) 0 0
\(682\) −17.4536 −0.668335
\(683\) −13.3356 + 23.0980i −0.510274 + 0.883821i 0.489655 + 0.871916i \(0.337123\pi\)
−0.999929 + 0.0119046i \(0.996211\pi\)
\(684\) 0 0
\(685\) −3.99773 −0.152745
\(686\) 0 0
\(687\) 0 0
\(688\) −6.59138 −0.251294
\(689\) −16.9480 29.3548i −0.645668 1.11833i
\(690\) 0 0
\(691\) −20.5220 + 35.5452i −0.780694 + 1.35220i 0.150844 + 0.988558i \(0.451801\pi\)
−0.931538 + 0.363644i \(0.881532\pi\)
\(692\) −27.5709 −1.04809
\(693\) 0 0
\(694\) −36.6671 −1.39187
\(695\) −11.9582 + 20.7121i −0.453599 + 0.785656i
\(696\) 0 0
\(697\) 9.38281 + 16.2515i 0.355399 + 0.615570i
\(698\) −67.6847 −2.56190
\(699\) 0 0
\(700\) 0 0
\(701\) −9.63355 −0.363854 −0.181927 0.983312i \(-0.558233\pi\)
−0.181927 + 0.983312i \(0.558233\pi\)
\(702\) 0 0
\(703\) 5.16148 8.93994i 0.194669 0.337176i
\(704\) −67.9575 −2.56125
\(705\) 0 0
\(706\) 2.89382 5.01224i 0.108910 0.188638i
\(707\) 0 0
\(708\) 0 0
\(709\) 5.07131 8.78376i 0.190457 0.329881i −0.754945 0.655788i \(-0.772336\pi\)
0.945402 + 0.325907i \(0.105670\pi\)
\(710\) 2.71448 4.70162i 0.101873 0.176449i
\(711\) 0 0
\(712\) 4.16286 + 7.21029i 0.156010 + 0.270217i
\(713\) −3.78954 6.56368i −0.141919 0.245812i
\(714\) 0 0
\(715\) −16.4826 + 28.5487i −0.616415 + 1.06766i
\(716\) 50.7380 1.89617
\(717\) 0 0
\(718\) −70.8235 −2.64311
\(719\) 20.6844 + 35.8264i 0.771397 + 1.33610i 0.936797 + 0.349873i \(0.113775\pi\)
−0.165400 + 0.986227i \(0.552891\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10.8350 + 18.7667i 0.403236 + 0.698425i
\(723\) 0 0
\(724\) −12.0533 20.8769i −0.447957 0.775884i
\(725\) 6.83904 + 11.8456i 0.253996 + 0.439934i
\(726\) 0 0
\(727\) 4.86372 + 8.42422i 0.180386 + 0.312437i 0.942012 0.335580i \(-0.108932\pi\)
−0.761626 + 0.648016i \(0.775599\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 14.5604 + 25.2194i 0.538906 + 0.933412i
\(731\) −15.9921 −0.591491
\(732\) 0 0
\(733\) −28.9108 −1.06784 −0.533922 0.845534i \(-0.679282\pi\)
−0.533922 + 0.845534i \(0.679282\pi\)
\(734\) −15.4013 + 26.6758i −0.568471 + 0.984621i
\(735\) 0 0
\(736\) −19.4766 33.7345i −0.717918 1.24347i
\(737\) −12.2503 21.2182i −0.451247 0.781582i
\(738\) 0 0
\(739\) 6.67467 11.5609i 0.245532 0.425273i −0.716749 0.697331i \(-0.754371\pi\)
0.962281 + 0.272058i \(0.0877041\pi\)
\(740\) −3.32876 + 5.76558i −0.122368 + 0.211947i
\(741\) 0 0
\(742\) 0 0
\(743\) −19.9100 + 34.4851i −0.730425 + 1.26513i 0.226276 + 0.974063i \(0.427345\pi\)
−0.956702 + 0.291071i \(0.905988\pi\)
\(744\) 0 0
\(745\) 26.9816 0.988530
\(746\) 2.91221 5.04410i 0.106624 0.184678i
\(747\) 0 0
\(748\) −72.1877 −2.63944
\(749\) 0 0
\(750\) 0 0
\(751\) −38.4345 −1.40250 −0.701248 0.712917i \(-0.747374\pi\)
−0.701248 + 0.712917i \(0.747374\pi\)
\(752\) 3.13204 + 5.42486i 0.114214 + 0.197824i
\(753\) 0 0
\(754\) 20.8258 36.0713i 0.758429 1.31364i
\(755\) 8.07344 0.293823
\(756\) 0 0
\(757\) −5.66698 −0.205970 −0.102985 0.994683i \(-0.532839\pi\)
−0.102985 + 0.994683i \(0.532839\pi\)
\(758\) −0.340516 + 0.589791i −0.0123681 + 0.0214222i
\(759\) 0 0
\(760\) −5.46839 9.47153i −0.198359 0.343569i
\(761\) 52.3321 1.89704 0.948519 0.316719i \(-0.102581\pi\)
0.948519 + 0.316719i \(0.102581\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13.4337 −0.486014
\(765\) 0 0
\(766\) −9.78121 + 16.9416i −0.353410 + 0.612123i
\(767\) 1.46481 0.0528912
\(768\) 0 0
\(769\) −1.17360 + 2.03274i −0.0423212 + 0.0733025i −0.886410 0.462901i \(-0.846809\pi\)
0.844089 + 0.536203i \(0.180142\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.3637 23.1466i 0.480970 0.833064i
\(773\) −18.1814 + 31.4912i −0.653941 + 1.13266i 0.328217 + 0.944602i \(0.393552\pi\)
−0.982158 + 0.188057i \(0.939781\pi\)
\(774\) 0 0
\(775\) 2.48285 + 4.30042i 0.0891866 + 0.154476i
\(776\) −3.98251 6.89790i −0.142964 0.247620i
\(777\) 0 0
\(778\) 29.3659 50.8633i 1.05282 1.82354i
\(779\) −20.9660 −0.751185
\(780\) 0 0
\(781\) 10.7733 0.385497
\(782\) −27.1292 46.9892i −0.970139 1.68033i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.885235 + 1.53327i 0.0315954 + 0.0547248i
\(786\) 0 0
\(787\) −15.8846 27.5129i −0.566224 0.980729i −0.996935 0.0782386i \(-0.975070\pi\)
0.430711 0.902490i \(-0.358263\pi\)
\(788\) 4.53472 + 7.85437i 0.161543 + 0.279800i
\(789\) 0 0
\(790\) −12.4435 21.5528i −0.442721 0.766816i
\(791\) 0 0
\(792\) 0 0
\(793\) 24.5403 + 42.5050i 0.871451 + 1.50940i
\(794\) 64.2024 2.27846
\(795\) 0 0
\(796\) −30.3422 −1.07545