Properties

Label 441.4.e.u.226.1
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.u.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +O(q^{10})\) \(q+(-0.207107 + 0.358719i) q^{2} +(3.91421 + 6.77962i) q^{4} +(-0.0502525 + 0.0870399i) q^{5} -6.55635 q^{8} +(-0.0208153 - 0.0360531i) q^{10} +(-21.9706 - 38.0541i) q^{11} -16.6447 q^{13} +(-29.9558 + 51.8850i) q^{16} +(-60.8198 - 105.343i) q^{17} +(63.5563 - 110.083i) q^{19} -0.786797 q^{20} +18.2010 q^{22} +(26.7990 - 46.4172i) q^{23} +(62.4949 + 108.244i) q^{25} +(3.44722 - 5.97076i) q^{26} -235.681 q^{29} +(9.35534 + 16.2039i) q^{31} +(-38.6335 - 66.9152i) q^{32} +50.3848 q^{34} +(95.9411 - 166.175i) q^{37} +(26.3259 + 45.5978i) q^{38} +(0.329473 - 0.570664i) q^{40} +319.713 q^{41} -218.579 q^{43} +(171.995 - 297.904i) q^{44} +(11.1005 + 19.2266i) q^{46} +(200.777 - 347.755i) q^{47} -51.7725 q^{50} +(-65.1508 - 112.844i) q^{52} +(321.558 + 556.956i) q^{53} +4.41631 q^{55} +(48.8112 - 84.5434i) q^{58} +(-5.80613 - 10.0565i) q^{59} +(6.12132 - 10.6024i) q^{61} -7.75022 q^{62} -447.288 q^{64} +(0.836436 - 1.44875i) q^{65} +(-334.524 - 579.412i) q^{67} +(476.123 - 824.670i) q^{68} -822.098 q^{71} +(-257.550 - 446.089i) q^{73} +(39.7401 + 68.8319i) q^{74} +995.092 q^{76} +(402.877 - 697.804i) q^{79} +(-3.01071 - 5.21471i) q^{80} +(-66.2147 + 114.687i) q^{82} +394.863 q^{83} +12.2254 q^{85} +(45.2691 - 78.4084i) q^{86} +(144.047 + 249.496i) q^{88} +(336.709 - 583.197i) q^{89} +419.588 q^{92} +(83.1644 + 144.045i) q^{94} +(6.38773 + 11.0639i) q^{95} -1091.11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 10q^{4} - 20q^{5} + 36q^{8} + O(q^{10}) \) \( 4q + 2q^{2} + 10q^{4} - 20q^{5} + 36q^{8} + 48q^{10} - 20q^{11} - 208q^{13} - 18q^{16} - 116q^{17} + 192q^{19} - 88q^{20} + 152q^{22} + 28q^{23} - 146q^{25} - 204q^{26} - 592q^{29} - 104q^{31} + 18q^{32} + 128q^{34} + 248q^{37} - 104q^{38} - 488q^{40} + 40q^{41} - 1440q^{43} + 292q^{44} + 84q^{46} + 96q^{47} - 1412q^{50} - 320q^{52} + 268q^{53} - 944q^{55} - 48q^{58} + 616q^{59} + 16q^{61} - 608q^{62} + 236q^{64} + 1740q^{65} + 144q^{67} + 940q^{68} - 1976q^{71} + 104q^{73} - 56q^{74} + 2272q^{76} + 944q^{79} + 828q^{80} - 856q^{82} + 2032q^{83} - 200q^{85} - 1120q^{86} + 876q^{88} + 388q^{89} + 728q^{92} + 904q^{94} + 1304q^{95} - 976q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 + 0.358719i −0.0732233 + 0.126826i −0.900312 0.435245i \(-0.856662\pi\)
0.827089 + 0.562071i \(0.189995\pi\)
\(3\) 0 0
\(4\) 3.91421 + 6.77962i 0.489277 + 0.847452i
\(5\) −0.0502525 + 0.0870399i −0.00449472 + 0.00778509i −0.868264 0.496102i \(-0.834764\pi\)
0.863769 + 0.503887i \(0.168097\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −6.55635 −0.289752
\(9\) 0 0
\(10\) −0.0208153 0.0360531i −0.000658237 0.00114010i
\(11\) −21.9706 38.0541i −0.602216 1.04307i −0.992485 0.122368i \(-0.960951\pi\)
0.390269 0.920701i \(-0.372382\pi\)
\(12\) 0 0
\(13\) −16.6447 −0.355108 −0.177554 0.984111i \(-0.556818\pi\)
−0.177554 + 0.984111i \(0.556818\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −29.9558 + 51.8850i −0.468060 + 0.810704i
\(17\) −60.8198 105.343i −0.867704 1.50291i −0.864337 0.502913i \(-0.832262\pi\)
−0.00336718 0.999994i \(-0.501072\pi\)
\(18\) 0 0
\(19\) 63.5563 110.083i 0.767412 1.32920i −0.171550 0.985175i \(-0.554878\pi\)
0.938962 0.344021i \(-0.111789\pi\)
\(20\) −0.786797 −0.00879665
\(21\) 0 0
\(22\) 18.2010 0.176385
\(23\) 26.7990 46.4172i 0.242955 0.420811i −0.718599 0.695424i \(-0.755216\pi\)
0.961555 + 0.274613i \(0.0885498\pi\)
\(24\) 0 0
\(25\) 62.4949 + 108.244i 0.499960 + 0.865955i
\(26\) 3.44722 5.97076i 0.0260021 0.0450370i
\(27\) 0 0
\(28\) 0 0
\(29\) −235.681 −1.50913 −0.754567 0.656223i \(-0.772153\pi\)
−0.754567 + 0.656223i \(0.772153\pi\)
\(30\) 0 0
\(31\) 9.35534 + 16.2039i 0.0542022 + 0.0938810i 0.891853 0.452324i \(-0.149405\pi\)
−0.837651 + 0.546205i \(0.816072\pi\)
\(32\) −38.6335 66.9152i −0.213422 0.369658i
\(33\) 0 0
\(34\) 50.3848 0.254145
\(35\) 0 0
\(36\) 0 0
\(37\) 95.9411 166.175i 0.426287 0.738351i −0.570253 0.821469i \(-0.693155\pi\)
0.996540 + 0.0831185i \(0.0264880\pi\)
\(38\) 26.3259 + 45.5978i 0.112385 + 0.194656i
\(39\) 0 0
\(40\) 0.329473 0.570664i 0.00130236 0.00225575i
\(41\) 319.713 1.21782 0.608912 0.793238i \(-0.291606\pi\)
0.608912 + 0.793238i \(0.291606\pi\)
\(42\) 0 0
\(43\) −218.579 −0.775184 −0.387592 0.921831i \(-0.626693\pi\)
−0.387592 + 0.921831i \(0.626693\pi\)
\(44\) 171.995 297.904i 0.589300 1.02070i
\(45\) 0 0
\(46\) 11.1005 + 19.2266i 0.0355800 + 0.0616264i
\(47\) 200.777 347.755i 0.623113 1.07926i −0.365790 0.930697i \(-0.619201\pi\)
0.988903 0.148565i \(-0.0474655\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −51.7725 −0.146435
\(51\) 0 0
\(52\) −65.1508 112.844i −0.173746 0.300937i
\(53\) 321.558 + 556.956i 0.833386 + 1.44347i 0.895338 + 0.445387i \(0.146934\pi\)
−0.0619521 + 0.998079i \(0.519733\pi\)
\(54\) 0 0
\(55\) 4.41631 0.0108272
\(56\) 0 0
\(57\) 0 0
\(58\) 48.8112 84.5434i 0.110504 0.191398i
\(59\) −5.80613 10.0565i −0.0128118 0.0221906i 0.859548 0.511054i \(-0.170745\pi\)
−0.872360 + 0.488864i \(0.837412\pi\)
\(60\) 0 0
\(61\) 6.12132 10.6024i 0.0128484 0.0222541i −0.859530 0.511086i \(-0.829243\pi\)
0.872378 + 0.488832i \(0.162577\pi\)
\(62\) −7.75022 −0.0158755
\(63\) 0 0
\(64\) −447.288 −0.873610
\(65\) 0.836436 1.44875i 0.00159611 0.00276454i
\(66\) 0 0
\(67\) −334.524 579.412i −0.609979 1.05651i −0.991243 0.132049i \(-0.957844\pi\)
0.381264 0.924466i \(-0.375489\pi\)
\(68\) 476.123 824.670i 0.849095 1.47068i
\(69\) 0 0
\(70\) 0 0
\(71\) −822.098 −1.37416 −0.687078 0.726584i \(-0.741107\pi\)
−0.687078 + 0.726584i \(0.741107\pi\)
\(72\) 0 0
\(73\) −257.550 446.089i −0.412930 0.715217i 0.582278 0.812990i \(-0.302161\pi\)
−0.995209 + 0.0977730i \(0.968828\pi\)
\(74\) 39.7401 + 68.8319i 0.0624283 + 0.108129i
\(75\) 0 0
\(76\) 995.092 1.50191
\(77\) 0 0
\(78\) 0 0
\(79\) 402.877 697.804i 0.573762 0.993786i −0.422413 0.906404i \(-0.638817\pi\)
0.996175 0.0873819i \(-0.0278500\pi\)
\(80\) −3.01071 5.21471i −0.00420760 0.00728778i
\(81\) 0 0
\(82\) −66.2147 + 114.687i −0.0891730 + 0.154452i
\(83\) 394.863 0.522191 0.261095 0.965313i \(-0.415916\pi\)
0.261095 + 0.965313i \(0.415916\pi\)
\(84\) 0 0
\(85\) 12.2254 0.0156004
\(86\) 45.2691 78.4084i 0.0567616 0.0983139i
\(87\) 0 0
\(88\) 144.047 + 249.496i 0.174493 + 0.302232i
\(89\) 336.709 583.197i 0.401024 0.694593i −0.592826 0.805331i \(-0.701988\pi\)
0.993850 + 0.110737i \(0.0353212\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 419.588 0.475490
\(93\) 0 0
\(94\) 83.1644 + 144.045i 0.0912527 + 0.158054i
\(95\) 6.38773 + 11.0639i 0.00689861 + 0.0119487i
\(96\) 0 0
\(97\) −1091.11 −1.14212 −0.571061 0.820908i \(-0.693468\pi\)
−0.571061 + 0.820908i \(0.693468\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −489.237 + 847.384i −0.489237 + 0.847384i
\(101\) −685.395 1187.14i −0.675242 1.16955i −0.976398 0.215978i \(-0.930706\pi\)
0.301157 0.953575i \(-0.402627\pi\)
\(102\) 0 0
\(103\) 706.978 1224.52i 0.676316 1.17141i −0.299766 0.954013i \(-0.596909\pi\)
0.976082 0.217401i \(-0.0697581\pi\)
\(104\) 109.128 0.102893
\(105\) 0 0
\(106\) −266.388 −0.244093
\(107\) −171.770 + 297.514i −0.155192 + 0.268801i −0.933129 0.359542i \(-0.882933\pi\)
0.777937 + 0.628343i \(0.216266\pi\)
\(108\) 0 0
\(109\) 158.828 + 275.099i 0.139569 + 0.241740i 0.927333 0.374236i \(-0.122095\pi\)
−0.787765 + 0.615976i \(0.788762\pi\)
\(110\) −0.914647 + 1.58421i −0.000792801 + 0.00137317i
\(111\) 0 0
\(112\) 0 0
\(113\) −798.373 −0.664643 −0.332321 0.943166i \(-0.607832\pi\)
−0.332321 + 0.943166i \(0.607832\pi\)
\(114\) 0 0
\(115\) 2.69343 + 4.66516i 0.00218404 + 0.00378286i
\(116\) −922.507 1597.83i −0.738384 1.27892i
\(117\) 0 0
\(118\) 4.80996 0.00375248
\(119\) 0 0
\(120\) 0 0
\(121\) −299.911 + 519.462i −0.225328 + 0.390279i
\(122\) 2.53553 + 4.39167i 0.00188161 + 0.00325904i
\(123\) 0 0
\(124\) −73.2376 + 126.851i −0.0530398 + 0.0918676i
\(125\) −25.1253 −0.0179782
\(126\) 0 0
\(127\) 1071.40 0.748593 0.374297 0.927309i \(-0.377884\pi\)
0.374297 + 0.927309i \(0.377884\pi\)
\(128\) 401.705 695.773i 0.277391 0.480455i
\(129\) 0 0
\(130\) 0.346463 + 0.600092i 0.000233745 + 0.000404858i
\(131\) −1257.51 + 2178.07i −0.838695 + 1.45266i 0.0522910 + 0.998632i \(0.483348\pi\)
−0.890986 + 0.454031i \(0.849986\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 277.129 0.178659
\(135\) 0 0
\(136\) 398.756 + 690.665i 0.251419 + 0.435471i
\(137\) 125.532 + 217.428i 0.0782841 + 0.135592i 0.902510 0.430670i \(-0.141723\pi\)
−0.824226 + 0.566262i \(0.808389\pi\)
\(138\) 0 0
\(139\) 886.067 0.540685 0.270343 0.962764i \(-0.412863\pi\)
0.270343 + 0.962764i \(0.412863\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 170.262 294.902i 0.100620 0.174279i
\(143\) 365.693 + 633.398i 0.213851 + 0.370401i
\(144\) 0 0
\(145\) 11.8436 20.5137i 0.00678314 0.0117487i
\(146\) 213.361 0.120945
\(147\) 0 0
\(148\) 1502.14 0.834289
\(149\) 291.313 504.569i 0.160170 0.277422i −0.774760 0.632256i \(-0.782129\pi\)
0.934929 + 0.354834i \(0.115463\pi\)
\(150\) 0 0
\(151\) 1405.88 + 2435.06i 0.757676 + 1.31233i 0.944033 + 0.329851i \(0.106999\pi\)
−0.186357 + 0.982482i \(0.559668\pi\)
\(152\) −416.698 + 721.741i −0.222359 + 0.385138i
\(153\) 0 0
\(154\) 0 0
\(155\) −1.88052 −0.000974496
\(156\) 0 0
\(157\) 845.672 + 1464.75i 0.429885 + 0.744583i 0.996863 0.0791504i \(-0.0252207\pi\)
−0.566978 + 0.823733i \(0.691887\pi\)
\(158\) 166.877 + 289.040i 0.0840256 + 0.145537i
\(159\) 0 0
\(160\) 7.76573 0.00383709
\(161\) 0 0
\(162\) 0 0
\(163\) 20.3616 35.2674i 0.00978432 0.0169469i −0.861092 0.508450i \(-0.830219\pi\)
0.870876 + 0.491503i \(0.163552\pi\)
\(164\) 1251.42 + 2167.53i 0.595852 + 1.03205i
\(165\) 0 0
\(166\) −81.7788 + 141.645i −0.0382365 + 0.0662276i
\(167\) −2900.47 −1.34398 −0.671990 0.740560i \(-0.734560\pi\)
−0.671990 + 0.740560i \(0.734560\pi\)
\(168\) 0 0
\(169\) −1919.96 −0.873899
\(170\) −2.53196 + 4.38549i −0.00114231 + 0.00197854i
\(171\) 0 0
\(172\) −855.563 1481.88i −0.379280 0.656932i
\(173\) −1073.07 + 1858.62i −0.471585 + 0.816810i −0.999472 0.0325052i \(-0.989651\pi\)
0.527886 + 0.849315i \(0.322985\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2632.59 1.12749
\(177\) 0 0
\(178\) 139.470 + 241.568i 0.0587286 + 0.101721i
\(179\) 601.770 + 1042.30i 0.251276 + 0.435222i 0.963877 0.266347i \(-0.0858166\pi\)
−0.712602 + 0.701569i \(0.752483\pi\)
\(180\) 0 0
\(181\) −2990.47 −1.22807 −0.614033 0.789280i \(-0.710454\pi\)
−0.614033 + 0.789280i \(0.710454\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −175.704 + 304.327i −0.0703969 + 0.121931i
\(185\) 9.64257 + 16.7014i 0.00383209 + 0.00663737i
\(186\) 0 0
\(187\) −2672.49 + 4628.89i −1.04509 + 1.81015i
\(188\) 3143.53 1.21950
\(189\) 0 0
\(190\) −5.29177 −0.00202056
\(191\) −1403.70 + 2431.29i −0.531772 + 0.921057i 0.467540 + 0.883972i \(0.345140\pi\)
−0.999312 + 0.0370847i \(0.988193\pi\)
\(192\) 0 0
\(193\) −1668.18 2889.38i −0.622169 1.07763i −0.989081 0.147372i \(-0.952919\pi\)
0.366913 0.930255i \(-0.380415\pi\)
\(194\) 225.977 391.404i 0.0836299 0.144851i
\(195\) 0 0
\(196\) 0 0
\(197\) 4226.65 1.52861 0.764305 0.644855i \(-0.223082\pi\)
0.764305 + 0.644855i \(0.223082\pi\)
\(198\) 0 0
\(199\) −2192.85 3798.12i −0.781140 1.35297i −0.931278 0.364309i \(-0.881305\pi\)
0.150139 0.988665i \(-0.452028\pi\)
\(200\) −409.739 709.688i −0.144865 0.250913i
\(201\) 0 0
\(202\) 567.800 0.197774
\(203\) 0 0
\(204\) 0 0
\(205\) −16.0664 + 27.8278i −0.00547378 + 0.00948086i
\(206\) 292.840 + 507.213i 0.0990442 + 0.171550i
\(207\) 0 0
\(208\) 498.605 863.609i 0.166212 0.287887i
\(209\) −5585.48 −1.84859
\(210\) 0 0
\(211\) 2291.56 0.747665 0.373833 0.927496i \(-0.378043\pi\)
0.373833 + 0.927496i \(0.378043\pi\)
\(212\) −2517.30 + 4360.09i −0.815513 + 1.41251i
\(213\) 0 0
\(214\) −71.1493 123.234i −0.0227274 0.0393650i
\(215\) 10.9841 19.0251i 0.00348424 0.00603488i
\(216\) 0 0
\(217\) 0 0
\(218\) −131.578 −0.0408788
\(219\) 0 0
\(220\) 17.2864 + 29.9409i 0.00529748 + 0.00917551i
\(221\) 1012.33 + 1753.40i 0.308128 + 0.533694i
\(222\) 0 0
\(223\) −217.970 −0.0654544 −0.0327272 0.999464i \(-0.510419\pi\)
−0.0327272 + 0.999464i \(0.510419\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 165.349 286.392i 0.0486674 0.0842943i
\(227\) 917.680 + 1589.47i 0.268320 + 0.464743i 0.968428 0.249293i \(-0.0801983\pi\)
−0.700108 + 0.714037i \(0.746865\pi\)
\(228\) 0 0
\(229\) −1387.00 + 2402.36i −0.400244 + 0.693243i −0.993755 0.111583i \(-0.964408\pi\)
0.593511 + 0.804826i \(0.297741\pi\)
\(230\) −2.23131 −0.000639689
\(231\) 0 0
\(232\) 1545.21 0.437275
\(233\) −494.356 + 856.250i −0.138997 + 0.240750i −0.927117 0.374771i \(-0.877721\pi\)
0.788120 + 0.615522i \(0.211055\pi\)
\(234\) 0 0
\(235\) 20.1791 + 34.9512i 0.00560144 + 0.00970197i
\(236\) 45.4529 78.7267i 0.0125370 0.0217147i
\(237\) 0 0
\(238\) 0 0
\(239\) 837.928 0.226783 0.113391 0.993550i \(-0.463829\pi\)
0.113391 + 0.993550i \(0.463829\pi\)
\(240\) 0 0
\(241\) 1727.49 + 2992.11i 0.461733 + 0.799745i 0.999047 0.0436371i \(-0.0138945\pi\)
−0.537315 + 0.843382i \(0.680561\pi\)
\(242\) −124.227 215.168i −0.0329985 0.0571551i
\(243\) 0 0
\(244\) 95.8406 0.0251458
\(245\) 0 0
\(246\) 0 0
\(247\) −1057.87 + 1832.29i −0.272514 + 0.472008i
\(248\) −61.3369 106.239i −0.0157052 0.0272022i
\(249\) 0 0
\(250\) 5.20361 9.01292i 0.00131642 0.00228011i
\(251\) −5635.01 −1.41705 −0.708523 0.705688i \(-0.750638\pi\)
−0.708523 + 0.705688i \(0.750638\pi\)
\(252\) 0 0
\(253\) −2355.16 −0.585246
\(254\) −221.894 + 384.332i −0.0548145 + 0.0949414i
\(255\) 0 0
\(256\) −1622.76 2810.71i −0.396182 0.686208i
\(257\) −1135.58 + 1966.88i −0.275624 + 0.477395i −0.970292 0.241935i \(-0.922218\pi\)
0.694668 + 0.719330i \(0.255551\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 13.0960 0.00312376
\(261\) 0 0
\(262\) −520.877 902.186i −0.122824 0.212737i
\(263\) 81.9336 + 141.913i 0.0192101 + 0.0332728i 0.875471 0.483271i \(-0.160552\pi\)
−0.856261 + 0.516544i \(0.827218\pi\)
\(264\) 0 0
\(265\) −64.6365 −0.0149834
\(266\) 0 0
\(267\) 0 0
\(268\) 2618.80 4535.89i 0.596897 1.03386i
\(269\) −2583.55 4474.84i −0.585582 1.01426i −0.994803 0.101823i \(-0.967533\pi\)
0.409220 0.912436i \(-0.365801\pi\)
\(270\) 0 0
\(271\) 811.136 1404.93i 0.181819 0.314920i −0.760681 0.649126i \(-0.775135\pi\)
0.942500 + 0.334206i \(0.108468\pi\)
\(272\) 7287.63 1.62455
\(273\) 0 0
\(274\) −103.994 −0.0229289
\(275\) 2746.10 4756.38i 0.602167 1.04298i
\(276\) 0 0
\(277\) 2306.18 + 3994.43i 0.500235 + 0.866433i 1.00000 0.000271708i \(8.64874e-5\pi\)
−0.499765 + 0.866161i \(0.666580\pi\)
\(278\) −183.511 + 317.850i −0.0395908 + 0.0685732i
\(279\) 0 0
\(280\) 0 0
\(281\) 2125.22 0.451174 0.225587 0.974223i \(-0.427570\pi\)
0.225587 + 0.974223i \(0.427570\pi\)
\(282\) 0 0
\(283\) −1285.77 2227.02i −0.270075 0.467783i 0.698806 0.715311i \(-0.253715\pi\)
−0.968881 + 0.247528i \(0.920382\pi\)
\(284\) −3217.87 5573.51i −0.672342 1.16453i
\(285\) 0 0
\(286\) −302.950 −0.0626356
\(287\) 0 0
\(288\) 0 0
\(289\) −4941.60 + 8559.10i −1.00582 + 1.74213i
\(290\) 4.90577 + 8.49704i 0.000993368 + 0.00172056i
\(291\) 0 0
\(292\) 2016.21 3492.18i 0.404075 0.699878i
\(293\) 3324.96 0.662957 0.331478 0.943463i \(-0.392453\pi\)
0.331478 + 0.943463i \(0.392453\pi\)
\(294\) 0 0
\(295\) 1.16709 0.000230341
\(296\) −629.024 + 1089.50i −0.123518 + 0.213939i
\(297\) 0 0
\(298\) 120.666 + 208.999i 0.0234563 + 0.0406275i
\(299\) −446.060 + 772.599i −0.0862753 + 0.149433i
\(300\) 0 0
\(301\) 0 0
\(302\) −1164.67 −0.221918
\(303\) 0 0
\(304\) 3807.77 + 6595.25i 0.718390 + 1.24429i
\(305\) 0.615224 + 1.06560i 0.000115500 + 0.000200052i
\(306\) 0 0
\(307\) 887.096 0.164916 0.0824580 0.996595i \(-0.473723\pi\)
0.0824580 + 0.996595i \(0.473723\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.389468 0.674578i 7.13558e−5 0.000123592i
\(311\) 2255.41 + 3906.48i 0.411230 + 0.712271i 0.995025 0.0996300i \(-0.0317659\pi\)
−0.583794 + 0.811902i \(0.698433\pi\)
\(312\) 0 0
\(313\) 1857.89 3217.96i 0.335509 0.581118i −0.648074 0.761578i \(-0.724425\pi\)
0.983582 + 0.180459i \(0.0577584\pi\)
\(314\) −700.577 −0.125910
\(315\) 0 0
\(316\) 6307.79 1.12291
\(317\) 3477.26 6022.79i 0.616096 1.06711i −0.374095 0.927390i \(-0.622047\pi\)
0.990191 0.139719i \(-0.0446200\pi\)
\(318\) 0 0
\(319\) 5178.05 + 8968.64i 0.908825 + 1.57413i
\(320\) 22.4774 38.9320i 0.00392664 0.00680113i
\(321\) 0 0
\(322\) 0 0
\(323\) −15461.9 −2.66355
\(324\) 0 0
\(325\) −1040.21 1801.69i −0.177539 0.307507i
\(326\) 8.43406 + 14.6082i 0.00143288 + 0.00248182i
\(327\) 0 0
\(328\) −2096.15 −0.352867
\(329\) 0 0
\(330\) 0 0
\(331\) 4931.59 8541.76i 0.818926 1.41842i −0.0875478 0.996160i \(-0.527903\pi\)
0.906474 0.422262i \(-0.138764\pi\)
\(332\) 1545.58 + 2677.02i 0.255496 + 0.442532i
\(333\) 0 0
\(334\) 600.706 1040.45i 0.0984107 0.170452i
\(335\) 67.2427 0.0109668
\(336\) 0 0
\(337\) −5945.06 −0.960974 −0.480487 0.877002i \(-0.659540\pi\)
−0.480487 + 0.877002i \(0.659540\pi\)
\(338\) 397.636 688.725i 0.0639897 0.110833i
\(339\) 0 0
\(340\) 47.8528 + 82.8835i 0.00763289 + 0.0132206i
\(341\) 411.084 712.019i 0.0652829 0.113073i
\(342\) 0 0
\(343\) 0 0
\(344\) 1433.08 0.224612
\(345\) 0 0
\(346\) −444.482 769.865i −0.0690621 0.119619i
\(347\) 584.786 + 1012.88i 0.0904697 + 0.156698i 0.907709 0.419601i \(-0.137830\pi\)
−0.817239 + 0.576299i \(0.804497\pi\)
\(348\) 0 0
\(349\) 9176.66 1.40749 0.703747 0.710451i \(-0.251509\pi\)
0.703747 + 0.710451i \(0.251509\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1697.60 + 2940.33i −0.257052 + 0.445228i
\(353\) −5293.60 9168.78i −0.798158 1.38245i −0.920814 0.390001i \(-0.872474\pi\)
0.122656 0.992449i \(-0.460859\pi\)
\(354\) 0 0
\(355\) 41.3125 71.5553i 0.00617645 0.0106979i
\(356\) 5271.81 0.784846
\(357\) 0 0
\(358\) −498.522 −0.0735970
\(359\) 4307.61 7460.99i 0.633278 1.09687i −0.353599 0.935397i \(-0.615042\pi\)
0.986877 0.161472i \(-0.0516243\pi\)
\(360\) 0 0
\(361\) −4649.32 8052.86i −0.677842 1.17406i
\(362\) 619.347 1072.74i 0.0899230 0.155751i
\(363\) 0 0
\(364\) 0 0
\(365\) 51.7701 0.00742403
\(366\) 0 0
\(367\) 4148.89 + 7186.10i 0.590110 + 1.02210i 0.994217 + 0.107389i \(0.0342492\pi\)
−0.404107 + 0.914712i \(0.632418\pi\)
\(368\) 1605.57 + 2780.93i 0.227436 + 0.393930i
\(369\) 0 0
\(370\) −7.98817 −0.00112239
\(371\) 0 0
\(372\) 0 0
\(373\) 2561.93 4437.39i 0.355634 0.615977i −0.631592 0.775301i \(-0.717598\pi\)
0.987226 + 0.159324i \(0.0509315\pi\)
\(374\) −1106.98 1917.35i −0.153050 0.265090i
\(375\) 0 0
\(376\) −1316.36 + 2280.01i −0.180548 + 0.312719i
\(377\) 3922.83 0.535905
\(378\) 0 0
\(379\) −1502.49 −0.203635 −0.101817 0.994803i \(-0.532466\pi\)
−0.101817 + 0.994803i \(0.532466\pi\)
\(380\) −50.0059 + 86.6128i −0.00675066 + 0.0116925i
\(381\) 0 0
\(382\) −581.434 1007.07i −0.0778763 0.134886i
\(383\) 5436.47 9416.24i 0.725301 1.25626i −0.233548 0.972345i \(-0.575034\pi\)
0.958850 0.283914i \(-0.0916330\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1381.97 0.182229
\(387\) 0 0
\(388\) −4270.85 7397.33i −0.558814 0.967894i
\(389\) 2309.50 + 4000.16i 0.301018 + 0.521379i 0.976367 0.216120i \(-0.0693402\pi\)
−0.675349 + 0.737499i \(0.736007\pi\)
\(390\) 0 0
\(391\) −6519.64 −0.843254
\(392\) 0 0
\(393\) 0 0
\(394\) −875.367 + 1516.18i −0.111930 + 0.193868i
\(395\) 40.4912 + 70.1328i 0.00515781 + 0.00893358i
\(396\) 0 0
\(397\) 4803.48 8319.86i 0.607253 1.05179i −0.384438 0.923151i \(-0.625605\pi\)
0.991691 0.128642i \(-0.0410620\pi\)
\(398\) 1816.61 0.228791
\(399\) 0 0
\(400\) −7488.36 −0.936044
\(401\) −5250.52 + 9094.17i −0.653862 + 1.13252i 0.328316 + 0.944568i \(0.393519\pi\)
−0.982178 + 0.187954i \(0.939814\pi\)
\(402\) 0 0
\(403\) −155.716 269.709i −0.0192476 0.0333378i
\(404\) 5365.57 9293.44i 0.660760 1.14447i
\(405\) 0 0
\(406\) 0 0
\(407\) −8431.52 −1.02687
\(408\) 0 0
\(409\) −6033.47 10450.3i −0.729427 1.26340i −0.957126 0.289673i \(-0.906453\pi\)
0.227699 0.973732i \(-0.426880\pi\)
\(410\) −6.65491 11.5266i −0.000801616 0.00138844i
\(411\) 0 0
\(412\) 11069.0 1.32362
\(413\) 0 0
\(414\) 0 0
\(415\) −19.8429 + 34.3688i −0.00234710 + 0.00406530i
\(416\) 643.042 + 1113.78i 0.0757878 + 0.131268i
\(417\) 0 0
\(418\) 1156.79 2003.62i 0.135360 0.234450i
\(419\) −6366.31 −0.742278 −0.371139 0.928577i \(-0.621033\pi\)
−0.371139 + 0.928577i \(0.621033\pi\)
\(420\) 0 0
\(421\) −4731.84 −0.547781 −0.273890 0.961761i \(-0.588311\pi\)
−0.273890 + 0.961761i \(0.588311\pi\)
\(422\) −474.597 + 822.026i −0.0547465 + 0.0948237i
\(423\) 0 0
\(424\) −2108.25 3651.60i −0.241476 0.418248i
\(425\) 7601.86 13166.8i 0.867634 1.50279i
\(426\) 0 0
\(427\) 0 0
\(428\) −2689.37 −0.303728
\(429\) 0 0
\(430\) 4.54978 + 7.88044i 0.000510255 + 0.000883788i
\(431\) 1876.39 + 3250.01i 0.209704 + 0.363219i 0.951621 0.307273i \(-0.0994165\pi\)
−0.741917 + 0.670492i \(0.766083\pi\)
\(432\) 0 0
\(433\) −11709.2 −1.29956 −0.649780 0.760122i \(-0.725139\pi\)
−0.649780 + 0.760122i \(0.725139\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1243.38 + 2153.59i −0.136576 + 0.236556i
\(437\) −3406.49 5900.22i −0.372894 0.645871i
\(438\) 0 0
\(439\) −7462.36 + 12925.2i −0.811296 + 1.40521i 0.100661 + 0.994921i \(0.467904\pi\)
−0.911957 + 0.410285i \(0.865429\pi\)
\(440\) −28.9548 −0.00313720
\(441\) 0 0
\(442\) −838.638 −0.0902487
\(443\) −4258.83 + 7376.51i −0.456756 + 0.791125i −0.998787 0.0492333i \(-0.984322\pi\)
0.542031 + 0.840359i \(0.317656\pi\)
\(444\) 0 0
\(445\) 33.8410 + 58.6143i 0.00360498 + 0.00624401i
\(446\) 45.1430 78.1900i 0.00479279 0.00830135i
\(447\) 0 0
\(448\) 0 0
\(449\) 5965.73 0.627038 0.313519 0.949582i \(-0.398492\pi\)
0.313519 + 0.949582i \(0.398492\pi\)
\(450\) 0 0
\(451\) −7024.27 12166.4i −0.733392 1.27027i
\(452\) −3125.00 5412.67i −0.325194 0.563253i
\(453\) 0 0
\(454\) −760.231 −0.0785890
\(455\) 0 0
\(456\) 0 0
\(457\) 6930.28 12003.6i 0.709376 1.22868i −0.255712 0.966753i \(-0.582310\pi\)
0.965089 0.261923i \(-0.0843567\pi\)
\(458\) −574.516 995.091i −0.0586143 0.101523i
\(459\) 0 0
\(460\) −21.0854 + 36.5209i −0.00213719 + 0.00370173i
\(461\) −149.312 −0.0150850 −0.00754249 0.999972i \(-0.502401\pi\)
−0.00754249 + 0.999972i \(0.502401\pi\)
\(462\) 0 0
\(463\) 5403.95 0.542425 0.271213 0.962519i \(-0.412575\pi\)
0.271213 + 0.962519i \(0.412575\pi\)
\(464\) 7060.03 12228.3i 0.706366 1.22346i
\(465\) 0 0
\(466\) −204.769 354.670i −0.0203557 0.0352571i
\(467\) −1852.33 + 3208.33i −0.183545 + 0.317909i −0.943085 0.332551i \(-0.892091\pi\)
0.759540 + 0.650460i \(0.225424\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.7169 −0.00164062
\(471\) 0 0
\(472\) 38.0670 + 65.9340i 0.00371224 + 0.00642979i
\(473\) 4802.30 + 8317.82i 0.466828 + 0.808570i
\(474\) 0 0
\(475\) 15887.8 1.53470
\(476\) 0 0
\(477\) 0 0
\(478\) −173.540 + 300.581i −0.0166058 + 0.0287620i
\(479\) 5335.88 + 9242.02i 0.508982 + 0.881583i 0.999946 + 0.0104033i \(0.00331152\pi\)
−0.490963 + 0.871180i \(0.663355\pi\)
\(480\) 0 0
\(481\) −1596.91 + 2765.92i −0.151378 + 0.262194i
\(482\) −1431.10 −0.135238
\(483\) 0 0
\(484\) −4695.67 −0.440990
\(485\) 54.8312 94.9705i 0.00513352 0.00889152i
\(486\) 0 0
\(487\) −2926.96 5069.65i −0.272348 0.471720i 0.697115 0.716959i \(-0.254467\pi\)
−0.969463 + 0.245239i \(0.921133\pi\)
\(488\) −40.1335 + 69.5133i −0.00372287 + 0.00644819i
\(489\) 0 0
\(490\) 0 0
\(491\) −4065.31 −0.373656 −0.186828 0.982393i \(-0.559821\pi\)
−0.186828 + 0.982393i \(0.559821\pi\)
\(492\) 0 0
\(493\) 14334.1 + 24827.4i 1.30948 + 2.26809i
\(494\) −438.186 758.960i −0.0399087 0.0691239i
\(495\) 0 0
\(496\) −1120.99 −0.101480
\(497\) 0 0
\(498\) 0 0
\(499\) −2405.59 + 4166.61i −0.215810 + 0.373794i −0.953523 0.301321i \(-0.902572\pi\)
0.737713 + 0.675115i \(0.235906\pi\)
\(500\) −98.3456 170.340i −0.00879630 0.0152356i
\(501\) 0 0
\(502\) 1167.05 2021.39i 0.103761 0.179719i
\(503\) 17001.2 1.50705 0.753526 0.657418i \(-0.228351\pi\)
0.753526 + 0.657418i \(0.228351\pi\)
\(504\) 0 0
\(505\) 137.771 0.0121401
\(506\) 487.769 844.840i 0.0428537 0.0742248i
\(507\) 0 0
\(508\) 4193.69 + 7263.68i 0.366269 + 0.634397i
\(509\) −6898.61 + 11948.7i −0.600738 + 1.04051i 0.391972 + 0.919977i \(0.371793\pi\)
−0.992710 + 0.120531i \(0.961540\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 7771.61 0.670820
\(513\) 0 0
\(514\) −470.372 814.708i −0.0403642 0.0699129i
\(515\) 71.0548 + 123.071i 0.00607971 + 0.0105304i
\(516\) 0 0
\(517\) −17644.7 −1.50099
\(518\) 0 0
\(519\) 0 0
\(520\) −5.48397 + 9.49851i −0.000462477 + 0.000801033i
\(521\) −1968.31 3409.21i −0.165515 0.286680i 0.771323 0.636443i \(-0.219595\pi\)
−0.936838 + 0.349764i \(0.886262\pi\)
\(522\) 0 0
\(523\) 8729.63 15120.2i 0.729866 1.26417i −0.227073 0.973878i \(-0.572916\pi\)
0.956939 0.290288i \(-0.0937510\pi\)
\(524\) −19688.6 −1.64142
\(525\) 0 0
\(526\) −67.8760 −0.00562649
\(527\) 1137.98 1971.04i 0.0940630 0.162922i
\(528\) 0 0
\(529\) 4647.13 + 8049.06i 0.381945 + 0.661549i
\(530\) 13.3867 23.1864i 0.00109713 0.00190029i
\(531\) 0 0
\(532\) 0 0
\(533\) −5321.51 −0.432458
\(534\) 0 0
\(535\) −17.2637 29.9016i −0.00139509 0.00241637i
\(536\) 2193.26 + 3798.83i 0.176743 + 0.306128i
\(537\) 0 0
\(538\) 2140.28 0.171513
\(539\) 0 0
\(540\) 0 0
\(541\) −9550.66 + 16542.2i −0.758992 + 1.31461i 0.184373 + 0.982856i \(0.440975\pi\)
−0.943365 + 0.331757i \(0.892359\pi\)
\(542\) 335.983 + 581.940i 0.0266268 + 0.0461190i
\(543\) 0 0
\(544\) −4699.37 + 8139.54i −0.370374 + 0.641507i
\(545\) −31.9261 −0.00250929
\(546\) 0 0
\(547\) 15413.5 1.20481 0.602407 0.798189i \(-0.294208\pi\)
0.602407 + 0.798189i \(0.294208\pi\)
\(548\) −982.718 + 1702.12i −0.0766052 + 0.132684i
\(549\) 0 0
\(550\) 1137.47 + 1970.16i 0.0881853 + 0.152741i
\(551\) −14979.0 + 25944.5i −1.15813 + 2.00594i
\(552\) 0 0
\(553\) 0 0
\(554\) −1910.51 −0.146516
\(555\) 0 0
\(556\) 3468.26 + 6007.20i 0.264545 + 0.458205i
\(557\) −10246.4 17747.3i −0.779453 1.35005i −0.932257 0.361796i \(-0.882164\pi\)
0.152804 0.988257i \(-0.451170\pi\)
\(558\) 0 0
\(559\) 3638.17 0.275274
\(560\) 0 0
\(561\) 0 0
\(562\) −440.147 + 762.357i −0.0330364 + 0.0572208i
\(563\) 3571.24 + 6185.57i 0.267336 + 0.463039i 0.968173 0.250282i \(-0.0805234\pi\)
−0.700837 + 0.713321i \(0.747190\pi\)
\(564\) 0 0
\(565\) 40.1203 69.4904i 0.00298739 0.00517430i
\(566\) 1065.17 0.0791030
\(567\) 0 0
\(568\) 5389.96 0.398165
\(569\) 2048.96 3548.90i 0.150961 0.261472i −0.780620 0.625006i \(-0.785097\pi\)
0.931581 + 0.363534i \(0.118430\pi\)
\(570\) 0 0
\(571\) 1419.24 + 2458.20i 0.104016 + 0.180162i 0.913336 0.407207i \(-0.133497\pi\)
−0.809320 + 0.587369i \(0.800164\pi\)
\(572\) −2862.80 + 4958.51i −0.209265 + 0.362458i
\(573\) 0 0
\(574\) 0 0
\(575\) 6699.21 0.485872
\(576\) 0 0
\(577\) −7732.23 13392.6i −0.557881 0.966277i −0.997673 0.0681781i \(-0.978281\pi\)
0.439793 0.898099i \(-0.355052\pi\)
\(578\) −2046.88 3545.29i −0.147299 0.255129i
\(579\) 0 0
\(580\) 185.433 0.0132753
\(581\) 0 0
\(582\) 0 0
\(583\) 14129.6 24473.3i 1.00376 1.73856i
\(584\) 1688.59 + 2924.72i 0.119648 + 0.207236i
\(585\) 0 0
\(586\) −688.622 + 1192.73i −0.0485439 + 0.0840805i
\(587\) 14003.6 0.984652 0.492326 0.870411i \(-0.336147\pi\)
0.492326 + 0.870411i \(0.336147\pi\)
\(588\) 0 0
\(589\) 2378.36 0.166382
\(590\) −0.241713 + 0.418658i −1.68664e−5 + 2.92134e-5i
\(591\) 0 0
\(592\) 5747.99 + 9955.82i 0.399056 + 0.691185i
\(593\) −3252.25 + 5633.06i −0.225217 + 0.390088i −0.956385 0.292110i \(-0.905643\pi\)
0.731167 + 0.682198i \(0.238976\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4561.04 0.313469
\(597\) 0 0
\(598\) −184.764 320.021i −0.0126347 0.0218840i
\(599\) −6308.05 10925.9i −0.430284 0.745273i 0.566614 0.823983i \(-0.308253\pi\)
−0.996898 + 0.0787104i \(0.974920\pi\)
\(600\) 0 0
\(601\) −8270.87 −0.561358 −0.280679 0.959802i \(-0.590560\pi\)
−0.280679 + 0.959802i \(0.590560\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −11005.8 + 19062.7i −0.741426 + 1.28419i
\(605\) −30.1426 52.2085i −0.00202557 0.00350839i
\(606\) 0 0
\(607\) 1905.92 3301.15i 0.127445 0.220740i −0.795241 0.606293i \(-0.792656\pi\)
0.922686 + 0.385553i \(0.125989\pi\)
\(608\) −9821.62 −0.655130
\(609\) 0 0
\(610\) −0.509668 −3.38293e−5
\(611\) −3341.86 + 5788.27i −0.221272 + 0.383254i
\(612\) 0 0
\(613\) −5679.63 9837.42i −0.374222 0.648172i 0.615988 0.787756i \(-0.288757\pi\)
−0.990210 + 0.139583i \(0.955424\pi\)
\(614\) −183.724 + 318.219i −0.0120757 + 0.0209157i
\(615\) 0 0
\(616\) 0 0
\(617\) 18272.2 1.19224 0.596118 0.802896i \(-0.296709\pi\)
0.596118 + 0.802896i \(0.296709\pi\)
\(618\) 0 0
\(619\) 14800.1 + 25634.6i 0.961013 + 1.66452i 0.719965 + 0.694010i \(0.244158\pi\)
0.241048 + 0.970513i \(0.422509\pi\)
\(620\) −7.36075 12.7492i −0.000476798 0.000825838i
\(621\) 0 0
\(622\) −1868.44 −0.120447
\(623\) 0 0
\(624\) 0 0
\(625\) −7810.61 + 13528.4i −0.499879 + 0.865815i
\(626\) 769.564 + 1332.92i 0.0491341 + 0.0851028i
\(627\) 0 0
\(628\) −6620.28 + 11466.7i −0.420665 + 0.728614i
\(629\) −23340.5 −1.47956
\(630\) 0 0
\(631\) 7185.41 0.453322 0.226661 0.973974i \(-0.427219\pi\)
0.226661 + 0.973974i \(0.427219\pi\)
\(632\) −2641.40 + 4575.05i −0.166249 + 0.287952i
\(633\) 0 0
\(634\) 1440.33 + 2494.72i 0.0902252 + 0.156275i
\(635\) −53.8405 + 93.2545i −0.00336472 + 0.00582786i
\(636\) 0 0
\(637\) 0 0
\(638\) −4289.64 −0.266189
\(639\) 0 0
\(640\) 40.3733 + 69.9287i 0.00249359 + 0.00431902i
\(641\) −116.491 201.768i −0.00717803 0.0124327i 0.862414 0.506203i \(-0.168952\pi\)
−0.869592 + 0.493771i \(0.835618\pi\)
\(642\) 0 0
\(643\) 1837.96 0.112725 0.0563624 0.998410i \(-0.482050\pi\)
0.0563624 + 0.998410i \(0.482050\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3202.27 5546.50i 0.195034 0.337808i
\(647\) 9297.35 + 16103.5i 0.564941 + 0.978506i 0.997055 + 0.0766874i \(0.0244343\pi\)
−0.432114 + 0.901819i \(0.642232\pi\)
\(648\) 0 0
\(649\) −255.128 + 441.895i −0.0154309 + 0.0267271i
\(650\) 861.736 0.0520001
\(651\) 0 0
\(652\) 318.799 0.0191490
\(653\) −14432.3 + 24997.6i −0.864902 + 1.49805i 0.00224162 + 0.999997i \(0.499286\pi\)
−0.867144 + 0.498057i \(0.834047\pi\)
\(654\) 0 0
\(655\) −126.386 218.907i −0.00753940 0.0130586i
\(656\) −9577.27 + 16588.3i −0.570014 + 0.987294i
\(657\) 0 0
\(658\) 0 0
\(659\) 29066.3 1.71815 0.859076 0.511847i \(-0.171039\pi\)
0.859076 + 0.511847i \(0.171039\pi\)
\(660\) 0 0
\(661\) −1989.75 3446.36i −0.117084 0.202795i 0.801527 0.597959i \(-0.204021\pi\)
−0.918611 + 0.395163i \(0.870688\pi\)
\(662\) 2042.73 + 3538.11i 0.119929 + 0.207723i
\(663\) 0 0
\(664\) −2588.86 −0.151306
\(665\) 0 0
\(666\) 0 0
\(667\) −6316.02 + 10939.7i −0.366653 + 0.635061i
\(668\) −11353.0 19664.0i −0.657578 1.13896i
\(669\) 0 0
\(670\) −13.9264 + 24.1213i −0.000803022 + 0.00139087i
\(671\) −537.955 −0.0309501
\(672\) 0 0
\(673\) −184.229 −0.0105520 −0.00527601 0.999986i \(-0.501679\pi\)
−0.00527601 + 0.999986i \(0.501679\pi\)
\(674\) 1231.26 2132.61i 0.0703657 0.121877i
\(675\) 0 0
\(676\) −7515.11 13016.6i −0.427578 0.740587i
\(677\) 8341.73 14448.3i 0.473558 0.820227i −0.525984 0.850495i \(-0.676303\pi\)
0.999542 + 0.0302680i \(0.00963607\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −80.1540 −0.00452024
\(681\) 0 0
\(682\) 170.277 + 294.928i 0.00956045 + 0.0165592i
\(683\) 8904.11 + 15422.4i 0.498838 + 0.864013i 0.999999 0.00134107i \(-0.000426875\pi\)
−0.501161 + 0.865354i \(0.667094\pi\)
\(684\) 0 0
\(685\) −25.2332 −0.00140746
\(686\) 0 0
\(687\) 0 0
\(688\) 6547.71 11341.0i 0.362833 0.628445i
\(689\) −5352.23 9270.34i −0.295942 0.512586i
\(690\) 0 0
\(691\) −10072.8 + 17446.7i −0.554542 + 0.960495i 0.443397 + 0.896325i \(0.353773\pi\)
−0.997939 + 0.0641695i \(0.979560\pi\)
\(692\) −16801.0 −0.922943
\(693\) 0 0
\(694\) −484.453 −0.0264980
\(695\) −44.5271 + 77.1232i −0.00243023 + 0.00420928i
\(696\) 0 0
\(697\) −19444.9 33679.5i −1.05671 1.83028i
\(698\) −1900.55 + 3291.85i −0.103061 + 0.178507i
\(699\) 0 0
\(700\) 0 0
\(701\) 2719.67 0.146534 0.0732672 0.997312i \(-0.476657\pi\)
0.0732672 + 0.997312i \(0.476657\pi\)
\(702\) 0 0
\(703\) −12195.3 21122.9i −0.654276 1.13324i
\(704\) 9827.18 + 17021.2i 0.526102 + 0.911235i
\(705\) 0 0
\(706\) 4385.36 0.233775
\(707\) 0 0
\(708\) 0 0
\(709\) 312.854 541.879i 0.0165719 0.0287034i −0.857621 0.514283i \(-0.828058\pi\)
0.874192 + 0.485580i \(0.161391\pi\)
\(710\) 17.1122 + 29.6392i 0.000904520 + 0.00156667i
\(711\) 0 0
\(712\) −2207.58 + 3823.65i −0.116198 + 0.201260i
\(713\) 1002.85 0.0526749
\(714\) 0 0
\(715\) −73.5079 −0.00384481
\(716\) −4710.91 + 8159.53i −0.245887 + 0.425888i
\(717\) 0 0
\(718\) 1784.27 + 3090.44i 0.0927414 + 0.160633i
\(719\) 4788.77 8294.39i 0.248388 0.430221i −0.714691 0.699441i \(-0.753433\pi\)
0.963079 + 0.269220i \(0.0867659\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3851.62 0.198535
\(723\) 0 0
\(724\) −11705.3 20274.2i −0.600864 1.04073i
\(725\) −14728.9 25511.2i −0.754506 1.30684i
\(726\) 0 0
\(727\) 16741.2 0.854053 0.427027 0.904239i \(-0.359561\pi\)
0.427027 + 0.904239i \(0.359561\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −10.7219 + 18.5710i −0.000543612 + 0.000941564i
\(731\) 13293.9 + 23025.7i 0.672631 + 1.16503i
\(732\) 0 0
\(733\) −3248.02 + 5625.74i −0.163668 + 0.283481i −0.936181 0.351517i \(-0.885666\pi\)
0.772514 + 0.634998i \(0.218999\pi\)
\(734\) −3437.06 −0.172839
\(735\) 0 0
\(736\) −4141.36 −0.207408
\(737\) −14699.4 + 25460.0i −0.734678 + 1.27250i
\(738\) 0 0
\(739\) −249.640 432.389i −0.0124265 0.0215233i 0.859745 0.510723i \(-0.170622\pi\)
−0.872172 + 0.489200i \(0.837289\pi\)
\(740\) −75.4861 + 130.746i −0.00374990 + 0.00649502i
\(741\) 0 0
\(742\) 0 0
\(743\) 6367.30 0.314393 0.157196 0.987567i \(-0.449754\pi\)
0.157196 + 0.987567i \(0.449754\pi\)
\(744\) 0 0
\(745\) 29.2784 + 50.7117i 0.00143984 + 0.00249387i
\(746\) 1061.19 + 1838.03i 0.0520814 + 0.0902077i
\(747\) 0 0
\(748\) −41842.8 −2.04535
\(749\) 0 0
\(750\) 0 0
\(751\) −248.049 + 429.634i −0.0120525 + 0.0208756i −0.871989 0.489526i \(-0.837170\pi\)
0.859936 + 0.510401i \(0.170503\pi\)
\(752\) 12028.9 + 20834.6i 0.583308 + 1.01032i
\(753\) 0 0
\(754\) −812.446 + 1407.20i −0.0392407 + 0.0679670i
\(755\) −282.597 −0.0136222
\(756\) 0 0
\(757\) 13025.9 0.625408 0.312704 0.949851i \(-0.398765\pi\)
0.312704 + 0.949851i \(0.398765\pi\)
\(758\) 311.175 538.971i 0.0149108 0.0258263i
\(759\) 0 0
\(760\) −41.8802 72.5387i −0.00199889 0.00346218i
\(761\) 12737.3 22061.6i 0.606736 1.05090i −0.385039 0.922900i \(-0.625812\pi\)
0.991775 0.127997i \(-0.0408548\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −21977.6 −1.04074
\(765\) 0 0
\(766\) 2251.86 + 3900.33i 0.106218 + 0.183975i
\(767\) 96.6411 + 167.387i 0.00454955 + 0.00788006i
\(768\) 0 0
\(769\) 29054.0 1.36244 0.681218 0.732080i \(-0.261450\pi\)
0.681218 + 0.732080i \(0.261450\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13059.3 22619.3i 0.608825 1.05452i
\(773\) −948.677 1643.16i −0.0441417 0.0764557i 0.843110 0.537740i \(-0.180722\pi\)
−0.887252 + 0.461285i \(0.847389\pi\)
\(774\) 0 0
\(775\) −1169.32 + 2025.33i −0.0541978 + 0.0938734i
\(776\) 7153.72 0.330933
\(777\) 0 0
\(778\) −1913.25 −0.0881662
\(779\) 20319.8 35194.9i 0.934572 1.61873i
\(780\) 0 0
\(781\) 18061.9 + 31284.2i 0.827538 + 1.43334i
\(782\) 1350.26 2338.72i 0.0617458 0.106947i
\(783\) 0 0
\(784\) 0 0
\(785\) −169.989 −0.00772886
\(786\) 0 0
\(787\) 21325.1 + 36936.2i 0.965895 + 1.67298i 0.707192 + 0.707021i \(0.249961\pi\)
0.258702 + 0.965957i \(0.416705\pi\)
\(788\) 16544.0 + 28655.0i 0.747913 + 1.29542i
\(789\) 0 0
\(790\) −33.5440