Properties

Label 441.4.p.d.80.16
Level $441$
Weight $4$
Character 441.80
Analytic conductor $26.020$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 80.16
Character \(\chi\) \(=\) 441.80
Dual form 441.4.p.d.215.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.40358 - 0.810356i) q^{2} +(-2.68665 + 4.65341i) q^{4} +(2.35993 + 4.08752i) q^{5} +21.6743i q^{8} +O(q^{10})\) \(q+(1.40358 - 0.810356i) q^{2} +(-2.68665 + 4.65341i) q^{4} +(2.35993 + 4.08752i) q^{5} +21.6743i q^{8} +(6.62469 + 3.82477i) q^{10} +(-25.9801 - 14.9996i) q^{11} +27.1586i q^{13} +(-3.92932 - 6.80578i) q^{16} +(8.92464 - 15.4579i) q^{17} +(-107.297 + 61.9477i) q^{19} -25.3612 q^{20} -48.6201 q^{22} +(71.0802 - 41.0382i) q^{23} +(51.3615 - 88.9606i) q^{25} +(22.0081 + 38.1191i) q^{26} +88.2194i q^{29} +(-220.389 - 127.242i) q^{31} +(-161.194 - 93.0653i) q^{32} -28.9285i q^{34} +(-107.695 - 186.533i) q^{37} +(-100.399 + 173.897i) q^{38} +(-88.5939 + 51.1497i) q^{40} -427.760 q^{41} +62.4602 q^{43} +(139.599 - 80.5974i) q^{44} +(66.5110 - 115.200i) q^{46} +(211.787 + 366.825i) q^{47} -166.484i q^{50} +(-126.380 - 72.9654i) q^{52} +(-587.234 - 339.039i) q^{53} -141.592i q^{55} +(71.4891 + 123.823i) q^{58} +(-383.719 + 664.621i) q^{59} +(-313.156 + 180.801i) q^{61} -412.444 q^{62} -238.795 q^{64} +(-111.011 + 64.0923i) q^{65} +(323.947 - 561.093i) q^{67} +(47.9547 + 83.0600i) q^{68} +536.663i q^{71} +(-547.293 - 315.980i) q^{73} +(-302.316 - 174.542i) q^{74} -665.726i q^{76} +(298.709 + 517.379i) q^{79} +(18.5458 - 32.1223i) q^{80} +(-600.395 + 346.638i) q^{82} +591.773 q^{83} +84.2461 q^{85} +(87.6677 - 50.6150i) q^{86} +(325.106 - 563.100i) q^{88} +(769.502 + 1332.82i) q^{89} +441.020i q^{92} +(594.517 + 343.245i) q^{94} +(-506.425 - 292.385i) q^{95} -654.102i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 96q^{4} + O(q^{10}) \) \( 48q + 96q^{4} - 144q^{16} + 1248q^{22} - 312q^{25} + 864q^{37} + 2496q^{43} + 3888q^{46} + 7440q^{58} - 6720q^{64} + 2688q^{67} - 480q^{79} + 26496q^{85} + 7248q^{88} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40358 0.810356i 0.496240 0.286504i −0.230920 0.972973i \(-0.574173\pi\)
0.727159 + 0.686469i \(0.240840\pi\)
\(3\) 0 0
\(4\) −2.68665 + 4.65341i −0.335831 + 0.581676i
\(5\) 2.35993 + 4.08752i 0.211079 + 0.365599i 0.952052 0.305935i \(-0.0989691\pi\)
−0.740974 + 0.671534i \(0.765636\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 21.6743i 0.957876i
\(9\) 0 0
\(10\) 6.62469 + 3.82477i 0.209491 + 0.120950i
\(11\) −25.9801 14.9996i −0.712118 0.411142i 0.0997267 0.995015i \(-0.468203\pi\)
−0.811845 + 0.583873i \(0.801536\pi\)
\(12\) 0 0
\(13\) 27.1586i 0.579417i 0.957115 + 0.289709i \(0.0935584\pi\)
−0.957115 + 0.289709i \(0.906442\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.92932 6.80578i −0.0613956 0.106340i
\(17\) 8.92464 15.4579i 0.127326 0.220535i −0.795314 0.606198i \(-0.792694\pi\)
0.922640 + 0.385663i \(0.126027\pi\)
\(18\) 0 0
\(19\) −107.297 + 61.9477i −1.29555 + 0.747988i −0.979633 0.200797i \(-0.935647\pi\)
−0.315921 + 0.948786i \(0.602313\pi\)
\(20\) −25.3612 −0.283547
\(21\) 0 0
\(22\) −48.6201 −0.471175
\(23\) 71.0802 41.0382i 0.644402 0.372046i −0.141906 0.989880i \(-0.545323\pi\)
0.786308 + 0.617835i \(0.211990\pi\)
\(24\) 0 0
\(25\) 51.3615 88.9606i 0.410892 0.711685i
\(26\) 22.0081 + 38.1191i 0.166005 + 0.287530i
\(27\) 0 0
\(28\) 0 0
\(29\) 88.2194i 0.564894i 0.959283 + 0.282447i \(0.0911462\pi\)
−0.959283 + 0.282447i \(0.908854\pi\)
\(30\) 0 0
\(31\) −220.389 127.242i −1.27687 0.737203i −0.300600 0.953750i \(-0.597187\pi\)
−0.976272 + 0.216548i \(0.930520\pi\)
\(32\) −161.194 93.0653i −0.890479 0.514118i
\(33\) 0 0
\(34\) 28.9285i 0.145918i
\(35\) 0 0
\(36\) 0 0
\(37\) −107.695 186.533i −0.478511 0.828805i 0.521186 0.853443i \(-0.325490\pi\)
−0.999696 + 0.0246385i \(0.992157\pi\)
\(38\) −100.399 + 173.897i −0.428603 + 0.742363i
\(39\) 0 0
\(40\) −88.5939 + 51.1497i −0.350198 + 0.202187i
\(41\) −427.760 −1.62939 −0.814695 0.579890i \(-0.803095\pi\)
−0.814695 + 0.579890i \(0.803095\pi\)
\(42\) 0 0
\(43\) 62.4602 0.221514 0.110757 0.993848i \(-0.464673\pi\)
0.110757 + 0.993848i \(0.464673\pi\)
\(44\) 139.599 80.5974i 0.478303 0.276148i
\(45\) 0 0
\(46\) 66.5110 115.200i 0.213185 0.369247i
\(47\) 211.787 + 366.825i 0.657282 + 1.13845i 0.981317 + 0.192400i \(0.0616271\pi\)
−0.324035 + 0.946045i \(0.605040\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 166.484i 0.470888i
\(51\) 0 0
\(52\) −126.380 72.9654i −0.337033 0.194586i
\(53\) −587.234 339.039i −1.52194 0.878692i −0.999664 0.0259140i \(-0.991750\pi\)
−0.522274 0.852778i \(-0.674916\pi\)
\(54\) 0 0
\(55\) 141.592i 0.347133i
\(56\) 0 0
\(57\) 0 0
\(58\) 71.4891 + 123.823i 0.161844 + 0.280323i
\(59\) −383.719 + 664.621i −0.846711 + 1.46655i 0.0374163 + 0.999300i \(0.488087\pi\)
−0.884127 + 0.467246i \(0.845246\pi\)
\(60\) 0 0
\(61\) −313.156 + 180.801i −0.657303 + 0.379494i −0.791249 0.611495i \(-0.790569\pi\)
0.133946 + 0.990989i \(0.457235\pi\)
\(62\) −412.444 −0.844846
\(63\) 0 0
\(64\) −238.795 −0.466396
\(65\) −111.011 + 64.0923i −0.211834 + 0.122303i
\(66\) 0 0
\(67\) 323.947 561.093i 0.590694 1.02311i −0.403446 0.915004i \(-0.632188\pi\)
0.994139 0.108108i \(-0.0344791\pi\)
\(68\) 47.9547 + 83.0600i 0.0855200 + 0.148125i
\(69\) 0 0
\(70\) 0 0
\(71\) 536.663i 0.897045i 0.893772 + 0.448522i \(0.148050\pi\)
−0.893772 + 0.448522i \(0.851950\pi\)
\(72\) 0 0
\(73\) −547.293 315.980i −0.877477 0.506612i −0.00765130 0.999971i \(-0.502436\pi\)
−0.869826 + 0.493359i \(0.835769\pi\)
\(74\) −302.316 174.542i −0.474912 0.274190i
\(75\) 0 0
\(76\) 665.726i 1.00479i
\(77\) 0 0
\(78\) 0 0
\(79\) 298.709 + 517.379i 0.425410 + 0.736832i 0.996459 0.0840844i \(-0.0267965\pi\)
−0.571049 + 0.820916i \(0.693463\pi\)
\(80\) 18.5458 32.1223i 0.0259186 0.0448923i
\(81\) 0 0
\(82\) −600.395 + 346.638i −0.808567 + 0.466827i
\(83\) 591.773 0.782597 0.391299 0.920264i \(-0.372026\pi\)
0.391299 + 0.920264i \(0.372026\pi\)
\(84\) 0 0
\(85\) 84.2461 0.107503
\(86\) 87.6677 50.6150i 0.109924 0.0634646i
\(87\) 0 0
\(88\) 325.106 563.100i 0.393823 0.682121i
\(89\) 769.502 + 1332.82i 0.916484 + 1.58740i 0.804714 + 0.593662i \(0.202318\pi\)
0.111769 + 0.993734i \(0.464348\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 441.020i 0.499778i
\(93\) 0 0
\(94\) 594.517 + 343.245i 0.652338 + 0.376628i
\(95\) −506.425 292.385i −0.546927 0.315769i
\(96\) 0 0
\(97\) 654.102i 0.684680i −0.939576 0.342340i \(-0.888781\pi\)
0.939576 0.342340i \(-0.111219\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 275.980 + 478.012i 0.275980 + 0.478012i
\(101\) −148.389 + 257.018i −0.146191 + 0.253210i −0.929817 0.368023i \(-0.880035\pi\)
0.783626 + 0.621233i \(0.213368\pi\)
\(102\) 0 0
\(103\) 387.255 223.582i 0.370460 0.213885i −0.303199 0.952927i \(-0.598055\pi\)
0.673660 + 0.739042i \(0.264721\pi\)
\(104\) −588.641 −0.555010
\(105\) 0 0
\(106\) −1098.97 −1.00699
\(107\) −655.418 + 378.406i −0.592165 + 0.341887i −0.765953 0.642896i \(-0.777733\pi\)
0.173788 + 0.984783i \(0.444399\pi\)
\(108\) 0 0
\(109\) −59.2503 + 102.625i −0.0520656 + 0.0901803i −0.890884 0.454232i \(-0.849914\pi\)
0.838818 + 0.544412i \(0.183247\pi\)
\(110\) −114.740 198.736i −0.0994550 0.172261i
\(111\) 0 0
\(112\) 0 0
\(113\) 90.4761i 0.0753210i 0.999291 + 0.0376605i \(0.0119905\pi\)
−0.999291 + 0.0376605i \(0.988009\pi\)
\(114\) 0 0
\(115\) 335.489 + 193.694i 0.272039 + 0.157062i
\(116\) −410.521 237.014i −0.328586 0.189709i
\(117\) 0 0
\(118\) 1243.80i 0.970344i
\(119\) 0 0
\(120\) 0 0
\(121\) −215.522 373.296i −0.161925 0.280463i
\(122\) −293.026 + 507.535i −0.217453 + 0.376640i
\(123\) 0 0
\(124\) 1184.22 683.707i 0.857626 0.495151i
\(125\) 1074.82 0.769079
\(126\) 0 0
\(127\) 324.991 0.227073 0.113536 0.993534i \(-0.463782\pi\)
0.113536 + 0.993534i \(0.463782\pi\)
\(128\) 954.384 551.014i 0.659034 0.380494i
\(129\) 0 0
\(130\) −103.875 + 179.917i −0.0700804 + 0.121383i
\(131\) 338.925 + 587.035i 0.226046 + 0.391523i 0.956633 0.291297i \(-0.0940868\pi\)
−0.730587 + 0.682820i \(0.760753\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1050.05i 0.676944i
\(135\) 0 0
\(136\) 335.039 + 193.435i 0.211245 + 0.121963i
\(137\) 1866.23 + 1077.47i 1.16381 + 0.671928i 0.952215 0.305429i \(-0.0987998\pi\)
0.211598 + 0.977357i \(0.432133\pi\)
\(138\) 0 0
\(139\) 719.518i 0.439055i −0.975606 0.219528i \(-0.929548\pi\)
0.975606 0.219528i \(-0.0704516\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 434.888 + 753.248i 0.257007 + 0.445149i
\(143\) 407.368 705.582i 0.238223 0.412614i
\(144\) 0 0
\(145\) −360.599 + 208.192i −0.206525 + 0.119237i
\(146\) −1024.22 −0.580585
\(147\) 0 0
\(148\) 1157.35 0.642795
\(149\) −1034.65 + 597.357i −0.568873 + 0.328439i −0.756699 0.653763i \(-0.773189\pi\)
0.187826 + 0.982202i \(0.439856\pi\)
\(150\) 0 0
\(151\) −536.066 + 928.494i −0.288904 + 0.500396i −0.973548 0.228481i \(-0.926624\pi\)
0.684645 + 0.728877i \(0.259957\pi\)
\(152\) −1342.67 2325.57i −0.716480 1.24098i
\(153\) 0 0
\(154\) 0 0
\(155\) 1201.13i 0.622431i
\(156\) 0 0
\(157\) −2022.12 1167.47i −1.02792 0.593468i −0.111530 0.993761i \(-0.535575\pi\)
−0.916387 + 0.400293i \(0.868908\pi\)
\(158\) 838.523 + 484.121i 0.422211 + 0.243763i
\(159\) 0 0
\(160\) 878.511i 0.434077i
\(161\) 0 0
\(162\) 0 0
\(163\) −1803.42 3123.61i −0.866592 1.50098i −0.865458 0.500982i \(-0.832972\pi\)
−0.00113428 0.999999i \(-0.500361\pi\)
\(164\) 1149.24 1990.54i 0.547199 0.947777i
\(165\) 0 0
\(166\) 830.600 479.547i 0.388356 0.224217i
\(167\) 2249.44 1.04232 0.521159 0.853460i \(-0.325500\pi\)
0.521159 + 0.853460i \(0.325500\pi\)
\(168\) 0 0
\(169\) 1459.41 0.664275
\(170\) 118.246 68.2693i 0.0533473 0.0308001i
\(171\) 0 0
\(172\) −167.809 + 290.653i −0.0743912 + 0.128849i
\(173\) −2022.40 3502.90i −0.888788 1.53943i −0.841310 0.540553i \(-0.818215\pi\)
−0.0474778 0.998872i \(-0.515118\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 235.753i 0.100969i
\(177\) 0 0
\(178\) 2160.11 + 1247.14i 0.909591 + 0.525153i
\(179\) 1843.22 + 1064.18i 0.769658 + 0.444362i 0.832753 0.553645i \(-0.186764\pi\)
−0.0630946 + 0.998008i \(0.520097\pi\)
\(180\) 0 0
\(181\) 4272.10i 1.75438i 0.480143 + 0.877190i \(0.340585\pi\)
−0.480143 + 0.877190i \(0.659415\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 889.472 + 1540.61i 0.356373 + 0.617257i
\(185\) 508.304 880.408i 0.202007 0.349886i
\(186\) 0 0
\(187\) −463.726 + 267.732i −0.181342 + 0.104698i
\(188\) −2275.98 −0.882942
\(189\) 0 0
\(190\) −947.742 −0.361876
\(191\) −670.762 + 387.265i −0.254108 + 0.146709i −0.621644 0.783300i \(-0.713535\pi\)
0.367536 + 0.930009i \(0.380202\pi\)
\(192\) 0 0
\(193\) −2456.61 + 4254.97i −0.916221 + 1.58694i −0.111117 + 0.993807i \(0.535443\pi\)
−0.805104 + 0.593134i \(0.797890\pi\)
\(194\) −530.055 918.082i −0.196164 0.339765i
\(195\) 0 0
\(196\) 0 0
\(197\) 1004.44i 0.363265i −0.983366 0.181632i \(-0.941862\pi\)
0.983366 0.181632i \(-0.0581381\pi\)
\(198\) 0 0
\(199\) 1734.53 + 1001.43i 0.617878 + 0.356732i 0.776042 0.630681i \(-0.217224\pi\)
−0.158164 + 0.987413i \(0.550558\pi\)
\(200\) 1928.16 + 1113.22i 0.681706 + 0.393583i
\(201\) 0 0
\(202\) 480.992i 0.167537i
\(203\) 0 0
\(204\) 0 0
\(205\) −1009.49 1748.48i −0.343929 0.595703i
\(206\) 362.362 627.629i 0.122558 0.212277i
\(207\) 0 0
\(208\) 184.835 106.715i 0.0616154 0.0355737i
\(209\) 3716.77 1.23012
\(210\) 0 0
\(211\) 2630.90 0.858383 0.429191 0.903214i \(-0.358799\pi\)
0.429191 + 0.903214i \(0.358799\pi\)
\(212\) 3155.38 1821.76i 1.02223 0.590184i
\(213\) 0 0
\(214\) −613.287 + 1062.24i −0.195904 + 0.339315i
\(215\) 147.402 + 255.307i 0.0467568 + 0.0809852i
\(216\) 0 0
\(217\) 0 0
\(218\) 192.055i 0.0596680i
\(219\) 0 0
\(220\) 658.887 + 380.409i 0.201919 + 0.116578i
\(221\) 419.815 + 242.380i 0.127782 + 0.0737749i
\(222\) 0 0
\(223\) 4972.20i 1.49311i 0.665324 + 0.746555i \(0.268293\pi\)
−0.665324 + 0.746555i \(0.731707\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 73.3178 + 126.990i 0.0215798 + 0.0373773i
\(227\) 1710.26 2962.26i 0.500062 0.866133i −0.499938 0.866061i \(-0.666644\pi\)
1.00000 7.18991e-5i \(-2.28862e-5\pi\)
\(228\) 0 0
\(229\) 2770.81 1599.73i 0.799566 0.461629i −0.0437537 0.999042i \(-0.513932\pi\)
0.843319 + 0.537413i \(0.180598\pi\)
\(230\) 627.846 0.179995
\(231\) 0 0
\(232\) −1912.09 −0.541099
\(233\) −1859.97 + 1073.85i −0.522964 + 0.301933i −0.738146 0.674641i \(-0.764299\pi\)
0.215183 + 0.976574i \(0.430965\pi\)
\(234\) 0 0
\(235\) −999.603 + 1731.36i −0.277476 + 0.480603i
\(236\) −2061.83 3571.20i −0.568703 0.985023i
\(237\) 0 0
\(238\) 0 0
\(239\) 2853.29i 0.772236i 0.922449 + 0.386118i \(0.126184\pi\)
−0.922449 + 0.386118i \(0.873816\pi\)
\(240\) 0 0
\(241\) 340.988 + 196.869i 0.0911409 + 0.0526202i 0.544878 0.838516i \(-0.316576\pi\)
−0.453737 + 0.891136i \(0.649909\pi\)
\(242\) −605.005 349.300i −0.160707 0.0927844i
\(243\) 0 0
\(244\) 1942.99i 0.509783i
\(245\) 0 0
\(246\) 0 0
\(247\) −1682.41 2914.02i −0.433397 0.750666i
\(248\) 2757.87 4776.77i 0.706149 1.22309i
\(249\) 0 0
\(250\) 1508.59 870.987i 0.381647 0.220344i
\(251\) 2520.34 0.633794 0.316897 0.948460i \(-0.397359\pi\)
0.316897 + 0.948460i \(0.397359\pi\)
\(252\) 0 0
\(253\) −2462.23 −0.611854
\(254\) 456.150 263.358i 0.112683 0.0650573i
\(255\) 0 0
\(256\) 1848.21 3201.20i 0.451224 0.781543i
\(257\) 2125.96 + 3682.26i 0.516006 + 0.893748i 0.999827 + 0.0185815i \(0.00591500\pi\)
−0.483822 + 0.875167i \(0.660752\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 688.774i 0.164292i
\(261\) 0 0
\(262\) 951.414 + 549.299i 0.224346 + 0.129526i
\(263\) 6145.87 + 3548.32i 1.44095 + 0.831935i 0.997913 0.0645666i \(-0.0205665\pi\)
0.443040 + 0.896502i \(0.353900\pi\)
\(264\) 0 0
\(265\) 3200.44i 0.741892i
\(266\) 0 0
\(267\) 0 0
\(268\) 1740.66 + 3014.92i 0.396746 + 0.687185i
\(269\) −2180.43 + 3776.61i −0.494212 + 0.856000i −0.999978 0.00667106i \(-0.997877\pi\)
0.505766 + 0.862671i \(0.331210\pi\)
\(270\) 0 0
\(271\) −3737.79 + 2158.02i −0.837841 + 0.483727i −0.856530 0.516098i \(-0.827384\pi\)
0.0186891 + 0.999825i \(0.494051\pi\)
\(272\) −140.271 −0.0312690
\(273\) 0 0
\(274\) 3492.52 0.770040
\(275\) −2668.75 + 1540.81i −0.585207 + 0.337869i
\(276\) 0 0
\(277\) 1319.46 2285.38i 0.286205 0.495722i −0.686696 0.726945i \(-0.740939\pi\)
0.972901 + 0.231223i \(0.0742728\pi\)
\(278\) −583.065 1009.90i −0.125791 0.217877i
\(279\) 0 0
\(280\) 0 0
\(281\) 5925.56i 1.25797i −0.777417 0.628985i \(-0.783471\pi\)
0.777417 0.628985i \(-0.216529\pi\)
\(282\) 0 0
\(283\) −2663.30 1537.65i −0.559422 0.322983i 0.193491 0.981102i \(-0.438019\pi\)
−0.752914 + 0.658119i \(0.771352\pi\)
\(284\) −2497.31 1441.82i −0.521789 0.301255i
\(285\) 0 0
\(286\) 1320.45i 0.273007i
\(287\) 0 0
\(288\) 0 0
\(289\) 2297.20 + 3978.87i 0.467576 + 0.809866i
\(290\) −337.419 + 584.426i −0.0683238 + 0.118340i
\(291\) 0 0
\(292\) 2940.77 1697.85i 0.589368 0.340272i
\(293\) −1557.31 −0.310509 −0.155254 0.987875i \(-0.549620\pi\)
−0.155254 + 0.987875i \(0.549620\pi\)
\(294\) 0 0
\(295\) −3622.20 −0.714890
\(296\) 4042.96 2334.20i 0.793892 0.458354i
\(297\) 0 0
\(298\) −968.144 + 1676.87i −0.188198 + 0.325969i
\(299\) 1114.54 + 1930.43i 0.215570 + 0.373378i
\(300\) 0 0
\(301\) 0 0
\(302\) 1737.62i 0.331088i
\(303\) 0 0
\(304\) 843.205 + 486.825i 0.159083 + 0.0918464i
\(305\) −1478.05 853.353i −0.277485 0.160206i
\(306\) 0 0
\(307\) 1802.67i 0.335127i 0.985861 + 0.167563i \(0.0535898\pi\)
−0.985861 + 0.167563i \(0.946410\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −973.340 1685.87i −0.178329 0.308875i
\(311\) −4769.98 + 8261.85i −0.869714 + 1.50639i −0.00742422 + 0.999972i \(0.502363\pi\)
−0.862289 + 0.506416i \(0.830970\pi\)
\(312\) 0 0
\(313\) −1095.23 + 632.332i −0.197783 + 0.114190i −0.595621 0.803266i \(-0.703094\pi\)
0.397838 + 0.917456i \(0.369761\pi\)
\(314\) −3784.27 −0.680124
\(315\) 0 0
\(316\) −3210.10 −0.571463
\(317\) −8265.68 + 4772.19i −1.46450 + 0.845530i −0.999214 0.0396301i \(-0.987382\pi\)
−0.465287 + 0.885160i \(0.654049\pi\)
\(318\) 0 0
\(319\) 1323.26 2291.95i 0.232252 0.402271i
\(320\) −563.539 976.079i −0.0984463 0.170514i
\(321\) 0 0
\(322\) 0 0
\(323\) 2211.44i 0.380954i
\(324\) 0 0
\(325\) 2416.04 + 1394.90i 0.412363 + 0.238078i
\(326\) −5062.47 2922.82i −0.860074 0.496564i
\(327\) 0 0
\(328\) 9271.39i 1.56075i
\(329\) 0 0
\(330\) 0 0
\(331\) 1353.22 + 2343.85i 0.224712 + 0.389213i 0.956233 0.292606i \(-0.0945225\pi\)
−0.731521 + 0.681819i \(0.761189\pi\)
\(332\) −1589.89 + 2753.76i −0.262820 + 0.455218i
\(333\) 0 0
\(334\) 3157.27 1822.85i 0.517239 0.298628i
\(335\) 3057.97 0.498731
\(336\) 0 0
\(337\) 10550.8 1.70545 0.852727 0.522357i \(-0.174947\pi\)
0.852727 + 0.522357i \(0.174947\pi\)
\(338\) 2048.40 1182.64i 0.329640 0.190318i
\(339\) 0 0
\(340\) −226.340 + 392.032i −0.0361029 + 0.0625321i
\(341\) 3817.16 + 6611.51i 0.606189 + 1.04995i
\(342\) 0 0
\(343\) 0 0
\(344\) 1353.78i 0.212183i
\(345\) 0 0
\(346\) −5677.19 3277.73i −0.882103 0.509283i
\(347\) −8636.09 4986.05i −1.33605 0.771369i −0.349831 0.936813i \(-0.613761\pi\)
−0.986219 + 0.165444i \(0.947094\pi\)
\(348\) 0 0
\(349\) 1653.11i 0.253549i −0.991932 0.126775i \(-0.959537\pi\)
0.991932 0.126775i \(-0.0404625\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2791.89 + 4835.69i 0.422751 + 0.732226i
\(353\) −1677.25 + 2905.09i −0.252893 + 0.438024i −0.964321 0.264735i \(-0.914715\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(354\) 0 0
\(355\) −2193.62 + 1266.49i −0.327959 + 0.189347i
\(356\) −8269.52 −1.23113
\(357\) 0 0
\(358\) 3449.47 0.509246
\(359\) 937.988 541.548i 0.137897 0.0796150i −0.429464 0.903084i \(-0.641298\pi\)
0.567361 + 0.823469i \(0.307964\pi\)
\(360\) 0 0
\(361\) 4245.53 7353.48i 0.618973 1.07209i
\(362\) 3461.92 + 5996.23i 0.502637 + 0.870593i
\(363\) 0 0
\(364\) 0 0
\(365\) 2982.76i 0.427739i
\(366\) 0 0
\(367\) −1823.53 1052.81i −0.259366 0.149745i 0.364679 0.931133i \(-0.381179\pi\)
−0.624045 + 0.781388i \(0.714512\pi\)
\(368\) −558.594 322.504i −0.0791269 0.0456839i
\(369\) 0 0
\(370\) 1647.63i 0.231503i
\(371\) 0 0
\(372\) 0 0
\(373\) −1867.35 3234.34i −0.259216 0.448975i 0.706816 0.707397i \(-0.250131\pi\)
−0.966032 + 0.258422i \(0.916797\pi\)
\(374\) −433.917 + 751.567i −0.0599928 + 0.103911i
\(375\) 0 0
\(376\) −7950.66 + 4590.31i −1.09049 + 0.629594i
\(377\) −2395.91 −0.327310
\(378\) 0 0
\(379\) −13141.6 −1.78111 −0.890555 0.454876i \(-0.849684\pi\)
−0.890555 + 0.454876i \(0.849684\pi\)
\(380\) 2721.17 1571.07i 0.367350 0.212090i
\(381\) 0 0
\(382\) −627.645 + 1087.11i −0.0840657 + 0.145606i
\(383\) 2671.88 + 4627.84i 0.356467 + 0.617419i 0.987368 0.158444i \(-0.0506479\pi\)
−0.630901 + 0.775863i \(0.717315\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7962.91i 1.05000i
\(387\) 0 0
\(388\) 3043.80 + 1757.34i 0.398262 + 0.229937i
\(389\) −1624.29 937.783i −0.211709 0.122230i 0.390397 0.920647i \(-0.372338\pi\)
−0.602105 + 0.798417i \(0.705671\pi\)
\(390\) 0 0
\(391\) 1465.00i 0.189484i
\(392\) 0 0
\(393\) 0 0
\(394\) −813.951 1409.81i −0.104077 0.180266i
\(395\) −1409.87 + 2441.96i −0.179590 + 0.311059i
\(396\) 0 0
\(397\) −8327.97 + 4808.16i −1.05282 + 0.607845i −0.923437 0.383750i \(-0.874633\pi\)
−0.129381 + 0.991595i \(0.541299\pi\)
\(398\) 3246.07 0.408821
\(399\) 0 0
\(400\) −807.262 −0.100908
\(401\) −562.762 + 324.911i −0.0700823 + 0.0404620i −0.534632 0.845085i \(-0.679550\pi\)
0.464549 + 0.885547i \(0.346216\pi\)
\(402\) 0 0
\(403\) 3455.70 5985.45i 0.427148 0.739842i
\(404\) −797.339 1381.03i −0.0981908 0.170072i
\(405\) 0 0
\(406\) 0 0
\(407\) 6461.52i 0.786943i
\(408\) 0 0
\(409\) −13491.6 7789.38i −1.63109 0.941711i −0.983757 0.179505i \(-0.942550\pi\)
−0.647334 0.762206i \(-0.724116\pi\)
\(410\) −2833.78 1636.08i −0.341343 0.197074i
\(411\) 0 0
\(412\) 2402.74i 0.287317i
\(413\) 0 0
\(414\) 0 0
\(415\) 1396.54 + 2418.89i 0.165190 + 0.286117i
\(416\) 2527.52 4377.79i 0.297889 0.515959i
\(417\) 0 0
\(418\) 5216.77 3011.91i 0.610432 0.352433i
\(419\) −5391.59 −0.628631 −0.314315 0.949319i \(-0.601775\pi\)
−0.314315 + 0.949319i \(0.601775\pi\)
\(420\) 0 0
\(421\) −12506.0 −1.44776 −0.723879 0.689927i \(-0.757642\pi\)
−0.723879 + 0.689927i \(0.757642\pi\)
\(422\) 3692.67 2131.97i 0.425963 0.245930i
\(423\) 0 0
\(424\) 7348.43 12727.8i 0.841677 1.45783i
\(425\) −916.765 1587.88i −0.104634 0.181232i
\(426\) 0 0
\(427\) 0 0
\(428\) 4066.57i 0.459264i
\(429\) 0 0
\(430\) 413.780 + 238.896i 0.0464052 + 0.0267920i
\(431\) −7648.94 4416.12i −0.854841 0.493543i 0.00744041 0.999972i \(-0.497632\pi\)
−0.862281 + 0.506430i \(0.830965\pi\)
\(432\) 0 0
\(433\) 5550.41i 0.616017i 0.951384 + 0.308009i \(0.0996626\pi\)
−0.951384 + 0.308009i \(0.900337\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −318.369 551.432i −0.0349705 0.0605707i
\(437\) −5084.44 + 8806.51i −0.556571 + 0.964010i
\(438\) 0 0
\(439\) −9848.19 + 5685.86i −1.07068 + 0.618157i −0.928367 0.371664i \(-0.878787\pi\)
−0.142313 + 0.989822i \(0.545454\pi\)
\(440\) 3068.91 0.332510
\(441\) 0 0
\(442\) 785.657 0.0845473
\(443\) 6944.93 4009.66i 0.744839 0.430033i −0.0789873 0.996876i \(-0.525169\pi\)
0.823826 + 0.566843i \(0.191835\pi\)
\(444\) 0 0
\(445\) −3631.94 + 6290.71i −0.386900 + 0.670131i
\(446\) 4029.25 + 6978.87i 0.427782 + 0.740940i
\(447\) 0 0
\(448\) 0 0
\(449\) 1039.67i 0.109276i 0.998506 + 0.0546379i \(0.0174005\pi\)
−0.998506 + 0.0546379i \(0.982600\pi\)
\(450\) 0 0
\(451\) 11113.3 + 6416.25i 1.16032 + 0.669910i
\(452\) −421.022 243.077i −0.0438124 0.0252951i
\(453\) 0 0
\(454\) 5543.69i 0.573079i
\(455\) 0 0
\(456\) 0 0
\(457\) −7151.36 12386.5i −0.732005 1.26787i −0.956025 0.293286i \(-0.905251\pi\)
0.224019 0.974585i \(-0.428082\pi\)
\(458\) 2592.70 4490.69i 0.264517 0.458158i
\(459\) 0 0
\(460\) −1802.68 + 1040.78i −0.182718 + 0.105492i
\(461\) −12732.1 −1.28632 −0.643159 0.765733i \(-0.722377\pi\)
−0.643159 + 0.765733i \(0.722377\pi\)
\(462\) 0 0
\(463\) 12358.7 1.24051 0.620256 0.784400i \(-0.287029\pi\)
0.620256 + 0.784400i \(0.287029\pi\)
\(464\) 600.402 346.642i 0.0600711 0.0346820i
\(465\) 0 0
\(466\) −1740.41 + 3014.47i −0.173010 + 0.299662i
\(467\) 6288.06 + 10891.2i 0.623077 + 1.07920i 0.988909 + 0.148520i \(0.0474509\pi\)
−0.365833 + 0.930681i \(0.619216\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 3240.14i 0.317992i
\(471\) 0 0
\(472\) −14405.2 8316.82i −1.40477 0.811044i
\(473\) −1622.72 936.880i −0.157744 0.0910735i
\(474\) 0 0
\(475\) 12726.9i 1.22937i
\(476\) 0 0
\(477\) 0 0
\(478\) 2312.18 + 4004.82i 0.221249 + 0.383214i
\(479\) 6137.19 10629.9i 0.585418 1.01397i −0.409405 0.912353i \(-0.634264\pi\)
0.994823 0.101621i \(-0.0324030\pi\)
\(480\) 0 0
\(481\) 5065.96 2924.83i 0.480224 0.277257i
\(482\) 638.137 0.0603036
\(483\) 0 0
\(484\) 2316.13 0.217518
\(485\) 2673.65 1543.63i 0.250318 0.144521i
\(486\) 0 0
\(487\) −3769.96 + 6529.76i −0.350787 + 0.607581i −0.986388 0.164437i \(-0.947419\pi\)
0.635601 + 0.772018i \(0.280753\pi\)
\(488\) −3918.72 6787.42i −0.363508 0.629614i
\(489\) 0 0
\(490\) 0 0
\(491\) 406.618i 0.0373735i −0.999825 0.0186868i \(-0.994051\pi\)
0.999825 0.0186868i \(-0.00594853\pi\)
\(492\) 0 0
\(493\) 1363.69 + 787.326i 0.124579 + 0.0719258i
\(494\) −4722.78 2726.70i −0.430138 0.248340i
\(495\) 0 0
\(496\) 1999.89i 0.181044i
\(497\) 0 0
\(498\) 0 0
\(499\) −2752.48 4767.44i −0.246930 0.427695i 0.715742 0.698364i \(-0.246088\pi\)
−0.962672 + 0.270669i \(0.912755\pi\)
\(500\) −2887.66 + 5001.58i −0.258280 + 0.447355i
\(501\) 0 0
\(502\) 3537.49 2042.37i 0.314514 0.181585i
\(503\) 6535.76 0.579354 0.289677 0.957124i \(-0.406452\pi\)
0.289677 + 0.957124i \(0.406452\pi\)
\(504\) 0 0
\(505\) −1400.75 −0.123431
\(506\) −3455.93 + 1995.28i −0.303626 + 0.175299i
\(507\) 0 0
\(508\) −873.135 + 1512.31i −0.0762581 + 0.132083i
\(509\) −8953.46 15507.9i −0.779677 1.35044i −0.932128 0.362128i \(-0.882050\pi\)
0.152452 0.988311i \(-0.451283\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 2825.37i 0.243877i
\(513\) 0 0
\(514\) 5967.89 + 3445.56i 0.512125 + 0.295675i
\(515\) 1827.79 + 1055.28i 0.156392 + 0.0902932i
\(516\) 0 0
\(517\) 12706.9i 1.08094i
\(518\) 0 0
\(519\) 0 0
\(520\) −1389.15 2406.08i −0.117151 0.202911i
\(521\) −5445.98 + 9432.71i −0.457951 + 0.793195i −0.998853 0.0478914i \(-0.984750\pi\)
0.540901 + 0.841086i \(0.318083\pi\)
\(522\) 0 0
\(523\) 2311.20 1334.37i 0.193235 0.111564i −0.400261 0.916401i \(-0.631081\pi\)
0.593496 + 0.804837i \(0.297747\pi\)
\(524\) −3642.28 −0.303652
\(525\) 0 0
\(526\) 11501.6 0.953411
\(527\) −3933.79 + 2271.17i −0.325158 + 0.187730i
\(528\) 0 0
\(529\) −2715.24 + 4702.93i −0.223164 + 0.386532i
\(530\) −2593.49 4492.06i −0.212555 0.368156i
\(531\) 0 0
\(532\) 0 0
\(533\) 11617.4i 0.944097i
\(534\) 0 0
\(535\) −3093.48 1786.02i −0.249987 0.144330i
\(536\) 12161.3 + 7021.32i 0.980013 + 0.565811i
\(537\) 0 0
\(538\) 7067.68i 0.566374i
\(539\) 0 0
\(540\) 0 0
\(541\) 5388.29 + 9332.80i 0.428209 + 0.741679i 0.996714 0.0810005i \(-0.0258115\pi\)
−0.568506 + 0.822679i \(0.692478\pi\)
\(542\) −3497.52 + 6057.89i −0.277180 + 0.480089i
\(543\) 0 0
\(544\) −2877.19 + 1661.15i −0.226762 + 0.130921i
\(545\) −559.307 −0.0439598
\(546\) 0 0
\(547\) −6796.09 −0.531225 −0.265612 0.964080i \(-0.585574\pi\)
−0.265612 + 0.964080i \(0.585574\pi\)
\(548\) −10027.8 + 5789.54i −0.781689 + 0.451308i
\(549\) 0 0
\(550\) −2497.20 + 4325.28i −0.193602 + 0.335328i
\(551\) −5464.99 9465.64i −0.422534 0.731851i
\(552\) 0 0
\(553\) 0 0
\(554\) 4276.94i 0.327996i
\(555\) 0 0
\(556\) 3348.21 + 1933.09i 0.255388 + 0.147448i
\(557\) 15641.9 + 9030.85i 1.18989 + 0.686983i 0.958282 0.285826i \(-0.0922680\pi\)
0.231608 + 0.972809i \(0.425601\pi\)
\(558\) 0 0
\(559\) 1696.33i 0.128349i
\(560\) 0 0
\(561\) 0 0
\(562\) −4801.82 8316.99i −0.360413 0.624254i
\(563\) 10523.3 18227.0i 0.787755 1.36443i −0.139585 0.990210i \(-0.544577\pi\)
0.927339 0.374221i \(-0.122090\pi\)
\(564\) 0 0
\(565\) −369.823 + 213.517i −0.0275373 + 0.0158986i
\(566\) −4984.19 −0.370143
\(567\) 0 0
\(568\) −11631.8 −0.859257
\(569\) 10497.9 6060.98i 0.773455 0.446554i −0.0606509 0.998159i \(-0.519318\pi\)
0.834106 + 0.551605i \(0.185984\pi\)
\(570\) 0 0
\(571\) 1472.07 2549.70i 0.107888 0.186868i −0.807026 0.590516i \(-0.798924\pi\)
0.914915 + 0.403647i \(0.132258\pi\)
\(572\) 2188.91 + 3791.30i 0.160005 + 0.277137i
\(573\) 0 0
\(574\) 0 0
\(575\) 8431.12i 0.611482i
\(576\) 0 0
\(577\) 4495.86 + 2595.69i 0.324376 + 0.187279i 0.653342 0.757063i \(-0.273367\pi\)
−0.328965 + 0.944342i \(0.606700\pi\)
\(578\) 6448.60 + 3723.10i 0.464060 + 0.267925i
\(579\) 0 0
\(580\) 2237.35i 0.160174i
\(581\) 0 0
\(582\) 0 0
\(583\) 10170.9 + 17616.6i 0.722533 + 1.25146i
\(584\) 6848.63 11862.2i 0.485271 0.840514i
\(585\) 0 0
\(586\) −2185.81 + 1261.98i −0.154087 + 0.0889620i
\(587\) 21918.4 1.54118 0.770588 0.637334i \(-0.219963\pi\)
0.770588 + 0.637334i \(0.219963\pi\)
\(588\) 0 0
\(589\) 31529.3 2.20568
\(590\) −5084.04 + 2935.27i −0.354757 + 0.204819i
\(591\) 0 0
\(592\) −846.334 + 1465.89i −0.0587569 + 0.101770i
\(593\) −10119.7 17527.9i −0.700788 1.21380i −0.968190 0.250216i \(-0.919499\pi\)
0.267402 0.963585i \(-0.413835\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6419.55i 0.441200i
\(597\) 0 0
\(598\) 3128.68 + 1806.34i 0.213948 + 0.123523i
\(599\) 7376.06 + 4258.57i 0.503135 + 0.290485i 0.730007 0.683439i \(-0.239517\pi\)
−0.226872 + 0.973925i \(0.572850\pi\)
\(600\) 0 0
\(601\) 5040.33i 0.342096i −0.985263 0.171048i \(-0.945285\pi\)
0.985263 0.171048i \(-0.0547152\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2880.44 4989.07i −0.194046 0.336097i
\(605\) 1017.24 1761.90i 0.0683579 0.118399i
\(606\) 0 0
\(607\) 23489.5 13561.6i 1.57069 0.906837i 0.574604 0.818432i \(-0.305156\pi\)
0.996085 0.0884057i \(-0.0281772\pi\)
\(608\) 23060.7 1.53822
\(609\) 0 0
\(610\) −2766.08 −0.183599
\(611\) −9962.44 + 5751.81i −0.659635 + 0.380840i
\(612\) 0 0
\(613\) −1467.22 + 2541.30i −0.0966730 + 0.167443i −0.910306 0.413937i \(-0.864153\pi\)
0.813633 + 0.581379i \(0.197487\pi\)
\(614\) 1460.80 + 2530.19i 0.0960151 + 0.166303i
\(615\) 0 0
\(616\) 0 0
\(617\) 2908.86i 0.189799i 0.995487 + 0.0948996i \(0.0302530\pi\)
−0.995487 + 0.0948996i \(0.969747\pi\)
\(618\) 0 0
\(619\) 13814.4 + 7975.77i 0.897010 + 0.517889i 0.876229 0.481895i \(-0.160051\pi\)
0.0207811 + 0.999784i \(0.493385\pi\)
\(620\) 5589.33 + 3227.00i 0.362053 + 0.209032i
\(621\) 0 0
\(622\) 15461.5i 0.996706i
\(623\) 0 0
\(624\) 0 0
\(625\) −3883.68 6726.73i −0.248556 0.430511i
\(626\) −1024.83 + 1775.05i −0.0654319 + 0.113331i
\(627\) 0 0
\(628\) 10865.5 6273.18i 0.690412 0.398610i
\(629\) −3844.54 −0.243707
\(630\) 0 0
\(631\) −31218.8 −1.96957 −0.984786 0.173771i \(-0.944405\pi\)
−0.984786 + 0.173771i \(0.944405\pi\)
\(632\) −11213.8 + 6474.30i −0.705793 + 0.407490i
\(633\) 0 0
\(634\) −7734.35 + 13396.3i −0.484496 + 0.839171i
\(635\) 766.955 + 1328.41i 0.0479302 + 0.0830176i
\(636\) 0 0
\(637\) 0 0
\(638\) 4289.24i 0.266164i
\(639\) 0 0
\(640\) 4504.56 + 2600.71i 0.278216 + 0.160628i
\(641\) 4720.80 + 2725.55i 0.290890 + 0.167945i 0.638343 0.769752i \(-0.279620\pi\)
−0.347453 + 0.937697i \(0.612953\pi\)
\(642\) 0 0
\(643\) 15700.8i 0.962956i −0.876458 0.481478i \(-0.840100\pi\)
0.876458 0.481478i \(-0.159900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1792.06 + 3103.93i 0.109145 + 0.189044i
\(647\) 11372.0 19696.9i 0.691006 1.19686i −0.280502 0.959853i \(-0.590501\pi\)
0.971509 0.237004i \(-0.0761656\pi\)
\(648\) 0 0
\(649\) 19938.1 11511.3i 1.20592 0.696236i
\(650\) 4521.47 0.272841
\(651\) 0 0
\(652\) 19380.6 1.16411
\(653\) 4984.17 2877.61i 0.298691 0.172450i −0.343163 0.939276i \(-0.611498\pi\)
0.641855 + 0.766826i \(0.278165\pi\)
\(654\) 0 0
\(655\) −1599.68 + 2770.72i −0.0954268 + 0.165284i
\(656\) 1680.81 + 2911.24i 0.100037 + 0.173270i
\(657\) 0 0
\(658\) 0 0
\(659\) 24579.2i 1.45292i 0.687211 + 0.726458i \(0.258835\pi\)
−0.687211 + 0.726458i \(0.741165\pi\)
\(660\) 0 0
\(661\) 4251.57 + 2454.64i 0.250177 + 0.144440i 0.619845 0.784724i \(-0.287195\pi\)
−0.369669 + 0.929164i \(0.620529\pi\)
\(662\) 3798.70 + 2193.18i 0.223022 + 0.128762i
\(663\) 0 0
\(664\) 12826.2i 0.749631i
\(665\) 0 0
\(666\) 0 0
\(667\) 3620.36 + 6270.65i 0.210166 + 0.364019i
\(668\) −6043.46 + 10467.6i −0.350043 + 0.606291i
\(669\) 0 0
\(670\) 4292.10 2478.05i 0.247490 0.142888i
\(671\) 10847.8 0.624103
\(672\) 0 0
\(673\) 2635.70 0.150964 0.0754819 0.997147i \(-0.475950\pi\)
0.0754819 + 0.997147i \(0.475950\pi\)
\(674\) 14808.8 8549.89i 0.846314 0.488619i
\(675\) 0 0
\(676\) −3920.93 + 6791.25i −0.223084 + 0.386393i
\(677\) 3191.45 + 5527.76i 0.181178 + 0.313809i 0.942282 0.334821i \(-0.108676\pi\)
−0.761104 + 0.648630i \(0.775342\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1825.97i 0.102975i
\(681\) 0 0
\(682\) 10715.3 + 6186.51i 0.601630 + 0.347351i
\(683\) 11952.8 + 6900.95i 0.669636 + 0.386614i 0.795939 0.605377i \(-0.206978\pi\)
−0.126303 + 0.991992i \(0.540311\pi\)
\(684\) 0 0
\(685\) 10171.0i 0.567318i
\(686\) 0 0
\(687\) 0 0
\(688\) −245.426 425.091i −0.0136000 0.0235559i
\(689\) 9207.82 15948.4i 0.509129 0.881838i
\(690\) 0 0
\(691\) −1516.12 + 875.333i −0.0834674 + 0.0481899i −0.541153 0.840924i \(-0.682012\pi\)
0.457685 + 0.889114i \(0.348679\pi\)
\(692\) 21733.9 1.19393
\(693\) 0 0
\(694\) −16161.9 −0.884001
\(695\) 2941.04 1698.01i 0.160518 0.0926752i
\(696\) 0 0
\(697\) −3817.61 + 6612.29i −0.207464 + 0.359338i
\(698\) −1339.60 2320.26i −0.0726429 0.125821i
\(699\) 0 0
\(700\) 0 0
\(701\) 26927.8i 1.45085i −0.688300 0.725426i \(-0.741643\pi\)
0.688300 0.725426i \(-0.258357\pi\)
\(702\) 0 0
\(703\) 23110.5 + 13342.9i 1.23987 + 0.715841i
\(704\) 6203.92 + 3581.83i 0.332129 + 0.191755i
\(705\) 0 0
\(706\) 5436.69i 0.289819i
\(707\) 0 0
\(708\) 0 0
\(709\) 5801.80 + 10049.0i 0.307322 + 0.532297i 0.977776 0.209654i \(-0.0672338\pi\)
−0.670454 + 0.741952i \(0.733900\pi\)
\(710\) −2052.61 + 3555.23i −0.108497 + 0.187923i
\(711\) 0 0
\(712\) −28887.8 + 16678.4i −1.52053 + 0.877877i
\(713\) −20887.1 −1.09709
\(714\) 0 0
\(715\) 3845.44 0.201135
\(716\) −9904.17 + 5718.17i −0.516950 + 0.298461i
\(717\) 0 0
\(718\) 877.693 1520.21i 0.0456201 0.0790163i
\(719\) −6750.67 11692.5i −0.350150 0.606477i 0.636126 0.771585i \(-0.280536\pi\)
−0.986275 + 0.165108i \(0.947203\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13761.6i 0.709353i
\(723\) 0 0
\(724\) −19879.8 11477.6i −1.02048 0.589175i
\(725\) 7848.06 + 4531.08i 0.402027 + 0.232110i
\(726\) 0 0
\(727\) 1116.75i 0.0569708i 0.999594 + 0.0284854i \(0.00906842\pi\)
−0.999594 + 0.0284854i \(0.990932\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2417.10 4186.54i −0.122549 0.212261i
\(731\) 557.435 965.505i 0.0282045 0.0488516i
\(732\) 0 0
\(733\) 25019.4 14444.9i 1.26072 0.727879i 0.287510 0.957778i \(-0.407173\pi\)
0.973215 + 0.229898i \(0.0738394\pi\)
\(734\) −3412.62 −0.171610
\(735\) 0 0
\(736\) −15276.9 −0.765101
\(737\) −16832.4 + 9718.18i −0.841287 + 0.485717i
\(738\) 0 0
\(739\) 996.244 1725.55i 0.0495906 0.0858934i −0.840165 0.542332i \(-0.817542\pi\)
0.889755 + 0.456438i \(0.150875\pi\)
\(740\) 2731.27 + 4730.69i 0.135680 + 0.235005i
\(741\) 0 0
\(742\) 0 0
\(743\) 32395.7i 1.59957i 0.600284 + 0.799787i \(0.295054\pi\)
−0.600284 + 0.799787i \(0.704946\pi\)
\(744\) 0 0
\(745\) −4883.42 2819.44i −0.240154 0.138653i
\(746\) −5241.93 3026.43i −0.257266 0.148533i
\(747\) 0 0
\(748\) 2877.21i 0.140643i
\(749\) 0 0
\(750\) 0 0
\(751\) 3796.22 + 6575.24i 0.184455 + 0.319486i 0.943393 0.331677i \(-0.107615\pi\)
−0.758937 + 0.651163i \(0.774281\pi\)
\(752\) 1664.35 2882.75i 0.0807084 0.139791i
\(753\) 0 0
\(754\) −3362.85 + 1941.54i −0.162424 + 0.0937755i
\(755\) −5060.32 −0.243926
\(756\) 0 0
\(757\) 29398.9 1.41152 0.705760 0.708451i \(-0.250605\pi\)
0.705760 + 0.708451i \(0.250605\pi\)
\(758\) −18445.3 + 10649.4i −0.883857 + 0.510295i
\(759\) 0 0
\(760\) 6337.22 10976.4i 0.302467 0.523888i
\(761\) −16277.5 28193.4i −0.775373 1.34299i −0.934585 0.355741i \(-0.884229\pi\)
0.159212 0.987244i \(-0.449105\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4161.78i 0.197078i
\(765\) 0 0
\(766\) 7500.39 + 4330.35i 0.353786 + 0.204258i
\(767\) −18050.1 10421.2i −0.849742 0.490599i
\(768\) 0 0
\(769\) 34767.8i 1.63038i −0.579195 0.815189i \(-0.696633\pi\)
0.579195 0.815189i \(-0.303367\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −13200.1 22863.2i −0.615391 1.06589i
\(773\) −2994.63 + 5186.85i −0.139339 + 0.241343i −0.927247 0.374451i \(-0.877831\pi\)
0.787907 + 0.615794i \(0.211165\pi\)
\(774\) 0 0
\(775\) −22639.0 + 13070.6i −1.04931 + 0.605821i
\(776\) 14177.2 0.655838
\(777\) 0 0
\(778\) −3039.75 −0.140078
\(779\) 45897.2 26498.8i 2.11096 1.21876i
\(780\) 0 0
\(781\) 8049.74 13942.6i 0.368812 0.638802i
\(782\) −1187.17 2056.25i −0.0542880 0.0940296i
\(783\) 0 0
\(784\) 0 0
\(785\) 11020.6i 0.501074i
\(786\) 0 0
\(787\) −36037.5 20806.3i −1.63227 0.942393i −0.983390 0.181504i \(-0.941903\pi\)
−0.648882 0.760889i \(-0.724763\pi\)
\(788\) 4674.06 + 2698.57i 0.211302 + 0.121996i
\(789\) 0 0
\(790\) 4569.97i 0.205813i
\(791\) 0 0
\(792\) 0 0