Properties

Label 882.4.g.j.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.j.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +(8.00000 - 13.8564i) q^{10} +(20.0000 - 34.6410i) q^{11} +4.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-74.0000 - 128.172i) q^{19} -32.0000 q^{20} -80.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(30.5000 - 52.8275i) q^{25} +(-4.00000 - 6.92820i) q^{26} -58.0000 q^{29} +(68.0000 - 117.779i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(111.000 + 192.258i) q^{37} +(-148.000 + 256.344i) q^{38} +(32.0000 + 55.4256i) q^{40} -420.000 q^{41} -164.000 q^{43} +(80.0000 + 138.564i) q^{44} +(84.0000 - 145.492i) q^{46} +(244.000 + 422.620i) q^{47} -122.000 q^{50} +(-8.00000 + 13.8564i) q^{52} +(239.000 - 413.960i) q^{53} +320.000 q^{55} +(58.0000 + 100.459i) q^{58} +(274.000 - 474.582i) q^{59} +(-346.000 - 599.290i) q^{61} -272.000 q^{62} +64.0000 q^{64} +(16.0000 + 27.7128i) q^{65} +(454.000 - 786.351i) q^{67} +(-168.000 - 290.985i) q^{68} +524.000 q^{71} +(-220.000 + 381.051i) q^{73} +(222.000 - 384.515i) q^{74} +592.000 q^{76} +(-608.000 - 1053.09i) q^{79} +(64.0000 - 110.851i) q^{80} +(420.000 + 727.461i) q^{82} +684.000 q^{83} -672.000 q^{85} +(164.000 + 284.056i) q^{86} +(160.000 - 277.128i) q^{88} +(302.000 + 523.079i) q^{89} -336.000 q^{92} +(488.000 - 845.241i) q^{94} +(592.000 - 1025.37i) q^{95} -832.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 8q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 8q^{5} + 16q^{8} + 16q^{10} + 40q^{11} + 8q^{13} - 16q^{16} - 84q^{17} - 148q^{19} - 64q^{20} - 160q^{22} + 84q^{23} + 61q^{25} - 8q^{26} - 116q^{29} + 136q^{31} - 32q^{32} + 336q^{34} + 222q^{37} - 296q^{38} + 64q^{40} - 840q^{41} - 328q^{43} + 160q^{44} + 168q^{46} + 488q^{47} - 244q^{50} - 16q^{52} + 478q^{53} + 640q^{55} + 116q^{58} + 548q^{59} - 692q^{61} - 544q^{62} + 128q^{64} + 32q^{65} + 908q^{67} - 336q^{68} + 1048q^{71} - 440q^{73} + 444q^{74} + 1184q^{76} - 1216q^{79} + 128q^{80} + 840q^{82} + 1368q^{83} - 1344q^{85} + 328q^{86} + 320q^{88} + 604q^{89} - 672q^{92} + 976q^{94} + 1184q^{95} - 1664q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 4.00000 + 6.92820i 0.357771 + 0.619677i 0.987588 0.157066i \(-0.0502036\pi\)
−0.629817 + 0.776743i \(0.716870\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 8.00000 13.8564i 0.252982 0.438178i
\(11\) 20.0000 34.6410i 0.548202 0.949514i −0.450195 0.892930i \(-0.648646\pi\)
0.998398 0.0565844i \(-0.0180210\pi\)
\(12\) 0 0
\(13\) 4.00000 0.0853385 0.0426692 0.999089i \(-0.486414\pi\)
0.0426692 + 0.999089i \(0.486414\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −42.0000 + 72.7461i −0.599206 + 1.03785i 0.393733 + 0.919225i \(0.371183\pi\)
−0.992939 + 0.118630i \(0.962150\pi\)
\(18\) 0 0
\(19\) −74.0000 128.172i −0.893514 1.54761i −0.835633 0.549288i \(-0.814899\pi\)
−0.0578808 0.998324i \(-0.518434\pi\)
\(20\) −32.0000 −0.357771
\(21\) 0 0
\(22\) −80.0000 −0.775275
\(23\) 42.0000 + 72.7461i 0.380765 + 0.659505i 0.991172 0.132583i \(-0.0423272\pi\)
−0.610406 + 0.792088i \(0.708994\pi\)
\(24\) 0 0
\(25\) 30.5000 52.8275i 0.244000 0.422620i
\(26\) −4.00000 6.92820i −0.0301717 0.0522589i
\(27\) 0 0
\(28\) 0 0
\(29\) −58.0000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 68.0000 117.779i 0.393973 0.682381i −0.598997 0.800752i \(-0.704434\pi\)
0.992970 + 0.118370i \(0.0377670\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 168.000 0.847405
\(35\) 0 0
\(36\) 0 0
\(37\) 111.000 + 192.258i 0.493197 + 0.854242i 0.999969 0.00783774i \(-0.00249486\pi\)
−0.506772 + 0.862080i \(0.669162\pi\)
\(38\) −148.000 + 256.344i −0.631810 + 1.09433i
\(39\) 0 0
\(40\) 32.0000 + 55.4256i 0.126491 + 0.219089i
\(41\) −420.000 −1.59983 −0.799914 0.600114i \(-0.795122\pi\)
−0.799914 + 0.600114i \(0.795122\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) 80.0000 + 138.564i 0.274101 + 0.474757i
\(45\) 0 0
\(46\) 84.0000 145.492i 0.269242 0.466341i
\(47\) 244.000 + 422.620i 0.757257 + 1.31161i 0.944245 + 0.329245i \(0.106794\pi\)
−0.186988 + 0.982362i \(0.559873\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −122.000 −0.345068
\(51\) 0 0
\(52\) −8.00000 + 13.8564i −0.0213346 + 0.0369527i
\(53\) 239.000 413.960i 0.619418 1.07286i −0.370174 0.928963i \(-0.620702\pi\)
0.989592 0.143902i \(-0.0459649\pi\)
\(54\) 0 0
\(55\) 320.000 0.784523
\(56\) 0 0
\(57\) 0 0
\(58\) 58.0000 + 100.459i 0.131306 + 0.227429i
\(59\) 274.000 474.582i 0.604606 1.04721i −0.387507 0.921867i \(-0.626664\pi\)
0.992114 0.125342i \(-0.0400028\pi\)
\(60\) 0 0
\(61\) −346.000 599.290i −0.726242 1.25789i −0.958461 0.285224i \(-0.907932\pi\)
0.232219 0.972664i \(-0.425401\pi\)
\(62\) −272.000 −0.557162
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 16.0000 + 27.7128i 0.0305316 + 0.0528823i
\(66\) 0 0
\(67\) 454.000 786.351i 0.827835 1.43385i −0.0718987 0.997412i \(-0.522906\pi\)
0.899733 0.436440i \(-0.143761\pi\)
\(68\) −168.000 290.985i −0.299603 0.518927i
\(69\) 0 0
\(70\) 0 0
\(71\) 524.000 0.875878 0.437939 0.899005i \(-0.355709\pi\)
0.437939 + 0.899005i \(0.355709\pi\)
\(72\) 0 0
\(73\) −220.000 + 381.051i −0.352727 + 0.610941i −0.986726 0.162393i \(-0.948079\pi\)
0.633999 + 0.773334i \(0.281412\pi\)
\(74\) 222.000 384.515i 0.348743 0.604040i
\(75\) 0 0
\(76\) 592.000 0.893514
\(77\) 0 0
\(78\) 0 0
\(79\) −608.000 1053.09i −0.865890 1.49977i −0.866160 0.499766i \(-0.833419\pi\)
0.000269874 1.00000i \(-0.499914\pi\)
\(80\) 64.0000 110.851i 0.0894427 0.154919i
\(81\) 0 0
\(82\) 420.000 + 727.461i 0.565625 + 0.979691i
\(83\) 684.000 0.904563 0.452282 0.891875i \(-0.350610\pi\)
0.452282 + 0.891875i \(0.350610\pi\)
\(84\) 0 0
\(85\) −672.000 −0.857513
\(86\) 164.000 + 284.056i 0.205635 + 0.356170i
\(87\) 0 0
\(88\) 160.000 277.128i 0.193819 0.335704i
\(89\) 302.000 + 523.079i 0.359685 + 0.622992i 0.987908 0.155041i \(-0.0495509\pi\)
−0.628223 + 0.778033i \(0.716218\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) 0 0
\(94\) 488.000 845.241i 0.535461 0.927446i
\(95\) 592.000 1025.37i 0.639347 1.10738i
\(96\) 0 0
\(97\) −832.000 −0.870895 −0.435447 0.900214i \(-0.643410\pi\)
−0.435447 + 0.900214i \(0.643410\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 122.000 + 211.310i 0.122000 + 0.211310i
\(101\) 232.000 401.836i 0.228563 0.395883i −0.728819 0.684706i \(-0.759931\pi\)
0.957382 + 0.288823i \(0.0932640\pi\)
\(102\) 0 0
\(103\) 316.000 + 547.328i 0.302295 + 0.523591i 0.976655 0.214812i \(-0.0689138\pi\)
−0.674360 + 0.738402i \(0.735580\pi\)
\(104\) 32.0000 0.0301717
\(105\) 0 0
\(106\) −956.000 −0.875990
\(107\) −80.0000 138.564i −0.0722794 0.125192i 0.827621 0.561288i \(-0.189694\pi\)
−0.899900 + 0.436096i \(0.856361\pi\)
\(108\) 0 0
\(109\) 1099.00 1903.52i 0.965735 1.67270i 0.258108 0.966116i \(-0.416901\pi\)
0.707627 0.706586i \(-0.249766\pi\)
\(110\) −320.000 554.256i −0.277371 0.480421i
\(111\) 0 0
\(112\) 0 0
\(113\) −770.000 −0.641022 −0.320511 0.947245i \(-0.603855\pi\)
−0.320511 + 0.947245i \(0.603855\pi\)
\(114\) 0 0
\(115\) −336.000 + 581.969i −0.272454 + 0.471903i
\(116\) 116.000 200.918i 0.0928477 0.160817i
\(117\) 0 0
\(118\) −1096.00 −0.855042
\(119\) 0 0
\(120\) 0 0
\(121\) −134.500 232.961i −0.101052 0.175027i
\(122\) −692.000 + 1198.58i −0.513531 + 0.889461i
\(123\) 0 0
\(124\) 272.000 + 471.118i 0.196986 + 0.341191i
\(125\) 1488.00 1.06473
\(126\) 0 0
\(127\) −184.000 −0.128562 −0.0642809 0.997932i \(-0.520475\pi\)
−0.0642809 + 0.997932i \(0.520475\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 32.0000 55.4256i 0.0215891 0.0373935i
\(131\) −726.000 1257.47i −0.484205 0.838668i 0.515630 0.856811i \(-0.327558\pi\)
−0.999835 + 0.0181429i \(0.994225\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1816.00 −1.17074
\(135\) 0 0
\(136\) −336.000 + 581.969i −0.211851 + 0.366937i
\(137\) 323.000 559.452i 0.201429 0.348885i −0.747560 0.664194i \(-0.768775\pi\)
0.948989 + 0.315309i \(0.102108\pi\)
\(138\) 0 0
\(139\) −3012.00 −1.83795 −0.918973 0.394320i \(-0.870980\pi\)
−0.918973 + 0.394320i \(0.870980\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −524.000 907.595i −0.309670 0.536364i
\(143\) 80.0000 138.564i 0.0467828 0.0810301i
\(144\) 0 0
\(145\) −232.000 401.836i −0.132873 0.230142i
\(146\) 880.000 0.498831
\(147\) 0 0
\(148\) −888.000 −0.493197
\(149\) −1585.00 2745.30i −0.871465 1.50942i −0.860482 0.509482i \(-0.829837\pi\)
−0.0109833 0.999940i \(-0.503496\pi\)
\(150\) 0 0
\(151\) 940.000 1628.13i 0.506597 0.877451i −0.493374 0.869817i \(-0.664237\pi\)
0.999971 0.00763414i \(-0.00243005\pi\)
\(152\) −592.000 1025.37i −0.315905 0.547163i
\(153\) 0 0
\(154\) 0 0
\(155\) 1088.00 0.563808
\(156\) 0 0
\(157\) −302.000 + 523.079i −0.153517 + 0.265900i −0.932518 0.361123i \(-0.882393\pi\)
0.779001 + 0.627023i \(0.215727\pi\)
\(158\) −1216.00 + 2106.17i −0.612277 + 1.06049i
\(159\) 0 0
\(160\) −256.000 −0.126491
\(161\) 0 0
\(162\) 0 0
\(163\) −558.000 966.484i −0.268135 0.464423i 0.700246 0.713902i \(-0.253074\pi\)
−0.968380 + 0.249479i \(0.919741\pi\)
\(164\) 840.000 1454.92i 0.399957 0.692746i
\(165\) 0 0
\(166\) −684.000 1184.72i −0.319811 0.553930i
\(167\) 1784.00 0.826647 0.413324 0.910584i \(-0.364368\pi\)
0.413324 + 0.910584i \(0.364368\pi\)
\(168\) 0 0
\(169\) −2181.00 −0.992717
\(170\) 672.000 + 1163.94i 0.303177 + 0.525118i
\(171\) 0 0
\(172\) 328.000 568.113i 0.145406 0.251850i
\(173\) −172.000 297.913i −0.0755891 0.130924i 0.825753 0.564032i \(-0.190750\pi\)
−0.901342 + 0.433107i \(0.857417\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −640.000 −0.274101
\(177\) 0 0
\(178\) 604.000 1046.16i 0.254335 0.440522i
\(179\) 696.000 1205.51i 0.290623 0.503373i −0.683334 0.730106i \(-0.739471\pi\)
0.973957 + 0.226732i \(0.0728042\pi\)
\(180\) 0 0
\(181\) 4052.00 1.66399 0.831997 0.554781i \(-0.187198\pi\)
0.831997 + 0.554781i \(0.187198\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 336.000 + 581.969i 0.134621 + 0.233170i
\(185\) −888.000 + 1538.06i −0.352903 + 0.611246i
\(186\) 0 0
\(187\) 1680.00 + 2909.85i 0.656972 + 1.13791i
\(188\) −1952.00 −0.757257
\(189\) 0 0
\(190\) −2368.00 −0.904173
\(191\) −1554.00 2691.61i −0.588709 1.01967i −0.994402 0.105665i \(-0.966303\pi\)
0.405692 0.914010i \(-0.367030\pi\)
\(192\) 0 0
\(193\) −25.0000 + 43.3013i −0.00932404 + 0.0161497i −0.870650 0.491903i \(-0.836301\pi\)
0.861326 + 0.508053i \(0.169635\pi\)
\(194\) 832.000 + 1441.07i 0.307908 + 0.533312i
\(195\) 0 0
\(196\) 0 0
\(197\) 162.000 0.0585889 0.0292945 0.999571i \(-0.490674\pi\)
0.0292945 + 0.999571i \(0.490674\pi\)
\(198\) 0 0
\(199\) −772.000 + 1337.14i −0.275003 + 0.476319i −0.970136 0.242562i \(-0.922012\pi\)
0.695133 + 0.718881i \(0.255346\pi\)
\(200\) 244.000 422.620i 0.0862670 0.149419i
\(201\) 0 0
\(202\) −928.000 −0.323237
\(203\) 0 0
\(204\) 0 0
\(205\) −1680.00 2909.85i −0.572372 0.991378i
\(206\) 632.000 1094.66i 0.213755 0.370234i
\(207\) 0 0
\(208\) −32.0000 55.4256i −0.0106673 0.0184763i
\(209\) −5920.00 −1.95931
\(210\) 0 0
\(211\) −1204.00 −0.392828 −0.196414 0.980521i \(-0.562930\pi\)
−0.196414 + 0.980521i \(0.562930\pi\)
\(212\) 956.000 + 1655.84i 0.309709 + 0.536432i
\(213\) 0 0
\(214\) −160.000 + 277.128i −0.0511092 + 0.0885238i
\(215\) −656.000 1136.23i −0.208088 0.360418i
\(216\) 0 0
\(217\) 0 0
\(218\) −4396.00 −1.36576
\(219\) 0 0
\(220\) −640.000 + 1108.51i −0.196131 + 0.339709i
\(221\) −168.000 + 290.985i −0.0511353 + 0.0885690i
\(222\) 0 0
\(223\) 2000.00 0.600583 0.300291 0.953848i \(-0.402916\pi\)
0.300291 + 0.953848i \(0.402916\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 770.000 + 1333.68i 0.226636 + 0.392544i
\(227\) 194.000 336.018i 0.0567235 0.0982480i −0.836269 0.548319i \(-0.815268\pi\)
0.892993 + 0.450071i \(0.148601\pi\)
\(228\) 0 0
\(229\) −2090.00 3619.99i −0.603105 1.04461i −0.992348 0.123474i \(-0.960597\pi\)
0.389243 0.921135i \(-0.372737\pi\)
\(230\) 1344.00 0.385308
\(231\) 0 0
\(232\) −464.000 −0.131306
\(233\) −661.000 1144.89i −0.185852 0.321905i 0.758011 0.652242i \(-0.226171\pi\)
−0.943863 + 0.330336i \(0.892838\pi\)
\(234\) 0 0
\(235\) −1952.00 + 3380.96i −0.541849 + 0.938509i
\(236\) 1096.00 + 1898.33i 0.302303 + 0.523604i
\(237\) 0 0
\(238\) 0 0
\(239\) −2412.00 −0.652800 −0.326400 0.945232i \(-0.605836\pi\)
−0.326400 + 0.945232i \(0.605836\pi\)
\(240\) 0 0
\(241\) 2168.00 3755.09i 0.579474 1.00368i −0.416066 0.909334i \(-0.636591\pi\)
0.995540 0.0943434i \(-0.0300752\pi\)
\(242\) −269.000 + 465.922i −0.0714544 + 0.123763i
\(243\) 0 0
\(244\) 2768.00 0.726242
\(245\) 0 0
\(246\) 0 0
\(247\) −296.000 512.687i −0.0762511 0.132071i
\(248\) 544.000 942.236i 0.139290 0.241258i
\(249\) 0 0
\(250\) −1488.00 2577.29i −0.376438 0.652009i
\(251\) −764.000 −0.192125 −0.0960623 0.995375i \(-0.530625\pi\)
−0.0960623 + 0.995375i \(0.530625\pi\)
\(252\) 0 0
\(253\) 3360.00 0.834946
\(254\) 184.000 + 318.697i 0.0454535 + 0.0787278i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2150.00 + 3723.91i 0.521842 + 0.903856i 0.999677 + 0.0254070i \(0.00808817\pi\)
−0.477835 + 0.878449i \(0.658579\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −128.000 −0.0305316
\(261\) 0 0
\(262\) −1452.00 + 2514.94i −0.342385 + 0.593028i
\(263\) −1930.00 + 3342.86i −0.452505 + 0.783762i −0.998541 0.0539998i \(-0.982803\pi\)
0.546036 + 0.837762i \(0.316136\pi\)
\(264\) 0 0
\(265\) 3824.00 0.886439
\(266\) 0 0
\(267\) 0 0
\(268\) 1816.00 + 3145.40i 0.413917 + 0.716926i
\(269\) −1400.00 + 2424.87i −0.317322 + 0.549617i −0.979928 0.199350i \(-0.936117\pi\)
0.662607 + 0.748968i \(0.269450\pi\)
\(270\) 0 0
\(271\) 2440.00 + 4226.20i 0.546935 + 0.947320i 0.998482 + 0.0550723i \(0.0175389\pi\)
−0.451547 + 0.892247i \(0.649128\pi\)
\(272\) 1344.00 0.299603
\(273\) 0 0
\(274\) −1292.00 −0.284863
\(275\) −1220.00 2113.10i −0.267523 0.463363i
\(276\) 0 0
\(277\) 3337.00 5779.85i 0.723830 1.25371i −0.235624 0.971844i \(-0.575713\pi\)
0.959454 0.281866i \(-0.0909533\pi\)
\(278\) 3012.00 + 5216.94i 0.649812 + 1.12551i
\(279\) 0 0
\(280\) 0 0
\(281\) 9402.00 1.99600 0.998001 0.0632056i \(-0.0201324\pi\)
0.998001 + 0.0632056i \(0.0201324\pi\)
\(282\) 0 0
\(283\) 4550.00 7880.83i 0.955722 1.65536i 0.223016 0.974815i \(-0.428410\pi\)
0.732706 0.680545i \(-0.238257\pi\)
\(284\) −1048.00 + 1815.19i −0.218970 + 0.379266i
\(285\) 0 0
\(286\) −320.000 −0.0661608
\(287\) 0 0
\(288\) 0 0
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) −464.000 + 803.672i −0.0939552 + 0.162735i
\(291\) 0 0
\(292\) −880.000 1524.20i −0.176363 0.305470i
\(293\) −5952.00 −1.18676 −0.593378 0.804924i \(-0.702206\pi\)
−0.593378 + 0.804924i \(0.702206\pi\)
\(294\) 0 0
\(295\) 4384.00 0.865242
\(296\) 888.000 + 1538.06i 0.174371 + 0.302020i
\(297\) 0 0
\(298\) −3170.00 + 5490.60i −0.616219 + 1.06732i
\(299\) 168.000 + 290.985i 0.0324939 + 0.0562812i
\(300\) 0 0
\(301\) 0 0
\(302\) −3760.00 −0.716436
\(303\) 0 0
\(304\) −1184.00 + 2050.75i −0.223378 + 0.386903i
\(305\) 2768.00 4794.32i 0.519656 0.900071i
\(306\) 0 0
\(307\) −3004.00 −0.558460 −0.279230 0.960224i \(-0.590079\pi\)
−0.279230 + 0.960224i \(0.590079\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1088.00 1884.47i −0.199336 0.345261i
\(311\) 344.000 595.825i 0.0627217 0.108637i −0.832959 0.553334i \(-0.813355\pi\)
0.895681 + 0.444697i \(0.146689\pi\)
\(312\) 0 0
\(313\) −2796.00 4842.81i −0.504918 0.874543i −0.999984 0.00568790i \(-0.998189\pi\)
0.495066 0.868855i \(-0.335144\pi\)
\(314\) 1208.00 0.217106
\(315\) 0 0
\(316\) 4864.00 0.865890
\(317\) −1461.00 2530.53i −0.258858 0.448355i 0.707078 0.707135i \(-0.250013\pi\)
−0.965936 + 0.258780i \(0.916679\pi\)
\(318\) 0 0
\(319\) −1160.00 + 2009.18i −0.203597 + 0.352641i
\(320\) 256.000 + 443.405i 0.0447214 + 0.0774597i
\(321\) 0 0
\(322\) 0 0
\(323\) 12432.0 2.14159
\(324\) 0 0
\(325\) 122.000 211.310i 0.0208226 0.0360658i
\(326\) −1116.00 + 1932.97i −0.189600 + 0.328396i
\(327\) 0 0
\(328\) −3360.00 −0.565625
\(329\) 0 0
\(330\) 0 0
\(331\) 3746.00 + 6488.26i 0.622051 + 1.07742i 0.989103 + 0.147223i \(0.0470336\pi\)
−0.367053 + 0.930200i \(0.619633\pi\)
\(332\) −1368.00 + 2369.45i −0.226141 + 0.391687i
\(333\) 0 0
\(334\) −1784.00 3089.98i −0.292264 0.506216i
\(335\) 7264.00 1.18470
\(336\) 0 0
\(337\) 10766.0 1.74024 0.870121 0.492839i \(-0.164041\pi\)
0.870121 + 0.492839i \(0.164041\pi\)
\(338\) 2181.00 + 3777.60i 0.350979 + 0.607913i
\(339\) 0 0
\(340\) 1344.00 2327.88i 0.214378 0.371314i
\(341\) −2720.00 4711.18i −0.431954 0.748166i
\(342\) 0 0
\(343\) 0 0
\(344\) −1312.00 −0.205635
\(345\) 0 0
\(346\) −344.000 + 595.825i −0.0534496 + 0.0925774i
\(347\) −1992.00 + 3450.25i −0.308173 + 0.533772i −0.977963 0.208779i \(-0.933051\pi\)
0.669789 + 0.742551i \(0.266384\pi\)
\(348\) 0 0
\(349\) −180.000 −0.0276080 −0.0138040 0.999905i \(-0.504394\pi\)
−0.0138040 + 0.999905i \(0.504394\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 640.000 + 1108.51i 0.0969094 + 0.167852i
\(353\) −5214.00 + 9030.91i −0.786156 + 1.36166i 0.142149 + 0.989845i \(0.454599\pi\)
−0.928306 + 0.371818i \(0.878735\pi\)
\(354\) 0 0
\(355\) 2096.00 + 3630.38i 0.313364 + 0.542762i
\(356\) −2416.00 −0.359685
\(357\) 0 0
\(358\) −2784.00 −0.411003
\(359\) 4342.00 + 7520.56i 0.638334 + 1.10563i 0.985798 + 0.167934i \(0.0537096\pi\)
−0.347464 + 0.937693i \(0.612957\pi\)
\(360\) 0 0
\(361\) −7522.50 + 13029.4i −1.09673 + 1.89960i
\(362\) −4052.00 7018.27i −0.588310 1.01898i
\(363\) 0 0
\(364\) 0 0
\(365\) −3520.00 −0.504781
\(366\) 0 0
\(367\) −2824.00 + 4891.31i −0.401666 + 0.695707i −0.993927 0.110040i \(-0.964902\pi\)
0.592261 + 0.805746i \(0.298236\pi\)
\(368\) 672.000 1163.94i 0.0951914 0.164876i
\(369\) 0 0
\(370\) 3552.00 0.499080
\(371\) 0 0
\(372\) 0 0
\(373\) 1273.00 + 2204.90i 0.176712 + 0.306074i 0.940752 0.339095i \(-0.110121\pi\)
−0.764041 + 0.645168i \(0.776787\pi\)
\(374\) 3360.00 5819.69i 0.464549 0.804623i
\(375\) 0 0
\(376\) 1952.00 + 3380.96i 0.267731 + 0.463723i
\(377\) −232.000 −0.0316939
\(378\) 0 0
\(379\) 8268.00 1.12058 0.560288 0.828298i \(-0.310690\pi\)
0.560288 + 0.828298i \(0.310690\pi\)
\(380\) 2368.00 + 4101.50i 0.319673 + 0.553690i
\(381\) 0 0
\(382\) −3108.00 + 5383.21i −0.416280 + 0.721019i
\(383\) −5436.00 9415.43i −0.725239 1.25615i −0.958875 0.283827i \(-0.908396\pi\)
0.233636 0.972324i \(-0.424938\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 100.000 0.0131862
\(387\) 0 0
\(388\) 1664.00 2882.13i 0.217724 0.377109i
\(389\) 5217.00 9036.11i 0.679980 1.17776i −0.295006 0.955495i \(-0.595322\pi\)
0.974986 0.222265i \(-0.0713451\pi\)
\(390\) 0 0
\(391\) −7056.00 −0.912627
\(392\) 0 0
\(393\) 0 0
\(394\) −162.000 280.592i −0.0207143 0.0358783i
\(395\) 4864.00 8424.70i 0.619581 1.07315i
\(396\) 0 0
\(397\) 1522.00 + 2636.18i 0.192411 + 0.333265i 0.946049 0.324025i \(-0.105036\pi\)
−0.753638 + 0.657290i \(0.771703\pi\)
\(398\) 3088.00 0.388913
\(399\) 0 0
\(400\) −976.000 −0.122000
\(401\) 4455.00 + 7716.29i 0.554793 + 0.960930i 0.997920 + 0.0644709i \(0.0205360\pi\)
−0.443126 + 0.896459i \(0.646131\pi\)
\(402\) 0 0
\(403\) 272.000 471.118i 0.0336211 0.0582334i
\(404\) 928.000 + 1607.34i 0.114281 + 0.197941i
\(405\) 0 0
\(406\) 0 0
\(407\) 8880.00 1.08149
\(408\) 0 0
\(409\) −2808.00 + 4863.60i −0.339478 + 0.587994i −0.984335 0.176310i \(-0.943584\pi\)
0.644856 + 0.764304i \(0.276917\pi\)
\(410\) −3360.00 + 5819.69i −0.404728 + 0.701010i
\(411\) 0 0
\(412\) −2528.00 −0.302295
\(413\) 0 0
\(414\) 0 0
\(415\) 2736.00 + 4738.89i 0.323626 + 0.560537i
\(416\) −64.0000 + 110.851i −0.00754293 + 0.0130647i
\(417\) 0 0
\(418\) 5920.00 + 10253.7i 0.692719 + 1.19983i
\(419\) 8932.00 1.04142 0.520712 0.853732i \(-0.325666\pi\)
0.520712 + 0.853732i \(0.325666\pi\)
\(420\) 0 0
\(421\) −5538.00 −0.641106 −0.320553 0.947231i \(-0.603869\pi\)
−0.320553 + 0.947231i \(0.603869\pi\)
\(422\) 1204.00 + 2085.39i 0.138886 + 0.240557i
\(423\) 0 0
\(424\) 1912.00 3311.68i 0.218997 0.379315i
\(425\) 2562.00 + 4437.51i 0.292412 + 0.506473i
\(426\) 0 0
\(427\) 0 0
\(428\) 640.000 0.0722794
\(429\) 0 0
\(430\) −1312.00 + 2272.45i −0.147140 + 0.254854i
\(431\) −3350.00 + 5802.37i −0.374394 + 0.648469i −0.990236 0.139400i \(-0.955483\pi\)
0.615842 + 0.787870i \(0.288816\pi\)
\(432\) 0 0
\(433\) −5048.00 −0.560257 −0.280129 0.959962i \(-0.590377\pi\)
−0.280129 + 0.959962i \(0.590377\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4396.00 + 7614.10i 0.482867 + 0.836351i
\(437\) 6216.00 10766.4i 0.680438 1.17855i
\(438\) 0 0
\(439\) 672.000 + 1163.94i 0.0730588 + 0.126542i 0.900240 0.435393i \(-0.143391\pi\)
−0.827182 + 0.561935i \(0.810057\pi\)
\(440\) 2560.00 0.277371
\(441\) 0 0
\(442\) 672.000 0.0723162
\(443\) −2196.00 3803.58i −0.235519 0.407932i 0.723904 0.689901i \(-0.242346\pi\)
−0.959424 + 0.281969i \(0.909012\pi\)
\(444\) 0 0
\(445\) −2416.00 + 4184.63i −0.257369 + 0.445777i
\(446\) −2000.00 3464.10i −0.212338 0.367780i
\(447\) 0 0
\(448\) 0 0
\(449\) −3666.00 −0.385321 −0.192661 0.981265i \(-0.561712\pi\)
−0.192661 + 0.981265i \(0.561712\pi\)
\(450\) 0 0
\(451\) −8400.00 + 14549.2i −0.877030 + 1.51906i
\(452\) 1540.00 2667.36i 0.160256 0.277571i
\(453\) 0 0
\(454\) −776.000 −0.0802191
\(455\) 0 0
\(456\) 0 0
\(457\) −13.0000 22.5167i −0.00133067 0.00230478i 0.865359 0.501152i \(-0.167090\pi\)
−0.866690 + 0.498847i \(0.833757\pi\)
\(458\) −4180.00 + 7239.97i −0.426460 + 0.738650i
\(459\) 0 0
\(460\) −1344.00 2327.88i −0.136227 0.235952i
\(461\) −7656.00 −0.773483 −0.386741 0.922188i \(-0.626399\pi\)
−0.386741 + 0.922188i \(0.626399\pi\)
\(462\) 0 0
\(463\) 12608.0 1.26554 0.632768 0.774341i \(-0.281919\pi\)
0.632768 + 0.774341i \(0.281919\pi\)
\(464\) 464.000 + 803.672i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −1322.00 + 2289.77i −0.131417 + 0.227621i
\(467\) −1534.00 2656.97i −0.152002 0.263276i 0.779961 0.625828i \(-0.215239\pi\)
−0.931963 + 0.362552i \(0.881905\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7808.00 0.766290
\(471\) 0 0
\(472\) 2192.00 3796.66i 0.213761 0.370244i
\(473\) −3280.00 + 5681.13i −0.318847 + 0.552259i
\(474\) 0 0
\(475\) −9028.00 −0.872070
\(476\) 0 0
\(477\) 0 0
\(478\) 2412.00 + 4177.71i 0.230800 + 0.399757i
\(479\) 3228.00 5591.06i 0.307915 0.533324i −0.669991 0.742369i \(-0.733702\pi\)
0.977906 + 0.209045i \(0.0670356\pi\)
\(480\) 0 0
\(481\) 444.000 + 769.031i 0.0420887 + 0.0728997i
\(482\) −8672.00 −0.819500
\(483\) 0 0
\(484\) 1076.00 0.101052
\(485\) −3328.00 5764.27i −0.311581 0.539674i
\(486\) 0 0
\(487\) −5948.00 + 10302.2i −0.553449 + 0.958602i 0.444574 + 0.895742i \(0.353355\pi\)
−0.998022 + 0.0628592i \(0.979978\pi\)
\(488\) −2768.00 4794.32i −0.256765 0.444731i
\(489\) 0 0
\(490\) 0 0
\(491\) 264.000 0.0242651 0.0121325 0.999926i \(-0.496138\pi\)
0.0121325 + 0.999926i \(0.496138\pi\)
\(492\) 0 0
\(493\) 2436.00 4219.28i 0.222539 0.385450i
\(494\) −592.000 + 1025.37i −0.0539177 + 0.0933882i
\(495\) 0 0
\(496\) −2176.00 −0.196986
\(497\) 0 0
\(498\) 0 0
\(499\) 1314.00 + 2275.91i 0.117881 + 0.204176i 0.918928 0.394426i \(-0.129056\pi\)
−0.801047 + 0.598602i \(0.795723\pi\)
\(500\) −2976.00 + 5154.58i −0.266182 + 0.461040i
\(501\) 0 0
\(502\) 764.000 + 1323.29i 0.0679263 + 0.117652i
\(503\) 13568.0 1.20272 0.601359 0.798979i \(-0.294626\pi\)
0.601359 + 0.798979i \(0.294626\pi\)
\(504\) 0 0
\(505\) 3712.00 0.327093
\(506\) −3360.00 5819.69i −0.295198 0.511298i
\(507\) 0 0
\(508\) 368.000 637.395i 0.0321405 0.0556689i
\(509\) 10328.0 + 17888.6i 0.899372 + 1.55776i 0.828298 + 0.560288i \(0.189309\pi\)
0.0710743 + 0.997471i \(0.477357\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 4300.00 7447.82i 0.368998 0.639123i
\(515\) −2528.00 + 4378.62i −0.216305 + 0.374651i
\(516\) 0 0
\(517\) 19520.0 1.66052
\(518\) 0 0
\(519\) 0 0
\(520\) 128.000 + 221.703i 0.0107946 + 0.0186967i
\(521\) 1814.00 3141.94i 0.152539 0.264205i −0.779621 0.626251i \(-0.784588\pi\)
0.932160 + 0.362046i \(0.117922\pi\)
\(522\) 0 0
\(523\) −2426.00 4201.96i −0.202833 0.351317i 0.746607 0.665265i \(-0.231681\pi\)
−0.949440 + 0.313948i \(0.898348\pi\)
\(524\) 5808.00 0.484205
\(525\) 0 0
\(526\) 7720.00 0.639939
\(527\) 5712.00 + 9893.47i 0.472142 + 0.817773i
\(528\) 0 0
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) −3824.00 6623.36i −0.313404 0.542831i
\(531\) 0 0
\(532\) 0 0
\(533\) −1680.00 −0.136527
\(534\) 0 0
\(535\) 640.000 1108.51i 0.0517189 0.0895798i
\(536\) 3632.00 6290.81i 0.292684 0.506943i
\(537\) 0 0
\(538\) 5600.00 0.448760
\(539\) 0 0
\(540\) 0 0
\(541\) 3565.00 + 6174.76i 0.283311 + 0.490709i 0.972198 0.234159i \(-0.0752338\pi\)
−0.688887 + 0.724869i \(0.741900\pi\)
\(542\) 4880.00 8452.41i 0.386742 0.669856i
\(543\) 0 0
\(544\) −1344.00 2327.88i −0.105926 0.183469i
\(545\) 17584.0 1.38205
\(546\) 0 0
\(547\) −12788.0 −0.999589 −0.499795 0.866144i \(-0.666591\pi\)
−0.499795 + 0.866144i \(0.666591\pi\)
\(548\) 1292.00 + 2237.81i 0.100714 + 0.174443i
\(549\) 0 0
\(550\) −2440.00 + 4226.20i −0.189167 + 0.327647i
\(551\) 4292.00 + 7433.96i 0.331843 + 0.574768i
\(552\) 0 0
\(553\) 0 0
\(554\) −13348.0 −1.02365
\(555\) 0 0
\(556\) 6024.00 10433.9i 0.459487 0.795854i
\(557\) 1203.00 2083.66i 0.0915130 0.158505i −0.816635 0.577155i \(-0.804163\pi\)
0.908148 + 0.418649i \(0.137496\pi\)
\(558\) 0 0
\(559\) −656.000 −0.0496348
\(560\) 0 0
\(561\) 0 0
\(562\) −9402.00 16284.7i −0.705693 1.22230i
\(563\) −12706.0 + 22007.4i −0.951144 + 1.64743i −0.208189 + 0.978089i \(0.566757\pi\)
−0.742955 + 0.669341i \(0.766577\pi\)
\(564\) 0 0
\(565\) −3080.00 5334.72i −0.229339 0.397227i
\(566\) −18200.0 −1.35160
\(567\) 0 0
\(568\) 4192.00 0.309670
\(569\) −4845.00 8391.79i −0.356965 0.618281i 0.630487 0.776199i \(-0.282855\pi\)
−0.987452 + 0.157918i \(0.949522\pi\)
\(570\) 0 0
\(571\) −2802.00 + 4853.21i −0.205359 + 0.355692i −0.950247 0.311497i \(-0.899170\pi\)
0.744888 + 0.667190i \(0.232503\pi\)
\(572\) 320.000 + 554.256i 0.0233914 + 0.0405151i
\(573\) 0 0
\(574\) 0 0
\(575\) 5124.00 0.371627
\(576\) 0 0
\(577\) 10784.0 18678.4i 0.778066 1.34765i −0.154990 0.987916i \(-0.549534\pi\)
0.933055 0.359733i \(-0.117132\pi\)
\(578\) −2143.00 + 3711.78i −0.154216 + 0.267111i
\(579\) 0 0
\(580\) 1856.00 0.132873
\(581\) 0 0
\(582\) 0 0
\(583\) −9560.00 16558.4i −0.679133 1.17629i
\(584\) −1760.00 + 3048.41i −0.124708 + 0.216000i
\(585\) 0 0
\(586\) 5952.00 + 10309.2i 0.419582 + 0.726737i
\(587\) −20300.0 −1.42738 −0.713689 0.700463i \(-0.752977\pi\)
−0.713689 + 0.700463i \(0.752977\pi\)
\(588\) 0 0
\(589\) −20128.0 −1.40808
\(590\) −4384.00 7593.31i −0.305909 0.529850i
\(591\) 0 0
\(592\) 1776.00 3076.12i 0.123299 0.213561i
\(593\) 6906.00 + 11961.5i 0.478238 + 0.828333i 0.999689 0.0249483i \(-0.00794212\pi\)
−0.521450 + 0.853282i \(0.674609\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12680.0 0.871465
\(597\) 0 0
\(598\) 336.000 581.969i 0.0229767 0.0397968i
\(599\) −10998.0 + 19049.1i −0.750194 + 1.29937i 0.197535 + 0.980296i \(0.436706\pi\)
−0.947728 + 0.319078i \(0.896627\pi\)
\(600\) 0 0
\(601\) 8368.00 0.567950 0.283975 0.958832i \(-0.408347\pi\)
0.283975 + 0.958832i \(0.408347\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3760.00 + 6512.51i 0.253298 + 0.438726i
\(605\) 1076.00 1863.69i 0.0723068 0.125239i
\(606\) 0 0
\(607\) −10752.0 18623.0i −0.718962 1.24528i −0.961411 0.275115i \(-0.911284\pi\)
0.242449 0.970164i \(-0.422049\pi\)
\(608\) 4736.00 0.315905
\(609\) 0 0
\(610\) −11072.0 −0.734905
\(611\) 976.000 + 1690.48i 0.0646231 + 0.111931i
\(612\) 0 0
\(613\) 5135.00 8894.08i 0.338337 0.586017i −0.645783 0.763521i \(-0.723469\pi\)
0.984120 + 0.177504i \(0.0568022\pi\)
\(614\) 3004.00 + 5203.08i 0.197446 + 0.341986i
\(615\) 0 0
\(616\) 0 0
\(617\) −28358.0 −1.85032 −0.925162 0.379572i \(-0.876071\pi\)
−0.925162 + 0.379572i \(0.876071\pi\)
\(618\) 0 0
\(619\) −8146.00 + 14109.3i −0.528942 + 0.916155i 0.470488 + 0.882406i \(0.344078\pi\)
−0.999430 + 0.0337488i \(0.989255\pi\)
\(620\) −2176.00 + 3768.94i −0.140952 + 0.244136i
\(621\) 0 0
\(622\) −1376.00 −0.0887019
\(623\) 0 0
\(624\) 0 0
\(625\) 2139.50 + 3705.72i 0.136928 + 0.237166i
\(626\) −5592.00 + 9685.63i −0.357031 + 0.618395i
\(627\) 0 0
\(628\) −1208.00 2092.32i −0.0767587 0.132950i
\(629\) −18648.0 −1.18211
\(630\) 0 0
\(631\) 11256.0 0.710134 0.355067 0.934841i \(-0.384458\pi\)
0.355067 + 0.934841i \(0.384458\pi\)
\(632\) −4864.00 8424.70i −0.306138 0.530247i
\(633\) 0 0
\(634\) −2922.00 + 5061.05i −0.183040 + 0.317035i
\(635\) −736.000 1274.79i −0.0459957 0.0796669i
\(636\) 0 0
\(637\) 0 0
\(638\) 4640.00 0.287930
\(639\) 0 0
\(640\) 512.000 886.810i 0.0316228 0.0547723i
\(641\) 7759.00 13439.0i 0.478100 0.828093i −0.521585 0.853199i \(-0.674659\pi\)
0.999685 + 0.0251060i \(0.00799233\pi\)
\(642\) 0 0
\(643\) −10452.0 −0.641037 −0.320518 0.947242i \(-0.603857\pi\)
−0.320518 + 0.947242i \(0.603857\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12432.0 21532.9i −0.757168 1.31145i
\(647\) 36.0000 62.3538i 0.00218749 0.00378884i −0.864930 0.501893i \(-0.832637\pi\)
0.867117 + 0.498104i \(0.165970\pi\)
\(648\) 0 0
\(649\) −10960.0 18983.3i −0.662893 1.14816i
\(650\) −488.000 −0.0294476
\(651\) 0 0
\(652\) 4464.00 0.268135
\(653\) 5981.00 + 10359.4i 0.358430 + 0.620819i 0.987699 0.156369i \(-0.0499789\pi\)
−0.629269 + 0.777188i \(0.716646\pi\)
\(654\) 0 0
\(655\) 5808.00 10059.8i 0.346469 0.600102i
\(656\) 3360.00 + 5819.69i 0.199979 + 0.346373i
\(657\) 0 0
\(658\) 0 0
\(659\) 6016.00 0.355615 0.177807 0.984065i \(-0.443100\pi\)
0.177807 + 0.984065i \(0.443100\pi\)
\(660\) 0 0
\(661\) −13034.0 + 22575.6i −0.766965 + 1.32842i 0.172236 + 0.985056i \(0.444901\pi\)
−0.939201 + 0.343367i \(0.888433\pi\)
\(662\) 7492.00 12976.5i 0.439856 0.761853i
\(663\) 0 0
\(664\) 5472.00 0.319811
\(665\) 0 0
\(666\) 0 0
\(667\) −2436.00 4219.28i −0.141413 0.244934i
\(668\) −3568.00 + 6179.96i −0.206662 + 0.357949i
\(669\) 0 0
\(670\) −7264.00 12581.6i −0.418855 0.725478i
\(671\) −27680.0 −1.59251
\(672\) 0 0
\(673\) −20530.0 −1.17589 −0.587945 0.808901i \(-0.700063\pi\)
−0.587945 + 0.808901i \(0.700063\pi\)
\(674\) −10766.0 18647.3i −0.615268 1.06568i
\(675\) 0 0
\(676\) 4362.00 7555.21i 0.248179 0.429859i
\(677\) −5028.00 8708.75i −0.285438 0.494394i 0.687277 0.726395i \(-0.258806\pi\)
−0.972715 + 0.232002i \(0.925473\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −5376.00 −0.303177
\(681\) 0 0
\(682\) −5440.00 + 9422.36i −0.305437 + 0.529033i
\(683\) 3076.00 5327.79i 0.172328 0.298480i −0.766905 0.641760i \(-0.778205\pi\)
0.939233 + 0.343280i \(0.111538\pi\)
\(684\) 0 0
\(685\) 5168.00 0.288262
\(686\) 0 0
\(687\) 0 0
\(688\) 1312.00 + 2272.45i 0.0727028 + 0.125925i
\(689\) 956.000 1655.84i 0.0528602 0.0915566i
\(690\) 0 0
\(691\) 7358.00 + 12744.4i 0.405082 + 0.701622i 0.994331 0.106329i \(-0.0339097\pi\)
−0.589249 + 0.807951i \(0.700576\pi\)
\(692\) 1376.00 0.0755891
\(693\) 0 0
\(694\) 7968.00 0.435823
\(695\) −12048.0 20867.7i −0.657564 1.13893i
\(696\) 0 0
\(697\) 17640.0 30553.4i 0.958626 1.66039i
\(698\) 180.000 + 311.769i 0.00976089 + 0.0169064i
\(699\) 0 0
\(700\) 0 0
\(701\) −28202.0 −1.51951 −0.759754 0.650211i \(-0.774681\pi\)
−0.759754 + 0.650211i \(0.774681\pi\)
\(702\) 0 0
\(703\) 16428.0 28454.1i 0.881357 1.52655i
\(704\) 1280.00 2217.03i 0.0685253 0.118689i
\(705\) 0 0
\(706\) 20856.0 1.11179
\(707\) 0 0
\(708\) 0 0
\(709\) −11057.0 19151.3i −0.585690 1.01445i −0.994789 0.101955i \(-0.967490\pi\)
0.409099 0.912490i \(-0.365843\pi\)
\(710\) 4192.00 7260.76i 0.221582 0.383791i
\(711\) 0 0
\(712\) 2416.00 + 4184.63i 0.127168 + 0.220261i
\(713\) 11424.0 0.600045
\(714\) 0 0
\(715\) 1280.00 0.0669501
\(716\) 2784.00 + 4822.03i 0.145311 + 0.251687i
\(717\) 0 0
\(718\) 8684.00 15041.1i 0.451370 0.781797i
\(719\) −4644.00 8043.64i −0.240879 0.417215i 0.720086 0.693885i \(-0.244102\pi\)
−0.960965 + 0.276670i \(0.910769\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 30090.0 1.55102
\(723\) 0 0
\(724\) −8104.00 + 14036.5i −0.415998 + 0.720530i
\(725\) −1769.00 + 3064.00i −0.0906193 + 0.156957i
\(726\) 0 0
\(727\) 23848.0 1.21661 0.608304 0.793704i \(-0.291850\pi\)
0.608304 + 0.793704i \(0.291850\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3520.00 + 6096.82i 0.178467 + 0.309114i
\(731\) 6888.00 11930.4i 0.348511 0.603640i
\(732\) 0 0
\(733\) 17378.0 + 30099.6i 0.875677 + 1.51672i 0.856040 + 0.516909i \(0.172918\pi\)
0.0196367 + 0.999807i \(0.493749\pi\)
\(734\) 11296.0 0.568042
\(735\) 0 0
\(736\) −2688.00 −0.134621
\(737\) −18160.0 31454.0i −0.907642 1.57208i
\(738\) 0 0
\(739\) −13022.0 + 22554.8i −0.648203 + 1.12272i 0.335349 + 0.942094i \(0.391146\pi\)
−0.983552 + 0.180626i \(0.942187\pi\)
\(740\) −3552.00 6152.24i −0.176452 0.305623i
\(741\) 0 0
\(742\) 0 0
\(743\) −36204.0 −1.78761 −0.893806 0.448454i \(-0.851975\pi\)
−0.893806 + 0.448454i \(0.851975\pi\)
\(744\) 0 0
\(745\) 12680.0 21962.4i 0.623569 1.08005i
\(746\) 2546.00 4409.80i 0.124954 0.216427i
\(747\) 0 0
\(748\) −13440.0 −0.656972
\(749\) 0 0
\(750\) 0 0
\(751\) 5712.00 + 9893.47i 0.277542 + 0.480716i 0.970773 0.239999i \(-0.0771470\pi\)
−0.693232 + 0.720715i \(0.743814\pi\)
\(752\) 3904.00 6761.93i 0.189314 0.327902i
\(753\) 0 0
\(754\) 232.000 + 401.836i 0.0112055 + 0.0194085i
\(755\) 15040.0 0.724982
\(756\) 0 0
\(757\) −16622.0 −0.798067 −0.399034 0.916936i \(-0.630654\pi\)
−0.399034 + 0.916936i \(0.630654\pi\)
\(758\) −8268.00 14320.6i −0.396184 0.686210i
\(759\) 0 0
\(760\) 4736.00 8202.99i 0.226043 0.391518i
\(761\) −19262.0 33362.8i −0.917539 1.58922i −0.803141 0.595789i \(-0.796840\pi\)
−0.114397 0.993435i \(-0.536494\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 12432.0 0.588709
\(765\) 0 0
\(766\) −10872.0 + 18830.9i −0.512822 + 0.888233i
\(767\) 1096.00 1898.33i 0.0515962 0.0893672i
\(768\) 0 0
\(769\) −18440.0 −0.864712 −0.432356 0.901703i \(-0.642318\pi\)
−0.432356 + 0.901703i \(0.642318\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −100.000 173.205i −0.00466202 0.00807485i
\(773\) −6984.00 + 12096.6i −0.324964 + 0.562854i −0.981505 0.191436i \(-0.938685\pi\)
0.656541 + 0.754290i \(0.272019\pi\)
\(774\) 0 0
\(775\) −4148.00 7184.55i −0.192259 0.333002i
\(776\) −6656.00 −0.307908
\(777\) 0 0
\(778\) −20868.0 −0.961638
\(779\) 31080.0 + 53832.1i 1.42947 + 2.47591i
\(780\) 0 0
\(781\) 10480.0 18151.9i 0.480159 0.831659i
\(782\) 7056.00 + 12221.4i 0.322662 + 0.558868i
\(783\) 0 0
\(784\) 0 0
\(785\) −4832.00 −0.219696
\(786\) 0 0
\(787\) −5458.00 + 9453.53i −0.247213 + 0.428186i −0.962752 0.270388i \(-0.912848\pi\)
0.715538 + 0.698573i \(0.246181\pi\)
\(788\) −324.000 + 561.184i −0.0146472 + 0.0253698i
\(789\) 0 0
\(790\) −19456.0 −0.876220
\(791\) 0 0