Properties

Label 882.4.g.c.667.1
Level $882$
Weight $4$
Character 882.667
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 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.c.361.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 \(-0.949796\pi\)
0.629817 + 0.776743i \(0.283130\pi\)
\(6\) 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 0.998398 + 0.0565844i \(0.0180210\pi\)
−0.450195 + 0.892930i \(0.648646\pi\)
\(12\) 0 0
\(13\) −4.00000 −0.0853385 −0.0426692 0.999089i \(-0.513586\pi\)
−0.0426692 + 0.999089i \(0.513586\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 42.0000 + 72.7461i 0.599206 + 1.03785i 0.992939 + 0.118630i \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) 0 0
\(19\) 74.0000 128.172i 0.893514 1.54761i 0.0578808 0.998324i \(-0.481566\pi\)
0.835633 0.549288i \(-0.185101\pi\)
\(20\) 32.0000 0.357771
\(21\) 0 0
\(22\) −80.0000 −0.775275
\(23\) 42.0000 72.7461i 0.380765 0.659505i −0.610406 0.792088i \(-0.708994\pi\)
0.991172 + 0.132583i \(0.0423272\pi\)
\(24\) 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 \(-0.295566\pi\)
−0.992970 + 0.118370i \(0.962233\pi\)
\(32\) −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 −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 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 \(-0.204878\pi\)
0.799914 + 0.600114i \(0.204878\pi\)
\(42\) 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 0.186988 + 0.982362i \(0.440127\pi\)
−0.944245 + 0.329245i \(0.893206\pi\)
\(48\) 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 0.989592 + 0.143902i \(0.0459649\pi\)
−0.370174 + 0.928963i \(0.620702\pi\)
\(54\) 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 −0.992114 0.125342i \(-0.959997\pi\)
0.387507 0.921867i \(-0.373336\pi\)
\(60\) 0 0
\(61\) 346.000 599.290i 0.726242 1.25789i −0.232219 0.972664i \(-0.574599\pi\)
0.958461 0.285224i \(-0.0920681\pi\)
\(62\) 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 0.899733 + 0.436440i \(0.143761\pi\)
−0.0718987 + 0.997412i \(0.522906\pi\)
\(68\) 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 \(-0.0519212\pi\)
−0.633999 + 0.773334i \(0.718588\pi\)
\(74\) 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 0.000269874 1.00000i \(0.499914\pi\)
−0.866160 + 0.499766i \(0.833419\pi\)
\(80\) −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 \(-0.649390\pi\)
−0.452282 + 0.891875i \(0.649390\pi\)
\(84\) 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 \(-0.950449\pi\)
0.628223 + 0.778033i \(0.283782\pi\)
\(90\) 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 \(-0.356590\pi\)
0.435447 + 0.900214i \(0.356590\pi\)
\(98\) 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 \(-0.240069\pi\)
−0.957382 + 0.288823i \(0.906736\pi\)
\(102\) 0 0
\(103\) −316.000 + 547.328i −0.302295 + 0.523591i −0.976655 0.214812i \(-0.931086\pi\)
0.674360 + 0.738402i \(0.264420\pi\)
\(104\) −32.0000 −0.0301717
\(105\) 0 0
\(106\) −956.000 −0.875990
\(107\) −80.0000 + 138.564i −0.0722794 + 0.125192i −0.899900 0.436096i \(-0.856361\pi\)
0.827621 + 0.561288i \(0.189694\pi\)
\(108\) 0 0
\(109\) 1099.00 + 1903.52i 0.965735 + 1.67270i 0.707627 + 0.706586i \(0.249766\pi\)
0.258108 + 0.966116i \(0.416901\pi\)
\(110\) 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 \(-0.672442\pi\)
0.999835 + 0.0181429i \(0.00577539\pi\)
\(132\) 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 0.948989 0.315309i \(-0.102108\pi\)
−0.747560 + 0.664194i \(0.768775\pi\)
\(138\) 0 0
\(139\) 3012.00 1.83795 0.918973 0.394320i \(-0.129020\pi\)
0.918973 + 0.394320i \(0.129020\pi\)
\(140\) 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 −0.0109833 + 0.999940i \(0.503496\pi\)
−0.860482 + 0.509482i \(0.829837\pi\)
\(150\) 0 0
\(151\) 940.000 + 1628.13i 0.506597 + 0.877451i 0.999971 + 0.00763414i \(0.00243005\pi\)
−0.493374 + 0.869817i \(0.664237\pi\)
\(152\) 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 \(-0.117607\pi\)
−0.779001 + 0.627023i \(0.784273\pi\)
\(158\) −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 −0.968380 0.249479i \(-0.919741\pi\)
0.700246 + 0.713902i \(0.253074\pi\)
\(164\) −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 \(-0.635632\pi\)
−0.413324 + 0.910584i \(0.635632\pi\)
\(168\) 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 \(-0.809250\pi\)
0.901342 + 0.433107i \(0.142583\pi\)
\(174\) 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 0.973957 0.226732i \(-0.0728042\pi\)
−0.683334 + 0.730106i \(0.739471\pi\)
\(180\) 0 0
\(181\) −4052.00 −1.66399 −0.831997 0.554781i \(-0.812802\pi\)
−0.831997 + 0.554781i \(0.812802\pi\)
\(182\) 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 0.405692 + 0.914010i \(0.367030\pi\)
−0.994402 + 0.105665i \(0.966303\pi\)
\(192\) 0 0
\(193\) −25.0000 43.3013i −0.00932404 0.0161497i 0.861326 0.508053i \(-0.169635\pi\)
−0.870650 + 0.491903i \(0.836301\pi\)
\(194\) −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 \(-0.0779878\pi\)
−0.695133 + 0.718881i \(0.744654\pi\)
\(200\) 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 \(-0.597084\pi\)
−0.300291 + 0.953848i \(0.597084\pi\)
\(224\) 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 \(-0.184732\pi\)
−0.892993 + 0.450071i \(0.851399\pi\)
\(228\) 0 0
\(229\) 2090.00 3619.99i 0.603105 1.04461i −0.389243 0.921135i \(-0.627263\pi\)
0.992348 0.123474i \(-0.0394034\pi\)
\(230\) −1344.00 −0.385308
\(231\) 0 0
\(232\) −464.000 −0.131306
\(233\) −661.000 + 1144.89i −0.185852 + 0.321905i −0.943863 0.330336i \(-0.892838\pi\)
0.758011 + 0.652242i \(0.226171\pi\)
\(234\) 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 −0.995540 0.0943434i \(-0.969925\pi\)
0.416066 0.909334i \(-0.363409\pi\)
\(242\) −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 \(-0.469375\pi\)
0.0960623 + 0.995375i \(0.469375\pi\)
\(252\) 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 0.477835 + 0.878449i \(0.341421\pi\)
−0.999677 + 0.0254070i \(0.991912\pi\)
\(258\) 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 0.546036 0.837762i \(-0.316136\pi\)
−0.998541 + 0.0539998i \(0.982803\pi\)
\(264\) 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 \(-0.0638832\pi\)
−0.662607 + 0.748968i \(0.730550\pi\)
\(270\) 0 0
\(271\) −2440.00 + 4226.20i −0.546935 + 0.947320i 0.451547 + 0.892247i \(0.350872\pi\)
−0.998482 + 0.0550723i \(0.982461\pi\)
\(272\) −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 0.959454 + 0.281866i \(0.0909533\pi\)
−0.235624 + 0.971844i \(0.575713\pi\)
\(278\) −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 −0.732706 0.680545i \(-0.761743\pi\)
−0.223016 0.974815i \(-0.571590\pi\)
\(284\) −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 \(-0.297794\pi\)
0.593378 + 0.804924i \(0.297794\pi\)
\(294\) 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 \(-0.409921\pi\)
0.279230 + 0.960224i \(0.409921\pi\)
\(308\) 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 \(-0.186645\pi\)
−0.895681 + 0.444697i \(0.853311\pi\)
\(312\) 0 0
\(313\) 2796.00 4842.81i 0.504918 0.874543i −0.495066 0.868855i \(-0.664856\pi\)
0.999984 0.00568790i \(-0.00181052\pi\)
\(314\) −1208.00 −0.217106
\(315\) 0 0
\(316\) 4864.00 0.865890
\(317\) −1461.00 + 2530.53i −0.258858 + 0.448355i −0.965936 0.258780i \(-0.916679\pi\)
0.707078 + 0.707135i \(0.250013\pi\)
\(318\) 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 −0.367053 0.930200i \(-0.619633\pi\)
0.989103 0.147223i \(-0.0470336\pi\)
\(332\) 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 0.669789 0.742551i \(-0.266384\pi\)
−0.977963 + 0.208779i \(0.933051\pi\)
\(348\) 0 0
\(349\) 180.000 0.0276080 0.0138040 0.999905i \(-0.495606\pi\)
0.0138040 + 0.999905i \(0.495606\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 640.000 1108.51i 0.0969094 0.167852i
\(353\) 5214.00 + 9030.91i 0.786156 + 1.36166i 0.928306 + 0.371818i \(0.121265\pi\)
−0.142149 + 0.989845i \(0.545401\pi\)
\(354\) 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 −0.347464 0.937693i \(-0.612957\pi\)
0.985798 0.167934i \(-0.0537096\pi\)
\(360\) 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 \(-0.0350978\pi\)
−0.592261 + 0.805746i \(0.701764\pi\)
\(368\) 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 −0.764041 0.645168i \(-0.776787\pi\)
0.940752 + 0.339095i \(0.110121\pi\)
\(374\) −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 −0.233636 0.972324i \(-0.575062\pi\)
0.958875 0.283827i \(-0.0916042\pi\)
\(384\) 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 0.974986 + 0.222265i \(0.0713451\pi\)
−0.295006 + 0.955495i \(0.595322\pi\)
\(390\) 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 \(-0.894964\pi\)
0.753638 + 0.657290i \(0.228297\pi\)
\(398\) −3088.00 −0.388913
\(399\) 0 0
\(400\) −976.000 −0.122000
\(401\) 4455.00 7716.29i 0.554793 0.960930i −0.443126 0.896459i \(-0.646131\pi\)
0.997920 0.0644709i \(-0.0205360\pi\)
\(402\) 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 \(-0.0564161\pi\)
−0.644856 + 0.764304i \(0.723083\pi\)
\(410\) −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 \(-0.674334\pi\)
−0.520712 + 0.853732i \(0.674334\pi\)
\(420\) 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 0.615842 0.787870i \(-0.288816\pi\)
−0.990236 + 0.139400i \(0.955483\pi\)
\(432\) 0 0
\(433\) 5048.00 0.560257 0.280129 0.959962i \(-0.409623\pi\)
0.280129 + 0.959962i \(0.409623\pi\)
\(434\) 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 \(-0.856609\pi\)
0.827182 + 0.561935i \(0.189943\pi\)
\(440\) −2560.00 −0.277371
\(441\) 0 0
\(442\) 672.000 0.0723162
\(443\) −2196.00 + 3803.58i −0.235519 + 0.407932i −0.959424 0.281969i \(-0.909012\pi\)
0.723904 + 0.689901i \(0.242346\pi\)
\(444\) 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 −0.866690 0.498847i \(-0.833757\pi\)
0.865359 + 0.501152i \(0.167090\pi\)
\(458\) 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 \(-0.373601\pi\)
0.386741 + 0.922188i \(0.373601\pi\)
\(462\) 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 \(-0.784761\pi\)
0.931963 + 0.362552i \(0.118095\pi\)
\(468\) 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 \(-0.266298\pi\)
−0.977906 + 0.209045i \(0.932964\pi\)
\(480\) 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 −0.998022 0.0628592i \(-0.979978\pi\)
0.444574 0.895742i \(-0.353355\pi\)
\(488\) 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 −0.801047 0.598602i \(-0.795723\pi\)
0.918928 + 0.394426i \(0.129056\pi\)
\(500\) 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 \(-0.705374\pi\)
−0.601359 + 0.798979i \(0.705374\pi\)
\(504\) 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 −0.0710743 + 0.997471i \(0.522643\pi\)
−0.828298 + 0.560288i \(0.810691\pi\)
\(510\) 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 \(-0.215412\pi\)
−0.932160 + 0.362046i \(0.882078\pi\)
\(522\) 0 0
\(523\) 2426.00 4201.96i 0.202833 0.351317i −0.746607 0.665265i \(-0.768319\pi\)
0.949440 + 0.313948i \(0.101652\pi\)
\(524\) −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 −0.688887 0.724869i \(-0.741900\pi\)
0.972198 + 0.234159i \(0.0752338\pi\)
\(542\) −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 0.908148 0.418649i \(-0.137496\pi\)
−0.816635 + 0.577155i \(0.804163\pi\)
\(558\) 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 0.742955 + 0.669341i \(0.233423\pi\)
0.208189 + 0.978089i \(0.433243\pi\)
\(564\) 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 −0.987452 0.157918i \(-0.949522\pi\)
0.630487 + 0.776199i \(0.282855\pi\)
\(570\) 0 0
\(571\) −2802.00 4853.21i −0.205359 0.355692i 0.744888 0.667190i \(-0.232503\pi\)
−0.950247 + 0.311497i \(0.899170\pi\)
\(572\) −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 −0.933055 0.359733i \(-0.882868\pi\)
0.154990 0.987916i \(-0.450466\pi\)
\(578\) −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 \(-0.247023\pi\)
0.713689 + 0.700463i \(0.247023\pi\)
\(588\) 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 \(-0.992058\pi\)
0.521450 + 0.853282i \(0.325391\pi\)
\(594\) 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 −0.947728 0.319078i \(-0.896627\pi\)
0.197535 0.980296i \(-0.436706\pi\)
\(600\) 0 0
\(601\) −8368.00 −0.567950 −0.283975 0.958832i \(-0.591653\pi\)
−0.283975 + 0.958832i \(0.591653\pi\)
\(602\) 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 −0.242449 0.970164i \(-0.577951\pi\)
0.961411 0.275115i \(-0.0887160\pi\)
\(608\) −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 0.984120 0.177504i \(-0.0568022\pi\)
−0.645783 + 0.763521i \(0.723469\pi\)
\(614\) −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 0.999430 + 0.0337488i \(0.0107446\pi\)
−0.470488 + 0.882406i \(0.655922\pi\)
\(620\) −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 0.999685 0.0251060i \(-0.00799233\pi\)
−0.521585 + 0.853199i \(0.674659\pi\)
\(642\) 0 0
\(643\) 10452.0 0.641037 0.320518 0.947242i \(-0.396143\pi\)
0.320518 + 0.947242i \(0.396143\pi\)
\(644\) 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 \(-0.167363\pi\)
−0.867117 + 0.498104i \(0.834030\pi\)
\(648\) 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 −0.629269 0.777188i \(-0.716646\pi\)
0.987699 + 0.156369i \(0.0499789\pi\)
\(654\) 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 0.939201 + 0.343367i \(0.111567\pi\)
−0.172236 + 0.985056i \(0.555099\pi\)
\(662\) 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 \(-0.741194\pi\)
0.972715 + 0.232002i \(0.0745275\pi\)
\(678\) 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 0.939233 0.343280i \(-0.111538\pi\)
−0.766905 + 0.641760i \(0.778205\pi\)
\(684\) 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 \(-0.966090\pi\)
0.589249 + 0.807951i \(0.299424\pi\)
\(692\) −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 0.409099 + 0.912490i \(0.365843\pi\)
−0.994789 + 0.101955i \(0.967490\pi\)
\(710\) −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 \(-0.755898\pi\)
0.960965 + 0.276670i \(0.0892310\pi\)
\(720\) 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 \(-0.708150\pi\)
−0.608304 + 0.793704i \(0.708150\pi\)
\(728\) 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 −0.0196367 + 0.999807i \(0.506251\pi\)
−0.856040 + 0.516909i \(0.827082\pi\)
\(734\) −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 −0.983552 0.180626i \(-0.942187\pi\)
0.335349 0.942094i \(-0.391146\pi\)
\(740\) 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 −0.693232 0.720715i \(-0.743814\pi\)
0.970773 + 0.239999i \(0.0771470\pi\)
\(752\) −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 0.114397 0.993435i \(-0.463506\pi\)
0.803141 0.595789i \(-0.203160\pi\)
\(762\) 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 \(-0.357682\pi\)
0.432356 + 0.901703i \(0.357682\pi\)
\(770\) 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 \(-0.0613145\pi\)
−0.656541 + 0.754290i \(0.727981\pi\)
\(774\) 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 \(-0.0871519\pi\)
−0.715538 + 0.698573i \(0.753819\pi\)
\(788\) −324.000 561.184i −0.0146472 0.0253698i
\(789\) 0 0
\(790\) 19456.0 0.876220