Properties

Label 882.4.g.c.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.c.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 0.629817 0.776743i \(-0.283130\pi\)
−0.987588 + 0.157066i \(0.949796\pi\)
\(6\) 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 \(-0.513586\pi\)
−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 −0.393733 0.919225i \(-0.628817\pi\)
0.992939 0.118630i \(-0.0378502\pi\)
\(18\) 0 0
\(19\) 74.0000 + 128.172i 0.893514 + 1.54761i 0.835633 + 0.549288i \(0.185101\pi\)
0.0578808 + 0.998324i \(0.481566\pi\)
\(20\) 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 −0.992970 0.118370i \(-0.962233\pi\)
0.598997 + 0.800752i \(0.295566\pi\)
\(32\) −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 \(-0.204878\pi\)
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 −0.944245 0.329245i \(-0.893206\pi\)
0.186988 0.982362i \(-0.440127\pi\)
\(48\) 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 \(0.373336\pi\)
−0.992114 + 0.125342i \(0.959997\pi\)
\(60\) 0 0
\(61\) 346.000 + 599.290i 0.726242 + 1.25789i 0.958461 + 0.285224i \(0.0920681\pi\)
−0.232219 + 0.972664i \(0.574599\pi\)
\(62\) 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 −0.633999 0.773334i \(-0.718588\pi\)
0.986726 + 0.162393i \(0.0519212\pi\)
\(74\) 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 \(-0.649390\pi\)
−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 0.628223 0.778033i \(-0.283782\pi\)
−0.987908 + 0.155041i \(0.950449\pi\)
\(90\) 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 −0.957382 0.288823i \(-0.906736\pi\)
0.728819 + 0.684706i \(0.240069\pi\)
\(102\) 0 0
\(103\) −316.000 547.328i −0.302295 0.523591i 0.674360 0.738402i \(-0.264420\pi\)
−0.976655 + 0.214812i \(0.931086\pi\)
\(104\) −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 0.999835 0.0181429i \(-0.00577539\pi\)
−0.515630 + 0.856811i \(0.672442\pi\)
\(132\) 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 \(-0.129020\pi\)
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 −0.860482 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 −0.779001 0.627023i \(-0.784273\pi\)
0.932518 + 0.361123i \(0.117607\pi\)
\(158\) −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 \(-0.635632\pi\)
−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 0.901342 0.433107i \(-0.142583\pi\)
−0.825753 + 0.564032i \(0.809250\pi\)
\(174\) 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 \(-0.812802\pi\)
−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 −0.994402 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 −0.695133 0.718881i \(-0.744654\pi\)
0.970136 + 0.242562i \(0.0779878\pi\)
\(200\) 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 −0.892993 0.450071i \(-0.851399\pi\)
0.836269 + 0.548319i \(0.184732\pi\)
\(228\) 0 0
\(229\) 2090.00 + 3619.99i 0.603105 + 1.04461i 0.992348 + 0.123474i \(0.0394034\pi\)
−0.389243 + 0.921135i \(0.627263\pi\)
\(230\) −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 \(0.363409\pi\)
−0.995540 + 0.0943434i \(0.969925\pi\)
\(242\) −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 −0.999677 0.0254070i \(-0.991912\pi\)
0.477835 0.878449i \(-0.341421\pi\)
\(258\) 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 −0.662607 0.748968i \(-0.730550\pi\)
0.979928 + 0.199350i \(0.0638832\pi\)
\(270\) 0 0
\(271\) −2440.00 4226.20i −0.546935 0.947320i −0.998482 0.0550723i \(-0.982461\pi\)
0.451547 0.892247i \(-0.350872\pi\)
\(272\) −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 \(0.571590\pi\)
−0.732706 + 0.680545i \(0.761743\pi\)
\(284\) −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 −0.895681 0.444697i \(-0.853311\pi\)
0.832959 + 0.553334i \(0.186645\pi\)
\(312\) 0 0
\(313\) 2796.00 + 4842.81i 0.504918 + 0.874543i 0.999984 + 0.00568790i \(0.00181052\pi\)
−0.495066 + 0.868855i \(0.664856\pi\)
\(314\) −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 \(-0.495606\pi\)
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 −0.142149 0.989845i \(-0.545401\pi\)
0.928306 0.371818i \(-0.121265\pi\)
\(354\) 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 −0.592261 0.805746i \(-0.701764\pi\)
0.993927 + 0.110040i \(0.0350978\pi\)
\(368\) 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 \(0.0916042\pi\)
−0.233636 + 0.972324i \(0.575062\pi\)
\(384\) 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 0.753638 0.657290i \(-0.228297\pi\)
−0.946049 + 0.324025i \(0.894964\pi\)
\(398\) −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 −0.644856 0.764304i \(-0.723083\pi\)
0.984335 + 0.176310i \(0.0564161\pi\)
\(410\) −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 −0.990236 0.139400i \(-0.955483\pi\)
0.615842 + 0.787870i \(0.288816\pi\)
\(432\) 0 0
\(433\) 5048.00 0.560257 0.280129 0.959962i \(-0.409623\pi\)
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 0.827182 0.561935i \(-0.189943\pi\)
−0.900240 + 0.435393i \(0.856609\pi\)
\(440\) −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 \(-0.373601\pi\)
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 0.931963 0.362552i \(-0.118095\pi\)
−0.779961 + 0.625828i \(0.784761\pi\)
\(468\) 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 −0.977906 0.209045i \(-0.932964\pi\)
0.669991 + 0.742369i \(0.266298\pi\)
\(480\) 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 \(-0.705374\pi\)
−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 −0.828298 0.560288i \(-0.810691\pi\)
−0.0710743 0.997471i \(-0.522643\pi\)
\(510\) 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 −0.932160 0.362046i \(-0.882078\pi\)
0.779621 + 0.626251i \(0.215412\pi\)
\(522\) 0 0
\(523\) 2426.00 + 4201.96i 0.202833 + 0.351317i 0.949440 0.313948i \(-0.101652\pi\)
−0.746607 + 0.665265i \(0.768319\pi\)
\(524\) −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 \(-0.433243\pi\)
0.742955 0.669341i \(-0.233423\pi\)
\(564\) 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 \(0.450466\pi\)
−0.933055 + 0.359733i \(0.882868\pi\)
\(578\) −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 0.521450 0.853282i \(-0.325391\pi\)
−0.999689 + 0.0249483i \(0.992058\pi\)
\(594\) 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 \(-0.591653\pi\)
−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 0.961411 + 0.275115i \(0.0887160\pi\)
−0.242449 + 0.970164i \(0.577951\pi\)
\(608\) −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 \(-0.655922\pi\)
0.999430 0.0337488i \(-0.0107446\pi\)
\(620\) −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 \(-0.396143\pi\)
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 −0.867117 0.498104i \(-0.834030\pi\)
0.864930 + 0.501893i \(0.167363\pi\)
\(648\) 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 \(-0.555099\pi\)
0.939201 0.343367i \(-0.111567\pi\)
\(662\) 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 0.972715 0.232002i \(-0.0745275\pi\)
−0.687277 + 0.726395i \(0.741194\pi\)
\(678\) 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 0.589249 0.807951i \(-0.299424\pi\)
−0.994331 + 0.106329i \(0.966090\pi\)
\(692\) −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 0.960965 0.276670i \(-0.0892310\pi\)
−0.720086 + 0.693885i \(0.755898\pi\)
\(720\) 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 −0.856040 0.516909i \(-0.827082\pi\)
−0.0196367 0.999807i \(-0.506251\pi\)
\(734\) −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 \(0.203160\pi\)
0.114397 + 0.993435i \(0.463506\pi\)
\(762\) 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 −0.656541 0.754290i \(-0.727981\pi\)
0.981505 + 0.191436i \(0.0613145\pi\)
\(774\) 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 −0.715538 0.698573i \(-0.753819\pi\)
0.962752 + 0.270388i \(0.0871519\pi\)
\(788\) −324.000 + 561.184i −0.0146472 + 0.0253698i
\(789\) 0 0
\(790\) 19456.0 0.876220