Properties

Label 882.4.g.y.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.y.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.94975 - 13.7694i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.94975 - 13.7694i) q^{5} +8.00000 q^{8} +(-15.8995 + 27.5387i) q^{10} +(28.6985 - 49.7072i) q^{11} +5.69848 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-25.9497 + 44.9463i) q^{17} +(-8.10051 - 14.0305i) q^{19} +63.5980 q^{20} -114.794 q^{22} +(-106.698 - 184.807i) q^{23} +(-63.8970 + 110.673i) q^{25} +(-5.69848 - 9.87007i) q^{26} +218.191 q^{29} +(125.698 - 217.716i) q^{31} +(-16.0000 + 27.7128i) q^{32} +103.799 q^{34} +(-193.397 - 334.973i) q^{37} +(-16.2010 + 28.0610i) q^{38} +(-63.5980 - 110.155i) q^{40} +328.503 q^{41} -37.5879 q^{43} +(114.794 + 198.829i) q^{44} +(-213.397 + 369.614i) q^{46} +(-127.497 - 220.832i) q^{47} +255.588 q^{50} +(-11.3970 + 19.7401i) q^{52} +(105.794 - 183.240i) q^{53} -912.583 q^{55} +(-218.191 - 377.918i) q^{58} +(-206.101 + 356.977i) q^{59} +(418.347 + 724.598i) q^{61} -502.794 q^{62} +64.0000 q^{64} +(-45.3015 - 78.4645i) q^{65} +(82.7939 - 143.403i) q^{67} +(-103.799 - 179.785i) q^{68} +465.015 q^{71} +(-224.829 + 389.415i) q^{73} +(-386.794 + 669.947i) q^{74} +64.8040 q^{76} +(171.779 + 297.530i) q^{79} +(-127.196 + 220.310i) q^{80} +(-328.503 - 568.983i) q^{82} -1502.33 q^{83} +825.176 q^{85} +(37.5879 + 65.1041i) q^{86} +(229.588 - 397.658i) q^{88} +(-170.543 - 295.389i) q^{89} +853.588 q^{92} +(-254.995 + 441.664i) q^{94} +(-128.794 + 223.078i) q^{95} -865.437 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} - 12q^{5} + 32q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} - 12q^{5} + 32q^{8} - 24q^{10} - 4q^{11} - 96q^{13} - 32q^{16} - 84q^{17} - 72q^{19} + 96q^{20} + 16q^{22} - 308q^{23} - 18q^{25} + 96q^{26} + 160q^{29} + 384q^{31} - 64q^{32} + 336q^{34} - 536q^{37} - 144q^{38} - 96q^{40} + 1512q^{41} + 800q^{43} - 16q^{44} - 616q^{46} - 312q^{47} + 72q^{50} + 192q^{52} - 52q^{53} - 2304q^{55} - 160q^{58} - 864q^{59} + 1416q^{61} - 1536q^{62} + 256q^{64} - 300q^{65} - 144q^{67} - 336q^{68} + 3048q^{71} + 744q^{73} - 1072q^{74} + 576q^{76} - 976q^{79} - 192q^{80} - 1512q^{82} - 624q^{83} + 1400q^{85} - 800q^{86} - 32q^{88} - 108q^{89} + 2464q^{92} - 624q^{94} - 40q^{95} + 1488q^{97} + O(q^{100}) \)

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
\(5\) −7.94975 13.7694i −0.711047 1.23157i −0.964464 0.264213i \(-0.914888\pi\)
0.253417 0.967357i \(-0.418445\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −15.8995 + 27.5387i −0.502786 + 0.870851i
\(11\) 28.6985 49.7072i 0.786629 1.36248i −0.141392 0.989954i \(-0.545158\pi\)
0.928021 0.372528i \(-0.121509\pi\)
\(12\) 0 0
\(13\) 5.69848 0.121575 0.0607875 0.998151i \(-0.480639\pi\)
0.0607875 + 0.998151i \(0.480639\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −25.9497 + 44.9463i −0.370220 + 0.641240i −0.989599 0.143852i \(-0.954051\pi\)
0.619379 + 0.785092i \(0.287384\pi\)
\(18\) 0 0
\(19\) −8.10051 14.0305i −0.0978096 0.169411i 0.812968 0.582308i \(-0.197850\pi\)
−0.910778 + 0.412897i \(0.864517\pi\)
\(20\) 63.5980 0.711047
\(21\) 0 0
\(22\) −114.794 −1.11246
\(23\) −106.698 184.807i −0.967312 1.67543i −0.703271 0.710922i \(-0.748278\pi\)
−0.264041 0.964512i \(-0.585055\pi\)
\(24\) 0 0
\(25\) −63.8970 + 110.673i −0.511176 + 0.885382i
\(26\) −5.69848 9.87007i −0.0429833 0.0744492i
\(27\) 0 0
\(28\) 0 0
\(29\) 218.191 1.39714 0.698570 0.715542i \(-0.253820\pi\)
0.698570 + 0.715542i \(0.253820\pi\)
\(30\) 0 0
\(31\) 125.698 217.716i 0.728262 1.26139i −0.229356 0.973343i \(-0.573662\pi\)
0.957617 0.288044i \(-0.0930048\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 103.799 0.523570
\(35\) 0 0
\(36\) 0 0
\(37\) −193.397 334.973i −0.859304 1.48836i −0.872593 0.488447i \(-0.837563\pi\)
0.0132889 0.999912i \(-0.495770\pi\)
\(38\) −16.2010 + 28.0610i −0.0691619 + 0.119792i
\(39\) 0 0
\(40\) −63.5980 110.155i −0.251393 0.435426i
\(41\) 328.503 1.25130 0.625652 0.780102i \(-0.284833\pi\)
0.625652 + 0.780102i \(0.284833\pi\)
\(42\) 0 0
\(43\) −37.5879 −0.133305 −0.0666523 0.997776i \(-0.521232\pi\)
−0.0666523 + 0.997776i \(0.521232\pi\)
\(44\) 114.794 + 198.829i 0.393314 + 0.681241i
\(45\) 0 0
\(46\) −213.397 + 369.614i −0.683993 + 1.18471i
\(47\) −127.497 220.832i −0.395690 0.685355i 0.597499 0.801869i \(-0.296161\pi\)
−0.993189 + 0.116515i \(0.962828\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 255.588 0.722912
\(51\) 0 0
\(52\) −11.3970 + 19.7401i −0.0303938 + 0.0526435i
\(53\) 105.794 183.240i 0.274187 0.474906i −0.695743 0.718291i \(-0.744925\pi\)
0.969930 + 0.243385i \(0.0782579\pi\)
\(54\) 0 0
\(55\) −912.583 −2.23732
\(56\) 0 0
\(57\) 0 0
\(58\) −218.191 377.918i −0.493963 0.855569i
\(59\) −206.101 + 356.977i −0.454780 + 0.787701i −0.998676 0.0514512i \(-0.983615\pi\)
0.543896 + 0.839153i \(0.316949\pi\)
\(60\) 0 0
\(61\) 418.347 + 724.598i 0.878095 + 1.52091i 0.853429 + 0.521210i \(0.174519\pi\)
0.0246666 + 0.999696i \(0.492148\pi\)
\(62\) −502.794 −1.02992
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −45.3015 78.4645i −0.0864456 0.149728i
\(66\) 0 0
\(67\) 82.7939 143.403i 0.150969 0.261485i −0.780615 0.625012i \(-0.785094\pi\)
0.931584 + 0.363527i \(0.118427\pi\)
\(68\) −103.799 179.785i −0.185110 0.320620i
\(69\) 0 0
\(70\) 0 0
\(71\) 465.015 0.777284 0.388642 0.921389i \(-0.372944\pi\)
0.388642 + 0.921389i \(0.372944\pi\)
\(72\) 0 0
\(73\) −224.829 + 389.415i −0.360469 + 0.624351i −0.988038 0.154210i \(-0.950717\pi\)
0.627569 + 0.778561i \(0.284050\pi\)
\(74\) −386.794 + 669.947i −0.607620 + 1.05243i
\(75\) 0 0
\(76\) 64.8040 0.0978096
\(77\) 0 0
\(78\) 0 0
\(79\) 171.779 + 297.530i 0.244641 + 0.423730i 0.962031 0.272942i \(-0.0879966\pi\)
−0.717390 + 0.696672i \(0.754663\pi\)
\(80\) −127.196 + 220.310i −0.177762 + 0.307892i
\(81\) 0 0
\(82\) −328.503 568.983i −0.442403 0.766264i
\(83\) −1502.33 −1.98677 −0.993387 0.114812i \(-0.963373\pi\)
−0.993387 + 0.114812i \(0.963373\pi\)
\(84\) 0 0
\(85\) 825.176 1.05298
\(86\) 37.5879 + 65.1041i 0.0471303 + 0.0816321i
\(87\) 0 0
\(88\) 229.588 397.658i 0.278115 0.481710i
\(89\) −170.543 295.389i −0.203118 0.351810i 0.746414 0.665482i \(-0.231774\pi\)
−0.949531 + 0.313672i \(0.898441\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 853.588 0.967312
\(93\) 0 0
\(94\) −254.995 + 441.664i −0.279795 + 0.484619i
\(95\) −128.794 + 223.078i −0.139095 + 0.240919i
\(96\) 0 0
\(97\) −865.437 −0.905895 −0.452947 0.891537i \(-0.649627\pi\)
−0.452947 + 0.891537i \(0.649627\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −255.588 442.691i −0.255588 0.442691i
\(101\) −121.628 + 210.666i −0.119826 + 0.207545i −0.919699 0.392625i \(-0.871567\pi\)
0.799873 + 0.600170i \(0.204900\pi\)
\(102\) 0 0
\(103\) 476.673 + 825.622i 0.456000 + 0.789815i 0.998745 0.0500822i \(-0.0159483\pi\)
−0.542745 + 0.839898i \(0.682615\pi\)
\(104\) 45.5879 0.0429833
\(105\) 0 0
\(106\) −423.176 −0.387759
\(107\) −672.477 1164.76i −0.607578 1.05236i −0.991638 0.129048i \(-0.958808\pi\)
0.384061 0.923308i \(-0.374525\pi\)
\(108\) 0 0
\(109\) −867.176 + 1501.99i −0.762022 + 1.31986i 0.179785 + 0.983706i \(0.442460\pi\)
−0.941807 + 0.336155i \(0.890874\pi\)
\(110\) 912.583 + 1580.64i 0.791012 + 1.37007i
\(111\) 0 0
\(112\) 0 0
\(113\) −1441.18 −1.19977 −0.599887 0.800085i \(-0.704788\pi\)
−0.599887 + 0.800085i \(0.704788\pi\)
\(114\) 0 0
\(115\) −1696.45 + 2938.34i −1.37561 + 2.38262i
\(116\) −436.382 + 755.835i −0.349285 + 0.604979i
\(117\) 0 0
\(118\) 824.402 0.643156
\(119\) 0 0
\(120\) 0 0
\(121\) −981.706 1700.36i −0.737570 1.27751i
\(122\) 836.693 1449.20i 0.620907 1.07544i
\(123\) 0 0
\(124\) 502.794 + 870.865i 0.364131 + 0.630693i
\(125\) 44.4222 0.0317860
\(126\) 0 0
\(127\) 1184.70 0.827759 0.413880 0.910332i \(-0.364173\pi\)
0.413880 + 0.910332i \(0.364173\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −90.6030 + 156.929i −0.0611262 + 0.105874i
\(131\) 148.794 + 257.719i 0.0992381 + 0.171885i 0.911369 0.411589i \(-0.135026\pi\)
−0.812131 + 0.583475i \(0.801693\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −331.176 −0.213502
\(135\) 0 0
\(136\) −207.598 + 359.570i −0.130892 + 0.226712i
\(137\) 310.492 537.789i 0.193629 0.335375i −0.752821 0.658225i \(-0.771308\pi\)
0.946450 + 0.322850i \(0.104641\pi\)
\(138\) 0 0
\(139\) −898.754 −0.548426 −0.274213 0.961669i \(-0.588417\pi\)
−0.274213 + 0.961669i \(0.588417\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −465.015 805.430i −0.274811 0.475987i
\(143\) 163.538 283.256i 0.0956344 0.165644i
\(144\) 0 0
\(145\) −1734.56 3004.35i −0.993432 1.72067i
\(146\) 899.316 0.509780
\(147\) 0 0
\(148\) 1547.18 0.859304
\(149\) −1527.35 2645.45i −0.839769 1.45452i −0.890088 0.455789i \(-0.849357\pi\)
0.0503195 0.998733i \(-0.483976\pi\)
\(150\) 0 0
\(151\) 32.5727 56.4176i 0.0175545 0.0304053i −0.857115 0.515126i \(-0.827745\pi\)
0.874669 + 0.484720i \(0.161079\pi\)
\(152\) −64.8040 112.244i −0.0345809 0.0598959i
\(153\) 0 0
\(154\) 0 0
\(155\) −3997.08 −2.07131
\(156\) 0 0
\(157\) −771.110 + 1335.60i −0.391983 + 0.678934i −0.992711 0.120519i \(-0.961544\pi\)
0.600728 + 0.799453i \(0.294877\pi\)
\(158\) 343.558 595.059i 0.172987 0.299623i
\(159\) 0 0
\(160\) 508.784 0.251393
\(161\) 0 0
\(162\) 0 0
\(163\) 1257.37 + 2177.82i 0.604200 + 1.04650i 0.992177 + 0.124836i \(0.0398404\pi\)
−0.387978 + 0.921669i \(0.626826\pi\)
\(164\) −657.005 + 1137.97i −0.312826 + 0.541831i
\(165\) 0 0
\(166\) 1502.33 + 2602.11i 0.702431 + 1.21665i
\(167\) −528.643 −0.244956 −0.122478 0.992471i \(-0.539084\pi\)
−0.122478 + 0.992471i \(0.539084\pi\)
\(168\) 0 0
\(169\) −2164.53 −0.985220
\(170\) −825.176 1429.25i −0.372283 0.644813i
\(171\) 0 0
\(172\) 75.1758 130.208i 0.0333261 0.0577226i
\(173\) 48.4220 + 83.8693i 0.0212801 + 0.0368582i 0.876469 0.481458i \(-0.159892\pi\)
−0.855189 + 0.518316i \(0.826559\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −918.352 −0.393314
\(177\) 0 0
\(178\) −341.085 + 590.777i −0.143626 + 0.248768i
\(179\) −267.271 + 462.927i −0.111602 + 0.193301i −0.916416 0.400226i \(-0.868932\pi\)
0.804814 + 0.593527i \(0.202265\pi\)
\(180\) 0 0
\(181\) 2087.00 0.857049 0.428524 0.903530i \(-0.359034\pi\)
0.428524 + 0.903530i \(0.359034\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −853.588 1478.46i −0.341996 0.592355i
\(185\) −3074.91 + 5325.91i −1.22201 + 2.11659i
\(186\) 0 0
\(187\) 1489.44 + 2579.78i 0.582451 + 1.00884i
\(188\) 1019.98 0.395690
\(189\) 0 0
\(190\) 515.176 0.196709
\(191\) 1693.84 + 2933.82i 0.641687 + 1.11143i 0.985056 + 0.172234i \(0.0550986\pi\)
−0.343369 + 0.939201i \(0.611568\pi\)
\(192\) 0 0
\(193\) 954.176 1652.68i 0.355871 0.616386i −0.631396 0.775461i \(-0.717518\pi\)
0.987267 + 0.159074i \(0.0508510\pi\)
\(194\) 865.437 + 1498.98i 0.320282 + 0.554745i
\(195\) 0 0
\(196\) 0 0
\(197\) 2061.88 0.745699 0.372850 0.927892i \(-0.378381\pi\)
0.372850 + 0.927892i \(0.378381\pi\)
\(198\) 0 0
\(199\) −1585.75 + 2746.60i −0.564878 + 0.978397i 0.432183 + 0.901786i \(0.357743\pi\)
−0.997061 + 0.0766115i \(0.975590\pi\)
\(200\) −511.176 + 885.382i −0.180728 + 0.313030i
\(201\) 0 0
\(202\) 486.512 0.169460
\(203\) 0 0
\(204\) 0 0
\(205\) −2611.51 4523.27i −0.889736 1.54107i
\(206\) 953.346 1651.24i 0.322441 0.558484i
\(207\) 0 0
\(208\) −45.5879 78.9605i −0.0151969 0.0263218i
\(209\) −929.889 −0.307760
\(210\) 0 0
\(211\) 1349.97 0.440454 0.220227 0.975449i \(-0.429320\pi\)
0.220227 + 0.975449i \(0.429320\pi\)
\(212\) 423.176 + 732.962i 0.137094 + 0.237453i
\(213\) 0 0
\(214\) −1344.95 + 2329.53i −0.429622 + 0.744128i
\(215\) 298.814 + 517.561i 0.0947858 + 0.164174i
\(216\) 0 0
\(217\) 0 0
\(218\) 3468.70 1.07766
\(219\) 0 0
\(220\) 1825.17 3161.28i 0.559330 0.968788i
\(221\) −147.874 + 256.126i −0.0450095 + 0.0779587i
\(222\) 0 0
\(223\) −1361.85 −0.408951 −0.204476 0.978872i \(-0.565549\pi\)
−0.204476 + 0.978872i \(0.565549\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1441.18 + 2496.19i 0.424184 + 0.734708i
\(227\) 930.905 1612.37i 0.272186 0.471441i −0.697235 0.716843i \(-0.745587\pi\)
0.969421 + 0.245402i \(0.0789199\pi\)
\(228\) 0 0
\(229\) 2679.39 + 4640.84i 0.773184 + 1.33919i 0.935809 + 0.352506i \(0.114671\pi\)
−0.162625 + 0.986688i \(0.551996\pi\)
\(230\) 6785.81 1.94540
\(231\) 0 0
\(232\) 1745.53 0.493963
\(233\) 2720.56 + 4712.15i 0.764935 + 1.32491i 0.940281 + 0.340400i \(0.110562\pi\)
−0.175345 + 0.984507i \(0.556104\pi\)
\(234\) 0 0
\(235\) −2027.15 + 3511.12i −0.562708 + 0.974639i
\(236\) −824.402 1427.91i −0.227390 0.393851i
\(237\) 0 0
\(238\) 0 0
\(239\) 1157.28 0.313213 0.156607 0.987661i \(-0.449945\pi\)
0.156607 + 0.987661i \(0.449945\pi\)
\(240\) 0 0
\(241\) 1984.69 3437.58i 0.530477 0.918814i −0.468890 0.883256i \(-0.655346\pi\)
0.999368 0.0355573i \(-0.0113206\pi\)
\(242\) −1963.41 + 3400.73i −0.521541 + 0.903335i
\(243\) 0 0
\(244\) −3346.77 −0.878095
\(245\) 0 0
\(246\) 0 0
\(247\) −46.1606 79.9525i −0.0118912 0.0205962i
\(248\) 1005.59 1741.73i 0.257479 0.445967i
\(249\) 0 0
\(250\) −44.4222 76.9415i −0.0112380 0.0194648i
\(251\) −5978.75 −1.50349 −0.751744 0.659455i \(-0.770787\pi\)
−0.751744 + 0.659455i \(0.770787\pi\)
\(252\) 0 0
\(253\) −12248.3 −3.04366
\(254\) −1184.70 2051.97i −0.292657 0.506897i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 2325.07 + 4027.15i 0.564335 + 0.977458i 0.997111 + 0.0759560i \(0.0242008\pi\)
−0.432776 + 0.901502i \(0.642466\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 362.412 0.0864456
\(261\) 0 0
\(262\) 297.588 515.437i 0.0701719 0.121541i
\(263\) 1847.68 3200.28i 0.433205 0.750334i −0.563942 0.825815i \(-0.690716\pi\)
0.997147 + 0.0754807i \(0.0240491\pi\)
\(264\) 0 0
\(265\) −3364.14 −0.779840
\(266\) 0 0
\(267\) 0 0
\(268\) 331.176 + 573.613i 0.0754843 + 0.130743i
\(269\) −3578.84 + 6198.74i −0.811175 + 1.40500i 0.100868 + 0.994900i \(0.467838\pi\)
−0.912042 + 0.410096i \(0.865495\pi\)
\(270\) 0 0
\(271\) −2019.19 3497.33i −0.452608 0.783940i 0.545939 0.837825i \(-0.316173\pi\)
−0.998547 + 0.0538847i \(0.982840\pi\)
\(272\) 830.392 0.185110
\(273\) 0 0
\(274\) −1241.97 −0.273833
\(275\) 3667.49 + 6352.28i 0.804211 + 1.39293i
\(276\) 0 0
\(277\) 1377.41 2385.75i 0.298775 0.517493i −0.677081 0.735909i \(-0.736755\pi\)
0.975856 + 0.218415i \(0.0700887\pi\)
\(278\) 898.754 + 1556.69i 0.193898 + 0.335841i
\(279\) 0 0
\(280\) 0 0
\(281\) 772.742 0.164050 0.0820248 0.996630i \(-0.473861\pi\)
0.0820248 + 0.996630i \(0.473861\pi\)
\(282\) 0 0
\(283\) 3372.74 5841.76i 0.708441 1.22706i −0.256995 0.966413i \(-0.582732\pi\)
0.965435 0.260643i \(-0.0839344\pi\)
\(284\) −930.030 + 1610.86i −0.194321 + 0.336574i
\(285\) 0 0
\(286\) −654.152 −0.135248
\(287\) 0 0
\(288\) 0 0
\(289\) 1109.72 + 1922.09i 0.225874 + 0.391226i
\(290\) −3469.13 + 6008.70i −0.702462 + 1.21670i
\(291\) 0 0
\(292\) −899.316 1557.66i −0.180235 0.312175i
\(293\) −1922.69 −0.383362 −0.191681 0.981457i \(-0.561394\pi\)
−0.191681 + 0.981457i \(0.561394\pi\)
\(294\) 0 0
\(295\) 6553.79 1.29348
\(296\) −1547.18 2679.79i −0.303810 0.526214i
\(297\) 0 0
\(298\) −3054.70 + 5290.90i −0.593806 + 1.02850i
\(299\) −608.020 1053.12i −0.117601 0.203691i
\(300\) 0 0
\(301\) 0 0
\(302\) −130.291 −0.0248258
\(303\) 0 0
\(304\) −129.608 + 224.488i −0.0244524 + 0.0423528i
\(305\) 6651.50 11520.7i 1.24873 2.16287i
\(306\) 0 0
\(307\) 2016.68 0.374913 0.187456 0.982273i \(-0.439976\pi\)
0.187456 + 0.982273i \(0.439976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3997.08 + 6923.15i 0.732320 + 1.26842i
\(311\) 3574.99 6192.07i 0.651831 1.12900i −0.330848 0.943684i \(-0.607335\pi\)
0.982678 0.185320i \(-0.0593320\pi\)
\(312\) 0 0
\(313\) −4298.25 7444.78i −0.776202 1.34442i −0.934116 0.356969i \(-0.883810\pi\)
0.157914 0.987453i \(-0.449523\pi\)
\(314\) 3084.44 0.554347
\(315\) 0 0
\(316\) −1374.23 −0.244641
\(317\) −1426.62 2470.98i −0.252766 0.437804i 0.711520 0.702666i \(-0.248007\pi\)
−0.964286 + 0.264862i \(0.914674\pi\)
\(318\) 0 0
\(319\) 6261.75 10845.7i 1.09903 1.90358i
\(320\) −508.784 881.239i −0.0888809 0.153946i
\(321\) 0 0
\(322\) 0 0
\(323\) 840.824 0.144844
\(324\) 0 0
\(325\) −364.116 + 630.667i −0.0621462 + 0.107640i
\(326\) 2514.73 4355.65i 0.427234 0.739991i
\(327\) 0 0
\(328\) 2628.02 0.442403
\(329\) 0 0
\(330\) 0 0
\(331\) −809.558 1402.19i −0.134433 0.232845i 0.790948 0.611884i \(-0.209588\pi\)
−0.925381 + 0.379039i \(0.876255\pi\)
\(332\) 3004.66 5204.23i 0.496694 0.860299i
\(333\) 0 0
\(334\) 528.643 + 915.637i 0.0866050 + 0.150004i
\(335\) −2632.76 −0.429383
\(336\) 0 0
\(337\) −3278.67 −0.529972 −0.264986 0.964252i \(-0.585367\pi\)
−0.264986 + 0.964252i \(0.585367\pi\)
\(338\) 2164.53 + 3749.07i 0.348328 + 0.603321i
\(339\) 0 0
\(340\) −1650.35 + 2858.49i −0.263244 + 0.455952i
\(341\) −7214.71 12496.2i −1.14574 1.98449i
\(342\) 0 0
\(343\) 0 0
\(344\) −300.703 −0.0471303
\(345\) 0 0
\(346\) 96.8439 167.739i 0.0150473 0.0260627i
\(347\) −1425.15 + 2468.43i −0.220479 + 0.381880i −0.954953 0.296756i \(-0.904095\pi\)
0.734475 + 0.678636i \(0.237429\pi\)
\(348\) 0 0
\(349\) −4725.32 −0.724758 −0.362379 0.932031i \(-0.618035\pi\)
−0.362379 + 0.932031i \(0.618035\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 918.352 + 1590.63i 0.139058 + 0.240855i
\(353\) 3363.72 5826.13i 0.507175 0.878452i −0.492791 0.870148i \(-0.664023\pi\)
0.999966 0.00830453i \(-0.00264345\pi\)
\(354\) 0 0
\(355\) −3696.75 6402.96i −0.552685 0.957279i
\(356\) 1364.34 0.203118
\(357\) 0 0
\(358\) 1069.08 0.157829
\(359\) −3665.94 6349.60i −0.538945 0.933479i −0.998961 0.0455691i \(-0.985490\pi\)
0.460017 0.887910i \(-0.347843\pi\)
\(360\) 0 0
\(361\) 3298.26 5712.76i 0.480867 0.832885i
\(362\) −2087.00 3614.80i −0.303012 0.524833i
\(363\) 0 0
\(364\) 0 0
\(365\) 7149.34 1.02524
\(366\) 0 0
\(367\) −1387.22 + 2402.73i −0.197308 + 0.341748i −0.947655 0.319297i \(-0.896553\pi\)
0.750347 + 0.661045i \(0.229887\pi\)
\(368\) −1707.18 + 2956.92i −0.241828 + 0.418858i
\(369\) 0 0
\(370\) 12299.7 1.72819
\(371\) 0 0
\(372\) 0 0
\(373\) −1263.67 2188.75i −0.175417 0.303831i 0.764889 0.644163i \(-0.222794\pi\)
−0.940305 + 0.340332i \(0.889461\pi\)
\(374\) 2978.87 5159.56i 0.411855 0.713354i
\(375\) 0 0
\(376\) −1019.98 1766.66i −0.139897 0.242309i
\(377\) 1243.36 0.169857
\(378\) 0 0
\(379\) 3116.40 0.422371 0.211186 0.977446i \(-0.432268\pi\)
0.211186 + 0.977446i \(0.432268\pi\)
\(380\) −515.176 892.311i −0.0695473 0.120459i
\(381\) 0 0
\(382\) 3387.69 5867.65i 0.453741 0.785903i
\(383\) 759.035 + 1314.69i 0.101266 + 0.175398i 0.912207 0.409731i \(-0.134377\pi\)
−0.810940 + 0.585129i \(0.801044\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3816.70 −0.503277
\(387\) 0 0
\(388\) 1730.87 2997.96i 0.226474 0.392264i
\(389\) −1623.39 + 2811.79i −0.211591 + 0.366487i −0.952213 0.305436i \(-0.901198\pi\)
0.740622 + 0.671922i \(0.234531\pi\)
\(390\) 0 0
\(391\) 11075.2 1.43247
\(392\) 0 0
\(393\) 0 0
\(394\) −2061.88 3571.28i −0.263645 0.456646i
\(395\) 2731.20 4730.57i 0.347902 0.602584i
\(396\) 0 0
\(397\) 915.312 + 1585.37i 0.115713 + 0.200421i 0.918065 0.396431i \(-0.129751\pi\)
−0.802351 + 0.596852i \(0.796418\pi\)
\(398\) 6342.99 0.798858
\(399\) 0 0
\(400\) 2044.70 0.255588
\(401\) −1692.90 2932.20i −0.210822 0.365154i 0.741150 0.671339i \(-0.234281\pi\)
−0.951972 + 0.306185i \(0.900947\pi\)
\(402\) 0 0
\(403\) 716.291 1240.65i 0.0885384 0.153353i
\(404\) −486.512 842.664i −0.0599131 0.103772i
\(405\) 0 0
\(406\) 0 0
\(407\) −22200.8 −2.70382
\(408\) 0 0
\(409\) 4626.59 8013.48i 0.559340 0.968805i −0.438212 0.898872i \(-0.644388\pi\)
0.997552 0.0699333i \(-0.0222787\pi\)
\(410\) −5223.02 + 9046.54i −0.629138 + 1.08970i
\(411\) 0 0
\(412\) −3813.39 −0.456000
\(413\) 0 0
\(414\) 0 0
\(415\) 11943.2 + 20686.2i 1.41269 + 2.44685i
\(416\) −91.1758 + 157.921i −0.0107458 + 0.0186123i
\(417\) 0 0
\(418\) 929.889 + 1610.61i 0.108809 + 0.188464i
\(419\) 3547.52 0.413622 0.206811 0.978381i \(-0.433692\pi\)
0.206811 + 0.978381i \(0.433692\pi\)
\(420\) 0 0
\(421\) 7848.87 0.908624 0.454312 0.890843i \(-0.349885\pi\)
0.454312 + 0.890843i \(0.349885\pi\)
\(422\) −1349.97 2338.22i −0.155724 0.269722i
\(423\) 0 0
\(424\) 846.352 1465.92i 0.0969398 0.167905i
\(425\) −3316.22 5743.86i −0.378495 0.655572i
\(426\) 0 0
\(427\) 0 0
\(428\) 5379.82 0.607578
\(429\) 0 0
\(430\) 597.628 1035.12i 0.0670237 0.116088i
\(431\) −2223.66 + 3851.50i −0.248515 + 0.430441i −0.963114 0.269094i \(-0.913276\pi\)
0.714599 + 0.699534i \(0.246609\pi\)
\(432\) 0 0
\(433\) 6994.82 0.776327 0.388164 0.921590i \(-0.373110\pi\)
0.388164 + 0.921590i \(0.373110\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3468.70 6007.97i −0.381011 0.659930i
\(437\) −1728.62 + 2994.06i −0.189225 + 0.327747i
\(438\) 0 0
\(439\) 318.091 + 550.950i 0.0345823 + 0.0598984i 0.882799 0.469752i \(-0.155657\pi\)
−0.848216 + 0.529650i \(0.822323\pi\)
\(440\) −7300.66 −0.791012
\(441\) 0 0
\(442\) 591.497 0.0636530
\(443\) −2237.12 3874.80i −0.239929 0.415570i 0.720764 0.693180i \(-0.243791\pi\)
−0.960694 + 0.277610i \(0.910458\pi\)
\(444\) 0 0
\(445\) −2711.54 + 4696.53i −0.288853 + 0.500308i
\(446\) 1361.85 + 2358.79i 0.144586 + 0.250430i
\(447\) 0 0
\(448\) 0 0
\(449\) 2389.42 0.251144 0.125572 0.992085i \(-0.459923\pi\)
0.125572 + 0.992085i \(0.459923\pi\)
\(450\) 0 0
\(451\) 9427.52 16329.0i 0.984312 1.70488i
\(452\) 2882.35 4992.38i 0.299943 0.519517i
\(453\) 0 0
\(454\) −3723.62 −0.384930
\(455\) 0 0
\(456\) 0 0
\(457\) 2219.17 + 3843.71i 0.227152 + 0.393438i 0.956963 0.290210i \(-0.0937253\pi\)
−0.729811 + 0.683649i \(0.760392\pi\)
\(458\) 5358.78 9281.68i 0.546724 0.946953i
\(459\) 0 0
\(460\) −6785.81 11753.4i −0.687804 1.19131i
\(461\) −14079.8 −1.42248 −0.711240 0.702949i \(-0.751866\pi\)
−0.711240 + 0.702949i \(0.751866\pi\)
\(462\) 0 0
\(463\) 4687.50 0.470511 0.235255 0.971934i \(-0.424407\pi\)
0.235255 + 0.971934i \(0.424407\pi\)
\(464\) −1745.53 3023.34i −0.174642 0.302489i
\(465\) 0 0
\(466\) 5441.12 9424.30i 0.540891 0.936851i
\(467\) −4223.63 7315.54i −0.418514 0.724888i 0.577276 0.816549i \(-0.304116\pi\)
−0.995790 + 0.0916611i \(0.970782\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8108.58 0.795789
\(471\) 0 0
\(472\) −1648.80 + 2855.81i −0.160789 + 0.278495i
\(473\) −1078.72 + 1868.39i −0.104861 + 0.181625i
\(474\) 0 0
\(475\) 2070.39 0.199992
\(476\) 0 0
\(477\) 0 0
\(478\) −1157.28 2004.46i −0.110738 0.191803i
\(479\) 2184.70 3784.02i 0.208396 0.360952i −0.742814 0.669498i \(-0.766509\pi\)
0.951209 + 0.308546i \(0.0998424\pi\)
\(480\) 0 0
\(481\) −1102.07 1908.84i −0.104470 0.180947i
\(482\) −7938.75 −0.750208
\(483\) 0 0
\(484\) 7853.65 0.737570
\(485\) 6880.00 + 11916.5i 0.644134 + 1.11567i
\(486\) 0 0
\(487\) 7238.86 12538.1i 0.673561 1.16664i −0.303326 0.952887i \(-0.598097\pi\)
0.976887 0.213755i \(-0.0685695\pi\)
\(488\) 3346.77 + 5796.78i 0.310454 + 0.537721i
\(489\) 0 0
\(490\) 0 0
\(491\) −9306.12 −0.855355 −0.427677 0.903931i \(-0.640668\pi\)
−0.427677 + 0.903931i \(0.640668\pi\)
\(492\) 0 0
\(493\) −5662.00 + 9806.87i −0.517249 + 0.895901i
\(494\) −92.3212 + 159.905i −0.00840836 + 0.0145637i
\(495\) 0 0
\(496\) −4022.35 −0.364131
\(497\) 0 0
\(498\) 0 0
\(499\) 6118.77 + 10598.0i 0.548926 + 0.950767i 0.998349 + 0.0574479i \(0.0182963\pi\)
−0.449423 + 0.893319i \(0.648370\pi\)
\(500\) −88.8444 + 153.883i −0.00794649 + 0.0137637i
\(501\) 0 0
\(502\) 5978.75 + 10355.5i 0.531563 + 0.920695i
\(503\) 5524.30 0.489694 0.244847 0.969562i \(-0.421262\pi\)
0.244847 + 0.969562i \(0.421262\pi\)
\(504\) 0 0
\(505\) 3867.65 0.340808
\(506\) 12248.3 + 21214.7i 1.07610 + 1.86385i
\(507\) 0 0
\(508\) −2369.41 + 4103.93i −0.206940 + 0.358430i
\(509\) 5039.81 + 8729.20i 0.438871 + 0.760148i 0.997603 0.0692012i \(-0.0220450\pi\)
−0.558731 + 0.829349i \(0.688712\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 4650.15 8054.30i 0.399045 0.691167i
\(515\) 7578.86 13127.0i 0.648475 1.12319i
\(516\) 0 0
\(517\) −14635.9 −1.24504
\(518\) 0 0
\(519\) 0 0
\(520\) −362.412 627.716i −0.0305631 0.0529369i
\(521\) −2853.31 + 4942.07i −0.239934 + 0.415578i −0.960695 0.277606i \(-0.910459\pi\)
0.720761 + 0.693184i \(0.243792\pi\)
\(522\) 0 0
\(523\) −5328.63 9229.46i −0.445516 0.771656i 0.552572 0.833465i \(-0.313646\pi\)
−0.998088 + 0.0618088i \(0.980313\pi\)
\(524\) −1190.35 −0.0992381
\(525\) 0 0
\(526\) −7390.73 −0.612645
\(527\) 6523.69 + 11299.4i 0.539234 + 0.933981i
\(528\) 0 0
\(529\) −16685.6 + 28900.4i −1.37138 + 2.37531i
\(530\) 3364.14 + 5826.86i 0.275715 + 0.477552i
\(531\) 0 0
\(532\) 0 0
\(533\) 1871.97 0.152127
\(534\) 0 0
\(535\) −10692.0 + 18519.2i −0.864033 + 1.49655i
\(536\) 662.352 1147.23i 0.0533754 0.0924489i
\(537\) 0 0
\(538\) 14315.4 1.14717
\(539\) 0 0
\(540\) 0 0
\(541\) 2005.24 + 3473.18i 0.159357 + 0.276014i 0.934637 0.355603i \(-0.115725\pi\)
−0.775280 + 0.631618i \(0.782391\pi\)
\(542\) −4038.37 + 6994.66i −0.320042 + 0.554329i
\(543\) 0 0
\(544\) −830.392 1438.28i −0.0654462 0.113356i
\(545\) 27575.3 2.16733
\(546\) 0 0
\(547\) −17619.8 −1.37728 −0.688638 0.725105i \(-0.741791\pi\)
−0.688638 + 0.725105i \(0.741791\pi\)
\(548\) 1241.97 + 2151.15i 0.0968144 + 0.167688i
\(549\) 0 0
\(550\) 7334.98 12704.6i 0.568663 0.984954i
\(551\) −1767.46 3061.32i −0.136654 0.236691i
\(552\) 0 0
\(553\) 0 0
\(554\) −5509.65 −0.422532
\(555\) 0 0
\(556\) 1797.51 3113.37i 0.137107 0.237476i
\(557\) −5168.85 + 8952.71i −0.393198 + 0.681038i −0.992869 0.119208i \(-0.961965\pi\)
0.599672 + 0.800246i \(0.295298\pi\)
\(558\) 0 0
\(559\) −214.194 −0.0162065
\(560\) 0 0
\(561\) 0 0
\(562\) −772.742 1338.43i −0.0580003 0.100459i
\(563\) 12011.8 20805.1i 0.899180 1.55742i 0.0706347 0.997502i \(-0.477498\pi\)
0.828545 0.559923i \(-0.189169\pi\)
\(564\) 0 0
\(565\) 11457.0 + 19844.1i 0.853095 + 1.47760i
\(566\) −13491.0 −1.00189
\(567\) 0 0
\(568\) 3720.12 0.274811
\(569\) −6589.59 11413.5i −0.485501 0.840912i 0.514361 0.857574i \(-0.328029\pi\)
−0.999861 + 0.0166623i \(0.994696\pi\)
\(570\) 0 0
\(571\) −3888.13 + 6734.44i −0.284962 + 0.493568i −0.972600 0.232485i \(-0.925314\pi\)
0.687638 + 0.726054i \(0.258648\pi\)
\(572\) 654.152 + 1133.02i 0.0478172 + 0.0828219i
\(573\) 0 0
\(574\) 0 0
\(575\) 27270.8 1.97787
\(576\) 0 0
\(577\) 10083.5 17465.2i 0.727525 1.26011i −0.230401 0.973096i \(-0.574004\pi\)
0.957926 0.287015i \(-0.0926630\pi\)
\(578\) 2219.44 3844.19i 0.159717 0.276639i
\(579\) 0 0
\(580\) 13876.5 0.993432
\(581\) 0 0
\(582\) 0 0
\(583\) −6072.25 10517.4i −0.431367 0.747150i
\(584\) −1798.63 + 3115.32i −0.127445 + 0.220741i
\(585\) 0 0
\(586\) 1922.69 + 3330.20i 0.135539 + 0.234760i
\(587\) −8365.08 −0.588184 −0.294092 0.955777i \(-0.595017\pi\)
−0.294092 + 0.955777i \(0.595017\pi\)
\(588\) 0 0
\(589\) −4072.88 −0.284924
\(590\) −6553.79 11351.5i −0.457314 0.792091i
\(591\) 0 0
\(592\) −3094.35 + 5359.57i −0.214826 + 0.372090i
\(593\) 13810.9 + 23921.2i 0.956403 + 1.65654i 0.731124 + 0.682244i \(0.238996\pi\)
0.225279 + 0.974294i \(0.427671\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12218.8 0.839769
\(597\) 0 0
\(598\) −1216.04 + 2106.24i −0.0831564 + 0.144031i
\(599\) 269.159 466.197i 0.0183598 0.0318002i −0.856700 0.515816i \(-0.827489\pi\)
0.875059 + 0.484016i \(0.160822\pi\)
\(600\) 0 0
\(601\) −6958.64 −0.472294 −0.236147 0.971717i \(-0.575885\pi\)
−0.236147 + 0.971717i \(0.575885\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 130.291 + 225.670i 0.00877725 + 0.0152027i
\(605\) −15608.6 + 27034.9i −1.04889 + 1.81674i
\(606\) 0 0
\(607\) −8648.80 14980.2i −0.578326 1.00169i −0.995671 0.0929425i \(-0.970373\pi\)
0.417345 0.908748i \(-0.362961\pi\)
\(608\) 518.432 0.0345809
\(609\) 0 0
\(610\) −26606.0 −1.76598
\(611\) −726.542 1258.41i −0.0481060 0.0833220i
\(612\) 0 0
\(613\) 419.579 726.732i 0.0276454 0.0478832i −0.851872 0.523751i \(-0.824532\pi\)
0.879517 + 0.475867i \(0.157866\pi\)
\(614\) −2016.68 3493.00i −0.132552 0.229586i
\(615\) 0 0
\(616\) 0 0
\(617\) 16040.0 1.04659 0.523295 0.852152i \(-0.324703\pi\)
0.523295 + 0.852152i \(0.324703\pi\)
\(618\) 0 0
\(619\) −2714.64 + 4701.90i −0.176269 + 0.305307i −0.940600 0.339517i \(-0.889736\pi\)
0.764331 + 0.644825i \(0.223070\pi\)
\(620\) 7994.17 13846.3i 0.517828 0.896905i
\(621\) 0 0
\(622\) −14300.0 −0.921828
\(623\) 0 0
\(624\) 0 0
\(625\) 7633.98 + 13222.4i 0.488574 + 0.846236i
\(626\) −8596.49 + 14889.6i −0.548858 + 0.950649i
\(627\) 0 0
\(628\) −3084.44 5342.41i −0.195991 0.339467i
\(629\) 20074.4 1.27253
\(630\) 0 0
\(631\) −1807.86 −0.114057 −0.0570284 0.998373i \(-0.518163\pi\)
−0.0570284 + 0.998373i \(0.518163\pi\)
\(632\) 1374.23 + 2380.24i 0.0864936 + 0.149811i
\(633\) 0 0
\(634\) −2853.24 + 4941.95i −0.178733 + 0.309574i
\(635\) −9418.09 16312.6i −0.588576 1.01944i
\(636\) 0 0
\(637\) 0 0
\(638\) −25047.0 −1.55426
\(639\) 0 0
\(640\) −1017.57 + 1762.48i −0.0628483 + 0.108856i
\(641\) −2952.28 + 5113.50i −0.181916 + 0.315087i −0.942533 0.334113i \(-0.891563\pi\)
0.760617 + 0.649201i \(0.224897\pi\)
\(642\) 0 0
\(643\) −8092.42 −0.496320 −0.248160 0.968719i \(-0.579826\pi\)
−0.248160 + 0.968719i \(0.579826\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −840.824 1456.35i −0.0512102 0.0886987i
\(647\) −10096.3 + 17487.4i −0.613490 + 1.06260i 0.377157 + 0.926149i \(0.376902\pi\)
−0.990647 + 0.136447i \(0.956432\pi\)
\(648\) 0 0
\(649\) 11829.5 + 20489.4i 0.715486 + 1.23926i
\(650\) 1456.46 0.0878880
\(651\) 0 0
\(652\) −10058.9 −0.604200
\(653\) −10590.4 18343.2i −0.634664 1.09927i −0.986586 0.163240i \(-0.947805\pi\)
0.351923 0.936029i \(-0.385528\pi\)
\(654\) 0 0
\(655\) 2365.75 4097.60i 0.141126 0.244437i
\(656\) −2628.02 4551.86i −0.156413 0.270915i
\(657\) 0 0
\(658\) 0 0
\(659\) −28411.3 −1.67944 −0.839718 0.543023i \(-0.817280\pi\)
−0.839718 + 0.543023i \(0.817280\pi\)
\(660\) 0 0
\(661\) 8352.47 14466.9i 0.491488 0.851282i −0.508464 0.861083i \(-0.669787\pi\)
0.999952 + 0.00980149i \(0.00311996\pi\)
\(662\) −1619.12 + 2804.39i −0.0950585 + 0.164646i
\(663\) 0 0
\(664\) −12018.7 −0.702431
\(665\) 0 0
\(666\) 0 0
\(667\) −23280.6 40323.3i −1.35147 2.34081i
\(668\) 1057.29 1831.27i 0.0612390 0.106069i
\(669\) 0 0
\(670\) 2632.76 + 4560.08i 0.151810 + 0.262942i
\(671\) 48023.7 2.76294
\(672\) 0 0
\(673\) −9047.09 −0.518187 −0.259093 0.965852i \(-0.583424\pi\)
−0.259093 + 0.965852i \(0.583424\pi\)
\(674\) 3278.67 + 5678.83i 0.187374 + 0.324540i
\(675\) 0 0
\(676\) 4329.05 7498.14i 0.246305 0.426613i
\(677\) 3922.13 + 6793.32i 0.222658 + 0.385655i 0.955614 0.294621i \(-0.0951933\pi\)
−0.732956 + 0.680276i \(0.761860\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6601.41 0.372283
\(681\) 0 0
\(682\) −14429.4 + 24992.5i −0.810163 + 1.40324i
\(683\) 12883.0 22314.1i 0.721751 1.25011i −0.238547 0.971131i \(-0.576671\pi\)
0.960298 0.278978i \(-0.0899956\pi\)
\(684\) 0 0
\(685\) −9873.35 −0.550717
\(686\) 0 0
\(687\) 0 0
\(688\) 300.703 + 520.833i 0.0166631 + 0.0288613i
\(689\) 602.865 1044.19i 0.0333343 0.0577367i
\(690\) 0 0
\(691\) 12337.1 + 21368.4i 0.679195 + 1.17640i 0.975224 + 0.221221i \(0.0710042\pi\)
−0.296029 + 0.955179i \(0.595662\pi\)
\(692\) −387.376 −0.0212801
\(693\) 0 0
\(694\) 5700.60 0.311804
\(695\) 7144.86 + 12375.3i 0.389957 + 0.675425i
\(696\) 0 0
\(697\) −8524.56 + 14765.0i −0.463258 + 0.802386i
\(698\) 4725.32 + 8184.49i 0.256241 + 0.443822i
\(699\) 0 0
\(700\) 0 0
\(701\) −29377.9 −1.58286 −0.791431 0.611258i \(-0.790664\pi\)
−0.791431 + 0.611258i \(0.790664\pi\)
\(702\) 0 0
\(703\) −3133.23 + 5426.91i −0.168097 + 0.291152i
\(704\) 1836.70 3181.26i 0.0983286 0.170310i
\(705\) 0 0
\(706\) −13454.9 −0.717253
\(707\) 0 0
\(708\) 0 0
\(709\) −15297.1 26495.4i −0.810291 1.40347i −0.912660 0.408719i \(-0.865976\pi\)
0.102369 0.994746i \(-0.467358\pi\)
\(710\) −7393.51 + 12805.9i −0.390808 + 0.676898i
\(711\) 0 0
\(712\) −1364.34 2363.11i −0.0718130 0.124384i
\(713\) −53647.4 −2.81782
\(714\) 0 0
\(715\) −5200.34 −0.272002
\(716\) −1069.08 1851.71i −0.0558011 0.0966503i
\(717\) 0 0
\(718\) −7331.89 + 12699.2i −0.381091 + 0.660070i
\(719\) −973.469 1686.10i −0.0504927 0.0874559i 0.839674 0.543090i \(-0.182746\pi\)
−0.890167 + 0.455634i \(0.849412\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −13193.1 −0.680048
\(723\) 0 0
\(724\) −4174.01 + 7229.60i −0.214262 + 0.371113i
\(725\) −13941.7 + 24147.8i −0.714184 + 1.23700i
\(726\) 0 0
\(727\) 15750.6 0.803518 0.401759 0.915745i \(-0.368399\pi\)
0.401759 + 0.915745i \(0.368399\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7149.34 12383.0i −0.362478 0.627830i
\(731\) 975.396 1689.44i 0.0493520 0.0854802i
\(732\) 0 0
\(733\) −7174.78 12427.1i −0.361537 0.626200i 0.626677 0.779279i \(-0.284414\pi\)
−0.988214 + 0.153079i \(0.951081\pi\)
\(734\) 5548.86 0.279036
\(735\) 0 0
\(736\) 6828.70 0.341996
\(737\) −4752.12 8230.92i −0.237512 0.411384i
\(738\) 0 0
\(739\) 8879.03 15378.9i 0.441976 0.765525i −0.555860 0.831276i \(-0.687611\pi\)
0.997836 + 0.0657506i \(0.0209442\pi\)
\(740\) −12299.7 21303.6i −0.611006 1.05829i
\(741\) 0 0
\(742\) 0 0
\(743\) 29187.6 1.44117 0.720586 0.693366i \(-0.243873\pi\)
0.720586 + 0.693366i \(0.243873\pi\)
\(744\) 0 0
\(745\) −24284.1 + 42061.3i −1.19423 + 2.06847i
\(746\) −2527.35 + 4377.49i −0.124038 + 0.214841i
\(747\) 0 0
\(748\) −11915.5 −0.582451
\(749\) 0 0
\(750\) 0 0
\(751\) −6890.97 11935.5i −0.334827 0.579938i 0.648624 0.761109i \(-0.275345\pi\)
−0.983452 + 0.181171i \(0.942011\pi\)
\(752\) −2039.96 + 3533.31i −0.0989224 + 0.171339i
\(753\) 0 0
\(754\) −1243.36 2153.56i −0.0600536 0.104016i
\(755\) −1035.78 −0.0499283
\(756\) 0 0
\(757\) 36952.7 1.77420 0.887099 0.461579i \(-0.152717\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(758\) −3116.40 5397.76i −0.149331 0.258649i
\(759\) 0 0
\(760\) −1030.35 + 1784.62i −0.0491773 + 0.0851776i
\(761\) 14408.2 + 24955.8i 0.686332 + 1.18876i 0.973016 + 0.230737i \(0.0741136\pi\)
−0.286684 + 0.958025i \(0.592553\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13550.8 −0.641687
\(765\) 0 0
\(766\) 1518.07 2629.38i 0.0716059 0.124025i
\(767\) −1174.46 + 2034.23i −0.0552898 + 0.0957648i
\(768\) 0 0
\(769\) 25285.2 1.18571 0.592854 0.805310i \(-0.298001\pi\)
0.592854 + 0.805310i \(0.298001\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3816.70 + 6610.72i 0.177935 + 0.308193i
\(773\) −9209.10 + 15950.6i −0.428497 + 0.742179i −0.996740 0.0806820i \(-0.974290\pi\)
0.568243 + 0.822861i \(0.307624\pi\)
\(774\) 0 0
\(775\) 16063.5 + 27822.8i 0.744540 + 1.28958i
\(776\) −6923.49 −0.320282
\(777\) 0 0
\(778\) 6493.55 0.299235
\(779\) −2661.04 4609.05i −0.122390 0.211985i
\(780\) 0 0
\(781\) 13345.2 23114.6i 0.611434 1.05903i
\(782\) −11075.2 19182.8i −0.506455 0.877207i
\(783\) 0 0
\(784\) 0 0
\(785\) 24520.5 1.11487
\(786\) 0 0
\(787\) 5537.90 9591.92i 0.250832 0.434454i −0.712923 0.701242i \(-0.752629\pi\)
0.963755 + 0.266788i \(0.0859625\pi\)
\(788\) −4123.76 + 7142.56i −0.186425 + 0.322897i
\(789\) 0 0
\(790\) −10924.8 −0.492008