Properties

Label 252.4.x.a.41.1
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.1
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +O(q^{10})\) \(q+(-5.19208 - 0.205661i) q^{3} +(2.34269 - 4.05766i) q^{5} +(-10.9369 + 14.9461i) q^{7} +(26.9154 + 2.13562i) q^{9} +(16.1150 - 9.30397i) q^{11} +(44.1430 + 25.4860i) q^{13} +(-12.9980 + 20.5859i) q^{15} -112.833 q^{17} -111.459i q^{19} +(59.8590 - 75.3518i) q^{21} +(-124.503 - 71.8819i) q^{23} +(51.5236 + 89.2414i) q^{25} +(-139.308 - 16.6238i) q^{27} +(206.907 - 119.458i) q^{29} +(-179.999 - 103.923i) q^{31} +(-85.5836 + 44.9928i) q^{33} +(35.0243 + 79.3922i) q^{35} -227.815 q^{37} +(-223.953 - 141.404i) q^{39} +(133.141 - 230.607i) q^{41} +(-170.287 - 294.946i) q^{43} +(71.7202 - 104.211i) q^{45} +(-111.979 - 193.952i) q^{47} +(-103.769 - 326.927i) q^{49} +(585.836 + 23.2053i) q^{51} -547.974i q^{53} -87.1854i q^{55} +(-22.9227 + 578.703i) q^{57} +(-43.9483 + 76.1207i) q^{59} +(-312.398 + 180.363i) q^{61} +(-326.290 + 378.922i) q^{63} +(206.827 - 119.412i) q^{65} +(-372.426 + 645.060i) q^{67} +(631.647 + 398.822i) q^{69} -135.948i q^{71} -467.289i q^{73} +(-249.161 - 473.945i) q^{75} +(-37.1896 + 342.612i) q^{77} +(192.171 + 332.850i) q^{79} +(719.878 + 114.962i) q^{81} +(597.216 + 1034.41i) q^{83} +(-264.332 + 457.836i) q^{85} +(-1098.85 + 577.683i) q^{87} +1385.63 q^{89} +(-863.702 + 381.027i) q^{91} +(913.198 + 576.594i) q^{93} +(-452.262 - 261.114i) q^{95} +(1070.10 - 617.821i) q^{97} +(453.610 - 216.005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −5.19208 0.205661i −0.999216 0.0395795i
\(4\) 0 0
\(5\) 2.34269 4.05766i 0.209537 0.362929i −0.742032 0.670365i \(-0.766138\pi\)
0.951569 + 0.307436i \(0.0994710\pi\)
\(6\) 0 0
\(7\) −10.9369 + 14.9461i −0.590536 + 0.807011i
\(8\) 0 0
\(9\) 26.9154 + 2.13562i 0.996867 + 0.0790970i
\(10\) 0 0
\(11\) 16.1150 9.30397i 0.441713 0.255023i −0.262611 0.964902i \(-0.584584\pi\)
0.704324 + 0.709879i \(0.251250\pi\)
\(12\) 0 0
\(13\) 44.1430 + 25.4860i 0.941775 + 0.543734i 0.890516 0.454951i \(-0.150343\pi\)
0.0512589 + 0.998685i \(0.483677\pi\)
\(14\) 0 0
\(15\) −12.9980 + 20.5859i −0.223737 + 0.354351i
\(16\) 0 0
\(17\) −112.833 −1.60976 −0.804880 0.593438i \(-0.797770\pi\)
−0.804880 + 0.593438i \(0.797770\pi\)
\(18\) 0 0
\(19\) 111.459i 1.34581i −0.739729 0.672905i \(-0.765046\pi\)
0.739729 0.672905i \(-0.234954\pi\)
\(20\) 0 0
\(21\) 59.8590 75.3518i 0.622014 0.783006i
\(22\) 0 0
\(23\) −124.503 71.8819i −1.12873 0.651671i −0.185112 0.982717i \(-0.559265\pi\)
−0.943614 + 0.331047i \(0.892598\pi\)
\(24\) 0 0
\(25\) 51.5236 + 89.2414i 0.412189 + 0.713932i
\(26\) 0 0
\(27\) −139.308 16.6238i −0.992955 0.118490i
\(28\) 0 0
\(29\) 206.907 119.458i 1.32489 0.764924i 0.340383 0.940287i \(-0.389443\pi\)
0.984504 + 0.175363i \(0.0561101\pi\)
\(30\) 0 0
\(31\) −179.999 103.923i −1.04287 0.602099i −0.122222 0.992503i \(-0.539002\pi\)
−0.920644 + 0.390404i \(0.872335\pi\)
\(32\) 0 0
\(33\) −85.5836 + 44.9928i −0.451460 + 0.237340i
\(34\) 0 0
\(35\) 35.0243 + 79.3922i 0.169148 + 0.383421i
\(36\) 0 0
\(37\) −227.815 −1.01223 −0.506115 0.862466i \(-0.668919\pi\)
−0.506115 + 0.862466i \(0.668919\pi\)
\(38\) 0 0
\(39\) −223.953 141.404i −0.919517 0.580583i
\(40\) 0 0
\(41\) 133.141 230.607i 0.507149 0.878407i −0.492817 0.870133i \(-0.664033\pi\)
0.999966 0.00827417i \(-0.00263378\pi\)
\(42\) 0 0
\(43\) −170.287 294.946i −0.603920 1.04602i −0.992221 0.124488i \(-0.960271\pi\)
0.388301 0.921533i \(-0.373062\pi\)
\(44\) 0 0
\(45\) 71.7202 104.211i 0.237587 0.345218i
\(46\) 0 0
\(47\) −111.979 193.952i −0.347527 0.601934i 0.638283 0.769802i \(-0.279645\pi\)
−0.985809 + 0.167868i \(0.946312\pi\)
\(48\) 0 0
\(49\) −103.769 326.927i −0.302534 0.953139i
\(50\) 0 0
\(51\) 585.836 + 23.2053i 1.60850 + 0.0637135i
\(52\) 0 0
\(53\) 547.974i 1.42019i −0.704107 0.710094i \(-0.748652\pi\)
0.704107 0.710094i \(-0.251348\pi\)
\(54\) 0 0
\(55\) 87.1854i 0.213747i
\(56\) 0 0
\(57\) −22.9227 + 578.703i −0.0532665 + 1.34476i
\(58\) 0 0
\(59\) −43.9483 + 76.1207i −0.0969760 + 0.167967i −0.910432 0.413660i \(-0.864250\pi\)
0.813456 + 0.581627i \(0.197584\pi\)
\(60\) 0 0
\(61\) −312.398 + 180.363i −0.655712 + 0.378575i −0.790641 0.612280i \(-0.790253\pi\)
0.134929 + 0.990855i \(0.456919\pi\)
\(62\) 0 0
\(63\) −326.290 + 378.922i −0.652518 + 0.757773i
\(64\) 0 0
\(65\) 206.827 119.412i 0.394673 0.227865i
\(66\) 0 0
\(67\) −372.426 + 645.060i −0.679090 + 1.17622i 0.296165 + 0.955137i \(0.404292\pi\)
−0.975255 + 0.221082i \(0.929041\pi\)
\(68\) 0 0
\(69\) 631.647 + 398.822i 1.10205 + 0.695834i
\(70\) 0 0
\(71\) 135.948i 0.227240i −0.993524 0.113620i \(-0.963755\pi\)
0.993524 0.113620i \(-0.0362447\pi\)
\(72\) 0 0
\(73\) 467.289i 0.749206i −0.927185 0.374603i \(-0.877779\pi\)
0.927185 0.374603i \(-0.122221\pi\)
\(74\) 0 0
\(75\) −249.161 473.945i −0.383609 0.729686i
\(76\) 0 0
\(77\) −37.1896 + 342.612i −0.0550409 + 0.507068i
\(78\) 0 0
\(79\) 192.171 + 332.850i 0.273683 + 0.474032i 0.969802 0.243894i \(-0.0784249\pi\)
−0.696119 + 0.717926i \(0.745092\pi\)
\(80\) 0 0
\(81\) 719.878 + 114.962i 0.987487 + 0.157698i
\(82\) 0 0
\(83\) 597.216 + 1034.41i 0.789795 + 1.36796i 0.926092 + 0.377297i \(0.123146\pi\)
−0.136297 + 0.990668i \(0.543520\pi\)
\(84\) 0 0
\(85\) −264.332 + 457.836i −0.337304 + 0.584228i
\(86\) 0 0
\(87\) −1098.85 + 577.683i −1.35412 + 0.711886i
\(88\) 0 0
\(89\) 1385.63 1.65030 0.825150 0.564914i \(-0.191091\pi\)
0.825150 + 0.564914i \(0.191091\pi\)
\(90\) 0 0
\(91\) −863.702 + 381.027i −0.994952 + 0.438929i
\(92\) 0 0
\(93\) 913.198 + 576.594i 1.01822 + 0.642903i
\(94\) 0 0
\(95\) −452.262 261.114i −0.488433 0.281997i
\(96\) 0 0
\(97\) 1070.10 617.821i 1.12012 0.646704i 0.178691 0.983905i \(-0.442814\pi\)
0.941432 + 0.337202i \(0.109480\pi\)
\(98\) 0 0
\(99\) 453.610 216.005i 0.460501 0.219286i
\(100\) 0 0
\(101\) −94.1707 163.108i −0.0927756 0.160692i 0.815902 0.578190i \(-0.196241\pi\)
−0.908678 + 0.417498i \(0.862907\pi\)
\(102\) 0 0
\(103\) 687.152 + 396.727i 0.657350 + 0.379521i 0.791267 0.611471i \(-0.209422\pi\)
−0.133916 + 0.990993i \(0.542755\pi\)
\(104\) 0 0
\(105\) −165.521 419.414i −0.153840 0.389815i
\(106\) 0 0
\(107\) 1399.55i 1.26448i −0.774773 0.632240i \(-0.782136\pi\)
0.774773 0.632240i \(-0.217864\pi\)
\(108\) 0 0
\(109\) −2137.48 −1.87829 −0.939145 0.343521i \(-0.888380\pi\)
−0.939145 + 0.343521i \(0.888380\pi\)
\(110\) 0 0
\(111\) 1182.83 + 46.8526i 1.01144 + 0.0400635i
\(112\) 0 0
\(113\) −1500.15 866.110i −1.24887 0.721034i −0.277984 0.960586i \(-0.589666\pi\)
−0.970884 + 0.239552i \(0.922999\pi\)
\(114\) 0 0
\(115\) −583.346 + 336.795i −0.473020 + 0.273098i
\(116\) 0 0
\(117\) 1133.70 + 780.239i 0.895817 + 0.616522i
\(118\) 0 0
\(119\) 1234.04 1686.40i 0.950621 1.29909i
\(120\) 0 0
\(121\) −492.372 + 852.814i −0.369926 + 0.640731i
\(122\) 0 0
\(123\) −738.704 + 1169.95i −0.541518 + 0.857646i
\(124\) 0 0
\(125\) 1068.49 0.764549
\(126\) 0 0
\(127\) −770.489 −0.538345 −0.269173 0.963092i \(-0.586750\pi\)
−0.269173 + 0.963092i \(0.586750\pi\)
\(128\) 0 0
\(129\) 823.487 + 1566.41i 0.562046 + 1.06910i
\(130\) 0 0
\(131\) −489.800 + 848.359i −0.326672 + 0.565813i −0.981849 0.189662i \(-0.939261\pi\)
0.655177 + 0.755475i \(0.272594\pi\)
\(132\) 0 0
\(133\) 1665.87 + 1219.01i 1.08608 + 0.794750i
\(134\) 0 0
\(135\) −393.809 + 526.320i −0.251064 + 0.335544i
\(136\) 0 0
\(137\) −182.458 + 105.342i −0.113784 + 0.0656932i −0.555812 0.831308i \(-0.687593\pi\)
0.442028 + 0.897001i \(0.354259\pi\)
\(138\) 0 0
\(139\) −730.515 421.763i −0.445766 0.257363i 0.260274 0.965535i \(-0.416187\pi\)
−0.706040 + 0.708172i \(0.749520\pi\)
\(140\) 0 0
\(141\) 541.513 + 1030.05i 0.323430 + 0.615217i
\(142\) 0 0
\(143\) 948.484 0.554659
\(144\) 0 0
\(145\) 1119.41i 0.641119i
\(146\) 0 0
\(147\) 471.542 + 1718.77i 0.264572 + 0.964366i
\(148\) 0 0
\(149\) 1137.32 + 656.632i 0.625321 + 0.361029i 0.778938 0.627101i \(-0.215759\pi\)
−0.153617 + 0.988131i \(0.549092\pi\)
\(150\) 0 0
\(151\) −1738.76 3011.62i −0.937074 1.62306i −0.770893 0.636965i \(-0.780190\pi\)
−0.166182 0.986095i \(-0.553144\pi\)
\(152\) 0 0
\(153\) −3036.93 240.967i −1.60472 0.127327i
\(154\) 0 0
\(155\) −843.366 + 486.918i −0.437038 + 0.252324i
\(156\) 0 0
\(157\) 499.729 + 288.519i 0.254030 + 0.146664i 0.621608 0.783328i \(-0.286480\pi\)
−0.367578 + 0.929993i \(0.619813\pi\)
\(158\) 0 0
\(159\) −112.697 + 2845.12i −0.0562103 + 1.41908i
\(160\) 0 0
\(161\) 2436.03 1074.67i 1.19246 0.526060i
\(162\) 0 0
\(163\) 1595.73 0.766794 0.383397 0.923584i \(-0.374754\pi\)
0.383397 + 0.923584i \(0.374754\pi\)
\(164\) 0 0
\(165\) −17.9307 + 452.674i −0.00846000 + 0.213579i
\(166\) 0 0
\(167\) 184.918 320.287i 0.0856850 0.148411i −0.819998 0.572366i \(-0.806025\pi\)
0.905683 + 0.423956i \(0.139359\pi\)
\(168\) 0 0
\(169\) 200.572 + 347.402i 0.0912938 + 0.158125i
\(170\) 0 0
\(171\) 238.033 2999.96i 0.106450 1.34159i
\(172\) 0 0
\(173\) −973.579 1686.29i −0.427860 0.741076i 0.568822 0.822460i \(-0.307399\pi\)
−0.996683 + 0.0813844i \(0.974066\pi\)
\(174\) 0 0
\(175\) −1897.31 205.949i −0.819563 0.0889615i
\(176\) 0 0
\(177\) 243.838 386.187i 0.103548 0.163997i
\(178\) 0 0
\(179\) 851.921i 0.355730i 0.984055 + 0.177865i \(0.0569190\pi\)
−0.984055 + 0.177865i \(0.943081\pi\)
\(180\) 0 0
\(181\) 639.259i 0.262518i 0.991348 + 0.131259i \(0.0419020\pi\)
−0.991348 + 0.131259i \(0.958098\pi\)
\(182\) 0 0
\(183\) 1659.09 872.210i 0.670182 0.352326i
\(184\) 0 0
\(185\) −533.700 + 924.395i −0.212099 + 0.367367i
\(186\) 0 0
\(187\) −1818.29 + 1049.79i −0.711051 + 0.410526i
\(188\) 0 0
\(189\) 1772.05 1900.29i 0.681999 0.731353i
\(190\) 0 0
\(191\) 3120.13 1801.41i 1.18201 0.682435i 0.225533 0.974235i \(-0.427588\pi\)
0.956479 + 0.291800i \(0.0942542\pi\)
\(192\) 0 0
\(193\) −1745.01 + 3022.44i −0.650821 + 1.12725i 0.332103 + 0.943243i \(0.392242\pi\)
−0.982924 + 0.184012i \(0.941092\pi\)
\(194\) 0 0
\(195\) −1098.42 + 577.459i −0.403383 + 0.212065i
\(196\) 0 0
\(197\) 1909.86i 0.690719i −0.938470 0.345360i \(-0.887757\pi\)
0.938470 0.345360i \(-0.112243\pi\)
\(198\) 0 0
\(199\) 713.005i 0.253988i −0.991903 0.126994i \(-0.959467\pi\)
0.991903 0.126994i \(-0.0405329\pi\)
\(200\) 0 0
\(201\) 2066.33 3272.61i 0.725112 1.14842i
\(202\) 0 0
\(203\) −477.494 + 4398.94i −0.165091 + 1.52091i
\(204\) 0 0
\(205\) −623.816 1080.48i −0.212533 0.368117i
\(206\) 0 0
\(207\) −3197.54 2200.62i −1.07364 0.738908i
\(208\) 0 0
\(209\) −1037.01 1796.15i −0.343213 0.594462i
\(210\) 0 0
\(211\) 788.596 1365.89i 0.257295 0.445648i −0.708221 0.705990i \(-0.750502\pi\)
0.965516 + 0.260343i \(0.0838355\pi\)
\(212\) 0 0
\(213\) −27.9592 + 705.853i −0.00899406 + 0.227062i
\(214\) 0 0
\(215\) −1595.72 −0.506174
\(216\) 0 0
\(217\) 3521.86 1553.69i 1.10175 0.486043i
\(218\) 0 0
\(219\) −96.1031 + 2426.20i −0.0296532 + 0.748618i
\(220\) 0 0
\(221\) −4980.77 2875.65i −1.51603 0.875281i
\(222\) 0 0
\(223\) 412.569 238.197i 0.123891 0.0715284i −0.436774 0.899571i \(-0.643879\pi\)
0.560665 + 0.828043i \(0.310546\pi\)
\(224\) 0 0
\(225\) 1196.19 + 2512.00i 0.354427 + 0.744298i
\(226\) 0 0
\(227\) −1386.85 2402.10i −0.405501 0.702348i 0.588879 0.808221i \(-0.299569\pi\)
−0.994380 + 0.105873i \(0.966236\pi\)
\(228\) 0 0
\(229\) −1698.53 980.646i −0.490139 0.282982i 0.234493 0.972118i \(-0.424657\pi\)
−0.724632 + 0.689136i \(0.757990\pi\)
\(230\) 0 0
\(231\) 263.553 1771.22i 0.0750673 0.504492i
\(232\) 0 0
\(233\) 4734.94i 1.33132i 0.746257 + 0.665658i \(0.231849\pi\)
−0.746257 + 0.665658i \(0.768151\pi\)
\(234\) 0 0
\(235\) −1049.33 −0.291279
\(236\) 0 0
\(237\) −929.313 1767.71i −0.254706 0.484493i
\(238\) 0 0
\(239\) −1055.48 609.379i −0.285661 0.164927i 0.350322 0.936629i \(-0.386072\pi\)
−0.635984 + 0.771703i \(0.719405\pi\)
\(240\) 0 0
\(241\) −1784.77 + 1030.43i −0.477041 + 0.275420i −0.719182 0.694821i \(-0.755483\pi\)
0.242142 + 0.970241i \(0.422150\pi\)
\(242\) 0 0
\(243\) −3714.02 744.943i −0.980472 0.196659i
\(244\) 0 0
\(245\) −1569.66 344.828i −0.409313 0.0899193i
\(246\) 0 0
\(247\) 2840.64 4920.13i 0.731763 1.26745i
\(248\) 0 0
\(249\) −2888.06 5493.56i −0.735033 1.39815i
\(250\) 0 0
\(251\) −2966.29 −0.745937 −0.372969 0.927844i \(-0.621660\pi\)
−0.372969 + 0.927844i \(0.621660\pi\)
\(252\) 0 0
\(253\) −2675.15 −0.664764
\(254\) 0 0
\(255\) 1466.59 2322.76i 0.360163 0.570419i
\(256\) 0 0
\(257\) 1133.09 1962.58i 0.275021 0.476351i −0.695119 0.718895i \(-0.744648\pi\)
0.970141 + 0.242543i \(0.0779817\pi\)
\(258\) 0 0
\(259\) 2491.58 3404.93i 0.597758 0.816880i
\(260\) 0 0
\(261\) 5824.11 2773.38i 1.38124 0.657732i
\(262\) 0 0
\(263\) −1580.16 + 912.308i −0.370483 + 0.213898i −0.673669 0.739033i \(-0.735283\pi\)
0.303186 + 0.952931i \(0.401950\pi\)
\(264\) 0 0
\(265\) −2223.49 1283.73i −0.515427 0.297582i
\(266\) 0 0
\(267\) −7194.31 284.971i −1.64901 0.0653180i
\(268\) 0 0
\(269\) 5616.89 1.27312 0.636558 0.771229i \(-0.280358\pi\)
0.636558 + 0.771229i \(0.280358\pi\)
\(270\) 0 0
\(271\) 5603.22i 1.25598i 0.778220 + 0.627992i \(0.216123\pi\)
−0.778220 + 0.627992i \(0.783877\pi\)
\(272\) 0 0
\(273\) 4562.78 1800.69i 1.01154 0.399205i
\(274\) 0 0
\(275\) 1660.60 + 958.748i 0.364138 + 0.210235i
\(276\) 0 0
\(277\) 2329.35 + 4034.55i 0.505260 + 0.875137i 0.999981 + 0.00608483i \(0.00193687\pi\)
−0.494721 + 0.869052i \(0.664730\pi\)
\(278\) 0 0
\(279\) −4622.82 3181.53i −0.991974 0.682700i
\(280\) 0 0
\(281\) 1939.85 1119.97i 0.411820 0.237765i −0.279751 0.960073i \(-0.590252\pi\)
0.691572 + 0.722308i \(0.256919\pi\)
\(282\) 0 0
\(283\) 2759.51 + 1593.21i 0.579633 + 0.334651i 0.760987 0.648767i \(-0.224715\pi\)
−0.181355 + 0.983418i \(0.558048\pi\)
\(284\) 0 0
\(285\) 2294.48 + 1448.74i 0.476889 + 0.301108i
\(286\) 0 0
\(287\) 1990.51 + 4512.05i 0.409395 + 0.928006i
\(288\) 0 0
\(289\) 7818.18 1.59132
\(290\) 0 0
\(291\) −5683.10 + 2987.70i −1.14484 + 0.601863i
\(292\) 0 0
\(293\) −4563.57 + 7904.34i −0.909921 + 1.57603i −0.0957489 + 0.995406i \(0.530525\pi\)
−0.814172 + 0.580624i \(0.802809\pi\)
\(294\) 0 0
\(295\) 205.915 + 356.655i 0.0406401 + 0.0703907i
\(296\) 0 0
\(297\) −2399.61 + 1028.22i −0.468819 + 0.200888i
\(298\) 0 0
\(299\) −3663.97 6346.18i −0.708671 1.22745i
\(300\) 0 0
\(301\) 6270.70 + 680.669i 1.20079 + 0.130342i
\(302\) 0 0
\(303\) 455.397 + 866.239i 0.0863428 + 0.164238i
\(304\) 0 0
\(305\) 1690.14i 0.317302i
\(306\) 0 0
\(307\) 4744.58i 0.882044i −0.897496 0.441022i \(-0.854616\pi\)
0.897496 0.441022i \(-0.145384\pi\)
\(308\) 0 0
\(309\) −3486.16 2201.16i −0.641814 0.405242i
\(310\) 0 0
\(311\) −1089.62 + 1887.29i −0.198672 + 0.344110i −0.948098 0.317978i \(-0.896996\pi\)
0.749426 + 0.662088i \(0.230329\pi\)
\(312\) 0 0
\(313\) −1752.85 + 1012.01i −0.316540 + 0.182754i −0.649849 0.760063i \(-0.725168\pi\)
0.333309 + 0.942818i \(0.391835\pi\)
\(314\) 0 0
\(315\) 773.142 + 2211.67i 0.138291 + 0.395599i
\(316\) 0 0
\(317\) 189.948 109.666i 0.0336547 0.0194305i −0.483078 0.875577i \(-0.660481\pi\)
0.516733 + 0.856147i \(0.327148\pi\)
\(318\) 0 0
\(319\) 2222.87 3850.12i 0.390146 0.675753i
\(320\) 0 0
\(321\) −287.833 + 7266.56i −0.0500475 + 1.26349i
\(322\) 0 0
\(323\) 12576.2i 2.16643i
\(324\) 0 0
\(325\) 5252.52i 0.896484i
\(326\) 0 0
\(327\) 11098.0 + 439.597i 1.87682 + 0.0743418i
\(328\) 0 0
\(329\) 4123.52 + 447.598i 0.690994 + 0.0750057i
\(330\) 0 0
\(331\) 1884.36 + 3263.81i 0.312912 + 0.541980i 0.978991 0.203901i \(-0.0653621\pi\)
−0.666079 + 0.745881i \(0.732029\pi\)
\(332\) 0 0
\(333\) −6131.72 486.525i −1.00906 0.0800643i
\(334\) 0 0
\(335\) 1744.96 + 3022.36i 0.284589 + 0.492922i
\(336\) 0 0
\(337\) 3056.60 5294.18i 0.494076 0.855764i −0.505901 0.862592i \(-0.668840\pi\)
0.999977 + 0.00682736i \(0.00217323\pi\)
\(338\) 0 0
\(339\) 7610.76 + 4805.44i 1.21935 + 0.769898i
\(340\) 0 0
\(341\) −3867.57 −0.614196
\(342\) 0 0
\(343\) 6021.17 + 2024.61i 0.947851 + 0.318714i
\(344\) 0 0
\(345\) 3098.04 1628.69i 0.483458 0.254162i
\(346\) 0 0
\(347\) 1143.36 + 660.117i 0.176883 + 0.102124i 0.585828 0.810436i \(-0.300770\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(348\) 0 0
\(349\) −2309.07 + 1333.14i −0.354159 + 0.204474i −0.666515 0.745491i \(-0.732215\pi\)
0.312357 + 0.949965i \(0.398882\pi\)
\(350\) 0 0
\(351\) −5725.80 4284.22i −0.870713 0.651495i
\(352\) 0 0
\(353\) −4725.05 8184.03i −0.712434 1.23397i −0.963941 0.266116i \(-0.914260\pi\)
0.251508 0.967855i \(-0.419074\pi\)
\(354\) 0 0
\(355\) −551.632 318.485i −0.0824720 0.0476152i
\(356\) 0 0
\(357\) −6754.04 + 8502.14i −1.00129 + 1.26045i
\(358\) 0 0
\(359\) 6846.88i 1.00659i 0.864116 + 0.503293i \(0.167878\pi\)
−0.864116 + 0.503293i \(0.832122\pi\)
\(360\) 0 0
\(361\) −5564.07 −0.811206
\(362\) 0 0
\(363\) 2731.83 4326.62i 0.394996 0.625588i
\(364\) 0 0
\(365\) −1896.10 1094.71i −0.271908 0.156986i
\(366\) 0 0
\(367\) 5440.63 3141.15i 0.773838 0.446775i −0.0604042 0.998174i \(-0.519239\pi\)
0.834242 + 0.551399i \(0.185906\pi\)
\(368\) 0 0
\(369\) 4076.02 5922.53i 0.575039 0.835541i
\(370\) 0 0
\(371\) 8190.05 + 5993.12i 1.14611 + 0.838672i
\(372\) 0 0
\(373\) −5253.75 + 9099.76i −0.729300 + 1.26318i 0.227880 + 0.973689i \(0.426821\pi\)
−0.957179 + 0.289495i \(0.906513\pi\)
\(374\) 0 0
\(375\) −5547.68 219.747i −0.763950 0.0302605i
\(376\) 0 0
\(377\) 12178.0 1.66366
\(378\) 0 0
\(379\) 5904.89 0.800301 0.400150 0.916450i \(-0.368958\pi\)
0.400150 + 0.916450i \(0.368958\pi\)
\(380\) 0 0
\(381\) 4000.44 + 158.460i 0.537923 + 0.0213074i
\(382\) 0 0
\(383\) −1175.26 + 2035.61i −0.156797 + 0.271580i −0.933712 0.358026i \(-0.883450\pi\)
0.776915 + 0.629605i \(0.216783\pi\)
\(384\) 0 0
\(385\) 1303.08 + 953.537i 0.172496 + 0.126225i
\(386\) 0 0
\(387\) −3953.46 8302.27i −0.519291 1.09051i
\(388\) 0 0
\(389\) −11034.6 + 6370.81i −1.43824 + 0.830368i −0.997727 0.0673794i \(-0.978536\pi\)
−0.440511 + 0.897747i \(0.645203\pi\)
\(390\) 0 0
\(391\) 14048.0 + 8110.62i 1.81698 + 1.04903i
\(392\) 0 0
\(393\) 2717.56 4304.02i 0.348811 0.552440i
\(394\) 0 0
\(395\) 1800.79 0.229386
\(396\) 0 0
\(397\) 13326.3i 1.68470i 0.538930 + 0.842350i \(0.318829\pi\)
−0.538930 + 0.842350i \(0.681171\pi\)
\(398\) 0 0
\(399\) −8398.63 6671.81i −1.05378 0.837114i
\(400\) 0 0
\(401\) −8090.75 4671.20i −1.00756 0.581717i −0.0970856 0.995276i \(-0.530952\pi\)
−0.910477 + 0.413559i \(0.864285\pi\)
\(402\) 0 0
\(403\) −5297.15 9174.92i −0.654763 1.13408i
\(404\) 0 0
\(405\) 2152.93 2651.70i 0.264148 0.325344i
\(406\) 0 0
\(407\) −3671.22 + 2119.58i −0.447115 + 0.258142i
\(408\) 0 0
\(409\) 268.033 + 154.749i 0.0324044 + 0.0187087i 0.516115 0.856519i \(-0.327378\pi\)
−0.483710 + 0.875228i \(0.660711\pi\)
\(410\) 0 0
\(411\) 968.999 509.419i 0.116295 0.0611382i
\(412\) 0 0
\(413\) −657.047 1489.38i −0.0782837 0.177452i
\(414\) 0 0
\(415\) 5596.38 0.661965
\(416\) 0 0
\(417\) 3706.15 + 2340.07i 0.435230 + 0.274805i
\(418\) 0 0
\(419\) −3008.72 + 5211.26i −0.350801 + 0.607605i −0.986390 0.164422i \(-0.947424\pi\)
0.635589 + 0.772028i \(0.280757\pi\)
\(420\) 0 0
\(421\) 1920.18 + 3325.85i 0.222289 + 0.385017i 0.955503 0.294982i \(-0.0953137\pi\)
−0.733213 + 0.679999i \(0.761980\pi\)
\(422\) 0 0
\(423\) −2599.74 5459.45i −0.298827 0.627536i
\(424\) 0 0
\(425\) −5813.53 10069.3i −0.663524 1.14926i
\(426\) 0 0
\(427\) 720.942 6641.72i 0.0817069 0.752729i
\(428\) 0 0
\(429\) −4924.61 195.066i −0.554224 0.0219531i
\(430\) 0 0
\(431\) 4510.80i 0.504125i 0.967711 + 0.252062i \(0.0811088\pi\)
−0.967711 + 0.252062i \(0.918891\pi\)
\(432\) 0 0
\(433\) 7012.84i 0.778328i −0.921169 0.389164i \(-0.872764\pi\)
0.921169 0.389164i \(-0.127236\pi\)
\(434\) 0 0
\(435\) −230.220 + 5812.09i −0.0253752 + 0.640616i
\(436\) 0 0
\(437\) −8011.88 + 13877.0i −0.877025 + 1.51905i
\(438\) 0 0
\(439\) −3220.45 + 1859.33i −0.350122 + 0.202143i −0.664739 0.747075i \(-0.731457\pi\)
0.314617 + 0.949219i \(0.398124\pi\)
\(440\) 0 0
\(441\) −2094.80 9020.97i −0.226196 0.974082i
\(442\) 0 0
\(443\) 5177.61 2989.29i 0.555295 0.320599i −0.195960 0.980612i \(-0.562782\pi\)
0.751255 + 0.660012i \(0.229449\pi\)
\(444\) 0 0
\(445\) 3246.11 5622.43i 0.345799 0.598941i
\(446\) 0 0
\(447\) −5770.01 3643.19i −0.610542 0.385496i
\(448\) 0 0
\(449\) 1188.91i 0.124963i 0.998046 + 0.0624813i \(0.0199014\pi\)
−0.998046 + 0.0624813i \(0.980099\pi\)
\(450\) 0 0
\(451\) 4954.95i 0.517338i
\(452\) 0 0
\(453\) 8408.41 + 15994.2i 0.872100 + 1.65888i
\(454\) 0 0
\(455\) −477.310 + 4397.24i −0.0491794 + 0.453068i
\(456\) 0 0
\(457\) 2039.30 + 3532.17i 0.208741 + 0.361549i 0.951318 0.308211i \(-0.0997302\pi\)
−0.742577 + 0.669760i \(0.766397\pi\)
\(458\) 0 0
\(459\) 15718.4 + 1875.70i 1.59842 + 0.190741i
\(460\) 0 0
\(461\) −3283.79 5687.69i −0.331760 0.574625i 0.651097 0.758995i \(-0.274309\pi\)
−0.982857 + 0.184369i \(0.940976\pi\)
\(462\) 0 0
\(463\) −4120.60 + 7137.09i −0.413608 + 0.716390i −0.995281 0.0970322i \(-0.969065\pi\)
0.581673 + 0.813423i \(0.302398\pi\)
\(464\) 0 0
\(465\) 4478.97 2354.67i 0.446682 0.234828i
\(466\) 0 0
\(467\) 11330.9 1.12276 0.561382 0.827557i \(-0.310270\pi\)
0.561382 + 0.827557i \(0.310270\pi\)
\(468\) 0 0
\(469\) −5567.93 12621.2i −0.548194 1.24263i
\(470\) 0 0
\(471\) −2535.30 1600.79i −0.248026 0.156604i
\(472\) 0 0
\(473\) −5488.35 3168.70i −0.533519 0.308027i
\(474\) 0 0
\(475\) 9946.74 5742.76i 0.960817 0.554728i
\(476\) 0 0
\(477\) 1170.26 14748.9i 0.112333 1.41574i
\(478\) 0 0
\(479\) −4151.12 7189.94i −0.395969 0.685839i 0.597255 0.802051i \(-0.296258\pi\)
−0.993224 + 0.116212i \(0.962925\pi\)
\(480\) 0 0
\(481\) −10056.4 5806.08i −0.953292 0.550384i
\(482\) 0 0
\(483\) −12869.1 + 5078.76i −1.21235 + 0.478451i
\(484\) 0 0
\(485\) 5789.46i 0.542033i
\(486\) 0 0
\(487\) −76.4693 −0.00711530 −0.00355765 0.999994i \(-0.501132\pi\)
−0.00355765 + 0.999994i \(0.501132\pi\)
\(488\) 0 0
\(489\) −8285.17 328.180i −0.766193 0.0303493i
\(490\) 0 0
\(491\) 6951.74 + 4013.59i 0.638957 + 0.368902i 0.784213 0.620492i \(-0.213067\pi\)
−0.145256 + 0.989394i \(0.546401\pi\)
\(492\) 0 0
\(493\) −23345.9 + 13478.7i −2.13275 + 1.23134i
\(494\) 0 0
\(495\) 186.195 2346.63i 0.0169067 0.213077i
\(496\) 0 0
\(497\) 2031.89 + 1486.85i 0.183386 + 0.134194i
\(498\) 0 0
\(499\) 8035.68 13918.2i 0.720895 1.24863i −0.239747 0.970836i \(-0.577064\pi\)
0.960641 0.277791i \(-0.0896023\pi\)
\(500\) 0 0
\(501\) −1025.98 + 1624.93i −0.0914918 + 0.144903i
\(502\) 0 0
\(503\) 7450.97 0.660481 0.330241 0.943897i \(-0.392870\pi\)
0.330241 + 0.943897i \(0.392870\pi\)
\(504\) 0 0
\(505\) −882.452 −0.0777596
\(506\) 0 0
\(507\) −969.941 1844.99i −0.0849637 0.161615i
\(508\) 0 0
\(509\) 6060.49 10497.1i 0.527753 0.914095i −0.471724 0.881746i \(-0.656368\pi\)
0.999477 0.0323486i \(-0.0102987\pi\)
\(510\) 0 0
\(511\) 6984.12 + 5110.68i 0.604617 + 0.442433i
\(512\) 0 0
\(513\) −1852.86 + 15527.1i −0.159466 + 1.33633i
\(514\) 0 0
\(515\) 3219.57 1858.82i 0.275478 0.159047i
\(516\) 0 0
\(517\) −3609.06 2083.69i −0.307014 0.177255i
\(518\) 0 0
\(519\) 4708.10 + 8955.57i 0.398194 + 0.757430i
\(520\) 0 0
\(521\) −10433.7 −0.877371 −0.438685 0.898641i \(-0.644556\pi\)
−0.438685 + 0.898641i \(0.644556\pi\)
\(522\) 0 0
\(523\) 22346.3i 1.86833i 0.356846 + 0.934163i \(0.383852\pi\)
−0.356846 + 0.934163i \(0.616148\pi\)
\(524\) 0 0
\(525\) 9808.66 + 1459.51i 0.815400 + 0.121330i
\(526\) 0 0
\(527\) 20309.8 + 11725.9i 1.67876 + 0.969234i
\(528\) 0 0
\(529\) 4250.53 + 7362.13i 0.349349 + 0.605090i
\(530\) 0 0
\(531\) −1345.45 + 1954.96i −0.109958 + 0.159771i
\(532\) 0 0
\(533\) 11754.5 6786.45i 0.955240 0.551508i
\(534\) 0 0
\(535\) −5678.89 3278.71i −0.458916 0.264955i
\(536\) 0 0
\(537\) 175.207 4423.24i 0.0140796 0.355451i
\(538\) 0 0
\(539\) −4713.95 4302.94i −0.376706 0.343860i
\(540\) 0 0
\(541\) −13690.0 −1.08794 −0.543972 0.839103i \(-0.683080\pi\)
−0.543972 + 0.839103i \(0.683080\pi\)
\(542\) 0 0
\(543\) 131.471 3319.09i 0.0103903 0.262312i
\(544\) 0 0
\(545\) −5007.46 + 8673.18i −0.393571 + 0.681685i
\(546\) 0 0
\(547\) −8042.35 13929.8i −0.628640 1.08884i −0.987825 0.155570i \(-0.950279\pi\)
0.359185 0.933266i \(-0.383055\pi\)
\(548\) 0 0
\(549\) −8793.49 + 4187.38i −0.683601 + 0.325524i
\(550\) 0 0
\(551\) −13314.6 23061.6i −1.02944 1.78305i
\(552\) 0 0
\(553\) −7076.54 768.141i −0.544169 0.0590682i
\(554\) 0 0
\(555\) 2961.12 4689.77i 0.226473 0.358684i
\(556\) 0 0
\(557\) 9207.28i 0.700404i −0.936674 0.350202i \(-0.886113\pi\)
0.936674 0.350202i \(-0.113887\pi\)
\(558\) 0 0
\(559\) 17359.8i 1.31349i
\(560\) 0 0
\(561\) 9656.61 5076.65i 0.726743 0.382061i
\(562\) 0 0
\(563\) 10095.6 17486.0i 0.755732 1.30897i −0.189278 0.981924i \(-0.560615\pi\)
0.945010 0.327042i \(-0.106052\pi\)
\(564\) 0 0
\(565\) −7028.77 + 4058.06i −0.523367 + 0.302166i
\(566\) 0 0
\(567\) −9591.45 + 9502.02i −0.710411 + 0.703787i
\(568\) 0 0
\(569\) −3118.35 + 1800.38i −0.229750 + 0.132646i −0.610457 0.792050i \(-0.709014\pi\)
0.380707 + 0.924696i \(0.375681\pi\)
\(570\) 0 0
\(571\) −1111.32 + 1924.86i −0.0814489 + 0.141074i −0.903873 0.427802i \(-0.859288\pi\)
0.822424 + 0.568876i \(0.192621\pi\)
\(572\) 0 0
\(573\) −16570.4 + 8711.36i −1.20810 + 0.635117i
\(574\) 0 0
\(575\) 14814.5i 1.07444i
\(576\) 0 0
\(577\) 8818.52i 0.636256i −0.948048 0.318128i \(-0.896946\pi\)
0.948048 0.318128i \(-0.103054\pi\)
\(578\) 0 0
\(579\) 9681.82 15333.9i 0.694927 1.10061i
\(580\) 0 0
\(581\) −21992.0 2387.18i −1.57037 0.170459i
\(582\) 0 0
\(583\) −5098.33 8830.57i −0.362181 0.627316i
\(584\) 0 0
\(585\) 5821.86 2772.31i 0.411460 0.195933i
\(586\) 0 0
\(587\) 9540.65 + 16524.9i 0.670843 + 1.16193i 0.977665 + 0.210167i \(0.0674008\pi\)
−0.306823 + 0.951767i \(0.599266\pi\)
\(588\) 0 0
\(589\) −11583.1 + 20062.5i −0.810311 + 1.40350i
\(590\) 0 0
\(591\) −392.783 + 9916.13i −0.0273383 + 0.690178i
\(592\) 0 0
\(593\) −7386.65 −0.511523 −0.255762 0.966740i \(-0.582326\pi\)
−0.255762 + 0.966740i \(0.582326\pi\)
\(594\) 0 0
\(595\) −3951.88 8958.02i −0.272288 0.617215i
\(596\) 0 0
\(597\) −146.638 + 3701.98i −0.0100527 + 0.253789i
\(598\) 0 0
\(599\) 5442.40 + 3142.17i 0.371236 + 0.214333i 0.673998 0.738733i \(-0.264575\pi\)
−0.302762 + 0.953066i \(0.597909\pi\)
\(600\) 0 0
\(601\) 23587.5 13618.2i 1.60092 0.924291i 0.609615 0.792697i \(-0.291324\pi\)
0.991304 0.131594i \(-0.0420094\pi\)
\(602\) 0 0
\(603\) −11401.6 + 16566.7i −0.769998 + 1.11882i
\(604\) 0 0
\(605\) 2306.95 + 3995.76i 0.155026 + 0.268514i
\(606\) 0 0
\(607\) −2294.69 1324.84i −0.153441 0.0885891i 0.421314 0.906915i \(-0.361569\pi\)
−0.574755 + 0.818326i \(0.694902\pi\)
\(608\) 0 0
\(609\) 3383.88 22741.5i 0.225159 1.51319i
\(610\) 0 0
\(611\) 11415.5i 0.755848i
\(612\) 0 0
\(613\) 19866.5 1.30897 0.654486 0.756074i \(-0.272885\pi\)
0.654486 + 0.756074i \(0.272885\pi\)
\(614\) 0 0
\(615\) 3016.69 + 5738.24i 0.197796 + 0.376241i
\(616\) 0 0
\(617\) −21498.0 12411.9i −1.40272 0.809858i −0.408044 0.912962i \(-0.633789\pi\)
−0.994671 + 0.103104i \(0.967123\pi\)
\(618\) 0 0
\(619\) 6535.31 3773.16i 0.424356 0.245002i −0.272583 0.962132i \(-0.587878\pi\)
0.696939 + 0.717130i \(0.254545\pi\)
\(620\) 0 0
\(621\) 16149.3 + 12083.4i 1.04356 + 0.780823i
\(622\) 0 0
\(623\) −15154.5 + 20709.7i −0.974562 + 1.33181i
\(624\) 0 0
\(625\) −3937.30 + 6819.61i −0.251987 + 0.436455i
\(626\) 0 0
\(627\) 5014.84 + 9539.05i 0.319415 + 0.607580i
\(628\) 0 0
\(629\) 25704.9 1.62944
\(630\) 0 0
\(631\) −10950.1 −0.690837 −0.345418 0.938449i \(-0.612263\pi\)
−0.345418 + 0.938449i \(0.612263\pi\)
\(632\) 0 0
\(633\) −4375.37 + 6929.62i −0.274732 + 0.435115i
\(634\) 0 0
\(635\) −1805.02 + 3126.39i −0.112803 + 0.195381i
\(636\) 0 0
\(637\) 3751.36 17076.2i 0.233335 1.06214i
\(638\) 0 0
\(639\) 290.333 3659.10i 0.0179740 0.226528i
\(640\) 0 0
\(641\) 27715.4 16001.5i 1.70779 0.985994i 0.770504 0.637435i \(-0.220004\pi\)
0.937287 0.348559i \(-0.113329\pi\)
\(642\) 0 0
\(643\) −4359.15 2516.76i −0.267353 0.154356i 0.360331 0.932824i \(-0.382664\pi\)
−0.627684 + 0.778468i \(0.715997\pi\)
\(644\) 0 0
\(645\) 8285.13 + 328.178i 0.505778 + 0.0200341i
\(646\) 0 0
\(647\) −5406.97 −0.328547 −0.164274 0.986415i \(-0.552528\pi\)
−0.164274 + 0.986415i \(0.552528\pi\)
\(648\) 0 0
\(649\) 1635.58i 0.0989245i
\(650\) 0 0
\(651\) −18605.3 + 7342.57i −1.12012 + 0.442056i
\(652\) 0 0
\(653\) −22480.8 12979.3i −1.34723 0.777826i −0.359377 0.933193i \(-0.617011\pi\)
−0.987857 + 0.155367i \(0.950344\pi\)
\(654\) 0 0
\(655\) 2294.90 + 3974.89i 0.136900 + 0.237117i
\(656\) 0 0
\(657\) 997.950 12577.3i 0.0592599 0.746858i
\(658\) 0 0
\(659\) 22849.6 13192.2i 1.35067 0.779811i 0.362328 0.932051i \(-0.381982\pi\)
0.988344 + 0.152240i \(0.0486486\pi\)
\(660\) 0 0
\(661\) 4642.84 + 2680.54i 0.273200 + 0.157732i 0.630341 0.776318i \(-0.282915\pi\)
−0.357141 + 0.934051i \(0.616248\pi\)
\(662\) 0 0
\(663\) 25269.2 + 15955.0i 1.48020 + 0.934599i
\(664\) 0 0
\(665\) 8848.96 3903.77i 0.516012 0.227642i
\(666\) 0 0
\(667\) −34347.5 −1.99391
\(668\) 0 0
\(669\) −2191.08 + 1151.89i −0.126625 + 0.0665688i
\(670\) 0 0
\(671\) −3356.18 + 5813.08i −0.193091 + 0.334443i
\(672\) 0 0
\(673\) 3378.73 + 5852.13i 0.193522 + 0.335190i 0.946415 0.322953i \(-0.104676\pi\)
−0.752893 + 0.658143i \(0.771342\pi\)
\(674\) 0 0
\(675\) −5694.11 13288.5i −0.324691 0.757742i
\(676\) 0 0
\(677\) −2962.04 5130.41i −0.168154 0.291252i 0.769617 0.638506i \(-0.220447\pi\)
−0.937771 + 0.347254i \(0.887114\pi\)
\(678\) 0 0
\(679\) −2469.54 + 22750.8i −0.139576 + 1.28585i
\(680\) 0 0
\(681\) 6706.63 + 12757.1i 0.377384 + 0.717847i
\(682\) 0 0
\(683\) 8838.52i 0.495163i −0.968867 0.247582i \(-0.920364\pi\)
0.968867 0.247582i \(-0.0796358\pi\)
\(684\) 0 0
\(685\) 987.135i 0.0550606i
\(686\) 0 0
\(687\) 8617.21 + 5440.91i 0.478555 + 0.302160i
\(688\) 0 0
\(689\) 13965.7 24189.2i 0.772205 1.33750i
\(690\) 0 0
\(691\) −25392.1 + 14660.1i −1.39792 + 0.807087i −0.994174 0.107787i \(-0.965624\pi\)
−0.403741 + 0.914873i \(0.632290\pi\)
\(692\) 0 0
\(693\) −1732.66 + 9142.11i −0.0949760 + 0.501125i
\(694\) 0 0
\(695\) −3422.75 + 1976.12i −0.186809 + 0.107854i
\(696\) 0 0
\(697\) −15022.6 + 26019.9i −0.816387 + 1.41402i
\(698\) 0 0
\(699\) 973.794 24584.2i 0.0526928 1.33027i
\(700\) 0 0
\(701\) 15890.7i 0.856184i 0.903735 + 0.428092i \(0.140814\pi\)
−0.903735 + 0.428092i \(0.859186\pi\)
\(702\) 0 0
\(703\) 25391.9i 1.36227i
\(704\) 0 0
\(705\) 5448.18 + 215.805i 0.291050 + 0.0115287i
\(706\) 0 0
\(707\) 3467.76 + 376.417i 0.184468 + 0.0200235i
\(708\) 0 0
\(709\) 1060.77 + 1837.31i 0.0561890 + 0.0973222i 0.892752 0.450549i \(-0.148772\pi\)
−0.836563 + 0.547871i \(0.815438\pi\)
\(710\) 0 0
\(711\) 4461.52 + 9369.19i 0.235331 + 0.494194i
\(712\) 0 0
\(713\) 14940.3 + 25877.4i 0.784740 + 1.35921i
\(714\) 0 0
\(715\) 2222.01 3848.63i 0.116222 0.201302i
\(716\) 0 0
\(717\) 5354.79 + 3381.02i 0.278910 + 0.176104i
\(718\) 0 0
\(719\) −23897.3 −1.23953 −0.619764 0.784789i \(-0.712772\pi\)
−0.619764 + 0.784789i \(0.712772\pi\)
\(720\) 0 0
\(721\) −13444.8 + 5931.25i −0.694467 + 0.306368i
\(722\) 0 0
\(723\) 9478.57 4983.04i 0.487568 0.256323i
\(724\) 0 0
\(725\) 21321.2 + 12309.8i 1.09221 + 0.630586i
\(726\) 0 0
\(727\) −10755.1 + 6209.44i −0.548670 + 0.316775i −0.748586 0.663038i \(-0.769267\pi\)
0.199915 + 0.979813i \(0.435933\pi\)
\(728\) 0 0
\(729\) 19130.3 + 4631.64i 0.971920 + 0.235311i
\(730\) 0 0
\(731\) 19213.9 + 33279.5i 0.972166 + 1.68384i
\(732\) 0 0
\(733\) 199.317 + 115.076i 0.0100436 + 0.00579865i 0.505013 0.863112i \(-0.331488\pi\)
−0.494970 + 0.868910i \(0.664821\pi\)
\(734\) 0 0
\(735\) 8078.87 + 2113.19i 0.405434 + 0.106049i
\(736\) 0 0
\(737\) 13860.2i 0.692734i
\(738\) 0 0
\(739\) 6421.89 0.319666 0.159833 0.987144i \(-0.448904\pi\)
0.159833 + 0.987144i \(0.448904\pi\)
\(740\) 0 0
\(741\) −15760.7 + 24961.5i −0.781355 + 1.23750i
\(742\) 0 0
\(743\) −693.090 400.156i −0.0342221 0.0197581i 0.482791 0.875735i \(-0.339623\pi\)
−0.517013 + 0.855977i \(0.672956\pi\)
\(744\) 0 0
\(745\) 5328.78 3076.58i 0.262056 0.151298i
\(746\) 0 0
\(747\) 13865.2 + 29117.0i 0.679119 + 1.42615i
\(748\) 0 0
\(749\) 20917.7 + 15306.7i 1.02045 + 0.746721i
\(750\) 0 0
\(751\) −971.585 + 1682.83i −0.0472086 + 0.0817676i −0.888664 0.458559i \(-0.848366\pi\)
0.841456 + 0.540326i \(0.181699\pi\)
\(752\) 0 0
\(753\) 15401.2 + 610.050i 0.745353 + 0.0295238i
\(754\) 0 0
\(755\) −16293.5 −0.785406
\(756\) 0 0
\(757\) 16016.6 0.768999 0.384500 0.923125i \(-0.374374\pi\)
0.384500 + 0.923125i \(0.374374\pi\)
\(758\) 0 0
\(759\) 13889.6 + 550.175i 0.664243 + 0.0263110i
\(760\) 0 0
\(761\) 20615.4 35706.8i 0.982005 1.70088i 0.327450 0.944869i \(-0.393811\pi\)
0.654555 0.756014i \(-0.272856\pi\)
\(762\) 0 0
\(763\) 23377.4 31946.9i 1.10920 1.51580i
\(764\) 0 0
\(765\) −8092.37 + 11758.3i −0.382458 + 0.555717i
\(766\) 0 0
\(767\) −3880.03 + 2240.13i −0.182659 + 0.105458i
\(768\) 0 0
\(769\) −4147.70 2394.68i −0.194499 0.112294i 0.399588 0.916695i \(-0.369153\pi\)
−0.594087 + 0.804401i \(0.702487\pi\)
\(770\) 0 0
\(771\) −6286.75 + 9956.83i −0.293660 + 0.465093i
\(772\) 0 0
\(773\) 12950.9 0.602601 0.301301 0.953529i \(-0.402579\pi\)
0.301301 + 0.953529i \(0.402579\pi\)
\(774\) 0 0
\(775\) 21417.9i 0.992713i
\(776\) 0 0
\(777\) −13636.7 + 17166.2i −0.629621 + 0.792581i
\(778\) 0 0
\(779\) −25703.1 14839.7i −1.18217 0.682526i
\(780\) 0 0
\(781\) −1264.86 2190.80i −0.0579515 0.100375i
\(782\) 0 0
\(783\) −30809.6 + 13201.8i −1.40619 + 0.602548i
\(784\) 0 0
\(785\) 2341.42 1351.82i 0.106457 0.0614632i
\(786\) 0 0
\(787\) 2678.82 + 1546.62i 0.121334 + 0.0700521i 0.559439 0.828872i \(-0.311017\pi\)
−0.438105 + 0.898924i \(0.644350\pi\)
\(788\) 0 0
\(789\) 8391.96 4411.80i 0.378659 0.199067i
\(790\) 0 0
\(791\) 29351.9 12948.7i 1.31938 0.582053i
\(792\) 0 0
\(793\) −18386.9 −0.823377
\(794\) 0 0
\(795\) 11280.5 + 7122.54i 0.503245 + 0.317749i