Properties

Label 624.4.bv.c.49.2
Level $624$
Weight $4$
Character 624.49
Analytic conductor $36.817$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-17})\)
Defining polynomial: \( x^{4} - 17x^{2} + 289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(-3.57071 + 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 624.49
Dual form 624.4.bv.c.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +13.4424i q^{5} +(27.2121 + 15.7109i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +13.4424i q^{5} +(27.2121 + 15.7109i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(35.0707 - 20.2481i) q^{11} +(42.1364 + 20.5310i) q^{13} +(34.9243 - 20.1635i) q^{15} +(-21.5707 + 37.3616i) q^{17} +(-23.3636 - 13.4890i) q^{19} -94.2656i q^{21} +(9.50500 + 16.4631i) q^{23} -55.6971 q^{25} +27.0000 q^{27} +(77.0557 + 133.464i) q^{29} -308.270i q^{31} +(-105.212 - 60.7443i) q^{33} +(-211.192 + 365.796i) q^{35} +(-37.6821 + 21.7558i) q^{37} +(-9.86357 - 140.270i) q^{39} +(41.4293 - 23.9192i) q^{41} +(-171.061 + 296.286i) q^{43} +(-104.773 - 60.4906i) q^{45} +133.468i q^{47} +(322.167 + 558.010i) q^{49} +129.424 q^{51} -438.454 q^{53} +(272.182 + 471.433i) q^{55} +80.9338i q^{57} +(-511.434 - 295.277i) q^{59} +(270.652 - 468.783i) q^{61} +(-244.909 + 141.398i) q^{63} +(-275.985 + 566.413i) q^{65} +(199.485 - 115.173i) q^{67} +(28.5150 - 49.3894i) q^{69} +(389.202 + 224.706i) q^{71} +389.711i q^{73} +(83.5457 + 144.705i) q^{75} +1272.47 q^{77} +897.820 q^{79} +(-40.5000 - 70.1481i) q^{81} +1300.24i q^{83} +(-502.228 - 289.961i) q^{85} +(231.167 - 400.393i) q^{87} +(801.113 - 462.523i) q^{89} +(824.061 + 1220.69i) q^{91} +(-800.910 + 462.406i) q^{93} +(181.324 - 314.062i) q^{95} +(1351.43 + 780.247i) q^{97} +364.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9} + 126 q^{11} + 40 q^{13} + 54 q^{15} - 72 q^{17} - 222 q^{19} + 138 q^{23} + 120 q^{25} + 108 q^{27} - 6 q^{29} - 378 q^{33} - 402 q^{35} + 492 q^{37} - 168 q^{39} + 180 q^{41} - 470 q^{43} - 162 q^{45} + 346 q^{49} + 432 q^{51} - 2268 q^{53} + 446 q^{55} - 2160 q^{59} - 160 q^{61} - 594 q^{63} - 804 q^{65} + 498 q^{67} + 414 q^{69} + 1314 q^{71} - 180 q^{75} + 2976 q^{77} - 8 q^{79} - 162 q^{81} - 852 q^{85} - 18 q^{87} - 252 q^{89} + 1668 q^{91} - 1404 q^{93} + 54 q^{95} - 336 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 0 0
\(5\) 13.4424i 1.20232i 0.799128 + 0.601161i \(0.205295\pi\)
−0.799128 + 0.601161i \(0.794705\pi\)
\(6\) 0 0
\(7\) 27.2121 + 15.7109i 1.46932 + 0.848311i 0.999408 0.0344037i \(-0.0109532\pi\)
0.469910 + 0.882715i \(0.344287\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 35.0707 20.2481i 0.961293 0.555003i 0.0647219 0.997903i \(-0.479384\pi\)
0.896571 + 0.442901i \(0.146051\pi\)
\(12\) 0 0
\(13\) 42.1364 + 20.5310i 0.898965 + 0.438021i
\(14\) 0 0
\(15\) 34.9243 20.1635i 0.601161 0.347080i
\(16\) 0 0
\(17\) −21.5707 + 37.3616i −0.307745 + 0.533030i −0.977869 0.209219i \(-0.932908\pi\)
0.670124 + 0.742249i \(0.266241\pi\)
\(18\) 0 0
\(19\) −23.3636 13.4890i −0.282104 0.162873i 0.352272 0.935898i \(-0.385409\pi\)
−0.634375 + 0.773025i \(0.718743\pi\)
\(20\) 0 0
\(21\) 94.2656i 0.979545i
\(22\) 0 0
\(23\) 9.50500 + 16.4631i 0.0861709 + 0.149252i 0.905890 0.423514i \(-0.139204\pi\)
−0.819719 + 0.572766i \(0.805870\pi\)
\(24\) 0 0
\(25\) −55.6971 −0.445577
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 77.0557 + 133.464i 0.493410 + 0.854611i 0.999971 0.00759297i \(-0.00241694\pi\)
−0.506561 + 0.862204i \(0.669084\pi\)
\(30\) 0 0
\(31\) 308.270i 1.78603i −0.450025 0.893016i \(-0.648585\pi\)
0.450025 0.893016i \(-0.351415\pi\)
\(32\) 0 0
\(33\) −105.212 60.7443i −0.555003 0.320431i
\(34\) 0 0
\(35\) −211.192 + 365.796i −1.01994 + 1.76659i
\(36\) 0 0
\(37\) −37.6821 + 21.7558i −0.167430 + 0.0966657i −0.581373 0.813637i \(-0.697484\pi\)
0.413944 + 0.910303i \(0.364151\pi\)
\(38\) 0 0
\(39\) −9.86357 140.270i −0.0404983 0.575928i
\(40\) 0 0
\(41\) 41.4293 23.9192i 0.157809 0.0911110i −0.419016 0.907979i \(-0.637625\pi\)
0.576825 + 0.816868i \(0.304292\pi\)
\(42\) 0 0
\(43\) −171.061 + 296.286i −0.606663 + 1.05077i 0.385123 + 0.922865i \(0.374159\pi\)
−0.991786 + 0.127906i \(0.959174\pi\)
\(44\) 0 0
\(45\) −104.773 60.4906i −0.347080 0.200387i
\(46\) 0 0
\(47\) 133.468i 0.414218i 0.978318 + 0.207109i \(0.0664055\pi\)
−0.978318 + 0.207109i \(0.933594\pi\)
\(48\) 0 0
\(49\) 322.167 + 558.010i 0.939263 + 1.62685i
\(50\) 0 0
\(51\) 129.424 0.355353
\(52\) 0 0
\(53\) −438.454 −1.13635 −0.568173 0.822909i \(-0.692350\pi\)
−0.568173 + 0.822909i \(0.692350\pi\)
\(54\) 0 0
\(55\) 272.182 + 471.433i 0.667291 + 1.15578i
\(56\) 0 0
\(57\) 80.9338i 0.188069i
\(58\) 0 0
\(59\) −511.434 295.277i −1.12853 0.651555i −0.184963 0.982746i \(-0.559216\pi\)
−0.943564 + 0.331190i \(0.892550\pi\)
\(60\) 0 0
\(61\) 270.652 468.783i 0.568089 0.983960i −0.428665 0.903463i \(-0.641016\pi\)
0.996755 0.0804965i \(-0.0256506\pi\)
\(62\) 0 0
\(63\) −244.909 + 141.398i −0.489773 + 0.282770i
\(64\) 0 0
\(65\) −275.985 + 566.413i −0.526642 + 1.08084i
\(66\) 0 0
\(67\) 199.485 115.173i 0.363746 0.210009i −0.306977 0.951717i \(-0.599317\pi\)
0.670723 + 0.741708i \(0.265984\pi\)
\(68\) 0 0
\(69\) 28.5150 49.3894i 0.0497508 0.0861709i
\(70\) 0 0
\(71\) 389.202 + 224.706i 0.650561 + 0.375601i 0.788671 0.614816i \(-0.210770\pi\)
−0.138110 + 0.990417i \(0.544103\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i 0.949946 + 0.312413i \(0.101137\pi\)
−0.949946 + 0.312413i \(0.898863\pi\)
\(74\) 0 0
\(75\) 83.5457 + 144.705i 0.128627 + 0.222789i
\(76\) 0 0
\(77\) 1272.47 1.88326
\(78\) 0 0
\(79\) 897.820 1.27864 0.639321 0.768940i \(-0.279216\pi\)
0.639321 + 0.768940i \(0.279216\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 1300.24i 1.71952i 0.510700 + 0.859759i \(0.329386\pi\)
−0.510700 + 0.859759i \(0.670614\pi\)
\(84\) 0 0
\(85\) −502.228 289.961i −0.640874 0.370009i
\(86\) 0 0
\(87\) 231.167 400.393i 0.284870 0.493410i
\(88\) 0 0
\(89\) 801.113 462.523i 0.954132 0.550869i 0.0597703 0.998212i \(-0.480963\pi\)
0.894362 + 0.447344i \(0.147630\pi\)
\(90\) 0 0
\(91\) 824.061 + 1220.69i 0.949287 + 1.40619i
\(92\) 0 0
\(93\) −800.910 + 462.406i −0.893016 + 0.515583i
\(94\) 0 0
\(95\) 181.324 314.062i 0.195825 0.339179i
\(96\) 0 0
\(97\) 1351.43 + 780.247i 1.41460 + 0.816722i 0.995818 0.0913623i \(-0.0291221\pi\)
0.418787 + 0.908085i \(0.362455\pi\)
\(98\) 0 0
\(99\) 364.466i 0.370002i
\(100\) 0 0
\(101\) 479.420 + 830.380i 0.472318 + 0.818078i 0.999498 0.0316752i \(-0.0100842\pi\)
−0.527181 + 0.849753i \(0.676751\pi\)
\(102\) 0 0
\(103\) 635.153 0.607606 0.303803 0.952735i \(-0.401743\pi\)
0.303803 + 0.952735i \(0.401743\pi\)
\(104\) 0 0
\(105\) 1267.15 1.17773
\(106\) 0 0
\(107\) −724.162 1254.29i −0.654275 1.13324i −0.982075 0.188490i \(-0.939641\pi\)
0.327800 0.944747i \(-0.393693\pi\)
\(108\) 0 0
\(109\) 331.084i 0.290937i −0.989363 0.145468i \(-0.953531\pi\)
0.989363 0.145468i \(-0.0464689\pi\)
\(110\) 0 0
\(111\) 113.046 + 65.2674i 0.0966657 + 0.0558100i
\(112\) 0 0
\(113\) −347.602 + 602.065i −0.289378 + 0.501217i −0.973661 0.227999i \(-0.926782\pi\)
0.684284 + 0.729216i \(0.260115\pi\)
\(114\) 0 0
\(115\) −221.304 + 127.770i −0.179449 + 0.103605i
\(116\) 0 0
\(117\) −349.637 + 236.032i −0.276273 + 0.186505i
\(118\) 0 0
\(119\) −1173.97 + 677.792i −0.904351 + 0.522127i
\(120\) 0 0
\(121\) 154.470 267.550i 0.116056 0.201014i
\(122\) 0 0
\(123\) −124.288 71.7576i −0.0911110 0.0526030i
\(124\) 0 0
\(125\) 931.594i 0.666595i
\(126\) 0 0
\(127\) −123.577 214.042i −0.0863441 0.149552i 0.819619 0.572909i \(-0.194185\pi\)
−0.905963 + 0.423357i \(0.860852\pi\)
\(128\) 0 0
\(129\) 1026.36 0.700514
\(130\) 0 0
\(131\) −472.243 −0.314962 −0.157481 0.987522i \(-0.550337\pi\)
−0.157481 + 0.987522i \(0.550337\pi\)
\(132\) 0 0
\(133\) −423.849 734.127i −0.276333 0.478623i
\(134\) 0 0
\(135\) 362.944i 0.231387i
\(136\) 0 0
\(137\) −1585.43 915.349i −0.988704 0.570829i −0.0838175 0.996481i \(-0.526711\pi\)
−0.904887 + 0.425652i \(0.860045\pi\)
\(138\) 0 0
\(139\) −50.0000 + 86.6025i −0.0305104 + 0.0528456i −0.880877 0.473344i \(-0.843047\pi\)
0.850367 + 0.526190i \(0.176380\pi\)
\(140\) 0 0
\(141\) 346.759 200.202i 0.207109 0.119575i
\(142\) 0 0
\(143\) 1893.47 133.146i 1.10727 0.0778615i
\(144\) 0 0
\(145\) −1794.08 + 1035.81i −1.02752 + 0.593237i
\(146\) 0 0
\(147\) 966.501 1674.03i 0.542284 0.939263i
\(148\) 0 0
\(149\) −129.520 74.7784i −0.0712127 0.0411147i 0.463971 0.885850i \(-0.346424\pi\)
−0.535184 + 0.844736i \(0.679758\pi\)
\(150\) 0 0
\(151\) 800.032i 0.431163i −0.976486 0.215582i \(-0.930835\pi\)
0.976486 0.215582i \(-0.0691647\pi\)
\(152\) 0 0
\(153\) −194.136 336.254i −0.102582 0.177677i
\(154\) 0 0
\(155\) 4143.88 2.14739
\(156\) 0 0
\(157\) −2706.16 −1.37564 −0.687818 0.725884i \(-0.741431\pi\)
−0.687818 + 0.725884i \(0.741431\pi\)
\(158\) 0 0
\(159\) 657.681 + 1139.14i 0.328035 + 0.568173i
\(160\) 0 0
\(161\) 597.330i 0.292399i
\(162\) 0 0
\(163\) −3185.46 1839.12i −1.53070 0.883750i −0.999330 0.0366108i \(-0.988344\pi\)
−0.531371 0.847139i \(-0.678323\pi\)
\(164\) 0 0
\(165\) 816.546 1414.30i 0.385261 0.667291i
\(166\) 0 0
\(167\) −2791.30 + 1611.56i −1.29339 + 0.746742i −0.979254 0.202635i \(-0.935050\pi\)
−0.314140 + 0.949377i \(0.601716\pi\)
\(168\) 0 0
\(169\) 1353.96 + 1730.20i 0.616275 + 0.787531i
\(170\) 0 0
\(171\) 210.272 121.401i 0.0940346 0.0542909i
\(172\) 0 0
\(173\) −1344.77 + 2329.21i −0.590988 + 1.02362i 0.403111 + 0.915151i \(0.367929\pi\)
−0.994100 + 0.108471i \(0.965405\pi\)
\(174\) 0 0
\(175\) −1515.64 875.054i −0.654694 0.377988i
\(176\) 0 0
\(177\) 1771.66i 0.752351i
\(178\) 0 0
\(179\) 762.021 + 1319.86i 0.318191 + 0.551122i 0.980111 0.198452i \(-0.0635915\pi\)
−0.661920 + 0.749574i \(0.730258\pi\)
\(180\) 0 0
\(181\) −476.881 −0.195836 −0.0979180 0.995194i \(-0.531218\pi\)
−0.0979180 + 0.995194i \(0.531218\pi\)
\(182\) 0 0
\(183\) −1623.91 −0.655973
\(184\) 0 0
\(185\) −292.449 506.537i −0.116223 0.201305i
\(186\) 0 0
\(187\) 1747.06i 0.683197i
\(188\) 0 0
\(189\) 734.728 + 424.195i 0.282770 + 0.163258i
\(190\) 0 0
\(191\) −684.871 + 1186.23i −0.259453 + 0.449386i −0.966096 0.258185i \(-0.916876\pi\)
0.706642 + 0.707571i \(0.250209\pi\)
\(192\) 0 0
\(193\) 1857.38 1072.36i 0.692732 0.399949i −0.111903 0.993719i \(-0.535695\pi\)
0.804635 + 0.593770i \(0.202361\pi\)
\(194\) 0 0
\(195\) 1885.56 132.590i 0.692451 0.0486920i
\(196\) 0 0
\(197\) −207.620 + 119.869i −0.0750879 + 0.0433520i −0.537074 0.843535i \(-0.680470\pi\)
0.461986 + 0.886887i \(0.347137\pi\)
\(198\) 0 0
\(199\) 794.969 1376.93i 0.283185 0.490491i −0.688982 0.724778i \(-0.741942\pi\)
0.972167 + 0.234287i \(0.0752755\pi\)
\(200\) 0 0
\(201\) −598.455 345.518i −0.210009 0.121249i
\(202\) 0 0
\(203\) 4842.47i 1.67426i
\(204\) 0 0
\(205\) 321.531 + 556.908i 0.109545 + 0.189737i
\(206\) 0 0
\(207\) −171.090 −0.0574472
\(208\) 0 0
\(209\) −1092.50 −0.361579
\(210\) 0 0
\(211\) −936.427 1621.94i −0.305527 0.529189i 0.671851 0.740686i \(-0.265499\pi\)
−0.977379 + 0.211497i \(0.932166\pi\)
\(212\) 0 0
\(213\) 1348.24i 0.433707i
\(214\) 0 0
\(215\) −3982.78 2299.46i −1.26337 0.729404i
\(216\) 0 0
\(217\) 4843.22 8388.70i 1.51511 2.62425i
\(218\) 0 0
\(219\) 1012.50 584.567i 0.312413 0.180372i
\(220\) 0 0
\(221\) −1675.98 + 1131.42i −0.510130 + 0.344377i
\(222\) 0 0
\(223\) 48.6085 28.0642i 0.0145967 0.00842742i −0.492684 0.870208i \(-0.663984\pi\)
0.507281 + 0.861781i \(0.330651\pi\)
\(224\) 0 0
\(225\) 250.637 434.116i 0.0742629 0.128627i
\(226\) 0 0
\(227\) −577.976 333.695i −0.168994 0.0975687i 0.413117 0.910678i \(-0.364440\pi\)
−0.582111 + 0.813109i \(0.697773\pi\)
\(228\) 0 0
\(229\) 723.299i 0.208720i −0.994540 0.104360i \(-0.966721\pi\)
0.994540 0.104360i \(-0.0332795\pi\)
\(230\) 0 0
\(231\) −1908.70 3305.96i −0.543650 0.941629i
\(232\) 0 0
\(233\) 275.451 0.0774482 0.0387241 0.999250i \(-0.487671\pi\)
0.0387241 + 0.999250i \(0.487671\pi\)
\(234\) 0 0
\(235\) −1794.12 −0.498024
\(236\) 0 0
\(237\) −1346.73 2332.60i −0.369112 0.639321i
\(238\) 0 0
\(239\) 1529.39i 0.413925i 0.978349 + 0.206963i \(0.0663579\pi\)
−0.978349 + 0.206963i \(0.933642\pi\)
\(240\) 0 0
\(241\) 844.830 + 487.763i 0.225810 + 0.130372i 0.608638 0.793448i \(-0.291716\pi\)
−0.382827 + 0.923820i \(0.625050\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −7500.97 + 4330.69i −1.95600 + 1.12930i
\(246\) 0 0
\(247\) −707.516 1048.05i −0.182260 0.269984i
\(248\) 0 0
\(249\) 3378.13 1950.36i 0.859759 0.496382i
\(250\) 0 0
\(251\) 937.070 1623.05i 0.235647 0.408152i −0.723814 0.689995i \(-0.757613\pi\)
0.959460 + 0.281843i \(0.0909458\pi\)
\(252\) 0 0
\(253\) 666.694 + 384.916i 0.165671 + 0.0956501i
\(254\) 0 0
\(255\) 1739.77i 0.427249i
\(256\) 0 0
\(257\) −909.094 1574.60i −0.220653 0.382181i 0.734354 0.678767i \(-0.237485\pi\)
−0.955006 + 0.296586i \(0.904152\pi\)
\(258\) 0 0
\(259\) −1367.22 −0.328010
\(260\) 0 0
\(261\) −1387.00 −0.328940
\(262\) 0 0
\(263\) 336.899 + 583.527i 0.0789890 + 0.136813i 0.902814 0.430031i \(-0.141497\pi\)
−0.823825 + 0.566844i \(0.808164\pi\)
\(264\) 0 0
\(265\) 5893.86i 1.36625i
\(266\) 0 0
\(267\) −2403.34 1387.57i −0.550869 0.318044i
\(268\) 0 0
\(269\) 1678.20 2906.73i 0.380378 0.658834i −0.610738 0.791833i \(-0.709127\pi\)
0.991116 + 0.132998i \(0.0424605\pi\)
\(270\) 0 0
\(271\) 7721.09 4457.77i 1.73071 0.999227i 0.845699 0.533660i \(-0.179184\pi\)
0.885013 0.465567i \(-0.154150\pi\)
\(272\) 0 0
\(273\) 1935.37 3972.02i 0.429061 0.880577i
\(274\) 0 0
\(275\) −1953.34 + 1127.76i −0.428330 + 0.247296i
\(276\) 0 0
\(277\) 2008.65 3479.09i 0.435698 0.754651i −0.561654 0.827372i \(-0.689835\pi\)
0.997352 + 0.0727208i \(0.0231682\pi\)
\(278\) 0 0
\(279\) 2402.73 + 1387.22i 0.515583 + 0.297672i
\(280\) 0 0
\(281\) 1841.12i 0.390860i −0.980718 0.195430i \(-0.937390\pi\)
0.980718 0.195430i \(-0.0626103\pi\)
\(282\) 0 0
\(283\) −2424.70 4199.70i −0.509305 0.882143i −0.999942 0.0107784i \(-0.996569\pi\)
0.490637 0.871364i \(-0.336764\pi\)
\(284\) 0 0
\(285\) −1087.94 −0.226120
\(286\) 0 0
\(287\) 1503.17 0.309162
\(288\) 0 0
\(289\) 1525.91 + 2642.95i 0.310586 + 0.537951i
\(290\) 0 0
\(291\) 4681.48i 0.943070i
\(292\) 0 0
\(293\) −1224.43 706.927i −0.244137 0.140953i 0.372940 0.927856i \(-0.378350\pi\)
−0.617077 + 0.786903i \(0.711683\pi\)
\(294\) 0 0
\(295\) 3969.22 6874.89i 0.783379 1.35685i
\(296\) 0 0
\(297\) 946.909 546.698i 0.185001 0.106810i
\(298\) 0 0
\(299\) 62.5022 + 888.845i 0.0120889 + 0.171917i
\(300\) 0 0
\(301\) −9309.86 + 5375.05i −1.78276 + 1.02928i
\(302\) 0 0
\(303\) 1438.26 2491.14i 0.272693 0.472318i
\(304\) 0 0
\(305\) 6301.55 + 3638.20i 1.18304 + 0.683026i
\(306\) 0 0
\(307\) 4625.64i 0.859932i −0.902845 0.429966i \(-0.858526\pi\)
0.902845 0.429966i \(-0.141474\pi\)
\(308\) 0 0
\(309\) −952.729 1650.18i −0.175401 0.303803i
\(310\) 0 0
\(311\) −6060.79 −1.10507 −0.552534 0.833490i \(-0.686339\pi\)
−0.552534 + 0.833490i \(0.686339\pi\)
\(312\) 0 0
\(313\) 969.946 0.175158 0.0875792 0.996158i \(-0.472087\pi\)
0.0875792 + 0.996158i \(0.472087\pi\)
\(314\) 0 0
\(315\) −1900.73 3292.16i −0.339981 0.588864i
\(316\) 0 0
\(317\) 8741.63i 1.54883i 0.632679 + 0.774414i \(0.281955\pi\)
−0.632679 + 0.774414i \(0.718045\pi\)
\(318\) 0 0
\(319\) 5404.80 + 3120.46i 0.948623 + 0.547687i
\(320\) 0 0
\(321\) −2172.49 + 3762.86i −0.377746 + 0.654275i
\(322\) 0 0
\(323\) 1007.94 581.933i 0.173632 0.100247i
\(324\) 0 0
\(325\) −2346.88 1143.52i −0.400558 0.195172i
\(326\) 0 0
\(327\) −860.181 + 496.626i −0.145468 + 0.0839862i
\(328\) 0 0
\(329\) −2096.90 + 3631.94i −0.351386 + 0.608618i
\(330\) 0 0
\(331\) 6051.57 + 3493.88i 1.00491 + 0.580184i 0.909697 0.415273i \(-0.136314\pi\)
0.0952114 + 0.995457i \(0.469647\pi\)
\(332\) 0 0
\(333\) 391.604i 0.0644438i
\(334\) 0 0
\(335\) 1548.19 + 2681.55i 0.252498 + 0.437339i
\(336\) 0 0
\(337\) 4156.59 0.671881 0.335940 0.941883i \(-0.390946\pi\)
0.335940 + 0.941883i \(0.390946\pi\)
\(338\) 0 0
\(339\) 2085.61 0.334144
\(340\) 0 0
\(341\) −6241.89 10811.3i −0.991252 1.71690i
\(342\) 0 0
\(343\) 9468.49i 1.49053i
\(344\) 0 0
\(345\) 663.911 + 383.309i 0.103605 + 0.0598164i
\(346\) 0 0
\(347\) −156.256 + 270.644i −0.0241737 + 0.0418701i −0.877859 0.478919i \(-0.841029\pi\)
0.853685 + 0.520789i \(0.174362\pi\)
\(348\) 0 0
\(349\) 3861.39 2229.37i 0.592251 0.341936i −0.173736 0.984792i \(-0.555584\pi\)
0.765987 + 0.642856i \(0.222251\pi\)
\(350\) 0 0
\(351\) 1137.68 + 554.337i 0.173006 + 0.0842972i
\(352\) 0 0
\(353\) −1947.84 + 1124.59i −0.293692 + 0.169563i −0.639605 0.768703i \(-0.720902\pi\)
0.345914 + 0.938266i \(0.387569\pi\)
\(354\) 0 0
\(355\) −3020.58 + 5231.80i −0.451594 + 0.782183i
\(356\) 0 0
\(357\) 3521.91 + 2033.38i 0.522127 + 0.301450i
\(358\) 0 0
\(359\) 7842.79i 1.15300i −0.817098 0.576499i \(-0.804418\pi\)
0.817098 0.576499i \(-0.195582\pi\)
\(360\) 0 0
\(361\) −3065.60 5309.77i −0.446945 0.774131i
\(362\) 0 0
\(363\) −926.820 −0.134009
\(364\) 0 0
\(365\) −5238.64 −0.751241
\(366\) 0 0
\(367\) 3330.12 + 5767.94i 0.473653 + 0.820392i 0.999545 0.0301597i \(-0.00960160\pi\)
−0.525892 + 0.850552i \(0.676268\pi\)
\(368\) 0 0
\(369\) 430.546i 0.0607407i
\(370\) 0 0
\(371\) −11931.3 6888.53i −1.66965 0.963975i
\(372\) 0 0
\(373\) 18.4936 32.0319i 0.00256720 0.00444651i −0.864739 0.502222i \(-0.832516\pi\)
0.867306 + 0.497775i \(0.165850\pi\)
\(374\) 0 0
\(375\) 2420.35 1397.39i 0.333297 0.192429i
\(376\) 0 0
\(377\) 506.696 + 7205.74i 0.0692207 + 0.984389i
\(378\) 0 0
\(379\) −10461.5 + 6039.93i −1.41786 + 0.818603i −0.996111 0.0881092i \(-0.971918\pi\)
−0.421751 + 0.906712i \(0.638584\pi\)
\(380\) 0 0
\(381\) −370.731 + 642.126i −0.0498508 + 0.0863441i
\(382\) 0 0
\(383\) −9151.63 5283.69i −1.22096 0.704919i −0.255835 0.966721i \(-0.582350\pi\)
−0.965122 + 0.261801i \(0.915684\pi\)
\(384\) 0 0
\(385\) 17104.9i 2.26428i
\(386\) 0 0
\(387\) −1539.55 2666.57i −0.202221 0.350257i
\(388\) 0 0
\(389\) 9757.49 1.27179 0.635893 0.771778i \(-0.280632\pi\)
0.635893 + 0.771778i \(0.280632\pi\)
\(390\) 0 0
\(391\) −820.119 −0.106075
\(392\) 0 0
\(393\) 708.364 + 1226.92i 0.0909218 + 0.157481i
\(394\) 0 0
\(395\) 12068.8i 1.53734i
\(396\) 0 0
\(397\) −12298.0 7100.26i −1.55471 0.897612i −0.997748 0.0670737i \(-0.978634\pi\)
−0.556962 0.830538i \(-0.688033\pi\)
\(398\) 0 0
\(399\) −1271.55 + 2202.38i −0.159541 + 0.276333i
\(400\) 0 0
\(401\) 10978.1 6338.19i 1.36713 0.789313i 0.376569 0.926389i \(-0.377104\pi\)
0.990561 + 0.137076i \(0.0437705\pi\)
\(402\) 0 0
\(403\) 6329.10 12989.4i 0.782319 1.60558i
\(404\) 0 0
\(405\) 942.956 544.416i 0.115693 0.0667956i
\(406\) 0 0
\(407\) −881.026 + 1525.98i −0.107299 + 0.185848i
\(408\) 0 0
\(409\) −1328.20 766.838i −0.160576 0.0927083i 0.417559 0.908650i \(-0.362886\pi\)
−0.578134 + 0.815942i \(0.696219\pi\)
\(410\) 0 0
\(411\) 5492.09i 0.659136i
\(412\) 0 0
\(413\) −9278.15 16070.2i −1.10544 1.91468i
\(414\) 0 0
\(415\) −17478.3 −2.06741
\(416\) 0 0
\(417\) 300.000 0.0352304
\(418\) 0 0
\(419\) −1082.95 1875.72i −0.126266 0.218699i 0.795961 0.605348i \(-0.206966\pi\)
−0.922227 + 0.386649i \(0.873633\pi\)
\(420\) 0 0
\(421\) 734.575i 0.0850380i 0.999096 + 0.0425190i \(0.0135383\pi\)
−0.999096 + 0.0425190i \(0.986462\pi\)
\(422\) 0 0
\(423\) −1040.28 600.605i −0.119575 0.0690364i
\(424\) 0 0
\(425\) 1201.43 2080.93i 0.137124 0.237506i
\(426\) 0 0
\(427\) 14730.0 8504.40i 1.66941 0.963833i
\(428\) 0 0
\(429\) −3186.12 4719.66i −0.358572 0.531159i
\(430\) 0 0
\(431\) 11872.6 6854.66i 1.32688 0.766073i 0.342061 0.939678i \(-0.388875\pi\)
0.984815 + 0.173605i \(0.0555416\pi\)
\(432\) 0 0
\(433\) 5024.97 8703.50i 0.557701 0.965967i −0.439987 0.898004i \(-0.645017\pi\)
0.997688 0.0679624i \(-0.0216498\pi\)
\(434\) 0 0
\(435\) 5382.23 + 3107.43i 0.593237 + 0.342506i
\(436\) 0 0
\(437\) 512.850i 0.0561395i
\(438\) 0 0
\(439\) 4066.73 + 7043.79i 0.442129 + 0.765790i 0.997847 0.0655807i \(-0.0208900\pi\)
−0.555718 + 0.831371i \(0.687557\pi\)
\(440\) 0 0
\(441\) −5799.01 −0.626175
\(442\) 0 0
\(443\) 2370.78 0.254264 0.127132 0.991886i \(-0.459423\pi\)
0.127132 + 0.991886i \(0.459423\pi\)
\(444\) 0 0
\(445\) 6217.40 + 10768.9i 0.662321 + 1.14717i
\(446\) 0 0
\(447\) 448.670i 0.0474751i
\(448\) 0 0
\(449\) 11191.8 + 6461.60i 1.17634 + 0.679158i 0.955164 0.296077i \(-0.0956785\pi\)
0.221172 + 0.975235i \(0.429012\pi\)
\(450\) 0 0
\(451\) 968.636 1677.73i 0.101134 0.175169i
\(452\) 0 0
\(453\) −2078.54 + 1200.05i −0.215582 + 0.124466i
\(454\) 0 0
\(455\) −16409.0 + 11077.3i −1.69070 + 1.14135i
\(456\) 0 0
\(457\) 7275.71 4200.63i 0.744734 0.429972i −0.0790543 0.996870i \(-0.525190\pi\)
0.823788 + 0.566898i \(0.191857\pi\)
\(458\) 0 0
\(459\) −582.409 + 1008.76i −0.0592256 + 0.102582i
\(460\) 0 0
\(461\) −15265.7 8813.67i −1.54229 0.890441i −0.998694 0.0510940i \(-0.983729\pi\)
−0.543596 0.839347i \(-0.682937\pi\)
\(462\) 0 0
\(463\) 5461.81i 0.548233i −0.961697 0.274116i \(-0.911615\pi\)
0.961697 0.274116i \(-0.0883853\pi\)
\(464\) 0 0
\(465\) −6215.82 10766.1i −0.619897 1.07369i
\(466\) 0 0
\(467\) 8262.19 0.818691 0.409345 0.912379i \(-0.365757\pi\)
0.409345 + 0.912379i \(0.365757\pi\)
\(468\) 0 0
\(469\) 7237.89 0.712611
\(470\) 0 0
\(471\) 4059.23 + 7030.80i 0.397112 + 0.687818i
\(472\) 0 0
\(473\) 13854.6i 1.34680i
\(474\) 0 0
\(475\) 1301.28 + 751.297i 0.125699 + 0.0725723i
\(476\) 0 0
\(477\) 1973.04 3417.41i 0.189391 0.328035i
\(478\) 0 0
\(479\) −1364.74 + 787.935i −0.130181 + 0.0751601i −0.563676 0.825996i \(-0.690613\pi\)
0.433495 + 0.901156i \(0.357280\pi\)
\(480\) 0 0
\(481\) −2034.46 + 143.060i −0.192855 + 0.0135613i
\(482\) 0 0
\(483\) 1551.91 895.995i 0.146199 0.0844082i
\(484\) 0 0
\(485\) −10488.4 + 18166.4i −0.981963 + 1.70081i
\(486\) 0 0
\(487\) −10908.2 6297.84i −1.01498 0.586001i −0.102337 0.994750i \(-0.532632\pi\)
−0.912647 + 0.408749i \(0.865965\pi\)
\(488\) 0 0
\(489\) 11034.7i 1.02047i
\(490\) 0 0
\(491\) 535.606 + 927.697i 0.0492293 + 0.0852676i 0.889590 0.456760i \(-0.150990\pi\)
−0.840361 + 0.542028i \(0.817657\pi\)
\(492\) 0 0
\(493\) −6648.59 −0.607378
\(494\) 0 0
\(495\) −4899.28 −0.444861
\(496\) 0 0
\(497\) 7060.68 + 12229.5i 0.637253 + 1.10376i
\(498\) 0 0
\(499\) 1422.30i 0.127597i 0.997963 + 0.0637985i \(0.0203215\pi\)
−0.997963 + 0.0637985i \(0.979678\pi\)
\(500\) 0 0
\(501\) 8373.89 + 4834.67i 0.746742 + 0.431132i
\(502\) 0 0
\(503\) −4674.67 + 8096.76i −0.414380 + 0.717727i −0.995363 0.0961884i \(-0.969335\pi\)
0.580983 + 0.813916i \(0.302668\pi\)
\(504\) 0 0
\(505\) −11162.3 + 6444.54i −0.983593 + 0.567878i
\(506\) 0 0
\(507\) 2464.27 6112.99i 0.215862 0.535478i
\(508\) 0 0
\(509\) 11896.0 6868.15i 1.03591 0.598086i 0.117241 0.993103i \(-0.462595\pi\)
0.918673 + 0.395018i \(0.129262\pi\)
\(510\) 0 0
\(511\) −6122.73 + 10604.9i −0.530046 + 0.918067i
\(512\) 0 0
\(513\) −630.816 364.202i −0.0542909 0.0313449i
\(514\) 0 0
\(515\) 8537.96i 0.730538i
\(516\) 0 0
\(517\) 2702.47 + 4680.81i 0.229892 + 0.398185i
\(518\) 0 0
\(519\) 8068.62 0.682414
\(520\) 0 0
\(521\) 11052.3 0.929386 0.464693 0.885472i \(-0.346165\pi\)
0.464693 + 0.885472i \(0.346165\pi\)
\(522\) 0 0
\(523\) 3238.52 + 5609.28i 0.270766 + 0.468980i 0.969058 0.246832i \(-0.0793897\pi\)
−0.698292 + 0.715813i \(0.746056\pi\)
\(524\) 0 0
\(525\) 5250.33i 0.436463i
\(526\) 0 0
\(527\) 11517.5 + 6649.61i 0.952009 + 0.549643i
\(528\) 0 0
\(529\) 5902.81 10224.0i 0.485149 0.840303i
\(530\) 0 0
\(531\) 4602.91 2657.49i 0.376176 0.217185i
\(532\) 0 0
\(533\) 2236.77 157.286i 0.181773 0.0127820i
\(534\) 0 0
\(535\) 16860.6 9734.45i 1.36252 0.786649i
\(536\) 0 0
\(537\) 2286.06 3959.58i 0.183707 0.318191i
\(538\) 0 0
\(539\) 22597.3 + 13046.5i 1.80581 + 1.04259i
\(540\) 0 0
\(541\) 18341.5i 1.45761i −0.684723 0.728803i \(-0.740077\pi\)
0.684723 0.728803i \(-0.259923\pi\)
\(542\) 0 0
\(543\) 715.322 + 1238.97i 0.0565330 + 0.0979180i
\(544\) 0 0
\(545\) 4450.55 0.349799
\(546\) 0 0
\(547\) 18943.1 1.48071 0.740356 0.672215i \(-0.234657\pi\)
0.740356 + 0.672215i \(0.234657\pi\)
\(548\) 0 0
\(549\) 2435.87 + 4219.05i 0.189363 + 0.327987i
\(550\) 0 0
\(551\) 4157.61i 0.321452i
\(552\) 0 0
\(553\) 24431.6 + 14105.6i 1.87873 + 1.08469i
\(554\) 0 0
\(555\) −877.348 + 1519.61i −0.0671015 + 0.116223i
\(556\) 0 0
\(557\) −359.861 + 207.766i −0.0273749 + 0.0158049i −0.513625 0.858015i \(-0.671698\pi\)
0.486250 + 0.873820i \(0.338364\pi\)
\(558\) 0 0
\(559\) −13290.9 + 8972.38i −1.00563 + 0.678875i
\(560\) 0 0
\(561\) 4539.00 2620.59i 0.341599 0.197222i
\(562\) 0 0
\(563\) −9145.90 + 15841.2i −0.684643 + 1.18584i 0.288907 + 0.957357i \(0.406708\pi\)
−0.973549 + 0.228478i \(0.926625\pi\)
\(564\) 0 0
\(565\) −8093.17 4672.59i −0.602623 0.347925i
\(566\) 0 0
\(567\) 2545.17i 0.188514i
\(568\) 0 0
\(569\) 2173.73 + 3765.02i 0.160154 + 0.277395i 0.934924 0.354848i \(-0.115468\pi\)
−0.774770 + 0.632244i \(0.782134\pi\)
\(570\) 0 0
\(571\) −16756.0 −1.22805 −0.614024 0.789288i \(-0.710450\pi\)
−0.614024 + 0.789288i \(0.710450\pi\)
\(572\) 0 0
\(573\) 4109.23 0.299591
\(574\) 0 0
\(575\) −529.401 916.950i −0.0383958 0.0665034i
\(576\) 0 0
\(577\) 19974.7i 1.44117i 0.693364 + 0.720587i \(0.256128\pi\)
−0.693364 + 0.720587i \(0.743872\pi\)
\(578\) 0 0
\(579\) −5572.14 3217.08i −0.399949 0.230911i
\(580\) 0 0
\(581\) −20428.0 + 35382.4i −1.45869 + 2.52652i
\(582\) 0 0
\(583\) −15376.9 + 8877.86i −1.09236 + 0.630675i
\(584\) 0 0
\(585\) −3172.82 4699.95i −0.224239 0.332169i
\(586\) 0 0
\(587\) 13638.7 7874.33i 0.958996 0.553677i 0.0631321 0.998005i \(-0.479891\pi\)
0.895864 + 0.444329i \(0.146558\pi\)
\(588\) 0 0
\(589\) −4158.25 + 7202.30i −0.290896 + 0.503846i
\(590\) 0 0
\(591\) 622.860 + 359.608i 0.0433520 + 0.0250293i
\(592\) 0 0
\(593\) 13318.4i 0.922297i −0.887323 0.461148i \(-0.847438\pi\)
0.887323 0.461148i \(-0.152562\pi\)
\(594\) 0 0
\(595\) −9111.13 15780.9i −0.627765 1.08732i
\(596\) 0 0
\(597\) −4769.82 −0.326994
\(598\) 0 0
\(599\) −2970.80 −0.202644 −0.101322 0.994854i \(-0.532307\pi\)
−0.101322 + 0.994854i \(0.532307\pi\)
\(600\) 0 0
\(601\) −5316.31 9208.13i −0.360827 0.624971i 0.627270 0.778802i \(-0.284172\pi\)
−0.988097 + 0.153831i \(0.950839\pi\)
\(602\) 0 0
\(603\) 2073.11i 0.140006i
\(604\) 0 0
\(605\) 3596.50 + 2076.44i 0.241684 + 0.139536i
\(606\) 0 0
\(607\) 5793.94 10035.4i 0.387428 0.671045i −0.604675 0.796472i \(-0.706697\pi\)
0.992103 + 0.125428i \(0.0400303\pi\)
\(608\) 0 0
\(609\) 12581.1 7263.71i 0.837130 0.483317i
\(610\) 0 0
\(611\) −2740.22 + 5623.85i −0.181436 + 0.372368i
\(612\) 0 0
\(613\) 18006.7 10396.2i 1.18643 0.684988i 0.228939 0.973441i \(-0.426474\pi\)
0.957494 + 0.288453i \(0.0931409\pi\)
\(614\) 0 0
\(615\) 964.592 1670.72i 0.0632457 0.109545i
\(616\) 0 0
\(617\) 1353.40 + 781.388i 0.0883079 + 0.0509846i 0.543504 0.839407i \(-0.317097\pi\)
−0.455196 + 0.890391i \(0.650431\pi\)
\(618\) 0 0
\(619\) 758.406i 0.0492454i 0.999697 + 0.0246227i \(0.00783844\pi\)
−0.999697 + 0.0246227i \(0.992162\pi\)
\(620\) 0 0
\(621\) 256.635 + 444.505i 0.0165836 + 0.0287236i
\(622\) 0 0
\(623\) 29066.7 1.86923
\(624\) 0 0
\(625\) −19485.0 −1.24704
\(626\) 0 0
\(627\) 1638.75 + 2838.41i 0.104379 + 0.180789i
\(628\) 0 0
\(629\) 1877.15i 0.118994i
\(630\) 0 0
\(631\) 12354.0 + 7132.59i 0.779406 + 0.449990i 0.836220 0.548394i \(-0.184761\pi\)
−0.0568136 + 0.998385i \(0.518094\pi\)
\(632\) 0 0
\(633\) −2809.28 + 4865.82i −0.176396 + 0.305527i
\(634\) 0 0
\(635\) 2877.23 1661.17i 0.179810 0.103813i
\(636\) 0 0
\(637\) 2118.48 + 30127.0i 0.131770 + 1.87390i
\(638\) 0 0
\(639\) −3502.82 + 2022.35i −0.216854 + 0.125200i
\(640\) 0 0
\(641\) 1992.82 3451.67i 0.122795 0.212688i −0.798074 0.602560i \(-0.794147\pi\)
0.920869 + 0.389872i \(0.127481\pi\)
\(642\) 0 0
\(643\) −7063.78 4078.28i −0.433232 0.250127i 0.267490 0.963561i \(-0.413806\pi\)
−0.700723 + 0.713434i \(0.747139\pi\)
\(644\) 0 0
\(645\) 13796.8i 0.842243i
\(646\) 0 0
\(647\) −5639.62 9768.11i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(648\) 0 0
\(649\) −23915.2 −1.44646
\(650\) 0 0
\(651\) −29059.3 −1.74950
\(652\) 0 0
\(653\) −3282.88 5686.11i −0.196736 0.340757i 0.750732 0.660607i \(-0.229701\pi\)
−0.947468 + 0.319850i \(0.896368\pi\)
\(654\) 0 0
\(655\) 6348.06i 0.378686i
\(656\) 0 0
\(657\) −3037.50 1753.70i −0.180372 0.104138i
\(658\) 0 0
\(659\) 2399.67 4156.36i 0.141848 0.245688i −0.786344 0.617788i \(-0.788029\pi\)
0.928193 + 0.372100i \(0.121362\pi\)
\(660\) 0 0
\(661\) −13504.5 + 7796.80i −0.794648 + 0.458790i −0.841596 0.540107i \(-0.818384\pi\)
0.0469482 + 0.998897i \(0.485050\pi\)
\(662\) 0 0
\(663\) 5453.48 + 2657.21i 0.319450 + 0.155652i
\(664\) 0 0
\(665\) 9868.41 5697.53i 0.575459 0.332242i
\(666\) 0 0
\(667\) −1464.83 + 2537.16i −0.0850351 + 0.147285i
\(668\) 0 0
\(669\) −145.826 84.1925i −0.00842742 0.00486557i
\(670\) 0 0
\(671\) 21920.8i 1.26116i
\(672\) 0 0
\(673\) −1102.77 1910.06i −0.0631630 0.109402i 0.832715 0.553702i \(-0.186785\pi\)
−0.895878 + 0.444301i \(0.853452\pi\)
\(674\) 0 0
\(675\) −1503.82 −0.0857514
\(676\) 0 0
\(677\) −15046.4 −0.854182 −0.427091 0.904209i \(-0.640462\pi\)
−0.427091 + 0.904209i \(0.640462\pi\)
\(678\) 0 0
\(679\) 24516.8 + 42464.4i 1.38567 + 2.40005i
\(680\) 0 0
\(681\) 2002.17i 0.112663i
\(682\) 0 0
\(683\) −26528.5 15316.3i −1.48622 0.858068i −0.486340 0.873770i \(-0.661668\pi\)
−0.999877 + 0.0157020i \(0.995002\pi\)
\(684\) 0 0
\(685\) 12304.5 21311.9i 0.686320 1.18874i
\(686\) 0 0
\(687\) −1879.19 + 1084.95i −0.104360 + 0.0602524i
\(688\) 0 0
\(689\) −18474.9 9001.90i −1.02153 0.497743i
\(690\) 0 0
\(691\) −1884.22 + 1087.86i −0.103733 + 0.0598901i −0.550969 0.834526i \(-0.685742\pi\)
0.447236 + 0.894416i \(0.352408\pi\)
\(692\) 0 0
\(693\) −5726.10 + 9917.89i −0.313876 + 0.543650i
\(694\) 0 0
\(695\) −1164.14 672.118i −0.0635373 0.0366833i
\(696\) 0 0
\(697\) 2063.82i 0.112156i
\(698\) 0 0
\(699\) −413.177 715.644i −0.0223574 0.0387241i
\(700\) 0 0
\(701\) 32718.2 1.76284 0.881419 0.472335i \(-0.156589\pi\)
0.881419 + 0.472335i \(0.156589\pi\)
\(702\) 0 0
\(703\) 1173.85 0.0629768
\(704\) 0 0
\(705\) 2691.18 + 4661.26i 0.143767 + 0.249012i
\(706\) 0 0
\(707\) 30128.6i 1.60269i
\(708\) 0 0
\(709\) −21840.9 12609.8i −1.15691 0.667945i −0.206352 0.978478i \(-0.566159\pi\)
−0.950563 + 0.310533i \(0.899492\pi\)
\(710\) 0 0
\(711\) −4040.19 + 6997.81i −0.213107 + 0.369112i
\(712\) 0 0
\(713\) 5075.10 2930.11i 0.266569 0.153904i
\(714\) 0 0
\(715\) 1789.79 + 25452.7i 0.0936146 + 1.33130i
\(716\) 0 0
\(717\) 3973.48 2294.09i 0.206963 0.119490i
\(718\) 0 0
\(719\) 17733.1 30714.6i 0.919796 1.59313i 0.120071 0.992765i \(-0.461688\pi\)
0.799724 0.600368i \(-0.204979\pi\)
\(720\) 0 0
\(721\) 17283.9 + 9978.85i 0.892767 + 0.515439i
\(722\) 0 0
\(723\) 2926.58i 0.150540i
\(724\) 0 0
\(725\) −4291.78 7433.59i −0.219852 0.380795i
\(726\) 0 0
\(727\) −14262.2 −0.727588 −0.363794 0.931479i \(-0.618519\pi\)
−0.363794 + 0.931479i \(0.618519\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −7379.80 12782.2i −0.373395 0.646739i
\(732\) 0 0
\(733\) 16022.5i 0.807371i 0.914898 + 0.403685i \(0.132271\pi\)
−0.914898 + 0.403685i \(0.867729\pi\)
\(734\) 0 0
\(735\) 22502.9 + 12992.1i 1.12930 + 0.651999i
\(736\) 0 0
\(737\) 4664.05 8078.38i 0.233111 0.403760i
\(738\) 0 0
\(739\) 3287.61 1898.11i 0.163649 0.0944830i −0.415939 0.909393i \(-0.636547\pi\)
0.579588 + 0.814910i \(0.303214\pi\)
\(740\) 0 0
\(741\) −1661.65 + 3410.26i −0.0823782 + 0.169068i
\(742\) 0 0
\(743\) 26266.0 15164.7i 1.29691 0.748772i 0.317042 0.948412i \(-0.397310\pi\)
0.979869 + 0.199639i \(0.0639771\pi\)
\(744\) 0 0
\(745\) 1005.20 1741.05i 0.0494331 0.0856206i
\(746\) 0 0
\(747\) −10134.4 5851.09i −0.496382 0.286586i
\(748\) 0 0
\(749\) 45509.1i 2.22011i
\(750\) 0 0
\(751\) −10775.9 18664.5i −0.523595 0.906893i −0.999623 0.0274629i \(-0.991257\pi\)
0.476028 0.879430i \(-0.342076\pi\)
\(752\) 0 0
\(753\) −5622.42 −0.272101
\(754\) 0 0
\(755\) 10754.3 0.518397
\(756\) 0 0
\(757\) 10208.8 + 17682.2i 0.490153 + 0.848970i 0.999936 0.0113335i \(-0.00360764\pi\)
−0.509783 + 0.860303i \(0.670274\pi\)
\(758\) 0 0
\(759\) 2309.50i 0.110447i
\(760\) 0 0
\(761\) −27171.9 15687.7i −1.29432 0.747278i −0.314906 0.949123i \(-0.601973\pi\)
−0.979417 + 0.201845i \(0.935306\pi\)
\(762\) 0 0
\(763\) 5201.64 9009.50i 0.246805 0.427478i
\(764\) 0 0
\(765\) 4520.05 2609.65i 0.213625 0.123336i
\(766\) 0 0
\(767\) −15487.7 22942.2i −0.729111 1.08004i
\(768\) 0 0
\(769\) 10784.3 6226.33i 0.505712 0.291973i −0.225357 0.974276i \(-0.572355\pi\)
0.731069 + 0.682303i \(0.239022\pi\)
\(770\) 0 0
\(771\) −2727.28 + 4723.79i −0.127394 + 0.220653i
\(772\) 0 0
\(773\) 32432.4 + 18724.9i 1.50907 + 0.871264i 0.999944 + 0.0105740i \(0.00336588\pi\)
0.509129 + 0.860690i \(0.329967\pi\)
\(774\) 0 0
\(775\) 17169.8i 0.795815i
\(776\) 0 0
\(777\) 2050.82 + 3552.13i 0.0946884 + 0.164005i
\(778\) 0 0
\(779\) −1290.58 −0.0593580
\(780\) 0 0
\(781\) 18199.5 0.833839
\(782\) 0 0
\(783\) 2080.50 + 3603.54i 0.0949568 + 0.164470i
\(784\) 0 0
\(785\) 36377.1i 1.65396i
\(786\) 0 0
\(787\) 22915.2 + 13230.1i 1.03791 + 0.599240i 0.919242 0.393694i \(-0.128803\pi\)
0.118672 + 0.992934i \(0.462136\pi\)
\(788\) 0 0
\(789\) 1010.70 1750.58i 0.0456043 0.0789890i