Properties

Label 336.4.q.k.289.3
Level $336$
Weight $4$
Character 336.289
Analytic conductor $19.825$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.9924270768.1
Defining polynomial: \(x^{6} - x^{5} + 25 x^{4} + 12 x^{3} + 582 x^{2} - 144 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.3
Root \(0.124036 - 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.4.q.k.193.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +(6.21730 - 10.7687i) q^{5} +(18.4385 + 1.73873i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(30.1558 + 52.2313i) q^{11} +36.4269 q^{13} -37.3038 q^{15} +(24.3731 + 42.2154i) q^{17} +(-25.2750 + 43.7776i) q^{19} +(-23.1403 - 50.5126i) q^{21} +(69.3962 - 120.198i) q^{23} +(-14.8097 - 25.6511i) q^{25} +27.0000 q^{27} -61.1345 q^{29} +(-0.584676 - 1.01269i) q^{31} +(90.4673 - 156.694i) q^{33} +(133.361 - 187.748i) q^{35} +(-34.7634 + 60.2120i) q^{37} +(-54.6403 - 94.6398i) q^{39} +308.115 q^{41} -174.443 q^{43} +(55.9557 + 96.9181i) q^{45} +(194.681 - 337.197i) q^{47} +(336.954 + 64.1190i) q^{49} +(73.1192 - 126.646i) q^{51} +(-157.467 - 272.742i) q^{53} +749.950 q^{55} +151.650 q^{57} +(422.263 + 731.381i) q^{59} +(169.269 - 293.182i) q^{61} +(-96.5251 + 135.889i) q^{63} +(226.477 - 392.270i) q^{65} +(-485.775 - 841.387i) q^{67} -416.377 q^{69} +98.4698 q^{71} +(-355.117 - 615.082i) q^{73} +(-44.4291 + 76.9534i) q^{75} +(465.210 + 1015.50i) q^{77} +(-243.442 + 421.654i) q^{79} +(-40.5000 - 70.1481i) q^{81} -605.688 q^{83} +606.139 q^{85} +(91.7017 + 158.832i) q^{87} +(-109.034 + 188.853i) q^{89} +(671.656 + 63.3365i) q^{91} +(-1.75403 + 3.03807i) q^{93} +(314.284 + 544.357i) q^{95} -782.288 q^{97} -542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 9q^{3} - 11q^{5} + 13q^{7} - 27q^{9} + O(q^{10}) \) \( 6q - 9q^{3} - 11q^{5} + 13q^{7} - 27q^{9} + 35q^{11} + 124q^{13} + 66q^{15} - 48q^{17} - 202q^{19} + 3q^{21} + 216q^{23} - 130q^{25} + 162q^{27} + 106q^{29} - 95q^{31} + 105q^{33} - 56q^{35} - 262q^{37} - 186q^{39} + 488q^{41} - 720q^{43} - 99q^{45} - 210q^{47} - 303q^{49} - 144q^{51} - 393q^{53} + 2062q^{55} + 1212q^{57} + 1143q^{59} + 70q^{61} - 126q^{63} + 472q^{65} - 628q^{67} - 1296q^{69} - 636q^{71} - 988q^{73} - 390q^{75} + 1073q^{77} + 861q^{79} - 243q^{81} - 1038q^{83} + 3600q^{85} - 159q^{87} - 1766q^{89} + 654q^{91} - 285q^{93} - 736q^{95} + 38q^{97} - 630q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 6.21730 10.7687i 0.556092 0.963180i −0.441725 0.897150i \(-0.645633\pi\)
0.997818 0.0660299i \(-0.0210333\pi\)
\(6\) 0 0
\(7\) 18.4385 + 1.73873i 0.995583 + 0.0938826i
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 30.1558 + 52.2313i 0.826573 + 1.43167i 0.900711 + 0.434419i \(0.143046\pi\)
−0.0741379 + 0.997248i \(0.523621\pi\)
\(12\) 0 0
\(13\) 36.4269 0.777154 0.388577 0.921416i \(-0.372967\pi\)
0.388577 + 0.921416i \(0.372967\pi\)
\(14\) 0 0
\(15\) −37.3038 −0.642120
\(16\) 0 0
\(17\) 24.3731 + 42.2154i 0.347726 + 0.602279i 0.985845 0.167659i \(-0.0536207\pi\)
−0.638119 + 0.769937i \(0.720287\pi\)
\(18\) 0 0
\(19\) −25.2750 + 43.7776i −0.305183 + 0.528593i −0.977302 0.211851i \(-0.932051\pi\)
0.672119 + 0.740443i \(0.265384\pi\)
\(20\) 0 0
\(21\) −23.1403 50.5126i −0.240459 0.524893i
\(22\) 0 0
\(23\) 69.3962 120.198i 0.629135 1.08969i −0.358590 0.933495i \(-0.616743\pi\)
0.987726 0.156199i \(-0.0499241\pi\)
\(24\) 0 0
\(25\) −14.8097 25.6511i −0.118478 0.205209i
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −61.1345 −0.391462 −0.195731 0.980658i \(-0.562708\pi\)
−0.195731 + 0.980658i \(0.562708\pi\)
\(30\) 0 0
\(31\) −0.584676 1.01269i −0.00338745 0.00586724i 0.864327 0.502931i \(-0.167745\pi\)
−0.867714 + 0.497064i \(0.834412\pi\)
\(32\) 0 0
\(33\) 90.4673 156.694i 0.477222 0.826573i
\(34\) 0 0
\(35\) 133.361 187.748i 0.644062 0.906719i
\(36\) 0 0
\(37\) −34.7634 + 60.2120i −0.154461 + 0.267535i −0.932863 0.360232i \(-0.882698\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(38\) 0 0
\(39\) −54.6403 94.6398i −0.224345 0.388577i
\(40\) 0 0
\(41\) 308.115 1.17365 0.586823 0.809715i \(-0.300378\pi\)
0.586823 + 0.809715i \(0.300378\pi\)
\(42\) 0 0
\(43\) −174.443 −0.618657 −0.309329 0.950955i \(-0.600104\pi\)
−0.309329 + 0.950955i \(0.600104\pi\)
\(44\) 0 0
\(45\) 55.9557 + 96.9181i 0.185364 + 0.321060i
\(46\) 0 0
\(47\) 194.681 337.197i 0.604194 1.04649i −0.387984 0.921666i \(-0.626828\pi\)
0.992178 0.124829i \(-0.0398382\pi\)
\(48\) 0 0
\(49\) 336.954 + 64.1190i 0.982372 + 0.186936i
\(50\) 0 0
\(51\) 73.1192 126.646i 0.200760 0.347726i
\(52\) 0 0
\(53\) −157.467 272.742i −0.408110 0.706867i 0.586568 0.809900i \(-0.300479\pi\)
−0.994678 + 0.103033i \(0.967145\pi\)
\(54\) 0 0
\(55\) 749.950 1.83860
\(56\) 0 0
\(57\) 151.650 0.352395
\(58\) 0 0
\(59\) 422.263 + 731.381i 0.931762 + 1.61386i 0.780308 + 0.625396i \(0.215062\pi\)
0.151455 + 0.988464i \(0.451604\pi\)
\(60\) 0 0
\(61\) 169.269 293.182i 0.355290 0.615380i −0.631878 0.775068i \(-0.717716\pi\)
0.987167 + 0.159688i \(0.0510489\pi\)
\(62\) 0 0
\(63\) −96.5251 + 135.889i −0.193032 + 0.271753i
\(64\) 0 0
\(65\) 226.477 392.270i 0.432169 0.748539i
\(66\) 0 0
\(67\) −485.775 841.387i −0.885774 1.53421i −0.844824 0.535044i \(-0.820295\pi\)
−0.0409498 0.999161i \(-0.513038\pi\)
\(68\) 0 0
\(69\) −416.377 −0.726463
\(70\) 0 0
\(71\) 98.4698 0.164595 0.0822973 0.996608i \(-0.473774\pi\)
0.0822973 + 0.996608i \(0.473774\pi\)
\(72\) 0 0
\(73\) −355.117 615.082i −0.569361 0.986162i −0.996629 0.0820374i \(-0.973857\pi\)
0.427268 0.904125i \(-0.359476\pi\)
\(74\) 0 0
\(75\) −44.4291 + 76.9534i −0.0684030 + 0.118478i
\(76\) 0 0
\(77\) 465.210 + 1015.50i 0.688514 + 1.50294i
\(78\) 0 0
\(79\) −243.442 + 421.654i −0.346701 + 0.600504i −0.985661 0.168736i \(-0.946031\pi\)
0.638960 + 0.769240i \(0.279365\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −605.688 −0.800999 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(84\) 0 0
\(85\) 606.139 0.773470
\(86\) 0 0
\(87\) 91.7017 + 158.832i 0.113005 + 0.195731i
\(88\) 0 0
\(89\) −109.034 + 188.853i −0.129861 + 0.224925i −0.923622 0.383303i \(-0.874786\pi\)
0.793762 + 0.608229i \(0.208120\pi\)
\(90\) 0 0
\(91\) 671.656 + 63.3365i 0.773722 + 0.0729612i
\(92\) 0 0
\(93\) −1.75403 + 3.03807i −0.00195575 + 0.00338745i
\(94\) 0 0
\(95\) 314.284 + 544.357i 0.339420 + 0.587893i
\(96\) 0 0
\(97\) −782.288 −0.818859 −0.409429 0.912342i \(-0.634272\pi\)
−0.409429 + 0.912342i \(0.634272\pi\)
\(98\) 0 0
\(99\) −542.804 −0.551049
\(100\) 0 0
\(101\) 155.823 + 269.893i 0.153514 + 0.265895i 0.932517 0.361126i \(-0.117608\pi\)
−0.779003 + 0.627021i \(0.784274\pi\)
\(102\) 0 0
\(103\) −74.6289 + 129.261i −0.0713922 + 0.123655i −0.899512 0.436897i \(-0.856078\pi\)
0.828119 + 0.560552i \(0.189411\pi\)
\(104\) 0 0
\(105\) −687.825 64.8613i −0.639284 0.0602839i
\(106\) 0 0
\(107\) 425.760 737.437i 0.384670 0.666269i −0.607053 0.794661i \(-0.707648\pi\)
0.991723 + 0.128393i \(0.0409818\pi\)
\(108\) 0 0
\(109\) −680.939 1179.42i −0.598369 1.03640i −0.993062 0.117592i \(-0.962483\pi\)
0.394694 0.918813i \(-0.370851\pi\)
\(110\) 0 0
\(111\) 208.581 0.178357
\(112\) 0 0
\(113\) 1048.55 0.872917 0.436459 0.899724i \(-0.356233\pi\)
0.436459 + 0.899724i \(0.356233\pi\)
\(114\) 0 0
\(115\) −862.914 1494.61i −0.699715 1.21194i
\(116\) 0 0
\(117\) −163.921 + 283.920i −0.129526 + 0.224345i
\(118\) 0 0
\(119\) 376.001 + 820.765i 0.289646 + 0.632264i
\(120\) 0 0
\(121\) −1153.24 + 1997.47i −0.866446 + 1.50073i
\(122\) 0 0
\(123\) −462.173 800.507i −0.338803 0.586823i
\(124\) 0 0
\(125\) 1186.02 0.848647
\(126\) 0 0
\(127\) −488.408 −0.341254 −0.170627 0.985336i \(-0.554579\pi\)
−0.170627 + 0.985336i \(0.554579\pi\)
\(128\) 0 0
\(129\) 261.664 + 453.215i 0.178591 + 0.309329i
\(130\) 0 0
\(131\) −927.114 + 1605.81i −0.618338 + 1.07099i 0.371451 + 0.928453i \(0.378861\pi\)
−0.989789 + 0.142541i \(0.954473\pi\)
\(132\) 0 0
\(133\) −542.149 + 763.244i −0.353461 + 0.497607i
\(134\) 0 0
\(135\) 167.867 290.754i 0.107020 0.185364i
\(136\) 0 0
\(137\) 255.558 + 442.639i 0.159370 + 0.276038i 0.934642 0.355591i \(-0.115720\pi\)
−0.775271 + 0.631628i \(0.782387\pi\)
\(138\) 0 0
\(139\) −2266.10 −1.38279 −0.691397 0.722475i \(-0.743005\pi\)
−0.691397 + 0.722475i \(0.743005\pi\)
\(140\) 0 0
\(141\) −1168.09 −0.697663
\(142\) 0 0
\(143\) 1098.48 + 1902.62i 0.642375 + 1.11263i
\(144\) 0 0
\(145\) −380.091 + 658.338i −0.217689 + 0.377048i
\(146\) 0 0
\(147\) −338.844 971.610i −0.190118 0.545150i
\(148\) 0 0
\(149\) −753.950 + 1305.88i −0.414537 + 0.717999i −0.995380 0.0960168i \(-0.969390\pi\)
0.580843 + 0.814016i \(0.302723\pi\)
\(150\) 0 0
\(151\) 795.913 + 1378.56i 0.428943 + 0.742952i 0.996780 0.0801897i \(-0.0255526\pi\)
−0.567836 + 0.823142i \(0.692219\pi\)
\(152\) 0 0
\(153\) −438.715 −0.231817
\(154\) 0 0
\(155\) −14.5404 −0.00753494
\(156\) 0 0
\(157\) −582.080 1008.19i −0.295892 0.512500i 0.679300 0.733861i \(-0.262283\pi\)
−0.975192 + 0.221361i \(0.928950\pi\)
\(158\) 0 0
\(159\) −472.402 + 818.225i −0.235622 + 0.408110i
\(160\) 0 0
\(161\) 1488.55 2095.60i 0.728660 1.02582i
\(162\) 0 0
\(163\) −577.940 + 1001.02i −0.277716 + 0.481019i −0.970817 0.239822i \(-0.922911\pi\)
0.693101 + 0.720841i \(0.256244\pi\)
\(164\) 0 0
\(165\) −1124.92 1948.43i −0.530759 0.919302i
\(166\) 0 0
\(167\) 2890.61 1.33941 0.669707 0.742626i \(-0.266420\pi\)
0.669707 + 0.742626i \(0.266420\pi\)
\(168\) 0 0
\(169\) −870.082 −0.396032
\(170\) 0 0
\(171\) −227.475 393.998i −0.101728 0.176198i
\(172\) 0 0
\(173\) −947.468 + 1641.06i −0.416385 + 0.721200i −0.995573 0.0939940i \(-0.970037\pi\)
0.579188 + 0.815194i \(0.303370\pi\)
\(174\) 0 0
\(175\) −228.467 498.718i −0.0986887 0.215426i
\(176\) 0 0
\(177\) 1266.79 2194.14i 0.537953 0.931762i
\(178\) 0 0
\(179\) −2144.25 3713.94i −0.895355 1.55080i −0.833365 0.552723i \(-0.813589\pi\)
−0.0619893 0.998077i \(-0.519744\pi\)
\(180\) 0 0
\(181\) 383.732 0.157583 0.0787917 0.996891i \(-0.474894\pi\)
0.0787917 + 0.996891i \(0.474894\pi\)
\(182\) 0 0
\(183\) −1015.61 −0.410253
\(184\) 0 0
\(185\) 432.269 + 748.712i 0.171790 + 0.297548i
\(186\) 0 0
\(187\) −1469.98 + 2546.07i −0.574841 + 0.995655i
\(188\) 0 0
\(189\) 497.838 + 46.9457i 0.191600 + 0.0180677i
\(190\) 0 0
\(191\) 192.655 333.689i 0.0729845 0.126413i −0.827224 0.561873i \(-0.810081\pi\)
0.900208 + 0.435460i \(0.143414\pi\)
\(192\) 0 0
\(193\) −315.112 545.790i −0.117525 0.203559i 0.801262 0.598314i \(-0.204163\pi\)
−0.918786 + 0.394756i \(0.870829\pi\)
\(194\) 0 0
\(195\) −1358.86 −0.499026
\(196\) 0 0
\(197\) −1250.23 −0.452158 −0.226079 0.974109i \(-0.572591\pi\)
−0.226079 + 0.974109i \(0.572591\pi\)
\(198\) 0 0
\(199\) −546.122 945.912i −0.194541 0.336954i 0.752209 0.658924i \(-0.228988\pi\)
−0.946750 + 0.321970i \(0.895655\pi\)
\(200\) 0 0
\(201\) −1457.32 + 2524.16i −0.511402 + 0.885774i
\(202\) 0 0
\(203\) −1127.23 106.296i −0.389733 0.0367514i
\(204\) 0 0
\(205\) 1915.65 3318.00i 0.652656 1.13043i
\(206\) 0 0
\(207\) 624.566 + 1081.78i 0.209712 + 0.363231i
\(208\) 0 0
\(209\) −3048.75 −1.00902
\(210\) 0 0
\(211\) 3620.05 1.18111 0.590556 0.806997i \(-0.298909\pi\)
0.590556 + 0.806997i \(0.298909\pi\)
\(212\) 0 0
\(213\) −147.705 255.832i −0.0475143 0.0822973i
\(214\) 0 0
\(215\) −1084.56 + 1878.52i −0.344030 + 0.595878i
\(216\) 0 0
\(217\) −9.01974 19.6890i −0.00282166 0.00615935i
\(218\) 0 0
\(219\) −1065.35 + 1845.24i −0.328721 + 0.569361i
\(220\) 0 0
\(221\) 887.835 + 1537.78i 0.270236 + 0.468063i
\(222\) 0 0
\(223\) 183.844 0.0552069 0.0276034 0.999619i \(-0.491212\pi\)
0.0276034 + 0.999619i \(0.491212\pi\)
\(224\) 0 0
\(225\) 266.574 0.0789850
\(226\) 0 0
\(227\) 1139.76 + 1974.12i 0.333253 + 0.577211i 0.983148 0.182813i \(-0.0585203\pi\)
−0.649895 + 0.760024i \(0.725187\pi\)
\(228\) 0 0
\(229\) −2706.34 + 4687.51i −0.780960 + 1.35266i 0.150424 + 0.988622i \(0.451936\pi\)
−0.931383 + 0.364040i \(0.881397\pi\)
\(230\) 0 0
\(231\) 1940.53 2731.90i 0.552715 0.778120i
\(232\) 0 0
\(233\) −569.184 + 985.856i −0.160036 + 0.277191i −0.934882 0.354960i \(-0.884494\pi\)
0.774845 + 0.632151i \(0.217828\pi\)
\(234\) 0 0
\(235\) −2420.78 4192.91i −0.671975 1.16390i
\(236\) 0 0
\(237\) 1460.65 0.400336
\(238\) 0 0
\(239\) 6226.36 1.68515 0.842573 0.538583i \(-0.181040\pi\)
0.842573 + 0.538583i \(0.181040\pi\)
\(240\) 0 0
\(241\) 1598.10 + 2767.99i 0.427147 + 0.739841i 0.996618 0.0821704i \(-0.0261852\pi\)
−0.569471 + 0.822012i \(0.692852\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 2785.42 3229.90i 0.726343 0.842248i
\(246\) 0 0
\(247\) −920.689 + 1594.68i −0.237174 + 0.410798i
\(248\) 0 0
\(249\) 908.532 + 1573.62i 0.231228 + 0.400499i
\(250\) 0 0
\(251\) −239.608 −0.0602546 −0.0301273 0.999546i \(-0.509591\pi\)
−0.0301273 + 0.999546i \(0.509591\pi\)
\(252\) 0 0
\(253\) 8370.78 2.08010
\(254\) 0 0
\(255\) −909.208 1574.79i −0.223282 0.386735i
\(256\) 0 0
\(257\) −349.559 + 605.453i −0.0848439 + 0.146954i −0.905325 0.424720i \(-0.860372\pi\)
0.820481 + 0.571674i \(0.193706\pi\)
\(258\) 0 0
\(259\) −745.676 + 1049.77i −0.178896 + 0.251852i
\(260\) 0 0
\(261\) 275.105 476.496i 0.0652436 0.113005i
\(262\) 0 0
\(263\) −459.520 795.912i −0.107738 0.186609i 0.807115 0.590394i \(-0.201028\pi\)
−0.914854 + 0.403785i \(0.867694\pi\)
\(264\) 0 0
\(265\) −3916.09 −0.907787
\(266\) 0 0
\(267\) 654.206 0.149950
\(268\) 0 0
\(269\) 1389.59 + 2406.84i 0.314961 + 0.545529i 0.979429 0.201788i \(-0.0646751\pi\)
−0.664468 + 0.747317i \(0.731342\pi\)
\(270\) 0 0
\(271\) 1113.49 1928.62i 0.249593 0.432308i −0.713820 0.700329i \(-0.753036\pi\)
0.963413 + 0.268021i \(0.0863698\pi\)
\(272\) 0 0
\(273\) −842.931 1840.02i −0.186874 0.407923i
\(274\) 0 0
\(275\) 893.195 1547.06i 0.195861 0.339241i
\(276\) 0 0
\(277\) −3653.85 6328.65i −0.792557 1.37275i −0.924379 0.381476i \(-0.875416\pi\)
0.131821 0.991273i \(-0.457917\pi\)
\(278\) 0 0
\(279\) 10.5242 0.00225830
\(280\) 0 0
\(281\) 2730.61 0.579696 0.289848 0.957073i \(-0.406395\pi\)
0.289848 + 0.957073i \(0.406395\pi\)
\(282\) 0 0
\(283\) −884.926 1532.74i −0.185878 0.321950i 0.757994 0.652261i \(-0.226179\pi\)
−0.943872 + 0.330312i \(0.892846\pi\)
\(284\) 0 0
\(285\) 942.853 1633.07i 0.195964 0.339420i
\(286\) 0 0
\(287\) 5681.17 + 535.729i 1.16846 + 0.110185i
\(288\) 0 0
\(289\) 1268.41 2196.95i 0.258174 0.447170i
\(290\) 0 0
\(291\) 1173.43 + 2032.44i 0.236384 + 0.409429i
\(292\) 0 0
\(293\) 8228.81 1.64072 0.820362 0.571844i \(-0.193772\pi\)
0.820362 + 0.571844i \(0.193772\pi\)
\(294\) 0 0
\(295\) 10501.4 2.07258
\(296\) 0 0
\(297\) 814.206 + 1410.25i 0.159074 + 0.275524i
\(298\) 0 0
\(299\) 2527.89 4378.43i 0.488935 0.846860i
\(300\) 0 0
\(301\) −3216.45 303.309i −0.615925 0.0580811i
\(302\) 0 0
\(303\) 467.468 809.679i 0.0886316 0.153514i
\(304\) 0 0
\(305\) −2104.79 3645.61i −0.395148 0.684416i
\(306\) 0 0
\(307\) −6019.62 −1.11908 −0.559541 0.828803i \(-0.689023\pi\)
−0.559541 + 0.828803i \(0.689023\pi\)
\(308\) 0 0
\(309\) 447.773 0.0824366
\(310\) 0 0
\(311\) 596.857 + 1033.79i 0.108825 + 0.188491i 0.915295 0.402785i \(-0.131958\pi\)
−0.806469 + 0.591276i \(0.798624\pi\)
\(312\) 0 0
\(313\) 4423.02 7660.89i 0.798734 1.38345i −0.121707 0.992566i \(-0.538837\pi\)
0.920441 0.390882i \(-0.127830\pi\)
\(314\) 0 0
\(315\) 863.223 + 1884.31i 0.154403 + 0.337045i
\(316\) 0 0
\(317\) −3040.72 + 5266.68i −0.538750 + 0.933142i 0.460222 + 0.887804i \(0.347770\pi\)
−0.998972 + 0.0453380i \(0.985564\pi\)
\(318\) 0 0
\(319\) −1843.56 3193.13i −0.323572 0.560442i
\(320\) 0 0
\(321\) −2554.56 −0.444179
\(322\) 0 0
\(323\) −2464.12 −0.424480
\(324\) 0 0
\(325\) −539.471 934.391i −0.0920753 0.159479i
\(326\) 0 0
\(327\) −2042.82 + 3538.26i −0.345468 + 0.598369i
\(328\) 0 0
\(329\) 4175.91 5878.90i 0.699773 0.985149i
\(330\) 0 0
\(331\) 1526.65 2644.23i 0.253511 0.439094i −0.710979 0.703213i \(-0.751748\pi\)
0.964490 + 0.264119i \(0.0850813\pi\)
\(332\) 0 0
\(333\) −312.871 541.908i −0.0514871 0.0891783i
\(334\) 0 0
\(335\) −12080.8 −1.97029
\(336\) 0 0
\(337\) 3865.80 0.624877 0.312438 0.949938i \(-0.398854\pi\)
0.312438 + 0.949938i \(0.398854\pi\)
\(338\) 0 0
\(339\) −1572.83 2724.22i −0.251989 0.436459i
\(340\) 0 0
\(341\) 35.2627 61.0768i 0.00559995 0.00969940i
\(342\) 0 0
\(343\) 6101.42 + 1768.13i 0.960483 + 0.278338i
\(344\) 0 0
\(345\) −2588.74 + 4483.83i −0.403980 + 0.699715i
\(346\) 0 0
\(347\) −49.7965 86.2501i −0.00770380 0.0133434i 0.862148 0.506657i \(-0.169119\pi\)
−0.869852 + 0.493313i \(0.835786\pi\)
\(348\) 0 0
\(349\) −3607.34 −0.553285 −0.276643 0.960973i \(-0.589222\pi\)
−0.276643 + 0.960973i \(0.589222\pi\)
\(350\) 0 0
\(351\) 983.526 0.149563
\(352\) 0 0
\(353\) −3565.37 6175.40i −0.537579 0.931114i −0.999034 0.0439501i \(-0.986006\pi\)
0.461455 0.887164i \(-0.347328\pi\)
\(354\) 0 0
\(355\) 612.216 1060.39i 0.0915298 0.158534i
\(356\) 0 0
\(357\) 1568.41 2208.03i 0.232518 0.327342i
\(358\) 0 0
\(359\) −3250.14 + 5629.41i −0.477816 + 0.827602i −0.999677 0.0254289i \(-0.991905\pi\)
0.521860 + 0.853031i \(0.325238\pi\)
\(360\) 0 0
\(361\) 2151.85 + 3727.11i 0.313727 + 0.543390i
\(362\) 0 0
\(363\) 6919.44 1.00049
\(364\) 0 0
\(365\) −8831.49 −1.26647
\(366\) 0 0
\(367\) 412.443 + 714.372i 0.0586631 + 0.101607i 0.893866 0.448335i \(-0.147983\pi\)
−0.835202 + 0.549943i \(0.814650\pi\)
\(368\) 0 0
\(369\) −1386.52 + 2401.52i −0.195608 + 0.338803i
\(370\) 0 0
\(371\) −2429.23 5302.73i −0.339945 0.742059i
\(372\) 0 0
\(373\) −666.925 + 1155.15i −0.0925793 + 0.160352i −0.908596 0.417677i \(-0.862845\pi\)
0.816016 + 0.578029i \(0.196178\pi\)
\(374\) 0 0
\(375\) −1779.03 3081.37i −0.244983 0.424324i
\(376\) 0 0
\(377\) −2226.94 −0.304226
\(378\) 0 0
\(379\) 1338.29 0.181380 0.0906902 0.995879i \(-0.471093\pi\)
0.0906902 + 0.995879i \(0.471093\pi\)
\(380\) 0 0
\(381\) 732.612 + 1268.92i 0.0985114 + 0.170627i
\(382\) 0 0
\(383\) 176.688 306.032i 0.0235727 0.0408290i −0.853998 0.520276i \(-0.825829\pi\)
0.877571 + 0.479447i \(0.159163\pi\)
\(384\) 0 0
\(385\) 13827.9 + 1303.96i 1.83048 + 0.172613i
\(386\) 0 0
\(387\) 784.992 1359.65i 0.103110 0.178591i
\(388\) 0 0
\(389\) −5868.59 10164.7i −0.764908 1.32486i −0.940295 0.340360i \(-0.889451\pi\)
0.175387 0.984500i \(-0.443882\pi\)
\(390\) 0 0
\(391\) 6765.59 0.875066
\(392\) 0 0
\(393\) 5562.68 0.713996
\(394\) 0 0
\(395\) 3027.11 + 5243.10i 0.385595 + 0.667871i
\(396\) 0 0
\(397\) −6640.71 + 11502.1i −0.839516 + 1.45408i 0.0507841 + 0.998710i \(0.483828\pi\)
−0.890300 + 0.455374i \(0.849505\pi\)
\(398\) 0 0
\(399\) 2796.19 + 263.678i 0.350839 + 0.0330838i
\(400\) 0 0
\(401\) 3741.18 6479.91i 0.465899 0.806961i −0.533343 0.845899i \(-0.679064\pi\)
0.999242 + 0.0389385i \(0.0123976\pi\)
\(402\) 0 0
\(403\) −21.2979 36.8891i −0.00263257 0.00455975i
\(404\) 0 0
\(405\) −1007.20 −0.123576
\(406\) 0 0
\(407\) −4193.27 −0.510694
\(408\) 0 0
\(409\) 6898.30 + 11948.2i 0.833983 + 1.44450i 0.894856 + 0.446355i \(0.147278\pi\)
−0.0608735 + 0.998145i \(0.519389\pi\)
\(410\) 0 0
\(411\) 766.673 1327.92i 0.0920126 0.159370i
\(412\) 0 0
\(413\) 6514.21 + 14219.7i 0.776134 + 1.69421i
\(414\) 0 0
\(415\) −3765.75 + 6522.46i −0.445429 + 0.771506i
\(416\) 0 0
\(417\) 3399.16 + 5887.51i 0.399179 + 0.691397i
\(418\) 0 0
\(419\) −9497.56 −1.10737 −0.553683 0.832728i \(-0.686778\pi\)
−0.553683 + 0.832728i \(0.686778\pi\)
\(420\) 0 0
\(421\) 624.367 0.0722797 0.0361399 0.999347i \(-0.488494\pi\)
0.0361399 + 0.999347i \(0.488494\pi\)
\(422\) 0 0
\(423\) 1752.13 + 3034.77i 0.201398 + 0.348832i
\(424\) 0 0
\(425\) 721.915 1250.39i 0.0823954 0.142713i
\(426\) 0 0
\(427\) 3630.82 5111.52i 0.411494 0.579306i
\(428\) 0 0
\(429\) 3295.44 5707.87i 0.370875 0.642375i
\(430\) 0 0
\(431\) −6698.64 11602.4i −0.748636 1.29668i −0.948476 0.316848i \(-0.897376\pi\)
0.199840 0.979829i \(-0.435958\pi\)
\(432\) 0 0
\(433\) −14057.3 −1.56016 −0.780079 0.625681i \(-0.784821\pi\)
−0.780079 + 0.625681i \(0.784821\pi\)
\(434\) 0 0
\(435\) 2280.55 0.251365
\(436\) 0 0
\(437\) 3507.98 + 6075.99i 0.384003 + 0.665112i
\(438\) 0 0
\(439\) −8184.42 + 14175.8i −0.889798 + 1.54117i −0.0496832 + 0.998765i \(0.515821\pi\)
−0.840114 + 0.542409i \(0.817512\pi\)
\(440\) 0 0
\(441\) −2016.05 + 2337.76i −0.217692 + 0.252430i
\(442\) 0 0
\(443\) −589.354 + 1020.79i −0.0632078 + 0.109479i −0.895898 0.444261i \(-0.853466\pi\)
0.832690 + 0.553740i \(0.186800\pi\)
\(444\) 0 0
\(445\) 1355.80 + 2348.31i 0.144429 + 0.250159i
\(446\) 0 0
\(447\) 4523.70 0.478666
\(448\) 0 0
\(449\) −12400.9 −1.30342 −0.651709 0.758469i \(-0.725948\pi\)
−0.651709 + 0.758469i \(0.725948\pi\)
\(450\) 0 0
\(451\) 9291.45 + 16093.3i 0.970105 + 1.68027i
\(452\) 0 0
\(453\) 2387.74 4135.68i 0.247651 0.428943i
\(454\) 0 0
\(455\) 4857.94 6839.07i 0.500535 0.704660i
\(456\) 0 0
\(457\) −4962.79 + 8595.81i −0.507986 + 0.879858i 0.491971 + 0.870611i \(0.336277\pi\)
−0.999957 + 0.00924618i \(0.997057\pi\)
\(458\) 0 0
\(459\) 658.073 + 1139.82i 0.0669198 + 0.115909i
\(460\) 0 0
\(461\) −16010.3 −1.61751 −0.808755 0.588146i \(-0.799858\pi\)
−0.808755 + 0.588146i \(0.799858\pi\)
\(462\) 0 0
\(463\) −17372.4 −1.74377 −0.871883 0.489714i \(-0.837101\pi\)
−0.871883 + 0.489714i \(0.837101\pi\)
\(464\) 0 0
\(465\) 21.8107 + 37.7772i 0.00217515 + 0.00376747i
\(466\) 0 0
\(467\) 1054.03 1825.64i 0.104443 0.180900i −0.809068 0.587716i \(-0.800027\pi\)
0.913510 + 0.406815i \(0.133361\pi\)
\(468\) 0 0
\(469\) −7494.00 16358.5i −0.737826 1.61059i
\(470\) 0 0
\(471\) −1746.24 + 3024.58i −0.170833 + 0.295892i
\(472\) 0 0
\(473\) −5260.45 9111.37i −0.511365 0.885711i
\(474\) 0 0
\(475\) 1497.26 0.144629
\(476\) 0 0
\(477\) 2834.41 0.272073
\(478\) 0 0
\(479\) −1225.02 2121.80i −0.116853 0.202395i 0.801666 0.597772i \(-0.203947\pi\)
−0.918519 + 0.395377i \(0.870614\pi\)
\(480\) 0 0
\(481\) −1266.32 + 2193.34i −0.120040 + 0.207916i
\(482\) 0 0
\(483\) −7677.35 723.967i −0.723254 0.0682022i
\(484\) 0 0
\(485\) −4863.72 + 8424.21i −0.455361 + 0.788709i
\(486\) 0 0
\(487\) 322.618 + 558.791i 0.0300189 + 0.0519943i 0.880645 0.473778i \(-0.157110\pi\)
−0.850626 + 0.525772i \(0.823777\pi\)
\(488\) 0 0
\(489\) 3467.64 0.320679
\(490\) 0 0
\(491\) −11766.1 −1.08146 −0.540731 0.841196i \(-0.681852\pi\)
−0.540731 + 0.841196i \(0.681852\pi\)
\(492\) 0 0
\(493\) −1490.03 2580.81i −0.136121 0.235769i
\(494\) 0 0
\(495\) −3374.77 + 5845.28i −0.306434 + 0.530759i
\(496\) 0 0
\(497\) 1815.63 + 171.212i 0.163868 + 0.0154526i
\(498\) 0 0
\(499\) −22.0104 + 38.1232i −0.00197459 + 0.00342010i −0.867011 0.498289i \(-0.833962\pi\)
0.865036 + 0.501709i \(0.167295\pi\)
\(500\) 0 0
\(501\) −4335.91 7510.02i −0.386655 0.669707i
\(502\) 0 0
\(503\) −8290.27 −0.734880 −0.367440 0.930047i \(-0.619766\pi\)
−0.367440 + 0.930047i \(0.619766\pi\)
\(504\) 0 0
\(505\) 3875.19 0.341473
\(506\) 0 0
\(507\) 1305.12 + 2260.54i 0.114324 + 0.198016i
\(508\) 0 0
\(509\) −3457.52 + 5988.60i −0.301084 + 0.521493i −0.976382 0.216052i \(-0.930682\pi\)
0.675298 + 0.737545i \(0.264015\pi\)
\(510\) 0 0
\(511\) −5478.36 11958.6i −0.474263 1.03526i
\(512\) 0 0
\(513\) −682.425 + 1181.99i −0.0587325 + 0.101728i
\(514\) 0 0
\(515\) 927.980 + 1607.31i 0.0794014 + 0.137527i
\(516\) 0 0
\(517\) 23483.0 1.99764
\(518\) 0 0
\(519\) 5684.81 0.480800
\(520\) 0 0
\(521\) −6699.64 11604.1i −0.563371 0.975788i −0.997199 0.0747919i \(-0.976171\pi\)
0.433828 0.900996i \(-0.357163\pi\)
\(522\) 0 0
\(523\) −4968.50 + 8605.69i −0.415406 + 0.719504i −0.995471 0.0950662i \(-0.969694\pi\)
0.580065 + 0.814570i \(0.303027\pi\)
\(524\) 0 0
\(525\) −953.005 + 1341.65i −0.0792239 + 0.111532i
\(526\) 0 0
\(527\) 28.5007 49.3647i 0.00235581 0.00408038i
\(528\) 0 0
\(529\) −3548.17 6145.60i −0.291622 0.505104i
\(530\) 0 0
\(531\) −7600.74 −0.621175
\(532\) 0 0
\(533\) 11223.7 0.912104
\(534\) 0 0
\(535\) −5294.15 9169.74i −0.427825 0.741014i
\(536\) 0 0
\(537\) −6432.74 + 11141.8i −0.516933 + 0.895355i
\(538\) 0 0
\(539\) 6812.07 + 19533.1i 0.544373 + 1.56095i
\(540\) 0 0
\(541\) −4643.08 + 8042.06i −0.368987 + 0.639103i −0.989407 0.145166i \(-0.953628\pi\)
0.620421 + 0.784269i \(0.286962\pi\)
\(542\) 0 0
\(543\) −575.599 996.966i −0.0454904 0.0787917i
\(544\) 0 0
\(545\) −16934.4 −1.33099
\(546\) 0 0
\(547\) 16821.6 1.31488 0.657438 0.753508i \(-0.271640\pi\)
0.657438 + 0.753508i \(0.271640\pi\)
\(548\) 0 0
\(549\) 1523.42 + 2638.64i 0.118430 + 0.205127i
\(550\) 0 0
\(551\) 1545.17 2676.32i 0.119467 0.206924i
\(552\) 0 0
\(553\) −5221.84 + 7351.37i −0.401546 + 0.565302i
\(554\) 0 0
\(555\) 1296.81 2246.14i 0.0991828 0.171790i
\(556\) 0 0
\(557\) −902.972 1563.99i −0.0686897 0.118974i 0.829635 0.558306i \(-0.188549\pi\)
−0.898325 + 0.439332i \(0.855215\pi\)
\(558\) 0 0
\(559\) −6354.40 −0.480792
\(560\) 0 0
\(561\) 8819.86 0.663770
\(562\) 0 0
\(563\) 6107.45 + 10578.4i 0.457190 + 0.791877i 0.998811 0.0487460i \(-0.0155225\pi\)
−0.541621 + 0.840623i \(0.682189\pi\)
\(564\) 0 0
\(565\) 6519.17 11291.5i 0.485423 0.840776i
\(566\) 0 0
\(567\) −624.789 1363.84i −0.0462763 0.101016i
\(568\) 0 0
\(569\) −2141.89 + 3709.86i −0.157808 + 0.273331i −0.934078 0.357070i \(-0.883776\pi\)
0.776270 + 0.630400i \(0.217109\pi\)
\(570\) 0 0
\(571\) 3179.97 + 5507.87i 0.233060 + 0.403673i 0.958707 0.284395i \(-0.0917927\pi\)
−0.725647 + 0.688067i \(0.758459\pi\)
\(572\) 0 0
\(573\) −1155.93 −0.0842753
\(574\) 0 0
\(575\) −4110.95 −0.298153
\(576\) 0 0
\(577\) −7234.36 12530.3i −0.521959 0.904059i −0.999674 0.0255444i \(-0.991868\pi\)
0.477715 0.878515i \(-0.341465\pi\)
\(578\) 0 0
\(579\) −945.335 + 1637.37i −0.0678528 + 0.117525i
\(580\) 0 0
\(581\) −11168.0 1053.13i −0.797461 0.0751998i
\(582\) 0 0
\(583\) 9497.10 16449.5i 0.674665 1.16855i
\(584\) 0 0
\(585\) 2038.29 + 3530.43i 0.144056 + 0.249513i
\(586\) 0 0
\(587\) 11132.6 0.782777 0.391388 0.920226i \(-0.371995\pi\)
0.391388 + 0.920226i \(0.371995\pi\)
\(588\) 0 0
\(589\) 59.1108 0.00413517
\(590\) 0 0
\(591\) 1875.34 + 3248.19i 0.130527 + 0.226079i
\(592\) 0 0
\(593\) 9887.81 17126.2i 0.684728 1.18598i −0.288794 0.957391i \(-0.593254\pi\)
0.973522 0.228592i \(-0.0734123\pi\)
\(594\) 0 0
\(595\) 11176.3 + 1053.91i 0.770054 + 0.0726154i
\(596\) 0 0
\(597\) −1638.37 + 2837.73i −0.112318 + 0.194541i
\(598\) 0 0
\(599\) −11945.5 20690.2i −0.814825 1.41132i −0.909453 0.415806i \(-0.863500\pi\)
0.0946282 0.995513i \(-0.469834\pi\)
\(600\) 0 0
\(601\) 19395.5 1.31641 0.658204 0.752840i \(-0.271317\pi\)
0.658204 + 0.752840i \(0.271317\pi\)
\(602\) 0 0
\(603\) 8743.95 0.590516
\(604\) 0 0
\(605\) 14340.1 + 24837.8i 0.963648 + 1.66909i
\(606\) 0 0
\(607\) 7298.36 12641.1i 0.488025 0.845285i −0.511880 0.859057i \(-0.671051\pi\)
0.999905 + 0.0137724i \(0.00438402\pi\)
\(608\) 0 0
\(609\) 1414.67 + 3088.06i 0.0941304 + 0.205475i
\(610\) 0 0
\(611\) 7091.62 12283.0i 0.469552 0.813288i
\(612\) 0 0
\(613\) −989.898 1714.55i −0.0652229 0.112969i 0.831570 0.555420i \(-0.187442\pi\)
−0.896793 + 0.442451i \(0.854109\pi\)
\(614\) 0 0
\(615\) −11493.9 −0.753622
\(616\) 0 0
\(617\) 16262.4 1.06110 0.530551 0.847653i \(-0.321985\pi\)
0.530551 + 0.847653i \(0.321985\pi\)
\(618\) 0 0
\(619\) −6010.49 10410.5i −0.390278 0.675981i 0.602208 0.798339i \(-0.294288\pi\)
−0.992486 + 0.122358i \(0.960954\pi\)
\(620\) 0 0
\(621\) 1873.70 3245.34i 0.121077 0.209712i
\(622\) 0 0
\(623\) −2338.79 + 3292.58i −0.150404 + 0.211740i
\(624\) 0 0
\(625\) 9225.06 15978.3i 0.590404 1.02261i
\(626\) 0 0
\(627\) 4573.12 + 7920.87i 0.291280 + 0.504512i
\(628\) 0 0
\(629\) −3389.16 −0.214841
\(630\) 0 0
\(631\) −25347.6 −1.59916 −0.799582 0.600557i \(-0.794945\pi\)
−0.799582 + 0.600557i \(0.794945\pi\)
\(632\) 0 0
\(633\) −5430.07 9405.16i −0.340957 0.590556i
\(634\) 0 0
\(635\) −3036.58 + 5259.51i −0.189769 + 0.328689i
\(636\) 0 0
\(637\) 12274.2 + 2335.66i 0.763454 + 0.145278i
\(638\) 0 0
\(639\) −443.114 + 767.496i −0.0274324 + 0.0475143i
\(640\) 0 0
\(641\) 2555.80 + 4426.78i 0.157485 + 0.272772i 0.933961 0.357374i \(-0.116328\pi\)
−0.776476 + 0.630147i \(0.782995\pi\)
\(642\) 0 0
\(643\) 10931.3 0.670435 0.335217 0.942141i \(-0.391190\pi\)
0.335217 + 0.942141i \(0.391190\pi\)
\(644\) 0 0
\(645\) 6507.38 0.397252
\(646\) 0 0
\(647\) −9203.06 15940.2i −0.559211 0.968582i −0.997563 0.0697783i \(-0.977771\pi\)
0.438352 0.898804i \(-0.355563\pi\)
\(648\) 0 0
\(649\) −25467.3 + 44110.7i −1.54034 + 2.66795i
\(650\) 0 0
\(651\) −37.6240 + 52.9675i −0.00226513 + 0.00318888i
\(652\) 0 0
\(653\) −9960.71 + 17252.5i −0.596926 + 1.03391i 0.396346 + 0.918101i \(0.370278\pi\)
−0.993272 + 0.115805i \(0.963055\pi\)
\(654\) 0 0
\(655\) 11528.3 + 19967.6i 0.687707 + 1.19114i
\(656\) 0 0
\(657\) 6392.11 0.379574
\(658\) 0 0
\(659\) 18858.8 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(660\) 0 0
\(661\) −12916.0 22371.2i −0.760023 1.31640i −0.942838 0.333251i \(-0.891854\pi\)
0.182815 0.983147i \(-0.441479\pi\)
\(662\) 0 0
\(663\) 2663.50 4613.33i 0.156021 0.270236i
\(664\) 0 0
\(665\) 4848.43 + 10583.6i 0.282728 + 0.617162i
\(666\) 0 0
\(667\) −4242.50 + 7348.22i −0.246282 + 0.426573i
\(668\) 0 0
\(669\) −275.767 477.642i −0.0159369 0.0276034i
\(670\) 0 0
\(671\) 20417.7 1.17469
\(672\) 0 0
\(673\) −16275.0 −0.932178 −0.466089 0.884738i \(-0.654337\pi\)
−0.466089 + 0.884738i \(0.654337\pi\)
\(674\) 0 0
\(675\) −399.862 692.581i −0.0228010 0.0394925i
\(676\) 0 0
\(677\) 13135.9 22752.0i 0.745720 1.29163i −0.204137 0.978942i \(-0.565439\pi\)
0.949857 0.312683i \(-0.101228\pi\)
\(678\) 0 0
\(679\) −14424.2 1360.19i −0.815242 0.0768766i
\(680\) 0 0
\(681\) 3419.28 5922.36i 0.192404 0.333253i
\(682\) 0 0
\(683\) −4036.14 6990.81i −0.226118 0.391648i 0.730536 0.682874i \(-0.239270\pi\)
−0.956654 + 0.291226i \(0.905937\pi\)
\(684\) 0 0
\(685\) 6355.51 0.354499
\(686\) 0 0
\(687\) 16238.0 0.901774
\(688\) 0 0
\(689\) −5736.05 9935.13i −0.317164 0.549344i
\(690\) 0 0
\(691\) −12242.6 + 21204.9i −0.673997 + 1.16740i 0.302763 + 0.953066i \(0.402091\pi\)
−0.976761 + 0.214332i \(0.931243\pi\)
\(692\) 0 0
\(693\) −10008.5 943.789i −0.548615 0.0517339i
\(694\) 0 0
\(695\) −14089.1 + 24403.0i −0.768962 + 1.33188i
\(696\) 0 0
\(697\) 7509.71 + 13007.2i 0.408107 + 0.706862i
\(698\) 0 0
\(699\) 3415.10 0.184794
\(700\) 0 0
\(701\) 778.448 0.0419423 0.0209712 0.999780i \(-0.493324\pi\)
0.0209712 + 0.999780i \(0.493324\pi\)
\(702\) 0 0
\(703\) −1757.29 3043.72i −0.0942780 0.163294i
\(704\) 0 0
\(705\) −7262.34 + 12578.7i −0.387965 + 0.671975i
\(706\) 0 0
\(707\) 2403.86 + 5247.35i 0.127873 + 0.279133i
\(708\) 0 0
\(709\) 12086.0 20933.6i 0.640197 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170322i \(-0.0544806\pi\)
\(710\) 0 0
\(711\) −2190.98 3794.89i −0.115567 0.200168i
\(712\) 0 0
\(713\) −162.297 −0.00852466
\(714\) 0 0
\(715\) 27318.3 1.42888
\(716\) 0 0
\(717\) −9339.54 16176.6i −0.486460 0.842573i
\(718\) 0 0
\(719\) −40.9418 + 70.9132i −0.00212360 + 0.00367819i −0.867085 0.498160i \(-0.834009\pi\)
0.864962 + 0.501838i \(0.167343\pi\)
\(720\) 0 0
\(721\) −1600.79 + 2253.61i −0.0826860 + 0.116406i
\(722\) 0 0
\(723\) 4794.29 8303.96i 0.246614 0.427147i
\(724\) 0 0
\(725\) 905.382 + 1568.17i 0.0463794 + 0.0803315i
\(726\) 0 0
\(727\) 32542.9 1.66018 0.830088 0.557632i \(-0.188290\pi\)
0.830088 + 0.557632i \(0.188290\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −4251.70 7364.16i −0.215123 0.372604i
\(732\) 0 0
\(733\) 2534.47 4389.83i 0.127712 0.221203i −0.795078 0.606507i \(-0.792570\pi\)
0.922790 + 0.385304i \(0.125903\pi\)
\(734\) 0 0
\(735\) −12569.7 2391.88i −0.630801 0.120035i
\(736\) 0 0
\(737\) 29297.8 50745.3i 1.46431 2.53627i
\(738\) 0 0
\(739\) −19214.2 33280.0i −0.956437 1.65660i −0.731045 0.682329i \(-0.760967\pi\)
−0.225392 0.974268i \(-0.572366\pi\)
\(740\) 0 0
\(741\) 5524.14 0.273865
\(742\) 0 0
\(743\) −21592.9 −1.06617 −0.533086 0.846061i \(-0.678968\pi\)
−0.533086 + 0.846061i \(0.678968\pi\)
\(744\) 0 0
\(745\) 9375.07 + 16238.1i 0.461042 + 0.798548i
\(746\) 0 0
\(747\) 2725.60 4720.87i 0.133500 0.231228i
\(748\) 0 0
\(749\) 9132.55 12856.9i 0.445522 0.627212i
\(750\) 0 0
\(751\) 4056.30 7025.72i 0.197093 0.341374i −0.750492 0.660880i \(-0.770183\pi\)
0.947585 + 0.319505i \(0.103517\pi\)
\(752\) 0 0
\(753\) 359.411 + 622.519i 0.0173940 + 0.0301273i
\(754\) 0 0
\(755\) 19793.7 0.954129
\(756\) 0 0
\(757\) 3108.01 0.149224 0.0746120 0.997213i \(-0.476228\pi\)
0.0746120 + 0.997213i \(0.476228\pi\)
\(758\) 0 0
\(759\) −12556.2 21747.9i −0.600475 1.04005i
\(760\) 0 0
\(761\) 3605.96 6245.71i 0.171769 0.297512i −0.767269 0.641325i \(-0.778385\pi\)
0.939038 + 0.343812i \(0.111718\pi\)
\(762\) 0 0
\(763\) −10504.8 22930.7i −0.498425 1.08800i
\(764\) 0 0
\(765\) −2727.62 + 4724.38i −0.128912 + 0.223282i
\(766\) 0 0
\(767\) 15381.7 + 26641.9i 0.724123 + 1.25422i
\(768\) 0 0
\(769\) −7533.07 −0.353250 −0.176625 0.984278i \(-0.556518\pi\)
−0.176625 + 0.984278i \(0.556518\pi\)
\(770\) 0 0
\(771\) 2097.35 0.0979693
\(772\) 0 0
\(773\) 12416.3 + 21505.7i 0.577728 + 1.00065i 0.995739 + 0.0922122i \(0.0293938\pi\)
−0.418012 + 0.908442i \(0.637273\pi\)
\(774\) 0 0
\(775\) −17.3178 + 29.9952i −0.000802674 + 0.00139027i
\(776\) 0 0
\(777\) 3845.90 + 362.665i 0.177569 + 0.0167446i
\(778\) 0 0
\(779\) −7787.61 + 13488.5i −0.358177 + 0.620381i
\(780\) 0 0
\(781\) 2969.43 + 5143.20i 0.136049 + 0.235644i
\(782\) 0 0
\(783\) −1650.63 −0.0753368
\(784\) 0 0
\(785\) −14475.9 −0.658173
\(786\) 0 0
\(787\) 18156.6 + 31448.1i 0.822378 + 1.42440i 0.903907 + 0.427730i \(0.140686\pi\)
−0.0815287 + 0.996671i \(0.525980\pi\)
\(788\) 0 0
\(789\) −1378.56 + 2387.74i −0.0622028 + 0.107738i
\(790\) 0 0
\(791\) 19333.7 + 1823.15i 0.869062 + 0.0819517i
\(792\) 0 0