Properties

Label 336.4.q.k.193.3
Level $336$
Weight $4$
Character 336.193
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 193.3
Root \(0.124036 + 0.214837i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.4.q.k.289.3

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.997818 + 0.0660299i \(0.0210333\pi\)
−0.441725 + 0.897150i \(0.645633\pi\)
\(6\) 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 −0.0741379 0.997248i \(-0.523621\pi\)
0.900711 0.434419i \(-0.143046\pi\)
\(12\) 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 −0.638119 0.769937i \(-0.720287\pi\)
0.985845 + 0.167659i \(0.0536207\pi\)
\(18\) 0 0
\(19\) −25.2750 43.7776i −0.305183 0.528593i 0.672119 0.740443i \(-0.265384\pi\)
−0.977302 + 0.211851i \(0.932051\pi\)
\(20\) 0 0
\(21\) −23.1403 + 50.5126i −0.240459 + 0.524893i
\(22\) 0 0
\(23\) 69.3962 + 120.198i 0.629135 + 1.08969i 0.987726 + 0.156199i \(0.0499241\pi\)
−0.358590 + 0.933495i \(0.616743\pi\)
\(24\) 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 −0.867714 0.497064i \(-0.834412\pi\)
0.864327 + 0.502931i \(0.167745\pi\)
\(32\) 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 0.778401 0.627767i \(-0.216031\pi\)
−0.932863 + 0.360232i \(0.882698\pi\)
\(38\) 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 0.992178 + 0.124829i \(0.0398382\pi\)
−0.387984 + 0.921666i \(0.626828\pi\)
\(48\) 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 −0.994678 0.103033i \(-0.967145\pi\)
0.586568 + 0.809900i \(0.300479\pi\)
\(54\) 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 0.151455 0.988464i \(-0.451604\pi\)
0.780308 0.625396i \(-0.215062\pi\)
\(60\) 0 0
\(61\) 169.269 + 293.182i 0.355290 + 0.615380i 0.987167 0.159688i \(-0.0510489\pi\)
−0.631878 + 0.775068i \(0.717716\pi\)
\(62\) 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 −0.0409498 + 0.999161i \(0.513038\pi\)
−0.844824 + 0.535044i \(0.820295\pi\)
\(68\) 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 0.427268 + 0.904125i \(0.359476\pi\)
−0.996629 + 0.0820374i \(0.973857\pi\)
\(74\) 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 0.638960 0.769240i \(-0.279365\pi\)
−0.985661 + 0.168736i \(0.946031\pi\)
\(80\) 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 0.793762 0.608229i \(-0.208120\pi\)
−0.923622 + 0.383303i \(0.874786\pi\)
\(90\) 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 −0.779003 0.627021i \(-0.784274\pi\)
0.932517 + 0.361126i \(0.117608\pi\)
\(102\) 0 0
\(103\) −74.6289 129.261i −0.0713922 0.123655i 0.828119 0.560552i \(-0.189411\pi\)
−0.899512 + 0.436897i \(0.856078\pi\)
\(104\) 0 0
\(105\) −687.825 + 64.8613i −0.639284 + 0.0602839i
\(106\) 0 0
\(107\) 425.760 + 737.437i 0.384670 + 0.666269i 0.991723 0.128393i \(-0.0409818\pi\)
−0.607053 + 0.794661i \(0.707648\pi\)
\(108\) 0 0
\(109\) −680.939 + 1179.42i −0.598369 + 1.03640i 0.394694 + 0.918813i \(0.370851\pi\)
−0.993062 + 0.117592i \(0.962483\pi\)
\(110\) 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 −0.989789 0.142541i \(-0.954473\pi\)
0.371451 0.928453i \(-0.378861\pi\)
\(132\) 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 −0.775271 0.631628i \(-0.782387\pi\)
0.934642 + 0.355591i \(0.115720\pi\)
\(138\) 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 0.580843 0.814016i \(-0.302723\pi\)
−0.995380 + 0.0960168i \(0.969390\pi\)
\(150\) 0 0
\(151\) 795.913 1378.56i 0.428943 0.742952i −0.567836 0.823142i \(-0.692219\pi\)
0.996780 + 0.0801897i \(0.0255526\pi\)
\(152\) 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 −0.975192 0.221361i \(-0.928950\pi\)
0.679300 + 0.733861i \(0.262283\pi\)
\(158\) 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 0.693101 0.720841i \(-0.256244\pi\)
−0.970817 + 0.239822i \(0.922911\pi\)
\(164\) 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 0.579188 0.815194i \(-0.303370\pi\)
−0.995573 + 0.0939940i \(0.970037\pi\)
\(174\) 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 −0.0619893 + 0.998077i \(0.519744\pi\)
−0.833365 + 0.552723i \(0.813589\pi\)
\(180\) 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 0.900208 0.435460i \(-0.143414\pi\)
−0.827224 + 0.561873i \(0.810081\pi\)
\(192\) 0 0
\(193\) −315.112 + 545.790i −0.117525 + 0.203559i −0.918786 0.394756i \(-0.870829\pi\)
0.801262 + 0.598314i \(0.204163\pi\)
\(194\) 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 −0.946750 0.321970i \(-0.895655\pi\)
0.752209 + 0.658924i \(0.228988\pi\)
\(200\) 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 −0.649895 0.760024i \(-0.725187\pi\)
0.983148 + 0.182813i \(0.0585203\pi\)
\(228\) 0 0
\(229\) −2706.34 4687.51i −0.780960 1.35266i −0.931383 0.364040i \(-0.881397\pi\)
0.150424 0.988622i \(-0.451936\pi\)
\(230\) 0 0
\(231\) 1940.53 + 2731.90i 0.552715 + 0.778120i
\(232\) 0 0
\(233\) −569.184 985.856i −0.160036 0.277191i 0.774845 0.632151i \(-0.217828\pi\)
−0.934882 + 0.354960i \(0.884494\pi\)
\(234\) 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 −0.569471 0.822012i \(-0.692852\pi\)
0.996618 + 0.0821704i \(0.0261852\pi\)
\(242\) 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 0.820481 0.571674i \(-0.193706\pi\)
−0.905325 + 0.424720i \(0.860372\pi\)
\(258\) 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 −0.914854 0.403785i \(-0.867694\pi\)
0.807115 + 0.590394i \(0.201028\pi\)
\(264\) 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 −0.664468 0.747317i \(-0.731342\pi\)
0.979429 + 0.201788i \(0.0646751\pi\)
\(270\) 0 0
\(271\) 1113.49 + 1928.62i 0.249593 + 0.432308i 0.963413 0.268021i \(-0.0863698\pi\)
−0.713820 + 0.700329i \(0.753036\pi\)
\(272\) 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 0.131821 + 0.991273i \(0.457917\pi\)
−0.924379 + 0.381476i \(0.875416\pi\)
\(278\) 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 −0.943872 0.330312i \(-0.892846\pi\)
0.757994 + 0.652261i \(0.226179\pi\)
\(284\) 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 −0.806469 0.591276i \(-0.798624\pi\)
0.915295 + 0.402785i \(0.131958\pi\)
\(312\) 0 0
\(313\) 4423.02 + 7660.89i 0.798734 + 1.38345i 0.920441 + 0.390882i \(0.127830\pi\)
−0.121707 + 0.992566i \(0.538837\pi\)
\(314\) 0 0
\(315\) 863.223 1884.31i 0.154403 0.337045i
\(316\) 0 0
\(317\) −3040.72 5266.68i −0.538750 0.933142i −0.998972 0.0453380i \(-0.985564\pi\)
0.460222 0.887804i \(-0.347770\pi\)
\(318\) 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 0.964490 0.264119i \(-0.0850813\pi\)
−0.710979 + 0.703213i \(0.751748\pi\)
\(332\) 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 −0.869852 0.493313i \(-0.835786\pi\)
0.862148 + 0.506657i \(0.169119\pi\)
\(348\) 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 0.461455 + 0.887164i \(0.347328\pi\)
−0.999034 + 0.0439501i \(0.986006\pi\)
\(354\) 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 0.521860 0.853031i \(-0.325238\pi\)
−0.999677 + 0.0254289i \(0.991905\pi\)
\(360\) 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 −0.835202 0.549943i \(-0.814650\pi\)
0.893866 + 0.448335i \(0.147983\pi\)
\(368\) 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 0.816016 0.578029i \(-0.196178\pi\)
−0.908596 + 0.417677i \(0.862845\pi\)
\(374\) 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 0.877571 0.479447i \(-0.159163\pi\)
−0.853998 + 0.520276i \(0.825829\pi\)
\(384\) 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 0.175387 + 0.984500i \(0.443882\pi\)
−0.940295 + 0.340360i \(0.889451\pi\)
\(390\) 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 −0.890300 0.455374i \(-0.849505\pi\)
0.0507841 0.998710i \(-0.483828\pi\)
\(398\) 0 0
\(399\) 2796.19 263.678i 0.350839 0.0330838i
\(400\) 0 0
\(401\) 3741.18 + 6479.91i 0.465899 + 0.806961i 0.999242 0.0389385i \(-0.0123976\pi\)
−0.533343 + 0.845899i \(0.679064\pi\)
\(402\) 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 −0.0608735 0.998145i \(-0.519389\pi\)
0.894856 0.446355i \(-0.147278\pi\)
\(410\) 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 0.199840 + 0.979829i \(0.435958\pi\)
−0.948476 + 0.316848i \(0.897376\pi\)
\(432\) 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 −0.840114 0.542409i \(-0.817512\pi\)
−0.0496832 0.998765i \(-0.515821\pi\)
\(440\) 0 0
\(441\) −2016.05 2337.76i −0.217692 0.252430i
\(442\) 0 0
\(443\) −589.354 1020.79i −0.0632078 0.109479i 0.832690 0.553740i \(-0.186800\pi\)
−0.895898 + 0.444261i \(0.853466\pi\)
\(444\) 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 −0.999957 0.00924618i \(-0.997057\pi\)
0.491971 0.870611i \(-0.336277\pi\)
\(458\) 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 0.913510 0.406815i \(-0.133361\pi\)
−0.809068 + 0.587716i \(0.800027\pi\)
\(468\) 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 −0.918519 0.395377i \(-0.870614\pi\)
0.801666 + 0.597772i \(0.203947\pi\)
\(480\) 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 −0.850626 0.525772i \(-0.823777\pi\)
0.880645 + 0.473778i \(0.157110\pi\)
\(488\) 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 0.865036 0.501709i \(-0.167295\pi\)
−0.867011 + 0.498289i \(0.833962\pi\)
\(500\) 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 0.675298 0.737545i \(-0.264015\pi\)
−0.976382 + 0.216052i \(0.930682\pi\)
\(510\) 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 0.433828 + 0.900996i \(0.357163\pi\)
−0.997199 + 0.0747919i \(0.976171\pi\)
\(522\) 0 0
\(523\) −4968.50 8605.69i −0.415406 0.719504i 0.580065 0.814570i \(-0.303027\pi\)
−0.995471 + 0.0950662i \(0.969694\pi\)
\(524\) 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 0.620421 0.784269i \(-0.286962\pi\)
−0.989407 + 0.145166i \(0.953628\pi\)
\(542\) 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 −0.898325 0.439332i \(-0.855215\pi\)
0.829635 + 0.558306i \(0.188549\pi\)
\(558\) 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 −0.541621 0.840623i \(-0.682189\pi\)
0.998811 + 0.0487460i \(0.0155225\pi\)
\(564\) 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 0.776270 0.630400i \(-0.217109\pi\)
−0.934078 + 0.357070i \(0.883776\pi\)
\(570\) 0 0
\(571\) 3179.97 5507.87i 0.233060 0.403673i −0.725647 0.688067i \(-0.758459\pi\)
0.958707 + 0.284395i \(0.0917927\pi\)
\(572\) 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 0.477715 + 0.878515i \(0.341465\pi\)
−0.999674 + 0.0255444i \(0.991868\pi\)
\(578\) 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 0.973522 + 0.228592i \(0.0734123\pi\)
−0.288794 + 0.957391i \(0.593254\pi\)
\(594\) 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 0.0946282 + 0.995513i \(0.469834\pi\)
−0.909453 + 0.415806i \(0.863500\pi\)
\(600\) 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 0.999905 0.0137724i \(-0.00438402\pi\)
−0.511880 + 0.859057i \(0.671051\pi\)
\(608\) 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 −0.896793 0.442451i \(-0.854109\pi\)
0.831570 + 0.555420i \(0.187442\pi\)
\(614\) 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 −0.992486 0.122358i \(-0.960954\pi\)
0.602208 + 0.798339i \(0.294288\pi\)
\(620\) 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 −0.776476 0.630147i \(-0.782995\pi\)
0.933961 + 0.357374i \(0.116328\pi\)
\(642\) 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 0.438352 + 0.898804i \(0.355563\pi\)
−0.997563 + 0.0697783i \(0.977771\pi\)
\(648\) 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 −0.993272 0.115805i \(-0.963055\pi\)
0.396346 0.918101i \(-0.370278\pi\)
\(654\) 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 0.182815 + 0.983147i \(0.441479\pi\)
−0.942838 + 0.333251i \(0.891854\pi\)
\(662\) 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 0.949857 + 0.312683i \(0.101228\pi\)
−0.204137 + 0.978942i \(0.565439\pi\)
\(678\) 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 −0.956654 0.291226i \(-0.905937\pi\)
0.730536 + 0.682874i \(0.239270\pi\)
\(684\) 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 −0.976761 0.214332i \(-0.931243\pi\)
0.302763 0.953066i \(-0.402091\pi\)
\(692\) 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 0.985389 + 0.170322i \(0.0544806\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(710\) 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 0.864962 0.501838i \(-0.167343\pi\)
−0.867085 + 0.498160i \(0.834009\pi\)
\(720\) 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 0.922790 0.385304i \(-0.125903\pi\)
−0.795078 + 0.606507i \(0.792570\pi\)
\(734\) 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 −0.225392 + 0.974268i \(0.572366\pi\)
−0.731045 + 0.682329i \(0.760967\pi\)
\(740\) 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 0.947585 0.319505i \(-0.103517\pi\)
−0.750492 + 0.660880i \(0.770183\pi\)
\(752\) 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 0.939038 0.343812i \(-0.111718\pi\)
−0.767269 + 0.641325i \(0.778385\pi\)
\(762\) 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 −0.418012 0.908442i \(-0.637273\pi\)
0.995739 0.0922122i \(-0.0293938\pi\)
\(774\) 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 −0.0815287 0.996671i \(-0.525980\pi\)
0.903907 0.427730i \(-0.140686\pi\)
\(788\) 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