Properties

Label 224.3.n.a.17.2
Level 224
Weight 3
Character 224.17
Analytic conductor 6.104
Analytic rank 0
Dimension 28
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.94818 + 3.37434i) q^{3} +(4.42985 + 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +O(q^{10})\) \(q+(-1.94818 + 3.37434i) q^{3} +(4.42985 + 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +(-3.15749 - 1.82298i) q^{11} +7.79378 q^{13} -34.5205 q^{15} +(-9.07152 - 5.23744i) q^{17} +(5.39264 + 9.34032i) q^{19} +(-16.9751 + 21.3482i) q^{21} +(-6.45553 - 11.1813i) q^{23} +(-26.7471 + 46.3273i) q^{25} -10.9817 q^{27} -17.2327i q^{29} +(26.1797 + 15.1148i) q^{31} +(12.3027 - 7.10296i) q^{33} +(22.7396 + 57.6986i) q^{35} +(-34.2810 + 19.7922i) q^{37} +(-15.1837 + 26.2989i) q^{39} -73.6801i q^{41} -40.8501i q^{43} +(27.3833 - 47.4293i) q^{45} +(36.2025 - 20.9015i) q^{47} +(46.8639 + 14.3100i) q^{49} +(35.3458 - 20.4069i) q^{51} +(5.55272 + 3.20586i) q^{53} -32.3020i q^{55} -42.0232 q^{57} +(-7.95742 + 13.7827i) q^{59} +(6.07848 + 10.5282i) q^{61} +(-15.8658 - 40.2572i) q^{63} +(34.5253 + 59.7995i) q^{65} +(6.75274 + 3.89870i) q^{67} +50.3060 q^{69} +41.3627 q^{71} +(77.6038 + 44.8046i) q^{73} +(-104.216 - 180.507i) q^{75} +(-19.9762 - 15.8842i) q^{77} +(35.3975 + 61.3103i) q^{79} +(49.2112 - 85.2363i) q^{81} -60.8673 q^{83} -92.8043i q^{85} +(58.1489 + 33.5723i) q^{87} +(-23.4004 + 13.5102i) q^{89} +(53.9586 + 8.05463i) q^{91} +(-102.005 + 58.8927i) q^{93} +(-47.7771 + 82.7524i) q^{95} +3.26608i q^{97} +22.5377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.94818 + 3.37434i −0.649392 + 1.12478i 0.333876 + 0.942617i \(0.391643\pi\)
−0.983268 + 0.182163i \(0.941690\pi\)
\(4\) 0 0
\(5\) 4.42985 + 7.67272i 0.885969 + 1.53454i 0.844599 + 0.535400i \(0.179839\pi\)
0.0413705 + 0.999144i \(0.486828\pi\)
\(6\) 0 0
\(7\) 6.92329 + 1.03347i 0.989041 + 0.147638i
\(8\) 0 0
\(9\) −3.09078 5.35338i −0.343420 0.594820i
\(10\) 0 0
\(11\) −3.15749 1.82298i −0.287045 0.165725i 0.349564 0.936913i \(-0.386330\pi\)
−0.636608 + 0.771187i \(0.719663\pi\)
\(12\) 0 0
\(13\) 7.79378 0.599522 0.299761 0.954014i \(-0.403093\pi\)
0.299761 + 0.954014i \(0.403093\pi\)
\(14\) 0 0
\(15\) −34.5205 −2.30136
\(16\) 0 0
\(17\) −9.07152 5.23744i −0.533619 0.308085i 0.208870 0.977943i \(-0.433021\pi\)
−0.742489 + 0.669858i \(0.766355\pi\)
\(18\) 0 0
\(19\) 5.39264 + 9.34032i 0.283823 + 0.491596i 0.972323 0.233640i \(-0.0750639\pi\)
−0.688500 + 0.725236i \(0.741731\pi\)
\(20\) 0 0
\(21\) −16.9751 + 21.3482i −0.808336 + 1.01658i
\(22\) 0 0
\(23\) −6.45553 11.1813i −0.280675 0.486144i 0.690876 0.722973i \(-0.257225\pi\)
−0.971551 + 0.236829i \(0.923892\pi\)
\(24\) 0 0
\(25\) −26.7471 + 46.3273i −1.06988 + 1.85309i
\(26\) 0 0
\(27\) −10.9817 −0.406728
\(28\) 0 0
\(29\) 17.2327i 0.594231i −0.954842 0.297115i \(-0.903975\pi\)
0.954842 0.297115i \(-0.0960246\pi\)
\(30\) 0 0
\(31\) 26.1797 + 15.1148i 0.844505 + 0.487575i 0.858793 0.512323i \(-0.171215\pi\)
−0.0142878 + 0.999898i \(0.504548\pi\)
\(32\) 0 0
\(33\) 12.3027 7.10296i 0.372809 0.215241i
\(34\) 0 0
\(35\) 22.7396 + 57.6986i 0.649703 + 1.64853i
\(36\) 0 0
\(37\) −34.2810 + 19.7922i −0.926515 + 0.534924i −0.885708 0.464244i \(-0.846326\pi\)
−0.0408071 + 0.999167i \(0.512993\pi\)
\(38\) 0 0
\(39\) −15.1837 + 26.2989i −0.389324 + 0.674330i
\(40\) 0 0
\(41\) 73.6801i 1.79707i −0.438897 0.898537i \(-0.644631\pi\)
0.438897 0.898537i \(-0.355369\pi\)
\(42\) 0 0
\(43\) 40.8501i 0.950002i −0.879985 0.475001i \(-0.842448\pi\)
0.879985 0.475001i \(-0.157552\pi\)
\(44\) 0 0
\(45\) 27.3833 47.4293i 0.608518 1.05398i
\(46\) 0 0
\(47\) 36.2025 20.9015i 0.770266 0.444713i −0.0627038 0.998032i \(-0.519972\pi\)
0.832969 + 0.553319i \(0.186639\pi\)
\(48\) 0 0
\(49\) 46.8639 + 14.3100i 0.956406 + 0.292041i
\(50\) 0 0
\(51\) 35.3458 20.4069i 0.693055 0.400136i
\(52\) 0 0
\(53\) 5.55272 + 3.20586i 0.104768 + 0.0604880i 0.551469 0.834196i \(-0.314068\pi\)
−0.446700 + 0.894684i \(0.647401\pi\)
\(54\) 0 0
\(55\) 32.3020i 0.587310i
\(56\) 0 0
\(57\) −42.0232 −0.737249
\(58\) 0 0
\(59\) −7.95742 + 13.7827i −0.134871 + 0.233604i −0.925548 0.378629i \(-0.876395\pi\)
0.790677 + 0.612234i \(0.209729\pi\)
\(60\) 0 0
\(61\) 6.07848 + 10.5282i 0.0996472 + 0.172594i 0.911539 0.411214i \(-0.134895\pi\)
−0.811891 + 0.583808i \(0.801562\pi\)
\(62\) 0 0
\(63\) −15.8658 40.2572i −0.251838 0.639004i
\(64\) 0 0
\(65\) 34.5253 + 59.7995i 0.531158 + 0.919992i
\(66\) 0 0
\(67\) 6.75274 + 3.89870i 0.100787 + 0.0581895i 0.549546 0.835463i \(-0.314801\pi\)
−0.448759 + 0.893653i \(0.648134\pi\)
\(68\) 0 0
\(69\) 50.3060 0.729073
\(70\) 0 0
\(71\) 41.3627 0.582574 0.291287 0.956636i \(-0.405917\pi\)
0.291287 + 0.956636i \(0.405917\pi\)
\(72\) 0 0
\(73\) 77.6038 + 44.8046i 1.06307 + 0.613761i 0.926279 0.376839i \(-0.122989\pi\)
0.136787 + 0.990601i \(0.456322\pi\)
\(74\) 0 0
\(75\) −104.216 180.507i −1.38955 2.40677i
\(76\) 0 0
\(77\) −19.9762 15.8842i −0.259432 0.206288i
\(78\) 0 0
\(79\) 35.3975 + 61.3103i 0.448070 + 0.776080i 0.998260 0.0589594i \(-0.0187783\pi\)
−0.550191 + 0.835039i \(0.685445\pi\)
\(80\) 0 0
\(81\) 49.2112 85.2363i 0.607546 1.05230i
\(82\) 0 0
\(83\) −60.8673 −0.733341 −0.366671 0.930351i \(-0.619502\pi\)
−0.366671 + 0.930351i \(0.619502\pi\)
\(84\) 0 0
\(85\) 92.8043i 1.09182i
\(86\) 0 0
\(87\) 58.1489 + 33.5723i 0.668379 + 0.385889i
\(88\) 0 0
\(89\) −23.4004 + 13.5102i −0.262926 + 0.151800i −0.625668 0.780089i \(-0.715174\pi\)
0.362743 + 0.931889i \(0.381840\pi\)
\(90\) 0 0
\(91\) 53.9586 + 8.05463i 0.592952 + 0.0885124i
\(92\) 0 0
\(93\) −102.005 + 58.8927i −1.09683 + 0.633255i
\(94\) 0 0
\(95\) −47.7771 + 82.7524i −0.502917 + 0.871078i
\(96\) 0 0
\(97\) 3.26608i 0.0336710i 0.999858 + 0.0168355i \(0.00535916\pi\)
−0.999858 + 0.0168355i \(0.994641\pi\)
\(98\) 0 0
\(99\) 22.5377i 0.227653i
\(100\) 0 0
\(101\) 68.8571 119.264i 0.681754 1.18083i −0.292691 0.956207i \(-0.594551\pi\)
0.974445 0.224625i \(-0.0721158\pi\)
\(102\) 0 0
\(103\) −86.3243 + 49.8393i −0.838100 + 0.483877i −0.856618 0.515952i \(-0.827438\pi\)
0.0185182 + 0.999829i \(0.494105\pi\)
\(104\) 0 0
\(105\) −238.995 35.6758i −2.27615 0.339770i
\(106\) 0 0
\(107\) −81.4157 + 47.0054i −0.760894 + 0.439302i −0.829617 0.558333i \(-0.811441\pi\)
0.0687226 + 0.997636i \(0.478108\pi\)
\(108\) 0 0
\(109\) 169.697 + 97.9745i 1.55685 + 0.898849i 0.997555 + 0.0698815i \(0.0222621\pi\)
0.559297 + 0.828967i \(0.311071\pi\)
\(110\) 0 0
\(111\) 154.234i 1.38950i
\(112\) 0 0
\(113\) 101.873 0.901527 0.450763 0.892643i \(-0.351152\pi\)
0.450763 + 0.892643i \(0.351152\pi\)
\(114\) 0 0
\(115\) 57.1940 99.0629i 0.497339 0.861417i
\(116\) 0 0
\(117\) −24.0888 41.7231i −0.205887 0.356608i
\(118\) 0 0
\(119\) −57.3920 45.6355i −0.482286 0.383491i
\(120\) 0 0
\(121\) −53.8535 93.2770i −0.445070 0.770884i
\(122\) 0 0
\(123\) 248.622 + 143.542i 2.02131 + 1.16701i
\(124\) 0 0
\(125\) −252.449 −2.01960
\(126\) 0 0
\(127\) 139.079 1.09511 0.547554 0.836770i \(-0.315559\pi\)
0.547554 + 0.836770i \(0.315559\pi\)
\(128\) 0 0
\(129\) 137.842 + 79.5831i 1.06854 + 0.616924i
\(130\) 0 0
\(131\) 45.8526 + 79.4190i 0.350020 + 0.606252i 0.986252 0.165245i \(-0.0528416\pi\)
−0.636233 + 0.771497i \(0.719508\pi\)
\(132\) 0 0
\(133\) 27.6819 + 70.2389i 0.208134 + 0.528112i
\(134\) 0 0
\(135\) −48.6471 84.2592i −0.360349 0.624142i
\(136\) 0 0
\(137\) −99.7904 + 172.842i −0.728397 + 1.26162i 0.229163 + 0.973388i \(0.426401\pi\)
−0.957560 + 0.288233i \(0.906932\pi\)
\(138\) 0 0
\(139\) −39.4768 −0.284006 −0.142003 0.989866i \(-0.545354\pi\)
−0.142003 + 0.989866i \(0.545354\pi\)
\(140\) 0 0
\(141\) 162.879i 1.15517i
\(142\) 0 0
\(143\) −24.6088 14.2079i −0.172089 0.0993559i
\(144\) 0 0
\(145\) 132.222 76.3382i 0.911873 0.526470i
\(146\) 0 0
\(147\) −139.586 + 130.256i −0.949564 + 0.886097i
\(148\) 0 0
\(149\) −82.0846 + 47.3916i −0.550903 + 0.318064i −0.749486 0.662020i \(-0.769699\pi\)
0.198583 + 0.980084i \(0.436366\pi\)
\(150\) 0 0
\(151\) 33.2843 57.6501i 0.220426 0.381789i −0.734511 0.678596i \(-0.762589\pi\)
0.954937 + 0.296807i \(0.0959220\pi\)
\(152\) 0 0
\(153\) 64.7511i 0.423210i
\(154\) 0 0
\(155\) 267.826i 1.72791i
\(156\) 0 0
\(157\) 12.7597 22.1004i 0.0812720 0.140767i −0.822525 0.568730i \(-0.807435\pi\)
0.903797 + 0.427962i \(0.140768\pi\)
\(158\) 0 0
\(159\) −21.6353 + 12.4912i −0.136071 + 0.0785608i
\(160\) 0 0
\(161\) −33.1380 84.0830i −0.205826 0.522255i
\(162\) 0 0
\(163\) 166.364 96.0504i 1.02064 0.589267i 0.106350 0.994329i \(-0.466083\pi\)
0.914289 + 0.405062i \(0.132750\pi\)
\(164\) 0 0
\(165\) 108.998 + 62.9301i 0.660594 + 0.381394i
\(166\) 0 0
\(167\) 184.150i 1.10269i 0.834276 + 0.551346i \(0.185886\pi\)
−0.834276 + 0.551346i \(0.814114\pi\)
\(168\) 0 0
\(169\) −108.257 −0.640574
\(170\) 0 0
\(171\) 33.3349 57.7377i 0.194941 0.337647i
\(172\) 0 0
\(173\) 34.9519 + 60.5384i 0.202034 + 0.349933i 0.949184 0.314723i \(-0.101912\pi\)
−0.747150 + 0.664656i \(0.768578\pi\)
\(174\) 0 0
\(175\) −233.056 + 293.095i −1.33175 + 1.67483i
\(176\) 0 0
\(177\) −31.0049 53.7021i −0.175169 0.303401i
\(178\) 0 0
\(179\) −207.251 119.657i −1.15783 0.668473i −0.207047 0.978331i \(-0.566385\pi\)
−0.950783 + 0.309858i \(0.899719\pi\)
\(180\) 0 0
\(181\) −36.2834 −0.200461 −0.100230 0.994964i \(-0.531958\pi\)
−0.100230 + 0.994964i \(0.531958\pi\)
\(182\) 0 0
\(183\) −47.3678 −0.258840
\(184\) 0 0
\(185\) −303.720 175.353i −1.64173 0.947852i
\(186\) 0 0
\(187\) 19.0955 + 33.0744i 0.102115 + 0.176868i
\(188\) 0 0
\(189\) −76.0292 11.3492i −0.402271 0.0600487i
\(190\) 0 0
\(191\) −162.622 281.669i −0.851422 1.47471i −0.879925 0.475113i \(-0.842407\pi\)
0.0285024 0.999594i \(-0.490926\pi\)
\(192\) 0 0
\(193\) −99.8198 + 172.893i −0.517201 + 0.895818i 0.482599 + 0.875841i \(0.339693\pi\)
−0.999800 + 0.0199772i \(0.993641\pi\)
\(194\) 0 0
\(195\) −269.045 −1.37972
\(196\) 0 0
\(197\) 15.5053i 0.0787071i −0.999225 0.0393536i \(-0.987470\pi\)
0.999225 0.0393536i \(-0.0125299\pi\)
\(198\) 0 0
\(199\) 48.6375 + 28.0809i 0.244409 + 0.141110i 0.617202 0.786805i \(-0.288266\pi\)
−0.372792 + 0.927915i \(0.621600\pi\)
\(200\) 0 0
\(201\) −26.3110 + 15.1907i −0.130901 + 0.0755756i
\(202\) 0 0
\(203\) 17.8094 119.307i 0.0877312 0.587719i
\(204\) 0 0
\(205\) 565.326 326.391i 2.75769 1.59215i
\(206\) 0 0
\(207\) −39.9052 + 69.1178i −0.192779 + 0.333903i
\(208\) 0 0
\(209\) 39.3226i 0.188147i
\(210\) 0 0
\(211\) 370.470i 1.75578i −0.478859 0.877892i \(-0.658949\pi\)
0.478859 0.877892i \(-0.341051\pi\)
\(212\) 0 0
\(213\) −80.5819 + 139.572i −0.378319 + 0.655267i
\(214\) 0 0
\(215\) 313.431 180.960i 1.45782 0.841673i
\(216\) 0 0
\(217\) 165.629 + 131.700i 0.763266 + 0.606914i
\(218\) 0 0
\(219\) −302.372 + 174.574i −1.38069 + 0.797143i
\(220\) 0 0
\(221\) −70.7014 40.8195i −0.319916 0.184704i
\(222\) 0 0
\(223\) 6.78533i 0.0304275i 0.999884 + 0.0152137i \(0.00484287\pi\)
−0.999884 + 0.0152137i \(0.995157\pi\)
\(224\) 0 0
\(225\) 330.677 1.46968
\(226\) 0 0
\(227\) 148.309 256.879i 0.653344 1.13163i −0.328962 0.944343i \(-0.606699\pi\)
0.982306 0.187282i \(-0.0599679\pi\)
\(228\) 0 0
\(229\) −89.0964 154.320i −0.389067 0.673885i 0.603257 0.797547i \(-0.293869\pi\)
−0.992324 + 0.123662i \(0.960536\pi\)
\(230\) 0 0
\(231\) 92.5158 36.4614i 0.400501 0.157842i
\(232\) 0 0
\(233\) −58.9011 102.020i −0.252795 0.437853i 0.711500 0.702687i \(-0.248016\pi\)
−0.964294 + 0.264833i \(0.914683\pi\)
\(234\) 0 0
\(235\) 320.743 + 185.181i 1.36486 + 0.788004i
\(236\) 0 0
\(237\) −275.842 −1.16389
\(238\) 0 0
\(239\) −46.3543 −0.193951 −0.0969755 0.995287i \(-0.530917\pi\)
−0.0969755 + 0.995287i \(0.530917\pi\)
\(240\) 0 0
\(241\) 317.501 + 183.309i 1.31743 + 0.760619i 0.983315 0.181914i \(-0.0582291\pi\)
0.334115 + 0.942532i \(0.391562\pi\)
\(242\) 0 0
\(243\) 142.327 + 246.517i 0.585706 + 1.01447i
\(244\) 0 0
\(245\) 97.8032 + 422.965i 0.399197 + 1.72639i
\(246\) 0 0
\(247\) 42.0290 + 72.7964i 0.170158 + 0.294722i
\(248\) 0 0
\(249\) 118.580 205.387i 0.476226 0.824847i
\(250\) 0 0
\(251\) 129.896 0.517513 0.258756 0.965943i \(-0.416687\pi\)
0.258756 + 0.965943i \(0.416687\pi\)
\(252\) 0 0
\(253\) 47.0732i 0.186060i
\(254\) 0 0
\(255\) 313.153 + 180.799i 1.22805 + 0.709016i
\(256\) 0 0
\(257\) 232.394 134.173i 0.904256 0.522073i 0.0256776 0.999670i \(-0.491826\pi\)
0.878579 + 0.477598i \(0.158492\pi\)
\(258\) 0 0
\(259\) −257.792 + 101.599i −0.995337 + 0.392272i
\(260\) 0 0
\(261\) −92.2532 + 53.2624i −0.353460 + 0.204070i
\(262\) 0 0
\(263\) −117.691 + 203.847i −0.447495 + 0.775085i −0.998222 0.0596008i \(-0.981017\pi\)
0.550727 + 0.834685i \(0.314351\pi\)
\(264\) 0 0
\(265\) 56.8059i 0.214362i
\(266\) 0 0
\(267\) 105.281i 0.394311i
\(268\) 0 0
\(269\) 177.348 307.175i 0.659285 1.14192i −0.321516 0.946904i \(-0.604192\pi\)
0.980801 0.195011i \(-0.0624743\pi\)
\(270\) 0 0
\(271\) 365.350 210.935i 1.34816 0.778358i 0.360168 0.932888i \(-0.382719\pi\)
0.987988 + 0.154529i \(0.0493861\pi\)
\(272\) 0 0
\(273\) −132.300 + 166.383i −0.484615 + 0.609461i
\(274\) 0 0
\(275\) 168.907 97.5186i 0.614208 0.354613i
\(276\) 0 0
\(277\) −319.155 184.264i −1.15218 0.665214i −0.202766 0.979227i \(-0.564993\pi\)
−0.949419 + 0.314013i \(0.898326\pi\)
\(278\) 0 0
\(279\) 186.866i 0.669772i
\(280\) 0 0
\(281\) −35.2868 −0.125576 −0.0627879 0.998027i \(-0.519999\pi\)
−0.0627879 + 0.998027i \(0.519999\pi\)
\(282\) 0 0
\(283\) 98.3087 170.276i 0.347380 0.601681i −0.638403 0.769702i \(-0.720405\pi\)
0.985783 + 0.168022i \(0.0537379\pi\)
\(284\) 0 0
\(285\) −186.156 322.432i −0.653180 1.13134i
\(286\) 0 0
\(287\) 76.1460 510.108i 0.265317 1.77738i
\(288\) 0 0
\(289\) −89.6384 155.258i −0.310167 0.537226i
\(290\) 0 0
\(291\) −11.0209 6.36291i −0.0378724 0.0218657i
\(292\) 0 0
\(293\) 317.573 1.08387 0.541933 0.840421i \(-0.317693\pi\)
0.541933 + 0.840421i \(0.317693\pi\)
\(294\) 0 0
\(295\) −141.001 −0.477968
\(296\) 0 0
\(297\) 34.6745 + 20.0193i 0.116749 + 0.0674051i
\(298\) 0 0
\(299\) −50.3130 87.1447i −0.168271 0.291454i
\(300\) 0 0
\(301\) 42.2173 282.817i 0.140257 0.939591i
\(302\) 0 0
\(303\) 268.292 + 464.695i 0.885451 + 1.53365i
\(304\) 0 0
\(305\) −53.8535 + 93.2769i −0.176569 + 0.305826i
\(306\) 0 0
\(307\) 132.193 0.430596 0.215298 0.976548i \(-0.430928\pi\)
0.215298 + 0.976548i \(0.430928\pi\)
\(308\) 0 0
\(309\) 388.383i 1.25690i
\(310\) 0 0
\(311\) −400.453 231.202i −1.28763 0.743414i −0.309400 0.950932i \(-0.600128\pi\)
−0.978231 + 0.207518i \(0.933462\pi\)
\(312\) 0 0
\(313\) −490.206 + 283.021i −1.56615 + 0.904220i −0.569544 + 0.821961i \(0.692880\pi\)
−0.996611 + 0.0822589i \(0.973787\pi\)
\(314\) 0 0
\(315\) 238.599 300.067i 0.757458 0.952594i
\(316\) 0 0
\(317\) −153.315 + 88.5163i −0.483643 + 0.279231i −0.721933 0.691963i \(-0.756746\pi\)
0.238291 + 0.971194i \(0.423413\pi\)
\(318\) 0 0
\(319\) −31.4148 + 54.4120i −0.0984790 + 0.170571i
\(320\) 0 0
\(321\) 366.299i 1.14112i
\(322\) 0 0
\(323\) 112.975i 0.349766i
\(324\) 0 0
\(325\) −208.461 + 361.065i −0.641418 + 1.11097i
\(326\) 0 0
\(327\) −661.199 + 381.743i −2.02201 + 1.16741i
\(328\) 0 0
\(329\) 272.241 107.293i 0.827481 0.326119i
\(330\) 0 0
\(331\) −429.688 + 248.080i −1.29815 + 0.749487i −0.980084 0.198582i \(-0.936366\pi\)
−0.318065 + 0.948069i \(0.603033\pi\)
\(332\) 0 0
\(333\) 211.910 + 122.346i 0.636367 + 0.367406i
\(334\) 0 0
\(335\) 69.0825i 0.206216i
\(336\) 0 0
\(337\) −206.191 −0.611843 −0.305922 0.952057i \(-0.598965\pi\)
−0.305922 + 0.952057i \(0.598965\pi\)
\(338\) 0 0
\(339\) −198.466 + 343.752i −0.585444 + 1.01402i
\(340\) 0 0
\(341\) −55.1080 95.4499i −0.161607 0.279912i
\(342\) 0 0
\(343\) 309.663 + 147.505i 0.902809 + 0.430043i
\(344\) 0 0
\(345\) 222.848 + 385.984i 0.645936 + 1.11879i
\(346\) 0 0
\(347\) −524.976 303.095i −1.51290 0.873472i −0.999886 0.0150913i \(-0.995196\pi\)
−0.513013 0.858381i \(1.32853\pi\)
\(348\) 0 0
\(349\) 136.343 0.390669 0.195335 0.980737i \(-0.437421\pi\)
0.195335 + 0.980737i \(0.437421\pi\)
\(350\) 0 0
\(351\) −85.5887 −0.243842
\(352\) 0 0
\(353\) −8.72457 5.03713i −0.0247155 0.0142695i 0.487591 0.873072i \(-0.337876\pi\)
−0.512307 + 0.858802i \(0.671209\pi\)
\(354\) 0 0
\(355\) 183.231 + 317.365i 0.516143 + 0.893985i
\(356\) 0 0
\(357\) 265.799 104.754i 0.744536 0.293429i
\(358\) 0 0
\(359\) 197.808 + 342.613i 0.550997 + 0.954354i 0.998203 + 0.0599236i \(0.0190857\pi\)
−0.447206 + 0.894431i \(0.647581\pi\)
\(360\) 0 0
\(361\) 122.339 211.897i 0.338889 0.586973i
\(362\) 0 0
\(363\) 419.664 1.15610
\(364\) 0 0
\(365\) 793.909i 2.17509i
\(366\) 0 0
\(367\) −164.486 94.9661i −0.448191 0.258763i 0.258875 0.965911i \(-0.416648\pi\)
−0.707066 + 0.707148i \(0.749982\pi\)
\(368\) 0 0
\(369\) −394.438 + 227.729i −1.06894 + 0.617151i
\(370\) 0 0
\(371\) 35.1299 + 27.9337i 0.0946898 + 0.0752930i
\(372\) 0 0
\(373\) −311.859 + 180.052i −0.836083 + 0.482713i −0.855931 0.517090i \(-0.827015\pi\)
0.0198479 + 0.999803i \(0.493682\pi\)
\(374\) 0 0
\(375\) 491.816 851.850i 1.31151 2.27160i
\(376\) 0 0
\(377\) 134.308i 0.356254i
\(378\) 0 0
\(379\) 11.2929i 0.0297966i 0.999889 + 0.0148983i \(0.00474246\pi\)
−0.999889 + 0.0148983i \(0.995258\pi\)
\(380\) 0 0
\(381\) −270.950 + 469.299i −0.711154 + 1.23176i
\(382\) 0 0
\(383\) −376.075 + 217.127i −0.981918 + 0.566910i −0.902849 0.429959i \(-0.858528\pi\)
−0.0790692 + 0.996869i \(0.525195\pi\)
\(384\) 0 0
\(385\) 33.3831 223.636i 0.0867095 0.580874i
\(386\) 0 0
\(387\) −218.686 + 126.258i −0.565080 + 0.326249i
\(388\) 0 0
\(389\) 37.3803 + 21.5816i 0.0960934 + 0.0554796i 0.547277 0.836952i \(-0.315665\pi\)
−0.451183 + 0.892431i \(0.648998\pi\)
\(390\) 0 0
\(391\) 135.242i 0.345887i
\(392\) 0 0
\(393\) −357.315 −0.909199
\(394\) 0 0
\(395\) −313.611 + 543.190i −0.793952 + 1.37517i
\(396\) 0 0
\(397\) 243.395 + 421.573i 0.613086 + 1.06190i 0.990717 + 0.135940i \(0.0434053\pi\)
−0.377631 + 0.925956i \(0.623261\pi\)
\(398\) 0 0
\(399\) −290.939 43.4297i −0.729170 0.108846i
\(400\) 0 0
\(401\) 273.457 + 473.641i 0.681938 + 1.18115i 0.974389 + 0.224870i \(0.0721958\pi\)
−0.292451 + 0.956280i \(0.594471\pi\)
\(402\) 0 0
\(403\) 204.039 + 117.802i 0.506299 + 0.292312i
\(404\) 0 0
\(405\) 871.992 2.15307
\(406\) 0 0
\(407\) 144.323 0.354601
\(408\) 0 0
\(409\) 57.8217 + 33.3834i 0.141373 + 0.0816220i 0.569018 0.822325i \(-0.307323\pi\)
−0.427645 + 0.903947i \(0.640657\pi\)
\(410\) 0 0
\(411\) −388.819 673.453i −0.946030 1.63857i
\(412\) 0 0
\(413\) −69.3354 + 87.1976i −0.167882 + 0.211132i
\(414\) 0 0
\(415\) −269.633 467.018i −0.649718 1.12534i
\(416\) 0 0
\(417\) 76.9077 133.208i 0.184431 0.319444i
\(418\) 0 0
\(419\) 550.169 1.31305 0.656527 0.754303i \(-0.272025\pi\)
0.656527 + 0.754303i \(0.272025\pi\)
\(420\) 0 0
\(421\) 579.599i 1.37672i −0.725369 0.688360i \(-0.758331\pi\)
0.725369 0.688360i \(-0.241669\pi\)
\(422\) 0 0
\(423\) −223.788 129.204i −0.529049 0.305446i
\(424\) 0 0
\(425\) 485.273 280.173i 1.14182 0.659230i
\(426\) 0 0
\(427\) 31.2025 + 79.1719i 0.0730737 + 0.185414i
\(428\) 0 0
\(429\) 95.8845 55.3589i 0.223507 0.129042i
\(430\) 0 0
\(431\) −215.935 + 374.010i −0.501009 + 0.867773i 0.498990 + 0.866607i \(0.333704\pi\)
−0.999999 + 0.00116534i \(0.999629\pi\)
\(432\) 0 0
\(433\) 0.143463i 0.000331322i −1.00000 0.000165661i \(-0.999947\pi\)
1.00000 0.000165661i \(-5.27316e-5\pi\)
\(434\) 0 0
\(435\) 594.881i 1.36754i
\(436\) 0 0
\(437\) 69.6247 120.593i 0.159324 0.275958i
\(438\) 0 0
\(439\) 165.713 95.6744i 0.377478 0.217937i −0.299242 0.954177i \(-0.596734\pi\)
0.676721 + 0.736240i \(0.263401\pi\)
\(440\) 0 0
\(441\) −68.2389 295.109i −0.154737 0.669182i
\(442\) 0 0
\(443\) 340.782 196.751i 0.769260 0.444133i −0.0633505 0.997991i \(-0.520179\pi\)
0.832611 + 0.553859i \(0.186845\pi\)
\(444\) 0 0
\(445\) −207.320 119.696i −0.465888 0.268981i
\(446\) 0 0
\(447\) 369.308i 0.826193i
\(448\) 0 0
\(449\) −725.831 −1.61655 −0.808275 0.588805i \(-0.799598\pi\)
−0.808275 + 0.588805i \(0.799598\pi\)
\(450\) 0 0
\(451\) −134.317 + 232.644i −0.297821 + 0.515841i
\(452\) 0 0
\(453\) 129.687 + 224.625i 0.286286 + 0.495861i
\(454\) 0 0
\(455\) 177.227 + 449.690i 0.389511 + 0.988330i
\(456\) 0 0
\(457\) 34.6713 + 60.0525i 0.0758673 + 0.131406i 0.901463 0.432856i \(-0.142494\pi\)
−0.825596 + 0.564262i \(0.809161\pi\)
\(458\) 0 0
\(459\) 99.6203 + 57.5158i 0.217038 + 0.125307i
\(460\) 0 0
\(461\) −768.006 −1.66596 −0.832978 0.553306i \(-0.813366\pi\)
−0.832978 + 0.553306i \(0.813366\pi\)
\(462\) 0 0
\(463\) −215.717 −0.465911 −0.232956 0.972487i \(-0.574840\pi\)
−0.232956 + 0.972487i \(0.574840\pi\)
\(464\) 0 0
\(465\) −903.734 521.771i −1.94351 1.12209i
\(466\) 0 0
\(467\) 14.4688 + 25.0607i 0.0309824 + 0.0536631i 0.881101 0.472928i \(-0.156803\pi\)
−0.850118 + 0.526592i \(0.823470\pi\)
\(468\) 0 0
\(469\) 42.7220 + 33.9705i 0.0910917 + 0.0724319i
\(470\) 0 0
\(471\) 49.7163 + 86.1111i 0.105555 + 0.182826i
\(472\) 0 0
\(473\) −74.4688 + 128.984i −0.157439 + 0.272693i
\(474\) 0 0
\(475\) −576.949 −1.21463
\(476\) 0 0
\(477\) 39.6344i 0.0830911i
\(478\) 0 0
\(479\) 695.377 + 401.476i 1.45173 + 0.838154i 0.998580 0.0532818i \(-0.0169682\pi\)
0.453146 + 0.891436i \(0.350302\pi\)
\(480\) 0 0
\(481\) −267.179 + 154.256i −0.555466 + 0.320698i
\(482\) 0 0
\(483\) 348.283 + 51.9897i 0.721083 + 0.107639i
\(484\) 0 0
\(485\) −25.0598 + 14.4683i −0.0516696 + 0.0298315i
\(486\) 0 0
\(487\) 9.96197 17.2546i 0.0204558 0.0354305i −0.855616 0.517611i \(-0.826822\pi\)
0.876072 + 0.482180i \(0.160155\pi\)
\(488\) 0 0
\(489\) 748.493i 1.53066i
\(490\) 0 0
\(491\) 76.2017i 0.155197i 0.996985 + 0.0775985i \(0.0247252\pi\)
−0.996985 + 0.0775985i \(0.975275\pi\)
\(492\) 0 0
\(493\) −90.2552 + 156.327i −0.183073 + 0.317093i
\(494\) 0 0
\(495\) −172.925 + 99.8384i −0.349344 + 0.201694i
\(496\) 0 0
\(497\) 286.366 + 42.7471i 0.576190 + 0.0860102i
\(498\) 0 0
\(499\) 452.819 261.435i 0.907454 0.523919i 0.0278428 0.999612i \(-0.491136\pi\)
0.879611 + 0.475694i \(0.157803\pi\)
\(500\) 0 0
\(501\) −621.384 358.756i −1.24029 0.716080i
\(502\) 0 0
\(503\) 132.060i 0.262545i 0.991346 + 0.131273i \(0.0419064\pi\)
−0.991346 + 0.131273i \(0.958094\pi\)
\(504\) 0 0
\(505\) 1220.11 2.41605
\(506\) 0 0
\(507\) 210.904 365.296i 0.415983 0.720504i
\(508\) 0 0
\(509\) 155.079 + 268.604i 0.304673 + 0.527709i 0.977189 0.212374i \(-0.0681194\pi\)
−0.672515 + 0.740083i \(0.734786\pi\)
\(510\) 0 0
\(511\) 490.969 + 390.396i 0.960801 + 0.763984i
\(512\) 0 0
\(513\) −59.2201 102.572i −0.115439 0.199946i
\(514\) 0 0
\(515\) −764.806 441.561i −1.48506 0.857400i
\(516\) 0 0
\(517\) −152.412 −0.294801
\(518\) 0 0
\(519\) −272.369 −0.524797
\(520\) 0 0
\(521\) 52.9121 + 30.5488i 0.101559 + 0.0586349i 0.549919 0.835218i \(-0.314659\pi\)
−0.448360 + 0.893853i \(0.647992\pi\)
\(522\) 0 0
\(523\) 256.923 + 445.004i 0.491249 + 0.850868i 0.999949 0.0100759i \(-0.00320730\pi\)
−0.508701 + 0.860944i \(0.669874\pi\)
\(524\) 0 0
\(525\) −534.969 1357.41i −1.01899 2.58554i
\(526\) 0 0
\(527\) −158.326 274.229i −0.300429 0.520359i
\(528\) 0 0
\(529\) 181.152 313.765i 0.342443 0.593128i
\(530\) 0 0
\(531\) 98.3784 0.185270
\(532\) 0 0
\(533\) 574.246i 1.07739i
\(534\) 0 0
\(535\) −721.318 416.453i −1.34826 0.778417i
\(536\) 0 0
\(537\) 807.525 466.225i 1.50377 0.868202i
\(538\) 0 0
\(539\) −121.885 130.616i −0.226133 0.242329i
\(540\) 0 0
\(541\) 92.7322 53.5390i 0.171409 0.0989630i −0.411841 0.911256i \(-0.635114\pi\)
0.583250 + 0.812293i \(0.301781\pi\)
\(542\) 0 0
\(543\) 70.6863 122.432i 0.130177 0.225474i
\(544\) 0 0
\(545\) 1736.05i 3.18541i
\(546\) 0 0
\(547\) 43.3240i 0.0792030i −0.999216 0.0396015i \(-0.987391\pi\)
0.999216 0.0396015i \(-0.0126088\pi\)
\(548\) 0 0
\(549\) 37.5744 65.0808i 0.0684416 0.118544i
\(550\) 0 0
\(551\) 160.959 92.9296i 0.292121 0.168656i
\(552\) 0 0
\(553\) 181.705 + 461.051i 0.328581 + 0.833727i
\(554\) 0 0
\(555\) 1183.40 683.235i 2.13225 1.23105i
\(556\) 0 0
\(557\) 62.7878 + 36.2506i 0.112725 + 0.0650818i 0.555302 0.831648i \(-0.312603\pi\)
−0.442577 + 0.896730i \(0.645936\pi\)
\(558\) 0 0
\(559\) 318.377i 0.569547i
\(560\) 0 0
\(561\) −148.805 −0.265250
\(562\) 0 0
\(563\) −292.471 + 506.575i −0.519487 + 0.899779i 0.480256 + 0.877128i \(0.340544\pi\)
−0.999743 + 0.0226503i \(0.992790\pi\)
\(564\) 0 0
\(565\) 451.280 + 781.639i 0.798725 + 1.38343i
\(566\) 0 0
\(567\) 428.792 539.257i 0.756247 0.951071i
\(568\) 0 0
\(569\) −371.765 643.915i −0.653365 1.13166i −0.982301 0.187309i \(-0.940023\pi\)
0.328936 0.944352i \(-0.393310\pi\)
\(570\) 0 0
\(571\) −893.793 516.031i −1.56531 0.903733i −0.996704 0.0811234i \(-0.974149\pi\)
−0.568607 0.822609i \(1.30748\pi\)
\(572\) 0 0
\(573\) 1267.26 2.21163
\(574\) 0 0
\(575\) 690.666 1.20116
\(576\) 0 0
\(577\) −825.404 476.547i −1.43051 0.825905i −0.433350 0.901226i \(-0.642668\pi\)
−0.997159 + 0.0753213i \(0.976002\pi\)
\(578\) 0 0
\(579\) −388.933 673.652i −0.671732 1.16347i
\(580\) 0 0
\(581\) −421.402 62.9044i −0.725305 0.108269i
\(582\) 0 0
\(583\) −11.6884 20.2450i −0.0200488 0.0347255i
\(584\) 0 0
\(585\) 213.420 369.654i 0.364820 0.631887i
\(586\) 0 0
\(587\) 96.2876 0.164033 0.0820167 0.996631i \(-0.473864\pi\)
0.0820167 + 0.996631i \(0.473864\pi\)
\(588\) 0 0
\(589\) 326.035i 0.553540i
\(590\) 0 0
\(591\) 52.3201 + 30.2071i 0.0885282 + 0.0511118i
\(592\) 0 0
\(593\) 44.1840 25.5096i 0.0745092 0.0430179i −0.462283 0.886733i \(-0.652969\pi\)
0.536792 + 0.843715i \(0.319636\pi\)
\(594\) 0 0
\(595\) 95.9103 642.511i 0.161194 1.07985i
\(596\) 0 0
\(597\) −189.509 + 109.413i −0.317435 + 0.183271i
\(598\) 0 0
\(599\) 451.118 781.359i 0.753119 1.30444i −0.193186 0.981162i \(-0.561882\pi\)
0.946304 0.323277i \(-0.104785\pi\)
\(600\) 0 0
\(601\) 903.595i 1.50349i −0.659456 0.751743i \(-0.729213\pi\)
0.659456 0.751743i \(-0.270787\pi\)
\(602\) 0 0
\(603\) 48.2000i 0.0799337i
\(604\) 0 0
\(605\) 477.125 826.406i 0.788637 1.36596i
\(606\) 0 0
\(607\) 306.928 177.205i 0.505648 0.291936i −0.225395 0.974267i \(-0.572367\pi\)
0.731043 + 0.682332i \(0.239034\pi\)
\(608\) 0 0
\(609\) 367.886 + 292.526i 0.604082 + 0.480338i
\(610\) 0 0
\(611\) 282.154 162.902i 0.461791 0.266615i
\(612\) 0 0
\(613\) −290.984 168.000i −0.474688 0.274061i 0.243512 0.969898i \(-0.421700\pi\)
−0.718200 + 0.695837i \(0.755034\pi\)
\(614\) 0 0
\(615\) 2543.47i 4.13573i
\(616\) 0 0
\(617\) 223.359 0.362008 0.181004 0.983482i \(-0.442065\pi\)
0.181004 + 0.983482i \(0.442065\pi\)
\(618\) 0 0
\(619\) −363.026 + 628.780i −0.586472 + 1.01580i 0.408218 + 0.912885i \(0.366150\pi\)
−0.994690 + 0.102915i \(0.967183\pi\)
\(620\) 0 0
\(621\) 70.8925 + 122.789i 0.114159 + 0.197728i
\(622\) 0 0
\(623\) −175.970 + 69.3516i −0.282456 + 0.111319i
\(624\) 0 0
\(625\) −449.635 778.791i −0.719416 1.24607i
\(626\) 0 0
\(627\) 132.688 + 76.6074i 0.211623 + 0.122181i
\(628\) 0 0
\(629\) 414.642 0.659208
\(630\) 0 0
\(631\) 326.157 0.516888 0.258444 0.966026i \(-0.416790\pi\)
0.258444 + 0.966026i \(0.416790\pi\)
\(632\) 0 0
\(633\) 1250.09 + 721.741i 1.97487 + 1.14019i
\(634\) 0 0
\(635\) 616.097 + 1067.11i 0.970232 + 1.68049i
\(636\) 0 0
\(637\) 365.247 + 111.529i 0.573386 + 0.175085i
\(638\) 0 0
\(639\) −127.843 221.431i −0.200067 0.346527i
\(640\) 0 0
\(641\) 299.187 518.208i 0.466751 0.808436i −0.532528 0.846413i \(-0.678758\pi\)
0.999279 + 0.0379764i \(0.0120912\pi\)
\(642\) 0 0
\(643\) −1008.20 −1.56796 −0.783979 0.620787i \(-0.786813\pi\)
−0.783979 + 0.620787i \(0.786813\pi\)
\(644\) 0 0
\(645\) 1410.16i 2.18630i
\(646\) 0 0
\(647\) −574.378 331.617i −0.887756 0.512546i −0.0145481 0.999894i \(-0.504631\pi\)
−0.873208 + 0.487348i \(0.837964\pi\)
\(648\) 0 0
\(649\) 50.2509 29.0124i 0.0774283 0.0447032i
\(650\) 0 0
\(651\) −767.075 + 302.312i −1.17830 + 0.464381i
\(652\) 0 0
\(653\) 857.892 495.304i 1.31377 0.758506i 0.331052 0.943612i \(-0.392596\pi\)
0.982718 + 0.185107i \(0.0592631\pi\)
\(654\) 0 0
\(655\) −406.240 + 703.628i −0.620213 + 1.07424i
\(656\) 0 0
\(657\) 553.924i 0.843110i
\(658\) 0 0
\(659\) 82.2318i 0.124783i 0.998052 + 0.0623914i \(0.0198727\pi\)
−0.998052 + 0.0623914i \(0.980127\pi\)
\(660\) 0 0
\(661\) −313.110 + 542.322i −0.473691 + 0.820457i −0.999546 0.0301171i \(-0.990412\pi\)
0.525855 + 0.850574i \(0.323745\pi\)
\(662\) 0 0
\(663\) 275.478 159.047i 0.415502 0.239890i
\(664\) 0 0
\(665\) −416.297 + 523.543i −0.626010 + 0.787282i
\(666\) 0 0
\(667\) −192.684 + 111.246i −0.288882 + 0.166786i
\(668\) 0 0
\(669\) −22.8960 13.2190i −0.0342242 0.0197594i
\(670\) 0 0
\(671\) 44.3237i 0.0660562i
\(672\) 0 0
\(673\) −150.211 −0.223196 −0.111598 0.993753i \(-0.535597\pi\)
−0.111598 + 0.993753i \(0.535597\pi\)
\(674\) 0 0
\(675\) 293.727 508.751i 0.435152 0.753705i
\(676\) 0 0
\(677\) −278.207 481.869i −0.410941 0.711771i 0.584052 0.811716i \(-0.301467\pi\)
−0.994993 + 0.0999455i \(0.968133\pi\)
\(678\) 0 0
\(679\) −3.37540 + 22.6121i −0.00497113 + 0.0333020i
\(680\) 0 0
\(681\) 577.865 + 1000.89i 0.848553 + 1.46974i
\(682\) 0 0
\(683\) 685.334 + 395.678i 1.00342 + 0.579323i 0.909258 0.416234i \(-0.136650\pi\)
0.0941597 + 0.995557i \(0.469984\pi\)
\(684\) 0 0
\(685\) −1768.22 −2.58135
\(686\) 0 0
\(687\) 694.302 1.01063
\(688\) 0 0
\(689\) 43.2767 + 24.9858i 0.0628109 + 0.0362639i
\(690\) 0 0
\(691\) −488.267 845.703i −0.706609 1.22388i −0.966108 0.258139i \(-0.916891\pi\)
0.259499 0.965743i \(1.58356\pi\)
\(692\) 0 0
\(693\) −23.2920 + 156.035i −0.0336103 + 0.225158i
\(694\) 0 0
\(695\) −174.876 302.894i −0.251620 0.435819i
\(696\) 0 0
\(697\) −385.895 + 668.390i −0.553652 + 0.958953i
\(698\) 0 0
\(699\) 458.999 0.656651
\(700\) 0 0
\(701\) 855.098i 1.21983i −0.792468 0.609913i \(-0.791204\pi\)
0.792468 0.609913i \(-0.208796\pi\)
\(702\) 0 0
\(703\) −369.730 213.464i −0.525932 0.303647i
\(704\) 0 0
\(705\) −1249.73 + 721.530i −1.77266 + 1.02345i
\(706\) 0 0
\(707\) 599.974 754.538i 0.848619 1.06724i
\(708\) 0 0
\(709\) −288.794 + 166.735i −0.407326 + 0.235170i −0.689640 0.724152i \(-0.742231\pi\)
0.282314 + 0.959322i \(0.408898\pi\)
\(710\) 0 0
\(711\) 218.812 378.993i 0.307752 0.533042i
\(712\) 0 0
\(713\) 390.297i 0.547401i
\(714\) 0 0
\(715\) 251.755i 0.352105i
\(716\) 0 0
\(717\) 90.3063 156.415i 0.125950 0.218152i
\(718\) 0 0
\(719\) 34.4877 19.9115i 0.0479662 0.0276933i −0.475825 0.879540i \(-0.657850\pi\)
0.523791 + 0.851847i \(0.324517\pi\)
\(720\) 0 0
\(721\) −649.155 + 255.839i −0.900354 + 0.354839i
\(722\) 0 0
\(723\) −1237.09 + 714.237i −1.71106 + 0.987879i
\(724\) 0 0
\(725\) 798.344 + 460.924i 1.10116 + 0.635757i
\(726\) 0 0
\(727\) 489.402i 0.673180i −0.941651 0.336590i \(-0.890726\pi\)
0.941651 0.336590i \(-0.109274\pi\)
\(728\) 0 0
\(729\) −223.307 −0.306320
\(730\) 0 0
\(731\) −213.950 + 370.572i −0.292681 + 0.506939i
\(732\) 0 0
\(733\) 89.1592 + 154.428i 0.121636 + 0.210680i 0.920413 0.390948i \(-0.127853\pi\)
−0.798777 + 0.601627i \(0.794519\pi\)
\(734\) 0 0
\(735\) −1617.76 493.988i −2.20104 0.672093i
\(736\) 0 0
\(737\) −14.2145 24.6202i −0.0192869 0.0334060i
\(738\) 0 0
\(739\) 764.182 + 441.200i 1.03408 + 0.597024i 0.918149 0.396234i \(-0.129683\pi\)
0.115926 + 0.993258i \(0.463017\pi\)
\(740\) 0 0
\(741\) −327.520 −0.441997
\(742\) 0 0
\(743\) −1404.00 −1.88964 −0.944819 0.327591i \(-0.893763\pi\)
−0.944819 + 0.327591i \(0.893763\pi\)
\(744\) 0 0
\(745\) −727.244 419.875i −0.976167 0.563590i
\(746\) 0 0
\(747\) 188.127 + 325.846i 0.251844 + 0.436206i
\(748\) 0 0
\(749\) −612.243 + 241.291i −0.817414 + 0.322151i
\(750\) 0 0
\(751\) 102.840 + 178.124i 0.136938 + 0.237183i 0.926336 0.376698i \(-0.122941\pi\)
−0.789398 + 0.613881i \(0.789607\pi\)
\(752\) 0 0
\(753\) −253.060 + 438.312i −0.336069 + 0.582088i
\(754\) 0 0
\(755\) 589.777 0.781162
\(756\) 0 0
\(757\) 15.0345i 0.0198606i −0.999951 0.00993032i \(-0.996839\pi\)
0.999951 0.00993032i \(-0.00316097\pi\)
\(758\) 0 0
\(759\) −158.841 91.7068i −0.209276 0.120826i
\(760\) 0 0
\(761\) −544.290 + 314.246i −0.715229 + 0.412938i −0.812994 0.582272i \(-0.802164\pi\)
0.0977649 + 0.995210i \(0.468831\pi\)
\(762\) 0 0
\(763\) 1073.61 + 853.682i 1.40709 + 1.11885i
\(764\) 0 0
\(765\) −496.817 + 286.837i −0.649434 + 0.374951i
\(766\) 0 0
\(767\) −62.0184 + 107.419i −0.0808584 + 0.140051i
\(768\) 0 0
\(769\) 442.918i 0.575967i −0.957635 0.287983i \(-0.907015\pi\)
0.957635 0.287983i \(-0.0929848\pi\)
\(770\) 0 0
\(771\) 1045.57i 1.35612i
\(772\) 0 0
\(773\) −84.5990 + 146.530i −0.109442 + 0.189560i −0.915545 0.402217i \(-0.868240\pi\)
0.806102 + 0.591777i \(0.201573\pi\)
\(774\) 0 0
\(775\) −1400.46 + 808.555i −1.80704 + 1.04330i
\(776\) 0 0
\(777\) 159.396 1067.81i 0.205143 1.37427i
\(778\) 0 0
\(779\) 688.196 397.330i 0.883435 0.510051i
\(780\) 0 0
\(781\) −130.602 75.4034i −0.167225 0.0965472i
\(782\) 0 0
\(783\) 189.244i 0.241690i
\(784\) 0 0
\(785\) 226.094 0.288018
\(786\) 0 0
\(787\) 23.2437 40.2593i 0.0295346 0.0511554i −0.850880 0.525360i \(-0.823931\pi\)
0.880415 + 0.474204i \(0.157264\pi\)