Properties

Label 224.3.n.a.145.13
Level 224
Weight 3
Character 224.145
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 145.13
Character \(\chi\) \(=\) 224.145
Dual form 224.3.n.a.17.13

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 0.983268 + 0.182163i \(0.0583098\pi\)
−0.333876 + 0.942617i \(0.608357\pi\)
\(4\) 0 0
\(5\) −4.42985 + 7.67272i −0.885969 + 1.53454i −0.0413705 + 0.999144i \(0.513172\pi\)
−0.844599 + 0.535400i \(0.820161\pi\)
\(6\) 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 \(-0.613670\pi\)
0.636608 + 0.771187i \(0.280337\pi\)
\(12\) 0 0
\(13\) −7.79378 −0.599522 −0.299761 0.954014i \(-0.596907\pi\)
−0.299761 + 0.954014i \(0.596907\pi\)
\(14\) 0 0
\(15\) −34.5205 −2.30136
\(16\) 0 0
\(17\) −9.07152 + 5.23744i −0.533619 + 0.308085i −0.742489 0.669858i \(-0.766355\pi\)
0.208870 + 0.977943i \(0.433021\pi\)
\(18\) 0 0
\(19\) −5.39264 + 9.34032i −0.283823 + 0.491596i −0.972323 0.233640i \(-0.924936\pi\)
0.688500 + 0.725236i \(0.258269\pi\)
\(20\) 0 0
\(21\) 16.9751 + 21.3482i 0.808336 + 1.01658i
\(22\) 0 0
\(23\) −6.45553 + 11.1813i −0.280675 + 0.486144i −0.971551 0.236829i \(-0.923892\pi\)
0.690876 + 0.722973i \(0.257225\pi\)
\(24\) 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 −0.0142878 0.999898i \(-0.504548\pi\)
0.858793 + 0.512323i \(0.171215\pi\)
\(32\) 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 \(-0.153674\pi\)
0.0408071 + 0.999167i \(0.487007\pi\)
\(38\) 0 0
\(39\) −15.1837 26.2989i −0.389324 0.674330i
\(40\) 0 0
\(41\) 73.6801i 1.79707i 0.438897 + 0.898537i \(0.355369\pi\)
−0.438897 + 0.898537i \(0.644631\pi\)
\(42\) 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 0.832969 0.553319i \(-0.186639\pi\)
−0.0627038 + 0.998032i \(0.519972\pi\)
\(48\) 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 \(-0.685932\pi\)
0.446700 + 0.894684i \(0.352599\pi\)
\(54\) 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 \(-0.123605\pi\)
−0.790677 + 0.612234i \(0.790271\pi\)
\(60\) 0 0
\(61\) −6.07848 + 10.5282i −0.0996472 + 0.172594i −0.911539 0.411214i \(-0.865105\pi\)
0.811891 + 0.583808i \(0.198438\pi\)
\(62\) 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 \(-0.685199\pi\)
0.448759 + 0.893653i \(0.351866\pi\)
\(68\) 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 0.136787 0.990601i \(-0.456322\pi\)
0.926279 + 0.376839i \(0.122989\pi\)
\(74\) 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 −0.550191 0.835039i \(-0.685445\pi\)
0.998260 + 0.0589594i \(0.0187783\pi\)
\(80\) 0 0
\(81\) 49.2112 + 85.2363i 0.607546 + 1.05230i
\(82\) 0 0
\(83\) 60.8673 0.733341 0.366671 0.930351i \(-0.380498\pi\)
0.366671 + 0.930351i \(0.380498\pi\)
\(84\) 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 0.362743 0.931889i \(-0.381840\pi\)
−0.625668 + 0.780089i \(0.715174\pi\)
\(90\) 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 \(-0.994641\pi\)
0.999858 0.0168355i \(-0.00535916\pi\)
\(98\) 0 0
\(99\) 22.5377i 0.227653i
\(100\) 0 0
\(101\) −68.8571 119.264i −0.681754 1.18083i −0.974445 0.224625i \(-0.927884\pi\)
0.292691 0.956207i \(1.59455\pi\)
\(102\) 0 0
\(103\) −86.3243 49.8393i −0.838100 0.483877i 0.0185182 0.999829i \(-0.494105\pi\)
−0.856618 + 0.515952i \(0.827438\pi\)
\(104\) 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 \(-0.188559\pi\)
−0.0687226 + 0.997636i \(0.521892\pi\)
\(108\) 0 0
\(109\) −169.697 + 97.9745i −1.55685 + 0.898849i −0.559297 + 0.828967i \(0.688929\pi\)
−0.997555 + 0.0698815i \(0.977738\pi\)
\(110\) 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 \(-0.947158\pi\)
0.636233 + 0.771497i \(0.280492\pi\)
\(132\) 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 −0.957560 0.288233i \(-0.906932\pi\)
0.229163 0.973388i \(-0.426401\pi\)
\(138\) 0 0
\(139\) 39.4768 0.284006 0.142003 0.989866i \(-0.454646\pi\)
0.142003 + 0.989866i \(0.454646\pi\)
\(140\) 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 \(-0.230301\pi\)
−0.198583 + 0.980084i \(0.563634\pi\)
\(150\) 0 0
\(151\) 33.2843 + 57.6501i 0.220426 + 0.381789i 0.954937 0.296807i \(-0.0959220\pi\)
−0.734511 + 0.678596i \(0.762589\pi\)
\(152\) 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 \(-0.192565\pi\)
−0.903797 + 0.427962i \(0.859232\pi\)
\(158\) 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 \(-0.533917\pi\)
−0.914289 + 0.405062i \(0.867250\pi\)
\(164\) 0 0
\(165\) −108.998 + 62.9301i −0.660594 + 0.381394i
\(166\) 0 0
\(167\) 184.150i 1.10269i −0.834276 0.551346i \(-0.814114\pi\)
0.834276 0.551346i \(-0.185886\pi\)
\(168\) 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 \(-0.898088\pi\)
0.747150 + 0.664656i \(0.231422\pi\)
\(174\) 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 \(-0.433615\pi\)
0.950783 + 0.309858i \(0.100281\pi\)
\(180\) 0 0
\(181\) 36.2834 0.200461 0.100230 0.994964i \(-0.468042\pi\)
0.100230 + 0.994964i \(0.468042\pi\)
\(182\) 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 0.0285024 + 0.999594i \(0.490926\pi\)
−0.879925 + 0.475113i \(0.842407\pi\)
\(192\) 0 0
\(193\) −99.8198 172.893i −0.517201 0.895818i −0.999800 0.0199772i \(-0.993641\pi\)
0.482599 0.875841i \(-0.339693\pi\)
\(194\) 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 −0.372792 0.927915i \(-0.621600\pi\)
0.617202 + 0.786805i \(0.288266\pi\)
\(200\) 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 \(-0.995157\pi\)
0.999884 0.0152137i \(-0.00484287\pi\)
\(224\) 0 0
\(225\) 330.677 1.46968
\(226\) 0 0
\(227\) −148.309 256.879i −0.653344 1.13163i −0.982306 0.187282i \(-0.940032\pi\)
0.328962 0.944343i \(1.60670\pi\)
\(228\) 0 0
\(229\) 89.0964 154.320i 0.389067 0.673885i −0.603257 0.797547i \(-0.706131\pi\)
0.992324 + 0.123662i \(0.0394640\pi\)
\(230\) 0 0
\(231\) 92.5158 + 36.4614i 0.400501 + 0.157842i
\(232\) 0 0
\(233\) −58.9011 + 102.020i −0.252795 + 0.437853i −0.964294 0.264833i \(-0.914683\pi\)
0.711500 + 0.702687i \(0.248016\pi\)
\(234\) 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 0.334115 0.942532i \(-0.391562\pi\)
0.983315 + 0.181914i \(0.0582291\pi\)
\(242\) 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 \(-0.583313\pi\)
−0.258756 + 0.965943i \(0.583313\pi\)
\(252\) 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 0.878579 0.477598i \(-0.158492\pi\)
0.0256776 + 0.999670i \(0.491826\pi\)
\(258\) 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 0.550727 0.834685i \(-0.314351\pi\)
−0.998222 + 0.0596008i \(0.981017\pi\)
\(264\) 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 −0.980801 0.195011i \(-0.937526\pi\)
0.321516 0.946904i \(1.60419\pi\)
\(270\) 0 0
\(271\) 365.350 + 210.935i 1.34816 + 0.778358i 0.987988 0.154529i \(-0.0493861\pi\)
0.360168 + 0.932888i \(0.382719\pi\)
\(272\) 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 \(-0.435007\pi\)
0.949419 + 0.314013i \(0.101674\pi\)
\(278\) 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 \(-0.279595\pi\)
−0.985783 + 0.168022i \(0.946262\pi\)
\(284\) 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 \(-0.682307\pi\)
−0.541933 + 0.840421i \(0.682307\pi\)
\(294\) 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 \(-0.569072\pi\)
−0.215298 + 0.976548i \(0.569072\pi\)
\(308\) 0 0
\(309\) 388.383i 1.25690i
\(310\) 0 0
\(311\) −400.453 + 231.202i −1.28763 + 0.743414i −0.978231 0.207518i \(-0.933462\pi\)
−0.309400 + 0.950932i \(0.600128\pi\)
\(312\) 0 0
\(313\) −490.206 283.021i −1.56615 0.904220i −0.996611 0.0822589i \(-0.973787\pi\)
−0.569544 0.821961i \(-0.692880\pi\)
\(314\) 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 \(-0.243254\pi\)
−0.238291 + 0.971194i \(0.576587\pi\)
\(318\) 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 \(-0.0636335\pi\)
0.318065 + 0.948069i \(0.396967\pi\)
\(332\) 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 0.513013 0.858381i \(-0.328529\pi\)
0.999886 0.0150913i \(-0.00480389\pi\)
\(348\) 0 0
\(349\) −136.343 −0.390669 −0.195335 0.980737i \(-0.562579\pi\)
−0.195335 + 0.980737i \(0.562579\pi\)
\(350\) 0 0
\(351\) −85.5887 −0.243842
\(352\) 0 0
\(353\) −8.72457 + 5.03713i −0.0247155 + 0.0142695i −0.512307 0.858802i \(-0.671209\pi\)
0.487591 + 0.873072i \(0.337876\pi\)
\(354\) 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 −0.447206 0.894431i \(-0.647581\pi\)
0.998203 0.0599236i \(-0.0190857\pi\)
\(360\) 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 −0.707066 0.707148i \(-0.749982\pi\)
0.258875 + 0.965911i \(0.416648\pi\)
\(368\) 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 \(-0.172985\pi\)
−0.0198479 + 0.999803i \(0.506318\pi\)
\(374\) 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 −0.0790692 0.996869i \(-0.525195\pi\)
−0.902849 + 0.429959i \(0.858528\pi\)
\(384\) 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 \(-0.684335\pi\)
0.451183 + 0.892431i \(0.351002\pi\)
\(390\) 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 0.377631 + 0.925956i \(0.376739\pi\)
−0.990717 + 0.135940i \(0.956595\pi\)
\(398\) 0 0
\(399\) −290.939 + 43.4297i −0.729170 + 0.108846i
\(400\) 0 0
\(401\) 273.457 473.641i 0.681938 1.18115i −0.292451 0.956280i \(-0.594471\pi\)
0.974389 0.224870i \(-0.0721958\pi\)
\(402\) 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 −0.427645 0.903947i \(-0.640657\pi\)
0.569018 + 0.822325i \(0.307323\pi\)
\(410\) 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 \(-0.727975\pi\)
−0.656527 + 0.754303i \(0.727975\pi\)
\(420\) 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 −0.999999 0.00116534i \(-0.999629\pi\)
0.498990 0.866607i \(-0.333704\pi\)
\(432\) 0 0
\(433\) 0.143463i 0.000331322i 1.00000 0.000165661i \(5.27316e-5\pi\)
−1.00000 0.000165661i \(0.999947\pi\)
\(434\) 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 0.676721 0.736240i \(-0.263401\pi\)
−0.299242 + 0.954177i \(0.596734\pi\)
\(440\) 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 \(-0.479821\pi\)
−0.832611 + 0.553859i \(0.813155\pi\)
\(444\) 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 −0.825596 0.564262i \(-0.809161\pi\)
0.901463 + 0.432856i \(0.142494\pi\)
\(458\) 0 0
\(459\) −99.6203 + 57.5158i −0.217038 + 0.125307i
\(460\) 0 0
\(461\) 768.006 1.66596 0.832978 0.553306i \(-0.186634\pi\)
0.832978 + 0.553306i \(0.186634\pi\)
\(462\) 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 \(-0.843197\pi\)
0.850118 + 0.526592i \(0.176530\pi\)
\(468\) 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 0.453146 0.891436i \(-0.350302\pi\)
0.998580 + 0.0532818i \(0.0169682\pi\)
\(480\) 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 0.876072 0.482180i \(-0.160155\pi\)
−0.855616 + 0.517611i \(0.826822\pi\)
\(488\) 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 \(-0.508864\pi\)
−0.879611 + 0.475694i \(0.842197\pi\)
\(500\) 0 0
\(501\) 621.384 358.756i 1.24029 0.716080i
\(502\) 0 0
\(503\) 132.060i 0.262545i −0.991346 0.131273i \(-0.958094\pi\)
0.991346 0.131273i \(-0.0419064\pi\)
\(504\) 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 \(-0.931881\pi\)
0.672515 + 0.740083i \(0.265214\pi\)
\(510\) 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 −0.448360 0.893853i \(-0.647992\pi\)
0.549919 + 0.835218i \(0.314659\pi\)
\(522\) 0 0
\(523\) −256.923 + 445.004i −0.491249 + 0.850868i −0.999949 0.0100759i \(-0.996793\pi\)
0.508701 + 0.860944i \(0.330126\pi\)
\(524\) 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 \(-0.364886\pi\)
−0.583250 + 0.812293i \(0.698219\pi\)
\(542\) 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 \(-0.687397\pi\)
0.442577 + 0.896730i \(0.354064\pi\)
\(558\) 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 0.999743 + 0.0226503i \(0.00721043\pi\)
−0.480256 + 0.877128i \(0.659456\pi\)
\(564\) 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 0.328936 + 0.944352i \(0.393310\pi\)
−0.982301 + 0.187309i \(0.940023\pi\)
\(570\) 0 0
\(571\) 893.793 516.031i 1.56531 0.903733i 0.568607 0.822609i \(-0.307483\pi\)
0.996704 0.0811234i \(-0.0258508\pi\)
\(572\) 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 −0.997159 0.0753213i \(-0.976002\pi\)
−0.433350 + 0.901226i \(0.642668\pi\)
\(578\) 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 \(-0.526136\pi\)
−0.0820167 + 0.996631i \(0.526136\pi\)
\(588\) 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 0.536792 0.843715i \(-0.319636\pi\)
−0.462283 + 0.886733i \(0.652969\pi\)
\(594\) 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 0.946304 + 0.323277i \(0.104785\pi\)
−0.193186 + 0.981162i \(0.561882\pi\)
\(600\) 0 0
\(601\) 903.595i 1.50349i 0.659456 + 0.751743i \(0.270787\pi\)
−0.659456 + 0.751743i \(0.729213\pi\)
\(602\) 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 0.731043 0.682332i \(-0.239034\pi\)
−0.225395 + 0.974267i \(0.572367\pi\)
\(608\) 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 \(-0.578300\pi\)
0.718200 + 0.695837i \(0.244966\pi\)
\(614\) 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 0.994690 + 0.102915i \(0.0328170\pi\)
−0.408218 + 0.912885i \(0.633850\pi\)
\(620\) 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 0.999279 0.0379764i \(-0.0120912\pi\)
−0.532528 + 0.846413i \(0.678758\pi\)
\(642\) 0 0
\(643\) 1008.20 1.56796 0.783979 0.620787i \(-0.213187\pi\)
0.783979 + 0.620787i \(0.213187\pi\)
\(644\) 0 0
\(645\) 1410.16i 2.18630i
\(646\) 0 0
\(647\) −574.378 + 331.617i −0.887756 + 0.512546i −0.873208 0.487348i \(-0.837964\pi\)
−0.0145481 + 0.999894i \(0.504631\pi\)
\(648\) 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 \(-0.607404\pi\)
−0.982718 + 0.185107i \(0.940737\pi\)
\(654\) 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 \(-0.00958802\pi\)
−0.525855 + 0.850574i \(0.676255\pi\)
\(662\) 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 \(-0.698533\pi\)
0.994993 + 0.0999455i \(0.0318668\pi\)
\(678\) 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 \(-0.863350\pi\)
−0.0941597 + 0.995557i \(0.530016\pi\)
\(684\) 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 −0.259499 0.965743i \(-0.583557\pi\)
0.966108 0.258139i \(-0.0831093\pi\)
\(692\) 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 \(-0.257769\pi\)
−0.282314 + 0.959322i \(0.591102\pi\)
\(710\) 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 0.523791 0.851847i \(-0.324517\pi\)
−0.475825 + 0.879540i \(0.657850\pi\)
\(720\) 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 \(0.109274\pi\)
−0.941651 + 0.336590i \(0.890726\pi\)
\(728\) 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 \(-0.872147\pi\)
0.798777 + 0.601627i \(0.205481\pi\)
\(734\) 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 \(-0.870317\pi\)
−0.115926 + 0.993258i \(0.536983\pi\)
\(740\) 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 −0.789398 0.613881i \(-0.789607\pi\)
0.926336 + 0.376698i \(0.122941\pi\)
\(752\) 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 0.0977649 0.995210i \(-0.468831\pi\)
−0.812994 + 0.582272i \(0.802164\pi\)
\(762\) 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 \(0.0929848\pi\)
−0.957635 + 0.287983i \(0.907015\pi\)
\(770\) 0 0
\(771\) 1045.57i 1.35612i
\(772\) 0 0
\(773\) 84.5990 + 146.530i 0.109442 + 0.189560i 0.915545 0.402217i \(-0.131760\pi\)
−0.806102 + 0.591777i \(0.798427\pi\)
\(774\) 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 \(-0.176069\pi\)
−0.880415 + 0.474204i \(0.842736\pi\)
\(788\) 0 0