Properties

Label 4028.2.a.d.1.19
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Root \(-3.17454\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.17454 q^{3} -4.27638 q^{5} -4.73492 q^{7} +7.07773 q^{9} +O(q^{10})\) \(q+3.17454 q^{3} -4.27638 q^{5} -4.73492 q^{7} +7.07773 q^{9} +3.63629 q^{11} +3.74027 q^{13} -13.5756 q^{15} -1.80496 q^{17} -1.00000 q^{19} -15.0312 q^{21} -2.48625 q^{23} +13.2874 q^{25} +12.9449 q^{27} +0.417081 q^{29} -6.42779 q^{31} +11.5436 q^{33} +20.2483 q^{35} -4.97711 q^{37} +11.8737 q^{39} -0.0129771 q^{41} -11.1876 q^{43} -30.2671 q^{45} -6.11779 q^{47} +15.4195 q^{49} -5.72994 q^{51} +1.00000 q^{53} -15.5502 q^{55} -3.17454 q^{57} -12.4760 q^{59} +4.40643 q^{61} -33.5125 q^{63} -15.9948 q^{65} -14.2338 q^{67} -7.89271 q^{69} +4.24339 q^{71} -10.7983 q^{73} +42.1815 q^{75} -17.2176 q^{77} -3.93332 q^{79} +19.8611 q^{81} -11.0579 q^{83} +7.71872 q^{85} +1.32404 q^{87} +3.91713 q^{89} -17.7099 q^{91} -20.4053 q^{93} +4.27638 q^{95} +7.08577 q^{97} +25.7367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 3.17454 1.83282 0.916412 0.400236i \(-0.131072\pi\)
0.916412 + 0.400236i \(0.131072\pi\)
\(4\) 0 0
\(5\) −4.27638 −1.91246 −0.956228 0.292623i \(-0.905472\pi\)
−0.956228 + 0.292623i \(0.905472\pi\)
\(6\) 0 0
\(7\) −4.73492 −1.78963 −0.894815 0.446436i \(-0.852693\pi\)
−0.894815 + 0.446436i \(0.852693\pi\)
\(8\) 0 0
\(9\) 7.07773 2.35924
\(10\) 0 0
\(11\) 3.63629 1.09638 0.548192 0.836352i \(-0.315316\pi\)
0.548192 + 0.836352i \(0.315316\pi\)
\(12\) 0 0
\(13\) 3.74027 1.03736 0.518682 0.854967i \(-0.326423\pi\)
0.518682 + 0.854967i \(0.326423\pi\)
\(14\) 0 0
\(15\) −13.5756 −3.50519
\(16\) 0 0
\(17\) −1.80496 −0.437768 −0.218884 0.975751i \(-0.570242\pi\)
−0.218884 + 0.975751i \(0.570242\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −15.0312 −3.28008
\(22\) 0 0
\(23\) −2.48625 −0.518419 −0.259210 0.965821i \(-0.583462\pi\)
−0.259210 + 0.965821i \(0.583462\pi\)
\(24\) 0 0
\(25\) 13.2874 2.65749
\(26\) 0 0
\(27\) 12.9449 2.49126
\(28\) 0 0
\(29\) 0.417081 0.0774499 0.0387250 0.999250i \(-0.487670\pi\)
0.0387250 + 0.999250i \(0.487670\pi\)
\(30\) 0 0
\(31\) −6.42779 −1.15447 −0.577233 0.816580i \(-0.695867\pi\)
−0.577233 + 0.816580i \(0.695867\pi\)
\(32\) 0 0
\(33\) 11.5436 2.00948
\(34\) 0 0
\(35\) 20.2483 3.42259
\(36\) 0 0
\(37\) −4.97711 −0.818231 −0.409116 0.912483i \(-0.634163\pi\)
−0.409116 + 0.912483i \(0.634163\pi\)
\(38\) 0 0
\(39\) 11.8737 1.90131
\(40\) 0 0
\(41\) −0.0129771 −0.00202668 −0.00101334 0.999999i \(-0.500323\pi\)
−0.00101334 + 0.999999i \(0.500323\pi\)
\(42\) 0 0
\(43\) −11.1876 −1.70609 −0.853044 0.521839i \(-0.825246\pi\)
−0.853044 + 0.521839i \(0.825246\pi\)
\(44\) 0 0
\(45\) −30.2671 −4.51195
\(46\) 0 0
\(47\) −6.11779 −0.892372 −0.446186 0.894940i \(-0.647218\pi\)
−0.446186 + 0.894940i \(0.647218\pi\)
\(48\) 0 0
\(49\) 15.4195 2.20278
\(50\) 0 0
\(51\) −5.72994 −0.802352
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −15.5502 −2.09679
\(56\) 0 0
\(57\) −3.17454 −0.420479
\(58\) 0 0
\(59\) −12.4760 −1.62424 −0.812120 0.583491i \(-0.801686\pi\)
−0.812120 + 0.583491i \(0.801686\pi\)
\(60\) 0 0
\(61\) 4.40643 0.564186 0.282093 0.959387i \(-0.408971\pi\)
0.282093 + 0.959387i \(0.408971\pi\)
\(62\) 0 0
\(63\) −33.5125 −4.22218
\(64\) 0 0
\(65\) −15.9948 −1.98391
\(66\) 0 0
\(67\) −14.2338 −1.73894 −0.869470 0.493986i \(-0.835539\pi\)
−0.869470 + 0.493986i \(0.835539\pi\)
\(68\) 0 0
\(69\) −7.89271 −0.950171
\(70\) 0 0
\(71\) 4.24339 0.503597 0.251799 0.967780i \(-0.418978\pi\)
0.251799 + 0.967780i \(0.418978\pi\)
\(72\) 0 0
\(73\) −10.7983 −1.26384 −0.631921 0.775033i \(-0.717733\pi\)
−0.631921 + 0.775033i \(0.717733\pi\)
\(74\) 0 0
\(75\) 42.1815 4.87071
\(76\) 0 0
\(77\) −17.2176 −1.96212
\(78\) 0 0
\(79\) −3.93332 −0.442533 −0.221267 0.975213i \(-0.571019\pi\)
−0.221267 + 0.975213i \(0.571019\pi\)
\(80\) 0 0
\(81\) 19.8611 2.20679
\(82\) 0 0
\(83\) −11.0579 −1.21376 −0.606882 0.794792i \(-0.707580\pi\)
−0.606882 + 0.794792i \(0.707580\pi\)
\(84\) 0 0
\(85\) 7.71872 0.837212
\(86\) 0 0
\(87\) 1.32404 0.141952
\(88\) 0 0
\(89\) 3.91713 0.415215 0.207608 0.978212i \(-0.433432\pi\)
0.207608 + 0.978212i \(0.433432\pi\)
\(90\) 0 0
\(91\) −17.7099 −1.85650
\(92\) 0 0
\(93\) −20.4053 −2.11593
\(94\) 0 0
\(95\) 4.27638 0.438747
\(96\) 0 0
\(97\) 7.08577 0.719451 0.359726 0.933058i \(-0.382870\pi\)
0.359726 + 0.933058i \(0.382870\pi\)
\(98\) 0 0
\(99\) 25.7367 2.58664
\(100\) 0 0
\(101\) 6.28317 0.625199 0.312600 0.949885i \(-0.398800\pi\)
0.312600 + 0.949885i \(0.398800\pi\)
\(102\) 0 0
\(103\) −1.36553 −0.134550 −0.0672750 0.997734i \(-0.521430\pi\)
−0.0672750 + 0.997734i \(0.521430\pi\)
\(104\) 0 0
\(105\) 64.2792 6.27301
\(106\) 0 0
\(107\) −14.7230 −1.42333 −0.711664 0.702520i \(-0.752058\pi\)
−0.711664 + 0.702520i \(0.752058\pi\)
\(108\) 0 0
\(109\) 17.0448 1.63260 0.816299 0.577630i \(-0.196022\pi\)
0.816299 + 0.577630i \(0.196022\pi\)
\(110\) 0 0
\(111\) −15.8000 −1.49967
\(112\) 0 0
\(113\) −5.32408 −0.500847 −0.250424 0.968136i \(-0.580570\pi\)
−0.250424 + 0.968136i \(0.580570\pi\)
\(114\) 0 0
\(115\) 10.6322 0.991453
\(116\) 0 0
\(117\) 26.4726 2.44740
\(118\) 0 0
\(119\) 8.54636 0.783444
\(120\) 0 0
\(121\) 2.22264 0.202058
\(122\) 0 0
\(123\) −0.0411964 −0.00371455
\(124\) 0 0
\(125\) −35.4402 −3.16987
\(126\) 0 0
\(127\) −11.2335 −0.996814 −0.498407 0.866943i \(-0.666081\pi\)
−0.498407 + 0.866943i \(0.666081\pi\)
\(128\) 0 0
\(129\) −35.5154 −3.12696
\(130\) 0 0
\(131\) −2.46946 −0.215758 −0.107879 0.994164i \(-0.534406\pi\)
−0.107879 + 0.994164i \(0.534406\pi\)
\(132\) 0 0
\(133\) 4.73492 0.410570
\(134\) 0 0
\(135\) −55.3575 −4.76442
\(136\) 0 0
\(137\) 8.84634 0.755794 0.377897 0.925848i \(-0.376647\pi\)
0.377897 + 0.925848i \(0.376647\pi\)
\(138\) 0 0
\(139\) 15.0915 1.28004 0.640021 0.768358i \(-0.278926\pi\)
0.640021 + 0.768358i \(0.278926\pi\)
\(140\) 0 0
\(141\) −19.4212 −1.63556
\(142\) 0 0
\(143\) 13.6007 1.13735
\(144\) 0 0
\(145\) −1.78360 −0.148120
\(146\) 0 0
\(147\) 48.9497 4.03731
\(148\) 0 0
\(149\) 3.63193 0.297540 0.148770 0.988872i \(-0.452469\pi\)
0.148770 + 0.988872i \(0.452469\pi\)
\(150\) 0 0
\(151\) 5.70641 0.464381 0.232190 0.972670i \(-0.425411\pi\)
0.232190 + 0.972670i \(0.425411\pi\)
\(152\) 0 0
\(153\) −12.7751 −1.03280
\(154\) 0 0
\(155\) 27.4877 2.20786
\(156\) 0 0
\(157\) −16.8079 −1.34142 −0.670709 0.741721i \(-0.734010\pi\)
−0.670709 + 0.741721i \(0.734010\pi\)
\(158\) 0 0
\(159\) 3.17454 0.251758
\(160\) 0 0
\(161\) 11.7722 0.927779
\(162\) 0 0
\(163\) −22.2051 −1.73924 −0.869619 0.493724i \(-0.835635\pi\)
−0.869619 + 0.493724i \(0.835635\pi\)
\(164\) 0 0
\(165\) −49.3647 −3.84304
\(166\) 0 0
\(167\) 10.4987 0.812417 0.406208 0.913780i \(-0.366851\pi\)
0.406208 + 0.913780i \(0.366851\pi\)
\(168\) 0 0
\(169\) 0.989635 0.0761258
\(170\) 0 0
\(171\) −7.07773 −0.541248
\(172\) 0 0
\(173\) −13.0826 −0.994649 −0.497324 0.867565i \(-0.665684\pi\)
−0.497324 + 0.867565i \(0.665684\pi\)
\(174\) 0 0
\(175\) −62.9149 −4.75592
\(176\) 0 0
\(177\) −39.6057 −2.97695
\(178\) 0 0
\(179\) 18.7498 1.40142 0.700712 0.713444i \(-0.252866\pi\)
0.700712 + 0.713444i \(0.252866\pi\)
\(180\) 0 0
\(181\) 17.9054 1.33090 0.665449 0.746443i \(-0.268240\pi\)
0.665449 + 0.746443i \(0.268240\pi\)
\(182\) 0 0
\(183\) 13.9884 1.03405
\(184\) 0 0
\(185\) 21.2840 1.56483
\(186\) 0 0
\(187\) −6.56338 −0.479962
\(188\) 0 0
\(189\) −61.2933 −4.45843
\(190\) 0 0
\(191\) −24.2695 −1.75608 −0.878039 0.478588i \(-0.841149\pi\)
−0.878039 + 0.478588i \(0.841149\pi\)
\(192\) 0 0
\(193\) −27.6589 −1.99093 −0.995467 0.0951104i \(-0.969680\pi\)
−0.995467 + 0.0951104i \(0.969680\pi\)
\(194\) 0 0
\(195\) −50.7763 −3.63617
\(196\) 0 0
\(197\) 17.5481 1.25025 0.625126 0.780524i \(-0.285047\pi\)
0.625126 + 0.780524i \(0.285047\pi\)
\(198\) 0 0
\(199\) −7.03326 −0.498575 −0.249287 0.968430i \(-0.580196\pi\)
−0.249287 + 0.968430i \(0.580196\pi\)
\(200\) 0 0
\(201\) −45.1859 −3.18717
\(202\) 0 0
\(203\) −1.97484 −0.138607
\(204\) 0 0
\(205\) 0.0554950 0.00387594
\(206\) 0 0
\(207\) −17.5970 −1.22308
\(208\) 0 0
\(209\) −3.63629 −0.251528
\(210\) 0 0
\(211\) −9.66387 −0.665288 −0.332644 0.943052i \(-0.607941\pi\)
−0.332644 + 0.943052i \(0.607941\pi\)
\(212\) 0 0
\(213\) 13.4708 0.923005
\(214\) 0 0
\(215\) 47.8423 3.26282
\(216\) 0 0
\(217\) 30.4351 2.06607
\(218\) 0 0
\(219\) −34.2796 −2.31640
\(220\) 0 0
\(221\) −6.75106 −0.454125
\(222\) 0 0
\(223\) 12.1280 0.812151 0.406075 0.913840i \(-0.366897\pi\)
0.406075 + 0.913840i \(0.366897\pi\)
\(224\) 0 0
\(225\) 94.0449 6.26966
\(226\) 0 0
\(227\) 18.5331 1.23009 0.615043 0.788493i \(-0.289139\pi\)
0.615043 + 0.788493i \(0.289139\pi\)
\(228\) 0 0
\(229\) −21.6898 −1.43330 −0.716650 0.697433i \(-0.754326\pi\)
−0.716650 + 0.697433i \(0.754326\pi\)
\(230\) 0 0
\(231\) −54.6579 −3.59623
\(232\) 0 0
\(233\) −6.77239 −0.443674 −0.221837 0.975084i \(-0.571205\pi\)
−0.221837 + 0.975084i \(0.571205\pi\)
\(234\) 0 0
\(235\) 26.1620 1.70662
\(236\) 0 0
\(237\) −12.4865 −0.811086
\(238\) 0 0
\(239\) 7.16525 0.463481 0.231741 0.972778i \(-0.425558\pi\)
0.231741 + 0.972778i \(0.425558\pi\)
\(240\) 0 0
\(241\) −2.06497 −0.133017 −0.0665083 0.997786i \(-0.521186\pi\)
−0.0665083 + 0.997786i \(0.521186\pi\)
\(242\) 0 0
\(243\) 24.2151 1.55340
\(244\) 0 0
\(245\) −65.9395 −4.21272
\(246\) 0 0
\(247\) −3.74027 −0.237988
\(248\) 0 0
\(249\) −35.1038 −2.22462
\(250\) 0 0
\(251\) 7.87980 0.497369 0.248684 0.968585i \(-0.420002\pi\)
0.248684 + 0.968585i \(0.420002\pi\)
\(252\) 0 0
\(253\) −9.04074 −0.568386
\(254\) 0 0
\(255\) 24.5034 1.53446
\(256\) 0 0
\(257\) 24.1450 1.50613 0.753063 0.657948i \(-0.228575\pi\)
0.753063 + 0.657948i \(0.228575\pi\)
\(258\) 0 0
\(259\) 23.5662 1.46433
\(260\) 0 0
\(261\) 2.95199 0.182723
\(262\) 0 0
\(263\) −9.62011 −0.593202 −0.296601 0.955002i \(-0.595853\pi\)
−0.296601 + 0.955002i \(0.595853\pi\)
\(264\) 0 0
\(265\) −4.27638 −0.262696
\(266\) 0 0
\(267\) 12.4351 0.761017
\(268\) 0 0
\(269\) 20.6103 1.25663 0.628316 0.777958i \(-0.283745\pi\)
0.628316 + 0.777958i \(0.283745\pi\)
\(270\) 0 0
\(271\) −14.7013 −0.893040 −0.446520 0.894774i \(-0.647337\pi\)
−0.446520 + 0.894774i \(0.647337\pi\)
\(272\) 0 0
\(273\) −56.2208 −3.40264
\(274\) 0 0
\(275\) 48.3170 2.91363
\(276\) 0 0
\(277\) 3.43234 0.206229 0.103115 0.994669i \(-0.467119\pi\)
0.103115 + 0.994669i \(0.467119\pi\)
\(278\) 0 0
\(279\) −45.4942 −2.72367
\(280\) 0 0
\(281\) −28.8272 −1.71968 −0.859842 0.510560i \(-0.829438\pi\)
−0.859842 + 0.510560i \(0.829438\pi\)
\(282\) 0 0
\(283\) 31.7392 1.88670 0.943349 0.331802i \(-0.107657\pi\)
0.943349 + 0.331802i \(0.107657\pi\)
\(284\) 0 0
\(285\) 13.5756 0.804147
\(286\) 0 0
\(287\) 0.0614455 0.00362701
\(288\) 0 0
\(289\) −13.7421 −0.808359
\(290\) 0 0
\(291\) 22.4941 1.31863
\(292\) 0 0
\(293\) −8.61913 −0.503535 −0.251767 0.967788i \(-0.581012\pi\)
−0.251767 + 0.967788i \(0.581012\pi\)
\(294\) 0 0
\(295\) 53.3522 3.10629
\(296\) 0 0
\(297\) 47.0716 2.73137
\(298\) 0 0
\(299\) −9.29925 −0.537790
\(300\) 0 0
\(301\) 52.9722 3.05327
\(302\) 0 0
\(303\) 19.9462 1.14588
\(304\) 0 0
\(305\) −18.8436 −1.07898
\(306\) 0 0
\(307\) 16.1844 0.923694 0.461847 0.886960i \(-0.347187\pi\)
0.461847 + 0.886960i \(0.347187\pi\)
\(308\) 0 0
\(309\) −4.33495 −0.246607
\(310\) 0 0
\(311\) −4.62784 −0.262421 −0.131210 0.991355i \(-0.541886\pi\)
−0.131210 + 0.991355i \(0.541886\pi\)
\(312\) 0 0
\(313\) −7.99505 −0.451907 −0.225953 0.974138i \(-0.572550\pi\)
−0.225953 + 0.974138i \(0.572550\pi\)
\(314\) 0 0
\(315\) 143.312 8.07473
\(316\) 0 0
\(317\) 23.0306 1.29353 0.646763 0.762691i \(-0.276122\pi\)
0.646763 + 0.762691i \(0.276122\pi\)
\(318\) 0 0
\(319\) 1.51663 0.0849149
\(320\) 0 0
\(321\) −46.7389 −2.60871
\(322\) 0 0
\(323\) 1.80496 0.100431
\(324\) 0 0
\(325\) 49.6986 2.75678
\(326\) 0 0
\(327\) 54.1095 2.99226
\(328\) 0 0
\(329\) 28.9672 1.59702
\(330\) 0 0
\(331\) 9.06911 0.498484 0.249242 0.968441i \(-0.419819\pi\)
0.249242 + 0.968441i \(0.419819\pi\)
\(332\) 0 0
\(333\) −35.2266 −1.93041
\(334\) 0 0
\(335\) 60.8693 3.32564
\(336\) 0 0
\(337\) −11.6223 −0.633108 −0.316554 0.948575i \(-0.602526\pi\)
−0.316554 + 0.948575i \(0.602526\pi\)
\(338\) 0 0
\(339\) −16.9015 −0.917965
\(340\) 0 0
\(341\) −23.3733 −1.26574
\(342\) 0 0
\(343\) −39.8654 −2.15253
\(344\) 0 0
\(345\) 33.7522 1.81716
\(346\) 0 0
\(347\) 9.64973 0.518024 0.259012 0.965874i \(-0.416603\pi\)
0.259012 + 0.965874i \(0.416603\pi\)
\(348\) 0 0
\(349\) 12.8659 0.688695 0.344347 0.938842i \(-0.388100\pi\)
0.344347 + 0.938842i \(0.388100\pi\)
\(350\) 0 0
\(351\) 48.4176 2.58434
\(352\) 0 0
\(353\) −25.3810 −1.35089 −0.675446 0.737410i \(-0.736049\pi\)
−0.675446 + 0.737410i \(0.736049\pi\)
\(354\) 0 0
\(355\) −18.1463 −0.963108
\(356\) 0 0
\(357\) 27.1308 1.43591
\(358\) 0 0
\(359\) −8.73670 −0.461106 −0.230553 0.973060i \(-0.574053\pi\)
−0.230553 + 0.973060i \(0.574053\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 7.05587 0.370337
\(364\) 0 0
\(365\) 46.1775 2.41704
\(366\) 0 0
\(367\) 10.8751 0.567675 0.283838 0.958872i \(-0.408392\pi\)
0.283838 + 0.958872i \(0.408392\pi\)
\(368\) 0 0
\(369\) −0.0918484 −0.00478144
\(370\) 0 0
\(371\) −4.73492 −0.245825
\(372\) 0 0
\(373\) −0.610842 −0.0316282 −0.0158141 0.999875i \(-0.505034\pi\)
−0.0158141 + 0.999875i \(0.505034\pi\)
\(374\) 0 0
\(375\) −112.507 −5.80981
\(376\) 0 0
\(377\) 1.56000 0.0803438
\(378\) 0 0
\(379\) −1.22331 −0.0628374 −0.0314187 0.999506i \(-0.510003\pi\)
−0.0314187 + 0.999506i \(0.510003\pi\)
\(380\) 0 0
\(381\) −35.6613 −1.82698
\(382\) 0 0
\(383\) −4.17965 −0.213570 −0.106785 0.994282i \(-0.534056\pi\)
−0.106785 + 0.994282i \(0.534056\pi\)
\(384\) 0 0
\(385\) 73.6288 3.75247
\(386\) 0 0
\(387\) −79.1826 −4.02508
\(388\) 0 0
\(389\) 11.6166 0.588984 0.294492 0.955654i \(-0.404850\pi\)
0.294492 + 0.955654i \(0.404850\pi\)
\(390\) 0 0
\(391\) 4.48759 0.226947
\(392\) 0 0
\(393\) −7.83941 −0.395446
\(394\) 0 0
\(395\) 16.8204 0.846325
\(396\) 0 0
\(397\) −17.0512 −0.855776 −0.427888 0.903832i \(-0.640742\pi\)
−0.427888 + 0.903832i \(0.640742\pi\)
\(398\) 0 0
\(399\) 15.0312 0.752502
\(400\) 0 0
\(401\) 7.21698 0.360399 0.180199 0.983630i \(-0.442326\pi\)
0.180199 + 0.983630i \(0.442326\pi\)
\(402\) 0 0
\(403\) −24.0417 −1.19760
\(404\) 0 0
\(405\) −84.9337 −4.22039
\(406\) 0 0
\(407\) −18.0982 −0.897096
\(408\) 0 0
\(409\) 31.7986 1.57234 0.786170 0.618010i \(-0.212061\pi\)
0.786170 + 0.618010i \(0.212061\pi\)
\(410\) 0 0
\(411\) 28.0831 1.38524
\(412\) 0 0
\(413\) 59.0729 2.90679
\(414\) 0 0
\(415\) 47.2879 2.32127
\(416\) 0 0
\(417\) 47.9085 2.34609
\(418\) 0 0
\(419\) 28.4319 1.38899 0.694494 0.719499i \(-0.255628\pi\)
0.694494 + 0.719499i \(0.255628\pi\)
\(420\) 0 0
\(421\) −22.8992 −1.11604 −0.558019 0.829828i \(-0.688438\pi\)
−0.558019 + 0.829828i \(0.688438\pi\)
\(422\) 0 0
\(423\) −43.3001 −2.10532
\(424\) 0 0
\(425\) −23.9834 −1.16336
\(426\) 0 0
\(427\) −20.8641 −1.00968
\(428\) 0 0
\(429\) 43.1761 2.08456
\(430\) 0 0
\(431\) 12.3161 0.593247 0.296623 0.954995i \(-0.404139\pi\)
0.296623 + 0.954995i \(0.404139\pi\)
\(432\) 0 0
\(433\) −0.236191 −0.0113506 −0.00567530 0.999984i \(-0.501807\pi\)
−0.00567530 + 0.999984i \(0.501807\pi\)
\(434\) 0 0
\(435\) −5.66210 −0.271477
\(436\) 0 0
\(437\) 2.48625 0.118933
\(438\) 0 0
\(439\) −4.88355 −0.233079 −0.116540 0.993186i \(-0.537180\pi\)
−0.116540 + 0.993186i \(0.537180\pi\)
\(440\) 0 0
\(441\) 109.135 5.19689
\(442\) 0 0
\(443\) 26.2317 1.24630 0.623152 0.782101i \(-0.285852\pi\)
0.623152 + 0.782101i \(0.285852\pi\)
\(444\) 0 0
\(445\) −16.7512 −0.794081
\(446\) 0 0
\(447\) 11.5297 0.545338
\(448\) 0 0
\(449\) 2.34028 0.110445 0.0552224 0.998474i \(-0.482413\pi\)
0.0552224 + 0.998474i \(0.482413\pi\)
\(450\) 0 0
\(451\) −0.0471885 −0.00222202
\(452\) 0 0
\(453\) 18.1152 0.851128
\(454\) 0 0
\(455\) 75.7342 3.55047
\(456\) 0 0
\(457\) 8.04674 0.376410 0.188205 0.982130i \(-0.439733\pi\)
0.188205 + 0.982130i \(0.439733\pi\)
\(458\) 0 0
\(459\) −23.3652 −1.09059
\(460\) 0 0
\(461\) 37.6901 1.75540 0.877702 0.479206i \(-0.159075\pi\)
0.877702 + 0.479206i \(0.159075\pi\)
\(462\) 0 0
\(463\) 5.57700 0.259185 0.129592 0.991567i \(-0.458633\pi\)
0.129592 + 0.991567i \(0.458633\pi\)
\(464\) 0 0
\(465\) 87.2609 4.04663
\(466\) 0 0
\(467\) −30.5446 −1.41343 −0.706717 0.707496i \(-0.749825\pi\)
−0.706717 + 0.707496i \(0.749825\pi\)
\(468\) 0 0
\(469\) 67.3960 3.11206
\(470\) 0 0
\(471\) −53.3575 −2.45858
\(472\) 0 0
\(473\) −40.6813 −1.87053
\(474\) 0 0
\(475\) −13.2874 −0.609669
\(476\) 0 0
\(477\) 7.07773 0.324067
\(478\) 0 0
\(479\) 1.63999 0.0749330 0.0374665 0.999298i \(-0.488071\pi\)
0.0374665 + 0.999298i \(0.488071\pi\)
\(480\) 0 0
\(481\) −18.6157 −0.848804
\(482\) 0 0
\(483\) 37.3714 1.70046
\(484\) 0 0
\(485\) −30.3015 −1.37592
\(486\) 0 0
\(487\) −10.3716 −0.469983 −0.234991 0.971997i \(-0.575506\pi\)
−0.234991 + 0.971997i \(0.575506\pi\)
\(488\) 0 0
\(489\) −70.4911 −3.18772
\(490\) 0 0
\(491\) −38.0504 −1.71719 −0.858595 0.512654i \(-0.828662\pi\)
−0.858595 + 0.512654i \(0.828662\pi\)
\(492\) 0 0
\(493\) −0.752816 −0.0339051
\(494\) 0 0
\(495\) −110.060 −4.94683
\(496\) 0 0
\(497\) −20.0921 −0.901253
\(498\) 0 0
\(499\) −33.9758 −1.52097 −0.760483 0.649358i \(-0.775038\pi\)
−0.760483 + 0.649358i \(0.775038\pi\)
\(500\) 0 0
\(501\) 33.3287 1.48902
\(502\) 0 0
\(503\) 13.4820 0.601132 0.300566 0.953761i \(-0.402824\pi\)
0.300566 + 0.953761i \(0.402824\pi\)
\(504\) 0 0
\(505\) −26.8692 −1.19567
\(506\) 0 0
\(507\) 3.14164 0.139525
\(508\) 0 0
\(509\) 13.3229 0.590529 0.295264 0.955416i \(-0.404592\pi\)
0.295264 + 0.955416i \(0.404592\pi\)
\(510\) 0 0
\(511\) 51.1289 2.26181
\(512\) 0 0
\(513\) −12.9449 −0.571533
\(514\) 0 0
\(515\) 5.83954 0.257321
\(516\) 0 0
\(517\) −22.2461 −0.978382
\(518\) 0 0
\(519\) −41.5312 −1.82302
\(520\) 0 0
\(521\) −6.51367 −0.285369 −0.142685 0.989768i \(-0.545573\pi\)
−0.142685 + 0.989768i \(0.545573\pi\)
\(522\) 0 0
\(523\) −9.38391 −0.410330 −0.205165 0.978727i \(-0.565773\pi\)
−0.205165 + 0.978727i \(0.565773\pi\)
\(524\) 0 0
\(525\) −199.726 −8.71677
\(526\) 0 0
\(527\) 11.6019 0.505388
\(528\) 0 0
\(529\) −16.8186 −0.731242
\(530\) 0 0
\(531\) −88.3019 −3.83198
\(532\) 0 0
\(533\) −0.0485379 −0.00210241
\(534\) 0 0
\(535\) 62.9612 2.72205
\(536\) 0 0
\(537\) 59.5220 2.56856
\(538\) 0 0
\(539\) 56.0697 2.41509
\(540\) 0 0
\(541\) −2.62461 −0.112841 −0.0564203 0.998407i \(-0.517969\pi\)
−0.0564203 + 0.998407i \(0.517969\pi\)
\(542\) 0 0
\(543\) 56.8415 2.43930
\(544\) 0 0
\(545\) −72.8901 −3.12227
\(546\) 0 0
\(547\) −1.94741 −0.0832651 −0.0416325 0.999133i \(-0.513256\pi\)
−0.0416325 + 0.999133i \(0.513256\pi\)
\(548\) 0 0
\(549\) 31.1876 1.33105
\(550\) 0 0
\(551\) −0.417081 −0.0177682
\(552\) 0 0
\(553\) 18.6240 0.791971
\(554\) 0 0
\(555\) 67.5670 2.86806
\(556\) 0 0
\(557\) 20.9226 0.886518 0.443259 0.896393i \(-0.353822\pi\)
0.443259 + 0.896393i \(0.353822\pi\)
\(558\) 0 0
\(559\) −41.8445 −1.76984
\(560\) 0 0
\(561\) −20.8358 −0.879686
\(562\) 0 0
\(563\) −19.8069 −0.834762 −0.417381 0.908732i \(-0.637052\pi\)
−0.417381 + 0.908732i \(0.637052\pi\)
\(564\) 0 0
\(565\) 22.7678 0.957848
\(566\) 0 0
\(567\) −94.0407 −3.94934
\(568\) 0 0
\(569\) 9.47854 0.397361 0.198680 0.980064i \(-0.436334\pi\)
0.198680 + 0.980064i \(0.436334\pi\)
\(570\) 0 0
\(571\) 20.5826 0.861356 0.430678 0.902506i \(-0.358275\pi\)
0.430678 + 0.902506i \(0.358275\pi\)
\(572\) 0 0
\(573\) −77.0446 −3.21858
\(574\) 0 0
\(575\) −33.0359 −1.37769
\(576\) 0 0
\(577\) 3.18773 0.132707 0.0663534 0.997796i \(-0.478864\pi\)
0.0663534 + 0.997796i \(0.478864\pi\)
\(578\) 0 0
\(579\) −87.8045 −3.64903
\(580\) 0 0
\(581\) 52.3583 2.17219
\(582\) 0 0
\(583\) 3.63629 0.150600
\(584\) 0 0
\(585\) −113.207 −4.68054
\(586\) 0 0
\(587\) 40.7227 1.68081 0.840403 0.541962i \(-0.182318\pi\)
0.840403 + 0.541962i \(0.182318\pi\)
\(588\) 0 0
\(589\) 6.42779 0.264852
\(590\) 0 0
\(591\) 55.7073 2.29149
\(592\) 0 0
\(593\) −0.612310 −0.0251446 −0.0125723 0.999921i \(-0.504002\pi\)
−0.0125723 + 0.999921i \(0.504002\pi\)
\(594\) 0 0
\(595\) −36.5475 −1.49830
\(596\) 0 0
\(597\) −22.3274 −0.913800
\(598\) 0 0
\(599\) −29.7994 −1.21757 −0.608785 0.793335i \(-0.708343\pi\)
−0.608785 + 0.793335i \(0.708343\pi\)
\(600\) 0 0
\(601\) 13.3764 0.545635 0.272818 0.962066i \(-0.412044\pi\)
0.272818 + 0.962066i \(0.412044\pi\)
\(602\) 0 0
\(603\) −100.743 −4.10258
\(604\) 0 0
\(605\) −9.50485 −0.386427
\(606\) 0 0
\(607\) −24.9370 −1.01216 −0.506080 0.862486i \(-0.668906\pi\)
−0.506080 + 0.862486i \(0.668906\pi\)
\(608\) 0 0
\(609\) −6.26923 −0.254042
\(610\) 0 0
\(611\) −22.8822 −0.925715
\(612\) 0 0
\(613\) 7.02600 0.283778 0.141889 0.989883i \(-0.454682\pi\)
0.141889 + 0.989883i \(0.454682\pi\)
\(614\) 0 0
\(615\) 0.176171 0.00710391
\(616\) 0 0
\(617\) 36.7738 1.48046 0.740229 0.672355i \(-0.234717\pi\)
0.740229 + 0.672355i \(0.234717\pi\)
\(618\) 0 0
\(619\) −17.6301 −0.708613 −0.354306 0.935129i \(-0.615283\pi\)
−0.354306 + 0.935129i \(0.615283\pi\)
\(620\) 0 0
\(621\) −32.1844 −1.29151
\(622\) 0 0
\(623\) −18.5473 −0.743082
\(624\) 0 0
\(625\) 85.1187 3.40475
\(626\) 0 0
\(627\) −11.5436 −0.461006
\(628\) 0 0
\(629\) 8.98350 0.358196
\(630\) 0 0
\(631\) 32.4321 1.29110 0.645551 0.763717i \(-0.276628\pi\)
0.645551 + 0.763717i \(0.276628\pi\)
\(632\) 0 0
\(633\) −30.6784 −1.21936
\(634\) 0 0
\(635\) 48.0388 1.90636
\(636\) 0 0
\(637\) 57.6729 2.28509
\(638\) 0 0
\(639\) 30.0336 1.18811
\(640\) 0 0
\(641\) −33.5398 −1.32474 −0.662371 0.749176i \(-0.730450\pi\)
−0.662371 + 0.749176i \(0.730450\pi\)
\(642\) 0 0
\(643\) 36.7000 1.44731 0.723654 0.690163i \(-0.242461\pi\)
0.723654 + 0.690163i \(0.242461\pi\)
\(644\) 0 0
\(645\) 151.877 5.98017
\(646\) 0 0
\(647\) 18.3697 0.722186 0.361093 0.932530i \(-0.382404\pi\)
0.361093 + 0.932530i \(0.382404\pi\)
\(648\) 0 0
\(649\) −45.3665 −1.78079
\(650\) 0 0
\(651\) 96.6175 3.78674
\(652\) 0 0
\(653\) −43.9517 −1.71996 −0.859982 0.510324i \(-0.829526\pi\)
−0.859982 + 0.510324i \(0.829526\pi\)
\(654\) 0 0
\(655\) 10.5604 0.412627
\(656\) 0 0
\(657\) −76.4273 −2.98171
\(658\) 0 0
\(659\) 15.3575 0.598245 0.299122 0.954215i \(-0.403306\pi\)
0.299122 + 0.954215i \(0.403306\pi\)
\(660\) 0 0
\(661\) −37.3749 −1.45372 −0.726858 0.686787i \(-0.759020\pi\)
−0.726858 + 0.686787i \(0.759020\pi\)
\(662\) 0 0
\(663\) −21.4315 −0.832332
\(664\) 0 0
\(665\) −20.2483 −0.785196
\(666\) 0 0
\(667\) −1.03697 −0.0401515
\(668\) 0 0
\(669\) 38.5009 1.48853
\(670\) 0 0
\(671\) 16.0231 0.618565
\(672\) 0 0
\(673\) 1.34765 0.0519481 0.0259741 0.999663i \(-0.491731\pi\)
0.0259741 + 0.999663i \(0.491731\pi\)
\(674\) 0 0
\(675\) 172.005 6.62048
\(676\) 0 0
\(677\) 42.4717 1.63232 0.816160 0.577825i \(-0.196099\pi\)
0.816160 + 0.577825i \(0.196099\pi\)
\(678\) 0 0
\(679\) −33.5505 −1.28755
\(680\) 0 0
\(681\) 58.8342 2.25453
\(682\) 0 0
\(683\) −16.6167 −0.635820 −0.317910 0.948121i \(-0.602981\pi\)
−0.317910 + 0.948121i \(0.602981\pi\)
\(684\) 0 0
\(685\) −37.8303 −1.44542
\(686\) 0 0
\(687\) −68.8552 −2.62699
\(688\) 0 0
\(689\) 3.74027 0.142493
\(690\) 0 0
\(691\) 36.2051 1.37731 0.688654 0.725090i \(-0.258202\pi\)
0.688654 + 0.725090i \(0.258202\pi\)
\(692\) 0 0
\(693\) −121.861 −4.62913
\(694\) 0 0
\(695\) −64.5368 −2.44802
\(696\) 0 0
\(697\) 0.0234232 0.000887217 0
\(698\) 0 0
\(699\) −21.4993 −0.813177
\(700\) 0 0
\(701\) 8.01274 0.302637 0.151319 0.988485i \(-0.451648\pi\)
0.151319 + 0.988485i \(0.451648\pi\)
\(702\) 0 0
\(703\) 4.97711 0.187715
\(704\) 0 0
\(705\) 83.0525 3.12794
\(706\) 0 0
\(707\) −29.7503 −1.11888
\(708\) 0 0
\(709\) −26.0454 −0.978155 −0.489077 0.872240i \(-0.662666\pi\)
−0.489077 + 0.872240i \(0.662666\pi\)
\(710\) 0 0
\(711\) −27.8390 −1.04404
\(712\) 0 0
\(713\) 15.9811 0.598497
\(714\) 0 0
\(715\) −58.1619 −2.17513
\(716\) 0 0
\(717\) 22.7464 0.849480
\(718\) 0 0
\(719\) 24.8824 0.927959 0.463979 0.885846i \(-0.346421\pi\)
0.463979 + 0.885846i \(0.346421\pi\)
\(720\) 0 0
\(721\) 6.46569 0.240795
\(722\) 0 0
\(723\) −6.55535 −0.243796
\(724\) 0 0
\(725\) 5.54193 0.205822
\(726\) 0 0
\(727\) 7.24276 0.268619 0.134309 0.990939i \(-0.457118\pi\)
0.134309 + 0.990939i \(0.457118\pi\)
\(728\) 0 0
\(729\) 17.2887 0.640322
\(730\) 0 0
\(731\) 20.1932 0.746871
\(732\) 0 0
\(733\) 1.98752 0.0734107 0.0367053 0.999326i \(-0.488314\pi\)
0.0367053 + 0.999326i \(0.488314\pi\)
\(734\) 0 0
\(735\) −209.328 −7.72117
\(736\) 0 0
\(737\) −51.7584 −1.90655
\(738\) 0 0
\(739\) −29.7505 −1.09439 −0.547195 0.837005i \(-0.684305\pi\)
−0.547195 + 0.837005i \(0.684305\pi\)
\(740\) 0 0
\(741\) −11.8737 −0.436190
\(742\) 0 0
\(743\) −18.9921 −0.696752 −0.348376 0.937355i \(-0.613267\pi\)
−0.348376 + 0.937355i \(0.613267\pi\)
\(744\) 0 0
\(745\) −15.5315 −0.569031
\(746\) 0 0
\(747\) −78.2650 −2.86357
\(748\) 0 0
\(749\) 69.7123 2.54723
\(750\) 0 0
\(751\) 37.1163 1.35439 0.677196 0.735802i \(-0.263195\pi\)
0.677196 + 0.735802i \(0.263195\pi\)
\(752\) 0 0
\(753\) 25.0148 0.911589
\(754\) 0 0
\(755\) −24.4028 −0.888108
\(756\) 0 0
\(757\) 13.1729 0.478776 0.239388 0.970924i \(-0.423053\pi\)
0.239388 + 0.970924i \(0.423053\pi\)
\(758\) 0 0
\(759\) −28.7002 −1.04175
\(760\) 0 0
\(761\) 54.5440 1.97722 0.988610 0.150503i \(-0.0480893\pi\)
0.988610 + 0.150503i \(0.0480893\pi\)
\(762\) 0 0
\(763\) −80.7058 −2.92175
\(764\) 0 0
\(765\) 54.6310 1.97519
\(766\) 0 0
\(767\) −46.6637 −1.68493
\(768\) 0 0
\(769\) −33.6028 −1.21175 −0.605873 0.795561i \(-0.707176\pi\)
−0.605873 + 0.795561i \(0.707176\pi\)
\(770\) 0 0
\(771\) 76.6495 2.76046
\(772\) 0 0
\(773\) −3.50565 −0.126090 −0.0630448 0.998011i \(-0.520081\pi\)
−0.0630448 + 0.998011i \(0.520081\pi\)
\(774\) 0 0
\(775\) −85.4088 −3.06798
\(776\) 0 0
\(777\) 74.8119 2.68386
\(778\) 0 0
\(779\) 0.0129771 0.000464953 0
\(780\) 0 0
\(781\) 15.4302 0.552136
\(782\) 0 0
\(783\) 5.39909 0.192948
\(784\) 0 0
\(785\) 71.8771 2.56540
\(786\) 0 0
\(787\) −20.7607 −0.740041 −0.370020 0.929024i \(-0.620649\pi\)
−0.370020 + 0.929024i \(0.620649\pi\)
\(788\) 0 0
\(789\) −30.5395 −1.08723
\(790\) 0 0
\(791\) 25.2091 0.896332
\(792\) 0 0
\(793\) 16.4813 0.585267
\(794\) 0 0
\(795\) −13.5756 −0.481476
\(796\) 0 0
\(797\) −16.5479 −0.586156 −0.293078 0.956088i \(-0.594680\pi\)
−0.293078 + 0.956088i \(0.594680\pi\)
\(798\) 0 0
\(799\) 11.0424 0.390652
\(800\) 0 0
\(801\) 27.7244 0.979595
\(802\) 0 0
\(803\) −39.2657 −1.38566
\(804\) 0 0
\(805\) −50.3424 −1.77434
\(806\) 0 0
\(807\) 65.4283 2.30319
\(808\) 0 0
\(809\) 49.4756 1.73947 0.869735 0.493519i \(-0.164290\pi\)
0.869735 + 0.493519i \(0.164290\pi\)
\(810\) 0 0
\(811\) −37.7298 −1.32487 −0.662436 0.749119i \(-0.730477\pi\)
−0.662436 + 0.749119i \(0.730477\pi\)
\(812\) 0 0
\(813\) −46.6699 −1.63679
\(814\) 0 0
\(815\) 94.9574 3.32621
\(816\) 0 0
\(817\) 11.1876 0.391403
\(818\) 0 0
\(819\) −125.346 −4.37994
\(820\) 0 0
\(821\) 3.71452 0.129638 0.0648188 0.997897i \(-0.479353\pi\)
0.0648188 + 0.997897i \(0.479353\pi\)
\(822\) 0 0
\(823\) 45.1834 1.57500 0.787498 0.616317i \(-0.211376\pi\)
0.787498 + 0.616317i \(0.211376\pi\)
\(824\) 0 0
\(825\) 153.385 5.34016
\(826\) 0 0
\(827\) −11.7935 −0.410099 −0.205050 0.978752i \(-0.565736\pi\)
−0.205050 + 0.978752i \(0.565736\pi\)
\(828\) 0 0
\(829\) −16.8515 −0.585276 −0.292638 0.956223i \(-0.594533\pi\)
−0.292638 + 0.956223i \(0.594533\pi\)
\(830\) 0 0
\(831\) 10.8961 0.377982
\(832\) 0 0
\(833\) −27.8316 −0.964307
\(834\) 0 0
\(835\) −44.8966 −1.55371
\(836\) 0 0
\(837\) −83.2074 −2.87607
\(838\) 0 0
\(839\) −4.25734 −0.146980 −0.0734898 0.997296i \(-0.523414\pi\)
−0.0734898 + 0.997296i \(0.523414\pi\)
\(840\) 0 0
\(841\) −28.8260 −0.994002
\(842\) 0 0
\(843\) −91.5131 −3.15188
\(844\) 0 0
\(845\) −4.23206 −0.145587
\(846\) 0 0
\(847\) −10.5240 −0.361609
\(848\) 0 0
\(849\) 100.757 3.45799
\(850\) 0 0
\(851\) 12.3743 0.424187
\(852\) 0 0
\(853\) 0.607038 0.0207846 0.0103923 0.999946i \(-0.496692\pi\)
0.0103923 + 0.999946i \(0.496692\pi\)
\(854\) 0 0
\(855\) 30.2671 1.03511
\(856\) 0 0
\(857\) 0.617490 0.0210931 0.0105465 0.999944i \(-0.496643\pi\)
0.0105465 + 0.999944i \(0.496643\pi\)
\(858\) 0 0
\(859\) 15.0494 0.513478 0.256739 0.966481i \(-0.417352\pi\)
0.256739 + 0.966481i \(0.417352\pi\)
\(860\) 0 0
\(861\) 0.195061 0.00664767
\(862\) 0 0
\(863\) −11.0514 −0.376195 −0.188097 0.982150i \(-0.560232\pi\)
−0.188097 + 0.982150i \(0.560232\pi\)
\(864\) 0 0
\(865\) 55.9460 1.90222
\(866\) 0 0
\(867\) −43.6249 −1.48158
\(868\) 0 0
\(869\) −14.3027 −0.485187
\(870\) 0 0
\(871\) −53.2384 −1.80391
\(872\) 0 0
\(873\) 50.1512 1.69736
\(874\) 0 0
\(875\) 167.807 5.67290
\(876\) 0 0
\(877\) −27.4907 −0.928294 −0.464147 0.885758i \(-0.653639\pi\)
−0.464147 + 0.885758i \(0.653639\pi\)
\(878\) 0 0
\(879\) −27.3618 −0.922891
\(880\) 0 0
\(881\) −8.63410 −0.290890 −0.145445 0.989366i \(-0.546461\pi\)
−0.145445 + 0.989366i \(0.546461\pi\)
\(882\) 0 0
\(883\) −33.3515 −1.12237 −0.561183 0.827691i \(-0.689654\pi\)
−0.561183 + 0.827691i \(0.689654\pi\)
\(884\) 0 0
\(885\) 169.369 5.69328
\(886\) 0 0
\(887\) 12.0868 0.405834 0.202917 0.979196i \(-0.434958\pi\)
0.202917 + 0.979196i \(0.434958\pi\)
\(888\) 0 0
\(889\) 53.1898 1.78393
\(890\) 0 0
\(891\) 72.2208 2.41949
\(892\) 0 0
\(893\) 6.11779 0.204724
\(894\) 0 0
\(895\) −80.1812 −2.68016
\(896\) 0 0
\(897\) −29.5209 −0.985674
\(898\) 0 0
\(899\) −2.68091 −0.0894132
\(900\) 0 0
\(901\) −1.80496 −0.0601321
\(902\) 0 0
\(903\) 168.163 5.59610
\(904\) 0 0
\(905\) −76.5703 −2.54528
\(906\) 0 0
\(907\) −10.4689 −0.347615 −0.173807 0.984780i \(-0.555607\pi\)
−0.173807 + 0.984780i \(0.555607\pi\)
\(908\) 0 0
\(909\) 44.4706 1.47500
\(910\) 0 0
\(911\) 35.2074 1.16647 0.583236 0.812303i \(-0.301786\pi\)
0.583236 + 0.812303i \(0.301786\pi\)
\(912\) 0 0
\(913\) −40.2098 −1.33075
\(914\) 0 0
\(915\) −59.8198 −1.97758
\(916\) 0 0
\(917\) 11.6927 0.386127
\(918\) 0 0
\(919\) −11.4368 −0.377266 −0.188633 0.982048i \(-0.560406\pi\)
−0.188633 + 0.982048i \(0.560406\pi\)
\(920\) 0 0
\(921\) 51.3782 1.69297
\(922\) 0 0
\(923\) 15.8714 0.522414
\(924\) 0 0
\(925\) −66.1330 −2.17444
\(926\) 0 0
\(927\) −9.66489 −0.317436
\(928\) 0 0
\(929\) −28.3131 −0.928921 −0.464461 0.885594i \(-0.653752\pi\)
−0.464461 + 0.885594i \(0.653752\pi\)
\(930\) 0 0
\(931\) −15.4195 −0.505352
\(932\) 0 0
\(933\) −14.6913 −0.480971
\(934\) 0 0
\(935\) 28.0675 0.917906
\(936\) 0 0
\(937\) −8.47783 −0.276959 −0.138479 0.990365i \(-0.544221\pi\)
−0.138479 + 0.990365i \(0.544221\pi\)
\(938\) 0 0
\(939\) −25.3806 −0.828266
\(940\) 0 0
\(941\) 17.6707 0.576049 0.288025 0.957623i \(-0.407001\pi\)
0.288025 + 0.957623i \(0.407001\pi\)
\(942\) 0 0
\(943\) 0.0322643 0.00105067
\(944\) 0 0
\(945\) 262.113 8.52655
\(946\) 0 0
\(947\) −13.9249 −0.452500 −0.226250 0.974069i \(-0.572647\pi\)
−0.226250 + 0.974069i \(0.572647\pi\)
\(948\) 0 0
\(949\) −40.3885 −1.31107
\(950\) 0 0
\(951\) 73.1116 2.37080
\(952\) 0 0
\(953\) 54.2582 1.75760 0.878798 0.477193i \(-0.158346\pi\)
0.878798 + 0.477193i \(0.158346\pi\)
\(954\) 0 0
\(955\) 103.786 3.35842
\(956\) 0 0
\(957\) 4.81460 0.155634
\(958\) 0 0
\(959\) −41.8867 −1.35259
\(960\) 0 0
\(961\) 10.3165 0.332790
\(962\) 0 0
\(963\) −104.206 −3.35798
\(964\) 0 0
\(965\) 118.280 3.80757
\(966\) 0 0
\(967\) −55.5567 −1.78658 −0.893292 0.449476i \(-0.851611\pi\)
−0.893292 + 0.449476i \(0.851611\pi\)
\(968\) 0 0
\(969\) 5.72994 0.184072
\(970\) 0 0
\(971\) −38.6461 −1.24021 −0.620106 0.784518i \(-0.712910\pi\)
−0.620106 + 0.784518i \(0.712910\pi\)
\(972\) 0 0
\(973\) −71.4569 −2.29080
\(974\) 0 0
\(975\) 157.770 5.05270
\(976\) 0 0
\(977\) 39.0149 1.24820 0.624099 0.781345i \(-0.285466\pi\)
0.624099 + 0.781345i \(0.285466\pi\)
\(978\) 0 0
\(979\) 14.2439 0.455236
\(980\) 0 0
\(981\) 120.639 3.85170
\(982\) 0 0
\(983\) 13.0682 0.416811 0.208406 0.978042i \(-0.433173\pi\)
0.208406 + 0.978042i \(0.433173\pi\)
\(984\) 0 0
\(985\) −75.0425 −2.39105
\(986\) 0 0
\(987\) 91.9578 2.92705
\(988\) 0 0
\(989\) 27.8151 0.884468
\(990\) 0 0
\(991\) −42.5907 −1.35294 −0.676468 0.736472i \(-0.736490\pi\)
−0.676468 + 0.736472i \(0.736490\pi\)
\(992\) 0 0
\(993\) 28.7903 0.913633
\(994\) 0 0
\(995\) 30.0769 0.953502
\(996\) 0 0
\(997\) 34.2479 1.08464 0.542321 0.840171i \(-0.317546\pi\)
0.542321 + 0.840171i \(0.317546\pi\)
\(998\) 0 0
\(999\) −64.4284 −2.03842
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 \(a_p\))