Properties

Label 8048.2.a.p.1.3
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.31567\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.315672 q^{3} +2.25024 q^{5} +3.20647 q^{7} -2.90035 q^{9} +O(q^{10})\) \(q-0.315672 q^{3} +2.25024 q^{5} +3.20647 q^{7} -2.90035 q^{9} +0.218022 q^{11} -4.17856 q^{13} -0.710339 q^{15} -4.68939 q^{17} -3.43926 q^{19} -1.01219 q^{21} +3.99816 q^{23} +0.0635992 q^{25} +1.86257 q^{27} -0.712153 q^{29} -1.04933 q^{31} -0.0688235 q^{33} +7.21534 q^{35} +1.70998 q^{37} +1.31905 q^{39} +3.18460 q^{41} +6.35890 q^{43} -6.52650 q^{45} +3.87861 q^{47} +3.28144 q^{49} +1.48031 q^{51} -10.8877 q^{53} +0.490604 q^{55} +1.08568 q^{57} +2.63793 q^{59} +11.1544 q^{61} -9.29988 q^{63} -9.40279 q^{65} -6.09170 q^{67} -1.26210 q^{69} -9.40515 q^{71} -2.78532 q^{73} -0.0200765 q^{75} +0.699082 q^{77} -5.16993 q^{79} +8.11309 q^{81} -1.83793 q^{83} -10.5523 q^{85} +0.224807 q^{87} -8.08786 q^{89} -13.3984 q^{91} +0.331245 q^{93} -7.73917 q^{95} -12.9058 q^{97} -0.632342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + O(q^{10}) \) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + 3q^{11} - 18q^{13} + 2q^{15} - 11q^{17} + q^{21} + 2q^{23} - 27q^{25} + 2q^{27} - 9q^{29} + 22q^{31} - 10q^{33} + 6q^{35} - 35q^{37} - 8q^{39} - 4q^{41} + 20q^{43} + 2q^{45} - 7q^{47} - 27q^{49} - 9q^{51} - 24q^{53} + 11q^{55} - 23q^{57} - 17q^{59} - 4q^{61} - 10q^{63} - 16q^{65} + 6q^{67} - 2q^{69} + q^{71} - 31q^{73} - 30q^{75} + 3q^{77} + 10q^{79} - 6q^{81} - 22q^{83} - 6q^{85} - 25q^{87} + q^{89} - 10q^{91} - 6q^{93} - 39q^{95} - 57q^{97} - 35q^{99} + O(q^{100}) \)

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
\(3\) −0.315672 −0.182253 −0.0911266 0.995839i \(-0.529047\pi\)
−0.0911266 + 0.995839i \(0.529047\pi\)
\(4\) 0 0
\(5\) 2.25024 1.00634 0.503170 0.864188i \(-0.332167\pi\)
0.503170 + 0.864188i \(0.332167\pi\)
\(6\) 0 0
\(7\) 3.20647 1.21193 0.605966 0.795491i \(-0.292787\pi\)
0.605966 + 0.795491i \(0.292787\pi\)
\(8\) 0 0
\(9\) −2.90035 −0.966784
\(10\) 0 0
\(11\) 0.218022 0.0657362 0.0328681 0.999460i \(-0.489536\pi\)
0.0328681 + 0.999460i \(0.489536\pi\)
\(12\) 0 0
\(13\) −4.17856 −1.15892 −0.579462 0.814999i \(-0.696737\pi\)
−0.579462 + 0.814999i \(0.696737\pi\)
\(14\) 0 0
\(15\) −0.710339 −0.183409
\(16\) 0 0
\(17\) −4.68939 −1.13734 −0.568672 0.822564i \(-0.692543\pi\)
−0.568672 + 0.822564i \(0.692543\pi\)
\(18\) 0 0
\(19\) −3.43926 −0.789020 −0.394510 0.918892i \(-0.629086\pi\)
−0.394510 + 0.918892i \(0.629086\pi\)
\(20\) 0 0
\(21\) −1.01219 −0.220878
\(22\) 0 0
\(23\) 3.99816 0.833673 0.416837 0.908981i \(-0.363139\pi\)
0.416837 + 0.908981i \(0.363139\pi\)
\(24\) 0 0
\(25\) 0.0635992 0.0127198
\(26\) 0 0
\(27\) 1.86257 0.358453
\(28\) 0 0
\(29\) −0.712153 −0.132243 −0.0661217 0.997812i \(-0.521063\pi\)
−0.0661217 + 0.997812i \(0.521063\pi\)
\(30\) 0 0
\(31\) −1.04933 −0.188466 −0.0942329 0.995550i \(-0.530040\pi\)
−0.0942329 + 0.995550i \(0.530040\pi\)
\(32\) 0 0
\(33\) −0.0688235 −0.0119806
\(34\) 0 0
\(35\) 7.21534 1.21961
\(36\) 0 0
\(37\) 1.70998 0.281119 0.140560 0.990072i \(-0.455110\pi\)
0.140560 + 0.990072i \(0.455110\pi\)
\(38\) 0 0
\(39\) 1.31905 0.211218
\(40\) 0 0
\(41\) 3.18460 0.497351 0.248675 0.968587i \(-0.420005\pi\)
0.248675 + 0.968587i \(0.420005\pi\)
\(42\) 0 0
\(43\) 6.35890 0.969723 0.484861 0.874591i \(-0.338870\pi\)
0.484861 + 0.874591i \(0.338870\pi\)
\(44\) 0 0
\(45\) −6.52650 −0.972913
\(46\) 0 0
\(47\) 3.87861 0.565754 0.282877 0.959156i \(-0.408711\pi\)
0.282877 + 0.959156i \(0.408711\pi\)
\(48\) 0 0
\(49\) 3.28144 0.468777
\(50\) 0 0
\(51\) 1.48031 0.207285
\(52\) 0 0
\(53\) −10.8877 −1.49555 −0.747773 0.663954i \(-0.768877\pi\)
−0.747773 + 0.663954i \(0.768877\pi\)
\(54\) 0 0
\(55\) 0.490604 0.0661530
\(56\) 0 0
\(57\) 1.08568 0.143801
\(58\) 0 0
\(59\) 2.63793 0.343429 0.171715 0.985147i \(-0.445069\pi\)
0.171715 + 0.985147i \(0.445069\pi\)
\(60\) 0 0
\(61\) 11.1544 1.42817 0.714084 0.700060i \(-0.246843\pi\)
0.714084 + 0.700060i \(0.246843\pi\)
\(62\) 0 0
\(63\) −9.29988 −1.17168
\(64\) 0 0
\(65\) −9.40279 −1.16627
\(66\) 0 0
\(67\) −6.09170 −0.744219 −0.372110 0.928189i \(-0.621365\pi\)
−0.372110 + 0.928189i \(0.621365\pi\)
\(68\) 0 0
\(69\) −1.26210 −0.151940
\(70\) 0 0
\(71\) −9.40515 −1.11619 −0.558093 0.829778i \(-0.688467\pi\)
−0.558093 + 0.829778i \(0.688467\pi\)
\(72\) 0 0
\(73\) −2.78532 −0.325997 −0.162998 0.986626i \(-0.552117\pi\)
−0.162998 + 0.986626i \(0.552117\pi\)
\(74\) 0 0
\(75\) −0.0200765 −0.00231823
\(76\) 0 0
\(77\) 0.699082 0.0796678
\(78\) 0 0
\(79\) −5.16993 −0.581662 −0.290831 0.956774i \(-0.593932\pi\)
−0.290831 + 0.956774i \(0.593932\pi\)
\(80\) 0 0
\(81\) 8.11309 0.901455
\(82\) 0 0
\(83\) −1.83793 −0.201739 −0.100870 0.994900i \(-0.532162\pi\)
−0.100870 + 0.994900i \(0.532162\pi\)
\(84\) 0 0
\(85\) −10.5523 −1.14455
\(86\) 0 0
\(87\) 0.224807 0.0241018
\(88\) 0 0
\(89\) −8.08786 −0.857311 −0.428656 0.903468i \(-0.641013\pi\)
−0.428656 + 0.903468i \(0.641013\pi\)
\(90\) 0 0
\(91\) −13.3984 −1.40454
\(92\) 0 0
\(93\) 0.331245 0.0343485
\(94\) 0 0
\(95\) −7.73917 −0.794022
\(96\) 0 0
\(97\) −12.9058 −1.31039 −0.655193 0.755462i \(-0.727413\pi\)
−0.655193 + 0.755462i \(0.727413\pi\)
\(98\) 0 0
\(99\) −0.632342 −0.0635527
\(100\) 0 0
\(101\) 2.17744 0.216663 0.108331 0.994115i \(-0.465449\pi\)
0.108331 + 0.994115i \(0.465449\pi\)
\(102\) 0 0
\(103\) −14.7612 −1.45447 −0.727234 0.686390i \(-0.759194\pi\)
−0.727234 + 0.686390i \(0.759194\pi\)
\(104\) 0 0
\(105\) −2.27768 −0.222279
\(106\) 0 0
\(107\) −10.4459 −1.00984 −0.504920 0.863166i \(-0.668478\pi\)
−0.504920 + 0.863166i \(0.668478\pi\)
\(108\) 0 0
\(109\) −5.69014 −0.545017 −0.272508 0.962153i \(-0.587853\pi\)
−0.272508 + 0.962153i \(0.587853\pi\)
\(110\) 0 0
\(111\) −0.539793 −0.0512348
\(112\) 0 0
\(113\) 20.9980 1.97533 0.987665 0.156584i \(-0.0500481\pi\)
0.987665 + 0.156584i \(0.0500481\pi\)
\(114\) 0 0
\(115\) 8.99683 0.838958
\(116\) 0 0
\(117\) 12.1193 1.12043
\(118\) 0 0
\(119\) −15.0364 −1.37838
\(120\) 0 0
\(121\) −10.9525 −0.995679
\(122\) 0 0
\(123\) −1.00529 −0.0906438
\(124\) 0 0
\(125\) −11.1081 −0.993539
\(126\) 0 0
\(127\) 0.0956906 0.00849117 0.00424558 0.999991i \(-0.498649\pi\)
0.00424558 + 0.999991i \(0.498649\pi\)
\(128\) 0 0
\(129\) −2.00732 −0.176735
\(130\) 0 0
\(131\) −14.5638 −1.27244 −0.636221 0.771507i \(-0.719504\pi\)
−0.636221 + 0.771507i \(0.719504\pi\)
\(132\) 0 0
\(133\) −11.0279 −0.956238
\(134\) 0 0
\(135\) 4.19125 0.360725
\(136\) 0 0
\(137\) −17.1079 −1.46162 −0.730811 0.682579i \(-0.760858\pi\)
−0.730811 + 0.682579i \(0.760858\pi\)
\(138\) 0 0
\(139\) 17.7270 1.50358 0.751791 0.659402i \(-0.229190\pi\)
0.751791 + 0.659402i \(0.229190\pi\)
\(140\) 0 0
\(141\) −1.22437 −0.103110
\(142\) 0 0
\(143\) −0.911020 −0.0761833
\(144\) 0 0
\(145\) −1.60252 −0.133082
\(146\) 0 0
\(147\) −1.03586 −0.0854361
\(148\) 0 0
\(149\) −3.37396 −0.276406 −0.138203 0.990404i \(-0.544133\pi\)
−0.138203 + 0.990404i \(0.544133\pi\)
\(150\) 0 0
\(151\) −2.76168 −0.224742 −0.112371 0.993666i \(-0.535845\pi\)
−0.112371 + 0.993666i \(0.535845\pi\)
\(152\) 0 0
\(153\) 13.6009 1.09957
\(154\) 0 0
\(155\) −2.36126 −0.189661
\(156\) 0 0
\(157\) −8.93566 −0.713144 −0.356572 0.934268i \(-0.616054\pi\)
−0.356572 + 0.934268i \(0.616054\pi\)
\(158\) 0 0
\(159\) 3.43695 0.272568
\(160\) 0 0
\(161\) 12.8200 1.01035
\(162\) 0 0
\(163\) 8.75660 0.685870 0.342935 0.939359i \(-0.388579\pi\)
0.342935 + 0.939359i \(0.388579\pi\)
\(164\) 0 0
\(165\) −0.154870 −0.0120566
\(166\) 0 0
\(167\) −14.3605 −1.11125 −0.555623 0.831434i \(-0.687520\pi\)
−0.555623 + 0.831434i \(0.687520\pi\)
\(168\) 0 0
\(169\) 4.46038 0.343106
\(170\) 0 0
\(171\) 9.97506 0.762812
\(172\) 0 0
\(173\) −11.0498 −0.840098 −0.420049 0.907501i \(-0.637987\pi\)
−0.420049 + 0.907501i \(0.637987\pi\)
\(174\) 0 0
\(175\) 0.203929 0.0154156
\(176\) 0 0
\(177\) −0.832720 −0.0625910
\(178\) 0 0
\(179\) 6.55060 0.489615 0.244808 0.969572i \(-0.421275\pi\)
0.244808 + 0.969572i \(0.421275\pi\)
\(180\) 0 0
\(181\) −13.9694 −1.03834 −0.519169 0.854672i \(-0.673758\pi\)
−0.519169 + 0.854672i \(0.673758\pi\)
\(182\) 0 0
\(183\) −3.52111 −0.260288
\(184\) 0 0
\(185\) 3.84787 0.282901
\(186\) 0 0
\(187\) −1.02239 −0.0747647
\(188\) 0 0
\(189\) 5.97229 0.434420
\(190\) 0 0
\(191\) −2.23996 −0.162078 −0.0810390 0.996711i \(-0.525824\pi\)
−0.0810390 + 0.996711i \(0.525824\pi\)
\(192\) 0 0
\(193\) 22.1924 1.59744 0.798722 0.601700i \(-0.205510\pi\)
0.798722 + 0.601700i \(0.205510\pi\)
\(194\) 0 0
\(195\) 2.96819 0.212557
\(196\) 0 0
\(197\) −11.0264 −0.785595 −0.392797 0.919625i \(-0.628493\pi\)
−0.392797 + 0.919625i \(0.628493\pi\)
\(198\) 0 0
\(199\) −14.6196 −1.03636 −0.518179 0.855272i \(-0.673390\pi\)
−0.518179 + 0.855272i \(0.673390\pi\)
\(200\) 0 0
\(201\) 1.92298 0.135636
\(202\) 0 0
\(203\) −2.28350 −0.160270
\(204\) 0 0
\(205\) 7.16612 0.500504
\(206\) 0 0
\(207\) −11.5961 −0.805982
\(208\) 0 0
\(209\) −0.749835 −0.0518672
\(210\) 0 0
\(211\) −1.54449 −0.106327 −0.0531635 0.998586i \(-0.516930\pi\)
−0.0531635 + 0.998586i \(0.516930\pi\)
\(212\) 0 0
\(213\) 2.96894 0.203428
\(214\) 0 0
\(215\) 14.3091 0.975871
\(216\) 0 0
\(217\) −3.36465 −0.228408
\(218\) 0 0
\(219\) 0.879246 0.0594139
\(220\) 0 0
\(221\) 19.5949 1.31810
\(222\) 0 0
\(223\) 26.6878 1.78715 0.893573 0.448918i \(-0.148190\pi\)
0.893573 + 0.448918i \(0.148190\pi\)
\(224\) 0 0
\(225\) −0.184460 −0.0122973
\(226\) 0 0
\(227\) 6.41989 0.426103 0.213052 0.977041i \(-0.431660\pi\)
0.213052 + 0.977041i \(0.431660\pi\)
\(228\) 0 0
\(229\) −27.8670 −1.84150 −0.920752 0.390149i \(-0.872423\pi\)
−0.920752 + 0.390149i \(0.872423\pi\)
\(230\) 0 0
\(231\) −0.220680 −0.0145197
\(232\) 0 0
\(233\) 0.647350 0.0424093 0.0212047 0.999775i \(-0.493250\pi\)
0.0212047 + 0.999775i \(0.493250\pi\)
\(234\) 0 0
\(235\) 8.72782 0.569340
\(236\) 0 0
\(237\) 1.63200 0.106010
\(238\) 0 0
\(239\) 12.3635 0.799727 0.399864 0.916575i \(-0.369057\pi\)
0.399864 + 0.916575i \(0.369057\pi\)
\(240\) 0 0
\(241\) −12.7531 −0.821497 −0.410748 0.911749i \(-0.634732\pi\)
−0.410748 + 0.911749i \(0.634732\pi\)
\(242\) 0 0
\(243\) −8.14880 −0.522746
\(244\) 0 0
\(245\) 7.38404 0.471749
\(246\) 0 0
\(247\) 14.3712 0.914415
\(248\) 0 0
\(249\) 0.580183 0.0367676
\(250\) 0 0
\(251\) 13.4917 0.851588 0.425794 0.904820i \(-0.359995\pi\)
0.425794 + 0.904820i \(0.359995\pi\)
\(252\) 0 0
\(253\) 0.871688 0.0548025
\(254\) 0 0
\(255\) 3.33105 0.208599
\(256\) 0 0
\(257\) −4.56318 −0.284643 −0.142322 0.989820i \(-0.545457\pi\)
−0.142322 + 0.989820i \(0.545457\pi\)
\(258\) 0 0
\(259\) 5.48300 0.340697
\(260\) 0 0
\(261\) 2.06549 0.127851
\(262\) 0 0
\(263\) −16.0985 −0.992674 −0.496337 0.868130i \(-0.665322\pi\)
−0.496337 + 0.868130i \(0.665322\pi\)
\(264\) 0 0
\(265\) −24.5001 −1.50503
\(266\) 0 0
\(267\) 2.55311 0.156248
\(268\) 0 0
\(269\) −7.49840 −0.457186 −0.228593 0.973522i \(-0.573412\pi\)
−0.228593 + 0.973522i \(0.573412\pi\)
\(270\) 0 0
\(271\) −6.47424 −0.393282 −0.196641 0.980476i \(-0.563003\pi\)
−0.196641 + 0.980476i \(0.563003\pi\)
\(272\) 0 0
\(273\) 4.22951 0.255981
\(274\) 0 0
\(275\) 0.0138660 0.000836154 0
\(276\) 0 0
\(277\) 8.32050 0.499930 0.249965 0.968255i \(-0.419581\pi\)
0.249965 + 0.968255i \(0.419581\pi\)
\(278\) 0 0
\(279\) 3.04344 0.182206
\(280\) 0 0
\(281\) −26.3798 −1.57369 −0.786844 0.617152i \(-0.788286\pi\)
−0.786844 + 0.617152i \(0.788286\pi\)
\(282\) 0 0
\(283\) 23.4048 1.39127 0.695637 0.718394i \(-0.255122\pi\)
0.695637 + 0.718394i \(0.255122\pi\)
\(284\) 0 0
\(285\) 2.44304 0.144713
\(286\) 0 0
\(287\) 10.2113 0.602755
\(288\) 0 0
\(289\) 4.99036 0.293551
\(290\) 0 0
\(291\) 4.07400 0.238822
\(292\) 0 0
\(293\) −3.57088 −0.208613 −0.104307 0.994545i \(-0.533262\pi\)
−0.104307 + 0.994545i \(0.533262\pi\)
\(294\) 0 0
\(295\) 5.93598 0.345606
\(296\) 0 0
\(297\) 0.406083 0.0235633
\(298\) 0 0
\(299\) −16.7065 −0.966164
\(300\) 0 0
\(301\) 20.3896 1.17524
\(302\) 0 0
\(303\) −0.687355 −0.0394875
\(304\) 0 0
\(305\) 25.1000 1.43722
\(306\) 0 0
\(307\) 2.46828 0.140872 0.0704362 0.997516i \(-0.477561\pi\)
0.0704362 + 0.997516i \(0.477561\pi\)
\(308\) 0 0
\(309\) 4.65970 0.265081
\(310\) 0 0
\(311\) 19.8949 1.12814 0.564069 0.825727i \(-0.309235\pi\)
0.564069 + 0.825727i \(0.309235\pi\)
\(312\) 0 0
\(313\) −10.0179 −0.566246 −0.283123 0.959084i \(-0.591370\pi\)
−0.283123 + 0.959084i \(0.591370\pi\)
\(314\) 0 0
\(315\) −20.9270 −1.17910
\(316\) 0 0
\(317\) −11.2440 −0.631529 −0.315764 0.948838i \(-0.602261\pi\)
−0.315764 + 0.948838i \(0.602261\pi\)
\(318\) 0 0
\(319\) −0.155265 −0.00869319
\(320\) 0 0
\(321\) 3.29747 0.184047
\(322\) 0 0
\(323\) 16.1280 0.897387
\(324\) 0 0
\(325\) −0.265753 −0.0147413
\(326\) 0 0
\(327\) 1.79622 0.0993311
\(328\) 0 0
\(329\) 12.4366 0.685654
\(330\) 0 0
\(331\) 30.0728 1.65295 0.826475 0.562974i \(-0.190343\pi\)
0.826475 + 0.562974i \(0.190343\pi\)
\(332\) 0 0
\(333\) −4.95954 −0.271781
\(334\) 0 0
\(335\) −13.7078 −0.748937
\(336\) 0 0
\(337\) −17.3224 −0.943613 −0.471807 0.881702i \(-0.656398\pi\)
−0.471807 + 0.881702i \(0.656398\pi\)
\(338\) 0 0
\(339\) −6.62849 −0.360010
\(340\) 0 0
\(341\) −0.228778 −0.0123890
\(342\) 0 0
\(343\) −11.9234 −0.643806
\(344\) 0 0
\(345\) −2.84004 −0.152903
\(346\) 0 0
\(347\) −21.2412 −1.14029 −0.570143 0.821545i \(-0.693112\pi\)
−0.570143 + 0.821545i \(0.693112\pi\)
\(348\) 0 0
\(349\) 11.6817 0.625308 0.312654 0.949867i \(-0.398782\pi\)
0.312654 + 0.949867i \(0.398782\pi\)
\(350\) 0 0
\(351\) −7.78288 −0.415420
\(352\) 0 0
\(353\) 14.0775 0.749271 0.374636 0.927172i \(-0.377768\pi\)
0.374636 + 0.927172i \(0.377768\pi\)
\(354\) 0 0
\(355\) −21.1639 −1.12326
\(356\) 0 0
\(357\) 4.74656 0.251215
\(358\) 0 0
\(359\) −7.85706 −0.414680 −0.207340 0.978269i \(-0.566481\pi\)
−0.207340 + 0.978269i \(0.566481\pi\)
\(360\) 0 0
\(361\) −7.17150 −0.377448
\(362\) 0 0
\(363\) 3.45738 0.181466
\(364\) 0 0
\(365\) −6.26764 −0.328063
\(366\) 0 0
\(367\) 19.7726 1.03212 0.516062 0.856551i \(-0.327398\pi\)
0.516062 + 0.856551i \(0.327398\pi\)
\(368\) 0 0
\(369\) −9.23646 −0.480831
\(370\) 0 0
\(371\) −34.9112 −1.81250
\(372\) 0 0
\(373\) 7.49088 0.387863 0.193931 0.981015i \(-0.437876\pi\)
0.193931 + 0.981015i \(0.437876\pi\)
\(374\) 0 0
\(375\) 3.50652 0.181076
\(376\) 0 0
\(377\) 2.97577 0.153260
\(378\) 0 0
\(379\) −27.5064 −1.41291 −0.706455 0.707758i \(-0.749707\pi\)
−0.706455 + 0.707758i \(0.749707\pi\)
\(380\) 0 0
\(381\) −0.0302068 −0.00154754
\(382\) 0 0
\(383\) −4.92412 −0.251611 −0.125805 0.992055i \(-0.540151\pi\)
−0.125805 + 0.992055i \(0.540151\pi\)
\(384\) 0 0
\(385\) 1.57311 0.0801729
\(386\) 0 0
\(387\) −18.4430 −0.937512
\(388\) 0 0
\(389\) 38.9916 1.97696 0.988478 0.151368i \(-0.0483678\pi\)
0.988478 + 0.151368i \(0.0483678\pi\)
\(390\) 0 0
\(391\) −18.7489 −0.948173
\(392\) 0 0
\(393\) 4.59737 0.231907
\(394\) 0 0
\(395\) −11.6336 −0.585350
\(396\) 0 0
\(397\) −12.6661 −0.635694 −0.317847 0.948142i \(-0.602960\pi\)
−0.317847 + 0.948142i \(0.602960\pi\)
\(398\) 0 0
\(399\) 3.48119 0.174277
\(400\) 0 0
\(401\) 26.7959 1.33812 0.669062 0.743207i \(-0.266696\pi\)
0.669062 + 0.743207i \(0.266696\pi\)
\(402\) 0 0
\(403\) 4.38471 0.218418
\(404\) 0 0
\(405\) 18.2564 0.907170
\(406\) 0 0
\(407\) 0.372814 0.0184797
\(408\) 0 0
\(409\) 35.3472 1.74781 0.873903 0.486101i \(-0.161581\pi\)
0.873903 + 0.486101i \(0.161581\pi\)
\(410\) 0 0
\(411\) 5.40047 0.266385
\(412\) 0 0
\(413\) 8.45844 0.416212
\(414\) 0 0
\(415\) −4.13580 −0.203018
\(416\) 0 0
\(417\) −5.59590 −0.274033
\(418\) 0 0
\(419\) 2.49358 0.121819 0.0609096 0.998143i \(-0.480600\pi\)
0.0609096 + 0.998143i \(0.480600\pi\)
\(420\) 0 0
\(421\) 17.2671 0.841547 0.420773 0.907166i \(-0.361759\pi\)
0.420773 + 0.907166i \(0.361759\pi\)
\(422\) 0 0
\(423\) −11.2493 −0.546961
\(424\) 0 0
\(425\) −0.298241 −0.0144668
\(426\) 0 0
\(427\) 35.7661 1.73084
\(428\) 0 0
\(429\) 0.287583 0.0138847
\(430\) 0 0
\(431\) −31.0699 −1.49659 −0.748293 0.663368i \(-0.769126\pi\)
−0.748293 + 0.663368i \(0.769126\pi\)
\(432\) 0 0
\(433\) 16.4828 0.792112 0.396056 0.918226i \(-0.370379\pi\)
0.396056 + 0.918226i \(0.370379\pi\)
\(434\) 0 0
\(435\) 0.505870 0.0242546
\(436\) 0 0
\(437\) −13.7507 −0.657785
\(438\) 0 0
\(439\) −33.0499 −1.57739 −0.788693 0.614787i \(-0.789242\pi\)
−0.788693 + 0.614787i \(0.789242\pi\)
\(440\) 0 0
\(441\) −9.51733 −0.453206
\(442\) 0 0
\(443\) 24.8330 1.17985 0.589925 0.807458i \(-0.299157\pi\)
0.589925 + 0.807458i \(0.299157\pi\)
\(444\) 0 0
\(445\) −18.1997 −0.862747
\(446\) 0 0
\(447\) 1.06506 0.0503758
\(448\) 0 0
\(449\) −18.6217 −0.878811 −0.439405 0.898289i \(-0.644811\pi\)
−0.439405 + 0.898289i \(0.644811\pi\)
\(450\) 0 0
\(451\) 0.694314 0.0326940
\(452\) 0 0
\(453\) 0.871784 0.0409600
\(454\) 0 0
\(455\) −30.1497 −1.41344
\(456\) 0 0
\(457\) −34.2762 −1.60337 −0.801686 0.597745i \(-0.796063\pi\)
−0.801686 + 0.597745i \(0.796063\pi\)
\(458\) 0 0
\(459\) −8.73433 −0.407684
\(460\) 0 0
\(461\) 11.2220 0.522659 0.261329 0.965250i \(-0.415839\pi\)
0.261329 + 0.965250i \(0.415839\pi\)
\(462\) 0 0
\(463\) 26.9770 1.25373 0.626863 0.779129i \(-0.284338\pi\)
0.626863 + 0.779129i \(0.284338\pi\)
\(464\) 0 0
\(465\) 0.745382 0.0345663
\(466\) 0 0
\(467\) −11.5336 −0.533711 −0.266856 0.963737i \(-0.585985\pi\)
−0.266856 + 0.963737i \(0.585985\pi\)
\(468\) 0 0
\(469\) −19.5328 −0.901942
\(470\) 0 0
\(471\) 2.82074 0.129973
\(472\) 0 0
\(473\) 1.38638 0.0637459
\(474\) 0 0
\(475\) −0.218734 −0.0100362
\(476\) 0 0
\(477\) 31.5783 1.44587
\(478\) 0 0
\(479\) 28.8893 1.31998 0.659992 0.751272i \(-0.270559\pi\)
0.659992 + 0.751272i \(0.270559\pi\)
\(480\) 0 0
\(481\) −7.14526 −0.325796
\(482\) 0 0
\(483\) −4.04690 −0.184140
\(484\) 0 0
\(485\) −29.0412 −1.31869
\(486\) 0 0
\(487\) −1.63083 −0.0739001 −0.0369501 0.999317i \(-0.511764\pi\)
−0.0369501 + 0.999317i \(0.511764\pi\)
\(488\) 0 0
\(489\) −2.76421 −0.125002
\(490\) 0 0
\(491\) 6.45592 0.291352 0.145676 0.989332i \(-0.453464\pi\)
0.145676 + 0.989332i \(0.453464\pi\)
\(492\) 0 0
\(493\) 3.33956 0.150406
\(494\) 0 0
\(495\) −1.42292 −0.0639556
\(496\) 0 0
\(497\) −30.1573 −1.35274
\(498\) 0 0
\(499\) −29.7187 −1.33039 −0.665196 0.746669i \(-0.731652\pi\)
−0.665196 + 0.746669i \(0.731652\pi\)
\(500\) 0 0
\(501\) 4.53320 0.202528
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 4.89976 0.218037
\(506\) 0 0
\(507\) −1.40802 −0.0625323
\(508\) 0 0
\(509\) 7.29140 0.323186 0.161593 0.986858i \(-0.448337\pi\)
0.161593 + 0.986858i \(0.448337\pi\)
\(510\) 0 0
\(511\) −8.93103 −0.395086
\(512\) 0 0
\(513\) −6.40587 −0.282826
\(514\) 0 0
\(515\) −33.2164 −1.46369
\(516\) 0 0
\(517\) 0.845624 0.0371905
\(518\) 0 0
\(519\) 3.48810 0.153110
\(520\) 0 0
\(521\) 1.73107 0.0758394 0.0379197 0.999281i \(-0.487927\pi\)
0.0379197 + 0.999281i \(0.487927\pi\)
\(522\) 0 0
\(523\) −15.8653 −0.693742 −0.346871 0.937913i \(-0.612756\pi\)
−0.346871 + 0.937913i \(0.612756\pi\)
\(524\) 0 0
\(525\) −0.0643745 −0.00280953
\(526\) 0 0
\(527\) 4.92073 0.214350
\(528\) 0 0
\(529\) −7.01475 −0.304989
\(530\) 0 0
\(531\) −7.65092 −0.332022
\(532\) 0 0
\(533\) −13.3070 −0.576392
\(534\) 0 0
\(535\) −23.5058 −1.01624
\(536\) 0 0
\(537\) −2.06784 −0.0892339
\(538\) 0 0
\(539\) 0.715427 0.0308156
\(540\) 0 0
\(541\) 0.384069 0.0165124 0.00825621 0.999966i \(-0.497372\pi\)
0.00825621 + 0.999966i \(0.497372\pi\)
\(542\) 0 0
\(543\) 4.40975 0.189240
\(544\) 0 0
\(545\) −12.8042 −0.548472
\(546\) 0 0
\(547\) −38.3367 −1.63916 −0.819579 0.572967i \(-0.805792\pi\)
−0.819579 + 0.572967i \(0.805792\pi\)
\(548\) 0 0
\(549\) −32.3515 −1.38073
\(550\) 0 0
\(551\) 2.44928 0.104343
\(552\) 0 0
\(553\) −16.5772 −0.704935
\(554\) 0 0
\(555\) −1.21467 −0.0515597
\(556\) 0 0
\(557\) 25.2935 1.07172 0.535860 0.844307i \(-0.319987\pi\)
0.535860 + 0.844307i \(0.319987\pi\)
\(558\) 0 0
\(559\) −26.5710 −1.12384
\(560\) 0 0
\(561\) 0.322740 0.0136261
\(562\) 0 0
\(563\) −32.5764 −1.37293 −0.686465 0.727163i \(-0.740839\pi\)
−0.686465 + 0.727163i \(0.740839\pi\)
\(564\) 0 0
\(565\) 47.2507 1.98785
\(566\) 0 0
\(567\) 26.0144 1.09250
\(568\) 0 0
\(569\) −36.9548 −1.54923 −0.774614 0.632435i \(-0.782056\pi\)
−0.774614 + 0.632435i \(0.782056\pi\)
\(570\) 0 0
\(571\) 32.4941 1.35984 0.679919 0.733288i \(-0.262015\pi\)
0.679919 + 0.733288i \(0.262015\pi\)
\(572\) 0 0
\(573\) 0.707093 0.0295393
\(574\) 0 0
\(575\) 0.254279 0.0106042
\(576\) 0 0
\(577\) −3.08889 −0.128592 −0.0642960 0.997931i \(-0.520480\pi\)
−0.0642960 + 0.997931i \(0.520480\pi\)
\(578\) 0 0
\(579\) −7.00552 −0.291139
\(580\) 0 0
\(581\) −5.89327 −0.244494
\(582\) 0 0
\(583\) −2.37377 −0.0983116
\(584\) 0 0
\(585\) 27.2714 1.12753
\(586\) 0 0
\(587\) 39.5581 1.63274 0.816369 0.577530i \(-0.195983\pi\)
0.816369 + 0.577530i \(0.195983\pi\)
\(588\) 0 0
\(589\) 3.60893 0.148703
\(590\) 0 0
\(591\) 3.48071 0.143177
\(592\) 0 0
\(593\) 37.0809 1.52273 0.761366 0.648323i \(-0.224529\pi\)
0.761366 + 0.648323i \(0.224529\pi\)
\(594\) 0 0
\(595\) −33.8355 −1.38712
\(596\) 0 0
\(597\) 4.61501 0.188880
\(598\) 0 0
\(599\) 7.21058 0.294616 0.147308 0.989091i \(-0.452939\pi\)
0.147308 + 0.989091i \(0.452939\pi\)
\(600\) 0 0
\(601\) −15.6443 −0.638145 −0.319072 0.947730i \(-0.603371\pi\)
−0.319072 + 0.947730i \(0.603371\pi\)
\(602\) 0 0
\(603\) 17.6681 0.719499
\(604\) 0 0
\(605\) −24.6457 −1.00199
\(606\) 0 0
\(607\) 5.03996 0.204566 0.102283 0.994755i \(-0.467385\pi\)
0.102283 + 0.994755i \(0.467385\pi\)
\(608\) 0 0
\(609\) 0.720835 0.0292097
\(610\) 0 0
\(611\) −16.2070 −0.655666
\(612\) 0 0
\(613\) −41.4393 −1.67372 −0.836858 0.547420i \(-0.815610\pi\)
−0.836858 + 0.547420i \(0.815610\pi\)
\(614\) 0 0
\(615\) −2.26214 −0.0912184
\(616\) 0 0
\(617\) 17.1685 0.691178 0.345589 0.938386i \(-0.387679\pi\)
0.345589 + 0.938386i \(0.387679\pi\)
\(618\) 0 0
\(619\) 16.9228 0.680186 0.340093 0.940392i \(-0.389541\pi\)
0.340093 + 0.940392i \(0.389541\pi\)
\(620\) 0 0
\(621\) 7.44686 0.298832
\(622\) 0 0
\(623\) −25.9335 −1.03900
\(624\) 0 0
\(625\) −25.3140 −1.01256
\(626\) 0 0
\(627\) 0.236702 0.00945296
\(628\) 0 0
\(629\) −8.01876 −0.319729
\(630\) 0 0
\(631\) −15.9640 −0.635518 −0.317759 0.948171i \(-0.602930\pi\)
−0.317759 + 0.948171i \(0.602930\pi\)
\(632\) 0 0
\(633\) 0.487551 0.0193784
\(634\) 0 0
\(635\) 0.215327 0.00854500
\(636\) 0 0
\(637\) −13.7117 −0.543277
\(638\) 0 0
\(639\) 27.2782 1.07911
\(640\) 0 0
\(641\) 34.1774 1.34993 0.674964 0.737851i \(-0.264159\pi\)
0.674964 + 0.737851i \(0.264159\pi\)
\(642\) 0 0
\(643\) 1.27460 0.0502653 0.0251326 0.999684i \(-0.491999\pi\)
0.0251326 + 0.999684i \(0.491999\pi\)
\(644\) 0 0
\(645\) −4.51697 −0.177856
\(646\) 0 0
\(647\) −16.4300 −0.645930 −0.322965 0.946411i \(-0.604680\pi\)
−0.322965 + 0.946411i \(0.604680\pi\)
\(648\) 0 0
\(649\) 0.575128 0.0225757
\(650\) 0 0
\(651\) 1.06213 0.0416280
\(652\) 0 0
\(653\) 46.5637 1.82218 0.911088 0.412211i \(-0.135243\pi\)
0.911088 + 0.412211i \(0.135243\pi\)
\(654\) 0 0
\(655\) −32.7720 −1.28051
\(656\) 0 0
\(657\) 8.07840 0.315168
\(658\) 0 0
\(659\) 21.2263 0.826861 0.413431 0.910536i \(-0.364330\pi\)
0.413431 + 0.910536i \(0.364330\pi\)
\(660\) 0 0
\(661\) 31.5049 1.22540 0.612700 0.790316i \(-0.290084\pi\)
0.612700 + 0.790316i \(0.290084\pi\)
\(662\) 0 0
\(663\) −6.18556 −0.240227
\(664\) 0 0
\(665\) −24.8154 −0.962300
\(666\) 0 0
\(667\) −2.84730 −0.110248
\(668\) 0 0
\(669\) −8.42458 −0.325713
\(670\) 0 0
\(671\) 2.43190 0.0938824
\(672\) 0 0
\(673\) −46.0920 −1.77672 −0.888359 0.459150i \(-0.848154\pi\)
−0.888359 + 0.459150i \(0.848154\pi\)
\(674\) 0 0
\(675\) 0.118458 0.00455946
\(676\) 0 0
\(677\) 5.22605 0.200853 0.100427 0.994944i \(-0.467979\pi\)
0.100427 + 0.994944i \(0.467979\pi\)
\(678\) 0 0
\(679\) −41.3820 −1.58810
\(680\) 0 0
\(681\) −2.02658 −0.0776587
\(682\) 0 0
\(683\) 26.7163 1.02227 0.511135 0.859500i \(-0.329225\pi\)
0.511135 + 0.859500i \(0.329225\pi\)
\(684\) 0 0
\(685\) −38.4969 −1.47089
\(686\) 0 0
\(687\) 8.79683 0.335620
\(688\) 0 0
\(689\) 45.4951 1.73323
\(690\) 0 0
\(691\) 20.7575 0.789653 0.394826 0.918756i \(-0.370805\pi\)
0.394826 + 0.918756i \(0.370805\pi\)
\(692\) 0 0
\(693\) −2.02758 −0.0770215
\(694\) 0 0
\(695\) 39.8900 1.51311
\(696\) 0 0
\(697\) −14.9338 −0.565659
\(698\) 0 0
\(699\) −0.204350 −0.00772924
\(700\) 0 0
\(701\) −48.5428 −1.83344 −0.916719 0.399533i \(-0.869172\pi\)
−0.916719 + 0.399533i \(0.869172\pi\)
\(702\) 0 0
\(703\) −5.88106 −0.221809
\(704\) 0 0
\(705\) −2.75513 −0.103764
\(706\) 0 0
\(707\) 6.98188 0.262581
\(708\) 0 0
\(709\) −21.9935 −0.825981 −0.412991 0.910735i \(-0.635516\pi\)
−0.412991 + 0.910735i \(0.635516\pi\)
\(710\) 0 0
\(711\) 14.9946 0.562342
\(712\) 0 0
\(713\) −4.19540 −0.157119
\(714\) 0 0
\(715\) −2.05002 −0.0766663
\(716\) 0 0
\(717\) −3.90280 −0.145753
\(718\) 0 0
\(719\) −9.78228 −0.364817 −0.182409 0.983223i \(-0.558389\pi\)
−0.182409 + 0.983223i \(0.558389\pi\)
\(720\) 0 0
\(721\) −47.3314 −1.76271
\(722\) 0 0
\(723\) 4.02578 0.149720
\(724\) 0 0
\(725\) −0.0452923 −0.00168211
\(726\) 0 0
\(727\) 41.0223 1.52143 0.760716 0.649085i \(-0.224848\pi\)
0.760716 + 0.649085i \(0.224848\pi\)
\(728\) 0 0
\(729\) −21.7669 −0.806183
\(730\) 0 0
\(731\) −29.8193 −1.10291
\(732\) 0 0
\(733\) 19.7580 0.729780 0.364890 0.931051i \(-0.381107\pi\)
0.364890 + 0.931051i \(0.381107\pi\)
\(734\) 0 0
\(735\) −2.33093 −0.0859777
\(736\) 0 0
\(737\) −1.32813 −0.0489222
\(738\) 0 0
\(739\) −8.08268 −0.297326 −0.148663 0.988888i \(-0.547497\pi\)
−0.148663 + 0.988888i \(0.547497\pi\)
\(740\) 0 0
\(741\) −4.53657 −0.166655
\(742\) 0 0
\(743\) −10.5995 −0.388859 −0.194429 0.980917i \(-0.562286\pi\)
−0.194429 + 0.980917i \(0.562286\pi\)
\(744\) 0 0
\(745\) −7.59224 −0.278158
\(746\) 0 0
\(747\) 5.33065 0.195038
\(748\) 0 0
\(749\) −33.4944 −1.22386
\(750\) 0 0
\(751\) −14.0003 −0.510877 −0.255438 0.966825i \(-0.582220\pi\)
−0.255438 + 0.966825i \(0.582220\pi\)
\(752\) 0 0
\(753\) −4.25895 −0.155205
\(754\) 0 0
\(755\) −6.21445 −0.226167
\(756\) 0 0
\(757\) −28.8413 −1.04826 −0.524128 0.851640i \(-0.675609\pi\)
−0.524128 + 0.851640i \(0.675609\pi\)
\(758\) 0 0
\(759\) −0.275167 −0.00998794
\(760\) 0 0
\(761\) −14.2005 −0.514767 −0.257383 0.966309i \(-0.582860\pi\)
−0.257383 + 0.966309i \(0.582860\pi\)
\(762\) 0 0
\(763\) −18.2453 −0.660523
\(764\) 0 0
\(765\) 30.6053 1.10654
\(766\) 0 0
\(767\) −11.0228 −0.398008
\(768\) 0 0
\(769\) 19.1077 0.689043 0.344521 0.938778i \(-0.388041\pi\)
0.344521 + 0.938778i \(0.388041\pi\)
\(770\) 0 0
\(771\) 1.44047 0.0518771
\(772\) 0 0
\(773\) −29.5204 −1.06178 −0.530888 0.847442i \(-0.678141\pi\)
−0.530888 + 0.847442i \(0.678141\pi\)
\(774\) 0 0
\(775\) −0.0667367 −0.00239725
\(776\) 0 0
\(777\) −1.73083 −0.0620931
\(778\) 0 0
\(779\) −10.9527 −0.392420
\(780\) 0 0
\(781\) −2.05053 −0.0733739
\(782\) 0 0
\(783\) −1.32644 −0.0474030
\(784\) 0 0
\(785\) −20.1074 −0.717665
\(786\) 0 0
\(787\) 20.3547 0.725568 0.362784 0.931873i \(-0.381826\pi\)
0.362784 + 0.931873i \(0.381826\pi\)
\(788\) 0 0
\(789\) 5.08183 0.180918
\(790\) 0 0
\(791\) 67.3295 2.39396
\(792\) 0 0
\(793\) −46.6092 −1.65514
\(794\) 0 0
\(795\) 7.73398 0.274296
\(796\) 0 0
\(797\) 51.2687 1.81603 0.908016 0.418935i \(-0.137597\pi\)
0.908016 + 0.418935i \(0.137597\pi\)
\(798\) 0 0
\(799\) −18.1883 −0.643456
\(800\) 0 0
\(801\) 23.4576 0.828835
\(802\) 0 0
\(803\) −0.607262 −0.0214298
\(804\) 0 0
\(805\) 28.8480 1.01676
\(806\) 0 0
\(807\) 2.36703 0.0833235
\(808\) 0 0
\(809\) 53.5568 1.88296 0.941478 0.337073i \(-0.109437\pi\)
0.941478 + 0.337073i \(0.109437\pi\)
\(810\) 0 0
\(811\) −42.8963 −1.50629 −0.753146 0.657854i \(-0.771465\pi\)
−0.753146 + 0.657854i \(0.771465\pi\)
\(812\) 0 0
\(813\) 2.04373 0.0716769
\(814\) 0 0
\(815\) 19.7045 0.690218
\(816\) 0 0
\(817\) −21.8699 −0.765130
\(818\) 0 0
\(819\) 38.8601 1.35788
\(820\) 0 0
\(821\) 5.52686 0.192889 0.0964444 0.995338i \(-0.469253\pi\)
0.0964444 + 0.995338i \(0.469253\pi\)
\(822\) 0 0
\(823\) 19.0939 0.665572 0.332786 0.943002i \(-0.392011\pi\)
0.332786 + 0.943002i \(0.392011\pi\)
\(824\) 0 0
\(825\) −0.00437712 −0.000152392 0
\(826\) 0 0
\(827\) 47.8774 1.66486 0.832430 0.554130i \(-0.186949\pi\)
0.832430 + 0.554130i \(0.186949\pi\)
\(828\) 0 0
\(829\) 13.1461 0.456583 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(830\) 0 0
\(831\) −2.62655 −0.0911139
\(832\) 0 0
\(833\) −15.3879 −0.533161
\(834\) 0 0
\(835\) −32.3146 −1.11829
\(836\) 0 0
\(837\) −1.95446 −0.0675561
\(838\) 0 0
\(839\) −33.7580 −1.16545 −0.582727 0.812668i \(-0.698014\pi\)
−0.582727 + 0.812668i \(0.698014\pi\)
\(840\) 0 0
\(841\) −28.4928 −0.982512
\(842\) 0 0
\(843\) 8.32736 0.286810
\(844\) 0 0
\(845\) 10.0370 0.345282
\(846\) 0 0
\(847\) −35.1187 −1.20669
\(848\) 0 0
\(849\) −7.38825 −0.253564
\(850\) 0 0
\(851\) 6.83677 0.234361
\(852\) 0 0
\(853\) 16.1494 0.552946 0.276473 0.961022i \(-0.410834\pi\)
0.276473 + 0.961022i \(0.410834\pi\)
\(854\) 0 0
\(855\) 22.4463 0.767648
\(856\) 0 0
\(857\) 21.1749 0.723322 0.361661 0.932310i \(-0.382210\pi\)
0.361661 + 0.932310i \(0.382210\pi\)
\(858\) 0 0
\(859\) 21.2136 0.723798 0.361899 0.932217i \(-0.382129\pi\)
0.361899 + 0.932217i \(0.382129\pi\)
\(860\) 0 0
\(861\) −3.22342 −0.109854
\(862\) 0 0
\(863\) 45.3619 1.54414 0.772068 0.635539i \(-0.219222\pi\)
0.772068 + 0.635539i \(0.219222\pi\)
\(864\) 0 0
\(865\) −24.8647 −0.845424
\(866\) 0 0
\(867\) −1.57532 −0.0535005
\(868\) 0 0
\(869\) −1.12716 −0.0382363
\(870\) 0 0
\(871\) 25.4545 0.862494
\(872\) 0 0
\(873\) 37.4313 1.26686
\(874\) 0 0
\(875\) −35.6178 −1.20410
\(876\) 0 0
\(877\) 12.1962 0.411837 0.205918 0.978569i \(-0.433982\pi\)
0.205918 + 0.978569i \(0.433982\pi\)
\(878\) 0 0
\(879\) 1.12723 0.0380204
\(880\) 0 0
\(881\) 8.50736 0.286620 0.143310 0.989678i \(-0.454225\pi\)
0.143310 + 0.989678i \(0.454225\pi\)
\(882\) 0 0
\(883\) 26.5027 0.891888 0.445944 0.895061i \(-0.352868\pi\)
0.445944 + 0.895061i \(0.352868\pi\)
\(884\) 0 0
\(885\) −1.87382 −0.0629879
\(886\) 0 0
\(887\) −33.1863 −1.11429 −0.557144 0.830416i \(-0.688103\pi\)
−0.557144 + 0.830416i \(0.688103\pi\)
\(888\) 0 0
\(889\) 0.306829 0.0102907
\(890\) 0 0
\(891\) 1.76884 0.0592582
\(892\) 0 0
\(893\) −13.3395 −0.446391
\(894\) 0 0
\(895\) 14.7405 0.492719
\(896\) 0 0
\(897\) 5.27378 0.176087
\(898\) 0 0
\(899\) 0.747286 0.0249234
\(900\) 0 0
\(901\) 51.0568 1.70095
\(902\) 0 0
\(903\) −6.43642 −0.214191
\(904\) 0 0
\(905\) −31.4346 −1.04492
\(906\) 0 0
\(907\) −6.31486 −0.209682 −0.104841 0.994489i \(-0.533433\pi\)
−0.104841 + 0.994489i \(0.533433\pi\)
\(908\) 0 0
\(909\) −6.31533 −0.209466
\(910\) 0 0
\(911\) −43.0949 −1.42780 −0.713898 0.700249i \(-0.753072\pi\)
−0.713898 + 0.700249i \(0.753072\pi\)
\(912\) 0 0
\(913\) −0.400710 −0.0132616
\(914\) 0 0
\(915\) −7.92337 −0.261938
\(916\) 0 0
\(917\) −46.6983 −1.54211
\(918\) 0 0
\(919\) 19.4088 0.640236 0.320118 0.947378i \(-0.396277\pi\)
0.320118 + 0.947378i \(0.396277\pi\)
\(920\) 0 0
\(921\) −0.779167 −0.0256744
\(922\) 0 0
\(923\) 39.3000 1.29358
\(924\) 0 0
\(925\) 0.108753 0.00357579
\(926\) 0 0
\(927\) 42.8128 1.40616
\(928\) 0 0
\(929\) −28.3914 −0.931493 −0.465747 0.884918i \(-0.654214\pi\)
−0.465747 + 0.884918i \(0.654214\pi\)
\(930\) 0 0
\(931\) −11.2857 −0.369874
\(932\) 0 0
\(933\) −6.28027 −0.205607
\(934\) 0 0
\(935\) −2.30063 −0.0752387
\(936\) 0 0
\(937\) −4.00280 −0.130766 −0.0653829 0.997860i \(-0.520827\pi\)
−0.0653829 + 0.997860i \(0.520827\pi\)
\(938\) 0 0
\(939\) 3.16237 0.103200
\(940\) 0 0
\(941\) 13.9675 0.455328 0.227664 0.973740i \(-0.426891\pi\)
0.227664 + 0.973740i \(0.426891\pi\)
\(942\) 0 0
\(943\) 12.7325 0.414628
\(944\) 0 0
\(945\) 13.4391 0.437174
\(946\) 0 0
\(947\) −57.2963 −1.86188 −0.930940 0.365171i \(-0.881010\pi\)
−0.930940 + 0.365171i \(0.881010\pi\)
\(948\) 0 0
\(949\) 11.6386 0.377806
\(950\) 0 0
\(951\) 3.54943 0.115098
\(952\) 0 0
\(953\) 5.29452 0.171506 0.0857532 0.996316i \(-0.472670\pi\)
0.0857532 + 0.996316i \(0.472670\pi\)
\(954\) 0 0
\(955\) −5.04047 −0.163106
\(956\) 0 0
\(957\) 0.0490129 0.00158436
\(958\) 0 0
\(959\) −54.8558 −1.77139
\(960\) 0 0
\(961\) −29.8989 −0.964481
\(962\) 0 0
\(963\) 30.2967 0.976298
\(964\) 0 0
\(965\) 49.9383 1.60757
\(966\) 0 0
\(967\) −44.3615 −1.42657 −0.713284 0.700875i \(-0.752793\pi\)
−0.713284 + 0.700875i \(0.752793\pi\)
\(968\) 0 0
\(969\) −5.09116 −0.163552
\(970\) 0 0
\(971\) −51.4789 −1.65204 −0.826018 0.563644i \(-0.809399\pi\)
−0.826018 + 0.563644i \(0.809399\pi\)
\(972\) 0 0
\(973\) 56.8410 1.82224
\(974\) 0 0
\(975\) 0.0838907 0.00268665
\(976\) 0 0
\(977\) −0.892938 −0.0285676 −0.0142838 0.999898i \(-0.504547\pi\)
−0.0142838 + 0.999898i \(0.504547\pi\)
\(978\) 0 0
\(979\) −1.76333 −0.0563564
\(980\) 0 0
\(981\) 16.5034 0.526913
\(982\) 0 0
\(983\) −36.2679 −1.15677 −0.578384 0.815765i \(-0.696316\pi\)
−0.578384 + 0.815765i \(0.696316\pi\)
\(984\) 0 0
\(985\) −24.8120 −0.790576
\(986\) 0 0
\(987\) −3.92590 −0.124963
\(988\) 0 0
\(989\) 25.4239 0.808432
\(990\) 0 0
\(991\) −29.3407 −0.932036 −0.466018 0.884775i \(-0.654312\pi\)
−0.466018 + 0.884775i \(0.654312\pi\)
\(992\) 0 0
\(993\) −9.49313 −0.301255
\(994\) 0 0
\(995\) −32.8977 −1.04293
\(996\) 0 0
\(997\) 18.6388 0.590296 0.295148 0.955452i \(-0.404631\pi\)
0.295148 + 0.955452i \(0.404631\pi\)
\(998\) 0 0
\(999\) 3.18497 0.100768
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 \(a_p\))