Properties

Label 8024.2.a.y.1.19
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.15021 q^{3} +1.53922 q^{5} -0.745521 q^{7} +1.62340 q^{9} +O(q^{10})\) \(q+2.15021 q^{3} +1.53922 q^{5} -0.745521 q^{7} +1.62340 q^{9} -4.48378 q^{11} +2.05215 q^{13} +3.30965 q^{15} -1.00000 q^{17} -5.76485 q^{19} -1.60303 q^{21} -4.38388 q^{23} -2.63080 q^{25} -2.95998 q^{27} +8.97480 q^{29} -0.172281 q^{31} -9.64106 q^{33} -1.14752 q^{35} +6.69182 q^{37} +4.41255 q^{39} +1.53239 q^{41} -3.47164 q^{43} +2.49877 q^{45} -10.8212 q^{47} -6.44420 q^{49} -2.15021 q^{51} +3.84980 q^{53} -6.90153 q^{55} -12.3956 q^{57} -1.00000 q^{59} +10.9327 q^{61} -1.21028 q^{63} +3.15871 q^{65} -1.23237 q^{67} -9.42627 q^{69} -3.83196 q^{71} -7.18903 q^{73} -5.65677 q^{75} +3.34275 q^{77} -9.93308 q^{79} -11.2348 q^{81} +14.6903 q^{83} -1.53922 q^{85} +19.2977 q^{87} -12.6751 q^{89} -1.52992 q^{91} -0.370439 q^{93} -8.87337 q^{95} +10.6498 q^{97} -7.27896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 6q^{3} - q^{7} + 23q^{9} + O(q^{10}) \) \( 23q - 6q^{3} - q^{7} + 23q^{9} - 3q^{11} - 7q^{13} - 2q^{15} - 23q^{17} - 16q^{19} - 11q^{21} - 29q^{23} + 31q^{25} - 3q^{27} - 5q^{29} - 41q^{31} + 8q^{33} - 22q^{35} + 5q^{37} + 16q^{39} + 11q^{41} + 13q^{43} - 26q^{45} - 39q^{47} + 16q^{49} + 6q^{51} - 2q^{53} - 35q^{55} + 13q^{57} - 23q^{59} - 37q^{61} + 33q^{65} - 34q^{67} - 66q^{69} - 13q^{71} - 14q^{73} - 81q^{75} - 4q^{77} - 61q^{79} - q^{81} - 9q^{83} - 16q^{87} + 28q^{89} - 18q^{91} - 62q^{93} - 33q^{95} - 5q^{99} + O(q^{100}) \)

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
\(3\) 2.15021 1.24142 0.620712 0.784039i \(-0.286844\pi\)
0.620712 + 0.784039i \(0.286844\pi\)
\(4\) 0 0
\(5\) 1.53922 0.688361 0.344180 0.938904i \(-0.388157\pi\)
0.344180 + 0.938904i \(0.388157\pi\)
\(6\) 0 0
\(7\) −0.745521 −0.281781 −0.140890 0.990025i \(-0.544996\pi\)
−0.140890 + 0.990025i \(0.544996\pi\)
\(8\) 0 0
\(9\) 1.62340 0.541133
\(10\) 0 0
\(11\) −4.48378 −1.35191 −0.675955 0.736943i \(-0.736269\pi\)
−0.675955 + 0.736943i \(0.736269\pi\)
\(12\) 0 0
\(13\) 2.05215 0.569164 0.284582 0.958652i \(-0.408145\pi\)
0.284582 + 0.958652i \(0.408145\pi\)
\(14\) 0 0
\(15\) 3.30965 0.854547
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −5.76485 −1.32255 −0.661273 0.750145i \(-0.729984\pi\)
−0.661273 + 0.750145i \(0.729984\pi\)
\(20\) 0 0
\(21\) −1.60303 −0.349809
\(22\) 0 0
\(23\) −4.38388 −0.914103 −0.457052 0.889440i \(-0.651095\pi\)
−0.457052 + 0.889440i \(0.651095\pi\)
\(24\) 0 0
\(25\) −2.63080 −0.526160
\(26\) 0 0
\(27\) −2.95998 −0.569649
\(28\) 0 0
\(29\) 8.97480 1.66658 0.833289 0.552838i \(-0.186455\pi\)
0.833289 + 0.552838i \(0.186455\pi\)
\(30\) 0 0
\(31\) −0.172281 −0.0309425 −0.0154713 0.999880i \(-0.504925\pi\)
−0.0154713 + 0.999880i \(0.504925\pi\)
\(32\) 0 0
\(33\) −9.64106 −1.67829
\(34\) 0 0
\(35\) −1.14752 −0.193967
\(36\) 0 0
\(37\) 6.69182 1.10013 0.550064 0.835122i \(-0.314603\pi\)
0.550064 + 0.835122i \(0.314603\pi\)
\(38\) 0 0
\(39\) 4.41255 0.706574
\(40\) 0 0
\(41\) 1.53239 0.239319 0.119660 0.992815i \(-0.461820\pi\)
0.119660 + 0.992815i \(0.461820\pi\)
\(42\) 0 0
\(43\) −3.47164 −0.529420 −0.264710 0.964328i \(-0.585276\pi\)
−0.264710 + 0.964328i \(0.585276\pi\)
\(44\) 0 0
\(45\) 2.49877 0.372495
\(46\) 0 0
\(47\) −10.8212 −1.57844 −0.789219 0.614112i \(-0.789514\pi\)
−0.789219 + 0.614112i \(0.789514\pi\)
\(48\) 0 0
\(49\) −6.44420 −0.920600
\(50\) 0 0
\(51\) −2.15021 −0.301089
\(52\) 0 0
\(53\) 3.84980 0.528811 0.264405 0.964412i \(-0.414824\pi\)
0.264405 + 0.964412i \(0.414824\pi\)
\(54\) 0 0
\(55\) −6.90153 −0.930602
\(56\) 0 0
\(57\) −12.3956 −1.64184
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 10.9327 1.39979 0.699897 0.714244i \(-0.253229\pi\)
0.699897 + 0.714244i \(0.253229\pi\)
\(62\) 0 0
\(63\) −1.21028 −0.152481
\(64\) 0 0
\(65\) 3.15871 0.391790
\(66\) 0 0
\(67\) −1.23237 −0.150558 −0.0752791 0.997163i \(-0.523985\pi\)
−0.0752791 + 0.997163i \(0.523985\pi\)
\(68\) 0 0
\(69\) −9.42627 −1.13479
\(70\) 0 0
\(71\) −3.83196 −0.454770 −0.227385 0.973805i \(-0.573018\pi\)
−0.227385 + 0.973805i \(0.573018\pi\)
\(72\) 0 0
\(73\) −7.18903 −0.841413 −0.420706 0.907197i \(-0.638218\pi\)
−0.420706 + 0.907197i \(0.638218\pi\)
\(74\) 0 0
\(75\) −5.65677 −0.653187
\(76\) 0 0
\(77\) 3.34275 0.380942
\(78\) 0 0
\(79\) −9.93308 −1.11756 −0.558779 0.829316i \(-0.688730\pi\)
−0.558779 + 0.829316i \(0.688730\pi\)
\(80\) 0 0
\(81\) −11.2348 −1.24831
\(82\) 0 0
\(83\) 14.6903 1.61247 0.806237 0.591593i \(-0.201501\pi\)
0.806237 + 0.591593i \(0.201501\pi\)
\(84\) 0 0
\(85\) −1.53922 −0.166952
\(86\) 0 0
\(87\) 19.2977 2.06893
\(88\) 0 0
\(89\) −12.6751 −1.34356 −0.671779 0.740752i \(-0.734469\pi\)
−0.671779 + 0.740752i \(0.734469\pi\)
\(90\) 0 0
\(91\) −1.52992 −0.160379
\(92\) 0 0
\(93\) −0.370439 −0.0384128
\(94\) 0 0
\(95\) −8.87337 −0.910389
\(96\) 0 0
\(97\) 10.6498 1.08133 0.540664 0.841238i \(-0.318173\pi\)
0.540664 + 0.841238i \(0.318173\pi\)
\(98\) 0 0
\(99\) −7.27896 −0.731563
\(100\) 0 0
\(101\) 0.365599 0.0363784 0.0181892 0.999835i \(-0.494210\pi\)
0.0181892 + 0.999835i \(0.494210\pi\)
\(102\) 0 0
\(103\) −14.9762 −1.47565 −0.737824 0.674993i \(-0.764147\pi\)
−0.737824 + 0.674993i \(0.764147\pi\)
\(104\) 0 0
\(105\) −2.46741 −0.240795
\(106\) 0 0
\(107\) −18.1951 −1.75899 −0.879495 0.475908i \(-0.842119\pi\)
−0.879495 + 0.475908i \(0.842119\pi\)
\(108\) 0 0
\(109\) −9.75098 −0.933975 −0.466987 0.884264i \(-0.654661\pi\)
−0.466987 + 0.884264i \(0.654661\pi\)
\(110\) 0 0
\(111\) 14.3888 1.36573
\(112\) 0 0
\(113\) −8.29832 −0.780640 −0.390320 0.920679i \(-0.627636\pi\)
−0.390320 + 0.920679i \(0.627636\pi\)
\(114\) 0 0
\(115\) −6.74777 −0.629233
\(116\) 0 0
\(117\) 3.33146 0.307993
\(118\) 0 0
\(119\) 0.745521 0.0683418
\(120\) 0 0
\(121\) 9.10427 0.827661
\(122\) 0 0
\(123\) 3.29496 0.297097
\(124\) 0 0
\(125\) −11.7455 −1.05055
\(126\) 0 0
\(127\) 8.99640 0.798301 0.399151 0.916885i \(-0.369305\pi\)
0.399151 + 0.916885i \(0.369305\pi\)
\(128\) 0 0
\(129\) −7.46475 −0.657235
\(130\) 0 0
\(131\) −16.8641 −1.47342 −0.736710 0.676209i \(-0.763622\pi\)
−0.736710 + 0.676209i \(0.763622\pi\)
\(132\) 0 0
\(133\) 4.29782 0.372668
\(134\) 0 0
\(135\) −4.55606 −0.392124
\(136\) 0 0
\(137\) −16.5922 −1.41757 −0.708783 0.705427i \(-0.750755\pi\)
−0.708783 + 0.705427i \(0.750755\pi\)
\(138\) 0 0
\(139\) 16.3366 1.38565 0.692827 0.721104i \(-0.256365\pi\)
0.692827 + 0.721104i \(0.256365\pi\)
\(140\) 0 0
\(141\) −23.2679 −1.95951
\(142\) 0 0
\(143\) −9.20139 −0.769459
\(144\) 0 0
\(145\) 13.8142 1.14721
\(146\) 0 0
\(147\) −13.8564 −1.14285
\(148\) 0 0
\(149\) 20.1693 1.65233 0.826167 0.563425i \(-0.190517\pi\)
0.826167 + 0.563425i \(0.190517\pi\)
\(150\) 0 0
\(151\) −19.2807 −1.56904 −0.784520 0.620104i \(-0.787090\pi\)
−0.784520 + 0.620104i \(0.787090\pi\)
\(152\) 0 0
\(153\) −1.62340 −0.131244
\(154\) 0 0
\(155\) −0.265178 −0.0212996
\(156\) 0 0
\(157\) 10.6201 0.847577 0.423789 0.905761i \(-0.360700\pi\)
0.423789 + 0.905761i \(0.360700\pi\)
\(158\) 0 0
\(159\) 8.27788 0.656478
\(160\) 0 0
\(161\) 3.26828 0.257577
\(162\) 0 0
\(163\) −8.00878 −0.627296 −0.313648 0.949539i \(-0.601551\pi\)
−0.313648 + 0.949539i \(0.601551\pi\)
\(164\) 0 0
\(165\) −14.8397 −1.15527
\(166\) 0 0
\(167\) 2.38685 0.184700 0.0923500 0.995727i \(-0.470562\pi\)
0.0923500 + 0.995727i \(0.470562\pi\)
\(168\) 0 0
\(169\) −8.78868 −0.676052
\(170\) 0 0
\(171\) −9.35864 −0.715673
\(172\) 0 0
\(173\) 2.38371 0.181230 0.0906152 0.995886i \(-0.471117\pi\)
0.0906152 + 0.995886i \(0.471117\pi\)
\(174\) 0 0
\(175\) 1.96132 0.148262
\(176\) 0 0
\(177\) −2.15021 −0.161620
\(178\) 0 0
\(179\) 4.62432 0.345638 0.172819 0.984954i \(-0.444712\pi\)
0.172819 + 0.984954i \(0.444712\pi\)
\(180\) 0 0
\(181\) 1.84379 0.137048 0.0685240 0.997649i \(-0.478171\pi\)
0.0685240 + 0.997649i \(0.478171\pi\)
\(182\) 0 0
\(183\) 23.5077 1.73774
\(184\) 0 0
\(185\) 10.3002 0.757285
\(186\) 0 0
\(187\) 4.48378 0.327886
\(188\) 0 0
\(189\) 2.20673 0.160516
\(190\) 0 0
\(191\) −3.51470 −0.254315 −0.127157 0.991883i \(-0.540585\pi\)
−0.127157 + 0.991883i \(0.540585\pi\)
\(192\) 0 0
\(193\) 0.663979 0.0477942 0.0238971 0.999714i \(-0.492393\pi\)
0.0238971 + 0.999714i \(0.492393\pi\)
\(194\) 0 0
\(195\) 6.79189 0.486377
\(196\) 0 0
\(197\) −4.61133 −0.328544 −0.164272 0.986415i \(-0.552527\pi\)
−0.164272 + 0.986415i \(0.552527\pi\)
\(198\) 0 0
\(199\) −4.07668 −0.288988 −0.144494 0.989506i \(-0.546155\pi\)
−0.144494 + 0.989506i \(0.546155\pi\)
\(200\) 0 0
\(201\) −2.64986 −0.186906
\(202\) 0 0
\(203\) −6.69090 −0.469609
\(204\) 0 0
\(205\) 2.35869 0.164738
\(206\) 0 0
\(207\) −7.11679 −0.494651
\(208\) 0 0
\(209\) 25.8483 1.78796
\(210\) 0 0
\(211\) 3.51118 0.241719 0.120860 0.992670i \(-0.461435\pi\)
0.120860 + 0.992670i \(0.461435\pi\)
\(212\) 0 0
\(213\) −8.23951 −0.564562
\(214\) 0 0
\(215\) −5.34362 −0.364432
\(216\) 0 0
\(217\) 0.128439 0.00871900
\(218\) 0 0
\(219\) −15.4579 −1.04455
\(220\) 0 0
\(221\) −2.05215 −0.138043
\(222\) 0 0
\(223\) −0.0878155 −0.00588056 −0.00294028 0.999996i \(-0.500936\pi\)
−0.00294028 + 0.999996i \(0.500936\pi\)
\(224\) 0 0
\(225\) −4.27083 −0.284722
\(226\) 0 0
\(227\) 9.17378 0.608885 0.304443 0.952531i \(-0.401530\pi\)
0.304443 + 0.952531i \(0.401530\pi\)
\(228\) 0 0
\(229\) −5.83455 −0.385558 −0.192779 0.981242i \(-0.561750\pi\)
−0.192779 + 0.981242i \(0.561750\pi\)
\(230\) 0 0
\(231\) 7.18762 0.472911
\(232\) 0 0
\(233\) −1.99857 −0.130931 −0.0654653 0.997855i \(-0.520853\pi\)
−0.0654653 + 0.997855i \(0.520853\pi\)
\(234\) 0 0
\(235\) −16.6563 −1.08653
\(236\) 0 0
\(237\) −21.3582 −1.38736
\(238\) 0 0
\(239\) 15.5793 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(240\) 0 0
\(241\) −30.2053 −1.94570 −0.972848 0.231447i \(-0.925654\pi\)
−0.972848 + 0.231447i \(0.925654\pi\)
\(242\) 0 0
\(243\) −15.2772 −0.980031
\(244\) 0 0
\(245\) −9.91904 −0.633705
\(246\) 0 0
\(247\) −11.8303 −0.752746
\(248\) 0 0
\(249\) 31.5873 2.00176
\(250\) 0 0
\(251\) 28.2254 1.78157 0.890785 0.454425i \(-0.150155\pi\)
0.890785 + 0.454425i \(0.150155\pi\)
\(252\) 0 0
\(253\) 19.6564 1.23579
\(254\) 0 0
\(255\) −3.30965 −0.207258
\(256\) 0 0
\(257\) 10.5690 0.659275 0.329637 0.944108i \(-0.393073\pi\)
0.329637 + 0.944108i \(0.393073\pi\)
\(258\) 0 0
\(259\) −4.98890 −0.309995
\(260\) 0 0
\(261\) 14.5697 0.901840
\(262\) 0 0
\(263\) 25.1130 1.54853 0.774267 0.632859i \(-0.218119\pi\)
0.774267 + 0.632859i \(0.218119\pi\)
\(264\) 0 0
\(265\) 5.92569 0.364013
\(266\) 0 0
\(267\) −27.2541 −1.66792
\(268\) 0 0
\(269\) −5.32331 −0.324568 −0.162284 0.986744i \(-0.551886\pi\)
−0.162284 + 0.986744i \(0.551886\pi\)
\(270\) 0 0
\(271\) 32.1286 1.95167 0.975837 0.218498i \(-0.0701158\pi\)
0.975837 + 0.218498i \(0.0701158\pi\)
\(272\) 0 0
\(273\) −3.28965 −0.199099
\(274\) 0 0
\(275\) 11.7959 0.711321
\(276\) 0 0
\(277\) −30.4389 −1.82890 −0.914448 0.404704i \(-0.867374\pi\)
−0.914448 + 0.404704i \(0.867374\pi\)
\(278\) 0 0
\(279\) −0.279680 −0.0167440
\(280\) 0 0
\(281\) −25.4173 −1.51627 −0.758135 0.652098i \(-0.773889\pi\)
−0.758135 + 0.652098i \(0.773889\pi\)
\(282\) 0 0
\(283\) −25.2985 −1.50384 −0.751920 0.659254i \(-0.770872\pi\)
−0.751920 + 0.659254i \(0.770872\pi\)
\(284\) 0 0
\(285\) −19.0796 −1.13018
\(286\) 0 0
\(287\) −1.14243 −0.0674356
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 22.8994 1.34239
\(292\) 0 0
\(293\) −8.72136 −0.509507 −0.254754 0.967006i \(-0.581994\pi\)
−0.254754 + 0.967006i \(0.581994\pi\)
\(294\) 0 0
\(295\) −1.53922 −0.0896169
\(296\) 0 0
\(297\) 13.2719 0.770114
\(298\) 0 0
\(299\) −8.99639 −0.520275
\(300\) 0 0
\(301\) 2.58818 0.149180
\(302\) 0 0
\(303\) 0.786113 0.0451610
\(304\) 0 0
\(305\) 16.8279 0.963563
\(306\) 0 0
\(307\) 13.7013 0.781974 0.390987 0.920396i \(-0.372134\pi\)
0.390987 + 0.920396i \(0.372134\pi\)
\(308\) 0 0
\(309\) −32.2019 −1.83190
\(310\) 0 0
\(311\) −27.8201 −1.57753 −0.788765 0.614695i \(-0.789279\pi\)
−0.788765 + 0.614695i \(0.789279\pi\)
\(312\) 0 0
\(313\) 2.59213 0.146516 0.0732579 0.997313i \(-0.476660\pi\)
0.0732579 + 0.997313i \(0.476660\pi\)
\(314\) 0 0
\(315\) −1.86289 −0.104962
\(316\) 0 0
\(317\) 1.06614 0.0598803 0.0299402 0.999552i \(-0.490468\pi\)
0.0299402 + 0.999552i \(0.490468\pi\)
\(318\) 0 0
\(319\) −40.2410 −2.25306
\(320\) 0 0
\(321\) −39.1233 −2.18365
\(322\) 0 0
\(323\) 5.76485 0.320765
\(324\) 0 0
\(325\) −5.39879 −0.299471
\(326\) 0 0
\(327\) −20.9667 −1.15946
\(328\) 0 0
\(329\) 8.06745 0.444773
\(330\) 0 0
\(331\) 7.91407 0.434997 0.217498 0.976061i \(-0.430210\pi\)
0.217498 + 0.976061i \(0.430210\pi\)
\(332\) 0 0
\(333\) 10.8635 0.595316
\(334\) 0 0
\(335\) −1.89689 −0.103638
\(336\) 0 0
\(337\) −0.500204 −0.0272478 −0.0136239 0.999907i \(-0.504337\pi\)
−0.0136239 + 0.999907i \(0.504337\pi\)
\(338\) 0 0
\(339\) −17.8431 −0.969105
\(340\) 0 0
\(341\) 0.772468 0.0418315
\(342\) 0 0
\(343\) 10.0229 0.541188
\(344\) 0 0
\(345\) −14.5091 −0.781144
\(346\) 0 0
\(347\) 32.4015 1.73940 0.869701 0.493578i \(-0.164311\pi\)
0.869701 + 0.493578i \(0.164311\pi\)
\(348\) 0 0
\(349\) −5.20961 −0.278864 −0.139432 0.990232i \(-0.544528\pi\)
−0.139432 + 0.990232i \(0.544528\pi\)
\(350\) 0 0
\(351\) −6.07432 −0.324223
\(352\) 0 0
\(353\) 13.1004 0.697264 0.348632 0.937260i \(-0.386646\pi\)
0.348632 + 0.937260i \(0.386646\pi\)
\(354\) 0 0
\(355\) −5.89823 −0.313046
\(356\) 0 0
\(357\) 1.60303 0.0848412
\(358\) 0 0
\(359\) 32.0851 1.69339 0.846693 0.532081i \(-0.178590\pi\)
0.846693 + 0.532081i \(0.178590\pi\)
\(360\) 0 0
\(361\) 14.2335 0.749129
\(362\) 0 0
\(363\) 19.5761 1.02748
\(364\) 0 0
\(365\) −11.0655 −0.579195
\(366\) 0 0
\(367\) −6.09787 −0.318306 −0.159153 0.987254i \(-0.550876\pi\)
−0.159153 + 0.987254i \(0.550876\pi\)
\(368\) 0 0
\(369\) 2.48768 0.129504
\(370\) 0 0
\(371\) −2.87011 −0.149009
\(372\) 0 0
\(373\) −16.9026 −0.875185 −0.437593 0.899173i \(-0.644169\pi\)
−0.437593 + 0.899173i \(0.644169\pi\)
\(374\) 0 0
\(375\) −25.2552 −1.30418
\(376\) 0 0
\(377\) 18.4176 0.948556
\(378\) 0 0
\(379\) 14.6925 0.754703 0.377352 0.926070i \(-0.376835\pi\)
0.377352 + 0.926070i \(0.376835\pi\)
\(380\) 0 0
\(381\) 19.3441 0.991030
\(382\) 0 0
\(383\) 24.9963 1.27725 0.638625 0.769518i \(-0.279504\pi\)
0.638625 + 0.769518i \(0.279504\pi\)
\(384\) 0 0
\(385\) 5.14524 0.262226
\(386\) 0 0
\(387\) −5.63586 −0.286487
\(388\) 0 0
\(389\) −23.4240 −1.18764 −0.593821 0.804597i \(-0.702381\pi\)
−0.593821 + 0.804597i \(0.702381\pi\)
\(390\) 0 0
\(391\) 4.38388 0.221703
\(392\) 0 0
\(393\) −36.2612 −1.82914
\(394\) 0 0
\(395\) −15.2892 −0.769283
\(396\) 0 0
\(397\) 30.3666 1.52406 0.762028 0.647544i \(-0.224204\pi\)
0.762028 + 0.647544i \(0.224204\pi\)
\(398\) 0 0
\(399\) 9.24120 0.462639
\(400\) 0 0
\(401\) 8.91678 0.445283 0.222641 0.974900i \(-0.428532\pi\)
0.222641 + 0.974900i \(0.428532\pi\)
\(402\) 0 0
\(403\) −0.353546 −0.0176114
\(404\) 0 0
\(405\) −17.2928 −0.859286
\(406\) 0 0
\(407\) −30.0046 −1.48727
\(408\) 0 0
\(409\) −15.9501 −0.788680 −0.394340 0.918965i \(-0.629027\pi\)
−0.394340 + 0.918965i \(0.629027\pi\)
\(410\) 0 0
\(411\) −35.6767 −1.75980
\(412\) 0 0
\(413\) 0.745521 0.0366847
\(414\) 0 0
\(415\) 22.6117 1.10996
\(416\) 0 0
\(417\) 35.1272 1.72018
\(418\) 0 0
\(419\) −38.1632 −1.86440 −0.932198 0.361950i \(-0.882111\pi\)
−0.932198 + 0.361950i \(0.882111\pi\)
\(420\) 0 0
\(421\) 27.3034 1.33069 0.665344 0.746537i \(-0.268285\pi\)
0.665344 + 0.746537i \(0.268285\pi\)
\(422\) 0 0
\(423\) −17.5672 −0.854144
\(424\) 0 0
\(425\) 2.63080 0.127612
\(426\) 0 0
\(427\) −8.15059 −0.394435
\(428\) 0 0
\(429\) −19.7849 −0.955224
\(430\) 0 0
\(431\) 25.7162 1.23870 0.619352 0.785114i \(-0.287395\pi\)
0.619352 + 0.785114i \(0.287395\pi\)
\(432\) 0 0
\(433\) 34.6860 1.66690 0.833451 0.552593i \(-0.186362\pi\)
0.833451 + 0.552593i \(0.186362\pi\)
\(434\) 0 0
\(435\) 29.7034 1.42417
\(436\) 0 0
\(437\) 25.2724 1.20894
\(438\) 0 0
\(439\) −34.3155 −1.63779 −0.818895 0.573944i \(-0.805413\pi\)
−0.818895 + 0.573944i \(0.805413\pi\)
\(440\) 0 0
\(441\) −10.4615 −0.498167
\(442\) 0 0
\(443\) 6.95278 0.330337 0.165168 0.986265i \(-0.447183\pi\)
0.165168 + 0.986265i \(0.447183\pi\)
\(444\) 0 0
\(445\) −19.5098 −0.924852
\(446\) 0 0
\(447\) 43.3682 2.05125
\(448\) 0 0
\(449\) −2.94322 −0.138899 −0.0694496 0.997585i \(-0.522124\pi\)
−0.0694496 + 0.997585i \(0.522124\pi\)
\(450\) 0 0
\(451\) −6.87091 −0.323538
\(452\) 0 0
\(453\) −41.4575 −1.94784
\(454\) 0 0
\(455\) −2.35489 −0.110399
\(456\) 0 0
\(457\) 23.2388 1.08706 0.543532 0.839389i \(-0.317087\pi\)
0.543532 + 0.839389i \(0.317087\pi\)
\(458\) 0 0
\(459\) 2.95998 0.138160
\(460\) 0 0
\(461\) −8.54846 −0.398141 −0.199071 0.979985i \(-0.563792\pi\)
−0.199071 + 0.979985i \(0.563792\pi\)
\(462\) 0 0
\(463\) 6.03185 0.280324 0.140162 0.990129i \(-0.455238\pi\)
0.140162 + 0.990129i \(0.455238\pi\)
\(464\) 0 0
\(465\) −0.570188 −0.0264418
\(466\) 0 0
\(467\) 22.0998 1.02265 0.511327 0.859386i \(-0.329154\pi\)
0.511327 + 0.859386i \(0.329154\pi\)
\(468\) 0 0
\(469\) 0.918760 0.0424244
\(470\) 0 0
\(471\) 22.8355 1.05220
\(472\) 0 0
\(473\) 15.5661 0.715728
\(474\) 0 0
\(475\) 15.1661 0.695871
\(476\) 0 0
\(477\) 6.24976 0.286157
\(478\) 0 0
\(479\) −34.0875 −1.55750 −0.778749 0.627335i \(-0.784146\pi\)
−0.778749 + 0.627335i \(0.784146\pi\)
\(480\) 0 0
\(481\) 13.7326 0.626153
\(482\) 0 0
\(483\) 7.02749 0.319762
\(484\) 0 0
\(485\) 16.3925 0.744344
\(486\) 0 0
\(487\) −38.2826 −1.73475 −0.867375 0.497655i \(-0.834195\pi\)
−0.867375 + 0.497655i \(0.834195\pi\)
\(488\) 0 0
\(489\) −17.2206 −0.778741
\(490\) 0 0
\(491\) 22.4833 1.01466 0.507328 0.861753i \(-0.330633\pi\)
0.507328 + 0.861753i \(0.330633\pi\)
\(492\) 0 0
\(493\) −8.97480 −0.404204
\(494\) 0 0
\(495\) −11.2039 −0.503579
\(496\) 0 0
\(497\) 2.85681 0.128145
\(498\) 0 0
\(499\) 43.4971 1.94720 0.973599 0.228267i \(-0.0733059\pi\)
0.973599 + 0.228267i \(0.0733059\pi\)
\(500\) 0 0
\(501\) 5.13223 0.229291
\(502\) 0 0
\(503\) 0.607269 0.0270768 0.0135384 0.999908i \(-0.495690\pi\)
0.0135384 + 0.999908i \(0.495690\pi\)
\(504\) 0 0
\(505\) 0.562737 0.0250415
\(506\) 0 0
\(507\) −18.8975 −0.839267
\(508\) 0 0
\(509\) 0.0966872 0.00428559 0.00214279 0.999998i \(-0.499318\pi\)
0.00214279 + 0.999998i \(0.499318\pi\)
\(510\) 0 0
\(511\) 5.35958 0.237094
\(512\) 0 0
\(513\) 17.0638 0.753387
\(514\) 0 0
\(515\) −23.0517 −1.01578
\(516\) 0 0
\(517\) 48.5200 2.13391
\(518\) 0 0
\(519\) 5.12548 0.224984
\(520\) 0 0
\(521\) 8.07749 0.353881 0.176941 0.984222i \(-0.443380\pi\)
0.176941 + 0.984222i \(0.443380\pi\)
\(522\) 0 0
\(523\) −12.6111 −0.551447 −0.275723 0.961237i \(-0.588917\pi\)
−0.275723 + 0.961237i \(0.588917\pi\)
\(524\) 0 0
\(525\) 4.21724 0.184055
\(526\) 0 0
\(527\) 0.172281 0.00750466
\(528\) 0 0
\(529\) −3.78155 −0.164415
\(530\) 0 0
\(531\) −1.62340 −0.0704495
\(532\) 0 0
\(533\) 3.14470 0.136212
\(534\) 0 0
\(535\) −28.0063 −1.21082
\(536\) 0 0
\(537\) 9.94325 0.429083
\(538\) 0 0
\(539\) 28.8944 1.24457
\(540\) 0 0
\(541\) 43.8815 1.88661 0.943306 0.331923i \(-0.107698\pi\)
0.943306 + 0.331923i \(0.107698\pi\)
\(542\) 0 0
\(543\) 3.96454 0.170135
\(544\) 0 0
\(545\) −15.0089 −0.642911
\(546\) 0 0
\(547\) 34.4073 1.47115 0.735576 0.677443i \(-0.236912\pi\)
0.735576 + 0.677443i \(0.236912\pi\)
\(548\) 0 0
\(549\) 17.7482 0.757474
\(550\) 0 0
\(551\) −51.7383 −2.20413
\(552\) 0 0
\(553\) 7.40532 0.314906
\(554\) 0 0
\(555\) 22.1476 0.940112
\(556\) 0 0
\(557\) 11.2200 0.475408 0.237704 0.971338i \(-0.423605\pi\)
0.237704 + 0.971338i \(0.423605\pi\)
\(558\) 0 0
\(559\) −7.12433 −0.301327
\(560\) 0 0
\(561\) 9.64106 0.407046
\(562\) 0 0
\(563\) 11.8439 0.499162 0.249581 0.968354i \(-0.419707\pi\)
0.249581 + 0.968354i \(0.419707\pi\)
\(564\) 0 0
\(565\) −12.7729 −0.537362
\(566\) 0 0
\(567\) 8.37576 0.351749
\(568\) 0 0
\(569\) −30.9566 −1.29777 −0.648883 0.760888i \(-0.724764\pi\)
−0.648883 + 0.760888i \(0.724764\pi\)
\(570\) 0 0
\(571\) 37.2197 1.55760 0.778799 0.627274i \(-0.215829\pi\)
0.778799 + 0.627274i \(0.215829\pi\)
\(572\) 0 0
\(573\) −7.55734 −0.315713
\(574\) 0 0
\(575\) 11.5331 0.480964
\(576\) 0 0
\(577\) −18.9600 −0.789316 −0.394658 0.918828i \(-0.629137\pi\)
−0.394658 + 0.918828i \(0.629137\pi\)
\(578\) 0 0
\(579\) 1.42769 0.0593329
\(580\) 0 0
\(581\) −10.9520 −0.454364
\(582\) 0 0
\(583\) −17.2617 −0.714905
\(584\) 0 0
\(585\) 5.12785 0.212010
\(586\) 0 0
\(587\) 14.3772 0.593413 0.296706 0.954969i \(-0.404112\pi\)
0.296706 + 0.954969i \(0.404112\pi\)
\(588\) 0 0
\(589\) 0.993171 0.0409229
\(590\) 0 0
\(591\) −9.91532 −0.407862
\(592\) 0 0
\(593\) −6.89753 −0.283248 −0.141624 0.989921i \(-0.545232\pi\)
−0.141624 + 0.989921i \(0.545232\pi\)
\(594\) 0 0
\(595\) 1.14752 0.0470438
\(596\) 0 0
\(597\) −8.76571 −0.358756
\(598\) 0 0
\(599\) −13.0784 −0.534370 −0.267185 0.963645i \(-0.586093\pi\)
−0.267185 + 0.963645i \(0.586093\pi\)
\(600\) 0 0
\(601\) −20.7866 −0.847902 −0.423951 0.905685i \(-0.639357\pi\)
−0.423951 + 0.905685i \(0.639357\pi\)
\(602\) 0 0
\(603\) −2.00063 −0.0814720
\(604\) 0 0
\(605\) 14.0135 0.569729
\(606\) 0 0
\(607\) 12.6434 0.513181 0.256591 0.966520i \(-0.417401\pi\)
0.256591 + 0.966520i \(0.417401\pi\)
\(608\) 0 0
\(609\) −14.3868 −0.582984
\(610\) 0 0
\(611\) −22.2068 −0.898390
\(612\) 0 0
\(613\) −35.0676 −1.41637 −0.708184 0.706028i \(-0.750485\pi\)
−0.708184 + 0.706028i \(0.750485\pi\)
\(614\) 0 0
\(615\) 5.07168 0.204510
\(616\) 0 0
\(617\) −2.63030 −0.105892 −0.0529460 0.998597i \(-0.516861\pi\)
−0.0529460 + 0.998597i \(0.516861\pi\)
\(618\) 0 0
\(619\) 29.3842 1.18105 0.590526 0.807018i \(-0.298920\pi\)
0.590526 + 0.807018i \(0.298920\pi\)
\(620\) 0 0
\(621\) 12.9762 0.520718
\(622\) 0 0
\(623\) 9.44956 0.378588
\(624\) 0 0
\(625\) −4.92491 −0.196996
\(626\) 0 0
\(627\) 55.5792 2.21962
\(628\) 0 0
\(629\) −6.69182 −0.266820
\(630\) 0 0
\(631\) 29.2093 1.16280 0.581401 0.813617i \(-0.302505\pi\)
0.581401 + 0.813617i \(0.302505\pi\)
\(632\) 0 0
\(633\) 7.54976 0.300076
\(634\) 0 0
\(635\) 13.8474 0.549519
\(636\) 0 0
\(637\) −13.2245 −0.523972
\(638\) 0 0
\(639\) −6.22080 −0.246091
\(640\) 0 0
\(641\) 40.7856 1.61094 0.805468 0.592640i \(-0.201914\pi\)
0.805468 + 0.592640i \(0.201914\pi\)
\(642\) 0 0
\(643\) −17.4632 −0.688682 −0.344341 0.938845i \(-0.611898\pi\)
−0.344341 + 0.938845i \(0.611898\pi\)
\(644\) 0 0
\(645\) −11.4899 −0.452414
\(646\) 0 0
\(647\) −18.9904 −0.746591 −0.373296 0.927712i \(-0.621772\pi\)
−0.373296 + 0.927712i \(0.621772\pi\)
\(648\) 0 0
\(649\) 4.48378 0.176004
\(650\) 0 0
\(651\) 0.276170 0.0108240
\(652\) 0 0
\(653\) −6.24228 −0.244279 −0.122140 0.992513i \(-0.538976\pi\)
−0.122140 + 0.992513i \(0.538976\pi\)
\(654\) 0 0
\(655\) −25.9575 −1.01424
\(656\) 0 0
\(657\) −11.6707 −0.455316
\(658\) 0 0
\(659\) −12.4617 −0.485441 −0.242720 0.970096i \(-0.578040\pi\)
−0.242720 + 0.970096i \(0.578040\pi\)
\(660\) 0 0
\(661\) −12.1220 −0.471492 −0.235746 0.971815i \(-0.575753\pi\)
−0.235746 + 0.971815i \(0.575753\pi\)
\(662\) 0 0
\(663\) −4.41255 −0.171369
\(664\) 0 0
\(665\) 6.61529 0.256530
\(666\) 0 0
\(667\) −39.3445 −1.52342
\(668\) 0 0
\(669\) −0.188822 −0.00730027
\(670\) 0 0
\(671\) −49.0200 −1.89239
\(672\) 0 0
\(673\) −26.7932 −1.03280 −0.516402 0.856346i \(-0.672729\pi\)
−0.516402 + 0.856346i \(0.672729\pi\)
\(674\) 0 0
\(675\) 7.78711 0.299726
\(676\) 0 0
\(677\) 10.3131 0.396366 0.198183 0.980165i \(-0.436496\pi\)
0.198183 + 0.980165i \(0.436496\pi\)
\(678\) 0 0
\(679\) −7.93969 −0.304697
\(680\) 0 0
\(681\) 19.7256 0.755885
\(682\) 0 0
\(683\) −8.09734 −0.309836 −0.154918 0.987927i \(-0.549511\pi\)
−0.154918 + 0.987927i \(0.549511\pi\)
\(684\) 0 0
\(685\) −25.5390 −0.975796
\(686\) 0 0
\(687\) −12.5455 −0.478641
\(688\) 0 0
\(689\) 7.90037 0.300980
\(690\) 0 0
\(691\) 17.3069 0.658386 0.329193 0.944263i \(-0.393223\pi\)
0.329193 + 0.944263i \(0.393223\pi\)
\(692\) 0 0
\(693\) 5.42662 0.206140
\(694\) 0 0
\(695\) 25.1457 0.953830
\(696\) 0 0
\(697\) −1.53239 −0.0580435
\(698\) 0 0
\(699\) −4.29734 −0.162540
\(700\) 0 0
\(701\) 16.4252 0.620372 0.310186 0.950676i \(-0.399609\pi\)
0.310186 + 0.950676i \(0.399609\pi\)
\(702\) 0 0
\(703\) −38.5773 −1.45497
\(704\) 0 0
\(705\) −35.8144 −1.34885
\(706\) 0 0
\(707\) −0.272562 −0.0102507
\(708\) 0 0
\(709\) 24.2689 0.911438 0.455719 0.890124i \(-0.349382\pi\)
0.455719 + 0.890124i \(0.349382\pi\)
\(710\) 0 0
\(711\) −16.1253 −0.604748
\(712\) 0 0
\(713\) 0.755258 0.0282846
\(714\) 0 0
\(715\) −14.1630 −0.529665
\(716\) 0 0
\(717\) 33.4988 1.25103
\(718\) 0 0
\(719\) 28.7681 1.07287 0.536435 0.843942i \(-0.319771\pi\)
0.536435 + 0.843942i \(0.319771\pi\)
\(720\) 0 0
\(721\) 11.1651 0.415809
\(722\) 0 0
\(723\) −64.9477 −2.41543
\(724\) 0 0
\(725\) −23.6109 −0.876886
\(726\) 0 0
\(727\) −12.1298 −0.449871 −0.224935 0.974374i \(-0.572217\pi\)
−0.224935 + 0.974374i \(0.572217\pi\)
\(728\) 0 0
\(729\) 0.855215 0.0316746
\(730\) 0 0
\(731\) 3.47164 0.128403
\(732\) 0 0
\(733\) 2.49693 0.0922264 0.0461132 0.998936i \(-0.485317\pi\)
0.0461132 + 0.998936i \(0.485317\pi\)
\(734\) 0 0
\(735\) −21.3280 −0.786696
\(736\) 0 0
\(737\) 5.52568 0.203541
\(738\) 0 0
\(739\) −40.6741 −1.49622 −0.748111 0.663574i \(-0.769039\pi\)
−0.748111 + 0.663574i \(0.769039\pi\)
\(740\) 0 0
\(741\) −25.4377 −0.934476
\(742\) 0 0
\(743\) −19.7646 −0.725093 −0.362546 0.931966i \(-0.618093\pi\)
−0.362546 + 0.931966i \(0.618093\pi\)
\(744\) 0 0
\(745\) 31.0450 1.13740
\(746\) 0 0
\(747\) 23.8483 0.872562
\(748\) 0 0
\(749\) 13.5649 0.495649
\(750\) 0 0
\(751\) 36.3940 1.32804 0.664018 0.747717i \(-0.268850\pi\)
0.664018 + 0.747717i \(0.268850\pi\)
\(752\) 0 0
\(753\) 60.6904 2.21168
\(754\) 0 0
\(755\) −29.6772 −1.08007
\(756\) 0 0
\(757\) −34.4852 −1.25339 −0.626693 0.779267i \(-0.715592\pi\)
−0.626693 + 0.779267i \(0.715592\pi\)
\(758\) 0 0
\(759\) 42.2653 1.53413
\(760\) 0 0
\(761\) 19.9649 0.723728 0.361864 0.932231i \(-0.382140\pi\)
0.361864 + 0.932231i \(0.382140\pi\)
\(762\) 0 0
\(763\) 7.26957 0.263176
\(764\) 0 0
\(765\) −2.49877 −0.0903432
\(766\) 0 0
\(767\) −2.05215 −0.0740988
\(768\) 0 0
\(769\) −21.8906 −0.789396 −0.394698 0.918811i \(-0.629151\pi\)
−0.394698 + 0.918811i \(0.629151\pi\)
\(770\) 0 0
\(771\) 22.7255 0.818439
\(772\) 0 0
\(773\) −36.3952 −1.30904 −0.654522 0.756043i \(-0.727130\pi\)
−0.654522 + 0.756043i \(0.727130\pi\)
\(774\) 0 0
\(775\) 0.453236 0.0162807
\(776\) 0 0
\(777\) −10.7272 −0.384835
\(778\) 0 0
\(779\) −8.83400 −0.316511
\(780\) 0 0
\(781\) 17.1817 0.614808
\(782\) 0 0
\(783\) −26.5652 −0.949363
\(784\) 0 0
\(785\) 16.3467 0.583439
\(786\) 0 0
\(787\) −33.4675 −1.19299 −0.596494 0.802618i \(-0.703440\pi\)
−0.596494 + 0.802618i \(0.703440\pi\)
\(788\) 0 0
\(789\) 53.9982 1.92239
\(790\) 0 0
\(791\) 6.18658 0.219969
\(792\) 0 0
\(793\) 22.4356 0.796712
\(794\) 0 0
\(795\) 12.7415 0.451894
\(796\) 0 0
\(797\) 44.7628 1.58558 0.792789 0.609496i \(-0.208628\pi\)
0.792789 + 0.609496i \(0.208628\pi\)
\(798\) 0 0
\(799\) 10.8212 0.382827
\(800\) 0 0
\(801\) −20.5767 −0.727043
\(802\) 0 0
\(803\) 32.2340 1.13751
\(804\) 0 0
\(805\) 5.03061 0.177306
\(806\) 0 0
\(807\) −11.4462 −0.402926
\(808\) 0 0
\(809\) −0.913247 −0.0321081 −0.0160540 0.999871i \(-0.505110\pi\)
−0.0160540 + 0.999871i \(0.505110\pi\)
\(810\) 0 0
\(811\) 18.8076 0.660426 0.330213 0.943907i \(-0.392879\pi\)
0.330213 + 0.943907i \(0.392879\pi\)
\(812\) 0 0
\(813\) 69.0832 2.42286
\(814\) 0 0
\(815\) −12.3273 −0.431806
\(816\) 0 0
\(817\) 20.0135 0.700183
\(818\) 0 0
\(819\) −2.48367 −0.0867866
\(820\) 0 0
\(821\) 17.2882 0.603361 0.301680 0.953409i \(-0.402452\pi\)
0.301680 + 0.953409i \(0.402452\pi\)
\(822\) 0 0
\(823\) 9.36213 0.326343 0.163172 0.986598i \(-0.447828\pi\)
0.163172 + 0.986598i \(0.447828\pi\)
\(824\) 0 0
\(825\) 25.3637 0.883050
\(826\) 0 0
\(827\) −5.53918 −0.192616 −0.0963081 0.995352i \(-0.530703\pi\)
−0.0963081 + 0.995352i \(0.530703\pi\)
\(828\) 0 0
\(829\) −26.5733 −0.922929 −0.461465 0.887159i \(-0.652676\pi\)
−0.461465 + 0.887159i \(0.652676\pi\)
\(830\) 0 0
\(831\) −65.4500 −2.27043
\(832\) 0 0
\(833\) 6.44420 0.223278
\(834\) 0 0
\(835\) 3.67389 0.127140
\(836\) 0 0
\(837\) 0.509947 0.0176264
\(838\) 0 0
\(839\) 52.1417 1.80013 0.900065 0.435755i \(-0.143519\pi\)
0.900065 + 0.435755i \(0.143519\pi\)
\(840\) 0 0
\(841\) 51.5469 1.77748
\(842\) 0 0
\(843\) −54.6525 −1.88233
\(844\) 0 0
\(845\) −13.5277 −0.465368
\(846\) 0 0
\(847\) −6.78743 −0.233219
\(848\) 0 0
\(849\) −54.3971 −1.86690
\(850\) 0 0
\(851\) −29.3362 −1.00563
\(852\) 0 0
\(853\) −17.2582 −0.590910 −0.295455 0.955357i \(-0.595471\pi\)
−0.295455 + 0.955357i \(0.595471\pi\)
\(854\) 0 0
\(855\) −14.4050 −0.492641
\(856\) 0 0
\(857\) −41.4174 −1.41479 −0.707396 0.706818i \(-0.750130\pi\)
−0.707396 + 0.706818i \(0.750130\pi\)
\(858\) 0 0
\(859\) −18.8381 −0.642747 −0.321374 0.946952i \(-0.604145\pi\)
−0.321374 + 0.946952i \(0.604145\pi\)
\(860\) 0 0
\(861\) −2.45647 −0.0837161
\(862\) 0 0
\(863\) −39.5843 −1.34746 −0.673732 0.738975i \(-0.735310\pi\)
−0.673732 + 0.738975i \(0.735310\pi\)
\(864\) 0 0
\(865\) 3.66906 0.124752
\(866\) 0 0
\(867\) 2.15021 0.0730249
\(868\) 0 0
\(869\) 44.5377 1.51084
\(870\) 0 0
\(871\) −2.52901 −0.0856923
\(872\) 0 0
\(873\) 17.2890 0.585142
\(874\) 0 0
\(875\) 8.75651 0.296024
\(876\) 0 0
\(877\) −38.1081 −1.28682 −0.643409 0.765522i \(-0.722481\pi\)
−0.643409 + 0.765522i \(0.722481\pi\)
\(878\) 0 0
\(879\) −18.7527 −0.632514
\(880\) 0 0
\(881\) 0.659310 0.0222127 0.0111064 0.999938i \(-0.496465\pi\)
0.0111064 + 0.999938i \(0.496465\pi\)
\(882\) 0 0
\(883\) −58.8386 −1.98008 −0.990038 0.140801i \(-0.955032\pi\)
−0.990038 + 0.140801i \(0.955032\pi\)
\(884\) 0 0
\(885\) −3.30965 −0.111253
\(886\) 0 0
\(887\) −13.6915 −0.459715 −0.229857 0.973224i \(-0.573826\pi\)
−0.229857 + 0.973224i \(0.573826\pi\)
\(888\) 0 0
\(889\) −6.70701 −0.224946
\(890\) 0 0
\(891\) 50.3742 1.68760
\(892\) 0 0
\(893\) 62.3827 2.08756
\(894\) 0 0
\(895\) 7.11785 0.237923
\(896\) 0 0
\(897\) −19.3441 −0.645881
\(898\) 0 0
\(899\) −1.54618 −0.0515681
\(900\) 0 0
\(901\) −3.84980 −0.128255
\(902\) 0 0
\(903\) 5.56513 0.185196
\(904\) 0 0
\(905\) 2.83800 0.0943384
\(906\) 0 0
\(907\) 36.6794 1.21792 0.608960 0.793201i \(-0.291587\pi\)
0.608960 + 0.793201i \(0.291587\pi\)
\(908\) 0 0
\(909\) 0.593512 0.0196856
\(910\) 0 0
\(911\) −50.4068 −1.67005 −0.835026 0.550211i \(-0.814547\pi\)
−0.835026 + 0.550211i \(0.814547\pi\)
\(912\) 0 0
\(913\) −65.8682 −2.17992
\(914\) 0 0
\(915\) 36.1835 1.19619
\(916\) 0 0
\(917\) 12.5725 0.415181
\(918\) 0 0
\(919\) −25.7697 −0.850065 −0.425033 0.905178i \(-0.639737\pi\)
−0.425033 + 0.905178i \(0.639737\pi\)
\(920\) 0 0
\(921\) 29.4606 0.970761
\(922\) 0 0
\(923\) −7.86375 −0.258839
\(924\) 0 0
\(925\) −17.6048 −0.578843
\(926\) 0 0
\(927\) −24.3123 −0.798522
\(928\) 0 0
\(929\) −25.1475 −0.825061 −0.412531 0.910944i \(-0.635355\pi\)
−0.412531 + 0.910944i \(0.635355\pi\)
\(930\) 0 0
\(931\) 37.1498 1.21754
\(932\) 0 0
\(933\) −59.8189 −1.95838
\(934\) 0 0
\(935\) 6.90153 0.225704
\(936\) 0 0
\(937\) 0.223784 0.00731069 0.00365534 0.999993i \(-0.498836\pi\)
0.00365534 + 0.999993i \(0.498836\pi\)
\(938\) 0 0
\(939\) 5.57362 0.181888
\(940\) 0 0
\(941\) 15.0456 0.490474 0.245237 0.969463i \(-0.421134\pi\)
0.245237 + 0.969463i \(0.421134\pi\)
\(942\) 0 0
\(943\) −6.71783 −0.218763
\(944\) 0 0
\(945\) 3.39664 0.110493
\(946\) 0 0
\(947\) 11.5924 0.376701 0.188351 0.982102i \(-0.439686\pi\)
0.188351 + 0.982102i \(0.439686\pi\)
\(948\) 0 0
\(949\) −14.7530 −0.478902
\(950\) 0 0
\(951\) 2.29242 0.0743368
\(952\) 0 0
\(953\) 46.7820 1.51542 0.757709 0.652593i \(-0.226319\pi\)
0.757709 + 0.652593i \(0.226319\pi\)
\(954\) 0 0
\(955\) −5.40990 −0.175060
\(956\) 0 0
\(957\) −86.5265 −2.79701
\(958\) 0 0
\(959\) 12.3698 0.399443
\(960\) 0 0
\(961\) −30.9703 −0.999043
\(962\) 0 0
\(963\) −29.5380 −0.951847
\(964\) 0 0
\(965\) 1.02201 0.0328997
\(966\) 0 0
\(967\) −24.0468 −0.773291 −0.386646 0.922228i \(-0.626366\pi\)
−0.386646 + 0.922228i \(0.626366\pi\)
\(968\) 0 0
\(969\) 12.3956 0.398205
\(970\) 0 0
\(971\) −42.6392 −1.36836 −0.684178 0.729315i \(-0.739839\pi\)
−0.684178 + 0.729315i \(0.739839\pi\)
\(972\) 0 0
\(973\) −12.1793 −0.390451
\(974\) 0 0
\(975\) −11.6085 −0.371771
\(976\) 0 0
\(977\) 5.77838 0.184867 0.0924334 0.995719i \(-0.470535\pi\)
0.0924334 + 0.995719i \(0.470535\pi\)
\(978\) 0 0
\(979\) 56.8323 1.81637
\(980\) 0 0
\(981\) −15.8297 −0.505405
\(982\) 0 0
\(983\) 16.0211 0.510993 0.255496 0.966810i \(-0.417761\pi\)
0.255496 + 0.966810i \(0.417761\pi\)
\(984\) 0 0
\(985\) −7.09785 −0.226156
\(986\) 0 0
\(987\) 17.3467 0.552152
\(988\) 0 0
\(989\) 15.2193 0.483945
\(990\) 0 0
\(991\) −18.3797 −0.583851 −0.291926 0.956441i \(-0.594296\pi\)
−0.291926 + 0.956441i \(0.594296\pi\)
\(992\) 0 0
\(993\) 17.0169 0.540015
\(994\) 0 0
\(995\) −6.27491 −0.198928
\(996\) 0 0
\(997\) −4.66918 −0.147874 −0.0739372 0.997263i \(-0.523556\pi\)
−0.0739372 + 0.997263i \(0.523556\pi\)
\(998\) 0 0
\(999\) −19.8077 −0.626687
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 \(a_p\))