Properties

Label 8016.2.a.bg.1.10
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.79706\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+2.79706 q^{5}\) \(-4.56518 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+2.79706 q^{5}\) \(-4.56518 q^{7}\) \(+1.00000 q^{9}\) \(-2.91073 q^{11}\) \(-0.850435 q^{13}\) \(-2.79706 q^{15}\) \(-7.79699 q^{17}\) \(-2.29761 q^{19}\) \(+4.56518 q^{21}\) \(-2.74788 q^{23}\) \(+2.82355 q^{25}\) \(-1.00000 q^{27}\) \(-6.57467 q^{29}\) \(+7.06047 q^{31}\) \(+2.91073 q^{33}\) \(-12.7691 q^{35}\) \(+8.35845 q^{37}\) \(+0.850435 q^{39}\) \(+4.96938 q^{41}\) \(-11.4328 q^{43}\) \(+2.79706 q^{45}\) \(-12.1758 q^{47}\) \(+13.8408 q^{49}\) \(+7.79699 q^{51}\) \(-6.03568 q^{53}\) \(-8.14149 q^{55}\) \(+2.29761 q^{57}\) \(+3.64159 q^{59}\) \(+3.09676 q^{61}\) \(-4.56518 q^{63}\) \(-2.37872 q^{65}\) \(+14.0723 q^{67}\) \(+2.74788 q^{69}\) \(+0.961653 q^{71}\) \(-6.57980 q^{73}\) \(-2.82355 q^{75}\) \(+13.2880 q^{77}\) \(-2.76849 q^{79}\) \(+1.00000 q^{81}\) \(+16.8645 q^{83}\) \(-21.8086 q^{85}\) \(+6.57467 q^{87}\) \(+8.20258 q^{89}\) \(+3.88239 q^{91}\) \(-7.06047 q^{93}\) \(-6.42656 q^{95}\) \(-8.44292 q^{97}\) \(-2.91073 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 2.79706 1.25088 0.625442 0.780271i \(-0.284919\pi\)
0.625442 + 0.780271i \(0.284919\pi\)
\(6\) 0 0
\(7\) −4.56518 −1.72547 −0.862737 0.505652i \(-0.831252\pi\)
−0.862737 + 0.505652i \(0.831252\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.91073 −0.877618 −0.438809 0.898580i \(-0.644599\pi\)
−0.438809 + 0.898580i \(0.644599\pi\)
\(12\) 0 0
\(13\) −0.850435 −0.235868 −0.117934 0.993021i \(-0.537627\pi\)
−0.117934 + 0.993021i \(0.537627\pi\)
\(14\) 0 0
\(15\) −2.79706 −0.722198
\(16\) 0 0
\(17\) −7.79699 −1.89105 −0.945523 0.325554i \(-0.894449\pi\)
−0.945523 + 0.325554i \(0.894449\pi\)
\(18\) 0 0
\(19\) −2.29761 −0.527108 −0.263554 0.964645i \(-0.584895\pi\)
−0.263554 + 0.964645i \(0.584895\pi\)
\(20\) 0 0
\(21\) 4.56518 0.996203
\(22\) 0 0
\(23\) −2.74788 −0.572972 −0.286486 0.958084i \(-0.592487\pi\)
−0.286486 + 0.958084i \(0.592487\pi\)
\(24\) 0 0
\(25\) 2.82355 0.564710
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.57467 −1.22088 −0.610442 0.792061i \(-0.709008\pi\)
−0.610442 + 0.792061i \(0.709008\pi\)
\(30\) 0 0
\(31\) 7.06047 1.26810 0.634049 0.773293i \(-0.281392\pi\)
0.634049 + 0.773293i \(0.281392\pi\)
\(32\) 0 0
\(33\) 2.91073 0.506693
\(34\) 0 0
\(35\) −12.7691 −2.15837
\(36\) 0 0
\(37\) 8.35845 1.37412 0.687060 0.726600i \(-0.258901\pi\)
0.687060 + 0.726600i \(0.258901\pi\)
\(38\) 0 0
\(39\) 0.850435 0.136179
\(40\) 0 0
\(41\) 4.96938 0.776087 0.388043 0.921641i \(-0.373151\pi\)
0.388043 + 0.921641i \(0.373151\pi\)
\(42\) 0 0
\(43\) −11.4328 −1.74349 −0.871745 0.489960i \(-0.837011\pi\)
−0.871745 + 0.489960i \(0.837011\pi\)
\(44\) 0 0
\(45\) 2.79706 0.416961
\(46\) 0 0
\(47\) −12.1758 −1.77602 −0.888010 0.459824i \(-0.847912\pi\)
−0.888010 + 0.459824i \(0.847912\pi\)
\(48\) 0 0
\(49\) 13.8408 1.97726
\(50\) 0 0
\(51\) 7.79699 1.09180
\(52\) 0 0
\(53\) −6.03568 −0.829065 −0.414532 0.910035i \(-0.636055\pi\)
−0.414532 + 0.910035i \(0.636055\pi\)
\(54\) 0 0
\(55\) −8.14149 −1.09780
\(56\) 0 0
\(57\) 2.29761 0.304326
\(58\) 0 0
\(59\) 3.64159 0.474094 0.237047 0.971498i \(-0.423820\pi\)
0.237047 + 0.971498i \(0.423820\pi\)
\(60\) 0 0
\(61\) 3.09676 0.396500 0.198250 0.980151i \(-0.436474\pi\)
0.198250 + 0.980151i \(0.436474\pi\)
\(62\) 0 0
\(63\) −4.56518 −0.575158
\(64\) 0 0
\(65\) −2.37872 −0.295044
\(66\) 0 0
\(67\) 14.0723 1.71921 0.859603 0.510963i \(-0.170711\pi\)
0.859603 + 0.510963i \(0.170711\pi\)
\(68\) 0 0
\(69\) 2.74788 0.330806
\(70\) 0 0
\(71\) 0.961653 0.114127 0.0570636 0.998371i \(-0.481826\pi\)
0.0570636 + 0.998371i \(0.481826\pi\)
\(72\) 0 0
\(73\) −6.57980 −0.770108 −0.385054 0.922894i \(-0.625817\pi\)
−0.385054 + 0.922894i \(0.625817\pi\)
\(74\) 0 0
\(75\) −2.82355 −0.326036
\(76\) 0 0
\(77\) 13.2880 1.51431
\(78\) 0 0
\(79\) −2.76849 −0.311479 −0.155740 0.987798i \(-0.549776\pi\)
−0.155740 + 0.987798i \(0.549776\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.8645 1.85112 0.925562 0.378596i \(-0.123593\pi\)
0.925562 + 0.378596i \(0.123593\pi\)
\(84\) 0 0
\(85\) −21.8086 −2.36548
\(86\) 0 0
\(87\) 6.57467 0.704878
\(88\) 0 0
\(89\) 8.20258 0.869472 0.434736 0.900558i \(-0.356842\pi\)
0.434736 + 0.900558i \(0.356842\pi\)
\(90\) 0 0
\(91\) 3.88239 0.406985
\(92\) 0 0
\(93\) −7.06047 −0.732136
\(94\) 0 0
\(95\) −6.42656 −0.659351
\(96\) 0 0
\(97\) −8.44292 −0.857249 −0.428624 0.903483i \(-0.641002\pi\)
−0.428624 + 0.903483i \(0.641002\pi\)
\(98\) 0 0
\(99\) −2.91073 −0.292539
\(100\) 0 0
\(101\) 1.35436 0.134764 0.0673821 0.997727i \(-0.478535\pi\)
0.0673821 + 0.997727i \(0.478535\pi\)
\(102\) 0 0
\(103\) 3.24034 0.319280 0.159640 0.987175i \(-0.448967\pi\)
0.159640 + 0.987175i \(0.448967\pi\)
\(104\) 0 0
\(105\) 12.7691 1.24613
\(106\) 0 0
\(107\) 12.4272 1.20138 0.600690 0.799482i \(-0.294893\pi\)
0.600690 + 0.799482i \(0.294893\pi\)
\(108\) 0 0
\(109\) 19.9444 1.91033 0.955163 0.296082i \(-0.0956800\pi\)
0.955163 + 0.296082i \(0.0956800\pi\)
\(110\) 0 0
\(111\) −8.35845 −0.793349
\(112\) 0 0
\(113\) 5.83295 0.548718 0.274359 0.961627i \(-0.411534\pi\)
0.274359 + 0.961627i \(0.411534\pi\)
\(114\) 0 0
\(115\) −7.68598 −0.716722
\(116\) 0 0
\(117\) −0.850435 −0.0786228
\(118\) 0 0
\(119\) 35.5946 3.26295
\(120\) 0 0
\(121\) −2.52766 −0.229787
\(122\) 0 0
\(123\) −4.96938 −0.448074
\(124\) 0 0
\(125\) −6.08766 −0.544497
\(126\) 0 0
\(127\) −1.57092 −0.139397 −0.0696984 0.997568i \(-0.522204\pi\)
−0.0696984 + 0.997568i \(0.522204\pi\)
\(128\) 0 0
\(129\) 11.4328 1.00660
\(130\) 0 0
\(131\) −1.67110 −0.146005 −0.0730025 0.997332i \(-0.523258\pi\)
−0.0730025 + 0.997332i \(0.523258\pi\)
\(132\) 0 0
\(133\) 10.4890 0.909511
\(134\) 0 0
\(135\) −2.79706 −0.240733
\(136\) 0 0
\(137\) 10.0249 0.856481 0.428240 0.903665i \(-0.359134\pi\)
0.428240 + 0.903665i \(0.359134\pi\)
\(138\) 0 0
\(139\) 12.6598 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(140\) 0 0
\(141\) 12.1758 1.02539
\(142\) 0 0
\(143\) 2.47539 0.207002
\(144\) 0 0
\(145\) −18.3897 −1.52719
\(146\) 0 0
\(147\) −13.8408 −1.14157
\(148\) 0 0
\(149\) −19.1913 −1.57221 −0.786107 0.618090i \(-0.787907\pi\)
−0.786107 + 0.618090i \(0.787907\pi\)
\(150\) 0 0
\(151\) −13.2906 −1.08157 −0.540786 0.841160i \(-0.681873\pi\)
−0.540786 + 0.841160i \(0.681873\pi\)
\(152\) 0 0
\(153\) −7.79699 −0.630349
\(154\) 0 0
\(155\) 19.7486 1.58624
\(156\) 0 0
\(157\) −0.624256 −0.0498211 −0.0249105 0.999690i \(-0.507930\pi\)
−0.0249105 + 0.999690i \(0.507930\pi\)
\(158\) 0 0
\(159\) 6.03568 0.478661
\(160\) 0 0
\(161\) 12.5445 0.988649
\(162\) 0 0
\(163\) −6.71759 −0.526163 −0.263081 0.964774i \(-0.584739\pi\)
−0.263081 + 0.964774i \(0.584739\pi\)
\(164\) 0 0
\(165\) 8.14149 0.633814
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.2768 −0.944366
\(170\) 0 0
\(171\) −2.29761 −0.175703
\(172\) 0 0
\(173\) 21.4371 1.62983 0.814917 0.579578i \(-0.196783\pi\)
0.814917 + 0.579578i \(0.196783\pi\)
\(174\) 0 0
\(175\) −12.8900 −0.974394
\(176\) 0 0
\(177\) −3.64159 −0.273718
\(178\) 0 0
\(179\) 0.637299 0.0476340 0.0238170 0.999716i \(-0.492418\pi\)
0.0238170 + 0.999716i \(0.492418\pi\)
\(180\) 0 0
\(181\) −14.5472 −1.08128 −0.540642 0.841253i \(-0.681819\pi\)
−0.540642 + 0.841253i \(0.681819\pi\)
\(182\) 0 0
\(183\) −3.09676 −0.228919
\(184\) 0 0
\(185\) 23.3791 1.71887
\(186\) 0 0
\(187\) 22.6949 1.65962
\(188\) 0 0
\(189\) 4.56518 0.332068
\(190\) 0 0
\(191\) 20.3497 1.47245 0.736225 0.676737i \(-0.236606\pi\)
0.736225 + 0.676737i \(0.236606\pi\)
\(192\) 0 0
\(193\) 10.0666 0.724612 0.362306 0.932059i \(-0.381990\pi\)
0.362306 + 0.932059i \(0.381990\pi\)
\(194\) 0 0
\(195\) 2.37872 0.170344
\(196\) 0 0
\(197\) −1.11488 −0.0794322 −0.0397161 0.999211i \(-0.512645\pi\)
−0.0397161 + 0.999211i \(0.512645\pi\)
\(198\) 0 0
\(199\) −3.21029 −0.227572 −0.113786 0.993505i \(-0.536298\pi\)
−0.113786 + 0.993505i \(0.536298\pi\)
\(200\) 0 0
\(201\) −14.0723 −0.992584
\(202\) 0 0
\(203\) 30.0145 2.10661
\(204\) 0 0
\(205\) 13.8997 0.970794
\(206\) 0 0
\(207\) −2.74788 −0.190991
\(208\) 0 0
\(209\) 6.68772 0.462599
\(210\) 0 0
\(211\) 24.1441 1.66215 0.831073 0.556164i \(-0.187727\pi\)
0.831073 + 0.556164i \(0.187727\pi\)
\(212\) 0 0
\(213\) −0.961653 −0.0658913
\(214\) 0 0
\(215\) −31.9783 −2.18090
\(216\) 0 0
\(217\) −32.2323 −2.18807
\(218\) 0 0
\(219\) 6.57980 0.444622
\(220\) 0 0
\(221\) 6.63083 0.446038
\(222\) 0 0
\(223\) 16.4018 1.09835 0.549174 0.835708i \(-0.314942\pi\)
0.549174 + 0.835708i \(0.314942\pi\)
\(224\) 0 0
\(225\) 2.82355 0.188237
\(226\) 0 0
\(227\) −18.8181 −1.24900 −0.624500 0.781025i \(-0.714697\pi\)
−0.624500 + 0.781025i \(0.714697\pi\)
\(228\) 0 0
\(229\) 12.7703 0.843885 0.421943 0.906623i \(-0.361348\pi\)
0.421943 + 0.906623i \(0.361348\pi\)
\(230\) 0 0
\(231\) −13.2880 −0.874286
\(232\) 0 0
\(233\) −18.2136 −1.19321 −0.596606 0.802534i \(-0.703485\pi\)
−0.596606 + 0.802534i \(0.703485\pi\)
\(234\) 0 0
\(235\) −34.0564 −2.22159
\(236\) 0 0
\(237\) 2.76849 0.179833
\(238\) 0 0
\(239\) 2.53425 0.163927 0.0819637 0.996635i \(-0.473881\pi\)
0.0819637 + 0.996635i \(0.473881\pi\)
\(240\) 0 0
\(241\) 10.9201 0.703426 0.351713 0.936108i \(-0.385599\pi\)
0.351713 + 0.936108i \(0.385599\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 38.7137 2.47333
\(246\) 0 0
\(247\) 1.95397 0.124328
\(248\) 0 0
\(249\) −16.8645 −1.06875
\(250\) 0 0
\(251\) −7.08878 −0.447440 −0.223720 0.974653i \(-0.571820\pi\)
−0.223720 + 0.974653i \(0.571820\pi\)
\(252\) 0 0
\(253\) 7.99833 0.502851
\(254\) 0 0
\(255\) 21.8086 1.36571
\(256\) 0 0
\(257\) −23.0298 −1.43656 −0.718280 0.695754i \(-0.755070\pi\)
−0.718280 + 0.695754i \(0.755070\pi\)
\(258\) 0 0
\(259\) −38.1578 −2.37101
\(260\) 0 0
\(261\) −6.57467 −0.406962
\(262\) 0 0
\(263\) −12.6362 −0.779181 −0.389591 0.920988i \(-0.627383\pi\)
−0.389591 + 0.920988i \(0.627383\pi\)
\(264\) 0 0
\(265\) −16.8822 −1.03706
\(266\) 0 0
\(267\) −8.20258 −0.501990
\(268\) 0 0
\(269\) 29.8615 1.82069 0.910343 0.413854i \(-0.135818\pi\)
0.910343 + 0.413854i \(0.135818\pi\)
\(270\) 0 0
\(271\) −6.38067 −0.387598 −0.193799 0.981041i \(-0.562081\pi\)
−0.193799 + 0.981041i \(0.562081\pi\)
\(272\) 0 0
\(273\) −3.88239 −0.234973
\(274\) 0 0
\(275\) −8.21859 −0.495600
\(276\) 0 0
\(277\) 23.5063 1.41235 0.706177 0.708035i \(-0.250418\pi\)
0.706177 + 0.708035i \(0.250418\pi\)
\(278\) 0 0
\(279\) 7.06047 0.422699
\(280\) 0 0
\(281\) −23.4338 −1.39794 −0.698972 0.715149i \(-0.746359\pi\)
−0.698972 + 0.715149i \(0.746359\pi\)
\(282\) 0 0
\(283\) −17.6525 −1.04933 −0.524666 0.851308i \(-0.675810\pi\)
−0.524666 + 0.851308i \(0.675810\pi\)
\(284\) 0 0
\(285\) 6.42656 0.380676
\(286\) 0 0
\(287\) −22.6861 −1.33912
\(288\) 0 0
\(289\) 43.7930 2.57606
\(290\) 0 0
\(291\) 8.44292 0.494933
\(292\) 0 0
\(293\) −28.9734 −1.69265 −0.846323 0.532671i \(-0.821188\pi\)
−0.846323 + 0.532671i \(0.821188\pi\)
\(294\) 0 0
\(295\) 10.1857 0.593037
\(296\) 0 0
\(297\) 2.91073 0.168898
\(298\) 0 0
\(299\) 2.33689 0.135146
\(300\) 0 0
\(301\) 52.1929 3.00835
\(302\) 0 0
\(303\) −1.35436 −0.0778062
\(304\) 0 0
\(305\) 8.66184 0.495975
\(306\) 0 0
\(307\) −26.5494 −1.51525 −0.757627 0.652688i \(-0.773641\pi\)
−0.757627 + 0.652688i \(0.773641\pi\)
\(308\) 0 0
\(309\) −3.24034 −0.184336
\(310\) 0 0
\(311\) 6.57114 0.372615 0.186308 0.982491i \(-0.440348\pi\)
0.186308 + 0.982491i \(0.440348\pi\)
\(312\) 0 0
\(313\) 1.39897 0.0790747 0.0395374 0.999218i \(-0.487412\pi\)
0.0395374 + 0.999218i \(0.487412\pi\)
\(314\) 0 0
\(315\) −12.7691 −0.719456
\(316\) 0 0
\(317\) −32.0982 −1.80282 −0.901408 0.432971i \(-0.857465\pi\)
−0.901408 + 0.432971i \(0.857465\pi\)
\(318\) 0 0
\(319\) 19.1371 1.07147
\(320\) 0 0
\(321\) −12.4272 −0.693617
\(322\) 0 0
\(323\) 17.9144 0.996786
\(324\) 0 0
\(325\) −2.40125 −0.133197
\(326\) 0 0
\(327\) −19.9444 −1.10293
\(328\) 0 0
\(329\) 55.5846 3.06448
\(330\) 0 0
\(331\) 30.4241 1.67226 0.836130 0.548532i \(-0.184813\pi\)
0.836130 + 0.548532i \(0.184813\pi\)
\(332\) 0 0
\(333\) 8.35845 0.458040
\(334\) 0 0
\(335\) 39.3611 2.15053
\(336\) 0 0
\(337\) 9.18567 0.500375 0.250188 0.968197i \(-0.419508\pi\)
0.250188 + 0.968197i \(0.419508\pi\)
\(338\) 0 0
\(339\) −5.83295 −0.316802
\(340\) 0 0
\(341\) −20.5511 −1.11290
\(342\) 0 0
\(343\) −31.2296 −1.68624
\(344\) 0 0
\(345\) 7.68598 0.413799
\(346\) 0 0
\(347\) 21.2584 1.14121 0.570604 0.821225i \(-0.306709\pi\)
0.570604 + 0.821225i \(0.306709\pi\)
\(348\) 0 0
\(349\) −5.23246 −0.280087 −0.140044 0.990145i \(-0.544724\pi\)
−0.140044 + 0.990145i \(0.544724\pi\)
\(350\) 0 0
\(351\) 0.850435 0.0453929
\(352\) 0 0
\(353\) −24.0428 −1.27967 −0.639834 0.768513i \(-0.720997\pi\)
−0.639834 + 0.768513i \(0.720997\pi\)
\(354\) 0 0
\(355\) 2.68980 0.142760
\(356\) 0 0
\(357\) −35.5946 −1.88387
\(358\) 0 0
\(359\) 5.99756 0.316539 0.158270 0.987396i \(-0.449409\pi\)
0.158270 + 0.987396i \(0.449409\pi\)
\(360\) 0 0
\(361\) −13.7210 −0.722157
\(362\) 0 0
\(363\) 2.52766 0.132668
\(364\) 0 0
\(365\) −18.4041 −0.963315
\(366\) 0 0
\(367\) 12.5632 0.655793 0.327896 0.944714i \(-0.393660\pi\)
0.327896 + 0.944714i \(0.393660\pi\)
\(368\) 0 0
\(369\) 4.96938 0.258696
\(370\) 0 0
\(371\) 27.5540 1.43053
\(372\) 0 0
\(373\) −0.156554 −0.00810604 −0.00405302 0.999992i \(-0.501290\pi\)
−0.00405302 + 0.999992i \(0.501290\pi\)
\(374\) 0 0
\(375\) 6.08766 0.314365
\(376\) 0 0
\(377\) 5.59133 0.287968
\(378\) 0 0
\(379\) −16.2254 −0.833444 −0.416722 0.909034i \(-0.636821\pi\)
−0.416722 + 0.909034i \(0.636821\pi\)
\(380\) 0 0
\(381\) 1.57092 0.0804808
\(382\) 0 0
\(383\) −12.9406 −0.661232 −0.330616 0.943765i \(-0.607257\pi\)
−0.330616 + 0.943765i \(0.607257\pi\)
\(384\) 0 0
\(385\) 37.1673 1.89422
\(386\) 0 0
\(387\) −11.4328 −0.581163
\(388\) 0 0
\(389\) 17.2828 0.876271 0.438136 0.898909i \(-0.355639\pi\)
0.438136 + 0.898909i \(0.355639\pi\)
\(390\) 0 0
\(391\) 21.4252 1.08352
\(392\) 0 0
\(393\) 1.67110 0.0842960
\(394\) 0 0
\(395\) −7.74363 −0.389624
\(396\) 0 0
\(397\) −12.2136 −0.612982 −0.306491 0.951873i \(-0.599155\pi\)
−0.306491 + 0.951873i \(0.599155\pi\)
\(398\) 0 0
\(399\) −10.4890 −0.525107
\(400\) 0 0
\(401\) 26.2780 1.31226 0.656129 0.754648i \(-0.272193\pi\)
0.656129 + 0.754648i \(0.272193\pi\)
\(402\) 0 0
\(403\) −6.00447 −0.299104
\(404\) 0 0
\(405\) 2.79706 0.138987
\(406\) 0 0
\(407\) −24.3292 −1.20595
\(408\) 0 0
\(409\) −3.32947 −0.164632 −0.0823159 0.996606i \(-0.526232\pi\)
−0.0823159 + 0.996606i \(0.526232\pi\)
\(410\) 0 0
\(411\) −10.0249 −0.494489
\(412\) 0 0
\(413\) −16.6245 −0.818038
\(414\) 0 0
\(415\) 47.1712 2.31554
\(416\) 0 0
\(417\) −12.6598 −0.619953
\(418\) 0 0
\(419\) −10.6768 −0.521594 −0.260797 0.965394i \(-0.583985\pi\)
−0.260797 + 0.965394i \(0.583985\pi\)
\(420\) 0 0
\(421\) −36.4760 −1.77773 −0.888866 0.458167i \(-0.848506\pi\)
−0.888866 + 0.458167i \(0.848506\pi\)
\(422\) 0 0
\(423\) −12.1758 −0.592007
\(424\) 0 0
\(425\) −22.0152 −1.06789
\(426\) 0 0
\(427\) −14.1373 −0.684151
\(428\) 0 0
\(429\) −2.47539 −0.119513
\(430\) 0 0
\(431\) 23.0164 1.10866 0.554330 0.832297i \(-0.312975\pi\)
0.554330 + 0.832297i \(0.312975\pi\)
\(432\) 0 0
\(433\) 24.8633 1.19486 0.597428 0.801923i \(-0.296190\pi\)
0.597428 + 0.801923i \(0.296190\pi\)
\(434\) 0 0
\(435\) 18.3897 0.881721
\(436\) 0 0
\(437\) 6.31355 0.302018
\(438\) 0 0
\(439\) −6.84142 −0.326523 −0.163262 0.986583i \(-0.552201\pi\)
−0.163262 + 0.986583i \(0.552201\pi\)
\(440\) 0 0
\(441\) 13.8408 0.659087
\(442\) 0 0
\(443\) 22.9161 1.08878 0.544389 0.838833i \(-0.316762\pi\)
0.544389 + 0.838833i \(0.316762\pi\)
\(444\) 0 0
\(445\) 22.9431 1.08761
\(446\) 0 0
\(447\) 19.1913 0.907719
\(448\) 0 0
\(449\) −2.55643 −0.120645 −0.0603226 0.998179i \(-0.519213\pi\)
−0.0603226 + 0.998179i \(0.519213\pi\)
\(450\) 0 0
\(451\) −14.4645 −0.681107
\(452\) 0 0
\(453\) 13.2906 0.624446
\(454\) 0 0
\(455\) 10.8593 0.509091
\(456\) 0 0
\(457\) 18.3051 0.856277 0.428139 0.903713i \(-0.359170\pi\)
0.428139 + 0.903713i \(0.359170\pi\)
\(458\) 0 0
\(459\) 7.79699 0.363932
\(460\) 0 0
\(461\) 15.9794 0.744236 0.372118 0.928185i \(-0.378632\pi\)
0.372118 + 0.928185i \(0.378632\pi\)
\(462\) 0 0
\(463\) 40.0301 1.86036 0.930178 0.367108i \(-0.119652\pi\)
0.930178 + 0.367108i \(0.119652\pi\)
\(464\) 0 0
\(465\) −19.7486 −0.915817
\(466\) 0 0
\(467\) −19.8776 −0.919825 −0.459913 0.887964i \(-0.652119\pi\)
−0.459913 + 0.887964i \(0.652119\pi\)
\(468\) 0 0
\(469\) −64.2426 −2.96645
\(470\) 0 0
\(471\) 0.624256 0.0287642
\(472\) 0 0
\(473\) 33.2779 1.53012
\(474\) 0 0
\(475\) −6.48742 −0.297663
\(476\) 0 0
\(477\) −6.03568 −0.276355
\(478\) 0 0
\(479\) 21.8981 1.00055 0.500274 0.865867i \(-0.333233\pi\)
0.500274 + 0.865867i \(0.333233\pi\)
\(480\) 0 0
\(481\) −7.10832 −0.324112
\(482\) 0 0
\(483\) −12.5445 −0.570797
\(484\) 0 0
\(485\) −23.6154 −1.07232
\(486\) 0 0
\(487\) −31.4280 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(488\) 0 0
\(489\) 6.71759 0.303780
\(490\) 0 0
\(491\) −26.9355 −1.21558 −0.607792 0.794097i \(-0.707944\pi\)
−0.607792 + 0.794097i \(0.707944\pi\)
\(492\) 0 0
\(493\) 51.2626 2.30875
\(494\) 0 0
\(495\) −8.14149 −0.365933
\(496\) 0 0
\(497\) −4.39011 −0.196924
\(498\) 0 0
\(499\) 24.9321 1.11611 0.558057 0.829802i \(-0.311547\pi\)
0.558057 + 0.829802i \(0.311547\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 23.9427 1.06755 0.533776 0.845626i \(-0.320773\pi\)
0.533776 + 0.845626i \(0.320773\pi\)
\(504\) 0 0
\(505\) 3.78824 0.168574
\(506\) 0 0
\(507\) 12.2768 0.545230
\(508\) 0 0
\(509\) −11.2763 −0.499813 −0.249906 0.968270i \(-0.580400\pi\)
−0.249906 + 0.968270i \(0.580400\pi\)
\(510\) 0 0
\(511\) 30.0380 1.32880
\(512\) 0 0
\(513\) 2.29761 0.101442
\(514\) 0 0
\(515\) 9.06343 0.399382
\(516\) 0 0
\(517\) 35.4404 1.55867
\(518\) 0 0
\(519\) −21.4371 −0.940985
\(520\) 0 0
\(521\) 18.3218 0.802693 0.401347 0.915926i \(-0.368542\pi\)
0.401347 + 0.915926i \(0.368542\pi\)
\(522\) 0 0
\(523\) −32.2678 −1.41097 −0.705487 0.708723i \(-0.749272\pi\)
−0.705487 + 0.708723i \(0.749272\pi\)
\(524\) 0 0
\(525\) 12.8900 0.562566
\(526\) 0 0
\(527\) −55.0504 −2.39803
\(528\) 0 0
\(529\) −15.4492 −0.671703
\(530\) 0 0
\(531\) 3.64159 0.158031
\(532\) 0 0
\(533\) −4.22614 −0.183054
\(534\) 0 0
\(535\) 34.7596 1.50279
\(536\) 0 0
\(537\) −0.637299 −0.0275015
\(538\) 0 0
\(539\) −40.2869 −1.73528
\(540\) 0 0
\(541\) 36.6203 1.57443 0.787215 0.616678i \(-0.211522\pi\)
0.787215 + 0.616678i \(0.211522\pi\)
\(542\) 0 0
\(543\) 14.5472 0.624280
\(544\) 0 0
\(545\) 55.7857 2.38960
\(546\) 0 0
\(547\) −29.7390 −1.27155 −0.635774 0.771875i \(-0.719319\pi\)
−0.635774 + 0.771875i \(0.719319\pi\)
\(548\) 0 0
\(549\) 3.09676 0.132167
\(550\) 0 0
\(551\) 15.1060 0.643538
\(552\) 0 0
\(553\) 12.6386 0.537450
\(554\) 0 0
\(555\) −23.3791 −0.992387
\(556\) 0 0
\(557\) −21.1579 −0.896490 −0.448245 0.893911i \(-0.647951\pi\)
−0.448245 + 0.893911i \(0.647951\pi\)
\(558\) 0 0
\(559\) 9.72288 0.411234
\(560\) 0 0
\(561\) −22.6949 −0.958180
\(562\) 0 0
\(563\) 35.7313 1.50589 0.752946 0.658082i \(-0.228632\pi\)
0.752946 + 0.658082i \(0.228632\pi\)
\(564\) 0 0
\(565\) 16.3151 0.686382
\(566\) 0 0
\(567\) −4.56518 −0.191719
\(568\) 0 0
\(569\) −12.2786 −0.514745 −0.257373 0.966312i \(-0.582857\pi\)
−0.257373 + 0.966312i \(0.582857\pi\)
\(570\) 0 0
\(571\) 13.8771 0.580740 0.290370 0.956914i \(-0.406222\pi\)
0.290370 + 0.956914i \(0.406222\pi\)
\(572\) 0 0
\(573\) −20.3497 −0.850120
\(574\) 0 0
\(575\) −7.75878 −0.323563
\(576\) 0 0
\(577\) 26.7746 1.11464 0.557321 0.830297i \(-0.311829\pi\)
0.557321 + 0.830297i \(0.311829\pi\)
\(578\) 0 0
\(579\) −10.0666 −0.418355
\(580\) 0 0
\(581\) −76.9896 −3.19407
\(582\) 0 0
\(583\) 17.5682 0.727602
\(584\) 0 0
\(585\) −2.37872 −0.0983480
\(586\) 0 0
\(587\) −0.941202 −0.0388476 −0.0194238 0.999811i \(-0.506183\pi\)
−0.0194238 + 0.999811i \(0.506183\pi\)
\(588\) 0 0
\(589\) −16.2222 −0.668424
\(590\) 0 0
\(591\) 1.11488 0.0458602
\(592\) 0 0
\(593\) 35.9662 1.47695 0.738477 0.674279i \(-0.235545\pi\)
0.738477 + 0.674279i \(0.235545\pi\)
\(594\) 0 0
\(595\) 99.5603 4.08158
\(596\) 0 0
\(597\) 3.21029 0.131388
\(598\) 0 0
\(599\) 26.9543 1.10132 0.550662 0.834728i \(-0.314375\pi\)
0.550662 + 0.834728i \(0.314375\pi\)
\(600\) 0 0
\(601\) 37.3201 1.52232 0.761159 0.648566i \(-0.224631\pi\)
0.761159 + 0.648566i \(0.224631\pi\)
\(602\) 0 0
\(603\) 14.0723 0.573069
\(604\) 0 0
\(605\) −7.07002 −0.287437
\(606\) 0 0
\(607\) −4.98231 −0.202226 −0.101113 0.994875i \(-0.532240\pi\)
−0.101113 + 0.994875i \(0.532240\pi\)
\(608\) 0 0
\(609\) −30.0145 −1.21625
\(610\) 0 0
\(611\) 10.3547 0.418907
\(612\) 0 0
\(613\) 17.9611 0.725441 0.362720 0.931898i \(-0.381848\pi\)
0.362720 + 0.931898i \(0.381848\pi\)
\(614\) 0 0
\(615\) −13.8997 −0.560488
\(616\) 0 0
\(617\) 14.8834 0.599184 0.299592 0.954067i \(-0.403149\pi\)
0.299592 + 0.954067i \(0.403149\pi\)
\(618\) 0 0
\(619\) −19.4829 −0.783086 −0.391543 0.920160i \(-0.628059\pi\)
−0.391543 + 0.920160i \(0.628059\pi\)
\(620\) 0 0
\(621\) 2.74788 0.110269
\(622\) 0 0
\(623\) −37.4462 −1.50025
\(624\) 0 0
\(625\) −31.1453 −1.24581
\(626\) 0 0
\(627\) −6.68772 −0.267082
\(628\) 0 0
\(629\) −65.1707 −2.59853
\(630\) 0 0
\(631\) −16.1689 −0.643674 −0.321837 0.946795i \(-0.604300\pi\)
−0.321837 + 0.946795i \(0.604300\pi\)
\(632\) 0 0
\(633\) −24.1441 −0.959640
\(634\) 0 0
\(635\) −4.39397 −0.174369
\(636\) 0 0
\(637\) −11.7707 −0.466374
\(638\) 0 0
\(639\) 0.961653 0.0380424
\(640\) 0 0
\(641\) −34.4316 −1.35997 −0.679984 0.733227i \(-0.738013\pi\)
−0.679984 + 0.733227i \(0.738013\pi\)
\(642\) 0 0
\(643\) 22.4242 0.884325 0.442163 0.896935i \(-0.354211\pi\)
0.442163 + 0.896935i \(0.354211\pi\)
\(644\) 0 0
\(645\) 31.9783 1.25915
\(646\) 0 0
\(647\) 6.63740 0.260943 0.130472 0.991452i \(-0.458351\pi\)
0.130472 + 0.991452i \(0.458351\pi\)
\(648\) 0 0
\(649\) −10.5997 −0.416074
\(650\) 0 0
\(651\) 32.2323 1.26328
\(652\) 0 0
\(653\) −29.1259 −1.13978 −0.569892 0.821720i \(-0.693015\pi\)
−0.569892 + 0.821720i \(0.693015\pi\)
\(654\) 0 0
\(655\) −4.67418 −0.182635
\(656\) 0 0
\(657\) −6.57980 −0.256703
\(658\) 0 0
\(659\) −25.0489 −0.975766 −0.487883 0.872909i \(-0.662231\pi\)
−0.487883 + 0.872909i \(0.662231\pi\)
\(660\) 0 0
\(661\) 19.1690 0.745589 0.372795 0.927914i \(-0.378400\pi\)
0.372795 + 0.927914i \(0.378400\pi\)
\(662\) 0 0
\(663\) −6.63083 −0.257520
\(664\) 0 0
\(665\) 29.3384 1.13769
\(666\) 0 0
\(667\) 18.0664 0.699533
\(668\) 0 0
\(669\) −16.4018 −0.634132
\(670\) 0 0
\(671\) −9.01384 −0.347975
\(672\) 0 0
\(673\) −28.4432 −1.09640 −0.548202 0.836346i \(-0.684687\pi\)
−0.548202 + 0.836346i \(0.684687\pi\)
\(674\) 0 0
\(675\) −2.82355 −0.108679
\(676\) 0 0
\(677\) −21.9968 −0.845405 −0.422703 0.906268i \(-0.638919\pi\)
−0.422703 + 0.906268i \(0.638919\pi\)
\(678\) 0 0
\(679\) 38.5434 1.47916
\(680\) 0 0
\(681\) 18.8181 0.721111
\(682\) 0 0
\(683\) 29.0973 1.11338 0.556689 0.830721i \(-0.312071\pi\)
0.556689 + 0.830721i \(0.312071\pi\)
\(684\) 0 0
\(685\) 28.0401 1.07136
\(686\) 0 0
\(687\) −12.7703 −0.487217
\(688\) 0 0
\(689\) 5.13296 0.195550
\(690\) 0 0
\(691\) −23.5824 −0.897118 −0.448559 0.893753i \(-0.648063\pi\)
−0.448559 + 0.893753i \(0.648063\pi\)
\(692\) 0 0
\(693\) 13.2880 0.504769
\(694\) 0 0
\(695\) 35.4102 1.34319
\(696\) 0 0
\(697\) −38.7462 −1.46762
\(698\) 0 0
\(699\) 18.2136 0.688902
\(700\) 0 0
\(701\) 23.2444 0.877928 0.438964 0.898505i \(-0.355346\pi\)
0.438964 + 0.898505i \(0.355346\pi\)
\(702\) 0 0
\(703\) −19.2045 −0.724310
\(704\) 0 0
\(705\) 34.0564 1.28264
\(706\) 0 0
\(707\) −6.18291 −0.232532
\(708\) 0 0
\(709\) −18.7991 −0.706016 −0.353008 0.935620i \(-0.614841\pi\)
−0.353008 + 0.935620i \(0.614841\pi\)
\(710\) 0 0
\(711\) −2.76849 −0.103826
\(712\) 0 0
\(713\) −19.4013 −0.726584
\(714\) 0 0
\(715\) 6.92381 0.258936
\(716\) 0 0
\(717\) −2.53425 −0.0946435
\(718\) 0 0
\(719\) 25.0101 0.932721 0.466360 0.884595i \(-0.345565\pi\)
0.466360 + 0.884595i \(0.345565\pi\)
\(720\) 0 0
\(721\) −14.7927 −0.550910
\(722\) 0 0
\(723\) −10.9201 −0.406123
\(724\) 0 0
\(725\) −18.5639 −0.689446
\(726\) 0 0
\(727\) 35.1165 1.30240 0.651199 0.758907i \(-0.274266\pi\)
0.651199 + 0.758907i \(0.274266\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 89.1416 3.29702
\(732\) 0 0
\(733\) 31.3756 1.15889 0.579443 0.815013i \(-0.303270\pi\)
0.579443 + 0.815013i \(0.303270\pi\)
\(734\) 0 0
\(735\) −38.7137 −1.42798
\(736\) 0 0
\(737\) −40.9607 −1.50881
\(738\) 0 0
\(739\) −17.6202 −0.648169 −0.324085 0.946028i \(-0.605056\pi\)
−0.324085 + 0.946028i \(0.605056\pi\)
\(740\) 0 0
\(741\) −1.95397 −0.0717808
\(742\) 0 0
\(743\) 42.3274 1.55284 0.776421 0.630214i \(-0.217033\pi\)
0.776421 + 0.630214i \(0.217033\pi\)
\(744\) 0 0
\(745\) −53.6793 −1.96666
\(746\) 0 0
\(747\) 16.8645 0.617041
\(748\) 0 0
\(749\) −56.7323 −2.07295
\(750\) 0 0
\(751\) 9.22171 0.336505 0.168253 0.985744i \(-0.446188\pi\)
0.168253 + 0.985744i \(0.446188\pi\)
\(752\) 0 0
\(753\) 7.08878 0.258329
\(754\) 0 0
\(755\) −37.1746 −1.35292
\(756\) 0 0
\(757\) 38.8185 1.41088 0.705441 0.708769i \(-0.250749\pi\)
0.705441 + 0.708769i \(0.250749\pi\)
\(758\) 0 0
\(759\) −7.99833 −0.290321
\(760\) 0 0
\(761\) −11.9586 −0.433498 −0.216749 0.976227i \(-0.569545\pi\)
−0.216749 + 0.976227i \(0.569545\pi\)
\(762\) 0 0
\(763\) −91.0496 −3.29622
\(764\) 0 0
\(765\) −21.8086 −0.788493
\(766\) 0 0
\(767\) −3.09693 −0.111824
\(768\) 0 0
\(769\) 33.8376 1.22021 0.610107 0.792319i \(-0.291127\pi\)
0.610107 + 0.792319i \(0.291127\pi\)
\(770\) 0 0
\(771\) 23.0298 0.829399
\(772\) 0 0
\(773\) 18.8998 0.679778 0.339889 0.940466i \(-0.389610\pi\)
0.339889 + 0.940466i \(0.389610\pi\)
\(774\) 0 0
\(775\) 19.9356 0.716108
\(776\) 0 0
\(777\) 38.1578 1.36890
\(778\) 0 0
\(779\) −11.4177 −0.409081
\(780\) 0 0
\(781\) −2.79911 −0.100160
\(782\) 0 0
\(783\) 6.57467 0.234959
\(784\) 0 0
\(785\) −1.74608 −0.0623204
\(786\) 0 0
\(787\) −5.91461 −0.210833 −0.105416 0.994428i \(-0.533618\pi\)
−0.105416 + 0.994428i \(0.533618\pi\)
\(788\) 0 0
\(789\) 12.6362 0.449860
\(790\) 0 0
\(791\) −26.6285 −0.946799
\(792\) 0 0
\(793\) −2.63360 −0.0935218
\(794\) 0 0
\(795\) 16.8822 0.598749
\(796\) 0 0
\(797\) 9.51329 0.336978 0.168489 0.985704i \(-0.446111\pi\)
0.168489 + 0.985704i \(0.446111\pi\)
\(798\) 0 0
\(799\) 94.9344 3.35854
\(800\) 0 0
\(801\) 8.20258 0.289824
\(802\) 0 0
\(803\) 19.1520 0.675860
\(804\) 0 0
\(805\) 35.0879 1.23668
\(806\) 0 0
\(807\) −29.8615 −1.05117
\(808\) 0 0
\(809\) −10.7944 −0.379510 −0.189755 0.981831i \(-0.560769\pi\)
−0.189755 + 0.981831i \(0.560769\pi\)
\(810\) 0 0
\(811\) −7.89452 −0.277214 −0.138607 0.990347i \(-0.544262\pi\)
−0.138607 + 0.990347i \(0.544262\pi\)
\(812\) 0 0
\(813\) 6.38067 0.223780
\(814\) 0 0
\(815\) −18.7895 −0.658168
\(816\) 0 0
\(817\) 26.2682 0.919007
\(818\) 0 0
\(819\) 3.88239 0.135662
\(820\) 0 0
\(821\) 8.60687 0.300382 0.150191 0.988657i \(-0.452011\pi\)
0.150191 + 0.988657i \(0.452011\pi\)
\(822\) 0 0
\(823\) −1.40078 −0.0488280 −0.0244140 0.999702i \(-0.507772\pi\)
−0.0244140 + 0.999702i \(0.507772\pi\)
\(824\) 0 0
\(825\) 8.21859 0.286135
\(826\) 0 0
\(827\) 16.7472 0.582358 0.291179 0.956669i \(-0.405952\pi\)
0.291179 + 0.956669i \(0.405952\pi\)
\(828\) 0 0
\(829\) −15.6416 −0.543256 −0.271628 0.962402i \(-0.587562\pi\)
−0.271628 + 0.962402i \(0.587562\pi\)
\(830\) 0 0
\(831\) −23.5063 −0.815423
\(832\) 0 0
\(833\) −107.917 −3.73910
\(834\) 0 0
\(835\) 2.79706 0.0967963
\(836\) 0 0
\(837\) −7.06047 −0.244045
\(838\) 0 0
\(839\) −34.9539 −1.20674 −0.603371 0.797461i \(-0.706176\pi\)
−0.603371 + 0.797461i \(0.706176\pi\)
\(840\) 0 0
\(841\) 14.2262 0.490560
\(842\) 0 0
\(843\) 23.4338 0.807103
\(844\) 0 0
\(845\) −34.3389 −1.18129
\(846\) 0 0
\(847\) 11.5392 0.396492
\(848\) 0 0
\(849\) 17.6525 0.605832
\(850\) 0 0
\(851\) −22.9680 −0.787333
\(852\) 0 0
\(853\) 6.43085 0.220188 0.110094 0.993921i \(-0.464885\pi\)
0.110094 + 0.993921i \(0.464885\pi\)
\(854\) 0 0
\(855\) −6.42656 −0.219784
\(856\) 0 0
\(857\) −13.2815 −0.453686 −0.226843 0.973931i \(-0.572840\pi\)
−0.226843 + 0.973931i \(0.572840\pi\)
\(858\) 0 0
\(859\) −29.8157 −1.01730 −0.508650 0.860974i \(-0.669855\pi\)
−0.508650 + 0.860974i \(0.669855\pi\)
\(860\) 0 0
\(861\) 22.6861 0.773140
\(862\) 0 0
\(863\) −17.5960 −0.598974 −0.299487 0.954100i \(-0.596816\pi\)
−0.299487 + 0.954100i \(0.596816\pi\)
\(864\) 0 0
\(865\) 59.9609 2.03873
\(866\) 0 0
\(867\) −43.7930 −1.48729
\(868\) 0 0
\(869\) 8.05832 0.273360
\(870\) 0 0
\(871\) −11.9676 −0.405506
\(872\) 0 0
\(873\) −8.44292 −0.285750
\(874\) 0 0
\(875\) 27.7912 0.939515
\(876\) 0 0
\(877\) −27.3636 −0.924003 −0.462001 0.886879i \(-0.652868\pi\)
−0.462001 + 0.886879i \(0.652868\pi\)
\(878\) 0 0
\(879\) 28.9734 0.977249
\(880\) 0 0
\(881\) 27.2657 0.918604 0.459302 0.888280i \(-0.348100\pi\)
0.459302 + 0.888280i \(0.348100\pi\)
\(882\) 0 0
\(883\) 14.1255 0.475360 0.237680 0.971344i \(-0.423613\pi\)
0.237680 + 0.971344i \(0.423613\pi\)
\(884\) 0 0
\(885\) −10.1857 −0.342390
\(886\) 0 0
\(887\) 14.1172 0.474010 0.237005 0.971508i \(-0.423834\pi\)
0.237005 + 0.971508i \(0.423834\pi\)
\(888\) 0 0
\(889\) 7.17154 0.240526
\(890\) 0 0
\(891\) −2.91073 −0.0975131
\(892\) 0 0
\(893\) 27.9752 0.936154
\(894\) 0 0
\(895\) 1.78257 0.0595846
\(896\) 0 0
\(897\) −2.33689 −0.0780266
\(898\) 0 0
\(899\) −46.4202 −1.54820
\(900\) 0 0
\(901\) 47.0601 1.56780
\(902\) 0 0
\(903\) −52.1929 −1.73687
\(904\) 0 0
\(905\) −40.6894 −1.35256
\(906\) 0 0
\(907\) 47.3644 1.57271 0.786354 0.617776i \(-0.211966\pi\)
0.786354 + 0.617776i \(0.211966\pi\)
\(908\) 0 0
\(909\) 1.35436 0.0449214
\(910\) 0 0
\(911\) 32.8073 1.08696 0.543478 0.839423i \(-0.317107\pi\)
0.543478 + 0.839423i \(0.317107\pi\)
\(912\) 0 0
\(913\) −49.0881 −1.62458
\(914\) 0 0
\(915\) −8.66184 −0.286352
\(916\) 0 0
\(917\) 7.62888 0.251928
\(918\) 0 0
\(919\) −5.12933 −0.169201 −0.0846005 0.996415i \(-0.526961\pi\)
−0.0846005 + 0.996415i \(0.526961\pi\)
\(920\) 0 0
\(921\) 26.5494 0.874832
\(922\) 0 0
\(923\) −0.817823 −0.0269190
\(924\) 0 0
\(925\) 23.6005 0.775980
\(926\) 0 0
\(927\) 3.24034 0.106427
\(928\) 0 0
\(929\) 57.3874 1.88282 0.941410 0.337264i \(-0.109501\pi\)
0.941410 + 0.337264i \(0.109501\pi\)
\(930\) 0 0
\(931\) −31.8008 −1.04223
\(932\) 0 0
\(933\) −6.57114 −0.215129
\(934\) 0 0
\(935\) 63.4791 2.07599
\(936\) 0 0
\(937\) 23.5812 0.770366 0.385183 0.922840i \(-0.374138\pi\)
0.385183 + 0.922840i \(0.374138\pi\)
\(938\) 0 0
\(939\) −1.39897 −0.0456538
\(940\) 0 0
\(941\) 12.3255 0.401800 0.200900 0.979612i \(-0.435613\pi\)
0.200900 + 0.979612i \(0.435613\pi\)
\(942\) 0 0
\(943\) −13.6552 −0.444676
\(944\) 0 0
\(945\) 12.7691 0.415378
\(946\) 0 0
\(947\) 2.48420 0.0807256 0.0403628 0.999185i \(-0.487149\pi\)
0.0403628 + 0.999185i \(0.487149\pi\)
\(948\) 0 0
\(949\) 5.59570 0.181644
\(950\) 0 0
\(951\) 32.0982 1.04086
\(952\) 0 0
\(953\) −35.7243 −1.15722 −0.578612 0.815603i \(-0.696405\pi\)
−0.578612 + 0.815603i \(0.696405\pi\)
\(954\) 0 0
\(955\) 56.9193 1.84186
\(956\) 0 0
\(957\) −19.1371 −0.618614
\(958\) 0 0
\(959\) −45.7652 −1.47784
\(960\) 0 0
\(961\) 18.8502 0.608071
\(962\) 0 0
\(963\) 12.4272 0.400460
\(964\) 0 0
\(965\) 28.1570 0.906405
\(966\) 0 0
\(967\) 14.3114 0.460224 0.230112 0.973164i \(-0.426091\pi\)
0.230112 + 0.973164i \(0.426091\pi\)
\(968\) 0 0
\(969\) −17.9144 −0.575494
\(970\) 0 0
\(971\) −7.01096 −0.224992 −0.112496 0.993652i \(-0.535885\pi\)
−0.112496 + 0.993652i \(0.535885\pi\)
\(972\) 0 0
\(973\) −57.7942 −1.85280
\(974\) 0 0
\(975\) 2.40125 0.0769015
\(976\) 0 0
\(977\) 23.2826 0.744876 0.372438 0.928057i \(-0.378522\pi\)
0.372438 + 0.928057i \(0.378522\pi\)
\(978\) 0 0
\(979\) −23.8755 −0.763064
\(980\) 0 0
\(981\) 19.9444 0.636775
\(982\) 0 0
\(983\) −3.28649 −0.104823 −0.0524114 0.998626i \(-0.516691\pi\)
−0.0524114 + 0.998626i \(0.516691\pi\)
\(984\) 0 0
\(985\) −3.11840 −0.0993605
\(986\) 0 0
\(987\) −55.5846 −1.76928
\(988\) 0 0
\(989\) 31.4160 0.998971
\(990\) 0 0
\(991\) −16.0707 −0.510502 −0.255251 0.966875i \(-0.582158\pi\)
−0.255251 + 0.966875i \(0.582158\pi\)
\(992\) 0 0
\(993\) −30.4241 −0.965479
\(994\) 0 0
\(995\) −8.97938 −0.284666
\(996\) 0 0
\(997\) −28.3838 −0.898924 −0.449462 0.893299i \(-0.648384\pi\)
−0.449462 + 0.893299i \(0.648384\pi\)
\(998\) 0 0
\(999\) −8.35845 −0.264450
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 \(a_p\))