Properties

Label 8046.2.a.h.1.2
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.58022\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -2.72526 q^{5} -2.79628 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -2.72526 q^{5} -2.79628 q^{7} +1.00000 q^{8} -2.72526 q^{10} +3.26105 q^{11} -2.91542 q^{13} -2.79628 q^{14} +1.00000 q^{16} +0.639779 q^{17} +5.70570 q^{19} -2.72526 q^{20} +3.26105 q^{22} -1.32811 q^{23} +2.42702 q^{25} -2.91542 q^{26} -2.79628 q^{28} -3.22092 q^{29} -4.53396 q^{31} +1.00000 q^{32} +0.639779 q^{34} +7.62059 q^{35} +3.32382 q^{37} +5.70570 q^{38} -2.72526 q^{40} +8.09895 q^{41} +11.8813 q^{43} +3.26105 q^{44} -1.32811 q^{46} +5.42908 q^{47} +0.819203 q^{49} +2.42702 q^{50} -2.91542 q^{52} -8.89160 q^{53} -8.88719 q^{55} -2.79628 q^{56} -3.22092 q^{58} +0.723299 q^{59} +3.58006 q^{61} -4.53396 q^{62} +1.00000 q^{64} +7.94526 q^{65} +11.3440 q^{67} +0.639779 q^{68} +7.62059 q^{70} -16.6286 q^{71} -14.5294 q^{73} +3.32382 q^{74} +5.70570 q^{76} -9.11882 q^{77} -14.8665 q^{79} -2.72526 q^{80} +8.09895 q^{82} +5.26159 q^{83} -1.74356 q^{85} +11.8813 q^{86} +3.26105 q^{88} -16.2962 q^{89} +8.15234 q^{91} -1.32811 q^{92} +5.42908 q^{94} -15.5495 q^{95} -16.0563 q^{97} +0.819203 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −2.72526 −1.21877 −0.609386 0.792874i \(-0.708584\pi\)
−0.609386 + 0.792874i \(0.708584\pi\)
\(6\) 0 0
\(7\) −2.79628 −1.05690 −0.528448 0.848966i \(-0.677226\pi\)
−0.528448 + 0.848966i \(0.677226\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −2.72526 −0.861802
\(11\) 3.26105 0.983243 0.491622 0.870809i \(-0.336404\pi\)
0.491622 + 0.870809i \(0.336404\pi\)
\(12\) 0 0
\(13\) −2.91542 −0.808591 −0.404296 0.914628i \(-0.632483\pi\)
−0.404296 + 0.914628i \(0.632483\pi\)
\(14\) −2.79628 −0.747338
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.639779 0.155169 0.0775846 0.996986i \(-0.475279\pi\)
0.0775846 + 0.996986i \(0.475279\pi\)
\(18\) 0 0
\(19\) 5.70570 1.30898 0.654489 0.756072i \(-0.272884\pi\)
0.654489 + 0.756072i \(0.272884\pi\)
\(20\) −2.72526 −0.609386
\(21\) 0 0
\(22\) 3.26105 0.695258
\(23\) −1.32811 −0.276930 −0.138465 0.990367i \(-0.544217\pi\)
−0.138465 + 0.990367i \(0.544217\pi\)
\(24\) 0 0
\(25\) 2.42702 0.485404
\(26\) −2.91542 −0.571761
\(27\) 0 0
\(28\) −2.79628 −0.528448
\(29\) −3.22092 −0.598110 −0.299055 0.954236i \(-0.596671\pi\)
−0.299055 + 0.954236i \(0.596671\pi\)
\(30\) 0 0
\(31\) −4.53396 −0.814323 −0.407162 0.913356i \(-0.633481\pi\)
−0.407162 + 0.913356i \(0.633481\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.639779 0.109721
\(35\) 7.62059 1.28811
\(36\) 0 0
\(37\) 3.32382 0.546433 0.273217 0.961953i \(-0.411912\pi\)
0.273217 + 0.961953i \(0.411912\pi\)
\(38\) 5.70570 0.925587
\(39\) 0 0
\(40\) −2.72526 −0.430901
\(41\) 8.09895 1.26484 0.632422 0.774624i \(-0.282061\pi\)
0.632422 + 0.774624i \(0.282061\pi\)
\(42\) 0 0
\(43\) 11.8813 1.81188 0.905940 0.423406i \(-0.139166\pi\)
0.905940 + 0.423406i \(0.139166\pi\)
\(44\) 3.26105 0.491622
\(45\) 0 0
\(46\) −1.32811 −0.195819
\(47\) 5.42908 0.791913 0.395957 0.918269i \(-0.370413\pi\)
0.395957 + 0.918269i \(0.370413\pi\)
\(48\) 0 0
\(49\) 0.819203 0.117029
\(50\) 2.42702 0.343232
\(51\) 0 0
\(52\) −2.91542 −0.404296
\(53\) −8.89160 −1.22135 −0.610677 0.791879i \(-0.709103\pi\)
−0.610677 + 0.791879i \(0.709103\pi\)
\(54\) 0 0
\(55\) −8.88719 −1.19835
\(56\) −2.79628 −0.373669
\(57\) 0 0
\(58\) −3.22092 −0.422927
\(59\) 0.723299 0.0941655 0.0470827 0.998891i \(-0.485008\pi\)
0.0470827 + 0.998891i \(0.485008\pi\)
\(60\) 0 0
\(61\) 3.58006 0.458380 0.229190 0.973382i \(-0.426392\pi\)
0.229190 + 0.973382i \(0.426392\pi\)
\(62\) −4.53396 −0.575813
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.94526 0.985488
\(66\) 0 0
\(67\) 11.3440 1.38588 0.692942 0.720993i \(-0.256314\pi\)
0.692942 + 0.720993i \(0.256314\pi\)
\(68\) 0.639779 0.0775846
\(69\) 0 0
\(70\) 7.62059 0.910835
\(71\) −16.6286 −1.97345 −0.986727 0.162387i \(-0.948081\pi\)
−0.986727 + 0.162387i \(0.948081\pi\)
\(72\) 0 0
\(73\) −14.5294 −1.70054 −0.850270 0.526346i \(-0.823562\pi\)
−0.850270 + 0.526346i \(0.823562\pi\)
\(74\) 3.32382 0.386387
\(75\) 0 0
\(76\) 5.70570 0.654489
\(77\) −9.11882 −1.03919
\(78\) 0 0
\(79\) −14.8665 −1.67261 −0.836304 0.548266i \(-0.815288\pi\)
−0.836304 + 0.548266i \(0.815288\pi\)
\(80\) −2.72526 −0.304693
\(81\) 0 0
\(82\) 8.09895 0.894379
\(83\) 5.26159 0.577534 0.288767 0.957399i \(-0.406755\pi\)
0.288767 + 0.957399i \(0.406755\pi\)
\(84\) 0 0
\(85\) −1.74356 −0.189116
\(86\) 11.8813 1.28119
\(87\) 0 0
\(88\) 3.26105 0.347629
\(89\) −16.2962 −1.72739 −0.863697 0.504011i \(-0.831857\pi\)
−0.863697 + 0.504011i \(0.831857\pi\)
\(90\) 0 0
\(91\) 8.15234 0.854597
\(92\) −1.32811 −0.138465
\(93\) 0 0
\(94\) 5.42908 0.559967
\(95\) −15.5495 −1.59534
\(96\) 0 0
\(97\) −16.0563 −1.63027 −0.815137 0.579268i \(-0.803338\pi\)
−0.815137 + 0.579268i \(0.803338\pi\)
\(98\) 0.819203 0.0827520
\(99\) 0 0
\(100\) 2.42702 0.242702
\(101\) 10.8277 1.07739 0.538697 0.842500i \(-0.318917\pi\)
0.538697 + 0.842500i \(0.318917\pi\)
\(102\) 0 0
\(103\) 10.1784 1.00291 0.501454 0.865184i \(-0.332799\pi\)
0.501454 + 0.865184i \(0.332799\pi\)
\(104\) −2.91542 −0.285880
\(105\) 0 0
\(106\) −8.89160 −0.863628
\(107\) −4.43299 −0.428553 −0.214277 0.976773i \(-0.568739\pi\)
−0.214277 + 0.976773i \(0.568739\pi\)
\(108\) 0 0
\(109\) −19.8234 −1.89874 −0.949368 0.314166i \(-0.898275\pi\)
−0.949368 + 0.314166i \(0.898275\pi\)
\(110\) −8.88719 −0.847360
\(111\) 0 0
\(112\) −2.79628 −0.264224
\(113\) −11.3336 −1.06618 −0.533088 0.846060i \(-0.678969\pi\)
−0.533088 + 0.846060i \(0.678969\pi\)
\(114\) 0 0
\(115\) 3.61944 0.337514
\(116\) −3.22092 −0.299055
\(117\) 0 0
\(118\) 0.723299 0.0665851
\(119\) −1.78900 −0.163998
\(120\) 0 0
\(121\) −0.365561 −0.0332328
\(122\) 3.58006 0.324124
\(123\) 0 0
\(124\) −4.53396 −0.407162
\(125\) 7.01203 0.627175
\(126\) 0 0
\(127\) −3.89207 −0.345365 −0.172683 0.984978i \(-0.555243\pi\)
−0.172683 + 0.984978i \(0.555243\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 7.94526 0.696845
\(131\) 1.37955 0.120532 0.0602660 0.998182i \(-0.480805\pi\)
0.0602660 + 0.998182i \(0.480805\pi\)
\(132\) 0 0
\(133\) −15.9548 −1.38345
\(134\) 11.3440 0.979968
\(135\) 0 0
\(136\) 0.639779 0.0548606
\(137\) 15.5769 1.33082 0.665411 0.746478i \(-0.268256\pi\)
0.665411 + 0.746478i \(0.268256\pi\)
\(138\) 0 0
\(139\) −3.71888 −0.315432 −0.157716 0.987485i \(-0.550413\pi\)
−0.157716 + 0.987485i \(0.550413\pi\)
\(140\) 7.62059 0.644057
\(141\) 0 0
\(142\) −16.6286 −1.39544
\(143\) −9.50732 −0.795042
\(144\) 0 0
\(145\) 8.77783 0.728959
\(146\) −14.5294 −1.20246
\(147\) 0 0
\(148\) 3.32382 0.273217
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) −3.55019 −0.288910 −0.144455 0.989511i \(-0.546143\pi\)
−0.144455 + 0.989511i \(0.546143\pi\)
\(152\) 5.70570 0.462794
\(153\) 0 0
\(154\) −9.11882 −0.734815
\(155\) 12.3562 0.992474
\(156\) 0 0
\(157\) −22.1681 −1.76921 −0.884603 0.466345i \(-0.845571\pi\)
−0.884603 + 0.466345i \(0.845571\pi\)
\(158\) −14.8665 −1.18271
\(159\) 0 0
\(160\) −2.72526 −0.215450
\(161\) 3.71377 0.292686
\(162\) 0 0
\(163\) −16.1548 −1.26534 −0.632670 0.774422i \(-0.718041\pi\)
−0.632670 + 0.774422i \(0.718041\pi\)
\(164\) 8.09895 0.632422
\(165\) 0 0
\(166\) 5.26159 0.408379
\(167\) −16.0147 −1.23926 −0.619628 0.784896i \(-0.712716\pi\)
−0.619628 + 0.784896i \(0.712716\pi\)
\(168\) 0 0
\(169\) −4.50034 −0.346180
\(170\) −1.74356 −0.133725
\(171\) 0 0
\(172\) 11.8813 0.905940
\(173\) 25.3904 1.93039 0.965197 0.261523i \(-0.0842246\pi\)
0.965197 + 0.261523i \(0.0842246\pi\)
\(174\) 0 0
\(175\) −6.78663 −0.513021
\(176\) 3.26105 0.245811
\(177\) 0 0
\(178\) −16.2962 −1.22145
\(179\) 7.95101 0.594286 0.297143 0.954833i \(-0.403966\pi\)
0.297143 + 0.954833i \(0.403966\pi\)
\(180\) 0 0
\(181\) 5.41497 0.402492 0.201246 0.979541i \(-0.435501\pi\)
0.201246 + 0.979541i \(0.435501\pi\)
\(182\) 8.15234 0.604291
\(183\) 0 0
\(184\) −1.32811 −0.0979095
\(185\) −9.05827 −0.665977
\(186\) 0 0
\(187\) 2.08635 0.152569
\(188\) 5.42908 0.395957
\(189\) 0 0
\(190\) −15.5495 −1.12808
\(191\) 8.24768 0.596781 0.298391 0.954444i \(-0.403550\pi\)
0.298391 + 0.954444i \(0.403550\pi\)
\(192\) 0 0
\(193\) 3.95012 0.284336 0.142168 0.989843i \(-0.454593\pi\)
0.142168 + 0.989843i \(0.454593\pi\)
\(194\) −16.0563 −1.15278
\(195\) 0 0
\(196\) 0.819203 0.0585145
\(197\) 18.1572 1.29364 0.646822 0.762641i \(-0.276097\pi\)
0.646822 + 0.762641i \(0.276097\pi\)
\(198\) 0 0
\(199\) −8.03230 −0.569395 −0.284697 0.958617i \(-0.591893\pi\)
−0.284697 + 0.958617i \(0.591893\pi\)
\(200\) 2.42702 0.171616
\(201\) 0 0
\(202\) 10.8277 0.761833
\(203\) 9.00661 0.632140
\(204\) 0 0
\(205\) −22.0717 −1.54155
\(206\) 10.1784 0.709163
\(207\) 0 0
\(208\) −2.91542 −0.202148
\(209\) 18.6066 1.28704
\(210\) 0 0
\(211\) −26.9038 −1.85213 −0.926065 0.377363i \(-0.876831\pi\)
−0.926065 + 0.377363i \(0.876831\pi\)
\(212\) −8.89160 −0.610677
\(213\) 0 0
\(214\) −4.43299 −0.303033
\(215\) −32.3796 −2.20827
\(216\) 0 0
\(217\) 12.6782 0.860655
\(218\) −19.8234 −1.34261
\(219\) 0 0
\(220\) −8.88719 −0.599174
\(221\) −1.86522 −0.125469
\(222\) 0 0
\(223\) 23.1746 1.55189 0.775945 0.630801i \(-0.217274\pi\)
0.775945 + 0.630801i \(0.217274\pi\)
\(224\) −2.79628 −0.186835
\(225\) 0 0
\(226\) −11.3336 −0.753901
\(227\) 11.7427 0.779388 0.389694 0.920944i \(-0.372581\pi\)
0.389694 + 0.920944i \(0.372581\pi\)
\(228\) 0 0
\(229\) −13.1092 −0.866279 −0.433140 0.901327i \(-0.642594\pi\)
−0.433140 + 0.901327i \(0.642594\pi\)
\(230\) 3.61944 0.238659
\(231\) 0 0
\(232\) −3.22092 −0.211464
\(233\) −4.00233 −0.262201 −0.131101 0.991369i \(-0.541851\pi\)
−0.131101 + 0.991369i \(0.541851\pi\)
\(234\) 0 0
\(235\) −14.7956 −0.965161
\(236\) 0.723299 0.0470827
\(237\) 0 0
\(238\) −1.78900 −0.115964
\(239\) 22.3878 1.44815 0.724074 0.689722i \(-0.242267\pi\)
0.724074 + 0.689722i \(0.242267\pi\)
\(240\) 0 0
\(241\) −22.8159 −1.46970 −0.734852 0.678228i \(-0.762748\pi\)
−0.734852 + 0.678228i \(0.762748\pi\)
\(242\) −0.365561 −0.0234992
\(243\) 0 0
\(244\) 3.58006 0.229190
\(245\) −2.23254 −0.142632
\(246\) 0 0
\(247\) −16.6345 −1.05843
\(248\) −4.53396 −0.287907
\(249\) 0 0
\(250\) 7.01203 0.443480
\(251\) 12.2272 0.771771 0.385885 0.922547i \(-0.373896\pi\)
0.385885 + 0.922547i \(0.373896\pi\)
\(252\) 0 0
\(253\) −4.33103 −0.272289
\(254\) −3.89207 −0.244210
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −7.64557 −0.476918 −0.238459 0.971153i \(-0.576642\pi\)
−0.238459 + 0.971153i \(0.576642\pi\)
\(258\) 0 0
\(259\) −9.29435 −0.577523
\(260\) 7.94526 0.492744
\(261\) 0 0
\(262\) 1.37955 0.0852290
\(263\) −23.0025 −1.41839 −0.709196 0.705011i \(-0.750942\pi\)
−0.709196 + 0.705011i \(0.750942\pi\)
\(264\) 0 0
\(265\) 24.2319 1.48855
\(266\) −15.9548 −0.978249
\(267\) 0 0
\(268\) 11.3440 0.692942
\(269\) −23.1234 −1.40986 −0.704929 0.709278i \(-0.749021\pi\)
−0.704929 + 0.709278i \(0.749021\pi\)
\(270\) 0 0
\(271\) −7.10401 −0.431538 −0.215769 0.976444i \(-0.569226\pi\)
−0.215769 + 0.976444i \(0.569226\pi\)
\(272\) 0.639779 0.0387923
\(273\) 0 0
\(274\) 15.5769 0.941033
\(275\) 7.91463 0.477270
\(276\) 0 0
\(277\) −16.2288 −0.975096 −0.487548 0.873096i \(-0.662109\pi\)
−0.487548 + 0.873096i \(0.662109\pi\)
\(278\) −3.71888 −0.223044
\(279\) 0 0
\(280\) 7.62059 0.455417
\(281\) −23.2687 −1.38809 −0.694047 0.719930i \(-0.744174\pi\)
−0.694047 + 0.719930i \(0.744174\pi\)
\(282\) 0 0
\(283\) 4.13901 0.246038 0.123019 0.992404i \(-0.460742\pi\)
0.123019 + 0.992404i \(0.460742\pi\)
\(284\) −16.6286 −0.986727
\(285\) 0 0
\(286\) −9.50732 −0.562180
\(287\) −22.6470 −1.33681
\(288\) 0 0
\(289\) −16.5907 −0.975923
\(290\) 8.77783 0.515452
\(291\) 0 0
\(292\) −14.5294 −0.850270
\(293\) −11.8774 −0.693888 −0.346944 0.937886i \(-0.612781\pi\)
−0.346944 + 0.937886i \(0.612781\pi\)
\(294\) 0 0
\(295\) −1.97117 −0.114766
\(296\) 3.32382 0.193193
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 3.87199 0.223923
\(300\) 0 0
\(301\) −33.2235 −1.91497
\(302\) −3.55019 −0.204290
\(303\) 0 0
\(304\) 5.70570 0.327244
\(305\) −9.75659 −0.558661
\(306\) 0 0
\(307\) 8.07771 0.461019 0.230510 0.973070i \(-0.425961\pi\)
0.230510 + 0.973070i \(0.425961\pi\)
\(308\) −9.11882 −0.519593
\(309\) 0 0
\(310\) 12.3562 0.701785
\(311\) 22.4413 1.27253 0.636266 0.771470i \(-0.280478\pi\)
0.636266 + 0.771470i \(0.280478\pi\)
\(312\) 0 0
\(313\) 1.79049 0.101204 0.0506022 0.998719i \(-0.483886\pi\)
0.0506022 + 0.998719i \(0.483886\pi\)
\(314\) −22.1681 −1.25102
\(315\) 0 0
\(316\) −14.8665 −0.836304
\(317\) −11.1489 −0.626185 −0.313092 0.949723i \(-0.601365\pi\)
−0.313092 + 0.949723i \(0.601365\pi\)
\(318\) 0 0
\(319\) −10.5036 −0.588087
\(320\) −2.72526 −0.152346
\(321\) 0 0
\(322\) 3.71377 0.206960
\(323\) 3.65039 0.203113
\(324\) 0 0
\(325\) −7.07577 −0.392493
\(326\) −16.1548 −0.894730
\(327\) 0 0
\(328\) 8.09895 0.447190
\(329\) −15.1813 −0.836970
\(330\) 0 0
\(331\) 3.96274 0.217812 0.108906 0.994052i \(-0.465265\pi\)
0.108906 + 0.994052i \(0.465265\pi\)
\(332\) 5.26159 0.288767
\(333\) 0 0
\(334\) −16.0147 −0.876286
\(335\) −30.9152 −1.68908
\(336\) 0 0
\(337\) −23.3207 −1.27036 −0.635179 0.772365i \(-0.719074\pi\)
−0.635179 + 0.772365i \(0.719074\pi\)
\(338\) −4.50034 −0.244786
\(339\) 0 0
\(340\) −1.74356 −0.0945579
\(341\) −14.7855 −0.800678
\(342\) 0 0
\(343\) 17.2833 0.933208
\(344\) 11.8813 0.640596
\(345\) 0 0
\(346\) 25.3904 1.36500
\(347\) 3.89827 0.209270 0.104635 0.994511i \(-0.466633\pi\)
0.104635 + 0.994511i \(0.466633\pi\)
\(348\) 0 0
\(349\) 20.7995 1.11337 0.556686 0.830723i \(-0.312073\pi\)
0.556686 + 0.830723i \(0.312073\pi\)
\(350\) −6.78663 −0.362761
\(351\) 0 0
\(352\) 3.26105 0.173814
\(353\) 9.98456 0.531424 0.265712 0.964052i \(-0.414393\pi\)
0.265712 + 0.964052i \(0.414393\pi\)
\(354\) 0 0
\(355\) 45.3172 2.40519
\(356\) −16.2962 −0.863697
\(357\) 0 0
\(358\) 7.95101 0.420224
\(359\) −30.8076 −1.62596 −0.812982 0.582288i \(-0.802157\pi\)
−0.812982 + 0.582288i \(0.802157\pi\)
\(360\) 0 0
\(361\) 13.5550 0.713423
\(362\) 5.41497 0.284605
\(363\) 0 0
\(364\) 8.15234 0.427299
\(365\) 39.5964 2.07257
\(366\) 0 0
\(367\) −32.2179 −1.68176 −0.840880 0.541221i \(-0.817962\pi\)
−0.840880 + 0.541221i \(0.817962\pi\)
\(368\) −1.32811 −0.0692325
\(369\) 0 0
\(370\) −9.05827 −0.470917
\(371\) 24.8634 1.29084
\(372\) 0 0
\(373\) −12.5090 −0.647691 −0.323845 0.946110i \(-0.604976\pi\)
−0.323845 + 0.946110i \(0.604976\pi\)
\(374\) 2.08635 0.107883
\(375\) 0 0
\(376\) 5.42908 0.279984
\(377\) 9.39033 0.483626
\(378\) 0 0
\(379\) 20.8180 1.06935 0.534675 0.845058i \(-0.320434\pi\)
0.534675 + 0.845058i \(0.320434\pi\)
\(380\) −15.5495 −0.797672
\(381\) 0 0
\(382\) 8.24768 0.421988
\(383\) −38.2768 −1.95585 −0.977926 0.208952i \(-0.932995\pi\)
−0.977926 + 0.208952i \(0.932995\pi\)
\(384\) 0 0
\(385\) 24.8511 1.26653
\(386\) 3.95012 0.201056
\(387\) 0 0
\(388\) −16.0563 −0.815137
\(389\) 20.5628 1.04257 0.521287 0.853382i \(-0.325452\pi\)
0.521287 + 0.853382i \(0.325452\pi\)
\(390\) 0 0
\(391\) −0.849696 −0.0429710
\(392\) 0.819203 0.0413760
\(393\) 0 0
\(394\) 18.1572 0.914745
\(395\) 40.5149 2.03853
\(396\) 0 0
\(397\) −29.0661 −1.45879 −0.729394 0.684094i \(-0.760198\pi\)
−0.729394 + 0.684094i \(0.760198\pi\)
\(398\) −8.03230 −0.402623
\(399\) 0 0
\(400\) 2.42702 0.121351
\(401\) 3.25582 0.162588 0.0812940 0.996690i \(-0.474095\pi\)
0.0812940 + 0.996690i \(0.474095\pi\)
\(402\) 0 0
\(403\) 13.2184 0.658455
\(404\) 10.8277 0.538697
\(405\) 0 0
\(406\) 9.00661 0.446990
\(407\) 10.8391 0.537277
\(408\) 0 0
\(409\) 39.5930 1.95775 0.978873 0.204471i \(-0.0655473\pi\)
0.978873 + 0.204471i \(0.0655473\pi\)
\(410\) −22.0717 −1.09004
\(411\) 0 0
\(412\) 10.1784 0.501454
\(413\) −2.02255 −0.0995231
\(414\) 0 0
\(415\) −14.3392 −0.703882
\(416\) −2.91542 −0.142940
\(417\) 0 0
\(418\) 18.6066 0.910077
\(419\) 7.77544 0.379855 0.189927 0.981798i \(-0.439175\pi\)
0.189927 + 0.981798i \(0.439175\pi\)
\(420\) 0 0
\(421\) −25.7009 −1.25259 −0.626293 0.779587i \(-0.715429\pi\)
−0.626293 + 0.779587i \(0.715429\pi\)
\(422\) −26.9038 −1.30965
\(423\) 0 0
\(424\) −8.89160 −0.431814
\(425\) 1.55276 0.0753197
\(426\) 0 0
\(427\) −10.0109 −0.484460
\(428\) −4.43299 −0.214277
\(429\) 0 0
\(430\) −32.3796 −1.56148
\(431\) 19.0736 0.918744 0.459372 0.888244i \(-0.348075\pi\)
0.459372 + 0.888244i \(0.348075\pi\)
\(432\) 0 0
\(433\) 18.1129 0.870451 0.435225 0.900321i \(-0.356669\pi\)
0.435225 + 0.900321i \(0.356669\pi\)
\(434\) 12.6782 0.608575
\(435\) 0 0
\(436\) −19.8234 −0.949368
\(437\) −7.57779 −0.362495
\(438\) 0 0
\(439\) 4.42989 0.211427 0.105714 0.994397i \(-0.466287\pi\)
0.105714 + 0.994397i \(0.466287\pi\)
\(440\) −8.88719 −0.423680
\(441\) 0 0
\(442\) −1.86522 −0.0887196
\(443\) 22.6132 1.07438 0.537192 0.843460i \(-0.319485\pi\)
0.537192 + 0.843460i \(0.319485\pi\)
\(444\) 0 0
\(445\) 44.4113 2.10530
\(446\) 23.1746 1.09735
\(447\) 0 0
\(448\) −2.79628 −0.132112
\(449\) −23.4810 −1.10814 −0.554069 0.832470i \(-0.686926\pi\)
−0.554069 + 0.832470i \(0.686926\pi\)
\(450\) 0 0
\(451\) 26.4111 1.24365
\(452\) −11.3336 −0.533088
\(453\) 0 0
\(454\) 11.7427 0.551110
\(455\) −22.2172 −1.04156
\(456\) 0 0
\(457\) −10.3125 −0.482400 −0.241200 0.970475i \(-0.577541\pi\)
−0.241200 + 0.970475i \(0.577541\pi\)
\(458\) −13.1092 −0.612552
\(459\) 0 0
\(460\) 3.61944 0.168757
\(461\) −28.1519 −1.31116 −0.655582 0.755124i \(-0.727576\pi\)
−0.655582 + 0.755124i \(0.727576\pi\)
\(462\) 0 0
\(463\) 23.6846 1.10072 0.550358 0.834929i \(-0.314491\pi\)
0.550358 + 0.834929i \(0.314491\pi\)
\(464\) −3.22092 −0.149527
\(465\) 0 0
\(466\) −4.00233 −0.185404
\(467\) −17.9826 −0.832133 −0.416067 0.909334i \(-0.636592\pi\)
−0.416067 + 0.909334i \(0.636592\pi\)
\(468\) 0 0
\(469\) −31.7209 −1.46474
\(470\) −14.7956 −0.682472
\(471\) 0 0
\(472\) 0.723299 0.0332925
\(473\) 38.7455 1.78152
\(474\) 0 0
\(475\) 13.8478 0.635383
\(476\) −1.78900 −0.0819989
\(477\) 0 0
\(478\) 22.3878 1.02400
\(479\) −8.58630 −0.392318 −0.196159 0.980572i \(-0.562847\pi\)
−0.196159 + 0.980572i \(0.562847\pi\)
\(480\) 0 0
\(481\) −9.69033 −0.441841
\(482\) −22.8159 −1.03924
\(483\) 0 0
\(484\) −0.365561 −0.0166164
\(485\) 43.7576 1.98693
\(486\) 0 0
\(487\) −4.72199 −0.213974 −0.106987 0.994260i \(-0.534120\pi\)
−0.106987 + 0.994260i \(0.534120\pi\)
\(488\) 3.58006 0.162062
\(489\) 0 0
\(490\) −2.23254 −0.100856
\(491\) −2.83154 −0.127786 −0.0638929 0.997957i \(-0.520352\pi\)
−0.0638929 + 0.997957i \(0.520352\pi\)
\(492\) 0 0
\(493\) −2.06068 −0.0928082
\(494\) −16.6345 −0.748422
\(495\) 0 0
\(496\) −4.53396 −0.203581
\(497\) 46.4983 2.08574
\(498\) 0 0
\(499\) −35.6782 −1.59718 −0.798588 0.601878i \(-0.794419\pi\)
−0.798588 + 0.601878i \(0.794419\pi\)
\(500\) 7.01203 0.313588
\(501\) 0 0
\(502\) 12.2272 0.545724
\(503\) 27.2478 1.21492 0.607461 0.794350i \(-0.292188\pi\)
0.607461 + 0.794350i \(0.292188\pi\)
\(504\) 0 0
\(505\) −29.5082 −1.31310
\(506\) −4.33103 −0.192538
\(507\) 0 0
\(508\) −3.89207 −0.172683
\(509\) −1.94505 −0.0862129 −0.0431064 0.999070i \(-0.513725\pi\)
−0.0431064 + 0.999070i \(0.513725\pi\)
\(510\) 0 0
\(511\) 40.6284 1.79729
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.64557 −0.337232
\(515\) −27.7387 −1.22232
\(516\) 0 0
\(517\) 17.7045 0.778643
\(518\) −9.29435 −0.408370
\(519\) 0 0
\(520\) 7.94526 0.348423
\(521\) 30.2679 1.32606 0.663031 0.748592i \(-0.269270\pi\)
0.663031 + 0.748592i \(0.269270\pi\)
\(522\) 0 0
\(523\) 4.47550 0.195700 0.0978501 0.995201i \(-0.468803\pi\)
0.0978501 + 0.995201i \(0.468803\pi\)
\(524\) 1.37955 0.0602660
\(525\) 0 0
\(526\) −23.0025 −1.00295
\(527\) −2.90073 −0.126358
\(528\) 0 0
\(529\) −21.2361 −0.923310
\(530\) 24.2319 1.05257
\(531\) 0 0
\(532\) −15.9548 −0.691727
\(533\) −23.6118 −1.02274
\(534\) 0 0
\(535\) 12.0810 0.522308
\(536\) 11.3440 0.489984
\(537\) 0 0
\(538\) −23.1234 −0.996920
\(539\) 2.67146 0.115068
\(540\) 0 0
\(541\) 1.13187 0.0486630 0.0243315 0.999704i \(-0.492254\pi\)
0.0243315 + 0.999704i \(0.492254\pi\)
\(542\) −7.10401 −0.305143
\(543\) 0 0
\(544\) 0.639779 0.0274303
\(545\) 54.0238 2.31413
\(546\) 0 0
\(547\) −20.4555 −0.874616 −0.437308 0.899312i \(-0.644068\pi\)
−0.437308 + 0.899312i \(0.644068\pi\)
\(548\) 15.5769 0.665411
\(549\) 0 0
\(550\) 7.91463 0.337481
\(551\) −18.3776 −0.782913
\(552\) 0 0
\(553\) 41.5709 1.76777
\(554\) −16.2288 −0.689497
\(555\) 0 0
\(556\) −3.71888 −0.157716
\(557\) 44.2761 1.87604 0.938020 0.346581i \(-0.112657\pi\)
0.938020 + 0.346581i \(0.112657\pi\)
\(558\) 0 0
\(559\) −34.6389 −1.46507
\(560\) 7.62059 0.322029
\(561\) 0 0
\(562\) −23.2687 −0.981530
\(563\) −30.8672 −1.30090 −0.650449 0.759550i \(-0.725419\pi\)
−0.650449 + 0.759550i \(0.725419\pi\)
\(564\) 0 0
\(565\) 30.8870 1.29943
\(566\) 4.13901 0.173975
\(567\) 0 0
\(568\) −16.6286 −0.697721
\(569\) 4.86745 0.204054 0.102027 0.994782i \(-0.467467\pi\)
0.102027 + 0.994782i \(0.467467\pi\)
\(570\) 0 0
\(571\) −27.5505 −1.15295 −0.576477 0.817113i \(-0.695573\pi\)
−0.576477 + 0.817113i \(0.695573\pi\)
\(572\) −9.50732 −0.397521
\(573\) 0 0
\(574\) −22.6470 −0.945266
\(575\) −3.22335 −0.134423
\(576\) 0 0
\(577\) 27.4508 1.14279 0.571397 0.820674i \(-0.306402\pi\)
0.571397 + 0.820674i \(0.306402\pi\)
\(578\) −16.5907 −0.690081
\(579\) 0 0
\(580\) 8.77783 0.364480
\(581\) −14.7129 −0.610394
\(582\) 0 0
\(583\) −28.9959 −1.20089
\(584\) −14.5294 −0.601232
\(585\) 0 0
\(586\) −11.8774 −0.490653
\(587\) −8.74701 −0.361028 −0.180514 0.983572i \(-0.557776\pi\)
−0.180514 + 0.983572i \(0.557776\pi\)
\(588\) 0 0
\(589\) −25.8694 −1.06593
\(590\) −1.97117 −0.0811520
\(591\) 0 0
\(592\) 3.32382 0.136608
\(593\) −46.3617 −1.90385 −0.951924 0.306334i \(-0.900898\pi\)
−0.951924 + 0.306334i \(0.900898\pi\)
\(594\) 0 0
\(595\) 4.87549 0.199876
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 3.87199 0.158338
\(599\) 6.12967 0.250451 0.125226 0.992128i \(-0.460035\pi\)
0.125226 + 0.992128i \(0.460035\pi\)
\(600\) 0 0
\(601\) 1.43528 0.0585463 0.0292732 0.999571i \(-0.490681\pi\)
0.0292732 + 0.999571i \(0.490681\pi\)
\(602\) −33.2235 −1.35409
\(603\) 0 0
\(604\) −3.55019 −0.144455
\(605\) 0.996248 0.0405032
\(606\) 0 0
\(607\) 20.8849 0.847693 0.423847 0.905734i \(-0.360680\pi\)
0.423847 + 0.905734i \(0.360680\pi\)
\(608\) 5.70570 0.231397
\(609\) 0 0
\(610\) −9.75659 −0.395033
\(611\) −15.8280 −0.640334
\(612\) 0 0
\(613\) −37.5686 −1.51738 −0.758691 0.651451i \(-0.774161\pi\)
−0.758691 + 0.651451i \(0.774161\pi\)
\(614\) 8.07771 0.325990
\(615\) 0 0
\(616\) −9.11882 −0.367408
\(617\) −4.84106 −0.194894 −0.0974468 0.995241i \(-0.531068\pi\)
−0.0974468 + 0.995241i \(0.531068\pi\)
\(618\) 0 0
\(619\) −7.70576 −0.309721 −0.154860 0.987936i \(-0.549493\pi\)
−0.154860 + 0.987936i \(0.549493\pi\)
\(620\) 12.3562 0.496237
\(621\) 0 0
\(622\) 22.4413 0.899815
\(623\) 45.5688 1.82568
\(624\) 0 0
\(625\) −31.2447 −1.24979
\(626\) 1.79049 0.0715624
\(627\) 0 0
\(628\) −22.1681 −0.884603
\(629\) 2.12651 0.0847896
\(630\) 0 0
\(631\) −2.62695 −0.104577 −0.0522887 0.998632i \(-0.516652\pi\)
−0.0522887 + 0.998632i \(0.516652\pi\)
\(632\) −14.8665 −0.591356
\(633\) 0 0
\(634\) −11.1489 −0.442779
\(635\) 10.6069 0.420921
\(636\) 0 0
\(637\) −2.38832 −0.0946287
\(638\) −10.5036 −0.415841
\(639\) 0 0
\(640\) −2.72526 −0.107725
\(641\) 22.1313 0.874132 0.437066 0.899429i \(-0.356018\pi\)
0.437066 + 0.899429i \(0.356018\pi\)
\(642\) 0 0
\(643\) 0.528582 0.0208452 0.0104226 0.999946i \(-0.496682\pi\)
0.0104226 + 0.999946i \(0.496682\pi\)
\(644\) 3.71377 0.146343
\(645\) 0 0
\(646\) 3.65039 0.143623
\(647\) −1.05402 −0.0414377 −0.0207189 0.999785i \(-0.506595\pi\)
−0.0207189 + 0.999785i \(0.506595\pi\)
\(648\) 0 0
\(649\) 2.35871 0.0925876
\(650\) −7.07577 −0.277535
\(651\) 0 0
\(652\) −16.1548 −0.632670
\(653\) −12.8500 −0.502860 −0.251430 0.967876i \(-0.580901\pi\)
−0.251430 + 0.967876i \(0.580901\pi\)
\(654\) 0 0
\(655\) −3.75963 −0.146901
\(656\) 8.09895 0.316211
\(657\) 0 0
\(658\) −15.1813 −0.591827
\(659\) −3.36625 −0.131130 −0.0655652 0.997848i \(-0.520885\pi\)
−0.0655652 + 0.997848i \(0.520885\pi\)
\(660\) 0 0
\(661\) −29.1141 −1.13241 −0.566203 0.824266i \(-0.691588\pi\)
−0.566203 + 0.824266i \(0.691588\pi\)
\(662\) 3.96274 0.154016
\(663\) 0 0
\(664\) 5.26159 0.204189
\(665\) 43.4808 1.68611
\(666\) 0 0
\(667\) 4.27773 0.165634
\(668\) −16.0147 −0.619628
\(669\) 0 0
\(670\) −30.9152 −1.19436
\(671\) 11.6748 0.450699
\(672\) 0 0
\(673\) 14.9029 0.574463 0.287232 0.957861i \(-0.407265\pi\)
0.287232 + 0.957861i \(0.407265\pi\)
\(674\) −23.3207 −0.898279
\(675\) 0 0
\(676\) −4.50034 −0.173090
\(677\) 21.7641 0.836462 0.418231 0.908341i \(-0.362650\pi\)
0.418231 + 0.908341i \(0.362650\pi\)
\(678\) 0 0
\(679\) 44.8981 1.72303
\(680\) −1.74356 −0.0668625
\(681\) 0 0
\(682\) −14.7855 −0.566165
\(683\) −22.9350 −0.877582 −0.438791 0.898589i \(-0.644593\pi\)
−0.438791 + 0.898589i \(0.644593\pi\)
\(684\) 0 0
\(685\) −42.4509 −1.62197
\(686\) 17.2833 0.659878
\(687\) 0 0
\(688\) 11.8813 0.452970
\(689\) 25.9227 0.987577
\(690\) 0 0
\(691\) 27.1459 1.03268 0.516339 0.856384i \(-0.327294\pi\)
0.516339 + 0.856384i \(0.327294\pi\)
\(692\) 25.3904 0.965197
\(693\) 0 0
\(694\) 3.89827 0.147976
\(695\) 10.1349 0.384439
\(696\) 0 0
\(697\) 5.18154 0.196265
\(698\) 20.7995 0.787273
\(699\) 0 0
\(700\) −6.78663 −0.256511
\(701\) −11.2381 −0.424459 −0.212229 0.977220i \(-0.568072\pi\)
−0.212229 + 0.977220i \(0.568072\pi\)
\(702\) 0 0
\(703\) 18.9647 0.715269
\(704\) 3.26105 0.122905
\(705\) 0 0
\(706\) 9.98456 0.375774
\(707\) −30.2773 −1.13869
\(708\) 0 0
\(709\) 32.9160 1.23619 0.618094 0.786105i \(-0.287905\pi\)
0.618094 + 0.786105i \(0.287905\pi\)
\(710\) 45.3172 1.70073
\(711\) 0 0
\(712\) −16.2962 −0.610726
\(713\) 6.02159 0.225510
\(714\) 0 0
\(715\) 25.9099 0.968975
\(716\) 7.95101 0.297143
\(717\) 0 0
\(718\) −30.8076 −1.14973
\(719\) 18.7416 0.698942 0.349471 0.936947i \(-0.386361\pi\)
0.349471 + 0.936947i \(0.386361\pi\)
\(720\) 0 0
\(721\) −28.4617 −1.05997
\(722\) 13.5550 0.504466
\(723\) 0 0
\(724\) 5.41497 0.201246
\(725\) −7.81723 −0.290325
\(726\) 0 0
\(727\) 45.3511 1.68198 0.840990 0.541051i \(-0.181973\pi\)
0.840990 + 0.541051i \(0.181973\pi\)
\(728\) 8.15234 0.302146
\(729\) 0 0
\(730\) 39.5964 1.46553
\(731\) 7.60140 0.281148
\(732\) 0 0
\(733\) 52.6932 1.94627 0.973133 0.230243i \(-0.0739523\pi\)
0.973133 + 0.230243i \(0.0739523\pi\)
\(734\) −32.2179 −1.18918
\(735\) 0 0
\(736\) −1.32811 −0.0489547
\(737\) 36.9932 1.36266
\(738\) 0 0
\(739\) −22.6834 −0.834421 −0.417211 0.908810i \(-0.636992\pi\)
−0.417211 + 0.908810i \(0.636992\pi\)
\(740\) −9.05827 −0.332989
\(741\) 0 0
\(742\) 24.8634 0.912765
\(743\) −17.9688 −0.659211 −0.329606 0.944119i \(-0.606916\pi\)
−0.329606 + 0.944119i \(0.606916\pi\)
\(744\) 0 0
\(745\) 2.72526 0.0998456
\(746\) −12.5090 −0.457986
\(747\) 0 0
\(748\) 2.08635 0.0762845
\(749\) 12.3959 0.452936
\(750\) 0 0
\(751\) 0.566495 0.0206717 0.0103359 0.999947i \(-0.496710\pi\)
0.0103359 + 0.999947i \(0.496710\pi\)
\(752\) 5.42908 0.197978
\(753\) 0 0
\(754\) 9.39033 0.341976
\(755\) 9.67518 0.352116
\(756\) 0 0
\(757\) 26.4143 0.960042 0.480021 0.877257i \(-0.340629\pi\)
0.480021 + 0.877257i \(0.340629\pi\)
\(758\) 20.8180 0.756144
\(759\) 0 0
\(760\) −15.5495 −0.564040
\(761\) −2.85181 −0.103378 −0.0516890 0.998663i \(-0.516460\pi\)
−0.0516890 + 0.998663i \(0.516460\pi\)
\(762\) 0 0
\(763\) 55.4318 2.00677
\(764\) 8.24768 0.298391
\(765\) 0 0
\(766\) −38.2768 −1.38300
\(767\) −2.10872 −0.0761414
\(768\) 0 0
\(769\) 10.3071 0.371683 0.185842 0.982580i \(-0.440499\pi\)
0.185842 + 0.982580i \(0.440499\pi\)
\(770\) 24.8511 0.895572
\(771\) 0 0
\(772\) 3.95012 0.142168
\(773\) 7.81989 0.281262 0.140631 0.990062i \(-0.455087\pi\)
0.140631 + 0.990062i \(0.455087\pi\)
\(774\) 0 0
\(775\) −11.0040 −0.395276
\(776\) −16.0563 −0.576389
\(777\) 0 0
\(778\) 20.5628 0.737210
\(779\) 46.2102 1.65565
\(780\) 0 0
\(781\) −54.2267 −1.94039
\(782\) −0.849696 −0.0303851
\(783\) 0 0
\(784\) 0.819203 0.0292573
\(785\) 60.4137 2.15626
\(786\) 0 0
\(787\) 2.48811 0.0886915 0.0443458 0.999016i \(-0.485880\pi\)
0.0443458 + 0.999016i \(0.485880\pi\)
\(788\) 18.1572 0.646822
\(789\) 0 0
\(790\) 40.5149 1.44146
\(791\) 31.6920 1.12684
\(792\) 0 0
\(793\) −10.4374 −0.370642
\(794\) −29.0661 −1.03152
\(795\) 0 0
\(796\) −8.03230 −0.284697
\(797\) 2.20148 0.0779805 0.0389902 0.999240i \(-0.487586\pi\)
0.0389902 + 0.999240i \(0.487586\pi\)
\(798\) 0 0
\(799\) 3.47341 0.122881
\(800\) 2.42702 0.0858081
\(801\) 0 0
\(802\) 3.25582 0.114967
\(803\) −47.3812 −1.67205
\(804\) 0 0
\(805\) −10.1210 −0.356717
\(806\) 13.2184 0.465598
\(807\) 0 0
\(808\) 10.8277 0.380916
\(809\) 31.9340 1.12274 0.561369 0.827565i \(-0.310275\pi\)
0.561369 + 0.827565i \(0.310275\pi\)
\(810\) 0 0
\(811\) −24.9375 −0.875675 −0.437837 0.899054i \(-0.644255\pi\)
−0.437837 + 0.899054i \(0.644255\pi\)
\(812\) 9.00661 0.316070
\(813\) 0 0
\(814\) 10.8391 0.379912
\(815\) 44.0259 1.54216
\(816\) 0 0
\(817\) 67.7911 2.37171
\(818\) 39.5930 1.38434
\(819\) 0 0
\(820\) −22.0717 −0.770777
\(821\) 53.9606 1.88324 0.941619 0.336681i \(-0.109304\pi\)
0.941619 + 0.336681i \(0.109304\pi\)
\(822\) 0 0
\(823\) −4.62304 −0.161149 −0.0805745 0.996749i \(-0.525675\pi\)
−0.0805745 + 0.996749i \(0.525675\pi\)
\(824\) 10.1784 0.354581
\(825\) 0 0
\(826\) −2.02255 −0.0703735
\(827\) −23.5970 −0.820549 −0.410274 0.911962i \(-0.634567\pi\)
−0.410274 + 0.911962i \(0.634567\pi\)
\(828\) 0 0
\(829\) −41.9815 −1.45808 −0.729039 0.684472i \(-0.760033\pi\)
−0.729039 + 0.684472i \(0.760033\pi\)
\(830\) −14.3392 −0.497720
\(831\) 0 0
\(832\) −2.91542 −0.101074
\(833\) 0.524109 0.0181593
\(834\) 0 0
\(835\) 43.6442 1.51037
\(836\) 18.6066 0.643522
\(837\) 0 0
\(838\) 7.77544 0.268598
\(839\) −10.7147 −0.369912 −0.184956 0.982747i \(-0.559214\pi\)
−0.184956 + 0.982747i \(0.559214\pi\)
\(840\) 0 0
\(841\) −18.6257 −0.642265
\(842\) −25.7009 −0.885713
\(843\) 0 0
\(844\) −26.9038 −0.926065
\(845\) 12.2646 0.421914
\(846\) 0 0
\(847\) 1.02221 0.0351237
\(848\) −8.89160 −0.305339
\(849\) 0 0
\(850\) 1.55276 0.0532591
\(851\) −4.41440 −0.151324
\(852\) 0 0
\(853\) 33.7916 1.15700 0.578500 0.815682i \(-0.303638\pi\)
0.578500 + 0.815682i \(0.303638\pi\)
\(854\) −10.0109 −0.342565
\(855\) 0 0
\(856\) −4.43299 −0.151516
\(857\) 30.3647 1.03724 0.518619 0.855005i \(-0.326446\pi\)
0.518619 + 0.855005i \(0.326446\pi\)
\(858\) 0 0
\(859\) −10.3030 −0.351533 −0.175767 0.984432i \(-0.556240\pi\)
−0.175767 + 0.984432i \(0.556240\pi\)
\(860\) −32.3796 −1.10413
\(861\) 0 0
\(862\) 19.0736 0.649650
\(863\) −16.8673 −0.574168 −0.287084 0.957905i \(-0.592686\pi\)
−0.287084 + 0.957905i \(0.592686\pi\)
\(864\) 0 0
\(865\) −69.1953 −2.35271
\(866\) 18.1129 0.615502
\(867\) 0 0
\(868\) 12.6782 0.430327
\(869\) −48.4803 −1.64458
\(870\) 0 0
\(871\) −33.0724 −1.12061
\(872\) −19.8234 −0.671305
\(873\) 0 0
\(874\) −7.57779 −0.256323
\(875\) −19.6076 −0.662859
\(876\) 0 0
\(877\) 27.9275 0.943044 0.471522 0.881854i \(-0.343705\pi\)
0.471522 + 0.881854i \(0.343705\pi\)
\(878\) 4.42989 0.149502
\(879\) 0 0
\(880\) −8.88719 −0.299587
\(881\) −37.2411 −1.25468 −0.627342 0.778744i \(-0.715857\pi\)
−0.627342 + 0.778744i \(0.715857\pi\)
\(882\) 0 0
\(883\) 19.0955 0.642616 0.321308 0.946975i \(-0.395878\pi\)
0.321308 + 0.946975i \(0.395878\pi\)
\(884\) −1.86522 −0.0627343
\(885\) 0 0
\(886\) 22.6132 0.759705
\(887\) 46.8091 1.57169 0.785847 0.618420i \(-0.212227\pi\)
0.785847 + 0.618420i \(0.212227\pi\)
\(888\) 0 0
\(889\) 10.8833 0.365015
\(890\) 44.4113 1.48867
\(891\) 0 0
\(892\) 23.1746 0.775945
\(893\) 30.9767 1.03660
\(894\) 0 0
\(895\) −21.6685 −0.724299
\(896\) −2.79628 −0.0934173
\(897\) 0 0
\(898\) −23.4810 −0.783573
\(899\) 14.6035 0.487055
\(900\) 0 0
\(901\) −5.68866 −0.189517
\(902\) 26.4111 0.879392
\(903\) 0 0
\(904\) −11.3336 −0.376950
\(905\) −14.7572 −0.490545
\(906\) 0 0
\(907\) −21.2858 −0.706784 −0.353392 0.935475i \(-0.614972\pi\)
−0.353392 + 0.935475i \(0.614972\pi\)
\(908\) 11.7427 0.389694
\(909\) 0 0
\(910\) −22.2172 −0.736493
\(911\) −44.5040 −1.47448 −0.737241 0.675629i \(-0.763872\pi\)
−0.737241 + 0.675629i \(0.763872\pi\)
\(912\) 0 0
\(913\) 17.1583 0.567857
\(914\) −10.3125 −0.341108
\(915\) 0 0
\(916\) −13.1092 −0.433140
\(917\) −3.85762 −0.127390
\(918\) 0 0
\(919\) −35.3524 −1.16617 −0.583083 0.812412i \(-0.698154\pi\)
−0.583083 + 0.812412i \(0.698154\pi\)
\(920\) 3.61944 0.119329
\(921\) 0 0
\(922\) −28.1519 −0.927132
\(923\) 48.4794 1.59572
\(924\) 0 0
\(925\) 8.06698 0.265241
\(926\) 23.6846 0.778323
\(927\) 0 0
\(928\) −3.22092 −0.105732
\(929\) 44.0940 1.44668 0.723338 0.690494i \(-0.242607\pi\)
0.723338 + 0.690494i \(0.242607\pi\)
\(930\) 0 0
\(931\) 4.67413 0.153188
\(932\) −4.00233 −0.131101
\(933\) 0 0
\(934\) −17.9826 −0.588407
\(935\) −5.68584 −0.185947
\(936\) 0 0
\(937\) 5.16133 0.168613 0.0843066 0.996440i \(-0.473132\pi\)
0.0843066 + 0.996440i \(0.473132\pi\)
\(938\) −31.7209 −1.03572
\(939\) 0 0
\(940\) −14.7956 −0.482581
\(941\) −25.8702 −0.843344 −0.421672 0.906748i \(-0.638557\pi\)
−0.421672 + 0.906748i \(0.638557\pi\)
\(942\) 0 0
\(943\) −10.7563 −0.350273
\(944\) 0.723299 0.0235414
\(945\) 0 0
\(946\) 38.7455 1.25972
\(947\) 14.1037 0.458308 0.229154 0.973390i \(-0.426404\pi\)
0.229154 + 0.973390i \(0.426404\pi\)
\(948\) 0 0
\(949\) 42.3594 1.37504
\(950\) 13.8478 0.449284
\(951\) 0 0
\(952\) −1.78900 −0.0579820
\(953\) 12.3360 0.399603 0.199801 0.979836i \(-0.435970\pi\)
0.199801 + 0.979836i \(0.435970\pi\)
\(954\) 0 0
\(955\) −22.4770 −0.727340
\(956\) 22.3878 0.724074
\(957\) 0 0
\(958\) −8.58630 −0.277411
\(959\) −43.5573 −1.40654
\(960\) 0 0
\(961\) −10.4432 −0.336878
\(962\) −9.69033 −0.312429
\(963\) 0 0
\(964\) −22.8159 −0.734852
\(965\) −10.7651 −0.346541
\(966\) 0 0
\(967\) −16.0689 −0.516740 −0.258370 0.966046i \(-0.583185\pi\)
−0.258370 + 0.966046i \(0.583185\pi\)
\(968\) −0.365561 −0.0117496
\(969\) 0 0
\(970\) 43.7576 1.40497
\(971\) 51.5433 1.65410 0.827051 0.562126i \(-0.190017\pi\)
0.827051 + 0.562126i \(0.190017\pi\)
\(972\) 0 0
\(973\) 10.3991 0.333378
\(974\) −4.72199 −0.151302
\(975\) 0 0
\(976\) 3.58006 0.114595
\(977\) 47.6254 1.52367 0.761836 0.647770i \(-0.224298\pi\)
0.761836 + 0.647770i \(0.224298\pi\)
\(978\) 0 0
\(979\) −53.1427 −1.69845
\(980\) −2.23254 −0.0713158
\(981\) 0 0
\(982\) −2.83154 −0.0903582
\(983\) −24.2854 −0.774585 −0.387293 0.921957i \(-0.626590\pi\)
−0.387293 + 0.921957i \(0.626590\pi\)
\(984\) 0 0
\(985\) −49.4829 −1.57666
\(986\) −2.06068 −0.0656253
\(987\) 0 0
\(988\) −16.6345 −0.529214
\(989\) −15.7796 −0.501764
\(990\) 0 0
\(991\) 16.8119 0.534048 0.267024 0.963690i \(-0.413960\pi\)
0.267024 + 0.963690i \(0.413960\pi\)
\(992\) −4.53396 −0.143953
\(993\) 0 0
\(994\) 46.4983 1.47484
\(995\) 21.8901 0.693962
\(996\) 0 0
\(997\) 33.9833 1.07626 0.538132 0.842861i \(-0.319130\pi\)
0.538132 + 0.842861i \(0.319130\pi\)
\(998\) −35.6782 −1.12937
\(999\) 0 0
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 \(a_p\))