Properties

Label 8008.2.a.v.1.6
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 11
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{4} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.447939\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.447939 q^{3} +3.28103 q^{5} -1.00000 q^{7} -2.79935 q^{9} +O(q^{10})\) \(q-0.447939 q^{3} +3.28103 q^{5} -1.00000 q^{7} -2.79935 q^{9} +1.00000 q^{11} -1.00000 q^{13} -1.46970 q^{15} +4.02477 q^{17} +1.40652 q^{19} +0.447939 q^{21} -4.52401 q^{23} +5.76518 q^{25} +2.59776 q^{27} -1.61567 q^{29} -2.93017 q^{31} -0.447939 q^{33} -3.28103 q^{35} -11.8490 q^{37} +0.447939 q^{39} -6.65896 q^{41} -3.31326 q^{43} -9.18476 q^{45} -4.52401 q^{47} +1.00000 q^{49} -1.80285 q^{51} +10.5741 q^{53} +3.28103 q^{55} -0.630036 q^{57} -5.53810 q^{59} +10.3262 q^{61} +2.79935 q^{63} -3.28103 q^{65} +4.73986 q^{67} +2.02648 q^{69} -9.78183 q^{71} -4.97428 q^{73} -2.58245 q^{75} -1.00000 q^{77} -0.859419 q^{79} +7.23441 q^{81} -17.7747 q^{83} +13.2054 q^{85} +0.723722 q^{87} +3.79972 q^{89} +1.00000 q^{91} +1.31254 q^{93} +4.61484 q^{95} -18.7636 q^{97} -2.79935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.447939 −0.258618 −0.129309 0.991604i \(-0.541276\pi\)
−0.129309 + 0.991604i \(0.541276\pi\)
\(4\) 0 0
\(5\) 3.28103 1.46732 0.733661 0.679515i \(-0.237810\pi\)
0.733661 + 0.679515i \(0.237810\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.79935 −0.933117
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.46970 −0.379476
\(16\) 0 0
\(17\) 4.02477 0.976150 0.488075 0.872802i \(-0.337699\pi\)
0.488075 + 0.872802i \(0.337699\pi\)
\(18\) 0 0
\(19\) 1.40652 0.322678 0.161339 0.986899i \(-0.448419\pi\)
0.161339 + 0.986899i \(0.448419\pi\)
\(20\) 0 0
\(21\) 0.447939 0.0977484
\(22\) 0 0
\(23\) −4.52401 −0.943320 −0.471660 0.881780i \(-0.656345\pi\)
−0.471660 + 0.881780i \(0.656345\pi\)
\(24\) 0 0
\(25\) 5.76518 1.15304
\(26\) 0 0
\(27\) 2.59776 0.499939
\(28\) 0 0
\(29\) −1.61567 −0.300022 −0.150011 0.988684i \(-0.547931\pi\)
−0.150011 + 0.988684i \(0.547931\pi\)
\(30\) 0 0
\(31\) −2.93017 −0.526274 −0.263137 0.964758i \(-0.584757\pi\)
−0.263137 + 0.964758i \(0.584757\pi\)
\(32\) 0 0
\(33\) −0.447939 −0.0779762
\(34\) 0 0
\(35\) −3.28103 −0.554596
\(36\) 0 0
\(37\) −11.8490 −1.94796 −0.973982 0.226623i \(-0.927231\pi\)
−0.973982 + 0.226623i \(0.927231\pi\)
\(38\) 0 0
\(39\) 0.447939 0.0717277
\(40\) 0 0
\(41\) −6.65896 −1.03995 −0.519977 0.854180i \(-0.674060\pi\)
−0.519977 + 0.854180i \(0.674060\pi\)
\(42\) 0 0
\(43\) −3.31326 −0.505268 −0.252634 0.967562i \(-0.581297\pi\)
−0.252634 + 0.967562i \(0.581297\pi\)
\(44\) 0 0
\(45\) −9.18476 −1.36918
\(46\) 0 0
\(47\) −4.52401 −0.659894 −0.329947 0.943999i \(-0.607031\pi\)
−0.329947 + 0.943999i \(0.607031\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.80285 −0.252450
\(52\) 0 0
\(53\) 10.5741 1.45247 0.726233 0.687448i \(-0.241269\pi\)
0.726233 + 0.687448i \(0.241269\pi\)
\(54\) 0 0
\(55\) 3.28103 0.442415
\(56\) 0 0
\(57\) −0.630036 −0.0834503
\(58\) 0 0
\(59\) −5.53810 −0.720999 −0.360499 0.932759i \(-0.617394\pi\)
−0.360499 + 0.932759i \(0.617394\pi\)
\(60\) 0 0
\(61\) 10.3262 1.32213 0.661065 0.750329i \(-0.270105\pi\)
0.661065 + 0.750329i \(0.270105\pi\)
\(62\) 0 0
\(63\) 2.79935 0.352685
\(64\) 0 0
\(65\) −3.28103 −0.406962
\(66\) 0 0
\(67\) 4.73986 0.579066 0.289533 0.957168i \(-0.406500\pi\)
0.289533 + 0.957168i \(0.406500\pi\)
\(68\) 0 0
\(69\) 2.02648 0.243960
\(70\) 0 0
\(71\) −9.78183 −1.16089 −0.580445 0.814300i \(-0.697121\pi\)
−0.580445 + 0.814300i \(0.697121\pi\)
\(72\) 0 0
\(73\) −4.97428 −0.582196 −0.291098 0.956693i \(-0.594021\pi\)
−0.291098 + 0.956693i \(0.594021\pi\)
\(74\) 0 0
\(75\) −2.58245 −0.298196
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −0.859419 −0.0966922 −0.0483461 0.998831i \(-0.515395\pi\)
−0.0483461 + 0.998831i \(0.515395\pi\)
\(80\) 0 0
\(81\) 7.23441 0.803824
\(82\) 0 0
\(83\) −17.7747 −1.95103 −0.975513 0.219942i \(-0.929413\pi\)
−0.975513 + 0.219942i \(0.929413\pi\)
\(84\) 0 0
\(85\) 13.2054 1.43233
\(86\) 0 0
\(87\) 0.723722 0.0775911
\(88\) 0 0
\(89\) 3.79972 0.402769 0.201385 0.979512i \(-0.435456\pi\)
0.201385 + 0.979512i \(0.435456\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 1.31254 0.136104
\(94\) 0 0
\(95\) 4.61484 0.473473
\(96\) 0 0
\(97\) −18.7636 −1.90516 −0.952578 0.304294i \(-0.901579\pi\)
−0.952578 + 0.304294i \(0.901579\pi\)
\(98\) 0 0
\(99\) −2.79935 −0.281345
\(100\) 0 0
\(101\) 13.4588 1.33920 0.669599 0.742722i \(-0.266466\pi\)
0.669599 + 0.742722i \(0.266466\pi\)
\(102\) 0 0
\(103\) 5.80963 0.572440 0.286220 0.958164i \(-0.407601\pi\)
0.286220 + 0.958164i \(0.407601\pi\)
\(104\) 0 0
\(105\) 1.46970 0.143428
\(106\) 0 0
\(107\) 4.92441 0.476061 0.238031 0.971258i \(-0.423498\pi\)
0.238031 + 0.971258i \(0.423498\pi\)
\(108\) 0 0
\(109\) −7.40719 −0.709480 −0.354740 0.934965i \(-0.615431\pi\)
−0.354740 + 0.934965i \(0.615431\pi\)
\(110\) 0 0
\(111\) 5.30764 0.503779
\(112\) 0 0
\(113\) 11.9253 1.12184 0.560921 0.827869i \(-0.310447\pi\)
0.560921 + 0.827869i \(0.310447\pi\)
\(114\) 0 0
\(115\) −14.8434 −1.38416
\(116\) 0 0
\(117\) 2.79935 0.258800
\(118\) 0 0
\(119\) −4.02477 −0.368950
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 2.98281 0.268951
\(124\) 0 0
\(125\) 2.51059 0.224554
\(126\) 0 0
\(127\) −6.98619 −0.619925 −0.309962 0.950749i \(-0.600316\pi\)
−0.309962 + 0.950749i \(0.600316\pi\)
\(128\) 0 0
\(129\) 1.48414 0.130671
\(130\) 0 0
\(131\) −5.64597 −0.493291 −0.246645 0.969106i \(-0.579328\pi\)
−0.246645 + 0.969106i \(0.579328\pi\)
\(132\) 0 0
\(133\) −1.40652 −0.121961
\(134\) 0 0
\(135\) 8.52333 0.733571
\(136\) 0 0
\(137\) −7.78732 −0.665315 −0.332658 0.943048i \(-0.607945\pi\)
−0.332658 + 0.943048i \(0.607945\pi\)
\(138\) 0 0
\(139\) −10.3891 −0.881191 −0.440596 0.897706i \(-0.645233\pi\)
−0.440596 + 0.897706i \(0.645233\pi\)
\(140\) 0 0
\(141\) 2.02648 0.170660
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −5.30107 −0.440230
\(146\) 0 0
\(147\) −0.447939 −0.0369454
\(148\) 0 0
\(149\) 4.17537 0.342060 0.171030 0.985266i \(-0.445291\pi\)
0.171030 + 0.985266i \(0.445291\pi\)
\(150\) 0 0
\(151\) 14.5117 1.18095 0.590474 0.807057i \(-0.298941\pi\)
0.590474 + 0.807057i \(0.298941\pi\)
\(152\) 0 0
\(153\) −11.2667 −0.910862
\(154\) 0 0
\(155\) −9.61399 −0.772214
\(156\) 0 0
\(157\) −0.900121 −0.0718375 −0.0359187 0.999355i \(-0.511436\pi\)
−0.0359187 + 0.999355i \(0.511436\pi\)
\(158\) 0 0
\(159\) −4.73656 −0.375634
\(160\) 0 0
\(161\) 4.52401 0.356542
\(162\) 0 0
\(163\) −11.2253 −0.879237 −0.439618 0.898185i \(-0.644886\pi\)
−0.439618 + 0.898185i \(0.644886\pi\)
\(164\) 0 0
\(165\) −1.46970 −0.114416
\(166\) 0 0
\(167\) −19.0047 −1.47062 −0.735312 0.677729i \(-0.762964\pi\)
−0.735312 + 0.677729i \(0.762964\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −3.93734 −0.301096
\(172\) 0 0
\(173\) −2.55089 −0.193940 −0.0969702 0.995287i \(-0.530915\pi\)
−0.0969702 + 0.995287i \(0.530915\pi\)
\(174\) 0 0
\(175\) −5.76518 −0.435807
\(176\) 0 0
\(177\) 2.48073 0.186463
\(178\) 0 0
\(179\) 10.4286 0.779472 0.389736 0.920927i \(-0.372566\pi\)
0.389736 + 0.920927i \(0.372566\pi\)
\(180\) 0 0
\(181\) 18.6854 1.38887 0.694436 0.719554i \(-0.255654\pi\)
0.694436 + 0.719554i \(0.255654\pi\)
\(182\) 0 0
\(183\) −4.62549 −0.341926
\(184\) 0 0
\(185\) −38.8770 −2.85829
\(186\) 0 0
\(187\) 4.02477 0.294320
\(188\) 0 0
\(189\) −2.59776 −0.188959
\(190\) 0 0
\(191\) −10.4631 −0.757080 −0.378540 0.925585i \(-0.623574\pi\)
−0.378540 + 0.925585i \(0.623574\pi\)
\(192\) 0 0
\(193\) −14.8324 −1.06766 −0.533828 0.845593i \(-0.679247\pi\)
−0.533828 + 0.845593i \(0.679247\pi\)
\(194\) 0 0
\(195\) 1.46970 0.105248
\(196\) 0 0
\(197\) 5.00417 0.356532 0.178266 0.983982i \(-0.442951\pi\)
0.178266 + 0.983982i \(0.442951\pi\)
\(198\) 0 0
\(199\) −21.8705 −1.55036 −0.775178 0.631742i \(-0.782340\pi\)
−0.775178 + 0.631742i \(0.782340\pi\)
\(200\) 0 0
\(201\) −2.12317 −0.149757
\(202\) 0 0
\(203\) 1.61567 0.113398
\(204\) 0 0
\(205\) −21.8483 −1.52595
\(206\) 0 0
\(207\) 12.6643 0.880228
\(208\) 0 0
\(209\) 1.40652 0.0972911
\(210\) 0 0
\(211\) −21.2994 −1.46631 −0.733156 0.680061i \(-0.761953\pi\)
−0.733156 + 0.680061i \(0.761953\pi\)
\(212\) 0 0
\(213\) 4.38167 0.300227
\(214\) 0 0
\(215\) −10.8709 −0.741392
\(216\) 0 0
\(217\) 2.93017 0.198913
\(218\) 0 0
\(219\) 2.22818 0.150566
\(220\) 0 0
\(221\) −4.02477 −0.270735
\(222\) 0 0
\(223\) 14.0607 0.941577 0.470788 0.882246i \(-0.343970\pi\)
0.470788 + 0.882246i \(0.343970\pi\)
\(224\) 0 0
\(225\) −16.1388 −1.07592
\(226\) 0 0
\(227\) 16.6931 1.10796 0.553980 0.832530i \(-0.313108\pi\)
0.553980 + 0.832530i \(0.313108\pi\)
\(228\) 0 0
\(229\) −20.4263 −1.34981 −0.674905 0.737905i \(-0.735815\pi\)
−0.674905 + 0.737905i \(0.735815\pi\)
\(230\) 0 0
\(231\) 0.447939 0.0294722
\(232\) 0 0
\(233\) 10.3057 0.675150 0.337575 0.941299i \(-0.390393\pi\)
0.337575 + 0.941299i \(0.390393\pi\)
\(234\) 0 0
\(235\) −14.8434 −0.968278
\(236\) 0 0
\(237\) 0.384968 0.0250063
\(238\) 0 0
\(239\) 5.58873 0.361505 0.180752 0.983529i \(-0.442147\pi\)
0.180752 + 0.983529i \(0.442147\pi\)
\(240\) 0 0
\(241\) −11.2193 −0.722701 −0.361350 0.932430i \(-0.617684\pi\)
−0.361350 + 0.932430i \(0.617684\pi\)
\(242\) 0 0
\(243\) −11.0339 −0.707822
\(244\) 0 0
\(245\) 3.28103 0.209618
\(246\) 0 0
\(247\) −1.40652 −0.0894948
\(248\) 0 0
\(249\) 7.96198 0.504570
\(250\) 0 0
\(251\) −1.01675 −0.0641770 −0.0320885 0.999485i \(-0.510216\pi\)
−0.0320885 + 0.999485i \(0.510216\pi\)
\(252\) 0 0
\(253\) −4.52401 −0.284422
\(254\) 0 0
\(255\) −5.91522 −0.370426
\(256\) 0 0
\(257\) −5.19821 −0.324256 −0.162128 0.986770i \(-0.551836\pi\)
−0.162128 + 0.986770i \(0.551836\pi\)
\(258\) 0 0
\(259\) 11.8490 0.736262
\(260\) 0 0
\(261\) 4.52283 0.279956
\(262\) 0 0
\(263\) −19.0413 −1.17413 −0.587067 0.809538i \(-0.699718\pi\)
−0.587067 + 0.809538i \(0.699718\pi\)
\(264\) 0 0
\(265\) 34.6940 2.13124
\(266\) 0 0
\(267\) −1.70204 −0.104163
\(268\) 0 0
\(269\) 25.7218 1.56829 0.784143 0.620580i \(-0.213103\pi\)
0.784143 + 0.620580i \(0.213103\pi\)
\(270\) 0 0
\(271\) −15.5256 −0.943113 −0.471557 0.881836i \(-0.656308\pi\)
−0.471557 + 0.881836i \(0.656308\pi\)
\(272\) 0 0
\(273\) −0.447939 −0.0271105
\(274\) 0 0
\(275\) 5.76518 0.347654
\(276\) 0 0
\(277\) 0.194004 0.0116566 0.00582829 0.999983i \(-0.498145\pi\)
0.00582829 + 0.999983i \(0.498145\pi\)
\(278\) 0 0
\(279\) 8.20257 0.491075
\(280\) 0 0
\(281\) 16.7248 0.997719 0.498859 0.866683i \(-0.333752\pi\)
0.498859 + 0.866683i \(0.333752\pi\)
\(282\) 0 0
\(283\) −8.74211 −0.519665 −0.259832 0.965654i \(-0.583667\pi\)
−0.259832 + 0.965654i \(0.583667\pi\)
\(284\) 0 0
\(285\) −2.06717 −0.122449
\(286\) 0 0
\(287\) 6.65896 0.393066
\(288\) 0 0
\(289\) −0.801224 −0.0471308
\(290\) 0 0
\(291\) 8.40496 0.492708
\(292\) 0 0
\(293\) 0.773173 0.0451693 0.0225846 0.999745i \(-0.492810\pi\)
0.0225846 + 0.999745i \(0.492810\pi\)
\(294\) 0 0
\(295\) −18.1707 −1.05794
\(296\) 0 0
\(297\) 2.59776 0.150737
\(298\) 0 0
\(299\) 4.52401 0.261630
\(300\) 0 0
\(301\) 3.31326 0.190973
\(302\) 0 0
\(303\) −6.02872 −0.346341
\(304\) 0 0
\(305\) 33.8805 1.93999
\(306\) 0 0
\(307\) 13.9348 0.795299 0.397650 0.917537i \(-0.369826\pi\)
0.397650 + 0.917537i \(0.369826\pi\)
\(308\) 0 0
\(309\) −2.60236 −0.148043
\(310\) 0 0
\(311\) −8.59928 −0.487620 −0.243810 0.969823i \(-0.578397\pi\)
−0.243810 + 0.969823i \(0.578397\pi\)
\(312\) 0 0
\(313\) 16.8743 0.953792 0.476896 0.878960i \(-0.341762\pi\)
0.476896 + 0.878960i \(0.341762\pi\)
\(314\) 0 0
\(315\) 9.18476 0.517503
\(316\) 0 0
\(317\) 10.8781 0.610976 0.305488 0.952196i \(-0.401180\pi\)
0.305488 + 0.952196i \(0.401180\pi\)
\(318\) 0 0
\(319\) −1.61567 −0.0904601
\(320\) 0 0
\(321\) −2.20584 −0.123118
\(322\) 0 0
\(323\) 5.66092 0.314982
\(324\) 0 0
\(325\) −5.76518 −0.319795
\(326\) 0 0
\(327\) 3.31797 0.183484
\(328\) 0 0
\(329\) 4.52401 0.249416
\(330\) 0 0
\(331\) −0.857840 −0.0471511 −0.0235756 0.999722i \(-0.507505\pi\)
−0.0235756 + 0.999722i \(0.507505\pi\)
\(332\) 0 0
\(333\) 33.1695 1.81768
\(334\) 0 0
\(335\) 15.5517 0.849677
\(336\) 0 0
\(337\) 20.4394 1.11340 0.556701 0.830713i \(-0.312067\pi\)
0.556701 + 0.830713i \(0.312067\pi\)
\(338\) 0 0
\(339\) −5.34183 −0.290129
\(340\) 0 0
\(341\) −2.93017 −0.158678
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 6.64895 0.357967
\(346\) 0 0
\(347\) −23.0289 −1.23626 −0.618129 0.786077i \(-0.712109\pi\)
−0.618129 + 0.786077i \(0.712109\pi\)
\(348\) 0 0
\(349\) −22.0666 −1.18120 −0.590598 0.806966i \(-0.701108\pi\)
−0.590598 + 0.806966i \(0.701108\pi\)
\(350\) 0 0
\(351\) −2.59776 −0.138658
\(352\) 0 0
\(353\) −13.7935 −0.734153 −0.367076 0.930191i \(-0.619641\pi\)
−0.367076 + 0.930191i \(0.619641\pi\)
\(354\) 0 0
\(355\) −32.0945 −1.70340
\(356\) 0 0
\(357\) 1.80285 0.0954171
\(358\) 0 0
\(359\) 0.247233 0.0130484 0.00652422 0.999979i \(-0.497923\pi\)
0.00652422 + 0.999979i \(0.497923\pi\)
\(360\) 0 0
\(361\) −17.0217 −0.895879
\(362\) 0 0
\(363\) −0.447939 −0.0235107
\(364\) 0 0
\(365\) −16.3208 −0.854270
\(366\) 0 0
\(367\) −13.5596 −0.707806 −0.353903 0.935282i \(-0.615146\pi\)
−0.353903 + 0.935282i \(0.615146\pi\)
\(368\) 0 0
\(369\) 18.6408 0.970399
\(370\) 0 0
\(371\) −10.5741 −0.548981
\(372\) 0 0
\(373\) 38.4069 1.98864 0.994318 0.106455i \(-0.0339499\pi\)
0.994318 + 0.106455i \(0.0339499\pi\)
\(374\) 0 0
\(375\) −1.12459 −0.0580738
\(376\) 0 0
\(377\) 1.61567 0.0832112
\(378\) 0 0
\(379\) 20.1382 1.03443 0.517215 0.855855i \(-0.326969\pi\)
0.517215 + 0.855855i \(0.326969\pi\)
\(380\) 0 0
\(381\) 3.12939 0.160324
\(382\) 0 0
\(383\) 9.70876 0.496094 0.248047 0.968748i \(-0.420211\pi\)
0.248047 + 0.968748i \(0.420211\pi\)
\(384\) 0 0
\(385\) −3.28103 −0.167217
\(386\) 0 0
\(387\) 9.27499 0.471474
\(388\) 0 0
\(389\) 13.9463 0.707104 0.353552 0.935415i \(-0.384974\pi\)
0.353552 + 0.935415i \(0.384974\pi\)
\(390\) 0 0
\(391\) −18.2081 −0.920822
\(392\) 0 0
\(393\) 2.52905 0.127574
\(394\) 0 0
\(395\) −2.81978 −0.141879
\(396\) 0 0
\(397\) −14.1889 −0.712121 −0.356060 0.934463i \(-0.615880\pi\)
−0.356060 + 0.934463i \(0.615880\pi\)
\(398\) 0 0
\(399\) 0.630036 0.0315412
\(400\) 0 0
\(401\) −27.7777 −1.38715 −0.693576 0.720384i \(-0.743966\pi\)
−0.693576 + 0.720384i \(0.743966\pi\)
\(402\) 0 0
\(403\) 2.93017 0.145962
\(404\) 0 0
\(405\) 23.7364 1.17947
\(406\) 0 0
\(407\) −11.8490 −0.587334
\(408\) 0 0
\(409\) −35.7851 −1.76946 −0.884729 0.466106i \(-0.845656\pi\)
−0.884729 + 0.466106i \(0.845656\pi\)
\(410\) 0 0
\(411\) 3.48825 0.172062
\(412\) 0 0
\(413\) 5.53810 0.272512
\(414\) 0 0
\(415\) −58.3194 −2.86279
\(416\) 0 0
\(417\) 4.65368 0.227892
\(418\) 0 0
\(419\) −2.62309 −0.128146 −0.0640731 0.997945i \(-0.520409\pi\)
−0.0640731 + 0.997945i \(0.520409\pi\)
\(420\) 0 0
\(421\) −0.181796 −0.00886017 −0.00443009 0.999990i \(-0.501410\pi\)
−0.00443009 + 0.999990i \(0.501410\pi\)
\(422\) 0 0
\(423\) 12.6643 0.615758
\(424\) 0 0
\(425\) 23.2035 1.12554
\(426\) 0 0
\(427\) −10.3262 −0.499718
\(428\) 0 0
\(429\) 0.447939 0.0216267
\(430\) 0 0
\(431\) −36.7451 −1.76995 −0.884974 0.465641i \(-0.845824\pi\)
−0.884974 + 0.465641i \(0.845824\pi\)
\(432\) 0 0
\(433\) 3.97484 0.191019 0.0955093 0.995429i \(-0.469552\pi\)
0.0955093 + 0.995429i \(0.469552\pi\)
\(434\) 0 0
\(435\) 2.37456 0.113851
\(436\) 0 0
\(437\) −6.36311 −0.304389
\(438\) 0 0
\(439\) 1.86289 0.0889107 0.0444554 0.999011i \(-0.485845\pi\)
0.0444554 + 0.999011i \(0.485845\pi\)
\(440\) 0 0
\(441\) −2.79935 −0.133302
\(442\) 0 0
\(443\) 8.71373 0.414002 0.207001 0.978341i \(-0.433630\pi\)
0.207001 + 0.978341i \(0.433630\pi\)
\(444\) 0 0
\(445\) 12.4670 0.590993
\(446\) 0 0
\(447\) −1.87031 −0.0884628
\(448\) 0 0
\(449\) 21.7433 1.02613 0.513064 0.858350i \(-0.328510\pi\)
0.513064 + 0.858350i \(0.328510\pi\)
\(450\) 0 0
\(451\) −6.65896 −0.313558
\(452\) 0 0
\(453\) −6.50038 −0.305414
\(454\) 0 0
\(455\) 3.28103 0.153817
\(456\) 0 0
\(457\) −14.7921 −0.691947 −0.345974 0.938244i \(-0.612451\pi\)
−0.345974 + 0.938244i \(0.612451\pi\)
\(458\) 0 0
\(459\) 10.4554 0.488015
\(460\) 0 0
\(461\) 15.1545 0.705817 0.352908 0.935658i \(-0.385193\pi\)
0.352908 + 0.935658i \(0.385193\pi\)
\(462\) 0 0
\(463\) −20.1333 −0.935675 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(464\) 0 0
\(465\) 4.30648 0.199708
\(466\) 0 0
\(467\) 20.9108 0.967635 0.483817 0.875169i \(-0.339250\pi\)
0.483817 + 0.875169i \(0.339250\pi\)
\(468\) 0 0
\(469\) −4.73986 −0.218867
\(470\) 0 0
\(471\) 0.403200 0.0185785
\(472\) 0 0
\(473\) −3.31326 −0.152344
\(474\) 0 0
\(475\) 8.10885 0.372060
\(476\) 0 0
\(477\) −29.6007 −1.35532
\(478\) 0 0
\(479\) −19.4194 −0.887294 −0.443647 0.896202i \(-0.646316\pi\)
−0.443647 + 0.896202i \(0.646316\pi\)
\(480\) 0 0
\(481\) 11.8490 0.540268
\(482\) 0 0
\(483\) −2.02648 −0.0922080
\(484\) 0 0
\(485\) −61.5641 −2.79548
\(486\) 0 0
\(487\) −28.6495 −1.29823 −0.649116 0.760689i \(-0.724861\pi\)
−0.649116 + 0.760689i \(0.724861\pi\)
\(488\) 0 0
\(489\) 5.02827 0.227386
\(490\) 0 0
\(491\) 20.7493 0.936403 0.468201 0.883622i \(-0.344902\pi\)
0.468201 + 0.883622i \(0.344902\pi\)
\(492\) 0 0
\(493\) −6.50270 −0.292867
\(494\) 0 0
\(495\) −9.18476 −0.412824
\(496\) 0 0
\(497\) 9.78183 0.438775
\(498\) 0 0
\(499\) 8.45028 0.378287 0.189143 0.981950i \(-0.439429\pi\)
0.189143 + 0.981950i \(0.439429\pi\)
\(500\) 0 0
\(501\) 8.51293 0.380330
\(502\) 0 0
\(503\) 4.15294 0.185170 0.0925851 0.995705i \(-0.470487\pi\)
0.0925851 + 0.995705i \(0.470487\pi\)
\(504\) 0 0
\(505\) 44.1587 1.96504
\(506\) 0 0
\(507\) −0.447939 −0.0198937
\(508\) 0 0
\(509\) 29.4711 1.30628 0.653142 0.757236i \(-0.273451\pi\)
0.653142 + 0.757236i \(0.273451\pi\)
\(510\) 0 0
\(511\) 4.97428 0.220049
\(512\) 0 0
\(513\) 3.65380 0.161319
\(514\) 0 0
\(515\) 19.0616 0.839954
\(516\) 0 0
\(517\) −4.52401 −0.198966
\(518\) 0 0
\(519\) 1.14264 0.0501565
\(520\) 0 0
\(521\) −13.7754 −0.603510 −0.301755 0.953386i \(-0.597572\pi\)
−0.301755 + 0.953386i \(0.597572\pi\)
\(522\) 0 0
\(523\) 12.7796 0.558814 0.279407 0.960173i \(-0.409862\pi\)
0.279407 + 0.960173i \(0.409862\pi\)
\(524\) 0 0
\(525\) 2.58245 0.112707
\(526\) 0 0
\(527\) −11.7933 −0.513723
\(528\) 0 0
\(529\) −2.53338 −0.110147
\(530\) 0 0
\(531\) 15.5031 0.672776
\(532\) 0 0
\(533\) 6.65896 0.288431
\(534\) 0 0
\(535\) 16.1572 0.698535
\(536\) 0 0
\(537\) −4.67139 −0.201586
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 3.21818 0.138360 0.0691801 0.997604i \(-0.477962\pi\)
0.0691801 + 0.997604i \(0.477962\pi\)
\(542\) 0 0
\(543\) −8.36991 −0.359187
\(544\) 0 0
\(545\) −24.3033 −1.04104
\(546\) 0 0
\(547\) −5.59881 −0.239388 −0.119694 0.992811i \(-0.538191\pi\)
−0.119694 + 0.992811i \(0.538191\pi\)
\(548\) 0 0
\(549\) −28.9065 −1.23370
\(550\) 0 0
\(551\) −2.27247 −0.0968106
\(552\) 0 0
\(553\) 0.859419 0.0365462
\(554\) 0 0
\(555\) 17.4145 0.739206
\(556\) 0 0
\(557\) −34.1662 −1.44767 −0.723835 0.689973i \(-0.757622\pi\)
−0.723835 + 0.689973i \(0.757622\pi\)
\(558\) 0 0
\(559\) 3.31326 0.140136
\(560\) 0 0
\(561\) −1.80285 −0.0761165
\(562\) 0 0
\(563\) 12.0881 0.509453 0.254726 0.967013i \(-0.418015\pi\)
0.254726 + 0.967013i \(0.418015\pi\)
\(564\) 0 0
\(565\) 39.1275 1.64611
\(566\) 0 0
\(567\) −7.23441 −0.303817
\(568\) 0 0
\(569\) −17.7546 −0.744312 −0.372156 0.928170i \(-0.621381\pi\)
−0.372156 + 0.928170i \(0.621381\pi\)
\(570\) 0 0
\(571\) 30.4778 1.27546 0.637728 0.770261i \(-0.279874\pi\)
0.637728 + 0.770261i \(0.279874\pi\)
\(572\) 0 0
\(573\) 4.68681 0.195794
\(574\) 0 0
\(575\) −26.0817 −1.08768
\(576\) 0 0
\(577\) −18.5397 −0.771819 −0.385909 0.922537i \(-0.626112\pi\)
−0.385909 + 0.922537i \(0.626112\pi\)
\(578\) 0 0
\(579\) 6.64400 0.276115
\(580\) 0 0
\(581\) 17.7747 0.737418
\(582\) 0 0
\(583\) 10.5741 0.437935
\(584\) 0 0
\(585\) 9.18476 0.379743
\(586\) 0 0
\(587\) 12.1426 0.501180 0.250590 0.968093i \(-0.419375\pi\)
0.250590 + 0.968093i \(0.419375\pi\)
\(588\) 0 0
\(589\) −4.12134 −0.169817
\(590\) 0 0
\(591\) −2.24157 −0.0922057
\(592\) 0 0
\(593\) 0.323537 0.0132861 0.00664304 0.999978i \(-0.497885\pi\)
0.00664304 + 0.999978i \(0.497885\pi\)
\(594\) 0 0
\(595\) −13.2054 −0.541369
\(596\) 0 0
\(597\) 9.79665 0.400950
\(598\) 0 0
\(599\) −10.6184 −0.433854 −0.216927 0.976188i \(-0.569603\pi\)
−0.216927 + 0.976188i \(0.569603\pi\)
\(600\) 0 0
\(601\) −4.61907 −0.188416 −0.0942078 0.995553i \(-0.530032\pi\)
−0.0942078 + 0.995553i \(0.530032\pi\)
\(602\) 0 0
\(603\) −13.2685 −0.540337
\(604\) 0 0
\(605\) 3.28103 0.133393
\(606\) 0 0
\(607\) 1.96513 0.0797622 0.0398811 0.999204i \(-0.487302\pi\)
0.0398811 + 0.999204i \(0.487302\pi\)
\(608\) 0 0
\(609\) −0.723722 −0.0293267
\(610\) 0 0
\(611\) 4.52401 0.183022
\(612\) 0 0
\(613\) −1.23085 −0.0497136 −0.0248568 0.999691i \(-0.507913\pi\)
−0.0248568 + 0.999691i \(0.507913\pi\)
\(614\) 0 0
\(615\) 9.78670 0.394638
\(616\) 0 0
\(617\) 21.4707 0.864377 0.432188 0.901783i \(-0.357742\pi\)
0.432188 + 0.901783i \(0.357742\pi\)
\(618\) 0 0
\(619\) −7.78189 −0.312780 −0.156390 0.987695i \(-0.549986\pi\)
−0.156390 + 0.987695i \(0.549986\pi\)
\(620\) 0 0
\(621\) −11.7523 −0.471602
\(622\) 0 0
\(623\) −3.79972 −0.152232
\(624\) 0 0
\(625\) −20.5886 −0.823543
\(626\) 0 0
\(627\) −0.630036 −0.0251612
\(628\) 0 0
\(629\) −47.6895 −1.90151
\(630\) 0 0
\(631\) 40.4400 1.60989 0.804945 0.593350i \(-0.202195\pi\)
0.804945 + 0.593350i \(0.202195\pi\)
\(632\) 0 0
\(633\) 9.54084 0.379214
\(634\) 0 0
\(635\) −22.9219 −0.909630
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 27.3828 1.08325
\(640\) 0 0
\(641\) 4.68498 0.185045 0.0925227 0.995711i \(-0.470507\pi\)
0.0925227 + 0.995711i \(0.470507\pi\)
\(642\) 0 0
\(643\) 9.04913 0.356863 0.178431 0.983952i \(-0.442898\pi\)
0.178431 + 0.983952i \(0.442898\pi\)
\(644\) 0 0
\(645\) 4.86952 0.191737
\(646\) 0 0
\(647\) −22.4978 −0.884478 −0.442239 0.896897i \(-0.645816\pi\)
−0.442239 + 0.896897i \(0.645816\pi\)
\(648\) 0 0
\(649\) −5.53810 −0.217389
\(650\) 0 0
\(651\) −1.31254 −0.0514424
\(652\) 0 0
\(653\) 30.9847 1.21253 0.606263 0.795264i \(-0.292668\pi\)
0.606263 + 0.795264i \(0.292668\pi\)
\(654\) 0 0
\(655\) −18.5246 −0.723817
\(656\) 0 0
\(657\) 13.9248 0.543257
\(658\) 0 0
\(659\) −33.4325 −1.30235 −0.651173 0.758929i \(-0.725723\pi\)
−0.651173 + 0.758929i \(0.725723\pi\)
\(660\) 0 0
\(661\) −24.9115 −0.968945 −0.484472 0.874807i \(-0.660988\pi\)
−0.484472 + 0.874807i \(0.660988\pi\)
\(662\) 0 0
\(663\) 1.80285 0.0700170
\(664\) 0 0
\(665\) −4.61484 −0.178956
\(666\) 0 0
\(667\) 7.30930 0.283017
\(668\) 0 0
\(669\) −6.29836 −0.243509
\(670\) 0 0
\(671\) 10.3262 0.398637
\(672\) 0 0
\(673\) −19.4048 −0.747999 −0.373999 0.927429i \(-0.622014\pi\)
−0.373999 + 0.927429i \(0.622014\pi\)
\(674\) 0 0
\(675\) 14.9765 0.576448
\(676\) 0 0
\(677\) −21.8427 −0.839481 −0.419741 0.907644i \(-0.637879\pi\)
−0.419741 + 0.907644i \(0.637879\pi\)
\(678\) 0 0
\(679\) 18.7636 0.720081
\(680\) 0 0
\(681\) −7.47750 −0.286538
\(682\) 0 0
\(683\) −49.4004 −1.89025 −0.945126 0.326706i \(-0.894061\pi\)
−0.945126 + 0.326706i \(0.894061\pi\)
\(684\) 0 0
\(685\) −25.5504 −0.976232
\(686\) 0 0
\(687\) 9.14976 0.349085
\(688\) 0 0
\(689\) −10.5741 −0.402842
\(690\) 0 0
\(691\) −2.77894 −0.105716 −0.0528580 0.998602i \(-0.516833\pi\)
−0.0528580 + 0.998602i \(0.516833\pi\)
\(692\) 0 0
\(693\) 2.79935 0.106339
\(694\) 0 0
\(695\) −34.0870 −1.29299
\(696\) 0 0
\(697\) −26.8008 −1.01515
\(698\) 0 0
\(699\) −4.61634 −0.174606
\(700\) 0 0
\(701\) −23.2999 −0.880023 −0.440012 0.897992i \(-0.645026\pi\)
−0.440012 + 0.897992i \(0.645026\pi\)
\(702\) 0 0
\(703\) −16.6659 −0.628565
\(704\) 0 0
\(705\) 6.64895 0.250414
\(706\) 0 0
\(707\) −13.4588 −0.506170
\(708\) 0 0
\(709\) 16.6855 0.626639 0.313319 0.949648i \(-0.398559\pi\)
0.313319 + 0.949648i \(0.398559\pi\)
\(710\) 0 0
\(711\) 2.40582 0.0902251
\(712\) 0 0
\(713\) 13.2561 0.496445
\(714\) 0 0
\(715\) −3.28103 −0.122704
\(716\) 0 0
\(717\) −2.50341 −0.0934917
\(718\) 0 0
\(719\) 32.3650 1.20701 0.603506 0.797359i \(-0.293770\pi\)
0.603506 + 0.797359i \(0.293770\pi\)
\(720\) 0 0
\(721\) −5.80963 −0.216362
\(722\) 0 0
\(723\) 5.02558 0.186903
\(724\) 0 0
\(725\) −9.31463 −0.345937
\(726\) 0 0
\(727\) 13.4062 0.497208 0.248604 0.968605i \(-0.420028\pi\)
0.248604 + 0.968605i \(0.420028\pi\)
\(728\) 0 0
\(729\) −16.7607 −0.620768
\(730\) 0 0
\(731\) −13.3351 −0.493218
\(732\) 0 0
\(733\) −40.1158 −1.48171 −0.740856 0.671664i \(-0.765580\pi\)
−0.740856 + 0.671664i \(0.765580\pi\)
\(734\) 0 0
\(735\) −1.46970 −0.0542109
\(736\) 0 0
\(737\) 4.73986 0.174595
\(738\) 0 0
\(739\) −11.5972 −0.426609 −0.213304 0.976986i \(-0.568423\pi\)
−0.213304 + 0.976986i \(0.568423\pi\)
\(740\) 0 0
\(741\) 0.630036 0.0231449
\(742\) 0 0
\(743\) −19.8775 −0.729235 −0.364618 0.931157i \(-0.618800\pi\)
−0.364618 + 0.931157i \(0.618800\pi\)
\(744\) 0 0
\(745\) 13.6995 0.501912
\(746\) 0 0
\(747\) 49.7576 1.82053
\(748\) 0 0
\(749\) −4.92441 −0.179934
\(750\) 0 0
\(751\) 42.4212 1.54797 0.773986 0.633203i \(-0.218260\pi\)
0.773986 + 0.633203i \(0.218260\pi\)
\(752\) 0 0
\(753\) 0.455444 0.0165973
\(754\) 0 0
\(755\) 47.6135 1.73283
\(756\) 0 0
\(757\) 1.25244 0.0455207 0.0227603 0.999741i \(-0.492755\pi\)
0.0227603 + 0.999741i \(0.492755\pi\)
\(758\) 0 0
\(759\) 2.02648 0.0735566
\(760\) 0 0
\(761\) 3.53131 0.128010 0.0640050 0.997950i \(-0.479613\pi\)
0.0640050 + 0.997950i \(0.479613\pi\)
\(762\) 0 0
\(763\) 7.40719 0.268158
\(764\) 0 0
\(765\) −36.9666 −1.33653
\(766\) 0 0
\(767\) 5.53810 0.199969
\(768\) 0 0
\(769\) −4.82723 −0.174075 −0.0870373 0.996205i \(-0.527740\pi\)
−0.0870373 + 0.996205i \(0.527740\pi\)
\(770\) 0 0
\(771\) 2.32848 0.0838583
\(772\) 0 0
\(773\) 2.30903 0.0830502 0.0415251 0.999137i \(-0.486778\pi\)
0.0415251 + 0.999137i \(0.486778\pi\)
\(774\) 0 0
\(775\) −16.8930 −0.606813
\(776\) 0 0
\(777\) −5.30764 −0.190410
\(778\) 0 0
\(779\) −9.36596 −0.335570
\(780\) 0 0
\(781\) −9.78183 −0.350021
\(782\) 0 0
\(783\) −4.19712 −0.149993
\(784\) 0 0
\(785\) −2.95333 −0.105409
\(786\) 0 0
\(787\) −45.8744 −1.63524 −0.817622 0.575755i \(-0.804708\pi\)
−0.817622 + 0.575755i \(0.804708\pi\)
\(788\) 0 0
\(789\) 8.52933 0.303652
\(790\) 0 0
\(791\) −11.9253 −0.424017
\(792\) 0 0
\(793\) −10.3262 −0.366693
\(794\) 0 0
\(795\) −15.5408 −0.551176
\(796\) 0 0
\(797\) −41.1585 −1.45791 −0.728954 0.684563i \(-0.759993\pi\)
−0.728954 + 0.684563i \(0.759993\pi\)
\(798\) 0 0
\(799\) −18.2081 −0.644156
\(800\) 0 0
\(801\) −10.6367 −0.375831
\(802\) 0 0
\(803\) −4.97428 −0.175539
\(804\) 0 0
\(805\) 14.8434 0.523162
\(806\) 0 0
\(807\) −11.5218 −0.405587
\(808\) 0 0
\(809\) 11.2111 0.394163 0.197081 0.980387i \(-0.436854\pi\)
0.197081 + 0.980387i \(0.436854\pi\)
\(810\) 0 0
\(811\) −18.2886 −0.642201 −0.321100 0.947045i \(-0.604053\pi\)
−0.321100 + 0.947045i \(0.604053\pi\)
\(812\) 0 0
\(813\) 6.95453 0.243906
\(814\) 0 0
\(815\) −36.8307 −1.29012
\(816\) 0 0
\(817\) −4.66018 −0.163039
\(818\) 0 0
\(819\) −2.79935 −0.0978172
\(820\) 0 0
\(821\) −5.66576 −0.197736 −0.0988682 0.995101i \(-0.531522\pi\)
−0.0988682 + 0.995101i \(0.531522\pi\)
\(822\) 0 0
\(823\) 6.89165 0.240228 0.120114 0.992760i \(-0.461674\pi\)
0.120114 + 0.992760i \(0.461674\pi\)
\(824\) 0 0
\(825\) −2.58245 −0.0899095
\(826\) 0 0
\(827\) 25.2955 0.879609 0.439804 0.898094i \(-0.355048\pi\)
0.439804 + 0.898094i \(0.355048\pi\)
\(828\) 0 0
\(829\) −46.2104 −1.60495 −0.802477 0.596683i \(-0.796485\pi\)
−0.802477 + 0.596683i \(0.796485\pi\)
\(830\) 0 0
\(831\) −0.0869020 −0.00301460
\(832\) 0 0
\(833\) 4.02477 0.139450
\(834\) 0 0
\(835\) −62.3549 −2.15788
\(836\) 0 0
\(837\) −7.61187 −0.263105
\(838\) 0 0
\(839\) 46.6446 1.61035 0.805175 0.593037i \(-0.202071\pi\)
0.805175 + 0.593037i \(0.202071\pi\)
\(840\) 0 0
\(841\) −26.3896 −0.909987
\(842\) 0 0
\(843\) −7.49170 −0.258028
\(844\) 0 0
\(845\) 3.28103 0.112871
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 3.91594 0.134395
\(850\) 0 0
\(851\) 53.6050 1.83755
\(852\) 0 0
\(853\) 22.1666 0.758970 0.379485 0.925198i \(-0.376101\pi\)
0.379485 + 0.925198i \(0.376101\pi\)
\(854\) 0 0
\(855\) −12.9186 −0.441805
\(856\) 0 0
\(857\) 18.9996 0.649015 0.324507 0.945883i \(-0.394802\pi\)
0.324507 + 0.945883i \(0.394802\pi\)
\(858\) 0 0
\(859\) 0.272422 0.00929493 0.00464746 0.999989i \(-0.498521\pi\)
0.00464746 + 0.999989i \(0.498521\pi\)
\(860\) 0 0
\(861\) −2.98281 −0.101654
\(862\) 0 0
\(863\) 26.5519 0.903836 0.451918 0.892059i \(-0.350740\pi\)
0.451918 + 0.892059i \(0.350740\pi\)
\(864\) 0 0
\(865\) −8.36955 −0.284573
\(866\) 0 0
\(867\) 0.358900 0.0121889
\(868\) 0 0
\(869\) −0.859419 −0.0291538
\(870\) 0 0
\(871\) −4.73986 −0.160604
\(872\) 0 0
\(873\) 52.5259 1.77773
\(874\) 0 0
\(875\) −2.51059 −0.0848736
\(876\) 0 0
\(877\) 32.6734 1.10330 0.551650 0.834075i \(-0.313998\pi\)
0.551650 + 0.834075i \(0.313998\pi\)
\(878\) 0 0
\(879\) −0.346335 −0.0116816
\(880\) 0 0
\(881\) 38.8204 1.30789 0.653946 0.756541i \(-0.273112\pi\)
0.653946 + 0.756541i \(0.273112\pi\)
\(882\) 0 0
\(883\) 17.6060 0.592488 0.296244 0.955112i \(-0.404266\pi\)
0.296244 + 0.955112i \(0.404266\pi\)
\(884\) 0 0
\(885\) 8.13937 0.273602
\(886\) 0 0
\(887\) −23.5297 −0.790050 −0.395025 0.918670i \(-0.629264\pi\)
−0.395025 + 0.918670i \(0.629264\pi\)
\(888\) 0 0
\(889\) 6.98619 0.234309
\(890\) 0 0
\(891\) 7.23441 0.242362
\(892\) 0 0
\(893\) −6.36311 −0.212933
\(894\) 0 0
\(895\) 34.2167 1.14374
\(896\) 0 0
\(897\) −2.02648 −0.0676622
\(898\) 0 0
\(899\) 4.73419 0.157894
\(900\) 0 0
\(901\) 42.5584 1.41783
\(902\) 0 0
\(903\) −1.48414 −0.0493891
\(904\) 0 0
\(905\) 61.3073 2.03792
\(906\) 0 0
\(907\) −40.7665 −1.35363 −0.676815 0.736153i \(-0.736640\pi\)
−0.676815 + 0.736153i \(0.736640\pi\)
\(908\) 0 0
\(909\) −37.6758 −1.24963
\(910\) 0 0
\(911\) 5.29899 0.175563 0.0877817 0.996140i \(-0.472022\pi\)
0.0877817 + 0.996140i \(0.472022\pi\)
\(912\) 0 0
\(913\) −17.7747 −0.588256
\(914\) 0 0
\(915\) −15.1764 −0.501716
\(916\) 0 0
\(917\) 5.64597 0.186446
\(918\) 0 0
\(919\) −50.9761 −1.68155 −0.840773 0.541388i \(-0.817899\pi\)
−0.840773 + 0.541388i \(0.817899\pi\)
\(920\) 0 0
\(921\) −6.24193 −0.205679
\(922\) 0 0
\(923\) 9.78183 0.321973
\(924\) 0 0
\(925\) −68.3117 −2.24608
\(926\) 0 0
\(927\) −16.2632 −0.534153
\(928\) 0 0
\(929\) −0.932456 −0.0305929 −0.0152964 0.999883i \(-0.504869\pi\)
−0.0152964 + 0.999883i \(0.504869\pi\)
\(930\) 0 0
\(931\) 1.40652 0.0460969
\(932\) 0 0
\(933\) 3.85196 0.126107
\(934\) 0 0
\(935\) 13.2054 0.431863
\(936\) 0 0
\(937\) −19.1283 −0.624893 −0.312447 0.949935i \(-0.601149\pi\)
−0.312447 + 0.949935i \(0.601149\pi\)
\(938\) 0 0
\(939\) −7.55867 −0.246668
\(940\) 0 0
\(941\) 16.2679 0.530318 0.265159 0.964205i \(-0.414576\pi\)
0.265159 + 0.964205i \(0.414576\pi\)
\(942\) 0 0
\(943\) 30.1252 0.981010
\(944\) 0 0
\(945\) −8.52333 −0.277264
\(946\) 0 0
\(947\) −50.7920 −1.65052 −0.825259 0.564754i \(-0.808971\pi\)
−0.825259 + 0.564754i \(0.808971\pi\)
\(948\) 0 0
\(949\) 4.97428 0.161472
\(950\) 0 0
\(951\) −4.87274 −0.158009
\(952\) 0 0
\(953\) −29.3455 −0.950594 −0.475297 0.879825i \(-0.657659\pi\)
−0.475297 + 0.879825i \(0.657659\pi\)
\(954\) 0 0
\(955\) −34.3296 −1.11088
\(956\) 0 0
\(957\) 0.723722 0.0233946
\(958\) 0 0
\(959\) 7.78732 0.251466
\(960\) 0 0
\(961\) −22.4141 −0.723036
\(962\) 0 0
\(963\) −13.7852 −0.444221
\(964\) 0 0
\(965\) −48.6655 −1.56660
\(966\) 0 0
\(967\) −4.30901 −0.138568 −0.0692841 0.997597i \(-0.522072\pi\)
−0.0692841 + 0.997597i \(0.522072\pi\)
\(968\) 0 0
\(969\) −2.53575 −0.0814600
\(970\) 0 0
\(971\) 19.4778 0.625074 0.312537 0.949906i \(-0.398821\pi\)
0.312537 + 0.949906i \(0.398821\pi\)
\(972\) 0 0
\(973\) 10.3891 0.333059
\(974\) 0 0
\(975\) 2.58245 0.0827047
\(976\) 0 0
\(977\) 38.5692 1.23394 0.616968 0.786988i \(-0.288361\pi\)
0.616968 + 0.786988i \(0.288361\pi\)
\(978\) 0 0
\(979\) 3.79972 0.121439
\(980\) 0 0
\(981\) 20.7353 0.662028
\(982\) 0 0
\(983\) 13.8737 0.442502 0.221251 0.975217i \(-0.428986\pi\)
0.221251 + 0.975217i \(0.428986\pi\)
\(984\) 0 0
\(985\) 16.4189 0.523148
\(986\) 0 0
\(987\) −2.02648 −0.0645036
\(988\) 0 0
\(989\) 14.9892 0.476630
\(990\) 0 0
\(991\) 46.2789 1.47010 0.735048 0.678015i \(-0.237159\pi\)
0.735048 + 0.678015i \(0.237159\pi\)
\(992\) 0 0
\(993\) 0.384260 0.0121941
\(994\) 0 0
\(995\) −71.7578 −2.27487
\(996\) 0 0
\(997\) 44.6421 1.41383 0.706915 0.707298i \(-0.250086\pi\)
0.706915 + 0.707298i \(0.250086\pi\)
\(998\) 0 0
\(999\) −30.7808 −0.973863
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 \(a_p\))