Properties

Label 8016.2.a.bg.1.11
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.11
Root \(3.18209\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+3.18209 q^{5}\) \(+1.39408 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+3.18209 q^{5}\) \(+1.39408 q^{7}\) \(+1.00000 q^{9}\) \(+2.54587 q^{11}\) \(+5.18156 q^{13}\) \(-3.18209 q^{15}\) \(-2.90365 q^{17}\) \(-6.55969 q^{19}\) \(-1.39408 q^{21}\) \(-2.68375 q^{23}\) \(+5.12570 q^{25}\) \(-1.00000 q^{27}\) \(-3.50556 q^{29}\) \(-6.85751 q^{31}\) \(-2.54587 q^{33}\) \(+4.43609 q^{35}\) \(+4.23682 q^{37}\) \(-5.18156 q^{39}\) \(-1.88971 q^{41}\) \(+6.49527 q^{43}\) \(+3.18209 q^{45}\) \(+7.80101 q^{47}\) \(-5.05654 q^{49}\) \(+2.90365 q^{51}\) \(+10.5299 q^{53}\) \(+8.10120 q^{55}\) \(+6.55969 q^{57}\) \(-0.200385 q^{59}\) \(+11.8595 q^{61}\) \(+1.39408 q^{63}\) \(+16.4882 q^{65}\) \(+12.5383 q^{67}\) \(+2.68375 q^{69}\) \(+2.92956 q^{71}\) \(+14.6356 q^{73}\) \(-5.12570 q^{75}\) \(+3.54915 q^{77}\) \(-1.95847 q^{79}\) \(+1.00000 q^{81}\) \(+3.16521 q^{83}\) \(-9.23968 q^{85}\) \(+3.50556 q^{87}\) \(+8.01635 q^{89}\) \(+7.22351 q^{91}\) \(+6.85751 q^{93}\) \(-20.8735 q^{95}\) \(+2.21764 q^{97}\) \(+2.54587 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 3.18209 1.42307 0.711537 0.702648i \(-0.247999\pi\)
0.711537 + 0.702648i \(0.247999\pi\)
\(6\) 0 0
\(7\) 1.39408 0.526912 0.263456 0.964671i \(-0.415138\pi\)
0.263456 + 0.964671i \(0.415138\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.54587 0.767609 0.383805 0.923414i \(-0.374614\pi\)
0.383805 + 0.923414i \(0.374614\pi\)
\(12\) 0 0
\(13\) 5.18156 1.43711 0.718554 0.695471i \(-0.244804\pi\)
0.718554 + 0.695471i \(0.244804\pi\)
\(14\) 0 0
\(15\) −3.18209 −0.821612
\(16\) 0 0
\(17\) −2.90365 −0.704238 −0.352119 0.935955i \(-0.614539\pi\)
−0.352119 + 0.935955i \(0.614539\pi\)
\(18\) 0 0
\(19\) −6.55969 −1.50490 −0.752448 0.658651i \(-0.771127\pi\)
−0.752448 + 0.658651i \(0.771127\pi\)
\(20\) 0 0
\(21\) −1.39408 −0.304213
\(22\) 0 0
\(23\) −2.68375 −0.559601 −0.279801 0.960058i \(-0.590268\pi\)
−0.279801 + 0.960058i \(0.590268\pi\)
\(24\) 0 0
\(25\) 5.12570 1.02514
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.50556 −0.650965 −0.325483 0.945548i \(-0.605527\pi\)
−0.325483 + 0.945548i \(0.605527\pi\)
\(30\) 0 0
\(31\) −6.85751 −1.23165 −0.615823 0.787885i \(-0.711176\pi\)
−0.615823 + 0.787885i \(0.711176\pi\)
\(32\) 0 0
\(33\) −2.54587 −0.443179
\(34\) 0 0
\(35\) 4.43609 0.749835
\(36\) 0 0
\(37\) 4.23682 0.696530 0.348265 0.937396i \(-0.386771\pi\)
0.348265 + 0.937396i \(0.386771\pi\)
\(38\) 0 0
\(39\) −5.18156 −0.829714
\(40\) 0 0
\(41\) −1.88971 −0.295122 −0.147561 0.989053i \(-0.547142\pi\)
−0.147561 + 0.989053i \(0.547142\pi\)
\(42\) 0 0
\(43\) 6.49527 0.990520 0.495260 0.868745i \(-0.335073\pi\)
0.495260 + 0.868745i \(0.335073\pi\)
\(44\) 0 0
\(45\) 3.18209 0.474358
\(46\) 0 0
\(47\) 7.80101 1.13789 0.568947 0.822374i \(-0.307351\pi\)
0.568947 + 0.822374i \(0.307351\pi\)
\(48\) 0 0
\(49\) −5.05654 −0.722364
\(50\) 0 0
\(51\) 2.90365 0.406592
\(52\) 0 0
\(53\) 10.5299 1.44640 0.723199 0.690639i \(-0.242671\pi\)
0.723199 + 0.690639i \(0.242671\pi\)
\(54\) 0 0
\(55\) 8.10120 1.09237
\(56\) 0 0
\(57\) 6.55969 0.868852
\(58\) 0 0
\(59\) −0.200385 −0.0260879 −0.0130439 0.999915i \(-0.504152\pi\)
−0.0130439 + 0.999915i \(0.504152\pi\)
\(60\) 0 0
\(61\) 11.8595 1.51845 0.759226 0.650827i \(-0.225578\pi\)
0.759226 + 0.650827i \(0.225578\pi\)
\(62\) 0 0
\(63\) 1.39408 0.175637
\(64\) 0 0
\(65\) 16.4882 2.04511
\(66\) 0 0
\(67\) 12.5383 1.53180 0.765901 0.642959i \(-0.222293\pi\)
0.765901 + 0.642959i \(0.222293\pi\)
\(68\) 0 0
\(69\) 2.68375 0.323086
\(70\) 0 0
\(71\) 2.92956 0.347674 0.173837 0.984774i \(-0.444383\pi\)
0.173837 + 0.984774i \(0.444383\pi\)
\(72\) 0 0
\(73\) 14.6356 1.71297 0.856487 0.516169i \(-0.172642\pi\)
0.856487 + 0.516169i \(0.172642\pi\)
\(74\) 0 0
\(75\) −5.12570 −0.591865
\(76\) 0 0
\(77\) 3.54915 0.404463
\(78\) 0 0
\(79\) −1.95847 −0.220346 −0.110173 0.993912i \(-0.535140\pi\)
−0.110173 + 0.993912i \(0.535140\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.16521 0.347427 0.173714 0.984796i \(-0.444423\pi\)
0.173714 + 0.984796i \(0.444423\pi\)
\(84\) 0 0
\(85\) −9.23968 −1.00218
\(86\) 0 0
\(87\) 3.50556 0.375835
\(88\) 0 0
\(89\) 8.01635 0.849732 0.424866 0.905256i \(-0.360321\pi\)
0.424866 + 0.905256i \(0.360321\pi\)
\(90\) 0 0
\(91\) 7.22351 0.757230
\(92\) 0 0
\(93\) 6.85751 0.711091
\(94\) 0 0
\(95\) −20.8735 −2.14158
\(96\) 0 0
\(97\) 2.21764 0.225167 0.112584 0.993642i \(-0.464087\pi\)
0.112584 + 0.993642i \(0.464087\pi\)
\(98\) 0 0
\(99\) 2.54587 0.255870
\(100\) 0 0
\(101\) −1.57057 −0.156277 −0.0781386 0.996943i \(-0.524898\pi\)
−0.0781386 + 0.996943i \(0.524898\pi\)
\(102\) 0 0
\(103\) −8.64913 −0.852224 −0.426112 0.904670i \(-0.640117\pi\)
−0.426112 + 0.904670i \(0.640117\pi\)
\(104\) 0 0
\(105\) −4.43609 −0.432918
\(106\) 0 0
\(107\) −9.32081 −0.901077 −0.450538 0.892757i \(-0.648768\pi\)
−0.450538 + 0.892757i \(0.648768\pi\)
\(108\) 0 0
\(109\) −2.99664 −0.287026 −0.143513 0.989648i \(-0.545840\pi\)
−0.143513 + 0.989648i \(0.545840\pi\)
\(110\) 0 0
\(111\) −4.23682 −0.402142
\(112\) 0 0
\(113\) 13.8938 1.30702 0.653508 0.756920i \(-0.273297\pi\)
0.653508 + 0.756920i \(0.273297\pi\)
\(114\) 0 0
\(115\) −8.53995 −0.796354
\(116\) 0 0
\(117\) 5.18156 0.479036
\(118\) 0 0
\(119\) −4.04792 −0.371072
\(120\) 0 0
\(121\) −4.51854 −0.410776
\(122\) 0 0
\(123\) 1.88971 0.170389
\(124\) 0 0
\(125\) 0.400003 0.0357773
\(126\) 0 0
\(127\) 7.49924 0.665450 0.332725 0.943024i \(-0.392032\pi\)
0.332725 + 0.943024i \(0.392032\pi\)
\(128\) 0 0
\(129\) −6.49527 −0.571877
\(130\) 0 0
\(131\) −1.66672 −0.145622 −0.0728110 0.997346i \(-0.523197\pi\)
−0.0728110 + 0.997346i \(0.523197\pi\)
\(132\) 0 0
\(133\) −9.14473 −0.792948
\(134\) 0 0
\(135\) −3.18209 −0.273871
\(136\) 0 0
\(137\) −11.1564 −0.953152 −0.476576 0.879133i \(-0.658122\pi\)
−0.476576 + 0.879133i \(0.658122\pi\)
\(138\) 0 0
\(139\) 4.80521 0.407573 0.203786 0.979015i \(-0.434675\pi\)
0.203786 + 0.979015i \(0.434675\pi\)
\(140\) 0 0
\(141\) −7.80101 −0.656964
\(142\) 0 0
\(143\) 13.1916 1.10314
\(144\) 0 0
\(145\) −11.1550 −0.926372
\(146\) 0 0
\(147\) 5.05654 0.417057
\(148\) 0 0
\(149\) 4.24977 0.348155 0.174077 0.984732i \(-0.444306\pi\)
0.174077 + 0.984732i \(0.444306\pi\)
\(150\) 0 0
\(151\) −12.8711 −1.04743 −0.523717 0.851892i \(-0.675455\pi\)
−0.523717 + 0.851892i \(0.675455\pi\)
\(152\) 0 0
\(153\) −2.90365 −0.234746
\(154\) 0 0
\(155\) −21.8212 −1.75272
\(156\) 0 0
\(157\) 4.92657 0.393183 0.196592 0.980485i \(-0.437013\pi\)
0.196592 + 0.980485i \(0.437013\pi\)
\(158\) 0 0
\(159\) −10.5299 −0.835079
\(160\) 0 0
\(161\) −3.74136 −0.294861
\(162\) 0 0
\(163\) 11.4770 0.898945 0.449472 0.893294i \(-0.351612\pi\)
0.449472 + 0.893294i \(0.351612\pi\)
\(164\) 0 0
\(165\) −8.10120 −0.630677
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 13.8486 1.06528
\(170\) 0 0
\(171\) −6.55969 −0.501632
\(172\) 0 0
\(173\) 14.6626 1.11478 0.557390 0.830251i \(-0.311803\pi\)
0.557390 + 0.830251i \(0.311803\pi\)
\(174\) 0 0
\(175\) 7.14564 0.540159
\(176\) 0 0
\(177\) 0.200385 0.0150618
\(178\) 0 0
\(179\) 19.5306 1.45979 0.729894 0.683560i \(-0.239569\pi\)
0.729894 + 0.683560i \(0.239569\pi\)
\(180\) 0 0
\(181\) 0.281329 0.0209110 0.0104555 0.999945i \(-0.496672\pi\)
0.0104555 + 0.999945i \(0.496672\pi\)
\(182\) 0 0
\(183\) −11.8595 −0.876678
\(184\) 0 0
\(185\) 13.4820 0.991213
\(186\) 0 0
\(187\) −7.39232 −0.540580
\(188\) 0 0
\(189\) −1.39408 −0.101404
\(190\) 0 0
\(191\) −2.32165 −0.167989 −0.0839943 0.996466i \(-0.526768\pi\)
−0.0839943 + 0.996466i \(0.526768\pi\)
\(192\) 0 0
\(193\) 22.7761 1.63946 0.819729 0.572751i \(-0.194124\pi\)
0.819729 + 0.572751i \(0.194124\pi\)
\(194\) 0 0
\(195\) −16.4882 −1.18075
\(196\) 0 0
\(197\) −10.4276 −0.742935 −0.371467 0.928446i \(-0.621145\pi\)
−0.371467 + 0.928446i \(0.621145\pi\)
\(198\) 0 0
\(199\) 16.0417 1.13716 0.568582 0.822626i \(-0.307492\pi\)
0.568582 + 0.822626i \(0.307492\pi\)
\(200\) 0 0
\(201\) −12.5383 −0.884386
\(202\) 0 0
\(203\) −4.88702 −0.343002
\(204\) 0 0
\(205\) −6.01321 −0.419981
\(206\) 0 0
\(207\) −2.68375 −0.186534
\(208\) 0 0
\(209\) −16.7001 −1.15517
\(210\) 0 0
\(211\) −11.5563 −0.795569 −0.397784 0.917479i \(-0.630221\pi\)
−0.397784 + 0.917479i \(0.630221\pi\)
\(212\) 0 0
\(213\) −2.92956 −0.200730
\(214\) 0 0
\(215\) 20.6685 1.40958
\(216\) 0 0
\(217\) −9.55991 −0.648969
\(218\) 0 0
\(219\) −14.6356 −0.988985
\(220\) 0 0
\(221\) −15.0454 −1.01207
\(222\) 0 0
\(223\) 10.2536 0.686631 0.343316 0.939220i \(-0.388450\pi\)
0.343316 + 0.939220i \(0.388450\pi\)
\(224\) 0 0
\(225\) 5.12570 0.341714
\(226\) 0 0
\(227\) 15.3493 1.01877 0.509383 0.860540i \(-0.329874\pi\)
0.509383 + 0.860540i \(0.329874\pi\)
\(228\) 0 0
\(229\) 9.12046 0.602697 0.301349 0.953514i \(-0.402563\pi\)
0.301349 + 0.953514i \(0.402563\pi\)
\(230\) 0 0
\(231\) −3.54915 −0.233517
\(232\) 0 0
\(233\) 28.7291 1.88211 0.941053 0.338258i \(-0.109838\pi\)
0.941053 + 0.338258i \(0.109838\pi\)
\(234\) 0 0
\(235\) 24.8235 1.61931
\(236\) 0 0
\(237\) 1.95847 0.127217
\(238\) 0 0
\(239\) 13.2277 0.855627 0.427814 0.903867i \(-0.359284\pi\)
0.427814 + 0.903867i \(0.359284\pi\)
\(240\) 0 0
\(241\) −19.0262 −1.22558 −0.612791 0.790245i \(-0.709953\pi\)
−0.612791 + 0.790245i \(0.709953\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −16.0904 −1.02798
\(246\) 0 0
\(247\) −33.9895 −2.16270
\(248\) 0 0
\(249\) −3.16521 −0.200587
\(250\) 0 0
\(251\) −2.12412 −0.134073 −0.0670365 0.997751i \(-0.521354\pi\)
−0.0670365 + 0.997751i \(0.521354\pi\)
\(252\) 0 0
\(253\) −6.83249 −0.429555
\(254\) 0 0
\(255\) 9.23968 0.578611
\(256\) 0 0
\(257\) −2.39914 −0.149654 −0.0748271 0.997197i \(-0.523841\pi\)
−0.0748271 + 0.997197i \(0.523841\pi\)
\(258\) 0 0
\(259\) 5.90647 0.367010
\(260\) 0 0
\(261\) −3.50556 −0.216988
\(262\) 0 0
\(263\) 3.69327 0.227737 0.113869 0.993496i \(-0.463676\pi\)
0.113869 + 0.993496i \(0.463676\pi\)
\(264\) 0 0
\(265\) 33.5072 2.05833
\(266\) 0 0
\(267\) −8.01635 −0.490593
\(268\) 0 0
\(269\) −5.45323 −0.332489 −0.166245 0.986085i \(-0.553164\pi\)
−0.166245 + 0.986085i \(0.553164\pi\)
\(270\) 0 0
\(271\) −25.6650 −1.55904 −0.779519 0.626378i \(-0.784537\pi\)
−0.779519 + 0.626378i \(0.784537\pi\)
\(272\) 0 0
\(273\) −7.22351 −0.437187
\(274\) 0 0
\(275\) 13.0494 0.786908
\(276\) 0 0
\(277\) −22.5266 −1.35349 −0.676745 0.736217i \(-0.736610\pi\)
−0.676745 + 0.736217i \(0.736610\pi\)
\(278\) 0 0
\(279\) −6.85751 −0.410549
\(280\) 0 0
\(281\) −10.8370 −0.646479 −0.323239 0.946317i \(-0.604772\pi\)
−0.323239 + 0.946317i \(0.604772\pi\)
\(282\) 0 0
\(283\) −2.38825 −0.141967 −0.0709834 0.997477i \(-0.522614\pi\)
−0.0709834 + 0.997477i \(0.522614\pi\)
\(284\) 0 0
\(285\) 20.8735 1.23644
\(286\) 0 0
\(287\) −2.63440 −0.155504
\(288\) 0 0
\(289\) −8.56882 −0.504048
\(290\) 0 0
\(291\) −2.21764 −0.130000
\(292\) 0 0
\(293\) −16.2580 −0.949800 −0.474900 0.880040i \(-0.657516\pi\)
−0.474900 + 0.880040i \(0.657516\pi\)
\(294\) 0 0
\(295\) −0.637642 −0.0371250
\(296\) 0 0
\(297\) −2.54587 −0.147726
\(298\) 0 0
\(299\) −13.9060 −0.804207
\(300\) 0 0
\(301\) 9.05492 0.521917
\(302\) 0 0
\(303\) 1.57057 0.0902267
\(304\) 0 0
\(305\) 37.7380 2.16087
\(306\) 0 0
\(307\) 10.5390 0.601491 0.300746 0.953704i \(-0.402765\pi\)
0.300746 + 0.953704i \(0.402765\pi\)
\(308\) 0 0
\(309\) 8.64913 0.492032
\(310\) 0 0
\(311\) −8.52271 −0.483279 −0.241639 0.970366i \(-0.577685\pi\)
−0.241639 + 0.970366i \(0.577685\pi\)
\(312\) 0 0
\(313\) −15.5929 −0.881362 −0.440681 0.897664i \(-0.645263\pi\)
−0.440681 + 0.897664i \(0.645263\pi\)
\(314\) 0 0
\(315\) 4.43609 0.249945
\(316\) 0 0
\(317\) −18.8386 −1.05808 −0.529042 0.848596i \(-0.677448\pi\)
−0.529042 + 0.848596i \(0.677448\pi\)
\(318\) 0 0
\(319\) −8.92470 −0.499687
\(320\) 0 0
\(321\) 9.32081 0.520237
\(322\) 0 0
\(323\) 19.0470 1.05981
\(324\) 0 0
\(325\) 26.5592 1.47324
\(326\) 0 0
\(327\) 2.99664 0.165714
\(328\) 0 0
\(329\) 10.8752 0.599571
\(330\) 0 0
\(331\) 24.3161 1.33653 0.668267 0.743921i \(-0.267036\pi\)
0.668267 + 0.743921i \(0.267036\pi\)
\(332\) 0 0
\(333\) 4.23682 0.232177
\(334\) 0 0
\(335\) 39.8981 2.17987
\(336\) 0 0
\(337\) −10.2241 −0.556944 −0.278472 0.960444i \(-0.589828\pi\)
−0.278472 + 0.960444i \(0.589828\pi\)
\(338\) 0 0
\(339\) −13.8938 −0.754606
\(340\) 0 0
\(341\) −17.4583 −0.945423
\(342\) 0 0
\(343\) −16.8078 −0.907534
\(344\) 0 0
\(345\) 8.53995 0.459775
\(346\) 0 0
\(347\) −2.09384 −0.112403 −0.0562017 0.998419i \(-0.517899\pi\)
−0.0562017 + 0.998419i \(0.517899\pi\)
\(348\) 0 0
\(349\) 25.7148 1.37648 0.688241 0.725482i \(-0.258383\pi\)
0.688241 + 0.725482i \(0.258383\pi\)
\(350\) 0 0
\(351\) −5.18156 −0.276571
\(352\) 0 0
\(353\) 10.3134 0.548929 0.274465 0.961597i \(-0.411499\pi\)
0.274465 + 0.961597i \(0.411499\pi\)
\(354\) 0 0
\(355\) 9.32212 0.494767
\(356\) 0 0
\(357\) 4.04792 0.214238
\(358\) 0 0
\(359\) −8.07605 −0.426237 −0.213119 0.977026i \(-0.568362\pi\)
−0.213119 + 0.977026i \(0.568362\pi\)
\(360\) 0 0
\(361\) 24.0296 1.26471
\(362\) 0 0
\(363\) 4.51854 0.237162
\(364\) 0 0
\(365\) 46.5720 2.43769
\(366\) 0 0
\(367\) −10.0400 −0.524082 −0.262041 0.965057i \(-0.584396\pi\)
−0.262041 + 0.965057i \(0.584396\pi\)
\(368\) 0 0
\(369\) −1.88971 −0.0983741
\(370\) 0 0
\(371\) 14.6796 0.762125
\(372\) 0 0
\(373\) −0.292570 −0.0151487 −0.00757435 0.999971i \(-0.502411\pi\)
−0.00757435 + 0.999971i \(0.502411\pi\)
\(374\) 0 0
\(375\) −0.400003 −0.0206561
\(376\) 0 0
\(377\) −18.1643 −0.935507
\(378\) 0 0
\(379\) 4.65909 0.239321 0.119661 0.992815i \(-0.461819\pi\)
0.119661 + 0.992815i \(0.461819\pi\)
\(380\) 0 0
\(381\) −7.49924 −0.384198
\(382\) 0 0
\(383\) −10.9662 −0.560345 −0.280173 0.959950i \(-0.590392\pi\)
−0.280173 + 0.959950i \(0.590392\pi\)
\(384\) 0 0
\(385\) 11.2937 0.575581
\(386\) 0 0
\(387\) 6.49527 0.330173
\(388\) 0 0
\(389\) −36.5417 −1.85274 −0.926370 0.376616i \(-0.877088\pi\)
−0.926370 + 0.376616i \(0.877088\pi\)
\(390\) 0 0
\(391\) 7.79268 0.394093
\(392\) 0 0
\(393\) 1.66672 0.0840750
\(394\) 0 0
\(395\) −6.23204 −0.313568
\(396\) 0 0
\(397\) −11.2781 −0.566032 −0.283016 0.959115i \(-0.591335\pi\)
−0.283016 + 0.959115i \(0.591335\pi\)
\(398\) 0 0
\(399\) 9.14473 0.457809
\(400\) 0 0
\(401\) 13.3097 0.664655 0.332328 0.943164i \(-0.392166\pi\)
0.332328 + 0.943164i \(0.392166\pi\)
\(402\) 0 0
\(403\) −35.5326 −1.77001
\(404\) 0 0
\(405\) 3.18209 0.158119
\(406\) 0 0
\(407\) 10.7864 0.534663
\(408\) 0 0
\(409\) 2.52181 0.124696 0.0623479 0.998054i \(-0.480141\pi\)
0.0623479 + 0.998054i \(0.480141\pi\)
\(410\) 0 0
\(411\) 11.1564 0.550303
\(412\) 0 0
\(413\) −0.279352 −0.0137460
\(414\) 0 0
\(415\) 10.0720 0.494415
\(416\) 0 0
\(417\) −4.80521 −0.235312
\(418\) 0 0
\(419\) 6.84632 0.334465 0.167232 0.985917i \(-0.446517\pi\)
0.167232 + 0.985917i \(0.446517\pi\)
\(420\) 0 0
\(421\) 29.8171 1.45320 0.726599 0.687061i \(-0.241100\pi\)
0.726599 + 0.687061i \(0.241100\pi\)
\(422\) 0 0
\(423\) 7.80101 0.379298
\(424\) 0 0
\(425\) −14.8832 −0.721944
\(426\) 0 0
\(427\) 16.5331 0.800091
\(428\) 0 0
\(429\) −13.1916 −0.636896
\(430\) 0 0
\(431\) −12.2712 −0.591082 −0.295541 0.955330i \(-0.595500\pi\)
−0.295541 + 0.955330i \(0.595500\pi\)
\(432\) 0 0
\(433\) 28.9314 1.39035 0.695177 0.718838i \(-0.255326\pi\)
0.695177 + 0.718838i \(0.255326\pi\)
\(434\) 0 0
\(435\) 11.1550 0.534841
\(436\) 0 0
\(437\) 17.6046 0.842142
\(438\) 0 0
\(439\) −11.2562 −0.537228 −0.268614 0.963248i \(-0.586566\pi\)
−0.268614 + 0.963248i \(0.586566\pi\)
\(440\) 0 0
\(441\) −5.05654 −0.240788
\(442\) 0 0
\(443\) −18.4501 −0.876591 −0.438296 0.898831i \(-0.644418\pi\)
−0.438296 + 0.898831i \(0.644418\pi\)
\(444\) 0 0
\(445\) 25.5088 1.20923
\(446\) 0 0
\(447\) −4.24977 −0.201007
\(448\) 0 0
\(449\) −27.1633 −1.28192 −0.640958 0.767576i \(-0.721463\pi\)
−0.640958 + 0.767576i \(0.721463\pi\)
\(450\) 0 0
\(451\) −4.81095 −0.226539
\(452\) 0 0
\(453\) 12.8711 0.604736
\(454\) 0 0
\(455\) 22.9859 1.07759
\(456\) 0 0
\(457\) 28.2604 1.32197 0.660983 0.750401i \(-0.270140\pi\)
0.660983 + 0.750401i \(0.270140\pi\)
\(458\) 0 0
\(459\) 2.90365 0.135531
\(460\) 0 0
\(461\) −26.9228 −1.25392 −0.626959 0.779052i \(-0.715701\pi\)
−0.626959 + 0.779052i \(0.715701\pi\)
\(462\) 0 0
\(463\) −8.70108 −0.404374 −0.202187 0.979347i \(-0.564805\pi\)
−0.202187 + 0.979347i \(0.564805\pi\)
\(464\) 0 0
\(465\) 21.8212 1.01194
\(466\) 0 0
\(467\) 27.8472 1.28862 0.644308 0.764766i \(-0.277145\pi\)
0.644308 + 0.764766i \(0.277145\pi\)
\(468\) 0 0
\(469\) 17.4794 0.807125
\(470\) 0 0
\(471\) −4.92657 −0.227005
\(472\) 0 0
\(473\) 16.5361 0.760332
\(474\) 0 0
\(475\) −33.6230 −1.54273
\(476\) 0 0
\(477\) 10.5299 0.482133
\(478\) 0 0
\(479\) 38.9578 1.78003 0.890014 0.455933i \(-0.150694\pi\)
0.890014 + 0.455933i \(0.150694\pi\)
\(480\) 0 0
\(481\) 21.9534 1.00099
\(482\) 0 0
\(483\) 3.74136 0.170238
\(484\) 0 0
\(485\) 7.05674 0.320430
\(486\) 0 0
\(487\) −16.7195 −0.757633 −0.378816 0.925472i \(-0.623669\pi\)
−0.378816 + 0.925472i \(0.623669\pi\)
\(488\) 0 0
\(489\) −11.4770 −0.519006
\(490\) 0 0
\(491\) −10.7073 −0.483213 −0.241607 0.970374i \(-0.577674\pi\)
−0.241607 + 0.970374i \(0.577674\pi\)
\(492\) 0 0
\(493\) 10.1789 0.458435
\(494\) 0 0
\(495\) 8.10120 0.364122
\(496\) 0 0
\(497\) 4.08403 0.183194
\(498\) 0 0
\(499\) 4.19869 0.187959 0.0939797 0.995574i \(-0.470041\pi\)
0.0939797 + 0.995574i \(0.470041\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 32.6725 1.45680 0.728398 0.685154i \(-0.240265\pi\)
0.728398 + 0.685154i \(0.240265\pi\)
\(504\) 0 0
\(505\) −4.99769 −0.222394
\(506\) 0 0
\(507\) −13.8486 −0.615039
\(508\) 0 0
\(509\) −3.56268 −0.157913 −0.0789564 0.996878i \(-0.525159\pi\)
−0.0789564 + 0.996878i \(0.525159\pi\)
\(510\) 0 0
\(511\) 20.4032 0.902586
\(512\) 0 0
\(513\) 6.55969 0.289617
\(514\) 0 0
\(515\) −27.5223 −1.21278
\(516\) 0 0
\(517\) 19.8604 0.873458
\(518\) 0 0
\(519\) −14.6626 −0.643619
\(520\) 0 0
\(521\) −4.09199 −0.179273 −0.0896367 0.995975i \(-0.528571\pi\)
−0.0896367 + 0.995975i \(0.528571\pi\)
\(522\) 0 0
\(523\) −12.8494 −0.561863 −0.280932 0.959728i \(-0.590643\pi\)
−0.280932 + 0.959728i \(0.590643\pi\)
\(524\) 0 0
\(525\) −7.14564 −0.311861
\(526\) 0 0
\(527\) 19.9118 0.867372
\(528\) 0 0
\(529\) −15.7975 −0.686847
\(530\) 0 0
\(531\) −0.200385 −0.00869596
\(532\) 0 0
\(533\) −9.79163 −0.424123
\(534\) 0 0
\(535\) −29.6597 −1.28230
\(536\) 0 0
\(537\) −19.5306 −0.842809
\(538\) 0 0
\(539\) −12.8733 −0.554493
\(540\) 0 0
\(541\) −23.8636 −1.02597 −0.512987 0.858396i \(-0.671461\pi\)
−0.512987 + 0.858396i \(0.671461\pi\)
\(542\) 0 0
\(543\) −0.281329 −0.0120730
\(544\) 0 0
\(545\) −9.53557 −0.408459
\(546\) 0 0
\(547\) 32.1923 1.37645 0.688223 0.725500i \(-0.258391\pi\)
0.688223 + 0.725500i \(0.258391\pi\)
\(548\) 0 0
\(549\) 11.8595 0.506151
\(550\) 0 0
\(551\) 22.9954 0.979636
\(552\) 0 0
\(553\) −2.73027 −0.116103
\(554\) 0 0
\(555\) −13.4820 −0.572277
\(556\) 0 0
\(557\) −10.1486 −0.430010 −0.215005 0.976613i \(-0.568977\pi\)
−0.215005 + 0.976613i \(0.568977\pi\)
\(558\) 0 0
\(559\) 33.6557 1.42348
\(560\) 0 0
\(561\) 7.39232 0.312104
\(562\) 0 0
\(563\) 5.29505 0.223160 0.111580 0.993755i \(-0.464409\pi\)
0.111580 + 0.993755i \(0.464409\pi\)
\(564\) 0 0
\(565\) 44.2112 1.85998
\(566\) 0 0
\(567\) 1.39408 0.0585458
\(568\) 0 0
\(569\) −18.4824 −0.774822 −0.387411 0.921907i \(-0.626631\pi\)
−0.387411 + 0.921907i \(0.626631\pi\)
\(570\) 0 0
\(571\) −46.1352 −1.93070 −0.965348 0.260966i \(-0.915959\pi\)
−0.965348 + 0.260966i \(0.915959\pi\)
\(572\) 0 0
\(573\) 2.32165 0.0969882
\(574\) 0 0
\(575\) −13.7561 −0.573670
\(576\) 0 0
\(577\) −13.1408 −0.547059 −0.273529 0.961864i \(-0.588191\pi\)
−0.273529 + 0.961864i \(0.588191\pi\)
\(578\) 0 0
\(579\) −22.7761 −0.946542
\(580\) 0 0
\(581\) 4.41256 0.183064
\(582\) 0 0
\(583\) 26.8079 1.11027
\(584\) 0 0
\(585\) 16.4882 0.681704
\(586\) 0 0
\(587\) −22.0037 −0.908189 −0.454095 0.890954i \(-0.650037\pi\)
−0.454095 + 0.890954i \(0.650037\pi\)
\(588\) 0 0
\(589\) 44.9832 1.85350
\(590\) 0 0
\(591\) 10.4276 0.428934
\(592\) 0 0
\(593\) −30.1594 −1.23850 −0.619249 0.785195i \(-0.712563\pi\)
−0.619249 + 0.785195i \(0.712563\pi\)
\(594\) 0 0
\(595\) −12.8808 −0.528063
\(596\) 0 0
\(597\) −16.0417 −0.656542
\(598\) 0 0
\(599\) −16.1500 −0.659871 −0.329935 0.944004i \(-0.607027\pi\)
−0.329935 + 0.944004i \(0.607027\pi\)
\(600\) 0 0
\(601\) 32.7075 1.33417 0.667083 0.744984i \(-0.267543\pi\)
0.667083 + 0.744984i \(0.267543\pi\)
\(602\) 0 0
\(603\) 12.5383 0.510600
\(604\) 0 0
\(605\) −14.3784 −0.584565
\(606\) 0 0
\(607\) 37.0158 1.50243 0.751213 0.660060i \(-0.229469\pi\)
0.751213 + 0.660060i \(0.229469\pi\)
\(608\) 0 0
\(609\) 4.88702 0.198032
\(610\) 0 0
\(611\) 40.4214 1.63528
\(612\) 0 0
\(613\) −29.4598 −1.18987 −0.594935 0.803774i \(-0.702822\pi\)
−0.594935 + 0.803774i \(0.702822\pi\)
\(614\) 0 0
\(615\) 6.01321 0.242476
\(616\) 0 0
\(617\) −29.4634 −1.18615 −0.593075 0.805147i \(-0.702086\pi\)
−0.593075 + 0.805147i \(0.702086\pi\)
\(618\) 0 0
\(619\) 11.7461 0.472117 0.236058 0.971739i \(-0.424144\pi\)
0.236058 + 0.971739i \(0.424144\pi\)
\(620\) 0 0
\(621\) 2.68375 0.107695
\(622\) 0 0
\(623\) 11.1754 0.447734
\(624\) 0 0
\(625\) −24.3557 −0.974227
\(626\) 0 0
\(627\) 16.7001 0.666939
\(628\) 0 0
\(629\) −12.3023 −0.490523
\(630\) 0 0
\(631\) 33.5462 1.33545 0.667727 0.744406i \(-0.267267\pi\)
0.667727 + 0.744406i \(0.267267\pi\)
\(632\) 0 0
\(633\) 11.5563 0.459322
\(634\) 0 0
\(635\) 23.8633 0.946985
\(636\) 0 0
\(637\) −26.2008 −1.03811
\(638\) 0 0
\(639\) 2.92956 0.115891
\(640\) 0 0
\(641\) 25.1843 0.994719 0.497360 0.867544i \(-0.334303\pi\)
0.497360 + 0.867544i \(0.334303\pi\)
\(642\) 0 0
\(643\) −1.64113 −0.0647197 −0.0323599 0.999476i \(-0.510302\pi\)
−0.0323599 + 0.999476i \(0.510302\pi\)
\(644\) 0 0
\(645\) −20.6685 −0.813823
\(646\) 0 0
\(647\) 40.8963 1.60780 0.803900 0.594764i \(-0.202755\pi\)
0.803900 + 0.594764i \(0.202755\pi\)
\(648\) 0 0
\(649\) −0.510154 −0.0200253
\(650\) 0 0
\(651\) 9.55991 0.374682
\(652\) 0 0
\(653\) 21.3875 0.836959 0.418479 0.908226i \(-0.362563\pi\)
0.418479 + 0.908226i \(0.362563\pi\)
\(654\) 0 0
\(655\) −5.30366 −0.207231
\(656\) 0 0
\(657\) 14.6356 0.570991
\(658\) 0 0
\(659\) −29.6553 −1.15521 −0.577604 0.816317i \(-0.696012\pi\)
−0.577604 + 0.816317i \(0.696012\pi\)
\(660\) 0 0
\(661\) 20.2127 0.786184 0.393092 0.919499i \(-0.371405\pi\)
0.393092 + 0.919499i \(0.371405\pi\)
\(662\) 0 0
\(663\) 15.0454 0.584317
\(664\) 0 0
\(665\) −29.0994 −1.12842
\(666\) 0 0
\(667\) 9.40805 0.364281
\(668\) 0 0
\(669\) −10.2536 −0.396427
\(670\) 0 0
\(671\) 30.1927 1.16558
\(672\) 0 0
\(673\) −26.3275 −1.01485 −0.507425 0.861696i \(-0.669403\pi\)
−0.507425 + 0.861696i \(0.669403\pi\)
\(674\) 0 0
\(675\) −5.12570 −0.197288
\(676\) 0 0
\(677\) −25.0308 −0.962013 −0.481006 0.876717i \(-0.659729\pi\)
−0.481006 + 0.876717i \(0.659729\pi\)
\(678\) 0 0
\(679\) 3.09157 0.118643
\(680\) 0 0
\(681\) −15.3493 −0.588185
\(682\) 0 0
\(683\) −46.9156 −1.79518 −0.897589 0.440834i \(-0.854683\pi\)
−0.897589 + 0.440834i \(0.854683\pi\)
\(684\) 0 0
\(685\) −35.5005 −1.35641
\(686\) 0 0
\(687\) −9.12046 −0.347967
\(688\) 0 0
\(689\) 54.5616 2.07863
\(690\) 0 0
\(691\) −29.6225 −1.12689 −0.563447 0.826152i \(-0.690525\pi\)
−0.563447 + 0.826152i \(0.690525\pi\)
\(692\) 0 0
\(693\) 3.54915 0.134821
\(694\) 0 0
\(695\) 15.2906 0.580007
\(696\) 0 0
\(697\) 5.48704 0.207837
\(698\) 0 0
\(699\) −28.7291 −1.08663
\(700\) 0 0
\(701\) −51.7652 −1.95514 −0.977572 0.210603i \(-0.932457\pi\)
−0.977572 + 0.210603i \(0.932457\pi\)
\(702\) 0 0
\(703\) −27.7923 −1.04821
\(704\) 0 0
\(705\) −24.8235 −0.934908
\(706\) 0 0
\(707\) −2.18949 −0.0823444
\(708\) 0 0
\(709\) 26.8216 1.00730 0.503652 0.863906i \(-0.331989\pi\)
0.503652 + 0.863906i \(0.331989\pi\)
\(710\) 0 0
\(711\) −1.95847 −0.0734485
\(712\) 0 0
\(713\) 18.4039 0.689230
\(714\) 0 0
\(715\) 41.9769 1.56985
\(716\) 0 0
\(717\) −13.2277 −0.493996
\(718\) 0 0
\(719\) −19.1436 −0.713934 −0.356967 0.934117i \(-0.616189\pi\)
−0.356967 + 0.934117i \(0.616189\pi\)
\(720\) 0 0
\(721\) −12.0576 −0.449047
\(722\) 0 0
\(723\) 19.0262 0.707591
\(724\) 0 0
\(725\) −17.9684 −0.667331
\(726\) 0 0
\(727\) 25.8740 0.959612 0.479806 0.877375i \(-0.340707\pi\)
0.479806 + 0.877375i \(0.340707\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.8600 −0.697562
\(732\) 0 0
\(733\) −7.91938 −0.292509 −0.146255 0.989247i \(-0.546722\pi\)
−0.146255 + 0.989247i \(0.546722\pi\)
\(734\) 0 0
\(735\) 16.0904 0.593503
\(736\) 0 0
\(737\) 31.9210 1.17582
\(738\) 0 0
\(739\) 13.5229 0.497446 0.248723 0.968575i \(-0.419989\pi\)
0.248723 + 0.968575i \(0.419989\pi\)
\(740\) 0 0
\(741\) 33.9895 1.24863
\(742\) 0 0
\(743\) −31.0296 −1.13836 −0.569182 0.822211i \(-0.692740\pi\)
−0.569182 + 0.822211i \(0.692740\pi\)
\(744\) 0 0
\(745\) 13.5232 0.495450
\(746\) 0 0
\(747\) 3.16521 0.115809
\(748\) 0 0
\(749\) −12.9939 −0.474788
\(750\) 0 0
\(751\) 34.5470 1.26064 0.630320 0.776336i \(-0.282924\pi\)
0.630320 + 0.776336i \(0.282924\pi\)
\(752\) 0 0
\(753\) 2.12412 0.0774071
\(754\) 0 0
\(755\) −40.9570 −1.49058
\(756\) 0 0
\(757\) −22.8028 −0.828781 −0.414391 0.910099i \(-0.636005\pi\)
−0.414391 + 0.910099i \(0.636005\pi\)
\(758\) 0 0
\(759\) 6.83249 0.248004
\(760\) 0 0
\(761\) −14.2303 −0.515847 −0.257923 0.966165i \(-0.583038\pi\)
−0.257923 + 0.966165i \(0.583038\pi\)
\(762\) 0 0
\(763\) −4.17755 −0.151237
\(764\) 0 0
\(765\) −9.23968 −0.334061
\(766\) 0 0
\(767\) −1.03831 −0.0374911
\(768\) 0 0
\(769\) 17.6897 0.637908 0.318954 0.947770i \(-0.396669\pi\)
0.318954 + 0.947770i \(0.396669\pi\)
\(770\) 0 0
\(771\) 2.39914 0.0864029
\(772\) 0 0
\(773\) −46.6405 −1.67754 −0.838771 0.544485i \(-0.816725\pi\)
−0.838771 + 0.544485i \(0.816725\pi\)
\(774\) 0 0
\(775\) −35.1496 −1.26261
\(776\) 0 0
\(777\) −5.90647 −0.211893
\(778\) 0 0
\(779\) 12.3959 0.444129
\(780\) 0 0
\(781\) 7.45828 0.266878
\(782\) 0 0
\(783\) 3.50556 0.125278
\(784\) 0 0
\(785\) 15.6768 0.559529
\(786\) 0 0
\(787\) 34.1135 1.21601 0.608007 0.793932i \(-0.291969\pi\)
0.608007 + 0.793932i \(0.291969\pi\)
\(788\) 0 0
\(789\) −3.69327 −0.131484
\(790\) 0 0
\(791\) 19.3690 0.688683
\(792\) 0 0
\(793\) 61.4507 2.18218
\(794\) 0 0
\(795\) −33.5072 −1.18838
\(796\) 0 0
\(797\) −11.1237 −0.394022 −0.197011 0.980401i \(-0.563123\pi\)
−0.197011 + 0.980401i \(0.563123\pi\)
\(798\) 0 0
\(799\) −22.6514 −0.801349
\(800\) 0 0
\(801\) 8.01635 0.283244
\(802\) 0 0
\(803\) 37.2605 1.31489
\(804\) 0 0
\(805\) −11.9054 −0.419609
\(806\) 0 0
\(807\) 5.45323 0.191963
\(808\) 0 0
\(809\) 12.8098 0.450369 0.225184 0.974316i \(-0.427702\pi\)
0.225184 + 0.974316i \(0.427702\pi\)
\(810\) 0 0
\(811\) −40.1149 −1.40863 −0.704313 0.709890i \(-0.748745\pi\)
−0.704313 + 0.709890i \(0.748745\pi\)
\(812\) 0 0
\(813\) 25.6650 0.900112
\(814\) 0 0
\(815\) 36.5207 1.27927
\(816\) 0 0
\(817\) −42.6070 −1.49063
\(818\) 0 0
\(819\) 7.22351 0.252410
\(820\) 0 0
\(821\) −46.9641 −1.63906 −0.819529 0.573037i \(-0.805765\pi\)
−0.819529 + 0.573037i \(0.805765\pi\)
\(822\) 0 0
\(823\) 24.9100 0.868309 0.434154 0.900839i \(-0.357047\pi\)
0.434154 + 0.900839i \(0.357047\pi\)
\(824\) 0 0
\(825\) −13.0494 −0.454321
\(826\) 0 0
\(827\) −10.0184 −0.348374 −0.174187 0.984713i \(-0.555730\pi\)
−0.174187 + 0.984713i \(0.555730\pi\)
\(828\) 0 0
\(829\) −30.3717 −1.05485 −0.527427 0.849600i \(-0.676843\pi\)
−0.527427 + 0.849600i \(0.676843\pi\)
\(830\) 0 0
\(831\) 22.5266 0.781438
\(832\) 0 0
\(833\) 14.6824 0.508716
\(834\) 0 0
\(835\) 3.18209 0.110121
\(836\) 0 0
\(837\) 6.85751 0.237030
\(838\) 0 0
\(839\) 54.1321 1.86885 0.934424 0.356162i \(-0.115915\pi\)
0.934424 + 0.356162i \(0.115915\pi\)
\(840\) 0 0
\(841\) −16.7111 −0.576244
\(842\) 0 0
\(843\) 10.8370 0.373245
\(844\) 0 0
\(845\) 44.0676 1.51597
\(846\) 0 0
\(847\) −6.29920 −0.216443
\(848\) 0 0
\(849\) 2.38825 0.0819646
\(850\) 0 0
\(851\) −11.3706 −0.389779
\(852\) 0 0
\(853\) −6.84450 −0.234351 −0.117176 0.993111i \(-0.537384\pi\)
−0.117176 + 0.993111i \(0.537384\pi\)
\(854\) 0 0
\(855\) −20.8735 −0.713860
\(856\) 0 0
\(857\) 0.266153 0.00909160 0.00454580 0.999990i \(-0.498553\pi\)
0.00454580 + 0.999990i \(0.498553\pi\)
\(858\) 0 0
\(859\) 42.6988 1.45686 0.728431 0.685119i \(-0.240250\pi\)
0.728431 + 0.685119i \(0.240250\pi\)
\(860\) 0 0
\(861\) 2.63440 0.0897800
\(862\) 0 0
\(863\) −46.4528 −1.58127 −0.790636 0.612286i \(-0.790250\pi\)
−0.790636 + 0.612286i \(0.790250\pi\)
\(864\) 0 0
\(865\) 46.6579 1.58642
\(866\) 0 0
\(867\) 8.56882 0.291012
\(868\) 0 0
\(869\) −4.98603 −0.169139
\(870\) 0 0
\(871\) 64.9682 2.20136
\(872\) 0 0
\(873\) 2.21764 0.0750558
\(874\) 0 0
\(875\) 0.557635 0.0188515
\(876\) 0 0
\(877\) 18.1097 0.611522 0.305761 0.952108i \(-0.401089\pi\)
0.305761 + 0.952108i \(0.401089\pi\)
\(878\) 0 0
\(879\) 16.2580 0.548367
\(880\) 0 0
\(881\) −34.6839 −1.16853 −0.584265 0.811563i \(-0.698617\pi\)
−0.584265 + 0.811563i \(0.698617\pi\)
\(882\) 0 0
\(883\) 4.11055 0.138331 0.0691655 0.997605i \(-0.477966\pi\)
0.0691655 + 0.997605i \(0.477966\pi\)
\(884\) 0 0
\(885\) 0.637642 0.0214341
\(886\) 0 0
\(887\) −33.6817 −1.13092 −0.565460 0.824776i \(-0.691301\pi\)
−0.565460 + 0.824776i \(0.691301\pi\)
\(888\) 0 0
\(889\) 10.4545 0.350634
\(890\) 0 0
\(891\) 2.54587 0.0852899
\(892\) 0 0
\(893\) −51.1722 −1.71241
\(894\) 0 0
\(895\) 62.1483 2.07739
\(896\) 0 0
\(897\) 13.9060 0.464309
\(898\) 0 0
\(899\) 24.0394 0.801759
\(900\) 0 0
\(901\) −30.5753 −1.01861
\(902\) 0 0
\(903\) −9.05492 −0.301329
\(904\) 0 0
\(905\) 0.895213 0.0297579
\(906\) 0 0
\(907\) −51.6896 −1.71632 −0.858162 0.513379i \(-0.828394\pi\)
−0.858162 + 0.513379i \(0.828394\pi\)
\(908\) 0 0
\(909\) −1.57057 −0.0520924
\(910\) 0 0
\(911\) −23.5298 −0.779578 −0.389789 0.920904i \(-0.627452\pi\)
−0.389789 + 0.920904i \(0.627452\pi\)
\(912\) 0 0
\(913\) 8.05823 0.266688
\(914\) 0 0
\(915\) −37.7380 −1.24758
\(916\) 0 0
\(917\) −2.32354 −0.0767301
\(918\) 0 0
\(919\) 55.4985 1.83073 0.915363 0.402629i \(-0.131904\pi\)
0.915363 + 0.402629i \(0.131904\pi\)
\(920\) 0 0
\(921\) −10.5390 −0.347271
\(922\) 0 0
\(923\) 15.1797 0.499646
\(924\) 0 0
\(925\) 21.7167 0.714041
\(926\) 0 0
\(927\) −8.64913 −0.284075
\(928\) 0 0
\(929\) 21.2800 0.698173 0.349086 0.937091i \(-0.386492\pi\)
0.349086 + 0.937091i \(0.386492\pi\)
\(930\) 0 0
\(931\) 33.1694 1.08708
\(932\) 0 0
\(933\) 8.52271 0.279021
\(934\) 0 0
\(935\) −23.5230 −0.769285
\(936\) 0 0
\(937\) −55.8852 −1.82569 −0.912844 0.408307i \(-0.866119\pi\)
−0.912844 + 0.408307i \(0.866119\pi\)
\(938\) 0 0
\(939\) 15.5929 0.508855
\(940\) 0 0
\(941\) 57.7285 1.88189 0.940947 0.338554i \(-0.109938\pi\)
0.940947 + 0.338554i \(0.109938\pi\)
\(942\) 0 0
\(943\) 5.07150 0.165151
\(944\) 0 0
\(945\) −4.43609 −0.144306
\(946\) 0 0
\(947\) 24.2287 0.787326 0.393663 0.919255i \(-0.371208\pi\)
0.393663 + 0.919255i \(0.371208\pi\)
\(948\) 0 0
\(949\) 75.8356 2.46173
\(950\) 0 0
\(951\) 18.8386 0.610885
\(952\) 0 0
\(953\) 18.6411 0.603845 0.301922 0.953333i \(-0.402372\pi\)
0.301922 + 0.953333i \(0.402372\pi\)
\(954\) 0 0
\(955\) −7.38769 −0.239060
\(956\) 0 0
\(957\) 8.92470 0.288494
\(958\) 0 0
\(959\) −15.5528 −0.502227
\(960\) 0 0
\(961\) 16.0255 0.516951
\(962\) 0 0
\(963\) −9.32081 −0.300359
\(964\) 0 0
\(965\) 72.4756 2.33307
\(966\) 0 0
\(967\) −15.5476 −0.499978 −0.249989 0.968249i \(-0.580427\pi\)
−0.249989 + 0.968249i \(0.580427\pi\)
\(968\) 0 0
\(969\) −19.0470 −0.611879
\(970\) 0 0
\(971\) 51.1943 1.64290 0.821451 0.570279i \(-0.193165\pi\)
0.821451 + 0.570279i \(0.193165\pi\)
\(972\) 0 0
\(973\) 6.69885 0.214755
\(974\) 0 0
\(975\) −26.5592 −0.850574
\(976\) 0 0
\(977\) 4.93866 0.158002 0.0790008 0.996875i \(-0.474827\pi\)
0.0790008 + 0.996875i \(0.474827\pi\)
\(978\) 0 0
\(979\) 20.4086 0.652262
\(980\) 0 0
\(981\) −2.99664 −0.0956752
\(982\) 0 0
\(983\) 40.5536 1.29346 0.646730 0.762719i \(-0.276136\pi\)
0.646730 + 0.762719i \(0.276136\pi\)
\(984\) 0 0
\(985\) −33.1815 −1.05725
\(986\) 0 0
\(987\) −10.8752 −0.346162
\(988\) 0 0
\(989\) −17.4317 −0.554296
\(990\) 0 0
\(991\) 46.0034 1.46135 0.730674 0.682727i \(-0.239206\pi\)
0.730674 + 0.682727i \(0.239206\pi\)
\(992\) 0 0
\(993\) −24.3161 −0.771648
\(994\) 0 0
\(995\) 51.0461 1.61827
\(996\) 0 0
\(997\) 38.4720 1.21842 0.609210 0.793009i \(-0.291486\pi\)
0.609210 + 0.793009i \(0.291486\pi\)
\(998\) 0 0
\(999\) −4.23682 −0.134047
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 \(a_p\))