Properties

Label 8008.2.a.v.1.8
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 1.8
Root \(-0.979305\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.979305 q^{3} +2.33286 q^{5} -1.00000 q^{7} -2.04096 q^{9} +O(q^{10})\) \(q+0.979305 q^{3} +2.33286 q^{5} -1.00000 q^{7} -2.04096 q^{9} +1.00000 q^{11} -1.00000 q^{13} +2.28458 q^{15} -2.60681 q^{17} +2.89553 q^{19} -0.979305 q^{21} +3.81847 q^{23} +0.442245 q^{25} -4.93664 q^{27} -3.10856 q^{29} -7.32534 q^{31} +0.979305 q^{33} -2.33286 q^{35} -1.46215 q^{37} -0.979305 q^{39} -0.286060 q^{41} -9.21304 q^{43} -4.76128 q^{45} +3.81847 q^{47} +1.00000 q^{49} -2.55286 q^{51} -11.8763 q^{53} +2.33286 q^{55} +2.83561 q^{57} -9.80563 q^{59} +1.26111 q^{61} +2.04096 q^{63} -2.33286 q^{65} -4.93124 q^{67} +3.73944 q^{69} +16.2180 q^{71} +0.183169 q^{73} +0.433093 q^{75} -1.00000 q^{77} -15.7288 q^{79} +1.28841 q^{81} +15.3290 q^{83} -6.08133 q^{85} -3.04423 q^{87} -10.7996 q^{89} +1.00000 q^{91} -7.17374 q^{93} +6.75487 q^{95} +4.70388 q^{97} -2.04096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) 0.979305 0.565402 0.282701 0.959208i \(-0.408770\pi\)
0.282701 + 0.959208i \(0.408770\pi\)
\(4\) 0 0
\(5\) 2.33286 1.04329 0.521644 0.853163i \(-0.325319\pi\)
0.521644 + 0.853163i \(0.325319\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.04096 −0.680320
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.28458 0.589877
\(16\) 0 0
\(17\) −2.60681 −0.632244 −0.316122 0.948719i \(-0.602381\pi\)
−0.316122 + 0.948719i \(0.602381\pi\)
\(18\) 0 0
\(19\) 2.89553 0.664280 0.332140 0.943230i \(-0.392229\pi\)
0.332140 + 0.943230i \(0.392229\pi\)
\(20\) 0 0
\(21\) −0.979305 −0.213702
\(22\) 0 0
\(23\) 3.81847 0.796205 0.398103 0.917341i \(-0.369669\pi\)
0.398103 + 0.917341i \(0.369669\pi\)
\(24\) 0 0
\(25\) 0.442245 0.0884490
\(26\) 0 0
\(27\) −4.93664 −0.950057
\(28\) 0 0
\(29\) −3.10856 −0.577245 −0.288623 0.957443i \(-0.593197\pi\)
−0.288623 + 0.957443i \(0.593197\pi\)
\(30\) 0 0
\(31\) −7.32534 −1.31567 −0.657835 0.753162i \(-0.728527\pi\)
−0.657835 + 0.753162i \(0.728527\pi\)
\(32\) 0 0
\(33\) 0.979305 0.170475
\(34\) 0 0
\(35\) −2.33286 −0.394326
\(36\) 0 0
\(37\) −1.46215 −0.240376 −0.120188 0.992751i \(-0.538350\pi\)
−0.120188 + 0.992751i \(0.538350\pi\)
\(38\) 0 0
\(39\) −0.979305 −0.156814
\(40\) 0 0
\(41\) −0.286060 −0.0446750 −0.0223375 0.999750i \(-0.507111\pi\)
−0.0223375 + 0.999750i \(0.507111\pi\)
\(42\) 0 0
\(43\) −9.21304 −1.40497 −0.702487 0.711696i \(-0.747927\pi\)
−0.702487 + 0.711696i \(0.747927\pi\)
\(44\) 0 0
\(45\) −4.76128 −0.709770
\(46\) 0 0
\(47\) 3.81847 0.556981 0.278490 0.960439i \(-0.410166\pi\)
0.278490 + 0.960439i \(0.410166\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −2.55286 −0.357472
\(52\) 0 0
\(53\) −11.8763 −1.63133 −0.815666 0.578523i \(-0.803629\pi\)
−0.815666 + 0.578523i \(0.803629\pi\)
\(54\) 0 0
\(55\) 2.33286 0.314563
\(56\) 0 0
\(57\) 2.83561 0.375585
\(58\) 0 0
\(59\) −9.80563 −1.27658 −0.638292 0.769794i \(-0.720359\pi\)
−0.638292 + 0.769794i \(0.720359\pi\)
\(60\) 0 0
\(61\) 1.26111 0.161469 0.0807343 0.996736i \(-0.474273\pi\)
0.0807343 + 0.996736i \(0.474273\pi\)
\(62\) 0 0
\(63\) 2.04096 0.257137
\(64\) 0 0
\(65\) −2.33286 −0.289356
\(66\) 0 0
\(67\) −4.93124 −0.602447 −0.301224 0.953554i \(-0.597395\pi\)
−0.301224 + 0.953554i \(0.597395\pi\)
\(68\) 0 0
\(69\) 3.73944 0.450176
\(70\) 0 0
\(71\) 16.2180 1.92472 0.962360 0.271780i \(-0.0876122\pi\)
0.962360 + 0.271780i \(0.0876122\pi\)
\(72\) 0 0
\(73\) 0.183169 0.0214383 0.0107191 0.999943i \(-0.496588\pi\)
0.0107191 + 0.999943i \(0.496588\pi\)
\(74\) 0 0
\(75\) 0.433093 0.0500092
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −15.7288 −1.76963 −0.884813 0.465947i \(-0.845714\pi\)
−0.884813 + 0.465947i \(0.845714\pi\)
\(80\) 0 0
\(81\) 1.28841 0.143156
\(82\) 0 0
\(83\) 15.3290 1.68257 0.841286 0.540591i \(-0.181799\pi\)
0.841286 + 0.540591i \(0.181799\pi\)
\(84\) 0 0
\(85\) −6.08133 −0.659612
\(86\) 0 0
\(87\) −3.04423 −0.326376
\(88\) 0 0
\(89\) −10.7996 −1.14476 −0.572379 0.819989i \(-0.693979\pi\)
−0.572379 + 0.819989i \(0.693979\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −7.17374 −0.743882
\(94\) 0 0
\(95\) 6.75487 0.693035
\(96\) 0 0
\(97\) 4.70388 0.477606 0.238803 0.971068i \(-0.423245\pi\)
0.238803 + 0.971068i \(0.423245\pi\)
\(98\) 0 0
\(99\) −2.04096 −0.205124
\(100\) 0 0
\(101\) −10.6825 −1.06294 −0.531472 0.847076i \(-0.678361\pi\)
−0.531472 + 0.847076i \(0.678361\pi\)
\(102\) 0 0
\(103\) −13.1224 −1.29299 −0.646494 0.762919i \(-0.723766\pi\)
−0.646494 + 0.762919i \(0.723766\pi\)
\(104\) 0 0
\(105\) −2.28458 −0.222953
\(106\) 0 0
\(107\) −2.16009 −0.208824 −0.104412 0.994534i \(-0.533296\pi\)
−0.104412 + 0.994534i \(0.533296\pi\)
\(108\) 0 0
\(109\) 13.2998 1.27389 0.636945 0.770909i \(-0.280198\pi\)
0.636945 + 0.770909i \(0.280198\pi\)
\(110\) 0 0
\(111\) −1.43189 −0.135909
\(112\) 0 0
\(113\) 12.1758 1.14540 0.572701 0.819764i \(-0.305895\pi\)
0.572701 + 0.819764i \(0.305895\pi\)
\(114\) 0 0
\(115\) 8.90795 0.830671
\(116\) 0 0
\(117\) 2.04096 0.188687
\(118\) 0 0
\(119\) 2.60681 0.238966
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −0.280140 −0.0252593
\(124\) 0 0
\(125\) −10.6326 −0.951010
\(126\) 0 0
\(127\) −1.59695 −0.141707 −0.0708533 0.997487i \(-0.522572\pi\)
−0.0708533 + 0.997487i \(0.522572\pi\)
\(128\) 0 0
\(129\) −9.02237 −0.794376
\(130\) 0 0
\(131\) 5.72718 0.500386 0.250193 0.968196i \(-0.419506\pi\)
0.250193 + 0.968196i \(0.419506\pi\)
\(132\) 0 0
\(133\) −2.89553 −0.251074
\(134\) 0 0
\(135\) −11.5165 −0.991182
\(136\) 0 0
\(137\) 13.7036 1.17078 0.585390 0.810752i \(-0.300941\pi\)
0.585390 + 0.810752i \(0.300941\pi\)
\(138\) 0 0
\(139\) −6.16193 −0.522648 −0.261324 0.965251i \(-0.584159\pi\)
−0.261324 + 0.965251i \(0.584159\pi\)
\(140\) 0 0
\(141\) 3.73944 0.314918
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −7.25185 −0.602233
\(146\) 0 0
\(147\) 0.979305 0.0807717
\(148\) 0 0
\(149\) 3.66700 0.300413 0.150206 0.988655i \(-0.452006\pi\)
0.150206 + 0.988655i \(0.452006\pi\)
\(150\) 0 0
\(151\) −16.4743 −1.34066 −0.670331 0.742062i \(-0.733848\pi\)
−0.670331 + 0.742062i \(0.733848\pi\)
\(152\) 0 0
\(153\) 5.32040 0.430129
\(154\) 0 0
\(155\) −17.0890 −1.37262
\(156\) 0 0
\(157\) −0.898098 −0.0716760 −0.0358380 0.999358i \(-0.511410\pi\)
−0.0358380 + 0.999358i \(0.511410\pi\)
\(158\) 0 0
\(159\) −11.6305 −0.922359
\(160\) 0 0
\(161\) −3.81847 −0.300937
\(162\) 0 0
\(163\) 6.05949 0.474616 0.237308 0.971435i \(-0.423735\pi\)
0.237308 + 0.971435i \(0.423735\pi\)
\(164\) 0 0
\(165\) 2.28458 0.177855
\(166\) 0 0
\(167\) −2.96978 −0.229809 −0.114904 0.993377i \(-0.536656\pi\)
−0.114904 + 0.993377i \(0.536656\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.90966 −0.451923
\(172\) 0 0
\(173\) −4.79498 −0.364556 −0.182278 0.983247i \(-0.558347\pi\)
−0.182278 + 0.983247i \(0.558347\pi\)
\(174\) 0 0
\(175\) −0.442245 −0.0334306
\(176\) 0 0
\(177\) −9.60271 −0.721784
\(178\) 0 0
\(179\) −15.6819 −1.17212 −0.586060 0.810268i \(-0.699322\pi\)
−0.586060 + 0.810268i \(0.699322\pi\)
\(180\) 0 0
\(181\) 21.5030 1.59830 0.799152 0.601129i \(-0.205282\pi\)
0.799152 + 0.601129i \(0.205282\pi\)
\(182\) 0 0
\(183\) 1.23501 0.0912946
\(184\) 0 0
\(185\) −3.41100 −0.250782
\(186\) 0 0
\(187\) −2.60681 −0.190629
\(188\) 0 0
\(189\) 4.93664 0.359088
\(190\) 0 0
\(191\) −12.9627 −0.937951 −0.468975 0.883211i \(-0.655377\pi\)
−0.468975 + 0.883211i \(0.655377\pi\)
\(192\) 0 0
\(193\) −10.8808 −0.783214 −0.391607 0.920133i \(-0.628081\pi\)
−0.391607 + 0.920133i \(0.628081\pi\)
\(194\) 0 0
\(195\) −2.28458 −0.163602
\(196\) 0 0
\(197\) −14.8956 −1.06127 −0.530635 0.847600i \(-0.678046\pi\)
−0.530635 + 0.847600i \(0.678046\pi\)
\(198\) 0 0
\(199\) 1.66656 0.118139 0.0590696 0.998254i \(-0.481187\pi\)
0.0590696 + 0.998254i \(0.481187\pi\)
\(200\) 0 0
\(201\) −4.82919 −0.340625
\(202\) 0 0
\(203\) 3.10856 0.218178
\(204\) 0 0
\(205\) −0.667338 −0.0466089
\(206\) 0 0
\(207\) −7.79334 −0.541675
\(208\) 0 0
\(209\) 2.89553 0.200288
\(210\) 0 0
\(211\) −16.7614 −1.15390 −0.576950 0.816780i \(-0.695757\pi\)
−0.576950 + 0.816780i \(0.695757\pi\)
\(212\) 0 0
\(213\) 15.8823 1.08824
\(214\) 0 0
\(215\) −21.4927 −1.46579
\(216\) 0 0
\(217\) 7.32534 0.497276
\(218\) 0 0
\(219\) 0.179378 0.0121212
\(220\) 0 0
\(221\) 2.60681 0.175353
\(222\) 0 0
\(223\) −4.79512 −0.321105 −0.160552 0.987027i \(-0.551328\pi\)
−0.160552 + 0.987027i \(0.551328\pi\)
\(224\) 0 0
\(225\) −0.902605 −0.0601736
\(226\) 0 0
\(227\) −11.5168 −0.764397 −0.382199 0.924080i \(-0.624833\pi\)
−0.382199 + 0.924080i \(0.624833\pi\)
\(228\) 0 0
\(229\) 14.1605 0.935754 0.467877 0.883794i \(-0.345019\pi\)
0.467877 + 0.883794i \(0.345019\pi\)
\(230\) 0 0
\(231\) −0.979305 −0.0644335
\(232\) 0 0
\(233\) −17.8496 −1.16936 −0.584682 0.811263i \(-0.698781\pi\)
−0.584682 + 0.811263i \(0.698781\pi\)
\(234\) 0 0
\(235\) 8.90795 0.581091
\(236\) 0 0
\(237\) −15.4033 −1.00055
\(238\) 0 0
\(239\) −25.0009 −1.61717 −0.808587 0.588377i \(-0.799767\pi\)
−0.808587 + 0.588377i \(0.799767\pi\)
\(240\) 0 0
\(241\) −3.85076 −0.248049 −0.124025 0.992279i \(-0.539580\pi\)
−0.124025 + 0.992279i \(0.539580\pi\)
\(242\) 0 0
\(243\) 16.0717 1.03100
\(244\) 0 0
\(245\) 2.33286 0.149041
\(246\) 0 0
\(247\) −2.89553 −0.184238
\(248\) 0 0
\(249\) 15.0117 0.951329
\(250\) 0 0
\(251\) 15.6235 0.986144 0.493072 0.869989i \(-0.335874\pi\)
0.493072 + 0.869989i \(0.335874\pi\)
\(252\) 0 0
\(253\) 3.81847 0.240065
\(254\) 0 0
\(255\) −5.95547 −0.372946
\(256\) 0 0
\(257\) 3.79105 0.236479 0.118239 0.992985i \(-0.462275\pi\)
0.118239 + 0.992985i \(0.462275\pi\)
\(258\) 0 0
\(259\) 1.46215 0.0908537
\(260\) 0 0
\(261\) 6.34445 0.392712
\(262\) 0 0
\(263\) 12.8208 0.790563 0.395282 0.918560i \(-0.370647\pi\)
0.395282 + 0.918560i \(0.370647\pi\)
\(264\) 0 0
\(265\) −27.7057 −1.70195
\(266\) 0 0
\(267\) −10.5761 −0.647249
\(268\) 0 0
\(269\) 17.2682 1.05286 0.526430 0.850218i \(-0.323530\pi\)
0.526430 + 0.850218i \(0.323530\pi\)
\(270\) 0 0
\(271\) 6.99630 0.424995 0.212497 0.977162i \(-0.431840\pi\)
0.212497 + 0.977162i \(0.431840\pi\)
\(272\) 0 0
\(273\) 0.979305 0.0592702
\(274\) 0 0
\(275\) 0.442245 0.0266684
\(276\) 0 0
\(277\) 21.5108 1.29246 0.646228 0.763144i \(-0.276345\pi\)
0.646228 + 0.763144i \(0.276345\pi\)
\(278\) 0 0
\(279\) 14.9507 0.895077
\(280\) 0 0
\(281\) 13.7124 0.818013 0.409007 0.912531i \(-0.365875\pi\)
0.409007 + 0.912531i \(0.365875\pi\)
\(282\) 0 0
\(283\) −26.2520 −1.56052 −0.780259 0.625457i \(-0.784913\pi\)
−0.780259 + 0.625457i \(0.784913\pi\)
\(284\) 0 0
\(285\) 6.61508 0.391844
\(286\) 0 0
\(287\) 0.286060 0.0168856
\(288\) 0 0
\(289\) −10.2045 −0.600267
\(290\) 0 0
\(291\) 4.60653 0.270040
\(292\) 0 0
\(293\) −2.63462 −0.153916 −0.0769581 0.997034i \(-0.524521\pi\)
−0.0769581 + 0.997034i \(0.524521\pi\)
\(294\) 0 0
\(295\) −22.8752 −1.33185
\(296\) 0 0
\(297\) −4.93664 −0.286453
\(298\) 0 0
\(299\) −3.81847 −0.220828
\(300\) 0 0
\(301\) 9.21304 0.531031
\(302\) 0 0
\(303\) −10.4614 −0.600991
\(304\) 0 0
\(305\) 2.94199 0.168458
\(306\) 0 0
\(307\) −15.6740 −0.894565 −0.447282 0.894393i \(-0.647608\pi\)
−0.447282 + 0.894393i \(0.647608\pi\)
\(308\) 0 0
\(309\) −12.8508 −0.731058
\(310\) 0 0
\(311\) 0.412463 0.0233886 0.0116943 0.999932i \(-0.496277\pi\)
0.0116943 + 0.999932i \(0.496277\pi\)
\(312\) 0 0
\(313\) −11.1735 −0.631563 −0.315782 0.948832i \(-0.602267\pi\)
−0.315782 + 0.948832i \(0.602267\pi\)
\(314\) 0 0
\(315\) 4.76128 0.268268
\(316\) 0 0
\(317\) 18.4553 1.03655 0.518276 0.855214i \(-0.326574\pi\)
0.518276 + 0.855214i \(0.326574\pi\)
\(318\) 0 0
\(319\) −3.10856 −0.174046
\(320\) 0 0
\(321\) −2.11539 −0.118070
\(322\) 0 0
\(323\) −7.54810 −0.419987
\(324\) 0 0
\(325\) −0.442245 −0.0245313
\(326\) 0 0
\(327\) 13.0246 0.720260
\(328\) 0 0
\(329\) −3.81847 −0.210519
\(330\) 0 0
\(331\) −17.1894 −0.944815 −0.472407 0.881380i \(-0.656615\pi\)
−0.472407 + 0.881380i \(0.656615\pi\)
\(332\) 0 0
\(333\) 2.98420 0.163533
\(334\) 0 0
\(335\) −11.5039 −0.628526
\(336\) 0 0
\(337\) −21.5406 −1.17339 −0.586697 0.809807i \(-0.699572\pi\)
−0.586697 + 0.809807i \(0.699572\pi\)
\(338\) 0 0
\(339\) 11.9238 0.647613
\(340\) 0 0
\(341\) −7.32534 −0.396689
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 8.72361 0.469663
\(346\) 0 0
\(347\) 7.68411 0.412505 0.206252 0.978499i \(-0.433873\pi\)
0.206252 + 0.978499i \(0.433873\pi\)
\(348\) 0 0
\(349\) −11.8842 −0.636145 −0.318073 0.948066i \(-0.603036\pi\)
−0.318073 + 0.948066i \(0.603036\pi\)
\(350\) 0 0
\(351\) 4.93664 0.263498
\(352\) 0 0
\(353\) 4.68606 0.249414 0.124707 0.992194i \(-0.460201\pi\)
0.124707 + 0.992194i \(0.460201\pi\)
\(354\) 0 0
\(355\) 37.8343 2.00804
\(356\) 0 0
\(357\) 2.55286 0.135112
\(358\) 0 0
\(359\) 14.1521 0.746918 0.373459 0.927647i \(-0.378172\pi\)
0.373459 + 0.927647i \(0.378172\pi\)
\(360\) 0 0
\(361\) −10.6159 −0.558732
\(362\) 0 0
\(363\) 0.979305 0.0514002
\(364\) 0 0
\(365\) 0.427307 0.0223663
\(366\) 0 0
\(367\) −16.9661 −0.885625 −0.442813 0.896614i \(-0.646019\pi\)
−0.442813 + 0.896614i \(0.646019\pi\)
\(368\) 0 0
\(369\) 0.583837 0.0303933
\(370\) 0 0
\(371\) 11.8763 0.616586
\(372\) 0 0
\(373\) 5.89452 0.305206 0.152603 0.988288i \(-0.451234\pi\)
0.152603 + 0.988288i \(0.451234\pi\)
\(374\) 0 0
\(375\) −10.4126 −0.537703
\(376\) 0 0
\(377\) 3.10856 0.160099
\(378\) 0 0
\(379\) 0.354818 0.0182258 0.00911289 0.999958i \(-0.497099\pi\)
0.00911289 + 0.999958i \(0.497099\pi\)
\(380\) 0 0
\(381\) −1.56390 −0.0801212
\(382\) 0 0
\(383\) −25.1046 −1.28279 −0.641393 0.767213i \(-0.721643\pi\)
−0.641393 + 0.767213i \(0.721643\pi\)
\(384\) 0 0
\(385\) −2.33286 −0.118894
\(386\) 0 0
\(387\) 18.8034 0.955833
\(388\) 0 0
\(389\) 17.4783 0.886187 0.443094 0.896475i \(-0.353881\pi\)
0.443094 + 0.896475i \(0.353881\pi\)
\(390\) 0 0
\(391\) −9.95401 −0.503396
\(392\) 0 0
\(393\) 5.60866 0.282919
\(394\) 0 0
\(395\) −36.6931 −1.84623
\(396\) 0 0
\(397\) 22.1899 1.11368 0.556840 0.830620i \(-0.312014\pi\)
0.556840 + 0.830620i \(0.312014\pi\)
\(398\) 0 0
\(399\) −2.83561 −0.141958
\(400\) 0 0
\(401\) 36.8152 1.83846 0.919230 0.393720i \(-0.128812\pi\)
0.919230 + 0.393720i \(0.128812\pi\)
\(402\) 0 0
\(403\) 7.32534 0.364901
\(404\) 0 0
\(405\) 3.00568 0.149353
\(406\) 0 0
\(407\) −1.46215 −0.0724762
\(408\) 0 0
\(409\) −4.59380 −0.227149 −0.113574 0.993529i \(-0.536230\pi\)
−0.113574 + 0.993529i \(0.536230\pi\)
\(410\) 0 0
\(411\) 13.4200 0.661961
\(412\) 0 0
\(413\) 9.80563 0.482504
\(414\) 0 0
\(415\) 35.7603 1.75541
\(416\) 0 0
\(417\) −6.03441 −0.295506
\(418\) 0 0
\(419\) 35.4748 1.73306 0.866528 0.499129i \(-0.166347\pi\)
0.866528 + 0.499129i \(0.166347\pi\)
\(420\) 0 0
\(421\) −10.7158 −0.522254 −0.261127 0.965304i \(-0.584094\pi\)
−0.261127 + 0.965304i \(0.584094\pi\)
\(422\) 0 0
\(423\) −7.79334 −0.378925
\(424\) 0 0
\(425\) −1.15285 −0.0559214
\(426\) 0 0
\(427\) −1.26111 −0.0610294
\(428\) 0 0
\(429\) −0.979305 −0.0472813
\(430\) 0 0
\(431\) 26.3325 1.26839 0.634197 0.773172i \(-0.281331\pi\)
0.634197 + 0.773172i \(0.281331\pi\)
\(432\) 0 0
\(433\) −20.8589 −1.00242 −0.501208 0.865327i \(-0.667111\pi\)
−0.501208 + 0.865327i \(0.667111\pi\)
\(434\) 0 0
\(435\) −7.10177 −0.340504
\(436\) 0 0
\(437\) 11.0565 0.528903
\(438\) 0 0
\(439\) −12.7517 −0.608606 −0.304303 0.952575i \(-0.598424\pi\)
−0.304303 + 0.952575i \(0.598424\pi\)
\(440\) 0 0
\(441\) −2.04096 −0.0971886
\(442\) 0 0
\(443\) −11.9295 −0.566789 −0.283395 0.959003i \(-0.591461\pi\)
−0.283395 + 0.959003i \(0.591461\pi\)
\(444\) 0 0
\(445\) −25.1940 −1.19431
\(446\) 0 0
\(447\) 3.59112 0.169854
\(448\) 0 0
\(449\) 0.651619 0.0307518 0.0153759 0.999882i \(-0.495106\pi\)
0.0153759 + 0.999882i \(0.495106\pi\)
\(450\) 0 0
\(451\) −0.286060 −0.0134700
\(452\) 0 0
\(453\) −16.1334 −0.758013
\(454\) 0 0
\(455\) 2.33286 0.109366
\(456\) 0 0
\(457\) 34.3642 1.60749 0.803745 0.594974i \(-0.202838\pi\)
0.803745 + 0.594974i \(0.202838\pi\)
\(458\) 0 0
\(459\) 12.8689 0.600668
\(460\) 0 0
\(461\) −10.1979 −0.474966 −0.237483 0.971392i \(-0.576322\pi\)
−0.237483 + 0.971392i \(0.576322\pi\)
\(462\) 0 0
\(463\) 29.6391 1.37745 0.688723 0.725025i \(-0.258172\pi\)
0.688723 + 0.725025i \(0.258172\pi\)
\(464\) 0 0
\(465\) −16.7353 −0.776083
\(466\) 0 0
\(467\) 5.97904 0.276677 0.138338 0.990385i \(-0.455824\pi\)
0.138338 + 0.990385i \(0.455824\pi\)
\(468\) 0 0
\(469\) 4.93124 0.227704
\(470\) 0 0
\(471\) −0.879512 −0.0405258
\(472\) 0 0
\(473\) −9.21304 −0.423616
\(474\) 0 0
\(475\) 1.28053 0.0587549
\(476\) 0 0
\(477\) 24.2390 1.10983
\(478\) 0 0
\(479\) −30.3925 −1.38867 −0.694334 0.719653i \(-0.744301\pi\)
−0.694334 + 0.719653i \(0.744301\pi\)
\(480\) 0 0
\(481\) 1.46215 0.0666684
\(482\) 0 0
\(483\) −3.73944 −0.170151
\(484\) 0 0
\(485\) 10.9735 0.498281
\(486\) 0 0
\(487\) 32.6920 1.48141 0.740707 0.671828i \(-0.234490\pi\)
0.740707 + 0.671828i \(0.234490\pi\)
\(488\) 0 0
\(489\) 5.93409 0.268349
\(490\) 0 0
\(491\) 30.6634 1.38382 0.691911 0.721983i \(-0.256769\pi\)
0.691911 + 0.721983i \(0.256769\pi\)
\(492\) 0 0
\(493\) 8.10343 0.364960
\(494\) 0 0
\(495\) −4.76128 −0.214004
\(496\) 0 0
\(497\) −16.2180 −0.727475
\(498\) 0 0
\(499\) 26.0432 1.16586 0.582928 0.812524i \(-0.301907\pi\)
0.582928 + 0.812524i \(0.301907\pi\)
\(500\) 0 0
\(501\) −2.90832 −0.129934
\(502\) 0 0
\(503\) −36.0360 −1.60677 −0.803384 0.595462i \(-0.796969\pi\)
−0.803384 + 0.595462i \(0.796969\pi\)
\(504\) 0 0
\(505\) −24.9207 −1.10896
\(506\) 0 0
\(507\) 0.979305 0.0434925
\(508\) 0 0
\(509\) −21.9584 −0.973290 −0.486645 0.873600i \(-0.661780\pi\)
−0.486645 + 0.873600i \(0.661780\pi\)
\(510\) 0 0
\(511\) −0.183169 −0.00810291
\(512\) 0 0
\(513\) −14.2942 −0.631104
\(514\) 0 0
\(515\) −30.6127 −1.34896
\(516\) 0 0
\(517\) 3.81847 0.167936
\(518\) 0 0
\(519\) −4.69575 −0.206120
\(520\) 0 0
\(521\) −19.5117 −0.854825 −0.427412 0.904057i \(-0.640575\pi\)
−0.427412 + 0.904057i \(0.640575\pi\)
\(522\) 0 0
\(523\) −27.8683 −1.21859 −0.609297 0.792942i \(-0.708548\pi\)
−0.609297 + 0.792942i \(0.708548\pi\)
\(524\) 0 0
\(525\) −0.433093 −0.0189017
\(526\) 0 0
\(527\) 19.0958 0.831824
\(528\) 0 0
\(529\) −8.41931 −0.366057
\(530\) 0 0
\(531\) 20.0129 0.868487
\(532\) 0 0
\(533\) 0.286060 0.0123906
\(534\) 0 0
\(535\) −5.03920 −0.217864
\(536\) 0 0
\(537\) −15.3574 −0.662719
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −15.9951 −0.687684 −0.343842 0.939027i \(-0.611728\pi\)
−0.343842 + 0.939027i \(0.611728\pi\)
\(542\) 0 0
\(543\) 21.0580 0.903685
\(544\) 0 0
\(545\) 31.0266 1.32903
\(546\) 0 0
\(547\) −39.3080 −1.68069 −0.840345 0.542053i \(-0.817647\pi\)
−0.840345 + 0.542053i \(0.817647\pi\)
\(548\) 0 0
\(549\) −2.57388 −0.109850
\(550\) 0 0
\(551\) −9.00093 −0.383453
\(552\) 0 0
\(553\) 15.7288 0.668856
\(554\) 0 0
\(555\) −3.34041 −0.141792
\(556\) 0 0
\(557\) −37.9317 −1.60722 −0.803608 0.595159i \(-0.797089\pi\)
−0.803608 + 0.595159i \(0.797089\pi\)
\(558\) 0 0
\(559\) 9.21304 0.389670
\(560\) 0 0
\(561\) −2.55286 −0.107782
\(562\) 0 0
\(563\) −34.9013 −1.47091 −0.735457 0.677571i \(-0.763032\pi\)
−0.735457 + 0.677571i \(0.763032\pi\)
\(564\) 0 0
\(565\) 28.4045 1.19498
\(566\) 0 0
\(567\) −1.28841 −0.0541080
\(568\) 0 0
\(569\) 23.3620 0.979384 0.489692 0.871895i \(-0.337109\pi\)
0.489692 + 0.871895i \(0.337109\pi\)
\(570\) 0 0
\(571\) 15.0498 0.629815 0.314907 0.949122i \(-0.398027\pi\)
0.314907 + 0.949122i \(0.398027\pi\)
\(572\) 0 0
\(573\) −12.6945 −0.530319
\(574\) 0 0
\(575\) 1.68870 0.0704235
\(576\) 0 0
\(577\) 17.8152 0.741656 0.370828 0.928702i \(-0.379074\pi\)
0.370828 + 0.928702i \(0.379074\pi\)
\(578\) 0 0
\(579\) −10.6556 −0.442831
\(580\) 0 0
\(581\) −15.3290 −0.635952
\(582\) 0 0
\(583\) −11.8763 −0.491865
\(584\) 0 0
\(585\) 4.76128 0.196855
\(586\) 0 0
\(587\) 28.4425 1.17395 0.586974 0.809606i \(-0.300319\pi\)
0.586974 + 0.809606i \(0.300319\pi\)
\(588\) 0 0
\(589\) −21.2107 −0.873973
\(590\) 0 0
\(591\) −14.5874 −0.600044
\(592\) 0 0
\(593\) 34.3548 1.41078 0.705392 0.708818i \(-0.250771\pi\)
0.705392 + 0.708818i \(0.250771\pi\)
\(594\) 0 0
\(595\) 6.08133 0.249310
\(596\) 0 0
\(597\) 1.63207 0.0667961
\(598\) 0 0
\(599\) −1.93947 −0.0792447 −0.0396223 0.999215i \(-0.512615\pi\)
−0.0396223 + 0.999215i \(0.512615\pi\)
\(600\) 0 0
\(601\) −19.9317 −0.813032 −0.406516 0.913644i \(-0.633256\pi\)
−0.406516 + 0.913644i \(0.633256\pi\)
\(602\) 0 0
\(603\) 10.0645 0.409857
\(604\) 0 0
\(605\) 2.33286 0.0948443
\(606\) 0 0
\(607\) −2.52805 −0.102611 −0.0513053 0.998683i \(-0.516338\pi\)
−0.0513053 + 0.998683i \(0.516338\pi\)
\(608\) 0 0
\(609\) 3.04423 0.123358
\(610\) 0 0
\(611\) −3.81847 −0.154479
\(612\) 0 0
\(613\) 13.3609 0.539641 0.269821 0.962911i \(-0.413036\pi\)
0.269821 + 0.962911i \(0.413036\pi\)
\(614\) 0 0
\(615\) −0.653527 −0.0263528
\(616\) 0 0
\(617\) 7.81741 0.314717 0.157359 0.987542i \(-0.449702\pi\)
0.157359 + 0.987542i \(0.449702\pi\)
\(618\) 0 0
\(619\) 23.8668 0.959288 0.479644 0.877463i \(-0.340766\pi\)
0.479644 + 0.877463i \(0.340766\pi\)
\(620\) 0 0
\(621\) −18.8504 −0.756440
\(622\) 0 0
\(623\) 10.7996 0.432678
\(624\) 0 0
\(625\) −27.0156 −1.08063
\(626\) 0 0
\(627\) 2.83561 0.113243
\(628\) 0 0
\(629\) 3.81155 0.151977
\(630\) 0 0
\(631\) −17.6974 −0.704523 −0.352262 0.935902i \(-0.614587\pi\)
−0.352262 + 0.935902i \(0.614587\pi\)
\(632\) 0 0
\(633\) −16.4145 −0.652417
\(634\) 0 0
\(635\) −3.72547 −0.147841
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −33.1003 −1.30943
\(640\) 0 0
\(641\) 33.6388 1.32865 0.664327 0.747442i \(-0.268718\pi\)
0.664327 + 0.747442i \(0.268718\pi\)
\(642\) 0 0
\(643\) 18.5558 0.731770 0.365885 0.930660i \(-0.380766\pi\)
0.365885 + 0.930660i \(0.380766\pi\)
\(644\) 0 0
\(645\) −21.0480 −0.828762
\(646\) 0 0
\(647\) 31.2113 1.22704 0.613521 0.789678i \(-0.289752\pi\)
0.613521 + 0.789678i \(0.289752\pi\)
\(648\) 0 0
\(649\) −9.80563 −0.384905
\(650\) 0 0
\(651\) 7.17374 0.281161
\(652\) 0 0
\(653\) −40.4228 −1.58186 −0.790932 0.611903i \(-0.790404\pi\)
−0.790932 + 0.611903i \(0.790404\pi\)
\(654\) 0 0
\(655\) 13.3607 0.522046
\(656\) 0 0
\(657\) −0.373840 −0.0145849
\(658\) 0 0
\(659\) −4.56349 −0.177768 −0.0888841 0.996042i \(-0.528330\pi\)
−0.0888841 + 0.996042i \(0.528330\pi\)
\(660\) 0 0
\(661\) −37.3024 −1.45090 −0.725448 0.688277i \(-0.758367\pi\)
−0.725448 + 0.688277i \(0.758367\pi\)
\(662\) 0 0
\(663\) 2.55286 0.0991449
\(664\) 0 0
\(665\) −6.75487 −0.261943
\(666\) 0 0
\(667\) −11.8699 −0.459606
\(668\) 0 0
\(669\) −4.69588 −0.181553
\(670\) 0 0
\(671\) 1.26111 0.0486846
\(672\) 0 0
\(673\) 38.2640 1.47497 0.737484 0.675365i \(-0.236014\pi\)
0.737484 + 0.675365i \(0.236014\pi\)
\(674\) 0 0
\(675\) −2.18320 −0.0840315
\(676\) 0 0
\(677\) 25.4686 0.978839 0.489419 0.872049i \(-0.337209\pi\)
0.489419 + 0.872049i \(0.337209\pi\)
\(678\) 0 0
\(679\) −4.70388 −0.180518
\(680\) 0 0
\(681\) −11.2785 −0.432192
\(682\) 0 0
\(683\) −12.6773 −0.485082 −0.242541 0.970141i \(-0.577981\pi\)
−0.242541 + 0.970141i \(0.577981\pi\)
\(684\) 0 0
\(685\) 31.9687 1.22146
\(686\) 0 0
\(687\) 13.8675 0.529077
\(688\) 0 0
\(689\) 11.8763 0.452450
\(690\) 0 0
\(691\) −33.9122 −1.29008 −0.645041 0.764148i \(-0.723160\pi\)
−0.645041 + 0.764148i \(0.723160\pi\)
\(692\) 0 0
\(693\) 2.04096 0.0775297
\(694\) 0 0
\(695\) −14.3749 −0.545272
\(696\) 0 0
\(697\) 0.745703 0.0282455
\(698\) 0 0
\(699\) −17.4802 −0.661161
\(700\) 0 0
\(701\) 43.5469 1.64474 0.822371 0.568951i \(-0.192651\pi\)
0.822371 + 0.568951i \(0.192651\pi\)
\(702\) 0 0
\(703\) −4.23371 −0.159677
\(704\) 0 0
\(705\) 8.72361 0.328550
\(706\) 0 0
\(707\) 10.6825 0.401755
\(708\) 0 0
\(709\) 44.5607 1.67351 0.836757 0.547574i \(-0.184449\pi\)
0.836757 + 0.547574i \(0.184449\pi\)
\(710\) 0 0
\(711\) 32.1018 1.20391
\(712\) 0 0
\(713\) −27.9716 −1.04754
\(714\) 0 0
\(715\) −2.33286 −0.0872441
\(716\) 0 0
\(717\) −24.4835 −0.914353
\(718\) 0 0
\(719\) −34.7805 −1.29709 −0.648546 0.761175i \(-0.724623\pi\)
−0.648546 + 0.761175i \(0.724623\pi\)
\(720\) 0 0
\(721\) 13.1224 0.488704
\(722\) 0 0
\(723\) −3.77107 −0.140248
\(724\) 0 0
\(725\) −1.37475 −0.0510568
\(726\) 0 0
\(727\) 28.7891 1.06773 0.533864 0.845571i \(-0.320740\pi\)
0.533864 + 0.845571i \(0.320740\pi\)
\(728\) 0 0
\(729\) 11.8738 0.439772
\(730\) 0 0
\(731\) 24.0166 0.888287
\(732\) 0 0
\(733\) 7.49094 0.276684 0.138342 0.990385i \(-0.455823\pi\)
0.138342 + 0.990385i \(0.455823\pi\)
\(734\) 0 0
\(735\) 2.28458 0.0842681
\(736\) 0 0
\(737\) −4.93124 −0.181645
\(738\) 0 0
\(739\) −34.5073 −1.26937 −0.634686 0.772770i \(-0.718871\pi\)
−0.634686 + 0.772770i \(0.718871\pi\)
\(740\) 0 0
\(741\) −2.83561 −0.104169
\(742\) 0 0
\(743\) −50.7560 −1.86206 −0.931028 0.364948i \(-0.881087\pi\)
−0.931028 + 0.364948i \(0.881087\pi\)
\(744\) 0 0
\(745\) 8.55462 0.313417
\(746\) 0 0
\(747\) −31.2858 −1.14469
\(748\) 0 0
\(749\) 2.16009 0.0789281
\(750\) 0 0
\(751\) −22.7913 −0.831666 −0.415833 0.909441i \(-0.636510\pi\)
−0.415833 + 0.909441i \(0.636510\pi\)
\(752\) 0 0
\(753\) 15.3001 0.557568
\(754\) 0 0
\(755\) −38.4323 −1.39870
\(756\) 0 0
\(757\) −7.70078 −0.279889 −0.139945 0.990159i \(-0.544692\pi\)
−0.139945 + 0.990159i \(0.544692\pi\)
\(758\) 0 0
\(759\) 3.73944 0.135733
\(760\) 0 0
\(761\) 0.329560 0.0119465 0.00597327 0.999982i \(-0.498099\pi\)
0.00597327 + 0.999982i \(0.498099\pi\)
\(762\) 0 0
\(763\) −13.2998 −0.481485
\(764\) 0 0
\(765\) 12.4118 0.448748
\(766\) 0 0
\(767\) 9.80563 0.354061
\(768\) 0 0
\(769\) 24.9152 0.898465 0.449233 0.893415i \(-0.351697\pi\)
0.449233 + 0.893415i \(0.351697\pi\)
\(770\) 0 0
\(771\) 3.71259 0.133706
\(772\) 0 0
\(773\) 36.0350 1.29609 0.648044 0.761603i \(-0.275587\pi\)
0.648044 + 0.761603i \(0.275587\pi\)
\(774\) 0 0
\(775\) −3.23959 −0.116370
\(776\) 0 0
\(777\) 1.43189 0.0513689
\(778\) 0 0
\(779\) −0.828294 −0.0296767
\(780\) 0 0
\(781\) 16.2180 0.580325
\(782\) 0 0
\(783\) 15.3458 0.548416
\(784\) 0 0
\(785\) −2.09514 −0.0747787
\(786\) 0 0
\(787\) −37.0281 −1.31991 −0.659955 0.751305i \(-0.729425\pi\)
−0.659955 + 0.751305i \(0.729425\pi\)
\(788\) 0 0
\(789\) 12.5555 0.446986
\(790\) 0 0
\(791\) −12.1758 −0.432922
\(792\) 0 0
\(793\) −1.26111 −0.0447833
\(794\) 0 0
\(795\) −27.1324 −0.962285
\(796\) 0 0
\(797\) −24.8666 −0.880820 −0.440410 0.897797i \(-0.645167\pi\)
−0.440410 + 0.897797i \(0.645167\pi\)
\(798\) 0 0
\(799\) −9.95401 −0.352148
\(800\) 0 0
\(801\) 22.0416 0.778803
\(802\) 0 0
\(803\) 0.183169 0.00646388
\(804\) 0 0
\(805\) −8.90795 −0.313964
\(806\) 0 0
\(807\) 16.9108 0.595290
\(808\) 0 0
\(809\) −38.9534 −1.36953 −0.684764 0.728765i \(-0.740095\pi\)
−0.684764 + 0.728765i \(0.740095\pi\)
\(810\) 0 0
\(811\) −4.20179 −0.147545 −0.0737724 0.997275i \(-0.523504\pi\)
−0.0737724 + 0.997275i \(0.523504\pi\)
\(812\) 0 0
\(813\) 6.85151 0.240293
\(814\) 0 0
\(815\) 14.1359 0.495161
\(816\) 0 0
\(817\) −26.6766 −0.933297
\(818\) 0 0
\(819\) −2.04096 −0.0713170
\(820\) 0 0
\(821\) 24.8090 0.865842 0.432921 0.901432i \(-0.357483\pi\)
0.432921 + 0.901432i \(0.357483\pi\)
\(822\) 0 0
\(823\) 14.1090 0.491809 0.245905 0.969294i \(-0.420915\pi\)
0.245905 + 0.969294i \(0.420915\pi\)
\(824\) 0 0
\(825\) 0.433093 0.0150784
\(826\) 0 0
\(827\) 37.9753 1.32053 0.660266 0.751032i \(-0.270444\pi\)
0.660266 + 0.751032i \(0.270444\pi\)
\(828\) 0 0
\(829\) 10.8367 0.376374 0.188187 0.982133i \(-0.439739\pi\)
0.188187 + 0.982133i \(0.439739\pi\)
\(830\) 0 0
\(831\) 21.0656 0.730757
\(832\) 0 0
\(833\) −2.60681 −0.0903206
\(834\) 0 0
\(835\) −6.92809 −0.239757
\(836\) 0 0
\(837\) 36.1626 1.24996
\(838\) 0 0
\(839\) 47.9990 1.65711 0.828555 0.559908i \(-0.189163\pi\)
0.828555 + 0.559908i \(0.189163\pi\)
\(840\) 0 0
\(841\) −19.3368 −0.666788
\(842\) 0 0
\(843\) 13.4286 0.462506
\(844\) 0 0
\(845\) 2.33286 0.0802529
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) −25.7087 −0.882320
\(850\) 0 0
\(851\) −5.58318 −0.191389
\(852\) 0 0
\(853\) −34.6149 −1.18519 −0.592595 0.805500i \(-0.701897\pi\)
−0.592595 + 0.805500i \(0.701897\pi\)
\(854\) 0 0
\(855\) −13.7864 −0.471486
\(856\) 0 0
\(857\) −26.3956 −0.901656 −0.450828 0.892611i \(-0.648871\pi\)
−0.450828 + 0.892611i \(0.648871\pi\)
\(858\) 0 0
\(859\) −28.1458 −0.960323 −0.480162 0.877180i \(-0.659422\pi\)
−0.480162 + 0.877180i \(0.659422\pi\)
\(860\) 0 0
\(861\) 0.280140 0.00954714
\(862\) 0 0
\(863\) −1.08423 −0.0369077 −0.0184539 0.999830i \(-0.505874\pi\)
−0.0184539 + 0.999830i \(0.505874\pi\)
\(864\) 0 0
\(865\) −11.1860 −0.380336
\(866\) 0 0
\(867\) −9.99336 −0.339392
\(868\) 0 0
\(869\) −15.7288 −0.533562
\(870\) 0 0
\(871\) 4.93124 0.167089
\(872\) 0 0
\(873\) −9.60043 −0.324925
\(874\) 0 0
\(875\) 10.6326 0.359448
\(876\) 0 0
\(877\) 15.7169 0.530723 0.265362 0.964149i \(-0.414509\pi\)
0.265362 + 0.964149i \(0.414509\pi\)
\(878\) 0 0
\(879\) −2.58010 −0.0870245
\(880\) 0 0
\(881\) −33.9150 −1.14262 −0.571312 0.820733i \(-0.693566\pi\)
−0.571312 + 0.820733i \(0.693566\pi\)
\(882\) 0 0
\(883\) −5.38111 −0.181089 −0.0905444 0.995892i \(-0.528861\pi\)
−0.0905444 + 0.995892i \(0.528861\pi\)
\(884\) 0 0
\(885\) −22.4018 −0.753028
\(886\) 0 0
\(887\) 18.0514 0.606107 0.303053 0.952974i \(-0.401994\pi\)
0.303053 + 0.952974i \(0.401994\pi\)
\(888\) 0 0
\(889\) 1.59695 0.0535600
\(890\) 0 0
\(891\) 1.28841 0.0431633
\(892\) 0 0
\(893\) 11.0565 0.369991
\(894\) 0 0
\(895\) −36.5837 −1.22286
\(896\) 0 0
\(897\) −3.73944 −0.124856
\(898\) 0 0
\(899\) 22.7713 0.759464
\(900\) 0 0
\(901\) 30.9592 1.03140
\(902\) 0 0
\(903\) 9.02237 0.300246
\(904\) 0 0
\(905\) 50.1635 1.66749
\(906\) 0 0
\(907\) 17.4949 0.580909 0.290454 0.956889i \(-0.406194\pi\)
0.290454 + 0.956889i \(0.406194\pi\)
\(908\) 0 0
\(909\) 21.8025 0.723143
\(910\) 0 0
\(911\) −43.7260 −1.44871 −0.724353 0.689429i \(-0.757861\pi\)
−0.724353 + 0.689429i \(0.757861\pi\)
\(912\) 0 0
\(913\) 15.3290 0.507314
\(914\) 0 0
\(915\) 2.88111 0.0952466
\(916\) 0 0
\(917\) −5.72718 −0.189128
\(918\) 0 0
\(919\) −5.76629 −0.190212 −0.0951061 0.995467i \(-0.530319\pi\)
−0.0951061 + 0.995467i \(0.530319\pi\)
\(920\) 0 0
\(921\) −15.3497 −0.505789
\(922\) 0 0
\(923\) −16.2180 −0.533821
\(924\) 0 0
\(925\) −0.646629 −0.0212610
\(926\) 0 0
\(927\) 26.7823 0.879646
\(928\) 0 0
\(929\) 0.993416 0.0325929 0.0162965 0.999867i \(-0.494812\pi\)
0.0162965 + 0.999867i \(0.494812\pi\)
\(930\) 0 0
\(931\) 2.89553 0.0948972
\(932\) 0 0
\(933\) 0.403927 0.0132240
\(934\) 0 0
\(935\) −6.08133 −0.198881
\(936\) 0 0
\(937\) 7.98084 0.260723 0.130361 0.991467i \(-0.458386\pi\)
0.130361 + 0.991467i \(0.458386\pi\)
\(938\) 0 0
\(939\) −10.9423 −0.357087
\(940\) 0 0
\(941\) 2.46084 0.0802212 0.0401106 0.999195i \(-0.487229\pi\)
0.0401106 + 0.999195i \(0.487229\pi\)
\(942\) 0 0
\(943\) −1.09231 −0.0355705
\(944\) 0 0
\(945\) 11.5165 0.374632
\(946\) 0 0
\(947\) −22.5354 −0.732301 −0.366150 0.930556i \(-0.619324\pi\)
−0.366150 + 0.930556i \(0.619324\pi\)
\(948\) 0 0
\(949\) −0.183169 −0.00594591
\(950\) 0 0
\(951\) 18.0733 0.586068
\(952\) 0 0
\(953\) −0.811014 −0.0262713 −0.0131357 0.999914i \(-0.504181\pi\)
−0.0131357 + 0.999914i \(0.504181\pi\)
\(954\) 0 0
\(955\) −30.2403 −0.978552
\(956\) 0 0
\(957\) −3.04423 −0.0984060
\(958\) 0 0
\(959\) −13.7036 −0.442513
\(960\) 0 0
\(961\) 22.6606 0.730986
\(962\) 0 0
\(963\) 4.40867 0.142067
\(964\) 0 0
\(965\) −25.3833 −0.817118
\(966\) 0 0
\(967\) 49.2075 1.58241 0.791203 0.611554i \(-0.209455\pi\)
0.791203 + 0.611554i \(0.209455\pi\)
\(968\) 0 0
\(969\) −7.39189 −0.237462
\(970\) 0 0
\(971\) 19.9554 0.640398 0.320199 0.947350i \(-0.396250\pi\)
0.320199 + 0.947350i \(0.396250\pi\)
\(972\) 0 0
\(973\) 6.16193 0.197542
\(974\) 0 0
\(975\) −0.433093 −0.0138701
\(976\) 0 0
\(977\) −29.0330 −0.928849 −0.464424 0.885613i \(-0.653739\pi\)
−0.464424 + 0.885613i \(0.653739\pi\)
\(978\) 0 0
\(979\) −10.7996 −0.345158
\(980\) 0 0
\(981\) −27.1444 −0.866653
\(982\) 0 0
\(983\) −0.451059 −0.0143866 −0.00719328 0.999974i \(-0.502290\pi\)
−0.00719328 + 0.999974i \(0.502290\pi\)
\(984\) 0 0
\(985\) −34.7495 −1.10721
\(986\) 0 0
\(987\) −3.73944 −0.119028
\(988\) 0 0
\(989\) −35.1797 −1.11865
\(990\) 0 0
\(991\) −12.7744 −0.405791 −0.202896 0.979200i \(-0.565035\pi\)
−0.202896 + 0.979200i \(0.565035\pi\)
\(992\) 0 0
\(993\) −16.8337 −0.534200
\(994\) 0 0
\(995\) 3.88785 0.123253
\(996\) 0 0
\(997\) 14.5482 0.460745 0.230373 0.973102i \(-0.426006\pi\)
0.230373 + 0.973102i \(0.426006\pi\)
\(998\) 0 0
\(999\) 7.21812 0.228371
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 \(a_p\))