Properties

Label 8008.2.a.v.1.3
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 1.3
Root \(1.49423\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.49423 q^{3} -2.57953 q^{5} -1.00000 q^{7} -0.767273 q^{9} +O(q^{10})\) \(q-1.49423 q^{3} -2.57953 q^{5} -1.00000 q^{7} -0.767273 q^{9} +1.00000 q^{11} -1.00000 q^{13} +3.85441 q^{15} -3.29504 q^{17} +3.91608 q^{19} +1.49423 q^{21} -2.83448 q^{23} +1.65397 q^{25} +5.62918 q^{27} -5.39617 q^{29} +7.50095 q^{31} -1.49423 q^{33} +2.57953 q^{35} +8.01604 q^{37} +1.49423 q^{39} -4.23796 q^{41} -2.91466 q^{43} +1.97920 q^{45} -2.83448 q^{47} +1.00000 q^{49} +4.92355 q^{51} +2.31459 q^{53} -2.57953 q^{55} -5.85154 q^{57} -5.37744 q^{59} +0.473694 q^{61} +0.767273 q^{63} +2.57953 q^{65} +4.81638 q^{67} +4.23537 q^{69} +12.6839 q^{71} +8.61377 q^{73} -2.47141 q^{75} -1.00000 q^{77} -1.69788 q^{79} -6.10948 q^{81} +5.19688 q^{83} +8.49965 q^{85} +8.06313 q^{87} +16.6460 q^{89} +1.00000 q^{91} -11.2082 q^{93} -10.1017 q^{95} +5.14154 q^{97} -0.767273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + O(q^{10}) \) \( 11q - 2q^{3} + 2q^{5} - 11q^{7} + 9q^{9} + 11q^{11} - 11q^{13} - 7q^{15} - 4q^{17} - 16q^{19} + 2q^{21} - 3q^{23} + 11q^{25} - 11q^{27} + q^{29} + 14q^{31} - 2q^{33} - 2q^{35} - 8q^{37} + 2q^{39} + 4q^{41} - 30q^{43} + 13q^{45} - 3q^{47} + 11q^{49} - 14q^{51} - 5q^{53} + 2q^{55} - 22q^{57} + 11q^{59} + 15q^{61} - 9q^{63} - 2q^{65} - 41q^{67} + 12q^{69} + q^{71} - 8q^{73} - 24q^{75} - 11q^{77} - 26q^{79} + 19q^{81} - 31q^{83} - 27q^{85} - 25q^{87} + 2q^{89} + 11q^{91} - 37q^{93} - 6q^{97} + 9q^{99} + O(q^{100}) \)

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
\(3\) −1.49423 −0.862695 −0.431347 0.902186i \(-0.641962\pi\)
−0.431347 + 0.902186i \(0.641962\pi\)
\(4\) 0 0
\(5\) −2.57953 −1.15360 −0.576800 0.816885i \(-0.695699\pi\)
−0.576800 + 0.816885i \(0.695699\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.767273 −0.255758
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 3.85441 0.995205
\(16\) 0 0
\(17\) −3.29504 −0.799165 −0.399582 0.916697i \(-0.630845\pi\)
−0.399582 + 0.916697i \(0.630845\pi\)
\(18\) 0 0
\(19\) 3.91608 0.898411 0.449206 0.893428i \(-0.351707\pi\)
0.449206 + 0.893428i \(0.351707\pi\)
\(20\) 0 0
\(21\) 1.49423 0.326068
\(22\) 0 0
\(23\) −2.83448 −0.591031 −0.295515 0.955338i \(-0.595491\pi\)
−0.295515 + 0.955338i \(0.595491\pi\)
\(24\) 0 0
\(25\) 1.65397 0.330794
\(26\) 0 0
\(27\) 5.62918 1.08334
\(28\) 0 0
\(29\) −5.39617 −1.00204 −0.501022 0.865435i \(-0.667042\pi\)
−0.501022 + 0.865435i \(0.667042\pi\)
\(30\) 0 0
\(31\) 7.50095 1.34721 0.673605 0.739091i \(-0.264745\pi\)
0.673605 + 0.739091i \(0.264745\pi\)
\(32\) 0 0
\(33\) −1.49423 −0.260112
\(34\) 0 0
\(35\) 2.57953 0.436020
\(36\) 0 0
\(37\) 8.01604 1.31783 0.658914 0.752218i \(-0.271016\pi\)
0.658914 + 0.752218i \(0.271016\pi\)
\(38\) 0 0
\(39\) 1.49423 0.239269
\(40\) 0 0
\(41\) −4.23796 −0.661858 −0.330929 0.943656i \(-0.607362\pi\)
−0.330929 + 0.943656i \(0.607362\pi\)
\(42\) 0 0
\(43\) −2.91466 −0.444482 −0.222241 0.974992i \(-0.571337\pi\)
−0.222241 + 0.974992i \(0.571337\pi\)
\(44\) 0 0
\(45\) 1.97920 0.295042
\(46\) 0 0
\(47\) −2.83448 −0.413452 −0.206726 0.978399i \(-0.566281\pi\)
−0.206726 + 0.978399i \(0.566281\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 4.92355 0.689436
\(52\) 0 0
\(53\) 2.31459 0.317933 0.158966 0.987284i \(-0.449184\pi\)
0.158966 + 0.987284i \(0.449184\pi\)
\(54\) 0 0
\(55\) −2.57953 −0.347824
\(56\) 0 0
\(57\) −5.85154 −0.775055
\(58\) 0 0
\(59\) −5.37744 −0.700083 −0.350041 0.936734i \(-0.613833\pi\)
−0.350041 + 0.936734i \(0.613833\pi\)
\(60\) 0 0
\(61\) 0.473694 0.0606503 0.0303252 0.999540i \(-0.490346\pi\)
0.0303252 + 0.999540i \(0.490346\pi\)
\(62\) 0 0
\(63\) 0.767273 0.0966673
\(64\) 0 0
\(65\) 2.57953 0.319951
\(66\) 0 0
\(67\) 4.81638 0.588414 0.294207 0.955742i \(-0.404944\pi\)
0.294207 + 0.955742i \(0.404944\pi\)
\(68\) 0 0
\(69\) 4.23537 0.509879
\(70\) 0 0
\(71\) 12.6839 1.50530 0.752650 0.658420i \(-0.228775\pi\)
0.752650 + 0.658420i \(0.228775\pi\)
\(72\) 0 0
\(73\) 8.61377 1.00817 0.504083 0.863655i \(-0.331831\pi\)
0.504083 + 0.863655i \(0.331831\pi\)
\(74\) 0 0
\(75\) −2.47141 −0.285374
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −1.69788 −0.191027 −0.0955133 0.995428i \(-0.530449\pi\)
−0.0955133 + 0.995428i \(0.530449\pi\)
\(80\) 0 0
\(81\) −6.10948 −0.678831
\(82\) 0 0
\(83\) 5.19688 0.570431 0.285216 0.958463i \(-0.407935\pi\)
0.285216 + 0.958463i \(0.407935\pi\)
\(84\) 0 0
\(85\) 8.49965 0.921917
\(86\) 0 0
\(87\) 8.06313 0.864458
\(88\) 0 0
\(89\) 16.6460 1.76447 0.882234 0.470812i \(-0.156039\pi\)
0.882234 + 0.470812i \(0.156039\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −11.2082 −1.16223
\(94\) 0 0
\(95\) −10.1017 −1.03641
\(96\) 0 0
\(97\) 5.14154 0.522044 0.261022 0.965333i \(-0.415940\pi\)
0.261022 + 0.965333i \(0.415940\pi\)
\(98\) 0 0
\(99\) −0.767273 −0.0771138
\(100\) 0 0
\(101\) −1.60983 −0.160184 −0.0800921 0.996787i \(-0.525521\pi\)
−0.0800921 + 0.996787i \(0.525521\pi\)
\(102\) 0 0
\(103\) 13.1504 1.29575 0.647874 0.761747i \(-0.275658\pi\)
0.647874 + 0.761747i \(0.275658\pi\)
\(104\) 0 0
\(105\) −3.85441 −0.376152
\(106\) 0 0
\(107\) −4.61859 −0.446496 −0.223248 0.974762i \(-0.571666\pi\)
−0.223248 + 0.974762i \(0.571666\pi\)
\(108\) 0 0
\(109\) −4.20419 −0.402688 −0.201344 0.979521i \(-0.564531\pi\)
−0.201344 + 0.979521i \(0.564531\pi\)
\(110\) 0 0
\(111\) −11.9778 −1.13688
\(112\) 0 0
\(113\) −1.27349 −0.119800 −0.0599001 0.998204i \(-0.519078\pi\)
−0.0599001 + 0.998204i \(0.519078\pi\)
\(114\) 0 0
\(115\) 7.31163 0.681813
\(116\) 0 0
\(117\) 0.767273 0.0709344
\(118\) 0 0
\(119\) 3.29504 0.302056
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 6.33249 0.570982
\(124\) 0 0
\(125\) 8.63118 0.771997
\(126\) 0 0
\(127\) −8.83489 −0.783970 −0.391985 0.919972i \(-0.628211\pi\)
−0.391985 + 0.919972i \(0.628211\pi\)
\(128\) 0 0
\(129\) 4.35518 0.383452
\(130\) 0 0
\(131\) −2.56430 −0.224044 −0.112022 0.993706i \(-0.535733\pi\)
−0.112022 + 0.993706i \(0.535733\pi\)
\(132\) 0 0
\(133\) −3.91608 −0.339568
\(134\) 0 0
\(135\) −14.5206 −1.24974
\(136\) 0 0
\(137\) −12.1840 −1.04095 −0.520475 0.853877i \(-0.674245\pi\)
−0.520475 + 0.853877i \(0.674245\pi\)
\(138\) 0 0
\(139\) −13.7940 −1.16999 −0.584996 0.811036i \(-0.698904\pi\)
−0.584996 + 0.811036i \(0.698904\pi\)
\(140\) 0 0
\(141\) 4.23537 0.356683
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 13.9196 1.15596
\(146\) 0 0
\(147\) −1.49423 −0.123242
\(148\) 0 0
\(149\) −4.27576 −0.350284 −0.175142 0.984543i \(-0.556038\pi\)
−0.175142 + 0.984543i \(0.556038\pi\)
\(150\) 0 0
\(151\) −7.18999 −0.585113 −0.292557 0.956248i \(-0.594506\pi\)
−0.292557 + 0.956248i \(0.594506\pi\)
\(152\) 0 0
\(153\) 2.52820 0.204392
\(154\) 0 0
\(155\) −19.3489 −1.55414
\(156\) 0 0
\(157\) 2.09003 0.166802 0.0834011 0.996516i \(-0.473422\pi\)
0.0834011 + 0.996516i \(0.473422\pi\)
\(158\) 0 0
\(159\) −3.45853 −0.274279
\(160\) 0 0
\(161\) 2.83448 0.223389
\(162\) 0 0
\(163\) 10.8065 0.846431 0.423215 0.906029i \(-0.360901\pi\)
0.423215 + 0.906029i \(0.360901\pi\)
\(164\) 0 0
\(165\) 3.85441 0.300066
\(166\) 0 0
\(167\) −21.8989 −1.69459 −0.847294 0.531124i \(-0.821770\pi\)
−0.847294 + 0.531124i \(0.821770\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −3.00470 −0.229775
\(172\) 0 0
\(173\) 2.45208 0.186428 0.0932142 0.995646i \(-0.470286\pi\)
0.0932142 + 0.995646i \(0.470286\pi\)
\(174\) 0 0
\(175\) −1.65397 −0.125028
\(176\) 0 0
\(177\) 8.03514 0.603958
\(178\) 0 0
\(179\) −2.27441 −0.169997 −0.0849987 0.996381i \(-0.527089\pi\)
−0.0849987 + 0.996381i \(0.527089\pi\)
\(180\) 0 0
\(181\) 18.4486 1.37128 0.685638 0.727942i \(-0.259523\pi\)
0.685638 + 0.727942i \(0.259523\pi\)
\(182\) 0 0
\(183\) −0.707809 −0.0523227
\(184\) 0 0
\(185\) −20.6776 −1.52025
\(186\) 0 0
\(187\) −3.29504 −0.240957
\(188\) 0 0
\(189\) −5.62918 −0.409462
\(190\) 0 0
\(191\) −3.15929 −0.228598 −0.114299 0.993446i \(-0.536462\pi\)
−0.114299 + 0.993446i \(0.536462\pi\)
\(192\) 0 0
\(193\) 2.87644 0.207050 0.103525 0.994627i \(-0.466988\pi\)
0.103525 + 0.994627i \(0.466988\pi\)
\(194\) 0 0
\(195\) −3.85441 −0.276020
\(196\) 0 0
\(197\) −1.42134 −0.101267 −0.0506333 0.998717i \(-0.516124\pi\)
−0.0506333 + 0.998717i \(0.516124\pi\)
\(198\) 0 0
\(199\) 11.3032 0.801260 0.400630 0.916240i \(-0.368791\pi\)
0.400630 + 0.916240i \(0.368791\pi\)
\(200\) 0 0
\(201\) −7.19679 −0.507622
\(202\) 0 0
\(203\) 5.39617 0.378737
\(204\) 0 0
\(205\) 10.9319 0.763520
\(206\) 0 0
\(207\) 2.17482 0.151161
\(208\) 0 0
\(209\) 3.91608 0.270881
\(210\) 0 0
\(211\) −12.8290 −0.883184 −0.441592 0.897216i \(-0.645586\pi\)
−0.441592 + 0.897216i \(0.645586\pi\)
\(212\) 0 0
\(213\) −18.9527 −1.29862
\(214\) 0 0
\(215\) 7.51846 0.512755
\(216\) 0 0
\(217\) −7.50095 −0.509198
\(218\) 0 0
\(219\) −12.8710 −0.869740
\(220\) 0 0
\(221\) 3.29504 0.221648
\(222\) 0 0
\(223\) 3.42508 0.229360 0.114680 0.993402i \(-0.463416\pi\)
0.114680 + 0.993402i \(0.463416\pi\)
\(224\) 0 0
\(225\) −1.26904 −0.0846030
\(226\) 0 0
\(227\) −15.5787 −1.03399 −0.516997 0.855987i \(-0.672950\pi\)
−0.516997 + 0.855987i \(0.672950\pi\)
\(228\) 0 0
\(229\) 8.82349 0.583073 0.291536 0.956560i \(-0.405834\pi\)
0.291536 + 0.956560i \(0.405834\pi\)
\(230\) 0 0
\(231\) 1.49423 0.0983132
\(232\) 0 0
\(233\) −3.65547 −0.239478 −0.119739 0.992805i \(-0.538206\pi\)
−0.119739 + 0.992805i \(0.538206\pi\)
\(234\) 0 0
\(235\) 7.31163 0.476958
\(236\) 0 0
\(237\) 2.53703 0.164798
\(238\) 0 0
\(239\) 19.8061 1.28115 0.640574 0.767896i \(-0.278696\pi\)
0.640574 + 0.767896i \(0.278696\pi\)
\(240\) 0 0
\(241\) 16.3948 1.05608 0.528042 0.849218i \(-0.322926\pi\)
0.528042 + 0.849218i \(0.322926\pi\)
\(242\) 0 0
\(243\) −7.75856 −0.497712
\(244\) 0 0
\(245\) −2.57953 −0.164800
\(246\) 0 0
\(247\) −3.91608 −0.249175
\(248\) 0 0
\(249\) −7.76534 −0.492108
\(250\) 0 0
\(251\) 10.7051 0.675697 0.337848 0.941201i \(-0.390301\pi\)
0.337848 + 0.941201i \(0.390301\pi\)
\(252\) 0 0
\(253\) −2.83448 −0.178202
\(254\) 0 0
\(255\) −12.7005 −0.795333
\(256\) 0 0
\(257\) 1.29828 0.0809843 0.0404921 0.999180i \(-0.487107\pi\)
0.0404921 + 0.999180i \(0.487107\pi\)
\(258\) 0 0
\(259\) −8.01604 −0.498092
\(260\) 0 0
\(261\) 4.14033 0.256280
\(262\) 0 0
\(263\) −0.476095 −0.0293573 −0.0146786 0.999892i \(-0.504673\pi\)
−0.0146786 + 0.999892i \(0.504673\pi\)
\(264\) 0 0
\(265\) −5.97054 −0.366767
\(266\) 0 0
\(267\) −24.8729 −1.52220
\(268\) 0 0
\(269\) −15.2027 −0.926925 −0.463462 0.886117i \(-0.653393\pi\)
−0.463462 + 0.886117i \(0.653393\pi\)
\(270\) 0 0
\(271\) 0.405689 0.0246438 0.0123219 0.999924i \(-0.496078\pi\)
0.0123219 + 0.999924i \(0.496078\pi\)
\(272\) 0 0
\(273\) −1.49423 −0.0904350
\(274\) 0 0
\(275\) 1.65397 0.0997381
\(276\) 0 0
\(277\) 3.09788 0.186133 0.0930667 0.995660i \(-0.470333\pi\)
0.0930667 + 0.995660i \(0.470333\pi\)
\(278\) 0 0
\(279\) −5.75527 −0.344559
\(280\) 0 0
\(281\) −21.7331 −1.29649 −0.648245 0.761432i \(-0.724497\pi\)
−0.648245 + 0.761432i \(0.724497\pi\)
\(282\) 0 0
\(283\) −27.1040 −1.61117 −0.805583 0.592483i \(-0.798148\pi\)
−0.805583 + 0.592483i \(0.798148\pi\)
\(284\) 0 0
\(285\) 15.0942 0.894104
\(286\) 0 0
\(287\) 4.23796 0.250159
\(288\) 0 0
\(289\) −6.14270 −0.361335
\(290\) 0 0
\(291\) −7.68265 −0.450365
\(292\) 0 0
\(293\) 5.04838 0.294929 0.147465 0.989067i \(-0.452889\pi\)
0.147465 + 0.989067i \(0.452889\pi\)
\(294\) 0 0
\(295\) 13.8713 0.807616
\(296\) 0 0
\(297\) 5.62918 0.326638
\(298\) 0 0
\(299\) 2.83448 0.163922
\(300\) 0 0
\(301\) 2.91466 0.167998
\(302\) 0 0
\(303\) 2.40546 0.138190
\(304\) 0 0
\(305\) −1.22191 −0.0699662
\(306\) 0 0
\(307\) −30.0630 −1.71579 −0.857894 0.513827i \(-0.828227\pi\)
−0.857894 + 0.513827i \(0.828227\pi\)
\(308\) 0 0
\(309\) −19.6498 −1.11784
\(310\) 0 0
\(311\) −31.4567 −1.78374 −0.891872 0.452287i \(-0.850608\pi\)
−0.891872 + 0.452287i \(0.850608\pi\)
\(312\) 0 0
\(313\) 25.5649 1.44501 0.722505 0.691365i \(-0.242990\pi\)
0.722505 + 0.691365i \(0.242990\pi\)
\(314\) 0 0
\(315\) −1.97920 −0.111515
\(316\) 0 0
\(317\) −11.5013 −0.645980 −0.322990 0.946402i \(-0.604688\pi\)
−0.322990 + 0.946402i \(0.604688\pi\)
\(318\) 0 0
\(319\) −5.39617 −0.302128
\(320\) 0 0
\(321\) 6.90124 0.385190
\(322\) 0 0
\(323\) −12.9037 −0.717979
\(324\) 0 0
\(325\) −1.65397 −0.0917457
\(326\) 0 0
\(327\) 6.28203 0.347397
\(328\) 0 0
\(329\) 2.83448 0.156270
\(330\) 0 0
\(331\) 14.3610 0.789350 0.394675 0.918821i \(-0.370857\pi\)
0.394675 + 0.918821i \(0.370857\pi\)
\(332\) 0 0
\(333\) −6.15048 −0.337044
\(334\) 0 0
\(335\) −12.4240 −0.678795
\(336\) 0 0
\(337\) −30.4289 −1.65757 −0.828785 0.559567i \(-0.810967\pi\)
−0.828785 + 0.559567i \(0.810967\pi\)
\(338\) 0 0
\(339\) 1.90289 0.103351
\(340\) 0 0
\(341\) 7.50095 0.406199
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −10.9253 −0.588197
\(346\) 0 0
\(347\) −17.1430 −0.920285 −0.460143 0.887845i \(-0.652202\pi\)
−0.460143 + 0.887845i \(0.652202\pi\)
\(348\) 0 0
\(349\) −4.83230 −0.258667 −0.129333 0.991601i \(-0.541284\pi\)
−0.129333 + 0.991601i \(0.541284\pi\)
\(350\) 0 0
\(351\) −5.62918 −0.300463
\(352\) 0 0
\(353\) −10.1721 −0.541407 −0.270704 0.962663i \(-0.587256\pi\)
−0.270704 + 0.962663i \(0.587256\pi\)
\(354\) 0 0
\(355\) −32.7185 −1.73652
\(356\) 0 0
\(357\) −4.92355 −0.260582
\(358\) 0 0
\(359\) 23.3972 1.23486 0.617429 0.786626i \(-0.288174\pi\)
0.617429 + 0.786626i \(0.288174\pi\)
\(360\) 0 0
\(361\) −3.66428 −0.192857
\(362\) 0 0
\(363\) −1.49423 −0.0784268
\(364\) 0 0
\(365\) −22.2195 −1.16302
\(366\) 0 0
\(367\) −31.4887 −1.64370 −0.821848 0.569707i \(-0.807057\pi\)
−0.821848 + 0.569707i \(0.807057\pi\)
\(368\) 0 0
\(369\) 3.25167 0.169275
\(370\) 0 0
\(371\) −2.31459 −0.120167
\(372\) 0 0
\(373\) −11.0174 −0.570457 −0.285229 0.958459i \(-0.592070\pi\)
−0.285229 + 0.958459i \(0.592070\pi\)
\(374\) 0 0
\(375\) −12.8970 −0.665998
\(376\) 0 0
\(377\) 5.39617 0.277917
\(378\) 0 0
\(379\) −4.11483 −0.211365 −0.105682 0.994400i \(-0.533703\pi\)
−0.105682 + 0.994400i \(0.533703\pi\)
\(380\) 0 0
\(381\) 13.2014 0.676327
\(382\) 0 0
\(383\) 29.2482 1.49452 0.747258 0.664534i \(-0.231370\pi\)
0.747258 + 0.664534i \(0.231370\pi\)
\(384\) 0 0
\(385\) 2.57953 0.131465
\(386\) 0 0
\(387\) 2.23634 0.113680
\(388\) 0 0
\(389\) −10.2580 −0.520102 −0.260051 0.965595i \(-0.583739\pi\)
−0.260051 + 0.965595i \(0.583739\pi\)
\(390\) 0 0
\(391\) 9.33974 0.472331
\(392\) 0 0
\(393\) 3.83166 0.193282
\(394\) 0 0
\(395\) 4.37974 0.220368
\(396\) 0 0
\(397\) −6.47211 −0.324826 −0.162413 0.986723i \(-0.551928\pi\)
−0.162413 + 0.986723i \(0.551928\pi\)
\(398\) 0 0
\(399\) 5.85154 0.292943
\(400\) 0 0
\(401\) 22.5862 1.12790 0.563950 0.825809i \(-0.309281\pi\)
0.563950 + 0.825809i \(0.309281\pi\)
\(402\) 0 0
\(403\) −7.50095 −0.373649
\(404\) 0 0
\(405\) 15.7596 0.783099
\(406\) 0 0
\(407\) 8.01604 0.397340
\(408\) 0 0
\(409\) 8.13278 0.402140 0.201070 0.979577i \(-0.435558\pi\)
0.201070 + 0.979577i \(0.435558\pi\)
\(410\) 0 0
\(411\) 18.2057 0.898022
\(412\) 0 0
\(413\) 5.37744 0.264606
\(414\) 0 0
\(415\) −13.4055 −0.658050
\(416\) 0 0
\(417\) 20.6114 1.00935
\(418\) 0 0
\(419\) −23.3448 −1.14047 −0.570235 0.821481i \(-0.693148\pi\)
−0.570235 + 0.821481i \(0.693148\pi\)
\(420\) 0 0
\(421\) −14.1121 −0.687782 −0.343891 0.939010i \(-0.611745\pi\)
−0.343891 + 0.939010i \(0.611745\pi\)
\(422\) 0 0
\(423\) 2.17482 0.105743
\(424\) 0 0
\(425\) −5.44989 −0.264359
\(426\) 0 0
\(427\) −0.473694 −0.0229237
\(428\) 0 0
\(429\) 1.49423 0.0721422
\(430\) 0 0
\(431\) −20.8369 −1.00368 −0.501840 0.864961i \(-0.667343\pi\)
−0.501840 + 0.864961i \(0.667343\pi\)
\(432\) 0 0
\(433\) 15.2556 0.733136 0.366568 0.930391i \(-0.380533\pi\)
0.366568 + 0.930391i \(0.380533\pi\)
\(434\) 0 0
\(435\) −20.7991 −0.997239
\(436\) 0 0
\(437\) −11.1001 −0.530989
\(438\) 0 0
\(439\) 30.2519 1.44385 0.721923 0.691973i \(-0.243258\pi\)
0.721923 + 0.691973i \(0.243258\pi\)
\(440\) 0 0
\(441\) −0.767273 −0.0365368
\(442\) 0 0
\(443\) −28.1710 −1.33844 −0.669222 0.743062i \(-0.733373\pi\)
−0.669222 + 0.743062i \(0.733373\pi\)
\(444\) 0 0
\(445\) −42.9387 −2.03549
\(446\) 0 0
\(447\) 6.38898 0.302188
\(448\) 0 0
\(449\) 6.53143 0.308237 0.154119 0.988052i \(-0.450746\pi\)
0.154119 + 0.988052i \(0.450746\pi\)
\(450\) 0 0
\(451\) −4.23796 −0.199558
\(452\) 0 0
\(453\) 10.7435 0.504774
\(454\) 0 0
\(455\) −2.57953 −0.120930
\(456\) 0 0
\(457\) −10.3265 −0.483052 −0.241526 0.970394i \(-0.577648\pi\)
−0.241526 + 0.970394i \(0.577648\pi\)
\(458\) 0 0
\(459\) −18.5484 −0.865764
\(460\) 0 0
\(461\) −14.4683 −0.673856 −0.336928 0.941530i \(-0.609388\pi\)
−0.336928 + 0.941530i \(0.609388\pi\)
\(462\) 0 0
\(463\) −16.2677 −0.756024 −0.378012 0.925801i \(-0.623392\pi\)
−0.378012 + 0.925801i \(0.623392\pi\)
\(464\) 0 0
\(465\) 28.9118 1.34075
\(466\) 0 0
\(467\) 3.75586 0.173800 0.0869001 0.996217i \(-0.472304\pi\)
0.0869001 + 0.996217i \(0.472304\pi\)
\(468\) 0 0
\(469\) −4.81638 −0.222400
\(470\) 0 0
\(471\) −3.12298 −0.143899
\(472\) 0 0
\(473\) −2.91466 −0.134016
\(474\) 0 0
\(475\) 6.47708 0.297189
\(476\) 0 0
\(477\) −1.77592 −0.0813137
\(478\) 0 0
\(479\) 31.0677 1.41952 0.709761 0.704443i \(-0.248803\pi\)
0.709761 + 0.704443i \(0.248803\pi\)
\(480\) 0 0
\(481\) −8.01604 −0.365500
\(482\) 0 0
\(483\) −4.23537 −0.192716
\(484\) 0 0
\(485\) −13.2628 −0.602231
\(486\) 0 0
\(487\) −37.4188 −1.69561 −0.847803 0.530312i \(-0.822075\pi\)
−0.847803 + 0.530312i \(0.822075\pi\)
\(488\) 0 0
\(489\) −16.1474 −0.730211
\(490\) 0 0
\(491\) 6.10841 0.275669 0.137834 0.990455i \(-0.455986\pi\)
0.137834 + 0.990455i \(0.455986\pi\)
\(492\) 0 0
\(493\) 17.7806 0.800798
\(494\) 0 0
\(495\) 1.97920 0.0889585
\(496\) 0 0
\(497\) −12.6839 −0.568950
\(498\) 0 0
\(499\) −1.46757 −0.0656973 −0.0328486 0.999460i \(-0.510458\pi\)
−0.0328486 + 0.999460i \(0.510458\pi\)
\(500\) 0 0
\(501\) 32.7220 1.46191
\(502\) 0 0
\(503\) 19.5934 0.873627 0.436814 0.899552i \(-0.356107\pi\)
0.436814 + 0.899552i \(0.356107\pi\)
\(504\) 0 0
\(505\) 4.15261 0.184789
\(506\) 0 0
\(507\) −1.49423 −0.0663611
\(508\) 0 0
\(509\) −0.544361 −0.0241284 −0.0120642 0.999927i \(-0.503840\pi\)
−0.0120642 + 0.999927i \(0.503840\pi\)
\(510\) 0 0
\(511\) −8.61377 −0.381051
\(512\) 0 0
\(513\) 22.0443 0.973281
\(514\) 0 0
\(515\) −33.9219 −1.49478
\(516\) 0 0
\(517\) −2.83448 −0.124660
\(518\) 0 0
\(519\) −3.66398 −0.160831
\(520\) 0 0
\(521\) 35.8589 1.57101 0.785503 0.618858i \(-0.212404\pi\)
0.785503 + 0.618858i \(0.212404\pi\)
\(522\) 0 0
\(523\) −5.23650 −0.228976 −0.114488 0.993425i \(-0.536523\pi\)
−0.114488 + 0.993425i \(0.536523\pi\)
\(524\) 0 0
\(525\) 2.47141 0.107861
\(526\) 0 0
\(527\) −24.7159 −1.07664
\(528\) 0 0
\(529\) −14.9657 −0.650683
\(530\) 0 0
\(531\) 4.12596 0.179051
\(532\) 0 0
\(533\) 4.23796 0.183566
\(534\) 0 0
\(535\) 11.9138 0.515078
\(536\) 0 0
\(537\) 3.39849 0.146656
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −11.0196 −0.473768 −0.236884 0.971538i \(-0.576126\pi\)
−0.236884 + 0.971538i \(0.576126\pi\)
\(542\) 0 0
\(543\) −27.5665 −1.18299
\(544\) 0 0
\(545\) 10.8448 0.464542
\(546\) 0 0
\(547\) −43.2865 −1.85080 −0.925399 0.378995i \(-0.876270\pi\)
−0.925399 + 0.378995i \(0.876270\pi\)
\(548\) 0 0
\(549\) −0.363453 −0.0155118
\(550\) 0 0
\(551\) −21.1319 −0.900248
\(552\) 0 0
\(553\) 1.69788 0.0722013
\(554\) 0 0
\(555\) 30.8971 1.31151
\(556\) 0 0
\(557\) 24.5314 1.03943 0.519714 0.854340i \(-0.326038\pi\)
0.519714 + 0.854340i \(0.326038\pi\)
\(558\) 0 0
\(559\) 2.91466 0.123277
\(560\) 0 0
\(561\) 4.92355 0.207873
\(562\) 0 0
\(563\) −13.0943 −0.551859 −0.275930 0.961178i \(-0.588986\pi\)
−0.275930 + 0.961178i \(0.588986\pi\)
\(564\) 0 0
\(565\) 3.28501 0.138202
\(566\) 0 0
\(567\) 6.10948 0.256574
\(568\) 0 0
\(569\) −23.3549 −0.979088 −0.489544 0.871978i \(-0.662837\pi\)
−0.489544 + 0.871978i \(0.662837\pi\)
\(570\) 0 0
\(571\) 13.8129 0.578052 0.289026 0.957321i \(-0.406669\pi\)
0.289026 + 0.957321i \(0.406669\pi\)
\(572\) 0 0
\(573\) 4.72071 0.197211
\(574\) 0 0
\(575\) −4.68815 −0.195509
\(576\) 0 0
\(577\) −18.0817 −0.752751 −0.376375 0.926467i \(-0.622830\pi\)
−0.376375 + 0.926467i \(0.622830\pi\)
\(578\) 0 0
\(579\) −4.29806 −0.178621
\(580\) 0 0
\(581\) −5.19688 −0.215603
\(582\) 0 0
\(583\) 2.31459 0.0958603
\(584\) 0 0
\(585\) −1.97920 −0.0818299
\(586\) 0 0
\(587\) 23.2681 0.960379 0.480190 0.877165i \(-0.340568\pi\)
0.480190 + 0.877165i \(0.340568\pi\)
\(588\) 0 0
\(589\) 29.3744 1.21035
\(590\) 0 0
\(591\) 2.12382 0.0873622
\(592\) 0 0
\(593\) −22.8212 −0.937155 −0.468577 0.883422i \(-0.655233\pi\)
−0.468577 + 0.883422i \(0.655233\pi\)
\(594\) 0 0
\(595\) −8.49965 −0.348452
\(596\) 0 0
\(597\) −16.8895 −0.691243
\(598\) 0 0
\(599\) 17.3672 0.709605 0.354803 0.934941i \(-0.384548\pi\)
0.354803 + 0.934941i \(0.384548\pi\)
\(600\) 0 0
\(601\) 40.8177 1.66499 0.832494 0.554035i \(-0.186912\pi\)
0.832494 + 0.554035i \(0.186912\pi\)
\(602\) 0 0
\(603\) −3.69548 −0.150491
\(604\) 0 0
\(605\) −2.57953 −0.104873
\(606\) 0 0
\(607\) 0.366059 0.0148579 0.00742894 0.999972i \(-0.497635\pi\)
0.00742894 + 0.999972i \(0.497635\pi\)
\(608\) 0 0
\(609\) −8.06313 −0.326735
\(610\) 0 0
\(611\) 2.83448 0.114671
\(612\) 0 0
\(613\) −2.82000 −0.113899 −0.0569493 0.998377i \(-0.518137\pi\)
−0.0569493 + 0.998377i \(0.518137\pi\)
\(614\) 0 0
\(615\) −16.3349 −0.658685
\(616\) 0 0
\(617\) 11.4175 0.459651 0.229826 0.973232i \(-0.426184\pi\)
0.229826 + 0.973232i \(0.426184\pi\)
\(618\) 0 0
\(619\) 41.2654 1.65860 0.829298 0.558806i \(-0.188740\pi\)
0.829298 + 0.558806i \(0.188740\pi\)
\(620\) 0 0
\(621\) −15.9558 −0.640285
\(622\) 0 0
\(623\) −16.6460 −0.666906
\(624\) 0 0
\(625\) −30.5342 −1.22137
\(626\) 0 0
\(627\) −5.85154 −0.233688
\(628\) 0 0
\(629\) −26.4132 −1.05316
\(630\) 0 0
\(631\) 12.9642 0.516095 0.258047 0.966132i \(-0.416921\pi\)
0.258047 + 0.966132i \(0.416921\pi\)
\(632\) 0 0
\(633\) 19.1695 0.761919
\(634\) 0 0
\(635\) 22.7899 0.904388
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −9.73200 −0.384992
\(640\) 0 0
\(641\) −9.66384 −0.381699 −0.190849 0.981619i \(-0.561124\pi\)
−0.190849 + 0.981619i \(0.561124\pi\)
\(642\) 0 0
\(643\) −43.4082 −1.71185 −0.855926 0.517099i \(-0.827012\pi\)
−0.855926 + 0.517099i \(0.827012\pi\)
\(644\) 0 0
\(645\) −11.2343 −0.442351
\(646\) 0 0
\(647\) 4.33148 0.170288 0.0851441 0.996369i \(-0.472865\pi\)
0.0851441 + 0.996369i \(0.472865\pi\)
\(648\) 0 0
\(649\) −5.37744 −0.211083
\(650\) 0 0
\(651\) 11.2082 0.439282
\(652\) 0 0
\(653\) 24.7314 0.967813 0.483907 0.875120i \(-0.339217\pi\)
0.483907 + 0.875120i \(0.339217\pi\)
\(654\) 0 0
\(655\) 6.61470 0.258458
\(656\) 0 0
\(657\) −6.60911 −0.257846
\(658\) 0 0
\(659\) −28.1814 −1.09779 −0.548895 0.835891i \(-0.684951\pi\)
−0.548895 + 0.835891i \(0.684951\pi\)
\(660\) 0 0
\(661\) −5.16968 −0.201077 −0.100539 0.994933i \(-0.532057\pi\)
−0.100539 + 0.994933i \(0.532057\pi\)
\(662\) 0 0
\(663\) −4.92355 −0.191215
\(664\) 0 0
\(665\) 10.1017 0.391725
\(666\) 0 0
\(667\) 15.2954 0.592239
\(668\) 0 0
\(669\) −5.11786 −0.197868
\(670\) 0 0
\(671\) 0.473694 0.0182868
\(672\) 0 0
\(673\) 8.58798 0.331042 0.165521 0.986206i \(-0.447069\pi\)
0.165521 + 0.986206i \(0.447069\pi\)
\(674\) 0 0
\(675\) 9.31048 0.358361
\(676\) 0 0
\(677\) 46.2692 1.77827 0.889135 0.457645i \(-0.151307\pi\)
0.889135 + 0.457645i \(0.151307\pi\)
\(678\) 0 0
\(679\) −5.14154 −0.197314
\(680\) 0 0
\(681\) 23.2782 0.892021
\(682\) 0 0
\(683\) −43.7891 −1.67554 −0.837772 0.546020i \(-0.816142\pi\)
−0.837772 + 0.546020i \(0.816142\pi\)
\(684\) 0 0
\(685\) 31.4290 1.20084
\(686\) 0 0
\(687\) −13.1843 −0.503014
\(688\) 0 0
\(689\) −2.31459 −0.0881787
\(690\) 0 0
\(691\) −15.1389 −0.575910 −0.287955 0.957644i \(-0.592975\pi\)
−0.287955 + 0.957644i \(0.592975\pi\)
\(692\) 0 0
\(693\) 0.767273 0.0291463
\(694\) 0 0
\(695\) 35.5820 1.34970
\(696\) 0 0
\(697\) 13.9643 0.528934
\(698\) 0 0
\(699\) 5.46212 0.206596
\(700\) 0 0
\(701\) −46.1822 −1.74428 −0.872138 0.489260i \(-0.837267\pi\)
−0.872138 + 0.489260i \(0.837267\pi\)
\(702\) 0 0
\(703\) 31.3915 1.18395
\(704\) 0 0
\(705\) −10.9253 −0.411469
\(706\) 0 0
\(707\) 1.60983 0.0605439
\(708\) 0 0
\(709\) −36.4983 −1.37072 −0.685362 0.728203i \(-0.740356\pi\)
−0.685362 + 0.728203i \(0.740356\pi\)
\(710\) 0 0
\(711\) 1.30274 0.0488565
\(712\) 0 0
\(713\) −21.2613 −0.796243
\(714\) 0 0
\(715\) 2.57953 0.0964689
\(716\) 0 0
\(717\) −29.5949 −1.10524
\(718\) 0 0
\(719\) −3.64090 −0.135782 −0.0678912 0.997693i \(-0.521627\pi\)
−0.0678912 + 0.997693i \(0.521627\pi\)
\(720\) 0 0
\(721\) −13.1504 −0.489747
\(722\) 0 0
\(723\) −24.4977 −0.911078
\(724\) 0 0
\(725\) −8.92510 −0.331470
\(726\) 0 0
\(727\) −17.7306 −0.657590 −0.328795 0.944401i \(-0.606642\pi\)
−0.328795 + 0.944401i \(0.606642\pi\)
\(728\) 0 0
\(729\) 29.9215 1.10820
\(730\) 0 0
\(731\) 9.60394 0.355214
\(732\) 0 0
\(733\) 1.39053 0.0513605 0.0256802 0.999670i \(-0.491825\pi\)
0.0256802 + 0.999670i \(0.491825\pi\)
\(734\) 0 0
\(735\) 3.85441 0.142172
\(736\) 0 0
\(737\) 4.81638 0.177414
\(738\) 0 0
\(739\) −7.83683 −0.288283 −0.144141 0.989557i \(-0.546042\pi\)
−0.144141 + 0.989557i \(0.546042\pi\)
\(740\) 0 0
\(741\) 5.85154 0.214962
\(742\) 0 0
\(743\) 13.5760 0.498057 0.249028 0.968496i \(-0.419889\pi\)
0.249028 + 0.968496i \(0.419889\pi\)
\(744\) 0 0
\(745\) 11.0294 0.404088
\(746\) 0 0
\(747\) −3.98742 −0.145892
\(748\) 0 0
\(749\) 4.61859 0.168759
\(750\) 0 0
\(751\) 13.0565 0.476438 0.238219 0.971211i \(-0.423436\pi\)
0.238219 + 0.971211i \(0.423436\pi\)
\(752\) 0 0
\(753\) −15.9958 −0.582920
\(754\) 0 0
\(755\) 18.5468 0.674987
\(756\) 0 0
\(757\) 2.63655 0.0958271 0.0479136 0.998851i \(-0.484743\pi\)
0.0479136 + 0.998851i \(0.484743\pi\)
\(758\) 0 0
\(759\) 4.23537 0.153734
\(760\) 0 0
\(761\) 0.974938 0.0353415 0.0176707 0.999844i \(-0.494375\pi\)
0.0176707 + 0.999844i \(0.494375\pi\)
\(762\) 0 0
\(763\) 4.20419 0.152202
\(764\) 0 0
\(765\) −6.52155 −0.235787
\(766\) 0 0
\(767\) 5.37744 0.194168
\(768\) 0 0
\(769\) 23.8205 0.858988 0.429494 0.903070i \(-0.358692\pi\)
0.429494 + 0.903070i \(0.358692\pi\)
\(770\) 0 0
\(771\) −1.93993 −0.0698647
\(772\) 0 0
\(773\) 27.1934 0.978079 0.489039 0.872262i \(-0.337347\pi\)
0.489039 + 0.872262i \(0.337347\pi\)
\(774\) 0 0
\(775\) 12.4063 0.445649
\(776\) 0 0
\(777\) 11.9778 0.429702
\(778\) 0 0
\(779\) −16.5962 −0.594621
\(780\) 0 0
\(781\) 12.6839 0.453865
\(782\) 0 0
\(783\) −30.3760 −1.08555
\(784\) 0 0
\(785\) −5.39128 −0.192423
\(786\) 0 0
\(787\) −12.1129 −0.431777 −0.215888 0.976418i \(-0.569265\pi\)
−0.215888 + 0.976418i \(0.569265\pi\)
\(788\) 0 0
\(789\) 0.711396 0.0253264
\(790\) 0 0
\(791\) 1.27349 0.0452802
\(792\) 0 0
\(793\) −0.473694 −0.0168214
\(794\) 0 0
\(795\) 8.92137 0.316408
\(796\) 0 0
\(797\) −28.5430 −1.01105 −0.505523 0.862813i \(-0.668700\pi\)
−0.505523 + 0.862813i \(0.668700\pi\)
\(798\) 0 0
\(799\) 9.33974 0.330416
\(800\) 0 0
\(801\) −12.7720 −0.451276
\(802\) 0 0
\(803\) 8.61377 0.303973
\(804\) 0 0
\(805\) −7.31163 −0.257701
\(806\) 0 0
\(807\) 22.7163 0.799653
\(808\) 0 0
\(809\) 2.00964 0.0706551 0.0353276 0.999376i \(-0.488753\pi\)
0.0353276 + 0.999376i \(0.488753\pi\)
\(810\) 0 0
\(811\) −30.7855 −1.08103 −0.540513 0.841336i \(-0.681770\pi\)
−0.540513 + 0.841336i \(0.681770\pi\)
\(812\) 0 0
\(813\) −0.606193 −0.0212601
\(814\) 0 0
\(815\) −27.8757 −0.976443
\(816\) 0 0
\(817\) −11.4141 −0.399328
\(818\) 0 0
\(819\) −0.767273 −0.0268107
\(820\) 0 0
\(821\) 9.35361 0.326443 0.163222 0.986589i \(-0.447811\pi\)
0.163222 + 0.986589i \(0.447811\pi\)
\(822\) 0 0
\(823\) −26.2028 −0.913372 −0.456686 0.889628i \(-0.650964\pi\)
−0.456686 + 0.889628i \(0.650964\pi\)
\(824\) 0 0
\(825\) −2.47141 −0.0860435
\(826\) 0 0
\(827\) 20.9106 0.727134 0.363567 0.931568i \(-0.381559\pi\)
0.363567 + 0.931568i \(0.381559\pi\)
\(828\) 0 0
\(829\) 30.3601 1.05445 0.527224 0.849726i \(-0.323233\pi\)
0.527224 + 0.849726i \(0.323233\pi\)
\(830\) 0 0
\(831\) −4.62895 −0.160576
\(832\) 0 0
\(833\) −3.29504 −0.114166
\(834\) 0 0
\(835\) 56.4889 1.95488
\(836\) 0 0
\(837\) 42.2242 1.45948
\(838\) 0 0
\(839\) 34.4247 1.18847 0.594236 0.804291i \(-0.297454\pi\)
0.594236 + 0.804291i \(0.297454\pi\)
\(840\) 0 0
\(841\) 0.118673 0.00409217
\(842\) 0 0
\(843\) 32.4743 1.11847
\(844\) 0 0
\(845\) −2.57953 −0.0887385
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 40.4997 1.38994
\(850\) 0 0
\(851\) −22.7213 −0.778877
\(852\) 0 0
\(853\) 12.3524 0.422938 0.211469 0.977385i \(-0.432175\pi\)
0.211469 + 0.977385i \(0.432175\pi\)
\(854\) 0 0
\(855\) 7.75072 0.265069
\(856\) 0 0
\(857\) 8.57700 0.292985 0.146492 0.989212i \(-0.453202\pi\)
0.146492 + 0.989212i \(0.453202\pi\)
\(858\) 0 0
\(859\) 1.66397 0.0567738 0.0283869 0.999597i \(-0.490963\pi\)
0.0283869 + 0.999597i \(0.490963\pi\)
\(860\) 0 0
\(861\) −6.33249 −0.215811
\(862\) 0 0
\(863\) −4.61861 −0.157219 −0.0786097 0.996905i \(-0.525048\pi\)
−0.0786097 + 0.996905i \(0.525048\pi\)
\(864\) 0 0
\(865\) −6.32522 −0.215064
\(866\) 0 0
\(867\) 9.17862 0.311722
\(868\) 0 0
\(869\) −1.69788 −0.0575967
\(870\) 0 0
\(871\) −4.81638 −0.163197
\(872\) 0 0
\(873\) −3.94496 −0.133517
\(874\) 0 0
\(875\) −8.63118 −0.291787
\(876\) 0 0
\(877\) −22.3029 −0.753114 −0.376557 0.926393i \(-0.622892\pi\)
−0.376557 + 0.926393i \(0.622892\pi\)
\(878\) 0 0
\(879\) −7.54344 −0.254434
\(880\) 0 0
\(881\) 7.74124 0.260809 0.130405 0.991461i \(-0.458372\pi\)
0.130405 + 0.991461i \(0.458372\pi\)
\(882\) 0 0
\(883\) −50.6229 −1.70360 −0.851798 0.523870i \(-0.824488\pi\)
−0.851798 + 0.523870i \(0.824488\pi\)
\(884\) 0 0
\(885\) −20.7269 −0.696726
\(886\) 0 0
\(887\) −12.6149 −0.423568 −0.211784 0.977317i \(-0.567927\pi\)
−0.211784 + 0.977317i \(0.567927\pi\)
\(888\) 0 0
\(889\) 8.83489 0.296313
\(890\) 0 0
\(891\) −6.10948 −0.204675
\(892\) 0 0
\(893\) −11.1001 −0.371450
\(894\) 0 0
\(895\) 5.86691 0.196109
\(896\) 0 0
\(897\) −4.23537 −0.141415
\(898\) 0 0
\(899\) −40.4764 −1.34996
\(900\) 0 0
\(901\) −7.62666 −0.254081
\(902\) 0 0
\(903\) −4.35518 −0.144931
\(904\) 0 0
\(905\) −47.5888 −1.58191
\(906\) 0 0
\(907\) −30.5182 −1.01334 −0.506669 0.862140i \(-0.669123\pi\)
−0.506669 + 0.862140i \(0.669123\pi\)
\(908\) 0 0
\(909\) 1.23518 0.0409683
\(910\) 0 0
\(911\) 48.2454 1.59844 0.799221 0.601037i \(-0.205246\pi\)
0.799221 + 0.601037i \(0.205246\pi\)
\(912\) 0 0
\(913\) 5.19688 0.171992
\(914\) 0 0
\(915\) 1.82581 0.0603595
\(916\) 0 0
\(917\) 2.56430 0.0846808
\(918\) 0 0
\(919\) 0.790659 0.0260814 0.0130407 0.999915i \(-0.495849\pi\)
0.0130407 + 0.999915i \(0.495849\pi\)
\(920\) 0 0
\(921\) 44.9211 1.48020
\(922\) 0 0
\(923\) −12.6839 −0.417495
\(924\) 0 0
\(925\) 13.2583 0.435929
\(926\) 0 0
\(927\) −10.0899 −0.331397
\(928\) 0 0
\(929\) −44.0940 −1.44668 −0.723338 0.690494i \(-0.757393\pi\)
−0.723338 + 0.690494i \(0.757393\pi\)
\(930\) 0 0
\(931\) 3.91608 0.128344
\(932\) 0 0
\(933\) 47.0036 1.53883
\(934\) 0 0
\(935\) 8.49965 0.277968
\(936\) 0 0
\(937\) 15.1449 0.494761 0.247381 0.968918i \(-0.420430\pi\)
0.247381 + 0.968918i \(0.420430\pi\)
\(938\) 0 0
\(939\) −38.1998 −1.24660
\(940\) 0 0
\(941\) −32.1274 −1.04732 −0.523662 0.851926i \(-0.675435\pi\)
−0.523662 + 0.851926i \(0.675435\pi\)
\(942\) 0 0
\(943\) 12.0124 0.391179
\(944\) 0 0
\(945\) 14.5206 0.472356
\(946\) 0 0
\(947\) −9.25694 −0.300810 −0.150405 0.988624i \(-0.548058\pi\)
−0.150405 + 0.988624i \(0.548058\pi\)
\(948\) 0 0
\(949\) −8.61377 −0.279615
\(950\) 0 0
\(951\) 17.1857 0.557284
\(952\) 0 0
\(953\) 50.6223 1.63982 0.819909 0.572493i \(-0.194024\pi\)
0.819909 + 0.572493i \(0.194024\pi\)
\(954\) 0 0
\(955\) 8.14949 0.263711
\(956\) 0 0
\(957\) 8.06313 0.260644
\(958\) 0 0
\(959\) 12.1840 0.393442
\(960\) 0 0
\(961\) 25.2643 0.814976
\(962\) 0 0
\(963\) 3.54372 0.114195
\(964\) 0 0
\(965\) −7.41985 −0.238853
\(966\) 0 0
\(967\) −1.23462 −0.0397029 −0.0198514 0.999803i \(-0.506319\pi\)
−0.0198514 + 0.999803i \(0.506319\pi\)
\(968\) 0 0
\(969\) 19.2811 0.619397
\(970\) 0 0
\(971\) 21.5929 0.692949 0.346474 0.938059i \(-0.387379\pi\)
0.346474 + 0.938059i \(0.387379\pi\)
\(972\) 0 0
\(973\) 13.7940 0.442215
\(974\) 0 0
\(975\) 2.47141 0.0791485
\(976\) 0 0
\(977\) 41.5818 1.33032 0.665159 0.746701i \(-0.268364\pi\)
0.665159 + 0.746701i \(0.268364\pi\)
\(978\) 0 0
\(979\) 16.6460 0.532007
\(980\) 0 0
\(981\) 3.22576 0.102991
\(982\) 0 0
\(983\) −40.7259 −1.29895 −0.649477 0.760381i \(-0.725012\pi\)
−0.649477 + 0.760381i \(0.725012\pi\)
\(984\) 0 0
\(985\) 3.66640 0.116821
\(986\) 0 0
\(987\) −4.23537 −0.134813
\(988\) 0 0
\(989\) 8.26157 0.262703
\(990\) 0 0
\(991\) −19.4013 −0.616304 −0.308152 0.951337i \(-0.599711\pi\)
−0.308152 + 0.951337i \(0.599711\pi\)
\(992\) 0 0
\(993\) −21.4586 −0.680968
\(994\) 0 0
\(995\) −29.1568 −0.924334
\(996\) 0 0
\(997\) −17.0561 −0.540172 −0.270086 0.962836i \(-0.587052\pi\)
−0.270086 + 0.962836i \(0.587052\pi\)
\(998\) 0 0
\(999\) 45.1237 1.42765
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 \(a_p\))