Properties

Label 4008.2.a.l.1.1
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.1
Root \(-3.64003\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.64003 q^{5}\) \(-1.45249 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.64003 q^{5}\) \(-1.45249 q^{7}\) \(+1.00000 q^{9}\) \(-6.42846 q^{11}\) \(-4.46811 q^{13}\) \(-3.64003 q^{15}\) \(-3.08793 q^{17}\) \(-1.23264 q^{19}\) \(-1.45249 q^{21}\) \(+1.06502 q^{23}\) \(+8.24979 q^{25}\) \(+1.00000 q^{27}\) \(+1.27384 q^{29}\) \(+4.58373 q^{31}\) \(-6.42846 q^{33}\) \(+5.28712 q^{35}\) \(+3.59595 q^{37}\) \(-4.46811 q^{39}\) \(-9.41085 q^{41}\) \(+1.44738 q^{43}\) \(-3.64003 q^{45}\) \(-3.82478 q^{47}\) \(-4.89026 q^{49}\) \(-3.08793 q^{51}\) \(+9.67640 q^{53}\) \(+23.3998 q^{55}\) \(-1.23264 q^{57}\) \(+7.68527 q^{59}\) \(+6.50606 q^{61}\) \(-1.45249 q^{63}\) \(+16.2640 q^{65}\) \(-7.73227 q^{67}\) \(+1.06502 q^{69}\) \(-10.4166 q^{71}\) \(+2.25213 q^{73}\) \(+8.24979 q^{75}\) \(+9.33730 q^{77}\) \(+15.3378 q^{79}\) \(+1.00000 q^{81}\) \(+2.64462 q^{83}\) \(+11.2401 q^{85}\) \(+1.27384 q^{87}\) \(+3.71818 q^{89}\) \(+6.48990 q^{91}\) \(+4.58373 q^{93}\) \(+4.48683 q^{95}\) \(+5.92298 q^{97}\) \(-6.42846 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −3.64003 −1.62787 −0.813935 0.580957i \(-0.802679\pi\)
−0.813935 + 0.580957i \(0.802679\pi\)
\(6\) 0 0
\(7\) −1.45249 −0.548991 −0.274496 0.961588i \(-0.588511\pi\)
−0.274496 + 0.961588i \(0.588511\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −6.42846 −1.93825 −0.969127 0.246561i \(-0.920699\pi\)
−0.969127 + 0.246561i \(0.920699\pi\)
\(12\) 0 0
\(13\) −4.46811 −1.23923 −0.619615 0.784906i \(-0.712711\pi\)
−0.619615 + 0.784906i \(0.712711\pi\)
\(14\) 0 0
\(15\) −3.64003 −0.939851
\(16\) 0 0
\(17\) −3.08793 −0.748932 −0.374466 0.927241i \(-0.622174\pi\)
−0.374466 + 0.927241i \(0.622174\pi\)
\(18\) 0 0
\(19\) −1.23264 −0.282787 −0.141393 0.989954i \(-0.545158\pi\)
−0.141393 + 0.989954i \(0.545158\pi\)
\(20\) 0 0
\(21\) −1.45249 −0.316960
\(22\) 0 0
\(23\) 1.06502 0.222071 0.111036 0.993816i \(-0.464583\pi\)
0.111036 + 0.993816i \(0.464583\pi\)
\(24\) 0 0
\(25\) 8.24979 1.64996
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.27384 0.236546 0.118273 0.992981i \(-0.462264\pi\)
0.118273 + 0.992981i \(0.462264\pi\)
\(30\) 0 0
\(31\) 4.58373 0.823262 0.411631 0.911351i \(-0.364959\pi\)
0.411631 + 0.911351i \(0.364959\pi\)
\(32\) 0 0
\(33\) −6.42846 −1.11905
\(34\) 0 0
\(35\) 5.28712 0.893686
\(36\) 0 0
\(37\) 3.59595 0.591171 0.295586 0.955316i \(-0.404485\pi\)
0.295586 + 0.955316i \(0.404485\pi\)
\(38\) 0 0
\(39\) −4.46811 −0.715470
\(40\) 0 0
\(41\) −9.41085 −1.46973 −0.734864 0.678214i \(-0.762754\pi\)
−0.734864 + 0.678214i \(0.762754\pi\)
\(42\) 0 0
\(43\) 1.44738 0.220724 0.110362 0.993891i \(-0.464799\pi\)
0.110362 + 0.993891i \(0.464799\pi\)
\(44\) 0 0
\(45\) −3.64003 −0.542623
\(46\) 0 0
\(47\) −3.82478 −0.557901 −0.278951 0.960305i \(-0.589987\pi\)
−0.278951 + 0.960305i \(0.589987\pi\)
\(48\) 0 0
\(49\) −4.89026 −0.698609
\(50\) 0 0
\(51\) −3.08793 −0.432396
\(52\) 0 0
\(53\) 9.67640 1.32916 0.664578 0.747219i \(-0.268611\pi\)
0.664578 + 0.747219i \(0.268611\pi\)
\(54\) 0 0
\(55\) 23.3998 3.15522
\(56\) 0 0
\(57\) −1.23264 −0.163267
\(58\) 0 0
\(59\) 7.68527 1.00054 0.500269 0.865870i \(-0.333235\pi\)
0.500269 + 0.865870i \(0.333235\pi\)
\(60\) 0 0
\(61\) 6.50606 0.833016 0.416508 0.909132i \(-0.363254\pi\)
0.416508 + 0.909132i \(0.363254\pi\)
\(62\) 0 0
\(63\) −1.45249 −0.182997
\(64\) 0 0
\(65\) 16.2640 2.01731
\(66\) 0 0
\(67\) −7.73227 −0.944647 −0.472324 0.881425i \(-0.656585\pi\)
−0.472324 + 0.881425i \(0.656585\pi\)
\(68\) 0 0
\(69\) 1.06502 0.128213
\(70\) 0 0
\(71\) −10.4166 −1.23622 −0.618109 0.786092i \(-0.712101\pi\)
−0.618109 + 0.786092i \(0.712101\pi\)
\(72\) 0 0
\(73\) 2.25213 0.263591 0.131796 0.991277i \(-0.457926\pi\)
0.131796 + 0.991277i \(0.457926\pi\)
\(74\) 0 0
\(75\) 8.24979 0.952604
\(76\) 0 0
\(77\) 9.33730 1.06408
\(78\) 0 0
\(79\) 15.3378 1.72564 0.862818 0.505515i \(-0.168698\pi\)
0.862818 + 0.505515i \(0.168698\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.64462 0.290285 0.145142 0.989411i \(-0.453636\pi\)
0.145142 + 0.989411i \(0.453636\pi\)
\(84\) 0 0
\(85\) 11.2401 1.21916
\(86\) 0 0
\(87\) 1.27384 0.136570
\(88\) 0 0
\(89\) 3.71818 0.394126 0.197063 0.980391i \(-0.436860\pi\)
0.197063 + 0.980391i \(0.436860\pi\)
\(90\) 0 0
\(91\) 6.48990 0.680327
\(92\) 0 0
\(93\) 4.58373 0.475311
\(94\) 0 0
\(95\) 4.48683 0.460340
\(96\) 0 0
\(97\) 5.92298 0.601388 0.300694 0.953721i \(-0.402782\pi\)
0.300694 + 0.953721i \(0.402782\pi\)
\(98\) 0 0
\(99\) −6.42846 −0.646085
\(100\) 0 0
\(101\) 13.6005 1.35330 0.676648 0.736307i \(-0.263432\pi\)
0.676648 + 0.736307i \(0.263432\pi\)
\(102\) 0 0
\(103\) 7.45117 0.734186 0.367093 0.930184i \(-0.380353\pi\)
0.367093 + 0.930184i \(0.380353\pi\)
\(104\) 0 0
\(105\) 5.28712 0.515970
\(106\) 0 0
\(107\) −16.0477 −1.55139 −0.775695 0.631108i \(-0.782601\pi\)
−0.775695 + 0.631108i \(0.782601\pi\)
\(108\) 0 0
\(109\) −17.8483 −1.70956 −0.854778 0.518994i \(-0.826307\pi\)
−0.854778 + 0.518994i \(0.826307\pi\)
\(110\) 0 0
\(111\) 3.59595 0.341313
\(112\) 0 0
\(113\) 6.77367 0.637213 0.318607 0.947887i \(-0.396785\pi\)
0.318607 + 0.947887i \(0.396785\pi\)
\(114\) 0 0
\(115\) −3.87669 −0.361503
\(116\) 0 0
\(117\) −4.46811 −0.413077
\(118\) 0 0
\(119\) 4.48520 0.411157
\(120\) 0 0
\(121\) 30.3251 2.75683
\(122\) 0 0
\(123\) −9.41085 −0.848548
\(124\) 0 0
\(125\) −11.8293 −1.05805
\(126\) 0 0
\(127\) 6.35044 0.563511 0.281755 0.959486i \(-0.409083\pi\)
0.281755 + 0.959486i \(0.409083\pi\)
\(128\) 0 0
\(129\) 1.44738 0.127435
\(130\) 0 0
\(131\) −6.51198 −0.568954 −0.284477 0.958683i \(-0.591820\pi\)
−0.284477 + 0.958683i \(0.591820\pi\)
\(132\) 0 0
\(133\) 1.79040 0.155247
\(134\) 0 0
\(135\) −3.64003 −0.313284
\(136\) 0 0
\(137\) −16.8446 −1.43914 −0.719568 0.694422i \(-0.755660\pi\)
−0.719568 + 0.694422i \(0.755660\pi\)
\(138\) 0 0
\(139\) −18.0810 −1.53361 −0.766806 0.641879i \(-0.778155\pi\)
−0.766806 + 0.641879i \(0.778155\pi\)
\(140\) 0 0
\(141\) −3.82478 −0.322104
\(142\) 0 0
\(143\) 28.7231 2.40194
\(144\) 0 0
\(145\) −4.63680 −0.385065
\(146\) 0 0
\(147\) −4.89026 −0.403342
\(148\) 0 0
\(149\) −17.4067 −1.42602 −0.713008 0.701156i \(-0.752667\pi\)
−0.713008 + 0.701156i \(0.752667\pi\)
\(150\) 0 0
\(151\) 12.0142 0.977702 0.488851 0.872367i \(-0.337416\pi\)
0.488851 + 0.872367i \(0.337416\pi\)
\(152\) 0 0
\(153\) −3.08793 −0.249644
\(154\) 0 0
\(155\) −16.6849 −1.34016
\(156\) 0 0
\(157\) −5.05762 −0.403642 −0.201821 0.979422i \(-0.564686\pi\)
−0.201821 + 0.979422i \(0.564686\pi\)
\(158\) 0 0
\(159\) 9.67640 0.767388
\(160\) 0 0
\(161\) −1.54693 −0.121915
\(162\) 0 0
\(163\) −11.8323 −0.926780 −0.463390 0.886155i \(-0.653367\pi\)
−0.463390 + 0.886155i \(0.653367\pi\)
\(164\) 0 0
\(165\) 23.3998 1.82167
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 6.96400 0.535692
\(170\) 0 0
\(171\) −1.23264 −0.0942622
\(172\) 0 0
\(173\) −1.55262 −0.118043 −0.0590216 0.998257i \(-0.518798\pi\)
−0.0590216 + 0.998257i \(0.518798\pi\)
\(174\) 0 0
\(175\) −11.9828 −0.905812
\(176\) 0 0
\(177\) 7.68527 0.577660
\(178\) 0 0
\(179\) −12.2516 −0.915726 −0.457863 0.889023i \(-0.651385\pi\)
−0.457863 + 0.889023i \(0.651385\pi\)
\(180\) 0 0
\(181\) 2.63499 0.195857 0.0979286 0.995193i \(-0.468778\pi\)
0.0979286 + 0.995193i \(0.468778\pi\)
\(182\) 0 0
\(183\) 6.50606 0.480942
\(184\) 0 0
\(185\) −13.0894 −0.962349
\(186\) 0 0
\(187\) 19.8506 1.45162
\(188\) 0 0
\(189\) −1.45249 −0.105653
\(190\) 0 0
\(191\) 10.3171 0.746519 0.373260 0.927727i \(-0.378240\pi\)
0.373260 + 0.927727i \(0.378240\pi\)
\(192\) 0 0
\(193\) −5.69351 −0.409828 −0.204914 0.978780i \(-0.565691\pi\)
−0.204914 + 0.978780i \(0.565691\pi\)
\(194\) 0 0
\(195\) 16.2640 1.16469
\(196\) 0 0
\(197\) 2.61257 0.186138 0.0930690 0.995660i \(-0.470332\pi\)
0.0930690 + 0.995660i \(0.470332\pi\)
\(198\) 0 0
\(199\) 26.1850 1.85620 0.928102 0.372325i \(-0.121439\pi\)
0.928102 + 0.372325i \(0.121439\pi\)
\(200\) 0 0
\(201\) −7.73227 −0.545392
\(202\) 0 0
\(203\) −1.85024 −0.129861
\(204\) 0 0
\(205\) 34.2557 2.39253
\(206\) 0 0
\(207\) 1.06502 0.0740237
\(208\) 0 0
\(209\) 7.92397 0.548112
\(210\) 0 0
\(211\) 17.2397 1.18683 0.593416 0.804896i \(-0.297779\pi\)
0.593416 + 0.804896i \(0.297779\pi\)
\(212\) 0 0
\(213\) −10.4166 −0.713731
\(214\) 0 0
\(215\) −5.26851 −0.359309
\(216\) 0 0
\(217\) −6.65784 −0.451964
\(218\) 0 0
\(219\) 2.25213 0.152185
\(220\) 0 0
\(221\) 13.7972 0.928100
\(222\) 0 0
\(223\) −15.2142 −1.01882 −0.509408 0.860525i \(-0.670135\pi\)
−0.509408 + 0.860525i \(0.670135\pi\)
\(224\) 0 0
\(225\) 8.24979 0.549986
\(226\) 0 0
\(227\) 27.6521 1.83533 0.917666 0.397353i \(-0.130071\pi\)
0.917666 + 0.397353i \(0.130071\pi\)
\(228\) 0 0
\(229\) −17.6115 −1.16380 −0.581900 0.813261i \(-0.697690\pi\)
−0.581900 + 0.813261i \(0.697690\pi\)
\(230\) 0 0
\(231\) 9.33730 0.614350
\(232\) 0 0
\(233\) −5.06669 −0.331930 −0.165965 0.986132i \(-0.553074\pi\)
−0.165965 + 0.986132i \(0.553074\pi\)
\(234\) 0 0
\(235\) 13.9223 0.908190
\(236\) 0 0
\(237\) 15.3378 0.996296
\(238\) 0 0
\(239\) 14.5435 0.940741 0.470371 0.882469i \(-0.344120\pi\)
0.470371 + 0.882469i \(0.344120\pi\)
\(240\) 0 0
\(241\) 14.4271 0.929328 0.464664 0.885487i \(-0.346175\pi\)
0.464664 + 0.885487i \(0.346175\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 17.8007 1.13724
\(246\) 0 0
\(247\) 5.50756 0.350438
\(248\) 0 0
\(249\) 2.64462 0.167596
\(250\) 0 0
\(251\) −18.0066 −1.13657 −0.568283 0.822833i \(-0.692392\pi\)
−0.568283 + 0.822833i \(0.692392\pi\)
\(252\) 0 0
\(253\) −6.84641 −0.430430
\(254\) 0 0
\(255\) 11.2401 0.703885
\(256\) 0 0
\(257\) 3.82924 0.238861 0.119431 0.992843i \(-0.461893\pi\)
0.119431 + 0.992843i \(0.461893\pi\)
\(258\) 0 0
\(259\) −5.22310 −0.324548
\(260\) 0 0
\(261\) 1.27384 0.0788485
\(262\) 0 0
\(263\) −20.9906 −1.29434 −0.647168 0.762348i \(-0.724047\pi\)
−0.647168 + 0.762348i \(0.724047\pi\)
\(264\) 0 0
\(265\) −35.2223 −2.16369
\(266\) 0 0
\(267\) 3.71818 0.227549
\(268\) 0 0
\(269\) −22.2290 −1.35533 −0.677664 0.735371i \(-0.737008\pi\)
−0.677664 + 0.735371i \(0.737008\pi\)
\(270\) 0 0
\(271\) 12.1552 0.738377 0.369189 0.929355i \(-0.379636\pi\)
0.369189 + 0.929355i \(0.379636\pi\)
\(272\) 0 0
\(273\) 6.48990 0.392787
\(274\) 0 0
\(275\) −53.0335 −3.19804
\(276\) 0 0
\(277\) −7.50659 −0.451027 −0.225514 0.974240i \(-0.572406\pi\)
−0.225514 + 0.974240i \(0.572406\pi\)
\(278\) 0 0
\(279\) 4.58373 0.274421
\(280\) 0 0
\(281\) 3.74128 0.223186 0.111593 0.993754i \(-0.464405\pi\)
0.111593 + 0.993754i \(0.464405\pi\)
\(282\) 0 0
\(283\) 2.47396 0.147062 0.0735309 0.997293i \(-0.476573\pi\)
0.0735309 + 0.997293i \(0.476573\pi\)
\(284\) 0 0
\(285\) 4.48683 0.265777
\(286\) 0 0
\(287\) 13.6692 0.806868
\(288\) 0 0
\(289\) −7.46471 −0.439100
\(290\) 0 0
\(291\) 5.92298 0.347212
\(292\) 0 0
\(293\) 26.1746 1.52914 0.764568 0.644543i \(-0.222952\pi\)
0.764568 + 0.644543i \(0.222952\pi\)
\(294\) 0 0
\(295\) −27.9746 −1.62874
\(296\) 0 0
\(297\) −6.42846 −0.373017
\(298\) 0 0
\(299\) −4.75861 −0.275197
\(300\) 0 0
\(301\) −2.10231 −0.121175
\(302\) 0 0
\(303\) 13.6005 0.781326
\(304\) 0 0
\(305\) −23.6822 −1.35604
\(306\) 0 0
\(307\) 28.4693 1.62483 0.812413 0.583082i \(-0.198154\pi\)
0.812413 + 0.583082i \(0.198154\pi\)
\(308\) 0 0
\(309\) 7.45117 0.423882
\(310\) 0 0
\(311\) −0.793105 −0.0449728 −0.0224864 0.999747i \(-0.507158\pi\)
−0.0224864 + 0.999747i \(0.507158\pi\)
\(312\) 0 0
\(313\) 11.1869 0.632319 0.316160 0.948706i \(-0.397606\pi\)
0.316160 + 0.948706i \(0.397606\pi\)
\(314\) 0 0
\(315\) 5.28712 0.297895
\(316\) 0 0
\(317\) −12.2513 −0.688103 −0.344052 0.938951i \(-0.611800\pi\)
−0.344052 + 0.938951i \(0.611800\pi\)
\(318\) 0 0
\(319\) −8.18881 −0.458485
\(320\) 0 0
\(321\) −16.0477 −0.895696
\(322\) 0 0
\(323\) 3.80630 0.211788
\(324\) 0 0
\(325\) −36.8610 −2.04468
\(326\) 0 0
\(327\) −17.8483 −0.987012
\(328\) 0 0
\(329\) 5.55547 0.306283
\(330\) 0 0
\(331\) 7.48597 0.411466 0.205733 0.978608i \(-0.434042\pi\)
0.205733 + 0.978608i \(0.434042\pi\)
\(332\) 0 0
\(333\) 3.59595 0.197057
\(334\) 0 0
\(335\) 28.1457 1.53776
\(336\) 0 0
\(337\) 24.8638 1.35442 0.677208 0.735792i \(-0.263190\pi\)
0.677208 + 0.735792i \(0.263190\pi\)
\(338\) 0 0
\(339\) 6.77367 0.367895
\(340\) 0 0
\(341\) −29.4663 −1.59569
\(342\) 0 0
\(343\) 17.2705 0.932521
\(344\) 0 0
\(345\) −3.87669 −0.208714
\(346\) 0 0
\(347\) −11.7194 −0.629132 −0.314566 0.949236i \(-0.601859\pi\)
−0.314566 + 0.949236i \(0.601859\pi\)
\(348\) 0 0
\(349\) −20.1366 −1.07789 −0.538945 0.842341i \(-0.681177\pi\)
−0.538945 + 0.842341i \(0.681177\pi\)
\(350\) 0 0
\(351\) −4.46811 −0.238490
\(352\) 0 0
\(353\) 25.7845 1.37237 0.686184 0.727428i \(-0.259284\pi\)
0.686184 + 0.727428i \(0.259284\pi\)
\(354\) 0 0
\(355\) 37.9165 2.01240
\(356\) 0 0
\(357\) 4.48520 0.237382
\(358\) 0 0
\(359\) 27.1422 1.43251 0.716256 0.697838i \(-0.245854\pi\)
0.716256 + 0.697838i \(0.245854\pi\)
\(360\) 0 0
\(361\) −17.4806 −0.920032
\(362\) 0 0
\(363\) 30.3251 1.59166
\(364\) 0 0
\(365\) −8.19779 −0.429092
\(366\) 0 0
\(367\) 26.6657 1.39194 0.695969 0.718072i \(-0.254975\pi\)
0.695969 + 0.718072i \(0.254975\pi\)
\(368\) 0 0
\(369\) −9.41085 −0.489909
\(370\) 0 0
\(371\) −14.0549 −0.729695
\(372\) 0 0
\(373\) −23.4526 −1.21433 −0.607165 0.794576i \(-0.707693\pi\)
−0.607165 + 0.794576i \(0.707693\pi\)
\(374\) 0 0
\(375\) −11.8293 −0.610863
\(376\) 0 0
\(377\) −5.69164 −0.293134
\(378\) 0 0
\(379\) 6.29453 0.323328 0.161664 0.986846i \(-0.448314\pi\)
0.161664 + 0.986846i \(0.448314\pi\)
\(380\) 0 0
\(381\) 6.35044 0.325343
\(382\) 0 0
\(383\) 17.7486 0.906913 0.453456 0.891278i \(-0.350191\pi\)
0.453456 + 0.891278i \(0.350191\pi\)
\(384\) 0 0
\(385\) −33.9880 −1.73219
\(386\) 0 0
\(387\) 1.44738 0.0735746
\(388\) 0 0
\(389\) 23.1572 1.17412 0.587058 0.809545i \(-0.300286\pi\)
0.587058 + 0.809545i \(0.300286\pi\)
\(390\) 0 0
\(391\) −3.28869 −0.166316
\(392\) 0 0
\(393\) −6.51198 −0.328486
\(394\) 0 0
\(395\) −55.8299 −2.80911
\(396\) 0 0
\(397\) −24.1170 −1.21040 −0.605198 0.796075i \(-0.706906\pi\)
−0.605198 + 0.796075i \(0.706906\pi\)
\(398\) 0 0
\(399\) 1.79040 0.0896321
\(400\) 0 0
\(401\) −5.17511 −0.258433 −0.129216 0.991616i \(-0.541246\pi\)
−0.129216 + 0.991616i \(0.541246\pi\)
\(402\) 0 0
\(403\) −20.4806 −1.02021
\(404\) 0 0
\(405\) −3.64003 −0.180874
\(406\) 0 0
\(407\) −23.1165 −1.14584
\(408\) 0 0
\(409\) −4.19365 −0.207363 −0.103681 0.994611i \(-0.533062\pi\)
−0.103681 + 0.994611i \(0.533062\pi\)
\(410\) 0 0
\(411\) −16.8446 −0.830885
\(412\) 0 0
\(413\) −11.1628 −0.549286
\(414\) 0 0
\(415\) −9.62649 −0.472546
\(416\) 0 0
\(417\) −18.0810 −0.885431
\(418\) 0 0
\(419\) −5.34361 −0.261053 −0.130526 0.991445i \(-0.541667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(420\) 0 0
\(421\) −19.8415 −0.967017 −0.483509 0.875340i \(-0.660638\pi\)
−0.483509 + 0.875340i \(0.660638\pi\)
\(422\) 0 0
\(423\) −3.82478 −0.185967
\(424\) 0 0
\(425\) −25.4747 −1.23571
\(426\) 0 0
\(427\) −9.45002 −0.457318
\(428\) 0 0
\(429\) 28.7231 1.38676
\(430\) 0 0
\(431\) 36.1172 1.73970 0.869852 0.493313i \(-0.164214\pi\)
0.869852 + 0.493313i \(0.164214\pi\)
\(432\) 0 0
\(433\) 22.4261 1.07773 0.538866 0.842392i \(-0.318853\pi\)
0.538866 + 0.842392i \(0.318853\pi\)
\(434\) 0 0
\(435\) −4.63680 −0.222318
\(436\) 0 0
\(437\) −1.31278 −0.0627987
\(438\) 0 0
\(439\) 31.0932 1.48400 0.741999 0.670401i \(-0.233878\pi\)
0.741999 + 0.670401i \(0.233878\pi\)
\(440\) 0 0
\(441\) −4.89026 −0.232870
\(442\) 0 0
\(443\) −21.4614 −1.01966 −0.509830 0.860275i \(-0.670292\pi\)
−0.509830 + 0.860275i \(0.670292\pi\)
\(444\) 0 0
\(445\) −13.5343 −0.641586
\(446\) 0 0
\(447\) −17.4067 −0.823310
\(448\) 0 0
\(449\) −34.3531 −1.62122 −0.810611 0.585585i \(-0.800865\pi\)
−0.810611 + 0.585585i \(0.800865\pi\)
\(450\) 0 0
\(451\) 60.4973 2.84871
\(452\) 0 0
\(453\) 12.0142 0.564476
\(454\) 0 0
\(455\) −23.6234 −1.10748
\(456\) 0 0
\(457\) −21.6954 −1.01487 −0.507434 0.861691i \(-0.669406\pi\)
−0.507434 + 0.861691i \(0.669406\pi\)
\(458\) 0 0
\(459\) −3.08793 −0.144132
\(460\) 0 0
\(461\) 9.58945 0.446625 0.223313 0.974747i \(-0.428313\pi\)
0.223313 + 0.974747i \(0.428313\pi\)
\(462\) 0 0
\(463\) 2.30946 0.107330 0.0536648 0.998559i \(-0.482910\pi\)
0.0536648 + 0.998559i \(0.482910\pi\)
\(464\) 0 0
\(465\) −16.6849 −0.773744
\(466\) 0 0
\(467\) 13.5368 0.626408 0.313204 0.949686i \(-0.398598\pi\)
0.313204 + 0.949686i \(0.398598\pi\)
\(468\) 0 0
\(469\) 11.2311 0.518603
\(470\) 0 0
\(471\) −5.05762 −0.233043
\(472\) 0 0
\(473\) −9.30444 −0.427819
\(474\) 0 0
\(475\) −10.1690 −0.466586
\(476\) 0 0
\(477\) 9.67640 0.443052
\(478\) 0 0
\(479\) 2.42006 0.110575 0.0552876 0.998470i \(-0.482392\pi\)
0.0552876 + 0.998470i \(0.482392\pi\)
\(480\) 0 0
\(481\) −16.0671 −0.732597
\(482\) 0 0
\(483\) −1.54693 −0.0703877
\(484\) 0 0
\(485\) −21.5598 −0.978981
\(486\) 0 0
\(487\) −24.3709 −1.10435 −0.552174 0.833729i \(-0.686202\pi\)
−0.552174 + 0.833729i \(0.686202\pi\)
\(488\) 0 0
\(489\) −11.8323 −0.535076
\(490\) 0 0
\(491\) −9.19207 −0.414832 −0.207416 0.978253i \(-0.566505\pi\)
−0.207416 + 0.978253i \(0.566505\pi\)
\(492\) 0 0
\(493\) −3.93352 −0.177157
\(494\) 0 0
\(495\) 23.3998 1.05174
\(496\) 0 0
\(497\) 15.1300 0.678673
\(498\) 0 0
\(499\) 42.8570 1.91854 0.959272 0.282483i \(-0.0911580\pi\)
0.959272 + 0.282483i \(0.0911580\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 19.5868 0.873332 0.436666 0.899624i \(-0.356159\pi\)
0.436666 + 0.899624i \(0.356159\pi\)
\(504\) 0 0
\(505\) −49.5060 −2.20299
\(506\) 0 0
\(507\) 6.96400 0.309282
\(508\) 0 0
\(509\) 6.59346 0.292250 0.146125 0.989266i \(-0.453320\pi\)
0.146125 + 0.989266i \(0.453320\pi\)
\(510\) 0 0
\(511\) −3.27120 −0.144709
\(512\) 0 0
\(513\) −1.23264 −0.0544223
\(514\) 0 0
\(515\) −27.1225 −1.19516
\(516\) 0 0
\(517\) 24.5874 1.08135
\(518\) 0 0
\(519\) −1.55262 −0.0681523
\(520\) 0 0
\(521\) −32.7504 −1.43482 −0.717410 0.696652i \(-0.754672\pi\)
−0.717410 + 0.696652i \(0.754672\pi\)
\(522\) 0 0
\(523\) 7.97133 0.348562 0.174281 0.984696i \(-0.444240\pi\)
0.174281 + 0.984696i \(0.444240\pi\)
\(524\) 0 0
\(525\) −11.9828 −0.522971
\(526\) 0 0
\(527\) −14.1542 −0.616568
\(528\) 0 0
\(529\) −21.8657 −0.950684
\(530\) 0 0
\(531\) 7.68527 0.333512
\(532\) 0 0
\(533\) 42.0487 1.82133
\(534\) 0 0
\(535\) 58.4141 2.52546
\(536\) 0 0
\(537\) −12.2516 −0.528695
\(538\) 0 0
\(539\) 31.4369 1.35408
\(540\) 0 0
\(541\) −21.8235 −0.938267 −0.469134 0.883127i \(-0.655434\pi\)
−0.469134 + 0.883127i \(0.655434\pi\)
\(542\) 0 0
\(543\) 2.63499 0.113078
\(544\) 0 0
\(545\) 64.9682 2.78293
\(546\) 0 0
\(547\) 19.2970 0.825080 0.412540 0.910939i \(-0.364642\pi\)
0.412540 + 0.910939i \(0.364642\pi\)
\(548\) 0 0
\(549\) 6.50606 0.277672
\(550\) 0 0
\(551\) −1.57018 −0.0668919
\(552\) 0 0
\(553\) −22.2780 −0.947359
\(554\) 0 0
\(555\) −13.0894 −0.555613
\(556\) 0 0
\(557\) 7.31531 0.309959 0.154980 0.987918i \(-0.450469\pi\)
0.154980 + 0.987918i \(0.450469\pi\)
\(558\) 0 0
\(559\) −6.46706 −0.273528
\(560\) 0 0
\(561\) 19.8506 0.838094
\(562\) 0 0
\(563\) 20.8755 0.879795 0.439898 0.898048i \(-0.355015\pi\)
0.439898 + 0.898048i \(0.355015\pi\)
\(564\) 0 0
\(565\) −24.6563 −1.03730
\(566\) 0 0
\(567\) −1.45249 −0.0609990
\(568\) 0 0
\(569\) 7.99366 0.335112 0.167556 0.985863i \(-0.446413\pi\)
0.167556 + 0.985863i \(0.446413\pi\)
\(570\) 0 0
\(571\) −2.10566 −0.0881193 −0.0440596 0.999029i \(-0.514029\pi\)
−0.0440596 + 0.999029i \(0.514029\pi\)
\(572\) 0 0
\(573\) 10.3171 0.431003
\(574\) 0 0
\(575\) 8.78616 0.366408
\(576\) 0 0
\(577\) −27.1596 −1.13067 −0.565334 0.824862i \(-0.691253\pi\)
−0.565334 + 0.824862i \(0.691253\pi\)
\(578\) 0 0
\(579\) −5.69351 −0.236614
\(580\) 0 0
\(581\) −3.84130 −0.159364
\(582\) 0 0
\(583\) −62.2043 −2.57624
\(584\) 0 0
\(585\) 16.2640 0.672435
\(586\) 0 0
\(587\) −18.0687 −0.745773 −0.372887 0.927877i \(-0.621632\pi\)
−0.372887 + 0.927877i \(0.621632\pi\)
\(588\) 0 0
\(589\) −5.65008 −0.232808
\(590\) 0 0
\(591\) 2.61257 0.107467
\(592\) 0 0
\(593\) −9.55608 −0.392421 −0.196211 0.980562i \(-0.562864\pi\)
−0.196211 + 0.980562i \(0.562864\pi\)
\(594\) 0 0
\(595\) −16.3262 −0.669310
\(596\) 0 0
\(597\) 26.1850 1.07168
\(598\) 0 0
\(599\) −24.3175 −0.993586 −0.496793 0.867869i \(-0.665489\pi\)
−0.496793 + 0.867869i \(0.665489\pi\)
\(600\) 0 0
\(601\) 37.5779 1.53284 0.766418 0.642343i \(-0.222037\pi\)
0.766418 + 0.642343i \(0.222037\pi\)
\(602\) 0 0
\(603\) −7.73227 −0.314882
\(604\) 0 0
\(605\) −110.384 −4.48776
\(606\) 0 0
\(607\) 28.2208 1.14545 0.572723 0.819749i \(-0.305887\pi\)
0.572723 + 0.819749i \(0.305887\pi\)
\(608\) 0 0
\(609\) −1.85024 −0.0749755
\(610\) 0 0
\(611\) 17.0895 0.691368
\(612\) 0 0
\(613\) 27.0371 1.09202 0.546009 0.837779i \(-0.316146\pi\)
0.546009 + 0.837779i \(0.316146\pi\)
\(614\) 0 0
\(615\) 34.2557 1.38133
\(616\) 0 0
\(617\) 13.1293 0.528565 0.264282 0.964445i \(-0.414865\pi\)
0.264282 + 0.964445i \(0.414865\pi\)
\(618\) 0 0
\(619\) −11.7358 −0.471702 −0.235851 0.971789i \(-0.575788\pi\)
−0.235851 + 0.971789i \(0.575788\pi\)
\(620\) 0 0
\(621\) 1.06502 0.0427376
\(622\) 0 0
\(623\) −5.40063 −0.216372
\(624\) 0 0
\(625\) 1.81008 0.0724031
\(626\) 0 0
\(627\) 7.92397 0.316453
\(628\) 0 0
\(629\) −11.1040 −0.442747
\(630\) 0 0
\(631\) −4.55833 −0.181464 −0.0907321 0.995875i \(-0.528921\pi\)
−0.0907321 + 0.995875i \(0.528921\pi\)
\(632\) 0 0
\(633\) 17.2397 0.685218
\(634\) 0 0
\(635\) −23.1158 −0.917322
\(636\) 0 0
\(637\) 21.8502 0.865737
\(638\) 0 0
\(639\) −10.4166 −0.412073
\(640\) 0 0
\(641\) −42.0838 −1.66221 −0.831105 0.556116i \(-0.812291\pi\)
−0.831105 + 0.556116i \(0.812291\pi\)
\(642\) 0 0
\(643\) −10.8426 −0.427590 −0.213795 0.976879i \(-0.568582\pi\)
−0.213795 + 0.976879i \(0.568582\pi\)
\(644\) 0 0
\(645\) −5.26851 −0.207447
\(646\) 0 0
\(647\) 29.1805 1.14721 0.573603 0.819134i \(-0.305545\pi\)
0.573603 + 0.819134i \(0.305545\pi\)
\(648\) 0 0
\(649\) −49.4045 −1.93930
\(650\) 0 0
\(651\) −6.65784 −0.260941
\(652\) 0 0
\(653\) 24.1983 0.946953 0.473477 0.880806i \(-0.342999\pi\)
0.473477 + 0.880806i \(0.342999\pi\)
\(654\) 0 0
\(655\) 23.7038 0.926183
\(656\) 0 0
\(657\) 2.25213 0.0878638
\(658\) 0 0
\(659\) 4.14327 0.161399 0.0806995 0.996738i \(-0.474285\pi\)
0.0806995 + 0.996738i \(0.474285\pi\)
\(660\) 0 0
\(661\) −16.6852 −0.648980 −0.324490 0.945889i \(-0.605193\pi\)
−0.324490 + 0.945889i \(0.605193\pi\)
\(662\) 0 0
\(663\) 13.7972 0.535839
\(664\) 0 0
\(665\) −6.51710 −0.252722
\(666\) 0 0
\(667\) 1.35666 0.0525299
\(668\) 0 0
\(669\) −15.2142 −0.588213
\(670\) 0 0
\(671\) −41.8240 −1.61460
\(672\) 0 0
\(673\) 35.7946 1.37978 0.689891 0.723914i \(-0.257659\pi\)
0.689891 + 0.723914i \(0.257659\pi\)
\(674\) 0 0
\(675\) 8.24979 0.317535
\(676\) 0 0
\(677\) −18.4624 −0.709567 −0.354783 0.934949i \(-0.615445\pi\)
−0.354783 + 0.934949i \(0.615445\pi\)
\(678\) 0 0
\(679\) −8.60310 −0.330157
\(680\) 0 0
\(681\) 27.6521 1.05963
\(682\) 0 0
\(683\) 2.16551 0.0828610 0.0414305 0.999141i \(-0.486808\pi\)
0.0414305 + 0.999141i \(0.486808\pi\)
\(684\) 0 0
\(685\) 61.3150 2.34272
\(686\) 0 0
\(687\) −17.6115 −0.671920
\(688\) 0 0
\(689\) −43.2352 −1.64713
\(690\) 0 0
\(691\) −15.9965 −0.608535 −0.304268 0.952587i \(-0.598412\pi\)
−0.304268 + 0.952587i \(0.598412\pi\)
\(692\) 0 0
\(693\) 9.33730 0.354695
\(694\) 0 0
\(695\) 65.8153 2.49652
\(696\) 0 0
\(697\) 29.0600 1.10073
\(698\) 0 0
\(699\) −5.06669 −0.191640
\(700\) 0 0
\(701\) 32.8720 1.24156 0.620779 0.783986i \(-0.286817\pi\)
0.620779 + 0.783986i \(0.286817\pi\)
\(702\) 0 0
\(703\) −4.43251 −0.167175
\(704\) 0 0
\(705\) 13.9223 0.524344
\(706\) 0 0
\(707\) −19.7546 −0.742948
\(708\) 0 0
\(709\) 36.9184 1.38650 0.693249 0.720698i \(-0.256178\pi\)
0.693249 + 0.720698i \(0.256178\pi\)
\(710\) 0 0
\(711\) 15.3378 0.575212
\(712\) 0 0
\(713\) 4.88175 0.182823
\(714\) 0 0
\(715\) −104.553 −3.91005
\(716\) 0 0
\(717\) 14.5435 0.543137
\(718\) 0 0
\(719\) −11.5566 −0.430989 −0.215494 0.976505i \(-0.569136\pi\)
−0.215494 + 0.976505i \(0.569136\pi\)
\(720\) 0 0
\(721\) −10.8228 −0.403062
\(722\) 0 0
\(723\) 14.4271 0.536548
\(724\) 0 0
\(725\) 10.5089 0.390290
\(726\) 0 0
\(727\) 15.0101 0.556696 0.278348 0.960480i \(-0.410213\pi\)
0.278348 + 0.960480i \(0.410213\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.46941 −0.165307
\(732\) 0 0
\(733\) 44.7907 1.65438 0.827191 0.561921i \(-0.189937\pi\)
0.827191 + 0.561921i \(0.189937\pi\)
\(734\) 0 0
\(735\) 17.8007 0.656588
\(736\) 0 0
\(737\) 49.7066 1.83097
\(738\) 0 0
\(739\) 7.53470 0.277168 0.138584 0.990351i \(-0.455745\pi\)
0.138584 + 0.990351i \(0.455745\pi\)
\(740\) 0 0
\(741\) 5.50756 0.202325
\(742\) 0 0
\(743\) −31.7204 −1.16371 −0.581855 0.813293i \(-0.697673\pi\)
−0.581855 + 0.813293i \(0.697673\pi\)
\(744\) 0 0
\(745\) 63.3610 2.32137
\(746\) 0 0
\(747\) 2.64462 0.0967616
\(748\) 0 0
\(749\) 23.3092 0.851700
\(750\) 0 0
\(751\) 42.8785 1.56466 0.782329 0.622866i \(-0.214032\pi\)
0.782329 + 0.622866i \(0.214032\pi\)
\(752\) 0 0
\(753\) −18.0066 −0.656196
\(754\) 0 0
\(755\) −43.7320 −1.59157
\(756\) 0 0
\(757\) −29.9811 −1.08968 −0.544841 0.838539i \(-0.683410\pi\)
−0.544841 + 0.838539i \(0.683410\pi\)
\(758\) 0 0
\(759\) −6.84641 −0.248509
\(760\) 0 0
\(761\) 37.2320 1.34966 0.674829 0.737974i \(-0.264217\pi\)
0.674829 + 0.737974i \(0.264217\pi\)
\(762\) 0 0
\(763\) 25.9245 0.938531
\(764\) 0 0
\(765\) 11.2401 0.406388
\(766\) 0 0
\(767\) −34.3386 −1.23990
\(768\) 0 0
\(769\) −14.3416 −0.517171 −0.258585 0.965988i \(-0.583256\pi\)
−0.258585 + 0.965988i \(0.583256\pi\)
\(770\) 0 0
\(771\) 3.82924 0.137907
\(772\) 0 0
\(773\) 19.2550 0.692553 0.346277 0.938132i \(-0.387446\pi\)
0.346277 + 0.938132i \(0.387446\pi\)
\(774\) 0 0
\(775\) 37.8148 1.35835
\(776\) 0 0
\(777\) −5.22310 −0.187378
\(778\) 0 0
\(779\) 11.6002 0.415619
\(780\) 0 0
\(781\) 66.9625 2.39611
\(782\) 0 0
\(783\) 1.27384 0.0455232
\(784\) 0 0
\(785\) 18.4099 0.657077
\(786\) 0 0
\(787\) −41.2670 −1.47101 −0.735504 0.677520i \(-0.763055\pi\)
−0.735504 + 0.677520i \(0.763055\pi\)
\(788\) 0 0
\(789\) −20.9906 −0.747285
\(790\) 0 0
\(791\) −9.83872 −0.349824
\(792\) 0 0
\(793\) −29.0698 −1.03230
\(794\) 0 0
\(795\) −35.2223 −1.24921
\(796\) 0 0
\(797\) −25.6409 −0.908248 −0.454124 0.890938i \(-0.650048\pi\)
−0.454124 + 0.890938i \(0.650048\pi\)
\(798\) 0 0
\(799\) 11.8106 0.417830
\(800\) 0 0
\(801\) 3.71818 0.131375
\(802\) 0 0
\(803\) −14.4777 −0.510907
\(804\) 0 0
\(805\) 5.63086 0.198462
\(806\) 0 0
\(807\) −22.2290 −0.782499
\(808\) 0 0
\(809\) 9.07049 0.318901 0.159451 0.987206i \(-0.449028\pi\)
0.159451 + 0.987206i \(0.449028\pi\)
\(810\) 0 0
\(811\) 26.9376 0.945906 0.472953 0.881088i \(-0.343188\pi\)
0.472953 + 0.881088i \(0.343188\pi\)
\(812\) 0 0
\(813\) 12.1552 0.426302
\(814\) 0 0
\(815\) 43.0700 1.50868
\(816\) 0 0
\(817\) −1.78410 −0.0624177
\(818\) 0 0
\(819\) 6.48990 0.226776
\(820\) 0 0
\(821\) −48.6191 −1.69682 −0.848410 0.529340i \(-0.822440\pi\)
−0.848410 + 0.529340i \(0.822440\pi\)
\(822\) 0 0
\(823\) −50.5500 −1.76206 −0.881032 0.473057i \(-0.843150\pi\)
−0.881032 + 0.473057i \(0.843150\pi\)
\(824\) 0 0
\(825\) −53.0335 −1.84639
\(826\) 0 0
\(827\) −7.92496 −0.275578 −0.137789 0.990462i \(-0.544000\pi\)
−0.137789 + 0.990462i \(0.544000\pi\)
\(828\) 0 0
\(829\) −3.81681 −0.132563 −0.0662816 0.997801i \(-0.521114\pi\)
−0.0662816 + 0.997801i \(0.521114\pi\)
\(830\) 0 0
\(831\) −7.50659 −0.260401
\(832\) 0 0
\(833\) 15.1008 0.523211
\(834\) 0 0
\(835\) −3.64003 −0.125968
\(836\) 0 0
\(837\) 4.58373 0.158437
\(838\) 0 0
\(839\) 19.7601 0.682193 0.341096 0.940028i \(-0.389202\pi\)
0.341096 + 0.940028i \(0.389202\pi\)
\(840\) 0 0
\(841\) −27.3773 −0.944046
\(842\) 0 0
\(843\) 3.74128 0.128857
\(844\) 0 0
\(845\) −25.3491 −0.872037
\(846\) 0 0
\(847\) −44.0471 −1.51348
\(848\) 0 0
\(849\) 2.47396 0.0849062
\(850\) 0 0
\(851\) 3.82975 0.131282
\(852\) 0 0
\(853\) −15.9023 −0.544485 −0.272242 0.962229i \(-0.587765\pi\)
−0.272242 + 0.962229i \(0.587765\pi\)
\(854\) 0 0
\(855\) 4.48683 0.153447
\(856\) 0 0
\(857\) 48.5947 1.65996 0.829981 0.557792i \(-0.188351\pi\)
0.829981 + 0.557792i \(0.188351\pi\)
\(858\) 0 0
\(859\) 17.4581 0.595662 0.297831 0.954619i \(-0.403737\pi\)
0.297831 + 0.954619i \(0.403737\pi\)
\(860\) 0 0
\(861\) 13.6692 0.465845
\(862\) 0 0
\(863\) 6.80517 0.231651 0.115825 0.993270i \(-0.463049\pi\)
0.115825 + 0.993270i \(0.463049\pi\)
\(864\) 0 0
\(865\) 5.65156 0.192159
\(866\) 0 0
\(867\) −7.46471 −0.253515
\(868\) 0 0
\(869\) −98.5984 −3.34472
\(870\) 0 0
\(871\) 34.5486 1.17064
\(872\) 0 0
\(873\) 5.92298 0.200463
\(874\) 0 0
\(875\) 17.1820 0.580858
\(876\) 0 0
\(877\) −13.6188 −0.459875 −0.229937 0.973205i \(-0.573852\pi\)
−0.229937 + 0.973205i \(0.573852\pi\)
\(878\) 0 0
\(879\) 26.1746 0.882847
\(880\) 0 0
\(881\) 25.7736 0.868336 0.434168 0.900832i \(-0.357042\pi\)
0.434168 + 0.900832i \(0.357042\pi\)
\(882\) 0 0
\(883\) 24.1106 0.811386 0.405693 0.914009i \(-0.367030\pi\)
0.405693 + 0.914009i \(0.367030\pi\)
\(884\) 0 0
\(885\) −27.9746 −0.940355
\(886\) 0 0
\(887\) −17.4973 −0.587503 −0.293751 0.955882i \(-0.594904\pi\)
−0.293751 + 0.955882i \(0.594904\pi\)
\(888\) 0 0
\(889\) −9.22398 −0.309362
\(890\) 0 0
\(891\) −6.42846 −0.215362
\(892\) 0 0
\(893\) 4.71457 0.157767
\(894\) 0 0
\(895\) 44.5961 1.49068
\(896\) 0 0
\(897\) −4.75861 −0.158885
\(898\) 0 0
\(899\) 5.83892 0.194739
\(900\) 0 0
\(901\) −29.8800 −0.995447
\(902\) 0 0
\(903\) −2.10231 −0.0699607
\(904\) 0 0
\(905\) −9.59143 −0.318830
\(906\) 0 0
\(907\) −41.0307 −1.36240 −0.681201 0.732097i \(-0.738542\pi\)
−0.681201 + 0.732097i \(0.738542\pi\)
\(908\) 0 0
\(909\) 13.6005 0.451099
\(910\) 0 0
\(911\) 21.4782 0.711606 0.355803 0.934561i \(-0.384207\pi\)
0.355803 + 0.934561i \(0.384207\pi\)
\(912\) 0 0
\(913\) −17.0008 −0.562646
\(914\) 0 0
\(915\) −23.6822 −0.782911
\(916\) 0 0
\(917\) 9.45861 0.312351
\(918\) 0 0
\(919\) −32.3806 −1.06814 −0.534068 0.845441i \(-0.679337\pi\)
−0.534068 + 0.845441i \(0.679337\pi\)
\(920\) 0 0
\(921\) 28.4693 0.938094
\(922\) 0 0
\(923\) 46.5423 1.53196
\(924\) 0 0
\(925\) 29.6659 0.975408
\(926\) 0 0
\(927\) 7.45117 0.244729
\(928\) 0 0
\(929\) −0.577842 −0.0189584 −0.00947918 0.999955i \(-0.503017\pi\)
−0.00947918 + 0.999955i \(0.503017\pi\)
\(930\) 0 0
\(931\) 6.02792 0.197557
\(932\) 0 0
\(933\) −0.793105 −0.0259651
\(934\) 0 0
\(935\) −72.2568 −2.36305
\(936\) 0 0
\(937\) −29.2764 −0.956417 −0.478209 0.878246i \(-0.658714\pi\)
−0.478209 + 0.878246i \(0.658714\pi\)
\(938\) 0 0
\(939\) 11.1869 0.365070
\(940\) 0 0
\(941\) 3.37113 0.109896 0.0549479 0.998489i \(-0.482501\pi\)
0.0549479 + 0.998489i \(0.482501\pi\)
\(942\) 0 0
\(943\) −10.0227 −0.326384
\(944\) 0 0
\(945\) 5.28712 0.171990
\(946\) 0 0
\(947\) 0.805786 0.0261845 0.0130923 0.999914i \(-0.495832\pi\)
0.0130923 + 0.999914i \(0.495832\pi\)
\(948\) 0 0
\(949\) −10.0627 −0.326650
\(950\) 0 0
\(951\) −12.2513 −0.397277
\(952\) 0 0
\(953\) −16.1015 −0.521580 −0.260790 0.965396i \(-0.583983\pi\)
−0.260790 + 0.965396i \(0.583983\pi\)
\(954\) 0 0
\(955\) −37.5545 −1.21524
\(956\) 0 0
\(957\) −8.18881 −0.264707
\(958\) 0 0
\(959\) 24.4668 0.790073
\(960\) 0 0
\(961\) −9.98941 −0.322239
\(962\) 0 0
\(963\) −16.0477 −0.517130
\(964\) 0 0
\(965\) 20.7245 0.667147
\(966\) 0 0
\(967\) −7.26784 −0.233718 −0.116859 0.993149i \(-0.537283\pi\)
−0.116859 + 0.993149i \(0.537283\pi\)
\(968\) 0 0
\(969\) 3.80630 0.122276
\(970\) 0 0
\(971\) −49.9617 −1.60335 −0.801674 0.597761i \(-0.796057\pi\)
−0.801674 + 0.597761i \(0.796057\pi\)
\(972\) 0 0
\(973\) 26.2626 0.841939
\(974\) 0 0
\(975\) −36.8610 −1.18050
\(976\) 0 0
\(977\) 15.2258 0.487117 0.243558 0.969886i \(-0.421685\pi\)
0.243558 + 0.969886i \(0.421685\pi\)
\(978\) 0 0
\(979\) −23.9022 −0.763917
\(980\) 0 0
\(981\) −17.8483 −0.569852
\(982\) 0 0
\(983\) 31.1238 0.992695 0.496348 0.868124i \(-0.334674\pi\)
0.496348 + 0.868124i \(0.334674\pi\)
\(984\) 0 0
\(985\) −9.50982 −0.303008
\(986\) 0 0
\(987\) 5.55547 0.176832
\(988\) 0 0
\(989\) 1.54149 0.0490164
\(990\) 0 0
\(991\) −54.9753 −1.74635 −0.873174 0.487409i \(-0.837942\pi\)
−0.873174 + 0.487409i \(0.837942\pi\)
\(992\) 0 0
\(993\) 7.48597 0.237560
\(994\) 0 0
\(995\) −95.3140 −3.02166
\(996\) 0 0
\(997\) −39.2882 −1.24427 −0.622135 0.782910i \(-0.713734\pi\)
−0.622135 + 0.782910i \(0.713734\pi\)
\(998\) 0 0
\(999\) 3.59595 0.113771
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 \(a_p\))