Properties

Label 6036.2.a.i.1.7
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.38993 q^{5}\) \(+0.588107 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.38993 q^{5}\) \(+0.588107 q^{7}\) \(+1.00000 q^{9}\) \(-6.40011 q^{11}\) \(-3.59160 q^{13}\) \(+2.38993 q^{15}\) \(-3.38286 q^{17}\) \(+7.29913 q^{19}\) \(-0.588107 q^{21}\) \(+0.312022 q^{23}\) \(+0.711742 q^{25}\) \(-1.00000 q^{27}\) \(-5.17403 q^{29}\) \(-0.272176 q^{31}\) \(+6.40011 q^{33}\) \(-1.40553 q^{35}\) \(-2.33784 q^{37}\) \(+3.59160 q^{39}\) \(-1.99835 q^{41}\) \(-4.73040 q^{43}\) \(-2.38993 q^{45}\) \(-9.43664 q^{47}\) \(-6.65413 q^{49}\) \(+3.38286 q^{51}\) \(-12.3484 q^{53}\) \(+15.2958 q^{55}\) \(-7.29913 q^{57}\) \(+6.36719 q^{59}\) \(+2.40187 q^{61}\) \(+0.588107 q^{63}\) \(+8.58365 q^{65}\) \(-9.64729 q^{67}\) \(-0.312022 q^{69}\) \(+14.8072 q^{71}\) \(+2.81016 q^{73}\) \(-0.711742 q^{75}\) \(-3.76395 q^{77}\) \(+2.41978 q^{79}\) \(+1.00000 q^{81}\) \(-13.8550 q^{83}\) \(+8.08479 q^{85}\) \(+5.17403 q^{87}\) \(-9.03526 q^{89}\) \(-2.11225 q^{91}\) \(+0.272176 q^{93}\) \(-17.4444 q^{95}\) \(+15.1732 q^{97}\) \(-6.40011 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −2.38993 −1.06881 −0.534404 0.845229i \(-0.679464\pi\)
−0.534404 + 0.845229i \(0.679464\pi\)
\(6\) 0 0
\(7\) 0.588107 0.222284 0.111142 0.993805i \(-0.464549\pi\)
0.111142 + 0.993805i \(0.464549\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −6.40011 −1.92970 −0.964852 0.262793i \(-0.915356\pi\)
−0.964852 + 0.262793i \(0.915356\pi\)
\(12\) 0 0
\(13\) −3.59160 −0.996130 −0.498065 0.867140i \(-0.665956\pi\)
−0.498065 + 0.867140i \(0.665956\pi\)
\(14\) 0 0
\(15\) 2.38993 0.617076
\(16\) 0 0
\(17\) −3.38286 −0.820465 −0.410232 0.911981i \(-0.634552\pi\)
−0.410232 + 0.911981i \(0.634552\pi\)
\(18\) 0 0
\(19\) 7.29913 1.67454 0.837268 0.546793i \(-0.184151\pi\)
0.837268 + 0.546793i \(0.184151\pi\)
\(20\) 0 0
\(21\) −0.588107 −0.128336
\(22\) 0 0
\(23\) 0.312022 0.0650611 0.0325306 0.999471i \(-0.489643\pi\)
0.0325306 + 0.999471i \(0.489643\pi\)
\(24\) 0 0
\(25\) 0.711742 0.142348
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.17403 −0.960793 −0.480397 0.877051i \(-0.659507\pi\)
−0.480397 + 0.877051i \(0.659507\pi\)
\(30\) 0 0
\(31\) −0.272176 −0.0488842 −0.0244421 0.999701i \(-0.507781\pi\)
−0.0244421 + 0.999701i \(0.507781\pi\)
\(32\) 0 0
\(33\) 6.40011 1.11412
\(34\) 0 0
\(35\) −1.40553 −0.237578
\(36\) 0 0
\(37\) −2.33784 −0.384339 −0.192169 0.981362i \(-0.561552\pi\)
−0.192169 + 0.981362i \(0.561552\pi\)
\(38\) 0 0
\(39\) 3.59160 0.575116
\(40\) 0 0
\(41\) −1.99835 −0.312089 −0.156045 0.987750i \(-0.549874\pi\)
−0.156045 + 0.987750i \(0.549874\pi\)
\(42\) 0 0
\(43\) −4.73040 −0.721379 −0.360689 0.932686i \(-0.617459\pi\)
−0.360689 + 0.932686i \(0.617459\pi\)
\(44\) 0 0
\(45\) −2.38993 −0.356269
\(46\) 0 0
\(47\) −9.43664 −1.37647 −0.688237 0.725486i \(-0.741615\pi\)
−0.688237 + 0.725486i \(0.741615\pi\)
\(48\) 0 0
\(49\) −6.65413 −0.950590
\(50\) 0 0
\(51\) 3.38286 0.473695
\(52\) 0 0
\(53\) −12.3484 −1.69618 −0.848091 0.529850i \(-0.822248\pi\)
−0.848091 + 0.529850i \(0.822248\pi\)
\(54\) 0 0
\(55\) 15.2958 2.06248
\(56\) 0 0
\(57\) −7.29913 −0.966794
\(58\) 0 0
\(59\) 6.36719 0.828937 0.414469 0.910064i \(-0.363968\pi\)
0.414469 + 0.910064i \(0.363968\pi\)
\(60\) 0 0
\(61\) 2.40187 0.307528 0.153764 0.988108i \(-0.450860\pi\)
0.153764 + 0.988108i \(0.450860\pi\)
\(62\) 0 0
\(63\) 0.588107 0.0740946
\(64\) 0 0
\(65\) 8.58365 1.06467
\(66\) 0 0
\(67\) −9.64729 −1.17860 −0.589302 0.807913i \(-0.700597\pi\)
−0.589302 + 0.807913i \(0.700597\pi\)
\(68\) 0 0
\(69\) −0.312022 −0.0375631
\(70\) 0 0
\(71\) 14.8072 1.75729 0.878647 0.477472i \(-0.158447\pi\)
0.878647 + 0.477472i \(0.158447\pi\)
\(72\) 0 0
\(73\) 2.81016 0.328904 0.164452 0.986385i \(-0.447414\pi\)
0.164452 + 0.986385i \(0.447414\pi\)
\(74\) 0 0
\(75\) −0.711742 −0.0821849
\(76\) 0 0
\(77\) −3.76395 −0.428942
\(78\) 0 0
\(79\) 2.41978 0.272247 0.136123 0.990692i \(-0.456536\pi\)
0.136123 + 0.990692i \(0.456536\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.8550 −1.52079 −0.760393 0.649463i \(-0.774994\pi\)
−0.760393 + 0.649463i \(0.774994\pi\)
\(84\) 0 0
\(85\) 8.08479 0.876918
\(86\) 0 0
\(87\) 5.17403 0.554714
\(88\) 0 0
\(89\) −9.03526 −0.957735 −0.478868 0.877887i \(-0.658953\pi\)
−0.478868 + 0.877887i \(0.658953\pi\)
\(90\) 0 0
\(91\) −2.11225 −0.221423
\(92\) 0 0
\(93\) 0.272176 0.0282233
\(94\) 0 0
\(95\) −17.4444 −1.78976
\(96\) 0 0
\(97\) 15.1732 1.54060 0.770301 0.637681i \(-0.220106\pi\)
0.770301 + 0.637681i \(0.220106\pi\)
\(98\) 0 0
\(99\) −6.40011 −0.643235
\(100\) 0 0
\(101\) −11.9767 −1.19172 −0.595862 0.803087i \(-0.703189\pi\)
−0.595862 + 0.803087i \(0.703189\pi\)
\(102\) 0 0
\(103\) 0.697308 0.0687078 0.0343539 0.999410i \(-0.489063\pi\)
0.0343539 + 0.999410i \(0.489063\pi\)
\(104\) 0 0
\(105\) 1.40553 0.137166
\(106\) 0 0
\(107\) −5.38252 −0.520348 −0.260174 0.965562i \(-0.583780\pi\)
−0.260174 + 0.965562i \(0.583780\pi\)
\(108\) 0 0
\(109\) 11.3581 1.08791 0.543953 0.839116i \(-0.316927\pi\)
0.543953 + 0.839116i \(0.316927\pi\)
\(110\) 0 0
\(111\) 2.33784 0.221898
\(112\) 0 0
\(113\) 18.3709 1.72819 0.864094 0.503330i \(-0.167892\pi\)
0.864094 + 0.503330i \(0.167892\pi\)
\(114\) 0 0
\(115\) −0.745710 −0.0695378
\(116\) 0 0
\(117\) −3.59160 −0.332043
\(118\) 0 0
\(119\) −1.98949 −0.182376
\(120\) 0 0
\(121\) 29.9613 2.72376
\(122\) 0 0
\(123\) 1.99835 0.180185
\(124\) 0 0
\(125\) 10.2486 0.916664
\(126\) 0 0
\(127\) 13.7453 1.21970 0.609848 0.792518i \(-0.291230\pi\)
0.609848 + 0.792518i \(0.291230\pi\)
\(128\) 0 0
\(129\) 4.73040 0.416488
\(130\) 0 0
\(131\) 4.90929 0.428926 0.214463 0.976732i \(-0.431200\pi\)
0.214463 + 0.976732i \(0.431200\pi\)
\(132\) 0 0
\(133\) 4.29267 0.372222
\(134\) 0 0
\(135\) 2.38993 0.205692
\(136\) 0 0
\(137\) −0.345498 −0.0295179 −0.0147589 0.999891i \(-0.504698\pi\)
−0.0147589 + 0.999891i \(0.504698\pi\)
\(138\) 0 0
\(139\) −20.9006 −1.77276 −0.886381 0.462956i \(-0.846789\pi\)
−0.886381 + 0.462956i \(0.846789\pi\)
\(140\) 0 0
\(141\) 9.43664 0.794708
\(142\) 0 0
\(143\) 22.9866 1.92224
\(144\) 0 0
\(145\) 12.3655 1.02690
\(146\) 0 0
\(147\) 6.65413 0.548823
\(148\) 0 0
\(149\) 16.3697 1.34106 0.670528 0.741884i \(-0.266068\pi\)
0.670528 + 0.741884i \(0.266068\pi\)
\(150\) 0 0
\(151\) −17.0850 −1.39036 −0.695180 0.718836i \(-0.744675\pi\)
−0.695180 + 0.718836i \(0.744675\pi\)
\(152\) 0 0
\(153\) −3.38286 −0.273488
\(154\) 0 0
\(155\) 0.650480 0.0522478
\(156\) 0 0
\(157\) 2.07454 0.165566 0.0827830 0.996568i \(-0.473619\pi\)
0.0827830 + 0.996568i \(0.473619\pi\)
\(158\) 0 0
\(159\) 12.3484 0.979292
\(160\) 0 0
\(161\) 0.183503 0.0144620
\(162\) 0 0
\(163\) −4.37975 −0.343049 −0.171524 0.985180i \(-0.554869\pi\)
−0.171524 + 0.985180i \(0.554869\pi\)
\(164\) 0 0
\(165\) −15.2958 −1.19077
\(166\) 0 0
\(167\) −5.72958 −0.443368 −0.221684 0.975119i \(-0.571155\pi\)
−0.221684 + 0.975119i \(0.571155\pi\)
\(168\) 0 0
\(169\) −0.100422 −0.00772473
\(170\) 0 0
\(171\) 7.29913 0.558179
\(172\) 0 0
\(173\) −5.49514 −0.417788 −0.208894 0.977938i \(-0.566986\pi\)
−0.208894 + 0.977938i \(0.566986\pi\)
\(174\) 0 0
\(175\) 0.418581 0.0316417
\(176\) 0 0
\(177\) −6.36719 −0.478587
\(178\) 0 0
\(179\) 13.4407 1.00461 0.502304 0.864691i \(-0.332486\pi\)
0.502304 + 0.864691i \(0.332486\pi\)
\(180\) 0 0
\(181\) −19.2230 −1.42884 −0.714418 0.699719i \(-0.753309\pi\)
−0.714418 + 0.699719i \(0.753309\pi\)
\(182\) 0 0
\(183\) −2.40187 −0.177552
\(184\) 0 0
\(185\) 5.58726 0.410784
\(186\) 0 0
\(187\) 21.6507 1.58325
\(188\) 0 0
\(189\) −0.588107 −0.0427785
\(190\) 0 0
\(191\) 14.5416 1.05219 0.526097 0.850425i \(-0.323655\pi\)
0.526097 + 0.850425i \(0.323655\pi\)
\(192\) 0 0
\(193\) −26.4953 −1.90718 −0.953588 0.301114i \(-0.902642\pi\)
−0.953588 + 0.301114i \(0.902642\pi\)
\(194\) 0 0
\(195\) −8.58365 −0.614688
\(196\) 0 0
\(197\) 1.72972 0.123238 0.0616188 0.998100i \(-0.480374\pi\)
0.0616188 + 0.998100i \(0.480374\pi\)
\(198\) 0 0
\(199\) −22.1817 −1.57242 −0.786211 0.617958i \(-0.787960\pi\)
−0.786211 + 0.617958i \(0.787960\pi\)
\(200\) 0 0
\(201\) 9.64729 0.680467
\(202\) 0 0
\(203\) −3.04288 −0.213569
\(204\) 0 0
\(205\) 4.77590 0.333563
\(206\) 0 0
\(207\) 0.312022 0.0216870
\(208\) 0 0
\(209\) −46.7152 −3.23136
\(210\) 0 0
\(211\) 28.3317 1.95044 0.975218 0.221245i \(-0.0710120\pi\)
0.975218 + 0.221245i \(0.0710120\pi\)
\(212\) 0 0
\(213\) −14.8072 −1.01457
\(214\) 0 0
\(215\) 11.3053 0.771015
\(216\) 0 0
\(217\) −0.160069 −0.0108662
\(218\) 0 0
\(219\) −2.81016 −0.189893
\(220\) 0 0
\(221\) 12.1499 0.817290
\(222\) 0 0
\(223\) 14.6429 0.980561 0.490281 0.871565i \(-0.336894\pi\)
0.490281 + 0.871565i \(0.336894\pi\)
\(224\) 0 0
\(225\) 0.711742 0.0474495
\(226\) 0 0
\(227\) −16.9117 −1.12247 −0.561236 0.827656i \(-0.689674\pi\)
−0.561236 + 0.827656i \(0.689674\pi\)
\(228\) 0 0
\(229\) 28.6468 1.89303 0.946516 0.322656i \(-0.104576\pi\)
0.946516 + 0.322656i \(0.104576\pi\)
\(230\) 0 0
\(231\) 3.76395 0.247650
\(232\) 0 0
\(233\) −11.9058 −0.779976 −0.389988 0.920820i \(-0.627521\pi\)
−0.389988 + 0.920820i \(0.627521\pi\)
\(234\) 0 0
\(235\) 22.5529 1.47119
\(236\) 0 0
\(237\) −2.41978 −0.157182
\(238\) 0 0
\(239\) 2.67752 0.173195 0.0865973 0.996243i \(-0.472401\pi\)
0.0865973 + 0.996243i \(0.472401\pi\)
\(240\) 0 0
\(241\) 16.2107 1.04422 0.522110 0.852878i \(-0.325145\pi\)
0.522110 + 0.852878i \(0.325145\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 15.9029 1.01600
\(246\) 0 0
\(247\) −26.2156 −1.66806
\(248\) 0 0
\(249\) 13.8550 0.878026
\(250\) 0 0
\(251\) −6.74504 −0.425743 −0.212872 0.977080i \(-0.568282\pi\)
−0.212872 + 0.977080i \(0.568282\pi\)
\(252\) 0 0
\(253\) −1.99698 −0.125549
\(254\) 0 0
\(255\) −8.08479 −0.506289
\(256\) 0 0
\(257\) 22.9551 1.43190 0.715950 0.698151i \(-0.245994\pi\)
0.715950 + 0.698151i \(0.245994\pi\)
\(258\) 0 0
\(259\) −1.37490 −0.0854322
\(260\) 0 0
\(261\) −5.17403 −0.320264
\(262\) 0 0
\(263\) −21.3876 −1.31881 −0.659407 0.751786i \(-0.729193\pi\)
−0.659407 + 0.751786i \(0.729193\pi\)
\(264\) 0 0
\(265\) 29.5117 1.81289
\(266\) 0 0
\(267\) 9.03526 0.552949
\(268\) 0 0
\(269\) 25.0659 1.52829 0.764146 0.645043i \(-0.223160\pi\)
0.764146 + 0.645043i \(0.223160\pi\)
\(270\) 0 0
\(271\) 16.4961 1.00206 0.501032 0.865429i \(-0.332954\pi\)
0.501032 + 0.865429i \(0.332954\pi\)
\(272\) 0 0
\(273\) 2.11225 0.127839
\(274\) 0 0
\(275\) −4.55523 −0.274690
\(276\) 0 0
\(277\) 19.0521 1.14473 0.572365 0.819999i \(-0.306026\pi\)
0.572365 + 0.819999i \(0.306026\pi\)
\(278\) 0 0
\(279\) −0.272176 −0.0162947
\(280\) 0 0
\(281\) −20.5003 −1.22294 −0.611472 0.791266i \(-0.709422\pi\)
−0.611472 + 0.791266i \(0.709422\pi\)
\(282\) 0 0
\(283\) −22.1389 −1.31602 −0.658011 0.753009i \(-0.728602\pi\)
−0.658011 + 0.753009i \(0.728602\pi\)
\(284\) 0 0
\(285\) 17.4444 1.03332
\(286\) 0 0
\(287\) −1.17524 −0.0693723
\(288\) 0 0
\(289\) −5.55624 −0.326838
\(290\) 0 0
\(291\) −15.1732 −0.889467
\(292\) 0 0
\(293\) −5.77896 −0.337611 −0.168805 0.985649i \(-0.553991\pi\)
−0.168805 + 0.985649i \(0.553991\pi\)
\(294\) 0 0
\(295\) −15.2171 −0.885974
\(296\) 0 0
\(297\) 6.40011 0.371372
\(298\) 0 0
\(299\) −1.12066 −0.0648094
\(300\) 0 0
\(301\) −2.78198 −0.160351
\(302\) 0 0
\(303\) 11.9767 0.688042
\(304\) 0 0
\(305\) −5.74030 −0.328689
\(306\) 0 0
\(307\) 12.3201 0.703146 0.351573 0.936160i \(-0.385647\pi\)
0.351573 + 0.936160i \(0.385647\pi\)
\(308\) 0 0
\(309\) −0.697308 −0.0396685
\(310\) 0 0
\(311\) −3.99551 −0.226565 −0.113282 0.993563i \(-0.536136\pi\)
−0.113282 + 0.993563i \(0.536136\pi\)
\(312\) 0 0
\(313\) −10.3980 −0.587731 −0.293865 0.955847i \(-0.594942\pi\)
−0.293865 + 0.955847i \(0.594942\pi\)
\(314\) 0 0
\(315\) −1.40553 −0.0791928
\(316\) 0 0
\(317\) 18.9689 1.06540 0.532700 0.846304i \(-0.321177\pi\)
0.532700 + 0.846304i \(0.321177\pi\)
\(318\) 0 0
\(319\) 33.1143 1.85405
\(320\) 0 0
\(321\) 5.38252 0.300423
\(322\) 0 0
\(323\) −24.6920 −1.37390
\(324\) 0 0
\(325\) −2.55629 −0.141798
\(326\) 0 0
\(327\) −11.3581 −0.628103
\(328\) 0 0
\(329\) −5.54975 −0.305968
\(330\) 0 0
\(331\) −7.95346 −0.437162 −0.218581 0.975819i \(-0.570143\pi\)
−0.218581 + 0.975819i \(0.570143\pi\)
\(332\) 0 0
\(333\) −2.33784 −0.128113
\(334\) 0 0
\(335\) 23.0563 1.25970
\(336\) 0 0
\(337\) −9.48324 −0.516585 −0.258292 0.966067i \(-0.583160\pi\)
−0.258292 + 0.966067i \(0.583160\pi\)
\(338\) 0 0
\(339\) −18.3709 −0.997770
\(340\) 0 0
\(341\) 1.74195 0.0943322
\(342\) 0 0
\(343\) −8.03009 −0.433584
\(344\) 0 0
\(345\) 0.745710 0.0401477
\(346\) 0 0
\(347\) 17.4217 0.935246 0.467623 0.883928i \(-0.345110\pi\)
0.467623 + 0.883928i \(0.345110\pi\)
\(348\) 0 0
\(349\) 2.28231 0.122169 0.0610847 0.998133i \(-0.480544\pi\)
0.0610847 + 0.998133i \(0.480544\pi\)
\(350\) 0 0
\(351\) 3.59160 0.191705
\(352\) 0 0
\(353\) 32.4238 1.72574 0.862872 0.505422i \(-0.168663\pi\)
0.862872 + 0.505422i \(0.168663\pi\)
\(354\) 0 0
\(355\) −35.3882 −1.87821
\(356\) 0 0
\(357\) 1.98949 0.105295
\(358\) 0 0
\(359\) 22.6046 1.19303 0.596513 0.802603i \(-0.296552\pi\)
0.596513 + 0.802603i \(0.296552\pi\)
\(360\) 0 0
\(361\) 34.2773 1.80407
\(362\) 0 0
\(363\) −29.9613 −1.57256
\(364\) 0 0
\(365\) −6.71607 −0.351535
\(366\) 0 0
\(367\) 11.4818 0.599347 0.299674 0.954042i \(-0.403122\pi\)
0.299674 + 0.954042i \(0.403122\pi\)
\(368\) 0 0
\(369\) −1.99835 −0.104030
\(370\) 0 0
\(371\) −7.26218 −0.377034
\(372\) 0 0
\(373\) −7.20131 −0.372870 −0.186435 0.982467i \(-0.559693\pi\)
−0.186435 + 0.982467i \(0.559693\pi\)
\(374\) 0 0
\(375\) −10.2486 −0.529236
\(376\) 0 0
\(377\) 18.5830 0.957075
\(378\) 0 0
\(379\) 30.5023 1.56680 0.783399 0.621519i \(-0.213484\pi\)
0.783399 + 0.621519i \(0.213484\pi\)
\(380\) 0 0
\(381\) −13.7453 −0.704192
\(382\) 0 0
\(383\) 22.4939 1.14939 0.574693 0.818369i \(-0.305122\pi\)
0.574693 + 0.818369i \(0.305122\pi\)
\(384\) 0 0
\(385\) 8.99556 0.458456
\(386\) 0 0
\(387\) −4.73040 −0.240460
\(388\) 0 0
\(389\) −3.76896 −0.191094 −0.0955469 0.995425i \(-0.530460\pi\)
−0.0955469 + 0.995425i \(0.530460\pi\)
\(390\) 0 0
\(391\) −1.05553 −0.0533804
\(392\) 0 0
\(393\) −4.90929 −0.247641
\(394\) 0 0
\(395\) −5.78309 −0.290979
\(396\) 0 0
\(397\) −17.5566 −0.881141 −0.440571 0.897718i \(-0.645224\pi\)
−0.440571 + 0.897718i \(0.645224\pi\)
\(398\) 0 0
\(399\) −4.29267 −0.214902
\(400\) 0 0
\(401\) 17.3227 0.865056 0.432528 0.901621i \(-0.357622\pi\)
0.432528 + 0.901621i \(0.357622\pi\)
\(402\) 0 0
\(403\) 0.977547 0.0486951
\(404\) 0 0
\(405\) −2.38993 −0.118756
\(406\) 0 0
\(407\) 14.9624 0.741660
\(408\) 0 0
\(409\) 13.2762 0.656465 0.328232 0.944597i \(-0.393547\pi\)
0.328232 + 0.944597i \(0.393547\pi\)
\(410\) 0 0
\(411\) 0.345498 0.0170422
\(412\) 0 0
\(413\) 3.74459 0.184259
\(414\) 0 0
\(415\) 33.1125 1.62543
\(416\) 0 0
\(417\) 20.9006 1.02351
\(418\) 0 0
\(419\) −8.62663 −0.421438 −0.210719 0.977547i \(-0.567581\pi\)
−0.210719 + 0.977547i \(0.567581\pi\)
\(420\) 0 0
\(421\) −5.48658 −0.267400 −0.133700 0.991022i \(-0.542686\pi\)
−0.133700 + 0.991022i \(0.542686\pi\)
\(422\) 0 0
\(423\) −9.43664 −0.458825
\(424\) 0 0
\(425\) −2.40773 −0.116792
\(426\) 0 0
\(427\) 1.41256 0.0683585
\(428\) 0 0
\(429\) −22.9866 −1.10980
\(430\) 0 0
\(431\) −5.86411 −0.282464 −0.141232 0.989976i \(-0.545106\pi\)
−0.141232 + 0.989976i \(0.545106\pi\)
\(432\) 0 0
\(433\) 19.5766 0.940793 0.470396 0.882455i \(-0.344111\pi\)
0.470396 + 0.882455i \(0.344111\pi\)
\(434\) 0 0
\(435\) −12.3655 −0.592882
\(436\) 0 0
\(437\) 2.27749 0.108947
\(438\) 0 0
\(439\) 8.97589 0.428396 0.214198 0.976790i \(-0.431286\pi\)
0.214198 + 0.976790i \(0.431286\pi\)
\(440\) 0 0
\(441\) −6.65413 −0.316863
\(442\) 0 0
\(443\) 13.3745 0.635440 0.317720 0.948185i \(-0.397083\pi\)
0.317720 + 0.948185i \(0.397083\pi\)
\(444\) 0 0
\(445\) 21.5936 1.02363
\(446\) 0 0
\(447\) −16.3697 −0.774259
\(448\) 0 0
\(449\) 21.6819 1.02323 0.511615 0.859215i \(-0.329047\pi\)
0.511615 + 0.859215i \(0.329047\pi\)
\(450\) 0 0
\(451\) 12.7896 0.602240
\(452\) 0 0
\(453\) 17.0850 0.802725
\(454\) 0 0
\(455\) 5.04811 0.236659
\(456\) 0 0
\(457\) 24.3867 1.14076 0.570380 0.821381i \(-0.306796\pi\)
0.570380 + 0.821381i \(0.306796\pi\)
\(458\) 0 0
\(459\) 3.38286 0.157898
\(460\) 0 0
\(461\) 35.6549 1.66061 0.830307 0.557306i \(-0.188165\pi\)
0.830307 + 0.557306i \(0.188165\pi\)
\(462\) 0 0
\(463\) 10.2832 0.477902 0.238951 0.971032i \(-0.423196\pi\)
0.238951 + 0.971032i \(0.423196\pi\)
\(464\) 0 0
\(465\) −0.650480 −0.0301653
\(466\) 0 0
\(467\) −3.45629 −0.159938 −0.0799691 0.996797i \(-0.525482\pi\)
−0.0799691 + 0.996797i \(0.525482\pi\)
\(468\) 0 0
\(469\) −5.67364 −0.261984
\(470\) 0 0
\(471\) −2.07454 −0.0955896
\(472\) 0 0
\(473\) 30.2750 1.39205
\(474\) 0 0
\(475\) 5.19510 0.238368
\(476\) 0 0
\(477\) −12.3484 −0.565394
\(478\) 0 0
\(479\) −40.0140 −1.82829 −0.914143 0.405393i \(-0.867135\pi\)
−0.914143 + 0.405393i \(0.867135\pi\)
\(480\) 0 0
\(481\) 8.39658 0.382851
\(482\) 0 0
\(483\) −0.183503 −0.00834966
\(484\) 0 0
\(485\) −36.2627 −1.64661
\(486\) 0 0
\(487\) 15.2621 0.691593 0.345796 0.938310i \(-0.387609\pi\)
0.345796 + 0.938310i \(0.387609\pi\)
\(488\) 0 0
\(489\) 4.37975 0.198059
\(490\) 0 0
\(491\) 36.1991 1.63364 0.816821 0.576891i \(-0.195734\pi\)
0.816821 + 0.576891i \(0.195734\pi\)
\(492\) 0 0
\(493\) 17.5030 0.788297
\(494\) 0 0
\(495\) 15.2958 0.687494
\(496\) 0 0
\(497\) 8.70824 0.390618
\(498\) 0 0
\(499\) −40.7341 −1.82351 −0.911754 0.410736i \(-0.865272\pi\)
−0.911754 + 0.410736i \(0.865272\pi\)
\(500\) 0 0
\(501\) 5.72958 0.255979
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 28.6234 1.27372
\(506\) 0 0
\(507\) 0.100422 0.00445988
\(508\) 0 0
\(509\) −16.1247 −0.714713 −0.357356 0.933968i \(-0.616322\pi\)
−0.357356 + 0.933968i \(0.616322\pi\)
\(510\) 0 0
\(511\) 1.65268 0.0731101
\(512\) 0 0
\(513\) −7.29913 −0.322265
\(514\) 0 0
\(515\) −1.66651 −0.0734354
\(516\) 0 0
\(517\) 60.3955 2.65619
\(518\) 0 0
\(519\) 5.49514 0.241210
\(520\) 0 0
\(521\) 9.76844 0.427963 0.213982 0.976838i \(-0.431357\pi\)
0.213982 + 0.976838i \(0.431357\pi\)
\(522\) 0 0
\(523\) 24.3708 1.06566 0.532829 0.846223i \(-0.321129\pi\)
0.532829 + 0.846223i \(0.321129\pi\)
\(524\) 0 0
\(525\) −0.418581 −0.0182684
\(526\) 0 0
\(527\) 0.920734 0.0401078
\(528\) 0 0
\(529\) −22.9026 −0.995767
\(530\) 0 0
\(531\) 6.36719 0.276312
\(532\) 0 0
\(533\) 7.17726 0.310881
\(534\) 0 0
\(535\) 12.8638 0.556152
\(536\) 0 0
\(537\) −13.4407 −0.580011
\(538\) 0 0
\(539\) 42.5871 1.83436
\(540\) 0 0
\(541\) 1.49822 0.0644135 0.0322067 0.999481i \(-0.489747\pi\)
0.0322067 + 0.999481i \(0.489747\pi\)
\(542\) 0 0
\(543\) 19.2230 0.824939
\(544\) 0 0
\(545\) −27.1450 −1.16276
\(546\) 0 0
\(547\) −15.0557 −0.643736 −0.321868 0.946785i \(-0.604311\pi\)
−0.321868 + 0.946785i \(0.604311\pi\)
\(548\) 0 0
\(549\) 2.40187 0.102509
\(550\) 0 0
\(551\) −37.7659 −1.60888
\(552\) 0 0
\(553\) 1.42309 0.0605159
\(554\) 0 0
\(555\) −5.58726 −0.237166
\(556\) 0 0
\(557\) −6.34801 −0.268974 −0.134487 0.990915i \(-0.542939\pi\)
−0.134487 + 0.990915i \(0.542939\pi\)
\(558\) 0 0
\(559\) 16.9897 0.718587
\(560\) 0 0
\(561\) −21.6507 −0.914092
\(562\) 0 0
\(563\) −24.4057 −1.02858 −0.514290 0.857617i \(-0.671944\pi\)
−0.514290 + 0.857617i \(0.671944\pi\)
\(564\) 0 0
\(565\) −43.9051 −1.84710
\(566\) 0 0
\(567\) 0.588107 0.0246982
\(568\) 0 0
\(569\) 16.3905 0.687124 0.343562 0.939130i \(-0.388366\pi\)
0.343562 + 0.939130i \(0.388366\pi\)
\(570\) 0 0
\(571\) −16.1798 −0.677103 −0.338552 0.940948i \(-0.609937\pi\)
−0.338552 + 0.940948i \(0.609937\pi\)
\(572\) 0 0
\(573\) −14.5416 −0.607484
\(574\) 0 0
\(575\) 0.222079 0.00926135
\(576\) 0 0
\(577\) 19.2936 0.803204 0.401602 0.915814i \(-0.368454\pi\)
0.401602 + 0.915814i \(0.368454\pi\)
\(578\) 0 0
\(579\) 26.4953 1.10111
\(580\) 0 0
\(581\) −8.14824 −0.338046
\(582\) 0 0
\(583\) 79.0310 3.27313
\(584\) 0 0
\(585\) 8.58365 0.354890
\(586\) 0 0
\(587\) −15.8376 −0.653688 −0.326844 0.945078i \(-0.605985\pi\)
−0.326844 + 0.945078i \(0.605985\pi\)
\(588\) 0 0
\(589\) −1.98665 −0.0818584
\(590\) 0 0
\(591\) −1.72972 −0.0711513
\(592\) 0 0
\(593\) −32.5864 −1.33816 −0.669082 0.743188i \(-0.733313\pi\)
−0.669082 + 0.743188i \(0.733313\pi\)
\(594\) 0 0
\(595\) 4.75472 0.194925
\(596\) 0 0
\(597\) 22.1817 0.907838
\(598\) 0 0
\(599\) −39.8792 −1.62942 −0.814709 0.579869i \(-0.803104\pi\)
−0.814709 + 0.579869i \(0.803104\pi\)
\(600\) 0 0
\(601\) 4.11864 0.168003 0.0840015 0.996466i \(-0.473230\pi\)
0.0840015 + 0.996466i \(0.473230\pi\)
\(602\) 0 0
\(603\) −9.64729 −0.392868
\(604\) 0 0
\(605\) −71.6054 −2.91117
\(606\) 0 0
\(607\) 32.6159 1.32384 0.661920 0.749575i \(-0.269742\pi\)
0.661920 + 0.749575i \(0.269742\pi\)
\(608\) 0 0
\(609\) 3.04288 0.123304
\(610\) 0 0
\(611\) 33.8926 1.37115
\(612\) 0 0
\(613\) −31.6708 −1.27917 −0.639587 0.768719i \(-0.720895\pi\)
−0.639587 + 0.768719i \(0.720895\pi\)
\(614\) 0 0
\(615\) −4.77590 −0.192583
\(616\) 0 0
\(617\) 42.5002 1.71099 0.855497 0.517808i \(-0.173252\pi\)
0.855497 + 0.517808i \(0.173252\pi\)
\(618\) 0 0
\(619\) −43.1901 −1.73596 −0.867979 0.496601i \(-0.834581\pi\)
−0.867979 + 0.496601i \(0.834581\pi\)
\(620\) 0 0
\(621\) −0.312022 −0.0125210
\(622\) 0 0
\(623\) −5.31370 −0.212889
\(624\) 0 0
\(625\) −28.0521 −1.12209
\(626\) 0 0
\(627\) 46.7152 1.86563
\(628\) 0 0
\(629\) 7.90859 0.315336
\(630\) 0 0
\(631\) −40.8635 −1.62675 −0.813374 0.581740i \(-0.802372\pi\)
−0.813374 + 0.581740i \(0.802372\pi\)
\(632\) 0 0
\(633\) −28.3317 −1.12609
\(634\) 0 0
\(635\) −32.8502 −1.30362
\(636\) 0 0
\(637\) 23.8990 0.946911
\(638\) 0 0
\(639\) 14.8072 0.585765
\(640\) 0 0
\(641\) −45.9590 −1.81527 −0.907637 0.419757i \(-0.862115\pi\)
−0.907637 + 0.419757i \(0.862115\pi\)
\(642\) 0 0
\(643\) −14.3778 −0.567004 −0.283502 0.958972i \(-0.591496\pi\)
−0.283502 + 0.958972i \(0.591496\pi\)
\(644\) 0 0
\(645\) −11.3053 −0.445145
\(646\) 0 0
\(647\) −38.4085 −1.50999 −0.754997 0.655729i \(-0.772362\pi\)
−0.754997 + 0.655729i \(0.772362\pi\)
\(648\) 0 0
\(649\) −40.7507 −1.59960
\(650\) 0 0
\(651\) 0.160069 0.00627359
\(652\) 0 0
\(653\) −15.6342 −0.611812 −0.305906 0.952062i \(-0.598959\pi\)
−0.305906 + 0.952062i \(0.598959\pi\)
\(654\) 0 0
\(655\) −11.7328 −0.458440
\(656\) 0 0
\(657\) 2.81016 0.109635
\(658\) 0 0
\(659\) 18.7437 0.730151 0.365076 0.930978i \(-0.381043\pi\)
0.365076 + 0.930978i \(0.381043\pi\)
\(660\) 0 0
\(661\) −21.6538 −0.842235 −0.421118 0.907006i \(-0.638362\pi\)
−0.421118 + 0.907006i \(0.638362\pi\)
\(662\) 0 0
\(663\) −12.1499 −0.471862
\(664\) 0 0
\(665\) −10.2592 −0.397833
\(666\) 0 0
\(667\) −1.61441 −0.0625103
\(668\) 0 0
\(669\) −14.6429 −0.566127
\(670\) 0 0
\(671\) −15.3722 −0.593439
\(672\) 0 0
\(673\) −18.7691 −0.723497 −0.361749 0.932276i \(-0.617820\pi\)
−0.361749 + 0.932276i \(0.617820\pi\)
\(674\) 0 0
\(675\) −0.711742 −0.0273950
\(676\) 0 0
\(677\) 1.75391 0.0674081 0.0337040 0.999432i \(-0.489270\pi\)
0.0337040 + 0.999432i \(0.489270\pi\)
\(678\) 0 0
\(679\) 8.92345 0.342451
\(680\) 0 0
\(681\) 16.9117 0.648059
\(682\) 0 0
\(683\) −47.3013 −1.80993 −0.904967 0.425481i \(-0.860105\pi\)
−0.904967 + 0.425481i \(0.860105\pi\)
\(684\) 0 0
\(685\) 0.825714 0.0315489
\(686\) 0 0
\(687\) −28.6468 −1.09294
\(688\) 0 0
\(689\) 44.3505 1.68962
\(690\) 0 0
\(691\) 20.8270 0.792295 0.396148 0.918187i \(-0.370347\pi\)
0.396148 + 0.918187i \(0.370347\pi\)
\(692\) 0 0
\(693\) −3.76395 −0.142981
\(694\) 0 0
\(695\) 49.9508 1.89474
\(696\) 0 0
\(697\) 6.76013 0.256058
\(698\) 0 0
\(699\) 11.9058 0.450319
\(700\) 0 0
\(701\) 20.1425 0.760772 0.380386 0.924828i \(-0.375791\pi\)
0.380386 + 0.924828i \(0.375791\pi\)
\(702\) 0 0
\(703\) −17.0642 −0.643589
\(704\) 0 0
\(705\) −22.5529 −0.849390
\(706\) 0 0
\(707\) −7.04357 −0.264901
\(708\) 0 0
\(709\) −39.6246 −1.48813 −0.744067 0.668105i \(-0.767106\pi\)
−0.744067 + 0.668105i \(0.767106\pi\)
\(710\) 0 0
\(711\) 2.41978 0.0907488
\(712\) 0 0
\(713\) −0.0849250 −0.00318047
\(714\) 0 0
\(715\) −54.9363 −2.05450
\(716\) 0 0
\(717\) −2.67752 −0.0999939
\(718\) 0 0
\(719\) 8.19406 0.305587 0.152793 0.988258i \(-0.451173\pi\)
0.152793 + 0.988258i \(0.451173\pi\)
\(720\) 0 0
\(721\) 0.410092 0.0152726
\(722\) 0 0
\(723\) −16.2107 −0.602881
\(724\) 0 0
\(725\) −3.68258 −0.136767
\(726\) 0 0
\(727\) −7.36758 −0.273249 −0.136624 0.990623i \(-0.543625\pi\)
−0.136624 + 0.990623i \(0.543625\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 16.0023 0.591866
\(732\) 0 0
\(733\) 16.3787 0.604962 0.302481 0.953155i \(-0.402185\pi\)
0.302481 + 0.953155i \(0.402185\pi\)
\(734\) 0 0
\(735\) −15.9029 −0.586586
\(736\) 0 0
\(737\) 61.7436 2.27436
\(738\) 0 0
\(739\) −8.99317 −0.330819 −0.165410 0.986225i \(-0.552895\pi\)
−0.165410 + 0.986225i \(0.552895\pi\)
\(740\) 0 0
\(741\) 26.2156 0.963052
\(742\) 0 0
\(743\) −12.6592 −0.464420 −0.232210 0.972666i \(-0.574596\pi\)
−0.232210 + 0.972666i \(0.574596\pi\)
\(744\) 0 0
\(745\) −39.1223 −1.43333
\(746\) 0 0
\(747\) −13.8550 −0.506929
\(748\) 0 0
\(749\) −3.16550 −0.115665
\(750\) 0 0
\(751\) 4.01514 0.146515 0.0732573 0.997313i \(-0.476661\pi\)
0.0732573 + 0.997313i \(0.476661\pi\)
\(752\) 0 0
\(753\) 6.74504 0.245803
\(754\) 0 0
\(755\) 40.8319 1.48603
\(756\) 0 0
\(757\) 22.0647 0.801954 0.400977 0.916088i \(-0.368671\pi\)
0.400977 + 0.916088i \(0.368671\pi\)
\(758\) 0 0
\(759\) 1.99698 0.0724856
\(760\) 0 0
\(761\) −2.68911 −0.0974801 −0.0487400 0.998811i \(-0.515521\pi\)
−0.0487400 + 0.998811i \(0.515521\pi\)
\(762\) 0 0
\(763\) 6.67977 0.241824
\(764\) 0 0
\(765\) 8.08479 0.292306
\(766\) 0 0
\(767\) −22.8684 −0.825729
\(768\) 0 0
\(769\) 26.1831 0.944187 0.472094 0.881548i \(-0.343498\pi\)
0.472094 + 0.881548i \(0.343498\pi\)
\(770\) 0 0
\(771\) −22.9551 −0.826708
\(772\) 0 0
\(773\) −28.9270 −1.04043 −0.520216 0.854035i \(-0.674149\pi\)
−0.520216 + 0.854035i \(0.674149\pi\)
\(774\) 0 0
\(775\) −0.193719 −0.00695860
\(776\) 0 0
\(777\) 1.37490 0.0493243
\(778\) 0 0
\(779\) −14.5862 −0.522605
\(780\) 0 0
\(781\) −94.7678 −3.39106
\(782\) 0 0
\(783\) 5.17403 0.184905
\(784\) 0 0
\(785\) −4.95799 −0.176958
\(786\) 0 0
\(787\) 17.9161 0.638641 0.319321 0.947647i \(-0.396545\pi\)
0.319321 + 0.947647i \(0.396545\pi\)
\(788\) 0 0
\(789\) 21.3876 0.761418
\(790\) 0 0
\(791\) 10.8041 0.384148
\(792\) 0 0
\(793\) −8.62657 −0.306338
\(794\) 0 0
\(795\) −29.5117 −1.04667
\(796\) 0 0
\(797\) 33.9111 1.20119 0.600597 0.799552i \(-0.294930\pi\)
0.600597 + 0.799552i \(0.294930\pi\)
\(798\) 0 0
\(799\) 31.9228 1.12935
\(800\) 0 0
\(801\) −9.03526 −0.319245
\(802\) 0 0
\(803\) −17.9853 −0.634688
\(804\) 0 0
\(805\) −0.438557 −0.0154571
\(806\) 0 0
\(807\) −25.0659 −0.882360
\(808\) 0 0
\(809\) −51.9598 −1.82681 −0.913405 0.407051i \(-0.866557\pi\)
−0.913405 + 0.407051i \(0.866557\pi\)
\(810\) 0 0
\(811\) −14.1320 −0.496240 −0.248120 0.968729i \(-0.579813\pi\)
−0.248120 + 0.968729i \(0.579813\pi\)
\(812\) 0 0
\(813\) −16.4961 −0.578542
\(814\) 0 0
\(815\) 10.4673 0.366653
\(816\) 0 0
\(817\) −34.5278 −1.20797
\(818\) 0 0
\(819\) −2.11225 −0.0738078
\(820\) 0 0
\(821\) −38.4230 −1.34097 −0.670485 0.741923i \(-0.733914\pi\)
−0.670485 + 0.741923i \(0.733914\pi\)
\(822\) 0 0
\(823\) 21.1853 0.738474 0.369237 0.929335i \(-0.379619\pi\)
0.369237 + 0.929335i \(0.379619\pi\)
\(824\) 0 0
\(825\) 4.55523 0.158593
\(826\) 0 0
\(827\) −29.2491 −1.01709 −0.508546 0.861035i \(-0.669817\pi\)
−0.508546 + 0.861035i \(0.669817\pi\)
\(828\) 0 0
\(829\) 3.15645 0.109628 0.0548140 0.998497i \(-0.482543\pi\)
0.0548140 + 0.998497i \(0.482543\pi\)
\(830\) 0 0
\(831\) −19.0521 −0.660910
\(832\) 0 0
\(833\) 22.5100 0.779925
\(834\) 0 0
\(835\) 13.6933 0.473875
\(836\) 0 0
\(837\) 0.272176 0.00940778
\(838\) 0 0
\(839\) −17.8210 −0.615250 −0.307625 0.951508i \(-0.599534\pi\)
−0.307625 + 0.951508i \(0.599534\pi\)
\(840\) 0 0
\(841\) −2.22941 −0.0768763
\(842\) 0 0
\(843\) 20.5003 0.706067
\(844\) 0 0
\(845\) 0.240000 0.00825625
\(846\) 0 0
\(847\) 17.6205 0.605447
\(848\) 0 0
\(849\) 22.1389 0.759805
\(850\) 0 0
\(851\) −0.729458 −0.0250055
\(852\) 0 0
\(853\) −24.0437 −0.823242 −0.411621 0.911355i \(-0.635037\pi\)
−0.411621 + 0.911355i \(0.635037\pi\)
\(854\) 0 0
\(855\) −17.4444 −0.596585
\(856\) 0 0
\(857\) 35.2784 1.20509 0.602544 0.798086i \(-0.294154\pi\)
0.602544 + 0.798086i \(0.294154\pi\)
\(858\) 0 0
\(859\) −44.0022 −1.50134 −0.750668 0.660680i \(-0.770268\pi\)
−0.750668 + 0.660680i \(0.770268\pi\)
\(860\) 0 0
\(861\) 1.17524 0.0400521
\(862\) 0 0
\(863\) 31.6997 1.07907 0.539535 0.841963i \(-0.318600\pi\)
0.539535 + 0.841963i \(0.318600\pi\)
\(864\) 0 0
\(865\) 13.1330 0.446535
\(866\) 0 0
\(867\) 5.55624 0.188700
\(868\) 0 0
\(869\) −15.4868 −0.525355
\(870\) 0 0
\(871\) 34.6492 1.17404
\(872\) 0 0
\(873\) 15.1732 0.513534
\(874\) 0 0
\(875\) 6.02729 0.203759
\(876\) 0 0
\(877\) 19.2543 0.650171 0.325086 0.945685i \(-0.394607\pi\)
0.325086 + 0.945685i \(0.394607\pi\)
\(878\) 0 0
\(879\) 5.77896 0.194920
\(880\) 0 0
\(881\) 46.2169 1.55709 0.778543 0.627591i \(-0.215959\pi\)
0.778543 + 0.627591i \(0.215959\pi\)
\(882\) 0 0
\(883\) 23.0857 0.776896 0.388448 0.921471i \(-0.373011\pi\)
0.388448 + 0.921471i \(0.373011\pi\)
\(884\) 0 0
\(885\) 15.2171 0.511517
\(886\) 0 0
\(887\) −30.7720 −1.03322 −0.516611 0.856220i \(-0.672807\pi\)
−0.516611 + 0.856220i \(0.672807\pi\)
\(888\) 0 0
\(889\) 8.08370 0.271119
\(890\) 0 0
\(891\) −6.40011 −0.214412
\(892\) 0 0
\(893\) −68.8793 −2.30496
\(894\) 0 0
\(895\) −32.1224 −1.07373
\(896\) 0 0
\(897\) 1.12066 0.0374177
\(898\) 0 0
\(899\) 1.40825 0.0469677
\(900\) 0 0
\(901\) 41.7729 1.39166
\(902\) 0 0
\(903\) 2.78198 0.0925785
\(904\) 0 0
\(905\) 45.9416 1.52715
\(906\) 0 0
\(907\) 0.611367 0.0203001 0.0101501 0.999948i \(-0.496769\pi\)
0.0101501 + 0.999948i \(0.496769\pi\)
\(908\) 0 0
\(909\) −11.9767 −0.397241
\(910\) 0 0
\(911\) −5.11765 −0.169555 −0.0847776 0.996400i \(-0.527018\pi\)
−0.0847776 + 0.996400i \(0.527018\pi\)
\(912\) 0 0
\(913\) 88.6736 2.93467
\(914\) 0 0
\(915\) 5.74030 0.189768
\(916\) 0 0
\(917\) 2.88719 0.0953433
\(918\) 0 0
\(919\) −32.2959 −1.06534 −0.532672 0.846322i \(-0.678812\pi\)
−0.532672 + 0.846322i \(0.678812\pi\)
\(920\) 0 0
\(921\) −12.3201 −0.405962
\(922\) 0 0
\(923\) −53.1816 −1.75049
\(924\) 0 0
\(925\) −1.66394 −0.0547100
\(926\) 0 0
\(927\) 0.697308 0.0229026
\(928\) 0 0
\(929\) 30.9312 1.01482 0.507410 0.861704i \(-0.330603\pi\)
0.507410 + 0.861704i \(0.330603\pi\)
\(930\) 0 0
\(931\) −48.5694 −1.59180
\(932\) 0 0
\(933\) 3.99551 0.130807
\(934\) 0 0
\(935\) −51.7435 −1.69219
\(936\) 0 0
\(937\) −35.0285 −1.14433 −0.572165 0.820138i \(-0.693896\pi\)
−0.572165 + 0.820138i \(0.693896\pi\)
\(938\) 0 0
\(939\) 10.3980 0.339327
\(940\) 0 0
\(941\) −0.459980 −0.0149949 −0.00749747 0.999972i \(-0.502387\pi\)
−0.00749747 + 0.999972i \(0.502387\pi\)
\(942\) 0 0
\(943\) −0.623528 −0.0203049
\(944\) 0 0
\(945\) 1.40553 0.0457220
\(946\) 0 0
\(947\) −8.99124 −0.292176 −0.146088 0.989272i \(-0.546668\pi\)
−0.146088 + 0.989272i \(0.546668\pi\)
\(948\) 0 0
\(949\) −10.0930 −0.327631
\(950\) 0 0
\(951\) −18.9689 −0.615109
\(952\) 0 0
\(953\) −20.6118 −0.667683 −0.333841 0.942629i \(-0.608345\pi\)
−0.333841 + 0.942629i \(0.608345\pi\)
\(954\) 0 0
\(955\) −34.7533 −1.12459
\(956\) 0 0
\(957\) −33.1143 −1.07043
\(958\) 0 0
\(959\) −0.203190 −0.00656134
\(960\) 0 0
\(961\) −30.9259 −0.997610
\(962\) 0 0
\(963\) −5.38252 −0.173449
\(964\) 0 0
\(965\) 63.3219 2.03840
\(966\) 0 0
\(967\) −20.7297 −0.666621 −0.333311 0.942817i \(-0.608166\pi\)
−0.333311 + 0.942817i \(0.608166\pi\)
\(968\) 0 0
\(969\) 24.6920 0.793220
\(970\) 0 0
\(971\) −22.5434 −0.723451 −0.361726 0.932285i \(-0.617812\pi\)
−0.361726 + 0.932285i \(0.617812\pi\)
\(972\) 0 0
\(973\) −12.2918 −0.394056
\(974\) 0 0
\(975\) 2.55629 0.0818669
\(976\) 0 0
\(977\) −42.8482 −1.37084 −0.685418 0.728150i \(-0.740381\pi\)
−0.685418 + 0.728150i \(0.740381\pi\)
\(978\) 0 0
\(979\) 57.8266 1.84815
\(980\) 0 0
\(981\) 11.3581 0.362635
\(982\) 0 0
\(983\) −9.34154 −0.297949 −0.148974 0.988841i \(-0.547597\pi\)
−0.148974 + 0.988841i \(0.547597\pi\)
\(984\) 0 0
\(985\) −4.13391 −0.131717
\(986\) 0 0
\(987\) 5.54975 0.176651
\(988\) 0 0
\(989\) −1.47599 −0.0469337
\(990\) 0 0
\(991\) 21.0204 0.667737 0.333868 0.942620i \(-0.391646\pi\)
0.333868 + 0.942620i \(0.391646\pi\)
\(992\) 0 0
\(993\) 7.95346 0.252396
\(994\) 0 0
\(995\) 53.0127 1.68062
\(996\) 0 0
\(997\) 26.9967 0.854994 0.427497 0.904017i \(-0.359395\pi\)
0.427497 + 0.904017i \(0.359395\pi\)
\(998\) 0 0
\(999\) 2.33784 0.0739660
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 \(a_p\))