Properties

Label 8020.2.a.c.1.11
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.750059 q^{3}\) \(-1.00000 q^{5}\) \(-4.31732 q^{7}\) \(-2.43741 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.750059 q^{3}\) \(-1.00000 q^{5}\) \(-4.31732 q^{7}\) \(-2.43741 q^{9}\) \(+1.26278 q^{11}\) \(+0.840199 q^{13}\) \(+0.750059 q^{15}\) \(+1.74261 q^{17}\) \(+4.53194 q^{19}\) \(+3.23824 q^{21}\) \(-7.00253 q^{23}\) \(+1.00000 q^{25}\) \(+4.07838 q^{27}\) \(-5.86477 q^{29}\) \(+5.85507 q^{31}\) \(-0.947155 q^{33}\) \(+4.31732 q^{35}\) \(+9.40647 q^{37}\) \(-0.630198 q^{39}\) \(-6.00340 q^{41}\) \(+6.28753 q^{43}\) \(+2.43741 q^{45}\) \(+1.12131 q^{47}\) \(+11.6393 q^{49}\) \(-1.30706 q^{51}\) \(+0.740586 q^{53}\) \(-1.26278 q^{55}\) \(-3.39922 q^{57}\) \(-1.87130 q^{59}\) \(-4.43841 q^{61}\) \(+10.5231 q^{63}\) \(-0.840199 q^{65}\) \(-2.32847 q^{67}\) \(+5.25231 q^{69}\) \(-11.5920 q^{71}\) \(+14.5436 q^{73}\) \(-0.750059 q^{75}\) \(-5.45181 q^{77}\) \(+16.2442 q^{79}\) \(+4.25321 q^{81}\) \(-6.59783 q^{83}\) \(-1.74261 q^{85}\) \(+4.39892 q^{87}\) \(-9.88080 q^{89}\) \(-3.62741 q^{91}\) \(-4.39165 q^{93}\) \(-4.53194 q^{95}\) \(+4.74520 q^{97}\) \(-3.07790 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.750059 −0.433047 −0.216523 0.976277i \(-0.569472\pi\)
−0.216523 + 0.976277i \(0.569472\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −4.31732 −1.63179 −0.815897 0.578197i \(-0.803756\pi\)
−0.815897 + 0.578197i \(0.803756\pi\)
\(8\) 0 0
\(9\) −2.43741 −0.812471
\(10\) 0 0
\(11\) 1.26278 0.380741 0.190371 0.981712i \(-0.439031\pi\)
0.190371 + 0.981712i \(0.439031\pi\)
\(12\) 0 0
\(13\) 0.840199 0.233029 0.116515 0.993189i \(-0.462828\pi\)
0.116515 + 0.993189i \(0.462828\pi\)
\(14\) 0 0
\(15\) 0.750059 0.193664
\(16\) 0 0
\(17\) 1.74261 0.422646 0.211323 0.977416i \(-0.432223\pi\)
0.211323 + 0.977416i \(0.432223\pi\)
\(18\) 0 0
\(19\) 4.53194 1.03970 0.519849 0.854258i \(-0.325988\pi\)
0.519849 + 0.854258i \(0.325988\pi\)
\(20\) 0 0
\(21\) 3.23824 0.706643
\(22\) 0 0
\(23\) −7.00253 −1.46013 −0.730065 0.683378i \(-0.760510\pi\)
−0.730065 + 0.683378i \(0.760510\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 4.07838 0.784884
\(28\) 0 0
\(29\) −5.86477 −1.08906 −0.544530 0.838741i \(-0.683292\pi\)
−0.544530 + 0.838741i \(0.683292\pi\)
\(30\) 0 0
\(31\) 5.85507 1.05160 0.525801 0.850608i \(-0.323766\pi\)
0.525801 + 0.850608i \(0.323766\pi\)
\(32\) 0 0
\(33\) −0.947155 −0.164879
\(34\) 0 0
\(35\) 4.31732 0.729760
\(36\) 0 0
\(37\) 9.40647 1.54641 0.773207 0.634154i \(-0.218651\pi\)
0.773207 + 0.634154i \(0.218651\pi\)
\(38\) 0 0
\(39\) −0.630198 −0.100913
\(40\) 0 0
\(41\) −6.00340 −0.937574 −0.468787 0.883311i \(-0.655309\pi\)
−0.468787 + 0.883311i \(0.655309\pi\)
\(42\) 0 0
\(43\) 6.28753 0.958840 0.479420 0.877586i \(-0.340847\pi\)
0.479420 + 0.877586i \(0.340847\pi\)
\(44\) 0 0
\(45\) 2.43741 0.363348
\(46\) 0 0
\(47\) 1.12131 0.163559 0.0817797 0.996650i \(-0.473940\pi\)
0.0817797 + 0.996650i \(0.473940\pi\)
\(48\) 0 0
\(49\) 11.6393 1.66275
\(50\) 0 0
\(51\) −1.30706 −0.183025
\(52\) 0 0
\(53\) 0.740586 0.101727 0.0508637 0.998706i \(-0.483803\pi\)
0.0508637 + 0.998706i \(0.483803\pi\)
\(54\) 0 0
\(55\) −1.26278 −0.170273
\(56\) 0 0
\(57\) −3.39922 −0.450237
\(58\) 0 0
\(59\) −1.87130 −0.243622 −0.121811 0.992553i \(-0.538870\pi\)
−0.121811 + 0.992553i \(0.538870\pi\)
\(60\) 0 0
\(61\) −4.43841 −0.568281 −0.284140 0.958783i \(-0.591708\pi\)
−0.284140 + 0.958783i \(0.591708\pi\)
\(62\) 0 0
\(63\) 10.5231 1.32578
\(64\) 0 0
\(65\) −0.840199 −0.104214
\(66\) 0 0
\(67\) −2.32847 −0.284468 −0.142234 0.989833i \(-0.545428\pi\)
−0.142234 + 0.989833i \(0.545428\pi\)
\(68\) 0 0
\(69\) 5.25231 0.632304
\(70\) 0 0
\(71\) −11.5920 −1.37571 −0.687857 0.725846i \(-0.741448\pi\)
−0.687857 + 0.725846i \(0.741448\pi\)
\(72\) 0 0
\(73\) 14.5436 1.70220 0.851099 0.525005i \(-0.175936\pi\)
0.851099 + 0.525005i \(0.175936\pi\)
\(74\) 0 0
\(75\) −0.750059 −0.0866093
\(76\) 0 0
\(77\) −5.45181 −0.621291
\(78\) 0 0
\(79\) 16.2442 1.82761 0.913805 0.406154i \(-0.133130\pi\)
0.913805 + 0.406154i \(0.133130\pi\)
\(80\) 0 0
\(81\) 4.25321 0.472579
\(82\) 0 0
\(83\) −6.59783 −0.724205 −0.362103 0.932138i \(-0.617941\pi\)
−0.362103 + 0.932138i \(0.617941\pi\)
\(84\) 0 0
\(85\) −1.74261 −0.189013
\(86\) 0 0
\(87\) 4.39892 0.471614
\(88\) 0 0
\(89\) −9.88080 −1.04736 −0.523681 0.851914i \(-0.675442\pi\)
−0.523681 + 0.851914i \(0.675442\pi\)
\(90\) 0 0
\(91\) −3.62741 −0.380256
\(92\) 0 0
\(93\) −4.39165 −0.455392
\(94\) 0 0
\(95\) −4.53194 −0.464967
\(96\) 0 0
\(97\) 4.74520 0.481802 0.240901 0.970550i \(-0.422557\pi\)
0.240901 + 0.970550i \(0.422557\pi\)
\(98\) 0 0
\(99\) −3.07790 −0.309341
\(100\) 0 0
\(101\) −7.87274 −0.783367 −0.391683 0.920100i \(-0.628107\pi\)
−0.391683 + 0.920100i \(0.628107\pi\)
\(102\) 0 0
\(103\) 17.8281 1.75665 0.878325 0.478063i \(-0.158661\pi\)
0.878325 + 0.478063i \(0.158661\pi\)
\(104\) 0 0
\(105\) −3.23824 −0.316020
\(106\) 0 0
\(107\) −0.215578 −0.0208407 −0.0104203 0.999946i \(-0.503317\pi\)
−0.0104203 + 0.999946i \(0.503317\pi\)
\(108\) 0 0
\(109\) 5.40467 0.517674 0.258837 0.965921i \(-0.416661\pi\)
0.258837 + 0.965921i \(0.416661\pi\)
\(110\) 0 0
\(111\) −7.05540 −0.669669
\(112\) 0 0
\(113\) 15.9257 1.49817 0.749083 0.662476i \(-0.230495\pi\)
0.749083 + 0.662476i \(0.230495\pi\)
\(114\) 0 0
\(115\) 7.00253 0.652990
\(116\) 0 0
\(117\) −2.04791 −0.189329
\(118\) 0 0
\(119\) −7.52343 −0.689671
\(120\) 0 0
\(121\) −9.40540 −0.855036
\(122\) 0 0
\(123\) 4.50290 0.406013
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 1.24363 0.110355 0.0551773 0.998477i \(-0.482428\pi\)
0.0551773 + 0.998477i \(0.482428\pi\)
\(128\) 0 0
\(129\) −4.71602 −0.415222
\(130\) 0 0
\(131\) 0.986253 0.0861693 0.0430846 0.999071i \(-0.486281\pi\)
0.0430846 + 0.999071i \(0.486281\pi\)
\(132\) 0 0
\(133\) −19.5658 −1.69657
\(134\) 0 0
\(135\) −4.07838 −0.351011
\(136\) 0 0
\(137\) −4.44041 −0.379369 −0.189685 0.981845i \(-0.560747\pi\)
−0.189685 + 0.981845i \(0.560747\pi\)
\(138\) 0 0
\(139\) −4.08344 −0.346352 −0.173176 0.984891i \(-0.555403\pi\)
−0.173176 + 0.984891i \(0.555403\pi\)
\(140\) 0 0
\(141\) −0.841045 −0.0708288
\(142\) 0 0
\(143\) 1.06098 0.0887238
\(144\) 0 0
\(145\) 5.86477 0.487043
\(146\) 0 0
\(147\) −8.73013 −0.720049
\(148\) 0 0
\(149\) 12.1336 0.994020 0.497010 0.867745i \(-0.334431\pi\)
0.497010 + 0.867745i \(0.334431\pi\)
\(150\) 0 0
\(151\) −7.99445 −0.650579 −0.325290 0.945614i \(-0.605462\pi\)
−0.325290 + 0.945614i \(0.605462\pi\)
\(152\) 0 0
\(153\) −4.24747 −0.343388
\(154\) 0 0
\(155\) −5.85507 −0.470291
\(156\) 0 0
\(157\) −15.1332 −1.20776 −0.603882 0.797074i \(-0.706380\pi\)
−0.603882 + 0.797074i \(0.706380\pi\)
\(158\) 0 0
\(159\) −0.555483 −0.0440527
\(160\) 0 0
\(161\) 30.2322 2.38263
\(162\) 0 0
\(163\) 21.4567 1.68062 0.840308 0.542109i \(-0.182374\pi\)
0.840308 + 0.542109i \(0.182374\pi\)
\(164\) 0 0
\(165\) 0.947155 0.0737360
\(166\) 0 0
\(167\) 9.37763 0.725663 0.362831 0.931855i \(-0.381810\pi\)
0.362831 + 0.931855i \(0.381810\pi\)
\(168\) 0 0
\(169\) −12.2941 −0.945697
\(170\) 0 0
\(171\) −11.0462 −0.844724
\(172\) 0 0
\(173\) 4.51979 0.343633 0.171817 0.985129i \(-0.445036\pi\)
0.171817 + 0.985129i \(0.445036\pi\)
\(174\) 0 0
\(175\) −4.31732 −0.326359
\(176\) 0 0
\(177\) 1.40358 0.105500
\(178\) 0 0
\(179\) 4.72827 0.353408 0.176704 0.984264i \(-0.443456\pi\)
0.176704 + 0.984264i \(0.443456\pi\)
\(180\) 0 0
\(181\) −24.3759 −1.81185 −0.905925 0.423438i \(-0.860823\pi\)
−0.905925 + 0.423438i \(0.860823\pi\)
\(182\) 0 0
\(183\) 3.32907 0.246092
\(184\) 0 0
\(185\) −9.40647 −0.691577
\(186\) 0 0
\(187\) 2.20053 0.160919
\(188\) 0 0
\(189\) −17.6077 −1.28077
\(190\) 0 0
\(191\) −17.4655 −1.26376 −0.631878 0.775068i \(-0.717716\pi\)
−0.631878 + 0.775068i \(0.717716\pi\)
\(192\) 0 0
\(193\) −13.6808 −0.984767 −0.492383 0.870378i \(-0.663874\pi\)
−0.492383 + 0.870378i \(0.663874\pi\)
\(194\) 0 0
\(195\) 0.630198 0.0451294
\(196\) 0 0
\(197\) −5.60348 −0.399231 −0.199616 0.979874i \(-0.563969\pi\)
−0.199616 + 0.979874i \(0.563969\pi\)
\(198\) 0 0
\(199\) −12.7383 −0.902995 −0.451497 0.892273i \(-0.649110\pi\)
−0.451497 + 0.892273i \(0.649110\pi\)
\(200\) 0 0
\(201\) 1.74649 0.123188
\(202\) 0 0
\(203\) 25.3201 1.77712
\(204\) 0 0
\(205\) 6.00340 0.419296
\(206\) 0 0
\(207\) 17.0681 1.18631
\(208\) 0 0
\(209\) 5.72282 0.395856
\(210\) 0 0
\(211\) −8.31509 −0.572435 −0.286217 0.958165i \(-0.592398\pi\)
−0.286217 + 0.958165i \(0.592398\pi\)
\(212\) 0 0
\(213\) 8.69466 0.595748
\(214\) 0 0
\(215\) −6.28753 −0.428806
\(216\) 0 0
\(217\) −25.2782 −1.71600
\(218\) 0 0
\(219\) −10.9085 −0.737131
\(220\) 0 0
\(221\) 1.46414 0.0984889
\(222\) 0 0
\(223\) −0.527641 −0.0353334 −0.0176667 0.999844i \(-0.505624\pi\)
−0.0176667 + 0.999844i \(0.505624\pi\)
\(224\) 0 0
\(225\) −2.43741 −0.162494
\(226\) 0 0
\(227\) −15.7014 −1.04214 −0.521070 0.853514i \(-0.674467\pi\)
−0.521070 + 0.853514i \(0.674467\pi\)
\(228\) 0 0
\(229\) 0.772461 0.0510457 0.0255228 0.999674i \(-0.491875\pi\)
0.0255228 + 0.999674i \(0.491875\pi\)
\(230\) 0 0
\(231\) 4.08917 0.269048
\(232\) 0 0
\(233\) −10.3255 −0.676445 −0.338223 0.941066i \(-0.609826\pi\)
−0.338223 + 0.941066i \(0.609826\pi\)
\(234\) 0 0
\(235\) −1.12131 −0.0731459
\(236\) 0 0
\(237\) −12.1841 −0.791440
\(238\) 0 0
\(239\) −3.56332 −0.230492 −0.115246 0.993337i \(-0.536766\pi\)
−0.115246 + 0.993337i \(0.536766\pi\)
\(240\) 0 0
\(241\) 2.28273 0.147043 0.0735217 0.997294i \(-0.476576\pi\)
0.0735217 + 0.997294i \(0.476576\pi\)
\(242\) 0 0
\(243\) −15.4253 −0.989533
\(244\) 0 0
\(245\) −11.6393 −0.743605
\(246\) 0 0
\(247\) 3.80773 0.242280
\(248\) 0 0
\(249\) 4.94876 0.313615
\(250\) 0 0
\(251\) 12.5000 0.788995 0.394497 0.918897i \(-0.370919\pi\)
0.394497 + 0.918897i \(0.370919\pi\)
\(252\) 0 0
\(253\) −8.84263 −0.555931
\(254\) 0 0
\(255\) 1.30706 0.0818515
\(256\) 0 0
\(257\) −23.4959 −1.46563 −0.732817 0.680426i \(-0.761795\pi\)
−0.732817 + 0.680426i \(0.761795\pi\)
\(258\) 0 0
\(259\) −40.6107 −2.52343
\(260\) 0 0
\(261\) 14.2949 0.884830
\(262\) 0 0
\(263\) −2.77922 −0.171374 −0.0856871 0.996322i \(-0.527309\pi\)
−0.0856871 + 0.996322i \(0.527309\pi\)
\(264\) 0 0
\(265\) −0.740586 −0.0454938
\(266\) 0 0
\(267\) 7.41118 0.453557
\(268\) 0 0
\(269\) −23.9484 −1.46016 −0.730079 0.683363i \(-0.760517\pi\)
−0.730079 + 0.683363i \(0.760517\pi\)
\(270\) 0 0
\(271\) −9.32023 −0.566164 −0.283082 0.959096i \(-0.591357\pi\)
−0.283082 + 0.959096i \(0.591357\pi\)
\(272\) 0 0
\(273\) 2.72077 0.164668
\(274\) 0 0
\(275\) 1.26278 0.0761482
\(276\) 0 0
\(277\) −13.2903 −0.798536 −0.399268 0.916834i \(-0.630736\pi\)
−0.399268 + 0.916834i \(0.630736\pi\)
\(278\) 0 0
\(279\) −14.2712 −0.854396
\(280\) 0 0
\(281\) 2.56864 0.153232 0.0766162 0.997061i \(-0.475588\pi\)
0.0766162 + 0.997061i \(0.475588\pi\)
\(282\) 0 0
\(283\) 8.92647 0.530623 0.265312 0.964163i \(-0.414525\pi\)
0.265312 + 0.964163i \(0.414525\pi\)
\(284\) 0 0
\(285\) 3.39922 0.201352
\(286\) 0 0
\(287\) 25.9186 1.52993
\(288\) 0 0
\(289\) −13.9633 −0.821370
\(290\) 0 0
\(291\) −3.55918 −0.208643
\(292\) 0 0
\(293\) −23.2424 −1.35783 −0.678917 0.734215i \(-0.737550\pi\)
−0.678917 + 0.734215i \(0.737550\pi\)
\(294\) 0 0
\(295\) 1.87130 0.108951
\(296\) 0 0
\(297\) 5.15007 0.298838
\(298\) 0 0
\(299\) −5.88352 −0.340253
\(300\) 0 0
\(301\) −27.1453 −1.56463
\(302\) 0 0
\(303\) 5.90502 0.339234
\(304\) 0 0
\(305\) 4.43841 0.254143
\(306\) 0 0
\(307\) −24.7518 −1.41266 −0.706329 0.707883i \(-0.749650\pi\)
−0.706329 + 0.707883i \(0.749650\pi\)
\(308\) 0 0
\(309\) −13.3721 −0.760712
\(310\) 0 0
\(311\) 31.4484 1.78328 0.891639 0.452747i \(-0.149556\pi\)
0.891639 + 0.452747i \(0.149556\pi\)
\(312\) 0 0
\(313\) 29.0008 1.63922 0.819612 0.572919i \(-0.194189\pi\)
0.819612 + 0.572919i \(0.194189\pi\)
\(314\) 0 0
\(315\) −10.5231 −0.592909
\(316\) 0 0
\(317\) −14.8857 −0.836063 −0.418032 0.908432i \(-0.637280\pi\)
−0.418032 + 0.908432i \(0.637280\pi\)
\(318\) 0 0
\(319\) −7.40589 −0.414650
\(320\) 0 0
\(321\) 0.161696 0.00902498
\(322\) 0 0
\(323\) 7.89742 0.439424
\(324\) 0 0
\(325\) 0.840199 0.0466059
\(326\) 0 0
\(327\) −4.05382 −0.224177
\(328\) 0 0
\(329\) −4.84104 −0.266895
\(330\) 0 0
\(331\) −8.99982 −0.494675 −0.247338 0.968929i \(-0.579556\pi\)
−0.247338 + 0.968929i \(0.579556\pi\)
\(332\) 0 0
\(333\) −22.9274 −1.25642
\(334\) 0 0
\(335\) 2.32847 0.127218
\(336\) 0 0
\(337\) 26.7997 1.45987 0.729935 0.683516i \(-0.239550\pi\)
0.729935 + 0.683516i \(0.239550\pi\)
\(338\) 0 0
\(339\) −11.9452 −0.648775
\(340\) 0 0
\(341\) 7.39364 0.400388
\(342\) 0 0
\(343\) −20.0292 −1.08147
\(344\) 0 0
\(345\) −5.25231 −0.282775
\(346\) 0 0
\(347\) −0.0900549 −0.00483440 −0.00241720 0.999997i \(-0.500769\pi\)
−0.00241720 + 0.999997i \(0.500769\pi\)
\(348\) 0 0
\(349\) −34.9049 −1.86842 −0.934209 0.356726i \(-0.883893\pi\)
−0.934209 + 0.356726i \(0.883893\pi\)
\(350\) 0 0
\(351\) 3.42665 0.182901
\(352\) 0 0
\(353\) −19.4246 −1.03386 −0.516932 0.856026i \(-0.672926\pi\)
−0.516932 + 0.856026i \(0.672926\pi\)
\(354\) 0 0
\(355\) 11.5920 0.615238
\(356\) 0 0
\(357\) 5.64301 0.298660
\(358\) 0 0
\(359\) 0.828543 0.0437288 0.0218644 0.999761i \(-0.493040\pi\)
0.0218644 + 0.999761i \(0.493040\pi\)
\(360\) 0 0
\(361\) 1.53845 0.0809712
\(362\) 0 0
\(363\) 7.05460 0.370270
\(364\) 0 0
\(365\) −14.5436 −0.761246
\(366\) 0 0
\(367\) −21.9404 −1.14528 −0.572640 0.819807i \(-0.694081\pi\)
−0.572640 + 0.819807i \(0.694081\pi\)
\(368\) 0 0
\(369\) 14.6328 0.761751
\(370\) 0 0
\(371\) −3.19735 −0.165998
\(372\) 0 0
\(373\) −10.4994 −0.543637 −0.271819 0.962349i \(-0.587625\pi\)
−0.271819 + 0.962349i \(0.587625\pi\)
\(374\) 0 0
\(375\) 0.750059 0.0387329
\(376\) 0 0
\(377\) −4.92757 −0.253783
\(378\) 0 0
\(379\) 1.36333 0.0700295 0.0350147 0.999387i \(-0.488852\pi\)
0.0350147 + 0.999387i \(0.488852\pi\)
\(380\) 0 0
\(381\) −0.932798 −0.0477887
\(382\) 0 0
\(383\) 15.7867 0.806661 0.403330 0.915054i \(-0.367853\pi\)
0.403330 + 0.915054i \(0.367853\pi\)
\(384\) 0 0
\(385\) 5.45181 0.277850
\(386\) 0 0
\(387\) −15.3253 −0.779029
\(388\) 0 0
\(389\) −23.7530 −1.20433 −0.602164 0.798373i \(-0.705694\pi\)
−0.602164 + 0.798373i \(0.705694\pi\)
\(390\) 0 0
\(391\) −12.2027 −0.617118
\(392\) 0 0
\(393\) −0.739747 −0.0373153
\(394\) 0 0
\(395\) −16.2442 −0.817332
\(396\) 0 0
\(397\) 9.80619 0.492158 0.246079 0.969250i \(-0.420858\pi\)
0.246079 + 0.969250i \(0.420858\pi\)
\(398\) 0 0
\(399\) 14.6755 0.734695
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 4.91942 0.245054
\(404\) 0 0
\(405\) −4.25321 −0.211344
\(406\) 0 0
\(407\) 11.8783 0.588783
\(408\) 0 0
\(409\) 35.4444 1.75261 0.876306 0.481754i \(-0.160000\pi\)
0.876306 + 0.481754i \(0.160000\pi\)
\(410\) 0 0
\(411\) 3.33056 0.164285
\(412\) 0 0
\(413\) 8.07899 0.397541
\(414\) 0 0
\(415\) 6.59783 0.323875
\(416\) 0 0
\(417\) 3.06282 0.149987
\(418\) 0 0
\(419\) 12.9094 0.630667 0.315334 0.948981i \(-0.397884\pi\)
0.315334 + 0.948981i \(0.397884\pi\)
\(420\) 0 0
\(421\) 19.2983 0.940544 0.470272 0.882522i \(-0.344156\pi\)
0.470272 + 0.882522i \(0.344156\pi\)
\(422\) 0 0
\(423\) −2.73309 −0.132887
\(424\) 0 0
\(425\) 1.74261 0.0845292
\(426\) 0 0
\(427\) 19.1621 0.927317
\(428\) 0 0
\(429\) −0.795799 −0.0384215
\(430\) 0 0
\(431\) 12.7813 0.615653 0.307826 0.951443i \(-0.400398\pi\)
0.307826 + 0.951443i \(0.400398\pi\)
\(432\) 0 0
\(433\) 35.9291 1.72664 0.863321 0.504655i \(-0.168380\pi\)
0.863321 + 0.504655i \(0.168380\pi\)
\(434\) 0 0
\(435\) −4.39892 −0.210912
\(436\) 0 0
\(437\) −31.7350 −1.51809
\(438\) 0 0
\(439\) −13.2146 −0.630696 −0.315348 0.948976i \(-0.602121\pi\)
−0.315348 + 0.948976i \(0.602121\pi\)
\(440\) 0 0
\(441\) −28.3697 −1.35094
\(442\) 0 0
\(443\) 33.6761 1.60000 0.800001 0.599999i \(-0.204832\pi\)
0.800001 + 0.599999i \(0.204832\pi\)
\(444\) 0 0
\(445\) 9.88080 0.468395
\(446\) 0 0
\(447\) −9.10088 −0.430457
\(448\) 0 0
\(449\) −9.39505 −0.443380 −0.221690 0.975117i \(-0.571157\pi\)
−0.221690 + 0.975117i \(0.571157\pi\)
\(450\) 0 0
\(451\) −7.58095 −0.356973
\(452\) 0 0
\(453\) 5.99631 0.281731
\(454\) 0 0
\(455\) 3.62741 0.170056
\(456\) 0 0
\(457\) −5.30725 −0.248263 −0.124131 0.992266i \(-0.539614\pi\)
−0.124131 + 0.992266i \(0.539614\pi\)
\(458\) 0 0
\(459\) 7.10704 0.331728
\(460\) 0 0
\(461\) 30.7981 1.43441 0.717206 0.696861i \(-0.245420\pi\)
0.717206 + 0.696861i \(0.245420\pi\)
\(462\) 0 0
\(463\) 37.7678 1.75522 0.877609 0.479377i \(-0.159137\pi\)
0.877609 + 0.479377i \(0.159137\pi\)
\(464\) 0 0
\(465\) 4.39165 0.203658
\(466\) 0 0
\(467\) −0.924859 −0.0427974 −0.0213987 0.999771i \(-0.506812\pi\)
−0.0213987 + 0.999771i \(0.506812\pi\)
\(468\) 0 0
\(469\) 10.0527 0.464192
\(470\) 0 0
\(471\) 11.3508 0.523018
\(472\) 0 0
\(473\) 7.93974 0.365070
\(474\) 0 0
\(475\) 4.53194 0.207940
\(476\) 0 0
\(477\) −1.80511 −0.0826505
\(478\) 0 0
\(479\) −0.230945 −0.0105522 −0.00527608 0.999986i \(-0.501679\pi\)
−0.00527608 + 0.999986i \(0.501679\pi\)
\(480\) 0 0
\(481\) 7.90330 0.360360
\(482\) 0 0
\(483\) −22.6759 −1.03179
\(484\) 0 0
\(485\) −4.74520 −0.215468
\(486\) 0 0
\(487\) −18.2318 −0.826162 −0.413081 0.910694i \(-0.635547\pi\)
−0.413081 + 0.910694i \(0.635547\pi\)
\(488\) 0 0
\(489\) −16.0938 −0.727785
\(490\) 0 0
\(491\) 11.6486 0.525694 0.262847 0.964838i \(-0.415339\pi\)
0.262847 + 0.964838i \(0.415339\pi\)
\(492\) 0 0
\(493\) −10.2200 −0.460287
\(494\) 0 0
\(495\) 3.07790 0.138341
\(496\) 0 0
\(497\) 50.0462 2.24488
\(498\) 0 0
\(499\) 1.40138 0.0627344 0.0313672 0.999508i \(-0.490014\pi\)
0.0313672 + 0.999508i \(0.490014\pi\)
\(500\) 0 0
\(501\) −7.03377 −0.314246
\(502\) 0 0
\(503\) −39.1078 −1.74373 −0.871865 0.489746i \(-0.837089\pi\)
−0.871865 + 0.489746i \(0.837089\pi\)
\(504\) 0 0
\(505\) 7.87274 0.350332
\(506\) 0 0
\(507\) 9.22127 0.409531
\(508\) 0 0
\(509\) −40.3500 −1.78848 −0.894242 0.447584i \(-0.852285\pi\)
−0.894242 + 0.447584i \(0.852285\pi\)
\(510\) 0 0
\(511\) −62.7893 −2.77764
\(512\) 0 0
\(513\) 18.4830 0.816042
\(514\) 0 0
\(515\) −17.8281 −0.785598
\(516\) 0 0
\(517\) 1.41596 0.0622737
\(518\) 0 0
\(519\) −3.39011 −0.148809
\(520\) 0 0
\(521\) −30.1444 −1.32065 −0.660324 0.750981i \(-0.729581\pi\)
−0.660324 + 0.750981i \(0.729581\pi\)
\(522\) 0 0
\(523\) 2.56645 0.112223 0.0561115 0.998425i \(-0.482130\pi\)
0.0561115 + 0.998425i \(0.482130\pi\)
\(524\) 0 0
\(525\) 3.23824 0.141329
\(526\) 0 0
\(527\) 10.2031 0.444455
\(528\) 0 0
\(529\) 26.0355 1.13198
\(530\) 0 0
\(531\) 4.56112 0.197936
\(532\) 0 0
\(533\) −5.04405 −0.218482
\(534\) 0 0
\(535\) 0.215578 0.00932023
\(536\) 0 0
\(537\) −3.54648 −0.153042
\(538\) 0 0
\(539\) 14.6978 0.633078
\(540\) 0 0
\(541\) 5.30796 0.228207 0.114104 0.993469i \(-0.463600\pi\)
0.114104 + 0.993469i \(0.463600\pi\)
\(542\) 0 0
\(543\) 18.2834 0.784615
\(544\) 0 0
\(545\) −5.40467 −0.231511
\(546\) 0 0
\(547\) −19.6184 −0.838821 −0.419411 0.907797i \(-0.637763\pi\)
−0.419411 + 0.907797i \(0.637763\pi\)
\(548\) 0 0
\(549\) 10.8182 0.461711
\(550\) 0 0
\(551\) −26.5788 −1.13229
\(552\) 0 0
\(553\) −70.1312 −2.98228
\(554\) 0 0
\(555\) 7.05540 0.299485
\(556\) 0 0
\(557\) −27.9723 −1.18522 −0.592612 0.805488i \(-0.701903\pi\)
−0.592612 + 0.805488i \(0.701903\pi\)
\(558\) 0 0
\(559\) 5.28278 0.223438
\(560\) 0 0
\(561\) −1.65053 −0.0696853
\(562\) 0 0
\(563\) 30.2689 1.27568 0.637842 0.770168i \(-0.279827\pi\)
0.637842 + 0.770168i \(0.279827\pi\)
\(564\) 0 0
\(565\) −15.9257 −0.670000
\(566\) 0 0
\(567\) −18.3625 −0.771152
\(568\) 0 0
\(569\) 32.2680 1.35275 0.676373 0.736560i \(-0.263551\pi\)
0.676373 + 0.736560i \(0.263551\pi\)
\(570\) 0 0
\(571\) −21.3512 −0.893518 −0.446759 0.894654i \(-0.647422\pi\)
−0.446759 + 0.894654i \(0.647422\pi\)
\(572\) 0 0
\(573\) 13.1001 0.547265
\(574\) 0 0
\(575\) −7.00253 −0.292026
\(576\) 0 0
\(577\) 6.18332 0.257415 0.128708 0.991683i \(-0.458917\pi\)
0.128708 + 0.991683i \(0.458917\pi\)
\(578\) 0 0
\(579\) 10.2614 0.426450
\(580\) 0 0
\(581\) 28.4849 1.18175
\(582\) 0 0
\(583\) 0.935194 0.0387318
\(584\) 0 0
\(585\) 2.04791 0.0846707
\(586\) 0 0
\(587\) 17.3892 0.717731 0.358866 0.933389i \(-0.383164\pi\)
0.358866 + 0.933389i \(0.383164\pi\)
\(588\) 0 0
\(589\) 26.5348 1.09335
\(590\) 0 0
\(591\) 4.20294 0.172886
\(592\) 0 0
\(593\) −14.7534 −0.605849 −0.302924 0.953015i \(-0.597963\pi\)
−0.302924 + 0.953015i \(0.597963\pi\)
\(594\) 0 0
\(595\) 7.52343 0.308430
\(596\) 0 0
\(597\) 9.55447 0.391039
\(598\) 0 0
\(599\) 32.6529 1.33416 0.667081 0.744985i \(-0.267543\pi\)
0.667081 + 0.744985i \(0.267543\pi\)
\(600\) 0 0
\(601\) 44.1895 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(602\) 0 0
\(603\) 5.67543 0.231122
\(604\) 0 0
\(605\) 9.40540 0.382384
\(606\) 0 0
\(607\) 19.3881 0.786940 0.393470 0.919338i \(-0.371275\pi\)
0.393470 + 0.919338i \(0.371275\pi\)
\(608\) 0 0
\(609\) −18.9916 −0.769577
\(610\) 0 0
\(611\) 0.942120 0.0381141
\(612\) 0 0
\(613\) −30.4845 −1.23126 −0.615629 0.788036i \(-0.711098\pi\)
−0.615629 + 0.788036i \(0.711098\pi\)
\(614\) 0 0
\(615\) −4.50290 −0.181575
\(616\) 0 0
\(617\) −39.5693 −1.59300 −0.796499 0.604640i \(-0.793317\pi\)
−0.796499 + 0.604640i \(0.793317\pi\)
\(618\) 0 0
\(619\) 9.87274 0.396819 0.198410 0.980119i \(-0.436422\pi\)
0.198410 + 0.980119i \(0.436422\pi\)
\(620\) 0 0
\(621\) −28.5590 −1.14603
\(622\) 0 0
\(623\) 42.6586 1.70908
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −4.29245 −0.171424
\(628\) 0 0
\(629\) 16.3918 0.653586
\(630\) 0 0
\(631\) −18.1507 −0.722568 −0.361284 0.932456i \(-0.617661\pi\)
−0.361284 + 0.932456i \(0.617661\pi\)
\(632\) 0 0
\(633\) 6.23681 0.247891
\(634\) 0 0
\(635\) −1.24363 −0.0493521
\(636\) 0 0
\(637\) 9.77929 0.387470
\(638\) 0 0
\(639\) 28.2544 1.11773
\(640\) 0 0
\(641\) 22.5290 0.889841 0.444921 0.895570i \(-0.353232\pi\)
0.444921 + 0.895570i \(0.353232\pi\)
\(642\) 0 0
\(643\) −10.7285 −0.423091 −0.211546 0.977368i \(-0.567850\pi\)
−0.211546 + 0.977368i \(0.567850\pi\)
\(644\) 0 0
\(645\) 4.71602 0.185693
\(646\) 0 0
\(647\) −39.3358 −1.54645 −0.773225 0.634132i \(-0.781358\pi\)
−0.773225 + 0.634132i \(0.781358\pi\)
\(648\) 0 0
\(649\) −2.36303 −0.0927570
\(650\) 0 0
\(651\) 18.9601 0.743107
\(652\) 0 0
\(653\) 22.7548 0.890464 0.445232 0.895415i \(-0.353121\pi\)
0.445232 + 0.895415i \(0.353121\pi\)
\(654\) 0 0
\(655\) −0.986253 −0.0385361
\(656\) 0 0
\(657\) −35.4487 −1.38299
\(658\) 0 0
\(659\) 18.7924 0.732050 0.366025 0.930605i \(-0.380719\pi\)
0.366025 + 0.930605i \(0.380719\pi\)
\(660\) 0 0
\(661\) −39.4244 −1.53343 −0.766716 0.641987i \(-0.778110\pi\)
−0.766716 + 0.641987i \(0.778110\pi\)
\(662\) 0 0
\(663\) −1.09819 −0.0426503
\(664\) 0 0
\(665\) 19.5658 0.758730
\(666\) 0 0
\(667\) 41.0683 1.59017
\(668\) 0 0
\(669\) 0.395762 0.0153010
\(670\) 0 0
\(671\) −5.60472 −0.216368
\(672\) 0 0
\(673\) −43.2657 −1.66777 −0.833885 0.551938i \(-0.813889\pi\)
−0.833885 + 0.551938i \(0.813889\pi\)
\(674\) 0 0
\(675\) 4.07838 0.156977
\(676\) 0 0
\(677\) −12.5311 −0.481608 −0.240804 0.970574i \(-0.577411\pi\)
−0.240804 + 0.970574i \(0.577411\pi\)
\(678\) 0 0
\(679\) −20.4866 −0.786202
\(680\) 0 0
\(681\) 11.7770 0.451295
\(682\) 0 0
\(683\) −5.48199 −0.209763 −0.104881 0.994485i \(-0.533446\pi\)
−0.104881 + 0.994485i \(0.533446\pi\)
\(684\) 0 0
\(685\) 4.44041 0.169659
\(686\) 0 0
\(687\) −0.579391 −0.0221052
\(688\) 0 0
\(689\) 0.622240 0.0237054
\(690\) 0 0
\(691\) −42.2665 −1.60790 −0.803948 0.594700i \(-0.797271\pi\)
−0.803948 + 0.594700i \(0.797271\pi\)
\(692\) 0 0
\(693\) 13.2883 0.504781
\(694\) 0 0
\(695\) 4.08344 0.154894
\(696\) 0 0
\(697\) −10.4616 −0.396262
\(698\) 0 0
\(699\) 7.74472 0.292932
\(700\) 0 0
\(701\) 19.7589 0.746284 0.373142 0.927774i \(-0.378280\pi\)
0.373142 + 0.927774i \(0.378280\pi\)
\(702\) 0 0
\(703\) 42.6295 1.60780
\(704\) 0 0
\(705\) 0.841045 0.0316756
\(706\) 0 0
\(707\) 33.9891 1.27829
\(708\) 0 0
\(709\) −31.3628 −1.17786 −0.588928 0.808186i \(-0.700450\pi\)
−0.588928 + 0.808186i \(0.700450\pi\)
\(710\) 0 0
\(711\) −39.5937 −1.48488
\(712\) 0 0
\(713\) −41.0003 −1.53547
\(714\) 0 0
\(715\) −1.06098 −0.0396785
\(716\) 0 0
\(717\) 2.67270 0.0998138
\(718\) 0 0
\(719\) −15.8563 −0.591341 −0.295670 0.955290i \(-0.595543\pi\)
−0.295670 + 0.955290i \(0.595543\pi\)
\(720\) 0 0
\(721\) −76.9694 −2.86649
\(722\) 0 0
\(723\) −1.71218 −0.0636766
\(724\) 0 0
\(725\) −5.86477 −0.217812
\(726\) 0 0
\(727\) −17.3941 −0.645110 −0.322555 0.946551i \(-0.604542\pi\)
−0.322555 + 0.946551i \(0.604542\pi\)
\(728\) 0 0
\(729\) −1.18977 −0.0440656
\(730\) 0 0
\(731\) 10.9567 0.405250
\(732\) 0 0
\(733\) 39.1108 1.44459 0.722295 0.691585i \(-0.243087\pi\)
0.722295 + 0.691585i \(0.243087\pi\)
\(734\) 0 0
\(735\) 8.73013 0.322016
\(736\) 0 0
\(737\) −2.94033 −0.108308
\(738\) 0 0
\(739\) 12.7603 0.469395 0.234697 0.972069i \(-0.424590\pi\)
0.234697 + 0.972069i \(0.424590\pi\)
\(740\) 0 0
\(741\) −2.85602 −0.104919
\(742\) 0 0
\(743\) 28.8539 1.05855 0.529274 0.848451i \(-0.322464\pi\)
0.529274 + 0.848451i \(0.322464\pi\)
\(744\) 0 0
\(745\) −12.1336 −0.444539
\(746\) 0 0
\(747\) 16.0816 0.588396
\(748\) 0 0
\(749\) 0.930718 0.0340077
\(750\) 0 0
\(751\) −4.43265 −0.161750 −0.0808749 0.996724i \(-0.525771\pi\)
−0.0808749 + 0.996724i \(0.525771\pi\)
\(752\) 0 0
\(753\) −9.37576 −0.341672
\(754\) 0 0
\(755\) 7.99445 0.290948
\(756\) 0 0
\(757\) −24.7646 −0.900084 −0.450042 0.893007i \(-0.648591\pi\)
−0.450042 + 0.893007i \(0.648591\pi\)
\(758\) 0 0
\(759\) 6.63249 0.240744
\(760\) 0 0
\(761\) −35.9830 −1.30438 −0.652191 0.758055i \(-0.726150\pi\)
−0.652191 + 0.758055i \(0.726150\pi\)
\(762\) 0 0
\(763\) −23.3337 −0.844737
\(764\) 0 0
\(765\) 4.24747 0.153568
\(766\) 0 0
\(767\) −1.57226 −0.0567711
\(768\) 0 0
\(769\) 38.3042 1.38128 0.690642 0.723197i \(-0.257328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(770\) 0 0
\(771\) 17.6233 0.634688
\(772\) 0 0
\(773\) 26.9499 0.969320 0.484660 0.874703i \(-0.338943\pi\)
0.484660 + 0.874703i \(0.338943\pi\)
\(774\) 0 0
\(775\) 5.85507 0.210320
\(776\) 0 0
\(777\) 30.4604 1.09276
\(778\) 0 0
\(779\) −27.2070 −0.974793
\(780\) 0 0
\(781\) −14.6381 −0.523791
\(782\) 0 0
\(783\) −23.9188 −0.854786
\(784\) 0 0
\(785\) 15.1332 0.540129
\(786\) 0 0
\(787\) −33.5166 −1.19474 −0.597369 0.801966i \(-0.703787\pi\)
−0.597369 + 0.801966i \(0.703787\pi\)
\(788\) 0 0
\(789\) 2.08458 0.0742130
\(790\) 0 0
\(791\) −68.7564 −2.44470
\(792\) 0 0
\(793\) −3.72915 −0.132426
\(794\) 0 0
\(795\) 0.555483 0.0197009
\(796\) 0 0
\(797\) 40.5353 1.43584 0.717918 0.696128i \(-0.245095\pi\)
0.717918 + 0.696128i \(0.245095\pi\)
\(798\) 0 0
\(799\) 1.95400 0.0691277
\(800\) 0 0
\(801\) 24.0836 0.850951
\(802\) 0 0
\(803\) 18.3653 0.648097
\(804\) 0 0
\(805\) −30.2322 −1.06554
\(806\) 0 0
\(807\) 17.9627 0.632316
\(808\) 0 0
\(809\) −29.3086 −1.03044 −0.515218 0.857059i \(-0.672289\pi\)
−0.515218 + 0.857059i \(0.672289\pi\)
\(810\) 0 0
\(811\) −9.48650 −0.333116 −0.166558 0.986032i \(-0.553265\pi\)
−0.166558 + 0.986032i \(0.553265\pi\)
\(812\) 0 0
\(813\) 6.99072 0.245175
\(814\) 0 0
\(815\) −21.4567 −0.751594
\(816\) 0 0
\(817\) 28.4947 0.996904
\(818\) 0 0
\(819\) 8.84149 0.308947
\(820\) 0 0
\(821\) −36.9014 −1.28787 −0.643934 0.765081i \(-0.722699\pi\)
−0.643934 + 0.765081i \(0.722699\pi\)
\(822\) 0 0
\(823\) 37.9089 1.32142 0.660711 0.750641i \(-0.270255\pi\)
0.660711 + 0.750641i \(0.270255\pi\)
\(824\) 0 0
\(825\) −0.947155 −0.0329757
\(826\) 0 0
\(827\) 9.35095 0.325165 0.162582 0.986695i \(-0.448018\pi\)
0.162582 + 0.986695i \(0.448018\pi\)
\(828\) 0 0
\(829\) −25.9832 −0.902433 −0.451216 0.892415i \(-0.649010\pi\)
−0.451216 + 0.892415i \(0.649010\pi\)
\(830\) 0 0
\(831\) 9.96850 0.345803
\(832\) 0 0
\(833\) 20.2827 0.702755
\(834\) 0 0
\(835\) −9.37763 −0.324526
\(836\) 0 0
\(837\) 23.8792 0.825385
\(838\) 0 0
\(839\) 22.1025 0.763063 0.381531 0.924356i \(-0.375397\pi\)
0.381531 + 0.924356i \(0.375397\pi\)
\(840\) 0 0
\(841\) 5.39554 0.186053
\(842\) 0 0
\(843\) −1.92663 −0.0663568
\(844\) 0 0
\(845\) 12.2941 0.422929
\(846\) 0 0
\(847\) 40.6061 1.39524
\(848\) 0 0
\(849\) −6.69537 −0.229785
\(850\) 0 0
\(851\) −65.8691 −2.25796
\(852\) 0 0
\(853\) −12.4183 −0.425193 −0.212596 0.977140i \(-0.568192\pi\)
−0.212596 + 0.977140i \(0.568192\pi\)
\(854\) 0 0
\(855\) 11.0462 0.377772
\(856\) 0 0
\(857\) −51.5011 −1.75924 −0.879622 0.475673i \(-0.842205\pi\)
−0.879622 + 0.475673i \(0.842205\pi\)
\(858\) 0 0
\(859\) −21.0721 −0.718969 −0.359485 0.933151i \(-0.617047\pi\)
−0.359485 + 0.933151i \(0.617047\pi\)
\(860\) 0 0
\(861\) −19.4405 −0.662530
\(862\) 0 0
\(863\) 14.4552 0.492061 0.246030 0.969262i \(-0.420874\pi\)
0.246030 + 0.969262i \(0.420874\pi\)
\(864\) 0 0
\(865\) −4.51979 −0.153677
\(866\) 0 0
\(867\) 10.4733 0.355692
\(868\) 0 0
\(869\) 20.5127 0.695846
\(870\) 0 0
\(871\) −1.95638 −0.0662893
\(872\) 0 0
\(873\) −11.5660 −0.391450
\(874\) 0 0
\(875\) 4.31732 0.145952
\(876\) 0 0
\(877\) −15.1108 −0.510255 −0.255127 0.966907i \(-0.582117\pi\)
−0.255127 + 0.966907i \(0.582117\pi\)
\(878\) 0 0
\(879\) 17.4331 0.588005
\(880\) 0 0
\(881\) −41.3918 −1.39452 −0.697262 0.716816i \(-0.745599\pi\)
−0.697262 + 0.716816i \(0.745599\pi\)
\(882\) 0 0
\(883\) 48.7179 1.63949 0.819744 0.572729i \(-0.194115\pi\)
0.819744 + 0.572729i \(0.194115\pi\)
\(884\) 0 0
\(885\) −1.40358 −0.0471809
\(886\) 0 0
\(887\) 2.80750 0.0942667 0.0471334 0.998889i \(-0.484991\pi\)
0.0471334 + 0.998889i \(0.484991\pi\)
\(888\) 0 0
\(889\) −5.36917 −0.180076
\(890\) 0 0
\(891\) 5.37085 0.179930
\(892\) 0 0
\(893\) 5.08169 0.170052
\(894\) 0 0
\(895\) −4.72827 −0.158049
\(896\) 0 0
\(897\) 4.41299 0.147345
\(898\) 0 0
\(899\) −34.3386 −1.14526
\(900\) 0 0
\(901\) 1.29056 0.0429947
\(902\) 0 0
\(903\) 20.3606 0.677557
\(904\) 0 0
\(905\) 24.3759 0.810284
\(906\) 0 0
\(907\) 2.03530 0.0675811 0.0337905 0.999429i \(-0.489242\pi\)
0.0337905 + 0.999429i \(0.489242\pi\)
\(908\) 0 0
\(909\) 19.1891 0.636463
\(910\) 0 0
\(911\) −47.0929 −1.56026 −0.780129 0.625618i \(-0.784847\pi\)
−0.780129 + 0.625618i \(0.784847\pi\)
\(912\) 0 0
\(913\) −8.33157 −0.275735
\(914\) 0 0
\(915\) −3.32907 −0.110056
\(916\) 0 0
\(917\) −4.25797 −0.140611
\(918\) 0 0
\(919\) 19.2868 0.636214 0.318107 0.948055i \(-0.396953\pi\)
0.318107 + 0.948055i \(0.396953\pi\)
\(920\) 0 0
\(921\) 18.5653 0.611747
\(922\) 0 0
\(923\) −9.73956 −0.320582
\(924\) 0 0
\(925\) 9.40647 0.309283
\(926\) 0 0
\(927\) −43.4543 −1.42723
\(928\) 0 0
\(929\) −37.9926 −1.24650 −0.623249 0.782024i \(-0.714188\pi\)
−0.623249 + 0.782024i \(0.714188\pi\)
\(930\) 0 0
\(931\) 52.7484 1.72876
\(932\) 0 0
\(933\) −23.5882 −0.772242
\(934\) 0 0
\(935\) −2.20053 −0.0719651
\(936\) 0 0
\(937\) 46.3448 1.51402 0.757010 0.653404i \(-0.226660\pi\)
0.757010 + 0.653404i \(0.226660\pi\)
\(938\) 0 0
\(939\) −21.7523 −0.709860
\(940\) 0 0
\(941\) 40.5059 1.32045 0.660227 0.751066i \(-0.270460\pi\)
0.660227 + 0.751066i \(0.270460\pi\)
\(942\) 0 0
\(943\) 42.0390 1.36898
\(944\) 0 0
\(945\) 17.6077 0.572777
\(946\) 0 0
\(947\) 59.7355 1.94114 0.970571 0.240815i \(-0.0774147\pi\)
0.970571 + 0.240815i \(0.0774147\pi\)
\(948\) 0 0
\(949\) 12.2195 0.396662
\(950\) 0 0
\(951\) 11.1651 0.362054
\(952\) 0 0
\(953\) −23.6121 −0.764872 −0.382436 0.923982i \(-0.624915\pi\)
−0.382436 + 0.923982i \(0.624915\pi\)
\(954\) 0 0
\(955\) 17.4655 0.565169
\(956\) 0 0
\(957\) 5.55485 0.179563
\(958\) 0 0
\(959\) 19.1707 0.619053
\(960\) 0 0
\(961\) 3.28184 0.105866
\(962\) 0 0
\(963\) 0.525452 0.0169324
\(964\) 0 0
\(965\) 13.6808 0.440401
\(966\) 0 0
\(967\) −41.5091 −1.33484 −0.667421 0.744681i \(-0.732602\pi\)
−0.667421 + 0.744681i \(0.732602\pi\)
\(968\) 0 0
\(969\) −5.92353 −0.190291
\(970\) 0 0
\(971\) 50.1683 1.60998 0.804988 0.593291i \(-0.202172\pi\)
0.804988 + 0.593291i \(0.202172\pi\)
\(972\) 0 0
\(973\) 17.6295 0.565176
\(974\) 0 0
\(975\) −0.630198 −0.0201825
\(976\) 0 0
\(977\) −2.47811 −0.0792818 −0.0396409 0.999214i \(-0.512621\pi\)
−0.0396409 + 0.999214i \(0.512621\pi\)
\(978\) 0 0
\(979\) −12.4772 −0.398774
\(980\) 0 0
\(981\) −13.1734 −0.420595
\(982\) 0 0
\(983\) 2.36744 0.0755096 0.0377548 0.999287i \(-0.487979\pi\)
0.0377548 + 0.999287i \(0.487979\pi\)
\(984\) 0 0
\(985\) 5.60348 0.178542
\(986\) 0 0
\(987\) 3.63106 0.115578
\(988\) 0 0
\(989\) −44.0287 −1.40003
\(990\) 0 0
\(991\) 42.5633 1.35207 0.676034 0.736870i \(-0.263697\pi\)
0.676034 + 0.736870i \(0.263697\pi\)
\(992\) 0 0
\(993\) 6.75040 0.214217
\(994\) 0 0
\(995\) 12.7383 0.403831
\(996\) 0 0
\(997\) 24.2874 0.769189 0.384594 0.923086i \(-0.374341\pi\)
0.384594 + 0.923086i \(0.374341\pi\)
\(998\) 0 0
\(999\) 38.3631 1.21376
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 \(a_p\))