Properties

Label 6004.2.a.g.1.18
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.739341 q^{3}\) \(+2.08289 q^{5}\) \(+4.12124 q^{7}\) \(-2.45337 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.739341 q^{3}\) \(+2.08289 q^{5}\) \(+4.12124 q^{7}\) \(-2.45337 q^{9}\) \(-4.72599 q^{11}\) \(-3.93062 q^{13}\) \(+1.53997 q^{15}\) \(+1.15203 q^{17}\) \(+1.00000 q^{19}\) \(+3.04700 q^{21}\) \(-5.67889 q^{23}\) \(-0.661576 q^{25}\) \(-4.03191 q^{27}\) \(-8.45054 q^{29}\) \(-2.39783 q^{31}\) \(-3.49412 q^{33}\) \(+8.58407 q^{35}\) \(+5.34502 q^{37}\) \(-2.90607 q^{39}\) \(+0.419643 q^{41}\) \(+8.48432 q^{43}\) \(-5.11010 q^{45}\) \(-7.51581 q^{47}\) \(+9.98458 q^{49}\) \(+0.851742 q^{51}\) \(-6.91969 q^{53}\) \(-9.84371 q^{55}\) \(+0.739341 q^{57}\) \(+1.82801 q^{59}\) \(-0.433477 q^{61}\) \(-10.1109 q^{63}\) \(-8.18705 q^{65}\) \(-9.55605 q^{67}\) \(-4.19864 q^{69}\) \(-12.4740 q^{71}\) \(+3.54045 q^{73}\) \(-0.489131 q^{75}\) \(-19.4769 q^{77}\) \(-1.00000 q^{79}\) \(+4.37917 q^{81}\) \(+8.27154 q^{83}\) \(+2.39955 q^{85}\) \(-6.24783 q^{87}\) \(-6.82753 q^{89}\) \(-16.1990 q^{91}\) \(-1.77281 q^{93}\) \(+2.08289 q^{95}\) \(+12.5877 q^{97}\) \(+11.5946 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.739341 0.426859 0.213429 0.976958i \(-0.431537\pi\)
0.213429 + 0.976958i \(0.431537\pi\)
\(4\) 0 0
\(5\) 2.08289 0.931496 0.465748 0.884917i \(-0.345785\pi\)
0.465748 + 0.884917i \(0.345785\pi\)
\(6\) 0 0
\(7\) 4.12124 1.55768 0.778840 0.627222i \(-0.215808\pi\)
0.778840 + 0.627222i \(0.215808\pi\)
\(8\) 0 0
\(9\) −2.45337 −0.817791
\(10\) 0 0
\(11\) −4.72599 −1.42494 −0.712470 0.701703i \(-0.752423\pi\)
−0.712470 + 0.701703i \(0.752423\pi\)
\(12\) 0 0
\(13\) −3.93062 −1.09016 −0.545079 0.838385i \(-0.683500\pi\)
−0.545079 + 0.838385i \(0.683500\pi\)
\(14\) 0 0
\(15\) 1.53997 0.397617
\(16\) 0 0
\(17\) 1.15203 0.279408 0.139704 0.990193i \(-0.455385\pi\)
0.139704 + 0.990193i \(0.455385\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 3.04700 0.664910
\(22\) 0 0
\(23\) −5.67889 −1.18413 −0.592066 0.805890i \(-0.701687\pi\)
−0.592066 + 0.805890i \(0.701687\pi\)
\(24\) 0 0
\(25\) −0.661576 −0.132315
\(26\) 0 0
\(27\) −4.03191 −0.775941
\(28\) 0 0
\(29\) −8.45054 −1.56923 −0.784613 0.619986i \(-0.787138\pi\)
−0.784613 + 0.619986i \(0.787138\pi\)
\(30\) 0 0
\(31\) −2.39783 −0.430662 −0.215331 0.976541i \(-0.569083\pi\)
−0.215331 + 0.976541i \(0.569083\pi\)
\(32\) 0 0
\(33\) −3.49412 −0.608248
\(34\) 0 0
\(35\) 8.58407 1.45097
\(36\) 0 0
\(37\) 5.34502 0.878716 0.439358 0.898312i \(-0.355206\pi\)
0.439358 + 0.898312i \(0.355206\pi\)
\(38\) 0 0
\(39\) −2.90607 −0.465344
\(40\) 0 0
\(41\) 0.419643 0.0655372 0.0327686 0.999463i \(-0.489568\pi\)
0.0327686 + 0.999463i \(0.489568\pi\)
\(42\) 0 0
\(43\) 8.48432 1.29385 0.646923 0.762555i \(-0.276055\pi\)
0.646923 + 0.762555i \(0.276055\pi\)
\(44\) 0 0
\(45\) −5.11010 −0.761769
\(46\) 0 0
\(47\) −7.51581 −1.09629 −0.548146 0.836382i \(-0.684666\pi\)
−0.548146 + 0.836382i \(0.684666\pi\)
\(48\) 0 0
\(49\) 9.98458 1.42637
\(50\) 0 0
\(51\) 0.851742 0.119268
\(52\) 0 0
\(53\) −6.91969 −0.950493 −0.475246 0.879853i \(-0.657641\pi\)
−0.475246 + 0.879853i \(0.657641\pi\)
\(54\) 0 0
\(55\) −9.84371 −1.32733
\(56\) 0 0
\(57\) 0.739341 0.0979282
\(58\) 0 0
\(59\) 1.82801 0.237987 0.118993 0.992895i \(-0.462033\pi\)
0.118993 + 0.992895i \(0.462033\pi\)
\(60\) 0 0
\(61\) −0.433477 −0.0555010 −0.0277505 0.999615i \(-0.508834\pi\)
−0.0277505 + 0.999615i \(0.508834\pi\)
\(62\) 0 0
\(63\) −10.1109 −1.27386
\(64\) 0 0
\(65\) −8.18705 −1.01548
\(66\) 0 0
\(67\) −9.55605 −1.16746 −0.583729 0.811949i \(-0.698407\pi\)
−0.583729 + 0.811949i \(0.698407\pi\)
\(68\) 0 0
\(69\) −4.19864 −0.505457
\(70\) 0 0
\(71\) −12.4740 −1.48039 −0.740196 0.672392i \(-0.765267\pi\)
−0.740196 + 0.672392i \(0.765267\pi\)
\(72\) 0 0
\(73\) 3.54045 0.414379 0.207189 0.978301i \(-0.433568\pi\)
0.207189 + 0.978301i \(0.433568\pi\)
\(74\) 0 0
\(75\) −0.489131 −0.0564800
\(76\) 0 0
\(77\) −19.4769 −2.21960
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 4.37917 0.486574
\(82\) 0 0
\(83\) 8.27154 0.907920 0.453960 0.891022i \(-0.350011\pi\)
0.453960 + 0.891022i \(0.350011\pi\)
\(84\) 0 0
\(85\) 2.39955 0.260267
\(86\) 0 0
\(87\) −6.24783 −0.669838
\(88\) 0 0
\(89\) −6.82753 −0.723716 −0.361858 0.932233i \(-0.617858\pi\)
−0.361858 + 0.932233i \(0.617858\pi\)
\(90\) 0 0
\(91\) −16.1990 −1.69812
\(92\) 0 0
\(93\) −1.77281 −0.183832
\(94\) 0 0
\(95\) 2.08289 0.213700
\(96\) 0 0
\(97\) 12.5877 1.27809 0.639043 0.769171i \(-0.279331\pi\)
0.639043 + 0.769171i \(0.279331\pi\)
\(98\) 0 0
\(99\) 11.5946 1.16530
\(100\) 0 0
\(101\) −4.65801 −0.463490 −0.231745 0.972777i \(-0.574443\pi\)
−0.231745 + 0.972777i \(0.574443\pi\)
\(102\) 0 0
\(103\) −9.36779 −0.923036 −0.461518 0.887131i \(-0.652695\pi\)
−0.461518 + 0.887131i \(0.652695\pi\)
\(104\) 0 0
\(105\) 6.34656 0.619361
\(106\) 0 0
\(107\) −8.58100 −0.829556 −0.414778 0.909923i \(-0.636141\pi\)
−0.414778 + 0.909923i \(0.636141\pi\)
\(108\) 0 0
\(109\) −6.44016 −0.616855 −0.308428 0.951248i \(-0.599803\pi\)
−0.308428 + 0.951248i \(0.599803\pi\)
\(110\) 0 0
\(111\) 3.95179 0.375088
\(112\) 0 0
\(113\) −16.8847 −1.58838 −0.794190 0.607670i \(-0.792104\pi\)
−0.794190 + 0.607670i \(0.792104\pi\)
\(114\) 0 0
\(115\) −11.8285 −1.10301
\(116\) 0 0
\(117\) 9.64329 0.891522
\(118\) 0 0
\(119\) 4.74778 0.435228
\(120\) 0 0
\(121\) 11.3350 1.03045
\(122\) 0 0
\(123\) 0.310260 0.0279752
\(124\) 0 0
\(125\) −11.7924 −1.05475
\(126\) 0 0
\(127\) 5.60549 0.497406 0.248703 0.968580i \(-0.419996\pi\)
0.248703 + 0.968580i \(0.419996\pi\)
\(128\) 0 0
\(129\) 6.27281 0.552290
\(130\) 0 0
\(131\) 9.04776 0.790507 0.395253 0.918572i \(-0.370657\pi\)
0.395253 + 0.918572i \(0.370657\pi\)
\(132\) 0 0
\(133\) 4.12124 0.357356
\(134\) 0 0
\(135\) −8.39801 −0.722785
\(136\) 0 0
\(137\) 13.1195 1.12088 0.560438 0.828196i \(-0.310633\pi\)
0.560438 + 0.828196i \(0.310633\pi\)
\(138\) 0 0
\(139\) −7.59356 −0.644077 −0.322038 0.946727i \(-0.604368\pi\)
−0.322038 + 0.946727i \(0.604368\pi\)
\(140\) 0 0
\(141\) −5.55675 −0.467962
\(142\) 0 0
\(143\) 18.5761 1.55341
\(144\) 0 0
\(145\) −17.6015 −1.46173
\(146\) 0 0
\(147\) 7.38201 0.608858
\(148\) 0 0
\(149\) 6.58035 0.539083 0.269542 0.962989i \(-0.413128\pi\)
0.269542 + 0.962989i \(0.413128\pi\)
\(150\) 0 0
\(151\) 5.05204 0.411129 0.205564 0.978644i \(-0.434097\pi\)
0.205564 + 0.978644i \(0.434097\pi\)
\(152\) 0 0
\(153\) −2.82636 −0.228497
\(154\) 0 0
\(155\) −4.99440 −0.401160
\(156\) 0 0
\(157\) −9.39745 −0.749998 −0.374999 0.927025i \(-0.622357\pi\)
−0.374999 + 0.927025i \(0.622357\pi\)
\(158\) 0 0
\(159\) −5.11601 −0.405726
\(160\) 0 0
\(161\) −23.4041 −1.84450
\(162\) 0 0
\(163\) 10.7835 0.844626 0.422313 0.906450i \(-0.361218\pi\)
0.422313 + 0.906450i \(0.361218\pi\)
\(164\) 0 0
\(165\) −7.27786 −0.566581
\(166\) 0 0
\(167\) 10.5522 0.816557 0.408279 0.912857i \(-0.366129\pi\)
0.408279 + 0.912857i \(0.366129\pi\)
\(168\) 0 0
\(169\) 2.44979 0.188445
\(170\) 0 0
\(171\) −2.45337 −0.187614
\(172\) 0 0
\(173\) 8.70718 0.661994 0.330997 0.943632i \(-0.392615\pi\)
0.330997 + 0.943632i \(0.392615\pi\)
\(174\) 0 0
\(175\) −2.72651 −0.206105
\(176\) 0 0
\(177\) 1.35152 0.101587
\(178\) 0 0
\(179\) −9.29291 −0.694584 −0.347292 0.937757i \(-0.612899\pi\)
−0.347292 + 0.937757i \(0.612899\pi\)
\(180\) 0 0
\(181\) 8.62428 0.641037 0.320519 0.947242i \(-0.396143\pi\)
0.320519 + 0.947242i \(0.396143\pi\)
\(182\) 0 0
\(183\) −0.320487 −0.0236911
\(184\) 0 0
\(185\) 11.1331 0.818520
\(186\) 0 0
\(187\) −5.44447 −0.398139
\(188\) 0 0
\(189\) −16.6164 −1.20867
\(190\) 0 0
\(191\) −16.8195 −1.21701 −0.608507 0.793549i \(-0.708231\pi\)
−0.608507 + 0.793549i \(0.708231\pi\)
\(192\) 0 0
\(193\) −0.807299 −0.0581106 −0.0290553 0.999578i \(-0.509250\pi\)
−0.0290553 + 0.999578i \(0.509250\pi\)
\(194\) 0 0
\(195\) −6.05302 −0.433466
\(196\) 0 0
\(197\) 9.03287 0.643565 0.321783 0.946814i \(-0.395718\pi\)
0.321783 + 0.946814i \(0.395718\pi\)
\(198\) 0 0
\(199\) −3.02866 −0.214696 −0.107348 0.994221i \(-0.534236\pi\)
−0.107348 + 0.994221i \(0.534236\pi\)
\(200\) 0 0
\(201\) −7.06518 −0.498340
\(202\) 0 0
\(203\) −34.8267 −2.44435
\(204\) 0 0
\(205\) 0.874070 0.0610477
\(206\) 0 0
\(207\) 13.9325 0.968372
\(208\) 0 0
\(209\) −4.72599 −0.326903
\(210\) 0 0
\(211\) 6.13392 0.422276 0.211138 0.977456i \(-0.432283\pi\)
0.211138 + 0.977456i \(0.432283\pi\)
\(212\) 0 0
\(213\) −9.22254 −0.631918
\(214\) 0 0
\(215\) 17.6719 1.20521
\(216\) 0 0
\(217\) −9.88200 −0.670834
\(218\) 0 0
\(219\) 2.61760 0.176881
\(220\) 0 0
\(221\) −4.52819 −0.304599
\(222\) 0 0
\(223\) 3.61310 0.241951 0.120976 0.992655i \(-0.461398\pi\)
0.120976 + 0.992655i \(0.461398\pi\)
\(224\) 0 0
\(225\) 1.62309 0.108206
\(226\) 0 0
\(227\) 7.79576 0.517423 0.258711 0.965955i \(-0.416702\pi\)
0.258711 + 0.965955i \(0.416702\pi\)
\(228\) 0 0
\(229\) −3.96487 −0.262006 −0.131003 0.991382i \(-0.541820\pi\)
−0.131003 + 0.991382i \(0.541820\pi\)
\(230\) 0 0
\(231\) −14.4001 −0.947456
\(232\) 0 0
\(233\) 4.16693 0.272984 0.136492 0.990641i \(-0.456417\pi\)
0.136492 + 0.990641i \(0.456417\pi\)
\(234\) 0 0
\(235\) −15.6546 −1.02119
\(236\) 0 0
\(237\) −0.739341 −0.0480254
\(238\) 0 0
\(239\) 16.7930 1.08625 0.543123 0.839653i \(-0.317242\pi\)
0.543123 + 0.839653i \(0.317242\pi\)
\(240\) 0 0
\(241\) 0.120350 0.00775245 0.00387623 0.999992i \(-0.498766\pi\)
0.00387623 + 0.999992i \(0.498766\pi\)
\(242\) 0 0
\(243\) 15.3334 0.983639
\(244\) 0 0
\(245\) 20.7968 1.32866
\(246\) 0 0
\(247\) −3.93062 −0.250099
\(248\) 0 0
\(249\) 6.11549 0.387554
\(250\) 0 0
\(251\) −19.0172 −1.20036 −0.600178 0.799867i \(-0.704903\pi\)
−0.600178 + 0.799867i \(0.704903\pi\)
\(252\) 0 0
\(253\) 26.8384 1.68732
\(254\) 0 0
\(255\) 1.77408 0.111097
\(256\) 0 0
\(257\) −2.46717 −0.153898 −0.0769488 0.997035i \(-0.524518\pi\)
−0.0769488 + 0.997035i \(0.524518\pi\)
\(258\) 0 0
\(259\) 22.0281 1.36876
\(260\) 0 0
\(261\) 20.7323 1.28330
\(262\) 0 0
\(263\) −2.30444 −0.142098 −0.0710488 0.997473i \(-0.522635\pi\)
−0.0710488 + 0.997473i \(0.522635\pi\)
\(264\) 0 0
\(265\) −14.4129 −0.885380
\(266\) 0 0
\(267\) −5.04787 −0.308925
\(268\) 0 0
\(269\) 9.58142 0.584190 0.292095 0.956389i \(-0.405648\pi\)
0.292095 + 0.956389i \(0.405648\pi\)
\(270\) 0 0
\(271\) −8.58153 −0.521291 −0.260645 0.965435i \(-0.583935\pi\)
−0.260645 + 0.965435i \(0.583935\pi\)
\(272\) 0 0
\(273\) −11.9766 −0.724857
\(274\) 0 0
\(275\) 3.12660 0.188541
\(276\) 0 0
\(277\) −2.99972 −0.180236 −0.0901179 0.995931i \(-0.528724\pi\)
−0.0901179 + 0.995931i \(0.528724\pi\)
\(278\) 0 0
\(279\) 5.88276 0.352192
\(280\) 0 0
\(281\) 8.48893 0.506407 0.253204 0.967413i \(-0.418516\pi\)
0.253204 + 0.967413i \(0.418516\pi\)
\(282\) 0 0
\(283\) 24.6141 1.46315 0.731577 0.681759i \(-0.238785\pi\)
0.731577 + 0.681759i \(0.238785\pi\)
\(284\) 0 0
\(285\) 1.53997 0.0912197
\(286\) 0 0
\(287\) 1.72945 0.102086
\(288\) 0 0
\(289\) −15.6728 −0.921931
\(290\) 0 0
\(291\) 9.30660 0.545562
\(292\) 0 0
\(293\) 11.7266 0.685076 0.342538 0.939504i \(-0.388713\pi\)
0.342538 + 0.939504i \(0.388713\pi\)
\(294\) 0 0
\(295\) 3.80754 0.221684
\(296\) 0 0
\(297\) 19.0547 1.10567
\(298\) 0 0
\(299\) 22.3216 1.29089
\(300\) 0 0
\(301\) 34.9659 2.01540
\(302\) 0 0
\(303\) −3.44386 −0.197845
\(304\) 0 0
\(305\) −0.902883 −0.0516989
\(306\) 0 0
\(307\) −7.82135 −0.446388 −0.223194 0.974774i \(-0.571648\pi\)
−0.223194 + 0.974774i \(0.571648\pi\)
\(308\) 0 0
\(309\) −6.92600 −0.394006
\(310\) 0 0
\(311\) 11.8983 0.674690 0.337345 0.941381i \(-0.390471\pi\)
0.337345 + 0.941381i \(0.390471\pi\)
\(312\) 0 0
\(313\) 11.1059 0.627744 0.313872 0.949465i \(-0.398374\pi\)
0.313872 + 0.949465i \(0.398374\pi\)
\(314\) 0 0
\(315\) −21.0599 −1.18659
\(316\) 0 0
\(317\) 9.49273 0.533165 0.266582 0.963812i \(-0.414106\pi\)
0.266582 + 0.963812i \(0.414106\pi\)
\(318\) 0 0
\(319\) 39.9371 2.23605
\(320\) 0 0
\(321\) −6.34429 −0.354104
\(322\) 0 0
\(323\) 1.15203 0.0641006
\(324\) 0 0
\(325\) 2.60041 0.144245
\(326\) 0 0
\(327\) −4.76148 −0.263310
\(328\) 0 0
\(329\) −30.9744 −1.70767
\(330\) 0 0
\(331\) 4.46699 0.245528 0.122764 0.992436i \(-0.460824\pi\)
0.122764 + 0.992436i \(0.460824\pi\)
\(332\) 0 0
\(333\) −13.1133 −0.718606
\(334\) 0 0
\(335\) −19.9042 −1.08748
\(336\) 0 0
\(337\) −29.6939 −1.61753 −0.808766 0.588131i \(-0.799864\pi\)
−0.808766 + 0.588131i \(0.799864\pi\)
\(338\) 0 0
\(339\) −12.4836 −0.678014
\(340\) 0 0
\(341\) 11.3321 0.613667
\(342\) 0 0
\(343\) 12.3002 0.664146
\(344\) 0 0
\(345\) −8.74530 −0.470831
\(346\) 0 0
\(347\) 11.0227 0.591730 0.295865 0.955230i \(-0.404392\pi\)
0.295865 + 0.955230i \(0.404392\pi\)
\(348\) 0 0
\(349\) 26.9037 1.44012 0.720061 0.693911i \(-0.244114\pi\)
0.720061 + 0.693911i \(0.244114\pi\)
\(350\) 0 0
\(351\) 15.8479 0.845898
\(352\) 0 0
\(353\) −34.6423 −1.84382 −0.921911 0.387403i \(-0.873372\pi\)
−0.921911 + 0.387403i \(0.873372\pi\)
\(354\) 0 0
\(355\) −25.9819 −1.37898
\(356\) 0 0
\(357\) 3.51023 0.185781
\(358\) 0 0
\(359\) 27.4384 1.44814 0.724071 0.689726i \(-0.242269\pi\)
0.724071 + 0.689726i \(0.242269\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 8.38041 0.439858
\(364\) 0 0
\(365\) 7.37437 0.385992
\(366\) 0 0
\(367\) −4.94281 −0.258013 −0.129006 0.991644i \(-0.541179\pi\)
−0.129006 + 0.991644i \(0.541179\pi\)
\(368\) 0 0
\(369\) −1.02954 −0.0535958
\(370\) 0 0
\(371\) −28.5177 −1.48056
\(372\) 0 0
\(373\) 11.7123 0.606440 0.303220 0.952921i \(-0.401938\pi\)
0.303220 + 0.952921i \(0.401938\pi\)
\(374\) 0 0
\(375\) −8.71863 −0.450228
\(376\) 0 0
\(377\) 33.2159 1.71070
\(378\) 0 0
\(379\) 35.0009 1.79787 0.898937 0.438078i \(-0.144341\pi\)
0.898937 + 0.438078i \(0.144341\pi\)
\(380\) 0 0
\(381\) 4.14437 0.212322
\(382\) 0 0
\(383\) −33.0184 −1.68716 −0.843582 0.537001i \(-0.819557\pi\)
−0.843582 + 0.537001i \(0.819557\pi\)
\(384\) 0 0
\(385\) −40.5682 −2.06755
\(386\) 0 0
\(387\) −20.8152 −1.05810
\(388\) 0 0
\(389\) 1.86200 0.0944069 0.0472035 0.998885i \(-0.484969\pi\)
0.0472035 + 0.998885i \(0.484969\pi\)
\(390\) 0 0
\(391\) −6.54225 −0.330856
\(392\) 0 0
\(393\) 6.68939 0.337435
\(394\) 0 0
\(395\) −2.08289 −0.104801
\(396\) 0 0
\(397\) −29.3594 −1.47350 −0.736752 0.676163i \(-0.763642\pi\)
−0.736752 + 0.676163i \(0.763642\pi\)
\(398\) 0 0
\(399\) 3.04700 0.152541
\(400\) 0 0
\(401\) 1.76234 0.0880069 0.0440035 0.999031i \(-0.485989\pi\)
0.0440035 + 0.999031i \(0.485989\pi\)
\(402\) 0 0
\(403\) 9.42494 0.469490
\(404\) 0 0
\(405\) 9.12132 0.453242
\(406\) 0 0
\(407\) −25.2605 −1.25212
\(408\) 0 0
\(409\) 8.46166 0.418402 0.209201 0.977873i \(-0.432914\pi\)
0.209201 + 0.977873i \(0.432914\pi\)
\(410\) 0 0
\(411\) 9.69980 0.478456
\(412\) 0 0
\(413\) 7.53366 0.370707
\(414\) 0 0
\(415\) 17.2287 0.845724
\(416\) 0 0
\(417\) −5.61423 −0.274930
\(418\) 0 0
\(419\) 24.9694 1.21984 0.609918 0.792464i \(-0.291202\pi\)
0.609918 + 0.792464i \(0.291202\pi\)
\(420\) 0 0
\(421\) −17.7267 −0.863949 −0.431974 0.901886i \(-0.642183\pi\)
−0.431974 + 0.901886i \(0.642183\pi\)
\(422\) 0 0
\(423\) 18.4391 0.896539
\(424\) 0 0
\(425\) −0.762155 −0.0369699
\(426\) 0 0
\(427\) −1.78646 −0.0864528
\(428\) 0 0
\(429\) 13.7341 0.663087
\(430\) 0 0
\(431\) −34.9629 −1.68410 −0.842052 0.539396i \(-0.818652\pi\)
−0.842052 + 0.539396i \(0.818652\pi\)
\(432\) 0 0
\(433\) −30.9133 −1.48560 −0.742800 0.669513i \(-0.766503\pi\)
−0.742800 + 0.669513i \(0.766503\pi\)
\(434\) 0 0
\(435\) −13.0135 −0.623951
\(436\) 0 0
\(437\) −5.67889 −0.271658
\(438\) 0 0
\(439\) 26.2183 1.25133 0.625666 0.780091i \(-0.284827\pi\)
0.625666 + 0.780091i \(0.284827\pi\)
\(440\) 0 0
\(441\) −24.4959 −1.16647
\(442\) 0 0
\(443\) −33.6509 −1.59880 −0.799402 0.600797i \(-0.794850\pi\)
−0.799402 + 0.600797i \(0.794850\pi\)
\(444\) 0 0
\(445\) −14.2210 −0.674139
\(446\) 0 0
\(447\) 4.86512 0.230112
\(448\) 0 0
\(449\) 16.6482 0.785676 0.392838 0.919608i \(-0.371493\pi\)
0.392838 + 0.919608i \(0.371493\pi\)
\(450\) 0 0
\(451\) −1.98323 −0.0933866
\(452\) 0 0
\(453\) 3.73518 0.175494
\(454\) 0 0
\(455\) −33.7407 −1.58179
\(456\) 0 0
\(457\) −17.6539 −0.825814 −0.412907 0.910773i \(-0.635487\pi\)
−0.412907 + 0.910773i \(0.635487\pi\)
\(458\) 0 0
\(459\) −4.64487 −0.216804
\(460\) 0 0
\(461\) −38.0865 −1.77387 −0.886933 0.461898i \(-0.847169\pi\)
−0.886933 + 0.461898i \(0.847169\pi\)
\(462\) 0 0
\(463\) −41.3005 −1.91940 −0.959698 0.281033i \(-0.909323\pi\)
−0.959698 + 0.281033i \(0.909323\pi\)
\(464\) 0 0
\(465\) −3.69257 −0.171239
\(466\) 0 0
\(467\) −36.9596 −1.71029 −0.855143 0.518393i \(-0.826531\pi\)
−0.855143 + 0.518393i \(0.826531\pi\)
\(468\) 0 0
\(469\) −39.3827 −1.81853
\(470\) 0 0
\(471\) −6.94792 −0.320143
\(472\) 0 0
\(473\) −40.0968 −1.84365
\(474\) 0 0
\(475\) −0.661576 −0.0303552
\(476\) 0 0
\(477\) 16.9766 0.777305
\(478\) 0 0
\(479\) 27.2702 1.24601 0.623004 0.782219i \(-0.285912\pi\)
0.623004 + 0.782219i \(0.285912\pi\)
\(480\) 0 0
\(481\) −21.0093 −0.957939
\(482\) 0 0
\(483\) −17.3036 −0.787341
\(484\) 0 0
\(485\) 26.2187 1.19053
\(486\) 0 0
\(487\) 27.2152 1.23324 0.616618 0.787262i \(-0.288502\pi\)
0.616618 + 0.787262i \(0.288502\pi\)
\(488\) 0 0
\(489\) 7.97266 0.360536
\(490\) 0 0
\(491\) 10.8541 0.489838 0.244919 0.969543i \(-0.421239\pi\)
0.244919 + 0.969543i \(0.421239\pi\)
\(492\) 0 0
\(493\) −9.73526 −0.438454
\(494\) 0 0
\(495\) 24.1503 1.08548
\(496\) 0 0
\(497\) −51.4083 −2.30598
\(498\) 0 0
\(499\) 4.10592 0.183806 0.0919031 0.995768i \(-0.470705\pi\)
0.0919031 + 0.995768i \(0.470705\pi\)
\(500\) 0 0
\(501\) 7.80171 0.348555
\(502\) 0 0
\(503\) −34.0451 −1.51800 −0.758999 0.651092i \(-0.774311\pi\)
−0.758999 + 0.651092i \(0.774311\pi\)
\(504\) 0 0
\(505\) −9.70212 −0.431739
\(506\) 0 0
\(507\) 1.81123 0.0804395
\(508\) 0 0
\(509\) 21.3079 0.944458 0.472229 0.881476i \(-0.343450\pi\)
0.472229 + 0.881476i \(0.343450\pi\)
\(510\) 0 0
\(511\) 14.5910 0.645470
\(512\) 0 0
\(513\) −4.03191 −0.178013
\(514\) 0 0
\(515\) −19.5121 −0.859804
\(516\) 0 0
\(517\) 35.5196 1.56215
\(518\) 0 0
\(519\) 6.43758 0.282578
\(520\) 0 0
\(521\) −21.7881 −0.954556 −0.477278 0.878752i \(-0.658377\pi\)
−0.477278 + 0.878752i \(0.658377\pi\)
\(522\) 0 0
\(523\) −26.9131 −1.17683 −0.588413 0.808561i \(-0.700247\pi\)
−0.588413 + 0.808561i \(0.700247\pi\)
\(524\) 0 0
\(525\) −2.01582 −0.0879777
\(526\) 0 0
\(527\) −2.76236 −0.120330
\(528\) 0 0
\(529\) 9.24984 0.402167
\(530\) 0 0
\(531\) −4.48480 −0.194624
\(532\) 0 0
\(533\) −1.64946 −0.0714460
\(534\) 0 0
\(535\) −17.8733 −0.772728
\(536\) 0 0
\(537\) −6.87063 −0.296490
\(538\) 0 0
\(539\) −47.1870 −2.03249
\(540\) 0 0
\(541\) −39.6871 −1.70628 −0.853142 0.521679i \(-0.825306\pi\)
−0.853142 + 0.521679i \(0.825306\pi\)
\(542\) 0 0
\(543\) 6.37628 0.273633
\(544\) 0 0
\(545\) −13.4141 −0.574598
\(546\) 0 0
\(547\) 19.9490 0.852959 0.426480 0.904497i \(-0.359754\pi\)
0.426480 + 0.904497i \(0.359754\pi\)
\(548\) 0 0
\(549\) 1.06348 0.0453882
\(550\) 0 0
\(551\) −8.45054 −0.360005
\(552\) 0 0
\(553\) −4.12124 −0.175253
\(554\) 0 0
\(555\) 8.23115 0.349393
\(556\) 0 0
\(557\) −14.1236 −0.598434 −0.299217 0.954185i \(-0.596725\pi\)
−0.299217 + 0.954185i \(0.596725\pi\)
\(558\) 0 0
\(559\) −33.3487 −1.41050
\(560\) 0 0
\(561\) −4.02532 −0.169949
\(562\) 0 0
\(563\) 43.5809 1.83672 0.918358 0.395750i \(-0.129515\pi\)
0.918358 + 0.395750i \(0.129515\pi\)
\(564\) 0 0
\(565\) −35.1690 −1.47957
\(566\) 0 0
\(567\) 18.0476 0.757927
\(568\) 0 0
\(569\) 16.3596 0.685832 0.342916 0.939366i \(-0.388585\pi\)
0.342916 + 0.939366i \(0.388585\pi\)
\(570\) 0 0
\(571\) 11.8795 0.497143 0.248571 0.968614i \(-0.420039\pi\)
0.248571 + 0.968614i \(0.420039\pi\)
\(572\) 0 0
\(573\) −12.4353 −0.519493
\(574\) 0 0
\(575\) 3.75702 0.156679
\(576\) 0 0
\(577\) 18.1374 0.755070 0.377535 0.925995i \(-0.376772\pi\)
0.377535 + 0.925995i \(0.376772\pi\)
\(578\) 0 0
\(579\) −0.596870 −0.0248050
\(580\) 0 0
\(581\) 34.0890 1.41425
\(582\) 0 0
\(583\) 32.7024 1.35439
\(584\) 0 0
\(585\) 20.0859 0.830449
\(586\) 0 0
\(587\) 15.9306 0.657528 0.328764 0.944412i \(-0.393368\pi\)
0.328764 + 0.944412i \(0.393368\pi\)
\(588\) 0 0
\(589\) −2.39783 −0.0988007
\(590\) 0 0
\(591\) 6.67837 0.274712
\(592\) 0 0
\(593\) 4.49689 0.184665 0.0923326 0.995728i \(-0.470568\pi\)
0.0923326 + 0.995728i \(0.470568\pi\)
\(594\) 0 0
\(595\) 9.88910 0.405413
\(596\) 0 0
\(597\) −2.23922 −0.0916451
\(598\) 0 0
\(599\) −24.2748 −0.991841 −0.495921 0.868368i \(-0.665169\pi\)
−0.495921 + 0.868368i \(0.665169\pi\)
\(600\) 0 0
\(601\) −37.4418 −1.52728 −0.763642 0.645640i \(-0.776591\pi\)
−0.763642 + 0.645640i \(0.776591\pi\)
\(602\) 0 0
\(603\) 23.4446 0.954737
\(604\) 0 0
\(605\) 23.6095 0.959862
\(606\) 0 0
\(607\) 16.6083 0.674110 0.337055 0.941485i \(-0.390569\pi\)
0.337055 + 0.941485i \(0.390569\pi\)
\(608\) 0 0
\(609\) −25.7488 −1.04339
\(610\) 0 0
\(611\) 29.5418 1.19513
\(612\) 0 0
\(613\) −45.6805 −1.84502 −0.922510 0.385974i \(-0.873865\pi\)
−0.922510 + 0.385974i \(0.873865\pi\)
\(614\) 0 0
\(615\) 0.646236 0.0260587
\(616\) 0 0
\(617\) −24.2230 −0.975180 −0.487590 0.873073i \(-0.662124\pi\)
−0.487590 + 0.873073i \(0.662124\pi\)
\(618\) 0 0
\(619\) 21.8914 0.879890 0.439945 0.898025i \(-0.354998\pi\)
0.439945 + 0.898025i \(0.354998\pi\)
\(620\) 0 0
\(621\) 22.8968 0.918815
\(622\) 0 0
\(623\) −28.1378 −1.12732
\(624\) 0 0
\(625\) −21.2544 −0.850177
\(626\) 0 0
\(627\) −3.49412 −0.139542
\(628\) 0 0
\(629\) 6.15761 0.245520
\(630\) 0 0
\(631\) 11.8130 0.470269 0.235134 0.971963i \(-0.424447\pi\)
0.235134 + 0.971963i \(0.424447\pi\)
\(632\) 0 0
\(633\) 4.53506 0.180252
\(634\) 0 0
\(635\) 11.6756 0.463332
\(636\) 0 0
\(637\) −39.2456 −1.55497
\(638\) 0 0
\(639\) 30.6034 1.21065
\(640\) 0 0
\(641\) −36.5371 −1.44313 −0.721564 0.692347i \(-0.756577\pi\)
−0.721564 + 0.692347i \(0.756577\pi\)
\(642\) 0 0
\(643\) 5.87043 0.231507 0.115754 0.993278i \(-0.463072\pi\)
0.115754 + 0.993278i \(0.463072\pi\)
\(644\) 0 0
\(645\) 13.0656 0.514456
\(646\) 0 0
\(647\) 13.6612 0.537075 0.268538 0.963269i \(-0.413460\pi\)
0.268538 + 0.963269i \(0.413460\pi\)
\(648\) 0 0
\(649\) −8.63916 −0.339117
\(650\) 0 0
\(651\) −7.30617 −0.286351
\(652\) 0 0
\(653\) 14.6411 0.572951 0.286475 0.958088i \(-0.407516\pi\)
0.286475 + 0.958088i \(0.407516\pi\)
\(654\) 0 0
\(655\) 18.8455 0.736354
\(656\) 0 0
\(657\) −8.68606 −0.338875
\(658\) 0 0
\(659\) −21.0821 −0.821242 −0.410621 0.911806i \(-0.634688\pi\)
−0.410621 + 0.911806i \(0.634688\pi\)
\(660\) 0 0
\(661\) −9.22331 −0.358745 −0.179373 0.983781i \(-0.557407\pi\)
−0.179373 + 0.983781i \(0.557407\pi\)
\(662\) 0 0
\(663\) −3.34788 −0.130021
\(664\) 0 0
\(665\) 8.58407 0.332876
\(666\) 0 0
\(667\) 47.9897 1.85817
\(668\) 0 0
\(669\) 2.67132 0.103279
\(670\) 0 0
\(671\) 2.04861 0.0790855
\(672\) 0 0
\(673\) 18.4164 0.709902 0.354951 0.934885i \(-0.384498\pi\)
0.354951 + 0.934885i \(0.384498\pi\)
\(674\) 0 0
\(675\) 2.66741 0.102669
\(676\) 0 0
\(677\) −46.3758 −1.78237 −0.891184 0.453642i \(-0.850124\pi\)
−0.891184 + 0.453642i \(0.850124\pi\)
\(678\) 0 0
\(679\) 51.8768 1.99085
\(680\) 0 0
\(681\) 5.76373 0.220866
\(682\) 0 0
\(683\) 29.5512 1.13075 0.565373 0.824835i \(-0.308732\pi\)
0.565373 + 0.824835i \(0.308732\pi\)
\(684\) 0 0
\(685\) 27.3265 1.04409
\(686\) 0 0
\(687\) −2.93139 −0.111840
\(688\) 0 0
\(689\) 27.1987 1.03619
\(690\) 0 0
\(691\) 11.4927 0.437203 0.218601 0.975814i \(-0.429851\pi\)
0.218601 + 0.975814i \(0.429851\pi\)
\(692\) 0 0
\(693\) 47.7842 1.81517
\(694\) 0 0
\(695\) −15.8165 −0.599955
\(696\) 0 0
\(697\) 0.483441 0.0183116
\(698\) 0 0
\(699\) 3.08078 0.116526
\(700\) 0 0
\(701\) 21.5496 0.813916 0.406958 0.913447i \(-0.366590\pi\)
0.406958 + 0.913447i \(0.366590\pi\)
\(702\) 0 0
\(703\) 5.34502 0.201591
\(704\) 0 0
\(705\) −11.5741 −0.435905
\(706\) 0 0
\(707\) −19.1968 −0.721969
\(708\) 0 0
\(709\) 11.5022 0.431974 0.215987 0.976396i \(-0.430703\pi\)
0.215987 + 0.976396i \(0.430703\pi\)
\(710\) 0 0
\(711\) 2.45337 0.0920087
\(712\) 0 0
\(713\) 13.6170 0.509961
\(714\) 0 0
\(715\) 38.6919 1.44699
\(716\) 0 0
\(717\) 12.4157 0.463674
\(718\) 0 0
\(719\) 44.3867 1.65535 0.827673 0.561210i \(-0.189664\pi\)
0.827673 + 0.561210i \(0.189664\pi\)
\(720\) 0 0
\(721\) −38.6069 −1.43780
\(722\) 0 0
\(723\) 0.0889800 0.00330920
\(724\) 0 0
\(725\) 5.59068 0.207632
\(726\) 0 0
\(727\) −44.0551 −1.63391 −0.816957 0.576699i \(-0.804341\pi\)
−0.816957 + 0.576699i \(0.804341\pi\)
\(728\) 0 0
\(729\) −1.80088 −0.0666992
\(730\) 0 0
\(731\) 9.77418 0.361511
\(732\) 0 0
\(733\) −21.8380 −0.806604 −0.403302 0.915067i \(-0.632138\pi\)
−0.403302 + 0.915067i \(0.632138\pi\)
\(734\) 0 0
\(735\) 15.3759 0.567149
\(736\) 0 0
\(737\) 45.1618 1.66356
\(738\) 0 0
\(739\) 26.1009 0.960139 0.480069 0.877231i \(-0.340612\pi\)
0.480069 + 0.877231i \(0.340612\pi\)
\(740\) 0 0
\(741\) −2.90607 −0.106757
\(742\) 0 0
\(743\) −11.3793 −0.417464 −0.208732 0.977973i \(-0.566934\pi\)
−0.208732 + 0.977973i \(0.566934\pi\)
\(744\) 0 0
\(745\) 13.7061 0.502154
\(746\) 0 0
\(747\) −20.2932 −0.742489
\(748\) 0 0
\(749\) −35.3643 −1.29218
\(750\) 0 0
\(751\) −36.5770 −1.33471 −0.667356 0.744739i \(-0.732574\pi\)
−0.667356 + 0.744739i \(0.732574\pi\)
\(752\) 0 0
\(753\) −14.0602 −0.512382
\(754\) 0 0
\(755\) 10.5228 0.382965
\(756\) 0 0
\(757\) −33.9887 −1.23534 −0.617669 0.786438i \(-0.711923\pi\)
−0.617669 + 0.786438i \(0.711923\pi\)
\(758\) 0 0
\(759\) 19.8427 0.720246
\(760\) 0 0
\(761\) 31.3768 1.13741 0.568704 0.822542i \(-0.307445\pi\)
0.568704 + 0.822542i \(0.307445\pi\)
\(762\) 0 0
\(763\) −26.5414 −0.960864
\(764\) 0 0
\(765\) −5.88699 −0.212844
\(766\) 0 0
\(767\) −7.18522 −0.259443
\(768\) 0 0
\(769\) 7.75894 0.279795 0.139897 0.990166i \(-0.455323\pi\)
0.139897 + 0.990166i \(0.455323\pi\)
\(770\) 0 0
\(771\) −1.82408 −0.0656926
\(772\) 0 0
\(773\) −7.66652 −0.275745 −0.137873 0.990450i \(-0.544026\pi\)
−0.137873 + 0.990450i \(0.544026\pi\)
\(774\) 0 0
\(775\) 1.58634 0.0569832
\(776\) 0 0
\(777\) 16.2863 0.584267
\(778\) 0 0
\(779\) 0.419643 0.0150353
\(780\) 0 0
\(781\) 58.9520 2.10947
\(782\) 0 0
\(783\) 34.0718 1.21763
\(784\) 0 0
\(785\) −19.5738 −0.698620
\(786\) 0 0
\(787\) 6.41451 0.228653 0.114326 0.993443i \(-0.463529\pi\)
0.114326 + 0.993443i \(0.463529\pi\)
\(788\) 0 0
\(789\) −1.70377 −0.0606557
\(790\) 0 0
\(791\) −69.5858 −2.47419
\(792\) 0 0
\(793\) 1.70383 0.0605049
\(794\) 0 0
\(795\) −10.6561 −0.377932
\(796\) 0 0
\(797\) 36.4077 1.28963 0.644813 0.764341i \(-0.276935\pi\)
0.644813 + 0.764341i \(0.276935\pi\)
\(798\) 0 0
\(799\) −8.65842 −0.306313
\(800\) 0 0
\(801\) 16.7505 0.591849
\(802\) 0 0
\(803\) −16.7321 −0.590465
\(804\) 0 0
\(805\) −48.7480 −1.71814
\(806\) 0 0
\(807\) 7.08394 0.249367
\(808\) 0 0
\(809\) −44.2454 −1.55558 −0.777792 0.628521i \(-0.783660\pi\)
−0.777792 + 0.628521i \(0.783660\pi\)
\(810\) 0 0
\(811\) −5.57319 −0.195701 −0.0978506 0.995201i \(-0.531197\pi\)
−0.0978506 + 0.995201i \(0.531197\pi\)
\(812\) 0 0
\(813\) −6.34468 −0.222518
\(814\) 0 0
\(815\) 22.4608 0.786766
\(816\) 0 0
\(817\) 8.48432 0.296829
\(818\) 0 0
\(819\) 39.7422 1.38871
\(820\) 0 0
\(821\) 37.7900 1.31888 0.659440 0.751757i \(-0.270794\pi\)
0.659440 + 0.751757i \(0.270794\pi\)
\(822\) 0 0
\(823\) 45.3652 1.58133 0.790665 0.612249i \(-0.209735\pi\)
0.790665 + 0.612249i \(0.209735\pi\)
\(824\) 0 0
\(825\) 2.31163 0.0804805
\(826\) 0 0
\(827\) −20.3768 −0.708570 −0.354285 0.935137i \(-0.615276\pi\)
−0.354285 + 0.935137i \(0.615276\pi\)
\(828\) 0 0
\(829\) 6.62674 0.230156 0.115078 0.993356i \(-0.463288\pi\)
0.115078 + 0.993356i \(0.463288\pi\)
\(830\) 0 0
\(831\) −2.21782 −0.0769352
\(832\) 0 0
\(833\) 11.5025 0.398539
\(834\) 0 0
\(835\) 21.9792 0.760620
\(836\) 0 0
\(837\) 9.66780 0.334168
\(838\) 0 0
\(839\) −49.2721 −1.70106 −0.850531 0.525925i \(-0.823719\pi\)
−0.850531 + 0.525925i \(0.823719\pi\)
\(840\) 0 0
\(841\) 42.4116 1.46247
\(842\) 0 0
\(843\) 6.27622 0.216164
\(844\) 0 0
\(845\) 5.10263 0.175536
\(846\) 0 0
\(847\) 46.7141 1.60511
\(848\) 0 0
\(849\) 18.1982 0.624560
\(850\) 0 0
\(851\) −30.3538 −1.04051
\(852\) 0 0
\(853\) −40.2178 −1.37703 −0.688516 0.725221i \(-0.741738\pi\)
−0.688516 + 0.725221i \(0.741738\pi\)
\(854\) 0 0
\(855\) −5.11010 −0.174762
\(856\) 0 0
\(857\) −26.1429 −0.893025 −0.446513 0.894777i \(-0.647334\pi\)
−0.446513 + 0.894777i \(0.647334\pi\)
\(858\) 0 0
\(859\) 36.1659 1.23397 0.616983 0.786977i \(-0.288355\pi\)
0.616983 + 0.786977i \(0.288355\pi\)
\(860\) 0 0
\(861\) 1.27865 0.0435764
\(862\) 0 0
\(863\) −4.52226 −0.153940 −0.0769698 0.997033i \(-0.524525\pi\)
−0.0769698 + 0.997033i \(0.524525\pi\)
\(864\) 0 0
\(865\) 18.1361 0.616645
\(866\) 0 0
\(867\) −11.5876 −0.393535
\(868\) 0 0
\(869\) 4.72599 0.160318
\(870\) 0 0
\(871\) 37.5612 1.27271
\(872\) 0 0
\(873\) −30.8823 −1.04521
\(874\) 0 0
\(875\) −48.5994 −1.64296
\(876\) 0 0
\(877\) 36.1854 1.22189 0.610947 0.791672i \(-0.290789\pi\)
0.610947 + 0.791672i \(0.290789\pi\)
\(878\) 0 0
\(879\) 8.66997 0.292431
\(880\) 0 0
\(881\) 14.1826 0.477825 0.238913 0.971041i \(-0.423209\pi\)
0.238913 + 0.971041i \(0.423209\pi\)
\(882\) 0 0
\(883\) 7.68689 0.258685 0.129342 0.991600i \(-0.458713\pi\)
0.129342 + 0.991600i \(0.458713\pi\)
\(884\) 0 0
\(885\) 2.81507 0.0946277
\(886\) 0 0
\(887\) −25.2096 −0.846457 −0.423228 0.906023i \(-0.639103\pi\)
−0.423228 + 0.906023i \(0.639103\pi\)
\(888\) 0 0
\(889\) 23.1015 0.774800
\(890\) 0 0
\(891\) −20.6959 −0.693339
\(892\) 0 0
\(893\) −7.51581 −0.251507
\(894\) 0 0
\(895\) −19.3561 −0.647003
\(896\) 0 0
\(897\) 16.5033 0.551028
\(898\) 0 0
\(899\) 20.2629 0.675806
\(900\) 0 0
\(901\) −7.97168 −0.265575
\(902\) 0 0
\(903\) 25.8517 0.860291
\(904\) 0 0
\(905\) 17.9634 0.597124
\(906\) 0 0
\(907\) −36.3700 −1.20765 −0.603823 0.797118i \(-0.706357\pi\)
−0.603823 + 0.797118i \(0.706357\pi\)
\(908\) 0 0
\(909\) 11.4278 0.379038
\(910\) 0 0
\(911\) 30.0116 0.994329 0.497165 0.867656i \(-0.334375\pi\)
0.497165 + 0.867656i \(0.334375\pi\)
\(912\) 0 0
\(913\) −39.0912 −1.29373
\(914\) 0 0
\(915\) −0.667539 −0.0220682
\(916\) 0 0
\(917\) 37.2880 1.23136
\(918\) 0 0
\(919\) −4.35013 −0.143497 −0.0717487 0.997423i \(-0.522858\pi\)
−0.0717487 + 0.997423i \(0.522858\pi\)
\(920\) 0 0
\(921\) −5.78265 −0.190545
\(922\) 0 0
\(923\) 49.0306 1.61386
\(924\) 0 0
\(925\) −3.53614 −0.116268
\(926\) 0 0
\(927\) 22.9827 0.754851
\(928\) 0 0
\(929\) −44.4786 −1.45929 −0.729647 0.683823i \(-0.760316\pi\)
−0.729647 + 0.683823i \(0.760316\pi\)
\(930\) 0 0
\(931\) 9.98458 0.327231
\(932\) 0 0
\(933\) 8.79690 0.287998
\(934\) 0 0
\(935\) −11.3402 −0.370865
\(936\) 0 0
\(937\) 3.56251 0.116382 0.0581911 0.998305i \(-0.481467\pi\)
0.0581911 + 0.998305i \(0.481467\pi\)
\(938\) 0 0
\(939\) 8.21107 0.267958
\(940\) 0 0
\(941\) −0.730714 −0.0238206 −0.0119103 0.999929i \(-0.503791\pi\)
−0.0119103 + 0.999929i \(0.503791\pi\)
\(942\) 0 0
\(943\) −2.38311 −0.0776047
\(944\) 0 0
\(945\) −34.6102 −1.12587
\(946\) 0 0
\(947\) 27.6492 0.898478 0.449239 0.893412i \(-0.351695\pi\)
0.449239 + 0.893412i \(0.351695\pi\)
\(948\) 0 0
\(949\) −13.9162 −0.451738
\(950\) 0 0
\(951\) 7.01837 0.227586
\(952\) 0 0
\(953\) 43.8360 1.41999 0.709994 0.704208i \(-0.248698\pi\)
0.709994 + 0.704208i \(0.248698\pi\)
\(954\) 0 0
\(955\) −35.0331 −1.13364
\(956\) 0 0
\(957\) 29.5272 0.954478
\(958\) 0 0
\(959\) 54.0686 1.74597
\(960\) 0 0
\(961\) −25.2504 −0.814530
\(962\) 0 0
\(963\) 21.0524 0.678404
\(964\) 0 0
\(965\) −1.68151 −0.0541298
\(966\) 0 0
\(967\) 46.6129 1.49897 0.749485 0.662022i \(-0.230301\pi\)
0.749485 + 0.662022i \(0.230301\pi\)
\(968\) 0 0
\(969\) 0.851742 0.0273619
\(970\) 0 0
\(971\) 15.2664 0.489923 0.244962 0.969533i \(-0.421225\pi\)
0.244962 + 0.969533i \(0.421225\pi\)
\(972\) 0 0
\(973\) −31.2948 −1.00327
\(974\) 0 0
\(975\) 1.92259 0.0615721
\(976\) 0 0
\(977\) 1.63813 0.0524084 0.0262042 0.999657i \(-0.491658\pi\)
0.0262042 + 0.999657i \(0.491658\pi\)
\(978\) 0 0
\(979\) 32.2668 1.03125
\(980\) 0 0
\(981\) 15.8001 0.504459
\(982\) 0 0
\(983\) 1.19798 0.0382096 0.0191048 0.999817i \(-0.493918\pi\)
0.0191048 + 0.999817i \(0.493918\pi\)
\(984\) 0 0
\(985\) 18.8145 0.599479
\(986\) 0 0
\(987\) −22.9007 −0.728936
\(988\) 0 0
\(989\) −48.1816 −1.53208
\(990\) 0 0
\(991\) −25.1683 −0.799497 −0.399749 0.916625i \(-0.630903\pi\)
−0.399749 + 0.916625i \(0.630903\pi\)
\(992\) 0 0
\(993\) 3.30263 0.104806
\(994\) 0 0
\(995\) −6.30837 −0.199989
\(996\) 0 0
\(997\) 57.3679 1.81686 0.908429 0.418038i \(-0.137282\pi\)
0.908429 + 0.418038i \(0.137282\pi\)
\(998\) 0 0
\(999\) −21.5506 −0.681831
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 \(a_p\))