Properties

Label 6036.2.a.i.1.13
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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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 1.13
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.0581310 q^{5}\) \(-2.78315 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.0581310 q^{5}\) \(-2.78315 q^{7}\) \(+1.00000 q^{9}\) \(+3.35646 q^{11}\) \(-1.13981 q^{13}\) \(-0.0581310 q^{15}\) \(+1.84368 q^{17}\) \(-0.820062 q^{19}\) \(+2.78315 q^{21}\) \(-4.45849 q^{23}\) \(-4.99662 q^{25}\) \(-1.00000 q^{27}\) \(+2.16313 q^{29}\) \(-4.12569 q^{31}\) \(-3.35646 q^{33}\) \(-0.161787 q^{35}\) \(+2.83415 q^{37}\) \(+1.13981 q^{39}\) \(+11.8611 q^{41}\) \(-2.14201 q^{43}\) \(+0.0581310 q^{45}\) \(+2.54359 q^{47}\) \(+0.745927 q^{49}\) \(-1.84368 q^{51}\) \(+9.14941 q^{53}\) \(+0.195114 q^{55}\) \(+0.820062 q^{57}\) \(-5.43274 q^{59}\) \(-3.80269 q^{61}\) \(-2.78315 q^{63}\) \(-0.0662585 q^{65}\) \(-8.54100 q^{67}\) \(+4.45849 q^{69}\) \(+7.66410 q^{71}\) \(+6.97047 q^{73}\) \(+4.99662 q^{75}\) \(-9.34154 q^{77}\) \(+3.92009 q^{79}\) \(+1.00000 q^{81}\) \(-7.00196 q^{83}\) \(+0.107175 q^{85}\) \(-2.16313 q^{87}\) \(-0.190479 q^{89}\) \(+3.17227 q^{91}\) \(+4.12569 q^{93}\) \(-0.0476711 q^{95}\) \(-5.39203 q^{97}\) \(+3.35646 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 0.0581310 0.0259970 0.0129985 0.999916i \(-0.495862\pi\)
0.0129985 + 0.999916i \(0.495862\pi\)
\(6\) 0 0
\(7\) −2.78315 −1.05193 −0.525966 0.850506i \(-0.676296\pi\)
−0.525966 + 0.850506i \(0.676296\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.35646 1.01201 0.506006 0.862530i \(-0.331121\pi\)
0.506006 + 0.862530i \(0.331121\pi\)
\(12\) 0 0
\(13\) −1.13981 −0.316127 −0.158064 0.987429i \(-0.550525\pi\)
−0.158064 + 0.987429i \(0.550525\pi\)
\(14\) 0 0
\(15\) −0.0581310 −0.0150094
\(16\) 0 0
\(17\) 1.84368 0.447158 0.223579 0.974686i \(-0.428226\pi\)
0.223579 + 0.974686i \(0.428226\pi\)
\(18\) 0 0
\(19\) −0.820062 −0.188135 −0.0940676 0.995566i \(-0.529987\pi\)
−0.0940676 + 0.995566i \(0.529987\pi\)
\(20\) 0 0
\(21\) 2.78315 0.607333
\(22\) 0 0
\(23\) −4.45849 −0.929660 −0.464830 0.885400i \(-0.653884\pi\)
−0.464830 + 0.885400i \(0.653884\pi\)
\(24\) 0 0
\(25\) −4.99662 −0.999324
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.16313 0.401684 0.200842 0.979624i \(-0.435632\pi\)
0.200842 + 0.979624i \(0.435632\pi\)
\(30\) 0 0
\(31\) −4.12569 −0.740995 −0.370498 0.928833i \(-0.620813\pi\)
−0.370498 + 0.928833i \(0.620813\pi\)
\(32\) 0 0
\(33\) −3.35646 −0.584285
\(34\) 0 0
\(35\) −0.161787 −0.0273471
\(36\) 0 0
\(37\) 2.83415 0.465932 0.232966 0.972485i \(-0.425157\pi\)
0.232966 + 0.972485i \(0.425157\pi\)
\(38\) 0 0
\(39\) 1.13981 0.182516
\(40\) 0 0
\(41\) 11.8611 1.85239 0.926196 0.377042i \(-0.123059\pi\)
0.926196 + 0.377042i \(0.123059\pi\)
\(42\) 0 0
\(43\) −2.14201 −0.326654 −0.163327 0.986572i \(-0.552223\pi\)
−0.163327 + 0.986572i \(0.552223\pi\)
\(44\) 0 0
\(45\) 0.0581310 0.00866566
\(46\) 0 0
\(47\) 2.54359 0.371021 0.185510 0.982642i \(-0.440606\pi\)
0.185510 + 0.982642i \(0.440606\pi\)
\(48\) 0 0
\(49\) 0.745927 0.106561
\(50\) 0 0
\(51\) −1.84368 −0.258167
\(52\) 0 0
\(53\) 9.14941 1.25677 0.628384 0.777903i \(-0.283717\pi\)
0.628384 + 0.777903i \(0.283717\pi\)
\(54\) 0 0
\(55\) 0.195114 0.0263092
\(56\) 0 0
\(57\) 0.820062 0.108620
\(58\) 0 0
\(59\) −5.43274 −0.707282 −0.353641 0.935381i \(-0.615057\pi\)
−0.353641 + 0.935381i \(0.615057\pi\)
\(60\) 0 0
\(61\) −3.80269 −0.486885 −0.243442 0.969915i \(-0.578277\pi\)
−0.243442 + 0.969915i \(0.578277\pi\)
\(62\) 0 0
\(63\) −2.78315 −0.350644
\(64\) 0 0
\(65\) −0.0662585 −0.00821835
\(66\) 0 0
\(67\) −8.54100 −1.04345 −0.521725 0.853114i \(-0.674711\pi\)
−0.521725 + 0.853114i \(0.674711\pi\)
\(68\) 0 0
\(69\) 4.45849 0.536739
\(70\) 0 0
\(71\) 7.66410 0.909562 0.454781 0.890603i \(-0.349718\pi\)
0.454781 + 0.890603i \(0.349718\pi\)
\(72\) 0 0
\(73\) 6.97047 0.815832 0.407916 0.913019i \(-0.366256\pi\)
0.407916 + 0.913019i \(0.366256\pi\)
\(74\) 0 0
\(75\) 4.99662 0.576960
\(76\) 0 0
\(77\) −9.34154 −1.06457
\(78\) 0 0
\(79\) 3.92009 0.441044 0.220522 0.975382i \(-0.429224\pi\)
0.220522 + 0.975382i \(0.429224\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.00196 −0.768565 −0.384282 0.923216i \(-0.625551\pi\)
−0.384282 + 0.923216i \(0.625551\pi\)
\(84\) 0 0
\(85\) 0.107175 0.0116248
\(86\) 0 0
\(87\) −2.16313 −0.231912
\(88\) 0 0
\(89\) −0.190479 −0.0201907 −0.0100953 0.999949i \(-0.503214\pi\)
−0.0100953 + 0.999949i \(0.503214\pi\)
\(90\) 0 0
\(91\) 3.17227 0.332544
\(92\) 0 0
\(93\) 4.12569 0.427814
\(94\) 0 0
\(95\) −0.0476711 −0.00489095
\(96\) 0 0
\(97\) −5.39203 −0.547478 −0.273739 0.961804i \(-0.588260\pi\)
−0.273739 + 0.961804i \(0.588260\pi\)
\(98\) 0 0
\(99\) 3.35646 0.337337
\(100\) 0 0
\(101\) −16.9622 −1.68780 −0.843899 0.536502i \(-0.819745\pi\)
−0.843899 + 0.536502i \(0.819745\pi\)
\(102\) 0 0
\(103\) 12.1345 1.19565 0.597826 0.801626i \(-0.296031\pi\)
0.597826 + 0.801626i \(0.296031\pi\)
\(104\) 0 0
\(105\) 0.161787 0.0157888
\(106\) 0 0
\(107\) 7.88121 0.761905 0.380953 0.924595i \(-0.375596\pi\)
0.380953 + 0.924595i \(0.375596\pi\)
\(108\) 0 0
\(109\) 13.0857 1.25338 0.626690 0.779268i \(-0.284409\pi\)
0.626690 + 0.779268i \(0.284409\pi\)
\(110\) 0 0
\(111\) −2.83415 −0.269006
\(112\) 0 0
\(113\) −19.0378 −1.79093 −0.895463 0.445136i \(-0.853155\pi\)
−0.895463 + 0.445136i \(0.853155\pi\)
\(114\) 0 0
\(115\) −0.259177 −0.0241683
\(116\) 0 0
\(117\) −1.13981 −0.105376
\(118\) 0 0
\(119\) −5.13124 −0.470380
\(120\) 0 0
\(121\) 0.265834 0.0241667
\(122\) 0 0
\(123\) −11.8611 −1.06948
\(124\) 0 0
\(125\) −0.581114 −0.0519764
\(126\) 0 0
\(127\) −14.0797 −1.24937 −0.624685 0.780877i \(-0.714772\pi\)
−0.624685 + 0.780877i \(0.714772\pi\)
\(128\) 0 0
\(129\) 2.14201 0.188594
\(130\) 0 0
\(131\) 13.9728 1.22081 0.610406 0.792089i \(-0.291006\pi\)
0.610406 + 0.792089i \(0.291006\pi\)
\(132\) 0 0
\(133\) 2.28236 0.197905
\(134\) 0 0
\(135\) −0.0581310 −0.00500312
\(136\) 0 0
\(137\) −4.93731 −0.421823 −0.210911 0.977505i \(-0.567643\pi\)
−0.210911 + 0.977505i \(0.567643\pi\)
\(138\) 0 0
\(139\) 14.7184 1.24840 0.624199 0.781266i \(-0.285426\pi\)
0.624199 + 0.781266i \(0.285426\pi\)
\(140\) 0 0
\(141\) −2.54359 −0.214209
\(142\) 0 0
\(143\) −3.82574 −0.319924
\(144\) 0 0
\(145\) 0.125745 0.0104426
\(146\) 0 0
\(147\) −0.745927 −0.0615230
\(148\) 0 0
\(149\) 20.8872 1.71115 0.855575 0.517679i \(-0.173204\pi\)
0.855575 + 0.517679i \(0.173204\pi\)
\(150\) 0 0
\(151\) −9.89692 −0.805400 −0.402700 0.915332i \(-0.631928\pi\)
−0.402700 + 0.915332i \(0.631928\pi\)
\(152\) 0 0
\(153\) 1.84368 0.149053
\(154\) 0 0
\(155\) −0.239830 −0.0192636
\(156\) 0 0
\(157\) −18.2131 −1.45357 −0.726784 0.686867i \(-0.758986\pi\)
−0.726784 + 0.686867i \(0.758986\pi\)
\(158\) 0 0
\(159\) −9.14941 −0.725595
\(160\) 0 0
\(161\) 12.4087 0.977939
\(162\) 0 0
\(163\) −6.70773 −0.525390 −0.262695 0.964879i \(-0.584611\pi\)
−0.262695 + 0.964879i \(0.584611\pi\)
\(164\) 0 0
\(165\) −0.195114 −0.0151896
\(166\) 0 0
\(167\) 16.7108 1.29312 0.646560 0.762863i \(-0.276207\pi\)
0.646560 + 0.762863i \(0.276207\pi\)
\(168\) 0 0
\(169\) −11.7008 −0.900064
\(170\) 0 0
\(171\) −0.820062 −0.0627117
\(172\) 0 0
\(173\) 11.0922 0.843321 0.421661 0.906754i \(-0.361447\pi\)
0.421661 + 0.906754i \(0.361447\pi\)
\(174\) 0 0
\(175\) 13.9063 1.05122
\(176\) 0 0
\(177\) 5.43274 0.408349
\(178\) 0 0
\(179\) 7.06107 0.527769 0.263885 0.964554i \(-0.414996\pi\)
0.263885 + 0.964554i \(0.414996\pi\)
\(180\) 0 0
\(181\) 12.1676 0.904413 0.452207 0.891913i \(-0.350637\pi\)
0.452207 + 0.891913i \(0.350637\pi\)
\(182\) 0 0
\(183\) 3.80269 0.281103
\(184\) 0 0
\(185\) 0.164752 0.0121128
\(186\) 0 0
\(187\) 6.18824 0.452529
\(188\) 0 0
\(189\) 2.78315 0.202444
\(190\) 0 0
\(191\) −1.17840 −0.0852661 −0.0426330 0.999091i \(-0.513575\pi\)
−0.0426330 + 0.999091i \(0.513575\pi\)
\(192\) 0 0
\(193\) 21.4923 1.54705 0.773523 0.633768i \(-0.218492\pi\)
0.773523 + 0.633768i \(0.218492\pi\)
\(194\) 0 0
\(195\) 0.0662585 0.00474487
\(196\) 0 0
\(197\) 24.4163 1.73959 0.869796 0.493412i \(-0.164250\pi\)
0.869796 + 0.493412i \(0.164250\pi\)
\(198\) 0 0
\(199\) −6.20550 −0.439896 −0.219948 0.975512i \(-0.570589\pi\)
−0.219948 + 0.975512i \(0.570589\pi\)
\(200\) 0 0
\(201\) 8.54100 0.602436
\(202\) 0 0
\(203\) −6.02033 −0.422544
\(204\) 0 0
\(205\) 0.689497 0.0481566
\(206\) 0 0
\(207\) −4.45849 −0.309887
\(208\) 0 0
\(209\) −2.75251 −0.190395
\(210\) 0 0
\(211\) 7.54531 0.519441 0.259720 0.965684i \(-0.416370\pi\)
0.259720 + 0.965684i \(0.416370\pi\)
\(212\) 0 0
\(213\) −7.66410 −0.525136
\(214\) 0 0
\(215\) −0.124517 −0.00849201
\(216\) 0 0
\(217\) 11.4824 0.779477
\(218\) 0 0
\(219\) −6.97047 −0.471021
\(220\) 0 0
\(221\) −2.10145 −0.141359
\(222\) 0 0
\(223\) 12.4707 0.835098 0.417549 0.908654i \(-0.362889\pi\)
0.417549 + 0.908654i \(0.362889\pi\)
\(224\) 0 0
\(225\) −4.99662 −0.333108
\(226\) 0 0
\(227\) −0.761779 −0.0505610 −0.0252805 0.999680i \(-0.508048\pi\)
−0.0252805 + 0.999680i \(0.508048\pi\)
\(228\) 0 0
\(229\) 26.6788 1.76298 0.881491 0.472201i \(-0.156540\pi\)
0.881491 + 0.472201i \(0.156540\pi\)
\(230\) 0 0
\(231\) 9.34154 0.614628
\(232\) 0 0
\(233\) 14.9373 0.978577 0.489288 0.872122i \(-0.337257\pi\)
0.489288 + 0.872122i \(0.337257\pi\)
\(234\) 0 0
\(235\) 0.147861 0.00964541
\(236\) 0 0
\(237\) −3.92009 −0.254637
\(238\) 0 0
\(239\) 23.1926 1.50020 0.750102 0.661322i \(-0.230004\pi\)
0.750102 + 0.661322i \(0.230004\pi\)
\(240\) 0 0
\(241\) 28.9557 1.86520 0.932599 0.360913i \(-0.117535\pi\)
0.932599 + 0.360913i \(0.117535\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0.0433615 0.00277026
\(246\) 0 0
\(247\) 0.934718 0.0594747
\(248\) 0 0
\(249\) 7.00196 0.443731
\(250\) 0 0
\(251\) −18.9642 −1.19701 −0.598506 0.801118i \(-0.704239\pi\)
−0.598506 + 0.801118i \(0.704239\pi\)
\(252\) 0 0
\(253\) −14.9648 −0.940826
\(254\) 0 0
\(255\) −0.107175 −0.00671156
\(256\) 0 0
\(257\) −3.05251 −0.190410 −0.0952052 0.995458i \(-0.530351\pi\)
−0.0952052 + 0.995458i \(0.530351\pi\)
\(258\) 0 0
\(259\) −7.88788 −0.490129
\(260\) 0 0
\(261\) 2.16313 0.133895
\(262\) 0 0
\(263\) −11.1032 −0.684655 −0.342327 0.939581i \(-0.611215\pi\)
−0.342327 + 0.939581i \(0.611215\pi\)
\(264\) 0 0
\(265\) 0.531864 0.0326722
\(266\) 0 0
\(267\) 0.190479 0.0116571
\(268\) 0 0
\(269\) 26.9690 1.64433 0.822165 0.569249i \(-0.192766\pi\)
0.822165 + 0.569249i \(0.192766\pi\)
\(270\) 0 0
\(271\) 18.4072 1.11816 0.559080 0.829114i \(-0.311154\pi\)
0.559080 + 0.829114i \(0.311154\pi\)
\(272\) 0 0
\(273\) −3.17227 −0.191995
\(274\) 0 0
\(275\) −16.7710 −1.01133
\(276\) 0 0
\(277\) 29.4623 1.77022 0.885109 0.465383i \(-0.154083\pi\)
0.885109 + 0.465383i \(0.154083\pi\)
\(278\) 0 0
\(279\) −4.12569 −0.246998
\(280\) 0 0
\(281\) −23.1967 −1.38380 −0.691899 0.721994i \(-0.743226\pi\)
−0.691899 + 0.721994i \(0.743226\pi\)
\(282\) 0 0
\(283\) 22.2312 1.32151 0.660753 0.750603i \(-0.270237\pi\)
0.660753 + 0.750603i \(0.270237\pi\)
\(284\) 0 0
\(285\) 0.0476711 0.00282379
\(286\) 0 0
\(287\) −33.0112 −1.94859
\(288\) 0 0
\(289\) −13.6008 −0.800050
\(290\) 0 0
\(291\) 5.39203 0.316087
\(292\) 0 0
\(293\) 12.6671 0.740019 0.370009 0.929028i \(-0.379355\pi\)
0.370009 + 0.929028i \(0.379355\pi\)
\(294\) 0 0
\(295\) −0.315810 −0.0183872
\(296\) 0 0
\(297\) −3.35646 −0.194762
\(298\) 0 0
\(299\) 5.08185 0.293891
\(300\) 0 0
\(301\) 5.96154 0.343618
\(302\) 0 0
\(303\) 16.9622 0.974451
\(304\) 0 0
\(305\) −0.221054 −0.0126575
\(306\) 0 0
\(307\) −24.1954 −1.38091 −0.690453 0.723377i \(-0.742589\pi\)
−0.690453 + 0.723377i \(0.742589\pi\)
\(308\) 0 0
\(309\) −12.1345 −0.690310
\(310\) 0 0
\(311\) −15.3821 −0.872238 −0.436119 0.899889i \(-0.643647\pi\)
−0.436119 + 0.899889i \(0.643647\pi\)
\(312\) 0 0
\(313\) 5.03233 0.284444 0.142222 0.989835i \(-0.454575\pi\)
0.142222 + 0.989835i \(0.454575\pi\)
\(314\) 0 0
\(315\) −0.161787 −0.00911568
\(316\) 0 0
\(317\) 30.0336 1.68685 0.843427 0.537244i \(-0.180535\pi\)
0.843427 + 0.537244i \(0.180535\pi\)
\(318\) 0 0
\(319\) 7.26048 0.406509
\(320\) 0 0
\(321\) −7.88121 −0.439886
\(322\) 0 0
\(323\) −1.51193 −0.0841262
\(324\) 0 0
\(325\) 5.69521 0.315914
\(326\) 0 0
\(327\) −13.0857 −0.723640
\(328\) 0 0
\(329\) −7.07919 −0.390288
\(330\) 0 0
\(331\) 2.46324 0.135392 0.0676958 0.997706i \(-0.478435\pi\)
0.0676958 + 0.997706i \(0.478435\pi\)
\(332\) 0 0
\(333\) 2.83415 0.155311
\(334\) 0 0
\(335\) −0.496497 −0.0271265
\(336\) 0 0
\(337\) −14.3358 −0.780920 −0.390460 0.920620i \(-0.627684\pi\)
−0.390460 + 0.920620i \(0.627684\pi\)
\(338\) 0 0
\(339\) 19.0378 1.03399
\(340\) 0 0
\(341\) −13.8477 −0.749895
\(342\) 0 0
\(343\) 17.4060 0.939837
\(344\) 0 0
\(345\) 0.259177 0.0139536
\(346\) 0 0
\(347\) 16.8417 0.904111 0.452056 0.891990i \(-0.350691\pi\)
0.452056 + 0.891990i \(0.350691\pi\)
\(348\) 0 0
\(349\) 16.4874 0.882552 0.441276 0.897372i \(-0.354526\pi\)
0.441276 + 0.897372i \(0.354526\pi\)
\(350\) 0 0
\(351\) 1.13981 0.0608387
\(352\) 0 0
\(353\) 14.7869 0.787025 0.393512 0.919319i \(-0.371260\pi\)
0.393512 + 0.919319i \(0.371260\pi\)
\(354\) 0 0
\(355\) 0.445522 0.0236458
\(356\) 0 0
\(357\) 5.13124 0.271574
\(358\) 0 0
\(359\) −15.1451 −0.799327 −0.399663 0.916662i \(-0.630873\pi\)
−0.399663 + 0.916662i \(0.630873\pi\)
\(360\) 0 0
\(361\) −18.3275 −0.964605
\(362\) 0 0
\(363\) −0.265834 −0.0139527
\(364\) 0 0
\(365\) 0.405200 0.0212092
\(366\) 0 0
\(367\) −2.49327 −0.130148 −0.0650739 0.997880i \(-0.520728\pi\)
−0.0650739 + 0.997880i \(0.520728\pi\)
\(368\) 0 0
\(369\) 11.8611 0.617464
\(370\) 0 0
\(371\) −25.4642 −1.32203
\(372\) 0 0
\(373\) 1.89166 0.0979463 0.0489732 0.998800i \(-0.484405\pi\)
0.0489732 + 0.998800i \(0.484405\pi\)
\(374\) 0 0
\(375\) 0.581114 0.0300086
\(376\) 0 0
\(377\) −2.46557 −0.126983
\(378\) 0 0
\(379\) 27.2330 1.39887 0.699433 0.714698i \(-0.253436\pi\)
0.699433 + 0.714698i \(0.253436\pi\)
\(380\) 0 0
\(381\) 14.0797 0.721324
\(382\) 0 0
\(383\) −19.0000 −0.970854 −0.485427 0.874277i \(-0.661336\pi\)
−0.485427 + 0.874277i \(0.661336\pi\)
\(384\) 0 0
\(385\) −0.543033 −0.0276755
\(386\) 0 0
\(387\) −2.14201 −0.108885
\(388\) 0 0
\(389\) 25.1295 1.27412 0.637058 0.770816i \(-0.280151\pi\)
0.637058 + 0.770816i \(0.280151\pi\)
\(390\) 0 0
\(391\) −8.22003 −0.415705
\(392\) 0 0
\(393\) −13.9728 −0.704836
\(394\) 0 0
\(395\) 0.227879 0.0114658
\(396\) 0 0
\(397\) −19.9219 −0.999852 −0.499926 0.866068i \(-0.666640\pi\)
−0.499926 + 0.866068i \(0.666640\pi\)
\(398\) 0 0
\(399\) −2.28236 −0.114261
\(400\) 0 0
\(401\) −20.2457 −1.01102 −0.505511 0.862820i \(-0.668696\pi\)
−0.505511 + 0.862820i \(0.668696\pi\)
\(402\) 0 0
\(403\) 4.70251 0.234249
\(404\) 0 0
\(405\) 0.0581310 0.00288855
\(406\) 0 0
\(407\) 9.51273 0.471528
\(408\) 0 0
\(409\) 31.4494 1.55507 0.777537 0.628837i \(-0.216469\pi\)
0.777537 + 0.628837i \(0.216469\pi\)
\(410\) 0 0
\(411\) 4.93731 0.243539
\(412\) 0 0
\(413\) 15.1201 0.744013
\(414\) 0 0
\(415\) −0.407031 −0.0199804
\(416\) 0 0
\(417\) −14.7184 −0.720762
\(418\) 0 0
\(419\) −2.65661 −0.129784 −0.0648919 0.997892i \(-0.520670\pi\)
−0.0648919 + 0.997892i \(0.520670\pi\)
\(420\) 0 0
\(421\) 16.9007 0.823688 0.411844 0.911254i \(-0.364885\pi\)
0.411844 + 0.911254i \(0.364885\pi\)
\(422\) 0 0
\(423\) 2.54359 0.123674
\(424\) 0 0
\(425\) −9.21217 −0.446856
\(426\) 0 0
\(427\) 10.5835 0.512170
\(428\) 0 0
\(429\) 3.82574 0.184708
\(430\) 0 0
\(431\) 5.25025 0.252896 0.126448 0.991973i \(-0.459642\pi\)
0.126448 + 0.991973i \(0.459642\pi\)
\(432\) 0 0
\(433\) −4.55545 −0.218921 −0.109461 0.993991i \(-0.534912\pi\)
−0.109461 + 0.993991i \(0.534912\pi\)
\(434\) 0 0
\(435\) −0.125745 −0.00602902
\(436\) 0 0
\(437\) 3.65624 0.174902
\(438\) 0 0
\(439\) 24.9849 1.19247 0.596233 0.802812i \(-0.296663\pi\)
0.596233 + 0.802812i \(0.296663\pi\)
\(440\) 0 0
\(441\) 0.745927 0.0355203
\(442\) 0 0
\(443\) −35.9441 −1.70776 −0.853879 0.520472i \(-0.825756\pi\)
−0.853879 + 0.520472i \(0.825756\pi\)
\(444\) 0 0
\(445\) −0.0110727 −0.000524897 0
\(446\) 0 0
\(447\) −20.8872 −0.987933
\(448\) 0 0
\(449\) 26.0892 1.23123 0.615613 0.788049i \(-0.288908\pi\)
0.615613 + 0.788049i \(0.288908\pi\)
\(450\) 0 0
\(451\) 39.8113 1.87464
\(452\) 0 0
\(453\) 9.89692 0.464998
\(454\) 0 0
\(455\) 0.184407 0.00864515
\(456\) 0 0
\(457\) −8.81754 −0.412467 −0.206233 0.978503i \(-0.566121\pi\)
−0.206233 + 0.978503i \(0.566121\pi\)
\(458\) 0 0
\(459\) −1.84368 −0.0860556
\(460\) 0 0
\(461\) 14.8329 0.690836 0.345418 0.938449i \(-0.387737\pi\)
0.345418 + 0.938449i \(0.387737\pi\)
\(462\) 0 0
\(463\) 20.0746 0.932945 0.466473 0.884536i \(-0.345525\pi\)
0.466473 + 0.884536i \(0.345525\pi\)
\(464\) 0 0
\(465\) 0.239830 0.0111219
\(466\) 0 0
\(467\) −7.23995 −0.335025 −0.167512 0.985870i \(-0.553573\pi\)
−0.167512 + 0.985870i \(0.553573\pi\)
\(468\) 0 0
\(469\) 23.7709 1.09764
\(470\) 0 0
\(471\) 18.2131 0.839217
\(472\) 0 0
\(473\) −7.18958 −0.330577
\(474\) 0 0
\(475\) 4.09754 0.188008
\(476\) 0 0
\(477\) 9.14941 0.418923
\(478\) 0 0
\(479\) −10.6712 −0.487580 −0.243790 0.969828i \(-0.578391\pi\)
−0.243790 + 0.969828i \(0.578391\pi\)
\(480\) 0 0
\(481\) −3.23040 −0.147294
\(482\) 0 0
\(483\) −12.4087 −0.564613
\(484\) 0 0
\(485\) −0.313444 −0.0142328
\(486\) 0 0
\(487\) 2.01733 0.0914139 0.0457070 0.998955i \(-0.485446\pi\)
0.0457070 + 0.998955i \(0.485446\pi\)
\(488\) 0 0
\(489\) 6.70773 0.303334
\(490\) 0 0
\(491\) −41.1887 −1.85882 −0.929411 0.369047i \(-0.879684\pi\)
−0.929411 + 0.369047i \(0.879684\pi\)
\(492\) 0 0
\(493\) 3.98813 0.179616
\(494\) 0 0
\(495\) 0.195114 0.00876974
\(496\) 0 0
\(497\) −21.3303 −0.956797
\(498\) 0 0
\(499\) −18.8212 −0.842554 −0.421277 0.906932i \(-0.638418\pi\)
−0.421277 + 0.906932i \(0.638418\pi\)
\(500\) 0 0
\(501\) −16.7108 −0.746583
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −0.986027 −0.0438776
\(506\) 0 0
\(507\) 11.7008 0.519652
\(508\) 0 0
\(509\) −11.5040 −0.509907 −0.254953 0.966953i \(-0.582060\pi\)
−0.254953 + 0.966953i \(0.582060\pi\)
\(510\) 0 0
\(511\) −19.3999 −0.858200
\(512\) 0 0
\(513\) 0.820062 0.0362066
\(514\) 0 0
\(515\) 0.705393 0.0310833
\(516\) 0 0
\(517\) 8.53746 0.375477
\(518\) 0 0
\(519\) −11.0922 −0.486892
\(520\) 0 0
\(521\) 29.4854 1.29178 0.645890 0.763430i \(-0.276486\pi\)
0.645890 + 0.763430i \(0.276486\pi\)
\(522\) 0 0
\(523\) −32.1450 −1.40560 −0.702801 0.711386i \(-0.748068\pi\)
−0.702801 + 0.711386i \(0.748068\pi\)
\(524\) 0 0
\(525\) −13.9063 −0.606923
\(526\) 0 0
\(527\) −7.60644 −0.331342
\(528\) 0 0
\(529\) −3.12186 −0.135733
\(530\) 0 0
\(531\) −5.43274 −0.235761
\(532\) 0 0
\(533\) −13.5194 −0.585592
\(534\) 0 0
\(535\) 0.458143 0.0198072
\(536\) 0 0
\(537\) −7.06107 −0.304708
\(538\) 0 0
\(539\) 2.50368 0.107841
\(540\) 0 0
\(541\) 1.64479 0.0707149 0.0353575 0.999375i \(-0.488743\pi\)
0.0353575 + 0.999375i \(0.488743\pi\)
\(542\) 0 0
\(543\) −12.1676 −0.522163
\(544\) 0 0
\(545\) 0.760684 0.0325841
\(546\) 0 0
\(547\) 8.37139 0.357935 0.178967 0.983855i \(-0.442724\pi\)
0.178967 + 0.983855i \(0.442724\pi\)
\(548\) 0 0
\(549\) −3.80269 −0.162295
\(550\) 0 0
\(551\) −1.77391 −0.0755709
\(552\) 0 0
\(553\) −10.9102 −0.463949
\(554\) 0 0
\(555\) −0.164752 −0.00699334
\(556\) 0 0
\(557\) −5.67421 −0.240424 −0.120212 0.992748i \(-0.538357\pi\)
−0.120212 + 0.992748i \(0.538357\pi\)
\(558\) 0 0
\(559\) 2.44149 0.103264
\(560\) 0 0
\(561\) −6.18824 −0.261268
\(562\) 0 0
\(563\) −19.4744 −0.820749 −0.410374 0.911917i \(-0.634602\pi\)
−0.410374 + 0.911917i \(0.634602\pi\)
\(564\) 0 0
\(565\) −1.10669 −0.0465587
\(566\) 0 0
\(567\) −2.78315 −0.116881
\(568\) 0 0
\(569\) 22.3961 0.938893 0.469447 0.882961i \(-0.344453\pi\)
0.469447 + 0.882961i \(0.344453\pi\)
\(570\) 0 0
\(571\) 44.2765 1.85292 0.926458 0.376398i \(-0.122838\pi\)
0.926458 + 0.376398i \(0.122838\pi\)
\(572\) 0 0
\(573\) 1.17840 0.0492284
\(574\) 0 0
\(575\) 22.2774 0.929031
\(576\) 0 0
\(577\) 46.7959 1.94814 0.974069 0.226253i \(-0.0726476\pi\)
0.974069 + 0.226253i \(0.0726476\pi\)
\(578\) 0 0
\(579\) −21.4923 −0.893188
\(580\) 0 0
\(581\) 19.4875 0.808478
\(582\) 0 0
\(583\) 30.7096 1.27186
\(584\) 0 0
\(585\) −0.0662585 −0.00273945
\(586\) 0 0
\(587\) −3.73755 −0.154265 −0.0771327 0.997021i \(-0.524577\pi\)
−0.0771327 + 0.997021i \(0.524577\pi\)
\(588\) 0 0
\(589\) 3.38332 0.139407
\(590\) 0 0
\(591\) −24.4163 −1.00435
\(592\) 0 0
\(593\) 21.4923 0.882584 0.441292 0.897364i \(-0.354520\pi\)
0.441292 + 0.897364i \(0.354520\pi\)
\(594\) 0 0
\(595\) −0.298284 −0.0122285
\(596\) 0 0
\(597\) 6.20550 0.253974
\(598\) 0 0
\(599\) 48.3413 1.97517 0.987586 0.157079i \(-0.0502078\pi\)
0.987586 + 0.157079i \(0.0502078\pi\)
\(600\) 0 0
\(601\) 19.9239 0.812711 0.406356 0.913715i \(-0.366799\pi\)
0.406356 + 0.913715i \(0.366799\pi\)
\(602\) 0 0
\(603\) −8.54100 −0.347816
\(604\) 0 0
\(605\) 0.0154532 0.000628262 0
\(606\) 0 0
\(607\) −45.1116 −1.83102 −0.915511 0.402292i \(-0.868214\pi\)
−0.915511 + 0.402292i \(0.868214\pi\)
\(608\) 0 0
\(609\) 6.02033 0.243956
\(610\) 0 0
\(611\) −2.89922 −0.117290
\(612\) 0 0
\(613\) −42.7630 −1.72718 −0.863591 0.504193i \(-0.831790\pi\)
−0.863591 + 0.504193i \(0.831790\pi\)
\(614\) 0 0
\(615\) −0.689497 −0.0278032
\(616\) 0 0
\(617\) −21.5529 −0.867688 −0.433844 0.900988i \(-0.642843\pi\)
−0.433844 + 0.900988i \(0.642843\pi\)
\(618\) 0 0
\(619\) −30.7810 −1.23719 −0.618597 0.785709i \(-0.712299\pi\)
−0.618597 + 0.785709i \(0.712299\pi\)
\(620\) 0 0
\(621\) 4.45849 0.178913
\(622\) 0 0
\(623\) 0.530131 0.0212392
\(624\) 0 0
\(625\) 24.9493 0.997973
\(626\) 0 0
\(627\) 2.75251 0.109925
\(628\) 0 0
\(629\) 5.22527 0.208345
\(630\) 0 0
\(631\) 43.8485 1.74558 0.872790 0.488096i \(-0.162308\pi\)
0.872790 + 0.488096i \(0.162308\pi\)
\(632\) 0 0
\(633\) −7.54531 −0.299899
\(634\) 0 0
\(635\) −0.818466 −0.0324798
\(636\) 0 0
\(637\) −0.850217 −0.0336868
\(638\) 0 0
\(639\) 7.66410 0.303187
\(640\) 0 0
\(641\) 13.4722 0.532119 0.266059 0.963957i \(-0.414278\pi\)
0.266059 + 0.963957i \(0.414278\pi\)
\(642\) 0 0
\(643\) 10.9000 0.429855 0.214928 0.976630i \(-0.431048\pi\)
0.214928 + 0.976630i \(0.431048\pi\)
\(644\) 0 0
\(645\) 0.124517 0.00490287
\(646\) 0 0
\(647\) −30.0981 −1.18328 −0.591639 0.806203i \(-0.701519\pi\)
−0.591639 + 0.806203i \(0.701519\pi\)
\(648\) 0 0
\(649\) −18.2348 −0.715777
\(650\) 0 0
\(651\) −11.4824 −0.450031
\(652\) 0 0
\(653\) −31.5775 −1.23572 −0.617862 0.786287i \(-0.712001\pi\)
−0.617862 + 0.786287i \(0.712001\pi\)
\(654\) 0 0
\(655\) 0.812254 0.0317374
\(656\) 0 0
\(657\) 6.97047 0.271944
\(658\) 0 0
\(659\) −36.5330 −1.42312 −0.711562 0.702624i \(-0.752012\pi\)
−0.711562 + 0.702624i \(0.752012\pi\)
\(660\) 0 0
\(661\) −10.1541 −0.394948 −0.197474 0.980308i \(-0.563274\pi\)
−0.197474 + 0.980308i \(0.563274\pi\)
\(662\) 0 0
\(663\) 2.10145 0.0816136
\(664\) 0 0
\(665\) 0.132676 0.00514494
\(666\) 0 0
\(667\) −9.64432 −0.373429
\(668\) 0 0
\(669\) −12.4707 −0.482144
\(670\) 0 0
\(671\) −12.7636 −0.492733
\(672\) 0 0
\(673\) 29.0219 1.11871 0.559355 0.828928i \(-0.311049\pi\)
0.559355 + 0.828928i \(0.311049\pi\)
\(674\) 0 0
\(675\) 4.99662 0.192320
\(676\) 0 0
\(677\) 13.8316 0.531591 0.265795 0.964029i \(-0.414365\pi\)
0.265795 + 0.964029i \(0.414365\pi\)
\(678\) 0 0
\(679\) 15.0068 0.575910
\(680\) 0 0
\(681\) 0.761779 0.0291914
\(682\) 0 0
\(683\) −23.7315 −0.908061 −0.454030 0.890986i \(-0.650014\pi\)
−0.454030 + 0.890986i \(0.650014\pi\)
\(684\) 0 0
\(685\) −0.287011 −0.0109661
\(686\) 0 0
\(687\) −26.6788 −1.01786
\(688\) 0 0
\(689\) −10.4286 −0.397299
\(690\) 0 0
\(691\) −2.48459 −0.0945184 −0.0472592 0.998883i \(-0.515049\pi\)
−0.0472592 + 0.998883i \(0.515049\pi\)
\(692\) 0 0
\(693\) −9.34154 −0.354856
\(694\) 0 0
\(695\) 0.855595 0.0324546
\(696\) 0 0
\(697\) 21.8681 0.828312
\(698\) 0 0
\(699\) −14.9373 −0.564981
\(700\) 0 0
\(701\) −24.7033 −0.933030 −0.466515 0.884513i \(-0.654491\pi\)
−0.466515 + 0.884513i \(0.654491\pi\)
\(702\) 0 0
\(703\) −2.32418 −0.0876582
\(704\) 0 0
\(705\) −0.147861 −0.00556878
\(706\) 0 0
\(707\) 47.2082 1.77545
\(708\) 0 0
\(709\) 16.7783 0.630124 0.315062 0.949071i \(-0.397975\pi\)
0.315062 + 0.949071i \(0.397975\pi\)
\(710\) 0 0
\(711\) 3.92009 0.147015
\(712\) 0 0
\(713\) 18.3943 0.688873
\(714\) 0 0
\(715\) −0.222394 −0.00831706
\(716\) 0 0
\(717\) −23.1926 −0.866143
\(718\) 0 0
\(719\) 45.2929 1.68914 0.844569 0.535447i \(-0.179857\pi\)
0.844569 + 0.535447i \(0.179857\pi\)
\(720\) 0 0
\(721\) −33.7723 −1.25774
\(722\) 0 0
\(723\) −28.9557 −1.07687
\(724\) 0 0
\(725\) −10.8084 −0.401413
\(726\) 0 0
\(727\) 41.3389 1.53317 0.766587 0.642141i \(-0.221954\pi\)
0.766587 + 0.642141i \(0.221954\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −3.94918 −0.146066
\(732\) 0 0
\(733\) 36.1694 1.33595 0.667974 0.744185i \(-0.267162\pi\)
0.667974 + 0.744185i \(0.267162\pi\)
\(734\) 0 0
\(735\) −0.0433615 −0.00159941
\(736\) 0 0
\(737\) −28.6675 −1.05598
\(738\) 0 0
\(739\) −29.4739 −1.08421 −0.542107 0.840309i \(-0.682373\pi\)
−0.542107 + 0.840309i \(0.682373\pi\)
\(740\) 0 0
\(741\) −0.934718 −0.0343377
\(742\) 0 0
\(743\) −32.7791 −1.20255 −0.601274 0.799043i \(-0.705340\pi\)
−0.601274 + 0.799043i \(0.705340\pi\)
\(744\) 0 0
\(745\) 1.21420 0.0444847
\(746\) 0 0
\(747\) −7.00196 −0.256188
\(748\) 0 0
\(749\) −21.9346 −0.801473
\(750\) 0 0
\(751\) 35.4109 1.29216 0.646082 0.763268i \(-0.276407\pi\)
0.646082 + 0.763268i \(0.276407\pi\)
\(752\) 0 0
\(753\) 18.9642 0.691096
\(754\) 0 0
\(755\) −0.575318 −0.0209380
\(756\) 0 0
\(757\) −29.8838 −1.08614 −0.543072 0.839686i \(-0.682739\pi\)
−0.543072 + 0.839686i \(0.682739\pi\)
\(758\) 0 0
\(759\) 14.9648 0.543186
\(760\) 0 0
\(761\) 39.6385 1.43689 0.718447 0.695582i \(-0.244853\pi\)
0.718447 + 0.695582i \(0.244853\pi\)
\(762\) 0 0
\(763\) −36.4194 −1.31847
\(764\) 0 0
\(765\) 0.107175 0.00387492
\(766\) 0 0
\(767\) 6.19230 0.223591
\(768\) 0 0
\(769\) −49.8197 −1.79654 −0.898272 0.439439i \(-0.855177\pi\)
−0.898272 + 0.439439i \(0.855177\pi\)
\(770\) 0 0
\(771\) 3.05251 0.109933
\(772\) 0 0
\(773\) −4.77408 −0.171712 −0.0858559 0.996308i \(-0.527362\pi\)
−0.0858559 + 0.996308i \(0.527362\pi\)
\(774\) 0 0
\(775\) 20.6145 0.740494
\(776\) 0 0
\(777\) 7.88788 0.282976
\(778\) 0 0
\(779\) −9.72684 −0.348500
\(780\) 0 0
\(781\) 25.7243 0.920486
\(782\) 0 0
\(783\) −2.16313 −0.0773041
\(784\) 0 0
\(785\) −1.05875 −0.0377883
\(786\) 0 0
\(787\) 11.6565 0.415508 0.207754 0.978181i \(-0.433385\pi\)
0.207754 + 0.978181i \(0.433385\pi\)
\(788\) 0 0
\(789\) 11.1032 0.395286
\(790\) 0 0
\(791\) 52.9851 1.88393
\(792\) 0 0
\(793\) 4.33436 0.153918
\(794\) 0 0
\(795\) −0.531864 −0.0188633
\(796\) 0 0
\(797\) −8.06073 −0.285526 −0.142763 0.989757i \(-0.545599\pi\)
−0.142763 + 0.989757i \(0.545599\pi\)
\(798\) 0 0
\(799\) 4.68956 0.165905
\(800\) 0 0
\(801\) −0.190479 −0.00673023
\(802\) 0 0
\(803\) 23.3961 0.825631
\(804\) 0 0
\(805\) 0.721327 0.0254234
\(806\) 0 0
\(807\) −26.9690 −0.949355
\(808\) 0 0
\(809\) 13.9913 0.491908 0.245954 0.969282i \(-0.420899\pi\)
0.245954 + 0.969282i \(0.420899\pi\)
\(810\) 0 0
\(811\) −15.1025 −0.530319 −0.265160 0.964205i \(-0.585425\pi\)
−0.265160 + 0.964205i \(0.585425\pi\)
\(812\) 0 0
\(813\) −18.4072 −0.645570
\(814\) 0 0
\(815\) −0.389927 −0.0136585
\(816\) 0 0
\(817\) 1.75658 0.0614551
\(818\) 0 0
\(819\) 3.17227 0.110848
\(820\) 0 0
\(821\) 26.3031 0.917983 0.458992 0.888441i \(-0.348211\pi\)
0.458992 + 0.888441i \(0.348211\pi\)
\(822\) 0 0
\(823\) −3.70649 −0.129200 −0.0646000 0.997911i \(-0.520577\pi\)
−0.0646000 + 0.997911i \(0.520577\pi\)
\(824\) 0 0
\(825\) 16.7710 0.583890
\(826\) 0 0
\(827\) −29.6775 −1.03199 −0.515993 0.856593i \(-0.672577\pi\)
−0.515993 + 0.856593i \(0.672577\pi\)
\(828\) 0 0
\(829\) 44.6254 1.54990 0.774952 0.632020i \(-0.217774\pi\)
0.774952 + 0.632020i \(0.217774\pi\)
\(830\) 0 0
\(831\) −29.4623 −1.02204
\(832\) 0 0
\(833\) 1.37525 0.0476496
\(834\) 0 0
\(835\) 0.971415 0.0336172
\(836\) 0 0
\(837\) 4.12569 0.142605
\(838\) 0 0
\(839\) −20.9652 −0.723798 −0.361899 0.932217i \(-0.617872\pi\)
−0.361899 + 0.932217i \(0.617872\pi\)
\(840\) 0 0
\(841\) −24.3208 −0.838650
\(842\) 0 0
\(843\) 23.1967 0.798937
\(844\) 0 0
\(845\) −0.680181 −0.0233989
\(846\) 0 0
\(847\) −0.739856 −0.0254218
\(848\) 0 0
\(849\) −22.2312 −0.762972
\(850\) 0 0
\(851\) −12.6360 −0.433158
\(852\) 0 0
\(853\) −29.6837 −1.01635 −0.508176 0.861253i \(-0.669680\pi\)
−0.508176 + 0.861253i \(0.669680\pi\)
\(854\) 0 0
\(855\) −0.0476711 −0.00163032
\(856\) 0 0
\(857\) 9.66189 0.330044 0.165022 0.986290i \(-0.447230\pi\)
0.165022 + 0.986290i \(0.447230\pi\)
\(858\) 0 0
\(859\) 3.90188 0.133131 0.0665653 0.997782i \(-0.478796\pi\)
0.0665653 + 0.997782i \(0.478796\pi\)
\(860\) 0 0
\(861\) 33.0112 1.12502
\(862\) 0 0
\(863\) 45.5026 1.54893 0.774463 0.632619i \(-0.218020\pi\)
0.774463 + 0.632619i \(0.218020\pi\)
\(864\) 0 0
\(865\) 0.644798 0.0219238
\(866\) 0 0
\(867\) 13.6008 0.461909
\(868\) 0 0
\(869\) 13.1576 0.446342
\(870\) 0 0
\(871\) 9.73514 0.329863
\(872\) 0 0
\(873\) −5.39203 −0.182493
\(874\) 0 0
\(875\) 1.61733 0.0546756
\(876\) 0 0
\(877\) 3.98385 0.134525 0.0672626 0.997735i \(-0.478573\pi\)
0.0672626 + 0.997735i \(0.478573\pi\)
\(878\) 0 0
\(879\) −12.6671 −0.427250
\(880\) 0 0
\(881\) 4.40623 0.148450 0.0742249 0.997242i \(-0.476352\pi\)
0.0742249 + 0.997242i \(0.476352\pi\)
\(882\) 0 0
\(883\) 41.9372 1.41130 0.705650 0.708561i \(-0.250655\pi\)
0.705650 + 0.708561i \(0.250655\pi\)
\(884\) 0 0
\(885\) 0.315810 0.0106159
\(886\) 0 0
\(887\) −39.7860 −1.33588 −0.667942 0.744213i \(-0.732825\pi\)
−0.667942 + 0.744213i \(0.732825\pi\)
\(888\) 0 0
\(889\) 39.1859 1.31425
\(890\) 0 0
\(891\) 3.35646 0.112446
\(892\) 0 0
\(893\) −2.08590 −0.0698020
\(894\) 0 0
\(895\) 0.410467 0.0137204
\(896\) 0 0
\(897\) −5.08185 −0.169678
\(898\) 0 0
\(899\) −8.92441 −0.297646
\(900\) 0 0
\(901\) 16.8686 0.561974
\(902\) 0 0
\(903\) −5.96154 −0.198388
\(904\) 0 0
\(905\) 0.707317 0.0235120
\(906\) 0 0
\(907\) −47.0209 −1.56130 −0.780652 0.624966i \(-0.785113\pi\)
−0.780652 + 0.624966i \(0.785113\pi\)
\(908\) 0 0
\(909\) −16.9622 −0.562599
\(910\) 0 0
\(911\) −58.4812 −1.93757 −0.968784 0.247906i \(-0.920258\pi\)
−0.968784 + 0.247906i \(0.920258\pi\)
\(912\) 0 0
\(913\) −23.5018 −0.777796
\(914\) 0 0
\(915\) 0.221054 0.00730783
\(916\) 0 0
\(917\) −38.8885 −1.28421
\(918\) 0 0
\(919\) 53.1235 1.75238 0.876192 0.481962i \(-0.160076\pi\)
0.876192 + 0.481962i \(0.160076\pi\)
\(920\) 0 0
\(921\) 24.1954 0.797267
\(922\) 0 0
\(923\) −8.73564 −0.287537
\(924\) 0 0
\(925\) −14.1612 −0.465617
\(926\) 0 0
\(927\) 12.1345 0.398551
\(928\) 0 0
\(929\) −31.2556 −1.02546 −0.512732 0.858549i \(-0.671366\pi\)
−0.512732 + 0.858549i \(0.671366\pi\)
\(930\) 0 0
\(931\) −0.611707 −0.0200479
\(932\) 0 0
\(933\) 15.3821 0.503587
\(934\) 0 0
\(935\) 0.359729 0.0117644
\(936\) 0 0
\(937\) −8.11164 −0.264996 −0.132498 0.991183i \(-0.542300\pi\)
−0.132498 + 0.991183i \(0.542300\pi\)
\(938\) 0 0
\(939\) −5.03233 −0.164224
\(940\) 0 0
\(941\) 3.77000 0.122898 0.0614492 0.998110i \(-0.480428\pi\)
0.0614492 + 0.998110i \(0.480428\pi\)
\(942\) 0 0
\(943\) −52.8826 −1.72209
\(944\) 0 0
\(945\) 0.161787 0.00526294
\(946\) 0 0
\(947\) −41.2792 −1.34139 −0.670696 0.741732i \(-0.734005\pi\)
−0.670696 + 0.741732i \(0.734005\pi\)
\(948\) 0 0
\(949\) −7.94503 −0.257907
\(950\) 0 0
\(951\) −30.0336 −0.973906
\(952\) 0 0
\(953\) 31.0552 1.00598 0.502989 0.864293i \(-0.332234\pi\)
0.502989 + 0.864293i \(0.332234\pi\)
\(954\) 0 0
\(955\) −0.0685016 −0.00221666
\(956\) 0 0
\(957\) −7.26048 −0.234698
\(958\) 0 0
\(959\) 13.7413 0.443729
\(960\) 0 0
\(961\) −13.9787 −0.450926
\(962\) 0 0
\(963\) 7.88121 0.253968
\(964\) 0 0
\(965\) 1.24937 0.0402185
\(966\) 0 0
\(967\) 46.1758 1.48491 0.742457 0.669894i \(-0.233660\pi\)
0.742457 + 0.669894i \(0.233660\pi\)
\(968\) 0 0
\(969\) 1.51193 0.0485703
\(970\) 0 0
\(971\) 40.9441 1.31396 0.656980 0.753908i \(-0.271834\pi\)
0.656980 + 0.753908i \(0.271834\pi\)
\(972\) 0 0
\(973\) −40.9635 −1.31323
\(974\) 0 0
\(975\) −5.69521 −0.182393
\(976\) 0 0
\(977\) 41.1402 1.31619 0.658095 0.752935i \(-0.271362\pi\)
0.658095 + 0.752935i \(0.271362\pi\)
\(978\) 0 0
\(979\) −0.639334 −0.0204332
\(980\) 0 0
\(981\) 13.0857 0.417794
\(982\) 0 0
\(983\) 17.1244 0.546184 0.273092 0.961988i \(-0.411954\pi\)
0.273092 + 0.961988i \(0.411954\pi\)
\(984\) 0 0
\(985\) 1.41935 0.0452241
\(986\) 0 0
\(987\) 7.07919 0.225333
\(988\) 0 0
\(989\) 9.55014 0.303677
\(990\) 0 0
\(991\) −8.63117 −0.274178 −0.137089 0.990559i \(-0.543775\pi\)
−0.137089 + 0.990559i \(0.543775\pi\)
\(992\) 0 0
\(993\) −2.46324 −0.0781684
\(994\) 0 0
\(995\) −0.360732 −0.0114360
\(996\) 0 0
\(997\) −39.3075 −1.24488 −0.622441 0.782667i \(-0.713859\pi\)
−0.622441 + 0.782667i \(0.713859\pi\)
\(998\) 0 0
\(999\) −2.83415 −0.0896686
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 \(a_p\))