Properties

Label 6004.2.a.g.1.2
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 1.2
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.81775 q^{3}\) \(-0.243389 q^{5}\) \(+0.929492 q^{7}\) \(+4.93969 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.81775 q^{3}\) \(-0.243389 q^{5}\) \(+0.929492 q^{7}\) \(+4.93969 q^{9}\) \(+4.38796 q^{11}\) \(-1.17004 q^{13}\) \(+0.685809 q^{15}\) \(+6.41492 q^{17}\) \(+1.00000 q^{19}\) \(-2.61907 q^{21}\) \(-6.17766 q^{23}\) \(-4.94076 q^{25}\) \(-5.46555 q^{27}\) \(-5.16503 q^{29}\) \(-8.29647 q^{31}\) \(-12.3642 q^{33}\) \(-0.226229 q^{35}\) \(-11.1767 q^{37}\) \(+3.29689 q^{39}\) \(+3.11040 q^{41}\) \(+5.53876 q^{43}\) \(-1.20227 q^{45}\) \(+8.81464 q^{47}\) \(-6.13604 q^{49}\) \(-18.0756 q^{51}\) \(+10.2900 q^{53}\) \(-1.06798 q^{55}\) \(-2.81775 q^{57}\) \(-11.0099 q^{59}\) \(+0.358578 q^{61}\) \(+4.59140 q^{63}\) \(+0.284776 q^{65}\) \(+11.8751 q^{67}\) \(+17.4071 q^{69}\) \(+7.27001 q^{71}\) \(-14.0340 q^{73}\) \(+13.9218 q^{75}\) \(+4.07858 q^{77}\) \(-1.00000 q^{79}\) \(+0.581451 q^{81}\) \(+6.31006 q^{83}\) \(-1.56132 q^{85}\) \(+14.5537 q^{87}\) \(+5.87396 q^{89}\) \(-1.08755 q^{91}\) \(+23.3773 q^{93}\) \(-0.243389 q^{95}\) \(-10.4974 q^{97}\) \(+21.6752 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.81775 −1.62683 −0.813413 0.581687i \(-0.802393\pi\)
−0.813413 + 0.581687i \(0.802393\pi\)
\(4\) 0 0
\(5\) −0.243389 −0.108847 −0.0544235 0.998518i \(-0.517332\pi\)
−0.0544235 + 0.998518i \(0.517332\pi\)
\(6\) 0 0
\(7\) 0.929492 0.351315 0.175658 0.984451i \(-0.443795\pi\)
0.175658 + 0.984451i \(0.443795\pi\)
\(8\) 0 0
\(9\) 4.93969 1.64656
\(10\) 0 0
\(11\) 4.38796 1.32302 0.661510 0.749936i \(-0.269916\pi\)
0.661510 + 0.749936i \(0.269916\pi\)
\(12\) 0 0
\(13\) −1.17004 −0.324512 −0.162256 0.986749i \(-0.551877\pi\)
−0.162256 + 0.986749i \(0.551877\pi\)
\(14\) 0 0
\(15\) 0.685809 0.177075
\(16\) 0 0
\(17\) 6.41492 1.55585 0.777923 0.628360i \(-0.216273\pi\)
0.777923 + 0.628360i \(0.216273\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −2.61907 −0.571528
\(22\) 0 0
\(23\) −6.17766 −1.28813 −0.644066 0.764970i \(-0.722754\pi\)
−0.644066 + 0.764970i \(0.722754\pi\)
\(24\) 0 0
\(25\) −4.94076 −0.988152
\(26\) 0 0
\(27\) −5.46555 −1.05184
\(28\) 0 0
\(29\) −5.16503 −0.959122 −0.479561 0.877508i \(-0.659204\pi\)
−0.479561 + 0.877508i \(0.659204\pi\)
\(30\) 0 0
\(31\) −8.29647 −1.49009 −0.745045 0.667015i \(-0.767572\pi\)
−0.745045 + 0.667015i \(0.767572\pi\)
\(32\) 0 0
\(33\) −12.3642 −2.15232
\(34\) 0 0
\(35\) −0.226229 −0.0382396
\(36\) 0 0
\(37\) −11.1767 −1.83744 −0.918718 0.394914i \(-0.870775\pi\)
−0.918718 + 0.394914i \(0.870775\pi\)
\(38\) 0 0
\(39\) 3.29689 0.527925
\(40\) 0 0
\(41\) 3.11040 0.485763 0.242881 0.970056i \(-0.421907\pi\)
0.242881 + 0.970056i \(0.421907\pi\)
\(42\) 0 0
\(43\) 5.53876 0.844653 0.422326 0.906444i \(-0.361214\pi\)
0.422326 + 0.906444i \(0.361214\pi\)
\(44\) 0 0
\(45\) −1.20227 −0.179223
\(46\) 0 0
\(47\) 8.81464 1.28575 0.642874 0.765972i \(-0.277742\pi\)
0.642874 + 0.765972i \(0.277742\pi\)
\(48\) 0 0
\(49\) −6.13604 −0.876578
\(50\) 0 0
\(51\) −18.0756 −2.53109
\(52\) 0 0
\(53\) 10.2900 1.41344 0.706720 0.707494i \(-0.250174\pi\)
0.706720 + 0.707494i \(0.250174\pi\)
\(54\) 0 0
\(55\) −1.06798 −0.144007
\(56\) 0 0
\(57\) −2.81775 −0.373219
\(58\) 0 0
\(59\) −11.0099 −1.43336 −0.716682 0.697400i \(-0.754340\pi\)
−0.716682 + 0.697400i \(0.754340\pi\)
\(60\) 0 0
\(61\) 0.358578 0.0459113 0.0229556 0.999736i \(-0.492692\pi\)
0.0229556 + 0.999736i \(0.492692\pi\)
\(62\) 0 0
\(63\) 4.59140 0.578462
\(64\) 0 0
\(65\) 0.284776 0.0353222
\(66\) 0 0
\(67\) 11.8751 1.45077 0.725385 0.688344i \(-0.241662\pi\)
0.725385 + 0.688344i \(0.241662\pi\)
\(68\) 0 0
\(69\) 17.4071 2.09557
\(70\) 0 0
\(71\) 7.27001 0.862792 0.431396 0.902163i \(-0.358021\pi\)
0.431396 + 0.902163i \(0.358021\pi\)
\(72\) 0 0
\(73\) −14.0340 −1.64255 −0.821276 0.570530i \(-0.806738\pi\)
−0.821276 + 0.570530i \(0.806738\pi\)
\(74\) 0 0
\(75\) 13.9218 1.60755
\(76\) 0 0
\(77\) 4.07858 0.464797
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 0.581451 0.0646056
\(82\) 0 0
\(83\) 6.31006 0.692619 0.346309 0.938120i \(-0.387435\pi\)
0.346309 + 0.938120i \(0.387435\pi\)
\(84\) 0 0
\(85\) −1.56132 −0.169349
\(86\) 0 0
\(87\) 14.5537 1.56033
\(88\) 0 0
\(89\) 5.87396 0.622639 0.311319 0.950305i \(-0.399229\pi\)
0.311319 + 0.950305i \(0.399229\pi\)
\(90\) 0 0
\(91\) −1.08755 −0.114006
\(92\) 0 0
\(93\) 23.3773 2.42412
\(94\) 0 0
\(95\) −0.243389 −0.0249712
\(96\) 0 0
\(97\) −10.4974 −1.06585 −0.532926 0.846162i \(-0.678908\pi\)
−0.532926 + 0.846162i \(0.678908\pi\)
\(98\) 0 0
\(99\) 21.6752 2.17844
\(100\) 0 0
\(101\) 1.14271 0.113704 0.0568519 0.998383i \(-0.481894\pi\)
0.0568519 + 0.998383i \(0.481894\pi\)
\(102\) 0 0
\(103\) −14.8972 −1.46787 −0.733934 0.679221i \(-0.762318\pi\)
−0.733934 + 0.679221i \(0.762318\pi\)
\(104\) 0 0
\(105\) 0.637454 0.0622092
\(106\) 0 0
\(107\) −12.8657 −1.24378 −0.621888 0.783106i \(-0.713634\pi\)
−0.621888 + 0.783106i \(0.713634\pi\)
\(108\) 0 0
\(109\) 1.90646 0.182606 0.0913030 0.995823i \(-0.470897\pi\)
0.0913030 + 0.995823i \(0.470897\pi\)
\(110\) 0 0
\(111\) 31.4931 2.98919
\(112\) 0 0
\(113\) 10.3402 0.972723 0.486362 0.873758i \(-0.338324\pi\)
0.486362 + 0.873758i \(0.338324\pi\)
\(114\) 0 0
\(115\) 1.50358 0.140209
\(116\) 0 0
\(117\) −5.77966 −0.534329
\(118\) 0 0
\(119\) 5.96262 0.546592
\(120\) 0 0
\(121\) 8.25422 0.750384
\(122\) 0 0
\(123\) −8.76431 −0.790251
\(124\) 0 0
\(125\) 2.41948 0.216404
\(126\) 0 0
\(127\) 6.81705 0.604915 0.302458 0.953163i \(-0.402193\pi\)
0.302458 + 0.953163i \(0.402193\pi\)
\(128\) 0 0
\(129\) −15.6068 −1.37410
\(130\) 0 0
\(131\) 8.88813 0.776559 0.388280 0.921542i \(-0.373069\pi\)
0.388280 + 0.921542i \(0.373069\pi\)
\(132\) 0 0
\(133\) 0.929492 0.0805972
\(134\) 0 0
\(135\) 1.33026 0.114490
\(136\) 0 0
\(137\) −3.19350 −0.272839 −0.136420 0.990651i \(-0.543560\pi\)
−0.136420 + 0.990651i \(0.543560\pi\)
\(138\) 0 0
\(139\) 10.6744 0.905392 0.452696 0.891665i \(-0.350462\pi\)
0.452696 + 0.891665i \(0.350462\pi\)
\(140\) 0 0
\(141\) −24.8374 −2.09169
\(142\) 0 0
\(143\) −5.13411 −0.429336
\(144\) 0 0
\(145\) 1.25711 0.104398
\(146\) 0 0
\(147\) 17.2898 1.42604
\(148\) 0 0
\(149\) −6.99354 −0.572933 −0.286467 0.958090i \(-0.592481\pi\)
−0.286467 + 0.958090i \(0.592481\pi\)
\(150\) 0 0
\(151\) 20.9826 1.70754 0.853771 0.520648i \(-0.174310\pi\)
0.853771 + 0.520648i \(0.174310\pi\)
\(152\) 0 0
\(153\) 31.6877 2.56180
\(154\) 0 0
\(155\) 2.01927 0.162192
\(156\) 0 0
\(157\) 7.91794 0.631921 0.315960 0.948772i \(-0.397673\pi\)
0.315960 + 0.948772i \(0.397673\pi\)
\(158\) 0 0
\(159\) −28.9946 −2.29942
\(160\) 0 0
\(161\) −5.74209 −0.452540
\(162\) 0 0
\(163\) 6.71896 0.526270 0.263135 0.964759i \(-0.415244\pi\)
0.263135 + 0.964759i \(0.415244\pi\)
\(164\) 0 0
\(165\) 3.00931 0.234274
\(166\) 0 0
\(167\) −10.9171 −0.844790 −0.422395 0.906412i \(-0.638810\pi\)
−0.422395 + 0.906412i \(0.638810\pi\)
\(168\) 0 0
\(169\) −11.6310 −0.894692
\(170\) 0 0
\(171\) 4.93969 0.377747
\(172\) 0 0
\(173\) −24.2211 −1.84149 −0.920747 0.390159i \(-0.872420\pi\)
−0.920747 + 0.390159i \(0.872420\pi\)
\(174\) 0 0
\(175\) −4.59240 −0.347153
\(176\) 0 0
\(177\) 31.0230 2.33183
\(178\) 0 0
\(179\) −21.3740 −1.59757 −0.798783 0.601619i \(-0.794522\pi\)
−0.798783 + 0.601619i \(0.794522\pi\)
\(180\) 0 0
\(181\) −16.2771 −1.20987 −0.604933 0.796277i \(-0.706800\pi\)
−0.604933 + 0.796277i \(0.706800\pi\)
\(182\) 0 0
\(183\) −1.01038 −0.0746896
\(184\) 0 0
\(185\) 2.72029 0.200000
\(186\) 0 0
\(187\) 28.1484 2.05842
\(188\) 0 0
\(189\) −5.08018 −0.369529
\(190\) 0 0
\(191\) −19.8455 −1.43597 −0.717984 0.696060i \(-0.754935\pi\)
−0.717984 + 0.696060i \(0.754935\pi\)
\(192\) 0 0
\(193\) −18.2372 −1.31274 −0.656371 0.754438i \(-0.727910\pi\)
−0.656371 + 0.754438i \(0.727910\pi\)
\(194\) 0 0
\(195\) −0.802427 −0.0574630
\(196\) 0 0
\(197\) −10.7045 −0.762666 −0.381333 0.924438i \(-0.624535\pi\)
−0.381333 + 0.924438i \(0.624535\pi\)
\(198\) 0 0
\(199\) −7.75540 −0.549766 −0.274883 0.961478i \(-0.588639\pi\)
−0.274883 + 0.961478i \(0.588639\pi\)
\(200\) 0 0
\(201\) −33.4609 −2.36015
\(202\) 0 0
\(203\) −4.80086 −0.336954
\(204\) 0 0
\(205\) −0.757038 −0.0528738
\(206\) 0 0
\(207\) −30.5157 −2.12099
\(208\) 0 0
\(209\) 4.38796 0.303522
\(210\) 0 0
\(211\) −26.6690 −1.83597 −0.917985 0.396615i \(-0.870185\pi\)
−0.917985 + 0.396615i \(0.870185\pi\)
\(212\) 0 0
\(213\) −20.4850 −1.40361
\(214\) 0 0
\(215\) −1.34808 −0.0919380
\(216\) 0 0
\(217\) −7.71150 −0.523491
\(218\) 0 0
\(219\) 39.5442 2.67215
\(220\) 0 0
\(221\) −7.50574 −0.504891
\(222\) 0 0
\(223\) 12.3667 0.828135 0.414067 0.910246i \(-0.364108\pi\)
0.414067 + 0.910246i \(0.364108\pi\)
\(224\) 0 0
\(225\) −24.4058 −1.62705
\(226\) 0 0
\(227\) 16.9197 1.12300 0.561499 0.827477i \(-0.310225\pi\)
0.561499 + 0.827477i \(0.310225\pi\)
\(228\) 0 0
\(229\) 16.3415 1.07988 0.539939 0.841704i \(-0.318447\pi\)
0.539939 + 0.841704i \(0.318447\pi\)
\(230\) 0 0
\(231\) −11.4924 −0.756144
\(232\) 0 0
\(233\) −8.98952 −0.588923 −0.294461 0.955663i \(-0.595140\pi\)
−0.294461 + 0.955663i \(0.595140\pi\)
\(234\) 0 0
\(235\) −2.14539 −0.139950
\(236\) 0 0
\(237\) 2.81775 0.183032
\(238\) 0 0
\(239\) 19.1449 1.23838 0.619191 0.785240i \(-0.287461\pi\)
0.619191 + 0.785240i \(0.287461\pi\)
\(240\) 0 0
\(241\) −10.0048 −0.644466 −0.322233 0.946660i \(-0.604433\pi\)
−0.322233 + 0.946660i \(0.604433\pi\)
\(242\) 0 0
\(243\) 14.7583 0.946743
\(244\) 0 0
\(245\) 1.49345 0.0954129
\(246\) 0 0
\(247\) −1.17004 −0.0744482
\(248\) 0 0
\(249\) −17.7801 −1.12677
\(250\) 0 0
\(251\) 4.33666 0.273727 0.136864 0.990590i \(-0.456298\pi\)
0.136864 + 0.990590i \(0.456298\pi\)
\(252\) 0 0
\(253\) −27.1074 −1.70422
\(254\) 0 0
\(255\) 4.39941 0.275502
\(256\) 0 0
\(257\) 28.4324 1.77356 0.886782 0.462187i \(-0.152935\pi\)
0.886782 + 0.462187i \(0.152935\pi\)
\(258\) 0 0
\(259\) −10.3886 −0.645519
\(260\) 0 0
\(261\) −25.5136 −1.57926
\(262\) 0 0
\(263\) −17.4259 −1.07453 −0.537263 0.843415i \(-0.680542\pi\)
−0.537263 + 0.843415i \(0.680542\pi\)
\(264\) 0 0
\(265\) −2.50447 −0.153849
\(266\) 0 0
\(267\) −16.5513 −1.01292
\(268\) 0 0
\(269\) −25.8170 −1.57409 −0.787045 0.616895i \(-0.788390\pi\)
−0.787045 + 0.616895i \(0.788390\pi\)
\(270\) 0 0
\(271\) −23.2688 −1.41348 −0.706739 0.707475i \(-0.749834\pi\)
−0.706739 + 0.707475i \(0.749834\pi\)
\(272\) 0 0
\(273\) 3.06443 0.185468
\(274\) 0 0
\(275\) −21.6799 −1.30735
\(276\) 0 0
\(277\) 11.8827 0.713962 0.356981 0.934112i \(-0.383806\pi\)
0.356981 + 0.934112i \(0.383806\pi\)
\(278\) 0 0
\(279\) −40.9820 −2.45353
\(280\) 0 0
\(281\) −10.6975 −0.638157 −0.319079 0.947728i \(-0.603373\pi\)
−0.319079 + 0.947728i \(0.603373\pi\)
\(282\) 0 0
\(283\) 9.06296 0.538737 0.269368 0.963037i \(-0.413185\pi\)
0.269368 + 0.963037i \(0.413185\pi\)
\(284\) 0 0
\(285\) 0.685809 0.0406238
\(286\) 0 0
\(287\) 2.89109 0.170656
\(288\) 0 0
\(289\) 24.1512 1.42066
\(290\) 0 0
\(291\) 29.5791 1.73396
\(292\) 0 0
\(293\) 28.2216 1.64872 0.824361 0.566064i \(-0.191535\pi\)
0.824361 + 0.566064i \(0.191535\pi\)
\(294\) 0 0
\(295\) 2.67969 0.156017
\(296\) 0 0
\(297\) −23.9826 −1.39161
\(298\) 0 0
\(299\) 7.22814 0.418014
\(300\) 0 0
\(301\) 5.14823 0.296739
\(302\) 0 0
\(303\) −3.21986 −0.184976
\(304\) 0 0
\(305\) −0.0872742 −0.00499731
\(306\) 0 0
\(307\) 30.9355 1.76558 0.882791 0.469765i \(-0.155661\pi\)
0.882791 + 0.469765i \(0.155661\pi\)
\(308\) 0 0
\(309\) 41.9766 2.38796
\(310\) 0 0
\(311\) −3.88612 −0.220361 −0.110181 0.993912i \(-0.535143\pi\)
−0.110181 + 0.993912i \(0.535143\pi\)
\(312\) 0 0
\(313\) −5.03801 −0.284765 −0.142383 0.989812i \(-0.545476\pi\)
−0.142383 + 0.989812i \(0.545476\pi\)
\(314\) 0 0
\(315\) −1.11750 −0.0629639
\(316\) 0 0
\(317\) 14.8736 0.835386 0.417693 0.908588i \(-0.362839\pi\)
0.417693 + 0.908588i \(0.362839\pi\)
\(318\) 0 0
\(319\) −22.6640 −1.26894
\(320\) 0 0
\(321\) 36.2523 2.02341
\(322\) 0 0
\(323\) 6.41492 0.356936
\(324\) 0 0
\(325\) 5.78091 0.320667
\(326\) 0 0
\(327\) −5.37193 −0.297068
\(328\) 0 0
\(329\) 8.19314 0.451703
\(330\) 0 0
\(331\) 28.8329 1.58480 0.792399 0.610003i \(-0.208832\pi\)
0.792399 + 0.610003i \(0.208832\pi\)
\(332\) 0 0
\(333\) −55.2094 −3.02545
\(334\) 0 0
\(335\) −2.89026 −0.157912
\(336\) 0 0
\(337\) −30.1520 −1.64249 −0.821243 0.570579i \(-0.806719\pi\)
−0.821243 + 0.570579i \(0.806719\pi\)
\(338\) 0 0
\(339\) −29.1360 −1.58245
\(340\) 0 0
\(341\) −36.4046 −1.97142
\(342\) 0 0
\(343\) −12.2099 −0.659270
\(344\) 0 0
\(345\) −4.23670 −0.228096
\(346\) 0 0
\(347\) 14.0836 0.756045 0.378023 0.925796i \(-0.376604\pi\)
0.378023 + 0.925796i \(0.376604\pi\)
\(348\) 0 0
\(349\) −2.47266 −0.132358 −0.0661792 0.997808i \(-0.521081\pi\)
−0.0661792 + 0.997808i \(0.521081\pi\)
\(350\) 0 0
\(351\) 6.39493 0.341336
\(352\) 0 0
\(353\) 8.95360 0.476552 0.238276 0.971197i \(-0.423418\pi\)
0.238276 + 0.971197i \(0.423418\pi\)
\(354\) 0 0
\(355\) −1.76944 −0.0939123
\(356\) 0 0
\(357\) −16.8011 −0.889210
\(358\) 0 0
\(359\) 7.84896 0.414252 0.207126 0.978314i \(-0.433589\pi\)
0.207126 + 0.978314i \(0.433589\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −23.2583 −1.22074
\(364\) 0 0
\(365\) 3.41572 0.178787
\(366\) 0 0
\(367\) −26.8354 −1.40079 −0.700397 0.713753i \(-0.746994\pi\)
−0.700397 + 0.713753i \(0.746994\pi\)
\(368\) 0 0
\(369\) 15.3644 0.799839
\(370\) 0 0
\(371\) 9.56447 0.496563
\(372\) 0 0
\(373\) −19.5460 −1.01205 −0.506027 0.862517i \(-0.668887\pi\)
−0.506027 + 0.862517i \(0.668887\pi\)
\(374\) 0 0
\(375\) −6.81747 −0.352052
\(376\) 0 0
\(377\) 6.04332 0.311247
\(378\) 0 0
\(379\) 8.31232 0.426975 0.213488 0.976946i \(-0.431518\pi\)
0.213488 + 0.976946i \(0.431518\pi\)
\(380\) 0 0
\(381\) −19.2087 −0.984092
\(382\) 0 0
\(383\) −4.08070 −0.208514 −0.104257 0.994550i \(-0.533246\pi\)
−0.104257 + 0.994550i \(0.533246\pi\)
\(384\) 0 0
\(385\) −0.992682 −0.0505918
\(386\) 0 0
\(387\) 27.3597 1.39077
\(388\) 0 0
\(389\) −18.2795 −0.926808 −0.463404 0.886147i \(-0.653372\pi\)
−0.463404 + 0.886147i \(0.653372\pi\)
\(390\) 0 0
\(391\) −39.6292 −2.00413
\(392\) 0 0
\(393\) −25.0445 −1.26333
\(394\) 0 0
\(395\) 0.243389 0.0122462
\(396\) 0 0
\(397\) 5.50119 0.276097 0.138048 0.990426i \(-0.455917\pi\)
0.138048 + 0.990426i \(0.455917\pi\)
\(398\) 0 0
\(399\) −2.61907 −0.131118
\(400\) 0 0
\(401\) −4.46487 −0.222965 −0.111482 0.993766i \(-0.535560\pi\)
−0.111482 + 0.993766i \(0.535560\pi\)
\(402\) 0 0
\(403\) 9.70724 0.483552
\(404\) 0 0
\(405\) −0.141519 −0.00703213
\(406\) 0 0
\(407\) −49.0429 −2.43097
\(408\) 0 0
\(409\) 13.5789 0.671432 0.335716 0.941963i \(-0.391022\pi\)
0.335716 + 0.941963i \(0.391022\pi\)
\(410\) 0 0
\(411\) 8.99847 0.443862
\(412\) 0 0
\(413\) −10.2336 −0.503562
\(414\) 0 0
\(415\) −1.53580 −0.0753895
\(416\) 0 0
\(417\) −30.0778 −1.47292
\(418\) 0 0
\(419\) 30.8314 1.50621 0.753106 0.657899i \(-0.228555\pi\)
0.753106 + 0.657899i \(0.228555\pi\)
\(420\) 0 0
\(421\) −16.4084 −0.799697 −0.399849 0.916581i \(-0.630937\pi\)
−0.399849 + 0.916581i \(0.630937\pi\)
\(422\) 0 0
\(423\) 43.5416 2.11706
\(424\) 0 0
\(425\) −31.6946 −1.53741
\(426\) 0 0
\(427\) 0.333296 0.0161293
\(428\) 0 0
\(429\) 14.4666 0.698455
\(430\) 0 0
\(431\) −40.2586 −1.93919 −0.969594 0.244718i \(-0.921305\pi\)
−0.969594 + 0.244718i \(0.921305\pi\)
\(432\) 0 0
\(433\) 0.477039 0.0229250 0.0114625 0.999934i \(-0.496351\pi\)
0.0114625 + 0.999934i \(0.496351\pi\)
\(434\) 0 0
\(435\) −3.54223 −0.169837
\(436\) 0 0
\(437\) −6.17766 −0.295518
\(438\) 0 0
\(439\) −26.8587 −1.28190 −0.640948 0.767584i \(-0.721459\pi\)
−0.640948 + 0.767584i \(0.721459\pi\)
\(440\) 0 0
\(441\) −30.3101 −1.44334
\(442\) 0 0
\(443\) −24.0326 −1.14182 −0.570912 0.821011i \(-0.693410\pi\)
−0.570912 + 0.821011i \(0.693410\pi\)
\(444\) 0 0
\(445\) −1.42966 −0.0677724
\(446\) 0 0
\(447\) 19.7060 0.932063
\(448\) 0 0
\(449\) −40.9547 −1.93277 −0.966386 0.257097i \(-0.917234\pi\)
−0.966386 + 0.257097i \(0.917234\pi\)
\(450\) 0 0
\(451\) 13.6483 0.642674
\(452\) 0 0
\(453\) −59.1237 −2.77787
\(454\) 0 0
\(455\) 0.264698 0.0124092
\(456\) 0 0
\(457\) 2.32008 0.108529 0.0542644 0.998527i \(-0.482719\pi\)
0.0542644 + 0.998527i \(0.482719\pi\)
\(458\) 0 0
\(459\) −35.0610 −1.63651
\(460\) 0 0
\(461\) 4.92454 0.229359 0.114679 0.993403i \(-0.463416\pi\)
0.114679 + 0.993403i \(0.463416\pi\)
\(462\) 0 0
\(463\) −13.1476 −0.611021 −0.305511 0.952189i \(-0.598827\pi\)
−0.305511 + 0.952189i \(0.598827\pi\)
\(464\) 0 0
\(465\) −5.68979 −0.263858
\(466\) 0 0
\(467\) −16.5271 −0.764784 −0.382392 0.924000i \(-0.624900\pi\)
−0.382392 + 0.924000i \(0.624900\pi\)
\(468\) 0 0
\(469\) 11.0378 0.509677
\(470\) 0 0
\(471\) −22.3107 −1.02802
\(472\) 0 0
\(473\) 24.3039 1.11749
\(474\) 0 0
\(475\) −4.94076 −0.226698
\(476\) 0 0
\(477\) 50.8294 2.32732
\(478\) 0 0
\(479\) 20.2636 0.925869 0.462934 0.886393i \(-0.346797\pi\)
0.462934 + 0.886393i \(0.346797\pi\)
\(480\) 0 0
\(481\) 13.0772 0.596270
\(482\) 0 0
\(483\) 16.1797 0.736204
\(484\) 0 0
\(485\) 2.55496 0.116015
\(486\) 0 0
\(487\) 27.7595 1.25791 0.628953 0.777444i \(-0.283484\pi\)
0.628953 + 0.777444i \(0.283484\pi\)
\(488\) 0 0
\(489\) −18.9323 −0.856149
\(490\) 0 0
\(491\) −20.9007 −0.943235 −0.471617 0.881803i \(-0.656330\pi\)
−0.471617 + 0.881803i \(0.656330\pi\)
\(492\) 0 0
\(493\) −33.1333 −1.49225
\(494\) 0 0
\(495\) −5.27550 −0.237116
\(496\) 0 0
\(497\) 6.75742 0.303112
\(498\) 0 0
\(499\) 18.9602 0.848775 0.424387 0.905481i \(-0.360490\pi\)
0.424387 + 0.905481i \(0.360490\pi\)
\(500\) 0 0
\(501\) 30.7616 1.37433
\(502\) 0 0
\(503\) 9.88996 0.440972 0.220486 0.975390i \(-0.429236\pi\)
0.220486 + 0.975390i \(0.429236\pi\)
\(504\) 0 0
\(505\) −0.278123 −0.0123763
\(506\) 0 0
\(507\) 32.7732 1.45551
\(508\) 0 0
\(509\) −5.67539 −0.251557 −0.125779 0.992058i \(-0.540143\pi\)
−0.125779 + 0.992058i \(0.540143\pi\)
\(510\) 0 0
\(511\) −13.0445 −0.577054
\(512\) 0 0
\(513\) −5.46555 −0.241310
\(514\) 0 0
\(515\) 3.62583 0.159773
\(516\) 0 0
\(517\) 38.6783 1.70107
\(518\) 0 0
\(519\) 68.2488 2.99579
\(520\) 0 0
\(521\) −31.6584 −1.38698 −0.693490 0.720466i \(-0.743928\pi\)
−0.693490 + 0.720466i \(0.743928\pi\)
\(522\) 0 0
\(523\) −1.52863 −0.0668423 −0.0334212 0.999441i \(-0.510640\pi\)
−0.0334212 + 0.999441i \(0.510640\pi\)
\(524\) 0 0
\(525\) 12.9402 0.564757
\(526\) 0 0
\(527\) −53.2211 −2.31835
\(528\) 0 0
\(529\) 15.1635 0.659282
\(530\) 0 0
\(531\) −54.3854 −2.36012
\(532\) 0 0
\(533\) −3.63931 −0.157636
\(534\) 0 0
\(535\) 3.13138 0.135381
\(536\) 0 0
\(537\) 60.2264 2.59896
\(538\) 0 0
\(539\) −26.9247 −1.15973
\(540\) 0 0
\(541\) −28.5133 −1.22588 −0.612942 0.790128i \(-0.710014\pi\)
−0.612942 + 0.790128i \(0.710014\pi\)
\(542\) 0 0
\(543\) 45.8646 1.96824
\(544\) 0 0
\(545\) −0.464013 −0.0198761
\(546\) 0 0
\(547\) −5.90948 −0.252671 −0.126336 0.991988i \(-0.540322\pi\)
−0.126336 + 0.991988i \(0.540322\pi\)
\(548\) 0 0
\(549\) 1.77127 0.0755958
\(550\) 0 0
\(551\) −5.16503 −0.220038
\(552\) 0 0
\(553\) −0.929492 −0.0395260
\(554\) 0 0
\(555\) −7.66508 −0.325364
\(556\) 0 0
\(557\) −22.9039 −0.970467 −0.485234 0.874385i \(-0.661265\pi\)
−0.485234 + 0.874385i \(0.661265\pi\)
\(558\) 0 0
\(559\) −6.48060 −0.274100
\(560\) 0 0
\(561\) −79.3151 −3.34869
\(562\) 0 0
\(563\) −11.6582 −0.491333 −0.245667 0.969354i \(-0.579007\pi\)
−0.245667 + 0.969354i \(0.579007\pi\)
\(564\) 0 0
\(565\) −2.51669 −0.105878
\(566\) 0 0
\(567\) 0.540454 0.0226969
\(568\) 0 0
\(569\) 1.57711 0.0661160 0.0330580 0.999453i \(-0.489475\pi\)
0.0330580 + 0.999453i \(0.489475\pi\)
\(570\) 0 0
\(571\) 30.3873 1.27167 0.635834 0.771826i \(-0.280656\pi\)
0.635834 + 0.771826i \(0.280656\pi\)
\(572\) 0 0
\(573\) 55.9195 2.33607
\(574\) 0 0
\(575\) 30.5224 1.27287
\(576\) 0 0
\(577\) −24.6605 −1.02663 −0.513315 0.858200i \(-0.671583\pi\)
−0.513315 + 0.858200i \(0.671583\pi\)
\(578\) 0 0
\(579\) 51.3878 2.13560
\(580\) 0 0
\(581\) 5.86515 0.243327
\(582\) 0 0
\(583\) 45.1521 1.87001
\(584\) 0 0
\(585\) 1.40671 0.0581602
\(586\) 0 0
\(587\) −26.9821 −1.11367 −0.556835 0.830623i \(-0.687985\pi\)
−0.556835 + 0.830623i \(0.687985\pi\)
\(588\) 0 0
\(589\) −8.29647 −0.341850
\(590\) 0 0
\(591\) 30.1626 1.24073
\(592\) 0 0
\(593\) −15.7153 −0.645351 −0.322676 0.946510i \(-0.604582\pi\)
−0.322676 + 0.946510i \(0.604582\pi\)
\(594\) 0 0
\(595\) −1.45124 −0.0594949
\(596\) 0 0
\(597\) 21.8527 0.894373
\(598\) 0 0
\(599\) 17.2265 0.703856 0.351928 0.936027i \(-0.385526\pi\)
0.351928 + 0.936027i \(0.385526\pi\)
\(600\) 0 0
\(601\) −36.2061 −1.47688 −0.738438 0.674321i \(-0.764436\pi\)
−0.738438 + 0.674321i \(0.764436\pi\)
\(602\) 0 0
\(603\) 58.6591 2.38878
\(604\) 0 0
\(605\) −2.00899 −0.0816770
\(606\) 0 0
\(607\) 10.7548 0.436525 0.218263 0.975890i \(-0.429961\pi\)
0.218263 + 0.975890i \(0.429961\pi\)
\(608\) 0 0
\(609\) 13.5276 0.548166
\(610\) 0 0
\(611\) −10.3135 −0.417241
\(612\) 0 0
\(613\) −5.77027 −0.233059 −0.116530 0.993187i \(-0.537177\pi\)
−0.116530 + 0.993187i \(0.537177\pi\)
\(614\) 0 0
\(615\) 2.13314 0.0860165
\(616\) 0 0
\(617\) −1.48806 −0.0599069 −0.0299535 0.999551i \(-0.509536\pi\)
−0.0299535 + 0.999551i \(0.509536\pi\)
\(618\) 0 0
\(619\) −38.1127 −1.53188 −0.765940 0.642913i \(-0.777726\pi\)
−0.765940 + 0.642913i \(0.777726\pi\)
\(620\) 0 0
\(621\) 33.7643 1.35491
\(622\) 0 0
\(623\) 5.45980 0.218742
\(624\) 0 0
\(625\) 24.1149 0.964597
\(626\) 0 0
\(627\) −12.3642 −0.493777
\(628\) 0 0
\(629\) −71.6975 −2.85877
\(630\) 0 0
\(631\) 12.2918 0.489329 0.244664 0.969608i \(-0.421322\pi\)
0.244664 + 0.969608i \(0.421322\pi\)
\(632\) 0 0
\(633\) 75.1465 2.98680
\(634\) 0 0
\(635\) −1.65920 −0.0658432
\(636\) 0 0
\(637\) 7.17945 0.284460
\(638\) 0 0
\(639\) 35.9116 1.42064
\(640\) 0 0
\(641\) −36.1875 −1.42932 −0.714659 0.699473i \(-0.753418\pi\)
−0.714659 + 0.699473i \(0.753418\pi\)
\(642\) 0 0
\(643\) −19.1619 −0.755672 −0.377836 0.925872i \(-0.623332\pi\)
−0.377836 + 0.925872i \(0.623332\pi\)
\(644\) 0 0
\(645\) 3.79853 0.149567
\(646\) 0 0
\(647\) 41.0331 1.61318 0.806589 0.591113i \(-0.201311\pi\)
0.806589 + 0.591113i \(0.201311\pi\)
\(648\) 0 0
\(649\) −48.3109 −1.89637
\(650\) 0 0
\(651\) 21.7290 0.851628
\(652\) 0 0
\(653\) 9.30259 0.364038 0.182019 0.983295i \(-0.441737\pi\)
0.182019 + 0.983295i \(0.441737\pi\)
\(654\) 0 0
\(655\) −2.16328 −0.0845262
\(656\) 0 0
\(657\) −69.3235 −2.70457
\(658\) 0 0
\(659\) 11.9866 0.466931 0.233466 0.972365i \(-0.424993\pi\)
0.233466 + 0.972365i \(0.424993\pi\)
\(660\) 0 0
\(661\) −15.0263 −0.584455 −0.292228 0.956349i \(-0.594396\pi\)
−0.292228 + 0.956349i \(0.594396\pi\)
\(662\) 0 0
\(663\) 21.1493 0.821369
\(664\) 0 0
\(665\) −0.226229 −0.00877277
\(666\) 0 0
\(667\) 31.9078 1.23548
\(668\) 0 0
\(669\) −34.8462 −1.34723
\(670\) 0 0
\(671\) 1.57343 0.0607416
\(672\) 0 0
\(673\) −0.447914 −0.0172658 −0.00863291 0.999963i \(-0.502748\pi\)
−0.00863291 + 0.999963i \(0.502748\pi\)
\(674\) 0 0
\(675\) 27.0040 1.03938
\(676\) 0 0
\(677\) −15.7839 −0.606624 −0.303312 0.952891i \(-0.598092\pi\)
−0.303312 + 0.952891i \(0.598092\pi\)
\(678\) 0 0
\(679\) −9.75728 −0.374450
\(680\) 0 0
\(681\) −47.6753 −1.82692
\(682\) 0 0
\(683\) 41.9490 1.60513 0.802566 0.596563i \(-0.203467\pi\)
0.802566 + 0.596563i \(0.203467\pi\)
\(684\) 0 0
\(685\) 0.777264 0.0296977
\(686\) 0 0
\(687\) −46.0462 −1.75677
\(688\) 0 0
\(689\) −12.0398 −0.458678
\(690\) 0 0
\(691\) 12.9636 0.493160 0.246580 0.969122i \(-0.420693\pi\)
0.246580 + 0.969122i \(0.420693\pi\)
\(692\) 0 0
\(693\) 20.1469 0.765318
\(694\) 0 0
\(695\) −2.59804 −0.0985492
\(696\) 0 0
\(697\) 19.9529 0.755772
\(698\) 0 0
\(699\) 25.3302 0.958075
\(700\) 0 0
\(701\) −41.7159 −1.57559 −0.787795 0.615938i \(-0.788777\pi\)
−0.787795 + 0.615938i \(0.788777\pi\)
\(702\) 0 0
\(703\) −11.1767 −0.421537
\(704\) 0 0
\(705\) 6.04516 0.227674
\(706\) 0 0
\(707\) 1.06214 0.0399458
\(708\) 0 0
\(709\) −17.9243 −0.673160 −0.336580 0.941655i \(-0.609270\pi\)
−0.336580 + 0.941655i \(0.609270\pi\)
\(710\) 0 0
\(711\) −4.93969 −0.185253
\(712\) 0 0
\(713\) 51.2528 1.91943
\(714\) 0 0
\(715\) 1.24959 0.0467320
\(716\) 0 0
\(717\) −53.9455 −2.01463
\(718\) 0 0
\(719\) −25.7196 −0.959180 −0.479590 0.877493i \(-0.659215\pi\)
−0.479590 + 0.877493i \(0.659215\pi\)
\(720\) 0 0
\(721\) −13.8469 −0.515684
\(722\) 0 0
\(723\) 28.1910 1.04843
\(724\) 0 0
\(725\) 25.5192 0.947759
\(726\) 0 0
\(727\) −39.8235 −1.47697 −0.738485 0.674270i \(-0.764459\pi\)
−0.738485 + 0.674270i \(0.764459\pi\)
\(728\) 0 0
\(729\) −43.3294 −1.60479
\(730\) 0 0
\(731\) 35.5307 1.31415
\(732\) 0 0
\(733\) 32.2629 1.19166 0.595829 0.803111i \(-0.296823\pi\)
0.595829 + 0.803111i \(0.296823\pi\)
\(734\) 0 0
\(735\) −4.20816 −0.155220
\(736\) 0 0
\(737\) 52.1073 1.91940
\(738\) 0 0
\(739\) −51.8038 −1.90563 −0.952816 0.303548i \(-0.901829\pi\)
−0.952816 + 0.303548i \(0.901829\pi\)
\(740\) 0 0
\(741\) 3.29689 0.121114
\(742\) 0 0
\(743\) −14.9802 −0.549570 −0.274785 0.961506i \(-0.588607\pi\)
−0.274785 + 0.961506i \(0.588607\pi\)
\(744\) 0 0
\(745\) 1.70215 0.0623621
\(746\) 0 0
\(747\) 31.1697 1.14044
\(748\) 0 0
\(749\) −11.9586 −0.436957
\(750\) 0 0
\(751\) −12.6191 −0.460477 −0.230238 0.973134i \(-0.573951\pi\)
−0.230238 + 0.973134i \(0.573951\pi\)
\(752\) 0 0
\(753\) −12.2196 −0.445307
\(754\) 0 0
\(755\) −5.10695 −0.185861
\(756\) 0 0
\(757\) −10.6477 −0.386997 −0.193499 0.981101i \(-0.561984\pi\)
−0.193499 + 0.981101i \(0.561984\pi\)
\(758\) 0 0
\(759\) 76.3816 2.77248
\(760\) 0 0
\(761\) 26.9322 0.976293 0.488146 0.872762i \(-0.337673\pi\)
0.488146 + 0.872762i \(0.337673\pi\)
\(762\) 0 0
\(763\) 1.77204 0.0641523
\(764\) 0 0
\(765\) −7.71245 −0.278844
\(766\) 0 0
\(767\) 12.8821 0.465144
\(768\) 0 0
\(769\) 21.3676 0.770536 0.385268 0.922805i \(-0.374109\pi\)
0.385268 + 0.922805i \(0.374109\pi\)
\(770\) 0 0
\(771\) −80.1153 −2.88528
\(772\) 0 0
\(773\) −10.1433 −0.364829 −0.182415 0.983222i \(-0.558391\pi\)
−0.182415 + 0.983222i \(0.558391\pi\)
\(774\) 0 0
\(775\) 40.9909 1.47244
\(776\) 0 0
\(777\) 29.2726 1.05015
\(778\) 0 0
\(779\) 3.11040 0.111442
\(780\) 0 0
\(781\) 31.9005 1.14149
\(782\) 0 0
\(783\) 28.2297 1.00885
\(784\) 0 0
\(785\) −1.92714 −0.0687827
\(786\) 0 0
\(787\) 28.2597 1.00735 0.503675 0.863893i \(-0.331981\pi\)
0.503675 + 0.863893i \(0.331981\pi\)
\(788\) 0 0
\(789\) 49.1017 1.74807
\(790\) 0 0
\(791\) 9.61113 0.341732
\(792\) 0 0
\(793\) −0.419553 −0.0148988
\(794\) 0 0
\(795\) 7.05697 0.250285
\(796\) 0 0
\(797\) 53.3864 1.89104 0.945522 0.325557i \(-0.105552\pi\)
0.945522 + 0.325557i \(0.105552\pi\)
\(798\) 0 0
\(799\) 56.5452 2.00043
\(800\) 0 0
\(801\) 29.0155 1.02521
\(802\) 0 0
\(803\) −61.5806 −2.17313
\(804\) 0 0
\(805\) 1.39756 0.0492576
\(806\) 0 0
\(807\) 72.7457 2.56077
\(808\) 0 0
\(809\) −1.13616 −0.0399453 −0.0199726 0.999801i \(-0.506358\pi\)
−0.0199726 + 0.999801i \(0.506358\pi\)
\(810\) 0 0
\(811\) −39.5890 −1.39016 −0.695078 0.718934i \(-0.744630\pi\)
−0.695078 + 0.718934i \(0.744630\pi\)
\(812\) 0 0
\(813\) 65.5655 2.29948
\(814\) 0 0
\(815\) −1.63532 −0.0572829
\(816\) 0 0
\(817\) 5.53876 0.193777
\(818\) 0 0
\(819\) −5.37215 −0.187718
\(820\) 0 0
\(821\) −11.1082 −0.387677 −0.193839 0.981033i \(-0.562094\pi\)
−0.193839 + 0.981033i \(0.562094\pi\)
\(822\) 0 0
\(823\) −8.81783 −0.307370 −0.153685 0.988120i \(-0.549114\pi\)
−0.153685 + 0.988120i \(0.549114\pi\)
\(824\) 0 0
\(825\) 61.0884 2.12682
\(826\) 0 0
\(827\) 48.3086 1.67985 0.839927 0.542699i \(-0.182598\pi\)
0.839927 + 0.542699i \(0.182598\pi\)
\(828\) 0 0
\(829\) −20.9899 −0.729008 −0.364504 0.931202i \(-0.618761\pi\)
−0.364504 + 0.931202i \(0.618761\pi\)
\(830\) 0 0
\(831\) −33.4824 −1.16149
\(832\) 0 0
\(833\) −39.3622 −1.36382
\(834\) 0 0
\(835\) 2.65710 0.0919528
\(836\) 0 0
\(837\) 45.3447 1.56734
\(838\) 0 0
\(839\) −12.6224 −0.435774 −0.217887 0.975974i \(-0.569916\pi\)
−0.217887 + 0.975974i \(0.569916\pi\)
\(840\) 0 0
\(841\) −2.32244 −0.0800841
\(842\) 0 0
\(843\) 30.1427 1.03817
\(844\) 0 0
\(845\) 2.83086 0.0973846
\(846\) 0 0
\(847\) 7.67224 0.263621
\(848\) 0 0
\(849\) −25.5371 −0.876431
\(850\) 0 0
\(851\) 69.0458 2.36686
\(852\) 0 0
\(853\) 28.2597 0.967592 0.483796 0.875181i \(-0.339258\pi\)
0.483796 + 0.875181i \(0.339258\pi\)
\(854\) 0 0
\(855\) −1.20227 −0.0411167
\(856\) 0 0
\(857\) 7.10377 0.242660 0.121330 0.992612i \(-0.461284\pi\)
0.121330 + 0.992612i \(0.461284\pi\)
\(858\) 0 0
\(859\) 25.6812 0.876232 0.438116 0.898918i \(-0.355646\pi\)
0.438116 + 0.898918i \(0.355646\pi\)
\(860\) 0 0
\(861\) −8.14636 −0.277627
\(862\) 0 0
\(863\) −52.1636 −1.77567 −0.887835 0.460161i \(-0.847792\pi\)
−0.887835 + 0.460161i \(0.847792\pi\)
\(864\) 0 0
\(865\) 5.89515 0.200441
\(866\) 0 0
\(867\) −68.0518 −2.31116
\(868\) 0 0
\(869\) −4.38796 −0.148851
\(870\) 0 0
\(871\) −13.8944 −0.470792
\(872\) 0 0
\(873\) −51.8540 −1.75499
\(874\) 0 0
\(875\) 2.24888 0.0760262
\(876\) 0 0
\(877\) −25.2518 −0.852692 −0.426346 0.904560i \(-0.640199\pi\)
−0.426346 + 0.904560i \(0.640199\pi\)
\(878\) 0 0
\(879\) −79.5212 −2.68218
\(880\) 0 0
\(881\) −53.7053 −1.80938 −0.904689 0.426072i \(-0.859897\pi\)
−0.904689 + 0.426072i \(0.859897\pi\)
\(882\) 0 0
\(883\) −7.33046 −0.246690 −0.123345 0.992364i \(-0.539362\pi\)
−0.123345 + 0.992364i \(0.539362\pi\)
\(884\) 0 0
\(885\) −7.55067 −0.253813
\(886\) 0 0
\(887\) 46.5751 1.56384 0.781920 0.623379i \(-0.214241\pi\)
0.781920 + 0.623379i \(0.214241\pi\)
\(888\) 0 0
\(889\) 6.33639 0.212516
\(890\) 0 0
\(891\) 2.55138 0.0854746
\(892\) 0 0
\(893\) 8.81464 0.294971
\(894\) 0 0
\(895\) 5.20220 0.173890
\(896\) 0 0
\(897\) −20.3671 −0.680036
\(898\) 0 0
\(899\) 42.8515 1.42918
\(900\) 0 0
\(901\) 66.0095 2.19909
\(902\) 0 0
\(903\) −14.5064 −0.482743
\(904\) 0 0
\(905\) 3.96167 0.131690
\(906\) 0 0
\(907\) 52.2496 1.73492 0.867460 0.497508i \(-0.165751\pi\)
0.867460 + 0.497508i \(0.165751\pi\)
\(908\) 0 0
\(909\) 5.64462 0.187220
\(910\) 0 0
\(911\) −39.5725 −1.31109 −0.655547 0.755154i \(-0.727562\pi\)
−0.655547 + 0.755154i \(0.727562\pi\)
\(912\) 0 0
\(913\) 27.6883 0.916349
\(914\) 0 0
\(915\) 0.245916 0.00812975
\(916\) 0 0
\(917\) 8.26145 0.272817
\(918\) 0 0
\(919\) −20.1585 −0.664968 −0.332484 0.943109i \(-0.607887\pi\)
−0.332484 + 0.943109i \(0.607887\pi\)
\(920\) 0 0
\(921\) −87.1684 −2.87230
\(922\) 0 0
\(923\) −8.50624 −0.279986
\(924\) 0 0
\(925\) 55.2214 1.81567
\(926\) 0 0
\(927\) −73.5876 −2.41694
\(928\) 0 0
\(929\) 11.9692 0.392696 0.196348 0.980534i \(-0.437092\pi\)
0.196348 + 0.980534i \(0.437092\pi\)
\(930\) 0 0
\(931\) −6.13604 −0.201101
\(932\) 0 0
\(933\) 10.9501 0.358490
\(934\) 0 0
\(935\) −6.85103 −0.224053
\(936\) 0 0
\(937\) 14.8914 0.486480 0.243240 0.969966i \(-0.421790\pi\)
0.243240 + 0.969966i \(0.421790\pi\)
\(938\) 0 0
\(939\) 14.1958 0.463263
\(940\) 0 0
\(941\) −13.8992 −0.453103 −0.226551 0.973999i \(-0.572745\pi\)
−0.226551 + 0.973999i \(0.572745\pi\)
\(942\) 0 0
\(943\) −19.2150 −0.625726
\(944\) 0 0
\(945\) 1.23646 0.0402221
\(946\) 0 0
\(947\) −44.8171 −1.45636 −0.728180 0.685386i \(-0.759633\pi\)
−0.728180 + 0.685386i \(0.759633\pi\)
\(948\) 0 0
\(949\) 16.4204 0.533028
\(950\) 0 0
\(951\) −41.9101 −1.35903
\(952\) 0 0
\(953\) 34.2210 1.10853 0.554264 0.832341i \(-0.313000\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(954\) 0 0
\(955\) 4.83018 0.156301
\(956\) 0 0
\(957\) 63.8613 2.06434
\(958\) 0 0
\(959\) −2.96833 −0.0958525
\(960\) 0 0
\(961\) 37.8313 1.22037
\(962\) 0 0
\(963\) −63.5526 −2.04796
\(964\) 0 0
\(965\) 4.43874 0.142888
\(966\) 0 0
\(967\) 48.2353 1.55114 0.775571 0.631260i \(-0.217462\pi\)
0.775571 + 0.631260i \(0.217462\pi\)
\(968\) 0 0
\(969\) −18.0756 −0.580672
\(970\) 0 0
\(971\) 35.7510 1.14730 0.573652 0.819099i \(-0.305526\pi\)
0.573652 + 0.819099i \(0.305526\pi\)
\(972\) 0 0
\(973\) 9.92179 0.318078
\(974\) 0 0
\(975\) −16.2891 −0.521670
\(976\) 0 0
\(977\) −2.06258 −0.0659876 −0.0329938 0.999456i \(-0.510504\pi\)
−0.0329938 + 0.999456i \(0.510504\pi\)
\(978\) 0 0
\(979\) 25.7747 0.823764
\(980\) 0 0
\(981\) 9.41733 0.300672
\(982\) 0 0
\(983\) −23.1827 −0.739413 −0.369707 0.929149i \(-0.620542\pi\)
−0.369707 + 0.929149i \(0.620542\pi\)
\(984\) 0 0
\(985\) 2.60537 0.0830140
\(986\) 0 0
\(987\) −23.0862 −0.734841
\(988\) 0 0
\(989\) −34.2166 −1.08802
\(990\) 0 0
\(991\) −12.8141 −0.407053 −0.203526 0.979069i \(-0.565240\pi\)
−0.203526 + 0.979069i \(0.565240\pi\)
\(992\) 0 0
\(993\) −81.2437 −2.57819
\(994\) 0 0
\(995\) 1.88758 0.0598404
\(996\) 0 0
\(997\) 30.1866 0.956019 0.478010 0.878355i \(-0.341358\pi\)
0.478010 + 0.878355i \(0.341358\pi\)
\(998\) 0 0
\(999\) 61.0867 1.93270
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 \(a_p\))