Properties

Label 6040.2.a.l.1.6
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.68790\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.325171 q^{3}\) \(+1.00000 q^{5}\) \(+2.31586 q^{7}\) \(-2.89426 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.325171 q^{3}\) \(+1.00000 q^{5}\) \(+2.31586 q^{7}\) \(-2.89426 q^{9}\) \(+0.0563199 q^{11}\) \(-6.43408 q^{13}\) \(+0.325171 q^{15}\) \(+3.42872 q^{17}\) \(-2.17512 q^{19}\) \(+0.753050 q^{21}\) \(-3.43828 q^{23}\) \(+1.00000 q^{25}\) \(-1.91664 q^{27}\) \(+9.17899 q^{29}\) \(-4.04276 q^{31}\) \(+0.0183136 q^{33}\) \(+2.31586 q^{35}\) \(-2.68712 q^{37}\) \(-2.09218 q^{39}\) \(+0.966020 q^{41}\) \(+3.65204 q^{43}\) \(-2.89426 q^{45}\) \(+9.41359 q^{47}\) \(-1.63680 q^{49}\) \(+1.11492 q^{51}\) \(-3.66245 q^{53}\) \(+0.0563199 q^{55}\) \(-0.707288 q^{57}\) \(-8.00799 q^{59}\) \(+0.207095 q^{61}\) \(-6.70271 q^{63}\) \(-6.43408 q^{65}\) \(-3.39983 q^{67}\) \(-1.11803 q^{69}\) \(-5.80306 q^{71}\) \(-6.19683 q^{73}\) \(+0.325171 q^{75}\) \(+0.130429 q^{77}\) \(-13.8221 q^{79}\) \(+8.05955 q^{81}\) \(-6.06544 q^{83}\) \(+3.42872 q^{85}\) \(+2.98474 q^{87}\) \(-5.64338 q^{89}\) \(-14.9004 q^{91}\) \(-1.31459 q^{93}\) \(-2.17512 q^{95}\) \(-7.46595 q^{97}\) \(-0.163005 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.325171 0.187738 0.0938688 0.995585i \(-0.470077\pi\)
0.0938688 + 0.995585i \(0.470077\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.31586 0.875313 0.437656 0.899142i \(-0.355809\pi\)
0.437656 + 0.899142i \(0.355809\pi\)
\(8\) 0 0
\(9\) −2.89426 −0.964755
\(10\) 0 0
\(11\) 0.0563199 0.0169811 0.00849054 0.999964i \(-0.497297\pi\)
0.00849054 + 0.999964i \(0.497297\pi\)
\(12\) 0 0
\(13\) −6.43408 −1.78449 −0.892246 0.451550i \(-0.850871\pi\)
−0.892246 + 0.451550i \(0.850871\pi\)
\(14\) 0 0
\(15\) 0.325171 0.0839588
\(16\) 0 0
\(17\) 3.42872 0.831586 0.415793 0.909459i \(-0.363504\pi\)
0.415793 + 0.909459i \(0.363504\pi\)
\(18\) 0 0
\(19\) −2.17512 −0.499008 −0.249504 0.968374i \(-0.580268\pi\)
−0.249504 + 0.968374i \(0.580268\pi\)
\(20\) 0 0
\(21\) 0.753050 0.164329
\(22\) 0 0
\(23\) −3.43828 −0.716931 −0.358466 0.933543i \(-0.616700\pi\)
−0.358466 + 0.933543i \(0.616700\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.91664 −0.368858
\(28\) 0 0
\(29\) 9.17899 1.70450 0.852248 0.523138i \(-0.175239\pi\)
0.852248 + 0.523138i \(0.175239\pi\)
\(30\) 0 0
\(31\) −4.04276 −0.726101 −0.363050 0.931769i \(-0.618265\pi\)
−0.363050 + 0.931769i \(0.618265\pi\)
\(32\) 0 0
\(33\) 0.0183136 0.00318799
\(34\) 0 0
\(35\) 2.31586 0.391452
\(36\) 0 0
\(37\) −2.68712 −0.441760 −0.220880 0.975301i \(-0.570893\pi\)
−0.220880 + 0.975301i \(0.570893\pi\)
\(38\) 0 0
\(39\) −2.09218 −0.335016
\(40\) 0 0
\(41\) 0.966020 0.150867 0.0754335 0.997151i \(-0.475966\pi\)
0.0754335 + 0.997151i \(0.475966\pi\)
\(42\) 0 0
\(43\) 3.65204 0.556931 0.278466 0.960446i \(-0.410174\pi\)
0.278466 + 0.960446i \(0.410174\pi\)
\(44\) 0 0
\(45\) −2.89426 −0.431451
\(46\) 0 0
\(47\) 9.41359 1.37311 0.686557 0.727076i \(-0.259121\pi\)
0.686557 + 0.727076i \(0.259121\pi\)
\(48\) 0 0
\(49\) −1.63680 −0.233828
\(50\) 0 0
\(51\) 1.11492 0.156120
\(52\) 0 0
\(53\) −3.66245 −0.503076 −0.251538 0.967847i \(-0.580936\pi\)
−0.251538 + 0.967847i \(0.580936\pi\)
\(54\) 0 0
\(55\) 0.0563199 0.00759417
\(56\) 0 0
\(57\) −0.707288 −0.0936825
\(58\) 0 0
\(59\) −8.00799 −1.04255 −0.521276 0.853388i \(-0.674544\pi\)
−0.521276 + 0.853388i \(0.674544\pi\)
\(60\) 0 0
\(61\) 0.207095 0.0265158 0.0132579 0.999912i \(-0.495780\pi\)
0.0132579 + 0.999912i \(0.495780\pi\)
\(62\) 0 0
\(63\) −6.70271 −0.844462
\(64\) 0 0
\(65\) −6.43408 −0.798049
\(66\) 0 0
\(67\) −3.39983 −0.415356 −0.207678 0.978197i \(-0.566591\pi\)
−0.207678 + 0.978197i \(0.566591\pi\)
\(68\) 0 0
\(69\) −1.11803 −0.134595
\(70\) 0 0
\(71\) −5.80306 −0.688696 −0.344348 0.938842i \(-0.611900\pi\)
−0.344348 + 0.938842i \(0.611900\pi\)
\(72\) 0 0
\(73\) −6.19683 −0.725284 −0.362642 0.931928i \(-0.618125\pi\)
−0.362642 + 0.931928i \(0.618125\pi\)
\(74\) 0 0
\(75\) 0.325171 0.0375475
\(76\) 0 0
\(77\) 0.130429 0.0148637
\(78\) 0 0
\(79\) −13.8221 −1.55511 −0.777554 0.628816i \(-0.783540\pi\)
−0.777554 + 0.628816i \(0.783540\pi\)
\(80\) 0 0
\(81\) 8.05955 0.895506
\(82\) 0 0
\(83\) −6.06544 −0.665769 −0.332884 0.942968i \(-0.608022\pi\)
−0.332884 + 0.942968i \(0.608022\pi\)
\(84\) 0 0
\(85\) 3.42872 0.371897
\(86\) 0 0
\(87\) 2.98474 0.319998
\(88\) 0 0
\(89\) −5.64338 −0.598197 −0.299099 0.954222i \(-0.596686\pi\)
−0.299099 + 0.954222i \(0.596686\pi\)
\(90\) 0 0
\(91\) −14.9004 −1.56199
\(92\) 0 0
\(93\) −1.31459 −0.136316
\(94\) 0 0
\(95\) −2.17512 −0.223163
\(96\) 0 0
\(97\) −7.46595 −0.758052 −0.379026 0.925386i \(-0.623741\pi\)
−0.379026 + 0.925386i \(0.623741\pi\)
\(98\) 0 0
\(99\) −0.163005 −0.0163826
\(100\) 0 0
\(101\) −2.32488 −0.231334 −0.115667 0.993288i \(-0.536901\pi\)
−0.115667 + 0.993288i \(0.536901\pi\)
\(102\) 0 0
\(103\) −5.82507 −0.573961 −0.286981 0.957936i \(-0.592652\pi\)
−0.286981 + 0.957936i \(0.592652\pi\)
\(104\) 0 0
\(105\) 0.753050 0.0734902
\(106\) 0 0
\(107\) 5.39889 0.521930 0.260965 0.965348i \(-0.415959\pi\)
0.260965 + 0.965348i \(0.415959\pi\)
\(108\) 0 0
\(109\) −2.01104 −0.192623 −0.0963115 0.995351i \(-0.530705\pi\)
−0.0963115 + 0.995351i \(0.530705\pi\)
\(110\) 0 0
\(111\) −0.873775 −0.0829350
\(112\) 0 0
\(113\) 0.0960389 0.00903458 0.00451729 0.999990i \(-0.498562\pi\)
0.00451729 + 0.999990i \(0.498562\pi\)
\(114\) 0 0
\(115\) −3.43828 −0.320621
\(116\) 0 0
\(117\) 18.6219 1.72160
\(118\) 0 0
\(119\) 7.94043 0.727898
\(120\) 0 0
\(121\) −10.9968 −0.999712
\(122\) 0 0
\(123\) 0.314122 0.0283234
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.76321 −0.688874 −0.344437 0.938809i \(-0.611930\pi\)
−0.344437 + 0.938809i \(0.611930\pi\)
\(128\) 0 0
\(129\) 1.18754 0.104557
\(130\) 0 0
\(131\) 7.22872 0.631576 0.315788 0.948830i \(-0.397731\pi\)
0.315788 + 0.948830i \(0.397731\pi\)
\(132\) 0 0
\(133\) −5.03728 −0.436788
\(134\) 0 0
\(135\) −1.91664 −0.164958
\(136\) 0 0
\(137\) −13.5309 −1.15603 −0.578013 0.816028i \(-0.696172\pi\)
−0.578013 + 0.816028i \(0.696172\pi\)
\(138\) 0 0
\(139\) −12.6203 −1.07044 −0.535221 0.844712i \(-0.679771\pi\)
−0.535221 + 0.844712i \(0.679771\pi\)
\(140\) 0 0
\(141\) 3.06103 0.257785
\(142\) 0 0
\(143\) −0.362366 −0.0303026
\(144\) 0 0
\(145\) 9.17899 0.762274
\(146\) 0 0
\(147\) −0.532238 −0.0438983
\(148\) 0 0
\(149\) −1.62093 −0.132792 −0.0663958 0.997793i \(-0.521150\pi\)
−0.0663958 + 0.997793i \(0.521150\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −9.92361 −0.802277
\(154\) 0 0
\(155\) −4.04276 −0.324722
\(156\) 0 0
\(157\) 18.2972 1.46028 0.730139 0.683298i \(-0.239455\pi\)
0.730139 + 0.683298i \(0.239455\pi\)
\(158\) 0 0
\(159\) −1.19092 −0.0944464
\(160\) 0 0
\(161\) −7.96257 −0.627539
\(162\) 0 0
\(163\) −9.80387 −0.767898 −0.383949 0.923354i \(-0.625436\pi\)
−0.383949 + 0.923354i \(0.625436\pi\)
\(164\) 0 0
\(165\) 0.0183136 0.00142571
\(166\) 0 0
\(167\) −2.51591 −0.194687 −0.0973434 0.995251i \(-0.531035\pi\)
−0.0973434 + 0.995251i \(0.531035\pi\)
\(168\) 0 0
\(169\) 28.3973 2.18441
\(170\) 0 0
\(171\) 6.29538 0.481420
\(172\) 0 0
\(173\) −20.9962 −1.59631 −0.798156 0.602450i \(-0.794191\pi\)
−0.798156 + 0.602450i \(0.794191\pi\)
\(174\) 0 0
\(175\) 2.31586 0.175063
\(176\) 0 0
\(177\) −2.60397 −0.195726
\(178\) 0 0
\(179\) 7.11164 0.531549 0.265774 0.964035i \(-0.414372\pi\)
0.265774 + 0.964035i \(0.414372\pi\)
\(180\) 0 0
\(181\) −9.61795 −0.714897 −0.357448 0.933933i \(-0.616353\pi\)
−0.357448 + 0.933933i \(0.616353\pi\)
\(182\) 0 0
\(183\) 0.0673413 0.00497801
\(184\) 0 0
\(185\) −2.68712 −0.197561
\(186\) 0 0
\(187\) 0.193105 0.0141212
\(188\) 0 0
\(189\) −4.43868 −0.322866
\(190\) 0 0
\(191\) −6.46910 −0.468087 −0.234044 0.972226i \(-0.575196\pi\)
−0.234044 + 0.972226i \(0.575196\pi\)
\(192\) 0 0
\(193\) −22.8585 −1.64539 −0.822696 0.568482i \(-0.807531\pi\)
−0.822696 + 0.568482i \(0.807531\pi\)
\(194\) 0 0
\(195\) −2.09218 −0.149824
\(196\) 0 0
\(197\) −13.2245 −0.942206 −0.471103 0.882078i \(-0.656144\pi\)
−0.471103 + 0.882078i \(0.656144\pi\)
\(198\) 0 0
\(199\) 15.9888 1.13342 0.566709 0.823918i \(-0.308216\pi\)
0.566709 + 0.823918i \(0.308216\pi\)
\(200\) 0 0
\(201\) −1.10553 −0.0779779
\(202\) 0 0
\(203\) 21.2573 1.49197
\(204\) 0 0
\(205\) 0.966020 0.0674698
\(206\) 0 0
\(207\) 9.95129 0.691663
\(208\) 0 0
\(209\) −0.122503 −0.00847369
\(210\) 0 0
\(211\) 27.6637 1.90445 0.952224 0.305401i \(-0.0987905\pi\)
0.952224 + 0.305401i \(0.0987905\pi\)
\(212\) 0 0
\(213\) −1.88699 −0.129294
\(214\) 0 0
\(215\) 3.65204 0.249067
\(216\) 0 0
\(217\) −9.36246 −0.635565
\(218\) 0 0
\(219\) −2.01503 −0.136163
\(220\) 0 0
\(221\) −22.0606 −1.48396
\(222\) 0 0
\(223\) −23.4451 −1.57000 −0.784999 0.619497i \(-0.787337\pi\)
−0.784999 + 0.619497i \(0.787337\pi\)
\(224\) 0 0
\(225\) −2.89426 −0.192951
\(226\) 0 0
\(227\) 26.5443 1.76181 0.880905 0.473294i \(-0.156935\pi\)
0.880905 + 0.473294i \(0.156935\pi\)
\(228\) 0 0
\(229\) −11.2223 −0.741592 −0.370796 0.928714i \(-0.620915\pi\)
−0.370796 + 0.928714i \(0.620915\pi\)
\(230\) 0 0
\(231\) 0.0424117 0.00279048
\(232\) 0 0
\(233\) 6.19435 0.405805 0.202903 0.979199i \(-0.434963\pi\)
0.202903 + 0.979199i \(0.434963\pi\)
\(234\) 0 0
\(235\) 9.41359 0.614075
\(236\) 0 0
\(237\) −4.49455 −0.291952
\(238\) 0 0
\(239\) 17.0596 1.10349 0.551747 0.834012i \(-0.313962\pi\)
0.551747 + 0.834012i \(0.313962\pi\)
\(240\) 0 0
\(241\) −10.0660 −0.648408 −0.324204 0.945987i \(-0.605096\pi\)
−0.324204 + 0.945987i \(0.605096\pi\)
\(242\) 0 0
\(243\) 8.37067 0.536978
\(244\) 0 0
\(245\) −1.63680 −0.104571
\(246\) 0 0
\(247\) 13.9949 0.890475
\(248\) 0 0
\(249\) −1.97231 −0.124990
\(250\) 0 0
\(251\) 2.20064 0.138903 0.0694516 0.997585i \(-0.477875\pi\)
0.0694516 + 0.997585i \(0.477875\pi\)
\(252\) 0 0
\(253\) −0.193643 −0.0121743
\(254\) 0 0
\(255\) 1.11492 0.0698190
\(256\) 0 0
\(257\) −4.42680 −0.276136 −0.138068 0.990423i \(-0.544089\pi\)
−0.138068 + 0.990423i \(0.544089\pi\)
\(258\) 0 0
\(259\) −6.22300 −0.386678
\(260\) 0 0
\(261\) −26.5664 −1.64442
\(262\) 0 0
\(263\) 16.1049 0.993071 0.496535 0.868016i \(-0.334605\pi\)
0.496535 + 0.868016i \(0.334605\pi\)
\(264\) 0 0
\(265\) −3.66245 −0.224983
\(266\) 0 0
\(267\) −1.83506 −0.112304
\(268\) 0 0
\(269\) 6.82264 0.415984 0.207992 0.978131i \(-0.433307\pi\)
0.207992 + 0.978131i \(0.433307\pi\)
\(270\) 0 0
\(271\) 0.306947 0.0186457 0.00932284 0.999957i \(-0.497032\pi\)
0.00932284 + 0.999957i \(0.497032\pi\)
\(272\) 0 0
\(273\) −4.84518 −0.293244
\(274\) 0 0
\(275\) 0.0563199 0.00339622
\(276\) 0 0
\(277\) 16.0066 0.961741 0.480871 0.876792i \(-0.340321\pi\)
0.480871 + 0.876792i \(0.340321\pi\)
\(278\) 0 0
\(279\) 11.7008 0.700509
\(280\) 0 0
\(281\) −7.87401 −0.469724 −0.234862 0.972029i \(-0.575464\pi\)
−0.234862 + 0.972029i \(0.575464\pi\)
\(282\) 0 0
\(283\) −3.03592 −0.180467 −0.0902335 0.995921i \(-0.528761\pi\)
−0.0902335 + 0.995921i \(0.528761\pi\)
\(284\) 0 0
\(285\) −0.707288 −0.0418961
\(286\) 0 0
\(287\) 2.23717 0.132056
\(288\) 0 0
\(289\) −5.24389 −0.308464
\(290\) 0 0
\(291\) −2.42771 −0.142315
\(292\) 0 0
\(293\) 0.769903 0.0449782 0.0224891 0.999747i \(-0.492841\pi\)
0.0224891 + 0.999747i \(0.492841\pi\)
\(294\) 0 0
\(295\) −8.00799 −0.466243
\(296\) 0 0
\(297\) −0.107945 −0.00626361
\(298\) 0 0
\(299\) 22.1222 1.27936
\(300\) 0 0
\(301\) 8.45761 0.487489
\(302\) 0 0
\(303\) −0.755984 −0.0434302
\(304\) 0 0
\(305\) 0.207095 0.0118582
\(306\) 0 0
\(307\) 8.91000 0.508521 0.254260 0.967136i \(-0.418168\pi\)
0.254260 + 0.967136i \(0.418168\pi\)
\(308\) 0 0
\(309\) −1.89414 −0.107754
\(310\) 0 0
\(311\) 1.97993 0.112271 0.0561357 0.998423i \(-0.482122\pi\)
0.0561357 + 0.998423i \(0.482122\pi\)
\(312\) 0 0
\(313\) 1.28314 0.0725271 0.0362636 0.999342i \(-0.488454\pi\)
0.0362636 + 0.999342i \(0.488454\pi\)
\(314\) 0 0
\(315\) −6.70271 −0.377655
\(316\) 0 0
\(317\) −2.47251 −0.138870 −0.0694350 0.997586i \(-0.522120\pi\)
−0.0694350 + 0.997586i \(0.522120\pi\)
\(318\) 0 0
\(319\) 0.516960 0.0289442
\(320\) 0 0
\(321\) 1.75556 0.0979859
\(322\) 0 0
\(323\) −7.45789 −0.414968
\(324\) 0 0
\(325\) −6.43408 −0.356898
\(326\) 0 0
\(327\) −0.653933 −0.0361626
\(328\) 0 0
\(329\) 21.8006 1.20190
\(330\) 0 0
\(331\) 17.9394 0.986037 0.493019 0.870019i \(-0.335893\pi\)
0.493019 + 0.870019i \(0.335893\pi\)
\(332\) 0 0
\(333\) 7.77724 0.426190
\(334\) 0 0
\(335\) −3.39983 −0.185753
\(336\) 0 0
\(337\) −29.3588 −1.59928 −0.799639 0.600481i \(-0.794976\pi\)
−0.799639 + 0.600481i \(0.794976\pi\)
\(338\) 0 0
\(339\) 0.0312291 0.00169613
\(340\) 0 0
\(341\) −0.227688 −0.0123300
\(342\) 0 0
\(343\) −20.0016 −1.07999
\(344\) 0 0
\(345\) −1.11803 −0.0601927
\(346\) 0 0
\(347\) −6.33413 −0.340034 −0.170017 0.985441i \(-0.554382\pi\)
−0.170017 + 0.985441i \(0.554382\pi\)
\(348\) 0 0
\(349\) 9.10874 0.487580 0.243790 0.969828i \(-0.421609\pi\)
0.243790 + 0.969828i \(0.421609\pi\)
\(350\) 0 0
\(351\) 12.3318 0.658224
\(352\) 0 0
\(353\) 3.92130 0.208710 0.104355 0.994540i \(-0.466722\pi\)
0.104355 + 0.994540i \(0.466722\pi\)
\(354\) 0 0
\(355\) −5.80306 −0.307994
\(356\) 0 0
\(357\) 2.58200 0.136654
\(358\) 0 0
\(359\) −8.00756 −0.422623 −0.211311 0.977419i \(-0.567773\pi\)
−0.211311 + 0.977419i \(0.567773\pi\)
\(360\) 0 0
\(361\) −14.2688 −0.750991
\(362\) 0 0
\(363\) −3.57585 −0.187683
\(364\) 0 0
\(365\) −6.19683 −0.324357
\(366\) 0 0
\(367\) 8.07193 0.421351 0.210676 0.977556i \(-0.432434\pi\)
0.210676 + 0.977556i \(0.432434\pi\)
\(368\) 0 0
\(369\) −2.79592 −0.145550
\(370\) 0 0
\(371\) −8.48172 −0.440349
\(372\) 0 0
\(373\) 29.0443 1.50386 0.751928 0.659246i \(-0.229124\pi\)
0.751928 + 0.659246i \(0.229124\pi\)
\(374\) 0 0
\(375\) 0.325171 0.0167918
\(376\) 0 0
\(377\) −59.0583 −3.04166
\(378\) 0 0
\(379\) −9.84651 −0.505781 −0.252891 0.967495i \(-0.581381\pi\)
−0.252891 + 0.967495i \(0.581381\pi\)
\(380\) 0 0
\(381\) −2.52437 −0.129327
\(382\) 0 0
\(383\) −1.68356 −0.0860259 −0.0430130 0.999075i \(-0.513696\pi\)
−0.0430130 + 0.999075i \(0.513696\pi\)
\(384\) 0 0
\(385\) 0.130429 0.00664727
\(386\) 0 0
\(387\) −10.5700 −0.537302
\(388\) 0 0
\(389\) −26.4042 −1.33875 −0.669373 0.742926i \(-0.733437\pi\)
−0.669373 + 0.742926i \(0.733437\pi\)
\(390\) 0 0
\(391\) −11.7889 −0.596190
\(392\) 0 0
\(393\) 2.35057 0.118571
\(394\) 0 0
\(395\) −13.8221 −0.695466
\(396\) 0 0
\(397\) −7.81175 −0.392060 −0.196030 0.980598i \(-0.562805\pi\)
−0.196030 + 0.980598i \(0.562805\pi\)
\(398\) 0 0
\(399\) −1.63798 −0.0820015
\(400\) 0 0
\(401\) −4.32525 −0.215993 −0.107996 0.994151i \(-0.534443\pi\)
−0.107996 + 0.994151i \(0.534443\pi\)
\(402\) 0 0
\(403\) 26.0114 1.29572
\(404\) 0 0
\(405\) 8.05955 0.400482
\(406\) 0 0
\(407\) −0.151338 −0.00750157
\(408\) 0 0
\(409\) 32.7052 1.61717 0.808585 0.588379i \(-0.200234\pi\)
0.808585 + 0.588379i \(0.200234\pi\)
\(410\) 0 0
\(411\) −4.39987 −0.217029
\(412\) 0 0
\(413\) −18.5454 −0.912559
\(414\) 0 0
\(415\) −6.06544 −0.297741
\(416\) 0 0
\(417\) −4.10376 −0.200962
\(418\) 0 0
\(419\) −10.9558 −0.535225 −0.267613 0.963527i \(-0.586235\pi\)
−0.267613 + 0.963527i \(0.586235\pi\)
\(420\) 0 0
\(421\) 1.67343 0.0815582 0.0407791 0.999168i \(-0.487016\pi\)
0.0407791 + 0.999168i \(0.487016\pi\)
\(422\) 0 0
\(423\) −27.2454 −1.32472
\(424\) 0 0
\(425\) 3.42872 0.166317
\(426\) 0 0
\(427\) 0.479603 0.0232096
\(428\) 0 0
\(429\) −0.117831 −0.00568893
\(430\) 0 0
\(431\) −32.0330 −1.54297 −0.771487 0.636245i \(-0.780487\pi\)
−0.771487 + 0.636245i \(0.780487\pi\)
\(432\) 0 0
\(433\) 22.2092 1.06731 0.533654 0.845703i \(-0.320819\pi\)
0.533654 + 0.845703i \(0.320819\pi\)
\(434\) 0 0
\(435\) 2.98474 0.143107
\(436\) 0 0
\(437\) 7.47869 0.357754
\(438\) 0 0
\(439\) 28.3150 1.35140 0.675700 0.737176i \(-0.263841\pi\)
0.675700 + 0.737176i \(0.263841\pi\)
\(440\) 0 0
\(441\) 4.73732 0.225587
\(442\) 0 0
\(443\) 13.0614 0.620564 0.310282 0.950645i \(-0.399577\pi\)
0.310282 + 0.950645i \(0.399577\pi\)
\(444\) 0 0
\(445\) −5.64338 −0.267522
\(446\) 0 0
\(447\) −0.527079 −0.0249300
\(448\) 0 0
\(449\) 6.51186 0.307314 0.153657 0.988124i \(-0.450895\pi\)
0.153657 + 0.988124i \(0.450895\pi\)
\(450\) 0 0
\(451\) 0.0544061 0.00256188
\(452\) 0 0
\(453\) −0.325171 −0.0152779
\(454\) 0 0
\(455\) −14.9004 −0.698542
\(456\) 0 0
\(457\) −14.7695 −0.690890 −0.345445 0.938439i \(-0.612272\pi\)
−0.345445 + 0.938439i \(0.612272\pi\)
\(458\) 0 0
\(459\) −6.57163 −0.306737
\(460\) 0 0
\(461\) 6.06159 0.282317 0.141158 0.989987i \(-0.454917\pi\)
0.141158 + 0.989987i \(0.454917\pi\)
\(462\) 0 0
\(463\) 31.2815 1.45377 0.726887 0.686758i \(-0.240967\pi\)
0.726887 + 0.686758i \(0.240967\pi\)
\(464\) 0 0
\(465\) −1.31459 −0.0609626
\(466\) 0 0
\(467\) 11.1705 0.516911 0.258456 0.966023i \(-0.416786\pi\)
0.258456 + 0.966023i \(0.416786\pi\)
\(468\) 0 0
\(469\) −7.87354 −0.363566
\(470\) 0 0
\(471\) 5.94973 0.274149
\(472\) 0 0
\(473\) 0.205682 0.00945729
\(474\) 0 0
\(475\) −2.17512 −0.0998016
\(476\) 0 0
\(477\) 10.6001 0.485345
\(478\) 0 0
\(479\) −22.4107 −1.02397 −0.511986 0.858994i \(-0.671090\pi\)
−0.511986 + 0.858994i \(0.671090\pi\)
\(480\) 0 0
\(481\) 17.2892 0.788318
\(482\) 0 0
\(483\) −2.58920 −0.117813
\(484\) 0 0
\(485\) −7.46595 −0.339011
\(486\) 0 0
\(487\) 1.70131 0.0770939 0.0385470 0.999257i \(-0.487727\pi\)
0.0385470 + 0.999257i \(0.487727\pi\)
\(488\) 0 0
\(489\) −3.18793 −0.144163
\(490\) 0 0
\(491\) −13.0364 −0.588324 −0.294162 0.955756i \(-0.595040\pi\)
−0.294162 + 0.955756i \(0.595040\pi\)
\(492\) 0 0
\(493\) 31.4722 1.41744
\(494\) 0 0
\(495\) −0.163005 −0.00732651
\(496\) 0 0
\(497\) −13.4391 −0.602825
\(498\) 0 0
\(499\) −20.6803 −0.925780 −0.462890 0.886416i \(-0.653187\pi\)
−0.462890 + 0.886416i \(0.653187\pi\)
\(500\) 0 0
\(501\) −0.818100 −0.0365500
\(502\) 0 0
\(503\) 1.83106 0.0816431 0.0408216 0.999166i \(-0.487002\pi\)
0.0408216 + 0.999166i \(0.487002\pi\)
\(504\) 0 0
\(505\) −2.32488 −0.103456
\(506\) 0 0
\(507\) 9.23399 0.410096
\(508\) 0 0
\(509\) −34.4468 −1.52683 −0.763413 0.645911i \(-0.776478\pi\)
−0.763413 + 0.645911i \(0.776478\pi\)
\(510\) 0 0
\(511\) −14.3510 −0.634851
\(512\) 0 0
\(513\) 4.16894 0.184063
\(514\) 0 0
\(515\) −5.82507 −0.256683
\(516\) 0 0
\(517\) 0.530172 0.0233169
\(518\) 0 0
\(519\) −6.82736 −0.299688
\(520\) 0 0
\(521\) −11.8029 −0.517097 −0.258548 0.965998i \(-0.583244\pi\)
−0.258548 + 0.965998i \(0.583244\pi\)
\(522\) 0 0
\(523\) 16.3976 0.717015 0.358507 0.933527i \(-0.383286\pi\)
0.358507 + 0.933527i \(0.383286\pi\)
\(524\) 0 0
\(525\) 0.753050 0.0328658
\(526\) 0 0
\(527\) −13.8615 −0.603816
\(528\) 0 0
\(529\) −11.1782 −0.486010
\(530\) 0 0
\(531\) 23.1772 1.00581
\(532\) 0 0
\(533\) −6.21545 −0.269221
\(534\) 0 0
\(535\) 5.39889 0.233414
\(536\) 0 0
\(537\) 2.31250 0.0997917
\(538\) 0 0
\(539\) −0.0921841 −0.00397065
\(540\) 0 0
\(541\) −21.8874 −0.941012 −0.470506 0.882397i \(-0.655929\pi\)
−0.470506 + 0.882397i \(0.655929\pi\)
\(542\) 0 0
\(543\) −3.12748 −0.134213
\(544\) 0 0
\(545\) −2.01104 −0.0861437
\(546\) 0 0
\(547\) −24.3436 −1.04086 −0.520429 0.853905i \(-0.674228\pi\)
−0.520429 + 0.853905i \(0.674228\pi\)
\(548\) 0 0
\(549\) −0.599387 −0.0255812
\(550\) 0 0
\(551\) −19.9655 −0.850557
\(552\) 0 0
\(553\) −32.0101 −1.36121
\(554\) 0 0
\(555\) −0.873775 −0.0370897
\(556\) 0 0
\(557\) −26.3618 −1.11699 −0.558494 0.829509i \(-0.688620\pi\)
−0.558494 + 0.829509i \(0.688620\pi\)
\(558\) 0 0
\(559\) −23.4975 −0.993839
\(560\) 0 0
\(561\) 0.0627921 0.00265109
\(562\) 0 0
\(563\) 12.5418 0.528574 0.264287 0.964444i \(-0.414863\pi\)
0.264287 + 0.964444i \(0.414863\pi\)
\(564\) 0 0
\(565\) 0.0960389 0.00404039
\(566\) 0 0
\(567\) 18.6648 0.783848
\(568\) 0 0
\(569\) 18.0058 0.754844 0.377422 0.926041i \(-0.376811\pi\)
0.377422 + 0.926041i \(0.376811\pi\)
\(570\) 0 0
\(571\) 12.7538 0.533731 0.266866 0.963734i \(-0.414012\pi\)
0.266866 + 0.963734i \(0.414012\pi\)
\(572\) 0 0
\(573\) −2.10356 −0.0878776
\(574\) 0 0
\(575\) −3.43828 −0.143386
\(576\) 0 0
\(577\) −20.1902 −0.840527 −0.420264 0.907402i \(-0.638062\pi\)
−0.420264 + 0.907402i \(0.638062\pi\)
\(578\) 0 0
\(579\) −7.43293 −0.308902
\(580\) 0 0
\(581\) −14.0467 −0.582756
\(582\) 0 0
\(583\) −0.206269 −0.00854278
\(584\) 0 0
\(585\) 18.6219 0.769921
\(586\) 0 0
\(587\) 7.08622 0.292479 0.146240 0.989249i \(-0.453283\pi\)
0.146240 + 0.989249i \(0.453283\pi\)
\(588\) 0 0
\(589\) 8.79350 0.362330
\(590\) 0 0
\(591\) −4.30022 −0.176887
\(592\) 0 0
\(593\) 3.05023 0.125258 0.0626290 0.998037i \(-0.480052\pi\)
0.0626290 + 0.998037i \(0.480052\pi\)
\(594\) 0 0
\(595\) 7.94043 0.325526
\(596\) 0 0
\(597\) 5.19910 0.212785
\(598\) 0 0
\(599\) 27.1790 1.11050 0.555252 0.831682i \(-0.312622\pi\)
0.555252 + 0.831682i \(0.312622\pi\)
\(600\) 0 0
\(601\) 2.03409 0.0829724 0.0414862 0.999139i \(-0.486791\pi\)
0.0414862 + 0.999139i \(0.486791\pi\)
\(602\) 0 0
\(603\) 9.84002 0.400716
\(604\) 0 0
\(605\) −10.9968 −0.447085
\(606\) 0 0
\(607\) −8.22738 −0.333939 −0.166969 0.985962i \(-0.553398\pi\)
−0.166969 + 0.985962i \(0.553398\pi\)
\(608\) 0 0
\(609\) 6.91224 0.280098
\(610\) 0 0
\(611\) −60.5678 −2.45031
\(612\) 0 0
\(613\) 33.9482 1.37116 0.685578 0.727999i \(-0.259549\pi\)
0.685578 + 0.727999i \(0.259549\pi\)
\(614\) 0 0
\(615\) 0.314122 0.0126666
\(616\) 0 0
\(617\) −12.3280 −0.496305 −0.248153 0.968721i \(-0.579823\pi\)
−0.248153 + 0.968721i \(0.579823\pi\)
\(618\) 0 0
\(619\) −20.5233 −0.824901 −0.412450 0.910980i \(-0.635327\pi\)
−0.412450 + 0.910980i \(0.635327\pi\)
\(620\) 0 0
\(621\) 6.58996 0.264446
\(622\) 0 0
\(623\) −13.0693 −0.523609
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.0398343 −0.00159083
\(628\) 0 0
\(629\) −9.21339 −0.367362
\(630\) 0 0
\(631\) 14.4763 0.576294 0.288147 0.957586i \(-0.406961\pi\)
0.288147 + 0.957586i \(0.406961\pi\)
\(632\) 0 0
\(633\) 8.99543 0.357536
\(634\) 0 0
\(635\) −7.76321 −0.308074
\(636\) 0 0
\(637\) 10.5313 0.417264
\(638\) 0 0
\(639\) 16.7956 0.664423
\(640\) 0 0
\(641\) −28.2070 −1.11411 −0.557055 0.830476i \(-0.688069\pi\)
−0.557055 + 0.830476i \(0.688069\pi\)
\(642\) 0 0
\(643\) 21.1243 0.833059 0.416530 0.909122i \(-0.363246\pi\)
0.416530 + 0.909122i \(0.363246\pi\)
\(644\) 0 0
\(645\) 1.18754 0.0467593
\(646\) 0 0
\(647\) 43.5932 1.71382 0.856912 0.515463i \(-0.172380\pi\)
0.856912 + 0.515463i \(0.172380\pi\)
\(648\) 0 0
\(649\) −0.451009 −0.0177037
\(650\) 0 0
\(651\) −3.04440 −0.119319
\(652\) 0 0
\(653\) −42.7553 −1.67314 −0.836572 0.547857i \(-0.815444\pi\)
−0.836572 + 0.547857i \(0.815444\pi\)
\(654\) 0 0
\(655\) 7.22872 0.282449
\(656\) 0 0
\(657\) 17.9353 0.699722
\(658\) 0 0
\(659\) 40.6170 1.58221 0.791107 0.611678i \(-0.209505\pi\)
0.791107 + 0.611678i \(0.209505\pi\)
\(660\) 0 0
\(661\) −47.7230 −1.85621 −0.928105 0.372318i \(-0.878563\pi\)
−0.928105 + 0.372318i \(0.878563\pi\)
\(662\) 0 0
\(663\) −7.17348 −0.278595
\(664\) 0 0
\(665\) −5.03728 −0.195337
\(666\) 0 0
\(667\) −31.5600 −1.22201
\(668\) 0 0
\(669\) −7.62366 −0.294748
\(670\) 0 0
\(671\) 0.0116636 0.000450267 0
\(672\) 0 0
\(673\) 25.2841 0.974630 0.487315 0.873226i \(-0.337976\pi\)
0.487315 + 0.873226i \(0.337976\pi\)
\(674\) 0 0
\(675\) −1.91664 −0.0737717
\(676\) 0 0
\(677\) 32.8260 1.26161 0.630803 0.775943i \(-0.282726\pi\)
0.630803 + 0.775943i \(0.282726\pi\)
\(678\) 0 0
\(679\) −17.2901 −0.663532
\(680\) 0 0
\(681\) 8.63145 0.330758
\(682\) 0 0
\(683\) −6.92474 −0.264968 −0.132484 0.991185i \(-0.542295\pi\)
−0.132484 + 0.991185i \(0.542295\pi\)
\(684\) 0 0
\(685\) −13.5309 −0.516990
\(686\) 0 0
\(687\) −3.64917 −0.139225
\(688\) 0 0
\(689\) 23.5645 0.897736
\(690\) 0 0
\(691\) −15.7452 −0.598976 −0.299488 0.954100i \(-0.596816\pi\)
−0.299488 + 0.954100i \(0.596816\pi\)
\(692\) 0 0
\(693\) −0.377496 −0.0143399
\(694\) 0 0
\(695\) −12.6203 −0.478716
\(696\) 0 0
\(697\) 3.31221 0.125459
\(698\) 0 0
\(699\) 2.01422 0.0761849
\(700\) 0 0
\(701\) 20.2907 0.766370 0.383185 0.923672i \(-0.374827\pi\)
0.383185 + 0.923672i \(0.374827\pi\)
\(702\) 0 0
\(703\) 5.84483 0.220442
\(704\) 0 0
\(705\) 3.06103 0.115285
\(706\) 0 0
\(707\) −5.38410 −0.202490
\(708\) 0 0
\(709\) −1.50205 −0.0564106 −0.0282053 0.999602i \(-0.508979\pi\)
−0.0282053 + 0.999602i \(0.508979\pi\)
\(710\) 0 0
\(711\) 40.0048 1.50030
\(712\) 0 0
\(713\) 13.9001 0.520564
\(714\) 0 0
\(715\) −0.362366 −0.0135517
\(716\) 0 0
\(717\) 5.54728 0.207167
\(718\) 0 0
\(719\) −16.1931 −0.603900 −0.301950 0.953324i \(-0.597638\pi\)
−0.301950 + 0.953324i \(0.597638\pi\)
\(720\) 0 0
\(721\) −13.4900 −0.502395
\(722\) 0 0
\(723\) −3.27317 −0.121731
\(724\) 0 0
\(725\) 9.17899 0.340899
\(726\) 0 0
\(727\) 51.7644 1.91984 0.959918 0.280279i \(-0.0904271\pi\)
0.959918 + 0.280279i \(0.0904271\pi\)
\(728\) 0 0
\(729\) −21.4568 −0.794695
\(730\) 0 0
\(731\) 12.5218 0.463136
\(732\) 0 0
\(733\) 53.4407 1.97388 0.986938 0.161102i \(-0.0515048\pi\)
0.986938 + 0.161102i \(0.0515048\pi\)
\(734\) 0 0
\(735\) −0.532238 −0.0196319
\(736\) 0 0
\(737\) −0.191478 −0.00705319
\(738\) 0 0
\(739\) 15.9949 0.588382 0.294191 0.955747i \(-0.404950\pi\)
0.294191 + 0.955747i \(0.404950\pi\)
\(740\) 0 0
\(741\) 4.55074 0.167176
\(742\) 0 0
\(743\) 42.3285 1.55288 0.776442 0.630189i \(-0.217023\pi\)
0.776442 + 0.630189i \(0.217023\pi\)
\(744\) 0 0
\(745\) −1.62093 −0.0593862
\(746\) 0 0
\(747\) 17.5550 0.642303
\(748\) 0 0
\(749\) 12.5031 0.456852
\(750\) 0 0
\(751\) −48.2051 −1.75903 −0.879515 0.475872i \(-0.842133\pi\)
−0.879515 + 0.475872i \(0.842133\pi\)
\(752\) 0 0
\(753\) 0.715585 0.0260774
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −19.5650 −0.711101 −0.355550 0.934657i \(-0.615707\pi\)
−0.355550 + 0.934657i \(0.615707\pi\)
\(758\) 0 0
\(759\) −0.0629673 −0.00228557
\(760\) 0 0
\(761\) 10.4368 0.378335 0.189167 0.981945i \(-0.439421\pi\)
0.189167 + 0.981945i \(0.439421\pi\)
\(762\) 0 0
\(763\) −4.65730 −0.168605
\(764\) 0 0
\(765\) −9.92361 −0.358789
\(766\) 0 0
\(767\) 51.5240 1.86042
\(768\) 0 0
\(769\) −17.3916 −0.627158 −0.313579 0.949562i \(-0.601528\pi\)
−0.313579 + 0.949562i \(0.601528\pi\)
\(770\) 0 0
\(771\) −1.43947 −0.0518412
\(772\) 0 0
\(773\) −13.8077 −0.496629 −0.248314 0.968680i \(-0.579877\pi\)
−0.248314 + 0.968680i \(0.579877\pi\)
\(774\) 0 0
\(775\) −4.04276 −0.145220
\(776\) 0 0
\(777\) −2.02354 −0.0725941
\(778\) 0 0
\(779\) −2.10121 −0.0752838
\(780\) 0 0
\(781\) −0.326827 −0.0116948
\(782\) 0 0
\(783\) −17.5929 −0.628717
\(784\) 0 0
\(785\) 18.2972 0.653057
\(786\) 0 0
\(787\) 36.7967 1.31166 0.655831 0.754908i \(-0.272318\pi\)
0.655831 + 0.754908i \(0.272318\pi\)
\(788\) 0 0
\(789\) 5.23685 0.186437
\(790\) 0 0
\(791\) 0.222413 0.00790808
\(792\) 0 0
\(793\) −1.33246 −0.0473172
\(794\) 0 0
\(795\) −1.19092 −0.0422377
\(796\) 0 0
\(797\) −2.79694 −0.0990726 −0.0495363 0.998772i \(-0.515774\pi\)
−0.0495363 + 0.998772i \(0.515774\pi\)
\(798\) 0 0
\(799\) 32.2766 1.14186
\(800\) 0 0
\(801\) 16.3334 0.577113
\(802\) 0 0
\(803\) −0.349005 −0.0123161
\(804\) 0 0
\(805\) −7.96257 −0.280644
\(806\) 0 0
\(807\) 2.21853 0.0780958
\(808\) 0 0
\(809\) −28.5043 −1.00216 −0.501079 0.865401i \(-0.667064\pi\)
−0.501079 + 0.865401i \(0.667064\pi\)
\(810\) 0 0
\(811\) −38.8251 −1.36333 −0.681666 0.731663i \(-0.738744\pi\)
−0.681666 + 0.731663i \(0.738744\pi\)
\(812\) 0 0
\(813\) 0.0998102 0.00350049
\(814\) 0 0
\(815\) −9.80387 −0.343415
\(816\) 0 0
\(817\) −7.94364 −0.277913
\(818\) 0 0
\(819\) 43.1257 1.50694
\(820\) 0 0
\(821\) 19.1085 0.666890 0.333445 0.942769i \(-0.391789\pi\)
0.333445 + 0.942769i \(0.391789\pi\)
\(822\) 0 0
\(823\) 21.7891 0.759521 0.379761 0.925085i \(-0.376006\pi\)
0.379761 + 0.925085i \(0.376006\pi\)
\(824\) 0 0
\(825\) 0.0183136 0.000637597 0
\(826\) 0 0
\(827\) 1.49055 0.0518317 0.0259158 0.999664i \(-0.491750\pi\)
0.0259158 + 0.999664i \(0.491750\pi\)
\(828\) 0 0
\(829\) 15.9080 0.552509 0.276254 0.961085i \(-0.410907\pi\)
0.276254 + 0.961085i \(0.410907\pi\)
\(830\) 0 0
\(831\) 5.20487 0.180555
\(832\) 0 0
\(833\) −5.61211 −0.194448
\(834\) 0 0
\(835\) −2.51591 −0.0870666
\(836\) 0 0
\(837\) 7.74853 0.267828
\(838\) 0 0
\(839\) 3.58777 0.123864 0.0619318 0.998080i \(-0.480274\pi\)
0.0619318 + 0.998080i \(0.480274\pi\)
\(840\) 0 0
\(841\) 55.2539 1.90531
\(842\) 0 0
\(843\) −2.56040 −0.0881848
\(844\) 0 0
\(845\) 28.3973 0.976898
\(846\) 0 0
\(847\) −25.4671 −0.875060
\(848\) 0 0
\(849\) −0.987194 −0.0338804
\(850\) 0 0
\(851\) 9.23908 0.316712
\(852\) 0 0
\(853\) 35.0955 1.20165 0.600823 0.799382i \(-0.294840\pi\)
0.600823 + 0.799382i \(0.294840\pi\)
\(854\) 0 0
\(855\) 6.29538 0.215298
\(856\) 0 0
\(857\) 21.8544 0.746534 0.373267 0.927724i \(-0.378238\pi\)
0.373267 + 0.927724i \(0.378238\pi\)
\(858\) 0 0
\(859\) 15.3375 0.523308 0.261654 0.965162i \(-0.415732\pi\)
0.261654 + 0.965162i \(0.415732\pi\)
\(860\) 0 0
\(861\) 0.727462 0.0247918
\(862\) 0 0
\(863\) −26.5648 −0.904276 −0.452138 0.891948i \(-0.649338\pi\)
−0.452138 + 0.891948i \(0.649338\pi\)
\(864\) 0 0
\(865\) −20.9962 −0.713893
\(866\) 0 0
\(867\) −1.70516 −0.0579103
\(868\) 0 0
\(869\) −0.778459 −0.0264074
\(870\) 0 0
\(871\) 21.8748 0.741199
\(872\) 0 0
\(873\) 21.6084 0.731334
\(874\) 0 0
\(875\) 2.31586 0.0782903
\(876\) 0 0
\(877\) 9.18843 0.310271 0.155136 0.987893i \(-0.450419\pi\)
0.155136 + 0.987893i \(0.450419\pi\)
\(878\) 0 0
\(879\) 0.250350 0.00844410
\(880\) 0 0
\(881\) 22.6391 0.762731 0.381365 0.924424i \(-0.375454\pi\)
0.381365 + 0.924424i \(0.375454\pi\)
\(882\) 0 0
\(883\) −30.3049 −1.01984 −0.509920 0.860222i \(-0.670325\pi\)
−0.509920 + 0.860222i \(0.670325\pi\)
\(884\) 0 0
\(885\) −2.60397 −0.0875314
\(886\) 0 0
\(887\) 17.9430 0.602468 0.301234 0.953550i \(-0.402601\pi\)
0.301234 + 0.953550i \(0.402601\pi\)
\(888\) 0 0
\(889\) −17.9785 −0.602980
\(890\) 0 0
\(891\) 0.453913 0.0152067
\(892\) 0 0
\(893\) −20.4757 −0.685194
\(894\) 0 0
\(895\) 7.11164 0.237716
\(896\) 0 0
\(897\) 7.19349 0.240183
\(898\) 0 0
\(899\) −37.1084 −1.23764
\(900\) 0 0
\(901\) −12.5575 −0.418351
\(902\) 0 0
\(903\) 2.75017 0.0915200
\(904\) 0 0
\(905\) −9.61795 −0.319712
\(906\) 0 0
\(907\) 51.5996 1.71333 0.856667 0.515869i \(-0.172531\pi\)
0.856667 + 0.515869i \(0.172531\pi\)
\(908\) 0 0
\(909\) 6.72882 0.223181
\(910\) 0 0
\(911\) −28.5238 −0.945036 −0.472518 0.881321i \(-0.656655\pi\)
−0.472518 + 0.881321i \(0.656655\pi\)
\(912\) 0 0
\(913\) −0.341605 −0.0113055
\(914\) 0 0
\(915\) 0.0673413 0.00222623
\(916\) 0 0
\(917\) 16.7407 0.552826
\(918\) 0 0
\(919\) 36.8287 1.21487 0.607433 0.794371i \(-0.292199\pi\)
0.607433 + 0.794371i \(0.292199\pi\)
\(920\) 0 0
\(921\) 2.89727 0.0954684
\(922\) 0 0
\(923\) 37.3373 1.22897
\(924\) 0 0
\(925\) −2.68712 −0.0883521
\(926\) 0 0
\(927\) 16.8593 0.553732
\(928\) 0 0
\(929\) 22.0355 0.722961 0.361481 0.932380i \(-0.382271\pi\)
0.361481 + 0.932380i \(0.382271\pi\)
\(930\) 0 0
\(931\) 3.56023 0.116682
\(932\) 0 0
\(933\) 0.643815 0.0210776
\(934\) 0 0
\(935\) 0.193105 0.00631521
\(936\) 0 0
\(937\) −22.3699 −0.730792 −0.365396 0.930852i \(-0.619066\pi\)
−0.365396 + 0.930852i \(0.619066\pi\)
\(938\) 0 0
\(939\) 0.417239 0.0136161
\(940\) 0 0
\(941\) −59.0733 −1.92573 −0.962867 0.269976i \(-0.912984\pi\)
−0.962867 + 0.269976i \(0.912984\pi\)
\(942\) 0 0
\(943\) −3.32145 −0.108161
\(944\) 0 0
\(945\) −4.43868 −0.144390
\(946\) 0 0
\(947\) −20.1454 −0.654639 −0.327320 0.944914i \(-0.606145\pi\)
−0.327320 + 0.944914i \(0.606145\pi\)
\(948\) 0 0
\(949\) 39.8709 1.29426
\(950\) 0 0
\(951\) −0.803988 −0.0260711
\(952\) 0 0
\(953\) −39.6801 −1.28537 −0.642683 0.766133i \(-0.722179\pi\)
−0.642683 + 0.766133i \(0.722179\pi\)
\(954\) 0 0
\(955\) −6.46910 −0.209335
\(956\) 0 0
\(957\) 0.168100 0.00543391
\(958\) 0 0
\(959\) −31.3357 −1.01188
\(960\) 0 0
\(961\) −14.6561 −0.472777
\(962\) 0 0
\(963\) −15.6258 −0.503535
\(964\) 0 0
\(965\) −22.8585 −0.735841
\(966\) 0 0
\(967\) 36.5096 1.17407 0.587034 0.809562i \(-0.300295\pi\)
0.587034 + 0.809562i \(0.300295\pi\)
\(968\) 0 0
\(969\) −2.42509 −0.0779051
\(970\) 0 0
\(971\) −13.0888 −0.420038 −0.210019 0.977697i \(-0.567353\pi\)
−0.210019 + 0.977697i \(0.567353\pi\)
\(972\) 0 0
\(973\) −29.2269 −0.936971
\(974\) 0 0
\(975\) −2.09218 −0.0670032
\(976\) 0 0
\(977\) −5.45304 −0.174458 −0.0872291 0.996188i \(-0.527801\pi\)
−0.0872291 + 0.996188i \(0.527801\pi\)
\(978\) 0 0
\(979\) −0.317834 −0.0101580
\(980\) 0 0
\(981\) 5.82049 0.185834
\(982\) 0 0
\(983\) −24.6518 −0.786270 −0.393135 0.919481i \(-0.628610\pi\)
−0.393135 + 0.919481i \(0.628610\pi\)
\(984\) 0 0
\(985\) −13.2245 −0.421367
\(986\) 0 0
\(987\) 7.08891 0.225642
\(988\) 0 0
\(989\) −12.5567 −0.399281
\(990\) 0 0
\(991\) −16.7680 −0.532654 −0.266327 0.963883i \(-0.585810\pi\)
−0.266327 + 0.963883i \(0.585810\pi\)
\(992\) 0 0
\(993\) 5.83337 0.185116
\(994\) 0 0
\(995\) 15.9888 0.506880
\(996\) 0 0
\(997\) −4.30387 −0.136305 −0.0681524 0.997675i \(-0.521710\pi\)
−0.0681524 + 0.997675i \(0.521710\pi\)
\(998\) 0 0
\(999\) 5.15026 0.162947
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 \(a_p\))