Properties

Label 8001.2.a.z.1.8
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.63487 q^{2}\) \(+0.672794 q^{4}\) \(+0.107826 q^{5}\) \(-1.00000 q^{7}\) \(+2.16981 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.63487 q^{2}\) \(+0.672794 q^{4}\) \(+0.107826 q^{5}\) \(-1.00000 q^{7}\) \(+2.16981 q^{8}\) \(-0.176281 q^{10}\) \(-1.23406 q^{11}\) \(-2.67752 q^{13}\) \(+1.63487 q^{14}\) \(-4.89294 q^{16}\) \(-6.14025 q^{17}\) \(+1.57630 q^{19}\) \(+0.0725448 q^{20}\) \(+2.01753 q^{22}\) \(-5.97787 q^{23}\) \(-4.98837 q^{25}\) \(+4.37740 q^{26}\) \(-0.672794 q^{28}\) \(+9.60657 q^{29}\) \(+1.81504 q^{31}\) \(+3.65969 q^{32}\) \(+10.0385 q^{34}\) \(-0.107826 q^{35}\) \(+7.63656 q^{37}\) \(-2.57704 q^{38}\) \(+0.233962 q^{40}\) \(+4.73470 q^{41}\) \(+8.65406 q^{43}\) \(-0.830270 q^{44}\) \(+9.77303 q^{46}\) \(+11.0930 q^{47}\) \(+1.00000 q^{49}\) \(+8.15533 q^{50}\) \(-1.80142 q^{52}\) \(+13.7545 q^{53}\) \(-0.133064 q^{55}\) \(-2.16981 q^{56}\) \(-15.7055 q^{58}\) \(-5.68940 q^{59}\) \(-8.36686 q^{61}\) \(-2.96735 q^{62}\) \(+3.80276 q^{64}\) \(-0.288707 q^{65}\) \(-4.40536 q^{67}\) \(-4.13113 q^{68}\) \(+0.176281 q^{70}\) \(+13.9036 q^{71}\) \(-8.13243 q^{73}\) \(-12.4848 q^{74}\) \(+1.06052 q^{76}\) \(+1.23406 q^{77}\) \(+10.6927 q^{79}\) \(-0.527586 q^{80}\) \(-7.74061 q^{82}\) \(-10.3228 q^{83}\) \(-0.662079 q^{85}\) \(-14.1482 q^{86}\) \(-2.67768 q^{88}\) \(-15.7224 q^{89}\) \(+2.67752 q^{91}\) \(-4.02188 q^{92}\) \(-18.1355 q^{94}\) \(+0.169966 q^{95}\) \(-12.2148 q^{97}\) \(-1.63487 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63487 −1.15603 −0.578013 0.816027i \(-0.696172\pi\)
−0.578013 + 0.816027i \(0.696172\pi\)
\(3\) 0 0
\(4\) 0.672794 0.336397
\(5\) 0.107826 0.0482213 0.0241106 0.999709i \(-0.492325\pi\)
0.0241106 + 0.999709i \(0.492325\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.16981 0.767142
\(9\) 0 0
\(10\) −0.176281 −0.0557451
\(11\) −1.23406 −0.372084 −0.186042 0.982542i \(-0.559566\pi\)
−0.186042 + 0.982542i \(0.559566\pi\)
\(12\) 0 0
\(13\) −2.67752 −0.742611 −0.371306 0.928511i \(-0.621090\pi\)
−0.371306 + 0.928511i \(0.621090\pi\)
\(14\) 1.63487 0.436937
\(15\) 0 0
\(16\) −4.89294 −1.22323
\(17\) −6.14025 −1.48923 −0.744615 0.667494i \(-0.767367\pi\)
−0.744615 + 0.667494i \(0.767367\pi\)
\(18\) 0 0
\(19\) 1.57630 0.361628 0.180814 0.983517i \(-0.442127\pi\)
0.180814 + 0.983517i \(0.442127\pi\)
\(20\) 0.0725448 0.0162215
\(21\) 0 0
\(22\) 2.01753 0.430139
\(23\) −5.97787 −1.24647 −0.623236 0.782034i \(-0.714182\pi\)
−0.623236 + 0.782034i \(0.714182\pi\)
\(24\) 0 0
\(25\) −4.98837 −0.997675
\(26\) 4.37740 0.858478
\(27\) 0 0
\(28\) −0.672794 −0.127146
\(29\) 9.60657 1.78389 0.891947 0.452139i \(-0.149339\pi\)
0.891947 + 0.452139i \(0.149339\pi\)
\(30\) 0 0
\(31\) 1.81504 0.325990 0.162995 0.986627i \(-0.447885\pi\)
0.162995 + 0.986627i \(0.447885\pi\)
\(32\) 3.65969 0.646949
\(33\) 0 0
\(34\) 10.0385 1.72159
\(35\) −0.107826 −0.0182259
\(36\) 0 0
\(37\) 7.63656 1.25544 0.627721 0.778438i \(-0.283988\pi\)
0.627721 + 0.778438i \(0.283988\pi\)
\(38\) −2.57704 −0.418051
\(39\) 0 0
\(40\) 0.233962 0.0369926
\(41\) 4.73470 0.739436 0.369718 0.929144i \(-0.379454\pi\)
0.369718 + 0.929144i \(0.379454\pi\)
\(42\) 0 0
\(43\) 8.65406 1.31973 0.659866 0.751384i \(-0.270613\pi\)
0.659866 + 0.751384i \(0.270613\pi\)
\(44\) −0.830270 −0.125168
\(45\) 0 0
\(46\) 9.77303 1.44095
\(47\) 11.0930 1.61807 0.809037 0.587758i \(-0.199989\pi\)
0.809037 + 0.587758i \(0.199989\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 8.15533 1.15334
\(51\) 0 0
\(52\) −1.80142 −0.249812
\(53\) 13.7545 1.88933 0.944665 0.328038i \(-0.106387\pi\)
0.944665 + 0.328038i \(0.106387\pi\)
\(54\) 0 0
\(55\) −0.133064 −0.0179424
\(56\) −2.16981 −0.289953
\(57\) 0 0
\(58\) −15.7055 −2.06223
\(59\) −5.68940 −0.740697 −0.370348 0.928893i \(-0.620762\pi\)
−0.370348 + 0.928893i \(0.620762\pi\)
\(60\) 0 0
\(61\) −8.36686 −1.07127 −0.535634 0.844450i \(-0.679927\pi\)
−0.535634 + 0.844450i \(0.679927\pi\)
\(62\) −2.96735 −0.376853
\(63\) 0 0
\(64\) 3.80276 0.475344
\(65\) −0.288707 −0.0358097
\(66\) 0 0
\(67\) −4.40536 −0.538200 −0.269100 0.963112i \(-0.586726\pi\)
−0.269100 + 0.963112i \(0.586726\pi\)
\(68\) −4.13113 −0.500973
\(69\) 0 0
\(70\) 0.176281 0.0210697
\(71\) 13.9036 1.65006 0.825030 0.565089i \(-0.191158\pi\)
0.825030 + 0.565089i \(0.191158\pi\)
\(72\) 0 0
\(73\) −8.13243 −0.951829 −0.475914 0.879492i \(-0.657883\pi\)
−0.475914 + 0.879492i \(0.657883\pi\)
\(74\) −12.4848 −1.45133
\(75\) 0 0
\(76\) 1.06052 0.121651
\(77\) 1.23406 0.140634
\(78\) 0 0
\(79\) 10.6927 1.20302 0.601510 0.798865i \(-0.294566\pi\)
0.601510 + 0.798865i \(0.294566\pi\)
\(80\) −0.527586 −0.0589859
\(81\) 0 0
\(82\) −7.74061 −0.854807
\(83\) −10.3228 −1.13307 −0.566535 0.824038i \(-0.691716\pi\)
−0.566535 + 0.824038i \(0.691716\pi\)
\(84\) 0 0
\(85\) −0.662079 −0.0718126
\(86\) −14.1482 −1.52564
\(87\) 0 0
\(88\) −2.67768 −0.285441
\(89\) −15.7224 −1.66658 −0.833288 0.552839i \(-0.813544\pi\)
−0.833288 + 0.552839i \(0.813544\pi\)
\(90\) 0 0
\(91\) 2.67752 0.280681
\(92\) −4.02188 −0.419310
\(93\) 0 0
\(94\) −18.1355 −1.87054
\(95\) 0.169966 0.0174382
\(96\) 0 0
\(97\) −12.2148 −1.24022 −0.620111 0.784514i \(-0.712912\pi\)
−0.620111 + 0.784514i \(0.712912\pi\)
\(98\) −1.63487 −0.165147
\(99\) 0 0
\(100\) −3.35615 −0.335615
\(101\) 4.73958 0.471606 0.235803 0.971801i \(-0.424228\pi\)
0.235803 + 0.971801i \(0.424228\pi\)
\(102\) 0 0
\(103\) 4.33072 0.426718 0.213359 0.976974i \(-0.431560\pi\)
0.213359 + 0.976974i \(0.431560\pi\)
\(104\) −5.80971 −0.569689
\(105\) 0 0
\(106\) −22.4868 −2.18411
\(107\) −3.48445 −0.336854 −0.168427 0.985714i \(-0.553869\pi\)
−0.168427 + 0.985714i \(0.553869\pi\)
\(108\) 0 0
\(109\) −15.1221 −1.44843 −0.724217 0.689572i \(-0.757799\pi\)
−0.724217 + 0.689572i \(0.757799\pi\)
\(110\) 0.217542 0.0207419
\(111\) 0 0
\(112\) 4.89294 0.462339
\(113\) 11.6269 1.09377 0.546885 0.837208i \(-0.315813\pi\)
0.546885 + 0.837208i \(0.315813\pi\)
\(114\) 0 0
\(115\) −0.644570 −0.0601065
\(116\) 6.46324 0.600097
\(117\) 0 0
\(118\) 9.30142 0.856265
\(119\) 6.14025 0.562876
\(120\) 0 0
\(121\) −9.47709 −0.861554
\(122\) 13.6787 1.23841
\(123\) 0 0
\(124\) 1.22115 0.109662
\(125\) −1.07701 −0.0963305
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −13.5364 −1.19646
\(129\) 0 0
\(130\) 0.471998 0.0413969
\(131\) 2.66536 0.232873 0.116437 0.993198i \(-0.462853\pi\)
0.116437 + 0.993198i \(0.462853\pi\)
\(132\) 0 0
\(133\) −1.57630 −0.136682
\(134\) 7.20218 0.622174
\(135\) 0 0
\(136\) −13.3232 −1.14245
\(137\) 18.7227 1.59959 0.799795 0.600274i \(-0.204942\pi\)
0.799795 + 0.600274i \(0.204942\pi\)
\(138\) 0 0
\(139\) −13.7227 −1.16395 −0.581973 0.813208i \(-0.697719\pi\)
−0.581973 + 0.813208i \(0.697719\pi\)
\(140\) −0.0725448 −0.00613115
\(141\) 0 0
\(142\) −22.7306 −1.90751
\(143\) 3.30423 0.276314
\(144\) 0 0
\(145\) 1.03584 0.0860217
\(146\) 13.2954 1.10034
\(147\) 0 0
\(148\) 5.13784 0.422327
\(149\) −0.137822 −0.0112908 −0.00564541 0.999984i \(-0.501797\pi\)
−0.00564541 + 0.999984i \(0.501797\pi\)
\(150\) 0 0
\(151\) −5.95504 −0.484614 −0.242307 0.970200i \(-0.577904\pi\)
−0.242307 + 0.970200i \(0.577904\pi\)
\(152\) 3.42026 0.277420
\(153\) 0 0
\(154\) −2.01753 −0.162577
\(155\) 0.195708 0.0157197
\(156\) 0 0
\(157\) −11.1340 −0.888588 −0.444294 0.895881i \(-0.646545\pi\)
−0.444294 + 0.895881i \(0.646545\pi\)
\(158\) −17.4811 −1.39072
\(159\) 0 0
\(160\) 0.394611 0.0311967
\(161\) 5.97787 0.471122
\(162\) 0 0
\(163\) 11.5262 0.902799 0.451400 0.892322i \(-0.350925\pi\)
0.451400 + 0.892322i \(0.350925\pi\)
\(164\) 3.18548 0.248744
\(165\) 0 0
\(166\) 16.8763 1.30986
\(167\) 19.8842 1.53869 0.769344 0.638835i \(-0.220583\pi\)
0.769344 + 0.638835i \(0.220583\pi\)
\(168\) 0 0
\(169\) −5.83087 −0.448529
\(170\) 1.08241 0.0830173
\(171\) 0 0
\(172\) 5.82240 0.443954
\(173\) 22.1209 1.68182 0.840909 0.541177i \(-0.182021\pi\)
0.840909 + 0.541177i \(0.182021\pi\)
\(174\) 0 0
\(175\) 4.98837 0.377086
\(176\) 6.03819 0.455146
\(177\) 0 0
\(178\) 25.7041 1.92661
\(179\) −8.04366 −0.601211 −0.300606 0.953749i \(-0.597189\pi\)
−0.300606 + 0.953749i \(0.597189\pi\)
\(180\) 0 0
\(181\) 8.83086 0.656392 0.328196 0.944610i \(-0.393559\pi\)
0.328196 + 0.944610i \(0.393559\pi\)
\(182\) −4.37740 −0.324474
\(183\) 0 0
\(184\) −12.9708 −0.956221
\(185\) 0.823421 0.0605391
\(186\) 0 0
\(187\) 7.57745 0.554118
\(188\) 7.46328 0.544315
\(189\) 0 0
\(190\) −0.277872 −0.0201590
\(191\) −11.0056 −0.796337 −0.398169 0.917312i \(-0.630354\pi\)
−0.398169 + 0.917312i \(0.630354\pi\)
\(192\) 0 0
\(193\) 6.67906 0.480769 0.240385 0.970678i \(-0.422726\pi\)
0.240385 + 0.970678i \(0.422726\pi\)
\(194\) 19.9695 1.43373
\(195\) 0 0
\(196\) 0.672794 0.0480567
\(197\) −14.2032 −1.01194 −0.505970 0.862551i \(-0.668865\pi\)
−0.505970 + 0.862551i \(0.668865\pi\)
\(198\) 0 0
\(199\) −8.78561 −0.622795 −0.311398 0.950280i \(-0.600797\pi\)
−0.311398 + 0.950280i \(0.600797\pi\)
\(200\) −10.8238 −0.765359
\(201\) 0 0
\(202\) −7.74859 −0.545189
\(203\) −9.60657 −0.674249
\(204\) 0 0
\(205\) 0.510524 0.0356565
\(206\) −7.08015 −0.493298
\(207\) 0 0
\(208\) 13.1009 0.908387
\(209\) −1.94525 −0.134556
\(210\) 0 0
\(211\) −17.0024 −1.17049 −0.585247 0.810855i \(-0.699002\pi\)
−0.585247 + 0.810855i \(0.699002\pi\)
\(212\) 9.25397 0.635565
\(213\) 0 0
\(214\) 5.69662 0.389413
\(215\) 0.933133 0.0636392
\(216\) 0 0
\(217\) −1.81504 −0.123213
\(218\) 24.7226 1.67443
\(219\) 0 0
\(220\) −0.0895248 −0.00603576
\(221\) 16.4407 1.10592
\(222\) 0 0
\(223\) −1.34976 −0.0903867 −0.0451934 0.998978i \(-0.514390\pi\)
−0.0451934 + 0.998978i \(0.514390\pi\)
\(224\) −3.65969 −0.244524
\(225\) 0 0
\(226\) −19.0085 −1.26443
\(227\) 12.2240 0.811338 0.405669 0.914020i \(-0.367039\pi\)
0.405669 + 0.914020i \(0.367039\pi\)
\(228\) 0 0
\(229\) −6.61263 −0.436975 −0.218488 0.975840i \(-0.570112\pi\)
−0.218488 + 0.975840i \(0.570112\pi\)
\(230\) 1.05379 0.0694847
\(231\) 0 0
\(232\) 20.8444 1.36850
\(233\) 7.28567 0.477300 0.238650 0.971106i \(-0.423295\pi\)
0.238650 + 0.971106i \(0.423295\pi\)
\(234\) 0 0
\(235\) 1.19611 0.0780256
\(236\) −3.82780 −0.249168
\(237\) 0 0
\(238\) −10.0385 −0.650699
\(239\) 10.5610 0.683135 0.341567 0.939857i \(-0.389042\pi\)
0.341567 + 0.939857i \(0.389042\pi\)
\(240\) 0 0
\(241\) 21.1530 1.36258 0.681292 0.732012i \(-0.261418\pi\)
0.681292 + 0.732012i \(0.261418\pi\)
\(242\) 15.4938 0.995979
\(243\) 0 0
\(244\) −5.62918 −0.360371
\(245\) 0.107826 0.00688876
\(246\) 0 0
\(247\) −4.22057 −0.268549
\(248\) 3.93828 0.250081
\(249\) 0 0
\(250\) 1.76077 0.111361
\(251\) −4.58972 −0.289700 −0.144850 0.989454i \(-0.546270\pi\)
−0.144850 + 0.989454i \(0.546270\pi\)
\(252\) 0 0
\(253\) 7.37707 0.463792
\(254\) 1.63487 0.102581
\(255\) 0 0
\(256\) 14.5247 0.907794
\(257\) −22.0168 −1.37337 −0.686687 0.726954i \(-0.740936\pi\)
−0.686687 + 0.726954i \(0.740936\pi\)
\(258\) 0 0
\(259\) −7.63656 −0.474513
\(260\) −0.194240 −0.0120463
\(261\) 0 0
\(262\) −4.35750 −0.269208
\(263\) 1.29988 0.0801540 0.0400770 0.999197i \(-0.487240\pi\)
0.0400770 + 0.999197i \(0.487240\pi\)
\(264\) 0 0
\(265\) 1.48310 0.0911059
\(266\) 2.57704 0.158008
\(267\) 0 0
\(268\) −2.96390 −0.181049
\(269\) −5.22689 −0.318689 −0.159345 0.987223i \(-0.550938\pi\)
−0.159345 + 0.987223i \(0.550938\pi\)
\(270\) 0 0
\(271\) −30.8828 −1.87600 −0.937999 0.346637i \(-0.887324\pi\)
−0.937999 + 0.346637i \(0.887324\pi\)
\(272\) 30.0439 1.82168
\(273\) 0 0
\(274\) −30.6092 −1.84917
\(275\) 6.15597 0.371219
\(276\) 0 0
\(277\) 1.95927 0.117721 0.0588606 0.998266i \(-0.481253\pi\)
0.0588606 + 0.998266i \(0.481253\pi\)
\(278\) 22.4349 1.34555
\(279\) 0 0
\(280\) −0.233962 −0.0139819
\(281\) −24.0387 −1.43403 −0.717015 0.697058i \(-0.754492\pi\)
−0.717015 + 0.697058i \(0.754492\pi\)
\(282\) 0 0
\(283\) −19.8765 −1.18154 −0.590768 0.806841i \(-0.701175\pi\)
−0.590768 + 0.806841i \(0.701175\pi\)
\(284\) 9.35430 0.555075
\(285\) 0 0
\(286\) −5.40198 −0.319426
\(287\) −4.73470 −0.279480
\(288\) 0 0
\(289\) 20.7027 1.21781
\(290\) −1.69346 −0.0994434
\(291\) 0 0
\(292\) −5.47145 −0.320192
\(293\) 12.0901 0.706313 0.353156 0.935564i \(-0.385108\pi\)
0.353156 + 0.935564i \(0.385108\pi\)
\(294\) 0 0
\(295\) −0.613466 −0.0357174
\(296\) 16.5699 0.963103
\(297\) 0 0
\(298\) 0.225321 0.0130525
\(299\) 16.0059 0.925644
\(300\) 0 0
\(301\) −8.65406 −0.498812
\(302\) 9.73571 0.560227
\(303\) 0 0
\(304\) −7.71273 −0.442355
\(305\) −0.902166 −0.0516579
\(306\) 0 0
\(307\) −27.6351 −1.57722 −0.788608 0.614896i \(-0.789198\pi\)
−0.788608 + 0.614896i \(0.789198\pi\)
\(308\) 0.830270 0.0473090
\(309\) 0 0
\(310\) −0.319957 −0.0181724
\(311\) −23.9836 −1.35999 −0.679994 0.733218i \(-0.738017\pi\)
−0.679994 + 0.733218i \(0.738017\pi\)
\(312\) 0 0
\(313\) 23.6714 1.33799 0.668993 0.743269i \(-0.266726\pi\)
0.668993 + 0.743269i \(0.266726\pi\)
\(314\) 18.2026 1.02723
\(315\) 0 0
\(316\) 7.19397 0.404693
\(317\) 21.3847 1.20108 0.600542 0.799593i \(-0.294951\pi\)
0.600542 + 0.799593i \(0.294951\pi\)
\(318\) 0 0
\(319\) −11.8551 −0.663758
\(320\) 0.410036 0.0229217
\(321\) 0 0
\(322\) −9.77303 −0.544630
\(323\) −9.67887 −0.538547
\(324\) 0 0
\(325\) 13.3565 0.740884
\(326\) −18.8438 −1.04366
\(327\) 0 0
\(328\) 10.2734 0.567252
\(329\) −11.0930 −0.611574
\(330\) 0 0
\(331\) 2.40761 0.132334 0.0661670 0.997809i \(-0.478923\pi\)
0.0661670 + 0.997809i \(0.478923\pi\)
\(332\) −6.94509 −0.381161
\(333\) 0 0
\(334\) −32.5081 −1.77876
\(335\) −0.475013 −0.0259527
\(336\) 0 0
\(337\) −27.4338 −1.49442 −0.747208 0.664590i \(-0.768606\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(338\) 9.53271 0.518511
\(339\) 0 0
\(340\) −0.445443 −0.0241576
\(341\) −2.23987 −0.121296
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 18.7776 1.01242
\(345\) 0 0
\(346\) −36.1647 −1.94423
\(347\) −24.7643 −1.32942 −0.664709 0.747103i \(-0.731444\pi\)
−0.664709 + 0.747103i \(0.731444\pi\)
\(348\) 0 0
\(349\) −33.4203 −1.78895 −0.894473 0.447123i \(-0.852449\pi\)
−0.894473 + 0.447123i \(0.852449\pi\)
\(350\) −8.15533 −0.435921
\(351\) 0 0
\(352\) −4.51629 −0.240719
\(353\) −9.29165 −0.494545 −0.247272 0.968946i \(-0.579534\pi\)
−0.247272 + 0.968946i \(0.579534\pi\)
\(354\) 0 0
\(355\) 1.49918 0.0795680
\(356\) −10.5780 −0.560631
\(357\) 0 0
\(358\) 13.1503 0.695016
\(359\) −2.66632 −0.140723 −0.0703614 0.997522i \(-0.522415\pi\)
−0.0703614 + 0.997522i \(0.522415\pi\)
\(360\) 0 0
\(361\) −16.5153 −0.869225
\(362\) −14.4373 −0.758807
\(363\) 0 0
\(364\) 1.80142 0.0944202
\(365\) −0.876888 −0.0458984
\(366\) 0 0
\(367\) 5.53961 0.289165 0.144583 0.989493i \(-0.453816\pi\)
0.144583 + 0.989493i \(0.453816\pi\)
\(368\) 29.2493 1.52473
\(369\) 0 0
\(370\) −1.34618 −0.0699848
\(371\) −13.7545 −0.714099
\(372\) 0 0
\(373\) 7.13583 0.369479 0.184740 0.982788i \(-0.440856\pi\)
0.184740 + 0.982788i \(0.440856\pi\)
\(374\) −12.3881 −0.640576
\(375\) 0 0
\(376\) 24.0696 1.24129
\(377\) −25.7218 −1.32474
\(378\) 0 0
\(379\) 22.1188 1.13617 0.568083 0.822971i \(-0.307685\pi\)
0.568083 + 0.822971i \(0.307685\pi\)
\(380\) 0.114352 0.00586615
\(381\) 0 0
\(382\) 17.9927 0.920587
\(383\) −5.74924 −0.293773 −0.146886 0.989153i \(-0.546925\pi\)
−0.146886 + 0.989153i \(0.546925\pi\)
\(384\) 0 0
\(385\) 0.133064 0.00678158
\(386\) −10.9194 −0.555782
\(387\) 0 0
\(388\) −8.21803 −0.417207
\(389\) 18.0335 0.914335 0.457167 0.889381i \(-0.348864\pi\)
0.457167 + 0.889381i \(0.348864\pi\)
\(390\) 0 0
\(391\) 36.7056 1.85628
\(392\) 2.16981 0.109592
\(393\) 0 0
\(394\) 23.2204 1.16983
\(395\) 1.15295 0.0580112
\(396\) 0 0
\(397\) 22.5113 1.12981 0.564906 0.825156i \(-0.308913\pi\)
0.564906 + 0.825156i \(0.308913\pi\)
\(398\) 14.3633 0.719968
\(399\) 0 0
\(400\) 24.4078 1.22039
\(401\) −33.0927 −1.65257 −0.826284 0.563253i \(-0.809550\pi\)
−0.826284 + 0.563253i \(0.809550\pi\)
\(402\) 0 0
\(403\) −4.85980 −0.242084
\(404\) 3.18876 0.158647
\(405\) 0 0
\(406\) 15.7055 0.779449
\(407\) −9.42399 −0.467130
\(408\) 0 0
\(409\) −10.6802 −0.528103 −0.264051 0.964509i \(-0.585059\pi\)
−0.264051 + 0.964509i \(0.585059\pi\)
\(410\) −0.834640 −0.0412199
\(411\) 0 0
\(412\) 2.91368 0.143547
\(413\) 5.68940 0.279957
\(414\) 0 0
\(415\) −1.11306 −0.0546381
\(416\) −9.79891 −0.480431
\(417\) 0 0
\(418\) 3.18023 0.155550
\(419\) 8.09996 0.395709 0.197855 0.980231i \(-0.436603\pi\)
0.197855 + 0.980231i \(0.436603\pi\)
\(420\) 0 0
\(421\) 22.9457 1.11830 0.559152 0.829065i \(-0.311127\pi\)
0.559152 + 0.829065i \(0.311127\pi\)
\(422\) 27.7967 1.35312
\(423\) 0 0
\(424\) 29.8447 1.44938
\(425\) 30.6299 1.48577
\(426\) 0 0
\(427\) 8.36686 0.404901
\(428\) −2.34432 −0.113317
\(429\) 0 0
\(430\) −1.52555 −0.0735686
\(431\) −18.5620 −0.894099 −0.447049 0.894509i \(-0.647525\pi\)
−0.447049 + 0.894509i \(0.647525\pi\)
\(432\) 0 0
\(433\) −9.97229 −0.479238 −0.239619 0.970867i \(-0.577023\pi\)
−0.239619 + 0.970867i \(0.577023\pi\)
\(434\) 2.96735 0.142437
\(435\) 0 0
\(436\) −10.1741 −0.487249
\(437\) −9.42290 −0.450759
\(438\) 0 0
\(439\) −13.8980 −0.663316 −0.331658 0.943400i \(-0.607608\pi\)
−0.331658 + 0.943400i \(0.607608\pi\)
\(440\) −0.288723 −0.0137644
\(441\) 0 0
\(442\) −26.8783 −1.27847
\(443\) −26.4427 −1.25633 −0.628165 0.778080i \(-0.716194\pi\)
−0.628165 + 0.778080i \(0.716194\pi\)
\(444\) 0 0
\(445\) −1.69529 −0.0803644
\(446\) 2.20668 0.104489
\(447\) 0 0
\(448\) −3.80276 −0.179663
\(449\) −12.1557 −0.573664 −0.286832 0.957981i \(-0.592602\pi\)
−0.286832 + 0.957981i \(0.592602\pi\)
\(450\) 0 0
\(451\) −5.84291 −0.275132
\(452\) 7.82254 0.367941
\(453\) 0 0
\(454\) −19.9847 −0.937928
\(455\) 0.288707 0.0135348
\(456\) 0 0
\(457\) −13.8183 −0.646395 −0.323197 0.946332i \(-0.604758\pi\)
−0.323197 + 0.946332i \(0.604758\pi\)
\(458\) 10.8108 0.505155
\(459\) 0 0
\(460\) −0.433663 −0.0202197
\(461\) 11.8257 0.550779 0.275389 0.961333i \(-0.411193\pi\)
0.275389 + 0.961333i \(0.411193\pi\)
\(462\) 0 0
\(463\) 23.5068 1.09245 0.546227 0.837637i \(-0.316064\pi\)
0.546227 + 0.837637i \(0.316064\pi\)
\(464\) −47.0043 −2.18212
\(465\) 0 0
\(466\) −11.9111 −0.551772
\(467\) −31.0128 −1.43510 −0.717551 0.696506i \(-0.754737\pi\)
−0.717551 + 0.696506i \(0.754737\pi\)
\(468\) 0 0
\(469\) 4.40536 0.203421
\(470\) −1.95548 −0.0901997
\(471\) 0 0
\(472\) −12.3449 −0.568220
\(473\) −10.6797 −0.491051
\(474\) 0 0
\(475\) −7.86316 −0.360787
\(476\) 4.13113 0.189350
\(477\) 0 0
\(478\) −17.2659 −0.789722
\(479\) 21.5723 0.985664 0.492832 0.870125i \(-0.335962\pi\)
0.492832 + 0.870125i \(0.335962\pi\)
\(480\) 0 0
\(481\) −20.4471 −0.932306
\(482\) −34.5824 −1.57518
\(483\) 0 0
\(484\) −6.37613 −0.289824
\(485\) −1.31707 −0.0598051
\(486\) 0 0
\(487\) −16.3925 −0.742813 −0.371407 0.928470i \(-0.621124\pi\)
−0.371407 + 0.928470i \(0.621124\pi\)
\(488\) −18.1545 −0.821815
\(489\) 0 0
\(490\) −0.176281 −0.00796359
\(491\) −5.03723 −0.227327 −0.113663 0.993519i \(-0.536259\pi\)
−0.113663 + 0.993519i \(0.536259\pi\)
\(492\) 0 0
\(493\) −58.9867 −2.65663
\(494\) 6.90008 0.310449
\(495\) 0 0
\(496\) −8.88086 −0.398762
\(497\) −13.9036 −0.623664
\(498\) 0 0
\(499\) 10.7980 0.483387 0.241693 0.970353i \(-0.422297\pi\)
0.241693 + 0.970353i \(0.422297\pi\)
\(500\) −0.724605 −0.0324053
\(501\) 0 0
\(502\) 7.50359 0.334901
\(503\) 7.50427 0.334599 0.167299 0.985906i \(-0.446495\pi\)
0.167299 + 0.985906i \(0.446495\pi\)
\(504\) 0 0
\(505\) 0.511050 0.0227414
\(506\) −12.0605 −0.536156
\(507\) 0 0
\(508\) −0.672794 −0.0298504
\(509\) −23.3270 −1.03395 −0.516976 0.856000i \(-0.672942\pi\)
−0.516976 + 0.856000i \(0.672942\pi\)
\(510\) 0 0
\(511\) 8.13243 0.359757
\(512\) 3.32680 0.147025
\(513\) 0 0
\(514\) 35.9946 1.58766
\(515\) 0.466964 0.0205769
\(516\) 0 0
\(517\) −13.6894 −0.602059
\(518\) 12.4848 0.548549
\(519\) 0 0
\(520\) −0.626438 −0.0274711
\(521\) −25.1871 −1.10347 −0.551734 0.834020i \(-0.686034\pi\)
−0.551734 + 0.834020i \(0.686034\pi\)
\(522\) 0 0
\(523\) −5.75769 −0.251766 −0.125883 0.992045i \(-0.540176\pi\)
−0.125883 + 0.992045i \(0.540176\pi\)
\(524\) 1.79324 0.0783379
\(525\) 0 0
\(526\) −2.12513 −0.0926601
\(527\) −11.1448 −0.485474
\(528\) 0 0
\(529\) 12.7349 0.553692
\(530\) −2.42467 −0.105321
\(531\) 0 0
\(532\) −1.06052 −0.0459796
\(533\) −12.6773 −0.549113
\(534\) 0 0
\(535\) −0.375715 −0.0162436
\(536\) −9.55877 −0.412876
\(537\) 0 0
\(538\) 8.54528 0.368413
\(539\) −1.23406 −0.0531548
\(540\) 0 0
\(541\) 0.385713 0.0165831 0.00829154 0.999966i \(-0.497361\pi\)
0.00829154 + 0.999966i \(0.497361\pi\)
\(542\) 50.4894 2.16870
\(543\) 0 0
\(544\) −22.4714 −0.963455
\(545\) −1.63056 −0.0698454
\(546\) 0 0
\(547\) −18.7454 −0.801495 −0.400747 0.916189i \(-0.631249\pi\)
−0.400747 + 0.916189i \(0.631249\pi\)
\(548\) 12.5965 0.538097
\(549\) 0 0
\(550\) −10.0642 −0.429139
\(551\) 15.1428 0.645106
\(552\) 0 0
\(553\) −10.6927 −0.454699
\(554\) −3.20315 −0.136089
\(555\) 0 0
\(556\) −9.23258 −0.391548
\(557\) −10.1358 −0.429467 −0.214734 0.976673i \(-0.568888\pi\)
−0.214734 + 0.976673i \(0.568888\pi\)
\(558\) 0 0
\(559\) −23.1714 −0.980047
\(560\) 0.527586 0.0222946
\(561\) 0 0
\(562\) 39.3002 1.65778
\(563\) 0.675398 0.0284646 0.0142323 0.999899i \(-0.495470\pi\)
0.0142323 + 0.999899i \(0.495470\pi\)
\(564\) 0 0
\(565\) 1.25369 0.0527430
\(566\) 32.4955 1.36589
\(567\) 0 0
\(568\) 30.1682 1.26583
\(569\) 16.3639 0.686009 0.343004 0.939334i \(-0.388555\pi\)
0.343004 + 0.939334i \(0.388555\pi\)
\(570\) 0 0
\(571\) −7.26607 −0.304075 −0.152038 0.988375i \(-0.548584\pi\)
−0.152038 + 0.988375i \(0.548584\pi\)
\(572\) 2.22307 0.0929511
\(573\) 0 0
\(574\) 7.74061 0.323087
\(575\) 29.8198 1.24357
\(576\) 0 0
\(577\) −25.9010 −1.07827 −0.539137 0.842218i \(-0.681250\pi\)
−0.539137 + 0.842218i \(0.681250\pi\)
\(578\) −33.8462 −1.40782
\(579\) 0 0
\(580\) 0.696906 0.0289375
\(581\) 10.3228 0.428260
\(582\) 0 0
\(583\) −16.9739 −0.702989
\(584\) −17.6458 −0.730188
\(585\) 0 0
\(586\) −19.7658 −0.816516
\(587\) −9.99126 −0.412383 −0.206192 0.978512i \(-0.566107\pi\)
−0.206192 + 0.978512i \(0.566107\pi\)
\(588\) 0 0
\(589\) 2.86104 0.117887
\(590\) 1.00294 0.0412902
\(591\) 0 0
\(592\) −37.3652 −1.53570
\(593\) 32.8401 1.34858 0.674291 0.738466i \(-0.264449\pi\)
0.674291 + 0.738466i \(0.264449\pi\)
\(594\) 0 0
\(595\) 0.662079 0.0271426
\(596\) −0.0927258 −0.00379820
\(597\) 0 0
\(598\) −26.1675 −1.07007
\(599\) −33.2490 −1.35852 −0.679258 0.733900i \(-0.737698\pi\)
−0.679258 + 0.733900i \(0.737698\pi\)
\(600\) 0 0
\(601\) 9.22830 0.376430 0.188215 0.982128i \(-0.439730\pi\)
0.188215 + 0.982128i \(0.439730\pi\)
\(602\) 14.1482 0.576639
\(603\) 0 0
\(604\) −4.00652 −0.163023
\(605\) −1.02188 −0.0415452
\(606\) 0 0
\(607\) 43.9163 1.78251 0.891253 0.453506i \(-0.149827\pi\)
0.891253 + 0.453506i \(0.149827\pi\)
\(608\) 5.76877 0.233954
\(609\) 0 0
\(610\) 1.47492 0.0597179
\(611\) −29.7016 −1.20160
\(612\) 0 0
\(613\) 41.6037 1.68036 0.840179 0.542309i \(-0.182450\pi\)
0.840179 + 0.542309i \(0.182450\pi\)
\(614\) 45.1797 1.82330
\(615\) 0 0
\(616\) 2.67768 0.107887
\(617\) 17.5822 0.707833 0.353916 0.935277i \(-0.384850\pi\)
0.353916 + 0.935277i \(0.384850\pi\)
\(618\) 0 0
\(619\) −19.9761 −0.802909 −0.401455 0.915879i \(-0.631495\pi\)
−0.401455 + 0.915879i \(0.631495\pi\)
\(620\) 0.131672 0.00528806
\(621\) 0 0
\(622\) 39.2101 1.57218
\(623\) 15.7224 0.629906
\(624\) 0 0
\(625\) 24.8257 0.993030
\(626\) −38.6996 −1.54675
\(627\) 0 0
\(628\) −7.49088 −0.298919
\(629\) −46.8904 −1.86964
\(630\) 0 0
\(631\) 23.2542 0.925733 0.462867 0.886428i \(-0.346821\pi\)
0.462867 + 0.886428i \(0.346821\pi\)
\(632\) 23.2010 0.922888
\(633\) 0 0
\(634\) −34.9612 −1.38849
\(635\) −0.107826 −0.00427895
\(636\) 0 0
\(637\) −2.67752 −0.106087
\(638\) 19.3815 0.767322
\(639\) 0 0
\(640\) −1.45958 −0.0576948
\(641\) 9.68321 0.382464 0.191232 0.981545i \(-0.438752\pi\)
0.191232 + 0.981545i \(0.438752\pi\)
\(642\) 0 0
\(643\) −24.4462 −0.964063 −0.482032 0.876154i \(-0.660101\pi\)
−0.482032 + 0.876154i \(0.660101\pi\)
\(644\) 4.02188 0.158484
\(645\) 0 0
\(646\) 15.8237 0.622574
\(647\) 48.3444 1.90062 0.950308 0.311312i \(-0.100769\pi\)
0.950308 + 0.311312i \(0.100769\pi\)
\(648\) 0 0
\(649\) 7.02107 0.275601
\(650\) −21.8361 −0.856482
\(651\) 0 0
\(652\) 7.75474 0.303699
\(653\) −2.27517 −0.0890342 −0.0445171 0.999009i \(-0.514175\pi\)
−0.0445171 + 0.999009i \(0.514175\pi\)
\(654\) 0 0
\(655\) 0.287395 0.0112294
\(656\) −23.1666 −0.904503
\(657\) 0 0
\(658\) 18.1355 0.706996
\(659\) −21.4031 −0.833745 −0.416873 0.908965i \(-0.636874\pi\)
−0.416873 + 0.908965i \(0.636874\pi\)
\(660\) 0 0
\(661\) −17.6134 −0.685083 −0.342541 0.939503i \(-0.611288\pi\)
−0.342541 + 0.939503i \(0.611288\pi\)
\(662\) −3.93612 −0.152982
\(663\) 0 0
\(664\) −22.3984 −0.869225
\(665\) −0.169966 −0.00659100
\(666\) 0 0
\(667\) −57.4268 −2.22357
\(668\) 13.3780 0.517610
\(669\) 0 0
\(670\) 0.776583 0.0300020
\(671\) 10.3252 0.398601
\(672\) 0 0
\(673\) 18.3102 0.705805 0.352903 0.935660i \(-0.385195\pi\)
0.352903 + 0.935660i \(0.385195\pi\)
\(674\) 44.8507 1.72758
\(675\) 0 0
\(676\) −3.92298 −0.150884
\(677\) 27.3081 1.04954 0.524769 0.851245i \(-0.324152\pi\)
0.524769 + 0.851245i \(0.324152\pi\)
\(678\) 0 0
\(679\) 12.2148 0.468760
\(680\) −1.43658 −0.0550905
\(681\) 0 0
\(682\) 3.66189 0.140221
\(683\) 14.9870 0.573461 0.286731 0.958011i \(-0.407432\pi\)
0.286731 + 0.958011i \(0.407432\pi\)
\(684\) 0 0
\(685\) 2.01880 0.0771343
\(686\) 1.63487 0.0624196
\(687\) 0 0
\(688\) −42.3438 −1.61434
\(689\) −36.8281 −1.40304
\(690\) 0 0
\(691\) −42.1601 −1.60384 −0.801922 0.597428i \(-0.796189\pi\)
−0.801922 + 0.597428i \(0.796189\pi\)
\(692\) 14.8828 0.565759
\(693\) 0 0
\(694\) 40.4864 1.53684
\(695\) −1.47967 −0.0561270
\(696\) 0 0
\(697\) −29.0722 −1.10119
\(698\) 54.6377 2.06807
\(699\) 0 0
\(700\) 3.35615 0.126851
\(701\) −32.7665 −1.23757 −0.618786 0.785559i \(-0.712375\pi\)
−0.618786 + 0.785559i \(0.712375\pi\)
\(702\) 0 0
\(703\) 12.0375 0.454003
\(704\) −4.69284 −0.176868
\(705\) 0 0
\(706\) 15.1906 0.571707
\(707\) −4.73958 −0.178250
\(708\) 0 0
\(709\) 25.0222 0.939728 0.469864 0.882739i \(-0.344303\pi\)
0.469864 + 0.882739i \(0.344303\pi\)
\(710\) −2.45096 −0.0919827
\(711\) 0 0
\(712\) −34.1147 −1.27850
\(713\) −10.8501 −0.406338
\(714\) 0 0
\(715\) 0.356282 0.0133242
\(716\) −5.41173 −0.202246
\(717\) 0 0
\(718\) 4.35908 0.162679
\(719\) 41.1989 1.53646 0.768230 0.640174i \(-0.221138\pi\)
0.768230 + 0.640174i \(0.221138\pi\)
\(720\) 0 0
\(721\) −4.33072 −0.161284
\(722\) 27.0003 1.00485
\(723\) 0 0
\(724\) 5.94135 0.220809
\(725\) −47.9211 −1.77975
\(726\) 0 0
\(727\) −2.12027 −0.0786366 −0.0393183 0.999227i \(-0.512519\pi\)
−0.0393183 + 0.999227i \(0.512519\pi\)
\(728\) 5.80971 0.215322
\(729\) 0 0
\(730\) 1.43360 0.0530598
\(731\) −53.1381 −1.96538
\(732\) 0 0
\(733\) −26.4888 −0.978385 −0.489192 0.872176i \(-0.662708\pi\)
−0.489192 + 0.872176i \(0.662708\pi\)
\(734\) −9.05653 −0.334282
\(735\) 0 0
\(736\) −21.8772 −0.806403
\(737\) 5.43649 0.200256
\(738\) 0 0
\(739\) 36.6556 1.34840 0.674199 0.738549i \(-0.264489\pi\)
0.674199 + 0.738549i \(0.264489\pi\)
\(740\) 0.553993 0.0203652
\(741\) 0 0
\(742\) 22.4868 0.825518
\(743\) 16.4701 0.604231 0.302115 0.953271i \(-0.402307\pi\)
0.302115 + 0.953271i \(0.402307\pi\)
\(744\) 0 0
\(745\) −0.0148608 −0.000544458 0
\(746\) −11.6661 −0.427128
\(747\) 0 0
\(748\) 5.09807 0.186404
\(749\) 3.48445 0.127319
\(750\) 0 0
\(751\) 15.7106 0.573288 0.286644 0.958037i \(-0.407460\pi\)
0.286644 + 0.958037i \(0.407460\pi\)
\(752\) −54.2771 −1.97928
\(753\) 0 0
\(754\) 42.0518 1.53143
\(755\) −0.642109 −0.0233687
\(756\) 0 0
\(757\) −14.4985 −0.526957 −0.263478 0.964665i \(-0.584870\pi\)
−0.263478 + 0.964665i \(0.584870\pi\)
\(758\) −36.1613 −1.31344
\(759\) 0 0
\(760\) 0.368794 0.0133775
\(761\) −28.2418 −1.02376 −0.511882 0.859056i \(-0.671051\pi\)
−0.511882 + 0.859056i \(0.671051\pi\)
\(762\) 0 0
\(763\) 15.1221 0.547457
\(764\) −7.40451 −0.267886
\(765\) 0 0
\(766\) 9.39926 0.339609
\(767\) 15.2335 0.550050
\(768\) 0 0
\(769\) 14.1456 0.510103 0.255051 0.966928i \(-0.417908\pi\)
0.255051 + 0.966928i \(0.417908\pi\)
\(770\) −0.217542 −0.00783968
\(771\) 0 0
\(772\) 4.49364 0.161729
\(773\) −13.2490 −0.476534 −0.238267 0.971200i \(-0.576579\pi\)
−0.238267 + 0.971200i \(0.576579\pi\)
\(774\) 0 0
\(775\) −9.05408 −0.325232
\(776\) −26.5037 −0.951427
\(777\) 0 0
\(778\) −29.4824 −1.05700
\(779\) 7.46330 0.267400
\(780\) 0 0
\(781\) −17.1580 −0.613961
\(782\) −60.0089 −2.14591
\(783\) 0 0
\(784\) −4.89294 −0.174748
\(785\) −1.20053 −0.0428489
\(786\) 0 0
\(787\) 51.2817 1.82800 0.913998 0.405718i \(-0.132979\pi\)
0.913998 + 0.405718i \(0.132979\pi\)
\(788\) −9.55586 −0.340414
\(789\) 0 0
\(790\) −1.88492 −0.0670625
\(791\) −11.6269 −0.413406
\(792\) 0 0
\(793\) 22.4025 0.795535
\(794\) −36.8031 −1.30609
\(795\) 0 0
\(796\) −5.91091 −0.209507
\(797\) −49.0876 −1.73877 −0.869385 0.494135i \(-0.835485\pi\)
−0.869385 + 0.494135i \(0.835485\pi\)
\(798\) 0 0
\(799\) −68.1135 −2.40968
\(800\) −18.2559 −0.645444
\(801\) 0 0
\(802\) 54.1021 1.91041
\(803\) 10.0359 0.354160
\(804\) 0 0
\(805\) 0.644570 0.0227181
\(806\) 7.94514 0.279856
\(807\) 0 0
\(808\) 10.2840 0.361789
\(809\) −8.25607 −0.290268 −0.145134 0.989412i \(-0.546361\pi\)
−0.145134 + 0.989412i \(0.546361\pi\)
\(810\) 0 0
\(811\) 10.1645 0.356923 0.178461 0.983947i \(-0.442888\pi\)
0.178461 + 0.983947i \(0.442888\pi\)
\(812\) −6.46324 −0.226815
\(813\) 0 0
\(814\) 15.4070 0.540015
\(815\) 1.24282 0.0435342
\(816\) 0 0
\(817\) 13.6414 0.477251
\(818\) 17.4608 0.610501
\(819\) 0 0
\(820\) 0.343478 0.0119948
\(821\) −11.6755 −0.407478 −0.203739 0.979025i \(-0.565309\pi\)
−0.203739 + 0.979025i \(0.565309\pi\)
\(822\) 0 0
\(823\) −46.4146 −1.61791 −0.808956 0.587870i \(-0.799967\pi\)
−0.808956 + 0.587870i \(0.799967\pi\)
\(824\) 9.39682 0.327354
\(825\) 0 0
\(826\) −9.30142 −0.323638
\(827\) −31.2992 −1.08838 −0.544190 0.838962i \(-0.683163\pi\)
−0.544190 + 0.838962i \(0.683163\pi\)
\(828\) 0 0
\(829\) 13.8062 0.479510 0.239755 0.970833i \(-0.422933\pi\)
0.239755 + 0.970833i \(0.422933\pi\)
\(830\) 1.81971 0.0631630
\(831\) 0 0
\(832\) −10.1820 −0.352996
\(833\) −6.14025 −0.212747
\(834\) 0 0
\(835\) 2.14404 0.0741975
\(836\) −1.30875 −0.0452642
\(837\) 0 0
\(838\) −13.2424 −0.457450
\(839\) 29.4290 1.01600 0.508000 0.861357i \(-0.330385\pi\)
0.508000 + 0.861357i \(0.330385\pi\)
\(840\) 0 0
\(841\) 63.2861 2.18228
\(842\) −37.5132 −1.29279
\(843\) 0 0
\(844\) −11.4391 −0.393751
\(845\) −0.628720 −0.0216286
\(846\) 0 0
\(847\) 9.47709 0.325637
\(848\) −67.3000 −2.31109
\(849\) 0 0
\(850\) −50.0758 −1.71759
\(851\) −45.6504 −1.56487
\(852\) 0 0
\(853\) 17.7046 0.606195 0.303097 0.952960i \(-0.401979\pi\)
0.303097 + 0.952960i \(0.401979\pi\)
\(854\) −13.6787 −0.468076
\(855\) 0 0
\(856\) −7.56058 −0.258415
\(857\) −0.809325 −0.0276460 −0.0138230 0.999904i \(-0.504400\pi\)
−0.0138230 + 0.999904i \(0.504400\pi\)
\(858\) 0 0
\(859\) −3.42756 −0.116947 −0.0584734 0.998289i \(-0.518623\pi\)
−0.0584734 + 0.998289i \(0.518623\pi\)
\(860\) 0.627807 0.0214080
\(861\) 0 0
\(862\) 30.3464 1.03360
\(863\) −13.9962 −0.476436 −0.238218 0.971212i \(-0.576563\pi\)
−0.238218 + 0.971212i \(0.576563\pi\)
\(864\) 0 0
\(865\) 2.38521 0.0810994
\(866\) 16.3034 0.554012
\(867\) 0 0
\(868\) −1.22115 −0.0414484
\(869\) −13.1954 −0.447624
\(870\) 0 0
\(871\) 11.7954 0.399673
\(872\) −32.8120 −1.11116
\(873\) 0 0
\(874\) 15.4052 0.521089
\(875\) 1.07701 0.0364095
\(876\) 0 0
\(877\) −39.9269 −1.34824 −0.674118 0.738624i \(-0.735476\pi\)
−0.674118 + 0.738624i \(0.735476\pi\)
\(878\) 22.7214 0.766810
\(879\) 0 0
\(880\) 0.651075 0.0219477
\(881\) 26.7623 0.901646 0.450823 0.892613i \(-0.351131\pi\)
0.450823 + 0.892613i \(0.351131\pi\)
\(882\) 0 0
\(883\) −26.3077 −0.885326 −0.442663 0.896688i \(-0.645966\pi\)
−0.442663 + 0.896688i \(0.645966\pi\)
\(884\) 11.0612 0.372028
\(885\) 0 0
\(886\) 43.2303 1.45235
\(887\) 47.3136 1.58864 0.794318 0.607502i \(-0.207828\pi\)
0.794318 + 0.607502i \(0.207828\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 2.77158 0.0929034
\(891\) 0 0
\(892\) −0.908112 −0.0304058
\(893\) 17.4858 0.585140
\(894\) 0 0
\(895\) −0.867316 −0.0289912
\(896\) 13.5364 0.452219
\(897\) 0 0
\(898\) 19.8730 0.663171
\(899\) 17.4363 0.581532
\(900\) 0 0
\(901\) −84.4562 −2.81365
\(902\) 9.55240 0.318060
\(903\) 0 0
\(904\) 25.2282 0.839078
\(905\) 0.952197 0.0316521
\(906\) 0 0
\(907\) 18.1057 0.601191 0.300596 0.953752i \(-0.402815\pi\)
0.300596 + 0.953752i \(0.402815\pi\)
\(908\) 8.22426 0.272932
\(909\) 0 0
\(910\) −0.471998 −0.0156466
\(911\) 10.1254 0.335471 0.167735 0.985832i \(-0.446355\pi\)
0.167735 + 0.985832i \(0.446355\pi\)
\(912\) 0 0
\(913\) 12.7389 0.421597
\(914\) 22.5912 0.747249
\(915\) 0 0
\(916\) −4.44894 −0.146997
\(917\) −2.66536 −0.0880178
\(918\) 0 0
\(919\) 25.0065 0.824889 0.412444 0.910983i \(-0.364675\pi\)
0.412444 + 0.910983i \(0.364675\pi\)
\(920\) −1.39859 −0.0461102
\(921\) 0 0
\(922\) −19.3335 −0.636715
\(923\) −37.2273 −1.22535
\(924\) 0 0
\(925\) −38.0940 −1.25252
\(926\) −38.4305 −1.26291
\(927\) 0 0
\(928\) 35.1571 1.15409
\(929\) 12.6245 0.414196 0.207098 0.978320i \(-0.433598\pi\)
0.207098 + 0.978320i \(0.433598\pi\)
\(930\) 0 0
\(931\) 1.57630 0.0516611
\(932\) 4.90176 0.160563
\(933\) 0 0
\(934\) 50.7019 1.65902
\(935\) 0.817047 0.0267203
\(936\) 0 0
\(937\) 4.17602 0.136425 0.0682123 0.997671i \(-0.478270\pi\)
0.0682123 + 0.997671i \(0.478270\pi\)
\(938\) −7.20218 −0.235160
\(939\) 0 0
\(940\) 0.804736 0.0262476
\(941\) 4.50287 0.146789 0.0733946 0.997303i \(-0.476617\pi\)
0.0733946 + 0.997303i \(0.476617\pi\)
\(942\) 0 0
\(943\) −28.3034 −0.921686
\(944\) 27.8379 0.906045
\(945\) 0 0
\(946\) 17.4598 0.567668
\(947\) 10.8130 0.351377 0.175688 0.984446i \(-0.443785\pi\)
0.175688 + 0.984446i \(0.443785\pi\)
\(948\) 0 0
\(949\) 21.7748 0.706839
\(950\) 12.8552 0.417079
\(951\) 0 0
\(952\) 13.3232 0.431806
\(953\) −1.02312 −0.0331420 −0.0165710 0.999863i \(-0.505275\pi\)
−0.0165710 + 0.999863i \(0.505275\pi\)
\(954\) 0 0
\(955\) −1.18669 −0.0384004
\(956\) 7.10539 0.229805
\(957\) 0 0
\(958\) −35.2679 −1.13945
\(959\) −18.7227 −0.604588
\(960\) 0 0
\(961\) −27.7056 −0.893730
\(962\) 33.4283 1.07777
\(963\) 0 0
\(964\) 14.2316 0.458369
\(965\) 0.720177 0.0231833
\(966\) 0 0
\(967\) −33.4538 −1.07580 −0.537902 0.843008i \(-0.680783\pi\)
−0.537902 + 0.843008i \(0.680783\pi\)
\(968\) −20.5634 −0.660934
\(969\) 0 0
\(970\) 2.15324 0.0691363
\(971\) −16.1758 −0.519106 −0.259553 0.965729i \(-0.583575\pi\)
−0.259553 + 0.965729i \(0.583575\pi\)
\(972\) 0 0
\(973\) 13.7227 0.439931
\(974\) 26.7995 0.858712
\(975\) 0 0
\(976\) 40.9385 1.31041
\(977\) −24.4857 −0.783368 −0.391684 0.920100i \(-0.628107\pi\)
−0.391684 + 0.920100i \(0.628107\pi\)
\(978\) 0 0
\(979\) 19.4025 0.620106
\(980\) 0.0725448 0.00231736
\(981\) 0 0
\(982\) 8.23520 0.262796
\(983\) 27.0424 0.862518 0.431259 0.902228i \(-0.358069\pi\)
0.431259 + 0.902228i \(0.358069\pi\)
\(984\) 0 0
\(985\) −1.53148 −0.0487970
\(986\) 96.4355 3.07113
\(987\) 0 0
\(988\) −2.83958 −0.0903390
\(989\) −51.7328 −1.64501
\(990\) 0 0
\(991\) −34.0897 −1.08290 −0.541448 0.840734i \(-0.682124\pi\)
−0.541448 + 0.840734i \(0.682124\pi\)
\(992\) 6.64248 0.210899
\(993\) 0 0
\(994\) 22.7306 0.720972
\(995\) −0.947318 −0.0300320
\(996\) 0 0
\(997\) −18.0695 −0.572266 −0.286133 0.958190i \(-0.592370\pi\)
−0.286133 + 0.958190i \(0.592370\pi\)
\(998\) −17.6534 −0.558808
\(999\) 0 0
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 \(a_p\))