Properties

Label 8008.2.a.u.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.0822465\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0822465 q^{3} -4.16696 q^{5} -1.00000 q^{7} -2.99324 q^{9} +O(q^{10})\) \(q+0.0822465 q^{3} -4.16696 q^{5} -1.00000 q^{7} -2.99324 q^{9} -1.00000 q^{11} -1.00000 q^{13} -0.342718 q^{15} +3.55835 q^{17} +5.09522 q^{19} -0.0822465 q^{21} -0.867395 q^{23} +12.3635 q^{25} -0.492922 q^{27} -8.23108 q^{29} +2.28590 q^{31} -0.0822465 q^{33} +4.16696 q^{35} +6.74793 q^{37} -0.0822465 q^{39} +2.15690 q^{41} +6.41607 q^{43} +12.4727 q^{45} -13.3368 q^{47} +1.00000 q^{49} +0.292662 q^{51} -2.36261 q^{53} +4.16696 q^{55} +0.419064 q^{57} +2.85455 q^{59} +3.08242 q^{61} +2.99324 q^{63} +4.16696 q^{65} +7.23118 q^{67} -0.0713401 q^{69} +1.56955 q^{71} +4.34423 q^{73} +1.01686 q^{75} +1.00000 q^{77} +0.0822696 q^{79} +8.93917 q^{81} -5.58917 q^{83} -14.8275 q^{85} -0.676977 q^{87} +5.43343 q^{89} +1.00000 q^{91} +0.188007 q^{93} -21.2316 q^{95} -11.8362 q^{97} +2.99324 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 0.0822465 0.0474850 0.0237425 0.999718i \(-0.492442\pi\)
0.0237425 + 0.999718i \(0.492442\pi\)
\(4\) 0 0
\(5\) −4.16696 −1.86352 −0.931760 0.363074i \(-0.881727\pi\)
−0.931760 + 0.363074i \(0.881727\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −2.99324 −0.997745
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −0.342718 −0.0884893
\(16\) 0 0
\(17\) 3.55835 0.863027 0.431514 0.902106i \(-0.357980\pi\)
0.431514 + 0.902106i \(0.357980\pi\)
\(18\) 0 0
\(19\) 5.09522 1.16892 0.584462 0.811421i \(-0.301306\pi\)
0.584462 + 0.811421i \(0.301306\pi\)
\(20\) 0 0
\(21\) −0.0822465 −0.0179476
\(22\) 0 0
\(23\) −0.867395 −0.180864 −0.0904321 0.995903i \(-0.528825\pi\)
−0.0904321 + 0.995903i \(0.528825\pi\)
\(24\) 0 0
\(25\) 12.3635 2.47271
\(26\) 0 0
\(27\) −0.492922 −0.0948629
\(28\) 0 0
\(29\) −8.23108 −1.52847 −0.764236 0.644936i \(-0.776884\pi\)
−0.764236 + 0.644936i \(0.776884\pi\)
\(30\) 0 0
\(31\) 2.28590 0.410559 0.205280 0.978703i \(-0.434190\pi\)
0.205280 + 0.978703i \(0.434190\pi\)
\(32\) 0 0
\(33\) −0.0822465 −0.0143173
\(34\) 0 0
\(35\) 4.16696 0.704345
\(36\) 0 0
\(37\) 6.74793 1.10935 0.554676 0.832066i \(-0.312842\pi\)
0.554676 + 0.832066i \(0.312842\pi\)
\(38\) 0 0
\(39\) −0.0822465 −0.0131700
\(40\) 0 0
\(41\) 2.15690 0.336851 0.168425 0.985714i \(-0.446132\pi\)
0.168425 + 0.985714i \(0.446132\pi\)
\(42\) 0 0
\(43\) 6.41607 0.978441 0.489221 0.872160i \(-0.337281\pi\)
0.489221 + 0.872160i \(0.337281\pi\)
\(44\) 0 0
\(45\) 12.4727 1.85932
\(46\) 0 0
\(47\) −13.3368 −1.94537 −0.972686 0.232126i \(-0.925432\pi\)
−0.972686 + 0.232126i \(0.925432\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0.292662 0.0409808
\(52\) 0 0
\(53\) −2.36261 −0.324530 −0.162265 0.986747i \(-0.551880\pi\)
−0.162265 + 0.986747i \(0.551880\pi\)
\(54\) 0 0
\(55\) 4.16696 0.561873
\(56\) 0 0
\(57\) 0.419064 0.0555063
\(58\) 0 0
\(59\) 2.85455 0.371631 0.185815 0.982585i \(-0.440507\pi\)
0.185815 + 0.982585i \(0.440507\pi\)
\(60\) 0 0
\(61\) 3.08242 0.394663 0.197332 0.980337i \(-0.436772\pi\)
0.197332 + 0.980337i \(0.436772\pi\)
\(62\) 0 0
\(63\) 2.99324 0.377112
\(64\) 0 0
\(65\) 4.16696 0.516848
\(66\) 0 0
\(67\) 7.23118 0.883430 0.441715 0.897156i \(-0.354370\pi\)
0.441715 + 0.897156i \(0.354370\pi\)
\(68\) 0 0
\(69\) −0.0713401 −0.00858834
\(70\) 0 0
\(71\) 1.56955 0.186271 0.0931354 0.995653i \(-0.470311\pi\)
0.0931354 + 0.995653i \(0.470311\pi\)
\(72\) 0 0
\(73\) 4.34423 0.508453 0.254227 0.967145i \(-0.418179\pi\)
0.254227 + 0.967145i \(0.418179\pi\)
\(74\) 0 0
\(75\) 1.01686 0.117417
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 0.0822696 0.00925605 0.00462802 0.999989i \(-0.498527\pi\)
0.00462802 + 0.999989i \(0.498527\pi\)
\(80\) 0 0
\(81\) 8.93917 0.993241
\(82\) 0 0
\(83\) −5.58917 −0.613491 −0.306746 0.951792i \(-0.599240\pi\)
−0.306746 + 0.951792i \(0.599240\pi\)
\(84\) 0 0
\(85\) −14.8275 −1.60827
\(86\) 0 0
\(87\) −0.676977 −0.0725796
\(88\) 0 0
\(89\) 5.43343 0.575942 0.287971 0.957639i \(-0.407019\pi\)
0.287971 + 0.957639i \(0.407019\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0.188007 0.0194954
\(94\) 0 0
\(95\) −21.2316 −2.17831
\(96\) 0 0
\(97\) −11.8362 −1.20179 −0.600894 0.799328i \(-0.705189\pi\)
−0.600894 + 0.799328i \(0.705189\pi\)
\(98\) 0 0
\(99\) 2.99324 0.300831
\(100\) 0 0
\(101\) 13.1574 1.30921 0.654605 0.755971i \(-0.272835\pi\)
0.654605 + 0.755971i \(0.272835\pi\)
\(102\) 0 0
\(103\) −2.45911 −0.242303 −0.121152 0.992634i \(-0.538659\pi\)
−0.121152 + 0.992634i \(0.538659\pi\)
\(104\) 0 0
\(105\) 0.342718 0.0334458
\(106\) 0 0
\(107\) 3.15058 0.304578 0.152289 0.988336i \(-0.451336\pi\)
0.152289 + 0.988336i \(0.451336\pi\)
\(108\) 0 0
\(109\) 19.2113 1.84011 0.920055 0.391789i \(-0.128144\pi\)
0.920055 + 0.391789i \(0.128144\pi\)
\(110\) 0 0
\(111\) 0.554993 0.0526776
\(112\) 0 0
\(113\) 9.78708 0.920691 0.460345 0.887740i \(-0.347726\pi\)
0.460345 + 0.887740i \(0.347726\pi\)
\(114\) 0 0
\(115\) 3.61440 0.337044
\(116\) 0 0
\(117\) 2.99324 0.276725
\(118\) 0 0
\(119\) −3.55835 −0.326194
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.177397 0.0159954
\(124\) 0 0
\(125\) −30.6836 −2.74442
\(126\) 0 0
\(127\) −9.25558 −0.821300 −0.410650 0.911793i \(-0.634698\pi\)
−0.410650 + 0.911793i \(0.634698\pi\)
\(128\) 0 0
\(129\) 0.527699 0.0464613
\(130\) 0 0
\(131\) −4.72266 −0.412620 −0.206310 0.978487i \(-0.566146\pi\)
−0.206310 + 0.978487i \(0.566146\pi\)
\(132\) 0 0
\(133\) −5.09522 −0.441812
\(134\) 0 0
\(135\) 2.05399 0.176779
\(136\) 0 0
\(137\) −14.8620 −1.26975 −0.634875 0.772615i \(-0.718948\pi\)
−0.634875 + 0.772615i \(0.718948\pi\)
\(138\) 0 0
\(139\) 12.0767 1.02433 0.512164 0.858888i \(-0.328844\pi\)
0.512164 + 0.858888i \(0.328844\pi\)
\(140\) 0 0
\(141\) −1.09690 −0.0923760
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) 34.2986 2.84834
\(146\) 0 0
\(147\) 0.0822465 0.00678357
\(148\) 0 0
\(149\) −16.0424 −1.31424 −0.657120 0.753786i \(-0.728226\pi\)
−0.657120 + 0.753786i \(0.728226\pi\)
\(150\) 0 0
\(151\) −2.36830 −0.192729 −0.0963647 0.995346i \(-0.530722\pi\)
−0.0963647 + 0.995346i \(0.530722\pi\)
\(152\) 0 0
\(153\) −10.6510 −0.861081
\(154\) 0 0
\(155\) −9.52524 −0.765086
\(156\) 0 0
\(157\) 0.920932 0.0734984 0.0367492 0.999325i \(-0.488300\pi\)
0.0367492 + 0.999325i \(0.488300\pi\)
\(158\) 0 0
\(159\) −0.194316 −0.0154103
\(160\) 0 0
\(161\) 0.867395 0.0683603
\(162\) 0 0
\(163\) −16.8658 −1.32103 −0.660516 0.750812i \(-0.729663\pi\)
−0.660516 + 0.750812i \(0.729663\pi\)
\(164\) 0 0
\(165\) 0.342718 0.0266805
\(166\) 0 0
\(167\) −0.272664 −0.0210994 −0.0105497 0.999944i \(-0.503358\pi\)
−0.0105497 + 0.999944i \(0.503358\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −15.2512 −1.16629
\(172\) 0 0
\(173\) −7.79353 −0.592531 −0.296266 0.955106i \(-0.595741\pi\)
−0.296266 + 0.955106i \(0.595741\pi\)
\(174\) 0 0
\(175\) −12.3635 −0.934596
\(176\) 0 0
\(177\) 0.234776 0.0176469
\(178\) 0 0
\(179\) −2.03030 −0.151752 −0.0758759 0.997117i \(-0.524175\pi\)
−0.0758759 + 0.997117i \(0.524175\pi\)
\(180\) 0 0
\(181\) 3.60659 0.268075 0.134038 0.990976i \(-0.457206\pi\)
0.134038 + 0.990976i \(0.457206\pi\)
\(182\) 0 0
\(183\) 0.253518 0.0187406
\(184\) 0 0
\(185\) −28.1183 −2.06730
\(186\) 0 0
\(187\) −3.55835 −0.260212
\(188\) 0 0
\(189\) 0.492922 0.0358548
\(190\) 0 0
\(191\) 7.49107 0.542035 0.271017 0.962574i \(-0.412640\pi\)
0.271017 + 0.962574i \(0.412640\pi\)
\(192\) 0 0
\(193\) −8.29214 −0.596882 −0.298441 0.954428i \(-0.596467\pi\)
−0.298441 + 0.954428i \(0.596467\pi\)
\(194\) 0 0
\(195\) 0.342718 0.0245425
\(196\) 0 0
\(197\) 19.0417 1.35667 0.678333 0.734754i \(-0.262703\pi\)
0.678333 + 0.734754i \(0.262703\pi\)
\(198\) 0 0
\(199\) −15.1220 −1.07197 −0.535986 0.844227i \(-0.680060\pi\)
−0.535986 + 0.844227i \(0.680060\pi\)
\(200\) 0 0
\(201\) 0.594739 0.0419497
\(202\) 0 0
\(203\) 8.23108 0.577708
\(204\) 0 0
\(205\) −8.98770 −0.627728
\(206\) 0 0
\(207\) 2.59632 0.180456
\(208\) 0 0
\(209\) −5.09522 −0.352444
\(210\) 0 0
\(211\) −23.7605 −1.63574 −0.817872 0.575401i \(-0.804846\pi\)
−0.817872 + 0.575401i \(0.804846\pi\)
\(212\) 0 0
\(213\) 0.129090 0.00884507
\(214\) 0 0
\(215\) −26.7355 −1.82335
\(216\) 0 0
\(217\) −2.28590 −0.155177
\(218\) 0 0
\(219\) 0.357297 0.0241439
\(220\) 0 0
\(221\) −3.55835 −0.239361
\(222\) 0 0
\(223\) −5.23733 −0.350718 −0.175359 0.984505i \(-0.556109\pi\)
−0.175359 + 0.984505i \(0.556109\pi\)
\(224\) 0 0
\(225\) −37.0070 −2.46713
\(226\) 0 0
\(227\) 0.629276 0.0417665 0.0208833 0.999782i \(-0.493352\pi\)
0.0208833 + 0.999782i \(0.493352\pi\)
\(228\) 0 0
\(229\) −15.1243 −0.999439 −0.499720 0.866187i \(-0.666564\pi\)
−0.499720 + 0.866187i \(0.666564\pi\)
\(230\) 0 0
\(231\) 0.0822465 0.00541142
\(232\) 0 0
\(233\) −6.49987 −0.425820 −0.212910 0.977072i \(-0.568294\pi\)
−0.212910 + 0.977072i \(0.568294\pi\)
\(234\) 0 0
\(235\) 55.5739 3.62524
\(236\) 0 0
\(237\) 0.00676638 0.000439524 0
\(238\) 0 0
\(239\) −24.6722 −1.59591 −0.797955 0.602717i \(-0.794085\pi\)
−0.797955 + 0.602717i \(0.794085\pi\)
\(240\) 0 0
\(241\) −18.5382 −1.19415 −0.597074 0.802186i \(-0.703670\pi\)
−0.597074 + 0.802186i \(0.703670\pi\)
\(242\) 0 0
\(243\) 2.21398 0.142027
\(244\) 0 0
\(245\) −4.16696 −0.266217
\(246\) 0 0
\(247\) −5.09522 −0.324201
\(248\) 0 0
\(249\) −0.459690 −0.0291316
\(250\) 0 0
\(251\) 25.0435 1.58073 0.790365 0.612636i \(-0.209891\pi\)
0.790365 + 0.612636i \(0.209891\pi\)
\(252\) 0 0
\(253\) 0.867395 0.0545326
\(254\) 0 0
\(255\) −1.21951 −0.0763686
\(256\) 0 0
\(257\) −1.87197 −0.116770 −0.0583851 0.998294i \(-0.518595\pi\)
−0.0583851 + 0.998294i \(0.518595\pi\)
\(258\) 0 0
\(259\) −6.74793 −0.419296
\(260\) 0 0
\(261\) 24.6376 1.52503
\(262\) 0 0
\(263\) −18.4354 −1.13678 −0.568389 0.822760i \(-0.692433\pi\)
−0.568389 + 0.822760i \(0.692433\pi\)
\(264\) 0 0
\(265\) 9.84490 0.604768
\(266\) 0 0
\(267\) 0.446880 0.0273486
\(268\) 0 0
\(269\) −9.63833 −0.587659 −0.293830 0.955858i \(-0.594930\pi\)
−0.293830 + 0.955858i \(0.594930\pi\)
\(270\) 0 0
\(271\) −2.11167 −0.128275 −0.0641374 0.997941i \(-0.520430\pi\)
−0.0641374 + 0.997941i \(0.520430\pi\)
\(272\) 0 0
\(273\) 0.0822465 0.00497778
\(274\) 0 0
\(275\) −12.3635 −0.745550
\(276\) 0 0
\(277\) −13.5147 −0.812019 −0.406010 0.913869i \(-0.633080\pi\)
−0.406010 + 0.913869i \(0.633080\pi\)
\(278\) 0 0
\(279\) −6.84223 −0.409634
\(280\) 0 0
\(281\) −12.4079 −0.740193 −0.370097 0.928993i \(-0.620675\pi\)
−0.370097 + 0.928993i \(0.620675\pi\)
\(282\) 0 0
\(283\) 20.5515 1.22166 0.610830 0.791762i \(-0.290836\pi\)
0.610830 + 0.791762i \(0.290836\pi\)
\(284\) 0 0
\(285\) −1.74622 −0.103437
\(286\) 0 0
\(287\) −2.15690 −0.127318
\(288\) 0 0
\(289\) −4.33813 −0.255184
\(290\) 0 0
\(291\) −0.973489 −0.0570669
\(292\) 0 0
\(293\) −9.74122 −0.569088 −0.284544 0.958663i \(-0.591842\pi\)
−0.284544 + 0.958663i \(0.591842\pi\)
\(294\) 0 0
\(295\) −11.8948 −0.692541
\(296\) 0 0
\(297\) 0.492922 0.0286023
\(298\) 0 0
\(299\) 0.867395 0.0501627
\(300\) 0 0
\(301\) −6.41607 −0.369816
\(302\) 0 0
\(303\) 1.08215 0.0621679
\(304\) 0 0
\(305\) −12.8443 −0.735463
\(306\) 0 0
\(307\) 8.98907 0.513034 0.256517 0.966540i \(-0.417425\pi\)
0.256517 + 0.966540i \(0.417425\pi\)
\(308\) 0 0
\(309\) −0.202253 −0.0115058
\(310\) 0 0
\(311\) −6.04639 −0.342860 −0.171430 0.985196i \(-0.554839\pi\)
−0.171430 + 0.985196i \(0.554839\pi\)
\(312\) 0 0
\(313\) 3.86492 0.218458 0.109229 0.994017i \(-0.465162\pi\)
0.109229 + 0.994017i \(0.465162\pi\)
\(314\) 0 0
\(315\) −12.4727 −0.702756
\(316\) 0 0
\(317\) 20.2825 1.13918 0.569588 0.821930i \(-0.307103\pi\)
0.569588 + 0.821930i \(0.307103\pi\)
\(318\) 0 0
\(319\) 8.23108 0.460852
\(320\) 0 0
\(321\) 0.259124 0.0144629
\(322\) 0 0
\(323\) 18.1306 1.00881
\(324\) 0 0
\(325\) −12.3635 −0.685806
\(326\) 0 0
\(327\) 1.58006 0.0873776
\(328\) 0 0
\(329\) 13.3368 0.735281
\(330\) 0 0
\(331\) −13.3781 −0.735329 −0.367665 0.929958i \(-0.619843\pi\)
−0.367665 + 0.929958i \(0.619843\pi\)
\(332\) 0 0
\(333\) −20.1981 −1.10685
\(334\) 0 0
\(335\) −30.1320 −1.64629
\(336\) 0 0
\(337\) −12.1252 −0.660503 −0.330251 0.943893i \(-0.607133\pi\)
−0.330251 + 0.943893i \(0.607133\pi\)
\(338\) 0 0
\(339\) 0.804952 0.0437190
\(340\) 0 0
\(341\) −2.28590 −0.123788
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.297271 0.0160046
\(346\) 0 0
\(347\) −34.5746 −1.85606 −0.928032 0.372501i \(-0.878500\pi\)
−0.928032 + 0.372501i \(0.878500\pi\)
\(348\) 0 0
\(349\) −26.7103 −1.42977 −0.714884 0.699243i \(-0.753521\pi\)
−0.714884 + 0.699243i \(0.753521\pi\)
\(350\) 0 0
\(351\) 0.492922 0.0263102
\(352\) 0 0
\(353\) 21.7511 1.15769 0.578847 0.815436i \(-0.303503\pi\)
0.578847 + 0.815436i \(0.303503\pi\)
\(354\) 0 0
\(355\) −6.54023 −0.347119
\(356\) 0 0
\(357\) −0.292662 −0.0154893
\(358\) 0 0
\(359\) −22.6345 −1.19460 −0.597301 0.802017i \(-0.703760\pi\)
−0.597301 + 0.802017i \(0.703760\pi\)
\(360\) 0 0
\(361\) 6.96126 0.366382
\(362\) 0 0
\(363\) 0.0822465 0.00431682
\(364\) 0 0
\(365\) −18.1022 −0.947513
\(366\) 0 0
\(367\) 28.2933 1.47690 0.738449 0.674309i \(-0.235558\pi\)
0.738449 + 0.674309i \(0.235558\pi\)
\(368\) 0 0
\(369\) −6.45610 −0.336091
\(370\) 0 0
\(371\) 2.36261 0.122661
\(372\) 0 0
\(373\) 25.8464 1.33827 0.669137 0.743139i \(-0.266664\pi\)
0.669137 + 0.743139i \(0.266664\pi\)
\(374\) 0 0
\(375\) −2.52361 −0.130319
\(376\) 0 0
\(377\) 8.23108 0.423922
\(378\) 0 0
\(379\) 2.00688 0.103086 0.0515431 0.998671i \(-0.483586\pi\)
0.0515431 + 0.998671i \(0.483586\pi\)
\(380\) 0 0
\(381\) −0.761239 −0.0389994
\(382\) 0 0
\(383\) 25.7837 1.31749 0.658744 0.752367i \(-0.271088\pi\)
0.658744 + 0.752367i \(0.271088\pi\)
\(384\) 0 0
\(385\) −4.16696 −0.212368
\(386\) 0 0
\(387\) −19.2048 −0.976235
\(388\) 0 0
\(389\) 5.03712 0.255392 0.127696 0.991813i \(-0.459242\pi\)
0.127696 + 0.991813i \(0.459242\pi\)
\(390\) 0 0
\(391\) −3.08649 −0.156091
\(392\) 0 0
\(393\) −0.388422 −0.0195933
\(394\) 0 0
\(395\) −0.342814 −0.0172488
\(396\) 0 0
\(397\) −9.26949 −0.465222 −0.232611 0.972570i \(-0.574727\pi\)
−0.232611 + 0.972570i \(0.574727\pi\)
\(398\) 0 0
\(399\) −0.419064 −0.0209794
\(400\) 0 0
\(401\) 25.3355 1.26519 0.632596 0.774482i \(-0.281989\pi\)
0.632596 + 0.774482i \(0.281989\pi\)
\(402\) 0 0
\(403\) −2.28590 −0.113869
\(404\) 0 0
\(405\) −37.2491 −1.85092
\(406\) 0 0
\(407\) −6.74793 −0.334482
\(408\) 0 0
\(409\) −37.9974 −1.87885 −0.939426 0.342751i \(-0.888641\pi\)
−0.939426 + 0.342751i \(0.888641\pi\)
\(410\) 0 0
\(411\) −1.22235 −0.0602941
\(412\) 0 0
\(413\) −2.85455 −0.140463
\(414\) 0 0
\(415\) 23.2899 1.14325
\(416\) 0 0
\(417\) 0.993262 0.0486402
\(418\) 0 0
\(419\) 16.9918 0.830105 0.415053 0.909797i \(-0.363763\pi\)
0.415053 + 0.909797i \(0.363763\pi\)
\(420\) 0 0
\(421\) −1.52547 −0.0743471 −0.0371735 0.999309i \(-0.511835\pi\)
−0.0371735 + 0.999309i \(0.511835\pi\)
\(422\) 0 0
\(423\) 39.9202 1.94099
\(424\) 0 0
\(425\) 43.9938 2.13401
\(426\) 0 0
\(427\) −3.08242 −0.149169
\(428\) 0 0
\(429\) 0.0822465 0.00397090
\(430\) 0 0
\(431\) −4.34282 −0.209186 −0.104593 0.994515i \(-0.533354\pi\)
−0.104593 + 0.994515i \(0.533354\pi\)
\(432\) 0 0
\(433\) −7.42087 −0.356624 −0.178312 0.983974i \(-0.557064\pi\)
−0.178312 + 0.983974i \(0.557064\pi\)
\(434\) 0 0
\(435\) 2.82093 0.135253
\(436\) 0 0
\(437\) −4.41957 −0.211417
\(438\) 0 0
\(439\) 34.8332 1.66250 0.831249 0.555901i \(-0.187627\pi\)
0.831249 + 0.555901i \(0.187627\pi\)
\(440\) 0 0
\(441\) −2.99324 −0.142535
\(442\) 0 0
\(443\) 21.2656 1.01036 0.505180 0.863014i \(-0.331426\pi\)
0.505180 + 0.863014i \(0.331426\pi\)
\(444\) 0 0
\(445\) −22.6409 −1.07328
\(446\) 0 0
\(447\) −1.31943 −0.0624067
\(448\) 0 0
\(449\) −40.0150 −1.88842 −0.944212 0.329339i \(-0.893174\pi\)
−0.944212 + 0.329339i \(0.893174\pi\)
\(450\) 0 0
\(451\) −2.15690 −0.101564
\(452\) 0 0
\(453\) −0.194784 −0.00915176
\(454\) 0 0
\(455\) −4.16696 −0.195350
\(456\) 0 0
\(457\) −3.96588 −0.185516 −0.0927580 0.995689i \(-0.529568\pi\)
−0.0927580 + 0.995689i \(0.529568\pi\)
\(458\) 0 0
\(459\) −1.75399 −0.0818693
\(460\) 0 0
\(461\) 11.0325 0.513837 0.256918 0.966433i \(-0.417293\pi\)
0.256918 + 0.966433i \(0.417293\pi\)
\(462\) 0 0
\(463\) −0.180837 −0.00840419 −0.00420210 0.999991i \(-0.501338\pi\)
−0.00420210 + 0.999991i \(0.501338\pi\)
\(464\) 0 0
\(465\) −0.783417 −0.0363301
\(466\) 0 0
\(467\) 26.2015 1.21246 0.606229 0.795290i \(-0.292681\pi\)
0.606229 + 0.795290i \(0.292681\pi\)
\(468\) 0 0
\(469\) −7.23118 −0.333905
\(470\) 0 0
\(471\) 0.0757434 0.00349007
\(472\) 0 0
\(473\) −6.41607 −0.295011
\(474\) 0 0
\(475\) 62.9950 2.89041
\(476\) 0 0
\(477\) 7.07185 0.323798
\(478\) 0 0
\(479\) 11.7491 0.536828 0.268414 0.963304i \(-0.413501\pi\)
0.268414 + 0.963304i \(0.413501\pi\)
\(480\) 0 0
\(481\) −6.74793 −0.307679
\(482\) 0 0
\(483\) 0.0713401 0.00324609
\(484\) 0 0
\(485\) 49.3211 2.23956
\(486\) 0 0
\(487\) −8.18584 −0.370936 −0.185468 0.982650i \(-0.559380\pi\)
−0.185468 + 0.982650i \(0.559380\pi\)
\(488\) 0 0
\(489\) −1.38715 −0.0627292
\(490\) 0 0
\(491\) −23.5403 −1.06236 −0.531179 0.847260i \(-0.678251\pi\)
−0.531179 + 0.847260i \(0.678251\pi\)
\(492\) 0 0
\(493\) −29.2891 −1.31911
\(494\) 0 0
\(495\) −12.4727 −0.560606
\(496\) 0 0
\(497\) −1.56955 −0.0704037
\(498\) 0 0
\(499\) 17.2794 0.773532 0.386766 0.922178i \(-0.373592\pi\)
0.386766 + 0.922178i \(0.373592\pi\)
\(500\) 0 0
\(501\) −0.0224256 −0.00100190
\(502\) 0 0
\(503\) 33.6467 1.50023 0.750117 0.661306i \(-0.229997\pi\)
0.750117 + 0.661306i \(0.229997\pi\)
\(504\) 0 0
\(505\) −54.8264 −2.43974
\(506\) 0 0
\(507\) 0.0822465 0.00365269
\(508\) 0 0
\(509\) 18.4079 0.815918 0.407959 0.913000i \(-0.366241\pi\)
0.407959 + 0.913000i \(0.366241\pi\)
\(510\) 0 0
\(511\) −4.34423 −0.192177
\(512\) 0 0
\(513\) −2.51155 −0.110888
\(514\) 0 0
\(515\) 10.2470 0.451537
\(516\) 0 0
\(517\) 13.3368 0.586552
\(518\) 0 0
\(519\) −0.640991 −0.0281364
\(520\) 0 0
\(521\) 6.80001 0.297914 0.148957 0.988844i \(-0.452408\pi\)
0.148957 + 0.988844i \(0.452408\pi\)
\(522\) 0 0
\(523\) −7.68243 −0.335929 −0.167965 0.985793i \(-0.553719\pi\)
−0.167965 + 0.985793i \(0.553719\pi\)
\(524\) 0 0
\(525\) −1.01686 −0.0443793
\(526\) 0 0
\(527\) 8.13403 0.354324
\(528\) 0 0
\(529\) −22.2476 −0.967288
\(530\) 0 0
\(531\) −8.54433 −0.370793
\(532\) 0 0
\(533\) −2.15690 −0.0934256
\(534\) 0 0
\(535\) −13.1283 −0.567587
\(536\) 0 0
\(537\) −0.166985 −0.00720593
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 24.1763 1.03942 0.519710 0.854343i \(-0.326040\pi\)
0.519710 + 0.854343i \(0.326040\pi\)
\(542\) 0 0
\(543\) 0.296629 0.0127296
\(544\) 0 0
\(545\) −80.0527 −3.42908
\(546\) 0 0
\(547\) 2.80666 0.120004 0.0600020 0.998198i \(-0.480889\pi\)
0.0600020 + 0.998198i \(0.480889\pi\)
\(548\) 0 0
\(549\) −9.22640 −0.393773
\(550\) 0 0
\(551\) −41.9392 −1.78667
\(552\) 0 0
\(553\) −0.0822696 −0.00349846
\(554\) 0 0
\(555\) −2.31263 −0.0981658
\(556\) 0 0
\(557\) −39.9857 −1.69425 −0.847123 0.531396i \(-0.821667\pi\)
−0.847123 + 0.531396i \(0.821667\pi\)
\(558\) 0 0
\(559\) −6.41607 −0.271371
\(560\) 0 0
\(561\) −0.292662 −0.0123562
\(562\) 0 0
\(563\) 11.8498 0.499411 0.249706 0.968322i \(-0.419666\pi\)
0.249706 + 0.968322i \(0.419666\pi\)
\(564\) 0 0
\(565\) −40.7823 −1.71573
\(566\) 0 0
\(567\) −8.93917 −0.375410
\(568\) 0 0
\(569\) 23.0663 0.966990 0.483495 0.875347i \(-0.339367\pi\)
0.483495 + 0.875347i \(0.339367\pi\)
\(570\) 0 0
\(571\) −44.7513 −1.87279 −0.936393 0.350954i \(-0.885857\pi\)
−0.936393 + 0.350954i \(0.885857\pi\)
\(572\) 0 0
\(573\) 0.616114 0.0257385
\(574\) 0 0
\(575\) −10.7241 −0.447225
\(576\) 0 0
\(577\) −29.6341 −1.23368 −0.616842 0.787087i \(-0.711588\pi\)
−0.616842 + 0.787087i \(0.711588\pi\)
\(578\) 0 0
\(579\) −0.681999 −0.0283429
\(580\) 0 0
\(581\) 5.58917 0.231878
\(582\) 0 0
\(583\) 2.36261 0.0978494
\(584\) 0 0
\(585\) −12.4727 −0.515682
\(586\) 0 0
\(587\) −27.4384 −1.13250 −0.566251 0.824233i \(-0.691607\pi\)
−0.566251 + 0.824233i \(0.691607\pi\)
\(588\) 0 0
\(589\) 11.6471 0.479912
\(590\) 0 0
\(591\) 1.56611 0.0644213
\(592\) 0 0
\(593\) 22.4208 0.920712 0.460356 0.887734i \(-0.347722\pi\)
0.460356 + 0.887734i \(0.347722\pi\)
\(594\) 0 0
\(595\) 14.8275 0.607868
\(596\) 0 0
\(597\) −1.24373 −0.0509026
\(598\) 0 0
\(599\) −5.58800 −0.228319 −0.114160 0.993462i \(-0.536418\pi\)
−0.114160 + 0.993462i \(0.536418\pi\)
\(600\) 0 0
\(601\) −42.2270 −1.72247 −0.861237 0.508204i \(-0.830310\pi\)
−0.861237 + 0.508204i \(0.830310\pi\)
\(602\) 0 0
\(603\) −21.6446 −0.881438
\(604\) 0 0
\(605\) −4.16696 −0.169411
\(606\) 0 0
\(607\) 46.2906 1.87888 0.939438 0.342720i \(-0.111348\pi\)
0.939438 + 0.342720i \(0.111348\pi\)
\(608\) 0 0
\(609\) 0.676977 0.0274325
\(610\) 0 0
\(611\) 13.3368 0.539549
\(612\) 0 0
\(613\) −21.4942 −0.868143 −0.434071 0.900878i \(-0.642923\pi\)
−0.434071 + 0.900878i \(0.642923\pi\)
\(614\) 0 0
\(615\) −0.739206 −0.0298077
\(616\) 0 0
\(617\) −36.2196 −1.45815 −0.729073 0.684436i \(-0.760048\pi\)
−0.729073 + 0.684436i \(0.760048\pi\)
\(618\) 0 0
\(619\) 4.84542 0.194754 0.0973770 0.995248i \(-0.468955\pi\)
0.0973770 + 0.995248i \(0.468955\pi\)
\(620\) 0 0
\(621\) 0.427558 0.0171573
\(622\) 0 0
\(623\) −5.43343 −0.217686
\(624\) 0 0
\(625\) 66.0394 2.64158
\(626\) 0 0
\(627\) −0.419064 −0.0167358
\(628\) 0 0
\(629\) 24.0115 0.957401
\(630\) 0 0
\(631\) −15.7269 −0.626079 −0.313040 0.949740i \(-0.601347\pi\)
−0.313040 + 0.949740i \(0.601347\pi\)
\(632\) 0 0
\(633\) −1.95422 −0.0776733
\(634\) 0 0
\(635\) 38.5676 1.53051
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −4.69802 −0.185851
\(640\) 0 0
\(641\) 30.5557 1.20688 0.603439 0.797409i \(-0.293797\pi\)
0.603439 + 0.797409i \(0.293797\pi\)
\(642\) 0 0
\(643\) 30.5681 1.20549 0.602744 0.797934i \(-0.294074\pi\)
0.602744 + 0.797934i \(0.294074\pi\)
\(644\) 0 0
\(645\) −2.19890 −0.0865816
\(646\) 0 0
\(647\) 41.3237 1.62460 0.812302 0.583237i \(-0.198214\pi\)
0.812302 + 0.583237i \(0.198214\pi\)
\(648\) 0 0
\(649\) −2.85455 −0.112051
\(650\) 0 0
\(651\) −0.188007 −0.00736857
\(652\) 0 0
\(653\) −32.2029 −1.26020 −0.630099 0.776515i \(-0.716986\pi\)
−0.630099 + 0.776515i \(0.716986\pi\)
\(654\) 0 0
\(655\) 19.6791 0.768926
\(656\) 0 0
\(657\) −13.0033 −0.507307
\(658\) 0 0
\(659\) 14.6458 0.570519 0.285260 0.958450i \(-0.407920\pi\)
0.285260 + 0.958450i \(0.407920\pi\)
\(660\) 0 0
\(661\) 16.9684 0.659996 0.329998 0.943982i \(-0.392952\pi\)
0.329998 + 0.943982i \(0.392952\pi\)
\(662\) 0 0
\(663\) −0.292662 −0.0113660
\(664\) 0 0
\(665\) 21.2316 0.823325
\(666\) 0 0
\(667\) 7.13959 0.276446
\(668\) 0 0
\(669\) −0.430752 −0.0166538
\(670\) 0 0
\(671\) −3.08242 −0.118995
\(672\) 0 0
\(673\) 15.1240 0.582988 0.291494 0.956573i \(-0.405848\pi\)
0.291494 + 0.956573i \(0.405848\pi\)
\(674\) 0 0
\(675\) −6.09427 −0.234568
\(676\) 0 0
\(677\) 1.25538 0.0482482 0.0241241 0.999709i \(-0.492320\pi\)
0.0241241 + 0.999709i \(0.492320\pi\)
\(678\) 0 0
\(679\) 11.8362 0.454233
\(680\) 0 0
\(681\) 0.0517557 0.00198328
\(682\) 0 0
\(683\) 12.4488 0.476338 0.238169 0.971224i \(-0.423453\pi\)
0.238169 + 0.971224i \(0.423453\pi\)
\(684\) 0 0
\(685\) 61.9295 2.36620
\(686\) 0 0
\(687\) −1.24392 −0.0474584
\(688\) 0 0
\(689\) 2.36261 0.0900083
\(690\) 0 0
\(691\) −44.2277 −1.68250 −0.841251 0.540645i \(-0.818180\pi\)
−0.841251 + 0.540645i \(0.818180\pi\)
\(692\) 0 0
\(693\) −2.99324 −0.113704
\(694\) 0 0
\(695\) −50.3229 −1.90886
\(696\) 0 0
\(697\) 7.67500 0.290711
\(698\) 0 0
\(699\) −0.534591 −0.0202201
\(700\) 0 0
\(701\) 3.19359 0.120620 0.0603101 0.998180i \(-0.480791\pi\)
0.0603101 + 0.998180i \(0.480791\pi\)
\(702\) 0 0
\(703\) 34.3822 1.29675
\(704\) 0 0
\(705\) 4.57075 0.172145
\(706\) 0 0
\(707\) −13.1574 −0.494835
\(708\) 0 0
\(709\) 3.46491 0.130128 0.0650638 0.997881i \(-0.479275\pi\)
0.0650638 + 0.997881i \(0.479275\pi\)
\(710\) 0 0
\(711\) −0.246252 −0.00923518
\(712\) 0 0
\(713\) −1.98277 −0.0742555
\(714\) 0 0
\(715\) −4.16696 −0.155835
\(716\) 0 0
\(717\) −2.02920 −0.0757818
\(718\) 0 0
\(719\) −37.9362 −1.41478 −0.707390 0.706823i \(-0.750128\pi\)
−0.707390 + 0.706823i \(0.750128\pi\)
\(720\) 0 0
\(721\) 2.45911 0.0915820
\(722\) 0 0
\(723\) −1.52470 −0.0567042
\(724\) 0 0
\(725\) −101.765 −3.77947
\(726\) 0 0
\(727\) −12.4357 −0.461216 −0.230608 0.973047i \(-0.574071\pi\)
−0.230608 + 0.973047i \(0.574071\pi\)
\(728\) 0 0
\(729\) −26.6354 −0.986496
\(730\) 0 0
\(731\) 22.8306 0.844421
\(732\) 0 0
\(733\) −19.0836 −0.704868 −0.352434 0.935837i \(-0.614646\pi\)
−0.352434 + 0.935837i \(0.614646\pi\)
\(734\) 0 0
\(735\) −0.342718 −0.0126413
\(736\) 0 0
\(737\) −7.23118 −0.266364
\(738\) 0 0
\(739\) 31.7132 1.16659 0.583295 0.812260i \(-0.301763\pi\)
0.583295 + 0.812260i \(0.301763\pi\)
\(740\) 0 0
\(741\) −0.419064 −0.0153947
\(742\) 0 0
\(743\) −19.9621 −0.732339 −0.366169 0.930548i \(-0.619331\pi\)
−0.366169 + 0.930548i \(0.619331\pi\)
\(744\) 0 0
\(745\) 66.8478 2.44911
\(746\) 0 0
\(747\) 16.7297 0.612108
\(748\) 0 0
\(749\) −3.15058 −0.115120
\(750\) 0 0
\(751\) 47.7508 1.74245 0.871225 0.490884i \(-0.163326\pi\)
0.871225 + 0.490884i \(0.163326\pi\)
\(752\) 0 0
\(753\) 2.05974 0.0750610
\(754\) 0 0
\(755\) 9.86860 0.359155
\(756\) 0 0
\(757\) −42.7254 −1.55288 −0.776441 0.630190i \(-0.782977\pi\)
−0.776441 + 0.630190i \(0.782977\pi\)
\(758\) 0 0
\(759\) 0.0713401 0.00258948
\(760\) 0 0
\(761\) 27.1507 0.984214 0.492107 0.870535i \(-0.336227\pi\)
0.492107 + 0.870535i \(0.336227\pi\)
\(762\) 0 0
\(763\) −19.2113 −0.695496
\(764\) 0 0
\(765\) 44.3822 1.60464
\(766\) 0 0
\(767\) −2.85455 −0.103072
\(768\) 0 0
\(769\) −6.51555 −0.234957 −0.117478 0.993075i \(-0.537481\pi\)
−0.117478 + 0.993075i \(0.537481\pi\)
\(770\) 0 0
\(771\) −0.153963 −0.00554483
\(772\) 0 0
\(773\) 15.6440 0.562675 0.281338 0.959609i \(-0.409222\pi\)
0.281338 + 0.959609i \(0.409222\pi\)
\(774\) 0 0
\(775\) 28.2618 1.01519
\(776\) 0 0
\(777\) −0.554993 −0.0199103
\(778\) 0 0
\(779\) 10.9899 0.393753
\(780\) 0 0
\(781\) −1.56955 −0.0561628
\(782\) 0 0
\(783\) 4.05728 0.144995
\(784\) 0 0
\(785\) −3.83749 −0.136966
\(786\) 0 0
\(787\) 40.6488 1.44897 0.724486 0.689290i \(-0.242077\pi\)
0.724486 + 0.689290i \(0.242077\pi\)
\(788\) 0 0
\(789\) −1.51625 −0.0539799
\(790\) 0 0
\(791\) −9.78708 −0.347988
\(792\) 0 0
\(793\) −3.08242 −0.109460
\(794\) 0 0
\(795\) 0.809708 0.0287174
\(796\) 0 0
\(797\) 4.44704 0.157522 0.0787611 0.996894i \(-0.474904\pi\)
0.0787611 + 0.996894i \(0.474904\pi\)
\(798\) 0 0
\(799\) −47.4570 −1.67891
\(800\) 0 0
\(801\) −16.2635 −0.574644
\(802\) 0 0
\(803\) −4.34423 −0.153304
\(804\) 0 0
\(805\) −3.61440 −0.127391
\(806\) 0 0
\(807\) −0.792718 −0.0279050
\(808\) 0 0
\(809\) −45.2670 −1.59150 −0.795752 0.605623i \(-0.792924\pi\)
−0.795752 + 0.605623i \(0.792924\pi\)
\(810\) 0 0
\(811\) 9.64362 0.338633 0.169317 0.985562i \(-0.445844\pi\)
0.169317 + 0.985562i \(0.445844\pi\)
\(812\) 0 0
\(813\) −0.173677 −0.00609113
\(814\) 0 0
\(815\) 70.2791 2.46177
\(816\) 0 0
\(817\) 32.6913 1.14372
\(818\) 0 0
\(819\) −2.99324 −0.104592
\(820\) 0 0
\(821\) −2.70516 −0.0944107 −0.0472054 0.998885i \(-0.515032\pi\)
−0.0472054 + 0.998885i \(0.515032\pi\)
\(822\) 0 0
\(823\) 10.5217 0.366765 0.183383 0.983042i \(-0.441295\pi\)
0.183383 + 0.983042i \(0.441295\pi\)
\(824\) 0 0
\(825\) −1.01686 −0.0354024
\(826\) 0 0
\(827\) −28.2336 −0.981780 −0.490890 0.871222i \(-0.663328\pi\)
−0.490890 + 0.871222i \(0.663328\pi\)
\(828\) 0 0
\(829\) 37.9146 1.31683 0.658415 0.752655i \(-0.271227\pi\)
0.658415 + 0.752655i \(0.271227\pi\)
\(830\) 0 0
\(831\) −1.11154 −0.0385587
\(832\) 0 0
\(833\) 3.55835 0.123290
\(834\) 0 0
\(835\) 1.13618 0.0393191
\(836\) 0 0
\(837\) −1.12677 −0.0389469
\(838\) 0 0
\(839\) 7.26159 0.250698 0.125349 0.992113i \(-0.459995\pi\)
0.125349 + 0.992113i \(0.459995\pi\)
\(840\) 0 0
\(841\) 38.7507 1.33623
\(842\) 0 0
\(843\) −1.02051 −0.0351481
\(844\) 0 0
\(845\) −4.16696 −0.143348
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 1.69029 0.0580105
\(850\) 0 0
\(851\) −5.85312 −0.200642
\(852\) 0 0
\(853\) −1.87833 −0.0643127 −0.0321563 0.999483i \(-0.510237\pi\)
−0.0321563 + 0.999483i \(0.510237\pi\)
\(854\) 0 0
\(855\) 63.5511 2.17340
\(856\) 0 0
\(857\) −46.7916 −1.59837 −0.799185 0.601085i \(-0.794735\pi\)
−0.799185 + 0.601085i \(0.794735\pi\)
\(858\) 0 0
\(859\) 37.8374 1.29099 0.645497 0.763762i \(-0.276650\pi\)
0.645497 + 0.763762i \(0.276650\pi\)
\(860\) 0 0
\(861\) −0.177397 −0.00604568
\(862\) 0 0
\(863\) −14.9426 −0.508651 −0.254325 0.967119i \(-0.581853\pi\)
−0.254325 + 0.967119i \(0.581853\pi\)
\(864\) 0 0
\(865\) 32.4753 1.10419
\(866\) 0 0
\(867\) −0.356796 −0.0121174
\(868\) 0 0
\(869\) −0.0822696 −0.00279080
\(870\) 0 0
\(871\) −7.23118 −0.245019
\(872\) 0 0
\(873\) 35.4287 1.19908
\(874\) 0 0
\(875\) 30.6836 1.03729
\(876\) 0 0
\(877\) 28.2606 0.954292 0.477146 0.878824i \(-0.341671\pi\)
0.477146 + 0.878824i \(0.341671\pi\)
\(878\) 0 0
\(879\) −0.801181 −0.0270232
\(880\) 0 0
\(881\) 33.7099 1.13572 0.567858 0.823126i \(-0.307772\pi\)
0.567858 + 0.823126i \(0.307772\pi\)
\(882\) 0 0
\(883\) −24.1577 −0.812971 −0.406485 0.913657i \(-0.633246\pi\)
−0.406485 + 0.913657i \(0.633246\pi\)
\(884\) 0 0
\(885\) −0.978304 −0.0328853
\(886\) 0 0
\(887\) 17.5637 0.589731 0.294865 0.955539i \(-0.404725\pi\)
0.294865 + 0.955539i \(0.404725\pi\)
\(888\) 0 0
\(889\) 9.25558 0.310422
\(890\) 0 0
\(891\) −8.93917 −0.299473
\(892\) 0 0
\(893\) −67.9539 −2.27399
\(894\) 0 0
\(895\) 8.46018 0.282793
\(896\) 0 0
\(897\) 0.0713401 0.00238198
\(898\) 0 0
\(899\) −18.8154 −0.627529
\(900\) 0 0
\(901\) −8.40700 −0.280078
\(902\) 0 0
\(903\) −0.527699 −0.0175607
\(904\) 0 0
\(905\) −15.0285 −0.499564
\(906\) 0 0
\(907\) 42.3794 1.40718 0.703592 0.710604i \(-0.251578\pi\)
0.703592 + 0.710604i \(0.251578\pi\)
\(908\) 0 0
\(909\) −39.3832 −1.30626
\(910\) 0 0
\(911\) −5.13819 −0.170236 −0.0851180 0.996371i \(-0.527127\pi\)
−0.0851180 + 0.996371i \(0.527127\pi\)
\(912\) 0 0
\(913\) 5.58917 0.184975
\(914\) 0 0
\(915\) −1.05640 −0.0349235
\(916\) 0 0
\(917\) 4.72266 0.155956
\(918\) 0 0
\(919\) 15.2237 0.502182 0.251091 0.967963i \(-0.419211\pi\)
0.251091 + 0.967963i \(0.419211\pi\)
\(920\) 0 0
\(921\) 0.739319 0.0243614
\(922\) 0 0
\(923\) −1.56955 −0.0516622
\(924\) 0 0
\(925\) 83.4283 2.74311
\(926\) 0 0
\(927\) 7.36069 0.241757
\(928\) 0 0
\(929\) 32.5560 1.06813 0.534064 0.845444i \(-0.320664\pi\)
0.534064 + 0.845444i \(0.320664\pi\)
\(930\) 0 0
\(931\) 5.09522 0.166989
\(932\) 0 0
\(933\) −0.497294 −0.0162807
\(934\) 0 0
\(935\) 14.8275 0.484911
\(936\) 0 0
\(937\) 31.3946 1.02562 0.512808 0.858503i \(-0.328605\pi\)
0.512808 + 0.858503i \(0.328605\pi\)
\(938\) 0 0
\(939\) 0.317876 0.0103735
\(940\) 0 0
\(941\) −16.7638 −0.546484 −0.273242 0.961945i \(-0.588096\pi\)
−0.273242 + 0.961945i \(0.588096\pi\)
\(942\) 0 0
\(943\) −1.87088 −0.0609243
\(944\) 0 0
\(945\) −2.05399 −0.0668162
\(946\) 0 0
\(947\) −28.5661 −0.928274 −0.464137 0.885763i \(-0.653635\pi\)
−0.464137 + 0.885763i \(0.653635\pi\)
\(948\) 0 0
\(949\) −4.34423 −0.141020
\(950\) 0 0
\(951\) 1.66816 0.0540938
\(952\) 0 0
\(953\) −19.7225 −0.638875 −0.319437 0.947607i \(-0.603494\pi\)
−0.319437 + 0.947607i \(0.603494\pi\)
\(954\) 0 0
\(955\) −31.2150 −1.01009
\(956\) 0 0
\(957\) 0.676977 0.0218836
\(958\) 0 0
\(959\) 14.8620 0.479920
\(960\) 0 0
\(961\) −25.7747 −0.831441
\(962\) 0 0
\(963\) −9.43042 −0.303891
\(964\) 0 0
\(965\) 34.5530 1.11230
\(966\) 0 0
\(967\) −46.9802 −1.51078 −0.755391 0.655274i \(-0.772553\pi\)
−0.755391 + 0.655274i \(0.772553\pi\)
\(968\) 0 0
\(969\) 1.49118 0.0479035
\(970\) 0 0
\(971\) 2.03048 0.0651613 0.0325807 0.999469i \(-0.489627\pi\)
0.0325807 + 0.999469i \(0.489627\pi\)
\(972\) 0 0
\(973\) −12.0767 −0.387160
\(974\) 0 0
\(975\) −1.01686 −0.0325655
\(976\) 0 0
\(977\) −10.7899 −0.345199 −0.172599 0.984992i \(-0.555217\pi\)
−0.172599 + 0.984992i \(0.555217\pi\)
\(978\) 0 0
\(979\) −5.43343 −0.173653
\(980\) 0 0
\(981\) −57.5040 −1.83596
\(982\) 0 0
\(983\) −38.1755 −1.21761 −0.608804 0.793321i \(-0.708350\pi\)
−0.608804 + 0.793321i \(0.708350\pi\)
\(984\) 0 0
\(985\) −79.3461 −2.52818
\(986\) 0 0
\(987\) 1.09690 0.0349148
\(988\) 0 0
\(989\) −5.56526 −0.176965
\(990\) 0 0
\(991\) 3.98288 0.126520 0.0632602 0.997997i \(-0.479850\pi\)
0.0632602 + 0.997997i \(0.479850\pi\)
\(992\) 0 0
\(993\) −1.10030 −0.0349171
\(994\) 0 0
\(995\) 63.0129 1.99764
\(996\) 0 0
\(997\) −48.5499 −1.53759 −0.768795 0.639496i \(-0.779143\pi\)
−0.768795 + 0.639496i \(0.779143\pi\)
\(998\) 0 0
\(999\) −3.32620 −0.105236
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 \(a_p\))