Properties

Label 8016.2.a.bg.1.4
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-2.71099\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.71099 q^{5}\) \(+0.775439 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.71099 q^{5}\) \(+0.775439 q^{7}\) \(+1.00000 q^{9}\) \(-3.70739 q^{11}\) \(-6.16847 q^{13}\) \(+2.71099 q^{15}\) \(+6.36353 q^{17}\) \(-0.922209 q^{19}\) \(-0.775439 q^{21}\) \(+4.47047 q^{23}\) \(+2.34945 q^{25}\) \(-1.00000 q^{27}\) \(-5.18433 q^{29}\) \(-1.35539 q^{31}\) \(+3.70739 q^{33}\) \(-2.10220 q^{35}\) \(+11.5076 q^{37}\) \(+6.16847 q^{39}\) \(-8.90644 q^{41}\) \(-5.52092 q^{43}\) \(-2.71099 q^{45}\) \(-8.07634 q^{47}\) \(-6.39869 q^{49}\) \(-6.36353 q^{51}\) \(-2.23790 q^{53}\) \(+10.0507 q^{55}\) \(+0.922209 q^{57}\) \(-12.3284 q^{59}\) \(-5.08112 q^{61}\) \(+0.775439 q^{63}\) \(+16.7226 q^{65}\) \(-0.628889 q^{67}\) \(-4.47047 q^{69}\) \(-3.07457 q^{71}\) \(+3.83167 q^{73}\) \(-2.34945 q^{75}\) \(-2.87486 q^{77}\) \(-15.8763 q^{79}\) \(+1.00000 q^{81}\) \(+4.76483 q^{83}\) \(-17.2514 q^{85}\) \(+5.18433 q^{87}\) \(+0.390848 q^{89}\) \(-4.78327 q^{91}\) \(+1.35539 q^{93}\) \(+2.50010 q^{95}\) \(+15.5125 q^{97}\) \(-3.70739 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −2.71099 −1.21239 −0.606195 0.795316i \(-0.707305\pi\)
−0.606195 + 0.795316i \(0.707305\pi\)
\(6\) 0 0
\(7\) 0.775439 0.293088 0.146544 0.989204i \(-0.453185\pi\)
0.146544 + 0.989204i \(0.453185\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.70739 −1.11782 −0.558911 0.829228i \(-0.688781\pi\)
−0.558911 + 0.829228i \(0.688781\pi\)
\(12\) 0 0
\(13\) −6.16847 −1.71083 −0.855413 0.517947i \(-0.826697\pi\)
−0.855413 + 0.517947i \(0.826697\pi\)
\(14\) 0 0
\(15\) 2.71099 0.699974
\(16\) 0 0
\(17\) 6.36353 1.54338 0.771691 0.635998i \(-0.219411\pi\)
0.771691 + 0.635998i \(0.219411\pi\)
\(18\) 0 0
\(19\) −0.922209 −0.211569 −0.105785 0.994389i \(-0.533735\pi\)
−0.105785 + 0.994389i \(0.533735\pi\)
\(20\) 0 0
\(21\) −0.775439 −0.169215
\(22\) 0 0
\(23\) 4.47047 0.932157 0.466079 0.884743i \(-0.345666\pi\)
0.466079 + 0.884743i \(0.345666\pi\)
\(24\) 0 0
\(25\) 2.34945 0.469889
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.18433 −0.962705 −0.481353 0.876527i \(-0.659854\pi\)
−0.481353 + 0.876527i \(0.659854\pi\)
\(30\) 0 0
\(31\) −1.35539 −0.243436 −0.121718 0.992565i \(-0.538840\pi\)
−0.121718 + 0.992565i \(0.538840\pi\)
\(32\) 0 0
\(33\) 3.70739 0.645375
\(34\) 0 0
\(35\) −2.10220 −0.355337
\(36\) 0 0
\(37\) 11.5076 1.89183 0.945915 0.324414i \(-0.105167\pi\)
0.945915 + 0.324414i \(0.105167\pi\)
\(38\) 0 0
\(39\) 6.16847 0.987746
\(40\) 0 0
\(41\) −8.90644 −1.39095 −0.695476 0.718549i \(-0.744806\pi\)
−0.695476 + 0.718549i \(0.744806\pi\)
\(42\) 0 0
\(43\) −5.52092 −0.841933 −0.420966 0.907076i \(-0.638309\pi\)
−0.420966 + 0.907076i \(0.638309\pi\)
\(44\) 0 0
\(45\) −2.71099 −0.404130
\(46\) 0 0
\(47\) −8.07634 −1.17806 −0.589028 0.808113i \(-0.700489\pi\)
−0.589028 + 0.808113i \(0.700489\pi\)
\(48\) 0 0
\(49\) −6.39869 −0.914099
\(50\) 0 0
\(51\) −6.36353 −0.891072
\(52\) 0 0
\(53\) −2.23790 −0.307399 −0.153700 0.988118i \(-0.549119\pi\)
−0.153700 + 0.988118i \(0.549119\pi\)
\(54\) 0 0
\(55\) 10.0507 1.35524
\(56\) 0 0
\(57\) 0.922209 0.122150
\(58\) 0 0
\(59\) −12.3284 −1.60502 −0.802509 0.596640i \(-0.796502\pi\)
−0.802509 + 0.596640i \(0.796502\pi\)
\(60\) 0 0
\(61\) −5.08112 −0.650571 −0.325285 0.945616i \(-0.605460\pi\)
−0.325285 + 0.945616i \(0.605460\pi\)
\(62\) 0 0
\(63\) 0.775439 0.0976961
\(64\) 0 0
\(65\) 16.7226 2.07419
\(66\) 0 0
\(67\) −0.628889 −0.0768311 −0.0384155 0.999262i \(-0.512231\pi\)
−0.0384155 + 0.999262i \(0.512231\pi\)
\(68\) 0 0
\(69\) −4.47047 −0.538181
\(70\) 0 0
\(71\) −3.07457 −0.364884 −0.182442 0.983217i \(-0.558400\pi\)
−0.182442 + 0.983217i \(0.558400\pi\)
\(72\) 0 0
\(73\) 3.83167 0.448463 0.224232 0.974536i \(-0.428013\pi\)
0.224232 + 0.974536i \(0.428013\pi\)
\(74\) 0 0
\(75\) −2.34945 −0.271291
\(76\) 0 0
\(77\) −2.87486 −0.327620
\(78\) 0 0
\(79\) −15.8763 −1.78622 −0.893111 0.449837i \(-0.851482\pi\)
−0.893111 + 0.449837i \(0.851482\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.76483 0.523009 0.261504 0.965202i \(-0.415781\pi\)
0.261504 + 0.965202i \(0.415781\pi\)
\(84\) 0 0
\(85\) −17.2514 −1.87118
\(86\) 0 0
\(87\) 5.18433 0.555818
\(88\) 0 0
\(89\) 0.390848 0.0414298 0.0207149 0.999785i \(-0.493406\pi\)
0.0207149 + 0.999785i \(0.493406\pi\)
\(90\) 0 0
\(91\) −4.78327 −0.501423
\(92\) 0 0
\(93\) 1.35539 0.140548
\(94\) 0 0
\(95\) 2.50010 0.256504
\(96\) 0 0
\(97\) 15.5125 1.57506 0.787529 0.616277i \(-0.211360\pi\)
0.787529 + 0.616277i \(0.211360\pi\)
\(98\) 0 0
\(99\) −3.70739 −0.372607
\(100\) 0 0
\(101\) 14.2133 1.41428 0.707140 0.707074i \(-0.249985\pi\)
0.707140 + 0.707074i \(0.249985\pi\)
\(102\) 0 0
\(103\) 11.6148 1.14444 0.572219 0.820101i \(-0.306083\pi\)
0.572219 + 0.820101i \(0.306083\pi\)
\(104\) 0 0
\(105\) 2.10220 0.205154
\(106\) 0 0
\(107\) −13.1267 −1.26901 −0.634503 0.772920i \(-0.718795\pi\)
−0.634503 + 0.772920i \(0.718795\pi\)
\(108\) 0 0
\(109\) 3.37165 0.322945 0.161473 0.986877i \(-0.448376\pi\)
0.161473 + 0.986877i \(0.448376\pi\)
\(110\) 0 0
\(111\) −11.5076 −1.09225
\(112\) 0 0
\(113\) −12.9419 −1.21747 −0.608735 0.793374i \(-0.708323\pi\)
−0.608735 + 0.793374i \(0.708323\pi\)
\(114\) 0 0
\(115\) −12.1194 −1.13014
\(116\) 0 0
\(117\) −6.16847 −0.570275
\(118\) 0 0
\(119\) 4.93452 0.452347
\(120\) 0 0
\(121\) 2.74477 0.249525
\(122\) 0 0
\(123\) 8.90644 0.803066
\(124\) 0 0
\(125\) 7.18562 0.642701
\(126\) 0 0
\(127\) 5.24079 0.465045 0.232522 0.972591i \(-0.425302\pi\)
0.232522 + 0.972591i \(0.425302\pi\)
\(128\) 0 0
\(129\) 5.52092 0.486090
\(130\) 0 0
\(131\) −4.29290 −0.375072 −0.187536 0.982258i \(-0.560050\pi\)
−0.187536 + 0.982258i \(0.560050\pi\)
\(132\) 0 0
\(133\) −0.715117 −0.0620085
\(134\) 0 0
\(135\) 2.71099 0.233325
\(136\) 0 0
\(137\) −2.17341 −0.185687 −0.0928433 0.995681i \(-0.529596\pi\)
−0.0928433 + 0.995681i \(0.529596\pi\)
\(138\) 0 0
\(139\) −18.0691 −1.53260 −0.766300 0.642483i \(-0.777904\pi\)
−0.766300 + 0.642483i \(0.777904\pi\)
\(140\) 0 0
\(141\) 8.07634 0.680150
\(142\) 0 0
\(143\) 22.8689 1.91240
\(144\) 0 0
\(145\) 14.0546 1.16717
\(146\) 0 0
\(147\) 6.39869 0.527755
\(148\) 0 0
\(149\) −0.330735 −0.0270949 −0.0135474 0.999908i \(-0.504312\pi\)
−0.0135474 + 0.999908i \(0.504312\pi\)
\(150\) 0 0
\(151\) 3.69073 0.300347 0.150174 0.988660i \(-0.452017\pi\)
0.150174 + 0.988660i \(0.452017\pi\)
\(152\) 0 0
\(153\) 6.36353 0.514461
\(154\) 0 0
\(155\) 3.67445 0.295139
\(156\) 0 0
\(157\) 15.7517 1.25712 0.628560 0.777761i \(-0.283645\pi\)
0.628560 + 0.777761i \(0.283645\pi\)
\(158\) 0 0
\(159\) 2.23790 0.177477
\(160\) 0 0
\(161\) 3.46657 0.273204
\(162\) 0 0
\(163\) −15.5320 −1.21656 −0.608280 0.793722i \(-0.708140\pi\)
−0.608280 + 0.793722i \(0.708140\pi\)
\(164\) 0 0
\(165\) −10.0507 −0.782446
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 25.0500 1.92692
\(170\) 0 0
\(171\) −0.922209 −0.0705231
\(172\) 0 0
\(173\) 16.8363 1.28004 0.640020 0.768358i \(-0.278926\pi\)
0.640020 + 0.768358i \(0.278926\pi\)
\(174\) 0 0
\(175\) 1.82185 0.137719
\(176\) 0 0
\(177\) 12.3284 0.926658
\(178\) 0 0
\(179\) 14.7443 1.10204 0.551020 0.834492i \(-0.314239\pi\)
0.551020 + 0.834492i \(0.314239\pi\)
\(180\) 0 0
\(181\) 11.7286 0.871783 0.435891 0.899999i \(-0.356433\pi\)
0.435891 + 0.899999i \(0.356433\pi\)
\(182\) 0 0
\(183\) 5.08112 0.375607
\(184\) 0 0
\(185\) −31.1968 −2.29364
\(186\) 0 0
\(187\) −23.5921 −1.72523
\(188\) 0 0
\(189\) −0.775439 −0.0564049
\(190\) 0 0
\(191\) −1.61629 −0.116951 −0.0584753 0.998289i \(-0.518624\pi\)
−0.0584753 + 0.998289i \(0.518624\pi\)
\(192\) 0 0
\(193\) 18.7212 1.34758 0.673792 0.738921i \(-0.264664\pi\)
0.673792 + 0.738921i \(0.264664\pi\)
\(194\) 0 0
\(195\) −16.7226 −1.19753
\(196\) 0 0
\(197\) −12.1950 −0.868856 −0.434428 0.900707i \(-0.643049\pi\)
−0.434428 + 0.900707i \(0.643049\pi\)
\(198\) 0 0
\(199\) 1.48491 0.105262 0.0526312 0.998614i \(-0.483239\pi\)
0.0526312 + 0.998614i \(0.483239\pi\)
\(200\) 0 0
\(201\) 0.628889 0.0443584
\(202\) 0 0
\(203\) −4.02013 −0.282158
\(204\) 0 0
\(205\) 24.1452 1.68638
\(206\) 0 0
\(207\) 4.47047 0.310719
\(208\) 0 0
\(209\) 3.41899 0.236497
\(210\) 0 0
\(211\) −14.9344 −1.02813 −0.514063 0.857752i \(-0.671860\pi\)
−0.514063 + 0.857752i \(0.671860\pi\)
\(212\) 0 0
\(213\) 3.07457 0.210666
\(214\) 0 0
\(215\) 14.9671 1.02075
\(216\) 0 0
\(217\) −1.05102 −0.0713482
\(218\) 0 0
\(219\) −3.83167 −0.258920
\(220\) 0 0
\(221\) −39.2532 −2.64046
\(222\) 0 0
\(223\) 10.3483 0.692975 0.346487 0.938055i \(-0.387374\pi\)
0.346487 + 0.938055i \(0.387374\pi\)
\(224\) 0 0
\(225\) 2.34945 0.156630
\(226\) 0 0
\(227\) 7.31500 0.485513 0.242757 0.970087i \(-0.421948\pi\)
0.242757 + 0.970087i \(0.421948\pi\)
\(228\) 0 0
\(229\) 17.3272 1.14502 0.572508 0.819899i \(-0.305970\pi\)
0.572508 + 0.819899i \(0.305970\pi\)
\(230\) 0 0
\(231\) 2.87486 0.189152
\(232\) 0 0
\(233\) −16.4242 −1.07599 −0.537994 0.842949i \(-0.680818\pi\)
−0.537994 + 0.842949i \(0.680818\pi\)
\(234\) 0 0
\(235\) 21.8948 1.42826
\(236\) 0 0
\(237\) 15.8763 1.03128
\(238\) 0 0
\(239\) 4.16870 0.269651 0.134825 0.990869i \(-0.456953\pi\)
0.134825 + 0.990869i \(0.456953\pi\)
\(240\) 0 0
\(241\) 10.1175 0.651725 0.325862 0.945417i \(-0.394345\pi\)
0.325862 + 0.945417i \(0.394345\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 17.3468 1.10824
\(246\) 0 0
\(247\) 5.68862 0.361958
\(248\) 0 0
\(249\) −4.76483 −0.301959
\(250\) 0 0
\(251\) −11.9898 −0.756790 −0.378395 0.925644i \(-0.623524\pi\)
−0.378395 + 0.925644i \(0.623524\pi\)
\(252\) 0 0
\(253\) −16.5738 −1.04199
\(254\) 0 0
\(255\) 17.2514 1.08033
\(256\) 0 0
\(257\) 12.0253 0.750117 0.375059 0.927001i \(-0.377623\pi\)
0.375059 + 0.927001i \(0.377623\pi\)
\(258\) 0 0
\(259\) 8.92340 0.554473
\(260\) 0 0
\(261\) −5.18433 −0.320902
\(262\) 0 0
\(263\) 0.941771 0.0580721 0.0290360 0.999578i \(-0.490756\pi\)
0.0290360 + 0.999578i \(0.490756\pi\)
\(264\) 0 0
\(265\) 6.06691 0.372688
\(266\) 0 0
\(267\) −0.390848 −0.0239195
\(268\) 0 0
\(269\) 3.56306 0.217243 0.108622 0.994083i \(-0.465356\pi\)
0.108622 + 0.994083i \(0.465356\pi\)
\(270\) 0 0
\(271\) −21.3869 −1.29916 −0.649582 0.760292i \(-0.725056\pi\)
−0.649582 + 0.760292i \(0.725056\pi\)
\(272\) 0 0
\(273\) 4.78327 0.289497
\(274\) 0 0
\(275\) −8.71032 −0.525252
\(276\) 0 0
\(277\) 28.5165 1.71339 0.856695 0.515823i \(-0.172514\pi\)
0.856695 + 0.515823i \(0.172514\pi\)
\(278\) 0 0
\(279\) −1.35539 −0.0811453
\(280\) 0 0
\(281\) −26.7452 −1.59549 −0.797744 0.602997i \(-0.793973\pi\)
−0.797744 + 0.602997i \(0.793973\pi\)
\(282\) 0 0
\(283\) 2.76889 0.164594 0.0822968 0.996608i \(-0.473774\pi\)
0.0822968 + 0.996608i \(0.473774\pi\)
\(284\) 0 0
\(285\) −2.50010 −0.148093
\(286\) 0 0
\(287\) −6.90640 −0.407672
\(288\) 0 0
\(289\) 23.4945 1.38203
\(290\) 0 0
\(291\) −15.5125 −0.909360
\(292\) 0 0
\(293\) −17.3417 −1.01311 −0.506555 0.862208i \(-0.669081\pi\)
−0.506555 + 0.862208i \(0.669081\pi\)
\(294\) 0 0
\(295\) 33.4221 1.94591
\(296\) 0 0
\(297\) 3.70739 0.215125
\(298\) 0 0
\(299\) −27.5759 −1.59476
\(300\) 0 0
\(301\) −4.28114 −0.246761
\(302\) 0 0
\(303\) −14.2133 −0.816535
\(304\) 0 0
\(305\) 13.7748 0.788745
\(306\) 0 0
\(307\) 17.3038 0.987578 0.493789 0.869582i \(-0.335612\pi\)
0.493789 + 0.869582i \(0.335612\pi\)
\(308\) 0 0
\(309\) −11.6148 −0.660742
\(310\) 0 0
\(311\) −23.3959 −1.32666 −0.663329 0.748328i \(-0.730857\pi\)
−0.663329 + 0.748328i \(0.730857\pi\)
\(312\) 0 0
\(313\) 0.191470 0.0108225 0.00541127 0.999985i \(-0.498278\pi\)
0.00541127 + 0.999985i \(0.498278\pi\)
\(314\) 0 0
\(315\) −2.10220 −0.118446
\(316\) 0 0
\(317\) −3.25612 −0.182882 −0.0914410 0.995810i \(-0.529147\pi\)
−0.0914410 + 0.995810i \(0.529147\pi\)
\(318\) 0 0
\(319\) 19.2203 1.07613
\(320\) 0 0
\(321\) 13.1267 0.732661
\(322\) 0 0
\(323\) −5.86850 −0.326532
\(324\) 0 0
\(325\) −14.4925 −0.803898
\(326\) 0 0
\(327\) −3.37165 −0.186452
\(328\) 0 0
\(329\) −6.26271 −0.345274
\(330\) 0 0
\(331\) 30.7585 1.69064 0.845320 0.534260i \(-0.179410\pi\)
0.845320 + 0.534260i \(0.179410\pi\)
\(332\) 0 0
\(333\) 11.5076 0.630610
\(334\) 0 0
\(335\) 1.70491 0.0931492
\(336\) 0 0
\(337\) 2.60466 0.141885 0.0709425 0.997480i \(-0.477399\pi\)
0.0709425 + 0.997480i \(0.477399\pi\)
\(338\) 0 0
\(339\) 12.9419 0.702906
\(340\) 0 0
\(341\) 5.02498 0.272118
\(342\) 0 0
\(343\) −10.3899 −0.561000
\(344\) 0 0
\(345\) 12.1194 0.652485
\(346\) 0 0
\(347\) 20.1851 1.08359 0.541796 0.840510i \(-0.317745\pi\)
0.541796 + 0.840510i \(0.317745\pi\)
\(348\) 0 0
\(349\) 13.7950 0.738431 0.369216 0.929344i \(-0.379626\pi\)
0.369216 + 0.929344i \(0.379626\pi\)
\(350\) 0 0
\(351\) 6.16847 0.329249
\(352\) 0 0
\(353\) −6.65454 −0.354185 −0.177093 0.984194i \(-0.556669\pi\)
−0.177093 + 0.984194i \(0.556669\pi\)
\(354\) 0 0
\(355\) 8.33510 0.442381
\(356\) 0 0
\(357\) −4.93452 −0.261163
\(358\) 0 0
\(359\) −18.5216 −0.977535 −0.488768 0.872414i \(-0.662553\pi\)
−0.488768 + 0.872414i \(0.662553\pi\)
\(360\) 0 0
\(361\) −18.1495 −0.955238
\(362\) 0 0
\(363\) −2.74477 −0.144063
\(364\) 0 0
\(365\) −10.3876 −0.543712
\(366\) 0 0
\(367\) 17.6276 0.920152 0.460076 0.887880i \(-0.347822\pi\)
0.460076 + 0.887880i \(0.347822\pi\)
\(368\) 0 0
\(369\) −8.90644 −0.463651
\(370\) 0 0
\(371\) −1.73535 −0.0900951
\(372\) 0 0
\(373\) 4.37087 0.226315 0.113158 0.993577i \(-0.463904\pi\)
0.113158 + 0.993577i \(0.463904\pi\)
\(374\) 0 0
\(375\) −7.18562 −0.371064
\(376\) 0 0
\(377\) 31.9794 1.64702
\(378\) 0 0
\(379\) 31.2802 1.60676 0.803379 0.595468i \(-0.203033\pi\)
0.803379 + 0.595468i \(0.203033\pi\)
\(380\) 0 0
\(381\) −5.24079 −0.268494
\(382\) 0 0
\(383\) 6.10351 0.311875 0.155937 0.987767i \(-0.450160\pi\)
0.155937 + 0.987767i \(0.450160\pi\)
\(384\) 0 0
\(385\) 7.79370 0.397204
\(386\) 0 0
\(387\) −5.52092 −0.280644
\(388\) 0 0
\(389\) −7.97649 −0.404424 −0.202212 0.979342i \(-0.564813\pi\)
−0.202212 + 0.979342i \(0.564813\pi\)
\(390\) 0 0
\(391\) 28.4479 1.43867
\(392\) 0 0
\(393\) 4.29290 0.216548
\(394\) 0 0
\(395\) 43.0404 2.16560
\(396\) 0 0
\(397\) 24.2101 1.21507 0.607535 0.794293i \(-0.292158\pi\)
0.607535 + 0.794293i \(0.292158\pi\)
\(398\) 0 0
\(399\) 0.715117 0.0358006
\(400\) 0 0
\(401\) −17.9420 −0.895982 −0.447991 0.894038i \(-0.647860\pi\)
−0.447991 + 0.894038i \(0.647860\pi\)
\(402\) 0 0
\(403\) 8.36071 0.416476
\(404\) 0 0
\(405\) −2.71099 −0.134710
\(406\) 0 0
\(407\) −42.6630 −2.11473
\(408\) 0 0
\(409\) −10.9929 −0.543562 −0.271781 0.962359i \(-0.587613\pi\)
−0.271781 + 0.962359i \(0.587613\pi\)
\(410\) 0 0
\(411\) 2.17341 0.107206
\(412\) 0 0
\(413\) −9.55990 −0.470412
\(414\) 0 0
\(415\) −12.9174 −0.634090
\(416\) 0 0
\(417\) 18.0691 0.884847
\(418\) 0 0
\(419\) 20.5571 1.00428 0.502139 0.864787i \(-0.332547\pi\)
0.502139 + 0.864787i \(0.332547\pi\)
\(420\) 0 0
\(421\) 15.2776 0.744583 0.372291 0.928116i \(-0.378572\pi\)
0.372291 + 0.928116i \(0.378572\pi\)
\(422\) 0 0
\(423\) −8.07634 −0.392685
\(424\) 0 0
\(425\) 14.9508 0.725218
\(426\) 0 0
\(427\) −3.94010 −0.190675
\(428\) 0 0
\(429\) −22.8689 −1.10412
\(430\) 0 0
\(431\) 24.6247 1.18613 0.593066 0.805154i \(-0.297917\pi\)
0.593066 + 0.805154i \(0.297917\pi\)
\(432\) 0 0
\(433\) −30.2365 −1.45307 −0.726537 0.687127i \(-0.758872\pi\)
−0.726537 + 0.687127i \(0.758872\pi\)
\(434\) 0 0
\(435\) −14.0546 −0.673868
\(436\) 0 0
\(437\) −4.12271 −0.197216
\(438\) 0 0
\(439\) −5.07328 −0.242134 −0.121067 0.992644i \(-0.538632\pi\)
−0.121067 + 0.992644i \(0.538632\pi\)
\(440\) 0 0
\(441\) −6.39869 −0.304700
\(442\) 0 0
\(443\) 11.3097 0.537339 0.268670 0.963232i \(-0.413416\pi\)
0.268670 + 0.963232i \(0.413416\pi\)
\(444\) 0 0
\(445\) −1.05958 −0.0502291
\(446\) 0 0
\(447\) 0.330735 0.0156432
\(448\) 0 0
\(449\) −23.0503 −1.08781 −0.543906 0.839146i \(-0.683055\pi\)
−0.543906 + 0.839146i \(0.683055\pi\)
\(450\) 0 0
\(451\) 33.0197 1.55484
\(452\) 0 0
\(453\) −3.69073 −0.173406
\(454\) 0 0
\(455\) 12.9674 0.607920
\(456\) 0 0
\(457\) 38.1775 1.78587 0.892935 0.450185i \(-0.148642\pi\)
0.892935 + 0.450185i \(0.148642\pi\)
\(458\) 0 0
\(459\) −6.36353 −0.297024
\(460\) 0 0
\(461\) −3.19692 −0.148895 −0.0744477 0.997225i \(-0.523719\pi\)
−0.0744477 + 0.997225i \(0.523719\pi\)
\(462\) 0 0
\(463\) −29.8591 −1.38767 −0.693834 0.720135i \(-0.744080\pi\)
−0.693834 + 0.720135i \(0.744080\pi\)
\(464\) 0 0
\(465\) −3.67445 −0.170399
\(466\) 0 0
\(467\) 34.0326 1.57484 0.787421 0.616415i \(-0.211416\pi\)
0.787421 + 0.616415i \(0.211416\pi\)
\(468\) 0 0
\(469\) −0.487665 −0.0225183
\(470\) 0 0
\(471\) −15.7517 −0.725798
\(472\) 0 0
\(473\) 20.4682 0.941131
\(474\) 0 0
\(475\) −2.16668 −0.0994141
\(476\) 0 0
\(477\) −2.23790 −0.102466
\(478\) 0 0
\(479\) 30.2683 1.38300 0.691498 0.722378i \(-0.256951\pi\)
0.691498 + 0.722378i \(0.256951\pi\)
\(480\) 0 0
\(481\) −70.9840 −3.23659
\(482\) 0 0
\(483\) −3.46657 −0.157735
\(484\) 0 0
\(485\) −42.0542 −1.90958
\(486\) 0 0
\(487\) 18.1702 0.823369 0.411684 0.911327i \(-0.364941\pi\)
0.411684 + 0.911327i \(0.364941\pi\)
\(488\) 0 0
\(489\) 15.5320 0.702381
\(490\) 0 0
\(491\) 32.7025 1.47584 0.737922 0.674886i \(-0.235807\pi\)
0.737922 + 0.674886i \(0.235807\pi\)
\(492\) 0 0
\(493\) −32.9906 −1.48582
\(494\) 0 0
\(495\) 10.0507 0.451745
\(496\) 0 0
\(497\) −2.38414 −0.106943
\(498\) 0 0
\(499\) 3.70087 0.165674 0.0828368 0.996563i \(-0.473602\pi\)
0.0828368 + 0.996563i \(0.473602\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −17.4615 −0.778569 −0.389285 0.921118i \(-0.627278\pi\)
−0.389285 + 0.921118i \(0.627278\pi\)
\(504\) 0 0
\(505\) −38.5322 −1.71466
\(506\) 0 0
\(507\) −25.0500 −1.11251
\(508\) 0 0
\(509\) 12.8296 0.568662 0.284331 0.958726i \(-0.408229\pi\)
0.284331 + 0.958726i \(0.408229\pi\)
\(510\) 0 0
\(511\) 2.97123 0.131439
\(512\) 0 0
\(513\) 0.922209 0.0407165
\(514\) 0 0
\(515\) −31.4875 −1.38751
\(516\) 0 0
\(517\) 29.9422 1.31686
\(518\) 0 0
\(519\) −16.8363 −0.739032
\(520\) 0 0
\(521\) 14.7753 0.647316 0.323658 0.946174i \(-0.395087\pi\)
0.323658 + 0.946174i \(0.395087\pi\)
\(522\) 0 0
\(523\) −18.6247 −0.814402 −0.407201 0.913339i \(-0.633495\pi\)
−0.407201 + 0.913339i \(0.633495\pi\)
\(524\) 0 0
\(525\) −1.82185 −0.0795121
\(526\) 0 0
\(527\) −8.62508 −0.375715
\(528\) 0 0
\(529\) −3.01492 −0.131083
\(530\) 0 0
\(531\) −12.3284 −0.535006
\(532\) 0 0
\(533\) 54.9391 2.37968
\(534\) 0 0
\(535\) 35.5863 1.53853
\(536\) 0 0
\(537\) −14.7443 −0.636263
\(538\) 0 0
\(539\) 23.7225 1.02180
\(540\) 0 0
\(541\) 12.5963 0.541558 0.270779 0.962641i \(-0.412719\pi\)
0.270779 + 0.962641i \(0.412719\pi\)
\(542\) 0 0
\(543\) −11.7286 −0.503324
\(544\) 0 0
\(545\) −9.14048 −0.391535
\(546\) 0 0
\(547\) −11.0198 −0.471172 −0.235586 0.971853i \(-0.575701\pi\)
−0.235586 + 0.971853i \(0.575701\pi\)
\(548\) 0 0
\(549\) −5.08112 −0.216857
\(550\) 0 0
\(551\) 4.78103 0.203679
\(552\) 0 0
\(553\) −12.3111 −0.523521
\(554\) 0 0
\(555\) 31.1968 1.32423
\(556\) 0 0
\(557\) 25.8382 1.09480 0.547401 0.836871i \(-0.315617\pi\)
0.547401 + 0.836871i \(0.315617\pi\)
\(558\) 0 0
\(559\) 34.0556 1.44040
\(560\) 0 0
\(561\) 23.5921 0.996059
\(562\) 0 0
\(563\) −34.8221 −1.46757 −0.733787 0.679379i \(-0.762249\pi\)
−0.733787 + 0.679379i \(0.762249\pi\)
\(564\) 0 0
\(565\) 35.0853 1.47605
\(566\) 0 0
\(567\) 0.775439 0.0325654
\(568\) 0 0
\(569\) −2.62357 −0.109986 −0.0549929 0.998487i \(-0.517514\pi\)
−0.0549929 + 0.998487i \(0.517514\pi\)
\(570\) 0 0
\(571\) −9.52229 −0.398495 −0.199248 0.979949i \(-0.563850\pi\)
−0.199248 + 0.979949i \(0.563850\pi\)
\(572\) 0 0
\(573\) 1.61629 0.0675215
\(574\) 0 0
\(575\) 10.5031 0.438010
\(576\) 0 0
\(577\) 31.2255 1.29994 0.649968 0.759962i \(-0.274782\pi\)
0.649968 + 0.759962i \(0.274782\pi\)
\(578\) 0 0
\(579\) −18.7212 −0.778028
\(580\) 0 0
\(581\) 3.69484 0.153288
\(582\) 0 0
\(583\) 8.29678 0.343617
\(584\) 0 0
\(585\) 16.7226 0.691396
\(586\) 0 0
\(587\) −6.02985 −0.248878 −0.124439 0.992227i \(-0.539713\pi\)
−0.124439 + 0.992227i \(0.539713\pi\)
\(588\) 0 0
\(589\) 1.24996 0.0515036
\(590\) 0 0
\(591\) 12.1950 0.501634
\(592\) 0 0
\(593\) 27.7573 1.13986 0.569929 0.821694i \(-0.306971\pi\)
0.569929 + 0.821694i \(0.306971\pi\)
\(594\) 0 0
\(595\) −13.3774 −0.548421
\(596\) 0 0
\(597\) −1.48491 −0.0607733
\(598\) 0 0
\(599\) 35.4573 1.44874 0.724372 0.689409i \(-0.242130\pi\)
0.724372 + 0.689409i \(0.242130\pi\)
\(600\) 0 0
\(601\) 31.3416 1.27845 0.639225 0.769020i \(-0.279255\pi\)
0.639225 + 0.769020i \(0.279255\pi\)
\(602\) 0 0
\(603\) −0.628889 −0.0256104
\(604\) 0 0
\(605\) −7.44104 −0.302521
\(606\) 0 0
\(607\) 31.9080 1.29510 0.647552 0.762021i \(-0.275793\pi\)
0.647552 + 0.762021i \(0.275793\pi\)
\(608\) 0 0
\(609\) 4.02013 0.162904
\(610\) 0 0
\(611\) 49.8187 2.01545
\(612\) 0 0
\(613\) 3.53486 0.142772 0.0713859 0.997449i \(-0.477258\pi\)
0.0713859 + 0.997449i \(0.477258\pi\)
\(614\) 0 0
\(615\) −24.1452 −0.973630
\(616\) 0 0
\(617\) −6.53527 −0.263100 −0.131550 0.991310i \(-0.541995\pi\)
−0.131550 + 0.991310i \(0.541995\pi\)
\(618\) 0 0
\(619\) 27.3866 1.10076 0.550381 0.834914i \(-0.314483\pi\)
0.550381 + 0.834914i \(0.314483\pi\)
\(620\) 0 0
\(621\) −4.47047 −0.179394
\(622\) 0 0
\(623\) 0.303079 0.0121426
\(624\) 0 0
\(625\) −31.2273 −1.24909
\(626\) 0 0
\(627\) −3.41899 −0.136541
\(628\) 0 0
\(629\) 73.2286 2.91982
\(630\) 0 0
\(631\) 12.8036 0.509704 0.254852 0.966980i \(-0.417973\pi\)
0.254852 + 0.966980i \(0.417973\pi\)
\(632\) 0 0
\(633\) 14.9344 0.593589
\(634\) 0 0
\(635\) −14.2077 −0.563815
\(636\) 0 0
\(637\) 39.4702 1.56386
\(638\) 0 0
\(639\) −3.07457 −0.121628
\(640\) 0 0
\(641\) −2.32208 −0.0917165 −0.0458583 0.998948i \(-0.514602\pi\)
−0.0458583 + 0.998948i \(0.514602\pi\)
\(642\) 0 0
\(643\) −1.60321 −0.0632245 −0.0316122 0.999500i \(-0.510064\pi\)
−0.0316122 + 0.999500i \(0.510064\pi\)
\(644\) 0 0
\(645\) −14.9671 −0.589331
\(646\) 0 0
\(647\) −43.0337 −1.69183 −0.845915 0.533317i \(-0.820945\pi\)
−0.845915 + 0.533317i \(0.820945\pi\)
\(648\) 0 0
\(649\) 45.7062 1.79412
\(650\) 0 0
\(651\) 1.05102 0.0411929
\(652\) 0 0
\(653\) 18.3118 0.716596 0.358298 0.933607i \(-0.383357\pi\)
0.358298 + 0.933607i \(0.383357\pi\)
\(654\) 0 0
\(655\) 11.6380 0.454734
\(656\) 0 0
\(657\) 3.83167 0.149488
\(658\) 0 0
\(659\) −4.81736 −0.187658 −0.0938289 0.995588i \(-0.529911\pi\)
−0.0938289 + 0.995588i \(0.529911\pi\)
\(660\) 0 0
\(661\) 42.4346 1.65051 0.825257 0.564757i \(-0.191030\pi\)
0.825257 + 0.564757i \(0.191030\pi\)
\(662\) 0 0
\(663\) 39.2532 1.52447
\(664\) 0 0
\(665\) 1.93867 0.0751785
\(666\) 0 0
\(667\) −23.1764 −0.897392
\(668\) 0 0
\(669\) −10.3483 −0.400089
\(670\) 0 0
\(671\) 18.8377 0.727222
\(672\) 0 0
\(673\) 23.4211 0.902815 0.451408 0.892318i \(-0.350922\pi\)
0.451408 + 0.892318i \(0.350922\pi\)
\(674\) 0 0
\(675\) −2.34945 −0.0904302
\(676\) 0 0
\(677\) 31.8529 1.22421 0.612104 0.790777i \(-0.290323\pi\)
0.612104 + 0.790777i \(0.290323\pi\)
\(678\) 0 0
\(679\) 12.0290 0.461631
\(680\) 0 0
\(681\) −7.31500 −0.280311
\(682\) 0 0
\(683\) −35.9939 −1.37727 −0.688635 0.725108i \(-0.741790\pi\)
−0.688635 + 0.725108i \(0.741790\pi\)
\(684\) 0 0
\(685\) 5.89207 0.225124
\(686\) 0 0
\(687\) −17.3272 −0.661076
\(688\) 0 0
\(689\) 13.8044 0.525906
\(690\) 0 0
\(691\) 27.9417 1.06295 0.531476 0.847073i \(-0.321638\pi\)
0.531476 + 0.847073i \(0.321638\pi\)
\(692\) 0 0
\(693\) −2.87486 −0.109207
\(694\) 0 0
\(695\) 48.9850 1.85811
\(696\) 0 0
\(697\) −56.6763 −2.14677
\(698\) 0 0
\(699\) 16.4242 0.621222
\(700\) 0 0
\(701\) −11.3135 −0.427306 −0.213653 0.976910i \(-0.568536\pi\)
−0.213653 + 0.976910i \(0.568536\pi\)
\(702\) 0 0
\(703\) −10.6124 −0.400253
\(704\) 0 0
\(705\) −21.8948 −0.824607
\(706\) 0 0
\(707\) 11.0216 0.414509
\(708\) 0 0
\(709\) −33.8151 −1.26995 −0.634976 0.772532i \(-0.718990\pi\)
−0.634976 + 0.772532i \(0.718990\pi\)
\(710\) 0 0
\(711\) −15.8763 −0.595407
\(712\) 0 0
\(713\) −6.05924 −0.226920
\(714\) 0 0
\(715\) −61.9974 −2.31857
\(716\) 0 0
\(717\) −4.16870 −0.155683
\(718\) 0 0
\(719\) 38.3845 1.43150 0.715749 0.698357i \(-0.246085\pi\)
0.715749 + 0.698357i \(0.246085\pi\)
\(720\) 0 0
\(721\) 9.00655 0.335421
\(722\) 0 0
\(723\) −10.1175 −0.376273
\(724\) 0 0
\(725\) −12.1803 −0.452365
\(726\) 0 0
\(727\) 12.6807 0.470301 0.235150 0.971959i \(-0.424442\pi\)
0.235150 + 0.971959i \(0.424442\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −35.1325 −1.29942
\(732\) 0 0
\(733\) 4.51823 0.166885 0.0834423 0.996513i \(-0.473409\pi\)
0.0834423 + 0.996513i \(0.473409\pi\)
\(734\) 0 0
\(735\) −17.3468 −0.639845
\(736\) 0 0
\(737\) 2.33154 0.0858834
\(738\) 0 0
\(739\) −49.4318 −1.81838 −0.909189 0.416383i \(-0.863297\pi\)
−0.909189 + 0.416383i \(0.863297\pi\)
\(740\) 0 0
\(741\) −5.68862 −0.208977
\(742\) 0 0
\(743\) 11.0292 0.404623 0.202312 0.979321i \(-0.435155\pi\)
0.202312 + 0.979321i \(0.435155\pi\)
\(744\) 0 0
\(745\) 0.896619 0.0328496
\(746\) 0 0
\(747\) 4.76483 0.174336
\(748\) 0 0
\(749\) −10.1790 −0.371931
\(750\) 0 0
\(751\) −50.2471 −1.83354 −0.916771 0.399412i \(-0.869214\pi\)
−0.916771 + 0.399412i \(0.869214\pi\)
\(752\) 0 0
\(753\) 11.9898 0.436933
\(754\) 0 0
\(755\) −10.0055 −0.364138
\(756\) 0 0
\(757\) −40.6067 −1.47588 −0.737938 0.674869i \(-0.764200\pi\)
−0.737938 + 0.674869i \(0.764200\pi\)
\(758\) 0 0
\(759\) 16.5738 0.601590
\(760\) 0 0
\(761\) −29.3817 −1.06509 −0.532543 0.846403i \(-0.678764\pi\)
−0.532543 + 0.846403i \(0.678764\pi\)
\(762\) 0 0
\(763\) 2.61450 0.0946514
\(764\) 0 0
\(765\) −17.2514 −0.623727
\(766\) 0 0
\(767\) 76.0473 2.74591
\(768\) 0 0
\(769\) 29.1206 1.05012 0.525058 0.851067i \(-0.324044\pi\)
0.525058 + 0.851067i \(0.324044\pi\)
\(770\) 0 0
\(771\) −12.0253 −0.433081
\(772\) 0 0
\(773\) −0.665280 −0.0239285 −0.0119642 0.999928i \(-0.503808\pi\)
−0.0119642 + 0.999928i \(0.503808\pi\)
\(774\) 0 0
\(775\) −3.18442 −0.114388
\(776\) 0 0
\(777\) −8.92340 −0.320125
\(778\) 0 0
\(779\) 8.21360 0.294283
\(780\) 0 0
\(781\) 11.3986 0.407875
\(782\) 0 0
\(783\) 5.18433 0.185273
\(784\) 0 0
\(785\) −42.7025 −1.52412
\(786\) 0 0
\(787\) 32.0421 1.14218 0.571089 0.820888i \(-0.306521\pi\)
0.571089 + 0.820888i \(0.306521\pi\)
\(788\) 0 0
\(789\) −0.941771 −0.0335279
\(790\) 0 0
\(791\) −10.0356 −0.356826
\(792\) 0 0
\(793\) 31.3427 1.11301
\(794\) 0 0
\(795\) −6.06691 −0.215171
\(796\) 0 0
\(797\) −41.1598 −1.45795 −0.728977 0.684538i \(-0.760004\pi\)
−0.728977 + 0.684538i \(0.760004\pi\)
\(798\) 0 0
\(799\) −51.3940 −1.81819
\(800\) 0 0
\(801\) 0.390848 0.0138099
\(802\) 0 0
\(803\) −14.2055 −0.501302
\(804\) 0 0
\(805\) −9.39783 −0.331230
\(806\) 0 0
\(807\) −3.56306 −0.125426
\(808\) 0 0
\(809\) 31.4775 1.10669 0.553345 0.832952i \(-0.313351\pi\)
0.553345 + 0.832952i \(0.313351\pi\)
\(810\) 0 0
\(811\) 15.1659 0.532546 0.266273 0.963898i \(-0.414208\pi\)
0.266273 + 0.963898i \(0.414208\pi\)
\(812\) 0 0
\(813\) 21.3869 0.750072
\(814\) 0 0
\(815\) 42.1070 1.47495
\(816\) 0 0
\(817\) 5.09145 0.178127
\(818\) 0 0
\(819\) −4.78327 −0.167141
\(820\) 0 0
\(821\) −50.3086 −1.75578 −0.877890 0.478862i \(-0.841050\pi\)
−0.877890 + 0.478862i \(0.841050\pi\)
\(822\) 0 0
\(823\) 31.2887 1.09066 0.545328 0.838222i \(-0.316405\pi\)
0.545328 + 0.838222i \(0.316405\pi\)
\(824\) 0 0
\(825\) 8.71032 0.303254
\(826\) 0 0
\(827\) −21.5291 −0.748639 −0.374320 0.927300i \(-0.622124\pi\)
−0.374320 + 0.927300i \(0.622124\pi\)
\(828\) 0 0
\(829\) −30.7206 −1.06697 −0.533486 0.845809i \(-0.679118\pi\)
−0.533486 + 0.845809i \(0.679118\pi\)
\(830\) 0 0
\(831\) −28.5165 −0.989227
\(832\) 0 0
\(833\) −40.7183 −1.41080
\(834\) 0 0
\(835\) −2.71099 −0.0938175
\(836\) 0 0
\(837\) 1.35539 0.0468493
\(838\) 0 0
\(839\) −6.94057 −0.239615 −0.119808 0.992797i \(-0.538228\pi\)
−0.119808 + 0.992797i \(0.538228\pi\)
\(840\) 0 0
\(841\) −2.12277 −0.0731989
\(842\) 0 0
\(843\) 26.7452 0.921155
\(844\) 0 0
\(845\) −67.9103 −2.33618
\(846\) 0 0
\(847\) 2.12840 0.0731328
\(848\) 0 0
\(849\) −2.76889 −0.0950281
\(850\) 0 0
\(851\) 51.4442 1.76348
\(852\) 0 0
\(853\) −5.88185 −0.201391 −0.100695 0.994917i \(-0.532107\pi\)
−0.100695 + 0.994917i \(0.532107\pi\)
\(854\) 0 0
\(855\) 2.50010 0.0855015
\(856\) 0 0
\(857\) −24.9088 −0.850869 −0.425435 0.904989i \(-0.639879\pi\)
−0.425435 + 0.904989i \(0.639879\pi\)
\(858\) 0 0
\(859\) −9.86029 −0.336429 −0.168214 0.985750i \(-0.553800\pi\)
−0.168214 + 0.985750i \(0.553800\pi\)
\(860\) 0 0
\(861\) 6.90640 0.235369
\(862\) 0 0
\(863\) −37.4522 −1.27489 −0.637444 0.770497i \(-0.720008\pi\)
−0.637444 + 0.770497i \(0.720008\pi\)
\(864\) 0 0
\(865\) −45.6430 −1.55191
\(866\) 0 0
\(867\) −23.4945 −0.797914
\(868\) 0 0
\(869\) 58.8597 1.99668
\(870\) 0 0
\(871\) 3.87928 0.131445
\(872\) 0 0
\(873\) 15.5125 0.525019
\(874\) 0 0
\(875\) 5.57200 0.188368
\(876\) 0 0
\(877\) −33.7918 −1.14107 −0.570534 0.821274i \(-0.693264\pi\)
−0.570534 + 0.821274i \(0.693264\pi\)
\(878\) 0 0
\(879\) 17.3417 0.584920
\(880\) 0 0
\(881\) 50.8128 1.71193 0.855963 0.517038i \(-0.172965\pi\)
0.855963 + 0.517038i \(0.172965\pi\)
\(882\) 0 0
\(883\) −46.4246 −1.56231 −0.781156 0.624336i \(-0.785370\pi\)
−0.781156 + 0.624336i \(0.785370\pi\)
\(884\) 0 0
\(885\) −33.4221 −1.12347
\(886\) 0 0
\(887\) −7.20134 −0.241797 −0.120899 0.992665i \(-0.538578\pi\)
−0.120899 + 0.992665i \(0.538578\pi\)
\(888\) 0 0
\(889\) 4.06391 0.136299
\(890\) 0 0
\(891\) −3.70739 −0.124202
\(892\) 0 0
\(893\) 7.44807 0.249240
\(894\) 0 0
\(895\) −39.9716 −1.33610
\(896\) 0 0
\(897\) 27.5759 0.920734
\(898\) 0 0
\(899\) 7.02680 0.234357
\(900\) 0 0
\(901\) −14.2409 −0.474434
\(902\) 0 0
\(903\) 4.28114 0.142467
\(904\) 0 0
\(905\) −31.7962 −1.05694
\(906\) 0 0
\(907\) 35.0271 1.16305 0.581527 0.813527i \(-0.302455\pi\)
0.581527 + 0.813527i \(0.302455\pi\)
\(908\) 0 0
\(909\) 14.2133 0.471427
\(910\) 0 0
\(911\) 30.7886 1.02007 0.510036 0.860153i \(-0.329632\pi\)
0.510036 + 0.860153i \(0.329632\pi\)
\(912\) 0 0
\(913\) −17.6651 −0.584630
\(914\) 0 0
\(915\) −13.7748 −0.455382
\(916\) 0 0
\(917\) −3.32888 −0.109929
\(918\) 0 0
\(919\) −23.8564 −0.786949 −0.393474 0.919336i \(-0.628727\pi\)
−0.393474 + 0.919336i \(0.628727\pi\)
\(920\) 0 0
\(921\) −17.3038 −0.570178
\(922\) 0 0
\(923\) 18.9654 0.624252
\(924\) 0 0
\(925\) 27.0364 0.888951
\(926\) 0 0
\(927\) 11.6148 0.381479
\(928\) 0 0
\(929\) −41.8969 −1.37459 −0.687297 0.726377i \(-0.741203\pi\)
−0.687297 + 0.726377i \(0.741203\pi\)
\(930\) 0 0
\(931\) 5.90094 0.193395
\(932\) 0 0
\(933\) 23.3959 0.765947
\(934\) 0 0
\(935\) 63.9579 2.09165
\(936\) 0 0
\(937\) −38.6906 −1.26397 −0.631983 0.774983i \(-0.717759\pi\)
−0.631983 + 0.774983i \(0.717759\pi\)
\(938\) 0 0
\(939\) −0.191470 −0.00624839
\(940\) 0 0
\(941\) −49.1394 −1.60190 −0.800949 0.598732i \(-0.795671\pi\)
−0.800949 + 0.598732i \(0.795671\pi\)
\(942\) 0 0
\(943\) −39.8159 −1.29659
\(944\) 0 0
\(945\) 2.10220 0.0683847
\(946\) 0 0
\(947\) −60.1778 −1.95552 −0.977758 0.209736i \(-0.932740\pi\)
−0.977758 + 0.209736i \(0.932740\pi\)
\(948\) 0 0
\(949\) −23.6355 −0.767242
\(950\) 0 0
\(951\) 3.25612 0.105587
\(952\) 0 0
\(953\) 6.03764 0.195578 0.0977892 0.995207i \(-0.468823\pi\)
0.0977892 + 0.995207i \(0.468823\pi\)
\(954\) 0 0
\(955\) 4.38174 0.141790
\(956\) 0 0
\(957\) −19.2203 −0.621305
\(958\) 0 0
\(959\) −1.68534 −0.0544225
\(960\) 0 0
\(961\) −29.1629 −0.940739
\(962\) 0 0
\(963\) −13.1267 −0.423002
\(964\) 0 0
\(965\) −50.7530 −1.63380
\(966\) 0 0
\(967\) 17.4074 0.559785 0.279892 0.960031i \(-0.409701\pi\)
0.279892 + 0.960031i \(0.409701\pi\)
\(968\) 0 0
\(969\) 5.86850 0.188523
\(970\) 0 0
\(971\) 18.2201 0.584711 0.292356 0.956310i \(-0.405561\pi\)
0.292356 + 0.956310i \(0.405561\pi\)
\(972\) 0 0
\(973\) −14.0115 −0.449187
\(974\) 0 0
\(975\) 14.4925 0.464131
\(976\) 0 0
\(977\) −40.7926 −1.30507 −0.652535 0.757758i \(-0.726295\pi\)
−0.652535 + 0.757758i \(0.726295\pi\)
\(978\) 0 0
\(979\) −1.44903 −0.0463111
\(980\) 0 0
\(981\) 3.37165 0.107648
\(982\) 0 0
\(983\) −56.5978 −1.80519 −0.902594 0.430492i \(-0.858340\pi\)
−0.902594 + 0.430492i \(0.858340\pi\)
\(984\) 0 0
\(985\) 33.0604 1.05339
\(986\) 0 0
\(987\) 6.26271 0.199344
\(988\) 0 0
\(989\) −24.6811 −0.784814
\(990\) 0 0
\(991\) 15.0500 0.478081 0.239040 0.971010i \(-0.423167\pi\)
0.239040 + 0.971010i \(0.423167\pi\)
\(992\) 0 0
\(993\) −30.7585 −0.976092
\(994\) 0 0
\(995\) −4.02557 −0.127619
\(996\) 0 0
\(997\) −23.2414 −0.736063 −0.368031 0.929813i \(-0.619968\pi\)
−0.368031 + 0.929813i \(0.619968\pi\)
\(998\) 0 0
\(999\) −11.5076 −0.364083
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 \(a_p\))