Properties

Label 8020.2.a.c.1.16
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.356039 q^{3}\) \(-1.00000 q^{5}\) \(-0.400497 q^{7}\) \(-2.87324 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.356039 q^{3}\) \(-1.00000 q^{5}\) \(-0.400497 q^{7}\) \(-2.87324 q^{9}\) \(-0.436499 q^{11}\) \(-0.615654 q^{13}\) \(-0.356039 q^{15}\) \(-0.540511 q^{17}\) \(+1.98251 q^{19}\) \(-0.142593 q^{21}\) \(+0.0321294 q^{23}\) \(+1.00000 q^{25}\) \(-2.09110 q^{27}\) \(+7.32938 q^{29}\) \(-1.85305 q^{31}\) \(-0.155411 q^{33}\) \(+0.400497 q^{35}\) \(+1.34276 q^{37}\) \(-0.219197 q^{39}\) \(+7.68506 q^{41}\) \(+4.12708 q^{43}\) \(+2.87324 q^{45}\) \(+11.3077 q^{47}\) \(-6.83960 q^{49}\) \(-0.192443 q^{51}\) \(-3.77405 q^{53}\) \(+0.436499 q^{55}\) \(+0.705850 q^{57}\) \(+3.82501 q^{59}\) \(-1.59871 q^{61}\) \(+1.15072 q^{63}\) \(+0.615654 q^{65}\) \(-10.1573 q^{67}\) \(+0.0114393 q^{69}\) \(-8.53890 q^{71}\) \(+1.94694 q^{73}\) \(+0.356039 q^{75}\) \(+0.174817 q^{77}\) \(-2.05854 q^{79}\) \(+7.87520 q^{81}\) \(+3.42087 q^{83}\) \(+0.540511 q^{85}\) \(+2.60954 q^{87}\) \(-9.88151 q^{89}\) \(+0.246568 q^{91}\) \(-0.659760 q^{93}\) \(-1.98251 q^{95}\) \(-4.60530 q^{97}\) \(+1.25417 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.356039 0.205559 0.102780 0.994704i \(-0.467226\pi\)
0.102780 + 0.994704i \(0.467226\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.400497 −0.151374 −0.0756869 0.997132i \(-0.524115\pi\)
−0.0756869 + 0.997132i \(0.524115\pi\)
\(8\) 0 0
\(9\) −2.87324 −0.957745
\(10\) 0 0
\(11\) −0.436499 −0.131610 −0.0658048 0.997833i \(-0.520961\pi\)
−0.0658048 + 0.997833i \(0.520961\pi\)
\(12\) 0 0
\(13\) −0.615654 −0.170752 −0.0853758 0.996349i \(-0.527209\pi\)
−0.0853758 + 0.996349i \(0.527209\pi\)
\(14\) 0 0
\(15\) −0.356039 −0.0919288
\(16\) 0 0
\(17\) −0.540511 −0.131093 −0.0655466 0.997850i \(-0.520879\pi\)
−0.0655466 + 0.997850i \(0.520879\pi\)
\(18\) 0 0
\(19\) 1.98251 0.454819 0.227409 0.973799i \(-0.426974\pi\)
0.227409 + 0.973799i \(0.426974\pi\)
\(20\) 0 0
\(21\) −0.142593 −0.0311163
\(22\) 0 0
\(23\) 0.0321294 0.00669945 0.00334972 0.999994i \(-0.498934\pi\)
0.00334972 + 0.999994i \(0.498934\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −2.09110 −0.402433
\(28\) 0 0
\(29\) 7.32938 1.36103 0.680516 0.732733i \(-0.261756\pi\)
0.680516 + 0.732733i \(0.261756\pi\)
\(30\) 0 0
\(31\) −1.85305 −0.332818 −0.166409 0.986057i \(-0.553217\pi\)
−0.166409 + 0.986057i \(0.553217\pi\)
\(32\) 0 0
\(33\) −0.155411 −0.0270535
\(34\) 0 0
\(35\) 0.400497 0.0676964
\(36\) 0 0
\(37\) 1.34276 0.220748 0.110374 0.993890i \(-0.464795\pi\)
0.110374 + 0.993890i \(0.464795\pi\)
\(38\) 0 0
\(39\) −0.219197 −0.0350996
\(40\) 0 0
\(41\) 7.68506 1.20020 0.600102 0.799923i \(-0.295126\pi\)
0.600102 + 0.799923i \(0.295126\pi\)
\(42\) 0 0
\(43\) 4.12708 0.629374 0.314687 0.949195i \(-0.398100\pi\)
0.314687 + 0.949195i \(0.398100\pi\)
\(44\) 0 0
\(45\) 2.87324 0.428317
\(46\) 0 0
\(47\) 11.3077 1.64939 0.824695 0.565577i \(-0.191347\pi\)
0.824695 + 0.565577i \(0.191347\pi\)
\(48\) 0 0
\(49\) −6.83960 −0.977086
\(50\) 0 0
\(51\) −0.192443 −0.0269474
\(52\) 0 0
\(53\) −3.77405 −0.518405 −0.259203 0.965823i \(-0.583460\pi\)
−0.259203 + 0.965823i \(0.583460\pi\)
\(54\) 0 0
\(55\) 0.436499 0.0588576
\(56\) 0 0
\(57\) 0.705850 0.0934921
\(58\) 0 0
\(59\) 3.82501 0.497973 0.248987 0.968507i \(-0.419902\pi\)
0.248987 + 0.968507i \(0.419902\pi\)
\(60\) 0 0
\(61\) −1.59871 −0.204693 −0.102347 0.994749i \(-0.532635\pi\)
−0.102347 + 0.994749i \(0.532635\pi\)
\(62\) 0 0
\(63\) 1.15072 0.144978
\(64\) 0 0
\(65\) 0.615654 0.0763625
\(66\) 0 0
\(67\) −10.1573 −1.24092 −0.620458 0.784239i \(-0.713053\pi\)
−0.620458 + 0.784239i \(0.713053\pi\)
\(68\) 0 0
\(69\) 0.0114393 0.00137713
\(70\) 0 0
\(71\) −8.53890 −1.01338 −0.506690 0.862128i \(-0.669131\pi\)
−0.506690 + 0.862128i \(0.669131\pi\)
\(72\) 0 0
\(73\) 1.94694 0.227872 0.113936 0.993488i \(-0.463654\pi\)
0.113936 + 0.993488i \(0.463654\pi\)
\(74\) 0 0
\(75\) 0.356039 0.0411118
\(76\) 0 0
\(77\) 0.174817 0.0199222
\(78\) 0 0
\(79\) −2.05854 −0.231604 −0.115802 0.993272i \(-0.536944\pi\)
−0.115802 + 0.993272i \(0.536944\pi\)
\(80\) 0 0
\(81\) 7.87520 0.875022
\(82\) 0 0
\(83\) 3.42087 0.375490 0.187745 0.982218i \(-0.439882\pi\)
0.187745 + 0.982218i \(0.439882\pi\)
\(84\) 0 0
\(85\) 0.540511 0.0586267
\(86\) 0 0
\(87\) 2.60954 0.279772
\(88\) 0 0
\(89\) −9.88151 −1.04744 −0.523719 0.851891i \(-0.675456\pi\)
−0.523719 + 0.851891i \(0.675456\pi\)
\(90\) 0 0
\(91\) 0.246568 0.0258473
\(92\) 0 0
\(93\) −0.659760 −0.0684139
\(94\) 0 0
\(95\) −1.98251 −0.203401
\(96\) 0 0
\(97\) −4.60530 −0.467597 −0.233799 0.972285i \(-0.575116\pi\)
−0.233799 + 0.972285i \(0.575116\pi\)
\(98\) 0 0
\(99\) 1.25417 0.126048
\(100\) 0 0
\(101\) −14.7271 −1.46540 −0.732701 0.680550i \(-0.761741\pi\)
−0.732701 + 0.680550i \(0.761741\pi\)
\(102\) 0 0
\(103\) −7.01280 −0.690992 −0.345496 0.938420i \(-0.612289\pi\)
−0.345496 + 0.938420i \(0.612289\pi\)
\(104\) 0 0
\(105\) 0.142593 0.0139156
\(106\) 0 0
\(107\) −14.0600 −1.35923 −0.679616 0.733568i \(-0.737853\pi\)
−0.679616 + 0.733568i \(0.737853\pi\)
\(108\) 0 0
\(109\) −5.24267 −0.502157 −0.251079 0.967967i \(-0.580785\pi\)
−0.251079 + 0.967967i \(0.580785\pi\)
\(110\) 0 0
\(111\) 0.478074 0.0453768
\(112\) 0 0
\(113\) 6.01042 0.565413 0.282706 0.959207i \(-0.408768\pi\)
0.282706 + 0.959207i \(0.408768\pi\)
\(114\) 0 0
\(115\) −0.0321294 −0.00299608
\(116\) 0 0
\(117\) 1.76892 0.163537
\(118\) 0 0
\(119\) 0.216473 0.0198441
\(120\) 0 0
\(121\) −10.8095 −0.982679
\(122\) 0 0
\(123\) 2.73618 0.246713
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.232932 0.0206694 0.0103347 0.999947i \(-0.496710\pi\)
0.0103347 + 0.999947i \(0.496710\pi\)
\(128\) 0 0
\(129\) 1.46940 0.129374
\(130\) 0 0
\(131\) −7.38264 −0.645025 −0.322512 0.946565i \(-0.604527\pi\)
−0.322512 + 0.946565i \(0.604527\pi\)
\(132\) 0 0
\(133\) −0.793990 −0.0688476
\(134\) 0 0
\(135\) 2.09110 0.179973
\(136\) 0 0
\(137\) 10.8082 0.923408 0.461704 0.887034i \(-0.347238\pi\)
0.461704 + 0.887034i \(0.347238\pi\)
\(138\) 0 0
\(139\) 6.01742 0.510391 0.255196 0.966889i \(-0.417860\pi\)
0.255196 + 0.966889i \(0.417860\pi\)
\(140\) 0 0
\(141\) 4.02596 0.339047
\(142\) 0 0
\(143\) 0.268733 0.0224726
\(144\) 0 0
\(145\) −7.32938 −0.608672
\(146\) 0 0
\(147\) −2.43516 −0.200849
\(148\) 0 0
\(149\) −0.190471 −0.0156040 −0.00780202 0.999970i \(-0.502483\pi\)
−0.00780202 + 0.999970i \(0.502483\pi\)
\(150\) 0 0
\(151\) −12.8656 −1.04699 −0.523495 0.852029i \(-0.675372\pi\)
−0.523495 + 0.852029i \(0.675372\pi\)
\(152\) 0 0
\(153\) 1.55302 0.125554
\(154\) 0 0
\(155\) 1.85305 0.148841
\(156\) 0 0
\(157\) 3.08796 0.246446 0.123223 0.992379i \(-0.460677\pi\)
0.123223 + 0.992379i \(0.460677\pi\)
\(158\) 0 0
\(159\) −1.34371 −0.106563
\(160\) 0 0
\(161\) −0.0128678 −0.00101412
\(162\) 0 0
\(163\) −5.25329 −0.411470 −0.205735 0.978608i \(-0.565958\pi\)
−0.205735 + 0.978608i \(0.565958\pi\)
\(164\) 0 0
\(165\) 0.155411 0.0120987
\(166\) 0 0
\(167\) −18.8138 −1.45585 −0.727926 0.685656i \(-0.759516\pi\)
−0.727926 + 0.685656i \(0.759516\pi\)
\(168\) 0 0
\(169\) −12.6210 −0.970844
\(170\) 0 0
\(171\) −5.69622 −0.435600
\(172\) 0 0
\(173\) −17.7085 −1.34635 −0.673177 0.739481i \(-0.735071\pi\)
−0.673177 + 0.739481i \(0.735071\pi\)
\(174\) 0 0
\(175\) −0.400497 −0.0302748
\(176\) 0 0
\(177\) 1.36185 0.102363
\(178\) 0 0
\(179\) −15.1574 −1.13292 −0.566460 0.824089i \(-0.691687\pi\)
−0.566460 + 0.824089i \(0.691687\pi\)
\(180\) 0 0
\(181\) 14.7964 1.09981 0.549905 0.835227i \(-0.314664\pi\)
0.549905 + 0.835227i \(0.314664\pi\)
\(182\) 0 0
\(183\) −0.569201 −0.0420766
\(184\) 0 0
\(185\) −1.34276 −0.0987215
\(186\) 0 0
\(187\) 0.235933 0.0172531
\(188\) 0 0
\(189\) 0.837480 0.0609177
\(190\) 0 0
\(191\) 26.1176 1.88981 0.944903 0.327352i \(-0.106156\pi\)
0.944903 + 0.327352i \(0.106156\pi\)
\(192\) 0 0
\(193\) −5.54721 −0.399297 −0.199649 0.979868i \(-0.563980\pi\)
−0.199649 + 0.979868i \(0.563980\pi\)
\(194\) 0 0
\(195\) 0.219197 0.0156970
\(196\) 0 0
\(197\) −3.16628 −0.225588 −0.112794 0.993618i \(-0.535980\pi\)
−0.112794 + 0.993618i \(0.535980\pi\)
\(198\) 0 0
\(199\) −0.965855 −0.0684677 −0.0342338 0.999414i \(-0.510899\pi\)
−0.0342338 + 0.999414i \(0.510899\pi\)
\(200\) 0 0
\(201\) −3.61641 −0.255082
\(202\) 0 0
\(203\) −2.93540 −0.206024
\(204\) 0 0
\(205\) −7.68506 −0.536748
\(206\) 0 0
\(207\) −0.0923154 −0.00641637
\(208\) 0 0
\(209\) −0.865364 −0.0598585
\(210\) 0 0
\(211\) 10.8110 0.744263 0.372132 0.928180i \(-0.378627\pi\)
0.372132 + 0.928180i \(0.378627\pi\)
\(212\) 0 0
\(213\) −3.04018 −0.208310
\(214\) 0 0
\(215\) −4.12708 −0.281465
\(216\) 0 0
\(217\) 0.742144 0.0503800
\(218\) 0 0
\(219\) 0.693186 0.0468411
\(220\) 0 0
\(221\) 0.332768 0.0223844
\(222\) 0 0
\(223\) −8.10871 −0.543000 −0.271500 0.962438i \(-0.587520\pi\)
−0.271500 + 0.962438i \(0.587520\pi\)
\(224\) 0 0
\(225\) −2.87324 −0.191549
\(226\) 0 0
\(227\) −26.2653 −1.74329 −0.871644 0.490139i \(-0.836946\pi\)
−0.871644 + 0.490139i \(0.836946\pi\)
\(228\) 0 0
\(229\) 19.4473 1.28511 0.642557 0.766238i \(-0.277874\pi\)
0.642557 + 0.766238i \(0.277874\pi\)
\(230\) 0 0
\(231\) 0.0622416 0.00409520
\(232\) 0 0
\(233\) 20.7846 1.36165 0.680823 0.732448i \(-0.261622\pi\)
0.680823 + 0.732448i \(0.261622\pi\)
\(234\) 0 0
\(235\) −11.3077 −0.737630
\(236\) 0 0
\(237\) −0.732921 −0.0476083
\(238\) 0 0
\(239\) −13.6909 −0.885590 −0.442795 0.896623i \(-0.646013\pi\)
−0.442795 + 0.896623i \(0.646013\pi\)
\(240\) 0 0
\(241\) 2.64027 0.170075 0.0850375 0.996378i \(-0.472899\pi\)
0.0850375 + 0.996378i \(0.472899\pi\)
\(242\) 0 0
\(243\) 9.07718 0.582301
\(244\) 0 0
\(245\) 6.83960 0.436966
\(246\) 0 0
\(247\) −1.22054 −0.0776610
\(248\) 0 0
\(249\) 1.21796 0.0771854
\(250\) 0 0
\(251\) −5.53695 −0.349489 −0.174745 0.984614i \(-0.555910\pi\)
−0.174745 + 0.984614i \(0.555910\pi\)
\(252\) 0 0
\(253\) −0.0140245 −0.000881711 0
\(254\) 0 0
\(255\) 0.192443 0.0120512
\(256\) 0 0
\(257\) −27.5774 −1.72023 −0.860115 0.510101i \(-0.829608\pi\)
−0.860115 + 0.510101i \(0.829608\pi\)
\(258\) 0 0
\(259\) −0.537771 −0.0334155
\(260\) 0 0
\(261\) −21.0590 −1.30352
\(262\) 0 0
\(263\) 16.2506 1.00206 0.501028 0.865431i \(-0.332955\pi\)
0.501028 + 0.865431i \(0.332955\pi\)
\(264\) 0 0
\(265\) 3.77405 0.231838
\(266\) 0 0
\(267\) −3.51820 −0.215310
\(268\) 0 0
\(269\) −17.9729 −1.09583 −0.547913 0.836535i \(-0.684577\pi\)
−0.547913 + 0.836535i \(0.684577\pi\)
\(270\) 0 0
\(271\) −17.5126 −1.06381 −0.531907 0.846803i \(-0.678524\pi\)
−0.531907 + 0.846803i \(0.678524\pi\)
\(272\) 0 0
\(273\) 0.0877877 0.00531316
\(274\) 0 0
\(275\) −0.436499 −0.0263219
\(276\) 0 0
\(277\) −3.23224 −0.194206 −0.0971031 0.995274i \(-0.530958\pi\)
−0.0971031 + 0.995274i \(0.530958\pi\)
\(278\) 0 0
\(279\) 5.32426 0.318755
\(280\) 0 0
\(281\) −1.92462 −0.114813 −0.0574065 0.998351i \(-0.518283\pi\)
−0.0574065 + 0.998351i \(0.518283\pi\)
\(282\) 0 0
\(283\) 4.99800 0.297100 0.148550 0.988905i \(-0.452539\pi\)
0.148550 + 0.988905i \(0.452539\pi\)
\(284\) 0 0
\(285\) −0.705850 −0.0418110
\(286\) 0 0
\(287\) −3.07785 −0.181680
\(288\) 0 0
\(289\) −16.7078 −0.982815
\(290\) 0 0
\(291\) −1.63967 −0.0961189
\(292\) 0 0
\(293\) −4.66831 −0.272726 −0.136363 0.990659i \(-0.543541\pi\)
−0.136363 + 0.990659i \(0.543541\pi\)
\(294\) 0 0
\(295\) −3.82501 −0.222700
\(296\) 0 0
\(297\) 0.912764 0.0529640
\(298\) 0 0
\(299\) −0.0197806 −0.00114394
\(300\) 0 0
\(301\) −1.65289 −0.0952708
\(302\) 0 0
\(303\) −5.24343 −0.301227
\(304\) 0 0
\(305\) 1.59871 0.0915416
\(306\) 0 0
\(307\) −18.1043 −1.03327 −0.516634 0.856206i \(-0.672815\pi\)
−0.516634 + 0.856206i \(0.672815\pi\)
\(308\) 0 0
\(309\) −2.49683 −0.142040
\(310\) 0 0
\(311\) −33.4713 −1.89798 −0.948992 0.315300i \(-0.897895\pi\)
−0.948992 + 0.315300i \(0.897895\pi\)
\(312\) 0 0
\(313\) 3.67831 0.207910 0.103955 0.994582i \(-0.466850\pi\)
0.103955 + 0.994582i \(0.466850\pi\)
\(314\) 0 0
\(315\) −1.15072 −0.0648359
\(316\) 0 0
\(317\) −12.0864 −0.678841 −0.339420 0.940635i \(-0.610231\pi\)
−0.339420 + 0.940635i \(0.610231\pi\)
\(318\) 0 0
\(319\) −3.19927 −0.179125
\(320\) 0 0
\(321\) −5.00591 −0.279402
\(322\) 0 0
\(323\) −1.07157 −0.0596236
\(324\) 0 0
\(325\) −0.615654 −0.0341503
\(326\) 0 0
\(327\) −1.86660 −0.103223
\(328\) 0 0
\(329\) −4.52869 −0.249674
\(330\) 0 0
\(331\) 4.19704 0.230690 0.115345 0.993325i \(-0.463203\pi\)
0.115345 + 0.993325i \(0.463203\pi\)
\(332\) 0 0
\(333\) −3.85806 −0.211420
\(334\) 0 0
\(335\) 10.1573 0.554955
\(336\) 0 0
\(337\) 30.4211 1.65714 0.828571 0.559884i \(-0.189154\pi\)
0.828571 + 0.559884i \(0.189154\pi\)
\(338\) 0 0
\(339\) 2.13994 0.116226
\(340\) 0 0
\(341\) 0.808858 0.0438021
\(342\) 0 0
\(343\) 5.54272 0.299279
\(344\) 0 0
\(345\) −0.0114393 −0.000615873 0
\(346\) 0 0
\(347\) −36.3677 −1.95232 −0.976161 0.217047i \(-0.930357\pi\)
−0.976161 + 0.217047i \(0.930357\pi\)
\(348\) 0 0
\(349\) 28.0876 1.50349 0.751747 0.659452i \(-0.229212\pi\)
0.751747 + 0.659452i \(0.229212\pi\)
\(350\) 0 0
\(351\) 1.28739 0.0687160
\(352\) 0 0
\(353\) 19.9754 1.06318 0.531591 0.847001i \(-0.321594\pi\)
0.531591 + 0.847001i \(0.321594\pi\)
\(354\) 0 0
\(355\) 8.53890 0.453198
\(356\) 0 0
\(357\) 0.0770729 0.00407913
\(358\) 0 0
\(359\) 35.5820 1.87795 0.938973 0.343990i \(-0.111779\pi\)
0.938973 + 0.343990i \(0.111779\pi\)
\(360\) 0 0
\(361\) −15.0697 −0.793140
\(362\) 0 0
\(363\) −3.84859 −0.201999
\(364\) 0 0
\(365\) −1.94694 −0.101907
\(366\) 0 0
\(367\) 35.1552 1.83508 0.917542 0.397638i \(-0.130170\pi\)
0.917542 + 0.397638i \(0.130170\pi\)
\(368\) 0 0
\(369\) −22.0810 −1.14949
\(370\) 0 0
\(371\) 1.51150 0.0784730
\(372\) 0 0
\(373\) 24.4843 1.26775 0.633874 0.773437i \(-0.281464\pi\)
0.633874 + 0.773437i \(0.281464\pi\)
\(374\) 0 0
\(375\) −0.356039 −0.0183858
\(376\) 0 0
\(377\) −4.51236 −0.232398
\(378\) 0 0
\(379\) 31.2262 1.60398 0.801991 0.597336i \(-0.203774\pi\)
0.801991 + 0.597336i \(0.203774\pi\)
\(380\) 0 0
\(381\) 0.0829328 0.00424878
\(382\) 0 0
\(383\) −12.9086 −0.659598 −0.329799 0.944051i \(-0.606981\pi\)
−0.329799 + 0.944051i \(0.606981\pi\)
\(384\) 0 0
\(385\) −0.174817 −0.00890950
\(386\) 0 0
\(387\) −11.8581 −0.602780
\(388\) 0 0
\(389\) 1.62994 0.0826410 0.0413205 0.999146i \(-0.486844\pi\)
0.0413205 + 0.999146i \(0.486844\pi\)
\(390\) 0 0
\(391\) −0.0173663 −0.000878252 0
\(392\) 0 0
\(393\) −2.62851 −0.132591
\(394\) 0 0
\(395\) 2.05854 0.103577
\(396\) 0 0
\(397\) −32.7581 −1.64408 −0.822040 0.569430i \(-0.807164\pi\)
−0.822040 + 0.569430i \(0.807164\pi\)
\(398\) 0 0
\(399\) −0.282691 −0.0141523
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 1.14084 0.0568293
\(404\) 0 0
\(405\) −7.87520 −0.391322
\(406\) 0 0
\(407\) −0.586113 −0.0290525
\(408\) 0 0
\(409\) 33.7689 1.66977 0.834883 0.550427i \(-0.185535\pi\)
0.834883 + 0.550427i \(0.185535\pi\)
\(410\) 0 0
\(411\) 3.84815 0.189815
\(412\) 0 0
\(413\) −1.53191 −0.0753801
\(414\) 0 0
\(415\) −3.42087 −0.167924
\(416\) 0 0
\(417\) 2.14244 0.104916
\(418\) 0 0
\(419\) −21.2504 −1.03815 −0.519075 0.854729i \(-0.673724\pi\)
−0.519075 + 0.854729i \(0.673724\pi\)
\(420\) 0 0
\(421\) −5.61538 −0.273677 −0.136839 0.990593i \(-0.543694\pi\)
−0.136839 + 0.990593i \(0.543694\pi\)
\(422\) 0 0
\(423\) −32.4896 −1.57970
\(424\) 0 0
\(425\) −0.540511 −0.0262186
\(426\) 0 0
\(427\) 0.640278 0.0309852
\(428\) 0 0
\(429\) 0.0956793 0.00461944
\(430\) 0 0
\(431\) 31.9645 1.53968 0.769838 0.638239i \(-0.220337\pi\)
0.769838 + 0.638239i \(0.220337\pi\)
\(432\) 0 0
\(433\) −11.6145 −0.558158 −0.279079 0.960268i \(-0.590029\pi\)
−0.279079 + 0.960268i \(0.590029\pi\)
\(434\) 0 0
\(435\) −2.60954 −0.125118
\(436\) 0 0
\(437\) 0.0636969 0.00304703
\(438\) 0 0
\(439\) −3.73907 −0.178456 −0.0892281 0.996011i \(-0.528440\pi\)
−0.0892281 + 0.996011i \(0.528440\pi\)
\(440\) 0 0
\(441\) 19.6518 0.935800
\(442\) 0 0
\(443\) 15.3407 0.728858 0.364429 0.931231i \(-0.381264\pi\)
0.364429 + 0.931231i \(0.381264\pi\)
\(444\) 0 0
\(445\) 9.88151 0.468428
\(446\) 0 0
\(447\) −0.0678153 −0.00320755
\(448\) 0 0
\(449\) −17.2372 −0.813472 −0.406736 0.913546i \(-0.633333\pi\)
−0.406736 + 0.913546i \(0.633333\pi\)
\(450\) 0 0
\(451\) −3.35453 −0.157958
\(452\) 0 0
\(453\) −4.58066 −0.215218
\(454\) 0 0
\(455\) −0.246568 −0.0115593
\(456\) 0 0
\(457\) −34.5103 −1.61433 −0.807163 0.590329i \(-0.798998\pi\)
−0.807163 + 0.590329i \(0.798998\pi\)
\(458\) 0 0
\(459\) 1.13026 0.0527562
\(460\) 0 0
\(461\) −18.0567 −0.840984 −0.420492 0.907296i \(-0.638142\pi\)
−0.420492 + 0.907296i \(0.638142\pi\)
\(462\) 0 0
\(463\) −6.67140 −0.310046 −0.155023 0.987911i \(-0.549545\pi\)
−0.155023 + 0.987911i \(0.549545\pi\)
\(464\) 0 0
\(465\) 0.659760 0.0305956
\(466\) 0 0
\(467\) 11.5080 0.532527 0.266263 0.963900i \(-0.414211\pi\)
0.266263 + 0.963900i \(0.414211\pi\)
\(468\) 0 0
\(469\) 4.06799 0.187842
\(470\) 0 0
\(471\) 1.09943 0.0506592
\(472\) 0 0
\(473\) −1.80147 −0.0828317
\(474\) 0 0
\(475\) 1.98251 0.0909637
\(476\) 0 0
\(477\) 10.8437 0.496500
\(478\) 0 0
\(479\) −13.5921 −0.621040 −0.310520 0.950567i \(-0.600503\pi\)
−0.310520 + 0.950567i \(0.600503\pi\)
\(480\) 0 0
\(481\) −0.826674 −0.0376931
\(482\) 0 0
\(483\) −0.00458142 −0.000208462 0
\(484\) 0 0
\(485\) 4.60530 0.209116
\(486\) 0 0
\(487\) −5.70563 −0.258547 −0.129273 0.991609i \(-0.541264\pi\)
−0.129273 + 0.991609i \(0.541264\pi\)
\(488\) 0 0
\(489\) −1.87038 −0.0845814
\(490\) 0 0
\(491\) −35.8351 −1.61721 −0.808607 0.588350i \(-0.799778\pi\)
−0.808607 + 0.588350i \(0.799778\pi\)
\(492\) 0 0
\(493\) −3.96161 −0.178422
\(494\) 0 0
\(495\) −1.25417 −0.0563706
\(496\) 0 0
\(497\) 3.41981 0.153399
\(498\) 0 0
\(499\) 23.7161 1.06168 0.530838 0.847473i \(-0.321877\pi\)
0.530838 + 0.847473i \(0.321877\pi\)
\(500\) 0 0
\(501\) −6.69843 −0.299264
\(502\) 0 0
\(503\) 9.85775 0.439535 0.219768 0.975552i \(-0.429470\pi\)
0.219768 + 0.975552i \(0.429470\pi\)
\(504\) 0 0
\(505\) 14.7271 0.655348
\(506\) 0 0
\(507\) −4.49356 −0.199566
\(508\) 0 0
\(509\) −24.7129 −1.09538 −0.547691 0.836681i \(-0.684493\pi\)
−0.547691 + 0.836681i \(0.684493\pi\)
\(510\) 0 0
\(511\) −0.779744 −0.0344938
\(512\) 0 0
\(513\) −4.14562 −0.183034
\(514\) 0 0
\(515\) 7.01280 0.309021
\(516\) 0 0
\(517\) −4.93578 −0.217076
\(518\) 0 0
\(519\) −6.30493 −0.276756
\(520\) 0 0
\(521\) 0.0849929 0.00372361 0.00186180 0.999998i \(-0.499407\pi\)
0.00186180 + 0.999998i \(0.499407\pi\)
\(522\) 0 0
\(523\) 34.5506 1.51079 0.755397 0.655267i \(-0.227444\pi\)
0.755397 + 0.655267i \(0.227444\pi\)
\(524\) 0 0
\(525\) −0.142593 −0.00622325
\(526\) 0 0
\(527\) 1.00160 0.0436302
\(528\) 0 0
\(529\) −22.9990 −0.999955
\(530\) 0 0
\(531\) −10.9901 −0.476932
\(532\) 0 0
\(533\) −4.73134 −0.204937
\(534\) 0 0
\(535\) 14.0600 0.607867
\(536\) 0 0
\(537\) −5.39664 −0.232882
\(538\) 0 0
\(539\) 2.98548 0.128594
\(540\) 0 0
\(541\) −19.2339 −0.826932 −0.413466 0.910520i \(-0.635682\pi\)
−0.413466 + 0.910520i \(0.635682\pi\)
\(542\) 0 0
\(543\) 5.26810 0.226076
\(544\) 0 0
\(545\) 5.24267 0.224571
\(546\) 0 0
\(547\) 18.5792 0.794391 0.397195 0.917734i \(-0.369984\pi\)
0.397195 + 0.917734i \(0.369984\pi\)
\(548\) 0 0
\(549\) 4.59346 0.196044
\(550\) 0 0
\(551\) 14.5306 0.619022
\(552\) 0 0
\(553\) 0.824441 0.0350588
\(554\) 0 0
\(555\) −0.478074 −0.0202931
\(556\) 0 0
\(557\) −21.8733 −0.926802 −0.463401 0.886149i \(-0.653371\pi\)
−0.463401 + 0.886149i \(0.653371\pi\)
\(558\) 0 0
\(559\) −2.54086 −0.107467
\(560\) 0 0
\(561\) 0.0840013 0.00354654
\(562\) 0 0
\(563\) −8.25953 −0.348098 −0.174049 0.984737i \(-0.555685\pi\)
−0.174049 + 0.984737i \(0.555685\pi\)
\(564\) 0 0
\(565\) −6.01042 −0.252860
\(566\) 0 0
\(567\) −3.15400 −0.132455
\(568\) 0 0
\(569\) 7.00280 0.293573 0.146786 0.989168i \(-0.453107\pi\)
0.146786 + 0.989168i \(0.453107\pi\)
\(570\) 0 0
\(571\) 3.81284 0.159562 0.0797812 0.996812i \(-0.474578\pi\)
0.0797812 + 0.996812i \(0.474578\pi\)
\(572\) 0 0
\(573\) 9.29889 0.388467
\(574\) 0 0
\(575\) 0.0321294 0.00133989
\(576\) 0 0
\(577\) 12.5748 0.523497 0.261749 0.965136i \(-0.415701\pi\)
0.261749 + 0.965136i \(0.415701\pi\)
\(578\) 0 0
\(579\) −1.97502 −0.0820792
\(580\) 0 0
\(581\) −1.37005 −0.0568393
\(582\) 0 0
\(583\) 1.64737 0.0682271
\(584\) 0 0
\(585\) −1.76892 −0.0731358
\(586\) 0 0
\(587\) 8.55733 0.353199 0.176599 0.984283i \(-0.443490\pi\)
0.176599 + 0.984283i \(0.443490\pi\)
\(588\) 0 0
\(589\) −3.67370 −0.151372
\(590\) 0 0
\(591\) −1.12732 −0.0463717
\(592\) 0 0
\(593\) −24.5437 −1.00789 −0.503944 0.863736i \(-0.668118\pi\)
−0.503944 + 0.863736i \(0.668118\pi\)
\(594\) 0 0
\(595\) −0.216473 −0.00887454
\(596\) 0 0
\(597\) −0.343882 −0.0140742
\(598\) 0 0
\(599\) −1.13865 −0.0465239 −0.0232619 0.999729i \(-0.507405\pi\)
−0.0232619 + 0.999729i \(0.507405\pi\)
\(600\) 0 0
\(601\) 19.5084 0.795765 0.397883 0.917436i \(-0.369745\pi\)
0.397883 + 0.917436i \(0.369745\pi\)
\(602\) 0 0
\(603\) 29.1844 1.18848
\(604\) 0 0
\(605\) 10.8095 0.439467
\(606\) 0 0
\(607\) −8.22651 −0.333904 −0.166952 0.985965i \(-0.553392\pi\)
−0.166952 + 0.985965i \(0.553392\pi\)
\(608\) 0 0
\(609\) −1.04512 −0.0423502
\(610\) 0 0
\(611\) −6.96160 −0.281636
\(612\) 0 0
\(613\) −21.8604 −0.882933 −0.441466 0.897278i \(-0.645542\pi\)
−0.441466 + 0.897278i \(0.645542\pi\)
\(614\) 0 0
\(615\) −2.73618 −0.110333
\(616\) 0 0
\(617\) −34.7716 −1.39985 −0.699927 0.714215i \(-0.746784\pi\)
−0.699927 + 0.714215i \(0.746784\pi\)
\(618\) 0 0
\(619\) −30.8902 −1.24158 −0.620791 0.783976i \(-0.713189\pi\)
−0.620791 + 0.783976i \(0.713189\pi\)
\(620\) 0 0
\(621\) −0.0671859 −0.00269608
\(622\) 0 0
\(623\) 3.95752 0.158555
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.308103 −0.0123045
\(628\) 0 0
\(629\) −0.725775 −0.0289386
\(630\) 0 0
\(631\) −16.1831 −0.644238 −0.322119 0.946699i \(-0.604395\pi\)
−0.322119 + 0.946699i \(0.604395\pi\)
\(632\) 0 0
\(633\) 3.84915 0.152990
\(634\) 0 0
\(635\) −0.232932 −0.00924362
\(636\) 0 0
\(637\) 4.21083 0.166839
\(638\) 0 0
\(639\) 24.5343 0.970561
\(640\) 0 0
\(641\) −46.4255 −1.83370 −0.916849 0.399234i \(-0.869276\pi\)
−0.916849 + 0.399234i \(0.869276\pi\)
\(642\) 0 0
\(643\) 34.9269 1.37738 0.688691 0.725055i \(-0.258186\pi\)
0.688691 + 0.725055i \(0.258186\pi\)
\(644\) 0 0
\(645\) −1.46940 −0.0578577
\(646\) 0 0
\(647\) 22.2857 0.876139 0.438070 0.898941i \(-0.355662\pi\)
0.438070 + 0.898941i \(0.355662\pi\)
\(648\) 0 0
\(649\) −1.66961 −0.0655381
\(650\) 0 0
\(651\) 0.264232 0.0103561
\(652\) 0 0
\(653\) 5.67149 0.221943 0.110971 0.993824i \(-0.464604\pi\)
0.110971 + 0.993824i \(0.464604\pi\)
\(654\) 0 0
\(655\) 7.38264 0.288464
\(656\) 0 0
\(657\) −5.59401 −0.218243
\(658\) 0 0
\(659\) 28.7446 1.11973 0.559865 0.828584i \(-0.310853\pi\)
0.559865 + 0.828584i \(0.310853\pi\)
\(660\) 0 0
\(661\) 11.7992 0.458934 0.229467 0.973316i \(-0.426302\pi\)
0.229467 + 0.973316i \(0.426302\pi\)
\(662\) 0 0
\(663\) 0.118478 0.00460132
\(664\) 0 0
\(665\) 0.793990 0.0307896
\(666\) 0 0
\(667\) 0.235489 0.00911816
\(668\) 0 0
\(669\) −2.88702 −0.111619
\(670\) 0 0
\(671\) 0.697834 0.0269396
\(672\) 0 0
\(673\) 22.2674 0.858345 0.429173 0.903222i \(-0.358805\pi\)
0.429173 + 0.903222i \(0.358805\pi\)
\(674\) 0 0
\(675\) −2.09110 −0.0804865
\(676\) 0 0
\(677\) 0.463396 0.0178097 0.00890487 0.999960i \(-0.497165\pi\)
0.00890487 + 0.999960i \(0.497165\pi\)
\(678\) 0 0
\(679\) 1.84441 0.0707820
\(680\) 0 0
\(681\) −9.35147 −0.358349
\(682\) 0 0
\(683\) 51.7674 1.98083 0.990413 0.138139i \(-0.0441120\pi\)
0.990413 + 0.138139i \(0.0441120\pi\)
\(684\) 0 0
\(685\) −10.8082 −0.412961
\(686\) 0 0
\(687\) 6.92400 0.264167
\(688\) 0 0
\(689\) 2.32351 0.0885186
\(690\) 0 0
\(691\) 1.94058 0.0738231 0.0369116 0.999319i \(-0.488248\pi\)
0.0369116 + 0.999319i \(0.488248\pi\)
\(692\) 0 0
\(693\) −0.502290 −0.0190804
\(694\) 0 0
\(695\) −6.01742 −0.228254
\(696\) 0 0
\(697\) −4.15386 −0.157339
\(698\) 0 0
\(699\) 7.40014 0.279899
\(700\) 0 0
\(701\) −49.2092 −1.85861 −0.929303 0.369319i \(-0.879591\pi\)
−0.929303 + 0.369319i \(0.879591\pi\)
\(702\) 0 0
\(703\) 2.66203 0.100400
\(704\) 0 0
\(705\) −4.02596 −0.151627
\(706\) 0 0
\(707\) 5.89817 0.221824
\(708\) 0 0
\(709\) −18.2333 −0.684766 −0.342383 0.939560i \(-0.611234\pi\)
−0.342383 + 0.939560i \(0.611234\pi\)
\(710\) 0 0
\(711\) 5.91468 0.221818
\(712\) 0 0
\(713\) −0.0595376 −0.00222970
\(714\) 0 0
\(715\) −0.268733 −0.0100500
\(716\) 0 0
\(717\) −4.87449 −0.182041
\(718\) 0 0
\(719\) −37.5673 −1.40102 −0.700512 0.713640i \(-0.747045\pi\)
−0.700512 + 0.713640i \(0.747045\pi\)
\(720\) 0 0
\(721\) 2.80861 0.104598
\(722\) 0 0
\(723\) 0.940040 0.0349605
\(724\) 0 0
\(725\) 7.32938 0.272206
\(726\) 0 0
\(727\) 16.3326 0.605742 0.302871 0.953032i \(-0.402055\pi\)
0.302871 + 0.953032i \(0.402055\pi\)
\(728\) 0 0
\(729\) −20.3938 −0.755324
\(730\) 0 0
\(731\) −2.23073 −0.0825067
\(732\) 0 0
\(733\) −40.6423 −1.50116 −0.750578 0.660781i \(-0.770225\pi\)
−0.750578 + 0.660781i \(0.770225\pi\)
\(734\) 0 0
\(735\) 2.43516 0.0898224
\(736\) 0 0
\(737\) 4.43367 0.163316
\(738\) 0 0
\(739\) −22.7567 −0.837119 −0.418559 0.908189i \(-0.637465\pi\)
−0.418559 + 0.908189i \(0.637465\pi\)
\(740\) 0 0
\(741\) −0.434559 −0.0159639
\(742\) 0 0
\(743\) 38.4053 1.40895 0.704477 0.709727i \(-0.251182\pi\)
0.704477 + 0.709727i \(0.251182\pi\)
\(744\) 0 0
\(745\) 0.190471 0.00697834
\(746\) 0 0
\(747\) −9.82898 −0.359624
\(748\) 0 0
\(749\) 5.63099 0.205752
\(750\) 0 0
\(751\) −10.4702 −0.382063 −0.191032 0.981584i \(-0.561183\pi\)
−0.191032 + 0.981584i \(0.561183\pi\)
\(752\) 0 0
\(753\) −1.97137 −0.0718408
\(754\) 0 0
\(755\) 12.8656 0.468228
\(756\) 0 0
\(757\) −30.5176 −1.10918 −0.554591 0.832123i \(-0.687125\pi\)
−0.554591 + 0.832123i \(0.687125\pi\)
\(758\) 0 0
\(759\) −0.00499326 −0.000181244 0
\(760\) 0 0
\(761\) 49.9403 1.81034 0.905168 0.425055i \(-0.139745\pi\)
0.905168 + 0.425055i \(0.139745\pi\)
\(762\) 0 0
\(763\) 2.09968 0.0760134
\(764\) 0 0
\(765\) −1.55302 −0.0561494
\(766\) 0 0
\(767\) −2.35488 −0.0850298
\(768\) 0 0
\(769\) −22.5588 −0.813492 −0.406746 0.913541i \(-0.633337\pi\)
−0.406746 + 0.913541i \(0.633337\pi\)
\(770\) 0 0
\(771\) −9.81862 −0.353609
\(772\) 0 0
\(773\) −16.3025 −0.586360 −0.293180 0.956057i \(-0.594714\pi\)
−0.293180 + 0.956057i \(0.594714\pi\)
\(774\) 0 0
\(775\) −1.85305 −0.0665637
\(776\) 0 0
\(777\) −0.191467 −0.00686885
\(778\) 0 0
\(779\) 15.2357 0.545876
\(780\) 0 0
\(781\) 3.72722 0.133371
\(782\) 0 0
\(783\) −15.3265 −0.547723
\(784\) 0 0
\(785\) −3.08796 −0.110214
\(786\) 0 0
\(787\) 10.6865 0.380933 0.190467 0.981694i \(-0.439000\pi\)
0.190467 + 0.981694i \(0.439000\pi\)
\(788\) 0 0
\(789\) 5.78585 0.205982
\(790\) 0 0
\(791\) −2.40716 −0.0855887
\(792\) 0 0
\(793\) 0.984249 0.0349517
\(794\) 0 0
\(795\) 1.34371 0.0476564
\(796\) 0 0
\(797\) 31.3307 1.10979 0.554895 0.831921i \(-0.312759\pi\)
0.554895 + 0.831921i \(0.312759\pi\)
\(798\) 0 0
\(799\) −6.11191 −0.216224
\(800\) 0 0
\(801\) 28.3919 1.00318
\(802\) 0 0
\(803\) −0.849837 −0.0299901
\(804\) 0 0
\(805\) 0.0128678 0.000453529 0
\(806\) 0 0
\(807\) −6.39904 −0.225257
\(808\) 0 0
\(809\) −30.6531 −1.07770 −0.538852 0.842400i \(-0.681142\pi\)
−0.538852 + 0.842400i \(0.681142\pi\)
\(810\) 0 0
\(811\) −1.55427 −0.0545779 −0.0272890 0.999628i \(-0.508687\pi\)
−0.0272890 + 0.999628i \(0.508687\pi\)
\(812\) 0 0
\(813\) −6.23516 −0.218677
\(814\) 0 0
\(815\) 5.25329 0.184015
\(816\) 0 0
\(817\) 8.18198 0.286251
\(818\) 0 0
\(819\) −0.708448 −0.0247552
\(820\) 0 0
\(821\) 50.3493 1.75720 0.878602 0.477555i \(-0.158477\pi\)
0.878602 + 0.477555i \(0.158477\pi\)
\(822\) 0 0
\(823\) −1.33143 −0.0464108 −0.0232054 0.999731i \(-0.507387\pi\)
−0.0232054 + 0.999731i \(0.507387\pi\)
\(824\) 0 0
\(825\) −0.155411 −0.00541071
\(826\) 0 0
\(827\) 34.6659 1.20545 0.602726 0.797948i \(-0.294081\pi\)
0.602726 + 0.797948i \(0.294081\pi\)
\(828\) 0 0
\(829\) −11.0049 −0.382214 −0.191107 0.981569i \(-0.561208\pi\)
−0.191107 + 0.981569i \(0.561208\pi\)
\(830\) 0 0
\(831\) −1.15080 −0.0399209
\(832\) 0 0
\(833\) 3.69688 0.128089
\(834\) 0 0
\(835\) 18.8138 0.651077
\(836\) 0 0
\(837\) 3.87492 0.133937
\(838\) 0 0
\(839\) −48.4008 −1.67098 −0.835490 0.549505i \(-0.814816\pi\)
−0.835490 + 0.549505i \(0.814816\pi\)
\(840\) 0 0
\(841\) 24.7198 0.852406
\(842\) 0 0
\(843\) −0.685239 −0.0236009
\(844\) 0 0
\(845\) 12.6210 0.434175
\(846\) 0 0
\(847\) 4.32916 0.148752
\(848\) 0 0
\(849\) 1.77948 0.0610717
\(850\) 0 0
\(851\) 0.0431420 0.00147889
\(852\) 0 0
\(853\) −9.13891 −0.312910 −0.156455 0.987685i \(-0.550007\pi\)
−0.156455 + 0.987685i \(0.550007\pi\)
\(854\) 0 0
\(855\) 5.69622 0.194806
\(856\) 0 0
\(857\) 56.3654 1.92541 0.962704 0.270559i \(-0.0872084\pi\)
0.962704 + 0.270559i \(0.0872084\pi\)
\(858\) 0 0
\(859\) −2.13001 −0.0726749 −0.0363375 0.999340i \(-0.511569\pi\)
−0.0363375 + 0.999340i \(0.511569\pi\)
\(860\) 0 0
\(861\) −1.09583 −0.0373459
\(862\) 0 0
\(863\) −41.8224 −1.42365 −0.711826 0.702355i \(-0.752132\pi\)
−0.711826 + 0.702355i \(0.752132\pi\)
\(864\) 0 0
\(865\) 17.7085 0.602108
\(866\) 0 0
\(867\) −5.94864 −0.202027
\(868\) 0 0
\(869\) 0.898553 0.0304813
\(870\) 0 0
\(871\) 6.25341 0.211889
\(872\) 0 0
\(873\) 13.2321 0.447839
\(874\) 0 0
\(875\) 0.400497 0.0135393
\(876\) 0 0
\(877\) 15.6853 0.529656 0.264828 0.964296i \(-0.414685\pi\)
0.264828 + 0.964296i \(0.414685\pi\)
\(878\) 0 0
\(879\) −1.66210 −0.0560613
\(880\) 0 0
\(881\) −26.9249 −0.907122 −0.453561 0.891225i \(-0.649847\pi\)
−0.453561 + 0.891225i \(0.649847\pi\)
\(882\) 0 0
\(883\) −4.96791 −0.167184 −0.0835918 0.996500i \(-0.526639\pi\)
−0.0835918 + 0.996500i \(0.526639\pi\)
\(884\) 0 0
\(885\) −1.36185 −0.0457781
\(886\) 0 0
\(887\) −16.2180 −0.544546 −0.272273 0.962220i \(-0.587775\pi\)
−0.272273 + 0.962220i \(0.587775\pi\)
\(888\) 0 0
\(889\) −0.0932886 −0.00312880
\(890\) 0 0
\(891\) −3.43752 −0.115161
\(892\) 0 0
\(893\) 22.4175 0.750173
\(894\) 0 0
\(895\) 15.1574 0.506657
\(896\) 0 0
\(897\) −0.00704267 −0.000235148 0
\(898\) 0 0
\(899\) −13.5817 −0.452976
\(900\) 0 0
\(901\) 2.03991 0.0679594
\(902\) 0 0
\(903\) −0.588492 −0.0195838
\(904\) 0 0
\(905\) −14.7964 −0.491850
\(906\) 0 0
\(907\) −21.9005 −0.727194 −0.363597 0.931556i \(-0.618451\pi\)
−0.363597 + 0.931556i \(0.618451\pi\)
\(908\) 0 0
\(909\) 42.3145 1.40348
\(910\) 0 0
\(911\) −29.4363 −0.975268 −0.487634 0.873048i \(-0.662140\pi\)
−0.487634 + 0.873048i \(0.662140\pi\)
\(912\) 0 0
\(913\) −1.49321 −0.0494180
\(914\) 0 0
\(915\) 0.569201 0.0188172
\(916\) 0 0
\(917\) 2.95673 0.0976398
\(918\) 0 0
\(919\) −30.2212 −0.996906 −0.498453 0.866917i \(-0.666098\pi\)
−0.498453 + 0.866917i \(0.666098\pi\)
\(920\) 0 0
\(921\) −6.44584 −0.212398
\(922\) 0 0
\(923\) 5.25701 0.173036
\(924\) 0 0
\(925\) 1.34276 0.0441496
\(926\) 0 0
\(927\) 20.1494 0.661795
\(928\) 0 0
\(929\) −47.2151 −1.54908 −0.774538 0.632528i \(-0.782017\pi\)
−0.774538 + 0.632528i \(0.782017\pi\)
\(930\) 0 0
\(931\) −13.5596 −0.444397
\(932\) 0 0
\(933\) −11.9171 −0.390148
\(934\) 0 0
\(935\) −0.235933 −0.00771583
\(936\) 0 0
\(937\) −16.5255 −0.539864 −0.269932 0.962879i \(-0.587001\pi\)
−0.269932 + 0.962879i \(0.587001\pi\)
\(938\) 0 0
\(939\) 1.30962 0.0427378
\(940\) 0 0
\(941\) −39.9812 −1.30335 −0.651675 0.758498i \(-0.725934\pi\)
−0.651675 + 0.758498i \(0.725934\pi\)
\(942\) 0 0
\(943\) 0.246917 0.00804071
\(944\) 0 0
\(945\) −0.837480 −0.0272432
\(946\) 0 0
\(947\) −23.8596 −0.775334 −0.387667 0.921800i \(-0.626719\pi\)
−0.387667 + 0.921800i \(0.626719\pi\)
\(948\) 0 0
\(949\) −1.19864 −0.0389095
\(950\) 0 0
\(951\) −4.30323 −0.139542
\(952\) 0 0
\(953\) 12.1617 0.393955 0.196977 0.980408i \(-0.436887\pi\)
0.196977 + 0.980408i \(0.436887\pi\)
\(954\) 0 0
\(955\) −26.1176 −0.845147
\(956\) 0 0
\(957\) −1.13906 −0.0368207
\(958\) 0 0
\(959\) −4.32866 −0.139780
\(960\) 0 0
\(961\) −27.5662 −0.889232
\(962\) 0 0
\(963\) 40.3977 1.30180
\(964\) 0 0
\(965\) 5.54721 0.178571
\(966\) 0 0
\(967\) 30.2333 0.972238 0.486119 0.873893i \(-0.338412\pi\)
0.486119 + 0.873893i \(0.338412\pi\)
\(968\) 0 0
\(969\) −0.381520 −0.0122562
\(970\) 0 0
\(971\) −31.5007 −1.01091 −0.505453 0.862854i \(-0.668675\pi\)
−0.505453 + 0.862854i \(0.668675\pi\)
\(972\) 0 0
\(973\) −2.40996 −0.0772598
\(974\) 0 0
\(975\) −0.219197 −0.00701991
\(976\) 0 0
\(977\) 23.9078 0.764878 0.382439 0.923981i \(-0.375084\pi\)
0.382439 + 0.923981i \(0.375084\pi\)
\(978\) 0 0
\(979\) 4.31327 0.137853
\(980\) 0 0
\(981\) 15.0634 0.480939
\(982\) 0 0
\(983\) 14.2823 0.455534 0.227767 0.973716i \(-0.426858\pi\)
0.227767 + 0.973716i \(0.426858\pi\)
\(984\) 0 0
\(985\) 3.16628 0.100886
\(986\) 0 0
\(987\) −1.61239 −0.0513229
\(988\) 0 0
\(989\) 0.132601 0.00421646
\(990\) 0 0
\(991\) 29.6236 0.941025 0.470513 0.882393i \(-0.344069\pi\)
0.470513 + 0.882393i \(0.344069\pi\)
\(992\) 0 0
\(993\) 1.49431 0.0474205
\(994\) 0 0
\(995\) 0.965855 0.0306197
\(996\) 0 0
\(997\) 5.51954 0.174806 0.0874028 0.996173i \(-0.472143\pi\)
0.0874028 + 0.996173i \(0.472143\pi\)
\(998\) 0 0
\(999\) −2.80784 −0.0888361
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 \(a_p\))