Properties

Label 8004.2.a.j.1.4
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 0
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-2.34509\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-2.34509 q^{5}\) \(-1.25807 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-2.34509 q^{5}\) \(-1.25807 q^{7}\) \(+1.00000 q^{9}\) \(-6.44999 q^{11}\) \(+1.34717 q^{13}\) \(-2.34509 q^{15}\) \(-7.39461 q^{17}\) \(-4.27627 q^{19}\) \(-1.25807 q^{21}\) \(+1.00000 q^{23}\) \(+0.499463 q^{25}\) \(+1.00000 q^{27}\) \(-1.00000 q^{29}\) \(+10.1300 q^{31}\) \(-6.44999 q^{33}\) \(+2.95030 q^{35}\) \(-5.20798 q^{37}\) \(+1.34717 q^{39}\) \(-10.6226 q^{41}\) \(+0.118668 q^{43}\) \(-2.34509 q^{45}\) \(+9.08470 q^{47}\) \(-5.41725 q^{49}\) \(-7.39461 q^{51}\) \(+10.4167 q^{53}\) \(+15.1258 q^{55}\) \(-4.27627 q^{57}\) \(-3.39629 q^{59}\) \(-2.23961 q^{61}\) \(-1.25807 q^{63}\) \(-3.15925 q^{65}\) \(+7.85081 q^{67}\) \(+1.00000 q^{69}\) \(-10.7923 q^{71}\) \(+7.17561 q^{73}\) \(+0.499463 q^{75}\) \(+8.11456 q^{77}\) \(-4.24131 q^{79}\) \(+1.00000 q^{81}\) \(-7.91341 q^{83}\) \(+17.3410 q^{85}\) \(-1.00000 q^{87}\) \(-4.52488 q^{89}\) \(-1.69484 q^{91}\) \(+10.1300 q^{93}\) \(+10.0282 q^{95}\) \(-0.279080 q^{97}\) \(-6.44999 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 11q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 19q^{53} \) \(\mathstrut +\mathstrut 31q^{55} \) \(\mathstrut +\mathstrut 11q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 19q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 33q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut +\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 33q^{97} \) \(\mathstrut +\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.34509 −1.04876 −0.524379 0.851485i \(-0.675702\pi\)
−0.524379 + 0.851485i \(0.675702\pi\)
\(6\) 0 0
\(7\) −1.25807 −0.475507 −0.237754 0.971326i \(-0.576411\pi\)
−0.237754 + 0.971326i \(0.576411\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −6.44999 −1.94475 −0.972373 0.233434i \(-0.925004\pi\)
−0.972373 + 0.233434i \(0.925004\pi\)
\(12\) 0 0
\(13\) 1.34717 0.373639 0.186819 0.982394i \(-0.440182\pi\)
0.186819 + 0.982394i \(0.440182\pi\)
\(14\) 0 0
\(15\) −2.34509 −0.605501
\(16\) 0 0
\(17\) −7.39461 −1.79346 −0.896728 0.442582i \(-0.854063\pi\)
−0.896728 + 0.442582i \(0.854063\pi\)
\(18\) 0 0
\(19\) −4.27627 −0.981043 −0.490521 0.871429i \(-0.663194\pi\)
−0.490521 + 0.871429i \(0.663194\pi\)
\(20\) 0 0
\(21\) −1.25807 −0.274534
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0.499463 0.0998926
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 10.1300 1.81941 0.909704 0.415256i \(-0.136308\pi\)
0.909704 + 0.415256i \(0.136308\pi\)
\(32\) 0 0
\(33\) −6.44999 −1.12280
\(34\) 0 0
\(35\) 2.95030 0.498692
\(36\) 0 0
\(37\) −5.20798 −0.856187 −0.428093 0.903735i \(-0.640815\pi\)
−0.428093 + 0.903735i \(0.640815\pi\)
\(38\) 0 0
\(39\) 1.34717 0.215720
\(40\) 0 0
\(41\) −10.6226 −1.65898 −0.829489 0.558523i \(-0.811368\pi\)
−0.829489 + 0.558523i \(0.811368\pi\)
\(42\) 0 0
\(43\) 0.118668 0.0180967 0.00904836 0.999959i \(-0.497120\pi\)
0.00904836 + 0.999959i \(0.497120\pi\)
\(44\) 0 0
\(45\) −2.34509 −0.349586
\(46\) 0 0
\(47\) 9.08470 1.32514 0.662570 0.749000i \(-0.269466\pi\)
0.662570 + 0.749000i \(0.269466\pi\)
\(48\) 0 0
\(49\) −5.41725 −0.773893
\(50\) 0 0
\(51\) −7.39461 −1.03545
\(52\) 0 0
\(53\) 10.4167 1.43085 0.715423 0.698691i \(-0.246234\pi\)
0.715423 + 0.698691i \(0.246234\pi\)
\(54\) 0 0
\(55\) 15.1258 2.03957
\(56\) 0 0
\(57\) −4.27627 −0.566405
\(58\) 0 0
\(59\) −3.39629 −0.442159 −0.221080 0.975256i \(-0.570958\pi\)
−0.221080 + 0.975256i \(0.570958\pi\)
\(60\) 0 0
\(61\) −2.23961 −0.286753 −0.143377 0.989668i \(-0.545796\pi\)
−0.143377 + 0.989668i \(0.545796\pi\)
\(62\) 0 0
\(63\) −1.25807 −0.158502
\(64\) 0 0
\(65\) −3.15925 −0.391857
\(66\) 0 0
\(67\) 7.85081 0.959130 0.479565 0.877506i \(-0.340795\pi\)
0.479565 + 0.877506i \(0.340795\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −10.7923 −1.28081 −0.640404 0.768038i \(-0.721233\pi\)
−0.640404 + 0.768038i \(0.721233\pi\)
\(72\) 0 0
\(73\) 7.17561 0.839842 0.419921 0.907561i \(-0.362058\pi\)
0.419921 + 0.907561i \(0.362058\pi\)
\(74\) 0 0
\(75\) 0.499463 0.0576730
\(76\) 0 0
\(77\) 8.11456 0.924740
\(78\) 0 0
\(79\) −4.24131 −0.477185 −0.238592 0.971120i \(-0.576686\pi\)
−0.238592 + 0.971120i \(0.576686\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.91341 −0.868609 −0.434305 0.900766i \(-0.643006\pi\)
−0.434305 + 0.900766i \(0.643006\pi\)
\(84\) 0 0
\(85\) 17.3410 1.88090
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) −4.52488 −0.479636 −0.239818 0.970818i \(-0.577088\pi\)
−0.239818 + 0.970818i \(0.577088\pi\)
\(90\) 0 0
\(91\) −1.69484 −0.177668
\(92\) 0 0
\(93\) 10.1300 1.05044
\(94\) 0 0
\(95\) 10.0282 1.02888
\(96\) 0 0
\(97\) −0.279080 −0.0283363 −0.0141681 0.999900i \(-0.504510\pi\)
−0.0141681 + 0.999900i \(0.504510\pi\)
\(98\) 0 0
\(99\) −6.44999 −0.648248
\(100\) 0 0
\(101\) 1.46268 0.145542 0.0727709 0.997349i \(-0.476816\pi\)
0.0727709 + 0.997349i \(0.476816\pi\)
\(102\) 0 0
\(103\) 16.7654 1.65194 0.825970 0.563714i \(-0.190628\pi\)
0.825970 + 0.563714i \(0.190628\pi\)
\(104\) 0 0
\(105\) 2.95030 0.287920
\(106\) 0 0
\(107\) 4.86261 0.470087 0.235043 0.971985i \(-0.424477\pi\)
0.235043 + 0.971985i \(0.424477\pi\)
\(108\) 0 0
\(109\) −3.10927 −0.297814 −0.148907 0.988851i \(-0.547575\pi\)
−0.148907 + 0.988851i \(0.547575\pi\)
\(110\) 0 0
\(111\) −5.20798 −0.494320
\(112\) 0 0
\(113\) −11.8302 −1.11290 −0.556448 0.830883i \(-0.687836\pi\)
−0.556448 + 0.830883i \(0.687836\pi\)
\(114\) 0 0
\(115\) −2.34509 −0.218681
\(116\) 0 0
\(117\) 1.34717 0.124546
\(118\) 0 0
\(119\) 9.30296 0.852801
\(120\) 0 0
\(121\) 30.6024 2.78203
\(122\) 0 0
\(123\) −10.6226 −0.957812
\(124\) 0 0
\(125\) 10.5542 0.943995
\(126\) 0 0
\(127\) 11.0935 0.984392 0.492196 0.870484i \(-0.336194\pi\)
0.492196 + 0.870484i \(0.336194\pi\)
\(128\) 0 0
\(129\) 0.118668 0.0104482
\(130\) 0 0
\(131\) 16.1623 1.41211 0.706055 0.708157i \(-0.250473\pi\)
0.706055 + 0.708157i \(0.250473\pi\)
\(132\) 0 0
\(133\) 5.37986 0.466493
\(134\) 0 0
\(135\) −2.34509 −0.201834
\(136\) 0 0
\(137\) 4.08719 0.349192 0.174596 0.984640i \(-0.444138\pi\)
0.174596 + 0.984640i \(0.444138\pi\)
\(138\) 0 0
\(139\) 8.11732 0.688503 0.344251 0.938878i \(-0.388133\pi\)
0.344251 + 0.938878i \(0.388133\pi\)
\(140\) 0 0
\(141\) 9.08470 0.765069
\(142\) 0 0
\(143\) −8.68926 −0.726632
\(144\) 0 0
\(145\) 2.34509 0.194749
\(146\) 0 0
\(147\) −5.41725 −0.446807
\(148\) 0 0
\(149\) 7.82849 0.641335 0.320667 0.947192i \(-0.396093\pi\)
0.320667 + 0.947192i \(0.396093\pi\)
\(150\) 0 0
\(151\) −19.0112 −1.54711 −0.773554 0.633730i \(-0.781523\pi\)
−0.773554 + 0.633730i \(0.781523\pi\)
\(152\) 0 0
\(153\) −7.39461 −0.597819
\(154\) 0 0
\(155\) −23.7559 −1.90812
\(156\) 0 0
\(157\) 13.2471 1.05723 0.528615 0.848862i \(-0.322712\pi\)
0.528615 + 0.848862i \(0.322712\pi\)
\(158\) 0 0
\(159\) 10.4167 0.826100
\(160\) 0 0
\(161\) −1.25807 −0.0991501
\(162\) 0 0
\(163\) −1.77321 −0.138889 −0.0694443 0.997586i \(-0.522123\pi\)
−0.0694443 + 0.997586i \(0.522123\pi\)
\(164\) 0 0
\(165\) 15.1258 1.17754
\(166\) 0 0
\(167\) 1.42037 0.109911 0.0549557 0.998489i \(-0.482498\pi\)
0.0549557 + 0.998489i \(0.482498\pi\)
\(168\) 0 0
\(169\) −11.1851 −0.860394
\(170\) 0 0
\(171\) −4.27627 −0.327014
\(172\) 0 0
\(173\) 13.6543 1.03812 0.519058 0.854739i \(-0.326283\pi\)
0.519058 + 0.854739i \(0.326283\pi\)
\(174\) 0 0
\(175\) −0.628361 −0.0474996
\(176\) 0 0
\(177\) −3.39629 −0.255281
\(178\) 0 0
\(179\) −9.98920 −0.746628 −0.373314 0.927705i \(-0.621779\pi\)
−0.373314 + 0.927705i \(0.621779\pi\)
\(180\) 0 0
\(181\) 5.29509 0.393581 0.196790 0.980446i \(-0.436948\pi\)
0.196790 + 0.980446i \(0.436948\pi\)
\(182\) 0 0
\(183\) −2.23961 −0.165557
\(184\) 0 0
\(185\) 12.2132 0.897932
\(186\) 0 0
\(187\) 47.6952 3.48782
\(188\) 0 0
\(189\) −1.25807 −0.0915114
\(190\) 0 0
\(191\) −11.3030 −0.817856 −0.408928 0.912567i \(-0.634097\pi\)
−0.408928 + 0.912567i \(0.634097\pi\)
\(192\) 0 0
\(193\) 24.2983 1.74903 0.874514 0.485001i \(-0.161181\pi\)
0.874514 + 0.485001i \(0.161181\pi\)
\(194\) 0 0
\(195\) −3.15925 −0.226238
\(196\) 0 0
\(197\) −0.204036 −0.0145370 −0.00726848 0.999974i \(-0.502314\pi\)
−0.00726848 + 0.999974i \(0.502314\pi\)
\(198\) 0 0
\(199\) −3.69588 −0.261994 −0.130997 0.991383i \(-0.541818\pi\)
−0.130997 + 0.991383i \(0.541818\pi\)
\(200\) 0 0
\(201\) 7.85081 0.553754
\(202\) 0 0
\(203\) 1.25807 0.0882994
\(204\) 0 0
\(205\) 24.9111 1.73987
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 27.5819 1.90788
\(210\) 0 0
\(211\) −10.3858 −0.714989 −0.357495 0.933915i \(-0.616369\pi\)
−0.357495 + 0.933915i \(0.616369\pi\)
\(212\) 0 0
\(213\) −10.7923 −0.739475
\(214\) 0 0
\(215\) −0.278288 −0.0189791
\(216\) 0 0
\(217\) −12.7443 −0.865142
\(218\) 0 0
\(219\) 7.17561 0.484883
\(220\) 0 0
\(221\) −9.96183 −0.670105
\(222\) 0 0
\(223\) 2.39453 0.160350 0.0801749 0.996781i \(-0.474452\pi\)
0.0801749 + 0.996781i \(0.474452\pi\)
\(224\) 0 0
\(225\) 0.499463 0.0332975
\(226\) 0 0
\(227\) −8.00245 −0.531141 −0.265571 0.964091i \(-0.585560\pi\)
−0.265571 + 0.964091i \(0.585560\pi\)
\(228\) 0 0
\(229\) −10.7641 −0.711312 −0.355656 0.934617i \(-0.615743\pi\)
−0.355656 + 0.934617i \(0.615743\pi\)
\(230\) 0 0
\(231\) 8.11456 0.533899
\(232\) 0 0
\(233\) −0.554990 −0.0363586 −0.0181793 0.999835i \(-0.505787\pi\)
−0.0181793 + 0.999835i \(0.505787\pi\)
\(234\) 0 0
\(235\) −21.3045 −1.38975
\(236\) 0 0
\(237\) −4.24131 −0.275503
\(238\) 0 0
\(239\) −17.4662 −1.12979 −0.564897 0.825162i \(-0.691084\pi\)
−0.564897 + 0.825162i \(0.691084\pi\)
\(240\) 0 0
\(241\) 16.5598 1.06671 0.533354 0.845892i \(-0.320931\pi\)
0.533354 + 0.845892i \(0.320931\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 12.7040 0.811626
\(246\) 0 0
\(247\) −5.76087 −0.366556
\(248\) 0 0
\(249\) −7.91341 −0.501492
\(250\) 0 0
\(251\) 4.55045 0.287222 0.143611 0.989634i \(-0.454129\pi\)
0.143611 + 0.989634i \(0.454129\pi\)
\(252\) 0 0
\(253\) −6.44999 −0.405507
\(254\) 0 0
\(255\) 17.3410 1.08594
\(256\) 0 0
\(257\) −18.8900 −1.17833 −0.589163 0.808014i \(-0.700543\pi\)
−0.589163 + 0.808014i \(0.700543\pi\)
\(258\) 0 0
\(259\) 6.55202 0.407123
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) −0.490569 −0.0302498 −0.0151249 0.999886i \(-0.504815\pi\)
−0.0151249 + 0.999886i \(0.504815\pi\)
\(264\) 0 0
\(265\) −24.4282 −1.50061
\(266\) 0 0
\(267\) −4.52488 −0.276918
\(268\) 0 0
\(269\) 19.1733 1.16902 0.584508 0.811388i \(-0.301288\pi\)
0.584508 + 0.811388i \(0.301288\pi\)
\(270\) 0 0
\(271\) −28.7636 −1.74726 −0.873631 0.486588i \(-0.838241\pi\)
−0.873631 + 0.486588i \(0.838241\pi\)
\(272\) 0 0
\(273\) −1.69484 −0.102577
\(274\) 0 0
\(275\) −3.22153 −0.194266
\(276\) 0 0
\(277\) −24.2754 −1.45857 −0.729283 0.684212i \(-0.760146\pi\)
−0.729283 + 0.684212i \(0.760146\pi\)
\(278\) 0 0
\(279\) 10.1300 0.606470
\(280\) 0 0
\(281\) −2.36539 −0.141107 −0.0705537 0.997508i \(-0.522477\pi\)
−0.0705537 + 0.997508i \(0.522477\pi\)
\(282\) 0 0
\(283\) −2.24568 −0.133492 −0.0667459 0.997770i \(-0.521262\pi\)
−0.0667459 + 0.997770i \(0.521262\pi\)
\(284\) 0 0
\(285\) 10.0282 0.594022
\(286\) 0 0
\(287\) 13.3641 0.788856
\(288\) 0 0
\(289\) 37.6803 2.21649
\(290\) 0 0
\(291\) −0.279080 −0.0163599
\(292\) 0 0
\(293\) 27.7523 1.62131 0.810655 0.585525i \(-0.199111\pi\)
0.810655 + 0.585525i \(0.199111\pi\)
\(294\) 0 0
\(295\) 7.96461 0.463718
\(296\) 0 0
\(297\) −6.44999 −0.374266
\(298\) 0 0
\(299\) 1.34717 0.0779091
\(300\) 0 0
\(301\) −0.149293 −0.00860512
\(302\) 0 0
\(303\) 1.46268 0.0840286
\(304\) 0 0
\(305\) 5.25210 0.300735
\(306\) 0 0
\(307\) −4.01961 −0.229411 −0.114706 0.993400i \(-0.536592\pi\)
−0.114706 + 0.993400i \(0.536592\pi\)
\(308\) 0 0
\(309\) 16.7654 0.953748
\(310\) 0 0
\(311\) −24.4335 −1.38550 −0.692748 0.721180i \(-0.743600\pi\)
−0.692748 + 0.721180i \(0.743600\pi\)
\(312\) 0 0
\(313\) −16.4118 −0.927648 −0.463824 0.885927i \(-0.653523\pi\)
−0.463824 + 0.885927i \(0.653523\pi\)
\(314\) 0 0
\(315\) 2.95030 0.166231
\(316\) 0 0
\(317\) 21.1766 1.18939 0.594697 0.803950i \(-0.297272\pi\)
0.594697 + 0.803950i \(0.297272\pi\)
\(318\) 0 0
\(319\) 6.44999 0.361130
\(320\) 0 0
\(321\) 4.86261 0.271405
\(322\) 0 0
\(323\) 31.6213 1.75946
\(324\) 0 0
\(325\) 0.672863 0.0373237
\(326\) 0 0
\(327\) −3.10927 −0.171943
\(328\) 0 0
\(329\) −11.4292 −0.630113
\(330\) 0 0
\(331\) −10.9757 −0.603278 −0.301639 0.953422i \(-0.597534\pi\)
−0.301639 + 0.953422i \(0.597534\pi\)
\(332\) 0 0
\(333\) −5.20798 −0.285396
\(334\) 0 0
\(335\) −18.4109 −1.00589
\(336\) 0 0
\(337\) 20.0132 1.09019 0.545094 0.838375i \(-0.316494\pi\)
0.545094 + 0.838375i \(0.316494\pi\)
\(338\) 0 0
\(339\) −11.8302 −0.642531
\(340\) 0 0
\(341\) −65.3387 −3.53829
\(342\) 0 0
\(343\) 15.6218 0.843499
\(344\) 0 0
\(345\) −2.34509 −0.126256
\(346\) 0 0
\(347\) 16.3958 0.880171 0.440085 0.897956i \(-0.354948\pi\)
0.440085 + 0.897956i \(0.354948\pi\)
\(348\) 0 0
\(349\) −5.00885 −0.268117 −0.134059 0.990973i \(-0.542801\pi\)
−0.134059 + 0.990973i \(0.542801\pi\)
\(350\) 0 0
\(351\) 1.34717 0.0719068
\(352\) 0 0
\(353\) −4.40928 −0.234682 −0.117341 0.993092i \(-0.537437\pi\)
−0.117341 + 0.993092i \(0.537437\pi\)
\(354\) 0 0
\(355\) 25.3089 1.34326
\(356\) 0 0
\(357\) 9.30296 0.492365
\(358\) 0 0
\(359\) 1.94966 0.102899 0.0514495 0.998676i \(-0.483616\pi\)
0.0514495 + 0.998676i \(0.483616\pi\)
\(360\) 0 0
\(361\) −0.713549 −0.0375552
\(362\) 0 0
\(363\) 30.6024 1.60621
\(364\) 0 0
\(365\) −16.8275 −0.880791
\(366\) 0 0
\(367\) 12.5834 0.656847 0.328424 0.944531i \(-0.393483\pi\)
0.328424 + 0.944531i \(0.393483\pi\)
\(368\) 0 0
\(369\) −10.6226 −0.552993
\(370\) 0 0
\(371\) −13.1050 −0.680378
\(372\) 0 0
\(373\) −18.3078 −0.947941 −0.473970 0.880541i \(-0.657180\pi\)
−0.473970 + 0.880541i \(0.657180\pi\)
\(374\) 0 0
\(375\) 10.5542 0.545016
\(376\) 0 0
\(377\) −1.34717 −0.0693830
\(378\) 0 0
\(379\) 26.2890 1.35038 0.675188 0.737646i \(-0.264063\pi\)
0.675188 + 0.737646i \(0.264063\pi\)
\(380\) 0 0
\(381\) 11.0935 0.568339
\(382\) 0 0
\(383\) −8.06675 −0.412192 −0.206096 0.978532i \(-0.566076\pi\)
−0.206096 + 0.978532i \(0.566076\pi\)
\(384\) 0 0
\(385\) −19.0294 −0.969828
\(386\) 0 0
\(387\) 0.118668 0.00603224
\(388\) 0 0
\(389\) 34.4242 1.74538 0.872688 0.488279i \(-0.162375\pi\)
0.872688 + 0.488279i \(0.162375\pi\)
\(390\) 0 0
\(391\) −7.39461 −0.373961
\(392\) 0 0
\(393\) 16.1623 0.815283
\(394\) 0 0
\(395\) 9.94627 0.500451
\(396\) 0 0
\(397\) −24.7751 −1.24343 −0.621714 0.783244i \(-0.713563\pi\)
−0.621714 + 0.783244i \(0.713563\pi\)
\(398\) 0 0
\(399\) 5.37986 0.269330
\(400\) 0 0
\(401\) 4.97629 0.248504 0.124252 0.992251i \(-0.460347\pi\)
0.124252 + 0.992251i \(0.460347\pi\)
\(402\) 0 0
\(403\) 13.6469 0.679802
\(404\) 0 0
\(405\) −2.34509 −0.116529
\(406\) 0 0
\(407\) 33.5914 1.66507
\(408\) 0 0
\(409\) −21.3193 −1.05417 −0.527087 0.849811i \(-0.676716\pi\)
−0.527087 + 0.849811i \(0.676716\pi\)
\(410\) 0 0
\(411\) 4.08719 0.201606
\(412\) 0 0
\(413\) 4.27278 0.210250
\(414\) 0 0
\(415\) 18.5577 0.910961
\(416\) 0 0
\(417\) 8.11732 0.397507
\(418\) 0 0
\(419\) 34.4117 1.68112 0.840561 0.541717i \(-0.182226\pi\)
0.840561 + 0.541717i \(0.182226\pi\)
\(420\) 0 0
\(421\) −13.3508 −0.650680 −0.325340 0.945597i \(-0.605479\pi\)
−0.325340 + 0.945597i \(0.605479\pi\)
\(422\) 0 0
\(423\) 9.08470 0.441713
\(424\) 0 0
\(425\) −3.69333 −0.179153
\(426\) 0 0
\(427\) 2.81760 0.136353
\(428\) 0 0
\(429\) −8.68926 −0.419521
\(430\) 0 0
\(431\) −38.0934 −1.83490 −0.917448 0.397856i \(-0.869754\pi\)
−0.917448 + 0.397856i \(0.869754\pi\)
\(432\) 0 0
\(433\) 22.6448 1.08824 0.544120 0.839008i \(-0.316864\pi\)
0.544120 + 0.839008i \(0.316864\pi\)
\(434\) 0 0
\(435\) 2.34509 0.112439
\(436\) 0 0
\(437\) −4.27627 −0.204562
\(438\) 0 0
\(439\) 29.9826 1.43099 0.715495 0.698618i \(-0.246201\pi\)
0.715495 + 0.698618i \(0.246201\pi\)
\(440\) 0 0
\(441\) −5.41725 −0.257964
\(442\) 0 0
\(443\) −14.1631 −0.672910 −0.336455 0.941699i \(-0.609228\pi\)
−0.336455 + 0.941699i \(0.609228\pi\)
\(444\) 0 0
\(445\) 10.6113 0.503022
\(446\) 0 0
\(447\) 7.82849 0.370275
\(448\) 0 0
\(449\) 33.1865 1.56617 0.783084 0.621915i \(-0.213645\pi\)
0.783084 + 0.621915i \(0.213645\pi\)
\(450\) 0 0
\(451\) 68.5160 3.22629
\(452\) 0 0
\(453\) −19.0112 −0.893223
\(454\) 0 0
\(455\) 3.97457 0.186331
\(456\) 0 0
\(457\) −4.41745 −0.206640 −0.103320 0.994648i \(-0.532947\pi\)
−0.103320 + 0.994648i \(0.532947\pi\)
\(458\) 0 0
\(459\) −7.39461 −0.345151
\(460\) 0 0
\(461\) 39.2457 1.82785 0.913927 0.405878i \(-0.133034\pi\)
0.913927 + 0.405878i \(0.133034\pi\)
\(462\) 0 0
\(463\) 26.2262 1.21883 0.609416 0.792850i \(-0.291404\pi\)
0.609416 + 0.792850i \(0.291404\pi\)
\(464\) 0 0
\(465\) −23.7559 −1.10165
\(466\) 0 0
\(467\) 12.1356 0.561571 0.280785 0.959771i \(-0.409405\pi\)
0.280785 + 0.959771i \(0.409405\pi\)
\(468\) 0 0
\(469\) −9.87690 −0.456073
\(470\) 0 0
\(471\) 13.2471 0.610392
\(472\) 0 0
\(473\) −0.765409 −0.0351935
\(474\) 0 0
\(475\) −2.13584 −0.0979989
\(476\) 0 0
\(477\) 10.4167 0.476949
\(478\) 0 0
\(479\) 11.9110 0.544229 0.272115 0.962265i \(-0.412277\pi\)
0.272115 + 0.962265i \(0.412277\pi\)
\(480\) 0 0
\(481\) −7.01606 −0.319905
\(482\) 0 0
\(483\) −1.25807 −0.0572443
\(484\) 0 0
\(485\) 0.654468 0.0297179
\(486\) 0 0
\(487\) 19.9032 0.901899 0.450950 0.892549i \(-0.351085\pi\)
0.450950 + 0.892549i \(0.351085\pi\)
\(488\) 0 0
\(489\) −1.77321 −0.0801874
\(490\) 0 0
\(491\) 18.2515 0.823680 0.411840 0.911256i \(-0.364886\pi\)
0.411840 + 0.911256i \(0.364886\pi\)
\(492\) 0 0
\(493\) 7.39461 0.333036
\(494\) 0 0
\(495\) 15.1258 0.679855
\(496\) 0 0
\(497\) 13.5775 0.609033
\(498\) 0 0
\(499\) −5.11958 −0.229184 −0.114592 0.993413i \(-0.536556\pi\)
−0.114592 + 0.993413i \(0.536556\pi\)
\(500\) 0 0
\(501\) 1.42037 0.0634573
\(502\) 0 0
\(503\) −20.4327 −0.911048 −0.455524 0.890224i \(-0.650548\pi\)
−0.455524 + 0.890224i \(0.650548\pi\)
\(504\) 0 0
\(505\) −3.43011 −0.152638
\(506\) 0 0
\(507\) −11.1851 −0.496749
\(508\) 0 0
\(509\) 9.82286 0.435390 0.217695 0.976017i \(-0.430146\pi\)
0.217695 + 0.976017i \(0.430146\pi\)
\(510\) 0 0
\(511\) −9.02745 −0.399351
\(512\) 0 0
\(513\) −4.27627 −0.188802
\(514\) 0 0
\(515\) −39.3163 −1.73248
\(516\) 0 0
\(517\) −58.5962 −2.57706
\(518\) 0 0
\(519\) 13.6543 0.599356
\(520\) 0 0
\(521\) −26.3946 −1.15637 −0.578184 0.815906i \(-0.696238\pi\)
−0.578184 + 0.815906i \(0.696238\pi\)
\(522\) 0 0
\(523\) −32.4210 −1.41767 −0.708835 0.705375i \(-0.750779\pi\)
−0.708835 + 0.705375i \(0.750779\pi\)
\(524\) 0 0
\(525\) −0.628361 −0.0274239
\(526\) 0 0
\(527\) −74.9077 −3.26303
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −3.39629 −0.147386
\(532\) 0 0
\(533\) −14.3106 −0.619859
\(534\) 0 0
\(535\) −11.4033 −0.493007
\(536\) 0 0
\(537\) −9.98920 −0.431066
\(538\) 0 0
\(539\) 34.9412 1.50502
\(540\) 0 0
\(541\) 36.1436 1.55393 0.776967 0.629541i \(-0.216757\pi\)
0.776967 + 0.629541i \(0.216757\pi\)
\(542\) 0 0
\(543\) 5.29509 0.227234
\(544\) 0 0
\(545\) 7.29152 0.312334
\(546\) 0 0
\(547\) 11.5761 0.494958 0.247479 0.968893i \(-0.420398\pi\)
0.247479 + 0.968893i \(0.420398\pi\)
\(548\) 0 0
\(549\) −2.23961 −0.0955844
\(550\) 0 0
\(551\) 4.27627 0.182175
\(552\) 0 0
\(553\) 5.33588 0.226905
\(554\) 0 0
\(555\) 12.2132 0.518422
\(556\) 0 0
\(557\) −1.45992 −0.0618589 −0.0309295 0.999522i \(-0.509847\pi\)
−0.0309295 + 0.999522i \(0.509847\pi\)
\(558\) 0 0
\(559\) 0.159867 0.00676164
\(560\) 0 0
\(561\) 47.6952 2.01369
\(562\) 0 0
\(563\) −41.1215 −1.73307 −0.866533 0.499120i \(-0.833657\pi\)
−0.866533 + 0.499120i \(0.833657\pi\)
\(564\) 0 0
\(565\) 27.7430 1.16716
\(566\) 0 0
\(567\) −1.25807 −0.0528341
\(568\) 0 0
\(569\) −42.9105 −1.79890 −0.899451 0.437023i \(-0.856033\pi\)
−0.899451 + 0.437023i \(0.856033\pi\)
\(570\) 0 0
\(571\) 22.2812 0.932439 0.466220 0.884669i \(-0.345616\pi\)
0.466220 + 0.884669i \(0.345616\pi\)
\(572\) 0 0
\(573\) −11.3030 −0.472189
\(574\) 0 0
\(575\) 0.499463 0.0208290
\(576\) 0 0
\(577\) −1.03746 −0.0431899 −0.0215950 0.999767i \(-0.506874\pi\)
−0.0215950 + 0.999767i \(0.506874\pi\)
\(578\) 0 0
\(579\) 24.2983 1.00980
\(580\) 0 0
\(581\) 9.95565 0.413030
\(582\) 0 0
\(583\) −67.1878 −2.78263
\(584\) 0 0
\(585\) −3.15925 −0.130619
\(586\) 0 0
\(587\) 4.14391 0.171038 0.0855188 0.996337i \(-0.472745\pi\)
0.0855188 + 0.996337i \(0.472745\pi\)
\(588\) 0 0
\(589\) −43.3187 −1.78492
\(590\) 0 0
\(591\) −0.204036 −0.00839292
\(592\) 0 0
\(593\) −38.4566 −1.57922 −0.789612 0.613607i \(-0.789718\pi\)
−0.789612 + 0.613607i \(0.789718\pi\)
\(594\) 0 0
\(595\) −21.8163 −0.894382
\(596\) 0 0
\(597\) −3.69588 −0.151262
\(598\) 0 0
\(599\) 1.86570 0.0762303 0.0381151 0.999273i \(-0.487865\pi\)
0.0381151 + 0.999273i \(0.487865\pi\)
\(600\) 0 0
\(601\) 29.4674 1.20200 0.600999 0.799250i \(-0.294769\pi\)
0.600999 + 0.799250i \(0.294769\pi\)
\(602\) 0 0
\(603\) 7.85081 0.319710
\(604\) 0 0
\(605\) −71.7654 −2.91768
\(606\) 0 0
\(607\) 18.3829 0.746141 0.373070 0.927803i \(-0.378305\pi\)
0.373070 + 0.927803i \(0.378305\pi\)
\(608\) 0 0
\(609\) 1.25807 0.0509797
\(610\) 0 0
\(611\) 12.2387 0.495123
\(612\) 0 0
\(613\) 14.0636 0.568022 0.284011 0.958821i \(-0.408335\pi\)
0.284011 + 0.958821i \(0.408335\pi\)
\(614\) 0 0
\(615\) 24.9111 1.00451
\(616\) 0 0
\(617\) 41.3676 1.66540 0.832699 0.553726i \(-0.186795\pi\)
0.832699 + 0.553726i \(0.186795\pi\)
\(618\) 0 0
\(619\) −13.9854 −0.562121 −0.281060 0.959690i \(-0.590686\pi\)
−0.281060 + 0.959690i \(0.590686\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 5.69263 0.228070
\(624\) 0 0
\(625\) −27.2479 −1.08991
\(626\) 0 0
\(627\) 27.5819 1.10151
\(628\) 0 0
\(629\) 38.5110 1.53553
\(630\) 0 0
\(631\) −5.28654 −0.210454 −0.105227 0.994448i \(-0.533557\pi\)
−0.105227 + 0.994448i \(0.533557\pi\)
\(632\) 0 0
\(633\) −10.3858 −0.412799
\(634\) 0 0
\(635\) −26.0154 −1.03239
\(636\) 0 0
\(637\) −7.29798 −0.289156
\(638\) 0 0
\(639\) −10.7923 −0.426936
\(640\) 0 0
\(641\) 6.20988 0.245276 0.122638 0.992451i \(-0.460865\pi\)
0.122638 + 0.992451i \(0.460865\pi\)
\(642\) 0 0
\(643\) −16.7158 −0.659205 −0.329603 0.944120i \(-0.606915\pi\)
−0.329603 + 0.944120i \(0.606915\pi\)
\(644\) 0 0
\(645\) −0.278288 −0.0109576
\(646\) 0 0
\(647\) −36.2631 −1.42565 −0.712825 0.701342i \(-0.752584\pi\)
−0.712825 + 0.701342i \(0.752584\pi\)
\(648\) 0 0
\(649\) 21.9060 0.859887
\(650\) 0 0
\(651\) −12.7443 −0.499490
\(652\) 0 0
\(653\) 17.4650 0.683458 0.341729 0.939799i \(-0.388988\pi\)
0.341729 + 0.939799i \(0.388988\pi\)
\(654\) 0 0
\(655\) −37.9022 −1.48096
\(656\) 0 0
\(657\) 7.17561 0.279947
\(658\) 0 0
\(659\) 39.1244 1.52407 0.762034 0.647536i \(-0.224201\pi\)
0.762034 + 0.647536i \(0.224201\pi\)
\(660\) 0 0
\(661\) −38.5339 −1.49879 −0.749397 0.662121i \(-0.769656\pi\)
−0.749397 + 0.662121i \(0.769656\pi\)
\(662\) 0 0
\(663\) −9.96183 −0.386885
\(664\) 0 0
\(665\) −12.6163 −0.489238
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 2.39453 0.0925780
\(670\) 0 0
\(671\) 14.4455 0.557662
\(672\) 0 0
\(673\) 1.56580 0.0603570 0.0301785 0.999545i \(-0.490392\pi\)
0.0301785 + 0.999545i \(0.490392\pi\)
\(674\) 0 0
\(675\) 0.499463 0.0192243
\(676\) 0 0
\(677\) 15.1966 0.584051 0.292026 0.956410i \(-0.405671\pi\)
0.292026 + 0.956410i \(0.405671\pi\)
\(678\) 0 0
\(679\) 0.351103 0.0134741
\(680\) 0 0
\(681\) −8.00245 −0.306655
\(682\) 0 0
\(683\) −26.3797 −1.00939 −0.504695 0.863298i \(-0.668395\pi\)
−0.504695 + 0.863298i \(0.668395\pi\)
\(684\) 0 0
\(685\) −9.58485 −0.366218
\(686\) 0 0
\(687\) −10.7641 −0.410676
\(688\) 0 0
\(689\) 14.0331 0.534620
\(690\) 0 0
\(691\) −15.0803 −0.573681 −0.286840 0.957978i \(-0.592605\pi\)
−0.286840 + 0.957978i \(0.592605\pi\)
\(692\) 0 0
\(693\) 8.11456 0.308247
\(694\) 0 0
\(695\) −19.0359 −0.722072
\(696\) 0 0
\(697\) 78.5503 2.97531
\(698\) 0 0
\(699\) −0.554990 −0.0209917
\(700\) 0 0
\(701\) −35.4316 −1.33823 −0.669116 0.743158i \(-0.733327\pi\)
−0.669116 + 0.743158i \(0.733327\pi\)
\(702\) 0 0
\(703\) 22.2707 0.839956
\(704\) 0 0
\(705\) −21.3045 −0.802372
\(706\) 0 0
\(707\) −1.84015 −0.0692061
\(708\) 0 0
\(709\) −19.0617 −0.715877 −0.357939 0.933745i \(-0.616520\pi\)
−0.357939 + 0.933745i \(0.616520\pi\)
\(710\) 0 0
\(711\) −4.24131 −0.159062
\(712\) 0 0
\(713\) 10.1300 0.379373
\(714\) 0 0
\(715\) 20.3771 0.762061
\(716\) 0 0
\(717\) −17.4662 −0.652286
\(718\) 0 0
\(719\) −6.27886 −0.234162 −0.117081 0.993122i \(-0.537354\pi\)
−0.117081 + 0.993122i \(0.537354\pi\)
\(720\) 0 0
\(721\) −21.0920 −0.785509
\(722\) 0 0
\(723\) 16.5598 0.615864
\(724\) 0 0
\(725\) −0.499463 −0.0185496
\(726\) 0 0
\(727\) −14.8619 −0.551199 −0.275599 0.961273i \(-0.588876\pi\)
−0.275599 + 0.961273i \(0.588876\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.877505 −0.0324557
\(732\) 0 0
\(733\) 52.6052 1.94302 0.971509 0.237004i \(-0.0761653\pi\)
0.971509 + 0.237004i \(0.0761653\pi\)
\(734\) 0 0
\(735\) 12.7040 0.468593
\(736\) 0 0
\(737\) −50.6377 −1.86526
\(738\) 0 0
\(739\) −0.794958 −0.0292430 −0.0146215 0.999893i \(-0.504654\pi\)
−0.0146215 + 0.999893i \(0.504654\pi\)
\(740\) 0 0
\(741\) −5.76087 −0.211631
\(742\) 0 0
\(743\) 5.73978 0.210572 0.105286 0.994442i \(-0.466424\pi\)
0.105286 + 0.994442i \(0.466424\pi\)
\(744\) 0 0
\(745\) −18.3585 −0.672605
\(746\) 0 0
\(747\) −7.91341 −0.289536
\(748\) 0 0
\(749\) −6.11752 −0.223529
\(750\) 0 0
\(751\) −14.7146 −0.536944 −0.268472 0.963287i \(-0.586519\pi\)
−0.268472 + 0.963287i \(0.586519\pi\)
\(752\) 0 0
\(753\) 4.55045 0.165828
\(754\) 0 0
\(755\) 44.5830 1.62254
\(756\) 0 0
\(757\) 25.8286 0.938756 0.469378 0.882997i \(-0.344478\pi\)
0.469378 + 0.882997i \(0.344478\pi\)
\(758\) 0 0
\(759\) −6.44999 −0.234120
\(760\) 0 0
\(761\) 20.2387 0.733651 0.366826 0.930290i \(-0.380445\pi\)
0.366826 + 0.930290i \(0.380445\pi\)
\(762\) 0 0
\(763\) 3.91169 0.141613
\(764\) 0 0
\(765\) 17.3410 0.626967
\(766\) 0 0
\(767\) −4.57539 −0.165208
\(768\) 0 0
\(769\) −48.6534 −1.75449 −0.877244 0.480045i \(-0.840620\pi\)
−0.877244 + 0.480045i \(0.840620\pi\)
\(770\) 0 0
\(771\) −18.8900 −0.680307
\(772\) 0 0
\(773\) 23.0404 0.828707 0.414353 0.910116i \(-0.364008\pi\)
0.414353 + 0.910116i \(0.364008\pi\)
\(774\) 0 0
\(775\) 5.05958 0.181745
\(776\) 0 0
\(777\) 6.55202 0.235052
\(778\) 0 0
\(779\) 45.4253 1.62753
\(780\) 0 0
\(781\) 69.6101 2.49085
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) 0 0
\(785\) −31.0656 −1.10878
\(786\) 0 0
\(787\) −2.48766 −0.0886756 −0.0443378 0.999017i \(-0.514118\pi\)
−0.0443378 + 0.999017i \(0.514118\pi\)
\(788\) 0 0
\(789\) −0.490569 −0.0174647
\(790\) 0 0
\(791\) 14.8833 0.529190
\(792\) 0 0
\(793\) −3.01715 −0.107142
\(794\) 0 0
\(795\) −24.4282 −0.866378
\(796\) 0 0
\(797\) −47.1618 −1.67056 −0.835278 0.549828i \(-0.814693\pi\)
−0.835278 + 0.549828i \(0.814693\pi\)
\(798\) 0 0
\(799\) −67.1778 −2.37658
\(800\) 0 0
\(801\) −4.52488 −0.159879
\(802\) 0 0
\(803\) −46.2826 −1.63328
\(804\) 0 0
\(805\) 2.95030 0.103984
\(806\) 0 0
\(807\) 19.1733 0.674931
\(808\) 0 0
\(809\) 35.7581 1.25719 0.628593 0.777734i \(-0.283631\pi\)
0.628593 + 0.777734i \(0.283631\pi\)
\(810\) 0 0
\(811\) −21.0722 −0.739945 −0.369973 0.929043i \(-0.620633\pi\)
−0.369973 + 0.929043i \(0.620633\pi\)
\(812\) 0 0
\(813\) −28.7636 −1.00878
\(814\) 0 0
\(815\) 4.15835 0.145661
\(816\) 0 0
\(817\) −0.507457 −0.0177537
\(818\) 0 0
\(819\) −1.69484 −0.0592226
\(820\) 0 0
\(821\) −29.8141 −1.04052 −0.520260 0.854008i \(-0.674165\pi\)
−0.520260 + 0.854008i \(0.674165\pi\)
\(822\) 0 0
\(823\) 42.3600 1.47658 0.738289 0.674485i \(-0.235634\pi\)
0.738289 + 0.674485i \(0.235634\pi\)
\(824\) 0 0
\(825\) −3.22153 −0.112159
\(826\) 0 0
\(827\) −30.7101 −1.06789 −0.533947 0.845518i \(-0.679292\pi\)
−0.533947 + 0.845518i \(0.679292\pi\)
\(828\) 0 0
\(829\) −1.49418 −0.0518952 −0.0259476 0.999663i \(-0.508260\pi\)
−0.0259476 + 0.999663i \(0.508260\pi\)
\(830\) 0 0
\(831\) −24.2754 −0.842104
\(832\) 0 0
\(833\) 40.0585 1.38794
\(834\) 0 0
\(835\) −3.33089 −0.115270
\(836\) 0 0
\(837\) 10.1300 0.350145
\(838\) 0 0
\(839\) 23.4228 0.808643 0.404322 0.914617i \(-0.367508\pi\)
0.404322 + 0.914617i \(0.367508\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −2.36539 −0.0814685
\(844\) 0 0
\(845\) 26.2302 0.902345
\(846\) 0 0
\(847\) −38.5000 −1.32288
\(848\) 0 0
\(849\) −2.24568 −0.0770715
\(850\) 0 0
\(851\) −5.20798 −0.178527
\(852\) 0 0
\(853\) 23.4457 0.802764 0.401382 0.915911i \(-0.368530\pi\)
0.401382 + 0.915911i \(0.368530\pi\)
\(854\) 0 0
\(855\) 10.0282 0.342959
\(856\) 0 0
\(857\) 34.2988 1.17163 0.585813 0.810446i \(-0.300775\pi\)
0.585813 + 0.810446i \(0.300775\pi\)
\(858\) 0 0
\(859\) 39.9851 1.36428 0.682138 0.731224i \(-0.261051\pi\)
0.682138 + 0.731224i \(0.261051\pi\)
\(860\) 0 0
\(861\) 13.3641 0.455446
\(862\) 0 0
\(863\) 16.3589 0.556864 0.278432 0.960456i \(-0.410185\pi\)
0.278432 + 0.960456i \(0.410185\pi\)
\(864\) 0 0
\(865\) −32.0206 −1.08873
\(866\) 0 0
\(867\) 37.6803 1.27969
\(868\) 0 0
\(869\) 27.3564 0.928003
\(870\) 0 0
\(871\) 10.5764 0.358368
\(872\) 0 0
\(873\) −0.279080 −0.00944542
\(874\) 0 0
\(875\) −13.2779 −0.448876
\(876\) 0 0
\(877\) 21.8906 0.739192 0.369596 0.929192i \(-0.379496\pi\)
0.369596 + 0.929192i \(0.379496\pi\)
\(878\) 0 0
\(879\) 27.7523 0.936063
\(880\) 0 0
\(881\) 10.5595 0.355759 0.177880 0.984052i \(-0.443076\pi\)
0.177880 + 0.984052i \(0.443076\pi\)
\(882\) 0 0
\(883\) 18.8359 0.633879 0.316939 0.948446i \(-0.397345\pi\)
0.316939 + 0.948446i \(0.397345\pi\)
\(884\) 0 0
\(885\) 7.96461 0.267728
\(886\) 0 0
\(887\) 35.7738 1.20117 0.600584 0.799562i \(-0.294935\pi\)
0.600584 + 0.799562i \(0.294935\pi\)
\(888\) 0 0
\(889\) −13.9565 −0.468086
\(890\) 0 0
\(891\) −6.44999 −0.216083
\(892\) 0 0
\(893\) −38.8486 −1.30002
\(894\) 0 0
\(895\) 23.4256 0.783032
\(896\) 0 0
\(897\) 1.34717 0.0449808
\(898\) 0 0
\(899\) −10.1300 −0.337856
\(900\) 0 0
\(901\) −77.0276 −2.56616
\(902\) 0 0
\(903\) −0.149293 −0.00496817
\(904\) 0 0
\(905\) −12.4175 −0.412771
\(906\) 0 0
\(907\) 33.6997 1.11898 0.559491 0.828837i \(-0.310997\pi\)
0.559491 + 0.828837i \(0.310997\pi\)
\(908\) 0 0
\(909\) 1.46268 0.0485139
\(910\) 0 0
\(911\) −24.7400 −0.819672 −0.409836 0.912159i \(-0.634414\pi\)
−0.409836 + 0.912159i \(0.634414\pi\)
\(912\) 0 0
\(913\) 51.0414 1.68922
\(914\) 0 0
\(915\) 5.25210 0.173629
\(916\) 0 0
\(917\) −20.3334 −0.671469
\(918\) 0 0
\(919\) −49.1870 −1.62253 −0.811264 0.584680i \(-0.801220\pi\)
−0.811264 + 0.584680i \(0.801220\pi\)
\(920\) 0 0
\(921\) −4.01961 −0.132451
\(922\) 0 0
\(923\) −14.5391 −0.478560
\(924\) 0 0
\(925\) −2.60119 −0.0855267
\(926\) 0 0
\(927\) 16.7654 0.550646
\(928\) 0 0
\(929\) −32.2541 −1.05822 −0.529112 0.848552i \(-0.677475\pi\)
−0.529112 + 0.848552i \(0.677475\pi\)
\(930\) 0 0
\(931\) 23.1656 0.759222
\(932\) 0 0
\(933\) −24.4335 −0.799916
\(934\) 0 0
\(935\) −111.850 −3.65787
\(936\) 0 0
\(937\) 3.64033 0.118924 0.0594622 0.998231i \(-0.481061\pi\)
0.0594622 + 0.998231i \(0.481061\pi\)
\(938\) 0 0
\(939\) −16.4118 −0.535578
\(940\) 0 0
\(941\) −43.7029 −1.42467 −0.712336 0.701838i \(-0.752363\pi\)
−0.712336 + 0.701838i \(0.752363\pi\)
\(942\) 0 0
\(943\) −10.6226 −0.345921
\(944\) 0 0
\(945\) 2.95030 0.0959732
\(946\) 0 0
\(947\) −17.2115 −0.559297 −0.279649 0.960102i \(-0.590218\pi\)
−0.279649 + 0.960102i \(0.590218\pi\)
\(948\) 0 0
\(949\) 9.66680 0.313798
\(950\) 0 0
\(951\) 21.1766 0.686697
\(952\) 0 0
\(953\) −44.0372 −1.42651 −0.713253 0.700907i \(-0.752779\pi\)
−0.713253 + 0.700907i \(0.752779\pi\)
\(954\) 0 0
\(955\) 26.5066 0.857733
\(956\) 0 0
\(957\) 6.44999 0.208499
\(958\) 0 0
\(959\) −5.14199 −0.166043
\(960\) 0 0
\(961\) 71.6177 2.31025
\(962\) 0 0
\(963\) 4.86261 0.156696
\(964\) 0 0
\(965\) −56.9817 −1.83431
\(966\) 0 0
\(967\) −8.47069 −0.272399 −0.136200 0.990681i \(-0.543489\pi\)
−0.136200 + 0.990681i \(0.543489\pi\)
\(968\) 0 0
\(969\) 31.6213 1.01582
\(970\) 0 0
\(971\) 51.8562 1.66414 0.832072 0.554667i \(-0.187154\pi\)
0.832072 + 0.554667i \(0.187154\pi\)
\(972\) 0 0
\(973\) −10.2122 −0.327388
\(974\) 0 0
\(975\) 0.672863 0.0215489
\(976\) 0 0
\(977\) −35.2841 −1.12884 −0.564420 0.825488i \(-0.690900\pi\)
−0.564420 + 0.825488i \(0.690900\pi\)
\(978\) 0 0
\(979\) 29.1854 0.932770
\(980\) 0 0
\(981\) −3.10927 −0.0992712
\(982\) 0 0
\(983\) −24.4820 −0.780854 −0.390427 0.920634i \(-0.627673\pi\)
−0.390427 + 0.920634i \(0.627673\pi\)
\(984\) 0 0
\(985\) 0.478484 0.0152458
\(986\) 0 0
\(987\) −11.4292 −0.363796
\(988\) 0 0
\(989\) 0.118668 0.00377343
\(990\) 0 0
\(991\) −30.8045 −0.978538 −0.489269 0.872133i \(-0.662736\pi\)
−0.489269 + 0.872133i \(0.662736\pi\)
\(992\) 0 0
\(993\) −10.9757 −0.348303
\(994\) 0 0
\(995\) 8.66719 0.274768
\(996\) 0 0
\(997\) −29.1338 −0.922676 −0.461338 0.887224i \(-0.652631\pi\)
−0.461338 + 0.887224i \(0.652631\pi\)
\(998\) 0 0
\(999\) −5.20798 −0.164773
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 \(a_p\))