Properties

Label 8048.2.a.v.1.12
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.799349 q^{3}\) \(+0.626001 q^{5}\) \(+0.555593 q^{7}\) \(-2.36104 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.799349 q^{3}\) \(+0.626001 q^{5}\) \(+0.555593 q^{7}\) \(-2.36104 q^{9}\) \(+1.34364 q^{11}\) \(+2.90044 q^{13}\) \(-0.500394 q^{15}\) \(+2.10341 q^{17}\) \(+8.54470 q^{19}\) \(-0.444113 q^{21}\) \(-8.01796 q^{23}\) \(-4.60812 q^{25}\) \(+4.28534 q^{27}\) \(-2.10061 q^{29}\) \(-3.16291 q^{31}\) \(-1.07404 q^{33}\) \(+0.347802 q^{35}\) \(-10.9692 q^{37}\) \(-2.31847 q^{39}\) \(-0.458903 q^{41}\) \(-2.58754 q^{43}\) \(-1.47801 q^{45}\) \(-10.5539 q^{47}\) \(-6.69132 q^{49}\) \(-1.68136 q^{51}\) \(-5.54386 q^{53}\) \(+0.841122 q^{55}\) \(-6.83020 q^{57}\) \(+9.89005 q^{59}\) \(+0.357146 q^{61}\) \(-1.31178 q^{63}\) \(+1.81568 q^{65}\) \(+2.78050 q^{67}\) \(+6.40915 q^{69}\) \(-4.26348 q^{71}\) \(-4.79073 q^{73}\) \(+3.68350 q^{75}\) \(+0.746518 q^{77}\) \(+12.7953 q^{79}\) \(+3.65763 q^{81}\) \(+11.7232 q^{83}\) \(+1.31674 q^{85}\) \(+1.67912 q^{87}\) \(+16.1805 q^{89}\) \(+1.61146 q^{91}\) \(+2.52827 q^{93}\) \(+5.34899 q^{95}\) \(-13.3066 q^{97}\) \(-3.17239 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.799349 −0.461505 −0.230752 0.973013i \(-0.574119\pi\)
−0.230752 + 0.973013i \(0.574119\pi\)
\(4\) 0 0
\(5\) 0.626001 0.279956 0.139978 0.990155i \(-0.455297\pi\)
0.139978 + 0.990155i \(0.455297\pi\)
\(6\) 0 0
\(7\) 0.555593 0.209994 0.104997 0.994473i \(-0.466517\pi\)
0.104997 + 0.994473i \(0.466517\pi\)
\(8\) 0 0
\(9\) −2.36104 −0.787013
\(10\) 0 0
\(11\) 1.34364 0.405123 0.202562 0.979270i \(-0.435073\pi\)
0.202562 + 0.979270i \(0.435073\pi\)
\(12\) 0 0
\(13\) 2.90044 0.804438 0.402219 0.915544i \(-0.368239\pi\)
0.402219 + 0.915544i \(0.368239\pi\)
\(14\) 0 0
\(15\) −0.500394 −0.129201
\(16\) 0 0
\(17\) 2.10341 0.510152 0.255076 0.966921i \(-0.417899\pi\)
0.255076 + 0.966921i \(0.417899\pi\)
\(18\) 0 0
\(19\) 8.54470 1.96029 0.980144 0.198288i \(-0.0635380\pi\)
0.980144 + 0.198288i \(0.0635380\pi\)
\(20\) 0 0
\(21\) −0.444113 −0.0969133
\(22\) 0 0
\(23\) −8.01796 −1.67186 −0.835930 0.548836i \(-0.815071\pi\)
−0.835930 + 0.548836i \(0.815071\pi\)
\(24\) 0 0
\(25\) −4.60812 −0.921624
\(26\) 0 0
\(27\) 4.28534 0.824715
\(28\) 0 0
\(29\) −2.10061 −0.390073 −0.195036 0.980796i \(-0.562483\pi\)
−0.195036 + 0.980796i \(0.562483\pi\)
\(30\) 0 0
\(31\) −3.16291 −0.568076 −0.284038 0.958813i \(-0.591674\pi\)
−0.284038 + 0.958813i \(0.591674\pi\)
\(32\) 0 0
\(33\) −1.07404 −0.186966
\(34\) 0 0
\(35\) 0.347802 0.0587892
\(36\) 0 0
\(37\) −10.9692 −1.80333 −0.901665 0.432436i \(-0.857654\pi\)
−0.901665 + 0.432436i \(0.857654\pi\)
\(38\) 0 0
\(39\) −2.31847 −0.371252
\(40\) 0 0
\(41\) −0.458903 −0.0716686 −0.0358343 0.999358i \(-0.511409\pi\)
−0.0358343 + 0.999358i \(0.511409\pi\)
\(42\) 0 0
\(43\) −2.58754 −0.394595 −0.197298 0.980344i \(-0.563217\pi\)
−0.197298 + 0.980344i \(0.563217\pi\)
\(44\) 0 0
\(45\) −1.47801 −0.220329
\(46\) 0 0
\(47\) −10.5539 −1.53944 −0.769722 0.638379i \(-0.779605\pi\)
−0.769722 + 0.638379i \(0.779605\pi\)
\(48\) 0 0
\(49\) −6.69132 −0.955902
\(50\) 0 0
\(51\) −1.68136 −0.235438
\(52\) 0 0
\(53\) −5.54386 −0.761508 −0.380754 0.924676i \(-0.624336\pi\)
−0.380754 + 0.924676i \(0.624336\pi\)
\(54\) 0 0
\(55\) 0.841122 0.113417
\(56\) 0 0
\(57\) −6.83020 −0.904682
\(58\) 0 0
\(59\) 9.89005 1.28757 0.643787 0.765204i \(-0.277362\pi\)
0.643787 + 0.765204i \(0.277362\pi\)
\(60\) 0 0
\(61\) 0.357146 0.0457278 0.0228639 0.999739i \(-0.492722\pi\)
0.0228639 + 0.999739i \(0.492722\pi\)
\(62\) 0 0
\(63\) −1.31178 −0.165268
\(64\) 0 0
\(65\) 1.81568 0.225207
\(66\) 0 0
\(67\) 2.78050 0.339693 0.169846 0.985471i \(-0.445673\pi\)
0.169846 + 0.985471i \(0.445673\pi\)
\(68\) 0 0
\(69\) 6.40915 0.771571
\(70\) 0 0
\(71\) −4.26348 −0.505982 −0.252991 0.967469i \(-0.581414\pi\)
−0.252991 + 0.967469i \(0.581414\pi\)
\(72\) 0 0
\(73\) −4.79073 −0.560713 −0.280357 0.959896i \(-0.590453\pi\)
−0.280357 + 0.959896i \(0.590453\pi\)
\(74\) 0 0
\(75\) 3.68350 0.425334
\(76\) 0 0
\(77\) 0.746518 0.0850736
\(78\) 0 0
\(79\) 12.7953 1.43958 0.719791 0.694191i \(-0.244238\pi\)
0.719791 + 0.694191i \(0.244238\pi\)
\(80\) 0 0
\(81\) 3.65763 0.406404
\(82\) 0 0
\(83\) 11.7232 1.28679 0.643395 0.765535i \(-0.277525\pi\)
0.643395 + 0.765535i \(0.277525\pi\)
\(84\) 0 0
\(85\) 1.31674 0.142820
\(86\) 0 0
\(87\) 1.67912 0.180020
\(88\) 0 0
\(89\) 16.1805 1.71513 0.857563 0.514379i \(-0.171978\pi\)
0.857563 + 0.514379i \(0.171978\pi\)
\(90\) 0 0
\(91\) 1.61146 0.168927
\(92\) 0 0
\(93\) 2.52827 0.262169
\(94\) 0 0
\(95\) 5.34899 0.548795
\(96\) 0 0
\(97\) −13.3066 −1.35108 −0.675540 0.737323i \(-0.736089\pi\)
−0.675540 + 0.737323i \(0.736089\pi\)
\(98\) 0 0
\(99\) −3.17239 −0.318838
\(100\) 0 0
\(101\) −10.6747 −1.06217 −0.531087 0.847317i \(-0.678216\pi\)
−0.531087 + 0.847317i \(0.678216\pi\)
\(102\) 0 0
\(103\) −7.17714 −0.707184 −0.353592 0.935400i \(-0.615040\pi\)
−0.353592 + 0.935400i \(0.615040\pi\)
\(104\) 0 0
\(105\) −0.278015 −0.0271315
\(106\) 0 0
\(107\) 8.23427 0.796037 0.398018 0.917377i \(-0.369698\pi\)
0.398018 + 0.917377i \(0.369698\pi\)
\(108\) 0 0
\(109\) 14.3637 1.37580 0.687898 0.725807i \(-0.258534\pi\)
0.687898 + 0.725807i \(0.258534\pi\)
\(110\) 0 0
\(111\) 8.76825 0.832245
\(112\) 0 0
\(113\) −0.429783 −0.0404306 −0.0202153 0.999796i \(-0.506435\pi\)
−0.0202153 + 0.999796i \(0.506435\pi\)
\(114\) 0 0
\(115\) −5.01926 −0.468048
\(116\) 0 0
\(117\) −6.84806 −0.633103
\(118\) 0 0
\(119\) 1.16864 0.107129
\(120\) 0 0
\(121\) −9.19463 −0.835875
\(122\) 0 0
\(123\) 0.366824 0.0330754
\(124\) 0 0
\(125\) −6.01470 −0.537971
\(126\) 0 0
\(127\) 17.8935 1.58779 0.793895 0.608055i \(-0.208050\pi\)
0.793895 + 0.608055i \(0.208050\pi\)
\(128\) 0 0
\(129\) 2.06835 0.182108
\(130\) 0 0
\(131\) 0.614900 0.0537241 0.0268620 0.999639i \(-0.491449\pi\)
0.0268620 + 0.999639i \(0.491449\pi\)
\(132\) 0 0
\(133\) 4.74737 0.411649
\(134\) 0 0
\(135\) 2.68263 0.230884
\(136\) 0 0
\(137\) −5.09359 −0.435175 −0.217587 0.976041i \(-0.569819\pi\)
−0.217587 + 0.976041i \(0.569819\pi\)
\(138\) 0 0
\(139\) 6.43213 0.545566 0.272783 0.962076i \(-0.412056\pi\)
0.272783 + 0.962076i \(0.412056\pi\)
\(140\) 0 0
\(141\) 8.43625 0.710461
\(142\) 0 0
\(143\) 3.89715 0.325896
\(144\) 0 0
\(145\) −1.31498 −0.109203
\(146\) 0 0
\(147\) 5.34870 0.441153
\(148\) 0 0
\(149\) 5.91770 0.484796 0.242398 0.970177i \(-0.422066\pi\)
0.242398 + 0.970177i \(0.422066\pi\)
\(150\) 0 0
\(151\) −3.65713 −0.297613 −0.148807 0.988866i \(-0.547543\pi\)
−0.148807 + 0.988866i \(0.547543\pi\)
\(152\) 0 0
\(153\) −4.96624 −0.401497
\(154\) 0 0
\(155\) −1.97999 −0.159036
\(156\) 0 0
\(157\) −18.4656 −1.47371 −0.736857 0.676048i \(-0.763691\pi\)
−0.736857 + 0.676048i \(0.763691\pi\)
\(158\) 0 0
\(159\) 4.43148 0.351439
\(160\) 0 0
\(161\) −4.45472 −0.351081
\(162\) 0 0
\(163\) −23.8373 −1.86708 −0.933540 0.358472i \(-0.883298\pi\)
−0.933540 + 0.358472i \(0.883298\pi\)
\(164\) 0 0
\(165\) −0.672350 −0.0523424
\(166\) 0 0
\(167\) −3.11519 −0.241061 −0.120530 0.992710i \(-0.538460\pi\)
−0.120530 + 0.992710i \(0.538460\pi\)
\(168\) 0 0
\(169\) −4.58744 −0.352880
\(170\) 0 0
\(171\) −20.1744 −1.54277
\(172\) 0 0
\(173\) −23.3868 −1.77806 −0.889032 0.457845i \(-0.848621\pi\)
−0.889032 + 0.457845i \(0.848621\pi\)
\(174\) 0 0
\(175\) −2.56024 −0.193536
\(176\) 0 0
\(177\) −7.90560 −0.594222
\(178\) 0 0
\(179\) −1.70833 −0.127687 −0.0638434 0.997960i \(-0.520336\pi\)
−0.0638434 + 0.997960i \(0.520336\pi\)
\(180\) 0 0
\(181\) 8.03069 0.596916 0.298458 0.954423i \(-0.403528\pi\)
0.298458 + 0.954423i \(0.403528\pi\)
\(182\) 0 0
\(183\) −0.285484 −0.0211036
\(184\) 0 0
\(185\) −6.86675 −0.504854
\(186\) 0 0
\(187\) 2.82623 0.206675
\(188\) 0 0
\(189\) 2.38091 0.173185
\(190\) 0 0
\(191\) 5.33287 0.385873 0.192937 0.981211i \(-0.438199\pi\)
0.192937 + 0.981211i \(0.438199\pi\)
\(192\) 0 0
\(193\) −18.0996 −1.30284 −0.651419 0.758718i \(-0.725826\pi\)
−0.651419 + 0.758718i \(0.725826\pi\)
\(194\) 0 0
\(195\) −1.45136 −0.103934
\(196\) 0 0
\(197\) 6.36431 0.453438 0.226719 0.973960i \(-0.427200\pi\)
0.226719 + 0.973960i \(0.427200\pi\)
\(198\) 0 0
\(199\) −23.3253 −1.65348 −0.826742 0.562581i \(-0.809808\pi\)
−0.826742 + 0.562581i \(0.809808\pi\)
\(200\) 0 0
\(201\) −2.22260 −0.156770
\(202\) 0 0
\(203\) −1.16708 −0.0819131
\(204\) 0 0
\(205\) −0.287274 −0.0200641
\(206\) 0 0
\(207\) 18.9307 1.31578
\(208\) 0 0
\(209\) 11.4810 0.794158
\(210\) 0 0
\(211\) −1.96717 −0.135426 −0.0677129 0.997705i \(-0.521570\pi\)
−0.0677129 + 0.997705i \(0.521570\pi\)
\(212\) 0 0
\(213\) 3.40801 0.233513
\(214\) 0 0
\(215\) −1.61980 −0.110469
\(216\) 0 0
\(217\) −1.75729 −0.119293
\(218\) 0 0
\(219\) 3.82947 0.258772
\(220\) 0 0
\(221\) 6.10082 0.410386
\(222\) 0 0
\(223\) −13.9131 −0.931693 −0.465847 0.884865i \(-0.654250\pi\)
−0.465847 + 0.884865i \(0.654250\pi\)
\(224\) 0 0
\(225\) 10.8800 0.725331
\(226\) 0 0
\(227\) 20.2586 1.34461 0.672304 0.740275i \(-0.265305\pi\)
0.672304 + 0.740275i \(0.265305\pi\)
\(228\) 0 0
\(229\) 0.859061 0.0567683 0.0283842 0.999597i \(-0.490964\pi\)
0.0283842 + 0.999597i \(0.490964\pi\)
\(230\) 0 0
\(231\) −0.596729 −0.0392619
\(232\) 0 0
\(233\) 14.8692 0.974113 0.487057 0.873370i \(-0.338071\pi\)
0.487057 + 0.873370i \(0.338071\pi\)
\(234\) 0 0
\(235\) −6.60676 −0.430977
\(236\) 0 0
\(237\) −10.2279 −0.664374
\(238\) 0 0
\(239\) 1.39190 0.0900346 0.0450173 0.998986i \(-0.485666\pi\)
0.0450173 + 0.998986i \(0.485666\pi\)
\(240\) 0 0
\(241\) 21.8940 1.41032 0.705160 0.709048i \(-0.250875\pi\)
0.705160 + 0.709048i \(0.250875\pi\)
\(242\) 0 0
\(243\) −15.7798 −1.01227
\(244\) 0 0
\(245\) −4.18877 −0.267611
\(246\) 0 0
\(247\) 24.7834 1.57693
\(248\) 0 0
\(249\) −9.37094 −0.593859
\(250\) 0 0
\(251\) 0.829354 0.0523484 0.0261742 0.999657i \(-0.491668\pi\)
0.0261742 + 0.999657i \(0.491668\pi\)
\(252\) 0 0
\(253\) −10.7733 −0.677310
\(254\) 0 0
\(255\) −1.05253 −0.0659122
\(256\) 0 0
\(257\) −23.8402 −1.48711 −0.743556 0.668674i \(-0.766862\pi\)
−0.743556 + 0.668674i \(0.766862\pi\)
\(258\) 0 0
\(259\) −6.09442 −0.378689
\(260\) 0 0
\(261\) 4.95962 0.306993
\(262\) 0 0
\(263\) −4.32891 −0.266932 −0.133466 0.991053i \(-0.542611\pi\)
−0.133466 + 0.991053i \(0.542611\pi\)
\(264\) 0 0
\(265\) −3.47046 −0.213189
\(266\) 0 0
\(267\) −12.9338 −0.791538
\(268\) 0 0
\(269\) −26.3997 −1.60962 −0.804808 0.593535i \(-0.797732\pi\)
−0.804808 + 0.593535i \(0.797732\pi\)
\(270\) 0 0
\(271\) −14.7676 −0.897070 −0.448535 0.893765i \(-0.648054\pi\)
−0.448535 + 0.893765i \(0.648054\pi\)
\(272\) 0 0
\(273\) −1.28812 −0.0779607
\(274\) 0 0
\(275\) −6.19167 −0.373372
\(276\) 0 0
\(277\) 10.7332 0.644893 0.322446 0.946588i \(-0.395495\pi\)
0.322446 + 0.946588i \(0.395495\pi\)
\(278\) 0 0
\(279\) 7.46776 0.447083
\(280\) 0 0
\(281\) −15.9698 −0.952676 −0.476338 0.879262i \(-0.658036\pi\)
−0.476338 + 0.879262i \(0.658036\pi\)
\(282\) 0 0
\(283\) −31.4609 −1.87015 −0.935077 0.354445i \(-0.884670\pi\)
−0.935077 + 0.354445i \(0.884670\pi\)
\(284\) 0 0
\(285\) −4.27571 −0.253271
\(286\) 0 0
\(287\) −0.254963 −0.0150500
\(288\) 0 0
\(289\) −12.5757 −0.739745
\(290\) 0 0
\(291\) 10.6366 0.623530
\(292\) 0 0
\(293\) −0.125371 −0.00732426 −0.00366213 0.999993i \(-0.501166\pi\)
−0.00366213 + 0.999993i \(0.501166\pi\)
\(294\) 0 0
\(295\) 6.19118 0.360465
\(296\) 0 0
\(297\) 5.75797 0.334111
\(298\) 0 0
\(299\) −23.2556 −1.34491
\(300\) 0 0
\(301\) −1.43762 −0.0828628
\(302\) 0 0
\(303\) 8.53283 0.490198
\(304\) 0 0
\(305\) 0.223574 0.0128018
\(306\) 0 0
\(307\) −3.33839 −0.190532 −0.0952660 0.995452i \(-0.530370\pi\)
−0.0952660 + 0.995452i \(0.530370\pi\)
\(308\) 0 0
\(309\) 5.73704 0.326369
\(310\) 0 0
\(311\) 4.02727 0.228366 0.114183 0.993460i \(-0.463575\pi\)
0.114183 + 0.993460i \(0.463575\pi\)
\(312\) 0 0
\(313\) −12.5613 −0.710009 −0.355005 0.934865i \(-0.615521\pi\)
−0.355005 + 0.934865i \(0.615521\pi\)
\(314\) 0 0
\(315\) −0.821174 −0.0462679
\(316\) 0 0
\(317\) 15.1813 0.852669 0.426335 0.904566i \(-0.359805\pi\)
0.426335 + 0.904566i \(0.359805\pi\)
\(318\) 0 0
\(319\) −2.82246 −0.158028
\(320\) 0 0
\(321\) −6.58206 −0.367375
\(322\) 0 0
\(323\) 17.9730 1.00004
\(324\) 0 0
\(325\) −13.3656 −0.741389
\(326\) 0 0
\(327\) −11.4816 −0.634936
\(328\) 0 0
\(329\) −5.86367 −0.323275
\(330\) 0 0
\(331\) −21.9585 −1.20695 −0.603473 0.797383i \(-0.706217\pi\)
−0.603473 + 0.797383i \(0.706217\pi\)
\(332\) 0 0
\(333\) 25.8988 1.41924
\(334\) 0 0
\(335\) 1.74060 0.0950991
\(336\) 0 0
\(337\) −15.5450 −0.846788 −0.423394 0.905946i \(-0.639161\pi\)
−0.423394 + 0.905946i \(0.639161\pi\)
\(338\) 0 0
\(339\) 0.343547 0.0186589
\(340\) 0 0
\(341\) −4.24982 −0.230141
\(342\) 0 0
\(343\) −7.60679 −0.410728
\(344\) 0 0
\(345\) 4.01214 0.216006
\(346\) 0 0
\(347\) −27.1596 −1.45800 −0.729001 0.684512i \(-0.760015\pi\)
−0.729001 + 0.684512i \(0.760015\pi\)
\(348\) 0 0
\(349\) −10.5102 −0.562598 −0.281299 0.959620i \(-0.590765\pi\)
−0.281299 + 0.959620i \(0.590765\pi\)
\(350\) 0 0
\(351\) 12.4294 0.663432
\(352\) 0 0
\(353\) 17.5220 0.932602 0.466301 0.884626i \(-0.345586\pi\)
0.466301 + 0.884626i \(0.345586\pi\)
\(354\) 0 0
\(355\) −2.66894 −0.141653
\(356\) 0 0
\(357\) −0.934151 −0.0494405
\(358\) 0 0
\(359\) 4.12608 0.217766 0.108883 0.994055i \(-0.465273\pi\)
0.108883 + 0.994055i \(0.465273\pi\)
\(360\) 0 0
\(361\) 54.0118 2.84273
\(362\) 0 0
\(363\) 7.34972 0.385760
\(364\) 0 0
\(365\) −2.99901 −0.156975
\(366\) 0 0
\(367\) 11.6987 0.610669 0.305335 0.952245i \(-0.401232\pi\)
0.305335 + 0.952245i \(0.401232\pi\)
\(368\) 0 0
\(369\) 1.08349 0.0564041
\(370\) 0 0
\(371\) −3.08013 −0.159912
\(372\) 0 0
\(373\) −15.6029 −0.807888 −0.403944 0.914784i \(-0.632361\pi\)
−0.403944 + 0.914784i \(0.632361\pi\)
\(374\) 0 0
\(375\) 4.80785 0.248276
\(376\) 0 0
\(377\) −6.09269 −0.313789
\(378\) 0 0
\(379\) −18.7859 −0.964966 −0.482483 0.875905i \(-0.660265\pi\)
−0.482483 + 0.875905i \(0.660265\pi\)
\(380\) 0 0
\(381\) −14.3031 −0.732772
\(382\) 0 0
\(383\) 34.5809 1.76700 0.883500 0.468431i \(-0.155181\pi\)
0.883500 + 0.468431i \(0.155181\pi\)
\(384\) 0 0
\(385\) 0.467321 0.0238169
\(386\) 0 0
\(387\) 6.10928 0.310552
\(388\) 0 0
\(389\) −16.2021 −0.821479 −0.410739 0.911753i \(-0.634729\pi\)
−0.410739 + 0.911753i \(0.634729\pi\)
\(390\) 0 0
\(391\) −16.8651 −0.852903
\(392\) 0 0
\(393\) −0.491520 −0.0247939
\(394\) 0 0
\(395\) 8.00987 0.403020
\(396\) 0 0
\(397\) −16.9437 −0.850380 −0.425190 0.905104i \(-0.639793\pi\)
−0.425190 + 0.905104i \(0.639793\pi\)
\(398\) 0 0
\(399\) −3.79481 −0.189978
\(400\) 0 0
\(401\) 11.1156 0.555085 0.277542 0.960713i \(-0.410480\pi\)
0.277542 + 0.960713i \(0.410480\pi\)
\(402\) 0 0
\(403\) −9.17384 −0.456981
\(404\) 0 0
\(405\) 2.28968 0.113775
\(406\) 0 0
\(407\) −14.7387 −0.730571
\(408\) 0 0
\(409\) −20.7477 −1.02591 −0.512953 0.858417i \(-0.671448\pi\)
−0.512953 + 0.858417i \(0.671448\pi\)
\(410\) 0 0
\(411\) 4.07156 0.200835
\(412\) 0 0
\(413\) 5.49484 0.270383
\(414\) 0 0
\(415\) 7.33875 0.360245
\(416\) 0 0
\(417\) −5.14152 −0.251781
\(418\) 0 0
\(419\) 4.57319 0.223415 0.111707 0.993741i \(-0.464368\pi\)
0.111707 + 0.993741i \(0.464368\pi\)
\(420\) 0 0
\(421\) 3.78180 0.184314 0.0921569 0.995744i \(-0.470624\pi\)
0.0921569 + 0.995744i \(0.470624\pi\)
\(422\) 0 0
\(423\) 24.9182 1.21156
\(424\) 0 0
\(425\) −9.69277 −0.470169
\(426\) 0 0
\(427\) 0.198428 0.00960258
\(428\) 0 0
\(429\) −3.11519 −0.150403
\(430\) 0 0
\(431\) 2.19119 0.105546 0.0527729 0.998607i \(-0.483194\pi\)
0.0527729 + 0.998607i \(0.483194\pi\)
\(432\) 0 0
\(433\) 29.5781 1.42143 0.710717 0.703478i \(-0.248371\pi\)
0.710717 + 0.703478i \(0.248371\pi\)
\(434\) 0 0
\(435\) 1.05113 0.0503979
\(436\) 0 0
\(437\) −68.5111 −3.27733
\(438\) 0 0
\(439\) 0.470781 0.0224692 0.0112346 0.999937i \(-0.496424\pi\)
0.0112346 + 0.999937i \(0.496424\pi\)
\(440\) 0 0
\(441\) 15.7985 0.752308
\(442\) 0 0
\(443\) 34.4202 1.63536 0.817678 0.575676i \(-0.195261\pi\)
0.817678 + 0.575676i \(0.195261\pi\)
\(444\) 0 0
\(445\) 10.1290 0.480160
\(446\) 0 0
\(447\) −4.73031 −0.223736
\(448\) 0 0
\(449\) 5.30590 0.250401 0.125200 0.992131i \(-0.460043\pi\)
0.125200 + 0.992131i \(0.460043\pi\)
\(450\) 0 0
\(451\) −0.616601 −0.0290346
\(452\) 0 0
\(453\) 2.92333 0.137350
\(454\) 0 0
\(455\) 1.00878 0.0472923
\(456\) 0 0
\(457\) −18.1205 −0.847643 −0.423821 0.905746i \(-0.639312\pi\)
−0.423821 + 0.905746i \(0.639312\pi\)
\(458\) 0 0
\(459\) 9.01384 0.420730
\(460\) 0 0
\(461\) −16.9439 −0.789155 −0.394577 0.918863i \(-0.629109\pi\)
−0.394577 + 0.918863i \(0.629109\pi\)
\(462\) 0 0
\(463\) 29.1117 1.35294 0.676468 0.736472i \(-0.263510\pi\)
0.676468 + 0.736472i \(0.263510\pi\)
\(464\) 0 0
\(465\) 1.58270 0.0733960
\(466\) 0 0
\(467\) −14.0748 −0.651304 −0.325652 0.945490i \(-0.605584\pi\)
−0.325652 + 0.945490i \(0.605584\pi\)
\(468\) 0 0
\(469\) 1.54483 0.0713335
\(470\) 0 0
\(471\) 14.7605 0.680126
\(472\) 0 0
\(473\) −3.47672 −0.159860
\(474\) 0 0
\(475\) −39.3750 −1.80665
\(476\) 0 0
\(477\) 13.0893 0.599317
\(478\) 0 0
\(479\) −14.5663 −0.665550 −0.332775 0.943006i \(-0.607985\pi\)
−0.332775 + 0.943006i \(0.607985\pi\)
\(480\) 0 0
\(481\) −31.8156 −1.45067
\(482\) 0 0
\(483\) 3.56088 0.162026
\(484\) 0 0
\(485\) −8.32995 −0.378243
\(486\) 0 0
\(487\) −21.4294 −0.971061 −0.485530 0.874220i \(-0.661373\pi\)
−0.485530 + 0.874220i \(0.661373\pi\)
\(488\) 0 0
\(489\) 19.0543 0.861666
\(490\) 0 0
\(491\) 5.61968 0.253613 0.126806 0.991927i \(-0.459527\pi\)
0.126806 + 0.991927i \(0.459527\pi\)
\(492\) 0 0
\(493\) −4.41844 −0.198996
\(494\) 0 0
\(495\) −1.98592 −0.0892606
\(496\) 0 0
\(497\) −2.36876 −0.106253
\(498\) 0 0
\(499\) 33.1712 1.48495 0.742474 0.669875i \(-0.233653\pi\)
0.742474 + 0.669875i \(0.233653\pi\)
\(500\) 0 0
\(501\) 2.49013 0.111251
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −6.68239 −0.297362
\(506\) 0 0
\(507\) 3.66697 0.162856
\(508\) 0 0
\(509\) 20.2202 0.896245 0.448123 0.893972i \(-0.352093\pi\)
0.448123 + 0.893972i \(0.352093\pi\)
\(510\) 0 0
\(511\) −2.66170 −0.117747
\(512\) 0 0
\(513\) 36.6170 1.61668
\(514\) 0 0
\(515\) −4.49290 −0.197981
\(516\) 0 0
\(517\) −14.1807 −0.623665
\(518\) 0 0
\(519\) 18.6942 0.820585
\(520\) 0 0
\(521\) −1.99252 −0.0872940 −0.0436470 0.999047i \(-0.513898\pi\)
−0.0436470 + 0.999047i \(0.513898\pi\)
\(522\) 0 0
\(523\) 9.47470 0.414300 0.207150 0.978309i \(-0.433581\pi\)
0.207150 + 0.978309i \(0.433581\pi\)
\(524\) 0 0
\(525\) 2.04653 0.0893177
\(526\) 0 0
\(527\) −6.65290 −0.289805
\(528\) 0 0
\(529\) 41.2877 1.79512
\(530\) 0 0
\(531\) −23.3508 −1.01334
\(532\) 0 0
\(533\) −1.33102 −0.0576529
\(534\) 0 0
\(535\) 5.15466 0.222856
\(536\) 0 0
\(537\) 1.36556 0.0589281
\(538\) 0 0
\(539\) −8.99074 −0.387258
\(540\) 0 0
\(541\) 4.41783 0.189937 0.0949686 0.995480i \(-0.469725\pi\)
0.0949686 + 0.995480i \(0.469725\pi\)
\(542\) 0 0
\(543\) −6.41933 −0.275480
\(544\) 0 0
\(545\) 8.99172 0.385163
\(546\) 0 0
\(547\) −0.631365 −0.0269952 −0.0134976 0.999909i \(-0.504297\pi\)
−0.0134976 + 0.999909i \(0.504297\pi\)
\(548\) 0 0
\(549\) −0.843236 −0.0359884
\(550\) 0 0
\(551\) −17.9490 −0.764655
\(552\) 0 0
\(553\) 7.10897 0.302304
\(554\) 0 0
\(555\) 5.48893 0.232992
\(556\) 0 0
\(557\) 20.2181 0.856670 0.428335 0.903620i \(-0.359100\pi\)
0.428335 + 0.903620i \(0.359100\pi\)
\(558\) 0 0
\(559\) −7.50499 −0.317427
\(560\) 0 0
\(561\) −2.25915 −0.0953812
\(562\) 0 0
\(563\) −19.7104 −0.830693 −0.415346 0.909663i \(-0.636340\pi\)
−0.415346 + 0.909663i \(0.636340\pi\)
\(564\) 0 0
\(565\) −0.269045 −0.0113188
\(566\) 0 0
\(567\) 2.03215 0.0853424
\(568\) 0 0
\(569\) 0.0802769 0.00336538 0.00168269 0.999999i \(-0.499464\pi\)
0.00168269 + 0.999999i \(0.499464\pi\)
\(570\) 0 0
\(571\) −21.8823 −0.915746 −0.457873 0.889018i \(-0.651389\pi\)
−0.457873 + 0.889018i \(0.651389\pi\)
\(572\) 0 0
\(573\) −4.26283 −0.178082
\(574\) 0 0
\(575\) 36.9478 1.54083
\(576\) 0 0
\(577\) 16.1912 0.674048 0.337024 0.941496i \(-0.390580\pi\)
0.337024 + 0.941496i \(0.390580\pi\)
\(578\) 0 0
\(579\) 14.4679 0.601266
\(580\) 0 0
\(581\) 6.51333 0.270218
\(582\) 0 0
\(583\) −7.44897 −0.308505
\(584\) 0 0
\(585\) −4.28689 −0.177241
\(586\) 0 0
\(587\) −6.72740 −0.277670 −0.138835 0.990316i \(-0.544336\pi\)
−0.138835 + 0.990316i \(0.544336\pi\)
\(588\) 0 0
\(589\) −27.0261 −1.11359
\(590\) 0 0
\(591\) −5.08731 −0.209264
\(592\) 0 0
\(593\) −32.9777 −1.35423 −0.677116 0.735876i \(-0.736771\pi\)
−0.677116 + 0.735876i \(0.736771\pi\)
\(594\) 0 0
\(595\) 0.731570 0.0299914
\(596\) 0 0
\(597\) 18.6450 0.763090
\(598\) 0 0
\(599\) −39.4962 −1.61377 −0.806885 0.590709i \(-0.798848\pi\)
−0.806885 + 0.590709i \(0.798848\pi\)
\(600\) 0 0
\(601\) 30.9618 1.26296 0.631479 0.775393i \(-0.282448\pi\)
0.631479 + 0.775393i \(0.282448\pi\)
\(602\) 0 0
\(603\) −6.56488 −0.267343
\(604\) 0 0
\(605\) −5.75585 −0.234009
\(606\) 0 0
\(607\) −22.0700 −0.895795 −0.447898 0.894085i \(-0.647827\pi\)
−0.447898 + 0.894085i \(0.647827\pi\)
\(608\) 0 0
\(609\) 0.932906 0.0378033
\(610\) 0 0
\(611\) −30.6110 −1.23839
\(612\) 0 0
\(613\) −22.1152 −0.893225 −0.446612 0.894728i \(-0.647370\pi\)
−0.446612 + 0.894728i \(0.647370\pi\)
\(614\) 0 0
\(615\) 0.229632 0.00925966
\(616\) 0 0
\(617\) −19.9062 −0.801394 −0.400697 0.916211i \(-0.631232\pi\)
−0.400697 + 0.916211i \(0.631232\pi\)
\(618\) 0 0
\(619\) −3.52776 −0.141793 −0.0708964 0.997484i \(-0.522586\pi\)
−0.0708964 + 0.997484i \(0.522586\pi\)
\(620\) 0 0
\(621\) −34.3597 −1.37881
\(622\) 0 0
\(623\) 8.98975 0.360167
\(624\) 0 0
\(625\) 19.2754 0.771016
\(626\) 0 0
\(627\) −9.17734 −0.366508
\(628\) 0 0
\(629\) −23.0728 −0.919972
\(630\) 0 0
\(631\) −7.82512 −0.311513 −0.155757 0.987795i \(-0.549782\pi\)
−0.155757 + 0.987795i \(0.549782\pi\)
\(632\) 0 0
\(633\) 1.57246 0.0624997
\(634\) 0 0
\(635\) 11.2013 0.444512
\(636\) 0 0
\(637\) −19.4078 −0.768964
\(638\) 0 0
\(639\) 10.0662 0.398214
\(640\) 0 0
\(641\) 24.7259 0.976615 0.488307 0.872672i \(-0.337615\pi\)
0.488307 + 0.872672i \(0.337615\pi\)
\(642\) 0 0
\(643\) 23.8969 0.942403 0.471201 0.882026i \(-0.343820\pi\)
0.471201 + 0.882026i \(0.343820\pi\)
\(644\) 0 0
\(645\) 1.29479 0.0509822
\(646\) 0 0
\(647\) −1.92521 −0.0756878 −0.0378439 0.999284i \(-0.512049\pi\)
−0.0378439 + 0.999284i \(0.512049\pi\)
\(648\) 0 0
\(649\) 13.2887 0.521627
\(650\) 0 0
\(651\) 1.40469 0.0550541
\(652\) 0 0
\(653\) −23.8640 −0.933869 −0.466934 0.884292i \(-0.654642\pi\)
−0.466934 + 0.884292i \(0.654642\pi\)
\(654\) 0 0
\(655\) 0.384928 0.0150404
\(656\) 0 0
\(657\) 11.3111 0.441289
\(658\) 0 0
\(659\) −5.51936 −0.215004 −0.107502 0.994205i \(-0.534285\pi\)
−0.107502 + 0.994205i \(0.534285\pi\)
\(660\) 0 0
\(661\) −3.94338 −0.153380 −0.0766898 0.997055i \(-0.524435\pi\)
−0.0766898 + 0.997055i \(0.524435\pi\)
\(662\) 0 0
\(663\) −4.87669 −0.189395
\(664\) 0 0
\(665\) 2.97186 0.115244
\(666\) 0 0
\(667\) 16.8426 0.652147
\(668\) 0 0
\(669\) 11.1215 0.429981
\(670\) 0 0
\(671\) 0.479876 0.0185254
\(672\) 0 0
\(673\) 12.7473 0.491373 0.245687 0.969349i \(-0.420987\pi\)
0.245687 + 0.969349i \(0.420987\pi\)
\(674\) 0 0
\(675\) −19.7474 −0.760078
\(676\) 0 0
\(677\) 31.5077 1.21094 0.605469 0.795869i \(-0.292986\pi\)
0.605469 + 0.795869i \(0.292986\pi\)
\(678\) 0 0
\(679\) −7.39305 −0.283719
\(680\) 0 0
\(681\) −16.1937 −0.620543
\(682\) 0 0
\(683\) −22.1126 −0.846117 −0.423058 0.906102i \(-0.639043\pi\)
−0.423058 + 0.906102i \(0.639043\pi\)
\(684\) 0 0
\(685\) −3.18859 −0.121830
\(686\) 0 0
\(687\) −0.686690 −0.0261989
\(688\) 0 0
\(689\) −16.0796 −0.612586
\(690\) 0 0
\(691\) 36.4525 1.38672 0.693360 0.720591i \(-0.256130\pi\)
0.693360 + 0.720591i \(0.256130\pi\)
\(692\) 0 0
\(693\) −1.76256 −0.0669541
\(694\) 0 0
\(695\) 4.02652 0.152735
\(696\) 0 0
\(697\) −0.965261 −0.0365619
\(698\) 0 0
\(699\) −11.8857 −0.449558
\(700\) 0 0
\(701\) 25.1084 0.948330 0.474165 0.880436i \(-0.342750\pi\)
0.474165 + 0.880436i \(0.342750\pi\)
\(702\) 0 0
\(703\) −93.7287 −3.53505
\(704\) 0 0
\(705\) 5.28111 0.198898
\(706\) 0 0
\(707\) −5.93079 −0.223050
\(708\) 0 0
\(709\) −31.2932 −1.17524 −0.587619 0.809137i \(-0.699935\pi\)
−0.587619 + 0.809137i \(0.699935\pi\)
\(710\) 0 0
\(711\) −30.2102 −1.13297
\(712\) 0 0
\(713\) 25.3601 0.949743
\(714\) 0 0
\(715\) 2.43962 0.0912368
\(716\) 0 0
\(717\) −1.11262 −0.0415514
\(718\) 0 0
\(719\) −39.9603 −1.49027 −0.745134 0.666915i \(-0.767614\pi\)
−0.745134 + 0.666915i \(0.767614\pi\)
\(720\) 0 0
\(721\) −3.98756 −0.148505
\(722\) 0 0
\(723\) −17.5010 −0.650869
\(724\) 0 0
\(725\) 9.67985 0.359501
\(726\) 0 0
\(727\) −49.4728 −1.83484 −0.917422 0.397915i \(-0.869734\pi\)
−0.917422 + 0.397915i \(0.869734\pi\)
\(728\) 0 0
\(729\) 1.64065 0.0607646
\(730\) 0 0
\(731\) −5.44265 −0.201304
\(732\) 0 0
\(733\) 19.1027 0.705576 0.352788 0.935703i \(-0.385234\pi\)
0.352788 + 0.935703i \(0.385234\pi\)
\(734\) 0 0
\(735\) 3.34829 0.123504
\(736\) 0 0
\(737\) 3.73600 0.137617
\(738\) 0 0
\(739\) −15.3657 −0.565236 −0.282618 0.959233i \(-0.591203\pi\)
−0.282618 + 0.959233i \(0.591203\pi\)
\(740\) 0 0
\(741\) −19.8106 −0.727760
\(742\) 0 0
\(743\) −22.7367 −0.834127 −0.417064 0.908877i \(-0.636941\pi\)
−0.417064 + 0.908877i \(0.636941\pi\)
\(744\) 0 0
\(745\) 3.70449 0.135722
\(746\) 0 0
\(747\) −27.6790 −1.01272
\(748\) 0 0
\(749\) 4.57490 0.167163
\(750\) 0 0
\(751\) 14.4892 0.528717 0.264359 0.964424i \(-0.414840\pi\)
0.264359 + 0.964424i \(0.414840\pi\)
\(752\) 0 0
\(753\) −0.662944 −0.0241590
\(754\) 0 0
\(755\) −2.28937 −0.0833187
\(756\) 0 0
\(757\) −6.95561 −0.252806 −0.126403 0.991979i \(-0.540343\pi\)
−0.126403 + 0.991979i \(0.540343\pi\)
\(758\) 0 0
\(759\) 8.61161 0.312582
\(760\) 0 0
\(761\) −29.1935 −1.05826 −0.529132 0.848540i \(-0.677482\pi\)
−0.529132 + 0.848540i \(0.677482\pi\)
\(762\) 0 0
\(763\) 7.98038 0.288909
\(764\) 0 0
\(765\) −3.10887 −0.112402
\(766\) 0 0
\(767\) 28.6855 1.03577
\(768\) 0 0
\(769\) −17.5303 −0.632158 −0.316079 0.948733i \(-0.602367\pi\)
−0.316079 + 0.948733i \(0.602367\pi\)
\(770\) 0 0
\(771\) 19.0567 0.686309
\(772\) 0 0
\(773\) 31.8089 1.14409 0.572043 0.820223i \(-0.306151\pi\)
0.572043 + 0.820223i \(0.306151\pi\)
\(774\) 0 0
\(775\) 14.5751 0.523552
\(776\) 0 0
\(777\) 4.87157 0.174767
\(778\) 0 0
\(779\) −3.92119 −0.140491
\(780\) 0 0
\(781\) −5.72859 −0.204985
\(782\) 0 0
\(783\) −9.00182 −0.321699
\(784\) 0 0
\(785\) −11.5595 −0.412576
\(786\) 0 0
\(787\) 9.11212 0.324812 0.162406 0.986724i \(-0.448075\pi\)
0.162406 + 0.986724i \(0.448075\pi\)
\(788\) 0 0
\(789\) 3.46031 0.123190
\(790\) 0 0
\(791\) −0.238784 −0.00849019
\(792\) 0 0
\(793\) 1.03588 0.0367852
\(794\) 0 0
\(795\) 2.77411 0.0983877
\(796\) 0 0
\(797\) 10.0593 0.356320 0.178160 0.984002i \(-0.442986\pi\)
0.178160 + 0.984002i \(0.442986\pi\)
\(798\) 0 0
\(799\) −22.1992 −0.785351
\(800\) 0 0
\(801\) −38.2027 −1.34983
\(802\) 0 0
\(803\) −6.43703 −0.227158
\(804\) 0 0
\(805\) −2.78866 −0.0982874
\(806\) 0 0
\(807\) 21.1026 0.742845
\(808\) 0 0
\(809\) 35.3441 1.24263 0.621316 0.783560i \(-0.286598\pi\)
0.621316 + 0.783560i \(0.286598\pi\)
\(810\) 0 0
\(811\) 46.0787 1.61804 0.809021 0.587779i \(-0.199998\pi\)
0.809021 + 0.587779i \(0.199998\pi\)
\(812\) 0 0
\(813\) 11.8045 0.414002
\(814\) 0 0
\(815\) −14.9222 −0.522701
\(816\) 0 0
\(817\) −22.1097 −0.773521
\(818\) 0 0
\(819\) −3.80473 −0.132948
\(820\) 0 0
\(821\) 0.787685 0.0274904 0.0137452 0.999906i \(-0.495625\pi\)
0.0137452 + 0.999906i \(0.495625\pi\)
\(822\) 0 0
\(823\) 25.2719 0.880924 0.440462 0.897771i \(-0.354815\pi\)
0.440462 + 0.897771i \(0.354815\pi\)
\(824\) 0 0
\(825\) 4.94931 0.172313
\(826\) 0 0
\(827\) −8.39440 −0.291902 −0.145951 0.989292i \(-0.546624\pi\)
−0.145951 + 0.989292i \(0.546624\pi\)
\(828\) 0 0
\(829\) −15.5001 −0.538341 −0.269170 0.963093i \(-0.586750\pi\)
−0.269170 + 0.963093i \(0.586750\pi\)
\(830\) 0 0
\(831\) −8.57954 −0.297621
\(832\) 0 0
\(833\) −14.0746 −0.487656
\(834\) 0 0
\(835\) −1.95012 −0.0674865
\(836\) 0 0
\(837\) −13.5542 −0.468500
\(838\) 0 0
\(839\) −46.7422 −1.61372 −0.806860 0.590743i \(-0.798835\pi\)
−0.806860 + 0.590743i \(0.798835\pi\)
\(840\) 0 0
\(841\) −24.5875 −0.847843
\(842\) 0 0
\(843\) 12.7654 0.439665
\(844\) 0 0
\(845\) −2.87174 −0.0987910
\(846\) 0 0
\(847\) −5.10847 −0.175529
\(848\) 0 0
\(849\) 25.1482 0.863085
\(850\) 0 0
\(851\) 87.9508 3.01492
\(852\) 0 0
\(853\) 22.8445 0.782181 0.391090 0.920352i \(-0.372098\pi\)
0.391090 + 0.920352i \(0.372098\pi\)
\(854\) 0 0
\(855\) −12.6292 −0.431909
\(856\) 0 0
\(857\) 12.5208 0.427702 0.213851 0.976866i \(-0.431399\pi\)
0.213851 + 0.976866i \(0.431399\pi\)
\(858\) 0 0
\(859\) −20.3285 −0.693598 −0.346799 0.937940i \(-0.612731\pi\)
−0.346799 + 0.937940i \(0.612731\pi\)
\(860\) 0 0
\(861\) 0.203805 0.00694564
\(862\) 0 0
\(863\) 47.5849 1.61981 0.809905 0.586562i \(-0.199519\pi\)
0.809905 + 0.586562i \(0.199519\pi\)
\(864\) 0 0
\(865\) −14.6402 −0.497780
\(866\) 0 0
\(867\) 10.0523 0.341396
\(868\) 0 0
\(869\) 17.1923 0.583208
\(870\) 0 0
\(871\) 8.06469 0.273262
\(872\) 0 0
\(873\) 31.4174 1.06332
\(874\) 0 0
\(875\) −3.34172 −0.112971
\(876\) 0 0
\(877\) 10.2959 0.347667 0.173833 0.984775i \(-0.444385\pi\)
0.173833 + 0.984775i \(0.444385\pi\)
\(878\) 0 0
\(879\) 0.100215 0.00338018
\(880\) 0 0
\(881\) 29.4676 0.992788 0.496394 0.868097i \(-0.334657\pi\)
0.496394 + 0.868097i \(0.334657\pi\)
\(882\) 0 0
\(883\) 4.61286 0.155235 0.0776176 0.996983i \(-0.475269\pi\)
0.0776176 + 0.996983i \(0.475269\pi\)
\(884\) 0 0
\(885\) −4.94892 −0.166356
\(886\) 0 0
\(887\) −10.6445 −0.357407 −0.178704 0.983903i \(-0.557190\pi\)
−0.178704 + 0.983903i \(0.557190\pi\)
\(888\) 0 0
\(889\) 9.94149 0.333427
\(890\) 0 0
\(891\) 4.91455 0.164644
\(892\) 0 0
\(893\) −90.1799 −3.01775
\(894\) 0 0
\(895\) −1.06942 −0.0357468
\(896\) 0 0
\(897\) 18.5894 0.620681
\(898\) 0 0
\(899\) 6.64403 0.221591
\(900\) 0 0
\(901\) −11.6610 −0.388485
\(902\) 0 0
\(903\) 1.14916 0.0382416
\(904\) 0 0
\(905\) 5.02722 0.167111
\(906\) 0 0
\(907\) −19.3731 −0.643272 −0.321636 0.946863i \(-0.604233\pi\)
−0.321636 + 0.946863i \(0.604233\pi\)
\(908\) 0 0
\(909\) 25.2034 0.835945
\(910\) 0 0
\(911\) 31.9169 1.05745 0.528727 0.848792i \(-0.322670\pi\)
0.528727 + 0.848792i \(0.322670\pi\)
\(912\) 0 0
\(913\) 15.7518 0.521308
\(914\) 0 0
\(915\) −0.178714 −0.00590809
\(916\) 0 0
\(917\) 0.341634 0.0112817
\(918\) 0 0
\(919\) 31.1320 1.02695 0.513474 0.858105i \(-0.328358\pi\)
0.513474 + 0.858105i \(0.328358\pi\)
\(920\) 0 0
\(921\) 2.66854 0.0879314
\(922\) 0 0
\(923\) −12.3660 −0.407031
\(924\) 0 0
\(925\) 50.5475 1.66199
\(926\) 0 0
\(927\) 16.9455 0.556564
\(928\) 0 0
\(929\) −33.2020 −1.08932 −0.544661 0.838656i \(-0.683342\pi\)
−0.544661 + 0.838656i \(0.683342\pi\)
\(930\) 0 0
\(931\) −57.1753 −1.87384
\(932\) 0 0
\(933\) −3.21920 −0.105392
\(934\) 0 0
\(935\) 1.76922 0.0578598
\(936\) 0 0
\(937\) 7.71287 0.251969 0.125984 0.992032i \(-0.459791\pi\)
0.125984 + 0.992032i \(0.459791\pi\)
\(938\) 0 0
\(939\) 10.0409 0.327673
\(940\) 0 0
\(941\) −39.7214 −1.29488 −0.647440 0.762117i \(-0.724160\pi\)
−0.647440 + 0.762117i \(0.724160\pi\)
\(942\) 0 0
\(943\) 3.67947 0.119820
\(944\) 0 0
\(945\) 1.49045 0.0484844
\(946\) 0 0
\(947\) 3.37654 0.109723 0.0548614 0.998494i \(-0.482528\pi\)
0.0548614 + 0.998494i \(0.482528\pi\)
\(948\) 0 0
\(949\) −13.8952 −0.451059
\(950\) 0 0
\(951\) −12.1352 −0.393511
\(952\) 0 0
\(953\) 53.4780 1.73232 0.866161 0.499766i \(-0.166581\pi\)
0.866161 + 0.499766i \(0.166581\pi\)
\(954\) 0 0
\(955\) 3.33839 0.108028
\(956\) 0 0
\(957\) 2.25613 0.0729305
\(958\) 0 0
\(959\) −2.82996 −0.0913842
\(960\) 0 0
\(961\) −20.9960 −0.677290
\(962\) 0 0
\(963\) −19.4414 −0.626492
\(964\) 0 0
\(965\) −11.3304 −0.364738
\(966\) 0 0
\(967\) 0.790292 0.0254141 0.0127070 0.999919i \(-0.495955\pi\)
0.0127070 + 0.999919i \(0.495955\pi\)
\(968\) 0 0
\(969\) −14.3667 −0.461525
\(970\) 0 0
\(971\) −38.7817 −1.24456 −0.622282 0.782793i \(-0.713794\pi\)
−0.622282 + 0.782793i \(0.713794\pi\)
\(972\) 0 0
\(973\) 3.57365 0.114566
\(974\) 0 0
\(975\) 10.6838 0.342155
\(976\) 0 0
\(977\) 0.126026 0.00403193 0.00201597 0.999998i \(-0.499358\pi\)
0.00201597 + 0.999998i \(0.499358\pi\)
\(978\) 0 0
\(979\) 21.7408 0.694837
\(980\) 0 0
\(981\) −33.9134 −1.08277
\(982\) 0 0
\(983\) 6.93750 0.221272 0.110636 0.993861i \(-0.464711\pi\)
0.110636 + 0.993861i \(0.464711\pi\)
\(984\) 0 0
\(985\) 3.98407 0.126943
\(986\) 0 0
\(987\) 4.68712 0.149193
\(988\) 0 0
\(989\) 20.7468 0.659709
\(990\) 0 0
\(991\) −5.83365 −0.185312 −0.0926560 0.995698i \(-0.529536\pi\)
−0.0926560 + 0.995698i \(0.529536\pi\)
\(992\) 0 0
\(993\) 17.5525 0.557011
\(994\) 0 0
\(995\) −14.6016 −0.462903
\(996\) 0 0
\(997\) −40.2725 −1.27544 −0.637721 0.770267i \(-0.720123\pi\)
−0.637721 + 0.770267i \(0.720123\pi\)
\(998\) 0 0
\(999\) −47.0069 −1.48723
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 \(a_p\))