Properties

Label 8048.2.a.p.1.4
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.07636\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0763625 q^{3} +1.17276 q^{5} -0.469303 q^{7} -2.99417 q^{9} +O(q^{10})\) \(q-0.0763625 q^{3} +1.17276 q^{5} -0.469303 q^{7} -2.99417 q^{9} +5.74596 q^{11} -1.85873 q^{13} -0.0895546 q^{15} +5.22916 q^{17} -2.12602 q^{19} +0.0358371 q^{21} -0.171951 q^{23} -3.62464 q^{25} +0.457730 q^{27} -6.19149 q^{29} +0.396234 q^{31} -0.438776 q^{33} -0.550377 q^{35} -8.17999 q^{37} +0.141937 q^{39} -12.4282 q^{41} +4.97920 q^{43} -3.51143 q^{45} +0.521599 q^{47} -6.77976 q^{49} -0.399312 q^{51} +8.76106 q^{53} +6.73861 q^{55} +0.162349 q^{57} -3.35297 q^{59} -5.38243 q^{61} +1.40517 q^{63} -2.17983 q^{65} -8.42823 q^{67} +0.0131306 q^{69} -7.47643 q^{71} -4.60009 q^{73} +0.276787 q^{75} -2.69660 q^{77} +17.1992 q^{79} +8.94755 q^{81} -5.97721 q^{83} +6.13253 q^{85} +0.472798 q^{87} -4.25595 q^{89} +0.872306 q^{91} -0.0302574 q^{93} -2.49331 q^{95} -2.64532 q^{97} -17.2044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + O(q^{10}) \) \( 10q + 8q^{3} - q^{5} + 5q^{7} - 2q^{9} + 3q^{11} - 18q^{13} + 2q^{15} - 11q^{17} + q^{21} + 2q^{23} - 27q^{25} + 2q^{27} - 9q^{29} + 22q^{31} - 10q^{33} + 6q^{35} - 35q^{37} - 8q^{39} - 4q^{41} + 20q^{43} + 2q^{45} - 7q^{47} - 27q^{49} - 9q^{51} - 24q^{53} + 11q^{55} - 23q^{57} - 17q^{59} - 4q^{61} - 10q^{63} - 16q^{65} + 6q^{67} - 2q^{69} + q^{71} - 31q^{73} - 30q^{75} + 3q^{77} + 10q^{79} - 6q^{81} - 22q^{83} - 6q^{85} - 25q^{87} + q^{89} - 10q^{91} - 6q^{93} - 39q^{95} - 57q^{97} - 35q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.0763625 −0.0440879 −0.0220440 0.999757i \(-0.507017\pi\)
−0.0220440 + 0.999757i \(0.507017\pi\)
\(4\) 0 0
\(5\) 1.17276 0.524472 0.262236 0.965004i \(-0.415540\pi\)
0.262236 + 0.965004i \(0.415540\pi\)
\(6\) 0 0
\(7\) −0.469303 −0.177380 −0.0886899 0.996059i \(-0.528268\pi\)
−0.0886899 + 0.996059i \(0.528268\pi\)
\(8\) 0 0
\(9\) −2.99417 −0.998056
\(10\) 0 0
\(11\) 5.74596 1.73247 0.866237 0.499634i \(-0.166532\pi\)
0.866237 + 0.499634i \(0.166532\pi\)
\(12\) 0 0
\(13\) −1.85873 −0.515518 −0.257759 0.966209i \(-0.582984\pi\)
−0.257759 + 0.966209i \(0.582984\pi\)
\(14\) 0 0
\(15\) −0.0895546 −0.0231229
\(16\) 0 0
\(17\) 5.22916 1.26826 0.634129 0.773228i \(-0.281359\pi\)
0.634129 + 0.773228i \(0.281359\pi\)
\(18\) 0 0
\(19\) −2.12602 −0.487743 −0.243872 0.969808i \(-0.578418\pi\)
−0.243872 + 0.969808i \(0.578418\pi\)
\(20\) 0 0
\(21\) 0.0358371 0.00782030
\(22\) 0 0
\(23\) −0.171951 −0.0358543 −0.0179271 0.999839i \(-0.505707\pi\)
−0.0179271 + 0.999839i \(0.505707\pi\)
\(24\) 0 0
\(25\) −3.62464 −0.724929
\(26\) 0 0
\(27\) 0.457730 0.0880902
\(28\) 0 0
\(29\) −6.19149 −1.14973 −0.574865 0.818248i \(-0.694946\pi\)
−0.574865 + 0.818248i \(0.694946\pi\)
\(30\) 0 0
\(31\) 0.396234 0.0711658 0.0355829 0.999367i \(-0.488671\pi\)
0.0355829 + 0.999367i \(0.488671\pi\)
\(32\) 0 0
\(33\) −0.438776 −0.0763812
\(34\) 0 0
\(35\) −0.550377 −0.0930307
\(36\) 0 0
\(37\) −8.17999 −1.34478 −0.672391 0.740196i \(-0.734733\pi\)
−0.672391 + 0.740196i \(0.734733\pi\)
\(38\) 0 0
\(39\) 0.141937 0.0227281
\(40\) 0 0
\(41\) −12.4282 −1.94095 −0.970477 0.241193i \(-0.922461\pi\)
−0.970477 + 0.241193i \(0.922461\pi\)
\(42\) 0 0
\(43\) 4.97920 0.759321 0.379661 0.925126i \(-0.376041\pi\)
0.379661 + 0.925126i \(0.376041\pi\)
\(44\) 0 0
\(45\) −3.51143 −0.523453
\(46\) 0 0
\(47\) 0.521599 0.0760831 0.0380415 0.999276i \(-0.487888\pi\)
0.0380415 + 0.999276i \(0.487888\pi\)
\(48\) 0 0
\(49\) −6.77976 −0.968536
\(50\) 0 0
\(51\) −0.399312 −0.0559148
\(52\) 0 0
\(53\) 8.76106 1.20342 0.601712 0.798713i \(-0.294486\pi\)
0.601712 + 0.798713i \(0.294486\pi\)
\(54\) 0 0
\(55\) 6.73861 0.908634
\(56\) 0 0
\(57\) 0.162349 0.0215036
\(58\) 0 0
\(59\) −3.35297 −0.436519 −0.218260 0.975891i \(-0.570038\pi\)
−0.218260 + 0.975891i \(0.570038\pi\)
\(60\) 0 0
\(61\) −5.38243 −0.689150 −0.344575 0.938759i \(-0.611977\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(62\) 0 0
\(63\) 1.40517 0.177035
\(64\) 0 0
\(65\) −2.17983 −0.270375
\(66\) 0 0
\(67\) −8.42823 −1.02967 −0.514836 0.857289i \(-0.672147\pi\)
−0.514836 + 0.857289i \(0.672147\pi\)
\(68\) 0 0
\(69\) 0.0131306 0.00158074
\(70\) 0 0
\(71\) −7.47643 −0.887289 −0.443644 0.896203i \(-0.646315\pi\)
−0.443644 + 0.896203i \(0.646315\pi\)
\(72\) 0 0
\(73\) −4.60009 −0.538400 −0.269200 0.963084i \(-0.586759\pi\)
−0.269200 + 0.963084i \(0.586759\pi\)
\(74\) 0 0
\(75\) 0.276787 0.0319606
\(76\) 0 0
\(77\) −2.69660 −0.307306
\(78\) 0 0
\(79\) 17.1992 1.93506 0.967530 0.252758i \(-0.0813376\pi\)
0.967530 + 0.252758i \(0.0813376\pi\)
\(80\) 0 0
\(81\) 8.94755 0.994173
\(82\) 0 0
\(83\) −5.97721 −0.656084 −0.328042 0.944663i \(-0.606389\pi\)
−0.328042 + 0.944663i \(0.606389\pi\)
\(84\) 0 0
\(85\) 6.13253 0.665166
\(86\) 0 0
\(87\) 0.472798 0.0506892
\(88\) 0 0
\(89\) −4.25595 −0.451130 −0.225565 0.974228i \(-0.572423\pi\)
−0.225565 + 0.974228i \(0.572423\pi\)
\(90\) 0 0
\(91\) 0.872306 0.0914425
\(92\) 0 0
\(93\) −0.0302574 −0.00313755
\(94\) 0 0
\(95\) −2.49331 −0.255808
\(96\) 0 0
\(97\) −2.64532 −0.268592 −0.134296 0.990941i \(-0.542877\pi\)
−0.134296 + 0.990941i \(0.542877\pi\)
\(98\) 0 0
\(99\) −17.2044 −1.72911
\(100\) 0 0
\(101\) 6.39045 0.635873 0.317937 0.948112i \(-0.397010\pi\)
0.317937 + 0.948112i \(0.397010\pi\)
\(102\) 0 0
\(103\) 16.6014 1.63578 0.817890 0.575375i \(-0.195144\pi\)
0.817890 + 0.575375i \(0.195144\pi\)
\(104\) 0 0
\(105\) 0.0420282 0.00410153
\(106\) 0 0
\(107\) −9.15760 −0.885299 −0.442649 0.896695i \(-0.645961\pi\)
−0.442649 + 0.896695i \(0.645961\pi\)
\(108\) 0 0
\(109\) 6.51891 0.624398 0.312199 0.950017i \(-0.398934\pi\)
0.312199 + 0.950017i \(0.398934\pi\)
\(110\) 0 0
\(111\) 0.624645 0.0592887
\(112\) 0 0
\(113\) 1.36694 0.128591 0.0642954 0.997931i \(-0.479520\pi\)
0.0642954 + 0.997931i \(0.479520\pi\)
\(114\) 0 0
\(115\) −0.201656 −0.0188046
\(116\) 0 0
\(117\) 5.56535 0.514516
\(118\) 0 0
\(119\) −2.45406 −0.224963
\(120\) 0 0
\(121\) 22.0161 2.00146
\(122\) 0 0
\(123\) 0.949047 0.0855726
\(124\) 0 0
\(125\) −10.1146 −0.904677
\(126\) 0 0
\(127\) −6.77469 −0.601157 −0.300578 0.953757i \(-0.597180\pi\)
−0.300578 + 0.953757i \(0.597180\pi\)
\(128\) 0 0
\(129\) −0.380225 −0.0334769
\(130\) 0 0
\(131\) −16.6839 −1.45768 −0.728838 0.684687i \(-0.759939\pi\)
−0.728838 + 0.684687i \(0.759939\pi\)
\(132\) 0 0
\(133\) 0.997748 0.0865158
\(134\) 0 0
\(135\) 0.536805 0.0462008
\(136\) 0 0
\(137\) 13.0662 1.11632 0.558162 0.829732i \(-0.311507\pi\)
0.558162 + 0.829732i \(0.311507\pi\)
\(138\) 0 0
\(139\) 10.8468 0.920017 0.460008 0.887915i \(-0.347846\pi\)
0.460008 + 0.887915i \(0.347846\pi\)
\(140\) 0 0
\(141\) −0.0398306 −0.00335434
\(142\) 0 0
\(143\) −10.6802 −0.893122
\(144\) 0 0
\(145\) −7.26110 −0.603002
\(146\) 0 0
\(147\) 0.517719 0.0427008
\(148\) 0 0
\(149\) 0.0210826 0.00172716 0.000863578 1.00000i \(-0.499725\pi\)
0.000863578 1.00000i \(0.499725\pi\)
\(150\) 0 0
\(151\) −15.1704 −1.23455 −0.617276 0.786746i \(-0.711764\pi\)
−0.617276 + 0.786746i \(0.711764\pi\)
\(152\) 0 0
\(153\) −15.6570 −1.26579
\(154\) 0 0
\(155\) 0.464686 0.0373245
\(156\) 0 0
\(157\) 11.1437 0.889367 0.444684 0.895688i \(-0.353316\pi\)
0.444684 + 0.895688i \(0.353316\pi\)
\(158\) 0 0
\(159\) −0.669016 −0.0530565
\(160\) 0 0
\(161\) 0.0806970 0.00635982
\(162\) 0 0
\(163\) 10.3388 0.809797 0.404899 0.914362i \(-0.367307\pi\)
0.404899 + 0.914362i \(0.367307\pi\)
\(164\) 0 0
\(165\) −0.514578 −0.0400598
\(166\) 0 0
\(167\) 15.6444 1.21060 0.605300 0.795998i \(-0.293053\pi\)
0.605300 + 0.795998i \(0.293053\pi\)
\(168\) 0 0
\(169\) −9.54513 −0.734241
\(170\) 0 0
\(171\) 6.36567 0.486795
\(172\) 0 0
\(173\) −5.69316 −0.432843 −0.216422 0.976300i \(-0.569439\pi\)
−0.216422 + 0.976300i \(0.569439\pi\)
\(174\) 0 0
\(175\) 1.70105 0.128588
\(176\) 0 0
\(177\) 0.256041 0.0192452
\(178\) 0 0
\(179\) −10.8571 −0.811495 −0.405748 0.913985i \(-0.632989\pi\)
−0.405748 + 0.913985i \(0.632989\pi\)
\(180\) 0 0
\(181\) 6.26595 0.465744 0.232872 0.972507i \(-0.425188\pi\)
0.232872 + 0.972507i \(0.425188\pi\)
\(182\) 0 0
\(183\) 0.411016 0.0303832
\(184\) 0 0
\(185\) −9.59313 −0.705301
\(186\) 0 0
\(187\) 30.0466 2.19722
\(188\) 0 0
\(189\) −0.214814 −0.0156254
\(190\) 0 0
\(191\) −8.26296 −0.597887 −0.298943 0.954271i \(-0.596634\pi\)
−0.298943 + 0.954271i \(0.596634\pi\)
\(192\) 0 0
\(193\) −19.8469 −1.42861 −0.714306 0.699833i \(-0.753258\pi\)
−0.714306 + 0.699833i \(0.753258\pi\)
\(194\) 0 0
\(195\) 0.166458 0.0119203
\(196\) 0 0
\(197\) −4.24866 −0.302704 −0.151352 0.988480i \(-0.548363\pi\)
−0.151352 + 0.988480i \(0.548363\pi\)
\(198\) 0 0
\(199\) −4.63286 −0.328415 −0.164207 0.986426i \(-0.552507\pi\)
−0.164207 + 0.986426i \(0.552507\pi\)
\(200\) 0 0
\(201\) 0.643601 0.0453961
\(202\) 0 0
\(203\) 2.90568 0.203939
\(204\) 0 0
\(205\) −14.5752 −1.01798
\(206\) 0 0
\(207\) 0.514850 0.0357846
\(208\) 0 0
\(209\) −12.2161 −0.845002
\(210\) 0 0
\(211\) −10.2699 −0.707007 −0.353503 0.935433i \(-0.615010\pi\)
−0.353503 + 0.935433i \(0.615010\pi\)
\(212\) 0 0
\(213\) 0.570919 0.0391187
\(214\) 0 0
\(215\) 5.83939 0.398243
\(216\) 0 0
\(217\) −0.185954 −0.0126234
\(218\) 0 0
\(219\) 0.351275 0.0237369
\(220\) 0 0
\(221\) −9.71958 −0.653810
\(222\) 0 0
\(223\) −14.7887 −0.990326 −0.495163 0.868800i \(-0.664892\pi\)
−0.495163 + 0.868800i \(0.664892\pi\)
\(224\) 0 0
\(225\) 10.8528 0.723520
\(226\) 0 0
\(227\) −14.9154 −0.989969 −0.494984 0.868902i \(-0.664826\pi\)
−0.494984 + 0.868902i \(0.664826\pi\)
\(228\) 0 0
\(229\) −18.2488 −1.20592 −0.602959 0.797772i \(-0.706012\pi\)
−0.602959 + 0.797772i \(0.706012\pi\)
\(230\) 0 0
\(231\) 0.205919 0.0135485
\(232\) 0 0
\(233\) −16.6741 −1.09235 −0.546177 0.837670i \(-0.683918\pi\)
−0.546177 + 0.837670i \(0.683918\pi\)
\(234\) 0 0
\(235\) 0.611708 0.0399035
\(236\) 0 0
\(237\) −1.31337 −0.0853127
\(238\) 0 0
\(239\) −24.3691 −1.57631 −0.788153 0.615479i \(-0.788963\pi\)
−0.788153 + 0.615479i \(0.788963\pi\)
\(240\) 0 0
\(241\) 18.1071 1.16638 0.583190 0.812336i \(-0.301804\pi\)
0.583190 + 0.812336i \(0.301804\pi\)
\(242\) 0 0
\(243\) −2.05645 −0.131921
\(244\) 0 0
\(245\) −7.95100 −0.507971
\(246\) 0 0
\(247\) 3.95170 0.251441
\(248\) 0 0
\(249\) 0.456435 0.0289254
\(250\) 0 0
\(251\) −26.9687 −1.70225 −0.851124 0.524965i \(-0.824078\pi\)
−0.851124 + 0.524965i \(0.824078\pi\)
\(252\) 0 0
\(253\) −0.988024 −0.0621165
\(254\) 0 0
\(255\) −0.468295 −0.0293258
\(256\) 0 0
\(257\) 20.3022 1.26642 0.633208 0.773982i \(-0.281738\pi\)
0.633208 + 0.773982i \(0.281738\pi\)
\(258\) 0 0
\(259\) 3.83889 0.238537
\(260\) 0 0
\(261\) 18.5384 1.14750
\(262\) 0 0
\(263\) 12.0595 0.743622 0.371811 0.928309i \(-0.378737\pi\)
0.371811 + 0.928309i \(0.378737\pi\)
\(264\) 0 0
\(265\) 10.2746 0.631162
\(266\) 0 0
\(267\) 0.324995 0.0198894
\(268\) 0 0
\(269\) −25.0120 −1.52501 −0.762506 0.646982i \(-0.776031\pi\)
−0.762506 + 0.646982i \(0.776031\pi\)
\(270\) 0 0
\(271\) 18.0354 1.09557 0.547787 0.836618i \(-0.315470\pi\)
0.547787 + 0.836618i \(0.315470\pi\)
\(272\) 0 0
\(273\) −0.0666115 −0.00403151
\(274\) 0 0
\(275\) −20.8271 −1.25592
\(276\) 0 0
\(277\) −29.3688 −1.76460 −0.882301 0.470686i \(-0.844006\pi\)
−0.882301 + 0.470686i \(0.844006\pi\)
\(278\) 0 0
\(279\) −1.18639 −0.0710274
\(280\) 0 0
\(281\) 12.0977 0.721686 0.360843 0.932626i \(-0.382489\pi\)
0.360843 + 0.932626i \(0.382489\pi\)
\(282\) 0 0
\(283\) 8.04149 0.478017 0.239009 0.971017i \(-0.423178\pi\)
0.239009 + 0.971017i \(0.423178\pi\)
\(284\) 0 0
\(285\) 0.190395 0.0112780
\(286\) 0 0
\(287\) 5.83257 0.344286
\(288\) 0 0
\(289\) 10.3441 0.608477
\(290\) 0 0
\(291\) 0.202003 0.0118416
\(292\) 0 0
\(293\) −13.5236 −0.790056 −0.395028 0.918669i \(-0.629265\pi\)
−0.395028 + 0.918669i \(0.629265\pi\)
\(294\) 0 0
\(295\) −3.93221 −0.228942
\(296\) 0 0
\(297\) 2.63010 0.152614
\(298\) 0 0
\(299\) 0.319610 0.0184835
\(300\) 0 0
\(301\) −2.33675 −0.134688
\(302\) 0 0
\(303\) −0.487991 −0.0280343
\(304\) 0 0
\(305\) −6.31228 −0.361440
\(306\) 0 0
\(307\) −3.60632 −0.205824 −0.102912 0.994690i \(-0.532816\pi\)
−0.102912 + 0.994690i \(0.532816\pi\)
\(308\) 0 0
\(309\) −1.26772 −0.0721181
\(310\) 0 0
\(311\) 27.5438 1.56187 0.780934 0.624613i \(-0.214743\pi\)
0.780934 + 0.624613i \(0.214743\pi\)
\(312\) 0 0
\(313\) −30.2190 −1.70808 −0.854039 0.520209i \(-0.825854\pi\)
−0.854039 + 0.520209i \(0.825854\pi\)
\(314\) 0 0
\(315\) 1.64792 0.0928499
\(316\) 0 0
\(317\) −5.23152 −0.293831 −0.146916 0.989149i \(-0.546935\pi\)
−0.146916 + 0.989149i \(0.546935\pi\)
\(318\) 0 0
\(319\) −35.5761 −1.99188
\(320\) 0 0
\(321\) 0.699298 0.0390310
\(322\) 0 0
\(323\) −11.1173 −0.618584
\(324\) 0 0
\(325\) 6.73723 0.373714
\(326\) 0 0
\(327\) −0.497800 −0.0275284
\(328\) 0 0
\(329\) −0.244788 −0.0134956
\(330\) 0 0
\(331\) 5.56111 0.305666 0.152833 0.988252i \(-0.451160\pi\)
0.152833 + 0.988252i \(0.451160\pi\)
\(332\) 0 0
\(333\) 24.4923 1.34217
\(334\) 0 0
\(335\) −9.88426 −0.540035
\(336\) 0 0
\(337\) 1.20314 0.0655392 0.0327696 0.999463i \(-0.489567\pi\)
0.0327696 + 0.999463i \(0.489567\pi\)
\(338\) 0 0
\(339\) −0.104383 −0.00566930
\(340\) 0 0
\(341\) 2.27675 0.123293
\(342\) 0 0
\(343\) 6.46688 0.349178
\(344\) 0 0
\(345\) 0.0153990 0.000829054 0
\(346\) 0 0
\(347\) −18.8760 −1.01332 −0.506659 0.862147i \(-0.669120\pi\)
−0.506659 + 0.862147i \(0.669120\pi\)
\(348\) 0 0
\(349\) 18.3633 0.982966 0.491483 0.870887i \(-0.336455\pi\)
0.491483 + 0.870887i \(0.336455\pi\)
\(350\) 0 0
\(351\) −0.850795 −0.0454121
\(352\) 0 0
\(353\) −2.06519 −0.109919 −0.0549596 0.998489i \(-0.517503\pi\)
−0.0549596 + 0.998489i \(0.517503\pi\)
\(354\) 0 0
\(355\) −8.76802 −0.465358
\(356\) 0 0
\(357\) 0.187398 0.00991816
\(358\) 0 0
\(359\) 7.83605 0.413571 0.206786 0.978386i \(-0.433700\pi\)
0.206786 + 0.978386i \(0.433700\pi\)
\(360\) 0 0
\(361\) −14.4800 −0.762107
\(362\) 0 0
\(363\) −1.68121 −0.0882404
\(364\) 0 0
\(365\) −5.39478 −0.282376
\(366\) 0 0
\(367\) −27.3479 −1.42755 −0.713775 0.700375i \(-0.753016\pi\)
−0.713775 + 0.700375i \(0.753016\pi\)
\(368\) 0 0
\(369\) 37.2120 1.93718
\(370\) 0 0
\(371\) −4.11159 −0.213463
\(372\) 0 0
\(373\) 31.3381 1.62263 0.811313 0.584612i \(-0.198753\pi\)
0.811313 + 0.584612i \(0.198753\pi\)
\(374\) 0 0
\(375\) 0.772376 0.0398853
\(376\) 0 0
\(377\) 11.5083 0.592707
\(378\) 0 0
\(379\) 1.97192 0.101291 0.0506454 0.998717i \(-0.483872\pi\)
0.0506454 + 0.998717i \(0.483872\pi\)
\(380\) 0 0
\(381\) 0.517333 0.0265038
\(382\) 0 0
\(383\) 24.9455 1.27466 0.637328 0.770593i \(-0.280040\pi\)
0.637328 + 0.770593i \(0.280040\pi\)
\(384\) 0 0
\(385\) −3.16245 −0.161173
\(386\) 0 0
\(387\) −14.9086 −0.757845
\(388\) 0 0
\(389\) −8.98152 −0.455381 −0.227691 0.973734i \(-0.573117\pi\)
−0.227691 + 0.973734i \(0.573117\pi\)
\(390\) 0 0
\(391\) −0.899159 −0.0454724
\(392\) 0 0
\(393\) 1.27402 0.0642659
\(394\) 0 0
\(395\) 20.1704 1.01488
\(396\) 0 0
\(397\) −10.3125 −0.517569 −0.258784 0.965935i \(-0.583322\pi\)
−0.258784 + 0.965935i \(0.583322\pi\)
\(398\) 0 0
\(399\) −0.0761906 −0.00381430
\(400\) 0 0
\(401\) −22.2691 −1.11207 −0.556033 0.831160i \(-0.687677\pi\)
−0.556033 + 0.831160i \(0.687677\pi\)
\(402\) 0 0
\(403\) −0.736492 −0.0366873
\(404\) 0 0
\(405\) 10.4933 0.521416
\(406\) 0 0
\(407\) −47.0019 −2.32980
\(408\) 0 0
\(409\) −9.36108 −0.462876 −0.231438 0.972850i \(-0.574343\pi\)
−0.231438 + 0.972850i \(0.574343\pi\)
\(410\) 0 0
\(411\) −0.997771 −0.0492164
\(412\) 0 0
\(413\) 1.57356 0.0774297
\(414\) 0 0
\(415\) −7.00980 −0.344098
\(416\) 0 0
\(417\) −0.828292 −0.0405616
\(418\) 0 0
\(419\) 34.9797 1.70887 0.854436 0.519557i \(-0.173903\pi\)
0.854436 + 0.519557i \(0.173903\pi\)
\(420\) 0 0
\(421\) 15.9244 0.776107 0.388054 0.921637i \(-0.373147\pi\)
0.388054 + 0.921637i \(0.373147\pi\)
\(422\) 0 0
\(423\) −1.56176 −0.0759352
\(424\) 0 0
\(425\) −18.9538 −0.919396
\(426\) 0 0
\(427\) 2.52599 0.122241
\(428\) 0 0
\(429\) 0.815566 0.0393759
\(430\) 0 0
\(431\) 37.5257 1.80755 0.903775 0.428008i \(-0.140785\pi\)
0.903775 + 0.428008i \(0.140785\pi\)
\(432\) 0 0
\(433\) 27.7776 1.33491 0.667454 0.744651i \(-0.267384\pi\)
0.667454 + 0.744651i \(0.267384\pi\)
\(434\) 0 0
\(435\) 0.554476 0.0265851
\(436\) 0 0
\(437\) 0.365572 0.0174877
\(438\) 0 0
\(439\) −37.3507 −1.78265 −0.891327 0.453362i \(-0.850225\pi\)
−0.891327 + 0.453362i \(0.850225\pi\)
\(440\) 0 0
\(441\) 20.2997 0.966654
\(442\) 0 0
\(443\) −15.8245 −0.751844 −0.375922 0.926651i \(-0.622674\pi\)
−0.375922 + 0.926651i \(0.622674\pi\)
\(444\) 0 0
\(445\) −4.99119 −0.236605
\(446\) 0 0
\(447\) −0.00160992 −7.61467e−5 0
\(448\) 0 0
\(449\) −33.0395 −1.55923 −0.779616 0.626258i \(-0.784586\pi\)
−0.779616 + 0.626258i \(0.784586\pi\)
\(450\) 0 0
\(451\) −71.4118 −3.36265
\(452\) 0 0
\(453\) 1.15845 0.0544289
\(454\) 0 0
\(455\) 1.02300 0.0479591
\(456\) 0 0
\(457\) −6.38585 −0.298717 −0.149359 0.988783i \(-0.547721\pi\)
−0.149359 + 0.988783i \(0.547721\pi\)
\(458\) 0 0
\(459\) 2.39354 0.111721
\(460\) 0 0
\(461\) 4.10510 0.191193 0.0955967 0.995420i \(-0.469524\pi\)
0.0955967 + 0.995420i \(0.469524\pi\)
\(462\) 0 0
\(463\) 21.9482 1.02002 0.510011 0.860168i \(-0.329641\pi\)
0.510011 + 0.860168i \(0.329641\pi\)
\(464\) 0 0
\(465\) −0.0354846 −0.00164556
\(466\) 0 0
\(467\) 20.9539 0.969633 0.484816 0.874616i \(-0.338886\pi\)
0.484816 + 0.874616i \(0.338886\pi\)
\(468\) 0 0
\(469\) 3.95539 0.182643
\(470\) 0 0
\(471\) −0.850964 −0.0392104
\(472\) 0 0
\(473\) 28.6103 1.31550
\(474\) 0 0
\(475\) 7.70608 0.353579
\(476\) 0 0
\(477\) −26.2321 −1.20108
\(478\) 0 0
\(479\) −40.1617 −1.83503 −0.917517 0.397698i \(-0.869809\pi\)
−0.917517 + 0.397698i \(0.869809\pi\)
\(480\) 0 0
\(481\) 15.2044 0.693260
\(482\) 0 0
\(483\) −0.00616223 −0.000280391 0
\(484\) 0 0
\(485\) −3.10232 −0.140869
\(486\) 0 0
\(487\) 1.56804 0.0710547 0.0355273 0.999369i \(-0.488689\pi\)
0.0355273 + 0.999369i \(0.488689\pi\)
\(488\) 0 0
\(489\) −0.789497 −0.0357023
\(490\) 0 0
\(491\) −9.66243 −0.436059 −0.218030 0.975942i \(-0.569963\pi\)
−0.218030 + 0.975942i \(0.569963\pi\)
\(492\) 0 0
\(493\) −32.3763 −1.45815
\(494\) 0 0
\(495\) −20.1765 −0.906868
\(496\) 0 0
\(497\) 3.50871 0.157387
\(498\) 0 0
\(499\) 20.6363 0.923810 0.461905 0.886930i \(-0.347166\pi\)
0.461905 + 0.886930i \(0.347166\pi\)
\(500\) 0 0
\(501\) −1.19465 −0.0533728
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 7.49444 0.333498
\(506\) 0 0
\(507\) 0.728890 0.0323712
\(508\) 0 0
\(509\) −23.3284 −1.03401 −0.517006 0.855982i \(-0.672953\pi\)
−0.517006 + 0.855982i \(0.672953\pi\)
\(510\) 0 0
\(511\) 2.15883 0.0955012
\(512\) 0 0
\(513\) −0.973144 −0.0429654
\(514\) 0 0
\(515\) 19.4693 0.857921
\(516\) 0 0
\(517\) 2.99709 0.131812
\(518\) 0 0
\(519\) 0.434744 0.0190832
\(520\) 0 0
\(521\) −43.2647 −1.89546 −0.947730 0.319073i \(-0.896629\pi\)
−0.947730 + 0.319073i \(0.896629\pi\)
\(522\) 0 0
\(523\) 43.4082 1.89811 0.949054 0.315112i \(-0.102042\pi\)
0.949054 + 0.315112i \(0.102042\pi\)
\(524\) 0 0
\(525\) −0.129897 −0.00566916
\(526\) 0 0
\(527\) 2.07197 0.0902565
\(528\) 0 0
\(529\) −22.9704 −0.998714
\(530\) 0 0
\(531\) 10.0394 0.435671
\(532\) 0 0
\(533\) 23.1006 1.00060
\(534\) 0 0
\(535\) −10.7396 −0.464315
\(536\) 0 0
\(537\) 0.829073 0.0357771
\(538\) 0 0
\(539\) −38.9562 −1.67796
\(540\) 0 0
\(541\) 32.5657 1.40011 0.700054 0.714090i \(-0.253159\pi\)
0.700054 + 0.714090i \(0.253159\pi\)
\(542\) 0 0
\(543\) −0.478484 −0.0205337
\(544\) 0 0
\(545\) 7.64509 0.327480
\(546\) 0 0
\(547\) −27.8377 −1.19025 −0.595127 0.803631i \(-0.702898\pi\)
−0.595127 + 0.803631i \(0.702898\pi\)
\(548\) 0 0
\(549\) 16.1159 0.687811
\(550\) 0 0
\(551\) 13.1633 0.560773
\(552\) 0 0
\(553\) −8.07162 −0.343240
\(554\) 0 0
\(555\) 0.732556 0.0310953
\(556\) 0 0
\(557\) 15.7225 0.666182 0.333091 0.942895i \(-0.391908\pi\)
0.333091 + 0.942895i \(0.391908\pi\)
\(558\) 0 0
\(559\) −9.25498 −0.391444
\(560\) 0 0
\(561\) −2.29443 −0.0968710
\(562\) 0 0
\(563\) 24.7817 1.04442 0.522212 0.852816i \(-0.325107\pi\)
0.522212 + 0.852816i \(0.325107\pi\)
\(564\) 0 0
\(565\) 1.60309 0.0674423
\(566\) 0 0
\(567\) −4.19911 −0.176346
\(568\) 0 0
\(569\) 2.95346 0.123816 0.0619078 0.998082i \(-0.480282\pi\)
0.0619078 + 0.998082i \(0.480282\pi\)
\(570\) 0 0
\(571\) 10.7926 0.451656 0.225828 0.974167i \(-0.427491\pi\)
0.225828 + 0.974167i \(0.427491\pi\)
\(572\) 0 0
\(573\) 0.630981 0.0263596
\(574\) 0 0
\(575\) 0.623261 0.0259918
\(576\) 0 0
\(577\) −5.92593 −0.246700 −0.123350 0.992363i \(-0.539364\pi\)
−0.123350 + 0.992363i \(0.539364\pi\)
\(578\) 0 0
\(579\) 1.51556 0.0629845
\(580\) 0 0
\(581\) 2.80512 0.116376
\(582\) 0 0
\(583\) 50.3407 2.08490
\(584\) 0 0
\(585\) 6.52679 0.269850
\(586\) 0 0
\(587\) 14.8090 0.611234 0.305617 0.952155i \(-0.401137\pi\)
0.305617 + 0.952155i \(0.401137\pi\)
\(588\) 0 0
\(589\) −0.842403 −0.0347106
\(590\) 0 0
\(591\) 0.324438 0.0133456
\(592\) 0 0
\(593\) 33.4465 1.37348 0.686741 0.726902i \(-0.259041\pi\)
0.686741 + 0.726902i \(0.259041\pi\)
\(594\) 0 0
\(595\) −2.87801 −0.117987
\(596\) 0 0
\(597\) 0.353777 0.0144791
\(598\) 0 0
\(599\) −9.35823 −0.382367 −0.191183 0.981554i \(-0.561233\pi\)
−0.191183 + 0.981554i \(0.561233\pi\)
\(600\) 0 0
\(601\) −6.16182 −0.251346 −0.125673 0.992072i \(-0.540109\pi\)
−0.125673 + 0.992072i \(0.540109\pi\)
\(602\) 0 0
\(603\) 25.2355 1.02767
\(604\) 0 0
\(605\) 25.8195 1.04971
\(606\) 0 0
\(607\) −35.7361 −1.45048 −0.725242 0.688494i \(-0.758272\pi\)
−0.725242 + 0.688494i \(0.758272\pi\)
\(608\) 0 0
\(609\) −0.221885 −0.00899124
\(610\) 0 0
\(611\) −0.969511 −0.0392222
\(612\) 0 0
\(613\) −1.96528 −0.0793771 −0.0396885 0.999212i \(-0.512637\pi\)
−0.0396885 + 0.999212i \(0.512637\pi\)
\(614\) 0 0
\(615\) 1.11300 0.0448805
\(616\) 0 0
\(617\) −35.4461 −1.42701 −0.713503 0.700652i \(-0.752893\pi\)
−0.713503 + 0.700652i \(0.752893\pi\)
\(618\) 0 0
\(619\) 34.4643 1.38524 0.692618 0.721304i \(-0.256457\pi\)
0.692618 + 0.721304i \(0.256457\pi\)
\(620\) 0 0
\(621\) −0.0787071 −0.00315841
\(622\) 0 0
\(623\) 1.99733 0.0800213
\(624\) 0 0
\(625\) 6.26126 0.250451
\(626\) 0 0
\(627\) 0.932849 0.0372544
\(628\) 0 0
\(629\) −42.7745 −1.70553
\(630\) 0 0
\(631\) 29.7560 1.18457 0.592284 0.805729i \(-0.298226\pi\)
0.592284 + 0.805729i \(0.298226\pi\)
\(632\) 0 0
\(633\) 0.784233 0.0311705
\(634\) 0 0
\(635\) −7.94506 −0.315290
\(636\) 0 0
\(637\) 12.6017 0.499298
\(638\) 0 0
\(639\) 22.3857 0.885564
\(640\) 0 0
\(641\) −32.9327 −1.30077 −0.650383 0.759607i \(-0.725391\pi\)
−0.650383 + 0.759607i \(0.725391\pi\)
\(642\) 0 0
\(643\) 0.492253 0.0194126 0.00970628 0.999953i \(-0.496910\pi\)
0.00970628 + 0.999953i \(0.496910\pi\)
\(644\) 0 0
\(645\) −0.445911 −0.0175577
\(646\) 0 0
\(647\) −3.76376 −0.147969 −0.0739844 0.997259i \(-0.523571\pi\)
−0.0739844 + 0.997259i \(0.523571\pi\)
\(648\) 0 0
\(649\) −19.2660 −0.756258
\(650\) 0 0
\(651\) 0.0141999 0.000556538 0
\(652\) 0 0
\(653\) 18.5728 0.726809 0.363404 0.931631i \(-0.381614\pi\)
0.363404 + 0.931631i \(0.381614\pi\)
\(654\) 0 0
\(655\) −19.5661 −0.764510
\(656\) 0 0
\(657\) 13.7734 0.537353
\(658\) 0 0
\(659\) 34.1930 1.33197 0.665985 0.745965i \(-0.268012\pi\)
0.665985 + 0.745965i \(0.268012\pi\)
\(660\) 0 0
\(661\) 29.5439 1.14912 0.574562 0.818461i \(-0.305173\pi\)
0.574562 + 0.818461i \(0.305173\pi\)
\(662\) 0 0
\(663\) 0.742212 0.0288251
\(664\) 0 0
\(665\) 1.17012 0.0453751
\(666\) 0 0
\(667\) 1.06463 0.0412227
\(668\) 0 0
\(669\) 1.12930 0.0436614
\(670\) 0 0
\(671\) −30.9273 −1.19393
\(672\) 0 0
\(673\) −9.15185 −0.352778 −0.176389 0.984321i \(-0.556442\pi\)
−0.176389 + 0.984321i \(0.556442\pi\)
\(674\) 0 0
\(675\) −1.65911 −0.0638591
\(676\) 0 0
\(677\) −33.1256 −1.27312 −0.636561 0.771227i \(-0.719644\pi\)
−0.636561 + 0.771227i \(0.719644\pi\)
\(678\) 0 0
\(679\) 1.24146 0.0476427
\(680\) 0 0
\(681\) 1.13898 0.0436457
\(682\) 0 0
\(683\) −49.1452 −1.88049 −0.940245 0.340498i \(-0.889404\pi\)
−0.940245 + 0.340498i \(0.889404\pi\)
\(684\) 0 0
\(685\) 15.3235 0.585481
\(686\) 0 0
\(687\) 1.39353 0.0531664
\(688\) 0 0
\(689\) −16.2844 −0.620387
\(690\) 0 0
\(691\) −34.1013 −1.29727 −0.648637 0.761098i \(-0.724661\pi\)
−0.648637 + 0.761098i \(0.724661\pi\)
\(692\) 0 0
\(693\) 8.07406 0.306708
\(694\) 0 0
\(695\) 12.7207 0.482523
\(696\) 0 0
\(697\) −64.9889 −2.46163
\(698\) 0 0
\(699\) 1.27327 0.0481596
\(700\) 0 0
\(701\) 26.2590 0.991787 0.495894 0.868383i \(-0.334841\pi\)
0.495894 + 0.868383i \(0.334841\pi\)
\(702\) 0 0
\(703\) 17.3909 0.655909
\(704\) 0 0
\(705\) −0.0467116 −0.00175926
\(706\) 0 0
\(707\) −2.99905 −0.112791
\(708\) 0 0
\(709\) 28.4811 1.06963 0.534815 0.844969i \(-0.320381\pi\)
0.534815 + 0.844969i \(0.320381\pi\)
\(710\) 0 0
\(711\) −51.4973 −1.93130
\(712\) 0 0
\(713\) −0.0681329 −0.00255160
\(714\) 0 0
\(715\) −12.5252 −0.468418
\(716\) 0 0
\(717\) 1.86089 0.0694961
\(718\) 0 0
\(719\) −13.8368 −0.516024 −0.258012 0.966142i \(-0.583067\pi\)
−0.258012 + 0.966142i \(0.583067\pi\)
\(720\) 0 0
\(721\) −7.79106 −0.290154
\(722\) 0 0
\(723\) −1.38270 −0.0514233
\(724\) 0 0
\(725\) 22.4419 0.833473
\(726\) 0 0
\(727\) −9.61759 −0.356697 −0.178348 0.983967i \(-0.557075\pi\)
−0.178348 + 0.983967i \(0.557075\pi\)
\(728\) 0 0
\(729\) −26.6856 −0.988356
\(730\) 0 0
\(731\) 26.0370 0.963015
\(732\) 0 0
\(733\) −16.9530 −0.626175 −0.313087 0.949724i \(-0.601363\pi\)
−0.313087 + 0.949724i \(0.601363\pi\)
\(734\) 0 0
\(735\) 0.607158 0.0223954
\(736\) 0 0
\(737\) −48.4283 −1.78388
\(738\) 0 0
\(739\) −9.82452 −0.361401 −0.180700 0.983538i \(-0.557836\pi\)
−0.180700 + 0.983538i \(0.557836\pi\)
\(740\) 0 0
\(741\) −0.301762 −0.0110855
\(742\) 0 0
\(743\) −28.8650 −1.05896 −0.529478 0.848324i \(-0.677612\pi\)
−0.529478 + 0.848324i \(0.677612\pi\)
\(744\) 0 0
\(745\) 0.0247248 0.000905845 0
\(746\) 0 0
\(747\) 17.8968 0.654808
\(748\) 0 0
\(749\) 4.29769 0.157034
\(750\) 0 0
\(751\) 9.70834 0.354262 0.177131 0.984187i \(-0.443318\pi\)
0.177131 + 0.984187i \(0.443318\pi\)
\(752\) 0 0
\(753\) 2.05940 0.0750486
\(754\) 0 0
\(755\) −17.7912 −0.647489
\(756\) 0 0
\(757\) −5.99476 −0.217883 −0.108942 0.994048i \(-0.534746\pi\)
−0.108942 + 0.994048i \(0.534746\pi\)
\(758\) 0 0
\(759\) 0.0754480 0.00273859
\(760\) 0 0
\(761\) 15.4793 0.561123 0.280562 0.959836i \(-0.409479\pi\)
0.280562 + 0.959836i \(0.409479\pi\)
\(762\) 0 0
\(763\) −3.05934 −0.110756
\(764\) 0 0
\(765\) −18.3618 −0.663873
\(766\) 0 0
\(767\) 6.23226 0.225034
\(768\) 0 0
\(769\) −27.9740 −1.00877 −0.504384 0.863480i \(-0.668280\pi\)
−0.504384 + 0.863480i \(0.668280\pi\)
\(770\) 0 0
\(771\) −1.55033 −0.0558336
\(772\) 0 0
\(773\) 31.7330 1.14136 0.570679 0.821173i \(-0.306680\pi\)
0.570679 + 0.821173i \(0.306680\pi\)
\(774\) 0 0
\(775\) −1.43621 −0.0515901
\(776\) 0 0
\(777\) −0.293147 −0.0105166
\(778\) 0 0
\(779\) 26.4226 0.946687
\(780\) 0 0
\(781\) −42.9593 −1.53720
\(782\) 0 0
\(783\) −2.83403 −0.101280
\(784\) 0 0
\(785\) 13.0689 0.466448
\(786\) 0 0
\(787\) −19.1339 −0.682051 −0.341025 0.940054i \(-0.610774\pi\)
−0.341025 + 0.940054i \(0.610774\pi\)
\(788\) 0 0
\(789\) −0.920895 −0.0327847
\(790\) 0 0
\(791\) −0.641508 −0.0228094
\(792\) 0 0
\(793\) 10.0045 0.355270
\(794\) 0 0
\(795\) −0.784593 −0.0278266
\(796\) 0 0
\(797\) −2.45993 −0.0871352 −0.0435676 0.999050i \(-0.513872\pi\)
−0.0435676 + 0.999050i \(0.513872\pi\)
\(798\) 0 0
\(799\) 2.72752 0.0964929
\(800\) 0 0
\(801\) 12.7430 0.450253
\(802\) 0 0
\(803\) −26.4320 −0.932764
\(804\) 0 0
\(805\) 0.0946379 0.00333555
\(806\) 0 0
\(807\) 1.90998 0.0672346
\(808\) 0 0
\(809\) 16.9350 0.595404 0.297702 0.954659i \(-0.403780\pi\)
0.297702 + 0.954659i \(0.403780\pi\)
\(810\) 0 0
\(811\) 23.7584 0.834269 0.417135 0.908845i \(-0.363034\pi\)
0.417135 + 0.908845i \(0.363034\pi\)
\(812\) 0 0
\(813\) −1.37723 −0.0483016
\(814\) 0 0
\(815\) 12.1249 0.424716
\(816\) 0 0
\(817\) −10.5859 −0.370354
\(818\) 0 0
\(819\) −2.61183 −0.0912648
\(820\) 0 0
\(821\) 19.2765 0.672755 0.336378 0.941727i \(-0.390798\pi\)
0.336378 + 0.941727i \(0.390798\pi\)
\(822\) 0 0
\(823\) −52.8192 −1.84116 −0.920580 0.390553i \(-0.872284\pi\)
−0.920580 + 0.390553i \(0.872284\pi\)
\(824\) 0 0
\(825\) 1.59041 0.0553709
\(826\) 0 0
\(827\) 25.7144 0.894176 0.447088 0.894490i \(-0.352461\pi\)
0.447088 + 0.894490i \(0.352461\pi\)
\(828\) 0 0
\(829\) 23.3380 0.810562 0.405281 0.914192i \(-0.367174\pi\)
0.405281 + 0.914192i \(0.367174\pi\)
\(830\) 0 0
\(831\) 2.24268 0.0777976
\(832\) 0 0
\(833\) −35.4524 −1.22835
\(834\) 0 0
\(835\) 18.3471 0.634926
\(836\) 0 0
\(837\) 0.181368 0.00626900
\(838\) 0 0
\(839\) −18.8028 −0.649144 −0.324572 0.945861i \(-0.605220\pi\)
−0.324572 + 0.945861i \(0.605220\pi\)
\(840\) 0 0
\(841\) 9.33453 0.321880
\(842\) 0 0
\(843\) −0.923809 −0.0318177
\(844\) 0 0
\(845\) −11.1941 −0.385089
\(846\) 0 0
\(847\) −10.3322 −0.355019
\(848\) 0 0
\(849\) −0.614069 −0.0210748
\(850\) 0 0
\(851\) 1.40656 0.0482162
\(852\) 0 0
\(853\) −45.0553 −1.54266 −0.771332 0.636433i \(-0.780409\pi\)
−0.771332 + 0.636433i \(0.780409\pi\)
\(854\) 0 0
\(855\) 7.46538 0.255311
\(856\) 0 0
\(857\) −33.4362 −1.14216 −0.571079 0.820895i \(-0.693475\pi\)
−0.571079 + 0.820895i \(0.693475\pi\)
\(858\) 0 0
\(859\) −19.4483 −0.663567 −0.331784 0.943355i \(-0.607650\pi\)
−0.331784 + 0.943355i \(0.607650\pi\)
\(860\) 0 0
\(861\) −0.445390 −0.0151789
\(862\) 0 0
\(863\) 16.1628 0.550186 0.275093 0.961418i \(-0.411291\pi\)
0.275093 + 0.961418i \(0.411291\pi\)
\(864\) 0 0
\(865\) −6.67669 −0.227014
\(866\) 0 0
\(867\) −0.789902 −0.0268265
\(868\) 0 0
\(869\) 98.8259 3.35244
\(870\) 0 0
\(871\) 15.6658 0.530815
\(872\) 0 0
\(873\) 7.92054 0.268070
\(874\) 0 0
\(875\) 4.74681 0.160471
\(876\) 0 0
\(877\) −22.3959 −0.756255 −0.378127 0.925754i \(-0.623432\pi\)
−0.378127 + 0.925754i \(0.623432\pi\)
\(878\) 0 0
\(879\) 1.03269 0.0348319
\(880\) 0 0
\(881\) 10.4074 0.350633 0.175316 0.984512i \(-0.443905\pi\)
0.175316 + 0.984512i \(0.443905\pi\)
\(882\) 0 0
\(883\) 18.3582 0.617803 0.308902 0.951094i \(-0.400039\pi\)
0.308902 + 0.951094i \(0.400039\pi\)
\(884\) 0 0
\(885\) 0.300274 0.0100936
\(886\) 0 0
\(887\) 22.9758 0.771453 0.385726 0.922613i \(-0.373951\pi\)
0.385726 + 0.922613i \(0.373951\pi\)
\(888\) 0 0
\(889\) 3.17938 0.106633
\(890\) 0 0
\(891\) 51.4123 1.72238
\(892\) 0 0
\(893\) −1.10893 −0.0371090
\(894\) 0 0
\(895\) −12.7327 −0.425607
\(896\) 0 0
\(897\) −0.0244062 −0.000814900 0
\(898\) 0 0
\(899\) −2.45328 −0.0818215
\(900\) 0 0
\(901\) 45.8130 1.52625
\(902\) 0 0
\(903\) 0.178440 0.00593812
\(904\) 0 0
\(905\) 7.34843 0.244270
\(906\) 0 0
\(907\) −0.415835 −0.0138076 −0.00690378 0.999976i \(-0.502198\pi\)
−0.00690378 + 0.999976i \(0.502198\pi\)
\(908\) 0 0
\(909\) −19.1341 −0.634638
\(910\) 0 0
\(911\) 13.6089 0.450881 0.225441 0.974257i \(-0.427618\pi\)
0.225441 + 0.974257i \(0.427618\pi\)
\(912\) 0 0
\(913\) −34.3448 −1.13665
\(914\) 0 0
\(915\) 0.482022 0.0159351
\(916\) 0 0
\(917\) 7.82978 0.258562
\(918\) 0 0
\(919\) 14.8913 0.491218 0.245609 0.969369i \(-0.421012\pi\)
0.245609 + 0.969369i \(0.421012\pi\)
\(920\) 0 0
\(921\) 0.275388 0.00907433
\(922\) 0 0
\(923\) 13.8966 0.457414
\(924\) 0 0
\(925\) 29.6496 0.974871
\(926\) 0 0
\(927\) −49.7072 −1.63260
\(928\) 0 0
\(929\) −19.4977 −0.639699 −0.319850 0.947468i \(-0.603632\pi\)
−0.319850 + 0.947468i \(0.603632\pi\)
\(930\) 0 0
\(931\) 14.4139 0.472397
\(932\) 0 0
\(933\) −2.10332 −0.0688595
\(934\) 0 0
\(935\) 35.2373 1.15238
\(936\) 0 0
\(937\) 12.5125 0.408764 0.204382 0.978891i \(-0.434481\pi\)
0.204382 + 0.978891i \(0.434481\pi\)
\(938\) 0 0
\(939\) 2.30760 0.0753056
\(940\) 0 0
\(941\) 4.08256 0.133088 0.0665439 0.997783i \(-0.478803\pi\)
0.0665439 + 0.997783i \(0.478803\pi\)
\(942\) 0 0
\(943\) 2.13704 0.0695915
\(944\) 0 0
\(945\) −0.251924 −0.00819509
\(946\) 0 0
\(947\) 0.698574 0.0227006 0.0113503 0.999936i \(-0.496387\pi\)
0.0113503 + 0.999936i \(0.496387\pi\)
\(948\) 0 0
\(949\) 8.55032 0.277555
\(950\) 0 0
\(951\) 0.399492 0.0129544
\(952\) 0 0
\(953\) 7.31223 0.236866 0.118433 0.992962i \(-0.462213\pi\)
0.118433 + 0.992962i \(0.462213\pi\)
\(954\) 0 0
\(955\) −9.69044 −0.313575
\(956\) 0 0
\(957\) 2.71668 0.0878178
\(958\) 0 0
\(959\) −6.13202 −0.198013
\(960\) 0 0
\(961\) −30.8430 −0.994935
\(962\) 0 0
\(963\) 27.4194 0.883578
\(964\) 0 0
\(965\) −23.2756 −0.749267
\(966\) 0 0
\(967\) −38.1107 −1.22556 −0.612778 0.790255i \(-0.709948\pi\)
−0.612778 + 0.790255i \(0.709948\pi\)
\(968\) 0 0
\(969\) 0.848946 0.0272721
\(970\) 0 0
\(971\) 51.0424 1.63803 0.819014 0.573773i \(-0.194521\pi\)
0.819014 + 0.573773i \(0.194521\pi\)
\(972\) 0 0
\(973\) −5.09045 −0.163192
\(974\) 0 0
\(975\) −0.514472 −0.0164763
\(976\) 0 0
\(977\) 53.4134 1.70885 0.854424 0.519577i \(-0.173910\pi\)
0.854424 + 0.519577i \(0.173910\pi\)
\(978\) 0 0
\(979\) −24.4546 −0.781571
\(980\) 0 0
\(981\) −19.5187 −0.623185
\(982\) 0 0
\(983\) −1.20932 −0.0385714 −0.0192857 0.999814i \(-0.506139\pi\)
−0.0192857 + 0.999814i \(0.506139\pi\)
\(984\) 0 0
\(985\) −4.98264 −0.158760
\(986\) 0 0
\(987\) 0.0186926 0.000594993 0
\(988\) 0 0
\(989\) −0.856179 −0.0272249
\(990\) 0 0
\(991\) 13.3298 0.423433 0.211717 0.977331i \(-0.432095\pi\)
0.211717 + 0.977331i \(0.432095\pi\)
\(992\) 0 0
\(993\) −0.424660 −0.0134762
\(994\) 0 0
\(995\) −5.43321 −0.172244
\(996\) 0 0
\(997\) −39.2475 −1.24298 −0.621490 0.783422i \(-0.713472\pi\)
−0.621490 + 0.783422i \(0.713472\pi\)
\(998\) 0 0
\(999\) −3.74423 −0.118462
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 \(a_p\))