Properties

Label 8036.2.a.q.1.10
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
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 1.10
Root \(-0.741382\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.741382 q^{3} -2.48663 q^{5} -2.45035 q^{9} +O(q^{10})\) \(q+0.741382 q^{3} -2.48663 q^{5} -2.45035 q^{9} -5.32934 q^{11} +4.45475 q^{13} -1.84354 q^{15} -5.22789 q^{17} +1.97370 q^{19} -6.97574 q^{23} +1.18331 q^{25} -4.04079 q^{27} +3.94874 q^{29} +4.03917 q^{31} -3.95108 q^{33} +8.44085 q^{37} +3.30267 q^{39} -1.00000 q^{41} -10.5890 q^{43} +6.09311 q^{45} -4.67102 q^{47} -3.87586 q^{51} +2.15249 q^{53} +13.2521 q^{55} +1.46327 q^{57} +3.06901 q^{59} -12.0271 q^{61} -11.0773 q^{65} -15.6266 q^{67} -5.17169 q^{69} -0.549015 q^{71} -6.10132 q^{73} +0.877284 q^{75} +14.5674 q^{79} +4.35529 q^{81} -16.2369 q^{83} +12.9998 q^{85} +2.92752 q^{87} +3.02391 q^{89} +2.99457 q^{93} -4.90786 q^{95} +11.3079 q^{97} +13.0588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) 0.741382 0.428037 0.214019 0.976830i \(-0.431345\pi\)
0.214019 + 0.976830i \(0.431345\pi\)
\(4\) 0 0
\(5\) −2.48663 −1.11205 −0.556026 0.831165i \(-0.687675\pi\)
−0.556026 + 0.831165i \(0.687675\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.45035 −0.816784
\(10\) 0 0
\(11\) −5.32934 −1.60686 −0.803428 0.595401i \(-0.796993\pi\)
−0.803428 + 0.595401i \(0.796993\pi\)
\(12\) 0 0
\(13\) 4.45475 1.23553 0.617763 0.786364i \(-0.288039\pi\)
0.617763 + 0.786364i \(0.288039\pi\)
\(14\) 0 0
\(15\) −1.84354 −0.476000
\(16\) 0 0
\(17\) −5.22789 −1.26795 −0.633975 0.773354i \(-0.718578\pi\)
−0.633975 + 0.773354i \(0.718578\pi\)
\(18\) 0 0
\(19\) 1.97370 0.452798 0.226399 0.974035i \(-0.427305\pi\)
0.226399 + 0.974035i \(0.427305\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.97574 −1.45454 −0.727271 0.686351i \(-0.759212\pi\)
−0.727271 + 0.686351i \(0.759212\pi\)
\(24\) 0 0
\(25\) 1.18331 0.236662
\(26\) 0 0
\(27\) −4.04079 −0.777651
\(28\) 0 0
\(29\) 3.94874 0.733262 0.366631 0.930366i \(-0.380511\pi\)
0.366631 + 0.930366i \(0.380511\pi\)
\(30\) 0 0
\(31\) 4.03917 0.725456 0.362728 0.931895i \(-0.381845\pi\)
0.362728 + 0.931895i \(0.381845\pi\)
\(32\) 0 0
\(33\) −3.95108 −0.687794
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.44085 1.38767 0.693833 0.720136i \(-0.255920\pi\)
0.693833 + 0.720136i \(0.255920\pi\)
\(38\) 0 0
\(39\) 3.30267 0.528851
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −10.5890 −1.61481 −0.807406 0.589996i \(-0.799129\pi\)
−0.807406 + 0.589996i \(0.799129\pi\)
\(44\) 0 0
\(45\) 6.09311 0.908307
\(46\) 0 0
\(47\) −4.67102 −0.681338 −0.340669 0.940183i \(-0.610654\pi\)
−0.340669 + 0.940183i \(0.610654\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.87586 −0.542729
\(52\) 0 0
\(53\) 2.15249 0.295667 0.147833 0.989012i \(-0.452770\pi\)
0.147833 + 0.989012i \(0.452770\pi\)
\(54\) 0 0
\(55\) 13.2521 1.78691
\(56\) 0 0
\(57\) 1.46327 0.193814
\(58\) 0 0
\(59\) 3.06901 0.399551 0.199775 0.979842i \(-0.435979\pi\)
0.199775 + 0.979842i \(0.435979\pi\)
\(60\) 0 0
\(61\) −12.0271 −1.53992 −0.769958 0.638094i \(-0.779723\pi\)
−0.769958 + 0.638094i \(0.779723\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −11.0773 −1.37397
\(66\) 0 0
\(67\) −15.6266 −1.90909 −0.954546 0.298065i \(-0.903659\pi\)
−0.954546 + 0.298065i \(0.903659\pi\)
\(68\) 0 0
\(69\) −5.17169 −0.622598
\(70\) 0 0
\(71\) −0.549015 −0.0651560 −0.0325780 0.999469i \(-0.510372\pi\)
−0.0325780 + 0.999469i \(0.510372\pi\)
\(72\) 0 0
\(73\) −6.10132 −0.714106 −0.357053 0.934084i \(-0.616218\pi\)
−0.357053 + 0.934084i \(0.616218\pi\)
\(74\) 0 0
\(75\) 0.877284 0.101300
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 14.5674 1.63896 0.819478 0.573110i \(-0.194263\pi\)
0.819478 + 0.573110i \(0.194263\pi\)
\(80\) 0 0
\(81\) 4.35529 0.483921
\(82\) 0 0
\(83\) −16.2369 −1.78223 −0.891116 0.453776i \(-0.850077\pi\)
−0.891116 + 0.453776i \(0.850077\pi\)
\(84\) 0 0
\(85\) 12.9998 1.41003
\(86\) 0 0
\(87\) 2.92752 0.313863
\(88\) 0 0
\(89\) 3.02391 0.320534 0.160267 0.987074i \(-0.448764\pi\)
0.160267 + 0.987074i \(0.448764\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.99457 0.310522
\(94\) 0 0
\(95\) −4.90786 −0.503535
\(96\) 0 0
\(97\) 11.3079 1.14814 0.574070 0.818806i \(-0.305364\pi\)
0.574070 + 0.818806i \(0.305364\pi\)
\(98\) 0 0
\(99\) 13.0588 1.31246
\(100\) 0 0
\(101\) 9.36685 0.932037 0.466018 0.884775i \(-0.345688\pi\)
0.466018 + 0.884775i \(0.345688\pi\)
\(102\) 0 0
\(103\) 0.128628 0.0126741 0.00633703 0.999980i \(-0.497983\pi\)
0.00633703 + 0.999980i \(0.497983\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.7155 1.80930 0.904649 0.426157i \(-0.140133\pi\)
0.904649 + 0.426157i \(0.140133\pi\)
\(108\) 0 0
\(109\) 10.5776 1.01315 0.506577 0.862194i \(-0.330910\pi\)
0.506577 + 0.862194i \(0.330910\pi\)
\(110\) 0 0
\(111\) 6.25789 0.593973
\(112\) 0 0
\(113\) −5.86842 −0.552054 −0.276027 0.961150i \(-0.589018\pi\)
−0.276027 + 0.961150i \(0.589018\pi\)
\(114\) 0 0
\(115\) 17.3460 1.61753
\(116\) 0 0
\(117\) −10.9157 −1.00916
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 17.4019 1.58199
\(122\) 0 0
\(123\) −0.741382 −0.0668482
\(124\) 0 0
\(125\) 9.49068 0.848873
\(126\) 0 0
\(127\) 1.77348 0.157371 0.0786856 0.996899i \(-0.474928\pi\)
0.0786856 + 0.996899i \(0.474928\pi\)
\(128\) 0 0
\(129\) −7.85051 −0.691199
\(130\) 0 0
\(131\) −5.95356 −0.520165 −0.260083 0.965586i \(-0.583750\pi\)
−0.260083 + 0.965586i \(0.583750\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 10.0479 0.864789
\(136\) 0 0
\(137\) 22.2147 1.89793 0.948965 0.315380i \(-0.102132\pi\)
0.948965 + 0.315380i \(0.102132\pi\)
\(138\) 0 0
\(139\) −8.81730 −0.747873 −0.373937 0.927454i \(-0.621992\pi\)
−0.373937 + 0.927454i \(0.621992\pi\)
\(140\) 0 0
\(141\) −3.46301 −0.291638
\(142\) 0 0
\(143\) −23.7409 −1.98531
\(144\) 0 0
\(145\) −9.81903 −0.815426
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 12.1559 0.995853 0.497926 0.867219i \(-0.334095\pi\)
0.497926 + 0.867219i \(0.334095\pi\)
\(150\) 0 0
\(151\) 19.8222 1.61311 0.806553 0.591161i \(-0.201330\pi\)
0.806553 + 0.591161i \(0.201330\pi\)
\(152\) 0 0
\(153\) 12.8102 1.03564
\(154\) 0 0
\(155\) −10.0439 −0.806746
\(156\) 0 0
\(157\) −14.1217 −1.12704 −0.563519 0.826103i \(-0.690553\pi\)
−0.563519 + 0.826103i \(0.690553\pi\)
\(158\) 0 0
\(159\) 1.59581 0.126556
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.03291 −0.315882 −0.157941 0.987449i \(-0.550486\pi\)
−0.157941 + 0.987449i \(0.550486\pi\)
\(164\) 0 0
\(165\) 9.82485 0.764864
\(166\) 0 0
\(167\) −19.4677 −1.50646 −0.753229 0.657758i \(-0.771505\pi\)
−0.753229 + 0.657758i \(0.771505\pi\)
\(168\) 0 0
\(169\) 6.84483 0.526525
\(170\) 0 0
\(171\) −4.83626 −0.369838
\(172\) 0 0
\(173\) −3.03063 −0.230415 −0.115207 0.993341i \(-0.536753\pi\)
−0.115207 + 0.993341i \(0.536753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.27531 0.171022
\(178\) 0 0
\(179\) −4.73289 −0.353753 −0.176876 0.984233i \(-0.556599\pi\)
−0.176876 + 0.984233i \(0.556599\pi\)
\(180\) 0 0
\(181\) 23.6349 1.75677 0.878383 0.477957i \(-0.158623\pi\)
0.878383 + 0.477957i \(0.158623\pi\)
\(182\) 0 0
\(183\) −8.91670 −0.659141
\(184\) 0 0
\(185\) −20.9892 −1.54316
\(186\) 0 0
\(187\) 27.8612 2.03741
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 19.6528 1.42203 0.711014 0.703178i \(-0.248236\pi\)
0.711014 + 0.703178i \(0.248236\pi\)
\(192\) 0 0
\(193\) −21.7887 −1.56839 −0.784193 0.620517i \(-0.786923\pi\)
−0.784193 + 0.620517i \(0.786923\pi\)
\(194\) 0 0
\(195\) −8.21251 −0.588110
\(196\) 0 0
\(197\) −16.4791 −1.17409 −0.587044 0.809555i \(-0.699709\pi\)
−0.587044 + 0.809555i \(0.699709\pi\)
\(198\) 0 0
\(199\) 14.5780 1.03341 0.516705 0.856164i \(-0.327158\pi\)
0.516705 + 0.856164i \(0.327158\pi\)
\(200\) 0 0
\(201\) −11.5853 −0.817162
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.48663 0.173673
\(206\) 0 0
\(207\) 17.0930 1.18805
\(208\) 0 0
\(209\) −10.5185 −0.727582
\(210\) 0 0
\(211\) 18.7405 1.29015 0.645075 0.764119i \(-0.276826\pi\)
0.645075 + 0.764119i \(0.276826\pi\)
\(212\) 0 0
\(213\) −0.407029 −0.0278892
\(214\) 0 0
\(215\) 26.3310 1.79576
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −4.52341 −0.305664
\(220\) 0 0
\(221\) −23.2890 −1.56659
\(222\) 0 0
\(223\) 22.6617 1.51754 0.758770 0.651359i \(-0.225801\pi\)
0.758770 + 0.651359i \(0.225801\pi\)
\(224\) 0 0
\(225\) −2.89952 −0.193302
\(226\) 0 0
\(227\) −16.4497 −1.09180 −0.545901 0.837850i \(-0.683813\pi\)
−0.545901 + 0.837850i \(0.683813\pi\)
\(228\) 0 0
\(229\) 20.3549 1.34509 0.672546 0.740055i \(-0.265201\pi\)
0.672546 + 0.740055i \(0.265201\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.08432 0.136548 0.0682740 0.997667i \(-0.478251\pi\)
0.0682740 + 0.997667i \(0.478251\pi\)
\(234\) 0 0
\(235\) 11.6151 0.757684
\(236\) 0 0
\(237\) 10.8000 0.701534
\(238\) 0 0
\(239\) −1.18128 −0.0764108 −0.0382054 0.999270i \(-0.512164\pi\)
−0.0382054 + 0.999270i \(0.512164\pi\)
\(240\) 0 0
\(241\) −4.25967 −0.274390 −0.137195 0.990544i \(-0.543809\pi\)
−0.137195 + 0.990544i \(0.543809\pi\)
\(242\) 0 0
\(243\) 15.3513 0.984787
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.79235 0.559444
\(248\) 0 0
\(249\) −12.0377 −0.762861
\(250\) 0 0
\(251\) 25.1506 1.58749 0.793745 0.608251i \(-0.208128\pi\)
0.793745 + 0.608251i \(0.208128\pi\)
\(252\) 0 0
\(253\) 37.1761 2.33724
\(254\) 0 0
\(255\) 9.63782 0.603544
\(256\) 0 0
\(257\) −2.04026 −0.127268 −0.0636338 0.997973i \(-0.520269\pi\)
−0.0636338 + 0.997973i \(0.520269\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −9.67580 −0.598917
\(262\) 0 0
\(263\) 6.76783 0.417322 0.208661 0.977988i \(-0.433089\pi\)
0.208661 + 0.977988i \(0.433089\pi\)
\(264\) 0 0
\(265\) −5.35243 −0.328797
\(266\) 0 0
\(267\) 2.24188 0.137201
\(268\) 0 0
\(269\) −9.32017 −0.568261 −0.284130 0.958786i \(-0.591705\pi\)
−0.284130 + 0.958786i \(0.591705\pi\)
\(270\) 0 0
\(271\) 8.55575 0.519724 0.259862 0.965646i \(-0.416323\pi\)
0.259862 + 0.965646i \(0.416323\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.30626 −0.380282
\(276\) 0 0
\(277\) 23.8689 1.43414 0.717071 0.697000i \(-0.245482\pi\)
0.717071 + 0.697000i \(0.245482\pi\)
\(278\) 0 0
\(279\) −9.89739 −0.592541
\(280\) 0 0
\(281\) −5.77742 −0.344652 −0.172326 0.985040i \(-0.555128\pi\)
−0.172326 + 0.985040i \(0.555128\pi\)
\(282\) 0 0
\(283\) −12.9250 −0.768311 −0.384156 0.923268i \(-0.625507\pi\)
−0.384156 + 0.923268i \(0.625507\pi\)
\(284\) 0 0
\(285\) −3.63860 −0.215532
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 10.3308 0.607696
\(290\) 0 0
\(291\) 8.38345 0.491447
\(292\) 0 0
\(293\) −18.1943 −1.06292 −0.531460 0.847083i \(-0.678357\pi\)
−0.531460 + 0.847083i \(0.678357\pi\)
\(294\) 0 0
\(295\) −7.63147 −0.444321
\(296\) 0 0
\(297\) 21.5348 1.24957
\(298\) 0 0
\(299\) −31.0752 −1.79712
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 6.94442 0.398946
\(304\) 0 0
\(305\) 29.9070 1.71247
\(306\) 0 0
\(307\) −17.8287 −1.01754 −0.508769 0.860903i \(-0.669899\pi\)
−0.508769 + 0.860903i \(0.669899\pi\)
\(308\) 0 0
\(309\) 0.0953623 0.00542497
\(310\) 0 0
\(311\) 24.8260 1.40775 0.703877 0.710322i \(-0.251451\pi\)
0.703877 + 0.710322i \(0.251451\pi\)
\(312\) 0 0
\(313\) 5.38319 0.304276 0.152138 0.988359i \(-0.451384\pi\)
0.152138 + 0.988359i \(0.451384\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.6539 1.16004 0.580019 0.814603i \(-0.303045\pi\)
0.580019 + 0.814603i \(0.303045\pi\)
\(318\) 0 0
\(319\) −21.0442 −1.17825
\(320\) 0 0
\(321\) 13.8754 0.774447
\(322\) 0 0
\(323\) −10.3183 −0.574125
\(324\) 0 0
\(325\) 5.27135 0.292402
\(326\) 0 0
\(327\) 7.84208 0.433668
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −20.2209 −1.11144 −0.555721 0.831369i \(-0.687558\pi\)
−0.555721 + 0.831369i \(0.687558\pi\)
\(332\) 0 0
\(333\) −20.6831 −1.13342
\(334\) 0 0
\(335\) 38.8575 2.12301
\(336\) 0 0
\(337\) 11.9748 0.652308 0.326154 0.945317i \(-0.394247\pi\)
0.326154 + 0.945317i \(0.394247\pi\)
\(338\) 0 0
\(339\) −4.35074 −0.236300
\(340\) 0 0
\(341\) −21.5261 −1.16570
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 12.8600 0.692362
\(346\) 0 0
\(347\) −2.01201 −0.108011 −0.0540053 0.998541i \(-0.517199\pi\)
−0.0540053 + 0.998541i \(0.517199\pi\)
\(348\) 0 0
\(349\) −6.51102 −0.348527 −0.174264 0.984699i \(-0.555754\pi\)
−0.174264 + 0.984699i \(0.555754\pi\)
\(350\) 0 0
\(351\) −18.0007 −0.960808
\(352\) 0 0
\(353\) 20.0590 1.06763 0.533816 0.845601i \(-0.320757\pi\)
0.533816 + 0.845601i \(0.320757\pi\)
\(354\) 0 0
\(355\) 1.36519 0.0724570
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.73717 0.0916843 0.0458422 0.998949i \(-0.485403\pi\)
0.0458422 + 0.998949i \(0.485403\pi\)
\(360\) 0 0
\(361\) −15.1045 −0.794974
\(362\) 0 0
\(363\) 12.9014 0.677150
\(364\) 0 0
\(365\) 15.1717 0.794124
\(366\) 0 0
\(367\) −9.24439 −0.482553 −0.241276 0.970456i \(-0.577566\pi\)
−0.241276 + 0.970456i \(0.577566\pi\)
\(368\) 0 0
\(369\) 2.45035 0.127560
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.407031 −0.0210753 −0.0105376 0.999944i \(-0.503354\pi\)
−0.0105376 + 0.999944i \(0.503354\pi\)
\(374\) 0 0
\(375\) 7.03622 0.363349
\(376\) 0 0
\(377\) 17.5907 0.905965
\(378\) 0 0
\(379\) 18.4222 0.946284 0.473142 0.880986i \(-0.343120\pi\)
0.473142 + 0.880986i \(0.343120\pi\)
\(380\) 0 0
\(381\) 1.31483 0.0673607
\(382\) 0 0
\(383\) −2.29414 −0.117225 −0.0586124 0.998281i \(-0.518668\pi\)
−0.0586124 + 0.998281i \(0.518668\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 25.9469 1.31895
\(388\) 0 0
\(389\) −7.05178 −0.357540 −0.178770 0.983891i \(-0.557212\pi\)
−0.178770 + 0.983891i \(0.557212\pi\)
\(390\) 0 0
\(391\) 36.4684 1.84429
\(392\) 0 0
\(393\) −4.41386 −0.222650
\(394\) 0 0
\(395\) −36.2236 −1.82261
\(396\) 0 0
\(397\) −18.9163 −0.949383 −0.474691 0.880152i \(-0.657440\pi\)
−0.474691 + 0.880152i \(0.657440\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −28.7668 −1.43655 −0.718274 0.695761i \(-0.755067\pi\)
−0.718274 + 0.695761i \(0.755067\pi\)
\(402\) 0 0
\(403\) 17.9935 0.896321
\(404\) 0 0
\(405\) −10.8300 −0.538146
\(406\) 0 0
\(407\) −44.9842 −2.22978
\(408\) 0 0
\(409\) −5.08393 −0.251384 −0.125692 0.992069i \(-0.540115\pi\)
−0.125692 + 0.992069i \(0.540115\pi\)
\(410\) 0 0
\(411\) 16.4696 0.812385
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 40.3751 1.98194
\(416\) 0 0
\(417\) −6.53699 −0.320118
\(418\) 0 0
\(419\) 31.5598 1.54180 0.770899 0.636958i \(-0.219807\pi\)
0.770899 + 0.636958i \(0.219807\pi\)
\(420\) 0 0
\(421\) 31.7675 1.54825 0.774127 0.633031i \(-0.218189\pi\)
0.774127 + 0.633031i \(0.218189\pi\)
\(422\) 0 0
\(423\) 11.4456 0.556506
\(424\) 0 0
\(425\) −6.18621 −0.300075
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −17.6011 −0.849788
\(430\) 0 0
\(431\) −4.89423 −0.235747 −0.117873 0.993029i \(-0.537608\pi\)
−0.117873 + 0.993029i \(0.537608\pi\)
\(432\) 0 0
\(433\) 15.3722 0.738739 0.369369 0.929283i \(-0.379574\pi\)
0.369369 + 0.929283i \(0.379574\pi\)
\(434\) 0 0
\(435\) −7.27965 −0.349033
\(436\) 0 0
\(437\) −13.7680 −0.658614
\(438\) 0 0
\(439\) −7.49024 −0.357490 −0.178745 0.983895i \(-0.557204\pi\)
−0.178745 + 0.983895i \(0.557204\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.33920 −0.206162 −0.103081 0.994673i \(-0.532870\pi\)
−0.103081 + 0.994673i \(0.532870\pi\)
\(444\) 0 0
\(445\) −7.51935 −0.356451
\(446\) 0 0
\(447\) 9.01219 0.426262
\(448\) 0 0
\(449\) −18.4206 −0.869324 −0.434662 0.900594i \(-0.643132\pi\)
−0.434662 + 0.900594i \(0.643132\pi\)
\(450\) 0 0
\(451\) 5.32934 0.250949
\(452\) 0 0
\(453\) 14.6958 0.690469
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 34.3293 1.60586 0.802929 0.596075i \(-0.203274\pi\)
0.802929 + 0.596075i \(0.203274\pi\)
\(458\) 0 0
\(459\) 21.1248 0.986022
\(460\) 0 0
\(461\) 3.11137 0.144911 0.0724556 0.997372i \(-0.476916\pi\)
0.0724556 + 0.997372i \(0.476916\pi\)
\(462\) 0 0
\(463\) −16.1968 −0.752730 −0.376365 0.926471i \(-0.622826\pi\)
−0.376365 + 0.926471i \(0.622826\pi\)
\(464\) 0 0
\(465\) −7.44637 −0.345317
\(466\) 0 0
\(467\) −27.3607 −1.26610 −0.633052 0.774110i \(-0.718198\pi\)
−0.633052 + 0.774110i \(0.718198\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10.4696 −0.482414
\(472\) 0 0
\(473\) 56.4325 2.59477
\(474\) 0 0
\(475\) 2.33550 0.107160
\(476\) 0 0
\(477\) −5.27435 −0.241496
\(478\) 0 0
\(479\) 10.3553 0.473147 0.236573 0.971614i \(-0.423976\pi\)
0.236573 + 0.971614i \(0.423976\pi\)
\(480\) 0 0
\(481\) 37.6019 1.71450
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −28.1185 −1.27679
\(486\) 0 0
\(487\) 11.5693 0.524255 0.262128 0.965033i \(-0.415576\pi\)
0.262128 + 0.965033i \(0.415576\pi\)
\(488\) 0 0
\(489\) −2.98993 −0.135209
\(490\) 0 0
\(491\) −1.18896 −0.0536571 −0.0268286 0.999640i \(-0.508541\pi\)
−0.0268286 + 0.999640i \(0.508541\pi\)
\(492\) 0 0
\(493\) −20.6436 −0.929740
\(494\) 0 0
\(495\) −32.4723 −1.45952
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 15.5433 0.695812 0.347906 0.937529i \(-0.386893\pi\)
0.347906 + 0.937529i \(0.386893\pi\)
\(500\) 0 0
\(501\) −14.4330 −0.644820
\(502\) 0 0
\(503\) 0.661991 0.0295167 0.0147584 0.999891i \(-0.495302\pi\)
0.0147584 + 0.999891i \(0.495302\pi\)
\(504\) 0 0
\(505\) −23.2919 −1.03647
\(506\) 0 0
\(507\) 5.07463 0.225372
\(508\) 0 0
\(509\) −42.2412 −1.87231 −0.936154 0.351590i \(-0.885641\pi\)
−0.936154 + 0.351590i \(0.885641\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −7.97532 −0.352119
\(514\) 0 0
\(515\) −0.319849 −0.0140942
\(516\) 0 0
\(517\) 24.8934 1.09481
\(518\) 0 0
\(519\) −2.24685 −0.0986260
\(520\) 0 0
\(521\) −3.19485 −0.139969 −0.0699844 0.997548i \(-0.522295\pi\)
−0.0699844 + 0.997548i \(0.522295\pi\)
\(522\) 0 0
\(523\) 22.6853 0.991960 0.495980 0.868334i \(-0.334809\pi\)
0.495980 + 0.868334i \(0.334809\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.1163 −0.919842
\(528\) 0 0
\(529\) 25.6609 1.11569
\(530\) 0 0
\(531\) −7.52015 −0.326347
\(532\) 0 0
\(533\) −4.45475 −0.192957
\(534\) 0 0
\(535\) −46.5385 −2.01204
\(536\) 0 0
\(537\) −3.50888 −0.151419
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 9.75666 0.419472 0.209736 0.977758i \(-0.432740\pi\)
0.209736 + 0.977758i \(0.432740\pi\)
\(542\) 0 0
\(543\) 17.5225 0.751961
\(544\) 0 0
\(545\) −26.3027 −1.12668
\(546\) 0 0
\(547\) −28.2506 −1.20791 −0.603954 0.797020i \(-0.706409\pi\)
−0.603954 + 0.797020i \(0.706409\pi\)
\(548\) 0 0
\(549\) 29.4707 1.25778
\(550\) 0 0
\(551\) 7.79363 0.332020
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −15.5610 −0.660529
\(556\) 0 0
\(557\) 3.14602 0.133301 0.0666505 0.997776i \(-0.478769\pi\)
0.0666505 + 0.997776i \(0.478769\pi\)
\(558\) 0 0
\(559\) −47.1715 −1.99514
\(560\) 0 0
\(561\) 20.6558 0.872088
\(562\) 0 0
\(563\) 16.0597 0.676835 0.338418 0.940996i \(-0.390108\pi\)
0.338418 + 0.940996i \(0.390108\pi\)
\(564\) 0 0
\(565\) 14.5926 0.613913
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.87323 0.371985 0.185993 0.982551i \(-0.440450\pi\)
0.185993 + 0.982551i \(0.440450\pi\)
\(570\) 0 0
\(571\) −21.5143 −0.900343 −0.450172 0.892942i \(-0.648637\pi\)
−0.450172 + 0.892942i \(0.648637\pi\)
\(572\) 0 0
\(573\) 14.5702 0.608681
\(574\) 0 0
\(575\) −8.25445 −0.344234
\(576\) 0 0
\(577\) −12.1462 −0.505654 −0.252827 0.967512i \(-0.581360\pi\)
−0.252827 + 0.967512i \(0.581360\pi\)
\(578\) 0 0
\(579\) −16.1538 −0.671327
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −11.4713 −0.475094
\(584\) 0 0
\(585\) 27.1433 1.12224
\(586\) 0 0
\(587\) 35.2739 1.45591 0.727955 0.685625i \(-0.240471\pi\)
0.727955 + 0.685625i \(0.240471\pi\)
\(588\) 0 0
\(589\) 7.97211 0.328485
\(590\) 0 0
\(591\) −12.2173 −0.502553
\(592\) 0 0
\(593\) −15.7141 −0.645302 −0.322651 0.946518i \(-0.604574\pi\)
−0.322651 + 0.946518i \(0.604574\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.8079 0.442338
\(598\) 0 0
\(599\) −4.99253 −0.203989 −0.101995 0.994785i \(-0.532522\pi\)
−0.101995 + 0.994785i \(0.532522\pi\)
\(600\) 0 0
\(601\) −4.58505 −0.187028 −0.0935140 0.995618i \(-0.529810\pi\)
−0.0935140 + 0.995618i \(0.529810\pi\)
\(602\) 0 0
\(603\) 38.2906 1.55932
\(604\) 0 0
\(605\) −43.2720 −1.75926
\(606\) 0 0
\(607\) −20.5291 −0.833249 −0.416624 0.909079i \(-0.636787\pi\)
−0.416624 + 0.909079i \(0.636787\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.8082 −0.841811
\(612\) 0 0
\(613\) −37.8528 −1.52886 −0.764430 0.644707i \(-0.776980\pi\)
−0.764430 + 0.644707i \(0.776980\pi\)
\(614\) 0 0
\(615\) 1.84354 0.0743387
\(616\) 0 0
\(617\) 7.91820 0.318775 0.159387 0.987216i \(-0.449048\pi\)
0.159387 + 0.987216i \(0.449048\pi\)
\(618\) 0 0
\(619\) −9.12484 −0.366758 −0.183379 0.983042i \(-0.558704\pi\)
−0.183379 + 0.983042i \(0.558704\pi\)
\(620\) 0 0
\(621\) 28.1875 1.13113
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −29.5163 −1.18065
\(626\) 0 0
\(627\) −7.79824 −0.311432
\(628\) 0 0
\(629\) −44.1278 −1.75949
\(630\) 0 0
\(631\) −1.35091 −0.0537790 −0.0268895 0.999638i \(-0.508560\pi\)
−0.0268895 + 0.999638i \(0.508560\pi\)
\(632\) 0 0
\(633\) 13.8939 0.552232
\(634\) 0 0
\(635\) −4.40999 −0.175005
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.34528 0.0532184
\(640\) 0 0
\(641\) 29.5152 1.16578 0.582890 0.812551i \(-0.301922\pi\)
0.582890 + 0.812551i \(0.301922\pi\)
\(642\) 0 0
\(643\) 12.8306 0.505988 0.252994 0.967468i \(-0.418585\pi\)
0.252994 + 0.967468i \(0.418585\pi\)
\(644\) 0 0
\(645\) 19.5213 0.768650
\(646\) 0 0
\(647\) −38.2023 −1.50189 −0.750943 0.660367i \(-0.770401\pi\)
−0.750943 + 0.660367i \(0.770401\pi\)
\(648\) 0 0
\(649\) −16.3558 −0.642021
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.5985 0.414750 0.207375 0.978261i \(-0.433508\pi\)
0.207375 + 0.978261i \(0.433508\pi\)
\(654\) 0 0
\(655\) 14.8043 0.578451
\(656\) 0 0
\(657\) 14.9504 0.583271
\(658\) 0 0
\(659\) 21.7450 0.847065 0.423533 0.905881i \(-0.360790\pi\)
0.423533 + 0.905881i \(0.360790\pi\)
\(660\) 0 0
\(661\) 20.5702 0.800089 0.400045 0.916496i \(-0.368995\pi\)
0.400045 + 0.916496i \(0.368995\pi\)
\(662\) 0 0
\(663\) −17.2660 −0.670557
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −27.5454 −1.06656
\(668\) 0 0
\(669\) 16.8010 0.649563
\(670\) 0 0
\(671\) 64.0967 2.47443
\(672\) 0 0
\(673\) 0.627387 0.0241840 0.0120920 0.999927i \(-0.496151\pi\)
0.0120920 + 0.999927i \(0.496151\pi\)
\(674\) 0 0
\(675\) −4.78151 −0.184040
\(676\) 0 0
\(677\) −33.8225 −1.29990 −0.649951 0.759976i \(-0.725211\pi\)
−0.649951 + 0.759976i \(0.725211\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −12.1955 −0.467332
\(682\) 0 0
\(683\) 47.8189 1.82974 0.914869 0.403751i \(-0.132294\pi\)
0.914869 + 0.403751i \(0.132294\pi\)
\(684\) 0 0
\(685\) −55.2397 −2.11060
\(686\) 0 0
\(687\) 15.0908 0.575749
\(688\) 0 0
\(689\) 9.58880 0.365304
\(690\) 0 0
\(691\) −34.8561 −1.32599 −0.662995 0.748624i \(-0.730715\pi\)
−0.662995 + 0.748624i \(0.730715\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.9253 0.831675
\(696\) 0 0
\(697\) 5.22789 0.198020
\(698\) 0 0
\(699\) 1.54527 0.0584476
\(700\) 0 0
\(701\) 38.9927 1.47274 0.736368 0.676582i \(-0.236539\pi\)
0.736368 + 0.676582i \(0.236539\pi\)
\(702\) 0 0
\(703\) 16.6597 0.628333
\(704\) 0 0
\(705\) 8.61120 0.324317
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 36.8075 1.38233 0.691167 0.722695i \(-0.257097\pi\)
0.691167 + 0.722695i \(0.257097\pi\)
\(710\) 0 0
\(711\) −35.6952 −1.33867
\(712\) 0 0
\(713\) −28.1762 −1.05521
\(714\) 0 0
\(715\) 59.0347 2.20777
\(716\) 0 0
\(717\) −0.875782 −0.0327067
\(718\) 0 0
\(719\) 5.14550 0.191895 0.0959474 0.995386i \(-0.469412\pi\)
0.0959474 + 0.995386i \(0.469412\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.15804 −0.117449
\(724\) 0 0
\(725\) 4.67258 0.173535
\(726\) 0 0
\(727\) −20.7881 −0.770987 −0.385493 0.922711i \(-0.625969\pi\)
−0.385493 + 0.922711i \(0.625969\pi\)
\(728\) 0 0
\(729\) −1.68468 −0.0623955
\(730\) 0 0
\(731\) 55.3583 2.04750
\(732\) 0 0
\(733\) 1.34880 0.0498191 0.0249096 0.999690i \(-0.492070\pi\)
0.0249096 + 0.999690i \(0.492070\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 83.2794 3.06764
\(738\) 0 0
\(739\) 12.1004 0.445119 0.222559 0.974919i \(-0.428559\pi\)
0.222559 + 0.974919i \(0.428559\pi\)
\(740\) 0 0
\(741\) 6.51849 0.239463
\(742\) 0 0
\(743\) 0.927403 0.0340231 0.0170116 0.999855i \(-0.494585\pi\)
0.0170116 + 0.999855i \(0.494585\pi\)
\(744\) 0 0
\(745\) −30.2273 −1.10744
\(746\) 0 0
\(747\) 39.7861 1.45570
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −3.82085 −0.139425 −0.0697124 0.997567i \(-0.522208\pi\)
−0.0697124 + 0.997567i \(0.522208\pi\)
\(752\) 0 0
\(753\) 18.6462 0.679505
\(754\) 0 0
\(755\) −49.2904 −1.79386
\(756\) 0 0
\(757\) 11.5073 0.418240 0.209120 0.977890i \(-0.432940\pi\)
0.209120 + 0.977890i \(0.432940\pi\)
\(758\) 0 0
\(759\) 27.5617 1.00043
\(760\) 0 0
\(761\) −16.9439 −0.614215 −0.307108 0.951675i \(-0.599361\pi\)
−0.307108 + 0.951675i \(0.599361\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −31.8541 −1.15169
\(766\) 0 0
\(767\) 13.6717 0.493655
\(768\) 0 0
\(769\) −26.5516 −0.957476 −0.478738 0.877958i \(-0.658906\pi\)
−0.478738 + 0.877958i \(0.658906\pi\)
\(770\) 0 0
\(771\) −1.51261 −0.0544753
\(772\) 0 0
\(773\) −17.1372 −0.616382 −0.308191 0.951325i \(-0.599724\pi\)
−0.308191 + 0.951325i \(0.599724\pi\)
\(774\) 0 0
\(775\) 4.77959 0.171688
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.97370 −0.0707152
\(780\) 0 0
\(781\) 2.92589 0.104696
\(782\) 0 0
\(783\) −15.9560 −0.570222
\(784\) 0 0
\(785\) 35.1155 1.25333
\(786\) 0 0
\(787\) −14.2517 −0.508017 −0.254008 0.967202i \(-0.581749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(788\) 0 0
\(789\) 5.01755 0.178629
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −53.5779 −1.90261
\(794\) 0 0
\(795\) −3.96819 −0.140737
\(796\) 0 0
\(797\) −21.5237 −0.762409 −0.381205 0.924491i \(-0.624491\pi\)
−0.381205 + 0.924491i \(0.624491\pi\)
\(798\) 0 0
\(799\) 24.4196 0.863902
\(800\) 0 0
\(801\) −7.40966 −0.261807
\(802\) 0 0
\(803\) 32.5160 1.14747
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −6.90981 −0.243237
\(808\) 0 0
\(809\) −2.97942 −0.104751 −0.0523755 0.998627i \(-0.516679\pi\)
−0.0523755 + 0.998627i \(0.516679\pi\)
\(810\) 0 0
\(811\) 14.2556 0.500582 0.250291 0.968171i \(-0.419474\pi\)
0.250291 + 0.968171i \(0.419474\pi\)
\(812\) 0 0
\(813\) 6.34307 0.222461
\(814\) 0 0
\(815\) 10.0283 0.351277
\(816\) 0 0
\(817\) −20.8996 −0.731183
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 30.5905 1.06762 0.533808 0.845606i \(-0.320760\pi\)
0.533808 + 0.845606i \(0.320760\pi\)
\(822\) 0 0
\(823\) −1.42460 −0.0496586 −0.0248293 0.999692i \(-0.507904\pi\)
−0.0248293 + 0.999692i \(0.507904\pi\)
\(824\) 0 0
\(825\) −4.67534 −0.162775
\(826\) 0 0
\(827\) −52.6818 −1.83193 −0.915963 0.401263i \(-0.868571\pi\)
−0.915963 + 0.401263i \(0.868571\pi\)
\(828\) 0 0
\(829\) 1.57709 0.0547746 0.0273873 0.999625i \(-0.491281\pi\)
0.0273873 + 0.999625i \(0.491281\pi\)
\(830\) 0 0
\(831\) 17.6960 0.613866
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 48.4090 1.67526
\(836\) 0 0
\(837\) −16.3215 −0.564152
\(838\) 0 0
\(839\) 27.1309 0.936662 0.468331 0.883553i \(-0.344856\pi\)
0.468331 + 0.883553i \(0.344856\pi\)
\(840\) 0 0
\(841\) −13.4075 −0.462326
\(842\) 0 0
\(843\) −4.28327 −0.147524
\(844\) 0 0
\(845\) −17.0205 −0.585524
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −9.58236 −0.328866
\(850\) 0 0
\(851\) −58.8811 −2.01842
\(852\) 0 0
\(853\) 25.8997 0.886788 0.443394 0.896327i \(-0.353774\pi\)
0.443394 + 0.896327i \(0.353774\pi\)
\(854\) 0 0
\(855\) 12.0260 0.411280
\(856\) 0 0
\(857\) 30.3188 1.03567 0.517836 0.855480i \(-0.326738\pi\)
0.517836 + 0.855480i \(0.326738\pi\)
\(858\) 0 0
\(859\) 8.94984 0.305365 0.152682 0.988275i \(-0.451209\pi\)
0.152682 + 0.988275i \(0.451209\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 21.3881 0.728059 0.364029 0.931387i \(-0.381401\pi\)
0.364029 + 0.931387i \(0.381401\pi\)
\(864\) 0 0
\(865\) 7.53604 0.256233
\(866\) 0 0
\(867\) 7.65910 0.260117
\(868\) 0 0
\(869\) −77.6345 −2.63357
\(870\) 0 0
\(871\) −69.6126 −2.35873
\(872\) 0 0
\(873\) −27.7083 −0.937783
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 49.4718 1.67055 0.835273 0.549836i \(-0.185310\pi\)
0.835273 + 0.549836i \(0.185310\pi\)
\(878\) 0 0
\(879\) −13.4889 −0.454969
\(880\) 0 0
\(881\) −47.6776 −1.60630 −0.803149 0.595778i \(-0.796844\pi\)
−0.803149 + 0.595778i \(0.796844\pi\)
\(882\) 0 0
\(883\) 5.47242 0.184162 0.0920809 0.995752i \(-0.470648\pi\)
0.0920809 + 0.995752i \(0.470648\pi\)
\(884\) 0 0
\(885\) −5.65783 −0.190186
\(886\) 0 0
\(887\) −31.9348 −1.07226 −0.536132 0.844134i \(-0.680115\pi\)
−0.536132 + 0.844134i \(0.680115\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −23.2108 −0.777591
\(892\) 0 0
\(893\) −9.21919 −0.308508
\(894\) 0 0
\(895\) 11.7689 0.393392
\(896\) 0 0
\(897\) −23.0386 −0.769236
\(898\) 0 0
\(899\) 15.9496 0.531950
\(900\) 0 0
\(901\) −11.2530 −0.374891
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −58.7711 −1.95362
\(906\) 0 0
\(907\) −17.3838 −0.577220 −0.288610 0.957447i \(-0.593193\pi\)
−0.288610 + 0.957447i \(0.593193\pi\)
\(908\) 0 0
\(909\) −22.9521 −0.761273
\(910\) 0 0
\(911\) 5.20564 0.172471 0.0862353 0.996275i \(-0.472516\pi\)
0.0862353 + 0.996275i \(0.472516\pi\)
\(912\) 0 0
\(913\) 86.5320 2.86379
\(914\) 0 0
\(915\) 22.1725 0.733000
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −32.9641 −1.08738 −0.543692 0.839285i \(-0.682974\pi\)
−0.543692 + 0.839285i \(0.682974\pi\)
\(920\) 0 0
\(921\) −13.2179 −0.435544
\(922\) 0 0
\(923\) −2.44572 −0.0805020
\(924\) 0 0
\(925\) 9.98813 0.328408
\(926\) 0 0
\(927\) −0.315183 −0.0103520
\(928\) 0 0
\(929\) 25.5028 0.836720 0.418360 0.908281i \(-0.362605\pi\)
0.418360 + 0.908281i \(0.362605\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 18.4056 0.602571
\(934\) 0 0
\(935\) −69.2804 −2.26571
\(936\) 0 0
\(937\) −47.1388 −1.53996 −0.769979 0.638070i \(-0.779733\pi\)
−0.769979 + 0.638070i \(0.779733\pi\)
\(938\) 0 0
\(939\) 3.99100 0.130241
\(940\) 0 0
\(941\) 23.2555 0.758108 0.379054 0.925374i \(-0.376249\pi\)
0.379054 + 0.925374i \(0.376249\pi\)
\(942\) 0 0
\(943\) 6.97574 0.227161
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −24.1710 −0.785453 −0.392727 0.919655i \(-0.628468\pi\)
−0.392727 + 0.919655i \(0.628468\pi\)
\(948\) 0 0
\(949\) −27.1799 −0.882297
\(950\) 0 0
\(951\) 15.3124 0.496540
\(952\) 0 0
\(953\) 23.9082 0.774464 0.387232 0.921982i \(-0.373431\pi\)
0.387232 + 0.921982i \(0.373431\pi\)
\(954\) 0 0
\(955\) −48.8692 −1.58137
\(956\) 0 0
\(957\) −15.6018 −0.504334
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −14.6851 −0.473713
\(962\) 0 0
\(963\) −45.8597 −1.47781
\(964\) 0 0
\(965\) 54.1804 1.74413
\(966\) 0 0
\(967\) −23.7841 −0.764846 −0.382423 0.923987i \(-0.624910\pi\)
−0.382423 + 0.923987i \(0.624910\pi\)
\(968\) 0 0
\(969\) −7.64979 −0.245747
\(970\) 0 0
\(971\) 5.88609 0.188894 0.0944468 0.995530i \(-0.469892\pi\)
0.0944468 + 0.995530i \(0.469892\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 3.90808 0.125159
\(976\) 0 0
\(977\) 39.8602 1.27524 0.637620 0.770351i \(-0.279919\pi\)
0.637620 + 0.770351i \(0.279919\pi\)
\(978\) 0 0
\(979\) −16.1155 −0.515053
\(980\) 0 0
\(981\) −25.9190 −0.827529
\(982\) 0 0
\(983\) −12.6127 −0.402282 −0.201141 0.979562i \(-0.564465\pi\)
−0.201141 + 0.979562i \(0.564465\pi\)
\(984\) 0 0
\(985\) 40.9774 1.30565
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 73.8663 2.34881
\(990\) 0 0
\(991\) −4.60602 −0.146315 −0.0731575 0.997320i \(-0.523308\pi\)
−0.0731575 + 0.997320i \(0.523308\pi\)
\(992\) 0 0
\(993\) −14.9914 −0.475738
\(994\) 0 0
\(995\) −36.2501 −1.14921
\(996\) 0 0
\(997\) 57.7765 1.82980 0.914900 0.403680i \(-0.132269\pi\)
0.914900 + 0.403680i \(0.132269\pi\)
\(998\) 0 0
\(999\) −34.1077 −1.07912
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 \(a_p\))