Properties

Label 4028.2.a.d.1.7
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.76613\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.76613 q^{3} -1.36988 q^{5} +0.174249 q^{7} +0.119213 q^{9} +O(q^{10})\) \(q-1.76613 q^{3} -1.36988 q^{5} +0.174249 q^{7} +0.119213 q^{9} +1.83583 q^{11} +3.53740 q^{13} +2.41939 q^{15} -6.42129 q^{17} -1.00000 q^{19} -0.307747 q^{21} +4.41263 q^{23} -3.12342 q^{25} +5.08784 q^{27} +0.386227 q^{29} -6.29764 q^{31} -3.24231 q^{33} -0.238701 q^{35} +7.89972 q^{37} -6.24751 q^{39} -1.09598 q^{41} +5.58442 q^{43} -0.163308 q^{45} +8.67933 q^{47} -6.96964 q^{49} +11.3408 q^{51} +1.00000 q^{53} -2.51487 q^{55} +1.76613 q^{57} -10.0639 q^{59} +10.1283 q^{61} +0.0207728 q^{63} -4.84582 q^{65} -12.8009 q^{67} -7.79327 q^{69} +11.4879 q^{71} +2.20188 q^{73} +5.51637 q^{75} +0.319892 q^{77} -12.3063 q^{79} -9.34343 q^{81} +9.89130 q^{83} +8.79642 q^{85} -0.682127 q^{87} +11.8290 q^{89} +0.616389 q^{91} +11.1224 q^{93} +1.36988 q^{95} +14.5083 q^{97} +0.218855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) −1.76613 −1.01968 −0.509838 0.860271i \(-0.670295\pi\)
−0.509838 + 0.860271i \(0.670295\pi\)
\(4\) 0 0
\(5\) −1.36988 −0.612630 −0.306315 0.951930i \(-0.599096\pi\)
−0.306315 + 0.951930i \(0.599096\pi\)
\(6\) 0 0
\(7\) 0.174249 0.0658600 0.0329300 0.999458i \(-0.489516\pi\)
0.0329300 + 0.999458i \(0.489516\pi\)
\(8\) 0 0
\(9\) 0.119213 0.0397377
\(10\) 0 0
\(11\) 1.83583 0.553524 0.276762 0.960939i \(-0.410739\pi\)
0.276762 + 0.960939i \(0.410739\pi\)
\(12\) 0 0
\(13\) 3.53740 0.981098 0.490549 0.871414i \(-0.336796\pi\)
0.490549 + 0.871414i \(0.336796\pi\)
\(14\) 0 0
\(15\) 2.41939 0.624684
\(16\) 0 0
\(17\) −6.42129 −1.55739 −0.778696 0.627401i \(-0.784119\pi\)
−0.778696 + 0.627401i \(0.784119\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.307747 −0.0671558
\(22\) 0 0
\(23\) 4.41263 0.920096 0.460048 0.887894i \(-0.347832\pi\)
0.460048 + 0.887894i \(0.347832\pi\)
\(24\) 0 0
\(25\) −3.12342 −0.624684
\(26\) 0 0
\(27\) 5.08784 0.979156
\(28\) 0 0
\(29\) 0.386227 0.0717206 0.0358603 0.999357i \(-0.488583\pi\)
0.0358603 + 0.999357i \(0.488583\pi\)
\(30\) 0 0
\(31\) −6.29764 −1.13109 −0.565544 0.824718i \(-0.691334\pi\)
−0.565544 + 0.824718i \(0.691334\pi\)
\(32\) 0 0
\(33\) −3.24231 −0.564414
\(34\) 0 0
\(35\) −0.238701 −0.0403478
\(36\) 0 0
\(37\) 7.89972 1.29871 0.649353 0.760487i \(-0.275040\pi\)
0.649353 + 0.760487i \(0.275040\pi\)
\(38\) 0 0
\(39\) −6.24751 −1.00040
\(40\) 0 0
\(41\) −1.09598 −0.171164 −0.0855818 0.996331i \(-0.527275\pi\)
−0.0855818 + 0.996331i \(0.527275\pi\)
\(42\) 0 0
\(43\) 5.58442 0.851616 0.425808 0.904814i \(-0.359990\pi\)
0.425808 + 0.904814i \(0.359990\pi\)
\(44\) 0 0
\(45\) −0.163308 −0.0243445
\(46\) 0 0
\(47\) 8.67933 1.26601 0.633005 0.774148i \(-0.281821\pi\)
0.633005 + 0.774148i \(0.281821\pi\)
\(48\) 0 0
\(49\) −6.96964 −0.995662
\(50\) 0 0
\(51\) 11.3408 1.58803
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −2.51487 −0.339105
\(56\) 0 0
\(57\) 1.76613 0.233930
\(58\) 0 0
\(59\) −10.0639 −1.31021 −0.655103 0.755539i \(-0.727375\pi\)
−0.655103 + 0.755539i \(0.727375\pi\)
\(60\) 0 0
\(61\) 10.1283 1.29679 0.648395 0.761304i \(-0.275440\pi\)
0.648395 + 0.761304i \(0.275440\pi\)
\(62\) 0 0
\(63\) 0.0207728 0.00261713
\(64\) 0 0
\(65\) −4.84582 −0.601050
\(66\) 0 0
\(67\) −12.8009 −1.56388 −0.781940 0.623354i \(-0.785770\pi\)
−0.781940 + 0.623354i \(0.785770\pi\)
\(68\) 0 0
\(69\) −7.79327 −0.938200
\(70\) 0 0
\(71\) 11.4879 1.36336 0.681678 0.731652i \(-0.261250\pi\)
0.681678 + 0.731652i \(0.261250\pi\)
\(72\) 0 0
\(73\) 2.20188 0.257711 0.128855 0.991663i \(-0.458870\pi\)
0.128855 + 0.991663i \(0.458870\pi\)
\(74\) 0 0
\(75\) 5.51637 0.636975
\(76\) 0 0
\(77\) 0.319892 0.0364551
\(78\) 0 0
\(79\) −12.3063 −1.38457 −0.692284 0.721625i \(-0.743395\pi\)
−0.692284 + 0.721625i \(0.743395\pi\)
\(80\) 0 0
\(81\) −9.34343 −1.03816
\(82\) 0 0
\(83\) 9.89130 1.08571 0.542855 0.839826i \(-0.317343\pi\)
0.542855 + 0.839826i \(0.317343\pi\)
\(84\) 0 0
\(85\) 8.79642 0.954105
\(86\) 0 0
\(87\) −0.682127 −0.0731317
\(88\) 0 0
\(89\) 11.8290 1.25387 0.626935 0.779071i \(-0.284309\pi\)
0.626935 + 0.779071i \(0.284309\pi\)
\(90\) 0 0
\(91\) 0.616389 0.0646151
\(92\) 0 0
\(93\) 11.1224 1.15334
\(94\) 0 0
\(95\) 1.36988 0.140547
\(96\) 0 0
\(97\) 14.5083 1.47310 0.736550 0.676383i \(-0.236454\pi\)
0.736550 + 0.676383i \(0.236454\pi\)
\(98\) 0 0
\(99\) 0.218855 0.0219958
\(100\) 0 0
\(101\) 7.76242 0.772389 0.386195 0.922417i \(-0.373789\pi\)
0.386195 + 0.922417i \(0.373789\pi\)
\(102\) 0 0
\(103\) −7.46178 −0.735231 −0.367615 0.929978i \(-0.619826\pi\)
−0.367615 + 0.929978i \(0.619826\pi\)
\(104\) 0 0
\(105\) 0.421577 0.0411417
\(106\) 0 0
\(107\) −12.2830 −1.18745 −0.593723 0.804670i \(-0.702342\pi\)
−0.593723 + 0.804670i \(0.702342\pi\)
\(108\) 0 0
\(109\) −11.0121 −1.05477 −0.527383 0.849628i \(-0.676827\pi\)
−0.527383 + 0.849628i \(0.676827\pi\)
\(110\) 0 0
\(111\) −13.9519 −1.32426
\(112\) 0 0
\(113\) −3.45472 −0.324993 −0.162496 0.986709i \(-0.551955\pi\)
−0.162496 + 0.986709i \(0.551955\pi\)
\(114\) 0 0
\(115\) −6.04478 −0.563679
\(116\) 0 0
\(117\) 0.421705 0.0389866
\(118\) 0 0
\(119\) −1.11890 −0.102570
\(120\) 0 0
\(121\) −7.62973 −0.693612
\(122\) 0 0
\(123\) 1.93565 0.174531
\(124\) 0 0
\(125\) 11.1281 0.995331
\(126\) 0 0
\(127\) −4.67880 −0.415176 −0.207588 0.978216i \(-0.566561\pi\)
−0.207588 + 0.978216i \(0.566561\pi\)
\(128\) 0 0
\(129\) −9.86281 −0.868372
\(130\) 0 0
\(131\) −15.1421 −1.32297 −0.661486 0.749957i \(-0.730074\pi\)
−0.661486 + 0.749957i \(0.730074\pi\)
\(132\) 0 0
\(133\) −0.174249 −0.0151093
\(134\) 0 0
\(135\) −6.96975 −0.599860
\(136\) 0 0
\(137\) −20.5502 −1.75572 −0.877860 0.478918i \(-0.841029\pi\)
−0.877860 + 0.478918i \(0.841029\pi\)
\(138\) 0 0
\(139\) −8.75156 −0.742298 −0.371149 0.928573i \(-0.621036\pi\)
−0.371149 + 0.928573i \(0.621036\pi\)
\(140\) 0 0
\(141\) −15.3288 −1.29092
\(142\) 0 0
\(143\) 6.49406 0.543061
\(144\) 0 0
\(145\) −0.529086 −0.0439382
\(146\) 0 0
\(147\) 12.3093 1.01525
\(148\) 0 0
\(149\) 1.94152 0.159055 0.0795277 0.996833i \(-0.474659\pi\)
0.0795277 + 0.996833i \(0.474659\pi\)
\(150\) 0 0
\(151\) 12.8236 1.04357 0.521786 0.853076i \(-0.325266\pi\)
0.521786 + 0.853076i \(0.325266\pi\)
\(152\) 0 0
\(153\) −0.765503 −0.0618873
\(154\) 0 0
\(155\) 8.62702 0.692939
\(156\) 0 0
\(157\) −7.98964 −0.637643 −0.318822 0.947815i \(-0.603287\pi\)
−0.318822 + 0.947815i \(0.603287\pi\)
\(158\) 0 0
\(159\) −1.76613 −0.140063
\(160\) 0 0
\(161\) 0.768896 0.0605975
\(162\) 0 0
\(163\) −24.2580 −1.90003 −0.950015 0.312205i \(-0.898932\pi\)
−0.950015 + 0.312205i \(0.898932\pi\)
\(164\) 0 0
\(165\) 4.44159 0.345777
\(166\) 0 0
\(167\) 4.31541 0.333937 0.166968 0.985962i \(-0.446602\pi\)
0.166968 + 0.985962i \(0.446602\pi\)
\(168\) 0 0
\(169\) −0.486805 −0.0374465
\(170\) 0 0
\(171\) −0.119213 −0.00911646
\(172\) 0 0
\(173\) −3.10440 −0.236023 −0.118012 0.993012i \(-0.537652\pi\)
−0.118012 + 0.993012i \(0.537652\pi\)
\(174\) 0 0
\(175\) −0.544254 −0.0411417
\(176\) 0 0
\(177\) 17.7741 1.33599
\(178\) 0 0
\(179\) −4.88429 −0.365069 −0.182535 0.983199i \(-0.558430\pi\)
−0.182535 + 0.983199i \(0.558430\pi\)
\(180\) 0 0
\(181\) 9.38893 0.697874 0.348937 0.937146i \(-0.386543\pi\)
0.348937 + 0.937146i \(0.386543\pi\)
\(182\) 0 0
\(183\) −17.8878 −1.32231
\(184\) 0 0
\(185\) −10.8217 −0.795626
\(186\) 0 0
\(187\) −11.7884 −0.862053
\(188\) 0 0
\(189\) 0.886552 0.0644872
\(190\) 0 0
\(191\) 2.77372 0.200700 0.100350 0.994952i \(-0.468004\pi\)
0.100350 + 0.994952i \(0.468004\pi\)
\(192\) 0 0
\(193\) −4.29614 −0.309243 −0.154621 0.987974i \(-0.549416\pi\)
−0.154621 + 0.987974i \(0.549416\pi\)
\(194\) 0 0
\(195\) 8.55835 0.612876
\(196\) 0 0
\(197\) −17.4574 −1.24379 −0.621894 0.783101i \(-0.713637\pi\)
−0.621894 + 0.783101i \(0.713637\pi\)
\(198\) 0 0
\(199\) −10.1602 −0.720238 −0.360119 0.932906i \(-0.617264\pi\)
−0.360119 + 0.932906i \(0.617264\pi\)
\(200\) 0 0
\(201\) 22.6081 1.59465
\(202\) 0 0
\(203\) 0.0672997 0.00472352
\(204\) 0 0
\(205\) 1.50137 0.104860
\(206\) 0 0
\(207\) 0.526044 0.0365626
\(208\) 0 0
\(209\) −1.83583 −0.126987
\(210\) 0 0
\(211\) −26.4394 −1.82016 −0.910080 0.414432i \(-0.863980\pi\)
−0.910080 + 0.414432i \(0.863980\pi\)
\(212\) 0 0
\(213\) −20.2890 −1.39018
\(214\) 0 0
\(215\) −7.65000 −0.521726
\(216\) 0 0
\(217\) −1.09736 −0.0744935
\(218\) 0 0
\(219\) −3.88881 −0.262781
\(220\) 0 0
\(221\) −22.7147 −1.52795
\(222\) 0 0
\(223\) −28.6328 −1.91739 −0.958697 0.284431i \(-0.908195\pi\)
−0.958697 + 0.284431i \(0.908195\pi\)
\(224\) 0 0
\(225\) −0.372353 −0.0248235
\(226\) 0 0
\(227\) −25.5461 −1.69555 −0.847777 0.530353i \(-0.822059\pi\)
−0.847777 + 0.530353i \(0.822059\pi\)
\(228\) 0 0
\(229\) 14.3725 0.949761 0.474881 0.880050i \(-0.342491\pi\)
0.474881 + 0.880050i \(0.342491\pi\)
\(230\) 0 0
\(231\) −0.564970 −0.0371723
\(232\) 0 0
\(233\) 18.6238 1.22008 0.610042 0.792369i \(-0.291153\pi\)
0.610042 + 0.792369i \(0.291153\pi\)
\(234\) 0 0
\(235\) −11.8897 −0.775596
\(236\) 0 0
\(237\) 21.7345 1.41181
\(238\) 0 0
\(239\) −9.72660 −0.629161 −0.314581 0.949231i \(-0.601864\pi\)
−0.314581 + 0.949231i \(0.601864\pi\)
\(240\) 0 0
\(241\) −15.2510 −0.982401 −0.491201 0.871046i \(-0.663442\pi\)
−0.491201 + 0.871046i \(0.663442\pi\)
\(242\) 0 0
\(243\) 1.23818 0.0794290
\(244\) 0 0
\(245\) 9.54758 0.609973
\(246\) 0 0
\(247\) −3.53740 −0.225079
\(248\) 0 0
\(249\) −17.4693 −1.10707
\(250\) 0 0
\(251\) 5.62526 0.355063 0.177532 0.984115i \(-0.443189\pi\)
0.177532 + 0.984115i \(0.443189\pi\)
\(252\) 0 0
\(253\) 8.10083 0.509295
\(254\) 0 0
\(255\) −15.5356 −0.972878
\(256\) 0 0
\(257\) 2.39109 0.149152 0.0745759 0.997215i \(-0.476240\pi\)
0.0745759 + 0.997215i \(0.476240\pi\)
\(258\) 0 0
\(259\) 1.37652 0.0855327
\(260\) 0 0
\(261\) 0.0460434 0.00285001
\(262\) 0 0
\(263\) 9.97017 0.614787 0.307393 0.951583i \(-0.400543\pi\)
0.307393 + 0.951583i \(0.400543\pi\)
\(264\) 0 0
\(265\) −1.36988 −0.0841512
\(266\) 0 0
\(267\) −20.8915 −1.27854
\(268\) 0 0
\(269\) 7.03028 0.428644 0.214322 0.976763i \(-0.431246\pi\)
0.214322 + 0.976763i \(0.431246\pi\)
\(270\) 0 0
\(271\) 9.46965 0.575240 0.287620 0.957745i \(-0.407136\pi\)
0.287620 + 0.957745i \(0.407136\pi\)
\(272\) 0 0
\(273\) −1.08862 −0.0658864
\(274\) 0 0
\(275\) −5.73407 −0.345777
\(276\) 0 0
\(277\) −22.0357 −1.32399 −0.661997 0.749506i \(-0.730291\pi\)
−0.661997 + 0.749506i \(0.730291\pi\)
\(278\) 0 0
\(279\) −0.750762 −0.0449469
\(280\) 0 0
\(281\) 5.64111 0.336520 0.168260 0.985743i \(-0.446185\pi\)
0.168260 + 0.985743i \(0.446185\pi\)
\(282\) 0 0
\(283\) 11.0684 0.657947 0.328973 0.944339i \(-0.393297\pi\)
0.328973 + 0.944339i \(0.393297\pi\)
\(284\) 0 0
\(285\) −2.41939 −0.143312
\(286\) 0 0
\(287\) −0.190974 −0.0112728
\(288\) 0 0
\(289\) 24.2330 1.42547
\(290\) 0 0
\(291\) −25.6236 −1.50208
\(292\) 0 0
\(293\) 5.58229 0.326121 0.163060 0.986616i \(-0.447863\pi\)
0.163060 + 0.986616i \(0.447863\pi\)
\(294\) 0 0
\(295\) 13.7863 0.802672
\(296\) 0 0
\(297\) 9.34041 0.541986
\(298\) 0 0
\(299\) 15.6092 0.902705
\(300\) 0 0
\(301\) 0.973080 0.0560874
\(302\) 0 0
\(303\) −13.7094 −0.787586
\(304\) 0 0
\(305\) −13.8745 −0.794453
\(306\) 0 0
\(307\) −5.68897 −0.324687 −0.162343 0.986734i \(-0.551905\pi\)
−0.162343 + 0.986734i \(0.551905\pi\)
\(308\) 0 0
\(309\) 13.1785 0.749697
\(310\) 0 0
\(311\) 3.40086 0.192845 0.0964225 0.995340i \(-0.469260\pi\)
0.0964225 + 0.995340i \(0.469260\pi\)
\(312\) 0 0
\(313\) −23.8936 −1.35055 −0.675273 0.737568i \(-0.735974\pi\)
−0.675273 + 0.737568i \(0.735974\pi\)
\(314\) 0 0
\(315\) −0.0284563 −0.00160333
\(316\) 0 0
\(317\) −0.318310 −0.0178781 −0.00893904 0.999960i \(-0.502845\pi\)
−0.00893904 + 0.999960i \(0.502845\pi\)
\(318\) 0 0
\(319\) 0.709047 0.0396990
\(320\) 0 0
\(321\) 21.6934 1.21081
\(322\) 0 0
\(323\) 6.42129 0.357290
\(324\) 0 0
\(325\) −11.0488 −0.612877
\(326\) 0 0
\(327\) 19.4487 1.07552
\(328\) 0 0
\(329\) 1.51237 0.0833794
\(330\) 0 0
\(331\) −7.36958 −0.405069 −0.202534 0.979275i \(-0.564918\pi\)
−0.202534 + 0.979275i \(0.564918\pi\)
\(332\) 0 0
\(333\) 0.941751 0.0516076
\(334\) 0 0
\(335\) 17.5357 0.958080
\(336\) 0 0
\(337\) 3.30089 0.179811 0.0899055 0.995950i \(-0.471344\pi\)
0.0899055 + 0.995950i \(0.471344\pi\)
\(338\) 0 0
\(339\) 6.10148 0.331387
\(340\) 0 0
\(341\) −11.5614 −0.626084
\(342\) 0 0
\(343\) −2.43420 −0.131434
\(344\) 0 0
\(345\) 10.6759 0.574769
\(346\) 0 0
\(347\) −23.6717 −1.27076 −0.635381 0.772199i \(-0.719157\pi\)
−0.635381 + 0.772199i \(0.719157\pi\)
\(348\) 0 0
\(349\) −0.312831 −0.0167455 −0.00837274 0.999965i \(-0.502665\pi\)
−0.00837274 + 0.999965i \(0.502665\pi\)
\(350\) 0 0
\(351\) 17.9977 0.960648
\(352\) 0 0
\(353\) 6.51566 0.346793 0.173397 0.984852i \(-0.444526\pi\)
0.173397 + 0.984852i \(0.444526\pi\)
\(354\) 0 0
\(355\) −15.7370 −0.835234
\(356\) 0 0
\(357\) 1.97613 0.104588
\(358\) 0 0
\(359\) 22.5474 1.19000 0.595002 0.803724i \(-0.297151\pi\)
0.595002 + 0.803724i \(0.297151\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 13.4751 0.707259
\(364\) 0 0
\(365\) −3.01632 −0.157881
\(366\) 0 0
\(367\) −4.73263 −0.247041 −0.123521 0.992342i \(-0.539418\pi\)
−0.123521 + 0.992342i \(0.539418\pi\)
\(368\) 0 0
\(369\) −0.130656 −0.00680165
\(370\) 0 0
\(371\) 0.174249 0.00904656
\(372\) 0 0
\(373\) −19.0542 −0.986588 −0.493294 0.869863i \(-0.664207\pi\)
−0.493294 + 0.869863i \(0.664207\pi\)
\(374\) 0 0
\(375\) −19.6537 −1.01491
\(376\) 0 0
\(377\) 1.36624 0.0703649
\(378\) 0 0
\(379\) 21.7120 1.11527 0.557634 0.830087i \(-0.311709\pi\)
0.557634 + 0.830087i \(0.311709\pi\)
\(380\) 0 0
\(381\) 8.26336 0.423345
\(382\) 0 0
\(383\) 6.51509 0.332906 0.166453 0.986049i \(-0.446769\pi\)
0.166453 + 0.986049i \(0.446769\pi\)
\(384\) 0 0
\(385\) −0.438214 −0.0223335
\(386\) 0 0
\(387\) 0.665737 0.0338413
\(388\) 0 0
\(389\) −14.0965 −0.714723 −0.357361 0.933966i \(-0.616324\pi\)
−0.357361 + 0.933966i \(0.616324\pi\)
\(390\) 0 0
\(391\) −28.3348 −1.43295
\(392\) 0 0
\(393\) 26.7429 1.34900
\(394\) 0 0
\(395\) 16.8582 0.848228
\(396\) 0 0
\(397\) 27.0017 1.35518 0.677588 0.735442i \(-0.263025\pi\)
0.677588 + 0.735442i \(0.263025\pi\)
\(398\) 0 0
\(399\) 0.307747 0.0154066
\(400\) 0 0
\(401\) −25.1494 −1.25590 −0.627950 0.778253i \(-0.716106\pi\)
−0.627950 + 0.778253i \(0.716106\pi\)
\(402\) 0 0
\(403\) −22.2773 −1.10971
\(404\) 0 0
\(405\) 12.7994 0.636007
\(406\) 0 0
\(407\) 14.5025 0.718864
\(408\) 0 0
\(409\) 21.0864 1.04265 0.521327 0.853357i \(-0.325437\pi\)
0.521327 + 0.853357i \(0.325437\pi\)
\(410\) 0 0
\(411\) 36.2943 1.79026
\(412\) 0 0
\(413\) −1.75362 −0.0862902
\(414\) 0 0
\(415\) −13.5499 −0.665139
\(416\) 0 0
\(417\) 15.4564 0.756903
\(418\) 0 0
\(419\) −19.2247 −0.939187 −0.469593 0.882883i \(-0.655599\pi\)
−0.469593 + 0.882883i \(0.655599\pi\)
\(420\) 0 0
\(421\) −4.78295 −0.233107 −0.116553 0.993184i \(-0.537185\pi\)
−0.116553 + 0.993184i \(0.537185\pi\)
\(422\) 0 0
\(423\) 1.03469 0.0503084
\(424\) 0 0
\(425\) 20.0564 0.972878
\(426\) 0 0
\(427\) 1.76484 0.0854066
\(428\) 0 0
\(429\) −11.4694 −0.553746
\(430\) 0 0
\(431\) 6.20085 0.298685 0.149342 0.988786i \(-0.452284\pi\)
0.149342 + 0.988786i \(0.452284\pi\)
\(432\) 0 0
\(433\) −18.5071 −0.889396 −0.444698 0.895681i \(-0.646689\pi\)
−0.444698 + 0.895681i \(0.646689\pi\)
\(434\) 0 0
\(435\) 0.934434 0.0448027
\(436\) 0 0
\(437\) −4.41263 −0.211085
\(438\) 0 0
\(439\) −19.5302 −0.932124 −0.466062 0.884752i \(-0.654328\pi\)
−0.466062 + 0.884752i \(0.654328\pi\)
\(440\) 0 0
\(441\) −0.830873 −0.0395654
\(442\) 0 0
\(443\) −36.6212 −1.73992 −0.869962 0.493118i \(-0.835857\pi\)
−0.869962 + 0.493118i \(0.835857\pi\)
\(444\) 0 0
\(445\) −16.2043 −0.768159
\(446\) 0 0
\(447\) −3.42897 −0.162185
\(448\) 0 0
\(449\) −7.77823 −0.367077 −0.183539 0.983012i \(-0.558755\pi\)
−0.183539 + 0.983012i \(0.558755\pi\)
\(450\) 0 0
\(451\) −2.01204 −0.0947431
\(452\) 0 0
\(453\) −22.6482 −1.06410
\(454\) 0 0
\(455\) −0.844380 −0.0395852
\(456\) 0 0
\(457\) −0.00559014 −0.000261496 0 −0.000130748 1.00000i \(-0.500042\pi\)
−0.000130748 1.00000i \(0.500042\pi\)
\(458\) 0 0
\(459\) −32.6705 −1.52493
\(460\) 0 0
\(461\) −4.52873 −0.210924 −0.105462 0.994423i \(-0.533632\pi\)
−0.105462 + 0.994423i \(0.533632\pi\)
\(462\) 0 0
\(463\) −11.0424 −0.513182 −0.256591 0.966520i \(-0.582599\pi\)
−0.256591 + 0.966520i \(0.582599\pi\)
\(464\) 0 0
\(465\) −15.2364 −0.706573
\(466\) 0 0
\(467\) −14.0357 −0.649494 −0.324747 0.945801i \(-0.605279\pi\)
−0.324747 + 0.945801i \(0.605279\pi\)
\(468\) 0 0
\(469\) −2.23055 −0.102997
\(470\) 0 0
\(471\) 14.1107 0.650189
\(472\) 0 0
\(473\) 10.2520 0.471390
\(474\) 0 0
\(475\) 3.12342 0.143312
\(476\) 0 0
\(477\) 0.119213 0.00545840
\(478\) 0 0
\(479\) 41.7101 1.90578 0.952892 0.303311i \(-0.0980920\pi\)
0.952892 + 0.303311i \(0.0980920\pi\)
\(480\) 0 0
\(481\) 27.9445 1.27416
\(482\) 0 0
\(483\) −1.35797 −0.0617898
\(484\) 0 0
\(485\) −19.8747 −0.902465
\(486\) 0 0
\(487\) −8.43394 −0.382178 −0.191089 0.981573i \(-0.561202\pi\)
−0.191089 + 0.981573i \(0.561202\pi\)
\(488\) 0 0
\(489\) 42.8427 1.93741
\(490\) 0 0
\(491\) 14.2449 0.642862 0.321431 0.946933i \(-0.395836\pi\)
0.321431 + 0.946933i \(0.395836\pi\)
\(492\) 0 0
\(493\) −2.48008 −0.111697
\(494\) 0 0
\(495\) −0.299806 −0.0134753
\(496\) 0 0
\(497\) 2.00175 0.0897907
\(498\) 0 0
\(499\) −35.8944 −1.60685 −0.803426 0.595404i \(-0.796992\pi\)
−0.803426 + 0.595404i \(0.796992\pi\)
\(500\) 0 0
\(501\) −7.62157 −0.340507
\(502\) 0 0
\(503\) −40.3858 −1.80071 −0.900357 0.435152i \(-0.856694\pi\)
−0.900357 + 0.435152i \(0.856694\pi\)
\(504\) 0 0
\(505\) −10.6336 −0.473189
\(506\) 0 0
\(507\) 0.859760 0.0381833
\(508\) 0 0
\(509\) 41.8060 1.85302 0.926508 0.376274i \(-0.122795\pi\)
0.926508 + 0.376274i \(0.122795\pi\)
\(510\) 0 0
\(511\) 0.383676 0.0169728
\(512\) 0 0
\(513\) −5.08784 −0.224634
\(514\) 0 0
\(515\) 10.2218 0.450425
\(516\) 0 0
\(517\) 15.9338 0.700766
\(518\) 0 0
\(519\) 5.48278 0.240667
\(520\) 0 0
\(521\) 8.78143 0.384721 0.192361 0.981324i \(-0.438386\pi\)
0.192361 + 0.981324i \(0.438386\pi\)
\(522\) 0 0
\(523\) 39.4697 1.72589 0.862946 0.505297i \(-0.168617\pi\)
0.862946 + 0.505297i \(0.168617\pi\)
\(524\) 0 0
\(525\) 0.961222 0.0419512
\(526\) 0 0
\(527\) 40.4390 1.76155
\(528\) 0 0
\(529\) −3.52872 −0.153423
\(530\) 0 0
\(531\) −1.19975 −0.0520646
\(532\) 0 0
\(533\) −3.87692 −0.167928
\(534\) 0 0
\(535\) 16.8263 0.727465
\(536\) 0 0
\(537\) 8.62630 0.372252
\(538\) 0 0
\(539\) −12.7951 −0.551123
\(540\) 0 0
\(541\) −41.8505 −1.79929 −0.899646 0.436620i \(-0.856175\pi\)
−0.899646 + 0.436620i \(0.856175\pi\)
\(542\) 0 0
\(543\) −16.5821 −0.711605
\(544\) 0 0
\(545\) 15.0852 0.646181
\(546\) 0 0
\(547\) 31.1956 1.33383 0.666915 0.745134i \(-0.267615\pi\)
0.666915 + 0.745134i \(0.267615\pi\)
\(548\) 0 0
\(549\) 1.20742 0.0515315
\(550\) 0 0
\(551\) −0.386227 −0.0164538
\(552\) 0 0
\(553\) −2.14436 −0.0911876
\(554\) 0 0
\(555\) 19.1125 0.811280
\(556\) 0 0
\(557\) −41.2850 −1.74930 −0.874650 0.484754i \(-0.838909\pi\)
−0.874650 + 0.484754i \(0.838909\pi\)
\(558\) 0 0
\(559\) 19.7543 0.835519
\(560\) 0 0
\(561\) 20.8198 0.879014
\(562\) 0 0
\(563\) −32.5099 −1.37013 −0.685064 0.728483i \(-0.740226\pi\)
−0.685064 + 0.728483i \(0.740226\pi\)
\(564\) 0 0
\(565\) 4.73256 0.199100
\(566\) 0 0
\(567\) −1.62808 −0.0683731
\(568\) 0 0
\(569\) −4.62215 −0.193771 −0.0968854 0.995296i \(-0.530888\pi\)
−0.0968854 + 0.995296i \(0.530888\pi\)
\(570\) 0 0
\(571\) −42.9927 −1.79919 −0.899593 0.436728i \(-0.856137\pi\)
−0.899593 + 0.436728i \(0.856137\pi\)
\(572\) 0 0
\(573\) −4.89876 −0.204648
\(574\) 0 0
\(575\) −13.7825 −0.574770
\(576\) 0 0
\(577\) 29.9759 1.24791 0.623957 0.781459i \(-0.285524\pi\)
0.623957 + 0.781459i \(0.285524\pi\)
\(578\) 0 0
\(579\) 7.58754 0.315327
\(580\) 0 0
\(581\) 1.72355 0.0715049
\(582\) 0 0
\(583\) 1.83583 0.0760323
\(584\) 0 0
\(585\) −0.577686 −0.0238844
\(586\) 0 0
\(587\) −37.8181 −1.56092 −0.780460 0.625206i \(-0.785015\pi\)
−0.780460 + 0.625206i \(0.785015\pi\)
\(588\) 0 0
\(589\) 6.29764 0.259490
\(590\) 0 0
\(591\) 30.8320 1.26826
\(592\) 0 0
\(593\) −22.5076 −0.924278 −0.462139 0.886807i \(-0.652918\pi\)
−0.462139 + 0.886807i \(0.652918\pi\)
\(594\) 0 0
\(595\) 1.53277 0.0628374
\(596\) 0 0
\(597\) 17.9442 0.734408
\(598\) 0 0
\(599\) 36.4783 1.49046 0.745232 0.666806i \(-0.232339\pi\)
0.745232 + 0.666806i \(0.232339\pi\)
\(600\) 0 0
\(601\) −2.84200 −0.115928 −0.0579638 0.998319i \(-0.518461\pi\)
−0.0579638 + 0.998319i \(0.518461\pi\)
\(602\) 0 0
\(603\) −1.52604 −0.0621451
\(604\) 0 0
\(605\) 10.4518 0.424927
\(606\) 0 0
\(607\) −23.8080 −0.966335 −0.483168 0.875528i \(-0.660514\pi\)
−0.483168 + 0.875528i \(0.660514\pi\)
\(608\) 0 0
\(609\) −0.118860 −0.00481645
\(610\) 0 0
\(611\) 30.7022 1.24208
\(612\) 0 0
\(613\) 23.6638 0.955770 0.477885 0.878422i \(-0.341403\pi\)
0.477885 + 0.878422i \(0.341403\pi\)
\(614\) 0 0
\(615\) −2.65161 −0.106923
\(616\) 0 0
\(617\) 14.7357 0.593236 0.296618 0.954996i \(-0.404141\pi\)
0.296618 + 0.954996i \(0.404141\pi\)
\(618\) 0 0
\(619\) 6.03783 0.242681 0.121340 0.992611i \(-0.461281\pi\)
0.121340 + 0.992611i \(0.461281\pi\)
\(620\) 0 0
\(621\) 22.4508 0.900918
\(622\) 0 0
\(623\) 2.06119 0.0825799
\(624\) 0 0
\(625\) 0.372871 0.0149148
\(626\) 0 0
\(627\) 3.24231 0.129486
\(628\) 0 0
\(629\) −50.7264 −2.02259
\(630\) 0 0
\(631\) 10.9794 0.437084 0.218542 0.975828i \(-0.429870\pi\)
0.218542 + 0.975828i \(0.429870\pi\)
\(632\) 0 0
\(633\) 46.6953 1.85597
\(634\) 0 0
\(635\) 6.40941 0.254350
\(636\) 0 0
\(637\) −24.6544 −0.976843
\(638\) 0 0
\(639\) 1.36950 0.0541767
\(640\) 0 0
\(641\) 45.6726 1.80396 0.901979 0.431780i \(-0.142114\pi\)
0.901979 + 0.431780i \(0.142114\pi\)
\(642\) 0 0
\(643\) −10.3798 −0.409339 −0.204669 0.978831i \(-0.565612\pi\)
−0.204669 + 0.978831i \(0.565612\pi\)
\(644\) 0 0
\(645\) 13.5109 0.531991
\(646\) 0 0
\(647\) 8.92658 0.350940 0.175470 0.984485i \(-0.443856\pi\)
0.175470 + 0.984485i \(0.443856\pi\)
\(648\) 0 0
\(649\) −18.4756 −0.725230
\(650\) 0 0
\(651\) 1.93808 0.0759592
\(652\) 0 0
\(653\) −11.4895 −0.449617 −0.224809 0.974403i \(-0.572176\pi\)
−0.224809 + 0.974403i \(0.572176\pi\)
\(654\) 0 0
\(655\) 20.7429 0.810493
\(656\) 0 0
\(657\) 0.262493 0.0102408
\(658\) 0 0
\(659\) −0.576352 −0.0224515 −0.0112257 0.999937i \(-0.503573\pi\)
−0.0112257 + 0.999937i \(0.503573\pi\)
\(660\) 0 0
\(661\) 29.1219 1.13271 0.566356 0.824161i \(-0.308353\pi\)
0.566356 + 0.824161i \(0.308353\pi\)
\(662\) 0 0
\(663\) 40.1171 1.55802
\(664\) 0 0
\(665\) 0.238701 0.00925642
\(666\) 0 0
\(667\) 1.70428 0.0659898
\(668\) 0 0
\(669\) 50.5692 1.95512
\(670\) 0 0
\(671\) 18.5938 0.717804
\(672\) 0 0
\(673\) 24.5808 0.947521 0.473761 0.880654i \(-0.342896\pi\)
0.473761 + 0.880654i \(0.342896\pi\)
\(674\) 0 0
\(675\) −15.8915 −0.611663
\(676\) 0 0
\(677\) 31.6663 1.21704 0.608518 0.793540i \(-0.291764\pi\)
0.608518 + 0.793540i \(0.291764\pi\)
\(678\) 0 0
\(679\) 2.52807 0.0970183
\(680\) 0 0
\(681\) 45.1177 1.72891
\(682\) 0 0
\(683\) 6.46482 0.247370 0.123685 0.992322i \(-0.460529\pi\)
0.123685 + 0.992322i \(0.460529\pi\)
\(684\) 0 0
\(685\) 28.1513 1.07561
\(686\) 0 0
\(687\) −25.3837 −0.968448
\(688\) 0 0
\(689\) 3.53740 0.134764
\(690\) 0 0
\(691\) 18.5987 0.707527 0.353763 0.935335i \(-0.384902\pi\)
0.353763 + 0.935335i \(0.384902\pi\)
\(692\) 0 0
\(693\) 0.0381353 0.00144864
\(694\) 0 0
\(695\) 11.9886 0.454754
\(696\) 0 0
\(697\) 7.03762 0.266569
\(698\) 0 0
\(699\) −32.8920 −1.24409
\(700\) 0 0
\(701\) 43.7131 1.65102 0.825511 0.564387i \(-0.190887\pi\)
0.825511 + 0.564387i \(0.190887\pi\)
\(702\) 0 0
\(703\) −7.89972 −0.297943
\(704\) 0 0
\(705\) 20.9987 0.790856
\(706\) 0 0
\(707\) 1.35259 0.0508695
\(708\) 0 0
\(709\) −12.2792 −0.461156 −0.230578 0.973054i \(-0.574062\pi\)
−0.230578 + 0.973054i \(0.574062\pi\)
\(710\) 0 0
\(711\) −1.46707 −0.0550196
\(712\) 0 0
\(713\) −27.7891 −1.04071
\(714\) 0 0
\(715\) −8.89611 −0.332695
\(716\) 0 0
\(717\) 17.1784 0.641540
\(718\) 0 0
\(719\) −5.04974 −0.188323 −0.0941617 0.995557i \(-0.530017\pi\)
−0.0941617 + 0.995557i \(0.530017\pi\)
\(720\) 0 0
\(721\) −1.30021 −0.0484223
\(722\) 0 0
\(723\) 26.9352 1.00173
\(724\) 0 0
\(725\) −1.20635 −0.0448027
\(726\) 0 0
\(727\) −51.1591 −1.89739 −0.948694 0.316196i \(-0.897594\pi\)
−0.948694 + 0.316196i \(0.897594\pi\)
\(728\) 0 0
\(729\) 25.8435 0.957167
\(730\) 0 0
\(731\) −35.8592 −1.32630
\(732\) 0 0
\(733\) 45.8535 1.69364 0.846819 0.531882i \(-0.178515\pi\)
0.846819 + 0.531882i \(0.178515\pi\)
\(734\) 0 0
\(735\) −16.8623 −0.621974
\(736\) 0 0
\(737\) −23.5003 −0.865644
\(738\) 0 0
\(739\) 8.43358 0.310234 0.155117 0.987896i \(-0.450425\pi\)
0.155117 + 0.987896i \(0.450425\pi\)
\(740\) 0 0
\(741\) 6.24751 0.229508
\(742\) 0 0
\(743\) −41.8989 −1.53712 −0.768560 0.639777i \(-0.779027\pi\)
−0.768560 + 0.639777i \(0.779027\pi\)
\(744\) 0 0
\(745\) −2.65965 −0.0974421
\(746\) 0 0
\(747\) 1.17917 0.0431437
\(748\) 0 0
\(749\) −2.14031 −0.0782051
\(750\) 0 0
\(751\) 23.8017 0.868536 0.434268 0.900784i \(-0.357007\pi\)
0.434268 + 0.900784i \(0.357007\pi\)
\(752\) 0 0
\(753\) −9.93494 −0.362049
\(754\) 0 0
\(755\) −17.5669 −0.639324
\(756\) 0 0
\(757\) −33.3321 −1.21147 −0.605737 0.795665i \(-0.707122\pi\)
−0.605737 + 0.795665i \(0.707122\pi\)
\(758\) 0 0
\(759\) −14.3071 −0.519316
\(760\) 0 0
\(761\) 19.0974 0.692282 0.346141 0.938183i \(-0.387492\pi\)
0.346141 + 0.938183i \(0.387492\pi\)
\(762\) 0 0
\(763\) −1.91884 −0.0694668
\(764\) 0 0
\(765\) 1.04865 0.0379140
\(766\) 0 0
\(767\) −35.6000 −1.28544
\(768\) 0 0
\(769\) −10.8020 −0.389532 −0.194766 0.980850i \(-0.562395\pi\)
−0.194766 + 0.980850i \(0.562395\pi\)
\(770\) 0 0
\(771\) −4.22297 −0.152086
\(772\) 0 0
\(773\) 31.7904 1.14342 0.571711 0.820455i \(-0.306280\pi\)
0.571711 + 0.820455i \(0.306280\pi\)
\(774\) 0 0
\(775\) 19.6702 0.706573
\(776\) 0 0
\(777\) −2.43111 −0.0872156
\(778\) 0 0
\(779\) 1.09598 0.0392676
\(780\) 0 0
\(781\) 21.0897 0.754650
\(782\) 0 0
\(783\) 1.96506 0.0702256
\(784\) 0 0
\(785\) 10.9449 0.390639
\(786\) 0 0
\(787\) 16.3732 0.583640 0.291820 0.956473i \(-0.405739\pi\)
0.291820 + 0.956473i \(0.405739\pi\)
\(788\) 0 0
\(789\) −17.6086 −0.626883
\(790\) 0 0
\(791\) −0.601982 −0.0214040
\(792\) 0 0
\(793\) 35.8277 1.27228
\(794\) 0 0
\(795\) 2.41939 0.0858069
\(796\) 0 0
\(797\) −20.9402 −0.741741 −0.370871 0.928685i \(-0.620941\pi\)
−0.370871 + 0.928685i \(0.620941\pi\)
\(798\) 0 0
\(799\) −55.7325 −1.97167
\(800\) 0 0
\(801\) 1.41017 0.0498260
\(802\) 0 0
\(803\) 4.04228 0.142649
\(804\) 0 0
\(805\) −1.05330 −0.0371239
\(806\) 0 0
\(807\) −12.4164 −0.437077
\(808\) 0 0
\(809\) 23.0817 0.811510 0.405755 0.913982i \(-0.367009\pi\)
0.405755 + 0.913982i \(0.367009\pi\)
\(810\) 0 0
\(811\) 46.1158 1.61935 0.809673 0.586882i \(-0.199645\pi\)
0.809673 + 0.586882i \(0.199645\pi\)
\(812\) 0 0
\(813\) −16.7246 −0.586558
\(814\) 0 0
\(815\) 33.2305 1.16402
\(816\) 0 0
\(817\) −5.58442 −0.195374
\(818\) 0 0
\(819\) 0.0734817 0.00256766
\(820\) 0 0
\(821\) −3.36631 −0.117485 −0.0587426 0.998273i \(-0.518709\pi\)
−0.0587426 + 0.998273i \(0.518709\pi\)
\(822\) 0 0
\(823\) 10.0847 0.351532 0.175766 0.984432i \(-0.443760\pi\)
0.175766 + 0.984432i \(0.443760\pi\)
\(824\) 0 0
\(825\) 10.1271 0.352581
\(826\) 0 0
\(827\) −17.3024 −0.601663 −0.300832 0.953677i \(-0.597264\pi\)
−0.300832 + 0.953677i \(0.597264\pi\)
\(828\) 0 0
\(829\) 27.2250 0.945564 0.472782 0.881180i \(-0.343250\pi\)
0.472782 + 0.881180i \(0.343250\pi\)
\(830\) 0 0
\(831\) 38.9178 1.35004
\(832\) 0 0
\(833\) 44.7541 1.55064
\(834\) 0 0
\(835\) −5.91161 −0.204580
\(836\) 0 0
\(837\) −32.0414 −1.10751
\(838\) 0 0
\(839\) 53.2889 1.83974 0.919869 0.392226i \(-0.128295\pi\)
0.919869 + 0.392226i \(0.128295\pi\)
\(840\) 0 0
\(841\) −28.8508 −0.994856
\(842\) 0 0
\(843\) −9.96293 −0.343142
\(844\) 0 0
\(845\) 0.666865 0.0229409
\(846\) 0 0
\(847\) −1.32947 −0.0456813
\(848\) 0 0
\(849\) −19.5482 −0.670892
\(850\) 0 0
\(851\) 34.8585 1.19493
\(852\) 0 0
\(853\) −53.9727 −1.84799 −0.923996 0.382403i \(-0.875097\pi\)
−0.923996 + 0.382403i \(0.875097\pi\)
\(854\) 0 0
\(855\) 0.163308 0.00558502
\(856\) 0 0
\(857\) 45.3914 1.55054 0.775270 0.631630i \(-0.217614\pi\)
0.775270 + 0.631630i \(0.217614\pi\)
\(858\) 0 0
\(859\) 42.3659 1.44551 0.722753 0.691106i \(-0.242876\pi\)
0.722753 + 0.691106i \(0.242876\pi\)
\(860\) 0 0
\(861\) 0.337284 0.0114946
\(862\) 0 0
\(863\) 3.56657 0.121407 0.0607037 0.998156i \(-0.480666\pi\)
0.0607037 + 0.998156i \(0.480666\pi\)
\(864\) 0 0
\(865\) 4.25267 0.144595
\(866\) 0 0
\(867\) −42.7986 −1.45352
\(868\) 0 0
\(869\) −22.5923 −0.766391
\(870\) 0 0
\(871\) −45.2819 −1.53432
\(872\) 0 0
\(873\) 1.72959 0.0585377
\(874\) 0 0
\(875\) 1.93907 0.0655525
\(876\) 0 0
\(877\) 27.6030 0.932087 0.466043 0.884762i \(-0.345679\pi\)
0.466043 + 0.884762i \(0.345679\pi\)
\(878\) 0 0
\(879\) −9.85904 −0.332537
\(880\) 0 0
\(881\) 26.6725 0.898621 0.449310 0.893376i \(-0.351670\pi\)
0.449310 + 0.893376i \(0.351670\pi\)
\(882\) 0 0
\(883\) −7.22789 −0.243238 −0.121619 0.992577i \(-0.538809\pi\)
−0.121619 + 0.992577i \(0.538809\pi\)
\(884\) 0 0
\(885\) −24.3485 −0.818465
\(886\) 0 0
\(887\) −55.9296 −1.87793 −0.938966 0.344009i \(-0.888215\pi\)
−0.938966 + 0.344009i \(0.888215\pi\)
\(888\) 0 0
\(889\) −0.815277 −0.0273435
\(890\) 0 0
\(891\) −17.1529 −0.574645
\(892\) 0 0
\(893\) −8.67933 −0.290443
\(894\) 0 0
\(895\) 6.69091 0.223652
\(896\) 0 0
\(897\) −27.5679 −0.920466
\(898\) 0 0
\(899\) −2.43232 −0.0811223
\(900\) 0 0
\(901\) −6.42129 −0.213924
\(902\) 0 0
\(903\) −1.71859 −0.0571910
\(904\) 0 0
\(905\) −12.8617 −0.427539
\(906\) 0 0
\(907\) −37.4857 −1.24469 −0.622346 0.782742i \(-0.713820\pi\)
−0.622346 + 0.782742i \(0.713820\pi\)
\(908\) 0 0
\(909\) 0.925383 0.0306930
\(910\) 0 0
\(911\) −11.8543 −0.392749 −0.196375 0.980529i \(-0.562917\pi\)
−0.196375 + 0.980529i \(0.562917\pi\)
\(912\) 0 0
\(913\) 18.1587 0.600967
\(914\) 0 0
\(915\) 24.5042 0.810084
\(916\) 0 0
\(917\) −2.63850 −0.0871309
\(918\) 0 0
\(919\) −30.5585 −1.00803 −0.504015 0.863695i \(-0.668145\pi\)
−0.504015 + 0.863695i \(0.668145\pi\)
\(920\) 0 0
\(921\) 10.0475 0.331075
\(922\) 0 0
\(923\) 40.6371 1.33759
\(924\) 0 0
\(925\) −24.6741 −0.811281
\(926\) 0 0
\(927\) −0.889543 −0.0292164
\(928\) 0 0
\(929\) −20.7104 −0.679486 −0.339743 0.940518i \(-0.610340\pi\)
−0.339743 + 0.940518i \(0.610340\pi\)
\(930\) 0 0
\(931\) 6.96964 0.228421
\(932\) 0 0
\(933\) −6.00636 −0.196639
\(934\) 0 0
\(935\) 16.1487 0.528120
\(936\) 0 0
\(937\) −17.7638 −0.580317 −0.290158 0.956979i \(-0.593708\pi\)
−0.290158 + 0.956979i \(0.593708\pi\)
\(938\) 0 0
\(939\) 42.1992 1.37712
\(940\) 0 0
\(941\) 39.8581 1.29934 0.649668 0.760218i \(-0.274908\pi\)
0.649668 + 0.760218i \(0.274908\pi\)
\(942\) 0 0
\(943\) −4.83616 −0.157487
\(944\) 0 0
\(945\) −1.21447 −0.0395068
\(946\) 0 0
\(947\) 25.1937 0.818684 0.409342 0.912381i \(-0.365758\pi\)
0.409342 + 0.912381i \(0.365758\pi\)
\(948\) 0 0
\(949\) 7.78893 0.252839
\(950\) 0 0
\(951\) 0.562177 0.0182298
\(952\) 0 0
\(953\) 12.8841 0.417357 0.208678 0.977984i \(-0.433084\pi\)
0.208678 + 0.977984i \(0.433084\pi\)
\(954\) 0 0
\(955\) −3.79968 −0.122955
\(956\) 0 0
\(957\) −1.25227 −0.0404801
\(958\) 0 0
\(959\) −3.58085 −0.115632
\(960\) 0 0
\(961\) 8.66022 0.279362
\(962\) 0 0
\(963\) −1.46430 −0.0471864
\(964\) 0 0
\(965\) 5.88521 0.189451
\(966\) 0 0
\(967\) −15.5160 −0.498961 −0.249481 0.968380i \(-0.580260\pi\)
−0.249481 + 0.968380i \(0.580260\pi\)
\(968\) 0 0
\(969\) −11.3408 −0.364320
\(970\) 0 0
\(971\) 24.0964 0.773289 0.386644 0.922229i \(-0.373634\pi\)
0.386644 + 0.922229i \(0.373634\pi\)
\(972\) 0 0
\(973\) −1.52495 −0.0488877
\(974\) 0 0
\(975\) 19.5136 0.624935
\(976\) 0 0
\(977\) −27.2529 −0.871897 −0.435949 0.899972i \(-0.643587\pi\)
−0.435949 + 0.899972i \(0.643587\pi\)
\(978\) 0 0
\(979\) 21.7160 0.694047
\(980\) 0 0
\(981\) −1.31278 −0.0419140
\(982\) 0 0
\(983\) −6.30774 −0.201186 −0.100593 0.994928i \(-0.532074\pi\)
−0.100593 + 0.994928i \(0.532074\pi\)
\(984\) 0 0
\(985\) 23.9146 0.761982
\(986\) 0 0
\(987\) −2.67103 −0.0850199
\(988\) 0 0
\(989\) 24.6420 0.783569
\(990\) 0 0
\(991\) 6.43876 0.204534 0.102267 0.994757i \(-0.467390\pi\)
0.102267 + 0.994757i \(0.467390\pi\)
\(992\) 0 0
\(993\) 13.0156 0.413038
\(994\) 0 0
\(995\) 13.9183 0.441239
\(996\) 0 0
\(997\) 8.86331 0.280704 0.140352 0.990102i \(-0.455177\pi\)
0.140352 + 0.990102i \(0.455177\pi\)
\(998\) 0 0
\(999\) 40.1925 1.27163
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 \(a_p\))