Properties

Label 6008.2.a.e.1.5
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.83142 q^{3} +4.26484 q^{5} +3.89972 q^{7} +5.01693 q^{9} +O(q^{10})\) \(q-2.83142 q^{3} +4.26484 q^{5} +3.89972 q^{7} +5.01693 q^{9} +2.11918 q^{11} +2.93611 q^{13} -12.0755 q^{15} -2.84435 q^{17} -7.25277 q^{19} -11.0417 q^{21} +0.341822 q^{23} +13.1888 q^{25} -5.71078 q^{27} +0.780311 q^{29} +5.53879 q^{31} -6.00029 q^{33} +16.6317 q^{35} +6.82954 q^{37} -8.31336 q^{39} -8.86143 q^{41} -4.55369 q^{43} +21.3964 q^{45} -9.00906 q^{47} +8.20784 q^{49} +8.05354 q^{51} +4.97585 q^{53} +9.03796 q^{55} +20.5356 q^{57} +1.52810 q^{59} +7.97529 q^{61} +19.5646 q^{63} +12.5220 q^{65} +10.5064 q^{67} -0.967841 q^{69} +13.1735 q^{71} +8.40366 q^{73} -37.3432 q^{75} +8.26421 q^{77} -2.38763 q^{79} +1.11882 q^{81} -10.0730 q^{83} -12.1307 q^{85} -2.20939 q^{87} +3.91403 q^{89} +11.4500 q^{91} -15.6826 q^{93} -30.9319 q^{95} +4.05224 q^{97} +10.6318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.83142 −1.63472 −0.817360 0.576127i \(-0.804563\pi\)
−0.817360 + 0.576127i \(0.804563\pi\)
\(4\) 0 0
\(5\) 4.26484 1.90729 0.953647 0.300928i \(-0.0972964\pi\)
0.953647 + 0.300928i \(0.0972964\pi\)
\(6\) 0 0
\(7\) 3.89972 1.47396 0.736978 0.675916i \(-0.236252\pi\)
0.736978 + 0.675916i \(0.236252\pi\)
\(8\) 0 0
\(9\) 5.01693 1.67231
\(10\) 0 0
\(11\) 2.11918 0.638957 0.319478 0.947594i \(-0.396492\pi\)
0.319478 + 0.947594i \(0.396492\pi\)
\(12\) 0 0
\(13\) 2.93611 0.814330 0.407165 0.913355i \(-0.366517\pi\)
0.407165 + 0.913355i \(0.366517\pi\)
\(14\) 0 0
\(15\) −12.0755 −3.11789
\(16\) 0 0
\(17\) −2.84435 −0.689856 −0.344928 0.938629i \(-0.612097\pi\)
−0.344928 + 0.938629i \(0.612097\pi\)
\(18\) 0 0
\(19\) −7.25277 −1.66390 −0.831950 0.554850i \(-0.812776\pi\)
−0.831950 + 0.554850i \(0.812776\pi\)
\(20\) 0 0
\(21\) −11.0417 −2.40951
\(22\) 0 0
\(23\) 0.341822 0.0712748 0.0356374 0.999365i \(-0.488654\pi\)
0.0356374 + 0.999365i \(0.488654\pi\)
\(24\) 0 0
\(25\) 13.1888 2.63777
\(26\) 0 0
\(27\) −5.71078 −1.09904
\(28\) 0 0
\(29\) 0.780311 0.144900 0.0724501 0.997372i \(-0.476918\pi\)
0.0724501 + 0.997372i \(0.476918\pi\)
\(30\) 0 0
\(31\) 5.53879 0.994796 0.497398 0.867522i \(-0.334289\pi\)
0.497398 + 0.867522i \(0.334289\pi\)
\(32\) 0 0
\(33\) −6.00029 −1.04452
\(34\) 0 0
\(35\) 16.6317 2.81127
\(36\) 0 0
\(37\) 6.82954 1.12277 0.561385 0.827555i \(-0.310269\pi\)
0.561385 + 0.827555i \(0.310269\pi\)
\(38\) 0 0
\(39\) −8.31336 −1.33120
\(40\) 0 0
\(41\) −8.86143 −1.38392 −0.691962 0.721934i \(-0.743253\pi\)
−0.691962 + 0.721934i \(0.743253\pi\)
\(42\) 0 0
\(43\) −4.55369 −0.694431 −0.347215 0.937785i \(-0.612873\pi\)
−0.347215 + 0.937785i \(0.612873\pi\)
\(44\) 0 0
\(45\) 21.3964 3.18959
\(46\) 0 0
\(47\) −9.00906 −1.31411 −0.657053 0.753844i \(-0.728197\pi\)
−0.657053 + 0.753844i \(0.728197\pi\)
\(48\) 0 0
\(49\) 8.20784 1.17255
\(50\) 0 0
\(51\) 8.05354 1.12772
\(52\) 0 0
\(53\) 4.97585 0.683485 0.341742 0.939794i \(-0.388983\pi\)
0.341742 + 0.939794i \(0.388983\pi\)
\(54\) 0 0
\(55\) 9.03796 1.21868
\(56\) 0 0
\(57\) 20.5356 2.72001
\(58\) 0 0
\(59\) 1.52810 0.198941 0.0994707 0.995040i \(-0.468285\pi\)
0.0994707 + 0.995040i \(0.468285\pi\)
\(60\) 0 0
\(61\) 7.97529 1.02113 0.510566 0.859839i \(-0.329436\pi\)
0.510566 + 0.859839i \(0.329436\pi\)
\(62\) 0 0
\(63\) 19.5646 2.46491
\(64\) 0 0
\(65\) 12.5220 1.55317
\(66\) 0 0
\(67\) 10.5064 1.28356 0.641778 0.766891i \(-0.278197\pi\)
0.641778 + 0.766891i \(0.278197\pi\)
\(68\) 0 0
\(69\) −0.967841 −0.116514
\(70\) 0 0
\(71\) 13.1735 1.56341 0.781706 0.623648i \(-0.214350\pi\)
0.781706 + 0.623648i \(0.214350\pi\)
\(72\) 0 0
\(73\) 8.40366 0.983574 0.491787 0.870716i \(-0.336344\pi\)
0.491787 + 0.870716i \(0.336344\pi\)
\(74\) 0 0
\(75\) −37.3432 −4.31202
\(76\) 0 0
\(77\) 8.26421 0.941795
\(78\) 0 0
\(79\) −2.38763 −0.268630 −0.134315 0.990939i \(-0.542883\pi\)
−0.134315 + 0.990939i \(0.542883\pi\)
\(80\) 0 0
\(81\) 1.11882 0.124313
\(82\) 0 0
\(83\) −10.0730 −1.10566 −0.552830 0.833294i \(-0.686452\pi\)
−0.552830 + 0.833294i \(0.686452\pi\)
\(84\) 0 0
\(85\) −12.1307 −1.31576
\(86\) 0 0
\(87\) −2.20939 −0.236871
\(88\) 0 0
\(89\) 3.91403 0.414886 0.207443 0.978247i \(-0.433486\pi\)
0.207443 + 0.978247i \(0.433486\pi\)
\(90\) 0 0
\(91\) 11.4500 1.20029
\(92\) 0 0
\(93\) −15.6826 −1.62621
\(94\) 0 0
\(95\) −30.9319 −3.17355
\(96\) 0 0
\(97\) 4.05224 0.411442 0.205721 0.978611i \(-0.434046\pi\)
0.205721 + 0.978611i \(0.434046\pi\)
\(98\) 0 0
\(99\) 10.6318 1.06853
\(100\) 0 0
\(101\) 12.3529 1.22916 0.614580 0.788854i \(-0.289325\pi\)
0.614580 + 0.788854i \(0.289325\pi\)
\(102\) 0 0
\(103\) 18.1312 1.78652 0.893262 0.449536i \(-0.148411\pi\)
0.893262 + 0.449536i \(0.148411\pi\)
\(104\) 0 0
\(105\) −47.0913 −4.59564
\(106\) 0 0
\(107\) −17.8437 −1.72501 −0.862506 0.506047i \(-0.831106\pi\)
−0.862506 + 0.506047i \(0.831106\pi\)
\(108\) 0 0
\(109\) 17.0803 1.63600 0.817999 0.575220i \(-0.195084\pi\)
0.817999 + 0.575220i \(0.195084\pi\)
\(110\) 0 0
\(111\) −19.3373 −1.83541
\(112\) 0 0
\(113\) −9.34564 −0.879164 −0.439582 0.898203i \(-0.644873\pi\)
−0.439582 + 0.898203i \(0.644873\pi\)
\(114\) 0 0
\(115\) 1.45782 0.135942
\(116\) 0 0
\(117\) 14.7303 1.36181
\(118\) 0 0
\(119\) −11.0922 −1.01682
\(120\) 0 0
\(121\) −6.50908 −0.591734
\(122\) 0 0
\(123\) 25.0904 2.26233
\(124\) 0 0
\(125\) 34.9241 3.12371
\(126\) 0 0
\(127\) −16.2726 −1.44396 −0.721982 0.691912i \(-0.756769\pi\)
−0.721982 + 0.691912i \(0.756769\pi\)
\(128\) 0 0
\(129\) 12.8934 1.13520
\(130\) 0 0
\(131\) 0.0185339 0.00161931 0.000809655 1.00000i \(-0.499742\pi\)
0.000809655 1.00000i \(0.499742\pi\)
\(132\) 0 0
\(133\) −28.2838 −2.45252
\(134\) 0 0
\(135\) −24.3556 −2.09619
\(136\) 0 0
\(137\) 1.93835 0.165605 0.0828023 0.996566i \(-0.473613\pi\)
0.0828023 + 0.996566i \(0.473613\pi\)
\(138\) 0 0
\(139\) −11.6399 −0.987284 −0.493642 0.869665i \(-0.664335\pi\)
−0.493642 + 0.869665i \(0.664335\pi\)
\(140\) 0 0
\(141\) 25.5084 2.14820
\(142\) 0 0
\(143\) 6.22215 0.520322
\(144\) 0 0
\(145\) 3.32790 0.276367
\(146\) 0 0
\(147\) −23.2398 −1.91679
\(148\) 0 0
\(149\) 2.32221 0.190243 0.0951215 0.995466i \(-0.469676\pi\)
0.0951215 + 0.995466i \(0.469676\pi\)
\(150\) 0 0
\(151\) −10.9111 −0.887933 −0.443966 0.896043i \(-0.646429\pi\)
−0.443966 + 0.896043i \(0.646429\pi\)
\(152\) 0 0
\(153\) −14.2699 −1.15365
\(154\) 0 0
\(155\) 23.6221 1.89737
\(156\) 0 0
\(157\) −10.3549 −0.826413 −0.413207 0.910637i \(-0.635591\pi\)
−0.413207 + 0.910637i \(0.635591\pi\)
\(158\) 0 0
\(159\) −14.0887 −1.11731
\(160\) 0 0
\(161\) 1.33301 0.105056
\(162\) 0 0
\(163\) −3.98006 −0.311742 −0.155871 0.987777i \(-0.549818\pi\)
−0.155871 + 0.987777i \(0.549818\pi\)
\(164\) 0 0
\(165\) −25.5903 −1.99220
\(166\) 0 0
\(167\) 15.3238 1.18579 0.592894 0.805280i \(-0.297985\pi\)
0.592894 + 0.805280i \(0.297985\pi\)
\(168\) 0 0
\(169\) −4.37926 −0.336866
\(170\) 0 0
\(171\) −36.3867 −2.78256
\(172\) 0 0
\(173\) 6.23052 0.473697 0.236849 0.971547i \(-0.423885\pi\)
0.236849 + 0.971547i \(0.423885\pi\)
\(174\) 0 0
\(175\) 51.4328 3.88796
\(176\) 0 0
\(177\) −4.32668 −0.325214
\(178\) 0 0
\(179\) 1.69979 0.127049 0.0635243 0.997980i \(-0.479766\pi\)
0.0635243 + 0.997980i \(0.479766\pi\)
\(180\) 0 0
\(181\) −13.5760 −1.00910 −0.504549 0.863383i \(-0.668341\pi\)
−0.504549 + 0.863383i \(0.668341\pi\)
\(182\) 0 0
\(183\) −22.5814 −1.66926
\(184\) 0 0
\(185\) 29.1269 2.14145
\(186\) 0 0
\(187\) −6.02769 −0.440788
\(188\) 0 0
\(189\) −22.2705 −1.61994
\(190\) 0 0
\(191\) −14.5539 −1.05308 −0.526542 0.850149i \(-0.676512\pi\)
−0.526542 + 0.850149i \(0.676512\pi\)
\(192\) 0 0
\(193\) −24.9503 −1.79596 −0.897981 0.440034i \(-0.854966\pi\)
−0.897981 + 0.440034i \(0.854966\pi\)
\(194\) 0 0
\(195\) −35.4551 −2.53899
\(196\) 0 0
\(197\) −19.0165 −1.35487 −0.677436 0.735582i \(-0.736909\pi\)
−0.677436 + 0.735582i \(0.736909\pi\)
\(198\) 0 0
\(199\) 19.9265 1.41255 0.706277 0.707935i \(-0.250373\pi\)
0.706277 + 0.707935i \(0.250373\pi\)
\(200\) 0 0
\(201\) −29.7479 −2.09825
\(202\) 0 0
\(203\) 3.04300 0.213576
\(204\) 0 0
\(205\) −37.7926 −2.63955
\(206\) 0 0
\(207\) 1.71490 0.119194
\(208\) 0 0
\(209\) −15.3699 −1.06316
\(210\) 0 0
\(211\) 23.9950 1.65189 0.825943 0.563754i \(-0.190643\pi\)
0.825943 + 0.563754i \(0.190643\pi\)
\(212\) 0 0
\(213\) −37.2998 −2.55574
\(214\) 0 0
\(215\) −19.4207 −1.32448
\(216\) 0 0
\(217\) 21.5998 1.46629
\(218\) 0 0
\(219\) −23.7943 −1.60787
\(220\) 0 0
\(221\) −8.35132 −0.561770
\(222\) 0 0
\(223\) 8.43959 0.565157 0.282579 0.959244i \(-0.408810\pi\)
0.282579 + 0.959244i \(0.408810\pi\)
\(224\) 0 0
\(225\) 66.1676 4.41117
\(226\) 0 0
\(227\) 5.51956 0.366346 0.183173 0.983081i \(-0.441363\pi\)
0.183173 + 0.983081i \(0.441363\pi\)
\(228\) 0 0
\(229\) 16.8298 1.11214 0.556072 0.831134i \(-0.312308\pi\)
0.556072 + 0.831134i \(0.312308\pi\)
\(230\) 0 0
\(231\) −23.3995 −1.53957
\(232\) 0 0
\(233\) −5.63332 −0.369051 −0.184526 0.982828i \(-0.559075\pi\)
−0.184526 + 0.982828i \(0.559075\pi\)
\(234\) 0 0
\(235\) −38.4222 −2.50639
\(236\) 0 0
\(237\) 6.76039 0.439135
\(238\) 0 0
\(239\) −23.2855 −1.50621 −0.753106 0.657900i \(-0.771445\pi\)
−0.753106 + 0.657900i \(0.771445\pi\)
\(240\) 0 0
\(241\) −22.5636 −1.45345 −0.726724 0.686929i \(-0.758958\pi\)
−0.726724 + 0.686929i \(0.758958\pi\)
\(242\) 0 0
\(243\) 13.9645 0.895823
\(244\) 0 0
\(245\) 35.0051 2.23639
\(246\) 0 0
\(247\) −21.2949 −1.35496
\(248\) 0 0
\(249\) 28.5210 1.80744
\(250\) 0 0
\(251\) 14.5747 0.919947 0.459974 0.887933i \(-0.347859\pi\)
0.459974 + 0.887933i \(0.347859\pi\)
\(252\) 0 0
\(253\) 0.724382 0.0455415
\(254\) 0 0
\(255\) 34.3471 2.15090
\(256\) 0 0
\(257\) 12.5815 0.784810 0.392405 0.919793i \(-0.371643\pi\)
0.392405 + 0.919793i \(0.371643\pi\)
\(258\) 0 0
\(259\) 26.6333 1.65491
\(260\) 0 0
\(261\) 3.91477 0.242318
\(262\) 0 0
\(263\) −4.60784 −0.284132 −0.142066 0.989857i \(-0.545374\pi\)
−0.142066 + 0.989857i \(0.545374\pi\)
\(264\) 0 0
\(265\) 21.2212 1.30361
\(266\) 0 0
\(267\) −11.0823 −0.678223
\(268\) 0 0
\(269\) 11.5415 0.703698 0.351849 0.936057i \(-0.385553\pi\)
0.351849 + 0.936057i \(0.385553\pi\)
\(270\) 0 0
\(271\) 29.6168 1.79909 0.899547 0.436823i \(-0.143897\pi\)
0.899547 + 0.436823i \(0.143897\pi\)
\(272\) 0 0
\(273\) −32.4198 −1.96213
\(274\) 0 0
\(275\) 27.9495 1.68542
\(276\) 0 0
\(277\) 28.2029 1.69455 0.847273 0.531158i \(-0.178243\pi\)
0.847273 + 0.531158i \(0.178243\pi\)
\(278\) 0 0
\(279\) 27.7877 1.66361
\(280\) 0 0
\(281\) 1.55832 0.0929616 0.0464808 0.998919i \(-0.485199\pi\)
0.0464808 + 0.998919i \(0.485199\pi\)
\(282\) 0 0
\(283\) −3.61488 −0.214883 −0.107441 0.994211i \(-0.534266\pi\)
−0.107441 + 0.994211i \(0.534266\pi\)
\(284\) 0 0
\(285\) 87.5812 5.18786
\(286\) 0 0
\(287\) −34.5571 −2.03984
\(288\) 0 0
\(289\) −8.90968 −0.524099
\(290\) 0 0
\(291\) −11.4736 −0.672593
\(292\) 0 0
\(293\) 15.6850 0.916327 0.458163 0.888868i \(-0.348507\pi\)
0.458163 + 0.888868i \(0.348507\pi\)
\(294\) 0 0
\(295\) 6.51709 0.379440
\(296\) 0 0
\(297\) −12.1022 −0.702239
\(298\) 0 0
\(299\) 1.00363 0.0580412
\(300\) 0 0
\(301\) −17.7581 −1.02356
\(302\) 0 0
\(303\) −34.9763 −2.00933
\(304\) 0 0
\(305\) 34.0133 1.94760
\(306\) 0 0
\(307\) 25.4816 1.45431 0.727155 0.686473i \(-0.240842\pi\)
0.727155 + 0.686473i \(0.240842\pi\)
\(308\) 0 0
\(309\) −51.3371 −2.92047
\(310\) 0 0
\(311\) 26.7911 1.51918 0.759592 0.650400i \(-0.225399\pi\)
0.759592 + 0.650400i \(0.225399\pi\)
\(312\) 0 0
\(313\) 32.6430 1.84509 0.922546 0.385886i \(-0.126104\pi\)
0.922546 + 0.385886i \(0.126104\pi\)
\(314\) 0 0
\(315\) 83.4401 4.70131
\(316\) 0 0
\(317\) 5.25413 0.295101 0.147551 0.989054i \(-0.452861\pi\)
0.147551 + 0.989054i \(0.452861\pi\)
\(318\) 0 0
\(319\) 1.65362 0.0925849
\(320\) 0 0
\(321\) 50.5229 2.81991
\(322\) 0 0
\(323\) 20.6294 1.14785
\(324\) 0 0
\(325\) 38.7239 2.14802
\(326\) 0 0
\(327\) −48.3615 −2.67440
\(328\) 0 0
\(329\) −35.1328 −1.93694
\(330\) 0 0
\(331\) −20.8852 −1.14795 −0.573976 0.818872i \(-0.694600\pi\)
−0.573976 + 0.818872i \(0.694600\pi\)
\(332\) 0 0
\(333\) 34.2634 1.87762
\(334\) 0 0
\(335\) 44.8079 2.44812
\(336\) 0 0
\(337\) 6.38006 0.347544 0.173772 0.984786i \(-0.444404\pi\)
0.173772 + 0.984786i \(0.444404\pi\)
\(338\) 0 0
\(339\) 26.4614 1.43719
\(340\) 0 0
\(341\) 11.7377 0.635632
\(342\) 0 0
\(343\) 4.71022 0.254328
\(344\) 0 0
\(345\) −4.12769 −0.222227
\(346\) 0 0
\(347\) −6.57016 −0.352705 −0.176352 0.984327i \(-0.556430\pi\)
−0.176352 + 0.984327i \(0.556430\pi\)
\(348\) 0 0
\(349\) −15.2031 −0.813801 −0.406901 0.913472i \(-0.633390\pi\)
−0.406901 + 0.913472i \(0.633390\pi\)
\(350\) 0 0
\(351\) −16.7675 −0.894982
\(352\) 0 0
\(353\) −15.7242 −0.836916 −0.418458 0.908236i \(-0.637429\pi\)
−0.418458 + 0.908236i \(0.637429\pi\)
\(354\) 0 0
\(355\) 56.1830 2.98188
\(356\) 0 0
\(357\) 31.4066 1.66221
\(358\) 0 0
\(359\) −25.5096 −1.34635 −0.673174 0.739484i \(-0.735069\pi\)
−0.673174 + 0.739484i \(0.735069\pi\)
\(360\) 0 0
\(361\) 33.6027 1.76857
\(362\) 0 0
\(363\) 18.4299 0.967320
\(364\) 0 0
\(365\) 35.8403 1.87596
\(366\) 0 0
\(367\) −8.13935 −0.424871 −0.212435 0.977175i \(-0.568139\pi\)
−0.212435 + 0.977175i \(0.568139\pi\)
\(368\) 0 0
\(369\) −44.4572 −2.31435
\(370\) 0 0
\(371\) 19.4044 1.00743
\(372\) 0 0
\(373\) 8.29033 0.429257 0.214628 0.976696i \(-0.431146\pi\)
0.214628 + 0.976696i \(0.431146\pi\)
\(374\) 0 0
\(375\) −98.8848 −5.10639
\(376\) 0 0
\(377\) 2.29108 0.117997
\(378\) 0 0
\(379\) 13.5481 0.695921 0.347960 0.937509i \(-0.386874\pi\)
0.347960 + 0.937509i \(0.386874\pi\)
\(380\) 0 0
\(381\) 46.0747 2.36048
\(382\) 0 0
\(383\) −21.0800 −1.07714 −0.538568 0.842582i \(-0.681034\pi\)
−0.538568 + 0.842582i \(0.681034\pi\)
\(384\) 0 0
\(385\) 35.2455 1.79628
\(386\) 0 0
\(387\) −22.8455 −1.16130
\(388\) 0 0
\(389\) −9.07613 −0.460178 −0.230089 0.973170i \(-0.573902\pi\)
−0.230089 + 0.973170i \(0.573902\pi\)
\(390\) 0 0
\(391\) −0.972261 −0.0491693
\(392\) 0 0
\(393\) −0.0524771 −0.00264712
\(394\) 0 0
\(395\) −10.1829 −0.512356
\(396\) 0 0
\(397\) −16.3595 −0.821060 −0.410530 0.911847i \(-0.634656\pi\)
−0.410530 + 0.911847i \(0.634656\pi\)
\(398\) 0 0
\(399\) 80.0833 4.00918
\(400\) 0 0
\(401\) 21.7143 1.08436 0.542180 0.840263i \(-0.317599\pi\)
0.542180 + 0.840263i \(0.317599\pi\)
\(402\) 0 0
\(403\) 16.2625 0.810093
\(404\) 0 0
\(405\) 4.77157 0.237101
\(406\) 0 0
\(407\) 14.4730 0.717402
\(408\) 0 0
\(409\) −33.0374 −1.63360 −0.816798 0.576924i \(-0.804253\pi\)
−0.816798 + 0.576924i \(0.804253\pi\)
\(410\) 0 0
\(411\) −5.48829 −0.270717
\(412\) 0 0
\(413\) 5.95916 0.293231
\(414\) 0 0
\(415\) −42.9599 −2.10882
\(416\) 0 0
\(417\) 32.9574 1.61393
\(418\) 0 0
\(419\) −28.2484 −1.38003 −0.690013 0.723797i \(-0.742395\pi\)
−0.690013 + 0.723797i \(0.742395\pi\)
\(420\) 0 0
\(421\) −7.83979 −0.382088 −0.191044 0.981581i \(-0.561187\pi\)
−0.191044 + 0.981581i \(0.561187\pi\)
\(422\) 0 0
\(423\) −45.1978 −2.19759
\(424\) 0 0
\(425\) −37.5137 −1.81968
\(426\) 0 0
\(427\) 31.1014 1.50510
\(428\) 0 0
\(429\) −17.6175 −0.850581
\(430\) 0 0
\(431\) −13.0936 −0.630697 −0.315348 0.948976i \(-0.602121\pi\)
−0.315348 + 0.948976i \(0.602121\pi\)
\(432\) 0 0
\(433\) 3.22919 0.155185 0.0775926 0.996985i \(-0.475277\pi\)
0.0775926 + 0.996985i \(0.475277\pi\)
\(434\) 0 0
\(435\) −9.42268 −0.451783
\(436\) 0 0
\(437\) −2.47916 −0.118594
\(438\) 0 0
\(439\) −10.1627 −0.485039 −0.242520 0.970147i \(-0.577974\pi\)
−0.242520 + 0.970147i \(0.577974\pi\)
\(440\) 0 0
\(441\) 41.1782 1.96086
\(442\) 0 0
\(443\) −1.09206 −0.0518855 −0.0259427 0.999663i \(-0.508259\pi\)
−0.0259427 + 0.999663i \(0.508259\pi\)
\(444\) 0 0
\(445\) 16.6927 0.791310
\(446\) 0 0
\(447\) −6.57516 −0.310994
\(448\) 0 0
\(449\) 9.18522 0.433477 0.216739 0.976230i \(-0.430458\pi\)
0.216739 + 0.976230i \(0.430458\pi\)
\(450\) 0 0
\(451\) −18.7790 −0.884267
\(452\) 0 0
\(453\) 30.8939 1.45152
\(454\) 0 0
\(455\) 48.8325 2.28930
\(456\) 0 0
\(457\) −1.62771 −0.0761412 −0.0380706 0.999275i \(-0.512121\pi\)
−0.0380706 + 0.999275i \(0.512121\pi\)
\(458\) 0 0
\(459\) 16.2435 0.758179
\(460\) 0 0
\(461\) −16.6795 −0.776842 −0.388421 0.921482i \(-0.626979\pi\)
−0.388421 + 0.921482i \(0.626979\pi\)
\(462\) 0 0
\(463\) 4.78496 0.222376 0.111188 0.993799i \(-0.464534\pi\)
0.111188 + 0.993799i \(0.464534\pi\)
\(464\) 0 0
\(465\) −66.8839 −3.10167
\(466\) 0 0
\(467\) 37.6881 1.74400 0.871999 0.489508i \(-0.162824\pi\)
0.871999 + 0.489508i \(0.162824\pi\)
\(468\) 0 0
\(469\) 40.9719 1.89190
\(470\) 0 0
\(471\) 29.3191 1.35095
\(472\) 0 0
\(473\) −9.65009 −0.443711
\(474\) 0 0
\(475\) −95.6557 −4.38899
\(476\) 0 0
\(477\) 24.9635 1.14300
\(478\) 0 0
\(479\) −2.57745 −0.117767 −0.0588834 0.998265i \(-0.518754\pi\)
−0.0588834 + 0.998265i \(0.518754\pi\)
\(480\) 0 0
\(481\) 20.0523 0.914306
\(482\) 0 0
\(483\) −3.77431 −0.171737
\(484\) 0 0
\(485\) 17.2821 0.784741
\(486\) 0 0
\(487\) 4.99998 0.226571 0.113285 0.993562i \(-0.463863\pi\)
0.113285 + 0.993562i \(0.463863\pi\)
\(488\) 0 0
\(489\) 11.2692 0.509612
\(490\) 0 0
\(491\) 16.9889 0.766699 0.383350 0.923603i \(-0.374770\pi\)
0.383350 + 0.923603i \(0.374770\pi\)
\(492\) 0 0
\(493\) −2.21948 −0.0999602
\(494\) 0 0
\(495\) 45.3428 2.03801
\(496\) 0 0
\(497\) 51.3731 2.30440
\(498\) 0 0
\(499\) 13.9474 0.624373 0.312187 0.950021i \(-0.398939\pi\)
0.312187 + 0.950021i \(0.398939\pi\)
\(500\) 0 0
\(501\) −43.3880 −1.93843
\(502\) 0 0
\(503\) −21.7036 −0.967717 −0.483858 0.875146i \(-0.660765\pi\)
−0.483858 + 0.875146i \(0.660765\pi\)
\(504\) 0 0
\(505\) 52.6832 2.34437
\(506\) 0 0
\(507\) 12.3995 0.550682
\(508\) 0 0
\(509\) −21.7333 −0.963311 −0.481656 0.876361i \(-0.659964\pi\)
−0.481656 + 0.876361i \(0.659964\pi\)
\(510\) 0 0
\(511\) 32.7719 1.44975
\(512\) 0 0
\(513\) 41.4190 1.82869
\(514\) 0 0
\(515\) 77.3268 3.40743
\(516\) 0 0
\(517\) −19.0918 −0.839657
\(518\) 0 0
\(519\) −17.6412 −0.774363
\(520\) 0 0
\(521\) 17.0548 0.747186 0.373593 0.927593i \(-0.378126\pi\)
0.373593 + 0.927593i \(0.378126\pi\)
\(522\) 0 0
\(523\) 41.3195 1.80678 0.903388 0.428824i \(-0.141072\pi\)
0.903388 + 0.428824i \(0.141072\pi\)
\(524\) 0 0
\(525\) −145.628 −6.35572
\(526\) 0 0
\(527\) −15.7543 −0.686266
\(528\) 0 0
\(529\) −22.8832 −0.994920
\(530\) 0 0
\(531\) 7.66636 0.332692
\(532\) 0 0
\(533\) −26.0181 −1.12697
\(534\) 0 0
\(535\) −76.1003 −3.29010
\(536\) 0 0
\(537\) −4.81283 −0.207689
\(538\) 0 0
\(539\) 17.3939 0.749208
\(540\) 0 0
\(541\) −38.4177 −1.65170 −0.825852 0.563887i \(-0.809305\pi\)
−0.825852 + 0.563887i \(0.809305\pi\)
\(542\) 0 0
\(543\) 38.4394 1.64959
\(544\) 0 0
\(545\) 72.8448 3.12033
\(546\) 0 0
\(547\) −34.4323 −1.47222 −0.736109 0.676864i \(-0.763339\pi\)
−0.736109 + 0.676864i \(0.763339\pi\)
\(548\) 0 0
\(549\) 40.0115 1.70765
\(550\) 0 0
\(551\) −5.65942 −0.241099
\(552\) 0 0
\(553\) −9.31111 −0.395949
\(554\) 0 0
\(555\) −82.4704 −3.50068
\(556\) 0 0
\(557\) −31.8370 −1.34898 −0.674488 0.738286i \(-0.735636\pi\)
−0.674488 + 0.738286i \(0.735636\pi\)
\(558\) 0 0
\(559\) −13.3701 −0.565496
\(560\) 0 0
\(561\) 17.0669 0.720565
\(562\) 0 0
\(563\) −11.4508 −0.482592 −0.241296 0.970452i \(-0.577572\pi\)
−0.241296 + 0.970452i \(0.577572\pi\)
\(564\) 0 0
\(565\) −39.8576 −1.67682
\(566\) 0 0
\(567\) 4.36308 0.183232
\(568\) 0 0
\(569\) −25.5735 −1.07210 −0.536049 0.844187i \(-0.680084\pi\)
−0.536049 + 0.844187i \(0.680084\pi\)
\(570\) 0 0
\(571\) 6.15130 0.257424 0.128712 0.991682i \(-0.458916\pi\)
0.128712 + 0.991682i \(0.458916\pi\)
\(572\) 0 0
\(573\) 41.2082 1.72150
\(574\) 0 0
\(575\) 4.50824 0.188007
\(576\) 0 0
\(577\) −17.0654 −0.710444 −0.355222 0.934782i \(-0.615595\pi\)
−0.355222 + 0.934782i \(0.615595\pi\)
\(578\) 0 0
\(579\) 70.6448 2.93590
\(580\) 0 0
\(581\) −39.2821 −1.62969
\(582\) 0 0
\(583\) 10.5447 0.436717
\(584\) 0 0
\(585\) 62.8222 2.59738
\(586\) 0 0
\(587\) 26.9333 1.11166 0.555828 0.831298i \(-0.312401\pi\)
0.555828 + 0.831298i \(0.312401\pi\)
\(588\) 0 0
\(589\) −40.1716 −1.65524
\(590\) 0 0
\(591\) 53.8437 2.21484
\(592\) 0 0
\(593\) −24.1893 −0.993334 −0.496667 0.867941i \(-0.665443\pi\)
−0.496667 + 0.867941i \(0.665443\pi\)
\(594\) 0 0
\(595\) −47.3063 −1.93937
\(596\) 0 0
\(597\) −56.4204 −2.30913
\(598\) 0 0
\(599\) −7.86196 −0.321231 −0.160615 0.987017i \(-0.551348\pi\)
−0.160615 + 0.987017i \(0.551348\pi\)
\(600\) 0 0
\(601\) −11.6031 −0.473300 −0.236650 0.971595i \(-0.576049\pi\)
−0.236650 + 0.971595i \(0.576049\pi\)
\(602\) 0 0
\(603\) 52.7097 2.14650
\(604\) 0 0
\(605\) −27.7602 −1.12861
\(606\) 0 0
\(607\) −16.6568 −0.676080 −0.338040 0.941132i \(-0.609764\pi\)
−0.338040 + 0.941132i \(0.609764\pi\)
\(608\) 0 0
\(609\) −8.61600 −0.349138
\(610\) 0 0
\(611\) −26.4516 −1.07012
\(612\) 0 0
\(613\) 9.70838 0.392118 0.196059 0.980592i \(-0.437186\pi\)
0.196059 + 0.980592i \(0.437186\pi\)
\(614\) 0 0
\(615\) 107.007 4.31492
\(616\) 0 0
\(617\) 24.9271 1.00353 0.501764 0.865004i \(-0.332684\pi\)
0.501764 + 0.865004i \(0.332684\pi\)
\(618\) 0 0
\(619\) −24.2158 −0.973316 −0.486658 0.873593i \(-0.661784\pi\)
−0.486658 + 0.873593i \(0.661784\pi\)
\(620\) 0 0
\(621\) −1.95207 −0.0783339
\(622\) 0 0
\(623\) 15.2636 0.611524
\(624\) 0 0
\(625\) 83.0015 3.32006
\(626\) 0 0
\(627\) 43.5187 1.73797
\(628\) 0 0
\(629\) −19.4256 −0.774549
\(630\) 0 0
\(631\) 9.57832 0.381307 0.190653 0.981657i \(-0.438939\pi\)
0.190653 + 0.981657i \(0.438939\pi\)
\(632\) 0 0
\(633\) −67.9400 −2.70037
\(634\) 0 0
\(635\) −69.4002 −2.75406
\(636\) 0 0
\(637\) 24.0991 0.954841
\(638\) 0 0
\(639\) 66.0907 2.61451
\(640\) 0 0
\(641\) −30.2024 −1.19292 −0.596461 0.802642i \(-0.703427\pi\)
−0.596461 + 0.802642i \(0.703427\pi\)
\(642\) 0 0
\(643\) −29.2715 −1.15436 −0.577178 0.816618i \(-0.695846\pi\)
−0.577178 + 0.816618i \(0.695846\pi\)
\(644\) 0 0
\(645\) 54.9883 2.16516
\(646\) 0 0
\(647\) 27.8158 1.09355 0.546776 0.837279i \(-0.315855\pi\)
0.546776 + 0.837279i \(0.315855\pi\)
\(648\) 0 0
\(649\) 3.23831 0.127115
\(650\) 0 0
\(651\) −61.1579 −2.39697
\(652\) 0 0
\(653\) −5.73215 −0.224316 −0.112158 0.993690i \(-0.535776\pi\)
−0.112158 + 0.993690i \(0.535776\pi\)
\(654\) 0 0
\(655\) 0.0790439 0.00308850
\(656\) 0 0
\(657\) 42.1606 1.64484
\(658\) 0 0
\(659\) 32.2628 1.25678 0.628390 0.777898i \(-0.283714\pi\)
0.628390 + 0.777898i \(0.283714\pi\)
\(660\) 0 0
\(661\) −12.2122 −0.474999 −0.237500 0.971388i \(-0.576328\pi\)
−0.237500 + 0.971388i \(0.576328\pi\)
\(662\) 0 0
\(663\) 23.6461 0.918338
\(664\) 0 0
\(665\) −120.626 −4.67767
\(666\) 0 0
\(667\) 0.266728 0.0103277
\(668\) 0 0
\(669\) −23.8960 −0.923874
\(670\) 0 0
\(671\) 16.9011 0.652459
\(672\) 0 0
\(673\) 4.21631 0.162527 0.0812635 0.996693i \(-0.474104\pi\)
0.0812635 + 0.996693i \(0.474104\pi\)
\(674\) 0 0
\(675\) −75.3186 −2.89902
\(676\) 0 0
\(677\) 37.3291 1.43467 0.717337 0.696726i \(-0.245361\pi\)
0.717337 + 0.696726i \(0.245361\pi\)
\(678\) 0 0
\(679\) 15.8026 0.606448
\(680\) 0 0
\(681\) −15.6282 −0.598873
\(682\) 0 0
\(683\) 28.4120 1.08715 0.543577 0.839359i \(-0.317069\pi\)
0.543577 + 0.839359i \(0.317069\pi\)
\(684\) 0 0
\(685\) 8.26676 0.315857
\(686\) 0 0
\(687\) −47.6522 −1.81804
\(688\) 0 0
\(689\) 14.6096 0.556582
\(690\) 0 0
\(691\) −32.8252 −1.24873 −0.624364 0.781134i \(-0.714642\pi\)
−0.624364 + 0.781134i \(0.714642\pi\)
\(692\) 0 0
\(693\) 41.4610 1.57497
\(694\) 0 0
\(695\) −49.6423 −1.88304
\(696\) 0 0
\(697\) 25.2050 0.954707
\(698\) 0 0
\(699\) 15.9503 0.603295
\(700\) 0 0
\(701\) −31.2548 −1.18048 −0.590239 0.807229i \(-0.700967\pi\)
−0.590239 + 0.807229i \(0.700967\pi\)
\(702\) 0 0
\(703\) −49.5331 −1.86818
\(704\) 0 0
\(705\) 108.789 4.09724
\(706\) 0 0
\(707\) 48.1729 1.81173
\(708\) 0 0
\(709\) −2.69132 −0.101075 −0.0505373 0.998722i \(-0.516093\pi\)
−0.0505373 + 0.998722i \(0.516093\pi\)
\(710\) 0 0
\(711\) −11.9786 −0.449233
\(712\) 0 0
\(713\) 1.89328 0.0709039
\(714\) 0 0
\(715\) 26.5364 0.992407
\(716\) 0 0
\(717\) 65.9309 2.46223
\(718\) 0 0
\(719\) −5.33934 −0.199124 −0.0995620 0.995031i \(-0.531744\pi\)
−0.0995620 + 0.995031i \(0.531744\pi\)
\(720\) 0 0
\(721\) 70.7068 2.63326
\(722\) 0 0
\(723\) 63.8870 2.37598
\(724\) 0 0
\(725\) 10.2914 0.382213
\(726\) 0 0
\(727\) −13.9052 −0.515716 −0.257858 0.966183i \(-0.583017\pi\)
−0.257858 + 0.966183i \(0.583017\pi\)
\(728\) 0 0
\(729\) −42.8958 −1.58873
\(730\) 0 0
\(731\) 12.9523 0.479057
\(732\) 0 0
\(733\) 10.5028 0.387931 0.193965 0.981008i \(-0.437865\pi\)
0.193965 + 0.981008i \(0.437865\pi\)
\(734\) 0 0
\(735\) −99.1141 −3.65588
\(736\) 0 0
\(737\) 22.2649 0.820136
\(738\) 0 0
\(739\) −31.6931 −1.16585 −0.582925 0.812526i \(-0.698092\pi\)
−0.582925 + 0.812526i \(0.698092\pi\)
\(740\) 0 0
\(741\) 60.2949 2.21499
\(742\) 0 0
\(743\) 9.02988 0.331274 0.165637 0.986187i \(-0.447032\pi\)
0.165637 + 0.986187i \(0.447032\pi\)
\(744\) 0 0
\(745\) 9.90386 0.362849
\(746\) 0 0
\(747\) −50.5358 −1.84901
\(748\) 0 0
\(749\) −69.5853 −2.54259
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −41.2671 −1.50386
\(754\) 0 0
\(755\) −46.5341 −1.69355
\(756\) 0 0
\(757\) −16.5770 −0.602503 −0.301251 0.953545i \(-0.597404\pi\)
−0.301251 + 0.953545i \(0.597404\pi\)
\(758\) 0 0
\(759\) −2.05103 −0.0744477
\(760\) 0 0
\(761\) 25.0104 0.906627 0.453313 0.891351i \(-0.350242\pi\)
0.453313 + 0.891351i \(0.350242\pi\)
\(762\) 0 0
\(763\) 66.6085 2.41139
\(764\) 0 0
\(765\) −60.8588 −2.20036
\(766\) 0 0
\(767\) 4.48666 0.162004
\(768\) 0 0
\(769\) 26.5552 0.957606 0.478803 0.877922i \(-0.341071\pi\)
0.478803 + 0.877922i \(0.341071\pi\)
\(770\) 0 0
\(771\) −35.6234 −1.28294
\(772\) 0 0
\(773\) −6.05848 −0.217908 −0.108954 0.994047i \(-0.534750\pi\)
−0.108954 + 0.994047i \(0.534750\pi\)
\(774\) 0 0
\(775\) 73.0503 2.62404
\(776\) 0 0
\(777\) −75.4101 −2.70532
\(778\) 0 0
\(779\) 64.2700 2.30271
\(780\) 0 0
\(781\) 27.9171 0.998952
\(782\) 0 0
\(783\) −4.45619 −0.159251
\(784\) 0 0
\(785\) −44.1621 −1.57621
\(786\) 0 0
\(787\) 5.26096 0.187533 0.0937665 0.995594i \(-0.470109\pi\)
0.0937665 + 0.995594i \(0.470109\pi\)
\(788\) 0 0
\(789\) 13.0467 0.464476
\(790\) 0 0
\(791\) −36.4454 −1.29585
\(792\) 0 0
\(793\) 23.4163 0.831538
\(794\) 0 0
\(795\) −60.0860 −2.13103
\(796\) 0 0
\(797\) 4.80092 0.170057 0.0850287 0.996378i \(-0.472902\pi\)
0.0850287 + 0.996378i \(0.472902\pi\)
\(798\) 0 0
\(799\) 25.6249 0.906544
\(800\) 0 0
\(801\) 19.6364 0.693819
\(802\) 0 0
\(803\) 17.8089 0.628461
\(804\) 0 0
\(805\) 5.68508 0.200373
\(806\) 0 0
\(807\) −32.6789 −1.15035
\(808\) 0 0
\(809\) −38.2087 −1.34335 −0.671674 0.740847i \(-0.734424\pi\)
−0.671674 + 0.740847i \(0.734424\pi\)
\(810\) 0 0
\(811\) 30.7417 1.07949 0.539743 0.841830i \(-0.318521\pi\)
0.539743 + 0.841830i \(0.318521\pi\)
\(812\) 0 0
\(813\) −83.8577 −2.94102
\(814\) 0 0
\(815\) −16.9743 −0.594584
\(816\) 0 0
\(817\) 33.0269 1.15546
\(818\) 0 0
\(819\) 57.4439 2.00725
\(820\) 0 0
\(821\) 17.2126 0.600725 0.300363 0.953825i \(-0.402892\pi\)
0.300363 + 0.953825i \(0.402892\pi\)
\(822\) 0 0
\(823\) −7.02994 −0.245048 −0.122524 0.992466i \(-0.539099\pi\)
−0.122524 + 0.992466i \(0.539099\pi\)
\(824\) 0 0
\(825\) −79.1369 −2.75519
\(826\) 0 0
\(827\) 46.4072 1.61374 0.806869 0.590731i \(-0.201161\pi\)
0.806869 + 0.590731i \(0.201161\pi\)
\(828\) 0 0
\(829\) −45.7914 −1.59040 −0.795201 0.606346i \(-0.792635\pi\)
−0.795201 + 0.606346i \(0.792635\pi\)
\(830\) 0 0
\(831\) −79.8541 −2.77011
\(832\) 0 0
\(833\) −23.3459 −0.808889
\(834\) 0 0
\(835\) 65.3534 2.26165
\(836\) 0 0
\(837\) −31.6308 −1.09332
\(838\) 0 0
\(839\) −7.11008 −0.245467 −0.122734 0.992440i \(-0.539166\pi\)
−0.122734 + 0.992440i \(0.539166\pi\)
\(840\) 0 0
\(841\) −28.3911 −0.979004
\(842\) 0 0
\(843\) −4.41226 −0.151966
\(844\) 0 0
\(845\) −18.6768 −0.642503
\(846\) 0 0
\(847\) −25.3836 −0.872190
\(848\) 0 0
\(849\) 10.2353 0.351273
\(850\) 0 0
\(851\) 2.33449 0.0800252
\(852\) 0 0
\(853\) 19.4543 0.666102 0.333051 0.942909i \(-0.391922\pi\)
0.333051 + 0.942909i \(0.391922\pi\)
\(854\) 0 0
\(855\) −155.183 −5.30716
\(856\) 0 0
\(857\) −21.4375 −0.732290 −0.366145 0.930558i \(-0.619323\pi\)
−0.366145 + 0.930558i \(0.619323\pi\)
\(858\) 0 0
\(859\) −30.0759 −1.02618 −0.513089 0.858335i \(-0.671499\pi\)
−0.513089 + 0.858335i \(0.671499\pi\)
\(860\) 0 0
\(861\) 97.8457 3.33457
\(862\) 0 0
\(863\) 24.2949 0.827008 0.413504 0.910502i \(-0.364305\pi\)
0.413504 + 0.910502i \(0.364305\pi\)
\(864\) 0 0
\(865\) 26.5722 0.903480
\(866\) 0 0
\(867\) 25.2270 0.856755
\(868\) 0 0
\(869\) −5.05983 −0.171643
\(870\) 0 0
\(871\) 30.8478 1.04524
\(872\) 0 0
\(873\) 20.3298 0.688059
\(874\) 0 0
\(875\) 136.194 4.60421
\(876\) 0 0
\(877\) 31.2901 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(878\) 0 0
\(879\) −44.4108 −1.49794
\(880\) 0 0
\(881\) 1.89954 0.0639970 0.0319985 0.999488i \(-0.489813\pi\)
0.0319985 + 0.999488i \(0.489813\pi\)
\(882\) 0 0
\(883\) 55.1920 1.85736 0.928679 0.370884i \(-0.120945\pi\)
0.928679 + 0.370884i \(0.120945\pi\)
\(884\) 0 0
\(885\) −18.4526 −0.620278
\(886\) 0 0
\(887\) −29.6398 −0.995206 −0.497603 0.867405i \(-0.665786\pi\)
−0.497603 + 0.867405i \(0.665786\pi\)
\(888\) 0 0
\(889\) −63.4588 −2.12834
\(890\) 0 0
\(891\) 2.37098 0.0794307
\(892\) 0 0
\(893\) 65.3407 2.18654
\(894\) 0 0
\(895\) 7.24935 0.242319
\(896\) 0 0
\(897\) −2.84169 −0.0948812
\(898\) 0 0
\(899\) 4.32198 0.144146
\(900\) 0 0
\(901\) −14.1530 −0.471506
\(902\) 0 0
\(903\) 50.2807 1.67324
\(904\) 0 0
\(905\) −57.8995 −1.92465
\(906\) 0 0
\(907\) 48.0318 1.59487 0.797436 0.603404i \(-0.206189\pi\)
0.797436 + 0.603404i \(0.206189\pi\)
\(908\) 0 0
\(909\) 61.9737 2.05554
\(910\) 0 0
\(911\) −20.2868 −0.672133 −0.336066 0.941838i \(-0.609097\pi\)
−0.336066 + 0.941838i \(0.609097\pi\)
\(912\) 0 0
\(913\) −21.3466 −0.706469
\(914\) 0 0
\(915\) −96.3060 −3.18378
\(916\) 0 0
\(917\) 0.0722769 0.00238679
\(918\) 0 0
\(919\) 20.4138 0.673389 0.336694 0.941614i \(-0.390691\pi\)
0.336694 + 0.941614i \(0.390691\pi\)
\(920\) 0 0
\(921\) −72.1490 −2.37739
\(922\) 0 0
\(923\) 38.6789 1.27313
\(924\) 0 0
\(925\) 90.0738 2.96161
\(926\) 0 0
\(927\) 90.9632 2.98762
\(928\) 0 0
\(929\) 15.9611 0.523666 0.261833 0.965113i \(-0.415673\pi\)
0.261833 + 0.965113i \(0.415673\pi\)
\(930\) 0 0
\(931\) −59.5296 −1.95100
\(932\) 0 0
\(933\) −75.8568 −2.48344
\(934\) 0 0
\(935\) −25.7071 −0.840712
\(936\) 0 0
\(937\) 21.6107 0.705991 0.352996 0.935625i \(-0.385163\pi\)
0.352996 + 0.935625i \(0.385163\pi\)
\(938\) 0 0
\(939\) −92.4261 −3.01621
\(940\) 0 0
\(941\) 27.0829 0.882876 0.441438 0.897292i \(-0.354469\pi\)
0.441438 + 0.897292i \(0.354469\pi\)
\(942\) 0 0
\(943\) −3.02903 −0.0986389
\(944\) 0 0
\(945\) −94.9799 −3.08970
\(946\) 0 0
\(947\) 51.6301 1.67775 0.838876 0.544323i \(-0.183213\pi\)
0.838876 + 0.544323i \(0.183213\pi\)
\(948\) 0 0
\(949\) 24.6741 0.800954
\(950\) 0 0
\(951\) −14.8766 −0.482408
\(952\) 0 0
\(953\) −58.6944 −1.90130 −0.950649 0.310270i \(-0.899581\pi\)
−0.950649 + 0.310270i \(0.899581\pi\)
\(954\) 0 0
\(955\) −62.0701 −2.00854
\(956\) 0 0
\(957\) −4.68209 −0.151350
\(958\) 0 0
\(959\) 7.55903 0.244094
\(960\) 0 0
\(961\) −0.321783 −0.0103801
\(962\) 0 0
\(963\) −89.5205 −2.88476
\(964\) 0 0
\(965\) −106.409 −3.42543
\(966\) 0 0
\(967\) 40.5109 1.30274 0.651371 0.758759i \(-0.274194\pi\)
0.651371 + 0.758759i \(0.274194\pi\)
\(968\) 0 0
\(969\) −58.4105 −1.87642
\(970\) 0 0
\(971\) 12.3299 0.395686 0.197843 0.980234i \(-0.436606\pi\)
0.197843 + 0.980234i \(0.436606\pi\)
\(972\) 0 0
\(973\) −45.3924 −1.45521
\(974\) 0 0
\(975\) −109.644 −3.51141
\(976\) 0 0
\(977\) 19.6190 0.627666 0.313833 0.949478i \(-0.398387\pi\)
0.313833 + 0.949478i \(0.398387\pi\)
\(978\) 0 0
\(979\) 8.29453 0.265094
\(980\) 0 0
\(981\) 85.6908 2.73590
\(982\) 0 0
\(983\) 16.6017 0.529512 0.264756 0.964315i \(-0.414709\pi\)
0.264756 + 0.964315i \(0.414709\pi\)
\(984\) 0 0
\(985\) −81.1024 −2.58414
\(986\) 0 0
\(987\) 99.4757 3.16635
\(988\) 0 0
\(989\) −1.55655 −0.0494954
\(990\) 0 0
\(991\) 12.4425 0.395249 0.197624 0.980278i \(-0.436677\pi\)
0.197624 + 0.980278i \(0.436677\pi\)
\(992\) 0 0
\(993\) 59.1346 1.87658
\(994\) 0 0
\(995\) 84.9835 2.69416
\(996\) 0 0
\(997\) −30.4078 −0.963023 −0.481512 0.876440i \(-0.659912\pi\)
−0.481512 + 0.876440i \(0.659912\pi\)
\(998\) 0 0
\(999\) −39.0020 −1.23397
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 \(a_p\))