Properties

Label 8013.2.a.d.1.4
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69326 q^{2} +1.00000 q^{3} +5.25363 q^{4} -3.14797 q^{5} -2.69326 q^{6} +0.0430508 q^{7} -8.76286 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.69326 q^{2} +1.00000 q^{3} +5.25363 q^{4} -3.14797 q^{5} -2.69326 q^{6} +0.0430508 q^{7} -8.76286 q^{8} +1.00000 q^{9} +8.47829 q^{10} -3.97005 q^{11} +5.25363 q^{12} +0.212754 q^{13} -0.115947 q^{14} -3.14797 q^{15} +13.0934 q^{16} -6.24792 q^{17} -2.69326 q^{18} -1.70064 q^{19} -16.5383 q^{20} +0.0430508 q^{21} +10.6924 q^{22} -1.61766 q^{23} -8.76286 q^{24} +4.90972 q^{25} -0.573002 q^{26} +1.00000 q^{27} +0.226173 q^{28} -8.54219 q^{29} +8.47829 q^{30} -6.57126 q^{31} -17.7381 q^{32} -3.97005 q^{33} +16.8273 q^{34} -0.135523 q^{35} +5.25363 q^{36} -7.20692 q^{37} +4.58026 q^{38} +0.212754 q^{39} +27.5852 q^{40} +6.68846 q^{41} -0.115947 q^{42} -8.46296 q^{43} -20.8572 q^{44} -3.14797 q^{45} +4.35677 q^{46} +1.17838 q^{47} +13.0934 q^{48} -6.99815 q^{49} -13.2231 q^{50} -6.24792 q^{51} +1.11773 q^{52} -8.24058 q^{53} -2.69326 q^{54} +12.4976 q^{55} -0.377248 q^{56} -1.70064 q^{57} +23.0063 q^{58} +6.26247 q^{59} -16.5383 q^{60} -1.14722 q^{61} +17.6981 q^{62} +0.0430508 q^{63} +21.5865 q^{64} -0.669744 q^{65} +10.6924 q^{66} -0.662651 q^{67} -32.8243 q^{68} -1.61766 q^{69} +0.364997 q^{70} -10.3048 q^{71} -8.76286 q^{72} +13.1083 q^{73} +19.4101 q^{74} +4.90972 q^{75} -8.93454 q^{76} -0.170914 q^{77} -0.573002 q^{78} -14.5271 q^{79} -41.2176 q^{80} +1.00000 q^{81} -18.0137 q^{82} +10.4232 q^{83} +0.226173 q^{84} +19.6683 q^{85} +22.7929 q^{86} -8.54219 q^{87} +34.7890 q^{88} -1.48612 q^{89} +8.47829 q^{90} +0.00915924 q^{91} -8.49858 q^{92} -6.57126 q^{93} -3.17369 q^{94} +5.35357 q^{95} -17.7381 q^{96} +0.764689 q^{97} +18.8478 q^{98} -3.97005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69326 −1.90442 −0.952210 0.305444i \(-0.901195\pi\)
−0.952210 + 0.305444i \(0.901195\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.25363 2.62682
\(5\) −3.14797 −1.40782 −0.703908 0.710292i \(-0.748563\pi\)
−0.703908 + 0.710292i \(0.748563\pi\)
\(6\) −2.69326 −1.09952
\(7\) 0.0430508 0.0162717 0.00813583 0.999967i \(-0.497410\pi\)
0.00813583 + 0.999967i \(0.497410\pi\)
\(8\) −8.76286 −3.09814
\(9\) 1.00000 0.333333
\(10\) 8.47829 2.68107
\(11\) −3.97005 −1.19702 −0.598508 0.801117i \(-0.704240\pi\)
−0.598508 + 0.801117i \(0.704240\pi\)
\(12\) 5.25363 1.51659
\(13\) 0.212754 0.0590074 0.0295037 0.999565i \(-0.490607\pi\)
0.0295037 + 0.999565i \(0.490607\pi\)
\(14\) −0.115947 −0.0309881
\(15\) −3.14797 −0.812803
\(16\) 13.0934 3.27335
\(17\) −6.24792 −1.51534 −0.757672 0.652636i \(-0.773663\pi\)
−0.757672 + 0.652636i \(0.773663\pi\)
\(18\) −2.69326 −0.634807
\(19\) −1.70064 −0.390154 −0.195077 0.980788i \(-0.562496\pi\)
−0.195077 + 0.980788i \(0.562496\pi\)
\(20\) −16.5383 −3.69807
\(21\) 0.0430508 0.00939445
\(22\) 10.6924 2.27962
\(23\) −1.61766 −0.337305 −0.168653 0.985676i \(-0.553942\pi\)
−0.168653 + 0.985676i \(0.553942\pi\)
\(24\) −8.76286 −1.78871
\(25\) 4.90972 0.981944
\(26\) −0.573002 −0.112375
\(27\) 1.00000 0.192450
\(28\) 0.226173 0.0427427
\(29\) −8.54219 −1.58625 −0.793123 0.609062i \(-0.791546\pi\)
−0.793123 + 0.609062i \(0.791546\pi\)
\(30\) 8.47829 1.54792
\(31\) −6.57126 −1.18023 −0.590116 0.807318i \(-0.700918\pi\)
−0.590116 + 0.807318i \(0.700918\pi\)
\(32\) −17.7381 −3.13568
\(33\) −3.97005 −0.691097
\(34\) 16.8273 2.88585
\(35\) −0.135523 −0.0229075
\(36\) 5.25363 0.875605
\(37\) −7.20692 −1.18481 −0.592405 0.805640i \(-0.701821\pi\)
−0.592405 + 0.805640i \(0.701821\pi\)
\(38\) 4.58026 0.743017
\(39\) 0.212754 0.0340680
\(40\) 27.5852 4.36161
\(41\) 6.68846 1.04456 0.522281 0.852774i \(-0.325081\pi\)
0.522281 + 0.852774i \(0.325081\pi\)
\(42\) −0.115947 −0.0178910
\(43\) −8.46296 −1.29059 −0.645295 0.763934i \(-0.723265\pi\)
−0.645295 + 0.763934i \(0.723265\pi\)
\(44\) −20.8572 −3.14434
\(45\) −3.14797 −0.469272
\(46\) 4.35677 0.642371
\(47\) 1.17838 0.171885 0.0859425 0.996300i \(-0.472610\pi\)
0.0859425 + 0.996300i \(0.472610\pi\)
\(48\) 13.0934 1.88987
\(49\) −6.99815 −0.999735
\(50\) −13.2231 −1.87003
\(51\) −6.24792 −0.874884
\(52\) 1.11773 0.155002
\(53\) −8.24058 −1.13193 −0.565965 0.824429i \(-0.691496\pi\)
−0.565965 + 0.824429i \(0.691496\pi\)
\(54\) −2.69326 −0.366506
\(55\) 12.4976 1.68518
\(56\) −0.377248 −0.0504119
\(57\) −1.70064 −0.225255
\(58\) 23.0063 3.02088
\(59\) 6.26247 0.815304 0.407652 0.913137i \(-0.366348\pi\)
0.407652 + 0.913137i \(0.366348\pi\)
\(60\) −16.5383 −2.13508
\(61\) −1.14722 −0.146887 −0.0734435 0.997299i \(-0.523399\pi\)
−0.0734435 + 0.997299i \(0.523399\pi\)
\(62\) 17.6981 2.24766
\(63\) 0.0430508 0.00542389
\(64\) 21.5865 2.69831
\(65\) −0.669744 −0.0830716
\(66\) 10.6924 1.31614
\(67\) −0.662651 −0.0809557 −0.0404779 0.999180i \(-0.512888\pi\)
−0.0404779 + 0.999180i \(0.512888\pi\)
\(68\) −32.8243 −3.98053
\(69\) −1.61766 −0.194743
\(70\) 0.364997 0.0436255
\(71\) −10.3048 −1.22296 −0.611479 0.791261i \(-0.709425\pi\)
−0.611479 + 0.791261i \(0.709425\pi\)
\(72\) −8.76286 −1.03271
\(73\) 13.1083 1.53422 0.767108 0.641518i \(-0.221695\pi\)
0.767108 + 0.641518i \(0.221695\pi\)
\(74\) 19.4101 2.25638
\(75\) 4.90972 0.566926
\(76\) −8.93454 −1.02486
\(77\) −0.170914 −0.0194774
\(78\) −0.573002 −0.0648797
\(79\) −14.5271 −1.63443 −0.817214 0.576334i \(-0.804483\pi\)
−0.817214 + 0.576334i \(0.804483\pi\)
\(80\) −41.2176 −4.60827
\(81\) 1.00000 0.111111
\(82\) −18.0137 −1.98928
\(83\) 10.4232 1.14410 0.572049 0.820220i \(-0.306149\pi\)
0.572049 + 0.820220i \(0.306149\pi\)
\(84\) 0.226173 0.0246775
\(85\) 19.6683 2.13332
\(86\) 22.7929 2.45782
\(87\) −8.54219 −0.915819
\(88\) 34.7890 3.70852
\(89\) −1.48612 −0.157529 −0.0787643 0.996893i \(-0.525097\pi\)
−0.0787643 + 0.996893i \(0.525097\pi\)
\(90\) 8.47829 0.893691
\(91\) 0.00915924 0.000960149 0
\(92\) −8.49858 −0.886038
\(93\) −6.57126 −0.681408
\(94\) −3.17369 −0.327341
\(95\) 5.35357 0.549265
\(96\) −17.7381 −1.81039
\(97\) 0.764689 0.0776424 0.0388212 0.999246i \(-0.487640\pi\)
0.0388212 + 0.999246i \(0.487640\pi\)
\(98\) 18.8478 1.90392
\(99\) −3.97005 −0.399005
\(100\) 25.7939 2.57939
\(101\) −6.48839 −0.645618 −0.322809 0.946464i \(-0.604627\pi\)
−0.322809 + 0.946464i \(0.604627\pi\)
\(102\) 16.8273 1.66615
\(103\) 0.608752 0.0599821 0.0299911 0.999550i \(-0.490452\pi\)
0.0299911 + 0.999550i \(0.490452\pi\)
\(104\) −1.86434 −0.182813
\(105\) −0.135523 −0.0132256
\(106\) 22.1940 2.15567
\(107\) 10.1347 0.979754 0.489877 0.871792i \(-0.337042\pi\)
0.489877 + 0.871792i \(0.337042\pi\)
\(108\) 5.25363 0.505531
\(109\) −2.02593 −0.194049 −0.0970245 0.995282i \(-0.530933\pi\)
−0.0970245 + 0.995282i \(0.530933\pi\)
\(110\) −33.6593 −3.20929
\(111\) −7.20692 −0.684050
\(112\) 0.563680 0.0532628
\(113\) −14.2966 −1.34491 −0.672455 0.740138i \(-0.734760\pi\)
−0.672455 + 0.740138i \(0.734760\pi\)
\(114\) 4.58026 0.428981
\(115\) 5.09234 0.474863
\(116\) −44.8775 −4.16677
\(117\) 0.212754 0.0196691
\(118\) −16.8664 −1.55268
\(119\) −0.268978 −0.0246571
\(120\) 27.5852 2.51818
\(121\) 4.76132 0.432847
\(122\) 3.08977 0.279735
\(123\) 6.68846 0.603078
\(124\) −34.5230 −3.10025
\(125\) 0.284200 0.0254197
\(126\) −0.115947 −0.0103294
\(127\) −21.4040 −1.89930 −0.949648 0.313320i \(-0.898559\pi\)
−0.949648 + 0.313320i \(0.898559\pi\)
\(128\) −22.6618 −2.00304
\(129\) −8.46296 −0.745122
\(130\) 1.80379 0.158203
\(131\) −1.98638 −0.173550 −0.0867752 0.996228i \(-0.527656\pi\)
−0.0867752 + 0.996228i \(0.527656\pi\)
\(132\) −20.8572 −1.81539
\(133\) −0.0732139 −0.00634845
\(134\) 1.78469 0.154174
\(135\) −3.14797 −0.270934
\(136\) 54.7497 4.69475
\(137\) 6.48064 0.553679 0.276839 0.960916i \(-0.410713\pi\)
0.276839 + 0.960916i \(0.410713\pi\)
\(138\) 4.35677 0.370873
\(139\) 10.8856 0.923301 0.461651 0.887062i \(-0.347257\pi\)
0.461651 + 0.887062i \(0.347257\pi\)
\(140\) −0.711986 −0.0601738
\(141\) 1.17838 0.0992378
\(142\) 27.7535 2.32903
\(143\) −0.844646 −0.0706328
\(144\) 13.0934 1.09112
\(145\) 26.8906 2.23314
\(146\) −35.3041 −2.92179
\(147\) −6.99815 −0.577197
\(148\) −37.8625 −3.11228
\(149\) 9.48025 0.776653 0.388326 0.921522i \(-0.373053\pi\)
0.388326 + 0.921522i \(0.373053\pi\)
\(150\) −13.2231 −1.07966
\(151\) −16.2086 −1.31904 −0.659519 0.751688i \(-0.729240\pi\)
−0.659519 + 0.751688i \(0.729240\pi\)
\(152\) 14.9025 1.20875
\(153\) −6.24792 −0.505114
\(154\) 0.460315 0.0370932
\(155\) 20.6861 1.66155
\(156\) 1.11773 0.0894902
\(157\) 8.08975 0.645632 0.322816 0.946462i \(-0.395371\pi\)
0.322816 + 0.946462i \(0.395371\pi\)
\(158\) 39.1252 3.11264
\(159\) −8.24058 −0.653521
\(160\) 55.8390 4.41446
\(161\) −0.0696414 −0.00548851
\(162\) −2.69326 −0.211602
\(163\) 12.8992 1.01034 0.505172 0.863019i \(-0.331429\pi\)
0.505172 + 0.863019i \(0.331429\pi\)
\(164\) 35.1387 2.74387
\(165\) 12.4976 0.972938
\(166\) −28.0724 −2.17884
\(167\) 11.3998 0.882141 0.441070 0.897473i \(-0.354599\pi\)
0.441070 + 0.897473i \(0.354599\pi\)
\(168\) −0.377248 −0.0291053
\(169\) −12.9547 −0.996518
\(170\) −52.9717 −4.06274
\(171\) −1.70064 −0.130051
\(172\) −44.4613 −3.39014
\(173\) −8.14401 −0.619177 −0.309589 0.950871i \(-0.600191\pi\)
−0.309589 + 0.950871i \(0.600191\pi\)
\(174\) 23.0063 1.74410
\(175\) 0.211367 0.0159779
\(176\) −51.9814 −3.91825
\(177\) 6.26247 0.470716
\(178\) 4.00251 0.300001
\(179\) −21.9234 −1.63864 −0.819318 0.573340i \(-0.805647\pi\)
−0.819318 + 0.573340i \(0.805647\pi\)
\(180\) −16.5383 −1.23269
\(181\) 0.291204 0.0216450 0.0108225 0.999941i \(-0.496555\pi\)
0.0108225 + 0.999941i \(0.496555\pi\)
\(182\) −0.0246682 −0.00182853
\(183\) −1.14722 −0.0848053
\(184\) 14.1753 1.04502
\(185\) 22.6872 1.66799
\(186\) 17.6981 1.29769
\(187\) 24.8046 1.81389
\(188\) 6.19080 0.451510
\(189\) 0.0430508 0.00313148
\(190\) −14.4185 −1.04603
\(191\) 6.48551 0.469275 0.234638 0.972083i \(-0.424610\pi\)
0.234638 + 0.972083i \(0.424610\pi\)
\(192\) 21.5865 1.55787
\(193\) −21.6045 −1.55513 −0.777564 0.628804i \(-0.783545\pi\)
−0.777564 + 0.628804i \(0.783545\pi\)
\(194\) −2.05950 −0.147864
\(195\) −0.669744 −0.0479614
\(196\) −36.7657 −2.62612
\(197\) −16.1402 −1.14994 −0.574971 0.818174i \(-0.694987\pi\)
−0.574971 + 0.818174i \(0.694987\pi\)
\(198\) 10.6924 0.759874
\(199\) −2.42626 −0.171993 −0.0859965 0.996295i \(-0.527407\pi\)
−0.0859965 + 0.996295i \(0.527407\pi\)
\(200\) −43.0232 −3.04220
\(201\) −0.662651 −0.0467398
\(202\) 17.4749 1.22953
\(203\) −0.367748 −0.0258109
\(204\) −32.8243 −2.29816
\(205\) −21.0551 −1.47055
\(206\) −1.63953 −0.114231
\(207\) −1.61766 −0.112435
\(208\) 2.78567 0.193152
\(209\) 6.75164 0.467020
\(210\) 0.364997 0.0251872
\(211\) −19.3488 −1.33203 −0.666015 0.745939i \(-0.732001\pi\)
−0.666015 + 0.745939i \(0.732001\pi\)
\(212\) −43.2930 −2.97337
\(213\) −10.3048 −0.706075
\(214\) −27.2952 −1.86586
\(215\) 26.6412 1.81691
\(216\) −8.76286 −0.596237
\(217\) −0.282898 −0.0192043
\(218\) 5.45635 0.369551
\(219\) 13.1083 0.885780
\(220\) 65.6578 4.42665
\(221\) −1.32927 −0.0894165
\(222\) 19.4101 1.30272
\(223\) −19.6443 −1.31548 −0.657741 0.753245i \(-0.728488\pi\)
−0.657741 + 0.753245i \(0.728488\pi\)
\(224\) −0.763639 −0.0510228
\(225\) 4.90972 0.327315
\(226\) 38.5044 2.56127
\(227\) −17.1918 −1.14106 −0.570529 0.821278i \(-0.693262\pi\)
−0.570529 + 0.821278i \(0.693262\pi\)
\(228\) −8.93454 −0.591705
\(229\) −0.447614 −0.0295791 −0.0147896 0.999891i \(-0.504708\pi\)
−0.0147896 + 0.999891i \(0.504708\pi\)
\(230\) −13.7150 −0.904339
\(231\) −0.170914 −0.0112453
\(232\) 74.8541 4.91441
\(233\) 4.91670 0.322104 0.161052 0.986946i \(-0.448511\pi\)
0.161052 + 0.986946i \(0.448511\pi\)
\(234\) −0.573002 −0.0374583
\(235\) −3.70952 −0.241982
\(236\) 32.9007 2.14165
\(237\) −14.5271 −0.943637
\(238\) 0.724426 0.0469576
\(239\) 19.3251 1.25004 0.625019 0.780610i \(-0.285091\pi\)
0.625019 + 0.780610i \(0.285091\pi\)
\(240\) −41.2176 −2.66058
\(241\) 5.97867 0.385120 0.192560 0.981285i \(-0.438321\pi\)
0.192560 + 0.981285i \(0.438321\pi\)
\(242\) −12.8235 −0.824323
\(243\) 1.00000 0.0641500
\(244\) −6.02710 −0.385845
\(245\) 22.0300 1.40744
\(246\) −18.0137 −1.14851
\(247\) −0.361819 −0.0230220
\(248\) 57.5830 3.65653
\(249\) 10.4232 0.660545
\(250\) −0.765425 −0.0484097
\(251\) 13.7369 0.867065 0.433532 0.901138i \(-0.357267\pi\)
0.433532 + 0.901138i \(0.357267\pi\)
\(252\) 0.226173 0.0142476
\(253\) 6.42219 0.403760
\(254\) 57.6464 3.61706
\(255\) 19.6683 1.23167
\(256\) 17.8610 1.11631
\(257\) 10.2362 0.638514 0.319257 0.947668i \(-0.396567\pi\)
0.319257 + 0.947668i \(0.396567\pi\)
\(258\) 22.7929 1.41903
\(259\) −0.310263 −0.0192788
\(260\) −3.51859 −0.218214
\(261\) −8.54219 −0.528749
\(262\) 5.34982 0.330513
\(263\) 24.6857 1.52219 0.761093 0.648642i \(-0.224663\pi\)
0.761093 + 0.648642i \(0.224663\pi\)
\(264\) 34.7890 2.14112
\(265\) 25.9411 1.59355
\(266\) 0.197184 0.0120901
\(267\) −1.48612 −0.0909492
\(268\) −3.48132 −0.212656
\(269\) 1.46734 0.0894652 0.0447326 0.998999i \(-0.485756\pi\)
0.0447326 + 0.998999i \(0.485756\pi\)
\(270\) 8.47829 0.515972
\(271\) −19.9447 −1.21156 −0.605778 0.795634i \(-0.707138\pi\)
−0.605778 + 0.795634i \(0.707138\pi\)
\(272\) −81.8064 −4.96024
\(273\) 0.00915924 0.000554342 0
\(274\) −17.4540 −1.05444
\(275\) −19.4918 −1.17540
\(276\) −8.49858 −0.511554
\(277\) 15.5404 0.933734 0.466867 0.884327i \(-0.345383\pi\)
0.466867 + 0.884327i \(0.345383\pi\)
\(278\) −29.3176 −1.75835
\(279\) −6.57126 −0.393411
\(280\) 1.18757 0.0709706
\(281\) 9.32142 0.556069 0.278035 0.960571i \(-0.410317\pi\)
0.278035 + 0.960571i \(0.410317\pi\)
\(282\) −3.17369 −0.188991
\(283\) 16.2950 0.968636 0.484318 0.874892i \(-0.339068\pi\)
0.484318 + 0.874892i \(0.339068\pi\)
\(284\) −54.1378 −3.21248
\(285\) 5.35357 0.317118
\(286\) 2.27485 0.134515
\(287\) 0.287943 0.0169967
\(288\) −17.7381 −1.04523
\(289\) 22.0365 1.29626
\(290\) −72.4232 −4.25284
\(291\) 0.764689 0.0448269
\(292\) 68.8664 4.03010
\(293\) 7.15965 0.418271 0.209136 0.977887i \(-0.432935\pi\)
0.209136 + 0.977887i \(0.432935\pi\)
\(294\) 18.8478 1.09923
\(295\) −19.7141 −1.14780
\(296\) 63.1532 3.67071
\(297\) −3.97005 −0.230366
\(298\) −25.5328 −1.47907
\(299\) −0.344164 −0.0199035
\(300\) 25.7939 1.48921
\(301\) −0.364337 −0.0210000
\(302\) 43.6540 2.51200
\(303\) −6.48839 −0.372748
\(304\) −22.2671 −1.27711
\(305\) 3.61143 0.206790
\(306\) 16.8273 0.961950
\(307\) 21.1676 1.20810 0.604049 0.796947i \(-0.293553\pi\)
0.604049 + 0.796947i \(0.293553\pi\)
\(308\) −0.897918 −0.0511636
\(309\) 0.608752 0.0346307
\(310\) −55.7130 −3.16429
\(311\) 5.06551 0.287239 0.143619 0.989633i \(-0.454126\pi\)
0.143619 + 0.989633i \(0.454126\pi\)
\(312\) −1.86434 −0.105547
\(313\) 0.834190 0.0471512 0.0235756 0.999722i \(-0.492495\pi\)
0.0235756 + 0.999722i \(0.492495\pi\)
\(314\) −21.7878 −1.22955
\(315\) −0.135523 −0.00763583
\(316\) −76.3201 −4.29334
\(317\) −22.2444 −1.24937 −0.624685 0.780877i \(-0.714773\pi\)
−0.624685 + 0.780877i \(0.714773\pi\)
\(318\) 22.1940 1.24458
\(319\) 33.9130 1.89876
\(320\) −67.9537 −3.79873
\(321\) 10.1347 0.565661
\(322\) 0.187562 0.0104524
\(323\) 10.6255 0.591217
\(324\) 5.25363 0.291868
\(325\) 1.04456 0.0579420
\(326\) −34.7409 −1.92412
\(327\) −2.02593 −0.112034
\(328\) −58.6100 −3.23620
\(329\) 0.0507303 0.00279685
\(330\) −33.6593 −1.85288
\(331\) 10.7556 0.591181 0.295591 0.955315i \(-0.404484\pi\)
0.295591 + 0.955315i \(0.404484\pi\)
\(332\) 54.7598 3.00533
\(333\) −7.20692 −0.394937
\(334\) −30.7025 −1.67997
\(335\) 2.08601 0.113971
\(336\) 0.563680 0.0307513
\(337\) 32.0241 1.74446 0.872232 0.489093i \(-0.162672\pi\)
0.872232 + 0.489093i \(0.162672\pi\)
\(338\) 34.8904 1.89779
\(339\) −14.2966 −0.776484
\(340\) 103.330 5.60385
\(341\) 26.0882 1.41276
\(342\) 4.58026 0.247672
\(343\) −0.602631 −0.0325390
\(344\) 74.1598 3.99843
\(345\) 5.09234 0.274162
\(346\) 21.9339 1.17917
\(347\) −20.3762 −1.09385 −0.546926 0.837181i \(-0.684202\pi\)
−0.546926 + 0.837181i \(0.684202\pi\)
\(348\) −44.8775 −2.40569
\(349\) 12.6317 0.676161 0.338081 0.941117i \(-0.390222\pi\)
0.338081 + 0.941117i \(0.390222\pi\)
\(350\) −0.569266 −0.0304286
\(351\) 0.212754 0.0113560
\(352\) 70.4212 3.75346
\(353\) 8.98285 0.478109 0.239054 0.971006i \(-0.423163\pi\)
0.239054 + 0.971006i \(0.423163\pi\)
\(354\) −16.8664 −0.896441
\(355\) 32.4393 1.72170
\(356\) −7.80754 −0.413799
\(357\) −0.268978 −0.0142358
\(358\) 59.0455 3.12065
\(359\) 9.13891 0.482333 0.241167 0.970484i \(-0.422470\pi\)
0.241167 + 0.970484i \(0.422470\pi\)
\(360\) 27.5852 1.45387
\(361\) −16.1078 −0.847780
\(362\) −0.784286 −0.0412211
\(363\) 4.76132 0.249904
\(364\) 0.0481193 0.00252213
\(365\) −41.2647 −2.15989
\(366\) 3.08977 0.161505
\(367\) −20.1263 −1.05058 −0.525291 0.850922i \(-0.676044\pi\)
−0.525291 + 0.850922i \(0.676044\pi\)
\(368\) −21.1806 −1.10412
\(369\) 6.68846 0.348187
\(370\) −61.1024 −3.17656
\(371\) −0.354763 −0.0184184
\(372\) −34.5230 −1.78993
\(373\) 1.96957 0.101981 0.0509903 0.998699i \(-0.483762\pi\)
0.0509903 + 0.998699i \(0.483762\pi\)
\(374\) −66.8051 −3.45441
\(375\) 0.284200 0.0146760
\(376\) −10.3260 −0.532524
\(377\) −1.81739 −0.0936003
\(378\) −0.115947 −0.00596366
\(379\) −4.66433 −0.239591 −0.119795 0.992799i \(-0.538224\pi\)
−0.119795 + 0.992799i \(0.538224\pi\)
\(380\) 28.1257 1.44282
\(381\) −21.4040 −1.09656
\(382\) −17.4671 −0.893697
\(383\) −8.15198 −0.416547 −0.208273 0.978071i \(-0.566784\pi\)
−0.208273 + 0.978071i \(0.566784\pi\)
\(384\) −22.6618 −1.15645
\(385\) 0.538032 0.0274206
\(386\) 58.1865 2.96162
\(387\) −8.46296 −0.430197
\(388\) 4.01740 0.203952
\(389\) 22.3259 1.13197 0.565984 0.824416i \(-0.308496\pi\)
0.565984 + 0.824416i \(0.308496\pi\)
\(390\) 1.80379 0.0913386
\(391\) 10.1070 0.511133
\(392\) 61.3238 3.09732
\(393\) −1.98638 −0.100199
\(394\) 43.4697 2.18997
\(395\) 45.7309 2.30097
\(396\) −20.8572 −1.04811
\(397\) −4.17190 −0.209382 −0.104691 0.994505i \(-0.533385\pi\)
−0.104691 + 0.994505i \(0.533385\pi\)
\(398\) 6.53454 0.327547
\(399\) −0.0732139 −0.00366528
\(400\) 64.2848 3.21424
\(401\) −28.8507 −1.44074 −0.720368 0.693592i \(-0.756027\pi\)
−0.720368 + 0.693592i \(0.756027\pi\)
\(402\) 1.78469 0.0890122
\(403\) −1.39806 −0.0696425
\(404\) −34.0876 −1.69592
\(405\) −3.14797 −0.156424
\(406\) 0.990440 0.0491547
\(407\) 28.6118 1.41824
\(408\) 54.7497 2.71051
\(409\) −9.32567 −0.461125 −0.230562 0.973058i \(-0.574057\pi\)
−0.230562 + 0.973058i \(0.574057\pi\)
\(410\) 56.7067 2.80054
\(411\) 6.48064 0.319667
\(412\) 3.19816 0.157562
\(413\) 0.269604 0.0132664
\(414\) 4.35677 0.214124
\(415\) −32.8120 −1.61068
\(416\) −3.77386 −0.185029
\(417\) 10.8856 0.533068
\(418\) −18.1839 −0.889403
\(419\) −32.8357 −1.60413 −0.802064 0.597238i \(-0.796265\pi\)
−0.802064 + 0.597238i \(0.796265\pi\)
\(420\) −0.711986 −0.0347413
\(421\) −32.2409 −1.57133 −0.785663 0.618655i \(-0.787678\pi\)
−0.785663 + 0.618655i \(0.787678\pi\)
\(422\) 52.1114 2.53674
\(423\) 1.17838 0.0572950
\(424\) 72.2111 3.50688
\(425\) −30.6755 −1.48798
\(426\) 27.7535 1.34466
\(427\) −0.0493889 −0.00239010
\(428\) 53.2437 2.57363
\(429\) −0.844646 −0.0407799
\(430\) −71.7515 −3.46016
\(431\) 10.2569 0.494057 0.247028 0.969008i \(-0.420546\pi\)
0.247028 + 0.969008i \(0.420546\pi\)
\(432\) 13.0934 0.629956
\(433\) 1.65518 0.0795430 0.0397715 0.999209i \(-0.487337\pi\)
0.0397715 + 0.999209i \(0.487337\pi\)
\(434\) 0.761916 0.0365731
\(435\) 26.8906 1.28930
\(436\) −10.6435 −0.509731
\(437\) 2.75106 0.131601
\(438\) −35.3041 −1.68690
\(439\) −7.25909 −0.346457 −0.173229 0.984882i \(-0.555420\pi\)
−0.173229 + 0.984882i \(0.555420\pi\)
\(440\) −109.515 −5.22092
\(441\) −6.99815 −0.333245
\(442\) 3.58007 0.170287
\(443\) 13.0817 0.621529 0.310764 0.950487i \(-0.399415\pi\)
0.310764 + 0.950487i \(0.399415\pi\)
\(444\) −37.8625 −1.79687
\(445\) 4.67827 0.221771
\(446\) 52.9072 2.50523
\(447\) 9.48025 0.448401
\(448\) 0.929316 0.0439060
\(449\) −30.2153 −1.42595 −0.712973 0.701191i \(-0.752652\pi\)
−0.712973 + 0.701191i \(0.752652\pi\)
\(450\) −13.2231 −0.623345
\(451\) −26.5535 −1.25036
\(452\) −75.1090 −3.53283
\(453\) −16.2086 −0.761547
\(454\) 46.3018 2.17305
\(455\) −0.0288330 −0.00135171
\(456\) 14.9025 0.697873
\(457\) 13.7250 0.642030 0.321015 0.947074i \(-0.395976\pi\)
0.321015 + 0.947074i \(0.395976\pi\)
\(458\) 1.20554 0.0563311
\(459\) −6.24792 −0.291628
\(460\) 26.7533 1.24738
\(461\) −24.7390 −1.15221 −0.576105 0.817376i \(-0.695428\pi\)
−0.576105 + 0.817376i \(0.695428\pi\)
\(462\) 0.460315 0.0214158
\(463\) 5.41303 0.251565 0.125782 0.992058i \(-0.459856\pi\)
0.125782 + 0.992058i \(0.459856\pi\)
\(464\) −111.846 −5.19233
\(465\) 20.6861 0.959296
\(466\) −13.2419 −0.613421
\(467\) −12.7700 −0.590925 −0.295463 0.955354i \(-0.595474\pi\)
−0.295463 + 0.955354i \(0.595474\pi\)
\(468\) 1.11773 0.0516672
\(469\) −0.0285276 −0.00131728
\(470\) 9.99069 0.460836
\(471\) 8.08975 0.372756
\(472\) −54.8772 −2.52593
\(473\) 33.5984 1.54486
\(474\) 39.1252 1.79708
\(475\) −8.34967 −0.383109
\(476\) −1.41311 −0.0647698
\(477\) −8.24058 −0.377310
\(478\) −52.0475 −2.38060
\(479\) −27.3049 −1.24759 −0.623797 0.781587i \(-0.714411\pi\)
−0.623797 + 0.781587i \(0.714411\pi\)
\(480\) 55.8390 2.54869
\(481\) −1.53330 −0.0699126
\(482\) −16.1021 −0.733430
\(483\) −0.0696414 −0.00316880
\(484\) 25.0142 1.13701
\(485\) −2.40722 −0.109306
\(486\) −2.69326 −0.122169
\(487\) 32.2183 1.45995 0.729974 0.683475i \(-0.239532\pi\)
0.729974 + 0.683475i \(0.239532\pi\)
\(488\) 10.0530 0.455077
\(489\) 12.8992 0.583323
\(490\) −59.3323 −2.68036
\(491\) −36.8943 −1.66502 −0.832508 0.554013i \(-0.813096\pi\)
−0.832508 + 0.554013i \(0.813096\pi\)
\(492\) 35.1387 1.58417
\(493\) 53.3709 2.40371
\(494\) 0.974471 0.0438435
\(495\) 12.4976 0.561726
\(496\) −86.0400 −3.86331
\(497\) −0.443631 −0.0198996
\(498\) −28.0724 −1.25796
\(499\) −29.1658 −1.30564 −0.652820 0.757513i \(-0.726414\pi\)
−0.652820 + 0.757513i \(0.726414\pi\)
\(500\) 1.49308 0.0667727
\(501\) 11.3998 0.509304
\(502\) −36.9970 −1.65126
\(503\) −21.5005 −0.958660 −0.479330 0.877635i \(-0.659120\pi\)
−0.479330 + 0.877635i \(0.659120\pi\)
\(504\) −0.377248 −0.0168040
\(505\) 20.4252 0.908912
\(506\) −17.2966 −0.768928
\(507\) −12.9547 −0.575340
\(508\) −112.449 −4.98910
\(509\) 7.84723 0.347822 0.173911 0.984761i \(-0.444359\pi\)
0.173911 + 0.984761i \(0.444359\pi\)
\(510\) −52.9717 −2.34563
\(511\) 0.564324 0.0249642
\(512\) −2.78071 −0.122891
\(513\) −1.70064 −0.0750851
\(514\) −27.5686 −1.21600
\(515\) −1.91633 −0.0844438
\(516\) −44.4613 −1.95730
\(517\) −4.67825 −0.205749
\(518\) 0.835619 0.0367150
\(519\) −8.14401 −0.357482
\(520\) 5.86888 0.257367
\(521\) −9.57773 −0.419608 −0.209804 0.977743i \(-0.567283\pi\)
−0.209804 + 0.977743i \(0.567283\pi\)
\(522\) 23.0063 1.00696
\(523\) −16.3655 −0.715611 −0.357806 0.933796i \(-0.616475\pi\)
−0.357806 + 0.933796i \(0.616475\pi\)
\(524\) −10.4357 −0.455885
\(525\) 0.211367 0.00922482
\(526\) −66.4850 −2.89888
\(527\) 41.0567 1.78846
\(528\) −51.9814 −2.26220
\(529\) −20.3832 −0.886225
\(530\) −69.8661 −3.03479
\(531\) 6.26247 0.271768
\(532\) −0.384639 −0.0166762
\(533\) 1.42300 0.0616369
\(534\) 4.00251 0.173206
\(535\) −31.9036 −1.37931
\(536\) 5.80672 0.250812
\(537\) −21.9234 −0.946066
\(538\) −3.95192 −0.170379
\(539\) 27.7830 1.19670
\(540\) −16.5383 −0.711694
\(541\) 21.6362 0.930212 0.465106 0.885255i \(-0.346016\pi\)
0.465106 + 0.885255i \(0.346016\pi\)
\(542\) 53.7162 2.30731
\(543\) 0.291204 0.0124967
\(544\) 110.826 4.75164
\(545\) 6.37757 0.273185
\(546\) −0.0246682 −0.00105570
\(547\) −17.0895 −0.730694 −0.365347 0.930871i \(-0.619050\pi\)
−0.365347 + 0.930871i \(0.619050\pi\)
\(548\) 34.0469 1.45441
\(549\) −1.14722 −0.0489624
\(550\) 52.4965 2.23846
\(551\) 14.5272 0.618880
\(552\) 14.1753 0.603342
\(553\) −0.625403 −0.0265949
\(554\) −41.8544 −1.77822
\(555\) 22.6872 0.963017
\(556\) 57.1887 2.42534
\(557\) −29.8407 −1.26439 −0.632196 0.774808i \(-0.717846\pi\)
−0.632196 + 0.774808i \(0.717846\pi\)
\(558\) 17.6981 0.749219
\(559\) −1.80053 −0.0761544
\(560\) −1.77445 −0.0749841
\(561\) 24.8046 1.04725
\(562\) −25.1050 −1.05899
\(563\) −43.5907 −1.83713 −0.918564 0.395272i \(-0.870650\pi\)
−0.918564 + 0.395272i \(0.870650\pi\)
\(564\) 6.19080 0.260680
\(565\) 45.0053 1.89339
\(566\) −43.8866 −1.84469
\(567\) 0.0430508 0.00180796
\(568\) 90.2998 3.78889
\(569\) −30.5079 −1.27896 −0.639480 0.768808i \(-0.720850\pi\)
−0.639480 + 0.768808i \(0.720850\pi\)
\(570\) −14.4185 −0.603926
\(571\) 34.2415 1.43296 0.716480 0.697607i \(-0.245752\pi\)
0.716480 + 0.697607i \(0.245752\pi\)
\(572\) −4.43746 −0.185539
\(573\) 6.48551 0.270936
\(574\) −0.775505 −0.0323689
\(575\) −7.94225 −0.331215
\(576\) 21.5865 0.899438
\(577\) −21.3609 −0.889266 −0.444633 0.895713i \(-0.646666\pi\)
−0.444633 + 0.895713i \(0.646666\pi\)
\(578\) −59.3499 −2.46863
\(579\) −21.6045 −0.897853
\(580\) 141.273 5.86605
\(581\) 0.448728 0.0186164
\(582\) −2.05950 −0.0853692
\(583\) 32.7155 1.35494
\(584\) −114.867 −4.75322
\(585\) −0.669744 −0.0276905
\(586\) −19.2828 −0.796564
\(587\) 29.5178 1.21833 0.609165 0.793043i \(-0.291505\pi\)
0.609165 + 0.793043i \(0.291505\pi\)
\(588\) −36.7657 −1.51619
\(589\) 11.1753 0.460472
\(590\) 53.0951 2.18589
\(591\) −16.1402 −0.663919
\(592\) −94.3629 −3.87829
\(593\) −3.23084 −0.132675 −0.0663373 0.997797i \(-0.521131\pi\)
−0.0663373 + 0.997797i \(0.521131\pi\)
\(594\) 10.6924 0.438713
\(595\) 0.846734 0.0347127
\(596\) 49.8058 2.04012
\(597\) −2.42626 −0.0993002
\(598\) 0.926922 0.0379046
\(599\) −47.5239 −1.94178 −0.970888 0.239534i \(-0.923005\pi\)
−0.970888 + 0.239534i \(0.923005\pi\)
\(600\) −43.0232 −1.75642
\(601\) 35.1770 1.43490 0.717449 0.696611i \(-0.245309\pi\)
0.717449 + 0.696611i \(0.245309\pi\)
\(602\) 0.981253 0.0399929
\(603\) −0.662651 −0.0269852
\(604\) −85.1541 −3.46487
\(605\) −14.9885 −0.609369
\(606\) 17.4749 0.709869
\(607\) 47.6240 1.93300 0.966499 0.256670i \(-0.0826254\pi\)
0.966499 + 0.256670i \(0.0826254\pi\)
\(608\) 30.1662 1.22340
\(609\) −0.367748 −0.0149019
\(610\) −9.72651 −0.393815
\(611\) 0.250706 0.0101425
\(612\) −32.8243 −1.32684
\(613\) −23.0412 −0.930626 −0.465313 0.885146i \(-0.654058\pi\)
−0.465313 + 0.885146i \(0.654058\pi\)
\(614\) −57.0097 −2.30072
\(615\) −21.0551 −0.849022
\(616\) 1.49769 0.0603438
\(617\) −3.66906 −0.147711 −0.0738553 0.997269i \(-0.523530\pi\)
−0.0738553 + 0.997269i \(0.523530\pi\)
\(618\) −1.63953 −0.0659514
\(619\) 20.9193 0.840817 0.420409 0.907335i \(-0.361887\pi\)
0.420409 + 0.907335i \(0.361887\pi\)
\(620\) 108.677 4.36458
\(621\) −1.61766 −0.0649144
\(622\) −13.6427 −0.547023
\(623\) −0.0639787 −0.00256325
\(624\) 2.78567 0.111516
\(625\) −25.4433 −1.01773
\(626\) −2.24669 −0.0897957
\(627\) 6.75164 0.269634
\(628\) 42.5005 1.69596
\(629\) 45.0282 1.79539
\(630\) 0.364997 0.0145418
\(631\) 10.3667 0.412690 0.206345 0.978479i \(-0.433843\pi\)
0.206345 + 0.978479i \(0.433843\pi\)
\(632\) 127.299 5.06369
\(633\) −19.3488 −0.769047
\(634\) 59.9099 2.37933
\(635\) 67.3791 2.67386
\(636\) −43.2930 −1.71668
\(637\) −1.48889 −0.0589918
\(638\) −91.3363 −3.61604
\(639\) −10.3048 −0.407653
\(640\) 71.3387 2.81991
\(641\) 12.1861 0.481322 0.240661 0.970609i \(-0.422636\pi\)
0.240661 + 0.970609i \(0.422636\pi\)
\(642\) −27.2952 −1.07726
\(643\) 27.4309 1.08177 0.540884 0.841097i \(-0.318090\pi\)
0.540884 + 0.841097i \(0.318090\pi\)
\(644\) −0.365870 −0.0144173
\(645\) 26.6412 1.04899
\(646\) −28.6171 −1.12593
\(647\) 24.1269 0.948525 0.474263 0.880383i \(-0.342715\pi\)
0.474263 + 0.880383i \(0.342715\pi\)
\(648\) −8.76286 −0.344238
\(649\) −24.8623 −0.975932
\(650\) −2.81328 −0.110346
\(651\) −0.282898 −0.0110876
\(652\) 67.7677 2.65399
\(653\) 24.6003 0.962683 0.481342 0.876533i \(-0.340150\pi\)
0.481342 + 0.876533i \(0.340150\pi\)
\(654\) 5.45635 0.213360
\(655\) 6.25305 0.244327
\(656\) 87.5745 3.41921
\(657\) 13.1083 0.511405
\(658\) −0.136630 −0.00532639
\(659\) 35.7993 1.39454 0.697271 0.716807i \(-0.254397\pi\)
0.697271 + 0.716807i \(0.254397\pi\)
\(660\) 65.6578 2.55573
\(661\) 47.1408 1.83357 0.916783 0.399386i \(-0.130777\pi\)
0.916783 + 0.399386i \(0.130777\pi\)
\(662\) −28.9676 −1.12586
\(663\) −1.32927 −0.0516246
\(664\) −91.3373 −3.54457
\(665\) 0.230475 0.00893745
\(666\) 19.4101 0.752125
\(667\) 13.8184 0.535049
\(668\) 59.8902 2.31722
\(669\) −19.6443 −0.759493
\(670\) −5.61815 −0.217048
\(671\) 4.55454 0.175826
\(672\) −0.763639 −0.0294580
\(673\) −45.2055 −1.74254 −0.871272 0.490801i \(-0.836704\pi\)
−0.871272 + 0.490801i \(0.836704\pi\)
\(674\) −86.2491 −3.32219
\(675\) 4.90972 0.188975
\(676\) −68.0594 −2.61767
\(677\) 15.9940 0.614700 0.307350 0.951597i \(-0.400558\pi\)
0.307350 + 0.951597i \(0.400558\pi\)
\(678\) 38.5044 1.47875
\(679\) 0.0329205 0.00126337
\(680\) −172.350 −6.60933
\(681\) −17.1918 −0.658790
\(682\) −70.2623 −2.69048
\(683\) −13.4672 −0.515308 −0.257654 0.966237i \(-0.582949\pi\)
−0.257654 + 0.966237i \(0.582949\pi\)
\(684\) −8.93454 −0.341621
\(685\) −20.4009 −0.779478
\(686\) 1.62304 0.0619680
\(687\) −0.447614 −0.0170775
\(688\) −110.809 −4.22455
\(689\) −1.75322 −0.0667923
\(690\) −13.7150 −0.522120
\(691\) 36.2228 1.37798 0.688991 0.724770i \(-0.258054\pi\)
0.688991 + 0.724770i \(0.258054\pi\)
\(692\) −42.7856 −1.62646
\(693\) −0.170914 −0.00649248
\(694\) 54.8783 2.08315
\(695\) −34.2674 −1.29984
\(696\) 74.8541 2.83734
\(697\) −41.7889 −1.58287
\(698\) −34.0205 −1.28769
\(699\) 4.91670 0.185967
\(700\) 1.11045 0.0419709
\(701\) 29.0413 1.09688 0.548438 0.836191i \(-0.315223\pi\)
0.548438 + 0.836191i \(0.315223\pi\)
\(702\) −0.573002 −0.0216266
\(703\) 12.2564 0.462258
\(704\) −85.6996 −3.22992
\(705\) −3.70952 −0.139709
\(706\) −24.1931 −0.910520
\(707\) −0.279330 −0.0105053
\(708\) 32.9007 1.23648
\(709\) 0.0797127 0.00299367 0.00149684 0.999999i \(-0.499524\pi\)
0.00149684 + 0.999999i \(0.499524\pi\)
\(710\) −87.3673 −3.27884
\(711\) −14.5271 −0.544809
\(712\) 13.0227 0.488046
\(713\) 10.6300 0.398098
\(714\) 0.724426 0.0271110
\(715\) 2.65892 0.0994380
\(716\) −115.178 −4.30439
\(717\) 19.3251 0.721709
\(718\) −24.6134 −0.918565
\(719\) −5.28187 −0.196980 −0.0984902 0.995138i \(-0.531401\pi\)
−0.0984902 + 0.995138i \(0.531401\pi\)
\(720\) −41.2176 −1.53609
\(721\) 0.0262073 0.000976009 0
\(722\) 43.3825 1.61453
\(723\) 5.97867 0.222349
\(724\) 1.52988 0.0568574
\(725\) −41.9398 −1.55760
\(726\) −12.8235 −0.475923
\(727\) 25.8097 0.957228 0.478614 0.878025i \(-0.341139\pi\)
0.478614 + 0.878025i \(0.341139\pi\)
\(728\) −0.0802612 −0.00297468
\(729\) 1.00000 0.0370370
\(730\) 111.136 4.11334
\(731\) 52.8759 1.95569
\(732\) −6.02710 −0.222768
\(733\) 19.3541 0.714860 0.357430 0.933940i \(-0.383653\pi\)
0.357430 + 0.933940i \(0.383653\pi\)
\(734\) 54.2052 2.00075
\(735\) 22.0300 0.812587
\(736\) 28.6942 1.05768
\(737\) 2.63076 0.0969053
\(738\) −18.0137 −0.663094
\(739\) 3.59517 0.132250 0.0661252 0.997811i \(-0.478936\pi\)
0.0661252 + 0.997811i \(0.478936\pi\)
\(740\) 119.190 4.38151
\(741\) −0.361819 −0.0132917
\(742\) 0.955469 0.0350764
\(743\) 14.5914 0.535307 0.267653 0.963515i \(-0.413752\pi\)
0.267653 + 0.963515i \(0.413752\pi\)
\(744\) 57.5830 2.11110
\(745\) −29.8436 −1.09338
\(746\) −5.30456 −0.194214
\(747\) 10.4232 0.381366
\(748\) 130.314 4.76475
\(749\) 0.436305 0.0159422
\(750\) −0.765425 −0.0279494
\(751\) −44.1301 −1.61033 −0.805165 0.593051i \(-0.797923\pi\)
−0.805165 + 0.593051i \(0.797923\pi\)
\(752\) 15.4290 0.562639
\(753\) 13.7369 0.500600
\(754\) 4.89469 0.178254
\(755\) 51.0243 1.85696
\(756\) 0.226173 0.00822583
\(757\) −33.7818 −1.22782 −0.613911 0.789375i \(-0.710405\pi\)
−0.613911 + 0.789375i \(0.710405\pi\)
\(758\) 12.5622 0.456281
\(759\) 6.42219 0.233111
\(760\) −46.9126 −1.70170
\(761\) −30.1995 −1.09473 −0.547365 0.836894i \(-0.684369\pi\)
−0.547365 + 0.836894i \(0.684369\pi\)
\(762\) 57.6464 2.08831
\(763\) −0.0872179 −0.00315750
\(764\) 34.0725 1.23270
\(765\) 19.6683 0.711108
\(766\) 21.9554 0.793280
\(767\) 1.33237 0.0481090
\(768\) 17.8610 0.644504
\(769\) 33.5653 1.21040 0.605199 0.796075i \(-0.293094\pi\)
0.605199 + 0.796075i \(0.293094\pi\)
\(770\) −1.44906 −0.0522204
\(771\) 10.2362 0.368646
\(772\) −113.502 −4.08503
\(773\) −32.9732 −1.18596 −0.592982 0.805216i \(-0.702049\pi\)
−0.592982 + 0.805216i \(0.702049\pi\)
\(774\) 22.7929 0.819275
\(775\) −32.2630 −1.15892
\(776\) −6.70087 −0.240547
\(777\) −0.310263 −0.0111306
\(778\) −60.1294 −2.15574
\(779\) −11.3747 −0.407540
\(780\) −3.51859 −0.125986
\(781\) 40.9107 1.46390
\(782\) −27.2207 −0.973412
\(783\) −8.54219 −0.305273
\(784\) −91.6294 −3.27248
\(785\) −25.4663 −0.908931
\(786\) 5.34982 0.190822
\(787\) 21.9281 0.781653 0.390827 0.920464i \(-0.372189\pi\)
0.390827 + 0.920464i \(0.372189\pi\)
\(788\) −84.7947 −3.02068
\(789\) 24.6857 0.878835
\(790\) −123.165 −4.38202
\(791\) −0.615479 −0.0218839
\(792\) 34.7890 1.23617
\(793\) −0.244077 −0.00866743
\(794\) 11.2360 0.398750
\(795\) 25.9411 0.920036
\(796\) −12.7467 −0.451794
\(797\) −6.14979 −0.217837 −0.108918 0.994051i \(-0.534739\pi\)
−0.108918 + 0.994051i \(0.534739\pi\)
\(798\) 0.197184 0.00698023
\(799\) −7.36245 −0.260465
\(800\) −87.0891 −3.07907
\(801\) −1.48612 −0.0525096
\(802\) 77.7024 2.74377
\(803\) −52.0408 −1.83648
\(804\) −3.48132 −0.122777
\(805\) 0.219229 0.00772681
\(806\) 3.76534 0.132629
\(807\) 1.46734 0.0516527
\(808\) 56.8568 2.00022
\(809\) 12.5388 0.440840 0.220420 0.975405i \(-0.429257\pi\)
0.220420 + 0.975405i \(0.429257\pi\)
\(810\) 8.47829 0.297897
\(811\) 44.9269 1.57760 0.788798 0.614653i \(-0.210704\pi\)
0.788798 + 0.614653i \(0.210704\pi\)
\(812\) −1.93201 −0.0678003
\(813\) −19.9447 −0.699492
\(814\) −77.0590 −2.70092
\(815\) −40.6064 −1.42238
\(816\) −81.8064 −2.86380
\(817\) 14.3925 0.503529
\(818\) 25.1164 0.878175
\(819\) 0.00915924 0.000320050 0
\(820\) −110.616 −3.86286
\(821\) 26.8584 0.937364 0.468682 0.883367i \(-0.344729\pi\)
0.468682 + 0.883367i \(0.344729\pi\)
\(822\) −17.4540 −0.608780
\(823\) −18.6761 −0.651009 −0.325505 0.945540i \(-0.605534\pi\)
−0.325505 + 0.945540i \(0.605534\pi\)
\(824\) −5.33441 −0.185833
\(825\) −19.4918 −0.678619
\(826\) −0.726113 −0.0252647
\(827\) −28.7854 −1.00097 −0.500484 0.865746i \(-0.666845\pi\)
−0.500484 + 0.865746i \(0.666845\pi\)
\(828\) −8.49858 −0.295346
\(829\) −37.8459 −1.31444 −0.657220 0.753698i \(-0.728268\pi\)
−0.657220 + 0.753698i \(0.728268\pi\)
\(830\) 88.3712 3.06741
\(831\) 15.5404 0.539092
\(832\) 4.59262 0.159221
\(833\) 43.7239 1.51494
\(834\) −29.3176 −1.01519
\(835\) −35.8861 −1.24189
\(836\) 35.4706 1.22678
\(837\) −6.57126 −0.227136
\(838\) 88.4349 3.05493
\(839\) 36.1131 1.24676 0.623380 0.781919i \(-0.285759\pi\)
0.623380 + 0.781919i \(0.285759\pi\)
\(840\) 1.18757 0.0409749
\(841\) 43.9691 1.51617
\(842\) 86.8330 2.99246
\(843\) 9.32142 0.321047
\(844\) −101.652 −3.49900
\(845\) 40.7811 1.40291
\(846\) −3.17369 −0.109114
\(847\) 0.204978 0.00704314
\(848\) −107.897 −3.70520
\(849\) 16.2950 0.559242
\(850\) 82.6171 2.83374
\(851\) 11.6583 0.399642
\(852\) −54.1378 −1.85473
\(853\) 36.3723 1.24536 0.622682 0.782475i \(-0.286043\pi\)
0.622682 + 0.782475i \(0.286043\pi\)
\(854\) 0.133017 0.00455175
\(855\) 5.35357 0.183088
\(856\) −88.8086 −3.03542
\(857\) −3.82716 −0.130733 −0.0653666 0.997861i \(-0.520822\pi\)
−0.0653666 + 0.997861i \(0.520822\pi\)
\(858\) 2.27485 0.0776620
\(859\) −4.60465 −0.157109 −0.0785544 0.996910i \(-0.525030\pi\)
−0.0785544 + 0.996910i \(0.525030\pi\)
\(860\) 139.963 4.77269
\(861\) 0.287943 0.00981308
\(862\) −27.6244 −0.940892
\(863\) −46.6427 −1.58774 −0.793868 0.608090i \(-0.791936\pi\)
−0.793868 + 0.608090i \(0.791936\pi\)
\(864\) −17.7381 −0.603463
\(865\) 25.6371 0.871687
\(866\) −4.45783 −0.151483
\(867\) 22.0365 0.748399
\(868\) −1.48624 −0.0504463
\(869\) 57.6734 1.95644
\(870\) −72.4232 −2.45538
\(871\) −0.140982 −0.00477699
\(872\) 17.7530 0.601191
\(873\) 0.764689 0.0258808
\(874\) −7.40930 −0.250623
\(875\) 0.0122350 0.000413620 0
\(876\) 68.8664 2.32678
\(877\) 8.13899 0.274834 0.137417 0.990513i \(-0.456120\pi\)
0.137417 + 0.990513i \(0.456120\pi\)
\(878\) 19.5506 0.659801
\(879\) 7.15965 0.241489
\(880\) 163.636 5.51617
\(881\) 49.3414 1.66235 0.831177 0.556008i \(-0.187668\pi\)
0.831177 + 0.556008i \(0.187668\pi\)
\(882\) 18.8478 0.634639
\(883\) 34.2071 1.15116 0.575581 0.817745i \(-0.304776\pi\)
0.575581 + 0.817745i \(0.304776\pi\)
\(884\) −6.98350 −0.234881
\(885\) −19.7141 −0.662681
\(886\) −35.2323 −1.18365
\(887\) 1.71402 0.0575510 0.0287755 0.999586i \(-0.490839\pi\)
0.0287755 + 0.999586i \(0.490839\pi\)
\(888\) 63.1532 2.11928
\(889\) −0.921458 −0.0309047
\(890\) −12.5998 −0.422346
\(891\) −3.97005 −0.133002
\(892\) −103.204 −3.45553
\(893\) −2.00401 −0.0670616
\(894\) −25.5328 −0.853943
\(895\) 69.0144 2.30690
\(896\) −0.975608 −0.0325928
\(897\) −0.344164 −0.0114913
\(898\) 81.3774 2.71560
\(899\) 56.1329 1.87214
\(900\) 25.7939 0.859795
\(901\) 51.4865 1.71526
\(902\) 71.5154 2.38120
\(903\) −0.364337 −0.0121244
\(904\) 125.279 4.16672
\(905\) −0.916700 −0.0304721
\(906\) 43.6540 1.45031
\(907\) 11.3809 0.377897 0.188949 0.981987i \(-0.439492\pi\)
0.188949 + 0.981987i \(0.439492\pi\)
\(908\) −90.3192 −2.99735
\(909\) −6.48839 −0.215206
\(910\) 0.0776547 0.00257423
\(911\) 5.12921 0.169938 0.0849691 0.996384i \(-0.472921\pi\)
0.0849691 + 0.996384i \(0.472921\pi\)
\(912\) −22.2671 −0.737339
\(913\) −41.3808 −1.36950
\(914\) −36.9650 −1.22269
\(915\) 3.61143 0.119390
\(916\) −2.35160 −0.0776990
\(917\) −0.0855150 −0.00282395
\(918\) 16.8273 0.555382
\(919\) 28.4185 0.937440 0.468720 0.883347i \(-0.344715\pi\)
0.468720 + 0.883347i \(0.344715\pi\)
\(920\) −44.6235 −1.47119
\(921\) 21.1676 0.697495
\(922\) 66.6285 2.19429
\(923\) −2.19240 −0.0721636
\(924\) −0.897918 −0.0295393
\(925\) −35.3839 −1.16342
\(926\) −14.5787 −0.479085
\(927\) 0.608752 0.0199940
\(928\) 151.522 4.97396
\(929\) −17.1314 −0.562062 −0.281031 0.959699i \(-0.590676\pi\)
−0.281031 + 0.959699i \(0.590676\pi\)
\(930\) −55.7130 −1.82690
\(931\) 11.9013 0.390051
\(932\) 25.8306 0.846108
\(933\) 5.06551 0.165837
\(934\) 34.3929 1.12537
\(935\) −78.0841 −2.55362
\(936\) −1.86434 −0.0609378
\(937\) 58.9549 1.92597 0.962986 0.269552i \(-0.0868757\pi\)
0.962986 + 0.269552i \(0.0868757\pi\)
\(938\) 0.0768323 0.00250866
\(939\) 0.834190 0.0272228
\(940\) −19.4884 −0.635643
\(941\) 4.06419 0.132489 0.0662444 0.997803i \(-0.478898\pi\)
0.0662444 + 0.997803i \(0.478898\pi\)
\(942\) −21.7878 −0.709884
\(943\) −10.8196 −0.352336
\(944\) 81.9969 2.66877
\(945\) −0.135523 −0.00440855
\(946\) −90.4891 −2.94206
\(947\) 43.0426 1.39870 0.699349 0.714780i \(-0.253473\pi\)
0.699349 + 0.714780i \(0.253473\pi\)
\(948\) −76.3201 −2.47876
\(949\) 2.78886 0.0905301
\(950\) 22.4878 0.729601
\(951\) −22.2444 −0.721324
\(952\) 2.35702 0.0763913
\(953\) 8.56721 0.277519 0.138760 0.990326i \(-0.455688\pi\)
0.138760 + 0.990326i \(0.455688\pi\)
\(954\) 22.1940 0.718557
\(955\) −20.4162 −0.660653
\(956\) 101.527 3.28362
\(957\) 33.9130 1.09625
\(958\) 73.5391 2.37594
\(959\) 0.278997 0.00900928
\(960\) −67.9537 −2.19320
\(961\) 12.1814 0.392949
\(962\) 4.12958 0.133143
\(963\) 10.1347 0.326585
\(964\) 31.4097 1.01164
\(965\) 68.0104 2.18933
\(966\) 0.187562 0.00603472
\(967\) 24.1298 0.775963 0.387982 0.921667i \(-0.373172\pi\)
0.387982 + 0.921667i \(0.373172\pi\)
\(968\) −41.7228 −1.34102
\(969\) 10.6255 0.341339
\(970\) 6.48326 0.208165
\(971\) −31.5150 −1.01136 −0.505681 0.862720i \(-0.668759\pi\)
−0.505681 + 0.862720i \(0.668759\pi\)
\(972\) 5.25363 0.168510
\(973\) 0.468632 0.0150236
\(974\) −86.7720 −2.78036
\(975\) 1.04456 0.0334528
\(976\) −15.0211 −0.480812
\(977\) −22.3005 −0.713455 −0.356727 0.934208i \(-0.616108\pi\)
−0.356727 + 0.934208i \(0.616108\pi\)
\(978\) −34.7409 −1.11089
\(979\) 5.89998 0.188564
\(980\) 115.737 3.69709
\(981\) −2.02593 −0.0646830
\(982\) 99.3658 3.17089
\(983\) −4.38519 −0.139866 −0.0699330 0.997552i \(-0.522279\pi\)
−0.0699330 + 0.997552i \(0.522279\pi\)
\(984\) −58.6100 −1.86842
\(985\) 50.8089 1.61891
\(986\) −143.742 −4.57767
\(987\) 0.0507303 0.00161476
\(988\) −1.90086 −0.0604745
\(989\) 13.6902 0.435322
\(990\) −33.6593 −1.06976
\(991\) −53.6221 −1.70336 −0.851681 0.524060i \(-0.824417\pi\)
−0.851681 + 0.524060i \(0.824417\pi\)
\(992\) 116.562 3.70084
\(993\) 10.7556 0.341319
\(994\) 1.19481 0.0378971
\(995\) 7.63779 0.242134
\(996\) 54.7598 1.73513
\(997\) 13.8753 0.439435 0.219717 0.975564i \(-0.429486\pi\)
0.219717 + 0.975564i \(0.429486\pi\)
\(998\) 78.5510 2.48649
\(999\) −7.20692 −0.228017
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 \(a_p\))