Properties

Label 8027.2.a.f.1.3
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +O(q^{10})\) \(q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +2.68266 q^{10} +0.00376926 q^{11} -17.7442 q^{12} +6.25341 q^{13} -12.9558 q^{14} +3.00200 q^{15} +17.1884 q^{16} +4.19620 q^{17} -18.4807 q^{18} +2.54249 q^{19} -5.51691 q^{20} -14.4981 q^{21} -0.0104664 q^{22} +1.00000 q^{23} +32.0151 q^{24} -4.06664 q^{25} -17.3643 q^{26} -11.3587 q^{27} +26.6438 q^{28} +2.76292 q^{29} -8.33588 q^{30} -1.73444 q^{31} -27.1221 q^{32} -0.0117123 q^{33} -11.6519 q^{34} -4.50764 q^{35} +38.0057 q^{36} +9.51286 q^{37} -7.05992 q^{38} -19.4314 q^{39} +9.95389 q^{40} -2.36385 q^{41} +40.2579 q^{42} -5.09898 q^{43} +0.0215242 q^{44} -6.42988 q^{45} -2.77677 q^{46} -7.55988 q^{47} -53.4100 q^{48} +14.7695 q^{49} +11.2921 q^{50} -13.0390 q^{51} +35.7099 q^{52} +11.8266 q^{53} +31.5405 q^{54} -0.00364151 q^{55} -48.0720 q^{56} -7.90034 q^{57} -7.67200 q^{58} +9.51316 q^{59} +17.1428 q^{60} -11.2164 q^{61} +4.81615 q^{62} +31.0529 q^{63} +40.9351 q^{64} -6.04146 q^{65} +0.0325224 q^{66} +3.65836 q^{67} +23.9622 q^{68} -3.10732 q^{69} +12.5167 q^{70} +2.25856 q^{71} -68.5718 q^{72} +1.57815 q^{73} -26.4150 q^{74} +12.6364 q^{75} +14.5188 q^{76} +0.0175866 q^{77} +53.9565 q^{78} +0.604109 q^{79} -16.6058 q^{80} +15.3288 q^{81} +6.56388 q^{82} -15.9342 q^{83} -82.7908 q^{84} -4.05398 q^{85} +14.1587 q^{86} -8.58529 q^{87} -0.0388351 q^{88} -3.32964 q^{89} +17.8543 q^{90} +29.1771 q^{91} +5.71046 q^{92} +5.38948 q^{93} +20.9921 q^{94} -2.45632 q^{95} +84.2772 q^{96} +10.5025 q^{97} -41.0116 q^{98} +0.0250862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77677 −1.96347 −0.981737 0.190244i \(-0.939072\pi\)
−0.981737 + 0.190244i \(0.939072\pi\)
\(3\) −3.10732 −1.79401 −0.897007 0.442016i \(-0.854263\pi\)
−0.897007 + 0.442016i \(0.854263\pi\)
\(4\) 5.71046 2.85523
\(5\) −0.966106 −0.432056 −0.216028 0.976387i \(-0.569310\pi\)
−0.216028 + 0.976387i \(0.569310\pi\)
\(6\) 8.62833 3.52250
\(7\) 4.66578 1.76350 0.881750 0.471717i \(-0.156366\pi\)
0.881750 + 0.471717i \(0.156366\pi\)
\(8\) −10.3031 −3.64269
\(9\) 6.65546 2.21849
\(10\) 2.68266 0.848330
\(11\) 0.00376926 0.00113648 0.000568238 1.00000i \(-0.499819\pi\)
0.000568238 1.00000i \(0.499819\pi\)
\(12\) −17.7442 −5.12232
\(13\) 6.25341 1.73438 0.867192 0.497974i \(-0.165922\pi\)
0.867192 + 0.497974i \(0.165922\pi\)
\(14\) −12.9558 −3.46259
\(15\) 3.00200 0.775114
\(16\) 17.1884 4.29711
\(17\) 4.19620 1.01773 0.508864 0.860847i \(-0.330066\pi\)
0.508864 + 0.860847i \(0.330066\pi\)
\(18\) −18.4807 −4.35594
\(19\) 2.54249 0.583288 0.291644 0.956527i \(-0.405798\pi\)
0.291644 + 0.956527i \(0.405798\pi\)
\(20\) −5.51691 −1.23362
\(21\) −14.4981 −3.16374
\(22\) −0.0104664 −0.00223144
\(23\) 1.00000 0.208514
\(24\) 32.0151 6.53505
\(25\) −4.06664 −0.813328
\(26\) −17.3643 −3.40542
\(27\) −11.3587 −2.18598
\(28\) 26.6438 5.03520
\(29\) 2.76292 0.513061 0.256531 0.966536i \(-0.417421\pi\)
0.256531 + 0.966536i \(0.417421\pi\)
\(30\) −8.33588 −1.52192
\(31\) −1.73444 −0.311515 −0.155758 0.987795i \(-0.549782\pi\)
−0.155758 + 0.987795i \(0.549782\pi\)
\(32\) −27.1221 −4.79456
\(33\) −0.0117123 −0.00203885
\(34\) −11.6519 −1.99828
\(35\) −4.50764 −0.761930
\(36\) 38.0057 6.33429
\(37\) 9.51286 1.56390 0.781952 0.623338i \(-0.214224\pi\)
0.781952 + 0.623338i \(0.214224\pi\)
\(38\) −7.05992 −1.14527
\(39\) −19.4314 −3.11151
\(40\) 9.95389 1.57385
\(41\) −2.36385 −0.369172 −0.184586 0.982816i \(-0.559094\pi\)
−0.184586 + 0.982816i \(0.559094\pi\)
\(42\) 40.2579 6.21193
\(43\) −5.09898 −0.777588 −0.388794 0.921325i \(-0.627108\pi\)
−0.388794 + 0.921325i \(0.627108\pi\)
\(44\) 0.0215242 0.00324490
\(45\) −6.42988 −0.958510
\(46\) −2.77677 −0.409413
\(47\) −7.55988 −1.10272 −0.551361 0.834267i \(-0.685891\pi\)
−0.551361 + 0.834267i \(0.685891\pi\)
\(48\) −53.4100 −7.70907
\(49\) 14.7695 2.10993
\(50\) 11.2921 1.59695
\(51\) −13.0390 −1.82582
\(52\) 35.7099 4.95207
\(53\) 11.8266 1.62451 0.812254 0.583304i \(-0.198240\pi\)
0.812254 + 0.583304i \(0.198240\pi\)
\(54\) 31.5405 4.29212
\(55\) −0.00364151 −0.000491021 0
\(56\) −48.0720 −6.42389
\(57\) −7.90034 −1.04643
\(58\) −7.67200 −1.00738
\(59\) 9.51316 1.23851 0.619254 0.785191i \(-0.287435\pi\)
0.619254 + 0.785191i \(0.287435\pi\)
\(60\) 17.1428 2.21313
\(61\) −11.2164 −1.43611 −0.718053 0.695988i \(-0.754967\pi\)
−0.718053 + 0.695988i \(0.754967\pi\)
\(62\) 4.81615 0.611652
\(63\) 31.0529 3.91230
\(64\) 40.9351 5.11689
\(65\) −6.04146 −0.749351
\(66\) 0.0325224 0.00400323
\(67\) 3.65836 0.446940 0.223470 0.974711i \(-0.428262\pi\)
0.223470 + 0.974711i \(0.428262\pi\)
\(68\) 23.9622 2.90585
\(69\) −3.10732 −0.374078
\(70\) 12.5167 1.49603
\(71\) 2.25856 0.268042 0.134021 0.990979i \(-0.457211\pi\)
0.134021 + 0.990979i \(0.457211\pi\)
\(72\) −68.5718 −8.08127
\(73\) 1.57815 0.184709 0.0923545 0.995726i \(-0.470561\pi\)
0.0923545 + 0.995726i \(0.470561\pi\)
\(74\) −26.4150 −3.07069
\(75\) 12.6364 1.45912
\(76\) 14.5188 1.66542
\(77\) 0.0175866 0.00200417
\(78\) 53.9565 6.10937
\(79\) 0.604109 0.0679676 0.0339838 0.999422i \(-0.489181\pi\)
0.0339838 + 0.999422i \(0.489181\pi\)
\(80\) −16.6058 −1.85659
\(81\) 15.3288 1.70319
\(82\) 6.56388 0.724859
\(83\) −15.9342 −1.74900 −0.874500 0.485025i \(-0.838810\pi\)
−0.874500 + 0.485025i \(0.838810\pi\)
\(84\) −82.7908 −9.03321
\(85\) −4.05398 −0.439715
\(86\) 14.1587 1.52677
\(87\) −8.58529 −0.920439
\(88\) −0.0388351 −0.00413983
\(89\) −3.32964 −0.352941 −0.176471 0.984306i \(-0.556468\pi\)
−0.176471 + 0.984306i \(0.556468\pi\)
\(90\) 17.8543 1.88201
\(91\) 29.1771 3.05859
\(92\) 5.71046 0.595357
\(93\) 5.38948 0.558863
\(94\) 20.9921 2.16516
\(95\) −2.45632 −0.252013
\(96\) 84.2772 8.60151
\(97\) 10.5025 1.06636 0.533182 0.846000i \(-0.320996\pi\)
0.533182 + 0.846000i \(0.320996\pi\)
\(98\) −41.0116 −4.14280
\(99\) 0.0250862 0.00252126
\(100\) −23.2224 −2.32224
\(101\) 7.22212 0.718627 0.359314 0.933217i \(-0.383011\pi\)
0.359314 + 0.933217i \(0.383011\pi\)
\(102\) 36.2062 3.58495
\(103\) 13.3741 1.31779 0.658895 0.752235i \(-0.271024\pi\)
0.658895 + 0.752235i \(0.271024\pi\)
\(104\) −64.4295 −6.31783
\(105\) 14.0067 1.36691
\(106\) −32.8398 −3.18968
\(107\) −3.71905 −0.359534 −0.179767 0.983709i \(-0.557534\pi\)
−0.179767 + 0.983709i \(0.557534\pi\)
\(108\) −64.8633 −6.24148
\(109\) −8.34626 −0.799426 −0.399713 0.916640i \(-0.630890\pi\)
−0.399713 + 0.916640i \(0.630890\pi\)
\(110\) 0.0101116 0.000964107 0
\(111\) −29.5595 −2.80567
\(112\) 80.1975 7.57795
\(113\) 19.5324 1.83746 0.918728 0.394891i \(-0.129218\pi\)
0.918728 + 0.394891i \(0.129218\pi\)
\(114\) 21.9374 2.05463
\(115\) −0.966106 −0.0900899
\(116\) 15.7775 1.46491
\(117\) 41.6193 3.84771
\(118\) −26.4159 −2.43178
\(119\) 19.5786 1.79476
\(120\) −30.9299 −2.82350
\(121\) −11.0000 −0.999999
\(122\) 31.1452 2.81976
\(123\) 7.34525 0.662299
\(124\) −9.90447 −0.889447
\(125\) 8.75934 0.783459
\(126\) −86.2269 −7.68170
\(127\) 3.50952 0.311419 0.155710 0.987803i \(-0.450234\pi\)
0.155710 + 0.987803i \(0.450234\pi\)
\(128\) −59.4232 −5.25232
\(129\) 15.8442 1.39500
\(130\) 16.7758 1.47133
\(131\) −2.74298 −0.239655 −0.119827 0.992795i \(-0.538234\pi\)
−0.119827 + 0.992795i \(0.538234\pi\)
\(132\) −0.0668827 −0.00582139
\(133\) 11.8627 1.02863
\(134\) −10.1584 −0.877554
\(135\) 10.9737 0.944466
\(136\) −43.2339 −3.70727
\(137\) 7.87604 0.672895 0.336448 0.941702i \(-0.390774\pi\)
0.336448 + 0.941702i \(0.390774\pi\)
\(138\) 8.62833 0.734492
\(139\) 15.8297 1.34266 0.671330 0.741159i \(-0.265723\pi\)
0.671330 + 0.741159i \(0.265723\pi\)
\(140\) −25.7407 −2.17549
\(141\) 23.4910 1.97830
\(142\) −6.27150 −0.526292
\(143\) 0.0235708 0.00197109
\(144\) 114.397 9.53307
\(145\) −2.66927 −0.221671
\(146\) −4.38217 −0.362671
\(147\) −45.8937 −3.78525
\(148\) 54.3228 4.46531
\(149\) 12.7538 1.04483 0.522415 0.852691i \(-0.325031\pi\)
0.522415 + 0.852691i \(0.325031\pi\)
\(150\) −35.0883 −2.86495
\(151\) −18.5514 −1.50969 −0.754844 0.655904i \(-0.772287\pi\)
−0.754844 + 0.655904i \(0.772287\pi\)
\(152\) −26.1955 −2.12474
\(153\) 27.9276 2.25782
\(154\) −0.0488339 −0.00393514
\(155\) 1.67566 0.134592
\(156\) −110.962 −8.88408
\(157\) 16.1506 1.28896 0.644481 0.764620i \(-0.277074\pi\)
0.644481 + 0.764620i \(0.277074\pi\)
\(158\) −1.67747 −0.133453
\(159\) −36.7491 −2.91439
\(160\) 26.2029 2.07152
\(161\) 4.66578 0.367715
\(162\) −42.5644 −3.34418
\(163\) 10.7399 0.841216 0.420608 0.907243i \(-0.361817\pi\)
0.420608 + 0.907243i \(0.361817\pi\)
\(164\) −13.4987 −1.05407
\(165\) 0.0113153 0.000880898 0
\(166\) 44.2455 3.43412
\(167\) 13.6364 1.05522 0.527609 0.849487i \(-0.323089\pi\)
0.527609 + 0.849487i \(0.323089\pi\)
\(168\) 149.375 11.5246
\(169\) 26.1052 2.00809
\(170\) 11.2570 0.863370
\(171\) 16.9214 1.29402
\(172\) −29.1175 −2.22019
\(173\) 12.8624 0.977912 0.488956 0.872308i \(-0.337378\pi\)
0.488956 + 0.872308i \(0.337378\pi\)
\(174\) 23.8394 1.80726
\(175\) −18.9741 −1.43430
\(176\) 0.0647877 0.00488356
\(177\) −29.5605 −2.22190
\(178\) 9.24566 0.692991
\(179\) 21.2095 1.58527 0.792637 0.609693i \(-0.208707\pi\)
0.792637 + 0.609693i \(0.208707\pi\)
\(180\) −36.7176 −2.73677
\(181\) −16.4164 −1.22022 −0.610110 0.792317i \(-0.708875\pi\)
−0.610110 + 0.792317i \(0.708875\pi\)
\(182\) −81.0180 −6.00546
\(183\) 34.8528 2.57640
\(184\) −10.3031 −0.759554
\(185\) −9.19043 −0.675694
\(186\) −14.9653 −1.09731
\(187\) 0.0158166 0.00115662
\(188\) −43.1704 −3.14852
\(189\) −52.9972 −3.85498
\(190\) 6.82063 0.494820
\(191\) 9.12693 0.660401 0.330201 0.943911i \(-0.392884\pi\)
0.330201 + 0.943911i \(0.392884\pi\)
\(192\) −127.199 −9.17977
\(193\) 16.3956 1.18018 0.590091 0.807337i \(-0.299092\pi\)
0.590091 + 0.807337i \(0.299092\pi\)
\(194\) −29.1630 −2.09378
\(195\) 18.7728 1.34435
\(196\) 84.3408 6.02434
\(197\) −5.22362 −0.372168 −0.186084 0.982534i \(-0.559580\pi\)
−0.186084 + 0.982534i \(0.559580\pi\)
\(198\) −0.0696586 −0.00495042
\(199\) −7.55778 −0.535757 −0.267879 0.963453i \(-0.586323\pi\)
−0.267879 + 0.963453i \(0.586323\pi\)
\(200\) 41.8990 2.96270
\(201\) −11.3677 −0.801816
\(202\) −20.0542 −1.41101
\(203\) 12.8912 0.904784
\(204\) −74.4584 −5.21313
\(205\) 2.28373 0.159503
\(206\) −37.1369 −2.58745
\(207\) 6.65546 0.462586
\(208\) 107.486 7.45283
\(209\) 0.00958332 0.000662892 0
\(210\) −38.8934 −2.68390
\(211\) −16.3145 −1.12314 −0.561570 0.827429i \(-0.689802\pi\)
−0.561570 + 0.827429i \(0.689802\pi\)
\(212\) 67.5353 4.63834
\(213\) −7.01807 −0.480870
\(214\) 10.3270 0.705936
\(215\) 4.92616 0.335961
\(216\) 117.030 7.96286
\(217\) −8.09253 −0.549357
\(218\) 23.1756 1.56965
\(219\) −4.90384 −0.331370
\(220\) −0.0207947 −0.00140198
\(221\) 26.2406 1.76513
\(222\) 82.0801 5.50885
\(223\) 10.5430 0.706009 0.353004 0.935622i \(-0.385160\pi\)
0.353004 + 0.935622i \(0.385160\pi\)
\(224\) −126.546 −8.45521
\(225\) −27.0653 −1.80436
\(226\) −54.2371 −3.60780
\(227\) −21.8618 −1.45102 −0.725508 0.688214i \(-0.758395\pi\)
−0.725508 + 0.688214i \(0.758395\pi\)
\(228\) −45.1146 −2.98779
\(229\) 6.79922 0.449305 0.224653 0.974439i \(-0.427875\pi\)
0.224653 + 0.974439i \(0.427875\pi\)
\(230\) 2.68266 0.176889
\(231\) −0.0546471 −0.00359552
\(232\) −28.4666 −1.86893
\(233\) −24.7658 −1.62246 −0.811231 0.584726i \(-0.801202\pi\)
−0.811231 + 0.584726i \(0.801202\pi\)
\(234\) −115.567 −7.55487
\(235\) 7.30364 0.476437
\(236\) 54.3245 3.53622
\(237\) −1.87716 −0.121935
\(238\) −54.3652 −3.52397
\(239\) 14.5875 0.943584 0.471792 0.881710i \(-0.343607\pi\)
0.471792 + 0.881710i \(0.343607\pi\)
\(240\) 51.5997 3.33075
\(241\) −4.10431 −0.264382 −0.132191 0.991224i \(-0.542201\pi\)
−0.132191 + 0.991224i \(0.542201\pi\)
\(242\) 30.5444 1.96347
\(243\) −13.5553 −0.869574
\(244\) −64.0505 −4.10041
\(245\) −14.2689 −0.911609
\(246\) −20.3961 −1.30041
\(247\) 15.8992 1.01164
\(248\) 17.8701 1.13475
\(249\) 49.5126 3.13773
\(250\) −24.3227 −1.53830
\(251\) −19.9574 −1.25970 −0.629850 0.776716i \(-0.716884\pi\)
−0.629850 + 0.776716i \(0.716884\pi\)
\(252\) 177.326 11.1705
\(253\) 0.00376926 0.000236972 0
\(254\) −9.74513 −0.611464
\(255\) 12.5970 0.788856
\(256\) 83.1344 5.19590
\(257\) −26.6907 −1.66492 −0.832460 0.554086i \(-0.813068\pi\)
−0.832460 + 0.554086i \(0.813068\pi\)
\(258\) −43.9957 −2.73905
\(259\) 44.3849 2.75795
\(260\) −34.4995 −2.13957
\(261\) 18.3885 1.13822
\(262\) 7.61662 0.470556
\(263\) −15.6514 −0.965105 −0.482553 0.875867i \(-0.660290\pi\)
−0.482553 + 0.875867i \(0.660290\pi\)
\(264\) 0.120673 0.00742692
\(265\) −11.4258 −0.701878
\(266\) −32.9400 −2.01968
\(267\) 10.3463 0.633182
\(268\) 20.8909 1.27612
\(269\) 5.45580 0.332646 0.166323 0.986071i \(-0.446811\pi\)
0.166323 + 0.986071i \(0.446811\pi\)
\(270\) −30.4715 −1.85443
\(271\) −11.3918 −0.692006 −0.346003 0.938233i \(-0.612461\pi\)
−0.346003 + 0.938233i \(0.612461\pi\)
\(272\) 72.1261 4.37329
\(273\) −90.6626 −5.48715
\(274\) −21.8700 −1.32121
\(275\) −0.0153282 −0.000924327 0
\(276\) −17.7442 −1.06808
\(277\) −15.3705 −0.923524 −0.461762 0.887004i \(-0.652783\pi\)
−0.461762 + 0.887004i \(0.652783\pi\)
\(278\) −43.9555 −2.63628
\(279\) −11.5435 −0.691092
\(280\) 46.4427 2.77548
\(281\) −24.2522 −1.44677 −0.723383 0.690447i \(-0.757414\pi\)
−0.723383 + 0.690447i \(0.757414\pi\)
\(282\) −65.2291 −3.88434
\(283\) −15.0284 −0.893345 −0.446673 0.894697i \(-0.647391\pi\)
−0.446673 + 0.894697i \(0.647391\pi\)
\(284\) 12.8974 0.765320
\(285\) 7.63257 0.452114
\(286\) −0.0654506 −0.00387017
\(287\) −11.0292 −0.651034
\(288\) −180.510 −10.6367
\(289\) 0.608105 0.0357709
\(290\) 7.41197 0.435246
\(291\) −32.6346 −1.91307
\(292\) 9.01199 0.527387
\(293\) −17.3221 −1.01197 −0.505983 0.862543i \(-0.668870\pi\)
−0.505983 + 0.862543i \(0.668870\pi\)
\(294\) 127.436 7.43224
\(295\) −9.19072 −0.535104
\(296\) −98.0119 −5.69683
\(297\) −0.0428139 −0.00248431
\(298\) −35.4143 −2.05150
\(299\) 6.25341 0.361644
\(300\) 72.1594 4.16613
\(301\) −23.7908 −1.37128
\(302\) 51.5129 2.96423
\(303\) −22.4415 −1.28923
\(304\) 43.7014 2.50645
\(305\) 10.8362 0.620478
\(306\) −77.5487 −4.43316
\(307\) 28.5097 1.62713 0.813567 0.581471i \(-0.197523\pi\)
0.813567 + 0.581471i \(0.197523\pi\)
\(308\) 0.100427 0.00572238
\(309\) −41.5577 −2.36413
\(310\) −4.65291 −0.264268
\(311\) −17.0880 −0.968972 −0.484486 0.874799i \(-0.660993\pi\)
−0.484486 + 0.874799i \(0.660993\pi\)
\(312\) 200.203 11.3343
\(313\) −3.60663 −0.203859 −0.101929 0.994792i \(-0.532502\pi\)
−0.101929 + 0.994792i \(0.532502\pi\)
\(314\) −44.8467 −2.53084
\(315\) −30.0004 −1.69033
\(316\) 3.44974 0.194063
\(317\) 24.7512 1.39017 0.695084 0.718929i \(-0.255367\pi\)
0.695084 + 0.718929i \(0.255367\pi\)
\(318\) 102.044 5.72233
\(319\) 0.0104142 0.000583082 0
\(320\) −39.5477 −2.21078
\(321\) 11.5563 0.645009
\(322\) −12.9558 −0.721999
\(323\) 10.6688 0.593628
\(324\) 87.5342 4.86301
\(325\) −25.4304 −1.41062
\(326\) −29.8223 −1.65170
\(327\) 25.9345 1.43418
\(328\) 24.3550 1.34478
\(329\) −35.2727 −1.94465
\(330\) −0.0314201 −0.00172962
\(331\) −12.4592 −0.684821 −0.342410 0.939550i \(-0.611243\pi\)
−0.342410 + 0.939550i \(0.611243\pi\)
\(332\) −90.9913 −4.99380
\(333\) 63.3125 3.46950
\(334\) −37.8652 −2.07189
\(335\) −3.53436 −0.193103
\(336\) −249.199 −13.5949
\(337\) −3.12830 −0.170409 −0.0852046 0.996363i \(-0.527154\pi\)
−0.0852046 + 0.996363i \(0.527154\pi\)
\(338\) −72.4881 −3.94283
\(339\) −60.6936 −3.29642
\(340\) −23.1501 −1.25549
\(341\) −0.00653757 −0.000354029 0
\(342\) −46.9870 −2.54077
\(343\) 36.2509 1.95737
\(344\) 52.5353 2.83252
\(345\) 3.00200 0.161622
\(346\) −35.7160 −1.92011
\(347\) 35.7568 1.91953 0.959763 0.280812i \(-0.0906038\pi\)
0.959763 + 0.280812i \(0.0906038\pi\)
\(348\) −49.0259 −2.62807
\(349\) −1.00000 −0.0535288
\(350\) 52.6866 2.81622
\(351\) −71.0306 −3.79133
\(352\) −0.102230 −0.00544890
\(353\) 13.8709 0.738272 0.369136 0.929375i \(-0.379654\pi\)
0.369136 + 0.929375i \(0.379654\pi\)
\(354\) 82.0826 4.36264
\(355\) −2.18201 −0.115809
\(356\) −19.0138 −1.00773
\(357\) −60.8369 −3.21983
\(358\) −58.8940 −3.11265
\(359\) −3.68549 −0.194513 −0.0972563 0.995259i \(-0.531007\pi\)
−0.0972563 + 0.995259i \(0.531007\pi\)
\(360\) 66.2477 3.49156
\(361\) −12.5357 −0.659776
\(362\) 45.5845 2.39587
\(363\) 34.1805 1.79401
\(364\) 166.614 8.73297
\(365\) −1.52466 −0.0798046
\(366\) −96.7784 −5.05869
\(367\) −10.0369 −0.523920 −0.261960 0.965079i \(-0.584369\pi\)
−0.261960 + 0.965079i \(0.584369\pi\)
\(368\) 17.1884 0.896009
\(369\) −15.7325 −0.819002
\(370\) 25.5197 1.32671
\(371\) 55.1803 2.86482
\(372\) 30.7764 1.59568
\(373\) 12.2772 0.635692 0.317846 0.948142i \(-0.397041\pi\)
0.317846 + 0.948142i \(0.397041\pi\)
\(374\) −0.0439190 −0.00227100
\(375\) −27.2181 −1.40554
\(376\) 77.8901 4.01688
\(377\) 17.2777 0.889846
\(378\) 147.161 7.56915
\(379\) 19.6035 1.00696 0.503481 0.864006i \(-0.332052\pi\)
0.503481 + 0.864006i \(0.332052\pi\)
\(380\) −14.0267 −0.719554
\(381\) −10.9052 −0.558691
\(382\) −25.3434 −1.29668
\(383\) −2.26773 −0.115876 −0.0579378 0.998320i \(-0.518453\pi\)
−0.0579378 + 0.998320i \(0.518453\pi\)
\(384\) 184.647 9.42273
\(385\) −0.0169905 −0.000865915 0
\(386\) −45.5269 −2.31726
\(387\) −33.9361 −1.72507
\(388\) 59.9739 3.04471
\(389\) 9.45152 0.479211 0.239606 0.970870i \(-0.422982\pi\)
0.239606 + 0.970870i \(0.422982\pi\)
\(390\) −52.1277 −2.63959
\(391\) 4.19620 0.212211
\(392\) −152.172 −7.68584
\(393\) 8.52331 0.429944
\(394\) 14.5048 0.730741
\(395\) −0.583634 −0.0293658
\(396\) 0.143254 0.00719876
\(397\) 29.5184 1.48149 0.740743 0.671789i \(-0.234474\pi\)
0.740743 + 0.671789i \(0.234474\pi\)
\(398\) 20.9862 1.05195
\(399\) −36.8613 −1.84537
\(400\) −69.8991 −3.49496
\(401\) 28.7987 1.43814 0.719070 0.694937i \(-0.244568\pi\)
0.719070 + 0.694937i \(0.244568\pi\)
\(402\) 31.5655 1.57434
\(403\) −10.8462 −0.540287
\(404\) 41.2416 2.05185
\(405\) −14.8092 −0.735875
\(406\) −35.7959 −1.77652
\(407\) 0.0358565 0.00177734
\(408\) 134.342 6.65090
\(409\) −25.3140 −1.25169 −0.625847 0.779945i \(-0.715247\pi\)
−0.625847 + 0.779945i \(0.715247\pi\)
\(410\) −6.34140 −0.313179
\(411\) −24.4734 −1.20718
\(412\) 76.3723 3.76259
\(413\) 44.3863 2.18411
\(414\) −18.4807 −0.908276
\(415\) 15.3941 0.755666
\(416\) −169.606 −8.31561
\(417\) −49.1881 −2.40875
\(418\) −0.0266107 −0.00130157
\(419\) −2.74753 −0.134225 −0.0671127 0.997745i \(-0.521379\pi\)
−0.0671127 + 0.997745i \(0.521379\pi\)
\(420\) 79.9847 3.90285
\(421\) 0.573424 0.0279470 0.0139735 0.999902i \(-0.495552\pi\)
0.0139735 + 0.999902i \(0.495552\pi\)
\(422\) 45.3018 2.20526
\(423\) −50.3144 −2.44637
\(424\) −121.851 −5.91759
\(425\) −17.0644 −0.827747
\(426\) 19.4876 0.944176
\(427\) −52.3331 −2.53257
\(428\) −21.2375 −1.02655
\(429\) −0.0732419 −0.00353615
\(430\) −13.6788 −0.659651
\(431\) −19.3644 −0.932750 −0.466375 0.884587i \(-0.654440\pi\)
−0.466375 + 0.884587i \(0.654440\pi\)
\(432\) −195.238 −9.39339
\(433\) −13.3963 −0.643787 −0.321893 0.946776i \(-0.604319\pi\)
−0.321893 + 0.946776i \(0.604319\pi\)
\(434\) 22.4711 1.07865
\(435\) 8.29430 0.397681
\(436\) −47.6610 −2.28255
\(437\) 2.54249 0.121624
\(438\) 13.6168 0.650637
\(439\) −9.02989 −0.430973 −0.215487 0.976507i \(-0.569134\pi\)
−0.215487 + 0.976507i \(0.569134\pi\)
\(440\) 0.0375188 0.00178864
\(441\) 98.2980 4.68086
\(442\) −72.8641 −3.46579
\(443\) −26.0447 −1.23742 −0.618712 0.785618i \(-0.712345\pi\)
−0.618712 + 0.785618i \(0.712345\pi\)
\(444\) −168.799 −8.01082
\(445\) 3.21679 0.152490
\(446\) −29.2754 −1.38623
\(447\) −39.6301 −1.87444
\(448\) 190.994 9.02363
\(449\) −13.9042 −0.656181 −0.328090 0.944646i \(-0.606405\pi\)
−0.328090 + 0.944646i \(0.606405\pi\)
\(450\) 75.1543 3.54281
\(451\) −0.00890998 −0.000419555 0
\(452\) 111.539 5.24636
\(453\) 57.6451 2.70840
\(454\) 60.7051 2.84903
\(455\) −28.1881 −1.32148
\(456\) 81.3980 3.81181
\(457\) −6.47558 −0.302915 −0.151457 0.988464i \(-0.548397\pi\)
−0.151457 + 0.988464i \(0.548397\pi\)
\(458\) −18.8799 −0.882199
\(459\) −47.6634 −2.22474
\(460\) −5.51691 −0.257227
\(461\) −15.1618 −0.706157 −0.353078 0.935594i \(-0.614865\pi\)
−0.353078 + 0.935594i \(0.614865\pi\)
\(462\) 0.151743 0.00705970
\(463\) 19.1112 0.888171 0.444086 0.895984i \(-0.353529\pi\)
0.444086 + 0.895984i \(0.353529\pi\)
\(464\) 47.4903 2.20468
\(465\) −5.20681 −0.241460
\(466\) 68.7690 3.18566
\(467\) 15.7093 0.726938 0.363469 0.931606i \(-0.381592\pi\)
0.363469 + 0.931606i \(0.381592\pi\)
\(468\) 237.665 10.9861
\(469\) 17.0691 0.788178
\(470\) −20.2805 −0.935472
\(471\) −50.1853 −2.31242
\(472\) −98.0150 −4.51150
\(473\) −0.0192194 −0.000883710 0
\(474\) 5.21245 0.239416
\(475\) −10.3394 −0.474404
\(476\) 111.803 5.12446
\(477\) 78.7115 3.60395
\(478\) −40.5060 −1.85270
\(479\) −38.0748 −1.73968 −0.869840 0.493334i \(-0.835778\pi\)
−0.869840 + 0.493334i \(0.835778\pi\)
\(480\) −81.4208 −3.71633
\(481\) 59.4878 2.71241
\(482\) 11.3967 0.519106
\(483\) −14.4981 −0.659686
\(484\) −62.8150 −2.85523
\(485\) −10.1465 −0.460729
\(486\) 37.6400 1.70739
\(487\) 10.0164 0.453885 0.226942 0.973908i \(-0.427127\pi\)
0.226942 + 0.973908i \(0.427127\pi\)
\(488\) 115.563 5.23130
\(489\) −33.3724 −1.50915
\(490\) 39.6216 1.78992
\(491\) −20.0866 −0.906495 −0.453248 0.891385i \(-0.649735\pi\)
−0.453248 + 0.891385i \(0.649735\pi\)
\(492\) 41.9448 1.89102
\(493\) 11.5938 0.522157
\(494\) −44.1486 −1.98634
\(495\) −0.0242359 −0.00108932
\(496\) −29.8123 −1.33861
\(497\) 10.5379 0.472691
\(498\) −137.485 −6.16085
\(499\) −27.1958 −1.21745 −0.608725 0.793382i \(-0.708319\pi\)
−0.608725 + 0.793382i \(0.708319\pi\)
\(500\) 50.0198 2.23695
\(501\) −42.3728 −1.89308
\(502\) 55.4172 2.47339
\(503\) −12.6464 −0.563875 −0.281938 0.959433i \(-0.590977\pi\)
−0.281938 + 0.959433i \(0.590977\pi\)
\(504\) −319.941 −14.2513
\(505\) −6.97733 −0.310487
\(506\) −0.0104664 −0.000465287 0
\(507\) −81.1172 −3.60254
\(508\) 20.0410 0.889174
\(509\) 31.2951 1.38713 0.693566 0.720393i \(-0.256039\pi\)
0.693566 + 0.720393i \(0.256039\pi\)
\(510\) −34.9790 −1.54890
\(511\) 7.36332 0.325734
\(512\) −111.999 −4.94969
\(513\) −28.8794 −1.27506
\(514\) 74.1139 3.26903
\(515\) −12.9208 −0.569359
\(516\) 90.4776 3.98306
\(517\) −0.0284952 −0.00125322
\(518\) −123.247 −5.41516
\(519\) −39.9677 −1.75439
\(520\) 62.2457 2.72966
\(521\) 39.1149 1.71366 0.856828 0.515603i \(-0.172432\pi\)
0.856828 + 0.515603i \(0.172432\pi\)
\(522\) −51.0607 −2.23486
\(523\) −9.51402 −0.416019 −0.208010 0.978127i \(-0.566699\pi\)
−0.208010 + 0.978127i \(0.566699\pi\)
\(524\) −15.6637 −0.684270
\(525\) 58.9585 2.57316
\(526\) 43.4603 1.89496
\(527\) −7.27807 −0.317038
\(528\) −0.201316 −0.00876117
\(529\) 1.00000 0.0434783
\(530\) 31.7267 1.37812
\(531\) 63.3144 2.74761
\(532\) 67.7415 2.93697
\(533\) −14.7821 −0.640286
\(534\) −28.7292 −1.24324
\(535\) 3.59300 0.155339
\(536\) −37.6924 −1.62806
\(537\) −65.9049 −2.84401
\(538\) −15.1495 −0.653142
\(539\) 0.0556702 0.00239789
\(540\) 62.6649 2.69667
\(541\) −16.1246 −0.693250 −0.346625 0.938004i \(-0.612672\pi\)
−0.346625 + 0.938004i \(0.612672\pi\)
\(542\) 31.6326 1.35873
\(543\) 51.0110 2.18909
\(544\) −113.810 −4.87956
\(545\) 8.06337 0.345397
\(546\) 251.749 10.7739
\(547\) 12.5283 0.535673 0.267836 0.963464i \(-0.413691\pi\)
0.267836 + 0.963464i \(0.413691\pi\)
\(548\) 44.9758 1.92127
\(549\) −74.6500 −3.18598
\(550\) 0.0425630 0.00181489
\(551\) 7.02470 0.299262
\(552\) 32.0151 1.36265
\(553\) 2.81864 0.119861
\(554\) 42.6804 1.81332
\(555\) 28.5577 1.21220
\(556\) 90.3950 3.83360
\(557\) −5.87314 −0.248853 −0.124427 0.992229i \(-0.539709\pi\)
−0.124427 + 0.992229i \(0.539709\pi\)
\(558\) 32.0537 1.35694
\(559\) −31.8861 −1.34864
\(560\) −77.4793 −3.27410
\(561\) −0.0491472 −0.00207500
\(562\) 67.3428 2.84069
\(563\) 34.6058 1.45846 0.729231 0.684267i \(-0.239878\pi\)
0.729231 + 0.684267i \(0.239878\pi\)
\(564\) 134.144 5.64849
\(565\) −18.8704 −0.793884
\(566\) 41.7304 1.75406
\(567\) 71.5206 3.00358
\(568\) −23.2701 −0.976393
\(569\) −15.4399 −0.647273 −0.323637 0.946181i \(-0.604906\pi\)
−0.323637 + 0.946181i \(0.604906\pi\)
\(570\) −21.1939 −0.887715
\(571\) 44.4391 1.85972 0.929858 0.367918i \(-0.119929\pi\)
0.929858 + 0.367918i \(0.119929\pi\)
\(572\) 0.134600 0.00562790
\(573\) −28.3603 −1.18477
\(574\) 30.6256 1.27829
\(575\) −4.06664 −0.169591
\(576\) 272.442 11.3517
\(577\) −37.5616 −1.56371 −0.781855 0.623460i \(-0.785726\pi\)
−0.781855 + 0.623460i \(0.785726\pi\)
\(578\) −1.68857 −0.0702352
\(579\) −50.9465 −2.11726
\(580\) −15.2428 −0.632922
\(581\) −74.3453 −3.08436
\(582\) 90.6187 3.75627
\(583\) 0.0445776 0.00184621
\(584\) −16.2599 −0.672838
\(585\) −40.2087 −1.66242
\(586\) 48.0995 1.98697
\(587\) 6.98871 0.288455 0.144227 0.989545i \(-0.453930\pi\)
0.144227 + 0.989545i \(0.453930\pi\)
\(588\) −262.074 −10.8078
\(589\) −4.40981 −0.181703
\(590\) 25.5205 1.05066
\(591\) 16.2315 0.667674
\(592\) 163.511 6.72027
\(593\) 41.4073 1.70039 0.850197 0.526465i \(-0.176483\pi\)
0.850197 + 0.526465i \(0.176483\pi\)
\(594\) 0.118884 0.00487789
\(595\) −18.9150 −0.775438
\(596\) 72.8299 2.98323
\(597\) 23.4845 0.961156
\(598\) −17.3643 −0.710079
\(599\) 2.15507 0.0880539 0.0440270 0.999030i \(-0.485981\pi\)
0.0440270 + 0.999030i \(0.485981\pi\)
\(600\) −130.194 −5.31513
\(601\) −30.3806 −1.23925 −0.619625 0.784898i \(-0.712715\pi\)
−0.619625 + 0.784898i \(0.712715\pi\)
\(602\) 66.0615 2.69247
\(603\) 24.3481 0.991529
\(604\) −105.937 −4.31051
\(605\) 10.6272 0.432055
\(606\) 62.3148 2.53137
\(607\) 23.1999 0.941653 0.470827 0.882226i \(-0.343956\pi\)
0.470827 + 0.882226i \(0.343956\pi\)
\(608\) −68.9578 −2.79661
\(609\) −40.0571 −1.62320
\(610\) −30.0896 −1.21829
\(611\) −47.2750 −1.91254
\(612\) 159.480 6.44658
\(613\) 26.2793 1.06141 0.530706 0.847556i \(-0.321927\pi\)
0.530706 + 0.847556i \(0.321927\pi\)
\(614\) −79.1649 −3.19484
\(615\) −7.09629 −0.286150
\(616\) −0.181196 −0.00730060
\(617\) 8.59311 0.345946 0.172973 0.984927i \(-0.444663\pi\)
0.172973 + 0.984927i \(0.444663\pi\)
\(618\) 115.396 4.64192
\(619\) 47.5426 1.91090 0.955448 0.295159i \(-0.0953725\pi\)
0.955448 + 0.295159i \(0.0953725\pi\)
\(620\) 9.56877 0.384291
\(621\) −11.3587 −0.455809
\(622\) 47.4495 1.90255
\(623\) −15.5354 −0.622412
\(624\) −333.995 −13.3705
\(625\) 11.8707 0.474830
\(626\) 10.0148 0.400271
\(627\) −0.0297785 −0.00118924
\(628\) 92.2276 3.68028
\(629\) 39.9179 1.59163
\(630\) 83.3043 3.31892
\(631\) −36.5823 −1.45632 −0.728160 0.685408i \(-0.759624\pi\)
−0.728160 + 0.685408i \(0.759624\pi\)
\(632\) −6.22419 −0.247585
\(633\) 50.6946 2.01493
\(634\) −68.7285 −2.72956
\(635\) −3.39057 −0.134551
\(636\) −209.854 −8.32126
\(637\) 92.3599 3.65943
\(638\) −0.0289178 −0.00114487
\(639\) 15.0317 0.594646
\(640\) 57.4091 2.26929
\(641\) −7.49147 −0.295895 −0.147948 0.988995i \(-0.547267\pi\)
−0.147948 + 0.988995i \(0.547267\pi\)
\(642\) −32.0892 −1.26646
\(643\) 8.82930 0.348193 0.174097 0.984729i \(-0.444299\pi\)
0.174097 + 0.984729i \(0.444299\pi\)
\(644\) 26.6438 1.04991
\(645\) −15.3072 −0.602719
\(646\) −29.6248 −1.16557
\(647\) 47.8933 1.88288 0.941439 0.337182i \(-0.109474\pi\)
0.941439 + 0.337182i \(0.109474\pi\)
\(648\) −157.934 −6.20422
\(649\) 0.0358576 0.00140753
\(650\) 70.6143 2.76972
\(651\) 25.1461 0.985554
\(652\) 61.3299 2.40186
\(653\) 27.8575 1.09015 0.545074 0.838388i \(-0.316502\pi\)
0.545074 + 0.838388i \(0.316502\pi\)
\(654\) −72.0142 −2.81598
\(655\) 2.65001 0.103544
\(656\) −40.6309 −1.58637
\(657\) 10.5033 0.409774
\(658\) 97.9443 3.81827
\(659\) 14.8348 0.577882 0.288941 0.957347i \(-0.406697\pi\)
0.288941 + 0.957347i \(0.406697\pi\)
\(660\) 0.0646158 0.00251517
\(661\) 8.31497 0.323415 0.161707 0.986839i \(-0.448300\pi\)
0.161707 + 0.986839i \(0.448300\pi\)
\(662\) 34.5964 1.34463
\(663\) −81.5380 −3.16667
\(664\) 164.171 6.37107
\(665\) −11.4606 −0.444425
\(666\) −175.804 −6.81228
\(667\) 2.76292 0.106981
\(668\) 77.8702 3.01289
\(669\) −32.7604 −1.26659
\(670\) 9.81412 0.379152
\(671\) −0.0422774 −0.00163210
\(672\) 393.219 15.1688
\(673\) −13.4063 −0.516774 −0.258387 0.966041i \(-0.583191\pi\)
−0.258387 + 0.966041i \(0.583191\pi\)
\(674\) 8.68657 0.334594
\(675\) 46.1917 1.77792
\(676\) 149.072 5.73356
\(677\) −2.56649 −0.0986382 −0.0493191 0.998783i \(-0.515705\pi\)
−0.0493191 + 0.998783i \(0.515705\pi\)
\(678\) 168.532 6.47244
\(679\) 49.0022 1.88053
\(680\) 41.7685 1.60175
\(681\) 67.9316 2.60314
\(682\) 0.0181533 0.000695127 0
\(683\) −22.5405 −0.862488 −0.431244 0.902235i \(-0.641925\pi\)
−0.431244 + 0.902235i \(0.641925\pi\)
\(684\) 96.6292 3.69471
\(685\) −7.60909 −0.290728
\(686\) −100.661 −3.84324
\(687\) −21.1274 −0.806060
\(688\) −87.6435 −3.34138
\(689\) 73.9566 2.81752
\(690\) −8.33588 −0.317342
\(691\) 6.49505 0.247083 0.123542 0.992339i \(-0.460575\pi\)
0.123542 + 0.992339i \(0.460575\pi\)
\(692\) 73.4504 2.79216
\(693\) 0.117047 0.00444623
\(694\) −99.2884 −3.76894
\(695\) −15.2932 −0.580104
\(696\) 88.4551 3.35288
\(697\) −9.91920 −0.375716
\(698\) 2.77677 0.105102
\(699\) 76.9553 2.91072
\(700\) −108.351 −4.09527
\(701\) 15.9523 0.602511 0.301256 0.953543i \(-0.402594\pi\)
0.301256 + 0.953543i \(0.402594\pi\)
\(702\) 197.236 7.44418
\(703\) 24.1864 0.912206
\(704\) 0.154295 0.00581522
\(705\) −22.6948 −0.854735
\(706\) −38.5162 −1.44958
\(707\) 33.6968 1.26730
\(708\) −168.804 −6.34403
\(709\) 14.1416 0.531098 0.265549 0.964097i \(-0.414447\pi\)
0.265549 + 0.964097i \(0.414447\pi\)
\(710\) 6.05893 0.227388
\(711\) 4.02062 0.150785
\(712\) 34.3056 1.28566
\(713\) −1.73444 −0.0649554
\(714\) 168.930 6.32206
\(715\) −0.0227718 −0.000851619 0
\(716\) 121.116 4.52632
\(717\) −45.3279 −1.69280
\(718\) 10.2338 0.381920
\(719\) 31.9387 1.19111 0.595557 0.803313i \(-0.296931\pi\)
0.595557 + 0.803313i \(0.296931\pi\)
\(720\) −110.520 −4.11882
\(721\) 62.4007 2.32392
\(722\) 34.8089 1.29545
\(723\) 12.7534 0.474304
\(724\) −93.7450 −3.48401
\(725\) −11.2358 −0.417287
\(726\) −94.9115 −3.52250
\(727\) −22.3862 −0.830258 −0.415129 0.909762i \(-0.636264\pi\)
−0.415129 + 0.909762i \(0.636264\pi\)
\(728\) −300.614 −11.1415
\(729\) −3.86550 −0.143167
\(730\) 4.23364 0.156694
\(731\) −21.3964 −0.791373
\(732\) 199.026 7.35620
\(733\) −3.63197 −0.134150 −0.0670750 0.997748i \(-0.521367\pi\)
−0.0670750 + 0.997748i \(0.521367\pi\)
\(734\) 27.8701 1.02870
\(735\) 44.3382 1.63544
\(736\) −27.1221 −0.999735
\(737\) 0.0137893 0.000507936 0
\(738\) 43.6856 1.60809
\(739\) 3.00310 0.110471 0.0552355 0.998473i \(-0.482409\pi\)
0.0552355 + 0.998473i \(0.482409\pi\)
\(740\) −52.4816 −1.92926
\(741\) −49.4041 −1.81490
\(742\) −153.223 −5.62500
\(743\) −18.2384 −0.669101 −0.334550 0.942378i \(-0.608584\pi\)
−0.334550 + 0.942378i \(0.608584\pi\)
\(744\) −55.5283 −2.03577
\(745\) −12.3215 −0.451425
\(746\) −34.0911 −1.24816
\(747\) −106.049 −3.88013
\(748\) 0.0903200 0.00330242
\(749\) −17.3523 −0.634039
\(750\) 75.5784 2.75973
\(751\) −28.7223 −1.04809 −0.524046 0.851690i \(-0.675578\pi\)
−0.524046 + 0.851690i \(0.675578\pi\)
\(752\) −129.942 −4.73851
\(753\) 62.0141 2.25992
\(754\) −47.9762 −1.74719
\(755\) 17.9226 0.652269
\(756\) −302.638 −11.0068
\(757\) −15.7574 −0.572712 −0.286356 0.958123i \(-0.592444\pi\)
−0.286356 + 0.958123i \(0.592444\pi\)
\(758\) −54.4344 −1.97715
\(759\) −0.0117123 −0.000425130 0
\(760\) 25.3077 0.918006
\(761\) −27.0461 −0.980421 −0.490210 0.871604i \(-0.663080\pi\)
−0.490210 + 0.871604i \(0.663080\pi\)
\(762\) 30.2813 1.09697
\(763\) −38.9418 −1.40979
\(764\) 52.1190 1.88560
\(765\) −26.9811 −0.975503
\(766\) 6.29697 0.227519
\(767\) 59.4897 2.14805
\(768\) −258.325 −9.32151
\(769\) 11.8466 0.427199 0.213600 0.976921i \(-0.431481\pi\)
0.213600 + 0.976921i \(0.431481\pi\)
\(770\) 0.0471787 0.00170020
\(771\) 82.9366 2.98689
\(772\) 93.6264 3.36969
\(773\) 30.6942 1.10399 0.551997 0.833846i \(-0.313866\pi\)
0.551997 + 0.833846i \(0.313866\pi\)
\(774\) 94.2327 3.38713
\(775\) 7.05335 0.253364
\(776\) −108.208 −3.88444
\(777\) −137.918 −4.94779
\(778\) −26.2447 −0.940919
\(779\) −6.01007 −0.215333
\(780\) 107.201 3.83842
\(781\) 0.00851310 0.000304623 0
\(782\) −11.6519 −0.416671
\(783\) −31.3832 −1.12154
\(784\) 253.865 9.06660
\(785\) −15.6032 −0.556903
\(786\) −23.6673 −0.844184
\(787\) −22.4534 −0.800376 −0.400188 0.916433i \(-0.631055\pi\)
−0.400188 + 0.916433i \(0.631055\pi\)
\(788\) −29.8293 −1.06262
\(789\) 48.6339 1.73141
\(790\) 1.62062 0.0576590
\(791\) 91.1340 3.24035
\(792\) −0.258465 −0.00918416
\(793\) −70.1405 −2.49076
\(794\) −81.9658 −2.90886
\(795\) 35.5035 1.25918
\(796\) −43.1584 −1.52971
\(797\) −33.1848 −1.17547 −0.587733 0.809055i \(-0.699979\pi\)
−0.587733 + 0.809055i \(0.699979\pi\)
\(798\) 102.355 3.62334
\(799\) −31.7228 −1.12227
\(800\) 110.296 3.89955
\(801\) −22.1603 −0.782996
\(802\) −79.9675 −2.82375
\(803\) 0.00594848 0.000209917 0
\(804\) −64.9148 −2.28937
\(805\) −4.50764 −0.158873
\(806\) 30.1174 1.06084
\(807\) −16.9529 −0.596772
\(808\) −74.4102 −2.61774
\(809\) −34.4832 −1.21236 −0.606182 0.795326i \(-0.707300\pi\)
−0.606182 + 0.795326i \(0.707300\pi\)
\(810\) 41.1218 1.44487
\(811\) −12.2159 −0.428958 −0.214479 0.976729i \(-0.568805\pi\)
−0.214479 + 0.976729i \(0.568805\pi\)
\(812\) 73.6146 2.58337
\(813\) 35.3982 1.24147
\(814\) −0.0995652 −0.00348976
\(815\) −10.3759 −0.363452
\(816\) −224.119 −7.84574
\(817\) −12.9641 −0.453557
\(818\) 70.2911 2.45767
\(819\) 194.187 6.78543
\(820\) 13.0412 0.455417
\(821\) −11.2220 −0.391651 −0.195826 0.980639i \(-0.562739\pi\)
−0.195826 + 0.980639i \(0.562739\pi\)
\(822\) 67.9570 2.37027
\(823\) 4.48470 0.156327 0.0781635 0.996941i \(-0.475094\pi\)
0.0781635 + 0.996941i \(0.475094\pi\)
\(824\) −137.795 −4.80031
\(825\) 0.0476298 0.00165826
\(826\) −123.251 −4.28844
\(827\) 1.94021 0.0674679 0.0337339 0.999431i \(-0.489260\pi\)
0.0337339 + 0.999431i \(0.489260\pi\)
\(828\) 38.0057 1.32079
\(829\) 22.3122 0.774934 0.387467 0.921884i \(-0.373350\pi\)
0.387467 + 0.921884i \(0.373350\pi\)
\(830\) −42.7458 −1.48373
\(831\) 47.7611 1.65681
\(832\) 255.984 8.87465
\(833\) 61.9759 2.14734
\(834\) 136.584 4.72952
\(835\) −13.1742 −0.455913
\(836\) 0.0547251 0.00189271
\(837\) 19.7010 0.680966
\(838\) 7.62925 0.263548
\(839\) −20.7837 −0.717533 −0.358766 0.933427i \(-0.616803\pi\)
−0.358766 + 0.933427i \(0.616803\pi\)
\(840\) −144.312 −4.97925
\(841\) −21.3663 −0.736768
\(842\) −1.59227 −0.0548731
\(843\) 75.3594 2.59552
\(844\) −93.1635 −3.20682
\(845\) −25.2204 −0.867607
\(846\) 139.712 4.80339
\(847\) −51.3235 −1.76350
\(848\) 203.281 6.98069
\(849\) 46.6981 1.60267
\(850\) 47.3840 1.62526
\(851\) 9.51286 0.326097
\(852\) −40.0764 −1.37299
\(853\) −16.5772 −0.567592 −0.283796 0.958885i \(-0.591594\pi\)
−0.283796 + 0.958885i \(0.591594\pi\)
\(854\) 145.317 4.97264
\(855\) −16.3479 −0.559087
\(856\) 38.3177 1.30967
\(857\) −1.99969 −0.0683081 −0.0341540 0.999417i \(-0.510874\pi\)
−0.0341540 + 0.999417i \(0.510874\pi\)
\(858\) 0.203376 0.00694315
\(859\) −55.5358 −1.89486 −0.947428 0.319969i \(-0.896327\pi\)
−0.947428 + 0.319969i \(0.896327\pi\)
\(860\) 28.1306 0.959247
\(861\) 34.2713 1.16796
\(862\) 53.7705 1.83143
\(863\) −52.5776 −1.78976 −0.894882 0.446304i \(-0.852740\pi\)
−0.894882 + 0.446304i \(0.852740\pi\)
\(864\) 308.072 10.4808
\(865\) −12.4265 −0.422513
\(866\) 37.1986 1.26406
\(867\) −1.88958 −0.0641735
\(868\) −46.2121 −1.56854
\(869\) 0.00227705 7.72435e−5 0
\(870\) −23.0314 −0.780837
\(871\) 22.8772 0.775165
\(872\) 85.9923 2.91207
\(873\) 69.8988 2.36571
\(874\) −7.05992 −0.238805
\(875\) 40.8692 1.38163
\(876\) −28.0032 −0.946139
\(877\) 21.4147 0.723122 0.361561 0.932349i \(-0.382244\pi\)
0.361561 + 0.932349i \(0.382244\pi\)
\(878\) 25.0739 0.846205
\(879\) 53.8253 1.81548
\(880\) −0.0625918 −0.00210997
\(881\) 46.1941 1.55632 0.778159 0.628068i \(-0.216154\pi\)
0.778159 + 0.628068i \(0.216154\pi\)
\(882\) −272.951 −9.19074
\(883\) −37.3661 −1.25747 −0.628734 0.777620i \(-0.716427\pi\)
−0.628734 + 0.777620i \(0.716427\pi\)
\(884\) 149.846 5.03986
\(885\) 28.5585 0.959985
\(886\) 72.3203 2.42965
\(887\) −9.32904 −0.313238 −0.156619 0.987659i \(-0.550060\pi\)
−0.156619 + 0.987659i \(0.550060\pi\)
\(888\) 304.555 10.2202
\(889\) 16.3747 0.549188
\(890\) −8.93229 −0.299411
\(891\) 0.0577781 0.00193564
\(892\) 60.2051 2.01582
\(893\) −19.2209 −0.643204
\(894\) 110.044 3.68041
\(895\) −20.4907 −0.684927
\(896\) −277.256 −9.26246
\(897\) −19.4314 −0.648795
\(898\) 38.6088 1.28839
\(899\) −4.79213 −0.159826
\(900\) −154.556 −5.15185
\(901\) 49.6268 1.65331
\(902\) 0.0247410 0.000823784 0
\(903\) 73.9256 2.46009
\(904\) −201.244 −6.69329
\(905\) 15.8600 0.527203
\(906\) −160.067 −5.31788
\(907\) −34.5079 −1.14582 −0.572908 0.819620i \(-0.694185\pi\)
−0.572908 + 0.819620i \(0.694185\pi\)
\(908\) −124.841 −4.14298
\(909\) 48.0665 1.59427
\(910\) 78.2720 2.59469
\(911\) 7.67345 0.254233 0.127116 0.991888i \(-0.459428\pi\)
0.127116 + 0.991888i \(0.459428\pi\)
\(912\) −135.794 −4.49660
\(913\) −0.0600600 −0.00198770
\(914\) 17.9812 0.594766
\(915\) −33.6715 −1.11315
\(916\) 38.8267 1.28287
\(917\) −12.7981 −0.422632
\(918\) 132.350 4.36821
\(919\) 53.5890 1.76774 0.883868 0.467736i \(-0.154930\pi\)
0.883868 + 0.467736i \(0.154930\pi\)
\(920\) 9.95389 0.328170
\(921\) −88.5888 −2.91910
\(922\) 42.1009 1.38652
\(923\) 14.1237 0.464887
\(924\) −0.312060 −0.0102660
\(925\) −38.6854 −1.27197
\(926\) −53.0673 −1.74390
\(927\) 89.0109 2.92350
\(928\) −74.9363 −2.45990
\(929\) 17.6799 0.580058 0.290029 0.957018i \(-0.406335\pi\)
0.290029 + 0.957018i \(0.406335\pi\)
\(930\) 14.4581 0.474100
\(931\) 37.5514 1.23070
\(932\) −141.424 −4.63250
\(933\) 53.0980 1.73835
\(934\) −43.6210 −1.42732
\(935\) −0.0152805 −0.000499726 0
\(936\) −428.808 −14.0160
\(937\) −23.6700 −0.773266 −0.386633 0.922234i \(-0.626362\pi\)
−0.386633 + 0.922234i \(0.626362\pi\)
\(938\) −47.3970 −1.54757
\(939\) 11.2070 0.365725
\(940\) 41.7072 1.36034
\(941\) 8.42218 0.274555 0.137278 0.990533i \(-0.456165\pi\)
0.137278 + 0.990533i \(0.456165\pi\)
\(942\) 139.353 4.54037
\(943\) −2.36385 −0.0769776
\(944\) 163.516 5.32200
\(945\) 51.2009 1.66557
\(946\) 0.0533679 0.00173514
\(947\) −2.56544 −0.0833655 −0.0416827 0.999131i \(-0.513272\pi\)
−0.0416827 + 0.999131i \(0.513272\pi\)
\(948\) −10.7195 −0.348152
\(949\) 9.86885 0.320356
\(950\) 28.7101 0.931480
\(951\) −76.9100 −2.49398
\(952\) −201.720 −6.53778
\(953\) 28.2310 0.914490 0.457245 0.889341i \(-0.348836\pi\)
0.457245 + 0.889341i \(0.348836\pi\)
\(954\) −218.564 −7.07626
\(955\) −8.81758 −0.285330
\(956\) 83.3011 2.69415
\(957\) −0.0323602 −0.00104606
\(958\) 105.725 3.41582
\(959\) 36.7479 1.18665
\(960\) 122.887 3.96617
\(961\) −27.9917 −0.902958
\(962\) −165.184 −5.32575
\(963\) −24.7520 −0.797622
\(964\) −23.4375 −0.754870
\(965\) −15.8399 −0.509904
\(966\) 40.2579 1.29528
\(967\) −46.6689 −1.50077 −0.750385 0.661001i \(-0.770132\pi\)
−0.750385 + 0.661001i \(0.770132\pi\)
\(968\) 113.334 3.64269
\(969\) −33.1514 −1.06498
\(970\) 28.1745 0.904629
\(971\) 21.4465 0.688252 0.344126 0.938923i \(-0.388175\pi\)
0.344126 + 0.938923i \(0.388175\pi\)
\(972\) −77.4071 −2.48283
\(973\) 73.8580 2.36778
\(974\) −27.8132 −0.891191
\(975\) 79.0204 2.53068
\(976\) −192.791 −6.17110
\(977\) 36.1272 1.15581 0.577906 0.816104i \(-0.303870\pi\)
0.577906 + 0.816104i \(0.303870\pi\)
\(978\) 92.6676 2.96318
\(979\) −0.0125503 −0.000401109 0
\(980\) −81.4822 −2.60285
\(981\) −55.5482 −1.77352
\(982\) 55.7759 1.77988
\(983\) 10.8979 0.347588 0.173794 0.984782i \(-0.444397\pi\)
0.173794 + 0.984782i \(0.444397\pi\)
\(984\) −75.6788 −2.41255
\(985\) 5.04657 0.160797
\(986\) −32.1933 −1.02524
\(987\) 109.604 3.48873
\(988\) 90.7920 2.88848
\(989\) −5.09898 −0.162138
\(990\) 0.0672976 0.00213886
\(991\) 31.8596 1.01205 0.506026 0.862518i \(-0.331114\pi\)
0.506026 + 0.862518i \(0.331114\pi\)
\(992\) 47.0418 1.49358
\(993\) 38.7148 1.22858
\(994\) −29.2615 −0.928117
\(995\) 7.30162 0.231477
\(996\) 282.739 8.95894
\(997\) −7.65486 −0.242432 −0.121216 0.992626i \(-0.538679\pi\)
−0.121216 + 0.992626i \(0.538679\pi\)
\(998\) 75.5164 2.39043
\(999\) −108.054 −3.41867
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 \(a_p\))