Properties

Label 8027.2.a.f.1.5
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

Related objects

Downloads

Learn more about

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 1.5
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73308 q^{2} +2.04263 q^{3} +5.46974 q^{4} +2.78212 q^{5} -5.58268 q^{6} +3.87331 q^{7} -9.48308 q^{8} +1.17234 q^{9} +O(q^{10})\) \(q-2.73308 q^{2} +2.04263 q^{3} +5.46974 q^{4} +2.78212 q^{5} -5.58268 q^{6} +3.87331 q^{7} -9.48308 q^{8} +1.17234 q^{9} -7.60375 q^{10} -0.942573 q^{11} +11.1727 q^{12} +6.23637 q^{13} -10.5861 q^{14} +5.68284 q^{15} +14.9786 q^{16} -5.28749 q^{17} -3.20411 q^{18} +2.29285 q^{19} +15.2175 q^{20} +7.91174 q^{21} +2.57613 q^{22} +1.00000 q^{23} -19.3704 q^{24} +2.74017 q^{25} -17.0445 q^{26} -3.73323 q^{27} +21.1860 q^{28} -4.07188 q^{29} -15.5317 q^{30} +8.08494 q^{31} -21.9715 q^{32} -1.92533 q^{33} +14.4511 q^{34} +10.7760 q^{35} +6.41241 q^{36} -2.48169 q^{37} -6.26656 q^{38} +12.7386 q^{39} -26.3830 q^{40} +0.934218 q^{41} -21.6235 q^{42} +8.66302 q^{43} -5.15563 q^{44} +3.26160 q^{45} -2.73308 q^{46} +0.619143 q^{47} +30.5957 q^{48} +8.00253 q^{49} -7.48912 q^{50} -10.8004 q^{51} +34.1113 q^{52} +7.33471 q^{53} +10.2032 q^{54} -2.62235 q^{55} -36.7309 q^{56} +4.68345 q^{57} +11.1288 q^{58} -8.98731 q^{59} +31.0836 q^{60} +3.84620 q^{61} -22.0968 q^{62} +4.54085 q^{63} +30.0928 q^{64} +17.3503 q^{65} +5.26208 q^{66} -1.86292 q^{67} -28.9212 q^{68} +2.04263 q^{69} -29.4517 q^{70} +11.9901 q^{71} -11.1174 q^{72} -10.9820 q^{73} +6.78266 q^{74} +5.59716 q^{75} +12.5413 q^{76} -3.65088 q^{77} -34.8157 q^{78} +4.89120 q^{79} +41.6721 q^{80} -11.1426 q^{81} -2.55329 q^{82} +14.3163 q^{83} +43.2752 q^{84} -14.7104 q^{85} -23.6767 q^{86} -8.31735 q^{87} +8.93849 q^{88} -7.02322 q^{89} -8.91421 q^{90} +24.1554 q^{91} +5.46974 q^{92} +16.5146 q^{93} -1.69217 q^{94} +6.37898 q^{95} -44.8797 q^{96} +0.753121 q^{97} -21.8716 q^{98} -1.10502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73308 −1.93258 −0.966291 0.257454i \(-0.917116\pi\)
−0.966291 + 0.257454i \(0.917116\pi\)
\(3\) 2.04263 1.17931 0.589657 0.807654i \(-0.299263\pi\)
0.589657 + 0.807654i \(0.299263\pi\)
\(4\) 5.46974 2.73487
\(5\) 2.78212 1.24420 0.622100 0.782938i \(-0.286280\pi\)
0.622100 + 0.782938i \(0.286280\pi\)
\(6\) −5.58268 −2.27912
\(7\) 3.87331 1.46397 0.731987 0.681319i \(-0.238593\pi\)
0.731987 + 0.681319i \(0.238593\pi\)
\(8\) −9.48308 −3.35278
\(9\) 1.17234 0.390781
\(10\) −7.60375 −2.40452
\(11\) −0.942573 −0.284196 −0.142098 0.989853i \(-0.545385\pi\)
−0.142098 + 0.989853i \(0.545385\pi\)
\(12\) 11.1727 3.22527
\(13\) 6.23637 1.72966 0.864829 0.502067i \(-0.167427\pi\)
0.864829 + 0.502067i \(0.167427\pi\)
\(14\) −10.5861 −2.82925
\(15\) 5.68284 1.46730
\(16\) 14.9786 3.74464
\(17\) −5.28749 −1.28240 −0.641202 0.767372i \(-0.721564\pi\)
−0.641202 + 0.767372i \(0.721564\pi\)
\(18\) −3.20411 −0.755216
\(19\) 2.29285 0.526017 0.263008 0.964794i \(-0.415285\pi\)
0.263008 + 0.964794i \(0.415285\pi\)
\(20\) 15.2175 3.40273
\(21\) 7.91174 1.72648
\(22\) 2.57613 0.549232
\(23\) 1.00000 0.208514
\(24\) −19.3704 −3.95398
\(25\) 2.74017 0.548035
\(26\) −17.0445 −3.34270
\(27\) −3.73323 −0.718460
\(28\) 21.1860 4.00378
\(29\) −4.07188 −0.756129 −0.378065 0.925779i \(-0.623410\pi\)
−0.378065 + 0.925779i \(0.623410\pi\)
\(30\) −15.5317 −2.83568
\(31\) 8.08494 1.45210 0.726049 0.687643i \(-0.241355\pi\)
0.726049 + 0.687643i \(0.241355\pi\)
\(32\) −21.9715 −3.88405
\(33\) −1.92533 −0.335157
\(34\) 14.4511 2.47835
\(35\) 10.7760 1.82148
\(36\) 6.41241 1.06874
\(37\) −2.48169 −0.407987 −0.203993 0.978972i \(-0.565392\pi\)
−0.203993 + 0.978972i \(0.565392\pi\)
\(38\) −6.26656 −1.01657
\(39\) 12.7386 2.03981
\(40\) −26.3830 −4.17153
\(41\) 0.934218 0.145900 0.0729502 0.997336i \(-0.476759\pi\)
0.0729502 + 0.997336i \(0.476759\pi\)
\(42\) −21.6235 −3.33657
\(43\) 8.66302 1.32110 0.660549 0.750783i \(-0.270324\pi\)
0.660549 + 0.750783i \(0.270324\pi\)
\(44\) −5.15563 −0.777240
\(45\) 3.26160 0.486210
\(46\) −2.73308 −0.402971
\(47\) 0.619143 0.0903113 0.0451557 0.998980i \(-0.485622\pi\)
0.0451557 + 0.998980i \(0.485622\pi\)
\(48\) 30.5957 4.41611
\(49\) 8.00253 1.14322
\(50\) −7.48912 −1.05912
\(51\) −10.8004 −1.51236
\(52\) 34.1113 4.73039
\(53\) 7.33471 1.00750 0.503750 0.863850i \(-0.331953\pi\)
0.503750 + 0.863850i \(0.331953\pi\)
\(54\) 10.2032 1.38848
\(55\) −2.62235 −0.353597
\(56\) −36.7309 −4.90838
\(57\) 4.68345 0.620339
\(58\) 11.1288 1.46128
\(59\) −8.98731 −1.17005 −0.585024 0.811016i \(-0.698915\pi\)
−0.585024 + 0.811016i \(0.698915\pi\)
\(60\) 31.0836 4.01288
\(61\) 3.84620 0.492455 0.246228 0.969212i \(-0.420809\pi\)
0.246228 + 0.969212i \(0.420809\pi\)
\(62\) −22.0968 −2.80630
\(63\) 4.54085 0.572093
\(64\) 30.0928 3.76160
\(65\) 17.3503 2.15204
\(66\) 5.26208 0.647717
\(67\) −1.86292 −0.227592 −0.113796 0.993504i \(-0.536301\pi\)
−0.113796 + 0.993504i \(0.536301\pi\)
\(68\) −28.9212 −3.50721
\(69\) 2.04263 0.245904
\(70\) −29.4517 −3.52015
\(71\) 11.9901 1.42296 0.711481 0.702705i \(-0.248025\pi\)
0.711481 + 0.702705i \(0.248025\pi\)
\(72\) −11.1174 −1.31020
\(73\) −10.9820 −1.28535 −0.642674 0.766140i \(-0.722175\pi\)
−0.642674 + 0.766140i \(0.722175\pi\)
\(74\) 6.78266 0.788468
\(75\) 5.59716 0.646305
\(76\) 12.5413 1.43859
\(77\) −3.65088 −0.416056
\(78\) −34.8157 −3.94210
\(79\) 4.89120 0.550302 0.275151 0.961401i \(-0.411272\pi\)
0.275151 + 0.961401i \(0.411272\pi\)
\(80\) 41.6721 4.65909
\(81\) −11.1426 −1.23807
\(82\) −2.55329 −0.281964
\(83\) 14.3163 1.57142 0.785709 0.618597i \(-0.212298\pi\)
0.785709 + 0.618597i \(0.212298\pi\)
\(84\) 43.2752 4.72171
\(85\) −14.7104 −1.59557
\(86\) −23.6767 −2.55313
\(87\) −8.31735 −0.891714
\(88\) 8.93849 0.952847
\(89\) −7.02322 −0.744460 −0.372230 0.928141i \(-0.621407\pi\)
−0.372230 + 0.928141i \(0.621407\pi\)
\(90\) −8.91421 −0.939640
\(91\) 24.1554 2.53217
\(92\) 5.46974 0.570260
\(93\) 16.5146 1.71248
\(94\) −1.69217 −0.174534
\(95\) 6.37898 0.654470
\(96\) −44.8797 −4.58051
\(97\) 0.753121 0.0764679 0.0382339 0.999269i \(-0.487827\pi\)
0.0382339 + 0.999269i \(0.487827\pi\)
\(98\) −21.8716 −2.20936
\(99\) −1.10502 −0.111059
\(100\) 14.9880 1.49880
\(101\) 2.80490 0.279098 0.139549 0.990215i \(-0.455435\pi\)
0.139549 + 0.990215i \(0.455435\pi\)
\(102\) 29.5184 2.92275
\(103\) −4.53348 −0.446697 −0.223349 0.974739i \(-0.571699\pi\)
−0.223349 + 0.974739i \(0.571699\pi\)
\(104\) −59.1400 −5.79915
\(105\) 22.0114 2.14809
\(106\) −20.0464 −1.94707
\(107\) 2.00021 0.193368 0.0966838 0.995315i \(-0.469176\pi\)
0.0966838 + 0.995315i \(0.469176\pi\)
\(108\) −20.4198 −1.96490
\(109\) −5.36771 −0.514134 −0.257067 0.966394i \(-0.582756\pi\)
−0.257067 + 0.966394i \(0.582756\pi\)
\(110\) 7.16709 0.683355
\(111\) −5.06917 −0.481145
\(112\) 58.0166 5.48206
\(113\) −11.1257 −1.04662 −0.523308 0.852143i \(-0.675302\pi\)
−0.523308 + 0.852143i \(0.675302\pi\)
\(114\) −12.8003 −1.19885
\(115\) 2.78212 0.259434
\(116\) −22.2721 −2.06792
\(117\) 7.31116 0.675917
\(118\) 24.5631 2.26121
\(119\) −20.4801 −1.87741
\(120\) −53.8908 −4.91954
\(121\) −10.1116 −0.919232
\(122\) −10.5120 −0.951709
\(123\) 1.90826 0.172062
\(124\) 44.2225 3.97130
\(125\) −6.28710 −0.562336
\(126\) −12.4105 −1.10562
\(127\) 4.25550 0.377614 0.188807 0.982014i \(-0.439538\pi\)
0.188807 + 0.982014i \(0.439538\pi\)
\(128\) −38.3030 −3.38554
\(129\) 17.6954 1.55799
\(130\) −47.4198 −4.15899
\(131\) −19.0901 −1.66791 −0.833955 0.551833i \(-0.813929\pi\)
−0.833955 + 0.551833i \(0.813929\pi\)
\(132\) −10.5310 −0.916610
\(133\) 8.88093 0.770074
\(134\) 5.09151 0.439839
\(135\) −10.3863 −0.893909
\(136\) 50.1417 4.29961
\(137\) 3.44025 0.293921 0.146960 0.989142i \(-0.453051\pi\)
0.146960 + 0.989142i \(0.453051\pi\)
\(138\) −5.58268 −0.475229
\(139\) 10.9624 0.929820 0.464910 0.885358i \(-0.346087\pi\)
0.464910 + 0.885358i \(0.346087\pi\)
\(140\) 58.9419 4.98150
\(141\) 1.26468 0.106505
\(142\) −32.7699 −2.74999
\(143\) −5.87823 −0.491562
\(144\) 17.5600 1.46334
\(145\) −11.3284 −0.940777
\(146\) 30.0147 2.48404
\(147\) 16.3462 1.34821
\(148\) −13.5742 −1.11579
\(149\) −4.59518 −0.376452 −0.188226 0.982126i \(-0.560274\pi\)
−0.188226 + 0.982126i \(0.560274\pi\)
\(150\) −15.2975 −1.24904
\(151\) −7.46353 −0.607373 −0.303687 0.952772i \(-0.598218\pi\)
−0.303687 + 0.952772i \(0.598218\pi\)
\(152\) −21.7433 −1.76362
\(153\) −6.19875 −0.501139
\(154\) 9.97814 0.804062
\(155\) 22.4932 1.80670
\(156\) 69.6768 5.57861
\(157\) 14.0427 1.12073 0.560365 0.828245i \(-0.310661\pi\)
0.560365 + 0.828245i \(0.310661\pi\)
\(158\) −13.3680 −1.06350
\(159\) 14.9821 1.18816
\(160\) −61.1273 −4.83253
\(161\) 3.87331 0.305260
\(162\) 30.4538 2.39267
\(163\) −14.2419 −1.11551 −0.557755 0.830006i \(-0.688337\pi\)
−0.557755 + 0.830006i \(0.688337\pi\)
\(164\) 5.10993 0.399018
\(165\) −5.35649 −0.417002
\(166\) −39.1276 −3.03689
\(167\) 19.2444 1.48918 0.744588 0.667525i \(-0.232646\pi\)
0.744588 + 0.667525i \(0.232646\pi\)
\(168\) −75.0277 −5.78852
\(169\) 25.8923 1.99172
\(170\) 40.2048 3.08356
\(171\) 2.68801 0.205557
\(172\) 47.3845 3.61303
\(173\) 16.7795 1.27572 0.637861 0.770151i \(-0.279819\pi\)
0.637861 + 0.770151i \(0.279819\pi\)
\(174\) 22.7320 1.72331
\(175\) 10.6135 0.802308
\(176\) −14.1184 −1.06421
\(177\) −18.3578 −1.37985
\(178\) 19.1950 1.43873
\(179\) 18.4207 1.37683 0.688415 0.725317i \(-0.258307\pi\)
0.688415 + 0.725317i \(0.258307\pi\)
\(180\) 17.8401 1.32972
\(181\) −1.81569 −0.134959 −0.0674797 0.997721i \(-0.521496\pi\)
−0.0674797 + 0.997721i \(0.521496\pi\)
\(182\) −66.0187 −4.89363
\(183\) 7.85636 0.580759
\(184\) −9.48308 −0.699102
\(185\) −6.90434 −0.507617
\(186\) −45.1356 −3.30951
\(187\) 4.98384 0.364455
\(188\) 3.38655 0.246990
\(189\) −14.4600 −1.05181
\(190\) −17.4343 −1.26482
\(191\) 14.1955 1.02715 0.513574 0.858045i \(-0.328321\pi\)
0.513574 + 0.858045i \(0.328321\pi\)
\(192\) 61.4684 4.43610
\(193\) −21.4627 −1.54492 −0.772460 0.635064i \(-0.780974\pi\)
−0.772460 + 0.635064i \(0.780974\pi\)
\(194\) −2.05834 −0.147780
\(195\) 35.4403 2.53793
\(196\) 43.7718 3.12655
\(197\) 1.70146 0.121224 0.0606119 0.998161i \(-0.480695\pi\)
0.0606119 + 0.998161i \(0.480695\pi\)
\(198\) 3.02011 0.214630
\(199\) 22.4715 1.59296 0.796479 0.604666i \(-0.206693\pi\)
0.796479 + 0.604666i \(0.206693\pi\)
\(200\) −25.9853 −1.83744
\(201\) −3.80526 −0.268402
\(202\) −7.66602 −0.539379
\(203\) −15.7717 −1.10695
\(204\) −59.0753 −4.13610
\(205\) 2.59910 0.181529
\(206\) 12.3904 0.863279
\(207\) 1.17234 0.0814835
\(208\) 93.4119 6.47695
\(209\) −2.16118 −0.149492
\(210\) −60.1590 −4.15136
\(211\) −19.3898 −1.33485 −0.667424 0.744678i \(-0.732603\pi\)
−0.667424 + 0.744678i \(0.732603\pi\)
\(212\) 40.1189 2.75538
\(213\) 24.4913 1.67812
\(214\) −5.46674 −0.373698
\(215\) 24.1015 1.64371
\(216\) 35.4025 2.40884
\(217\) 31.3155 2.12583
\(218\) 14.6704 0.993605
\(219\) −22.4322 −1.51583
\(220\) −14.3436 −0.967042
\(221\) −32.9747 −2.21812
\(222\) 13.8545 0.929851
\(223\) −7.89058 −0.528392 −0.264196 0.964469i \(-0.585107\pi\)
−0.264196 + 0.964469i \(0.585107\pi\)
\(224\) −85.1024 −5.68614
\(225\) 3.21242 0.214162
\(226\) 30.4074 2.02267
\(227\) 19.9342 1.32308 0.661538 0.749911i \(-0.269904\pi\)
0.661538 + 0.749911i \(0.269904\pi\)
\(228\) 25.6173 1.69655
\(229\) −0.278942 −0.0184330 −0.00921649 0.999958i \(-0.502934\pi\)
−0.00921649 + 0.999958i \(0.502934\pi\)
\(230\) −7.60375 −0.501377
\(231\) −7.45739 −0.490660
\(232\) 38.6140 2.53513
\(233\) −23.5257 −1.54122 −0.770611 0.637306i \(-0.780049\pi\)
−0.770611 + 0.637306i \(0.780049\pi\)
\(234\) −19.9820 −1.30627
\(235\) 1.72253 0.112365
\(236\) −49.1583 −3.19993
\(237\) 9.99091 0.648979
\(238\) 55.9737 3.62824
\(239\) −6.77337 −0.438133 −0.219066 0.975710i \(-0.570301\pi\)
−0.219066 + 0.975710i \(0.570301\pi\)
\(240\) 85.1208 5.49452
\(241\) 16.6401 1.07188 0.535942 0.844255i \(-0.319956\pi\)
0.535942 + 0.844255i \(0.319956\pi\)
\(242\) 27.6357 1.77649
\(243\) −11.5606 −0.741614
\(244\) 21.0377 1.34680
\(245\) 22.2640 1.42239
\(246\) −5.21544 −0.332524
\(247\) 14.2991 0.909829
\(248\) −76.6702 −4.86856
\(249\) 29.2429 1.85319
\(250\) 17.1832 1.08676
\(251\) 24.9509 1.57489 0.787443 0.616387i \(-0.211404\pi\)
0.787443 + 0.616387i \(0.211404\pi\)
\(252\) 24.8373 1.56460
\(253\) −0.942573 −0.0592590
\(254\) −11.6306 −0.729770
\(255\) −30.0479 −1.88168
\(256\) 44.4998 2.78124
\(257\) 17.4782 1.09026 0.545130 0.838352i \(-0.316480\pi\)
0.545130 + 0.838352i \(0.316480\pi\)
\(258\) −48.3629 −3.01094
\(259\) −9.61234 −0.597282
\(260\) 94.9017 5.88555
\(261\) −4.77364 −0.295481
\(262\) 52.1748 3.22337
\(263\) 10.8108 0.666624 0.333312 0.942817i \(-0.391834\pi\)
0.333312 + 0.942817i \(0.391834\pi\)
\(264\) 18.2580 1.12371
\(265\) 20.4060 1.25353
\(266\) −24.2723 −1.48823
\(267\) −14.3459 −0.877952
\(268\) −10.1897 −0.622434
\(269\) 11.0911 0.676237 0.338118 0.941104i \(-0.390210\pi\)
0.338118 + 0.941104i \(0.390210\pi\)
\(270\) 28.3866 1.72755
\(271\) −12.7216 −0.772785 −0.386392 0.922335i \(-0.626279\pi\)
−0.386392 + 0.922335i \(0.626279\pi\)
\(272\) −79.1990 −4.80215
\(273\) 49.3406 2.98623
\(274\) −9.40250 −0.568026
\(275\) −2.58281 −0.155749
\(276\) 11.1727 0.672515
\(277\) −25.5788 −1.53688 −0.768440 0.639922i \(-0.778967\pi\)
−0.768440 + 0.639922i \(0.778967\pi\)
\(278\) −29.9612 −1.79695
\(279\) 9.47832 0.567452
\(280\) −102.190 −6.10700
\(281\) 18.0598 1.07736 0.538678 0.842511i \(-0.318924\pi\)
0.538678 + 0.842511i \(0.318924\pi\)
\(282\) −3.45648 −0.205830
\(283\) −6.89252 −0.409718 −0.204859 0.978792i \(-0.565674\pi\)
−0.204859 + 0.978792i \(0.565674\pi\)
\(284\) 65.5827 3.89162
\(285\) 13.0299 0.771826
\(286\) 16.0657 0.949984
\(287\) 3.61852 0.213594
\(288\) −25.7581 −1.51781
\(289\) 10.9575 0.644561
\(290\) 30.9616 1.81813
\(291\) 1.53835 0.0901796
\(292\) −60.0687 −3.51526
\(293\) −14.1139 −0.824545 −0.412272 0.911061i \(-0.635265\pi\)
−0.412272 + 0.911061i \(0.635265\pi\)
\(294\) −44.6756 −2.60553
\(295\) −25.0038 −1.45577
\(296\) 23.5340 1.36789
\(297\) 3.51884 0.204184
\(298\) 12.5590 0.727523
\(299\) 6.23637 0.360659
\(300\) 30.6150 1.76756
\(301\) 33.5546 1.93405
\(302\) 20.3984 1.17380
\(303\) 5.72937 0.329144
\(304\) 34.3437 1.96974
\(305\) 10.7006 0.612713
\(306\) 16.9417 0.968492
\(307\) −21.4365 −1.22345 −0.611724 0.791071i \(-0.709524\pi\)
−0.611724 + 0.791071i \(0.709524\pi\)
\(308\) −19.9693 −1.13786
\(309\) −9.26023 −0.526796
\(310\) −61.4759 −3.49160
\(311\) 14.7226 0.834841 0.417420 0.908714i \(-0.362934\pi\)
0.417420 + 0.908714i \(0.362934\pi\)
\(312\) −120.801 −6.83902
\(313\) 7.13170 0.403107 0.201554 0.979477i \(-0.435401\pi\)
0.201554 + 0.979477i \(0.435401\pi\)
\(314\) −38.3799 −2.16590
\(315\) 12.6332 0.711798
\(316\) 26.7536 1.50501
\(317\) 24.4872 1.37534 0.687669 0.726024i \(-0.258634\pi\)
0.687669 + 0.726024i \(0.258634\pi\)
\(318\) −40.9473 −2.29621
\(319\) 3.83804 0.214889
\(320\) 83.7216 4.68018
\(321\) 4.08569 0.228041
\(322\) −10.5861 −0.589939
\(323\) −12.1234 −0.674566
\(324\) −60.9473 −3.38596
\(325\) 17.0887 0.947912
\(326\) 38.9242 2.15581
\(327\) −10.9643 −0.606325
\(328\) −8.85927 −0.489171
\(329\) 2.39813 0.132213
\(330\) 14.6397 0.805890
\(331\) 24.6321 1.35390 0.676951 0.736028i \(-0.263301\pi\)
0.676951 + 0.736028i \(0.263301\pi\)
\(332\) 78.3064 4.29762
\(333\) −2.90939 −0.159434
\(334\) −52.5965 −2.87795
\(335\) −5.18286 −0.283170
\(336\) 118.507 6.46507
\(337\) −23.9929 −1.30697 −0.653487 0.756938i \(-0.726695\pi\)
−0.653487 + 0.756938i \(0.726695\pi\)
\(338\) −70.7658 −3.84915
\(339\) −22.7257 −1.23429
\(340\) −80.4621 −4.36367
\(341\) −7.62064 −0.412681
\(342\) −7.34655 −0.397256
\(343\) 3.88311 0.209668
\(344\) −82.1521 −4.42935
\(345\) 5.68284 0.305954
\(346\) −45.8598 −2.46544
\(347\) −22.3332 −1.19891 −0.599453 0.800410i \(-0.704615\pi\)
−0.599453 + 0.800410i \(0.704615\pi\)
\(348\) −45.4938 −2.43872
\(349\) −1.00000 −0.0535288
\(350\) −29.0077 −1.55053
\(351\) −23.2818 −1.24269
\(352\) 20.7097 1.10383
\(353\) 34.9582 1.86064 0.930318 0.366754i \(-0.119531\pi\)
0.930318 + 0.366754i \(0.119531\pi\)
\(354\) 50.1733 2.66668
\(355\) 33.3578 1.77045
\(356\) −38.4152 −2.03600
\(357\) −41.8333 −2.21405
\(358\) −50.3454 −2.66084
\(359\) −14.4297 −0.761571 −0.380786 0.924663i \(-0.624346\pi\)
−0.380786 + 0.924663i \(0.624346\pi\)
\(360\) −30.9300 −1.63015
\(361\) −13.7428 −0.723307
\(362\) 4.96244 0.260820
\(363\) −20.6542 −1.08406
\(364\) 132.124 6.92516
\(365\) −30.5532 −1.59923
\(366\) −21.4721 −1.12236
\(367\) 17.8581 0.932183 0.466092 0.884736i \(-0.345662\pi\)
0.466092 + 0.884736i \(0.345662\pi\)
\(368\) 14.9786 0.780812
\(369\) 1.09522 0.0570151
\(370\) 18.8701 0.981012
\(371\) 28.4096 1.47495
\(372\) 90.3303 4.68341
\(373\) −28.1443 −1.45726 −0.728629 0.684909i \(-0.759842\pi\)
−0.728629 + 0.684909i \(0.759842\pi\)
\(374\) −13.6212 −0.704338
\(375\) −12.8422 −0.663170
\(376\) −5.87139 −0.302794
\(377\) −25.3938 −1.30785
\(378\) 39.5202 2.03270
\(379\) −13.8648 −0.712187 −0.356093 0.934450i \(-0.615891\pi\)
−0.356093 + 0.934450i \(0.615891\pi\)
\(380\) 34.8914 1.78989
\(381\) 8.69241 0.445326
\(382\) −38.7974 −1.98505
\(383\) 9.54260 0.487604 0.243802 0.969825i \(-0.421605\pi\)
0.243802 + 0.969825i \(0.421605\pi\)
\(384\) −78.2390 −3.99262
\(385\) −10.1572 −0.517657
\(386\) 58.6594 2.98568
\(387\) 10.1560 0.516260
\(388\) 4.11938 0.209130
\(389\) −6.82269 −0.345924 −0.172962 0.984928i \(-0.555334\pi\)
−0.172962 + 0.984928i \(0.555334\pi\)
\(390\) −96.8612 −4.90476
\(391\) −5.28749 −0.267400
\(392\) −75.8887 −3.83296
\(393\) −38.9940 −1.96699
\(394\) −4.65022 −0.234275
\(395\) 13.6079 0.684687
\(396\) −6.04416 −0.303731
\(397\) −38.6015 −1.93735 −0.968677 0.248325i \(-0.920120\pi\)
−0.968677 + 0.248325i \(0.920120\pi\)
\(398\) −61.4163 −3.07852
\(399\) 18.1405 0.908159
\(400\) 41.0439 2.05219
\(401\) 1.44966 0.0723926 0.0361963 0.999345i \(-0.488476\pi\)
0.0361963 + 0.999345i \(0.488476\pi\)
\(402\) 10.4001 0.518709
\(403\) 50.4207 2.51163
\(404\) 15.3421 0.763296
\(405\) −31.0001 −1.54041
\(406\) 43.1052 2.13928
\(407\) 2.33917 0.115948
\(408\) 102.421 5.07059
\(409\) 5.40343 0.267182 0.133591 0.991037i \(-0.457349\pi\)
0.133591 + 0.991037i \(0.457349\pi\)
\(410\) −7.10356 −0.350820
\(411\) 7.02717 0.346625
\(412\) −24.7970 −1.22166
\(413\) −34.8106 −1.71292
\(414\) −3.20411 −0.157473
\(415\) 39.8296 1.95516
\(416\) −137.022 −6.71807
\(417\) 22.3922 1.09655
\(418\) 5.90668 0.288905
\(419\) 28.6602 1.40014 0.700071 0.714073i \(-0.253152\pi\)
0.700071 + 0.714073i \(0.253152\pi\)
\(420\) 120.397 5.87475
\(421\) −30.3688 −1.48008 −0.740042 0.672560i \(-0.765195\pi\)
−0.740042 + 0.672560i \(0.765195\pi\)
\(422\) 52.9939 2.57970
\(423\) 0.725848 0.0352919
\(424\) −69.5556 −3.37792
\(425\) −14.4886 −0.702802
\(426\) −66.9369 −3.24310
\(427\) 14.8975 0.720941
\(428\) 10.9406 0.528835
\(429\) −12.0071 −0.579706
\(430\) −65.8715 −3.17660
\(431\) −25.3620 −1.22165 −0.610823 0.791767i \(-0.709161\pi\)
−0.610823 + 0.791767i \(0.709161\pi\)
\(432\) −55.9184 −2.69038
\(433\) −3.49367 −0.167895 −0.0839475 0.996470i \(-0.526753\pi\)
−0.0839475 + 0.996470i \(0.526753\pi\)
\(434\) −85.5878 −4.10835
\(435\) −23.1398 −1.10947
\(436\) −29.3600 −1.40609
\(437\) 2.29285 0.109682
\(438\) 61.3091 2.92946
\(439\) −38.6739 −1.84581 −0.922903 0.385032i \(-0.874190\pi\)
−0.922903 + 0.385032i \(0.874190\pi\)
\(440\) 24.8679 1.18553
\(441\) 9.38171 0.446748
\(442\) 90.1226 4.28670
\(443\) 35.5796 1.69044 0.845218 0.534422i \(-0.179471\pi\)
0.845218 + 0.534422i \(0.179471\pi\)
\(444\) −27.7271 −1.31587
\(445\) −19.5394 −0.926257
\(446\) 21.5656 1.02116
\(447\) −9.38625 −0.443954
\(448\) 116.559 5.50688
\(449\) 27.5738 1.30129 0.650645 0.759382i \(-0.274499\pi\)
0.650645 + 0.759382i \(0.274499\pi\)
\(450\) −8.77982 −0.413884
\(451\) −0.880568 −0.0414643
\(452\) −60.8546 −2.86236
\(453\) −15.2452 −0.716284
\(454\) −54.4817 −2.55695
\(455\) 67.2031 3.15053
\(456\) −44.4136 −2.07986
\(457\) −6.11373 −0.285988 −0.142994 0.989724i \(-0.545673\pi\)
−0.142994 + 0.989724i \(0.545673\pi\)
\(458\) 0.762370 0.0356232
\(459\) 19.7394 0.921357
\(460\) 15.2175 0.709517
\(461\) −10.1165 −0.471171 −0.235586 0.971854i \(-0.575701\pi\)
−0.235586 + 0.971854i \(0.575701\pi\)
\(462\) 20.3817 0.948241
\(463\) 11.2538 0.523009 0.261505 0.965202i \(-0.415781\pi\)
0.261505 + 0.965202i \(0.415781\pi\)
\(464\) −60.9910 −2.83143
\(465\) 45.9454 2.13067
\(466\) 64.2978 2.97854
\(467\) −24.2736 −1.12325 −0.561624 0.827393i \(-0.689823\pi\)
−0.561624 + 0.827393i \(0.689823\pi\)
\(468\) 39.9902 1.84855
\(469\) −7.21566 −0.333188
\(470\) −4.70781 −0.217155
\(471\) 28.6841 1.32169
\(472\) 85.2274 3.92291
\(473\) −8.16552 −0.375451
\(474\) −27.3060 −1.25421
\(475\) 6.28281 0.288275
\(476\) −112.021 −5.13446
\(477\) 8.59879 0.393712
\(478\) 18.5122 0.846727
\(479\) 5.02143 0.229435 0.114717 0.993398i \(-0.463404\pi\)
0.114717 + 0.993398i \(0.463404\pi\)
\(480\) −124.860 −5.69908
\(481\) −15.4767 −0.705678
\(482\) −45.4788 −2.07150
\(483\) 7.91174 0.359997
\(484\) −55.3076 −2.51398
\(485\) 2.09527 0.0951413
\(486\) 31.5961 1.43323
\(487\) −4.00272 −0.181380 −0.0906902 0.995879i \(-0.528907\pi\)
−0.0906902 + 0.995879i \(0.528907\pi\)
\(488\) −36.4738 −1.65109
\(489\) −29.0909 −1.31554
\(490\) −60.8493 −2.74889
\(491\) −30.3756 −1.37083 −0.685415 0.728152i \(-0.740379\pi\)
−0.685415 + 0.728152i \(0.740379\pi\)
\(492\) 10.4377 0.470568
\(493\) 21.5300 0.969664
\(494\) −39.0806 −1.75832
\(495\) −3.07429 −0.138179
\(496\) 121.101 5.43759
\(497\) 46.4414 2.08318
\(498\) −79.9233 −3.58145
\(499\) 44.0095 1.97013 0.985067 0.172172i \(-0.0550786\pi\)
0.985067 + 0.172172i \(0.0550786\pi\)
\(500\) −34.3888 −1.53791
\(501\) 39.3092 1.75621
\(502\) −68.1928 −3.04360
\(503\) −39.8200 −1.77549 −0.887744 0.460338i \(-0.847728\pi\)
−0.887744 + 0.460338i \(0.847728\pi\)
\(504\) −43.0612 −1.91810
\(505\) 7.80356 0.347254
\(506\) 2.57613 0.114523
\(507\) 52.8884 2.34886
\(508\) 23.2764 1.03273
\(509\) 6.46687 0.286639 0.143319 0.989676i \(-0.454222\pi\)
0.143319 + 0.989676i \(0.454222\pi\)
\(510\) 82.1235 3.63649
\(511\) −42.5367 −1.88171
\(512\) −45.0156 −1.98943
\(513\) −8.55975 −0.377922
\(514\) −47.7694 −2.10702
\(515\) −12.6127 −0.555781
\(516\) 96.7890 4.26090
\(517\) −0.583587 −0.0256661
\(518\) 26.2713 1.15430
\(519\) 34.2743 1.50448
\(520\) −164.534 −7.21531
\(521\) −32.7710 −1.43572 −0.717861 0.696187i \(-0.754879\pi\)
−0.717861 + 0.696187i \(0.754879\pi\)
\(522\) 13.0468 0.571041
\(523\) −21.4335 −0.937223 −0.468611 0.883404i \(-0.655246\pi\)
−0.468611 + 0.883404i \(0.655246\pi\)
\(524\) −104.418 −4.56151
\(525\) 21.6795 0.946173
\(526\) −29.5469 −1.28830
\(527\) −42.7490 −1.86218
\(528\) −28.8387 −1.25504
\(529\) 1.00000 0.0434783
\(530\) −55.7713 −2.42255
\(531\) −10.5362 −0.457233
\(532\) 48.5764 2.10605
\(533\) 5.82613 0.252358
\(534\) 39.2084 1.69671
\(535\) 5.56482 0.240588
\(536\) 17.6662 0.763064
\(537\) 37.6268 1.62372
\(538\) −30.3129 −1.30688
\(539\) −7.54297 −0.324899
\(540\) −56.8102 −2.44472
\(541\) −15.1599 −0.651773 −0.325887 0.945409i \(-0.605663\pi\)
−0.325887 + 0.945409i \(0.605663\pi\)
\(542\) 34.7693 1.49347
\(543\) −3.70879 −0.159159
\(544\) 116.174 4.98092
\(545\) −14.9336 −0.639685
\(546\) −134.852 −5.77113
\(547\) 16.8025 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(548\) 18.8173 0.803835
\(549\) 4.50906 0.192442
\(550\) 7.05904 0.300998
\(551\) −9.33623 −0.397737
\(552\) −19.3704 −0.824461
\(553\) 18.9451 0.805628
\(554\) 69.9089 2.97015
\(555\) −14.1030 −0.598640
\(556\) 59.9615 2.54294
\(557\) −20.8609 −0.883905 −0.441952 0.897038i \(-0.645714\pi\)
−0.441952 + 0.897038i \(0.645714\pi\)
\(558\) −25.9050 −1.09665
\(559\) 54.0258 2.28505
\(560\) 161.409 6.82078
\(561\) 10.1802 0.429806
\(562\) −49.3589 −2.08208
\(563\) 17.9910 0.758232 0.379116 0.925349i \(-0.376228\pi\)
0.379116 + 0.925349i \(0.376228\pi\)
\(564\) 6.91748 0.291278
\(565\) −30.9530 −1.30220
\(566\) 18.8378 0.791813
\(567\) −43.1589 −1.81250
\(568\) −113.703 −4.77087
\(569\) 6.51137 0.272971 0.136485 0.990642i \(-0.456419\pi\)
0.136485 + 0.990642i \(0.456419\pi\)
\(570\) −35.6118 −1.49162
\(571\) 25.2674 1.05741 0.528704 0.848806i \(-0.322678\pi\)
0.528704 + 0.848806i \(0.322678\pi\)
\(572\) −32.1524 −1.34436
\(573\) 28.9961 1.21133
\(574\) −9.88970 −0.412788
\(575\) 2.74017 0.114273
\(576\) 35.2791 1.46996
\(577\) −29.9989 −1.24887 −0.624436 0.781076i \(-0.714671\pi\)
−0.624436 + 0.781076i \(0.714671\pi\)
\(578\) −29.9478 −1.24567
\(579\) −43.8404 −1.82195
\(580\) −61.9637 −2.57290
\(581\) 55.4514 2.30051
\(582\) −4.20443 −0.174279
\(583\) −6.91349 −0.286328
\(584\) 104.143 4.30948
\(585\) 20.3405 0.840977
\(586\) 38.5745 1.59350
\(587\) −12.7845 −0.527671 −0.263836 0.964568i \(-0.584988\pi\)
−0.263836 + 0.964568i \(0.584988\pi\)
\(588\) 89.4096 3.68719
\(589\) 18.5376 0.763828
\(590\) 68.3373 2.81340
\(591\) 3.47545 0.142961
\(592\) −37.1721 −1.52777
\(593\) −21.5496 −0.884935 −0.442468 0.896784i \(-0.645897\pi\)
−0.442468 + 0.896784i \(0.645897\pi\)
\(594\) −9.61728 −0.394602
\(595\) −56.9780 −2.33587
\(596\) −25.1344 −1.02955
\(597\) 45.9009 1.87860
\(598\) −17.0445 −0.697002
\(599\) 25.7240 1.05105 0.525527 0.850777i \(-0.323868\pi\)
0.525527 + 0.850777i \(0.323868\pi\)
\(600\) −53.0784 −2.16692
\(601\) 18.8968 0.770816 0.385408 0.922746i \(-0.374061\pi\)
0.385408 + 0.922746i \(0.374061\pi\)
\(602\) −91.7074 −3.73771
\(603\) −2.18398 −0.0889385
\(604\) −40.8235 −1.66109
\(605\) −28.1315 −1.14371
\(606\) −15.6589 −0.636097
\(607\) 3.69895 0.150136 0.0750678 0.997178i \(-0.476083\pi\)
0.0750678 + 0.997178i \(0.476083\pi\)
\(608\) −50.3774 −2.04307
\(609\) −32.2157 −1.30545
\(610\) −29.2455 −1.18412
\(611\) 3.86120 0.156208
\(612\) −33.9055 −1.37055
\(613\) 18.9216 0.764236 0.382118 0.924114i \(-0.375195\pi\)
0.382118 + 0.924114i \(0.375195\pi\)
\(614\) 58.5878 2.36441
\(615\) 5.30901 0.214080
\(616\) 34.6216 1.39494
\(617\) 7.26011 0.292281 0.146140 0.989264i \(-0.453315\pi\)
0.146140 + 0.989264i \(0.453315\pi\)
\(618\) 25.3090 1.01808
\(619\) −37.9918 −1.52702 −0.763510 0.645796i \(-0.776526\pi\)
−0.763510 + 0.645796i \(0.776526\pi\)
\(620\) 123.032 4.94109
\(621\) −3.73323 −0.149809
\(622\) −40.2380 −1.61340
\(623\) −27.2031 −1.08987
\(624\) 190.806 7.63836
\(625\) −31.1923 −1.24769
\(626\) −19.4915 −0.779038
\(627\) −4.41449 −0.176298
\(628\) 76.8100 3.06505
\(629\) 13.1219 0.523204
\(630\) −34.5275 −1.37561
\(631\) −27.6573 −1.10102 −0.550510 0.834829i \(-0.685567\pi\)
−0.550510 + 0.834829i \(0.685567\pi\)
\(632\) −46.3836 −1.84504
\(633\) −39.6062 −1.57421
\(634\) −66.9256 −2.65795
\(635\) 11.8393 0.469828
\(636\) 81.9482 3.24946
\(637\) 49.9067 1.97738
\(638\) −10.4897 −0.415291
\(639\) 14.0565 0.556067
\(640\) −106.564 −4.21229
\(641\) −23.6208 −0.932964 −0.466482 0.884531i \(-0.654479\pi\)
−0.466482 + 0.884531i \(0.654479\pi\)
\(642\) −11.1665 −0.440708
\(643\) −25.4284 −1.00280 −0.501400 0.865216i \(-0.667181\pi\)
−0.501400 + 0.865216i \(0.667181\pi\)
\(644\) 21.1860 0.834845
\(645\) 49.2305 1.93845
\(646\) 33.1343 1.30365
\(647\) −19.5984 −0.770494 −0.385247 0.922813i \(-0.625884\pi\)
−0.385247 + 0.922813i \(0.625884\pi\)
\(648\) 105.667 4.15098
\(649\) 8.47119 0.332523
\(650\) −46.7049 −1.83192
\(651\) 63.9660 2.50702
\(652\) −77.8994 −3.05077
\(653\) −33.3385 −1.30464 −0.652318 0.757945i \(-0.726203\pi\)
−0.652318 + 0.757945i \(0.726203\pi\)
\(654\) 29.9662 1.17177
\(655\) −53.1109 −2.07521
\(656\) 13.9932 0.546345
\(657\) −12.8747 −0.502289
\(658\) −6.55430 −0.255513
\(659\) −12.8480 −0.500488 −0.250244 0.968183i \(-0.580511\pi\)
−0.250244 + 0.968183i \(0.580511\pi\)
\(660\) −29.2986 −1.14045
\(661\) −38.7225 −1.50613 −0.753066 0.657945i \(-0.771426\pi\)
−0.753066 + 0.657945i \(0.771426\pi\)
\(662\) −67.3215 −2.61652
\(663\) −67.3552 −2.61586
\(664\) −135.763 −5.26861
\(665\) 24.7078 0.958127
\(666\) 7.95160 0.308118
\(667\) −4.07188 −0.157664
\(668\) 105.262 4.07270
\(669\) −16.1176 −0.623141
\(670\) 14.1652 0.547248
\(671\) −3.62532 −0.139954
\(672\) −173.833 −6.70575
\(673\) −4.39145 −0.169278 −0.0846390 0.996412i \(-0.526974\pi\)
−0.0846390 + 0.996412i \(0.526974\pi\)
\(674\) 65.5745 2.52583
\(675\) −10.2297 −0.393741
\(676\) 141.624 5.44708
\(677\) 45.8801 1.76332 0.881658 0.471888i \(-0.156427\pi\)
0.881658 + 0.471888i \(0.156427\pi\)
\(678\) 62.1112 2.38536
\(679\) 2.91707 0.111947
\(680\) 139.500 5.34958
\(681\) 40.7181 1.56032
\(682\) 20.8278 0.797539
\(683\) 19.2047 0.734847 0.367424 0.930054i \(-0.380240\pi\)
0.367424 + 0.930054i \(0.380240\pi\)
\(684\) 14.7027 0.562172
\(685\) 9.57119 0.365696
\(686\) −10.6129 −0.405201
\(687\) −0.569775 −0.0217383
\(688\) 129.760 4.94704
\(689\) 45.7419 1.74263
\(690\) −15.5317 −0.591280
\(691\) −22.6353 −0.861089 −0.430544 0.902569i \(-0.641678\pi\)
−0.430544 + 0.902569i \(0.641678\pi\)
\(692\) 91.7795 3.48893
\(693\) −4.28008 −0.162587
\(694\) 61.0384 2.31698
\(695\) 30.4987 1.15688
\(696\) 78.8742 2.98972
\(697\) −4.93967 −0.187103
\(698\) 2.73308 0.103449
\(699\) −48.0544 −1.81758
\(700\) 58.0533 2.19421
\(701\) −0.676650 −0.0255567 −0.0127784 0.999918i \(-0.504068\pi\)
−0.0127784 + 0.999918i \(0.504068\pi\)
\(702\) 63.6311 2.40160
\(703\) −5.69014 −0.214608
\(704\) −28.3646 −1.06903
\(705\) 3.51849 0.132514
\(706\) −95.5436 −3.59583
\(707\) 10.8642 0.408592
\(708\) −100.412 −3.77372
\(709\) 40.9875 1.53932 0.769659 0.638456i \(-0.220426\pi\)
0.769659 + 0.638456i \(0.220426\pi\)
\(710\) −91.1697 −3.42154
\(711\) 5.73416 0.215048
\(712\) 66.6018 2.49601
\(713\) 8.08494 0.302783
\(714\) 114.334 4.27883
\(715\) −16.3539 −0.611602
\(716\) 100.757 3.76545
\(717\) −13.8355 −0.516696
\(718\) 39.4376 1.47180
\(719\) 40.4073 1.50694 0.753468 0.657484i \(-0.228379\pi\)
0.753468 + 0.657484i \(0.228379\pi\)
\(720\) 48.8540 1.82068
\(721\) −17.5596 −0.653953
\(722\) 37.5603 1.39785
\(723\) 33.9897 1.26409
\(724\) −9.93136 −0.369096
\(725\) −11.1577 −0.414385
\(726\) 56.4496 2.09504
\(727\) 0.588702 0.0218337 0.0109169 0.999940i \(-0.496525\pi\)
0.0109169 + 0.999940i \(0.496525\pi\)
\(728\) −229.068 −8.48981
\(729\) 9.81384 0.363475
\(730\) 83.5045 3.09064
\(731\) −45.8056 −1.69418
\(732\) 42.9723 1.58830
\(733\) 16.3991 0.605714 0.302857 0.953036i \(-0.402060\pi\)
0.302857 + 0.953036i \(0.402060\pi\)
\(734\) −48.8076 −1.80152
\(735\) 45.4771 1.67745
\(736\) −21.9715 −0.809880
\(737\) 1.75594 0.0646807
\(738\) −2.99334 −0.110186
\(739\) 7.30562 0.268741 0.134371 0.990931i \(-0.457099\pi\)
0.134371 + 0.990931i \(0.457099\pi\)
\(740\) −37.7650 −1.38827
\(741\) 29.2077 1.07297
\(742\) −77.6458 −2.85047
\(743\) 4.26066 0.156308 0.0781542 0.996941i \(-0.475097\pi\)
0.0781542 + 0.996941i \(0.475097\pi\)
\(744\) −156.609 −5.74156
\(745\) −12.7843 −0.468381
\(746\) 76.9207 2.81627
\(747\) 16.7836 0.614080
\(748\) 27.2603 0.996736
\(749\) 7.74743 0.283085
\(750\) 35.0989 1.28163
\(751\) −18.9634 −0.691985 −0.345992 0.938237i \(-0.612458\pi\)
−0.345992 + 0.938237i \(0.612458\pi\)
\(752\) 9.27388 0.338184
\(753\) 50.9655 1.85728
\(754\) 69.4032 2.52752
\(755\) −20.7644 −0.755694
\(756\) −79.0922 −2.87656
\(757\) 43.4896 1.58065 0.790327 0.612685i \(-0.209910\pi\)
0.790327 + 0.612685i \(0.209910\pi\)
\(758\) 37.8936 1.37636
\(759\) −1.92533 −0.0698850
\(760\) −60.4924 −2.19429
\(761\) −19.0485 −0.690507 −0.345253 0.938509i \(-0.612207\pi\)
−0.345253 + 0.938509i \(0.612207\pi\)
\(762\) −23.7571 −0.860628
\(763\) −20.7908 −0.752678
\(764\) 77.6455 2.80912
\(765\) −17.2456 −0.623518
\(766\) −26.0807 −0.942335
\(767\) −56.0482 −2.02378
\(768\) 90.8967 3.27995
\(769\) 21.7746 0.785212 0.392606 0.919707i \(-0.371574\pi\)
0.392606 + 0.919707i \(0.371574\pi\)
\(770\) 27.7604 1.00041
\(771\) 35.7015 1.28576
\(772\) −117.395 −4.22515
\(773\) 22.1364 0.796192 0.398096 0.917344i \(-0.369671\pi\)
0.398096 + 0.917344i \(0.369671\pi\)
\(774\) −27.7573 −0.997714
\(775\) 22.1541 0.795800
\(776\) −7.14191 −0.256380
\(777\) −19.6345 −0.704383
\(778\) 18.6470 0.668527
\(779\) 2.14202 0.0767460
\(780\) 193.849 6.94091
\(781\) −11.3015 −0.404401
\(782\) 14.4511 0.516772
\(783\) 15.2013 0.543249
\(784\) 119.866 4.28095
\(785\) 39.0685 1.39441
\(786\) 106.574 3.80136
\(787\) −40.0312 −1.42696 −0.713480 0.700676i \(-0.752882\pi\)
−0.713480 + 0.700676i \(0.752882\pi\)
\(788\) 9.30653 0.331531
\(789\) 22.0825 0.786159
\(790\) −37.1914 −1.32321
\(791\) −43.0932 −1.53222
\(792\) 10.4790 0.372354
\(793\) 23.9863 0.851779
\(794\) 105.501 3.74409
\(795\) 41.6820 1.47831
\(796\) 122.913 4.35654
\(797\) −15.4518 −0.547330 −0.273665 0.961825i \(-0.588236\pi\)
−0.273665 + 0.961825i \(0.588236\pi\)
\(798\) −49.5794 −1.75509
\(799\) −3.27371 −0.115816
\(800\) −60.2057 −2.12859
\(801\) −8.23362 −0.290921
\(802\) −3.96204 −0.139904
\(803\) 10.3513 0.365291
\(804\) −20.8138 −0.734045
\(805\) 10.7760 0.379804
\(806\) −137.804 −4.85393
\(807\) 22.6550 0.797495
\(808\) −26.5991 −0.935753
\(809\) −37.6144 −1.32245 −0.661226 0.750187i \(-0.729964\pi\)
−0.661226 + 0.750187i \(0.729964\pi\)
\(810\) 84.7259 2.97696
\(811\) 15.7131 0.551760 0.275880 0.961192i \(-0.411031\pi\)
0.275880 + 0.961192i \(0.411031\pi\)
\(812\) −86.2669 −3.02737
\(813\) −25.9856 −0.911356
\(814\) −6.39315 −0.224080
\(815\) −39.6226 −1.38792
\(816\) −161.774 −5.66324
\(817\) 19.8630 0.694920
\(818\) −14.7680 −0.516351
\(819\) 28.3184 0.989525
\(820\) 14.2164 0.496459
\(821\) 6.17012 0.215339 0.107669 0.994187i \(-0.465661\pi\)
0.107669 + 0.994187i \(0.465661\pi\)
\(822\) −19.2058 −0.669880
\(823\) 0.237237 0.00826955 0.00413478 0.999991i \(-0.498684\pi\)
0.00413478 + 0.999991i \(0.498684\pi\)
\(824\) 42.9914 1.49768
\(825\) −5.27573 −0.183677
\(826\) 95.1404 3.31036
\(827\) −7.61192 −0.264692 −0.132346 0.991204i \(-0.542251\pi\)
−0.132346 + 0.991204i \(0.542251\pi\)
\(828\) 6.41241 0.222847
\(829\) −48.3466 −1.67915 −0.839573 0.543247i \(-0.817195\pi\)
−0.839573 + 0.543247i \(0.817195\pi\)
\(830\) −108.858 −3.77850
\(831\) −52.2480 −1.81246
\(832\) 187.670 6.50627
\(833\) −42.3133 −1.46607
\(834\) −61.1996 −2.11917
\(835\) 53.5401 1.85283
\(836\) −11.8211 −0.408841
\(837\) −30.1829 −1.04327
\(838\) −78.3307 −2.70589
\(839\) −42.3724 −1.46286 −0.731430 0.681917i \(-0.761147\pi\)
−0.731430 + 0.681917i \(0.761147\pi\)
\(840\) −208.736 −7.20207
\(841\) −12.4198 −0.428268
\(842\) 83.0004 2.86038
\(843\) 36.8895 1.27054
\(844\) −106.057 −3.65064
\(845\) 72.0354 2.47809
\(846\) −1.98380 −0.0682045
\(847\) −39.1652 −1.34573
\(848\) 109.863 3.77273
\(849\) −14.0789 −0.483186
\(850\) 39.5986 1.35822
\(851\) −2.48169 −0.0850711
\(852\) 133.961 4.58944
\(853\) 32.1190 1.09973 0.549866 0.835253i \(-0.314679\pi\)
0.549866 + 0.835253i \(0.314679\pi\)
\(854\) −40.7161 −1.39328
\(855\) 7.47836 0.255754
\(856\) −18.9682 −0.648318
\(857\) −24.7390 −0.845067 −0.422534 0.906347i \(-0.638859\pi\)
−0.422534 + 0.906347i \(0.638859\pi\)
\(858\) 32.8163 1.12033
\(859\) −26.5520 −0.905943 −0.452971 0.891525i \(-0.649636\pi\)
−0.452971 + 0.891525i \(0.649636\pi\)
\(860\) 131.829 4.49533
\(861\) 7.39129 0.251895
\(862\) 69.3165 2.36093
\(863\) −17.5678 −0.598015 −0.299007 0.954251i \(-0.596656\pi\)
−0.299007 + 0.954251i \(0.596656\pi\)
\(864\) 82.0246 2.79054
\(865\) 46.6825 1.58725
\(866\) 9.54848 0.324471
\(867\) 22.3822 0.760139
\(868\) 171.288 5.81388
\(869\) −4.61031 −0.156394
\(870\) 63.2431 2.14414
\(871\) −11.6178 −0.393656
\(872\) 50.9025 1.72377
\(873\) 0.882916 0.0298822
\(874\) −6.26656 −0.211969
\(875\) −24.3519 −0.823244
\(876\) −122.698 −4.14559
\(877\) 8.87287 0.299615 0.149808 0.988715i \(-0.452135\pi\)
0.149808 + 0.988715i \(0.452135\pi\)
\(878\) 105.699 3.56717
\(879\) −28.8296 −0.972397
\(880\) −39.2790 −1.32409
\(881\) −24.7791 −0.834828 −0.417414 0.908717i \(-0.637063\pi\)
−0.417414 + 0.908717i \(0.637063\pi\)
\(882\) −25.6410 −0.863377
\(883\) 36.4867 1.22788 0.613938 0.789354i \(-0.289585\pi\)
0.613938 + 0.789354i \(0.289585\pi\)
\(884\) −180.363 −6.06627
\(885\) −51.0734 −1.71682
\(886\) −97.2418 −3.26690
\(887\) 24.5993 0.825962 0.412981 0.910740i \(-0.364488\pi\)
0.412981 + 0.910740i \(0.364488\pi\)
\(888\) 48.0714 1.61317
\(889\) 16.4829 0.552817
\(890\) 53.4028 1.79007
\(891\) 10.5027 0.351855
\(892\) −43.1594 −1.44508
\(893\) 1.41960 0.0475052
\(894\) 25.6534 0.857978
\(895\) 51.2486 1.71305
\(896\) −148.360 −4.95634
\(897\) 12.7386 0.425330
\(898\) −75.3615 −2.51485
\(899\) −32.9209 −1.09797
\(900\) 17.5711 0.585704
\(901\) −38.7822 −1.29202
\(902\) 2.40667 0.0801332
\(903\) 68.5396 2.28086
\(904\) 105.506 3.50907
\(905\) −5.05147 −0.167916
\(906\) 41.6665 1.38428
\(907\) 25.9062 0.860201 0.430100 0.902781i \(-0.358478\pi\)
0.430100 + 0.902781i \(0.358478\pi\)
\(908\) 109.035 3.61844
\(909\) 3.28830 0.109066
\(910\) −183.672 −6.08866
\(911\) −42.2403 −1.39948 −0.699741 0.714396i \(-0.746701\pi\)
−0.699741 + 0.714396i \(0.746701\pi\)
\(912\) 70.1514 2.32295
\(913\) −13.4941 −0.446591
\(914\) 16.7093 0.552695
\(915\) 21.8573 0.722581
\(916\) −1.52574 −0.0504118
\(917\) −73.9418 −2.44177
\(918\) −53.9494 −1.78060
\(919\) −16.8877 −0.557075 −0.278538 0.960425i \(-0.589850\pi\)
−0.278538 + 0.960425i \(0.589850\pi\)
\(920\) −26.3830 −0.869823
\(921\) −43.7870 −1.44283
\(922\) 27.6492 0.910577
\(923\) 74.7747 2.46124
\(924\) −40.7900 −1.34189
\(925\) −6.80025 −0.223591
\(926\) −30.7576 −1.01076
\(927\) −5.31480 −0.174561
\(928\) 89.4653 2.93684
\(929\) −22.8538 −0.749809 −0.374905 0.927063i \(-0.622325\pi\)
−0.374905 + 0.927063i \(0.622325\pi\)
\(930\) −125.573 −4.11769
\(931\) 18.3486 0.601352
\(932\) −128.680 −4.21504
\(933\) 30.0728 0.984539
\(934\) 66.3417 2.17077
\(935\) 13.8656 0.453454
\(936\) −69.3324 −2.26620
\(937\) −15.7344 −0.514021 −0.257011 0.966409i \(-0.582738\pi\)
−0.257011 + 0.966409i \(0.582738\pi\)
\(938\) 19.7210 0.643913
\(939\) 14.5674 0.475390
\(940\) 9.42178 0.307305
\(941\) −30.0213 −0.978666 −0.489333 0.872097i \(-0.662760\pi\)
−0.489333 + 0.872097i \(0.662760\pi\)
\(942\) −78.3960 −2.55428
\(943\) 0.934218 0.0304223
\(944\) −134.617 −4.38141
\(945\) −40.2293 −1.30866
\(946\) 22.3171 0.725590
\(947\) −43.7036 −1.42018 −0.710088 0.704113i \(-0.751345\pi\)
−0.710088 + 0.704113i \(0.751345\pi\)
\(948\) 54.6477 1.77487
\(949\) −68.4879 −2.22321
\(950\) −17.1714 −0.557115
\(951\) 50.0183 1.62196
\(952\) 194.214 6.29452
\(953\) 25.3980 0.822723 0.411362 0.911472i \(-0.365053\pi\)
0.411362 + 0.911472i \(0.365053\pi\)
\(954\) −23.5012 −0.760880
\(955\) 39.4934 1.27798
\(956\) −37.0485 −1.19824
\(957\) 7.83971 0.253422
\(958\) −13.7240 −0.443401
\(959\) 13.3252 0.430292
\(960\) 171.012 5.51940
\(961\) 34.3663 1.10859
\(962\) 42.2991 1.36378
\(963\) 2.34493 0.0755644
\(964\) 91.0172 2.93147
\(965\) −59.7118 −1.92219
\(966\) −21.6235 −0.695723
\(967\) 35.9116 1.15484 0.577419 0.816448i \(-0.304060\pi\)
0.577419 + 0.816448i \(0.304060\pi\)
\(968\) 95.8887 3.08198
\(969\) −24.7637 −0.795525
\(970\) −5.72655 −0.183868
\(971\) 1.29273 0.0414858 0.0207429 0.999785i \(-0.493397\pi\)
0.0207429 + 0.999785i \(0.493397\pi\)
\(972\) −63.2336 −2.02822
\(973\) 42.4608 1.36123
\(974\) 10.9398 0.350532
\(975\) 34.9060 1.11789
\(976\) 57.6105 1.84407
\(977\) −17.8166 −0.570005 −0.285002 0.958527i \(-0.591994\pi\)
−0.285002 + 0.958527i \(0.591994\pi\)
\(978\) 79.5078 2.54238
\(979\) 6.61990 0.211573
\(980\) 121.778 3.89006
\(981\) −6.29280 −0.200914
\(982\) 83.0189 2.64924
\(983\) −35.9823 −1.14766 −0.573829 0.818975i \(-0.694543\pi\)
−0.573829 + 0.818975i \(0.694543\pi\)
\(984\) −18.0962 −0.576886
\(985\) 4.73365 0.150827
\(986\) −58.8433 −1.87395
\(987\) 4.89850 0.155921
\(988\) 78.2122 2.48826
\(989\) 8.66302 0.275468
\(990\) 8.40229 0.267042
\(991\) 28.4414 0.903472 0.451736 0.892152i \(-0.350805\pi\)
0.451736 + 0.892152i \(0.350805\pi\)
\(992\) −177.638 −5.64002
\(993\) 50.3143 1.59667
\(994\) −126.928 −4.02591
\(995\) 62.5182 1.98196
\(996\) 159.951 5.06824
\(997\) 29.7994 0.943758 0.471879 0.881663i \(-0.343576\pi\)
0.471879 + 0.881663i \(0.343576\pi\)
\(998\) −120.281 −3.80744
\(999\) 9.26471 0.293122
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 \(a_p\))