Properties

Label 8027.2.a.f.1.1
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 1.1
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.81854 q^{2} -0.267983 q^{3} +5.94415 q^{4} -3.79404 q^{5} +0.755319 q^{6} -0.324133 q^{7} -11.1167 q^{8} -2.92819 q^{9} +O(q^{10})\) \(q-2.81854 q^{2} -0.267983 q^{3} +5.94415 q^{4} -3.79404 q^{5} +0.755319 q^{6} -0.324133 q^{7} -11.1167 q^{8} -2.92819 q^{9} +10.6936 q^{10} +1.85803 q^{11} -1.59293 q^{12} +5.15183 q^{13} +0.913581 q^{14} +1.01674 q^{15} +19.4446 q^{16} +0.693605 q^{17} +8.25320 q^{18} +1.82537 q^{19} -22.5523 q^{20} +0.0868621 q^{21} -5.23694 q^{22} +1.00000 q^{23} +2.97909 q^{24} +9.39471 q^{25} -14.5206 q^{26} +1.58865 q^{27} -1.92669 q^{28} -6.16549 q^{29} -2.86571 q^{30} -2.72225 q^{31} -32.5718 q^{32} -0.497921 q^{33} -1.95495 q^{34} +1.22977 q^{35} -17.4056 q^{36} +2.45632 q^{37} -5.14487 q^{38} -1.38060 q^{39} +42.1772 q^{40} -0.589626 q^{41} -0.244824 q^{42} -0.677822 q^{43} +11.0444 q^{44} +11.1096 q^{45} -2.81854 q^{46} +11.0837 q^{47} -5.21081 q^{48} -6.89494 q^{49} -26.4793 q^{50} -0.185874 q^{51} +30.6232 q^{52} -1.42941 q^{53} -4.47767 q^{54} -7.04945 q^{55} +3.60329 q^{56} -0.489168 q^{57} +17.3777 q^{58} +5.83870 q^{59} +6.04363 q^{60} +13.0099 q^{61} +7.67276 q^{62} +0.949122 q^{63} +52.9156 q^{64} -19.5462 q^{65} +1.40341 q^{66} -4.11044 q^{67} +4.12289 q^{68} -0.267983 q^{69} -3.46616 q^{70} -0.762409 q^{71} +32.5518 q^{72} -3.96717 q^{73} -6.92321 q^{74} -2.51762 q^{75} +10.8503 q^{76} -0.602250 q^{77} +3.89128 q^{78} +14.5022 q^{79} -73.7734 q^{80} +8.35882 q^{81} +1.66188 q^{82} +13.7861 q^{83} +0.516321 q^{84} -2.63156 q^{85} +1.91047 q^{86} +1.65224 q^{87} -20.6552 q^{88} +7.51916 q^{89} -31.3129 q^{90} -1.66988 q^{91} +5.94415 q^{92} +0.729516 q^{93} -31.2399 q^{94} -6.92552 q^{95} +8.72868 q^{96} +0.659690 q^{97} +19.4336 q^{98} -5.44067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81854 −1.99301 −0.996503 0.0835574i \(-0.973372\pi\)
−0.996503 + 0.0835574i \(0.973372\pi\)
\(3\) −0.267983 −0.154720 −0.0773600 0.997003i \(-0.524649\pi\)
−0.0773600 + 0.997003i \(0.524649\pi\)
\(4\) 5.94415 2.97207
\(5\) −3.79404 −1.69674 −0.848372 0.529400i \(-0.822417\pi\)
−0.848372 + 0.529400i \(0.822417\pi\)
\(6\) 0.755319 0.308358
\(7\) −0.324133 −0.122511 −0.0612554 0.998122i \(-0.519510\pi\)
−0.0612554 + 0.998122i \(0.519510\pi\)
\(8\) −11.1167 −3.93035
\(9\) −2.92819 −0.976062
\(10\) 10.6936 3.38162
\(11\) 1.85803 0.560218 0.280109 0.959968i \(-0.409629\pi\)
0.280109 + 0.959968i \(0.409629\pi\)
\(12\) −1.59293 −0.459839
\(13\) 5.15183 1.42886 0.714431 0.699706i \(-0.246686\pi\)
0.714431 + 0.699706i \(0.246686\pi\)
\(14\) 0.913581 0.244165
\(15\) 1.01674 0.262520
\(16\) 19.4446 4.86114
\(17\) 0.693605 0.168224 0.0841120 0.996456i \(-0.473195\pi\)
0.0841120 + 0.996456i \(0.473195\pi\)
\(18\) 8.25320 1.94530
\(19\) 1.82537 0.418769 0.209384 0.977833i \(-0.432854\pi\)
0.209384 + 0.977833i \(0.432854\pi\)
\(20\) −22.5523 −5.04285
\(21\) 0.0868621 0.0189549
\(22\) −5.23694 −1.11652
\(23\) 1.00000 0.208514
\(24\) 2.97909 0.608104
\(25\) 9.39471 1.87894
\(26\) −14.5206 −2.84773
\(27\) 1.58865 0.305736
\(28\) −1.92669 −0.364111
\(29\) −6.16549 −1.14490 −0.572451 0.819939i \(-0.694007\pi\)
−0.572451 + 0.819939i \(0.694007\pi\)
\(30\) −2.86571 −0.523204
\(31\) −2.72225 −0.488930 −0.244465 0.969658i \(-0.578612\pi\)
−0.244465 + 0.969658i \(0.578612\pi\)
\(32\) −32.5718 −5.75793
\(33\) −0.497921 −0.0866769
\(34\) −1.95495 −0.335271
\(35\) 1.22977 0.207869
\(36\) −17.4056 −2.90093
\(37\) 2.45632 0.403816 0.201908 0.979405i \(-0.435286\pi\)
0.201908 + 0.979405i \(0.435286\pi\)
\(38\) −5.14487 −0.834608
\(39\) −1.38060 −0.221073
\(40\) 42.1772 6.66880
\(41\) −0.589626 −0.0920842 −0.0460421 0.998940i \(-0.514661\pi\)
−0.0460421 + 0.998940i \(0.514661\pi\)
\(42\) −0.244824 −0.0377771
\(43\) −0.677822 −0.103367 −0.0516835 0.998664i \(-0.516459\pi\)
−0.0516835 + 0.998664i \(0.516459\pi\)
\(44\) 11.0444 1.66501
\(45\) 11.1096 1.65613
\(46\) −2.81854 −0.415570
\(47\) 11.0837 1.61673 0.808364 0.588683i \(-0.200353\pi\)
0.808364 + 0.588683i \(0.200353\pi\)
\(48\) −5.21081 −0.752116
\(49\) −6.89494 −0.984991
\(50\) −26.4793 −3.74474
\(51\) −0.185874 −0.0260276
\(52\) 30.6232 4.24668
\(53\) −1.42941 −0.196345 −0.0981726 0.995169i \(-0.531300\pi\)
−0.0981726 + 0.995169i \(0.531300\pi\)
\(54\) −4.47767 −0.609334
\(55\) −7.04945 −0.950547
\(56\) 3.60329 0.481510
\(57\) −0.489168 −0.0647919
\(58\) 17.3777 2.28180
\(59\) 5.83870 0.760134 0.380067 0.924959i \(-0.375901\pi\)
0.380067 + 0.924959i \(0.375901\pi\)
\(60\) 6.04363 0.780229
\(61\) 13.0099 1.66574 0.832872 0.553466i \(-0.186695\pi\)
0.832872 + 0.553466i \(0.186695\pi\)
\(62\) 7.67276 0.974441
\(63\) 0.949122 0.119578
\(64\) 52.9156 6.61445
\(65\) −19.5462 −2.42441
\(66\) 1.40341 0.172748
\(67\) −4.11044 −0.502171 −0.251085 0.967965i \(-0.580787\pi\)
−0.251085 + 0.967965i \(0.580787\pi\)
\(68\) 4.12289 0.499974
\(69\) −0.267983 −0.0322613
\(70\) −3.46616 −0.414285
\(71\) −0.762409 −0.0904814 −0.0452407 0.998976i \(-0.514405\pi\)
−0.0452407 + 0.998976i \(0.514405\pi\)
\(72\) 32.5518 3.83627
\(73\) −3.96717 −0.464322 −0.232161 0.972677i \(-0.574580\pi\)
−0.232161 + 0.972677i \(0.574580\pi\)
\(74\) −6.92321 −0.804807
\(75\) −2.51762 −0.290710
\(76\) 10.8503 1.24461
\(77\) −0.602250 −0.0686328
\(78\) 3.89128 0.440600
\(79\) 14.5022 1.63162 0.815812 0.578317i \(-0.196290\pi\)
0.815812 + 0.578317i \(0.196290\pi\)
\(80\) −73.7734 −8.24812
\(81\) 8.35882 0.928758
\(82\) 1.66188 0.183524
\(83\) 13.7861 1.51322 0.756608 0.653868i \(-0.226855\pi\)
0.756608 + 0.653868i \(0.226855\pi\)
\(84\) 0.516321 0.0563352
\(85\) −2.63156 −0.285433
\(86\) 1.91047 0.206011
\(87\) 1.65224 0.177139
\(88\) −20.6552 −2.20186
\(89\) 7.51916 0.797030 0.398515 0.917162i \(-0.369526\pi\)
0.398515 + 0.917162i \(0.369526\pi\)
\(90\) −31.3129 −3.30067
\(91\) −1.66988 −0.175051
\(92\) 5.94415 0.619720
\(93\) 0.729516 0.0756473
\(94\) −31.2399 −3.22215
\(95\) −6.92552 −0.710543
\(96\) 8.72868 0.890867
\(97\) 0.659690 0.0669814 0.0334907 0.999439i \(-0.489338\pi\)
0.0334907 + 0.999439i \(0.489338\pi\)
\(98\) 19.4336 1.96309
\(99\) −5.44067 −0.546808
\(100\) 55.8435 5.58435
\(101\) −5.69095 −0.566270 −0.283135 0.959080i \(-0.591375\pi\)
−0.283135 + 0.959080i \(0.591375\pi\)
\(102\) 0.523893 0.0518732
\(103\) −1.20101 −0.118339 −0.0591695 0.998248i \(-0.518845\pi\)
−0.0591695 + 0.998248i \(0.518845\pi\)
\(104\) −57.2715 −5.61593
\(105\) −0.329558 −0.0321615
\(106\) 4.02886 0.391317
\(107\) −5.55369 −0.536896 −0.268448 0.963294i \(-0.586511\pi\)
−0.268448 + 0.963294i \(0.586511\pi\)
\(108\) 9.44317 0.908670
\(109\) −5.86430 −0.561698 −0.280849 0.959752i \(-0.590616\pi\)
−0.280849 + 0.959752i \(0.590616\pi\)
\(110\) 19.8691 1.89445
\(111\) −0.658250 −0.0624783
\(112\) −6.30263 −0.595542
\(113\) −0.943382 −0.0887459 −0.0443729 0.999015i \(-0.514129\pi\)
−0.0443729 + 0.999015i \(0.514129\pi\)
\(114\) 1.37874 0.129131
\(115\) −3.79404 −0.353796
\(116\) −36.6486 −3.40273
\(117\) −15.0855 −1.39466
\(118\) −16.4566 −1.51495
\(119\) −0.224820 −0.0206092
\(120\) −11.3028 −1.03180
\(121\) −7.54771 −0.686155
\(122\) −36.6688 −3.31984
\(123\) 0.158010 0.0142473
\(124\) −16.1814 −1.45314
\(125\) −16.6737 −1.49134
\(126\) −2.67513 −0.238320
\(127\) −6.29139 −0.558270 −0.279135 0.960252i \(-0.590048\pi\)
−0.279135 + 0.960252i \(0.590048\pi\)
\(128\) −84.0010 −7.42471
\(129\) 0.181645 0.0159929
\(130\) 55.0918 4.83187
\(131\) 6.29335 0.549852 0.274926 0.961465i \(-0.411347\pi\)
0.274926 + 0.961465i \(0.411347\pi\)
\(132\) −2.95972 −0.257610
\(133\) −0.591663 −0.0513037
\(134\) 11.5854 1.00083
\(135\) −6.02740 −0.518756
\(136\) −7.71061 −0.661180
\(137\) 6.84600 0.584893 0.292446 0.956282i \(-0.405531\pi\)
0.292446 + 0.956282i \(0.405531\pi\)
\(138\) 0.755319 0.0642970
\(139\) −0.469084 −0.0397871 −0.0198936 0.999802i \(-0.506333\pi\)
−0.0198936 + 0.999802i \(0.506333\pi\)
\(140\) 7.30994 0.617803
\(141\) −2.97025 −0.250140
\(142\) 2.14888 0.180330
\(143\) 9.57228 0.800474
\(144\) −56.9373 −4.74478
\(145\) 23.3921 1.94261
\(146\) 11.1816 0.925397
\(147\) 1.84772 0.152398
\(148\) 14.6007 1.20017
\(149\) −18.0840 −1.48150 −0.740748 0.671783i \(-0.765529\pi\)
−0.740748 + 0.671783i \(0.765529\pi\)
\(150\) 7.09600 0.579386
\(151\) −4.47189 −0.363918 −0.181959 0.983306i \(-0.558244\pi\)
−0.181959 + 0.983306i \(0.558244\pi\)
\(152\) −20.2921 −1.64591
\(153\) −2.03100 −0.164197
\(154\) 1.69746 0.136786
\(155\) 10.3283 0.829590
\(156\) −8.20650 −0.657046
\(157\) −21.0337 −1.67867 −0.839336 0.543614i \(-0.817056\pi\)
−0.839336 + 0.543614i \(0.817056\pi\)
\(158\) −40.8750 −3.25184
\(159\) 0.383058 0.0303785
\(160\) 123.579 9.76974
\(161\) −0.324133 −0.0255453
\(162\) −23.5596 −1.85102
\(163\) −6.52007 −0.510692 −0.255346 0.966850i \(-0.582189\pi\)
−0.255346 + 0.966850i \(0.582189\pi\)
\(164\) −3.50483 −0.273681
\(165\) 1.88913 0.147069
\(166\) −38.8565 −3.01585
\(167\) 10.5852 0.819108 0.409554 0.912286i \(-0.365684\pi\)
0.409554 + 0.912286i \(0.365684\pi\)
\(168\) −0.965621 −0.0744993
\(169\) 13.5414 1.04165
\(170\) 7.41715 0.568870
\(171\) −5.34502 −0.408744
\(172\) −4.02907 −0.307214
\(173\) −23.9742 −1.82272 −0.911361 0.411608i \(-0.864967\pi\)
−0.911361 + 0.411608i \(0.864967\pi\)
\(174\) −4.65691 −0.353040
\(175\) −3.04513 −0.230191
\(176\) 36.1287 2.72330
\(177\) −1.56467 −0.117608
\(178\) −21.1930 −1.58848
\(179\) −7.46864 −0.558232 −0.279116 0.960257i \(-0.590041\pi\)
−0.279116 + 0.960257i \(0.590041\pi\)
\(180\) 66.0373 4.92213
\(181\) −5.56778 −0.413850 −0.206925 0.978357i \(-0.566346\pi\)
−0.206925 + 0.978357i \(0.566346\pi\)
\(182\) 4.70661 0.348878
\(183\) −3.48642 −0.257724
\(184\) −11.1167 −0.819535
\(185\) −9.31935 −0.685172
\(186\) −2.05617 −0.150765
\(187\) 1.28874 0.0942422
\(188\) 65.8833 4.80503
\(189\) −0.514934 −0.0374560
\(190\) 19.5198 1.41612
\(191\) −18.1693 −1.31469 −0.657343 0.753592i \(-0.728320\pi\)
−0.657343 + 0.753592i \(0.728320\pi\)
\(192\) −14.1805 −1.02339
\(193\) −0.703618 −0.0506475 −0.0253238 0.999679i \(-0.508062\pi\)
−0.0253238 + 0.999679i \(0.508062\pi\)
\(194\) −1.85936 −0.133494
\(195\) 5.23805 0.375105
\(196\) −40.9845 −2.92747
\(197\) 18.5015 1.31818 0.659090 0.752064i \(-0.270942\pi\)
0.659090 + 0.752064i \(0.270942\pi\)
\(198\) 15.3347 1.08979
\(199\) 2.09032 0.148179 0.0740893 0.997252i \(-0.476395\pi\)
0.0740893 + 0.997252i \(0.476395\pi\)
\(200\) −104.438 −7.38490
\(201\) 1.10153 0.0776958
\(202\) 16.0401 1.12858
\(203\) 1.99844 0.140263
\(204\) −1.10486 −0.0773559
\(205\) 2.23706 0.156243
\(206\) 3.38509 0.235850
\(207\) −2.92819 −0.203523
\(208\) 100.175 6.94590
\(209\) 3.39160 0.234602
\(210\) 0.928870 0.0640981
\(211\) −20.4856 −1.41028 −0.705142 0.709066i \(-0.749117\pi\)
−0.705142 + 0.709066i \(0.749117\pi\)
\(212\) −8.49665 −0.583552
\(213\) 0.204313 0.0139993
\(214\) 15.6533 1.07004
\(215\) 2.57168 0.175387
\(216\) −17.6606 −1.20165
\(217\) 0.882371 0.0598992
\(218\) 16.5287 1.11947
\(219\) 1.06313 0.0718399
\(220\) −41.9029 −2.82510
\(221\) 3.57334 0.240369
\(222\) 1.85530 0.124520
\(223\) 18.6326 1.24773 0.623864 0.781533i \(-0.285562\pi\)
0.623864 + 0.781533i \(0.285562\pi\)
\(224\) 10.5576 0.705409
\(225\) −27.5094 −1.83396
\(226\) 2.65896 0.176871
\(227\) 11.6564 0.773665 0.386832 0.922150i \(-0.373569\pi\)
0.386832 + 0.922150i \(0.373569\pi\)
\(228\) −2.90768 −0.192566
\(229\) 16.1122 1.06472 0.532362 0.846517i \(-0.321305\pi\)
0.532362 + 0.846517i \(0.321305\pi\)
\(230\) 10.6936 0.705117
\(231\) 0.161393 0.0106189
\(232\) 68.5400 4.49987
\(233\) 18.0067 1.17966 0.589830 0.807528i \(-0.299195\pi\)
0.589830 + 0.807528i \(0.299195\pi\)
\(234\) 42.5191 2.77956
\(235\) −42.0521 −2.74317
\(236\) 34.7061 2.25917
\(237\) −3.88634 −0.252445
\(238\) 0.633664 0.0410744
\(239\) −21.5384 −1.39320 −0.696602 0.717458i \(-0.745306\pi\)
−0.696602 + 0.717458i \(0.745306\pi\)
\(240\) 19.7700 1.27615
\(241\) −11.5565 −0.744422 −0.372211 0.928148i \(-0.621400\pi\)
−0.372211 + 0.928148i \(0.621400\pi\)
\(242\) 21.2735 1.36751
\(243\) −7.00597 −0.449433
\(244\) 77.3326 4.95071
\(245\) 26.1596 1.67128
\(246\) −0.445356 −0.0283949
\(247\) 9.40400 0.598362
\(248\) 30.2625 1.92167
\(249\) −3.69443 −0.234125
\(250\) 46.9954 2.97225
\(251\) −13.1944 −0.832825 −0.416412 0.909176i \(-0.636713\pi\)
−0.416412 + 0.909176i \(0.636713\pi\)
\(252\) 5.64172 0.355395
\(253\) 1.85803 0.116814
\(254\) 17.7325 1.11264
\(255\) 0.705213 0.0441622
\(256\) 130.929 8.18304
\(257\) 25.0317 1.56143 0.780717 0.624885i \(-0.214854\pi\)
0.780717 + 0.624885i \(0.214854\pi\)
\(258\) −0.511972 −0.0318740
\(259\) −0.796173 −0.0494718
\(260\) −116.186 −7.20553
\(261\) 18.0537 1.11750
\(262\) −17.7380 −1.09586
\(263\) −8.74632 −0.539321 −0.269660 0.962955i \(-0.586911\pi\)
−0.269660 + 0.962955i \(0.586911\pi\)
\(264\) 5.53525 0.340671
\(265\) 5.42325 0.333148
\(266\) 1.66762 0.102249
\(267\) −2.01501 −0.123316
\(268\) −24.4331 −1.49249
\(269\) 14.4746 0.882534 0.441267 0.897376i \(-0.354529\pi\)
0.441267 + 0.897376i \(0.354529\pi\)
\(270\) 16.9884 1.03388
\(271\) −27.4726 −1.66884 −0.834421 0.551128i \(-0.814198\pi\)
−0.834421 + 0.551128i \(0.814198\pi\)
\(272\) 13.4869 0.817761
\(273\) 0.447499 0.0270839
\(274\) −19.2957 −1.16570
\(275\) 17.4557 1.05262
\(276\) −1.59293 −0.0958830
\(277\) 6.00630 0.360884 0.180442 0.983586i \(-0.442247\pi\)
0.180442 + 0.983586i \(0.442247\pi\)
\(278\) 1.32213 0.0792960
\(279\) 7.97125 0.477226
\(280\) −13.6710 −0.817000
\(281\) −19.8236 −1.18257 −0.591287 0.806461i \(-0.701380\pi\)
−0.591287 + 0.806461i \(0.701380\pi\)
\(282\) 8.37175 0.498531
\(283\) −25.6160 −1.52271 −0.761357 0.648333i \(-0.775466\pi\)
−0.761357 + 0.648333i \(0.775466\pi\)
\(284\) −4.53187 −0.268917
\(285\) 1.85592 0.109935
\(286\) −26.9798 −1.59535
\(287\) 0.191117 0.0112813
\(288\) 95.3763 5.62010
\(289\) −16.5189 −0.971701
\(290\) −65.9314 −3.87163
\(291\) −0.176786 −0.0103634
\(292\) −23.5814 −1.38000
\(293\) 11.0535 0.645753 0.322876 0.946441i \(-0.395350\pi\)
0.322876 + 0.946441i \(0.395350\pi\)
\(294\) −5.20788 −0.303730
\(295\) −22.1522 −1.28975
\(296\) −27.3062 −1.58714
\(297\) 2.95177 0.171279
\(298\) 50.9703 2.95263
\(299\) 5.15183 0.297938
\(300\) −14.9651 −0.864010
\(301\) 0.219705 0.0126636
\(302\) 12.6042 0.725290
\(303\) 1.52508 0.0876133
\(304\) 35.4935 2.03569
\(305\) −49.3599 −2.82634
\(306\) 5.72446 0.327246
\(307\) 32.5870 1.85984 0.929920 0.367763i \(-0.119876\pi\)
0.929920 + 0.367763i \(0.119876\pi\)
\(308\) −3.57986 −0.203982
\(309\) 0.321850 0.0183094
\(310\) −29.1107 −1.65338
\(311\) −9.57836 −0.543139 −0.271570 0.962419i \(-0.587543\pi\)
−0.271570 + 0.962419i \(0.587543\pi\)
\(312\) 15.3478 0.868896
\(313\) −33.2840 −1.88132 −0.940662 0.339346i \(-0.889794\pi\)
−0.940662 + 0.339346i \(0.889794\pi\)
\(314\) 59.2842 3.34560
\(315\) −3.60100 −0.202893
\(316\) 86.2032 4.84931
\(317\) 0.529211 0.0297235 0.0148617 0.999890i \(-0.495269\pi\)
0.0148617 + 0.999890i \(0.495269\pi\)
\(318\) −1.07966 −0.0605446
\(319\) −11.4557 −0.641396
\(320\) −200.764 −11.2230
\(321\) 1.48829 0.0830684
\(322\) 0.913581 0.0509119
\(323\) 1.26609 0.0704469
\(324\) 49.6861 2.76034
\(325\) 48.4000 2.68475
\(326\) 18.3771 1.01781
\(327\) 1.57153 0.0869059
\(328\) 6.55471 0.361923
\(329\) −3.59260 −0.198067
\(330\) −5.32458 −0.293109
\(331\) 29.9481 1.64609 0.823047 0.567973i \(-0.192272\pi\)
0.823047 + 0.567973i \(0.192272\pi\)
\(332\) 81.9463 4.49739
\(333\) −7.19255 −0.394149
\(334\) −29.8348 −1.63249
\(335\) 15.5952 0.852055
\(336\) 1.68900 0.0921423
\(337\) 2.52615 0.137608 0.0688041 0.997630i \(-0.478082\pi\)
0.0688041 + 0.997630i \(0.478082\pi\)
\(338\) −38.1669 −2.07600
\(339\) 0.252810 0.0137308
\(340\) −15.6424 −0.848328
\(341\) −5.05803 −0.273908
\(342\) 15.0651 0.814629
\(343\) 4.50381 0.243183
\(344\) 7.53516 0.406268
\(345\) 1.01674 0.0547392
\(346\) 67.5720 3.63270
\(347\) −9.84212 −0.528353 −0.264176 0.964474i \(-0.585100\pi\)
−0.264176 + 0.964474i \(0.585100\pi\)
\(348\) 9.82118 0.526471
\(349\) −1.00000 −0.0535288
\(350\) 8.58282 0.458771
\(351\) 8.18447 0.436855
\(352\) −60.5195 −3.22570
\(353\) 6.68229 0.355662 0.177831 0.984061i \(-0.443092\pi\)
0.177831 + 0.984061i \(0.443092\pi\)
\(354\) 4.41008 0.234393
\(355\) 2.89261 0.153524
\(356\) 44.6950 2.36883
\(357\) 0.0602480 0.00318866
\(358\) 21.0506 1.11256
\(359\) 3.13552 0.165486 0.0827431 0.996571i \(-0.473632\pi\)
0.0827431 + 0.996571i \(0.473632\pi\)
\(360\) −123.503 −6.50916
\(361\) −15.6680 −0.824633
\(362\) 15.6930 0.824806
\(363\) 2.02266 0.106162
\(364\) −9.92601 −0.520264
\(365\) 15.0516 0.787836
\(366\) 9.82660 0.513645
\(367\) 23.2393 1.21308 0.606541 0.795052i \(-0.292556\pi\)
0.606541 + 0.795052i \(0.292556\pi\)
\(368\) 19.4446 1.01362
\(369\) 1.72654 0.0898798
\(370\) 26.2669 1.36555
\(371\) 0.463321 0.0240544
\(372\) 4.33635 0.224829
\(373\) 33.0523 1.71138 0.855691 0.517488i \(-0.173133\pi\)
0.855691 + 0.517488i \(0.173133\pi\)
\(374\) −3.63237 −0.187825
\(375\) 4.46826 0.230740
\(376\) −123.215 −6.35431
\(377\) −31.7636 −1.63591
\(378\) 1.45136 0.0746500
\(379\) 21.0593 1.08175 0.540873 0.841105i \(-0.318094\pi\)
0.540873 + 0.841105i \(0.318094\pi\)
\(380\) −41.1663 −2.11179
\(381\) 1.68598 0.0863756
\(382\) 51.2109 2.62018
\(383\) −19.3439 −0.988429 −0.494214 0.869340i \(-0.664544\pi\)
−0.494214 + 0.869340i \(0.664544\pi\)
\(384\) 22.5108 1.14875
\(385\) 2.28496 0.116452
\(386\) 1.98317 0.100941
\(387\) 1.98479 0.100892
\(388\) 3.92130 0.199074
\(389\) −21.0726 −1.06842 −0.534211 0.845351i \(-0.679391\pi\)
−0.534211 + 0.845351i \(0.679391\pi\)
\(390\) −14.7636 −0.747586
\(391\) 0.693605 0.0350771
\(392\) 76.6491 3.87136
\(393\) −1.68651 −0.0850731
\(394\) −52.1472 −2.62714
\(395\) −55.0218 −2.76845
\(396\) −32.3401 −1.62515
\(397\) 4.08912 0.205227 0.102614 0.994721i \(-0.467279\pi\)
0.102614 + 0.994721i \(0.467279\pi\)
\(398\) −5.89163 −0.295321
\(399\) 0.158555 0.00793770
\(400\) 182.676 9.13380
\(401\) 24.8241 1.23966 0.619828 0.784738i \(-0.287202\pi\)
0.619828 + 0.784738i \(0.287202\pi\)
\(402\) −3.10470 −0.154848
\(403\) −14.0246 −0.698614
\(404\) −33.8278 −1.68300
\(405\) −31.7137 −1.57587
\(406\) −5.63267 −0.279545
\(407\) 4.56392 0.226225
\(408\) 2.06631 0.102298
\(409\) −32.6092 −1.61242 −0.806210 0.591630i \(-0.798485\pi\)
−0.806210 + 0.591630i \(0.798485\pi\)
\(410\) −6.30524 −0.311394
\(411\) −1.83461 −0.0904946
\(412\) −7.13897 −0.351712
\(413\) −1.89252 −0.0931247
\(414\) 8.25320 0.405622
\(415\) −52.3048 −2.56754
\(416\) −167.804 −8.22729
\(417\) 0.125706 0.00615586
\(418\) −9.55935 −0.467563
\(419\) 16.7037 0.816027 0.408014 0.912976i \(-0.366222\pi\)
0.408014 + 0.912976i \(0.366222\pi\)
\(420\) −1.95894 −0.0955864
\(421\) 5.53715 0.269864 0.134932 0.990855i \(-0.456918\pi\)
0.134932 + 0.990855i \(0.456918\pi\)
\(422\) 57.7393 2.81071
\(423\) −32.4552 −1.57803
\(424\) 15.8904 0.771706
\(425\) 6.51622 0.316083
\(426\) −0.575862 −0.0279006
\(427\) −4.21693 −0.204072
\(428\) −33.0119 −1.59569
\(429\) −2.56521 −0.123849
\(430\) −7.24838 −0.349548
\(431\) 25.0882 1.20845 0.604227 0.796812i \(-0.293482\pi\)
0.604227 + 0.796812i \(0.293482\pi\)
\(432\) 30.8906 1.48623
\(433\) −12.3063 −0.591401 −0.295700 0.955281i \(-0.595553\pi\)
−0.295700 + 0.955281i \(0.595553\pi\)
\(434\) −2.48699 −0.119380
\(435\) −6.26868 −0.300560
\(436\) −34.8582 −1.66941
\(437\) 1.82537 0.0873193
\(438\) −2.99648 −0.143177
\(439\) 15.5771 0.743456 0.371728 0.928342i \(-0.378765\pi\)
0.371728 + 0.928342i \(0.378765\pi\)
\(440\) 78.3667 3.73599
\(441\) 20.1897 0.961412
\(442\) −10.0716 −0.479056
\(443\) −6.67638 −0.317204 −0.158602 0.987343i \(-0.550699\pi\)
−0.158602 + 0.987343i \(0.550699\pi\)
\(444\) −3.91274 −0.185690
\(445\) −28.5280 −1.35236
\(446\) −52.5166 −2.48673
\(447\) 4.84619 0.229217
\(448\) −17.1517 −0.810342
\(449\) −34.4039 −1.62362 −0.811811 0.583920i \(-0.801518\pi\)
−0.811811 + 0.583920i \(0.801518\pi\)
\(450\) 77.5364 3.65510
\(451\) −1.09555 −0.0515872
\(452\) −5.60760 −0.263759
\(453\) 1.19839 0.0563053
\(454\) −32.8541 −1.54192
\(455\) 6.33558 0.297017
\(456\) 5.43794 0.254655
\(457\) 6.97757 0.326397 0.163199 0.986593i \(-0.447819\pi\)
0.163199 + 0.986593i \(0.447819\pi\)
\(458\) −45.4128 −2.12200
\(459\) 1.10190 0.0514321
\(460\) −22.5523 −1.05151
\(461\) 8.59245 0.400190 0.200095 0.979776i \(-0.435875\pi\)
0.200095 + 0.979776i \(0.435875\pi\)
\(462\) −0.454891 −0.0211634
\(463\) 17.5167 0.814068 0.407034 0.913413i \(-0.366563\pi\)
0.407034 + 0.913413i \(0.366563\pi\)
\(464\) −119.885 −5.56554
\(465\) −2.76781 −0.128354
\(466\) −50.7526 −2.35107
\(467\) 7.44382 0.344459 0.172229 0.985057i \(-0.444903\pi\)
0.172229 + 0.985057i \(0.444903\pi\)
\(468\) −89.6705 −4.14502
\(469\) 1.33233 0.0615213
\(470\) 118.525 5.46716
\(471\) 5.63667 0.259724
\(472\) −64.9072 −2.98760
\(473\) −1.25942 −0.0579080
\(474\) 10.9538 0.503124
\(475\) 17.1488 0.786842
\(476\) −1.33636 −0.0612522
\(477\) 4.18559 0.191645
\(478\) 60.7068 2.77666
\(479\) 35.7964 1.63558 0.817790 0.575516i \(-0.195199\pi\)
0.817790 + 0.575516i \(0.195199\pi\)
\(480\) −33.1169 −1.51157
\(481\) 12.6545 0.576997
\(482\) 32.5725 1.48364
\(483\) 0.0868621 0.00395236
\(484\) −44.8647 −2.03930
\(485\) −2.50289 −0.113650
\(486\) 19.7466 0.895724
\(487\) 33.0024 1.49548 0.747741 0.663990i \(-0.231138\pi\)
0.747741 + 0.663990i \(0.231138\pi\)
\(488\) −144.627 −6.54696
\(489\) 1.74727 0.0790142
\(490\) −73.7319 −3.33087
\(491\) 27.4658 1.23951 0.619756 0.784794i \(-0.287231\pi\)
0.619756 + 0.784794i \(0.287231\pi\)
\(492\) 0.939233 0.0423439
\(493\) −4.27642 −0.192600
\(494\) −26.5055 −1.19254
\(495\) 20.6421 0.927793
\(496\) −52.9330 −2.37676
\(497\) 0.247122 0.0110849
\(498\) 10.4129 0.466612
\(499\) −37.8760 −1.69556 −0.847782 0.530345i \(-0.822063\pi\)
−0.847782 + 0.530345i \(0.822063\pi\)
\(500\) −99.1107 −4.43237
\(501\) −2.83665 −0.126732
\(502\) 37.1890 1.65982
\(503\) 42.2944 1.88582 0.942908 0.333054i \(-0.108079\pi\)
0.942908 + 0.333054i \(0.108079\pi\)
\(504\) −10.5511 −0.469984
\(505\) 21.5917 0.960816
\(506\) −5.23694 −0.232810
\(507\) −3.62886 −0.161163
\(508\) −37.3969 −1.65922
\(509\) −17.8524 −0.791292 −0.395646 0.918403i \(-0.629479\pi\)
−0.395646 + 0.918403i \(0.629479\pi\)
\(510\) −1.98767 −0.0880155
\(511\) 1.28589 0.0568844
\(512\) −201.025 −8.88414
\(513\) 2.89988 0.128033
\(514\) −70.5527 −3.11195
\(515\) 4.55667 0.200791
\(516\) 1.07972 0.0475321
\(517\) 20.5940 0.905721
\(518\) 2.24404 0.0985976
\(519\) 6.42466 0.282011
\(520\) 217.290 9.52880
\(521\) −23.7181 −1.03911 −0.519554 0.854438i \(-0.673902\pi\)
−0.519554 + 0.854438i \(0.673902\pi\)
\(522\) −50.8850 −2.22718
\(523\) −1.14530 −0.0500803 −0.0250402 0.999686i \(-0.507971\pi\)
−0.0250402 + 0.999686i \(0.507971\pi\)
\(524\) 37.4086 1.63420
\(525\) 0.816044 0.0356151
\(526\) 24.6518 1.07487
\(527\) −1.88817 −0.0822498
\(528\) −9.68186 −0.421349
\(529\) 1.00000 0.0434783
\(530\) −15.2856 −0.663965
\(531\) −17.0968 −0.741938
\(532\) −3.51693 −0.152478
\(533\) −3.03766 −0.131576
\(534\) 5.67937 0.245770
\(535\) 21.0709 0.910975
\(536\) 45.6946 1.97371
\(537\) 2.00147 0.0863696
\(538\) −40.7973 −1.75890
\(539\) −12.8110 −0.551810
\(540\) −35.8277 −1.54178
\(541\) −3.93514 −0.169185 −0.0845924 0.996416i \(-0.526959\pi\)
−0.0845924 + 0.996416i \(0.526959\pi\)
\(542\) 77.4325 3.32601
\(543\) 1.49207 0.0640308
\(544\) −22.5920 −0.968623
\(545\) 22.2494 0.953058
\(546\) −1.26129 −0.0539783
\(547\) −9.28526 −0.397009 −0.198504 0.980100i \(-0.563608\pi\)
−0.198504 + 0.980100i \(0.563608\pi\)
\(548\) 40.6936 1.73834
\(549\) −38.0953 −1.62587
\(550\) −49.1995 −2.09787
\(551\) −11.2543 −0.479449
\(552\) 2.97909 0.126798
\(553\) −4.70064 −0.199892
\(554\) −16.9290 −0.719243
\(555\) 2.49742 0.106010
\(556\) −2.78830 −0.118250
\(557\) 25.1594 1.06604 0.533020 0.846103i \(-0.321057\pi\)
0.533020 + 0.846103i \(0.321057\pi\)
\(558\) −22.4673 −0.951115
\(559\) −3.49203 −0.147697
\(560\) 23.9124 1.01048
\(561\) −0.345361 −0.0145811
\(562\) 55.8734 2.35688
\(563\) 38.3463 1.61610 0.808052 0.589111i \(-0.200522\pi\)
0.808052 + 0.589111i \(0.200522\pi\)
\(564\) −17.6556 −0.743434
\(565\) 3.57922 0.150579
\(566\) 72.1996 3.03478
\(567\) −2.70937 −0.113783
\(568\) 8.47549 0.355624
\(569\) 40.5380 1.69944 0.849721 0.527232i \(-0.176770\pi\)
0.849721 + 0.527232i \(0.176770\pi\)
\(570\) −5.23098 −0.219102
\(571\) 21.8284 0.913491 0.456746 0.889597i \(-0.349015\pi\)
0.456746 + 0.889597i \(0.349015\pi\)
\(572\) 56.8990 2.37907
\(573\) 4.86906 0.203408
\(574\) −0.538671 −0.0224837
\(575\) 9.39471 0.391786
\(576\) −154.947 −6.45612
\(577\) 3.31806 0.138133 0.0690663 0.997612i \(-0.477998\pi\)
0.0690663 + 0.997612i \(0.477998\pi\)
\(578\) 46.5591 1.93661
\(579\) 0.188557 0.00783618
\(580\) 139.046 5.77357
\(581\) −4.46852 −0.185385
\(582\) 0.498277 0.0206542
\(583\) −2.65590 −0.109996
\(584\) 44.1019 1.82495
\(585\) 57.2350 2.36638
\(586\) −31.1547 −1.28699
\(587\) 37.1140 1.53186 0.765929 0.642926i \(-0.222280\pi\)
0.765929 + 0.642926i \(0.222280\pi\)
\(588\) 10.9831 0.452937
\(589\) −4.96911 −0.204749
\(590\) 62.4369 2.57049
\(591\) −4.95809 −0.203949
\(592\) 47.7620 1.96301
\(593\) −2.21354 −0.0908992 −0.0454496 0.998967i \(-0.514472\pi\)
−0.0454496 + 0.998967i \(0.514472\pi\)
\(594\) −8.31967 −0.341360
\(595\) 0.852976 0.0349686
\(596\) −107.494 −4.40311
\(597\) −0.560169 −0.0229262
\(598\) −14.5206 −0.593793
\(599\) 33.6880 1.37645 0.688227 0.725495i \(-0.258389\pi\)
0.688227 + 0.725495i \(0.258389\pi\)
\(600\) 27.9877 1.14259
\(601\) 26.8841 1.09663 0.548313 0.836273i \(-0.315270\pi\)
0.548313 + 0.836273i \(0.315270\pi\)
\(602\) −0.619245 −0.0252386
\(603\) 12.0361 0.490150
\(604\) −26.5816 −1.08159
\(605\) 28.6363 1.16423
\(606\) −4.29848 −0.174614
\(607\) −18.9227 −0.768047 −0.384023 0.923323i \(-0.625462\pi\)
−0.384023 + 0.923323i \(0.625462\pi\)
\(608\) −59.4556 −2.41124
\(609\) −0.535547 −0.0217015
\(610\) 139.123 5.63291
\(611\) 57.1015 2.31008
\(612\) −12.0726 −0.488005
\(613\) −16.1660 −0.652938 −0.326469 0.945208i \(-0.605859\pi\)
−0.326469 + 0.945208i \(0.605859\pi\)
\(614\) −91.8477 −3.70667
\(615\) −0.599494 −0.0241740
\(616\) 6.69504 0.269751
\(617\) 14.9047 0.600042 0.300021 0.953933i \(-0.403006\pi\)
0.300021 + 0.953933i \(0.403006\pi\)
\(618\) −0.907145 −0.0364907
\(619\) 7.58313 0.304792 0.152396 0.988320i \(-0.451301\pi\)
0.152396 + 0.988320i \(0.451301\pi\)
\(620\) 61.3930 2.46560
\(621\) 1.58865 0.0637504
\(622\) 26.9970 1.08248
\(623\) −2.43721 −0.0976447
\(624\) −26.8452 −1.07467
\(625\) 16.2870 0.651479
\(626\) 93.8122 3.74949
\(627\) −0.908890 −0.0362976
\(628\) −125.027 −4.98913
\(629\) 1.70371 0.0679315
\(630\) 10.1496 0.404368
\(631\) −26.7709 −1.06573 −0.532865 0.846200i \(-0.678885\pi\)
−0.532865 + 0.846200i \(0.678885\pi\)
\(632\) −161.217 −6.41286
\(633\) 5.48978 0.218199
\(634\) −1.49160 −0.0592390
\(635\) 23.8698 0.947242
\(636\) 2.27696 0.0902871
\(637\) −35.5216 −1.40742
\(638\) 32.2883 1.27831
\(639\) 2.23248 0.0883154
\(640\) 318.703 12.5978
\(641\) −29.3579 −1.15957 −0.579784 0.814770i \(-0.696863\pi\)
−0.579784 + 0.814770i \(0.696863\pi\)
\(642\) −4.19481 −0.165556
\(643\) 36.6279 1.44446 0.722232 0.691651i \(-0.243116\pi\)
0.722232 + 0.691651i \(0.243116\pi\)
\(644\) −1.92669 −0.0759224
\(645\) −0.689166 −0.0271359
\(646\) −3.56851 −0.140401
\(647\) −1.55802 −0.0612522 −0.0306261 0.999531i \(-0.509750\pi\)
−0.0306261 + 0.999531i \(0.509750\pi\)
\(648\) −92.9227 −3.65035
\(649\) 10.8485 0.425841
\(650\) −136.417 −5.35072
\(651\) −0.236460 −0.00926760
\(652\) −38.7563 −1.51781
\(653\) 10.9090 0.426902 0.213451 0.976954i \(-0.431530\pi\)
0.213451 + 0.976954i \(0.431530\pi\)
\(654\) −4.42942 −0.173204
\(655\) −23.8772 −0.932959
\(656\) −11.4650 −0.447634
\(657\) 11.6166 0.453207
\(658\) 10.1259 0.394748
\(659\) −13.7070 −0.533949 −0.266974 0.963704i \(-0.586024\pi\)
−0.266974 + 0.963704i \(0.586024\pi\)
\(660\) 11.2293 0.437099
\(661\) −8.52238 −0.331482 −0.165741 0.986169i \(-0.553002\pi\)
−0.165741 + 0.986169i \(0.553002\pi\)
\(662\) −84.4097 −3.28068
\(663\) −0.957593 −0.0371898
\(664\) −153.256 −5.94747
\(665\) 2.24479 0.0870492
\(666\) 20.2725 0.785542
\(667\) −6.16549 −0.238729
\(668\) 62.9200 2.43445
\(669\) −4.99321 −0.193048
\(670\) −43.9556 −1.69815
\(671\) 24.1728 0.933180
\(672\) −2.82925 −0.109141
\(673\) 50.4719 1.94555 0.972774 0.231754i \(-0.0744464\pi\)
0.972774 + 0.231754i \(0.0744464\pi\)
\(674\) −7.12004 −0.274254
\(675\) 14.9249 0.574460
\(676\) 80.4920 3.09584
\(677\) 5.86499 0.225410 0.112705 0.993628i \(-0.464049\pi\)
0.112705 + 0.993628i \(0.464049\pi\)
\(678\) −0.712554 −0.0273655
\(679\) −0.213827 −0.00820594
\(680\) 29.2543 1.12185
\(681\) −3.12372 −0.119701
\(682\) 14.2562 0.545900
\(683\) 31.9577 1.22283 0.611414 0.791311i \(-0.290601\pi\)
0.611414 + 0.791311i \(0.290601\pi\)
\(684\) −31.7716 −1.21482
\(685\) −25.9740 −0.992414
\(686\) −12.6941 −0.484665
\(687\) −4.31779 −0.164734
\(688\) −13.1800 −0.502481
\(689\) −7.36411 −0.280550
\(690\) −2.86571 −0.109096
\(691\) 0.550965 0.0209597 0.0104799 0.999945i \(-0.496664\pi\)
0.0104799 + 0.999945i \(0.496664\pi\)
\(692\) −142.506 −5.41726
\(693\) 1.76350 0.0669898
\(694\) 27.7404 1.05301
\(695\) 1.77972 0.0675086
\(696\) −18.3675 −0.696220
\(697\) −0.408968 −0.0154908
\(698\) 2.81854 0.106683
\(699\) −4.82549 −0.182517
\(700\) −18.1007 −0.684143
\(701\) −34.8659 −1.31687 −0.658434 0.752639i \(-0.728781\pi\)
−0.658434 + 0.752639i \(0.728781\pi\)
\(702\) −23.0682 −0.870654
\(703\) 4.48369 0.169105
\(704\) 98.3191 3.70554
\(705\) 11.2692 0.424424
\(706\) −18.8343 −0.708837
\(707\) 1.84462 0.0693742
\(708\) −9.30064 −0.349539
\(709\) −22.6223 −0.849597 −0.424798 0.905288i \(-0.639655\pi\)
−0.424798 + 0.905288i \(0.639655\pi\)
\(710\) −8.15292 −0.305974
\(711\) −42.4651 −1.59257
\(712\) −83.5884 −3.13261
\(713\) −2.72225 −0.101949
\(714\) −0.169811 −0.00635502
\(715\) −36.3176 −1.35820
\(716\) −44.3947 −1.65911
\(717\) 5.77192 0.215556
\(718\) −8.83756 −0.329815
\(719\) 32.7072 1.21977 0.609887 0.792489i \(-0.291215\pi\)
0.609887 + 0.792489i \(0.291215\pi\)
\(720\) 216.022 8.05067
\(721\) 0.389287 0.0144978
\(722\) 44.1609 1.64350
\(723\) 3.09695 0.115177
\(724\) −33.0957 −1.22999
\(725\) −57.9230 −2.15121
\(726\) −5.70093 −0.211581
\(727\) 21.6151 0.801659 0.400830 0.916153i \(-0.368722\pi\)
0.400830 + 0.916153i \(0.368722\pi\)
\(728\) 18.5636 0.688012
\(729\) −23.1990 −0.859222
\(730\) −42.4234 −1.57016
\(731\) −0.470141 −0.0173888
\(732\) −20.7238 −0.765974
\(733\) 7.34628 0.271341 0.135670 0.990754i \(-0.456681\pi\)
0.135670 + 0.990754i \(0.456681\pi\)
\(734\) −65.5009 −2.41768
\(735\) −7.01033 −0.258580
\(736\) −32.5718 −1.20061
\(737\) −7.63735 −0.281325
\(738\) −4.86630 −0.179131
\(739\) 6.53886 0.240536 0.120268 0.992741i \(-0.461625\pi\)
0.120268 + 0.992741i \(0.461625\pi\)
\(740\) −55.3956 −2.03638
\(741\) −2.52011 −0.0925786
\(742\) −1.30589 −0.0479406
\(743\) −13.3405 −0.489416 −0.244708 0.969597i \(-0.578692\pi\)
−0.244708 + 0.969597i \(0.578692\pi\)
\(744\) −8.10982 −0.297320
\(745\) 68.6112 2.51372
\(746\) −93.1590 −3.41079
\(747\) −40.3681 −1.47699
\(748\) 7.66047 0.280095
\(749\) 1.80013 0.0657755
\(750\) −12.5939 −0.459866
\(751\) −12.4598 −0.454664 −0.227332 0.973817i \(-0.573000\pi\)
−0.227332 + 0.973817i \(0.573000\pi\)
\(752\) 215.518 7.85915
\(753\) 3.53588 0.128855
\(754\) 89.5268 3.26037
\(755\) 16.9665 0.617475
\(756\) −3.06084 −0.111322
\(757\) 14.5537 0.528965 0.264482 0.964391i \(-0.414799\pi\)
0.264482 + 0.964391i \(0.414799\pi\)
\(758\) −59.3565 −2.15592
\(759\) −0.497921 −0.0180734
\(760\) 76.9890 2.79269
\(761\) 21.6147 0.783532 0.391766 0.920065i \(-0.371864\pi\)
0.391766 + 0.920065i \(0.371864\pi\)
\(762\) −4.75201 −0.172147
\(763\) 1.90081 0.0688141
\(764\) −108.001 −3.90734
\(765\) 7.70570 0.278600
\(766\) 54.5216 1.96994
\(767\) 30.0800 1.08613
\(768\) −35.0866 −1.26608
\(769\) 17.7367 0.639603 0.319801 0.947485i \(-0.396384\pi\)
0.319801 + 0.947485i \(0.396384\pi\)
\(770\) −6.44024 −0.232090
\(771\) −6.70806 −0.241585
\(772\) −4.18241 −0.150528
\(773\) −48.9806 −1.76171 −0.880856 0.473385i \(-0.843032\pi\)
−0.880856 + 0.473385i \(0.843032\pi\)
\(774\) −5.59420 −0.201079
\(775\) −25.5747 −0.918671
\(776\) −7.33359 −0.263261
\(777\) 0.213361 0.00765427
\(778\) 59.3938 2.12937
\(779\) −1.07629 −0.0385620
\(780\) 31.1358 1.11484
\(781\) −1.41658 −0.0506893
\(782\) −1.95495 −0.0699089
\(783\) −9.79481 −0.350038
\(784\) −134.069 −4.78818
\(785\) 79.8026 2.84828
\(786\) 4.75348 0.169551
\(787\) −22.6953 −0.809001 −0.404501 0.914538i \(-0.632555\pi\)
−0.404501 + 0.914538i \(0.632555\pi\)
\(788\) 109.976 3.91773
\(789\) 2.34386 0.0834437
\(790\) 155.081 5.51754
\(791\) 0.305781 0.0108723
\(792\) 60.4824 2.14915
\(793\) 67.0247 2.38012
\(794\) −11.5253 −0.409019
\(795\) −1.45334 −0.0515446
\(796\) 12.4251 0.440397
\(797\) −20.2681 −0.717935 −0.358967 0.933350i \(-0.616871\pi\)
−0.358967 + 0.933350i \(0.616871\pi\)
\(798\) −0.446894 −0.0158199
\(799\) 7.68773 0.271972
\(800\) −306.002 −10.8188
\(801\) −22.0175 −0.777950
\(802\) −69.9676 −2.47064
\(803\) −7.37114 −0.260122
\(804\) 6.54764 0.230918
\(805\) 1.22977 0.0433438
\(806\) 39.5288 1.39234
\(807\) −3.87895 −0.136546
\(808\) 63.2646 2.22564
\(809\) −25.0165 −0.879534 −0.439767 0.898112i \(-0.644939\pi\)
−0.439767 + 0.898112i \(0.644939\pi\)
\(810\) 89.3861 3.14071
\(811\) 30.3600 1.06608 0.533041 0.846089i \(-0.321049\pi\)
0.533041 + 0.846089i \(0.321049\pi\)
\(812\) 11.8790 0.416872
\(813\) 7.36218 0.258203
\(814\) −12.8636 −0.450868
\(815\) 24.7374 0.866513
\(816\) −3.61424 −0.126524
\(817\) −1.23728 −0.0432868
\(818\) 91.9101 3.21356
\(819\) 4.88972 0.170860
\(820\) 13.2974 0.464366
\(821\) −29.1515 −1.01739 −0.508697 0.860945i \(-0.669873\pi\)
−0.508697 + 0.860945i \(0.669873\pi\)
\(822\) 5.17091 0.180356
\(823\) −6.30843 −0.219898 −0.109949 0.993937i \(-0.535069\pi\)
−0.109949 + 0.993937i \(0.535069\pi\)
\(824\) 13.3513 0.465114
\(825\) −4.67782 −0.162861
\(826\) 5.33413 0.185598
\(827\) −40.3336 −1.40254 −0.701269 0.712897i \(-0.747383\pi\)
−0.701269 + 0.712897i \(0.747383\pi\)
\(828\) −17.4056 −0.604885
\(829\) 2.83129 0.0983347 0.0491673 0.998791i \(-0.484343\pi\)
0.0491673 + 0.998791i \(0.484343\pi\)
\(830\) 147.423 5.11713
\(831\) −1.60958 −0.0558359
\(832\) 272.613 9.45114
\(833\) −4.78236 −0.165699
\(834\) −0.354308 −0.0122687
\(835\) −40.1607 −1.38982
\(836\) 20.1602 0.697254
\(837\) −4.32470 −0.149484
\(838\) −47.0799 −1.62635
\(839\) 42.8674 1.47995 0.739973 0.672637i \(-0.234838\pi\)
0.739973 + 0.672637i \(0.234838\pi\)
\(840\) 3.66360 0.126406
\(841\) 9.01327 0.310802
\(842\) −15.6067 −0.537841
\(843\) 5.31237 0.182968
\(844\) −121.769 −4.19147
\(845\) −51.3765 −1.76741
\(846\) 91.4762 3.14502
\(847\) 2.44646 0.0840614
\(848\) −27.7944 −0.954462
\(849\) 6.86465 0.235594
\(850\) −18.3662 −0.629955
\(851\) 2.45632 0.0842014
\(852\) 1.21446 0.0416068
\(853\) 35.7999 1.22577 0.612883 0.790174i \(-0.290010\pi\)
0.612883 + 0.790174i \(0.290010\pi\)
\(854\) 11.8856 0.406716
\(855\) 20.2792 0.693534
\(856\) 61.7388 2.11019
\(857\) −13.7457 −0.469543 −0.234772 0.972051i \(-0.575434\pi\)
−0.234772 + 0.972051i \(0.575434\pi\)
\(858\) 7.23013 0.246832
\(859\) −28.2863 −0.965118 −0.482559 0.875864i \(-0.660293\pi\)
−0.482559 + 0.875864i \(0.660293\pi\)
\(860\) 15.2865 0.521264
\(861\) −0.0512162 −0.00174544
\(862\) −70.7119 −2.40846
\(863\) 37.7777 1.28597 0.642983 0.765880i \(-0.277696\pi\)
0.642983 + 0.765880i \(0.277696\pi\)
\(864\) −51.7452 −1.76041
\(865\) 90.9588 3.09269
\(866\) 34.6856 1.17867
\(867\) 4.42678 0.150341
\(868\) 5.24494 0.178025
\(869\) 26.9456 0.914066
\(870\) 17.6685 0.599018
\(871\) −21.1763 −0.717532
\(872\) 65.1918 2.20767
\(873\) −1.93170 −0.0653780
\(874\) −5.14487 −0.174028
\(875\) 5.40449 0.182705
\(876\) 6.31942 0.213513
\(877\) 27.0297 0.912729 0.456365 0.889793i \(-0.349151\pi\)
0.456365 + 0.889793i \(0.349151\pi\)
\(878\) −43.9047 −1.48171
\(879\) −2.96215 −0.0999108
\(880\) −137.073 −4.62075
\(881\) −5.56956 −0.187643 −0.0938215 0.995589i \(-0.529908\pi\)
−0.0938215 + 0.995589i \(0.529908\pi\)
\(882\) −56.9053 −1.91610
\(883\) −20.4513 −0.688241 −0.344121 0.938925i \(-0.611823\pi\)
−0.344121 + 0.938925i \(0.611823\pi\)
\(884\) 21.2404 0.714393
\(885\) 5.93642 0.199551
\(886\) 18.8176 0.632190
\(887\) 49.0006 1.64528 0.822639 0.568564i \(-0.192501\pi\)
0.822639 + 0.568564i \(0.192501\pi\)
\(888\) 7.31758 0.245562
\(889\) 2.03925 0.0683941
\(890\) 80.4071 2.69525
\(891\) 15.5310 0.520307
\(892\) 110.755 3.70834
\(893\) 20.2319 0.677035
\(894\) −13.6592 −0.456831
\(895\) 28.3363 0.947177
\(896\) 27.2275 0.909607
\(897\) −1.38060 −0.0460970
\(898\) 96.9687 3.23589
\(899\) 16.7840 0.559778
\(900\) −163.520 −5.45067
\(901\) −0.991449 −0.0330300
\(902\) 3.08784 0.102814
\(903\) −0.0588770 −0.00195930
\(904\) 10.4873 0.348803
\(905\) 21.1244 0.702198
\(906\) −3.37771 −0.112217
\(907\) 32.0713 1.06491 0.532454 0.846459i \(-0.321270\pi\)
0.532454 + 0.846459i \(0.321270\pi\)
\(908\) 69.2875 2.29939
\(909\) 16.6641 0.552715
\(910\) −17.8571 −0.591956
\(911\) 8.18820 0.271287 0.135644 0.990758i \(-0.456690\pi\)
0.135644 + 0.990758i \(0.456690\pi\)
\(912\) −9.51166 −0.314962
\(913\) 25.6150 0.847732
\(914\) −19.6665 −0.650511
\(915\) 13.2276 0.437291
\(916\) 95.7732 3.16443
\(917\) −2.03988 −0.0673628
\(918\) −3.10574 −0.102505
\(919\) 18.5535 0.612025 0.306012 0.952028i \(-0.401005\pi\)
0.306012 + 0.952028i \(0.401005\pi\)
\(920\) 42.1772 1.39054
\(921\) −8.73276 −0.287754
\(922\) −24.2181 −0.797582
\(923\) −3.92781 −0.129285
\(924\) 0.959341 0.0315600
\(925\) 23.0764 0.758746
\(926\) −49.3713 −1.62244
\(927\) 3.51678 0.115506
\(928\) 200.821 6.59228
\(929\) 17.3367 0.568797 0.284399 0.958706i \(-0.408206\pi\)
0.284399 + 0.958706i \(0.408206\pi\)
\(930\) 7.80117 0.255810
\(931\) −12.5858 −0.412483
\(932\) 107.035 3.50603
\(933\) 2.56684 0.0840345
\(934\) −20.9807 −0.686508
\(935\) −4.88953 −0.159905
\(936\) 167.701 5.48149
\(937\) 50.4371 1.64771 0.823855 0.566801i \(-0.191819\pi\)
0.823855 + 0.566801i \(0.191819\pi\)
\(938\) −3.75522 −0.122612
\(939\) 8.91954 0.291078
\(940\) −249.964 −8.15292
\(941\) 14.9229 0.486471 0.243236 0.969967i \(-0.421791\pi\)
0.243236 + 0.969967i \(0.421791\pi\)
\(942\) −15.8871 −0.517631
\(943\) −0.589626 −0.0192009
\(944\) 113.531 3.69512
\(945\) 1.95368 0.0635532
\(946\) 3.54971 0.115411
\(947\) 7.22419 0.234755 0.117377 0.993087i \(-0.462551\pi\)
0.117377 + 0.993087i \(0.462551\pi\)
\(948\) −23.1010 −0.750284
\(949\) −20.4382 −0.663452
\(950\) −48.3346 −1.56818
\(951\) −0.141819 −0.00459881
\(952\) 2.49926 0.0810016
\(953\) −49.1250 −1.59132 −0.795658 0.605747i \(-0.792875\pi\)
−0.795658 + 0.605747i \(0.792875\pi\)
\(954\) −11.7972 −0.381950
\(955\) 68.9350 2.23069
\(956\) −128.027 −4.14071
\(957\) 3.06993 0.0992367
\(958\) −100.894 −3.25972
\(959\) −2.21901 −0.0716557
\(960\) 53.8012 1.73643
\(961\) −23.5894 −0.760947
\(962\) −35.6672 −1.14996
\(963\) 16.2622 0.524043
\(964\) −68.6937 −2.21247
\(965\) 2.66955 0.0859359
\(966\) −0.244824 −0.00787708
\(967\) 34.3913 1.10595 0.552975 0.833198i \(-0.313492\pi\)
0.552975 + 0.833198i \(0.313492\pi\)
\(968\) 83.9057 2.69683
\(969\) −0.339289 −0.0108995
\(970\) 7.05448 0.226506
\(971\) 23.1930 0.744298 0.372149 0.928173i \(-0.378621\pi\)
0.372149 + 0.928173i \(0.378621\pi\)
\(972\) −41.6445 −1.33575
\(973\) 0.152045 0.00487435
\(974\) −93.0185 −2.98051
\(975\) −12.9704 −0.415384
\(976\) 252.971 8.09742
\(977\) 20.7243 0.663028 0.331514 0.943450i \(-0.392441\pi\)
0.331514 + 0.943450i \(0.392441\pi\)
\(978\) −4.92474 −0.157476
\(979\) 13.9709 0.446511
\(980\) 155.497 4.96716
\(981\) 17.1718 0.548252
\(982\) −77.4132 −2.47036
\(983\) 15.1307 0.482593 0.241297 0.970451i \(-0.422427\pi\)
0.241297 + 0.970451i \(0.422427\pi\)
\(984\) −1.75655 −0.0559967
\(985\) −70.1955 −2.23661
\(986\) 12.0532 0.383853
\(987\) 0.962756 0.0306449
\(988\) 55.8988 1.77838
\(989\) −0.677822 −0.0215535
\(990\) −58.1805 −1.84910
\(991\) −40.9248 −1.30002 −0.650010 0.759926i \(-0.725235\pi\)
−0.650010 + 0.759926i \(0.725235\pi\)
\(992\) 88.6685 2.81523
\(993\) −8.02556 −0.254684
\(994\) −0.696523 −0.0220924
\(995\) −7.93073 −0.251421
\(996\) −21.9602 −0.695836
\(997\) 15.9243 0.504329 0.252165 0.967684i \(-0.418858\pi\)
0.252165 + 0.967684i \(0.418858\pi\)
\(998\) 106.755 3.37927
\(999\) 3.90223 0.123461
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 \(a_p\))