Properties

Label 8027.2.a.f.1.4
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 1.4
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} +O(q^{10})\) \(q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} -10.0514 q^{10} -2.24646 q^{11} +16.7590 q^{12} +0.738634 q^{13} +8.36221 q^{14} +11.1755 q^{15} +15.2760 q^{16} +0.0553671 q^{17} -17.1882 q^{18} +0.775812 q^{19} +20.1930 q^{20} -9.29747 q^{21} +6.15336 q^{22} +1.00000 q^{23} -29.2212 q^{24} +8.46546 q^{25} -2.02322 q^{26} +9.97411 q^{27} -16.7995 q^{28} -3.19125 q^{29} -30.6113 q^{30} -7.96425 q^{31} -22.6532 q^{32} -6.84157 q^{33} -0.151658 q^{34} -11.2026 q^{35} +34.5308 q^{36} +8.51519 q^{37} -2.12506 q^{38} +2.24951 q^{39} -35.2087 q^{40} +10.8407 q^{41} +25.4671 q^{42} -5.13365 q^{43} -12.3620 q^{44} +23.0264 q^{45} -2.73914 q^{46} +10.2451 q^{47} +46.5229 q^{48} +2.31996 q^{49} -23.1881 q^{50} +0.168620 q^{51} +4.06462 q^{52} -7.81563 q^{53} -27.3205 q^{54} -8.24344 q^{55} +29.2919 q^{56} +2.36273 q^{57} +8.74128 q^{58} -0.0595952 q^{59} +61.4977 q^{60} +7.07771 q^{61} +21.8152 q^{62} -19.1568 q^{63} +31.4984 q^{64} +2.71044 q^{65} +18.7400 q^{66} +5.42949 q^{67} +0.304679 q^{68} +3.04549 q^{69} +30.6854 q^{70} +0.0177997 q^{71} -60.2083 q^{72} +11.1647 q^{73} -23.3243 q^{74} +25.7815 q^{75} +4.26920 q^{76} +6.85812 q^{77} -6.16171 q^{78} +10.6633 q^{79} +56.0556 q^{80} +11.5510 q^{81} -29.6941 q^{82} +3.41030 q^{83} -51.1629 q^{84} +0.203171 q^{85} +14.0618 q^{86} -9.71894 q^{87} +21.5545 q^{88} +14.1474 q^{89} -63.0726 q^{90} -2.25495 q^{91} +5.50288 q^{92} -24.2551 q^{93} -28.0627 q^{94} +2.84687 q^{95} -68.9903 q^{96} +10.3611 q^{97} -6.35469 q^{98} -14.0966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73914 −1.93686 −0.968432 0.249278i \(-0.919807\pi\)
−0.968432 + 0.249278i \(0.919807\pi\)
\(3\) 3.04549 1.75832 0.879159 0.476529i \(-0.158105\pi\)
0.879159 + 0.476529i \(0.158105\pi\)
\(4\) 5.50288 2.75144
\(5\) 3.66953 1.64106 0.820532 0.571601i \(-0.193677\pi\)
0.820532 + 0.571601i \(0.193677\pi\)
\(6\) −8.34203 −3.40562
\(7\) −3.05286 −1.15387 −0.576936 0.816789i \(-0.695752\pi\)
−0.576936 + 0.816789i \(0.695752\pi\)
\(8\) −9.59489 −3.39231
\(9\) 6.27504 2.09168
\(10\) −10.0514 −3.17852
\(11\) −2.24646 −0.677332 −0.338666 0.940907i \(-0.609976\pi\)
−0.338666 + 0.940907i \(0.609976\pi\)
\(12\) 16.7590 4.83791
\(13\) 0.738634 0.204860 0.102430 0.994740i \(-0.467338\pi\)
0.102430 + 0.994740i \(0.467338\pi\)
\(14\) 8.36221 2.23489
\(15\) 11.1755 2.88551
\(16\) 15.2760 3.81899
\(17\) 0.0553671 0.0134285 0.00671424 0.999977i \(-0.497863\pi\)
0.00671424 + 0.999977i \(0.497863\pi\)
\(18\) −17.1882 −4.05130
\(19\) 0.775812 0.177984 0.0889918 0.996032i \(-0.471636\pi\)
0.0889918 + 0.996032i \(0.471636\pi\)
\(20\) 20.1930 4.51529
\(21\) −9.29747 −2.02887
\(22\) 6.15336 1.31190
\(23\) 1.00000 0.208514
\(24\) −29.2212 −5.96475
\(25\) 8.46546 1.69309
\(26\) −2.02322 −0.396786
\(27\) 9.97411 1.91952
\(28\) −16.7995 −3.17481
\(29\) −3.19125 −0.592600 −0.296300 0.955095i \(-0.595753\pi\)
−0.296300 + 0.955095i \(0.595753\pi\)
\(30\) −30.6113 −5.58884
\(31\) −7.96425 −1.43042 −0.715210 0.698909i \(-0.753669\pi\)
−0.715210 + 0.698909i \(0.753669\pi\)
\(32\) −22.6532 −4.00456
\(33\) −6.84157 −1.19096
\(34\) −0.151658 −0.0260091
\(35\) −11.2026 −1.89358
\(36\) 34.5308 5.75513
\(37\) 8.51519 1.39989 0.699944 0.714198i \(-0.253208\pi\)
0.699944 + 0.714198i \(0.253208\pi\)
\(38\) −2.12506 −0.344730
\(39\) 2.24951 0.360209
\(40\) −35.2087 −5.56699
\(41\) 10.8407 1.69303 0.846514 0.532366i \(-0.178697\pi\)
0.846514 + 0.532366i \(0.178697\pi\)
\(42\) 25.4671 3.92965
\(43\) −5.13365 −0.782874 −0.391437 0.920205i \(-0.628022\pi\)
−0.391437 + 0.920205i \(0.628022\pi\)
\(44\) −12.3620 −1.86364
\(45\) 23.0264 3.43258
\(46\) −2.73914 −0.403864
\(47\) 10.2451 1.49440 0.747200 0.664600i \(-0.231398\pi\)
0.747200 + 0.664600i \(0.231398\pi\)
\(48\) 46.5229 6.71500
\(49\) 2.31996 0.331423
\(50\) −23.1881 −3.27929
\(51\) 0.168620 0.0236115
\(52\) 4.06462 0.563661
\(53\) −7.81563 −1.07356 −0.536779 0.843723i \(-0.680359\pi\)
−0.536779 + 0.843723i \(0.680359\pi\)
\(54\) −27.3205 −3.71785
\(55\) −8.24344 −1.11154
\(56\) 29.2919 3.91429
\(57\) 2.36273 0.312951
\(58\) 8.74128 1.14779
\(59\) −0.0595952 −0.00775863 −0.00387931 0.999992i \(-0.501235\pi\)
−0.00387931 + 0.999992i \(0.501235\pi\)
\(60\) 61.4977 7.93932
\(61\) 7.07771 0.906208 0.453104 0.891458i \(-0.350317\pi\)
0.453104 + 0.891458i \(0.350317\pi\)
\(62\) 21.8152 2.77053
\(63\) −19.1568 −2.41353
\(64\) 31.4984 3.93730
\(65\) 2.71044 0.336189
\(66\) 18.7400 2.30674
\(67\) 5.42949 0.663318 0.331659 0.943399i \(-0.392392\pi\)
0.331659 + 0.943399i \(0.392392\pi\)
\(68\) 0.304679 0.0369477
\(69\) 3.04549 0.366634
\(70\) 30.6854 3.66761
\(71\) 0.0177997 0.00211243 0.00105622 0.999999i \(-0.499664\pi\)
0.00105622 + 0.999999i \(0.499664\pi\)
\(72\) −60.2083 −7.09561
\(73\) 11.1647 1.30673 0.653367 0.757041i \(-0.273356\pi\)
0.653367 + 0.757041i \(0.273356\pi\)
\(74\) −23.3243 −2.71139
\(75\) 25.7815 2.97699
\(76\) 4.26920 0.489711
\(77\) 6.85812 0.781555
\(78\) −6.16171 −0.697676
\(79\) 10.6633 1.19972 0.599858 0.800107i \(-0.295224\pi\)
0.599858 + 0.800107i \(0.295224\pi\)
\(80\) 56.0556 6.26721
\(81\) 11.5510 1.28344
\(82\) −29.6941 −3.27917
\(83\) 3.41030 0.374329 0.187165 0.982329i \(-0.440070\pi\)
0.187165 + 0.982329i \(0.440070\pi\)
\(84\) −51.1629 −5.58233
\(85\) 0.203171 0.0220370
\(86\) 14.0618 1.51632
\(87\) −9.71894 −1.04198
\(88\) 21.5545 2.29772
\(89\) 14.1474 1.49962 0.749812 0.661651i \(-0.230144\pi\)
0.749812 + 0.661651i \(0.230144\pi\)
\(90\) −63.0726 −6.64844
\(91\) −2.25495 −0.236383
\(92\) 5.50288 0.573715
\(93\) −24.2551 −2.51513
\(94\) −28.0627 −2.89445
\(95\) 2.84687 0.292082
\(96\) −68.9903 −7.04129
\(97\) 10.3611 1.05201 0.526003 0.850483i \(-0.323690\pi\)
0.526003 + 0.850483i \(0.323690\pi\)
\(98\) −6.35469 −0.641920
\(99\) −14.0966 −1.41676
\(100\) 46.5844 4.65844
\(101\) 3.07768 0.306241 0.153120 0.988208i \(-0.451068\pi\)
0.153120 + 0.988208i \(0.451068\pi\)
\(102\) −0.461874 −0.0457323
\(103\) −4.10831 −0.404804 −0.202402 0.979303i \(-0.564875\pi\)
−0.202402 + 0.979303i \(0.564875\pi\)
\(104\) −7.08711 −0.694949
\(105\) −34.1174 −3.32951
\(106\) 21.4081 2.07934
\(107\) −8.32094 −0.804416 −0.402208 0.915548i \(-0.631757\pi\)
−0.402208 + 0.915548i \(0.631757\pi\)
\(108\) 54.8864 5.28144
\(109\) −0.0205040 −0.00196393 −0.000981966 1.00000i \(-0.500313\pi\)
−0.000981966 1.00000i \(0.500313\pi\)
\(110\) 22.5799 2.15291
\(111\) 25.9330 2.46145
\(112\) −46.6354 −4.40663
\(113\) 7.98310 0.750987 0.375493 0.926825i \(-0.377473\pi\)
0.375493 + 0.926825i \(0.377473\pi\)
\(114\) −6.47185 −0.606144
\(115\) 3.66953 0.342186
\(116\) −17.5611 −1.63051
\(117\) 4.63496 0.428502
\(118\) 0.163239 0.0150274
\(119\) −0.169028 −0.0154948
\(120\) −107.228 −9.78853
\(121\) −5.95344 −0.541222
\(122\) −19.3868 −1.75520
\(123\) 33.0152 2.97688
\(124\) −43.8263 −3.93572
\(125\) 12.7166 1.13741
\(126\) 52.4732 4.67468
\(127\) 2.38707 0.211819 0.105909 0.994376i \(-0.466225\pi\)
0.105909 + 0.994376i \(0.466225\pi\)
\(128\) −40.9721 −3.62145
\(129\) −15.6345 −1.37654
\(130\) −7.42427 −0.651152
\(131\) −13.9131 −1.21559 −0.607796 0.794093i \(-0.707946\pi\)
−0.607796 + 0.794093i \(0.707946\pi\)
\(132\) −37.6484 −3.27687
\(133\) −2.36845 −0.205370
\(134\) −14.8721 −1.28476
\(135\) 36.6003 3.15005
\(136\) −0.531241 −0.0455535
\(137\) −0.793301 −0.0677763 −0.0338882 0.999426i \(-0.510789\pi\)
−0.0338882 + 0.999426i \(0.510789\pi\)
\(138\) −8.34203 −0.710121
\(139\) −20.2076 −1.71398 −0.856992 0.515330i \(-0.827669\pi\)
−0.856992 + 0.515330i \(0.827669\pi\)
\(140\) −61.6464 −5.21007
\(141\) 31.2014 2.62763
\(142\) −0.0487558 −0.00409150
\(143\) −1.65931 −0.138758
\(144\) 95.8573 7.98810
\(145\) −11.7104 −0.972495
\(146\) −30.5818 −2.53097
\(147\) 7.06542 0.582746
\(148\) 46.8581 3.85171
\(149\) 9.21907 0.755255 0.377628 0.925958i \(-0.376740\pi\)
0.377628 + 0.925958i \(0.376740\pi\)
\(150\) −70.6191 −5.76603
\(151\) 3.64387 0.296534 0.148267 0.988947i \(-0.452631\pi\)
0.148267 + 0.988947i \(0.452631\pi\)
\(152\) −7.44383 −0.603774
\(153\) 0.347430 0.0280881
\(154\) −18.7853 −1.51377
\(155\) −29.2250 −2.34741
\(156\) 12.3788 0.991095
\(157\) 17.1895 1.37187 0.685935 0.727662i \(-0.259393\pi\)
0.685935 + 0.727662i \(0.259393\pi\)
\(158\) −29.2083 −2.32369
\(159\) −23.8024 −1.88766
\(160\) −83.1267 −6.57174
\(161\) −3.05286 −0.240599
\(162\) −31.6397 −2.48585
\(163\) 5.66005 0.443330 0.221665 0.975123i \(-0.428851\pi\)
0.221665 + 0.975123i \(0.428851\pi\)
\(164\) 59.6550 4.65827
\(165\) −25.1053 −1.95445
\(166\) −9.34129 −0.725025
\(167\) 3.47812 0.269145 0.134572 0.990904i \(-0.457034\pi\)
0.134572 + 0.990904i \(0.457034\pi\)
\(168\) 89.2082 6.88256
\(169\) −12.4544 −0.958032
\(170\) −0.556514 −0.0426827
\(171\) 4.86825 0.372284
\(172\) −28.2499 −2.15403
\(173\) −7.37480 −0.560695 −0.280348 0.959899i \(-0.590450\pi\)
−0.280348 + 0.959899i \(0.590450\pi\)
\(174\) 26.6215 2.01817
\(175\) −25.8439 −1.95361
\(176\) −34.3168 −2.58672
\(177\) −0.181497 −0.0136421
\(178\) −38.7518 −2.90457
\(179\) −16.0596 −1.20035 −0.600175 0.799869i \(-0.704902\pi\)
−0.600175 + 0.799869i \(0.704902\pi\)
\(180\) 126.712 9.44454
\(181\) 20.6116 1.53205 0.766025 0.642811i \(-0.222232\pi\)
0.766025 + 0.642811i \(0.222232\pi\)
\(182\) 6.17661 0.457841
\(183\) 21.5551 1.59340
\(184\) −9.59489 −0.707345
\(185\) 31.2467 2.29731
\(186\) 66.4380 4.87147
\(187\) −0.124380 −0.00909554
\(188\) 56.3775 4.11175
\(189\) −30.4496 −2.21488
\(190\) −7.79796 −0.565724
\(191\) −12.0323 −0.870630 −0.435315 0.900278i \(-0.643363\pi\)
−0.435315 + 0.900278i \(0.643363\pi\)
\(192\) 95.9282 6.92302
\(193\) 25.9405 1.86724 0.933619 0.358267i \(-0.116632\pi\)
0.933619 + 0.358267i \(0.116632\pi\)
\(194\) −28.3804 −2.03759
\(195\) 8.25463 0.591127
\(196\) 12.7665 0.911890
\(197\) 8.14552 0.580344 0.290172 0.956974i \(-0.406287\pi\)
0.290172 + 0.956974i \(0.406287\pi\)
\(198\) 38.6125 2.74407
\(199\) 15.5337 1.10116 0.550579 0.834783i \(-0.314407\pi\)
0.550579 + 0.834783i \(0.314407\pi\)
\(200\) −81.2251 −5.74348
\(201\) 16.5355 1.16632
\(202\) −8.43020 −0.593147
\(203\) 9.74244 0.683786
\(204\) 0.927897 0.0649658
\(205\) 39.7802 2.77837
\(206\) 11.2532 0.784050
\(207\) 6.27504 0.436145
\(208\) 11.2834 0.782360
\(209\) −1.74283 −0.120554
\(210\) 93.4522 6.44881
\(211\) 15.0562 1.03651 0.518256 0.855226i \(-0.326582\pi\)
0.518256 + 0.855226i \(0.326582\pi\)
\(212\) −43.0085 −2.95383
\(213\) 0.0542088 0.00371433
\(214\) 22.7922 1.55804
\(215\) −18.8381 −1.28475
\(216\) −95.7004 −6.51159
\(217\) 24.3137 1.65052
\(218\) 0.0561634 0.00380387
\(219\) 34.0022 2.29765
\(220\) −45.3627 −3.05835
\(221\) 0.0408960 0.00275096
\(222\) −71.0340 −4.76749
\(223\) −20.0138 −1.34022 −0.670111 0.742261i \(-0.733753\pi\)
−0.670111 + 0.742261i \(0.733753\pi\)
\(224\) 69.1571 4.62076
\(225\) 53.1210 3.54140
\(226\) −21.8668 −1.45456
\(227\) 0.761637 0.0505516 0.0252758 0.999681i \(-0.491954\pi\)
0.0252758 + 0.999681i \(0.491954\pi\)
\(228\) 13.0018 0.861068
\(229\) −14.2284 −0.940238 −0.470119 0.882603i \(-0.655789\pi\)
−0.470119 + 0.882603i \(0.655789\pi\)
\(230\) −10.0514 −0.662767
\(231\) 20.8864 1.37422
\(232\) 30.6197 2.01028
\(233\) 27.6578 1.81192 0.905961 0.423362i \(-0.139150\pi\)
0.905961 + 0.423362i \(0.139150\pi\)
\(234\) −12.6958 −0.829950
\(235\) 37.5947 2.45241
\(236\) −0.327945 −0.0213474
\(237\) 32.4750 2.10948
\(238\) 0.462991 0.0300112
\(239\) 8.17092 0.528533 0.264267 0.964450i \(-0.414870\pi\)
0.264267 + 0.964450i \(0.414870\pi\)
\(240\) 170.717 11.0197
\(241\) 12.4461 0.801724 0.400862 0.916138i \(-0.368711\pi\)
0.400862 + 0.916138i \(0.368711\pi\)
\(242\) 16.3073 1.04827
\(243\) 5.25612 0.337180
\(244\) 38.9478 2.49338
\(245\) 8.51316 0.543886
\(246\) −90.4333 −5.76581
\(247\) 0.573041 0.0364617
\(248\) 76.4160 4.85242
\(249\) 10.3861 0.658190
\(250\) −34.8325 −2.20300
\(251\) −7.47593 −0.471877 −0.235938 0.971768i \(-0.575816\pi\)
−0.235938 + 0.971768i \(0.575816\pi\)
\(252\) −105.418 −6.64069
\(253\) −2.24646 −0.141233
\(254\) −6.53853 −0.410264
\(255\) 0.618757 0.0387480
\(256\) 49.2314 3.07696
\(257\) −22.4630 −1.40120 −0.700602 0.713552i \(-0.747085\pi\)
−0.700602 + 0.713552i \(0.747085\pi\)
\(258\) 42.8251 2.66617
\(259\) −25.9957 −1.61529
\(260\) 14.9152 0.925004
\(261\) −20.0252 −1.23953
\(262\) 38.1099 2.35444
\(263\) 23.0547 1.42161 0.710806 0.703388i \(-0.248330\pi\)
0.710806 + 0.703388i \(0.248330\pi\)
\(264\) 65.6441 4.04011
\(265\) −28.6797 −1.76178
\(266\) 6.48750 0.397774
\(267\) 43.0859 2.63681
\(268\) 29.8779 1.82508
\(269\) 27.2824 1.66344 0.831720 0.555195i \(-0.187356\pi\)
0.831720 + 0.555195i \(0.187356\pi\)
\(270\) −100.253 −6.10122
\(271\) 21.2293 1.28959 0.644793 0.764357i \(-0.276943\pi\)
0.644793 + 0.764357i \(0.276943\pi\)
\(272\) 0.845785 0.0512833
\(273\) −6.86743 −0.415636
\(274\) 2.17296 0.131273
\(275\) −19.0173 −1.14678
\(276\) 16.7590 1.00877
\(277\) −19.0331 −1.14359 −0.571793 0.820398i \(-0.693752\pi\)
−0.571793 + 0.820398i \(0.693752\pi\)
\(278\) 55.3514 3.31975
\(279\) −49.9759 −2.99198
\(280\) 107.487 6.42360
\(281\) −16.0127 −0.955237 −0.477618 0.878567i \(-0.658500\pi\)
−0.477618 + 0.878567i \(0.658500\pi\)
\(282\) −85.4649 −5.08936
\(283\) −28.6557 −1.70341 −0.851703 0.524024i \(-0.824430\pi\)
−0.851703 + 0.524024i \(0.824430\pi\)
\(284\) 0.0979496 0.00581224
\(285\) 8.67012 0.513573
\(286\) 4.54508 0.268756
\(287\) −33.0951 −1.95354
\(288\) −142.150 −8.37626
\(289\) −16.9969 −0.999820
\(290\) 32.0764 1.88359
\(291\) 31.5545 1.84976
\(292\) 61.4383 3.59541
\(293\) −30.7297 −1.79525 −0.897625 0.440760i \(-0.854709\pi\)
−0.897625 + 0.440760i \(0.854709\pi\)
\(294\) −19.3532 −1.12870
\(295\) −0.218686 −0.0127324
\(296\) −81.7023 −4.74885
\(297\) −22.4064 −1.30015
\(298\) −25.2523 −1.46283
\(299\) 0.738634 0.0427163
\(300\) 141.873 8.19102
\(301\) 15.6723 0.903337
\(302\) −9.98107 −0.574346
\(303\) 9.37307 0.538469
\(304\) 11.8513 0.679717
\(305\) 25.9719 1.48715
\(306\) −0.951660 −0.0544028
\(307\) −17.8027 −1.01605 −0.508026 0.861342i \(-0.669624\pi\)
−0.508026 + 0.861342i \(0.669624\pi\)
\(308\) 37.7394 2.15040
\(309\) −12.5118 −0.711774
\(310\) 80.0515 4.54662
\(311\) 22.7848 1.29200 0.646002 0.763335i \(-0.276440\pi\)
0.646002 + 0.763335i \(0.276440\pi\)
\(312\) −21.5838 −1.22194
\(313\) 10.2601 0.579935 0.289968 0.957036i \(-0.406355\pi\)
0.289968 + 0.957036i \(0.406355\pi\)
\(314\) −47.0844 −2.65713
\(315\) −70.2965 −3.96076
\(316\) 58.6789 3.30095
\(317\) −13.2436 −0.743836 −0.371918 0.928266i \(-0.621300\pi\)
−0.371918 + 0.928266i \(0.621300\pi\)
\(318\) 65.1982 3.65613
\(319\) 7.16900 0.401387
\(320\) 115.584 6.46136
\(321\) −25.3414 −1.41442
\(322\) 8.36221 0.466008
\(323\) 0.0429544 0.00239005
\(324\) 63.5637 3.53132
\(325\) 6.25287 0.346847
\(326\) −15.5037 −0.858669
\(327\) −0.0624450 −0.00345321
\(328\) −104.015 −5.74327
\(329\) −31.2768 −1.72435
\(330\) 68.7670 3.78550
\(331\) 31.6674 1.74060 0.870298 0.492526i \(-0.163926\pi\)
0.870298 + 0.492526i \(0.163926\pi\)
\(332\) 18.7665 1.02995
\(333\) 53.4331 2.92812
\(334\) −9.52705 −0.521297
\(335\) 19.9237 1.08855
\(336\) −142.028 −7.74825
\(337\) −10.6152 −0.578247 −0.289123 0.957292i \(-0.593364\pi\)
−0.289123 + 0.957292i \(0.593364\pi\)
\(338\) 34.1144 1.85558
\(339\) 24.3125 1.32047
\(340\) 1.11803 0.0606335
\(341\) 17.8913 0.968870
\(342\) −13.3348 −0.721064
\(343\) 14.2875 0.771453
\(344\) 49.2568 2.65575
\(345\) 11.1755 0.601671
\(346\) 20.2006 1.08599
\(347\) 23.8718 1.28150 0.640752 0.767748i \(-0.278622\pi\)
0.640752 + 0.767748i \(0.278622\pi\)
\(348\) −53.4822 −2.86695
\(349\) −1.00000 −0.0535288
\(350\) 70.7899 3.78388
\(351\) 7.36722 0.393233
\(352\) 50.8895 2.71242
\(353\) −1.65728 −0.0882081 −0.0441041 0.999027i \(-0.514043\pi\)
−0.0441041 + 0.999027i \(0.514043\pi\)
\(354\) 0.497145 0.0264229
\(355\) 0.0653165 0.00346664
\(356\) 77.8516 4.12613
\(357\) −0.514774 −0.0272447
\(358\) 43.9894 2.32491
\(359\) −12.9085 −0.681287 −0.340643 0.940193i \(-0.610645\pi\)
−0.340643 + 0.940193i \(0.610645\pi\)
\(360\) −220.936 −11.6444
\(361\) −18.3981 −0.968322
\(362\) −56.4581 −2.96737
\(363\) −18.1312 −0.951639
\(364\) −12.4087 −0.650393
\(365\) 40.9694 2.14444
\(366\) −59.0425 −3.08620
\(367\) −22.4526 −1.17202 −0.586008 0.810305i \(-0.699301\pi\)
−0.586008 + 0.810305i \(0.699301\pi\)
\(368\) 15.2760 0.796315
\(369\) 68.0256 3.54127
\(370\) −85.5892 −4.44957
\(371\) 23.8600 1.23875
\(372\) −133.473 −6.92024
\(373\) 8.62205 0.446433 0.223216 0.974769i \(-0.428344\pi\)
0.223216 + 0.974769i \(0.428344\pi\)
\(374\) 0.340693 0.0176168
\(375\) 38.7283 1.99992
\(376\) −98.3005 −5.06946
\(377\) −2.35717 −0.121400
\(378\) 83.4056 4.28992
\(379\) −5.42924 −0.278881 −0.139441 0.990230i \(-0.544530\pi\)
−0.139441 + 0.990230i \(0.544530\pi\)
\(380\) 15.6660 0.803648
\(381\) 7.26982 0.372444
\(382\) 32.9583 1.68629
\(383\) 2.45778 0.125587 0.0627934 0.998027i \(-0.479999\pi\)
0.0627934 + 0.998027i \(0.479999\pi\)
\(384\) −124.780 −6.36766
\(385\) 25.1661 1.28258
\(386\) −71.0547 −3.61659
\(387\) −32.2138 −1.63752
\(388\) 57.0157 2.89453
\(389\) −2.75378 −0.139622 −0.0698110 0.997560i \(-0.522240\pi\)
−0.0698110 + 0.997560i \(0.522240\pi\)
\(390\) −22.6106 −1.14493
\(391\) 0.0553671 0.00280003
\(392\) −22.2597 −1.12429
\(393\) −42.3722 −2.13740
\(394\) −22.3117 −1.12405
\(395\) 39.1293 1.96881
\(396\) −77.5719 −3.89814
\(397\) 24.9136 1.25038 0.625190 0.780473i \(-0.285022\pi\)
0.625190 + 0.780473i \(0.285022\pi\)
\(398\) −42.5491 −2.13279
\(399\) −7.21309 −0.361106
\(400\) 129.318 6.46590
\(401\) −29.4505 −1.47069 −0.735344 0.677694i \(-0.762979\pi\)
−0.735344 + 0.677694i \(0.762979\pi\)
\(402\) −45.2930 −2.25901
\(403\) −5.88266 −0.293036
\(404\) 16.9361 0.842604
\(405\) 42.3867 2.10621
\(406\) −26.6859 −1.32440
\(407\) −19.1290 −0.948189
\(408\) −1.61789 −0.0800975
\(409\) 30.5647 1.51133 0.755664 0.654959i \(-0.227314\pi\)
0.755664 + 0.654959i \(0.227314\pi\)
\(410\) −108.963 −5.38132
\(411\) −2.41600 −0.119172
\(412\) −22.6076 −1.11379
\(413\) 0.181936 0.00895247
\(414\) −17.1882 −0.844754
\(415\) 12.5142 0.614298
\(416\) −16.7324 −0.820376
\(417\) −61.5421 −3.01373
\(418\) 4.77385 0.233497
\(419\) −21.1148 −1.03153 −0.515763 0.856731i \(-0.672492\pi\)
−0.515763 + 0.856731i \(0.672492\pi\)
\(420\) −187.744 −9.16096
\(421\) −29.0037 −1.41356 −0.706778 0.707436i \(-0.749852\pi\)
−0.706778 + 0.707436i \(0.749852\pi\)
\(422\) −41.2410 −2.00758
\(423\) 64.2883 3.12580
\(424\) 74.9900 3.64184
\(425\) 0.468707 0.0227356
\(426\) −0.148486 −0.00719415
\(427\) −21.6073 −1.04565
\(428\) −45.7892 −2.21330
\(429\) −5.05342 −0.243981
\(430\) 51.6001 2.48838
\(431\) 2.54481 0.122579 0.0612896 0.998120i \(-0.480479\pi\)
0.0612896 + 0.998120i \(0.480479\pi\)
\(432\) 152.364 7.33062
\(433\) −8.36502 −0.401997 −0.200999 0.979592i \(-0.564419\pi\)
−0.200999 + 0.979592i \(0.564419\pi\)
\(434\) −66.5987 −3.19684
\(435\) −35.6639 −1.70995
\(436\) −0.112831 −0.00540364
\(437\) 0.775812 0.0371121
\(438\) −93.1367 −4.45024
\(439\) 19.3675 0.924361 0.462181 0.886786i \(-0.347067\pi\)
0.462181 + 0.886786i \(0.347067\pi\)
\(440\) 79.0949 3.77070
\(441\) 14.5578 0.693230
\(442\) −0.112020 −0.00532824
\(443\) −6.60978 −0.314040 −0.157020 0.987595i \(-0.550189\pi\)
−0.157020 + 0.987595i \(0.550189\pi\)
\(444\) 142.706 6.77253
\(445\) 51.9144 2.46098
\(446\) 54.8205 2.59583
\(447\) 28.0766 1.32798
\(448\) −96.1602 −4.54314
\(449\) 2.90523 0.137106 0.0685532 0.997647i \(-0.478162\pi\)
0.0685532 + 0.997647i \(0.478162\pi\)
\(450\) −145.506 −6.85922
\(451\) −24.3531 −1.14674
\(452\) 43.9301 2.06630
\(453\) 11.0974 0.521401
\(454\) −2.08623 −0.0979116
\(455\) −8.27460 −0.387919
\(456\) −22.6701 −1.06163
\(457\) 15.4182 0.721234 0.360617 0.932714i \(-0.382566\pi\)
0.360617 + 0.932714i \(0.382566\pi\)
\(458\) 38.9735 1.82111
\(459\) 0.552237 0.0257762
\(460\) 20.1930 0.941504
\(461\) −27.3017 −1.27156 −0.635782 0.771868i \(-0.719322\pi\)
−0.635782 + 0.771868i \(0.719322\pi\)
\(462\) −57.2106 −2.66168
\(463\) 26.8286 1.24683 0.623415 0.781891i \(-0.285745\pi\)
0.623415 + 0.781891i \(0.285745\pi\)
\(464\) −48.7494 −2.26314
\(465\) −89.0047 −4.12749
\(466\) −75.7585 −3.50944
\(467\) 15.9554 0.738328 0.369164 0.929364i \(-0.379644\pi\)
0.369164 + 0.929364i \(0.379644\pi\)
\(468\) 25.5056 1.17900
\(469\) −16.5755 −0.765385
\(470\) −102.977 −4.74998
\(471\) 52.3505 2.41218
\(472\) 0.571809 0.0263196
\(473\) 11.5325 0.530265
\(474\) −88.9536 −4.08578
\(475\) 6.56760 0.301342
\(476\) −0.930141 −0.0426329
\(477\) −49.0433 −2.24554
\(478\) −22.3813 −1.02370
\(479\) −39.7623 −1.81679 −0.908393 0.418118i \(-0.862690\pi\)
−0.908393 + 0.418118i \(0.862690\pi\)
\(480\) −253.162 −11.5552
\(481\) 6.28961 0.286781
\(482\) −34.0916 −1.55283
\(483\) −9.29747 −0.423050
\(484\) −32.7611 −1.48914
\(485\) 38.0202 1.72641
\(486\) −14.3972 −0.653072
\(487\) −15.2660 −0.691769 −0.345885 0.938277i \(-0.612421\pi\)
−0.345885 + 0.938277i \(0.612421\pi\)
\(488\) −67.9099 −3.07414
\(489\) 17.2377 0.779514
\(490\) −23.3187 −1.05343
\(491\) −22.6591 −1.02259 −0.511294 0.859406i \(-0.670834\pi\)
−0.511294 + 0.859406i \(0.670834\pi\)
\(492\) 181.679 8.19072
\(493\) −0.176690 −0.00795773
\(494\) −1.56964 −0.0706214
\(495\) −51.7279 −2.32500
\(496\) −121.662 −5.46276
\(497\) −0.0543399 −0.00243748
\(498\) −28.4489 −1.27482
\(499\) 25.0963 1.12346 0.561732 0.827319i \(-0.310135\pi\)
0.561732 + 0.827319i \(0.310135\pi\)
\(500\) 69.9780 3.12951
\(501\) 10.5926 0.473242
\(502\) 20.4776 0.913961
\(503\) 2.54563 0.113504 0.0567520 0.998388i \(-0.481926\pi\)
0.0567520 + 0.998388i \(0.481926\pi\)
\(504\) 183.807 8.18744
\(505\) 11.2937 0.502561
\(506\) 6.15336 0.273550
\(507\) −37.9299 −1.68452
\(508\) 13.1358 0.582806
\(509\) 12.4161 0.550336 0.275168 0.961396i \(-0.411267\pi\)
0.275168 + 0.961396i \(0.411267\pi\)
\(510\) −1.69486 −0.0750497
\(511\) −34.0844 −1.50781
\(512\) −52.9075 −2.33820
\(513\) 7.73803 0.341643
\(514\) 61.5293 2.71394
\(515\) −15.0756 −0.664309
\(516\) −86.0348 −3.78747
\(517\) −23.0151 −1.01220
\(518\) 71.2058 3.12860
\(519\) −22.4599 −0.985880
\(520\) −26.0064 −1.14045
\(521\) 16.7968 0.735883 0.367941 0.929849i \(-0.380063\pi\)
0.367941 + 0.929849i \(0.380063\pi\)
\(522\) 54.8519 2.40080
\(523\) 1.32237 0.0578233 0.0289117 0.999582i \(-0.490796\pi\)
0.0289117 + 0.999582i \(0.490796\pi\)
\(524\) −76.5621 −3.34463
\(525\) −78.7073 −3.43507
\(526\) −63.1500 −2.75347
\(527\) −0.440957 −0.0192084
\(528\) −104.512 −4.54828
\(529\) 1.00000 0.0434783
\(530\) 78.5576 3.41233
\(531\) −0.373962 −0.0162286
\(532\) −13.0333 −0.565065
\(533\) 8.00729 0.346834
\(534\) −118.018 −5.10715
\(535\) −30.5340 −1.32010
\(536\) −52.0954 −2.25018
\(537\) −48.9094 −2.11060
\(538\) −74.7304 −3.22186
\(539\) −5.21168 −0.224483
\(540\) 201.407 8.66718
\(541\) −30.4727 −1.31012 −0.655062 0.755575i \(-0.727358\pi\)
−0.655062 + 0.755575i \(0.727358\pi\)
\(542\) −58.1500 −2.49775
\(543\) 62.7726 2.69383
\(544\) −1.25424 −0.0537752
\(545\) −0.0752402 −0.00322294
\(546\) 18.8108 0.805030
\(547\) 17.9399 0.767056 0.383528 0.923529i \(-0.374709\pi\)
0.383528 + 0.923529i \(0.374709\pi\)
\(548\) −4.36545 −0.186483
\(549\) 44.4129 1.89550
\(550\) 52.0910 2.22117
\(551\) −2.47581 −0.105473
\(552\) −29.2212 −1.24374
\(553\) −32.5536 −1.38432
\(554\) 52.1343 2.21497
\(555\) 95.1618 4.03939
\(556\) −111.200 −4.71593
\(557\) 16.4865 0.698555 0.349278 0.937019i \(-0.386427\pi\)
0.349278 + 0.937019i \(0.386427\pi\)
\(558\) 136.891 5.79506
\(559\) −3.79189 −0.160380
\(560\) −171.130 −7.23156
\(561\) −0.378798 −0.0159928
\(562\) 43.8610 1.85016
\(563\) −12.5139 −0.527398 −0.263699 0.964605i \(-0.584943\pi\)
−0.263699 + 0.964605i \(0.584943\pi\)
\(564\) 171.697 7.22977
\(565\) 29.2942 1.23242
\(566\) 78.4921 3.29927
\(567\) −35.2635 −1.48093
\(568\) −0.170786 −0.00716602
\(569\) −39.5993 −1.66009 −0.830044 0.557697i \(-0.811685\pi\)
−0.830044 + 0.557697i \(0.811685\pi\)
\(570\) −23.7487 −0.994722
\(571\) −35.1400 −1.47056 −0.735282 0.677761i \(-0.762950\pi\)
−0.735282 + 0.677761i \(0.762950\pi\)
\(572\) −9.13098 −0.381786
\(573\) −36.6444 −1.53084
\(574\) 90.6520 3.78374
\(575\) 8.46546 0.353034
\(576\) 197.654 8.23557
\(577\) −4.03699 −0.168062 −0.0840310 0.996463i \(-0.526779\pi\)
−0.0840310 + 0.996463i \(0.526779\pi\)
\(578\) 46.5570 1.93651
\(579\) 79.0017 3.28320
\(580\) −64.4409 −2.67576
\(581\) −10.4112 −0.431928
\(582\) −86.4323 −3.58273
\(583\) 17.5575 0.727155
\(584\) −107.124 −4.43284
\(585\) 17.0081 0.703199
\(586\) 84.1730 3.47715
\(587\) 22.4935 0.928407 0.464204 0.885729i \(-0.346341\pi\)
0.464204 + 0.885729i \(0.346341\pi\)
\(588\) 38.8802 1.60339
\(589\) −6.17876 −0.254591
\(590\) 0.599012 0.0246609
\(591\) 24.8071 1.02043
\(592\) 130.078 5.34616
\(593\) 15.5820 0.639877 0.319939 0.947438i \(-0.396338\pi\)
0.319939 + 0.947438i \(0.396338\pi\)
\(594\) 61.3742 2.51821
\(595\) −0.620253 −0.0254279
\(596\) 50.7315 2.07804
\(597\) 47.3079 1.93618
\(598\) −2.02322 −0.0827357
\(599\) −9.00051 −0.367751 −0.183875 0.982950i \(-0.558864\pi\)
−0.183875 + 0.982950i \(0.558864\pi\)
\(600\) −247.371 −10.0989
\(601\) 16.5712 0.675955 0.337978 0.941154i \(-0.390257\pi\)
0.337978 + 0.941154i \(0.390257\pi\)
\(602\) −42.9286 −1.74964
\(603\) 34.0703 1.38745
\(604\) 20.0518 0.815896
\(605\) −21.8463 −0.888179
\(606\) −25.6741 −1.04294
\(607\) 38.1517 1.54853 0.774266 0.632861i \(-0.218119\pi\)
0.774266 + 0.632861i \(0.218119\pi\)
\(608\) −17.5746 −0.712746
\(609\) 29.6706 1.20231
\(610\) −71.1406 −2.88040
\(611\) 7.56737 0.306143
\(612\) 1.91187 0.0772827
\(613\) 24.3774 0.984594 0.492297 0.870427i \(-0.336157\pi\)
0.492297 + 0.870427i \(0.336157\pi\)
\(614\) 48.7640 1.96795
\(615\) 121.150 4.88525
\(616\) −65.8029 −2.65127
\(617\) −37.1540 −1.49576 −0.747882 0.663831i \(-0.768929\pi\)
−0.747882 + 0.663831i \(0.768929\pi\)
\(618\) 34.2717 1.37861
\(619\) 9.95045 0.399943 0.199971 0.979802i \(-0.435915\pi\)
0.199971 + 0.979802i \(0.435915\pi\)
\(620\) −160.822 −6.45877
\(621\) 9.97411 0.400247
\(622\) −62.4106 −2.50244
\(623\) −43.1901 −1.73037
\(624\) 34.3634 1.37564
\(625\) 4.33666 0.173466
\(626\) −28.1039 −1.12326
\(627\) −5.30777 −0.211972
\(628\) 94.5918 3.77462
\(629\) 0.471461 0.0187984
\(630\) 192.552 7.67145
\(631\) 39.2464 1.56238 0.781188 0.624296i \(-0.214614\pi\)
0.781188 + 0.624296i \(0.214614\pi\)
\(632\) −102.313 −4.06980
\(633\) 45.8536 1.82252
\(634\) 36.2761 1.44071
\(635\) 8.75944 0.347608
\(636\) −130.982 −5.19378
\(637\) 1.71360 0.0678953
\(638\) −19.6369 −0.777432
\(639\) 0.111694 0.00441853
\(640\) −150.348 −5.94304
\(641\) −42.7464 −1.68838 −0.844190 0.536044i \(-0.819918\pi\)
−0.844190 + 0.536044i \(0.819918\pi\)
\(642\) 69.4136 2.73954
\(643\) 9.46931 0.373433 0.186717 0.982414i \(-0.440215\pi\)
0.186717 + 0.982414i \(0.440215\pi\)
\(644\) −16.7995 −0.661995
\(645\) −57.3713 −2.25899
\(646\) −0.117658 −0.00462920
\(647\) 28.9451 1.13795 0.568974 0.822355i \(-0.307340\pi\)
0.568974 + 0.822355i \(0.307340\pi\)
\(648\) −110.830 −4.35383
\(649\) 0.133878 0.00525517
\(650\) −17.1275 −0.671796
\(651\) 74.0473 2.90214
\(652\) 31.1466 1.21980
\(653\) −10.8682 −0.425306 −0.212653 0.977128i \(-0.568210\pi\)
−0.212653 + 0.977128i \(0.568210\pi\)
\(654\) 0.171045 0.00668841
\(655\) −51.0545 −1.99486
\(656\) 165.602 6.46566
\(657\) 70.0592 2.73327
\(658\) 85.6716 3.33983
\(659\) −47.5005 −1.85036 −0.925179 0.379532i \(-0.876085\pi\)
−0.925179 + 0.379532i \(0.876085\pi\)
\(660\) −138.152 −5.37755
\(661\) −29.5725 −1.15024 −0.575119 0.818069i \(-0.695044\pi\)
−0.575119 + 0.818069i \(0.695044\pi\)
\(662\) −86.7413 −3.37130
\(663\) 0.124549 0.00483706
\(664\) −32.7215 −1.26984
\(665\) −8.69109 −0.337026
\(666\) −146.361 −5.67136
\(667\) −3.19125 −0.123566
\(668\) 19.1397 0.740536
\(669\) −60.9519 −2.35654
\(670\) −54.5738 −2.10837
\(671\) −15.8998 −0.613804
\(672\) 210.618 8.12475
\(673\) 42.4783 1.63742 0.818710 0.574208i \(-0.194690\pi\)
0.818710 + 0.574208i \(0.194690\pi\)
\(674\) 29.0765 1.11999
\(675\) 84.4354 3.24992
\(676\) −68.5352 −2.63597
\(677\) −46.0877 −1.77129 −0.885647 0.464359i \(-0.846285\pi\)
−0.885647 + 0.464359i \(0.846285\pi\)
\(678\) −66.5953 −2.55758
\(679\) −31.6309 −1.21388
\(680\) −1.94940 −0.0747562
\(681\) 2.31956 0.0888858
\(682\) −49.0068 −1.87657
\(683\) 22.6343 0.866076 0.433038 0.901376i \(-0.357442\pi\)
0.433038 + 0.901376i \(0.357442\pi\)
\(684\) 26.7894 1.02432
\(685\) −2.91104 −0.111225
\(686\) −39.1355 −1.49420
\(687\) −43.3325 −1.65324
\(688\) −78.4214 −2.98979
\(689\) −5.77289 −0.219930
\(690\) −30.6113 −1.16535
\(691\) −36.8299 −1.40108 −0.700538 0.713615i \(-0.747057\pi\)
−0.700538 + 0.713615i \(0.747057\pi\)
\(692\) −40.5826 −1.54272
\(693\) 43.0349 1.63476
\(694\) −65.3882 −2.48210
\(695\) −74.1523 −2.81276
\(696\) 93.2521 3.53471
\(697\) 0.600216 0.0227348
\(698\) 2.73914 0.103678
\(699\) 84.2316 3.18593
\(700\) −142.216 −5.37525
\(701\) 28.0858 1.06078 0.530392 0.847752i \(-0.322045\pi\)
0.530392 + 0.847752i \(0.322045\pi\)
\(702\) −20.1798 −0.761639
\(703\) 6.60619 0.249157
\(704\) −70.7598 −2.66686
\(705\) 114.494 4.31211
\(706\) 4.53952 0.170847
\(707\) −9.39574 −0.353363
\(708\) −0.998755 −0.0375355
\(709\) −30.4881 −1.14500 −0.572502 0.819903i \(-0.694027\pi\)
−0.572502 + 0.819903i \(0.694027\pi\)
\(710\) −0.178911 −0.00671441
\(711\) 66.9126 2.50942
\(712\) −135.743 −5.08718
\(713\) −7.96425 −0.298263
\(714\) 1.41004 0.0527693
\(715\) −6.08888 −0.227711
\(716\) −88.3740 −3.30269
\(717\) 24.8845 0.929329
\(718\) 35.3583 1.31956
\(719\) −24.0643 −0.897446 −0.448723 0.893671i \(-0.648121\pi\)
−0.448723 + 0.893671i \(0.648121\pi\)
\(720\) 351.751 13.1090
\(721\) 12.5421 0.467092
\(722\) 50.3950 1.87551
\(723\) 37.9045 1.40968
\(724\) 113.423 4.21535
\(725\) −27.0154 −1.00333
\(726\) 49.6638 1.84320
\(727\) 20.8021 0.771508 0.385754 0.922602i \(-0.373941\pi\)
0.385754 + 0.922602i \(0.373941\pi\)
\(728\) 21.6360 0.801882
\(729\) −18.6454 −0.690572
\(730\) −112.221 −4.15348
\(731\) −0.284235 −0.0105128
\(732\) 118.615 4.38415
\(733\) 30.0374 1.10946 0.554728 0.832032i \(-0.312822\pi\)
0.554728 + 0.832032i \(0.312822\pi\)
\(734\) 61.5008 2.27004
\(735\) 25.9268 0.956323
\(736\) −22.6532 −0.835009
\(737\) −12.1971 −0.449287
\(738\) −186.332 −6.85896
\(739\) 1.88716 0.0694202 0.0347101 0.999397i \(-0.488949\pi\)
0.0347101 + 0.999397i \(0.488949\pi\)
\(740\) 171.947 6.32090
\(741\) 1.74519 0.0641113
\(742\) −65.3559 −2.39929
\(743\) −49.7854 −1.82645 −0.913225 0.407456i \(-0.866416\pi\)
−0.913225 + 0.407456i \(0.866416\pi\)
\(744\) 232.725 8.53210
\(745\) 33.8296 1.23942
\(746\) −23.6170 −0.864680
\(747\) 21.3998 0.782977
\(748\) −0.684447 −0.0250259
\(749\) 25.4027 0.928194
\(750\) −106.082 −3.87358
\(751\) 29.7926 1.08715 0.543573 0.839362i \(-0.317071\pi\)
0.543573 + 0.839362i \(0.317071\pi\)
\(752\) 156.504 5.70710
\(753\) −22.7679 −0.829709
\(754\) 6.45661 0.235136
\(755\) 13.3713 0.486631
\(756\) −167.560 −6.09411
\(757\) −38.2894 −1.39165 −0.695826 0.718211i \(-0.744961\pi\)
−0.695826 + 0.718211i \(0.744961\pi\)
\(758\) 14.8714 0.540155
\(759\) −6.84157 −0.248333
\(760\) −27.3154 −0.990832
\(761\) −41.0478 −1.48798 −0.743991 0.668190i \(-0.767069\pi\)
−0.743991 + 0.668190i \(0.767069\pi\)
\(762\) −19.9130 −0.721374
\(763\) 0.0625960 0.00226613
\(764\) −66.2126 −2.39549
\(765\) 1.27491 0.0460943
\(766\) −6.73221 −0.243245
\(767\) −0.0440190 −0.00158943
\(768\) 149.934 5.41028
\(769\) −1.79045 −0.0645651 −0.0322826 0.999479i \(-0.510278\pi\)
−0.0322826 + 0.999479i \(0.510278\pi\)
\(770\) −68.9334 −2.48419
\(771\) −68.4110 −2.46376
\(772\) 142.748 5.13760
\(773\) −9.75549 −0.350880 −0.175440 0.984490i \(-0.556135\pi\)
−0.175440 + 0.984490i \(0.556135\pi\)
\(774\) 88.2382 3.17166
\(775\) −67.4210 −2.42183
\(776\) −99.4132 −3.56872
\(777\) −79.1697 −2.84020
\(778\) 7.54297 0.270429
\(779\) 8.41032 0.301331
\(780\) 45.4243 1.62645
\(781\) −0.0399862 −0.00143082
\(782\) −0.151658 −0.00542328
\(783\) −31.8299 −1.13751
\(784\) 35.4396 1.26570
\(785\) 63.0774 2.25133
\(786\) 116.063 4.13985
\(787\) −31.5872 −1.12596 −0.562982 0.826469i \(-0.690346\pi\)
−0.562982 + 0.826469i \(0.690346\pi\)
\(788\) 44.8239 1.59678
\(789\) 70.2129 2.49964
\(790\) −107.181 −3.81332
\(791\) −24.3713 −0.866543
\(792\) 135.255 4.80609
\(793\) 5.22784 0.185646
\(794\) −68.2419 −2.42182
\(795\) −87.3438 −3.09777
\(796\) 85.4804 3.02977
\(797\) −5.95512 −0.210941 −0.105471 0.994422i \(-0.533635\pi\)
−0.105471 + 0.994422i \(0.533635\pi\)
\(798\) 19.7577 0.699414
\(799\) 0.567240 0.0200675
\(800\) −191.770 −6.78009
\(801\) 88.7756 3.13673
\(802\) 80.6690 2.84852
\(803\) −25.0811 −0.885093
\(804\) 90.9929 3.20907
\(805\) −11.2026 −0.394839
\(806\) 16.1134 0.567572
\(807\) 83.0885 2.92486
\(808\) −29.5300 −1.03886
\(809\) −26.4722 −0.930714 −0.465357 0.885123i \(-0.654074\pi\)
−0.465357 + 0.885123i \(0.654074\pi\)
\(810\) −116.103 −4.07944
\(811\) 47.8933 1.68176 0.840880 0.541222i \(-0.182038\pi\)
0.840880 + 0.541222i \(0.182038\pi\)
\(812\) 53.6115 1.88140
\(813\) 64.6537 2.26750
\(814\) 52.3970 1.83651
\(815\) 20.7697 0.727532
\(816\) 2.57583 0.0901722
\(817\) −3.98275 −0.139339
\(818\) −83.7211 −2.92724
\(819\) −14.1499 −0.494437
\(820\) 218.906 7.64452
\(821\) −48.1732 −1.68126 −0.840629 0.541612i \(-0.817814\pi\)
−0.840629 + 0.541612i \(0.817814\pi\)
\(822\) 6.61775 0.230820
\(823\) −23.6930 −0.825884 −0.412942 0.910757i \(-0.635499\pi\)
−0.412942 + 0.910757i \(0.635499\pi\)
\(824\) 39.4188 1.37322
\(825\) −57.9170 −2.01641
\(826\) −0.498347 −0.0173397
\(827\) −37.3999 −1.30052 −0.650260 0.759712i \(-0.725340\pi\)
−0.650260 + 0.759712i \(0.725340\pi\)
\(828\) 34.5308 1.20003
\(829\) −0.0528682 −0.00183619 −0.000918095 1.00000i \(-0.500292\pi\)
−0.000918095 1.00000i \(0.500292\pi\)
\(830\) −34.2782 −1.18981
\(831\) −57.9651 −2.01079
\(832\) 23.2658 0.806596
\(833\) 0.128449 0.00445050
\(834\) 168.572 5.83718
\(835\) 12.7631 0.441684
\(836\) −9.59058 −0.331697
\(837\) −79.4362 −2.74572
\(838\) 57.8364 1.99793
\(839\) −14.9417 −0.515843 −0.257922 0.966166i \(-0.583038\pi\)
−0.257922 + 0.966166i \(0.583038\pi\)
\(840\) 327.352 11.2947
\(841\) −18.8159 −0.648825
\(842\) 79.4452 2.73786
\(843\) −48.7666 −1.67961
\(844\) 82.8525 2.85190
\(845\) −45.7019 −1.57219
\(846\) −176.095 −6.05426
\(847\) 18.1750 0.624501
\(848\) −119.391 −4.09991
\(849\) −87.2709 −2.99513
\(850\) −1.28385 −0.0440359
\(851\) 8.51519 0.291897
\(852\) 0.298305 0.0102198
\(853\) 48.1257 1.64779 0.823897 0.566740i \(-0.191796\pi\)
0.823897 + 0.566740i \(0.191796\pi\)
\(854\) 59.1853 2.02528
\(855\) 17.8642 0.610942
\(856\) 79.8385 2.72882
\(857\) 31.9873 1.09267 0.546333 0.837568i \(-0.316023\pi\)
0.546333 + 0.837568i \(0.316023\pi\)
\(858\) 13.8420 0.472558
\(859\) −15.4341 −0.526605 −0.263303 0.964713i \(-0.584812\pi\)
−0.263303 + 0.964713i \(0.584812\pi\)
\(860\) −103.664 −3.53490
\(861\) −100.791 −3.43494
\(862\) −6.97059 −0.237419
\(863\) −18.4689 −0.628687 −0.314344 0.949309i \(-0.601784\pi\)
−0.314344 + 0.949309i \(0.601784\pi\)
\(864\) −225.946 −7.68683
\(865\) −27.0620 −0.920137
\(866\) 22.9130 0.778614
\(867\) −51.7641 −1.75800
\(868\) 133.796 4.54132
\(869\) −23.9546 −0.812605
\(870\) 97.6885 3.31195
\(871\) 4.01041 0.135888
\(872\) 0.196734 0.00666225
\(873\) 65.0160 2.20046
\(874\) −2.12506 −0.0718811
\(875\) −38.8220 −1.31242
\(876\) 187.110 6.32186
\(877\) 30.2670 1.02204 0.511021 0.859568i \(-0.329267\pi\)
0.511021 + 0.859568i \(0.329267\pi\)
\(878\) −53.0503 −1.79036
\(879\) −93.5872 −3.15662
\(880\) −125.926 −4.24498
\(881\) 15.5556 0.524080 0.262040 0.965057i \(-0.415605\pi\)
0.262040 + 0.965057i \(0.415605\pi\)
\(882\) −39.8759 −1.34269
\(883\) 26.3816 0.887813 0.443907 0.896073i \(-0.353592\pi\)
0.443907 + 0.896073i \(0.353592\pi\)
\(884\) 0.225046 0.00756911
\(885\) −0.666008 −0.0223876
\(886\) 18.1051 0.608253
\(887\) 2.65217 0.0890511 0.0445255 0.999008i \(-0.485822\pi\)
0.0445255 + 0.999008i \(0.485822\pi\)
\(888\) −248.824 −8.34998
\(889\) −7.28740 −0.244412
\(890\) −142.201 −4.76658
\(891\) −25.9488 −0.869316
\(892\) −110.134 −3.68754
\(893\) 7.94826 0.265978
\(894\) −76.9058 −2.57211
\(895\) −58.9311 −1.96985
\(896\) 125.082 4.17870
\(897\) 2.24951 0.0751088
\(898\) −7.95784 −0.265556
\(899\) 25.4159 0.847668
\(900\) 292.319 9.74397
\(901\) −0.432728 −0.0144163
\(902\) 66.7065 2.22108
\(903\) 47.7299 1.58835
\(904\) −76.5969 −2.54758
\(905\) 75.6350 2.51419
\(906\) −30.3973 −1.00988
\(907\) −6.91578 −0.229635 −0.114817 0.993387i \(-0.536628\pi\)
−0.114817 + 0.993387i \(0.536628\pi\)
\(908\) 4.19120 0.139090
\(909\) 19.3126 0.640558
\(910\) 22.6653 0.751347
\(911\) −20.9531 −0.694206 −0.347103 0.937827i \(-0.612835\pi\)
−0.347103 + 0.937827i \(0.612835\pi\)
\(912\) 36.0930 1.19516
\(913\) −7.66109 −0.253545
\(914\) −42.2327 −1.39693
\(915\) 79.0972 2.61487
\(916\) −78.2971 −2.58701
\(917\) 42.4747 1.40264
\(918\) −1.51265 −0.0499250
\(919\) −5.53493 −0.182581 −0.0912903 0.995824i \(-0.529099\pi\)
−0.0912903 + 0.995824i \(0.529099\pi\)
\(920\) −35.2087 −1.16080
\(921\) −54.2179 −1.78654
\(922\) 74.7830 2.46285
\(923\) 0.0131475 0.000432754 0
\(924\) 114.935 3.78109
\(925\) 72.0849 2.37014
\(926\) −73.4873 −2.41494
\(927\) −25.7798 −0.846720
\(928\) 72.2921 2.37311
\(929\) −49.3768 −1.62000 −0.810000 0.586430i \(-0.800533\pi\)
−0.810000 + 0.586430i \(0.800533\pi\)
\(930\) 243.796 7.99440
\(931\) 1.79985 0.0589877
\(932\) 152.198 4.98540
\(933\) 69.3908 2.27175
\(934\) −43.7041 −1.43004
\(935\) −0.456415 −0.0149264
\(936\) −44.4719 −1.45361
\(937\) 25.8597 0.844798 0.422399 0.906410i \(-0.361188\pi\)
0.422399 + 0.906410i \(0.361188\pi\)
\(938\) 45.4026 1.48245
\(939\) 31.2471 1.01971
\(940\) 206.879 6.74765
\(941\) 8.93513 0.291277 0.145638 0.989338i \(-0.453476\pi\)
0.145638 + 0.989338i \(0.453476\pi\)
\(942\) −143.395 −4.67207
\(943\) 10.8407 0.353021
\(944\) −0.910374 −0.0296301
\(945\) −111.736 −3.63476
\(946\) −31.5892 −1.02705
\(947\) 2.10446 0.0683859 0.0341929 0.999415i \(-0.489114\pi\)
0.0341929 + 0.999415i \(0.489114\pi\)
\(948\) 178.706 5.80411
\(949\) 8.24666 0.267698
\(950\) −17.9896 −0.583659
\(951\) −40.3334 −1.30790
\(952\) 1.62180 0.0525630
\(953\) −0.672703 −0.0217910 −0.0108955 0.999941i \(-0.503468\pi\)
−0.0108955 + 0.999941i \(0.503468\pi\)
\(954\) 134.337 4.34931
\(955\) −44.1531 −1.42876
\(956\) 44.9637 1.45423
\(957\) 21.8332 0.705766
\(958\) 108.914 3.51887
\(959\) 2.42184 0.0782052
\(960\) 352.012 11.3611
\(961\) 32.4292 1.04610
\(962\) −17.2281 −0.555457
\(963\) −52.2142 −1.68258
\(964\) 68.4895 2.20590
\(965\) 95.1895 3.06426
\(966\) 25.4671 0.819389
\(967\) 1.55537 0.0500174 0.0250087 0.999687i \(-0.492039\pi\)
0.0250087 + 0.999687i \(0.492039\pi\)
\(968\) 57.1226 1.83599
\(969\) 0.130817 0.00420246
\(970\) −104.143 −3.34382
\(971\) 22.9694 0.737123 0.368561 0.929603i \(-0.379850\pi\)
0.368561 + 0.929603i \(0.379850\pi\)
\(972\) 28.9238 0.927732
\(973\) 61.6909 1.97772
\(974\) 41.8157 1.33986
\(975\) 19.0431 0.609867
\(976\) 108.119 3.46080
\(977\) −49.9392 −1.59770 −0.798848 0.601533i \(-0.794557\pi\)
−0.798848 + 0.601533i \(0.794557\pi\)
\(978\) −47.2164 −1.50981
\(979\) −31.7816 −1.01574
\(980\) 46.8469 1.49647
\(981\) −0.128664 −0.00410791
\(982\) 62.0663 1.98062
\(983\) −15.1476 −0.483133 −0.241567 0.970384i \(-0.577661\pi\)
−0.241567 + 0.970384i \(0.577661\pi\)
\(984\) −316.777 −10.0985
\(985\) 29.8902 0.952382
\(986\) 0.483979 0.0154130
\(987\) −95.2534 −3.03195
\(988\) 3.15338 0.100322
\(989\) −5.13365 −0.163240
\(990\) 141.690 4.50320
\(991\) 58.4748 1.85751 0.928756 0.370691i \(-0.120879\pi\)
0.928756 + 0.370691i \(0.120879\pi\)
\(992\) 180.416 5.72821
\(993\) 96.4428 3.06052
\(994\) 0.148845 0.00472107
\(995\) 57.0015 1.80707
\(996\) 57.1533 1.81097
\(997\) 53.7018 1.70075 0.850377 0.526174i \(-0.176374\pi\)
0.850377 + 0.526174i \(0.176374\pi\)
\(998\) −68.7422 −2.17600
\(999\) 84.9314 2.68711
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 \(a_p\))