Properties

Label 8047.2.a.b.1.12
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51095 q^{2} -2.93259 q^{3} +4.30485 q^{4} -3.06715 q^{5} +7.36357 q^{6} +3.82085 q^{7} -5.78735 q^{8} +5.60007 q^{9} +O(q^{10})\) \(q-2.51095 q^{2} -2.93259 q^{3} +4.30485 q^{4} -3.06715 q^{5} +7.36357 q^{6} +3.82085 q^{7} -5.78735 q^{8} +5.60007 q^{9} +7.70146 q^{10} -0.749081 q^{11} -12.6243 q^{12} +1.00000 q^{13} -9.59395 q^{14} +8.99470 q^{15} +5.92201 q^{16} -6.57187 q^{17} -14.0615 q^{18} +5.95299 q^{19} -13.2036 q^{20} -11.2050 q^{21} +1.88090 q^{22} +7.17254 q^{23} +16.9719 q^{24} +4.40744 q^{25} -2.51095 q^{26} -7.62494 q^{27} +16.4482 q^{28} +0.412040 q^{29} -22.5852 q^{30} +0.475285 q^{31} -3.29516 q^{32} +2.19675 q^{33} +16.5016 q^{34} -11.7191 q^{35} +24.1075 q^{36} +7.83017 q^{37} -14.9476 q^{38} -2.93259 q^{39} +17.7507 q^{40} -6.09709 q^{41} +28.1351 q^{42} +3.56425 q^{43} -3.22468 q^{44} -17.1763 q^{45} -18.0099 q^{46} -7.17897 q^{47} -17.3668 q^{48} +7.59890 q^{49} -11.0668 q^{50} +19.2726 q^{51} +4.30485 q^{52} +11.7259 q^{53} +19.1458 q^{54} +2.29755 q^{55} -22.1126 q^{56} -17.4577 q^{57} -1.03461 q^{58} -8.83797 q^{59} +38.7208 q^{60} -4.24712 q^{61} -1.19342 q^{62} +21.3970 q^{63} -3.57005 q^{64} -3.06715 q^{65} -5.51591 q^{66} -11.6021 q^{67} -28.2909 q^{68} -21.0341 q^{69} +29.4261 q^{70} +12.4021 q^{71} -32.4095 q^{72} +2.64223 q^{73} -19.6611 q^{74} -12.9252 q^{75} +25.6267 q^{76} -2.86213 q^{77} +7.36357 q^{78} -4.45566 q^{79} -18.1637 q^{80} +5.56059 q^{81} +15.3095 q^{82} -13.0176 q^{83} -48.2357 q^{84} +20.1569 q^{85} -8.94963 q^{86} -1.20834 q^{87} +4.33519 q^{88} +18.6311 q^{89} +43.1287 q^{90} +3.82085 q^{91} +30.8767 q^{92} -1.39382 q^{93} +18.0260 q^{94} -18.2588 q^{95} +9.66336 q^{96} -17.0653 q^{97} -19.0804 q^{98} -4.19491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51095 −1.77551 −0.887753 0.460320i \(-0.847735\pi\)
−0.887753 + 0.460320i \(0.847735\pi\)
\(3\) −2.93259 −1.69313 −0.846565 0.532285i \(-0.821333\pi\)
−0.846565 + 0.532285i \(0.821333\pi\)
\(4\) 4.30485 2.15242
\(5\) −3.06715 −1.37167 −0.685837 0.727755i \(-0.740564\pi\)
−0.685837 + 0.727755i \(0.740564\pi\)
\(6\) 7.36357 3.00616
\(7\) 3.82085 1.44415 0.722073 0.691817i \(-0.243189\pi\)
0.722073 + 0.691817i \(0.243189\pi\)
\(8\) −5.78735 −2.04614
\(9\) 5.60007 1.86669
\(10\) 7.70146 2.43542
\(11\) −0.749081 −0.225856 −0.112928 0.993603i \(-0.536023\pi\)
−0.112928 + 0.993603i \(0.536023\pi\)
\(12\) −12.6243 −3.64433
\(13\) 1.00000 0.277350
\(14\) −9.59395 −2.56409
\(15\) 8.99470 2.32242
\(16\) 5.92201 1.48050
\(17\) −6.57187 −1.59391 −0.796956 0.604037i \(-0.793558\pi\)
−0.796956 + 0.604037i \(0.793558\pi\)
\(18\) −14.0615 −3.31432
\(19\) 5.95299 1.36571 0.682855 0.730554i \(-0.260738\pi\)
0.682855 + 0.730554i \(0.260738\pi\)
\(20\) −13.2036 −2.95242
\(21\) −11.2050 −2.44513
\(22\) 1.88090 0.401009
\(23\) 7.17254 1.49558 0.747789 0.663937i \(-0.231116\pi\)
0.747789 + 0.663937i \(0.231116\pi\)
\(24\) 16.9719 3.46437
\(25\) 4.40744 0.881488
\(26\) −2.51095 −0.492437
\(27\) −7.62494 −1.46742
\(28\) 16.4482 3.10841
\(29\) 0.412040 0.0765140 0.0382570 0.999268i \(-0.487819\pi\)
0.0382570 + 0.999268i \(0.487819\pi\)
\(30\) −22.5852 −4.12348
\(31\) 0.475285 0.0853638 0.0426819 0.999089i \(-0.486410\pi\)
0.0426819 + 0.999089i \(0.486410\pi\)
\(32\) −3.29516 −0.582508
\(33\) 2.19675 0.382404
\(34\) 16.5016 2.83000
\(35\) −11.7191 −1.98090
\(36\) 24.1075 4.01791
\(37\) 7.83017 1.28727 0.643636 0.765332i \(-0.277425\pi\)
0.643636 + 0.765332i \(0.277425\pi\)
\(38\) −14.9476 −2.42483
\(39\) −2.93259 −0.469590
\(40\) 17.7507 2.80663
\(41\) −6.09709 −0.952206 −0.476103 0.879390i \(-0.657951\pi\)
−0.476103 + 0.879390i \(0.657951\pi\)
\(42\) 28.1351 4.34134
\(43\) 3.56425 0.543542 0.271771 0.962362i \(-0.412391\pi\)
0.271771 + 0.962362i \(0.412391\pi\)
\(44\) −3.22468 −0.486138
\(45\) −17.1763 −2.56049
\(46\) −18.0099 −2.65541
\(47\) −7.17897 −1.04716 −0.523580 0.851976i \(-0.675404\pi\)
−0.523580 + 0.851976i \(0.675404\pi\)
\(48\) −17.3668 −2.50669
\(49\) 7.59890 1.08556
\(50\) −11.0668 −1.56509
\(51\) 19.2726 2.69870
\(52\) 4.30485 0.596975
\(53\) 11.7259 1.61068 0.805338 0.592816i \(-0.201984\pi\)
0.805338 + 0.592816i \(0.201984\pi\)
\(54\) 19.1458 2.60541
\(55\) 2.29755 0.309801
\(56\) −22.1126 −2.95492
\(57\) −17.4577 −2.31233
\(58\) −1.03461 −0.135851
\(59\) −8.83797 −1.15061 −0.575303 0.817940i \(-0.695116\pi\)
−0.575303 + 0.817940i \(0.695116\pi\)
\(60\) 38.7208 4.99884
\(61\) −4.24712 −0.543788 −0.271894 0.962327i \(-0.587650\pi\)
−0.271894 + 0.962327i \(0.587650\pi\)
\(62\) −1.19342 −0.151564
\(63\) 21.3970 2.69577
\(64\) −3.57005 −0.446256
\(65\) −3.06715 −0.380434
\(66\) −5.51591 −0.678961
\(67\) −11.6021 −1.41743 −0.708713 0.705497i \(-0.750724\pi\)
−0.708713 + 0.705497i \(0.750724\pi\)
\(68\) −28.2909 −3.43078
\(69\) −21.0341 −2.53221
\(70\) 29.4261 3.51709
\(71\) 12.4021 1.47185 0.735927 0.677061i \(-0.236747\pi\)
0.735927 + 0.677061i \(0.236747\pi\)
\(72\) −32.4095 −3.81950
\(73\) 2.64223 0.309250 0.154625 0.987973i \(-0.450583\pi\)
0.154625 + 0.987973i \(0.450583\pi\)
\(74\) −19.6611 −2.28556
\(75\) −12.9252 −1.49247
\(76\) 25.6267 2.93959
\(77\) −2.86213 −0.326169
\(78\) 7.36357 0.833760
\(79\) −4.45566 −0.501300 −0.250650 0.968078i \(-0.580644\pi\)
−0.250650 + 0.968078i \(0.580644\pi\)
\(80\) −18.1637 −2.03077
\(81\) 5.56059 0.617843
\(82\) 15.3095 1.69065
\(83\) −13.0176 −1.42887 −0.714434 0.699703i \(-0.753316\pi\)
−0.714434 + 0.699703i \(0.753316\pi\)
\(84\) −48.2357 −5.26295
\(85\) 20.1569 2.18633
\(86\) −8.94963 −0.965063
\(87\) −1.20834 −0.129548
\(88\) 4.33519 0.462133
\(89\) 18.6311 1.97490 0.987448 0.157943i \(-0.0504864\pi\)
0.987448 + 0.157943i \(0.0504864\pi\)
\(90\) 43.1287 4.54617
\(91\) 3.82085 0.400534
\(92\) 30.8767 3.21912
\(93\) −1.39382 −0.144532
\(94\) 18.0260 1.85924
\(95\) −18.2588 −1.87331
\(96\) 9.66336 0.986263
\(97\) −17.0653 −1.73272 −0.866359 0.499421i \(-0.833546\pi\)
−0.866359 + 0.499421i \(0.833546\pi\)
\(98\) −19.0804 −1.92741
\(99\) −4.19491 −0.421604
\(100\) 18.9734 1.89734
\(101\) 8.21460 0.817383 0.408691 0.912673i \(-0.365985\pi\)
0.408691 + 0.912673i \(0.365985\pi\)
\(102\) −48.3924 −4.79156
\(103\) −12.6003 −1.24155 −0.620774 0.783989i \(-0.713182\pi\)
−0.620774 + 0.783989i \(0.713182\pi\)
\(104\) −5.78735 −0.567496
\(105\) 34.3674 3.35392
\(106\) −29.4431 −2.85976
\(107\) −4.80628 −0.464641 −0.232320 0.972639i \(-0.574632\pi\)
−0.232320 + 0.972639i \(0.574632\pi\)
\(108\) −32.8242 −3.15851
\(109\) 0.0196813 0.00188513 0.000942564 1.00000i \(-0.499700\pi\)
0.000942564 1.00000i \(0.499700\pi\)
\(110\) −5.76901 −0.550054
\(111\) −22.9627 −2.17952
\(112\) 22.6271 2.13806
\(113\) −17.5678 −1.65264 −0.826318 0.563203i \(-0.809569\pi\)
−0.826318 + 0.563203i \(0.809569\pi\)
\(114\) 43.8353 4.10555
\(115\) −21.9993 −2.05144
\(116\) 1.77377 0.164691
\(117\) 5.60007 0.517727
\(118\) 22.1917 2.04291
\(119\) −25.1101 −2.30184
\(120\) −52.0554 −4.75199
\(121\) −10.4389 −0.948989
\(122\) 10.6643 0.965498
\(123\) 17.8803 1.61221
\(124\) 2.04603 0.183739
\(125\) 1.81748 0.162560
\(126\) −53.7268 −4.78636
\(127\) −18.2482 −1.61926 −0.809631 0.586939i \(-0.800333\pi\)
−0.809631 + 0.586939i \(0.800333\pi\)
\(128\) 15.5545 1.37484
\(129\) −10.4525 −0.920288
\(130\) 7.70146 0.675463
\(131\) −2.35837 −0.206052 −0.103026 0.994679i \(-0.532853\pi\)
−0.103026 + 0.994679i \(0.532853\pi\)
\(132\) 9.45665 0.823096
\(133\) 22.7455 1.97228
\(134\) 29.1323 2.51665
\(135\) 23.3869 2.01282
\(136\) 38.0337 3.26136
\(137\) −23.0178 −1.96654 −0.983271 0.182149i \(-0.941695\pi\)
−0.983271 + 0.182149i \(0.941695\pi\)
\(138\) 52.8155 4.49595
\(139\) 1.43869 0.122028 0.0610139 0.998137i \(-0.480567\pi\)
0.0610139 + 0.998137i \(0.480567\pi\)
\(140\) −50.4491 −4.26373
\(141\) 21.0530 1.77298
\(142\) −31.1409 −2.61329
\(143\) −0.749081 −0.0626413
\(144\) 33.1637 2.76364
\(145\) −1.26379 −0.104952
\(146\) −6.63450 −0.549075
\(147\) −22.2844 −1.83799
\(148\) 33.7077 2.77075
\(149\) 4.54911 0.372678 0.186339 0.982486i \(-0.440338\pi\)
0.186339 + 0.982486i \(0.440338\pi\)
\(150\) 32.4545 2.64990
\(151\) −10.0100 −0.814600 −0.407300 0.913294i \(-0.633530\pi\)
−0.407300 + 0.913294i \(0.633530\pi\)
\(152\) −34.4520 −2.79443
\(153\) −36.8029 −2.97534
\(154\) 7.18664 0.579116
\(155\) −1.45777 −0.117091
\(156\) −12.6243 −1.01076
\(157\) 14.8366 1.18409 0.592043 0.805906i \(-0.298321\pi\)
0.592043 + 0.805906i \(0.298321\pi\)
\(158\) 11.1879 0.890062
\(159\) −34.3872 −2.72708
\(160\) 10.1068 0.799011
\(161\) 27.4052 2.15983
\(162\) −13.9623 −1.09698
\(163\) 15.7145 1.23086 0.615428 0.788193i \(-0.288983\pi\)
0.615428 + 0.788193i \(0.288983\pi\)
\(164\) −26.2470 −2.04955
\(165\) −6.73776 −0.524534
\(166\) 32.6865 2.53696
\(167\) 2.36711 0.183172 0.0915861 0.995797i \(-0.470806\pi\)
0.0915861 + 0.995797i \(0.470806\pi\)
\(168\) 64.8471 5.00306
\(169\) 1.00000 0.0769231
\(170\) −50.6130 −3.88184
\(171\) 33.3372 2.54936
\(172\) 15.3435 1.16993
\(173\) −15.5318 −1.18086 −0.590432 0.807087i \(-0.701043\pi\)
−0.590432 + 0.807087i \(0.701043\pi\)
\(174\) 3.03409 0.230014
\(175\) 16.8402 1.27300
\(176\) −4.43607 −0.334381
\(177\) 25.9181 1.94813
\(178\) −46.7818 −3.50644
\(179\) 11.5547 0.863635 0.431818 0.901961i \(-0.357872\pi\)
0.431818 + 0.901961i \(0.357872\pi\)
\(180\) −73.9413 −5.51126
\(181\) 18.7197 1.39142 0.695712 0.718321i \(-0.255089\pi\)
0.695712 + 0.718321i \(0.255089\pi\)
\(182\) −9.59395 −0.711151
\(183\) 12.4550 0.920703
\(184\) −41.5100 −3.06015
\(185\) −24.0163 −1.76572
\(186\) 3.49980 0.256617
\(187\) 4.92286 0.359995
\(188\) −30.9044 −2.25393
\(189\) −29.1338 −2.11917
\(190\) 45.8467 3.32607
\(191\) 22.8428 1.65285 0.826423 0.563050i \(-0.190372\pi\)
0.826423 + 0.563050i \(0.190372\pi\)
\(192\) 10.4695 0.755570
\(193\) −0.741921 −0.0534046 −0.0267023 0.999643i \(-0.508501\pi\)
−0.0267023 + 0.999643i \(0.508501\pi\)
\(194\) 42.8500 3.07645
\(195\) 8.99470 0.644124
\(196\) 32.7121 2.33658
\(197\) 7.14733 0.509226 0.254613 0.967043i \(-0.418052\pi\)
0.254613 + 0.967043i \(0.418052\pi\)
\(198\) 10.5332 0.748560
\(199\) 1.89945 0.134649 0.0673244 0.997731i \(-0.478554\pi\)
0.0673244 + 0.997731i \(0.478554\pi\)
\(200\) −25.5074 −1.80364
\(201\) 34.0243 2.39989
\(202\) −20.6264 −1.45127
\(203\) 1.57435 0.110497
\(204\) 82.9655 5.80875
\(205\) 18.7007 1.30612
\(206\) 31.6388 2.20438
\(207\) 40.1667 2.79178
\(208\) 5.92201 0.410618
\(209\) −4.45927 −0.308454
\(210\) −86.2947 −5.95490
\(211\) −0.153142 −0.0105427 −0.00527136 0.999986i \(-0.501678\pi\)
−0.00527136 + 0.999986i \(0.501678\pi\)
\(212\) 50.4782 3.46686
\(213\) −36.3701 −2.49204
\(214\) 12.0683 0.824972
\(215\) −10.9321 −0.745563
\(216\) 44.1282 3.00254
\(217\) 1.81599 0.123278
\(218\) −0.0494187 −0.00334706
\(219\) −7.74857 −0.523600
\(220\) 9.89059 0.666823
\(221\) −6.57187 −0.442072
\(222\) 57.6580 3.86975
\(223\) −23.4689 −1.57159 −0.785797 0.618485i \(-0.787747\pi\)
−0.785797 + 0.618485i \(0.787747\pi\)
\(224\) −12.5903 −0.841227
\(225\) 24.6820 1.64547
\(226\) 44.1117 2.93427
\(227\) −2.07557 −0.137760 −0.0688802 0.997625i \(-0.521943\pi\)
−0.0688802 + 0.997625i \(0.521943\pi\)
\(228\) −75.1526 −4.97710
\(229\) −19.0655 −1.25988 −0.629942 0.776642i \(-0.716921\pi\)
−0.629942 + 0.776642i \(0.716921\pi\)
\(230\) 55.2390 3.64235
\(231\) 8.39343 0.552247
\(232\) −2.38462 −0.156558
\(233\) 9.65407 0.632459 0.316230 0.948683i \(-0.397583\pi\)
0.316230 + 0.948683i \(0.397583\pi\)
\(234\) −14.0615 −0.919227
\(235\) 22.0190 1.43636
\(236\) −38.0461 −2.47659
\(237\) 13.0666 0.848767
\(238\) 63.0502 4.08694
\(239\) 5.68936 0.368014 0.184007 0.982925i \(-0.441093\pi\)
0.184007 + 0.982925i \(0.441093\pi\)
\(240\) 53.2668 3.43835
\(241\) 14.6817 0.945732 0.472866 0.881134i \(-0.343219\pi\)
0.472866 + 0.881134i \(0.343219\pi\)
\(242\) 26.2115 1.68494
\(243\) 6.56790 0.421331
\(244\) −18.2832 −1.17046
\(245\) −23.3070 −1.48903
\(246\) −44.8964 −2.86249
\(247\) 5.95299 0.378780
\(248\) −2.75064 −0.174666
\(249\) 38.1753 2.41926
\(250\) −4.56358 −0.288626
\(251\) 8.85729 0.559067 0.279534 0.960136i \(-0.409820\pi\)
0.279534 + 0.960136i \(0.409820\pi\)
\(252\) 92.1110 5.80245
\(253\) −5.37281 −0.337786
\(254\) 45.8201 2.87501
\(255\) −59.1120 −3.70174
\(256\) −31.9165 −1.99478
\(257\) −3.33415 −0.207979 −0.103989 0.994578i \(-0.533161\pi\)
−0.103989 + 0.994578i \(0.533161\pi\)
\(258\) 26.2456 1.63398
\(259\) 29.9179 1.85901
\(260\) −13.2036 −0.818855
\(261\) 2.30746 0.142828
\(262\) 5.92175 0.365847
\(263\) −11.3542 −0.700130 −0.350065 0.936725i \(-0.613840\pi\)
−0.350065 + 0.936725i \(0.613840\pi\)
\(264\) −12.7133 −0.782451
\(265\) −35.9651 −2.20932
\(266\) −57.1127 −3.50180
\(267\) −54.6374 −3.34376
\(268\) −49.9454 −3.05090
\(269\) 0.573796 0.0349850 0.0174925 0.999847i \(-0.494432\pi\)
0.0174925 + 0.999847i \(0.494432\pi\)
\(270\) −58.7231 −3.57378
\(271\) −25.0626 −1.52245 −0.761223 0.648490i \(-0.775401\pi\)
−0.761223 + 0.648490i \(0.775401\pi\)
\(272\) −38.9187 −2.35979
\(273\) −11.2050 −0.678156
\(274\) 57.7964 3.49161
\(275\) −3.30153 −0.199090
\(276\) −90.5486 −5.45038
\(277\) −5.48033 −0.329281 −0.164641 0.986354i \(-0.552646\pi\)
−0.164641 + 0.986354i \(0.552646\pi\)
\(278\) −3.61247 −0.216661
\(279\) 2.66163 0.159348
\(280\) 67.8227 4.05318
\(281\) 31.4182 1.87425 0.937126 0.348992i \(-0.113476\pi\)
0.937126 + 0.348992i \(0.113476\pi\)
\(282\) −52.8628 −3.14794
\(283\) −5.70825 −0.339320 −0.169660 0.985503i \(-0.554267\pi\)
−0.169660 + 0.985503i \(0.554267\pi\)
\(284\) 53.3890 3.16805
\(285\) 53.5454 3.17176
\(286\) 1.88090 0.111220
\(287\) −23.2961 −1.37512
\(288\) −18.4532 −1.08736
\(289\) 26.1895 1.54056
\(290\) 3.17331 0.186343
\(291\) 50.0455 2.93372
\(292\) 11.3744 0.665636
\(293\) 18.3929 1.07453 0.537263 0.843415i \(-0.319458\pi\)
0.537263 + 0.843415i \(0.319458\pi\)
\(294\) 55.9550 3.26336
\(295\) 27.1074 1.57826
\(296\) −45.3159 −2.63393
\(297\) 5.71169 0.331426
\(298\) −11.4226 −0.661692
\(299\) 7.17254 0.414799
\(300\) −55.6410 −3.21244
\(301\) 13.6185 0.784954
\(302\) 25.1345 1.44633
\(303\) −24.0900 −1.38394
\(304\) 35.2537 2.02194
\(305\) 13.0266 0.745899
\(306\) 92.4102 5.28274
\(307\) −13.6422 −0.778599 −0.389299 0.921111i \(-0.627283\pi\)
−0.389299 + 0.921111i \(0.627283\pi\)
\(308\) −12.3210 −0.702055
\(309\) 36.9516 2.10210
\(310\) 3.66039 0.207896
\(311\) 10.8019 0.612518 0.306259 0.951948i \(-0.400923\pi\)
0.306259 + 0.951948i \(0.400923\pi\)
\(312\) 16.9719 0.960845
\(313\) −10.5925 −0.598722 −0.299361 0.954140i \(-0.596774\pi\)
−0.299361 + 0.954140i \(0.596774\pi\)
\(314\) −37.2538 −2.10235
\(315\) −65.6280 −3.69772
\(316\) −19.1809 −1.07901
\(317\) 22.1119 1.24193 0.620963 0.783840i \(-0.286742\pi\)
0.620963 + 0.783840i \(0.286742\pi\)
\(318\) 86.3444 4.84195
\(319\) −0.308652 −0.0172812
\(320\) 10.9499 0.612118
\(321\) 14.0948 0.786697
\(322\) −68.8130 −3.83480
\(323\) −39.1223 −2.17682
\(324\) 23.9375 1.32986
\(325\) 4.40744 0.244481
\(326\) −39.4583 −2.18539
\(327\) −0.0577172 −0.00319177
\(328\) 35.2860 1.94834
\(329\) −27.4298 −1.51225
\(330\) 16.9181 0.931313
\(331\) 20.2468 1.11287 0.556433 0.830893i \(-0.312170\pi\)
0.556433 + 0.830893i \(0.312170\pi\)
\(332\) −56.0388 −3.07553
\(333\) 43.8495 2.40294
\(334\) −5.94368 −0.325224
\(335\) 35.5855 1.94425
\(336\) −66.3561 −3.62002
\(337\) 3.44942 0.187902 0.0939510 0.995577i \(-0.470050\pi\)
0.0939510 + 0.995577i \(0.470050\pi\)
\(338\) −2.51095 −0.136577
\(339\) 51.5190 2.79813
\(340\) 86.7726 4.70590
\(341\) −0.356027 −0.0192799
\(342\) −83.7079 −4.52640
\(343\) 2.28831 0.123557
\(344\) −20.6275 −1.11216
\(345\) 64.5148 3.47336
\(346\) 38.9996 2.09663
\(347\) −19.7336 −1.05935 −0.529677 0.848199i \(-0.677687\pi\)
−0.529677 + 0.848199i \(0.677687\pi\)
\(348\) −5.20174 −0.278843
\(349\) −10.1289 −0.542189 −0.271094 0.962553i \(-0.587386\pi\)
−0.271094 + 0.962553i \(0.587386\pi\)
\(350\) −42.2847 −2.26021
\(351\) −7.62494 −0.406989
\(352\) 2.46834 0.131563
\(353\) 17.2160 0.916313 0.458157 0.888871i \(-0.348510\pi\)
0.458157 + 0.888871i \(0.348510\pi\)
\(354\) −65.0790 −3.45891
\(355\) −38.0390 −2.01890
\(356\) 80.2042 4.25081
\(357\) 73.6377 3.89732
\(358\) −29.0131 −1.53339
\(359\) −29.4540 −1.55452 −0.777261 0.629178i \(-0.783392\pi\)
−0.777261 + 0.629178i \(0.783392\pi\)
\(360\) 99.4051 5.23911
\(361\) 16.4381 0.865164
\(362\) −47.0041 −2.47048
\(363\) 30.6129 1.60676
\(364\) 16.4482 0.862119
\(365\) −8.10413 −0.424190
\(366\) −31.2739 −1.63471
\(367\) −35.7815 −1.86778 −0.933891 0.357558i \(-0.883609\pi\)
−0.933891 + 0.357558i \(0.883609\pi\)
\(368\) 42.4759 2.21421
\(369\) −34.1442 −1.77747
\(370\) 60.3037 3.13504
\(371\) 44.8029 2.32605
\(372\) −6.00016 −0.311094
\(373\) −1.08646 −0.0562545 −0.0281273 0.999604i \(-0.508954\pi\)
−0.0281273 + 0.999604i \(0.508954\pi\)
\(374\) −12.3610 −0.639174
\(375\) −5.32991 −0.275235
\(376\) 41.5472 2.14263
\(377\) 0.412040 0.0212212
\(378\) 73.1533 3.76260
\(379\) 7.08196 0.363776 0.181888 0.983319i \(-0.441779\pi\)
0.181888 + 0.983319i \(0.441779\pi\)
\(380\) −78.6011 −4.03215
\(381\) 53.5143 2.74162
\(382\) −57.3570 −2.93464
\(383\) 16.7244 0.854578 0.427289 0.904115i \(-0.359469\pi\)
0.427289 + 0.904115i \(0.359469\pi\)
\(384\) −45.6150 −2.32778
\(385\) 8.77858 0.447398
\(386\) 1.86292 0.0948203
\(387\) 19.9600 1.01463
\(388\) −73.4635 −3.72955
\(389\) −19.5849 −0.992992 −0.496496 0.868039i \(-0.665380\pi\)
−0.496496 + 0.868039i \(0.665380\pi\)
\(390\) −22.5852 −1.14365
\(391\) −47.1370 −2.38382
\(392\) −43.9775 −2.22120
\(393\) 6.91614 0.348873
\(394\) −17.9466 −0.904134
\(395\) 13.6662 0.687621
\(396\) −18.0584 −0.907470
\(397\) −16.6132 −0.833792 −0.416896 0.908954i \(-0.636882\pi\)
−0.416896 + 0.908954i \(0.636882\pi\)
\(398\) −4.76943 −0.239070
\(399\) −66.7032 −3.33934
\(400\) 26.1009 1.30505
\(401\) 17.1393 0.855894 0.427947 0.903804i \(-0.359237\pi\)
0.427947 + 0.903804i \(0.359237\pi\)
\(402\) −85.4331 −4.26101
\(403\) 0.475285 0.0236756
\(404\) 35.3626 1.75935
\(405\) −17.0552 −0.847479
\(406\) −3.95309 −0.196189
\(407\) −5.86543 −0.290738
\(408\) −111.537 −5.52191
\(409\) 16.8137 0.831382 0.415691 0.909506i \(-0.363540\pi\)
0.415691 + 0.909506i \(0.363540\pi\)
\(410\) −46.9565 −2.31902
\(411\) 67.5017 3.32961
\(412\) −54.2425 −2.67234
\(413\) −33.7686 −1.66164
\(414\) −100.856 −4.95682
\(415\) 39.9270 1.95994
\(416\) −3.29516 −0.161559
\(417\) −4.21908 −0.206609
\(418\) 11.1970 0.547663
\(419\) 12.5347 0.612360 0.306180 0.951974i \(-0.400949\pi\)
0.306180 + 0.951974i \(0.400949\pi\)
\(420\) 147.946 7.21905
\(421\) −33.0625 −1.61137 −0.805685 0.592344i \(-0.798203\pi\)
−0.805685 + 0.592344i \(0.798203\pi\)
\(422\) 0.384531 0.0187187
\(423\) −40.2027 −1.95472
\(424\) −67.8618 −3.29566
\(425\) −28.9651 −1.40501
\(426\) 91.3234 4.42463
\(427\) −16.2276 −0.785309
\(428\) −20.6903 −1.00010
\(429\) 2.19675 0.106060
\(430\) 27.4499 1.32375
\(431\) 36.8853 1.77670 0.888350 0.459167i \(-0.151852\pi\)
0.888350 + 0.459167i \(0.151852\pi\)
\(432\) −45.1550 −2.17252
\(433\) 15.1503 0.728075 0.364038 0.931384i \(-0.381398\pi\)
0.364038 + 0.931384i \(0.381398\pi\)
\(434\) −4.55986 −0.218880
\(435\) 3.70618 0.177698
\(436\) 0.0847250 0.00405759
\(437\) 42.6981 2.04253
\(438\) 19.4562 0.929655
\(439\) 27.5223 1.31357 0.656784 0.754078i \(-0.271916\pi\)
0.656784 + 0.754078i \(0.271916\pi\)
\(440\) −13.2967 −0.633895
\(441\) 42.5544 2.02640
\(442\) 16.5016 0.784901
\(443\) 11.6361 0.552849 0.276425 0.961036i \(-0.410850\pi\)
0.276425 + 0.961036i \(0.410850\pi\)
\(444\) −98.8507 −4.69125
\(445\) −57.1446 −2.70891
\(446\) 58.9291 2.79037
\(447\) −13.3407 −0.630992
\(448\) −13.6406 −0.644459
\(449\) −24.4068 −1.15183 −0.575914 0.817510i \(-0.695354\pi\)
−0.575914 + 0.817510i \(0.695354\pi\)
\(450\) −61.9751 −2.92153
\(451\) 4.56721 0.215062
\(452\) −75.6266 −3.55717
\(453\) 29.3551 1.37922
\(454\) 5.21164 0.244594
\(455\) −11.7191 −0.549402
\(456\) 101.034 4.73133
\(457\) 8.27890 0.387270 0.193635 0.981074i \(-0.437972\pi\)
0.193635 + 0.981074i \(0.437972\pi\)
\(458\) 47.8724 2.23693
\(459\) 50.1101 2.33894
\(460\) −94.7036 −4.41558
\(461\) −6.89724 −0.321236 −0.160618 0.987017i \(-0.551349\pi\)
−0.160618 + 0.987017i \(0.551349\pi\)
\(462\) −21.0755 −0.980519
\(463\) 9.61766 0.446970 0.223485 0.974707i \(-0.428257\pi\)
0.223485 + 0.974707i \(0.428257\pi\)
\(464\) 2.44011 0.113279
\(465\) 4.27505 0.198251
\(466\) −24.2408 −1.12294
\(467\) −34.1652 −1.58098 −0.790488 0.612477i \(-0.790173\pi\)
−0.790488 + 0.612477i \(0.790173\pi\)
\(468\) 24.1075 1.11437
\(469\) −44.3300 −2.04697
\(470\) −55.2885 −2.55027
\(471\) −43.5095 −2.00481
\(472\) 51.1484 2.35430
\(473\) −2.66991 −0.122762
\(474\) −32.8095 −1.50699
\(475\) 26.2375 1.20386
\(476\) −108.095 −4.95454
\(477\) 65.6658 3.00663
\(478\) −14.2857 −0.653411
\(479\) 18.1797 0.830654 0.415327 0.909672i \(-0.363667\pi\)
0.415327 + 0.909672i \(0.363667\pi\)
\(480\) −29.6390 −1.35283
\(481\) 7.83017 0.357025
\(482\) −36.8650 −1.67915
\(483\) −80.3681 −3.65688
\(484\) −44.9378 −2.04263
\(485\) 52.3419 2.37672
\(486\) −16.4917 −0.748076
\(487\) 3.03173 0.137381 0.0686904 0.997638i \(-0.478118\pi\)
0.0686904 + 0.997638i \(0.478118\pi\)
\(488\) 24.5795 1.11266
\(489\) −46.0842 −2.08400
\(490\) 58.5226 2.64378
\(491\) 30.2964 1.36726 0.683629 0.729829i \(-0.260401\pi\)
0.683629 + 0.729829i \(0.260401\pi\)
\(492\) 76.9718 3.47016
\(493\) −2.70788 −0.121957
\(494\) −14.9476 −0.672526
\(495\) 12.8664 0.578303
\(496\) 2.81465 0.126381
\(497\) 47.3864 2.12557
\(498\) −95.8560 −4.29541
\(499\) 15.0802 0.675082 0.337541 0.941311i \(-0.390405\pi\)
0.337541 + 0.941311i \(0.390405\pi\)
\(500\) 7.82395 0.349898
\(501\) −6.94175 −0.310135
\(502\) −22.2402 −0.992627
\(503\) −40.5273 −1.80702 −0.903512 0.428562i \(-0.859020\pi\)
−0.903512 + 0.428562i \(0.859020\pi\)
\(504\) −123.832 −5.51592
\(505\) −25.1954 −1.12118
\(506\) 13.4908 0.599741
\(507\) −2.93259 −0.130241
\(508\) −78.5555 −3.48534
\(509\) −24.9313 −1.10506 −0.552531 0.833492i \(-0.686338\pi\)
−0.552531 + 0.833492i \(0.686338\pi\)
\(510\) 148.427 6.57246
\(511\) 10.0956 0.446602
\(512\) 49.0315 2.16691
\(513\) −45.3912 −2.00407
\(514\) 8.37187 0.369267
\(515\) 38.6472 1.70300
\(516\) −44.9963 −1.98085
\(517\) 5.37763 0.236508
\(518\) −75.1222 −3.30068
\(519\) 45.5485 1.99936
\(520\) 17.7507 0.778419
\(521\) −11.7291 −0.513862 −0.256931 0.966430i \(-0.582711\pi\)
−0.256931 + 0.966430i \(0.582711\pi\)
\(522\) −5.79390 −0.253592
\(523\) 31.7559 1.38859 0.694294 0.719692i \(-0.255717\pi\)
0.694294 + 0.719692i \(0.255717\pi\)
\(524\) −10.1524 −0.443512
\(525\) −49.3853 −2.15535
\(526\) 28.5098 1.24308
\(527\) −3.12351 −0.136062
\(528\) 13.0092 0.566151
\(529\) 28.4453 1.23675
\(530\) 90.3065 3.92266
\(531\) −49.4933 −2.14783
\(532\) 97.9159 4.24519
\(533\) −6.09709 −0.264094
\(534\) 137.192 5.93686
\(535\) 14.7416 0.637335
\(536\) 67.1455 2.90025
\(537\) −33.8850 −1.46225
\(538\) −1.44077 −0.0621160
\(539\) −5.69219 −0.245180
\(540\) 100.677 4.33244
\(541\) −1.98254 −0.0852361 −0.0426181 0.999091i \(-0.513570\pi\)
−0.0426181 + 0.999091i \(0.513570\pi\)
\(542\) 62.9309 2.70311
\(543\) −54.8971 −2.35586
\(544\) 21.6554 0.928467
\(545\) −0.0603656 −0.00258578
\(546\) 28.1351 1.20407
\(547\) 5.77163 0.246777 0.123389 0.992358i \(-0.460624\pi\)
0.123389 + 0.992358i \(0.460624\pi\)
\(548\) −99.0880 −4.23283
\(549\) −23.7842 −1.01508
\(550\) 8.28996 0.353485
\(551\) 2.45287 0.104496
\(552\) 121.732 5.18124
\(553\) −17.0244 −0.723951
\(554\) 13.7608 0.584641
\(555\) 70.4300 2.98959
\(556\) 6.19333 0.262656
\(557\) 17.1828 0.728059 0.364029 0.931387i \(-0.381401\pi\)
0.364029 + 0.931387i \(0.381401\pi\)
\(558\) −6.68321 −0.282923
\(559\) 3.56425 0.150752
\(560\) −69.4009 −2.93272
\(561\) −14.4367 −0.609519
\(562\) −78.8893 −3.32775
\(563\) 21.7127 0.915081 0.457540 0.889189i \(-0.348731\pi\)
0.457540 + 0.889189i \(0.348731\pi\)
\(564\) 90.6298 3.81620
\(565\) 53.8831 2.26688
\(566\) 14.3331 0.602465
\(567\) 21.2462 0.892255
\(568\) −71.7750 −3.01161
\(569\) −46.7764 −1.96097 −0.980484 0.196598i \(-0.937011\pi\)
−0.980484 + 0.196598i \(0.937011\pi\)
\(570\) −134.450 −5.63147
\(571\) 36.8554 1.54235 0.771176 0.636622i \(-0.219669\pi\)
0.771176 + 0.636622i \(0.219669\pi\)
\(572\) −3.22468 −0.134831
\(573\) −66.9884 −2.79848
\(574\) 58.4952 2.44154
\(575\) 31.6125 1.31833
\(576\) −19.9925 −0.833022
\(577\) 4.67849 0.194768 0.0973840 0.995247i \(-0.468953\pi\)
0.0973840 + 0.995247i \(0.468953\pi\)
\(578\) −65.7604 −2.73527
\(579\) 2.17575 0.0904210
\(580\) −5.44043 −0.225902
\(581\) −49.7383 −2.06349
\(582\) −125.662 −5.20884
\(583\) −8.78364 −0.363781
\(584\) −15.2915 −0.632767
\(585\) −17.1763 −0.710152
\(586\) −46.1836 −1.90783
\(587\) −6.23092 −0.257178 −0.128589 0.991698i \(-0.541045\pi\)
−0.128589 + 0.991698i \(0.541045\pi\)
\(588\) −95.9311 −3.95613
\(589\) 2.82937 0.116582
\(590\) −68.0653 −2.80220
\(591\) −20.9602 −0.862186
\(592\) 46.3704 1.90581
\(593\) 2.84182 0.116699 0.0583497 0.998296i \(-0.481416\pi\)
0.0583497 + 0.998296i \(0.481416\pi\)
\(594\) −14.3418 −0.588449
\(595\) 77.0167 3.15738
\(596\) 19.5832 0.802160
\(597\) −5.57032 −0.227978
\(598\) −18.0099 −0.736478
\(599\) −45.8994 −1.87540 −0.937699 0.347449i \(-0.887048\pi\)
−0.937699 + 0.347449i \(0.887048\pi\)
\(600\) 74.8026 3.05380
\(601\) −12.4576 −0.508155 −0.254077 0.967184i \(-0.581772\pi\)
−0.254077 + 0.967184i \(0.581772\pi\)
\(602\) −34.1952 −1.39369
\(603\) −64.9728 −2.64590
\(604\) −43.0914 −1.75336
\(605\) 32.0177 1.30170
\(606\) 60.4887 2.45719
\(607\) −2.81382 −0.114209 −0.0571046 0.998368i \(-0.518187\pi\)
−0.0571046 + 0.998368i \(0.518187\pi\)
\(608\) −19.6161 −0.795538
\(609\) −4.61691 −0.187086
\(610\) −32.7090 −1.32435
\(611\) −7.17897 −0.290430
\(612\) −158.431 −6.40420
\(613\) 31.3727 1.26713 0.633566 0.773689i \(-0.281591\pi\)
0.633566 + 0.773689i \(0.281591\pi\)
\(614\) 34.2547 1.38241
\(615\) −54.8415 −2.21142
\(616\) 16.5641 0.667387
\(617\) −16.2240 −0.653152 −0.326576 0.945171i \(-0.605895\pi\)
−0.326576 + 0.945171i \(0.605895\pi\)
\(618\) −92.7835 −3.73230
\(619\) 1.00000 0.0401934
\(620\) −6.27549 −0.252030
\(621\) −54.6902 −2.19464
\(622\) −27.1229 −1.08753
\(623\) 71.1868 2.85204
\(624\) −17.3668 −0.695230
\(625\) −27.6117 −1.10447
\(626\) 26.5971 1.06304
\(627\) 13.0772 0.522253
\(628\) 63.8691 2.54866
\(629\) −51.4588 −2.05180
\(630\) 164.788 6.56533
\(631\) 7.61067 0.302976 0.151488 0.988459i \(-0.451594\pi\)
0.151488 + 0.988459i \(0.451594\pi\)
\(632\) 25.7864 1.02573
\(633\) 0.449102 0.0178502
\(634\) −55.5217 −2.20505
\(635\) 55.9699 2.22110
\(636\) −148.032 −5.86984
\(637\) 7.59890 0.301079
\(638\) 0.775007 0.0306828
\(639\) 69.4524 2.74749
\(640\) −47.7082 −1.88583
\(641\) −12.0456 −0.475773 −0.237887 0.971293i \(-0.576455\pi\)
−0.237887 + 0.971293i \(0.576455\pi\)
\(642\) −35.3914 −1.39679
\(643\) −8.31163 −0.327779 −0.163889 0.986479i \(-0.552404\pi\)
−0.163889 + 0.986479i \(0.552404\pi\)
\(644\) 117.975 4.64887
\(645\) 32.0593 1.26233
\(646\) 98.2340 3.86496
\(647\) −32.3214 −1.27069 −0.635343 0.772230i \(-0.719141\pi\)
−0.635343 + 0.772230i \(0.719141\pi\)
\(648\) −32.1810 −1.26419
\(649\) 6.62036 0.259872
\(650\) −11.0668 −0.434077
\(651\) −5.32556 −0.208725
\(652\) 67.6486 2.64932
\(653\) −19.4110 −0.759612 −0.379806 0.925066i \(-0.624009\pi\)
−0.379806 + 0.925066i \(0.624009\pi\)
\(654\) 0.144925 0.00566700
\(655\) 7.23350 0.282636
\(656\) −36.1071 −1.40974
\(657\) 14.7967 0.577274
\(658\) 68.8747 2.68501
\(659\) −18.5649 −0.723185 −0.361592 0.932336i \(-0.617767\pi\)
−0.361592 + 0.932336i \(0.617767\pi\)
\(660\) −29.0050 −1.12902
\(661\) −44.1347 −1.71664 −0.858320 0.513114i \(-0.828492\pi\)
−0.858320 + 0.513114i \(0.828492\pi\)
\(662\) −50.8387 −1.97590
\(663\) 19.2726 0.748485
\(664\) 75.3374 2.92366
\(665\) −69.7640 −2.70533
\(666\) −110.104 −4.26643
\(667\) 2.95538 0.114433
\(668\) 10.1900 0.394264
\(669\) 68.8246 2.66091
\(670\) −89.3533 −3.45202
\(671\) 3.18143 0.122818
\(672\) 36.9223 1.42431
\(673\) −26.0350 −1.00357 −0.501787 0.864991i \(-0.667324\pi\)
−0.501787 + 0.864991i \(0.667324\pi\)
\(674\) −8.66131 −0.333621
\(675\) −33.6065 −1.29351
\(676\) 4.30485 0.165571
\(677\) −36.4331 −1.40024 −0.700118 0.714027i \(-0.746869\pi\)
−0.700118 + 0.714027i \(0.746869\pi\)
\(678\) −129.361 −4.96810
\(679\) −65.2040 −2.50230
\(680\) −116.655 −4.47352
\(681\) 6.08679 0.233246
\(682\) 0.893964 0.0342317
\(683\) 10.3166 0.394754 0.197377 0.980328i \(-0.436758\pi\)
0.197377 + 0.980328i \(0.436758\pi\)
\(684\) 143.511 5.48730
\(685\) 70.5991 2.69745
\(686\) −5.74582 −0.219376
\(687\) 55.9112 2.13315
\(688\) 21.1075 0.804716
\(689\) 11.7259 0.446721
\(690\) −161.993 −6.16698
\(691\) 10.4846 0.398853 0.199427 0.979913i \(-0.436092\pi\)
0.199427 + 0.979913i \(0.436092\pi\)
\(692\) −66.8622 −2.54172
\(693\) −16.0281 −0.608857
\(694\) 49.5500 1.88089
\(695\) −4.41268 −0.167382
\(696\) 6.99311 0.265073
\(697\) 40.0693 1.51773
\(698\) 25.4332 0.962660
\(699\) −28.3114 −1.07084
\(700\) 72.4943 2.74003
\(701\) 2.50436 0.0945885 0.0472943 0.998881i \(-0.484940\pi\)
0.0472943 + 0.998881i \(0.484940\pi\)
\(702\) 19.1458 0.722612
\(703\) 46.6129 1.75804
\(704\) 2.67426 0.100790
\(705\) −64.5727 −2.43195
\(706\) −43.2283 −1.62692
\(707\) 31.3867 1.18042
\(708\) 111.574 4.19319
\(709\) −5.59934 −0.210288 −0.105144 0.994457i \(-0.533530\pi\)
−0.105144 + 0.994457i \(0.533530\pi\)
\(710\) 95.5139 3.58457
\(711\) −24.9520 −0.935773
\(712\) −107.825 −4.04091
\(713\) 3.40900 0.127668
\(714\) −184.900 −6.91972
\(715\) 2.29755 0.0859234
\(716\) 49.7410 1.85891
\(717\) −16.6845 −0.623096
\(718\) 73.9574 2.76006
\(719\) −5.25914 −0.196133 −0.0980665 0.995180i \(-0.531266\pi\)
−0.0980665 + 0.995180i \(0.531266\pi\)
\(720\) −101.718 −3.79081
\(721\) −48.1440 −1.79298
\(722\) −41.2752 −1.53610
\(723\) −43.0554 −1.60125
\(724\) 80.5854 2.99493
\(725\) 1.81604 0.0674462
\(726\) −76.8674 −2.85282
\(727\) 19.0262 0.705643 0.352821 0.935691i \(-0.385222\pi\)
0.352821 + 0.935691i \(0.385222\pi\)
\(728\) −22.1126 −0.819547
\(729\) −35.9427 −1.33121
\(730\) 20.3490 0.753151
\(731\) −23.4238 −0.866359
\(732\) 53.6171 1.98174
\(733\) 37.8883 1.39944 0.699718 0.714419i \(-0.253309\pi\)
0.699718 + 0.714419i \(0.253309\pi\)
\(734\) 89.8455 3.31626
\(735\) 68.3498 2.52112
\(736\) −23.6347 −0.871186
\(737\) 8.69093 0.320135
\(738\) 85.7341 3.15592
\(739\) 21.4831 0.790268 0.395134 0.918623i \(-0.370698\pi\)
0.395134 + 0.918623i \(0.370698\pi\)
\(740\) −103.387 −3.80057
\(741\) −17.4577 −0.641324
\(742\) −112.498 −4.12992
\(743\) 49.7677 1.82580 0.912900 0.408184i \(-0.133838\pi\)
0.912900 + 0.408184i \(0.133838\pi\)
\(744\) 8.06649 0.295732
\(745\) −13.9528 −0.511192
\(746\) 2.72803 0.0998803
\(747\) −72.8995 −2.66725
\(748\) 21.1922 0.774862
\(749\) −18.3641 −0.671009
\(750\) 13.3831 0.488682
\(751\) −49.1593 −1.79385 −0.896924 0.442186i \(-0.854203\pi\)
−0.896924 + 0.442186i \(0.854203\pi\)
\(752\) −42.5140 −1.55032
\(753\) −25.9748 −0.946574
\(754\) −1.03461 −0.0376783
\(755\) 30.7021 1.11736
\(756\) −125.416 −4.56135
\(757\) 20.9112 0.760032 0.380016 0.924980i \(-0.375918\pi\)
0.380016 + 0.924980i \(0.375918\pi\)
\(758\) −17.7824 −0.645886
\(759\) 15.7562 0.571915
\(760\) 105.670 3.83304
\(761\) −8.72024 −0.316108 −0.158054 0.987430i \(-0.550522\pi\)
−0.158054 + 0.987430i \(0.550522\pi\)
\(762\) −134.372 −4.86777
\(763\) 0.0751994 0.00272240
\(764\) 98.3347 3.55762
\(765\) 112.880 4.08120
\(766\) −41.9941 −1.51731
\(767\) −8.83797 −0.319121
\(768\) 93.5979 3.37742
\(769\) 28.6009 1.03137 0.515687 0.856777i \(-0.327537\pi\)
0.515687 + 0.856777i \(0.327537\pi\)
\(770\) −22.0425 −0.794358
\(771\) 9.77769 0.352135
\(772\) −3.19386 −0.114949
\(773\) −9.93121 −0.357201 −0.178600 0.983922i \(-0.557157\pi\)
−0.178600 + 0.983922i \(0.557157\pi\)
\(774\) −50.1185 −1.80147
\(775\) 2.09479 0.0752471
\(776\) 98.7628 3.54538
\(777\) −87.7369 −3.14754
\(778\) 49.1765 1.76306
\(779\) −36.2959 −1.30044
\(780\) 38.7208 1.38643
\(781\) −9.29014 −0.332427
\(782\) 118.358 4.23249
\(783\) −3.14178 −0.112278
\(784\) 45.0008 1.60717
\(785\) −45.5060 −1.62418
\(786\) −17.3661 −0.619427
\(787\) 1.23055 0.0438644 0.0219322 0.999759i \(-0.493018\pi\)
0.0219322 + 0.999759i \(0.493018\pi\)
\(788\) 30.7682 1.09607
\(789\) 33.2972 1.18541
\(790\) −34.3151 −1.22087
\(791\) −67.1238 −2.38665
\(792\) 24.2774 0.862659
\(793\) −4.24712 −0.150820
\(794\) 41.7148 1.48040
\(795\) 105.471 3.74067
\(796\) 8.17686 0.289821
\(797\) 18.0324 0.638741 0.319370 0.947630i \(-0.396529\pi\)
0.319370 + 0.947630i \(0.396529\pi\)
\(798\) 167.488 5.92901
\(799\) 47.1793 1.66908
\(800\) −14.5232 −0.513474
\(801\) 104.336 3.68652
\(802\) −43.0358 −1.51965
\(803\) −1.97924 −0.0698460
\(804\) 146.469 5.16557
\(805\) −84.0560 −2.96258
\(806\) −1.19342 −0.0420363
\(807\) −1.68271 −0.0592341
\(808\) −47.5407 −1.67248
\(809\) −18.2396 −0.641271 −0.320636 0.947203i \(-0.603896\pi\)
−0.320636 + 0.947203i \(0.603896\pi\)
\(810\) 42.8246 1.50470
\(811\) 5.62309 0.197453 0.0987266 0.995115i \(-0.468523\pi\)
0.0987266 + 0.995115i \(0.468523\pi\)
\(812\) 6.77732 0.237837
\(813\) 73.4984 2.57770
\(814\) 14.7278 0.516208
\(815\) −48.1988 −1.68833
\(816\) 114.133 3.99544
\(817\) 21.2179 0.742321
\(818\) −42.2182 −1.47612
\(819\) 21.3970 0.747673
\(820\) 80.5038 2.81131
\(821\) −7.54530 −0.263333 −0.131666 0.991294i \(-0.542033\pi\)
−0.131666 + 0.991294i \(0.542033\pi\)
\(822\) −169.493 −5.91175
\(823\) −2.50448 −0.0873006 −0.0436503 0.999047i \(-0.513899\pi\)
−0.0436503 + 0.999047i \(0.513899\pi\)
\(824\) 72.9225 2.54038
\(825\) 9.68202 0.337085
\(826\) 84.7911 2.95026
\(827\) −2.94367 −0.102361 −0.0511807 0.998689i \(-0.516298\pi\)
−0.0511807 + 0.998689i \(0.516298\pi\)
\(828\) 172.912 6.00909
\(829\) −31.1995 −1.08360 −0.541801 0.840507i \(-0.682257\pi\)
−0.541801 + 0.840507i \(0.682257\pi\)
\(830\) −100.255 −3.47988
\(831\) 16.0715 0.557516
\(832\) −3.57005 −0.123769
\(833\) −49.9390 −1.73028
\(834\) 10.5939 0.366836
\(835\) −7.26029 −0.251253
\(836\) −19.1965 −0.663924
\(837\) −3.62402 −0.125264
\(838\) −31.4739 −1.08725
\(839\) 1.50613 0.0519975 0.0259987 0.999662i \(-0.491723\pi\)
0.0259987 + 0.999662i \(0.491723\pi\)
\(840\) −198.896 −6.86257
\(841\) −28.8302 −0.994146
\(842\) 83.0183 2.86100
\(843\) −92.1366 −3.17335
\(844\) −0.659252 −0.0226924
\(845\) −3.06715 −0.105513
\(846\) 100.947 3.47063
\(847\) −39.8854 −1.37048
\(848\) 69.4409 2.38461
\(849\) 16.7399 0.574514
\(850\) 72.7298 2.49461
\(851\) 56.1622 1.92521
\(852\) −156.568 −5.36393
\(853\) −28.3662 −0.971241 −0.485620 0.874170i \(-0.661406\pi\)
−0.485620 + 0.874170i \(0.661406\pi\)
\(854\) 40.7466 1.39432
\(855\) −102.250 −3.49689
\(856\) 27.8156 0.950718
\(857\) 17.7051 0.604796 0.302398 0.953182i \(-0.402213\pi\)
0.302398 + 0.953182i \(0.402213\pi\)
\(858\) −5.51591 −0.188310
\(859\) 15.2851 0.521520 0.260760 0.965404i \(-0.416027\pi\)
0.260760 + 0.965404i \(0.416027\pi\)
\(860\) −47.0610 −1.60477
\(861\) 68.3178 2.32826
\(862\) −92.6169 −3.15454
\(863\) −8.30837 −0.282820 −0.141410 0.989951i \(-0.545164\pi\)
−0.141410 + 0.989951i \(0.545164\pi\)
\(864\) 25.1254 0.854784
\(865\) 47.6386 1.61976
\(866\) −38.0415 −1.29270
\(867\) −76.8030 −2.60837
\(868\) 7.81758 0.265346
\(869\) 3.33765 0.113222
\(870\) −9.30602 −0.315504
\(871\) −11.6021 −0.393123
\(872\) −0.113903 −0.00385723
\(873\) −95.5669 −3.23445
\(874\) −107.213 −3.62652
\(875\) 6.94430 0.234760
\(876\) −33.3564 −1.12701
\(877\) 34.6992 1.17171 0.585854 0.810417i \(-0.300759\pi\)
0.585854 + 0.810417i \(0.300759\pi\)
\(878\) −69.1070 −2.33225
\(879\) −53.9388 −1.81931
\(880\) 13.6061 0.458662
\(881\) 29.0239 0.977841 0.488920 0.872328i \(-0.337391\pi\)
0.488920 + 0.872328i \(0.337391\pi\)
\(882\) −106.852 −3.59789
\(883\) −26.6122 −0.895571 −0.447785 0.894141i \(-0.647787\pi\)
−0.447785 + 0.894141i \(0.647787\pi\)
\(884\) −28.2909 −0.951526
\(885\) −79.4949 −2.67219
\(886\) −29.2177 −0.981587
\(887\) 53.8416 1.80782 0.903911 0.427720i \(-0.140683\pi\)
0.903911 + 0.427720i \(0.140683\pi\)
\(888\) 132.893 4.45959
\(889\) −69.7235 −2.33845
\(890\) 143.487 4.80969
\(891\) −4.16533 −0.139544
\(892\) −101.030 −3.38273
\(893\) −42.7363 −1.43012
\(894\) 33.4977 1.12033
\(895\) −35.4399 −1.18463
\(896\) 59.4315 1.98547
\(897\) −21.0341 −0.702308
\(898\) 61.2842 2.04508
\(899\) 0.195837 0.00653152
\(900\) 106.252 3.54174
\(901\) −77.0611 −2.56728
\(902\) −11.4680 −0.381843
\(903\) −39.9373 −1.32903
\(904\) 101.671 3.38152
\(905\) −57.4162 −1.90858
\(906\) −73.7091 −2.44882
\(907\) 17.0271 0.565375 0.282688 0.959212i \(-0.408774\pi\)
0.282688 + 0.959212i \(0.408774\pi\)
\(908\) −8.93501 −0.296519
\(909\) 46.0023 1.52580
\(910\) 29.4261 0.975467
\(911\) −43.1106 −1.42832 −0.714160 0.699983i \(-0.753191\pi\)
−0.714160 + 0.699983i \(0.753191\pi\)
\(912\) −103.385 −3.42341
\(913\) 9.75123 0.322719
\(914\) −20.7879 −0.687601
\(915\) −38.2015 −1.26290
\(916\) −82.0740 −2.71180
\(917\) −9.01100 −0.297569
\(918\) −125.824 −4.15280
\(919\) −29.3492 −0.968141 −0.484071 0.875029i \(-0.660842\pi\)
−0.484071 + 0.875029i \(0.660842\pi\)
\(920\) 127.317 4.19753
\(921\) 40.0068 1.31827
\(922\) 17.3186 0.570357
\(923\) 12.4021 0.408219
\(924\) 36.1325 1.18867
\(925\) 34.5110 1.13471
\(926\) −24.1494 −0.793599
\(927\) −70.5628 −2.31759
\(928\) −1.35774 −0.0445700
\(929\) −10.4799 −0.343834 −0.171917 0.985111i \(-0.554996\pi\)
−0.171917 + 0.985111i \(0.554996\pi\)
\(930\) −10.7344 −0.351995
\(931\) 45.2362 1.48256
\(932\) 41.5593 1.36132
\(933\) −31.6774 −1.03707
\(934\) 85.7869 2.80703
\(935\) −15.0992 −0.493796
\(936\) −32.4095 −1.05934
\(937\) −25.8119 −0.843240 −0.421620 0.906773i \(-0.638538\pi\)
−0.421620 + 0.906773i \(0.638538\pi\)
\(938\) 111.310 3.63441
\(939\) 31.0634 1.01371
\(940\) 94.7885 3.09166
\(941\) 4.84424 0.157918 0.0789588 0.996878i \(-0.474840\pi\)
0.0789588 + 0.996878i \(0.474840\pi\)
\(942\) 109.250 3.55956
\(943\) −43.7316 −1.42410
\(944\) −52.3386 −1.70348
\(945\) 89.3577 2.90681
\(946\) 6.70399 0.217966
\(947\) −1.27499 −0.0414316 −0.0207158 0.999785i \(-0.506595\pi\)
−0.0207158 + 0.999785i \(0.506595\pi\)
\(948\) 56.2497 1.82691
\(949\) 2.64223 0.0857704
\(950\) −65.8808 −2.13746
\(951\) −64.8450 −2.10274
\(952\) 145.321 4.70988
\(953\) −16.6521 −0.539414 −0.269707 0.962942i \(-0.586927\pi\)
−0.269707 + 0.962942i \(0.586927\pi\)
\(954\) −164.883 −5.33830
\(955\) −70.0623 −2.26716
\(956\) 24.4918 0.792122
\(957\) 0.905148 0.0292593
\(958\) −45.6484 −1.47483
\(959\) −87.9475 −2.83997
\(960\) −32.1115 −1.03640
\(961\) −30.7741 −0.992713
\(962\) −19.6611 −0.633900
\(963\) −26.9155 −0.867340
\(964\) 63.2025 2.03562
\(965\) 2.27559 0.0732537
\(966\) 201.800 6.49281
\(967\) −41.3705 −1.33039 −0.665193 0.746671i \(-0.731651\pi\)
−0.665193 + 0.746671i \(0.731651\pi\)
\(968\) 60.4134 1.94176
\(969\) 114.730 3.68564
\(970\) −131.428 −4.21989
\(971\) −49.9053 −1.60154 −0.800769 0.598973i \(-0.795575\pi\)
−0.800769 + 0.598973i \(0.795575\pi\)
\(972\) 28.2738 0.906883
\(973\) 5.49701 0.176226
\(974\) −7.61251 −0.243921
\(975\) −12.9252 −0.413938
\(976\) −25.1515 −0.805079
\(977\) −17.7932 −0.569254 −0.284627 0.958638i \(-0.591870\pi\)
−0.284627 + 0.958638i \(0.591870\pi\)
\(978\) 115.715 3.70015
\(979\) −13.9562 −0.446043
\(980\) −100.333 −3.20502
\(981\) 0.110217 0.00351895
\(982\) −76.0727 −2.42758
\(983\) 12.9381 0.412660 0.206330 0.978482i \(-0.433848\pi\)
0.206330 + 0.978482i \(0.433848\pi\)
\(984\) −103.479 −3.29880
\(985\) −21.9220 −0.698492
\(986\) 6.79933 0.216535
\(987\) 80.4402 2.56044
\(988\) 25.6267 0.815295
\(989\) 25.5647 0.812910
\(990\) −32.3069 −1.02678
\(991\) 27.9144 0.886729 0.443365 0.896341i \(-0.353785\pi\)
0.443365 + 0.896341i \(0.353785\pi\)
\(992\) −1.56614 −0.0497251
\(993\) −59.3756 −1.88423
\(994\) −118.985 −3.77397
\(995\) −5.82592 −0.184694
\(996\) 164.339 5.20727
\(997\) −28.1399 −0.891198 −0.445599 0.895233i \(-0.647009\pi\)
−0.445599 + 0.895233i \(0.647009\pi\)
\(998\) −37.8655 −1.19861
\(999\) −59.7045 −1.88897
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 \(a_p\))