Properties

Label 8013.2.a.d.1.11
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} -8.23349 q^{10} +0.648462 q^{11} +4.34456 q^{12} -2.92940 q^{13} -10.2673 q^{14} +3.26876 q^{15} +6.18609 q^{16} +5.11297 q^{17} -2.51884 q^{18} +0.451729 q^{19} +14.2013 q^{20} +4.07622 q^{21} -1.63337 q^{22} -0.767548 q^{23} -5.90558 q^{24} +5.68479 q^{25} +7.37869 q^{26} +1.00000 q^{27} +17.7094 q^{28} +7.38455 q^{29} -8.23349 q^{30} +9.64925 q^{31} -3.77062 q^{32} +0.648462 q^{33} -12.8788 q^{34} +13.3242 q^{35} +4.34456 q^{36} +5.04246 q^{37} -1.13783 q^{38} -2.92940 q^{39} -19.3039 q^{40} -3.08641 q^{41} -10.2673 q^{42} +2.69609 q^{43} +2.81728 q^{44} +3.26876 q^{45} +1.93333 q^{46} +12.3720 q^{47} +6.18609 q^{48} +9.61554 q^{49} -14.3191 q^{50} +5.11297 q^{51} -12.7270 q^{52} -10.7907 q^{53} -2.51884 q^{54} +2.11967 q^{55} -24.0724 q^{56} +0.451729 q^{57} -18.6005 q^{58} -1.24993 q^{59} +14.2013 q^{60} +8.94667 q^{61} -24.3049 q^{62} +4.07622 q^{63} -2.87458 q^{64} -9.57550 q^{65} -1.63337 q^{66} -12.4383 q^{67} +22.2136 q^{68} -0.767548 q^{69} -33.5615 q^{70} -15.1732 q^{71} -5.90558 q^{72} +9.15289 q^{73} -12.7011 q^{74} +5.68479 q^{75} +1.96257 q^{76} +2.64327 q^{77} +7.37869 q^{78} +5.51966 q^{79} +20.2208 q^{80} +1.00000 q^{81} +7.77417 q^{82} -14.5915 q^{83} +17.7094 q^{84} +16.7131 q^{85} -6.79103 q^{86} +7.38455 q^{87} -3.82954 q^{88} -2.32441 q^{89} -8.23349 q^{90} -11.9409 q^{91} -3.33466 q^{92} +9.64925 q^{93} -31.1632 q^{94} +1.47659 q^{95} -3.77062 q^{96} -0.704230 q^{97} -24.2200 q^{98} +0.648462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + O(q^{10}) \) \( 129q + 15q^{2} + 129q^{3} + 151q^{4} + 16q^{5} + 15q^{6} + 61q^{7} + 42q^{8} + 129q^{9} + 41q^{10} + 51q^{11} + 151q^{12} + 56q^{13} + 5q^{14} + 16q^{15} + 195q^{16} + 18q^{17} + 15q^{18} + 93q^{19} + 44q^{20} + 61q^{21} + 46q^{22} + 50q^{23} + 42q^{24} + 193q^{25} + q^{26} + 129q^{27} + 145q^{28} + 24q^{29} + 41q^{30} + 67q^{31} + 89q^{32} + 51q^{33} + 73q^{34} + 56q^{35} + 151q^{36} + 95q^{37} + 9q^{38} + 56q^{39} + 103q^{40} + 7q^{41} + 5q^{42} + 150q^{43} + 69q^{44} + 16q^{45} + 72q^{46} + 53q^{47} + 195q^{48} + 240q^{49} + 17q^{50} + 18q^{51} + 124q^{52} + 34q^{53} + 15q^{54} + 66q^{55} - 17q^{56} + 93q^{57} + 57q^{58} + 49q^{59} + 44q^{60} + 113q^{61} + 27q^{62} + 61q^{63} + 262q^{64} + 22q^{65} + 46q^{66} + 185q^{67} + 2q^{68} + 50q^{69} + 25q^{70} + 41q^{71} + 42q^{72} + 153q^{73} - q^{74} + 193q^{75} + 190q^{76} + 39q^{77} + q^{78} + 101q^{79} + 48q^{80} + 129q^{81} + 15q^{82} + 162q^{83} + 145q^{84} + 99q^{85} + 13q^{86} + 24q^{87} + 86q^{88} - 4q^{89} + 41q^{90} + 117q^{91} + 56q^{92} + 67q^{93} + 49q^{94} + 71q^{95} + 89q^{96} + 159q^{97} + 40q^{98} + 51q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51884 −1.78109 −0.890545 0.454895i \(-0.849677\pi\)
−0.890545 + 0.454895i \(0.849677\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.34456 2.17228
\(5\) 3.26876 1.46183 0.730917 0.682467i \(-0.239093\pi\)
0.730917 + 0.682467i \(0.239093\pi\)
\(6\) −2.51884 −1.02831
\(7\) 4.07622 1.54066 0.770332 0.637642i \(-0.220090\pi\)
0.770332 + 0.637642i \(0.220090\pi\)
\(8\) −5.90558 −2.08794
\(9\) 1.00000 0.333333
\(10\) −8.23349 −2.60366
\(11\) 0.648462 0.195519 0.0977593 0.995210i \(-0.468832\pi\)
0.0977593 + 0.995210i \(0.468832\pi\)
\(12\) 4.34456 1.25417
\(13\) −2.92940 −0.812469 −0.406235 0.913769i \(-0.633158\pi\)
−0.406235 + 0.913769i \(0.633158\pi\)
\(14\) −10.2673 −2.74406
\(15\) 3.26876 0.843990
\(16\) 6.18609 1.54652
\(17\) 5.11297 1.24008 0.620039 0.784571i \(-0.287117\pi\)
0.620039 + 0.784571i \(0.287117\pi\)
\(18\) −2.51884 −0.593697
\(19\) 0.451729 0.103634 0.0518169 0.998657i \(-0.483499\pi\)
0.0518169 + 0.998657i \(0.483499\pi\)
\(20\) 14.2013 3.17551
\(21\) 4.07622 0.889503
\(22\) −1.63337 −0.348236
\(23\) −0.767548 −0.160045 −0.0800224 0.996793i \(-0.525499\pi\)
−0.0800224 + 0.996793i \(0.525499\pi\)
\(24\) −5.90558 −1.20547
\(25\) 5.68479 1.13696
\(26\) 7.37869 1.44708
\(27\) 1.00000 0.192450
\(28\) 17.7094 3.34676
\(29\) 7.38455 1.37128 0.685638 0.727943i \(-0.259523\pi\)
0.685638 + 0.727943i \(0.259523\pi\)
\(30\) −8.23349 −1.50322
\(31\) 9.64925 1.73306 0.866528 0.499129i \(-0.166346\pi\)
0.866528 + 0.499129i \(0.166346\pi\)
\(32\) −3.77062 −0.666558
\(33\) 0.648462 0.112883
\(34\) −12.8788 −2.20869
\(35\) 13.3242 2.25220
\(36\) 4.34456 0.724094
\(37\) 5.04246 0.828975 0.414487 0.910055i \(-0.363961\pi\)
0.414487 + 0.910055i \(0.363961\pi\)
\(38\) −1.13783 −0.184581
\(39\) −2.92940 −0.469079
\(40\) −19.3039 −3.05222
\(41\) −3.08641 −0.482016 −0.241008 0.970523i \(-0.577478\pi\)
−0.241008 + 0.970523i \(0.577478\pi\)
\(42\) −10.2673 −1.58429
\(43\) 2.69609 0.411150 0.205575 0.978641i \(-0.434094\pi\)
0.205575 + 0.978641i \(0.434094\pi\)
\(44\) 2.81728 0.424721
\(45\) 3.26876 0.487278
\(46\) 1.93333 0.285054
\(47\) 12.3720 1.80465 0.902323 0.431061i \(-0.141860\pi\)
0.902323 + 0.431061i \(0.141860\pi\)
\(48\) 6.18609 0.892885
\(49\) 9.61554 1.37365
\(50\) −14.3191 −2.02502
\(51\) 5.11297 0.715959
\(52\) −12.7270 −1.76491
\(53\) −10.7907 −1.48221 −0.741105 0.671389i \(-0.765698\pi\)
−0.741105 + 0.671389i \(0.765698\pi\)
\(54\) −2.51884 −0.342771
\(55\) 2.11967 0.285816
\(56\) −24.0724 −3.21681
\(57\) 0.451729 0.0598330
\(58\) −18.6005 −2.44236
\(59\) −1.24993 −0.162727 −0.0813633 0.996685i \(-0.525927\pi\)
−0.0813633 + 0.996685i \(0.525927\pi\)
\(60\) 14.2013 1.83338
\(61\) 8.94667 1.14550 0.572752 0.819729i \(-0.305876\pi\)
0.572752 + 0.819729i \(0.305876\pi\)
\(62\) −24.3049 −3.08673
\(63\) 4.07622 0.513555
\(64\) −2.87458 −0.359322
\(65\) −9.57550 −1.18769
\(66\) −1.63337 −0.201054
\(67\) −12.4383 −1.51958 −0.759791 0.650167i \(-0.774699\pi\)
−0.759791 + 0.650167i \(0.774699\pi\)
\(68\) 22.2136 2.69380
\(69\) −0.767548 −0.0924019
\(70\) −33.5615 −4.01136
\(71\) −15.1732 −1.80073 −0.900363 0.435139i \(-0.856699\pi\)
−0.900363 + 0.435139i \(0.856699\pi\)
\(72\) −5.90558 −0.695979
\(73\) 9.15289 1.07126 0.535632 0.844451i \(-0.320073\pi\)
0.535632 + 0.844451i \(0.320073\pi\)
\(74\) −12.7011 −1.47648
\(75\) 5.68479 0.656423
\(76\) 1.96257 0.225122
\(77\) 2.64327 0.301229
\(78\) 7.37869 0.835472
\(79\) 5.51966 0.621011 0.310505 0.950572i \(-0.399502\pi\)
0.310505 + 0.950572i \(0.399502\pi\)
\(80\) 20.2208 2.26076
\(81\) 1.00000 0.111111
\(82\) 7.77417 0.858513
\(83\) −14.5915 −1.60163 −0.800814 0.598913i \(-0.795600\pi\)
−0.800814 + 0.598913i \(0.795600\pi\)
\(84\) 17.7094 1.93225
\(85\) 16.7131 1.81279
\(86\) −6.79103 −0.732295
\(87\) 7.38455 0.791706
\(88\) −3.82954 −0.408231
\(89\) −2.32441 −0.246387 −0.123193 0.992383i \(-0.539314\pi\)
−0.123193 + 0.992383i \(0.539314\pi\)
\(90\) −8.23349 −0.867886
\(91\) −11.9409 −1.25174
\(92\) −3.33466 −0.347662
\(93\) 9.64925 1.00058
\(94\) −31.1632 −3.21424
\(95\) 1.47659 0.151495
\(96\) −3.77062 −0.384838
\(97\) −0.704230 −0.0715037 −0.0357519 0.999361i \(-0.511383\pi\)
−0.0357519 + 0.999361i \(0.511383\pi\)
\(98\) −24.2200 −2.44659
\(99\) 0.648462 0.0651729
\(100\) 24.6979 2.46979
\(101\) −15.3888 −1.53124 −0.765619 0.643294i \(-0.777567\pi\)
−0.765619 + 0.643294i \(0.777567\pi\)
\(102\) −12.8788 −1.27519
\(103\) 13.9462 1.37416 0.687078 0.726584i \(-0.258893\pi\)
0.687078 + 0.726584i \(0.258893\pi\)
\(104\) 17.2998 1.69638
\(105\) 13.3242 1.30031
\(106\) 27.1799 2.63995
\(107\) 14.1540 1.36832 0.684158 0.729334i \(-0.260170\pi\)
0.684158 + 0.729334i \(0.260170\pi\)
\(108\) 4.34456 0.418056
\(109\) −2.57625 −0.246760 −0.123380 0.992359i \(-0.539373\pi\)
−0.123380 + 0.992359i \(0.539373\pi\)
\(110\) −5.33910 −0.509063
\(111\) 5.04246 0.478609
\(112\) 25.2158 2.38267
\(113\) −15.2411 −1.43376 −0.716881 0.697195i \(-0.754431\pi\)
−0.716881 + 0.697195i \(0.754431\pi\)
\(114\) −1.13783 −0.106568
\(115\) −2.50893 −0.233959
\(116\) 32.0826 2.97880
\(117\) −2.92940 −0.270823
\(118\) 3.14837 0.289831
\(119\) 20.8416 1.91054
\(120\) −19.3039 −1.76220
\(121\) −10.5795 −0.961772
\(122\) −22.5352 −2.04024
\(123\) −3.08641 −0.278292
\(124\) 41.9217 3.76468
\(125\) 2.23840 0.200209
\(126\) −10.2673 −0.914688
\(127\) −13.3631 −1.18578 −0.592889 0.805284i \(-0.702013\pi\)
−0.592889 + 0.805284i \(0.702013\pi\)
\(128\) 14.7819 1.30654
\(129\) 2.69609 0.237378
\(130\) 24.1192 2.11539
\(131\) −18.2766 −1.59683 −0.798415 0.602108i \(-0.794328\pi\)
−0.798415 + 0.602108i \(0.794328\pi\)
\(132\) 2.81728 0.245213
\(133\) 1.84135 0.159665
\(134\) 31.3301 2.70651
\(135\) 3.26876 0.281330
\(136\) −30.1950 −2.58920
\(137\) −18.7483 −1.60177 −0.800886 0.598817i \(-0.795638\pi\)
−0.800886 + 0.598817i \(0.795638\pi\)
\(138\) 1.93333 0.164576
\(139\) −19.5104 −1.65485 −0.827425 0.561577i \(-0.810195\pi\)
−0.827425 + 0.561577i \(0.810195\pi\)
\(140\) 57.8877 4.89240
\(141\) 12.3720 1.04191
\(142\) 38.2189 3.20726
\(143\) −1.89960 −0.158853
\(144\) 6.18609 0.515508
\(145\) 24.1383 2.00458
\(146\) −23.0547 −1.90802
\(147\) 9.61554 0.793076
\(148\) 21.9073 1.80077
\(149\) 13.7429 1.12586 0.562929 0.826505i \(-0.309674\pi\)
0.562929 + 0.826505i \(0.309674\pi\)
\(150\) −14.3191 −1.16915
\(151\) −3.70655 −0.301635 −0.150817 0.988562i \(-0.548191\pi\)
−0.150817 + 0.988562i \(0.548191\pi\)
\(152\) −2.66772 −0.216381
\(153\) 5.11297 0.413359
\(154\) −6.65798 −0.536515
\(155\) 31.5411 2.53344
\(156\) −12.7270 −1.01897
\(157\) 2.96178 0.236376 0.118188 0.992991i \(-0.462291\pi\)
0.118188 + 0.992991i \(0.462291\pi\)
\(158\) −13.9032 −1.10608
\(159\) −10.7907 −0.855754
\(160\) −12.3253 −0.974397
\(161\) −3.12869 −0.246575
\(162\) −2.51884 −0.197899
\(163\) 17.3658 1.36019 0.680095 0.733124i \(-0.261938\pi\)
0.680095 + 0.733124i \(0.261938\pi\)
\(164\) −13.4091 −1.04707
\(165\) 2.11967 0.165016
\(166\) 36.7538 2.85264
\(167\) −13.9346 −1.07830 −0.539148 0.842211i \(-0.681254\pi\)
−0.539148 + 0.842211i \(0.681254\pi\)
\(168\) −24.0724 −1.85723
\(169\) −4.41862 −0.339894
\(170\) −42.0976 −3.22874
\(171\) 0.451729 0.0345446
\(172\) 11.7133 0.893133
\(173\) −19.1201 −1.45368 −0.726838 0.686809i \(-0.759011\pi\)
−0.726838 + 0.686809i \(0.759011\pi\)
\(174\) −18.6005 −1.41010
\(175\) 23.1724 1.75167
\(176\) 4.01144 0.302374
\(177\) −1.24993 −0.0939502
\(178\) 5.85481 0.438836
\(179\) −1.13929 −0.0851547 −0.0425773 0.999093i \(-0.513557\pi\)
−0.0425773 + 0.999093i \(0.513557\pi\)
\(180\) 14.2013 1.05850
\(181\) 17.1194 1.27247 0.636237 0.771494i \(-0.280490\pi\)
0.636237 + 0.771494i \(0.280490\pi\)
\(182\) 30.0771 2.22947
\(183\) 8.94667 0.661357
\(184\) 4.53281 0.334163
\(185\) 16.4826 1.21182
\(186\) −24.3049 −1.78212
\(187\) 3.31557 0.242458
\(188\) 53.7510 3.92020
\(189\) 4.07622 0.296501
\(190\) −3.71931 −0.269827
\(191\) 8.40422 0.608108 0.304054 0.952655i \(-0.401660\pi\)
0.304054 + 0.952655i \(0.401660\pi\)
\(192\) −2.87458 −0.207455
\(193\) 14.1958 1.02184 0.510920 0.859628i \(-0.329305\pi\)
0.510920 + 0.859628i \(0.329305\pi\)
\(194\) 1.77384 0.127355
\(195\) −9.57550 −0.685716
\(196\) 41.7753 2.98395
\(197\) 5.47194 0.389860 0.194930 0.980817i \(-0.437552\pi\)
0.194930 + 0.980817i \(0.437552\pi\)
\(198\) −1.63337 −0.116079
\(199\) 11.6424 0.825309 0.412654 0.910888i \(-0.364602\pi\)
0.412654 + 0.910888i \(0.364602\pi\)
\(200\) −33.5719 −2.37389
\(201\) −12.4383 −0.877331
\(202\) 38.7618 2.72727
\(203\) 30.1010 2.11268
\(204\) 22.2136 1.55526
\(205\) −10.0887 −0.704627
\(206\) −35.1282 −2.44749
\(207\) −0.767548 −0.0533483
\(208\) −18.1215 −1.25650
\(209\) 0.292929 0.0202623
\(210\) −33.5615 −2.31596
\(211\) −23.0003 −1.58341 −0.791704 0.610905i \(-0.790806\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(212\) −46.8806 −3.21978
\(213\) −15.1732 −1.03965
\(214\) −35.6516 −2.43709
\(215\) 8.81287 0.601033
\(216\) −5.90558 −0.401824
\(217\) 39.3324 2.67006
\(218\) 6.48917 0.439502
\(219\) 9.15289 0.618495
\(220\) 9.20902 0.620872
\(221\) −14.9779 −1.00752
\(222\) −12.7011 −0.852445
\(223\) −10.6453 −0.712861 −0.356431 0.934322i \(-0.616006\pi\)
−0.356431 + 0.934322i \(0.616006\pi\)
\(224\) −15.3699 −1.02694
\(225\) 5.68479 0.378986
\(226\) 38.3899 2.55366
\(227\) −3.66318 −0.243134 −0.121567 0.992583i \(-0.538792\pi\)
−0.121567 + 0.992583i \(0.538792\pi\)
\(228\) 1.96257 0.129974
\(229\) 10.3781 0.685801 0.342901 0.939372i \(-0.388591\pi\)
0.342901 + 0.939372i \(0.388591\pi\)
\(230\) 6.31959 0.416702
\(231\) 2.64327 0.173915
\(232\) −43.6100 −2.86314
\(233\) −10.4755 −0.686273 −0.343137 0.939285i \(-0.611489\pi\)
−0.343137 + 0.939285i \(0.611489\pi\)
\(234\) 7.37869 0.482360
\(235\) 40.4412 2.63809
\(236\) −5.43038 −0.353488
\(237\) 5.51966 0.358541
\(238\) −52.4966 −3.40285
\(239\) −14.6957 −0.950586 −0.475293 0.879828i \(-0.657658\pi\)
−0.475293 + 0.879828i \(0.657658\pi\)
\(240\) 20.2208 1.30525
\(241\) −23.0092 −1.48215 −0.741076 0.671421i \(-0.765684\pi\)
−0.741076 + 0.671421i \(0.765684\pi\)
\(242\) 26.6481 1.71300
\(243\) 1.00000 0.0641500
\(244\) 38.8694 2.48836
\(245\) 31.4309 2.00805
\(246\) 7.77417 0.495663
\(247\) −1.32330 −0.0841993
\(248\) −56.9844 −3.61851
\(249\) −14.5915 −0.924701
\(250\) −5.63817 −0.356589
\(251\) −6.73804 −0.425301 −0.212651 0.977128i \(-0.568210\pi\)
−0.212651 + 0.977128i \(0.568210\pi\)
\(252\) 17.7094 1.11559
\(253\) −0.497726 −0.0312917
\(254\) 33.6594 2.11198
\(255\) 16.7131 1.04661
\(256\) −31.4840 −1.96775
\(257\) −26.4634 −1.65074 −0.825370 0.564592i \(-0.809034\pi\)
−0.825370 + 0.564592i \(0.809034\pi\)
\(258\) −6.79103 −0.422791
\(259\) 20.5541 1.27717
\(260\) −41.6014 −2.58001
\(261\) 7.38455 0.457092
\(262\) 46.0357 2.84410
\(263\) 26.4099 1.62851 0.814253 0.580510i \(-0.197147\pi\)
0.814253 + 0.580510i \(0.197147\pi\)
\(264\) −3.82954 −0.235692
\(265\) −35.2720 −2.16674
\(266\) −4.63806 −0.284378
\(267\) −2.32441 −0.142251
\(268\) −54.0390 −3.30096
\(269\) 7.91517 0.482596 0.241298 0.970451i \(-0.422427\pi\)
0.241298 + 0.970451i \(0.422427\pi\)
\(270\) −8.23349 −0.501074
\(271\) 0.262801 0.0159640 0.00798201 0.999968i \(-0.497459\pi\)
0.00798201 + 0.999968i \(0.497459\pi\)
\(272\) 31.6293 1.91781
\(273\) −11.9409 −0.722694
\(274\) 47.2239 2.85290
\(275\) 3.68637 0.222296
\(276\) −3.33466 −0.200723
\(277\) 22.4788 1.35062 0.675311 0.737533i \(-0.264009\pi\)
0.675311 + 0.737533i \(0.264009\pi\)
\(278\) 49.1436 2.94744
\(279\) 9.64925 0.577685
\(280\) −78.6869 −4.70244
\(281\) 5.19041 0.309634 0.154817 0.987943i \(-0.450521\pi\)
0.154817 + 0.987943i \(0.450521\pi\)
\(282\) −31.1632 −1.85574
\(283\) 12.2072 0.725644 0.362822 0.931858i \(-0.381813\pi\)
0.362822 + 0.931858i \(0.381813\pi\)
\(284\) −65.9209 −3.91168
\(285\) 1.47659 0.0874659
\(286\) 4.78480 0.282931
\(287\) −12.5809 −0.742625
\(288\) −3.77062 −0.222186
\(289\) 9.14247 0.537792
\(290\) −60.8005 −3.57033
\(291\) −0.704230 −0.0412827
\(292\) 39.7653 2.32709
\(293\) 19.2073 1.12210 0.561051 0.827782i \(-0.310397\pi\)
0.561051 + 0.827782i \(0.310397\pi\)
\(294\) −24.2200 −1.41254
\(295\) −4.08571 −0.237879
\(296\) −29.7786 −1.73085
\(297\) 0.648462 0.0376276
\(298\) −34.6161 −2.00526
\(299\) 2.24845 0.130031
\(300\) 24.6979 1.42593
\(301\) 10.9898 0.633444
\(302\) 9.33622 0.537239
\(303\) −15.3888 −0.884061
\(304\) 2.79444 0.160272
\(305\) 29.2445 1.67454
\(306\) −12.8788 −0.736230
\(307\) −28.4591 −1.62425 −0.812124 0.583485i \(-0.801689\pi\)
−0.812124 + 0.583485i \(0.801689\pi\)
\(308\) 11.4839 0.654353
\(309\) 13.9462 0.793369
\(310\) −79.4469 −4.51228
\(311\) 18.7576 1.06365 0.531823 0.846856i \(-0.321507\pi\)
0.531823 + 0.846856i \(0.321507\pi\)
\(312\) 17.2998 0.979408
\(313\) −1.65575 −0.0935886 −0.0467943 0.998905i \(-0.514901\pi\)
−0.0467943 + 0.998905i \(0.514901\pi\)
\(314\) −7.46026 −0.421007
\(315\) 13.3242 0.750732
\(316\) 23.9805 1.34901
\(317\) −12.2014 −0.685298 −0.342649 0.939464i \(-0.611324\pi\)
−0.342649 + 0.939464i \(0.611324\pi\)
\(318\) 27.1799 1.52418
\(319\) 4.78860 0.268110
\(320\) −9.39630 −0.525269
\(321\) 14.1540 0.789997
\(322\) 7.88068 0.439173
\(323\) 2.30968 0.128514
\(324\) 4.34456 0.241365
\(325\) −16.6530 −0.923743
\(326\) −43.7416 −2.42262
\(327\) −2.57625 −0.142467
\(328\) 18.2270 1.00642
\(329\) 50.4311 2.78035
\(330\) −5.33910 −0.293908
\(331\) −9.21492 −0.506498 −0.253249 0.967401i \(-0.581499\pi\)
−0.253249 + 0.967401i \(0.581499\pi\)
\(332\) −63.3938 −3.47919
\(333\) 5.04246 0.276325
\(334\) 35.0992 1.92054
\(335\) −40.6579 −2.22138
\(336\) 25.2158 1.37564
\(337\) −0.296921 −0.0161743 −0.00808716 0.999967i \(-0.502574\pi\)
−0.00808716 + 0.999967i \(0.502574\pi\)
\(338\) 11.1298 0.605381
\(339\) −15.2411 −0.827783
\(340\) 72.6110 3.93788
\(341\) 6.25717 0.338845
\(342\) −1.13783 −0.0615270
\(343\) 10.6615 0.575667
\(344\) −15.9220 −0.858455
\(345\) −2.50893 −0.135076
\(346\) 48.1605 2.58913
\(347\) 2.31373 0.124208 0.0621038 0.998070i \(-0.480219\pi\)
0.0621038 + 0.998070i \(0.480219\pi\)
\(348\) 32.0826 1.71981
\(349\) 14.4172 0.771733 0.385867 0.922555i \(-0.373902\pi\)
0.385867 + 0.922555i \(0.373902\pi\)
\(350\) −58.3676 −3.11988
\(351\) −2.92940 −0.156360
\(352\) −2.44511 −0.130325
\(353\) −20.7594 −1.10491 −0.552457 0.833542i \(-0.686309\pi\)
−0.552457 + 0.833542i \(0.686309\pi\)
\(354\) 3.14837 0.167334
\(355\) −49.5975 −2.63236
\(356\) −10.0985 −0.535221
\(357\) 20.8416 1.10305
\(358\) 2.86970 0.151668
\(359\) −1.95160 −0.103002 −0.0515008 0.998673i \(-0.516400\pi\)
−0.0515008 + 0.998673i \(0.516400\pi\)
\(360\) −19.3039 −1.01741
\(361\) −18.7959 −0.989260
\(362\) −43.1210 −2.26639
\(363\) −10.5795 −0.555280
\(364\) −51.8778 −2.71914
\(365\) 29.9186 1.56601
\(366\) −22.5352 −1.17794
\(367\) −22.3819 −1.16833 −0.584164 0.811636i \(-0.698578\pi\)
−0.584164 + 0.811636i \(0.698578\pi\)
\(368\) −4.74812 −0.247513
\(369\) −3.08641 −0.160672
\(370\) −41.5170 −2.15837
\(371\) −43.9850 −2.28359
\(372\) 41.9217 2.17354
\(373\) −6.26236 −0.324253 −0.162126 0.986770i \(-0.551835\pi\)
−0.162126 + 0.986770i \(0.551835\pi\)
\(374\) −8.35139 −0.431840
\(375\) 2.23840 0.115590
\(376\) −73.0640 −3.76799
\(377\) −21.6323 −1.11412
\(378\) −10.2673 −0.528095
\(379\) −20.0025 −1.02746 −0.513730 0.857952i \(-0.671737\pi\)
−0.513730 + 0.857952i \(0.671737\pi\)
\(380\) 6.41516 0.329091
\(381\) −13.3631 −0.684610
\(382\) −21.1689 −1.08309
\(383\) −20.7570 −1.06063 −0.530317 0.847799i \(-0.677927\pi\)
−0.530317 + 0.847799i \(0.677927\pi\)
\(384\) 14.7819 0.754333
\(385\) 8.64022 0.440346
\(386\) −35.7571 −1.81999
\(387\) 2.69609 0.137050
\(388\) −3.05957 −0.155326
\(389\) −7.59223 −0.384941 −0.192471 0.981303i \(-0.561650\pi\)
−0.192471 + 0.981303i \(0.561650\pi\)
\(390\) 24.1192 1.22132
\(391\) −3.92445 −0.198468
\(392\) −56.7853 −2.86809
\(393\) −18.2766 −0.921930
\(394\) −13.7829 −0.694375
\(395\) 18.0425 0.907814
\(396\) 2.81728 0.141574
\(397\) 29.8494 1.49810 0.749050 0.662514i \(-0.230510\pi\)
0.749050 + 0.662514i \(0.230510\pi\)
\(398\) −29.3254 −1.46995
\(399\) 1.84135 0.0921826
\(400\) 35.1666 1.75833
\(401\) 9.98013 0.498384 0.249192 0.968454i \(-0.419835\pi\)
0.249192 + 0.968454i \(0.419835\pi\)
\(402\) 31.3301 1.56261
\(403\) −28.2665 −1.40805
\(404\) −66.8574 −3.32628
\(405\) 3.26876 0.162426
\(406\) −75.8197 −3.76287
\(407\) 3.26984 0.162080
\(408\) −30.1950 −1.49488
\(409\) 33.8654 1.67453 0.837267 0.546794i \(-0.184152\pi\)
0.837267 + 0.546794i \(0.184152\pi\)
\(410\) 25.4119 1.25500
\(411\) −18.7483 −0.924783
\(412\) 60.5899 2.98505
\(413\) −5.09497 −0.250707
\(414\) 1.93333 0.0950180
\(415\) −47.6962 −2.34131
\(416\) 11.0457 0.541558
\(417\) −19.5104 −0.955428
\(418\) −0.737843 −0.0360891
\(419\) 32.6422 1.59468 0.797339 0.603532i \(-0.206240\pi\)
0.797339 + 0.603532i \(0.206240\pi\)
\(420\) 57.8877 2.82463
\(421\) −9.37994 −0.457150 −0.228575 0.973526i \(-0.573407\pi\)
−0.228575 + 0.973526i \(0.573407\pi\)
\(422\) 57.9341 2.82019
\(423\) 12.3720 0.601549
\(424\) 63.7250 3.09476
\(425\) 29.0661 1.40992
\(426\) 38.2189 1.85171
\(427\) 36.4686 1.76484
\(428\) 61.4928 2.97237
\(429\) −1.89960 −0.0917138
\(430\) −22.1982 −1.07049
\(431\) 23.4793 1.13096 0.565480 0.824762i \(-0.308691\pi\)
0.565480 + 0.824762i \(0.308691\pi\)
\(432\) 6.18609 0.297628
\(433\) −37.1402 −1.78484 −0.892421 0.451203i \(-0.850995\pi\)
−0.892421 + 0.451203i \(0.850995\pi\)
\(434\) −99.0721 −4.75561
\(435\) 24.1383 1.15734
\(436\) −11.1927 −0.536032
\(437\) −0.346724 −0.0165861
\(438\) −23.0547 −1.10159
\(439\) 13.3938 0.639253 0.319627 0.947544i \(-0.396442\pi\)
0.319627 + 0.947544i \(0.396442\pi\)
\(440\) −12.5179 −0.596765
\(441\) 9.61554 0.457883
\(442\) 37.7270 1.79449
\(443\) −9.99995 −0.475112 −0.237556 0.971374i \(-0.576346\pi\)
−0.237556 + 0.971374i \(0.576346\pi\)
\(444\) 21.9073 1.03967
\(445\) −7.59792 −0.360176
\(446\) 26.8138 1.26967
\(447\) 13.7429 0.650015
\(448\) −11.7174 −0.553595
\(449\) 33.9889 1.60404 0.802019 0.597299i \(-0.203759\pi\)
0.802019 + 0.597299i \(0.203759\pi\)
\(450\) −14.3191 −0.675008
\(451\) −2.00142 −0.0942431
\(452\) −66.2159 −3.11454
\(453\) −3.70655 −0.174149
\(454\) 9.22697 0.433043
\(455\) −39.0318 −1.82984
\(456\) −2.66772 −0.124928
\(457\) 9.39491 0.439475 0.219738 0.975559i \(-0.429480\pi\)
0.219738 + 0.975559i \(0.429480\pi\)
\(458\) −26.1407 −1.22147
\(459\) 5.11297 0.238653
\(460\) −10.9002 −0.508224
\(461\) −29.2213 −1.36097 −0.680487 0.732760i \(-0.738232\pi\)
−0.680487 + 0.732760i \(0.738232\pi\)
\(462\) −6.65798 −0.309757
\(463\) −5.91392 −0.274843 −0.137422 0.990513i \(-0.543882\pi\)
−0.137422 + 0.990513i \(0.543882\pi\)
\(464\) 45.6815 2.12071
\(465\) 31.5411 1.46268
\(466\) 26.3861 1.22231
\(467\) 29.8913 1.38321 0.691603 0.722278i \(-0.256905\pi\)
0.691603 + 0.722278i \(0.256905\pi\)
\(468\) −12.7270 −0.588304
\(469\) −50.7013 −2.34117
\(470\) −101.865 −4.69868
\(471\) 2.96178 0.136472
\(472\) 7.38154 0.339763
\(473\) 1.74831 0.0803875
\(474\) −13.9032 −0.638593
\(475\) 2.56798 0.117827
\(476\) 90.5475 4.15024
\(477\) −10.7907 −0.494070
\(478\) 37.0161 1.69308
\(479\) −13.7282 −0.627259 −0.313630 0.949545i \(-0.601545\pi\)
−0.313630 + 0.949545i \(0.601545\pi\)
\(480\) −12.3253 −0.562569
\(481\) −14.7714 −0.673516
\(482\) 57.9565 2.63985
\(483\) −3.12869 −0.142360
\(484\) −45.9633 −2.08924
\(485\) −2.30196 −0.104527
\(486\) −2.51884 −0.114257
\(487\) 12.2678 0.555905 0.277953 0.960595i \(-0.410344\pi\)
0.277953 + 0.960595i \(0.410344\pi\)
\(488\) −52.8353 −2.39174
\(489\) 17.3658 0.785307
\(490\) −79.1694 −3.57651
\(491\) 31.2069 1.40835 0.704174 0.710028i \(-0.251318\pi\)
0.704174 + 0.710028i \(0.251318\pi\)
\(492\) −13.4091 −0.604528
\(493\) 37.7570 1.70049
\(494\) 3.33317 0.149967
\(495\) 2.11967 0.0952719
\(496\) 59.6911 2.68021
\(497\) −61.8492 −2.77432
\(498\) 36.7538 1.64698
\(499\) −5.47525 −0.245106 −0.122553 0.992462i \(-0.539108\pi\)
−0.122553 + 0.992462i \(0.539108\pi\)
\(500\) 9.72487 0.434909
\(501\) −13.9346 −0.622554
\(502\) 16.9721 0.757500
\(503\) −7.58932 −0.338391 −0.169195 0.985583i \(-0.554117\pi\)
−0.169195 + 0.985583i \(0.554117\pi\)
\(504\) −24.0724 −1.07227
\(505\) −50.3021 −2.23842
\(506\) 1.25369 0.0557334
\(507\) −4.41862 −0.196238
\(508\) −58.0566 −2.57584
\(509\) 16.7244 0.741294 0.370647 0.928774i \(-0.379136\pi\)
0.370647 + 0.928774i \(0.379136\pi\)
\(510\) −42.0976 −1.86411
\(511\) 37.3091 1.65046
\(512\) 49.7395 2.19819
\(513\) 0.451729 0.0199443
\(514\) 66.6571 2.94012
\(515\) 45.5866 2.00879
\(516\) 11.7133 0.515651
\(517\) 8.02279 0.352842
\(518\) −51.7726 −2.27476
\(519\) −19.1201 −0.839280
\(520\) 56.5489 2.47983
\(521\) −40.4749 −1.77324 −0.886620 0.462499i \(-0.846953\pi\)
−0.886620 + 0.462499i \(0.846953\pi\)
\(522\) −18.6005 −0.814122
\(523\) 34.7864 1.52110 0.760551 0.649278i \(-0.224929\pi\)
0.760551 + 0.649278i \(0.224929\pi\)
\(524\) −79.4036 −3.46876
\(525\) 23.1724 1.01133
\(526\) −66.5224 −2.90052
\(527\) 49.3363 2.14912
\(528\) 4.01144 0.174576
\(529\) −22.4109 −0.974386
\(530\) 88.8447 3.85917
\(531\) −1.24993 −0.0542422
\(532\) 7.99984 0.346837
\(533\) 9.04132 0.391623
\(534\) 5.85481 0.253362
\(535\) 46.2659 2.00025
\(536\) 73.4554 3.17279
\(537\) −1.13929 −0.0491641
\(538\) −19.9371 −0.859548
\(539\) 6.23531 0.268574
\(540\) 14.2013 0.611128
\(541\) 31.0638 1.33554 0.667768 0.744370i \(-0.267250\pi\)
0.667768 + 0.744370i \(0.267250\pi\)
\(542\) −0.661954 −0.0284333
\(543\) 17.1194 0.734663
\(544\) −19.2791 −0.826584
\(545\) −8.42114 −0.360722
\(546\) 30.0771 1.28718
\(547\) 42.0721 1.79887 0.899436 0.437053i \(-0.143978\pi\)
0.899436 + 0.437053i \(0.143978\pi\)
\(548\) −81.4529 −3.47950
\(549\) 8.94667 0.381835
\(550\) −9.28538 −0.395930
\(551\) 3.33582 0.142111
\(552\) 4.53281 0.192929
\(553\) 22.4993 0.956770
\(554\) −56.6206 −2.40558
\(555\) 16.4826 0.699646
\(556\) −84.7641 −3.59480
\(557\) −14.4813 −0.613591 −0.306796 0.951775i \(-0.599257\pi\)
−0.306796 + 0.951775i \(0.599257\pi\)
\(558\) −24.3049 −1.02891
\(559\) −7.89793 −0.334047
\(560\) 82.4245 3.48307
\(561\) 3.31557 0.139983
\(562\) −13.0738 −0.551485
\(563\) 9.12990 0.384779 0.192390 0.981319i \(-0.438376\pi\)
0.192390 + 0.981319i \(0.438376\pi\)
\(564\) 53.7510 2.26333
\(565\) −49.8195 −2.09592
\(566\) −30.7481 −1.29244
\(567\) 4.07622 0.171185
\(568\) 89.6065 3.75980
\(569\) 24.3208 1.01958 0.509790 0.860299i \(-0.329723\pi\)
0.509790 + 0.860299i \(0.329723\pi\)
\(570\) −3.71931 −0.155785
\(571\) −28.5261 −1.19378 −0.596891 0.802322i \(-0.703598\pi\)
−0.596891 + 0.802322i \(0.703598\pi\)
\(572\) −8.25295 −0.345073
\(573\) 8.40422 0.351091
\(574\) 31.6892 1.32268
\(575\) −4.36335 −0.181964
\(576\) −2.87458 −0.119774
\(577\) −15.0112 −0.624923 −0.312462 0.949930i \(-0.601154\pi\)
−0.312462 + 0.949930i \(0.601154\pi\)
\(578\) −23.0284 −0.957856
\(579\) 14.1958 0.589959
\(580\) 104.870 4.35450
\(581\) −59.4782 −2.46757
\(582\) 1.77384 0.0735282
\(583\) −6.99733 −0.289800
\(584\) −54.0531 −2.23673
\(585\) −9.57550 −0.395898
\(586\) −48.3801 −1.99856
\(587\) −18.0151 −0.743564 −0.371782 0.928320i \(-0.621253\pi\)
−0.371782 + 0.928320i \(0.621253\pi\)
\(588\) 41.7753 1.72278
\(589\) 4.35885 0.179603
\(590\) 10.2912 0.423684
\(591\) 5.47194 0.225086
\(592\) 31.1931 1.28203
\(593\) 8.31313 0.341379 0.170690 0.985325i \(-0.445400\pi\)
0.170690 + 0.985325i \(0.445400\pi\)
\(594\) −1.63337 −0.0670181
\(595\) 68.1261 2.79290
\(596\) 59.7067 2.44568
\(597\) 11.6424 0.476492
\(598\) −5.66350 −0.231598
\(599\) −17.1097 −0.699082 −0.349541 0.936921i \(-0.613662\pi\)
−0.349541 + 0.936921i \(0.613662\pi\)
\(600\) −33.5719 −1.37057
\(601\) 16.0414 0.654342 0.327171 0.944965i \(-0.393905\pi\)
0.327171 + 0.944965i \(0.393905\pi\)
\(602\) −27.6817 −1.12822
\(603\) −12.4383 −0.506527
\(604\) −16.1033 −0.655236
\(605\) −34.5818 −1.40595
\(606\) 38.7618 1.57459
\(607\) 23.9825 0.973418 0.486709 0.873564i \(-0.338197\pi\)
0.486709 + 0.873564i \(0.338197\pi\)
\(608\) −1.70330 −0.0690780
\(609\) 30.1010 1.21975
\(610\) −73.6623 −2.98250
\(611\) −36.2426 −1.46622
\(612\) 22.2136 0.897932
\(613\) −13.9768 −0.564518 −0.282259 0.959338i \(-0.591084\pi\)
−0.282259 + 0.959338i \(0.591084\pi\)
\(614\) 71.6840 2.89293
\(615\) −10.0887 −0.406816
\(616\) −15.6100 −0.628947
\(617\) −42.8632 −1.72561 −0.862803 0.505540i \(-0.831293\pi\)
−0.862803 + 0.505540i \(0.831293\pi\)
\(618\) −35.1282 −1.41306
\(619\) 37.0699 1.48996 0.744982 0.667085i \(-0.232458\pi\)
0.744982 + 0.667085i \(0.232458\pi\)
\(620\) 137.032 5.50334
\(621\) −0.767548 −0.0308006
\(622\) −47.2474 −1.89445
\(623\) −9.47478 −0.379599
\(624\) −18.1215 −0.725442
\(625\) −21.1071 −0.844286
\(626\) 4.17058 0.166690
\(627\) 0.292929 0.0116985
\(628\) 12.8676 0.513475
\(629\) 25.7819 1.02799
\(630\) −33.5615 −1.33712
\(631\) −31.5036 −1.25414 −0.627070 0.778963i \(-0.715746\pi\)
−0.627070 + 0.778963i \(0.715746\pi\)
\(632\) −32.5968 −1.29663
\(633\) −23.0003 −0.914181
\(634\) 30.7333 1.22058
\(635\) −43.6806 −1.73341
\(636\) −46.8806 −1.85894
\(637\) −28.1678 −1.11605
\(638\) −12.0617 −0.477528
\(639\) −15.1732 −0.600242
\(640\) 48.3183 1.90995
\(641\) −21.0790 −0.832569 −0.416285 0.909234i \(-0.636668\pi\)
−0.416285 + 0.909234i \(0.636668\pi\)
\(642\) −35.6516 −1.40706
\(643\) −19.5545 −0.771155 −0.385578 0.922675i \(-0.625998\pi\)
−0.385578 + 0.922675i \(0.625998\pi\)
\(644\) −13.5928 −0.535631
\(645\) 8.81287 0.347006
\(646\) −5.81771 −0.228895
\(647\) 41.6117 1.63593 0.817963 0.575271i \(-0.195104\pi\)
0.817963 + 0.575271i \(0.195104\pi\)
\(648\) −5.90558 −0.231993
\(649\) −0.810530 −0.0318161
\(650\) 41.9463 1.64527
\(651\) 39.3324 1.54156
\(652\) 75.4466 2.95472
\(653\) 20.8080 0.814281 0.407140 0.913366i \(-0.366526\pi\)
0.407140 + 0.913366i \(0.366526\pi\)
\(654\) 6.48917 0.253746
\(655\) −59.7416 −2.33430
\(656\) −19.0928 −0.745448
\(657\) 9.15289 0.357088
\(658\) −127.028 −4.95206
\(659\) −30.2150 −1.17701 −0.588505 0.808494i \(-0.700283\pi\)
−0.588505 + 0.808494i \(0.700283\pi\)
\(660\) 9.20902 0.358461
\(661\) 3.16792 0.123218 0.0616090 0.998100i \(-0.480377\pi\)
0.0616090 + 0.998100i \(0.480377\pi\)
\(662\) 23.2109 0.902118
\(663\) −14.9779 −0.581695
\(664\) 86.1714 3.34410
\(665\) 6.01892 0.233404
\(666\) −12.7011 −0.492159
\(667\) −5.66799 −0.219466
\(668\) −60.5399 −2.34236
\(669\) −10.6453 −0.411571
\(670\) 102.411 3.95647
\(671\) 5.80158 0.223967
\(672\) −15.3699 −0.592906
\(673\) 6.05639 0.233457 0.116728 0.993164i \(-0.462759\pi\)
0.116728 + 0.993164i \(0.462759\pi\)
\(674\) 0.747897 0.0288079
\(675\) 5.68479 0.218808
\(676\) −19.1970 −0.738345
\(677\) 32.4954 1.24890 0.624450 0.781064i \(-0.285323\pi\)
0.624450 + 0.781064i \(0.285323\pi\)
\(678\) 38.3899 1.47436
\(679\) −2.87059 −0.110163
\(680\) −98.7003 −3.78498
\(681\) −3.66318 −0.140373
\(682\) −15.7608 −0.603513
\(683\) −21.7372 −0.831751 −0.415876 0.909422i \(-0.636525\pi\)
−0.415876 + 0.909422i \(0.636525\pi\)
\(684\) 1.96257 0.0750406
\(685\) −61.2835 −2.34152
\(686\) −26.8546 −1.02532
\(687\) 10.3781 0.395947
\(688\) 16.6783 0.635853
\(689\) 31.6101 1.20425
\(690\) 6.31959 0.240583
\(691\) 0.576970 0.0219490 0.0109745 0.999940i \(-0.496507\pi\)
0.0109745 + 0.999940i \(0.496507\pi\)
\(692\) −83.0685 −3.15779
\(693\) 2.64327 0.100410
\(694\) −5.82792 −0.221225
\(695\) −63.7748 −2.41911
\(696\) −43.6100 −1.65303
\(697\) −15.7807 −0.597737
\(698\) −36.3146 −1.37453
\(699\) −10.4755 −0.396220
\(700\) 100.674 3.80512
\(701\) 7.41499 0.280060 0.140030 0.990147i \(-0.455280\pi\)
0.140030 + 0.990147i \(0.455280\pi\)
\(702\) 7.37869 0.278491
\(703\) 2.27783 0.0859098
\(704\) −1.86405 −0.0702542
\(705\) 40.4412 1.52310
\(706\) 52.2897 1.96795
\(707\) −62.7279 −2.35913
\(708\) −5.43038 −0.204086
\(709\) −21.1226 −0.793277 −0.396638 0.917975i \(-0.629823\pi\)
−0.396638 + 0.917975i \(0.629823\pi\)
\(710\) 124.928 4.68847
\(711\) 5.51966 0.207004
\(712\) 13.7270 0.514440
\(713\) −7.40626 −0.277367
\(714\) −52.4966 −1.96464
\(715\) −6.20935 −0.232217
\(716\) −4.94972 −0.184980
\(717\) −14.6957 −0.548821
\(718\) 4.91578 0.183455
\(719\) −20.1583 −0.751779 −0.375890 0.926664i \(-0.622663\pi\)
−0.375890 + 0.926664i \(0.622663\pi\)
\(720\) 20.2208 0.753586
\(721\) 56.8476 2.11711
\(722\) 47.3440 1.76196
\(723\) −23.0092 −0.855721
\(724\) 74.3762 2.76417
\(725\) 41.9796 1.55908
\(726\) 26.6481 0.989003
\(727\) 27.5569 1.02203 0.511014 0.859572i \(-0.329270\pi\)
0.511014 + 0.859572i \(0.329270\pi\)
\(728\) 70.5177 2.61356
\(729\) 1.00000 0.0370370
\(730\) −75.3601 −2.78920
\(731\) 13.7850 0.509858
\(732\) 38.8694 1.43665
\(733\) 34.0174 1.25646 0.628231 0.778027i \(-0.283779\pi\)
0.628231 + 0.778027i \(0.283779\pi\)
\(734\) 56.3766 2.08090
\(735\) 31.4309 1.15935
\(736\) 2.89413 0.106679
\(737\) −8.06578 −0.297107
\(738\) 7.77417 0.286171
\(739\) −8.96461 −0.329769 −0.164884 0.986313i \(-0.552725\pi\)
−0.164884 + 0.986313i \(0.552725\pi\)
\(740\) 71.6095 2.63242
\(741\) −1.32330 −0.0486125
\(742\) 110.791 4.06728
\(743\) −41.3662 −1.51758 −0.758789 0.651336i \(-0.774209\pi\)
−0.758789 + 0.651336i \(0.774209\pi\)
\(744\) −56.9844 −2.08915
\(745\) 44.9221 1.64582
\(746\) 15.7739 0.577523
\(747\) −14.5915 −0.533876
\(748\) 14.4047 0.526687
\(749\) 57.6946 2.10812
\(750\) −5.63817 −0.205877
\(751\) 30.9437 1.12915 0.564576 0.825381i \(-0.309040\pi\)
0.564576 + 0.825381i \(0.309040\pi\)
\(752\) 76.5345 2.79093
\(753\) −6.73804 −0.245548
\(754\) 54.4883 1.98435
\(755\) −12.1158 −0.440940
\(756\) 17.7094 0.644084
\(757\) 6.65268 0.241796 0.120898 0.992665i \(-0.461423\pi\)
0.120898 + 0.992665i \(0.461423\pi\)
\(758\) 50.3832 1.83000
\(759\) −0.497726 −0.0180663
\(760\) −8.72014 −0.316313
\(761\) 1.37325 0.0497804 0.0248902 0.999690i \(-0.492076\pi\)
0.0248902 + 0.999690i \(0.492076\pi\)
\(762\) 33.6594 1.21935
\(763\) −10.5014 −0.380175
\(764\) 36.5126 1.32098
\(765\) 16.7131 0.604262
\(766\) 52.2836 1.88908
\(767\) 3.66153 0.132210
\(768\) −31.4840 −1.13608
\(769\) −3.70178 −0.133490 −0.0667448 0.997770i \(-0.521261\pi\)
−0.0667448 + 0.997770i \(0.521261\pi\)
\(770\) −21.7633 −0.784296
\(771\) −26.4634 −0.953056
\(772\) 61.6747 2.21972
\(773\) 34.7777 1.25087 0.625434 0.780277i \(-0.284922\pi\)
0.625434 + 0.780277i \(0.284922\pi\)
\(774\) −6.79103 −0.244098
\(775\) 54.8539 1.97041
\(776\) 4.15889 0.149295
\(777\) 20.5541 0.737376
\(778\) 19.1236 0.685615
\(779\) −1.39422 −0.0499531
\(780\) −41.6014 −1.48957
\(781\) −9.83924 −0.352076
\(782\) 9.88507 0.353489
\(783\) 7.38455 0.263902
\(784\) 59.4826 2.12438
\(785\) 9.68135 0.345542
\(786\) 46.0357 1.64204
\(787\) −5.47712 −0.195238 −0.0976192 0.995224i \(-0.531123\pi\)
−0.0976192 + 0.995224i \(0.531123\pi\)
\(788\) 23.7732 0.846884
\(789\) 26.4099 0.940218
\(790\) −45.4461 −1.61690
\(791\) −62.1261 −2.20895
\(792\) −3.82954 −0.136077
\(793\) −26.2084 −0.930687
\(794\) −75.1860 −2.66825
\(795\) −35.2720 −1.25097
\(796\) 50.5812 1.79280
\(797\) −8.91974 −0.315954 −0.157977 0.987443i \(-0.550497\pi\)
−0.157977 + 0.987443i \(0.550497\pi\)
\(798\) −4.63806 −0.164186
\(799\) 63.2578 2.23790
\(800\) −21.4352 −0.757848
\(801\) −2.32441 −0.0821288
\(802\) −25.1384 −0.887666
\(803\) 5.93530 0.209452
\(804\) −54.0390 −1.90581
\(805\) −10.2269 −0.360452
\(806\) 71.1988 2.50787
\(807\) 7.91517 0.278627
\(808\) 90.8795 3.19713
\(809\) −18.2549 −0.641807 −0.320904 0.947112i \(-0.603987\pi\)
−0.320904 + 0.947112i \(0.603987\pi\)
\(810\) −8.23349 −0.289295
\(811\) 32.4981 1.14116 0.570582 0.821241i \(-0.306718\pi\)
0.570582 + 0.821241i \(0.306718\pi\)
\(812\) 130.776 4.58933
\(813\) 0.262801 0.00921683
\(814\) −8.23621 −0.288679
\(815\) 56.7645 1.98837
\(816\) 31.6293 1.10725
\(817\) 1.21790 0.0426090
\(818\) −85.3015 −2.98250
\(819\) −11.9409 −0.417248
\(820\) −43.8311 −1.53065
\(821\) 26.4401 0.922765 0.461383 0.887201i \(-0.347354\pi\)
0.461383 + 0.887201i \(0.347354\pi\)
\(822\) 47.2239 1.64712
\(823\) 13.7959 0.480894 0.240447 0.970662i \(-0.422706\pi\)
0.240447 + 0.970662i \(0.422706\pi\)
\(824\) −82.3601 −2.86915
\(825\) 3.68637 0.128343
\(826\) 12.8334 0.446532
\(827\) 44.8415 1.55929 0.779646 0.626221i \(-0.215399\pi\)
0.779646 + 0.626221i \(0.215399\pi\)
\(828\) −3.33466 −0.115887
\(829\) −39.7665 −1.38115 −0.690574 0.723262i \(-0.742642\pi\)
−0.690574 + 0.723262i \(0.742642\pi\)
\(830\) 120.139 4.17009
\(831\) 22.4788 0.779782
\(832\) 8.42079 0.291938
\(833\) 49.1640 1.70343
\(834\) 49.1436 1.70170
\(835\) −45.5490 −1.57629
\(836\) 1.27265 0.0440155
\(837\) 9.64925 0.333527
\(838\) −82.2206 −2.84026
\(839\) 17.3221 0.598024 0.299012 0.954249i \(-0.403343\pi\)
0.299012 + 0.954249i \(0.403343\pi\)
\(840\) −78.6869 −2.71496
\(841\) 25.5315 0.880397
\(842\) 23.6266 0.814226
\(843\) 5.19041 0.178767
\(844\) −99.9263 −3.43960
\(845\) −14.4434 −0.496868
\(846\) −31.1632 −1.07141
\(847\) −43.1243 −1.48177
\(848\) −66.7519 −2.29227
\(849\) 12.2072 0.418951
\(850\) −73.2130 −2.51119
\(851\) −3.87033 −0.132673
\(852\) −65.9209 −2.25841
\(853\) 41.4809 1.42028 0.710139 0.704062i \(-0.248632\pi\)
0.710139 + 0.704062i \(0.248632\pi\)
\(854\) −91.8585 −3.14333
\(855\) 1.47659 0.0504985
\(856\) −83.5874 −2.85696
\(857\) 45.4569 1.55278 0.776389 0.630254i \(-0.217049\pi\)
0.776389 + 0.630254i \(0.217049\pi\)
\(858\) 4.78480 0.163350
\(859\) −27.6751 −0.944264 −0.472132 0.881528i \(-0.656515\pi\)
−0.472132 + 0.881528i \(0.656515\pi\)
\(860\) 38.2881 1.30561
\(861\) −12.5809 −0.428755
\(862\) −59.1407 −2.01434
\(863\) 25.7930 0.878003 0.439001 0.898486i \(-0.355332\pi\)
0.439001 + 0.898486i \(0.355332\pi\)
\(864\) −3.77062 −0.128279
\(865\) −62.4990 −2.12503
\(866\) 93.5502 3.17896
\(867\) 9.14247 0.310495
\(868\) 170.882 5.80012
\(869\) 3.57929 0.121419
\(870\) −60.8005 −2.06133
\(871\) 36.4368 1.23461
\(872\) 15.2142 0.515219
\(873\) −0.704230 −0.0238346
\(874\) 0.873342 0.0295412
\(875\) 9.12420 0.308454
\(876\) 39.7653 1.34354
\(877\) −50.9301 −1.71979 −0.859893 0.510474i \(-0.829470\pi\)
−0.859893 + 0.510474i \(0.829470\pi\)
\(878\) −33.7370 −1.13857
\(879\) 19.2073 0.647845
\(880\) 13.1124 0.442020
\(881\) −49.3800 −1.66365 −0.831827 0.555035i \(-0.812705\pi\)
−0.831827 + 0.555035i \(0.812705\pi\)
\(882\) −24.2200 −0.815530
\(883\) 8.67623 0.291978 0.145989 0.989286i \(-0.453364\pi\)
0.145989 + 0.989286i \(0.453364\pi\)
\(884\) −65.0726 −2.18863
\(885\) −4.08571 −0.137340
\(886\) 25.1883 0.846217
\(887\) −32.3831 −1.08732 −0.543660 0.839306i \(-0.682962\pi\)
−0.543660 + 0.839306i \(0.682962\pi\)
\(888\) −29.7786 −0.999305
\(889\) −54.4707 −1.82689
\(890\) 19.1380 0.641506
\(891\) 0.648462 0.0217243
\(892\) −46.2491 −1.54854
\(893\) 5.58881 0.187022
\(894\) −34.6161 −1.15773
\(895\) −3.72407 −0.124482
\(896\) 60.2540 2.01295
\(897\) 2.24845 0.0750737
\(898\) −85.6127 −2.85693
\(899\) 71.2553 2.37650
\(900\) 24.6979 0.823263
\(901\) −55.1723 −1.83806
\(902\) 5.04125 0.167855
\(903\) 10.9898 0.365719
\(904\) 90.0075 2.99361
\(905\) 55.9591 1.86014
\(906\) 9.33622 0.310175
\(907\) −26.3106 −0.873628 −0.436814 0.899552i \(-0.643893\pi\)
−0.436814 + 0.899552i \(0.643893\pi\)
\(908\) −15.9149 −0.528155
\(909\) −15.3888 −0.510413
\(910\) 98.3149 3.25911
\(911\) −58.8835 −1.95090 −0.975448 0.220230i \(-0.929319\pi\)
−0.975448 + 0.220230i \(0.929319\pi\)
\(912\) 2.79444 0.0925331
\(913\) −9.46206 −0.313148
\(914\) −23.6643 −0.782745
\(915\) 29.2445 0.966794
\(916\) 45.0881 1.48975
\(917\) −74.4992 −2.46018
\(918\) −12.8788 −0.425062
\(919\) 18.7209 0.617544 0.308772 0.951136i \(-0.400082\pi\)
0.308772 + 0.951136i \(0.400082\pi\)
\(920\) 14.8167 0.488491
\(921\) −28.4591 −0.937760
\(922\) 73.6039 2.42402
\(923\) 44.4483 1.46303
\(924\) 11.4839 0.377791
\(925\) 28.6653 0.942509
\(926\) 14.8962 0.489520
\(927\) 13.9462 0.458052
\(928\) −27.8443 −0.914035
\(929\) 6.85266 0.224828 0.112414 0.993661i \(-0.464142\pi\)
0.112414 + 0.993661i \(0.464142\pi\)
\(930\) −79.4469 −2.60517
\(931\) 4.34362 0.142356
\(932\) −45.5115 −1.49078
\(933\) 18.7576 0.614096
\(934\) −75.2915 −2.46361
\(935\) 10.8378 0.354434
\(936\) 17.2998 0.565462
\(937\) −10.2142 −0.333683 −0.166841 0.985984i \(-0.553357\pi\)
−0.166841 + 0.985984i \(0.553357\pi\)
\(938\) 127.708 4.16983
\(939\) −1.65575 −0.0540334
\(940\) 175.699 5.73068
\(941\) 38.1858 1.24482 0.622410 0.782691i \(-0.286154\pi\)
0.622410 + 0.782691i \(0.286154\pi\)
\(942\) −7.46026 −0.243068
\(943\) 2.36896 0.0771441
\(944\) −7.73216 −0.251660
\(945\) 13.3242 0.433435
\(946\) −4.40372 −0.143177
\(947\) 54.6170 1.77481 0.887407 0.460987i \(-0.152505\pi\)
0.887407 + 0.460987i \(0.152505\pi\)
\(948\) 23.9805 0.778851
\(949\) −26.8125 −0.870369
\(950\) −6.46835 −0.209861
\(951\) −12.2014 −0.395657
\(952\) −123.082 −3.98910
\(953\) −17.0279 −0.551589 −0.275795 0.961217i \(-0.588941\pi\)
−0.275795 + 0.961217i \(0.588941\pi\)
\(954\) 27.1799 0.879983
\(955\) 27.4714 0.888952
\(956\) −63.8464 −2.06494
\(957\) 4.78860 0.154793
\(958\) 34.5792 1.11720
\(959\) −76.4219 −2.46779
\(960\) −9.39630 −0.303264
\(961\) 62.1080 2.00348
\(962\) 37.2067 1.19959
\(963\) 14.1540 0.456105
\(964\) −99.9648 −3.21965
\(965\) 46.4028 1.49376
\(966\) 7.88068 0.253557
\(967\) 13.5986 0.437303 0.218651 0.975803i \(-0.429834\pi\)
0.218651 + 0.975803i \(0.429834\pi\)
\(968\) 62.4780 2.00812
\(969\) 2.30968 0.0741976
\(970\) 5.79827 0.186171
\(971\) 48.4625 1.55523 0.777617 0.628738i \(-0.216428\pi\)
0.777617 + 0.628738i \(0.216428\pi\)
\(972\) 4.34456 0.139352
\(973\) −79.5286 −2.54957
\(974\) −30.9005 −0.990117
\(975\) −16.6530 −0.533323
\(976\) 55.3449 1.77155
\(977\) −33.2269 −1.06302 −0.531512 0.847051i \(-0.678376\pi\)
−0.531512 + 0.847051i \(0.678376\pi\)
\(978\) −43.7416 −1.39870
\(979\) −1.50729 −0.0481732
\(980\) 136.553 4.36204
\(981\) −2.57625 −0.0822533
\(982\) −78.6052 −2.50839
\(983\) 1.85585 0.0591923 0.0295962 0.999562i \(-0.490578\pi\)
0.0295962 + 0.999562i \(0.490578\pi\)
\(984\) 18.2270 0.581056
\(985\) 17.8865 0.569910
\(986\) −95.1038 −3.02872
\(987\) 50.4311 1.60524
\(988\) −5.74914 −0.182905
\(989\) −2.06938 −0.0658024
\(990\) −5.33910 −0.169688
\(991\) −16.0289 −0.509175 −0.254587 0.967050i \(-0.581940\pi\)
−0.254587 + 0.967050i \(0.581940\pi\)
\(992\) −36.3837 −1.15518
\(993\) −9.21492 −0.292427
\(994\) 155.788 4.94131
\(995\) 38.0562 1.20646
\(996\) −63.3938 −2.00871
\(997\) 30.4200 0.963411 0.481706 0.876333i \(-0.340017\pi\)
0.481706 + 0.876333i \(0.340017\pi\)
\(998\) 13.7913 0.436555
\(999\) 5.04246 0.159536
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 \(a_p\))