Properties

Label 619.2.a.b.1.8
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.37056 q^{2} -0.725873 q^{3} -0.121559 q^{4} -0.225133 q^{5} +0.994855 q^{6} +2.47282 q^{7} +2.90773 q^{8} -2.47311 q^{9} +O(q^{10})\) \(q-1.37056 q^{2} -0.725873 q^{3} -0.121559 q^{4} -0.225133 q^{5} +0.994855 q^{6} +2.47282 q^{7} +2.90773 q^{8} -2.47311 q^{9} +0.308559 q^{10} -4.06256 q^{11} +0.0882365 q^{12} +2.26536 q^{13} -3.38915 q^{14} +0.163418 q^{15} -3.74211 q^{16} +7.19086 q^{17} +3.38955 q^{18} -7.47015 q^{19} +0.0273670 q^{20} -1.79495 q^{21} +5.56800 q^{22} -0.178059 q^{23} -2.11064 q^{24} -4.94931 q^{25} -3.10482 q^{26} +3.97278 q^{27} -0.300594 q^{28} +10.5609 q^{29} -0.223975 q^{30} +1.27650 q^{31} -0.686670 q^{32} +2.94891 q^{33} -9.85552 q^{34} -0.556714 q^{35} +0.300629 q^{36} +2.08508 q^{37} +10.2383 q^{38} -1.64436 q^{39} -0.654627 q^{40} +4.23367 q^{41} +2.46009 q^{42} +8.52011 q^{43} +0.493842 q^{44} +0.556779 q^{45} +0.244041 q^{46} +9.96677 q^{47} +2.71629 q^{48} -0.885174 q^{49} +6.78334 q^{50} -5.21965 q^{51} -0.275375 q^{52} +0.619984 q^{53} -5.44495 q^{54} +0.914619 q^{55} +7.19028 q^{56} +5.42238 q^{57} -14.4744 q^{58} +11.8540 q^{59} -0.0198650 q^{60} +6.30300 q^{61} -1.74952 q^{62} -6.11554 q^{63} +8.42533 q^{64} -0.510008 q^{65} -4.04166 q^{66} +12.5388 q^{67} -0.874114 q^{68} +0.129248 q^{69} +0.763011 q^{70} -9.50401 q^{71} -7.19113 q^{72} +5.14906 q^{73} -2.85773 q^{74} +3.59258 q^{75} +0.908065 q^{76} -10.0460 q^{77} +2.25370 q^{78} -16.3932 q^{79} +0.842473 q^{80} +4.53559 q^{81} -5.80251 q^{82} +4.79273 q^{83} +0.218193 q^{84} -1.61890 q^{85} -11.6773 q^{86} -7.66589 q^{87} -11.8128 q^{88} -1.64933 q^{89} -0.763100 q^{90} +5.60182 q^{91} +0.0216447 q^{92} -0.926577 q^{93} -13.6601 q^{94} +1.68178 q^{95} +0.498435 q^{96} +3.34400 q^{97} +1.21319 q^{98} +10.0472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.37056 −0.969134 −0.484567 0.874754i \(-0.661023\pi\)
−0.484567 + 0.874754i \(0.661023\pi\)
\(3\) −0.725873 −0.419083 −0.209542 0.977800i \(-0.567197\pi\)
−0.209542 + 0.977800i \(0.567197\pi\)
\(4\) −0.121559 −0.0607796
\(5\) −0.225133 −0.100683 −0.0503414 0.998732i \(-0.516031\pi\)
−0.0503414 + 0.998732i \(0.516031\pi\)
\(6\) 0.994855 0.406148
\(7\) 2.47282 0.934637 0.467319 0.884089i \(-0.345220\pi\)
0.467319 + 0.884089i \(0.345220\pi\)
\(8\) 2.90773 1.02804
\(9\) −2.47311 −0.824369
\(10\) 0.308559 0.0975750
\(11\) −4.06256 −1.22491 −0.612455 0.790506i \(-0.709818\pi\)
−0.612455 + 0.790506i \(0.709818\pi\)
\(12\) 0.0882365 0.0254717
\(13\) 2.26536 0.628298 0.314149 0.949374i \(-0.398281\pi\)
0.314149 + 0.949374i \(0.398281\pi\)
\(14\) −3.38915 −0.905788
\(15\) 0.163418 0.0421944
\(16\) −3.74211 −0.935526
\(17\) 7.19086 1.74404 0.872019 0.489471i \(-0.162810\pi\)
0.872019 + 0.489471i \(0.162810\pi\)
\(18\) 3.38955 0.798924
\(19\) −7.47015 −1.71377 −0.856885 0.515507i \(-0.827603\pi\)
−0.856885 + 0.515507i \(0.827603\pi\)
\(20\) 0.0273670 0.00611945
\(21\) −1.79495 −0.391691
\(22\) 5.56800 1.18710
\(23\) −0.178059 −0.0371279 −0.0185639 0.999828i \(-0.505909\pi\)
−0.0185639 + 0.999828i \(0.505909\pi\)
\(24\) −2.11064 −0.430833
\(25\) −4.94931 −0.989863
\(26\) −3.10482 −0.608905
\(27\) 3.97278 0.764562
\(28\) −0.300594 −0.0568068
\(29\) 10.5609 1.96111 0.980557 0.196232i \(-0.0628707\pi\)
0.980557 + 0.196232i \(0.0628707\pi\)
\(30\) −0.223975 −0.0408920
\(31\) 1.27650 0.229266 0.114633 0.993408i \(-0.463431\pi\)
0.114633 + 0.993408i \(0.463431\pi\)
\(32\) −0.686670 −0.121387
\(33\) 2.94891 0.513339
\(34\) −9.85552 −1.69021
\(35\) −0.556714 −0.0941018
\(36\) 0.300629 0.0501048
\(37\) 2.08508 0.342784 0.171392 0.985203i \(-0.445173\pi\)
0.171392 + 0.985203i \(0.445173\pi\)
\(38\) 10.2383 1.66087
\(39\) −1.64436 −0.263309
\(40\) −0.654627 −0.103506
\(41\) 4.23367 0.661188 0.330594 0.943773i \(-0.392751\pi\)
0.330594 + 0.943773i \(0.392751\pi\)
\(42\) 2.46009 0.379601
\(43\) 8.52011 1.29930 0.649652 0.760232i \(-0.274915\pi\)
0.649652 + 0.760232i \(0.274915\pi\)
\(44\) 0.493842 0.0744495
\(45\) 0.556779 0.0829997
\(46\) 0.244041 0.0359819
\(47\) 9.96677 1.45380 0.726901 0.686742i \(-0.240960\pi\)
0.726901 + 0.686742i \(0.240960\pi\)
\(48\) 2.71629 0.392063
\(49\) −0.885174 −0.126453
\(50\) 6.78334 0.959310
\(51\) −5.21965 −0.730897
\(52\) −0.275375 −0.0381877
\(53\) 0.619984 0.0851614 0.0425807 0.999093i \(-0.486442\pi\)
0.0425807 + 0.999093i \(0.486442\pi\)
\(54\) −5.44495 −0.740963
\(55\) 0.914619 0.123327
\(56\) 7.19028 0.960842
\(57\) 5.42238 0.718212
\(58\) −14.4744 −1.90058
\(59\) 11.8540 1.54326 0.771628 0.636074i \(-0.219443\pi\)
0.771628 + 0.636074i \(0.219443\pi\)
\(60\) −0.0198650 −0.00256456
\(61\) 6.30300 0.807017 0.403508 0.914976i \(-0.367791\pi\)
0.403508 + 0.914976i \(0.367791\pi\)
\(62\) −1.74952 −0.222190
\(63\) −6.11554 −0.770486
\(64\) 8.42533 1.05317
\(65\) −0.510008 −0.0632587
\(66\) −4.04166 −0.497494
\(67\) 12.5388 1.53186 0.765928 0.642927i \(-0.222280\pi\)
0.765928 + 0.642927i \(0.222280\pi\)
\(68\) −0.874114 −0.106002
\(69\) 0.129248 0.0155597
\(70\) 0.763011 0.0911972
\(71\) −9.50401 −1.12792 −0.563959 0.825803i \(-0.690723\pi\)
−0.563959 + 0.825803i \(0.690723\pi\)
\(72\) −7.19113 −0.847482
\(73\) 5.14906 0.602652 0.301326 0.953521i \(-0.402571\pi\)
0.301326 + 0.953521i \(0.402571\pi\)
\(74\) −2.85773 −0.332204
\(75\) 3.59258 0.414835
\(76\) 0.908065 0.104162
\(77\) −10.0460 −1.14485
\(78\) 2.25370 0.255182
\(79\) −16.3932 −1.84438 −0.922190 0.386737i \(-0.873602\pi\)
−0.922190 + 0.386737i \(0.873602\pi\)
\(80\) 0.842473 0.0941913
\(81\) 4.53559 0.503954
\(82\) −5.80251 −0.640780
\(83\) 4.79273 0.526071 0.263035 0.964786i \(-0.415276\pi\)
0.263035 + 0.964786i \(0.415276\pi\)
\(84\) 0.218193 0.0238068
\(85\) −1.61890 −0.175595
\(86\) −11.6773 −1.25920
\(87\) −7.66589 −0.821870
\(88\) −11.8128 −1.25925
\(89\) −1.64933 −0.174829 −0.0874143 0.996172i \(-0.527860\pi\)
−0.0874143 + 0.996172i \(0.527860\pi\)
\(90\) −0.763100 −0.0804379
\(91\) 5.60182 0.587231
\(92\) 0.0216447 0.00225662
\(93\) −0.926577 −0.0960816
\(94\) −13.6601 −1.40893
\(95\) 1.68178 0.172547
\(96\) 0.498435 0.0508713
\(97\) 3.34400 0.339531 0.169766 0.985484i \(-0.445699\pi\)
0.169766 + 0.985484i \(0.445699\pi\)
\(98\) 1.21319 0.122550
\(99\) 10.0472 1.00978
\(100\) 0.601634 0.0601634
\(101\) −12.6806 −1.26176 −0.630882 0.775878i \(-0.717307\pi\)
−0.630882 + 0.775878i \(0.717307\pi\)
\(102\) 7.15386 0.708337
\(103\) −4.47808 −0.441238 −0.220619 0.975360i \(-0.570808\pi\)
−0.220619 + 0.975360i \(0.570808\pi\)
\(104\) 6.58705 0.645914
\(105\) 0.404104 0.0394365
\(106\) −0.849727 −0.0825328
\(107\) 15.0754 1.45740 0.728699 0.684834i \(-0.240125\pi\)
0.728699 + 0.684834i \(0.240125\pi\)
\(108\) −0.482928 −0.0464698
\(109\) 3.66599 0.351138 0.175569 0.984467i \(-0.443823\pi\)
0.175569 + 0.984467i \(0.443823\pi\)
\(110\) −1.25354 −0.119521
\(111\) −1.51350 −0.143655
\(112\) −9.25354 −0.874378
\(113\) 6.54316 0.615528 0.307764 0.951463i \(-0.400419\pi\)
0.307764 + 0.951463i \(0.400419\pi\)
\(114\) −7.43171 −0.696044
\(115\) 0.0400870 0.00373814
\(116\) −1.28378 −0.119196
\(117\) −5.60248 −0.517949
\(118\) −16.2466 −1.49562
\(119\) 17.7817 1.63004
\(120\) 0.475176 0.0433774
\(121\) 5.50443 0.500403
\(122\) −8.63866 −0.782107
\(123\) −3.07311 −0.277093
\(124\) −0.155170 −0.0139347
\(125\) 2.23992 0.200345
\(126\) 8.38173 0.746704
\(127\) −15.0494 −1.33542 −0.667711 0.744420i \(-0.732726\pi\)
−0.667711 + 0.744420i \(0.732726\pi\)
\(128\) −10.1741 −0.899272
\(129\) −6.18452 −0.544516
\(130\) 0.698998 0.0613062
\(131\) 9.57374 0.836462 0.418231 0.908341i \(-0.362650\pi\)
0.418231 + 0.908341i \(0.362650\pi\)
\(132\) −0.358467 −0.0312005
\(133\) −18.4723 −1.60175
\(134\) −17.1852 −1.48457
\(135\) −0.894406 −0.0769782
\(136\) 20.9091 1.79294
\(137\) 2.15272 0.183919 0.0919595 0.995763i \(-0.470687\pi\)
0.0919595 + 0.995763i \(0.470687\pi\)
\(138\) −0.177143 −0.0150794
\(139\) 5.62106 0.476772 0.238386 0.971171i \(-0.423382\pi\)
0.238386 + 0.971171i \(0.423382\pi\)
\(140\) 0.0676736 0.00571947
\(141\) −7.23461 −0.609264
\(142\) 13.0258 1.09310
\(143\) −9.20317 −0.769608
\(144\) 9.25463 0.771219
\(145\) −2.37762 −0.197450
\(146\) −7.05711 −0.584050
\(147\) 0.642524 0.0529945
\(148\) −0.253460 −0.0208343
\(149\) 15.1382 1.24017 0.620086 0.784534i \(-0.287098\pi\)
0.620086 + 0.784534i \(0.287098\pi\)
\(150\) −4.92385 −0.402031
\(151\) −19.7193 −1.60474 −0.802369 0.596828i \(-0.796427\pi\)
−0.802369 + 0.596828i \(0.796427\pi\)
\(152\) −21.7212 −1.76182
\(153\) −17.7838 −1.43773
\(154\) 13.7686 1.10951
\(155\) −0.287383 −0.0230831
\(156\) 0.199888 0.0160038
\(157\) 15.7111 1.25389 0.626943 0.779065i \(-0.284306\pi\)
0.626943 + 0.779065i \(0.284306\pi\)
\(158\) 22.4679 1.78745
\(159\) −0.450030 −0.0356897
\(160\) 0.154592 0.0122216
\(161\) −0.440308 −0.0347011
\(162\) −6.21630 −0.488399
\(163\) −11.8717 −0.929864 −0.464932 0.885346i \(-0.653921\pi\)
−0.464932 + 0.885346i \(0.653921\pi\)
\(164\) −0.514641 −0.0401867
\(165\) −0.663897 −0.0516843
\(166\) −6.56874 −0.509833
\(167\) −5.37936 −0.416267 −0.208134 0.978100i \(-0.566739\pi\)
−0.208134 + 0.978100i \(0.566739\pi\)
\(168\) −5.21923 −0.402673
\(169\) −7.86814 −0.605242
\(170\) 2.21881 0.170175
\(171\) 18.4745 1.41278
\(172\) −1.03570 −0.0789711
\(173\) −18.6393 −1.41712 −0.708560 0.705651i \(-0.750655\pi\)
−0.708560 + 0.705651i \(0.750655\pi\)
\(174\) 10.5066 0.796502
\(175\) −12.2388 −0.925163
\(176\) 15.2025 1.14593
\(177\) −8.60448 −0.646753
\(178\) 2.26051 0.169432
\(179\) −22.6264 −1.69117 −0.845587 0.533837i \(-0.820750\pi\)
−0.845587 + 0.533837i \(0.820750\pi\)
\(180\) −0.0676816 −0.00504469
\(181\) 12.1002 0.899398 0.449699 0.893180i \(-0.351531\pi\)
0.449699 + 0.893180i \(0.351531\pi\)
\(182\) −7.67765 −0.569105
\(183\) −4.57518 −0.338207
\(184\) −0.517747 −0.0381688
\(185\) −0.469420 −0.0345124
\(186\) 1.26993 0.0931159
\(187\) −29.2133 −2.13629
\(188\) −1.21155 −0.0883615
\(189\) 9.82397 0.714588
\(190\) −2.30498 −0.167221
\(191\) −0.166765 −0.0120667 −0.00603336 0.999982i \(-0.501920\pi\)
−0.00603336 + 0.999982i \(0.501920\pi\)
\(192\) −6.11573 −0.441364
\(193\) −16.5260 −1.18956 −0.594782 0.803887i \(-0.702762\pi\)
−0.594782 + 0.803887i \(0.702762\pi\)
\(194\) −4.58316 −0.329051
\(195\) 0.370201 0.0265107
\(196\) 0.107601 0.00768578
\(197\) 9.82274 0.699841 0.349921 0.936779i \(-0.386209\pi\)
0.349921 + 0.936779i \(0.386209\pi\)
\(198\) −13.7703 −0.978610
\(199\) 11.5691 0.820113 0.410056 0.912060i \(-0.365509\pi\)
0.410056 + 0.912060i \(0.365509\pi\)
\(200\) −14.3913 −1.01762
\(201\) −9.10156 −0.641975
\(202\) 17.3795 1.22282
\(203\) 26.1152 1.83293
\(204\) 0.634496 0.0444236
\(205\) −0.953140 −0.0665702
\(206\) 6.13749 0.427619
\(207\) 0.440359 0.0306071
\(208\) −8.47722 −0.587789
\(209\) 30.3480 2.09921
\(210\) −0.553849 −0.0382192
\(211\) −19.2316 −1.32396 −0.661978 0.749523i \(-0.730283\pi\)
−0.661978 + 0.749523i \(0.730283\pi\)
\(212\) −0.0753647 −0.00517607
\(213\) 6.89871 0.472692
\(214\) −20.6618 −1.41241
\(215\) −1.91816 −0.130817
\(216\) 11.5518 0.785999
\(217\) 3.15655 0.214281
\(218\) −5.02447 −0.340300
\(219\) −3.73757 −0.252561
\(220\) −0.111180 −0.00749577
\(221\) 16.2899 1.09578
\(222\) 2.07435 0.139221
\(223\) −2.26463 −0.151651 −0.0758255 0.997121i \(-0.524159\pi\)
−0.0758255 + 0.997121i \(0.524159\pi\)
\(224\) −1.69801 −0.113453
\(225\) 12.2402 0.816013
\(226\) −8.96780 −0.596529
\(227\) 12.6616 0.840378 0.420189 0.907437i \(-0.361964\pi\)
0.420189 + 0.907437i \(0.361964\pi\)
\(228\) −0.659140 −0.0436526
\(229\) 27.7524 1.83393 0.916967 0.398964i \(-0.130630\pi\)
0.916967 + 0.398964i \(0.130630\pi\)
\(230\) −0.0549418 −0.00362275
\(231\) 7.29211 0.479786
\(232\) 30.7083 2.01610
\(233\) −10.9164 −0.715157 −0.357579 0.933883i \(-0.616398\pi\)
−0.357579 + 0.933883i \(0.616398\pi\)
\(234\) 7.67855 0.501962
\(235\) −2.24385 −0.146373
\(236\) −1.44096 −0.0937984
\(237\) 11.8994 0.772949
\(238\) −24.3709 −1.57973
\(239\) 6.41476 0.414936 0.207468 0.978242i \(-0.433478\pi\)
0.207468 + 0.978242i \(0.433478\pi\)
\(240\) −0.611529 −0.0394740
\(241\) 9.85126 0.634576 0.317288 0.948329i \(-0.397228\pi\)
0.317288 + 0.948329i \(0.397228\pi\)
\(242\) −7.54417 −0.484957
\(243\) −15.2106 −0.975761
\(244\) −0.766188 −0.0490501
\(245\) 0.199282 0.0127317
\(246\) 4.21189 0.268540
\(247\) −16.9226 −1.07676
\(248\) 3.71172 0.235694
\(249\) −3.47892 −0.220467
\(250\) −3.06995 −0.194161
\(251\) 5.56947 0.351542 0.175771 0.984431i \(-0.443758\pi\)
0.175771 + 0.984431i \(0.443758\pi\)
\(252\) 0.743400 0.0468298
\(253\) 0.723376 0.0454783
\(254\) 20.6262 1.29420
\(255\) 1.17512 0.0735887
\(256\) −2.90642 −0.181651
\(257\) 24.0328 1.49913 0.749564 0.661932i \(-0.230263\pi\)
0.749564 + 0.661932i \(0.230263\pi\)
\(258\) 8.47627 0.527709
\(259\) 5.15601 0.320379
\(260\) 0.0619962 0.00384484
\(261\) −26.1183 −1.61668
\(262\) −13.1214 −0.810643
\(263\) 14.9598 0.922463 0.461232 0.887280i \(-0.347408\pi\)
0.461232 + 0.887280i \(0.347408\pi\)
\(264\) 8.57462 0.527732
\(265\) −0.139579 −0.00857428
\(266\) 25.3175 1.55231
\(267\) 1.19720 0.0732677
\(268\) −1.52420 −0.0931055
\(269\) 13.4385 0.819357 0.409679 0.912230i \(-0.365641\pi\)
0.409679 + 0.912230i \(0.365641\pi\)
\(270\) 1.22584 0.0746022
\(271\) 5.72605 0.347833 0.173916 0.984760i \(-0.444358\pi\)
0.173916 + 0.984760i \(0.444358\pi\)
\(272\) −26.9089 −1.63159
\(273\) −4.06621 −0.246098
\(274\) −2.95043 −0.178242
\(275\) 20.1069 1.21249
\(276\) −0.0157113 −0.000945710 0
\(277\) 12.0981 0.726905 0.363452 0.931613i \(-0.381598\pi\)
0.363452 + 0.931613i \(0.381598\pi\)
\(278\) −7.70401 −0.462056
\(279\) −3.15692 −0.189000
\(280\) −1.61877 −0.0967402
\(281\) −6.21778 −0.370921 −0.185461 0.982652i \(-0.559378\pi\)
−0.185461 + 0.982652i \(0.559378\pi\)
\(282\) 9.91549 0.590459
\(283\) 12.9505 0.769826 0.384913 0.922953i \(-0.374231\pi\)
0.384913 + 0.922953i \(0.374231\pi\)
\(284\) 1.15530 0.0685544
\(285\) −1.22076 −0.0723116
\(286\) 12.6135 0.745853
\(287\) 10.4691 0.617971
\(288\) 1.69821 0.100068
\(289\) 34.7084 2.04167
\(290\) 3.25867 0.191356
\(291\) −2.42732 −0.142292
\(292\) −0.625915 −0.0366289
\(293\) 14.3490 0.838279 0.419139 0.907922i \(-0.362332\pi\)
0.419139 + 0.907922i \(0.362332\pi\)
\(294\) −0.880619 −0.0513588
\(295\) −2.66873 −0.155379
\(296\) 6.06283 0.352395
\(297\) −16.1397 −0.936520
\(298\) −20.7479 −1.20189
\(299\) −0.403368 −0.0233274
\(300\) −0.436710 −0.0252135
\(301\) 21.0687 1.21438
\(302\) 27.0266 1.55521
\(303\) 9.20450 0.528784
\(304\) 27.9541 1.60328
\(305\) −1.41902 −0.0812526
\(306\) 24.3738 1.39335
\(307\) −28.7422 −1.64040 −0.820202 0.572075i \(-0.806139\pi\)
−0.820202 + 0.572075i \(0.806139\pi\)
\(308\) 1.22118 0.0695832
\(309\) 3.25052 0.184916
\(310\) 0.393876 0.0223707
\(311\) −29.9677 −1.69931 −0.849655 0.527339i \(-0.823190\pi\)
−0.849655 + 0.527339i \(0.823190\pi\)
\(312\) −4.78137 −0.270692
\(313\) −13.6402 −0.770990 −0.385495 0.922710i \(-0.625969\pi\)
−0.385495 + 0.922710i \(0.625969\pi\)
\(314\) −21.5331 −1.21518
\(315\) 1.37681 0.0775746
\(316\) 1.99274 0.112101
\(317\) 12.9433 0.726967 0.363484 0.931601i \(-0.381587\pi\)
0.363484 + 0.931601i \(0.381587\pi\)
\(318\) 0.616794 0.0345881
\(319\) −42.9044 −2.40219
\(320\) −1.89682 −0.106036
\(321\) −10.9429 −0.610771
\(322\) 0.603469 0.0336300
\(323\) −53.7168 −2.98888
\(324\) −0.551342 −0.0306301
\(325\) −11.2120 −0.621929
\(326\) 16.2709 0.901163
\(327\) −2.66104 −0.147156
\(328\) 12.3104 0.679726
\(329\) 24.6460 1.35878
\(330\) 0.909913 0.0500891
\(331\) 8.48346 0.466293 0.233147 0.972442i \(-0.425098\pi\)
0.233147 + 0.972442i \(0.425098\pi\)
\(332\) −0.582600 −0.0319744
\(333\) −5.15662 −0.282581
\(334\) 7.37275 0.403419
\(335\) −2.82290 −0.154231
\(336\) 6.71690 0.366437
\(337\) −28.4431 −1.54939 −0.774697 0.632332i \(-0.782098\pi\)
−0.774697 + 0.632332i \(0.782098\pi\)
\(338\) 10.7838 0.586560
\(339\) −4.74950 −0.257958
\(340\) 0.196792 0.0106726
\(341\) −5.18586 −0.280830
\(342\) −25.3204 −1.36917
\(343\) −19.4986 −1.05283
\(344\) 24.7742 1.33573
\(345\) −0.0290981 −0.00156659
\(346\) 25.5463 1.37338
\(347\) 6.37057 0.341990 0.170995 0.985272i \(-0.445302\pi\)
0.170995 + 0.985272i \(0.445302\pi\)
\(348\) 0.931860 0.0499529
\(349\) −12.7281 −0.681317 −0.340659 0.940187i \(-0.610650\pi\)
−0.340659 + 0.940187i \(0.610650\pi\)
\(350\) 16.7740 0.896607
\(351\) 8.99978 0.480373
\(352\) 2.78964 0.148688
\(353\) 1.48049 0.0787984 0.0393992 0.999224i \(-0.487456\pi\)
0.0393992 + 0.999224i \(0.487456\pi\)
\(354\) 11.7930 0.626790
\(355\) 2.13967 0.113562
\(356\) 0.200491 0.0106260
\(357\) −12.9072 −0.683124
\(358\) 31.0109 1.63897
\(359\) −27.5753 −1.45537 −0.727685 0.685911i \(-0.759404\pi\)
−0.727685 + 0.685911i \(0.759404\pi\)
\(360\) 1.61896 0.0853268
\(361\) 36.8032 1.93701
\(362\) −16.5840 −0.871637
\(363\) −3.99552 −0.209710
\(364\) −0.680953 −0.0356916
\(365\) −1.15923 −0.0606766
\(366\) 6.27057 0.327768
\(367\) 6.08957 0.317873 0.158936 0.987289i \(-0.449193\pi\)
0.158936 + 0.987289i \(0.449193\pi\)
\(368\) 0.666316 0.0347341
\(369\) −10.4703 −0.545063
\(370\) 0.643369 0.0334472
\(371\) 1.53311 0.0795950
\(372\) 0.112634 0.00583980
\(373\) 22.4949 1.16474 0.582371 0.812923i \(-0.302125\pi\)
0.582371 + 0.812923i \(0.302125\pi\)
\(374\) 40.0387 2.07035
\(375\) −1.62590 −0.0839611
\(376\) 28.9807 1.49456
\(377\) 23.9243 1.23216
\(378\) −13.4644 −0.692532
\(379\) −14.1157 −0.725075 −0.362538 0.931969i \(-0.618090\pi\)
−0.362538 + 0.931969i \(0.618090\pi\)
\(380\) −0.204436 −0.0104873
\(381\) 10.9240 0.559653
\(382\) 0.228562 0.0116943
\(383\) 24.3617 1.24482 0.622412 0.782690i \(-0.286153\pi\)
0.622412 + 0.782690i \(0.286153\pi\)
\(384\) 7.38511 0.376870
\(385\) 2.26169 0.115266
\(386\) 22.6498 1.15285
\(387\) −21.0711 −1.07111
\(388\) −0.406493 −0.0206366
\(389\) −16.7319 −0.848341 −0.424170 0.905582i \(-0.639434\pi\)
−0.424170 + 0.905582i \(0.639434\pi\)
\(390\) −0.507384 −0.0256924
\(391\) −1.28040 −0.0647525
\(392\) −2.57385 −0.129999
\(393\) −6.94932 −0.350547
\(394\) −13.4627 −0.678240
\(395\) 3.69066 0.185697
\(396\) −1.22132 −0.0613739
\(397\) −21.7689 −1.09255 −0.546274 0.837607i \(-0.683954\pi\)
−0.546274 + 0.837607i \(0.683954\pi\)
\(398\) −15.8562 −0.794799
\(399\) 13.4086 0.671268
\(400\) 18.5209 0.926043
\(401\) 20.2269 1.01008 0.505041 0.863095i \(-0.331477\pi\)
0.505041 + 0.863095i \(0.331477\pi\)
\(402\) 12.4743 0.622159
\(403\) 2.89173 0.144047
\(404\) 1.54144 0.0766895
\(405\) −1.02111 −0.0507395
\(406\) −35.7926 −1.77636
\(407\) −8.47075 −0.419880
\(408\) −15.1773 −0.751390
\(409\) 28.5461 1.41151 0.705757 0.708454i \(-0.250607\pi\)
0.705757 + 0.708454i \(0.250607\pi\)
\(410\) 1.30634 0.0645155
\(411\) −1.56260 −0.0770773
\(412\) 0.544352 0.0268183
\(413\) 29.3127 1.44238
\(414\) −0.603540 −0.0296624
\(415\) −1.07900 −0.0529662
\(416\) −1.55555 −0.0762673
\(417\) −4.08018 −0.199807
\(418\) −41.5938 −2.03442
\(419\) −36.3207 −1.77438 −0.887192 0.461400i \(-0.847347\pi\)
−0.887192 + 0.461400i \(0.847347\pi\)
\(420\) −0.0491225 −0.00239693
\(421\) −20.8986 −1.01853 −0.509267 0.860609i \(-0.670083\pi\)
−0.509267 + 0.860609i \(0.670083\pi\)
\(422\) 26.3581 1.28309
\(423\) −24.6489 −1.19847
\(424\) 1.80275 0.0875491
\(425\) −35.5898 −1.72636
\(426\) −9.45511 −0.458102
\(427\) 15.5862 0.754268
\(428\) −1.83256 −0.0885800
\(429\) 6.68034 0.322530
\(430\) 2.62896 0.126780
\(431\) 5.65795 0.272534 0.136267 0.990672i \(-0.456490\pi\)
0.136267 + 0.990672i \(0.456490\pi\)
\(432\) −14.8666 −0.715268
\(433\) −0.797593 −0.0383299 −0.0191649 0.999816i \(-0.506101\pi\)
−0.0191649 + 0.999816i \(0.506101\pi\)
\(434\) −4.32625 −0.207667
\(435\) 1.72585 0.0827481
\(436\) −0.445635 −0.0213420
\(437\) 1.33013 0.0636286
\(438\) 5.12257 0.244766
\(439\) −18.2826 −0.872581 −0.436290 0.899806i \(-0.643708\pi\)
−0.436290 + 0.899806i \(0.643708\pi\)
\(440\) 2.65946 0.126785
\(441\) 2.18913 0.104244
\(442\) −22.3263 −1.06195
\(443\) −18.4038 −0.874391 −0.437195 0.899367i \(-0.644028\pi\)
−0.437195 + 0.899367i \(0.644028\pi\)
\(444\) 0.183980 0.00873130
\(445\) 0.371319 0.0176022
\(446\) 3.10382 0.146970
\(447\) −10.9884 −0.519735
\(448\) 20.8343 0.984329
\(449\) 2.95767 0.139581 0.0697905 0.997562i \(-0.477767\pi\)
0.0697905 + 0.997562i \(0.477767\pi\)
\(450\) −16.7759 −0.790825
\(451\) −17.1996 −0.809896
\(452\) −0.795381 −0.0374116
\(453\) 14.3138 0.672519
\(454\) −17.3535 −0.814439
\(455\) −1.26116 −0.0591240
\(456\) 15.7668 0.738349
\(457\) 18.1383 0.848472 0.424236 0.905552i \(-0.360543\pi\)
0.424236 + 0.905552i \(0.360543\pi\)
\(458\) −38.0365 −1.77733
\(459\) 28.5677 1.33343
\(460\) −0.00487295 −0.000227202 0
\(461\) −16.5572 −0.771145 −0.385573 0.922677i \(-0.625996\pi\)
−0.385573 + 0.922677i \(0.625996\pi\)
\(462\) −9.99429 −0.464976
\(463\) 4.01151 0.186430 0.0932152 0.995646i \(-0.470286\pi\)
0.0932152 + 0.995646i \(0.470286\pi\)
\(464\) −39.5201 −1.83467
\(465\) 0.208603 0.00967376
\(466\) 14.9616 0.693083
\(467\) −4.61263 −0.213447 −0.106724 0.994289i \(-0.534036\pi\)
−0.106724 + 0.994289i \(0.534036\pi\)
\(468\) 0.681033 0.0314807
\(469\) 31.0061 1.43173
\(470\) 3.07534 0.141855
\(471\) −11.4043 −0.525482
\(472\) 34.4681 1.58652
\(473\) −34.6135 −1.59153
\(474\) −16.3089 −0.749091
\(475\) 36.9721 1.69640
\(476\) −2.16153 −0.0990733
\(477\) −1.53329 −0.0702044
\(478\) −8.79182 −0.402129
\(479\) −37.2886 −1.70376 −0.851879 0.523739i \(-0.824537\pi\)
−0.851879 + 0.523739i \(0.824537\pi\)
\(480\) −0.112214 −0.00512186
\(481\) 4.72345 0.215371
\(482\) −13.5018 −0.614989
\(483\) 0.319607 0.0145426
\(484\) −0.669114 −0.0304143
\(485\) −0.752845 −0.0341849
\(486\) 20.8471 0.945643
\(487\) 25.0176 1.13366 0.566828 0.823836i \(-0.308170\pi\)
0.566828 + 0.823836i \(0.308170\pi\)
\(488\) 18.3274 0.829644
\(489\) 8.61736 0.389690
\(490\) −0.273129 −0.0123387
\(491\) −23.7021 −1.06966 −0.534830 0.844960i \(-0.679624\pi\)
−0.534830 + 0.844960i \(0.679624\pi\)
\(492\) 0.373564 0.0168416
\(493\) 75.9421 3.42026
\(494\) 23.1935 1.04352
\(495\) −2.26195 −0.101667
\(496\) −4.77680 −0.214485
\(497\) −23.5017 −1.05419
\(498\) 4.76807 0.213662
\(499\) 27.1748 1.21651 0.608255 0.793742i \(-0.291870\pi\)
0.608255 + 0.793742i \(0.291870\pi\)
\(500\) −0.272283 −0.0121769
\(501\) 3.90473 0.174451
\(502\) −7.63331 −0.340691
\(503\) 12.0746 0.538381 0.269191 0.963087i \(-0.413244\pi\)
0.269191 + 0.963087i \(0.413244\pi\)
\(504\) −17.7823 −0.792089
\(505\) 2.85482 0.127038
\(506\) −0.991432 −0.0440745
\(507\) 5.71128 0.253647
\(508\) 1.82940 0.0811664
\(509\) −43.7176 −1.93775 −0.968873 0.247557i \(-0.920372\pi\)
−0.968873 + 0.247557i \(0.920372\pi\)
\(510\) −1.61057 −0.0713173
\(511\) 12.7327 0.563261
\(512\) 24.3316 1.07532
\(513\) −29.6773 −1.31028
\(514\) −32.9385 −1.45286
\(515\) 1.00817 0.0444251
\(516\) 0.751785 0.0330955
\(517\) −40.4906 −1.78078
\(518\) −7.06663 −0.310490
\(519\) 13.5298 0.593891
\(520\) −1.48297 −0.0650323
\(521\) −35.3638 −1.54932 −0.774659 0.632379i \(-0.782078\pi\)
−0.774659 + 0.632379i \(0.782078\pi\)
\(522\) 35.7968 1.56678
\(523\) 19.8938 0.869897 0.434949 0.900455i \(-0.356767\pi\)
0.434949 + 0.900455i \(0.356767\pi\)
\(524\) −1.16378 −0.0508398
\(525\) 8.88378 0.387720
\(526\) −20.5034 −0.893990
\(527\) 9.17913 0.399849
\(528\) −11.0351 −0.480242
\(529\) −22.9683 −0.998622
\(530\) 0.191302 0.00830962
\(531\) −29.3162 −1.27221
\(532\) 2.24548 0.0973539
\(533\) 9.59079 0.415423
\(534\) −1.64084 −0.0710062
\(535\) −3.39399 −0.146735
\(536\) 36.4594 1.57480
\(537\) 16.4239 0.708743
\(538\) −18.4182 −0.794067
\(539\) 3.59608 0.154894
\(540\) 0.108723 0.00467870
\(541\) −15.3119 −0.658311 −0.329156 0.944276i \(-0.606764\pi\)
−0.329156 + 0.944276i \(0.606764\pi\)
\(542\) −7.84790 −0.337096
\(543\) −8.78319 −0.376923
\(544\) −4.93774 −0.211704
\(545\) −0.825337 −0.0353535
\(546\) 5.57300 0.238502
\(547\) 42.3037 1.80878 0.904388 0.426711i \(-0.140328\pi\)
0.904388 + 0.426711i \(0.140328\pi\)
\(548\) −0.261682 −0.0111785
\(549\) −15.5880 −0.665280
\(550\) −27.5578 −1.17507
\(551\) −78.8917 −3.36090
\(552\) 0.375819 0.0159959
\(553\) −40.5374 −1.72383
\(554\) −16.5812 −0.704468
\(555\) 0.340739 0.0144636
\(556\) −0.683291 −0.0289780
\(557\) 7.44351 0.315392 0.157696 0.987488i \(-0.449593\pi\)
0.157696 + 0.987488i \(0.449593\pi\)
\(558\) 4.32676 0.183166
\(559\) 19.3011 0.816350
\(560\) 2.08328 0.0880347
\(561\) 21.2052 0.895283
\(562\) 8.52185 0.359472
\(563\) −30.6551 −1.29196 −0.645978 0.763356i \(-0.723550\pi\)
−0.645978 + 0.763356i \(0.723550\pi\)
\(564\) 0.879433 0.0370308
\(565\) −1.47308 −0.0619731
\(566\) −17.7494 −0.746064
\(567\) 11.2157 0.471014
\(568\) −27.6351 −1.15954
\(569\) 45.0445 1.88836 0.944182 0.329425i \(-0.106855\pi\)
0.944182 + 0.329425i \(0.106855\pi\)
\(570\) 1.67313 0.0700796
\(571\) −20.5533 −0.860127 −0.430063 0.902799i \(-0.641509\pi\)
−0.430063 + 0.902799i \(0.641509\pi\)
\(572\) 1.11873 0.0467764
\(573\) 0.121051 0.00505696
\(574\) −14.3485 −0.598897
\(575\) 0.881270 0.0367515
\(576\) −20.8368 −0.868198
\(577\) 2.43980 0.101570 0.0507851 0.998710i \(-0.483828\pi\)
0.0507851 + 0.998710i \(0.483828\pi\)
\(578\) −47.5700 −1.97865
\(579\) 11.9957 0.498526
\(580\) 0.289021 0.0120009
\(581\) 11.8516 0.491685
\(582\) 3.32679 0.137900
\(583\) −2.51873 −0.104315
\(584\) 14.9721 0.619549
\(585\) 1.26131 0.0521486
\(586\) −19.6662 −0.812404
\(587\) 28.0624 1.15826 0.579129 0.815236i \(-0.303393\pi\)
0.579129 + 0.815236i \(0.303393\pi\)
\(588\) −0.0781047 −0.00322098
\(589\) −9.53565 −0.392910
\(590\) 3.65765 0.150583
\(591\) −7.13007 −0.293292
\(592\) −7.80257 −0.320684
\(593\) −20.1600 −0.827873 −0.413937 0.910306i \(-0.635847\pi\)
−0.413937 + 0.910306i \(0.635847\pi\)
\(594\) 22.1204 0.907613
\(595\) −4.00325 −0.164117
\(596\) −1.84019 −0.0753771
\(597\) −8.39771 −0.343696
\(598\) 0.552841 0.0226073
\(599\) 23.5060 0.960427 0.480214 0.877152i \(-0.340559\pi\)
0.480214 + 0.877152i \(0.340559\pi\)
\(600\) 10.4462 0.426466
\(601\) −20.9839 −0.855952 −0.427976 0.903790i \(-0.640773\pi\)
−0.427976 + 0.903790i \(0.640773\pi\)
\(602\) −28.8759 −1.17689
\(603\) −31.0097 −1.26281
\(604\) 2.39707 0.0975353
\(605\) −1.23923 −0.0503819
\(606\) −12.6153 −0.512463
\(607\) 32.2511 1.30903 0.654516 0.756048i \(-0.272872\pi\)
0.654516 + 0.756048i \(0.272872\pi\)
\(608\) 5.12953 0.208030
\(609\) −18.9564 −0.768150
\(610\) 1.94485 0.0787447
\(611\) 22.5783 0.913421
\(612\) 2.16178 0.0873847
\(613\) −37.2120 −1.50298 −0.751489 0.659746i \(-0.770664\pi\)
−0.751489 + 0.659746i \(0.770664\pi\)
\(614\) 39.3930 1.58977
\(615\) 0.691859 0.0278985
\(616\) −29.2110 −1.17694
\(617\) 38.3479 1.54383 0.771915 0.635726i \(-0.219299\pi\)
0.771915 + 0.635726i \(0.219299\pi\)
\(618\) −4.45504 −0.179208
\(619\) 1.00000 0.0401934
\(620\) 0.0349340 0.00140298
\(621\) −0.707390 −0.0283866
\(622\) 41.0726 1.64686
\(623\) −4.07849 −0.163401
\(624\) 6.15339 0.246333
\(625\) 24.2423 0.969692
\(626\) 18.6948 0.747193
\(627\) −22.0288 −0.879745
\(628\) −1.90983 −0.0762106
\(629\) 14.9935 0.597829
\(630\) −1.88701 −0.0751802
\(631\) 38.9829 1.55188 0.775942 0.630804i \(-0.217275\pi\)
0.775942 + 0.630804i \(0.217275\pi\)
\(632\) −47.6670 −1.89609
\(633\) 13.9597 0.554848
\(634\) −17.7396 −0.704529
\(635\) 3.38813 0.134454
\(636\) 0.0547052 0.00216920
\(637\) −2.00524 −0.0794504
\(638\) 58.8032 2.32804
\(639\) 23.5044 0.929822
\(640\) 2.29053 0.0905412
\(641\) −0.319675 −0.0126264 −0.00631321 0.999980i \(-0.502010\pi\)
−0.00631321 + 0.999980i \(0.502010\pi\)
\(642\) 14.9979 0.591919
\(643\) 0.159017 0.00627101 0.00313550 0.999995i \(-0.499002\pi\)
0.00313550 + 0.999995i \(0.499002\pi\)
\(644\) 0.0535234 0.00210912
\(645\) 1.39234 0.0548234
\(646\) 73.6222 2.89663
\(647\) 24.6688 0.969829 0.484915 0.874562i \(-0.338851\pi\)
0.484915 + 0.874562i \(0.338851\pi\)
\(648\) 13.1883 0.518084
\(649\) −48.1575 −1.89035
\(650\) 15.3667 0.602732
\(651\) −2.29126 −0.0898014
\(652\) 1.44311 0.0565167
\(653\) −28.3461 −1.10927 −0.554635 0.832094i \(-0.687142\pi\)
−0.554635 + 0.832094i \(0.687142\pi\)
\(654\) 3.64713 0.142614
\(655\) −2.15537 −0.0842172
\(656\) −15.8428 −0.618559
\(657\) −12.7342 −0.496808
\(658\) −33.7789 −1.31684
\(659\) 39.5061 1.53894 0.769470 0.638683i \(-0.220521\pi\)
0.769470 + 0.638683i \(0.220521\pi\)
\(660\) 0.0807028 0.00314135
\(661\) −15.7041 −0.610818 −0.305409 0.952221i \(-0.598793\pi\)
−0.305409 + 0.952221i \(0.598793\pi\)
\(662\) −11.6271 −0.451900
\(663\) −11.8244 −0.459221
\(664\) 13.9360 0.540820
\(665\) 4.15874 0.161269
\(666\) 7.06746 0.273859
\(667\) −1.88047 −0.0728120
\(668\) 0.653910 0.0253006
\(669\) 1.64384 0.0635544
\(670\) 3.86896 0.149471
\(671\) −25.6064 −0.988523
\(672\) 1.23254 0.0475462
\(673\) −23.0243 −0.887522 −0.443761 0.896145i \(-0.646356\pi\)
−0.443761 + 0.896145i \(0.646356\pi\)
\(674\) 38.9830 1.50157
\(675\) −19.6626 −0.756812
\(676\) 0.956445 0.0367863
\(677\) 7.63096 0.293282 0.146641 0.989190i \(-0.453154\pi\)
0.146641 + 0.989190i \(0.453154\pi\)
\(678\) 6.50949 0.249995
\(679\) 8.26909 0.317339
\(680\) −4.70733 −0.180518
\(681\) −9.19070 −0.352188
\(682\) 7.10755 0.272162
\(683\) 0.644724 0.0246697 0.0123348 0.999924i \(-0.496074\pi\)
0.0123348 + 0.999924i \(0.496074\pi\)
\(684\) −2.24574 −0.0858681
\(685\) −0.484648 −0.0185175
\(686\) 26.7240 1.02033
\(687\) −20.1448 −0.768571
\(688\) −31.8831 −1.21553
\(689\) 1.40449 0.0535067
\(690\) 0.0398808 0.00151823
\(691\) −29.5024 −1.12232 −0.561162 0.827706i \(-0.689646\pi\)
−0.561162 + 0.827706i \(0.689646\pi\)
\(692\) 2.26578 0.0861319
\(693\) 24.8448 0.943776
\(694\) −8.73126 −0.331434
\(695\) −1.26549 −0.0480027
\(696\) −22.2903 −0.844913
\(697\) 30.4437 1.15314
\(698\) 17.4446 0.660288
\(699\) 7.92393 0.299710
\(700\) 1.48773 0.0562310
\(701\) −30.4332 −1.14944 −0.574722 0.818348i \(-0.694890\pi\)
−0.574722 + 0.818348i \(0.694890\pi\)
\(702\) −12.3348 −0.465546
\(703\) −15.5758 −0.587453
\(704\) −34.2285 −1.29003
\(705\) 1.62875 0.0613424
\(706\) −2.02910 −0.0763662
\(707\) −31.3568 −1.17929
\(708\) 1.04595 0.0393093
\(709\) 10.4754 0.393413 0.196707 0.980462i \(-0.436975\pi\)
0.196707 + 0.980462i \(0.436975\pi\)
\(710\) −2.93255 −0.110057
\(711\) 40.5422 1.52045
\(712\) −4.79580 −0.179730
\(713\) −0.227292 −0.00851217
\(714\) 17.6902 0.662038
\(715\) 2.07194 0.0774862
\(716\) 2.75044 0.102789
\(717\) −4.65630 −0.173893
\(718\) 37.7937 1.41045
\(719\) 0.815327 0.0304066 0.0152033 0.999884i \(-0.495160\pi\)
0.0152033 + 0.999884i \(0.495160\pi\)
\(720\) −2.08353 −0.0776484
\(721\) −11.0735 −0.412398
\(722\) −50.4410 −1.87722
\(723\) −7.15077 −0.265940
\(724\) −1.47089 −0.0546650
\(725\) −52.2694 −1.94123
\(726\) 5.47611 0.203237
\(727\) 5.58478 0.207128 0.103564 0.994623i \(-0.466975\pi\)
0.103564 + 0.994623i \(0.466975\pi\)
\(728\) 16.2886 0.603695
\(729\) −2.56578 −0.0950290
\(730\) 1.58879 0.0588038
\(731\) 61.2669 2.26604
\(732\) 0.556155 0.0205561
\(733\) 27.7414 1.02465 0.512327 0.858791i \(-0.328784\pi\)
0.512327 + 0.858791i \(0.328784\pi\)
\(734\) −8.34613 −0.308061
\(735\) −0.144654 −0.00533563
\(736\) 0.122268 0.00450685
\(737\) −50.9396 −1.87638
\(738\) 14.3502 0.528239
\(739\) −10.9980 −0.404569 −0.202285 0.979327i \(-0.564837\pi\)
−0.202285 + 0.979327i \(0.564837\pi\)
\(740\) 0.0570623 0.00209765
\(741\) 12.2837 0.451251
\(742\) −2.10122 −0.0771382
\(743\) 27.5706 1.01147 0.505733 0.862690i \(-0.331222\pi\)
0.505733 + 0.862690i \(0.331222\pi\)
\(744\) −2.69424 −0.0987755
\(745\) −3.40812 −0.124864
\(746\) −30.8307 −1.12879
\(747\) −11.8529 −0.433677
\(748\) 3.55115 0.129843
\(749\) 37.2788 1.36214
\(750\) 2.22840 0.0813696
\(751\) 2.39041 0.0872274 0.0436137 0.999048i \(-0.486113\pi\)
0.0436137 + 0.999048i \(0.486113\pi\)
\(752\) −37.2967 −1.36007
\(753\) −4.04273 −0.147325
\(754\) −32.7897 −1.19413
\(755\) 4.43948 0.161569
\(756\) −1.19419 −0.0434324
\(757\) 22.8502 0.830505 0.415253 0.909706i \(-0.363693\pi\)
0.415253 + 0.909706i \(0.363693\pi\)
\(758\) 19.3465 0.702695
\(759\) −0.525080 −0.0190592
\(760\) 4.89016 0.177385
\(761\) 35.2537 1.27795 0.638974 0.769229i \(-0.279359\pi\)
0.638974 + 0.769229i \(0.279359\pi\)
\(762\) −14.9720 −0.542379
\(763\) 9.06532 0.328187
\(764\) 0.0202719 0.000733410 0
\(765\) 4.00372 0.144755
\(766\) −33.3892 −1.20640
\(767\) 26.8535 0.969625
\(768\) 2.10970 0.0761271
\(769\) 14.0283 0.505875 0.252937 0.967483i \(-0.418603\pi\)
0.252937 + 0.967483i \(0.418603\pi\)
\(770\) −3.09978 −0.111708
\(771\) −17.4448 −0.628259
\(772\) 2.00888 0.0723012
\(773\) 2.05297 0.0738401 0.0369200 0.999318i \(-0.488245\pi\)
0.0369200 + 0.999318i \(0.488245\pi\)
\(774\) 28.8793 1.03805
\(775\) −6.31780 −0.226942
\(776\) 9.72344 0.349051
\(777\) −3.74261 −0.134265
\(778\) 22.9321 0.822156
\(779\) −31.6262 −1.13312
\(780\) −0.0450014 −0.00161131
\(781\) 38.6107 1.38160
\(782\) 1.75486 0.0627538
\(783\) 41.9563 1.49939
\(784\) 3.31241 0.118300
\(785\) −3.53710 −0.126245
\(786\) 9.52448 0.339727
\(787\) −7.63128 −0.272026 −0.136013 0.990707i \(-0.543429\pi\)
−0.136013 + 0.990707i \(0.543429\pi\)
\(788\) −1.19404 −0.0425361
\(789\) −10.8589 −0.386589
\(790\) −5.05828 −0.179965
\(791\) 16.1800 0.575296
\(792\) 29.2144 1.03809
\(793\) 14.2786 0.507047
\(794\) 29.8356 1.05882
\(795\) 0.101317 0.00359333
\(796\) −1.40633 −0.0498461
\(797\) 23.8432 0.844570 0.422285 0.906463i \(-0.361228\pi\)
0.422285 + 0.906463i \(0.361228\pi\)
\(798\) −18.3773 −0.650548
\(799\) 71.6696 2.53549
\(800\) 3.39854 0.120157
\(801\) 4.07897 0.144123
\(802\) −27.7222 −0.978905
\(803\) −20.9184 −0.738194
\(804\) 1.10638 0.0390189
\(805\) 0.0991279 0.00349380
\(806\) −3.96330 −0.139601
\(807\) −9.75462 −0.343379
\(808\) −36.8717 −1.29714
\(809\) 19.9428 0.701152 0.350576 0.936534i \(-0.385986\pi\)
0.350576 + 0.936534i \(0.385986\pi\)
\(810\) 1.39950 0.0491733
\(811\) −24.3626 −0.855488 −0.427744 0.903900i \(-0.640692\pi\)
−0.427744 + 0.903900i \(0.640692\pi\)
\(812\) −3.17455 −0.111405
\(813\) −4.15639 −0.145771
\(814\) 11.6097 0.406920
\(815\) 2.67272 0.0936212
\(816\) 19.5325 0.683774
\(817\) −63.6465 −2.22671
\(818\) −39.1242 −1.36795
\(819\) −13.8539 −0.484095
\(820\) 0.115863 0.00404611
\(821\) −15.6976 −0.547850 −0.273925 0.961751i \(-0.588322\pi\)
−0.273925 + 0.961751i \(0.588322\pi\)
\(822\) 2.14164 0.0746982
\(823\) −7.38747 −0.257511 −0.128755 0.991676i \(-0.541098\pi\)
−0.128755 + 0.991676i \(0.541098\pi\)
\(824\) −13.0210 −0.453609
\(825\) −14.5951 −0.508135
\(826\) −40.1749 −1.39786
\(827\) 11.5262 0.400806 0.200403 0.979714i \(-0.435775\pi\)
0.200403 + 0.979714i \(0.435775\pi\)
\(828\) −0.0535297 −0.00186029
\(829\) −17.7336 −0.615914 −0.307957 0.951400i \(-0.599645\pi\)
−0.307957 + 0.951400i \(0.599645\pi\)
\(830\) 1.47884 0.0513314
\(831\) −8.78169 −0.304634
\(832\) 19.0864 0.661702
\(833\) −6.36516 −0.220540
\(834\) 5.59213 0.193640
\(835\) 1.21107 0.0419109
\(836\) −3.68907 −0.127589
\(837\) 5.07126 0.175288
\(838\) 49.7798 1.71962
\(839\) −28.6447 −0.988924 −0.494462 0.869199i \(-0.664635\pi\)
−0.494462 + 0.869199i \(0.664635\pi\)
\(840\) 1.17502 0.0405422
\(841\) 82.5332 2.84597
\(842\) 28.6428 0.987095
\(843\) 4.51332 0.155447
\(844\) 2.33777 0.0804695
\(845\) 1.77138 0.0609374
\(846\) 33.7828 1.16148
\(847\) 13.6115 0.467695
\(848\) −2.32005 −0.0796707
\(849\) −9.40041 −0.322621
\(850\) 48.7781 1.67307
\(851\) −0.371266 −0.0127269
\(852\) −0.838601 −0.0287300
\(853\) 41.6536 1.42619 0.713097 0.701066i \(-0.247292\pi\)
0.713097 + 0.701066i \(0.247292\pi\)
\(854\) −21.3618 −0.730987
\(855\) −4.15922 −0.142242
\(856\) 43.8353 1.49826
\(857\) −9.05282 −0.309238 −0.154619 0.987974i \(-0.549415\pi\)
−0.154619 + 0.987974i \(0.549415\pi\)
\(858\) −9.15582 −0.312574
\(859\) 9.47579 0.323310 0.161655 0.986847i \(-0.448317\pi\)
0.161655 + 0.986847i \(0.448317\pi\)
\(860\) 0.233170 0.00795103
\(861\) −7.59924 −0.258981
\(862\) −7.75457 −0.264122
\(863\) −34.6314 −1.17887 −0.589434 0.807817i \(-0.700649\pi\)
−0.589434 + 0.807817i \(0.700649\pi\)
\(864\) −2.72799 −0.0928081
\(865\) 4.19633 0.142679
\(866\) 1.09315 0.0371468
\(867\) −25.1939 −0.855630
\(868\) −0.383708 −0.0130239
\(869\) 66.5985 2.25920
\(870\) −2.36538 −0.0801940
\(871\) 28.4048 0.962461
\(872\) 10.6597 0.360983
\(873\) −8.27007 −0.279899
\(874\) −1.82302 −0.0616647
\(875\) 5.53892 0.187250
\(876\) 0.454335 0.0153506
\(877\) 15.5441 0.524886 0.262443 0.964947i \(-0.415472\pi\)
0.262443 + 0.964947i \(0.415472\pi\)
\(878\) 25.0574 0.845648
\(879\) −10.4156 −0.351308
\(880\) −3.42260 −0.115376
\(881\) 52.4905 1.76845 0.884224 0.467063i \(-0.154688\pi\)
0.884224 + 0.467063i \(0.154688\pi\)
\(882\) −3.00034 −0.101027
\(883\) −32.8989 −1.10713 −0.553567 0.832804i \(-0.686734\pi\)
−0.553567 + 0.832804i \(0.686734\pi\)
\(884\) −1.98018 −0.0666008
\(885\) 1.93716 0.0651168
\(886\) 25.2236 0.847402
\(887\) −40.9458 −1.37483 −0.687413 0.726267i \(-0.741254\pi\)
−0.687413 + 0.726267i \(0.741254\pi\)
\(888\) −4.40085 −0.147683
\(889\) −37.2145 −1.24814
\(890\) −0.508916 −0.0170589
\(891\) −18.4261 −0.617298
\(892\) 0.275287 0.00921729
\(893\) −74.4533 −2.49148
\(894\) 15.0603 0.503693
\(895\) 5.09395 0.170272
\(896\) −25.1587 −0.840493
\(897\) 0.292794 0.00977611
\(898\) −4.05367 −0.135273
\(899\) 13.4810 0.449617
\(900\) −1.48791 −0.0495969
\(901\) 4.45822 0.148525
\(902\) 23.5731 0.784897
\(903\) −15.2932 −0.508925
\(904\) 19.0257 0.632786
\(905\) −2.72415 −0.0905539
\(906\) −19.6179 −0.651761
\(907\) −22.3371 −0.741692 −0.370846 0.928694i \(-0.620932\pi\)
−0.370846 + 0.928694i \(0.620932\pi\)
\(908\) −1.53913 −0.0510778
\(909\) 31.3604 1.04016
\(910\) 1.72849 0.0572990
\(911\) 15.9284 0.527732 0.263866 0.964559i \(-0.415002\pi\)
0.263866 + 0.964559i \(0.415002\pi\)
\(912\) −20.2911 −0.671906
\(913\) −19.4708 −0.644389
\(914\) −24.8596 −0.822283
\(915\) 1.03003 0.0340516
\(916\) −3.37356 −0.111466
\(917\) 23.6741 0.781788
\(918\) −39.1538 −1.29227
\(919\) −40.6296 −1.34025 −0.670124 0.742249i \(-0.733759\pi\)
−0.670124 + 0.742249i \(0.733759\pi\)
\(920\) 0.116562 0.00384294
\(921\) 20.8632 0.687465
\(922\) 22.6927 0.747343
\(923\) −21.5300 −0.708669
\(924\) −0.886423 −0.0291612
\(925\) −10.3197 −0.339309
\(926\) −5.49802 −0.180676
\(927\) 11.0748 0.363743
\(928\) −7.25187 −0.238054
\(929\) −38.1089 −1.25031 −0.625155 0.780500i \(-0.714964\pi\)
−0.625155 + 0.780500i \(0.714964\pi\)
\(930\) −0.285904 −0.00937516
\(931\) 6.61238 0.216712
\(932\) 1.32699 0.0434670
\(933\) 21.7527 0.712152
\(934\) 6.32190 0.206859
\(935\) 6.57689 0.215087
\(936\) −16.2905 −0.532471
\(937\) 20.9882 0.685653 0.342827 0.939399i \(-0.388616\pi\)
0.342827 + 0.939399i \(0.388616\pi\)
\(938\) −42.4958 −1.38754
\(939\) 9.90106 0.323109
\(940\) 0.272761 0.00889648
\(941\) 0.271913 0.00886412 0.00443206 0.999990i \(-0.498589\pi\)
0.00443206 + 0.999990i \(0.498589\pi\)
\(942\) 15.6303 0.509263
\(943\) −0.753843 −0.0245485
\(944\) −44.3588 −1.44376
\(945\) −2.21170 −0.0719467
\(946\) 47.4399 1.54241
\(947\) 18.9489 0.615756 0.307878 0.951426i \(-0.400381\pi\)
0.307878 + 0.951426i \(0.400381\pi\)
\(948\) −1.44648 −0.0469795
\(949\) 11.6645 0.378645
\(950\) −50.6726 −1.64404
\(951\) −9.39519 −0.304660
\(952\) 51.7043 1.67575
\(953\) −2.67357 −0.0866055 −0.0433027 0.999062i \(-0.513788\pi\)
−0.0433027 + 0.999062i \(0.513788\pi\)
\(954\) 2.10147 0.0680375
\(955\) 0.0375445 0.00121491
\(956\) −0.779772 −0.0252196
\(957\) 31.1432 1.00672
\(958\) 51.1063 1.65117
\(959\) 5.32327 0.171897
\(960\) 1.37685 0.0444378
\(961\) −29.3705 −0.947437
\(962\) −6.47378 −0.208723
\(963\) −37.2832 −1.20143
\(964\) −1.19751 −0.0385692
\(965\) 3.72054 0.119769
\(966\) −0.438042 −0.0140938
\(967\) 20.1196 0.647004 0.323502 0.946227i \(-0.395140\pi\)
0.323502 + 0.946227i \(0.395140\pi\)
\(968\) 16.0054 0.514433
\(969\) 38.9916 1.25259
\(970\) 1.03182 0.0331298
\(971\) 15.9577 0.512106 0.256053 0.966663i \(-0.417578\pi\)
0.256053 + 0.966663i \(0.417578\pi\)
\(972\) 1.84899 0.0593063
\(973\) 13.8998 0.445609
\(974\) −34.2882 −1.09866
\(975\) 8.13848 0.260640
\(976\) −23.5865 −0.754985
\(977\) 42.1759 1.34933 0.674663 0.738126i \(-0.264289\pi\)
0.674663 + 0.738126i \(0.264289\pi\)
\(978\) −11.8106 −0.377662
\(979\) 6.70051 0.214149
\(980\) −0.0242246 −0.000773826 0
\(981\) −9.06639 −0.289467
\(982\) 32.4852 1.03664
\(983\) −31.8772 −1.01673 −0.508363 0.861143i \(-0.669749\pi\)
−0.508363 + 0.861143i \(0.669749\pi\)
\(984\) −8.93577 −0.284862
\(985\) −2.21143 −0.0704619
\(986\) −104.083 −3.31469
\(987\) −17.8899 −0.569441
\(988\) 2.05709 0.0654449
\(989\) −1.51708 −0.0482404
\(990\) 3.10015 0.0985291
\(991\) 28.4135 0.902584 0.451292 0.892376i \(-0.350963\pi\)
0.451292 + 0.892376i \(0.350963\pi\)
\(992\) −0.876534 −0.0278300
\(993\) −6.15792 −0.195416
\(994\) 32.2105 1.02166
\(995\) −2.60459 −0.0825712
\(996\) 0.422894 0.0133999
\(997\) −38.9058 −1.23216 −0.616079 0.787684i \(-0.711280\pi\)
−0.616079 + 0.787684i \(0.711280\pi\)
\(998\) −37.2447 −1.17896
\(999\) 8.28355 0.262080
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 \(a_p\))