Properties

Label 8015.2.a.l.1.60
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.60
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} +O(q^{10})\) \(q+2.63990 q^{2} +2.23988 q^{3} +4.96906 q^{4} -1.00000 q^{5} +5.91306 q^{6} -1.00000 q^{7} +7.83803 q^{8} +2.01707 q^{9} -2.63990 q^{10} +2.72136 q^{11} +11.1301 q^{12} +1.32703 q^{13} -2.63990 q^{14} -2.23988 q^{15} +10.7535 q^{16} +5.16286 q^{17} +5.32485 q^{18} +4.00409 q^{19} -4.96906 q^{20} -2.23988 q^{21} +7.18411 q^{22} +3.31628 q^{23} +17.5562 q^{24} +1.00000 q^{25} +3.50322 q^{26} -2.20166 q^{27} -4.96906 q^{28} -3.92085 q^{29} -5.91306 q^{30} -6.66906 q^{31} +12.7120 q^{32} +6.09552 q^{33} +13.6294 q^{34} +1.00000 q^{35} +10.0229 q^{36} -11.3033 q^{37} +10.5704 q^{38} +2.97238 q^{39} -7.83803 q^{40} +3.99615 q^{41} -5.91306 q^{42} -5.70472 q^{43} +13.5226 q^{44} -2.01707 q^{45} +8.75465 q^{46} +0.309767 q^{47} +24.0865 q^{48} +1.00000 q^{49} +2.63990 q^{50} +11.5642 q^{51} +6.59408 q^{52} -0.760981 q^{53} -5.81215 q^{54} -2.72136 q^{55} -7.83803 q^{56} +8.96869 q^{57} -10.3506 q^{58} +3.18259 q^{59} -11.1301 q^{60} -11.5545 q^{61} -17.6056 q^{62} -2.01707 q^{63} +12.0515 q^{64} -1.32703 q^{65} +16.0915 q^{66} +12.6942 q^{67} +25.6546 q^{68} +7.42808 q^{69} +2.63990 q^{70} +8.73450 q^{71} +15.8098 q^{72} -1.07664 q^{73} -29.8396 q^{74} +2.23988 q^{75} +19.8966 q^{76} -2.72136 q^{77} +7.84679 q^{78} +7.12680 q^{79} -10.7535 q^{80} -10.9826 q^{81} +10.5494 q^{82} +17.4892 q^{83} -11.1301 q^{84} -5.16286 q^{85} -15.0599 q^{86} -8.78223 q^{87} +21.3301 q^{88} -0.252692 q^{89} -5.32485 q^{90} -1.32703 q^{91} +16.4788 q^{92} -14.9379 q^{93} +0.817754 q^{94} -4.00409 q^{95} +28.4734 q^{96} -5.71617 q^{97} +2.63990 q^{98} +5.48916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.63990 1.86669 0.933345 0.358981i \(-0.116876\pi\)
0.933345 + 0.358981i \(0.116876\pi\)
\(3\) 2.23988 1.29320 0.646598 0.762831i \(-0.276191\pi\)
0.646598 + 0.762831i \(0.276191\pi\)
\(4\) 4.96906 2.48453
\(5\) −1.00000 −0.447214
\(6\) 5.91306 2.41400
\(7\) −1.00000 −0.377964
\(8\) 7.83803 2.77116
\(9\) 2.01707 0.672355
\(10\) −2.63990 −0.834809
\(11\) 2.72136 0.820520 0.410260 0.911969i \(-0.365438\pi\)
0.410260 + 0.911969i \(0.365438\pi\)
\(12\) 11.1301 3.21299
\(13\) 1.32703 0.368051 0.184026 0.982921i \(-0.441087\pi\)
0.184026 + 0.982921i \(0.441087\pi\)
\(14\) −2.63990 −0.705543
\(15\) −2.23988 −0.578335
\(16\) 10.7535 2.68837
\(17\) 5.16286 1.25218 0.626088 0.779752i \(-0.284655\pi\)
0.626088 + 0.779752i \(0.284655\pi\)
\(18\) 5.32485 1.25508
\(19\) 4.00409 0.918602 0.459301 0.888281i \(-0.348100\pi\)
0.459301 + 0.888281i \(0.348100\pi\)
\(20\) −4.96906 −1.11112
\(21\) −2.23988 −0.488782
\(22\) 7.18411 1.53166
\(23\) 3.31628 0.691493 0.345746 0.938328i \(-0.387626\pi\)
0.345746 + 0.938328i \(0.387626\pi\)
\(24\) 17.5562 3.58365
\(25\) 1.00000 0.200000
\(26\) 3.50322 0.687037
\(27\) −2.20166 −0.423709
\(28\) −4.96906 −0.939065
\(29\) −3.92085 −0.728083 −0.364041 0.931383i \(-0.618603\pi\)
−0.364041 + 0.931383i \(0.618603\pi\)
\(30\) −5.91306 −1.07957
\(31\) −6.66906 −1.19780 −0.598899 0.800824i \(-0.704395\pi\)
−0.598899 + 0.800824i \(0.704395\pi\)
\(32\) 12.7120 2.24719
\(33\) 6.09552 1.06109
\(34\) 13.6294 2.33743
\(35\) 1.00000 0.169031
\(36\) 10.0229 1.67049
\(37\) −11.3033 −1.85826 −0.929128 0.369759i \(-0.879440\pi\)
−0.929128 + 0.369759i \(0.879440\pi\)
\(38\) 10.5704 1.71475
\(39\) 2.97238 0.475962
\(40\) −7.83803 −1.23930
\(41\) 3.99615 0.624093 0.312047 0.950067i \(-0.398985\pi\)
0.312047 + 0.950067i \(0.398985\pi\)
\(42\) −5.91306 −0.912405
\(43\) −5.70472 −0.869961 −0.434981 0.900440i \(-0.643245\pi\)
−0.434981 + 0.900440i \(0.643245\pi\)
\(44\) 13.5226 2.03861
\(45\) −2.01707 −0.300686
\(46\) 8.75465 1.29080
\(47\) 0.309767 0.0451842 0.0225921 0.999745i \(-0.492808\pi\)
0.0225921 + 0.999745i \(0.492808\pi\)
\(48\) 24.0865 3.47658
\(49\) 1.00000 0.142857
\(50\) 2.63990 0.373338
\(51\) 11.5642 1.61931
\(52\) 6.59408 0.914435
\(53\) −0.760981 −0.104529 −0.0522644 0.998633i \(-0.516644\pi\)
−0.0522644 + 0.998633i \(0.516644\pi\)
\(54\) −5.81215 −0.790933
\(55\) −2.72136 −0.366948
\(56\) −7.83803 −1.04740
\(57\) 8.96869 1.18793
\(58\) −10.3506 −1.35910
\(59\) 3.18259 0.414338 0.207169 0.978305i \(-0.433575\pi\)
0.207169 + 0.978305i \(0.433575\pi\)
\(60\) −11.1301 −1.43689
\(61\) −11.5545 −1.47941 −0.739703 0.672933i \(-0.765034\pi\)
−0.739703 + 0.672933i \(0.765034\pi\)
\(62\) −17.6056 −2.23592
\(63\) −2.01707 −0.254126
\(64\) 12.0515 1.50643
\(65\) −1.32703 −0.164597
\(66\) 16.0915 1.98073
\(67\) 12.6942 1.55085 0.775424 0.631440i \(-0.217536\pi\)
0.775424 + 0.631440i \(0.217536\pi\)
\(68\) 25.6546 3.11107
\(69\) 7.42808 0.894236
\(70\) 2.63990 0.315528
\(71\) 8.73450 1.03659 0.518297 0.855201i \(-0.326566\pi\)
0.518297 + 0.855201i \(0.326566\pi\)
\(72\) 15.8098 1.86320
\(73\) −1.07664 −0.126011 −0.0630055 0.998013i \(-0.520069\pi\)
−0.0630055 + 0.998013i \(0.520069\pi\)
\(74\) −29.8396 −3.46879
\(75\) 2.23988 0.258639
\(76\) 19.8966 2.28230
\(77\) −2.72136 −0.310128
\(78\) 7.84679 0.888474
\(79\) 7.12680 0.801828 0.400914 0.916116i \(-0.368693\pi\)
0.400914 + 0.916116i \(0.368693\pi\)
\(80\) −10.7535 −1.20227
\(81\) −10.9826 −1.22029
\(82\) 10.5494 1.16499
\(83\) 17.4892 1.91969 0.959847 0.280523i \(-0.0905080\pi\)
0.959847 + 0.280523i \(0.0905080\pi\)
\(84\) −11.1301 −1.21439
\(85\) −5.16286 −0.559990
\(86\) −15.0599 −1.62395
\(87\) −8.78223 −0.941553
\(88\) 21.3301 2.27379
\(89\) −0.252692 −0.0267853 −0.0133927 0.999910i \(-0.504263\pi\)
−0.0133927 + 0.999910i \(0.504263\pi\)
\(90\) −5.32485 −0.561288
\(91\) −1.32703 −0.139110
\(92\) 16.4788 1.71804
\(93\) −14.9379 −1.54899
\(94\) 0.817754 0.0843448
\(95\) −4.00409 −0.410811
\(96\) 28.4734 2.90605
\(97\) −5.71617 −0.580389 −0.290194 0.956968i \(-0.593720\pi\)
−0.290194 + 0.956968i \(0.593720\pi\)
\(98\) 2.63990 0.266670
\(99\) 5.48916 0.551681
\(100\) 4.96906 0.496906
\(101\) 1.25145 0.124524 0.0622622 0.998060i \(-0.480169\pi\)
0.0622622 + 0.998060i \(0.480169\pi\)
\(102\) 30.5283 3.02275
\(103\) −8.30099 −0.817921 −0.408961 0.912552i \(-0.634109\pi\)
−0.408961 + 0.912552i \(0.634109\pi\)
\(104\) 10.4013 1.01993
\(105\) 2.23988 0.218590
\(106\) −2.00891 −0.195123
\(107\) 6.74619 0.652179 0.326089 0.945339i \(-0.394269\pi\)
0.326089 + 0.945339i \(0.394269\pi\)
\(108\) −10.9402 −1.05272
\(109\) 3.69105 0.353539 0.176769 0.984252i \(-0.443435\pi\)
0.176769 + 0.984252i \(0.443435\pi\)
\(110\) −7.18411 −0.684978
\(111\) −25.3181 −2.40309
\(112\) −10.7535 −1.01611
\(113\) −5.11147 −0.480847 −0.240423 0.970668i \(-0.577286\pi\)
−0.240423 + 0.970668i \(0.577286\pi\)
\(114\) 23.6764 2.21750
\(115\) −3.31628 −0.309245
\(116\) −19.4829 −1.80894
\(117\) 2.67670 0.247461
\(118\) 8.40171 0.773440
\(119\) −5.16286 −0.473278
\(120\) −17.5562 −1.60266
\(121\) −3.59421 −0.326746
\(122\) −30.5028 −2.76159
\(123\) 8.95089 0.807075
\(124\) −33.1390 −2.97597
\(125\) −1.00000 −0.0894427
\(126\) −5.32485 −0.474375
\(127\) 4.33688 0.384836 0.192418 0.981313i \(-0.438367\pi\)
0.192418 + 0.981313i \(0.438367\pi\)
\(128\) 6.39066 0.564860
\(129\) −12.7779 −1.12503
\(130\) −3.50322 −0.307252
\(131\) 6.76692 0.591228 0.295614 0.955307i \(-0.404476\pi\)
0.295614 + 0.955307i \(0.404476\pi\)
\(132\) 30.2890 2.63632
\(133\) −4.00409 −0.347199
\(134\) 33.5115 2.89495
\(135\) 2.20166 0.189488
\(136\) 40.4666 3.46998
\(137\) 0.0291688 0.00249206 0.00124603 0.999999i \(-0.499603\pi\)
0.00124603 + 0.999999i \(0.499603\pi\)
\(138\) 19.6094 1.66926
\(139\) 16.5953 1.40760 0.703798 0.710401i \(-0.251486\pi\)
0.703798 + 0.710401i \(0.251486\pi\)
\(140\) 4.96906 0.419963
\(141\) 0.693841 0.0584320
\(142\) 23.0582 1.93500
\(143\) 3.61132 0.301993
\(144\) 21.6905 1.80754
\(145\) 3.92085 0.325608
\(146\) −2.84222 −0.235223
\(147\) 2.23988 0.184742
\(148\) −56.1669 −4.61689
\(149\) −14.2460 −1.16708 −0.583540 0.812085i \(-0.698333\pi\)
−0.583540 + 0.812085i \(0.698333\pi\)
\(150\) 5.91306 0.482799
\(151\) −16.7246 −1.36103 −0.680515 0.732734i \(-0.738244\pi\)
−0.680515 + 0.732734i \(0.738244\pi\)
\(152\) 31.3842 2.54559
\(153\) 10.4138 0.841908
\(154\) −7.18411 −0.578912
\(155\) 6.66906 0.535672
\(156\) 14.7700 1.18254
\(157\) 1.44668 0.115458 0.0577288 0.998332i \(-0.481614\pi\)
0.0577288 + 0.998332i \(0.481614\pi\)
\(158\) 18.8140 1.49676
\(159\) −1.70451 −0.135176
\(160\) −12.7120 −1.00497
\(161\) −3.31628 −0.261360
\(162\) −28.9931 −2.27791
\(163\) −13.2714 −1.03950 −0.519748 0.854319i \(-0.673974\pi\)
−0.519748 + 0.854319i \(0.673974\pi\)
\(164\) 19.8571 1.55058
\(165\) −6.09552 −0.474535
\(166\) 46.1698 3.58347
\(167\) 8.80456 0.681318 0.340659 0.940187i \(-0.389350\pi\)
0.340659 + 0.940187i \(0.389350\pi\)
\(168\) −17.5562 −1.35449
\(169\) −11.2390 −0.864538
\(170\) −13.6294 −1.04533
\(171\) 8.07652 0.617627
\(172\) −28.3471 −2.16145
\(173\) −0.574156 −0.0436523 −0.0218261 0.999762i \(-0.506948\pi\)
−0.0218261 + 0.999762i \(0.506948\pi\)
\(174\) −23.1842 −1.75759
\(175\) −1.00000 −0.0755929
\(176\) 29.2640 2.20586
\(177\) 7.12862 0.535820
\(178\) −0.667082 −0.0499999
\(179\) −7.41062 −0.553896 −0.276948 0.960885i \(-0.589323\pi\)
−0.276948 + 0.960885i \(0.589323\pi\)
\(180\) −10.0229 −0.747065
\(181\) −3.65740 −0.271852 −0.135926 0.990719i \(-0.543401\pi\)
−0.135926 + 0.990719i \(0.543401\pi\)
\(182\) −3.50322 −0.259676
\(183\) −25.8808 −1.91316
\(184\) 25.9931 1.91624
\(185\) 11.3033 0.831037
\(186\) −39.4345 −2.89148
\(187\) 14.0500 1.02744
\(188\) 1.53925 0.112262
\(189\) 2.20166 0.160147
\(190\) −10.5704 −0.766857
\(191\) 8.12688 0.588041 0.294020 0.955799i \(-0.405007\pi\)
0.294020 + 0.955799i \(0.405007\pi\)
\(192\) 26.9939 1.94812
\(193\) −25.7690 −1.85489 −0.927446 0.373956i \(-0.878001\pi\)
−0.927446 + 0.373956i \(0.878001\pi\)
\(194\) −15.0901 −1.08341
\(195\) −2.97238 −0.212857
\(196\) 4.96906 0.354933
\(197\) 6.30826 0.449445 0.224722 0.974423i \(-0.427852\pi\)
0.224722 + 0.974423i \(0.427852\pi\)
\(198\) 14.4908 1.02982
\(199\) −11.7117 −0.830222 −0.415111 0.909771i \(-0.636257\pi\)
−0.415111 + 0.909771i \(0.636257\pi\)
\(200\) 7.83803 0.554232
\(201\) 28.4336 2.00555
\(202\) 3.30371 0.232448
\(203\) 3.92085 0.275189
\(204\) 57.4632 4.02323
\(205\) −3.99615 −0.279103
\(206\) −21.9138 −1.52681
\(207\) 6.68916 0.464929
\(208\) 14.2701 0.989457
\(209\) 10.8966 0.753732
\(210\) 5.91306 0.408040
\(211\) 1.19240 0.0820879 0.0410440 0.999157i \(-0.486932\pi\)
0.0410440 + 0.999157i \(0.486932\pi\)
\(212\) −3.78136 −0.259705
\(213\) 19.5642 1.34052
\(214\) 17.8093 1.21742
\(215\) 5.70472 0.389059
\(216\) −17.2566 −1.17417
\(217\) 6.66906 0.452725
\(218\) 9.74400 0.659947
\(219\) −2.41154 −0.162957
\(220\) −13.5226 −0.911694
\(221\) 6.85125 0.460865
\(222\) −66.8372 −4.48582
\(223\) −12.0722 −0.808412 −0.404206 0.914668i \(-0.632452\pi\)
−0.404206 + 0.914668i \(0.632452\pi\)
\(224\) −12.7120 −0.849357
\(225\) 2.01707 0.134471
\(226\) −13.4938 −0.897592
\(227\) −10.8524 −0.720302 −0.360151 0.932894i \(-0.617275\pi\)
−0.360151 + 0.932894i \(0.617275\pi\)
\(228\) 44.5660 2.95146
\(229\) 1.00000 0.0660819
\(230\) −8.75465 −0.577265
\(231\) −6.09552 −0.401056
\(232\) −30.7317 −2.01763
\(233\) −5.87257 −0.384725 −0.192362 0.981324i \(-0.561615\pi\)
−0.192362 + 0.981324i \(0.561615\pi\)
\(234\) 7.06622 0.461933
\(235\) −0.309767 −0.0202070
\(236\) 15.8145 1.02944
\(237\) 15.9632 1.03692
\(238\) −13.6294 −0.883464
\(239\) 9.94340 0.643185 0.321593 0.946878i \(-0.395782\pi\)
0.321593 + 0.946878i \(0.395782\pi\)
\(240\) −24.0865 −1.55478
\(241\) 2.73831 0.176390 0.0881951 0.996103i \(-0.471890\pi\)
0.0881951 + 0.996103i \(0.471890\pi\)
\(242\) −9.48835 −0.609934
\(243\) −17.9948 −1.15437
\(244\) −57.4152 −3.67563
\(245\) −1.00000 −0.0638877
\(246\) 23.6294 1.50656
\(247\) 5.31354 0.338093
\(248\) −52.2723 −3.31929
\(249\) 39.1738 2.48254
\(250\) −2.63990 −0.166962
\(251\) −7.79993 −0.492327 −0.246164 0.969228i \(-0.579170\pi\)
−0.246164 + 0.969228i \(0.579170\pi\)
\(252\) −10.0229 −0.631385
\(253\) 9.02479 0.567384
\(254\) 11.4489 0.718370
\(255\) −11.5642 −0.724177
\(256\) −7.23226 −0.452016
\(257\) 13.3254 0.831215 0.415607 0.909544i \(-0.363569\pi\)
0.415607 + 0.909544i \(0.363569\pi\)
\(258\) −33.7323 −2.10008
\(259\) 11.3033 0.702354
\(260\) −6.59408 −0.408948
\(261\) −7.90860 −0.489530
\(262\) 17.8640 1.10364
\(263\) 0.640300 0.0394826 0.0197413 0.999805i \(-0.493716\pi\)
0.0197413 + 0.999805i \(0.493716\pi\)
\(264\) 47.7768 2.94046
\(265\) 0.760981 0.0467467
\(266\) −10.5704 −0.648113
\(267\) −0.566001 −0.0346387
\(268\) 63.0785 3.85313
\(269\) 15.4945 0.944715 0.472357 0.881407i \(-0.343403\pi\)
0.472357 + 0.881407i \(0.343403\pi\)
\(270\) 5.81215 0.353716
\(271\) 14.7223 0.894316 0.447158 0.894455i \(-0.352436\pi\)
0.447158 + 0.894455i \(0.352436\pi\)
\(272\) 55.5186 3.36631
\(273\) −2.97238 −0.179897
\(274\) 0.0770027 0.00465190
\(275\) 2.72136 0.164104
\(276\) 36.9106 2.22176
\(277\) −4.23530 −0.254475 −0.127237 0.991872i \(-0.540611\pi\)
−0.127237 + 0.991872i \(0.540611\pi\)
\(278\) 43.8099 2.62754
\(279\) −13.4519 −0.805346
\(280\) 7.83803 0.468412
\(281\) −1.75422 −0.104648 −0.0523241 0.998630i \(-0.516663\pi\)
−0.0523241 + 0.998630i \(0.516663\pi\)
\(282\) 1.83167 0.109074
\(283\) −2.72124 −0.161761 −0.0808806 0.996724i \(-0.525773\pi\)
−0.0808806 + 0.996724i \(0.525773\pi\)
\(284\) 43.4023 2.57545
\(285\) −8.96869 −0.531259
\(286\) 9.53351 0.563728
\(287\) −3.99615 −0.235885
\(288\) 25.6410 1.51091
\(289\) 9.65509 0.567947
\(290\) 10.3506 0.607810
\(291\) −12.8035 −0.750556
\(292\) −5.34988 −0.313078
\(293\) 20.0547 1.17161 0.585803 0.810453i \(-0.300779\pi\)
0.585803 + 0.810453i \(0.300779\pi\)
\(294\) 5.91306 0.344857
\(295\) −3.18259 −0.185298
\(296\) −88.5958 −5.14952
\(297\) −5.99149 −0.347662
\(298\) −37.6080 −2.17858
\(299\) 4.40080 0.254505
\(300\) 11.1301 0.642597
\(301\) 5.70472 0.328814
\(302\) −44.1513 −2.54062
\(303\) 2.80311 0.161034
\(304\) 43.0579 2.46954
\(305\) 11.5545 0.661611
\(306\) 27.4914 1.57158
\(307\) −6.17627 −0.352498 −0.176249 0.984346i \(-0.556396\pi\)
−0.176249 + 0.984346i \(0.556396\pi\)
\(308\) −13.5226 −0.770522
\(309\) −18.5932 −1.05773
\(310\) 17.6056 0.999933
\(311\) −13.0898 −0.742254 −0.371127 0.928582i \(-0.621029\pi\)
−0.371127 + 0.928582i \(0.621029\pi\)
\(312\) 23.2976 1.31897
\(313\) −9.21662 −0.520954 −0.260477 0.965480i \(-0.583880\pi\)
−0.260477 + 0.965480i \(0.583880\pi\)
\(314\) 3.81909 0.215524
\(315\) 2.01707 0.113649
\(316\) 35.4135 1.99217
\(317\) −31.8480 −1.78876 −0.894382 0.447304i \(-0.852384\pi\)
−0.894382 + 0.447304i \(0.852384\pi\)
\(318\) −4.49973 −0.252332
\(319\) −10.6700 −0.597407
\(320\) −12.0515 −0.673698
\(321\) 15.1107 0.843395
\(322\) −8.75465 −0.487878
\(323\) 20.6726 1.15025
\(324\) −54.5735 −3.03186
\(325\) 1.32703 0.0736102
\(326\) −35.0352 −1.94042
\(327\) 8.26752 0.457195
\(328\) 31.3219 1.72946
\(329\) −0.309767 −0.0170780
\(330\) −16.0915 −0.885810
\(331\) 6.01438 0.330580 0.165290 0.986245i \(-0.447144\pi\)
0.165290 + 0.986245i \(0.447144\pi\)
\(332\) 86.9052 4.76954
\(333\) −22.7995 −1.24941
\(334\) 23.2432 1.27181
\(335\) −12.6942 −0.693561
\(336\) −24.0865 −1.31403
\(337\) −27.7321 −1.51067 −0.755333 0.655342i \(-0.772525\pi\)
−0.755333 + 0.655342i \(0.772525\pi\)
\(338\) −29.6698 −1.61383
\(339\) −11.4491 −0.621829
\(340\) −25.6546 −1.39131
\(341\) −18.1489 −0.982818
\(342\) 21.3212 1.15292
\(343\) −1.00000 −0.0539949
\(344\) −44.7137 −2.41080
\(345\) −7.42808 −0.399914
\(346\) −1.51571 −0.0814853
\(347\) 10.9230 0.586378 0.293189 0.956054i \(-0.405283\pi\)
0.293189 + 0.956054i \(0.405283\pi\)
\(348\) −43.6394 −2.33932
\(349\) 17.8963 0.957965 0.478983 0.877824i \(-0.341006\pi\)
0.478983 + 0.877824i \(0.341006\pi\)
\(350\) −2.63990 −0.141109
\(351\) −2.92166 −0.155947
\(352\) 34.5939 1.84386
\(353\) −5.67409 −0.302001 −0.151001 0.988534i \(-0.548250\pi\)
−0.151001 + 0.988534i \(0.548250\pi\)
\(354\) 18.8188 1.00021
\(355\) −8.73450 −0.463579
\(356\) −1.25564 −0.0665490
\(357\) −11.5642 −0.612042
\(358\) −19.5633 −1.03395
\(359\) −34.0656 −1.79791 −0.898957 0.438036i \(-0.855674\pi\)
−0.898957 + 0.438036i \(0.855674\pi\)
\(360\) −15.8098 −0.833250
\(361\) −2.96723 −0.156170
\(362\) −9.65515 −0.507464
\(363\) −8.05060 −0.422547
\(364\) −6.59408 −0.345624
\(365\) 1.07664 0.0563538
\(366\) −68.3226 −3.57128
\(367\) −18.3678 −0.958791 −0.479395 0.877599i \(-0.659144\pi\)
−0.479395 + 0.877599i \(0.659144\pi\)
\(368\) 35.6616 1.85899
\(369\) 8.06049 0.419612
\(370\) 29.8396 1.55129
\(371\) 0.760981 0.0395082
\(372\) −74.2274 −3.84851
\(373\) −14.4234 −0.746814 −0.373407 0.927668i \(-0.621811\pi\)
−0.373407 + 0.927668i \(0.621811\pi\)
\(374\) 37.0905 1.91791
\(375\) −2.23988 −0.115667
\(376\) 2.42796 0.125213
\(377\) −5.20307 −0.267972
\(378\) 5.81215 0.298945
\(379\) 12.1242 0.622777 0.311389 0.950283i \(-0.399206\pi\)
0.311389 + 0.950283i \(0.399206\pi\)
\(380\) −19.8966 −1.02067
\(381\) 9.71410 0.497669
\(382\) 21.4542 1.09769
\(383\) 31.6405 1.61675 0.808377 0.588665i \(-0.200346\pi\)
0.808377 + 0.588665i \(0.200346\pi\)
\(384\) 14.3143 0.730474
\(385\) 2.72136 0.138693
\(386\) −68.0275 −3.46251
\(387\) −11.5068 −0.584923
\(388\) −28.4040 −1.44199
\(389\) −1.22977 −0.0623518 −0.0311759 0.999514i \(-0.509925\pi\)
−0.0311759 + 0.999514i \(0.509925\pi\)
\(390\) −7.84679 −0.397338
\(391\) 17.1215 0.865871
\(392\) 7.83803 0.395880
\(393\) 15.1571 0.764574
\(394\) 16.6532 0.838974
\(395\) −7.12680 −0.358588
\(396\) 27.2760 1.37067
\(397\) 0.302888 0.0152015 0.00760075 0.999971i \(-0.497581\pi\)
0.00760075 + 0.999971i \(0.497581\pi\)
\(398\) −30.9178 −1.54977
\(399\) −8.96869 −0.448996
\(400\) 10.7535 0.537673
\(401\) −5.36444 −0.267887 −0.133944 0.990989i \(-0.542764\pi\)
−0.133944 + 0.990989i \(0.542764\pi\)
\(402\) 75.0618 3.74374
\(403\) −8.85003 −0.440851
\(404\) 6.21856 0.309385
\(405\) 10.9826 0.545732
\(406\) 10.3506 0.513693
\(407\) −30.7604 −1.52474
\(408\) 90.6404 4.48737
\(409\) 22.8874 1.13171 0.565856 0.824504i \(-0.308546\pi\)
0.565856 + 0.824504i \(0.308546\pi\)
\(410\) −10.5494 −0.520999
\(411\) 0.0653347 0.00322272
\(412\) −41.2482 −2.03215
\(413\) −3.18259 −0.156605
\(414\) 17.6587 0.867878
\(415\) −17.4892 −0.858513
\(416\) 16.8692 0.827080
\(417\) 37.1715 1.82030
\(418\) 28.7658 1.40698
\(419\) −4.65847 −0.227581 −0.113790 0.993505i \(-0.536299\pi\)
−0.113790 + 0.993505i \(0.536299\pi\)
\(420\) 11.1301 0.543094
\(421\) −32.3430 −1.57630 −0.788151 0.615482i \(-0.788961\pi\)
−0.788151 + 0.615482i \(0.788961\pi\)
\(422\) 3.14780 0.153233
\(423\) 0.624821 0.0303798
\(424\) −5.96459 −0.289666
\(425\) 5.16286 0.250435
\(426\) 51.6476 2.50233
\(427\) 11.5545 0.559163
\(428\) 33.5222 1.62036
\(429\) 8.08892 0.390537
\(430\) 15.0599 0.726252
\(431\) −27.6088 −1.32987 −0.664936 0.746901i \(-0.731541\pi\)
−0.664936 + 0.746901i \(0.731541\pi\)
\(432\) −23.6754 −1.13908
\(433\) 32.3761 1.55589 0.777947 0.628330i \(-0.216261\pi\)
0.777947 + 0.628330i \(0.216261\pi\)
\(434\) 17.6056 0.845098
\(435\) 8.78223 0.421075
\(436\) 18.3411 0.878378
\(437\) 13.2787 0.635207
\(438\) −6.36622 −0.304190
\(439\) −26.4892 −1.26426 −0.632131 0.774861i \(-0.717820\pi\)
−0.632131 + 0.774861i \(0.717820\pi\)
\(440\) −21.3301 −1.01687
\(441\) 2.01707 0.0960507
\(442\) 18.0866 0.860292
\(443\) 7.19720 0.341949 0.170975 0.985275i \(-0.445308\pi\)
0.170975 + 0.985275i \(0.445308\pi\)
\(444\) −125.807 −5.97055
\(445\) 0.252692 0.0119788
\(446\) −31.8693 −1.50905
\(447\) −31.9094 −1.50926
\(448\) −12.0515 −0.569379
\(449\) −5.04917 −0.238285 −0.119143 0.992877i \(-0.538015\pi\)
−0.119143 + 0.992877i \(0.538015\pi\)
\(450\) 5.32485 0.251016
\(451\) 10.8749 0.512081
\(452\) −25.3992 −1.19468
\(453\) −37.4612 −1.76008
\(454\) −28.6494 −1.34458
\(455\) 1.32703 0.0622120
\(456\) 70.2969 3.29195
\(457\) −4.26410 −0.199466 −0.0997332 0.995014i \(-0.531799\pi\)
−0.0997332 + 0.995014i \(0.531799\pi\)
\(458\) 2.63990 0.123354
\(459\) −11.3668 −0.530558
\(460\) −16.4788 −0.768329
\(461\) −37.7111 −1.75638 −0.878191 0.478309i \(-0.841250\pi\)
−0.878191 + 0.478309i \(0.841250\pi\)
\(462\) −16.0915 −0.748646
\(463\) −14.1039 −0.655462 −0.327731 0.944771i \(-0.606284\pi\)
−0.327731 + 0.944771i \(0.606284\pi\)
\(464\) −42.1627 −1.95735
\(465\) 14.9379 0.692729
\(466\) −15.5030 −0.718162
\(467\) −23.9737 −1.10937 −0.554686 0.832060i \(-0.687162\pi\)
−0.554686 + 0.832060i \(0.687162\pi\)
\(468\) 13.3007 0.614825
\(469\) −12.6942 −0.586166
\(470\) −0.817754 −0.0377202
\(471\) 3.24039 0.149309
\(472\) 24.9452 1.14820
\(473\) −15.5246 −0.713821
\(474\) 42.1412 1.93561
\(475\) 4.00409 0.183720
\(476\) −25.6546 −1.17588
\(477\) −1.53495 −0.0702805
\(478\) 26.2496 1.20063
\(479\) −9.96924 −0.455506 −0.227753 0.973719i \(-0.573138\pi\)
−0.227753 + 0.973719i \(0.573138\pi\)
\(480\) −28.4734 −1.29963
\(481\) −14.9998 −0.683933
\(482\) 7.22887 0.329266
\(483\) −7.42808 −0.337989
\(484\) −17.8599 −0.811812
\(485\) 5.71617 0.259558
\(486\) −47.5046 −2.15485
\(487\) 13.2821 0.601870 0.300935 0.953645i \(-0.402701\pi\)
0.300935 + 0.953645i \(0.402701\pi\)
\(488\) −90.5648 −4.09968
\(489\) −29.7264 −1.34427
\(490\) −2.63990 −0.119258
\(491\) 37.0532 1.67219 0.836094 0.548586i \(-0.184834\pi\)
0.836094 + 0.548586i \(0.184834\pi\)
\(492\) 44.4776 2.00520
\(493\) −20.2428 −0.911688
\(494\) 14.0272 0.631114
\(495\) −5.48916 −0.246719
\(496\) −71.7155 −3.22012
\(497\) −8.73450 −0.391796
\(498\) 103.415 4.63413
\(499\) −5.06473 −0.226728 −0.113364 0.993554i \(-0.536163\pi\)
−0.113364 + 0.993554i \(0.536163\pi\)
\(500\) −4.96906 −0.222223
\(501\) 19.7212 0.881077
\(502\) −20.5910 −0.919023
\(503\) 27.8765 1.24295 0.621476 0.783433i \(-0.286533\pi\)
0.621476 + 0.783433i \(0.286533\pi\)
\(504\) −15.8098 −0.704225
\(505\) −1.25145 −0.0556890
\(506\) 23.8245 1.05913
\(507\) −25.1740 −1.11802
\(508\) 21.5503 0.956138
\(509\) −2.66097 −0.117945 −0.0589727 0.998260i \(-0.518782\pi\)
−0.0589727 + 0.998260i \(0.518782\pi\)
\(510\) −30.5283 −1.35181
\(511\) 1.07664 0.0476277
\(512\) −31.8738 −1.40863
\(513\) −8.81564 −0.389220
\(514\) 35.1777 1.55162
\(515\) 8.30099 0.365785
\(516\) −63.4941 −2.79517
\(517\) 0.842987 0.0370745
\(518\) 29.8396 1.31108
\(519\) −1.28604 −0.0564509
\(520\) −10.4013 −0.456126
\(521\) 1.70664 0.0747691 0.0373845 0.999301i \(-0.488097\pi\)
0.0373845 + 0.999301i \(0.488097\pi\)
\(522\) −20.8779 −0.913801
\(523\) 12.1750 0.532375 0.266187 0.963921i \(-0.414236\pi\)
0.266187 + 0.963921i \(0.414236\pi\)
\(524\) 33.6252 1.46893
\(525\) −2.23988 −0.0977564
\(526\) 1.69033 0.0737017
\(527\) −34.4314 −1.49986
\(528\) 65.5480 2.85261
\(529\) −12.0023 −0.521838
\(530\) 2.00891 0.0872616
\(531\) 6.41949 0.278582
\(532\) −19.8966 −0.862627
\(533\) 5.30300 0.229698
\(534\) −1.49418 −0.0646597
\(535\) −6.74619 −0.291663
\(536\) 99.4978 4.29765
\(537\) −16.5989 −0.716295
\(538\) 40.9038 1.76349
\(539\) 2.72136 0.117217
\(540\) 10.9402 0.470790
\(541\) 21.2246 0.912515 0.456258 0.889848i \(-0.349190\pi\)
0.456258 + 0.889848i \(0.349190\pi\)
\(542\) 38.8654 1.66941
\(543\) −8.19213 −0.351558
\(544\) 65.6303 2.81388
\(545\) −3.69105 −0.158107
\(546\) −7.84679 −0.335812
\(547\) 19.7095 0.842716 0.421358 0.906894i \(-0.361554\pi\)
0.421358 + 0.906894i \(0.361554\pi\)
\(548\) 0.144942 0.00619160
\(549\) −23.3063 −0.994687
\(550\) 7.18411 0.306331
\(551\) −15.6994 −0.668818
\(552\) 58.2215 2.47807
\(553\) −7.12680 −0.303062
\(554\) −11.1808 −0.475025
\(555\) 25.3181 1.07469
\(556\) 82.4631 3.49722
\(557\) −36.6572 −1.55322 −0.776608 0.629984i \(-0.783062\pi\)
−0.776608 + 0.629984i \(0.783062\pi\)
\(558\) −35.5117 −1.50333
\(559\) −7.57032 −0.320190
\(560\) 10.7535 0.454417
\(561\) 31.4703 1.32868
\(562\) −4.63098 −0.195346
\(563\) −8.96692 −0.377911 −0.188955 0.981986i \(-0.560510\pi\)
−0.188955 + 0.981986i \(0.560510\pi\)
\(564\) 3.44774 0.145176
\(565\) 5.11147 0.215041
\(566\) −7.18381 −0.301958
\(567\) 10.9826 0.461228
\(568\) 68.4612 2.87257
\(569\) 13.0873 0.548647 0.274324 0.961637i \(-0.411546\pi\)
0.274324 + 0.961637i \(0.411546\pi\)
\(570\) −23.6764 −0.991697
\(571\) −27.0306 −1.13120 −0.565598 0.824681i \(-0.691355\pi\)
−0.565598 + 0.824681i \(0.691355\pi\)
\(572\) 17.9449 0.750312
\(573\) 18.2033 0.760452
\(574\) −10.5494 −0.440324
\(575\) 3.31628 0.138299
\(576\) 24.3086 1.01286
\(577\) 18.3851 0.765384 0.382692 0.923876i \(-0.374997\pi\)
0.382692 + 0.923876i \(0.374997\pi\)
\(578\) 25.4885 1.06018
\(579\) −57.7195 −2.39874
\(580\) 19.4829 0.808985
\(581\) −17.4892 −0.725576
\(582\) −33.8000 −1.40106
\(583\) −2.07090 −0.0857680
\(584\) −8.43872 −0.349197
\(585\) −2.67670 −0.110668
\(586\) 52.9423 2.18703
\(587\) 23.9544 0.988702 0.494351 0.869262i \(-0.335406\pi\)
0.494351 + 0.869262i \(0.335406\pi\)
\(588\) 11.1301 0.458998
\(589\) −26.7035 −1.10030
\(590\) −8.40171 −0.345893
\(591\) 14.1298 0.581220
\(592\) −121.550 −4.99567
\(593\) −5.42859 −0.222926 −0.111463 0.993769i \(-0.535554\pi\)
−0.111463 + 0.993769i \(0.535554\pi\)
\(594\) −15.8169 −0.648977
\(595\) 5.16286 0.211657
\(596\) −70.7894 −2.89965
\(597\) −26.2329 −1.07364
\(598\) 11.6177 0.475082
\(599\) 8.33216 0.340443 0.170221 0.985406i \(-0.445552\pi\)
0.170221 + 0.985406i \(0.445552\pi\)
\(600\) 17.5562 0.716731
\(601\) 7.66900 0.312825 0.156412 0.987692i \(-0.450007\pi\)
0.156412 + 0.987692i \(0.450007\pi\)
\(602\) 15.0599 0.613795
\(603\) 25.6051 1.04272
\(604\) −83.1057 −3.38152
\(605\) 3.59421 0.146125
\(606\) 7.39992 0.300601
\(607\) 27.8683 1.13114 0.565571 0.824700i \(-0.308656\pi\)
0.565571 + 0.824700i \(0.308656\pi\)
\(608\) 50.9001 2.06427
\(609\) 8.78223 0.355874
\(610\) 30.5028 1.23502
\(611\) 0.411069 0.0166301
\(612\) 51.7469 2.09175
\(613\) −38.5679 −1.55774 −0.778871 0.627184i \(-0.784207\pi\)
−0.778871 + 0.627184i \(0.784207\pi\)
\(614\) −16.3047 −0.658005
\(615\) −8.95089 −0.360935
\(616\) −21.3301 −0.859413
\(617\) 14.6163 0.588430 0.294215 0.955739i \(-0.404942\pi\)
0.294215 + 0.955739i \(0.404942\pi\)
\(618\) −49.0843 −1.97446
\(619\) 27.9837 1.12476 0.562379 0.826879i \(-0.309886\pi\)
0.562379 + 0.826879i \(0.309886\pi\)
\(620\) 33.1390 1.33089
\(621\) −7.30131 −0.292992
\(622\) −34.5557 −1.38556
\(623\) 0.252692 0.0101239
\(624\) 31.9634 1.27956
\(625\) 1.00000 0.0400000
\(626\) −24.3309 −0.972460
\(627\) 24.4070 0.974723
\(628\) 7.18864 0.286858
\(629\) −58.3575 −2.32686
\(630\) 5.32485 0.212147
\(631\) 38.9894 1.55214 0.776072 0.630644i \(-0.217209\pi\)
0.776072 + 0.630644i \(0.217209\pi\)
\(632\) 55.8601 2.22199
\(633\) 2.67083 0.106156
\(634\) −84.0756 −3.33907
\(635\) −4.33688 −0.172104
\(636\) −8.46980 −0.335850
\(637\) 1.32703 0.0525787
\(638\) −28.1678 −1.11517
\(639\) 17.6181 0.696960
\(640\) −6.39066 −0.252613
\(641\) 45.6963 1.80490 0.902448 0.430800i \(-0.141768\pi\)
0.902448 + 0.430800i \(0.141768\pi\)
\(642\) 39.8906 1.57436
\(643\) −38.9906 −1.53764 −0.768820 0.639465i \(-0.779156\pi\)
−0.768820 + 0.639465i \(0.779156\pi\)
\(644\) −16.4788 −0.649357
\(645\) 12.7779 0.503129
\(646\) 54.5735 2.14716
\(647\) 44.6786 1.75650 0.878248 0.478205i \(-0.158712\pi\)
0.878248 + 0.478205i \(0.158712\pi\)
\(648\) −86.0823 −3.38163
\(649\) 8.66096 0.339973
\(650\) 3.50322 0.137407
\(651\) 14.9379 0.585463
\(652\) −65.9465 −2.58266
\(653\) −17.1963 −0.672944 −0.336472 0.941694i \(-0.609234\pi\)
−0.336472 + 0.941694i \(0.609234\pi\)
\(654\) 21.8254 0.853441
\(655\) −6.76692 −0.264405
\(656\) 42.9724 1.67779
\(657\) −2.17165 −0.0847241
\(658\) −0.817754 −0.0318794
\(659\) 43.0517 1.67706 0.838529 0.544857i \(-0.183416\pi\)
0.838529 + 0.544857i \(0.183416\pi\)
\(660\) −30.2890 −1.17900
\(661\) 2.24574 0.0873492 0.0436746 0.999046i \(-0.486094\pi\)
0.0436746 + 0.999046i \(0.486094\pi\)
\(662\) 15.8773 0.617090
\(663\) 15.3460 0.595989
\(664\) 137.081 5.31978
\(665\) 4.00409 0.155272
\(666\) −60.1885 −2.33226
\(667\) −13.0026 −0.503464
\(668\) 43.7504 1.69276
\(669\) −27.0402 −1.04543
\(670\) −33.5115 −1.29466
\(671\) −31.4440 −1.21388
\(672\) −28.4734 −1.09838
\(673\) 42.1677 1.62545 0.812724 0.582649i \(-0.197984\pi\)
0.812724 + 0.582649i \(0.197984\pi\)
\(674\) −73.2100 −2.81994
\(675\) −2.20166 −0.0847418
\(676\) −55.8473 −2.14797
\(677\) −28.6806 −1.10228 −0.551142 0.834411i \(-0.685808\pi\)
−0.551142 + 0.834411i \(0.685808\pi\)
\(678\) −30.2244 −1.16076
\(679\) 5.71617 0.219366
\(680\) −40.4666 −1.55182
\(681\) −24.3082 −0.931492
\(682\) −47.9113 −1.83462
\(683\) −23.9411 −0.916080 −0.458040 0.888932i \(-0.651448\pi\)
−0.458040 + 0.888932i \(0.651448\pi\)
\(684\) 40.1327 1.53451
\(685\) −0.0291688 −0.00111448
\(686\) −2.63990 −0.100792
\(687\) 2.23988 0.0854568
\(688\) −61.3455 −2.33878
\(689\) −1.00984 −0.0384719
\(690\) −19.6094 −0.746516
\(691\) −17.7237 −0.674241 −0.337120 0.941462i \(-0.609453\pi\)
−0.337120 + 0.941462i \(0.609453\pi\)
\(692\) −2.85302 −0.108455
\(693\) −5.48916 −0.208516
\(694\) 28.8357 1.09459
\(695\) −16.5953 −0.629496
\(696\) −68.8353 −2.60920
\(697\) 20.6315 0.781475
\(698\) 47.2443 1.78822
\(699\) −13.1539 −0.497524
\(700\) −4.96906 −0.187813
\(701\) 24.2050 0.914212 0.457106 0.889412i \(-0.348886\pi\)
0.457106 + 0.889412i \(0.348886\pi\)
\(702\) −7.71288 −0.291104
\(703\) −45.2596 −1.70700
\(704\) 32.7964 1.23606
\(705\) −0.693841 −0.0261316
\(706\) −14.9790 −0.563743
\(707\) −1.25145 −0.0470658
\(708\) 35.4226 1.33126
\(709\) 2.52998 0.0950155 0.0475077 0.998871i \(-0.484872\pi\)
0.0475077 + 0.998871i \(0.484872\pi\)
\(710\) −23.0582 −0.865358
\(711\) 14.3752 0.539113
\(712\) −1.98061 −0.0742265
\(713\) −22.1165 −0.828269
\(714\) −30.5283 −1.14249
\(715\) −3.61132 −0.135056
\(716\) −36.8238 −1.37617
\(717\) 22.2720 0.831765
\(718\) −89.9298 −3.35615
\(719\) −34.1503 −1.27359 −0.636796 0.771033i \(-0.719741\pi\)
−0.636796 + 0.771033i \(0.719741\pi\)
\(720\) −21.6905 −0.808355
\(721\) 8.30099 0.309145
\(722\) −7.83320 −0.291521
\(723\) 6.13349 0.228107
\(724\) −18.1738 −0.675425
\(725\) −3.92085 −0.145617
\(726\) −21.2528 −0.788765
\(727\) 32.8998 1.22018 0.610092 0.792330i \(-0.291132\pi\)
0.610092 + 0.792330i \(0.291132\pi\)
\(728\) −10.4013 −0.385497
\(729\) −7.35838 −0.272532
\(730\) 2.84222 0.105195
\(731\) −29.4526 −1.08935
\(732\) −128.603 −4.75331
\(733\) −40.2033 −1.48494 −0.742471 0.669878i \(-0.766346\pi\)
−0.742471 + 0.669878i \(0.766346\pi\)
\(734\) −48.4891 −1.78977
\(735\) −2.23988 −0.0826192
\(736\) 42.1566 1.55391
\(737\) 34.5456 1.27250
\(738\) 21.2789 0.783286
\(739\) −2.29644 −0.0844758 −0.0422379 0.999108i \(-0.513449\pi\)
−0.0422379 + 0.999108i \(0.513449\pi\)
\(740\) 56.1669 2.06474
\(741\) 11.9017 0.437220
\(742\) 2.00891 0.0737495
\(743\) 31.0508 1.13914 0.569571 0.821942i \(-0.307109\pi\)
0.569571 + 0.821942i \(0.307109\pi\)
\(744\) −117.084 −4.29250
\(745\) 14.2460 0.521934
\(746\) −38.0763 −1.39407
\(747\) 35.2770 1.29072
\(748\) 69.8153 2.55270
\(749\) −6.74619 −0.246500
\(750\) −5.91306 −0.215914
\(751\) −43.9562 −1.60399 −0.801993 0.597334i \(-0.796227\pi\)
−0.801993 + 0.597334i \(0.796227\pi\)
\(752\) 3.33107 0.121472
\(753\) −17.4709 −0.636676
\(754\) −13.7356 −0.500220
\(755\) 16.7246 0.608671
\(756\) 10.9402 0.397890
\(757\) 41.5254 1.50927 0.754633 0.656147i \(-0.227815\pi\)
0.754633 + 0.656147i \(0.227815\pi\)
\(758\) 32.0066 1.16253
\(759\) 20.2145 0.733739
\(760\) −31.3842 −1.13842
\(761\) 26.8469 0.973198 0.486599 0.873625i \(-0.338237\pi\)
0.486599 + 0.873625i \(0.338237\pi\)
\(762\) 25.6442 0.928993
\(763\) −3.69105 −0.133625
\(764\) 40.3830 1.46101
\(765\) −10.4138 −0.376513
\(766\) 83.5277 3.01798
\(767\) 4.22338 0.152498
\(768\) −16.1994 −0.584546
\(769\) 20.1833 0.727829 0.363915 0.931432i \(-0.381440\pi\)
0.363915 + 0.931432i \(0.381440\pi\)
\(770\) 7.18411 0.258897
\(771\) 29.8473 1.07492
\(772\) −128.048 −4.60854
\(773\) −10.5727 −0.380272 −0.190136 0.981758i \(-0.560893\pi\)
−0.190136 + 0.981758i \(0.560893\pi\)
\(774\) −30.3768 −1.09187
\(775\) −6.66906 −0.239560
\(776\) −44.8035 −1.60835
\(777\) 25.3181 0.908282
\(778\) −3.24647 −0.116392
\(779\) 16.0009 0.573293
\(780\) −14.7700 −0.528849
\(781\) 23.7697 0.850547
\(782\) 45.1990 1.61631
\(783\) 8.63235 0.308495
\(784\) 10.7535 0.384052
\(785\) −1.44668 −0.0516342
\(786\) 40.0132 1.42722
\(787\) 25.1544 0.896657 0.448329 0.893869i \(-0.352019\pi\)
0.448329 + 0.893869i \(0.352019\pi\)
\(788\) 31.3462 1.11666
\(789\) 1.43420 0.0510587
\(790\) −18.8140 −0.669373
\(791\) 5.11147 0.181743
\(792\) 43.0242 1.52880
\(793\) −15.3332 −0.544497
\(794\) 0.799593 0.0283765
\(795\) 1.70451 0.0604526
\(796\) −58.1963 −2.06271
\(797\) 9.99175 0.353926 0.176963 0.984218i \(-0.443373\pi\)
0.176963 + 0.984218i \(0.443373\pi\)
\(798\) −23.6764 −0.838137
\(799\) 1.59928 0.0565786
\(800\) 12.7120 0.449437
\(801\) −0.509697 −0.0180093
\(802\) −14.1616 −0.500063
\(803\) −2.92992 −0.103395
\(804\) 141.288 4.98286
\(805\) 3.31628 0.116884
\(806\) −23.3632 −0.822933
\(807\) 34.7058 1.22170
\(808\) 9.80893 0.345077
\(809\) −24.5109 −0.861758 −0.430879 0.902410i \(-0.641796\pi\)
−0.430879 + 0.902410i \(0.641796\pi\)
\(810\) 28.9931 1.01871
\(811\) 13.4607 0.472668 0.236334 0.971672i \(-0.424054\pi\)
0.236334 + 0.971672i \(0.424054\pi\)
\(812\) 19.4829 0.683717
\(813\) 32.9762 1.15653
\(814\) −81.2043 −2.84621
\(815\) 13.2714 0.464877
\(816\) 124.355 4.35330
\(817\) −22.8422 −0.799148
\(818\) 60.4205 2.11255
\(819\) −2.67670 −0.0935315
\(820\) −19.8571 −0.693440
\(821\) 42.9090 1.49753 0.748767 0.662833i \(-0.230646\pi\)
0.748767 + 0.662833i \(0.230646\pi\)
\(822\) 0.172477 0.00601582
\(823\) −24.1142 −0.840567 −0.420283 0.907393i \(-0.638069\pi\)
−0.420283 + 0.907393i \(0.638069\pi\)
\(824\) −65.0634 −2.26659
\(825\) 6.09552 0.212219
\(826\) −8.40171 −0.292333
\(827\) 40.1335 1.39558 0.697789 0.716303i \(-0.254167\pi\)
0.697789 + 0.716303i \(0.254167\pi\)
\(828\) 33.2389 1.15513
\(829\) −32.8041 −1.13933 −0.569667 0.821875i \(-0.692928\pi\)
−0.569667 + 0.821875i \(0.692928\pi\)
\(830\) −46.1698 −1.60258
\(831\) −9.48657 −0.329086
\(832\) 15.9926 0.554445
\(833\) 5.16286 0.178882
\(834\) 98.1290 3.39793
\(835\) −8.80456 −0.304694
\(836\) 54.1458 1.87267
\(837\) 14.6830 0.507518
\(838\) −12.2979 −0.424823
\(839\) −45.4206 −1.56809 −0.784046 0.620703i \(-0.786847\pi\)
−0.784046 + 0.620703i \(0.786847\pi\)
\(840\) 17.5562 0.605748
\(841\) −13.6270 −0.469896
\(842\) −85.3823 −2.94247
\(843\) −3.92925 −0.135331
\(844\) 5.92509 0.203950
\(845\) 11.2390 0.386633
\(846\) 1.64946 0.0567097
\(847\) 3.59421 0.123499
\(848\) −8.18319 −0.281012
\(849\) −6.09526 −0.209189
\(850\) 13.6294 0.467485
\(851\) −37.4850 −1.28497
\(852\) 97.2159 3.33056
\(853\) 31.2210 1.06899 0.534494 0.845172i \(-0.320502\pi\)
0.534494 + 0.845172i \(0.320502\pi\)
\(854\) 30.5028 1.04378
\(855\) −8.07652 −0.276211
\(856\) 52.8768 1.80729
\(857\) 42.7198 1.45928 0.729640 0.683832i \(-0.239688\pi\)
0.729640 + 0.683832i \(0.239688\pi\)
\(858\) 21.3539 0.729011
\(859\) 0.868425 0.0296303 0.0148151 0.999890i \(-0.495284\pi\)
0.0148151 + 0.999890i \(0.495284\pi\)
\(860\) 28.3471 0.966628
\(861\) −8.95089 −0.305046
\(862\) −72.8845 −2.48246
\(863\) −16.9656 −0.577516 −0.288758 0.957402i \(-0.593242\pi\)
−0.288758 + 0.957402i \(0.593242\pi\)
\(864\) −27.9875 −0.952153
\(865\) 0.574156 0.0195219
\(866\) 85.4695 2.90437
\(867\) 21.6263 0.734466
\(868\) 33.1390 1.12481
\(869\) 19.3946 0.657916
\(870\) 23.1842 0.786017
\(871\) 16.8456 0.570792
\(872\) 28.9306 0.979712
\(873\) −11.5299 −0.390227
\(874\) 35.0544 1.18573
\(875\) 1.00000 0.0338062
\(876\) −11.9831 −0.404872
\(877\) −3.96249 −0.133804 −0.0669019 0.997760i \(-0.521311\pi\)
−0.0669019 + 0.997760i \(0.521311\pi\)
\(878\) −69.9289 −2.35999
\(879\) 44.9201 1.51512
\(880\) −29.2640 −0.986490
\(881\) −11.4958 −0.387302 −0.193651 0.981070i \(-0.562033\pi\)
−0.193651 + 0.981070i \(0.562033\pi\)
\(882\) 5.32485 0.179297
\(883\) −5.30517 −0.178533 −0.0892666 0.996008i \(-0.528452\pi\)
−0.0892666 + 0.996008i \(0.528452\pi\)
\(884\) 34.0443 1.14503
\(885\) −7.12862 −0.239626
\(886\) 18.9999 0.638313
\(887\) 26.9010 0.903249 0.451624 0.892208i \(-0.350845\pi\)
0.451624 + 0.892208i \(0.350845\pi\)
\(888\) −198.444 −6.65934
\(889\) −4.33688 −0.145454
\(890\) 0.667082 0.0223606
\(891\) −29.8877 −1.00128
\(892\) −59.9873 −2.00852
\(893\) 1.24034 0.0415063
\(894\) −84.2375 −2.81732
\(895\) 7.41062 0.247710
\(896\) −6.39066 −0.213497
\(897\) 9.85726 0.329124
\(898\) −13.3293 −0.444804
\(899\) 26.1484 0.872097
\(900\) 10.0229 0.334098
\(901\) −3.92884 −0.130889
\(902\) 28.7087 0.955897
\(903\) 12.7779 0.425221
\(904\) −40.0638 −1.33250
\(905\) 3.65740 0.121576
\(906\) −98.8937 −3.28552
\(907\) −48.6319 −1.61480 −0.807398 0.590007i \(-0.799125\pi\)
−0.807398 + 0.590007i \(0.799125\pi\)
\(908\) −53.9265 −1.78961
\(909\) 2.52427 0.0837246
\(910\) 3.50322 0.116131
\(911\) 44.0064 1.45800 0.728998 0.684515i \(-0.239986\pi\)
0.728998 + 0.684515i \(0.239986\pi\)
\(912\) 96.4445 3.19360
\(913\) 47.5945 1.57515
\(914\) −11.2568 −0.372342
\(915\) 25.8808 0.855592
\(916\) 4.96906 0.164182
\(917\) −6.76692 −0.223463
\(918\) −30.0073 −0.990388
\(919\) 13.1260 0.432988 0.216494 0.976284i \(-0.430538\pi\)
0.216494 + 0.976284i \(0.430538\pi\)
\(920\) −25.9931 −0.856968
\(921\) −13.8341 −0.455850
\(922\) −99.5536 −3.27862
\(923\) 11.5909 0.381520
\(924\) −30.2890 −0.996435
\(925\) −11.3033 −0.371651
\(926\) −37.2328 −1.22354
\(927\) −16.7436 −0.549934
\(928\) −49.8418 −1.63614
\(929\) −7.03062 −0.230667 −0.115334 0.993327i \(-0.536794\pi\)
−0.115334 + 0.993327i \(0.536794\pi\)
\(930\) 39.4345 1.29311
\(931\) 4.00409 0.131229
\(932\) −29.1812 −0.955861
\(933\) −29.3196 −0.959879
\(934\) −63.2882 −2.07085
\(935\) −14.0500 −0.459484
\(936\) 20.9801 0.685755
\(937\) 27.6516 0.903340 0.451670 0.892185i \(-0.350828\pi\)
0.451670 + 0.892185i \(0.350828\pi\)
\(938\) −33.5115 −1.09419
\(939\) −20.6441 −0.673696
\(940\) −1.53925 −0.0502049
\(941\) 37.8872 1.23509 0.617543 0.786537i \(-0.288128\pi\)
0.617543 + 0.786537i \(0.288128\pi\)
\(942\) 8.55430 0.278714
\(943\) 13.2524 0.431556
\(944\) 34.2239 1.11389
\(945\) −2.20166 −0.0716199
\(946\) −40.9833 −1.33248
\(947\) −37.0379 −1.20357 −0.601785 0.798658i \(-0.705544\pi\)
−0.601785 + 0.798658i \(0.705544\pi\)
\(948\) 79.3221 2.57626
\(949\) −1.42873 −0.0463785
\(950\) 10.5704 0.342949
\(951\) −71.3358 −2.31322
\(952\) −40.4666 −1.31153
\(953\) −32.2407 −1.04438 −0.522189 0.852830i \(-0.674884\pi\)
−0.522189 + 0.852830i \(0.674884\pi\)
\(954\) −4.05211 −0.131192
\(955\) −8.12688 −0.262980
\(956\) 49.4094 1.59801
\(957\) −23.8996 −0.772564
\(958\) −26.3178 −0.850289
\(959\) −0.0291688 −0.000941910 0
\(960\) −26.9939 −0.871224
\(961\) 13.4764 0.434722
\(962\) −39.5980 −1.27669
\(963\) 13.6075 0.438496
\(964\) 13.6069 0.438247
\(965\) 25.7690 0.829533
\(966\) −19.6094 −0.630921
\(967\) −52.9043 −1.70129 −0.850644 0.525742i \(-0.823788\pi\)
−0.850644 + 0.525742i \(0.823788\pi\)
\(968\) −28.1715 −0.905467
\(969\) 46.3041 1.48750
\(970\) 15.0901 0.484514
\(971\) −46.7245 −1.49946 −0.749730 0.661744i \(-0.769816\pi\)
−0.749730 + 0.661744i \(0.769816\pi\)
\(972\) −89.4175 −2.86807
\(973\) −16.5953 −0.532021
\(974\) 35.0634 1.12351
\(975\) 2.97238 0.0951924
\(976\) −124.251 −3.97719
\(977\) 35.0174 1.12031 0.560153 0.828389i \(-0.310742\pi\)
0.560153 + 0.828389i \(0.310742\pi\)
\(978\) −78.4746 −2.50934
\(979\) −0.687666 −0.0219779
\(980\) −4.96906 −0.158731
\(981\) 7.44509 0.237704
\(982\) 97.8167 3.12146
\(983\) 37.3695 1.19190 0.595951 0.803021i \(-0.296775\pi\)
0.595951 + 0.803021i \(0.296775\pi\)
\(984\) 70.1573 2.23653
\(985\) −6.30826 −0.200998
\(986\) −53.4388 −1.70184
\(987\) −0.693841 −0.0220852
\(988\) 26.4033 0.840002
\(989\) −18.9185 −0.601572
\(990\) −14.4908 −0.460548
\(991\) 33.9287 1.07778 0.538890 0.842376i \(-0.318844\pi\)
0.538890 + 0.842376i \(0.318844\pi\)
\(992\) −84.7772 −2.69168
\(993\) 13.4715 0.427505
\(994\) −23.0582 −0.731361
\(995\) 11.7117 0.371287
\(996\) 194.657 6.16795
\(997\) 7.56393 0.239552 0.119776 0.992801i \(-0.461782\pi\)
0.119776 + 0.992801i \(0.461782\pi\)
\(998\) −13.3704 −0.423231
\(999\) 24.8860 0.787359
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 \(a_p\))