Properties

Label 8002.2.a.e.1.7
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} -0.854809 q^{10} +1.39811 q^{11} -2.62668 q^{12} +4.58926 q^{13} -1.79286 q^{14} -2.24531 q^{15} +1.00000 q^{16} +4.16383 q^{17} -3.89945 q^{18} +7.03095 q^{19} +0.854809 q^{20} -4.70927 q^{21} -1.39811 q^{22} -6.43702 q^{23} +2.62668 q^{24} -4.26930 q^{25} -4.58926 q^{26} -2.36257 q^{27} +1.79286 q^{28} +4.33951 q^{29} +2.24531 q^{30} +3.24386 q^{31} -1.00000 q^{32} -3.67239 q^{33} -4.16383 q^{34} +1.53255 q^{35} +3.89945 q^{36} +3.51846 q^{37} -7.03095 q^{38} -12.0545 q^{39} -0.854809 q^{40} +7.42613 q^{41} +4.70927 q^{42} +5.43299 q^{43} +1.39811 q^{44} +3.33329 q^{45} +6.43702 q^{46} +9.18945 q^{47} -2.62668 q^{48} -3.78565 q^{49} +4.26930 q^{50} -10.9370 q^{51} +4.58926 q^{52} +13.3398 q^{53} +2.36257 q^{54} +1.19512 q^{55} -1.79286 q^{56} -18.4681 q^{57} -4.33951 q^{58} +15.0144 q^{59} -2.24531 q^{60} -10.2707 q^{61} -3.24386 q^{62} +6.99118 q^{63} +1.00000 q^{64} +3.92294 q^{65} +3.67239 q^{66} +3.19534 q^{67} +4.16383 q^{68} +16.9080 q^{69} -1.53255 q^{70} -5.20239 q^{71} -3.89945 q^{72} +4.59082 q^{73} -3.51846 q^{74} +11.2141 q^{75} +7.03095 q^{76} +2.50662 q^{77} +12.0545 q^{78} +12.9027 q^{79} +0.854809 q^{80} -5.49263 q^{81} -7.42613 q^{82} +8.96203 q^{83} -4.70927 q^{84} +3.55928 q^{85} -5.43299 q^{86} -11.3985 q^{87} -1.39811 q^{88} -2.56615 q^{89} -3.33329 q^{90} +8.22790 q^{91} -6.43702 q^{92} -8.52059 q^{93} -9.18945 q^{94} +6.01012 q^{95} +2.62668 q^{96} -13.9084 q^{97} +3.78565 q^{98} +5.45187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.62668 −1.51651 −0.758257 0.651955i \(-0.773949\pi\)
−0.758257 + 0.651955i \(0.773949\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.854809 0.382282 0.191141 0.981563i \(-0.438781\pi\)
0.191141 + 0.981563i \(0.438781\pi\)
\(6\) 2.62668 1.07234
\(7\) 1.79286 0.677638 0.338819 0.940852i \(-0.389973\pi\)
0.338819 + 0.940852i \(0.389973\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.89945 1.29982
\(10\) −0.854809 −0.270314
\(11\) 1.39811 0.421547 0.210773 0.977535i \(-0.432402\pi\)
0.210773 + 0.977535i \(0.432402\pi\)
\(12\) −2.62668 −0.758257
\(13\) 4.58926 1.27283 0.636416 0.771346i \(-0.280416\pi\)
0.636416 + 0.771346i \(0.280416\pi\)
\(14\) −1.79286 −0.479162
\(15\) −2.24531 −0.579737
\(16\) 1.00000 0.250000
\(17\) 4.16383 1.00988 0.504938 0.863155i \(-0.331515\pi\)
0.504938 + 0.863155i \(0.331515\pi\)
\(18\) −3.89945 −0.919110
\(19\) 7.03095 1.61301 0.806505 0.591228i \(-0.201356\pi\)
0.806505 + 0.591228i \(0.201356\pi\)
\(20\) 0.854809 0.191141
\(21\) −4.70927 −1.02765
\(22\) −1.39811 −0.298078
\(23\) −6.43702 −1.34221 −0.671105 0.741362i \(-0.734180\pi\)
−0.671105 + 0.741362i \(0.734180\pi\)
\(24\) 2.62668 0.536169
\(25\) −4.26930 −0.853860
\(26\) −4.58926 −0.900028
\(27\) −2.36257 −0.454677
\(28\) 1.79286 0.338819
\(29\) 4.33951 0.805827 0.402913 0.915238i \(-0.367998\pi\)
0.402913 + 0.915238i \(0.367998\pi\)
\(30\) 2.24531 0.409936
\(31\) 3.24386 0.582615 0.291307 0.956630i \(-0.405910\pi\)
0.291307 + 0.956630i \(0.405910\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.67239 −0.639282
\(34\) −4.16383 −0.714090
\(35\) 1.53255 0.259049
\(36\) 3.89945 0.649909
\(37\) 3.51846 0.578431 0.289215 0.957264i \(-0.406606\pi\)
0.289215 + 0.957264i \(0.406606\pi\)
\(38\) −7.03095 −1.14057
\(39\) −12.0545 −1.93027
\(40\) −0.854809 −0.135157
\(41\) 7.42613 1.15977 0.579883 0.814700i \(-0.303098\pi\)
0.579883 + 0.814700i \(0.303098\pi\)
\(42\) 4.70927 0.726657
\(43\) 5.43299 0.828523 0.414261 0.910158i \(-0.364040\pi\)
0.414261 + 0.910158i \(0.364040\pi\)
\(44\) 1.39811 0.210773
\(45\) 3.33329 0.496897
\(46\) 6.43702 0.949086
\(47\) 9.18945 1.34042 0.670210 0.742172i \(-0.266204\pi\)
0.670210 + 0.742172i \(0.266204\pi\)
\(48\) −2.62668 −0.379129
\(49\) −3.78565 −0.540807
\(50\) 4.26930 0.603770
\(51\) −10.9370 −1.53149
\(52\) 4.58926 0.636416
\(53\) 13.3398 1.83236 0.916179 0.400769i \(-0.131257\pi\)
0.916179 + 0.400769i \(0.131257\pi\)
\(54\) 2.36257 0.321505
\(55\) 1.19512 0.161150
\(56\) −1.79286 −0.239581
\(57\) −18.4681 −2.44615
\(58\) −4.33951 −0.569805
\(59\) 15.0144 1.95471 0.977353 0.211614i \(-0.0678721\pi\)
0.977353 + 0.211614i \(0.0678721\pi\)
\(60\) −2.24531 −0.289868
\(61\) −10.2707 −1.31503 −0.657514 0.753442i \(-0.728392\pi\)
−0.657514 + 0.753442i \(0.728392\pi\)
\(62\) −3.24386 −0.411971
\(63\) 6.99118 0.880805
\(64\) 1.00000 0.125000
\(65\) 3.92294 0.486581
\(66\) 3.67239 0.452040
\(67\) 3.19534 0.390373 0.195187 0.980766i \(-0.437469\pi\)
0.195187 + 0.980766i \(0.437469\pi\)
\(68\) 4.16383 0.504938
\(69\) 16.9080 2.03548
\(70\) −1.53255 −0.183175
\(71\) −5.20239 −0.617411 −0.308705 0.951158i \(-0.599896\pi\)
−0.308705 + 0.951158i \(0.599896\pi\)
\(72\) −3.89945 −0.459555
\(73\) 4.59082 0.537315 0.268657 0.963236i \(-0.413420\pi\)
0.268657 + 0.963236i \(0.413420\pi\)
\(74\) −3.51846 −0.409012
\(75\) 11.2141 1.29489
\(76\) 7.03095 0.806505
\(77\) 2.50662 0.285656
\(78\) 12.0545 1.36491
\(79\) 12.9027 1.45166 0.725832 0.687872i \(-0.241455\pi\)
0.725832 + 0.687872i \(0.241455\pi\)
\(80\) 0.854809 0.0955706
\(81\) −5.49263 −0.610292
\(82\) −7.42613 −0.820079
\(83\) 8.96203 0.983710 0.491855 0.870677i \(-0.336319\pi\)
0.491855 + 0.870677i \(0.336319\pi\)
\(84\) −4.70927 −0.513824
\(85\) 3.55928 0.386058
\(86\) −5.43299 −0.585854
\(87\) −11.3985 −1.22205
\(88\) −1.39811 −0.149039
\(89\) −2.56615 −0.272011 −0.136006 0.990708i \(-0.543426\pi\)
−0.136006 + 0.990708i \(0.543426\pi\)
\(90\) −3.33329 −0.351359
\(91\) 8.22790 0.862519
\(92\) −6.43702 −0.671105
\(93\) −8.52059 −0.883544
\(94\) −9.18945 −0.947819
\(95\) 6.01012 0.616625
\(96\) 2.62668 0.268084
\(97\) −13.9084 −1.41219 −0.706095 0.708118i \(-0.749545\pi\)
−0.706095 + 0.708118i \(0.749545\pi\)
\(98\) 3.78565 0.382408
\(99\) 5.45187 0.547933
\(100\) −4.26930 −0.426930
\(101\) −18.6206 −1.85282 −0.926411 0.376514i \(-0.877123\pi\)
−0.926411 + 0.376514i \(0.877123\pi\)
\(102\) 10.9370 1.08293
\(103\) −7.47862 −0.736890 −0.368445 0.929649i \(-0.620110\pi\)
−0.368445 + 0.929649i \(0.620110\pi\)
\(104\) −4.58926 −0.450014
\(105\) −4.02553 −0.392851
\(106\) −13.3398 −1.29567
\(107\) 16.1348 1.55981 0.779906 0.625897i \(-0.215267\pi\)
0.779906 + 0.625897i \(0.215267\pi\)
\(108\) −2.36257 −0.227339
\(109\) 14.6084 1.39923 0.699616 0.714519i \(-0.253354\pi\)
0.699616 + 0.714519i \(0.253354\pi\)
\(110\) −1.19512 −0.113950
\(111\) −9.24186 −0.877198
\(112\) 1.79286 0.169409
\(113\) −11.4365 −1.07586 −0.537928 0.842991i \(-0.680793\pi\)
−0.537928 + 0.842991i \(0.680793\pi\)
\(114\) 18.4681 1.72969
\(115\) −5.50242 −0.513103
\(116\) 4.33951 0.402913
\(117\) 17.8956 1.65445
\(118\) −15.0144 −1.38219
\(119\) 7.46516 0.684330
\(120\) 2.24531 0.204968
\(121\) −9.04528 −0.822298
\(122\) 10.2707 0.929866
\(123\) −19.5061 −1.75880
\(124\) 3.24386 0.291307
\(125\) −7.92348 −0.708698
\(126\) −6.99118 −0.622823
\(127\) 9.05839 0.803802 0.401901 0.915683i \(-0.368350\pi\)
0.401901 + 0.915683i \(0.368350\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −14.2707 −1.25647
\(130\) −3.92294 −0.344065
\(131\) −3.80330 −0.332296 −0.166148 0.986101i \(-0.553133\pi\)
−0.166148 + 0.986101i \(0.553133\pi\)
\(132\) −3.67239 −0.319641
\(133\) 12.6055 1.09304
\(134\) −3.19534 −0.276036
\(135\) −2.01955 −0.173815
\(136\) −4.16383 −0.357045
\(137\) 20.6547 1.76465 0.882326 0.470638i \(-0.155976\pi\)
0.882326 + 0.470638i \(0.155976\pi\)
\(138\) −16.9080 −1.43930
\(139\) 6.77841 0.574937 0.287469 0.957790i \(-0.407186\pi\)
0.287469 + 0.957790i \(0.407186\pi\)
\(140\) 1.53255 0.129524
\(141\) −24.1378 −2.03277
\(142\) 5.20239 0.436575
\(143\) 6.41630 0.536558
\(144\) 3.89945 0.324954
\(145\) 3.70945 0.308053
\(146\) −4.59082 −0.379939
\(147\) 9.94369 0.820142
\(148\) 3.51846 0.289215
\(149\) 5.51127 0.451500 0.225750 0.974185i \(-0.427517\pi\)
0.225750 + 0.974185i \(0.427517\pi\)
\(150\) −11.2141 −0.915627
\(151\) −9.42711 −0.767167 −0.383584 0.923506i \(-0.625310\pi\)
−0.383584 + 0.923506i \(0.625310\pi\)
\(152\) −7.03095 −0.570285
\(153\) 16.2366 1.31265
\(154\) −2.50662 −0.201989
\(155\) 2.77288 0.222723
\(156\) −12.0545 −0.965134
\(157\) −14.6278 −1.16743 −0.583715 0.811959i \(-0.698401\pi\)
−0.583715 + 0.811959i \(0.698401\pi\)
\(158\) −12.9027 −1.02648
\(159\) −35.0393 −2.77880
\(160\) −0.854809 −0.0675786
\(161\) −11.5407 −0.909533
\(162\) 5.49263 0.431542
\(163\) −1.17571 −0.0920884 −0.0460442 0.998939i \(-0.514662\pi\)
−0.0460442 + 0.998939i \(0.514662\pi\)
\(164\) 7.42613 0.579883
\(165\) −3.13919 −0.244386
\(166\) −8.96203 −0.695588
\(167\) 6.13476 0.474722 0.237361 0.971422i \(-0.423718\pi\)
0.237361 + 0.971422i \(0.423718\pi\)
\(168\) 4.70927 0.363328
\(169\) 8.06129 0.620099
\(170\) −3.55928 −0.272984
\(171\) 27.4168 2.09662
\(172\) 5.43299 0.414261
\(173\) 6.25113 0.475264 0.237632 0.971355i \(-0.423629\pi\)
0.237632 + 0.971355i \(0.423629\pi\)
\(174\) 11.3985 0.864118
\(175\) −7.65426 −0.578608
\(176\) 1.39811 0.105387
\(177\) −39.4380 −2.96434
\(178\) 2.56615 0.192341
\(179\) −3.65995 −0.273557 −0.136779 0.990602i \(-0.543675\pi\)
−0.136779 + 0.990602i \(0.543675\pi\)
\(180\) 3.33329 0.248449
\(181\) −17.3263 −1.28786 −0.643928 0.765086i \(-0.722696\pi\)
−0.643928 + 0.765086i \(0.722696\pi\)
\(182\) −8.22790 −0.609893
\(183\) 26.9779 1.99426
\(184\) 6.43702 0.474543
\(185\) 3.00761 0.221124
\(186\) 8.52059 0.624760
\(187\) 5.82150 0.425710
\(188\) 9.18945 0.670210
\(189\) −4.23576 −0.308106
\(190\) −6.01012 −0.436020
\(191\) 17.2881 1.25092 0.625460 0.780256i \(-0.284911\pi\)
0.625460 + 0.780256i \(0.284911\pi\)
\(192\) −2.62668 −0.189564
\(193\) −15.8238 −1.13902 −0.569512 0.821983i \(-0.692868\pi\)
−0.569512 + 0.821983i \(0.692868\pi\)
\(194\) 13.9084 0.998569
\(195\) −10.3043 −0.737907
\(196\) −3.78565 −0.270404
\(197\) −12.0973 −0.861899 −0.430950 0.902376i \(-0.641821\pi\)
−0.430950 + 0.902376i \(0.641821\pi\)
\(198\) −5.45187 −0.387447
\(199\) −18.1581 −1.28720 −0.643598 0.765364i \(-0.722559\pi\)
−0.643598 + 0.765364i \(0.722559\pi\)
\(200\) 4.26930 0.301885
\(201\) −8.39314 −0.592007
\(202\) 18.6206 1.31014
\(203\) 7.78014 0.546059
\(204\) −10.9370 −0.765746
\(205\) 6.34792 0.443358
\(206\) 7.47862 0.521060
\(207\) −25.1008 −1.74463
\(208\) 4.58926 0.318208
\(209\) 9.83005 0.679959
\(210\) 4.02553 0.277788
\(211\) −9.69641 −0.667529 −0.333764 0.942657i \(-0.608319\pi\)
−0.333764 + 0.942657i \(0.608319\pi\)
\(212\) 13.3398 0.916179
\(213\) 13.6650 0.936312
\(214\) −16.1348 −1.10295
\(215\) 4.64417 0.316730
\(216\) 2.36257 0.160753
\(217\) 5.81579 0.394802
\(218\) −14.6084 −0.989406
\(219\) −12.0586 −0.814846
\(220\) 1.19512 0.0805749
\(221\) 19.1089 1.28540
\(222\) 9.24186 0.620273
\(223\) −13.9655 −0.935200 −0.467600 0.883940i \(-0.654881\pi\)
−0.467600 + 0.883940i \(0.654881\pi\)
\(224\) −1.79286 −0.119791
\(225\) −16.6479 −1.10986
\(226\) 11.4365 0.760745
\(227\) 8.81918 0.585350 0.292675 0.956212i \(-0.405455\pi\)
0.292675 + 0.956212i \(0.405455\pi\)
\(228\) −18.4681 −1.22308
\(229\) −17.8260 −1.17797 −0.588986 0.808143i \(-0.700473\pi\)
−0.588986 + 0.808143i \(0.700473\pi\)
\(230\) 5.50242 0.362819
\(231\) −6.58409 −0.433201
\(232\) −4.33951 −0.284903
\(233\) −13.1809 −0.863511 −0.431755 0.901991i \(-0.642106\pi\)
−0.431755 + 0.901991i \(0.642106\pi\)
\(234\) −17.8956 −1.16987
\(235\) 7.85522 0.512418
\(236\) 15.0144 0.977353
\(237\) −33.8912 −2.20147
\(238\) −7.46516 −0.483895
\(239\) 13.2733 0.858579 0.429289 0.903167i \(-0.358764\pi\)
0.429289 + 0.903167i \(0.358764\pi\)
\(240\) −2.24531 −0.144934
\(241\) −9.51088 −0.612649 −0.306325 0.951927i \(-0.599099\pi\)
−0.306325 + 0.951927i \(0.599099\pi\)
\(242\) 9.04528 0.581453
\(243\) 21.5151 1.38019
\(244\) −10.2707 −0.657514
\(245\) −3.23601 −0.206741
\(246\) 19.5061 1.24366
\(247\) 32.2668 2.05309
\(248\) −3.24386 −0.205985
\(249\) −23.5404 −1.49181
\(250\) 7.92348 0.501125
\(251\) −25.2709 −1.59508 −0.797542 0.603263i \(-0.793867\pi\)
−0.797542 + 0.603263i \(0.793867\pi\)
\(252\) 6.99118 0.440403
\(253\) −8.99967 −0.565804
\(254\) −9.05839 −0.568374
\(255\) −9.34908 −0.585462
\(256\) 1.00000 0.0625000
\(257\) 0.815232 0.0508528 0.0254264 0.999677i \(-0.491906\pi\)
0.0254264 + 0.999677i \(0.491906\pi\)
\(258\) 14.2707 0.888457
\(259\) 6.30810 0.391966
\(260\) 3.92294 0.243290
\(261\) 16.9217 1.04743
\(262\) 3.80330 0.234969
\(263\) −25.4272 −1.56791 −0.783954 0.620819i \(-0.786800\pi\)
−0.783954 + 0.620819i \(0.786800\pi\)
\(264\) 3.67239 0.226020
\(265\) 11.4030 0.700478
\(266\) −12.6055 −0.772893
\(267\) 6.74045 0.412509
\(268\) 3.19534 0.195187
\(269\) −18.1899 −1.10906 −0.554530 0.832164i \(-0.687102\pi\)
−0.554530 + 0.832164i \(0.687102\pi\)
\(270\) 2.01955 0.122906
\(271\) −9.42443 −0.572493 −0.286247 0.958156i \(-0.592408\pi\)
−0.286247 + 0.958156i \(0.592408\pi\)
\(272\) 4.16383 0.252469
\(273\) −21.6121 −1.30802
\(274\) −20.6547 −1.24780
\(275\) −5.96896 −0.359942
\(276\) 16.9080 1.01774
\(277\) 22.4304 1.34771 0.673855 0.738864i \(-0.264637\pi\)
0.673855 + 0.738864i \(0.264637\pi\)
\(278\) −6.77841 −0.406542
\(279\) 12.6493 0.757293
\(280\) −1.53255 −0.0915876
\(281\) 9.63200 0.574597 0.287299 0.957841i \(-0.407243\pi\)
0.287299 + 0.957841i \(0.407243\pi\)
\(282\) 24.1378 1.43738
\(283\) −18.2230 −1.08324 −0.541622 0.840622i \(-0.682189\pi\)
−0.541622 + 0.840622i \(0.682189\pi\)
\(284\) −5.20239 −0.308705
\(285\) −15.7867 −0.935121
\(286\) −6.41630 −0.379404
\(287\) 13.3140 0.785901
\(288\) −3.89945 −0.229777
\(289\) 0.337458 0.0198505
\(290\) −3.70945 −0.217826
\(291\) 36.5331 2.14161
\(292\) 4.59082 0.268657
\(293\) 11.5816 0.676604 0.338302 0.941038i \(-0.390147\pi\)
0.338302 + 0.941038i \(0.390147\pi\)
\(294\) −9.94369 −0.579928
\(295\) 12.8344 0.747250
\(296\) −3.51846 −0.204506
\(297\) −3.30314 −0.191668
\(298\) −5.51127 −0.319259
\(299\) −29.5411 −1.70841
\(300\) 11.2141 0.647446
\(301\) 9.74059 0.561438
\(302\) 9.42711 0.542469
\(303\) 48.9104 2.80983
\(304\) 7.03095 0.403252
\(305\) −8.77949 −0.502712
\(306\) −16.2366 −0.928187
\(307\) −24.7384 −1.41189 −0.705947 0.708264i \(-0.749479\pi\)
−0.705947 + 0.708264i \(0.749479\pi\)
\(308\) 2.50662 0.142828
\(309\) 19.6440 1.11751
\(310\) −2.77288 −0.157489
\(311\) 19.6832 1.11613 0.558066 0.829796i \(-0.311544\pi\)
0.558066 + 0.829796i \(0.311544\pi\)
\(312\) 12.0545 0.682453
\(313\) 26.9784 1.52491 0.762456 0.647040i \(-0.223993\pi\)
0.762456 + 0.647040i \(0.223993\pi\)
\(314\) 14.6278 0.825497
\(315\) 5.97612 0.336716
\(316\) 12.9027 0.725832
\(317\) 5.08898 0.285826 0.142913 0.989735i \(-0.454353\pi\)
0.142913 + 0.989735i \(0.454353\pi\)
\(318\) 35.0393 1.96491
\(319\) 6.06712 0.339693
\(320\) 0.854809 0.0477853
\(321\) −42.3810 −2.36548
\(322\) 11.5407 0.643137
\(323\) 29.2756 1.62894
\(324\) −5.49263 −0.305146
\(325\) −19.5929 −1.08682
\(326\) 1.17571 0.0651163
\(327\) −38.3716 −2.12196
\(328\) −7.42613 −0.410039
\(329\) 16.4754 0.908319
\(330\) 3.13919 0.172807
\(331\) −17.9887 −0.988749 −0.494374 0.869249i \(-0.664603\pi\)
−0.494374 + 0.869249i \(0.664603\pi\)
\(332\) 8.96203 0.491855
\(333\) 13.7200 0.751854
\(334\) −6.13476 −0.335679
\(335\) 2.73141 0.149233
\(336\) −4.70927 −0.256912
\(337\) −12.0506 −0.656437 −0.328219 0.944602i \(-0.606448\pi\)
−0.328219 + 0.944602i \(0.606448\pi\)
\(338\) −8.06129 −0.438477
\(339\) 30.0400 1.63155
\(340\) 3.55928 0.193029
\(341\) 4.53528 0.245599
\(342\) −27.4168 −1.48253
\(343\) −19.3372 −1.04411
\(344\) −5.43299 −0.292927
\(345\) 14.4531 0.778129
\(346\) −6.25113 −0.336063
\(347\) 4.32749 0.232312 0.116156 0.993231i \(-0.462943\pi\)
0.116156 + 0.993231i \(0.462943\pi\)
\(348\) −11.3985 −0.611024
\(349\) 7.97325 0.426798 0.213399 0.976965i \(-0.431547\pi\)
0.213399 + 0.976965i \(0.431547\pi\)
\(350\) 7.65426 0.409138
\(351\) −10.8425 −0.578727
\(352\) −1.39811 −0.0745196
\(353\) 8.60601 0.458052 0.229026 0.973420i \(-0.426446\pi\)
0.229026 + 0.973420i \(0.426446\pi\)
\(354\) 39.4380 2.09611
\(355\) −4.44705 −0.236025
\(356\) −2.56615 −0.136006
\(357\) −19.6086 −1.03780
\(358\) 3.65995 0.193434
\(359\) −11.4828 −0.606040 −0.303020 0.952984i \(-0.597995\pi\)
−0.303020 + 0.952984i \(0.597995\pi\)
\(360\) −3.33329 −0.175680
\(361\) 30.4342 1.60180
\(362\) 17.3263 0.910652
\(363\) 23.7591 1.24703
\(364\) 8.22790 0.431259
\(365\) 3.92427 0.205406
\(366\) −26.9779 −1.41016
\(367\) −26.0578 −1.36021 −0.680104 0.733115i \(-0.738065\pi\)
−0.680104 + 0.733115i \(0.738065\pi\)
\(368\) −6.43702 −0.335553
\(369\) 28.9578 1.50748
\(370\) −3.00761 −0.156358
\(371\) 23.9163 1.24168
\(372\) −8.52059 −0.441772
\(373\) −28.1289 −1.45646 −0.728230 0.685333i \(-0.759657\pi\)
−0.728230 + 0.685333i \(0.759657\pi\)
\(374\) −5.82150 −0.301022
\(375\) 20.8125 1.07475
\(376\) −9.18945 −0.473910
\(377\) 19.9151 1.02568
\(378\) 4.23576 0.217864
\(379\) −21.9273 −1.12633 −0.563164 0.826345i \(-0.690416\pi\)
−0.563164 + 0.826345i \(0.690416\pi\)
\(380\) 6.01012 0.308312
\(381\) −23.7935 −1.21898
\(382\) −17.2881 −0.884534
\(383\) −18.4116 −0.940790 −0.470395 0.882456i \(-0.655889\pi\)
−0.470395 + 0.882456i \(0.655889\pi\)
\(384\) 2.62668 0.134042
\(385\) 2.14268 0.109201
\(386\) 15.8238 0.805412
\(387\) 21.1857 1.07693
\(388\) −13.9084 −0.706095
\(389\) −14.2023 −0.720086 −0.360043 0.932936i \(-0.617238\pi\)
−0.360043 + 0.932936i \(0.617238\pi\)
\(390\) 10.3043 0.521779
\(391\) −26.8026 −1.35547
\(392\) 3.78565 0.191204
\(393\) 9.99006 0.503932
\(394\) 12.0973 0.609455
\(395\) 11.0293 0.554945
\(396\) 5.45187 0.273967
\(397\) 12.4757 0.626140 0.313070 0.949730i \(-0.398643\pi\)
0.313070 + 0.949730i \(0.398643\pi\)
\(398\) 18.1581 0.910185
\(399\) −33.1106 −1.65761
\(400\) −4.26930 −0.213465
\(401\) −14.5417 −0.726176 −0.363088 0.931755i \(-0.618278\pi\)
−0.363088 + 0.931755i \(0.618278\pi\)
\(402\) 8.39314 0.418612
\(403\) 14.8869 0.741570
\(404\) −18.6206 −0.926411
\(405\) −4.69515 −0.233304
\(406\) −7.78014 −0.386122
\(407\) 4.91919 0.243835
\(408\) 10.9370 0.541464
\(409\) −33.6657 −1.66466 −0.832332 0.554278i \(-0.812994\pi\)
−0.832332 + 0.554278i \(0.812994\pi\)
\(410\) −6.34792 −0.313501
\(411\) −54.2534 −2.67612
\(412\) −7.47862 −0.368445
\(413\) 26.9187 1.32458
\(414\) 25.1008 1.23364
\(415\) 7.66082 0.376055
\(416\) −4.58926 −0.225007
\(417\) −17.8047 −0.871901
\(418\) −9.83005 −0.480803
\(419\) 14.6756 0.716952 0.358476 0.933539i \(-0.383296\pi\)
0.358476 + 0.933539i \(0.383296\pi\)
\(420\) −4.02553 −0.196426
\(421\) 8.02186 0.390962 0.195481 0.980708i \(-0.437373\pi\)
0.195481 + 0.980708i \(0.437373\pi\)
\(422\) 9.69641 0.472014
\(423\) 35.8338 1.74230
\(424\) −13.3398 −0.647836
\(425\) −17.7766 −0.862293
\(426\) −13.6650 −0.662073
\(427\) −18.4139 −0.891113
\(428\) 16.1348 0.779906
\(429\) −16.8536 −0.813698
\(430\) −4.64417 −0.223962
\(431\) −7.96699 −0.383757 −0.191878 0.981419i \(-0.561458\pi\)
−0.191878 + 0.981419i \(0.561458\pi\)
\(432\) −2.36257 −0.113669
\(433\) 11.7495 0.564647 0.282324 0.959319i \(-0.408895\pi\)
0.282324 + 0.959319i \(0.408895\pi\)
\(434\) −5.81579 −0.279167
\(435\) −9.74354 −0.467167
\(436\) 14.6084 0.699616
\(437\) −45.2583 −2.16500
\(438\) 12.0586 0.576183
\(439\) 23.9236 1.14181 0.570906 0.821016i \(-0.306592\pi\)
0.570906 + 0.821016i \(0.306592\pi\)
\(440\) −1.19512 −0.0569750
\(441\) −14.7620 −0.702950
\(442\) −19.1089 −0.908917
\(443\) −14.5183 −0.689785 −0.344893 0.938642i \(-0.612085\pi\)
−0.344893 + 0.938642i \(0.612085\pi\)
\(444\) −9.24186 −0.438599
\(445\) −2.19357 −0.103985
\(446\) 13.9655 0.661286
\(447\) −14.4763 −0.684707
\(448\) 1.79286 0.0847047
\(449\) −13.9199 −0.656923 −0.328461 0.944517i \(-0.606530\pi\)
−0.328461 + 0.944517i \(0.606530\pi\)
\(450\) 16.6479 0.784791
\(451\) 10.3826 0.488895
\(452\) −11.4365 −0.537928
\(453\) 24.7620 1.16342
\(454\) −8.81918 −0.413905
\(455\) 7.03329 0.329726
\(456\) 18.4681 0.864846
\(457\) 34.2333 1.60137 0.800683 0.599088i \(-0.204470\pi\)
0.800683 + 0.599088i \(0.204470\pi\)
\(458\) 17.8260 0.832952
\(459\) −9.83734 −0.459168
\(460\) −5.50242 −0.256552
\(461\) 30.6217 1.42619 0.713097 0.701065i \(-0.247292\pi\)
0.713097 + 0.701065i \(0.247292\pi\)
\(462\) 6.58409 0.306320
\(463\) 2.79958 0.130107 0.0650537 0.997882i \(-0.479278\pi\)
0.0650537 + 0.997882i \(0.479278\pi\)
\(464\) 4.33951 0.201457
\(465\) −7.28348 −0.337763
\(466\) 13.1809 0.610594
\(467\) 18.1898 0.841726 0.420863 0.907124i \(-0.361727\pi\)
0.420863 + 0.907124i \(0.361727\pi\)
\(468\) 17.8956 0.827224
\(469\) 5.72880 0.264532
\(470\) −7.85522 −0.362334
\(471\) 38.4227 1.77042
\(472\) −15.0144 −0.691093
\(473\) 7.59592 0.349261
\(474\) 33.8912 1.55667
\(475\) −30.0172 −1.37728
\(476\) 7.46516 0.342165
\(477\) 52.0178 2.38173
\(478\) −13.2733 −0.607107
\(479\) 11.2498 0.514014 0.257007 0.966409i \(-0.417264\pi\)
0.257007 + 0.966409i \(0.417264\pi\)
\(480\) 2.24531 0.102484
\(481\) 16.1471 0.736244
\(482\) 9.51088 0.433209
\(483\) 30.3137 1.37932
\(484\) −9.04528 −0.411149
\(485\) −11.8891 −0.539855
\(486\) −21.5151 −0.975945
\(487\) 0.183892 0.00833294 0.00416647 0.999991i \(-0.498674\pi\)
0.00416647 + 0.999991i \(0.498674\pi\)
\(488\) 10.2707 0.464933
\(489\) 3.08820 0.139653
\(490\) 3.23601 0.146188
\(491\) −13.3053 −0.600461 −0.300230 0.953867i \(-0.597064\pi\)
−0.300230 + 0.953867i \(0.597064\pi\)
\(492\) −19.5061 −0.879401
\(493\) 18.0690 0.813785
\(494\) −32.2668 −1.45175
\(495\) 4.66031 0.209465
\(496\) 3.24386 0.145654
\(497\) −9.32717 −0.418381
\(498\) 23.5404 1.05487
\(499\) −12.7933 −0.572707 −0.286353 0.958124i \(-0.592443\pi\)
−0.286353 + 0.958124i \(0.592443\pi\)
\(500\) −7.92348 −0.354349
\(501\) −16.1141 −0.719923
\(502\) 25.2709 1.12789
\(503\) 30.8891 1.37728 0.688638 0.725105i \(-0.258209\pi\)
0.688638 + 0.725105i \(0.258209\pi\)
\(504\) −6.99118 −0.311412
\(505\) −15.9171 −0.708301
\(506\) 8.99967 0.400084
\(507\) −21.1744 −0.940390
\(508\) 9.05839 0.401901
\(509\) −1.90594 −0.0844795 −0.0422397 0.999108i \(-0.513449\pi\)
−0.0422397 + 0.999108i \(0.513449\pi\)
\(510\) 9.34908 0.413984
\(511\) 8.23070 0.364105
\(512\) −1.00000 −0.0441942
\(513\) −16.6111 −0.733399
\(514\) −0.815232 −0.0359583
\(515\) −6.39279 −0.281700
\(516\) −14.2707 −0.628234
\(517\) 12.8479 0.565049
\(518\) −6.30810 −0.277162
\(519\) −16.4197 −0.720745
\(520\) −3.92294 −0.172032
\(521\) −13.2261 −0.579445 −0.289722 0.957111i \(-0.593563\pi\)
−0.289722 + 0.957111i \(0.593563\pi\)
\(522\) −16.9217 −0.740643
\(523\) −15.3727 −0.672200 −0.336100 0.941826i \(-0.609108\pi\)
−0.336100 + 0.941826i \(0.609108\pi\)
\(524\) −3.80330 −0.166148
\(525\) 20.1053 0.877468
\(526\) 25.4272 1.10868
\(527\) 13.5069 0.588369
\(528\) −3.67239 −0.159820
\(529\) 18.4352 0.801530
\(530\) −11.4030 −0.495313
\(531\) 58.5479 2.54076
\(532\) 12.6055 0.546518
\(533\) 34.0804 1.47619
\(534\) −6.74045 −0.291688
\(535\) 13.7922 0.596288
\(536\) −3.19534 −0.138018
\(537\) 9.61351 0.414853
\(538\) 18.1899 0.784223
\(539\) −5.29276 −0.227975
\(540\) −2.01955 −0.0869075
\(541\) 28.4009 1.22105 0.610525 0.791997i \(-0.290958\pi\)
0.610525 + 0.791997i \(0.290958\pi\)
\(542\) 9.42443 0.404814
\(543\) 45.5107 1.95305
\(544\) −4.16383 −0.178523
\(545\) 12.4874 0.534901
\(546\) 21.6121 0.924911
\(547\) 34.5878 1.47887 0.739434 0.673229i \(-0.235093\pi\)
0.739434 + 0.673229i \(0.235093\pi\)
\(548\) 20.6547 0.882326
\(549\) −40.0501 −1.70930
\(550\) 5.96896 0.254517
\(551\) 30.5109 1.29981
\(552\) −16.9080 −0.719652
\(553\) 23.1327 0.983702
\(554\) −22.4304 −0.952975
\(555\) −7.90002 −0.335337
\(556\) 6.77841 0.287469
\(557\) −24.9401 −1.05675 −0.528373 0.849012i \(-0.677198\pi\)
−0.528373 + 0.849012i \(0.677198\pi\)
\(558\) −12.6493 −0.535487
\(559\) 24.9334 1.05457
\(560\) 1.53255 0.0647622
\(561\) −15.2912 −0.645595
\(562\) −9.63200 −0.406302
\(563\) −26.1339 −1.10141 −0.550706 0.834699i \(-0.685642\pi\)
−0.550706 + 0.834699i \(0.685642\pi\)
\(564\) −24.1378 −1.01638
\(565\) −9.77603 −0.411280
\(566\) 18.2230 0.765969
\(567\) −9.84753 −0.413557
\(568\) 5.20239 0.218288
\(569\) −9.66767 −0.405290 −0.202645 0.979252i \(-0.564954\pi\)
−0.202645 + 0.979252i \(0.564954\pi\)
\(570\) 15.7867 0.661230
\(571\) 15.4616 0.647046 0.323523 0.946220i \(-0.395133\pi\)
0.323523 + 0.946220i \(0.395133\pi\)
\(572\) 6.41630 0.268279
\(573\) −45.4102 −1.89704
\(574\) −13.3140 −0.555716
\(575\) 27.4816 1.14606
\(576\) 3.89945 0.162477
\(577\) 26.6487 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(578\) −0.337458 −0.0140364
\(579\) 41.5641 1.72735
\(580\) 3.70945 0.154027
\(581\) 16.0677 0.666599
\(582\) −36.5331 −1.51434
\(583\) 18.6505 0.772424
\(584\) −4.59082 −0.189970
\(585\) 15.2973 0.632466
\(586\) −11.5816 −0.478432
\(587\) 5.65942 0.233589 0.116795 0.993156i \(-0.462738\pi\)
0.116795 + 0.993156i \(0.462738\pi\)
\(588\) 9.94369 0.410071
\(589\) 22.8074 0.939763
\(590\) −12.8344 −0.528385
\(591\) 31.7758 1.30708
\(592\) 3.51846 0.144608
\(593\) 18.9259 0.777195 0.388598 0.921408i \(-0.372960\pi\)
0.388598 + 0.921408i \(0.372960\pi\)
\(594\) 3.30314 0.135529
\(595\) 6.38129 0.261607
\(596\) 5.51127 0.225750
\(597\) 47.6956 1.95205
\(598\) 29.5411 1.20803
\(599\) −6.03648 −0.246644 −0.123322 0.992367i \(-0.539355\pi\)
−0.123322 + 0.992367i \(0.539355\pi\)
\(600\) −11.2141 −0.457813
\(601\) 13.7806 0.562122 0.281061 0.959690i \(-0.409314\pi\)
0.281061 + 0.959690i \(0.409314\pi\)
\(602\) −9.74059 −0.396997
\(603\) 12.4601 0.507414
\(604\) −9.42711 −0.383584
\(605\) −7.73199 −0.314350
\(606\) −48.9104 −1.98685
\(607\) 16.5217 0.670597 0.335298 0.942112i \(-0.391163\pi\)
0.335298 + 0.942112i \(0.391163\pi\)
\(608\) −7.03095 −0.285143
\(609\) −20.4359 −0.828106
\(610\) 8.77949 0.355471
\(611\) 42.1728 1.70613
\(612\) 16.2366 0.656327
\(613\) −26.2590 −1.06059 −0.530295 0.847813i \(-0.677919\pi\)
−0.530295 + 0.847813i \(0.677919\pi\)
\(614\) 24.7384 0.998360
\(615\) −16.6740 −0.672359
\(616\) −2.50662 −0.100995
\(617\) −32.8817 −1.32377 −0.661884 0.749607i \(-0.730243\pi\)
−0.661884 + 0.749607i \(0.730243\pi\)
\(618\) −19.6440 −0.790196
\(619\) −6.10571 −0.245409 −0.122705 0.992443i \(-0.539157\pi\)
−0.122705 + 0.992443i \(0.539157\pi\)
\(620\) 2.77288 0.111362
\(621\) 15.2079 0.610273
\(622\) −19.6832 −0.789225
\(623\) −4.60075 −0.184325
\(624\) −12.0545 −0.482567
\(625\) 14.5734 0.582938
\(626\) −26.9784 −1.07828
\(627\) −25.8204 −1.03117
\(628\) −14.6278 −0.583715
\(629\) 14.6502 0.584143
\(630\) −5.97612 −0.238094
\(631\) 41.1629 1.63867 0.819335 0.573315i \(-0.194343\pi\)
0.819335 + 0.573315i \(0.194343\pi\)
\(632\) −12.9027 −0.513241
\(633\) 25.4694 1.01232
\(634\) −5.08898 −0.202109
\(635\) 7.74319 0.307279
\(636\) −35.0393 −1.38940
\(637\) −17.3733 −0.688356
\(638\) −6.06712 −0.240200
\(639\) −20.2865 −0.802521
\(640\) −0.854809 −0.0337893
\(641\) −32.4758 −1.28272 −0.641359 0.767241i \(-0.721629\pi\)
−0.641359 + 0.767241i \(0.721629\pi\)
\(642\) 42.3810 1.67265
\(643\) 20.5401 0.810022 0.405011 0.914312i \(-0.367268\pi\)
0.405011 + 0.914312i \(0.367268\pi\)
\(644\) −11.5407 −0.454766
\(645\) −12.1987 −0.480325
\(646\) −29.2756 −1.15183
\(647\) −30.1269 −1.18441 −0.592205 0.805787i \(-0.701742\pi\)
−0.592205 + 0.805787i \(0.701742\pi\)
\(648\) 5.49263 0.215771
\(649\) 20.9918 0.824000
\(650\) 19.5929 0.768498
\(651\) −15.2762 −0.598723
\(652\) −1.17571 −0.0460442
\(653\) 42.0664 1.64619 0.823093 0.567906i \(-0.192246\pi\)
0.823093 + 0.567906i \(0.192246\pi\)
\(654\) 38.3716 1.50045
\(655\) −3.25110 −0.127031
\(656\) 7.42613 0.289942
\(657\) 17.9017 0.698411
\(658\) −16.4754 −0.642278
\(659\) −8.63696 −0.336448 −0.168224 0.985749i \(-0.553803\pi\)
−0.168224 + 0.985749i \(0.553803\pi\)
\(660\) −3.13919 −0.122193
\(661\) −46.9973 −1.82798 −0.913992 0.405733i \(-0.867016\pi\)
−0.913992 + 0.405733i \(0.867016\pi\)
\(662\) 17.9887 0.699151
\(663\) −50.1929 −1.94933
\(664\) −8.96203 −0.347794
\(665\) 10.7753 0.417848
\(666\) −13.7200 −0.531641
\(667\) −27.9335 −1.08159
\(668\) 6.13476 0.237361
\(669\) 36.6829 1.41824
\(670\) −2.73141 −0.105523
\(671\) −14.3596 −0.554346
\(672\) 4.70927 0.181664
\(673\) −5.05267 −0.194766 −0.0973830 0.995247i \(-0.531047\pi\)
−0.0973830 + 0.995247i \(0.531047\pi\)
\(674\) 12.0506 0.464171
\(675\) 10.0865 0.388231
\(676\) 8.06129 0.310050
\(677\) −8.93098 −0.343246 −0.171623 0.985163i \(-0.554901\pi\)
−0.171623 + 0.985163i \(0.554901\pi\)
\(678\) −30.0400 −1.15368
\(679\) −24.9359 −0.956953
\(680\) −3.55928 −0.136492
\(681\) −23.1652 −0.887691
\(682\) −4.53528 −0.173665
\(683\) 26.7911 1.02513 0.512566 0.858648i \(-0.328695\pi\)
0.512566 + 0.858648i \(0.328695\pi\)
\(684\) 27.4168 1.04831
\(685\) 17.6558 0.674595
\(686\) 19.3372 0.738297
\(687\) 46.8231 1.78641
\(688\) 5.43299 0.207131
\(689\) 61.2196 2.33228
\(690\) −14.4531 −0.550220
\(691\) 31.2062 1.18714 0.593571 0.804782i \(-0.297718\pi\)
0.593571 + 0.804782i \(0.297718\pi\)
\(692\) 6.25113 0.237632
\(693\) 9.77444 0.371300
\(694\) −4.32749 −0.164269
\(695\) 5.79425 0.219788
\(696\) 11.3985 0.432059
\(697\) 30.9211 1.17122
\(698\) −7.97325 −0.301792
\(699\) 34.6221 1.30953
\(700\) −7.65426 −0.289304
\(701\) −29.3651 −1.10910 −0.554552 0.832149i \(-0.687110\pi\)
−0.554552 + 0.832149i \(0.687110\pi\)
\(702\) 10.8425 0.409222
\(703\) 24.7381 0.933014
\(704\) 1.39811 0.0526933
\(705\) −20.6332 −0.777090
\(706\) −8.60601 −0.323892
\(707\) −33.3842 −1.25554
\(708\) −39.4380 −1.48217
\(709\) 19.6656 0.738558 0.369279 0.929319i \(-0.379605\pi\)
0.369279 + 0.929319i \(0.379605\pi\)
\(710\) 4.44705 0.166895
\(711\) 50.3133 1.88690
\(712\) 2.56615 0.0961704
\(713\) −20.8808 −0.781992
\(714\) 19.6086 0.733833
\(715\) 5.48471 0.205116
\(716\) −3.65995 −0.136779
\(717\) −34.8647 −1.30205
\(718\) 11.4828 0.428535
\(719\) −4.74756 −0.177054 −0.0885271 0.996074i \(-0.528216\pi\)
−0.0885271 + 0.996074i \(0.528216\pi\)
\(720\) 3.33329 0.124224
\(721\) −13.4081 −0.499345
\(722\) −30.4342 −1.13264
\(723\) 24.9820 0.929092
\(724\) −17.3263 −0.643928
\(725\) −18.5267 −0.688063
\(726\) −23.7591 −0.881782
\(727\) −3.26857 −0.121224 −0.0606122 0.998161i \(-0.519305\pi\)
−0.0606122 + 0.998161i \(0.519305\pi\)
\(728\) −8.22790 −0.304946
\(729\) −40.0354 −1.48279
\(730\) −3.92427 −0.145244
\(731\) 22.6220 0.836706
\(732\) 26.9779 0.997130
\(733\) −17.7987 −0.657411 −0.328706 0.944432i \(-0.606612\pi\)
−0.328706 + 0.944432i \(0.606612\pi\)
\(734\) 26.0578 0.961813
\(735\) 8.49996 0.313526
\(736\) 6.43702 0.237272
\(737\) 4.46745 0.164560
\(738\) −28.9578 −1.06595
\(739\) 22.1082 0.813262 0.406631 0.913593i \(-0.366704\pi\)
0.406631 + 0.913593i \(0.366704\pi\)
\(740\) 3.00761 0.110562
\(741\) −84.7547 −3.11354
\(742\) −23.9163 −0.877997
\(743\) 36.2103 1.32843 0.664214 0.747543i \(-0.268766\pi\)
0.664214 + 0.747543i \(0.268766\pi\)
\(744\) 8.52059 0.312380
\(745\) 4.71108 0.172601
\(746\) 28.1289 1.02987
\(747\) 34.9470 1.27864
\(748\) 5.82150 0.212855
\(749\) 28.9275 1.05699
\(750\) −20.8125 −0.759964
\(751\) 31.6501 1.15493 0.577465 0.816416i \(-0.304042\pi\)
0.577465 + 0.816416i \(0.304042\pi\)
\(752\) 9.18945 0.335105
\(753\) 66.3785 2.41897
\(754\) −19.9151 −0.725266
\(755\) −8.05838 −0.293274
\(756\) −4.23576 −0.154053
\(757\) 32.2734 1.17300 0.586499 0.809950i \(-0.300506\pi\)
0.586499 + 0.809950i \(0.300506\pi\)
\(758\) 21.9273 0.796434
\(759\) 23.6393 0.858051
\(760\) −6.01012 −0.218010
\(761\) 0.674180 0.0244390 0.0122195 0.999925i \(-0.496110\pi\)
0.0122195 + 0.999925i \(0.496110\pi\)
\(762\) 23.7935 0.861948
\(763\) 26.1909 0.948172
\(764\) 17.2881 0.625460
\(765\) 13.8792 0.501805
\(766\) 18.4116 0.665239
\(767\) 68.9049 2.48801
\(768\) −2.62668 −0.0947822
\(769\) 20.2062 0.728653 0.364326 0.931271i \(-0.381299\pi\)
0.364326 + 0.931271i \(0.381299\pi\)
\(770\) −2.14268 −0.0772169
\(771\) −2.14135 −0.0771190
\(772\) −15.8238 −0.569512
\(773\) −40.8794 −1.47033 −0.735165 0.677888i \(-0.762895\pi\)
−0.735165 + 0.677888i \(0.762895\pi\)
\(774\) −21.1857 −0.761503
\(775\) −13.8490 −0.497472
\(776\) 13.9084 0.499284
\(777\) −16.5694 −0.594423
\(778\) 14.2023 0.509178
\(779\) 52.2127 1.87071
\(780\) −10.3043 −0.368953
\(781\) −7.27353 −0.260267
\(782\) 26.8026 0.958460
\(783\) −10.2524 −0.366391
\(784\) −3.78565 −0.135202
\(785\) −12.5040 −0.446287
\(786\) −9.99006 −0.356334
\(787\) −0.586423 −0.0209037 −0.0104519 0.999945i \(-0.503327\pi\)
−0.0104519 + 0.999945i \(0.503327\pi\)
\(788\) −12.0973 −0.430950
\(789\) 66.7891 2.37776
\(790\) −11.0293 −0.392406
\(791\) −20.5041 −0.729040
\(792\) −5.45187 −0.193724
\(793\) −47.1349 −1.67381
\(794\) −12.4757 −0.442748
\(795\) −29.9519 −1.06229
\(796\) −18.1581 −0.643598
\(797\) 40.4574 1.43307 0.716537 0.697549i \(-0.245726\pi\)
0.716537 + 0.697549i \(0.245726\pi\)
\(798\) 33.1106 1.17210
\(799\) 38.2633 1.35366
\(800\) 4.26930 0.150943
\(801\) −10.0066 −0.353565
\(802\) 14.5417 0.513484
\(803\) 6.41848 0.226503
\(804\) −8.39314 −0.296003
\(805\) −9.86508 −0.347698
\(806\) −14.8869 −0.524369
\(807\) 47.7791 1.68190
\(808\) 18.6206 0.655071
\(809\) 26.7279 0.939704 0.469852 0.882745i \(-0.344307\pi\)
0.469852 + 0.882745i \(0.344307\pi\)
\(810\) 4.69515 0.164971
\(811\) −16.8999 −0.593435 −0.296717 0.954965i \(-0.595892\pi\)
−0.296717 + 0.954965i \(0.595892\pi\)
\(812\) 7.78014 0.273029
\(813\) 24.7550 0.868195
\(814\) −4.91919 −0.172418
\(815\) −1.00500 −0.0352038
\(816\) −10.9370 −0.382873
\(817\) 38.1990 1.33642
\(818\) 33.6657 1.17709
\(819\) 32.0843 1.12112
\(820\) 6.34792 0.221679
\(821\) −52.8740 −1.84532 −0.922658 0.385620i \(-0.873988\pi\)
−0.922658 + 0.385620i \(0.873988\pi\)
\(822\) 54.2534 1.89230
\(823\) 41.6115 1.45049 0.725243 0.688493i \(-0.241727\pi\)
0.725243 + 0.688493i \(0.241727\pi\)
\(824\) 7.47862 0.260530
\(825\) 15.6786 0.545857
\(826\) −26.9187 −0.936622
\(827\) −48.2422 −1.67754 −0.838772 0.544483i \(-0.816726\pi\)
−0.838772 + 0.544483i \(0.816726\pi\)
\(828\) −25.1008 −0.872314
\(829\) 27.6293 0.959605 0.479802 0.877377i \(-0.340708\pi\)
0.479802 + 0.877377i \(0.340708\pi\)
\(830\) −7.66082 −0.265911
\(831\) −58.9174 −2.04382
\(832\) 4.58926 0.159104
\(833\) −15.7628 −0.546148
\(834\) 17.8047 0.616527
\(835\) 5.24405 0.181478
\(836\) 9.83005 0.339979
\(837\) −7.66386 −0.264902
\(838\) −14.6756 −0.506962
\(839\) 38.7610 1.33818 0.669090 0.743182i \(-0.266684\pi\)
0.669090 + 0.743182i \(0.266684\pi\)
\(840\) 4.02553 0.138894
\(841\) −10.1687 −0.350643
\(842\) −8.02186 −0.276452
\(843\) −25.3002 −0.871385
\(844\) −9.69641 −0.333764
\(845\) 6.89087 0.237053
\(846\) −35.8338 −1.23199
\(847\) −16.2169 −0.557221
\(848\) 13.3398 0.458090
\(849\) 47.8659 1.64275
\(850\) 17.7766 0.609734
\(851\) −22.6484 −0.776376
\(852\) 13.6650 0.468156
\(853\) 26.2095 0.897397 0.448698 0.893683i \(-0.351888\pi\)
0.448698 + 0.893683i \(0.351888\pi\)
\(854\) 18.4139 0.630112
\(855\) 23.4362 0.801500
\(856\) −16.1348 −0.551477
\(857\) −18.9087 −0.645908 −0.322954 0.946415i \(-0.604676\pi\)
−0.322954 + 0.946415i \(0.604676\pi\)
\(858\) 16.8536 0.575371
\(859\) −44.9505 −1.53369 −0.766845 0.641832i \(-0.778175\pi\)
−0.766845 + 0.641832i \(0.778175\pi\)
\(860\) 4.64417 0.158365
\(861\) −34.9717 −1.19183
\(862\) 7.96699 0.271357
\(863\) 13.5828 0.462362 0.231181 0.972911i \(-0.425741\pi\)
0.231181 + 0.972911i \(0.425741\pi\)
\(864\) 2.36257 0.0803763
\(865\) 5.34352 0.181685
\(866\) −11.7495 −0.399266
\(867\) −0.886394 −0.0301035
\(868\) 5.81579 0.197401
\(869\) 18.0394 0.611944
\(870\) 9.74354 0.330337
\(871\) 14.6643 0.496879
\(872\) −14.6084 −0.494703
\(873\) −54.2353 −1.83559
\(874\) 45.2583 1.53089
\(875\) −14.2057 −0.480240
\(876\) −12.0586 −0.407423
\(877\) −21.6707 −0.731767 −0.365883 0.930661i \(-0.619233\pi\)
−0.365883 + 0.930661i \(0.619233\pi\)
\(878\) −23.9236 −0.807382
\(879\) −30.4212 −1.02608
\(880\) 1.19512 0.0402874
\(881\) −51.9407 −1.74993 −0.874963 0.484190i \(-0.839114\pi\)
−0.874963 + 0.484190i \(0.839114\pi\)
\(882\) 14.7620 0.497061
\(883\) −8.02180 −0.269955 −0.134978 0.990849i \(-0.543096\pi\)
−0.134978 + 0.990849i \(0.543096\pi\)
\(884\) 19.1089 0.642701
\(885\) −33.7120 −1.13321
\(886\) 14.5183 0.487752
\(887\) 53.2708 1.78866 0.894330 0.447408i \(-0.147653\pi\)
0.894330 + 0.447408i \(0.147653\pi\)
\(888\) 9.24186 0.310136
\(889\) 16.2404 0.544687
\(890\) 2.19357 0.0735285
\(891\) −7.67931 −0.257267
\(892\) −13.9655 −0.467600
\(893\) 64.6105 2.16211
\(894\) 14.4763 0.484161
\(895\) −3.12855 −0.104576
\(896\) −1.79286 −0.0598953
\(897\) 77.5951 2.59083
\(898\) 13.9199 0.464515
\(899\) 14.0768 0.469486
\(900\) −16.6479 −0.554931
\(901\) 55.5445 1.85046
\(902\) −10.3826 −0.345701
\(903\) −25.5854 −0.851430
\(904\) 11.4365 0.380372
\(905\) −14.8107 −0.492324
\(906\) −24.7620 −0.822663
\(907\) 35.1878 1.16839 0.584196 0.811613i \(-0.301410\pi\)
0.584196 + 0.811613i \(0.301410\pi\)
\(908\) 8.81918 0.292675
\(909\) −72.6102 −2.40833
\(910\) −7.03329 −0.233151
\(911\) 26.9190 0.891867 0.445934 0.895066i \(-0.352872\pi\)
0.445934 + 0.895066i \(0.352872\pi\)
\(912\) −18.4681 −0.611538
\(913\) 12.5299 0.414680
\(914\) −34.2333 −1.13234
\(915\) 23.0609 0.762370
\(916\) −17.8260 −0.588986
\(917\) −6.81879 −0.225176
\(918\) 9.83734 0.324681
\(919\) −18.4655 −0.609121 −0.304560 0.952493i \(-0.598510\pi\)
−0.304560 + 0.952493i \(0.598510\pi\)
\(920\) 5.50242 0.181409
\(921\) 64.9799 2.14116
\(922\) −30.6217 −1.00847
\(923\) −23.8751 −0.785859
\(924\) −6.58409 −0.216601
\(925\) −15.0213 −0.493899
\(926\) −2.79958 −0.0919998
\(927\) −29.1625 −0.957823
\(928\) −4.33951 −0.142451
\(929\) −7.28308 −0.238950 −0.119475 0.992837i \(-0.538121\pi\)
−0.119475 + 0.992837i \(0.538121\pi\)
\(930\) 7.28348 0.238835
\(931\) −26.6167 −0.872327
\(932\) −13.1809 −0.431755
\(933\) −51.7015 −1.69263
\(934\) −18.1898 −0.595190
\(935\) 4.97627 0.162741
\(936\) −17.8956 −0.584936
\(937\) −39.8225 −1.30095 −0.650473 0.759529i \(-0.725429\pi\)
−0.650473 + 0.759529i \(0.725429\pi\)
\(938\) −5.72880 −0.187052
\(939\) −70.8638 −2.31255
\(940\) 7.85522 0.256209
\(941\) −56.7318 −1.84940 −0.924702 0.380692i \(-0.875686\pi\)
−0.924702 + 0.380692i \(0.875686\pi\)
\(942\) −38.4227 −1.25188
\(943\) −47.8021 −1.55665
\(944\) 15.0144 0.488677
\(945\) −3.62077 −0.117784
\(946\) −7.59592 −0.246965
\(947\) 9.83411 0.319566 0.159783 0.987152i \(-0.448921\pi\)
0.159783 + 0.987152i \(0.448921\pi\)
\(948\) −33.8912 −1.10073
\(949\) 21.0685 0.683911
\(950\) 30.0172 0.973888
\(951\) −13.3671 −0.433459
\(952\) −7.46516 −0.241947
\(953\) 46.4862 1.50584 0.752918 0.658114i \(-0.228646\pi\)
0.752918 + 0.658114i \(0.228646\pi\)
\(954\) −52.0178 −1.68414
\(955\) 14.7780 0.478204
\(956\) 13.2733 0.429289
\(957\) −15.9364 −0.515150
\(958\) −11.2498 −0.363463
\(959\) 37.0311 1.19580
\(960\) −2.24531 −0.0724671
\(961\) −20.4774 −0.660560
\(962\) −16.1471 −0.520603
\(963\) 62.9170 2.02747
\(964\) −9.51088 −0.306325
\(965\) −13.5263 −0.435429
\(966\) −30.3137 −0.975327
\(967\) −43.1669 −1.38816 −0.694078 0.719900i \(-0.744188\pi\)
−0.694078 + 0.719900i \(0.744188\pi\)
\(968\) 9.04528 0.290726
\(969\) −76.8978 −2.47031
\(970\) 11.8891 0.381735
\(971\) −21.1048 −0.677287 −0.338643 0.940915i \(-0.609968\pi\)
−0.338643 + 0.940915i \(0.609968\pi\)
\(972\) 21.5151 0.690097
\(973\) 12.1527 0.389599
\(974\) −0.183892 −0.00589228
\(975\) 51.4644 1.64818
\(976\) −10.2707 −0.328757
\(977\) −55.5374 −1.77680 −0.888400 0.459070i \(-0.848183\pi\)
−0.888400 + 0.459070i \(0.848183\pi\)
\(978\) −3.08820 −0.0987499
\(979\) −3.58776 −0.114665
\(980\) −3.23601 −0.103370
\(981\) 56.9648 1.81875
\(982\) 13.3053 0.424590
\(983\) 16.7990 0.535803 0.267902 0.963446i \(-0.413670\pi\)
0.267902 + 0.963446i \(0.413670\pi\)
\(984\) 19.5061 0.621831
\(985\) −10.3409 −0.329489
\(986\) −18.0690 −0.575433
\(987\) −43.2756 −1.37748
\(988\) 32.2668 1.02654
\(989\) −34.9722 −1.11205
\(990\) −4.66031 −0.148114
\(991\) 36.2646 1.15198 0.575991 0.817456i \(-0.304616\pi\)
0.575991 + 0.817456i \(0.304616\pi\)
\(992\) −3.24386 −0.102993
\(993\) 47.2506 1.49945
\(994\) 9.32717 0.295840
\(995\) −15.5217 −0.492072
\(996\) −23.5404 −0.745906
\(997\) 35.8129 1.13420 0.567102 0.823647i \(-0.308064\pi\)
0.567102 + 0.823647i \(0.308064\pi\)
\(998\) 12.7933 0.404965
\(999\) −8.31261 −0.262999
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 \(a_p\))