Properties

Label 4003.2.a.b.1.10
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +O(q^{10})\) \(q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +6.62756 q^{10} -0.721924 q^{11} +9.48091 q^{12} -0.206828 q^{13} -11.1707 q^{14} -5.10977 q^{15} +8.96915 q^{16} -7.08863 q^{17} -2.60850 q^{18} -1.94126 q^{19} -12.0964 q^{20} +8.61246 q^{21} +1.87388 q^{22} +2.09017 q^{23} -14.2203 q^{24} +1.51939 q^{25} +0.536857 q^{26} -3.99258 q^{27} +20.3883 q^{28} +8.47645 q^{29} +13.2633 q^{30} +6.08423 q^{31} -9.06951 q^{32} -1.44474 q^{33} +18.3998 q^{34} -10.9884 q^{35} +4.76093 q^{36} -6.39528 q^{37} +5.03888 q^{38} -0.413911 q^{39} +18.1432 q^{40} -7.05441 q^{41} -22.3551 q^{42} +3.62781 q^{43} -3.42014 q^{44} -2.56592 q^{45} -5.42540 q^{46} +5.44070 q^{47} +17.9494 q^{48} +11.5207 q^{49} -3.94385 q^{50} -14.1860 q^{51} -0.979853 q^{52} -9.83848 q^{53} +10.3635 q^{54} +1.84330 q^{55} -30.5801 q^{56} -3.88491 q^{57} -22.0021 q^{58} +0.691090 q^{59} -24.2077 q^{60} -6.96355 q^{61} -15.7927 q^{62} +4.32483 q^{63} +5.60321 q^{64} +0.528095 q^{65} +3.75007 q^{66} -8.86068 q^{67} -33.5826 q^{68} +4.18291 q^{69} +28.5222 q^{70} +9.39470 q^{71} -7.14084 q^{72} +5.11110 q^{73} +16.6001 q^{74} +3.04066 q^{75} -9.19677 q^{76} -3.10685 q^{77} +1.07438 q^{78} -4.80909 q^{79} -22.9010 q^{80} -11.0049 q^{81} +18.3110 q^{82} -17.1284 q^{83} +40.8018 q^{84} +18.0995 q^{85} -9.41661 q^{86} +16.9634 q^{87} +5.12981 q^{88} -2.32434 q^{89} +6.66030 q^{90} -0.890098 q^{91} +9.90224 q^{92} +12.1760 q^{93} -14.1223 q^{94} +4.95663 q^{95} -18.1502 q^{96} -13.8575 q^{97} -29.9041 q^{98} -0.725489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59568 −1.83542 −0.917710 0.397251i \(-0.869964\pi\)
−0.917710 + 0.397251i \(0.869964\pi\)
\(3\) 2.00123 1.15541 0.577707 0.816245i \(-0.303948\pi\)
0.577707 + 0.816245i \(0.303948\pi\)
\(4\) 4.73753 2.36877
\(5\) −2.55331 −1.14187 −0.570937 0.820994i \(-0.693420\pi\)
−0.570937 + 0.820994i \(0.693420\pi\)
\(6\) −5.19456 −2.12067
\(7\) 4.30357 1.62660 0.813299 0.581846i \(-0.197669\pi\)
0.813299 + 0.581846i \(0.197669\pi\)
\(8\) −7.10575 −2.51226
\(9\) 1.00494 0.334980
\(10\) 6.62756 2.09582
\(11\) −0.721924 −0.217668 −0.108834 0.994060i \(-0.534712\pi\)
−0.108834 + 0.994060i \(0.534712\pi\)
\(12\) 9.48091 2.73690
\(13\) −0.206828 −0.0573637 −0.0286818 0.999589i \(-0.509131\pi\)
−0.0286818 + 0.999589i \(0.509131\pi\)
\(14\) −11.1707 −2.98549
\(15\) −5.10977 −1.31934
\(16\) 8.96915 2.24229
\(17\) −7.08863 −1.71925 −0.859623 0.510929i \(-0.829301\pi\)
−0.859623 + 0.510929i \(0.829301\pi\)
\(18\) −2.60850 −0.614828
\(19\) −1.94126 −0.445355 −0.222678 0.974892i \(-0.571480\pi\)
−0.222678 + 0.974892i \(0.571480\pi\)
\(20\) −12.0964 −2.70483
\(21\) 8.61246 1.87939
\(22\) 1.87388 0.399513
\(23\) 2.09017 0.435830 0.217915 0.975968i \(-0.430074\pi\)
0.217915 + 0.975968i \(0.430074\pi\)
\(24\) −14.2203 −2.90270
\(25\) 1.51939 0.303878
\(26\) 0.536857 0.105286
\(27\) −3.99258 −0.768373
\(28\) 20.3883 3.85303
\(29\) 8.47645 1.57404 0.787019 0.616929i \(-0.211624\pi\)
0.787019 + 0.616929i \(0.211624\pi\)
\(30\) 13.2633 2.42154
\(31\) 6.08423 1.09276 0.546380 0.837537i \(-0.316005\pi\)
0.546380 + 0.837537i \(0.316005\pi\)
\(32\) −9.06951 −1.60328
\(33\) −1.44474 −0.251497
\(34\) 18.3998 3.15554
\(35\) −10.9884 −1.85737
\(36\) 4.76093 0.793488
\(37\) −6.39528 −1.05138 −0.525689 0.850677i \(-0.676192\pi\)
−0.525689 + 0.850677i \(0.676192\pi\)
\(38\) 5.03888 0.817414
\(39\) −0.413911 −0.0662787
\(40\) 18.1432 2.86869
\(41\) −7.05441 −1.10171 −0.550857 0.834600i \(-0.685699\pi\)
−0.550857 + 0.834600i \(0.685699\pi\)
\(42\) −22.3551 −3.44947
\(43\) 3.62781 0.553236 0.276618 0.960980i \(-0.410786\pi\)
0.276618 + 0.960980i \(0.410786\pi\)
\(44\) −3.42014 −0.515605
\(45\) −2.56592 −0.382505
\(46\) −5.42540 −0.799931
\(47\) 5.44070 0.793608 0.396804 0.917903i \(-0.370119\pi\)
0.396804 + 0.917903i \(0.370119\pi\)
\(48\) 17.9494 2.59077
\(49\) 11.5207 1.64582
\(50\) −3.94385 −0.557744
\(51\) −14.1860 −1.98644
\(52\) −0.979853 −0.135881
\(53\) −9.83848 −1.35142 −0.675709 0.737168i \(-0.736163\pi\)
−0.675709 + 0.737168i \(0.736163\pi\)
\(54\) 10.3635 1.41029
\(55\) 1.84330 0.248550
\(56\) −30.5801 −4.08644
\(57\) −3.88491 −0.514569
\(58\) −22.0021 −2.88902
\(59\) 0.691090 0.0899722 0.0449861 0.998988i \(-0.485676\pi\)
0.0449861 + 0.998988i \(0.485676\pi\)
\(60\) −24.2077 −3.12520
\(61\) −6.96355 −0.891591 −0.445795 0.895135i \(-0.647079\pi\)
−0.445795 + 0.895135i \(0.647079\pi\)
\(62\) −15.7927 −2.00567
\(63\) 4.32483 0.544877
\(64\) 5.60321 0.700401
\(65\) 0.528095 0.0655021
\(66\) 3.75007 0.461602
\(67\) −8.86068 −1.08250 −0.541252 0.840860i \(-0.682050\pi\)
−0.541252 + 0.840860i \(0.682050\pi\)
\(68\) −33.5826 −4.07249
\(69\) 4.18291 0.503564
\(70\) 28.5222 3.40906
\(71\) 9.39470 1.11495 0.557473 0.830195i \(-0.311771\pi\)
0.557473 + 0.830195i \(0.311771\pi\)
\(72\) −7.14084 −0.841556
\(73\) 5.11110 0.598209 0.299105 0.954220i \(-0.403312\pi\)
0.299105 + 0.954220i \(0.403312\pi\)
\(74\) 16.6001 1.92972
\(75\) 3.04066 0.351105
\(76\) −9.19677 −1.05494
\(77\) −3.10685 −0.354059
\(78\) 1.07438 0.121649
\(79\) −4.80909 −0.541065 −0.270533 0.962711i \(-0.587200\pi\)
−0.270533 + 0.962711i \(0.587200\pi\)
\(80\) −22.9010 −2.56041
\(81\) −11.0049 −1.22277
\(82\) 18.3110 2.02211
\(83\) −17.1284 −1.88008 −0.940042 0.341060i \(-0.889214\pi\)
−0.940042 + 0.341060i \(0.889214\pi\)
\(84\) 40.8018 4.45184
\(85\) 18.0995 1.96316
\(86\) −9.41661 −1.01542
\(87\) 16.9634 1.81866
\(88\) 5.12981 0.546840
\(89\) −2.32434 −0.246379 −0.123190 0.992383i \(-0.539312\pi\)
−0.123190 + 0.992383i \(0.539312\pi\)
\(90\) 6.66030 0.702057
\(91\) −0.890098 −0.0933076
\(92\) 9.90224 1.03238
\(93\) 12.1760 1.26259
\(94\) −14.1223 −1.45660
\(95\) 4.95663 0.508540
\(96\) −18.1502 −1.85245
\(97\) −13.8575 −1.40701 −0.703506 0.710690i \(-0.748383\pi\)
−0.703506 + 0.710690i \(0.748383\pi\)
\(98\) −29.9041 −3.02077
\(99\) −0.725489 −0.0729144
\(100\) 7.19817 0.719817
\(101\) −3.60538 −0.358749 −0.179375 0.983781i \(-0.557407\pi\)
−0.179375 + 0.983781i \(0.557407\pi\)
\(102\) 36.8223 3.64595
\(103\) 8.87257 0.874240 0.437120 0.899403i \(-0.355999\pi\)
0.437120 + 0.899403i \(0.355999\pi\)
\(104\) 1.46966 0.144112
\(105\) −21.9903 −2.14603
\(106\) 25.5375 2.48042
\(107\) 16.8512 1.62906 0.814531 0.580120i \(-0.196994\pi\)
0.814531 + 0.580120i \(0.196994\pi\)
\(108\) −18.9150 −1.82010
\(109\) 16.7958 1.60875 0.804375 0.594122i \(-0.202500\pi\)
0.804375 + 0.594122i \(0.202500\pi\)
\(110\) −4.78460 −0.456194
\(111\) −12.7985 −1.21478
\(112\) 38.5994 3.64730
\(113\) −13.9405 −1.31141 −0.655705 0.755017i \(-0.727628\pi\)
−0.655705 + 0.755017i \(0.727628\pi\)
\(114\) 10.0840 0.944451
\(115\) −5.33685 −0.497663
\(116\) 40.1575 3.72853
\(117\) −0.207849 −0.0192157
\(118\) −1.79385 −0.165137
\(119\) −30.5064 −2.79652
\(120\) 36.3087 3.31452
\(121\) −10.4788 −0.952621
\(122\) 18.0751 1.63644
\(123\) −14.1175 −1.27293
\(124\) 28.8243 2.58849
\(125\) 8.88707 0.794884
\(126\) −11.2258 −1.00008
\(127\) −19.6273 −1.74164 −0.870821 0.491601i \(-0.836412\pi\)
−0.870821 + 0.491601i \(0.836412\pi\)
\(128\) 3.59490 0.317748
\(129\) 7.26009 0.639216
\(130\) −1.37076 −0.120224
\(131\) 3.23261 0.282434 0.141217 0.989979i \(-0.454898\pi\)
0.141217 + 0.989979i \(0.454898\pi\)
\(132\) −6.84450 −0.595737
\(133\) −8.35434 −0.724414
\(134\) 22.9995 1.98685
\(135\) 10.1943 0.877386
\(136\) 50.3700 4.31919
\(137\) −18.0969 −1.54612 −0.773059 0.634334i \(-0.781274\pi\)
−0.773059 + 0.634334i \(0.781274\pi\)
\(138\) −10.8575 −0.924251
\(139\) −13.6873 −1.16094 −0.580471 0.814281i \(-0.697132\pi\)
−0.580471 + 0.814281i \(0.697132\pi\)
\(140\) −52.0577 −4.39968
\(141\) 10.8881 0.916945
\(142\) −24.3856 −2.04639
\(143\) 0.149314 0.0124862
\(144\) 9.01345 0.751121
\(145\) −21.6430 −1.79735
\(146\) −13.2668 −1.09797
\(147\) 23.0557 1.90160
\(148\) −30.2979 −2.49047
\(149\) −23.1111 −1.89334 −0.946669 0.322209i \(-0.895575\pi\)
−0.946669 + 0.322209i \(0.895575\pi\)
\(150\) −7.89256 −0.644425
\(151\) −12.3167 −1.00232 −0.501160 0.865355i \(-0.667093\pi\)
−0.501160 + 0.865355i \(0.667093\pi\)
\(152\) 13.7941 1.11885
\(153\) −7.12364 −0.575912
\(154\) 8.06438 0.649846
\(155\) −15.5349 −1.24780
\(156\) −1.96091 −0.156999
\(157\) 13.6451 1.08900 0.544499 0.838761i \(-0.316720\pi\)
0.544499 + 0.838761i \(0.316720\pi\)
\(158\) 12.4828 0.993082
\(159\) −19.6891 −1.56145
\(160\) 23.1573 1.83074
\(161\) 8.99519 0.708920
\(162\) 28.5652 2.24429
\(163\) 8.61674 0.674915 0.337458 0.941341i \(-0.390433\pi\)
0.337458 + 0.941341i \(0.390433\pi\)
\(164\) −33.4205 −2.60970
\(165\) 3.68887 0.287178
\(166\) 44.4597 3.45074
\(167\) 6.94325 0.537285 0.268643 0.963240i \(-0.413425\pi\)
0.268643 + 0.963240i \(0.413425\pi\)
\(168\) −61.1979 −4.72152
\(169\) −12.9572 −0.996709
\(170\) −46.9804 −3.60323
\(171\) −1.95085 −0.149185
\(172\) 17.1869 1.31049
\(173\) 7.86537 0.597993 0.298996 0.954254i \(-0.403348\pi\)
0.298996 + 0.954254i \(0.403348\pi\)
\(174\) −44.0314 −3.33801
\(175\) 6.53881 0.494288
\(176\) −6.47504 −0.488075
\(177\) 1.38303 0.103955
\(178\) 6.03323 0.452210
\(179\) 2.97368 0.222264 0.111132 0.993806i \(-0.464552\pi\)
0.111132 + 0.993806i \(0.464552\pi\)
\(180\) −12.1561 −0.906065
\(181\) −5.08216 −0.377754 −0.188877 0.982001i \(-0.560485\pi\)
−0.188877 + 0.982001i \(0.560485\pi\)
\(182\) 2.31040 0.171259
\(183\) −13.9357 −1.03016
\(184\) −14.8522 −1.09492
\(185\) 16.3291 1.20054
\(186\) −31.6049 −2.31738
\(187\) 5.11745 0.374225
\(188\) 25.7755 1.87987
\(189\) −17.1824 −1.24983
\(190\) −12.8658 −0.933384
\(191\) 5.12984 0.371182 0.185591 0.982627i \(-0.440580\pi\)
0.185591 + 0.982627i \(0.440580\pi\)
\(192\) 11.2133 0.809253
\(193\) 0.0765360 0.00550918 0.00275459 0.999996i \(-0.499123\pi\)
0.00275459 + 0.999996i \(0.499123\pi\)
\(194\) 35.9695 2.58246
\(195\) 1.05684 0.0756820
\(196\) 54.5799 3.89856
\(197\) −3.04659 −0.217060 −0.108530 0.994093i \(-0.534614\pi\)
−0.108530 + 0.994093i \(0.534614\pi\)
\(198\) 1.88314 0.133829
\(199\) −7.88995 −0.559304 −0.279652 0.960101i \(-0.590219\pi\)
−0.279652 + 0.960101i \(0.590219\pi\)
\(200\) −10.7964 −0.763422
\(201\) −17.7323 −1.25074
\(202\) 9.35841 0.658455
\(203\) 36.4790 2.56033
\(204\) −67.2067 −4.70541
\(205\) 18.0121 1.25802
\(206\) −23.0303 −1.60460
\(207\) 2.10049 0.145994
\(208\) −1.85507 −0.128626
\(209\) 1.40144 0.0969397
\(210\) 57.0796 3.93887
\(211\) −6.42169 −0.442087 −0.221044 0.975264i \(-0.570946\pi\)
−0.221044 + 0.975264i \(0.570946\pi\)
\(212\) −46.6101 −3.20120
\(213\) 18.8010 1.28822
\(214\) −43.7401 −2.99001
\(215\) −9.26292 −0.631726
\(216\) 28.3703 1.93035
\(217\) 26.1839 1.77748
\(218\) −43.5965 −2.95273
\(219\) 10.2285 0.691179
\(220\) 8.73267 0.588757
\(221\) 1.46612 0.0986222
\(222\) 33.2206 2.22962
\(223\) 13.6758 0.915802 0.457901 0.889003i \(-0.348601\pi\)
0.457901 + 0.889003i \(0.348601\pi\)
\(224\) −39.0313 −2.60789
\(225\) 1.52690 0.101793
\(226\) 36.1850 2.40699
\(227\) −19.9865 −1.32655 −0.663275 0.748376i \(-0.730834\pi\)
−0.663275 + 0.748376i \(0.730834\pi\)
\(228\) −18.4049 −1.21889
\(229\) 11.7776 0.778287 0.389143 0.921177i \(-0.372771\pi\)
0.389143 + 0.921177i \(0.372771\pi\)
\(230\) 13.8527 0.913421
\(231\) −6.21754 −0.409084
\(232\) −60.2315 −3.95439
\(233\) 15.8305 1.03709 0.518546 0.855050i \(-0.326474\pi\)
0.518546 + 0.855050i \(0.326474\pi\)
\(234\) 0.539509 0.0352688
\(235\) −13.8918 −0.906201
\(236\) 3.27406 0.213123
\(237\) −9.62412 −0.625154
\(238\) 79.1848 5.13279
\(239\) 6.92240 0.447773 0.223886 0.974615i \(-0.428126\pi\)
0.223886 + 0.974615i \(0.428126\pi\)
\(240\) −45.8303 −2.95833
\(241\) 0.325562 0.0209713 0.0104857 0.999945i \(-0.496662\pi\)
0.0104857 + 0.999945i \(0.496662\pi\)
\(242\) 27.1996 1.74846
\(243\) −10.0457 −0.644429
\(244\) −32.9900 −2.11197
\(245\) −29.4160 −1.87932
\(246\) 36.6445 2.33637
\(247\) 0.401506 0.0255472
\(248\) −43.2330 −2.74530
\(249\) −34.2779 −2.17227
\(250\) −23.0680 −1.45895
\(251\) −21.4115 −1.35148 −0.675742 0.737139i \(-0.736176\pi\)
−0.675742 + 0.737139i \(0.736176\pi\)
\(252\) 20.4890 1.29069
\(253\) −1.50894 −0.0948664
\(254\) 50.9461 3.19664
\(255\) 36.2213 2.26826
\(256\) −20.5376 −1.28360
\(257\) −10.5944 −0.660859 −0.330429 0.943831i \(-0.607194\pi\)
−0.330429 + 0.943831i \(0.607194\pi\)
\(258\) −18.8449 −1.17323
\(259\) −27.5226 −1.71017
\(260\) 2.50187 0.155159
\(261\) 8.51831 0.527270
\(262\) −8.39080 −0.518385
\(263\) 17.4834 1.07807 0.539036 0.842283i \(-0.318789\pi\)
0.539036 + 0.842283i \(0.318789\pi\)
\(264\) 10.2660 0.631826
\(265\) 25.1207 1.54315
\(266\) 21.6852 1.32960
\(267\) −4.65155 −0.284670
\(268\) −41.9778 −2.56420
\(269\) −26.6456 −1.62461 −0.812304 0.583234i \(-0.801787\pi\)
−0.812304 + 0.583234i \(0.801787\pi\)
\(270\) −26.4611 −1.61037
\(271\) 20.5733 1.24974 0.624869 0.780729i \(-0.285152\pi\)
0.624869 + 0.780729i \(0.285152\pi\)
\(272\) −63.5790 −3.85504
\(273\) −1.78129 −0.107809
\(274\) 46.9736 2.83778
\(275\) −1.09689 −0.0661447
\(276\) 19.8167 1.19282
\(277\) −3.76363 −0.226135 −0.113067 0.993587i \(-0.536068\pi\)
−0.113067 + 0.993587i \(0.536068\pi\)
\(278\) 35.5278 2.13082
\(279\) 6.11428 0.366053
\(280\) 78.0805 4.66620
\(281\) −11.3890 −0.679410 −0.339705 0.940532i \(-0.610327\pi\)
−0.339705 + 0.940532i \(0.610327\pi\)
\(282\) −28.2620 −1.68298
\(283\) 0.567111 0.0337112 0.0168556 0.999858i \(-0.494634\pi\)
0.0168556 + 0.999858i \(0.494634\pi\)
\(284\) 44.5077 2.64105
\(285\) 9.91938 0.587574
\(286\) −0.387570 −0.0229175
\(287\) −30.3592 −1.79204
\(288\) −9.11430 −0.537066
\(289\) 33.2487 1.95580
\(290\) 56.1782 3.29890
\(291\) −27.7320 −1.62568
\(292\) 24.2140 1.41702
\(293\) 2.61408 0.152716 0.0763580 0.997080i \(-0.475671\pi\)
0.0763580 + 0.997080i \(0.475671\pi\)
\(294\) −59.8451 −3.49024
\(295\) −1.76457 −0.102737
\(296\) 45.4432 2.64134
\(297\) 2.88234 0.167250
\(298\) 59.9890 3.47507
\(299\) −0.432304 −0.0250008
\(300\) 14.4052 0.831686
\(301\) 15.6125 0.899892
\(302\) 31.9702 1.83968
\(303\) −7.21522 −0.414503
\(304\) −17.4114 −0.998614
\(305\) 17.7801 1.01809
\(306\) 18.4907 1.05704
\(307\) −8.62811 −0.492432 −0.246216 0.969215i \(-0.579187\pi\)
−0.246216 + 0.969215i \(0.579187\pi\)
\(308\) −14.7188 −0.838682
\(309\) 17.7561 1.01011
\(310\) 40.3236 2.29023
\(311\) 21.7248 1.23190 0.615950 0.787785i \(-0.288772\pi\)
0.615950 + 0.787785i \(0.288772\pi\)
\(312\) 2.94114 0.166509
\(313\) 10.7355 0.606808 0.303404 0.952862i \(-0.401877\pi\)
0.303404 + 0.952862i \(0.401877\pi\)
\(314\) −35.4183 −1.99877
\(315\) −11.0426 −0.622181
\(316\) −22.7832 −1.28166
\(317\) 18.6947 1.05000 0.524999 0.851103i \(-0.324066\pi\)
0.524999 + 0.851103i \(0.324066\pi\)
\(318\) 51.1065 2.86591
\(319\) −6.11935 −0.342618
\(320\) −14.3067 −0.799771
\(321\) 33.7231 1.88224
\(322\) −23.3486 −1.30117
\(323\) 13.7609 0.765675
\(324\) −52.1361 −2.89645
\(325\) −0.314252 −0.0174316
\(326\) −22.3663 −1.23875
\(327\) 33.6124 1.85877
\(328\) 50.1269 2.76779
\(329\) 23.4144 1.29088
\(330\) −9.57510 −0.527092
\(331\) −4.93993 −0.271523 −0.135762 0.990742i \(-0.543348\pi\)
−0.135762 + 0.990742i \(0.543348\pi\)
\(332\) −81.1462 −4.45348
\(333\) −6.42687 −0.352190
\(334\) −18.0224 −0.986144
\(335\) 22.6241 1.23608
\(336\) 77.2464 4.21414
\(337\) −7.88706 −0.429635 −0.214818 0.976654i \(-0.568916\pi\)
−0.214818 + 0.976654i \(0.568916\pi\)
\(338\) 33.6327 1.82938
\(339\) −27.8982 −1.51522
\(340\) 85.7468 4.65027
\(341\) −4.39235 −0.237859
\(342\) 5.06376 0.273817
\(343\) 19.4553 1.05049
\(344\) −25.7783 −1.38987
\(345\) −10.6803 −0.575007
\(346\) −20.4159 −1.09757
\(347\) −9.17487 −0.492533 −0.246266 0.969202i \(-0.579204\pi\)
−0.246266 + 0.969202i \(0.579204\pi\)
\(348\) 80.3645 4.30799
\(349\) 16.9457 0.907081 0.453541 0.891236i \(-0.350161\pi\)
0.453541 + 0.891236i \(0.350161\pi\)
\(350\) −16.9726 −0.907225
\(351\) 0.825777 0.0440767
\(352\) 6.54750 0.348983
\(353\) −29.5867 −1.57474 −0.787371 0.616480i \(-0.788558\pi\)
−0.787371 + 0.616480i \(0.788558\pi\)
\(354\) −3.58991 −0.190801
\(355\) −23.9876 −1.27313
\(356\) −11.0116 −0.583615
\(357\) −61.0505 −3.23114
\(358\) −7.71872 −0.407947
\(359\) 10.3798 0.547826 0.273913 0.961754i \(-0.411682\pi\)
0.273913 + 0.961754i \(0.411682\pi\)
\(360\) 18.2328 0.960952
\(361\) −15.2315 −0.801659
\(362\) 13.1916 0.693337
\(363\) −20.9706 −1.10067
\(364\) −4.21687 −0.221024
\(365\) −13.0502 −0.683080
\(366\) 36.1725 1.89077
\(367\) −13.6717 −0.713656 −0.356828 0.934170i \(-0.616142\pi\)
−0.356828 + 0.934170i \(0.616142\pi\)
\(368\) 18.7470 0.977256
\(369\) −7.08925 −0.369052
\(370\) −42.3851 −2.20350
\(371\) −42.3406 −2.19821
\(372\) 57.6841 2.99078
\(373\) −35.9774 −1.86284 −0.931421 0.363944i \(-0.881430\pi\)
−0.931421 + 0.363944i \(0.881430\pi\)
\(374\) −13.2832 −0.686860
\(375\) 17.7851 0.918419
\(376\) −38.6602 −1.99375
\(377\) −1.75316 −0.0902925
\(378\) 44.5999 2.29397
\(379\) −0.840472 −0.0431721 −0.0215861 0.999767i \(-0.506872\pi\)
−0.0215861 + 0.999767i \(0.506872\pi\)
\(380\) 23.4822 1.20461
\(381\) −39.2788 −2.01232
\(382\) −13.3154 −0.681275
\(383\) 12.6758 0.647701 0.323851 0.946108i \(-0.395022\pi\)
0.323851 + 0.946108i \(0.395022\pi\)
\(384\) 7.19425 0.367130
\(385\) 7.93276 0.404291
\(386\) −0.198663 −0.0101117
\(387\) 3.64573 0.185323
\(388\) −65.6501 −3.33288
\(389\) 28.9552 1.46809 0.734044 0.679102i \(-0.237631\pi\)
0.734044 + 0.679102i \(0.237631\pi\)
\(390\) −2.74322 −0.138908
\(391\) −14.8164 −0.749299
\(392\) −81.8634 −4.13473
\(393\) 6.46920 0.326328
\(394\) 7.90795 0.398397
\(395\) 12.2791 0.617829
\(396\) −3.43703 −0.172717
\(397\) −14.1889 −0.712122 −0.356061 0.934463i \(-0.615880\pi\)
−0.356061 + 0.934463i \(0.615880\pi\)
\(398\) 20.4797 1.02656
\(399\) −16.7190 −0.836997
\(400\) 13.6276 0.681382
\(401\) 19.1715 0.957377 0.478689 0.877985i \(-0.341112\pi\)
0.478689 + 0.877985i \(0.341112\pi\)
\(402\) 46.0273 2.29563
\(403\) −1.25839 −0.0626847
\(404\) −17.0806 −0.849793
\(405\) 28.0990 1.39625
\(406\) −94.6877 −4.69927
\(407\) 4.61691 0.228852
\(408\) 100.802 4.99045
\(409\) −0.791300 −0.0391273 −0.0195636 0.999809i \(-0.506228\pi\)
−0.0195636 + 0.999809i \(0.506228\pi\)
\(410\) −46.7536 −2.30899
\(411\) −36.2160 −1.78641
\(412\) 42.0341 2.07087
\(413\) 2.97416 0.146349
\(414\) −5.45219 −0.267961
\(415\) 43.7340 2.14682
\(416\) 1.87583 0.0919699
\(417\) −27.3915 −1.34137
\(418\) −3.63769 −0.177925
\(419\) −11.7406 −0.573566 −0.286783 0.957996i \(-0.592586\pi\)
−0.286783 + 0.957996i \(0.592586\pi\)
\(420\) −104.180 −5.08345
\(421\) −4.31636 −0.210366 −0.105183 0.994453i \(-0.533543\pi\)
−0.105183 + 0.994453i \(0.533543\pi\)
\(422\) 16.6686 0.811416
\(423\) 5.46757 0.265842
\(424\) 69.9097 3.39512
\(425\) −10.7704 −0.522441
\(426\) −48.8013 −2.36443
\(427\) −29.9681 −1.45026
\(428\) 79.8329 3.85887
\(429\) 0.298812 0.0144268
\(430\) 24.0435 1.15948
\(431\) −10.8071 −0.520558 −0.260279 0.965533i \(-0.583815\pi\)
−0.260279 + 0.965533i \(0.583815\pi\)
\(432\) −35.8101 −1.72291
\(433\) −3.33623 −0.160329 −0.0801644 0.996782i \(-0.525545\pi\)
−0.0801644 + 0.996782i \(0.525545\pi\)
\(434\) −67.9650 −3.26243
\(435\) −43.3127 −2.07669
\(436\) 79.5708 3.81075
\(437\) −4.05755 −0.194099
\(438\) −26.5499 −1.26860
\(439\) −22.6093 −1.07908 −0.539541 0.841960i \(-0.681402\pi\)
−0.539541 + 0.841960i \(0.681402\pi\)
\(440\) −13.0980 −0.624422
\(441\) 11.5776 0.551316
\(442\) −3.80558 −0.181013
\(443\) −41.8565 −1.98866 −0.994331 0.106331i \(-0.966090\pi\)
−0.994331 + 0.106331i \(0.966090\pi\)
\(444\) −60.6331 −2.87752
\(445\) 5.93476 0.281334
\(446\) −35.4980 −1.68088
\(447\) −46.2508 −2.18759
\(448\) 24.1138 1.13927
\(449\) 27.2518 1.28609 0.643045 0.765828i \(-0.277671\pi\)
0.643045 + 0.765828i \(0.277671\pi\)
\(450\) −3.96333 −0.186833
\(451\) 5.09275 0.239808
\(452\) −66.0435 −3.10642
\(453\) −24.6486 −1.15809
\(454\) 51.8785 2.43478
\(455\) 2.27270 0.106546
\(456\) 27.6052 1.29273
\(457\) 10.6382 0.497633 0.248817 0.968551i \(-0.419958\pi\)
0.248817 + 0.968551i \(0.419958\pi\)
\(458\) −30.5709 −1.42848
\(459\) 28.3020 1.32102
\(460\) −25.2835 −1.17885
\(461\) 18.9352 0.881900 0.440950 0.897532i \(-0.354642\pi\)
0.440950 + 0.897532i \(0.354642\pi\)
\(462\) 16.1387 0.750841
\(463\) −27.1296 −1.26082 −0.630409 0.776263i \(-0.717113\pi\)
−0.630409 + 0.776263i \(0.717113\pi\)
\(464\) 76.0266 3.52944
\(465\) −31.0890 −1.44172
\(466\) −41.0909 −1.90350
\(467\) −17.9118 −0.828858 −0.414429 0.910082i \(-0.636019\pi\)
−0.414429 + 0.910082i \(0.636019\pi\)
\(468\) −0.984692 −0.0455174
\(469\) −38.1326 −1.76080
\(470\) 36.0586 1.66326
\(471\) 27.3071 1.25824
\(472\) −4.91071 −0.226034
\(473\) −2.61900 −0.120422
\(474\) 24.9811 1.14742
\(475\) −2.94953 −0.135334
\(476\) −144.525 −6.62430
\(477\) −9.88707 −0.452698
\(478\) −17.9683 −0.821851
\(479\) 7.51390 0.343319 0.171659 0.985156i \(-0.445087\pi\)
0.171659 + 0.985156i \(0.445087\pi\)
\(480\) 46.3431 2.11526
\(481\) 1.32272 0.0603109
\(482\) −0.845054 −0.0384911
\(483\) 18.0015 0.819096
\(484\) −49.6438 −2.25654
\(485\) 35.3824 1.60663
\(486\) 26.0753 1.18280
\(487\) −35.4930 −1.60834 −0.804171 0.594398i \(-0.797390\pi\)
−0.804171 + 0.594398i \(0.797390\pi\)
\(488\) 49.4812 2.23991
\(489\) 17.2441 0.779806
\(490\) 76.3544 3.44934
\(491\) −16.9482 −0.764862 −0.382431 0.923984i \(-0.624913\pi\)
−0.382431 + 0.923984i \(0.624913\pi\)
\(492\) −66.8822 −3.01528
\(493\) −60.0864 −2.70616
\(494\) −1.04218 −0.0468898
\(495\) 1.85240 0.0832592
\(496\) 54.5704 2.45028
\(497\) 40.4308 1.81357
\(498\) 88.9743 3.98703
\(499\) −2.64920 −0.118594 −0.0592972 0.998240i \(-0.518886\pi\)
−0.0592972 + 0.998240i \(0.518886\pi\)
\(500\) 42.1028 1.88289
\(501\) 13.8951 0.620786
\(502\) 55.5774 2.48054
\(503\) −4.63993 −0.206884 −0.103442 0.994635i \(-0.532986\pi\)
−0.103442 + 0.994635i \(0.532986\pi\)
\(504\) −30.7311 −1.36887
\(505\) 9.20566 0.409647
\(506\) 3.91672 0.174120
\(507\) −25.9304 −1.15161
\(508\) −92.9850 −4.12554
\(509\) 16.2144 0.718691 0.359346 0.933205i \(-0.383000\pi\)
0.359346 + 0.933205i \(0.383000\pi\)
\(510\) −94.0187 −4.16322
\(511\) 21.9960 0.973046
\(512\) 46.1192 2.03820
\(513\) 7.75064 0.342199
\(514\) 27.4995 1.21295
\(515\) −22.6544 −0.998273
\(516\) 34.3949 1.51415
\(517\) −3.92777 −0.172743
\(518\) 71.4396 3.13888
\(519\) 15.7404 0.690929
\(520\) −3.75251 −0.164558
\(521\) 11.5085 0.504195 0.252098 0.967702i \(-0.418880\pi\)
0.252098 + 0.967702i \(0.418880\pi\)
\(522\) −22.1108 −0.967763
\(523\) −27.8895 −1.21952 −0.609760 0.792586i \(-0.708734\pi\)
−0.609760 + 0.792586i \(0.708734\pi\)
\(524\) 15.3146 0.669021
\(525\) 13.0857 0.571106
\(526\) −45.3812 −1.97871
\(527\) −43.1289 −1.87872
\(528\) −12.9581 −0.563928
\(529\) −18.6312 −0.810052
\(530\) −65.2052 −2.83233
\(531\) 0.694503 0.0301389
\(532\) −39.5790 −1.71597
\(533\) 1.45905 0.0631983
\(534\) 12.0739 0.522489
\(535\) −43.0262 −1.86019
\(536\) 62.9618 2.71953
\(537\) 5.95104 0.256806
\(538\) 69.1632 2.98184
\(539\) −8.31710 −0.358243
\(540\) 48.2959 2.07832
\(541\) 38.3438 1.64853 0.824264 0.566206i \(-0.191589\pi\)
0.824264 + 0.566206i \(0.191589\pi\)
\(542\) −53.4016 −2.29379
\(543\) −10.1706 −0.436462
\(544\) 64.2904 2.75643
\(545\) −42.8850 −1.83699
\(546\) 4.62366 0.197874
\(547\) −13.2293 −0.565646 −0.282823 0.959172i \(-0.591271\pi\)
−0.282823 + 0.959172i \(0.591271\pi\)
\(548\) −85.7344 −3.66239
\(549\) −6.99794 −0.298665
\(550\) 2.84716 0.121403
\(551\) −16.4550 −0.701006
\(552\) −29.7227 −1.26508
\(553\) −20.6963 −0.880095
\(554\) 9.76917 0.415052
\(555\) 32.6784 1.38712
\(556\) −64.8441 −2.75000
\(557\) 12.6579 0.536334 0.268167 0.963372i \(-0.413582\pi\)
0.268167 + 0.963372i \(0.413582\pi\)
\(558\) −15.8707 −0.671860
\(559\) −0.750331 −0.0317356
\(560\) −98.5562 −4.16476
\(561\) 10.2412 0.432385
\(562\) 29.5621 1.24700
\(563\) 36.0539 1.51949 0.759745 0.650221i \(-0.225324\pi\)
0.759745 + 0.650221i \(0.225324\pi\)
\(564\) 51.5828 2.17203
\(565\) 35.5944 1.49747
\(566\) −1.47204 −0.0618743
\(567\) −47.3604 −1.98895
\(568\) −66.7564 −2.80103
\(569\) −23.3823 −0.980238 −0.490119 0.871656i \(-0.663047\pi\)
−0.490119 + 0.871656i \(0.663047\pi\)
\(570\) −25.7475 −1.07844
\(571\) −24.1559 −1.01089 −0.505447 0.862858i \(-0.668672\pi\)
−0.505447 + 0.862858i \(0.668672\pi\)
\(572\) 0.707379 0.0295770
\(573\) 10.2660 0.428869
\(574\) 78.8026 3.28915
\(575\) 3.17578 0.132439
\(576\) 5.63088 0.234620
\(577\) 43.2095 1.79883 0.899417 0.437092i \(-0.143992\pi\)
0.899417 + 0.437092i \(0.143992\pi\)
\(578\) −86.3028 −3.58972
\(579\) 0.153166 0.00636538
\(580\) −102.534 −4.25751
\(581\) −73.7132 −3.05814
\(582\) 71.9833 2.98380
\(583\) 7.10263 0.294161
\(584\) −36.3182 −1.50286
\(585\) 0.530703 0.0219419
\(586\) −6.78529 −0.280298
\(587\) −34.1105 −1.40789 −0.703945 0.710254i \(-0.748580\pi\)
−0.703945 + 0.710254i \(0.748580\pi\)
\(588\) 109.227 4.50445
\(589\) −11.8111 −0.486667
\(590\) 4.58024 0.188566
\(591\) −6.09693 −0.250794
\(592\) −57.3602 −2.35749
\(593\) 15.7197 0.645529 0.322764 0.946479i \(-0.395388\pi\)
0.322764 + 0.946479i \(0.395388\pi\)
\(594\) −7.48163 −0.306975
\(595\) 77.8924 3.19328
\(596\) −109.490 −4.48487
\(597\) −15.7896 −0.646227
\(598\) 1.12212 0.0458870
\(599\) −19.6085 −0.801183 −0.400591 0.916257i \(-0.631195\pi\)
−0.400591 + 0.916257i \(0.631195\pi\)
\(600\) −21.6061 −0.882067
\(601\) −1.73398 −0.0707305 −0.0353653 0.999374i \(-0.511259\pi\)
−0.0353653 + 0.999374i \(0.511259\pi\)
\(602\) −40.5251 −1.65168
\(603\) −8.90444 −0.362617
\(604\) −58.3509 −2.37426
\(605\) 26.7557 1.08777
\(606\) 18.7284 0.760788
\(607\) 12.5419 0.509060 0.254530 0.967065i \(-0.418079\pi\)
0.254530 + 0.967065i \(0.418079\pi\)
\(608\) 17.6063 0.714028
\(609\) 73.0031 2.95823
\(610\) −46.1514 −1.86861
\(611\) −1.12529 −0.0455242
\(612\) −33.7485 −1.36420
\(613\) −32.5981 −1.31662 −0.658312 0.752746i \(-0.728729\pi\)
−0.658312 + 0.752746i \(0.728729\pi\)
\(614\) 22.3958 0.903820
\(615\) 36.0464 1.45353
\(616\) 22.0765 0.889488
\(617\) 2.35505 0.0948106 0.0474053 0.998876i \(-0.484905\pi\)
0.0474053 + 0.998876i \(0.484905\pi\)
\(618\) −46.0890 −1.85397
\(619\) 28.2721 1.13635 0.568177 0.822907i \(-0.307649\pi\)
0.568177 + 0.822907i \(0.307649\pi\)
\(620\) −73.5972 −2.95574
\(621\) −8.34517 −0.334880
\(622\) −56.3905 −2.26105
\(623\) −10.0030 −0.400760
\(624\) −3.71243 −0.148616
\(625\) −30.2884 −1.21154
\(626\) −27.8660 −1.11375
\(627\) 2.80461 0.112005
\(628\) 64.6442 2.57958
\(629\) 45.3338 1.80758
\(630\) 28.6631 1.14196
\(631\) 13.6288 0.542555 0.271278 0.962501i \(-0.412554\pi\)
0.271278 + 0.962501i \(0.412554\pi\)
\(632\) 34.1722 1.35930
\(633\) −12.8513 −0.510794
\(634\) −48.5254 −1.92719
\(635\) 50.1146 1.98874
\(636\) −93.2778 −3.69870
\(637\) −2.38281 −0.0944102
\(638\) 15.8839 0.628848
\(639\) 9.44110 0.373484
\(640\) −9.17891 −0.362828
\(641\) 35.7660 1.41267 0.706336 0.707877i \(-0.250347\pi\)
0.706336 + 0.707877i \(0.250347\pi\)
\(642\) −87.5342 −3.45470
\(643\) −18.8023 −0.741492 −0.370746 0.928734i \(-0.620898\pi\)
−0.370746 + 0.928734i \(0.620898\pi\)
\(644\) 42.6150 1.67927
\(645\) −18.5373 −0.729904
\(646\) −35.7187 −1.40533
\(647\) −48.5078 −1.90704 −0.953519 0.301333i \(-0.902568\pi\)
−0.953519 + 0.301333i \(0.902568\pi\)
\(648\) 78.1981 3.07191
\(649\) −0.498914 −0.0195841
\(650\) 0.815697 0.0319943
\(651\) 52.4002 2.05373
\(652\) 40.8221 1.59872
\(653\) −30.1179 −1.17861 −0.589303 0.807912i \(-0.700598\pi\)
−0.589303 + 0.807912i \(0.700598\pi\)
\(654\) −87.2469 −3.41162
\(655\) −8.25385 −0.322505
\(656\) −63.2721 −2.47036
\(657\) 5.13635 0.200388
\(658\) −60.7763 −2.36931
\(659\) −15.3081 −0.596320 −0.298160 0.954516i \(-0.596373\pi\)
−0.298160 + 0.954516i \(0.596373\pi\)
\(660\) 17.4761 0.680257
\(661\) −30.7490 −1.19600 −0.597998 0.801498i \(-0.704037\pi\)
−0.597998 + 0.801498i \(0.704037\pi\)
\(662\) 12.8225 0.498359
\(663\) 2.93406 0.113949
\(664\) 121.710 4.72326
\(665\) 21.3312 0.827190
\(666\) 16.6821 0.646417
\(667\) 17.7172 0.686013
\(668\) 32.8939 1.27270
\(669\) 27.3685 1.05813
\(670\) −58.7247 −2.26873
\(671\) 5.02715 0.194071
\(672\) −78.1108 −3.01319
\(673\) −1.94981 −0.0751598 −0.0375799 0.999294i \(-0.511965\pi\)
−0.0375799 + 0.999294i \(0.511965\pi\)
\(674\) 20.4722 0.788561
\(675\) −6.06630 −0.233492
\(676\) −61.3853 −2.36097
\(677\) 4.93627 0.189716 0.0948581 0.995491i \(-0.469760\pi\)
0.0948581 + 0.995491i \(0.469760\pi\)
\(678\) 72.4146 2.78107
\(679\) −59.6366 −2.28864
\(680\) −128.610 −4.93198
\(681\) −39.9977 −1.53271
\(682\) 11.4011 0.436572
\(683\) 19.1081 0.731152 0.365576 0.930781i \(-0.380872\pi\)
0.365576 + 0.930781i \(0.380872\pi\)
\(684\) −9.24220 −0.353384
\(685\) 46.2069 1.76547
\(686\) −50.4997 −1.92809
\(687\) 23.5698 0.899243
\(688\) 32.5384 1.24051
\(689\) 2.03487 0.0775223
\(690\) 27.7225 1.05538
\(691\) −14.4910 −0.551262 −0.275631 0.961263i \(-0.588887\pi\)
−0.275631 + 0.961263i \(0.588887\pi\)
\(692\) 37.2624 1.41650
\(693\) −3.12220 −0.118602
\(694\) 23.8150 0.904004
\(695\) 34.9479 1.32565
\(696\) −120.537 −4.56896
\(697\) 50.0061 1.89412
\(698\) −43.9855 −1.66487
\(699\) 31.6806 1.19827
\(700\) 30.9778 1.17085
\(701\) −0.379290 −0.0143256 −0.00716280 0.999974i \(-0.502280\pi\)
−0.00716280 + 0.999974i \(0.502280\pi\)
\(702\) −2.14345 −0.0808993
\(703\) 12.4149 0.468236
\(704\) −4.04509 −0.152455
\(705\) −27.8007 −1.04704
\(706\) 76.7975 2.89031
\(707\) −15.5160 −0.583540
\(708\) 6.55216 0.246245
\(709\) −46.3790 −1.74180 −0.870900 0.491461i \(-0.836463\pi\)
−0.870900 + 0.491461i \(0.836463\pi\)
\(710\) 62.2640 2.33673
\(711\) −4.83284 −0.181246
\(712\) 16.5162 0.618969
\(713\) 12.7171 0.476258
\(714\) 158.467 5.93049
\(715\) −0.381244 −0.0142577
\(716\) 14.0879 0.526491
\(717\) 13.8533 0.517363
\(718\) −26.9427 −1.00549
\(719\) −19.0781 −0.711494 −0.355747 0.934582i \(-0.615774\pi\)
−0.355747 + 0.934582i \(0.615774\pi\)
\(720\) −23.0141 −0.857686
\(721\) 38.1837 1.42204
\(722\) 39.5361 1.47138
\(723\) 0.651526 0.0242305
\(724\) −24.0769 −0.894811
\(725\) 12.8790 0.478316
\(726\) 54.4328 2.02019
\(727\) 50.2047 1.86199 0.930994 0.365033i \(-0.118942\pi\)
0.930994 + 0.365033i \(0.118942\pi\)
\(728\) 6.32481 0.234413
\(729\) 12.9110 0.478186
\(730\) 33.8742 1.25374
\(731\) −25.7162 −0.951148
\(732\) −66.0208 −2.44020
\(733\) 9.20267 0.339908 0.169954 0.985452i \(-0.445638\pi\)
0.169954 + 0.985452i \(0.445638\pi\)
\(734\) 35.4873 1.30986
\(735\) −58.8683 −2.17139
\(736\) −18.9568 −0.698757
\(737\) 6.39674 0.235627
\(738\) 18.4014 0.677365
\(739\) 3.35181 0.123298 0.0616491 0.998098i \(-0.480364\pi\)
0.0616491 + 0.998098i \(0.480364\pi\)
\(740\) 77.3598 2.84380
\(741\) 0.803507 0.0295176
\(742\) 109.902 4.03465
\(743\) 38.5447 1.41407 0.707035 0.707179i \(-0.250032\pi\)
0.707035 + 0.707179i \(0.250032\pi\)
\(744\) −86.5194 −3.17196
\(745\) 59.0099 2.16195
\(746\) 93.3858 3.41910
\(747\) −17.2130 −0.629790
\(748\) 24.2441 0.886452
\(749\) 72.5202 2.64983
\(750\) −46.1644 −1.68569
\(751\) 12.7559 0.465470 0.232735 0.972540i \(-0.425233\pi\)
0.232735 + 0.972540i \(0.425233\pi\)
\(752\) 48.7985 1.77950
\(753\) −42.8495 −1.56152
\(754\) 4.55065 0.165725
\(755\) 31.4484 1.14452
\(756\) −81.4021 −2.96056
\(757\) 39.9523 1.45209 0.726045 0.687647i \(-0.241356\pi\)
0.726045 + 0.687647i \(0.241356\pi\)
\(758\) 2.18159 0.0792390
\(759\) −3.01975 −0.109610
\(760\) −35.2206 −1.27758
\(761\) 47.2255 1.71192 0.855962 0.517038i \(-0.172966\pi\)
0.855962 + 0.517038i \(0.172966\pi\)
\(762\) 101.955 3.69344
\(763\) 72.2821 2.61679
\(764\) 24.3028 0.879244
\(765\) 18.1889 0.657620
\(766\) −32.9022 −1.18880
\(767\) −0.142936 −0.00516114
\(768\) −41.1006 −1.48309
\(769\) 30.7500 1.10887 0.554437 0.832226i \(-0.312934\pi\)
0.554437 + 0.832226i \(0.312934\pi\)
\(770\) −20.5909 −0.742043
\(771\) −21.2018 −0.763565
\(772\) 0.362592 0.0130500
\(773\) −38.1154 −1.37091 −0.685457 0.728113i \(-0.740398\pi\)
−0.685457 + 0.728113i \(0.740398\pi\)
\(774\) −9.46312 −0.340145
\(775\) 9.24433 0.332066
\(776\) 98.4675 3.53478
\(777\) −55.0791 −1.97595
\(778\) −75.1584 −2.69456
\(779\) 13.6944 0.490654
\(780\) 5.00682 0.179273
\(781\) −6.78226 −0.242688
\(782\) 38.4586 1.37528
\(783\) −33.8429 −1.20945
\(784\) 103.331 3.69040
\(785\) −34.8402 −1.24350
\(786\) −16.7920 −0.598949
\(787\) −10.3292 −0.368197 −0.184099 0.982908i \(-0.558937\pi\)
−0.184099 + 0.982908i \(0.558937\pi\)
\(788\) −14.4333 −0.514165
\(789\) 34.9883 1.24562
\(790\) −31.8726 −1.13398
\(791\) −59.9939 −2.13314
\(792\) 5.15514 0.183180
\(793\) 1.44025 0.0511449
\(794\) 36.8299 1.30704
\(795\) 50.2724 1.78298
\(796\) −37.3789 −1.32486
\(797\) 30.1903 1.06940 0.534698 0.845043i \(-0.320425\pi\)
0.534698 + 0.845043i \(0.320425\pi\)
\(798\) 43.3971 1.53624
\(799\) −38.5671 −1.36441
\(800\) −13.7801 −0.487201
\(801\) −2.33582 −0.0825321
\(802\) −49.7629 −1.75719
\(803\) −3.68983 −0.130211
\(804\) −84.0073 −2.96271
\(805\) −22.9675 −0.809498
\(806\) 3.26637 0.115053
\(807\) −53.3240 −1.87709
\(808\) 25.6189 0.901271
\(809\) −32.6664 −1.14849 −0.574244 0.818684i \(-0.694704\pi\)
−0.574244 + 0.818684i \(0.694704\pi\)
\(810\) −72.9358 −2.56270
\(811\) −36.5632 −1.28391 −0.641954 0.766743i \(-0.721876\pi\)
−0.641954 + 0.766743i \(0.721876\pi\)
\(812\) 172.821 6.06481
\(813\) 41.1720 1.44396
\(814\) −11.9840 −0.420039
\(815\) −22.0012 −0.770669
\(816\) −127.236 −4.45417
\(817\) −7.04251 −0.246386
\(818\) 2.05396 0.0718149
\(819\) −0.894494 −0.0312561
\(820\) 85.3329 2.97995
\(821\) 9.65378 0.336919 0.168460 0.985709i \(-0.446121\pi\)
0.168460 + 0.985709i \(0.446121\pi\)
\(822\) 94.0051 3.27880
\(823\) −4.01032 −0.139791 −0.0698954 0.997554i \(-0.522267\pi\)
−0.0698954 + 0.997554i \(0.522267\pi\)
\(824\) −63.0462 −2.19632
\(825\) −2.19512 −0.0764244
\(826\) −7.71994 −0.268611
\(827\) −4.10677 −0.142806 −0.0714032 0.997448i \(-0.522748\pi\)
−0.0714032 + 0.997448i \(0.522748\pi\)
\(828\) 9.95114 0.345826
\(829\) 28.6597 0.995393 0.497697 0.867351i \(-0.334179\pi\)
0.497697 + 0.867351i \(0.334179\pi\)
\(830\) −113.519 −3.94032
\(831\) −7.53191 −0.261279
\(832\) −1.15890 −0.0401776
\(833\) −81.6662 −2.82957
\(834\) 71.0995 2.46197
\(835\) −17.7283 −0.613512
\(836\) 6.63937 0.229627
\(837\) −24.2918 −0.839648
\(838\) 30.4748 1.05273
\(839\) −30.7012 −1.05992 −0.529962 0.848021i \(-0.677794\pi\)
−0.529962 + 0.848021i \(0.677794\pi\)
\(840\) 156.257 5.39139
\(841\) 42.8502 1.47759
\(842\) 11.2039 0.386111
\(843\) −22.7920 −0.784999
\(844\) −30.4230 −1.04720
\(845\) 33.0838 1.13812
\(846\) −14.1920 −0.487932
\(847\) −45.0964 −1.54953
\(848\) −88.2428 −3.03027
\(849\) 1.13492 0.0389504
\(850\) 27.9565 0.958899
\(851\) −13.3672 −0.458222
\(852\) 89.0703 3.05150
\(853\) 51.4675 1.76221 0.881107 0.472917i \(-0.156799\pi\)
0.881107 + 0.472917i \(0.156799\pi\)
\(854\) 77.7876 2.66184
\(855\) 4.98111 0.170350
\(856\) −119.740 −4.09263
\(857\) 4.72225 0.161309 0.0806545 0.996742i \(-0.474299\pi\)
0.0806545 + 0.996742i \(0.474299\pi\)
\(858\) −0.775619 −0.0264792
\(859\) 21.5474 0.735187 0.367594 0.929987i \(-0.380182\pi\)
0.367594 + 0.929987i \(0.380182\pi\)
\(860\) −43.8834 −1.49641
\(861\) −60.7558 −2.07055
\(862\) 28.0516 0.955442
\(863\) 45.4434 1.54691 0.773455 0.633851i \(-0.218527\pi\)
0.773455 + 0.633851i \(0.218527\pi\)
\(864\) 36.2108 1.23192
\(865\) −20.0827 −0.682833
\(866\) 8.65977 0.294271
\(867\) 66.5384 2.25976
\(868\) 124.047 4.21044
\(869\) 3.47180 0.117773
\(870\) 112.426 3.81159
\(871\) 1.83263 0.0620964
\(872\) −119.347 −4.04160
\(873\) −13.9259 −0.471320
\(874\) 10.5321 0.356253
\(875\) 38.2462 1.29296
\(876\) 48.4579 1.63724
\(877\) −24.3662 −0.822787 −0.411393 0.911458i \(-0.634958\pi\)
−0.411393 + 0.911458i \(0.634958\pi\)
\(878\) 58.6863 1.98057
\(879\) 5.23138 0.176450
\(880\) 16.5328 0.557320
\(881\) 4.79543 0.161562 0.0807811 0.996732i \(-0.474259\pi\)
0.0807811 + 0.996732i \(0.474259\pi\)
\(882\) −30.0518 −1.01190
\(883\) 29.3529 0.987804 0.493902 0.869518i \(-0.335570\pi\)
0.493902 + 0.869518i \(0.335570\pi\)
\(884\) 6.94581 0.233613
\(885\) −3.53131 −0.118704
\(886\) 108.646 3.65003
\(887\) 16.3611 0.549353 0.274677 0.961537i \(-0.411429\pi\)
0.274677 + 0.961537i \(0.411429\pi\)
\(888\) 90.9426 3.05183
\(889\) −84.4675 −2.83295
\(890\) −15.4047 −0.516367
\(891\) 7.94471 0.266158
\(892\) 64.7897 2.16932
\(893\) −10.5618 −0.353437
\(894\) 120.052 4.01514
\(895\) −7.59274 −0.253797
\(896\) 15.4709 0.516848
\(897\) −0.865142 −0.0288863
\(898\) −70.7367 −2.36052
\(899\) 51.5727 1.72005
\(900\) 7.23372 0.241124
\(901\) 69.7413 2.32342
\(902\) −13.2191 −0.440149
\(903\) 31.2443 1.03975
\(904\) 99.0575 3.29460
\(905\) 12.9763 0.431348
\(906\) 63.9799 2.12559
\(907\) −40.7918 −1.35447 −0.677235 0.735767i \(-0.736822\pi\)
−0.677235 + 0.735767i \(0.736822\pi\)
\(908\) −94.6867 −3.14229
\(909\) −3.62319 −0.120174
\(910\) −5.89918 −0.195556
\(911\) −32.1532 −1.06528 −0.532642 0.846341i \(-0.678801\pi\)
−0.532642 + 0.846341i \(0.678801\pi\)
\(912\) −34.8444 −1.15381
\(913\) 12.3654 0.409234
\(914\) −27.6133 −0.913366
\(915\) 35.5821 1.17631
\(916\) 55.7969 1.84358
\(917\) 13.9118 0.459407
\(918\) −73.4627 −2.42463
\(919\) −40.1221 −1.32351 −0.661753 0.749722i \(-0.730187\pi\)
−0.661753 + 0.749722i \(0.730187\pi\)
\(920\) 37.9223 1.25026
\(921\) −17.2669 −0.568963
\(922\) −49.1496 −1.61866
\(923\) −1.94308 −0.0639574
\(924\) −29.4558 −0.969025
\(925\) −9.71693 −0.319491
\(926\) 70.4196 2.31413
\(927\) 8.91639 0.292853
\(928\) −76.8773 −2.52362
\(929\) 57.9228 1.90039 0.950193 0.311661i \(-0.100885\pi\)
0.950193 + 0.311661i \(0.100885\pi\)
\(930\) 80.6971 2.64616
\(931\) −22.3647 −0.732974
\(932\) 74.9976 2.45663
\(933\) 43.4764 1.42335
\(934\) 46.4932 1.52130
\(935\) −13.0664 −0.427318
\(936\) 1.47692 0.0482747
\(937\) −9.48324 −0.309804 −0.154902 0.987930i \(-0.549506\pi\)
−0.154902 + 0.987930i \(0.549506\pi\)
\(938\) 98.9798 3.23181
\(939\) 21.4843 0.701114
\(940\) −65.8128 −2.14658
\(941\) 20.6449 0.673006 0.336503 0.941682i \(-0.390756\pi\)
0.336503 + 0.941682i \(0.390756\pi\)
\(942\) −70.8803 −2.30941
\(943\) −14.7449 −0.480160
\(944\) 6.19849 0.201744
\(945\) 43.8719 1.42715
\(946\) 6.79808 0.221025
\(947\) 33.4884 1.08823 0.544113 0.839012i \(-0.316866\pi\)
0.544113 + 0.839012i \(0.316866\pi\)
\(948\) −45.5946 −1.48084
\(949\) −1.05712 −0.0343155
\(950\) 7.65603 0.248394
\(951\) 37.4125 1.21318
\(952\) 216.771 7.02559
\(953\) −11.7983 −0.382184 −0.191092 0.981572i \(-0.561203\pi\)
−0.191092 + 0.981572i \(0.561203\pi\)
\(954\) 25.6636 0.830891
\(955\) −13.0981 −0.423844
\(956\) 32.7951 1.06067
\(957\) −12.2463 −0.395865
\(958\) −19.5037 −0.630134
\(959\) −77.8811 −2.51491
\(960\) −28.6311 −0.924066
\(961\) 6.01789 0.194126
\(962\) −3.43335 −0.110696
\(963\) 16.9344 0.545703
\(964\) 1.54236 0.0496761
\(965\) −0.195420 −0.00629080
\(966\) −46.7260 −1.50338
\(967\) 35.3563 1.13698 0.568491 0.822689i \(-0.307527\pi\)
0.568491 + 0.822689i \(0.307527\pi\)
\(968\) 74.4599 2.39323
\(969\) 27.5387 0.884671
\(970\) −91.8412 −2.94884
\(971\) −24.9563 −0.800885 −0.400442 0.916322i \(-0.631144\pi\)
−0.400442 + 0.916322i \(0.631144\pi\)
\(972\) −47.5916 −1.52650
\(973\) −58.9043 −1.88839
\(974\) 92.1283 2.95198
\(975\) −0.628892 −0.0201407
\(976\) −62.4571 −1.99920
\(977\) −41.5705 −1.32996 −0.664980 0.746861i \(-0.731560\pi\)
−0.664980 + 0.746861i \(0.731560\pi\)
\(978\) −44.7601 −1.43127
\(979\) 1.67800 0.0536290
\(980\) −139.359 −4.45167
\(981\) 16.8788 0.538898
\(982\) 43.9920 1.40384
\(983\) 7.32015 0.233477 0.116738 0.993163i \(-0.462756\pi\)
0.116738 + 0.993163i \(0.462756\pi\)
\(984\) 100.316 3.19794
\(985\) 7.77888 0.247856
\(986\) 155.965 4.96693
\(987\) 46.8578 1.49150
\(988\) 1.90215 0.0605154
\(989\) 7.58273 0.241117
\(990\) −4.80823 −0.152816
\(991\) 15.4030 0.489292 0.244646 0.969613i \(-0.421328\pi\)
0.244646 + 0.969613i \(0.421328\pi\)
\(992\) −55.1810 −1.75200
\(993\) −9.88597 −0.313722
\(994\) −104.945 −3.32866
\(995\) 20.1455 0.638655
\(996\) −162.393 −5.14561
\(997\) −16.6711 −0.527979 −0.263990 0.964526i \(-0.585038\pi\)
−0.263990 + 0.964526i \(0.585038\pi\)
\(998\) 6.87646 0.217671
\(999\) 25.5337 0.807851
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 \(a_p\))