Properties

Label 4003.2.a.b.1.14
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 1.14
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +O(q^{10})\) \(q-2.44543 q^{2} -1.15615 q^{3} +3.98012 q^{4} -3.94364 q^{5} +2.82729 q^{6} +3.67660 q^{7} -4.84225 q^{8} -1.66331 q^{9} +9.64388 q^{10} -4.34035 q^{11} -4.60163 q^{12} +2.56321 q^{13} -8.99086 q^{14} +4.55944 q^{15} +3.88114 q^{16} -1.43730 q^{17} +4.06751 q^{18} -3.57623 q^{19} -15.6962 q^{20} -4.25071 q^{21} +10.6140 q^{22} +7.56025 q^{23} +5.59838 q^{24} +10.5523 q^{25} -6.26814 q^{26} +5.39150 q^{27} +14.6333 q^{28} -10.0757 q^{29} -11.1498 q^{30} -3.66806 q^{31} +0.193461 q^{32} +5.01811 q^{33} +3.51480 q^{34} -14.4992 q^{35} -6.62019 q^{36} -0.492301 q^{37} +8.74543 q^{38} -2.96346 q^{39} +19.0961 q^{40} +6.34905 q^{41} +10.3948 q^{42} +2.05250 q^{43} -17.2751 q^{44} +6.55950 q^{45} -18.4880 q^{46} +5.80507 q^{47} -4.48718 q^{48} +6.51738 q^{49} -25.8048 q^{50} +1.66173 q^{51} +10.2019 q^{52} -3.51286 q^{53} -13.1845 q^{54} +17.1168 q^{55} -17.8030 q^{56} +4.13467 q^{57} +24.6393 q^{58} -8.67947 q^{59} +18.1471 q^{60} +7.65206 q^{61} +8.96998 q^{62} -6.11533 q^{63} -8.23537 q^{64} -10.1084 q^{65} -12.2714 q^{66} +0.0212825 q^{67} -5.72061 q^{68} -8.74079 q^{69} +35.4567 q^{70} -0.157222 q^{71} +8.05418 q^{72} -13.0624 q^{73} +1.20389 q^{74} -12.2000 q^{75} -14.2339 q^{76} -15.9577 q^{77} +7.24692 q^{78} -1.22358 q^{79} -15.3058 q^{80} -1.24345 q^{81} -15.5262 q^{82} +9.74164 q^{83} -16.9183 q^{84} +5.66817 q^{85} -5.01924 q^{86} +11.6490 q^{87} +21.0171 q^{88} +11.9571 q^{89} -16.0408 q^{90} +9.42389 q^{91} +30.0907 q^{92} +4.24084 q^{93} -14.1959 q^{94} +14.1034 q^{95} -0.223671 q^{96} +3.79864 q^{97} -15.9378 q^{98} +7.21936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44543 −1.72918 −0.864590 0.502478i \(-0.832422\pi\)
−0.864590 + 0.502478i \(0.832422\pi\)
\(3\) −1.15615 −0.667505 −0.333752 0.942661i \(-0.608315\pi\)
−0.333752 + 0.942661i \(0.608315\pi\)
\(4\) 3.98012 1.99006
\(5\) −3.94364 −1.76365 −0.881824 0.471579i \(-0.843684\pi\)
−0.881824 + 0.471579i \(0.843684\pi\)
\(6\) 2.82729 1.15424
\(7\) 3.67660 1.38962 0.694812 0.719191i \(-0.255488\pi\)
0.694812 + 0.719191i \(0.255488\pi\)
\(8\) −4.84225 −1.71199
\(9\) −1.66331 −0.554438
\(10\) 9.64388 3.04966
\(11\) −4.34035 −1.30867 −0.654333 0.756207i \(-0.727050\pi\)
−0.654333 + 0.756207i \(0.727050\pi\)
\(12\) −4.60163 −1.32838
\(13\) 2.56321 0.710906 0.355453 0.934694i \(-0.384327\pi\)
0.355453 + 0.934694i \(0.384327\pi\)
\(14\) −8.99086 −2.40291
\(15\) 4.55944 1.17724
\(16\) 3.88114 0.970284
\(17\) −1.43730 −0.348595 −0.174298 0.984693i \(-0.555765\pi\)
−0.174298 + 0.984693i \(0.555765\pi\)
\(18\) 4.06751 0.958722
\(19\) −3.57623 −0.820444 −0.410222 0.911986i \(-0.634549\pi\)
−0.410222 + 0.911986i \(0.634549\pi\)
\(20\) −15.6962 −3.50977
\(21\) −4.25071 −0.927580
\(22\) 10.6140 2.26292
\(23\) 7.56025 1.57642 0.788210 0.615406i \(-0.211008\pi\)
0.788210 + 0.615406i \(0.211008\pi\)
\(24\) 5.59838 1.14276
\(25\) 10.5523 2.11045
\(26\) −6.26814 −1.22928
\(27\) 5.39150 1.03759
\(28\) 14.6333 2.76544
\(29\) −10.0757 −1.87100 −0.935501 0.353324i \(-0.885051\pi\)
−0.935501 + 0.353324i \(0.885051\pi\)
\(30\) −11.1498 −2.03566
\(31\) −3.66806 −0.658803 −0.329402 0.944190i \(-0.606847\pi\)
−0.329402 + 0.944190i \(0.606847\pi\)
\(32\) 0.193461 0.0341994
\(33\) 5.01811 0.873540
\(34\) 3.51480 0.602784
\(35\) −14.4992 −2.45081
\(36\) −6.62019 −1.10336
\(37\) −0.492301 −0.0809339 −0.0404669 0.999181i \(-0.512885\pi\)
−0.0404669 + 0.999181i \(0.512885\pi\)
\(38\) 8.74543 1.41870
\(39\) −2.96346 −0.474533
\(40\) 19.0961 3.01936
\(41\) 6.34905 0.991555 0.495777 0.868450i \(-0.334883\pi\)
0.495777 + 0.868450i \(0.334883\pi\)
\(42\) 10.3948 1.60395
\(43\) 2.05250 0.313003 0.156501 0.987678i \(-0.449978\pi\)
0.156501 + 0.987678i \(0.449978\pi\)
\(44\) −17.2751 −2.60432
\(45\) 6.55950 0.977833
\(46\) −18.4880 −2.72591
\(47\) 5.80507 0.846757 0.423379 0.905953i \(-0.360844\pi\)
0.423379 + 0.905953i \(0.360844\pi\)
\(48\) −4.48718 −0.647669
\(49\) 6.51738 0.931055
\(50\) −25.8048 −3.64935
\(51\) 1.66173 0.232689
\(52\) 10.2019 1.41475
\(53\) −3.51286 −0.482528 −0.241264 0.970459i \(-0.577562\pi\)
−0.241264 + 0.970459i \(0.577562\pi\)
\(54\) −13.1845 −1.79419
\(55\) 17.1168 2.30803
\(56\) −17.8030 −2.37903
\(57\) 4.13467 0.547650
\(58\) 24.6393 3.23530
\(59\) −8.67947 −1.12997 −0.564986 0.825101i \(-0.691118\pi\)
−0.564986 + 0.825101i \(0.691118\pi\)
\(60\) 18.1471 2.34279
\(61\) 7.65206 0.979746 0.489873 0.871794i \(-0.337043\pi\)
0.489873 + 0.871794i \(0.337043\pi\)
\(62\) 8.96998 1.13919
\(63\) −6.11533 −0.770460
\(64\) −8.23537 −1.02942
\(65\) −10.1084 −1.25379
\(66\) −12.2714 −1.51051
\(67\) 0.0212825 0.00260007 0.00130004 0.999999i \(-0.499586\pi\)
0.00130004 + 0.999999i \(0.499586\pi\)
\(68\) −5.72061 −0.693726
\(69\) −8.74079 −1.05227
\(70\) 35.4567 4.23789
\(71\) −0.157222 −0.0186589 −0.00932943 0.999956i \(-0.502970\pi\)
−0.00932943 + 0.999956i \(0.502970\pi\)
\(72\) 8.05418 0.949194
\(73\) −13.0624 −1.52884 −0.764418 0.644720i \(-0.776974\pi\)
−0.764418 + 0.644720i \(0.776974\pi\)
\(74\) 1.20389 0.139949
\(75\) −12.2000 −1.40874
\(76\) −14.2339 −1.63273
\(77\) −15.9577 −1.81855
\(78\) 7.24692 0.820553
\(79\) −1.22358 −0.137663 −0.0688317 0.997628i \(-0.521927\pi\)
−0.0688317 + 0.997628i \(0.521927\pi\)
\(80\) −15.3058 −1.71124
\(81\) −1.24345 −0.138161
\(82\) −15.5262 −1.71458
\(83\) 9.74164 1.06928 0.534642 0.845079i \(-0.320446\pi\)
0.534642 + 0.845079i \(0.320446\pi\)
\(84\) −16.9183 −1.84594
\(85\) 5.66817 0.614799
\(86\) −5.01924 −0.541238
\(87\) 11.6490 1.24890
\(88\) 21.0171 2.24043
\(89\) 11.9571 1.26745 0.633727 0.773557i \(-0.281524\pi\)
0.633727 + 0.773557i \(0.281524\pi\)
\(90\) −16.0408 −1.69085
\(91\) 9.42389 0.987892
\(92\) 30.0907 3.13717
\(93\) 4.24084 0.439754
\(94\) −14.1959 −1.46419
\(95\) 14.1034 1.44697
\(96\) −0.223671 −0.0228283
\(97\) 3.79864 0.385694 0.192847 0.981229i \(-0.438228\pi\)
0.192847 + 0.981229i \(0.438228\pi\)
\(98\) −15.9378 −1.60996
\(99\) 7.21936 0.725573
\(100\) 41.9993 4.19993
\(101\) −7.78154 −0.774292 −0.387146 0.922018i \(-0.626539\pi\)
−0.387146 + 0.922018i \(0.626539\pi\)
\(102\) −4.06365 −0.402361
\(103\) −12.3739 −1.21923 −0.609617 0.792696i \(-0.708677\pi\)
−0.609617 + 0.792696i \(0.708677\pi\)
\(104\) −12.4117 −1.21707
\(105\) 16.7632 1.63593
\(106\) 8.59045 0.834378
\(107\) 12.8460 1.24187 0.620937 0.783861i \(-0.286752\pi\)
0.620937 + 0.783861i \(0.286752\pi\)
\(108\) 21.4588 2.06488
\(109\) 16.2967 1.56094 0.780470 0.625193i \(-0.214980\pi\)
0.780470 + 0.625193i \(0.214980\pi\)
\(110\) −41.8579 −3.99099
\(111\) 0.569175 0.0540237
\(112\) 14.2694 1.34833
\(113\) 16.5689 1.55867 0.779335 0.626607i \(-0.215557\pi\)
0.779335 + 0.626607i \(0.215557\pi\)
\(114\) −10.1110 −0.946986
\(115\) −29.8149 −2.78025
\(116\) −40.1023 −3.72341
\(117\) −4.26342 −0.394153
\(118\) 21.2250 1.95392
\(119\) −5.28436 −0.484416
\(120\) −22.0780 −2.01543
\(121\) 7.83866 0.712605
\(122\) −18.7126 −1.69416
\(123\) −7.34047 −0.661868
\(124\) −14.5993 −1.31106
\(125\) −21.8961 −1.95845
\(126\) 14.9546 1.33226
\(127\) −0.990646 −0.0879057 −0.0439528 0.999034i \(-0.513995\pi\)
−0.0439528 + 0.999034i \(0.513995\pi\)
\(128\) 19.7521 1.74585
\(129\) −2.37300 −0.208931
\(130\) 24.7193 2.16802
\(131\) 18.4777 1.61440 0.807201 0.590277i \(-0.200981\pi\)
0.807201 + 0.590277i \(0.200981\pi\)
\(132\) 19.9727 1.73840
\(133\) −13.1484 −1.14011
\(134\) −0.0520448 −0.00449599
\(135\) −21.2621 −1.82995
\(136\) 6.95975 0.596793
\(137\) 9.07582 0.775400 0.387700 0.921786i \(-0.373270\pi\)
0.387700 + 0.921786i \(0.373270\pi\)
\(138\) 21.3750 1.81956
\(139\) −11.6227 −0.985822 −0.492911 0.870080i \(-0.664067\pi\)
−0.492911 + 0.870080i \(0.664067\pi\)
\(140\) −57.7085 −4.87726
\(141\) −6.71155 −0.565214
\(142\) 0.384476 0.0322645
\(143\) −11.1252 −0.930338
\(144\) −6.45554 −0.537962
\(145\) 39.7347 3.29979
\(146\) 31.9431 2.64363
\(147\) −7.53509 −0.621483
\(148\) −1.95942 −0.161063
\(149\) 10.0783 0.825649 0.412824 0.910811i \(-0.364542\pi\)
0.412824 + 0.910811i \(0.364542\pi\)
\(150\) 29.8343 2.43596
\(151\) −2.89948 −0.235957 −0.117978 0.993016i \(-0.537641\pi\)
−0.117978 + 0.993016i \(0.537641\pi\)
\(152\) 17.3170 1.40460
\(153\) 2.39067 0.193274
\(154\) 39.0235 3.14460
\(155\) 14.4655 1.16190
\(156\) −11.7949 −0.944350
\(157\) 11.2788 0.900145 0.450072 0.892992i \(-0.351398\pi\)
0.450072 + 0.892992i \(0.351398\pi\)
\(158\) 2.99217 0.238045
\(159\) 4.06140 0.322090
\(160\) −0.762941 −0.0603158
\(161\) 27.7960 2.19063
\(162\) 3.04078 0.238906
\(163\) 0.268052 0.0209954 0.0104977 0.999945i \(-0.496658\pi\)
0.0104977 + 0.999945i \(0.496658\pi\)
\(164\) 25.2700 1.97326
\(165\) −19.7896 −1.54062
\(166\) −23.8225 −1.84898
\(167\) 14.8715 1.15079 0.575397 0.817874i \(-0.304847\pi\)
0.575397 + 0.817874i \(0.304847\pi\)
\(168\) 20.5830 1.58801
\(169\) −6.42997 −0.494613
\(170\) −13.8611 −1.06310
\(171\) 5.94839 0.454885
\(172\) 8.16919 0.622895
\(173\) −18.7577 −1.42612 −0.713059 0.701104i \(-0.752691\pi\)
−0.713059 + 0.701104i \(0.752691\pi\)
\(174\) −28.4868 −2.15958
\(175\) 38.7965 2.93274
\(176\) −16.8455 −1.26978
\(177\) 10.0348 0.754261
\(178\) −29.2403 −2.19166
\(179\) −6.32143 −0.472486 −0.236243 0.971694i \(-0.575916\pi\)
−0.236243 + 0.971694i \(0.575916\pi\)
\(180\) 26.1076 1.94595
\(181\) −1.36262 −0.101283 −0.0506415 0.998717i \(-0.516127\pi\)
−0.0506415 + 0.998717i \(0.516127\pi\)
\(182\) −23.0454 −1.70824
\(183\) −8.84694 −0.653985
\(184\) −36.6086 −2.69882
\(185\) 1.94146 0.142739
\(186\) −10.3707 −0.760414
\(187\) 6.23837 0.456195
\(188\) 23.1049 1.68510
\(189\) 19.8224 1.44187
\(190\) −34.4888 −2.50208
\(191\) −21.9818 −1.59055 −0.795274 0.606250i \(-0.792673\pi\)
−0.795274 + 0.606250i \(0.792673\pi\)
\(192\) 9.52133 0.687143
\(193\) 6.34397 0.456649 0.228324 0.973585i \(-0.426675\pi\)
0.228324 + 0.973585i \(0.426675\pi\)
\(194\) −9.28931 −0.666934
\(195\) 11.6868 0.836909
\(196\) 25.9400 1.85286
\(197\) −15.7382 −1.12130 −0.560649 0.828053i \(-0.689448\pi\)
−0.560649 + 0.828053i \(0.689448\pi\)
\(198\) −17.6544 −1.25465
\(199\) 7.17962 0.508950 0.254475 0.967079i \(-0.418097\pi\)
0.254475 + 0.967079i \(0.418097\pi\)
\(200\) −51.0968 −3.61309
\(201\) −0.0246058 −0.00173556
\(202\) 19.0292 1.33889
\(203\) −37.0441 −2.59999
\(204\) 6.61390 0.463065
\(205\) −25.0383 −1.74875
\(206\) 30.2594 2.10827
\(207\) −12.5751 −0.874027
\(208\) 9.94816 0.689780
\(209\) 15.5221 1.07369
\(210\) −40.9933 −2.82881
\(211\) 16.8062 1.15699 0.578494 0.815687i \(-0.303641\pi\)
0.578494 + 0.815687i \(0.303641\pi\)
\(212\) −13.9816 −0.960261
\(213\) 0.181773 0.0124549
\(214\) −31.4141 −2.14742
\(215\) −8.09430 −0.552027
\(216\) −26.1070 −1.77636
\(217\) −13.4860 −0.915489
\(218\) −39.8524 −2.69914
\(219\) 15.1021 1.02051
\(220\) 68.1269 4.59311
\(221\) −3.68409 −0.247818
\(222\) −1.39188 −0.0934167
\(223\) 16.1410 1.08088 0.540439 0.841383i \(-0.318258\pi\)
0.540439 + 0.841383i \(0.318258\pi\)
\(224\) 0.711279 0.0475243
\(225\) −17.5517 −1.17012
\(226\) −40.5180 −2.69522
\(227\) −8.36879 −0.555456 −0.277728 0.960660i \(-0.589581\pi\)
−0.277728 + 0.960660i \(0.589581\pi\)
\(228\) 16.4565 1.08986
\(229\) 1.20796 0.0798240 0.0399120 0.999203i \(-0.487292\pi\)
0.0399120 + 0.999203i \(0.487292\pi\)
\(230\) 72.9101 4.80755
\(231\) 18.4496 1.21389
\(232\) 48.7888 3.20314
\(233\) −20.9223 −1.37066 −0.685331 0.728231i \(-0.740343\pi\)
−0.685331 + 0.728231i \(0.740343\pi\)
\(234\) 10.4259 0.681561
\(235\) −22.8931 −1.49338
\(236\) −34.5454 −2.24871
\(237\) 1.41464 0.0918909
\(238\) 12.9225 0.837643
\(239\) 14.4069 0.931906 0.465953 0.884809i \(-0.345711\pi\)
0.465953 + 0.884809i \(0.345711\pi\)
\(240\) 17.6958 1.14226
\(241\) 1.60754 0.103551 0.0517754 0.998659i \(-0.483512\pi\)
0.0517754 + 0.998659i \(0.483512\pi\)
\(242\) −19.1689 −1.23222
\(243\) −14.7369 −0.945371
\(244\) 30.4561 1.94975
\(245\) −25.7022 −1.64205
\(246\) 17.9506 1.14449
\(247\) −9.16663 −0.583259
\(248\) 17.7617 1.12787
\(249\) −11.2628 −0.713752
\(250\) 53.5455 3.38651
\(251\) 13.7490 0.867832 0.433916 0.900953i \(-0.357132\pi\)
0.433916 + 0.900953i \(0.357132\pi\)
\(252\) −24.3398 −1.53326
\(253\) −32.8141 −2.06301
\(254\) 2.42256 0.152005
\(255\) −6.55327 −0.410382
\(256\) −31.8316 −1.98947
\(257\) −10.7570 −0.671001 −0.335501 0.942040i \(-0.608905\pi\)
−0.335501 + 0.942040i \(0.608905\pi\)
\(258\) 5.80300 0.361279
\(259\) −1.81000 −0.112468
\(260\) −40.2325 −2.49511
\(261\) 16.7590 1.03735
\(262\) −45.1858 −2.79159
\(263\) −7.44899 −0.459324 −0.229662 0.973270i \(-0.573762\pi\)
−0.229662 + 0.973270i \(0.573762\pi\)
\(264\) −24.2989 −1.49550
\(265\) 13.8534 0.851010
\(266\) 32.1534 1.97145
\(267\) −13.8243 −0.846031
\(268\) 0.0847069 0.00517430
\(269\) 8.37834 0.510837 0.255418 0.966831i \(-0.417787\pi\)
0.255418 + 0.966831i \(0.417787\pi\)
\(270\) 51.9950 3.16431
\(271\) 1.00504 0.0610516 0.0305258 0.999534i \(-0.490282\pi\)
0.0305258 + 0.999534i \(0.490282\pi\)
\(272\) −5.57834 −0.338236
\(273\) −10.8954 −0.659422
\(274\) −22.1943 −1.34081
\(275\) −45.8006 −2.76188
\(276\) −34.7894 −2.09408
\(277\) 23.3188 1.40109 0.700546 0.713607i \(-0.252940\pi\)
0.700546 + 0.713607i \(0.252940\pi\)
\(278\) 28.4224 1.70466
\(279\) 6.10113 0.365265
\(280\) 70.2086 4.19577
\(281\) 2.68923 0.160426 0.0802130 0.996778i \(-0.474440\pi\)
0.0802130 + 0.996778i \(0.474440\pi\)
\(282\) 16.4126 0.977357
\(283\) −15.9997 −0.951085 −0.475543 0.879693i \(-0.657748\pi\)
−0.475543 + 0.879693i \(0.657748\pi\)
\(284\) −0.625764 −0.0371323
\(285\) −16.3056 −0.965862
\(286\) 27.2059 1.60872
\(287\) 23.3429 1.37789
\(288\) −0.321786 −0.0189614
\(289\) −14.9342 −0.878481
\(290\) −97.1684 −5.70593
\(291\) −4.39181 −0.257452
\(292\) −51.9899 −3.04248
\(293\) 20.6283 1.20512 0.602560 0.798074i \(-0.294148\pi\)
0.602560 + 0.798074i \(0.294148\pi\)
\(294\) 18.4265 1.07466
\(295\) 34.2287 1.99287
\(296\) 2.38385 0.138558
\(297\) −23.4010 −1.35786
\(298\) −24.6458 −1.42770
\(299\) 19.3785 1.12069
\(300\) −48.5576 −2.80348
\(301\) 7.54621 0.434956
\(302\) 7.09048 0.408012
\(303\) 8.99664 0.516843
\(304\) −13.8798 −0.796064
\(305\) −30.1769 −1.72793
\(306\) −5.84622 −0.334206
\(307\) −16.2859 −0.929484 −0.464742 0.885446i \(-0.653853\pi\)
−0.464742 + 0.885446i \(0.653853\pi\)
\(308\) −63.5138 −3.61903
\(309\) 14.3061 0.813844
\(310\) −35.3744 −2.00913
\(311\) −23.8103 −1.35016 −0.675080 0.737744i \(-0.735891\pi\)
−0.675080 + 0.737744i \(0.735891\pi\)
\(312\) 14.3498 0.812398
\(313\) 6.58466 0.372187 0.186094 0.982532i \(-0.440417\pi\)
0.186094 + 0.982532i \(0.440417\pi\)
\(314\) −27.5815 −1.55651
\(315\) 24.1167 1.35882
\(316\) −4.86999 −0.273958
\(317\) 2.90341 0.163072 0.0815359 0.996670i \(-0.474017\pi\)
0.0815359 + 0.996670i \(0.474017\pi\)
\(318\) −9.93186 −0.556951
\(319\) 43.7319 2.44852
\(320\) 32.4773 1.81554
\(321\) −14.8520 −0.828956
\(322\) −67.9731 −3.78800
\(323\) 5.14010 0.286003
\(324\) −4.94909 −0.274950
\(325\) 27.0477 1.50033
\(326\) −0.655501 −0.0363049
\(327\) −18.8414 −1.04193
\(328\) −30.7437 −1.69754
\(329\) 21.3429 1.17667
\(330\) 48.3940 2.66400
\(331\) −23.5568 −1.29480 −0.647399 0.762151i \(-0.724143\pi\)
−0.647399 + 0.762151i \(0.724143\pi\)
\(332\) 38.7729 2.12794
\(333\) 0.818851 0.0448728
\(334\) −36.3673 −1.98993
\(335\) −0.0839304 −0.00458561
\(336\) −16.4976 −0.900016
\(337\) 27.4114 1.49320 0.746598 0.665275i \(-0.231686\pi\)
0.746598 + 0.665275i \(0.231686\pi\)
\(338\) 15.7240 0.855274
\(339\) −19.1562 −1.04042
\(340\) 22.5600 1.22349
\(341\) 15.9207 0.862153
\(342\) −14.5464 −0.786578
\(343\) −1.77438 −0.0958078
\(344\) −9.93871 −0.535859
\(345\) 34.4705 1.85583
\(346\) 45.8705 2.46601
\(347\) −34.1393 −1.83269 −0.916346 0.400388i \(-0.868875\pi\)
−0.916346 + 0.400388i \(0.868875\pi\)
\(348\) 46.3644 2.48539
\(349\) −1.72055 −0.0920988 −0.0460494 0.998939i \(-0.514663\pi\)
−0.0460494 + 0.998939i \(0.514663\pi\)
\(350\) −94.8740 −5.07123
\(351\) 13.8195 0.737632
\(352\) −0.839690 −0.0447556
\(353\) 26.1787 1.39335 0.696677 0.717385i \(-0.254661\pi\)
0.696677 + 0.717385i \(0.254661\pi\)
\(354\) −24.5394 −1.30425
\(355\) 0.620028 0.0329077
\(356\) 47.5909 2.52231
\(357\) 6.10952 0.323350
\(358\) 15.4586 0.817012
\(359\) 18.9369 0.999451 0.499725 0.866184i \(-0.333434\pi\)
0.499725 + 0.866184i \(0.333434\pi\)
\(360\) −31.7628 −1.67404
\(361\) −6.21055 −0.326871
\(362\) 3.33220 0.175137
\(363\) −9.06268 −0.475667
\(364\) 37.5082 1.96597
\(365\) 51.5133 2.69633
\(366\) 21.6346 1.13086
\(367\) −30.5112 −1.59267 −0.796337 0.604853i \(-0.793232\pi\)
−0.796337 + 0.604853i \(0.793232\pi\)
\(368\) 29.3423 1.52958
\(369\) −10.5605 −0.549755
\(370\) −4.74770 −0.246821
\(371\) −12.9154 −0.670533
\(372\) 16.8791 0.875138
\(373\) −14.8881 −0.770876 −0.385438 0.922734i \(-0.625950\pi\)
−0.385438 + 0.922734i \(0.625950\pi\)
\(374\) −15.2555 −0.788842
\(375\) 25.3153 1.30728
\(376\) −28.1096 −1.44964
\(377\) −25.8260 −1.33011
\(378\) −48.4742 −2.49324
\(379\) −29.6533 −1.52319 −0.761593 0.648055i \(-0.775583\pi\)
−0.761593 + 0.648055i \(0.775583\pi\)
\(380\) 56.1331 2.87957
\(381\) 1.14534 0.0586774
\(382\) 53.7550 2.75034
\(383\) 22.2739 1.13815 0.569073 0.822287i \(-0.307302\pi\)
0.569073 + 0.822287i \(0.307302\pi\)
\(384\) −22.8364 −1.16537
\(385\) 62.9315 3.20729
\(386\) −15.5137 −0.789627
\(387\) −3.41395 −0.173541
\(388\) 15.1191 0.767554
\(389\) −19.8382 −1.00583 −0.502917 0.864335i \(-0.667740\pi\)
−0.502917 + 0.864335i \(0.667740\pi\)
\(390\) −28.5792 −1.44717
\(391\) −10.8663 −0.549533
\(392\) −31.5588 −1.59396
\(393\) −21.3630 −1.07762
\(394\) 38.4866 1.93893
\(395\) 4.82535 0.242790
\(396\) 28.7340 1.44394
\(397\) 12.5398 0.629353 0.314676 0.949199i \(-0.398104\pi\)
0.314676 + 0.949199i \(0.398104\pi\)
\(398\) −17.5572 −0.880065
\(399\) 15.2015 0.761028
\(400\) 40.9548 2.04774
\(401\) −28.3753 −1.41700 −0.708498 0.705713i \(-0.750627\pi\)
−0.708498 + 0.705713i \(0.750627\pi\)
\(402\) 0.0601717 0.00300109
\(403\) −9.40200 −0.468347
\(404\) −30.9715 −1.54089
\(405\) 4.90373 0.243668
\(406\) 90.5888 4.49585
\(407\) 2.13676 0.105915
\(408\) −8.04652 −0.398362
\(409\) −32.7730 −1.62052 −0.810261 0.586070i \(-0.800675\pi\)
−0.810261 + 0.586070i \(0.800675\pi\)
\(410\) 61.2295 3.02391
\(411\) −10.4930 −0.517583
\(412\) −49.2495 −2.42635
\(413\) −31.9109 −1.57024
\(414\) 30.7514 1.51135
\(415\) −38.4175 −1.88584
\(416\) 0.495881 0.0243126
\(417\) 13.4376 0.658041
\(418\) −37.9582 −1.85660
\(419\) −37.7606 −1.84473 −0.922363 0.386325i \(-0.873744\pi\)
−0.922363 + 0.386325i \(0.873744\pi\)
\(420\) 66.7198 3.25559
\(421\) 19.6401 0.957201 0.478601 0.878033i \(-0.341144\pi\)
0.478601 + 0.878033i \(0.341144\pi\)
\(422\) −41.0984 −2.00064
\(423\) −9.65565 −0.469474
\(424\) 17.0101 0.826086
\(425\) −15.1667 −0.735695
\(426\) −0.444513 −0.0215367
\(427\) 28.1336 1.36148
\(428\) 51.1288 2.47140
\(429\) 12.8624 0.621005
\(430\) 19.7940 0.954554
\(431\) −18.4192 −0.887222 −0.443611 0.896219i \(-0.646303\pi\)
−0.443611 + 0.896219i \(0.646303\pi\)
\(432\) 20.9251 1.00676
\(433\) 7.03845 0.338246 0.169123 0.985595i \(-0.445906\pi\)
0.169123 + 0.985595i \(0.445906\pi\)
\(434\) 32.9790 1.58304
\(435\) −45.9394 −2.20262
\(436\) 64.8628 3.10637
\(437\) −27.0372 −1.29337
\(438\) −36.9311 −1.76464
\(439\) −8.01432 −0.382502 −0.191251 0.981541i \(-0.561255\pi\)
−0.191251 + 0.981541i \(0.561255\pi\)
\(440\) −82.8837 −3.95133
\(441\) −10.8404 −0.516212
\(442\) 9.00917 0.428523
\(443\) −3.17399 −0.150801 −0.0754005 0.997153i \(-0.524024\pi\)
−0.0754005 + 0.997153i \(0.524024\pi\)
\(444\) 2.26539 0.107511
\(445\) −47.1546 −2.23534
\(446\) −39.4716 −1.86903
\(447\) −11.6521 −0.551124
\(448\) −30.2781 −1.43051
\(449\) −34.3893 −1.62293 −0.811467 0.584398i \(-0.801331\pi\)
−0.811467 + 0.584398i \(0.801331\pi\)
\(450\) 42.9215 2.02334
\(451\) −27.5571 −1.29761
\(452\) 65.9462 3.10185
\(453\) 3.35225 0.157502
\(454\) 20.4653 0.960483
\(455\) −37.1644 −1.74229
\(456\) −20.0211 −0.937574
\(457\) −0.434926 −0.0203450 −0.0101725 0.999948i \(-0.503238\pi\)
−0.0101725 + 0.999948i \(0.503238\pi\)
\(458\) −2.95397 −0.138030
\(459\) −7.74918 −0.361701
\(460\) −118.667 −5.53287
\(461\) 7.34963 0.342307 0.171153 0.985244i \(-0.445251\pi\)
0.171153 + 0.985244i \(0.445251\pi\)
\(462\) −45.1171 −2.09904
\(463\) −12.5653 −0.583961 −0.291981 0.956424i \(-0.594314\pi\)
−0.291981 + 0.956424i \(0.594314\pi\)
\(464\) −39.1050 −1.81540
\(465\) −16.7243 −0.775572
\(466\) 51.1639 2.37012
\(467\) −38.9070 −1.80040 −0.900201 0.435475i \(-0.856580\pi\)
−0.900201 + 0.435475i \(0.856580\pi\)
\(468\) −16.9689 −0.784389
\(469\) 0.0782472 0.00361312
\(470\) 55.9835 2.58232
\(471\) −13.0400 −0.600851
\(472\) 42.0282 1.93450
\(473\) −8.90856 −0.409616
\(474\) −3.45941 −0.158896
\(475\) −37.7374 −1.73151
\(476\) −21.0324 −0.964019
\(477\) 5.84298 0.267532
\(478\) −35.2311 −1.61143
\(479\) −24.7758 −1.13204 −0.566018 0.824393i \(-0.691517\pi\)
−0.566018 + 0.824393i \(0.691517\pi\)
\(480\) 0.882075 0.0402610
\(481\) −1.26187 −0.0575364
\(482\) −3.93113 −0.179058
\(483\) −32.1364 −1.46226
\(484\) 31.1988 1.41813
\(485\) −14.9805 −0.680228
\(486\) 36.0380 1.63472
\(487\) −2.14050 −0.0969953 −0.0484977 0.998823i \(-0.515443\pi\)
−0.0484977 + 0.998823i \(0.515443\pi\)
\(488\) −37.0532 −1.67732
\(489\) −0.309909 −0.0140145
\(490\) 62.8529 2.83940
\(491\) −34.0031 −1.53454 −0.767268 0.641326i \(-0.778385\pi\)
−0.767268 + 0.641326i \(0.778385\pi\)
\(492\) −29.2160 −1.31716
\(493\) 14.4817 0.652222
\(494\) 22.4163 1.00856
\(495\) −28.4705 −1.27966
\(496\) −14.2362 −0.639226
\(497\) −0.578044 −0.0259288
\(498\) 27.5424 1.23421
\(499\) −23.0993 −1.03407 −0.517034 0.855965i \(-0.672964\pi\)
−0.517034 + 0.855965i \(0.672964\pi\)
\(500\) −87.1494 −3.89744
\(501\) −17.1938 −0.768161
\(502\) −33.6223 −1.50064
\(503\) 43.1977 1.92609 0.963045 0.269340i \(-0.0868054\pi\)
0.963045 + 0.269340i \(0.0868054\pi\)
\(504\) 29.6120 1.31902
\(505\) 30.6875 1.36558
\(506\) 80.2446 3.56731
\(507\) 7.43402 0.330156
\(508\) −3.94290 −0.174938
\(509\) −8.00645 −0.354880 −0.177440 0.984132i \(-0.556782\pi\)
−0.177440 + 0.984132i \(0.556782\pi\)
\(510\) 16.0256 0.709623
\(511\) −48.0252 −2.12451
\(512\) 38.3377 1.69430
\(513\) −19.2813 −0.851288
\(514\) 26.3054 1.16028
\(515\) 48.7981 2.15030
\(516\) −9.44483 −0.415785
\(517\) −25.1961 −1.10812
\(518\) 4.42621 0.194477
\(519\) 21.6867 0.951940
\(520\) 48.9472 2.14648
\(521\) 4.99808 0.218970 0.109485 0.993988i \(-0.465080\pi\)
0.109485 + 0.993988i \(0.465080\pi\)
\(522\) −40.9829 −1.79377
\(523\) −17.2405 −0.753872 −0.376936 0.926239i \(-0.623022\pi\)
−0.376936 + 0.926239i \(0.623022\pi\)
\(524\) 73.5434 3.21276
\(525\) −44.8546 −1.95762
\(526\) 18.2160 0.794254
\(527\) 5.27209 0.229656
\(528\) 19.4760 0.847582
\(529\) 34.1573 1.48510
\(530\) −33.8776 −1.47155
\(531\) 14.4367 0.626498
\(532\) −52.3322 −2.26889
\(533\) 16.2739 0.704902
\(534\) 33.8063 1.46294
\(535\) −50.6601 −2.19023
\(536\) −0.103055 −0.00445131
\(537\) 7.30853 0.315386
\(538\) −20.4886 −0.883328
\(539\) −28.2877 −1.21844
\(540\) −84.6258 −3.64172
\(541\) 8.62014 0.370609 0.185304 0.982681i \(-0.440673\pi\)
0.185304 + 0.982681i \(0.440673\pi\)
\(542\) −2.45774 −0.105569
\(543\) 1.57540 0.0676069
\(544\) −0.278061 −0.0119218
\(545\) −64.2682 −2.75295
\(546\) 26.6440 1.14026
\(547\) −44.9978 −1.92397 −0.961983 0.273110i \(-0.911948\pi\)
−0.961983 + 0.273110i \(0.911948\pi\)
\(548\) 36.1229 1.54309
\(549\) −12.7278 −0.543208
\(550\) 112.002 4.77578
\(551\) 36.0329 1.53505
\(552\) 42.3251 1.80148
\(553\) −4.49861 −0.191300
\(554\) −57.0246 −2.42274
\(555\) −2.24462 −0.0952788
\(556\) −46.2597 −1.96185
\(557\) 30.0011 1.27119 0.635594 0.772024i \(-0.280755\pi\)
0.635594 + 0.772024i \(0.280755\pi\)
\(558\) −14.9199 −0.631609
\(559\) 5.26098 0.222516
\(560\) −56.2733 −2.37798
\(561\) −7.21250 −0.304512
\(562\) −6.57632 −0.277405
\(563\) −7.71352 −0.325086 −0.162543 0.986701i \(-0.551970\pi\)
−0.162543 + 0.986701i \(0.551970\pi\)
\(564\) −26.7128 −1.12481
\(565\) −65.3417 −2.74895
\(566\) 39.1262 1.64460
\(567\) −4.57168 −0.191992
\(568\) 0.761310 0.0319439
\(569\) −26.3693 −1.10546 −0.552730 0.833361i \(-0.686414\pi\)
−0.552730 + 0.833361i \(0.686414\pi\)
\(570\) 39.8743 1.67015
\(571\) 10.5608 0.441954 0.220977 0.975279i \(-0.429075\pi\)
0.220977 + 0.975279i \(0.429075\pi\)
\(572\) −44.2798 −1.85143
\(573\) 25.4143 1.06170
\(574\) −57.0834 −2.38262
\(575\) 79.7778 3.32696
\(576\) 13.6980 0.570750
\(577\) −27.1978 −1.13226 −0.566129 0.824317i \(-0.691560\pi\)
−0.566129 + 0.824317i \(0.691560\pi\)
\(578\) 36.5205 1.51905
\(579\) −7.33459 −0.304815
\(580\) 158.149 6.56678
\(581\) 35.8161 1.48590
\(582\) 10.7399 0.445181
\(583\) 15.2470 0.631468
\(584\) 63.2514 2.61736
\(585\) 16.8134 0.695147
\(586\) −50.4451 −2.08387
\(587\) 20.5705 0.849034 0.424517 0.905420i \(-0.360444\pi\)
0.424517 + 0.905420i \(0.360444\pi\)
\(588\) −29.9906 −1.23679
\(589\) 13.1178 0.540511
\(590\) −83.7038 −3.44603
\(591\) 18.1957 0.748472
\(592\) −1.91069 −0.0785288
\(593\) −33.3908 −1.37120 −0.685598 0.727981i \(-0.740459\pi\)
−0.685598 + 0.727981i \(0.740459\pi\)
\(594\) 57.2255 2.34799
\(595\) 20.8396 0.854340
\(596\) 40.1130 1.64309
\(597\) −8.30073 −0.339726
\(598\) −47.3887 −1.93787
\(599\) 38.7384 1.58281 0.791405 0.611292i \(-0.209350\pi\)
0.791405 + 0.611292i \(0.209350\pi\)
\(600\) 59.0756 2.41175
\(601\) 2.64984 0.108089 0.0540446 0.998539i \(-0.482789\pi\)
0.0540446 + 0.998539i \(0.482789\pi\)
\(602\) −18.4537 −0.752118
\(603\) −0.0353994 −0.00144158
\(604\) −11.5403 −0.469568
\(605\) −30.9128 −1.25678
\(606\) −22.0006 −0.893715
\(607\) −11.3306 −0.459897 −0.229948 0.973203i \(-0.573856\pi\)
−0.229948 + 0.973203i \(0.573856\pi\)
\(608\) −0.691862 −0.0280587
\(609\) 42.8287 1.73550
\(610\) 73.7956 2.98790
\(611\) 14.8796 0.601965
\(612\) 9.51517 0.384628
\(613\) −19.0320 −0.768696 −0.384348 0.923188i \(-0.625574\pi\)
−0.384348 + 0.923188i \(0.625574\pi\)
\(614\) 39.8259 1.60724
\(615\) 28.9481 1.16730
\(616\) 77.2714 3.11335
\(617\) 36.6963 1.47734 0.738669 0.674068i \(-0.235454\pi\)
0.738669 + 0.674068i \(0.235454\pi\)
\(618\) −34.9845 −1.40728
\(619\) −34.4101 −1.38306 −0.691530 0.722348i \(-0.743063\pi\)
−0.691530 + 0.722348i \(0.743063\pi\)
\(620\) 57.5745 2.31225
\(621\) 40.7611 1.63568
\(622\) 58.2265 2.33467
\(623\) 43.9616 1.76128
\(624\) −11.5016 −0.460432
\(625\) 33.5891 1.34356
\(626\) −16.1023 −0.643579
\(627\) −17.9459 −0.716691
\(628\) 44.8909 1.79134
\(629\) 0.707583 0.0282132
\(630\) −58.9756 −2.34964
\(631\) 27.8881 1.11021 0.555104 0.831781i \(-0.312678\pi\)
0.555104 + 0.831781i \(0.312678\pi\)
\(632\) 5.92487 0.235679
\(633\) −19.4305 −0.772295
\(634\) −7.10008 −0.281980
\(635\) 3.90675 0.155035
\(636\) 16.1649 0.640979
\(637\) 16.7054 0.661892
\(638\) −106.943 −4.23392
\(639\) 0.261510 0.0103452
\(640\) −77.8950 −3.07907
\(641\) 39.2139 1.54886 0.774428 0.632663i \(-0.218038\pi\)
0.774428 + 0.632663i \(0.218038\pi\)
\(642\) 36.3194 1.43341
\(643\) 27.3908 1.08019 0.540093 0.841605i \(-0.318389\pi\)
0.540093 + 0.841605i \(0.318389\pi\)
\(644\) 110.632 4.35949
\(645\) 9.35825 0.368481
\(646\) −12.5698 −0.494551
\(647\) 10.1515 0.399098 0.199549 0.979888i \(-0.436052\pi\)
0.199549 + 0.979888i \(0.436052\pi\)
\(648\) 6.02111 0.236532
\(649\) 37.6720 1.47875
\(650\) −66.1431 −2.59435
\(651\) 15.5919 0.611093
\(652\) 1.06688 0.0417822
\(653\) −27.0495 −1.05853 −0.529264 0.848457i \(-0.677532\pi\)
−0.529264 + 0.848457i \(0.677532\pi\)
\(654\) 46.0754 1.80169
\(655\) −72.8693 −2.84724
\(656\) 24.6415 0.962090
\(657\) 21.7268 0.847645
\(658\) −52.1926 −2.03468
\(659\) −14.5738 −0.567715 −0.283857 0.958866i \(-0.591614\pi\)
−0.283857 + 0.958866i \(0.591614\pi\)
\(660\) −78.7650 −3.06592
\(661\) −17.1929 −0.668725 −0.334362 0.942445i \(-0.608521\pi\)
−0.334362 + 0.942445i \(0.608521\pi\)
\(662\) 57.6064 2.23894
\(663\) 4.25936 0.165420
\(664\) −47.1715 −1.83061
\(665\) 51.8524 2.01075
\(666\) −2.00244 −0.0775931
\(667\) −76.1744 −2.94949
\(668\) 59.1906 2.29015
\(669\) −18.6614 −0.721491
\(670\) 0.205246 0.00792934
\(671\) −33.2126 −1.28216
\(672\) −0.822347 −0.0317227
\(673\) −12.8796 −0.496471 −0.248235 0.968700i \(-0.579851\pi\)
−0.248235 + 0.968700i \(0.579851\pi\)
\(674\) −67.0327 −2.58200
\(675\) 56.8926 2.18980
\(676\) −25.5921 −0.984310
\(677\) −1.75429 −0.0674229 −0.0337115 0.999432i \(-0.510733\pi\)
−0.0337115 + 0.999432i \(0.510733\pi\)
\(678\) 46.8450 1.79907
\(679\) 13.9661 0.535969
\(680\) −27.4467 −1.05253
\(681\) 9.67559 0.370769
\(682\) −38.9329 −1.49082
\(683\) 36.0142 1.37804 0.689022 0.724741i \(-0.258040\pi\)
0.689022 + 0.724741i \(0.258040\pi\)
\(684\) 23.6753 0.905249
\(685\) −35.7918 −1.36753
\(686\) 4.33913 0.165669
\(687\) −1.39658 −0.0532829
\(688\) 7.96602 0.303702
\(689\) −9.00419 −0.343032
\(690\) −84.2952 −3.20906
\(691\) 25.1211 0.955651 0.477825 0.878455i \(-0.341425\pi\)
0.477825 + 0.878455i \(0.341425\pi\)
\(692\) −74.6578 −2.83806
\(693\) 26.5427 1.00827
\(694\) 83.4851 3.16905
\(695\) 45.8356 1.73864
\(696\) −56.4073 −2.13811
\(697\) −9.12546 −0.345651
\(698\) 4.20748 0.159255
\(699\) 24.1893 0.914924
\(700\) 154.415 5.83633
\(701\) −24.9904 −0.943873 −0.471937 0.881632i \(-0.656445\pi\)
−0.471937 + 0.881632i \(0.656445\pi\)
\(702\) −33.7947 −1.27550
\(703\) 1.76058 0.0664017
\(704\) 35.7444 1.34717
\(705\) 26.4679 0.996839
\(706\) −64.0182 −2.40936
\(707\) −28.6096 −1.07597
\(708\) 39.9397 1.50103
\(709\) −10.2121 −0.383523 −0.191761 0.981442i \(-0.561420\pi\)
−0.191761 + 0.981442i \(0.561420\pi\)
\(710\) −1.51623 −0.0569033
\(711\) 2.03519 0.0763257
\(712\) −57.8995 −2.16987
\(713\) −27.7314 −1.03855
\(714\) −14.9404 −0.559131
\(715\) 43.8738 1.64079
\(716\) −25.1601 −0.940275
\(717\) −16.6566 −0.622052
\(718\) −46.3088 −1.72823
\(719\) 17.7922 0.663538 0.331769 0.943361i \(-0.392354\pi\)
0.331769 + 0.943361i \(0.392354\pi\)
\(720\) 25.4583 0.948775
\(721\) −45.4938 −1.69428
\(722\) 15.1875 0.565219
\(723\) −1.85856 −0.0691206
\(724\) −5.42341 −0.201559
\(725\) −106.321 −3.94866
\(726\) 22.1621 0.822514
\(727\) 17.3192 0.642333 0.321166 0.947023i \(-0.395925\pi\)
0.321166 + 0.947023i \(0.395925\pi\)
\(728\) −45.6328 −1.69127
\(729\) 20.7684 0.769201
\(730\) −125.972 −4.66244
\(731\) −2.95005 −0.109111
\(732\) −35.2119 −1.30147
\(733\) −46.2614 −1.70870 −0.854351 0.519696i \(-0.826045\pi\)
−0.854351 + 0.519696i \(0.826045\pi\)
\(734\) 74.6131 2.75402
\(735\) 29.7156 1.09608
\(736\) 1.46261 0.0539127
\(737\) −0.0923735 −0.00340262
\(738\) 25.8248 0.950626
\(739\) −35.6200 −1.31030 −0.655151 0.755498i \(-0.727395\pi\)
−0.655151 + 0.755498i \(0.727395\pi\)
\(740\) 7.72724 0.284059
\(741\) 10.5980 0.389328
\(742\) 31.5836 1.15947
\(743\) 11.8628 0.435202 0.217601 0.976038i \(-0.430177\pi\)
0.217601 + 0.976038i \(0.430177\pi\)
\(744\) −20.5352 −0.752857
\(745\) −39.7453 −1.45615
\(746\) 36.4078 1.33298
\(747\) −16.2034 −0.592851
\(748\) 24.8295 0.907856
\(749\) 47.2297 1.72574
\(750\) −61.9067 −2.26051
\(751\) −39.4769 −1.44053 −0.720267 0.693697i \(-0.755981\pi\)
−0.720267 + 0.693697i \(0.755981\pi\)
\(752\) 22.5303 0.821595
\(753\) −15.8960 −0.579282
\(754\) 63.1556 2.29999
\(755\) 11.4345 0.416145
\(756\) 78.8955 2.86940
\(757\) 5.05330 0.183665 0.0918327 0.995774i \(-0.470728\pi\)
0.0918327 + 0.995774i \(0.470728\pi\)
\(758\) 72.5150 2.63386
\(759\) 37.9381 1.37707
\(760\) −68.2921 −2.47721
\(761\) 2.73522 0.0991518 0.0495759 0.998770i \(-0.484213\pi\)
0.0495759 + 0.998770i \(0.484213\pi\)
\(762\) −2.80084 −0.101464
\(763\) 59.9164 2.16912
\(764\) −87.4903 −3.16529
\(765\) −9.42794 −0.340868
\(766\) −54.4693 −1.96806
\(767\) −22.2473 −0.803303
\(768\) 36.8021 1.32798
\(769\) 8.97463 0.323633 0.161817 0.986821i \(-0.448265\pi\)
0.161817 + 0.986821i \(0.448265\pi\)
\(770\) −153.895 −5.54598
\(771\) 12.4367 0.447896
\(772\) 25.2498 0.908759
\(773\) 34.2513 1.23193 0.615967 0.787772i \(-0.288766\pi\)
0.615967 + 0.787772i \(0.288766\pi\)
\(774\) 8.34856 0.300083
\(775\) −38.7064 −1.39037
\(776\) −18.3940 −0.660305
\(777\) 2.09263 0.0750727
\(778\) 48.5128 1.73927
\(779\) −22.7057 −0.813516
\(780\) 46.5149 1.66550
\(781\) 0.682400 0.0244182
\(782\) 26.5728 0.950241
\(783\) −54.3229 −1.94134
\(784\) 25.2949 0.903388
\(785\) −44.4794 −1.58754
\(786\) 52.2417 1.86340
\(787\) 26.8581 0.957389 0.478694 0.877982i \(-0.341110\pi\)
0.478694 + 0.877982i \(0.341110\pi\)
\(788\) −62.6399 −2.23145
\(789\) 8.61216 0.306601
\(790\) −11.8000 −0.419827
\(791\) 60.9172 2.16597
\(792\) −34.9580 −1.24218
\(793\) 19.6138 0.696507
\(794\) −30.6651 −1.08826
\(795\) −16.0167 −0.568053
\(796\) 28.5758 1.01284
\(797\) −21.8180 −0.772834 −0.386417 0.922324i \(-0.626287\pi\)
−0.386417 + 0.922324i \(0.626287\pi\)
\(798\) −37.1742 −1.31595
\(799\) −8.34361 −0.295176
\(800\) 2.04146 0.0721763
\(801\) −19.8885 −0.702724
\(802\) 69.3898 2.45024
\(803\) 56.6954 2.00074
\(804\) −0.0979341 −0.00345387
\(805\) −109.617 −3.86350
\(806\) 22.9919 0.809856
\(807\) −9.68664 −0.340986
\(808\) 37.6801 1.32558
\(809\) 21.0055 0.738514 0.369257 0.929327i \(-0.379612\pi\)
0.369257 + 0.929327i \(0.379612\pi\)
\(810\) −11.9917 −0.421346
\(811\) 24.2269 0.850722 0.425361 0.905024i \(-0.360147\pi\)
0.425361 + 0.905024i \(0.360147\pi\)
\(812\) −147.440 −5.17414
\(813\) −1.16197 −0.0407522
\(814\) −5.22530 −0.183147
\(815\) −1.05710 −0.0370286
\(816\) 6.44941 0.225774
\(817\) −7.34021 −0.256801
\(818\) 80.1441 2.80217
\(819\) −15.6749 −0.547724
\(820\) −99.6557 −3.48013
\(821\) −23.1127 −0.806639 −0.403320 0.915059i \(-0.632144\pi\)
−0.403320 + 0.915059i \(0.632144\pi\)
\(822\) 25.6600 0.894994
\(823\) 14.6899 0.512059 0.256030 0.966669i \(-0.417586\pi\)
0.256030 + 0.966669i \(0.417586\pi\)
\(824\) 59.9174 2.08732
\(825\) 52.9524 1.84357
\(826\) 78.0360 2.71522
\(827\) −52.5408 −1.82702 −0.913511 0.406815i \(-0.866639\pi\)
−0.913511 + 0.406815i \(0.866639\pi\)
\(828\) −50.0503 −1.73937
\(829\) 24.1312 0.838112 0.419056 0.907960i \(-0.362361\pi\)
0.419056 + 0.907960i \(0.362361\pi\)
\(830\) 93.9473 3.26096
\(831\) −26.9601 −0.935236
\(832\) −21.1090 −0.731821
\(833\) −9.36741 −0.324561
\(834\) −32.8606 −1.13787
\(835\) −58.6480 −2.02960
\(836\) 61.7799 2.13670
\(837\) −19.7763 −0.683571
\(838\) 92.3408 3.18986
\(839\) 43.4372 1.49962 0.749809 0.661654i \(-0.230145\pi\)
0.749809 + 0.661654i \(0.230145\pi\)
\(840\) −81.1719 −2.80070
\(841\) 72.5188 2.50065
\(842\) −48.0285 −1.65517
\(843\) −3.10916 −0.107085
\(844\) 66.8908 2.30248
\(845\) 25.3575 0.872323
\(846\) 23.6122 0.811805
\(847\) 28.8196 0.990253
\(848\) −13.6339 −0.468190
\(849\) 18.4981 0.634854
\(850\) 37.0892 1.27215
\(851\) −3.72192 −0.127586
\(852\) 0.723479 0.0247860
\(853\) −30.1252 −1.03147 −0.515733 0.856749i \(-0.672480\pi\)
−0.515733 + 0.856749i \(0.672480\pi\)
\(854\) −68.7986 −2.35424
\(855\) −23.4583 −0.802257
\(856\) −62.2037 −2.12608
\(857\) −26.7327 −0.913171 −0.456586 0.889679i \(-0.650928\pi\)
−0.456586 + 0.889679i \(0.650928\pi\)
\(858\) −31.4542 −1.07383
\(859\) 54.2227 1.85006 0.925028 0.379900i \(-0.124042\pi\)
0.925028 + 0.379900i \(0.124042\pi\)
\(860\) −32.2163 −1.09857
\(861\) −26.9880 −0.919747
\(862\) 45.0429 1.53417
\(863\) 5.88736 0.200408 0.100204 0.994967i \(-0.468050\pi\)
0.100204 + 0.994967i \(0.468050\pi\)
\(864\) 1.04305 0.0354851
\(865\) 73.9734 2.51517
\(866\) −17.2120 −0.584889
\(867\) 17.2662 0.586390
\(868\) −53.6759 −1.82188
\(869\) 5.31076 0.180155
\(870\) 112.341 3.80873
\(871\) 0.0545514 0.00184841
\(872\) −78.9127 −2.67232
\(873\) −6.31833 −0.213843
\(874\) 66.1176 2.23646
\(875\) −80.5034 −2.72151
\(876\) 60.1082 2.03087
\(877\) 30.6843 1.03613 0.518067 0.855340i \(-0.326652\pi\)
0.518067 + 0.855340i \(0.326652\pi\)
\(878\) 19.5984 0.661415
\(879\) −23.8495 −0.804423
\(880\) 66.4325 2.23944
\(881\) 29.4768 0.993100 0.496550 0.868008i \(-0.334600\pi\)
0.496550 + 0.868008i \(0.334600\pi\)
\(882\) 26.5095 0.892623
\(883\) 48.1323 1.61978 0.809890 0.586582i \(-0.199527\pi\)
0.809890 + 0.586582i \(0.199527\pi\)
\(884\) −14.6631 −0.493174
\(885\) −39.5736 −1.33025
\(886\) 7.76177 0.260762
\(887\) −46.5561 −1.56320 −0.781601 0.623778i \(-0.785597\pi\)
−0.781601 + 0.623778i \(0.785597\pi\)
\(888\) −2.75609 −0.0924883
\(889\) −3.64221 −0.122156
\(890\) 115.313 3.86531
\(891\) 5.39702 0.180807
\(892\) 64.2430 2.15101
\(893\) −20.7603 −0.694717
\(894\) 28.4943 0.952993
\(895\) 24.9294 0.833298
\(896\) 72.6205 2.42608
\(897\) −22.4045 −0.748063
\(898\) 84.0967 2.80634
\(899\) 36.9581 1.23262
\(900\) −69.8581 −2.32860
\(901\) 5.04902 0.168207
\(902\) 67.3890 2.24381
\(903\) −8.72457 −0.290335
\(904\) −80.2307 −2.66843
\(905\) 5.37369 0.178628
\(906\) −8.19768 −0.272350
\(907\) 48.3460 1.60530 0.802651 0.596450i \(-0.203422\pi\)
0.802651 + 0.596450i \(0.203422\pi\)
\(908\) −33.3088 −1.10539
\(909\) 12.9431 0.429296
\(910\) 90.8829 3.01274
\(911\) 9.76175 0.323421 0.161711 0.986838i \(-0.448299\pi\)
0.161711 + 0.986838i \(0.448299\pi\)
\(912\) 16.0472 0.531376
\(913\) −42.2822 −1.39934
\(914\) 1.06358 0.0351801
\(915\) 34.8891 1.15340
\(916\) 4.80781 0.158855
\(917\) 67.9350 2.24341
\(918\) 18.9501 0.625445
\(919\) −0.514857 −0.0169836 −0.00849179 0.999964i \(-0.502703\pi\)
−0.00849179 + 0.999964i \(0.502703\pi\)
\(920\) 144.371 4.75977
\(921\) 18.8289 0.620435
\(922\) −17.9730 −0.591910
\(923\) −0.402994 −0.0132647
\(924\) 73.4316 2.41572
\(925\) −5.19490 −0.170807
\(926\) 30.7277 1.00977
\(927\) 20.5816 0.675989
\(928\) −1.94925 −0.0639872
\(929\) −12.8592 −0.421898 −0.210949 0.977497i \(-0.567655\pi\)
−0.210949 + 0.977497i \(0.567655\pi\)
\(930\) 40.8981 1.34110
\(931\) −23.3077 −0.763879
\(932\) −83.2732 −2.72770
\(933\) 27.5284 0.901238
\(934\) 95.1443 3.11322
\(935\) −24.6019 −0.804567
\(936\) 20.6445 0.674788
\(937\) 21.1431 0.690714 0.345357 0.938471i \(-0.387758\pi\)
0.345357 + 0.938471i \(0.387758\pi\)
\(938\) −0.191348 −0.00624773
\(939\) −7.61287 −0.248437
\(940\) −91.1174 −2.97192
\(941\) 12.8423 0.418647 0.209323 0.977846i \(-0.432874\pi\)
0.209323 + 0.977846i \(0.432874\pi\)
\(942\) 31.8884 1.03898
\(943\) 48.0004 1.56311
\(944\) −33.6862 −1.09639
\(945\) −78.1723 −2.54294
\(946\) 21.7853 0.708300
\(947\) −14.1061 −0.458388 −0.229194 0.973381i \(-0.573609\pi\)
−0.229194 + 0.973381i \(0.573609\pi\)
\(948\) 5.63045 0.182869
\(949\) −33.4816 −1.08686
\(950\) 92.2841 2.99409
\(951\) −3.35678 −0.108851
\(952\) 25.5882 0.829318
\(953\) −49.9114 −1.61679 −0.808395 0.588640i \(-0.799663\pi\)
−0.808395 + 0.588640i \(0.799663\pi\)
\(954\) −14.2886 −0.462611
\(955\) 86.6883 2.80517
\(956\) 57.3413 1.85455
\(957\) −50.5607 −1.63440
\(958\) 60.5875 1.95749
\(959\) 33.3682 1.07751
\(960\) −37.5487 −1.21188
\(961\) −17.5453 −0.565978
\(962\) 3.08582 0.0994907
\(963\) −21.3670 −0.688541
\(964\) 6.39821 0.206072
\(965\) −25.0183 −0.805368
\(966\) 78.5873 2.52850
\(967\) 50.4565 1.62257 0.811286 0.584649i \(-0.198768\pi\)
0.811286 + 0.584649i \(0.198768\pi\)
\(968\) −37.9567 −1.21998
\(969\) −5.94274 −0.190908
\(970\) 36.6337 1.17624
\(971\) −33.0044 −1.05916 −0.529581 0.848259i \(-0.677651\pi\)
−0.529581 + 0.848259i \(0.677651\pi\)
\(972\) −58.6546 −1.88135
\(973\) −42.7319 −1.36992
\(974\) 5.23444 0.167722
\(975\) −31.2712 −1.00148
\(976\) 29.6987 0.950632
\(977\) −32.3762 −1.03581 −0.517903 0.855440i \(-0.673287\pi\)
−0.517903 + 0.855440i \(0.673287\pi\)
\(978\) 0.757859 0.0242337
\(979\) −51.8982 −1.65867
\(980\) −102.298 −3.26779
\(981\) −27.1065 −0.865444
\(982\) 83.1521 2.65349
\(983\) −43.0429 −1.37286 −0.686428 0.727198i \(-0.740822\pi\)
−0.686428 + 0.727198i \(0.740822\pi\)
\(984\) 35.5444 1.13311
\(985\) 62.0656 1.97758
\(986\) −35.4139 −1.12781
\(987\) −24.6757 −0.785435
\(988\) −36.4843 −1.16072
\(989\) 15.5174 0.493424
\(990\) 69.6227 2.21275
\(991\) −53.0669 −1.68573 −0.842863 0.538129i \(-0.819131\pi\)
−0.842863 + 0.538129i \(0.819131\pi\)
\(992\) −0.709628 −0.0225307
\(993\) 27.2352 0.864283
\(994\) 1.41356 0.0448356
\(995\) −28.3138 −0.897608
\(996\) −44.8274 −1.42041
\(997\) −11.8393 −0.374954 −0.187477 0.982269i \(-0.560031\pi\)
−0.187477 + 0.982269i \(0.560031\pi\)
\(998\) 56.4878 1.78809
\(999\) −2.65424 −0.0839765
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 \(a_p\))