Properties

Label 8021.2.a.a.1.16
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +O(q^{10})\) \(q-2.25892 q^{2} +1.96923 q^{3} +3.10273 q^{4} -2.33615 q^{5} -4.44833 q^{6} -1.78149 q^{7} -2.49097 q^{8} +0.877859 q^{9} +5.27718 q^{10} +0.876358 q^{11} +6.10997 q^{12} +1.00000 q^{13} +4.02425 q^{14} -4.60042 q^{15} -0.578545 q^{16} -4.07944 q^{17} -1.98301 q^{18} -0.618616 q^{19} -7.24844 q^{20} -3.50816 q^{21} -1.97962 q^{22} +1.84925 q^{23} -4.90529 q^{24} +0.457608 q^{25} -2.25892 q^{26} -4.17898 q^{27} -5.52748 q^{28} -2.44360 q^{29} +10.3920 q^{30} -2.19500 q^{31} +6.28883 q^{32} +1.72575 q^{33} +9.21513 q^{34} +4.16183 q^{35} +2.72375 q^{36} +7.05873 q^{37} +1.39741 q^{38} +1.96923 q^{39} +5.81929 q^{40} +9.83684 q^{41} +7.92466 q^{42} +9.85045 q^{43} +2.71910 q^{44} -2.05081 q^{45} -4.17731 q^{46} +5.03215 q^{47} -1.13929 q^{48} -3.82629 q^{49} -1.03370 q^{50} -8.03334 q^{51} +3.10273 q^{52} +0.650174 q^{53} +9.43999 q^{54} -2.04731 q^{55} +4.43764 q^{56} -1.21820 q^{57} +5.51990 q^{58} +12.9876 q^{59} -14.2738 q^{60} +8.84685 q^{61} +4.95832 q^{62} -1.56390 q^{63} -13.0489 q^{64} -2.33615 q^{65} -3.89833 q^{66} -4.47938 q^{67} -12.6574 q^{68} +3.64159 q^{69} -9.40126 q^{70} +12.2604 q^{71} -2.18672 q^{72} +9.32880 q^{73} -15.9451 q^{74} +0.901134 q^{75} -1.91940 q^{76} -1.56122 q^{77} -4.44833 q^{78} -5.45394 q^{79} +1.35157 q^{80} -10.8629 q^{81} -22.2206 q^{82} -4.47644 q^{83} -10.8849 q^{84} +9.53019 q^{85} -22.2514 q^{86} -4.81200 q^{87} -2.18298 q^{88} -3.76320 q^{89} +4.63262 q^{90} -1.78149 q^{91} +5.73771 q^{92} -4.32245 q^{93} -11.3672 q^{94} +1.44518 q^{95} +12.3841 q^{96} -4.39280 q^{97} +8.64329 q^{98} +0.769319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25892 −1.59730 −0.798649 0.601797i \(-0.794452\pi\)
−0.798649 + 0.601797i \(0.794452\pi\)
\(3\) 1.96923 1.13693 0.568467 0.822706i \(-0.307537\pi\)
0.568467 + 0.822706i \(0.307537\pi\)
\(4\) 3.10273 1.55136
\(5\) −2.33615 −1.04476 −0.522380 0.852713i \(-0.674956\pi\)
−0.522380 + 0.852713i \(0.674956\pi\)
\(6\) −4.44833 −1.81602
\(7\) −1.78149 −0.673340 −0.336670 0.941623i \(-0.609301\pi\)
−0.336670 + 0.941623i \(0.609301\pi\)
\(8\) −2.49097 −0.880691
\(9\) 0.877859 0.292620
\(10\) 5.27718 1.66879
\(11\) 0.876358 0.264232 0.132116 0.991234i \(-0.457823\pi\)
0.132116 + 0.991234i \(0.457823\pi\)
\(12\) 6.10997 1.76380
\(13\) 1.00000 0.277350
\(14\) 4.02425 1.07553
\(15\) −4.60042 −1.18782
\(16\) −0.578545 −0.144636
\(17\) −4.07944 −0.989409 −0.494704 0.869061i \(-0.664724\pi\)
−0.494704 + 0.869061i \(0.664724\pi\)
\(18\) −1.98301 −0.467401
\(19\) −0.618616 −0.141920 −0.0709602 0.997479i \(-0.522606\pi\)
−0.0709602 + 0.997479i \(0.522606\pi\)
\(20\) −7.24844 −1.62080
\(21\) −3.50816 −0.765544
\(22\) −1.97962 −0.422057
\(23\) 1.84925 0.385595 0.192798 0.981239i \(-0.438244\pi\)
0.192798 + 0.981239i \(0.438244\pi\)
\(24\) −4.90529 −1.00129
\(25\) 0.457608 0.0915216
\(26\) −2.25892 −0.443011
\(27\) −4.17898 −0.804245
\(28\) −5.52748 −1.04460
\(29\) −2.44360 −0.453765 −0.226882 0.973922i \(-0.572853\pi\)
−0.226882 + 0.973922i \(0.572853\pi\)
\(30\) 10.3920 1.89731
\(31\) −2.19500 −0.394233 −0.197116 0.980380i \(-0.563158\pi\)
−0.197116 + 0.980380i \(0.563158\pi\)
\(32\) 6.28883 1.11172
\(33\) 1.72575 0.300414
\(34\) 9.21513 1.58038
\(35\) 4.16183 0.703478
\(36\) 2.72375 0.453959
\(37\) 7.05873 1.16045 0.580224 0.814457i \(-0.302965\pi\)
0.580224 + 0.814457i \(0.302965\pi\)
\(38\) 1.39741 0.226689
\(39\) 1.96923 0.315329
\(40\) 5.81929 0.920110
\(41\) 9.83684 1.53626 0.768128 0.640296i \(-0.221188\pi\)
0.768128 + 0.640296i \(0.221188\pi\)
\(42\) 7.92466 1.22280
\(43\) 9.85045 1.50218 0.751090 0.660200i \(-0.229528\pi\)
0.751090 + 0.660200i \(0.229528\pi\)
\(44\) 2.71910 0.409920
\(45\) −2.05081 −0.305717
\(46\) −4.17731 −0.615911
\(47\) 5.03215 0.734014 0.367007 0.930218i \(-0.380382\pi\)
0.367007 + 0.930218i \(0.380382\pi\)
\(48\) −1.13929 −0.164442
\(49\) −3.82629 −0.546613
\(50\) −1.03370 −0.146187
\(51\) −8.03334 −1.12489
\(52\) 3.10273 0.430271
\(53\) 0.650174 0.0893083 0.0446542 0.999003i \(-0.485781\pi\)
0.0446542 + 0.999003i \(0.485781\pi\)
\(54\) 9.43999 1.28462
\(55\) −2.04731 −0.276059
\(56\) 4.43764 0.593005
\(57\) −1.21820 −0.161354
\(58\) 5.51990 0.724798
\(59\) 12.9876 1.69084 0.845421 0.534101i \(-0.179350\pi\)
0.845421 + 0.534101i \(0.179350\pi\)
\(60\) −14.2738 −1.84274
\(61\) 8.84685 1.13272 0.566361 0.824157i \(-0.308351\pi\)
0.566361 + 0.824157i \(0.308351\pi\)
\(62\) 4.95832 0.629708
\(63\) −1.56390 −0.197033
\(64\) −13.0489 −1.63111
\(65\) −2.33615 −0.289764
\(66\) −3.89833 −0.479851
\(67\) −4.47938 −0.547244 −0.273622 0.961837i \(-0.588222\pi\)
−0.273622 + 0.961837i \(0.588222\pi\)
\(68\) −12.6574 −1.53493
\(69\) 3.64159 0.438396
\(70\) −9.40126 −1.12367
\(71\) 12.2604 1.45504 0.727519 0.686087i \(-0.240673\pi\)
0.727519 + 0.686087i \(0.240673\pi\)
\(72\) −2.18672 −0.257707
\(73\) 9.32880 1.09185 0.545927 0.837833i \(-0.316178\pi\)
0.545927 + 0.837833i \(0.316178\pi\)
\(74\) −15.9451 −1.85358
\(75\) 0.901134 0.104054
\(76\) −1.91940 −0.220170
\(77\) −1.56122 −0.177918
\(78\) −4.44833 −0.503674
\(79\) −5.45394 −0.613616 −0.306808 0.951771i \(-0.599261\pi\)
−0.306808 + 0.951771i \(0.599261\pi\)
\(80\) 1.35157 0.151110
\(81\) −10.8629 −1.20699
\(82\) −22.2206 −2.45386
\(83\) −4.47644 −0.491353 −0.245677 0.969352i \(-0.579010\pi\)
−0.245677 + 0.969352i \(0.579010\pi\)
\(84\) −10.8849 −1.18764
\(85\) 9.53019 1.03369
\(86\) −22.2514 −2.39943
\(87\) −4.81200 −0.515901
\(88\) −2.18298 −0.232707
\(89\) −3.76320 −0.398898 −0.199449 0.979908i \(-0.563915\pi\)
−0.199449 + 0.979908i \(0.563915\pi\)
\(90\) 4.63262 0.488321
\(91\) −1.78149 −0.186751
\(92\) 5.73771 0.598198
\(93\) −4.32245 −0.448217
\(94\) −11.3672 −1.17244
\(95\) 1.44518 0.148273
\(96\) 12.3841 1.26395
\(97\) −4.39280 −0.446021 −0.223011 0.974816i \(-0.571588\pi\)
−0.223011 + 0.974816i \(0.571588\pi\)
\(98\) 8.64329 0.873104
\(99\) 0.769319 0.0773194
\(100\) 1.41983 0.141983
\(101\) −11.1496 −1.10943 −0.554715 0.832040i \(-0.687173\pi\)
−0.554715 + 0.832040i \(0.687173\pi\)
\(102\) 18.1467 1.79679
\(103\) −16.4044 −1.61638 −0.808188 0.588924i \(-0.799552\pi\)
−0.808188 + 0.588924i \(0.799552\pi\)
\(104\) −2.49097 −0.244260
\(105\) 8.19560 0.799809
\(106\) −1.46869 −0.142652
\(107\) 4.15832 0.402000 0.201000 0.979591i \(-0.435581\pi\)
0.201000 + 0.979591i \(0.435581\pi\)
\(108\) −12.9662 −1.24768
\(109\) −13.5478 −1.29765 −0.648823 0.760939i \(-0.724739\pi\)
−0.648823 + 0.760939i \(0.724739\pi\)
\(110\) 4.62470 0.440948
\(111\) 13.9003 1.31935
\(112\) 1.03067 0.0973894
\(113\) −12.3110 −1.15812 −0.579060 0.815285i \(-0.696580\pi\)
−0.579060 + 0.815285i \(0.696580\pi\)
\(114\) 2.75181 0.257731
\(115\) −4.32013 −0.402854
\(116\) −7.58182 −0.703954
\(117\) 0.877859 0.0811581
\(118\) −29.3380 −2.70078
\(119\) 7.26748 0.666209
\(120\) 11.4595 1.04610
\(121\) −10.2320 −0.930181
\(122\) −19.9843 −1.80930
\(123\) 19.3710 1.74662
\(124\) −6.81047 −0.611598
\(125\) 10.6117 0.949141
\(126\) 3.53272 0.314720
\(127\) −19.2315 −1.70652 −0.853258 0.521488i \(-0.825377\pi\)
−0.853258 + 0.521488i \(0.825377\pi\)
\(128\) 16.8987 1.49365
\(129\) 19.3978 1.70788
\(130\) 5.27718 0.462840
\(131\) 7.93404 0.693200 0.346600 0.938013i \(-0.387336\pi\)
0.346600 + 0.938013i \(0.387336\pi\)
\(132\) 5.35453 0.466052
\(133\) 1.10206 0.0955607
\(134\) 10.1186 0.874112
\(135\) 9.76273 0.840242
\(136\) 10.1618 0.871363
\(137\) −1.72942 −0.147754 −0.0738770 0.997267i \(-0.523537\pi\)
−0.0738770 + 0.997267i \(0.523537\pi\)
\(138\) −8.22607 −0.700250
\(139\) −22.9671 −1.94805 −0.974023 0.226449i \(-0.927288\pi\)
−0.974023 + 0.226449i \(0.927288\pi\)
\(140\) 12.9130 1.09135
\(141\) 9.90944 0.834526
\(142\) −27.6952 −2.32413
\(143\) 0.876358 0.0732848
\(144\) −0.507881 −0.0423234
\(145\) 5.70862 0.474075
\(146\) −21.0730 −1.74402
\(147\) −7.53484 −0.621463
\(148\) 21.9013 1.80028
\(149\) −5.89663 −0.483071 −0.241535 0.970392i \(-0.577651\pi\)
−0.241535 + 0.970392i \(0.577651\pi\)
\(150\) −2.03559 −0.166205
\(151\) 20.5433 1.67179 0.835894 0.548890i \(-0.184950\pi\)
0.835894 + 0.548890i \(0.184950\pi\)
\(152\) 1.54096 0.124988
\(153\) −3.58117 −0.289520
\(154\) 3.52668 0.284188
\(155\) 5.12785 0.411879
\(156\) 6.10997 0.489189
\(157\) 4.33920 0.346306 0.173153 0.984895i \(-0.444604\pi\)
0.173153 + 0.984895i \(0.444604\pi\)
\(158\) 12.3200 0.980128
\(159\) 1.28034 0.101538
\(160\) −14.6917 −1.16148
\(161\) −3.29442 −0.259637
\(162\) 24.5385 1.92793
\(163\) −6.85601 −0.537004 −0.268502 0.963279i \(-0.586529\pi\)
−0.268502 + 0.963279i \(0.586529\pi\)
\(164\) 30.5210 2.38329
\(165\) −4.03161 −0.313861
\(166\) 10.1119 0.784838
\(167\) −5.81311 −0.449832 −0.224916 0.974378i \(-0.572211\pi\)
−0.224916 + 0.974378i \(0.572211\pi\)
\(168\) 8.73873 0.674207
\(169\) 1.00000 0.0769231
\(170\) −21.5279 −1.65112
\(171\) −0.543058 −0.0415287
\(172\) 30.5633 2.33043
\(173\) 16.8780 1.28321 0.641606 0.767034i \(-0.278268\pi\)
0.641606 + 0.767034i \(0.278268\pi\)
\(174\) 10.8699 0.824048
\(175\) −0.815224 −0.0616252
\(176\) −0.507013 −0.0382175
\(177\) 25.5755 1.92238
\(178\) 8.50077 0.637160
\(179\) 2.57803 0.192691 0.0963455 0.995348i \(-0.469285\pi\)
0.0963455 + 0.995348i \(0.469285\pi\)
\(180\) −6.36311 −0.474278
\(181\) 10.5920 0.787299 0.393649 0.919261i \(-0.371212\pi\)
0.393649 + 0.919261i \(0.371212\pi\)
\(182\) 4.02425 0.298297
\(183\) 17.4215 1.28783
\(184\) −4.60643 −0.339590
\(185\) −16.4903 −1.21239
\(186\) 9.76407 0.715936
\(187\) −3.57505 −0.261433
\(188\) 15.6134 1.13872
\(189\) 7.44482 0.541531
\(190\) −3.26455 −0.236836
\(191\) 10.1881 0.737185 0.368593 0.929591i \(-0.379840\pi\)
0.368593 + 0.929591i \(0.379840\pi\)
\(192\) −25.6962 −1.85446
\(193\) −3.07177 −0.221111 −0.110556 0.993870i \(-0.535263\pi\)
−0.110556 + 0.993870i \(0.535263\pi\)
\(194\) 9.92299 0.712429
\(195\) −4.60042 −0.329443
\(196\) −11.8719 −0.847995
\(197\) −18.3263 −1.30569 −0.652847 0.757490i \(-0.726426\pi\)
−0.652847 + 0.757490i \(0.726426\pi\)
\(198\) −1.73783 −0.123502
\(199\) 7.67756 0.544247 0.272124 0.962262i \(-0.412274\pi\)
0.272124 + 0.962262i \(0.412274\pi\)
\(200\) −1.13989 −0.0806022
\(201\) −8.82093 −0.622180
\(202\) 25.1862 1.77209
\(203\) 4.35325 0.305538
\(204\) −24.9253 −1.74512
\(205\) −22.9803 −1.60502
\(206\) 37.0563 2.58184
\(207\) 1.62338 0.112833
\(208\) −0.578545 −0.0401149
\(209\) −0.542130 −0.0374999
\(210\) −18.5132 −1.27753
\(211\) −0.622270 −0.0428388 −0.0214194 0.999771i \(-0.506819\pi\)
−0.0214194 + 0.999771i \(0.506819\pi\)
\(212\) 2.01731 0.138550
\(213\) 24.1435 1.65428
\(214\) −9.39333 −0.642115
\(215\) −23.0122 −1.56942
\(216\) 10.4097 0.708291
\(217\) 3.91037 0.265453
\(218\) 30.6035 2.07273
\(219\) 18.3705 1.24137
\(220\) −6.35223 −0.428267
\(221\) −4.07944 −0.274413
\(222\) −31.3996 −2.10740
\(223\) 7.29827 0.488728 0.244364 0.969684i \(-0.421421\pi\)
0.244364 + 0.969684i \(0.421421\pi\)
\(224\) −11.2035 −0.748565
\(225\) 0.401715 0.0267810
\(226\) 27.8095 1.84986
\(227\) −24.4719 −1.62426 −0.812130 0.583477i \(-0.801692\pi\)
−0.812130 + 0.583477i \(0.801692\pi\)
\(228\) −3.77973 −0.250319
\(229\) −9.11998 −0.602665 −0.301333 0.953519i \(-0.597431\pi\)
−0.301333 + 0.953519i \(0.597431\pi\)
\(230\) 9.75883 0.643478
\(231\) −3.07441 −0.202281
\(232\) 6.08693 0.399627
\(233\) −11.6853 −0.765527 −0.382763 0.923846i \(-0.625028\pi\)
−0.382763 + 0.923846i \(0.625028\pi\)
\(234\) −1.98301 −0.129634
\(235\) −11.7559 −0.766868
\(236\) 40.2970 2.62311
\(237\) −10.7400 −0.697641
\(238\) −16.4167 −1.06413
\(239\) 0.221982 0.0143588 0.00717942 0.999974i \(-0.497715\pi\)
0.00717942 + 0.999974i \(0.497715\pi\)
\(240\) 2.66155 0.171802
\(241\) −15.4671 −0.996325 −0.498163 0.867084i \(-0.665992\pi\)
−0.498163 + 0.867084i \(0.665992\pi\)
\(242\) 23.1133 1.48578
\(243\) −8.85466 −0.568027
\(244\) 27.4493 1.75726
\(245\) 8.93880 0.571079
\(246\) −43.7575 −2.78988
\(247\) −0.618616 −0.0393616
\(248\) 5.46767 0.347197
\(249\) −8.81513 −0.558636
\(250\) −23.9710 −1.51606
\(251\) −1.07569 −0.0678971 −0.0339486 0.999424i \(-0.510808\pi\)
−0.0339486 + 0.999424i \(0.510808\pi\)
\(252\) −4.85234 −0.305669
\(253\) 1.62061 0.101887
\(254\) 43.4424 2.72582
\(255\) 18.7671 1.17524
\(256\) −12.0752 −0.754697
\(257\) 25.8401 1.61186 0.805930 0.592011i \(-0.201666\pi\)
0.805930 + 0.592011i \(0.201666\pi\)
\(258\) −43.8181 −2.72799
\(259\) −12.5751 −0.781377
\(260\) −7.24844 −0.449529
\(261\) −2.14513 −0.132780
\(262\) −17.9224 −1.10725
\(263\) −31.2144 −1.92476 −0.962380 0.271706i \(-0.912412\pi\)
−0.962380 + 0.271706i \(0.912412\pi\)
\(264\) −4.29879 −0.264572
\(265\) −1.51891 −0.0933057
\(266\) −2.48947 −0.152639
\(267\) −7.41060 −0.453521
\(268\) −13.8983 −0.848974
\(269\) −22.5719 −1.37623 −0.688116 0.725601i \(-0.741562\pi\)
−0.688116 + 0.725601i \(0.741562\pi\)
\(270\) −22.0532 −1.34212
\(271\) −24.9509 −1.51566 −0.757830 0.652453i \(-0.773740\pi\)
−0.757830 + 0.652453i \(0.773740\pi\)
\(272\) 2.36014 0.143104
\(273\) −3.50816 −0.212324
\(274\) 3.90662 0.236007
\(275\) 0.401029 0.0241829
\(276\) 11.2989 0.680112
\(277\) −18.8341 −1.13163 −0.565816 0.824532i \(-0.691439\pi\)
−0.565816 + 0.824532i \(0.691439\pi\)
\(278\) 51.8809 3.11161
\(279\) −1.92690 −0.115360
\(280\) −10.3670 −0.619547
\(281\) 10.5244 0.627830 0.313915 0.949451i \(-0.398359\pi\)
0.313915 + 0.949451i \(0.398359\pi\)
\(282\) −22.3847 −1.33299
\(283\) 30.1203 1.79047 0.895234 0.445597i \(-0.147008\pi\)
0.895234 + 0.445597i \(0.147008\pi\)
\(284\) 38.0406 2.25729
\(285\) 2.84589 0.168576
\(286\) −1.97962 −0.117058
\(287\) −17.5242 −1.03442
\(288\) 5.52070 0.325310
\(289\) −0.358192 −0.0210701
\(290\) −12.8953 −0.757239
\(291\) −8.65042 −0.507097
\(292\) 28.9447 1.69386
\(293\) 11.8053 0.689674 0.344837 0.938663i \(-0.387934\pi\)
0.344837 + 0.938663i \(0.387934\pi\)
\(294\) 17.0206 0.992662
\(295\) −30.3410 −1.76652
\(296\) −17.5831 −1.02200
\(297\) −3.66228 −0.212507
\(298\) 13.3200 0.771609
\(299\) 1.84925 0.106945
\(300\) 2.79597 0.161426
\(301\) −17.5485 −1.01148
\(302\) −46.4057 −2.67035
\(303\) −21.9562 −1.26135
\(304\) 0.357897 0.0205268
\(305\) −20.6676 −1.18342
\(306\) 8.08958 0.462450
\(307\) −19.8524 −1.13303 −0.566517 0.824050i \(-0.691709\pi\)
−0.566517 + 0.824050i \(0.691709\pi\)
\(308\) −4.84405 −0.276015
\(309\) −32.3041 −1.83771
\(310\) −11.5834 −0.657893
\(311\) 10.8085 0.612896 0.306448 0.951887i \(-0.400860\pi\)
0.306448 + 0.951887i \(0.400860\pi\)
\(312\) −4.90529 −0.277707
\(313\) 25.2964 1.42984 0.714919 0.699208i \(-0.246464\pi\)
0.714919 + 0.699208i \(0.246464\pi\)
\(314\) −9.80192 −0.553154
\(315\) 3.65350 0.205852
\(316\) −16.9221 −0.951941
\(317\) 3.78100 0.212362 0.106181 0.994347i \(-0.466138\pi\)
0.106181 + 0.994347i \(0.466138\pi\)
\(318\) −2.89219 −0.162186
\(319\) −2.14147 −0.119899
\(320\) 30.4842 1.70412
\(321\) 8.18869 0.457048
\(322\) 7.44184 0.414717
\(323\) 2.52361 0.140417
\(324\) −33.7047 −1.87248
\(325\) 0.457608 0.0253835
\(326\) 15.4872 0.857755
\(327\) −26.6788 −1.47534
\(328\) −24.5033 −1.35297
\(329\) −8.96472 −0.494241
\(330\) 9.10710 0.501329
\(331\) −5.29120 −0.290831 −0.145415 0.989371i \(-0.546452\pi\)
−0.145415 + 0.989371i \(0.546452\pi\)
\(332\) −13.8892 −0.762267
\(333\) 6.19657 0.339570
\(334\) 13.1313 0.718516
\(335\) 10.4645 0.571738
\(336\) 2.02963 0.110725
\(337\) 9.27317 0.505142 0.252571 0.967578i \(-0.418724\pi\)
0.252571 + 0.967578i \(0.418724\pi\)
\(338\) −2.25892 −0.122869
\(339\) −24.2431 −1.31671
\(340\) 29.5696 1.60363
\(341\) −1.92360 −0.104169
\(342\) 1.22672 0.0663337
\(343\) 19.2869 1.04140
\(344\) −24.5372 −1.32296
\(345\) −8.50732 −0.458019
\(346\) −38.1261 −2.04967
\(347\) 24.1782 1.29796 0.648978 0.760807i \(-0.275197\pi\)
0.648978 + 0.760807i \(0.275197\pi\)
\(348\) −14.9303 −0.800349
\(349\) −18.5285 −0.991807 −0.495904 0.868378i \(-0.665163\pi\)
−0.495904 + 0.868378i \(0.665163\pi\)
\(350\) 1.84153 0.0984338
\(351\) −4.17898 −0.223057
\(352\) 5.51127 0.293752
\(353\) −22.1816 −1.18061 −0.590303 0.807182i \(-0.700992\pi\)
−0.590303 + 0.807182i \(0.700992\pi\)
\(354\) −57.7731 −3.07061
\(355\) −28.6421 −1.52017
\(356\) −11.6762 −0.618836
\(357\) 14.3113 0.757436
\(358\) −5.82357 −0.307785
\(359\) −0.818977 −0.0432240 −0.0216120 0.999766i \(-0.506880\pi\)
−0.0216120 + 0.999766i \(0.506880\pi\)
\(360\) 5.10851 0.269242
\(361\) −18.6173 −0.979859
\(362\) −23.9265 −1.25755
\(363\) −20.1491 −1.05756
\(364\) −5.52748 −0.289719
\(365\) −21.7935 −1.14072
\(366\) −39.3537 −2.05705
\(367\) −33.2391 −1.73507 −0.867535 0.497377i \(-0.834297\pi\)
−0.867535 + 0.497377i \(0.834297\pi\)
\(368\) −1.06987 −0.0557711
\(369\) 8.63535 0.449538
\(370\) 37.2502 1.93655
\(371\) −1.15828 −0.0601349
\(372\) −13.4114 −0.695347
\(373\) 3.45866 0.179083 0.0895413 0.995983i \(-0.471460\pi\)
0.0895413 + 0.995983i \(0.471460\pi\)
\(374\) 8.07575 0.417587
\(375\) 20.8969 1.07911
\(376\) −12.5349 −0.646440
\(377\) −2.44360 −0.125852
\(378\) −16.8173 −0.864986
\(379\) 18.5826 0.954522 0.477261 0.878762i \(-0.341630\pi\)
0.477261 + 0.878762i \(0.341630\pi\)
\(380\) 4.48400 0.230025
\(381\) −37.8711 −1.94020
\(382\) −23.0141 −1.17750
\(383\) −26.9089 −1.37498 −0.687491 0.726193i \(-0.741288\pi\)
−0.687491 + 0.726193i \(0.741288\pi\)
\(384\) 33.2775 1.69818
\(385\) 3.64726 0.185881
\(386\) 6.93889 0.353180
\(387\) 8.64730 0.439567
\(388\) −13.6296 −0.691941
\(389\) 4.87333 0.247088 0.123544 0.992339i \(-0.460574\pi\)
0.123544 + 0.992339i \(0.460574\pi\)
\(390\) 10.3920 0.526218
\(391\) −7.54390 −0.381511
\(392\) 9.53118 0.481397
\(393\) 15.6239 0.788123
\(394\) 41.3977 2.08558
\(395\) 12.7412 0.641081
\(396\) 2.38698 0.119950
\(397\) 34.9142 1.75229 0.876146 0.482046i \(-0.160106\pi\)
0.876146 + 0.482046i \(0.160106\pi\)
\(398\) −17.3430 −0.869326
\(399\) 2.17021 0.108646
\(400\) −0.264747 −0.0132373
\(401\) 10.5754 0.528108 0.264054 0.964508i \(-0.414940\pi\)
0.264054 + 0.964508i \(0.414940\pi\)
\(402\) 19.9258 0.993807
\(403\) −2.19500 −0.109341
\(404\) −34.5943 −1.72113
\(405\) 25.3775 1.26102
\(406\) −9.83365 −0.488036
\(407\) 6.18598 0.306628
\(408\) 20.0108 0.990683
\(409\) −23.6292 −1.16839 −0.584195 0.811614i \(-0.698589\pi\)
−0.584195 + 0.811614i \(0.698589\pi\)
\(410\) 51.9108 2.56369
\(411\) −3.40561 −0.167987
\(412\) −50.8984 −2.50759
\(413\) −23.1373 −1.13851
\(414\) −3.66709 −0.180227
\(415\) 10.4577 0.513346
\(416\) 6.28883 0.308335
\(417\) −45.2275 −2.21480
\(418\) 1.22463 0.0598985
\(419\) −7.03590 −0.343726 −0.171863 0.985121i \(-0.554979\pi\)
−0.171863 + 0.985121i \(0.554979\pi\)
\(420\) 25.4287 1.24079
\(421\) −4.81078 −0.234463 −0.117232 0.993105i \(-0.537402\pi\)
−0.117232 + 0.993105i \(0.537402\pi\)
\(422\) 1.40566 0.0684264
\(423\) 4.41751 0.214787
\(424\) −1.61957 −0.0786530
\(425\) −1.86678 −0.0905523
\(426\) −54.5382 −2.64238
\(427\) −15.7606 −0.762708
\(428\) 12.9021 0.623649
\(429\) 1.72575 0.0833200
\(430\) 51.9827 2.50683
\(431\) 32.0861 1.54553 0.772766 0.634691i \(-0.218873\pi\)
0.772766 + 0.634691i \(0.218873\pi\)
\(432\) 2.41773 0.116323
\(433\) −31.1169 −1.49538 −0.747692 0.664046i \(-0.768838\pi\)
−0.747692 + 0.664046i \(0.768838\pi\)
\(434\) −8.83321 −0.424008
\(435\) 11.2416 0.538992
\(436\) −42.0352 −2.01312
\(437\) −1.14398 −0.0547238
\(438\) −41.4976 −1.98283
\(439\) 28.2858 1.35001 0.675005 0.737813i \(-0.264142\pi\)
0.675005 + 0.737813i \(0.264142\pi\)
\(440\) 5.09978 0.243122
\(441\) −3.35894 −0.159950
\(442\) 9.21513 0.438319
\(443\) 34.5892 1.64338 0.821691 0.569933i \(-0.193031\pi\)
0.821691 + 0.569933i \(0.193031\pi\)
\(444\) 43.1287 2.04680
\(445\) 8.79141 0.416753
\(446\) −16.4862 −0.780645
\(447\) −11.6118 −0.549220
\(448\) 23.2465 1.09829
\(449\) −30.1250 −1.42168 −0.710842 0.703351i \(-0.751686\pi\)
−0.710842 + 0.703351i \(0.751686\pi\)
\(450\) −0.907443 −0.0427773
\(451\) 8.62059 0.405928
\(452\) −38.1976 −1.79666
\(453\) 40.4544 1.90071
\(454\) 55.2802 2.59443
\(455\) 4.16183 0.195110
\(456\) 3.03449 0.142103
\(457\) −0.372412 −0.0174207 −0.00871035 0.999962i \(-0.502773\pi\)
−0.00871035 + 0.999962i \(0.502773\pi\)
\(458\) 20.6013 0.962636
\(459\) 17.0479 0.795727
\(460\) −13.4042 −0.624973
\(461\) −19.8356 −0.923837 −0.461918 0.886922i \(-0.652839\pi\)
−0.461918 + 0.886922i \(0.652839\pi\)
\(462\) 6.94484 0.323103
\(463\) −22.2138 −1.03236 −0.516181 0.856479i \(-0.672647\pi\)
−0.516181 + 0.856479i \(0.672647\pi\)
\(464\) 1.41373 0.0656309
\(465\) 10.0979 0.468279
\(466\) 26.3961 1.22277
\(467\) −12.7511 −0.590052 −0.295026 0.955489i \(-0.595328\pi\)
−0.295026 + 0.955489i \(0.595328\pi\)
\(468\) 2.72375 0.125906
\(469\) 7.97998 0.368481
\(470\) 26.5556 1.22492
\(471\) 8.54488 0.393727
\(472\) −32.3517 −1.48911
\(473\) 8.63253 0.396924
\(474\) 24.2609 1.11434
\(475\) −0.283084 −0.0129888
\(476\) 22.5490 1.03353
\(477\) 0.570761 0.0261334
\(478\) −0.501441 −0.0229354
\(479\) −28.8385 −1.31766 −0.658832 0.752290i \(-0.728949\pi\)
−0.658832 + 0.752290i \(0.728949\pi\)
\(480\) −28.9312 −1.32052
\(481\) 7.05873 0.321850
\(482\) 34.9390 1.59143
\(483\) −6.48747 −0.295190
\(484\) −31.7471 −1.44305
\(485\) 10.2622 0.465985
\(486\) 20.0020 0.907309
\(487\) −0.966908 −0.0438148 −0.0219074 0.999760i \(-0.506974\pi\)
−0.0219074 + 0.999760i \(0.506974\pi\)
\(488\) −22.0372 −0.997579
\(489\) −13.5010 −0.610538
\(490\) −20.1920 −0.912183
\(491\) 15.3629 0.693316 0.346658 0.937992i \(-0.387316\pi\)
0.346658 + 0.937992i \(0.387316\pi\)
\(492\) 60.1028 2.70964
\(493\) 9.96851 0.448959
\(494\) 1.39741 0.0628723
\(495\) −1.79725 −0.0807802
\(496\) 1.26990 0.0570204
\(497\) −21.8417 −0.979736
\(498\) 19.9127 0.892309
\(499\) −3.14340 −0.140718 −0.0703591 0.997522i \(-0.522415\pi\)
−0.0703591 + 0.997522i \(0.522415\pi\)
\(500\) 32.9253 1.47246
\(501\) −11.4473 −0.511429
\(502\) 2.42991 0.108452
\(503\) 36.1941 1.61382 0.806908 0.590677i \(-0.201139\pi\)
0.806908 + 0.590677i \(0.201139\pi\)
\(504\) 3.89562 0.173525
\(505\) 26.0473 1.15909
\(506\) −3.66082 −0.162743
\(507\) 1.96923 0.0874565
\(508\) −59.6700 −2.64743
\(509\) 2.01204 0.0891820 0.0445910 0.999005i \(-0.485802\pi\)
0.0445910 + 0.999005i \(0.485802\pi\)
\(510\) −42.3934 −1.87721
\(511\) −16.6192 −0.735189
\(512\) −6.52065 −0.288175
\(513\) 2.58519 0.114139
\(514\) −58.3707 −2.57462
\(515\) 38.3232 1.68872
\(516\) 60.1860 2.64954
\(517\) 4.40996 0.193950
\(518\) 28.4061 1.24809
\(519\) 33.2367 1.45893
\(520\) 5.81929 0.255193
\(521\) 13.6550 0.598237 0.299119 0.954216i \(-0.403307\pi\)
0.299119 + 0.954216i \(0.403307\pi\)
\(522\) 4.84569 0.212090
\(523\) −9.58464 −0.419107 −0.209554 0.977797i \(-0.567201\pi\)
−0.209554 + 0.977797i \(0.567201\pi\)
\(524\) 24.6172 1.07541
\(525\) −1.60536 −0.0700638
\(526\) 70.5108 3.07442
\(527\) 8.95435 0.390058
\(528\) −0.998424 −0.0434508
\(529\) −19.5803 −0.851316
\(530\) 3.43109 0.149037
\(531\) 11.4013 0.494773
\(532\) 3.41939 0.148249
\(533\) 9.83684 0.426081
\(534\) 16.7400 0.724409
\(535\) −9.71448 −0.419994
\(536\) 11.1580 0.481953
\(537\) 5.07673 0.219077
\(538\) 50.9881 2.19825
\(539\) −3.35320 −0.144433
\(540\) 30.2911 1.30352
\(541\) −7.44070 −0.319901 −0.159950 0.987125i \(-0.551133\pi\)
−0.159950 + 0.987125i \(0.551133\pi\)
\(542\) 56.3621 2.42096
\(543\) 20.8581 0.895107
\(544\) −25.6549 −1.09994
\(545\) 31.6498 1.35573
\(546\) 7.92466 0.339144
\(547\) −14.0384 −0.600240 −0.300120 0.953901i \(-0.597027\pi\)
−0.300120 + 0.953901i \(0.597027\pi\)
\(548\) −5.36590 −0.229220
\(549\) 7.76628 0.331457
\(550\) −0.905892 −0.0386274
\(551\) 1.51165 0.0643985
\(552\) −9.07110 −0.386092
\(553\) 9.71614 0.413172
\(554\) 42.5447 1.80755
\(555\) −32.4731 −1.37841
\(556\) −71.2607 −3.02213
\(557\) 10.9468 0.463829 0.231915 0.972736i \(-0.425501\pi\)
0.231915 + 0.972736i \(0.425501\pi\)
\(558\) 4.35271 0.184265
\(559\) 9.85045 0.416630
\(560\) −2.40781 −0.101748
\(561\) −7.04009 −0.297233
\(562\) −23.7737 −1.00283
\(563\) −5.34071 −0.225084 −0.112542 0.993647i \(-0.535899\pi\)
−0.112542 + 0.993647i \(0.535899\pi\)
\(564\) 30.7463 1.29465
\(565\) 28.7603 1.20996
\(566\) −68.0395 −2.85991
\(567\) 19.3522 0.812717
\(568\) −30.5402 −1.28144
\(569\) −7.26970 −0.304762 −0.152381 0.988322i \(-0.548694\pi\)
−0.152381 + 0.988322i \(0.548694\pi\)
\(570\) −6.42865 −0.269266
\(571\) 29.3167 1.22686 0.613432 0.789747i \(-0.289788\pi\)
0.613432 + 0.789747i \(0.289788\pi\)
\(572\) 2.71910 0.113691
\(573\) 20.0627 0.838131
\(574\) 39.5859 1.65228
\(575\) 0.846231 0.0352903
\(576\) −11.4551 −0.477295
\(577\) −18.7341 −0.779909 −0.389955 0.920834i \(-0.627509\pi\)
−0.389955 + 0.920834i \(0.627509\pi\)
\(578\) 0.809128 0.0336553
\(579\) −6.04902 −0.251389
\(580\) 17.7123 0.735462
\(581\) 7.97474 0.330848
\(582\) 19.5406 0.809985
\(583\) 0.569786 0.0235981
\(584\) −23.2378 −0.961585
\(585\) −2.05081 −0.0847906
\(586\) −26.6673 −1.10162
\(587\) 8.76337 0.361703 0.180852 0.983510i \(-0.442115\pi\)
0.180852 + 0.983510i \(0.442115\pi\)
\(588\) −23.3785 −0.964114
\(589\) 1.35786 0.0559497
\(590\) 68.5380 2.82166
\(591\) −36.0886 −1.48449
\(592\) −4.08379 −0.167843
\(593\) −14.8228 −0.608700 −0.304350 0.952560i \(-0.598439\pi\)
−0.304350 + 0.952560i \(0.598439\pi\)
\(594\) 8.27281 0.339438
\(595\) −16.9779 −0.696028
\(596\) −18.2956 −0.749418
\(597\) 15.1189 0.618774
\(598\) −4.17731 −0.170823
\(599\) −47.4191 −1.93749 −0.968745 0.248057i \(-0.920208\pi\)
−0.968745 + 0.248057i \(0.920208\pi\)
\(600\) −2.24470 −0.0916395
\(601\) −2.15857 −0.0880498 −0.0440249 0.999030i \(-0.514018\pi\)
−0.0440249 + 0.999030i \(0.514018\pi\)
\(602\) 39.6407 1.61563
\(603\) −3.93226 −0.160134
\(604\) 63.7402 2.59355
\(605\) 23.9035 0.971816
\(606\) 49.5973 2.01475
\(607\) −24.8346 −1.00801 −0.504003 0.863702i \(-0.668140\pi\)
−0.504003 + 0.863702i \(0.668140\pi\)
\(608\) −3.89037 −0.157775
\(609\) 8.57254 0.347377
\(610\) 46.6864 1.89028
\(611\) 5.03215 0.203579
\(612\) −11.1114 −0.449151
\(613\) −34.4569 −1.39170 −0.695851 0.718186i \(-0.744973\pi\)
−0.695851 + 0.718186i \(0.744973\pi\)
\(614\) 44.8449 1.80979
\(615\) −45.2535 −1.82480
\(616\) 3.88896 0.156691
\(617\) 1.00000 0.0402585
\(618\) 72.9723 2.93538
\(619\) −17.4726 −0.702282 −0.351141 0.936323i \(-0.614206\pi\)
−0.351141 + 0.936323i \(0.614206\pi\)
\(620\) 15.9103 0.638973
\(621\) −7.72798 −0.310113
\(622\) −24.4156 −0.978977
\(623\) 6.70411 0.268594
\(624\) −1.13929 −0.0456080
\(625\) −27.0786 −1.08315
\(626\) −57.1426 −2.28388
\(627\) −1.06758 −0.0426349
\(628\) 13.4634 0.537246
\(629\) −28.7957 −1.14816
\(630\) −8.25297 −0.328806
\(631\) −26.2695 −1.04577 −0.522886 0.852403i \(-0.675144\pi\)
−0.522886 + 0.852403i \(0.675144\pi\)
\(632\) 13.5856 0.540406
\(633\) −1.22539 −0.0487049
\(634\) −8.54099 −0.339206
\(635\) 44.9276 1.78290
\(636\) 3.97255 0.157522
\(637\) −3.82629 −0.151603
\(638\) 4.83741 0.191515
\(639\) 10.7629 0.425773
\(640\) −39.4780 −1.56051
\(641\) −39.1106 −1.54478 −0.772389 0.635150i \(-0.780938\pi\)
−0.772389 + 0.635150i \(0.780938\pi\)
\(642\) −18.4976 −0.730042
\(643\) −43.8249 −1.72829 −0.864144 0.503245i \(-0.832139\pi\)
−0.864144 + 0.503245i \(0.832139\pi\)
\(644\) −10.2217 −0.402791
\(645\) −45.3162 −1.78432
\(646\) −5.70063 −0.224288
\(647\) 21.1081 0.829845 0.414923 0.909857i \(-0.363809\pi\)
0.414923 + 0.909857i \(0.363809\pi\)
\(648\) 27.0593 1.06299
\(649\) 11.3818 0.446774
\(650\) −1.03370 −0.0405451
\(651\) 7.70040 0.301803
\(652\) −21.2723 −0.833088
\(653\) 38.2859 1.49824 0.749121 0.662433i \(-0.230476\pi\)
0.749121 + 0.662433i \(0.230476\pi\)
\(654\) 60.2652 2.35656
\(655\) −18.5351 −0.724227
\(656\) −5.69105 −0.222198
\(657\) 8.18936 0.319498
\(658\) 20.2506 0.789451
\(659\) −24.0208 −0.935719 −0.467860 0.883803i \(-0.654975\pi\)
−0.467860 + 0.883803i \(0.654975\pi\)
\(660\) −12.5090 −0.486912
\(661\) −49.3872 −1.92094 −0.960471 0.278381i \(-0.910202\pi\)
−0.960471 + 0.278381i \(0.910202\pi\)
\(662\) 11.9524 0.464544
\(663\) −8.03334 −0.311989
\(664\) 11.1507 0.432730
\(665\) −2.57458 −0.0998379
\(666\) −13.9976 −0.542394
\(667\) −4.51882 −0.174970
\(668\) −18.0365 −0.697852
\(669\) 14.3720 0.555652
\(670\) −23.6385 −0.913236
\(671\) 7.75301 0.299301
\(672\) −22.0622 −0.851069
\(673\) 39.3540 1.51699 0.758493 0.651681i \(-0.225936\pi\)
0.758493 + 0.651681i \(0.225936\pi\)
\(674\) −20.9474 −0.806863
\(675\) −1.91233 −0.0736058
\(676\) 3.10273 0.119336
\(677\) 25.4560 0.978353 0.489177 0.872185i \(-0.337297\pi\)
0.489177 + 0.872185i \(0.337297\pi\)
\(678\) 54.7633 2.10317
\(679\) 7.82573 0.300324
\(680\) −23.7394 −0.910365
\(681\) −48.1908 −1.84668
\(682\) 4.34527 0.166389
\(683\) 2.30538 0.0882128 0.0441064 0.999027i \(-0.485956\pi\)
0.0441064 + 0.999027i \(0.485956\pi\)
\(684\) −1.68496 −0.0644260
\(685\) 4.04018 0.154367
\(686\) −43.5677 −1.66342
\(687\) −17.9593 −0.685191
\(688\) −5.69893 −0.217270
\(689\) 0.650174 0.0247697
\(690\) 19.2174 0.731593
\(691\) 4.29295 0.163312 0.0816558 0.996661i \(-0.473979\pi\)
0.0816558 + 0.996661i \(0.473979\pi\)
\(692\) 52.3679 1.99073
\(693\) −1.37053 −0.0520623
\(694\) −54.6167 −2.07322
\(695\) 53.6547 2.03524
\(696\) 11.9866 0.454349
\(697\) −40.1288 −1.51999
\(698\) 41.8544 1.58421
\(699\) −23.0109 −0.870353
\(700\) −2.52942 −0.0956030
\(701\) 11.0922 0.418946 0.209473 0.977814i \(-0.432825\pi\)
0.209473 + 0.977814i \(0.432825\pi\)
\(702\) 9.43999 0.356289
\(703\) −4.36665 −0.164691
\(704\) −11.4355 −0.430991
\(705\) −23.1500 −0.871878
\(706\) 50.1064 1.88578
\(707\) 19.8630 0.747024
\(708\) 79.3539 2.98230
\(709\) 47.2640 1.77504 0.887518 0.460774i \(-0.152428\pi\)
0.887518 + 0.460774i \(0.152428\pi\)
\(710\) 64.7003 2.42816
\(711\) −4.78778 −0.179556
\(712\) 9.37402 0.351306
\(713\) −4.05910 −0.152014
\(714\) −32.3282 −1.20985
\(715\) −2.04731 −0.0765649
\(716\) 7.99892 0.298934
\(717\) 0.437134 0.0163251
\(718\) 1.85001 0.0690416
\(719\) −47.1308 −1.75768 −0.878842 0.477113i \(-0.841683\pi\)
−0.878842 + 0.477113i \(0.841683\pi\)
\(720\) 1.18649 0.0442178
\(721\) 29.2243 1.08837
\(722\) 42.0550 1.56513
\(723\) −30.4583 −1.13276
\(724\) 32.8641 1.22139
\(725\) −1.11821 −0.0415293
\(726\) 45.5153 1.68923
\(727\) −22.2968 −0.826942 −0.413471 0.910517i \(-0.635684\pi\)
−0.413471 + 0.910517i \(0.635684\pi\)
\(728\) 4.43764 0.164470
\(729\) 15.1520 0.561184
\(730\) 49.2298 1.82208
\(731\) −40.1843 −1.48627
\(732\) 54.0540 1.99789
\(733\) 0.922949 0.0340899 0.0170450 0.999855i \(-0.494574\pi\)
0.0170450 + 0.999855i \(0.494574\pi\)
\(734\) 75.0846 2.77142
\(735\) 17.6025 0.649279
\(736\) 11.6296 0.428673
\(737\) −3.92554 −0.144599
\(738\) −19.5066 −0.718047
\(739\) 14.0292 0.516072 0.258036 0.966135i \(-0.416925\pi\)
0.258036 + 0.966135i \(0.416925\pi\)
\(740\) −51.1648 −1.88086
\(741\) −1.21820 −0.0447516
\(742\) 2.61646 0.0960534
\(743\) 49.3715 1.81126 0.905632 0.424064i \(-0.139397\pi\)
0.905632 + 0.424064i \(0.139397\pi\)
\(744\) 10.7671 0.394741
\(745\) 13.7754 0.504693
\(746\) −7.81284 −0.286048
\(747\) −3.92968 −0.143780
\(748\) −11.0924 −0.405578
\(749\) −7.40802 −0.270683
\(750\) −47.2044 −1.72366
\(751\) 40.6390 1.48294 0.741470 0.670986i \(-0.234129\pi\)
0.741470 + 0.670986i \(0.234129\pi\)
\(752\) −2.91132 −0.106165
\(753\) −2.11828 −0.0771946
\(754\) 5.51990 0.201023
\(755\) −47.9922 −1.74662
\(756\) 23.0992 0.840110
\(757\) −46.7699 −1.69988 −0.849941 0.526878i \(-0.823362\pi\)
−0.849941 + 0.526878i \(0.823362\pi\)
\(758\) −41.9765 −1.52466
\(759\) 3.19134 0.115838
\(760\) −3.59991 −0.130582
\(761\) −15.4921 −0.561587 −0.280794 0.959768i \(-0.590598\pi\)
−0.280794 + 0.959768i \(0.590598\pi\)
\(762\) 85.5479 3.09907
\(763\) 24.1353 0.873758
\(764\) 31.6109 1.14364
\(765\) 8.36616 0.302479
\(766\) 60.7852 2.19626
\(767\) 12.9876 0.468955
\(768\) −23.7787 −0.858041
\(769\) 8.02649 0.289443 0.144721 0.989472i \(-0.453771\pi\)
0.144721 + 0.989472i \(0.453771\pi\)
\(770\) −8.23887 −0.296908
\(771\) 50.8850 1.83258
\(772\) −9.53087 −0.343023
\(773\) −3.64341 −0.131045 −0.0655223 0.997851i \(-0.520871\pi\)
−0.0655223 + 0.997851i \(0.520871\pi\)
\(774\) −19.5336 −0.702120
\(775\) −1.00445 −0.0360808
\(776\) 10.9423 0.392807
\(777\) −24.7632 −0.888374
\(778\) −11.0085 −0.394673
\(779\) −6.08523 −0.218026
\(780\) −14.2738 −0.511085
\(781\) 10.7445 0.384468
\(782\) 17.0411 0.609387
\(783\) 10.2118 0.364938
\(784\) 2.21368 0.0790601
\(785\) −10.1370 −0.361806
\(786\) −35.2932 −1.25887
\(787\) −26.5431 −0.946158 −0.473079 0.881020i \(-0.656858\pi\)
−0.473079 + 0.881020i \(0.656858\pi\)
\(788\) −56.8615 −2.02561
\(789\) −61.4682 −2.18833
\(790\) −28.7814 −1.02400
\(791\) 21.9319 0.779809
\(792\) −1.91635 −0.0680945
\(793\) 8.84685 0.314161
\(794\) −78.8684 −2.79893
\(795\) −2.99107 −0.106082
\(796\) 23.8213 0.844325
\(797\) 6.65834 0.235850 0.117925 0.993022i \(-0.462376\pi\)
0.117925 + 0.993022i \(0.462376\pi\)
\(798\) −4.90233 −0.173540
\(799\) −20.5283 −0.726240
\(800\) 2.87782 0.101746
\(801\) −3.30356 −0.116725
\(802\) −23.8889 −0.843547
\(803\) 8.17537 0.288502
\(804\) −27.3689 −0.965227
\(805\) 7.69627 0.271258
\(806\) 4.95832 0.174650
\(807\) −44.4492 −1.56468
\(808\) 27.7734 0.977066
\(809\) −50.8010 −1.78607 −0.893035 0.449987i \(-0.851428\pi\)
−0.893035 + 0.449987i \(0.851428\pi\)
\(810\) −57.3257 −2.01422
\(811\) −11.8194 −0.415035 −0.207517 0.978231i \(-0.566538\pi\)
−0.207517 + 0.978231i \(0.566538\pi\)
\(812\) 13.5069 0.474001
\(813\) −49.1340 −1.72320
\(814\) −13.9736 −0.489776
\(815\) 16.0167 0.561040
\(816\) 4.64765 0.162700
\(817\) −6.09365 −0.213190
\(818\) 53.3765 1.86627
\(819\) −1.56390 −0.0546470
\(820\) −71.3017 −2.48996
\(821\) 36.9398 1.28921 0.644604 0.764517i \(-0.277022\pi\)
0.644604 + 0.764517i \(0.277022\pi\)
\(822\) 7.69302 0.268325
\(823\) −39.9145 −1.39133 −0.695666 0.718365i \(-0.744891\pi\)
−0.695666 + 0.718365i \(0.744891\pi\)
\(824\) 40.8629 1.42353
\(825\) 0.789717 0.0274944
\(826\) 52.2653 1.81854
\(827\) −11.7627 −0.409029 −0.204515 0.978863i \(-0.565562\pi\)
−0.204515 + 0.978863i \(0.565562\pi\)
\(828\) 5.03690 0.175044
\(829\) 11.4351 0.397157 0.198578 0.980085i \(-0.436368\pi\)
0.198578 + 0.980085i \(0.436368\pi\)
\(830\) −23.6230 −0.819967
\(831\) −37.0886 −1.28659
\(832\) −13.0489 −0.452388
\(833\) 15.6091 0.540824
\(834\) 102.165 3.53770
\(835\) 13.5803 0.469966
\(836\) −1.68208 −0.0581759
\(837\) 9.17285 0.317060
\(838\) 15.8935 0.549033
\(839\) 27.9130 0.963664 0.481832 0.876264i \(-0.339972\pi\)
0.481832 + 0.876264i \(0.339972\pi\)
\(840\) −20.4150 −0.704384
\(841\) −23.0288 −0.794097
\(842\) 10.8672 0.374508
\(843\) 20.7248 0.713802
\(844\) −1.93073 −0.0664585
\(845\) −2.33615 −0.0803661
\(846\) −9.97882 −0.343079
\(847\) 18.2282 0.626329
\(848\) −0.376155 −0.0129172
\(849\) 59.3138 2.03564
\(850\) 4.21692 0.144639
\(851\) 13.0534 0.447463
\(852\) 74.9106 2.56639
\(853\) 51.5658 1.76558 0.882789 0.469769i \(-0.155663\pi\)
0.882789 + 0.469769i \(0.155663\pi\)
\(854\) 35.6019 1.21827
\(855\) 1.26867 0.0433874
\(856\) −10.3583 −0.354038
\(857\) −32.5871 −1.11315 −0.556577 0.830796i \(-0.687886\pi\)
−0.556577 + 0.830796i \(0.687886\pi\)
\(858\) −3.89833 −0.133087
\(859\) −50.2963 −1.71609 −0.858044 0.513576i \(-0.828320\pi\)
−0.858044 + 0.513576i \(0.828320\pi\)
\(860\) −71.4004 −2.43473
\(861\) −34.5092 −1.17607
\(862\) −72.4799 −2.46868
\(863\) 48.3426 1.64560 0.822801 0.568329i \(-0.192410\pi\)
0.822801 + 0.568329i \(0.192410\pi\)
\(864\) −26.2809 −0.894094
\(865\) −39.4296 −1.34065
\(866\) 70.2907 2.38857
\(867\) −0.705362 −0.0239553
\(868\) 12.1328 0.411814
\(869\) −4.77960 −0.162137
\(870\) −25.3938 −0.860931
\(871\) −4.47938 −0.151778
\(872\) 33.7472 1.14283
\(873\) −3.85626 −0.130514
\(874\) 2.58415 0.0874102
\(875\) −18.9047 −0.639095
\(876\) 56.9987 1.92581
\(877\) 2.49265 0.0841707 0.0420854 0.999114i \(-0.486600\pi\)
0.0420854 + 0.999114i \(0.486600\pi\)
\(878\) −63.8955 −2.15637
\(879\) 23.2474 0.784114
\(880\) 1.18446 0.0399281
\(881\) −31.6659 −1.06685 −0.533426 0.845847i \(-0.679096\pi\)
−0.533426 + 0.845847i \(0.679096\pi\)
\(882\) 7.58758 0.255487
\(883\) 6.22698 0.209554 0.104777 0.994496i \(-0.466587\pi\)
0.104777 + 0.994496i \(0.466587\pi\)
\(884\) −12.6574 −0.425714
\(885\) −59.7484 −2.00842
\(886\) −78.1343 −2.62497
\(887\) 16.1820 0.543337 0.271669 0.962391i \(-0.412425\pi\)
0.271669 + 0.962391i \(0.412425\pi\)
\(888\) −34.6251 −1.16194
\(889\) 34.2607 1.14907
\(890\) −19.8591 −0.665679
\(891\) −9.51983 −0.318926
\(892\) 22.6445 0.758195
\(893\) −3.11297 −0.104172
\(894\) 26.2302 0.877268
\(895\) −6.02267 −0.201316
\(896\) −30.1049 −1.00574
\(897\) 3.64159 0.121589
\(898\) 68.0499 2.27086
\(899\) 5.36369 0.178889
\(900\) 1.24641 0.0415471
\(901\) −2.65235 −0.0883624
\(902\) −19.4732 −0.648388
\(903\) −34.5570 −1.14998
\(904\) 30.6663 1.01995
\(905\) −24.7446 −0.822537
\(906\) −91.3833 −3.03601
\(907\) 0.520372 0.0172787 0.00863933 0.999963i \(-0.497250\pi\)
0.00863933 + 0.999963i \(0.497250\pi\)
\(908\) −75.9297 −2.51982
\(909\) −9.78781 −0.324641
\(910\) −9.40126 −0.311649
\(911\) −25.1969 −0.834810 −0.417405 0.908721i \(-0.637060\pi\)
−0.417405 + 0.908721i \(0.637060\pi\)
\(912\) 0.704782 0.0233377
\(913\) −3.92297 −0.129831
\(914\) 0.841250 0.0278261
\(915\) −40.6992 −1.34547
\(916\) −28.2968 −0.934953
\(917\) −14.1344 −0.466760
\(918\) −38.5098 −1.27101
\(919\) 46.8070 1.54402 0.772010 0.635611i \(-0.219252\pi\)
0.772010 + 0.635611i \(0.219252\pi\)
\(920\) 10.7613 0.354790
\(921\) −39.0938 −1.28819
\(922\) 44.8071 1.47564
\(923\) 12.2604 0.403555
\(924\) −9.53904 −0.313811
\(925\) 3.23013 0.106206
\(926\) 50.1792 1.64899
\(927\) −14.4008 −0.472983
\(928\) −15.3674 −0.504459
\(929\) −29.9787 −0.983569 −0.491785 0.870717i \(-0.663655\pi\)
−0.491785 + 0.870717i \(0.663655\pi\)
\(930\) −22.8104 −0.747981
\(931\) 2.36701 0.0775755
\(932\) −36.2561 −1.18761
\(933\) 21.2845 0.696822
\(934\) 28.8038 0.942489
\(935\) 8.35186 0.273135
\(936\) −2.18672 −0.0714752
\(937\) −17.9571 −0.586632 −0.293316 0.956016i \(-0.594759\pi\)
−0.293316 + 0.956016i \(0.594759\pi\)
\(938\) −18.0261 −0.588575
\(939\) 49.8144 1.62563
\(940\) −36.4752 −1.18969
\(941\) −0.830816 −0.0270838 −0.0135419 0.999908i \(-0.504311\pi\)
−0.0135419 + 0.999908i \(0.504311\pi\)
\(942\) −19.3022 −0.628900
\(943\) 18.1908 0.592373
\(944\) −7.51391 −0.244557
\(945\) −17.3922 −0.565769
\(946\) −19.5002 −0.634006
\(947\) 25.4657 0.827524 0.413762 0.910385i \(-0.364215\pi\)
0.413762 + 0.910385i \(0.364215\pi\)
\(948\) −33.3234 −1.08229
\(949\) 9.32880 0.302826
\(950\) 0.639464 0.0207470
\(951\) 7.44566 0.241442
\(952\) −18.1031 −0.586724
\(953\) 20.3880 0.660432 0.330216 0.943905i \(-0.392878\pi\)
0.330216 + 0.943905i \(0.392878\pi\)
\(954\) −1.28930 −0.0417428
\(955\) −23.8010 −0.770181
\(956\) 0.688750 0.0222758
\(957\) −4.21704 −0.136317
\(958\) 65.1439 2.10470
\(959\) 3.08094 0.0994887
\(960\) 60.0303 1.93747
\(961\) −26.1820 −0.844580
\(962\) −15.9451 −0.514091
\(963\) 3.65042 0.117633
\(964\) −47.9902 −1.54566
\(965\) 7.17613 0.231008
\(966\) 14.6547 0.471507
\(967\) 55.1711 1.77418 0.887092 0.461592i \(-0.152722\pi\)
0.887092 + 0.461592i \(0.152722\pi\)
\(968\) 25.4876 0.819202
\(969\) 4.96956 0.159645
\(970\) −23.1816 −0.744317
\(971\) −9.35303 −0.300153 −0.150077 0.988674i \(-0.547952\pi\)
−0.150077 + 0.988674i \(0.547952\pi\)
\(972\) −27.4736 −0.881216
\(973\) 40.9157 1.31170
\(974\) 2.18417 0.0699853
\(975\) 0.901134 0.0288594
\(976\) −5.11830 −0.163833
\(977\) 16.8767 0.539934 0.269967 0.962870i \(-0.412987\pi\)
0.269967 + 0.962870i \(0.412987\pi\)
\(978\) 30.4978 0.975212
\(979\) −3.29791 −0.105402
\(980\) 27.7346 0.885950
\(981\) −11.8931 −0.379717
\(982\) −34.7035 −1.10743
\(983\) 31.5291 1.00562 0.502810 0.864397i \(-0.332299\pi\)
0.502810 + 0.864397i \(0.332299\pi\)
\(984\) −48.2525 −1.53823
\(985\) 42.8130 1.36414
\(986\) −22.5181 −0.717122
\(987\) −17.6536 −0.561920
\(988\) −1.91940 −0.0610641
\(989\) 18.2159 0.579233
\(990\) 4.05984 0.129030
\(991\) −36.9207 −1.17283 −0.586413 0.810012i \(-0.699460\pi\)
−0.586413 + 0.810012i \(0.699460\pi\)
\(992\) −13.8040 −0.438276
\(993\) −10.4196 −0.330656
\(994\) 49.3388 1.56493
\(995\) −17.9359 −0.568608
\(996\) −27.3509 −0.866648
\(997\) 31.1725 0.987244 0.493622 0.869677i \(-0.335673\pi\)
0.493622 + 0.869677i \(0.335673\pi\)
\(998\) 7.10070 0.224769
\(999\) −29.4983 −0.933285
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 \(a_p\))