Properties

Label 619.2.a.b.1.5
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73496 q^{2} -0.518455 q^{3} +1.01008 q^{4} -1.50291 q^{5} +0.899498 q^{6} -4.51257 q^{7} +1.71746 q^{8} -2.73120 q^{9} +O(q^{10})\) \(q-1.73496 q^{2} -0.518455 q^{3} +1.01008 q^{4} -1.50291 q^{5} +0.899498 q^{6} -4.51257 q^{7} +1.71746 q^{8} -2.73120 q^{9} +2.60748 q^{10} -3.30447 q^{11} -0.523683 q^{12} +1.38556 q^{13} +7.82912 q^{14} +0.779189 q^{15} -4.99990 q^{16} -0.194113 q^{17} +4.73853 q^{18} +2.90749 q^{19} -1.51806 q^{20} +2.33956 q^{21} +5.73313 q^{22} +2.25144 q^{23} -0.890427 q^{24} -2.74127 q^{25} -2.40388 q^{26} +2.97137 q^{27} -4.55807 q^{28} -1.21738 q^{29} -1.35186 q^{30} -2.87352 q^{31} +5.23970 q^{32} +1.71322 q^{33} +0.336779 q^{34} +6.78196 q^{35} -2.75875 q^{36} +2.81864 q^{37} -5.04438 q^{38} -0.718348 q^{39} -2.58118 q^{40} +8.65482 q^{41} -4.05905 q^{42} -4.18584 q^{43} -3.33780 q^{44} +4.10474 q^{45} -3.90616 q^{46} -4.41047 q^{47} +2.59222 q^{48} +13.3633 q^{49} +4.75600 q^{50} +0.100639 q^{51} +1.39953 q^{52} +6.95984 q^{53} -5.15521 q^{54} +4.96631 q^{55} -7.75017 q^{56} -1.50740 q^{57} +2.11211 q^{58} +11.7409 q^{59} +0.787047 q^{60} -4.50107 q^{61} +4.98544 q^{62} +12.3247 q^{63} +0.909137 q^{64} -2.08236 q^{65} -2.97237 q^{66} -14.1315 q^{67} -0.196071 q^{68} -1.16727 q^{69} -11.7664 q^{70} +12.0366 q^{71} -4.69074 q^{72} -1.49793 q^{73} -4.89023 q^{74} +1.42123 q^{75} +2.93681 q^{76} +14.9117 q^{77} +1.24630 q^{78} +14.9019 q^{79} +7.51438 q^{80} +6.65309 q^{81} -15.0158 q^{82} -8.73893 q^{83} +2.36316 q^{84} +0.291734 q^{85} +7.26226 q^{86} +0.631159 q^{87} -5.67531 q^{88} +14.0241 q^{89} -7.12156 q^{90} -6.25241 q^{91} +2.27414 q^{92} +1.48979 q^{93} +7.65198 q^{94} -4.36968 q^{95} -2.71655 q^{96} +5.37688 q^{97} -23.1847 q^{98} +9.02520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73496 −1.22680 −0.613401 0.789772i \(-0.710199\pi\)
−0.613401 + 0.789772i \(0.710199\pi\)
\(3\) −0.518455 −0.299330 −0.149665 0.988737i \(-0.547820\pi\)
−0.149665 + 0.988737i \(0.547820\pi\)
\(4\) 1.01008 0.505042
\(5\) −1.50291 −0.672120 −0.336060 0.941841i \(-0.609094\pi\)
−0.336060 + 0.941841i \(0.609094\pi\)
\(6\) 0.899498 0.367219
\(7\) −4.51257 −1.70559 −0.852795 0.522246i \(-0.825094\pi\)
−0.852795 + 0.522246i \(0.825094\pi\)
\(8\) 1.71746 0.607215
\(9\) −2.73120 −0.910401
\(10\) 2.60748 0.824558
\(11\) −3.30447 −0.996337 −0.498168 0.867080i \(-0.665994\pi\)
−0.498168 + 0.867080i \(0.665994\pi\)
\(12\) −0.523683 −0.151174
\(13\) 1.38556 0.384284 0.192142 0.981367i \(-0.438457\pi\)
0.192142 + 0.981367i \(0.438457\pi\)
\(14\) 7.82912 2.09242
\(15\) 0.779189 0.201186
\(16\) −4.99990 −1.24997
\(17\) −0.194113 −0.0470794 −0.0235397 0.999723i \(-0.507494\pi\)
−0.0235397 + 0.999723i \(0.507494\pi\)
\(18\) 4.73853 1.11688
\(19\) 2.90749 0.667024 0.333512 0.942746i \(-0.391766\pi\)
0.333512 + 0.942746i \(0.391766\pi\)
\(20\) −1.51806 −0.339449
\(21\) 2.33956 0.510534
\(22\) 5.73313 1.22231
\(23\) 2.25144 0.469457 0.234729 0.972061i \(-0.424580\pi\)
0.234729 + 0.972061i \(0.424580\pi\)
\(24\) −0.890427 −0.181758
\(25\) −2.74127 −0.548255
\(26\) −2.40388 −0.471440
\(27\) 2.97137 0.571841
\(28\) −4.55807 −0.861395
\(29\) −1.21738 −0.226063 −0.113031 0.993591i \(-0.536056\pi\)
−0.113031 + 0.993591i \(0.536056\pi\)
\(30\) −1.35186 −0.246815
\(31\) −2.87352 −0.516100 −0.258050 0.966132i \(-0.583080\pi\)
−0.258050 + 0.966132i \(0.583080\pi\)
\(32\) 5.23970 0.926256
\(33\) 1.71322 0.298233
\(34\) 0.336779 0.0577571
\(35\) 6.78196 1.14636
\(36\) −2.75875 −0.459791
\(37\) 2.81864 0.463382 0.231691 0.972789i \(-0.425574\pi\)
0.231691 + 0.972789i \(0.425574\pi\)
\(38\) −5.04438 −0.818306
\(39\) −0.718348 −0.115028
\(40\) −2.58118 −0.408121
\(41\) 8.65482 1.35166 0.675828 0.737060i \(-0.263786\pi\)
0.675828 + 0.737060i \(0.263786\pi\)
\(42\) −4.05905 −0.626324
\(43\) −4.18584 −0.638335 −0.319167 0.947698i \(-0.603403\pi\)
−0.319167 + 0.947698i \(0.603403\pi\)
\(44\) −3.33780 −0.503192
\(45\) 4.10474 0.611899
\(46\) −3.90616 −0.575931
\(47\) −4.41047 −0.643333 −0.321666 0.946853i \(-0.604243\pi\)
−0.321666 + 0.946853i \(0.604243\pi\)
\(48\) 2.59222 0.374155
\(49\) 13.3633 1.90904
\(50\) 4.75600 0.672600
\(51\) 0.100639 0.0140923
\(52\) 1.39953 0.194080
\(53\) 6.95984 0.956008 0.478004 0.878358i \(-0.341360\pi\)
0.478004 + 0.878358i \(0.341360\pi\)
\(54\) −5.15521 −0.701535
\(55\) 4.96631 0.669658
\(56\) −7.75017 −1.03566
\(57\) −1.50740 −0.199660
\(58\) 2.11211 0.277334
\(59\) 11.7409 1.52853 0.764265 0.644902i \(-0.223102\pi\)
0.764265 + 0.644902i \(0.223102\pi\)
\(60\) 0.787047 0.101607
\(61\) −4.50107 −0.576302 −0.288151 0.957585i \(-0.593041\pi\)
−0.288151 + 0.957585i \(0.593041\pi\)
\(62\) 4.98544 0.633152
\(63\) 12.3247 1.55277
\(64\) 0.909137 0.113642
\(65\) −2.08236 −0.258285
\(66\) −2.97237 −0.365873
\(67\) −14.1315 −1.72643 −0.863217 0.504834i \(-0.831554\pi\)
−0.863217 + 0.504834i \(0.831554\pi\)
\(68\) −0.196071 −0.0237771
\(69\) −1.16727 −0.140523
\(70\) −11.7664 −1.40636
\(71\) 12.0366 1.42848 0.714241 0.699899i \(-0.246772\pi\)
0.714241 + 0.699899i \(0.246772\pi\)
\(72\) −4.69074 −0.552809
\(73\) −1.49793 −0.175319 −0.0876595 0.996150i \(-0.527939\pi\)
−0.0876595 + 0.996150i \(0.527939\pi\)
\(74\) −4.89023 −0.568478
\(75\) 1.42123 0.164109
\(76\) 2.93681 0.336875
\(77\) 14.9117 1.69934
\(78\) 1.24630 0.141116
\(79\) 14.9019 1.67660 0.838299 0.545210i \(-0.183550\pi\)
0.838299 + 0.545210i \(0.183550\pi\)
\(80\) 7.51438 0.840133
\(81\) 6.65309 0.739232
\(82\) −15.0158 −1.65821
\(83\) −8.73893 −0.959223 −0.479611 0.877481i \(-0.659222\pi\)
−0.479611 + 0.877481i \(0.659222\pi\)
\(84\) 2.36316 0.257841
\(85\) 0.291734 0.0316430
\(86\) 7.26226 0.783110
\(87\) 0.631159 0.0676673
\(88\) −5.67531 −0.604990
\(89\) 14.0241 1.48655 0.743274 0.668988i \(-0.233272\pi\)
0.743274 + 0.668988i \(0.233272\pi\)
\(90\) −7.12156 −0.750679
\(91\) −6.25241 −0.655431
\(92\) 2.27414 0.237096
\(93\) 1.48979 0.154484
\(94\) 7.65198 0.789242
\(95\) −4.36968 −0.448320
\(96\) −2.71655 −0.277256
\(97\) 5.37688 0.545939 0.272970 0.962023i \(-0.411994\pi\)
0.272970 + 0.962023i \(0.411994\pi\)
\(98\) −23.1847 −2.34201
\(99\) 9.02520 0.907066
\(100\) −2.76892 −0.276892
\(101\) 9.64653 0.959866 0.479933 0.877305i \(-0.340661\pi\)
0.479933 + 0.877305i \(0.340661\pi\)
\(102\) −0.174605 −0.0172884
\(103\) −9.67018 −0.952831 −0.476415 0.879220i \(-0.658064\pi\)
−0.476415 + 0.879220i \(0.658064\pi\)
\(104\) 2.37964 0.233343
\(105\) −3.51614 −0.343140
\(106\) −12.0750 −1.17283
\(107\) −16.6067 −1.60543 −0.802717 0.596360i \(-0.796613\pi\)
−0.802717 + 0.596360i \(0.796613\pi\)
\(108\) 3.00134 0.288804
\(109\) −12.8215 −1.22807 −0.614037 0.789277i \(-0.710455\pi\)
−0.614037 + 0.789277i \(0.710455\pi\)
\(110\) −8.61635 −0.821537
\(111\) −1.46134 −0.138704
\(112\) 22.5624 2.13194
\(113\) −7.15191 −0.672795 −0.336397 0.941720i \(-0.609209\pi\)
−0.336397 + 0.941720i \(0.609209\pi\)
\(114\) 2.61528 0.244944
\(115\) −3.38370 −0.315532
\(116\) −1.22966 −0.114171
\(117\) −3.78424 −0.349853
\(118\) −20.3699 −1.87520
\(119\) 0.875950 0.0802982
\(120\) 1.33823 0.122163
\(121\) −0.0804492 −0.00731357
\(122\) 7.80917 0.707009
\(123\) −4.48713 −0.404591
\(124\) −2.90250 −0.260652
\(125\) 11.6344 1.04061
\(126\) −21.3829 −1.90494
\(127\) 2.98978 0.265300 0.132650 0.991163i \(-0.457651\pi\)
0.132650 + 0.991163i \(0.457651\pi\)
\(128\) −12.0567 −1.06567
\(129\) 2.17017 0.191073
\(130\) 3.61281 0.316864
\(131\) −15.6537 −1.36767 −0.683834 0.729637i \(-0.739689\pi\)
−0.683834 + 0.729637i \(0.739689\pi\)
\(132\) 1.73050 0.150621
\(133\) −13.1202 −1.13767
\(134\) 24.5175 2.11799
\(135\) −4.46569 −0.384345
\(136\) −0.333383 −0.0285873
\(137\) 12.0724 1.03141 0.515706 0.856765i \(-0.327530\pi\)
0.515706 + 0.856765i \(0.327530\pi\)
\(138\) 2.02517 0.172394
\(139\) 8.32237 0.705894 0.352947 0.935643i \(-0.385180\pi\)
0.352947 + 0.935643i \(0.385180\pi\)
\(140\) 6.85036 0.578961
\(141\) 2.28663 0.192569
\(142\) −20.8830 −1.75247
\(143\) −4.57853 −0.382876
\(144\) 13.6557 1.13798
\(145\) 1.82961 0.151941
\(146\) 2.59884 0.215082
\(147\) −6.92825 −0.571432
\(148\) 2.84707 0.234028
\(149\) 11.0933 0.908796 0.454398 0.890799i \(-0.349854\pi\)
0.454398 + 0.890799i \(0.349854\pi\)
\(150\) −2.46577 −0.201329
\(151\) −23.9637 −1.95014 −0.975070 0.221900i \(-0.928774\pi\)
−0.975070 + 0.221900i \(0.928774\pi\)
\(152\) 4.99351 0.405027
\(153\) 0.530163 0.0428612
\(154\) −25.8711 −2.08475
\(155\) 4.31863 0.346881
\(156\) −0.725592 −0.0580939
\(157\) −17.6311 −1.40711 −0.703557 0.710639i \(-0.748406\pi\)
−0.703557 + 0.710639i \(0.748406\pi\)
\(158\) −25.8543 −2.05685
\(159\) −3.60837 −0.286162
\(160\) −7.87477 −0.622555
\(161\) −10.1598 −0.800702
\(162\) −11.5428 −0.906892
\(163\) 0.231428 0.0181268 0.00906341 0.999959i \(-0.497115\pi\)
0.00906341 + 0.999959i \(0.497115\pi\)
\(164\) 8.74210 0.682643
\(165\) −2.57481 −0.200449
\(166\) 15.1617 1.17678
\(167\) 3.63672 0.281418 0.140709 0.990051i \(-0.455062\pi\)
0.140709 + 0.990051i \(0.455062\pi\)
\(168\) 4.01811 0.310004
\(169\) −11.0802 −0.852326
\(170\) −0.506147 −0.0388197
\(171\) −7.94095 −0.607259
\(172\) −4.22805 −0.322386
\(173\) 8.61296 0.654831 0.327416 0.944880i \(-0.393822\pi\)
0.327416 + 0.944880i \(0.393822\pi\)
\(174\) −1.09504 −0.0830144
\(175\) 12.3702 0.935098
\(176\) 16.5220 1.24540
\(177\) −6.08711 −0.457535
\(178\) −24.3312 −1.82370
\(179\) −10.7205 −0.801289 −0.400645 0.916234i \(-0.631214\pi\)
−0.400645 + 0.916234i \(0.631214\pi\)
\(180\) 4.14614 0.309035
\(181\) 3.27437 0.243382 0.121691 0.992568i \(-0.461168\pi\)
0.121691 + 0.992568i \(0.461168\pi\)
\(182\) 10.8477 0.804084
\(183\) 2.33360 0.172505
\(184\) 3.86676 0.285062
\(185\) −4.23615 −0.311448
\(186\) −2.58473 −0.189521
\(187\) 0.641443 0.0469069
\(188\) −4.45495 −0.324910
\(189\) −13.4085 −0.975326
\(190\) 7.58122 0.550000
\(191\) −0.683502 −0.0494565 −0.0247282 0.999694i \(-0.507872\pi\)
−0.0247282 + 0.999694i \(0.507872\pi\)
\(192\) −0.471347 −0.0340165
\(193\) −2.55423 −0.183858 −0.0919289 0.995766i \(-0.529303\pi\)
−0.0919289 + 0.995766i \(0.529303\pi\)
\(194\) −9.32867 −0.669759
\(195\) 1.07961 0.0773124
\(196\) 13.4980 0.964144
\(197\) 10.5804 0.753826 0.376913 0.926249i \(-0.376986\pi\)
0.376913 + 0.926249i \(0.376986\pi\)
\(198\) −15.6583 −1.11279
\(199\) 6.44383 0.456791 0.228396 0.973568i \(-0.426652\pi\)
0.228396 + 0.973568i \(0.426652\pi\)
\(200\) −4.70804 −0.332909
\(201\) 7.32653 0.516773
\(202\) −16.7363 −1.17757
\(203\) 5.49353 0.385570
\(204\) 0.101654 0.00711720
\(205\) −13.0074 −0.908475
\(206\) 16.7774 1.16893
\(207\) −6.14914 −0.427395
\(208\) −6.92764 −0.480345
\(209\) −9.60772 −0.664580
\(210\) 6.10036 0.420965
\(211\) 20.8889 1.43805 0.719025 0.694984i \(-0.244589\pi\)
0.719025 + 0.694984i \(0.244589\pi\)
\(212\) 7.03003 0.482825
\(213\) −6.24044 −0.427588
\(214\) 28.8120 1.96955
\(215\) 6.29092 0.429037
\(216\) 5.10322 0.347230
\(217\) 12.9670 0.880254
\(218\) 22.2447 1.50660
\(219\) 0.776607 0.0524783
\(220\) 5.01640 0.338205
\(221\) −0.268955 −0.0180919
\(222\) 2.53536 0.170163
\(223\) 9.26897 0.620696 0.310348 0.950623i \(-0.399554\pi\)
0.310348 + 0.950623i \(0.399554\pi\)
\(224\) −23.6445 −1.57981
\(225\) 7.48698 0.499132
\(226\) 12.4083 0.825386
\(227\) 12.1398 0.805745 0.402872 0.915256i \(-0.368012\pi\)
0.402872 + 0.915256i \(0.368012\pi\)
\(228\) −1.52260 −0.100837
\(229\) 1.91232 0.126370 0.0631848 0.998002i \(-0.479874\pi\)
0.0631848 + 0.998002i \(0.479874\pi\)
\(230\) 5.87058 0.387095
\(231\) −7.73102 −0.508664
\(232\) −2.09081 −0.137269
\(233\) −8.25019 −0.540488 −0.270244 0.962792i \(-0.587104\pi\)
−0.270244 + 0.962792i \(0.587104\pi\)
\(234\) 6.56550 0.429200
\(235\) 6.62852 0.432397
\(236\) 11.8593 0.771972
\(237\) −7.72598 −0.501856
\(238\) −1.51974 −0.0985099
\(239\) 4.33812 0.280610 0.140305 0.990108i \(-0.455192\pi\)
0.140305 + 0.990108i \(0.455192\pi\)
\(240\) −3.89586 −0.251477
\(241\) 4.75987 0.306610 0.153305 0.988179i \(-0.451008\pi\)
0.153305 + 0.988179i \(0.451008\pi\)
\(242\) 0.139576 0.00897230
\(243\) −12.3634 −0.793115
\(244\) −4.54646 −0.291057
\(245\) −20.0837 −1.28310
\(246\) 7.78500 0.496353
\(247\) 4.02849 0.256327
\(248\) −4.93517 −0.313383
\(249\) 4.53074 0.287124
\(250\) −20.1852 −1.27663
\(251\) 29.1937 1.84269 0.921346 0.388744i \(-0.127091\pi\)
0.921346 + 0.388744i \(0.127091\pi\)
\(252\) 12.4490 0.784215
\(253\) −7.43982 −0.467738
\(254\) −5.18714 −0.325470
\(255\) −0.151251 −0.00947170
\(256\) 19.0996 1.19373
\(257\) −11.0017 −0.686269 −0.343134 0.939286i \(-0.611489\pi\)
−0.343134 + 0.939286i \(0.611489\pi\)
\(258\) −3.76516 −0.234408
\(259\) −12.7193 −0.790340
\(260\) −2.10336 −0.130445
\(261\) 3.32493 0.205808
\(262\) 27.1585 1.67786
\(263\) −14.6308 −0.902172 −0.451086 0.892480i \(-0.648963\pi\)
−0.451086 + 0.892480i \(0.648963\pi\)
\(264\) 2.94239 0.181092
\(265\) −10.4600 −0.642552
\(266\) 22.7631 1.39569
\(267\) −7.27084 −0.444968
\(268\) −14.2740 −0.871922
\(269\) 23.5618 1.43659 0.718293 0.695740i \(-0.244924\pi\)
0.718293 + 0.695740i \(0.244924\pi\)
\(270\) 7.74779 0.471516
\(271\) 4.46665 0.271330 0.135665 0.990755i \(-0.456683\pi\)
0.135665 + 0.990755i \(0.456683\pi\)
\(272\) 0.970547 0.0588481
\(273\) 3.24159 0.196190
\(274\) −20.9451 −1.26534
\(275\) 9.05847 0.546246
\(276\) −1.17904 −0.0709699
\(277\) 28.3264 1.70197 0.850983 0.525193i \(-0.176007\pi\)
0.850983 + 0.525193i \(0.176007\pi\)
\(278\) −14.4390 −0.865992
\(279\) 7.84817 0.469858
\(280\) 11.6478 0.696087
\(281\) −5.74382 −0.342648 −0.171324 0.985215i \(-0.554804\pi\)
−0.171324 + 0.985215i \(0.554804\pi\)
\(282\) −3.96721 −0.236244
\(283\) 25.2992 1.50388 0.751940 0.659232i \(-0.229119\pi\)
0.751940 + 0.659232i \(0.229119\pi\)
\(284\) 12.1580 0.721444
\(285\) 2.26548 0.134196
\(286\) 7.94357 0.469713
\(287\) −39.0554 −2.30537
\(288\) −14.3107 −0.843265
\(289\) −16.9623 −0.997784
\(290\) −3.17431 −0.186402
\(291\) −2.78767 −0.163416
\(292\) −1.51303 −0.0885435
\(293\) 4.53285 0.264812 0.132406 0.991196i \(-0.457730\pi\)
0.132406 + 0.991196i \(0.457730\pi\)
\(294\) 12.0202 0.701034
\(295\) −17.6454 −1.02736
\(296\) 4.84092 0.281372
\(297\) −9.81882 −0.569746
\(298\) −19.2464 −1.11491
\(299\) 3.11949 0.180405
\(300\) 1.43556 0.0828821
\(301\) 18.8889 1.08874
\(302\) 41.5761 2.39243
\(303\) −5.00129 −0.287317
\(304\) −14.5372 −0.833763
\(305\) 6.76468 0.387344
\(306\) −0.919812 −0.0525822
\(307\) −3.56935 −0.203714 −0.101857 0.994799i \(-0.532478\pi\)
−0.101857 + 0.994799i \(0.532478\pi\)
\(308\) 15.0620 0.858239
\(309\) 5.01355 0.285211
\(310\) −7.49265 −0.425554
\(311\) −20.7076 −1.17422 −0.587110 0.809507i \(-0.699734\pi\)
−0.587110 + 0.809507i \(0.699734\pi\)
\(312\) −1.23374 −0.0698466
\(313\) 20.1581 1.13940 0.569702 0.821851i \(-0.307058\pi\)
0.569702 + 0.821851i \(0.307058\pi\)
\(314\) 30.5892 1.72625
\(315\) −18.5229 −1.04365
\(316\) 15.0522 0.846753
\(317\) 10.9957 0.617578 0.308789 0.951131i \(-0.400076\pi\)
0.308789 + 0.951131i \(0.400076\pi\)
\(318\) 6.26037 0.351064
\(319\) 4.02282 0.225234
\(320\) −1.36635 −0.0763812
\(321\) 8.60985 0.480555
\(322\) 17.6268 0.982302
\(323\) −0.564383 −0.0314031
\(324\) 6.72019 0.373344
\(325\) −3.79819 −0.210686
\(326\) −0.401518 −0.0222380
\(327\) 6.64735 0.367599
\(328\) 14.8643 0.820745
\(329\) 19.9025 1.09726
\(330\) 4.46719 0.245911
\(331\) 15.8325 0.870233 0.435116 0.900374i \(-0.356707\pi\)
0.435116 + 0.900374i \(0.356707\pi\)
\(332\) −8.82706 −0.484448
\(333\) −7.69829 −0.421864
\(334\) −6.30956 −0.345244
\(335\) 21.2383 1.16037
\(336\) −11.6976 −0.638155
\(337\) 20.0094 1.08998 0.544991 0.838442i \(-0.316533\pi\)
0.544991 + 0.838442i \(0.316533\pi\)
\(338\) 19.2238 1.04563
\(339\) 3.70794 0.201388
\(340\) 0.294676 0.0159811
\(341\) 9.49548 0.514209
\(342\) 13.7772 0.744987
\(343\) −28.7146 −1.55044
\(344\) −7.18903 −0.387606
\(345\) 1.75430 0.0944481
\(346\) −14.9431 −0.803348
\(347\) −8.37009 −0.449330 −0.224665 0.974436i \(-0.572129\pi\)
−0.224665 + 0.974436i \(0.572129\pi\)
\(348\) 0.637524 0.0341749
\(349\) 31.1228 1.66596 0.832982 0.553300i \(-0.186632\pi\)
0.832982 + 0.553300i \(0.186632\pi\)
\(350\) −21.4618 −1.14718
\(351\) 4.11700 0.219749
\(352\) −17.3144 −0.922863
\(353\) 30.7626 1.63733 0.818663 0.574274i \(-0.194715\pi\)
0.818663 + 0.574274i \(0.194715\pi\)
\(354\) 10.5609 0.561305
\(355\) −18.0899 −0.960112
\(356\) 14.1655 0.750769
\(357\) −0.454140 −0.0240357
\(358\) 18.5997 0.983023
\(359\) 12.3707 0.652902 0.326451 0.945214i \(-0.394147\pi\)
0.326451 + 0.945214i \(0.394147\pi\)
\(360\) 7.04974 0.371554
\(361\) −10.5465 −0.555079
\(362\) −5.68090 −0.298582
\(363\) 0.0417093 0.00218917
\(364\) −6.31547 −0.331020
\(365\) 2.25124 0.117835
\(366\) −4.04870 −0.211629
\(367\) −16.5405 −0.863405 −0.431702 0.902016i \(-0.642087\pi\)
−0.431702 + 0.902016i \(0.642087\pi\)
\(368\) −11.2570 −0.586810
\(369\) −23.6381 −1.23055
\(370\) 7.34956 0.382085
\(371\) −31.4068 −1.63056
\(372\) 1.50482 0.0780210
\(373\) 20.8471 1.07942 0.539710 0.841851i \(-0.318534\pi\)
0.539710 + 0.841851i \(0.318534\pi\)
\(374\) −1.11288 −0.0575455
\(375\) −6.03191 −0.311487
\(376\) −7.57482 −0.390641
\(377\) −1.68675 −0.0868722
\(378\) 23.2632 1.19653
\(379\) −22.9253 −1.17759 −0.588797 0.808281i \(-0.700398\pi\)
−0.588797 + 0.808281i \(0.700398\pi\)
\(380\) −4.41375 −0.226421
\(381\) −1.55007 −0.0794123
\(382\) 1.18585 0.0606733
\(383\) −27.6637 −1.41355 −0.706775 0.707439i \(-0.749850\pi\)
−0.706775 + 0.707439i \(0.749850\pi\)
\(384\) 6.25086 0.318988
\(385\) −22.4108 −1.14216
\(386\) 4.43149 0.225557
\(387\) 11.4324 0.581141
\(388\) 5.43110 0.275722
\(389\) −17.5299 −0.888800 −0.444400 0.895828i \(-0.646583\pi\)
−0.444400 + 0.895828i \(0.646583\pi\)
\(390\) −1.87308 −0.0948470
\(391\) −0.437034 −0.0221018
\(392\) 22.9509 1.15920
\(393\) 8.11573 0.409384
\(394\) −18.3566 −0.924794
\(395\) −22.3962 −1.12688
\(396\) 9.11621 0.458107
\(397\) 11.9244 0.598470 0.299235 0.954179i \(-0.403269\pi\)
0.299235 + 0.954179i \(0.403269\pi\)
\(398\) −11.1798 −0.560392
\(399\) 6.80225 0.340539
\(400\) 13.7061 0.685305
\(401\) −7.89074 −0.394045 −0.197022 0.980399i \(-0.563127\pi\)
−0.197022 + 0.980399i \(0.563127\pi\)
\(402\) −12.7112 −0.633979
\(403\) −3.98142 −0.198329
\(404\) 9.74382 0.484773
\(405\) −9.99897 −0.496853
\(406\) −9.53105 −0.473018
\(407\) −9.31413 −0.461684
\(408\) 0.172844 0.00855705
\(409\) −15.0680 −0.745063 −0.372532 0.928020i \(-0.621510\pi\)
−0.372532 + 0.928020i \(0.621510\pi\)
\(410\) 22.5673 1.11452
\(411\) −6.25898 −0.308733
\(412\) −9.76770 −0.481220
\(413\) −52.9814 −2.60705
\(414\) 10.6685 0.524329
\(415\) 13.1338 0.644712
\(416\) 7.25989 0.355945
\(417\) −4.31477 −0.211295
\(418\) 16.6690 0.815308
\(419\) −1.08911 −0.0532063 −0.0266031 0.999646i \(-0.508469\pi\)
−0.0266031 + 0.999646i \(0.508469\pi\)
\(420\) −3.55160 −0.173300
\(421\) 22.1667 1.08034 0.540170 0.841556i \(-0.318360\pi\)
0.540170 + 0.841556i \(0.318360\pi\)
\(422\) −36.2414 −1.76420
\(423\) 12.0459 0.585691
\(424\) 11.9533 0.580502
\(425\) 0.532118 0.0258115
\(426\) 10.8269 0.524566
\(427\) 20.3114 0.982936
\(428\) −16.7742 −0.810812
\(429\) 2.37376 0.114606
\(430\) −10.9145 −0.526344
\(431\) 20.1499 0.970585 0.485292 0.874352i \(-0.338713\pi\)
0.485292 + 0.874352i \(0.338713\pi\)
\(432\) −14.8566 −0.714786
\(433\) −23.8701 −1.14713 −0.573563 0.819162i \(-0.694439\pi\)
−0.573563 + 0.819162i \(0.694439\pi\)
\(434\) −22.4971 −1.07990
\(435\) −0.948572 −0.0454806
\(436\) −12.9508 −0.620229
\(437\) 6.54603 0.313139
\(438\) −1.34738 −0.0643804
\(439\) 8.01603 0.382584 0.191292 0.981533i \(-0.438732\pi\)
0.191292 + 0.981533i \(0.438732\pi\)
\(440\) 8.52946 0.406626
\(441\) −36.4978 −1.73799
\(442\) 0.466626 0.0221951
\(443\) 15.9908 0.759747 0.379874 0.925038i \(-0.375967\pi\)
0.379874 + 0.925038i \(0.375967\pi\)
\(444\) −1.47608 −0.0700515
\(445\) −21.0768 −0.999138
\(446\) −16.0813 −0.761471
\(447\) −5.75136 −0.272030
\(448\) −4.10254 −0.193827
\(449\) −0.889928 −0.0419983 −0.0209991 0.999779i \(-0.506685\pi\)
−0.0209991 + 0.999779i \(0.506685\pi\)
\(450\) −12.9896 −0.612336
\(451\) −28.5996 −1.34670
\(452\) −7.22403 −0.339790
\(453\) 12.4241 0.583735
\(454\) −21.0620 −0.988489
\(455\) 9.39678 0.440528
\(456\) −2.58891 −0.121237
\(457\) 32.2953 1.51071 0.755355 0.655315i \(-0.227464\pi\)
0.755355 + 0.655315i \(0.227464\pi\)
\(458\) −3.31780 −0.155031
\(459\) −0.576783 −0.0269219
\(460\) −3.41782 −0.159357
\(461\) 17.3578 0.808431 0.404216 0.914664i \(-0.367545\pi\)
0.404216 + 0.914664i \(0.367545\pi\)
\(462\) 13.4130 0.624030
\(463\) 22.4024 1.04113 0.520565 0.853822i \(-0.325721\pi\)
0.520565 + 0.853822i \(0.325721\pi\)
\(464\) 6.08680 0.282573
\(465\) −2.23902 −0.103832
\(466\) 14.3137 0.663071
\(467\) −7.43799 −0.344189 −0.172095 0.985080i \(-0.555054\pi\)
−0.172095 + 0.985080i \(0.555054\pi\)
\(468\) −3.82240 −0.176690
\(469\) 63.7692 2.94459
\(470\) −11.5002 −0.530465
\(471\) 9.14092 0.421191
\(472\) 20.1645 0.928146
\(473\) 13.8320 0.635996
\(474\) 13.4043 0.615678
\(475\) −7.97023 −0.365699
\(476\) 0.884783 0.0405540
\(477\) −19.0088 −0.870351
\(478\) −7.52646 −0.344252
\(479\) 18.4127 0.841297 0.420648 0.907224i \(-0.361803\pi\)
0.420648 + 0.907224i \(0.361803\pi\)
\(480\) 4.08271 0.186349
\(481\) 3.90539 0.178070
\(482\) −8.25819 −0.376150
\(483\) 5.26738 0.239674
\(484\) −0.0812605 −0.00369366
\(485\) −8.08094 −0.366937
\(486\) 21.4501 0.972995
\(487\) −5.09792 −0.231009 −0.115504 0.993307i \(-0.536848\pi\)
−0.115504 + 0.993307i \(0.536848\pi\)
\(488\) −7.73042 −0.349939
\(489\) −0.119985 −0.00542590
\(490\) 34.8444 1.57411
\(491\) −32.2378 −1.45487 −0.727436 0.686176i \(-0.759288\pi\)
−0.727436 + 0.686176i \(0.759288\pi\)
\(492\) −4.53238 −0.204336
\(493\) 0.236311 0.0106429
\(494\) −6.98926 −0.314462
\(495\) −13.5640 −0.609657
\(496\) 14.3673 0.645111
\(497\) −54.3160 −2.43641
\(498\) −7.86066 −0.352244
\(499\) 21.1194 0.945436 0.472718 0.881214i \(-0.343273\pi\)
0.472718 + 0.881214i \(0.343273\pi\)
\(500\) 11.7517 0.525554
\(501\) −1.88547 −0.0842367
\(502\) −50.6499 −2.26062
\(503\) −20.3300 −0.906472 −0.453236 0.891391i \(-0.649731\pi\)
−0.453236 + 0.891391i \(0.649731\pi\)
\(504\) 21.1673 0.942866
\(505\) −14.4978 −0.645145
\(506\) 12.9078 0.573821
\(507\) 5.74460 0.255127
\(508\) 3.01993 0.133988
\(509\) 6.22487 0.275913 0.137956 0.990438i \(-0.455947\pi\)
0.137956 + 0.990438i \(0.455947\pi\)
\(510\) 0.262414 0.0116199
\(511\) 6.75949 0.299022
\(512\) −9.02366 −0.398793
\(513\) 8.63923 0.381431
\(514\) 19.0875 0.841916
\(515\) 14.5334 0.640417
\(516\) 2.19206 0.0964998
\(517\) 14.5743 0.640976
\(518\) 22.0675 0.969590
\(519\) −4.46543 −0.196011
\(520\) −3.57637 −0.156834
\(521\) −26.4316 −1.15799 −0.578995 0.815331i \(-0.696555\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(522\) −5.76861 −0.252485
\(523\) −41.2067 −1.80184 −0.900922 0.433982i \(-0.857108\pi\)
−0.900922 + 0.433982i \(0.857108\pi\)
\(524\) −15.8115 −0.690731
\(525\) −6.41338 −0.279903
\(526\) 25.3838 1.10679
\(527\) 0.557789 0.0242977
\(528\) −8.56593 −0.372784
\(529\) −17.9310 −0.779610
\(530\) 18.1477 0.788284
\(531\) −32.0667 −1.39158
\(532\) −13.2526 −0.574571
\(533\) 11.9917 0.519420
\(534\) 12.6146 0.545888
\(535\) 24.9584 1.07904
\(536\) −24.2703 −1.04832
\(537\) 5.55810 0.239850
\(538\) −40.8787 −1.76241
\(539\) −44.1585 −1.90204
\(540\) −4.51073 −0.194111
\(541\) 9.44712 0.406163 0.203082 0.979162i \(-0.434904\pi\)
0.203082 + 0.979162i \(0.434904\pi\)
\(542\) −7.74946 −0.332868
\(543\) −1.69761 −0.0728516
\(544\) −1.01710 −0.0436076
\(545\) 19.2695 0.825413
\(546\) −5.62403 −0.240686
\(547\) −4.98270 −0.213045 −0.106522 0.994310i \(-0.533972\pi\)
−0.106522 + 0.994310i \(0.533972\pi\)
\(548\) 12.1941 0.520907
\(549\) 12.2933 0.524667
\(550\) −15.7161 −0.670136
\(551\) −3.53953 −0.150789
\(552\) −2.00474 −0.0853275
\(553\) −67.2460 −2.85959
\(554\) −49.1451 −2.08798
\(555\) 2.19626 0.0932258
\(556\) 8.40629 0.356506
\(557\) 3.57013 0.151271 0.0756355 0.997136i \(-0.475901\pi\)
0.0756355 + 0.997136i \(0.475901\pi\)
\(558\) −13.6163 −0.576422
\(559\) −5.79971 −0.245302
\(560\) −33.9091 −1.43292
\(561\) −0.332559 −0.0140407
\(562\) 9.96530 0.420361
\(563\) 0.338020 0.0142458 0.00712292 0.999975i \(-0.497733\pi\)
0.00712292 + 0.999975i \(0.497733\pi\)
\(564\) 2.30969 0.0972554
\(565\) 10.7486 0.452199
\(566\) −43.8930 −1.84496
\(567\) −30.0225 −1.26083
\(568\) 20.6724 0.867396
\(569\) 22.9509 0.962150 0.481075 0.876679i \(-0.340246\pi\)
0.481075 + 0.876679i \(0.340246\pi\)
\(570\) −3.93052 −0.164631
\(571\) 26.6717 1.11617 0.558087 0.829782i \(-0.311535\pi\)
0.558087 + 0.829782i \(0.311535\pi\)
\(572\) −4.62471 −0.193369
\(573\) 0.354365 0.0148038
\(574\) 67.7596 2.82823
\(575\) −6.17181 −0.257382
\(576\) −2.48304 −0.103460
\(577\) −8.02188 −0.333955 −0.166978 0.985961i \(-0.553401\pi\)
−0.166978 + 0.985961i \(0.553401\pi\)
\(578\) 29.4289 1.22408
\(579\) 1.32426 0.0550342
\(580\) 1.84807 0.0767367
\(581\) 39.4350 1.63604
\(582\) 4.83649 0.200479
\(583\) −22.9986 −0.952506
\(584\) −2.57263 −0.106456
\(585\) 5.68735 0.235143
\(586\) −7.86432 −0.324872
\(587\) −43.3150 −1.78780 −0.893902 0.448263i \(-0.852043\pi\)
−0.893902 + 0.448263i \(0.852043\pi\)
\(588\) −6.99812 −0.288597
\(589\) −8.35473 −0.344251
\(590\) 30.6141 1.26036
\(591\) −5.48548 −0.225643
\(592\) −14.0929 −0.579216
\(593\) 14.1489 0.581027 0.290513 0.956871i \(-0.406174\pi\)
0.290513 + 0.956871i \(0.406174\pi\)
\(594\) 17.0353 0.698965
\(595\) −1.31647 −0.0539700
\(596\) 11.2051 0.458981
\(597\) −3.34084 −0.136731
\(598\) −5.41220 −0.221321
\(599\) 0.997199 0.0407444 0.0203722 0.999792i \(-0.493515\pi\)
0.0203722 + 0.999792i \(0.493515\pi\)
\(600\) 2.44091 0.0996496
\(601\) 15.9527 0.650723 0.325362 0.945590i \(-0.394514\pi\)
0.325362 + 0.945590i \(0.394514\pi\)
\(602\) −32.7715 −1.33566
\(603\) 38.5959 1.57175
\(604\) −24.2054 −0.984903
\(605\) 0.120908 0.00491559
\(606\) 8.67704 0.352481
\(607\) 25.7954 1.04700 0.523501 0.852025i \(-0.324626\pi\)
0.523501 + 0.852025i \(0.324626\pi\)
\(608\) 15.2344 0.617835
\(609\) −2.84815 −0.115413
\(610\) −11.7364 −0.475195
\(611\) −6.11095 −0.247222
\(612\) 0.535510 0.0216467
\(613\) 3.08922 0.124773 0.0623863 0.998052i \(-0.480129\pi\)
0.0623863 + 0.998052i \(0.480129\pi\)
\(614\) 6.19269 0.249916
\(615\) 6.74374 0.271934
\(616\) 25.6102 1.03187
\(617\) 15.4825 0.623301 0.311650 0.950197i \(-0.399118\pi\)
0.311650 + 0.950197i \(0.399118\pi\)
\(618\) −8.69831 −0.349897
\(619\) 1.00000 0.0401934
\(620\) 4.36218 0.175189
\(621\) 6.68986 0.268455
\(622\) 35.9268 1.44054
\(623\) −63.2845 −2.53544
\(624\) 3.59167 0.143782
\(625\) −3.77904 −0.151162
\(626\) −34.9735 −1.39782
\(627\) 4.98117 0.198929
\(628\) −17.8089 −0.710652
\(629\) −0.547136 −0.0218158
\(630\) 32.1365 1.28035
\(631\) 46.9943 1.87081 0.935406 0.353575i \(-0.115034\pi\)
0.935406 + 0.353575i \(0.115034\pi\)
\(632\) 25.5935 1.01806
\(633\) −10.8299 −0.430452
\(634\) −19.0770 −0.757646
\(635\) −4.49335 −0.178313
\(636\) −3.64475 −0.144524
\(637\) 18.5155 0.733612
\(638\) −6.97942 −0.276318
\(639\) −32.8744 −1.30049
\(640\) 18.1201 0.716260
\(641\) 1.79472 0.0708874 0.0354437 0.999372i \(-0.488716\pi\)
0.0354437 + 0.999372i \(0.488716\pi\)
\(642\) −14.9377 −0.589545
\(643\) −17.3895 −0.685777 −0.342888 0.939376i \(-0.611405\pi\)
−0.342888 + 0.939376i \(0.611405\pi\)
\(644\) −10.2622 −0.404388
\(645\) −3.26156 −0.128424
\(646\) 0.979181 0.0385254
\(647\) 47.2406 1.85722 0.928610 0.371058i \(-0.121005\pi\)
0.928610 + 0.371058i \(0.121005\pi\)
\(648\) 11.4264 0.448873
\(649\) −38.7974 −1.52293
\(650\) 6.58970 0.258469
\(651\) −6.72278 −0.263487
\(652\) 0.233762 0.00915481
\(653\) 15.1733 0.593778 0.296889 0.954912i \(-0.404051\pi\)
0.296889 + 0.954912i \(0.404051\pi\)
\(654\) −11.5329 −0.450972
\(655\) 23.5260 0.919237
\(656\) −43.2732 −1.68954
\(657\) 4.09114 0.159611
\(658\) −34.5301 −1.34612
\(659\) −10.7807 −0.419957 −0.209978 0.977706i \(-0.567339\pi\)
−0.209978 + 0.977706i \(0.567339\pi\)
\(660\) −2.60078 −0.101235
\(661\) 11.7317 0.456311 0.228155 0.973625i \(-0.426731\pi\)
0.228155 + 0.973625i \(0.426731\pi\)
\(662\) −27.4687 −1.06760
\(663\) 0.139441 0.00541544
\(664\) −15.0088 −0.582454
\(665\) 19.7185 0.764650
\(666\) 13.3562 0.517543
\(667\) −2.74087 −0.106127
\(668\) 3.67339 0.142128
\(669\) −4.80554 −0.185793
\(670\) −36.8475 −1.42354
\(671\) 14.8737 0.574191
\(672\) 12.2586 0.472886
\(673\) 32.6738 1.25948 0.629742 0.776805i \(-0.283161\pi\)
0.629742 + 0.776805i \(0.283161\pi\)
\(674\) −34.7155 −1.33719
\(675\) −8.14534 −0.313514
\(676\) −11.1920 −0.430461
\(677\) 12.4914 0.480083 0.240042 0.970763i \(-0.422839\pi\)
0.240042 + 0.970763i \(0.422839\pi\)
\(678\) −6.43313 −0.247063
\(679\) −24.2635 −0.931148
\(680\) 0.501043 0.0192141
\(681\) −6.29392 −0.241184
\(682\) −16.4743 −0.630832
\(683\) 48.7463 1.86523 0.932614 0.360877i \(-0.117523\pi\)
0.932614 + 0.360877i \(0.117523\pi\)
\(684\) −8.02103 −0.306692
\(685\) −18.1436 −0.693233
\(686\) 49.8187 1.90209
\(687\) −0.991452 −0.0378262
\(688\) 20.9288 0.797902
\(689\) 9.64325 0.367379
\(690\) −3.04363 −0.115869
\(691\) −33.3676 −1.26936 −0.634682 0.772773i \(-0.718869\pi\)
−0.634682 + 0.772773i \(0.718869\pi\)
\(692\) 8.69982 0.330717
\(693\) −40.7268 −1.54708
\(694\) 14.5218 0.551239
\(695\) −12.5077 −0.474445
\(696\) 1.08399 0.0410886
\(697\) −1.68002 −0.0636352
\(698\) −53.9968 −2.04381
\(699\) 4.27735 0.161784
\(700\) 12.4949 0.472264
\(701\) −7.67606 −0.289921 −0.144960 0.989437i \(-0.546305\pi\)
−0.144960 + 0.989437i \(0.546305\pi\)
\(702\) −7.14283 −0.269589
\(703\) 8.19517 0.309087
\(704\) −3.00422 −0.113226
\(705\) −3.43659 −0.129429
\(706\) −53.3718 −2.00868
\(707\) −43.5306 −1.63714
\(708\) −6.14849 −0.231075
\(709\) 39.7313 1.49214 0.746071 0.665866i \(-0.231938\pi\)
0.746071 + 0.665866i \(0.231938\pi\)
\(710\) 31.3852 1.17787
\(711\) −40.7002 −1.52638
\(712\) 24.0858 0.902654
\(713\) −6.46956 −0.242287
\(714\) 0.787915 0.0294870
\(715\) 6.88110 0.257339
\(716\) −10.8286 −0.404685
\(717\) −2.24912 −0.0839949
\(718\) −21.4627 −0.800982
\(719\) 11.9781 0.446707 0.223354 0.974737i \(-0.428300\pi\)
0.223354 + 0.974737i \(0.428300\pi\)
\(720\) −20.5233 −0.764858
\(721\) 43.6373 1.62514
\(722\) 18.2978 0.680972
\(723\) −2.46778 −0.0917777
\(724\) 3.30739 0.122918
\(725\) 3.33719 0.123940
\(726\) −0.0723640 −0.00268568
\(727\) −13.5586 −0.502859 −0.251430 0.967876i \(-0.580901\pi\)
−0.251430 + 0.967876i \(0.580901\pi\)
\(728\) −10.7383 −0.397987
\(729\) −13.5494 −0.501829
\(730\) −3.90581 −0.144561
\(731\) 0.812528 0.0300524
\(732\) 2.35713 0.0871222
\(733\) −39.9169 −1.47436 −0.737182 0.675695i \(-0.763844\pi\)
−0.737182 + 0.675695i \(0.763844\pi\)
\(734\) 28.6970 1.05923
\(735\) 10.4125 0.384071
\(736\) 11.7969 0.434838
\(737\) 46.6971 1.72011
\(738\) 41.0111 1.50964
\(739\) −7.95341 −0.292571 −0.146286 0.989242i \(-0.546732\pi\)
−0.146286 + 0.989242i \(0.546732\pi\)
\(740\) −4.27887 −0.157295
\(741\) −2.08859 −0.0767262
\(742\) 54.4895 2.00037
\(743\) 52.7858 1.93652 0.968261 0.249941i \(-0.0804114\pi\)
0.968261 + 0.249941i \(0.0804114\pi\)
\(744\) 2.55866 0.0938051
\(745\) −16.6721 −0.610820
\(746\) −36.1688 −1.32424
\(747\) 23.8678 0.873278
\(748\) 0.647912 0.0236900
\(749\) 74.9390 2.73821
\(750\) 10.4651 0.382132
\(751\) −41.6111 −1.51841 −0.759205 0.650852i \(-0.774412\pi\)
−0.759205 + 0.650852i \(0.774412\pi\)
\(752\) 22.0519 0.804150
\(753\) −15.1356 −0.551573
\(754\) 2.92645 0.106575
\(755\) 36.0152 1.31073
\(756\) −13.5437 −0.492581
\(757\) 16.4361 0.597380 0.298690 0.954350i \(-0.403450\pi\)
0.298690 + 0.954350i \(0.403450\pi\)
\(758\) 39.7745 1.44467
\(759\) 3.85721 0.140008
\(760\) −7.50477 −0.272227
\(761\) 20.0857 0.728105 0.364052 0.931379i \(-0.381393\pi\)
0.364052 + 0.931379i \(0.381393\pi\)
\(762\) 2.68930 0.0974231
\(763\) 57.8577 2.09459
\(764\) −0.690395 −0.0249776
\(765\) −0.796786 −0.0288078
\(766\) 47.9954 1.73414
\(767\) 16.2676 0.587390
\(768\) −9.90229 −0.357318
\(769\) −31.4916 −1.13562 −0.567809 0.823160i \(-0.692209\pi\)
−0.567809 + 0.823160i \(0.692209\pi\)
\(770\) 38.8819 1.40121
\(771\) 5.70390 0.205421
\(772\) −2.57999 −0.0928560
\(773\) 4.51810 0.162505 0.0812523 0.996694i \(-0.474108\pi\)
0.0812523 + 0.996694i \(0.474108\pi\)
\(774\) −19.8347 −0.712945
\(775\) 7.87711 0.282954
\(776\) 9.23459 0.331502
\(777\) 6.59439 0.236572
\(778\) 30.4136 1.09038
\(779\) 25.1638 0.901586
\(780\) 1.09050 0.0390461
\(781\) −39.7747 −1.42325
\(782\) 0.758237 0.0271145
\(783\) −3.61730 −0.129272
\(784\) −66.8149 −2.38625
\(785\) 26.4978 0.945749
\(786\) −14.0805 −0.502234
\(787\) −44.4820 −1.58561 −0.792807 0.609473i \(-0.791381\pi\)
−0.792807 + 0.609473i \(0.791381\pi\)
\(788\) 10.6871 0.380714
\(789\) 7.58540 0.270047
\(790\) 38.8565 1.38245
\(791\) 32.2735 1.14751
\(792\) 15.5004 0.550784
\(793\) −6.23648 −0.221464
\(794\) −20.6884 −0.734204
\(795\) 5.42303 0.192335
\(796\) 6.50881 0.230699
\(797\) −18.9102 −0.669835 −0.334917 0.942247i \(-0.608708\pi\)
−0.334917 + 0.942247i \(0.608708\pi\)
\(798\) −11.8016 −0.417773
\(799\) 0.856131 0.0302877
\(800\) −14.3634 −0.507824
\(801\) −38.3026 −1.35335
\(802\) 13.6901 0.483415
\(803\) 4.94986 0.174677
\(804\) 7.40041 0.260992
\(805\) 15.2692 0.538168
\(806\) 6.90761 0.243310
\(807\) −12.2157 −0.430014
\(808\) 16.5676 0.582845
\(809\) 45.8737 1.61283 0.806417 0.591347i \(-0.201403\pi\)
0.806417 + 0.591347i \(0.201403\pi\)
\(810\) 17.3478 0.609540
\(811\) 25.5748 0.898053 0.449027 0.893518i \(-0.351771\pi\)
0.449027 + 0.893518i \(0.351771\pi\)
\(812\) 5.54893 0.194729
\(813\) −2.31576 −0.0812172
\(814\) 16.1596 0.566395
\(815\) −0.347814 −0.0121834
\(816\) −0.503185 −0.0176150
\(817\) −12.1703 −0.425784
\(818\) 26.1423 0.914045
\(819\) 17.0766 0.596705
\(820\) −13.1386 −0.458818
\(821\) 47.7151 1.66527 0.832634 0.553824i \(-0.186832\pi\)
0.832634 + 0.553824i \(0.186832\pi\)
\(822\) 10.8591 0.378754
\(823\) −43.3281 −1.51032 −0.755161 0.655540i \(-0.772441\pi\)
−0.755161 + 0.655540i \(0.772441\pi\)
\(824\) −16.6082 −0.578573
\(825\) −4.69641 −0.163508
\(826\) 91.9206 3.19833
\(827\) 8.05533 0.280111 0.140056 0.990144i \(-0.455272\pi\)
0.140056 + 0.990144i \(0.455272\pi\)
\(828\) −6.21115 −0.215852
\(829\) 0.671960 0.0233382 0.0116691 0.999932i \(-0.496286\pi\)
0.0116691 + 0.999932i \(0.496286\pi\)
\(830\) −22.7866 −0.790934
\(831\) −14.6859 −0.509450
\(832\) 1.25966 0.0436709
\(833\) −2.59399 −0.0898763
\(834\) 7.48595 0.259217
\(835\) −5.46564 −0.189146
\(836\) −9.70461 −0.335641
\(837\) −8.53830 −0.295127
\(838\) 1.88955 0.0652735
\(839\) 22.3206 0.770593 0.385297 0.922793i \(-0.374099\pi\)
0.385297 + 0.922793i \(0.374099\pi\)
\(840\) −6.03884 −0.208360
\(841\) −27.5180 −0.948896
\(842\) −38.4584 −1.32536
\(843\) 2.97791 0.102565
\(844\) 21.0995 0.726276
\(845\) 16.6525 0.572865
\(846\) −20.8991 −0.718527
\(847\) 0.363033 0.0124739
\(848\) −34.7985 −1.19499
\(849\) −13.1165 −0.450156
\(850\) −0.923203 −0.0316656
\(851\) 6.34600 0.217538
\(852\) −6.30337 −0.215950
\(853\) −6.50720 −0.222802 −0.111401 0.993776i \(-0.535534\pi\)
−0.111401 + 0.993776i \(0.535534\pi\)
\(854\) −35.2394 −1.20587
\(855\) 11.9345 0.408151
\(856\) −28.5215 −0.974844
\(857\) −35.0354 −1.19679 −0.598394 0.801202i \(-0.704194\pi\)
−0.598394 + 0.801202i \(0.704194\pi\)
\(858\) −4.11838 −0.140599
\(859\) 25.5301 0.871077 0.435538 0.900170i \(-0.356558\pi\)
0.435538 + 0.900170i \(0.356558\pi\)
\(860\) 6.35437 0.216682
\(861\) 20.2485 0.690067
\(862\) −34.9592 −1.19072
\(863\) −22.2782 −0.758358 −0.379179 0.925323i \(-0.623794\pi\)
−0.379179 + 0.925323i \(0.623794\pi\)
\(864\) 15.5691 0.529671
\(865\) −12.9445 −0.440125
\(866\) 41.4137 1.40730
\(867\) 8.79420 0.298667
\(868\) 13.0977 0.444566
\(869\) −49.2431 −1.67046
\(870\) 1.64573 0.0557956
\(871\) −19.5799 −0.663441
\(872\) −22.0204 −0.745705
\(873\) −14.6854 −0.497024
\(874\) −11.3571 −0.384160
\(875\) −52.5010 −1.77486
\(876\) 0.784439 0.0265037
\(877\) −5.81752 −0.196444 −0.0982219 0.995165i \(-0.531315\pi\)
−0.0982219 + 0.995165i \(0.531315\pi\)
\(878\) −13.9075 −0.469355
\(879\) −2.35008 −0.0792662
\(880\) −24.8311 −0.837055
\(881\) −28.2307 −0.951117 −0.475558 0.879684i \(-0.657754\pi\)
−0.475558 + 0.879684i \(0.657754\pi\)
\(882\) 63.3222 2.13217
\(883\) 27.4679 0.924367 0.462183 0.886784i \(-0.347066\pi\)
0.462183 + 0.886784i \(0.347066\pi\)
\(884\) −0.271667 −0.00913716
\(885\) 9.14835 0.307518
\(886\) −27.7434 −0.932059
\(887\) −12.6924 −0.426169 −0.213084 0.977034i \(-0.568351\pi\)
−0.213084 + 0.977034i \(0.568351\pi\)
\(888\) −2.50980 −0.0842232
\(889\) −13.4916 −0.452493
\(890\) 36.5675 1.22574
\(891\) −21.9850 −0.736524
\(892\) 9.36244 0.313478
\(893\) −12.8234 −0.429118
\(894\) 9.97838 0.333727
\(895\) 16.1119 0.538562
\(896\) 54.4067 1.81760
\(897\) −1.61732 −0.0540006
\(898\) 1.54399 0.0515236
\(899\) 3.49818 0.116671
\(900\) 7.56249 0.252083
\(901\) −1.35100 −0.0450083
\(902\) 49.6192 1.65214
\(903\) −9.79304 −0.325892
\(904\) −12.2831 −0.408531
\(905\) −4.92107 −0.163582
\(906\) −21.5553 −0.716127
\(907\) 20.7822 0.690062 0.345031 0.938591i \(-0.387868\pi\)
0.345031 + 0.938591i \(0.387868\pi\)
\(908\) 12.2622 0.406935
\(909\) −26.3467 −0.873863
\(910\) −16.3030 −0.540441
\(911\) −23.3716 −0.774337 −0.387169 0.922009i \(-0.626547\pi\)
−0.387169 + 0.922009i \(0.626547\pi\)
\(912\) 7.53686 0.249570
\(913\) 28.8776 0.955708
\(914\) −56.0311 −1.85334
\(915\) −3.50718 −0.115944
\(916\) 1.93161 0.0638220
\(917\) 70.6383 2.33268
\(918\) 1.00070 0.0330279
\(919\) −7.86778 −0.259534 −0.129767 0.991545i \(-0.541423\pi\)
−0.129767 + 0.991545i \(0.541423\pi\)
\(920\) −5.81138 −0.191596
\(921\) 1.85055 0.0609777
\(922\) −30.1150 −0.991785
\(923\) 16.6774 0.548943
\(924\) −7.80899 −0.256897
\(925\) −7.72667 −0.254051
\(926\) −38.8673 −1.27726
\(927\) 26.4112 0.867459
\(928\) −6.37872 −0.209392
\(929\) −18.4520 −0.605390 −0.302695 0.953087i \(-0.597886\pi\)
−0.302695 + 0.953087i \(0.597886\pi\)
\(930\) 3.88460 0.127381
\(931\) 38.8535 1.27337
\(932\) −8.33339 −0.272969
\(933\) 10.7360 0.351479
\(934\) 12.9046 0.422252
\(935\) −0.964028 −0.0315271
\(936\) −6.49928 −0.212436
\(937\) −11.4523 −0.374129 −0.187064 0.982348i \(-0.559897\pi\)
−0.187064 + 0.982348i \(0.559897\pi\)
\(938\) −110.637 −3.61242
\(939\) −10.4511 −0.341058
\(940\) 6.69536 0.218379
\(941\) 28.3239 0.923334 0.461667 0.887053i \(-0.347252\pi\)
0.461667 + 0.887053i \(0.347252\pi\)
\(942\) −15.8591 −0.516718
\(943\) 19.4858 0.634545
\(944\) −58.7031 −1.91062
\(945\) 20.1517 0.655536
\(946\) −23.9980 −0.780241
\(947\) −33.2241 −1.07964 −0.539820 0.841781i \(-0.681508\pi\)
−0.539820 + 0.841781i \(0.681508\pi\)
\(948\) −7.80390 −0.253459
\(949\) −2.07546 −0.0673723
\(950\) 13.8280 0.448640
\(951\) −5.70076 −0.184860
\(952\) 1.50441 0.0487582
\(953\) −22.6737 −0.734472 −0.367236 0.930128i \(-0.619696\pi\)
−0.367236 + 0.930128i \(0.619696\pi\)
\(954\) 32.9794 1.06775
\(955\) 1.02724 0.0332407
\(956\) 4.38187 0.141720
\(957\) −2.08565 −0.0674194
\(958\) −31.9453 −1.03210
\(959\) −54.4774 −1.75917
\(960\) 0.708390 0.0228632
\(961\) −22.7429 −0.733641
\(962\) −6.77569 −0.218457
\(963\) 45.3564 1.46159
\(964\) 4.80787 0.154851
\(965\) 3.83877 0.123574
\(966\) −9.13870 −0.294033
\(967\) 9.15541 0.294418 0.147209 0.989105i \(-0.452971\pi\)
0.147209 + 0.989105i \(0.452971\pi\)
\(968\) −0.138169 −0.00444091
\(969\) 0.292607 0.00939989
\(970\) 14.0201 0.450158
\(971\) −32.9295 −1.05676 −0.528379 0.849008i \(-0.677200\pi\)
−0.528379 + 0.849008i \(0.677200\pi\)
\(972\) −12.4881 −0.400557
\(973\) −37.5552 −1.20397
\(974\) 8.84469 0.283402
\(975\) 1.96919 0.0630645
\(976\) 22.5049 0.720363
\(977\) 53.9902 1.72730 0.863649 0.504093i \(-0.168173\pi\)
0.863649 + 0.504093i \(0.168173\pi\)
\(978\) 0.208169 0.00665651
\(979\) −46.3421 −1.48110
\(980\) −20.2863 −0.648021
\(981\) 35.0180 1.11804
\(982\) 55.9313 1.78484
\(983\) −22.8171 −0.727751 −0.363876 0.931448i \(-0.618547\pi\)
−0.363876 + 0.931448i \(0.618547\pi\)
\(984\) −7.70649 −0.245674
\(985\) −15.9014 −0.506661
\(986\) −0.409989 −0.0130567
\(987\) −10.3186 −0.328444
\(988\) 4.06911 0.129456
\(989\) −9.42416 −0.299671
\(990\) 23.5330 0.747928
\(991\) −42.9771 −1.36521 −0.682606 0.730787i \(-0.739153\pi\)
−0.682606 + 0.730787i \(0.739153\pi\)
\(992\) −15.0564 −0.478040
\(993\) −8.20843 −0.260487
\(994\) 94.2361 2.98899
\(995\) −9.68447 −0.307018
\(996\) 4.57643 0.145010
\(997\) 7.08860 0.224498 0.112249 0.993680i \(-0.464195\pi\)
0.112249 + 0.993680i \(0.464195\pi\)
\(998\) −36.6414 −1.15986
\(999\) 8.37523 0.264981
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 \(a_p\))