Properties

Label 4017.2.a.j.1.7
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +0.645786 q^{10} -1.77709 q^{11} +0.372378 q^{12} +1.00000 q^{13} +3.89444 q^{14} +0.506188 q^{15} -3.11658 q^{16} -3.59426 q^{17} -1.27578 q^{18} -0.715310 q^{19} +0.188493 q^{20} +3.05259 q^{21} +2.26719 q^{22} -0.238375 q^{23} -3.02664 q^{24} -4.74377 q^{25} -1.27578 q^{26} -1.00000 q^{27} +1.13672 q^{28} +2.95446 q^{29} -0.645786 q^{30} +0.136135 q^{31} -2.07720 q^{32} +1.77709 q^{33} +4.58550 q^{34} +1.54518 q^{35} -0.372378 q^{36} +5.90568 q^{37} +0.912581 q^{38} -1.00000 q^{39} -1.53205 q^{40} -5.81439 q^{41} -3.89444 q^{42} -2.36383 q^{43} +0.661750 q^{44} -0.506188 q^{45} +0.304115 q^{46} -7.27479 q^{47} +3.11658 q^{48} +2.31830 q^{49} +6.05203 q^{50} +3.59426 q^{51} -0.372378 q^{52} -4.12441 q^{53} +1.27578 q^{54} +0.899543 q^{55} -9.23908 q^{56} +0.715310 q^{57} -3.76926 q^{58} -4.06634 q^{59} -0.188493 q^{60} -3.05264 q^{61} -0.173679 q^{62} -3.05259 q^{63} +8.88321 q^{64} -0.506188 q^{65} -2.26719 q^{66} +12.3054 q^{67} +1.33842 q^{68} +0.238375 q^{69} -1.97132 q^{70} +6.06837 q^{71} +3.02664 q^{72} -13.9094 q^{73} -7.53436 q^{74} +4.74377 q^{75} +0.266366 q^{76} +5.42473 q^{77} +1.27578 q^{78} -10.1863 q^{79} +1.57758 q^{80} +1.00000 q^{81} +7.41791 q^{82} +1.65318 q^{83} -1.13672 q^{84} +1.81937 q^{85} +3.01574 q^{86} -2.95446 q^{87} -5.37862 q^{88} -12.4282 q^{89} +0.645786 q^{90} -3.05259 q^{91} +0.0887656 q^{92} -0.136135 q^{93} +9.28105 q^{94} +0.362082 q^{95} +2.07720 q^{96} -15.8471 q^{97} -2.95764 q^{98} -1.77709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27578 −0.902115 −0.451057 0.892495i \(-0.648953\pi\)
−0.451057 + 0.892495i \(0.648953\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.372378 −0.186189
\(5\) −0.506188 −0.226374 −0.113187 0.993574i \(-0.536106\pi\)
−0.113187 + 0.993574i \(0.536106\pi\)
\(6\) 1.27578 0.520836
\(7\) −3.05259 −1.15377 −0.576885 0.816825i \(-0.695732\pi\)
−0.576885 + 0.816825i \(0.695732\pi\)
\(8\) 3.02664 1.07008
\(9\) 1.00000 0.333333
\(10\) 0.645786 0.204215
\(11\) −1.77709 −0.535814 −0.267907 0.963445i \(-0.586332\pi\)
−0.267907 + 0.963445i \(0.586332\pi\)
\(12\) 0.372378 0.107496
\(13\) 1.00000 0.277350
\(14\) 3.89444 1.04083
\(15\) 0.506188 0.130697
\(16\) −3.11658 −0.779145
\(17\) −3.59426 −0.871737 −0.435869 0.900010i \(-0.643559\pi\)
−0.435869 + 0.900010i \(0.643559\pi\)
\(18\) −1.27578 −0.300705
\(19\) −0.715310 −0.164103 −0.0820517 0.996628i \(-0.526147\pi\)
−0.0820517 + 0.996628i \(0.526147\pi\)
\(20\) 0.188493 0.0421483
\(21\) 3.05259 0.666129
\(22\) 2.26719 0.483365
\(23\) −0.238375 −0.0497047 −0.0248523 0.999691i \(-0.507912\pi\)
−0.0248523 + 0.999691i \(0.507912\pi\)
\(24\) −3.02664 −0.617810
\(25\) −4.74377 −0.948755
\(26\) −1.27578 −0.250202
\(27\) −1.00000 −0.192450
\(28\) 1.13672 0.214819
\(29\) 2.95446 0.548630 0.274315 0.961640i \(-0.411549\pi\)
0.274315 + 0.961640i \(0.411549\pi\)
\(30\) −0.645786 −0.117904
\(31\) 0.136135 0.0244506 0.0122253 0.999925i \(-0.496108\pi\)
0.0122253 + 0.999925i \(0.496108\pi\)
\(32\) −2.07720 −0.367200
\(33\) 1.77709 0.309352
\(34\) 4.58550 0.786407
\(35\) 1.54518 0.261184
\(36\) −0.372378 −0.0620629
\(37\) 5.90568 0.970887 0.485444 0.874268i \(-0.338658\pi\)
0.485444 + 0.874268i \(0.338658\pi\)
\(38\) 0.912581 0.148040
\(39\) −1.00000 −0.160128
\(40\) −1.53205 −0.242238
\(41\) −5.81439 −0.908056 −0.454028 0.890987i \(-0.650013\pi\)
−0.454028 + 0.890987i \(0.650013\pi\)
\(42\) −3.89444 −0.600925
\(43\) −2.36383 −0.360481 −0.180241 0.983623i \(-0.557688\pi\)
−0.180241 + 0.983623i \(0.557688\pi\)
\(44\) 0.661750 0.0997625
\(45\) −0.506188 −0.0754580
\(46\) 0.304115 0.0448393
\(47\) −7.27479 −1.06114 −0.530568 0.847642i \(-0.678022\pi\)
−0.530568 + 0.847642i \(0.678022\pi\)
\(48\) 3.11658 0.449840
\(49\) 2.31830 0.331185
\(50\) 6.05203 0.855886
\(51\) 3.59426 0.503298
\(52\) −0.372378 −0.0516395
\(53\) −4.12441 −0.566531 −0.283266 0.959041i \(-0.591418\pi\)
−0.283266 + 0.959041i \(0.591418\pi\)
\(54\) 1.27578 0.173612
\(55\) 0.899543 0.121294
\(56\) −9.23908 −1.23462
\(57\) 0.715310 0.0947452
\(58\) −3.76926 −0.494927
\(59\) −4.06634 −0.529392 −0.264696 0.964332i \(-0.585272\pi\)
−0.264696 + 0.964332i \(0.585272\pi\)
\(60\) −0.188493 −0.0243343
\(61\) −3.05264 −0.390850 −0.195425 0.980719i \(-0.562609\pi\)
−0.195425 + 0.980719i \(0.562609\pi\)
\(62\) −0.173679 −0.0220573
\(63\) −3.05259 −0.384590
\(64\) 8.88321 1.11040
\(65\) −0.506188 −0.0627849
\(66\) −2.26719 −0.279071
\(67\) 12.3054 1.50335 0.751673 0.659536i \(-0.229247\pi\)
0.751673 + 0.659536i \(0.229247\pi\)
\(68\) 1.33842 0.162308
\(69\) 0.238375 0.0286970
\(70\) −1.97132 −0.235618
\(71\) 6.06837 0.720183 0.360091 0.932917i \(-0.382746\pi\)
0.360091 + 0.932917i \(0.382746\pi\)
\(72\) 3.02664 0.356693
\(73\) −13.9094 −1.62797 −0.813984 0.580888i \(-0.802705\pi\)
−0.813984 + 0.580888i \(0.802705\pi\)
\(74\) −7.53436 −0.875852
\(75\) 4.74377 0.547764
\(76\) 0.266366 0.0305542
\(77\) 5.42473 0.618206
\(78\) 1.27578 0.144454
\(79\) −10.1863 −1.14605 −0.573027 0.819537i \(-0.694231\pi\)
−0.573027 + 0.819537i \(0.694231\pi\)
\(80\) 1.57758 0.176378
\(81\) 1.00000 0.111111
\(82\) 7.41791 0.819171
\(83\) 1.65318 0.181460 0.0907298 0.995876i \(-0.471080\pi\)
0.0907298 + 0.995876i \(0.471080\pi\)
\(84\) −1.13672 −0.124026
\(85\) 1.81937 0.197339
\(86\) 3.01574 0.325196
\(87\) −2.95446 −0.316752
\(88\) −5.37862 −0.573363
\(89\) −12.4282 −1.31739 −0.658693 0.752412i \(-0.728890\pi\)
−0.658693 + 0.752412i \(0.728890\pi\)
\(90\) 0.645786 0.0680718
\(91\) −3.05259 −0.319998
\(92\) 0.0887656 0.00925445
\(93\) −0.136135 −0.0141166
\(94\) 9.28105 0.957267
\(95\) 0.362082 0.0371488
\(96\) 2.07720 0.212003
\(97\) −15.8471 −1.60903 −0.804515 0.593933i \(-0.797575\pi\)
−0.804515 + 0.593933i \(0.797575\pi\)
\(98\) −2.95764 −0.298767
\(99\) −1.77709 −0.178605
\(100\) 1.76648 0.176648
\(101\) −3.35478 −0.333814 −0.166907 0.985973i \(-0.553378\pi\)
−0.166907 + 0.985973i \(0.553378\pi\)
\(102\) −4.58550 −0.454032
\(103\) −1.00000 −0.0985329
\(104\) 3.02664 0.296786
\(105\) −1.54518 −0.150794
\(106\) 5.26185 0.511076
\(107\) 17.7894 1.71977 0.859883 0.510492i \(-0.170537\pi\)
0.859883 + 0.510492i \(0.170537\pi\)
\(108\) 0.372378 0.0358321
\(109\) −16.2712 −1.55849 −0.779247 0.626717i \(-0.784398\pi\)
−0.779247 + 0.626717i \(0.784398\pi\)
\(110\) −1.14762 −0.109421
\(111\) −5.90568 −0.560542
\(112\) 9.51363 0.898954
\(113\) −0.902316 −0.0848827 −0.0424414 0.999099i \(-0.513514\pi\)
−0.0424414 + 0.999099i \(0.513514\pi\)
\(114\) −0.912581 −0.0854710
\(115\) 0.120663 0.0112519
\(116\) −1.10018 −0.102149
\(117\) 1.00000 0.0924500
\(118\) 5.18777 0.477573
\(119\) 10.9718 1.00578
\(120\) 1.53205 0.139856
\(121\) −7.84194 −0.712904
\(122\) 3.89450 0.352592
\(123\) 5.81439 0.524266
\(124\) −0.0506938 −0.00455243
\(125\) 4.93218 0.441148
\(126\) 3.89444 0.346944
\(127\) −18.5786 −1.64858 −0.824290 0.566168i \(-0.808425\pi\)
−0.824290 + 0.566168i \(0.808425\pi\)
\(128\) −7.17866 −0.634510
\(129\) 2.36383 0.208124
\(130\) 0.645786 0.0566392
\(131\) −7.85737 −0.686501 −0.343251 0.939244i \(-0.611528\pi\)
−0.343251 + 0.939244i \(0.611528\pi\)
\(132\) −0.661750 −0.0575979
\(133\) 2.18355 0.189338
\(134\) −15.6990 −1.35619
\(135\) 0.506188 0.0435657
\(136\) −10.8785 −0.932827
\(137\) 14.1353 1.20766 0.603829 0.797114i \(-0.293641\pi\)
0.603829 + 0.797114i \(0.293641\pi\)
\(138\) −0.304115 −0.0258880
\(139\) 16.7119 1.41748 0.708742 0.705468i \(-0.249263\pi\)
0.708742 + 0.705468i \(0.249263\pi\)
\(140\) −0.575392 −0.0486295
\(141\) 7.27479 0.612648
\(142\) −7.74192 −0.649687
\(143\) −1.77709 −0.148608
\(144\) −3.11658 −0.259715
\(145\) −1.49551 −0.124196
\(146\) 17.7453 1.46861
\(147\) −2.31830 −0.191210
\(148\) −2.19914 −0.180768
\(149\) 1.64008 0.134361 0.0671803 0.997741i \(-0.478600\pi\)
0.0671803 + 0.997741i \(0.478600\pi\)
\(150\) −6.05203 −0.494146
\(151\) −3.05639 −0.248726 −0.124363 0.992237i \(-0.539689\pi\)
−0.124363 + 0.992237i \(0.539689\pi\)
\(152\) −2.16499 −0.175604
\(153\) −3.59426 −0.290579
\(154\) −6.92078 −0.557693
\(155\) −0.0689101 −0.00553499
\(156\) 0.372378 0.0298141
\(157\) 8.64949 0.690304 0.345152 0.938547i \(-0.387827\pi\)
0.345152 + 0.938547i \(0.387827\pi\)
\(158\) 12.9956 1.03387
\(159\) 4.12441 0.327087
\(160\) 1.05145 0.0831247
\(161\) 0.727661 0.0573477
\(162\) −1.27578 −0.100235
\(163\) 16.6605 1.30495 0.652474 0.757811i \(-0.273731\pi\)
0.652474 + 0.757811i \(0.273731\pi\)
\(164\) 2.16515 0.169070
\(165\) −0.899543 −0.0700293
\(166\) −2.10909 −0.163697
\(167\) 18.1176 1.40198 0.700989 0.713172i \(-0.252742\pi\)
0.700989 + 0.713172i \(0.252742\pi\)
\(168\) 9.23908 0.712811
\(169\) 1.00000 0.0769231
\(170\) −2.32113 −0.178022
\(171\) −0.715310 −0.0547012
\(172\) 0.880239 0.0671176
\(173\) −7.61457 −0.578925 −0.289462 0.957189i \(-0.593477\pi\)
−0.289462 + 0.957189i \(0.593477\pi\)
\(174\) 3.76926 0.285746
\(175\) 14.4808 1.09464
\(176\) 5.53845 0.417477
\(177\) 4.06634 0.305645
\(178\) 15.8557 1.18843
\(179\) 20.9646 1.56696 0.783482 0.621414i \(-0.213442\pi\)
0.783482 + 0.621414i \(0.213442\pi\)
\(180\) 0.188493 0.0140494
\(181\) −14.2964 −1.06264 −0.531321 0.847171i \(-0.678304\pi\)
−0.531321 + 0.847171i \(0.678304\pi\)
\(182\) 3.89444 0.288675
\(183\) 3.05264 0.225657
\(184\) −0.721476 −0.0531879
\(185\) −2.98938 −0.219784
\(186\) 0.173679 0.0127348
\(187\) 6.38734 0.467089
\(188\) 2.70897 0.197572
\(189\) 3.05259 0.222043
\(190\) −0.461937 −0.0335125
\(191\) 2.42083 0.175165 0.0875824 0.996157i \(-0.472086\pi\)
0.0875824 + 0.996157i \(0.472086\pi\)
\(192\) −8.88321 −0.641091
\(193\) −5.40273 −0.388897 −0.194449 0.980913i \(-0.562292\pi\)
−0.194449 + 0.980913i \(0.562292\pi\)
\(194\) 20.2175 1.45153
\(195\) 0.506188 0.0362489
\(196\) −0.863281 −0.0616629
\(197\) 19.6801 1.40215 0.701073 0.713089i \(-0.252705\pi\)
0.701073 + 0.713089i \(0.252705\pi\)
\(198\) 2.26719 0.161122
\(199\) −17.2785 −1.22484 −0.612422 0.790531i \(-0.709805\pi\)
−0.612422 + 0.790531i \(0.709805\pi\)
\(200\) −14.3577 −1.01524
\(201\) −12.3054 −0.867957
\(202\) 4.27998 0.301138
\(203\) −9.01876 −0.632993
\(204\) −1.33842 −0.0937084
\(205\) 2.94318 0.205560
\(206\) 1.27578 0.0888880
\(207\) −0.238375 −0.0165682
\(208\) −3.11658 −0.216096
\(209\) 1.27117 0.0879289
\(210\) 1.97132 0.136034
\(211\) 15.3626 1.05760 0.528802 0.848745i \(-0.322641\pi\)
0.528802 + 0.848745i \(0.322641\pi\)
\(212\) 1.53584 0.105482
\(213\) −6.06837 −0.415798
\(214\) −22.6954 −1.55143
\(215\) 1.19654 0.0816037
\(216\) −3.02664 −0.205937
\(217\) −0.415565 −0.0282104
\(218\) 20.7585 1.40594
\(219\) 13.9094 0.939907
\(220\) −0.334970 −0.0225837
\(221\) −3.59426 −0.241776
\(222\) 7.53436 0.505673
\(223\) 17.5213 1.17332 0.586658 0.809835i \(-0.300443\pi\)
0.586658 + 0.809835i \(0.300443\pi\)
\(224\) 6.34083 0.423665
\(225\) −4.74377 −0.316252
\(226\) 1.15116 0.0765740
\(227\) −24.0192 −1.59421 −0.797104 0.603842i \(-0.793636\pi\)
−0.797104 + 0.603842i \(0.793636\pi\)
\(228\) −0.266366 −0.0176405
\(229\) −2.09099 −0.138177 −0.0690884 0.997611i \(-0.522009\pi\)
−0.0690884 + 0.997611i \(0.522009\pi\)
\(230\) −0.153939 −0.0101505
\(231\) −5.42473 −0.356921
\(232\) 8.94210 0.587077
\(233\) −9.15311 −0.599640 −0.299820 0.953996i \(-0.596927\pi\)
−0.299820 + 0.953996i \(0.596927\pi\)
\(234\) −1.27578 −0.0834005
\(235\) 3.68241 0.240214
\(236\) 1.51421 0.0985669
\(237\) 10.1863 0.661674
\(238\) −13.9976 −0.907333
\(239\) 6.93850 0.448814 0.224407 0.974495i \(-0.427955\pi\)
0.224407 + 0.974495i \(0.427955\pi\)
\(240\) −1.57758 −0.101832
\(241\) 26.6620 1.71745 0.858724 0.512438i \(-0.171258\pi\)
0.858724 + 0.512438i \(0.171258\pi\)
\(242\) 10.0046 0.643121
\(243\) −1.00000 −0.0641500
\(244\) 1.13673 0.0727719
\(245\) −1.17349 −0.0749717
\(246\) −7.41791 −0.472948
\(247\) −0.715310 −0.0455141
\(248\) 0.412033 0.0261641
\(249\) −1.65318 −0.104766
\(250\) −6.29239 −0.397966
\(251\) 13.4503 0.848978 0.424489 0.905433i \(-0.360454\pi\)
0.424489 + 0.905433i \(0.360454\pi\)
\(252\) 1.13672 0.0716063
\(253\) 0.423615 0.0266324
\(254\) 23.7022 1.48721
\(255\) −1.81937 −0.113934
\(256\) −8.60802 −0.538001
\(257\) 26.9808 1.68302 0.841509 0.540243i \(-0.181668\pi\)
0.841509 + 0.540243i \(0.181668\pi\)
\(258\) −3.01574 −0.187752
\(259\) −18.0276 −1.12018
\(260\) 0.188493 0.0116898
\(261\) 2.95446 0.182877
\(262\) 10.0243 0.619303
\(263\) −5.11106 −0.315161 −0.157581 0.987506i \(-0.550369\pi\)
−0.157581 + 0.987506i \(0.550369\pi\)
\(264\) 5.37862 0.331031
\(265\) 2.08773 0.128248
\(266\) −2.78573 −0.170804
\(267\) 12.4282 0.760593
\(268\) −4.58226 −0.279906
\(269\) −5.04937 −0.307865 −0.153933 0.988081i \(-0.549194\pi\)
−0.153933 + 0.988081i \(0.549194\pi\)
\(270\) −0.645786 −0.0393013
\(271\) −10.8978 −0.661996 −0.330998 0.943632i \(-0.607385\pi\)
−0.330998 + 0.943632i \(0.607385\pi\)
\(272\) 11.2018 0.679209
\(273\) 3.05259 0.184751
\(274\) −18.0335 −1.08945
\(275\) 8.43013 0.508356
\(276\) −0.0887656 −0.00534306
\(277\) −3.91725 −0.235365 −0.117682 0.993051i \(-0.537546\pi\)
−0.117682 + 0.993051i \(0.537546\pi\)
\(278\) −21.3207 −1.27873
\(279\) 0.136135 0.00815021
\(280\) 4.67671 0.279487
\(281\) 6.75296 0.402848 0.201424 0.979504i \(-0.435443\pi\)
0.201424 + 0.979504i \(0.435443\pi\)
\(282\) −9.28105 −0.552679
\(283\) −6.30052 −0.374527 −0.187263 0.982310i \(-0.559962\pi\)
−0.187263 + 0.982310i \(0.559962\pi\)
\(284\) −2.25972 −0.134090
\(285\) −0.362082 −0.0214479
\(286\) 2.26719 0.134061
\(287\) 17.7490 1.04769
\(288\) −2.07720 −0.122400
\(289\) −4.08127 −0.240075
\(290\) 1.90795 0.112039
\(291\) 15.8471 0.928974
\(292\) 5.17953 0.303109
\(293\) −14.8568 −0.867943 −0.433971 0.900927i \(-0.642888\pi\)
−0.433971 + 0.900927i \(0.642888\pi\)
\(294\) 2.95764 0.172493
\(295\) 2.05833 0.119841
\(296\) 17.8744 1.03893
\(297\) 1.77709 0.103117
\(298\) −2.09239 −0.121209
\(299\) −0.238375 −0.0137856
\(300\) −1.76648 −0.101987
\(301\) 7.21581 0.415913
\(302\) 3.89929 0.224379
\(303\) 3.35478 0.192727
\(304\) 2.22932 0.127860
\(305\) 1.54521 0.0884784
\(306\) 4.58550 0.262136
\(307\) 2.47596 0.141310 0.0706552 0.997501i \(-0.477491\pi\)
0.0706552 + 0.997501i \(0.477491\pi\)
\(308\) −2.02005 −0.115103
\(309\) 1.00000 0.0568880
\(310\) 0.0879143 0.00499320
\(311\) 4.91918 0.278941 0.139471 0.990226i \(-0.455460\pi\)
0.139471 + 0.990226i \(0.455460\pi\)
\(312\) −3.02664 −0.171350
\(313\) −22.5452 −1.27433 −0.637166 0.770727i \(-0.719893\pi\)
−0.637166 + 0.770727i \(0.719893\pi\)
\(314\) −11.0349 −0.622734
\(315\) 1.54518 0.0870612
\(316\) 3.79317 0.213382
\(317\) 26.6686 1.49786 0.748930 0.662649i \(-0.230568\pi\)
0.748930 + 0.662649i \(0.230568\pi\)
\(318\) −5.26185 −0.295070
\(319\) −5.25036 −0.293964
\(320\) −4.49658 −0.251366
\(321\) −17.7894 −0.992907
\(322\) −0.928338 −0.0517343
\(323\) 2.57101 0.143055
\(324\) −0.372378 −0.0206876
\(325\) −4.74377 −0.263137
\(326\) −21.2551 −1.17721
\(327\) 16.2712 0.899797
\(328\) −17.5981 −0.971691
\(329\) 22.2069 1.22431
\(330\) 1.14762 0.0631745
\(331\) 27.3313 1.50226 0.751131 0.660153i \(-0.229509\pi\)
0.751131 + 0.660153i \(0.229509\pi\)
\(332\) −0.615606 −0.0337858
\(333\) 5.90568 0.323629
\(334\) −23.1141 −1.26475
\(335\) −6.22885 −0.340319
\(336\) −9.51363 −0.519011
\(337\) 30.3518 1.65337 0.826683 0.562668i \(-0.190225\pi\)
0.826683 + 0.562668i \(0.190225\pi\)
\(338\) −1.27578 −0.0693934
\(339\) 0.902316 0.0490071
\(340\) −0.677494 −0.0367423
\(341\) −0.241925 −0.0131010
\(342\) 0.912581 0.0493467
\(343\) 14.2913 0.771659
\(344\) −7.15448 −0.385743
\(345\) −0.120663 −0.00649626
\(346\) 9.71454 0.522257
\(347\) 25.3945 1.36325 0.681625 0.731702i \(-0.261274\pi\)
0.681625 + 0.731702i \(0.261274\pi\)
\(348\) 1.10018 0.0589756
\(349\) 13.8170 0.739607 0.369804 0.929110i \(-0.379425\pi\)
0.369804 + 0.929110i \(0.379425\pi\)
\(350\) −18.4743 −0.987495
\(351\) −1.00000 −0.0533761
\(352\) 3.69138 0.196751
\(353\) 10.9712 0.583941 0.291970 0.956427i \(-0.405689\pi\)
0.291970 + 0.956427i \(0.405689\pi\)
\(354\) −5.18777 −0.275727
\(355\) −3.07173 −0.163031
\(356\) 4.62798 0.245282
\(357\) −10.9718 −0.580690
\(358\) −26.7462 −1.41358
\(359\) 22.8471 1.20583 0.602913 0.797807i \(-0.294007\pi\)
0.602913 + 0.797807i \(0.294007\pi\)
\(360\) −1.53205 −0.0807460
\(361\) −18.4883 −0.973070
\(362\) 18.2391 0.958625
\(363\) 7.84194 0.411595
\(364\) 1.13672 0.0595801
\(365\) 7.04075 0.368530
\(366\) −3.89450 −0.203569
\(367\) −11.2060 −0.584947 −0.292474 0.956274i \(-0.594478\pi\)
−0.292474 + 0.956274i \(0.594478\pi\)
\(368\) 0.742915 0.0387271
\(369\) −5.81439 −0.302685
\(370\) 3.81380 0.198270
\(371\) 12.5901 0.653647
\(372\) 0.0506938 0.00262835
\(373\) −6.17534 −0.319747 −0.159874 0.987138i \(-0.551109\pi\)
−0.159874 + 0.987138i \(0.551109\pi\)
\(374\) −8.14886 −0.421368
\(375\) −4.93218 −0.254697
\(376\) −22.0182 −1.13550
\(377\) 2.95446 0.152163
\(378\) −3.89444 −0.200308
\(379\) 17.3821 0.892857 0.446428 0.894819i \(-0.352696\pi\)
0.446428 + 0.894819i \(0.352696\pi\)
\(380\) −0.134831 −0.00691669
\(381\) 18.5786 0.951808
\(382\) −3.08845 −0.158019
\(383\) 9.86224 0.503937 0.251969 0.967735i \(-0.418922\pi\)
0.251969 + 0.967735i \(0.418922\pi\)
\(384\) 7.17866 0.366334
\(385\) −2.74593 −0.139946
\(386\) 6.89271 0.350830
\(387\) −2.36383 −0.120160
\(388\) 5.90111 0.299583
\(389\) 14.5318 0.736791 0.368396 0.929669i \(-0.379907\pi\)
0.368396 + 0.929669i \(0.379907\pi\)
\(390\) −0.645786 −0.0327006
\(391\) 0.856783 0.0433294
\(392\) 7.01664 0.354394
\(393\) 7.85737 0.396352
\(394\) −25.1075 −1.26490
\(395\) 5.15621 0.259437
\(396\) 0.661750 0.0332542
\(397\) −21.6455 −1.08635 −0.543177 0.839618i \(-0.682779\pi\)
−0.543177 + 0.839618i \(0.682779\pi\)
\(398\) 22.0437 1.10495
\(399\) −2.18355 −0.109314
\(400\) 14.7843 0.739217
\(401\) 8.98126 0.448503 0.224251 0.974531i \(-0.428006\pi\)
0.224251 + 0.974531i \(0.428006\pi\)
\(402\) 15.6990 0.782997
\(403\) 0.136135 0.00678139
\(404\) 1.24925 0.0621523
\(405\) −0.506188 −0.0251527
\(406\) 11.5060 0.571032
\(407\) −10.4949 −0.520215
\(408\) 10.8785 0.538568
\(409\) −30.4957 −1.50791 −0.753957 0.656923i \(-0.771857\pi\)
−0.753957 + 0.656923i \(0.771857\pi\)
\(410\) −3.75485 −0.185439
\(411\) −14.1353 −0.697242
\(412\) 0.372378 0.0183457
\(413\) 12.4129 0.610797
\(414\) 0.304115 0.0149464
\(415\) −0.836818 −0.0410778
\(416\) −2.07720 −0.101843
\(417\) −16.7119 −0.818385
\(418\) −1.62174 −0.0793220
\(419\) −4.37964 −0.213959 −0.106980 0.994261i \(-0.534118\pi\)
−0.106980 + 0.994261i \(0.534118\pi\)
\(420\) 0.575392 0.0280762
\(421\) 5.87184 0.286176 0.143088 0.989710i \(-0.454297\pi\)
0.143088 + 0.989710i \(0.454297\pi\)
\(422\) −19.5993 −0.954080
\(423\) −7.27479 −0.353712
\(424\) −12.4831 −0.606233
\(425\) 17.0504 0.827065
\(426\) 7.74192 0.375097
\(427\) 9.31845 0.450951
\(428\) −6.62437 −0.320201
\(429\) 1.77709 0.0857989
\(430\) −1.52653 −0.0736159
\(431\) −18.9790 −0.914187 −0.457094 0.889419i \(-0.651110\pi\)
−0.457094 + 0.889419i \(0.651110\pi\)
\(432\) 3.11658 0.149947
\(433\) 31.1549 1.49721 0.748604 0.663017i \(-0.230724\pi\)
0.748604 + 0.663017i \(0.230724\pi\)
\(434\) 0.530171 0.0254490
\(435\) 1.49551 0.0717044
\(436\) 6.05901 0.290174
\(437\) 0.170512 0.00815671
\(438\) −17.7453 −0.847904
\(439\) −16.0983 −0.768332 −0.384166 0.923264i \(-0.625511\pi\)
−0.384166 + 0.923264i \(0.625511\pi\)
\(440\) 2.72259 0.129794
\(441\) 2.31830 0.110395
\(442\) 4.58550 0.218110
\(443\) −21.9726 −1.04395 −0.521975 0.852961i \(-0.674805\pi\)
−0.521975 + 0.852961i \(0.674805\pi\)
\(444\) 2.19914 0.104367
\(445\) 6.29100 0.298222
\(446\) −22.3534 −1.05847
\(447\) −1.64008 −0.0775732
\(448\) −27.1168 −1.28115
\(449\) 20.9980 0.990956 0.495478 0.868621i \(-0.334993\pi\)
0.495478 + 0.868621i \(0.334993\pi\)
\(450\) 6.05203 0.285295
\(451\) 10.3327 0.486549
\(452\) 0.336002 0.0158042
\(453\) 3.05639 0.143602
\(454\) 30.6432 1.43816
\(455\) 1.54518 0.0724393
\(456\) 2.16499 0.101385
\(457\) −7.24415 −0.338867 −0.169433 0.985542i \(-0.554194\pi\)
−0.169433 + 0.985542i \(0.554194\pi\)
\(458\) 2.66765 0.124651
\(459\) 3.59426 0.167766
\(460\) −0.0449321 −0.00209497
\(461\) 10.9642 0.510652 0.255326 0.966855i \(-0.417817\pi\)
0.255326 + 0.966855i \(0.417817\pi\)
\(462\) 6.92078 0.321984
\(463\) −29.2865 −1.36106 −0.680529 0.732721i \(-0.738250\pi\)
−0.680529 + 0.732721i \(0.738250\pi\)
\(464\) −9.20782 −0.427462
\(465\) 0.0689101 0.00319563
\(466\) 11.6774 0.540944
\(467\) 41.8942 1.93863 0.969317 0.245813i \(-0.0790548\pi\)
0.969317 + 0.245813i \(0.0790548\pi\)
\(468\) −0.372378 −0.0172132
\(469\) −37.5634 −1.73452
\(470\) −4.69796 −0.216701
\(471\) −8.64949 −0.398547
\(472\) −12.3073 −0.566491
\(473\) 4.20075 0.193151
\(474\) −12.9956 −0.596906
\(475\) 3.39327 0.155694
\(476\) −4.08566 −0.187266
\(477\) −4.12441 −0.188844
\(478\) −8.85202 −0.404882
\(479\) 1.31516 0.0600912 0.0300456 0.999549i \(-0.490435\pi\)
0.0300456 + 0.999549i \(0.490435\pi\)
\(480\) −1.05145 −0.0479920
\(481\) 5.90568 0.269276
\(482\) −34.0149 −1.54934
\(483\) −0.727661 −0.0331097
\(484\) 2.92016 0.132735
\(485\) 8.02161 0.364243
\(486\) 1.27578 0.0578707
\(487\) 29.8662 1.35337 0.676683 0.736274i \(-0.263417\pi\)
0.676683 + 0.736274i \(0.263417\pi\)
\(488\) −9.23923 −0.418240
\(489\) −16.6605 −0.753412
\(490\) 1.49712 0.0676331
\(491\) −8.17232 −0.368811 −0.184406 0.982850i \(-0.559036\pi\)
−0.184406 + 0.982850i \(0.559036\pi\)
\(492\) −2.16515 −0.0976125
\(493\) −10.6191 −0.478261
\(494\) 0.912581 0.0410590
\(495\) 0.899543 0.0404315
\(496\) −0.424277 −0.0190506
\(497\) −18.5242 −0.830925
\(498\) 2.10909 0.0945108
\(499\) 5.99482 0.268365 0.134183 0.990957i \(-0.457159\pi\)
0.134183 + 0.990957i \(0.457159\pi\)
\(500\) −1.83663 −0.0821368
\(501\) −18.1176 −0.809433
\(502\) −17.1597 −0.765876
\(503\) 36.3423 1.62042 0.810212 0.586137i \(-0.199352\pi\)
0.810212 + 0.586137i \(0.199352\pi\)
\(504\) −9.23908 −0.411541
\(505\) 1.69815 0.0755667
\(506\) −0.540441 −0.0240255
\(507\) −1.00000 −0.0444116
\(508\) 6.91824 0.306947
\(509\) 13.6721 0.606007 0.303003 0.952989i \(-0.402011\pi\)
0.303003 + 0.952989i \(0.402011\pi\)
\(510\) 2.32113 0.102781
\(511\) 42.4595 1.87830
\(512\) 25.3393 1.11985
\(513\) 0.715310 0.0315817
\(514\) −34.4217 −1.51828
\(515\) 0.506188 0.0223053
\(516\) −0.880239 −0.0387504
\(517\) 12.9280 0.568572
\(518\) 22.9993 1.01053
\(519\) 7.61457 0.334242
\(520\) −1.53205 −0.0671848
\(521\) −5.96539 −0.261348 −0.130674 0.991425i \(-0.541714\pi\)
−0.130674 + 0.991425i \(0.541714\pi\)
\(522\) −3.76926 −0.164976
\(523\) 18.0919 0.791106 0.395553 0.918443i \(-0.370553\pi\)
0.395553 + 0.918443i \(0.370553\pi\)
\(524\) 2.92591 0.127819
\(525\) −14.4808 −0.631993
\(526\) 6.52060 0.284312
\(527\) −0.489307 −0.0213145
\(528\) −5.53845 −0.241030
\(529\) −22.9432 −0.997529
\(530\) −2.66349 −0.115694
\(531\) −4.06634 −0.176464
\(532\) −0.813104 −0.0352525
\(533\) −5.81439 −0.251849
\(534\) −15.8557 −0.686142
\(535\) −9.00478 −0.389310
\(536\) 37.2441 1.60870
\(537\) −20.9646 −0.904687
\(538\) 6.44190 0.277730
\(539\) −4.11983 −0.177453
\(540\) −0.188493 −0.00811145
\(541\) −10.5646 −0.454208 −0.227104 0.973871i \(-0.572926\pi\)
−0.227104 + 0.973871i \(0.572926\pi\)
\(542\) 13.9033 0.597196
\(543\) 14.2964 0.613517
\(544\) 7.46600 0.320102
\(545\) 8.23626 0.352803
\(546\) −3.89444 −0.166667
\(547\) −23.2951 −0.996027 −0.498013 0.867169i \(-0.665937\pi\)
−0.498013 + 0.867169i \(0.665937\pi\)
\(548\) −5.26366 −0.224852
\(549\) −3.05264 −0.130283
\(550\) −10.7550 −0.458595
\(551\) −2.11336 −0.0900321
\(552\) 0.721476 0.0307080
\(553\) 31.0947 1.32228
\(554\) 4.99757 0.212326
\(555\) 2.98938 0.126892
\(556\) −6.22313 −0.263920
\(557\) −4.54236 −0.192466 −0.0962331 0.995359i \(-0.530679\pi\)
−0.0962331 + 0.995359i \(0.530679\pi\)
\(558\) −0.173679 −0.00735243
\(559\) −2.36383 −0.0999796
\(560\) −4.81569 −0.203500
\(561\) −6.38734 −0.269674
\(562\) −8.61531 −0.363415
\(563\) −11.5640 −0.487364 −0.243682 0.969855i \(-0.578355\pi\)
−0.243682 + 0.969855i \(0.578355\pi\)
\(564\) −2.70897 −0.114068
\(565\) 0.456741 0.0192153
\(566\) 8.03809 0.337866
\(567\) −3.05259 −0.128197
\(568\) 18.3668 0.770652
\(569\) 25.6662 1.07598 0.537991 0.842950i \(-0.319183\pi\)
0.537991 + 0.842950i \(0.319183\pi\)
\(570\) 0.461937 0.0193484
\(571\) −31.6651 −1.32514 −0.662572 0.748998i \(-0.730535\pi\)
−0.662572 + 0.748998i \(0.730535\pi\)
\(572\) 0.661750 0.0276691
\(573\) −2.42083 −0.101131
\(574\) −22.6438 −0.945134
\(575\) 1.13080 0.0471575
\(576\) 8.88321 0.370134
\(577\) 3.75953 0.156511 0.0782556 0.996933i \(-0.475065\pi\)
0.0782556 + 0.996933i \(0.475065\pi\)
\(578\) 5.20681 0.216575
\(579\) 5.40273 0.224530
\(580\) 0.556896 0.0231238
\(581\) −5.04647 −0.209363
\(582\) −20.2175 −0.838041
\(583\) 7.32946 0.303555
\(584\) −42.0986 −1.74205
\(585\) −0.506188 −0.0209283
\(586\) 18.9540 0.782984
\(587\) −9.25750 −0.382098 −0.191049 0.981580i \(-0.561189\pi\)
−0.191049 + 0.981580i \(0.561189\pi\)
\(588\) 0.863281 0.0356011
\(589\) −0.0973791 −0.00401243
\(590\) −2.62599 −0.108110
\(591\) −19.6801 −0.809530
\(592\) −18.4055 −0.756462
\(593\) 23.2842 0.956168 0.478084 0.878314i \(-0.341331\pi\)
0.478084 + 0.878314i \(0.341331\pi\)
\(594\) −2.26719 −0.0930237
\(595\) −5.55380 −0.227683
\(596\) −0.610729 −0.0250165
\(597\) 17.2785 0.707164
\(598\) 0.304115 0.0124362
\(599\) 31.4527 1.28512 0.642561 0.766235i \(-0.277872\pi\)
0.642561 + 0.766235i \(0.277872\pi\)
\(600\) 14.3577 0.586150
\(601\) 40.8070 1.66455 0.832275 0.554362i \(-0.187038\pi\)
0.832275 + 0.554362i \(0.187038\pi\)
\(602\) −9.20581 −0.375201
\(603\) 12.3054 0.501115
\(604\) 1.13813 0.0463099
\(605\) 3.96950 0.161383
\(606\) −4.27998 −0.173862
\(607\) 35.9070 1.45742 0.728709 0.684823i \(-0.240121\pi\)
0.728709 + 0.684823i \(0.240121\pi\)
\(608\) 1.48584 0.0602588
\(609\) 9.01876 0.365459
\(610\) −1.97135 −0.0798177
\(611\) −7.27479 −0.294306
\(612\) 1.33842 0.0541026
\(613\) 6.01339 0.242879 0.121439 0.992599i \(-0.461249\pi\)
0.121439 + 0.992599i \(0.461249\pi\)
\(614\) −3.15879 −0.127478
\(615\) −2.94318 −0.118680
\(616\) 16.4187 0.661529
\(617\) 42.9411 1.72874 0.864372 0.502852i \(-0.167716\pi\)
0.864372 + 0.502852i \(0.167716\pi\)
\(618\) −1.27578 −0.0513195
\(619\) 5.03275 0.202283 0.101142 0.994872i \(-0.467750\pi\)
0.101142 + 0.994872i \(0.467750\pi\)
\(620\) 0.0256606 0.00103055
\(621\) 0.238375 0.00956567
\(622\) −6.27581 −0.251637
\(623\) 37.9382 1.51996
\(624\) 3.11658 0.124763
\(625\) 21.2223 0.848890
\(626\) 28.7628 1.14959
\(627\) −1.27117 −0.0507658
\(628\) −3.22088 −0.128527
\(629\) −21.2266 −0.846358
\(630\) −1.97132 −0.0785392
\(631\) −29.7510 −1.18437 −0.592185 0.805802i \(-0.701734\pi\)
−0.592185 + 0.805802i \(0.701734\pi\)
\(632\) −30.8304 −1.22637
\(633\) −15.3626 −0.610608
\(634\) −34.0234 −1.35124
\(635\) 9.40424 0.373196
\(636\) −1.53584 −0.0608999
\(637\) 2.31830 0.0918542
\(638\) 6.69832 0.265189
\(639\) 6.06837 0.240061
\(640\) 3.63375 0.143637
\(641\) −38.8127 −1.53301 −0.766505 0.642238i \(-0.778006\pi\)
−0.766505 + 0.642238i \(0.778006\pi\)
\(642\) 22.6954 0.895716
\(643\) −34.5045 −1.36073 −0.680363 0.732875i \(-0.738178\pi\)
−0.680363 + 0.732875i \(0.738178\pi\)
\(644\) −0.270965 −0.0106775
\(645\) −1.19654 −0.0471139
\(646\) −3.28006 −0.129052
\(647\) −21.0735 −0.828483 −0.414241 0.910167i \(-0.635953\pi\)
−0.414241 + 0.910167i \(0.635953\pi\)
\(648\) 3.02664 0.118898
\(649\) 7.22626 0.283656
\(650\) 6.05203 0.237380
\(651\) 0.415565 0.0162873
\(652\) −6.20398 −0.242967
\(653\) 8.74814 0.342341 0.171171 0.985241i \(-0.445245\pi\)
0.171171 + 0.985241i \(0.445245\pi\)
\(654\) −20.7585 −0.811720
\(655\) 3.97730 0.155406
\(656\) 18.1210 0.707507
\(657\) −13.9094 −0.542656
\(658\) −28.3312 −1.10447
\(659\) −4.59733 −0.179087 −0.0895433 0.995983i \(-0.528541\pi\)
−0.0895433 + 0.995983i \(0.528541\pi\)
\(660\) 0.334970 0.0130387
\(661\) −7.30213 −0.284020 −0.142010 0.989865i \(-0.545357\pi\)
−0.142010 + 0.989865i \(0.545357\pi\)
\(662\) −34.8688 −1.35521
\(663\) 3.59426 0.139590
\(664\) 5.00357 0.194176
\(665\) −1.10529 −0.0428611
\(666\) −7.53436 −0.291951
\(667\) −0.704271 −0.0272695
\(668\) −6.74657 −0.261033
\(669\) −17.5213 −0.677414
\(670\) 7.94667 0.307006
\(671\) 5.42482 0.209423
\(672\) −6.34083 −0.244603
\(673\) −51.1172 −1.97042 −0.985211 0.171344i \(-0.945189\pi\)
−0.985211 + 0.171344i \(0.945189\pi\)
\(674\) −38.7223 −1.49153
\(675\) 4.74377 0.182588
\(676\) −0.372378 −0.0143222
\(677\) −12.0934 −0.464788 −0.232394 0.972622i \(-0.574656\pi\)
−0.232394 + 0.972622i \(0.574656\pi\)
\(678\) −1.15116 −0.0442100
\(679\) 48.3747 1.85645
\(680\) 5.50659 0.211168
\(681\) 24.0192 0.920417
\(682\) 0.308644 0.0118186
\(683\) 25.9836 0.994234 0.497117 0.867684i \(-0.334392\pi\)
0.497117 + 0.867684i \(0.334392\pi\)
\(684\) 0.266366 0.0101847
\(685\) −7.15510 −0.273382
\(686\) −18.2326 −0.696125
\(687\) 2.09099 0.0797764
\(688\) 7.36708 0.280867
\(689\) −4.12441 −0.157127
\(690\) 0.153939 0.00586037
\(691\) 30.7103 1.16828 0.584138 0.811654i \(-0.301433\pi\)
0.584138 + 0.811654i \(0.301433\pi\)
\(692\) 2.83549 0.107789
\(693\) 5.42473 0.206069
\(694\) −32.3979 −1.22981
\(695\) −8.45936 −0.320882
\(696\) −8.94210 −0.338949
\(697\) 20.8985 0.791586
\(698\) −17.6275 −0.667211
\(699\) 9.15311 0.346202
\(700\) −5.39232 −0.203811
\(701\) −51.8192 −1.95719 −0.978593 0.205806i \(-0.934018\pi\)
−0.978593 + 0.205806i \(0.934018\pi\)
\(702\) 1.27578 0.0481513
\(703\) −4.22439 −0.159326
\(704\) −15.7863 −0.594968
\(705\) −3.68241 −0.138688
\(706\) −13.9969 −0.526782
\(707\) 10.2408 0.385144
\(708\) −1.51421 −0.0569076
\(709\) −31.7882 −1.19383 −0.596915 0.802305i \(-0.703607\pi\)
−0.596915 + 0.802305i \(0.703607\pi\)
\(710\) 3.91887 0.147072
\(711\) −10.1863 −0.382018
\(712\) −37.6157 −1.40971
\(713\) −0.0324513 −0.00121531
\(714\) 13.9976 0.523849
\(715\) 0.899543 0.0336410
\(716\) −7.80673 −0.291751
\(717\) −6.93850 −0.259123
\(718\) −29.1480 −1.08779
\(719\) −33.9686 −1.26681 −0.633407 0.773819i \(-0.718344\pi\)
−0.633407 + 0.773819i \(0.718344\pi\)
\(720\) 1.57758 0.0587928
\(721\) 3.05259 0.113684
\(722\) 23.5871 0.877821
\(723\) −26.6620 −0.991569
\(724\) 5.32365 0.197852
\(725\) −14.0153 −0.520515
\(726\) −10.0046 −0.371306
\(727\) −16.9776 −0.629663 −0.314832 0.949148i \(-0.601948\pi\)
−0.314832 + 0.949148i \(0.601948\pi\)
\(728\) −9.23908 −0.342423
\(729\) 1.00000 0.0370370
\(730\) −8.98247 −0.332456
\(731\) 8.49625 0.314245
\(732\) −1.13673 −0.0420149
\(733\) −20.9167 −0.772576 −0.386288 0.922378i \(-0.626243\pi\)
−0.386288 + 0.922378i \(0.626243\pi\)
\(734\) 14.2964 0.527690
\(735\) 1.17349 0.0432849
\(736\) 0.495153 0.0182516
\(737\) −21.8679 −0.805513
\(738\) 7.41791 0.273057
\(739\) 12.0997 0.445095 0.222548 0.974922i \(-0.428563\pi\)
0.222548 + 0.974922i \(0.428563\pi\)
\(740\) 1.11318 0.0409213
\(741\) 0.715310 0.0262776
\(742\) −16.0623 −0.589664
\(743\) 15.0790 0.553194 0.276597 0.960986i \(-0.410793\pi\)
0.276597 + 0.960986i \(0.410793\pi\)
\(744\) −0.412033 −0.0151059
\(745\) −0.830189 −0.0304158
\(746\) 7.87840 0.288449
\(747\) 1.65318 0.0604866
\(748\) −2.37850 −0.0869667
\(749\) −54.3037 −1.98421
\(750\) 6.29239 0.229766
\(751\) 21.9237 0.800009 0.400004 0.916513i \(-0.369009\pi\)
0.400004 + 0.916513i \(0.369009\pi\)
\(752\) 22.6725 0.826779
\(753\) −13.4503 −0.490158
\(754\) −3.76926 −0.137268
\(755\) 1.54711 0.0563050
\(756\) −1.13672 −0.0413419
\(757\) −2.99591 −0.108888 −0.0544440 0.998517i \(-0.517339\pi\)
−0.0544440 + 0.998517i \(0.517339\pi\)
\(758\) −22.1757 −0.805459
\(759\) −0.423615 −0.0153762
\(760\) 1.09589 0.0397521
\(761\) 4.79728 0.173901 0.0869506 0.996213i \(-0.472288\pi\)
0.0869506 + 0.996213i \(0.472288\pi\)
\(762\) −23.7022 −0.858640
\(763\) 49.6691 1.79814
\(764\) −0.901461 −0.0326137
\(765\) 1.81937 0.0657796
\(766\) −12.5821 −0.454609
\(767\) −4.06634 −0.146827
\(768\) 8.60802 0.310615
\(769\) −31.6564 −1.14156 −0.570779 0.821103i \(-0.693359\pi\)
−0.570779 + 0.821103i \(0.693359\pi\)
\(770\) 3.50322 0.126247
\(771\) −26.9808 −0.971691
\(772\) 2.01186 0.0724083
\(773\) −38.0532 −1.36868 −0.684340 0.729163i \(-0.739910\pi\)
−0.684340 + 0.729163i \(0.739910\pi\)
\(774\) 3.01574 0.108399
\(775\) −0.645795 −0.0231977
\(776\) −47.9635 −1.72179
\(777\) 18.0276 0.646736
\(778\) −18.5394 −0.664671
\(779\) 4.15910 0.149015
\(780\) −0.188493 −0.00674913
\(781\) −10.7841 −0.385884
\(782\) −1.09307 −0.0390881
\(783\) −2.95446 −0.105584
\(784\) −7.22515 −0.258041
\(785\) −4.37827 −0.156267
\(786\) −10.0243 −0.357555
\(787\) 38.5758 1.37508 0.687539 0.726148i \(-0.258691\pi\)
0.687539 + 0.726148i \(0.258691\pi\)
\(788\) −7.32842 −0.261064
\(789\) 5.11106 0.181959
\(790\) −6.57820 −0.234042
\(791\) 2.75440 0.0979351
\(792\) −5.37862 −0.191121
\(793\) −3.05264 −0.108402
\(794\) 27.6149 0.980017
\(795\) −2.08773 −0.0740440
\(796\) 6.43414 0.228052
\(797\) 35.8686 1.27053 0.635266 0.772294i \(-0.280891\pi\)
0.635266 + 0.772294i \(0.280891\pi\)
\(798\) 2.78573 0.0986139
\(799\) 26.1475 0.925032
\(800\) 9.85376 0.348383
\(801\) −12.4282 −0.439129
\(802\) −11.4581 −0.404601
\(803\) 24.7182 0.872287
\(804\) 4.58226 0.161604
\(805\) −0.368333 −0.0129820
\(806\) −0.173679 −0.00611759
\(807\) 5.04937 0.177746
\(808\) −10.1537 −0.357207
\(809\) −43.6710 −1.53539 −0.767696 0.640814i \(-0.778597\pi\)
−0.767696 + 0.640814i \(0.778597\pi\)
\(810\) 0.645786 0.0226906
\(811\) 42.7642 1.50166 0.750828 0.660498i \(-0.229655\pi\)
0.750828 + 0.660498i \(0.229655\pi\)
\(812\) 3.35838 0.117856
\(813\) 10.8978 0.382203
\(814\) 13.3893 0.469293
\(815\) −8.43332 −0.295406
\(816\) −11.2018 −0.392142
\(817\) 1.69088 0.0591563
\(818\) 38.9059 1.36031
\(819\) −3.05259 −0.106666
\(820\) −1.09597 −0.0382730
\(821\) −2.57276 −0.0897898 −0.0448949 0.998992i \(-0.514295\pi\)
−0.0448949 + 0.998992i \(0.514295\pi\)
\(822\) 18.0335 0.628992
\(823\) 44.5744 1.55377 0.776883 0.629645i \(-0.216800\pi\)
0.776883 + 0.629645i \(0.216800\pi\)
\(824\) −3.02664 −0.105438
\(825\) −8.43013 −0.293499
\(826\) −15.8361 −0.551009
\(827\) 9.11085 0.316815 0.158408 0.987374i \(-0.449364\pi\)
0.158408 + 0.987374i \(0.449364\pi\)
\(828\) 0.0887656 0.00308482
\(829\) 12.1320 0.421361 0.210680 0.977555i \(-0.432432\pi\)
0.210680 + 0.977555i \(0.432432\pi\)
\(830\) 1.06760 0.0370569
\(831\) 3.91725 0.135888
\(832\) 8.88321 0.307970
\(833\) −8.33256 −0.288706
\(834\) 21.3207 0.738277
\(835\) −9.17089 −0.317372
\(836\) −0.473356 −0.0163714
\(837\) −0.136135 −0.00470553
\(838\) 5.58747 0.193016
\(839\) −53.8711 −1.85984 −0.929918 0.367767i \(-0.880122\pi\)
−0.929918 + 0.367767i \(0.880122\pi\)
\(840\) −4.67671 −0.161362
\(841\) −20.2711 −0.699005
\(842\) −7.49119 −0.258164
\(843\) −6.75296 −0.232584
\(844\) −5.72068 −0.196914
\(845\) −0.506188 −0.0174134
\(846\) 9.28105 0.319089
\(847\) 23.9382 0.822527
\(848\) 12.8541 0.441410
\(849\) 6.30052 0.216233
\(850\) −21.7526 −0.746107
\(851\) −1.40777 −0.0482576
\(852\) 2.25972 0.0774169
\(853\) 1.06628 0.0365089 0.0182544 0.999833i \(-0.494189\pi\)
0.0182544 + 0.999833i \(0.494189\pi\)
\(854\) −11.8883 −0.406810
\(855\) 0.362082 0.0123829
\(856\) 53.8421 1.84028
\(857\) −16.6961 −0.570328 −0.285164 0.958479i \(-0.592048\pi\)
−0.285164 + 0.958479i \(0.592048\pi\)
\(858\) −2.26719 −0.0774004
\(859\) −1.34068 −0.0457434 −0.0228717 0.999738i \(-0.507281\pi\)
−0.0228717 + 0.999738i \(0.507281\pi\)
\(860\) −0.445566 −0.0151937
\(861\) −17.7490 −0.604883
\(862\) 24.2131 0.824702
\(863\) −7.94115 −0.270320 −0.135160 0.990824i \(-0.543155\pi\)
−0.135160 + 0.990824i \(0.543155\pi\)
\(864\) 2.07720 0.0706677
\(865\) 3.85440 0.131054
\(866\) −39.7469 −1.35065
\(867\) 4.08127 0.138607
\(868\) 0.154747 0.00525246
\(869\) 18.1021 0.614071
\(870\) −1.90795 −0.0646856
\(871\) 12.3054 0.416953
\(872\) −49.2469 −1.66771
\(873\) −15.8471 −0.536343
\(874\) −0.217537 −0.00735829
\(875\) −15.0559 −0.508983
\(876\) −5.17953 −0.175000
\(877\) 51.0387 1.72346 0.861728 0.507370i \(-0.169382\pi\)
0.861728 + 0.507370i \(0.169382\pi\)
\(878\) 20.5380 0.693124
\(879\) 14.8568 0.501107
\(880\) −2.80350 −0.0945059
\(881\) 25.6095 0.862805 0.431403 0.902160i \(-0.358019\pi\)
0.431403 + 0.902160i \(0.358019\pi\)
\(882\) −2.95764 −0.0995890
\(883\) −53.5333 −1.80154 −0.900769 0.434298i \(-0.856997\pi\)
−0.900769 + 0.434298i \(0.856997\pi\)
\(884\) 1.33842 0.0450160
\(885\) −2.05833 −0.0691901
\(886\) 28.0323 0.941763
\(887\) 26.0123 0.873409 0.436704 0.899605i \(-0.356146\pi\)
0.436704 + 0.899605i \(0.356146\pi\)
\(888\) −17.8744 −0.599824
\(889\) 56.7127 1.90208
\(890\) −8.02595 −0.269031
\(891\) −1.77709 −0.0595349
\(892\) −6.52456 −0.218458
\(893\) 5.20373 0.174136
\(894\) 2.09239 0.0699799
\(895\) −10.6120 −0.354720
\(896\) 21.9135 0.732078
\(897\) 0.238375 0.00795912
\(898\) −26.7889 −0.893956
\(899\) 0.402207 0.0134144
\(900\) 1.76648 0.0588825
\(901\) 14.8242 0.493866
\(902\) −13.1823 −0.438923
\(903\) −7.21581 −0.240127
\(904\) −2.73098 −0.0908312
\(905\) 7.23666 0.240555
\(906\) −3.89929 −0.129545
\(907\) −14.1824 −0.470918 −0.235459 0.971884i \(-0.575659\pi\)
−0.235459 + 0.971884i \(0.575659\pi\)
\(908\) 8.94420 0.296824
\(909\) −3.35478 −0.111271
\(910\) −1.97132 −0.0653486
\(911\) −14.2700 −0.472786 −0.236393 0.971657i \(-0.575965\pi\)
−0.236393 + 0.971657i \(0.575965\pi\)
\(912\) −2.22932 −0.0738202
\(913\) −2.93785 −0.0972286
\(914\) 9.24196 0.305697
\(915\) −1.54521 −0.0510830
\(916\) 0.778639 0.0257270
\(917\) 23.9853 0.792065
\(918\) −4.58550 −0.151344
\(919\) −34.3479 −1.13303 −0.566517 0.824050i \(-0.691709\pi\)
−0.566517 + 0.824050i \(0.691709\pi\)
\(920\) 0.365202 0.0120404
\(921\) −2.47596 −0.0815856
\(922\) −13.9879 −0.460667
\(923\) 6.06837 0.199743
\(924\) 2.02005 0.0664547
\(925\) −28.0152 −0.921134
\(926\) 37.3632 1.22783
\(927\) −1.00000 −0.0328443
\(928\) −6.13701 −0.201457
\(929\) 16.2958 0.534647 0.267324 0.963607i \(-0.413861\pi\)
0.267324 + 0.963607i \(0.413861\pi\)
\(930\) −0.0879143 −0.00288282
\(931\) −1.65830 −0.0543486
\(932\) 3.40841 0.111646
\(933\) −4.91918 −0.161047
\(934\) −53.4480 −1.74887
\(935\) −3.23320 −0.105737
\(936\) 3.02664 0.0989288
\(937\) −33.8529 −1.10593 −0.552963 0.833206i \(-0.686503\pi\)
−0.552963 + 0.833206i \(0.686503\pi\)
\(938\) 47.9227 1.56473
\(939\) 22.5452 0.735736
\(940\) −1.37125 −0.0447251
\(941\) 46.8092 1.52594 0.762969 0.646435i \(-0.223741\pi\)
0.762969 + 0.646435i \(0.223741\pi\)
\(942\) 11.0349 0.359536
\(943\) 1.38601 0.0451346
\(944\) 12.6731 0.412473
\(945\) −1.54518 −0.0502648
\(946\) −5.35925 −0.174244
\(947\) −52.0261 −1.69062 −0.845311 0.534275i \(-0.820585\pi\)
−0.845311 + 0.534275i \(0.820585\pi\)
\(948\) −3.79317 −0.123196
\(949\) −13.9094 −0.451517
\(950\) −4.32908 −0.140454
\(951\) −26.6686 −0.864790
\(952\) 33.2077 1.07627
\(953\) 9.23155 0.299039 0.149520 0.988759i \(-0.452227\pi\)
0.149520 + 0.988759i \(0.452227\pi\)
\(954\) 5.26185 0.170359
\(955\) −1.22539 −0.0396528
\(956\) −2.58374 −0.0835642
\(957\) 5.25036 0.169720
\(958\) −1.67786 −0.0542092
\(959\) −43.1492 −1.39336
\(960\) 4.49658 0.145126
\(961\) −30.9815 −0.999402
\(962\) −7.53436 −0.242918
\(963\) 17.7894 0.573255
\(964\) −9.92832 −0.319770
\(965\) 2.73480 0.0880363
\(966\) 0.928338 0.0298688
\(967\) −36.9716 −1.18893 −0.594463 0.804123i \(-0.702635\pi\)
−0.594463 + 0.804123i \(0.702635\pi\)
\(968\) −23.7347 −0.762863
\(969\) −2.57101 −0.0825929
\(970\) −10.2338 −0.328589
\(971\) −34.7886 −1.11642 −0.558210 0.829700i \(-0.688512\pi\)
−0.558210 + 0.829700i \(0.688512\pi\)
\(972\) 0.372378 0.0119440
\(973\) −51.0145 −1.63545
\(974\) −38.1028 −1.22089
\(975\) 4.74377 0.151922
\(976\) 9.51379 0.304529
\(977\) −9.71591 −0.310839 −0.155420 0.987849i \(-0.549673\pi\)
−0.155420 + 0.987849i \(0.549673\pi\)
\(978\) 21.2551 0.679664
\(979\) 22.0861 0.705873
\(980\) 0.436983 0.0139589
\(981\) −16.2712 −0.519498
\(982\) 10.4261 0.332710
\(983\) 9.45583 0.301594 0.150797 0.988565i \(-0.451816\pi\)
0.150797 + 0.988565i \(0.451816\pi\)
\(984\) 17.5981 0.561006
\(985\) −9.96181 −0.317410
\(986\) 13.5477 0.431447
\(987\) −22.2069 −0.706854
\(988\) 0.266366 0.00847422
\(989\) 0.563480 0.0179176
\(990\) −1.14762 −0.0364738
\(991\) −10.9428 −0.347610 −0.173805 0.984780i \(-0.555606\pi\)
−0.173805 + 0.984780i \(0.555606\pi\)
\(992\) −0.282780 −0.00897828
\(993\) −27.3313 −0.867332
\(994\) 23.6329 0.749590
\(995\) 8.74619 0.277273
\(996\) 0.615606 0.0195062
\(997\) 34.6737 1.09813 0.549063 0.835781i \(-0.314985\pi\)
0.549063 + 0.835781i \(0.314985\pi\)
\(998\) −7.64810 −0.242096
\(999\) −5.90568 −0.186847
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 \(a_p\))