Properties

Label 619.2.a.b.1.17
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 1.17
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.431096 q^{2} -1.56278 q^{3} -1.81416 q^{4} +1.50079 q^{5} -0.673708 q^{6} -4.83036 q^{7} -1.64427 q^{8} -0.557720 q^{9} +O(q^{10})\) \(q+0.431096 q^{2} -1.56278 q^{3} -1.81416 q^{4} +1.50079 q^{5} -0.673708 q^{6} -4.83036 q^{7} -1.64427 q^{8} -0.557720 q^{9} +0.646986 q^{10} +2.60102 q^{11} +2.83513 q^{12} +5.36233 q^{13} -2.08235 q^{14} -2.34541 q^{15} +2.91948 q^{16} +6.13234 q^{17} -0.240431 q^{18} +1.28647 q^{19} -2.72267 q^{20} +7.54879 q^{21} +1.12129 q^{22} -3.55264 q^{23} +2.56963 q^{24} -2.74762 q^{25} +2.31168 q^{26} +5.55993 q^{27} +8.76304 q^{28} -1.96205 q^{29} -1.01110 q^{30} +7.06516 q^{31} +4.54711 q^{32} -4.06482 q^{33} +2.64363 q^{34} -7.24937 q^{35} +1.01179 q^{36} +3.47725 q^{37} +0.554591 q^{38} -8.38014 q^{39} -2.46770 q^{40} +5.18803 q^{41} +3.25425 q^{42} -8.24591 q^{43} -4.71865 q^{44} -0.837022 q^{45} -1.53153 q^{46} +4.95150 q^{47} -4.56250 q^{48} +16.3324 q^{49} -1.18449 q^{50} -9.58350 q^{51} -9.72810 q^{52} -5.85664 q^{53} +2.39686 q^{54} +3.90359 q^{55} +7.94241 q^{56} -2.01047 q^{57} -0.845830 q^{58} -9.60280 q^{59} +4.25494 q^{60} +6.86922 q^{61} +3.04576 q^{62} +2.69399 q^{63} -3.87871 q^{64} +8.04774 q^{65} -1.75233 q^{66} +14.9558 q^{67} -11.1250 q^{68} +5.55199 q^{69} -3.12518 q^{70} -5.87145 q^{71} +0.917041 q^{72} +4.41927 q^{73} +1.49903 q^{74} +4.29393 q^{75} -2.33385 q^{76} -12.5639 q^{77} -3.61264 q^{78} +8.82851 q^{79} +4.38153 q^{80} -7.01579 q^{81} +2.23654 q^{82} +1.16250 q^{83} -13.6947 q^{84} +9.20337 q^{85} -3.55478 q^{86} +3.06625 q^{87} -4.27677 q^{88} +14.0013 q^{89} -0.360837 q^{90} -25.9020 q^{91} +6.44504 q^{92} -11.0413 q^{93} +2.13457 q^{94} +1.93072 q^{95} -7.10613 q^{96} -5.05039 q^{97} +7.04084 q^{98} -1.45064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.431096 0.304831 0.152415 0.988317i \(-0.451295\pi\)
0.152415 + 0.988317i \(0.451295\pi\)
\(3\) −1.56278 −0.902271 −0.451136 0.892455i \(-0.648981\pi\)
−0.451136 + 0.892455i \(0.648981\pi\)
\(4\) −1.81416 −0.907078
\(5\) 1.50079 0.671175 0.335587 0.942009i \(-0.391065\pi\)
0.335587 + 0.942009i \(0.391065\pi\)
\(6\) −0.673708 −0.275040
\(7\) −4.83036 −1.82571 −0.912853 0.408288i \(-0.866126\pi\)
−0.912853 + 0.408288i \(0.866126\pi\)
\(8\) −1.64427 −0.581336
\(9\) −0.557720 −0.185907
\(10\) 0.646986 0.204595
\(11\) 2.60102 0.784237 0.392118 0.919915i \(-0.371742\pi\)
0.392118 + 0.919915i \(0.371742\pi\)
\(12\) 2.83513 0.818430
\(13\) 5.36233 1.48724 0.743621 0.668601i \(-0.233107\pi\)
0.743621 + 0.668601i \(0.233107\pi\)
\(14\) −2.08235 −0.556532
\(15\) −2.34541 −0.605582
\(16\) 2.91948 0.729869
\(17\) 6.13234 1.48731 0.743656 0.668563i \(-0.233090\pi\)
0.743656 + 0.668563i \(0.233090\pi\)
\(18\) −0.240431 −0.0566701
\(19\) 1.28647 0.295136 0.147568 0.989052i \(-0.452855\pi\)
0.147568 + 0.989052i \(0.452855\pi\)
\(20\) −2.72267 −0.608808
\(21\) 7.54879 1.64728
\(22\) 1.12129 0.239060
\(23\) −3.55264 −0.740776 −0.370388 0.928877i \(-0.620775\pi\)
−0.370388 + 0.928877i \(0.620775\pi\)
\(24\) 2.56963 0.524523
\(25\) −2.74762 −0.549524
\(26\) 2.31168 0.453357
\(27\) 5.55993 1.07001
\(28\) 8.76304 1.65606
\(29\) −1.96205 −0.364343 −0.182171 0.983267i \(-0.558313\pi\)
−0.182171 + 0.983267i \(0.558313\pi\)
\(30\) −1.01110 −0.184600
\(31\) 7.06516 1.26894 0.634470 0.772947i \(-0.281218\pi\)
0.634470 + 0.772947i \(0.281218\pi\)
\(32\) 4.54711 0.803823
\(33\) −4.06482 −0.707594
\(34\) 2.64363 0.453379
\(35\) −7.24937 −1.22537
\(36\) 1.01179 0.168632
\(37\) 3.47725 0.571656 0.285828 0.958281i \(-0.407731\pi\)
0.285828 + 0.958281i \(0.407731\pi\)
\(38\) 0.554591 0.0899666
\(39\) −8.38014 −1.34190
\(40\) −2.46770 −0.390178
\(41\) 5.18803 0.810234 0.405117 0.914265i \(-0.367231\pi\)
0.405117 + 0.914265i \(0.367231\pi\)
\(42\) 3.25425 0.502142
\(43\) −8.24591 −1.25749 −0.628745 0.777612i \(-0.716431\pi\)
−0.628745 + 0.777612i \(0.716431\pi\)
\(44\) −4.71865 −0.711364
\(45\) −0.837022 −0.124776
\(46\) −1.53153 −0.225811
\(47\) 4.95150 0.722250 0.361125 0.932517i \(-0.382393\pi\)
0.361125 + 0.932517i \(0.382393\pi\)
\(48\) −4.56250 −0.658540
\(49\) 16.3324 2.33320
\(50\) −1.18449 −0.167512
\(51\) −9.58350 −1.34196
\(52\) −9.72810 −1.34904
\(53\) −5.85664 −0.804472 −0.402236 0.915536i \(-0.631767\pi\)
−0.402236 + 0.915536i \(0.631767\pi\)
\(54\) 2.39686 0.326172
\(55\) 3.90359 0.526360
\(56\) 7.94241 1.06135
\(57\) −2.01047 −0.266293
\(58\) −0.845830 −0.111063
\(59\) −9.60280 −1.25018 −0.625089 0.780554i \(-0.714937\pi\)
−0.625089 + 0.780554i \(0.714937\pi\)
\(60\) 4.25494 0.549310
\(61\) 6.86922 0.879514 0.439757 0.898117i \(-0.355065\pi\)
0.439757 + 0.898117i \(0.355065\pi\)
\(62\) 3.04576 0.386812
\(63\) 2.69399 0.339411
\(64\) −3.87871 −0.484839
\(65\) 8.04774 0.998200
\(66\) −1.75233 −0.215697
\(67\) 14.9558 1.82714 0.913569 0.406683i \(-0.133315\pi\)
0.913569 + 0.406683i \(0.133315\pi\)
\(68\) −11.1250 −1.34911
\(69\) 5.55199 0.668381
\(70\) −3.12518 −0.373530
\(71\) −5.87145 −0.696813 −0.348407 0.937344i \(-0.613277\pi\)
−0.348407 + 0.937344i \(0.613277\pi\)
\(72\) 0.917041 0.108074
\(73\) 4.41927 0.517236 0.258618 0.965980i \(-0.416733\pi\)
0.258618 + 0.965980i \(0.416733\pi\)
\(74\) 1.49903 0.174258
\(75\) 4.29393 0.495820
\(76\) −2.33385 −0.267711
\(77\) −12.5639 −1.43179
\(78\) −3.61264 −0.409051
\(79\) 8.82851 0.993285 0.496642 0.867955i \(-0.334566\pi\)
0.496642 + 0.867955i \(0.334566\pi\)
\(80\) 4.38153 0.489870
\(81\) −7.01579 −0.779532
\(82\) 2.23654 0.246984
\(83\) 1.16250 0.127601 0.0638003 0.997963i \(-0.479678\pi\)
0.0638003 + 0.997963i \(0.479678\pi\)
\(84\) −13.6947 −1.49421
\(85\) 9.20337 0.998246
\(86\) −3.55478 −0.383322
\(87\) 3.06625 0.328736
\(88\) −4.27677 −0.455905
\(89\) 14.0013 1.48414 0.742068 0.670325i \(-0.233845\pi\)
0.742068 + 0.670325i \(0.233845\pi\)
\(90\) −0.360837 −0.0380356
\(91\) −25.9020 −2.71527
\(92\) 6.44504 0.671942
\(93\) −11.0413 −1.14493
\(94\) 2.13457 0.220164
\(95\) 1.93072 0.198088
\(96\) −7.10613 −0.725266
\(97\) −5.05039 −0.512790 −0.256395 0.966572i \(-0.582535\pi\)
−0.256395 + 0.966572i \(0.582535\pi\)
\(98\) 7.04084 0.711232
\(99\) −1.45064 −0.145795
\(100\) 4.98462 0.498462
\(101\) 8.50227 0.846007 0.423004 0.906128i \(-0.360976\pi\)
0.423004 + 0.906128i \(0.360976\pi\)
\(102\) −4.13141 −0.409070
\(103\) 7.04198 0.693867 0.346934 0.937890i \(-0.387223\pi\)
0.346934 + 0.937890i \(0.387223\pi\)
\(104\) −8.81710 −0.864588
\(105\) 11.3292 1.10561
\(106\) −2.52477 −0.245228
\(107\) −14.6155 −1.41293 −0.706465 0.707748i \(-0.749711\pi\)
−0.706465 + 0.707748i \(0.749711\pi\)
\(108\) −10.0866 −0.970582
\(109\) −3.64511 −0.349138 −0.174569 0.984645i \(-0.555853\pi\)
−0.174569 + 0.984645i \(0.555853\pi\)
\(110\) 1.68282 0.160451
\(111\) −5.43417 −0.515789
\(112\) −14.1021 −1.33253
\(113\) 9.10477 0.856505 0.428252 0.903659i \(-0.359129\pi\)
0.428252 + 0.903659i \(0.359129\pi\)
\(114\) −0.866704 −0.0811742
\(115\) −5.33177 −0.497190
\(116\) 3.55946 0.330487
\(117\) −2.99068 −0.276488
\(118\) −4.13973 −0.381093
\(119\) −29.6215 −2.71539
\(120\) 3.85648 0.352047
\(121\) −4.23470 −0.384973
\(122\) 2.96129 0.268103
\(123\) −8.10774 −0.731051
\(124\) −12.8173 −1.15103
\(125\) −11.6276 −1.04000
\(126\) 1.16137 0.103463
\(127\) −13.4174 −1.19060 −0.595300 0.803504i \(-0.702967\pi\)
−0.595300 + 0.803504i \(0.702967\pi\)
\(128\) −10.7663 −0.951617
\(129\) 12.8865 1.13460
\(130\) 3.46935 0.304282
\(131\) 16.5240 1.44371 0.721855 0.692044i \(-0.243290\pi\)
0.721855 + 0.692044i \(0.243290\pi\)
\(132\) 7.37422 0.641843
\(133\) −6.21411 −0.538832
\(134\) 6.44737 0.556968
\(135\) 8.34430 0.718163
\(136\) −10.0832 −0.864628
\(137\) −19.3142 −1.65013 −0.825063 0.565041i \(-0.808860\pi\)
−0.825063 + 0.565041i \(0.808860\pi\)
\(138\) 2.39344 0.203743
\(139\) −5.09316 −0.431997 −0.215998 0.976394i \(-0.569301\pi\)
−0.215998 + 0.976394i \(0.569301\pi\)
\(140\) 13.1515 1.11150
\(141\) −7.73810 −0.651666
\(142\) −2.53116 −0.212410
\(143\) 13.9475 1.16635
\(144\) −1.62825 −0.135688
\(145\) −2.94462 −0.244538
\(146\) 1.90513 0.157670
\(147\) −25.5240 −2.10518
\(148\) −6.30827 −0.518537
\(149\) 15.6367 1.28101 0.640504 0.767955i \(-0.278726\pi\)
0.640504 + 0.767955i \(0.278726\pi\)
\(150\) 1.85109 0.151141
\(151\) 14.9031 1.21279 0.606397 0.795162i \(-0.292614\pi\)
0.606397 + 0.795162i \(0.292614\pi\)
\(152\) −2.11530 −0.171573
\(153\) −3.42013 −0.276501
\(154\) −5.41623 −0.436452
\(155\) 10.6033 0.851681
\(156\) 15.2029 1.21720
\(157\) 16.9495 1.35272 0.676359 0.736572i \(-0.263557\pi\)
0.676359 + 0.736572i \(0.263557\pi\)
\(158\) 3.80593 0.302784
\(159\) 9.15264 0.725851
\(160\) 6.82427 0.539506
\(161\) 17.1605 1.35244
\(162\) −3.02448 −0.237625
\(163\) −15.9532 −1.24955 −0.624775 0.780805i \(-0.714809\pi\)
−0.624775 + 0.780805i \(0.714809\pi\)
\(164\) −9.41189 −0.734945
\(165\) −6.10045 −0.474919
\(166\) 0.501147 0.0388966
\(167\) 9.93294 0.768634 0.384317 0.923201i \(-0.374437\pi\)
0.384317 + 0.923201i \(0.374437\pi\)
\(168\) −12.4122 −0.957625
\(169\) 15.7546 1.21189
\(170\) 3.96754 0.304296
\(171\) −0.717489 −0.0548678
\(172\) 14.9594 1.14064
\(173\) −13.5963 −1.03371 −0.516855 0.856073i \(-0.672897\pi\)
−0.516855 + 0.856073i \(0.672897\pi\)
\(174\) 1.32185 0.100209
\(175\) 13.2720 1.00327
\(176\) 7.59361 0.572390
\(177\) 15.0071 1.12800
\(178\) 6.03591 0.452410
\(179\) 14.4590 1.08072 0.540358 0.841435i \(-0.318289\pi\)
0.540358 + 0.841435i \(0.318289\pi\)
\(180\) 1.51849 0.113181
\(181\) 5.91625 0.439752 0.219876 0.975528i \(-0.429435\pi\)
0.219876 + 0.975528i \(0.429435\pi\)
\(182\) −11.1662 −0.827697
\(183\) −10.7351 −0.793560
\(184\) 5.84149 0.430640
\(185\) 5.21863 0.383681
\(186\) −4.75986 −0.349010
\(187\) 15.9503 1.16640
\(188\) −8.98279 −0.655138
\(189\) −26.8565 −1.95352
\(190\) 0.832326 0.0603833
\(191\) 22.2794 1.61208 0.806039 0.591862i \(-0.201607\pi\)
0.806039 + 0.591862i \(0.201607\pi\)
\(192\) 6.06157 0.437456
\(193\) −12.8221 −0.922955 −0.461478 0.887152i \(-0.652681\pi\)
−0.461478 + 0.887152i \(0.652681\pi\)
\(194\) −2.17720 −0.156314
\(195\) −12.5768 −0.900647
\(196\) −29.6296 −2.11640
\(197\) 1.62495 0.115773 0.0578866 0.998323i \(-0.481564\pi\)
0.0578866 + 0.998323i \(0.481564\pi\)
\(198\) −0.625365 −0.0444428
\(199\) 12.0603 0.854933 0.427466 0.904031i \(-0.359406\pi\)
0.427466 + 0.904031i \(0.359406\pi\)
\(200\) 4.51783 0.319459
\(201\) −23.3726 −1.64857
\(202\) 3.66529 0.257889
\(203\) 9.47740 0.665183
\(204\) 17.3860 1.21726
\(205\) 7.78615 0.543809
\(206\) 3.03577 0.211512
\(207\) 1.98138 0.137715
\(208\) 15.6552 1.08549
\(209\) 3.34613 0.231456
\(210\) 4.88396 0.337025
\(211\) −21.0651 −1.45018 −0.725090 0.688654i \(-0.758202\pi\)
−0.725090 + 0.688654i \(0.758202\pi\)
\(212\) 10.6249 0.729719
\(213\) 9.17578 0.628714
\(214\) −6.30067 −0.430705
\(215\) −12.3754 −0.843995
\(216\) −9.14202 −0.622035
\(217\) −34.1273 −2.31671
\(218\) −1.57139 −0.106428
\(219\) −6.90634 −0.466687
\(220\) −7.08172 −0.477450
\(221\) 32.8836 2.21199
\(222\) −2.34265 −0.157228
\(223\) −2.07074 −0.138667 −0.0693336 0.997594i \(-0.522087\pi\)
−0.0693336 + 0.997594i \(0.522087\pi\)
\(224\) −21.9642 −1.46754
\(225\) 1.53240 0.102160
\(226\) 3.92503 0.261089
\(227\) 1.64406 0.109120 0.0545599 0.998510i \(-0.482624\pi\)
0.0545599 + 0.998510i \(0.482624\pi\)
\(228\) 3.64730 0.241548
\(229\) −12.7092 −0.839848 −0.419924 0.907559i \(-0.637943\pi\)
−0.419924 + 0.907559i \(0.637943\pi\)
\(230\) −2.29851 −0.151559
\(231\) 19.6346 1.29186
\(232\) 3.22613 0.211806
\(233\) 25.1543 1.64792 0.823958 0.566651i \(-0.191761\pi\)
0.823958 + 0.566651i \(0.191761\pi\)
\(234\) −1.28927 −0.0842822
\(235\) 7.43117 0.484756
\(236\) 17.4210 1.13401
\(237\) −13.7970 −0.896212
\(238\) −12.7697 −0.827736
\(239\) 3.76267 0.243387 0.121693 0.992568i \(-0.461168\pi\)
0.121693 + 0.992568i \(0.461168\pi\)
\(240\) −6.84736 −0.441995
\(241\) −5.67080 −0.365289 −0.182644 0.983179i \(-0.558466\pi\)
−0.182644 + 0.983179i \(0.558466\pi\)
\(242\) −1.82556 −0.117352
\(243\) −5.71567 −0.366660
\(244\) −12.4618 −0.797788
\(245\) 24.5116 1.56599
\(246\) −3.49522 −0.222847
\(247\) 6.89846 0.438939
\(248\) −11.6170 −0.737682
\(249\) −1.81673 −0.115130
\(250\) −5.01260 −0.317025
\(251\) 10.1988 0.643741 0.321871 0.946784i \(-0.395688\pi\)
0.321871 + 0.946784i \(0.395688\pi\)
\(252\) −4.88732 −0.307872
\(253\) −9.24048 −0.580944
\(254\) −5.78418 −0.362932
\(255\) −14.3828 −0.900689
\(256\) 3.11611 0.194757
\(257\) 0.739967 0.0461579 0.0230789 0.999734i \(-0.492653\pi\)
0.0230789 + 0.999734i \(0.492653\pi\)
\(258\) 5.55533 0.345860
\(259\) −16.7964 −1.04368
\(260\) −14.5999 −0.905445
\(261\) 1.09427 0.0677338
\(262\) 7.12344 0.440087
\(263\) 11.6292 0.717090 0.358545 0.933513i \(-0.383273\pi\)
0.358545 + 0.933513i \(0.383273\pi\)
\(264\) 6.68365 0.411350
\(265\) −8.78960 −0.539941
\(266\) −2.67888 −0.164252
\(267\) −21.8810 −1.33909
\(268\) −27.1321 −1.65736
\(269\) 20.9998 1.28038 0.640190 0.768217i \(-0.278856\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(270\) 3.59720 0.218918
\(271\) −20.4684 −1.24337 −0.621684 0.783268i \(-0.713551\pi\)
−0.621684 + 0.783268i \(0.713551\pi\)
\(272\) 17.9032 1.08554
\(273\) 40.4791 2.44991
\(274\) −8.32628 −0.503009
\(275\) −7.14662 −0.430957
\(276\) −10.0722 −0.606274
\(277\) 8.22513 0.494200 0.247100 0.968990i \(-0.420522\pi\)
0.247100 + 0.968990i \(0.420522\pi\)
\(278\) −2.19564 −0.131686
\(279\) −3.94038 −0.235905
\(280\) 11.9199 0.712351
\(281\) 13.8741 0.827658 0.413829 0.910355i \(-0.364191\pi\)
0.413829 + 0.910355i \(0.364191\pi\)
\(282\) −3.33586 −0.198648
\(283\) 30.4615 1.81075 0.905373 0.424616i \(-0.139591\pi\)
0.905373 + 0.424616i \(0.139591\pi\)
\(284\) 10.6517 0.632064
\(285\) −3.01729 −0.178729
\(286\) 6.01272 0.355540
\(287\) −25.0601 −1.47925
\(288\) −2.53601 −0.149436
\(289\) 20.6056 1.21210
\(290\) −1.26942 −0.0745427
\(291\) 7.89265 0.462675
\(292\) −8.01724 −0.469174
\(293\) −27.5968 −1.61222 −0.806111 0.591765i \(-0.798431\pi\)
−0.806111 + 0.591765i \(0.798431\pi\)
\(294\) −11.0033 −0.641724
\(295\) −14.4118 −0.839088
\(296\) −5.71752 −0.332324
\(297\) 14.4615 0.839141
\(298\) 6.74092 0.390491
\(299\) −19.0504 −1.10171
\(300\) −7.78986 −0.449748
\(301\) 39.8307 2.29581
\(302\) 6.42465 0.369697
\(303\) −13.2872 −0.763328
\(304\) 3.75581 0.215411
\(305\) 10.3093 0.590307
\(306\) −1.47441 −0.0842861
\(307\) −13.6959 −0.781667 −0.390834 0.920461i \(-0.627813\pi\)
−0.390834 + 0.920461i \(0.627813\pi\)
\(308\) 22.7928 1.29874
\(309\) −11.0051 −0.626056
\(310\) 4.57106 0.259619
\(311\) −0.171615 −0.00973139 −0.00486569 0.999988i \(-0.501549\pi\)
−0.00486569 + 0.999988i \(0.501549\pi\)
\(312\) 13.7792 0.780093
\(313\) −17.5584 −0.992461 −0.496230 0.868191i \(-0.665283\pi\)
−0.496230 + 0.868191i \(0.665283\pi\)
\(314\) 7.30686 0.412350
\(315\) 4.04312 0.227804
\(316\) −16.0163 −0.900987
\(317\) −1.72271 −0.0967569 −0.0483784 0.998829i \(-0.515405\pi\)
−0.0483784 + 0.998829i \(0.515405\pi\)
\(318\) 3.94567 0.221262
\(319\) −5.10332 −0.285731
\(320\) −5.82114 −0.325412
\(321\) 22.8408 1.27485
\(322\) 7.39784 0.412265
\(323\) 7.88906 0.438959
\(324\) 12.7277 0.707096
\(325\) −14.7337 −0.817276
\(326\) −6.87736 −0.380902
\(327\) 5.69650 0.315017
\(328\) −8.53051 −0.471018
\(329\) −23.9175 −1.31862
\(330\) −2.62988 −0.144770
\(331\) 23.5273 1.29318 0.646590 0.762838i \(-0.276195\pi\)
0.646590 + 0.762838i \(0.276195\pi\)
\(332\) −2.10895 −0.115744
\(333\) −1.93933 −0.106275
\(334\) 4.28205 0.234303
\(335\) 22.4455 1.22633
\(336\) 22.0385 1.20230
\(337\) −8.02169 −0.436969 −0.218485 0.975840i \(-0.570111\pi\)
−0.218485 + 0.975840i \(0.570111\pi\)
\(338\) 6.79173 0.369421
\(339\) −14.2287 −0.772799
\(340\) −16.6964 −0.905487
\(341\) 18.3766 0.995150
\(342\) −0.309307 −0.0167254
\(343\) −45.0790 −2.43404
\(344\) 13.5585 0.731024
\(345\) 8.33238 0.448600
\(346\) −5.86133 −0.315107
\(347\) −11.7465 −0.630584 −0.315292 0.948995i \(-0.602102\pi\)
−0.315292 + 0.948995i \(0.602102\pi\)
\(348\) −5.56265 −0.298189
\(349\) 11.8697 0.635373 0.317686 0.948196i \(-0.397094\pi\)
0.317686 + 0.948196i \(0.397094\pi\)
\(350\) 5.72151 0.305828
\(351\) 29.8142 1.59136
\(352\) 11.8271 0.630387
\(353\) 22.4752 1.19624 0.598118 0.801408i \(-0.295915\pi\)
0.598118 + 0.801408i \(0.295915\pi\)
\(354\) 6.46948 0.343849
\(355\) −8.81183 −0.467683
\(356\) −25.4006 −1.34623
\(357\) 46.2918 2.45002
\(358\) 6.23322 0.329436
\(359\) −24.8782 −1.31302 −0.656510 0.754317i \(-0.727968\pi\)
−0.656510 + 0.754317i \(0.727968\pi\)
\(360\) 1.37629 0.0725368
\(361\) −17.3450 −0.912895
\(362\) 2.55047 0.134050
\(363\) 6.61791 0.347350
\(364\) 46.9903 2.46296
\(365\) 6.63240 0.347156
\(366\) −4.62785 −0.241902
\(367\) 32.9944 1.72230 0.861148 0.508355i \(-0.169746\pi\)
0.861148 + 0.508355i \(0.169746\pi\)
\(368\) −10.3718 −0.540669
\(369\) −2.89347 −0.150628
\(370\) 2.24973 0.116958
\(371\) 28.2897 1.46873
\(372\) 20.0306 1.03854
\(373\) −9.20405 −0.476567 −0.238284 0.971196i \(-0.576585\pi\)
−0.238284 + 0.971196i \(0.576585\pi\)
\(374\) 6.87613 0.355556
\(375\) 18.1713 0.938364
\(376\) −8.14159 −0.419870
\(377\) −10.5211 −0.541866
\(378\) −11.5777 −0.595494
\(379\) 5.20872 0.267554 0.133777 0.991011i \(-0.457289\pi\)
0.133777 + 0.991011i \(0.457289\pi\)
\(380\) −3.50263 −0.179681
\(381\) 20.9684 1.07424
\(382\) 9.60455 0.491411
\(383\) −12.3327 −0.630174 −0.315087 0.949063i \(-0.602034\pi\)
−0.315087 + 0.949063i \(0.602034\pi\)
\(384\) 16.8254 0.858616
\(385\) −18.8558 −0.960978
\(386\) −5.52756 −0.281345
\(387\) 4.59891 0.233776
\(388\) 9.16220 0.465140
\(389\) −16.7375 −0.848626 −0.424313 0.905516i \(-0.639484\pi\)
−0.424313 + 0.905516i \(0.639484\pi\)
\(390\) −5.42183 −0.274545
\(391\) −21.7860 −1.10176
\(392\) −26.8549 −1.35638
\(393\) −25.8234 −1.30262
\(394\) 0.700511 0.0352912
\(395\) 13.2498 0.666668
\(396\) 2.63169 0.132247
\(397\) 23.7860 1.19378 0.596892 0.802322i \(-0.296402\pi\)
0.596892 + 0.802322i \(0.296402\pi\)
\(398\) 5.19915 0.260610
\(399\) 9.71128 0.486172
\(400\) −8.02161 −0.401081
\(401\) −2.86075 −0.142859 −0.0714295 0.997446i \(-0.522756\pi\)
−0.0714295 + 0.997446i \(0.522756\pi\)
\(402\) −10.0758 −0.502536
\(403\) 37.8857 1.88722
\(404\) −15.4244 −0.767395
\(405\) −10.5292 −0.523202
\(406\) 4.08567 0.202768
\(407\) 9.04439 0.448314
\(408\) 15.7578 0.780129
\(409\) −6.71964 −0.332265 −0.166132 0.986103i \(-0.553128\pi\)
−0.166132 + 0.986103i \(0.553128\pi\)
\(410\) 3.35658 0.165770
\(411\) 30.1839 1.48886
\(412\) −12.7753 −0.629392
\(413\) 46.3850 2.28246
\(414\) 0.854164 0.0419799
\(415\) 1.74467 0.0856423
\(416\) 24.3831 1.19548
\(417\) 7.95949 0.389778
\(418\) 1.44250 0.0705551
\(419\) −39.3202 −1.92092 −0.960459 0.278420i \(-0.910189\pi\)
−0.960459 + 0.278420i \(0.910189\pi\)
\(420\) −20.5529 −1.00288
\(421\) 5.48595 0.267369 0.133685 0.991024i \(-0.457319\pi\)
0.133685 + 0.991024i \(0.457319\pi\)
\(422\) −9.08108 −0.442060
\(423\) −2.76155 −0.134271
\(424\) 9.62988 0.467669
\(425\) −16.8494 −0.817314
\(426\) 3.95564 0.191652
\(427\) −33.1808 −1.60573
\(428\) 26.5147 1.28164
\(429\) −21.7969 −1.05236
\(430\) −5.33498 −0.257276
\(431\) −5.47777 −0.263855 −0.131927 0.991259i \(-0.542117\pi\)
−0.131927 + 0.991259i \(0.542117\pi\)
\(432\) 16.2321 0.780967
\(433\) −25.3491 −1.21820 −0.609099 0.793094i \(-0.708469\pi\)
−0.609099 + 0.793094i \(0.708469\pi\)
\(434\) −14.7121 −0.706206
\(435\) 4.60180 0.220639
\(436\) 6.61280 0.316696
\(437\) −4.57035 −0.218630
\(438\) −2.97730 −0.142261
\(439\) −8.92124 −0.425788 −0.212894 0.977075i \(-0.568289\pi\)
−0.212894 + 0.977075i \(0.568289\pi\)
\(440\) −6.41854 −0.305992
\(441\) −9.10892 −0.433758
\(442\) 14.1760 0.674284
\(443\) −39.4683 −1.87520 −0.937598 0.347720i \(-0.886956\pi\)
−0.937598 + 0.347720i \(0.886956\pi\)
\(444\) 9.85843 0.467861
\(445\) 21.0131 0.996114
\(446\) −0.892689 −0.0422700
\(447\) −24.4367 −1.15582
\(448\) 18.7356 0.885173
\(449\) −7.56629 −0.357075 −0.178538 0.983933i \(-0.557137\pi\)
−0.178538 + 0.983933i \(0.557137\pi\)
\(450\) 0.660613 0.0311416
\(451\) 13.4942 0.635415
\(452\) −16.5175 −0.776917
\(453\) −23.2902 −1.09427
\(454\) 0.708746 0.0332631
\(455\) −38.8735 −1.82242
\(456\) 3.30574 0.154806
\(457\) −40.5680 −1.89769 −0.948846 0.315740i \(-0.897747\pi\)
−0.948846 + 0.315740i \(0.897747\pi\)
\(458\) −5.47888 −0.256011
\(459\) 34.0954 1.59144
\(460\) 9.67267 0.450990
\(461\) −16.6102 −0.773613 −0.386807 0.922161i \(-0.626422\pi\)
−0.386807 + 0.922161i \(0.626422\pi\)
\(462\) 8.46438 0.393799
\(463\) −10.7052 −0.497514 −0.248757 0.968566i \(-0.580022\pi\)
−0.248757 + 0.968566i \(0.580022\pi\)
\(464\) −5.72815 −0.265922
\(465\) −16.5707 −0.768447
\(466\) 10.8439 0.502336
\(467\) −21.0194 −0.972664 −0.486332 0.873774i \(-0.661665\pi\)
−0.486332 + 0.873774i \(0.661665\pi\)
\(468\) 5.42556 0.250797
\(469\) −72.2418 −3.33582
\(470\) 3.20355 0.147769
\(471\) −26.4883 −1.22052
\(472\) 15.7896 0.726774
\(473\) −21.4478 −0.986169
\(474\) −5.94784 −0.273193
\(475\) −3.53473 −0.162184
\(476\) 53.7379 2.46307
\(477\) 3.26637 0.149557
\(478\) 1.62207 0.0741918
\(479\) 11.8653 0.542139 0.271070 0.962560i \(-0.412623\pi\)
0.271070 + 0.962560i \(0.412623\pi\)
\(480\) −10.6648 −0.486780
\(481\) 18.6461 0.850191
\(482\) −2.44466 −0.111351
\(483\) −26.8181 −1.22027
\(484\) 7.68241 0.349200
\(485\) −7.57959 −0.344171
\(486\) −2.46400 −0.111769
\(487\) 0.526452 0.0238558 0.0119279 0.999929i \(-0.496203\pi\)
0.0119279 + 0.999929i \(0.496203\pi\)
\(488\) −11.2948 −0.511293
\(489\) 24.9313 1.12743
\(490\) 10.5668 0.477361
\(491\) 26.2774 1.18588 0.592940 0.805246i \(-0.297967\pi\)
0.592940 + 0.805246i \(0.297967\pi\)
\(492\) 14.7087 0.663120
\(493\) −12.0319 −0.541891
\(494\) 2.97390 0.133802
\(495\) −2.17711 −0.0978538
\(496\) 20.6266 0.926160
\(497\) 28.3612 1.27218
\(498\) −0.783183 −0.0350953
\(499\) 19.1651 0.857950 0.428975 0.903316i \(-0.358875\pi\)
0.428975 + 0.903316i \(0.358875\pi\)
\(500\) 21.0942 0.943363
\(501\) −15.5230 −0.693516
\(502\) 4.39665 0.196232
\(503\) 22.4963 1.00306 0.501531 0.865140i \(-0.332770\pi\)
0.501531 + 0.865140i \(0.332770\pi\)
\(504\) −4.42964 −0.197312
\(505\) 12.7601 0.567819
\(506\) −3.98353 −0.177090
\(507\) −24.6209 −1.09345
\(508\) 24.3412 1.07997
\(509\) 11.4434 0.507222 0.253611 0.967306i \(-0.418382\pi\)
0.253611 + 0.967306i \(0.418382\pi\)
\(510\) −6.20039 −0.274558
\(511\) −21.3467 −0.944321
\(512\) 22.8760 1.01098
\(513\) 7.15267 0.315798
\(514\) 0.318997 0.0140703
\(515\) 10.5686 0.465706
\(516\) −23.3782 −1.02917
\(517\) 12.8789 0.566415
\(518\) −7.24085 −0.318145
\(519\) 21.2481 0.932687
\(520\) −13.2326 −0.580290
\(521\) −6.38668 −0.279805 −0.139903 0.990165i \(-0.544679\pi\)
−0.139903 + 0.990165i \(0.544679\pi\)
\(522\) 0.471737 0.0206474
\(523\) 34.8404 1.52347 0.761733 0.647891i \(-0.224349\pi\)
0.761733 + 0.647891i \(0.224349\pi\)
\(524\) −29.9772 −1.30956
\(525\) −20.7412 −0.905222
\(526\) 5.01332 0.218591
\(527\) 43.3260 1.88731
\(528\) −11.8671 −0.516451
\(529\) −10.3788 −0.451251
\(530\) −3.78916 −0.164591
\(531\) 5.35567 0.232416
\(532\) 11.2734 0.488762
\(533\) 27.8199 1.20501
\(534\) −9.43279 −0.408197
\(535\) −21.9348 −0.948324
\(536\) −24.5913 −1.06218
\(537\) −22.5962 −0.975099
\(538\) 9.05293 0.390299
\(539\) 42.4809 1.82978
\(540\) −15.1379 −0.651430
\(541\) −34.2589 −1.47291 −0.736453 0.676489i \(-0.763501\pi\)
−0.736453 + 0.676489i \(0.763501\pi\)
\(542\) −8.82386 −0.379017
\(543\) −9.24580 −0.396775
\(544\) 27.8844 1.19554
\(545\) −5.47055 −0.234333
\(546\) 17.4504 0.746807
\(547\) −21.6616 −0.926184 −0.463092 0.886310i \(-0.653260\pi\)
−0.463092 + 0.886310i \(0.653260\pi\)
\(548\) 35.0390 1.49679
\(549\) −3.83110 −0.163508
\(550\) −3.08088 −0.131369
\(551\) −2.52411 −0.107531
\(552\) −9.12895 −0.388554
\(553\) −42.6449 −1.81345
\(554\) 3.54582 0.150647
\(555\) −8.15556 −0.346184
\(556\) 9.23980 0.391855
\(557\) −25.7714 −1.09197 −0.545985 0.837795i \(-0.683844\pi\)
−0.545985 + 0.837795i \(0.683844\pi\)
\(558\) −1.69868 −0.0719110
\(559\) −44.2173 −1.87019
\(560\) −21.1644 −0.894358
\(561\) −24.9269 −1.05241
\(562\) 5.98106 0.252296
\(563\) 20.5069 0.864262 0.432131 0.901811i \(-0.357762\pi\)
0.432131 + 0.901811i \(0.357762\pi\)
\(564\) 14.0381 0.591112
\(565\) 13.6644 0.574864
\(566\) 13.1318 0.551972
\(567\) 33.8888 1.42320
\(568\) 9.65424 0.405083
\(569\) −44.5631 −1.86818 −0.934092 0.357032i \(-0.883789\pi\)
−0.934092 + 0.357032i \(0.883789\pi\)
\(570\) −1.30074 −0.0544821
\(571\) 28.8727 1.20829 0.604143 0.796876i \(-0.293515\pi\)
0.604143 + 0.796876i \(0.293515\pi\)
\(572\) −25.3030 −1.05797
\(573\) −34.8177 −1.45453
\(574\) −10.8033 −0.450921
\(575\) 9.76130 0.407075
\(576\) 2.16323 0.0901348
\(577\) −12.2296 −0.509124 −0.254562 0.967056i \(-0.581931\pi\)
−0.254562 + 0.967056i \(0.581931\pi\)
\(578\) 8.88301 0.369484
\(579\) 20.0381 0.832756
\(580\) 5.34201 0.221815
\(581\) −5.61528 −0.232961
\(582\) 3.40249 0.141038
\(583\) −15.2332 −0.630896
\(584\) −7.26646 −0.300688
\(585\) −4.48839 −0.185572
\(586\) −11.8969 −0.491455
\(587\) −17.2501 −0.711988 −0.355994 0.934488i \(-0.615858\pi\)
−0.355994 + 0.934488i \(0.615858\pi\)
\(588\) 46.3045 1.90956
\(589\) 9.08911 0.374510
\(590\) −6.21287 −0.255780
\(591\) −2.53944 −0.104459
\(592\) 10.1517 0.417234
\(593\) 35.4901 1.45740 0.728702 0.684831i \(-0.240124\pi\)
0.728702 + 0.684831i \(0.240124\pi\)
\(594\) 6.23429 0.255796
\(595\) −44.4557 −1.82250
\(596\) −28.3674 −1.16197
\(597\) −18.8476 −0.771381
\(598\) −8.21255 −0.335836
\(599\) −27.9759 −1.14306 −0.571532 0.820580i \(-0.693651\pi\)
−0.571532 + 0.820580i \(0.693651\pi\)
\(600\) −7.06037 −0.288238
\(601\) 3.04309 0.124130 0.0620652 0.998072i \(-0.480231\pi\)
0.0620652 + 0.998072i \(0.480231\pi\)
\(602\) 17.1709 0.699832
\(603\) −8.34114 −0.339677
\(604\) −27.0365 −1.10010
\(605\) −6.35541 −0.258384
\(606\) −5.72805 −0.232686
\(607\) −18.9064 −0.767387 −0.383694 0.923460i \(-0.625348\pi\)
−0.383694 + 0.923460i \(0.625348\pi\)
\(608\) 5.84971 0.237237
\(609\) −14.8111 −0.600175
\(610\) 4.44429 0.179944
\(611\) 26.5516 1.07416
\(612\) 6.20465 0.250808
\(613\) 44.2346 1.78662 0.893309 0.449442i \(-0.148377\pi\)
0.893309 + 0.449442i \(0.148377\pi\)
\(614\) −5.90426 −0.238276
\(615\) −12.1680 −0.490663
\(616\) 20.6584 0.832349
\(617\) −1.91143 −0.0769511 −0.0384756 0.999260i \(-0.512250\pi\)
−0.0384756 + 0.999260i \(0.512250\pi\)
\(618\) −4.74424 −0.190841
\(619\) 1.00000 0.0401934
\(620\) −19.2361 −0.772541
\(621\) −19.7524 −0.792637
\(622\) −0.0739825 −0.00296643
\(623\) −67.6314 −2.70960
\(624\) −24.4656 −0.979408
\(625\) −3.71246 −0.148499
\(626\) −7.56937 −0.302533
\(627\) −5.22926 −0.208836
\(628\) −30.7491 −1.22702
\(629\) 21.3237 0.850231
\(630\) 1.74297 0.0694417
\(631\) −11.2642 −0.448419 −0.224210 0.974541i \(-0.571980\pi\)
−0.224210 + 0.974541i \(0.571980\pi\)
\(632\) −14.5164 −0.577432
\(633\) 32.9201 1.30846
\(634\) −0.742652 −0.0294945
\(635\) −20.1367 −0.799100
\(636\) −16.6043 −0.658404
\(637\) 87.5798 3.47004
\(638\) −2.20002 −0.0870996
\(639\) 3.27463 0.129542
\(640\) −16.1580 −0.638701
\(641\) 48.5425 1.91731 0.958657 0.284565i \(-0.0918490\pi\)
0.958657 + 0.284565i \(0.0918490\pi\)
\(642\) 9.84656 0.388613
\(643\) −6.33981 −0.250018 −0.125009 0.992156i \(-0.539896\pi\)
−0.125009 + 0.992156i \(0.539896\pi\)
\(644\) −31.1319 −1.22677
\(645\) 19.3400 0.761512
\(646\) 3.40094 0.133808
\(647\) 5.36992 0.211113 0.105557 0.994413i \(-0.466338\pi\)
0.105557 + 0.994413i \(0.466338\pi\)
\(648\) 11.5358 0.453170
\(649\) −24.9771 −0.980435
\(650\) −6.35162 −0.249131
\(651\) 53.3335 2.09030
\(652\) 28.9416 1.13344
\(653\) 11.7733 0.460724 0.230362 0.973105i \(-0.426009\pi\)
0.230362 + 0.973105i \(0.426009\pi\)
\(654\) 2.45574 0.0960270
\(655\) 24.7991 0.968982
\(656\) 15.1463 0.591364
\(657\) −2.46471 −0.0961577
\(658\) −10.3108 −0.401955
\(659\) 0.123206 0.00479943 0.00239972 0.999997i \(-0.499236\pi\)
0.00239972 + 0.999997i \(0.499236\pi\)
\(660\) 11.0672 0.430789
\(661\) 9.04712 0.351892 0.175946 0.984400i \(-0.443702\pi\)
0.175946 + 0.984400i \(0.443702\pi\)
\(662\) 10.1425 0.394201
\(663\) −51.3899 −1.99582
\(664\) −1.91145 −0.0741788
\(665\) −9.32609 −0.361650
\(666\) −0.836038 −0.0323958
\(667\) 6.97044 0.269896
\(668\) −18.0199 −0.697211
\(669\) 3.23611 0.125115
\(670\) 9.67617 0.373823
\(671\) 17.8670 0.689747
\(672\) 34.3252 1.32412
\(673\) −6.36878 −0.245498 −0.122749 0.992438i \(-0.539171\pi\)
−0.122749 + 0.992438i \(0.539171\pi\)
\(674\) −3.45812 −0.133202
\(675\) −15.2766 −0.587996
\(676\) −28.5812 −1.09928
\(677\) 13.5905 0.522326 0.261163 0.965295i \(-0.415894\pi\)
0.261163 + 0.965295i \(0.415894\pi\)
\(678\) −6.13396 −0.235573
\(679\) 24.3952 0.936203
\(680\) −15.1328 −0.580317
\(681\) −2.56930 −0.0984556
\(682\) 7.92209 0.303352
\(683\) −33.0393 −1.26422 −0.632108 0.774881i \(-0.717810\pi\)
−0.632108 + 0.774881i \(0.717810\pi\)
\(684\) 1.30164 0.0497693
\(685\) −28.9866 −1.10752
\(686\) −19.4334 −0.741969
\(687\) 19.8617 0.757770
\(688\) −24.0737 −0.917802
\(689\) −31.4052 −1.19644
\(690\) 3.59206 0.136747
\(691\) 47.4035 1.80331 0.901657 0.432453i \(-0.142352\pi\)
0.901657 + 0.432453i \(0.142352\pi\)
\(692\) 24.6659 0.937656
\(693\) 7.00712 0.266179
\(694\) −5.06386 −0.192221
\(695\) −7.64378 −0.289945
\(696\) −5.04173 −0.191106
\(697\) 31.8148 1.20507
\(698\) 5.11700 0.193681
\(699\) −39.3107 −1.48687
\(700\) −24.0775 −0.910044
\(701\) −2.90566 −0.109745 −0.0548726 0.998493i \(-0.517475\pi\)
−0.0548726 + 0.998493i \(0.517475\pi\)
\(702\) 12.8528 0.485097
\(703\) 4.47337 0.168716
\(704\) −10.0886 −0.380228
\(705\) −11.6133 −0.437382
\(706\) 9.68898 0.364650
\(707\) −41.0691 −1.54456
\(708\) −27.2251 −1.02318
\(709\) −27.9104 −1.04820 −0.524099 0.851657i \(-0.675598\pi\)
−0.524099 + 0.851657i \(0.675598\pi\)
\(710\) −3.79874 −0.142564
\(711\) −4.92384 −0.184658
\(712\) −23.0219 −0.862782
\(713\) −25.1000 −0.940001
\(714\) 19.9562 0.746842
\(715\) 20.9323 0.782825
\(716\) −26.2309 −0.980294
\(717\) −5.88022 −0.219601
\(718\) −10.7249 −0.400249
\(719\) 25.7321 0.959646 0.479823 0.877365i \(-0.340701\pi\)
0.479823 + 0.877365i \(0.340701\pi\)
\(720\) −2.44367 −0.0910700
\(721\) −34.0153 −1.26680
\(722\) −7.47736 −0.278279
\(723\) 8.86221 0.329589
\(724\) −10.7330 −0.398889
\(725\) 5.39096 0.200215
\(726\) 2.85295 0.105883
\(727\) −46.8285 −1.73677 −0.868386 0.495889i \(-0.834842\pi\)
−0.868386 + 0.495889i \(0.834842\pi\)
\(728\) 42.5898 1.57848
\(729\) 29.9797 1.11036
\(730\) 2.85920 0.105824
\(731\) −50.5667 −1.87028
\(732\) 19.4751 0.719821
\(733\) −53.3687 −1.97122 −0.985609 0.169042i \(-0.945933\pi\)
−0.985609 + 0.169042i \(0.945933\pi\)
\(734\) 14.2238 0.525009
\(735\) −38.3062 −1.41294
\(736\) −16.1542 −0.595453
\(737\) 38.9002 1.43291
\(738\) −1.24736 −0.0459160
\(739\) 4.94427 0.181878 0.0909390 0.995856i \(-0.471013\pi\)
0.0909390 + 0.995856i \(0.471013\pi\)
\(740\) −9.46740 −0.348029
\(741\) −10.7808 −0.396042
\(742\) 12.1956 0.447714
\(743\) 6.46500 0.237178 0.118589 0.992943i \(-0.462163\pi\)
0.118589 + 0.992943i \(0.462163\pi\)
\(744\) 18.1548 0.665589
\(745\) 23.4674 0.859780
\(746\) −3.96783 −0.145272
\(747\) −0.648348 −0.0237218
\(748\) −28.9364 −1.05802
\(749\) 70.5980 2.57960
\(750\) 7.83359 0.286042
\(751\) 17.5196 0.639299 0.319649 0.947536i \(-0.396435\pi\)
0.319649 + 0.947536i \(0.396435\pi\)
\(752\) 14.4558 0.527148
\(753\) −15.9384 −0.580829
\(754\) −4.53562 −0.165178
\(755\) 22.3664 0.813997
\(756\) 48.7219 1.77200
\(757\) 22.6591 0.823560 0.411780 0.911283i \(-0.364907\pi\)
0.411780 + 0.911283i \(0.364907\pi\)
\(758\) 2.24546 0.0815587
\(759\) 14.4408 0.524169
\(760\) −3.17462 −0.115156
\(761\) 34.8860 1.26462 0.632308 0.774717i \(-0.282108\pi\)
0.632308 + 0.774717i \(0.282108\pi\)
\(762\) 9.03939 0.327463
\(763\) 17.6072 0.637424
\(764\) −40.4183 −1.46228
\(765\) −5.13291 −0.185581
\(766\) −5.31660 −0.192096
\(767\) −51.4934 −1.85932
\(768\) −4.86979 −0.175723
\(769\) −9.05317 −0.326466 −0.163233 0.986588i \(-0.552192\pi\)
−0.163233 + 0.986588i \(0.552192\pi\)
\(770\) −8.12864 −0.292936
\(771\) −1.15640 −0.0416469
\(772\) 23.2613 0.837192
\(773\) 25.6348 0.922020 0.461010 0.887395i \(-0.347487\pi\)
0.461010 + 0.887395i \(0.347487\pi\)
\(774\) 1.98257 0.0712621
\(775\) −19.4124 −0.697314
\(776\) 8.30420 0.298103
\(777\) 26.2490 0.941678
\(778\) −7.21548 −0.258688
\(779\) 6.67423 0.239129
\(780\) 22.8164 0.816957
\(781\) −15.2718 −0.546466
\(782\) −9.39185 −0.335852
\(783\) −10.9088 −0.389850
\(784\) 47.6821 1.70293
\(785\) 25.4377 0.907910
\(786\) −11.1324 −0.397078
\(787\) 0.199605 0.00711515 0.00355758 0.999994i \(-0.498868\pi\)
0.00355758 + 0.999994i \(0.498868\pi\)
\(788\) −2.94792 −0.105015
\(789\) −18.1739 −0.647009
\(790\) 5.71192 0.203221
\(791\) −43.9794 −1.56373
\(792\) 2.38524 0.0847559
\(793\) 36.8350 1.30805
\(794\) 10.2540 0.363902
\(795\) 13.7362 0.487173
\(796\) −21.8793 −0.775491
\(797\) −22.5822 −0.799904 −0.399952 0.916536i \(-0.630973\pi\)
−0.399952 + 0.916536i \(0.630973\pi\)
\(798\) 4.18649 0.148200
\(799\) 30.3643 1.07421
\(800\) −12.4937 −0.441720
\(801\) −7.80881 −0.275911
\(802\) −1.23326 −0.0435478
\(803\) 11.4946 0.405636
\(804\) 42.4015 1.49539
\(805\) 25.7544 0.907723
\(806\) 16.3324 0.575284
\(807\) −32.8180 −1.15525
\(808\) −13.9800 −0.491815
\(809\) −2.59131 −0.0911055 −0.0455527 0.998962i \(-0.514505\pi\)
−0.0455527 + 0.998962i \(0.514505\pi\)
\(810\) −4.53911 −0.159488
\(811\) −36.4445 −1.27974 −0.639870 0.768483i \(-0.721012\pi\)
−0.639870 + 0.768483i \(0.721012\pi\)
\(812\) −17.1935 −0.603373
\(813\) 31.9876 1.12186
\(814\) 3.89900 0.136660
\(815\) −23.9424 −0.838667
\(816\) −27.9788 −0.979454
\(817\) −10.6081 −0.371130
\(818\) −2.89681 −0.101285
\(819\) 14.4461 0.504786
\(820\) −14.1253 −0.493277
\(821\) 1.22959 0.0429129 0.0214565 0.999770i \(-0.493170\pi\)
0.0214565 + 0.999770i \(0.493170\pi\)
\(822\) 13.0121 0.453851
\(823\) 19.0447 0.663858 0.331929 0.943304i \(-0.392301\pi\)
0.331929 + 0.943304i \(0.392301\pi\)
\(824\) −11.5789 −0.403370
\(825\) 11.1686 0.388840
\(826\) 19.9964 0.695763
\(827\) −1.35730 −0.0471980 −0.0235990 0.999722i \(-0.507512\pi\)
−0.0235990 + 0.999722i \(0.507512\pi\)
\(828\) −3.59453 −0.124919
\(829\) 9.29337 0.322772 0.161386 0.986891i \(-0.448404\pi\)
0.161386 + 0.986891i \(0.448404\pi\)
\(830\) 0.752118 0.0261064
\(831\) −12.8541 −0.445902
\(832\) −20.7989 −0.721073
\(833\) 100.156 3.47020
\(834\) 3.43131 0.118816
\(835\) 14.9073 0.515888
\(836\) −6.07040 −0.209949
\(837\) 39.2818 1.35778
\(838\) −16.9508 −0.585555
\(839\) 41.4301 1.43033 0.715164 0.698957i \(-0.246352\pi\)
0.715164 + 0.698957i \(0.246352\pi\)
\(840\) −18.6282 −0.642734
\(841\) −25.1504 −0.867254
\(842\) 2.36497 0.0815023
\(843\) −21.6821 −0.746772
\(844\) 38.2154 1.31543
\(845\) 23.6443 0.813390
\(846\) −1.19049 −0.0409300
\(847\) 20.4552 0.702847
\(848\) −17.0983 −0.587159
\(849\) −47.6046 −1.63378
\(850\) −7.26369 −0.249143
\(851\) −12.3534 −0.423469
\(852\) −16.6463 −0.570293
\(853\) −36.7516 −1.25835 −0.629176 0.777263i \(-0.716607\pi\)
−0.629176 + 0.777263i \(0.716607\pi\)
\(854\) −14.3041 −0.489477
\(855\) −1.07680 −0.0368259
\(856\) 24.0317 0.821388
\(857\) 28.9515 0.988963 0.494481 0.869188i \(-0.335358\pi\)
0.494481 + 0.869188i \(0.335358\pi\)
\(858\) −9.39655 −0.320793
\(859\) 41.6194 1.42004 0.710018 0.704184i \(-0.248687\pi\)
0.710018 + 0.704184i \(0.248687\pi\)
\(860\) 22.4509 0.765569
\(861\) 39.1634 1.33468
\(862\) −2.36144 −0.0804311
\(863\) −28.4643 −0.968937 −0.484469 0.874809i \(-0.660987\pi\)
−0.484469 + 0.874809i \(0.660987\pi\)
\(864\) 25.2816 0.860098
\(865\) −20.4053 −0.693800
\(866\) −10.9279 −0.371345
\(867\) −32.2021 −1.09364
\(868\) 61.9123 2.10144
\(869\) 22.9631 0.778970
\(870\) 1.98382 0.0672577
\(871\) 80.1978 2.71740
\(872\) 5.99353 0.202967
\(873\) 2.81671 0.0953310
\(874\) −1.97026 −0.0666451
\(875\) 56.1654 1.89874
\(876\) 12.5292 0.423322
\(877\) 4.10040 0.138461 0.0692303 0.997601i \(-0.477946\pi\)
0.0692303 + 0.997601i \(0.477946\pi\)
\(878\) −3.84591 −0.129793
\(879\) 43.1277 1.45466
\(880\) 11.3964 0.384174
\(881\) 23.8628 0.803958 0.401979 0.915649i \(-0.368322\pi\)
0.401979 + 0.915649i \(0.368322\pi\)
\(882\) −3.92682 −0.132223
\(883\) −13.3019 −0.447645 −0.223822 0.974630i \(-0.571854\pi\)
−0.223822 + 0.974630i \(0.571854\pi\)
\(884\) −59.6561 −2.00645
\(885\) 22.5225 0.757085
\(886\) −17.0146 −0.571618
\(887\) −21.2442 −0.713310 −0.356655 0.934236i \(-0.616083\pi\)
−0.356655 + 0.934236i \(0.616083\pi\)
\(888\) 8.93523 0.299847
\(889\) 64.8108 2.17369
\(890\) 9.05864 0.303646
\(891\) −18.2482 −0.611338
\(892\) 3.75665 0.125782
\(893\) 6.36995 0.213162
\(894\) −10.5346 −0.352329
\(895\) 21.7000 0.725350
\(896\) 52.0052 1.73737
\(897\) 29.7716 0.994044
\(898\) −3.26180 −0.108848
\(899\) −13.8622 −0.462330
\(900\) −2.78002 −0.0926674
\(901\) −35.9149 −1.19650
\(902\) 5.81728 0.193694
\(903\) −62.2467 −2.07144
\(904\) −14.9707 −0.497917
\(905\) 8.87907 0.295150
\(906\) −10.0403 −0.333567
\(907\) −29.8311 −0.990525 −0.495262 0.868743i \(-0.664928\pi\)
−0.495262 + 0.868743i \(0.664928\pi\)
\(908\) −2.98257 −0.0989802
\(909\) −4.74189 −0.157278
\(910\) −16.7582 −0.555530
\(911\) 26.4575 0.876578 0.438289 0.898834i \(-0.355585\pi\)
0.438289 + 0.898834i \(0.355585\pi\)
\(912\) −5.86950 −0.194359
\(913\) 3.02367 0.100069
\(914\) −17.4887 −0.578475
\(915\) −16.1111 −0.532617
\(916\) 23.0565 0.761807
\(917\) −79.8170 −2.63579
\(918\) 14.6984 0.485119
\(919\) 48.0450 1.58486 0.792429 0.609964i \(-0.208816\pi\)
0.792429 + 0.609964i \(0.208816\pi\)
\(920\) 8.76686 0.289035
\(921\) 21.4037 0.705276
\(922\) −7.16058 −0.235821
\(923\) −31.4847 −1.03633
\(924\) −35.6202 −1.17182
\(925\) −9.55416 −0.314139
\(926\) −4.61498 −0.151658
\(927\) −3.92746 −0.128995
\(928\) −8.92164 −0.292867
\(929\) −17.1784 −0.563605 −0.281803 0.959472i \(-0.590932\pi\)
−0.281803 + 0.959472i \(0.590932\pi\)
\(930\) −7.14356 −0.234247
\(931\) 21.0111 0.688612
\(932\) −45.6339 −1.49479
\(933\) 0.268196 0.00878035
\(934\) −9.06140 −0.296498
\(935\) 23.9381 0.782861
\(936\) 4.91748 0.160733
\(937\) −51.5569 −1.68429 −0.842145 0.539252i \(-0.818707\pi\)
−0.842145 + 0.539252i \(0.818707\pi\)
\(938\) −31.1432 −1.01686
\(939\) 27.4399 0.895469
\(940\) −13.4813 −0.439712
\(941\) 39.2864 1.28070 0.640349 0.768084i \(-0.278790\pi\)
0.640349 + 0.768084i \(0.278790\pi\)
\(942\) −11.4190 −0.372052
\(943\) −18.4312 −0.600202
\(944\) −28.0351 −0.912466
\(945\) −40.3060 −1.31116
\(946\) −9.24604 −0.300615
\(947\) 15.5225 0.504413 0.252206 0.967673i \(-0.418844\pi\)
0.252206 + 0.967673i \(0.418844\pi\)
\(948\) 25.0299 0.812934
\(949\) 23.6976 0.769255
\(950\) −1.52381 −0.0494388
\(951\) 2.69221 0.0873009
\(952\) 48.7056 1.57856
\(953\) 22.1294 0.716842 0.358421 0.933560i \(-0.383315\pi\)
0.358421 + 0.933560i \(0.383315\pi\)
\(954\) 1.40812 0.0455895
\(955\) 33.4367 1.08199
\(956\) −6.82607 −0.220771
\(957\) 7.97536 0.257807
\(958\) 5.11508 0.165261
\(959\) 93.2947 3.01264
\(960\) 9.09716 0.293609
\(961\) 18.9165 0.610211
\(962\) 8.03828 0.259164
\(963\) 8.15134 0.262673
\(964\) 10.2877 0.331345
\(965\) −19.2433 −0.619464
\(966\) −11.5612 −0.371975
\(967\) −9.97343 −0.320724 −0.160362 0.987058i \(-0.551266\pi\)
−0.160362 + 0.987058i \(0.551266\pi\)
\(968\) 6.96298 0.223799
\(969\) −12.3289 −0.396060
\(970\) −3.26753 −0.104914
\(971\) −55.8372 −1.79190 −0.895951 0.444154i \(-0.853504\pi\)
−0.895951 + 0.444154i \(0.853504\pi\)
\(972\) 10.3691 0.332589
\(973\) 24.6018 0.788699
\(974\) 0.226952 0.00727200
\(975\) 23.0254 0.737405
\(976\) 20.0545 0.641930
\(977\) −26.9677 −0.862772 −0.431386 0.902167i \(-0.641975\pi\)
−0.431386 + 0.902167i \(0.641975\pi\)
\(978\) 10.7478 0.343677
\(979\) 36.4177 1.16391
\(980\) −44.4678 −1.42047
\(981\) 2.03295 0.0649071
\(982\) 11.3281 0.361493
\(983\) 25.7677 0.821862 0.410931 0.911666i \(-0.365204\pi\)
0.410931 + 0.911666i \(0.365204\pi\)
\(984\) 13.3313 0.424986
\(985\) 2.43872 0.0777040
\(986\) −5.18692 −0.165185
\(987\) 37.3779 1.18975
\(988\) −12.5149 −0.398152
\(989\) 29.2947 0.931518
\(990\) −0.938544 −0.0298289
\(991\) −45.7646 −1.45376 −0.726881 0.686763i \(-0.759031\pi\)
−0.726881 + 0.686763i \(0.759031\pi\)
\(992\) 32.1261 1.02000
\(993\) −36.7680 −1.16680
\(994\) 12.2264 0.387799
\(995\) 18.1000 0.573809
\(996\) 3.29582 0.104432
\(997\) −19.9914 −0.633133 −0.316567 0.948570i \(-0.602530\pi\)
−0.316567 + 0.948570i \(0.602530\pi\)
\(998\) 8.26202 0.261530
\(999\) 19.3333 0.611677
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 \(a_p\))