Properties

Label 4017.2.a.j.1.1
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 1.1
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} -9.62067 q^{10} +0.122675 q^{11} -5.03939 q^{12} +1.00000 q^{13} +4.50300 q^{14} -3.62608 q^{15} +11.3167 q^{16} +1.64880 q^{17} -2.65319 q^{18} +2.48476 q^{19} +18.2733 q^{20} +1.69720 q^{21} -0.325481 q^{22} +7.71361 q^{23} +8.06407 q^{24} +8.14847 q^{25} -2.65319 q^{26} -1.00000 q^{27} -8.55288 q^{28} -8.37984 q^{29} +9.62067 q^{30} -5.04198 q^{31} -13.8971 q^{32} -0.122675 q^{33} -4.37458 q^{34} -6.15420 q^{35} +5.03939 q^{36} +7.37109 q^{37} -6.59252 q^{38} -1.00000 q^{39} -29.2410 q^{40} -5.29852 q^{41} -4.50300 q^{42} +5.82960 q^{43} +0.618209 q^{44} +3.62608 q^{45} -20.4656 q^{46} +11.9749 q^{47} -11.3167 q^{48} -4.11950 q^{49} -21.6194 q^{50} -1.64880 q^{51} +5.03939 q^{52} -3.27337 q^{53} +2.65319 q^{54} +0.444831 q^{55} +13.6864 q^{56} -2.48476 q^{57} +22.2333 q^{58} +9.14392 q^{59} -18.2733 q^{60} -11.7962 q^{61} +13.3773 q^{62} -1.69720 q^{63} +14.2383 q^{64} +3.62608 q^{65} +0.325481 q^{66} -12.8241 q^{67} +8.30897 q^{68} -7.71361 q^{69} +16.3282 q^{70} +12.5788 q^{71} -8.06407 q^{72} -6.39645 q^{73} -19.5569 q^{74} -8.14847 q^{75} +12.5217 q^{76} -0.208205 q^{77} +2.65319 q^{78} +9.16008 q^{79} +41.0352 q^{80} +1.00000 q^{81} +14.0579 q^{82} +16.7645 q^{83} +8.55288 q^{84} +5.97870 q^{85} -15.4670 q^{86} +8.37984 q^{87} -0.989263 q^{88} +1.34263 q^{89} -9.62067 q^{90} -1.69720 q^{91} +38.8719 q^{92} +5.04198 q^{93} -31.7716 q^{94} +9.00994 q^{95} +13.8971 q^{96} +8.30957 q^{97} +10.9298 q^{98} +0.122675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65319 −1.87609 −0.938043 0.346520i \(-0.887363\pi\)
−0.938043 + 0.346520i \(0.887363\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.03939 2.51970
\(5\) 3.62608 1.62163 0.810817 0.585300i \(-0.199023\pi\)
0.810817 + 0.585300i \(0.199023\pi\)
\(6\) 2.65319 1.08316
\(7\) −1.69720 −0.641483 −0.320741 0.947167i \(-0.603932\pi\)
−0.320741 + 0.947167i \(0.603932\pi\)
\(8\) −8.06407 −2.85108
\(9\) 1.00000 0.333333
\(10\) −9.62067 −3.04232
\(11\) 0.122675 0.0369880 0.0184940 0.999829i \(-0.494113\pi\)
0.0184940 + 0.999829i \(0.494113\pi\)
\(12\) −5.03939 −1.45475
\(13\) 1.00000 0.277350
\(14\) 4.50300 1.20348
\(15\) −3.62608 −0.936250
\(16\) 11.3167 2.82917
\(17\) 1.64880 0.399894 0.199947 0.979807i \(-0.435923\pi\)
0.199947 + 0.979807i \(0.435923\pi\)
\(18\) −2.65319 −0.625362
\(19\) 2.48476 0.570043 0.285021 0.958521i \(-0.407999\pi\)
0.285021 + 0.958521i \(0.407999\pi\)
\(20\) 18.2733 4.08602
\(21\) 1.69720 0.370360
\(22\) −0.325481 −0.0693927
\(23\) 7.71361 1.60840 0.804200 0.594359i \(-0.202594\pi\)
0.804200 + 0.594359i \(0.202594\pi\)
\(24\) 8.06407 1.64607
\(25\) 8.14847 1.62969
\(26\) −2.65319 −0.520332
\(27\) −1.00000 −0.192450
\(28\) −8.55288 −1.61634
\(29\) −8.37984 −1.55610 −0.778049 0.628204i \(-0.783790\pi\)
−0.778049 + 0.628204i \(0.783790\pi\)
\(30\) 9.62067 1.75649
\(31\) −5.04198 −0.905567 −0.452783 0.891621i \(-0.649569\pi\)
−0.452783 + 0.891621i \(0.649569\pi\)
\(32\) −13.8971 −2.45669
\(33\) −0.122675 −0.0213550
\(34\) −4.37458 −0.750235
\(35\) −6.15420 −1.04025
\(36\) 5.03939 0.839899
\(37\) 7.37109 1.21180 0.605900 0.795541i \(-0.292813\pi\)
0.605900 + 0.795541i \(0.292813\pi\)
\(38\) −6.59252 −1.06945
\(39\) −1.00000 −0.160128
\(40\) −29.2410 −4.62341
\(41\) −5.29852 −0.827489 −0.413745 0.910393i \(-0.635779\pi\)
−0.413745 + 0.910393i \(0.635779\pi\)
\(42\) −4.50300 −0.694827
\(43\) 5.82960 0.889006 0.444503 0.895777i \(-0.353380\pi\)
0.444503 + 0.895777i \(0.353380\pi\)
\(44\) 0.618209 0.0931986
\(45\) 3.62608 0.540544
\(46\) −20.4656 −3.01749
\(47\) 11.9749 1.74672 0.873359 0.487077i \(-0.161937\pi\)
0.873359 + 0.487077i \(0.161937\pi\)
\(48\) −11.3167 −1.63342
\(49\) −4.11950 −0.588500
\(50\) −21.6194 −3.05745
\(51\) −1.64880 −0.230879
\(52\) 5.03939 0.698838
\(53\) −3.27337 −0.449633 −0.224816 0.974401i \(-0.572178\pi\)
−0.224816 + 0.974401i \(0.572178\pi\)
\(54\) 2.65319 0.361053
\(55\) 0.444831 0.0599810
\(56\) 13.6864 1.82892
\(57\) −2.48476 −0.329114
\(58\) 22.2333 2.91937
\(59\) 9.14392 1.19044 0.595218 0.803564i \(-0.297066\pi\)
0.595218 + 0.803564i \(0.297066\pi\)
\(60\) −18.2733 −2.35907
\(61\) −11.7962 −1.51035 −0.755177 0.655521i \(-0.772449\pi\)
−0.755177 + 0.655521i \(0.772449\pi\)
\(62\) 13.3773 1.69892
\(63\) −1.69720 −0.213828
\(64\) 14.2383 1.77979
\(65\) 3.62608 0.449760
\(66\) 0.325481 0.0400639
\(67\) −12.8241 −1.56672 −0.783359 0.621569i \(-0.786495\pi\)
−0.783359 + 0.621569i \(0.786495\pi\)
\(68\) 8.30897 1.00761
\(69\) −7.71361 −0.928610
\(70\) 16.3282 1.95160
\(71\) 12.5788 1.49283 0.746413 0.665483i \(-0.231775\pi\)
0.746413 + 0.665483i \(0.231775\pi\)
\(72\) −8.06407 −0.950360
\(73\) −6.39645 −0.748648 −0.374324 0.927298i \(-0.622125\pi\)
−0.374324 + 0.927298i \(0.622125\pi\)
\(74\) −19.5569 −2.27344
\(75\) −8.14847 −0.940905
\(76\) 12.5217 1.43633
\(77\) −0.208205 −0.0237272
\(78\) 2.65319 0.300414
\(79\) 9.16008 1.03059 0.515295 0.857013i \(-0.327682\pi\)
0.515295 + 0.857013i \(0.327682\pi\)
\(80\) 41.0352 4.58788
\(81\) 1.00000 0.111111
\(82\) 14.0579 1.55244
\(83\) 16.7645 1.84014 0.920071 0.391753i \(-0.128131\pi\)
0.920071 + 0.391753i \(0.128131\pi\)
\(84\) 8.55288 0.933195
\(85\) 5.97870 0.648481
\(86\) −15.4670 −1.66785
\(87\) 8.37984 0.898413
\(88\) −0.989263 −0.105456
\(89\) 1.34263 0.142319 0.0711595 0.997465i \(-0.477330\pi\)
0.0711595 + 0.997465i \(0.477330\pi\)
\(90\) −9.62067 −1.01411
\(91\) −1.69720 −0.177915
\(92\) 38.8719 4.05268
\(93\) 5.04198 0.522829
\(94\) −31.7716 −3.27699
\(95\) 9.00994 0.924400
\(96\) 13.8971 1.41837
\(97\) 8.30957 0.843709 0.421854 0.906664i \(-0.361379\pi\)
0.421854 + 0.906664i \(0.361379\pi\)
\(98\) 10.9298 1.10408
\(99\) 0.122675 0.0123293
\(100\) 41.0634 4.10634
\(101\) 13.7971 1.37286 0.686430 0.727196i \(-0.259177\pi\)
0.686430 + 0.727196i \(0.259177\pi\)
\(102\) 4.37458 0.433148
\(103\) −1.00000 −0.0985329
\(104\) −8.06407 −0.790747
\(105\) 6.15420 0.600589
\(106\) 8.68487 0.843549
\(107\) −18.8039 −1.81784 −0.908919 0.416972i \(-0.863091\pi\)
−0.908919 + 0.416972i \(0.863091\pi\)
\(108\) −5.03939 −0.484916
\(109\) 3.01954 0.289220 0.144610 0.989489i \(-0.453807\pi\)
0.144610 + 0.989489i \(0.453807\pi\)
\(110\) −1.18022 −0.112530
\(111\) −7.37109 −0.699633
\(112\) −19.2067 −1.81486
\(113\) 16.5599 1.55782 0.778911 0.627134i \(-0.215772\pi\)
0.778911 + 0.627134i \(0.215772\pi\)
\(114\) 6.59252 0.617446
\(115\) 27.9702 2.60823
\(116\) −42.2293 −3.92089
\(117\) 1.00000 0.0924500
\(118\) −24.2605 −2.23336
\(119\) −2.79836 −0.256525
\(120\) 29.2410 2.66932
\(121\) −10.9850 −0.998632
\(122\) 31.2976 2.83355
\(123\) 5.29852 0.477751
\(124\) −25.4085 −2.28175
\(125\) 11.4166 1.02113
\(126\) 4.50300 0.401159
\(127\) 8.09714 0.718505 0.359252 0.933240i \(-0.383032\pi\)
0.359252 + 0.933240i \(0.383032\pi\)
\(128\) −9.98254 −0.882341
\(129\) −5.82960 −0.513268
\(130\) −9.62067 −0.843788
\(131\) −6.12661 −0.535284 −0.267642 0.963518i \(-0.586244\pi\)
−0.267642 + 0.963518i \(0.586244\pi\)
\(132\) −0.618209 −0.0538082
\(133\) −4.21714 −0.365673
\(134\) 34.0248 2.93930
\(135\) −3.62608 −0.312083
\(136\) −13.2961 −1.14013
\(137\) 16.4654 1.40673 0.703366 0.710828i \(-0.251680\pi\)
0.703366 + 0.710828i \(0.251680\pi\)
\(138\) 20.4656 1.74215
\(139\) 6.84474 0.580563 0.290282 0.956941i \(-0.406251\pi\)
0.290282 + 0.956941i \(0.406251\pi\)
\(140\) −31.0134 −2.62111
\(141\) −11.9749 −1.00847
\(142\) −33.3738 −2.80067
\(143\) 0.122675 0.0102586
\(144\) 11.3167 0.943057
\(145\) −30.3860 −2.52342
\(146\) 16.9710 1.40453
\(147\) 4.11950 0.339771
\(148\) 37.1458 3.05337
\(149\) −9.62736 −0.788704 −0.394352 0.918959i \(-0.629031\pi\)
−0.394352 + 0.918959i \(0.629031\pi\)
\(150\) 21.6194 1.76522
\(151\) −22.5090 −1.83175 −0.915877 0.401458i \(-0.868504\pi\)
−0.915877 + 0.401458i \(0.868504\pi\)
\(152\) −20.0373 −1.62524
\(153\) 1.64880 0.133298
\(154\) 0.552407 0.0445142
\(155\) −18.2826 −1.46850
\(156\) −5.03939 −0.403474
\(157\) −13.9794 −1.11568 −0.557840 0.829948i \(-0.688370\pi\)
−0.557840 + 0.829948i \(0.688370\pi\)
\(158\) −24.3034 −1.93347
\(159\) 3.27337 0.259596
\(160\) −50.3921 −3.98385
\(161\) −13.0916 −1.03176
\(162\) −2.65319 −0.208454
\(163\) 12.7910 1.00187 0.500936 0.865485i \(-0.332989\pi\)
0.500936 + 0.865485i \(0.332989\pi\)
\(164\) −26.7013 −2.08502
\(165\) −0.444831 −0.0346301
\(166\) −44.4793 −3.45226
\(167\) 6.86951 0.531579 0.265789 0.964031i \(-0.414367\pi\)
0.265789 + 0.964031i \(0.414367\pi\)
\(168\) −13.6864 −1.05593
\(169\) 1.00000 0.0769231
\(170\) −15.8626 −1.21661
\(171\) 2.48476 0.190014
\(172\) 29.3776 2.24002
\(173\) −0.853628 −0.0649002 −0.0324501 0.999473i \(-0.510331\pi\)
−0.0324501 + 0.999473i \(0.510331\pi\)
\(174\) −22.2333 −1.68550
\(175\) −13.8296 −1.04542
\(176\) 1.38828 0.104645
\(177\) −9.14392 −0.687299
\(178\) −3.56226 −0.267003
\(179\) 0.172575 0.0128989 0.00644943 0.999979i \(-0.497947\pi\)
0.00644943 + 0.999979i \(0.497947\pi\)
\(180\) 18.2733 1.36201
\(181\) −16.3527 −1.21548 −0.607742 0.794135i \(-0.707924\pi\)
−0.607742 + 0.794135i \(0.707924\pi\)
\(182\) 4.50300 0.333784
\(183\) 11.7962 0.872003
\(184\) −62.2031 −4.58567
\(185\) 26.7282 1.96509
\(186\) −13.3773 −0.980872
\(187\) 0.202268 0.0147913
\(188\) 60.3462 4.40120
\(189\) 1.69720 0.123453
\(190\) −23.9050 −1.73425
\(191\) 4.28492 0.310046 0.155023 0.987911i \(-0.450455\pi\)
0.155023 + 0.987911i \(0.450455\pi\)
\(192\) −14.2383 −1.02756
\(193\) −22.8864 −1.64740 −0.823698 0.567029i \(-0.808093\pi\)
−0.823698 + 0.567029i \(0.808093\pi\)
\(194\) −22.0468 −1.58287
\(195\) −3.62608 −0.259669
\(196\) −20.7598 −1.48284
\(197\) 1.55653 0.110898 0.0554492 0.998462i \(-0.482341\pi\)
0.0554492 + 0.998462i \(0.482341\pi\)
\(198\) −0.325481 −0.0231309
\(199\) 6.78405 0.480908 0.240454 0.970660i \(-0.422704\pi\)
0.240454 + 0.970660i \(0.422704\pi\)
\(200\) −65.7099 −4.64639
\(201\) 12.8241 0.904545
\(202\) −36.6062 −2.57560
\(203\) 14.2223 0.998209
\(204\) −8.30897 −0.581744
\(205\) −19.2129 −1.34188
\(206\) 2.65319 0.184856
\(207\) 7.71361 0.536133
\(208\) 11.3167 0.784671
\(209\) 0.304819 0.0210848
\(210\) −16.3282 −1.12676
\(211\) 16.6781 1.14817 0.574083 0.818797i \(-0.305359\pi\)
0.574083 + 0.818797i \(0.305359\pi\)
\(212\) −16.4958 −1.13294
\(213\) −12.5788 −0.861883
\(214\) 49.8901 3.41042
\(215\) 21.1386 1.44164
\(216\) 8.06407 0.548690
\(217\) 8.55727 0.580905
\(218\) −8.01141 −0.542601
\(219\) 6.39645 0.432232
\(220\) 2.24168 0.151134
\(221\) 1.64880 0.110911
\(222\) 19.5569 1.31257
\(223\) 3.87678 0.259608 0.129804 0.991540i \(-0.458565\pi\)
0.129804 + 0.991540i \(0.458565\pi\)
\(224\) 23.5863 1.57592
\(225\) 8.14847 0.543232
\(226\) −43.9364 −2.92261
\(227\) −29.7814 −1.97666 −0.988332 0.152315i \(-0.951327\pi\)
−0.988332 + 0.152315i \(0.951327\pi\)
\(228\) −12.5217 −0.829268
\(229\) −15.9711 −1.05540 −0.527701 0.849430i \(-0.676946\pi\)
−0.527701 + 0.849430i \(0.676946\pi\)
\(230\) −74.2101 −4.89327
\(231\) 0.208205 0.0136989
\(232\) 67.5756 4.43656
\(233\) 14.3408 0.939497 0.469748 0.882800i \(-0.344345\pi\)
0.469748 + 0.882800i \(0.344345\pi\)
\(234\) −2.65319 −0.173444
\(235\) 43.4219 2.83254
\(236\) 46.0798 2.99954
\(237\) −9.16008 −0.595011
\(238\) 7.42456 0.481263
\(239\) −3.34738 −0.216524 −0.108262 0.994122i \(-0.534529\pi\)
−0.108262 + 0.994122i \(0.534529\pi\)
\(240\) −41.0352 −2.64881
\(241\) 7.97897 0.513971 0.256985 0.966415i \(-0.417271\pi\)
0.256985 + 0.966415i \(0.417271\pi\)
\(242\) 29.1451 1.87352
\(243\) −1.00000 −0.0641500
\(244\) −59.4459 −3.80563
\(245\) −14.9376 −0.954331
\(246\) −14.0579 −0.896302
\(247\) 2.48476 0.158101
\(248\) 40.6589 2.58184
\(249\) −16.7645 −1.06241
\(250\) −30.2904 −1.91574
\(251\) 16.3350 1.03105 0.515527 0.856873i \(-0.327596\pi\)
0.515527 + 0.856873i \(0.327596\pi\)
\(252\) −8.55288 −0.538780
\(253\) 0.946270 0.0594915
\(254\) −21.4832 −1.34798
\(255\) −5.97870 −0.374401
\(256\) −1.99103 −0.124439
\(257\) 5.39908 0.336786 0.168393 0.985720i \(-0.446142\pi\)
0.168393 + 0.985720i \(0.446142\pi\)
\(258\) 15.4670 0.962934
\(259\) −12.5102 −0.777348
\(260\) 18.2733 1.13326
\(261\) −8.37984 −0.518699
\(262\) 16.2550 1.00424
\(263\) 4.35020 0.268245 0.134123 0.990965i \(-0.457178\pi\)
0.134123 + 0.990965i \(0.457178\pi\)
\(264\) 0.989263 0.0608849
\(265\) −11.8695 −0.729139
\(266\) 11.1889 0.686033
\(267\) −1.34263 −0.0821679
\(268\) −64.6259 −3.94765
\(269\) −2.42763 −0.148015 −0.0740076 0.997258i \(-0.523579\pi\)
−0.0740076 + 0.997258i \(0.523579\pi\)
\(270\) 9.62067 0.585495
\(271\) 18.5705 1.12808 0.564038 0.825749i \(-0.309247\pi\)
0.564038 + 0.825749i \(0.309247\pi\)
\(272\) 18.6590 1.13137
\(273\) 1.69720 0.102719
\(274\) −43.6857 −2.63915
\(275\) 0.999617 0.0602792
\(276\) −38.8719 −2.33981
\(277\) 4.53094 0.272238 0.136119 0.990693i \(-0.456537\pi\)
0.136119 + 0.990693i \(0.456537\pi\)
\(278\) −18.1604 −1.08919
\(279\) −5.04198 −0.301856
\(280\) 49.6279 2.96583
\(281\) 18.8843 1.12655 0.563273 0.826271i \(-0.309542\pi\)
0.563273 + 0.826271i \(0.309542\pi\)
\(282\) 31.7716 1.89197
\(283\) 9.24039 0.549284 0.274642 0.961547i \(-0.411441\pi\)
0.274642 + 0.961547i \(0.411441\pi\)
\(284\) 63.3894 3.76147
\(285\) −9.00994 −0.533703
\(286\) −0.325481 −0.0192461
\(287\) 8.99266 0.530820
\(288\) −13.8971 −0.818896
\(289\) −14.2814 −0.840085
\(290\) 80.6197 4.73415
\(291\) −8.30957 −0.487115
\(292\) −32.2342 −1.88637
\(293\) −4.77518 −0.278969 −0.139484 0.990224i \(-0.544545\pi\)
−0.139484 + 0.990224i \(0.544545\pi\)
\(294\) −10.9298 −0.637439
\(295\) 33.1566 1.93045
\(296\) −59.4410 −3.45494
\(297\) −0.122675 −0.00711835
\(298\) 25.5432 1.47968
\(299\) 7.71361 0.446090
\(300\) −41.0634 −2.37079
\(301\) −9.89402 −0.570282
\(302\) 59.7205 3.43653
\(303\) −13.7971 −0.792621
\(304\) 28.1192 1.61275
\(305\) −42.7742 −2.44924
\(306\) −4.37458 −0.250078
\(307\) 24.1332 1.37735 0.688677 0.725068i \(-0.258192\pi\)
0.688677 + 0.725068i \(0.258192\pi\)
\(308\) −1.04923 −0.0597853
\(309\) 1.00000 0.0568880
\(310\) 48.5072 2.75503
\(311\) −1.20829 −0.0685157 −0.0342578 0.999413i \(-0.510907\pi\)
−0.0342578 + 0.999413i \(0.510907\pi\)
\(312\) 8.06407 0.456538
\(313\) 8.52454 0.481835 0.240918 0.970546i \(-0.422552\pi\)
0.240918 + 0.970546i \(0.422552\pi\)
\(314\) 37.0900 2.09311
\(315\) −6.15420 −0.346750
\(316\) 46.1612 2.59677
\(317\) 6.81411 0.382718 0.191359 0.981520i \(-0.438710\pi\)
0.191359 + 0.981520i \(0.438710\pi\)
\(318\) −8.68487 −0.487023
\(319\) −1.02800 −0.0575570
\(320\) 51.6292 2.88616
\(321\) 18.8039 1.04953
\(322\) 34.7344 1.93567
\(323\) 4.09688 0.227957
\(324\) 5.03939 0.279966
\(325\) 8.14847 0.451996
\(326\) −33.9370 −1.87960
\(327\) −3.01954 −0.166981
\(328\) 42.7276 2.35924
\(329\) −20.3238 −1.12049
\(330\) 1.18022 0.0649689
\(331\) 8.88374 0.488295 0.244147 0.969738i \(-0.421492\pi\)
0.244147 + 0.969738i \(0.421492\pi\)
\(332\) 84.4828 4.63660
\(333\) 7.37109 0.403933
\(334\) −18.2261 −0.997287
\(335\) −46.5014 −2.54064
\(336\) 19.2067 1.04781
\(337\) 14.4415 0.786678 0.393339 0.919394i \(-0.371320\pi\)
0.393339 + 0.919394i \(0.371320\pi\)
\(338\) −2.65319 −0.144314
\(339\) −16.5599 −0.899409
\(340\) 30.1290 1.63398
\(341\) −0.618527 −0.0334951
\(342\) −6.59252 −0.356483
\(343\) 18.8721 1.01900
\(344\) −47.0103 −2.53463
\(345\) −27.9702 −1.50586
\(346\) 2.26483 0.121758
\(347\) −19.1942 −1.03040 −0.515200 0.857070i \(-0.672282\pi\)
−0.515200 + 0.857070i \(0.672282\pi\)
\(348\) 42.2293 2.26373
\(349\) 22.0422 1.17989 0.589947 0.807442i \(-0.299149\pi\)
0.589947 + 0.807442i \(0.299149\pi\)
\(350\) 36.6925 1.96130
\(351\) −1.00000 −0.0533761
\(352\) −1.70484 −0.0908681
\(353\) −28.7933 −1.53251 −0.766256 0.642536i \(-0.777882\pi\)
−0.766256 + 0.642536i \(0.777882\pi\)
\(354\) 24.2605 1.28943
\(355\) 45.6117 2.42082
\(356\) 6.76606 0.358601
\(357\) 2.79836 0.148105
\(358\) −0.457873 −0.0241994
\(359\) 10.1538 0.535897 0.267949 0.963433i \(-0.413654\pi\)
0.267949 + 0.963433i \(0.413654\pi\)
\(360\) −29.2410 −1.54114
\(361\) −12.8260 −0.675051
\(362\) 43.3866 2.28035
\(363\) 10.9850 0.576560
\(364\) −8.55288 −0.448292
\(365\) −23.1941 −1.21403
\(366\) −31.2976 −1.63595
\(367\) −18.3419 −0.957441 −0.478721 0.877967i \(-0.658899\pi\)
−0.478721 + 0.877967i \(0.658899\pi\)
\(368\) 87.2925 4.55044
\(369\) −5.29852 −0.275830
\(370\) −70.9148 −3.68668
\(371\) 5.55558 0.288432
\(372\) 25.4085 1.31737
\(373\) −6.57033 −0.340199 −0.170099 0.985427i \(-0.554409\pi\)
−0.170099 + 0.985427i \(0.554409\pi\)
\(374\) −0.536654 −0.0277497
\(375\) −11.4166 −0.589552
\(376\) −96.5664 −4.98003
\(377\) −8.37984 −0.431584
\(378\) −4.50300 −0.231609
\(379\) 25.3617 1.30274 0.651371 0.758759i \(-0.274194\pi\)
0.651371 + 0.758759i \(0.274194\pi\)
\(380\) 45.4046 2.32921
\(381\) −8.09714 −0.414829
\(382\) −11.3687 −0.581673
\(383\) 7.27999 0.371990 0.185995 0.982551i \(-0.440449\pi\)
0.185995 + 0.982551i \(0.440449\pi\)
\(384\) 9.98254 0.509420
\(385\) −0.754969 −0.0384768
\(386\) 60.7217 3.09066
\(387\) 5.82960 0.296335
\(388\) 41.8752 2.12589
\(389\) −7.67944 −0.389363 −0.194681 0.980867i \(-0.562367\pi\)
−0.194681 + 0.980867i \(0.562367\pi\)
\(390\) 9.62067 0.487161
\(391\) 12.7182 0.643189
\(392\) 33.2199 1.67786
\(393\) 6.12661 0.309046
\(394\) −4.12977 −0.208055
\(395\) 33.2152 1.67124
\(396\) 0.618209 0.0310662
\(397\) 16.4485 0.825527 0.412764 0.910838i \(-0.364564\pi\)
0.412764 + 0.910838i \(0.364564\pi\)
\(398\) −17.9993 −0.902225
\(399\) 4.21714 0.211121
\(400\) 92.2137 4.61069
\(401\) 9.58200 0.478502 0.239251 0.970958i \(-0.423098\pi\)
0.239251 + 0.970958i \(0.423098\pi\)
\(402\) −34.0248 −1.69700
\(403\) −5.04198 −0.251159
\(404\) 69.5288 3.45919
\(405\) 3.62608 0.180181
\(406\) −37.7344 −1.87273
\(407\) 0.904251 0.0448221
\(408\) 13.2961 0.658254
\(409\) −6.85379 −0.338898 −0.169449 0.985539i \(-0.554199\pi\)
−0.169449 + 0.985539i \(0.554199\pi\)
\(410\) 50.9753 2.51749
\(411\) −16.4654 −0.812177
\(412\) −5.03939 −0.248273
\(413\) −15.5191 −0.763645
\(414\) −20.4656 −1.00583
\(415\) 60.7894 2.98403
\(416\) −13.8971 −0.681363
\(417\) −6.84474 −0.335188
\(418\) −0.808741 −0.0395568
\(419\) −39.3855 −1.92411 −0.962053 0.272863i \(-0.912029\pi\)
−0.962053 + 0.272863i \(0.912029\pi\)
\(420\) 31.0134 1.51330
\(421\) −15.5708 −0.758877 −0.379438 0.925217i \(-0.623883\pi\)
−0.379438 + 0.925217i \(0.623883\pi\)
\(422\) −44.2500 −2.15406
\(423\) 11.9749 0.582239
\(424\) 26.3967 1.28194
\(425\) 13.4352 0.651705
\(426\) 33.3738 1.61697
\(427\) 20.0206 0.968866
\(428\) −94.7601 −4.58040
\(429\) −0.122675 −0.00592282
\(430\) −56.0847 −2.70464
\(431\) −17.8741 −0.860967 −0.430484 0.902598i \(-0.641657\pi\)
−0.430484 + 0.902598i \(0.641657\pi\)
\(432\) −11.3167 −0.544474
\(433\) −7.56596 −0.363597 −0.181798 0.983336i \(-0.558192\pi\)
−0.181798 + 0.983336i \(0.558192\pi\)
\(434\) −22.7040 −1.08983
\(435\) 30.3860 1.45690
\(436\) 15.2167 0.728746
\(437\) 19.1665 0.916856
\(438\) −16.9710 −0.810905
\(439\) −9.55373 −0.455975 −0.227987 0.973664i \(-0.573215\pi\)
−0.227987 + 0.973664i \(0.573215\pi\)
\(440\) −3.58715 −0.171011
\(441\) −4.11950 −0.196167
\(442\) −4.37458 −0.208078
\(443\) −28.4283 −1.35067 −0.675335 0.737511i \(-0.736001\pi\)
−0.675335 + 0.737511i \(0.736001\pi\)
\(444\) −37.1458 −1.76286
\(445\) 4.86850 0.230789
\(446\) −10.2858 −0.487047
\(447\) 9.62736 0.455358
\(448\) −24.1653 −1.14170
\(449\) 23.9759 1.13149 0.565747 0.824579i \(-0.308588\pi\)
0.565747 + 0.824579i \(0.308588\pi\)
\(450\) −21.6194 −1.01915
\(451\) −0.649998 −0.0306072
\(452\) 83.4517 3.92524
\(453\) 22.5090 1.05756
\(454\) 79.0157 3.70839
\(455\) −6.15420 −0.288513
\(456\) 20.0373 0.938331
\(457\) 30.9830 1.44933 0.724663 0.689103i \(-0.241995\pi\)
0.724663 + 0.689103i \(0.241995\pi\)
\(458\) 42.3744 1.98002
\(459\) −1.64880 −0.0769596
\(460\) 140.953 6.57196
\(461\) 15.9537 0.743038 0.371519 0.928425i \(-0.378837\pi\)
0.371519 + 0.928425i \(0.378837\pi\)
\(462\) −0.552407 −0.0257003
\(463\) −26.9533 −1.25263 −0.626314 0.779571i \(-0.715437\pi\)
−0.626314 + 0.779571i \(0.715437\pi\)
\(464\) −94.8320 −4.40247
\(465\) 18.2826 0.847837
\(466\) −38.0488 −1.76258
\(467\) −25.1178 −1.16231 −0.581156 0.813792i \(-0.697399\pi\)
−0.581156 + 0.813792i \(0.697399\pi\)
\(468\) 5.03939 0.232946
\(469\) 21.7652 1.00502
\(470\) −115.206 −5.31408
\(471\) 13.9794 0.644138
\(472\) −73.7372 −3.39403
\(473\) 0.715149 0.0328826
\(474\) 24.3034 1.11629
\(475\) 20.2470 0.928996
\(476\) −14.1020 −0.646365
\(477\) −3.27337 −0.149878
\(478\) 8.88123 0.406218
\(479\) 40.4928 1.85017 0.925083 0.379766i \(-0.123995\pi\)
0.925083 + 0.379766i \(0.123995\pi\)
\(480\) 50.3921 2.30008
\(481\) 7.37109 0.336093
\(482\) −21.1697 −0.964253
\(483\) 13.0916 0.595687
\(484\) −55.3575 −2.51625
\(485\) 30.1312 1.36819
\(486\) 2.65319 0.120351
\(487\) 30.3711 1.37624 0.688122 0.725595i \(-0.258435\pi\)
0.688122 + 0.725595i \(0.258435\pi\)
\(488\) 95.1257 4.30614
\(489\) −12.7910 −0.578431
\(490\) 39.6323 1.79041
\(491\) 1.93259 0.0872166 0.0436083 0.999049i \(-0.486115\pi\)
0.0436083 + 0.999049i \(0.486115\pi\)
\(492\) 26.7013 1.20379
\(493\) −13.8167 −0.622274
\(494\) −6.59252 −0.296612
\(495\) 0.444831 0.0199937
\(496\) −57.0585 −2.56200
\(497\) −21.3487 −0.957622
\(498\) 44.4793 1.99316
\(499\) −17.8437 −0.798794 −0.399397 0.916778i \(-0.630780\pi\)
−0.399397 + 0.916778i \(0.630780\pi\)
\(500\) 57.5329 2.57295
\(501\) −6.86951 −0.306907
\(502\) −43.3397 −1.93435
\(503\) 38.1058 1.69905 0.849526 0.527547i \(-0.176888\pi\)
0.849526 + 0.527547i \(0.176888\pi\)
\(504\) 13.6864 0.609639
\(505\) 50.0293 2.22627
\(506\) −2.51063 −0.111611
\(507\) −1.00000 −0.0444116
\(508\) 40.8047 1.81041
\(509\) 31.1794 1.38200 0.691001 0.722854i \(-0.257170\pi\)
0.691001 + 0.722854i \(0.257170\pi\)
\(510\) 15.8626 0.702408
\(511\) 10.8561 0.480245
\(512\) 25.2477 1.11580
\(513\) −2.48476 −0.109705
\(514\) −14.3248 −0.631839
\(515\) −3.62608 −0.159784
\(516\) −29.3776 −1.29328
\(517\) 1.46902 0.0646076
\(518\) 33.1920 1.45837
\(519\) 0.853628 0.0374701
\(520\) −29.2410 −1.28230
\(521\) −3.67012 −0.160791 −0.0803954 0.996763i \(-0.525618\pi\)
−0.0803954 + 0.996763i \(0.525618\pi\)
\(522\) 22.2333 0.973124
\(523\) 14.4506 0.631880 0.315940 0.948779i \(-0.397680\pi\)
0.315940 + 0.948779i \(0.397680\pi\)
\(524\) −30.8744 −1.34875
\(525\) 13.8296 0.603574
\(526\) −11.5419 −0.503251
\(527\) −8.31324 −0.362130
\(528\) −1.38828 −0.0604171
\(529\) 36.4998 1.58695
\(530\) 31.4921 1.36793
\(531\) 9.14392 0.396812
\(532\) −21.2518 −0.921384
\(533\) −5.29852 −0.229504
\(534\) 3.56226 0.154154
\(535\) −68.1844 −2.94787
\(536\) 103.415 4.46684
\(537\) −0.172575 −0.00744716
\(538\) 6.44095 0.277689
\(539\) −0.505361 −0.0217674
\(540\) −18.2733 −0.786356
\(541\) 2.64398 0.113674 0.0568368 0.998383i \(-0.481899\pi\)
0.0568368 + 0.998383i \(0.481899\pi\)
\(542\) −49.2709 −2.11637
\(543\) 16.3527 0.701760
\(544\) −22.9136 −0.982415
\(545\) 10.9491 0.469009
\(546\) −4.50300 −0.192710
\(547\) −5.19347 −0.222057 −0.111028 0.993817i \(-0.535414\pi\)
−0.111028 + 0.993817i \(0.535414\pi\)
\(548\) 82.9755 3.54454
\(549\) −11.7962 −0.503451
\(550\) −2.65217 −0.113089
\(551\) −20.8219 −0.887042
\(552\) 62.2031 2.64754
\(553\) −15.5465 −0.661106
\(554\) −12.0214 −0.510742
\(555\) −26.7282 −1.13455
\(556\) 34.4933 1.46284
\(557\) 7.83612 0.332027 0.166013 0.986123i \(-0.446910\pi\)
0.166013 + 0.986123i \(0.446910\pi\)
\(558\) 13.3773 0.566307
\(559\) 5.82960 0.246566
\(560\) −69.6452 −2.94305
\(561\) −0.202268 −0.00853975
\(562\) −50.1037 −2.11350
\(563\) 7.13649 0.300767 0.150384 0.988628i \(-0.451949\pi\)
0.150384 + 0.988628i \(0.451949\pi\)
\(564\) −60.3462 −2.54103
\(565\) 60.0475 2.52622
\(566\) −24.5165 −1.03050
\(567\) −1.69720 −0.0712759
\(568\) −101.436 −4.25616
\(569\) 3.09009 0.129543 0.0647717 0.997900i \(-0.479368\pi\)
0.0647717 + 0.997900i \(0.479368\pi\)
\(570\) 23.9050 1.00127
\(571\) 6.74506 0.282272 0.141136 0.989990i \(-0.454925\pi\)
0.141136 + 0.989990i \(0.454925\pi\)
\(572\) 0.618209 0.0258486
\(573\) −4.28492 −0.179005
\(574\) −23.8592 −0.995864
\(575\) 62.8542 2.62120
\(576\) 14.2383 0.593262
\(577\) −12.9125 −0.537556 −0.268778 0.963202i \(-0.586620\pi\)
−0.268778 + 0.963202i \(0.586620\pi\)
\(578\) 37.8913 1.57607
\(579\) 22.8864 0.951124
\(580\) −153.127 −6.35825
\(581\) −28.4527 −1.18042
\(582\) 22.0468 0.913870
\(583\) −0.401563 −0.0166310
\(584\) 51.5815 2.13446
\(585\) 3.62608 0.149920
\(586\) 12.6694 0.523369
\(587\) 5.58930 0.230695 0.115348 0.993325i \(-0.463202\pi\)
0.115348 + 0.993325i \(0.463202\pi\)
\(588\) 20.7598 0.856119
\(589\) −12.5281 −0.516212
\(590\) −87.9706 −3.62169
\(591\) −1.55653 −0.0640272
\(592\) 83.4163 3.42839
\(593\) 28.2176 1.15876 0.579379 0.815058i \(-0.303295\pi\)
0.579379 + 0.815058i \(0.303295\pi\)
\(594\) 0.325481 0.0133546
\(595\) −10.1471 −0.415989
\(596\) −48.5160 −1.98729
\(597\) −6.78405 −0.277653
\(598\) −20.4656 −0.836902
\(599\) 11.1988 0.457569 0.228784 0.973477i \(-0.426525\pi\)
0.228784 + 0.973477i \(0.426525\pi\)
\(600\) 65.7099 2.68259
\(601\) −17.5761 −0.716943 −0.358471 0.933541i \(-0.616702\pi\)
−0.358471 + 0.933541i \(0.616702\pi\)
\(602\) 26.2507 1.06990
\(603\) −12.8241 −0.522240
\(604\) −113.432 −4.61547
\(605\) −39.8323 −1.61941
\(606\) 36.6062 1.48702
\(607\) −5.50321 −0.223368 −0.111684 0.993744i \(-0.535625\pi\)
−0.111684 + 0.993744i \(0.535625\pi\)
\(608\) −34.5310 −1.40042
\(609\) −14.2223 −0.576317
\(610\) 113.488 4.59498
\(611\) 11.9749 0.484452
\(612\) 8.30897 0.335870
\(613\) 28.5464 1.15298 0.576490 0.817104i \(-0.304422\pi\)
0.576490 + 0.817104i \(0.304422\pi\)
\(614\) −64.0298 −2.58403
\(615\) 19.2129 0.774737
\(616\) 1.67898 0.0676481
\(617\) 47.1027 1.89628 0.948141 0.317849i \(-0.102961\pi\)
0.948141 + 0.317849i \(0.102961\pi\)
\(618\) −2.65319 −0.106727
\(619\) −6.48009 −0.260457 −0.130228 0.991484i \(-0.541571\pi\)
−0.130228 + 0.991484i \(0.541571\pi\)
\(620\) −92.1334 −3.70017
\(621\) −7.71361 −0.309537
\(622\) 3.20581 0.128541
\(623\) −2.27872 −0.0912952
\(624\) −11.3167 −0.453030
\(625\) 0.655265 0.0262106
\(626\) −22.6172 −0.903964
\(627\) −0.304819 −0.0121733
\(628\) −70.4478 −2.81117
\(629\) 12.1535 0.484591
\(630\) 16.3282 0.650532
\(631\) 12.6135 0.502137 0.251068 0.967969i \(-0.419218\pi\)
0.251068 + 0.967969i \(0.419218\pi\)
\(632\) −73.8675 −2.93829
\(633\) −16.6781 −0.662894
\(634\) −18.0791 −0.718012
\(635\) 29.3609 1.16515
\(636\) 16.4958 0.654102
\(637\) −4.11950 −0.163221
\(638\) 2.72748 0.107982
\(639\) 12.5788 0.497608
\(640\) −36.1975 −1.43083
\(641\) −12.2027 −0.481977 −0.240988 0.970528i \(-0.577472\pi\)
−0.240988 + 0.970528i \(0.577472\pi\)
\(642\) −49.8901 −1.96901
\(643\) −6.29470 −0.248239 −0.124119 0.992267i \(-0.539611\pi\)
−0.124119 + 0.992267i \(0.539611\pi\)
\(644\) −65.9736 −2.59972
\(645\) −21.1386 −0.832332
\(646\) −10.8698 −0.427666
\(647\) −22.2602 −0.875139 −0.437569 0.899185i \(-0.644161\pi\)
−0.437569 + 0.899185i \(0.644161\pi\)
\(648\) −8.06407 −0.316787
\(649\) 1.12173 0.0440319
\(650\) −21.6194 −0.847983
\(651\) −8.55727 −0.335386
\(652\) 64.4590 2.52441
\(653\) 15.1065 0.591164 0.295582 0.955317i \(-0.404487\pi\)
0.295582 + 0.955317i \(0.404487\pi\)
\(654\) 8.01141 0.313271
\(655\) −22.2156 −0.868035
\(656\) −59.9617 −2.34111
\(657\) −6.39645 −0.249549
\(658\) 53.9229 2.10213
\(659\) 38.2470 1.48989 0.744945 0.667126i \(-0.232476\pi\)
0.744945 + 0.667126i \(0.232476\pi\)
\(660\) −2.24168 −0.0872572
\(661\) −48.5155 −1.88704 −0.943518 0.331323i \(-0.892505\pi\)
−0.943518 + 0.331323i \(0.892505\pi\)
\(662\) −23.5702 −0.916082
\(663\) −1.64880 −0.0640343
\(664\) −135.190 −5.24639
\(665\) −15.2917 −0.592987
\(666\) −19.5569 −0.757813
\(667\) −64.6388 −2.50283
\(668\) 34.6182 1.33942
\(669\) −3.87678 −0.149885
\(670\) 123.377 4.76646
\(671\) −1.44711 −0.0558650
\(672\) −23.5863 −0.909860
\(673\) −34.6677 −1.33634 −0.668170 0.744008i \(-0.732922\pi\)
−0.668170 + 0.744008i \(0.732922\pi\)
\(674\) −38.3159 −1.47587
\(675\) −8.14847 −0.313635
\(676\) 5.03939 0.193823
\(677\) −19.4973 −0.749340 −0.374670 0.927158i \(-0.622244\pi\)
−0.374670 + 0.927158i \(0.622244\pi\)
\(678\) 43.9364 1.68737
\(679\) −14.1030 −0.541225
\(680\) −48.2127 −1.84887
\(681\) 29.7814 1.14123
\(682\) 1.64107 0.0628397
\(683\) 40.3459 1.54379 0.771896 0.635748i \(-0.219308\pi\)
0.771896 + 0.635748i \(0.219308\pi\)
\(684\) 12.5217 0.478778
\(685\) 59.7048 2.28120
\(686\) −50.0711 −1.91172
\(687\) 15.9711 0.609337
\(688\) 65.9718 2.51515
\(689\) −3.27337 −0.124706
\(690\) 74.2101 2.82513
\(691\) 30.3413 1.15424 0.577118 0.816660i \(-0.304177\pi\)
0.577118 + 0.816660i \(0.304177\pi\)
\(692\) −4.30177 −0.163529
\(693\) −0.208205 −0.00790906
\(694\) 50.9258 1.93312
\(695\) 24.8196 0.941461
\(696\) −67.5756 −2.56145
\(697\) −8.73622 −0.330908
\(698\) −58.4821 −2.21358
\(699\) −14.3408 −0.542419
\(700\) −69.6929 −2.63414
\(701\) −12.8526 −0.485438 −0.242719 0.970097i \(-0.578039\pi\)
−0.242719 + 0.970097i \(0.578039\pi\)
\(702\) 2.65319 0.100138
\(703\) 18.3154 0.690777
\(704\) 1.74669 0.0658307
\(705\) −43.4219 −1.63537
\(706\) 76.3939 2.87512
\(707\) −23.4164 −0.880666
\(708\) −46.0798 −1.73178
\(709\) 38.8701 1.45980 0.729899 0.683555i \(-0.239567\pi\)
0.729899 + 0.683555i \(0.239567\pi\)
\(710\) −121.016 −4.54166
\(711\) 9.16008 0.343530
\(712\) −10.8271 −0.405763
\(713\) −38.8919 −1.45651
\(714\) −7.42456 −0.277857
\(715\) 0.444831 0.0166357
\(716\) 0.869673 0.0325012
\(717\) 3.34738 0.125010
\(718\) −26.9399 −1.00539
\(719\) −19.6238 −0.731843 −0.365922 0.930646i \(-0.619246\pi\)
−0.365922 + 0.930646i \(0.619246\pi\)
\(720\) 41.0352 1.52929
\(721\) 1.69720 0.0632072
\(722\) 34.0297 1.26645
\(723\) −7.97897 −0.296741
\(724\) −82.4075 −3.06265
\(725\) −68.2829 −2.53596
\(726\) −29.1451 −1.08168
\(727\) 10.9018 0.404326 0.202163 0.979352i \(-0.435203\pi\)
0.202163 + 0.979352i \(0.435203\pi\)
\(728\) 13.6864 0.507251
\(729\) 1.00000 0.0370370
\(730\) 61.5382 2.27763
\(731\) 9.61187 0.355508
\(732\) 59.4459 2.19718
\(733\) 42.8070 1.58111 0.790555 0.612391i \(-0.209792\pi\)
0.790555 + 0.612391i \(0.209792\pi\)
\(734\) 48.6645 1.79624
\(735\) 14.9376 0.550983
\(736\) −107.197 −3.95134
\(737\) −1.57321 −0.0579498
\(738\) 14.0579 0.517480
\(739\) −33.2915 −1.22465 −0.612323 0.790608i \(-0.709765\pi\)
−0.612323 + 0.790608i \(0.709765\pi\)
\(740\) 134.694 4.95144
\(741\) −2.48476 −0.0912799
\(742\) −14.7400 −0.541122
\(743\) −15.8368 −0.580994 −0.290497 0.956876i \(-0.593821\pi\)
−0.290497 + 0.956876i \(0.593821\pi\)
\(744\) −40.6589 −1.49063
\(745\) −34.9096 −1.27899
\(746\) 17.4323 0.638242
\(747\) 16.7645 0.613380
\(748\) 1.01931 0.0372695
\(749\) 31.9140 1.16611
\(750\) 30.2904 1.10605
\(751\) 49.7107 1.81397 0.906985 0.421163i \(-0.138378\pi\)
0.906985 + 0.421163i \(0.138378\pi\)
\(752\) 135.516 4.94176
\(753\) −16.3350 −0.595280
\(754\) 22.2333 0.809688
\(755\) −81.6194 −2.97043
\(756\) 8.55288 0.311065
\(757\) 47.0953 1.71171 0.855854 0.517217i \(-0.173032\pi\)
0.855854 + 0.517217i \(0.173032\pi\)
\(758\) −67.2893 −2.44406
\(759\) −0.946270 −0.0343474
\(760\) −72.6568 −2.63554
\(761\) −34.7500 −1.25969 −0.629843 0.776722i \(-0.716881\pi\)
−0.629843 + 0.776722i \(0.716881\pi\)
\(762\) 21.4832 0.778255
\(763\) −5.12478 −0.185530
\(764\) 21.5934 0.781222
\(765\) 5.97870 0.216160
\(766\) −19.3152 −0.697885
\(767\) 9.14392 0.330168
\(768\) 1.99103 0.0718450
\(769\) 22.6587 0.817093 0.408546 0.912738i \(-0.366036\pi\)
0.408546 + 0.912738i \(0.366036\pi\)
\(770\) 2.00307 0.0721857
\(771\) −5.39908 −0.194443
\(772\) −115.333 −4.15094
\(773\) −2.52607 −0.0908564 −0.0454282 0.998968i \(-0.514465\pi\)
−0.0454282 + 0.998968i \(0.514465\pi\)
\(774\) −15.4670 −0.555950
\(775\) −41.0845 −1.47580
\(776\) −67.0089 −2.40548
\(777\) 12.5102 0.448802
\(778\) 20.3750 0.730478
\(779\) −13.1655 −0.471704
\(780\) −18.2733 −0.654287
\(781\) 1.54311 0.0552167
\(782\) −33.7438 −1.20668
\(783\) 8.37984 0.299471
\(784\) −46.6191 −1.66497
\(785\) −50.6906 −1.80922
\(786\) −16.2550 −0.579798
\(787\) −20.2595 −0.722173 −0.361087 0.932532i \(-0.617594\pi\)
−0.361087 + 0.932532i \(0.617594\pi\)
\(788\) 7.84398 0.279430
\(789\) −4.35020 −0.154871
\(790\) −88.1261 −3.13539
\(791\) −28.1055 −0.999316
\(792\) −0.989263 −0.0351519
\(793\) −11.7962 −0.418897
\(794\) −43.6410 −1.54876
\(795\) 11.8695 0.420969
\(796\) 34.1875 1.21174
\(797\) −0.0330833 −0.00117187 −0.000585935 1.00000i \(-0.500187\pi\)
−0.000585935 1.00000i \(0.500187\pi\)
\(798\) −11.1889 −0.396081
\(799\) 19.7443 0.698502
\(800\) −113.240 −4.00365
\(801\) 1.34263 0.0474397
\(802\) −25.4228 −0.897711
\(803\) −0.784688 −0.0276910
\(804\) 64.6259 2.27918
\(805\) −47.4711 −1.67314
\(806\) 13.3773 0.471196
\(807\) 2.42763 0.0854566
\(808\) −111.261 −3.91413
\(809\) −4.39339 −0.154463 −0.0772316 0.997013i \(-0.524608\pi\)
−0.0772316 + 0.997013i \(0.524608\pi\)
\(810\) −9.62067 −0.338036
\(811\) −32.8133 −1.15223 −0.576116 0.817368i \(-0.695432\pi\)
−0.576116 + 0.817368i \(0.695432\pi\)
\(812\) 71.6717 2.51518
\(813\) −18.5705 −0.651295
\(814\) −2.39915 −0.0840900
\(815\) 46.3813 1.62467
\(816\) −18.6590 −0.653196
\(817\) 14.4851 0.506771
\(818\) 18.1844 0.635802
\(819\) −1.69720 −0.0593051
\(820\) −96.8211 −3.38114
\(821\) −25.2885 −0.882575 −0.441287 0.897366i \(-0.645478\pi\)
−0.441287 + 0.897366i \(0.645478\pi\)
\(822\) 43.6857 1.52371
\(823\) −31.6894 −1.10462 −0.552312 0.833638i \(-0.686254\pi\)
−0.552312 + 0.833638i \(0.686254\pi\)
\(824\) 8.06407 0.280925
\(825\) −0.999617 −0.0348022
\(826\) 41.1750 1.43266
\(827\) −42.8039 −1.48844 −0.744218 0.667936i \(-0.767178\pi\)
−0.744218 + 0.667936i \(0.767178\pi\)
\(828\) 38.8719 1.35089
\(829\) −26.7030 −0.927435 −0.463717 0.885983i \(-0.653485\pi\)
−0.463717 + 0.885983i \(0.653485\pi\)
\(830\) −161.286 −5.59830
\(831\) −4.53094 −0.157177
\(832\) 14.2383 0.493624
\(833\) −6.79225 −0.235337
\(834\) 18.1604 0.628842
\(835\) 24.9094 0.862026
\(836\) 1.53610 0.0531272
\(837\) 5.04198 0.174276
\(838\) 104.497 3.60979
\(839\) 10.0561 0.347174 0.173587 0.984818i \(-0.444464\pi\)
0.173587 + 0.984818i \(0.444464\pi\)
\(840\) −49.6279 −1.71233
\(841\) 41.2217 1.42144
\(842\) 41.3123 1.42372
\(843\) −18.8843 −0.650412
\(844\) 84.0473 2.89303
\(845\) 3.62608 0.124741
\(846\) −31.7716 −1.09233
\(847\) 18.6437 0.640605
\(848\) −37.0438 −1.27209
\(849\) −9.24039 −0.317129
\(850\) −35.6462 −1.22265
\(851\) 56.8577 1.94906
\(852\) −63.3894 −2.17168
\(853\) 19.2631 0.659558 0.329779 0.944058i \(-0.393026\pi\)
0.329779 + 0.944058i \(0.393026\pi\)
\(854\) −53.1184 −1.81768
\(855\) 9.00994 0.308133
\(856\) 151.636 5.18280
\(857\) 36.0152 1.23026 0.615128 0.788427i \(-0.289104\pi\)
0.615128 + 0.788427i \(0.289104\pi\)
\(858\) 0.325481 0.0111117
\(859\) 53.6352 1.83001 0.915004 0.403445i \(-0.132187\pi\)
0.915004 + 0.403445i \(0.132187\pi\)
\(860\) 106.526 3.63250
\(861\) −8.99266 −0.306469
\(862\) 47.4234 1.61525
\(863\) −0.00516474 −0.000175810 0 −8.79049e−5 1.00000i \(-0.500028\pi\)
−8.79049e−5 1.00000i \(0.500028\pi\)
\(864\) 13.8971 0.472790
\(865\) −3.09533 −0.105244
\(866\) 20.0739 0.682139
\(867\) 14.2814 0.485023
\(868\) 43.1234 1.46370
\(869\) 1.12372 0.0381195
\(870\) −80.6197 −2.73326
\(871\) −12.8241 −0.434530
\(872\) −24.3498 −0.824589
\(873\) 8.30957 0.281236
\(874\) −50.8522 −1.72010
\(875\) −19.3763 −0.655040
\(876\) 32.2342 1.08909
\(877\) −34.8877 −1.17807 −0.589037 0.808106i \(-0.700493\pi\)
−0.589037 + 0.808106i \(0.700493\pi\)
\(878\) 25.3478 0.855448
\(879\) 4.77518 0.161063
\(880\) 5.03402 0.169697
\(881\) −47.3217 −1.59431 −0.797155 0.603775i \(-0.793662\pi\)
−0.797155 + 0.603775i \(0.793662\pi\)
\(882\) 10.9298 0.368025
\(883\) 44.3753 1.49335 0.746673 0.665191i \(-0.231650\pi\)
0.746673 + 0.665191i \(0.231650\pi\)
\(884\) 8.30897 0.279461
\(885\) −33.1566 −1.11455
\(886\) 75.4256 2.53397
\(887\) −2.29556 −0.0770774 −0.0385387 0.999257i \(-0.512270\pi\)
−0.0385387 + 0.999257i \(0.512270\pi\)
\(888\) 59.4410 1.99471
\(889\) −13.7425 −0.460908
\(890\) −12.9170 −0.432980
\(891\) 0.122675 0.00410978
\(892\) 19.5366 0.654134
\(893\) 29.7547 0.995704
\(894\) −25.5432 −0.854291
\(895\) 0.625771 0.0209172
\(896\) 16.9424 0.566006
\(897\) −7.71361 −0.257550
\(898\) −63.6125 −2.12278
\(899\) 42.2510 1.40915
\(900\) 41.0634 1.36878
\(901\) −5.39715 −0.179805
\(902\) 1.72456 0.0574217
\(903\) 9.89402 0.329252
\(904\) −133.540 −4.44147
\(905\) −59.2961 −1.97107
\(906\) −59.7205 −1.98408
\(907\) 57.9664 1.92474 0.962371 0.271740i \(-0.0875990\pi\)
0.962371 + 0.271740i \(0.0875990\pi\)
\(908\) −150.080 −4.98059
\(909\) 13.7971 0.457620
\(910\) 16.3282 0.541276
\(911\) 44.9297 1.48859 0.744294 0.667852i \(-0.232786\pi\)
0.744294 + 0.667852i \(0.232786\pi\)
\(912\) −28.1192 −0.931121
\(913\) 2.05659 0.0680632
\(914\) −82.2038 −2.71906
\(915\) 42.7742 1.41407
\(916\) −80.4848 −2.65929
\(917\) 10.3981 0.343376
\(918\) 4.37458 0.144383
\(919\) 43.1119 1.42213 0.711064 0.703127i \(-0.248213\pi\)
0.711064 + 0.703127i \(0.248213\pi\)
\(920\) −225.554 −7.43628
\(921\) −24.1332 −0.795215
\(922\) −42.3281 −1.39400
\(923\) 12.5788 0.414035
\(924\) 1.04923 0.0345170
\(925\) 60.0631 1.97486
\(926\) 71.5122 2.35004
\(927\) −1.00000 −0.0328443
\(928\) 116.456 3.82285
\(929\) 57.7847 1.89585 0.947927 0.318486i \(-0.103175\pi\)
0.947927 + 0.318486i \(0.103175\pi\)
\(930\) −48.5072 −1.59061
\(931\) −10.2360 −0.335470
\(932\) 72.2689 2.36725
\(933\) 1.20829 0.0395575
\(934\) 66.6421 2.18060
\(935\) 0.733439 0.0239860
\(936\) −8.06407 −0.263582
\(937\) 16.0601 0.524662 0.262331 0.964978i \(-0.415509\pi\)
0.262331 + 0.964978i \(0.415509\pi\)
\(938\) −57.7471 −1.88551
\(939\) −8.52454 −0.278188
\(940\) 218.820 7.13713
\(941\) 46.5017 1.51591 0.757956 0.652306i \(-0.226198\pi\)
0.757956 + 0.652306i \(0.226198\pi\)
\(942\) −37.0900 −1.20846
\(943\) −40.8707 −1.33093
\(944\) 103.479 3.36795
\(945\) 6.15420 0.200196
\(946\) −1.89742 −0.0616905
\(947\) 39.3923 1.28008 0.640039 0.768343i \(-0.278918\pi\)
0.640039 + 0.768343i \(0.278918\pi\)
\(948\) −46.1612 −1.49925
\(949\) −6.39645 −0.207638
\(950\) −53.7190 −1.74288
\(951\) −6.81411 −0.220963
\(952\) 22.5661 0.731373
\(953\) −20.8160 −0.674297 −0.337149 0.941451i \(-0.609463\pi\)
−0.337149 + 0.941451i \(0.609463\pi\)
\(954\) 8.68487 0.281183
\(955\) 15.5375 0.502781
\(956\) −16.8688 −0.545575
\(957\) 1.02800 0.0332305
\(958\) −107.435 −3.47107
\(959\) −27.9451 −0.902394
\(960\) −51.6292 −1.66632
\(961\) −5.57842 −0.179949
\(962\) −19.5569 −0.630538
\(963\) −18.8039 −0.605946
\(964\) 40.2092 1.29505
\(965\) −82.9878 −2.67147
\(966\) −34.7344 −1.11756
\(967\) 9.03615 0.290583 0.145291 0.989389i \(-0.453588\pi\)
0.145291 + 0.989389i \(0.453588\pi\)
\(968\) 88.5834 2.84718
\(969\) −4.09688 −0.131611
\(970\) −79.9436 −2.56683
\(971\) −17.4820 −0.561025 −0.280513 0.959850i \(-0.590504\pi\)
−0.280513 + 0.959850i \(0.590504\pi\)
\(972\) −5.03939 −0.161639
\(973\) −11.6169 −0.372421
\(974\) −80.5801 −2.58195
\(975\) −8.14847 −0.260960
\(976\) −133.494 −4.27305
\(977\) −11.9914 −0.383640 −0.191820 0.981430i \(-0.561439\pi\)
−0.191820 + 0.981430i \(0.561439\pi\)
\(978\) 33.9370 1.08519
\(979\) 0.164708 0.00526410
\(980\) −75.2766 −2.40462
\(981\) 3.01954 0.0964066
\(982\) −5.12752 −0.163626
\(983\) 8.38753 0.267521 0.133760 0.991014i \(-0.457295\pi\)
0.133760 + 0.991014i \(0.457295\pi\)
\(984\) −42.7276 −1.36211
\(985\) 5.64412 0.179837
\(986\) 36.6583 1.16744
\(987\) 20.3238 0.646915
\(988\) 12.5217 0.398367
\(989\) 44.9673 1.42988
\(990\) −1.18022 −0.0375098
\(991\) 1.02483 0.0325548 0.0162774 0.999868i \(-0.494819\pi\)
0.0162774 + 0.999868i \(0.494819\pi\)
\(992\) 70.0691 2.22470
\(993\) −8.88374 −0.281917
\(994\) 56.6422 1.79658
\(995\) 24.5995 0.779857
\(996\) −84.4828 −2.67694
\(997\) −1.09020 −0.0345270 −0.0172635 0.999851i \(-0.505495\pi\)
−0.0172635 + 0.999851i \(0.505495\pi\)
\(998\) 47.3426 1.49860
\(999\) −7.37109 −0.233211
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 \(a_p\))