Properties

Label 8015.2.a.l.1.35
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.35
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.240720 q^{2} +1.90161 q^{3} -1.94205 q^{4} -1.00000 q^{5} +0.457756 q^{6} -1.00000 q^{7} -0.948933 q^{8} +0.616107 q^{9} +O(q^{10})\) \(q+0.240720 q^{2} +1.90161 q^{3} -1.94205 q^{4} -1.00000 q^{5} +0.457756 q^{6} -1.00000 q^{7} -0.948933 q^{8} +0.616107 q^{9} -0.240720 q^{10} -3.43257 q^{11} -3.69302 q^{12} +4.77707 q^{13} -0.240720 q^{14} -1.90161 q^{15} +3.65568 q^{16} -6.96074 q^{17} +0.148310 q^{18} +3.44519 q^{19} +1.94205 q^{20} -1.90161 q^{21} -0.826290 q^{22} -5.47122 q^{23} -1.80450 q^{24} +1.00000 q^{25} +1.14994 q^{26} -4.53323 q^{27} +1.94205 q^{28} +0.0420292 q^{29} -0.457756 q^{30} +5.53721 q^{31} +2.77786 q^{32} -6.52740 q^{33} -1.67559 q^{34} +1.00000 q^{35} -1.19651 q^{36} -10.4814 q^{37} +0.829329 q^{38} +9.08412 q^{39} +0.948933 q^{40} +0.619883 q^{41} -0.457756 q^{42} +10.9424 q^{43} +6.66623 q^{44} -0.616107 q^{45} -1.31703 q^{46} -1.77308 q^{47} +6.95166 q^{48} +1.00000 q^{49} +0.240720 q^{50} -13.2366 q^{51} -9.27734 q^{52} -0.380935 q^{53} -1.09124 q^{54} +3.43257 q^{55} +0.948933 q^{56} +6.55140 q^{57} +0.0101173 q^{58} +2.35082 q^{59} +3.69302 q^{60} -10.2438 q^{61} +1.33292 q^{62} -0.616107 q^{63} -6.64267 q^{64} -4.77707 q^{65} -1.57128 q^{66} +3.91925 q^{67} +13.5181 q^{68} -10.4041 q^{69} +0.240720 q^{70} -0.284027 q^{71} -0.584645 q^{72} +6.72141 q^{73} -2.52309 q^{74} +1.90161 q^{75} -6.69075 q^{76} +3.43257 q^{77} +2.18673 q^{78} +3.61811 q^{79} -3.65568 q^{80} -10.4687 q^{81} +0.149218 q^{82} +13.5758 q^{83} +3.69302 q^{84} +6.96074 q^{85} +2.63406 q^{86} +0.0799229 q^{87} +3.25728 q^{88} -12.0649 q^{89} -0.148310 q^{90} -4.77707 q^{91} +10.6254 q^{92} +10.5296 q^{93} -0.426816 q^{94} -3.44519 q^{95} +5.28240 q^{96} +5.20734 q^{97} +0.240720 q^{98} -2.11483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.240720 0.170215 0.0851075 0.996372i \(-0.472877\pi\)
0.0851075 + 0.996372i \(0.472877\pi\)
\(3\) 1.90161 1.09789 0.548947 0.835857i \(-0.315029\pi\)
0.548947 + 0.835857i \(0.315029\pi\)
\(4\) −1.94205 −0.971027
\(5\) −1.00000 −0.447214
\(6\) 0.457756 0.186878
\(7\) −1.00000 −0.377964
\(8\) −0.948933 −0.335498
\(9\) 0.616107 0.205369
\(10\) −0.240720 −0.0761225
\(11\) −3.43257 −1.03496 −0.517479 0.855696i \(-0.673130\pi\)
−0.517479 + 0.855696i \(0.673130\pi\)
\(12\) −3.69302 −1.06608
\(13\) 4.77707 1.32492 0.662461 0.749096i \(-0.269512\pi\)
0.662461 + 0.749096i \(0.269512\pi\)
\(14\) −0.240720 −0.0643353
\(15\) −1.90161 −0.490993
\(16\) 3.65568 0.913920
\(17\) −6.96074 −1.68823 −0.844114 0.536164i \(-0.819873\pi\)
−0.844114 + 0.536164i \(0.819873\pi\)
\(18\) 0.148310 0.0349569
\(19\) 3.44519 0.790382 0.395191 0.918599i \(-0.370678\pi\)
0.395191 + 0.918599i \(0.370678\pi\)
\(20\) 1.94205 0.434256
\(21\) −1.90161 −0.414965
\(22\) −0.826290 −0.176166
\(23\) −5.47122 −1.14083 −0.570414 0.821357i \(-0.693217\pi\)
−0.570414 + 0.821357i \(0.693217\pi\)
\(24\) −1.80450 −0.368341
\(25\) 1.00000 0.200000
\(26\) 1.14994 0.225522
\(27\) −4.53323 −0.872420
\(28\) 1.94205 0.367014
\(29\) 0.0420292 0.00780462 0.00390231 0.999992i \(-0.498758\pi\)
0.00390231 + 0.999992i \(0.498758\pi\)
\(30\) −0.457756 −0.0835744
\(31\) 5.53721 0.994513 0.497257 0.867604i \(-0.334341\pi\)
0.497257 + 0.867604i \(0.334341\pi\)
\(32\) 2.77786 0.491061
\(33\) −6.52740 −1.13627
\(34\) −1.67559 −0.287362
\(35\) 1.00000 0.169031
\(36\) −1.19651 −0.199419
\(37\) −10.4814 −1.72313 −0.861567 0.507644i \(-0.830517\pi\)
−0.861567 + 0.507644i \(0.830517\pi\)
\(38\) 0.829329 0.134535
\(39\) 9.08412 1.45462
\(40\) 0.948933 0.150039
\(41\) 0.619883 0.0968094 0.0484047 0.998828i \(-0.484586\pi\)
0.0484047 + 0.998828i \(0.484586\pi\)
\(42\) −0.457756 −0.0706332
\(43\) 10.9424 1.66870 0.834351 0.551233i \(-0.185843\pi\)
0.834351 + 0.551233i \(0.185843\pi\)
\(44\) 6.66623 1.00497
\(45\) −0.616107 −0.0918439
\(46\) −1.31703 −0.194186
\(47\) −1.77308 −0.258630 −0.129315 0.991604i \(-0.541278\pi\)
−0.129315 + 0.991604i \(0.541278\pi\)
\(48\) 6.95166 1.00339
\(49\) 1.00000 0.142857
\(50\) 0.240720 0.0340430
\(51\) −13.2366 −1.85349
\(52\) −9.27734 −1.28653
\(53\) −0.380935 −0.0523254 −0.0261627 0.999658i \(-0.508329\pi\)
−0.0261627 + 0.999658i \(0.508329\pi\)
\(54\) −1.09124 −0.148499
\(55\) 3.43257 0.462848
\(56\) 0.948933 0.126807
\(57\) 6.55140 0.867754
\(58\) 0.0101173 0.00132846
\(59\) 2.35082 0.306051 0.153025 0.988222i \(-0.451098\pi\)
0.153025 + 0.988222i \(0.451098\pi\)
\(60\) 3.69302 0.476767
\(61\) −10.2438 −1.31158 −0.655790 0.754943i \(-0.727664\pi\)
−0.655790 + 0.754943i \(0.727664\pi\)
\(62\) 1.33292 0.169281
\(63\) −0.616107 −0.0776222
\(64\) −6.64267 −0.830334
\(65\) −4.77707 −0.592523
\(66\) −1.57128 −0.193411
\(67\) 3.91925 0.478813 0.239406 0.970919i \(-0.423047\pi\)
0.239406 + 0.970919i \(0.423047\pi\)
\(68\) 13.5181 1.63931
\(69\) −10.4041 −1.25251
\(70\) 0.240720 0.0287716
\(71\) −0.284027 −0.0337079 −0.0168539 0.999858i \(-0.505365\pi\)
−0.0168539 + 0.999858i \(0.505365\pi\)
\(72\) −0.584645 −0.0689010
\(73\) 6.72141 0.786681 0.393341 0.919393i \(-0.371319\pi\)
0.393341 + 0.919393i \(0.371319\pi\)
\(74\) −2.52309 −0.293303
\(75\) 1.90161 0.219579
\(76\) −6.69075 −0.767482
\(77\) 3.43257 0.391178
\(78\) 2.18673 0.247599
\(79\) 3.61811 0.407070 0.203535 0.979068i \(-0.434757\pi\)
0.203535 + 0.979068i \(0.434757\pi\)
\(80\) −3.65568 −0.408717
\(81\) −10.4687 −1.16319
\(82\) 0.149218 0.0164784
\(83\) 13.5758 1.49014 0.745071 0.666985i \(-0.232415\pi\)
0.745071 + 0.666985i \(0.232415\pi\)
\(84\) 3.69302 0.402942
\(85\) 6.96074 0.754999
\(86\) 2.63406 0.284038
\(87\) 0.0799229 0.00856864
\(88\) 3.25728 0.347227
\(89\) −12.0649 −1.27888 −0.639440 0.768841i \(-0.720834\pi\)
−0.639440 + 0.768841i \(0.720834\pi\)
\(90\) −0.148310 −0.0156332
\(91\) −4.77707 −0.500773
\(92\) 10.6254 1.10777
\(93\) 10.5296 1.09187
\(94\) −0.426816 −0.0440227
\(95\) −3.44519 −0.353469
\(96\) 5.28240 0.539133
\(97\) 5.20734 0.528725 0.264363 0.964423i \(-0.414838\pi\)
0.264363 + 0.964423i \(0.414838\pi\)
\(98\) 0.240720 0.0243164
\(99\) −2.11483 −0.212549
\(100\) −1.94205 −0.194205
\(101\) 19.3942 1.92980 0.964898 0.262624i \(-0.0845878\pi\)
0.964898 + 0.262624i \(0.0845878\pi\)
\(102\) −3.18632 −0.315493
\(103\) 17.0188 1.67691 0.838457 0.544967i \(-0.183458\pi\)
0.838457 + 0.544967i \(0.183458\pi\)
\(104\) −4.53312 −0.444509
\(105\) 1.90161 0.185578
\(106\) −0.0916988 −0.00890657
\(107\) 0.0626541 0.00605701 0.00302850 0.999995i \(-0.499036\pi\)
0.00302850 + 0.999995i \(0.499036\pi\)
\(108\) 8.80377 0.847143
\(109\) −5.22432 −0.500399 −0.250200 0.968194i \(-0.580496\pi\)
−0.250200 + 0.968194i \(0.580496\pi\)
\(110\) 0.826290 0.0787836
\(111\) −19.9315 −1.89182
\(112\) −3.65568 −0.345429
\(113\) −12.4036 −1.16684 −0.583418 0.812172i \(-0.698285\pi\)
−0.583418 + 0.812172i \(0.698285\pi\)
\(114\) 1.57706 0.147705
\(115\) 5.47122 0.510194
\(116\) −0.0816229 −0.00757849
\(117\) 2.94319 0.272098
\(118\) 0.565890 0.0520944
\(119\) 6.96074 0.638090
\(120\) 1.80450 0.164727
\(121\) 0.782536 0.0711396
\(122\) −2.46589 −0.223251
\(123\) 1.17877 0.106286
\(124\) −10.7536 −0.965699
\(125\) −1.00000 −0.0894427
\(126\) −0.148310 −0.0132125
\(127\) 16.6744 1.47961 0.739805 0.672821i \(-0.234918\pi\)
0.739805 + 0.672821i \(0.234918\pi\)
\(128\) −7.15475 −0.632397
\(129\) 20.8082 1.83206
\(130\) −1.14994 −0.100856
\(131\) −15.9226 −1.39117 −0.695584 0.718445i \(-0.744854\pi\)
−0.695584 + 0.718445i \(0.744854\pi\)
\(132\) 12.6766 1.10335
\(133\) −3.44519 −0.298736
\(134\) 0.943444 0.0815011
\(135\) 4.53323 0.390158
\(136\) 6.60528 0.566398
\(137\) 19.3806 1.65580 0.827899 0.560878i \(-0.189536\pi\)
0.827899 + 0.560878i \(0.189536\pi\)
\(138\) −2.50448 −0.213196
\(139\) 12.7930 1.08509 0.542545 0.840027i \(-0.317461\pi\)
0.542545 + 0.840027i \(0.317461\pi\)
\(140\) −1.94205 −0.164133
\(141\) −3.37169 −0.283948
\(142\) −0.0683712 −0.00573758
\(143\) −16.3976 −1.37124
\(144\) 2.25229 0.187691
\(145\) −0.0420292 −0.00349033
\(146\) 1.61798 0.133905
\(147\) 1.90161 0.156842
\(148\) 20.3555 1.67321
\(149\) −6.74451 −0.552531 −0.276266 0.961081i \(-0.589097\pi\)
−0.276266 + 0.961081i \(0.589097\pi\)
\(150\) 0.457756 0.0373756
\(151\) 22.9170 1.86496 0.932480 0.361222i \(-0.117640\pi\)
0.932480 + 0.361222i \(0.117640\pi\)
\(152\) −3.26926 −0.265172
\(153\) −4.28857 −0.346710
\(154\) 0.826290 0.0665843
\(155\) −5.53721 −0.444760
\(156\) −17.6418 −1.41248
\(157\) 2.43932 0.194679 0.0973396 0.995251i \(-0.468967\pi\)
0.0973396 + 0.995251i \(0.468967\pi\)
\(158\) 0.870954 0.0692894
\(159\) −0.724388 −0.0574477
\(160\) −2.77786 −0.219609
\(161\) 5.47122 0.431192
\(162\) −2.52004 −0.197993
\(163\) 10.5314 0.824881 0.412440 0.910985i \(-0.364677\pi\)
0.412440 + 0.910985i \(0.364677\pi\)
\(164\) −1.20385 −0.0940045
\(165\) 6.52740 0.508157
\(166\) 3.26798 0.253645
\(167\) −4.49502 −0.347835 −0.173918 0.984760i \(-0.555643\pi\)
−0.173918 + 0.984760i \(0.555643\pi\)
\(168\) 1.80450 0.139220
\(169\) 9.82044 0.755419
\(170\) 1.67559 0.128512
\(171\) 2.12261 0.162320
\(172\) −21.2508 −1.62035
\(173\) −12.1400 −0.922989 −0.461495 0.887143i \(-0.652687\pi\)
−0.461495 + 0.887143i \(0.652687\pi\)
\(174\) 0.0192391 0.00145851
\(175\) −1.00000 −0.0755929
\(176\) −12.5484 −0.945869
\(177\) 4.47033 0.336011
\(178\) −2.90428 −0.217685
\(179\) 9.34481 0.698464 0.349232 0.937036i \(-0.386443\pi\)
0.349232 + 0.937036i \(0.386443\pi\)
\(180\) 1.19651 0.0891829
\(181\) −18.7845 −1.39624 −0.698121 0.715980i \(-0.745980\pi\)
−0.698121 + 0.715980i \(0.745980\pi\)
\(182\) −1.14994 −0.0852392
\(183\) −19.4796 −1.43998
\(184\) 5.19182 0.382746
\(185\) 10.4814 0.770609
\(186\) 2.53469 0.185853
\(187\) 23.8932 1.74725
\(188\) 3.44341 0.251136
\(189\) 4.53323 0.329744
\(190\) −0.829329 −0.0601658
\(191\) 18.7107 1.35386 0.676930 0.736048i \(-0.263310\pi\)
0.676930 + 0.736048i \(0.263310\pi\)
\(192\) −12.6317 −0.911618
\(193\) −4.43027 −0.318898 −0.159449 0.987206i \(-0.550972\pi\)
−0.159449 + 0.987206i \(0.550972\pi\)
\(194\) 1.25351 0.0899970
\(195\) −9.08412 −0.650527
\(196\) −1.94205 −0.138718
\(197\) −11.3196 −0.806485 −0.403243 0.915093i \(-0.632117\pi\)
−0.403243 + 0.915093i \(0.632117\pi\)
\(198\) −0.509083 −0.0361790
\(199\) 12.9061 0.914892 0.457446 0.889237i \(-0.348764\pi\)
0.457446 + 0.889237i \(0.348764\pi\)
\(200\) −0.948933 −0.0670997
\(201\) 7.45287 0.525685
\(202\) 4.66858 0.328480
\(203\) −0.0420292 −0.00294987
\(204\) 25.7062 1.79979
\(205\) −0.619883 −0.0432945
\(206\) 4.09678 0.285436
\(207\) −3.37086 −0.234291
\(208\) 17.4635 1.21087
\(209\) −11.8259 −0.818012
\(210\) 0.457756 0.0315881
\(211\) 13.4966 0.929147 0.464573 0.885535i \(-0.346208\pi\)
0.464573 + 0.885535i \(0.346208\pi\)
\(212\) 0.739795 0.0508094
\(213\) −0.540108 −0.0370076
\(214\) 0.0150821 0.00103099
\(215\) −10.9424 −0.746266
\(216\) 4.30173 0.292695
\(217\) −5.53721 −0.375891
\(218\) −1.25760 −0.0851755
\(219\) 12.7815 0.863692
\(220\) −6.66623 −0.449437
\(221\) −33.2520 −2.23677
\(222\) −4.79793 −0.322016
\(223\) 1.69038 0.113196 0.0565981 0.998397i \(-0.481975\pi\)
0.0565981 + 0.998397i \(0.481975\pi\)
\(224\) −2.77786 −0.185604
\(225\) 0.616107 0.0410738
\(226\) −2.98581 −0.198613
\(227\) −0.477040 −0.0316623 −0.0158311 0.999875i \(-0.505039\pi\)
−0.0158311 + 0.999875i \(0.505039\pi\)
\(228\) −12.7232 −0.842613
\(229\) 1.00000 0.0660819
\(230\) 1.31703 0.0868427
\(231\) 6.52740 0.429471
\(232\) −0.0398829 −0.00261844
\(233\) 20.8613 1.36667 0.683335 0.730105i \(-0.260529\pi\)
0.683335 + 0.730105i \(0.260529\pi\)
\(234\) 0.708486 0.0463152
\(235\) 1.77308 0.115663
\(236\) −4.56542 −0.297183
\(237\) 6.88023 0.446919
\(238\) 1.67559 0.108613
\(239\) −8.85965 −0.573083 −0.286542 0.958068i \(-0.592506\pi\)
−0.286542 + 0.958068i \(0.592506\pi\)
\(240\) −6.95166 −0.448728
\(241\) 7.27316 0.468505 0.234253 0.972176i \(-0.424736\pi\)
0.234253 + 0.972176i \(0.424736\pi\)
\(242\) 0.188372 0.0121090
\(243\) −6.30774 −0.404641
\(244\) 19.8940 1.27358
\(245\) −1.00000 −0.0638877
\(246\) 0.283755 0.0180915
\(247\) 16.4579 1.04719
\(248\) −5.25445 −0.333658
\(249\) 25.8159 1.63602
\(250\) −0.240720 −0.0152245
\(251\) 11.4601 0.723357 0.361679 0.932303i \(-0.382204\pi\)
0.361679 + 0.932303i \(0.382204\pi\)
\(252\) 1.19651 0.0753733
\(253\) 18.7803 1.18071
\(254\) 4.01386 0.251852
\(255\) 13.2366 0.828908
\(256\) 11.5630 0.722690
\(257\) −27.4959 −1.71515 −0.857575 0.514359i \(-0.828030\pi\)
−0.857575 + 0.514359i \(0.828030\pi\)
\(258\) 5.00895 0.311844
\(259\) 10.4814 0.651284
\(260\) 9.27734 0.575356
\(261\) 0.0258945 0.00160283
\(262\) −3.83290 −0.236798
\(263\) −25.2507 −1.55702 −0.778512 0.627630i \(-0.784025\pi\)
−0.778512 + 0.627630i \(0.784025\pi\)
\(264\) 6.19406 0.381218
\(265\) 0.380935 0.0234006
\(266\) −0.829329 −0.0508494
\(267\) −22.9428 −1.40407
\(268\) −7.61139 −0.464940
\(269\) 22.4767 1.37043 0.685215 0.728341i \(-0.259708\pi\)
0.685215 + 0.728341i \(0.259708\pi\)
\(270\) 1.09124 0.0664108
\(271\) −1.67279 −0.101615 −0.0508074 0.998708i \(-0.516179\pi\)
−0.0508074 + 0.998708i \(0.516179\pi\)
\(272\) −25.4462 −1.54291
\(273\) −9.08412 −0.549796
\(274\) 4.66531 0.281842
\(275\) −3.43257 −0.206992
\(276\) 20.2053 1.21622
\(277\) 28.7150 1.72532 0.862660 0.505784i \(-0.168797\pi\)
0.862660 + 0.505784i \(0.168797\pi\)
\(278\) 3.07954 0.184699
\(279\) 3.41152 0.204242
\(280\) −0.948933 −0.0567096
\(281\) 19.8058 1.18151 0.590756 0.806850i \(-0.298829\pi\)
0.590756 + 0.806850i \(0.298829\pi\)
\(282\) −0.811635 −0.0483322
\(283\) 30.0865 1.78846 0.894229 0.447610i \(-0.147725\pi\)
0.894229 + 0.447610i \(0.147725\pi\)
\(284\) 0.551596 0.0327312
\(285\) −6.55140 −0.388072
\(286\) −3.94725 −0.233406
\(287\) −0.619883 −0.0365905
\(288\) 1.71146 0.100849
\(289\) 31.4519 1.85011
\(290\) −0.0101173 −0.000594107 0
\(291\) 9.90231 0.580484
\(292\) −13.0533 −0.763889
\(293\) 1.45746 0.0851460 0.0425730 0.999093i \(-0.486444\pi\)
0.0425730 + 0.999093i \(0.486444\pi\)
\(294\) 0.457756 0.0266969
\(295\) −2.35082 −0.136870
\(296\) 9.94616 0.578109
\(297\) 15.5606 0.902918
\(298\) −1.62354 −0.0940492
\(299\) −26.1364 −1.51151
\(300\) −3.69302 −0.213217
\(301\) −10.9424 −0.630710
\(302\) 5.51659 0.317444
\(303\) 36.8802 2.11871
\(304\) 12.5945 0.722345
\(305\) 10.2438 0.586557
\(306\) −1.03235 −0.0590153
\(307\) −7.06213 −0.403057 −0.201529 0.979483i \(-0.564591\pi\)
−0.201529 + 0.979483i \(0.564591\pi\)
\(308\) −6.66623 −0.379844
\(309\) 32.3631 1.84107
\(310\) −1.33292 −0.0757048
\(311\) 21.7579 1.23378 0.616888 0.787051i \(-0.288393\pi\)
0.616888 + 0.787051i \(0.288393\pi\)
\(312\) −8.62022 −0.488024
\(313\) −20.7829 −1.17472 −0.587360 0.809326i \(-0.699833\pi\)
−0.587360 + 0.809326i \(0.699833\pi\)
\(314\) 0.587195 0.0331373
\(315\) 0.616107 0.0347137
\(316\) −7.02657 −0.395276
\(317\) 13.9354 0.782690 0.391345 0.920244i \(-0.372010\pi\)
0.391345 + 0.920244i \(0.372010\pi\)
\(318\) −0.174375 −0.00977846
\(319\) −0.144268 −0.00807746
\(320\) 6.64267 0.371337
\(321\) 0.119144 0.00664994
\(322\) 1.31703 0.0733954
\(323\) −23.9811 −1.33434
\(324\) 20.3308 1.12949
\(325\) 4.77707 0.264984
\(326\) 2.53512 0.140407
\(327\) −9.93461 −0.549385
\(328\) −0.588227 −0.0324794
\(329\) 1.77308 0.0977528
\(330\) 1.57128 0.0864960
\(331\) −7.36290 −0.404702 −0.202351 0.979313i \(-0.564858\pi\)
−0.202351 + 0.979313i \(0.564858\pi\)
\(332\) −26.3650 −1.44697
\(333\) −6.45768 −0.353879
\(334\) −1.08204 −0.0592068
\(335\) −3.91925 −0.214132
\(336\) −6.95166 −0.379244
\(337\) −20.6020 −1.12226 −0.561130 0.827727i \(-0.689633\pi\)
−0.561130 + 0.827727i \(0.689633\pi\)
\(338\) 2.36398 0.128584
\(339\) −23.5869 −1.28106
\(340\) −13.5181 −0.733124
\(341\) −19.0069 −1.02928
\(342\) 0.510956 0.0276293
\(343\) −1.00000 −0.0539949
\(344\) −10.3836 −0.559847
\(345\) 10.4041 0.560138
\(346\) −2.92235 −0.157107
\(347\) 31.3829 1.68472 0.842361 0.538913i \(-0.181165\pi\)
0.842361 + 0.538913i \(0.181165\pi\)
\(348\) −0.155215 −0.00832038
\(349\) 16.8136 0.900009 0.450005 0.893026i \(-0.351422\pi\)
0.450005 + 0.893026i \(0.351422\pi\)
\(350\) −0.240720 −0.0128671
\(351\) −21.6556 −1.15589
\(352\) −9.53521 −0.508228
\(353\) 6.75065 0.359301 0.179651 0.983730i \(-0.442503\pi\)
0.179651 + 0.983730i \(0.442503\pi\)
\(354\) 1.07610 0.0571941
\(355\) 0.284027 0.0150746
\(356\) 23.4307 1.24183
\(357\) 13.2366 0.700555
\(358\) 2.24949 0.118889
\(359\) 6.84940 0.361497 0.180749 0.983529i \(-0.442148\pi\)
0.180749 + 0.983529i \(0.442148\pi\)
\(360\) 0.584645 0.0308135
\(361\) −7.13064 −0.375297
\(362\) −4.52182 −0.237661
\(363\) 1.48808 0.0781037
\(364\) 9.27734 0.486264
\(365\) −6.72141 −0.351815
\(366\) −4.68914 −0.245106
\(367\) −5.06402 −0.264339 −0.132170 0.991227i \(-0.542194\pi\)
−0.132170 + 0.991227i \(0.542194\pi\)
\(368\) −20.0010 −1.04263
\(369\) 0.381914 0.0198817
\(370\) 2.52309 0.131169
\(371\) 0.380935 0.0197771
\(372\) −20.4491 −1.06023
\(373\) 4.75568 0.246240 0.123120 0.992392i \(-0.460710\pi\)
0.123120 + 0.992392i \(0.460710\pi\)
\(374\) 5.75159 0.297408
\(375\) −1.90161 −0.0981985
\(376\) 1.68253 0.0867698
\(377\) 0.200776 0.0103405
\(378\) 1.09124 0.0561273
\(379\) −20.0771 −1.03129 −0.515647 0.856801i \(-0.672448\pi\)
−0.515647 + 0.856801i \(0.672448\pi\)
\(380\) 6.69075 0.343228
\(381\) 31.7081 1.62445
\(382\) 4.50405 0.230447
\(383\) 9.67636 0.494439 0.247219 0.968960i \(-0.420483\pi\)
0.247219 + 0.968960i \(0.420483\pi\)
\(384\) −13.6055 −0.694304
\(385\) −3.43257 −0.174940
\(386\) −1.06646 −0.0542812
\(387\) 6.74170 0.342700
\(388\) −10.1129 −0.513406
\(389\) 8.46240 0.429061 0.214530 0.976717i \(-0.431178\pi\)
0.214530 + 0.976717i \(0.431178\pi\)
\(390\) −2.18673 −0.110730
\(391\) 38.0837 1.92598
\(392\) −0.948933 −0.0479284
\(393\) −30.2786 −1.52735
\(394\) −2.72485 −0.137276
\(395\) −3.61811 −0.182047
\(396\) 4.10712 0.206390
\(397\) 4.56559 0.229140 0.114570 0.993415i \(-0.463451\pi\)
0.114570 + 0.993415i \(0.463451\pi\)
\(398\) 3.10677 0.155728
\(399\) −6.55140 −0.327980
\(400\) 3.65568 0.182784
\(401\) −13.1330 −0.655830 −0.327915 0.944707i \(-0.606346\pi\)
−0.327915 + 0.944707i \(0.606346\pi\)
\(402\) 1.79406 0.0894795
\(403\) 26.4517 1.31765
\(404\) −37.6646 −1.87388
\(405\) 10.4687 0.520196
\(406\) −0.0101173 −0.000502112 0
\(407\) 35.9782 1.78337
\(408\) 12.5606 0.621844
\(409\) 14.0680 0.695618 0.347809 0.937565i \(-0.386926\pi\)
0.347809 + 0.937565i \(0.386926\pi\)
\(410\) −0.149218 −0.00736937
\(411\) 36.8543 1.81789
\(412\) −33.0515 −1.62833
\(413\) −2.35082 −0.115676
\(414\) −0.811435 −0.0398798
\(415\) −13.5758 −0.666412
\(416\) 13.2701 0.650618
\(417\) 24.3273 1.19131
\(418\) −2.84673 −0.139238
\(419\) −38.3143 −1.87177 −0.935887 0.352299i \(-0.885400\pi\)
−0.935887 + 0.352299i \(0.885400\pi\)
\(420\) −3.69302 −0.180201
\(421\) −7.79306 −0.379810 −0.189905 0.981802i \(-0.560818\pi\)
−0.189905 + 0.981802i \(0.560818\pi\)
\(422\) 3.24892 0.158155
\(423\) −1.09240 −0.0531145
\(424\) 0.361481 0.0175551
\(425\) −6.96074 −0.337646
\(426\) −0.130015 −0.00629925
\(427\) 10.2438 0.495731
\(428\) −0.121678 −0.00588151
\(429\) −31.1819 −1.50547
\(430\) −2.63406 −0.127026
\(431\) −13.6001 −0.655093 −0.327547 0.944835i \(-0.606222\pi\)
−0.327547 + 0.944835i \(0.606222\pi\)
\(432\) −16.5720 −0.797322
\(433\) −31.9761 −1.53667 −0.768336 0.640046i \(-0.778915\pi\)
−0.768336 + 0.640046i \(0.778915\pi\)
\(434\) −1.33292 −0.0639822
\(435\) −0.0799229 −0.00383201
\(436\) 10.1459 0.485901
\(437\) −18.8494 −0.901689
\(438\) 3.07676 0.147013
\(439\) 11.5839 0.552871 0.276435 0.961033i \(-0.410847\pi\)
0.276435 + 0.961033i \(0.410847\pi\)
\(440\) −3.25728 −0.155285
\(441\) 0.616107 0.0293384
\(442\) −8.00443 −0.380732
\(443\) 16.4484 0.781486 0.390743 0.920500i \(-0.372218\pi\)
0.390743 + 0.920500i \(0.372218\pi\)
\(444\) 38.7081 1.83701
\(445\) 12.0649 0.571933
\(446\) 0.406909 0.0192677
\(447\) −12.8254 −0.606620
\(448\) 6.64267 0.313837
\(449\) 22.3674 1.05558 0.527792 0.849374i \(-0.323020\pi\)
0.527792 + 0.849374i \(0.323020\pi\)
\(450\) 0.148310 0.00699139
\(451\) −2.12779 −0.100194
\(452\) 24.0885 1.13303
\(453\) 43.5791 2.04753
\(454\) −0.114833 −0.00538939
\(455\) 4.77707 0.223953
\(456\) −6.21684 −0.291130
\(457\) 33.0977 1.54825 0.774123 0.633035i \(-0.218191\pi\)
0.774123 + 0.633035i \(0.218191\pi\)
\(458\) 0.240720 0.0112481
\(459\) 31.5546 1.47284
\(460\) −10.6254 −0.495412
\(461\) −39.9378 −1.86009 −0.930045 0.367446i \(-0.880232\pi\)
−0.930045 + 0.367446i \(0.880232\pi\)
\(462\) 1.57128 0.0731025
\(463\) 20.4612 0.950915 0.475457 0.879739i \(-0.342283\pi\)
0.475457 + 0.879739i \(0.342283\pi\)
\(464\) 0.153645 0.00713280
\(465\) −10.5296 −0.488299
\(466\) 5.02174 0.232628
\(467\) −29.0159 −1.34270 −0.671348 0.741143i \(-0.734284\pi\)
−0.671348 + 0.741143i \(0.734284\pi\)
\(468\) −5.71584 −0.264215
\(469\) −3.91925 −0.180974
\(470\) 0.426816 0.0196875
\(471\) 4.63863 0.213737
\(472\) −2.23077 −0.102680
\(473\) −37.5606 −1.72704
\(474\) 1.65621 0.0760723
\(475\) 3.44519 0.158076
\(476\) −13.5181 −0.619603
\(477\) −0.234697 −0.0107460
\(478\) −2.13270 −0.0975474
\(479\) −8.55075 −0.390694 −0.195347 0.980734i \(-0.562583\pi\)
−0.195347 + 0.980734i \(0.562583\pi\)
\(480\) −5.28240 −0.241108
\(481\) −50.0705 −2.28302
\(482\) 1.75080 0.0797466
\(483\) 10.4041 0.473403
\(484\) −1.51973 −0.0690785
\(485\) −5.20734 −0.236453
\(486\) −1.51840 −0.0688761
\(487\) −2.28689 −0.103629 −0.0518145 0.998657i \(-0.516500\pi\)
−0.0518145 + 0.998657i \(0.516500\pi\)
\(488\) 9.72065 0.440033
\(489\) 20.0265 0.905631
\(490\) −0.240720 −0.0108746
\(491\) 25.0207 1.12917 0.564583 0.825376i \(-0.309037\pi\)
0.564583 + 0.825376i \(0.309037\pi\)
\(492\) −2.28924 −0.103207
\(493\) −0.292554 −0.0131760
\(494\) 3.96176 0.178248
\(495\) 2.11483 0.0950546
\(496\) 20.2423 0.908905
\(497\) 0.284027 0.0127404
\(498\) 6.21442 0.278475
\(499\) −18.9725 −0.849328 −0.424664 0.905351i \(-0.639608\pi\)
−0.424664 + 0.905351i \(0.639608\pi\)
\(500\) 1.94205 0.0868513
\(501\) −8.54776 −0.381886
\(502\) 2.75869 0.123126
\(503\) 5.13944 0.229156 0.114578 0.993414i \(-0.463448\pi\)
0.114578 + 0.993414i \(0.463448\pi\)
\(504\) 0.584645 0.0260421
\(505\) −19.3942 −0.863031
\(506\) 4.52081 0.200975
\(507\) 18.6746 0.829369
\(508\) −32.3825 −1.43674
\(509\) 9.25765 0.410338 0.205169 0.978727i \(-0.434226\pi\)
0.205169 + 0.978727i \(0.434226\pi\)
\(510\) 3.18632 0.141093
\(511\) −6.72141 −0.297338
\(512\) 17.0930 0.755410
\(513\) −15.6178 −0.689544
\(514\) −6.61884 −0.291944
\(515\) −17.0188 −0.749939
\(516\) −40.4106 −1.77898
\(517\) 6.08621 0.267671
\(518\) 2.52309 0.110858
\(519\) −23.0856 −1.01334
\(520\) 4.53312 0.198791
\(521\) 28.4912 1.24822 0.624111 0.781336i \(-0.285461\pi\)
0.624111 + 0.781336i \(0.285461\pi\)
\(522\) 0.00623333 0.000272825 0
\(523\) −12.0533 −0.527053 −0.263527 0.964652i \(-0.584886\pi\)
−0.263527 + 0.964652i \(0.584886\pi\)
\(524\) 30.9226 1.35086
\(525\) −1.90161 −0.0829929
\(526\) −6.07835 −0.265029
\(527\) −38.5431 −1.67896
\(528\) −23.8621 −1.03846
\(529\) 6.93422 0.301488
\(530\) 0.0916988 0.00398314
\(531\) 1.44836 0.0628534
\(532\) 6.69075 0.290081
\(533\) 2.96123 0.128265
\(534\) −5.52279 −0.238995
\(535\) −0.0626541 −0.00270878
\(536\) −3.71911 −0.160641
\(537\) 17.7702 0.766839
\(538\) 5.41061 0.233268
\(539\) −3.43257 −0.147851
\(540\) −8.80377 −0.378854
\(541\) 14.2180 0.611280 0.305640 0.952147i \(-0.401130\pi\)
0.305640 + 0.952147i \(0.401130\pi\)
\(542\) −0.402675 −0.0172964
\(543\) −35.7207 −1.53292
\(544\) −19.3360 −0.829024
\(545\) 5.22432 0.223785
\(546\) −2.18673 −0.0935835
\(547\) −7.81435 −0.334118 −0.167059 0.985947i \(-0.553427\pi\)
−0.167059 + 0.985947i \(0.553427\pi\)
\(548\) −37.6382 −1.60782
\(549\) −6.31126 −0.269358
\(550\) −0.826290 −0.0352331
\(551\) 0.144799 0.00616863
\(552\) 9.87280 0.420214
\(553\) −3.61811 −0.153858
\(554\) 6.91230 0.293675
\(555\) 19.9315 0.846046
\(556\) −24.8447 −1.05365
\(557\) 41.2413 1.74745 0.873725 0.486421i \(-0.161698\pi\)
0.873725 + 0.486421i \(0.161698\pi\)
\(558\) 0.821222 0.0347651
\(559\) 52.2727 2.21090
\(560\) 3.65568 0.154481
\(561\) 45.4355 1.91829
\(562\) 4.76765 0.201111
\(563\) 12.8622 0.542078 0.271039 0.962568i \(-0.412633\pi\)
0.271039 + 0.962568i \(0.412633\pi\)
\(564\) 6.54801 0.275721
\(565\) 12.4036 0.521825
\(566\) 7.24244 0.304423
\(567\) 10.4687 0.439646
\(568\) 0.269523 0.0113089
\(569\) 6.63973 0.278352 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(570\) −1.57706 −0.0660556
\(571\) −17.5331 −0.733739 −0.366870 0.930272i \(-0.619571\pi\)
−0.366870 + 0.930272i \(0.619571\pi\)
\(572\) 31.8451 1.33151
\(573\) 35.5804 1.48639
\(574\) −0.149218 −0.00622826
\(575\) −5.47122 −0.228166
\(576\) −4.09260 −0.170525
\(577\) 18.8259 0.783731 0.391865 0.920023i \(-0.371830\pi\)
0.391865 + 0.920023i \(0.371830\pi\)
\(578\) 7.57113 0.314917
\(579\) −8.42464 −0.350116
\(580\) 0.0816229 0.00338921
\(581\) −13.5758 −0.563221
\(582\) 2.38369 0.0988071
\(583\) 1.30758 0.0541546
\(584\) −6.37817 −0.263930
\(585\) −2.94319 −0.121686
\(586\) 0.350842 0.0144931
\(587\) 7.19043 0.296781 0.148390 0.988929i \(-0.452591\pi\)
0.148390 + 0.988929i \(0.452591\pi\)
\(588\) −3.69302 −0.152298
\(589\) 19.0768 0.786045
\(590\) −0.565890 −0.0232973
\(591\) −21.5253 −0.885434
\(592\) −38.3167 −1.57481
\(593\) 26.9700 1.10752 0.553762 0.832675i \(-0.313192\pi\)
0.553762 + 0.832675i \(0.313192\pi\)
\(594\) 3.74576 0.153690
\(595\) −6.96074 −0.285363
\(596\) 13.0982 0.536523
\(597\) 24.5424 1.00445
\(598\) −6.29157 −0.257281
\(599\) −22.0008 −0.898930 −0.449465 0.893298i \(-0.648385\pi\)
−0.449465 + 0.893298i \(0.648385\pi\)
\(600\) −1.80450 −0.0736683
\(601\) 27.7028 1.13002 0.565011 0.825083i \(-0.308872\pi\)
0.565011 + 0.825083i \(0.308872\pi\)
\(602\) −2.63406 −0.107356
\(603\) 2.41468 0.0983333
\(604\) −44.5061 −1.81093
\(605\) −0.782536 −0.0318146
\(606\) 8.87781 0.360636
\(607\) −43.0791 −1.74853 −0.874263 0.485452i \(-0.838655\pi\)
−0.874263 + 0.485452i \(0.838655\pi\)
\(608\) 9.57028 0.388126
\(609\) −0.0799229 −0.00323864
\(610\) 2.46589 0.0998408
\(611\) −8.47011 −0.342664
\(612\) 8.32862 0.336665
\(613\) 5.92926 0.239481 0.119740 0.992805i \(-0.461794\pi\)
0.119740 + 0.992805i \(0.461794\pi\)
\(614\) −1.70000 −0.0686064
\(615\) −1.17877 −0.0475327
\(616\) −3.25728 −0.131240
\(617\) 7.92132 0.318900 0.159450 0.987206i \(-0.449028\pi\)
0.159450 + 0.987206i \(0.449028\pi\)
\(618\) 7.79046 0.313378
\(619\) −38.7590 −1.55785 −0.778927 0.627114i \(-0.784236\pi\)
−0.778927 + 0.627114i \(0.784236\pi\)
\(620\) 10.7536 0.431874
\(621\) 24.8023 0.995281
\(622\) 5.23756 0.210007
\(623\) 12.0649 0.483371
\(624\) 33.2086 1.32941
\(625\) 1.00000 0.0400000
\(626\) −5.00287 −0.199955
\(627\) −22.4881 −0.898090
\(628\) −4.73730 −0.189039
\(629\) 72.9585 2.90904
\(630\) 0.148310 0.00590880
\(631\) −49.4613 −1.96902 −0.984512 0.175320i \(-0.943904\pi\)
−0.984512 + 0.175320i \(0.943904\pi\)
\(632\) −3.43335 −0.136571
\(633\) 25.6653 1.02010
\(634\) 3.35454 0.133226
\(635\) −16.6744 −0.661702
\(636\) 1.40680 0.0557832
\(637\) 4.77707 0.189275
\(638\) −0.0347283 −0.00137491
\(639\) −0.174991 −0.00692255
\(640\) 7.15475 0.282816
\(641\) −39.9368 −1.57741 −0.788705 0.614771i \(-0.789248\pi\)
−0.788705 + 0.614771i \(0.789248\pi\)
\(642\) 0.0286803 0.00113192
\(643\) −6.30833 −0.248776 −0.124388 0.992234i \(-0.539697\pi\)
−0.124388 + 0.992234i \(0.539697\pi\)
\(644\) −10.6254 −0.418699
\(645\) −20.8082 −0.819321
\(646\) −5.77274 −0.227126
\(647\) 8.87796 0.349029 0.174514 0.984655i \(-0.444164\pi\)
0.174514 + 0.984655i \(0.444164\pi\)
\(648\) 9.93413 0.390249
\(649\) −8.06935 −0.316750
\(650\) 1.14994 0.0451043
\(651\) −10.5296 −0.412688
\(652\) −20.4525 −0.800981
\(653\) 24.3737 0.953816 0.476908 0.878953i \(-0.341758\pi\)
0.476908 + 0.878953i \(0.341758\pi\)
\(654\) −2.39146 −0.0935136
\(655\) 15.9226 0.622149
\(656\) 2.26609 0.0884760
\(657\) 4.14111 0.161560
\(658\) 0.426816 0.0166390
\(659\) 26.5238 1.03322 0.516609 0.856221i \(-0.327194\pi\)
0.516609 + 0.856221i \(0.327194\pi\)
\(660\) −12.6766 −0.493434
\(661\) −48.0445 −1.86871 −0.934356 0.356340i \(-0.884024\pi\)
−0.934356 + 0.356340i \(0.884024\pi\)
\(662\) −1.77240 −0.0688863
\(663\) −63.2322 −2.45574
\(664\) −12.8826 −0.499941
\(665\) 3.44519 0.133599
\(666\) −1.55450 −0.0602355
\(667\) −0.229951 −0.00890373
\(668\) 8.72957 0.337757
\(669\) 3.21444 0.124277
\(670\) −0.943444 −0.0364484
\(671\) 35.1625 1.35743
\(672\) −5.28240 −0.203773
\(673\) 2.63014 0.101385 0.0506923 0.998714i \(-0.483857\pi\)
0.0506923 + 0.998714i \(0.483857\pi\)
\(674\) −4.95932 −0.191026
\(675\) −4.53323 −0.174484
\(676\) −19.0718 −0.733532
\(677\) 18.0691 0.694452 0.347226 0.937781i \(-0.387124\pi\)
0.347226 + 0.937781i \(0.387124\pi\)
\(678\) −5.67784 −0.218056
\(679\) −5.20734 −0.199839
\(680\) −6.60528 −0.253301
\(681\) −0.907142 −0.0347618
\(682\) −4.57534 −0.175199
\(683\) −44.7602 −1.71270 −0.856350 0.516395i \(-0.827274\pi\)
−0.856350 + 0.516395i \(0.827274\pi\)
\(684\) −4.12222 −0.157617
\(685\) −19.3806 −0.740495
\(686\) −0.240720 −0.00919075
\(687\) 1.90161 0.0725508
\(688\) 40.0020 1.52506
\(689\) −1.81975 −0.0693271
\(690\) 2.50448 0.0953440
\(691\) −28.2412 −1.07434 −0.537172 0.843473i \(-0.680507\pi\)
−0.537172 + 0.843473i \(0.680507\pi\)
\(692\) 23.5766 0.896247
\(693\) 2.11483 0.0803358
\(694\) 7.55451 0.286765
\(695\) −12.7930 −0.485267
\(696\) −0.0758415 −0.00287476
\(697\) −4.31484 −0.163436
\(698\) 4.04737 0.153195
\(699\) 39.6700 1.50046
\(700\) 1.94205 0.0734027
\(701\) 32.0276 1.20967 0.604833 0.796352i \(-0.293240\pi\)
0.604833 + 0.796352i \(0.293240\pi\)
\(702\) −5.21294 −0.196750
\(703\) −36.1105 −1.36193
\(704\) 22.8014 0.859361
\(705\) 3.37169 0.126985
\(706\) 1.62502 0.0611585
\(707\) −19.3942 −0.729395
\(708\) −8.68163 −0.326276
\(709\) 28.4060 1.06681 0.533405 0.845860i \(-0.320912\pi\)
0.533405 + 0.845860i \(0.320912\pi\)
\(710\) 0.0683712 0.00256593
\(711\) 2.22915 0.0835995
\(712\) 11.4488 0.429062
\(713\) −30.2953 −1.13457
\(714\) 3.18632 0.119245
\(715\) 16.3976 0.613237
\(716\) −18.1481 −0.678227
\(717\) −16.8476 −0.629184
\(718\) 1.64879 0.0615323
\(719\) −23.7667 −0.886349 −0.443175 0.896435i \(-0.646148\pi\)
−0.443175 + 0.896435i \(0.646148\pi\)
\(720\) −2.25229 −0.0839379
\(721\) −17.0188 −0.633814
\(722\) −1.71649 −0.0638812
\(723\) 13.8307 0.514368
\(724\) 36.4805 1.35579
\(725\) 0.0420292 0.00156092
\(726\) 0.358210 0.0132944
\(727\) 41.5438 1.54077 0.770387 0.637577i \(-0.220063\pi\)
0.770387 + 0.637577i \(0.220063\pi\)
\(728\) 4.53312 0.168009
\(729\) 19.4114 0.718940
\(730\) −1.61798 −0.0598842
\(731\) −76.1673 −2.81715
\(732\) 37.8305 1.39825
\(733\) −36.4602 −1.34669 −0.673344 0.739329i \(-0.735143\pi\)
−0.673344 + 0.739329i \(0.735143\pi\)
\(734\) −1.21901 −0.0449946
\(735\) −1.90161 −0.0701418
\(736\) −15.1983 −0.560217
\(737\) −13.4531 −0.495551
\(738\) 0.0919346 0.00338416
\(739\) 36.2979 1.33524 0.667620 0.744502i \(-0.267313\pi\)
0.667620 + 0.744502i \(0.267313\pi\)
\(740\) −20.3555 −0.748282
\(741\) 31.2965 1.14971
\(742\) 0.0916988 0.00336637
\(743\) 1.97196 0.0723441 0.0361721 0.999346i \(-0.488484\pi\)
0.0361721 + 0.999346i \(0.488484\pi\)
\(744\) −9.99189 −0.366320
\(745\) 6.74451 0.247100
\(746\) 1.14479 0.0419137
\(747\) 8.36418 0.306029
\(748\) −46.4019 −1.69662
\(749\) −0.0626541 −0.00228933
\(750\) −0.457756 −0.0167149
\(751\) 28.7317 1.04844 0.524218 0.851584i \(-0.324358\pi\)
0.524218 + 0.851584i \(0.324358\pi\)
\(752\) −6.48180 −0.236367
\(753\) 21.7927 0.794169
\(754\) 0.0483310 0.00176011
\(755\) −22.9170 −0.834035
\(756\) −8.80377 −0.320190
\(757\) 10.9738 0.398848 0.199424 0.979913i \(-0.436093\pi\)
0.199424 + 0.979913i \(0.436093\pi\)
\(758\) −4.83298 −0.175542
\(759\) 35.7128 1.29629
\(760\) 3.26926 0.118588
\(761\) −20.2201 −0.732978 −0.366489 0.930422i \(-0.619440\pi\)
−0.366489 + 0.930422i \(0.619440\pi\)
\(762\) 7.63278 0.276507
\(763\) 5.22432 0.189133
\(764\) −36.3372 −1.31463
\(765\) 4.28857 0.155053
\(766\) 2.32930 0.0841610
\(767\) 11.2300 0.405493
\(768\) 21.9884 0.793437
\(769\) −41.5057 −1.49673 −0.748367 0.663284i \(-0.769162\pi\)
−0.748367 + 0.663284i \(0.769162\pi\)
\(770\) −0.826290 −0.0297774
\(771\) −52.2865 −1.88305
\(772\) 8.60383 0.309659
\(773\) −31.5613 −1.13518 −0.567591 0.823311i \(-0.692124\pi\)
−0.567591 + 0.823311i \(0.692124\pi\)
\(774\) 1.62287 0.0583327
\(775\) 5.53721 0.198903
\(776\) −4.94142 −0.177387
\(777\) 19.9315 0.715040
\(778\) 2.03707 0.0730326
\(779\) 2.13562 0.0765164
\(780\) 17.6418 0.631679
\(781\) 0.974944 0.0348862
\(782\) 9.16754 0.327830
\(783\) −0.190528 −0.00680890
\(784\) 3.65568 0.130560
\(785\) −2.43932 −0.0870632
\(786\) −7.28868 −0.259978
\(787\) −17.3767 −0.619412 −0.309706 0.950832i \(-0.600231\pi\)
−0.309706 + 0.950832i \(0.600231\pi\)
\(788\) 21.9832 0.783119
\(789\) −48.0168 −1.70945
\(790\) −0.870954 −0.0309872
\(791\) 12.4036 0.441023
\(792\) 2.00683 0.0713097
\(793\) −48.9353 −1.73774
\(794\) 1.09903 0.0390032
\(795\) 0.724388 0.0256914
\(796\) −25.0644 −0.888385
\(797\) 13.4795 0.477470 0.238735 0.971085i \(-0.423267\pi\)
0.238735 + 0.971085i \(0.423267\pi\)
\(798\) −1.57706 −0.0558272
\(799\) 12.3419 0.436626
\(800\) 2.77786 0.0982123
\(801\) −7.43329 −0.262643
\(802\) −3.16138 −0.111632
\(803\) −23.0717 −0.814183
\(804\) −14.4739 −0.510454
\(805\) −5.47122 −0.192835
\(806\) 6.36746 0.224284
\(807\) 42.7419 1.50459
\(808\) −18.4038 −0.647444
\(809\) −10.5708 −0.371650 −0.185825 0.982583i \(-0.559496\pi\)
−0.185825 + 0.982583i \(0.559496\pi\)
\(810\) 2.52004 0.0885451
\(811\) 18.7735 0.659227 0.329614 0.944116i \(-0.393082\pi\)
0.329614 + 0.944116i \(0.393082\pi\)
\(812\) 0.0816229 0.00286440
\(813\) −3.18099 −0.111562
\(814\) 8.66069 0.303557
\(815\) −10.5314 −0.368898
\(816\) −48.3888 −1.69395
\(817\) 37.6987 1.31891
\(818\) 3.38646 0.118405
\(819\) −2.94319 −0.102843
\(820\) 1.20385 0.0420401
\(821\) 18.3521 0.640492 0.320246 0.947334i \(-0.396234\pi\)
0.320246 + 0.947334i \(0.396234\pi\)
\(822\) 8.87158 0.309432
\(823\) −17.1630 −0.598265 −0.299133 0.954212i \(-0.596697\pi\)
−0.299133 + 0.954212i \(0.596697\pi\)
\(824\) −16.1497 −0.562602
\(825\) −6.52740 −0.227255
\(826\) −0.565890 −0.0196898
\(827\) −13.8512 −0.481653 −0.240827 0.970568i \(-0.577419\pi\)
−0.240827 + 0.970568i \(0.577419\pi\)
\(828\) 6.54639 0.227503
\(829\) 2.51559 0.0873699 0.0436850 0.999045i \(-0.486090\pi\)
0.0436850 + 0.999045i \(0.486090\pi\)
\(830\) −3.26798 −0.113433
\(831\) 54.6047 1.89422
\(832\) −31.7325 −1.10013
\(833\) −6.96074 −0.241175
\(834\) 5.85607 0.202779
\(835\) 4.49502 0.155557
\(836\) 22.9665 0.794312
\(837\) −25.1014 −0.867633
\(838\) −9.22303 −0.318604
\(839\) 21.0497 0.726716 0.363358 0.931650i \(-0.381630\pi\)
0.363358 + 0.931650i \(0.381630\pi\)
\(840\) −1.80450 −0.0622611
\(841\) −28.9982 −0.999939
\(842\) −1.87595 −0.0646494
\(843\) 37.6628 1.29717
\(844\) −26.2112 −0.902226
\(845\) −9.82044 −0.337833
\(846\) −0.262964 −0.00904090
\(847\) −0.782536 −0.0268883
\(848\) −1.39257 −0.0478212
\(849\) 57.2127 1.96354
\(850\) −1.67559 −0.0574724
\(851\) 57.3461 1.96580
\(852\) 1.04892 0.0359354
\(853\) −13.0491 −0.446794 −0.223397 0.974728i \(-0.571715\pi\)
−0.223397 + 0.974728i \(0.571715\pi\)
\(854\) 2.46589 0.0843809
\(855\) −2.12261 −0.0725917
\(856\) −0.0594546 −0.00203212
\(857\) −13.6004 −0.464582 −0.232291 0.972646i \(-0.574622\pi\)
−0.232291 + 0.972646i \(0.574622\pi\)
\(858\) −7.50611 −0.256254
\(859\) 9.07681 0.309697 0.154848 0.987938i \(-0.450511\pi\)
0.154848 + 0.987938i \(0.450511\pi\)
\(860\) 21.2508 0.724645
\(861\) −1.17877 −0.0401725
\(862\) −3.27382 −0.111507
\(863\) −21.9141 −0.745966 −0.372983 0.927838i \(-0.621665\pi\)
−0.372983 + 0.927838i \(0.621665\pi\)
\(864\) −12.5927 −0.428412
\(865\) 12.1400 0.412773
\(866\) −7.69730 −0.261565
\(867\) 59.8092 2.03123
\(868\) 10.7536 0.365000
\(869\) −12.4194 −0.421300
\(870\) −0.0192391 −0.000652266 0
\(871\) 18.7225 0.634389
\(872\) 4.95753 0.167883
\(873\) 3.20828 0.108584
\(874\) −4.53744 −0.153481
\(875\) 1.00000 0.0338062
\(876\) −24.8223 −0.838668
\(877\) 5.63017 0.190117 0.0950586 0.995472i \(-0.469696\pi\)
0.0950586 + 0.995472i \(0.469696\pi\)
\(878\) 2.78849 0.0941069
\(879\) 2.77152 0.0934812
\(880\) 12.5484 0.423006
\(881\) 33.6477 1.13362 0.566810 0.823849i \(-0.308178\pi\)
0.566810 + 0.823849i \(0.308178\pi\)
\(882\) 0.148310 0.00499385
\(883\) −2.46340 −0.0828999 −0.0414499 0.999141i \(-0.513198\pi\)
−0.0414499 + 0.999141i \(0.513198\pi\)
\(884\) 64.5771 2.17196
\(885\) −4.47033 −0.150269
\(886\) 3.95946 0.133021
\(887\) −26.9713 −0.905606 −0.452803 0.891611i \(-0.649576\pi\)
−0.452803 + 0.891611i \(0.649576\pi\)
\(888\) 18.9137 0.634702
\(889\) −16.6744 −0.559240
\(890\) 2.90428 0.0973516
\(891\) 35.9347 1.20386
\(892\) −3.28281 −0.109917
\(893\) −6.10859 −0.204416
\(894\) −3.08734 −0.103256
\(895\) −9.34481 −0.312363
\(896\) 7.15475 0.239024
\(897\) −49.7012 −1.65947
\(898\) 5.38429 0.179676
\(899\) 0.232724 0.00776179
\(900\) −1.19651 −0.0398838
\(901\) 2.65159 0.0883372
\(902\) −0.512203 −0.0170545
\(903\) −20.8082 −0.692452
\(904\) 11.7702 0.391472
\(905\) 18.7845 0.624418
\(906\) 10.4904 0.348520
\(907\) −8.43003 −0.279915 −0.139957 0.990158i \(-0.544697\pi\)
−0.139957 + 0.990158i \(0.544697\pi\)
\(908\) 0.926437 0.0307449
\(909\) 11.9489 0.396321
\(910\) 1.14994 0.0381201
\(911\) −34.1000 −1.12978 −0.564891 0.825165i \(-0.691082\pi\)
−0.564891 + 0.825165i \(0.691082\pi\)
\(912\) 23.9498 0.793058
\(913\) −46.6000 −1.54224
\(914\) 7.96730 0.263535
\(915\) 19.4796 0.643977
\(916\) −1.94205 −0.0641673
\(917\) 15.9226 0.525812
\(918\) 7.59584 0.250700
\(919\) −4.08914 −0.134888 −0.0674441 0.997723i \(-0.521484\pi\)
−0.0674441 + 0.997723i \(0.521484\pi\)
\(920\) −5.19182 −0.171169
\(921\) −13.4294 −0.442514
\(922\) −9.61385 −0.316615
\(923\) −1.35682 −0.0446603
\(924\) −12.6766 −0.417028
\(925\) −10.4814 −0.344627
\(926\) 4.92544 0.161860
\(927\) 10.4854 0.344387
\(928\) 0.116751 0.00383255
\(929\) 1.81293 0.0594803 0.0297401 0.999558i \(-0.490532\pi\)
0.0297401 + 0.999558i \(0.490532\pi\)
\(930\) −2.53469 −0.0831158
\(931\) 3.44519 0.112912
\(932\) −40.5138 −1.32707
\(933\) 41.3749 1.35455
\(934\) −6.98472 −0.228547
\(935\) −23.8932 −0.781392
\(936\) −2.79289 −0.0912885
\(937\) 33.4446 1.09259 0.546293 0.837594i \(-0.316038\pi\)
0.546293 + 0.837594i \(0.316038\pi\)
\(938\) −0.943444 −0.0308045
\(939\) −39.5209 −1.28972
\(940\) −3.44341 −0.112312
\(941\) 26.8077 0.873908 0.436954 0.899484i \(-0.356057\pi\)
0.436954 + 0.899484i \(0.356057\pi\)
\(942\) 1.11661 0.0363812
\(943\) −3.39151 −0.110443
\(944\) 8.59384 0.279706
\(945\) −4.53323 −0.147466
\(946\) −9.04160 −0.293968
\(947\) −5.83037 −0.189462 −0.0947308 0.995503i \(-0.530199\pi\)
−0.0947308 + 0.995503i \(0.530199\pi\)
\(948\) −13.3618 −0.433970
\(949\) 32.1087 1.04229
\(950\) 0.829329 0.0269070
\(951\) 26.4997 0.859310
\(952\) −6.60528 −0.214078
\(953\) −44.2208 −1.43245 −0.716227 0.697868i \(-0.754132\pi\)
−0.716227 + 0.697868i \(0.754132\pi\)
\(954\) −0.0564963 −0.00182913
\(955\) −18.7107 −0.605465
\(956\) 17.2059 0.556479
\(957\) −0.274341 −0.00886819
\(958\) −2.05834 −0.0665020
\(959\) −19.3806 −0.625832
\(960\) 12.6317 0.407688
\(961\) −0.339257 −0.0109438
\(962\) −12.0530 −0.388604
\(963\) 0.0386017 0.00124392
\(964\) −14.1249 −0.454931
\(965\) 4.43027 0.142616
\(966\) 2.50448 0.0805803
\(967\) 25.3512 0.815238 0.407619 0.913152i \(-0.366359\pi\)
0.407619 + 0.913152i \(0.366359\pi\)
\(968\) −0.742574 −0.0238672
\(969\) −45.6026 −1.46497
\(970\) −1.25351 −0.0402479
\(971\) 12.5158 0.401652 0.200826 0.979627i \(-0.435637\pi\)
0.200826 + 0.979627i \(0.435637\pi\)
\(972\) 12.2500 0.392918
\(973\) −12.7930 −0.410125
\(974\) −0.550502 −0.0176392
\(975\) 9.08412 0.290925
\(976\) −37.4480 −1.19868
\(977\) −3.15070 −0.100800 −0.0504000 0.998729i \(-0.516050\pi\)
−0.0504000 + 0.998729i \(0.516050\pi\)
\(978\) 4.82079 0.154152
\(979\) 41.4137 1.32359
\(980\) 1.94205 0.0620366
\(981\) −3.21874 −0.102767
\(982\) 6.02298 0.192201
\(983\) −20.8144 −0.663878 −0.331939 0.943301i \(-0.607703\pi\)
−0.331939 + 0.943301i \(0.607703\pi\)
\(984\) −1.11858 −0.0356589
\(985\) 11.3196 0.360671
\(986\) −0.0704238 −0.00224275
\(987\) 3.37169 0.107322
\(988\) −31.9622 −1.01685
\(989\) −59.8683 −1.90370
\(990\) 0.509083 0.0161797
\(991\) −43.1370 −1.37029 −0.685146 0.728406i \(-0.740262\pi\)
−0.685146 + 0.728406i \(0.740262\pi\)
\(992\) 15.3816 0.488367
\(993\) −14.0013 −0.444319
\(994\) 0.0683712 0.00216860
\(995\) −12.9061 −0.409152
\(996\) −50.1359 −1.58862
\(997\) −16.0822 −0.509328 −0.254664 0.967030i \(-0.581965\pi\)
−0.254664 + 0.967030i \(0.581965\pi\)
\(998\) −4.56708 −0.144568
\(999\) 47.5146 1.50330
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 \(a_p\))