Properties

Label 8015.2.a.l.1.24
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 1.24
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +O(q^{10})\) \(q-0.737016 q^{2} +0.825255 q^{3} -1.45681 q^{4} -1.00000 q^{5} -0.608226 q^{6} -1.00000 q^{7} +2.54772 q^{8} -2.31895 q^{9} +0.737016 q^{10} +0.0628820 q^{11} -1.20224 q^{12} -0.351818 q^{13} +0.737016 q^{14} -0.825255 q^{15} +1.03591 q^{16} -2.54461 q^{17} +1.70911 q^{18} -5.35415 q^{19} +1.45681 q^{20} -0.825255 q^{21} -0.0463450 q^{22} +1.58772 q^{23} +2.10252 q^{24} +1.00000 q^{25} +0.259296 q^{26} -4.38949 q^{27} +1.45681 q^{28} -1.09035 q^{29} +0.608226 q^{30} -7.26184 q^{31} -5.85892 q^{32} +0.0518937 q^{33} +1.87541 q^{34} +1.00000 q^{35} +3.37827 q^{36} -5.46649 q^{37} +3.94609 q^{38} -0.290340 q^{39} -2.54772 q^{40} +1.65375 q^{41} +0.608226 q^{42} +11.9328 q^{43} -0.0916070 q^{44} +2.31895 q^{45} -1.17017 q^{46} -9.00250 q^{47} +0.854886 q^{48} +1.00000 q^{49} -0.737016 q^{50} -2.09995 q^{51} +0.512532 q^{52} -3.24267 q^{53} +3.23512 q^{54} -0.0628820 q^{55} -2.54772 q^{56} -4.41853 q^{57} +0.803602 q^{58} +8.82509 q^{59} +1.20224 q^{60} -3.79486 q^{61} +5.35209 q^{62} +2.31895 q^{63} +2.24631 q^{64} +0.351818 q^{65} -0.0382464 q^{66} +2.20636 q^{67} +3.70700 q^{68} +1.31027 q^{69} -0.737016 q^{70} -13.4509 q^{71} -5.90805 q^{72} -14.4189 q^{73} +4.02889 q^{74} +0.825255 q^{75} +7.79996 q^{76} -0.0628820 q^{77} +0.213985 q^{78} +0.110548 q^{79} -1.03591 q^{80} +3.33441 q^{81} -1.21884 q^{82} +13.1669 q^{83} +1.20224 q^{84} +2.54461 q^{85} -8.79468 q^{86} -0.899813 q^{87} +0.160206 q^{88} +17.4818 q^{89} -1.70911 q^{90} +0.351818 q^{91} -2.31300 q^{92} -5.99287 q^{93} +6.63498 q^{94} +5.35415 q^{95} -4.83510 q^{96} +9.00690 q^{97} -0.737016 q^{98} -0.145820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.737016 −0.521149 −0.260574 0.965454i \(-0.583912\pi\)
−0.260574 + 0.965454i \(0.583912\pi\)
\(3\) 0.825255 0.476461 0.238231 0.971209i \(-0.423433\pi\)
0.238231 + 0.971209i \(0.423433\pi\)
\(4\) −1.45681 −0.728404
\(5\) −1.00000 −0.447214
\(6\) −0.608226 −0.248307
\(7\) −1.00000 −0.377964
\(8\) 2.54772 0.900756
\(9\) −2.31895 −0.772985
\(10\) 0.737016 0.233065
\(11\) 0.0628820 0.0189596 0.00947982 0.999955i \(-0.496982\pi\)
0.00947982 + 0.999955i \(0.496982\pi\)
\(12\) −1.20224 −0.347056
\(13\) −0.351818 −0.0975768 −0.0487884 0.998809i \(-0.515536\pi\)
−0.0487884 + 0.998809i \(0.515536\pi\)
\(14\) 0.737016 0.196976
\(15\) −0.825255 −0.213080
\(16\) 1.03591 0.258976
\(17\) −2.54461 −0.617157 −0.308579 0.951199i \(-0.599853\pi\)
−0.308579 + 0.951199i \(0.599853\pi\)
\(18\) 1.70911 0.402840
\(19\) −5.35415 −1.22833 −0.614163 0.789179i \(-0.710506\pi\)
−0.614163 + 0.789179i \(0.710506\pi\)
\(20\) 1.45681 0.325752
\(21\) −0.825255 −0.180085
\(22\) −0.0463450 −0.00988079
\(23\) 1.58772 0.331062 0.165531 0.986205i \(-0.447066\pi\)
0.165531 + 0.986205i \(0.447066\pi\)
\(24\) 2.10252 0.429175
\(25\) 1.00000 0.200000
\(26\) 0.259296 0.0508521
\(27\) −4.38949 −0.844758
\(28\) 1.45681 0.275311
\(29\) −1.09035 −0.202472 −0.101236 0.994862i \(-0.532280\pi\)
−0.101236 + 0.994862i \(0.532280\pi\)
\(30\) 0.608226 0.111046
\(31\) −7.26184 −1.30426 −0.652132 0.758105i \(-0.726125\pi\)
−0.652132 + 0.758105i \(0.726125\pi\)
\(32\) −5.85892 −1.03572
\(33\) 0.0518937 0.00903353
\(34\) 1.87541 0.321631
\(35\) 1.00000 0.169031
\(36\) 3.37827 0.563045
\(37\) −5.46649 −0.898686 −0.449343 0.893359i \(-0.648342\pi\)
−0.449343 + 0.893359i \(0.648342\pi\)
\(38\) 3.94609 0.640140
\(39\) −0.290340 −0.0464916
\(40\) −2.54772 −0.402830
\(41\) 1.65375 0.258272 0.129136 0.991627i \(-0.458780\pi\)
0.129136 + 0.991627i \(0.458780\pi\)
\(42\) 0.608226 0.0938513
\(43\) 11.9328 1.81974 0.909870 0.414894i \(-0.136181\pi\)
0.909870 + 0.414894i \(0.136181\pi\)
\(44\) −0.0916070 −0.0138103
\(45\) 2.31895 0.345689
\(46\) −1.17017 −0.172532
\(47\) −9.00250 −1.31315 −0.656575 0.754261i \(-0.727995\pi\)
−0.656575 + 0.754261i \(0.727995\pi\)
\(48\) 0.854886 0.123392
\(49\) 1.00000 0.142857
\(50\) −0.737016 −0.104230
\(51\) −2.09995 −0.294051
\(52\) 0.512532 0.0710754
\(53\) −3.24267 −0.445415 −0.222708 0.974885i \(-0.571490\pi\)
−0.222708 + 0.974885i \(0.571490\pi\)
\(54\) 3.23512 0.440245
\(55\) −0.0628820 −0.00847901
\(56\) −2.54772 −0.340454
\(57\) −4.41853 −0.585249
\(58\) 0.803602 0.105518
\(59\) 8.82509 1.14893 0.574465 0.818529i \(-0.305210\pi\)
0.574465 + 0.818529i \(0.305210\pi\)
\(60\) 1.20224 0.155208
\(61\) −3.79486 −0.485882 −0.242941 0.970041i \(-0.578112\pi\)
−0.242941 + 0.970041i \(0.578112\pi\)
\(62\) 5.35209 0.679716
\(63\) 2.31895 0.292161
\(64\) 2.24631 0.280788
\(65\) 0.351818 0.0436377
\(66\) −0.0382464 −0.00470781
\(67\) 2.20636 0.269550 0.134775 0.990876i \(-0.456969\pi\)
0.134775 + 0.990876i \(0.456969\pi\)
\(68\) 3.70700 0.449540
\(69\) 1.31027 0.157738
\(70\) −0.737016 −0.0880902
\(71\) −13.4509 −1.59633 −0.798163 0.602441i \(-0.794195\pi\)
−0.798163 + 0.602441i \(0.794195\pi\)
\(72\) −5.90805 −0.696270
\(73\) −14.4189 −1.68761 −0.843804 0.536652i \(-0.819689\pi\)
−0.843804 + 0.536652i \(0.819689\pi\)
\(74\) 4.02889 0.468349
\(75\) 0.825255 0.0952922
\(76\) 7.79996 0.894717
\(77\) −0.0628820 −0.00716607
\(78\) 0.213985 0.0242290
\(79\) 0.110548 0.0124376 0.00621880 0.999981i \(-0.498020\pi\)
0.00621880 + 0.999981i \(0.498020\pi\)
\(80\) −1.03591 −0.115818
\(81\) 3.33441 0.370491
\(82\) −1.21884 −0.134598
\(83\) 13.1669 1.44526 0.722630 0.691235i \(-0.242933\pi\)
0.722630 + 0.691235i \(0.242933\pi\)
\(84\) 1.20224 0.131175
\(85\) 2.54461 0.276001
\(86\) −8.79468 −0.948355
\(87\) −0.899813 −0.0964701
\(88\) 0.160206 0.0170780
\(89\) 17.4818 1.85307 0.926535 0.376210i \(-0.122773\pi\)
0.926535 + 0.376210i \(0.122773\pi\)
\(90\) −1.70911 −0.180156
\(91\) 0.351818 0.0368806
\(92\) −2.31300 −0.241147
\(93\) −5.99287 −0.621431
\(94\) 6.63498 0.684346
\(95\) 5.35415 0.549324
\(96\) −4.83510 −0.493481
\(97\) 9.00690 0.914513 0.457256 0.889335i \(-0.348832\pi\)
0.457256 + 0.889335i \(0.348832\pi\)
\(98\) −0.737016 −0.0744498
\(99\) −0.145820 −0.0146555
\(100\) −1.45681 −0.145681
\(101\) −6.59130 −0.655859 −0.327930 0.944702i \(-0.606351\pi\)
−0.327930 + 0.944702i \(0.606351\pi\)
\(102\) 1.54769 0.153245
\(103\) −17.1071 −1.68561 −0.842807 0.538215i \(-0.819099\pi\)
−0.842807 + 0.538215i \(0.819099\pi\)
\(104\) −0.896335 −0.0878929
\(105\) 0.825255 0.0805366
\(106\) 2.38990 0.232128
\(107\) −1.56299 −0.151100 −0.0755502 0.997142i \(-0.524071\pi\)
−0.0755502 + 0.997142i \(0.524071\pi\)
\(108\) 6.39465 0.615325
\(109\) −0.349916 −0.0335159 −0.0167579 0.999860i \(-0.505334\pi\)
−0.0167579 + 0.999860i \(0.505334\pi\)
\(110\) 0.0463450 0.00441882
\(111\) −4.51125 −0.428189
\(112\) −1.03591 −0.0978839
\(113\) −4.74995 −0.446837 −0.223419 0.974723i \(-0.571722\pi\)
−0.223419 + 0.974723i \(0.571722\pi\)
\(114\) 3.25653 0.305002
\(115\) −1.58772 −0.148055
\(116\) 1.58842 0.147482
\(117\) 0.815851 0.0754254
\(118\) −6.50423 −0.598763
\(119\) 2.54461 0.233264
\(120\) −2.10252 −0.191933
\(121\) −10.9960 −0.999641
\(122\) 2.79687 0.253217
\(123\) 1.36476 0.123057
\(124\) 10.5791 0.950032
\(125\) −1.00000 −0.0894427
\(126\) −1.70911 −0.152259
\(127\) −11.5163 −1.02190 −0.510952 0.859609i \(-0.670707\pi\)
−0.510952 + 0.859609i \(0.670707\pi\)
\(128\) 10.0623 0.889388
\(129\) 9.84762 0.867035
\(130\) −0.259296 −0.0227417
\(131\) −2.69595 −0.235546 −0.117773 0.993041i \(-0.537576\pi\)
−0.117773 + 0.993041i \(0.537576\pi\)
\(132\) −0.0755991 −0.00658006
\(133\) 5.35415 0.464263
\(134\) −1.62612 −0.140476
\(135\) 4.38949 0.377787
\(136\) −6.48295 −0.555908
\(137\) −7.22672 −0.617421 −0.308710 0.951156i \(-0.599897\pi\)
−0.308710 + 0.951156i \(0.599897\pi\)
\(138\) −0.965690 −0.0822050
\(139\) 19.2883 1.63601 0.818005 0.575210i \(-0.195080\pi\)
0.818005 + 0.575210i \(0.195080\pi\)
\(140\) −1.45681 −0.123123
\(141\) −7.42935 −0.625664
\(142\) 9.91351 0.831924
\(143\) −0.0221230 −0.00185002
\(144\) −2.40222 −0.200185
\(145\) 1.09035 0.0905483
\(146\) 10.6270 0.879495
\(147\) 0.825255 0.0680659
\(148\) 7.96363 0.654606
\(149\) −4.86869 −0.398859 −0.199429 0.979912i \(-0.563909\pi\)
−0.199429 + 0.979912i \(0.563909\pi\)
\(150\) −0.608226 −0.0496614
\(151\) −16.0932 −1.30965 −0.654825 0.755781i \(-0.727258\pi\)
−0.654825 + 0.755781i \(0.727258\pi\)
\(152\) −13.6409 −1.10642
\(153\) 5.90082 0.477053
\(154\) 0.0463450 0.00373459
\(155\) 7.26184 0.583285
\(156\) 0.422969 0.0338646
\(157\) 24.2977 1.93916 0.969582 0.244765i \(-0.0787109\pi\)
0.969582 + 0.244765i \(0.0787109\pi\)
\(158\) −0.0814755 −0.00648184
\(159\) −2.67603 −0.212223
\(160\) 5.85892 0.463188
\(161\) −1.58772 −0.125130
\(162\) −2.45752 −0.193081
\(163\) 7.60415 0.595603 0.297802 0.954628i \(-0.403747\pi\)
0.297802 + 0.954628i \(0.403747\pi\)
\(164\) −2.40919 −0.188126
\(165\) −0.0518937 −0.00403992
\(166\) −9.70424 −0.753195
\(167\) −19.2358 −1.48851 −0.744256 0.667895i \(-0.767196\pi\)
−0.744256 + 0.667895i \(0.767196\pi\)
\(168\) −2.10252 −0.162213
\(169\) −12.8762 −0.990479
\(170\) −1.87541 −0.143838
\(171\) 12.4160 0.949477
\(172\) −17.3838 −1.32551
\(173\) −0.953843 −0.0725194 −0.0362597 0.999342i \(-0.511544\pi\)
−0.0362597 + 0.999342i \(0.511544\pi\)
\(174\) 0.663176 0.0502753
\(175\) −1.00000 −0.0755929
\(176\) 0.0651398 0.00491010
\(177\) 7.28295 0.547420
\(178\) −12.8844 −0.965725
\(179\) 7.32528 0.547517 0.273758 0.961798i \(-0.411733\pi\)
0.273758 + 0.961798i \(0.411733\pi\)
\(180\) −3.37827 −0.251802
\(181\) 18.6102 1.38329 0.691644 0.722238i \(-0.256887\pi\)
0.691644 + 0.722238i \(0.256887\pi\)
\(182\) −0.259296 −0.0192203
\(183\) −3.13173 −0.231504
\(184\) 4.04506 0.298206
\(185\) 5.46649 0.401905
\(186\) 4.41684 0.323858
\(187\) −0.160010 −0.0117011
\(188\) 13.1149 0.956503
\(189\) 4.38949 0.319289
\(190\) −3.94609 −0.286279
\(191\) 18.3205 1.32563 0.662814 0.748784i \(-0.269362\pi\)
0.662814 + 0.748784i \(0.269362\pi\)
\(192\) 1.85377 0.133785
\(193\) −9.41833 −0.677946 −0.338973 0.940796i \(-0.610080\pi\)
−0.338973 + 0.940796i \(0.610080\pi\)
\(194\) −6.63823 −0.476597
\(195\) 0.290340 0.0207917
\(196\) −1.45681 −0.104058
\(197\) 0.00829155 0.000590749 0 0.000295374 1.00000i \(-0.499906\pi\)
0.000295374 1.00000i \(0.499906\pi\)
\(198\) 0.107472 0.00763770
\(199\) −7.36505 −0.522094 −0.261047 0.965326i \(-0.584068\pi\)
−0.261047 + 0.965326i \(0.584068\pi\)
\(200\) 2.54772 0.180151
\(201\) 1.82081 0.128430
\(202\) 4.85789 0.341800
\(203\) 1.09035 0.0765273
\(204\) 3.05922 0.214188
\(205\) −1.65375 −0.115503
\(206\) 12.6082 0.878456
\(207\) −3.68184 −0.255906
\(208\) −0.364451 −0.0252701
\(209\) −0.336679 −0.0232886
\(210\) −0.608226 −0.0419716
\(211\) 7.58022 0.521844 0.260922 0.965360i \(-0.415973\pi\)
0.260922 + 0.965360i \(0.415973\pi\)
\(212\) 4.72395 0.324442
\(213\) −11.1004 −0.760587
\(214\) 1.15195 0.0787457
\(215\) −11.9328 −0.813812
\(216\) −11.1832 −0.760921
\(217\) 7.26184 0.492966
\(218\) 0.257894 0.0174668
\(219\) −11.8993 −0.804079
\(220\) 0.0916070 0.00617614
\(221\) 0.895239 0.0602203
\(222\) 3.32486 0.223150
\(223\) −14.7494 −0.987696 −0.493848 0.869548i \(-0.664410\pi\)
−0.493848 + 0.869548i \(0.664410\pi\)
\(224\) 5.85892 0.391466
\(225\) −2.31895 −0.154597
\(226\) 3.50078 0.232869
\(227\) 13.9472 0.925711 0.462856 0.886434i \(-0.346825\pi\)
0.462856 + 0.886434i \(0.346825\pi\)
\(228\) 6.43696 0.426298
\(229\) 1.00000 0.0660819
\(230\) 1.17017 0.0771588
\(231\) −0.0518937 −0.00341435
\(232\) −2.77790 −0.182378
\(233\) −12.1414 −0.795407 −0.397704 0.917514i \(-0.630193\pi\)
−0.397704 + 0.917514i \(0.630193\pi\)
\(234\) −0.601295 −0.0393079
\(235\) 9.00250 0.587258
\(236\) −12.8565 −0.836884
\(237\) 0.0912302 0.00592604
\(238\) −1.87541 −0.121565
\(239\) 15.4988 1.00253 0.501266 0.865294i \(-0.332868\pi\)
0.501266 + 0.865294i \(0.332868\pi\)
\(240\) −0.854886 −0.0551826
\(241\) 9.21320 0.593474 0.296737 0.954959i \(-0.404101\pi\)
0.296737 + 0.954959i \(0.404101\pi\)
\(242\) 8.10426 0.520961
\(243\) 15.9202 1.02128
\(244\) 5.52838 0.353918
\(245\) −1.00000 −0.0638877
\(246\) −1.00585 −0.0641308
\(247\) 1.88369 0.119856
\(248\) −18.5011 −1.17482
\(249\) 10.8661 0.688610
\(250\) 0.737016 0.0466130
\(251\) 3.58987 0.226591 0.113295 0.993561i \(-0.463859\pi\)
0.113295 + 0.993561i \(0.463859\pi\)
\(252\) −3.37827 −0.212811
\(253\) 0.0998387 0.00627681
\(254\) 8.48768 0.532564
\(255\) 2.09995 0.131504
\(256\) −11.9087 −0.744292
\(257\) 20.2690 1.26434 0.632171 0.774829i \(-0.282164\pi\)
0.632171 + 0.774829i \(0.282164\pi\)
\(258\) −7.25785 −0.451854
\(259\) 5.46649 0.339671
\(260\) −0.512532 −0.0317859
\(261\) 2.52846 0.156508
\(262\) 1.98696 0.122755
\(263\) 7.34119 0.452677 0.226339 0.974049i \(-0.427324\pi\)
0.226339 + 0.974049i \(0.427324\pi\)
\(264\) 0.132211 0.00813700
\(265\) 3.24267 0.199196
\(266\) −3.94609 −0.241950
\(267\) 14.4270 0.882915
\(268\) −3.21425 −0.196341
\(269\) −25.1085 −1.53089 −0.765446 0.643500i \(-0.777482\pi\)
−0.765446 + 0.643500i \(0.777482\pi\)
\(270\) −3.23512 −0.196883
\(271\) 20.4849 1.24437 0.622185 0.782870i \(-0.286245\pi\)
0.622185 + 0.782870i \(0.286245\pi\)
\(272\) −2.63597 −0.159829
\(273\) 0.290340 0.0175722
\(274\) 5.32621 0.321768
\(275\) 0.0628820 0.00379193
\(276\) −1.90881 −0.114897
\(277\) 2.11864 0.127297 0.0636485 0.997972i \(-0.479726\pi\)
0.0636485 + 0.997972i \(0.479726\pi\)
\(278\) −14.2158 −0.852605
\(279\) 16.8399 1.00818
\(280\) 2.54772 0.152255
\(281\) −6.29937 −0.375789 −0.187895 0.982189i \(-0.560166\pi\)
−0.187895 + 0.982189i \(0.560166\pi\)
\(282\) 5.47555 0.326064
\(283\) −2.33712 −0.138928 −0.0694638 0.997584i \(-0.522129\pi\)
−0.0694638 + 0.997584i \(0.522129\pi\)
\(284\) 19.5954 1.16277
\(285\) 4.41853 0.261731
\(286\) 0.0163050 0.000964136 0
\(287\) −1.65375 −0.0976176
\(288\) 13.5866 0.800596
\(289\) −10.5250 −0.619117
\(290\) −0.803602 −0.0471891
\(291\) 7.43299 0.435730
\(292\) 21.0056 1.22926
\(293\) 25.4594 1.48735 0.743676 0.668540i \(-0.233081\pi\)
0.743676 + 0.668540i \(0.233081\pi\)
\(294\) −0.608226 −0.0354724
\(295\) −8.82509 −0.513817
\(296\) −13.9271 −0.809496
\(297\) −0.276020 −0.0160163
\(298\) 3.58830 0.207865
\(299\) −0.558588 −0.0323040
\(300\) −1.20224 −0.0694112
\(301\) −11.9328 −0.687797
\(302\) 11.8610 0.682522
\(303\) −5.43951 −0.312491
\(304\) −5.54639 −0.318107
\(305\) 3.79486 0.217293
\(306\) −4.34900 −0.248616
\(307\) 26.6271 1.51969 0.759845 0.650104i \(-0.225275\pi\)
0.759845 + 0.650104i \(0.225275\pi\)
\(308\) 0.0916070 0.00521979
\(309\) −14.1177 −0.803130
\(310\) −5.35209 −0.303978
\(311\) 17.3663 0.984752 0.492376 0.870382i \(-0.336128\pi\)
0.492376 + 0.870382i \(0.336128\pi\)
\(312\) −0.739705 −0.0418775
\(313\) 10.8130 0.611189 0.305594 0.952162i \(-0.401145\pi\)
0.305594 + 0.952162i \(0.401145\pi\)
\(314\) −17.9078 −1.01059
\(315\) −2.31895 −0.130658
\(316\) −0.161047 −0.00905960
\(317\) 7.42801 0.417199 0.208599 0.978001i \(-0.433110\pi\)
0.208599 + 0.978001i \(0.433110\pi\)
\(318\) 1.97228 0.110600
\(319\) −0.0685631 −0.00383880
\(320\) −2.24631 −0.125572
\(321\) −1.28987 −0.0719934
\(322\) 1.17017 0.0652111
\(323\) 13.6242 0.758070
\(324\) −4.85760 −0.269867
\(325\) −0.351818 −0.0195154
\(326\) −5.60438 −0.310398
\(327\) −0.288770 −0.0159690
\(328\) 4.21329 0.232640
\(329\) 9.00250 0.496324
\(330\) 0.0382464 0.00210540
\(331\) −10.3159 −0.567013 −0.283507 0.958970i \(-0.591498\pi\)
−0.283507 + 0.958970i \(0.591498\pi\)
\(332\) −19.1817 −1.05273
\(333\) 12.6765 0.694671
\(334\) 14.1771 0.775736
\(335\) −2.20636 −0.120546
\(336\) −0.854886 −0.0466378
\(337\) −28.3060 −1.54193 −0.770964 0.636879i \(-0.780225\pi\)
−0.770964 + 0.636879i \(0.780225\pi\)
\(338\) 9.48998 0.516187
\(339\) −3.91992 −0.212901
\(340\) −3.70700 −0.201040
\(341\) −0.456639 −0.0247284
\(342\) −9.15080 −0.494819
\(343\) −1.00000 −0.0539949
\(344\) 30.4015 1.63914
\(345\) −1.31027 −0.0705426
\(346\) 0.702997 0.0377934
\(347\) −2.97376 −0.159640 −0.0798199 0.996809i \(-0.525435\pi\)
−0.0798199 + 0.996809i \(0.525435\pi\)
\(348\) 1.31085 0.0702692
\(349\) 13.9312 0.745721 0.372861 0.927887i \(-0.378377\pi\)
0.372861 + 0.927887i \(0.378377\pi\)
\(350\) 0.737016 0.0393951
\(351\) 1.54430 0.0824288
\(352\) −0.368421 −0.0196369
\(353\) 2.40986 0.128264 0.0641318 0.997941i \(-0.479572\pi\)
0.0641318 + 0.997941i \(0.479572\pi\)
\(354\) −5.36765 −0.285287
\(355\) 13.4509 0.713899
\(356\) −25.4677 −1.34978
\(357\) 2.09995 0.111141
\(358\) −5.39884 −0.285338
\(359\) 5.95394 0.314237 0.157119 0.987580i \(-0.449780\pi\)
0.157119 + 0.987580i \(0.449780\pi\)
\(360\) 5.90805 0.311382
\(361\) 9.66688 0.508783
\(362\) −13.7160 −0.720899
\(363\) −9.07454 −0.476290
\(364\) −0.512532 −0.0268640
\(365\) 14.4189 0.754721
\(366\) 2.30813 0.120648
\(367\) −36.1088 −1.88486 −0.942431 0.334401i \(-0.891466\pi\)
−0.942431 + 0.334401i \(0.891466\pi\)
\(368\) 1.64472 0.0857372
\(369\) −3.83497 −0.199640
\(370\) −4.02889 −0.209452
\(371\) 3.24267 0.168351
\(372\) 8.73046 0.452653
\(373\) 9.97325 0.516395 0.258198 0.966092i \(-0.416871\pi\)
0.258198 + 0.966092i \(0.416871\pi\)
\(374\) 0.117930 0.00609800
\(375\) −0.825255 −0.0426160
\(376\) −22.9359 −1.18283
\(377\) 0.383604 0.0197566
\(378\) −3.23512 −0.166397
\(379\) 11.8304 0.607685 0.303843 0.952722i \(-0.401730\pi\)
0.303843 + 0.952722i \(0.401730\pi\)
\(380\) −7.79996 −0.400130
\(381\) −9.50387 −0.486898
\(382\) −13.5025 −0.690849
\(383\) −17.8199 −0.910555 −0.455278 0.890349i \(-0.650460\pi\)
−0.455278 + 0.890349i \(0.650460\pi\)
\(384\) 8.30394 0.423759
\(385\) 0.0628820 0.00320476
\(386\) 6.94146 0.353311
\(387\) −27.6717 −1.40663
\(388\) −13.1213 −0.666135
\(389\) 33.3319 1.69000 0.844998 0.534770i \(-0.179602\pi\)
0.844998 + 0.534770i \(0.179602\pi\)
\(390\) −0.213985 −0.0108355
\(391\) −4.04011 −0.204317
\(392\) 2.54772 0.128679
\(393\) −2.22485 −0.112229
\(394\) −0.00611100 −0.000307868 0
\(395\) −0.110548 −0.00556227
\(396\) 0.212432 0.0106751
\(397\) 13.0985 0.657394 0.328697 0.944435i \(-0.393390\pi\)
0.328697 + 0.944435i \(0.393390\pi\)
\(398\) 5.42815 0.272089
\(399\) 4.41853 0.221203
\(400\) 1.03591 0.0517953
\(401\) 28.2307 1.40977 0.704886 0.709320i \(-0.250998\pi\)
0.704886 + 0.709320i \(0.250998\pi\)
\(402\) −1.34197 −0.0669312
\(403\) 2.55485 0.127266
\(404\) 9.60227 0.477731
\(405\) −3.33441 −0.165688
\(406\) −0.803602 −0.0398821
\(407\) −0.343744 −0.0170388
\(408\) −5.35008 −0.264869
\(409\) 21.5002 1.06312 0.531558 0.847022i \(-0.321607\pi\)
0.531558 + 0.847022i \(0.321607\pi\)
\(410\) 1.21884 0.0601941
\(411\) −5.96389 −0.294177
\(412\) 24.9218 1.22781
\(413\) −8.82509 −0.434254
\(414\) 2.71357 0.133365
\(415\) −13.1669 −0.646340
\(416\) 2.06128 0.101062
\(417\) 15.9177 0.779495
\(418\) 0.248138 0.0121368
\(419\) 10.8623 0.530656 0.265328 0.964158i \(-0.414520\pi\)
0.265328 + 0.964158i \(0.414520\pi\)
\(420\) −1.20224 −0.0586632
\(421\) 1.14036 0.0555777 0.0277888 0.999614i \(-0.491153\pi\)
0.0277888 + 0.999614i \(0.491153\pi\)
\(422\) −5.58674 −0.271958
\(423\) 20.8764 1.01504
\(424\) −8.26143 −0.401210
\(425\) −2.54461 −0.123431
\(426\) 8.18117 0.396379
\(427\) 3.79486 0.183646
\(428\) 2.27698 0.110062
\(429\) −0.0182571 −0.000881463 0
\(430\) 8.79468 0.424117
\(431\) −7.20406 −0.347008 −0.173504 0.984833i \(-0.555509\pi\)
−0.173504 + 0.984833i \(0.555509\pi\)
\(432\) −4.54710 −0.218772
\(433\) 33.1616 1.59364 0.796822 0.604214i \(-0.206513\pi\)
0.796822 + 0.604214i \(0.206513\pi\)
\(434\) −5.35209 −0.256908
\(435\) 0.899813 0.0431427
\(436\) 0.509761 0.0244131
\(437\) −8.50086 −0.406652
\(438\) 8.76996 0.419045
\(439\) 4.96485 0.236959 0.118480 0.992956i \(-0.462198\pi\)
0.118480 + 0.992956i \(0.462198\pi\)
\(440\) −0.160206 −0.00763751
\(441\) −2.31895 −0.110426
\(442\) −0.659805 −0.0313837
\(443\) 16.5571 0.786650 0.393325 0.919399i \(-0.371325\pi\)
0.393325 + 0.919399i \(0.371325\pi\)
\(444\) 6.57202 0.311894
\(445\) −17.4818 −0.828718
\(446\) 10.8706 0.514736
\(447\) −4.01791 −0.190041
\(448\) −2.24631 −0.106128
\(449\) −22.5413 −1.06379 −0.531894 0.846811i \(-0.678520\pi\)
−0.531894 + 0.846811i \(0.678520\pi\)
\(450\) 1.70911 0.0805680
\(451\) 0.103991 0.00489674
\(452\) 6.91976 0.325478
\(453\) −13.2810 −0.623997
\(454\) −10.2793 −0.482433
\(455\) −0.351818 −0.0164935
\(456\) −11.2572 −0.527166
\(457\) 23.1868 1.08463 0.542316 0.840175i \(-0.317548\pi\)
0.542316 + 0.840175i \(0.317548\pi\)
\(458\) −0.737016 −0.0344385
\(459\) 11.1695 0.521349
\(460\) 2.31300 0.107844
\(461\) 35.2320 1.64092 0.820458 0.571706i \(-0.193718\pi\)
0.820458 + 0.571706i \(0.193718\pi\)
\(462\) 0.0382464 0.00177939
\(463\) 24.8805 1.15629 0.578147 0.815932i \(-0.303776\pi\)
0.578147 + 0.815932i \(0.303776\pi\)
\(464\) −1.12950 −0.0524355
\(465\) 5.99287 0.277913
\(466\) 8.94838 0.414526
\(467\) −28.7261 −1.32929 −0.664644 0.747160i \(-0.731417\pi\)
−0.664644 + 0.747160i \(0.731417\pi\)
\(468\) −1.18854 −0.0549402
\(469\) −2.20636 −0.101880
\(470\) −6.63498 −0.306049
\(471\) 20.0518 0.923936
\(472\) 22.4839 1.03490
\(473\) 0.750360 0.0345016
\(474\) −0.0672381 −0.00308835
\(475\) −5.35415 −0.245665
\(476\) −3.70700 −0.169910
\(477\) 7.51961 0.344299
\(478\) −11.4228 −0.522468
\(479\) 6.99527 0.319622 0.159811 0.987148i \(-0.448911\pi\)
0.159811 + 0.987148i \(0.448911\pi\)
\(480\) 4.83510 0.220691
\(481\) 1.92321 0.0876909
\(482\) −6.79027 −0.309288
\(483\) −1.31027 −0.0596194
\(484\) 16.0191 0.728142
\(485\) −9.00690 −0.408982
\(486\) −11.7334 −0.532240
\(487\) −26.2201 −1.18815 −0.594074 0.804410i \(-0.702481\pi\)
−0.594074 + 0.804410i \(0.702481\pi\)
\(488\) −9.66824 −0.437661
\(489\) 6.27536 0.283782
\(490\) 0.737016 0.0332950
\(491\) 5.32237 0.240195 0.120098 0.992762i \(-0.461679\pi\)
0.120098 + 0.992762i \(0.461679\pi\)
\(492\) −1.98820 −0.0896349
\(493\) 2.77450 0.124957
\(494\) −1.38831 −0.0624629
\(495\) 0.145820 0.00655414
\(496\) −7.52258 −0.337774
\(497\) 13.4509 0.603355
\(498\) −8.00847 −0.358868
\(499\) −10.3197 −0.461972 −0.230986 0.972957i \(-0.574195\pi\)
−0.230986 + 0.972957i \(0.574195\pi\)
\(500\) 1.45681 0.0651504
\(501\) −15.8744 −0.709218
\(502\) −2.64579 −0.118087
\(503\) 13.8698 0.618424 0.309212 0.950993i \(-0.399935\pi\)
0.309212 + 0.950993i \(0.399935\pi\)
\(504\) 5.90805 0.263165
\(505\) 6.59130 0.293309
\(506\) −0.0735827 −0.00327115
\(507\) −10.6262 −0.471925
\(508\) 16.7770 0.744360
\(509\) −35.7747 −1.58568 −0.792842 0.609427i \(-0.791399\pi\)
−0.792842 + 0.609427i \(0.791399\pi\)
\(510\) −1.54769 −0.0685330
\(511\) 14.4189 0.637856
\(512\) −11.3477 −0.501502
\(513\) 23.5020 1.03764
\(514\) −14.9385 −0.658911
\(515\) 17.1071 0.753830
\(516\) −14.3461 −0.631552
\(517\) −0.566095 −0.0248968
\(518\) −4.02889 −0.177019
\(519\) −0.787164 −0.0345527
\(520\) 0.896335 0.0393069
\(521\) 21.2117 0.929300 0.464650 0.885494i \(-0.346180\pi\)
0.464650 + 0.885494i \(0.346180\pi\)
\(522\) −1.86352 −0.0815639
\(523\) −6.22479 −0.272191 −0.136096 0.990696i \(-0.543455\pi\)
−0.136096 + 0.990696i \(0.543455\pi\)
\(524\) 3.92748 0.171573
\(525\) −0.825255 −0.0360171
\(526\) −5.41057 −0.235912
\(527\) 18.4785 0.804937
\(528\) 0.0537569 0.00233947
\(529\) −20.4792 −0.890398
\(530\) −2.38990 −0.103811
\(531\) −20.4650 −0.888105
\(532\) −7.79996 −0.338171
\(533\) −0.581819 −0.0252014
\(534\) −10.6329 −0.460130
\(535\) 1.56299 0.0675741
\(536\) 5.62120 0.242799
\(537\) 6.04522 0.260870
\(538\) 18.5054 0.797823
\(539\) 0.0628820 0.00270852
\(540\) −6.39465 −0.275182
\(541\) −3.39171 −0.145821 −0.0729105 0.997338i \(-0.523229\pi\)
−0.0729105 + 0.997338i \(0.523229\pi\)
\(542\) −15.0977 −0.648502
\(543\) 15.3582 0.659083
\(544\) 14.9086 0.639203
\(545\) 0.349916 0.0149888
\(546\) −0.213985 −0.00915771
\(547\) 10.8320 0.463144 0.231572 0.972818i \(-0.425613\pi\)
0.231572 + 0.972818i \(0.425613\pi\)
\(548\) 10.5279 0.449732
\(549\) 8.80011 0.375579
\(550\) −0.0463450 −0.00197616
\(551\) 5.83787 0.248702
\(552\) 3.33820 0.142083
\(553\) −0.110548 −0.00470097
\(554\) −1.56147 −0.0663406
\(555\) 4.51125 0.191492
\(556\) −28.0993 −1.19168
\(557\) 41.3939 1.75392 0.876958 0.480567i \(-0.159569\pi\)
0.876958 + 0.480567i \(0.159569\pi\)
\(558\) −12.4112 −0.525410
\(559\) −4.19819 −0.177564
\(560\) 1.03591 0.0437750
\(561\) −0.132049 −0.00557511
\(562\) 4.64274 0.195842
\(563\) 18.0979 0.762734 0.381367 0.924424i \(-0.375453\pi\)
0.381367 + 0.924424i \(0.375453\pi\)
\(564\) 10.8231 0.455736
\(565\) 4.74995 0.199832
\(566\) 1.72250 0.0724019
\(567\) −3.33441 −0.140032
\(568\) −34.2691 −1.43790
\(569\) 15.9517 0.668729 0.334365 0.942444i \(-0.391478\pi\)
0.334365 + 0.942444i \(0.391478\pi\)
\(570\) −3.25653 −0.136401
\(571\) −9.44426 −0.395230 −0.197615 0.980280i \(-0.563320\pi\)
−0.197615 + 0.980280i \(0.563320\pi\)
\(572\) 0.0322290 0.00134756
\(573\) 15.1191 0.631610
\(574\) 1.21884 0.0508733
\(575\) 1.58772 0.0662123
\(576\) −5.20908 −0.217045
\(577\) 37.4000 1.55698 0.778491 0.627656i \(-0.215985\pi\)
0.778491 + 0.627656i \(0.215985\pi\)
\(578\) 7.75708 0.322652
\(579\) −7.77252 −0.323015
\(580\) −1.58842 −0.0659557
\(581\) −13.1669 −0.546257
\(582\) −5.47823 −0.227080
\(583\) −0.203906 −0.00844491
\(584\) −36.7354 −1.52012
\(585\) −0.815851 −0.0337313
\(586\) −18.7639 −0.775132
\(587\) 9.55110 0.394216 0.197108 0.980382i \(-0.436845\pi\)
0.197108 + 0.980382i \(0.436845\pi\)
\(588\) −1.20224 −0.0495794
\(589\) 38.8809 1.60206
\(590\) 6.50423 0.267775
\(591\) 0.00684264 0.000281469 0
\(592\) −5.66277 −0.232738
\(593\) −24.6023 −1.01029 −0.505147 0.863034i \(-0.668562\pi\)
−0.505147 + 0.863034i \(0.668562\pi\)
\(594\) 0.203431 0.00834688
\(595\) −2.54461 −0.104319
\(596\) 7.09275 0.290530
\(597\) −6.07804 −0.248758
\(598\) 0.411688 0.0168352
\(599\) 30.5245 1.24720 0.623598 0.781745i \(-0.285670\pi\)
0.623598 + 0.781745i \(0.285670\pi\)
\(600\) 2.10252 0.0858350
\(601\) −16.2353 −0.662251 −0.331126 0.943587i \(-0.607428\pi\)
−0.331126 + 0.943587i \(0.607428\pi\)
\(602\) 8.79468 0.358444
\(603\) −5.11645 −0.208358
\(604\) 23.4448 0.953954
\(605\) 10.9960 0.447053
\(606\) 4.00900 0.162855
\(607\) −8.82351 −0.358135 −0.179068 0.983837i \(-0.557308\pi\)
−0.179068 + 0.983837i \(0.557308\pi\)
\(608\) 31.3695 1.27220
\(609\) 0.899813 0.0364623
\(610\) −2.79687 −0.113242
\(611\) 3.16724 0.128133
\(612\) −8.59637 −0.347488
\(613\) 40.8478 1.64983 0.824913 0.565259i \(-0.191224\pi\)
0.824913 + 0.565259i \(0.191224\pi\)
\(614\) −19.6246 −0.791985
\(615\) −1.36476 −0.0550326
\(616\) −0.160206 −0.00645487
\(617\) 6.65236 0.267814 0.133907 0.990994i \(-0.457248\pi\)
0.133907 + 0.990994i \(0.457248\pi\)
\(618\) 10.4050 0.418550
\(619\) 45.8466 1.84273 0.921366 0.388696i \(-0.127074\pi\)
0.921366 + 0.388696i \(0.127074\pi\)
\(620\) −10.5791 −0.424867
\(621\) −6.96927 −0.279667
\(622\) −12.7992 −0.513202
\(623\) −17.4818 −0.700394
\(624\) −0.300765 −0.0120402
\(625\) 1.00000 0.0400000
\(626\) −7.96937 −0.318520
\(627\) −0.277846 −0.0110961
\(628\) −35.3970 −1.41250
\(629\) 13.9101 0.554631
\(630\) 1.70911 0.0680924
\(631\) 25.3598 1.00956 0.504778 0.863249i \(-0.331574\pi\)
0.504778 + 0.863249i \(0.331574\pi\)
\(632\) 0.281645 0.0112032
\(633\) 6.25561 0.248638
\(634\) −5.47456 −0.217422
\(635\) 11.5163 0.457010
\(636\) 3.89846 0.154584
\(637\) −0.351818 −0.0139395
\(638\) 0.0505321 0.00200058
\(639\) 31.1920 1.23394
\(640\) −10.0623 −0.397747
\(641\) −15.0457 −0.594271 −0.297135 0.954835i \(-0.596031\pi\)
−0.297135 + 0.954835i \(0.596031\pi\)
\(642\) 0.950653 0.0375193
\(643\) 24.0676 0.949135 0.474567 0.880219i \(-0.342605\pi\)
0.474567 + 0.880219i \(0.342605\pi\)
\(644\) 2.31300 0.0911449
\(645\) −9.84762 −0.387750
\(646\) −10.0412 −0.395067
\(647\) −37.5254 −1.47528 −0.737638 0.675196i \(-0.764059\pi\)
−0.737638 + 0.675196i \(0.764059\pi\)
\(648\) 8.49516 0.333721
\(649\) 0.554939 0.0217833
\(650\) 0.259296 0.0101704
\(651\) 5.99287 0.234879
\(652\) −11.0778 −0.433840
\(653\) −35.7378 −1.39853 −0.699264 0.714864i \(-0.746489\pi\)
−0.699264 + 0.714864i \(0.746489\pi\)
\(654\) 0.212828 0.00832223
\(655\) 2.69595 0.105340
\(656\) 1.71313 0.0668863
\(657\) 33.4368 1.30450
\(658\) −6.63498 −0.258659
\(659\) −5.85681 −0.228149 −0.114074 0.993472i \(-0.536390\pi\)
−0.114074 + 0.993472i \(0.536390\pi\)
\(660\) 0.0755991 0.00294269
\(661\) −42.2086 −1.64172 −0.820862 0.571127i \(-0.806507\pi\)
−0.820862 + 0.571127i \(0.806507\pi\)
\(662\) 7.60298 0.295498
\(663\) 0.738800 0.0286926
\(664\) 33.5457 1.30183
\(665\) −5.35415 −0.207625
\(666\) −9.34281 −0.362027
\(667\) −1.73116 −0.0670308
\(668\) 28.0229 1.08424
\(669\) −12.1720 −0.470598
\(670\) 1.62612 0.0628226
\(671\) −0.238628 −0.00921214
\(672\) 4.83510 0.186518
\(673\) −24.1384 −0.930466 −0.465233 0.885188i \(-0.654030\pi\)
−0.465233 + 0.885188i \(0.654030\pi\)
\(674\) 20.8620 0.803574
\(675\) −4.38949 −0.168952
\(676\) 18.7582 0.721469
\(677\) −7.57912 −0.291289 −0.145645 0.989337i \(-0.546526\pi\)
−0.145645 + 0.989337i \(0.546526\pi\)
\(678\) 2.88904 0.110953
\(679\) −9.00690 −0.345653
\(680\) 6.48295 0.248610
\(681\) 11.5100 0.441065
\(682\) 0.336550 0.0128872
\(683\) −23.8489 −0.912554 −0.456277 0.889838i \(-0.650817\pi\)
−0.456277 + 0.889838i \(0.650817\pi\)
\(684\) −18.0878 −0.691603
\(685\) 7.22672 0.276119
\(686\) 0.737016 0.0281394
\(687\) 0.825255 0.0314854
\(688\) 12.3613 0.471270
\(689\) 1.14083 0.0434622
\(690\) 0.965690 0.0367632
\(691\) −6.56434 −0.249719 −0.124860 0.992174i \(-0.539848\pi\)
−0.124860 + 0.992174i \(0.539848\pi\)
\(692\) 1.38957 0.0528234
\(693\) 0.145820 0.00553926
\(694\) 2.19171 0.0831961
\(695\) −19.2883 −0.731646
\(696\) −2.29247 −0.0868960
\(697\) −4.20814 −0.159394
\(698\) −10.2675 −0.388632
\(699\) −10.0197 −0.378981
\(700\) 1.45681 0.0550622
\(701\) −42.9343 −1.62161 −0.810803 0.585319i \(-0.800969\pi\)
−0.810803 + 0.585319i \(0.800969\pi\)
\(702\) −1.13818 −0.0429577
\(703\) 29.2684 1.10388
\(704\) 0.141252 0.00532364
\(705\) 7.42935 0.279806
\(706\) −1.77610 −0.0668445
\(707\) 6.59130 0.247892
\(708\) −10.6099 −0.398743
\(709\) −31.6571 −1.18891 −0.594454 0.804130i \(-0.702632\pi\)
−0.594454 + 0.804130i \(0.702632\pi\)
\(710\) −9.91351 −0.372048
\(711\) −0.256356 −0.00961408
\(712\) 44.5388 1.66916
\(713\) −11.5297 −0.431792
\(714\) −1.54769 −0.0579210
\(715\) 0.0221230 0.000827355 0
\(716\) −10.6715 −0.398813
\(717\) 12.7904 0.477667
\(718\) −4.38815 −0.163764
\(719\) −14.3345 −0.534585 −0.267293 0.963615i \(-0.586129\pi\)
−0.267293 + 0.963615i \(0.586129\pi\)
\(720\) 2.40222 0.0895254
\(721\) 17.1071 0.637102
\(722\) −7.12464 −0.265152
\(723\) 7.60324 0.282767
\(724\) −27.1115 −1.00759
\(725\) −1.09035 −0.0404944
\(726\) 6.68808 0.248218
\(727\) 26.6864 0.989743 0.494871 0.868966i \(-0.335215\pi\)
0.494871 + 0.868966i \(0.335215\pi\)
\(728\) 0.896335 0.0332204
\(729\) 3.13499 0.116111
\(730\) −10.6270 −0.393322
\(731\) −30.3643 −1.12307
\(732\) 4.56232 0.168628
\(733\) 16.3915 0.605433 0.302717 0.953081i \(-0.402106\pi\)
0.302717 + 0.953081i \(0.402106\pi\)
\(734\) 26.6127 0.982293
\(735\) −0.825255 −0.0304400
\(736\) −9.30230 −0.342887
\(737\) 0.138740 0.00511057
\(738\) 2.82643 0.104042
\(739\) 6.08143 0.223709 0.111854 0.993725i \(-0.464321\pi\)
0.111854 + 0.993725i \(0.464321\pi\)
\(740\) −7.96363 −0.292749
\(741\) 1.55452 0.0571068
\(742\) −2.38990 −0.0877360
\(743\) −0.353465 −0.0129674 −0.00648369 0.999979i \(-0.502064\pi\)
−0.00648369 + 0.999979i \(0.502064\pi\)
\(744\) −15.2682 −0.559758
\(745\) 4.86869 0.178375
\(746\) −7.35044 −0.269119
\(747\) −30.5335 −1.11716
\(748\) 0.233104 0.00852311
\(749\) 1.56299 0.0571106
\(750\) 0.608226 0.0222093
\(751\) −5.07656 −0.185246 −0.0926232 0.995701i \(-0.529525\pi\)
−0.0926232 + 0.995701i \(0.529525\pi\)
\(752\) −9.32574 −0.340075
\(753\) 2.96256 0.107962
\(754\) −0.282722 −0.0102961
\(755\) 16.0932 0.585693
\(756\) −6.39465 −0.232571
\(757\) −36.9443 −1.34276 −0.671382 0.741111i \(-0.734299\pi\)
−0.671382 + 0.741111i \(0.734299\pi\)
\(758\) −8.71917 −0.316694
\(759\) 0.0823924 0.00299065
\(760\) 13.6409 0.494806
\(761\) 28.1062 1.01885 0.509424 0.860516i \(-0.329858\pi\)
0.509424 + 0.860516i \(0.329858\pi\)
\(762\) 7.00450 0.253746
\(763\) 0.349916 0.0126678
\(764\) −26.6895 −0.965593
\(765\) −5.90082 −0.213345
\(766\) 13.1336 0.474535
\(767\) −3.10483 −0.112109
\(768\) −9.82769 −0.354626
\(769\) 4.42874 0.159704 0.0798522 0.996807i \(-0.474555\pi\)
0.0798522 + 0.996807i \(0.474555\pi\)
\(770\) −0.0463450 −0.00167016
\(771\) 16.7271 0.602410
\(772\) 13.7207 0.493819
\(773\) −20.7809 −0.747436 −0.373718 0.927542i \(-0.621917\pi\)
−0.373718 + 0.927542i \(0.621917\pi\)
\(774\) 20.3945 0.733064
\(775\) −7.26184 −0.260853
\(776\) 22.9471 0.823752
\(777\) 4.51125 0.161840
\(778\) −24.5661 −0.880739
\(779\) −8.85441 −0.317242
\(780\) −0.422969 −0.0151447
\(781\) −0.845819 −0.0302658
\(782\) 2.97762 0.106480
\(783\) 4.78606 0.171040
\(784\) 1.03591 0.0369966
\(785\) −24.2977 −0.867221
\(786\) 1.63975 0.0584878
\(787\) 23.6529 0.843136 0.421568 0.906797i \(-0.361480\pi\)
0.421568 + 0.906797i \(0.361480\pi\)
\(788\) −0.0120792 −0.000430304 0
\(789\) 6.05835 0.215683
\(790\) 0.0814755 0.00289877
\(791\) 4.74995 0.168889
\(792\) −0.371510 −0.0132010
\(793\) 1.33510 0.0474108
\(794\) −9.65379 −0.342600
\(795\) 2.67603 0.0949090
\(796\) 10.7295 0.380295
\(797\) −27.6194 −0.978330 −0.489165 0.872191i \(-0.662698\pi\)
−0.489165 + 0.872191i \(0.662698\pi\)
\(798\) −3.25653 −0.115280
\(799\) 22.9078 0.810420
\(800\) −5.85892 −0.207144
\(801\) −40.5395 −1.43239
\(802\) −20.8064 −0.734701
\(803\) −0.906691 −0.0319964
\(804\) −2.65257 −0.0935490
\(805\) 1.58772 0.0559596
\(806\) −1.88296 −0.0663245
\(807\) −20.7209 −0.729411
\(808\) −16.7928 −0.590769
\(809\) −41.1231 −1.44581 −0.722905 0.690947i \(-0.757194\pi\)
−0.722905 + 0.690947i \(0.757194\pi\)
\(810\) 2.45752 0.0863483
\(811\) 15.8233 0.555630 0.277815 0.960635i \(-0.410390\pi\)
0.277815 + 0.960635i \(0.410390\pi\)
\(812\) −1.58842 −0.0557428
\(813\) 16.9053 0.592894
\(814\) 0.253345 0.00887972
\(815\) −7.60415 −0.266362
\(816\) −2.17535 −0.0761524
\(817\) −63.8901 −2.23523
\(818\) −15.8460 −0.554041
\(819\) −0.815851 −0.0285081
\(820\) 2.40919 0.0841327
\(821\) −39.7137 −1.38602 −0.693010 0.720928i \(-0.743716\pi\)
−0.693010 + 0.720928i \(0.743716\pi\)
\(822\) 4.39548 0.153310
\(823\) 12.9518 0.451470 0.225735 0.974189i \(-0.427522\pi\)
0.225735 + 0.974189i \(0.427522\pi\)
\(824\) −43.5842 −1.51833
\(825\) 0.0518937 0.00180671
\(826\) 6.50423 0.226311
\(827\) −48.6843 −1.69292 −0.846459 0.532454i \(-0.821270\pi\)
−0.846459 + 0.532454i \(0.821270\pi\)
\(828\) 5.36374 0.186403
\(829\) −25.3416 −0.880149 −0.440075 0.897961i \(-0.645048\pi\)
−0.440075 + 0.897961i \(0.645048\pi\)
\(830\) 9.70424 0.336839
\(831\) 1.74842 0.0606520
\(832\) −0.790291 −0.0273984
\(833\) −2.54461 −0.0881654
\(834\) −11.7316 −0.406233
\(835\) 19.2358 0.665683
\(836\) 0.490477 0.0169635
\(837\) 31.8758 1.10179
\(838\) −8.00566 −0.276551
\(839\) −16.6907 −0.576226 −0.288113 0.957596i \(-0.593028\pi\)
−0.288113 + 0.957596i \(0.593028\pi\)
\(840\) 2.10252 0.0725438
\(841\) −27.8111 −0.959005
\(842\) −0.840462 −0.0289642
\(843\) −5.19859 −0.179049
\(844\) −11.0429 −0.380113
\(845\) 12.8762 0.442956
\(846\) −15.3862 −0.528989
\(847\) 10.9960 0.377829
\(848\) −3.35910 −0.115352
\(849\) −1.92872 −0.0661936
\(850\) 1.87541 0.0643262
\(851\) −8.67924 −0.297520
\(852\) 16.1712 0.554015
\(853\) 47.1905 1.61577 0.807886 0.589338i \(-0.200612\pi\)
0.807886 + 0.589338i \(0.200612\pi\)
\(854\) −2.79687 −0.0957069
\(855\) −12.4160 −0.424619
\(856\) −3.98207 −0.136104
\(857\) −32.8874 −1.12341 −0.561707 0.827336i \(-0.689855\pi\)
−0.561707 + 0.827336i \(0.689855\pi\)
\(858\) 0.0134558 0.000459373 0
\(859\) −23.8617 −0.814152 −0.407076 0.913394i \(-0.633452\pi\)
−0.407076 + 0.913394i \(0.633452\pi\)
\(860\) 17.3838 0.592784
\(861\) −1.36476 −0.0465110
\(862\) 5.30951 0.180843
\(863\) 21.9990 0.748854 0.374427 0.927256i \(-0.377840\pi\)
0.374427 + 0.927256i \(0.377840\pi\)
\(864\) 25.7177 0.874934
\(865\) 0.953843 0.0324316
\(866\) −24.4406 −0.830526
\(867\) −8.68579 −0.294985
\(868\) −10.5791 −0.359078
\(869\) 0.00695147 0.000235812 0
\(870\) −0.663176 −0.0224838
\(871\) −0.776239 −0.0263018
\(872\) −0.891489 −0.0301896
\(873\) −20.8866 −0.706904
\(874\) 6.26527 0.211926
\(875\) 1.00000 0.0338062
\(876\) 17.3350 0.585695
\(877\) 49.0339 1.65576 0.827878 0.560908i \(-0.189548\pi\)
0.827878 + 0.560908i \(0.189548\pi\)
\(878\) −3.65917 −0.123491
\(879\) 21.0105 0.708665
\(880\) −0.0651398 −0.00219586
\(881\) −1.35979 −0.0458125 −0.0229063 0.999738i \(-0.507292\pi\)
−0.0229063 + 0.999738i \(0.507292\pi\)
\(882\) 1.70911 0.0575486
\(883\) 28.7971 0.969099 0.484550 0.874764i \(-0.338983\pi\)
0.484550 + 0.874764i \(0.338983\pi\)
\(884\) −1.30419 −0.0438647
\(885\) −7.28295 −0.244814
\(886\) −12.2028 −0.409962
\(887\) 34.1659 1.14718 0.573590 0.819142i \(-0.305550\pi\)
0.573590 + 0.819142i \(0.305550\pi\)
\(888\) −11.4934 −0.385693
\(889\) 11.5163 0.386244
\(890\) 12.8844 0.431885
\(891\) 0.209675 0.00702436
\(892\) 21.4871 0.719441
\(893\) 48.2007 1.61297
\(894\) 2.96126 0.0990394
\(895\) −7.32528 −0.244857
\(896\) −10.0623 −0.336157
\(897\) −0.460977 −0.0153916
\(898\) 16.6133 0.554392
\(899\) 7.91791 0.264077
\(900\) 3.37827 0.112609
\(901\) 8.25132 0.274891
\(902\) −0.0766429 −0.00255193
\(903\) −9.84762 −0.327708
\(904\) −12.1015 −0.402491
\(905\) −18.6102 −0.618625
\(906\) 9.78832 0.325195
\(907\) 15.1748 0.503870 0.251935 0.967744i \(-0.418933\pi\)
0.251935 + 0.967744i \(0.418933\pi\)
\(908\) −20.3185 −0.674292
\(909\) 15.2849 0.506969
\(910\) 0.259296 0.00859557
\(911\) 25.5108 0.845212 0.422606 0.906314i \(-0.361115\pi\)
0.422606 + 0.906314i \(0.361115\pi\)
\(912\) −4.57718 −0.151566
\(913\) 0.827963 0.0274016
\(914\) −17.0890 −0.565254
\(915\) 3.13173 0.103532
\(916\) −1.45681 −0.0481343
\(917\) 2.69595 0.0890282
\(918\) −8.23212 −0.271700
\(919\) −30.9660 −1.02147 −0.510737 0.859737i \(-0.670627\pi\)
−0.510737 + 0.859737i \(0.670627\pi\)
\(920\) −4.04506 −0.133362
\(921\) 21.9742 0.724073
\(922\) −25.9665 −0.855162
\(923\) 4.73227 0.155765
\(924\) 0.0755991 0.00248703
\(925\) −5.46649 −0.179737
\(926\) −18.3373 −0.602602
\(927\) 39.6706 1.30295
\(928\) 6.38825 0.209705
\(929\) 40.0507 1.31402 0.657010 0.753881i \(-0.271821\pi\)
0.657010 + 0.753881i \(0.271821\pi\)
\(930\) −4.41684 −0.144834
\(931\) −5.35415 −0.175475
\(932\) 17.6876 0.579378
\(933\) 14.3316 0.469196
\(934\) 21.1716 0.692756
\(935\) 0.160010 0.00523288
\(936\) 2.07856 0.0679399
\(937\) −15.2995 −0.499813 −0.249907 0.968270i \(-0.580400\pi\)
−0.249907 + 0.968270i \(0.580400\pi\)
\(938\) 1.62612 0.0530948
\(939\) 8.92350 0.291208
\(940\) −13.1149 −0.427761
\(941\) 56.2127 1.83248 0.916241 0.400628i \(-0.131208\pi\)
0.916241 + 0.400628i \(0.131208\pi\)
\(942\) −14.7785 −0.481508
\(943\) 2.62568 0.0855040
\(944\) 9.14196 0.297545
\(945\) −4.38949 −0.142790
\(946\) −0.553027 −0.0179805
\(947\) −13.0122 −0.422838 −0.211419 0.977395i \(-0.567809\pi\)
−0.211419 + 0.977395i \(0.567809\pi\)
\(948\) −0.132905 −0.00431655
\(949\) 5.07284 0.164671
\(950\) 3.94609 0.128028
\(951\) 6.13000 0.198779
\(952\) 6.48295 0.210113
\(953\) 43.7835 1.41829 0.709144 0.705064i \(-0.249082\pi\)
0.709144 + 0.705064i \(0.249082\pi\)
\(954\) −5.54207 −0.179431
\(955\) −18.3205 −0.592839
\(956\) −22.5787 −0.730248
\(957\) −0.0565820 −0.00182904
\(958\) −5.15562 −0.166571
\(959\) 7.22672 0.233363
\(960\) −1.85377 −0.0598303
\(961\) 21.7343 0.701106
\(962\) −1.41744 −0.0457000
\(963\) 3.62451 0.116798
\(964\) −13.4219 −0.432289
\(965\) 9.41833 0.303187
\(966\) 0.965690 0.0310706
\(967\) 23.7562 0.763948 0.381974 0.924173i \(-0.375244\pi\)
0.381974 + 0.924173i \(0.375244\pi\)
\(968\) −28.0149 −0.900432
\(969\) 11.2434 0.361191
\(970\) 6.63823 0.213141
\(971\) 14.3197 0.459542 0.229771 0.973245i \(-0.426202\pi\)
0.229771 + 0.973245i \(0.426202\pi\)
\(972\) −23.1927 −0.743906
\(973\) −19.2883 −0.618354
\(974\) 19.3247 0.619202
\(975\) −0.290340 −0.00929831
\(976\) −3.93112 −0.125832
\(977\) 28.4418 0.909934 0.454967 0.890508i \(-0.349651\pi\)
0.454967 + 0.890508i \(0.349651\pi\)
\(978\) −4.62504 −0.147892
\(979\) 1.09929 0.0351335
\(980\) 1.45681 0.0465360
\(981\) 0.811440 0.0259073
\(982\) −3.92267 −0.125177
\(983\) −31.1926 −0.994888 −0.497444 0.867496i \(-0.665728\pi\)
−0.497444 + 0.867496i \(0.665728\pi\)
\(984\) 3.47704 0.110844
\(985\) −0.00829155 −0.000264191 0
\(986\) −2.04485 −0.0651213
\(987\) 7.42935 0.236479
\(988\) −2.74417 −0.0873037
\(989\) 18.9459 0.602446
\(990\) −0.107472 −0.00341568
\(991\) 43.1418 1.37044 0.685222 0.728335i \(-0.259705\pi\)
0.685222 + 0.728335i \(0.259705\pi\)
\(992\) 42.5465 1.35085
\(993\) −8.51325 −0.270160
\(994\) −9.91351 −0.314438
\(995\) 7.36505 0.233488
\(996\) −15.8298 −0.501586
\(997\) 25.4690 0.806611 0.403306 0.915065i \(-0.367861\pi\)
0.403306 + 0.915065i \(0.367861\pi\)
\(998\) 7.60576 0.240756
\(999\) 23.9951 0.759172
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 \(a_p\))