Properties

Label 8002.2.a.e.1.18
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.70235 q^{3} +1.00000 q^{4} +4.07630 q^{5} +1.70235 q^{6} +1.03752 q^{7} -1.00000 q^{8} -0.101993 q^{9} -4.07630 q^{10} -1.31126 q^{11} -1.70235 q^{12} +2.37232 q^{13} -1.03752 q^{14} -6.93930 q^{15} +1.00000 q^{16} -5.13379 q^{17} +0.101993 q^{18} +4.46798 q^{19} +4.07630 q^{20} -1.76623 q^{21} +1.31126 q^{22} +0.760254 q^{23} +1.70235 q^{24} +11.6162 q^{25} -2.37232 q^{26} +5.28069 q^{27} +1.03752 q^{28} +5.15882 q^{29} +6.93930 q^{30} -0.698242 q^{31} -1.00000 q^{32} +2.23223 q^{33} +5.13379 q^{34} +4.22925 q^{35} -0.101993 q^{36} -7.91187 q^{37} -4.46798 q^{38} -4.03853 q^{39} -4.07630 q^{40} +3.27999 q^{41} +1.76623 q^{42} +5.83497 q^{43} -1.31126 q^{44} -0.415754 q^{45} -0.760254 q^{46} -2.17474 q^{47} -1.70235 q^{48} -5.92355 q^{49} -11.6162 q^{50} +8.73953 q^{51} +2.37232 q^{52} -0.495898 q^{53} -5.28069 q^{54} -5.34510 q^{55} -1.03752 q^{56} -7.60608 q^{57} -5.15882 q^{58} -1.42763 q^{59} -6.93930 q^{60} -10.1785 q^{61} +0.698242 q^{62} -0.105820 q^{63} +1.00000 q^{64} +9.67029 q^{65} -2.23223 q^{66} +15.5856 q^{67} -5.13379 q^{68} -1.29422 q^{69} -4.22925 q^{70} -7.14382 q^{71} +0.101993 q^{72} -8.35550 q^{73} +7.91187 q^{74} -19.7749 q^{75} +4.46798 q^{76} -1.36046 q^{77} +4.03853 q^{78} +6.98878 q^{79} +4.07630 q^{80} -8.68362 q^{81} -3.27999 q^{82} +9.52981 q^{83} -1.76623 q^{84} -20.9269 q^{85} -5.83497 q^{86} -8.78213 q^{87} +1.31126 q^{88} +15.9239 q^{89} +0.415754 q^{90} +2.46133 q^{91} +0.760254 q^{92} +1.18865 q^{93} +2.17474 q^{94} +18.2128 q^{95} +1.70235 q^{96} +6.80293 q^{97} +5.92355 q^{98} +0.133740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.70235 −0.982854 −0.491427 0.870919i \(-0.663525\pi\)
−0.491427 + 0.870919i \(0.663525\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.07630 1.82298 0.911489 0.411325i \(-0.134934\pi\)
0.911489 + 0.411325i \(0.134934\pi\)
\(6\) 1.70235 0.694983
\(7\) 1.03752 0.392146 0.196073 0.980589i \(-0.437181\pi\)
0.196073 + 0.980589i \(0.437181\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.101993 −0.0339977
\(10\) −4.07630 −1.28904
\(11\) −1.31126 −0.395361 −0.197680 0.980267i \(-0.563341\pi\)
−0.197680 + 0.980267i \(0.563341\pi\)
\(12\) −1.70235 −0.491427
\(13\) 2.37232 0.657963 0.328982 0.944336i \(-0.393295\pi\)
0.328982 + 0.944336i \(0.393295\pi\)
\(14\) −1.03752 −0.277289
\(15\) −6.93930 −1.79172
\(16\) 1.00000 0.250000
\(17\) −5.13379 −1.24513 −0.622564 0.782569i \(-0.713909\pi\)
−0.622564 + 0.782569i \(0.713909\pi\)
\(18\) 0.101993 0.0240400
\(19\) 4.46798 1.02503 0.512513 0.858680i \(-0.328715\pi\)
0.512513 + 0.858680i \(0.328715\pi\)
\(20\) 4.07630 0.911489
\(21\) −1.76623 −0.385423
\(22\) 1.31126 0.279562
\(23\) 0.760254 0.158524 0.0792619 0.996854i \(-0.474744\pi\)
0.0792619 + 0.996854i \(0.474744\pi\)
\(24\) 1.70235 0.347491
\(25\) 11.6162 2.32325
\(26\) −2.37232 −0.465250
\(27\) 5.28069 1.01627
\(28\) 1.03752 0.196073
\(29\) 5.15882 0.957969 0.478984 0.877823i \(-0.341005\pi\)
0.478984 + 0.877823i \(0.341005\pi\)
\(30\) 6.93930 1.26694
\(31\) −0.698242 −0.125408 −0.0627040 0.998032i \(-0.519972\pi\)
−0.0627040 + 0.998032i \(0.519972\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.23223 0.388582
\(34\) 5.13379 0.880438
\(35\) 4.22925 0.714874
\(36\) −0.101993 −0.0169988
\(37\) −7.91187 −1.30070 −0.650352 0.759633i \(-0.725379\pi\)
−0.650352 + 0.759633i \(0.725379\pi\)
\(38\) −4.46798 −0.724802
\(39\) −4.03853 −0.646682
\(40\) −4.07630 −0.644520
\(41\) 3.27999 0.512249 0.256124 0.966644i \(-0.417554\pi\)
0.256124 + 0.966644i \(0.417554\pi\)
\(42\) 1.76623 0.272535
\(43\) 5.83497 0.889824 0.444912 0.895574i \(-0.353235\pi\)
0.444912 + 0.895574i \(0.353235\pi\)
\(44\) −1.31126 −0.197680
\(45\) −0.415754 −0.0619770
\(46\) −0.760254 −0.112093
\(47\) −2.17474 −0.317219 −0.158610 0.987341i \(-0.550701\pi\)
−0.158610 + 0.987341i \(0.550701\pi\)
\(48\) −1.70235 −0.245714
\(49\) −5.92355 −0.846221
\(50\) −11.6162 −1.64278
\(51\) 8.73953 1.22378
\(52\) 2.37232 0.328982
\(53\) −0.495898 −0.0681169 −0.0340584 0.999420i \(-0.510843\pi\)
−0.0340584 + 0.999420i \(0.510843\pi\)
\(54\) −5.28069 −0.718611
\(55\) −5.34510 −0.720734
\(56\) −1.03752 −0.138645
\(57\) −7.60608 −1.00745
\(58\) −5.15882 −0.677386
\(59\) −1.42763 −0.185862 −0.0929309 0.995673i \(-0.529624\pi\)
−0.0929309 + 0.995673i \(0.529624\pi\)
\(60\) −6.93930 −0.895860
\(61\) −10.1785 −1.30323 −0.651613 0.758551i \(-0.725908\pi\)
−0.651613 + 0.758551i \(0.725908\pi\)
\(62\) 0.698242 0.0886768
\(63\) −0.105820 −0.0133321
\(64\) 1.00000 0.125000
\(65\) 9.67029 1.19945
\(66\) −2.23223 −0.274769
\(67\) 15.5856 1.90408 0.952042 0.305966i \(-0.0989794\pi\)
0.952042 + 0.305966i \(0.0989794\pi\)
\(68\) −5.13379 −0.622564
\(69\) −1.29422 −0.155806
\(70\) −4.22925 −0.505492
\(71\) −7.14382 −0.847815 −0.423907 0.905706i \(-0.639342\pi\)
−0.423907 + 0.905706i \(0.639342\pi\)
\(72\) 0.101993 0.0120200
\(73\) −8.35550 −0.977937 −0.488969 0.872301i \(-0.662627\pi\)
−0.488969 + 0.872301i \(0.662627\pi\)
\(74\) 7.91187 0.919737
\(75\) −19.7749 −2.28341
\(76\) 4.46798 0.512513
\(77\) −1.36046 −0.155039
\(78\) 4.03853 0.457273
\(79\) 6.98878 0.786299 0.393150 0.919475i \(-0.371385\pi\)
0.393150 + 0.919475i \(0.371385\pi\)
\(80\) 4.07630 0.455744
\(81\) −8.68362 −0.964846
\(82\) −3.27999 −0.362215
\(83\) 9.52981 1.04603 0.523016 0.852323i \(-0.324807\pi\)
0.523016 + 0.852323i \(0.324807\pi\)
\(84\) −1.76623 −0.192711
\(85\) −20.9269 −2.26984
\(86\) −5.83497 −0.629201
\(87\) −8.78213 −0.941543
\(88\) 1.31126 0.139781
\(89\) 15.9239 1.68792 0.843962 0.536402i \(-0.180217\pi\)
0.843962 + 0.536402i \(0.180217\pi\)
\(90\) 0.415754 0.0438244
\(91\) 2.46133 0.258018
\(92\) 0.760254 0.0792619
\(93\) 1.18865 0.123258
\(94\) 2.17474 0.224308
\(95\) 18.2128 1.86860
\(96\) 1.70235 0.173746
\(97\) 6.80293 0.690733 0.345367 0.938468i \(-0.387755\pi\)
0.345367 + 0.938468i \(0.387755\pi\)
\(98\) 5.92355 0.598369
\(99\) 0.133740 0.0134413
\(100\) 11.6162 1.16162
\(101\) 10.7348 1.06815 0.534076 0.845436i \(-0.320660\pi\)
0.534076 + 0.845436i \(0.320660\pi\)
\(102\) −8.73953 −0.865342
\(103\) −8.94582 −0.881458 −0.440729 0.897640i \(-0.645280\pi\)
−0.440729 + 0.897640i \(0.645280\pi\)
\(104\) −2.37232 −0.232625
\(105\) −7.19968 −0.702617
\(106\) 0.495898 0.0481659
\(107\) −1.15600 −0.111755 −0.0558776 0.998438i \(-0.517796\pi\)
−0.0558776 + 0.998438i \(0.517796\pi\)
\(108\) 5.28069 0.508134
\(109\) 11.5722 1.10842 0.554208 0.832378i \(-0.313021\pi\)
0.554208 + 0.832378i \(0.313021\pi\)
\(110\) 5.34510 0.509636
\(111\) 13.4688 1.27840
\(112\) 1.03752 0.0980366
\(113\) 12.7261 1.19717 0.598584 0.801060i \(-0.295730\pi\)
0.598584 + 0.801060i \(0.295730\pi\)
\(114\) 7.60608 0.712375
\(115\) 3.09902 0.288985
\(116\) 5.15882 0.478984
\(117\) −0.241960 −0.0223692
\(118\) 1.42763 0.131424
\(119\) −5.32642 −0.488272
\(120\) 6.93930 0.633469
\(121\) −9.28059 −0.843690
\(122\) 10.1785 0.921521
\(123\) −5.58371 −0.503466
\(124\) −0.698242 −0.0627040
\(125\) 26.9697 2.41225
\(126\) 0.105820 0.00942720
\(127\) 15.6377 1.38762 0.693811 0.720157i \(-0.255930\pi\)
0.693811 + 0.720157i \(0.255930\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.93318 −0.874567
\(130\) −9.67029 −0.848141
\(131\) 9.26329 0.809338 0.404669 0.914463i \(-0.367387\pi\)
0.404669 + 0.914463i \(0.367387\pi\)
\(132\) 2.23223 0.194291
\(133\) 4.63563 0.401960
\(134\) −15.5856 −1.34639
\(135\) 21.5257 1.85264
\(136\) 5.13379 0.440219
\(137\) −0.0402046 −0.00343491 −0.00171746 0.999999i \(-0.500547\pi\)
−0.00171746 + 0.999999i \(0.500547\pi\)
\(138\) 1.29422 0.110171
\(139\) −19.9509 −1.69221 −0.846105 0.533016i \(-0.821058\pi\)
−0.846105 + 0.533016i \(0.821058\pi\)
\(140\) 4.22925 0.357437
\(141\) 3.70218 0.311780
\(142\) 7.14382 0.599496
\(143\) −3.11074 −0.260133
\(144\) −0.101993 −0.00849942
\(145\) 21.0289 1.74635
\(146\) 8.35550 0.691506
\(147\) 10.0840 0.831712
\(148\) −7.91187 −0.650352
\(149\) −12.8354 −1.05152 −0.525760 0.850633i \(-0.676219\pi\)
−0.525760 + 0.850633i \(0.676219\pi\)
\(150\) 19.7749 1.61462
\(151\) −16.1459 −1.31393 −0.656967 0.753919i \(-0.728161\pi\)
−0.656967 + 0.753919i \(0.728161\pi\)
\(152\) −4.46798 −0.362401
\(153\) 0.523611 0.0423314
\(154\) 1.36046 0.109629
\(155\) −2.84624 −0.228616
\(156\) −4.03853 −0.323341
\(157\) 12.0959 0.965358 0.482679 0.875797i \(-0.339664\pi\)
0.482679 + 0.875797i \(0.339664\pi\)
\(158\) −6.98878 −0.555998
\(159\) 0.844194 0.0669490
\(160\) −4.07630 −0.322260
\(161\) 0.788780 0.0621646
\(162\) 8.68362 0.682249
\(163\) 1.88880 0.147942 0.0739709 0.997260i \(-0.476433\pi\)
0.0739709 + 0.997260i \(0.476433\pi\)
\(164\) 3.27999 0.256124
\(165\) 9.09925 0.708376
\(166\) −9.52981 −0.739657
\(167\) 6.55728 0.507418 0.253709 0.967281i \(-0.418349\pi\)
0.253709 + 0.967281i \(0.418349\pi\)
\(168\) 1.76623 0.136268
\(169\) −7.37210 −0.567085
\(170\) 20.9269 1.60502
\(171\) −0.455703 −0.0348485
\(172\) 5.83497 0.444912
\(173\) 9.61367 0.730914 0.365457 0.930828i \(-0.380913\pi\)
0.365457 + 0.930828i \(0.380913\pi\)
\(174\) 8.78213 0.665772
\(175\) 12.0521 0.911053
\(176\) −1.31126 −0.0988402
\(177\) 2.43033 0.182675
\(178\) −15.9239 −1.19354
\(179\) 10.3741 0.775400 0.387700 0.921786i \(-0.373270\pi\)
0.387700 + 0.921786i \(0.373270\pi\)
\(180\) −0.415754 −0.0309885
\(181\) −5.78228 −0.429793 −0.214897 0.976637i \(-0.568941\pi\)
−0.214897 + 0.976637i \(0.568941\pi\)
\(182\) −2.46133 −0.182446
\(183\) 17.3274 1.28088
\(184\) −0.760254 −0.0560466
\(185\) −32.2512 −2.37115
\(186\) −1.18865 −0.0871564
\(187\) 6.73175 0.492274
\(188\) −2.17474 −0.158610
\(189\) 5.47883 0.398526
\(190\) −18.2128 −1.32130
\(191\) 8.94259 0.647063 0.323532 0.946217i \(-0.395130\pi\)
0.323532 + 0.946217i \(0.395130\pi\)
\(192\) −1.70235 −0.122857
\(193\) −17.8248 −1.28305 −0.641527 0.767100i \(-0.721699\pi\)
−0.641527 + 0.767100i \(0.721699\pi\)
\(194\) −6.80293 −0.488422
\(195\) −16.4623 −1.17889
\(196\) −5.92355 −0.423111
\(197\) 18.6669 1.32996 0.664982 0.746859i \(-0.268439\pi\)
0.664982 + 0.746859i \(0.268439\pi\)
\(198\) −0.133740 −0.00950447
\(199\) 13.4208 0.951375 0.475687 0.879614i \(-0.342199\pi\)
0.475687 + 0.879614i \(0.342199\pi\)
\(200\) −11.6162 −0.821392
\(201\) −26.5322 −1.87144
\(202\) −10.7348 −0.755298
\(203\) 5.35239 0.375664
\(204\) 8.73953 0.611889
\(205\) 13.3702 0.933818
\(206\) 8.94582 0.623285
\(207\) −0.0775406 −0.00538944
\(208\) 2.37232 0.164491
\(209\) −5.85870 −0.405255
\(210\) 7.19968 0.496825
\(211\) −3.72585 −0.256498 −0.128249 0.991742i \(-0.540936\pi\)
−0.128249 + 0.991742i \(0.540936\pi\)
\(212\) −0.495898 −0.0340584
\(213\) 12.1613 0.833278
\(214\) 1.15600 0.0790228
\(215\) 23.7851 1.62213
\(216\) −5.28069 −0.359305
\(217\) −0.724441 −0.0491783
\(218\) −11.5722 −0.783768
\(219\) 14.2240 0.961170
\(220\) −5.34510 −0.360367
\(221\) −12.1790 −0.819248
\(222\) −13.4688 −0.903967
\(223\) −3.81823 −0.255688 −0.127844 0.991794i \(-0.540806\pi\)
−0.127844 + 0.991794i \(0.540806\pi\)
\(224\) −1.03752 −0.0693223
\(225\) −1.18477 −0.0789850
\(226\) −12.7261 −0.846526
\(227\) 15.3243 1.01711 0.508554 0.861030i \(-0.330180\pi\)
0.508554 + 0.861030i \(0.330180\pi\)
\(228\) −7.60608 −0.503725
\(229\) 19.0411 1.25827 0.629136 0.777295i \(-0.283409\pi\)
0.629136 + 0.777295i \(0.283409\pi\)
\(230\) −3.09902 −0.204344
\(231\) 2.31599 0.152381
\(232\) −5.15882 −0.338693
\(233\) −12.6530 −0.828928 −0.414464 0.910066i \(-0.636031\pi\)
−0.414464 + 0.910066i \(0.636031\pi\)
\(234\) 0.241960 0.0158174
\(235\) −8.86491 −0.578283
\(236\) −1.42763 −0.0929309
\(237\) −11.8974 −0.772818
\(238\) 5.32642 0.345261
\(239\) −3.96287 −0.256337 −0.128169 0.991752i \(-0.540910\pi\)
−0.128169 + 0.991752i \(0.540910\pi\)
\(240\) −6.93930 −0.447930
\(241\) −20.3938 −1.31368 −0.656841 0.754029i \(-0.728108\pi\)
−0.656841 + 0.754029i \(0.728108\pi\)
\(242\) 9.28059 0.596579
\(243\) −1.05948 −0.0679656
\(244\) −10.1785 −0.651613
\(245\) −24.1462 −1.54264
\(246\) 5.58371 0.356004
\(247\) 10.5995 0.674429
\(248\) 0.698242 0.0443384
\(249\) −16.2231 −1.02810
\(250\) −26.9697 −1.70572
\(251\) 25.6553 1.61935 0.809674 0.586880i \(-0.199644\pi\)
0.809674 + 0.586880i \(0.199644\pi\)
\(252\) −0.105820 −0.00666603
\(253\) −0.996893 −0.0626741
\(254\) −15.6377 −0.981196
\(255\) 35.6249 2.23092
\(256\) 1.00000 0.0625000
\(257\) −21.0779 −1.31480 −0.657402 0.753540i \(-0.728345\pi\)
−0.657402 + 0.753540i \(0.728345\pi\)
\(258\) 9.93318 0.618413
\(259\) −8.20874 −0.510066
\(260\) 9.67029 0.599726
\(261\) −0.526164 −0.0325687
\(262\) −9.26329 −0.572288
\(263\) 15.9581 0.984019 0.492009 0.870590i \(-0.336263\pi\)
0.492009 + 0.870590i \(0.336263\pi\)
\(264\) −2.23223 −0.137384
\(265\) −2.02143 −0.124176
\(266\) −4.63563 −0.284229
\(267\) −27.1080 −1.65898
\(268\) 15.5856 0.952042
\(269\) −7.34367 −0.447752 −0.223876 0.974618i \(-0.571871\pi\)
−0.223876 + 0.974618i \(0.571871\pi\)
\(270\) −21.5257 −1.31001
\(271\) −3.56307 −0.216441 −0.108221 0.994127i \(-0.534515\pi\)
−0.108221 + 0.994127i \(0.534515\pi\)
\(272\) −5.13379 −0.311282
\(273\) −4.19006 −0.253594
\(274\) 0.0402046 0.00242885
\(275\) −15.2319 −0.918520
\(276\) −1.29422 −0.0779029
\(277\) −6.73812 −0.404855 −0.202427 0.979297i \(-0.564883\pi\)
−0.202427 + 0.979297i \(0.564883\pi\)
\(278\) 19.9509 1.19657
\(279\) 0.0712158 0.00426358
\(280\) −4.22925 −0.252746
\(281\) −24.8932 −1.48501 −0.742503 0.669843i \(-0.766361\pi\)
−0.742503 + 0.669843i \(0.766361\pi\)
\(282\) −3.70218 −0.220462
\(283\) 5.60601 0.333243 0.166621 0.986021i \(-0.446714\pi\)
0.166621 + 0.986021i \(0.446714\pi\)
\(284\) −7.14382 −0.423907
\(285\) −31.0047 −1.83656
\(286\) 3.11074 0.183942
\(287\) 3.40306 0.200877
\(288\) 0.101993 0.00601000
\(289\) 9.35582 0.550342
\(290\) −21.0289 −1.23486
\(291\) −11.5810 −0.678890
\(292\) −8.35550 −0.488969
\(293\) 2.56147 0.149643 0.0748214 0.997197i \(-0.476161\pi\)
0.0748214 + 0.997197i \(0.476161\pi\)
\(294\) −10.0840 −0.588109
\(295\) −5.81946 −0.338822
\(296\) 7.91187 0.459868
\(297\) −6.92437 −0.401793
\(298\) 12.8354 0.743537
\(299\) 1.80356 0.104303
\(300\) −19.7749 −1.14171
\(301\) 6.05391 0.348941
\(302\) 16.1459 0.929092
\(303\) −18.2744 −1.04984
\(304\) 4.46798 0.256256
\(305\) −41.4907 −2.37575
\(306\) −0.523611 −0.0299329
\(307\) 6.62710 0.378228 0.189114 0.981955i \(-0.439438\pi\)
0.189114 + 0.981955i \(0.439438\pi\)
\(308\) −1.36046 −0.0775196
\(309\) 15.2289 0.866344
\(310\) 2.84624 0.161656
\(311\) 14.4722 0.820643 0.410321 0.911941i \(-0.365417\pi\)
0.410321 + 0.911941i \(0.365417\pi\)
\(312\) 4.03853 0.228637
\(313\) −30.8995 −1.74655 −0.873273 0.487232i \(-0.838007\pi\)
−0.873273 + 0.487232i \(0.838007\pi\)
\(314\) −12.0959 −0.682611
\(315\) −0.431354 −0.0243041
\(316\) 6.98878 0.393150
\(317\) −11.4870 −0.645175 −0.322588 0.946540i \(-0.604553\pi\)
−0.322588 + 0.946540i \(0.604553\pi\)
\(318\) −0.844194 −0.0473401
\(319\) −6.76457 −0.378743
\(320\) 4.07630 0.227872
\(321\) 1.96793 0.109839
\(322\) −0.788780 −0.0439570
\(323\) −22.9377 −1.27629
\(324\) −8.68362 −0.482423
\(325\) 27.5574 1.52861
\(326\) −1.88880 −0.104611
\(327\) −19.7000 −1.08941
\(328\) −3.27999 −0.181107
\(329\) −2.25634 −0.124396
\(330\) −9.09925 −0.500897
\(331\) 9.23886 0.507814 0.253907 0.967229i \(-0.418284\pi\)
0.253907 + 0.967229i \(0.418284\pi\)
\(332\) 9.52981 0.523016
\(333\) 0.806956 0.0442209
\(334\) −6.55728 −0.358799
\(335\) 63.5316 3.47110
\(336\) −1.76623 −0.0963557
\(337\) 10.4779 0.570767 0.285384 0.958413i \(-0.407879\pi\)
0.285384 + 0.958413i \(0.407879\pi\)
\(338\) 7.37210 0.400989
\(339\) −21.6643 −1.17664
\(340\) −20.9269 −1.13492
\(341\) 0.915579 0.0495814
\(342\) 0.455703 0.0246416
\(343\) −13.4085 −0.723989
\(344\) −5.83497 −0.314600
\(345\) −5.27563 −0.284030
\(346\) −9.61367 −0.516834
\(347\) 13.3901 0.718818 0.359409 0.933180i \(-0.382978\pi\)
0.359409 + 0.933180i \(0.382978\pi\)
\(348\) −8.78213 −0.470772
\(349\) 28.3325 1.51660 0.758301 0.651905i \(-0.226030\pi\)
0.758301 + 0.651905i \(0.226030\pi\)
\(350\) −12.0521 −0.644211
\(351\) 12.5275 0.668667
\(352\) 1.31126 0.0698906
\(353\) 7.38649 0.393143 0.196572 0.980489i \(-0.437019\pi\)
0.196572 + 0.980489i \(0.437019\pi\)
\(354\) −2.43033 −0.129171
\(355\) −29.1203 −1.54555
\(356\) 15.9239 0.843962
\(357\) 9.06745 0.479900
\(358\) −10.3741 −0.548291
\(359\) −17.7601 −0.937341 −0.468670 0.883373i \(-0.655267\pi\)
−0.468670 + 0.883373i \(0.655267\pi\)
\(360\) 0.415754 0.0219122
\(361\) 0.962862 0.0506770
\(362\) 5.78228 0.303910
\(363\) 15.7988 0.829224
\(364\) 2.46133 0.129009
\(365\) −34.0595 −1.78276
\(366\) −17.3274 −0.905720
\(367\) 29.5891 1.54454 0.772269 0.635296i \(-0.219122\pi\)
0.772269 + 0.635296i \(0.219122\pi\)
\(368\) 0.760254 0.0396310
\(369\) −0.334536 −0.0174153
\(370\) 32.2512 1.67666
\(371\) −0.514505 −0.0267118
\(372\) 1.18865 0.0616289
\(373\) 29.1942 1.51162 0.755810 0.654791i \(-0.227243\pi\)
0.755810 + 0.654791i \(0.227243\pi\)
\(374\) −6.73175 −0.348091
\(375\) −45.9120 −2.37089
\(376\) 2.17474 0.112154
\(377\) 12.2384 0.630308
\(378\) −5.47883 −0.281801
\(379\) 8.17757 0.420054 0.210027 0.977696i \(-0.432645\pi\)
0.210027 + 0.977696i \(0.432645\pi\)
\(380\) 18.2128 0.934299
\(381\) −26.6209 −1.36383
\(382\) −8.94259 −0.457543
\(383\) 7.06134 0.360818 0.180409 0.983592i \(-0.442258\pi\)
0.180409 + 0.983592i \(0.442258\pi\)
\(384\) 1.70235 0.0868729
\(385\) −5.54566 −0.282633
\(386\) 17.8248 0.907256
\(387\) −0.595126 −0.0302520
\(388\) 6.80293 0.345367
\(389\) 4.21852 0.213888 0.106944 0.994265i \(-0.465894\pi\)
0.106944 + 0.994265i \(0.465894\pi\)
\(390\) 16.4623 0.833598
\(391\) −3.90298 −0.197382
\(392\) 5.92355 0.299184
\(393\) −15.7694 −0.795461
\(394\) −18.6669 −0.940427
\(395\) 28.4884 1.43341
\(396\) 0.133740 0.00672067
\(397\) 10.9084 0.547478 0.273739 0.961804i \(-0.411740\pi\)
0.273739 + 0.961804i \(0.411740\pi\)
\(398\) −13.4208 −0.672723
\(399\) −7.89148 −0.395068
\(400\) 11.6162 0.580812
\(401\) 25.6705 1.28192 0.640961 0.767574i \(-0.278536\pi\)
0.640961 + 0.767574i \(0.278536\pi\)
\(402\) 26.5322 1.32331
\(403\) −1.65645 −0.0825138
\(404\) 10.7348 0.534076
\(405\) −35.3970 −1.75889
\(406\) −5.35239 −0.265635
\(407\) 10.3745 0.514247
\(408\) −8.73953 −0.432671
\(409\) 27.2787 1.34885 0.674424 0.738345i \(-0.264392\pi\)
0.674424 + 0.738345i \(0.264392\pi\)
\(410\) −13.3702 −0.660309
\(411\) 0.0684424 0.00337602
\(412\) −8.94582 −0.440729
\(413\) −1.48120 −0.0728850
\(414\) 0.0775406 0.00381091
\(415\) 38.8464 1.90689
\(416\) −2.37232 −0.116313
\(417\) 33.9634 1.66320
\(418\) 5.85870 0.286558
\(419\) 11.8089 0.576901 0.288451 0.957495i \(-0.406860\pi\)
0.288451 + 0.957495i \(0.406860\pi\)
\(420\) −7.19968 −0.351308
\(421\) −38.9584 −1.89871 −0.949357 0.314198i \(-0.898264\pi\)
−0.949357 + 0.314198i \(0.898264\pi\)
\(422\) 3.72585 0.181371
\(423\) 0.221809 0.0107847
\(424\) 0.495898 0.0240830
\(425\) −59.6353 −2.89274
\(426\) −12.1613 −0.589217
\(427\) −10.5604 −0.511056
\(428\) −1.15600 −0.0558776
\(429\) 5.29557 0.255673
\(430\) −23.7851 −1.14702
\(431\) 10.2463 0.493547 0.246774 0.969073i \(-0.420630\pi\)
0.246774 + 0.969073i \(0.420630\pi\)
\(432\) 5.28069 0.254067
\(433\) −4.12687 −0.198325 −0.0991623 0.995071i \(-0.531616\pi\)
−0.0991623 + 0.995071i \(0.531616\pi\)
\(434\) 0.724441 0.0347743
\(435\) −35.7986 −1.71641
\(436\) 11.5722 0.554208
\(437\) 3.39680 0.162491
\(438\) −14.2240 −0.679650
\(439\) −19.6791 −0.939233 −0.469616 0.882871i \(-0.655608\pi\)
−0.469616 + 0.882871i \(0.655608\pi\)
\(440\) 5.34510 0.254818
\(441\) 0.604161 0.0287696
\(442\) 12.1790 0.579296
\(443\) 1.80713 0.0858591 0.0429296 0.999078i \(-0.486331\pi\)
0.0429296 + 0.999078i \(0.486331\pi\)
\(444\) 13.4688 0.639201
\(445\) 64.9104 3.07705
\(446\) 3.81823 0.180798
\(447\) 21.8505 1.03349
\(448\) 1.03752 0.0490183
\(449\) −19.7178 −0.930540 −0.465270 0.885169i \(-0.654043\pi\)
−0.465270 + 0.885169i \(0.654043\pi\)
\(450\) 1.18477 0.0558508
\(451\) −4.30093 −0.202523
\(452\) 12.7261 0.598584
\(453\) 27.4860 1.29141
\(454\) −15.3243 −0.719205
\(455\) 10.0331 0.470361
\(456\) 7.60608 0.356188
\(457\) 24.0627 1.12561 0.562804 0.826591i \(-0.309723\pi\)
0.562804 + 0.826591i \(0.309723\pi\)
\(458\) −19.0411 −0.889733
\(459\) −27.1100 −1.26538
\(460\) 3.09902 0.144493
\(461\) −9.06197 −0.422058 −0.211029 0.977480i \(-0.567681\pi\)
−0.211029 + 0.977480i \(0.567681\pi\)
\(462\) −2.31599 −0.107750
\(463\) −27.5234 −1.27912 −0.639560 0.768741i \(-0.720883\pi\)
−0.639560 + 0.768741i \(0.720883\pi\)
\(464\) 5.15882 0.239492
\(465\) 4.84531 0.224696
\(466\) 12.6530 0.586140
\(467\) 3.53732 0.163688 0.0818438 0.996645i \(-0.473919\pi\)
0.0818438 + 0.996645i \(0.473919\pi\)
\(468\) −0.241960 −0.0111846
\(469\) 16.1704 0.746680
\(470\) 8.86491 0.408908
\(471\) −20.5915 −0.948806
\(472\) 1.42763 0.0657121
\(473\) −7.65118 −0.351802
\(474\) 11.8974 0.546465
\(475\) 51.9011 2.38139
\(476\) −5.32642 −0.244136
\(477\) 0.0505782 0.00231582
\(478\) 3.96287 0.181258
\(479\) −1.80306 −0.0823839 −0.0411919 0.999151i \(-0.513116\pi\)
−0.0411919 + 0.999151i \(0.513116\pi\)
\(480\) 6.93930 0.316734
\(481\) −18.7695 −0.855815
\(482\) 20.3938 0.928913
\(483\) −1.34278 −0.0610987
\(484\) −9.28059 −0.421845
\(485\) 27.7308 1.25919
\(486\) 1.05948 0.0480589
\(487\) 13.8396 0.627131 0.313565 0.949567i \(-0.398477\pi\)
0.313565 + 0.949567i \(0.398477\pi\)
\(488\) 10.1785 0.460760
\(489\) −3.21540 −0.145405
\(490\) 24.1462 1.09081
\(491\) 40.3124 1.81927 0.909636 0.415406i \(-0.136360\pi\)
0.909636 + 0.415406i \(0.136360\pi\)
\(492\) −5.58371 −0.251733
\(493\) −26.4843 −1.19279
\(494\) −10.5995 −0.476893
\(495\) 0.545163 0.0245033
\(496\) −0.698242 −0.0313520
\(497\) −7.41186 −0.332468
\(498\) 16.2231 0.726975
\(499\) 32.4731 1.45370 0.726848 0.686798i \(-0.240985\pi\)
0.726848 + 0.686798i \(0.240985\pi\)
\(500\) 26.9697 1.20612
\(501\) −11.1628 −0.498718
\(502\) −25.6553 −1.14505
\(503\) −42.9514 −1.91511 −0.957553 0.288257i \(-0.906924\pi\)
−0.957553 + 0.288257i \(0.906924\pi\)
\(504\) 0.105820 0.00471360
\(505\) 43.7583 1.94722
\(506\) 0.996893 0.0443173
\(507\) 12.5499 0.557361
\(508\) 15.6377 0.693811
\(509\) −34.6615 −1.53634 −0.768172 0.640244i \(-0.778833\pi\)
−0.768172 + 0.640244i \(0.778833\pi\)
\(510\) −35.6249 −1.57750
\(511\) −8.66902 −0.383495
\(512\) −1.00000 −0.0441942
\(513\) 23.5940 1.04170
\(514\) 21.0779 0.929706
\(515\) −36.4658 −1.60688
\(516\) −9.93318 −0.437284
\(517\) 2.85166 0.125416
\(518\) 8.20874 0.360671
\(519\) −16.3659 −0.718382
\(520\) −9.67029 −0.424070
\(521\) 28.1674 1.23404 0.617019 0.786949i \(-0.288340\pi\)
0.617019 + 0.786949i \(0.288340\pi\)
\(522\) 0.526164 0.0230296
\(523\) 13.8014 0.603492 0.301746 0.953388i \(-0.402431\pi\)
0.301746 + 0.953388i \(0.402431\pi\)
\(524\) 9.26329 0.404669
\(525\) −20.5169 −0.895432
\(526\) −15.9581 −0.695806
\(527\) 3.58463 0.156149
\(528\) 2.23223 0.0971455
\(529\) −22.4220 −0.974870
\(530\) 2.02143 0.0878053
\(531\) 0.145609 0.00631887
\(532\) 4.63563 0.200980
\(533\) 7.78119 0.337041
\(534\) 27.1080 1.17308
\(535\) −4.71222 −0.203727
\(536\) −15.5856 −0.673196
\(537\) −17.6605 −0.762105
\(538\) 7.34367 0.316608
\(539\) 7.76733 0.334563
\(540\) 21.5257 0.926318
\(541\) 29.4943 1.26806 0.634030 0.773309i \(-0.281400\pi\)
0.634030 + 0.773309i \(0.281400\pi\)
\(542\) 3.56307 0.153047
\(543\) 9.84348 0.422424
\(544\) 5.13379 0.220110
\(545\) 47.1718 2.02062
\(546\) 4.19006 0.179318
\(547\) 12.4292 0.531434 0.265717 0.964051i \(-0.414391\pi\)
0.265717 + 0.964051i \(0.414391\pi\)
\(548\) −0.0402046 −0.00171746
\(549\) 1.03814 0.0443067
\(550\) 15.2319 0.649492
\(551\) 23.0495 0.981942
\(552\) 1.29422 0.0550857
\(553\) 7.25101 0.308344
\(554\) 6.73812 0.286275
\(555\) 54.9029 2.33050
\(556\) −19.9509 −0.846105
\(557\) −35.5304 −1.50547 −0.752736 0.658322i \(-0.771267\pi\)
−0.752736 + 0.658322i \(0.771267\pi\)
\(558\) −0.0712158 −0.00301481
\(559\) 13.8424 0.585472
\(560\) 4.22925 0.178718
\(561\) −11.4598 −0.483834
\(562\) 24.8932 1.05006
\(563\) −7.98426 −0.336497 −0.168248 0.985745i \(-0.553811\pi\)
−0.168248 + 0.985745i \(0.553811\pi\)
\(564\) 3.70218 0.155890
\(565\) 51.8753 2.18241
\(566\) −5.60601 −0.235638
\(567\) −9.00944 −0.378361
\(568\) 7.14382 0.299748
\(569\) −2.21774 −0.0929727 −0.0464863 0.998919i \(-0.514802\pi\)
−0.0464863 + 0.998919i \(0.514802\pi\)
\(570\) 31.0047 1.29864
\(571\) −33.0788 −1.38431 −0.692153 0.721751i \(-0.743338\pi\)
−0.692153 + 0.721751i \(0.743338\pi\)
\(572\) −3.11074 −0.130066
\(573\) −15.2235 −0.635969
\(574\) −3.40306 −0.142041
\(575\) 8.83128 0.368290
\(576\) −0.101993 −0.00424971
\(577\) −36.2739 −1.51010 −0.755050 0.655667i \(-0.772388\pi\)
−0.755050 + 0.655667i \(0.772388\pi\)
\(578\) −9.35582 −0.389151
\(579\) 30.3440 1.26106
\(580\) 21.0289 0.873177
\(581\) 9.88739 0.410198
\(582\) 11.5810 0.480048
\(583\) 0.650253 0.0269307
\(584\) 8.35550 0.345753
\(585\) −0.986302 −0.0407786
\(586\) −2.56147 −0.105813
\(587\) 45.8702 1.89326 0.946632 0.322315i \(-0.104461\pi\)
0.946632 + 0.322315i \(0.104461\pi\)
\(588\) 10.0840 0.415856
\(589\) −3.11973 −0.128546
\(590\) 5.81946 0.239583
\(591\) −31.7777 −1.30716
\(592\) −7.91187 −0.325176
\(593\) −26.2469 −1.07783 −0.538916 0.842360i \(-0.681166\pi\)
−0.538916 + 0.842360i \(0.681166\pi\)
\(594\) 6.92437 0.284110
\(595\) −21.7121 −0.890109
\(596\) −12.8354 −0.525760
\(597\) −22.8469 −0.935062
\(598\) −1.80356 −0.0737533
\(599\) −14.9251 −0.609824 −0.304912 0.952381i \(-0.598627\pi\)
−0.304912 + 0.952381i \(0.598627\pi\)
\(600\) 19.7749 0.807308
\(601\) −26.5058 −1.08120 −0.540598 0.841281i \(-0.681802\pi\)
−0.540598 + 0.841281i \(0.681802\pi\)
\(602\) −6.05391 −0.246739
\(603\) −1.58962 −0.0647345
\(604\) −16.1459 −0.656967
\(605\) −37.8305 −1.53803
\(606\) 18.2744 0.742348
\(607\) −24.2897 −0.985888 −0.492944 0.870061i \(-0.664079\pi\)
−0.492944 + 0.870061i \(0.664079\pi\)
\(608\) −4.46798 −0.181201
\(609\) −9.11165 −0.369223
\(610\) 41.4907 1.67991
\(611\) −5.15919 −0.208718
\(612\) 0.523611 0.0211657
\(613\) 8.53805 0.344848 0.172424 0.985023i \(-0.444840\pi\)
0.172424 + 0.985023i \(0.444840\pi\)
\(614\) −6.62710 −0.267448
\(615\) −22.7609 −0.917807
\(616\) 1.36046 0.0548147
\(617\) −32.7930 −1.32019 −0.660097 0.751180i \(-0.729485\pi\)
−0.660097 + 0.751180i \(0.729485\pi\)
\(618\) −15.2289 −0.612598
\(619\) −14.8820 −0.598158 −0.299079 0.954228i \(-0.596679\pi\)
−0.299079 + 0.954228i \(0.596679\pi\)
\(620\) −2.84624 −0.114308
\(621\) 4.01466 0.161103
\(622\) −14.4722 −0.580282
\(623\) 16.5213 0.661914
\(624\) −4.03853 −0.161670
\(625\) 51.8557 2.07423
\(626\) 30.8995 1.23499
\(627\) 9.97358 0.398306
\(628\) 12.0959 0.482679
\(629\) 40.6179 1.61954
\(630\) 0.431354 0.0171856
\(631\) 29.2178 1.16314 0.581572 0.813495i \(-0.302438\pi\)
0.581572 + 0.813495i \(0.302438\pi\)
\(632\) −6.98878 −0.277999
\(633\) 6.34271 0.252100
\(634\) 11.4870 0.456208
\(635\) 63.7440 2.52960
\(636\) 0.844194 0.0334745
\(637\) −14.0526 −0.556782
\(638\) 6.76457 0.267812
\(639\) 0.728620 0.0288237
\(640\) −4.07630 −0.161130
\(641\) 1.52056 0.0600584 0.0300292 0.999549i \(-0.490440\pi\)
0.0300292 + 0.999549i \(0.490440\pi\)
\(642\) −1.96793 −0.0776679
\(643\) 30.5898 1.20634 0.603172 0.797611i \(-0.293903\pi\)
0.603172 + 0.797611i \(0.293903\pi\)
\(644\) 0.788780 0.0310823
\(645\) −40.4906 −1.59432
\(646\) 22.9377 0.902471
\(647\) 1.90178 0.0747669 0.0373834 0.999301i \(-0.488098\pi\)
0.0373834 + 0.999301i \(0.488098\pi\)
\(648\) 8.68362 0.341125
\(649\) 1.87200 0.0734825
\(650\) −27.5574 −1.08089
\(651\) 1.23325 0.0483351
\(652\) 1.88880 0.0739709
\(653\) 24.2031 0.947139 0.473569 0.880756i \(-0.342965\pi\)
0.473569 + 0.880756i \(0.342965\pi\)
\(654\) 19.7000 0.770330
\(655\) 37.7600 1.47540
\(656\) 3.27999 0.128062
\(657\) 0.852203 0.0332476
\(658\) 2.25634 0.0879615
\(659\) 27.2315 1.06079 0.530395 0.847751i \(-0.322044\pi\)
0.530395 + 0.847751i \(0.322044\pi\)
\(660\) 9.09925 0.354188
\(661\) 16.3279 0.635081 0.317541 0.948245i \(-0.397143\pi\)
0.317541 + 0.948245i \(0.397143\pi\)
\(662\) −9.23886 −0.359079
\(663\) 20.7330 0.805201
\(664\) −9.52981 −0.369828
\(665\) 18.8962 0.732764
\(666\) −0.806956 −0.0312689
\(667\) 3.92201 0.151861
\(668\) 6.55728 0.253709
\(669\) 6.49998 0.251304
\(670\) −63.5316 −2.45444
\(671\) 13.3467 0.515245
\(672\) 1.76623 0.0681338
\(673\) 20.0018 0.771012 0.385506 0.922705i \(-0.374027\pi\)
0.385506 + 0.922705i \(0.374027\pi\)
\(674\) −10.4779 −0.403593
\(675\) 61.3417 2.36104
\(676\) −7.37210 −0.283542
\(677\) −15.5543 −0.597799 −0.298899 0.954285i \(-0.596619\pi\)
−0.298899 + 0.954285i \(0.596619\pi\)
\(678\) 21.6643 0.832011
\(679\) 7.05819 0.270869
\(680\) 20.9269 0.802509
\(681\) −26.0874 −0.999670
\(682\) −0.915579 −0.0350593
\(683\) −22.9697 −0.878910 −0.439455 0.898265i \(-0.644828\pi\)
−0.439455 + 0.898265i \(0.644828\pi\)
\(684\) −0.455703 −0.0174242
\(685\) −0.163886 −0.00626176
\(686\) 13.4085 0.511938
\(687\) −32.4147 −1.23670
\(688\) 5.83497 0.222456
\(689\) −1.17643 −0.0448184
\(690\) 5.27563 0.200840
\(691\) −26.6472 −1.01371 −0.506854 0.862032i \(-0.669192\pi\)
−0.506854 + 0.862032i \(0.669192\pi\)
\(692\) 9.61367 0.365457
\(693\) 0.138758 0.00527098
\(694\) −13.3901 −0.508281
\(695\) −81.3257 −3.08486
\(696\) 8.78213 0.332886
\(697\) −16.8388 −0.637815
\(698\) −28.3325 −1.07240
\(699\) 21.5399 0.814715
\(700\) 12.0521 0.455526
\(701\) 9.42887 0.356124 0.178062 0.984019i \(-0.443017\pi\)
0.178062 + 0.984019i \(0.443017\pi\)
\(702\) −12.5275 −0.472819
\(703\) −35.3501 −1.33325
\(704\) −1.31126 −0.0494201
\(705\) 15.0912 0.568368
\(706\) −7.38649 −0.277994
\(707\) 11.1376 0.418872
\(708\) 2.43033 0.0913375
\(709\) −31.0011 −1.16427 −0.582135 0.813092i \(-0.697783\pi\)
−0.582135 + 0.813092i \(0.697783\pi\)
\(710\) 29.1203 1.09287
\(711\) −0.712807 −0.0267324
\(712\) −15.9239 −0.596772
\(713\) −0.530841 −0.0198802
\(714\) −9.06745 −0.339341
\(715\) −12.6803 −0.474216
\(716\) 10.3741 0.387700
\(717\) 6.74621 0.251942
\(718\) 17.7601 0.662800
\(719\) 22.9014 0.854080 0.427040 0.904233i \(-0.359556\pi\)
0.427040 + 0.904233i \(0.359556\pi\)
\(720\) −0.415754 −0.0154943
\(721\) −9.28148 −0.345660
\(722\) −0.962862 −0.0358340
\(723\) 34.7175 1.29116
\(724\) −5.78228 −0.214897
\(725\) 59.9260 2.22560
\(726\) −15.7988 −0.586350
\(727\) −26.5340 −0.984092 −0.492046 0.870569i \(-0.663751\pi\)
−0.492046 + 0.870569i \(0.663751\pi\)
\(728\) −2.46133 −0.0912231
\(729\) 27.8545 1.03165
\(730\) 34.0595 1.26060
\(731\) −29.9555 −1.10794
\(732\) 17.3274 0.640441
\(733\) 4.32778 0.159850 0.0799250 0.996801i \(-0.474532\pi\)
0.0799250 + 0.996801i \(0.474532\pi\)
\(734\) −29.5891 −1.09215
\(735\) 41.1053 1.51619
\(736\) −0.760254 −0.0280233
\(737\) −20.4368 −0.752800
\(738\) 0.334536 0.0123145
\(739\) 28.1923 1.03707 0.518536 0.855056i \(-0.326477\pi\)
0.518536 + 0.855056i \(0.326477\pi\)
\(740\) −32.2512 −1.18558
\(741\) −18.0441 −0.662865
\(742\) 0.514505 0.0188881
\(743\) 7.65119 0.280695 0.140348 0.990102i \(-0.455178\pi\)
0.140348 + 0.990102i \(0.455178\pi\)
\(744\) −1.18865 −0.0435782
\(745\) −52.3211 −1.91690
\(746\) −29.1942 −1.06888
\(747\) −0.971975 −0.0355627
\(748\) 6.73175 0.246137
\(749\) −1.19938 −0.0438244
\(750\) 45.9120 1.67647
\(751\) 37.7778 1.37853 0.689266 0.724508i \(-0.257933\pi\)
0.689266 + 0.724508i \(0.257933\pi\)
\(752\) −2.17474 −0.0793048
\(753\) −43.6744 −1.59158
\(754\) −12.2384 −0.445695
\(755\) −65.8156 −2.39527
\(756\) 5.47883 0.199263
\(757\) 1.13336 0.0411928 0.0205964 0.999788i \(-0.493443\pi\)
0.0205964 + 0.999788i \(0.493443\pi\)
\(758\) −8.17757 −0.297023
\(759\) 1.69706 0.0615995
\(760\) −18.2128 −0.660649
\(761\) 1.72037 0.0623634 0.0311817 0.999514i \(-0.490073\pi\)
0.0311817 + 0.999514i \(0.490073\pi\)
\(762\) 26.6209 0.964373
\(763\) 12.0064 0.434661
\(764\) 8.94259 0.323532
\(765\) 2.13440 0.0771693
\(766\) −7.06134 −0.255137
\(767\) −3.38680 −0.122290
\(768\) −1.70235 −0.0614284
\(769\) 30.1413 1.08692 0.543461 0.839435i \(-0.317114\pi\)
0.543461 + 0.839435i \(0.317114\pi\)
\(770\) 5.54566 0.199852
\(771\) 35.8820 1.29226
\(772\) −17.8248 −0.641527
\(773\) 48.2615 1.73585 0.867924 0.496698i \(-0.165454\pi\)
0.867924 + 0.496698i \(0.165454\pi\)
\(774\) 0.595126 0.0213914
\(775\) −8.11094 −0.291354
\(776\) −6.80293 −0.244211
\(777\) 13.9742 0.501321
\(778\) −4.21852 −0.151241
\(779\) 14.6549 0.525068
\(780\) −16.4623 −0.589443
\(781\) 9.36742 0.335193
\(782\) 3.90298 0.139570
\(783\) 27.2421 0.973554
\(784\) −5.92355 −0.211555
\(785\) 49.3065 1.75983
\(786\) 15.7694 0.562476
\(787\) −46.3501 −1.65220 −0.826101 0.563522i \(-0.809446\pi\)
−0.826101 + 0.563522i \(0.809446\pi\)
\(788\) 18.6669 0.664982
\(789\) −27.1663 −0.967147
\(790\) −28.4884 −1.01357
\(791\) 13.2036 0.469465
\(792\) −0.133740 −0.00475223
\(793\) −24.1467 −0.857475
\(794\) −10.9084 −0.387125
\(795\) 3.44119 0.122046
\(796\) 13.4208 0.475687
\(797\) 37.0247 1.31148 0.655741 0.754985i \(-0.272356\pi\)
0.655741 + 0.754985i \(0.272356\pi\)
\(798\) 7.89148 0.279355
\(799\) 11.1647 0.394978
\(800\) −11.6162 −0.410696
\(801\) −1.62412 −0.0573855
\(802\) −25.6705 −0.906455
\(803\) 10.9563 0.386638
\(804\) −26.5322 −0.935719
\(805\) 3.21530 0.113325
\(806\) 1.65645 0.0583461
\(807\) 12.5015 0.440075
\(808\) −10.7348 −0.377649
\(809\) −10.3362 −0.363402 −0.181701 0.983354i \(-0.558160\pi\)
−0.181701 + 0.983354i \(0.558160\pi\)
\(810\) 35.3970 1.24373
\(811\) 31.7218 1.11390 0.556951 0.830545i \(-0.311971\pi\)
0.556951 + 0.830545i \(0.311971\pi\)
\(812\) 5.35239 0.187832
\(813\) 6.06561 0.212730
\(814\) −10.3745 −0.363628
\(815\) 7.69930 0.269695
\(816\) 8.73953 0.305945
\(817\) 26.0705 0.912092
\(818\) −27.2787 −0.953779
\(819\) −0.251039 −0.00877201
\(820\) 13.3702 0.466909
\(821\) 0.280146 0.00977716 0.00488858 0.999988i \(-0.498444\pi\)
0.00488858 + 0.999988i \(0.498444\pi\)
\(822\) −0.0684424 −0.00238720
\(823\) 36.5580 1.27433 0.637167 0.770726i \(-0.280106\pi\)
0.637167 + 0.770726i \(0.280106\pi\)
\(824\) 8.94582 0.311642
\(825\) 25.9301 0.902771
\(826\) 1.48120 0.0515375
\(827\) 36.4356 1.26699 0.633495 0.773747i \(-0.281620\pi\)
0.633495 + 0.773747i \(0.281620\pi\)
\(828\) −0.0775406 −0.00269472
\(829\) 1.02705 0.0356708 0.0178354 0.999841i \(-0.494323\pi\)
0.0178354 + 0.999841i \(0.494323\pi\)
\(830\) −38.8464 −1.34838
\(831\) 11.4707 0.397913
\(832\) 2.37232 0.0822454
\(833\) 30.4103 1.05365
\(834\) −33.9634 −1.17606
\(835\) 26.7295 0.925011
\(836\) −5.85870 −0.202627
\(837\) −3.68720 −0.127448
\(838\) −11.8089 −0.407931
\(839\) 12.2991 0.424614 0.212307 0.977203i \(-0.431902\pi\)
0.212307 + 0.977203i \(0.431902\pi\)
\(840\) 7.19968 0.248413
\(841\) −2.38659 −0.0822962
\(842\) 38.9584 1.34259
\(843\) 42.3771 1.45954
\(844\) −3.72585 −0.128249
\(845\) −30.0509 −1.03378
\(846\) −0.221809 −0.00762594
\(847\) −9.62881 −0.330850
\(848\) −0.495898 −0.0170292
\(849\) −9.54342 −0.327529
\(850\) 59.6353 2.04547
\(851\) −6.01503 −0.206193
\(852\) 12.1613 0.416639
\(853\) 31.0343 1.06260 0.531298 0.847185i \(-0.321705\pi\)
0.531298 + 0.847185i \(0.321705\pi\)
\(854\) 10.5604 0.361371
\(855\) −1.85758 −0.0635280
\(856\) 1.15600 0.0395114
\(857\) 33.9058 1.15820 0.579101 0.815256i \(-0.303404\pi\)
0.579101 + 0.815256i \(0.303404\pi\)
\(858\) −5.29557 −0.180788
\(859\) 7.08003 0.241568 0.120784 0.992679i \(-0.461459\pi\)
0.120784 + 0.992679i \(0.461459\pi\)
\(860\) 23.7851 0.811065
\(861\) −5.79322 −0.197432
\(862\) −10.2463 −0.348991
\(863\) 5.77788 0.196681 0.0983406 0.995153i \(-0.468647\pi\)
0.0983406 + 0.995153i \(0.468647\pi\)
\(864\) −5.28069 −0.179653
\(865\) 39.1882 1.33244
\(866\) 4.12687 0.140237
\(867\) −15.9269 −0.540906
\(868\) −0.724441 −0.0245891
\(869\) −9.16413 −0.310872
\(870\) 35.7986 1.21369
\(871\) 36.9740 1.25282
\(872\) −11.5722 −0.391884
\(873\) −0.693852 −0.0234833
\(874\) −3.39680 −0.114898
\(875\) 27.9817 0.945954
\(876\) 14.2240 0.480585
\(877\) 49.2301 1.66238 0.831191 0.555986i \(-0.187659\pi\)
0.831191 + 0.555986i \(0.187659\pi\)
\(878\) 19.6791 0.664138
\(879\) −4.36053 −0.147077
\(880\) −5.34510 −0.180183
\(881\) 17.9217 0.603797 0.301899 0.953340i \(-0.402380\pi\)
0.301899 + 0.953340i \(0.402380\pi\)
\(882\) −0.604161 −0.0203432
\(883\) 7.95247 0.267622 0.133811 0.991007i \(-0.457278\pi\)
0.133811 + 0.991007i \(0.457278\pi\)
\(884\) −12.1790 −0.409624
\(885\) 9.90677 0.333012
\(886\) −1.80713 −0.0607116
\(887\) −33.8122 −1.13530 −0.567652 0.823269i \(-0.692148\pi\)
−0.567652 + 0.823269i \(0.692148\pi\)
\(888\) −13.4688 −0.451984
\(889\) 16.2245 0.544151
\(890\) −64.9104 −2.17580
\(891\) 11.3865 0.381462
\(892\) −3.81823 −0.127844
\(893\) −9.71672 −0.325158
\(894\) −21.8505 −0.730789
\(895\) 42.2881 1.41354
\(896\) −1.03752 −0.0346612
\(897\) −3.07030 −0.102514
\(898\) 19.7178 0.657991
\(899\) −3.60210 −0.120137
\(900\) −1.18477 −0.0394925
\(901\) 2.54584 0.0848142
\(902\) 4.30093 0.143205
\(903\) −10.3059 −0.342958
\(904\) −12.7261 −0.423263
\(905\) −23.5703 −0.783503
\(906\) −27.4860 −0.913162
\(907\) −46.1789 −1.53335 −0.766673 0.642038i \(-0.778089\pi\)
−0.766673 + 0.642038i \(0.778089\pi\)
\(908\) 15.3243 0.508554
\(909\) −1.09487 −0.0363147
\(910\) −10.0331 −0.332595
\(911\) 18.2569 0.604877 0.302438 0.953169i \(-0.402199\pi\)
0.302438 + 0.953169i \(0.402199\pi\)
\(912\) −7.60608 −0.251863
\(913\) −12.4961 −0.413560
\(914\) −24.0627 −0.795925
\(915\) 70.6319 2.33502
\(916\) 19.0411 0.629136
\(917\) 9.61087 0.317379
\(918\) 27.1100 0.894762
\(919\) −35.1701 −1.16015 −0.580077 0.814562i \(-0.696977\pi\)
−0.580077 + 0.814562i \(0.696977\pi\)
\(920\) −3.09902 −0.102172
\(921\) −11.2817 −0.371743
\(922\) 9.06197 0.298440
\(923\) −16.9474 −0.557831
\(924\) 2.31599 0.0761905
\(925\) −91.9062 −3.02186
\(926\) 27.5234 0.904475
\(927\) 0.912411 0.0299675
\(928\) −5.15882 −0.169347
\(929\) 11.4417 0.375389 0.187695 0.982227i \(-0.439898\pi\)
0.187695 + 0.982227i \(0.439898\pi\)
\(930\) −4.84531 −0.158884
\(931\) −26.4663 −0.867398
\(932\) −12.6530 −0.414464
\(933\) −24.6368 −0.806572
\(934\) −3.53732 −0.115745
\(935\) 27.4406 0.897405
\(936\) 0.241960 0.00790871
\(937\) 29.1310 0.951669 0.475835 0.879535i \(-0.342146\pi\)
0.475835 + 0.879535i \(0.342146\pi\)
\(938\) −16.1704 −0.527982
\(939\) 52.6019 1.71660
\(940\) −8.86491 −0.289142
\(941\) −9.40037 −0.306443 −0.153222 0.988192i \(-0.548965\pi\)
−0.153222 + 0.988192i \(0.548965\pi\)
\(942\) 20.5915 0.670907
\(943\) 2.49363 0.0812036
\(944\) −1.42763 −0.0464655
\(945\) 22.3334 0.726504
\(946\) 7.65118 0.248761
\(947\) 55.4521 1.80195 0.900976 0.433870i \(-0.142852\pi\)
0.900976 + 0.433870i \(0.142852\pi\)
\(948\) −11.8974 −0.386409
\(949\) −19.8219 −0.643447
\(950\) −51.9011 −1.68389
\(951\) 19.5550 0.634113
\(952\) 5.32642 0.172630
\(953\) 35.5889 1.15284 0.576419 0.817154i \(-0.304449\pi\)
0.576419 + 0.817154i \(0.304449\pi\)
\(954\) −0.0505782 −0.00163753
\(955\) 36.4527 1.17958
\(956\) −3.96287 −0.128169
\(957\) 11.5157 0.372249
\(958\) 1.80306 0.0582542
\(959\) −0.0417131 −0.00134699
\(960\) −6.93930 −0.223965
\(961\) −30.5125 −0.984273
\(962\) 18.7695 0.605153
\(963\) 0.117904 0.00379942
\(964\) −20.3938 −0.656841
\(965\) −72.6591 −2.33898
\(966\) 1.34278 0.0432033
\(967\) 42.8153 1.37685 0.688424 0.725308i \(-0.258303\pi\)
0.688424 + 0.725308i \(0.258303\pi\)
\(968\) 9.28059 0.298289
\(969\) 39.0481 1.25440
\(970\) −27.7308 −0.890382
\(971\) 2.86244 0.0918601 0.0459300 0.998945i \(-0.485375\pi\)
0.0459300 + 0.998945i \(0.485375\pi\)
\(972\) −1.05948 −0.0339828
\(973\) −20.6995 −0.663594
\(974\) −13.8396 −0.443448
\(975\) −46.9125 −1.50240
\(976\) −10.1785 −0.325807
\(977\) −10.5258 −0.336750 −0.168375 0.985723i \(-0.553852\pi\)
−0.168375 + 0.985723i \(0.553852\pi\)
\(978\) 3.21540 0.102817
\(979\) −20.8804 −0.667339
\(980\) −24.1462 −0.771321
\(981\) −1.18028 −0.0376836
\(982\) −40.3124 −1.28642
\(983\) −9.29329 −0.296410 −0.148205 0.988957i \(-0.547350\pi\)
−0.148205 + 0.988957i \(0.547350\pi\)
\(984\) 5.58371 0.178002
\(985\) 76.0921 2.42450
\(986\) 26.4843 0.843432
\(987\) 3.84110 0.122263
\(988\) 10.5995 0.337214
\(989\) 4.43606 0.141058
\(990\) −0.545163 −0.0173264
\(991\) 9.97620 0.316904 0.158452 0.987367i \(-0.449350\pi\)
0.158452 + 0.987367i \(0.449350\pi\)
\(992\) 0.698242 0.0221692
\(993\) −15.7278 −0.499107
\(994\) 7.41186 0.235090
\(995\) 54.7072 1.73433
\(996\) −16.2231 −0.514049
\(997\) 52.2680 1.65535 0.827673 0.561211i \(-0.189664\pi\)
0.827673 + 0.561211i \(0.189664\pi\)
\(998\) −32.4731 −1.02792
\(999\) −41.7801 −1.32187
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 \(a_p\))