Properties

Label 6013.2.a.e.1.3
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +O(q^{10})\) \(q-2.65451 q^{2} -2.36774 q^{3} +5.04644 q^{4} -0.160322 q^{5} +6.28521 q^{6} +1.00000 q^{7} -8.08683 q^{8} +2.60621 q^{9} +0.425577 q^{10} -0.871782 q^{11} -11.9487 q^{12} +0.818140 q^{13} -2.65451 q^{14} +0.379601 q^{15} +11.3737 q^{16} +4.11170 q^{17} -6.91823 q^{18} -0.545295 q^{19} -0.809056 q^{20} -2.36774 q^{21} +2.31416 q^{22} +8.22459 q^{23} +19.1475 q^{24} -4.97430 q^{25} -2.17176 q^{26} +0.932389 q^{27} +5.04644 q^{28} +5.19127 q^{29} -1.00766 q^{30} -1.28470 q^{31} -14.0180 q^{32} +2.06416 q^{33} -10.9146 q^{34} -0.160322 q^{35} +13.1521 q^{36} -2.04257 q^{37} +1.44749 q^{38} -1.93715 q^{39} +1.29650 q^{40} +7.99035 q^{41} +6.28521 q^{42} -1.08034 q^{43} -4.39940 q^{44} -0.417833 q^{45} -21.8323 q^{46} +1.54043 q^{47} -26.9300 q^{48} +1.00000 q^{49} +13.2043 q^{50} -9.73545 q^{51} +4.12870 q^{52} -0.678971 q^{53} -2.47504 q^{54} +0.139766 q^{55} -8.08683 q^{56} +1.29112 q^{57} -13.7803 q^{58} -3.03261 q^{59} +1.91564 q^{60} +4.28301 q^{61} +3.41026 q^{62} +2.60621 q^{63} +14.4636 q^{64} -0.131166 q^{65} -5.47933 q^{66} +13.0086 q^{67} +20.7495 q^{68} -19.4737 q^{69} +0.425577 q^{70} +0.359103 q^{71} -21.0760 q^{72} +8.05664 q^{73} +5.42204 q^{74} +11.7779 q^{75} -2.75180 q^{76} -0.871782 q^{77} +5.14218 q^{78} -6.47312 q^{79} -1.82346 q^{80} -10.0263 q^{81} -21.2105 q^{82} +1.74046 q^{83} -11.9487 q^{84} -0.659196 q^{85} +2.86779 q^{86} -12.2916 q^{87} +7.04995 q^{88} +4.18555 q^{89} +1.10914 q^{90} +0.818140 q^{91} +41.5049 q^{92} +3.04185 q^{93} -4.08910 q^{94} +0.0874228 q^{95} +33.1911 q^{96} -14.0397 q^{97} -2.65451 q^{98} -2.27205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 109q + 19q^{2} + 38q^{3} + 111q^{4} + 43q^{5} + 14q^{6} + 109q^{7} + 48q^{8} + 119q^{9} + O(q^{10}) \) \( 109q + 19q^{2} + 38q^{3} + 111q^{4} + 43q^{5} + 14q^{6} + 109q^{7} + 48q^{8} + 119q^{9} + 15q^{10} + 48q^{11} + 72q^{12} + 29q^{13} + 19q^{14} + 29q^{15} + 115q^{16} + 72q^{17} + 33q^{18} + 58q^{19} + 88q^{20} + 38q^{21} + 4q^{22} + 65q^{23} + 46q^{24} + 124q^{25} + 49q^{26} + 131q^{27} + 111q^{28} + 25q^{29} + 2q^{30} + 41q^{31} + 75q^{32} + 54q^{33} + 23q^{34} + 43q^{35} + 111q^{36} + 25q^{37} + 54q^{38} + 27q^{39} + 30q^{40} + 109q^{41} + 14q^{42} + 38q^{43} + 68q^{44} + 84q^{45} - 9q^{46} + 121q^{47} + 106q^{48} + 109q^{49} + 14q^{50} + 36q^{51} + 38q^{52} + 61q^{53} + 31q^{54} + 50q^{55} + 48q^{56} + 5q^{57} - 20q^{58} + 181q^{59} + 25q^{60} + 34q^{61} + 75q^{62} + 119q^{63} + 96q^{64} + 12q^{65} + 19q^{66} + 87q^{67} + 150q^{68} + 89q^{69} + 15q^{70} + 83q^{71} + 65q^{72} + 32q^{73} - 19q^{74} + 112q^{75} + 84q^{76} + 48q^{77} - 34q^{78} - 9q^{79} + 137q^{80} + 109q^{81} - 19q^{82} + 136q^{83} + 72q^{84} - 32q^{85} - 24q^{86} + 28q^{87} - 24q^{88} + 142q^{89} + 19q^{90} + 29q^{91} + 96q^{92} + 29q^{93} + 9q^{94} + 52q^{95} + 88q^{96} + 75q^{97} + 19q^{98} + 84q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65451 −1.87702 −0.938512 0.345246i \(-0.887796\pi\)
−0.938512 + 0.345246i \(0.887796\pi\)
\(3\) −2.36774 −1.36702 −0.683509 0.729942i \(-0.739547\pi\)
−0.683509 + 0.729942i \(0.739547\pi\)
\(4\) 5.04644 2.52322
\(5\) −0.160322 −0.0716982 −0.0358491 0.999357i \(-0.511414\pi\)
−0.0358491 + 0.999357i \(0.511414\pi\)
\(6\) 6.28521 2.56593
\(7\) 1.00000 0.377964
\(8\) −8.08683 −2.85913
\(9\) 2.60621 0.868737
\(10\) 0.425577 0.134579
\(11\) −0.871782 −0.262852 −0.131426 0.991326i \(-0.541956\pi\)
−0.131426 + 0.991326i \(0.541956\pi\)
\(12\) −11.9487 −3.44929
\(13\) 0.818140 0.226911 0.113456 0.993543i \(-0.463808\pi\)
0.113456 + 0.993543i \(0.463808\pi\)
\(14\) −2.65451 −0.709449
\(15\) 0.379601 0.0980127
\(16\) 11.3737 2.84343
\(17\) 4.11170 0.997234 0.498617 0.866823i \(-0.333841\pi\)
0.498617 + 0.866823i \(0.333841\pi\)
\(18\) −6.91823 −1.63064
\(19\) −0.545295 −0.125099 −0.0625497 0.998042i \(-0.519923\pi\)
−0.0625497 + 0.998042i \(0.519923\pi\)
\(20\) −0.809056 −0.180910
\(21\) −2.36774 −0.516684
\(22\) 2.31416 0.493380
\(23\) 8.22459 1.71495 0.857473 0.514529i \(-0.172033\pi\)
0.857473 + 0.514529i \(0.172033\pi\)
\(24\) 19.1475 3.90847
\(25\) −4.97430 −0.994859
\(26\) −2.17176 −0.425918
\(27\) 0.932389 0.179438
\(28\) 5.04644 0.953688
\(29\) 5.19127 0.963994 0.481997 0.876173i \(-0.339912\pi\)
0.481997 + 0.876173i \(0.339912\pi\)
\(30\) −1.00766 −0.183972
\(31\) −1.28470 −0.230739 −0.115370 0.993323i \(-0.536805\pi\)
−0.115370 + 0.993323i \(0.536805\pi\)
\(32\) −14.0180 −2.47806
\(33\) 2.06416 0.359323
\(34\) −10.9146 −1.87183
\(35\) −0.160322 −0.0270994
\(36\) 13.1521 2.19202
\(37\) −2.04257 −0.335797 −0.167898 0.985804i \(-0.553698\pi\)
−0.167898 + 0.985804i \(0.553698\pi\)
\(38\) 1.44749 0.234814
\(39\) −1.93715 −0.310192
\(40\) 1.29650 0.204994
\(41\) 7.99035 1.24788 0.623942 0.781471i \(-0.285530\pi\)
0.623942 + 0.781471i \(0.285530\pi\)
\(42\) 6.28521 0.969829
\(43\) −1.08034 −0.164751 −0.0823755 0.996601i \(-0.526251\pi\)
−0.0823755 + 0.996601i \(0.526251\pi\)
\(44\) −4.39940 −0.663234
\(45\) −0.417833 −0.0622869
\(46\) −21.8323 −3.21900
\(47\) 1.54043 0.224695 0.112348 0.993669i \(-0.464163\pi\)
0.112348 + 0.993669i \(0.464163\pi\)
\(48\) −26.9300 −3.88701
\(49\) 1.00000 0.142857
\(50\) 13.2043 1.86738
\(51\) −9.73545 −1.36324
\(52\) 4.12870 0.572548
\(53\) −0.678971 −0.0932638 −0.0466319 0.998912i \(-0.514849\pi\)
−0.0466319 + 0.998912i \(0.514849\pi\)
\(54\) −2.47504 −0.336810
\(55\) 0.139766 0.0188460
\(56\) −8.08683 −1.08065
\(57\) 1.29112 0.171013
\(58\) −13.7803 −1.80944
\(59\) −3.03261 −0.394812 −0.197406 0.980322i \(-0.563252\pi\)
−0.197406 + 0.980322i \(0.563252\pi\)
\(60\) 1.91564 0.247308
\(61\) 4.28301 0.548383 0.274191 0.961675i \(-0.411590\pi\)
0.274191 + 0.961675i \(0.411590\pi\)
\(62\) 3.41026 0.433104
\(63\) 2.60621 0.328352
\(64\) 14.4636 1.80795
\(65\) −0.131166 −0.0162691
\(66\) −5.47933 −0.674459
\(67\) 13.0086 1.58925 0.794625 0.607100i \(-0.207667\pi\)
0.794625 + 0.607100i \(0.207667\pi\)
\(68\) 20.7495 2.51624
\(69\) −19.4737 −2.34436
\(70\) 0.425577 0.0508662
\(71\) 0.359103 0.0426177 0.0213088 0.999773i \(-0.493217\pi\)
0.0213088 + 0.999773i \(0.493217\pi\)
\(72\) −21.0760 −2.48383
\(73\) 8.05664 0.942959 0.471479 0.881877i \(-0.343720\pi\)
0.471479 + 0.881877i \(0.343720\pi\)
\(74\) 5.42204 0.630299
\(75\) 11.7779 1.35999
\(76\) −2.75180 −0.315653
\(77\) −0.871782 −0.0993487
\(78\) 5.14218 0.582238
\(79\) −6.47312 −0.728283 −0.364141 0.931344i \(-0.618638\pi\)
−0.364141 + 0.931344i \(0.618638\pi\)
\(80\) −1.82346 −0.203869
\(81\) −10.0263 −1.11403
\(82\) −21.2105 −2.34231
\(83\) 1.74046 0.191040 0.0955201 0.995427i \(-0.469549\pi\)
0.0955201 + 0.995427i \(0.469549\pi\)
\(84\) −11.9487 −1.30371
\(85\) −0.659196 −0.0714998
\(86\) 2.86779 0.309242
\(87\) −12.2916 −1.31780
\(88\) 7.04995 0.751527
\(89\) 4.18555 0.443668 0.221834 0.975084i \(-0.428796\pi\)
0.221834 + 0.975084i \(0.428796\pi\)
\(90\) 1.10914 0.116914
\(91\) 0.818140 0.0857644
\(92\) 41.5049 4.32719
\(93\) 3.04185 0.315425
\(94\) −4.08910 −0.421759
\(95\) 0.0874228 0.00896939
\(96\) 33.1911 3.38755
\(97\) −14.0397 −1.42551 −0.712755 0.701413i \(-0.752553\pi\)
−0.712755 + 0.701413i \(0.752553\pi\)
\(98\) −2.65451 −0.268146
\(99\) −2.27205 −0.228349
\(100\) −25.1025 −2.51025
\(101\) −9.56933 −0.952184 −0.476092 0.879395i \(-0.657947\pi\)
−0.476092 + 0.879395i \(0.657947\pi\)
\(102\) 25.8429 2.55883
\(103\) 14.4000 1.41888 0.709439 0.704767i \(-0.248948\pi\)
0.709439 + 0.704767i \(0.248948\pi\)
\(104\) −6.61616 −0.648768
\(105\) 0.379601 0.0370453
\(106\) 1.80234 0.175058
\(107\) 12.6857 1.22637 0.613184 0.789940i \(-0.289888\pi\)
0.613184 + 0.789940i \(0.289888\pi\)
\(108\) 4.70525 0.452763
\(109\) 18.5314 1.77498 0.887491 0.460825i \(-0.152446\pi\)
0.887491 + 0.460825i \(0.152446\pi\)
\(110\) −0.371010 −0.0353744
\(111\) 4.83629 0.459040
\(112\) 11.3737 1.07471
\(113\) 4.78955 0.450563 0.225282 0.974294i \(-0.427670\pi\)
0.225282 + 0.974294i \(0.427670\pi\)
\(114\) −3.42729 −0.320996
\(115\) −1.31858 −0.122958
\(116\) 26.1974 2.43237
\(117\) 2.13225 0.197126
\(118\) 8.05011 0.741073
\(119\) 4.11170 0.376919
\(120\) −3.06977 −0.280230
\(121\) −10.2400 −0.930909
\(122\) −11.3693 −1.02933
\(123\) −18.9191 −1.70588
\(124\) −6.48318 −0.582207
\(125\) 1.59910 0.143028
\(126\) −6.91823 −0.616325
\(127\) 15.4385 1.36995 0.684974 0.728567i \(-0.259814\pi\)
0.684974 + 0.728567i \(0.259814\pi\)
\(128\) −10.3578 −0.915506
\(129\) 2.55798 0.225217
\(130\) 0.348182 0.0305375
\(131\) 21.7764 1.90261 0.951305 0.308250i \(-0.0997434\pi\)
0.951305 + 0.308250i \(0.0997434\pi\)
\(132\) 10.4166 0.906653
\(133\) −0.545295 −0.0472831
\(134\) −34.5315 −2.98306
\(135\) −0.149482 −0.0128654
\(136\) −33.2506 −2.85122
\(137\) −0.154988 −0.0132415 −0.00662075 0.999978i \(-0.502107\pi\)
−0.00662075 + 0.999978i \(0.502107\pi\)
\(138\) 51.6933 4.40042
\(139\) −17.9616 −1.52348 −0.761740 0.647883i \(-0.775655\pi\)
−0.761740 + 0.647883i \(0.775655\pi\)
\(140\) −0.809056 −0.0683777
\(141\) −3.64735 −0.307163
\(142\) −0.953244 −0.0799945
\(143\) −0.713240 −0.0596441
\(144\) 29.6423 2.47019
\(145\) −0.832274 −0.0691166
\(146\) −21.3865 −1.76996
\(147\) −2.36774 −0.195288
\(148\) −10.3077 −0.847290
\(149\) 16.2665 1.33261 0.666303 0.745681i \(-0.267876\pi\)
0.666303 + 0.745681i \(0.267876\pi\)
\(150\) −31.2645 −2.55274
\(151\) −7.39737 −0.601990 −0.300995 0.953626i \(-0.597319\pi\)
−0.300995 + 0.953626i \(0.597319\pi\)
\(152\) 4.40971 0.357675
\(153\) 10.7160 0.866334
\(154\) 2.31416 0.186480
\(155\) 0.205966 0.0165436
\(156\) −9.77570 −0.782683
\(157\) −2.67073 −0.213147 −0.106574 0.994305i \(-0.533988\pi\)
−0.106574 + 0.994305i \(0.533988\pi\)
\(158\) 17.1830 1.36701
\(159\) 1.60763 0.127493
\(160\) 2.24740 0.177672
\(161\) 8.22459 0.648189
\(162\) 26.6149 2.09107
\(163\) 3.34208 0.261772 0.130886 0.991397i \(-0.458218\pi\)
0.130886 + 0.991397i \(0.458218\pi\)
\(164\) 40.3229 3.14869
\(165\) −0.330930 −0.0257628
\(166\) −4.62007 −0.358587
\(167\) −4.08377 −0.316011 −0.158006 0.987438i \(-0.550506\pi\)
−0.158006 + 0.987438i \(0.550506\pi\)
\(168\) 19.1475 1.47726
\(169\) −12.3306 −0.948511
\(170\) 1.74984 0.134207
\(171\) −1.42116 −0.108678
\(172\) −5.45190 −0.415703
\(173\) 1.93253 0.146928 0.0734639 0.997298i \(-0.476595\pi\)
0.0734639 + 0.997298i \(0.476595\pi\)
\(174\) 32.6282 2.47354
\(175\) −4.97430 −0.376021
\(176\) −9.91539 −0.747401
\(177\) 7.18045 0.539716
\(178\) −11.1106 −0.832775
\(179\) −10.8453 −0.810613 −0.405306 0.914181i \(-0.632835\pi\)
−0.405306 + 0.914181i \(0.632835\pi\)
\(180\) −2.10857 −0.157164
\(181\) −12.7640 −0.948743 −0.474372 0.880325i \(-0.657325\pi\)
−0.474372 + 0.880325i \(0.657325\pi\)
\(182\) −2.17176 −0.160982
\(183\) −10.1411 −0.749649
\(184\) −66.5108 −4.90324
\(185\) 0.327469 0.0240760
\(186\) −8.07463 −0.592060
\(187\) −3.58450 −0.262125
\(188\) 7.77371 0.566956
\(189\) 0.932389 0.0678213
\(190\) −0.232065 −0.0168358
\(191\) 3.49998 0.253250 0.126625 0.991951i \(-0.459586\pi\)
0.126625 + 0.991951i \(0.459586\pi\)
\(192\) −34.2461 −2.47150
\(193\) −16.8862 −1.21550 −0.607748 0.794130i \(-0.707927\pi\)
−0.607748 + 0.794130i \(0.707927\pi\)
\(194\) 37.2684 2.67572
\(195\) 0.310567 0.0222402
\(196\) 5.04644 0.360460
\(197\) −3.12436 −0.222601 −0.111301 0.993787i \(-0.535502\pi\)
−0.111301 + 0.993787i \(0.535502\pi\)
\(198\) 6.03118 0.428618
\(199\) −13.4626 −0.954340 −0.477170 0.878811i \(-0.658337\pi\)
−0.477170 + 0.878811i \(0.658337\pi\)
\(200\) 40.2263 2.84443
\(201\) −30.8010 −2.17253
\(202\) 25.4019 1.78727
\(203\) 5.19127 0.364355
\(204\) −49.1294 −3.43975
\(205\) −1.28103 −0.0894710
\(206\) −38.2251 −2.66327
\(207\) 21.4350 1.48984
\(208\) 9.30529 0.645206
\(209\) 0.475378 0.0328826
\(210\) −1.00766 −0.0695350
\(211\) 17.9534 1.23596 0.617980 0.786194i \(-0.287951\pi\)
0.617980 + 0.786194i \(0.287951\pi\)
\(212\) −3.42639 −0.235325
\(213\) −0.850264 −0.0582591
\(214\) −33.6742 −2.30192
\(215\) 0.173203 0.0118123
\(216\) −7.54007 −0.513037
\(217\) −1.28470 −0.0872113
\(218\) −49.1917 −3.33169
\(219\) −19.0761 −1.28904
\(220\) 0.705320 0.0475527
\(221\) 3.36395 0.226284
\(222\) −12.8380 −0.861630
\(223\) −3.55002 −0.237727 −0.118864 0.992911i \(-0.537925\pi\)
−0.118864 + 0.992911i \(0.537925\pi\)
\(224\) −14.0180 −0.936618
\(225\) −12.9641 −0.864272
\(226\) −12.7139 −0.845719
\(227\) 3.51755 0.233468 0.116734 0.993163i \(-0.462758\pi\)
0.116734 + 0.993163i \(0.462758\pi\)
\(228\) 6.51556 0.431504
\(229\) −12.4487 −0.822631 −0.411316 0.911493i \(-0.634931\pi\)
−0.411316 + 0.911493i \(0.634931\pi\)
\(230\) 3.50020 0.230796
\(231\) 2.06416 0.135811
\(232\) −41.9809 −2.75618
\(233\) −8.88291 −0.581938 −0.290969 0.956732i \(-0.593978\pi\)
−0.290969 + 0.956732i \(0.593978\pi\)
\(234\) −5.66008 −0.370011
\(235\) −0.246965 −0.0161102
\(236\) −15.3039 −0.996199
\(237\) 15.3267 0.995576
\(238\) −10.9146 −0.707486
\(239\) −19.4018 −1.25500 −0.627498 0.778618i \(-0.715921\pi\)
−0.627498 + 0.778618i \(0.715921\pi\)
\(240\) 4.31748 0.278692
\(241\) −18.0921 −1.16542 −0.582708 0.812682i \(-0.698007\pi\)
−0.582708 + 0.812682i \(0.698007\pi\)
\(242\) 27.1822 1.74734
\(243\) 20.9425 1.34346
\(244\) 21.6140 1.38369
\(245\) −0.160322 −0.0102426
\(246\) 50.2211 3.20198
\(247\) −0.446128 −0.0283864
\(248\) 10.3892 0.659713
\(249\) −4.12096 −0.261155
\(250\) −4.24483 −0.268467
\(251\) 3.95043 0.249349 0.124674 0.992198i \(-0.460211\pi\)
0.124674 + 0.992198i \(0.460211\pi\)
\(252\) 13.1521 0.828505
\(253\) −7.17005 −0.450777
\(254\) −40.9818 −2.57143
\(255\) 1.56081 0.0977415
\(256\) −1.43233 −0.0895204
\(257\) 2.91380 0.181758 0.0908788 0.995862i \(-0.471032\pi\)
0.0908788 + 0.995862i \(0.471032\pi\)
\(258\) −6.79019 −0.422739
\(259\) −2.04257 −0.126919
\(260\) −0.661921 −0.0410506
\(261\) 13.5295 0.837458
\(262\) −57.8057 −3.57125
\(263\) −11.3419 −0.699373 −0.349686 0.936867i \(-0.613712\pi\)
−0.349686 + 0.936867i \(0.613712\pi\)
\(264\) −16.6925 −1.02735
\(265\) 0.108854 0.00668684
\(266\) 1.44749 0.0887515
\(267\) −9.91032 −0.606501
\(268\) 65.6471 4.01003
\(269\) 2.54216 0.154998 0.0774992 0.996992i \(-0.475306\pi\)
0.0774992 + 0.996992i \(0.475306\pi\)
\(270\) 0.396803 0.0241487
\(271\) −3.70597 −0.225122 −0.112561 0.993645i \(-0.535905\pi\)
−0.112561 + 0.993645i \(0.535905\pi\)
\(272\) 46.7653 2.83556
\(273\) −1.93715 −0.117241
\(274\) 0.411417 0.0248546
\(275\) 4.33650 0.261501
\(276\) −98.2731 −5.91534
\(277\) −16.1960 −0.973124 −0.486562 0.873646i \(-0.661749\pi\)
−0.486562 + 0.873646i \(0.661749\pi\)
\(278\) 47.6792 2.85961
\(279\) −3.34821 −0.200452
\(280\) 1.29650 0.0774805
\(281\) −13.5976 −0.811165 −0.405583 0.914058i \(-0.632931\pi\)
−0.405583 + 0.914058i \(0.632931\pi\)
\(282\) 9.68195 0.576552
\(283\) −9.17040 −0.545123 −0.272562 0.962138i \(-0.587871\pi\)
−0.272562 + 0.962138i \(0.587871\pi\)
\(284\) 1.81219 0.107534
\(285\) −0.206995 −0.0122613
\(286\) 1.89330 0.111953
\(287\) 7.99035 0.471656
\(288\) −36.5339 −2.15278
\(289\) −0.0939266 −0.00552510
\(290\) 2.20928 0.129734
\(291\) 33.2423 1.94870
\(292\) 40.6574 2.37929
\(293\) 29.0939 1.69969 0.849843 0.527036i \(-0.176697\pi\)
0.849843 + 0.527036i \(0.176697\pi\)
\(294\) 6.28521 0.366561
\(295\) 0.486194 0.0283073
\(296\) 16.5179 0.960085
\(297\) −0.812839 −0.0471657
\(298\) −43.1797 −2.50133
\(299\) 6.72887 0.389141
\(300\) 59.4363 3.43156
\(301\) −1.08034 −0.0622700
\(302\) 19.6364 1.12995
\(303\) 22.6577 1.30165
\(304\) −6.20203 −0.355711
\(305\) −0.686660 −0.0393181
\(306\) −28.4457 −1.62613
\(307\) 31.5622 1.80135 0.900675 0.434494i \(-0.143073\pi\)
0.900675 + 0.434494i \(0.143073\pi\)
\(308\) −4.39940 −0.250679
\(309\) −34.0956 −1.93963
\(310\) −0.546740 −0.0310527
\(311\) −1.77430 −0.100611 −0.0503056 0.998734i \(-0.516020\pi\)
−0.0503056 + 0.998734i \(0.516020\pi\)
\(312\) 15.6654 0.886877
\(313\) −5.14132 −0.290604 −0.145302 0.989387i \(-0.546415\pi\)
−0.145302 + 0.989387i \(0.546415\pi\)
\(314\) 7.08948 0.400082
\(315\) −0.417833 −0.0235422
\(316\) −32.6662 −1.83762
\(317\) 18.0776 1.01534 0.507670 0.861552i \(-0.330507\pi\)
0.507670 + 0.861552i \(0.330507\pi\)
\(318\) −4.26747 −0.239308
\(319\) −4.52565 −0.253388
\(320\) −2.31883 −0.129627
\(321\) −30.0364 −1.67647
\(322\) −21.8323 −1.21667
\(323\) −2.24209 −0.124753
\(324\) −50.5971 −2.81095
\(325\) −4.06967 −0.225745
\(326\) −8.87159 −0.491352
\(327\) −43.8775 −2.42643
\(328\) −64.6166 −3.56786
\(329\) 1.54043 0.0849269
\(330\) 0.878457 0.0483575
\(331\) −17.3737 −0.954943 −0.477472 0.878647i \(-0.658447\pi\)
−0.477472 + 0.878647i \(0.658447\pi\)
\(332\) 8.78313 0.482037
\(333\) −5.32338 −0.291719
\(334\) 10.8404 0.593161
\(335\) −2.08556 −0.113946
\(336\) −26.9300 −1.46915
\(337\) −1.95690 −0.106599 −0.0532995 0.998579i \(-0.516974\pi\)
−0.0532995 + 0.998579i \(0.516974\pi\)
\(338\) 32.7319 1.78038
\(339\) −11.3404 −0.615928
\(340\) −3.32659 −0.180410
\(341\) 1.11998 0.0606504
\(342\) 3.77248 0.203992
\(343\) 1.00000 0.0539949
\(344\) 8.73656 0.471043
\(345\) 3.12207 0.168086
\(346\) −5.12994 −0.275787
\(347\) −16.0927 −0.863904 −0.431952 0.901897i \(-0.642175\pi\)
−0.431952 + 0.901897i \(0.642175\pi\)
\(348\) −62.0288 −3.32509
\(349\) 5.96157 0.319116 0.159558 0.987189i \(-0.448993\pi\)
0.159558 + 0.987189i \(0.448993\pi\)
\(350\) 13.2043 0.705802
\(351\) 0.762825 0.0407166
\(352\) 12.2206 0.651363
\(353\) 13.0092 0.692411 0.346206 0.938159i \(-0.387470\pi\)
0.346206 + 0.938159i \(0.387470\pi\)
\(354\) −19.0606 −1.01306
\(355\) −0.0575721 −0.00305561
\(356\) 21.1222 1.11947
\(357\) −9.73545 −0.515255
\(358\) 28.7889 1.52154
\(359\) −6.18525 −0.326445 −0.163222 0.986589i \(-0.552189\pi\)
−0.163222 + 0.986589i \(0.552189\pi\)
\(360\) 3.37894 0.178086
\(361\) −18.7027 −0.984350
\(362\) 33.8823 1.78081
\(363\) 24.2457 1.27257
\(364\) 4.12870 0.216403
\(365\) −1.29166 −0.0676084
\(366\) 26.9196 1.40711
\(367\) −30.2767 −1.58043 −0.790215 0.612830i \(-0.790031\pi\)
−0.790215 + 0.612830i \(0.790031\pi\)
\(368\) 93.5441 4.87632
\(369\) 20.8246 1.08408
\(370\) −0.869272 −0.0451913
\(371\) −0.678971 −0.0352504
\(372\) 15.3505 0.795887
\(373\) −6.60106 −0.341790 −0.170895 0.985289i \(-0.554666\pi\)
−0.170895 + 0.985289i \(0.554666\pi\)
\(374\) 9.51512 0.492015
\(375\) −3.78626 −0.195521
\(376\) −12.4572 −0.642432
\(377\) 4.24718 0.218741
\(378\) −2.47504 −0.127302
\(379\) 29.7626 1.52880 0.764401 0.644741i \(-0.223035\pi\)
0.764401 + 0.644741i \(0.223035\pi\)
\(380\) 0.441174 0.0226318
\(381\) −36.5545 −1.87274
\(382\) −9.29074 −0.475356
\(383\) −8.62935 −0.440939 −0.220470 0.975394i \(-0.570759\pi\)
−0.220470 + 0.975394i \(0.570759\pi\)
\(384\) 24.5246 1.25151
\(385\) 0.139766 0.00712312
\(386\) 44.8247 2.28152
\(387\) −2.81561 −0.143125
\(388\) −70.8503 −3.59688
\(389\) −36.6144 −1.85643 −0.928213 0.372050i \(-0.878655\pi\)
−0.928213 + 0.372050i \(0.878655\pi\)
\(390\) −0.824405 −0.0417454
\(391\) 33.8170 1.71020
\(392\) −8.08683 −0.408446
\(393\) −51.5609 −2.60090
\(394\) 8.29366 0.417828
\(395\) 1.03778 0.0522166
\(396\) −11.4658 −0.576176
\(397\) 15.3182 0.768798 0.384399 0.923167i \(-0.374409\pi\)
0.384399 + 0.923167i \(0.374409\pi\)
\(398\) 35.7367 1.79132
\(399\) 1.29112 0.0646368
\(400\) −56.5762 −2.82881
\(401\) 0.244011 0.0121853 0.00609266 0.999981i \(-0.498061\pi\)
0.00609266 + 0.999981i \(0.498061\pi\)
\(402\) 81.7616 4.07790
\(403\) −1.05107 −0.0523574
\(404\) −48.2911 −2.40257
\(405\) 1.60744 0.0798741
\(406\) −13.7803 −0.683904
\(407\) 1.78068 0.0882649
\(408\) 78.7289 3.89766
\(409\) 17.4133 0.861031 0.430516 0.902583i \(-0.358332\pi\)
0.430516 + 0.902583i \(0.358332\pi\)
\(410\) 3.40051 0.167939
\(411\) 0.366971 0.0181014
\(412\) 72.6690 3.58015
\(413\) −3.03261 −0.149225
\(414\) −56.8996 −2.79646
\(415\) −0.279034 −0.0136972
\(416\) −11.4687 −0.562299
\(417\) 42.5284 2.08262
\(418\) −1.26190 −0.0617215
\(419\) 24.3426 1.18921 0.594606 0.804017i \(-0.297308\pi\)
0.594606 + 0.804017i \(0.297308\pi\)
\(420\) 1.91564 0.0934735
\(421\) 12.2674 0.597878 0.298939 0.954272i \(-0.403367\pi\)
0.298939 + 0.954272i \(0.403367\pi\)
\(422\) −47.6574 −2.31993
\(423\) 4.01470 0.195201
\(424\) 5.49072 0.266653
\(425\) −20.4528 −0.992107
\(426\) 2.25704 0.109354
\(427\) 4.28301 0.207269
\(428\) 64.0174 3.09440
\(429\) 1.68877 0.0815345
\(430\) −0.459769 −0.0221721
\(431\) 11.3563 0.547014 0.273507 0.961870i \(-0.411816\pi\)
0.273507 + 0.961870i \(0.411816\pi\)
\(432\) 10.6047 0.510220
\(433\) 26.0576 1.25225 0.626124 0.779724i \(-0.284641\pi\)
0.626124 + 0.779724i \(0.284641\pi\)
\(434\) 3.41026 0.163698
\(435\) 1.97061 0.0944836
\(436\) 93.5175 4.47867
\(437\) −4.48483 −0.214539
\(438\) 50.6377 2.41956
\(439\) −5.70087 −0.272088 −0.136044 0.990703i \(-0.543439\pi\)
−0.136044 + 0.990703i \(0.543439\pi\)
\(440\) −1.13026 −0.0538831
\(441\) 2.60621 0.124105
\(442\) −8.92964 −0.424740
\(443\) −16.8267 −0.799460 −0.399730 0.916633i \(-0.630896\pi\)
−0.399730 + 0.916633i \(0.630896\pi\)
\(444\) 24.4061 1.15826
\(445\) −0.671036 −0.0318102
\(446\) 9.42358 0.446220
\(447\) −38.5150 −1.82170
\(448\) 14.4636 0.683340
\(449\) −9.93629 −0.468922 −0.234461 0.972125i \(-0.575333\pi\)
−0.234461 + 0.972125i \(0.575333\pi\)
\(450\) 34.4133 1.62226
\(451\) −6.96584 −0.328009
\(452\) 24.1702 1.13687
\(453\) 17.5151 0.822931
\(454\) −9.33738 −0.438225
\(455\) −0.131166 −0.00614915
\(456\) −10.4411 −0.488947
\(457\) −7.80932 −0.365305 −0.182652 0.983178i \(-0.558468\pi\)
−0.182652 + 0.983178i \(0.558468\pi\)
\(458\) 33.0452 1.54410
\(459\) 3.83370 0.178942
\(460\) −6.65415 −0.310252
\(461\) 20.2544 0.943342 0.471671 0.881775i \(-0.343651\pi\)
0.471671 + 0.881775i \(0.343651\pi\)
\(462\) −5.47933 −0.254922
\(463\) 7.66482 0.356214 0.178107 0.984011i \(-0.443003\pi\)
0.178107 + 0.984011i \(0.443003\pi\)
\(464\) 59.0439 2.74105
\(465\) −0.487675 −0.0226154
\(466\) 23.5798 1.09231
\(467\) 32.2178 1.49086 0.745431 0.666583i \(-0.232244\pi\)
0.745431 + 0.666583i \(0.232244\pi\)
\(468\) 10.7603 0.497393
\(469\) 13.0086 0.600680
\(470\) 0.655573 0.0302393
\(471\) 6.32359 0.291376
\(472\) 24.5242 1.12882
\(473\) 0.941824 0.0433051
\(474\) −40.6849 −1.86872
\(475\) 2.71246 0.124456
\(476\) 20.7495 0.951050
\(477\) −1.76954 −0.0810217
\(478\) 51.5023 2.35566
\(479\) 9.24461 0.422397 0.211199 0.977443i \(-0.432263\pi\)
0.211199 + 0.977443i \(0.432263\pi\)
\(480\) −5.32126 −0.242881
\(481\) −1.67111 −0.0761961
\(482\) 48.0258 2.18752
\(483\) −19.4737 −0.886085
\(484\) −51.6756 −2.34889
\(485\) 2.25086 0.102206
\(486\) −55.5922 −2.52172
\(487\) −7.44636 −0.337427 −0.168713 0.985665i \(-0.553961\pi\)
−0.168713 + 0.985665i \(0.553961\pi\)
\(488\) −34.6359 −1.56790
\(489\) −7.91318 −0.357846
\(490\) 0.425577 0.0192256
\(491\) −26.1677 −1.18093 −0.590466 0.807063i \(-0.701056\pi\)
−0.590466 + 0.807063i \(0.701056\pi\)
\(492\) −95.4743 −4.30431
\(493\) 21.3449 0.961327
\(494\) 1.18425 0.0532821
\(495\) 0.364259 0.0163722
\(496\) −14.6118 −0.656091
\(497\) 0.359103 0.0161080
\(498\) 10.9392 0.490195
\(499\) 15.8236 0.708360 0.354180 0.935177i \(-0.384760\pi\)
0.354180 + 0.935177i \(0.384760\pi\)
\(500\) 8.06976 0.360891
\(501\) 9.66932 0.431993
\(502\) −10.4865 −0.468034
\(503\) 11.2296 0.500702 0.250351 0.968155i \(-0.419454\pi\)
0.250351 + 0.968155i \(0.419454\pi\)
\(504\) −21.0760 −0.938799
\(505\) 1.53417 0.0682698
\(506\) 19.0330 0.846120
\(507\) 29.1958 1.29663
\(508\) 77.9097 3.45668
\(509\) −0.0613138 −0.00271769 −0.00135884 0.999999i \(-0.500433\pi\)
−0.00135884 + 0.999999i \(0.500433\pi\)
\(510\) −4.14318 −0.183463
\(511\) 8.05664 0.356405
\(512\) 24.5177 1.08354
\(513\) −0.508427 −0.0224476
\(514\) −7.73471 −0.341163
\(515\) −2.30864 −0.101731
\(516\) 12.9087 0.568274
\(517\) −1.34292 −0.0590617
\(518\) 5.42204 0.238231
\(519\) −4.57575 −0.200853
\(520\) 1.06072 0.0465155
\(521\) −30.5822 −1.33983 −0.669915 0.742438i \(-0.733669\pi\)
−0.669915 + 0.742438i \(0.733669\pi\)
\(522\) −35.9144 −1.57193
\(523\) 42.6032 1.86291 0.931453 0.363861i \(-0.118542\pi\)
0.931453 + 0.363861i \(0.118542\pi\)
\(524\) 109.893 4.80071
\(525\) 11.7779 0.514028
\(526\) 30.1073 1.31274
\(527\) −5.28231 −0.230101
\(528\) 23.4771 1.02171
\(529\) 44.6439 1.94104
\(530\) −0.288954 −0.0125514
\(531\) −7.90363 −0.342988
\(532\) −2.75180 −0.119306
\(533\) 6.53723 0.283159
\(534\) 26.3071 1.13842
\(535\) −2.03379 −0.0879284
\(536\) −105.198 −4.54387
\(537\) 25.6788 1.10812
\(538\) −6.74820 −0.290936
\(539\) −0.871782 −0.0375503
\(540\) −0.754355 −0.0324623
\(541\) −32.0468 −1.37780 −0.688900 0.724856i \(-0.741906\pi\)
−0.688900 + 0.724856i \(0.741906\pi\)
\(542\) 9.83755 0.422559
\(543\) 30.2220 1.29695
\(544\) −57.6378 −2.47120
\(545\) −2.97098 −0.127263
\(546\) 5.14218 0.220065
\(547\) 2.73729 0.117038 0.0585190 0.998286i \(-0.481362\pi\)
0.0585190 + 0.998286i \(0.481362\pi\)
\(548\) −0.782137 −0.0334112
\(549\) 11.1624 0.476401
\(550\) −11.5113 −0.490844
\(551\) −2.83077 −0.120595
\(552\) 157.481 6.70282
\(553\) −6.47312 −0.275265
\(554\) 42.9926 1.82658
\(555\) −0.775363 −0.0329123
\(556\) −90.6420 −3.84408
\(557\) 24.8221 1.05175 0.525873 0.850563i \(-0.323739\pi\)
0.525873 + 0.850563i \(0.323739\pi\)
\(558\) 8.88787 0.376253
\(559\) −0.883873 −0.0373838
\(560\) −1.82346 −0.0770551
\(561\) 8.48719 0.358329
\(562\) 36.0950 1.52258
\(563\) 21.6853 0.913926 0.456963 0.889486i \(-0.348937\pi\)
0.456963 + 0.889486i \(0.348937\pi\)
\(564\) −18.4062 −0.775039
\(565\) −0.767871 −0.0323046
\(566\) 24.3429 1.02321
\(567\) −10.0263 −0.421065
\(568\) −2.90400 −0.121849
\(569\) 4.39910 0.184420 0.0922099 0.995740i \(-0.470607\pi\)
0.0922099 + 0.995740i \(0.470607\pi\)
\(570\) 0.549471 0.0230148
\(571\) −25.3632 −1.06142 −0.530708 0.847555i \(-0.678074\pi\)
−0.530708 + 0.847555i \(0.678074\pi\)
\(572\) −3.59932 −0.150495
\(573\) −8.28705 −0.346197
\(574\) −21.2105 −0.885309
\(575\) −40.9116 −1.70613
\(576\) 37.6952 1.57063
\(577\) 9.61388 0.400231 0.200115 0.979772i \(-0.435868\pi\)
0.200115 + 0.979772i \(0.435868\pi\)
\(578\) 0.249330 0.0103707
\(579\) 39.9823 1.66161
\(580\) −4.20002 −0.174397
\(581\) 1.74046 0.0722064
\(582\) −88.2421 −3.65775
\(583\) 0.591914 0.0245146
\(584\) −65.1527 −2.69604
\(585\) −0.341846 −0.0141336
\(586\) −77.2302 −3.19035
\(587\) 4.30109 0.177525 0.0887625 0.996053i \(-0.471709\pi\)
0.0887625 + 0.996053i \(0.471709\pi\)
\(588\) −11.9487 −0.492756
\(589\) 0.700542 0.0288654
\(590\) −1.29061 −0.0531336
\(591\) 7.39769 0.304300
\(592\) −23.2316 −0.954814
\(593\) 1.93282 0.0793715 0.0396857 0.999212i \(-0.487364\pi\)
0.0396857 + 0.999212i \(0.487364\pi\)
\(594\) 2.15769 0.0885312
\(595\) −0.659196 −0.0270244
\(596\) 82.0881 3.36246
\(597\) 31.8760 1.30460
\(598\) −17.8619 −0.730426
\(599\) 3.89070 0.158970 0.0794848 0.996836i \(-0.474672\pi\)
0.0794848 + 0.996836i \(0.474672\pi\)
\(600\) −95.2455 −3.88838
\(601\) 24.2303 0.988373 0.494186 0.869356i \(-0.335466\pi\)
0.494186 + 0.869356i \(0.335466\pi\)
\(602\) 2.86779 0.116882
\(603\) 33.9031 1.38064
\(604\) −37.3304 −1.51895
\(605\) 1.64170 0.0667445
\(606\) −60.1452 −2.44323
\(607\) −9.10323 −0.369489 −0.184744 0.982787i \(-0.559146\pi\)
−0.184744 + 0.982787i \(0.559146\pi\)
\(608\) 7.64395 0.310003
\(609\) −12.2916 −0.498080
\(610\) 1.82275 0.0738010
\(611\) 1.26029 0.0509859
\(612\) 54.0775 2.18595
\(613\) −3.55619 −0.143633 −0.0718165 0.997418i \(-0.522880\pi\)
−0.0718165 + 0.997418i \(0.522880\pi\)
\(614\) −83.7823 −3.38118
\(615\) 3.03315 0.122308
\(616\) 7.04995 0.284050
\(617\) −18.4776 −0.743879 −0.371940 0.928257i \(-0.621307\pi\)
−0.371940 + 0.928257i \(0.621307\pi\)
\(618\) 90.5073 3.64074
\(619\) −25.4725 −1.02383 −0.511913 0.859037i \(-0.671063\pi\)
−0.511913 + 0.859037i \(0.671063\pi\)
\(620\) 1.03940 0.0417432
\(621\) 7.66852 0.307727
\(622\) 4.70990 0.188850
\(623\) 4.18555 0.167691
\(624\) −22.0325 −0.882008
\(625\) 24.6151 0.984605
\(626\) 13.6477 0.545472
\(627\) −1.12557 −0.0449511
\(628\) −13.4777 −0.537817
\(629\) −8.39844 −0.334868
\(630\) 1.10914 0.0441893
\(631\) 48.9831 1.94999 0.974993 0.222234i \(-0.0713349\pi\)
0.974993 + 0.222234i \(0.0713349\pi\)
\(632\) 52.3470 2.08225
\(633\) −42.5090 −1.68958
\(634\) −47.9873 −1.90582
\(635\) −2.47514 −0.0982228
\(636\) 8.11281 0.321694
\(637\) 0.818140 0.0324159
\(638\) 12.0134 0.475615
\(639\) 0.935899 0.0370236
\(640\) 1.66058 0.0656401
\(641\) 10.7418 0.424276 0.212138 0.977240i \(-0.431957\pi\)
0.212138 + 0.977240i \(0.431957\pi\)
\(642\) 79.7320 3.14677
\(643\) −18.7523 −0.739517 −0.369758 0.929128i \(-0.620560\pi\)
−0.369758 + 0.929128i \(0.620560\pi\)
\(644\) 41.5049 1.63552
\(645\) −0.410100 −0.0161477
\(646\) 5.95166 0.234165
\(647\) 21.1648 0.832073 0.416037 0.909348i \(-0.363419\pi\)
0.416037 + 0.909348i \(0.363419\pi\)
\(648\) 81.0809 3.18516
\(649\) 2.64378 0.103777
\(650\) 10.8030 0.423729
\(651\) 3.04185 0.119219
\(652\) 16.8656 0.660508
\(653\) 27.7865 1.08737 0.543685 0.839290i \(-0.317029\pi\)
0.543685 + 0.839290i \(0.317029\pi\)
\(654\) 116.473 4.55447
\(655\) −3.49123 −0.136414
\(656\) 90.8800 3.54827
\(657\) 20.9973 0.819183
\(658\) −4.08910 −0.159410
\(659\) −31.5549 −1.22920 −0.614602 0.788838i \(-0.710683\pi\)
−0.614602 + 0.788838i \(0.710683\pi\)
\(660\) −1.67002 −0.0650053
\(661\) 27.3255 1.06284 0.531420 0.847108i \(-0.321659\pi\)
0.531420 + 0.847108i \(0.321659\pi\)
\(662\) 46.1187 1.79245
\(663\) −7.96497 −0.309334
\(664\) −14.0748 −0.546208
\(665\) 0.0874228 0.00339011
\(666\) 14.1310 0.547564
\(667\) 42.6960 1.65320
\(668\) −20.6085 −0.797367
\(669\) 8.40554 0.324977
\(670\) 5.53615 0.213880
\(671\) −3.73385 −0.144144
\(672\) 33.1911 1.28037
\(673\) −30.4742 −1.17469 −0.587347 0.809335i \(-0.699828\pi\)
−0.587347 + 0.809335i \(0.699828\pi\)
\(674\) 5.19461 0.200089
\(675\) −4.63798 −0.178516
\(676\) −62.2259 −2.39330
\(677\) −5.51373 −0.211910 −0.105955 0.994371i \(-0.533790\pi\)
−0.105955 + 0.994371i \(0.533790\pi\)
\(678\) 30.1034 1.15611
\(679\) −14.0397 −0.538792
\(680\) 5.33080 0.204427
\(681\) −8.32865 −0.319155
\(682\) −2.97300 −0.113842
\(683\) −18.9400 −0.724720 −0.362360 0.932038i \(-0.618029\pi\)
−0.362360 + 0.932038i \(0.618029\pi\)
\(684\) −7.17178 −0.274220
\(685\) 0.0248479 0.000949391 0
\(686\) −2.65451 −0.101350
\(687\) 29.4753 1.12455
\(688\) −12.2875 −0.468457
\(689\) −0.555493 −0.0211626
\(690\) −8.28757 −0.315502
\(691\) 26.8931 1.02306 0.511532 0.859264i \(-0.329078\pi\)
0.511532 + 0.859264i \(0.329078\pi\)
\(692\) 9.75242 0.370732
\(693\) −2.27205 −0.0863080
\(694\) 42.7184 1.62157
\(695\) 2.87963 0.109231
\(696\) 99.4000 3.76775
\(697\) 32.8539 1.24443
\(698\) −15.8251 −0.598988
\(699\) 21.0324 0.795520
\(700\) −25.1025 −0.948786
\(701\) −36.3110 −1.37145 −0.685724 0.727862i \(-0.740514\pi\)
−0.685724 + 0.727862i \(0.740514\pi\)
\(702\) −2.02493 −0.0764260
\(703\) 1.11380 0.0420080
\(704\) −12.6091 −0.475223
\(705\) 0.584751 0.0220230
\(706\) −34.5332 −1.29967
\(707\) −9.56933 −0.359892
\(708\) 36.2357 1.36182
\(709\) 16.3740 0.614940 0.307470 0.951558i \(-0.400518\pi\)
0.307470 + 0.951558i \(0.400518\pi\)
\(710\) 0.152826 0.00573546
\(711\) −16.8703 −0.632687
\(712\) −33.8478 −1.26850
\(713\) −10.5662 −0.395706
\(714\) 25.8429 0.967146
\(715\) 0.114348 0.00427637
\(716\) −54.7300 −2.04536
\(717\) 45.9384 1.71560
\(718\) 16.4188 0.612745
\(719\) 33.2297 1.23926 0.619630 0.784894i \(-0.287283\pi\)
0.619630 + 0.784894i \(0.287283\pi\)
\(720\) −4.75231 −0.177108
\(721\) 14.4000 0.536286
\(722\) 49.6465 1.84765
\(723\) 42.8375 1.59314
\(724\) −64.4130 −2.39389
\(725\) −25.8229 −0.959038
\(726\) −64.3605 −2.38864
\(727\) −7.03577 −0.260942 −0.130471 0.991452i \(-0.541649\pi\)
−0.130471 + 0.991452i \(0.541649\pi\)
\(728\) −6.61616 −0.245211
\(729\) −19.5077 −0.722507
\(730\) 3.42872 0.126903
\(731\) −4.44205 −0.164295
\(732\) −51.1763 −1.89153
\(733\) 6.62622 0.244745 0.122372 0.992484i \(-0.460950\pi\)
0.122372 + 0.992484i \(0.460950\pi\)
\(734\) 80.3699 2.96651
\(735\) 0.379601 0.0140018
\(736\) −115.292 −4.24973
\(737\) −11.3406 −0.417738
\(738\) −55.2791 −2.03485
\(739\) 44.0172 1.61920 0.809600 0.586982i \(-0.199684\pi\)
0.809600 + 0.586982i \(0.199684\pi\)
\(740\) 1.65256 0.0607491
\(741\) 1.05632 0.0388048
\(742\) 1.80234 0.0661659
\(743\) −7.95982 −0.292017 −0.146009 0.989283i \(-0.546643\pi\)
−0.146009 + 0.989283i \(0.546643\pi\)
\(744\) −24.5989 −0.901839
\(745\) −2.60788 −0.0955454
\(746\) 17.5226 0.641548
\(747\) 4.53601 0.165964
\(748\) −18.0890 −0.661399
\(749\) 12.6857 0.463524
\(750\) 10.0507 0.366999
\(751\) −22.0631 −0.805094 −0.402547 0.915399i \(-0.631875\pi\)
−0.402547 + 0.915399i \(0.631875\pi\)
\(752\) 17.5204 0.638905
\(753\) −9.35360 −0.340864
\(754\) −11.2742 −0.410582
\(755\) 1.18596 0.0431616
\(756\) 4.70525 0.171128
\(757\) 51.8506 1.88454 0.942271 0.334850i \(-0.108686\pi\)
0.942271 + 0.334850i \(0.108686\pi\)
\(758\) −79.0052 −2.86960
\(759\) 16.9768 0.616220
\(760\) −0.706973 −0.0256446
\(761\) 5.39729 0.195652 0.0978258 0.995204i \(-0.468811\pi\)
0.0978258 + 0.995204i \(0.468811\pi\)
\(762\) 97.0344 3.51519
\(763\) 18.5314 0.670880
\(764\) 17.6624 0.639005
\(765\) −1.71800 −0.0621146
\(766\) 22.9067 0.827654
\(767\) −2.48110 −0.0895874
\(768\) 3.39138 0.122376
\(769\) 41.5476 1.49824 0.749122 0.662432i \(-0.230476\pi\)
0.749122 + 0.662432i \(0.230476\pi\)
\(770\) −0.371010 −0.0133703
\(771\) −6.89912 −0.248466
\(772\) −85.2154 −3.06697
\(773\) −46.4125 −1.66934 −0.834671 0.550749i \(-0.814342\pi\)
−0.834671 + 0.550749i \(0.814342\pi\)
\(774\) 7.47406 0.268650
\(775\) 6.39049 0.229553
\(776\) 113.536 4.07571
\(777\) 4.83629 0.173501
\(778\) 97.1935 3.48456
\(779\) −4.35710 −0.156109
\(780\) 1.56726 0.0561169
\(781\) −0.313059 −0.0112021
\(782\) −89.7678 −3.21009
\(783\) 4.84028 0.172977
\(784\) 11.3737 0.406204
\(785\) 0.428176 0.0152823
\(786\) 136.869 4.88196
\(787\) 16.8877 0.601980 0.300990 0.953627i \(-0.402683\pi\)
0.300990 + 0.953627i \(0.402683\pi\)
\(788\) −15.7669 −0.561673
\(789\) 26.8548 0.956055
\(790\) −2.75481 −0.0980118
\(791\) 4.78955 0.170297
\(792\) 18.3737 0.652880
\(793\) 3.50410 0.124434
\(794\) −40.6623 −1.44305
\(795\) −0.257738 −0.00914103
\(796\) −67.9384 −2.40801
\(797\) −2.82269 −0.0999848 −0.0499924 0.998750i \(-0.515920\pi\)
−0.0499924 + 0.998750i \(0.515920\pi\)
\(798\) −3.42729 −0.121325
\(799\) 6.33380 0.224074
\(800\) 69.7297 2.46532
\(801\) 10.9084 0.385431
\(802\) −0.647731 −0.0228722
\(803\) −7.02363 −0.247859
\(804\) −155.435 −5.48179
\(805\) −1.31858 −0.0464739
\(806\) 2.79007 0.0982761
\(807\) −6.01919 −0.211886
\(808\) 77.3855 2.72241
\(809\) 25.1135 0.882942 0.441471 0.897276i \(-0.354457\pi\)
0.441471 + 0.897276i \(0.354457\pi\)
\(810\) −4.26696 −0.149926
\(811\) 4.49743 0.157926 0.0789631 0.996878i \(-0.474839\pi\)
0.0789631 + 0.996878i \(0.474839\pi\)
\(812\) 26.1974 0.919350
\(813\) 8.77479 0.307745
\(814\) −4.72683 −0.165675
\(815\) −0.535808 −0.0187685
\(816\) −110.728 −3.87626
\(817\) 0.589106 0.0206102
\(818\) −46.2238 −1.61618
\(819\) 2.13225 0.0745067
\(820\) −6.46464 −0.225755
\(821\) −23.7925 −0.830364 −0.415182 0.909738i \(-0.636282\pi\)
−0.415182 + 0.909738i \(0.636282\pi\)
\(822\) −0.974130 −0.0339767
\(823\) 19.9148 0.694186 0.347093 0.937831i \(-0.387169\pi\)
0.347093 + 0.937831i \(0.387169\pi\)
\(824\) −116.451 −4.05675
\(825\) −10.2677 −0.357476
\(826\) 8.05011 0.280099
\(827\) 45.3978 1.57863 0.789317 0.613985i \(-0.210435\pi\)
0.789317 + 0.613985i \(0.210435\pi\)
\(828\) 108.171 3.75919
\(829\) −33.5410 −1.16493 −0.582464 0.812857i \(-0.697911\pi\)
−0.582464 + 0.812857i \(0.697911\pi\)
\(830\) 0.740699 0.0257101
\(831\) 38.3480 1.33028
\(832\) 11.8332 0.410244
\(833\) 4.11170 0.142462
\(834\) −112.892 −3.90914
\(835\) 0.654718 0.0226574
\(836\) 2.39897 0.0829701
\(837\) −1.19784 −0.0414035
\(838\) −64.6177 −2.23218
\(839\) 38.9873 1.34599 0.672996 0.739646i \(-0.265007\pi\)
0.672996 + 0.739646i \(0.265007\pi\)
\(840\) −3.06977 −0.105917
\(841\) −2.05076 −0.0707157
\(842\) −32.5641 −1.12223
\(843\) 32.1957 1.10888
\(844\) 90.6006 3.11860
\(845\) 1.97687 0.0680065
\(846\) −10.6571 −0.366398
\(847\) −10.2400 −0.351850
\(848\) −7.72241 −0.265189
\(849\) 21.7132 0.745193
\(850\) 54.2923 1.86221
\(851\) −16.7993 −0.575873
\(852\) −4.29081 −0.147001
\(853\) −7.23337 −0.247666 −0.123833 0.992303i \(-0.539519\pi\)
−0.123833 + 0.992303i \(0.539519\pi\)
\(854\) −11.3693 −0.389050
\(855\) 0.227842 0.00779205
\(856\) −102.587 −3.50634
\(857\) −37.1725 −1.26979 −0.634894 0.772599i \(-0.718956\pi\)
−0.634894 + 0.772599i \(0.718956\pi\)
\(858\) −4.48286 −0.153042
\(859\) −1.00000 −0.0341196
\(860\) 0.874059 0.0298052
\(861\) −18.9191 −0.644762
\(862\) −30.1455 −1.02676
\(863\) 14.7733 0.502889 0.251444 0.967872i \(-0.419094\pi\)
0.251444 + 0.967872i \(0.419094\pi\)
\(864\) −13.0702 −0.444658
\(865\) −0.309828 −0.0105345
\(866\) −69.1702 −2.35050
\(867\) 0.222394 0.00755290
\(868\) −6.48318 −0.220054
\(869\) 5.64315 0.191431
\(870\) −5.23102 −0.177348
\(871\) 10.6428 0.360619
\(872\) −149.860 −5.07490
\(873\) −36.5903 −1.23839
\(874\) 11.9050 0.402694
\(875\) 1.59910 0.0540594
\(876\) −96.2663 −3.25254
\(877\) 42.6673 1.44077 0.720387 0.693572i \(-0.243964\pi\)
0.720387 + 0.693572i \(0.243964\pi\)
\(878\) 15.1330 0.510715
\(879\) −68.8870 −2.32350
\(880\) 1.58965 0.0535873
\(881\) 22.1657 0.746782 0.373391 0.927674i \(-0.378195\pi\)
0.373391 + 0.927674i \(0.378195\pi\)
\(882\) −6.91823 −0.232949
\(883\) −5.95627 −0.200444 −0.100222 0.994965i \(-0.531955\pi\)
−0.100222 + 0.994965i \(0.531955\pi\)
\(884\) 16.9760 0.570964
\(885\) −1.15118 −0.0386966
\(886\) 44.6667 1.50061
\(887\) 45.9360 1.54238 0.771190 0.636604i \(-0.219662\pi\)
0.771190 + 0.636604i \(0.219662\pi\)
\(888\) −39.1102 −1.31245
\(889\) 15.4385 0.517792
\(890\) 1.78127 0.0597084
\(891\) 8.74074 0.292826
\(892\) −17.9150 −0.599838
\(893\) −0.839991 −0.0281092
\(894\) 102.239 3.41937
\(895\) 1.73873 0.0581195
\(896\) −10.3578 −0.346029
\(897\) −15.9322 −0.531962
\(898\) 26.3760 0.880179
\(899\) −6.66924 −0.222431
\(900\) −65.4225 −2.18075
\(901\) −2.79172 −0.0930058
\(902\) 18.4909 0.615681
\(903\) 2.55798 0.0851242
\(904\) −38.7323 −1.28822
\(905\) 2.04635 0.0680231
\(906\) −46.4940 −1.54466
\(907\) 9.54805 0.317038 0.158519 0.987356i \(-0.449328\pi\)
0.158519 + 0.987356i \(0.449328\pi\)
\(908\) 17.7511 0.589091
\(909\) −24.9397 −0.827198
\(910\) 0.348182 0.0115421
\(911\) 7.71705 0.255677 0.127839 0.991795i \(-0.459196\pi\)
0.127839 + 0.991795i \(0.459196\pi\)
\(912\) 14.6848 0.486263
\(913\) −1.51730 −0.0502153
\(914\) 20.7299 0.685686
\(915\) 1.62584 0.0537485
\(916\) −62.8215 −2.07568
\(917\) 21.7764 0.719119
\(918\) −10.1766 −0.335878
\(919\) 46.0963 1.52058 0.760289 0.649585i \(-0.225057\pi\)
0.760289 + 0.649585i \(0.225057\pi\)
\(920\) 10.6632 0.351554
\(921\) −74.7312 −2.46248
\(922\) −53.7656 −1.77068
\(923\) 0.293797 0.00967044
\(924\) 10.4166 0.342683
\(925\) 10.1604 0.334071
\(926\) −20.3464 −0.668623
\(927\) 37.5296 1.23263
\(928\) −72.7712 −2.38883
\(929\) 34.2048 1.12222 0.561111 0.827740i \(-0.310374\pi\)
0.561111 + 0.827740i \(0.310374\pi\)
\(930\) 1.29454 0.0424497
\(931\) −0.545295 −0.0178713
\(932\) −44.8271 −1.46836
\(933\) 4.20108 0.137537
\(934\) −85.5226 −2.79839
\(935\) 0.574675 0.0187939
\(936\) −17.2431 −0.563609
\(937\) −38.8829 −1.27025 −0.635125 0.772410i \(-0.719051\pi\)
−0.635125 + 0.772410i \(0.719051\pi\)
\(938\) −34.5315 −1.12749
\(939\) 12.1733 0.397261
\(940\) −1.24630 −0.0406497
\(941\) −24.5173 −0.799241 −0.399620 0.916681i \(-0.630858\pi\)
−0.399620 + 0.916681i \(0.630858\pi\)
\(942\) −16.7861 −0.546920
\(943\) 65.7174 2.14005
\(944\) −34.4920 −1.12262
\(945\) −0.149482 −0.00486266
\(946\) −2.50009 −0.0812848
\(947\) −44.4261 −1.44366 −0.721828 0.692073i \(-0.756698\pi\)
−0.721828 + 0.692073i \(0.756698\pi\)
\(948\) 77.3453 2.51206
\(949\) 6.59146 0.213968
\(950\) −7.20026 −0.233607
\(951\) −42.8031 −1.38799
\(952\) −33.2506 −1.07766
\(953\) −32.8599 −1.06444 −0.532218 0.846608i \(-0.678641\pi\)
−0.532218 + 0.846608i \(0.678641\pi\)
\(954\) 4.69727 0.152080
\(955\) −0.561123 −0.0181575
\(956\) −97.9100 −3.16664
\(957\) 10.7156 0.346386
\(958\) −24.5400 −0.792850
\(959\) −0.154988 −0.00500481
\(960\) 5.49040 0.177202
\(961\) −29.3495 −0.946759
\(962\) 4.43599 0.143022
\(963\) 33.0615 1.06539
\(964\) −91.3009 −2.94060
\(965\) 2.70723 0.0871489
\(966\) 51.6933 1.66320
\(967\) 30.7949 0.990297 0.495149 0.868808i \(-0.335114\pi\)
0.495149 + 0.868808i \(0.335114\pi\)
\(968\) 82.8091 2.66158
\(969\) 5.30870 0.170540
\(970\) −5.97495 −0.191844
\(971\) 28.7419 0.922373 0.461186 0.887303i \(-0.347424\pi\)
0.461186 + 0.887303i \(0.347424\pi\)
\(972\) 105.685 3.38986
\(973\) −17.9616 −0.575821
\(974\) 19.7665 0.633358
\(975\) 9.63594 0.308597
\(976\) 48.7137 1.55929
\(977\) −42.6844 −1.36560 −0.682798 0.730607i \(-0.739237\pi\)
−0.682798 + 0.730607i \(0.739237\pi\)
\(978\) 21.0056 0.671687
\(979\) −3.64889 −0.116619
\(980\) −0.809056 −0.0258443
\(981\) 48.2966 1.54199
\(982\) 69.4625 2.21664
\(983\) −9.12448 −0.291026 −0.145513 0.989356i \(-0.546483\pi\)
−0.145513 + 0.989356i \(0.546483\pi\)
\(984\) 152.996 4.87732
\(985\) 0.500904 0.0159601
\(986\) −56.6604 −1.80443
\(987\) −3.64735 −0.116097
\(988\) −2.25136 −0.0716253
\(989\) −8.88539 −0.282539
\(990\) −0.966931 −0.0307311
\(991\) 25.9732 0.825067 0.412533 0.910943i \(-0.364644\pi\)
0.412533 + 0.910943i \(0.364644\pi\)
\(992\) 18.0090 0.571786
\(993\) 41.1364 1.30542
\(994\) −0.953244 −0.0302351
\(995\) 2.15835 0.0684244
\(996\) −20.7962 −0.658953
\(997\) −33.7048 −1.06744 −0.533721 0.845661i \(-0.679207\pi\)
−0.533721 + 0.845661i \(0.679207\pi\)
\(998\) −42.0039 −1.32961
\(999\) −1.90447 −0.0602548
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 \(a_p\))