Properties

Label 4010.2.a.k.1.7
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.95650\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.918908 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.918908 q^{6} -3.92602 q^{7} -1.00000 q^{8} -2.15561 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.918908 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.918908 q^{6} -3.92602 q^{7} -1.00000 q^{8} -2.15561 q^{9} +1.00000 q^{10} +1.54426 q^{11} -0.918908 q^{12} -0.562082 q^{13} +3.92602 q^{14} +0.918908 q^{15} +1.00000 q^{16} -6.59798 q^{17} +2.15561 q^{18} +6.11315 q^{19} -1.00000 q^{20} +3.60766 q^{21} -1.54426 q^{22} +4.55514 q^{23} +0.918908 q^{24} +1.00000 q^{25} +0.562082 q^{26} +4.73753 q^{27} -3.92602 q^{28} +4.69768 q^{29} -0.918908 q^{30} +5.10220 q^{31} -1.00000 q^{32} -1.41903 q^{33} +6.59798 q^{34} +3.92602 q^{35} -2.15561 q^{36} -2.86189 q^{37} -6.11315 q^{38} +0.516502 q^{39} +1.00000 q^{40} +6.29523 q^{41} -3.60766 q^{42} -3.87296 q^{43} +1.54426 q^{44} +2.15561 q^{45} -4.55514 q^{46} -2.99679 q^{47} -0.918908 q^{48} +8.41366 q^{49} -1.00000 q^{50} +6.06294 q^{51} -0.562082 q^{52} +8.81050 q^{53} -4.73753 q^{54} -1.54426 q^{55} +3.92602 q^{56} -5.61743 q^{57} -4.69768 q^{58} +8.63699 q^{59} +0.918908 q^{60} -5.01728 q^{61} -5.10220 q^{62} +8.46297 q^{63} +1.00000 q^{64} +0.562082 q^{65} +1.41903 q^{66} +1.74019 q^{67} -6.59798 q^{68} -4.18576 q^{69} -3.92602 q^{70} -7.67511 q^{71} +2.15561 q^{72} +3.93595 q^{73} +2.86189 q^{74} -0.918908 q^{75} +6.11315 q^{76} -6.06278 q^{77} -0.516502 q^{78} -14.4964 q^{79} -1.00000 q^{80} +2.11347 q^{81} -6.29523 q^{82} +4.99765 q^{83} +3.60766 q^{84} +6.59798 q^{85} +3.87296 q^{86} -4.31674 q^{87} -1.54426 q^{88} -14.6418 q^{89} -2.15561 q^{90} +2.20675 q^{91} +4.55514 q^{92} -4.68846 q^{93} +2.99679 q^{94} -6.11315 q^{95} +0.918908 q^{96} -4.83469 q^{97} -8.41366 q^{98} -3.32881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −0.918908 −0.530532 −0.265266 0.964175i \(-0.585460\pi\)
−0.265266 + 0.964175i \(0.585460\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.918908 0.375143
\(7\) −3.92602 −1.48390 −0.741949 0.670457i \(-0.766098\pi\)
−0.741949 + 0.670457i \(0.766098\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.15561 −0.718536
\(10\) 1.00000 0.316228
\(11\) 1.54426 0.465611 0.232805 0.972523i \(-0.425210\pi\)
0.232805 + 0.972523i \(0.425210\pi\)
\(12\) −0.918908 −0.265266
\(13\) −0.562082 −0.155894 −0.0779468 0.996958i \(-0.524836\pi\)
−0.0779468 + 0.996958i \(0.524836\pi\)
\(14\) 3.92602 1.04927
\(15\) 0.918908 0.237261
\(16\) 1.00000 0.250000
\(17\) −6.59798 −1.60024 −0.800122 0.599837i \(-0.795232\pi\)
−0.800122 + 0.599837i \(0.795232\pi\)
\(18\) 2.15561 0.508082
\(19\) 6.11315 1.40245 0.701226 0.712939i \(-0.252636\pi\)
0.701226 + 0.712939i \(0.252636\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.60766 0.787255
\(22\) −1.54426 −0.329236
\(23\) 4.55514 0.949813 0.474907 0.880036i \(-0.342482\pi\)
0.474907 + 0.880036i \(0.342482\pi\)
\(24\) 0.918908 0.187571
\(25\) 1.00000 0.200000
\(26\) 0.562082 0.110233
\(27\) 4.73753 0.911738
\(28\) −3.92602 −0.741949
\(29\) 4.69768 0.872338 0.436169 0.899865i \(-0.356335\pi\)
0.436169 + 0.899865i \(0.356335\pi\)
\(30\) −0.918908 −0.167769
\(31\) 5.10220 0.916383 0.458191 0.888854i \(-0.348497\pi\)
0.458191 + 0.888854i \(0.348497\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.41903 −0.247021
\(34\) 6.59798 1.13154
\(35\) 3.92602 0.663619
\(36\) −2.15561 −0.359268
\(37\) −2.86189 −0.470492 −0.235246 0.971936i \(-0.575590\pi\)
−0.235246 + 0.971936i \(0.575590\pi\)
\(38\) −6.11315 −0.991684
\(39\) 0.516502 0.0827065
\(40\) 1.00000 0.158114
\(41\) 6.29523 0.983150 0.491575 0.870835i \(-0.336421\pi\)
0.491575 + 0.870835i \(0.336421\pi\)
\(42\) −3.60766 −0.556673
\(43\) −3.87296 −0.590621 −0.295311 0.955401i \(-0.595423\pi\)
−0.295311 + 0.955401i \(0.595423\pi\)
\(44\) 1.54426 0.232805
\(45\) 2.15561 0.321339
\(46\) −4.55514 −0.671619
\(47\) −2.99679 −0.437127 −0.218564 0.975823i \(-0.570137\pi\)
−0.218564 + 0.975823i \(0.570137\pi\)
\(48\) −0.918908 −0.132633
\(49\) 8.41366 1.20195
\(50\) −1.00000 −0.141421
\(51\) 6.06294 0.848981
\(52\) −0.562082 −0.0779468
\(53\) 8.81050 1.21022 0.605108 0.796144i \(-0.293130\pi\)
0.605108 + 0.796144i \(0.293130\pi\)
\(54\) −4.73753 −0.644696
\(55\) −1.54426 −0.208227
\(56\) 3.92602 0.524637
\(57\) −5.61743 −0.744046
\(58\) −4.69768 −0.616836
\(59\) 8.63699 1.12444 0.562220 0.826988i \(-0.309947\pi\)
0.562220 + 0.826988i \(0.309947\pi\)
\(60\) 0.918908 0.118631
\(61\) −5.01728 −0.642396 −0.321198 0.947012i \(-0.604086\pi\)
−0.321198 + 0.947012i \(0.604086\pi\)
\(62\) −5.10220 −0.647980
\(63\) 8.46297 1.06623
\(64\) 1.00000 0.125000
\(65\) 0.562082 0.0697177
\(66\) 1.41903 0.174670
\(67\) 1.74019 0.212598 0.106299 0.994334i \(-0.466100\pi\)
0.106299 + 0.994334i \(0.466100\pi\)
\(68\) −6.59798 −0.800122
\(69\) −4.18576 −0.503906
\(70\) −3.92602 −0.469250
\(71\) −7.67511 −0.910868 −0.455434 0.890270i \(-0.650516\pi\)
−0.455434 + 0.890270i \(0.650516\pi\)
\(72\) 2.15561 0.254041
\(73\) 3.93595 0.460668 0.230334 0.973112i \(-0.426018\pi\)
0.230334 + 0.973112i \(0.426018\pi\)
\(74\) 2.86189 0.332688
\(75\) −0.918908 −0.106106
\(76\) 6.11315 0.701226
\(77\) −6.06278 −0.690918
\(78\) −0.516502 −0.0584823
\(79\) −14.4964 −1.63097 −0.815486 0.578777i \(-0.803530\pi\)
−0.815486 + 0.578777i \(0.803530\pi\)
\(80\) −1.00000 −0.111803
\(81\) 2.11347 0.234830
\(82\) −6.29523 −0.695192
\(83\) 4.99765 0.548564 0.274282 0.961649i \(-0.411560\pi\)
0.274282 + 0.961649i \(0.411560\pi\)
\(84\) 3.60766 0.393628
\(85\) 6.59798 0.715651
\(86\) 3.87296 0.417632
\(87\) −4.31674 −0.462803
\(88\) −1.54426 −0.164618
\(89\) −14.6418 −1.55202 −0.776012 0.630719i \(-0.782760\pi\)
−0.776012 + 0.630719i \(0.782760\pi\)
\(90\) −2.15561 −0.227221
\(91\) 2.20675 0.231330
\(92\) 4.55514 0.474907
\(93\) −4.68846 −0.486170
\(94\) 2.99679 0.309096
\(95\) −6.11315 −0.627196
\(96\) 0.918908 0.0937857
\(97\) −4.83469 −0.490888 −0.245444 0.969411i \(-0.578934\pi\)
−0.245444 + 0.969411i \(0.578934\pi\)
\(98\) −8.41366 −0.849908
\(99\) −3.32881 −0.334558
\(100\) 1.00000 0.100000
\(101\) −8.29206 −0.825090 −0.412545 0.910937i \(-0.635360\pi\)
−0.412545 + 0.910937i \(0.635360\pi\)
\(102\) −6.06294 −0.600320
\(103\) −0.0164182 −0.00161774 −0.000808868 1.00000i \(-0.500257\pi\)
−0.000808868 1.00000i \(0.500257\pi\)
\(104\) 0.562082 0.0551167
\(105\) −3.60766 −0.352071
\(106\) −8.81050 −0.855752
\(107\) −8.49762 −0.821496 −0.410748 0.911749i \(-0.634732\pi\)
−0.410748 + 0.911749i \(0.634732\pi\)
\(108\) 4.73753 0.455869
\(109\) 8.07761 0.773694 0.386847 0.922144i \(-0.373564\pi\)
0.386847 + 0.922144i \(0.373564\pi\)
\(110\) 1.54426 0.147239
\(111\) 2.62982 0.249611
\(112\) −3.92602 −0.370974
\(113\) −9.68966 −0.911527 −0.455763 0.890101i \(-0.650634\pi\)
−0.455763 + 0.890101i \(0.650634\pi\)
\(114\) 5.61743 0.526120
\(115\) −4.55514 −0.424769
\(116\) 4.69768 0.436169
\(117\) 1.21163 0.112015
\(118\) −8.63699 −0.795100
\(119\) 25.9038 2.37460
\(120\) −0.918908 −0.0838845
\(121\) −8.61527 −0.783207
\(122\) 5.01728 0.454243
\(123\) −5.78474 −0.521592
\(124\) 5.10220 0.458191
\(125\) −1.00000 −0.0894427
\(126\) −8.46297 −0.753941
\(127\) 16.5317 1.46695 0.733477 0.679715i \(-0.237896\pi\)
0.733477 + 0.679715i \(0.237896\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.55890 0.313343
\(130\) −0.562082 −0.0492979
\(131\) −10.2662 −0.896966 −0.448483 0.893791i \(-0.648036\pi\)
−0.448483 + 0.893791i \(0.648036\pi\)
\(132\) −1.41903 −0.123511
\(133\) −24.0004 −2.08110
\(134\) −1.74019 −0.150329
\(135\) −4.73753 −0.407742
\(136\) 6.59798 0.565772
\(137\) −2.55263 −0.218086 −0.109043 0.994037i \(-0.534779\pi\)
−0.109043 + 0.994037i \(0.534779\pi\)
\(138\) 4.18576 0.356316
\(139\) 1.40272 0.118977 0.0594885 0.998229i \(-0.481053\pi\)
0.0594885 + 0.998229i \(0.481053\pi\)
\(140\) 3.92602 0.331810
\(141\) 2.75378 0.231910
\(142\) 7.67511 0.644081
\(143\) −0.867999 −0.0725857
\(144\) −2.15561 −0.179634
\(145\) −4.69768 −0.390121
\(146\) −3.93595 −0.325741
\(147\) −7.73139 −0.637674
\(148\) −2.86189 −0.235246
\(149\) 23.7432 1.94512 0.972558 0.232659i \(-0.0747424\pi\)
0.972558 + 0.232659i \(0.0747424\pi\)
\(150\) 0.918908 0.0750286
\(151\) −18.6292 −1.51602 −0.758012 0.652241i \(-0.773829\pi\)
−0.758012 + 0.652241i \(0.773829\pi\)
\(152\) −6.11315 −0.495842
\(153\) 14.2226 1.14983
\(154\) 6.06278 0.488553
\(155\) −5.10220 −0.409819
\(156\) 0.516502 0.0413533
\(157\) −6.43230 −0.513354 −0.256677 0.966497i \(-0.582628\pi\)
−0.256677 + 0.966497i \(0.582628\pi\)
\(158\) 14.4964 1.15327
\(159\) −8.09604 −0.642058
\(160\) 1.00000 0.0790569
\(161\) −17.8836 −1.40943
\(162\) −2.11347 −0.166050
\(163\) 16.4413 1.28778 0.643892 0.765117i \(-0.277319\pi\)
0.643892 + 0.765117i \(0.277319\pi\)
\(164\) 6.29523 0.491575
\(165\) 1.41903 0.110471
\(166\) −4.99765 −0.387893
\(167\) 3.26012 0.252275 0.126138 0.992013i \(-0.459742\pi\)
0.126138 + 0.992013i \(0.459742\pi\)
\(168\) −3.60766 −0.278337
\(169\) −12.6841 −0.975697
\(170\) −6.59798 −0.506042
\(171\) −13.1776 −1.00771
\(172\) −3.87296 −0.295311
\(173\) 17.5469 1.33407 0.667035 0.745026i \(-0.267563\pi\)
0.667035 + 0.745026i \(0.267563\pi\)
\(174\) 4.31674 0.327251
\(175\) −3.92602 −0.296780
\(176\) 1.54426 0.116403
\(177\) −7.93660 −0.596552
\(178\) 14.6418 1.09745
\(179\) −1.40640 −0.105119 −0.0525597 0.998618i \(-0.516738\pi\)
−0.0525597 + 0.998618i \(0.516738\pi\)
\(180\) 2.15561 0.160669
\(181\) 8.51792 0.633132 0.316566 0.948571i \(-0.397470\pi\)
0.316566 + 0.948571i \(0.397470\pi\)
\(182\) −2.20675 −0.163575
\(183\) 4.61042 0.340812
\(184\) −4.55514 −0.335810
\(185\) 2.86189 0.210410
\(186\) 4.68846 0.343774
\(187\) −10.1890 −0.745091
\(188\) −2.99679 −0.218564
\(189\) −18.5997 −1.35293
\(190\) 6.11315 0.443495
\(191\) 0.207405 0.0150073 0.00750365 0.999972i \(-0.497611\pi\)
0.00750365 + 0.999972i \(0.497611\pi\)
\(192\) −0.918908 −0.0663165
\(193\) −18.1703 −1.30793 −0.653964 0.756525i \(-0.726895\pi\)
−0.653964 + 0.756525i \(0.726895\pi\)
\(194\) 4.83469 0.347110
\(195\) −0.516502 −0.0369875
\(196\) 8.41366 0.600976
\(197\) 12.9568 0.923132 0.461566 0.887106i \(-0.347288\pi\)
0.461566 + 0.887106i \(0.347288\pi\)
\(198\) 3.32881 0.236568
\(199\) −12.2094 −0.865503 −0.432751 0.901513i \(-0.642457\pi\)
−0.432751 + 0.901513i \(0.642457\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −1.59907 −0.112790
\(202\) 8.29206 0.583427
\(203\) −18.4432 −1.29446
\(204\) 6.06294 0.424490
\(205\) −6.29523 −0.439678
\(206\) 0.0164182 0.00114391
\(207\) −9.81910 −0.682475
\(208\) −0.562082 −0.0389734
\(209\) 9.44027 0.652997
\(210\) 3.60766 0.248952
\(211\) 12.0336 0.828430 0.414215 0.910179i \(-0.364056\pi\)
0.414215 + 0.910179i \(0.364056\pi\)
\(212\) 8.81050 0.605108
\(213\) 7.05272 0.483245
\(214\) 8.49762 0.580886
\(215\) 3.87296 0.264134
\(216\) −4.73753 −0.322348
\(217\) −20.0314 −1.35982
\(218\) −8.07761 −0.547085
\(219\) −3.61677 −0.244399
\(220\) −1.54426 −0.104114
\(221\) 3.70861 0.249468
\(222\) −2.62982 −0.176502
\(223\) −17.7792 −1.19058 −0.595292 0.803510i \(-0.702964\pi\)
−0.595292 + 0.803510i \(0.702964\pi\)
\(224\) 3.92602 0.262319
\(225\) −2.15561 −0.143707
\(226\) 9.68966 0.644547
\(227\) −10.8774 −0.721956 −0.360978 0.932574i \(-0.617557\pi\)
−0.360978 + 0.932574i \(0.617557\pi\)
\(228\) −5.61743 −0.372023
\(229\) −10.1215 −0.668845 −0.334422 0.942423i \(-0.608541\pi\)
−0.334422 + 0.942423i \(0.608541\pi\)
\(230\) 4.55514 0.300357
\(231\) 5.57114 0.366554
\(232\) −4.69768 −0.308418
\(233\) −7.83644 −0.513382 −0.256691 0.966493i \(-0.582632\pi\)
−0.256691 + 0.966493i \(0.582632\pi\)
\(234\) −1.21163 −0.0792066
\(235\) 2.99679 0.195489
\(236\) 8.63699 0.562220
\(237\) 13.3209 0.865283
\(238\) −25.9038 −1.67910
\(239\) 7.90410 0.511274 0.255637 0.966773i \(-0.417715\pi\)
0.255637 + 0.966773i \(0.417715\pi\)
\(240\) 0.918908 0.0593153
\(241\) 15.6685 1.00930 0.504650 0.863324i \(-0.331622\pi\)
0.504650 + 0.863324i \(0.331622\pi\)
\(242\) 8.61527 0.553811
\(243\) −16.1547 −1.03632
\(244\) −5.01728 −0.321198
\(245\) −8.41366 −0.537529
\(246\) 5.78474 0.368822
\(247\) −3.43609 −0.218633
\(248\) −5.10220 −0.323990
\(249\) −4.59239 −0.291031
\(250\) 1.00000 0.0632456
\(251\) 5.67050 0.357919 0.178959 0.983856i \(-0.442727\pi\)
0.178959 + 0.983856i \(0.442727\pi\)
\(252\) 8.46297 0.533117
\(253\) 7.03431 0.442243
\(254\) −16.5317 −1.03729
\(255\) −6.06294 −0.379676
\(256\) 1.00000 0.0625000
\(257\) −6.28655 −0.392144 −0.196072 0.980590i \(-0.562819\pi\)
−0.196072 + 0.980590i \(0.562819\pi\)
\(258\) −3.55890 −0.221567
\(259\) 11.2359 0.698162
\(260\) 0.562082 0.0348589
\(261\) −10.1264 −0.626806
\(262\) 10.2662 0.634251
\(263\) −28.9758 −1.78673 −0.893363 0.449336i \(-0.851660\pi\)
−0.893363 + 0.449336i \(0.851660\pi\)
\(264\) 1.41903 0.0873352
\(265\) −8.81050 −0.541225
\(266\) 24.0004 1.47156
\(267\) 13.4544 0.823398
\(268\) 1.74019 0.106299
\(269\) 22.5756 1.37646 0.688228 0.725495i \(-0.258389\pi\)
0.688228 + 0.725495i \(0.258389\pi\)
\(270\) 4.73753 0.288317
\(271\) −5.19284 −0.315443 −0.157721 0.987484i \(-0.550415\pi\)
−0.157721 + 0.987484i \(0.550415\pi\)
\(272\) −6.59798 −0.400061
\(273\) −2.02780 −0.122728
\(274\) 2.55263 0.154210
\(275\) 1.54426 0.0931221
\(276\) −4.18576 −0.251953
\(277\) −4.42858 −0.266088 −0.133044 0.991110i \(-0.542475\pi\)
−0.133044 + 0.991110i \(0.542475\pi\)
\(278\) −1.40272 −0.0841295
\(279\) −10.9983 −0.658454
\(280\) −3.92602 −0.234625
\(281\) 15.4096 0.919258 0.459629 0.888111i \(-0.347982\pi\)
0.459629 + 0.888111i \(0.347982\pi\)
\(282\) −2.75378 −0.163985
\(283\) 3.11244 0.185015 0.0925077 0.995712i \(-0.470512\pi\)
0.0925077 + 0.995712i \(0.470512\pi\)
\(284\) −7.67511 −0.455434
\(285\) 5.61743 0.332748
\(286\) 0.867999 0.0513258
\(287\) −24.7152 −1.45889
\(288\) 2.15561 0.127020
\(289\) 26.5333 1.56078
\(290\) 4.69768 0.275857
\(291\) 4.44264 0.260432
\(292\) 3.93595 0.230334
\(293\) 22.9346 1.33985 0.669926 0.742428i \(-0.266326\pi\)
0.669926 + 0.742428i \(0.266326\pi\)
\(294\) 7.73139 0.450904
\(295\) −8.63699 −0.502865
\(296\) 2.86189 0.166344
\(297\) 7.31596 0.424515
\(298\) −23.7432 −1.37541
\(299\) −2.56037 −0.148070
\(300\) −0.918908 −0.0530532
\(301\) 15.2053 0.876422
\(302\) 18.6292 1.07199
\(303\) 7.61964 0.437737
\(304\) 6.11315 0.350613
\(305\) 5.01728 0.287288
\(306\) −14.2226 −0.813055
\(307\) 9.29961 0.530757 0.265378 0.964144i \(-0.414503\pi\)
0.265378 + 0.964144i \(0.414503\pi\)
\(308\) −6.06278 −0.345459
\(309\) 0.0150869 0.000858261 0
\(310\) 5.10220 0.289786
\(311\) −16.6788 −0.945771 −0.472885 0.881124i \(-0.656788\pi\)
−0.472885 + 0.881124i \(0.656788\pi\)
\(312\) −0.516502 −0.0292412
\(313\) 7.07243 0.399757 0.199879 0.979821i \(-0.435945\pi\)
0.199879 + 0.979821i \(0.435945\pi\)
\(314\) 6.43230 0.362996
\(315\) −8.46297 −0.476834
\(316\) −14.4964 −0.815486
\(317\) 10.9145 0.613021 0.306511 0.951867i \(-0.400839\pi\)
0.306511 + 0.951867i \(0.400839\pi\)
\(318\) 8.09604 0.454004
\(319\) 7.25442 0.406170
\(320\) −1.00000 −0.0559017
\(321\) 7.80854 0.435830
\(322\) 17.8836 0.996614
\(323\) −40.3344 −2.24427
\(324\) 2.11347 0.117415
\(325\) −0.562082 −0.0311787
\(326\) −16.4413 −0.910600
\(327\) −7.42258 −0.410470
\(328\) −6.29523 −0.347596
\(329\) 11.7655 0.648652
\(330\) −1.41903 −0.0781150
\(331\) −8.13592 −0.447191 −0.223595 0.974682i \(-0.571779\pi\)
−0.223595 + 0.974682i \(0.571779\pi\)
\(332\) 4.99765 0.274282
\(333\) 6.16911 0.338065
\(334\) −3.26012 −0.178386
\(335\) −1.74019 −0.0950765
\(336\) 3.60766 0.196814
\(337\) −26.1203 −1.42286 −0.711432 0.702755i \(-0.751953\pi\)
−0.711432 + 0.702755i \(0.751953\pi\)
\(338\) 12.6841 0.689922
\(339\) 8.90391 0.483594
\(340\) 6.59798 0.357826
\(341\) 7.87910 0.426677
\(342\) 13.1776 0.712560
\(343\) −5.55007 −0.299676
\(344\) 3.87296 0.208816
\(345\) 4.18576 0.225354
\(346\) −17.5469 −0.943330
\(347\) 4.10689 0.220470 0.110235 0.993906i \(-0.464840\pi\)
0.110235 + 0.993906i \(0.464840\pi\)
\(348\) −4.31674 −0.231402
\(349\) −25.9138 −1.38713 −0.693566 0.720393i \(-0.743962\pi\)
−0.693566 + 0.720393i \(0.743962\pi\)
\(350\) 3.92602 0.209855
\(351\) −2.66288 −0.142134
\(352\) −1.54426 −0.0823091
\(353\) −11.8873 −0.632697 −0.316349 0.948643i \(-0.602457\pi\)
−0.316349 + 0.948643i \(0.602457\pi\)
\(354\) 7.93660 0.421826
\(355\) 7.67511 0.407353
\(356\) −14.6418 −0.776012
\(357\) −23.8032 −1.25980
\(358\) 1.40640 0.0743306
\(359\) −12.0315 −0.635000 −0.317500 0.948258i \(-0.602843\pi\)
−0.317500 + 0.948258i \(0.602843\pi\)
\(360\) −2.15561 −0.113610
\(361\) 18.3706 0.966874
\(362\) −8.51792 −0.447692
\(363\) 7.91665 0.415516
\(364\) 2.20675 0.115665
\(365\) −3.93595 −0.206017
\(366\) −4.61042 −0.240990
\(367\) −10.8051 −0.564022 −0.282011 0.959411i \(-0.591001\pi\)
−0.282011 + 0.959411i \(0.591001\pi\)
\(368\) 4.55514 0.237453
\(369\) −13.5700 −0.706428
\(370\) −2.86189 −0.148783
\(371\) −34.5902 −1.79584
\(372\) −4.68846 −0.243085
\(373\) 29.1390 1.50876 0.754380 0.656438i \(-0.227938\pi\)
0.754380 + 0.656438i \(0.227938\pi\)
\(374\) 10.1890 0.526859
\(375\) 0.918908 0.0474522
\(376\) 2.99679 0.154548
\(377\) −2.64048 −0.135992
\(378\) 18.5997 0.956663
\(379\) −27.4798 −1.41154 −0.705771 0.708440i \(-0.749399\pi\)
−0.705771 + 0.708440i \(0.749399\pi\)
\(380\) −6.11315 −0.313598
\(381\) −15.1911 −0.778266
\(382\) −0.207405 −0.0106118
\(383\) −6.59847 −0.337166 −0.168583 0.985687i \(-0.553919\pi\)
−0.168583 + 0.985687i \(0.553919\pi\)
\(384\) 0.918908 0.0468928
\(385\) 6.06278 0.308988
\(386\) 18.1703 0.924845
\(387\) 8.34859 0.424383
\(388\) −4.83469 −0.245444
\(389\) −13.2124 −0.669894 −0.334947 0.942237i \(-0.608718\pi\)
−0.334947 + 0.942237i \(0.608718\pi\)
\(390\) 0.516502 0.0261541
\(391\) −30.0547 −1.51993
\(392\) −8.41366 −0.424954
\(393\) 9.43374 0.475869
\(394\) −12.9568 −0.652753
\(395\) 14.4964 0.729393
\(396\) −3.32881 −0.167279
\(397\) 16.6594 0.836112 0.418056 0.908421i \(-0.362712\pi\)
0.418056 + 0.908421i \(0.362712\pi\)
\(398\) 12.2094 0.612003
\(399\) 22.0541 1.10409
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 1.59907 0.0797544
\(403\) −2.86786 −0.142858
\(404\) −8.29206 −0.412545
\(405\) −2.11347 −0.105019
\(406\) 18.4432 0.915321
\(407\) −4.41949 −0.219066
\(408\) −6.06294 −0.300160
\(409\) 27.9156 1.38034 0.690168 0.723649i \(-0.257537\pi\)
0.690168 + 0.723649i \(0.257537\pi\)
\(410\) 6.29523 0.310899
\(411\) 2.34564 0.115702
\(412\) −0.0164182 −0.000808868 0
\(413\) −33.9090 −1.66855
\(414\) 9.81910 0.482583
\(415\) −4.99765 −0.245325
\(416\) 0.562082 0.0275583
\(417\) −1.28897 −0.0631211
\(418\) −9.44027 −0.461739
\(419\) 4.77625 0.233335 0.116668 0.993171i \(-0.462779\pi\)
0.116668 + 0.993171i \(0.462779\pi\)
\(420\) −3.60766 −0.176036
\(421\) −29.3901 −1.43238 −0.716192 0.697903i \(-0.754117\pi\)
−0.716192 + 0.697903i \(0.754117\pi\)
\(422\) −12.0336 −0.585789
\(423\) 6.45991 0.314092
\(424\) −8.81050 −0.427876
\(425\) −6.59798 −0.320049
\(426\) −7.05272 −0.341705
\(427\) 19.6979 0.953250
\(428\) −8.49762 −0.410748
\(429\) 0.797611 0.0385090
\(430\) −3.87296 −0.186771
\(431\) 21.6388 1.04230 0.521151 0.853464i \(-0.325503\pi\)
0.521151 + 0.853464i \(0.325503\pi\)
\(432\) 4.73753 0.227935
\(433\) −30.3104 −1.45662 −0.728312 0.685246i \(-0.759695\pi\)
−0.728312 + 0.685246i \(0.759695\pi\)
\(434\) 20.0314 0.961537
\(435\) 4.31674 0.206972
\(436\) 8.07761 0.386847
\(437\) 27.8463 1.33207
\(438\) 3.61677 0.172816
\(439\) −14.8601 −0.709235 −0.354617 0.935012i \(-0.615389\pi\)
−0.354617 + 0.935012i \(0.615389\pi\)
\(440\) 1.54426 0.0736195
\(441\) −18.1366 −0.863645
\(442\) −3.70861 −0.176400
\(443\) −24.8300 −1.17971 −0.589853 0.807510i \(-0.700814\pi\)
−0.589853 + 0.807510i \(0.700814\pi\)
\(444\) 2.62982 0.124806
\(445\) 14.6418 0.694086
\(446\) 17.7792 0.841870
\(447\) −21.8178 −1.03195
\(448\) −3.92602 −0.185487
\(449\) −1.04233 −0.0491905 −0.0245953 0.999697i \(-0.507830\pi\)
−0.0245953 + 0.999697i \(0.507830\pi\)
\(450\) 2.15561 0.101616
\(451\) 9.72144 0.457765
\(452\) −9.68966 −0.455763
\(453\) 17.1185 0.804299
\(454\) 10.8774 0.510500
\(455\) −2.20675 −0.103454
\(456\) 5.61743 0.263060
\(457\) 15.2698 0.714292 0.357146 0.934049i \(-0.383750\pi\)
0.357146 + 0.934049i \(0.383750\pi\)
\(458\) 10.1215 0.472945
\(459\) −31.2581 −1.45900
\(460\) −4.55514 −0.212385
\(461\) −7.72789 −0.359924 −0.179962 0.983674i \(-0.557597\pi\)
−0.179962 + 0.983674i \(0.557597\pi\)
\(462\) −5.57114 −0.259193
\(463\) −24.4397 −1.13581 −0.567906 0.823094i \(-0.692246\pi\)
−0.567906 + 0.823094i \(0.692246\pi\)
\(464\) 4.69768 0.218084
\(465\) 4.68846 0.217422
\(466\) 7.83644 0.363016
\(467\) −30.9905 −1.43407 −0.717034 0.697038i \(-0.754501\pi\)
−0.717034 + 0.697038i \(0.754501\pi\)
\(468\) 1.21163 0.0560076
\(469\) −6.83201 −0.315473
\(470\) −2.99679 −0.138232
\(471\) 5.91070 0.272351
\(472\) −8.63699 −0.397550
\(473\) −5.98084 −0.275000
\(474\) −13.3209 −0.611847
\(475\) 6.11315 0.280491
\(476\) 25.9038 1.18730
\(477\) −18.9920 −0.869583
\(478\) −7.90410 −0.361525
\(479\) −22.0256 −1.00638 −0.503188 0.864177i \(-0.667840\pi\)
−0.503188 + 0.864177i \(0.667840\pi\)
\(480\) −0.918908 −0.0419422
\(481\) 1.60862 0.0733467
\(482\) −15.6685 −0.713683
\(483\) 16.4334 0.747745
\(484\) −8.61527 −0.391603
\(485\) 4.83469 0.219532
\(486\) 16.1547 0.732791
\(487\) −21.0036 −0.951766 −0.475883 0.879509i \(-0.657871\pi\)
−0.475883 + 0.879509i \(0.657871\pi\)
\(488\) 5.01728 0.227121
\(489\) −15.1081 −0.683210
\(490\) 8.41366 0.380091
\(491\) 0.318350 0.0143669 0.00718346 0.999974i \(-0.497713\pi\)
0.00718346 + 0.999974i \(0.497713\pi\)
\(492\) −5.78474 −0.260796
\(493\) −30.9952 −1.39595
\(494\) 3.43609 0.154597
\(495\) 3.32881 0.149619
\(496\) 5.10220 0.229096
\(497\) 30.1327 1.35163
\(498\) 4.59239 0.205790
\(499\) 0.281372 0.0125959 0.00629796 0.999980i \(-0.497995\pi\)
0.00629796 + 0.999980i \(0.497995\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −2.99575 −0.133840
\(502\) −5.67050 −0.253087
\(503\) −9.01237 −0.401842 −0.200921 0.979607i \(-0.564393\pi\)
−0.200921 + 0.979607i \(0.564393\pi\)
\(504\) −8.46297 −0.376970
\(505\) 8.29206 0.368992
\(506\) −7.03431 −0.312713
\(507\) 11.6555 0.517639
\(508\) 16.5317 0.733477
\(509\) 34.6649 1.53650 0.768248 0.640153i \(-0.221129\pi\)
0.768248 + 0.640153i \(0.221129\pi\)
\(510\) 6.06294 0.268471
\(511\) −15.4526 −0.683584
\(512\) −1.00000 −0.0441942
\(513\) 28.9612 1.27867
\(514\) 6.28655 0.277288
\(515\) 0.0164182 0.000723474 0
\(516\) 3.55890 0.156672
\(517\) −4.62782 −0.203531
\(518\) −11.2359 −0.493675
\(519\) −16.1240 −0.707767
\(520\) −0.562082 −0.0246489
\(521\) −7.84551 −0.343718 −0.171859 0.985122i \(-0.554977\pi\)
−0.171859 + 0.985122i \(0.554977\pi\)
\(522\) 10.1264 0.443219
\(523\) −20.5593 −0.898995 −0.449498 0.893282i \(-0.648397\pi\)
−0.449498 + 0.893282i \(0.648397\pi\)
\(524\) −10.2662 −0.448483
\(525\) 3.60766 0.157451
\(526\) 28.9758 1.26341
\(527\) −33.6642 −1.46644
\(528\) −1.41903 −0.0617553
\(529\) −2.25065 −0.0978545
\(530\) 8.81050 0.382704
\(531\) −18.6180 −0.807951
\(532\) −24.0004 −1.04055
\(533\) −3.53844 −0.153267
\(534\) −13.4544 −0.582230
\(535\) 8.49762 0.367384
\(536\) −1.74019 −0.0751646
\(537\) 1.29235 0.0557692
\(538\) −22.5756 −0.973301
\(539\) 12.9928 0.559641
\(540\) −4.73753 −0.203871
\(541\) −45.8817 −1.97261 −0.986303 0.164942i \(-0.947256\pi\)
−0.986303 + 0.164942i \(0.947256\pi\)
\(542\) 5.19284 0.223052
\(543\) −7.82719 −0.335897
\(544\) 6.59798 0.282886
\(545\) −8.07761 −0.346007
\(546\) 2.02780 0.0867818
\(547\) 3.60148 0.153988 0.0769941 0.997032i \(-0.475468\pi\)
0.0769941 + 0.997032i \(0.475468\pi\)
\(548\) −2.55263 −0.109043
\(549\) 10.8153 0.461585
\(550\) −1.54426 −0.0658473
\(551\) 28.7176 1.22341
\(552\) 4.18576 0.178158
\(553\) 56.9132 2.42019
\(554\) 4.42858 0.188152
\(555\) −2.62982 −0.111629
\(556\) 1.40272 0.0594885
\(557\) 4.64386 0.196767 0.0983833 0.995149i \(-0.468633\pi\)
0.0983833 + 0.995149i \(0.468633\pi\)
\(558\) 10.9983 0.465597
\(559\) 2.17692 0.0920741
\(560\) 3.92602 0.165905
\(561\) 9.36272 0.395294
\(562\) −15.4096 −0.650014
\(563\) 40.3282 1.69963 0.849815 0.527081i \(-0.176714\pi\)
0.849815 + 0.527081i \(0.176714\pi\)
\(564\) 2.75378 0.115955
\(565\) 9.68966 0.407647
\(566\) −3.11244 −0.130826
\(567\) −8.29752 −0.348463
\(568\) 7.67511 0.322040
\(569\) 13.7368 0.575876 0.287938 0.957649i \(-0.407030\pi\)
0.287938 + 0.957649i \(0.407030\pi\)
\(570\) −5.61743 −0.235288
\(571\) −22.4222 −0.938340 −0.469170 0.883108i \(-0.655447\pi\)
−0.469170 + 0.883108i \(0.655447\pi\)
\(572\) −0.867999 −0.0362928
\(573\) −0.190586 −0.00796186
\(574\) 24.7152 1.03159
\(575\) 4.55514 0.189963
\(576\) −2.15561 −0.0898170
\(577\) −31.6058 −1.31577 −0.657883 0.753120i \(-0.728548\pi\)
−0.657883 + 0.753120i \(0.728548\pi\)
\(578\) −26.5333 −1.10364
\(579\) 16.6969 0.693898
\(580\) −4.69768 −0.195061
\(581\) −19.6209 −0.814012
\(582\) −4.44264 −0.184153
\(583\) 13.6057 0.563489
\(584\) −3.93595 −0.162871
\(585\) −1.21163 −0.0500947
\(586\) −22.9346 −0.947418
\(587\) −3.40326 −0.140468 −0.0702339 0.997531i \(-0.522375\pi\)
−0.0702339 + 0.997531i \(0.522375\pi\)
\(588\) −7.73139 −0.318837
\(589\) 31.1905 1.28518
\(590\) 8.63699 0.355579
\(591\) −11.9061 −0.489751
\(592\) −2.86189 −0.117623
\(593\) 33.9699 1.39498 0.697489 0.716596i \(-0.254301\pi\)
0.697489 + 0.716596i \(0.254301\pi\)
\(594\) −7.31596 −0.300177
\(595\) −25.9038 −1.06195
\(596\) 23.7432 0.972558
\(597\) 11.2193 0.459177
\(598\) 2.56037 0.104701
\(599\) 0.760709 0.0310817 0.0155409 0.999879i \(-0.495053\pi\)
0.0155409 + 0.999879i \(0.495053\pi\)
\(600\) 0.918908 0.0375143
\(601\) −43.2346 −1.76357 −0.881787 0.471648i \(-0.843659\pi\)
−0.881787 + 0.471648i \(0.843659\pi\)
\(602\) −15.2053 −0.619724
\(603\) −3.75116 −0.152759
\(604\) −18.6292 −0.758012
\(605\) 8.61527 0.350261
\(606\) −7.61964 −0.309527
\(607\) −35.2370 −1.43022 −0.715112 0.699010i \(-0.753624\pi\)
−0.715112 + 0.699010i \(0.753624\pi\)
\(608\) −6.11315 −0.247921
\(609\) 16.9476 0.686752
\(610\) −5.01728 −0.203144
\(611\) 1.68445 0.0681454
\(612\) 14.2226 0.574917
\(613\) −15.5644 −0.628639 −0.314319 0.949317i \(-0.601776\pi\)
−0.314319 + 0.949317i \(0.601776\pi\)
\(614\) −9.29961 −0.375302
\(615\) 5.78474 0.233263
\(616\) 6.06278 0.244277
\(617\) −47.6815 −1.91958 −0.959792 0.280713i \(-0.909429\pi\)
−0.959792 + 0.280713i \(0.909429\pi\)
\(618\) −0.0150869 −0.000606882 0
\(619\) −12.4244 −0.499380 −0.249690 0.968326i \(-0.580329\pi\)
−0.249690 + 0.968326i \(0.580329\pi\)
\(620\) −5.10220 −0.204909
\(621\) 21.5801 0.865981
\(622\) 16.6788 0.668761
\(623\) 57.4839 2.30304
\(624\) 0.516502 0.0206766
\(625\) 1.00000 0.0400000
\(626\) −7.07243 −0.282671
\(627\) −8.67474 −0.346436
\(628\) −6.43230 −0.256677
\(629\) 18.8827 0.752902
\(630\) 8.46297 0.337173
\(631\) 0.0738847 0.00294130 0.00147065 0.999999i \(-0.499532\pi\)
0.00147065 + 0.999999i \(0.499532\pi\)
\(632\) 14.4964 0.576636
\(633\) −11.0578 −0.439509
\(634\) −10.9145 −0.433471
\(635\) −16.5317 −0.656042
\(636\) −8.09604 −0.321029
\(637\) −4.72917 −0.187377
\(638\) −7.25442 −0.287205
\(639\) 16.5445 0.654491
\(640\) 1.00000 0.0395285
\(641\) 22.3087 0.881139 0.440569 0.897719i \(-0.354777\pi\)
0.440569 + 0.897719i \(0.354777\pi\)
\(642\) −7.80854 −0.308178
\(643\) −31.3979 −1.23821 −0.619105 0.785308i \(-0.712505\pi\)
−0.619105 + 0.785308i \(0.712505\pi\)
\(644\) −17.8836 −0.704713
\(645\) −3.55890 −0.140131
\(646\) 40.3344 1.58694
\(647\) 44.2051 1.73788 0.868941 0.494916i \(-0.164801\pi\)
0.868941 + 0.494916i \(0.164801\pi\)
\(648\) −2.11347 −0.0830248
\(649\) 13.3377 0.523551
\(650\) 0.562082 0.0220467
\(651\) 18.4070 0.721427
\(652\) 16.4413 0.643892
\(653\) −17.4459 −0.682711 −0.341355 0.939934i \(-0.610886\pi\)
−0.341355 + 0.939934i \(0.610886\pi\)
\(654\) 7.42258 0.290246
\(655\) 10.2662 0.401135
\(656\) 6.29523 0.245787
\(657\) −8.48435 −0.331006
\(658\) −11.7655 −0.458666
\(659\) 9.85922 0.384061 0.192030 0.981389i \(-0.438493\pi\)
0.192030 + 0.981389i \(0.438493\pi\)
\(660\) 1.41903 0.0552356
\(661\) 7.32314 0.284837 0.142419 0.989807i \(-0.454512\pi\)
0.142419 + 0.989807i \(0.454512\pi\)
\(662\) 8.13592 0.316212
\(663\) −3.40787 −0.132351
\(664\) −4.99765 −0.193947
\(665\) 24.0004 0.930695
\(666\) −6.16911 −0.239048
\(667\) 21.3986 0.828558
\(668\) 3.26012 0.126138
\(669\) 16.3375 0.631643
\(670\) 1.74019 0.0672293
\(671\) −7.74795 −0.299106
\(672\) −3.60766 −0.139168
\(673\) 28.9692 1.11668 0.558341 0.829611i \(-0.311438\pi\)
0.558341 + 0.829611i \(0.311438\pi\)
\(674\) 26.1203 1.00612
\(675\) 4.73753 0.182348
\(676\) −12.6841 −0.487849
\(677\) −5.04167 −0.193767 −0.0968835 0.995296i \(-0.530887\pi\)
−0.0968835 + 0.995296i \(0.530887\pi\)
\(678\) −8.90391 −0.341953
\(679\) 18.9811 0.728428
\(680\) −6.59798 −0.253021
\(681\) 9.99530 0.383021
\(682\) −7.87910 −0.301707
\(683\) 8.39087 0.321068 0.160534 0.987030i \(-0.448678\pi\)
0.160534 + 0.987030i \(0.448678\pi\)
\(684\) −13.1776 −0.503856
\(685\) 2.55263 0.0975311
\(686\) 5.55007 0.211903
\(687\) 9.30069 0.354844
\(688\) −3.87296 −0.147655
\(689\) −4.95223 −0.188665
\(690\) −4.18576 −0.159349
\(691\) −18.7907 −0.714831 −0.357415 0.933946i \(-0.616342\pi\)
−0.357415 + 0.933946i \(0.616342\pi\)
\(692\) 17.5469 0.667035
\(693\) 13.0690 0.496450
\(694\) −4.10689 −0.155896
\(695\) −1.40272 −0.0532081
\(696\) 4.31674 0.163626
\(697\) −41.5358 −1.57328
\(698\) 25.9138 0.980851
\(699\) 7.20097 0.272366
\(700\) −3.92602 −0.148390
\(701\) 24.0207 0.907251 0.453625 0.891192i \(-0.350130\pi\)
0.453625 + 0.891192i \(0.350130\pi\)
\(702\) 2.66288 0.100504
\(703\) −17.4952 −0.659843
\(704\) 1.54426 0.0582013
\(705\) −2.75378 −0.103713
\(706\) 11.8873 0.447384
\(707\) 32.5548 1.22435
\(708\) −7.93660 −0.298276
\(709\) 40.3710 1.51616 0.758082 0.652159i \(-0.226137\pi\)
0.758082 + 0.652159i \(0.226137\pi\)
\(710\) −7.67511 −0.288042
\(711\) 31.2485 1.17191
\(712\) 14.6418 0.548723
\(713\) 23.2413 0.870393
\(714\) 23.8032 0.890814
\(715\) 0.867999 0.0324613
\(716\) −1.40640 −0.0525597
\(717\) −7.26314 −0.271247
\(718\) 12.0315 0.449013
\(719\) 1.59930 0.0596438 0.0298219 0.999555i \(-0.490506\pi\)
0.0298219 + 0.999555i \(0.490506\pi\)
\(720\) 2.15561 0.0803347
\(721\) 0.0644584 0.00240056
\(722\) −18.3706 −0.683683
\(723\) −14.3980 −0.535466
\(724\) 8.51792 0.316566
\(725\) 4.69768 0.174468
\(726\) −7.91665 −0.293814
\(727\) 39.5408 1.46649 0.733243 0.679966i \(-0.238006\pi\)
0.733243 + 0.679966i \(0.238006\pi\)
\(728\) −2.20675 −0.0817875
\(729\) 8.50427 0.314973
\(730\) 3.93595 0.145676
\(731\) 25.5537 0.945139
\(732\) 4.61042 0.170406
\(733\) −26.7411 −0.987703 −0.493852 0.869546i \(-0.664411\pi\)
−0.493852 + 0.869546i \(0.664411\pi\)
\(734\) 10.8051 0.398824
\(735\) 7.73139 0.285176
\(736\) −4.55514 −0.167905
\(737\) 2.68729 0.0989877
\(738\) 13.5700 0.499520
\(739\) 23.5912 0.867816 0.433908 0.900957i \(-0.357134\pi\)
0.433908 + 0.900957i \(0.357134\pi\)
\(740\) 2.86189 0.105205
\(741\) 3.15746 0.115992
\(742\) 34.5902 1.26985
\(743\) −17.6125 −0.646139 −0.323070 0.946375i \(-0.604715\pi\)
−0.323070 + 0.946375i \(0.604715\pi\)
\(744\) 4.68846 0.171887
\(745\) −23.7432 −0.869883
\(746\) −29.1390 −1.06685
\(747\) −10.7730 −0.394163
\(748\) −10.1890 −0.372545
\(749\) 33.3619 1.21902
\(750\) −0.918908 −0.0335538
\(751\) −22.8931 −0.835380 −0.417690 0.908590i \(-0.637160\pi\)
−0.417690 + 0.908590i \(0.637160\pi\)
\(752\) −2.99679 −0.109282
\(753\) −5.21067 −0.189887
\(754\) 2.64048 0.0961607
\(755\) 18.6292 0.677986
\(756\) −18.5997 −0.676463
\(757\) 11.8800 0.431784 0.215892 0.976417i \(-0.430734\pi\)
0.215892 + 0.976417i \(0.430734\pi\)
\(758\) 27.4798 0.998111
\(759\) −6.46388 −0.234624
\(760\) 6.11315 0.221747
\(761\) 4.84736 0.175717 0.0878584 0.996133i \(-0.471998\pi\)
0.0878584 + 0.996133i \(0.471998\pi\)
\(762\) 15.1911 0.550317
\(763\) −31.7129 −1.14808
\(764\) 0.207405 0.00750365
\(765\) −14.2226 −0.514221
\(766\) 6.59847 0.238412
\(767\) −4.85470 −0.175293
\(768\) −0.918908 −0.0331582
\(769\) −44.5829 −1.60770 −0.803849 0.594833i \(-0.797218\pi\)
−0.803849 + 0.594833i \(0.797218\pi\)
\(770\) −6.06278 −0.218488
\(771\) 5.77676 0.208045
\(772\) −18.1703 −0.653964
\(773\) −2.80103 −0.100746 −0.0503730 0.998730i \(-0.516041\pi\)
−0.0503730 + 0.998730i \(0.516041\pi\)
\(774\) −8.34859 −0.300084
\(775\) 5.10220 0.183277
\(776\) 4.83469 0.173555
\(777\) −10.3247 −0.370397
\(778\) 13.2124 0.473686
\(779\) 38.4837 1.37882
\(780\) −0.516502 −0.0184937
\(781\) −11.8523 −0.424110
\(782\) 30.0547 1.07476
\(783\) 22.2554 0.795344
\(784\) 8.41366 0.300488
\(785\) 6.43230 0.229579
\(786\) −9.43374 −0.336490
\(787\) 54.9251 1.95787 0.978934 0.204175i \(-0.0654510\pi\)
0.978934 + 0.204175i \(0.0654510\pi\)
\(788\) 12.9568 0.461566
\(789\) 26.6261 0.947915
\(790\) −14.4964 −0.515759
\(791\) 38.0419 1.35261
\(792\) 3.32881 0.118284
\(793\) 2.82012 0.100145
\(794\) −16.6594 −0.591220
\(795\) 8.09604 0.287137
\(796\) −12.2094 −0.432751
\(797\) 34.6507 1.22739 0.613696 0.789542i \(-0.289682\pi\)
0.613696 + 0.789542i \(0.289682\pi\)
\(798\) −22.0541 −0.780708
\(799\) 19.7728 0.699511
\(800\) −1.00000 −0.0353553
\(801\) 31.5619 1.11518
\(802\) 1.00000 0.0353112
\(803\) 6.07811 0.214492
\(804\) −1.59907 −0.0563949
\(805\) 17.8836 0.630314
\(806\) 2.86786 0.101016
\(807\) −20.7449 −0.730254
\(808\) 8.29206 0.291714
\(809\) 11.0131 0.387201 0.193600 0.981080i \(-0.437984\pi\)
0.193600 + 0.981080i \(0.437984\pi\)
\(810\) 2.11347 0.0742596
\(811\) 40.8479 1.43436 0.717182 0.696886i \(-0.245432\pi\)
0.717182 + 0.696886i \(0.245432\pi\)
\(812\) −18.4432 −0.647230
\(813\) 4.77175 0.167352
\(814\) 4.41949 0.154903
\(815\) −16.4413 −0.575914
\(816\) 6.06294 0.212245
\(817\) −23.6760 −0.828319
\(818\) −27.9156 −0.976045
\(819\) −4.75688 −0.166219
\(820\) −6.29523 −0.219839
\(821\) −29.8030 −1.04013 −0.520066 0.854126i \(-0.674093\pi\)
−0.520066 + 0.854126i \(0.674093\pi\)
\(822\) −2.34564 −0.0818135
\(823\) −12.8083 −0.446470 −0.223235 0.974765i \(-0.571662\pi\)
−0.223235 + 0.974765i \(0.571662\pi\)
\(824\) 0.0164182 0.000571956 0
\(825\) −1.41903 −0.0494043
\(826\) 33.9090 1.17985
\(827\) −23.1998 −0.806736 −0.403368 0.915038i \(-0.632160\pi\)
−0.403368 + 0.915038i \(0.632160\pi\)
\(828\) −9.81910 −0.341237
\(829\) 25.7076 0.892861 0.446430 0.894818i \(-0.352695\pi\)
0.446430 + 0.894818i \(0.352695\pi\)
\(830\) 4.99765 0.173471
\(831\) 4.06946 0.141168
\(832\) −0.562082 −0.0194867
\(833\) −55.5132 −1.92342
\(834\) 1.28897 0.0446334
\(835\) −3.26012 −0.112821
\(836\) 9.44027 0.326498
\(837\) 24.1718 0.835501
\(838\) −4.77625 −0.164993
\(839\) 30.1805 1.04195 0.520973 0.853573i \(-0.325569\pi\)
0.520973 + 0.853573i \(0.325569\pi\)
\(840\) 3.60766 0.124476
\(841\) −6.93178 −0.239027
\(842\) 29.3901 1.01285
\(843\) −14.1600 −0.487696
\(844\) 12.0336 0.414215
\(845\) 12.6841 0.436345
\(846\) −6.45991 −0.222096
\(847\) 33.8238 1.16220
\(848\) 8.81050 0.302554
\(849\) −2.86005 −0.0981566
\(850\) 6.59798 0.226309
\(851\) −13.0363 −0.446880
\(852\) 7.05272 0.241622
\(853\) 37.1996 1.27369 0.636845 0.770992i \(-0.280239\pi\)
0.636845 + 0.770992i \(0.280239\pi\)
\(854\) −19.6979 −0.674050
\(855\) 13.1776 0.450663
\(856\) 8.49762 0.290443
\(857\) 36.9242 1.26131 0.630653 0.776065i \(-0.282787\pi\)
0.630653 + 0.776065i \(0.282787\pi\)
\(858\) −0.797611 −0.0272300
\(859\) −40.7939 −1.39187 −0.695935 0.718105i \(-0.745010\pi\)
−0.695935 + 0.718105i \(0.745010\pi\)
\(860\) 3.87296 0.132067
\(861\) 22.7110 0.773990
\(862\) −21.6388 −0.737019
\(863\) −16.6230 −0.565855 −0.282927 0.959141i \(-0.591306\pi\)
−0.282927 + 0.959141i \(0.591306\pi\)
\(864\) −4.73753 −0.161174
\(865\) −17.5469 −0.596614
\(866\) 30.3104 1.02999
\(867\) −24.3817 −0.828045
\(868\) −20.0314 −0.679909
\(869\) −22.3861 −0.759398
\(870\) −4.31674 −0.146351
\(871\) −0.978128 −0.0331426
\(872\) −8.07761 −0.273542
\(873\) 10.4217 0.352721
\(874\) −27.8463 −0.941915
\(875\) 3.92602 0.132724
\(876\) −3.61677 −0.122199
\(877\) 49.9734 1.68748 0.843741 0.536751i \(-0.180349\pi\)
0.843741 + 0.536751i \(0.180349\pi\)
\(878\) 14.8601 0.501505
\(879\) −21.0748 −0.710834
\(880\) −1.54426 −0.0520568
\(881\) −12.2411 −0.412413 −0.206207 0.978508i \(-0.566112\pi\)
−0.206207 + 0.978508i \(0.566112\pi\)
\(882\) 18.1366 0.610690
\(883\) 37.7681 1.27100 0.635498 0.772102i \(-0.280795\pi\)
0.635498 + 0.772102i \(0.280795\pi\)
\(884\) 3.70861 0.124734
\(885\) 7.93660 0.266786
\(886\) 24.8300 0.834179
\(887\) 52.1678 1.75162 0.875811 0.482654i \(-0.160327\pi\)
0.875811 + 0.482654i \(0.160327\pi\)
\(888\) −2.62982 −0.0882508
\(889\) −64.9039 −2.17681
\(890\) −14.6418 −0.490793
\(891\) 3.26373 0.109339
\(892\) −17.7792 −0.595292
\(893\) −18.3199 −0.613051
\(894\) 21.8178 0.729697
\(895\) 1.40640 0.0470108
\(896\) 3.92602 0.131159
\(897\) 2.35274 0.0785558
\(898\) 1.04233 0.0347830
\(899\) 23.9685 0.799395
\(900\) −2.15561 −0.0718536
\(901\) −58.1315 −1.93664
\(902\) −9.72144 −0.323689
\(903\) −13.9723 −0.464970
\(904\) 9.68966 0.322273
\(905\) −8.51792 −0.283145
\(906\) −17.1185 −0.568725
\(907\) −59.4904 −1.97535 −0.987674 0.156527i \(-0.949970\pi\)
−0.987674 + 0.156527i \(0.949970\pi\)
\(908\) −10.8774 −0.360978
\(909\) 17.8744 0.592857
\(910\) 2.20675 0.0731530
\(911\) 7.66753 0.254037 0.127018 0.991900i \(-0.459459\pi\)
0.127018 + 0.991900i \(0.459459\pi\)
\(912\) −5.61743 −0.186012
\(913\) 7.71765 0.255417
\(914\) −15.2698 −0.505081
\(915\) −4.61042 −0.152416
\(916\) −10.1215 −0.334422
\(917\) 40.3055 1.33101
\(918\) 31.2581 1.03167
\(919\) 17.8523 0.588894 0.294447 0.955668i \(-0.404865\pi\)
0.294447 + 0.955668i \(0.404865\pi\)
\(920\) 4.55514 0.150179
\(921\) −8.54549 −0.281584
\(922\) 7.72789 0.254505
\(923\) 4.31404 0.141998
\(924\) 5.57114 0.183277
\(925\) −2.86189 −0.0940984
\(926\) 24.4397 0.803140
\(927\) 0.0353913 0.00116240
\(928\) −4.69768 −0.154209
\(929\) 15.2945 0.501796 0.250898 0.968014i \(-0.419274\pi\)
0.250898 + 0.968014i \(0.419274\pi\)
\(930\) −4.68846 −0.153741
\(931\) 51.4340 1.68568
\(932\) −7.83644 −0.256691
\(933\) 15.3263 0.501762
\(934\) 30.9905 1.01404
\(935\) 10.1890 0.333215
\(936\) −1.21163 −0.0396033
\(937\) −11.8289 −0.386433 −0.193217 0.981156i \(-0.561892\pi\)
−0.193217 + 0.981156i \(0.561892\pi\)
\(938\) 6.83201 0.223073
\(939\) −6.49892 −0.212084
\(940\) 2.99679 0.0977447
\(941\) −47.0046 −1.53231 −0.766153 0.642658i \(-0.777832\pi\)
−0.766153 + 0.642658i \(0.777832\pi\)
\(942\) −5.91070 −0.192581
\(943\) 28.6757 0.933809
\(944\) 8.63699 0.281110
\(945\) 18.5997 0.605047
\(946\) 5.98084 0.194454
\(947\) −58.9092 −1.91429 −0.957146 0.289607i \(-0.906475\pi\)
−0.957146 + 0.289607i \(0.906475\pi\)
\(948\) 13.3209 0.432641
\(949\) −2.21233 −0.0718151
\(950\) −6.11315 −0.198337
\(951\) −10.0295 −0.325227
\(952\) −25.9038 −0.839548
\(953\) 13.5554 0.439103 0.219551 0.975601i \(-0.429541\pi\)
0.219551 + 0.975601i \(0.429541\pi\)
\(954\) 18.9920 0.614888
\(955\) −0.207405 −0.00671147
\(956\) 7.90410 0.255637
\(957\) −6.66615 −0.215486
\(958\) 22.0256 0.711616
\(959\) 10.0217 0.323618
\(960\) 0.918908 0.0296576
\(961\) −4.96752 −0.160243
\(962\) −1.60862 −0.0518639
\(963\) 18.3175 0.590274
\(964\) 15.6685 0.504650
\(965\) 18.1703 0.584923
\(966\) −16.4334 −0.528736
\(967\) −23.0039 −0.739756 −0.369878 0.929080i \(-0.620600\pi\)
−0.369878 + 0.929080i \(0.620600\pi\)
\(968\) 8.61527 0.276905
\(969\) 37.0636 1.19066
\(970\) −4.83469 −0.155232
\(971\) 23.0033 0.738212 0.369106 0.929387i \(-0.379664\pi\)
0.369106 + 0.929387i \(0.379664\pi\)
\(972\) −16.1547 −0.518161
\(973\) −5.50711 −0.176550
\(974\) 21.0036 0.673000
\(975\) 0.516502 0.0165413
\(976\) −5.01728 −0.160599
\(977\) 38.8437 1.24272 0.621361 0.783525i \(-0.286580\pi\)
0.621361 + 0.783525i \(0.286580\pi\)
\(978\) 15.1081 0.483103
\(979\) −22.6106 −0.722638
\(980\) −8.41366 −0.268765
\(981\) −17.4122 −0.555927
\(982\) −0.318350 −0.0101589
\(983\) 12.6053 0.402047 0.201024 0.979586i \(-0.435573\pi\)
0.201024 + 0.979586i \(0.435573\pi\)
\(984\) 5.78474 0.184411
\(985\) −12.9568 −0.412837
\(986\) 30.9952 0.987088
\(987\) −10.8114 −0.344131
\(988\) −3.43609 −0.109317
\(989\) −17.6419 −0.560980
\(990\) −3.32881 −0.105796
\(991\) −54.7272 −1.73847 −0.869234 0.494401i \(-0.835388\pi\)
−0.869234 + 0.494401i \(0.835388\pi\)
\(992\) −5.10220 −0.161995
\(993\) 7.47617 0.237249
\(994\) −30.1327 −0.955750
\(995\) 12.2094 0.387065
\(996\) −4.59239 −0.145515
\(997\) −4.45414 −0.141064 −0.0705321 0.997510i \(-0.522470\pi\)
−0.0705321 + 0.997510i \(0.522470\pi\)
\(998\) −0.281372 −0.00890666
\(999\) −13.5583 −0.428966
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 \(a_p\))