Properties

Label 6027.2.a.bk.1.9
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-0.712717\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.712717 q^{2} +1.00000 q^{3} -1.49203 q^{4} -0.415066 q^{5} +0.712717 q^{6} -2.48883 q^{8} +1.00000 q^{9} -0.295824 q^{10} +2.75935 q^{11} -1.49203 q^{12} -4.20250 q^{13} -0.415066 q^{15} +1.21024 q^{16} +4.39412 q^{17} +0.712717 q^{18} -1.26769 q^{19} +0.619292 q^{20} +1.96663 q^{22} +4.53011 q^{23} -2.48883 q^{24} -4.82772 q^{25} -2.99519 q^{26} +1.00000 q^{27} -5.42809 q^{29} -0.295824 q^{30} -8.86379 q^{31} +5.84022 q^{32} +2.75935 q^{33} +3.13176 q^{34} -1.49203 q^{36} -2.60043 q^{37} -0.903505 q^{38} -4.20250 q^{39} +1.03303 q^{40} -1.00000 q^{41} +4.38379 q^{43} -4.11704 q^{44} -0.415066 q^{45} +3.22869 q^{46} +10.9478 q^{47} +1.21024 q^{48} -3.44080 q^{50} +4.39412 q^{51} +6.27028 q^{52} -2.30090 q^{53} +0.712717 q^{54} -1.14531 q^{55} -1.26769 q^{57} -3.86869 q^{58} -1.43254 q^{59} +0.619292 q^{60} -12.2775 q^{61} -6.31737 q^{62} +1.74195 q^{64} +1.74431 q^{65} +1.96663 q^{66} -1.10634 q^{67} -6.55618 q^{68} +4.53011 q^{69} +2.83634 q^{71} -2.48883 q^{72} -3.91272 q^{73} -1.85337 q^{74} -4.82772 q^{75} +1.89144 q^{76} -2.99519 q^{78} -15.3997 q^{79} -0.502327 q^{80} +1.00000 q^{81} -0.712717 q^{82} +4.04351 q^{83} -1.82385 q^{85} +3.12440 q^{86} -5.42809 q^{87} -6.86756 q^{88} +1.02847 q^{89} -0.295824 q^{90} -6.75908 q^{92} -8.86379 q^{93} +7.80271 q^{94} +0.526175 q^{95} +5.84022 q^{96} +7.88278 q^{97} +2.75935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.712717 0.503967 0.251983 0.967732i \(-0.418917\pi\)
0.251983 + 0.967732i \(0.418917\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.49203 −0.746017
\(5\) −0.415066 −0.185623 −0.0928115 0.995684i \(-0.529585\pi\)
−0.0928115 + 0.995684i \(0.529585\pi\)
\(6\) 0.712717 0.290965
\(7\) 0 0
\(8\) −2.48883 −0.879935
\(9\) 1.00000 0.333333
\(10\) −0.295824 −0.0935479
\(11\) 2.75935 0.831975 0.415988 0.909370i \(-0.363436\pi\)
0.415988 + 0.909370i \(0.363436\pi\)
\(12\) −1.49203 −0.430713
\(13\) −4.20250 −1.16556 −0.582782 0.812628i \(-0.698036\pi\)
−0.582782 + 0.812628i \(0.698036\pi\)
\(14\) 0 0
\(15\) −0.415066 −0.107169
\(16\) 1.21024 0.302559
\(17\) 4.39412 1.06573 0.532865 0.846200i \(-0.321115\pi\)
0.532865 + 0.846200i \(0.321115\pi\)
\(18\) 0.712717 0.167989
\(19\) −1.26769 −0.290828 −0.145414 0.989371i \(-0.546451\pi\)
−0.145414 + 0.989371i \(0.546451\pi\)
\(20\) 0.619292 0.138478
\(21\) 0 0
\(22\) 1.96663 0.419288
\(23\) 4.53011 0.944594 0.472297 0.881440i \(-0.343425\pi\)
0.472297 + 0.881440i \(0.343425\pi\)
\(24\) −2.48883 −0.508031
\(25\) −4.82772 −0.965544
\(26\) −2.99519 −0.587406
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.42809 −1.00797 −0.503985 0.863712i \(-0.668133\pi\)
−0.503985 + 0.863712i \(0.668133\pi\)
\(30\) −0.295824 −0.0540099
\(31\) −8.86379 −1.59198 −0.795992 0.605307i \(-0.793050\pi\)
−0.795992 + 0.605307i \(0.793050\pi\)
\(32\) 5.84022 1.03241
\(33\) 2.75935 0.480341
\(34\) 3.13176 0.537093
\(35\) 0 0
\(36\) −1.49203 −0.248672
\(37\) −2.60043 −0.427508 −0.213754 0.976887i \(-0.568569\pi\)
−0.213754 + 0.976887i \(0.568569\pi\)
\(38\) −0.903505 −0.146568
\(39\) −4.20250 −0.672939
\(40\) 1.03303 0.163336
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 4.38379 0.668522 0.334261 0.942480i \(-0.391513\pi\)
0.334261 + 0.942480i \(0.391513\pi\)
\(44\) −4.11704 −0.620668
\(45\) −0.415066 −0.0618743
\(46\) 3.22869 0.476044
\(47\) 10.9478 1.59691 0.798453 0.602057i \(-0.205652\pi\)
0.798453 + 0.602057i \(0.205652\pi\)
\(48\) 1.21024 0.174683
\(49\) 0 0
\(50\) −3.44080 −0.486602
\(51\) 4.39412 0.615300
\(52\) 6.27028 0.869531
\(53\) −2.30090 −0.316053 −0.158027 0.987435i \(-0.550513\pi\)
−0.158027 + 0.987435i \(0.550513\pi\)
\(54\) 0.712717 0.0969885
\(55\) −1.14531 −0.154434
\(56\) 0 0
\(57\) −1.26769 −0.167910
\(58\) −3.86869 −0.507984
\(59\) −1.43254 −0.186501 −0.0932506 0.995643i \(-0.529726\pi\)
−0.0932506 + 0.995643i \(0.529726\pi\)
\(60\) 0.619292 0.0799503
\(61\) −12.2775 −1.57197 −0.785986 0.618245i \(-0.787844\pi\)
−0.785986 + 0.618245i \(0.787844\pi\)
\(62\) −6.31737 −0.802307
\(63\) 0 0
\(64\) 1.74195 0.217744
\(65\) 1.74431 0.216356
\(66\) 1.96663 0.242076
\(67\) −1.10634 −0.135161 −0.0675806 0.997714i \(-0.521528\pi\)
−0.0675806 + 0.997714i \(0.521528\pi\)
\(68\) −6.55618 −0.795054
\(69\) 4.53011 0.545361
\(70\) 0 0
\(71\) 2.83634 0.336611 0.168306 0.985735i \(-0.446170\pi\)
0.168306 + 0.985735i \(0.446170\pi\)
\(72\) −2.48883 −0.293312
\(73\) −3.91272 −0.457949 −0.228975 0.973432i \(-0.573537\pi\)
−0.228975 + 0.973432i \(0.573537\pi\)
\(74\) −1.85337 −0.215450
\(75\) −4.82772 −0.557457
\(76\) 1.89144 0.216963
\(77\) 0 0
\(78\) −2.99519 −0.339139
\(79\) −15.3997 −1.73260 −0.866298 0.499527i \(-0.833507\pi\)
−0.866298 + 0.499527i \(0.833507\pi\)
\(80\) −0.502327 −0.0561619
\(81\) 1.00000 0.111111
\(82\) −0.712717 −0.0787064
\(83\) 4.04351 0.443833 0.221916 0.975066i \(-0.428769\pi\)
0.221916 + 0.975066i \(0.428769\pi\)
\(84\) 0 0
\(85\) −1.82385 −0.197824
\(86\) 3.12440 0.336913
\(87\) −5.42809 −0.581952
\(88\) −6.86756 −0.732084
\(89\) 1.02847 0.109018 0.0545090 0.998513i \(-0.482641\pi\)
0.0545090 + 0.998513i \(0.482641\pi\)
\(90\) −0.295824 −0.0311826
\(91\) 0 0
\(92\) −6.75908 −0.704683
\(93\) −8.86379 −0.919132
\(94\) 7.80271 0.804788
\(95\) 0.526175 0.0539844
\(96\) 5.84022 0.596065
\(97\) 7.88278 0.800375 0.400187 0.916433i \(-0.368945\pi\)
0.400187 + 0.916433i \(0.368945\pi\)
\(98\) 0 0
\(99\) 2.75935 0.277325
\(100\) 7.20313 0.720313
\(101\) 8.38909 0.834746 0.417373 0.908735i \(-0.362951\pi\)
0.417373 + 0.908735i \(0.362951\pi\)
\(102\) 3.13176 0.310091
\(103\) −17.2901 −1.70365 −0.851823 0.523830i \(-0.824503\pi\)
−0.851823 + 0.523830i \(0.824503\pi\)
\(104\) 10.4593 1.02562
\(105\) 0 0
\(106\) −1.63989 −0.159281
\(107\) −9.58485 −0.926602 −0.463301 0.886201i \(-0.653335\pi\)
−0.463301 + 0.886201i \(0.653335\pi\)
\(108\) −1.49203 −0.143571
\(109\) −0.616655 −0.0590648 −0.0295324 0.999564i \(-0.509402\pi\)
−0.0295324 + 0.999564i \(0.509402\pi\)
\(110\) −0.816283 −0.0778295
\(111\) −2.60043 −0.246822
\(112\) 0 0
\(113\) 14.7844 1.39080 0.695401 0.718622i \(-0.255227\pi\)
0.695401 + 0.718622i \(0.255227\pi\)
\(114\) −0.903505 −0.0846210
\(115\) −1.88029 −0.175338
\(116\) 8.09889 0.751963
\(117\) −4.20250 −0.388521
\(118\) −1.02100 −0.0939904
\(119\) 0 0
\(120\) 1.03303 0.0943022
\(121\) −3.38599 −0.307817
\(122\) −8.75037 −0.792222
\(123\) −1.00000 −0.0901670
\(124\) 13.2251 1.18765
\(125\) 4.07915 0.364850
\(126\) 0 0
\(127\) 17.0528 1.51319 0.756594 0.653885i \(-0.226862\pi\)
0.756594 + 0.653885i \(0.226862\pi\)
\(128\) −10.4389 −0.922679
\(129\) 4.38379 0.385972
\(130\) 1.24320 0.109036
\(131\) −22.2167 −1.94108 −0.970540 0.240939i \(-0.922544\pi\)
−0.970540 + 0.240939i \(0.922544\pi\)
\(132\) −4.11704 −0.358343
\(133\) 0 0
\(134\) −0.788509 −0.0681168
\(135\) −0.415066 −0.0357232
\(136\) −10.9362 −0.937774
\(137\) 8.05455 0.688147 0.344073 0.938943i \(-0.388193\pi\)
0.344073 + 0.938943i \(0.388193\pi\)
\(138\) 3.22869 0.274844
\(139\) −22.4539 −1.90451 −0.952257 0.305299i \(-0.901244\pi\)
−0.952257 + 0.305299i \(0.901244\pi\)
\(140\) 0 0
\(141\) 10.9478 0.921974
\(142\) 2.02150 0.169641
\(143\) −11.5962 −0.969721
\(144\) 1.21024 0.100853
\(145\) 2.25301 0.187103
\(146\) −2.78866 −0.230791
\(147\) 0 0
\(148\) 3.87993 0.318929
\(149\) −5.09508 −0.417405 −0.208702 0.977979i \(-0.566924\pi\)
−0.208702 + 0.977979i \(0.566924\pi\)
\(150\) −3.44080 −0.280940
\(151\) −17.6500 −1.43634 −0.718168 0.695870i \(-0.755019\pi\)
−0.718168 + 0.695870i \(0.755019\pi\)
\(152\) 3.15507 0.255910
\(153\) 4.39412 0.355244
\(154\) 0 0
\(155\) 3.67906 0.295509
\(156\) 6.27028 0.502024
\(157\) 5.78121 0.461391 0.230695 0.973026i \(-0.425900\pi\)
0.230695 + 0.973026i \(0.425900\pi\)
\(158\) −10.9756 −0.873172
\(159\) −2.30090 −0.182474
\(160\) −2.42407 −0.191640
\(161\) 0 0
\(162\) 0.712717 0.0559963
\(163\) −0.157705 −0.0123524 −0.00617621 0.999981i \(-0.501966\pi\)
−0.00617621 + 0.999981i \(0.501966\pi\)
\(164\) 1.49203 0.116508
\(165\) −1.14531 −0.0891623
\(166\) 2.88188 0.223677
\(167\) −22.1528 −1.71424 −0.857118 0.515120i \(-0.827747\pi\)
−0.857118 + 0.515120i \(0.827747\pi\)
\(168\) 0 0
\(169\) 4.66102 0.358540
\(170\) −1.29989 −0.0996969
\(171\) −1.26769 −0.0969428
\(172\) −6.54077 −0.498729
\(173\) −18.2812 −1.38989 −0.694947 0.719061i \(-0.744572\pi\)
−0.694947 + 0.719061i \(0.744572\pi\)
\(174\) −3.86869 −0.293285
\(175\) 0 0
\(176\) 3.33946 0.251722
\(177\) −1.43254 −0.107677
\(178\) 0.733010 0.0549414
\(179\) −19.7583 −1.47680 −0.738402 0.674361i \(-0.764419\pi\)
−0.738402 + 0.674361i \(0.764419\pi\)
\(180\) 0.619292 0.0461593
\(181\) −13.0870 −0.972748 −0.486374 0.873751i \(-0.661681\pi\)
−0.486374 + 0.873751i \(0.661681\pi\)
\(182\) 0 0
\(183\) −12.2775 −0.907578
\(184\) −11.2747 −0.831181
\(185\) 1.07935 0.0793554
\(186\) −6.31737 −0.463212
\(187\) 12.1249 0.886661
\(188\) −16.3345 −1.19132
\(189\) 0 0
\(190\) 0.375014 0.0272064
\(191\) −22.8221 −1.65135 −0.825675 0.564146i \(-0.809205\pi\)
−0.825675 + 0.564146i \(0.809205\pi\)
\(192\) 1.74195 0.125715
\(193\) 13.0794 0.941472 0.470736 0.882274i \(-0.343988\pi\)
0.470736 + 0.882274i \(0.343988\pi\)
\(194\) 5.61819 0.403362
\(195\) 1.74431 0.124913
\(196\) 0 0
\(197\) −0.844299 −0.0601538 −0.0300769 0.999548i \(-0.509575\pi\)
−0.0300769 + 0.999548i \(0.509575\pi\)
\(198\) 1.96663 0.139763
\(199\) −8.12795 −0.576175 −0.288088 0.957604i \(-0.593019\pi\)
−0.288088 + 0.957604i \(0.593019\pi\)
\(200\) 12.0154 0.849616
\(201\) −1.10634 −0.0780353
\(202\) 5.97905 0.420684
\(203\) 0 0
\(204\) −6.55618 −0.459024
\(205\) 0.415066 0.0289894
\(206\) −12.3230 −0.858581
\(207\) 4.53011 0.314865
\(208\) −5.08602 −0.352652
\(209\) −3.49800 −0.241962
\(210\) 0 0
\(211\) 11.6549 0.802357 0.401178 0.916000i \(-0.368601\pi\)
0.401178 + 0.916000i \(0.368601\pi\)
\(212\) 3.43303 0.235781
\(213\) 2.83634 0.194342
\(214\) −6.83128 −0.466977
\(215\) −1.81956 −0.124093
\(216\) −2.48883 −0.169344
\(217\) 0 0
\(218\) −0.439500 −0.0297667
\(219\) −3.91272 −0.264397
\(220\) 1.70884 0.115210
\(221\) −18.4663 −1.24218
\(222\) −1.85337 −0.124390
\(223\) −11.7288 −0.785416 −0.392708 0.919663i \(-0.628462\pi\)
−0.392708 + 0.919663i \(0.628462\pi\)
\(224\) 0 0
\(225\) −4.82772 −0.321848
\(226\) 10.5371 0.700919
\(227\) 1.94495 0.129091 0.0645455 0.997915i \(-0.479440\pi\)
0.0645455 + 0.997915i \(0.479440\pi\)
\(228\) 1.89144 0.125264
\(229\) −11.2389 −0.742686 −0.371343 0.928496i \(-0.621103\pi\)
−0.371343 + 0.928496i \(0.621103\pi\)
\(230\) −1.34012 −0.0883647
\(231\) 0 0
\(232\) 13.5096 0.886949
\(233\) 13.3117 0.872079 0.436039 0.899928i \(-0.356381\pi\)
0.436039 + 0.899928i \(0.356381\pi\)
\(234\) −2.99519 −0.195802
\(235\) −4.54407 −0.296423
\(236\) 2.13740 0.139133
\(237\) −15.3997 −1.00032
\(238\) 0 0
\(239\) 15.1521 0.980106 0.490053 0.871693i \(-0.336977\pi\)
0.490053 + 0.871693i \(0.336977\pi\)
\(240\) −0.502327 −0.0324251
\(241\) −25.5139 −1.64350 −0.821749 0.569850i \(-0.807001\pi\)
−0.821749 + 0.569850i \(0.807001\pi\)
\(242\) −2.41325 −0.155130
\(243\) 1.00000 0.0641500
\(244\) 18.3184 1.17272
\(245\) 0 0
\(246\) −0.712717 −0.0454412
\(247\) 5.32748 0.338979
\(248\) 22.0605 1.40084
\(249\) 4.04351 0.256247
\(250\) 2.90728 0.183872
\(251\) −9.41888 −0.594514 −0.297257 0.954797i \(-0.596072\pi\)
−0.297257 + 0.954797i \(0.596072\pi\)
\(252\) 0 0
\(253\) 12.5002 0.785878
\(254\) 12.1538 0.762597
\(255\) −1.82385 −0.114214
\(256\) −10.9239 −0.682744
\(257\) −1.07261 −0.0669075 −0.0334537 0.999440i \(-0.510651\pi\)
−0.0334537 + 0.999440i \(0.510651\pi\)
\(258\) 3.12440 0.194517
\(259\) 0 0
\(260\) −2.60258 −0.161405
\(261\) −5.42809 −0.335990
\(262\) −15.8342 −0.978240
\(263\) 26.2752 1.62020 0.810100 0.586292i \(-0.199413\pi\)
0.810100 + 0.586292i \(0.199413\pi\)
\(264\) −6.86756 −0.422669
\(265\) 0.955026 0.0586668
\(266\) 0 0
\(267\) 1.02847 0.0629415
\(268\) 1.65070 0.100833
\(269\) −19.8799 −1.21210 −0.606049 0.795427i \(-0.707247\pi\)
−0.606049 + 0.795427i \(0.707247\pi\)
\(270\) −0.295824 −0.0180033
\(271\) 15.1791 0.922062 0.461031 0.887384i \(-0.347480\pi\)
0.461031 + 0.887384i \(0.347480\pi\)
\(272\) 5.31792 0.322446
\(273\) 0 0
\(274\) 5.74062 0.346803
\(275\) −13.3214 −0.803309
\(276\) −6.75908 −0.406849
\(277\) 14.8072 0.889681 0.444840 0.895610i \(-0.353260\pi\)
0.444840 + 0.895610i \(0.353260\pi\)
\(278\) −16.0033 −0.959812
\(279\) −8.86379 −0.530661
\(280\) 0 0
\(281\) 12.5292 0.747429 0.373715 0.927544i \(-0.378084\pi\)
0.373715 + 0.927544i \(0.378084\pi\)
\(282\) 7.80271 0.464645
\(283\) −0.286081 −0.0170058 −0.00850289 0.999964i \(-0.502707\pi\)
−0.00850289 + 0.999964i \(0.502707\pi\)
\(284\) −4.23191 −0.251118
\(285\) 0.526175 0.0311679
\(286\) −8.26479 −0.488707
\(287\) 0 0
\(288\) 5.84022 0.344138
\(289\) 2.30830 0.135782
\(290\) 1.60576 0.0942935
\(291\) 7.88278 0.462096
\(292\) 5.83792 0.341638
\(293\) −16.1124 −0.941299 −0.470650 0.882320i \(-0.655980\pi\)
−0.470650 + 0.882320i \(0.655980\pi\)
\(294\) 0 0
\(295\) 0.594599 0.0346189
\(296\) 6.47204 0.376180
\(297\) 2.75935 0.160114
\(298\) −3.63135 −0.210358
\(299\) −19.0378 −1.10098
\(300\) 7.20313 0.415873
\(301\) 0 0
\(302\) −12.5794 −0.723866
\(303\) 8.38909 0.481941
\(304\) −1.53421 −0.0879927
\(305\) 5.09596 0.291794
\(306\) 3.13176 0.179031
\(307\) 8.82967 0.503936 0.251968 0.967736i \(-0.418922\pi\)
0.251968 + 0.967736i \(0.418922\pi\)
\(308\) 0 0
\(309\) −17.2901 −0.983600
\(310\) 2.62213 0.148927
\(311\) −6.70085 −0.379971 −0.189985 0.981787i \(-0.560844\pi\)
−0.189985 + 0.981787i \(0.560844\pi\)
\(312\) 10.4593 0.592143
\(313\) −2.34758 −0.132693 −0.0663465 0.997797i \(-0.521134\pi\)
−0.0663465 + 0.997797i \(0.521134\pi\)
\(314\) 4.12037 0.232526
\(315\) 0 0
\(316\) 22.9768 1.29255
\(317\) 22.8746 1.28477 0.642384 0.766383i \(-0.277945\pi\)
0.642384 + 0.766383i \(0.277945\pi\)
\(318\) −1.63989 −0.0919606
\(319\) −14.9780 −0.838606
\(320\) −0.723024 −0.0404183
\(321\) −9.58485 −0.534974
\(322\) 0 0
\(323\) −5.57039 −0.309945
\(324\) −1.49203 −0.0828908
\(325\) 20.2885 1.12540
\(326\) −0.112399 −0.00622521
\(327\) −0.616655 −0.0341011
\(328\) 2.48883 0.137423
\(329\) 0 0
\(330\) −0.816283 −0.0449349
\(331\) −10.6287 −0.584209 −0.292104 0.956386i \(-0.594355\pi\)
−0.292104 + 0.956386i \(0.594355\pi\)
\(332\) −6.03306 −0.331107
\(333\) −2.60043 −0.142503
\(334\) −15.7887 −0.863918
\(335\) 0.459205 0.0250890
\(336\) 0 0
\(337\) −16.0676 −0.875259 −0.437630 0.899155i \(-0.644182\pi\)
−0.437630 + 0.899155i \(0.644182\pi\)
\(338\) 3.32199 0.180692
\(339\) 14.7844 0.802980
\(340\) 2.72125 0.147580
\(341\) −24.4583 −1.32449
\(342\) −0.903505 −0.0488560
\(343\) 0 0
\(344\) −10.9105 −0.588256
\(345\) −1.88029 −0.101232
\(346\) −13.0293 −0.700460
\(347\) 31.3886 1.68503 0.842515 0.538674i \(-0.181074\pi\)
0.842515 + 0.538674i \(0.181074\pi\)
\(348\) 8.09889 0.434146
\(349\) 24.1638 1.29346 0.646728 0.762720i \(-0.276137\pi\)
0.646728 + 0.762720i \(0.276137\pi\)
\(350\) 0 0
\(351\) −4.20250 −0.224313
\(352\) 16.1152 0.858943
\(353\) 26.2342 1.39631 0.698153 0.715949i \(-0.254006\pi\)
0.698153 + 0.715949i \(0.254006\pi\)
\(354\) −1.02100 −0.0542654
\(355\) −1.17727 −0.0624828
\(356\) −1.53452 −0.0813293
\(357\) 0 0
\(358\) −14.0821 −0.744260
\(359\) 20.7642 1.09589 0.547945 0.836514i \(-0.315410\pi\)
0.547945 + 0.836514i \(0.315410\pi\)
\(360\) 1.03303 0.0544454
\(361\) −17.3930 −0.915419
\(362\) −9.32732 −0.490233
\(363\) −3.38599 −0.177718
\(364\) 0 0
\(365\) 1.62404 0.0850060
\(366\) −8.75037 −0.457389
\(367\) −25.4996 −1.33107 −0.665534 0.746368i \(-0.731796\pi\)
−0.665534 + 0.746368i \(0.731796\pi\)
\(368\) 5.48250 0.285795
\(369\) −1.00000 −0.0520579
\(370\) 0.769271 0.0399925
\(371\) 0 0
\(372\) 13.2251 0.685689
\(373\) −24.8633 −1.28737 −0.643685 0.765290i \(-0.722595\pi\)
−0.643685 + 0.765290i \(0.722595\pi\)
\(374\) 8.64163 0.446848
\(375\) 4.07915 0.210646
\(376\) −27.2473 −1.40517
\(377\) 22.8115 1.17485
\(378\) 0 0
\(379\) 15.7940 0.811285 0.405642 0.914032i \(-0.367048\pi\)
0.405642 + 0.914032i \(0.367048\pi\)
\(380\) −0.785072 −0.0402733
\(381\) 17.0528 0.873639
\(382\) −16.2657 −0.832226
\(383\) −13.6516 −0.697563 −0.348781 0.937204i \(-0.613404\pi\)
−0.348781 + 0.937204i \(0.613404\pi\)
\(384\) −10.4389 −0.532709
\(385\) 0 0
\(386\) 9.32188 0.474471
\(387\) 4.38379 0.222841
\(388\) −11.7614 −0.597093
\(389\) −15.8822 −0.805260 −0.402630 0.915363i \(-0.631904\pi\)
−0.402630 + 0.915363i \(0.631904\pi\)
\(390\) 1.24320 0.0629520
\(391\) 19.9059 1.00668
\(392\) 0 0
\(393\) −22.2167 −1.12068
\(394\) −0.601746 −0.0303155
\(395\) 6.39187 0.321610
\(396\) −4.11704 −0.206889
\(397\) 0.506673 0.0254292 0.0127146 0.999919i \(-0.495953\pi\)
0.0127146 + 0.999919i \(0.495953\pi\)
\(398\) −5.79293 −0.290373
\(399\) 0 0
\(400\) −5.84268 −0.292134
\(401\) −11.8880 −0.593660 −0.296830 0.954930i \(-0.595929\pi\)
−0.296830 + 0.954930i \(0.595929\pi\)
\(402\) −0.788509 −0.0393272
\(403\) 37.2501 1.85556
\(404\) −12.5168 −0.622735
\(405\) −0.415066 −0.0206248
\(406\) 0 0
\(407\) −7.17550 −0.355676
\(408\) −10.9362 −0.541424
\(409\) −27.4784 −1.35872 −0.679359 0.733806i \(-0.737742\pi\)
−0.679359 + 0.733806i \(0.737742\pi\)
\(410\) 0.295824 0.0146097
\(411\) 8.05455 0.397302
\(412\) 25.7974 1.27095
\(413\) 0 0
\(414\) 3.22869 0.158681
\(415\) −1.67832 −0.0823856
\(416\) −24.5435 −1.20335
\(417\) −22.4539 −1.09957
\(418\) −2.49309 −0.121941
\(419\) 3.97916 0.194394 0.0971972 0.995265i \(-0.469012\pi\)
0.0971972 + 0.995265i \(0.469012\pi\)
\(420\) 0 0
\(421\) −10.5438 −0.513874 −0.256937 0.966428i \(-0.582713\pi\)
−0.256937 + 0.966428i \(0.582713\pi\)
\(422\) 8.30665 0.404361
\(423\) 10.9478 0.532302
\(424\) 5.72656 0.278107
\(425\) −21.2136 −1.02901
\(426\) 2.02150 0.0979422
\(427\) 0 0
\(428\) 14.3009 0.691261
\(429\) −11.5962 −0.559868
\(430\) −1.29683 −0.0625389
\(431\) −14.7089 −0.708503 −0.354252 0.935150i \(-0.615264\pi\)
−0.354252 + 0.935150i \(0.615264\pi\)
\(432\) 1.21024 0.0582275
\(433\) −4.20424 −0.202043 −0.101021 0.994884i \(-0.532211\pi\)
−0.101021 + 0.994884i \(0.532211\pi\)
\(434\) 0 0
\(435\) 2.25301 0.108024
\(436\) 0.920070 0.0440634
\(437\) −5.74278 −0.274715
\(438\) −2.78866 −0.133247
\(439\) 9.46738 0.451854 0.225927 0.974144i \(-0.427459\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(440\) 2.85049 0.135892
\(441\) 0 0
\(442\) −13.1612 −0.626017
\(443\) −14.5808 −0.692753 −0.346377 0.938096i \(-0.612588\pi\)
−0.346377 + 0.938096i \(0.612588\pi\)
\(444\) 3.87993 0.184134
\(445\) −0.426884 −0.0202362
\(446\) −8.35929 −0.395824
\(447\) −5.09508 −0.240989
\(448\) 0 0
\(449\) 20.0362 0.945567 0.472783 0.881179i \(-0.343249\pi\)
0.472783 + 0.881179i \(0.343249\pi\)
\(450\) −3.44080 −0.162201
\(451\) −2.75935 −0.129933
\(452\) −22.0589 −1.03756
\(453\) −17.6500 −0.829269
\(454\) 1.38620 0.0650576
\(455\) 0 0
\(456\) 3.15507 0.147750
\(457\) 27.5760 1.28995 0.644975 0.764204i \(-0.276868\pi\)
0.644975 + 0.764204i \(0.276868\pi\)
\(458\) −8.01014 −0.374289
\(459\) 4.39412 0.205100
\(460\) 2.80546 0.130805
\(461\) 27.9697 1.30268 0.651340 0.758786i \(-0.274207\pi\)
0.651340 + 0.758786i \(0.274207\pi\)
\(462\) 0 0
\(463\) 8.96307 0.416549 0.208275 0.978070i \(-0.433215\pi\)
0.208275 + 0.978070i \(0.433215\pi\)
\(464\) −6.56927 −0.304971
\(465\) 3.67906 0.170612
\(466\) 9.48748 0.439499
\(467\) 20.6797 0.956944 0.478472 0.878103i \(-0.341191\pi\)
0.478472 + 0.878103i \(0.341191\pi\)
\(468\) 6.27028 0.289844
\(469\) 0 0
\(470\) −3.23864 −0.149387
\(471\) 5.78121 0.266384
\(472\) 3.56536 0.164109
\(473\) 12.0964 0.556194
\(474\) −10.9756 −0.504126
\(475\) 6.12006 0.280808
\(476\) 0 0
\(477\) −2.30090 −0.105351
\(478\) 10.7991 0.493941
\(479\) −0.0182962 −0.000835976 0 −0.000417988 1.00000i \(-0.500133\pi\)
−0.000417988 1.00000i \(0.500133\pi\)
\(480\) −2.42407 −0.110643
\(481\) 10.9283 0.498289
\(482\) −18.1842 −0.828268
\(483\) 0 0
\(484\) 5.05202 0.229637
\(485\) −3.27187 −0.148568
\(486\) 0.712717 0.0323295
\(487\) 26.5955 1.20516 0.602579 0.798059i \(-0.294140\pi\)
0.602579 + 0.798059i \(0.294140\pi\)
\(488\) 30.5566 1.38323
\(489\) −0.157705 −0.00713168
\(490\) 0 0
\(491\) −26.4915 −1.19555 −0.597773 0.801665i \(-0.703948\pi\)
−0.597773 + 0.801665i \(0.703948\pi\)
\(492\) 1.49203 0.0672661
\(493\) −23.8517 −1.07423
\(494\) 3.79698 0.170834
\(495\) −1.14531 −0.0514779
\(496\) −10.7273 −0.481669
\(497\) 0 0
\(498\) 2.88188 0.129140
\(499\) −2.14122 −0.0958541 −0.0479270 0.998851i \(-0.515261\pi\)
−0.0479270 + 0.998851i \(0.515261\pi\)
\(500\) −6.08623 −0.272185
\(501\) −22.1528 −0.989715
\(502\) −6.71299 −0.299616
\(503\) 14.0491 0.626417 0.313209 0.949684i \(-0.398596\pi\)
0.313209 + 0.949684i \(0.398596\pi\)
\(504\) 0 0
\(505\) −3.48203 −0.154948
\(506\) 8.90908 0.396057
\(507\) 4.66102 0.207003
\(508\) −25.4433 −1.12886
\(509\) −8.88531 −0.393834 −0.196917 0.980420i \(-0.563093\pi\)
−0.196917 + 0.980420i \(0.563093\pi\)
\(510\) −1.29989 −0.0575600
\(511\) 0 0
\(512\) 13.0922 0.578599
\(513\) −1.26769 −0.0559699
\(514\) −0.764466 −0.0337192
\(515\) 7.17653 0.316236
\(516\) −6.54077 −0.287941
\(517\) 30.2089 1.32859
\(518\) 0 0
\(519\) −18.2812 −0.802455
\(520\) −4.34131 −0.190379
\(521\) 12.9008 0.565194 0.282597 0.959239i \(-0.408804\pi\)
0.282597 + 0.959239i \(0.408804\pi\)
\(522\) −3.86869 −0.169328
\(523\) −8.93640 −0.390762 −0.195381 0.980727i \(-0.562594\pi\)
−0.195381 + 0.980727i \(0.562594\pi\)
\(524\) 33.1481 1.44808
\(525\) 0 0
\(526\) 18.7268 0.816527
\(527\) −38.9486 −1.69663
\(528\) 3.33946 0.145332
\(529\) −2.47809 −0.107743
\(530\) 0.680663 0.0295661
\(531\) −1.43254 −0.0621671
\(532\) 0 0
\(533\) 4.20250 0.182031
\(534\) 0.733010 0.0317205
\(535\) 3.97834 0.171999
\(536\) 2.75350 0.118933
\(537\) −19.7583 −0.852633
\(538\) −14.1687 −0.610858
\(539\) 0 0
\(540\) 0.619292 0.0266501
\(541\) 30.4024 1.30710 0.653550 0.756884i \(-0.273279\pi\)
0.653550 + 0.756884i \(0.273279\pi\)
\(542\) 10.8184 0.464689
\(543\) −13.0870 −0.561616
\(544\) 25.6626 1.10028
\(545\) 0.255952 0.0109638
\(546\) 0 0
\(547\) −32.5850 −1.39323 −0.696617 0.717443i \(-0.745312\pi\)
−0.696617 + 0.717443i \(0.745312\pi\)
\(548\) −12.0177 −0.513369
\(549\) −12.2775 −0.523990
\(550\) −9.49436 −0.404841
\(551\) 6.88114 0.293146
\(552\) −11.2747 −0.479883
\(553\) 0 0
\(554\) 10.5534 0.448370
\(555\) 1.07935 0.0458159
\(556\) 33.5020 1.42080
\(557\) −16.0876 −0.681654 −0.340827 0.940126i \(-0.610707\pi\)
−0.340827 + 0.940126i \(0.610707\pi\)
\(558\) −6.31737 −0.267436
\(559\) −18.4229 −0.779206
\(560\) 0 0
\(561\) 12.1249 0.511914
\(562\) 8.92977 0.376680
\(563\) 33.1478 1.39701 0.698507 0.715603i \(-0.253848\pi\)
0.698507 + 0.715603i \(0.253848\pi\)
\(564\) −16.3345 −0.687809
\(565\) −6.13651 −0.258165
\(566\) −0.203895 −0.00857035
\(567\) 0 0
\(568\) −7.05916 −0.296196
\(569\) 19.8175 0.830791 0.415396 0.909641i \(-0.363643\pi\)
0.415396 + 0.909641i \(0.363643\pi\)
\(570\) 0.375014 0.0157076
\(571\) 29.5390 1.23617 0.618085 0.786112i \(-0.287909\pi\)
0.618085 + 0.786112i \(0.287909\pi\)
\(572\) 17.3019 0.723428
\(573\) −22.8221 −0.953407
\(574\) 0 0
\(575\) −21.8701 −0.912047
\(576\) 1.74195 0.0725813
\(577\) −32.6770 −1.36036 −0.680181 0.733044i \(-0.738099\pi\)
−0.680181 + 0.733044i \(0.738099\pi\)
\(578\) 1.64516 0.0684298
\(579\) 13.0794 0.543559
\(580\) −3.36157 −0.139582
\(581\) 0 0
\(582\) 5.61819 0.232881
\(583\) −6.34900 −0.262949
\(584\) 9.73811 0.402966
\(585\) 1.74431 0.0721185
\(586\) −11.4836 −0.474384
\(587\) 40.6133 1.67629 0.838146 0.545447i \(-0.183640\pi\)
0.838146 + 0.545447i \(0.183640\pi\)
\(588\) 0 0
\(589\) 11.2366 0.462994
\(590\) 0.423781 0.0174468
\(591\) −0.844299 −0.0347298
\(592\) −3.14714 −0.129347
\(593\) −11.9727 −0.491660 −0.245830 0.969313i \(-0.579060\pi\)
−0.245830 + 0.969313i \(0.579060\pi\)
\(594\) 1.96663 0.0806920
\(595\) 0 0
\(596\) 7.60203 0.311391
\(597\) −8.12795 −0.332655
\(598\) −13.5686 −0.554860
\(599\) −6.16091 −0.251728 −0.125864 0.992048i \(-0.540170\pi\)
−0.125864 + 0.992048i \(0.540170\pi\)
\(600\) 12.0154 0.490526
\(601\) 33.4325 1.36374 0.681871 0.731473i \(-0.261167\pi\)
0.681871 + 0.731473i \(0.261167\pi\)
\(602\) 0 0
\(603\) −1.10634 −0.0450537
\(604\) 26.3344 1.07153
\(605\) 1.40541 0.0571380
\(606\) 5.97905 0.242882
\(607\) 39.8822 1.61877 0.809385 0.587279i \(-0.199801\pi\)
0.809385 + 0.587279i \(0.199801\pi\)
\(608\) −7.40360 −0.300256
\(609\) 0 0
\(610\) 3.63198 0.147055
\(611\) −46.0083 −1.86130
\(612\) −6.55618 −0.265018
\(613\) 9.30534 0.375839 0.187920 0.982184i \(-0.439826\pi\)
0.187920 + 0.982184i \(0.439826\pi\)
\(614\) 6.29306 0.253967
\(615\) 0.415066 0.0167371
\(616\) 0 0
\(617\) 35.3926 1.42485 0.712426 0.701747i \(-0.247596\pi\)
0.712426 + 0.701747i \(0.247596\pi\)
\(618\) −12.3230 −0.495702
\(619\) 5.72703 0.230189 0.115094 0.993355i \(-0.463283\pi\)
0.115094 + 0.993355i \(0.463283\pi\)
\(620\) −5.48928 −0.220455
\(621\) 4.53011 0.181787
\(622\) −4.77581 −0.191493
\(623\) 0 0
\(624\) −5.08602 −0.203604
\(625\) 22.4455 0.897820
\(626\) −1.67316 −0.0668729
\(627\) −3.49800 −0.139697
\(628\) −8.62576 −0.344205
\(629\) −11.4266 −0.455609
\(630\) 0 0
\(631\) 2.10310 0.0837233 0.0418616 0.999123i \(-0.486671\pi\)
0.0418616 + 0.999123i \(0.486671\pi\)
\(632\) 38.3272 1.52457
\(633\) 11.6549 0.463241
\(634\) 16.3031 0.647481
\(635\) −7.07802 −0.280882
\(636\) 3.43303 0.136128
\(637\) 0 0
\(638\) −10.6751 −0.422630
\(639\) 2.83634 0.112204
\(640\) 4.33284 0.171270
\(641\) −7.39557 −0.292107 −0.146054 0.989277i \(-0.546657\pi\)
−0.146054 + 0.989277i \(0.546657\pi\)
\(642\) −6.83128 −0.269609
\(643\) −13.9177 −0.548861 −0.274431 0.961607i \(-0.588489\pi\)
−0.274431 + 0.961607i \(0.588489\pi\)
\(644\) 0 0
\(645\) −1.81956 −0.0716452
\(646\) −3.97011 −0.156202
\(647\) −22.1622 −0.871287 −0.435643 0.900119i \(-0.643479\pi\)
−0.435643 + 0.900119i \(0.643479\pi\)
\(648\) −2.48883 −0.0977706
\(649\) −3.95289 −0.155164
\(650\) 14.4600 0.567166
\(651\) 0 0
\(652\) 0.235302 0.00921512
\(653\) −9.10805 −0.356425 −0.178213 0.983992i \(-0.557032\pi\)
−0.178213 + 0.983992i \(0.557032\pi\)
\(654\) −0.439500 −0.0171858
\(655\) 9.22138 0.360309
\(656\) −1.21024 −0.0472518
\(657\) −3.91272 −0.152650
\(658\) 0 0
\(659\) −15.1797 −0.591318 −0.295659 0.955294i \(-0.595539\pi\)
−0.295659 + 0.955294i \(0.595539\pi\)
\(660\) 1.70884 0.0665167
\(661\) 19.9463 0.775823 0.387911 0.921697i \(-0.373197\pi\)
0.387911 + 0.921697i \(0.373197\pi\)
\(662\) −7.57529 −0.294422
\(663\) −18.4663 −0.717172
\(664\) −10.0636 −0.390544
\(665\) 0 0
\(666\) −1.85337 −0.0718167
\(667\) −24.5898 −0.952123
\(668\) 33.0528 1.27885
\(669\) −11.7288 −0.453460
\(670\) 0.327283 0.0126440
\(671\) −33.8779 −1.30784
\(672\) 0 0
\(673\) 24.3373 0.938136 0.469068 0.883162i \(-0.344590\pi\)
0.469068 + 0.883162i \(0.344590\pi\)
\(674\) −11.4517 −0.441102
\(675\) −4.82772 −0.185819
\(676\) −6.95441 −0.267477
\(677\) 16.7296 0.642971 0.321485 0.946915i \(-0.395818\pi\)
0.321485 + 0.946915i \(0.395818\pi\)
\(678\) 10.5371 0.404676
\(679\) 0 0
\(680\) 4.53925 0.174072
\(681\) 1.94495 0.0745307
\(682\) −17.4318 −0.667500
\(683\) −13.7682 −0.526827 −0.263413 0.964683i \(-0.584848\pi\)
−0.263413 + 0.964683i \(0.584848\pi\)
\(684\) 1.89144 0.0723210
\(685\) −3.34317 −0.127736
\(686\) 0 0
\(687\) −11.2389 −0.428790
\(688\) 5.30543 0.202268
\(689\) 9.66955 0.368381
\(690\) −1.34012 −0.0510174
\(691\) −14.5283 −0.552684 −0.276342 0.961059i \(-0.589122\pi\)
−0.276342 + 0.961059i \(0.589122\pi\)
\(692\) 27.2762 1.03688
\(693\) 0 0
\(694\) 22.3712 0.849199
\(695\) 9.31983 0.353521
\(696\) 13.5096 0.512080
\(697\) −4.39412 −0.166439
\(698\) 17.2219 0.651860
\(699\) 13.3117 0.503495
\(700\) 0 0
\(701\) 41.6703 1.57386 0.786932 0.617040i \(-0.211668\pi\)
0.786932 + 0.617040i \(0.211668\pi\)
\(702\) −2.99519 −0.113046
\(703\) 3.29655 0.124332
\(704\) 4.80665 0.181158
\(705\) −4.54407 −0.171140
\(706\) 18.6976 0.703692
\(707\) 0 0
\(708\) 2.13740 0.0803285
\(709\) 9.18522 0.344958 0.172479 0.985013i \(-0.444822\pi\)
0.172479 + 0.985013i \(0.444822\pi\)
\(710\) −0.839057 −0.0314892
\(711\) −15.3997 −0.577532
\(712\) −2.55970 −0.0959287
\(713\) −40.1540 −1.50378
\(714\) 0 0
\(715\) 4.81317 0.180002
\(716\) 29.4800 1.10172
\(717\) 15.1521 0.565864
\(718\) 14.7990 0.552292
\(719\) 9.93068 0.370352 0.185176 0.982705i \(-0.440714\pi\)
0.185176 + 0.982705i \(0.440714\pi\)
\(720\) −0.502327 −0.0187206
\(721\) 0 0
\(722\) −12.3963 −0.461341
\(723\) −25.5139 −0.948874
\(724\) 19.5262 0.725687
\(725\) 26.2053 0.973240
\(726\) −2.41325 −0.0895643
\(727\) 34.7960 1.29051 0.645256 0.763966i \(-0.276751\pi\)
0.645256 + 0.763966i \(0.276751\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.15748 0.0428402
\(731\) 19.2629 0.712465
\(732\) 18.3184 0.677069
\(733\) −3.15245 −0.116438 −0.0582192 0.998304i \(-0.518542\pi\)
−0.0582192 + 0.998304i \(0.518542\pi\)
\(734\) −18.1740 −0.670814
\(735\) 0 0
\(736\) 26.4569 0.975212
\(737\) −3.05278 −0.112451
\(738\) −0.712717 −0.0262355
\(739\) 46.0474 1.69388 0.846941 0.531686i \(-0.178441\pi\)
0.846941 + 0.531686i \(0.178441\pi\)
\(740\) −1.61043 −0.0592005
\(741\) 5.32748 0.195710
\(742\) 0 0
\(743\) 35.9816 1.32004 0.660019 0.751249i \(-0.270548\pi\)
0.660019 + 0.751249i \(0.270548\pi\)
\(744\) 22.0605 0.808777
\(745\) 2.11479 0.0774799
\(746\) −17.7205 −0.648792
\(747\) 4.04351 0.147944
\(748\) −18.0908 −0.661465
\(749\) 0 0
\(750\) 2.90728 0.106159
\(751\) −29.6433 −1.08170 −0.540850 0.841119i \(-0.681897\pi\)
−0.540850 + 0.841119i \(0.681897\pi\)
\(752\) 13.2495 0.483158
\(753\) −9.41888 −0.343243
\(754\) 16.2582 0.592088
\(755\) 7.32590 0.266617
\(756\) 0 0
\(757\) 16.7775 0.609790 0.304895 0.952386i \(-0.401379\pi\)
0.304895 + 0.952386i \(0.401379\pi\)
\(758\) 11.2567 0.408861
\(759\) 12.5002 0.453727
\(760\) −1.30956 −0.0475028
\(761\) 23.0227 0.834574 0.417287 0.908775i \(-0.362981\pi\)
0.417287 + 0.908775i \(0.362981\pi\)
\(762\) 12.1538 0.440285
\(763\) 0 0
\(764\) 34.0514 1.23194
\(765\) −1.82385 −0.0659414
\(766\) −9.72971 −0.351549
\(767\) 6.02026 0.217379
\(768\) −10.9239 −0.394182
\(769\) −6.17449 −0.222658 −0.111329 0.993784i \(-0.535511\pi\)
−0.111329 + 0.993784i \(0.535511\pi\)
\(770\) 0 0
\(771\) −1.07261 −0.0386291
\(772\) −19.5148 −0.702355
\(773\) −37.5482 −1.35051 −0.675257 0.737583i \(-0.735967\pi\)
−0.675257 + 0.737583i \(0.735967\pi\)
\(774\) 3.12440 0.112304
\(775\) 42.7919 1.53713
\(776\) −19.6189 −0.704278
\(777\) 0 0
\(778\) −11.3195 −0.405825
\(779\) 1.26769 0.0454198
\(780\) −2.60258 −0.0931872
\(781\) 7.82644 0.280052
\(782\) 14.1872 0.507335
\(783\) −5.42809 −0.193984
\(784\) 0 0
\(785\) −2.39958 −0.0856447
\(786\) −15.8342 −0.564787
\(787\) −37.2802 −1.32890 −0.664448 0.747335i \(-0.731333\pi\)
−0.664448 + 0.747335i \(0.731333\pi\)
\(788\) 1.25972 0.0448758
\(789\) 26.2752 0.935422
\(790\) 4.55559 0.162081
\(791\) 0 0
\(792\) −6.86756 −0.244028
\(793\) 51.5962 1.83223
\(794\) 0.361114 0.0128155
\(795\) 0.955026 0.0338713
\(796\) 12.1272 0.429837
\(797\) −22.0377 −0.780617 −0.390308 0.920684i \(-0.627632\pi\)
−0.390308 + 0.920684i \(0.627632\pi\)
\(798\) 0 0
\(799\) 48.1061 1.70187
\(800\) −28.1950 −0.996842
\(801\) 1.02847 0.0363393
\(802\) −8.47280 −0.299185
\(803\) −10.7966 −0.381003
\(804\) 1.65070 0.0582157
\(805\) 0 0
\(806\) 26.5488 0.935141
\(807\) −19.8799 −0.699806
\(808\) −20.8790 −0.734522
\(809\) 34.8178 1.22413 0.612065 0.790807i \(-0.290339\pi\)
0.612065 + 0.790807i \(0.290339\pi\)
\(810\) −0.295824 −0.0103942
\(811\) 9.01482 0.316553 0.158277 0.987395i \(-0.449406\pi\)
0.158277 + 0.987395i \(0.449406\pi\)
\(812\) 0 0
\(813\) 15.1791 0.532353
\(814\) −5.11410 −0.179249
\(815\) 0.0654580 0.00229289
\(816\) 5.31792 0.186165
\(817\) −5.55730 −0.194425
\(818\) −19.5843 −0.684749
\(819\) 0 0
\(820\) −0.619292 −0.0216266
\(821\) −15.2878 −0.533547 −0.266774 0.963759i \(-0.585958\pi\)
−0.266774 + 0.963759i \(0.585958\pi\)
\(822\) 5.74062 0.200227
\(823\) −32.2809 −1.12524 −0.562621 0.826715i \(-0.690207\pi\)
−0.562621 + 0.826715i \(0.690207\pi\)
\(824\) 43.0322 1.49910
\(825\) −13.3214 −0.463790
\(826\) 0 0
\(827\) −41.5227 −1.44389 −0.721943 0.691952i \(-0.756751\pi\)
−0.721943 + 0.691952i \(0.756751\pi\)
\(828\) −6.75908 −0.234894
\(829\) −5.55425 −0.192907 −0.0964535 0.995337i \(-0.530750\pi\)
−0.0964535 + 0.995337i \(0.530750\pi\)
\(830\) −1.19617 −0.0415196
\(831\) 14.8072 0.513657
\(832\) −7.32056 −0.253795
\(833\) 0 0
\(834\) −16.0033 −0.554148
\(835\) 9.19487 0.318202
\(836\) 5.21914 0.180508
\(837\) −8.86379 −0.306377
\(838\) 2.83601 0.0979684
\(839\) 40.4477 1.39641 0.698204 0.715899i \(-0.253983\pi\)
0.698204 + 0.715899i \(0.253983\pi\)
\(840\) 0 0
\(841\) 0.464135 0.0160046
\(842\) −7.51476 −0.258976
\(843\) 12.5292 0.431528
\(844\) −17.3895 −0.598572
\(845\) −1.93463 −0.0665533
\(846\) 7.80271 0.268263
\(847\) 0 0
\(848\) −2.78464 −0.0956248
\(849\) −0.286081 −0.00981829
\(850\) −15.1193 −0.518587
\(851\) −11.7802 −0.403822
\(852\) −4.23191 −0.144983
\(853\) −16.5141 −0.565431 −0.282715 0.959204i \(-0.591235\pi\)
−0.282715 + 0.959204i \(0.591235\pi\)
\(854\) 0 0
\(855\) 0.526175 0.0179948
\(856\) 23.8551 0.815350
\(857\) −14.7078 −0.502410 −0.251205 0.967934i \(-0.580827\pi\)
−0.251205 + 0.967934i \(0.580827\pi\)
\(858\) −8.26479 −0.282155
\(859\) −42.3688 −1.44561 −0.722803 0.691055i \(-0.757146\pi\)
−0.722803 + 0.691055i \(0.757146\pi\)
\(860\) 2.71485 0.0925756
\(861\) 0 0
\(862\) −10.4833 −0.357062
\(863\) −57.6490 −1.96239 −0.981197 0.193009i \(-0.938175\pi\)
−0.981197 + 0.193009i \(0.938175\pi\)
\(864\) 5.84022 0.198688
\(865\) 7.58790 0.257996
\(866\) −2.99643 −0.101823
\(867\) 2.30830 0.0783939
\(868\) 0 0
\(869\) −42.4930 −1.44148
\(870\) 1.60576 0.0544404
\(871\) 4.64940 0.157539
\(872\) 1.53475 0.0519732
\(873\) 7.88278 0.266792
\(874\) −4.09298 −0.138447
\(875\) 0 0
\(876\) 5.83792 0.197245
\(877\) −40.9161 −1.38164 −0.690819 0.723028i \(-0.742750\pi\)
−0.690819 + 0.723028i \(0.742750\pi\)
\(878\) 6.74757 0.227719
\(879\) −16.1124 −0.543459
\(880\) −1.38610 −0.0467253
\(881\) −4.58413 −0.154443 −0.0772216 0.997014i \(-0.524605\pi\)
−0.0772216 + 0.997014i \(0.524605\pi\)
\(882\) 0 0
\(883\) −38.8738 −1.30821 −0.654104 0.756404i \(-0.726954\pi\)
−0.654104 + 0.756404i \(0.726954\pi\)
\(884\) 27.5524 0.926686
\(885\) 0.594599 0.0199872
\(886\) −10.3920 −0.349125
\(887\) 8.32382 0.279487 0.139743 0.990188i \(-0.455372\pi\)
0.139743 + 0.990188i \(0.455372\pi\)
\(888\) 6.47204 0.217187
\(889\) 0 0
\(890\) −0.304247 −0.0101984
\(891\) 2.75935 0.0924417
\(892\) 17.4997 0.585934
\(893\) −13.8785 −0.464426
\(894\) −3.63135 −0.121450
\(895\) 8.20098 0.274129
\(896\) 0 0
\(897\) −19.0378 −0.635654
\(898\) 14.2801 0.476534
\(899\) 48.1134 1.60467
\(900\) 7.20313 0.240104
\(901\) −10.1104 −0.336828
\(902\) −1.96663 −0.0654818
\(903\) 0 0
\(904\) −36.7960 −1.22382
\(905\) 5.43196 0.180564
\(906\) −12.5794 −0.417924
\(907\) 28.0918 0.932772 0.466386 0.884581i \(-0.345556\pi\)
0.466386 + 0.884581i \(0.345556\pi\)
\(908\) −2.90194 −0.0963041
\(909\) 8.38909 0.278249
\(910\) 0 0
\(911\) −55.7190 −1.84605 −0.923027 0.384736i \(-0.874292\pi\)
−0.923027 + 0.384736i \(0.874292\pi\)
\(912\) −1.53421 −0.0508026
\(913\) 11.1575 0.369258
\(914\) 19.6539 0.650092
\(915\) 5.09596 0.168467
\(916\) 16.7688 0.554057
\(917\) 0 0
\(918\) 3.13176 0.103364
\(919\) −12.6642 −0.417752 −0.208876 0.977942i \(-0.566981\pi\)
−0.208876 + 0.977942i \(0.566981\pi\)
\(920\) 4.67974 0.154286
\(921\) 8.82967 0.290948
\(922\) 19.9345 0.656508
\(923\) −11.9197 −0.392342
\(924\) 0 0
\(925\) 12.5542 0.412778
\(926\) 6.38813 0.209927
\(927\) −17.2901 −0.567882
\(928\) −31.7012 −1.04064
\(929\) −38.2432 −1.25472 −0.627359 0.778730i \(-0.715864\pi\)
−0.627359 + 0.778730i \(0.715864\pi\)
\(930\) 2.62213 0.0859829
\(931\) 0 0
\(932\) −19.8615 −0.650586
\(933\) −6.70085 −0.219376
\(934\) 14.7388 0.482268
\(935\) −5.03264 −0.164585
\(936\) 10.4593 0.341874
\(937\) −49.0781 −1.60331 −0.801656 0.597785i \(-0.796048\pi\)
−0.801656 + 0.597785i \(0.796048\pi\)
\(938\) 0 0
\(939\) −2.34758 −0.0766103
\(940\) 6.77991 0.221136
\(941\) −31.8341 −1.03776 −0.518882 0.854846i \(-0.673651\pi\)
−0.518882 + 0.854846i \(0.673651\pi\)
\(942\) 4.12037 0.134249
\(943\) −4.53011 −0.147521
\(944\) −1.73372 −0.0564276
\(945\) 0 0
\(946\) 8.62132 0.280303
\(947\) 33.8537 1.10010 0.550049 0.835132i \(-0.314609\pi\)
0.550049 + 0.835132i \(0.314609\pi\)
\(948\) 22.9768 0.746252
\(949\) 16.4432 0.533770
\(950\) 4.36187 0.141518
\(951\) 22.8746 0.741761
\(952\) 0 0
\(953\) −41.1049 −1.33152 −0.665759 0.746167i \(-0.731892\pi\)
−0.665759 + 0.746167i \(0.731892\pi\)
\(954\) −1.63989 −0.0530935
\(955\) 9.47267 0.306528
\(956\) −22.6074 −0.731176
\(957\) −14.9780 −0.484170
\(958\) −0.0130400 −0.000421304 0
\(959\) 0 0
\(960\) −0.723024 −0.0233355
\(961\) 47.5668 1.53441
\(962\) 7.78880 0.251121
\(963\) −9.58485 −0.308867
\(964\) 38.0677 1.22608
\(965\) −5.42879 −0.174759
\(966\) 0 0
\(967\) 44.3207 1.42526 0.712628 0.701542i \(-0.247505\pi\)
0.712628 + 0.701542i \(0.247505\pi\)
\(968\) 8.42717 0.270859
\(969\) −5.57039 −0.178947
\(970\) −2.33192 −0.0748733
\(971\) −24.4418 −0.784374 −0.392187 0.919885i \(-0.628281\pi\)
−0.392187 + 0.919885i \(0.628281\pi\)
\(972\) −1.49203 −0.0478570
\(973\) 0 0
\(974\) 18.9551 0.607360
\(975\) 20.2885 0.649752
\(976\) −14.8587 −0.475614
\(977\) 15.7803 0.504857 0.252429 0.967615i \(-0.418771\pi\)
0.252429 + 0.967615i \(0.418771\pi\)
\(978\) −0.112399 −0.00359413
\(979\) 2.83792 0.0907002
\(980\) 0 0
\(981\) −0.616655 −0.0196883
\(982\) −18.8810 −0.602516
\(983\) 25.3592 0.808832 0.404416 0.914575i \(-0.367475\pi\)
0.404416 + 0.914575i \(0.367475\pi\)
\(984\) 2.48883 0.0793411
\(985\) 0.350439 0.0111659
\(986\) −16.9995 −0.541374
\(987\) 0 0
\(988\) −7.94878 −0.252884
\(989\) 19.8591 0.631482
\(990\) −0.816283 −0.0259432
\(991\) −9.51391 −0.302219 −0.151110 0.988517i \(-0.548285\pi\)
−0.151110 + 0.988517i \(0.548285\pi\)
\(992\) −51.7665 −1.64359
\(993\) −10.6287 −0.337293
\(994\) 0 0
\(995\) 3.37363 0.106951
\(996\) −6.03306 −0.191165
\(997\) −44.0831 −1.39612 −0.698062 0.716037i \(-0.745954\pi\)
−0.698062 + 0.716037i \(0.745954\pi\)
\(998\) −1.52608 −0.0483073
\(999\) −2.60043 −0.0822740
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 \(a_p\))