Properties

Label 6036.2.a.g.1.10
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(1.03500\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +0.0349978 q^{5} +0.637505 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +0.0349978 q^{5} +0.637505 q^{7} +1.00000 q^{9} -0.863742 q^{11} -4.36921 q^{13} +0.0349978 q^{15} -2.27774 q^{17} -4.02205 q^{19} +0.637505 q^{21} +8.23006 q^{23} -4.99878 q^{25} +1.00000 q^{27} +1.29094 q^{29} -1.21322 q^{31} -0.863742 q^{33} +0.0223113 q^{35} +7.14619 q^{37} -4.36921 q^{39} +2.42495 q^{41} +0.00158582 q^{43} +0.0349978 q^{45} -3.98820 q^{47} -6.59359 q^{49} -2.27774 q^{51} +7.67263 q^{53} -0.0302291 q^{55} -4.02205 q^{57} -1.59240 q^{59} -3.50074 q^{61} +0.637505 q^{63} -0.152913 q^{65} -15.8723 q^{67} +8.23006 q^{69} -12.8739 q^{71} -2.85083 q^{73} -4.99878 q^{75} -0.550640 q^{77} +7.20069 q^{79} +1.00000 q^{81} -13.4282 q^{83} -0.0797159 q^{85} +1.29094 q^{87} -10.0457 q^{89} -2.78539 q^{91} -1.21322 q^{93} -0.140763 q^{95} +11.8338 q^{97} -0.863742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} + O(q^{10}) \) \( 15q + 15q^{3} - 11q^{5} - 4q^{7} + 15q^{9} - 5q^{11} - 14q^{13} - 11q^{15} - 5q^{17} + 3q^{19} - 4q^{21} - 32q^{23} + 2q^{25} + 15q^{27} - 23q^{29} - 13q^{31} - 5q^{33} - 16q^{35} - 10q^{37} - 14q^{39} - 14q^{41} + 4q^{43} - 11q^{45} - 20q^{47} - 9q^{49} - 5q^{51} - 30q^{53} - 10q^{55} + 3q^{57} - 14q^{59} - 38q^{61} - 4q^{63} - 24q^{65} - 8q^{67} - 32q^{69} - 41q^{71} - 19q^{73} + 2q^{75} - 39q^{77} - 27q^{79} + 15q^{81} - 17q^{83} - 6q^{85} - 23q^{87} - 23q^{89} + 4q^{91} - 13q^{93} - 30q^{95} - 18q^{97} - 5q^{99} + O(q^{100}) \)

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 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.0349978 0.0156515 0.00782575 0.999969i \(-0.497509\pi\)
0.00782575 + 0.999969i \(0.497509\pi\)
\(6\) 0 0
\(7\) 0.637505 0.240954 0.120477 0.992716i \(-0.461558\pi\)
0.120477 + 0.992716i \(0.461558\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.863742 −0.260428 −0.130214 0.991486i \(-0.541566\pi\)
−0.130214 + 0.991486i \(0.541566\pi\)
\(12\) 0 0
\(13\) −4.36921 −1.21180 −0.605900 0.795541i \(-0.707187\pi\)
−0.605900 + 0.795541i \(0.707187\pi\)
\(14\) 0 0
\(15\) 0.0349978 0.00903639
\(16\) 0 0
\(17\) −2.27774 −0.552433 −0.276217 0.961095i \(-0.589081\pi\)
−0.276217 + 0.961095i \(0.589081\pi\)
\(18\) 0 0
\(19\) −4.02205 −0.922722 −0.461361 0.887213i \(-0.652639\pi\)
−0.461361 + 0.887213i \(0.652639\pi\)
\(20\) 0 0
\(21\) 0.637505 0.139115
\(22\) 0 0
\(23\) 8.23006 1.71609 0.858043 0.513577i \(-0.171680\pi\)
0.858043 + 0.513577i \(0.171680\pi\)
\(24\) 0 0
\(25\) −4.99878 −0.999755
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.29094 0.239721 0.119860 0.992791i \(-0.461755\pi\)
0.119860 + 0.992791i \(0.461755\pi\)
\(30\) 0 0
\(31\) −1.21322 −0.217901 −0.108951 0.994047i \(-0.534749\pi\)
−0.108951 + 0.994047i \(0.534749\pi\)
\(32\) 0 0
\(33\) −0.863742 −0.150358
\(34\) 0 0
\(35\) 0.0223113 0.00377129
\(36\) 0 0
\(37\) 7.14619 1.17483 0.587413 0.809287i \(-0.300146\pi\)
0.587413 + 0.809287i \(0.300146\pi\)
\(38\) 0 0
\(39\) −4.36921 −0.699633
\(40\) 0 0
\(41\) 2.42495 0.378714 0.189357 0.981908i \(-0.439360\pi\)
0.189357 + 0.981908i \(0.439360\pi\)
\(42\) 0 0
\(43\) 0.00158582 0.000241836 0 0.000120918 1.00000i \(-0.499962\pi\)
0.000120918 1.00000i \(0.499962\pi\)
\(44\) 0 0
\(45\) 0.0349978 0.00521716
\(46\) 0 0
\(47\) −3.98820 −0.581739 −0.290870 0.956763i \(-0.593945\pi\)
−0.290870 + 0.956763i \(0.593945\pi\)
\(48\) 0 0
\(49\) −6.59359 −0.941941
\(50\) 0 0
\(51\) −2.27774 −0.318947
\(52\) 0 0
\(53\) 7.67263 1.05392 0.526958 0.849891i \(-0.323332\pi\)
0.526958 + 0.849891i \(0.323332\pi\)
\(54\) 0 0
\(55\) −0.0302291 −0.00407609
\(56\) 0 0
\(57\) −4.02205 −0.532734
\(58\) 0 0
\(59\) −1.59240 −0.207313 −0.103657 0.994613i \(-0.533054\pi\)
−0.103657 + 0.994613i \(0.533054\pi\)
\(60\) 0 0
\(61\) −3.50074 −0.448224 −0.224112 0.974563i \(-0.571948\pi\)
−0.224112 + 0.974563i \(0.571948\pi\)
\(62\) 0 0
\(63\) 0.637505 0.0803181
\(64\) 0 0
\(65\) −0.152913 −0.0189665
\(66\) 0 0
\(67\) −15.8723 −1.93911 −0.969557 0.244866i \(-0.921256\pi\)
−0.969557 + 0.244866i \(0.921256\pi\)
\(68\) 0 0
\(69\) 8.23006 0.990783
\(70\) 0 0
\(71\) −12.8739 −1.52786 −0.763928 0.645302i \(-0.776732\pi\)
−0.763928 + 0.645302i \(0.776732\pi\)
\(72\) 0 0
\(73\) −2.85083 −0.333665 −0.166832 0.985985i \(-0.553354\pi\)
−0.166832 + 0.985985i \(0.553354\pi\)
\(74\) 0 0
\(75\) −4.99878 −0.577209
\(76\) 0 0
\(77\) −0.550640 −0.0627512
\(78\) 0 0
\(79\) 7.20069 0.810141 0.405070 0.914286i \(-0.367247\pi\)
0.405070 + 0.914286i \(0.367247\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.4282 −1.47394 −0.736970 0.675925i \(-0.763744\pi\)
−0.736970 + 0.675925i \(0.763744\pi\)
\(84\) 0 0
\(85\) −0.0797159 −0.00864640
\(86\) 0 0
\(87\) 1.29094 0.138403
\(88\) 0 0
\(89\) −10.0457 −1.06484 −0.532420 0.846481i \(-0.678717\pi\)
−0.532420 + 0.846481i \(0.678717\pi\)
\(90\) 0 0
\(91\) −2.78539 −0.291988
\(92\) 0 0
\(93\) −1.21322 −0.125805
\(94\) 0 0
\(95\) −0.140763 −0.0144420
\(96\) 0 0
\(97\) 11.8338 1.20154 0.600770 0.799422i \(-0.294861\pi\)
0.600770 + 0.799422i \(0.294861\pi\)
\(98\) 0 0
\(99\) −0.863742 −0.0868094
\(100\) 0 0
\(101\) −15.7416 −1.56635 −0.783175 0.621801i \(-0.786401\pi\)
−0.783175 + 0.621801i \(0.786401\pi\)
\(102\) 0 0
\(103\) −11.4296 −1.12619 −0.563094 0.826393i \(-0.690389\pi\)
−0.563094 + 0.826393i \(0.690389\pi\)
\(104\) 0 0
\(105\) 0.0223113 0.00217736
\(106\) 0 0
\(107\) −8.44980 −0.816873 −0.408437 0.912787i \(-0.633926\pi\)
−0.408437 + 0.912787i \(0.633926\pi\)
\(108\) 0 0
\(109\) 7.81853 0.748879 0.374440 0.927251i \(-0.377835\pi\)
0.374440 + 0.927251i \(0.377835\pi\)
\(110\) 0 0
\(111\) 7.14619 0.678287
\(112\) 0 0
\(113\) −2.40154 −0.225918 −0.112959 0.993600i \(-0.536033\pi\)
−0.112959 + 0.993600i \(0.536033\pi\)
\(114\) 0 0
\(115\) 0.288034 0.0268593
\(116\) 0 0
\(117\) −4.36921 −0.403933
\(118\) 0 0
\(119\) −1.45207 −0.133111
\(120\) 0 0
\(121\) −10.2539 −0.932177
\(122\) 0 0
\(123\) 2.42495 0.218651
\(124\) 0 0
\(125\) −0.349935 −0.0312992
\(126\) 0 0
\(127\) −7.45717 −0.661717 −0.330858 0.943680i \(-0.607338\pi\)
−0.330858 + 0.943680i \(0.607338\pi\)
\(128\) 0 0
\(129\) 0.00158582 0.000139624 0
\(130\) 0 0
\(131\) −0.0329360 −0.00287763 −0.00143882 0.999999i \(-0.500458\pi\)
−0.00143882 + 0.999999i \(0.500458\pi\)
\(132\) 0 0
\(133\) −2.56408 −0.222334
\(134\) 0 0
\(135\) 0.0349978 0.00301213
\(136\) 0 0
\(137\) −13.7940 −1.17850 −0.589252 0.807949i \(-0.700577\pi\)
−0.589252 + 0.807949i \(0.700577\pi\)
\(138\) 0 0
\(139\) 6.22618 0.528098 0.264049 0.964509i \(-0.414942\pi\)
0.264049 + 0.964509i \(0.414942\pi\)
\(140\) 0 0
\(141\) −3.98820 −0.335867
\(142\) 0 0
\(143\) 3.77387 0.315587
\(144\) 0 0
\(145\) 0.0451800 0.00375199
\(146\) 0 0
\(147\) −6.59359 −0.543830
\(148\) 0 0
\(149\) 13.5572 1.11065 0.555326 0.831633i \(-0.312594\pi\)
0.555326 + 0.831633i \(0.312594\pi\)
\(150\) 0 0
\(151\) 4.23542 0.344674 0.172337 0.985038i \(-0.444868\pi\)
0.172337 + 0.985038i \(0.444868\pi\)
\(152\) 0 0
\(153\) −2.27774 −0.184144
\(154\) 0 0
\(155\) −0.0424601 −0.00341048
\(156\) 0 0
\(157\) 9.88889 0.789219 0.394610 0.918849i \(-0.370880\pi\)
0.394610 + 0.918849i \(0.370880\pi\)
\(158\) 0 0
\(159\) 7.67263 0.608479
\(160\) 0 0
\(161\) 5.24671 0.413498
\(162\) 0 0
\(163\) 7.43335 0.582225 0.291112 0.956689i \(-0.405975\pi\)
0.291112 + 0.956689i \(0.405975\pi\)
\(164\) 0 0
\(165\) −0.0302291 −0.00235333
\(166\) 0 0
\(167\) −4.80704 −0.371980 −0.185990 0.982552i \(-0.559549\pi\)
−0.185990 + 0.982552i \(0.559549\pi\)
\(168\) 0 0
\(169\) 6.08997 0.468459
\(170\) 0 0
\(171\) −4.02205 −0.307574
\(172\) 0 0
\(173\) −20.4319 −1.55341 −0.776704 0.629866i \(-0.783110\pi\)
−0.776704 + 0.629866i \(0.783110\pi\)
\(174\) 0 0
\(175\) −3.18674 −0.240895
\(176\) 0 0
\(177\) −1.59240 −0.119692
\(178\) 0 0
\(179\) −1.81895 −0.135955 −0.0679774 0.997687i \(-0.521655\pi\)
−0.0679774 + 0.997687i \(0.521655\pi\)
\(180\) 0 0
\(181\) −5.92712 −0.440559 −0.220280 0.975437i \(-0.570697\pi\)
−0.220280 + 0.975437i \(0.570697\pi\)
\(182\) 0 0
\(183\) −3.50074 −0.258782
\(184\) 0 0
\(185\) 0.250101 0.0183878
\(186\) 0 0
\(187\) 1.96738 0.143869
\(188\) 0 0
\(189\) 0.637505 0.0463717
\(190\) 0 0
\(191\) 0.852539 0.0616876 0.0308438 0.999524i \(-0.490181\pi\)
0.0308438 + 0.999524i \(0.490181\pi\)
\(192\) 0 0
\(193\) −0.273987 −0.0197220 −0.00986099 0.999951i \(-0.503139\pi\)
−0.00986099 + 0.999951i \(0.503139\pi\)
\(194\) 0 0
\(195\) −0.152913 −0.0109503
\(196\) 0 0
\(197\) −5.07126 −0.361313 −0.180656 0.983546i \(-0.557822\pi\)
−0.180656 + 0.983546i \(0.557822\pi\)
\(198\) 0 0
\(199\) 4.29664 0.304581 0.152290 0.988336i \(-0.451335\pi\)
0.152290 + 0.988336i \(0.451335\pi\)
\(200\) 0 0
\(201\) −15.8723 −1.11955
\(202\) 0 0
\(203\) 0.822979 0.0577618
\(204\) 0 0
\(205\) 0.0848680 0.00592744
\(206\) 0 0
\(207\) 8.23006 0.572029
\(208\) 0 0
\(209\) 3.47401 0.240303
\(210\) 0 0
\(211\) 19.7928 1.36259 0.681295 0.732009i \(-0.261417\pi\)
0.681295 + 0.732009i \(0.261417\pi\)
\(212\) 0 0
\(213\) −12.8739 −0.882108
\(214\) 0 0
\(215\) 5.55004e−5 0 3.78509e−6 0
\(216\) 0 0
\(217\) −0.773435 −0.0525042
\(218\) 0 0
\(219\) −2.85083 −0.192642
\(220\) 0 0
\(221\) 9.95192 0.669438
\(222\) 0 0
\(223\) −0.948794 −0.0635360 −0.0317680 0.999495i \(-0.510114\pi\)
−0.0317680 + 0.999495i \(0.510114\pi\)
\(224\) 0 0
\(225\) −4.99878 −0.333252
\(226\) 0 0
\(227\) 15.3021 1.01563 0.507817 0.861465i \(-0.330453\pi\)
0.507817 + 0.861465i \(0.330453\pi\)
\(228\) 0 0
\(229\) −14.9304 −0.986626 −0.493313 0.869852i \(-0.664214\pi\)
−0.493313 + 0.869852i \(0.664214\pi\)
\(230\) 0 0
\(231\) −0.550640 −0.0362294
\(232\) 0 0
\(233\) 1.04199 0.0682630 0.0341315 0.999417i \(-0.489133\pi\)
0.0341315 + 0.999417i \(0.489133\pi\)
\(234\) 0 0
\(235\) −0.139578 −0.00910509
\(236\) 0 0
\(237\) 7.20069 0.467735
\(238\) 0 0
\(239\) −4.80544 −0.310838 −0.155419 0.987849i \(-0.549673\pi\)
−0.155419 + 0.987849i \(0.549673\pi\)
\(240\) 0 0
\(241\) 24.4322 1.57381 0.786907 0.617071i \(-0.211681\pi\)
0.786907 + 0.617071i \(0.211681\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −0.230761 −0.0147428
\(246\) 0 0
\(247\) 17.5732 1.11815
\(248\) 0 0
\(249\) −13.4282 −0.850980
\(250\) 0 0
\(251\) −4.80461 −0.303264 −0.151632 0.988437i \(-0.548453\pi\)
−0.151632 + 0.988437i \(0.548453\pi\)
\(252\) 0 0
\(253\) −7.10865 −0.446917
\(254\) 0 0
\(255\) −0.0797159 −0.00499200
\(256\) 0 0
\(257\) −18.2299 −1.13715 −0.568576 0.822631i \(-0.692505\pi\)
−0.568576 + 0.822631i \(0.692505\pi\)
\(258\) 0 0
\(259\) 4.55573 0.283079
\(260\) 0 0
\(261\) 1.29094 0.0799070
\(262\) 0 0
\(263\) −27.2527 −1.68047 −0.840235 0.542222i \(-0.817583\pi\)
−0.840235 + 0.542222i \(0.817583\pi\)
\(264\) 0 0
\(265\) 0.268525 0.0164954
\(266\) 0 0
\(267\) −10.0457 −0.614785
\(268\) 0 0
\(269\) 15.4718 0.943335 0.471667 0.881777i \(-0.343652\pi\)
0.471667 + 0.881777i \(0.343652\pi\)
\(270\) 0 0
\(271\) 12.3488 0.750138 0.375069 0.926997i \(-0.377619\pi\)
0.375069 + 0.926997i \(0.377619\pi\)
\(272\) 0 0
\(273\) −2.78539 −0.168580
\(274\) 0 0
\(275\) 4.31765 0.260364
\(276\) 0 0
\(277\) 13.0131 0.781883 0.390941 0.920416i \(-0.372150\pi\)
0.390941 + 0.920416i \(0.372150\pi\)
\(278\) 0 0
\(279\) −1.21322 −0.0726337
\(280\) 0 0
\(281\) 14.6624 0.874683 0.437341 0.899296i \(-0.355920\pi\)
0.437341 + 0.899296i \(0.355920\pi\)
\(282\) 0 0
\(283\) 4.37195 0.259886 0.129943 0.991521i \(-0.458521\pi\)
0.129943 + 0.991521i \(0.458521\pi\)
\(284\) 0 0
\(285\) −0.140763 −0.00833808
\(286\) 0 0
\(287\) 1.54592 0.0912527
\(288\) 0 0
\(289\) −11.8119 −0.694818
\(290\) 0 0
\(291\) 11.8338 0.693710
\(292\) 0 0
\(293\) −23.6309 −1.38053 −0.690267 0.723555i \(-0.742507\pi\)
−0.690267 + 0.723555i \(0.742507\pi\)
\(294\) 0 0
\(295\) −0.0557306 −0.00324476
\(296\) 0 0
\(297\) −0.863742 −0.0501194
\(298\) 0 0
\(299\) −35.9588 −2.07955
\(300\) 0 0
\(301\) 0.00101097 5.82714e−5 0
\(302\) 0 0
\(303\) −15.7416 −0.904333
\(304\) 0 0
\(305\) −0.122518 −0.00701538
\(306\) 0 0
\(307\) 16.8530 0.961851 0.480926 0.876761i \(-0.340301\pi\)
0.480926 + 0.876761i \(0.340301\pi\)
\(308\) 0 0
\(309\) −11.4296 −0.650205
\(310\) 0 0
\(311\) −8.09954 −0.459283 −0.229641 0.973275i \(-0.573755\pi\)
−0.229641 + 0.973275i \(0.573755\pi\)
\(312\) 0 0
\(313\) −27.5042 −1.55463 −0.777315 0.629112i \(-0.783419\pi\)
−0.777315 + 0.629112i \(0.783419\pi\)
\(314\) 0 0
\(315\) 0.0223113 0.00125710
\(316\) 0 0
\(317\) −22.0581 −1.23891 −0.619454 0.785033i \(-0.712646\pi\)
−0.619454 + 0.785033i \(0.712646\pi\)
\(318\) 0 0
\(319\) −1.11504 −0.0624301
\(320\) 0 0
\(321\) −8.44980 −0.471622
\(322\) 0 0
\(323\) 9.16118 0.509742
\(324\) 0 0
\(325\) 21.8407 1.21150
\(326\) 0 0
\(327\) 7.81853 0.432366
\(328\) 0 0
\(329\) −2.54250 −0.140173
\(330\) 0 0
\(331\) 22.3009 1.22577 0.612883 0.790174i \(-0.290010\pi\)
0.612883 + 0.790174i \(0.290010\pi\)
\(332\) 0 0
\(333\) 7.14619 0.391609
\(334\) 0 0
\(335\) −0.555497 −0.0303500
\(336\) 0 0
\(337\) 14.1121 0.768735 0.384368 0.923180i \(-0.374420\pi\)
0.384368 + 0.923180i \(0.374420\pi\)
\(338\) 0 0
\(339\) −2.40154 −0.130434
\(340\) 0 0
\(341\) 1.04791 0.0567476
\(342\) 0 0
\(343\) −8.66598 −0.467919
\(344\) 0 0
\(345\) 0.288034 0.0155072
\(346\) 0 0
\(347\) 15.3510 0.824087 0.412043 0.911164i \(-0.364815\pi\)
0.412043 + 0.911164i \(0.364815\pi\)
\(348\) 0 0
\(349\) −10.2174 −0.546925 −0.273462 0.961883i \(-0.588169\pi\)
−0.273462 + 0.961883i \(0.588169\pi\)
\(350\) 0 0
\(351\) −4.36921 −0.233211
\(352\) 0 0
\(353\) 15.3114 0.814944 0.407472 0.913218i \(-0.366410\pi\)
0.407472 + 0.913218i \(0.366410\pi\)
\(354\) 0 0
\(355\) −0.450560 −0.0239132
\(356\) 0 0
\(357\) −1.45207 −0.0768517
\(358\) 0 0
\(359\) −12.8431 −0.677833 −0.338917 0.940816i \(-0.610060\pi\)
−0.338917 + 0.940816i \(0.610060\pi\)
\(360\) 0 0
\(361\) −2.82311 −0.148585
\(362\) 0 0
\(363\) −10.2539 −0.538193
\(364\) 0 0
\(365\) −0.0997730 −0.00522236
\(366\) 0 0
\(367\) −24.5432 −1.28114 −0.640571 0.767899i \(-0.721302\pi\)
−0.640571 + 0.767899i \(0.721302\pi\)
\(368\) 0 0
\(369\) 2.42495 0.126238
\(370\) 0 0
\(371\) 4.89134 0.253946
\(372\) 0 0
\(373\) −11.9642 −0.619485 −0.309743 0.950820i \(-0.600243\pi\)
−0.309743 + 0.950820i \(0.600243\pi\)
\(374\) 0 0
\(375\) −0.349935 −0.0180706
\(376\) 0 0
\(377\) −5.64037 −0.290494
\(378\) 0 0
\(379\) −13.6386 −0.700568 −0.350284 0.936643i \(-0.613915\pi\)
−0.350284 + 0.936643i \(0.613915\pi\)
\(380\) 0 0
\(381\) −7.45717 −0.382042
\(382\) 0 0
\(383\) −3.00991 −0.153799 −0.0768996 0.997039i \(-0.524502\pi\)
−0.0768996 + 0.997039i \(0.524502\pi\)
\(384\) 0 0
\(385\) −0.0192712 −0.000982151 0
\(386\) 0 0
\(387\) 0.00158582 8.06120e−5 0
\(388\) 0 0
\(389\) 20.9575 1.06259 0.531295 0.847187i \(-0.321706\pi\)
0.531295 + 0.847187i \(0.321706\pi\)
\(390\) 0 0
\(391\) −18.7459 −0.948023
\(392\) 0 0
\(393\) −0.0329360 −0.00166140
\(394\) 0 0
\(395\) 0.252008 0.0126799
\(396\) 0 0
\(397\) 7.01282 0.351963 0.175982 0.984393i \(-0.443690\pi\)
0.175982 + 0.984393i \(0.443690\pi\)
\(398\) 0 0
\(399\) −2.56408 −0.128364
\(400\) 0 0
\(401\) −24.2870 −1.21284 −0.606418 0.795146i \(-0.707394\pi\)
−0.606418 + 0.795146i \(0.707394\pi\)
\(402\) 0 0
\(403\) 5.30082 0.264053
\(404\) 0 0
\(405\) 0.0349978 0.00173905
\(406\) 0 0
\(407\) −6.17247 −0.305958
\(408\) 0 0
\(409\) −19.3926 −0.958901 −0.479450 0.877569i \(-0.659164\pi\)
−0.479450 + 0.877569i \(0.659164\pi\)
\(410\) 0 0
\(411\) −13.7940 −0.680410
\(412\) 0 0
\(413\) −1.01517 −0.0499530
\(414\) 0 0
\(415\) −0.469959 −0.0230694
\(416\) 0 0
\(417\) 6.22618 0.304897
\(418\) 0 0
\(419\) 18.6325 0.910256 0.455128 0.890426i \(-0.349594\pi\)
0.455128 + 0.890426i \(0.349594\pi\)
\(420\) 0 0
\(421\) −22.8703 −1.11463 −0.557315 0.830301i \(-0.688168\pi\)
−0.557315 + 0.830301i \(0.688168\pi\)
\(422\) 0 0
\(423\) −3.98820 −0.193913
\(424\) 0 0
\(425\) 11.3859 0.552298
\(426\) 0 0
\(427\) −2.23174 −0.108001
\(428\) 0 0
\(429\) 3.77387 0.182204
\(430\) 0 0
\(431\) 25.2271 1.21515 0.607573 0.794264i \(-0.292143\pi\)
0.607573 + 0.794264i \(0.292143\pi\)
\(432\) 0 0
\(433\) −5.95961 −0.286400 −0.143200 0.989694i \(-0.545739\pi\)
−0.143200 + 0.989694i \(0.545739\pi\)
\(434\) 0 0
\(435\) 0.0451800 0.00216621
\(436\) 0 0
\(437\) −33.1017 −1.58347
\(438\) 0 0
\(439\) −0.672432 −0.0320934 −0.0160467 0.999871i \(-0.505108\pi\)
−0.0160467 + 0.999871i \(0.505108\pi\)
\(440\) 0 0
\(441\) −6.59359 −0.313980
\(442\) 0 0
\(443\) 32.4879 1.54354 0.771772 0.635899i \(-0.219370\pi\)
0.771772 + 0.635899i \(0.219370\pi\)
\(444\) 0 0
\(445\) −0.351577 −0.0166663
\(446\) 0 0
\(447\) 13.5572 0.641235
\(448\) 0 0
\(449\) 2.54165 0.119948 0.0599740 0.998200i \(-0.480898\pi\)
0.0599740 + 0.998200i \(0.480898\pi\)
\(450\) 0 0
\(451\) −2.09453 −0.0986277
\(452\) 0 0
\(453\) 4.23542 0.198998
\(454\) 0 0
\(455\) −0.0974826 −0.00457005
\(456\) 0 0
\(457\) 14.7451 0.689747 0.344873 0.938649i \(-0.387922\pi\)
0.344873 + 0.938649i \(0.387922\pi\)
\(458\) 0 0
\(459\) −2.27774 −0.106316
\(460\) 0 0
\(461\) 11.0554 0.514900 0.257450 0.966292i \(-0.417118\pi\)
0.257450 + 0.966292i \(0.417118\pi\)
\(462\) 0 0
\(463\) 9.73323 0.452341 0.226171 0.974088i \(-0.427379\pi\)
0.226171 + 0.974088i \(0.427379\pi\)
\(464\) 0 0
\(465\) −0.0424601 −0.00196904
\(466\) 0 0
\(467\) −19.1438 −0.885867 −0.442934 0.896554i \(-0.646062\pi\)
−0.442934 + 0.896554i \(0.646062\pi\)
\(468\) 0 0
\(469\) −10.1187 −0.467238
\(470\) 0 0
\(471\) 9.88889 0.455656
\(472\) 0 0
\(473\) −0.00136974 −6.29809e−5 0
\(474\) 0 0
\(475\) 20.1053 0.922496
\(476\) 0 0
\(477\) 7.67263 0.351305
\(478\) 0 0
\(479\) −6.43999 −0.294251 −0.147125 0.989118i \(-0.547002\pi\)
−0.147125 + 0.989118i \(0.547002\pi\)
\(480\) 0 0
\(481\) −31.2232 −1.42366
\(482\) 0 0
\(483\) 5.24671 0.238733
\(484\) 0 0
\(485\) 0.414157 0.0188059
\(486\) 0 0
\(487\) −37.0468 −1.67875 −0.839376 0.543552i \(-0.817079\pi\)
−0.839376 + 0.543552i \(0.817079\pi\)
\(488\) 0 0
\(489\) 7.43335 0.336148
\(490\) 0 0
\(491\) −0.353508 −0.0159536 −0.00797680 0.999968i \(-0.502539\pi\)
−0.00797680 + 0.999968i \(0.502539\pi\)
\(492\) 0 0
\(493\) −2.94042 −0.132430
\(494\) 0 0
\(495\) −0.0302291 −0.00135870
\(496\) 0 0
\(497\) −8.20720 −0.368143
\(498\) 0 0
\(499\) 3.01632 0.135029 0.0675144 0.997718i \(-0.478493\pi\)
0.0675144 + 0.997718i \(0.478493\pi\)
\(500\) 0 0
\(501\) −4.80704 −0.214763
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −0.550922 −0.0245157
\(506\) 0 0
\(507\) 6.08997 0.270465
\(508\) 0 0
\(509\) 22.6447 1.00371 0.501855 0.864952i \(-0.332651\pi\)
0.501855 + 0.864952i \(0.332651\pi\)
\(510\) 0 0
\(511\) −1.81742 −0.0803980
\(512\) 0 0
\(513\) −4.02205 −0.177578
\(514\) 0 0
\(515\) −0.400009 −0.0176265
\(516\) 0 0
\(517\) 3.44478 0.151501
\(518\) 0 0
\(519\) −20.4319 −0.896860
\(520\) 0 0
\(521\) −36.5888 −1.60298 −0.801492 0.598006i \(-0.795960\pi\)
−0.801492 + 0.598006i \(0.795960\pi\)
\(522\) 0 0
\(523\) 5.01297 0.219202 0.109601 0.993976i \(-0.465043\pi\)
0.109601 + 0.993976i \(0.465043\pi\)
\(524\) 0 0
\(525\) −3.18674 −0.139081
\(526\) 0 0
\(527\) 2.76341 0.120376
\(528\) 0 0
\(529\) 44.7339 1.94495
\(530\) 0 0
\(531\) −1.59240 −0.0691044
\(532\) 0 0
\(533\) −10.5951 −0.458925
\(534\) 0 0
\(535\) −0.295725 −0.0127853
\(536\) 0 0
\(537\) −1.81895 −0.0784936
\(538\) 0 0
\(539\) 5.69516 0.245308
\(540\) 0 0
\(541\) 23.3051 1.00197 0.500983 0.865457i \(-0.332972\pi\)
0.500983 + 0.865457i \(0.332972\pi\)
\(542\) 0 0
\(543\) −5.92712 −0.254357
\(544\) 0 0
\(545\) 0.273631 0.0117211
\(546\) 0 0
\(547\) 10.8082 0.462126 0.231063 0.972939i \(-0.425780\pi\)
0.231063 + 0.972939i \(0.425780\pi\)
\(548\) 0 0
\(549\) −3.50074 −0.149408
\(550\) 0 0
\(551\) −5.19221 −0.221196
\(552\) 0 0
\(553\) 4.59047 0.195207
\(554\) 0 0
\(555\) 0.250101 0.0106162
\(556\) 0 0
\(557\) 28.5876 1.21130 0.605648 0.795733i \(-0.292914\pi\)
0.605648 + 0.795733i \(0.292914\pi\)
\(558\) 0 0
\(559\) −0.00692879 −0.000293057 0
\(560\) 0 0
\(561\) 1.96738 0.0830629
\(562\) 0 0
\(563\) 8.89314 0.374801 0.187401 0.982284i \(-0.439994\pi\)
0.187401 + 0.982284i \(0.439994\pi\)
\(564\) 0 0
\(565\) −0.0840487 −0.00353596
\(566\) 0 0
\(567\) 0.637505 0.0267727
\(568\) 0 0
\(569\) −16.6552 −0.698222 −0.349111 0.937081i \(-0.613516\pi\)
−0.349111 + 0.937081i \(0.613516\pi\)
\(570\) 0 0
\(571\) −4.35772 −0.182365 −0.0911825 0.995834i \(-0.529065\pi\)
−0.0911825 + 0.995834i \(0.529065\pi\)
\(572\) 0 0
\(573\) 0.852539 0.0356153
\(574\) 0 0
\(575\) −41.1402 −1.71567
\(576\) 0 0
\(577\) 3.48423 0.145050 0.0725251 0.997367i \(-0.476894\pi\)
0.0725251 + 0.997367i \(0.476894\pi\)
\(578\) 0 0
\(579\) −0.273987 −0.0113865
\(580\) 0 0
\(581\) −8.56057 −0.355152
\(582\) 0 0
\(583\) −6.62717 −0.274469
\(584\) 0 0
\(585\) −0.152913 −0.00632216
\(586\) 0 0
\(587\) −8.60458 −0.355149 −0.177575 0.984107i \(-0.556825\pi\)
−0.177575 + 0.984107i \(0.556825\pi\)
\(588\) 0 0
\(589\) 4.87964 0.201062
\(590\) 0 0
\(591\) −5.07126 −0.208604
\(592\) 0 0
\(593\) 30.3841 1.24773 0.623863 0.781533i \(-0.285562\pi\)
0.623863 + 0.781533i \(0.285562\pi\)
\(594\) 0 0
\(595\) −0.0508193 −0.00208339
\(596\) 0 0
\(597\) 4.29664 0.175850
\(598\) 0 0
\(599\) 23.5843 0.963626 0.481813 0.876274i \(-0.339978\pi\)
0.481813 + 0.876274i \(0.339978\pi\)
\(600\) 0 0
\(601\) 10.6263 0.433455 0.216728 0.976232i \(-0.430462\pi\)
0.216728 + 0.976232i \(0.430462\pi\)
\(602\) 0 0
\(603\) −15.8723 −0.646371
\(604\) 0 0
\(605\) −0.358866 −0.0145900
\(606\) 0 0
\(607\) 9.78081 0.396991 0.198495 0.980102i \(-0.436395\pi\)
0.198495 + 0.980102i \(0.436395\pi\)
\(608\) 0 0
\(609\) 0.822979 0.0333488
\(610\) 0 0
\(611\) 17.4253 0.704952
\(612\) 0 0
\(613\) 24.6552 0.995813 0.497906 0.867231i \(-0.334102\pi\)
0.497906 + 0.867231i \(0.334102\pi\)
\(614\) 0 0
\(615\) 0.0848680 0.00342221
\(616\) 0 0
\(617\) −17.2052 −0.692657 −0.346328 0.938113i \(-0.612572\pi\)
−0.346328 + 0.938113i \(0.612572\pi\)
\(618\) 0 0
\(619\) 18.2401 0.733133 0.366567 0.930392i \(-0.380533\pi\)
0.366567 + 0.930392i \(0.380533\pi\)
\(620\) 0 0
\(621\) 8.23006 0.330261
\(622\) 0 0
\(623\) −6.40417 −0.256578
\(624\) 0 0
\(625\) 24.9816 0.999265
\(626\) 0 0
\(627\) 3.47401 0.138739
\(628\) 0 0
\(629\) −16.2772 −0.649013
\(630\) 0 0
\(631\) 25.3591 1.00953 0.504766 0.863256i \(-0.331579\pi\)
0.504766 + 0.863256i \(0.331579\pi\)
\(632\) 0 0
\(633\) 19.7928 0.786692
\(634\) 0 0
\(635\) −0.260985 −0.0103569
\(636\) 0 0
\(637\) 28.8087 1.14144
\(638\) 0 0
\(639\) −12.8739 −0.509285
\(640\) 0 0
\(641\) 7.75302 0.306226 0.153113 0.988209i \(-0.451070\pi\)
0.153113 + 0.988209i \(0.451070\pi\)
\(642\) 0 0
\(643\) 22.4658 0.885966 0.442983 0.896530i \(-0.353920\pi\)
0.442983 + 0.896530i \(0.353920\pi\)
\(644\) 0 0
\(645\) 5.55004e−5 0 2.18532e−6 0
\(646\) 0 0
\(647\) 5.50543 0.216441 0.108220 0.994127i \(-0.465485\pi\)
0.108220 + 0.994127i \(0.465485\pi\)
\(648\) 0 0
\(649\) 1.37543 0.0539902
\(650\) 0 0
\(651\) −0.773435 −0.0303133
\(652\) 0 0
\(653\) 8.38115 0.327980 0.163990 0.986462i \(-0.447564\pi\)
0.163990 + 0.986462i \(0.447564\pi\)
\(654\) 0 0
\(655\) −0.00115269 −4.50393e−5 0
\(656\) 0 0
\(657\) −2.85083 −0.111222
\(658\) 0 0
\(659\) 24.1879 0.942225 0.471112 0.882073i \(-0.343853\pi\)
0.471112 + 0.882073i \(0.343853\pi\)
\(660\) 0 0
\(661\) 13.8859 0.540098 0.270049 0.962847i \(-0.412960\pi\)
0.270049 + 0.962847i \(0.412960\pi\)
\(662\) 0 0
\(663\) 9.95192 0.386500
\(664\) 0 0
\(665\) −0.0897371 −0.00347985
\(666\) 0 0
\(667\) 10.6245 0.411382
\(668\) 0 0
\(669\) −0.948794 −0.0366825
\(670\) 0 0
\(671\) 3.02374 0.116730
\(672\) 0 0
\(673\) −36.6544 −1.41292 −0.706461 0.707752i \(-0.749709\pi\)
−0.706461 + 0.707752i \(0.749709\pi\)
\(674\) 0 0
\(675\) −4.99878 −0.192403
\(676\) 0 0
\(677\) −32.4036 −1.24537 −0.622685 0.782473i \(-0.713958\pi\)
−0.622685 + 0.782473i \(0.713958\pi\)
\(678\) 0 0
\(679\) 7.54410 0.289516
\(680\) 0 0
\(681\) 15.3021 0.586377
\(682\) 0 0
\(683\) 31.3861 1.20095 0.600477 0.799642i \(-0.294977\pi\)
0.600477 + 0.799642i \(0.294977\pi\)
\(684\) 0 0
\(685\) −0.482761 −0.0184453
\(686\) 0 0
\(687\) −14.9304 −0.569629
\(688\) 0 0
\(689\) −33.5233 −1.27714
\(690\) 0 0
\(691\) −4.62328 −0.175878 −0.0879389 0.996126i \(-0.528028\pi\)
−0.0879389 + 0.996126i \(0.528028\pi\)
\(692\) 0 0
\(693\) −0.550640 −0.0209171
\(694\) 0 0
\(695\) 0.217903 0.00826552
\(696\) 0 0
\(697\) −5.52341 −0.209214
\(698\) 0 0
\(699\) 1.04199 0.0394117
\(700\) 0 0
\(701\) −18.8324 −0.711288 −0.355644 0.934621i \(-0.615738\pi\)
−0.355644 + 0.934621i \(0.615738\pi\)
\(702\) 0 0
\(703\) −28.7423 −1.08404
\(704\) 0 0
\(705\) −0.139578 −0.00525683
\(706\) 0 0
\(707\) −10.0354 −0.377419
\(708\) 0 0
\(709\) −27.1420 −1.01934 −0.509671 0.860370i \(-0.670233\pi\)
−0.509671 + 0.860370i \(0.670233\pi\)
\(710\) 0 0
\(711\) 7.20069 0.270047
\(712\) 0 0
\(713\) −9.98490 −0.373937
\(714\) 0 0
\(715\) 0.132077 0.00493940
\(716\) 0 0
\(717\) −4.80544 −0.179462
\(718\) 0 0
\(719\) −48.9125 −1.82413 −0.912065 0.410046i \(-0.865513\pi\)
−0.912065 + 0.410046i \(0.865513\pi\)
\(720\) 0 0
\(721\) −7.28640 −0.271360
\(722\) 0 0
\(723\) 24.4322 0.908642
\(724\) 0 0
\(725\) −6.45310 −0.239662
\(726\) 0 0
\(727\) 47.3184 1.75494 0.877471 0.479630i \(-0.159229\pi\)
0.877471 + 0.479630i \(0.159229\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.00361209 −0.000133598 0
\(732\) 0 0
\(733\) 22.1527 0.818230 0.409115 0.912483i \(-0.365837\pi\)
0.409115 + 0.912483i \(0.365837\pi\)
\(734\) 0 0
\(735\) −0.230761 −0.00851175
\(736\) 0 0
\(737\) 13.7096 0.505000
\(738\) 0 0
\(739\) 23.6128 0.868612 0.434306 0.900765i \(-0.356994\pi\)
0.434306 + 0.900765i \(0.356994\pi\)
\(740\) 0 0
\(741\) 17.5732 0.645566
\(742\) 0 0
\(743\) 18.2444 0.669321 0.334661 0.942339i \(-0.391378\pi\)
0.334661 + 0.942339i \(0.391378\pi\)
\(744\) 0 0
\(745\) 0.474473 0.0173833
\(746\) 0 0
\(747\) −13.4282 −0.491313
\(748\) 0 0
\(749\) −5.38679 −0.196829
\(750\) 0 0
\(751\) −38.7717 −1.41480 −0.707399 0.706815i \(-0.750132\pi\)
−0.707399 + 0.706815i \(0.750132\pi\)
\(752\) 0 0
\(753\) −4.80461 −0.175090
\(754\) 0 0
\(755\) 0.148231 0.00539466
\(756\) 0 0
\(757\) 46.9590 1.70675 0.853377 0.521293i \(-0.174550\pi\)
0.853377 + 0.521293i \(0.174550\pi\)
\(758\) 0 0
\(759\) −7.10865 −0.258028
\(760\) 0 0
\(761\) −11.4071 −0.413507 −0.206754 0.978393i \(-0.566290\pi\)
−0.206754 + 0.978393i \(0.566290\pi\)
\(762\) 0 0
\(763\) 4.98435 0.180446
\(764\) 0 0
\(765\) −0.0797159 −0.00288213
\(766\) 0 0
\(767\) 6.95754 0.251222
\(768\) 0 0
\(769\) 21.6809 0.781833 0.390917 0.920426i \(-0.372158\pi\)
0.390917 + 0.920426i \(0.372158\pi\)
\(770\) 0 0
\(771\) −18.2299 −0.656535
\(772\) 0 0
\(773\) −8.81854 −0.317181 −0.158590 0.987344i \(-0.550695\pi\)
−0.158590 + 0.987344i \(0.550695\pi\)
\(774\) 0 0
\(775\) 6.06463 0.217848
\(776\) 0 0
\(777\) 4.55573 0.163436
\(778\) 0 0
\(779\) −9.75328 −0.349448
\(780\) 0 0
\(781\) 11.1198 0.397896
\(782\) 0 0
\(783\) 1.29094 0.0461343
\(784\) 0 0
\(785\) 0.346089 0.0123525
\(786\) 0 0
\(787\) −9.74371 −0.347326 −0.173663 0.984805i \(-0.555560\pi\)
−0.173663 + 0.984805i \(0.555560\pi\)
\(788\) 0 0
\(789\) −27.2527 −0.970220
\(790\) 0 0
\(791\) −1.53100 −0.0544359
\(792\) 0 0
\(793\) 15.2955 0.543158
\(794\) 0 0
\(795\) 0.268525 0.00952360
\(796\) 0 0
\(797\) −40.7895 −1.44484 −0.722419 0.691456i \(-0.756970\pi\)
−0.722419 + 0.691456i \(0.756970\pi\)
\(798\) 0 0
\(799\) 9.08409 0.321372
\(800\) 0 0
\(801\) −10.0457 −0.354946
\(802\) 0 0
\(803\) 2.46239 0.0868957
\(804\) 0 0
\(805\) 0.183623 0.00647187
\(806\) 0 0
\(807\) 15.4718 0.544635
\(808\) 0 0
\(809\) 28.4540 1.00039 0.500195 0.865913i \(-0.333262\pi\)
0.500195 + 0.865913i \(0.333262\pi\)
\(810\) 0 0
\(811\) 22.2541 0.781447 0.390723 0.920508i \(-0.372225\pi\)
0.390723 + 0.920508i \(0.372225\pi\)
\(812\) 0 0
\(813\) 12.3488 0.433092
\(814\) 0 0
\(815\) 0.260151 0.00911269
\(816\) 0 0
\(817\) −0.00637826 −0.000223147 0
\(818\) 0 0
\(819\) −2.78539 −0.0973294
\(820\) 0 0
\(821\) −44.4240 −1.55041 −0.775203 0.631712i \(-0.782353\pi\)
−0.775203 + 0.631712i \(0.782353\pi\)
\(822\) 0 0
\(823\) −47.1094 −1.64213 −0.821065 0.570835i \(-0.806619\pi\)
−0.821065 + 0.570835i \(0.806619\pi\)
\(824\) 0 0
\(825\) 4.31765 0.150321
\(826\) 0 0
\(827\) −33.0786 −1.15026 −0.575128 0.818063i \(-0.695048\pi\)
−0.575128 + 0.818063i \(0.695048\pi\)
\(828\) 0 0
\(829\) −40.0005 −1.38927 −0.694637 0.719361i \(-0.744435\pi\)
−0.694637 + 0.719361i \(0.744435\pi\)
\(830\) 0 0
\(831\) 13.0131 0.451420
\(832\) 0 0
\(833\) 15.0185 0.520359
\(834\) 0 0
\(835\) −0.168236 −0.00582204
\(836\) 0 0
\(837\) −1.21322 −0.0419351
\(838\) 0 0
\(839\) −23.4299 −0.808889 −0.404444 0.914563i \(-0.632535\pi\)
−0.404444 + 0.914563i \(0.632535\pi\)
\(840\) 0 0
\(841\) −27.3335 −0.942534
\(842\) 0 0
\(843\) 14.6624 0.504998
\(844\) 0 0
\(845\) 0.213135 0.00733208
\(846\) 0 0
\(847\) −6.53694 −0.224612
\(848\) 0 0
\(849\) 4.37195 0.150045
\(850\) 0 0
\(851\) 58.8136 2.01610
\(852\) 0 0
\(853\) −30.5289 −1.04529 −0.522645 0.852551i \(-0.675055\pi\)
−0.522645 + 0.852551i \(0.675055\pi\)
\(854\) 0 0
\(855\) −0.140763 −0.00481399
\(856\) 0 0
\(857\) 13.3434 0.455803 0.227902 0.973684i \(-0.426814\pi\)
0.227902 + 0.973684i \(0.426814\pi\)
\(858\) 0 0
\(859\) −33.1185 −1.12999 −0.564994 0.825095i \(-0.691122\pi\)
−0.564994 + 0.825095i \(0.691122\pi\)
\(860\) 0 0
\(861\) 1.54592 0.0526848
\(862\) 0 0
\(863\) −38.8602 −1.32282 −0.661409 0.750026i \(-0.730041\pi\)
−0.661409 + 0.750026i \(0.730041\pi\)
\(864\) 0 0
\(865\) −0.715071 −0.0243131
\(866\) 0 0
\(867\) −11.8119 −0.401153
\(868\) 0 0
\(869\) −6.21954 −0.210983
\(870\) 0 0
\(871\) 69.3495 2.34982
\(872\) 0 0
\(873\) 11.8338 0.400513
\(874\) 0 0
\(875\) −0.223085 −0.00754166
\(876\) 0 0
\(877\) 48.6809 1.64384 0.821919 0.569604i \(-0.192904\pi\)
0.821919 + 0.569604i \(0.192904\pi\)
\(878\) 0 0
\(879\) −23.6309 −0.797052
\(880\) 0 0
\(881\) 9.27848 0.312600 0.156300 0.987710i \(-0.450043\pi\)
0.156300 + 0.987710i \(0.450043\pi\)
\(882\) 0 0
\(883\) 20.7522 0.698368 0.349184 0.937054i \(-0.386459\pi\)
0.349184 + 0.937054i \(0.386459\pi\)
\(884\) 0 0
\(885\) −0.0557306 −0.00187336
\(886\) 0 0
\(887\) 47.6183 1.59887 0.799433 0.600756i \(-0.205134\pi\)
0.799433 + 0.600756i \(0.205134\pi\)
\(888\) 0 0
\(889\) −4.75398 −0.159443
\(890\) 0 0
\(891\) −0.863742 −0.0289365
\(892\) 0 0
\(893\) 16.0408 0.536783
\(894\) 0 0
\(895\) −0.0636593 −0.00212790
\(896\) 0 0
\(897\) −35.9588 −1.20063
\(898\) 0 0
\(899\) −1.56619 −0.0522355
\(900\) 0 0
\(901\) −17.4762 −0.582218
\(902\) 0 0
\(903\) 0.00101097 3.36430e−5 0
\(904\) 0 0
\(905\) −0.207436 −0.00689541
\(906\) 0 0
\(907\) 22.5067 0.747323 0.373662 0.927565i \(-0.378102\pi\)
0.373662 + 0.927565i \(0.378102\pi\)
\(908\) 0 0
\(909\) −15.7416 −0.522117
\(910\) 0 0
\(911\) 23.9254 0.792685 0.396343 0.918103i \(-0.370279\pi\)
0.396343 + 0.918103i \(0.370279\pi\)
\(912\) 0 0
\(913\) 11.5985 0.383855
\(914\) 0 0
\(915\) −0.122518 −0.00405033
\(916\) 0 0
\(917\) −0.0209969 −0.000693378 0
\(918\) 0 0
\(919\) 40.6929 1.34234 0.671168 0.741305i \(-0.265793\pi\)
0.671168 + 0.741305i \(0.265793\pi\)
\(920\) 0 0
\(921\) 16.8530 0.555325
\(922\) 0 0
\(923\) 56.2489 1.85145
\(924\) 0 0
\(925\) −35.7222 −1.17454
\(926\) 0 0
\(927\) −11.4296 −0.375396
\(928\) 0 0
\(929\) −1.00948 −0.0331198 −0.0165599 0.999863i \(-0.505271\pi\)
−0.0165599 + 0.999863i \(0.505271\pi\)
\(930\) 0 0
\(931\) 26.5197 0.869149
\(932\) 0 0
\(933\) −8.09954 −0.265167
\(934\) 0 0
\(935\) 0.0688540 0.00225177
\(936\) 0 0
\(937\) −12.0701 −0.394314 −0.197157 0.980372i \(-0.563171\pi\)
−0.197157 + 0.980372i \(0.563171\pi\)
\(938\) 0 0
\(939\) −27.5042 −0.897566
\(940\) 0 0
\(941\) −12.1525 −0.396161 −0.198080 0.980186i \(-0.563471\pi\)
−0.198080 + 0.980186i \(0.563471\pi\)
\(942\) 0 0
\(943\) 19.9575 0.649906
\(944\) 0 0
\(945\) 0.0223113 0.000725786 0
\(946\) 0 0
\(947\) −19.0889 −0.620306 −0.310153 0.950687i \(-0.600380\pi\)
−0.310153 + 0.950687i \(0.600380\pi\)
\(948\) 0 0
\(949\) 12.4559 0.404335
\(950\) 0 0
\(951\) −22.0581 −0.715284
\(952\) 0 0
\(953\) −20.4334 −0.661904 −0.330952 0.943648i \(-0.607370\pi\)
−0.330952 + 0.943648i \(0.607370\pi\)
\(954\) 0 0
\(955\) 0.0298370 0.000965503 0
\(956\) 0 0
\(957\) −1.11504 −0.0360440
\(958\) 0 0
\(959\) −8.79377 −0.283966
\(960\) 0 0
\(961\) −29.5281 −0.952519
\(962\) 0 0
\(963\) −8.44980 −0.272291
\(964\) 0 0
\(965\) −0.00958893 −0.000308679 0
\(966\) 0 0
\(967\) 41.4076 1.33158 0.665790 0.746140i \(-0.268095\pi\)
0.665790 + 0.746140i \(0.268095\pi\)
\(968\) 0 0
\(969\) 9.16118 0.294300
\(970\) 0 0
\(971\) −15.5077 −0.497667 −0.248834 0.968546i \(-0.580047\pi\)
−0.248834 + 0.968546i \(0.580047\pi\)
\(972\) 0 0
\(973\) 3.96922 0.127247
\(974\) 0 0
\(975\) 21.8407 0.699462
\(976\) 0 0
\(977\) 43.6653 1.39698 0.698489 0.715621i \(-0.253856\pi\)
0.698489 + 0.715621i \(0.253856\pi\)
\(978\) 0 0
\(979\) 8.67687 0.277314
\(980\) 0 0
\(981\) 7.81853 0.249626
\(982\) 0 0
\(983\) 16.1033 0.513615 0.256807 0.966463i \(-0.417329\pi\)
0.256807 + 0.966463i \(0.417329\pi\)
\(984\) 0 0
\(985\) −0.177483 −0.00565508
\(986\) 0 0
\(987\) −2.54250 −0.0809287
\(988\) 0 0
\(989\) 0.0130514 0.000415011 0
\(990\) 0 0
\(991\) 22.2551 0.706957 0.353479 0.935443i \(-0.384999\pi\)
0.353479 + 0.935443i \(0.384999\pi\)
\(992\) 0 0
\(993\) 22.3009 0.707696
\(994\) 0 0
\(995\) 0.150373 0.00476714
\(996\) 0 0
\(997\) −14.7582 −0.467396 −0.233698 0.972309i \(-0.575083\pi\)
−0.233698 + 0.972309i \(0.575083\pi\)
\(998\) 0 0
\(999\) 7.14619 0.226096
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 \(a_p\))