Properties

Label 6003.2.a.t.1.12
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.144466 q^{2} -1.97913 q^{4} -4.08805 q^{5} -0.828594 q^{7} -0.574849 q^{8} +O(q^{10})\) \(q+0.144466 q^{2} -1.97913 q^{4} -4.08805 q^{5} -0.828594 q^{7} -0.574849 q^{8} -0.590584 q^{10} +0.0328797 q^{11} -3.12976 q^{13} -0.119704 q^{14} +3.87521 q^{16} +1.27064 q^{17} -4.11917 q^{19} +8.09078 q^{20} +0.00474999 q^{22} +1.00000 q^{23} +11.7122 q^{25} -0.452143 q^{26} +1.63989 q^{28} +1.00000 q^{29} +6.85696 q^{31} +1.70953 q^{32} +0.183564 q^{34} +3.38733 q^{35} -3.30243 q^{37} -0.595079 q^{38} +2.35001 q^{40} +6.64755 q^{41} -1.68035 q^{43} -0.0650731 q^{44} +0.144466 q^{46} +5.69373 q^{47} -6.31343 q^{49} +1.69201 q^{50} +6.19419 q^{52} +7.40328 q^{53} -0.134414 q^{55} +0.476316 q^{56} +0.144466 q^{58} -2.70220 q^{59} +7.51934 q^{61} +0.990597 q^{62} -7.50346 q^{64} +12.7946 q^{65} -4.02039 q^{67} -2.51476 q^{68} +0.489354 q^{70} -3.73962 q^{71} +2.01339 q^{73} -0.477089 q^{74} +8.15236 q^{76} -0.0272439 q^{77} +15.8864 q^{79} -15.8421 q^{80} +0.960344 q^{82} +11.5703 q^{83} -5.19443 q^{85} -0.242754 q^{86} -0.0189008 q^{88} -7.36813 q^{89} +2.59330 q^{91} -1.97913 q^{92} +0.822550 q^{94} +16.8394 q^{95} -17.3350 q^{97} -0.912076 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.144466 0.102153 0.0510764 0.998695i \(-0.483735\pi\)
0.0510764 + 0.998695i \(0.483735\pi\)
\(3\) 0 0
\(4\) −1.97913 −0.989565
\(5\) −4.08805 −1.82823 −0.914116 0.405452i \(-0.867114\pi\)
−0.914116 + 0.405452i \(0.867114\pi\)
\(6\) 0 0
\(7\) −0.828594 −0.313179 −0.156589 0.987664i \(-0.550050\pi\)
−0.156589 + 0.987664i \(0.550050\pi\)
\(8\) −0.574849 −0.203240
\(9\) 0 0
\(10\) −0.590584 −0.186759
\(11\) 0.0328797 0.00991359 0.00495680 0.999988i \(-0.498422\pi\)
0.00495680 + 0.999988i \(0.498422\pi\)
\(12\) 0 0
\(13\) −3.12976 −0.868038 −0.434019 0.900904i \(-0.642905\pi\)
−0.434019 + 0.900904i \(0.642905\pi\)
\(14\) −0.119704 −0.0319921
\(15\) 0 0
\(16\) 3.87521 0.968803
\(17\) 1.27064 0.308175 0.154087 0.988057i \(-0.450756\pi\)
0.154087 + 0.988057i \(0.450756\pi\)
\(18\) 0 0
\(19\) −4.11917 −0.945001 −0.472501 0.881330i \(-0.656649\pi\)
−0.472501 + 0.881330i \(0.656649\pi\)
\(20\) 8.09078 1.80915
\(21\) 0 0
\(22\) 0.00474999 0.00101270
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.7122 2.34243
\(26\) −0.452143 −0.0886726
\(27\) 0 0
\(28\) 1.63989 0.309911
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 6.85696 1.23155 0.615773 0.787924i \(-0.288844\pi\)
0.615773 + 0.787924i \(0.288844\pi\)
\(32\) 1.70953 0.302206
\(33\) 0 0
\(34\) 0.183564 0.0314809
\(35\) 3.38733 0.572564
\(36\) 0 0
\(37\) −3.30243 −0.542917 −0.271458 0.962450i \(-0.587506\pi\)
−0.271458 + 0.962450i \(0.587506\pi\)
\(38\) −0.595079 −0.0965346
\(39\) 0 0
\(40\) 2.35001 0.371569
\(41\) 6.64755 1.03817 0.519086 0.854722i \(-0.326272\pi\)
0.519086 + 0.854722i \(0.326272\pi\)
\(42\) 0 0
\(43\) −1.68035 −0.256251 −0.128126 0.991758i \(-0.540896\pi\)
−0.128126 + 0.991758i \(0.540896\pi\)
\(44\) −0.0650731 −0.00981014
\(45\) 0 0
\(46\) 0.144466 0.0213003
\(47\) 5.69373 0.830515 0.415258 0.909704i \(-0.363691\pi\)
0.415258 + 0.909704i \(0.363691\pi\)
\(48\) 0 0
\(49\) −6.31343 −0.901919
\(50\) 1.69201 0.239286
\(51\) 0 0
\(52\) 6.19419 0.858980
\(53\) 7.40328 1.01692 0.508459 0.861086i \(-0.330215\pi\)
0.508459 + 0.861086i \(0.330215\pi\)
\(54\) 0 0
\(55\) −0.134414 −0.0181243
\(56\) 0.476316 0.0636504
\(57\) 0 0
\(58\) 0.144466 0.0189693
\(59\) −2.70220 −0.351796 −0.175898 0.984408i \(-0.556283\pi\)
−0.175898 + 0.984408i \(0.556283\pi\)
\(60\) 0 0
\(61\) 7.51934 0.962753 0.481376 0.876514i \(-0.340137\pi\)
0.481376 + 0.876514i \(0.340137\pi\)
\(62\) 0.990597 0.125806
\(63\) 0 0
\(64\) −7.50346 −0.937932
\(65\) 12.7946 1.58698
\(66\) 0 0
\(67\) −4.02039 −0.491169 −0.245585 0.969375i \(-0.578980\pi\)
−0.245585 + 0.969375i \(0.578980\pi\)
\(68\) −2.51476 −0.304959
\(69\) 0 0
\(70\) 0.489354 0.0584890
\(71\) −3.73962 −0.443812 −0.221906 0.975068i \(-0.571228\pi\)
−0.221906 + 0.975068i \(0.571228\pi\)
\(72\) 0 0
\(73\) 2.01339 0.235649 0.117825 0.993034i \(-0.462408\pi\)
0.117825 + 0.993034i \(0.462408\pi\)
\(74\) −0.477089 −0.0554605
\(75\) 0 0
\(76\) 8.15236 0.935140
\(77\) −0.0272439 −0.00310473
\(78\) 0 0
\(79\) 15.8864 1.78736 0.893682 0.448702i \(-0.148113\pi\)
0.893682 + 0.448702i \(0.148113\pi\)
\(80\) −15.8421 −1.77120
\(81\) 0 0
\(82\) 0.960344 0.106052
\(83\) 11.5703 1.27000 0.635002 0.772511i \(-0.280999\pi\)
0.635002 + 0.772511i \(0.280999\pi\)
\(84\) 0 0
\(85\) −5.19443 −0.563415
\(86\) −0.242754 −0.0261768
\(87\) 0 0
\(88\) −0.0189008 −0.00201484
\(89\) −7.36813 −0.781020 −0.390510 0.920599i \(-0.627701\pi\)
−0.390510 + 0.920599i \(0.627701\pi\)
\(90\) 0 0
\(91\) 2.59330 0.271851
\(92\) −1.97913 −0.206339
\(93\) 0 0
\(94\) 0.822550 0.0848395
\(95\) 16.8394 1.72768
\(96\) 0 0
\(97\) −17.3350 −1.76010 −0.880051 0.474879i \(-0.842492\pi\)
−0.880051 + 0.474879i \(0.842492\pi\)
\(98\) −0.912076 −0.0921336
\(99\) 0 0
\(100\) −23.1799 −2.31799
\(101\) −2.51480 −0.250232 −0.125116 0.992142i \(-0.539930\pi\)
−0.125116 + 0.992142i \(0.539930\pi\)
\(102\) 0 0
\(103\) −7.00357 −0.690083 −0.345041 0.938588i \(-0.612135\pi\)
−0.345041 + 0.938588i \(0.612135\pi\)
\(104\) 1.79914 0.176420
\(105\) 0 0
\(106\) 1.06952 0.103881
\(107\) 5.54507 0.536062 0.268031 0.963410i \(-0.413627\pi\)
0.268031 + 0.963410i \(0.413627\pi\)
\(108\) 0 0
\(109\) −5.88688 −0.563860 −0.281930 0.959435i \(-0.590975\pi\)
−0.281930 + 0.959435i \(0.590975\pi\)
\(110\) −0.0194182 −0.00185145
\(111\) 0 0
\(112\) −3.21098 −0.303409
\(113\) 18.6370 1.75322 0.876611 0.481199i \(-0.159799\pi\)
0.876611 + 0.481199i \(0.159799\pi\)
\(114\) 0 0
\(115\) −4.08805 −0.381213
\(116\) −1.97913 −0.183758
\(117\) 0 0
\(118\) −0.390376 −0.0359370
\(119\) −1.05284 −0.0965139
\(120\) 0 0
\(121\) −10.9989 −0.999902
\(122\) 1.08629 0.0983480
\(123\) 0 0
\(124\) −13.5708 −1.21869
\(125\) −27.4397 −2.45428
\(126\) 0 0
\(127\) −15.5960 −1.38393 −0.691963 0.721933i \(-0.743254\pi\)
−0.691963 + 0.721933i \(0.743254\pi\)
\(128\) −4.50306 −0.398018
\(129\) 0 0
\(130\) 1.84838 0.162114
\(131\) −6.67906 −0.583552 −0.291776 0.956487i \(-0.594246\pi\)
−0.291776 + 0.956487i \(0.594246\pi\)
\(132\) 0 0
\(133\) 3.41311 0.295955
\(134\) −0.580810 −0.0501743
\(135\) 0 0
\(136\) −0.730424 −0.0626334
\(137\) 13.8703 1.18502 0.592508 0.805565i \(-0.298138\pi\)
0.592508 + 0.805565i \(0.298138\pi\)
\(138\) 0 0
\(139\) 4.53966 0.385049 0.192524 0.981292i \(-0.438333\pi\)
0.192524 + 0.981292i \(0.438333\pi\)
\(140\) −6.70397 −0.566589
\(141\) 0 0
\(142\) −0.540248 −0.0453366
\(143\) −0.102905 −0.00860538
\(144\) 0 0
\(145\) −4.08805 −0.339494
\(146\) 0.290866 0.0240723
\(147\) 0 0
\(148\) 6.53594 0.537251
\(149\) 15.0677 1.23440 0.617199 0.786807i \(-0.288267\pi\)
0.617199 + 0.786807i \(0.288267\pi\)
\(150\) 0 0
\(151\) 4.02276 0.327368 0.163684 0.986513i \(-0.447662\pi\)
0.163684 + 0.986513i \(0.447662\pi\)
\(152\) 2.36790 0.192062
\(153\) 0 0
\(154\) −0.00393581 −0.000317157 0
\(155\) −28.0316 −2.25155
\(156\) 0 0
\(157\) −0.424831 −0.0339052 −0.0169526 0.999856i \(-0.505396\pi\)
−0.0169526 + 0.999856i \(0.505396\pi\)
\(158\) 2.29505 0.182584
\(159\) 0 0
\(160\) −6.98866 −0.552502
\(161\) −0.828594 −0.0653023
\(162\) 0 0
\(163\) −10.2009 −0.798993 −0.399497 0.916735i \(-0.630815\pi\)
−0.399497 + 0.916735i \(0.630815\pi\)
\(164\) −13.1564 −1.02734
\(165\) 0 0
\(166\) 1.67151 0.129735
\(167\) −19.4197 −1.50274 −0.751370 0.659882i \(-0.770606\pi\)
−0.751370 + 0.659882i \(0.770606\pi\)
\(168\) 0 0
\(169\) −3.20463 −0.246510
\(170\) −0.750419 −0.0575545
\(171\) 0 0
\(172\) 3.32564 0.253577
\(173\) −22.8330 −1.73596 −0.867979 0.496601i \(-0.834581\pi\)
−0.867979 + 0.496601i \(0.834581\pi\)
\(174\) 0 0
\(175\) −9.70463 −0.733601
\(176\) 0.127416 0.00960432
\(177\) 0 0
\(178\) −1.06444 −0.0797834
\(179\) 9.79123 0.731831 0.365915 0.930648i \(-0.380756\pi\)
0.365915 + 0.930648i \(0.380756\pi\)
\(180\) 0 0
\(181\) 20.8077 1.54662 0.773310 0.634028i \(-0.218599\pi\)
0.773310 + 0.634028i \(0.218599\pi\)
\(182\) 0.374643 0.0277704
\(183\) 0 0
\(184\) −0.574849 −0.0423784
\(185\) 13.5005 0.992578
\(186\) 0 0
\(187\) 0.0417781 0.00305512
\(188\) −11.2686 −0.821849
\(189\) 0 0
\(190\) 2.43271 0.176488
\(191\) −4.12720 −0.298634 −0.149317 0.988789i \(-0.547707\pi\)
−0.149317 + 0.988789i \(0.547707\pi\)
\(192\) 0 0
\(193\) 23.4133 1.68533 0.842664 0.538440i \(-0.180986\pi\)
0.842664 + 0.538440i \(0.180986\pi\)
\(194\) −2.50432 −0.179799
\(195\) 0 0
\(196\) 12.4951 0.892507
\(197\) −14.0371 −1.00010 −0.500051 0.865996i \(-0.666686\pi\)
−0.500051 + 0.865996i \(0.666686\pi\)
\(198\) 0 0
\(199\) 0.624891 0.0442973 0.0221487 0.999755i \(-0.492949\pi\)
0.0221487 + 0.999755i \(0.492949\pi\)
\(200\) −6.73273 −0.476076
\(201\) 0 0
\(202\) −0.363303 −0.0255619
\(203\) −0.828594 −0.0581559
\(204\) 0 0
\(205\) −27.1755 −1.89802
\(206\) −1.01178 −0.0704939
\(207\) 0 0
\(208\) −12.1285 −0.840958
\(209\) −0.135437 −0.00936836
\(210\) 0 0
\(211\) −13.4759 −0.927717 −0.463858 0.885909i \(-0.653535\pi\)
−0.463858 + 0.885909i \(0.653535\pi\)
\(212\) −14.6521 −1.00631
\(213\) 0 0
\(214\) 0.801074 0.0547603
\(215\) 6.86937 0.468487
\(216\) 0 0
\(217\) −5.68163 −0.385694
\(218\) −0.850453 −0.0576000
\(219\) 0 0
\(220\) 0.266022 0.0179352
\(221\) −3.97679 −0.267508
\(222\) 0 0
\(223\) 3.35902 0.224937 0.112468 0.993655i \(-0.464124\pi\)
0.112468 + 0.993655i \(0.464124\pi\)
\(224\) −1.41651 −0.0946445
\(225\) 0 0
\(226\) 2.69241 0.179097
\(227\) 15.9164 1.05641 0.528204 0.849118i \(-0.322866\pi\)
0.528204 + 0.849118i \(0.322866\pi\)
\(228\) 0 0
\(229\) −17.0653 −1.12771 −0.563853 0.825875i \(-0.690682\pi\)
−0.563853 + 0.825875i \(0.690682\pi\)
\(230\) −0.590584 −0.0389420
\(231\) 0 0
\(232\) −0.574849 −0.0377407
\(233\) 17.5655 1.15076 0.575378 0.817887i \(-0.304855\pi\)
0.575378 + 0.817887i \(0.304855\pi\)
\(234\) 0 0
\(235\) −23.2763 −1.51838
\(236\) 5.34800 0.348125
\(237\) 0 0
\(238\) −0.152100 −0.00985917
\(239\) −18.2475 −1.18033 −0.590166 0.807282i \(-0.700938\pi\)
−0.590166 + 0.807282i \(0.700938\pi\)
\(240\) 0 0
\(241\) −5.35400 −0.344882 −0.172441 0.985020i \(-0.555165\pi\)
−0.172441 + 0.985020i \(0.555165\pi\)
\(242\) −1.58897 −0.102143
\(243\) 0 0
\(244\) −14.8817 −0.952706
\(245\) 25.8096 1.64892
\(246\) 0 0
\(247\) 12.8920 0.820297
\(248\) −3.94171 −0.250299
\(249\) 0 0
\(250\) −3.96410 −0.250712
\(251\) 14.0396 0.886170 0.443085 0.896480i \(-0.353884\pi\)
0.443085 + 0.896480i \(0.353884\pi\)
\(252\) 0 0
\(253\) 0.0328797 0.00206713
\(254\) −2.25310 −0.141372
\(255\) 0 0
\(256\) 14.3564 0.897273
\(257\) −9.51274 −0.593388 −0.296694 0.954973i \(-0.595884\pi\)
−0.296694 + 0.954973i \(0.595884\pi\)
\(258\) 0 0
\(259\) 2.73637 0.170030
\(260\) −25.3222 −1.57042
\(261\) 0 0
\(262\) −0.964896 −0.0596115
\(263\) −4.44916 −0.274347 −0.137174 0.990547i \(-0.543802\pi\)
−0.137174 + 0.990547i \(0.543802\pi\)
\(264\) 0 0
\(265\) −30.2650 −1.85916
\(266\) 0.493079 0.0302326
\(267\) 0 0
\(268\) 7.95688 0.486044
\(269\) −25.7794 −1.57180 −0.785899 0.618355i \(-0.787799\pi\)
−0.785899 + 0.618355i \(0.787799\pi\)
\(270\) 0 0
\(271\) 25.2632 1.53463 0.767314 0.641272i \(-0.221593\pi\)
0.767314 + 0.641272i \(0.221593\pi\)
\(272\) 4.92399 0.298561
\(273\) 0 0
\(274\) 2.00378 0.121053
\(275\) 0.385092 0.0232219
\(276\) 0 0
\(277\) −23.9622 −1.43975 −0.719875 0.694104i \(-0.755801\pi\)
−0.719875 + 0.694104i \(0.755801\pi\)
\(278\) 0.655826 0.0393338
\(279\) 0 0
\(280\) −1.94720 −0.116368
\(281\) 15.0553 0.898123 0.449062 0.893501i \(-0.351758\pi\)
0.449062 + 0.893501i \(0.351758\pi\)
\(282\) 0 0
\(283\) 23.6312 1.40473 0.702365 0.711817i \(-0.252128\pi\)
0.702365 + 0.711817i \(0.252128\pi\)
\(284\) 7.40120 0.439180
\(285\) 0 0
\(286\) −0.0148663 −0.000879064 0
\(287\) −5.50811 −0.325134
\(288\) 0 0
\(289\) −15.3855 −0.905028
\(290\) −0.590584 −0.0346803
\(291\) 0 0
\(292\) −3.98476 −0.233190
\(293\) 6.33215 0.369928 0.184964 0.982745i \(-0.440783\pi\)
0.184964 + 0.982745i \(0.440783\pi\)
\(294\) 0 0
\(295\) 11.0467 0.643165
\(296\) 1.89840 0.110342
\(297\) 0 0
\(298\) 2.17678 0.126097
\(299\) −3.12976 −0.180998
\(300\) 0 0
\(301\) 1.39233 0.0802525
\(302\) 0.581152 0.0334416
\(303\) 0 0
\(304\) −15.9626 −0.915520
\(305\) −30.7395 −1.76014
\(306\) 0 0
\(307\) −13.6720 −0.780301 −0.390150 0.920751i \(-0.627577\pi\)
−0.390150 + 0.920751i \(0.627577\pi\)
\(308\) 0.0539192 0.00307233
\(309\) 0 0
\(310\) −4.04961 −0.230002
\(311\) −21.5379 −1.22130 −0.610651 0.791900i \(-0.709092\pi\)
−0.610651 + 0.791900i \(0.709092\pi\)
\(312\) 0 0
\(313\) −17.1243 −0.967921 −0.483961 0.875090i \(-0.660802\pi\)
−0.483961 + 0.875090i \(0.660802\pi\)
\(314\) −0.0613736 −0.00346351
\(315\) 0 0
\(316\) −31.4413 −1.76871
\(317\) 15.7386 0.883971 0.441985 0.897022i \(-0.354274\pi\)
0.441985 + 0.897022i \(0.354274\pi\)
\(318\) 0 0
\(319\) 0.0328797 0.00184091
\(320\) 30.6745 1.71476
\(321\) 0 0
\(322\) −0.119704 −0.00667082
\(323\) −5.23397 −0.291226
\(324\) 0 0
\(325\) −36.6562 −2.03332
\(326\) −1.47368 −0.0816194
\(327\) 0 0
\(328\) −3.82133 −0.210998
\(329\) −4.71779 −0.260100
\(330\) 0 0
\(331\) −3.18162 −0.174878 −0.0874389 0.996170i \(-0.527868\pi\)
−0.0874389 + 0.996170i \(0.527868\pi\)
\(332\) −22.8991 −1.25675
\(333\) 0 0
\(334\) −2.80548 −0.153509
\(335\) 16.4356 0.897971
\(336\) 0 0
\(337\) −6.70392 −0.365186 −0.182593 0.983189i \(-0.558449\pi\)
−0.182593 + 0.983189i \(0.558449\pi\)
\(338\) −0.462959 −0.0251817
\(339\) 0 0
\(340\) 10.2805 0.557536
\(341\) 0.225454 0.0122090
\(342\) 0 0
\(343\) 11.0314 0.595641
\(344\) 0.965949 0.0520805
\(345\) 0 0
\(346\) −3.29859 −0.177333
\(347\) −11.8806 −0.637785 −0.318893 0.947791i \(-0.603311\pi\)
−0.318893 + 0.947791i \(0.603311\pi\)
\(348\) 0 0
\(349\) −21.8783 −1.17112 −0.585558 0.810630i \(-0.699125\pi\)
−0.585558 + 0.810630i \(0.699125\pi\)
\(350\) −1.40199 −0.0749394
\(351\) 0 0
\(352\) 0.0562089 0.00299594
\(353\) 10.4828 0.557943 0.278971 0.960299i \(-0.410007\pi\)
0.278971 + 0.960299i \(0.410007\pi\)
\(354\) 0 0
\(355\) 15.2878 0.811391
\(356\) 14.5825 0.772870
\(357\) 0 0
\(358\) 1.41450 0.0747586
\(359\) 30.0157 1.58417 0.792085 0.610411i \(-0.208996\pi\)
0.792085 + 0.610411i \(0.208996\pi\)
\(360\) 0 0
\(361\) −2.03248 −0.106972
\(362\) 3.00600 0.157992
\(363\) 0 0
\(364\) −5.13247 −0.269014
\(365\) −8.23084 −0.430822
\(366\) 0 0
\(367\) −31.6753 −1.65344 −0.826719 0.562615i \(-0.809795\pi\)
−0.826719 + 0.562615i \(0.809795\pi\)
\(368\) 3.87521 0.202009
\(369\) 0 0
\(370\) 1.95037 0.101395
\(371\) −6.13431 −0.318478
\(372\) 0 0
\(373\) −27.6937 −1.43392 −0.716962 0.697113i \(-0.754468\pi\)
−0.716962 + 0.697113i \(0.754468\pi\)
\(374\) 0.00603552 0.000312089 0
\(375\) 0 0
\(376\) −3.27303 −0.168794
\(377\) −3.12976 −0.161191
\(378\) 0 0
\(379\) −18.4048 −0.945393 −0.472696 0.881225i \(-0.656719\pi\)
−0.472696 + 0.881225i \(0.656719\pi\)
\(380\) −33.3273 −1.70965
\(381\) 0 0
\(382\) −0.596240 −0.0305063
\(383\) 33.8734 1.73085 0.865425 0.501038i \(-0.167048\pi\)
0.865425 + 0.501038i \(0.167048\pi\)
\(384\) 0 0
\(385\) 0.111374 0.00567616
\(386\) 3.38243 0.172161
\(387\) 0 0
\(388\) 34.3082 1.74173
\(389\) 14.9510 0.758045 0.379023 0.925387i \(-0.376260\pi\)
0.379023 + 0.925387i \(0.376260\pi\)
\(390\) 0 0
\(391\) 1.27064 0.0642589
\(392\) 3.62927 0.183306
\(393\) 0 0
\(394\) −2.02788 −0.102163
\(395\) −64.9446 −3.26772
\(396\) 0 0
\(397\) −18.7899 −0.943036 −0.471518 0.881856i \(-0.656294\pi\)
−0.471518 + 0.881856i \(0.656294\pi\)
\(398\) 0.0902754 0.00452510
\(399\) 0 0
\(400\) 45.3871 2.26936
\(401\) 18.9879 0.948213 0.474106 0.880468i \(-0.342771\pi\)
0.474106 + 0.880468i \(0.342771\pi\)
\(402\) 0 0
\(403\) −21.4606 −1.06903
\(404\) 4.97712 0.247621
\(405\) 0 0
\(406\) −0.119704 −0.00594079
\(407\) −0.108583 −0.00538225
\(408\) 0 0
\(409\) 6.58997 0.325853 0.162927 0.986638i \(-0.447907\pi\)
0.162927 + 0.986638i \(0.447907\pi\)
\(410\) −3.92594 −0.193888
\(411\) 0 0
\(412\) 13.8610 0.682881
\(413\) 2.23902 0.110175
\(414\) 0 0
\(415\) −47.2999 −2.32186
\(416\) −5.35042 −0.262326
\(417\) 0 0
\(418\) −0.0195660 −0.000957004 0
\(419\) 22.2270 1.08586 0.542931 0.839778i \(-0.317315\pi\)
0.542931 + 0.839778i \(0.317315\pi\)
\(420\) 0 0
\(421\) 8.80239 0.429002 0.214501 0.976724i \(-0.431187\pi\)
0.214501 + 0.976724i \(0.431187\pi\)
\(422\) −1.94680 −0.0947689
\(423\) 0 0
\(424\) −4.25577 −0.206678
\(425\) 14.8819 0.721879
\(426\) 0 0
\(427\) −6.23048 −0.301514
\(428\) −10.9744 −0.530468
\(429\) 0 0
\(430\) 0.992390 0.0478573
\(431\) −19.7085 −0.949324 −0.474662 0.880168i \(-0.657430\pi\)
−0.474662 + 0.880168i \(0.657430\pi\)
\(432\) 0 0
\(433\) 17.9153 0.860953 0.430476 0.902602i \(-0.358346\pi\)
0.430476 + 0.902602i \(0.358346\pi\)
\(434\) −0.820802 −0.0393998
\(435\) 0 0
\(436\) 11.6509 0.557976
\(437\) −4.11917 −0.197046
\(438\) 0 0
\(439\) −11.9184 −0.568834 −0.284417 0.958701i \(-0.591800\pi\)
−0.284417 + 0.958701i \(0.591800\pi\)
\(440\) 0.0772676 0.00368359
\(441\) 0 0
\(442\) −0.574510 −0.0273267
\(443\) −19.4540 −0.924286 −0.462143 0.886805i \(-0.652919\pi\)
−0.462143 + 0.886805i \(0.652919\pi\)
\(444\) 0 0
\(445\) 30.1213 1.42789
\(446\) 0.485264 0.0229779
\(447\) 0 0
\(448\) 6.21732 0.293741
\(449\) −3.01378 −0.142229 −0.0711146 0.997468i \(-0.522656\pi\)
−0.0711146 + 0.997468i \(0.522656\pi\)
\(450\) 0 0
\(451\) 0.218569 0.0102920
\(452\) −36.8851 −1.73493
\(453\) 0 0
\(454\) 2.29938 0.107915
\(455\) −10.6015 −0.497007
\(456\) 0 0
\(457\) 4.97040 0.232506 0.116253 0.993220i \(-0.462912\pi\)
0.116253 + 0.993220i \(0.462912\pi\)
\(458\) −2.46535 −0.115198
\(459\) 0 0
\(460\) 8.09078 0.377235
\(461\) 9.83599 0.458108 0.229054 0.973414i \(-0.426437\pi\)
0.229054 + 0.973414i \(0.426437\pi\)
\(462\) 0 0
\(463\) 5.42753 0.252239 0.126119 0.992015i \(-0.459748\pi\)
0.126119 + 0.992015i \(0.459748\pi\)
\(464\) 3.87521 0.179902
\(465\) 0 0
\(466\) 2.53762 0.117553
\(467\) −18.0781 −0.836556 −0.418278 0.908319i \(-0.637366\pi\)
−0.418278 + 0.908319i \(0.637366\pi\)
\(468\) 0 0
\(469\) 3.33127 0.153824
\(470\) −3.36263 −0.155106
\(471\) 0 0
\(472\) 1.55336 0.0714990
\(473\) −0.0552494 −0.00254037
\(474\) 0 0
\(475\) −48.2444 −2.21360
\(476\) 2.08371 0.0955067
\(477\) 0 0
\(478\) −2.63614 −0.120574
\(479\) −5.90145 −0.269644 −0.134822 0.990870i \(-0.543046\pi\)
−0.134822 + 0.990870i \(0.543046\pi\)
\(480\) 0 0
\(481\) 10.3358 0.471272
\(482\) −0.773471 −0.0352306
\(483\) 0 0
\(484\) 21.7683 0.989468
\(485\) 70.8664 3.21788
\(486\) 0 0
\(487\) −8.42154 −0.381617 −0.190808 0.981627i \(-0.561111\pi\)
−0.190808 + 0.981627i \(0.561111\pi\)
\(488\) −4.32248 −0.195670
\(489\) 0 0
\(490\) 3.72861 0.168442
\(491\) −20.5960 −0.929485 −0.464743 0.885446i \(-0.653853\pi\)
−0.464743 + 0.885446i \(0.653853\pi\)
\(492\) 0 0
\(493\) 1.27064 0.0572266
\(494\) 1.86245 0.0837957
\(495\) 0 0
\(496\) 26.5722 1.19313
\(497\) 3.09863 0.138992
\(498\) 0 0
\(499\) 27.4511 1.22888 0.614439 0.788964i \(-0.289382\pi\)
0.614439 + 0.788964i \(0.289382\pi\)
\(500\) 54.3067 2.42867
\(501\) 0 0
\(502\) 2.02824 0.0905248
\(503\) −16.4801 −0.734810 −0.367405 0.930061i \(-0.619754\pi\)
−0.367405 + 0.930061i \(0.619754\pi\)
\(504\) 0 0
\(505\) 10.2806 0.457483
\(506\) 0.00474999 0.000211163 0
\(507\) 0 0
\(508\) 30.8666 1.36948
\(509\) 37.8732 1.67870 0.839351 0.543590i \(-0.182936\pi\)
0.839351 + 0.543590i \(0.182936\pi\)
\(510\) 0 0
\(511\) −1.66828 −0.0738004
\(512\) 11.0801 0.489677
\(513\) 0 0
\(514\) −1.37427 −0.0606163
\(515\) 28.6310 1.26163
\(516\) 0 0
\(517\) 0.187208 0.00823339
\(518\) 0.395313 0.0173691
\(519\) 0 0
\(520\) −7.35496 −0.322536
\(521\) 3.02822 0.132669 0.0663343 0.997797i \(-0.478870\pi\)
0.0663343 + 0.997797i \(0.478870\pi\)
\(522\) 0 0
\(523\) −31.3330 −1.37010 −0.685049 0.728497i \(-0.740219\pi\)
−0.685049 + 0.728497i \(0.740219\pi\)
\(524\) 13.2187 0.577462
\(525\) 0 0
\(526\) −0.642753 −0.0280253
\(527\) 8.71271 0.379531
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −4.37226 −0.189919
\(531\) 0 0
\(532\) −6.75500 −0.292866
\(533\) −20.8052 −0.901173
\(534\) 0 0
\(535\) −22.6685 −0.980046
\(536\) 2.31112 0.0998251
\(537\) 0 0
\(538\) −3.72425 −0.160564
\(539\) −0.207584 −0.00894126
\(540\) 0 0
\(541\) −6.56857 −0.282405 −0.141202 0.989981i \(-0.545097\pi\)
−0.141202 + 0.989981i \(0.545097\pi\)
\(542\) 3.64967 0.156767
\(543\) 0 0
\(544\) 2.17220 0.0931322
\(545\) 24.0659 1.03087
\(546\) 0 0
\(547\) 3.77035 0.161209 0.0806043 0.996746i \(-0.474315\pi\)
0.0806043 + 0.996746i \(0.474315\pi\)
\(548\) −27.4510 −1.17265
\(549\) 0 0
\(550\) 0.0556327 0.00237219
\(551\) −4.11917 −0.175482
\(552\) 0 0
\(553\) −13.1634 −0.559765
\(554\) −3.46172 −0.147075
\(555\) 0 0
\(556\) −8.98457 −0.381031
\(557\) −16.1536 −0.684452 −0.342226 0.939618i \(-0.611181\pi\)
−0.342226 + 0.939618i \(0.611181\pi\)
\(558\) 0 0
\(559\) 5.25909 0.222436
\(560\) 13.1266 0.554702
\(561\) 0 0
\(562\) 2.17498 0.0917458
\(563\) −12.6580 −0.533469 −0.266735 0.963770i \(-0.585945\pi\)
−0.266735 + 0.963770i \(0.585945\pi\)
\(564\) 0 0
\(565\) −76.1891 −3.20530
\(566\) 3.41390 0.143497
\(567\) 0 0
\(568\) 2.14972 0.0902002
\(569\) −10.4132 −0.436543 −0.218272 0.975888i \(-0.570042\pi\)
−0.218272 + 0.975888i \(0.570042\pi\)
\(570\) 0 0
\(571\) −23.0090 −0.962897 −0.481449 0.876474i \(-0.659889\pi\)
−0.481449 + 0.876474i \(0.659889\pi\)
\(572\) 0.203663 0.00851558
\(573\) 0 0
\(574\) −0.795735 −0.0332133
\(575\) 11.7122 0.488431
\(576\) 0 0
\(577\) 24.7624 1.03087 0.515435 0.856928i \(-0.327630\pi\)
0.515435 + 0.856928i \(0.327630\pi\)
\(578\) −2.22268 −0.0924512
\(579\) 0 0
\(580\) 8.09078 0.335952
\(581\) −9.58706 −0.397738
\(582\) 0 0
\(583\) 0.243417 0.0100813
\(584\) −1.15739 −0.0478933
\(585\) 0 0
\(586\) 0.914780 0.0377892
\(587\) 10.1827 0.420283 0.210142 0.977671i \(-0.432608\pi\)
0.210142 + 0.977671i \(0.432608\pi\)
\(588\) 0 0
\(589\) −28.2449 −1.16381
\(590\) 1.59588 0.0657012
\(591\) 0 0
\(592\) −12.7976 −0.525979
\(593\) 15.1467 0.621998 0.310999 0.950410i \(-0.399336\pi\)
0.310999 + 0.950410i \(0.399336\pi\)
\(594\) 0 0
\(595\) 4.30407 0.176450
\(596\) −29.8210 −1.22152
\(597\) 0 0
\(598\) −0.452143 −0.0184895
\(599\) 7.06037 0.288479 0.144239 0.989543i \(-0.453926\pi\)
0.144239 + 0.989543i \(0.453926\pi\)
\(600\) 0 0
\(601\) 14.9345 0.609193 0.304596 0.952482i \(-0.401478\pi\)
0.304596 + 0.952482i \(0.401478\pi\)
\(602\) 0.201144 0.00819802
\(603\) 0 0
\(604\) −7.96157 −0.323952
\(605\) 44.9642 1.82805
\(606\) 0 0
\(607\) 4.17525 0.169468 0.0847341 0.996404i \(-0.472996\pi\)
0.0847341 + 0.996404i \(0.472996\pi\)
\(608\) −7.04185 −0.285585
\(609\) 0 0
\(610\) −4.44080 −0.179803
\(611\) −17.8200 −0.720919
\(612\) 0 0
\(613\) −2.61552 −0.105640 −0.0528198 0.998604i \(-0.516821\pi\)
−0.0528198 + 0.998604i \(0.516821\pi\)
\(614\) −1.97513 −0.0797099
\(615\) 0 0
\(616\) 0.0156611 0.000631004 0
\(617\) 29.8600 1.20212 0.601060 0.799204i \(-0.294745\pi\)
0.601060 + 0.799204i \(0.294745\pi\)
\(618\) 0 0
\(619\) 3.08187 0.123871 0.0619354 0.998080i \(-0.480273\pi\)
0.0619354 + 0.998080i \(0.480273\pi\)
\(620\) 55.4782 2.22806
\(621\) 0 0
\(622\) −3.11149 −0.124760
\(623\) 6.10518 0.244599
\(624\) 0 0
\(625\) 53.6140 2.14456
\(626\) −2.47388 −0.0988759
\(627\) 0 0
\(628\) 0.840795 0.0335514
\(629\) −4.19619 −0.167313
\(630\) 0 0
\(631\) 29.1425 1.16014 0.580072 0.814565i \(-0.303024\pi\)
0.580072 + 0.814565i \(0.303024\pi\)
\(632\) −9.13230 −0.363263
\(633\) 0 0
\(634\) 2.27370 0.0903001
\(635\) 63.7575 2.53014
\(636\) 0 0
\(637\) 19.7595 0.782900
\(638\) 0.00474999 0.000188054 0
\(639\) 0 0
\(640\) 18.4088 0.727670
\(641\) 7.05943 0.278831 0.139415 0.990234i \(-0.455478\pi\)
0.139415 + 0.990234i \(0.455478\pi\)
\(642\) 0 0
\(643\) −13.9954 −0.551923 −0.275962 0.961169i \(-0.588996\pi\)
−0.275962 + 0.961169i \(0.588996\pi\)
\(644\) 1.63989 0.0646209
\(645\) 0 0
\(646\) −0.756130 −0.0297495
\(647\) −9.22726 −0.362761 −0.181381 0.983413i \(-0.558057\pi\)
−0.181381 + 0.983413i \(0.558057\pi\)
\(648\) 0 0
\(649\) −0.0888474 −0.00348756
\(650\) −5.29558 −0.207710
\(651\) 0 0
\(652\) 20.1888 0.790656
\(653\) 18.2056 0.712440 0.356220 0.934402i \(-0.384065\pi\)
0.356220 + 0.934402i \(0.384065\pi\)
\(654\) 0 0
\(655\) 27.3043 1.06687
\(656\) 25.7607 1.00578
\(657\) 0 0
\(658\) −0.681559 −0.0265700
\(659\) −13.3730 −0.520937 −0.260469 0.965482i \(-0.583877\pi\)
−0.260469 + 0.965482i \(0.583877\pi\)
\(660\) 0 0
\(661\) 28.4406 1.10621 0.553106 0.833111i \(-0.313443\pi\)
0.553106 + 0.833111i \(0.313443\pi\)
\(662\) −0.459636 −0.0178643
\(663\) 0 0
\(664\) −6.65116 −0.258115
\(665\) −13.9530 −0.541074
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 38.4340 1.48706
\(669\) 0 0
\(670\) 2.37438 0.0917303
\(671\) 0.247233 0.00954434
\(672\) 0 0
\(673\) −8.48921 −0.327235 −0.163618 0.986524i \(-0.552316\pi\)
−0.163618 + 0.986524i \(0.552316\pi\)
\(674\) −0.968489 −0.0373048
\(675\) 0 0
\(676\) 6.34237 0.243937
\(677\) 25.5811 0.983163 0.491582 0.870832i \(-0.336419\pi\)
0.491582 + 0.870832i \(0.336419\pi\)
\(678\) 0 0
\(679\) 14.3637 0.551227
\(680\) 2.98601 0.114508
\(681\) 0 0
\(682\) 0.0325705 0.00124719
\(683\) 17.8005 0.681116 0.340558 0.940224i \(-0.389384\pi\)
0.340558 + 0.940224i \(0.389384\pi\)
\(684\) 0 0
\(685\) −56.7023 −2.16648
\(686\) 1.59367 0.0608464
\(687\) 0 0
\(688\) −6.51172 −0.248257
\(689\) −23.1705 −0.882724
\(690\) 0 0
\(691\) −4.62167 −0.175817 −0.0879084 0.996129i \(-0.528018\pi\)
−0.0879084 + 0.996129i \(0.528018\pi\)
\(692\) 45.1894 1.71784
\(693\) 0 0
\(694\) −1.71635 −0.0651516
\(695\) −18.5584 −0.703958
\(696\) 0 0
\(697\) 8.44662 0.319939
\(698\) −3.16066 −0.119633
\(699\) 0 0
\(700\) 19.2067 0.725946
\(701\) −40.4095 −1.52625 −0.763123 0.646254i \(-0.776335\pi\)
−0.763123 + 0.646254i \(0.776335\pi\)
\(702\) 0 0
\(703\) 13.6033 0.513057
\(704\) −0.246711 −0.00929828
\(705\) 0 0
\(706\) 1.51441 0.0569955
\(707\) 2.08375 0.0783674
\(708\) 0 0
\(709\) −21.3793 −0.802917 −0.401459 0.915877i \(-0.631497\pi\)
−0.401459 + 0.915877i \(0.631497\pi\)
\(710\) 2.20856 0.0828859
\(711\) 0 0
\(712\) 4.23556 0.158734
\(713\) 6.85696 0.256795
\(714\) 0 0
\(715\) 0.420682 0.0157326
\(716\) −19.3781 −0.724194
\(717\) 0 0
\(718\) 4.33625 0.161827
\(719\) −3.84124 −0.143254 −0.0716270 0.997431i \(-0.522819\pi\)
−0.0716270 + 0.997431i \(0.522819\pi\)
\(720\) 0 0
\(721\) 5.80312 0.216119
\(722\) −0.293624 −0.0109275
\(723\) 0 0
\(724\) −41.1810 −1.53048
\(725\) 11.7122 0.434979
\(726\) 0 0
\(727\) −23.2952 −0.863972 −0.431986 0.901880i \(-0.642187\pi\)
−0.431986 + 0.901880i \(0.642187\pi\)
\(728\) −1.49075 −0.0552510
\(729\) 0 0
\(730\) −1.18908 −0.0440097
\(731\) −2.13512 −0.0789702
\(732\) 0 0
\(733\) 26.1377 0.965419 0.482709 0.875781i \(-0.339653\pi\)
0.482709 + 0.875781i \(0.339653\pi\)
\(734\) −4.57601 −0.168903
\(735\) 0 0
\(736\) 1.70953 0.0630143
\(737\) −0.132189 −0.00486925
\(738\) 0 0
\(739\) 48.0772 1.76855 0.884274 0.466969i \(-0.154654\pi\)
0.884274 + 0.466969i \(0.154654\pi\)
\(740\) −26.7193 −0.982220
\(741\) 0 0
\(742\) −0.886199 −0.0325334
\(743\) −28.8522 −1.05849 −0.529243 0.848470i \(-0.677524\pi\)
−0.529243 + 0.848470i \(0.677524\pi\)
\(744\) 0 0
\(745\) −61.5977 −2.25677
\(746\) −4.00079 −0.146479
\(747\) 0 0
\(748\) −0.0826843 −0.00302324
\(749\) −4.59461 −0.167883
\(750\) 0 0
\(751\) 30.4943 1.11275 0.556376 0.830930i \(-0.312191\pi\)
0.556376 + 0.830930i \(0.312191\pi\)
\(752\) 22.0644 0.804606
\(753\) 0 0
\(754\) −0.452143 −0.0164661
\(755\) −16.4453 −0.598504
\(756\) 0 0
\(757\) 1.88355 0.0684587 0.0342294 0.999414i \(-0.489102\pi\)
0.0342294 + 0.999414i \(0.489102\pi\)
\(758\) −2.65887 −0.0965746
\(759\) 0 0
\(760\) −9.68009 −0.351134
\(761\) 37.0313 1.34238 0.671192 0.741283i \(-0.265782\pi\)
0.671192 + 0.741283i \(0.265782\pi\)
\(762\) 0 0
\(763\) 4.87783 0.176589
\(764\) 8.16826 0.295517
\(765\) 0 0
\(766\) 4.89356 0.176811
\(767\) 8.45722 0.305373
\(768\) 0 0
\(769\) 45.3148 1.63409 0.817046 0.576572i \(-0.195610\pi\)
0.817046 + 0.576572i \(0.195610\pi\)
\(770\) 0.0160898 0.000579836 0
\(771\) 0 0
\(772\) −46.3380 −1.66774
\(773\) 22.0003 0.791297 0.395648 0.918402i \(-0.370520\pi\)
0.395648 + 0.918402i \(0.370520\pi\)
\(774\) 0 0
\(775\) 80.3098 2.88481
\(776\) 9.96500 0.357723
\(777\) 0 0
\(778\) 2.15991 0.0774365
\(779\) −27.3823 −0.981074
\(780\) 0 0
\(781\) −0.122958 −0.00439977
\(782\) 0.183564 0.00656423
\(783\) 0 0
\(784\) −24.4659 −0.873782
\(785\) 1.73673 0.0619866
\(786\) 0 0
\(787\) −11.0240 −0.392962 −0.196481 0.980508i \(-0.562951\pi\)
−0.196481 + 0.980508i \(0.562951\pi\)
\(788\) 27.7813 0.989666
\(789\) 0 0
\(790\) −9.38228 −0.333806
\(791\) −15.4425 −0.549072
\(792\) 0 0
\(793\) −23.5337 −0.835706
\(794\) −2.71450 −0.0963339
\(795\) 0 0
\(796\) −1.23674 −0.0438351
\(797\) −43.6770 −1.54712 −0.773559 0.633724i \(-0.781525\pi\)
−0.773559 + 0.633724i \(0.781525\pi\)
\(798\) 0 0
\(799\) 7.23466 0.255944
\(800\) 20.0223 0.707897
\(801\) 0 0
\(802\) 2.74311 0.0968626
\(803\) 0.0661995 0.00233613
\(804\) 0 0
\(805\) 3.38733 0.119388
\(806\) −3.10033 −0.109204
\(807\) 0 0
\(808\) 1.44563 0.0508571
\(809\) 40.8283 1.43544 0.717722 0.696329i \(-0.245185\pi\)
0.717722 + 0.696329i \(0.245185\pi\)
\(810\) 0 0
\(811\) −46.1439 −1.62033 −0.810165 0.586202i \(-0.800622\pi\)
−0.810165 + 0.586202i \(0.800622\pi\)
\(812\) 1.63989 0.0575490
\(813\) 0 0
\(814\) −0.0156865 −0.000549813 0
\(815\) 41.7017 1.46075
\(816\) 0 0
\(817\) 6.92165 0.242158
\(818\) 0.952027 0.0332868
\(819\) 0 0
\(820\) 53.7839 1.87821
\(821\) −4.16325 −0.145298 −0.0726491 0.997358i \(-0.523145\pi\)
−0.0726491 + 0.997358i \(0.523145\pi\)
\(822\) 0 0
\(823\) 23.8760 0.832265 0.416132 0.909304i \(-0.363385\pi\)
0.416132 + 0.909304i \(0.363385\pi\)
\(824\) 4.02600 0.140252
\(825\) 0 0
\(826\) 0.323463 0.0112547
\(827\) −0.634486 −0.0220633 −0.0110316 0.999939i \(-0.503512\pi\)
−0.0110316 + 0.999939i \(0.503512\pi\)
\(828\) 0 0
\(829\) −1.12420 −0.0390449 −0.0195225 0.999809i \(-0.506215\pi\)
−0.0195225 + 0.999809i \(0.506215\pi\)
\(830\) −6.83323 −0.237185
\(831\) 0 0
\(832\) 23.4840 0.814161
\(833\) −8.02208 −0.277949
\(834\) 0 0
\(835\) 79.3886 2.74736
\(836\) 0.268047 0.00927060
\(837\) 0 0
\(838\) 3.21105 0.110924
\(839\) −53.5715 −1.84949 −0.924747 0.380583i \(-0.875723\pi\)
−0.924747 + 0.380583i \(0.875723\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 1.27165 0.0438238
\(843\) 0 0
\(844\) 26.6705 0.918036
\(845\) 13.1007 0.450677
\(846\) 0 0
\(847\) 9.11363 0.313148
\(848\) 28.6893 0.985194
\(849\) 0 0
\(850\) 2.14993 0.0737420
\(851\) −3.30243 −0.113206
\(852\) 0 0
\(853\) 7.24339 0.248009 0.124005 0.992282i \(-0.460426\pi\)
0.124005 + 0.992282i \(0.460426\pi\)
\(854\) −0.900092 −0.0308005
\(855\) 0 0
\(856\) −3.18758 −0.108949
\(857\) −40.9608 −1.39919 −0.699597 0.714537i \(-0.746637\pi\)
−0.699597 + 0.714537i \(0.746637\pi\)
\(858\) 0 0
\(859\) −5.68806 −0.194074 −0.0970370 0.995281i \(-0.530937\pi\)
−0.0970370 + 0.995281i \(0.530937\pi\)
\(860\) −13.5954 −0.463598
\(861\) 0 0
\(862\) −2.84720 −0.0969761
\(863\) −28.9336 −0.984911 −0.492455 0.870338i \(-0.663901\pi\)
−0.492455 + 0.870338i \(0.663901\pi\)
\(864\) 0 0
\(865\) 93.3423 3.17373
\(866\) 2.58815 0.0879488
\(867\) 0 0
\(868\) 11.2447 0.381669
\(869\) 0.522341 0.0177192
\(870\) 0 0
\(871\) 12.5828 0.426354
\(872\) 3.38406 0.114599
\(873\) 0 0
\(874\) −0.595079 −0.0201289
\(875\) 22.7364 0.768629
\(876\) 0 0
\(877\) 40.0680 1.35300 0.676500 0.736443i \(-0.263496\pi\)
0.676500 + 0.736443i \(0.263496\pi\)
\(878\) −1.72180 −0.0581081
\(879\) 0 0
\(880\) −0.520882 −0.0175589
\(881\) 15.0697 0.507709 0.253855 0.967242i \(-0.418301\pi\)
0.253855 + 0.967242i \(0.418301\pi\)
\(882\) 0 0
\(883\) −40.9333 −1.37751 −0.688757 0.724992i \(-0.741843\pi\)
−0.688757 + 0.724992i \(0.741843\pi\)
\(884\) 7.87057 0.264716
\(885\) 0 0
\(886\) −2.81044 −0.0944185
\(887\) −4.17043 −0.140029 −0.0700147 0.997546i \(-0.522305\pi\)
−0.0700147 + 0.997546i \(0.522305\pi\)
\(888\) 0 0
\(889\) 12.9228 0.433416
\(890\) 4.35150 0.145863
\(891\) 0 0
\(892\) −6.64794 −0.222589
\(893\) −23.4534 −0.784838
\(894\) 0 0
\(895\) −40.0270 −1.33796
\(896\) 3.73121 0.124651
\(897\) 0 0
\(898\) −0.435389 −0.0145291
\(899\) 6.85696 0.228692
\(900\) 0 0
\(901\) 9.40689 0.313389
\(902\) 0.0315758 0.00105136
\(903\) 0 0
\(904\) −10.7135 −0.356325
\(905\) −85.0628 −2.82758
\(906\) 0 0
\(907\) −23.2656 −0.772523 −0.386262 0.922389i \(-0.626234\pi\)
−0.386262 + 0.922389i \(0.626234\pi\)
\(908\) −31.5006 −1.04538
\(909\) 0 0
\(910\) −1.53156 −0.0507707
\(911\) −2.66516 −0.0883007 −0.0441504 0.999025i \(-0.514058\pi\)
−0.0441504 + 0.999025i \(0.514058\pi\)
\(912\) 0 0
\(913\) 0.380427 0.0125903
\(914\) 0.718054 0.0237511
\(915\) 0 0
\(916\) 33.7744 1.11594
\(917\) 5.53422 0.182756
\(918\) 0 0
\(919\) 16.2554 0.536218 0.268109 0.963389i \(-0.413601\pi\)
0.268109 + 0.963389i \(0.413601\pi\)
\(920\) 2.35001 0.0774776
\(921\) 0 0
\(922\) 1.42097 0.0467970
\(923\) 11.7041 0.385246
\(924\) 0 0
\(925\) −38.6786 −1.27175
\(926\) 0.784093 0.0257669
\(927\) 0 0
\(928\) 1.70953 0.0561182
\(929\) −38.1670 −1.25222 −0.626109 0.779735i \(-0.715354\pi\)
−0.626109 + 0.779735i \(0.715354\pi\)
\(930\) 0 0
\(931\) 26.0061 0.852315
\(932\) −34.7645 −1.13875
\(933\) 0 0
\(934\) −2.61168 −0.0854566
\(935\) −0.170791 −0.00558547
\(936\) 0 0
\(937\) 19.8536 0.648588 0.324294 0.945956i \(-0.394873\pi\)
0.324294 + 0.945956i \(0.394873\pi\)
\(938\) 0.481255 0.0157135
\(939\) 0 0
\(940\) 46.0667 1.50253
\(941\) −53.3118 −1.73791 −0.868957 0.494887i \(-0.835209\pi\)
−0.868957 + 0.494887i \(0.835209\pi\)
\(942\) 0 0
\(943\) 6.64755 0.216474
\(944\) −10.4716 −0.340821
\(945\) 0 0
\(946\) −0.00798166 −0.000259506 0
\(947\) 13.6427 0.443330 0.221665 0.975123i \(-0.428851\pi\)
0.221665 + 0.975123i \(0.428851\pi\)
\(948\) 0 0
\(949\) −6.30142 −0.204553
\(950\) −6.96967 −0.226126
\(951\) 0 0
\(952\) 0.605225 0.0196155
\(953\) −11.6267 −0.376625 −0.188312 0.982109i \(-0.560302\pi\)
−0.188312 + 0.982109i \(0.560302\pi\)
\(954\) 0 0
\(955\) 16.8722 0.545972
\(956\) 36.1141 1.16801
\(957\) 0 0
\(958\) −0.852558 −0.0275449
\(959\) −11.4928 −0.371122
\(960\) 0 0
\(961\) 16.0179 0.516705
\(962\) 1.49317 0.0481418
\(963\) 0 0
\(964\) 10.5963 0.341283
\(965\) −95.7149 −3.08117
\(966\) 0 0
\(967\) 24.1651 0.777099 0.388549 0.921428i \(-0.372976\pi\)
0.388549 + 0.921428i \(0.372976\pi\)
\(968\) 6.32272 0.203220
\(969\) 0 0
\(970\) 10.2378 0.328715
\(971\) 13.0260 0.418023 0.209011 0.977913i \(-0.432975\pi\)
0.209011 + 0.977913i \(0.432975\pi\)
\(972\) 0 0
\(973\) −3.76153 −0.120589
\(974\) −1.21663 −0.0389832
\(975\) 0 0
\(976\) 29.1390 0.932718
\(977\) 57.2221 1.83070 0.915348 0.402664i \(-0.131916\pi\)
0.915348 + 0.402664i \(0.131916\pi\)
\(978\) 0 0
\(979\) −0.242262 −0.00774271
\(980\) −51.0806 −1.63171
\(981\) 0 0
\(982\) −2.97542 −0.0949496
\(983\) −1.19935 −0.0382533 −0.0191267 0.999817i \(-0.506089\pi\)
−0.0191267 + 0.999817i \(0.506089\pi\)
\(984\) 0 0
\(985\) 57.3844 1.82842
\(986\) 0.183564 0.00584586
\(987\) 0 0
\(988\) −25.5149 −0.811737
\(989\) −1.68035 −0.0534321
\(990\) 0 0
\(991\) −8.08001 −0.256670 −0.128335 0.991731i \(-0.540963\pi\)
−0.128335 + 0.991731i \(0.540963\pi\)
\(992\) 11.7222 0.372180
\(993\) 0 0
\(994\) 0.447646 0.0141985
\(995\) −2.55459 −0.0809858
\(996\) 0 0
\(997\) −45.2942 −1.43448 −0.717241 0.696825i \(-0.754595\pi\)
−0.717241 + 0.696825i \(0.754595\pi\)
\(998\) 3.96574 0.125533
\(999\) 0 0
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 \(a_p\))