Properties

Label 6003.2.a.t.1.15
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

Related objects

Downloads

Learn more about

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 1.15
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.05077 q^{2} -0.895876 q^{4} +3.10634 q^{5} +3.07400 q^{7} -3.04291 q^{8} +O(q^{10})\) \(q+1.05077 q^{2} -0.895876 q^{4} +3.10634 q^{5} +3.07400 q^{7} -3.04291 q^{8} +3.26406 q^{10} -3.20654 q^{11} -0.0429964 q^{13} +3.23008 q^{14} -1.40566 q^{16} -4.01221 q^{17} -7.31997 q^{19} -2.78289 q^{20} -3.36935 q^{22} +1.00000 q^{23} +4.64934 q^{25} -0.0451795 q^{26} -2.75393 q^{28} +1.00000 q^{29} +0.714345 q^{31} +4.60879 q^{32} -4.21592 q^{34} +9.54890 q^{35} -6.91091 q^{37} -7.69163 q^{38} -9.45231 q^{40} -5.11513 q^{41} -11.9603 q^{43} +2.87266 q^{44} +1.05077 q^{46} -5.42059 q^{47} +2.44951 q^{49} +4.88541 q^{50} +0.0385194 q^{52} +2.84097 q^{53} -9.96061 q^{55} -9.35392 q^{56} +1.05077 q^{58} -10.8989 q^{59} -8.48818 q^{61} +0.750615 q^{62} +7.65411 q^{64} -0.133561 q^{65} +3.06291 q^{67} +3.59444 q^{68} +10.0337 q^{70} -3.65634 q^{71} +9.89771 q^{73} -7.26180 q^{74} +6.55778 q^{76} -9.85692 q^{77} +3.31014 q^{79} -4.36644 q^{80} -5.37484 q^{82} +12.8843 q^{83} -12.4633 q^{85} -12.5676 q^{86} +9.75721 q^{88} +6.29940 q^{89} -0.132171 q^{91} -0.895876 q^{92} -5.69581 q^{94} -22.7383 q^{95} -0.736499 q^{97} +2.57387 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05077 0.743009 0.371504 0.928431i \(-0.378842\pi\)
0.371504 + 0.928431i \(0.378842\pi\)
\(3\) 0 0
\(4\) −0.895876 −0.447938
\(5\) 3.10634 1.38920 0.694599 0.719398i \(-0.255582\pi\)
0.694599 + 0.719398i \(0.255582\pi\)
\(6\) 0 0
\(7\) 3.07400 1.16186 0.580932 0.813952i \(-0.302688\pi\)
0.580932 + 0.813952i \(0.302688\pi\)
\(8\) −3.04291 −1.07583
\(9\) 0 0
\(10\) 3.26406 1.03219
\(11\) −3.20654 −0.966809 −0.483404 0.875397i \(-0.660600\pi\)
−0.483404 + 0.875397i \(0.660600\pi\)
\(12\) 0 0
\(13\) −0.0429964 −0.0119251 −0.00596253 0.999982i \(-0.501898\pi\)
−0.00596253 + 0.999982i \(0.501898\pi\)
\(14\) 3.23008 0.863276
\(15\) 0 0
\(16\) −1.40566 −0.351414
\(17\) −4.01221 −0.973104 −0.486552 0.873652i \(-0.661746\pi\)
−0.486552 + 0.873652i \(0.661746\pi\)
\(18\) 0 0
\(19\) −7.31997 −1.67932 −0.839658 0.543116i \(-0.817244\pi\)
−0.839658 + 0.543116i \(0.817244\pi\)
\(20\) −2.78289 −0.622274
\(21\) 0 0
\(22\) −3.36935 −0.718347
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 4.64934 0.929869
\(26\) −0.0451795 −0.00886042
\(27\) 0 0
\(28\) −2.75393 −0.520443
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 0.714345 0.128300 0.0641501 0.997940i \(-0.479566\pi\)
0.0641501 + 0.997940i \(0.479566\pi\)
\(32\) 4.60879 0.814727
\(33\) 0 0
\(34\) −4.21592 −0.723025
\(35\) 9.54890 1.61406
\(36\) 0 0
\(37\) −6.91091 −1.13615 −0.568074 0.822978i \(-0.692311\pi\)
−0.568074 + 0.822978i \(0.692311\pi\)
\(38\) −7.69163 −1.24775
\(39\) 0 0
\(40\) −9.45231 −1.49454
\(41\) −5.11513 −0.798848 −0.399424 0.916766i \(-0.630790\pi\)
−0.399424 + 0.916766i \(0.630790\pi\)
\(42\) 0 0
\(43\) −11.9603 −1.82393 −0.911967 0.410263i \(-0.865437\pi\)
−0.911967 + 0.410263i \(0.865437\pi\)
\(44\) 2.87266 0.433070
\(45\) 0 0
\(46\) 1.05077 0.154928
\(47\) −5.42059 −0.790675 −0.395337 0.918536i \(-0.629372\pi\)
−0.395337 + 0.918536i \(0.629372\pi\)
\(48\) 0 0
\(49\) 2.44951 0.349929
\(50\) 4.88541 0.690901
\(51\) 0 0
\(52\) 0.0385194 0.00534168
\(53\) 2.84097 0.390237 0.195119 0.980780i \(-0.437491\pi\)
0.195119 + 0.980780i \(0.437491\pi\)
\(54\) 0 0
\(55\) −9.96061 −1.34309
\(56\) −9.35392 −1.24997
\(57\) 0 0
\(58\) 1.05077 0.137973
\(59\) −10.8989 −1.41892 −0.709458 0.704748i \(-0.751060\pi\)
−0.709458 + 0.704748i \(0.751060\pi\)
\(60\) 0 0
\(61\) −8.48818 −1.08680 −0.543400 0.839474i \(-0.682863\pi\)
−0.543400 + 0.839474i \(0.682863\pi\)
\(62\) 0.750615 0.0953281
\(63\) 0 0
\(64\) 7.65411 0.956763
\(65\) −0.133561 −0.0165662
\(66\) 0 0
\(67\) 3.06291 0.374194 0.187097 0.982341i \(-0.440092\pi\)
0.187097 + 0.982341i \(0.440092\pi\)
\(68\) 3.59444 0.435890
\(69\) 0 0
\(70\) 10.0337 1.19926
\(71\) −3.65634 −0.433927 −0.216964 0.976180i \(-0.569615\pi\)
−0.216964 + 0.976180i \(0.569615\pi\)
\(72\) 0 0
\(73\) 9.89771 1.15844 0.579220 0.815172i \(-0.303357\pi\)
0.579220 + 0.815172i \(0.303357\pi\)
\(74\) −7.26180 −0.844168
\(75\) 0 0
\(76\) 6.55778 0.752229
\(77\) −9.85692 −1.12330
\(78\) 0 0
\(79\) 3.31014 0.372419 0.186210 0.982510i \(-0.440380\pi\)
0.186210 + 0.982510i \(0.440380\pi\)
\(80\) −4.36644 −0.488183
\(81\) 0 0
\(82\) −5.37484 −0.593551
\(83\) 12.8843 1.41423 0.707115 0.707098i \(-0.249996\pi\)
0.707115 + 0.707098i \(0.249996\pi\)
\(84\) 0 0
\(85\) −12.4633 −1.35183
\(86\) −12.5676 −1.35520
\(87\) 0 0
\(88\) 9.75721 1.04012
\(89\) 6.29940 0.667735 0.333867 0.942620i \(-0.391646\pi\)
0.333867 + 0.942620i \(0.391646\pi\)
\(90\) 0 0
\(91\) −0.132171 −0.0138553
\(92\) −0.895876 −0.0934015
\(93\) 0 0
\(94\) −5.69581 −0.587478
\(95\) −22.7383 −2.33290
\(96\) 0 0
\(97\) −0.736499 −0.0747801 −0.0373901 0.999301i \(-0.511904\pi\)
−0.0373901 + 0.999301i \(0.511904\pi\)
\(98\) 2.57387 0.260001
\(99\) 0 0
\(100\) −4.16523 −0.416523
\(101\) −7.08667 −0.705150 −0.352575 0.935784i \(-0.614694\pi\)
−0.352575 + 0.935784i \(0.614694\pi\)
\(102\) 0 0
\(103\) 10.0369 0.988963 0.494481 0.869188i \(-0.335358\pi\)
0.494481 + 0.869188i \(0.335358\pi\)
\(104\) 0.130834 0.0128293
\(105\) 0 0
\(106\) 2.98522 0.289950
\(107\) 19.2040 1.85652 0.928261 0.371929i \(-0.121304\pi\)
0.928261 + 0.371929i \(0.121304\pi\)
\(108\) 0 0
\(109\) −13.5333 −1.29625 −0.648127 0.761533i \(-0.724447\pi\)
−0.648127 + 0.761533i \(0.724447\pi\)
\(110\) −10.4663 −0.997926
\(111\) 0 0
\(112\) −4.32099 −0.408295
\(113\) −15.6808 −1.47512 −0.737562 0.675280i \(-0.764023\pi\)
−0.737562 + 0.675280i \(0.764023\pi\)
\(114\) 0 0
\(115\) 3.10634 0.289668
\(116\) −0.895876 −0.0831800
\(117\) 0 0
\(118\) −11.4523 −1.05427
\(119\) −12.3336 −1.13062
\(120\) 0 0
\(121\) −0.718091 −0.0652810
\(122\) −8.91915 −0.807502
\(123\) 0 0
\(124\) −0.639964 −0.0574705
\(125\) −1.08926 −0.0974263
\(126\) 0 0
\(127\) 6.23438 0.553212 0.276606 0.960983i \(-0.410790\pi\)
0.276606 + 0.960983i \(0.410790\pi\)
\(128\) −1.17486 −0.103843
\(129\) 0 0
\(130\) −0.140343 −0.0123089
\(131\) −14.7195 −1.28605 −0.643025 0.765845i \(-0.722321\pi\)
−0.643025 + 0.765845i \(0.722321\pi\)
\(132\) 0 0
\(133\) −22.5016 −1.95114
\(134\) 3.21842 0.278029
\(135\) 0 0
\(136\) 12.2088 1.04690
\(137\) 14.3504 1.22604 0.613021 0.790067i \(-0.289954\pi\)
0.613021 + 0.790067i \(0.289954\pi\)
\(138\) 0 0
\(139\) −6.86612 −0.582377 −0.291188 0.956666i \(-0.594051\pi\)
−0.291188 + 0.956666i \(0.594051\pi\)
\(140\) −8.55463 −0.722998
\(141\) 0 0
\(142\) −3.84198 −0.322412
\(143\) 0.137870 0.0115292
\(144\) 0 0
\(145\) 3.10634 0.257967
\(146\) 10.4002 0.860731
\(147\) 0 0
\(148\) 6.19132 0.508923
\(149\) 2.26630 0.185662 0.0928312 0.995682i \(-0.470408\pi\)
0.0928312 + 0.995682i \(0.470408\pi\)
\(150\) 0 0
\(151\) 17.1474 1.39543 0.697716 0.716375i \(-0.254200\pi\)
0.697716 + 0.716375i \(0.254200\pi\)
\(152\) 22.2740 1.80666
\(153\) 0 0
\(154\) −10.3574 −0.834622
\(155\) 2.21900 0.178234
\(156\) 0 0
\(157\) −18.3834 −1.46715 −0.733576 0.679608i \(-0.762150\pi\)
−0.733576 + 0.679608i \(0.762150\pi\)
\(158\) 3.47820 0.276711
\(159\) 0 0
\(160\) 14.3165 1.13182
\(161\) 3.07400 0.242266
\(162\) 0 0
\(163\) 12.5756 0.984995 0.492497 0.870314i \(-0.336084\pi\)
0.492497 + 0.870314i \(0.336084\pi\)
\(164\) 4.58252 0.357834
\(165\) 0 0
\(166\) 13.5384 1.05079
\(167\) 5.05267 0.390988 0.195494 0.980705i \(-0.437369\pi\)
0.195494 + 0.980705i \(0.437369\pi\)
\(168\) 0 0
\(169\) −12.9982 −0.999858
\(170\) −13.0961 −1.00442
\(171\) 0 0
\(172\) 10.7150 0.817009
\(173\) −9.98395 −0.759066 −0.379533 0.925178i \(-0.623915\pi\)
−0.379533 + 0.925178i \(0.623915\pi\)
\(174\) 0 0
\(175\) 14.2921 1.08038
\(176\) 4.50729 0.339750
\(177\) 0 0
\(178\) 6.61924 0.496133
\(179\) 7.70479 0.575883 0.287942 0.957648i \(-0.407029\pi\)
0.287942 + 0.957648i \(0.407029\pi\)
\(180\) 0 0
\(181\) −15.2801 −1.13576 −0.567881 0.823111i \(-0.692236\pi\)
−0.567881 + 0.823111i \(0.692236\pi\)
\(182\) −0.138882 −0.0102946
\(183\) 0 0
\(184\) −3.04291 −0.224326
\(185\) −21.4676 −1.57833
\(186\) 0 0
\(187\) 12.8653 0.940806
\(188\) 4.85618 0.354173
\(189\) 0 0
\(190\) −23.8928 −1.73337
\(191\) 8.19768 0.593163 0.296582 0.955007i \(-0.404153\pi\)
0.296582 + 0.955007i \(0.404153\pi\)
\(192\) 0 0
\(193\) 14.6875 1.05723 0.528615 0.848862i \(-0.322712\pi\)
0.528615 + 0.848862i \(0.322712\pi\)
\(194\) −0.773893 −0.0555623
\(195\) 0 0
\(196\) −2.19445 −0.156747
\(197\) −6.90137 −0.491702 −0.245851 0.969308i \(-0.579067\pi\)
−0.245851 + 0.969308i \(0.579067\pi\)
\(198\) 0 0
\(199\) 14.1987 1.00652 0.503259 0.864136i \(-0.332134\pi\)
0.503259 + 0.864136i \(0.332134\pi\)
\(200\) −14.1475 −1.00038
\(201\) 0 0
\(202\) −7.44648 −0.523932
\(203\) 3.07400 0.215753
\(204\) 0 0
\(205\) −15.8893 −1.10976
\(206\) 10.5465 0.734808
\(207\) 0 0
\(208\) 0.0604381 0.00419063
\(209\) 23.4718 1.62358
\(210\) 0 0
\(211\) 12.9150 0.889102 0.444551 0.895754i \(-0.353363\pi\)
0.444551 + 0.895754i \(0.353363\pi\)
\(212\) −2.54516 −0.174802
\(213\) 0 0
\(214\) 20.1791 1.37941
\(215\) −37.1529 −2.53380
\(216\) 0 0
\(217\) 2.19590 0.149067
\(218\) −14.2204 −0.963128
\(219\) 0 0
\(220\) 8.92346 0.601620
\(221\) 0.172511 0.0116043
\(222\) 0 0
\(223\) −6.99684 −0.468543 −0.234271 0.972171i \(-0.575270\pi\)
−0.234271 + 0.972171i \(0.575270\pi\)
\(224\) 14.1674 0.946603
\(225\) 0 0
\(226\) −16.4769 −1.09603
\(227\) 20.8089 1.38114 0.690569 0.723267i \(-0.257360\pi\)
0.690569 + 0.723267i \(0.257360\pi\)
\(228\) 0 0
\(229\) 8.58224 0.567131 0.283565 0.958953i \(-0.408483\pi\)
0.283565 + 0.958953i \(0.408483\pi\)
\(230\) 3.26406 0.215226
\(231\) 0 0
\(232\) −3.04291 −0.199777
\(233\) 20.1645 1.32102 0.660511 0.750817i \(-0.270340\pi\)
0.660511 + 0.750817i \(0.270340\pi\)
\(234\) 0 0
\(235\) −16.8382 −1.09840
\(236\) 9.76406 0.635586
\(237\) 0 0
\(238\) −12.9598 −0.840057
\(239\) 19.3093 1.24901 0.624507 0.781019i \(-0.285300\pi\)
0.624507 + 0.781019i \(0.285300\pi\)
\(240\) 0 0
\(241\) −4.32842 −0.278818 −0.139409 0.990235i \(-0.544520\pi\)
−0.139409 + 0.990235i \(0.544520\pi\)
\(242\) −0.754551 −0.0485044
\(243\) 0 0
\(244\) 7.60435 0.486819
\(245\) 7.60900 0.486121
\(246\) 0 0
\(247\) 0.314732 0.0200259
\(248\) −2.17369 −0.138029
\(249\) 0 0
\(250\) −1.14456 −0.0723886
\(251\) 7.41999 0.468345 0.234173 0.972195i \(-0.424762\pi\)
0.234173 + 0.972195i \(0.424762\pi\)
\(252\) 0 0
\(253\) −3.20654 −0.201594
\(254\) 6.55092 0.411041
\(255\) 0 0
\(256\) −16.5427 −1.03392
\(257\) −24.9240 −1.55472 −0.777359 0.629057i \(-0.783441\pi\)
−0.777359 + 0.629057i \(0.783441\pi\)
\(258\) 0 0
\(259\) −21.2442 −1.32005
\(260\) 0.119654 0.00742065
\(261\) 0 0
\(262\) −15.4669 −0.955547
\(263\) −8.09672 −0.499265 −0.249633 0.968341i \(-0.580310\pi\)
−0.249633 + 0.968341i \(0.580310\pi\)
\(264\) 0 0
\(265\) 8.82502 0.542117
\(266\) −23.6441 −1.44971
\(267\) 0 0
\(268\) −2.74398 −0.167615
\(269\) 10.3743 0.632533 0.316267 0.948670i \(-0.397571\pi\)
0.316267 + 0.948670i \(0.397571\pi\)
\(270\) 0 0
\(271\) −31.9369 −1.94003 −0.970014 0.243050i \(-0.921852\pi\)
−0.970014 + 0.243050i \(0.921852\pi\)
\(272\) 5.63979 0.341962
\(273\) 0 0
\(274\) 15.0791 0.910960
\(275\) −14.9083 −0.899005
\(276\) 0 0
\(277\) 26.8274 1.61190 0.805951 0.591982i \(-0.201655\pi\)
0.805951 + 0.591982i \(0.201655\pi\)
\(278\) −7.21473 −0.432711
\(279\) 0 0
\(280\) −29.0564 −1.73645
\(281\) −1.09966 −0.0656000 −0.0328000 0.999462i \(-0.510442\pi\)
−0.0328000 + 0.999462i \(0.510442\pi\)
\(282\) 0 0
\(283\) −16.7079 −0.993182 −0.496591 0.867985i \(-0.665415\pi\)
−0.496591 + 0.867985i \(0.665415\pi\)
\(284\) 3.27562 0.194372
\(285\) 0 0
\(286\) 0.144870 0.00856633
\(287\) −15.7239 −0.928154
\(288\) 0 0
\(289\) −0.902157 −0.0530681
\(290\) 3.26406 0.191672
\(291\) 0 0
\(292\) −8.86712 −0.518909
\(293\) 2.31072 0.134994 0.0674970 0.997719i \(-0.478499\pi\)
0.0674970 + 0.997719i \(0.478499\pi\)
\(294\) 0 0
\(295\) −33.8557 −1.97115
\(296\) 21.0293 1.22230
\(297\) 0 0
\(298\) 2.38137 0.137949
\(299\) −0.0429964 −0.00248655
\(300\) 0 0
\(301\) −36.7661 −2.11916
\(302\) 18.0180 1.03682
\(303\) 0 0
\(304\) 10.2894 0.590135
\(305\) −26.3672 −1.50978
\(306\) 0 0
\(307\) −22.2607 −1.27049 −0.635243 0.772312i \(-0.719100\pi\)
−0.635243 + 0.772312i \(0.719100\pi\)
\(308\) 8.83058 0.503169
\(309\) 0 0
\(310\) 2.33166 0.132430
\(311\) 16.0897 0.912361 0.456181 0.889887i \(-0.349217\pi\)
0.456181 + 0.889887i \(0.349217\pi\)
\(312\) 0 0
\(313\) 9.19668 0.519827 0.259914 0.965632i \(-0.416306\pi\)
0.259914 + 0.965632i \(0.416306\pi\)
\(314\) −19.3167 −1.09011
\(315\) 0 0
\(316\) −2.96547 −0.166821
\(317\) 2.73116 0.153397 0.0766986 0.997054i \(-0.475562\pi\)
0.0766986 + 0.997054i \(0.475562\pi\)
\(318\) 0 0
\(319\) −3.20654 −0.179532
\(320\) 23.7762 1.32913
\(321\) 0 0
\(322\) 3.23008 0.180005
\(323\) 29.3693 1.63415
\(324\) 0 0
\(325\) −0.199905 −0.0110887
\(326\) 13.2141 0.731860
\(327\) 0 0
\(328\) 15.5649 0.859426
\(329\) −16.6629 −0.918657
\(330\) 0 0
\(331\) −24.6627 −1.35559 −0.677794 0.735252i \(-0.737064\pi\)
−0.677794 + 0.735252i \(0.737064\pi\)
\(332\) −11.5427 −0.633487
\(333\) 0 0
\(334\) 5.30921 0.290507
\(335\) 9.51443 0.519829
\(336\) 0 0
\(337\) −5.08897 −0.277214 −0.138607 0.990347i \(-0.544262\pi\)
−0.138607 + 0.990347i \(0.544262\pi\)
\(338\) −13.6581 −0.742903
\(339\) 0 0
\(340\) 11.1656 0.605537
\(341\) −2.29058 −0.124042
\(342\) 0 0
\(343\) −13.9882 −0.755294
\(344\) 36.3942 1.96224
\(345\) 0 0
\(346\) −10.4909 −0.563992
\(347\) −26.6514 −1.43072 −0.715360 0.698756i \(-0.753737\pi\)
−0.715360 + 0.698756i \(0.753737\pi\)
\(348\) 0 0
\(349\) −33.2848 −1.78170 −0.890848 0.454301i \(-0.849889\pi\)
−0.890848 + 0.454301i \(0.849889\pi\)
\(350\) 15.0178 0.802733
\(351\) 0 0
\(352\) −14.7783 −0.787685
\(353\) −28.5065 −1.51725 −0.758623 0.651530i \(-0.774127\pi\)
−0.758623 + 0.651530i \(0.774127\pi\)
\(354\) 0 0
\(355\) −11.3578 −0.602811
\(356\) −5.64348 −0.299104
\(357\) 0 0
\(358\) 8.09599 0.427886
\(359\) 12.3505 0.651832 0.325916 0.945399i \(-0.394327\pi\)
0.325916 + 0.945399i \(0.394327\pi\)
\(360\) 0 0
\(361\) 34.5819 1.82010
\(362\) −16.0559 −0.843881
\(363\) 0 0
\(364\) 0.118409 0.00620631
\(365\) 30.7456 1.60930
\(366\) 0 0
\(367\) −19.7884 −1.03294 −0.516472 0.856304i \(-0.672755\pi\)
−0.516472 + 0.856304i \(0.672755\pi\)
\(368\) −1.40566 −0.0732748
\(369\) 0 0
\(370\) −22.5576 −1.17272
\(371\) 8.73316 0.453403
\(372\) 0 0
\(373\) 0.00491154 0.000254310 0 0.000127155 1.00000i \(-0.499960\pi\)
0.000127155 1.00000i \(0.499960\pi\)
\(374\) 13.5185 0.699027
\(375\) 0 0
\(376\) 16.4944 0.850632
\(377\) −0.0429964 −0.00221443
\(378\) 0 0
\(379\) −29.3054 −1.50532 −0.752658 0.658411i \(-0.771229\pi\)
−0.752658 + 0.658411i \(0.771229\pi\)
\(380\) 20.3707 1.04499
\(381\) 0 0
\(382\) 8.61390 0.440726
\(383\) 2.27253 0.116121 0.0580604 0.998313i \(-0.481508\pi\)
0.0580604 + 0.998313i \(0.481508\pi\)
\(384\) 0 0
\(385\) −30.6189 −1.56049
\(386\) 15.4332 0.785531
\(387\) 0 0
\(388\) 0.659811 0.0334968
\(389\) 29.8019 1.51101 0.755507 0.655140i \(-0.227391\pi\)
0.755507 + 0.655140i \(0.227391\pi\)
\(390\) 0 0
\(391\) −4.01221 −0.202906
\(392\) −7.45362 −0.376465
\(393\) 0 0
\(394\) −7.25178 −0.365339
\(395\) 10.2824 0.517364
\(396\) 0 0
\(397\) −13.7498 −0.690081 −0.345040 0.938588i \(-0.612135\pi\)
−0.345040 + 0.938588i \(0.612135\pi\)
\(398\) 14.9196 0.747852
\(399\) 0 0
\(400\) −6.53537 −0.326769
\(401\) 11.4510 0.571836 0.285918 0.958254i \(-0.407701\pi\)
0.285918 + 0.958254i \(0.407701\pi\)
\(402\) 0 0
\(403\) −0.0307143 −0.00152999
\(404\) 6.34877 0.315863
\(405\) 0 0
\(406\) 3.23008 0.160306
\(407\) 22.1601 1.09844
\(408\) 0 0
\(409\) −6.99053 −0.345660 −0.172830 0.984952i \(-0.555291\pi\)
−0.172830 + 0.984952i \(0.555291\pi\)
\(410\) −16.6961 −0.824560
\(411\) 0 0
\(412\) −8.99179 −0.442994
\(413\) −33.5033 −1.64859
\(414\) 0 0
\(415\) 40.0229 1.96464
\(416\) −0.198161 −0.00971566
\(417\) 0 0
\(418\) 24.6635 1.20633
\(419\) −18.8803 −0.922364 −0.461182 0.887305i \(-0.652575\pi\)
−0.461182 + 0.887305i \(0.652575\pi\)
\(420\) 0 0
\(421\) 5.75470 0.280467 0.140233 0.990118i \(-0.455215\pi\)
0.140233 + 0.990118i \(0.455215\pi\)
\(422\) 13.5707 0.660611
\(423\) 0 0
\(424\) −8.64482 −0.419829
\(425\) −18.6541 −0.904859
\(426\) 0 0
\(427\) −26.0927 −1.26271
\(428\) −17.2044 −0.831607
\(429\) 0 0
\(430\) −39.0392 −1.88264
\(431\) −19.6675 −0.947350 −0.473675 0.880700i \(-0.657073\pi\)
−0.473675 + 0.880700i \(0.657073\pi\)
\(432\) 0 0
\(433\) −25.5240 −1.22660 −0.613302 0.789849i \(-0.710159\pi\)
−0.613302 + 0.789849i \(0.710159\pi\)
\(434\) 2.30739 0.110758
\(435\) 0 0
\(436\) 12.1241 0.580641
\(437\) −7.31997 −0.350162
\(438\) 0 0
\(439\) −8.99635 −0.429372 −0.214686 0.976683i \(-0.568873\pi\)
−0.214686 + 0.976683i \(0.568873\pi\)
\(440\) 30.3092 1.44493
\(441\) 0 0
\(442\) 0.181270 0.00862211
\(443\) 1.63232 0.0775541 0.0387770 0.999248i \(-0.487654\pi\)
0.0387770 + 0.999248i \(0.487654\pi\)
\(444\) 0 0
\(445\) 19.5681 0.927615
\(446\) −7.35209 −0.348131
\(447\) 0 0
\(448\) 23.5288 1.11163
\(449\) 36.0363 1.70066 0.850329 0.526251i \(-0.176403\pi\)
0.850329 + 0.526251i \(0.176403\pi\)
\(450\) 0 0
\(451\) 16.4019 0.772334
\(452\) 14.0480 0.660764
\(453\) 0 0
\(454\) 21.8655 1.02620
\(455\) −0.410568 −0.0192477
\(456\) 0 0
\(457\) −4.27483 −0.199968 −0.0999841 0.994989i \(-0.531879\pi\)
−0.0999841 + 0.994989i \(0.531879\pi\)
\(458\) 9.01799 0.421383
\(459\) 0 0
\(460\) −2.78289 −0.129753
\(461\) −23.0578 −1.07391 −0.536954 0.843612i \(-0.680425\pi\)
−0.536954 + 0.843612i \(0.680425\pi\)
\(462\) 0 0
\(463\) 34.6421 1.60996 0.804978 0.593305i \(-0.202177\pi\)
0.804978 + 0.593305i \(0.202177\pi\)
\(464\) −1.40566 −0.0652559
\(465\) 0 0
\(466\) 21.1883 0.981531
\(467\) 6.60876 0.305817 0.152908 0.988240i \(-0.451136\pi\)
0.152908 + 0.988240i \(0.451136\pi\)
\(468\) 0 0
\(469\) 9.41539 0.434762
\(470\) −17.6931 −0.816123
\(471\) 0 0
\(472\) 33.1644 1.52651
\(473\) 38.3513 1.76340
\(474\) 0 0
\(475\) −34.0330 −1.56154
\(476\) 11.0493 0.506445
\(477\) 0 0
\(478\) 20.2897 0.928029
\(479\) 14.1027 0.644368 0.322184 0.946677i \(-0.395583\pi\)
0.322184 + 0.946677i \(0.395583\pi\)
\(480\) 0 0
\(481\) 0.297144 0.0135486
\(482\) −4.54819 −0.207164
\(483\) 0 0
\(484\) 0.643321 0.0292418
\(485\) −2.28781 −0.103884
\(486\) 0 0
\(487\) −16.1971 −0.733962 −0.366981 0.930228i \(-0.619609\pi\)
−0.366981 + 0.930228i \(0.619609\pi\)
\(488\) 25.8287 1.16921
\(489\) 0 0
\(490\) 7.99533 0.361192
\(491\) −35.1704 −1.58722 −0.793609 0.608428i \(-0.791800\pi\)
−0.793609 + 0.608428i \(0.791800\pi\)
\(492\) 0 0
\(493\) −4.01221 −0.180701
\(494\) 0.330712 0.0148794
\(495\) 0 0
\(496\) −1.00412 −0.0450864
\(497\) −11.2396 −0.504165
\(498\) 0 0
\(499\) −29.0912 −1.30230 −0.651150 0.758949i \(-0.725713\pi\)
−0.651150 + 0.758949i \(0.725713\pi\)
\(500\) 0.975841 0.0436409
\(501\) 0 0
\(502\) 7.79672 0.347985
\(503\) 42.0281 1.87394 0.936970 0.349411i \(-0.113618\pi\)
0.936970 + 0.349411i \(0.113618\pi\)
\(504\) 0 0
\(505\) −22.0136 −0.979592
\(506\) −3.36935 −0.149786
\(507\) 0 0
\(508\) −5.58523 −0.247804
\(509\) −1.26068 −0.0558787 −0.0279394 0.999610i \(-0.508895\pi\)
−0.0279394 + 0.999610i \(0.508895\pi\)
\(510\) 0 0
\(511\) 30.4256 1.34595
\(512\) −15.0329 −0.664368
\(513\) 0 0
\(514\) −26.1895 −1.15517
\(515\) 31.1779 1.37386
\(516\) 0 0
\(517\) 17.3814 0.764431
\(518\) −22.3228 −0.980808
\(519\) 0 0
\(520\) 0.406415 0.0178225
\(521\) −27.7996 −1.21792 −0.608961 0.793200i \(-0.708413\pi\)
−0.608961 + 0.793200i \(0.708413\pi\)
\(522\) 0 0
\(523\) 34.2875 1.49929 0.749644 0.661842i \(-0.230225\pi\)
0.749644 + 0.661842i \(0.230225\pi\)
\(524\) 13.1869 0.576070
\(525\) 0 0
\(526\) −8.50782 −0.370958
\(527\) −2.86610 −0.124849
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 9.27310 0.402798
\(531\) 0 0
\(532\) 20.1586 0.873988
\(533\) 0.219932 0.00952631
\(534\) 0 0
\(535\) 59.6542 2.57908
\(536\) −9.32015 −0.402569
\(537\) 0 0
\(538\) 10.9011 0.469978
\(539\) −7.85444 −0.338315
\(540\) 0 0
\(541\) 39.2929 1.68933 0.844666 0.535293i \(-0.179799\pi\)
0.844666 + 0.535293i \(0.179799\pi\)
\(542\) −33.5584 −1.44146
\(543\) 0 0
\(544\) −18.4914 −0.792814
\(545\) −42.0390 −1.80075
\(546\) 0 0
\(547\) −25.1700 −1.07619 −0.538095 0.842884i \(-0.680856\pi\)
−0.538095 + 0.842884i \(0.680856\pi\)
\(548\) −12.8562 −0.549190
\(549\) 0 0
\(550\) −15.6653 −0.667969
\(551\) −7.31997 −0.311841
\(552\) 0 0
\(553\) 10.1754 0.432701
\(554\) 28.1895 1.19766
\(555\) 0 0
\(556\) 6.15119 0.260869
\(557\) −18.8437 −0.798433 −0.399217 0.916857i \(-0.630718\pi\)
−0.399217 + 0.916857i \(0.630718\pi\)
\(558\) 0 0
\(559\) 0.514251 0.0217505
\(560\) −13.4225 −0.567203
\(561\) 0 0
\(562\) −1.15549 −0.0487414
\(563\) 18.4647 0.778196 0.389098 0.921196i \(-0.372787\pi\)
0.389098 + 0.921196i \(0.372787\pi\)
\(564\) 0 0
\(565\) −48.7098 −2.04924
\(566\) −17.5562 −0.737943
\(567\) 0 0
\(568\) 11.1259 0.466832
\(569\) −24.5751 −1.03024 −0.515121 0.857117i \(-0.672253\pi\)
−0.515121 + 0.857117i \(0.672253\pi\)
\(570\) 0 0
\(571\) 32.1662 1.34612 0.673058 0.739590i \(-0.264981\pi\)
0.673058 + 0.739590i \(0.264981\pi\)
\(572\) −0.123514 −0.00516438
\(573\) 0 0
\(574\) −16.5223 −0.689626
\(575\) 4.64934 0.193891
\(576\) 0 0
\(577\) 3.94261 0.164133 0.0820664 0.996627i \(-0.473848\pi\)
0.0820664 + 0.996627i \(0.473848\pi\)
\(578\) −0.947962 −0.0394300
\(579\) 0 0
\(580\) −2.78289 −0.115553
\(581\) 39.6063 1.64314
\(582\) 0 0
\(583\) −9.10969 −0.377285
\(584\) −30.1178 −1.24628
\(585\) 0 0
\(586\) 2.42805 0.100302
\(587\) −31.9270 −1.31777 −0.658885 0.752244i \(-0.728971\pi\)
−0.658885 + 0.752244i \(0.728971\pi\)
\(588\) 0 0
\(589\) −5.22898 −0.215456
\(590\) −35.5746 −1.46458
\(591\) 0 0
\(592\) 9.71436 0.399258
\(593\) 9.21942 0.378596 0.189298 0.981920i \(-0.439379\pi\)
0.189298 + 0.981920i \(0.439379\pi\)
\(594\) 0 0
\(595\) −38.3122 −1.57065
\(596\) −2.03032 −0.0831652
\(597\) 0 0
\(598\) −0.0451795 −0.00184753
\(599\) 26.7668 1.09366 0.546831 0.837243i \(-0.315834\pi\)
0.546831 + 0.837243i \(0.315834\pi\)
\(600\) 0 0
\(601\) −22.6788 −0.925088 −0.462544 0.886596i \(-0.653063\pi\)
−0.462544 + 0.886596i \(0.653063\pi\)
\(602\) −38.6329 −1.57456
\(603\) 0 0
\(604\) −15.3619 −0.625067
\(605\) −2.23064 −0.0906882
\(606\) 0 0
\(607\) −29.7375 −1.20701 −0.603503 0.797360i \(-0.706229\pi\)
−0.603503 + 0.797360i \(0.706229\pi\)
\(608\) −33.7362 −1.36818
\(609\) 0 0
\(610\) −27.7059 −1.12178
\(611\) 0.233066 0.00942884
\(612\) 0 0
\(613\) −10.4654 −0.422695 −0.211347 0.977411i \(-0.567785\pi\)
−0.211347 + 0.977411i \(0.567785\pi\)
\(614\) −23.3910 −0.943982
\(615\) 0 0
\(616\) 29.9937 1.20848
\(617\) −1.84782 −0.0743905 −0.0371953 0.999308i \(-0.511842\pi\)
−0.0371953 + 0.999308i \(0.511842\pi\)
\(618\) 0 0
\(619\) 4.67510 0.187908 0.0939540 0.995577i \(-0.470049\pi\)
0.0939540 + 0.995577i \(0.470049\pi\)
\(620\) −1.98795 −0.0798378
\(621\) 0 0
\(622\) 16.9066 0.677892
\(623\) 19.3644 0.775817
\(624\) 0 0
\(625\) −26.6303 −1.06521
\(626\) 9.66363 0.386236
\(627\) 0 0
\(628\) 16.4692 0.657193
\(629\) 27.7281 1.10559
\(630\) 0 0
\(631\) −42.2191 −1.68072 −0.840358 0.542031i \(-0.817655\pi\)
−0.840358 + 0.542031i \(0.817655\pi\)
\(632\) −10.0724 −0.400660
\(633\) 0 0
\(634\) 2.86983 0.113975
\(635\) 19.3661 0.768520
\(636\) 0 0
\(637\) −0.105320 −0.00417293
\(638\) −3.36935 −0.133394
\(639\) 0 0
\(640\) −3.64950 −0.144259
\(641\) −29.1294 −1.15054 −0.575271 0.817963i \(-0.695103\pi\)
−0.575271 + 0.817963i \(0.695103\pi\)
\(642\) 0 0
\(643\) 13.8177 0.544916 0.272458 0.962168i \(-0.412163\pi\)
0.272458 + 0.962168i \(0.412163\pi\)
\(644\) −2.75393 −0.108520
\(645\) 0 0
\(646\) 30.8604 1.21419
\(647\) 42.2780 1.66212 0.831059 0.556184i \(-0.187735\pi\)
0.831059 + 0.556184i \(0.187735\pi\)
\(648\) 0 0
\(649\) 34.9478 1.37182
\(650\) −0.210055 −0.00823903
\(651\) 0 0
\(652\) −11.2661 −0.441216
\(653\) 29.2866 1.14607 0.573037 0.819529i \(-0.305765\pi\)
0.573037 + 0.819529i \(0.305765\pi\)
\(654\) 0 0
\(655\) −45.7238 −1.78658
\(656\) 7.19010 0.280726
\(657\) 0 0
\(658\) −17.5090 −0.682570
\(659\) −6.15767 −0.239869 −0.119934 0.992782i \(-0.538268\pi\)
−0.119934 + 0.992782i \(0.538268\pi\)
\(660\) 0 0
\(661\) −20.9869 −0.816295 −0.408148 0.912916i \(-0.633825\pi\)
−0.408148 + 0.912916i \(0.633825\pi\)
\(662\) −25.9150 −1.00721
\(663\) 0 0
\(664\) −39.2056 −1.52147
\(665\) −69.8976 −2.71051
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −4.52657 −0.175138
\(669\) 0 0
\(670\) 9.99751 0.386237
\(671\) 27.2177 1.05073
\(672\) 0 0
\(673\) 18.9550 0.730660 0.365330 0.930878i \(-0.380956\pi\)
0.365330 + 0.930878i \(0.380956\pi\)
\(674\) −5.34736 −0.205972
\(675\) 0 0
\(676\) 11.6447 0.447874
\(677\) −2.63505 −0.101273 −0.0506366 0.998717i \(-0.516125\pi\)
−0.0506366 + 0.998717i \(0.516125\pi\)
\(678\) 0 0
\(679\) −2.26400 −0.0868844
\(680\) 37.9247 1.45434
\(681\) 0 0
\(682\) −2.40688 −0.0921641
\(683\) 18.5862 0.711180 0.355590 0.934642i \(-0.384280\pi\)
0.355590 + 0.934642i \(0.384280\pi\)
\(684\) 0 0
\(685\) 44.5774 1.70321
\(686\) −14.6985 −0.561190
\(687\) 0 0
\(688\) 16.8121 0.640956
\(689\) −0.122152 −0.00465360
\(690\) 0 0
\(691\) 43.6567 1.66078 0.830389 0.557184i \(-0.188118\pi\)
0.830389 + 0.557184i \(0.188118\pi\)
\(692\) 8.94438 0.340014
\(693\) 0 0
\(694\) −28.0045 −1.06304
\(695\) −21.3285 −0.809036
\(696\) 0 0
\(697\) 20.5230 0.777363
\(698\) −34.9748 −1.32382
\(699\) 0 0
\(700\) −12.8039 −0.483944
\(701\) −22.0312 −0.832107 −0.416054 0.909340i \(-0.636587\pi\)
−0.416054 + 0.909340i \(0.636587\pi\)
\(702\) 0 0
\(703\) 50.5877 1.90795
\(704\) −24.5432 −0.925007
\(705\) 0 0
\(706\) −29.9538 −1.12733
\(707\) −21.7844 −0.819288
\(708\) 0 0
\(709\) −33.9056 −1.27335 −0.636676 0.771131i \(-0.719691\pi\)
−0.636676 + 0.771131i \(0.719691\pi\)
\(710\) −11.9345 −0.447894
\(711\) 0 0
\(712\) −19.1685 −0.718369
\(713\) 0.714345 0.0267524
\(714\) 0 0
\(715\) 0.428270 0.0160164
\(716\) −6.90253 −0.257960
\(717\) 0 0
\(718\) 12.9775 0.484317
\(719\) −10.7651 −0.401472 −0.200736 0.979645i \(-0.564333\pi\)
−0.200736 + 0.979645i \(0.564333\pi\)
\(720\) 0 0
\(721\) 30.8534 1.14904
\(722\) 36.3378 1.35235
\(723\) 0 0
\(724\) 13.6891 0.508750
\(725\) 4.64934 0.172672
\(726\) 0 0
\(727\) 48.9953 1.81714 0.908568 0.417737i \(-0.137177\pi\)
0.908568 + 0.417737i \(0.137177\pi\)
\(728\) 0.402185 0.0149060
\(729\) 0 0
\(730\) 32.3067 1.19572
\(731\) 47.9874 1.77488
\(732\) 0 0
\(733\) 30.4364 1.12420 0.562098 0.827071i \(-0.309995\pi\)
0.562098 + 0.827071i \(0.309995\pi\)
\(734\) −20.7931 −0.767487
\(735\) 0 0
\(736\) 4.60879 0.169882
\(737\) −9.82134 −0.361774
\(738\) 0 0
\(739\) 2.83114 0.104145 0.0520727 0.998643i \(-0.483417\pi\)
0.0520727 + 0.998643i \(0.483417\pi\)
\(740\) 19.2323 0.706995
\(741\) 0 0
\(742\) 9.17657 0.336883
\(743\) 18.5983 0.682307 0.341153 0.940008i \(-0.389182\pi\)
0.341153 + 0.940008i \(0.389182\pi\)
\(744\) 0 0
\(745\) 7.03989 0.257922
\(746\) 0.00516091 0.000188954 0
\(747\) 0 0
\(748\) −11.5257 −0.421422
\(749\) 59.0332 2.15703
\(750\) 0 0
\(751\) −24.7942 −0.904752 −0.452376 0.891827i \(-0.649424\pi\)
−0.452376 + 0.891827i \(0.649424\pi\)
\(752\) 7.61948 0.277854
\(753\) 0 0
\(754\) −0.0451795 −0.00164534
\(755\) 53.2655 1.93853
\(756\) 0 0
\(757\) −2.63450 −0.0957527 −0.0478763 0.998853i \(-0.515245\pi\)
−0.0478763 + 0.998853i \(0.515245\pi\)
\(758\) −30.7933 −1.11846
\(759\) 0 0
\(760\) 69.1906 2.50981
\(761\) 22.7357 0.824168 0.412084 0.911146i \(-0.364801\pi\)
0.412084 + 0.911146i \(0.364801\pi\)
\(762\) 0 0
\(763\) −41.6014 −1.50607
\(764\) −7.34410 −0.265700
\(765\) 0 0
\(766\) 2.38791 0.0862788
\(767\) 0.468613 0.0169206
\(768\) 0 0
\(769\) 0.477039 0.0172025 0.00860123 0.999963i \(-0.497262\pi\)
0.00860123 + 0.999963i \(0.497262\pi\)
\(770\) −32.1736 −1.15946
\(771\) 0 0
\(772\) −13.1582 −0.473573
\(773\) 4.06587 0.146239 0.0731197 0.997323i \(-0.476704\pi\)
0.0731197 + 0.997323i \(0.476704\pi\)
\(774\) 0 0
\(775\) 3.32123 0.119302
\(776\) 2.24110 0.0804507
\(777\) 0 0
\(778\) 31.3150 1.12270
\(779\) 37.4426 1.34152
\(780\) 0 0
\(781\) 11.7242 0.419525
\(782\) −4.21592 −0.150761
\(783\) 0 0
\(784\) −3.44316 −0.122970
\(785\) −57.1049 −2.03816
\(786\) 0 0
\(787\) −22.2517 −0.793188 −0.396594 0.917994i \(-0.629808\pi\)
−0.396594 + 0.917994i \(0.629808\pi\)
\(788\) 6.18277 0.220252
\(789\) 0 0
\(790\) 10.8045 0.384406
\(791\) −48.2028 −1.71389
\(792\) 0 0
\(793\) 0.364961 0.0129601
\(794\) −14.4479 −0.512736
\(795\) 0 0
\(796\) −12.7203 −0.450858
\(797\) 55.3496 1.96058 0.980291 0.197559i \(-0.0633015\pi\)
0.980291 + 0.197559i \(0.0633015\pi\)
\(798\) 0 0
\(799\) 21.7486 0.769409
\(800\) 21.4279 0.757589
\(801\) 0 0
\(802\) 12.0324 0.424879
\(803\) −31.7374 −1.11999
\(804\) 0 0
\(805\) 9.54890 0.336555
\(806\) −0.0322737 −0.00113679
\(807\) 0 0
\(808\) 21.5641 0.758621
\(809\) 10.4303 0.366711 0.183356 0.983047i \(-0.441304\pi\)
0.183356 + 0.983047i \(0.441304\pi\)
\(810\) 0 0
\(811\) −28.7760 −1.01046 −0.505232 0.862984i \(-0.668593\pi\)
−0.505232 + 0.862984i \(0.668593\pi\)
\(812\) −2.75393 −0.0966439
\(813\) 0 0
\(814\) 23.2853 0.816148
\(815\) 39.0640 1.36835
\(816\) 0 0
\(817\) 87.5493 3.06296
\(818\) −7.34546 −0.256828
\(819\) 0 0
\(820\) 14.2349 0.497103
\(821\) 19.8123 0.691453 0.345727 0.938335i \(-0.387632\pi\)
0.345727 + 0.938335i \(0.387632\pi\)
\(822\) 0 0
\(823\) −18.5275 −0.645828 −0.322914 0.946428i \(-0.604662\pi\)
−0.322914 + 0.946428i \(0.604662\pi\)
\(824\) −30.5413 −1.06396
\(825\) 0 0
\(826\) −35.2043 −1.22492
\(827\) 6.68508 0.232463 0.116232 0.993222i \(-0.462919\pi\)
0.116232 + 0.993222i \(0.462919\pi\)
\(828\) 0 0
\(829\) 32.6286 1.13324 0.566620 0.823980i \(-0.308251\pi\)
0.566620 + 0.823980i \(0.308251\pi\)
\(830\) 42.0549 1.45975
\(831\) 0 0
\(832\) −0.329099 −0.0114095
\(833\) −9.82794 −0.340518
\(834\) 0 0
\(835\) 15.6953 0.543159
\(836\) −21.0278 −0.727262
\(837\) 0 0
\(838\) −19.8389 −0.685325
\(839\) −14.7983 −0.510894 −0.255447 0.966823i \(-0.582223\pi\)
−0.255447 + 0.966823i \(0.582223\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 6.04688 0.208389
\(843\) 0 0
\(844\) −11.5702 −0.398262
\(845\) −40.3767 −1.38900
\(846\) 0 0
\(847\) −2.20742 −0.0758477
\(848\) −3.99343 −0.137135
\(849\) 0 0
\(850\) −19.6013 −0.672318
\(851\) −6.91091 −0.236903
\(852\) 0 0
\(853\) 16.3532 0.559922 0.279961 0.960011i \(-0.409679\pi\)
0.279961 + 0.960011i \(0.409679\pi\)
\(854\) −27.4175 −0.938208
\(855\) 0 0
\(856\) −58.4361 −1.99730
\(857\) 47.5474 1.62419 0.812094 0.583527i \(-0.198328\pi\)
0.812094 + 0.583527i \(0.198328\pi\)
\(858\) 0 0
\(859\) 5.87247 0.200366 0.100183 0.994969i \(-0.468057\pi\)
0.100183 + 0.994969i \(0.468057\pi\)
\(860\) 33.2843 1.13499
\(861\) 0 0
\(862\) −20.6661 −0.703889
\(863\) 30.9619 1.05396 0.526978 0.849879i \(-0.323325\pi\)
0.526978 + 0.849879i \(0.323325\pi\)
\(864\) 0 0
\(865\) −31.0135 −1.05449
\(866\) −26.8199 −0.911377
\(867\) 0 0
\(868\) −1.96725 −0.0667729
\(869\) −10.6141 −0.360058
\(870\) 0 0
\(871\) −0.131694 −0.00446228
\(872\) 41.1805 1.39455
\(873\) 0 0
\(874\) −7.69163 −0.260173
\(875\) −3.34839 −0.113196
\(876\) 0 0
\(877\) −17.6154 −0.594830 −0.297415 0.954748i \(-0.596124\pi\)
−0.297415 + 0.954748i \(0.596124\pi\)
\(878\) −9.45312 −0.319027
\(879\) 0 0
\(880\) 14.0012 0.471980
\(881\) −4.21972 −0.142166 −0.0710831 0.997470i \(-0.522646\pi\)
−0.0710831 + 0.997470i \(0.522646\pi\)
\(882\) 0 0
\(883\) 6.73658 0.226704 0.113352 0.993555i \(-0.463841\pi\)
0.113352 + 0.993555i \(0.463841\pi\)
\(884\) −0.154548 −0.00519801
\(885\) 0 0
\(886\) 1.71520 0.0576234
\(887\) 56.2580 1.88896 0.944479 0.328571i \(-0.106567\pi\)
0.944479 + 0.328571i \(0.106567\pi\)
\(888\) 0 0
\(889\) 19.1645 0.642757
\(890\) 20.5616 0.689226
\(891\) 0 0
\(892\) 6.26829 0.209878
\(893\) 39.6786 1.32779
\(894\) 0 0
\(895\) 23.9337 0.800015
\(896\) −3.61151 −0.120652
\(897\) 0 0
\(898\) 37.8660 1.26360
\(899\) 0.714345 0.0238247
\(900\) 0 0
\(901\) −11.3986 −0.379742
\(902\) 17.2346 0.573851
\(903\) 0 0
\(904\) 47.7152 1.58698
\(905\) −47.4652 −1.57780
\(906\) 0 0
\(907\) 32.6879 1.08538 0.542691 0.839932i \(-0.317405\pi\)
0.542691 + 0.839932i \(0.317405\pi\)
\(908\) −18.6422 −0.618664
\(909\) 0 0
\(910\) −0.431414 −0.0143012
\(911\) −27.6041 −0.914565 −0.457283 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(912\) 0 0
\(913\) −41.3139 −1.36729
\(914\) −4.49188 −0.148578
\(915\) 0 0
\(916\) −7.68862 −0.254039
\(917\) −45.2479 −1.49422
\(918\) 0 0
\(919\) 13.4419 0.443409 0.221704 0.975114i \(-0.428838\pi\)
0.221704 + 0.975114i \(0.428838\pi\)
\(920\) −9.45231 −0.311633
\(921\) 0 0
\(922\) −24.2285 −0.797923
\(923\) 0.157209 0.00517461
\(924\) 0 0
\(925\) −32.1312 −1.05647
\(926\) 36.4010 1.19621
\(927\) 0 0
\(928\) 4.60879 0.151291
\(929\) 29.7370 0.975640 0.487820 0.872944i \(-0.337792\pi\)
0.487820 + 0.872944i \(0.337792\pi\)
\(930\) 0 0
\(931\) −17.9303 −0.587642
\(932\) −18.0649 −0.591735
\(933\) 0 0
\(934\) 6.94431 0.227225
\(935\) 39.9641 1.30696
\(936\) 0 0
\(937\) −1.43663 −0.0469325 −0.0234663 0.999725i \(-0.507470\pi\)
−0.0234663 + 0.999725i \(0.507470\pi\)
\(938\) 9.89344 0.323032
\(939\) 0 0
\(940\) 15.0849 0.492016
\(941\) 6.73354 0.219507 0.109754 0.993959i \(-0.464994\pi\)
0.109754 + 0.993959i \(0.464994\pi\)
\(942\) 0 0
\(943\) −5.11513 −0.166571
\(944\) 15.3201 0.498627
\(945\) 0 0
\(946\) 40.2985 1.31022
\(947\) −14.0154 −0.455440 −0.227720 0.973727i \(-0.573127\pi\)
−0.227720 + 0.973727i \(0.573127\pi\)
\(948\) 0 0
\(949\) −0.425566 −0.0138144
\(950\) −35.7610 −1.16024
\(951\) 0 0
\(952\) 37.5299 1.21635
\(953\) −12.8306 −0.415624 −0.207812 0.978169i \(-0.566634\pi\)
−0.207812 + 0.978169i \(0.566634\pi\)
\(954\) 0 0
\(955\) 25.4648 0.824021
\(956\) −17.2987 −0.559481
\(957\) 0 0
\(958\) 14.8187 0.478771
\(959\) 44.1134 1.42449
\(960\) 0 0
\(961\) −30.4897 −0.983539
\(962\) 0.312231 0.0100667
\(963\) 0 0
\(964\) 3.87773 0.124893
\(965\) 45.6244 1.46870
\(966\) 0 0
\(967\) 30.6661 0.986156 0.493078 0.869985i \(-0.335872\pi\)
0.493078 + 0.869985i \(0.335872\pi\)
\(968\) 2.18509 0.0702313
\(969\) 0 0
\(970\) −2.40397 −0.0771870
\(971\) −12.6876 −0.407166 −0.203583 0.979058i \(-0.565259\pi\)
−0.203583 + 0.979058i \(0.565259\pi\)
\(972\) 0 0
\(973\) −21.1065 −0.676643
\(974\) −17.0195 −0.545340
\(975\) 0 0
\(976\) 11.9315 0.381916
\(977\) −34.7063 −1.11035 −0.555177 0.831732i \(-0.687350\pi\)
−0.555177 + 0.831732i \(0.687350\pi\)
\(978\) 0 0
\(979\) −20.1993 −0.645572
\(980\) −6.81671 −0.217752
\(981\) 0 0
\(982\) −36.9561 −1.17932
\(983\) 59.0415 1.88313 0.941566 0.336828i \(-0.109354\pi\)
0.941566 + 0.336828i \(0.109354\pi\)
\(984\) 0 0
\(985\) −21.4380 −0.683072
\(986\) −4.21592 −0.134262
\(987\) 0 0
\(988\) −0.281961 −0.00897037
\(989\) −11.9603 −0.380317
\(990\) 0 0
\(991\) −48.1877 −1.53073 −0.765367 0.643594i \(-0.777442\pi\)
−0.765367 + 0.643594i \(0.777442\pi\)
\(992\) 3.29227 0.104530
\(993\) 0 0
\(994\) −11.8103 −0.374599
\(995\) 44.1059 1.39825
\(996\) 0 0
\(997\) 38.0886 1.20628 0.603139 0.797636i \(-0.293916\pi\)
0.603139 + 0.797636i \(0.293916\pi\)
\(998\) −30.5682 −0.967620
\(999\) 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 \(a_p\))