Properties

Label 6003.2.a.t.1.19
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 1.19
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.93234 q^{2} +1.73393 q^{4} +2.82056 q^{5} -3.97268 q^{7} -0.514145 q^{8} +O(q^{10})\) \(q+1.93234 q^{2} +1.73393 q^{4} +2.82056 q^{5} -3.97268 q^{7} -0.514145 q^{8} +5.45026 q^{10} +4.70087 q^{11} -5.71953 q^{13} -7.67656 q^{14} -4.46135 q^{16} -5.11092 q^{17} +0.224637 q^{19} +4.89063 q^{20} +9.08366 q^{22} +1.00000 q^{23} +2.95554 q^{25} -11.0521 q^{26} -6.88834 q^{28} +1.00000 q^{29} +5.16107 q^{31} -7.59255 q^{32} -9.87602 q^{34} -11.2052 q^{35} -5.77440 q^{37} +0.434074 q^{38} -1.45017 q^{40} +0.469446 q^{41} +2.68640 q^{43} +8.15096 q^{44} +1.93234 q^{46} -12.2820 q^{47} +8.78220 q^{49} +5.71109 q^{50} -9.91724 q^{52} +3.63780 q^{53} +13.2591 q^{55} +2.04253 q^{56} +1.93234 q^{58} -8.78187 q^{59} +4.68255 q^{61} +9.97293 q^{62} -5.74865 q^{64} -16.1323 q^{65} -15.9642 q^{67} -8.86195 q^{68} -21.6522 q^{70} -10.0253 q^{71} +8.41059 q^{73} -11.1581 q^{74} +0.389504 q^{76} -18.6751 q^{77} -12.9991 q^{79} -12.5835 q^{80} +0.907129 q^{82} -11.6167 q^{83} -14.4156 q^{85} +5.19102 q^{86} -2.41693 q^{88} -10.7508 q^{89} +22.7219 q^{91} +1.73393 q^{92} -23.7330 q^{94} +0.633601 q^{95} -5.53357 q^{97} +16.9702 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93234 1.36637 0.683184 0.730246i \(-0.260595\pi\)
0.683184 + 0.730246i \(0.260595\pi\)
\(3\) 0 0
\(4\) 1.73393 0.866963
\(5\) 2.82056 1.26139 0.630696 0.776030i \(-0.282770\pi\)
0.630696 + 0.776030i \(0.282770\pi\)
\(6\) 0 0
\(7\) −3.97268 −1.50153 −0.750766 0.660568i \(-0.770316\pi\)
−0.750766 + 0.660568i \(0.770316\pi\)
\(8\) −0.514145 −0.181778
\(9\) 0 0
\(10\) 5.45026 1.72352
\(11\) 4.70087 1.41737 0.708683 0.705527i \(-0.249290\pi\)
0.708683 + 0.705527i \(0.249290\pi\)
\(12\) 0 0
\(13\) −5.71953 −1.58631 −0.793156 0.609018i \(-0.791564\pi\)
−0.793156 + 0.609018i \(0.791564\pi\)
\(14\) −7.67656 −2.05165
\(15\) 0 0
\(16\) −4.46135 −1.11534
\(17\) −5.11092 −1.23958 −0.619790 0.784768i \(-0.712782\pi\)
−0.619790 + 0.784768i \(0.712782\pi\)
\(18\) 0 0
\(19\) 0.224637 0.0515353 0.0257676 0.999668i \(-0.491797\pi\)
0.0257676 + 0.999668i \(0.491797\pi\)
\(20\) 4.89063 1.09358
\(21\) 0 0
\(22\) 9.08366 1.93664
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 2.95554 0.591107
\(26\) −11.0521 −2.16749
\(27\) 0 0
\(28\) −6.88834 −1.30177
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 5.16107 0.926956 0.463478 0.886108i \(-0.346601\pi\)
0.463478 + 0.886108i \(0.346601\pi\)
\(32\) −7.59255 −1.34219
\(33\) 0 0
\(34\) −9.87602 −1.69372
\(35\) −11.2052 −1.89402
\(36\) 0 0
\(37\) −5.77440 −0.949305 −0.474652 0.880173i \(-0.657426\pi\)
−0.474652 + 0.880173i \(0.657426\pi\)
\(38\) 0.434074 0.0704162
\(39\) 0 0
\(40\) −1.45017 −0.229293
\(41\) 0.469446 0.0733152 0.0366576 0.999328i \(-0.488329\pi\)
0.0366576 + 0.999328i \(0.488329\pi\)
\(42\) 0 0
\(43\) 2.68640 0.409672 0.204836 0.978796i \(-0.434334\pi\)
0.204836 + 0.978796i \(0.434334\pi\)
\(44\) 8.15096 1.22880
\(45\) 0 0
\(46\) 1.93234 0.284908
\(47\) −12.2820 −1.79152 −0.895759 0.444540i \(-0.853367\pi\)
−0.895759 + 0.444540i \(0.853367\pi\)
\(48\) 0 0
\(49\) 8.78220 1.25460
\(50\) 5.71109 0.807670
\(51\) 0 0
\(52\) −9.91724 −1.37527
\(53\) 3.63780 0.499690 0.249845 0.968286i \(-0.419620\pi\)
0.249845 + 0.968286i \(0.419620\pi\)
\(54\) 0 0
\(55\) 13.2591 1.78785
\(56\) 2.04253 0.272945
\(57\) 0 0
\(58\) 1.93234 0.253728
\(59\) −8.78187 −1.14330 −0.571651 0.820497i \(-0.693697\pi\)
−0.571651 + 0.820497i \(0.693697\pi\)
\(60\) 0 0
\(61\) 4.68255 0.599539 0.299770 0.954012i \(-0.403090\pi\)
0.299770 + 0.954012i \(0.403090\pi\)
\(62\) 9.97293 1.26656
\(63\) 0 0
\(64\) −5.74865 −0.718582
\(65\) −16.1323 −2.00096
\(66\) 0 0
\(67\) −15.9642 −1.95034 −0.975170 0.221457i \(-0.928919\pi\)
−0.975170 + 0.221457i \(0.928919\pi\)
\(68\) −8.86195 −1.07467
\(69\) 0 0
\(70\) −21.6522 −2.58793
\(71\) −10.0253 −1.18979 −0.594894 0.803804i \(-0.702806\pi\)
−0.594894 + 0.803804i \(0.702806\pi\)
\(72\) 0 0
\(73\) 8.41059 0.984385 0.492193 0.870486i \(-0.336196\pi\)
0.492193 + 0.870486i \(0.336196\pi\)
\(74\) −11.1581 −1.29710
\(75\) 0 0
\(76\) 0.389504 0.0446792
\(77\) −18.6751 −2.12822
\(78\) 0 0
\(79\) −12.9991 −1.46251 −0.731254 0.682105i \(-0.761065\pi\)
−0.731254 + 0.682105i \(0.761065\pi\)
\(80\) −12.5835 −1.40688
\(81\) 0 0
\(82\) 0.907129 0.100176
\(83\) −11.6167 −1.27509 −0.637547 0.770412i \(-0.720051\pi\)
−0.637547 + 0.770412i \(0.720051\pi\)
\(84\) 0 0
\(85\) −14.4156 −1.56360
\(86\) 5.19102 0.559762
\(87\) 0 0
\(88\) −2.41693 −0.257645
\(89\) −10.7508 −1.13958 −0.569790 0.821790i \(-0.692975\pi\)
−0.569790 + 0.821790i \(0.692975\pi\)
\(90\) 0 0
\(91\) 22.7219 2.38190
\(92\) 1.73393 0.180774
\(93\) 0 0
\(94\) −23.7330 −2.44787
\(95\) 0.633601 0.0650061
\(96\) 0 0
\(97\) −5.53357 −0.561849 −0.280924 0.959730i \(-0.590641\pi\)
−0.280924 + 0.959730i \(0.590641\pi\)
\(98\) 16.9702 1.71425
\(99\) 0 0
\(100\) 5.12468 0.512468
\(101\) 0.789577 0.0785659 0.0392829 0.999228i \(-0.487493\pi\)
0.0392829 + 0.999228i \(0.487493\pi\)
\(102\) 0 0
\(103\) −1.12240 −0.110593 −0.0552967 0.998470i \(-0.517610\pi\)
−0.0552967 + 0.998470i \(0.517610\pi\)
\(104\) 2.94067 0.288356
\(105\) 0 0
\(106\) 7.02945 0.682761
\(107\) 9.39437 0.908188 0.454094 0.890954i \(-0.349963\pi\)
0.454094 + 0.890954i \(0.349963\pi\)
\(108\) 0 0
\(109\) 8.34828 0.799620 0.399810 0.916598i \(-0.369076\pi\)
0.399810 + 0.916598i \(0.369076\pi\)
\(110\) 25.6210 2.44286
\(111\) 0 0
\(112\) 17.7235 1.67472
\(113\) −0.894306 −0.0841292 −0.0420646 0.999115i \(-0.513394\pi\)
−0.0420646 + 0.999115i \(0.513394\pi\)
\(114\) 0 0
\(115\) 2.82056 0.263018
\(116\) 1.73393 0.160991
\(117\) 0 0
\(118\) −16.9695 −1.56217
\(119\) 20.3041 1.86127
\(120\) 0 0
\(121\) 11.0982 1.00893
\(122\) 9.04827 0.819192
\(123\) 0 0
\(124\) 8.94892 0.803637
\(125\) −5.76652 −0.515774
\(126\) 0 0
\(127\) −10.1089 −0.897018 −0.448509 0.893778i \(-0.648045\pi\)
−0.448509 + 0.893778i \(0.648045\pi\)
\(128\) 4.07676 0.360338
\(129\) 0 0
\(130\) −31.1730 −2.73405
\(131\) 14.7583 1.28944 0.644718 0.764420i \(-0.276975\pi\)
0.644718 + 0.764420i \(0.276975\pi\)
\(132\) 0 0
\(133\) −0.892411 −0.0773819
\(134\) −30.8483 −2.66488
\(135\) 0 0
\(136\) 2.62775 0.225328
\(137\) 9.23341 0.788864 0.394432 0.918925i \(-0.370941\pi\)
0.394432 + 0.918925i \(0.370941\pi\)
\(138\) 0 0
\(139\) 10.4024 0.882319 0.441160 0.897429i \(-0.354567\pi\)
0.441160 + 0.897429i \(0.354567\pi\)
\(140\) −19.4289 −1.64204
\(141\) 0 0
\(142\) −19.3723 −1.62569
\(143\) −26.8868 −2.24838
\(144\) 0 0
\(145\) 2.82056 0.234234
\(146\) 16.2521 1.34503
\(147\) 0 0
\(148\) −10.0124 −0.823012
\(149\) −13.6004 −1.11419 −0.557093 0.830450i \(-0.688083\pi\)
−0.557093 + 0.830450i \(0.688083\pi\)
\(150\) 0 0
\(151\) −2.89036 −0.235214 −0.117607 0.993060i \(-0.537522\pi\)
−0.117607 + 0.993060i \(0.537522\pi\)
\(152\) −0.115496 −0.00936796
\(153\) 0 0
\(154\) −36.0865 −2.90793
\(155\) 14.5571 1.16925
\(156\) 0 0
\(157\) 11.9053 0.950150 0.475075 0.879945i \(-0.342421\pi\)
0.475075 + 0.879945i \(0.342421\pi\)
\(158\) −25.1186 −1.99833
\(159\) 0 0
\(160\) −21.4152 −1.69302
\(161\) −3.97268 −0.313091
\(162\) 0 0
\(163\) 7.05697 0.552745 0.276372 0.961051i \(-0.410868\pi\)
0.276372 + 0.961051i \(0.410868\pi\)
\(164\) 0.813985 0.0635616
\(165\) 0 0
\(166\) −22.4473 −1.74225
\(167\) −12.2598 −0.948689 −0.474344 0.880339i \(-0.657315\pi\)
−0.474344 + 0.880339i \(0.657315\pi\)
\(168\) 0 0
\(169\) 19.7130 1.51639
\(170\) −27.8559 −2.13645
\(171\) 0 0
\(172\) 4.65801 0.355170
\(173\) 2.41040 0.183259 0.0916296 0.995793i \(-0.470792\pi\)
0.0916296 + 0.995793i \(0.470792\pi\)
\(174\) 0 0
\(175\) −11.7414 −0.887567
\(176\) −20.9722 −1.58084
\(177\) 0 0
\(178\) −20.7741 −1.55709
\(179\) 5.21330 0.389661 0.194830 0.980837i \(-0.437584\pi\)
0.194830 + 0.980837i \(0.437584\pi\)
\(180\) 0 0
\(181\) −15.8370 −1.17715 −0.588576 0.808442i \(-0.700311\pi\)
−0.588576 + 0.808442i \(0.700311\pi\)
\(182\) 43.9063 3.25455
\(183\) 0 0
\(184\) −0.514145 −0.0379033
\(185\) −16.2870 −1.19744
\(186\) 0 0
\(187\) −24.0258 −1.75694
\(188\) −21.2961 −1.55318
\(189\) 0 0
\(190\) 1.22433 0.0888223
\(191\) 25.5745 1.85051 0.925254 0.379349i \(-0.123852\pi\)
0.925254 + 0.379349i \(0.123852\pi\)
\(192\) 0 0
\(193\) 9.38745 0.675723 0.337862 0.941196i \(-0.390296\pi\)
0.337862 + 0.941196i \(0.390296\pi\)
\(194\) −10.6927 −0.767692
\(195\) 0 0
\(196\) 15.2277 1.08769
\(197\) −10.9347 −0.779066 −0.389533 0.921012i \(-0.627364\pi\)
−0.389533 + 0.921012i \(0.627364\pi\)
\(198\) 0 0
\(199\) 19.0802 1.35256 0.676281 0.736644i \(-0.263590\pi\)
0.676281 + 0.736644i \(0.263590\pi\)
\(200\) −1.51957 −0.107450
\(201\) 0 0
\(202\) 1.52573 0.107350
\(203\) −3.97268 −0.278828
\(204\) 0 0
\(205\) 1.32410 0.0924792
\(206\) −2.16886 −0.151111
\(207\) 0 0
\(208\) 25.5168 1.76927
\(209\) 1.05599 0.0730443
\(210\) 0 0
\(211\) −9.96719 −0.686170 −0.343085 0.939304i \(-0.611472\pi\)
−0.343085 + 0.939304i \(0.611472\pi\)
\(212\) 6.30767 0.433213
\(213\) 0 0
\(214\) 18.1531 1.24092
\(215\) 7.57713 0.516756
\(216\) 0 0
\(217\) −20.5033 −1.39185
\(218\) 16.1317 1.09258
\(219\) 0 0
\(220\) 22.9902 1.55000
\(221\) 29.2321 1.96636
\(222\) 0 0
\(223\) 12.5991 0.843695 0.421847 0.906667i \(-0.361382\pi\)
0.421847 + 0.906667i \(0.361382\pi\)
\(224\) 30.1628 2.01534
\(225\) 0 0
\(226\) −1.72810 −0.114952
\(227\) 8.62488 0.572453 0.286227 0.958162i \(-0.407599\pi\)
0.286227 + 0.958162i \(0.407599\pi\)
\(228\) 0 0
\(229\) −26.6654 −1.76210 −0.881050 0.473022i \(-0.843163\pi\)
−0.881050 + 0.473022i \(0.843163\pi\)
\(230\) 5.45026 0.359380
\(231\) 0 0
\(232\) −0.514145 −0.0337553
\(233\) 3.28507 0.215212 0.107606 0.994194i \(-0.465681\pi\)
0.107606 + 0.994194i \(0.465681\pi\)
\(234\) 0 0
\(235\) −34.6421 −2.25980
\(236\) −15.2271 −0.991200
\(237\) 0 0
\(238\) 39.2343 2.54318
\(239\) 13.3297 0.862224 0.431112 0.902298i \(-0.358121\pi\)
0.431112 + 0.902298i \(0.358121\pi\)
\(240\) 0 0
\(241\) 6.39449 0.411906 0.205953 0.978562i \(-0.433971\pi\)
0.205953 + 0.978562i \(0.433971\pi\)
\(242\) 21.4454 1.37856
\(243\) 0 0
\(244\) 8.11920 0.519778
\(245\) 24.7707 1.58254
\(246\) 0 0
\(247\) −1.28482 −0.0817510
\(248\) −2.65354 −0.168500
\(249\) 0 0
\(250\) −11.1429 −0.704737
\(251\) −15.6412 −0.987262 −0.493631 0.869671i \(-0.664331\pi\)
−0.493631 + 0.869671i \(0.664331\pi\)
\(252\) 0 0
\(253\) 4.70087 0.295541
\(254\) −19.5338 −1.22566
\(255\) 0 0
\(256\) 19.3750 1.21094
\(257\) 9.59553 0.598552 0.299276 0.954167i \(-0.403255\pi\)
0.299276 + 0.954167i \(0.403255\pi\)
\(258\) 0 0
\(259\) 22.9398 1.42541
\(260\) −27.9721 −1.73476
\(261\) 0 0
\(262\) 28.5180 1.76185
\(263\) −8.20978 −0.506237 −0.253118 0.967435i \(-0.581456\pi\)
−0.253118 + 0.967435i \(0.581456\pi\)
\(264\) 0 0
\(265\) 10.2606 0.630305
\(266\) −1.72444 −0.105732
\(267\) 0 0
\(268\) −27.6808 −1.69087
\(269\) −2.60278 −0.158694 −0.0793471 0.996847i \(-0.525284\pi\)
−0.0793471 + 0.996847i \(0.525284\pi\)
\(270\) 0 0
\(271\) 14.9550 0.908452 0.454226 0.890887i \(-0.349916\pi\)
0.454226 + 0.890887i \(0.349916\pi\)
\(272\) 22.8016 1.38255
\(273\) 0 0
\(274\) 17.8421 1.07788
\(275\) 13.8936 0.837815
\(276\) 0 0
\(277\) −18.0554 −1.08484 −0.542422 0.840106i \(-0.682493\pi\)
−0.542422 + 0.840106i \(0.682493\pi\)
\(278\) 20.1009 1.20557
\(279\) 0 0
\(280\) 5.76108 0.344291
\(281\) −6.43104 −0.383644 −0.191822 0.981430i \(-0.561440\pi\)
−0.191822 + 0.981430i \(0.561440\pi\)
\(282\) 0 0
\(283\) −6.16593 −0.366526 −0.183263 0.983064i \(-0.558666\pi\)
−0.183263 + 0.983064i \(0.558666\pi\)
\(284\) −17.3832 −1.03150
\(285\) 0 0
\(286\) −51.9543 −3.07212
\(287\) −1.86496 −0.110085
\(288\) 0 0
\(289\) 9.12150 0.536559
\(290\) 5.45026 0.320051
\(291\) 0 0
\(292\) 14.5833 0.853425
\(293\) −6.44220 −0.376357 −0.188179 0.982135i \(-0.560258\pi\)
−0.188179 + 0.982135i \(0.560258\pi\)
\(294\) 0 0
\(295\) −24.7697 −1.44215
\(296\) 2.96888 0.172562
\(297\) 0 0
\(298\) −26.2805 −1.52239
\(299\) −5.71953 −0.330769
\(300\) 0 0
\(301\) −10.6722 −0.615135
\(302\) −5.58514 −0.321389
\(303\) 0 0
\(304\) −1.00218 −0.0574792
\(305\) 13.2074 0.756253
\(306\) 0 0
\(307\) 15.0115 0.856749 0.428374 0.903601i \(-0.359086\pi\)
0.428374 + 0.903601i \(0.359086\pi\)
\(308\) −32.3812 −1.84509
\(309\) 0 0
\(310\) 28.1292 1.59763
\(311\) −22.3886 −1.26954 −0.634771 0.772700i \(-0.718906\pi\)
−0.634771 + 0.772700i \(0.718906\pi\)
\(312\) 0 0
\(313\) −13.3858 −0.756613 −0.378306 0.925680i \(-0.623493\pi\)
−0.378306 + 0.925680i \(0.623493\pi\)
\(314\) 23.0051 1.29825
\(315\) 0 0
\(316\) −22.5394 −1.26794
\(317\) 20.2458 1.13712 0.568559 0.822642i \(-0.307501\pi\)
0.568559 + 0.822642i \(0.307501\pi\)
\(318\) 0 0
\(319\) 4.70087 0.263198
\(320\) −16.2144 −0.906412
\(321\) 0 0
\(322\) −7.67656 −0.427798
\(323\) −1.14810 −0.0638821
\(324\) 0 0
\(325\) −16.9043 −0.937681
\(326\) 13.6364 0.755253
\(327\) 0 0
\(328\) −0.241364 −0.0133271
\(329\) 48.7926 2.69002
\(330\) 0 0
\(331\) 28.2462 1.55255 0.776275 0.630394i \(-0.217107\pi\)
0.776275 + 0.630394i \(0.217107\pi\)
\(332\) −20.1424 −1.10546
\(333\) 0 0
\(334\) −23.6900 −1.29626
\(335\) −45.0280 −2.46014
\(336\) 0 0
\(337\) 13.9484 0.759818 0.379909 0.925024i \(-0.375955\pi\)
0.379909 + 0.925024i \(0.375955\pi\)
\(338\) 38.0922 2.07194
\(339\) 0 0
\(340\) −24.9956 −1.35558
\(341\) 24.2615 1.31384
\(342\) 0 0
\(343\) −7.08012 −0.382291
\(344\) −1.38120 −0.0744692
\(345\) 0 0
\(346\) 4.65770 0.250400
\(347\) −13.0430 −0.700186 −0.350093 0.936715i \(-0.613850\pi\)
−0.350093 + 0.936715i \(0.613850\pi\)
\(348\) 0 0
\(349\) −25.9323 −1.38813 −0.694063 0.719914i \(-0.744181\pi\)
−0.694063 + 0.719914i \(0.744181\pi\)
\(350\) −22.6884 −1.21274
\(351\) 0 0
\(352\) −35.6916 −1.90237
\(353\) −19.7060 −1.04884 −0.524422 0.851459i \(-0.675718\pi\)
−0.524422 + 0.851459i \(0.675718\pi\)
\(354\) 0 0
\(355\) −28.2770 −1.50079
\(356\) −18.6410 −0.987973
\(357\) 0 0
\(358\) 10.0739 0.532420
\(359\) 35.4959 1.87340 0.936701 0.350129i \(-0.113862\pi\)
0.936701 + 0.350129i \(0.113862\pi\)
\(360\) 0 0
\(361\) −18.9495 −0.997344
\(362\) −30.6023 −1.60842
\(363\) 0 0
\(364\) 39.3980 2.06502
\(365\) 23.7225 1.24169
\(366\) 0 0
\(367\) −13.8149 −0.721134 −0.360567 0.932733i \(-0.617417\pi\)
−0.360567 + 0.932733i \(0.617417\pi\)
\(368\) −4.46135 −0.232564
\(369\) 0 0
\(370\) −31.4720 −1.63615
\(371\) −14.4518 −0.750301
\(372\) 0 0
\(373\) 26.9343 1.39460 0.697301 0.716778i \(-0.254384\pi\)
0.697301 + 0.716778i \(0.254384\pi\)
\(374\) −46.4259 −2.40062
\(375\) 0 0
\(376\) 6.31474 0.325658
\(377\) −5.71953 −0.294571
\(378\) 0 0
\(379\) 32.3899 1.66376 0.831880 0.554956i \(-0.187265\pi\)
0.831880 + 0.554956i \(0.187265\pi\)
\(380\) 1.09862 0.0563579
\(381\) 0 0
\(382\) 49.4186 2.52848
\(383\) 36.9727 1.88922 0.944608 0.328200i \(-0.106442\pi\)
0.944608 + 0.328200i \(0.106442\pi\)
\(384\) 0 0
\(385\) −52.6741 −2.68452
\(386\) 18.1397 0.923287
\(387\) 0 0
\(388\) −9.59479 −0.487102
\(389\) −4.21678 −0.213799 −0.106900 0.994270i \(-0.534092\pi\)
−0.106900 + 0.994270i \(0.534092\pi\)
\(390\) 0 0
\(391\) −5.11092 −0.258470
\(392\) −4.51533 −0.228058
\(393\) 0 0
\(394\) −21.1296 −1.06449
\(395\) −36.6646 −1.84480
\(396\) 0 0
\(397\) −1.67840 −0.0842364 −0.0421182 0.999113i \(-0.513411\pi\)
−0.0421182 + 0.999113i \(0.513411\pi\)
\(398\) 36.8694 1.84810
\(399\) 0 0
\(400\) −13.1857 −0.659285
\(401\) −35.0056 −1.74810 −0.874048 0.485839i \(-0.838514\pi\)
−0.874048 + 0.485839i \(0.838514\pi\)
\(402\) 0 0
\(403\) −29.5189 −1.47044
\(404\) 1.36907 0.0681137
\(405\) 0 0
\(406\) −7.67656 −0.380981
\(407\) −27.1447 −1.34551
\(408\) 0 0
\(409\) 7.76285 0.383848 0.191924 0.981410i \(-0.438527\pi\)
0.191924 + 0.981410i \(0.438527\pi\)
\(410\) 2.55861 0.126361
\(411\) 0 0
\(412\) −1.94616 −0.0958804
\(413\) 34.8876 1.71670
\(414\) 0 0
\(415\) −32.7654 −1.60839
\(416\) 43.4258 2.12913
\(417\) 0 0
\(418\) 2.04053 0.0998054
\(419\) −4.61054 −0.225240 −0.112620 0.993638i \(-0.535924\pi\)
−0.112620 + 0.993638i \(0.535924\pi\)
\(420\) 0 0
\(421\) −32.4865 −1.58329 −0.791647 0.610979i \(-0.790776\pi\)
−0.791647 + 0.610979i \(0.790776\pi\)
\(422\) −19.2600 −0.937560
\(423\) 0 0
\(424\) −1.87036 −0.0908325
\(425\) −15.1055 −0.732725
\(426\) 0 0
\(427\) −18.6023 −0.900228
\(428\) 16.2891 0.787365
\(429\) 0 0
\(430\) 14.6416 0.706079
\(431\) 0.775560 0.0373574 0.0186787 0.999826i \(-0.494054\pi\)
0.0186787 + 0.999826i \(0.494054\pi\)
\(432\) 0 0
\(433\) −6.57931 −0.316181 −0.158091 0.987425i \(-0.550534\pi\)
−0.158091 + 0.987425i \(0.550534\pi\)
\(434\) −39.6193 −1.90179
\(435\) 0 0
\(436\) 14.4753 0.693241
\(437\) 0.224637 0.0107458
\(438\) 0 0
\(439\) 35.1830 1.67919 0.839595 0.543212i \(-0.182792\pi\)
0.839595 + 0.543212i \(0.182792\pi\)
\(440\) −6.81708 −0.324992
\(441\) 0 0
\(442\) 56.4862 2.68677
\(443\) 24.4074 1.15963 0.579815 0.814748i \(-0.303125\pi\)
0.579815 + 0.814748i \(0.303125\pi\)
\(444\) 0 0
\(445\) −30.3232 −1.43746
\(446\) 24.3456 1.15280
\(447\) 0 0
\(448\) 22.8376 1.07897
\(449\) 5.62450 0.265437 0.132718 0.991154i \(-0.457629\pi\)
0.132718 + 0.991154i \(0.457629\pi\)
\(450\) 0 0
\(451\) 2.20681 0.103914
\(452\) −1.55066 −0.0729369
\(453\) 0 0
\(454\) 16.6662 0.782182
\(455\) 64.0883 3.00451
\(456\) 0 0
\(457\) 6.51862 0.304928 0.152464 0.988309i \(-0.451279\pi\)
0.152464 + 0.988309i \(0.451279\pi\)
\(458\) −51.5266 −2.40768
\(459\) 0 0
\(460\) 4.89063 0.228027
\(461\) −4.33185 −0.201754 −0.100877 0.994899i \(-0.532165\pi\)
−0.100877 + 0.994899i \(0.532165\pi\)
\(462\) 0 0
\(463\) −22.2599 −1.03451 −0.517254 0.855832i \(-0.673046\pi\)
−0.517254 + 0.855832i \(0.673046\pi\)
\(464\) −4.46135 −0.207113
\(465\) 0 0
\(466\) 6.34786 0.294059
\(467\) −4.41272 −0.204196 −0.102098 0.994774i \(-0.532556\pi\)
−0.102098 + 0.994774i \(0.532556\pi\)
\(468\) 0 0
\(469\) 63.4208 2.92850
\(470\) −66.9403 −3.08773
\(471\) 0 0
\(472\) 4.51515 0.207827
\(473\) 12.6284 0.580654
\(474\) 0 0
\(475\) 0.663923 0.0304629
\(476\) 35.2057 1.61365
\(477\) 0 0
\(478\) 25.7574 1.17812
\(479\) −9.33238 −0.426407 −0.213204 0.977008i \(-0.568390\pi\)
−0.213204 + 0.977008i \(0.568390\pi\)
\(480\) 0 0
\(481\) 33.0268 1.50589
\(482\) 12.3563 0.562815
\(483\) 0 0
\(484\) 19.2434 0.874701
\(485\) −15.6077 −0.708711
\(486\) 0 0
\(487\) 6.00747 0.272225 0.136112 0.990693i \(-0.456539\pi\)
0.136112 + 0.990693i \(0.456539\pi\)
\(488\) −2.40751 −0.108983
\(489\) 0 0
\(490\) 47.8653 2.16233
\(491\) 16.0494 0.724299 0.362149 0.932120i \(-0.382043\pi\)
0.362149 + 0.932120i \(0.382043\pi\)
\(492\) 0 0
\(493\) −5.11092 −0.230184
\(494\) −2.48270 −0.111702
\(495\) 0 0
\(496\) −23.0254 −1.03387
\(497\) 39.8275 1.78651
\(498\) 0 0
\(499\) −24.7809 −1.10935 −0.554674 0.832068i \(-0.687157\pi\)
−0.554674 + 0.832068i \(0.687157\pi\)
\(500\) −9.99872 −0.447157
\(501\) 0 0
\(502\) −30.2240 −1.34896
\(503\) −38.0583 −1.69694 −0.848469 0.529245i \(-0.822475\pi\)
−0.848469 + 0.529245i \(0.822475\pi\)
\(504\) 0 0
\(505\) 2.22705 0.0991023
\(506\) 9.08366 0.403818
\(507\) 0 0
\(508\) −17.5281 −0.777682
\(509\) −19.2146 −0.851671 −0.425836 0.904800i \(-0.640020\pi\)
−0.425836 + 0.904800i \(0.640020\pi\)
\(510\) 0 0
\(511\) −33.4126 −1.47809
\(512\) 29.2855 1.29425
\(513\) 0 0
\(514\) 18.5418 0.817843
\(515\) −3.16579 −0.139502
\(516\) 0 0
\(517\) −57.7362 −2.53924
\(518\) 44.3275 1.94764
\(519\) 0 0
\(520\) 8.29432 0.363730
\(521\) −19.4926 −0.853988 −0.426994 0.904254i \(-0.640427\pi\)
−0.426994 + 0.904254i \(0.640427\pi\)
\(522\) 0 0
\(523\) 28.4432 1.24373 0.621866 0.783124i \(-0.286375\pi\)
0.621866 + 0.783124i \(0.286375\pi\)
\(524\) 25.5898 1.11789
\(525\) 0 0
\(526\) −15.8641 −0.691706
\(527\) −26.3778 −1.14904
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 19.8270 0.861228
\(531\) 0 0
\(532\) −1.54737 −0.0670872
\(533\) −2.68501 −0.116301
\(534\) 0 0
\(535\) 26.4973 1.14558
\(536\) 8.20793 0.354528
\(537\) 0 0
\(538\) −5.02945 −0.216835
\(539\) 41.2840 1.77823
\(540\) 0 0
\(541\) −6.26466 −0.269339 −0.134669 0.990891i \(-0.542997\pi\)
−0.134669 + 0.990891i \(0.542997\pi\)
\(542\) 28.8981 1.24128
\(543\) 0 0
\(544\) 38.8049 1.66375
\(545\) 23.5468 1.00863
\(546\) 0 0
\(547\) −32.9269 −1.40785 −0.703927 0.710272i \(-0.748572\pi\)
−0.703927 + 0.710272i \(0.748572\pi\)
\(548\) 16.0101 0.683916
\(549\) 0 0
\(550\) 26.8471 1.14476
\(551\) 0.224637 0.00956986
\(552\) 0 0
\(553\) 51.6411 2.19600
\(554\) −34.8891 −1.48230
\(555\) 0 0
\(556\) 18.0370 0.764938
\(557\) 36.0931 1.52931 0.764657 0.644438i \(-0.222908\pi\)
0.764657 + 0.644438i \(0.222908\pi\)
\(558\) 0 0
\(559\) −15.3649 −0.649867
\(560\) 49.9902 2.11247
\(561\) 0 0
\(562\) −12.4269 −0.524199
\(563\) 24.8551 1.04752 0.523758 0.851867i \(-0.324529\pi\)
0.523758 + 0.851867i \(0.324529\pi\)
\(564\) 0 0
\(565\) −2.52244 −0.106120
\(566\) −11.9147 −0.500810
\(567\) 0 0
\(568\) 5.15448 0.216277
\(569\) −24.2965 −1.01856 −0.509281 0.860600i \(-0.670089\pi\)
−0.509281 + 0.860600i \(0.670089\pi\)
\(570\) 0 0
\(571\) 36.3348 1.52056 0.760282 0.649593i \(-0.225061\pi\)
0.760282 + 0.649593i \(0.225061\pi\)
\(572\) −46.6197 −1.94927
\(573\) 0 0
\(574\) −3.60373 −0.150417
\(575\) 2.95554 0.123254
\(576\) 0 0
\(577\) 6.50544 0.270825 0.135412 0.990789i \(-0.456764\pi\)
0.135412 + 0.990789i \(0.456764\pi\)
\(578\) 17.6258 0.733137
\(579\) 0 0
\(580\) 4.89063 0.203073
\(581\) 46.1493 1.91459
\(582\) 0 0
\(583\) 17.1008 0.708243
\(584\) −4.32426 −0.178939
\(585\) 0 0
\(586\) −12.4485 −0.514242
\(587\) −44.9379 −1.85479 −0.927394 0.374087i \(-0.877956\pi\)
−0.927394 + 0.374087i \(0.877956\pi\)
\(588\) 0 0
\(589\) 1.15937 0.0477709
\(590\) −47.8635 −1.97051
\(591\) 0 0
\(592\) 25.7616 1.05880
\(593\) 48.0280 1.97227 0.986136 0.165939i \(-0.0530656\pi\)
0.986136 + 0.165939i \(0.0530656\pi\)
\(594\) 0 0
\(595\) 57.2687 2.34779
\(596\) −23.5821 −0.965958
\(597\) 0 0
\(598\) −11.0521 −0.451952
\(599\) −8.51888 −0.348072 −0.174036 0.984739i \(-0.555681\pi\)
−0.174036 + 0.984739i \(0.555681\pi\)
\(600\) 0 0
\(601\) −21.6288 −0.882257 −0.441129 0.897444i \(-0.645422\pi\)
−0.441129 + 0.897444i \(0.645422\pi\)
\(602\) −20.6223 −0.840501
\(603\) 0 0
\(604\) −5.01166 −0.203922
\(605\) 31.3030 1.27265
\(606\) 0 0
\(607\) −2.96277 −0.120255 −0.0601275 0.998191i \(-0.519151\pi\)
−0.0601275 + 0.998191i \(0.519151\pi\)
\(608\) −1.70557 −0.0691699
\(609\) 0 0
\(610\) 25.5211 1.03332
\(611\) 70.2474 2.84191
\(612\) 0 0
\(613\) −33.7840 −1.36452 −0.682262 0.731108i \(-0.739004\pi\)
−0.682262 + 0.731108i \(0.739004\pi\)
\(614\) 29.0072 1.17063
\(615\) 0 0
\(616\) 9.60169 0.386863
\(617\) 16.0811 0.647400 0.323700 0.946160i \(-0.395073\pi\)
0.323700 + 0.946160i \(0.395073\pi\)
\(618\) 0 0
\(619\) 28.1296 1.13062 0.565312 0.824877i \(-0.308756\pi\)
0.565312 + 0.824877i \(0.308756\pi\)
\(620\) 25.2409 1.01370
\(621\) 0 0
\(622\) −43.2624 −1.73466
\(623\) 42.7094 1.71112
\(624\) 0 0
\(625\) −31.0425 −1.24170
\(626\) −25.8660 −1.03381
\(627\) 0 0
\(628\) 20.6430 0.823745
\(629\) 29.5125 1.17674
\(630\) 0 0
\(631\) 26.6943 1.06268 0.531341 0.847158i \(-0.321688\pi\)
0.531341 + 0.847158i \(0.321688\pi\)
\(632\) 6.68340 0.265851
\(633\) 0 0
\(634\) 39.1218 1.55372
\(635\) −28.5127 −1.13149
\(636\) 0 0
\(637\) −50.2301 −1.99019
\(638\) 9.08366 0.359626
\(639\) 0 0
\(640\) 11.4987 0.454527
\(641\) 15.2742 0.603296 0.301648 0.953419i \(-0.402463\pi\)
0.301648 + 0.953419i \(0.402463\pi\)
\(642\) 0 0
\(643\) −37.1583 −1.46538 −0.732690 0.680562i \(-0.761736\pi\)
−0.732690 + 0.680562i \(0.761736\pi\)
\(644\) −6.88834 −0.271438
\(645\) 0 0
\(646\) −2.21852 −0.0872865
\(647\) −4.05766 −0.159523 −0.0797615 0.996814i \(-0.525416\pi\)
−0.0797615 + 0.996814i \(0.525416\pi\)
\(648\) 0 0
\(649\) −41.2824 −1.62048
\(650\) −32.6648 −1.28122
\(651\) 0 0
\(652\) 12.2363 0.479209
\(653\) 39.9199 1.56219 0.781093 0.624415i \(-0.214663\pi\)
0.781093 + 0.624415i \(0.214663\pi\)
\(654\) 0 0
\(655\) 41.6265 1.62648
\(656\) −2.09437 −0.0817713
\(657\) 0 0
\(658\) 94.2837 3.67556
\(659\) 8.93986 0.348248 0.174124 0.984724i \(-0.444291\pi\)
0.174124 + 0.984724i \(0.444291\pi\)
\(660\) 0 0
\(661\) −19.2868 −0.750171 −0.375086 0.926990i \(-0.622387\pi\)
−0.375086 + 0.926990i \(0.622387\pi\)
\(662\) 54.5811 2.12136
\(663\) 0 0
\(664\) 5.97265 0.231784
\(665\) −2.51710 −0.0976088
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −21.2575 −0.822478
\(669\) 0 0
\(670\) −87.0092 −3.36146
\(671\) 22.0121 0.849766
\(672\) 0 0
\(673\) 6.74414 0.259967 0.129984 0.991516i \(-0.458507\pi\)
0.129984 + 0.991516i \(0.458507\pi\)
\(674\) 26.9530 1.03819
\(675\) 0 0
\(676\) 34.1809 1.31465
\(677\) −30.5313 −1.17341 −0.586706 0.809800i \(-0.699575\pi\)
−0.586706 + 0.809800i \(0.699575\pi\)
\(678\) 0 0
\(679\) 21.9831 0.843634
\(680\) 7.41173 0.284227
\(681\) 0 0
\(682\) 46.8815 1.79518
\(683\) −50.6678 −1.93875 −0.969376 0.245583i \(-0.921021\pi\)
−0.969376 + 0.245583i \(0.921021\pi\)
\(684\) 0 0
\(685\) 26.0434 0.995066
\(686\) −13.6812 −0.522350
\(687\) 0 0
\(688\) −11.9850 −0.456922
\(689\) −20.8065 −0.792664
\(690\) 0 0
\(691\) 5.90345 0.224578 0.112289 0.993676i \(-0.464182\pi\)
0.112289 + 0.993676i \(0.464182\pi\)
\(692\) 4.17945 0.158879
\(693\) 0 0
\(694\) −25.2035 −0.956713
\(695\) 29.3405 1.11295
\(696\) 0 0
\(697\) −2.39930 −0.0908801
\(698\) −50.1100 −1.89669
\(699\) 0 0
\(700\) −20.3587 −0.769488
\(701\) 41.5271 1.56846 0.784228 0.620473i \(-0.213059\pi\)
0.784228 + 0.620473i \(0.213059\pi\)
\(702\) 0 0
\(703\) −1.29714 −0.0489227
\(704\) −27.0237 −1.01849
\(705\) 0 0
\(706\) −38.0786 −1.43311
\(707\) −3.13674 −0.117969
\(708\) 0 0
\(709\) 35.6554 1.33907 0.669534 0.742781i \(-0.266494\pi\)
0.669534 + 0.742781i \(0.266494\pi\)
\(710\) −54.6407 −2.05063
\(711\) 0 0
\(712\) 5.52746 0.207150
\(713\) 5.16107 0.193284
\(714\) 0 0
\(715\) −75.8356 −2.83609
\(716\) 9.03948 0.337821
\(717\) 0 0
\(718\) 68.5901 2.55976
\(719\) 8.21784 0.306474 0.153237 0.988189i \(-0.451030\pi\)
0.153237 + 0.988189i \(0.451030\pi\)
\(720\) 0 0
\(721\) 4.45894 0.166060
\(722\) −36.6169 −1.36274
\(723\) 0 0
\(724\) −27.4601 −1.02055
\(725\) 2.95554 0.109766
\(726\) 0 0
\(727\) −41.0160 −1.52120 −0.760599 0.649222i \(-0.775095\pi\)
−0.760599 + 0.649222i \(0.775095\pi\)
\(728\) −11.6823 −0.432976
\(729\) 0 0
\(730\) 45.8399 1.69661
\(731\) −13.7300 −0.507821
\(732\) 0 0
\(733\) −14.0254 −0.518040 −0.259020 0.965872i \(-0.583400\pi\)
−0.259020 + 0.965872i \(0.583400\pi\)
\(734\) −26.6951 −0.985334
\(735\) 0 0
\(736\) −7.59255 −0.279865
\(737\) −75.0457 −2.76434
\(738\) 0 0
\(739\) −28.3370 −1.04239 −0.521197 0.853437i \(-0.674514\pi\)
−0.521197 + 0.853437i \(0.674514\pi\)
\(740\) −28.2405 −1.03814
\(741\) 0 0
\(742\) −27.9258 −1.02519
\(743\) 13.0956 0.480433 0.240216 0.970719i \(-0.422782\pi\)
0.240216 + 0.970719i \(0.422782\pi\)
\(744\) 0 0
\(745\) −38.3606 −1.40543
\(746\) 52.0460 1.90554
\(747\) 0 0
\(748\) −41.6589 −1.52320
\(749\) −37.3208 −1.36367
\(750\) 0 0
\(751\) −40.4975 −1.47778 −0.738888 0.673828i \(-0.764649\pi\)
−0.738888 + 0.673828i \(0.764649\pi\)
\(752\) 54.7945 1.99815
\(753\) 0 0
\(754\) −11.0521 −0.402492
\(755\) −8.15241 −0.296697
\(756\) 0 0
\(757\) −43.3831 −1.57679 −0.788394 0.615171i \(-0.789087\pi\)
−0.788394 + 0.615171i \(0.789087\pi\)
\(758\) 62.5883 2.27331
\(759\) 0 0
\(760\) −0.325763 −0.0118167
\(761\) −33.3792 −1.21000 −0.604998 0.796227i \(-0.706826\pi\)
−0.604998 + 0.796227i \(0.706826\pi\)
\(762\) 0 0
\(763\) −33.1650 −1.20066
\(764\) 44.3443 1.60432
\(765\) 0 0
\(766\) 71.4437 2.58137
\(767\) 50.2281 1.81363
\(768\) 0 0
\(769\) 15.9543 0.575327 0.287663 0.957732i \(-0.407122\pi\)
0.287663 + 0.957732i \(0.407122\pi\)
\(770\) −101.784 −3.66804
\(771\) 0 0
\(772\) 16.2771 0.585827
\(773\) 36.1871 1.30156 0.650780 0.759266i \(-0.274442\pi\)
0.650780 + 0.759266i \(0.274442\pi\)
\(774\) 0 0
\(775\) 15.2537 0.547931
\(776\) 2.84506 0.102132
\(777\) 0 0
\(778\) −8.14824 −0.292129
\(779\) 0.105455 0.00377832
\(780\) 0 0
\(781\) −47.1278 −1.68637
\(782\) −9.87602 −0.353166
\(783\) 0 0
\(784\) −39.1805 −1.39930
\(785\) 33.5797 1.19851
\(786\) 0 0
\(787\) 32.4245 1.15581 0.577905 0.816104i \(-0.303870\pi\)
0.577905 + 0.816104i \(0.303870\pi\)
\(788\) −18.9600 −0.675421
\(789\) 0 0
\(790\) −70.8483 −2.52067
\(791\) 3.55279 0.126323
\(792\) 0 0
\(793\) −26.7820 −0.951056
\(794\) −3.24323 −0.115098
\(795\) 0 0
\(796\) 33.0837 1.17262
\(797\) 43.9980 1.55849 0.779245 0.626720i \(-0.215603\pi\)
0.779245 + 0.626720i \(0.215603\pi\)
\(798\) 0 0
\(799\) 62.7724 2.22073
\(800\) −22.4401 −0.793376
\(801\) 0 0
\(802\) −67.6426 −2.38854
\(803\) 39.5371 1.39523
\(804\) 0 0
\(805\) −11.2052 −0.394930
\(806\) −57.0405 −2.00917
\(807\) 0 0
\(808\) −0.405957 −0.0142815
\(809\) 0.740559 0.0260367 0.0130183 0.999915i \(-0.495856\pi\)
0.0130183 + 0.999915i \(0.495856\pi\)
\(810\) 0 0
\(811\) −48.6291 −1.70760 −0.853800 0.520602i \(-0.825708\pi\)
−0.853800 + 0.520602i \(0.825708\pi\)
\(812\) −6.88834 −0.241733
\(813\) 0 0
\(814\) −52.4527 −1.83847
\(815\) 19.9046 0.697227
\(816\) 0 0
\(817\) 0.603464 0.0211125
\(818\) 15.0004 0.524478
\(819\) 0 0
\(820\) 2.29589 0.0801760
\(821\) −3.00633 −0.104922 −0.0524608 0.998623i \(-0.516706\pi\)
−0.0524608 + 0.998623i \(0.516706\pi\)
\(822\) 0 0
\(823\) 11.4507 0.399146 0.199573 0.979883i \(-0.436045\pi\)
0.199573 + 0.979883i \(0.436045\pi\)
\(824\) 0.577077 0.0201034
\(825\) 0 0
\(826\) 67.4145 2.34565
\(827\) 24.1302 0.839089 0.419544 0.907735i \(-0.362190\pi\)
0.419544 + 0.907735i \(0.362190\pi\)
\(828\) 0 0
\(829\) −8.02376 −0.278677 −0.139338 0.990245i \(-0.544498\pi\)
−0.139338 + 0.990245i \(0.544498\pi\)
\(830\) −63.3138 −2.19766
\(831\) 0 0
\(832\) 32.8796 1.13989
\(833\) −44.8851 −1.55518
\(834\) 0 0
\(835\) −34.5793 −1.19667
\(836\) 1.83101 0.0633267
\(837\) 0 0
\(838\) −8.90912 −0.307760
\(839\) −29.8644 −1.03103 −0.515516 0.856880i \(-0.672400\pi\)
−0.515516 + 0.856880i \(0.672400\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −62.7748 −2.16336
\(843\) 0 0
\(844\) −17.2824 −0.594884
\(845\) 55.6017 1.91276
\(846\) 0 0
\(847\) −44.0895 −1.51493
\(848\) −16.2295 −0.557323
\(849\) 0 0
\(850\) −29.1889 −1.00117
\(851\) −5.77440 −0.197944
\(852\) 0 0
\(853\) −51.1122 −1.75005 −0.875023 0.484081i \(-0.839154\pi\)
−0.875023 + 0.484081i \(0.839154\pi\)
\(854\) −35.9459 −1.23004
\(855\) 0 0
\(856\) −4.83007 −0.165088
\(857\) −13.5277 −0.462096 −0.231048 0.972942i \(-0.574215\pi\)
−0.231048 + 0.972942i \(0.574215\pi\)
\(858\) 0 0
\(859\) 42.5821 1.45288 0.726440 0.687229i \(-0.241173\pi\)
0.726440 + 0.687229i \(0.241173\pi\)
\(860\) 13.1382 0.448008
\(861\) 0 0
\(862\) 1.49864 0.0510440
\(863\) 40.9531 1.39406 0.697031 0.717041i \(-0.254504\pi\)
0.697031 + 0.717041i \(0.254504\pi\)
\(864\) 0 0
\(865\) 6.79867 0.231162
\(866\) −12.7134 −0.432020
\(867\) 0 0
\(868\) −35.5512 −1.20669
\(869\) −61.1069 −2.07291
\(870\) 0 0
\(871\) 91.3078 3.09385
\(872\) −4.29222 −0.145353
\(873\) 0 0
\(874\) 0.434074 0.0146828
\(875\) 22.9086 0.774451
\(876\) 0 0
\(877\) 24.6726 0.833136 0.416568 0.909105i \(-0.363233\pi\)
0.416568 + 0.909105i \(0.363233\pi\)
\(878\) 67.9853 2.29439
\(879\) 0 0
\(880\) −59.1534 −1.99406
\(881\) −44.4515 −1.49761 −0.748804 0.662791i \(-0.769372\pi\)
−0.748804 + 0.662791i \(0.769372\pi\)
\(882\) 0 0
\(883\) −0.759374 −0.0255550 −0.0127775 0.999918i \(-0.504067\pi\)
−0.0127775 + 0.999918i \(0.504067\pi\)
\(884\) 50.6862 1.70476
\(885\) 0 0
\(886\) 47.1633 1.58448
\(887\) 39.0346 1.31065 0.655326 0.755346i \(-0.272531\pi\)
0.655326 + 0.755346i \(0.272531\pi\)
\(888\) 0 0
\(889\) 40.1594 1.34690
\(890\) −58.5946 −1.96409
\(891\) 0 0
\(892\) 21.8458 0.731452
\(893\) −2.75900 −0.0923263
\(894\) 0 0
\(895\) 14.7044 0.491514
\(896\) −16.1957 −0.541060
\(897\) 0 0
\(898\) 10.8684 0.362684
\(899\) 5.16107 0.172131
\(900\) 0 0
\(901\) −18.5925 −0.619406
\(902\) 4.26429 0.141985
\(903\) 0 0
\(904\) 0.459803 0.0152928
\(905\) −44.6690 −1.48485
\(906\) 0 0
\(907\) 0.394908 0.0131127 0.00655636 0.999979i \(-0.497913\pi\)
0.00655636 + 0.999979i \(0.497913\pi\)
\(908\) 14.9549 0.496296
\(909\) 0 0
\(910\) 123.840 4.10526
\(911\) −24.8847 −0.824468 −0.412234 0.911078i \(-0.635251\pi\)
−0.412234 + 0.911078i \(0.635251\pi\)
\(912\) 0 0
\(913\) −54.6084 −1.80727
\(914\) 12.5962 0.416644
\(915\) 0 0
\(916\) −46.2359 −1.52768
\(917\) −58.6299 −1.93613
\(918\) 0 0
\(919\) −48.2769 −1.59251 −0.796254 0.604963i \(-0.793188\pi\)
−0.796254 + 0.604963i \(0.793188\pi\)
\(920\) −1.45017 −0.0478108
\(921\) 0 0
\(922\) −8.37060 −0.275671
\(923\) 57.3402 1.88738
\(924\) 0 0
\(925\) −17.0664 −0.561141
\(926\) −43.0137 −1.41352
\(927\) 0 0
\(928\) −7.59255 −0.249238
\(929\) −15.2969 −0.501874 −0.250937 0.968003i \(-0.580739\pi\)
−0.250937 + 0.968003i \(0.580739\pi\)
\(930\) 0 0
\(931\) 1.97281 0.0646562
\(932\) 5.69607 0.186581
\(933\) 0 0
\(934\) −8.52686 −0.279007
\(935\) −67.7660 −2.21619
\(936\) 0 0
\(937\) −39.1270 −1.27822 −0.639111 0.769114i \(-0.720698\pi\)
−0.639111 + 0.769114i \(0.720698\pi\)
\(938\) 122.550 4.00141
\(939\) 0 0
\(940\) −60.0669 −1.95917
\(941\) −0.719765 −0.0234637 −0.0117318 0.999931i \(-0.503734\pi\)
−0.0117318 + 0.999931i \(0.503734\pi\)
\(942\) 0 0
\(943\) 0.469446 0.0152873
\(944\) 39.1790 1.27517
\(945\) 0 0
\(946\) 24.4023 0.793388
\(947\) −29.9337 −0.972714 −0.486357 0.873760i \(-0.661675\pi\)
−0.486357 + 0.873760i \(0.661675\pi\)
\(948\) 0 0
\(949\) −48.1046 −1.56154
\(950\) 1.28292 0.0416235
\(951\) 0 0
\(952\) −10.4392 −0.338337
\(953\) −46.7453 −1.51423 −0.757114 0.653282i \(-0.773391\pi\)
−0.757114 + 0.653282i \(0.773391\pi\)
\(954\) 0 0
\(955\) 72.1344 2.33421
\(956\) 23.1126 0.747516
\(957\) 0 0
\(958\) −18.0333 −0.582629
\(959\) −36.6814 −1.18450
\(960\) 0 0
\(961\) −4.36332 −0.140752
\(962\) 63.8190 2.05761
\(963\) 0 0
\(964\) 11.0876 0.357107
\(965\) 26.4778 0.852351
\(966\) 0 0
\(967\) 36.9325 1.18767 0.593834 0.804587i \(-0.297613\pi\)
0.593834 + 0.804587i \(0.297613\pi\)
\(968\) −5.70607 −0.183400
\(969\) 0 0
\(970\) −30.1594 −0.968360
\(971\) −10.7651 −0.345469 −0.172735 0.984968i \(-0.555260\pi\)
−0.172735 + 0.984968i \(0.555260\pi\)
\(972\) 0 0
\(973\) −41.3254 −1.32483
\(974\) 11.6085 0.371959
\(975\) 0 0
\(976\) −20.8905 −0.668689
\(977\) 8.98778 0.287545 0.143772 0.989611i \(-0.454077\pi\)
0.143772 + 0.989611i \(0.454077\pi\)
\(978\) 0 0
\(979\) −50.5380 −1.61520
\(980\) 42.9505 1.37200
\(981\) 0 0
\(982\) 31.0128 0.989659
\(983\) 41.4053 1.32062 0.660312 0.750991i \(-0.270424\pi\)
0.660312 + 0.750991i \(0.270424\pi\)
\(984\) 0 0
\(985\) −30.8420 −0.982707
\(986\) −9.87602 −0.314516
\(987\) 0 0
\(988\) −2.22778 −0.0708751
\(989\) 2.68640 0.0854224
\(990\) 0 0
\(991\) 40.0411 1.27195 0.635974 0.771710i \(-0.280598\pi\)
0.635974 + 0.771710i \(0.280598\pi\)
\(992\) −39.1857 −1.24415
\(993\) 0 0
\(994\) 76.9601 2.44103
\(995\) 53.8169 1.70611
\(996\) 0 0
\(997\) −11.3402 −0.359149 −0.179575 0.983744i \(-0.557472\pi\)
−0.179575 + 0.983744i \(0.557472\pi\)
\(998\) −47.8851 −1.51578
\(999\) 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 \(a_p\))