Properties

Label 6003.2.a.t.1.8
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 1.8
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.24737 q^{2} -0.444068 q^{4} -1.99313 q^{5} -4.26394 q^{7} +3.04866 q^{8} +O(q^{10})\) \(q-1.24737 q^{2} -0.444068 q^{4} -1.99313 q^{5} -4.26394 q^{7} +3.04866 q^{8} +2.48617 q^{10} -2.17945 q^{11} +0.563290 q^{13} +5.31871 q^{14} -2.91467 q^{16} -2.08203 q^{17} +7.02640 q^{19} +0.885084 q^{20} +2.71858 q^{22} +1.00000 q^{23} -1.02744 q^{25} -0.702630 q^{26} +1.89348 q^{28} +1.00000 q^{29} -5.22820 q^{31} -2.46165 q^{32} +2.59706 q^{34} +8.49858 q^{35} -3.21412 q^{37} -8.76453 q^{38} -6.07636 q^{40} +4.83996 q^{41} -12.2884 q^{43} +0.967826 q^{44} -1.24737 q^{46} -6.11511 q^{47} +11.1812 q^{49} +1.28160 q^{50} -0.250139 q^{52} +8.92910 q^{53} +4.34393 q^{55} -12.9993 q^{56} -1.24737 q^{58} +6.86887 q^{59} +1.96328 q^{61} +6.52150 q^{62} +8.89992 q^{64} -1.12271 q^{65} +13.0683 q^{67} +0.924563 q^{68} -10.6009 q^{70} +9.69199 q^{71} +7.14377 q^{73} +4.00920 q^{74} -3.12020 q^{76} +9.29306 q^{77} +11.3234 q^{79} +5.80930 q^{80} -6.03722 q^{82} +6.81709 q^{83} +4.14975 q^{85} +15.3282 q^{86} -6.64441 q^{88} +5.39987 q^{89} -2.40183 q^{91} -0.444068 q^{92} +7.62781 q^{94} -14.0045 q^{95} -3.65219 q^{97} -13.9471 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24737 −0.882024 −0.441012 0.897501i \(-0.645380\pi\)
−0.441012 + 0.897501i \(0.645380\pi\)
\(3\) 0 0
\(4\) −0.444068 −0.222034
\(5\) −1.99313 −0.891354 −0.445677 0.895194i \(-0.647037\pi\)
−0.445677 + 0.895194i \(0.647037\pi\)
\(6\) 0 0
\(7\) −4.26394 −1.61162 −0.805809 0.592175i \(-0.798269\pi\)
−0.805809 + 0.592175i \(0.798269\pi\)
\(8\) 3.04866 1.07786
\(9\) 0 0
\(10\) 2.48617 0.786195
\(11\) −2.17945 −0.657130 −0.328565 0.944481i \(-0.606565\pi\)
−0.328565 + 0.944481i \(0.606565\pi\)
\(12\) 0 0
\(13\) 0.563290 0.156228 0.0781142 0.996944i \(-0.475110\pi\)
0.0781142 + 0.996944i \(0.475110\pi\)
\(14\) 5.31871 1.42149
\(15\) 0 0
\(16\) −2.91467 −0.728667
\(17\) −2.08203 −0.504966 −0.252483 0.967601i \(-0.581247\pi\)
−0.252483 + 0.967601i \(0.581247\pi\)
\(18\) 0 0
\(19\) 7.02640 1.61197 0.805984 0.591938i \(-0.201637\pi\)
0.805984 + 0.591938i \(0.201637\pi\)
\(20\) 0.885084 0.197911
\(21\) 0 0
\(22\) 2.71858 0.579604
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −1.02744 −0.205489
\(26\) −0.702630 −0.137797
\(27\) 0 0
\(28\) 1.89348 0.357834
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −5.22820 −0.939012 −0.469506 0.882929i \(-0.655568\pi\)
−0.469506 + 0.882929i \(0.655568\pi\)
\(32\) −2.46165 −0.435162
\(33\) 0 0
\(34\) 2.59706 0.445392
\(35\) 8.49858 1.43652
\(36\) 0 0
\(37\) −3.21412 −0.528398 −0.264199 0.964468i \(-0.585108\pi\)
−0.264199 + 0.964468i \(0.585108\pi\)
\(38\) −8.76453 −1.42179
\(39\) 0 0
\(40\) −6.07636 −0.960757
\(41\) 4.83996 0.755875 0.377937 0.925831i \(-0.376633\pi\)
0.377937 + 0.925831i \(0.376633\pi\)
\(42\) 0 0
\(43\) −12.2884 −1.87397 −0.936985 0.349368i \(-0.886396\pi\)
−0.936985 + 0.349368i \(0.886396\pi\)
\(44\) 0.967826 0.145905
\(45\) 0 0
\(46\) −1.24737 −0.183915
\(47\) −6.11511 −0.891981 −0.445990 0.895038i \(-0.647148\pi\)
−0.445990 + 0.895038i \(0.647148\pi\)
\(48\) 0 0
\(49\) 11.1812 1.59731
\(50\) 1.28160 0.181246
\(51\) 0 0
\(52\) −0.250139 −0.0346880
\(53\) 8.92910 1.22651 0.613253 0.789887i \(-0.289861\pi\)
0.613253 + 0.789887i \(0.289861\pi\)
\(54\) 0 0
\(55\) 4.34393 0.585735
\(56\) −12.9993 −1.73710
\(57\) 0 0
\(58\) −1.24737 −0.163788
\(59\) 6.86887 0.894251 0.447126 0.894471i \(-0.352448\pi\)
0.447126 + 0.894471i \(0.352448\pi\)
\(60\) 0 0
\(61\) 1.96328 0.251372 0.125686 0.992070i \(-0.459887\pi\)
0.125686 + 0.992070i \(0.459887\pi\)
\(62\) 6.52150 0.828231
\(63\) 0 0
\(64\) 8.89992 1.11249
\(65\) −1.12271 −0.139255
\(66\) 0 0
\(67\) 13.0683 1.59655 0.798276 0.602292i \(-0.205746\pi\)
0.798276 + 0.602292i \(0.205746\pi\)
\(68\) 0.924563 0.112120
\(69\) 0 0
\(70\) −10.6009 −1.26705
\(71\) 9.69199 1.15023 0.575114 0.818073i \(-0.304958\pi\)
0.575114 + 0.818073i \(0.304958\pi\)
\(72\) 0 0
\(73\) 7.14377 0.836115 0.418057 0.908421i \(-0.362711\pi\)
0.418057 + 0.908421i \(0.362711\pi\)
\(74\) 4.00920 0.466060
\(75\) 0 0
\(76\) −3.12020 −0.357912
\(77\) 9.29306 1.05904
\(78\) 0 0
\(79\) 11.3234 1.27399 0.636994 0.770869i \(-0.280178\pi\)
0.636994 + 0.770869i \(0.280178\pi\)
\(80\) 5.80930 0.649500
\(81\) 0 0
\(82\) −6.03722 −0.666699
\(83\) 6.81709 0.748273 0.374136 0.927374i \(-0.377939\pi\)
0.374136 + 0.927374i \(0.377939\pi\)
\(84\) 0 0
\(85\) 4.14975 0.450103
\(86\) 15.3282 1.65289
\(87\) 0 0
\(88\) −6.64441 −0.708296
\(89\) 5.39987 0.572385 0.286192 0.958172i \(-0.407610\pi\)
0.286192 + 0.958172i \(0.407610\pi\)
\(90\) 0 0
\(91\) −2.40183 −0.251781
\(92\) −0.444068 −0.0462973
\(93\) 0 0
\(94\) 7.62781 0.786748
\(95\) −14.0045 −1.43683
\(96\) 0 0
\(97\) −3.65219 −0.370824 −0.185412 0.982661i \(-0.559362\pi\)
−0.185412 + 0.982661i \(0.559362\pi\)
\(98\) −13.9471 −1.40887
\(99\) 0 0
\(100\) 0.456255 0.0456255
\(101\) 4.27417 0.425296 0.212648 0.977129i \(-0.431791\pi\)
0.212648 + 0.977129i \(0.431791\pi\)
\(102\) 0 0
\(103\) 10.4801 1.03263 0.516316 0.856398i \(-0.327303\pi\)
0.516316 + 0.856398i \(0.327303\pi\)
\(104\) 1.71728 0.168393
\(105\) 0 0
\(106\) −11.1379 −1.08181
\(107\) 5.55127 0.536661 0.268331 0.963327i \(-0.413528\pi\)
0.268331 + 0.963327i \(0.413528\pi\)
\(108\) 0 0
\(109\) −16.4184 −1.57260 −0.786298 0.617848i \(-0.788005\pi\)
−0.786298 + 0.617848i \(0.788005\pi\)
\(110\) −5.41849 −0.516632
\(111\) 0 0
\(112\) 12.4280 1.17433
\(113\) −7.72206 −0.726430 −0.363215 0.931705i \(-0.618321\pi\)
−0.363215 + 0.931705i \(0.618321\pi\)
\(114\) 0 0
\(115\) −1.99313 −0.185860
\(116\) −0.444068 −0.0412307
\(117\) 0 0
\(118\) −8.56803 −0.788751
\(119\) 8.87765 0.813813
\(120\) 0 0
\(121\) −6.24998 −0.568180
\(122\) −2.44894 −0.221717
\(123\) 0 0
\(124\) 2.32168 0.208493
\(125\) 12.0135 1.07452
\(126\) 0 0
\(127\) −13.9951 −1.24186 −0.620932 0.783864i \(-0.713246\pi\)
−0.620932 + 0.783864i \(0.713246\pi\)
\(128\) −6.17820 −0.546081
\(129\) 0 0
\(130\) 1.40043 0.122826
\(131\) 10.9144 0.953598 0.476799 0.879012i \(-0.341797\pi\)
0.476799 + 0.879012i \(0.341797\pi\)
\(132\) 0 0
\(133\) −29.9602 −2.59788
\(134\) −16.3011 −1.40820
\(135\) 0 0
\(136\) −6.34739 −0.544284
\(137\) 9.28667 0.793414 0.396707 0.917945i \(-0.370153\pi\)
0.396707 + 0.917945i \(0.370153\pi\)
\(138\) 0 0
\(139\) 17.3020 1.46754 0.733768 0.679400i \(-0.237760\pi\)
0.733768 + 0.679400i \(0.237760\pi\)
\(140\) −3.77395 −0.318957
\(141\) 0 0
\(142\) −12.0895 −1.01453
\(143\) −1.22766 −0.102662
\(144\) 0 0
\(145\) −1.99313 −0.165520
\(146\) −8.91092 −0.737473
\(147\) 0 0
\(148\) 1.42729 0.117322
\(149\) 14.1617 1.16017 0.580085 0.814556i \(-0.303019\pi\)
0.580085 + 0.814556i \(0.303019\pi\)
\(150\) 0 0
\(151\) −13.2366 −1.07718 −0.538591 0.842567i \(-0.681043\pi\)
−0.538591 + 0.842567i \(0.681043\pi\)
\(152\) 21.4211 1.73748
\(153\) 0 0
\(154\) −11.5919 −0.934101
\(155\) 10.4205 0.836992
\(156\) 0 0
\(157\) −15.3147 −1.22225 −0.611124 0.791535i \(-0.709282\pi\)
−0.611124 + 0.791535i \(0.709282\pi\)
\(158\) −14.1245 −1.12369
\(159\) 0 0
\(160\) 4.90637 0.387883
\(161\) −4.26394 −0.336046
\(162\) 0 0
\(163\) −14.1835 −1.11094 −0.555469 0.831537i \(-0.687461\pi\)
−0.555469 + 0.831537i \(0.687461\pi\)
\(164\) −2.14927 −0.167830
\(165\) 0 0
\(166\) −8.50343 −0.659994
\(167\) 4.84408 0.374846 0.187423 0.982279i \(-0.439986\pi\)
0.187423 + 0.982279i \(0.439986\pi\)
\(168\) 0 0
\(169\) −12.6827 −0.975593
\(170\) −5.17627 −0.397002
\(171\) 0 0
\(172\) 5.45691 0.416085
\(173\) 20.4992 1.55853 0.779263 0.626697i \(-0.215593\pi\)
0.779263 + 0.626697i \(0.215593\pi\)
\(174\) 0 0
\(175\) 4.38096 0.331169
\(176\) 6.35238 0.478829
\(177\) 0 0
\(178\) −6.73563 −0.504857
\(179\) 9.34936 0.698804 0.349402 0.936973i \(-0.386385\pi\)
0.349402 + 0.936973i \(0.386385\pi\)
\(180\) 0 0
\(181\) −4.92860 −0.366340 −0.183170 0.983081i \(-0.558636\pi\)
−0.183170 + 0.983081i \(0.558636\pi\)
\(182\) 2.99598 0.222076
\(183\) 0 0
\(184\) 3.04866 0.224750
\(185\) 6.40616 0.470990
\(186\) 0 0
\(187\) 4.53768 0.331828
\(188\) 2.71553 0.198050
\(189\) 0 0
\(190\) 17.4688 1.26732
\(191\) −7.11425 −0.514769 −0.257385 0.966309i \(-0.582861\pi\)
−0.257385 + 0.966309i \(0.582861\pi\)
\(192\) 0 0
\(193\) −19.6914 −1.41742 −0.708709 0.705501i \(-0.750722\pi\)
−0.708709 + 0.705501i \(0.750722\pi\)
\(194\) 4.55563 0.327075
\(195\) 0 0
\(196\) −4.96522 −0.354658
\(197\) −19.9579 −1.42194 −0.710971 0.703222i \(-0.751744\pi\)
−0.710971 + 0.703222i \(0.751744\pi\)
\(198\) 0 0
\(199\) 7.39027 0.523882 0.261941 0.965084i \(-0.415637\pi\)
0.261941 + 0.965084i \(0.415637\pi\)
\(200\) −3.13232 −0.221489
\(201\) 0 0
\(202\) −5.33147 −0.375121
\(203\) −4.26394 −0.299270
\(204\) 0 0
\(205\) −9.64665 −0.673752
\(206\) −13.0725 −0.910806
\(207\) 0 0
\(208\) −1.64180 −0.113838
\(209\) −15.3137 −1.05927
\(210\) 0 0
\(211\) −12.6942 −0.873904 −0.436952 0.899485i \(-0.643942\pi\)
−0.436952 + 0.899485i \(0.643942\pi\)
\(212\) −3.96513 −0.272326
\(213\) 0 0
\(214\) −6.92448 −0.473348
\(215\) 24.4924 1.67037
\(216\) 0 0
\(217\) 22.2927 1.51333
\(218\) 20.4798 1.38707
\(219\) 0 0
\(220\) −1.92900 −0.130053
\(221\) −1.17279 −0.0788901
\(222\) 0 0
\(223\) −10.5554 −0.706840 −0.353420 0.935465i \(-0.614981\pi\)
−0.353420 + 0.935465i \(0.614981\pi\)
\(224\) 10.4963 0.701315
\(225\) 0 0
\(226\) 9.63227 0.640729
\(227\) −8.54370 −0.567065 −0.283533 0.958963i \(-0.591506\pi\)
−0.283533 + 0.958963i \(0.591506\pi\)
\(228\) 0 0
\(229\) −0.974063 −0.0643679 −0.0321840 0.999482i \(-0.510246\pi\)
−0.0321840 + 0.999482i \(0.510246\pi\)
\(230\) 2.48617 0.163933
\(231\) 0 0
\(232\) 3.04866 0.200154
\(233\) −21.7532 −1.42510 −0.712549 0.701622i \(-0.752459\pi\)
−0.712549 + 0.701622i \(0.752459\pi\)
\(234\) 0 0
\(235\) 12.1882 0.795071
\(236\) −3.05025 −0.198554
\(237\) 0 0
\(238\) −11.0737 −0.717802
\(239\) −26.1349 −1.69053 −0.845264 0.534349i \(-0.820557\pi\)
−0.845264 + 0.534349i \(0.820557\pi\)
\(240\) 0 0
\(241\) 21.9026 1.41087 0.705436 0.708773i \(-0.250751\pi\)
0.705436 + 0.708773i \(0.250751\pi\)
\(242\) 7.79604 0.501149
\(243\) 0 0
\(244\) −0.871831 −0.0558133
\(245\) −22.2856 −1.42377
\(246\) 0 0
\(247\) 3.95790 0.251835
\(248\) −15.9390 −1.01213
\(249\) 0 0
\(250\) −14.9852 −0.947749
\(251\) −25.5717 −1.61407 −0.807036 0.590502i \(-0.798930\pi\)
−0.807036 + 0.590502i \(0.798930\pi\)
\(252\) 0 0
\(253\) −2.17945 −0.137021
\(254\) 17.4571 1.09535
\(255\) 0 0
\(256\) −10.0933 −0.630834
\(257\) −3.90624 −0.243664 −0.121832 0.992551i \(-0.538877\pi\)
−0.121832 + 0.992551i \(0.538877\pi\)
\(258\) 0 0
\(259\) 13.7048 0.851577
\(260\) 0.498559 0.0309193
\(261\) 0 0
\(262\) −13.6143 −0.841096
\(263\) −2.64870 −0.163326 −0.0816630 0.996660i \(-0.526023\pi\)
−0.0816630 + 0.996660i \(0.526023\pi\)
\(264\) 0 0
\(265\) −17.7968 −1.09325
\(266\) 37.3714 2.29139
\(267\) 0 0
\(268\) −5.80323 −0.354489
\(269\) 19.8887 1.21264 0.606319 0.795222i \(-0.292646\pi\)
0.606319 + 0.795222i \(0.292646\pi\)
\(270\) 0 0
\(271\) −9.52010 −0.578305 −0.289152 0.957283i \(-0.593373\pi\)
−0.289152 + 0.957283i \(0.593373\pi\)
\(272\) 6.06842 0.367952
\(273\) 0 0
\(274\) −11.5839 −0.699810
\(275\) 2.23926 0.135033
\(276\) 0 0
\(277\) −29.3962 −1.76625 −0.883124 0.469140i \(-0.844564\pi\)
−0.883124 + 0.469140i \(0.844564\pi\)
\(278\) −21.5820 −1.29440
\(279\) 0 0
\(280\) 25.9093 1.54837
\(281\) 27.3246 1.63005 0.815026 0.579425i \(-0.196723\pi\)
0.815026 + 0.579425i \(0.196723\pi\)
\(282\) 0 0
\(283\) 11.2542 0.668990 0.334495 0.942398i \(-0.391434\pi\)
0.334495 + 0.942398i \(0.391434\pi\)
\(284\) −4.30390 −0.255390
\(285\) 0 0
\(286\) 1.53135 0.0905506
\(287\) −20.6373 −1.21818
\(288\) 0 0
\(289\) −12.6652 −0.745009
\(290\) 2.48617 0.145993
\(291\) 0 0
\(292\) −3.17232 −0.185646
\(293\) −12.4019 −0.724526 −0.362263 0.932076i \(-0.617996\pi\)
−0.362263 + 0.932076i \(0.617996\pi\)
\(294\) 0 0
\(295\) −13.6905 −0.797094
\(296\) −9.79876 −0.569541
\(297\) 0 0
\(298\) −17.6648 −1.02330
\(299\) 0.563290 0.0325759
\(300\) 0 0
\(301\) 52.3972 3.02013
\(302\) 16.5110 0.950101
\(303\) 0 0
\(304\) −20.4796 −1.17459
\(305\) −3.91307 −0.224062
\(306\) 0 0
\(307\) 2.27939 0.130092 0.0650460 0.997882i \(-0.479281\pi\)
0.0650460 + 0.997882i \(0.479281\pi\)
\(308\) −4.12675 −0.235144
\(309\) 0 0
\(310\) −12.9982 −0.738247
\(311\) −33.4135 −1.89470 −0.947352 0.320194i \(-0.896252\pi\)
−0.947352 + 0.320194i \(0.896252\pi\)
\(312\) 0 0
\(313\) 3.95340 0.223459 0.111730 0.993739i \(-0.464361\pi\)
0.111730 + 0.993739i \(0.464361\pi\)
\(314\) 19.1031 1.07805
\(315\) 0 0
\(316\) −5.02838 −0.282869
\(317\) 33.7297 1.89445 0.947225 0.320570i \(-0.103875\pi\)
0.947225 + 0.320570i \(0.103875\pi\)
\(318\) 0 0
\(319\) −2.17945 −0.122026
\(320\) −17.7387 −0.991622
\(321\) 0 0
\(322\) 5.31871 0.296400
\(323\) −14.6292 −0.813989
\(324\) 0 0
\(325\) −0.578748 −0.0321032
\(326\) 17.6921 0.979874
\(327\) 0 0
\(328\) 14.7554 0.814729
\(329\) 26.0745 1.43753
\(330\) 0 0
\(331\) −16.8294 −0.925028 −0.462514 0.886612i \(-0.653052\pi\)
−0.462514 + 0.886612i \(0.653052\pi\)
\(332\) −3.02725 −0.166142
\(333\) 0 0
\(334\) −6.04236 −0.330623
\(335\) −26.0469 −1.42309
\(336\) 0 0
\(337\) −12.4562 −0.678532 −0.339266 0.940690i \(-0.610179\pi\)
−0.339266 + 0.940690i \(0.610179\pi\)
\(338\) 15.8200 0.860496
\(339\) 0 0
\(340\) −1.84277 −0.0999383
\(341\) 11.3946 0.617053
\(342\) 0 0
\(343\) −17.8284 −0.962644
\(344\) −37.4633 −2.01988
\(345\) 0 0
\(346\) −25.5701 −1.37466
\(347\) 23.6920 1.27185 0.635926 0.771750i \(-0.280618\pi\)
0.635926 + 0.771750i \(0.280618\pi\)
\(348\) 0 0
\(349\) −15.4566 −0.827374 −0.413687 0.910419i \(-0.635759\pi\)
−0.413687 + 0.910419i \(0.635759\pi\)
\(350\) −5.46467 −0.292099
\(351\) 0 0
\(352\) 5.36504 0.285958
\(353\) −25.4882 −1.35660 −0.678300 0.734785i \(-0.737283\pi\)
−0.678300 + 0.734785i \(0.737283\pi\)
\(354\) 0 0
\(355\) −19.3174 −1.02526
\(356\) −2.39791 −0.127089
\(357\) 0 0
\(358\) −11.6621 −0.616362
\(359\) 18.4212 0.972232 0.486116 0.873894i \(-0.338413\pi\)
0.486116 + 0.873894i \(0.338413\pi\)
\(360\) 0 0
\(361\) 30.3704 1.59844
\(362\) 6.14779 0.323121
\(363\) 0 0
\(364\) 1.06658 0.0559039
\(365\) −14.2384 −0.745274
\(366\) 0 0
\(367\) 26.3389 1.37488 0.687440 0.726241i \(-0.258734\pi\)
0.687440 + 0.726241i \(0.258734\pi\)
\(368\) −2.91467 −0.151938
\(369\) 0 0
\(370\) −7.99085 −0.415424
\(371\) −38.0732 −1.97666
\(372\) 0 0
\(373\) 37.3063 1.93165 0.965824 0.259198i \(-0.0834582\pi\)
0.965824 + 0.259198i \(0.0834582\pi\)
\(374\) −5.66017 −0.292681
\(375\) 0 0
\(376\) −18.6429 −0.961433
\(377\) 0.563290 0.0290109
\(378\) 0 0
\(379\) 11.7605 0.604099 0.302049 0.953292i \(-0.402329\pi\)
0.302049 + 0.953292i \(0.402329\pi\)
\(380\) 6.21896 0.319026
\(381\) 0 0
\(382\) 8.87411 0.454039
\(383\) −29.6295 −1.51400 −0.756998 0.653417i \(-0.773335\pi\)
−0.756998 + 0.653417i \(0.773335\pi\)
\(384\) 0 0
\(385\) −18.5223 −0.943982
\(386\) 24.5625 1.25020
\(387\) 0 0
\(388\) 1.62182 0.0823355
\(389\) −29.2796 −1.48454 −0.742268 0.670103i \(-0.766250\pi\)
−0.742268 + 0.670103i \(0.766250\pi\)
\(390\) 0 0
\(391\) −2.08203 −0.105293
\(392\) 34.0877 1.72169
\(393\) 0 0
\(394\) 24.8949 1.25419
\(395\) −22.5691 −1.13557
\(396\) 0 0
\(397\) −34.7591 −1.74451 −0.872256 0.489050i \(-0.837344\pi\)
−0.872256 + 0.489050i \(0.837344\pi\)
\(398\) −9.21840 −0.462077
\(399\) 0 0
\(400\) 2.99465 0.149733
\(401\) −16.4277 −0.820361 −0.410181 0.912004i \(-0.634534\pi\)
−0.410181 + 0.912004i \(0.634534\pi\)
\(402\) 0 0
\(403\) −2.94499 −0.146700
\(404\) −1.89802 −0.0944301
\(405\) 0 0
\(406\) 5.31871 0.263963
\(407\) 7.00503 0.347226
\(408\) 0 0
\(409\) 25.1263 1.24242 0.621208 0.783646i \(-0.286642\pi\)
0.621208 + 0.783646i \(0.286642\pi\)
\(410\) 12.0329 0.594265
\(411\) 0 0
\(412\) −4.65387 −0.229280
\(413\) −29.2885 −1.44119
\(414\) 0 0
\(415\) −13.5873 −0.666976
\(416\) −1.38662 −0.0679846
\(417\) 0 0
\(418\) 19.1019 0.934303
\(419\) 34.9848 1.70912 0.854560 0.519353i \(-0.173827\pi\)
0.854560 + 0.519353i \(0.173827\pi\)
\(420\) 0 0
\(421\) 10.9782 0.535042 0.267521 0.963552i \(-0.413795\pi\)
0.267521 + 0.963552i \(0.413795\pi\)
\(422\) 15.8344 0.770804
\(423\) 0 0
\(424\) 27.2218 1.32201
\(425\) 2.13917 0.103765
\(426\) 0 0
\(427\) −8.37132 −0.405117
\(428\) −2.46514 −0.119157
\(429\) 0 0
\(430\) −30.5511 −1.47331
\(431\) 26.9852 1.29983 0.649915 0.760007i \(-0.274805\pi\)
0.649915 + 0.760007i \(0.274805\pi\)
\(432\) 0 0
\(433\) −5.30372 −0.254881 −0.127440 0.991846i \(-0.540676\pi\)
−0.127440 + 0.991846i \(0.540676\pi\)
\(434\) −27.8073 −1.33479
\(435\) 0 0
\(436\) 7.29088 0.349170
\(437\) 7.02640 0.336118
\(438\) 0 0
\(439\) 16.0713 0.767040 0.383520 0.923533i \(-0.374712\pi\)
0.383520 + 0.923533i \(0.374712\pi\)
\(440\) 13.2431 0.631342
\(441\) 0 0
\(442\) 1.46290 0.0695829
\(443\) 28.9967 1.37767 0.688837 0.724916i \(-0.258121\pi\)
0.688837 + 0.724916i \(0.258121\pi\)
\(444\) 0 0
\(445\) −10.7626 −0.510197
\(446\) 13.1665 0.623450
\(447\) 0 0
\(448\) −37.9487 −1.79291
\(449\) −16.5954 −0.783186 −0.391593 0.920139i \(-0.628076\pi\)
−0.391593 + 0.920139i \(0.628076\pi\)
\(450\) 0 0
\(451\) −10.5485 −0.496708
\(452\) 3.42912 0.161292
\(453\) 0 0
\(454\) 10.6572 0.500165
\(455\) 4.78716 0.224426
\(456\) 0 0
\(457\) −15.1292 −0.707713 −0.353857 0.935300i \(-0.615130\pi\)
−0.353857 + 0.935300i \(0.615130\pi\)
\(458\) 1.21502 0.0567740
\(459\) 0 0
\(460\) 0.885084 0.0412673
\(461\) −34.1418 −1.59014 −0.795071 0.606516i \(-0.792567\pi\)
−0.795071 + 0.606516i \(0.792567\pi\)
\(462\) 0 0
\(463\) 0.401403 0.0186548 0.00932740 0.999956i \(-0.497031\pi\)
0.00932740 + 0.999956i \(0.497031\pi\)
\(464\) −2.91467 −0.135310
\(465\) 0 0
\(466\) 27.1343 1.25697
\(467\) 28.5366 1.32052 0.660258 0.751039i \(-0.270447\pi\)
0.660258 + 0.751039i \(0.270447\pi\)
\(468\) 0 0
\(469\) −55.7226 −2.57303
\(470\) −15.2032 −0.701271
\(471\) 0 0
\(472\) 20.9408 0.963880
\(473\) 26.7821 1.23144
\(474\) 0 0
\(475\) −7.21923 −0.331241
\(476\) −3.94228 −0.180694
\(477\) 0 0
\(478\) 32.5999 1.49109
\(479\) −4.20402 −0.192087 −0.0960434 0.995377i \(-0.530619\pi\)
−0.0960434 + 0.995377i \(0.530619\pi\)
\(480\) 0 0
\(481\) −1.81048 −0.0825509
\(482\) −27.3207 −1.24442
\(483\) 0 0
\(484\) 2.77542 0.126155
\(485\) 7.27928 0.330535
\(486\) 0 0
\(487\) 11.7731 0.533492 0.266746 0.963767i \(-0.414051\pi\)
0.266746 + 0.963767i \(0.414051\pi\)
\(488\) 5.98537 0.270945
\(489\) 0 0
\(490\) 27.7983 1.25580
\(491\) −23.4405 −1.05785 −0.528927 0.848667i \(-0.677405\pi\)
−0.528927 + 0.848667i \(0.677405\pi\)
\(492\) 0 0
\(493\) −2.08203 −0.0937699
\(494\) −4.93697 −0.222125
\(495\) 0 0
\(496\) 15.2385 0.684227
\(497\) −41.3261 −1.85373
\(498\) 0 0
\(499\) 9.65443 0.432192 0.216096 0.976372i \(-0.430668\pi\)
0.216096 + 0.976372i \(0.430668\pi\)
\(500\) −5.33480 −0.238579
\(501\) 0 0
\(502\) 31.8974 1.42365
\(503\) −11.2210 −0.500320 −0.250160 0.968204i \(-0.580483\pi\)
−0.250160 + 0.968204i \(0.580483\pi\)
\(504\) 0 0
\(505\) −8.51896 −0.379089
\(506\) 2.71858 0.120856
\(507\) 0 0
\(508\) 6.21478 0.275736
\(509\) −9.20808 −0.408141 −0.204070 0.978956i \(-0.565417\pi\)
−0.204070 + 0.978956i \(0.565417\pi\)
\(510\) 0 0
\(511\) −30.4606 −1.34750
\(512\) 24.9465 1.10249
\(513\) 0 0
\(514\) 4.87252 0.214918
\(515\) −20.8881 −0.920441
\(516\) 0 0
\(517\) 13.3276 0.586147
\(518\) −17.0950 −0.751111
\(519\) 0 0
\(520\) −3.42275 −0.150098
\(521\) −20.6804 −0.906023 −0.453011 0.891505i \(-0.649650\pi\)
−0.453011 + 0.891505i \(0.649650\pi\)
\(522\) 0 0
\(523\) 7.40668 0.323872 0.161936 0.986801i \(-0.448226\pi\)
0.161936 + 0.986801i \(0.448226\pi\)
\(524\) −4.84675 −0.211731
\(525\) 0 0
\(526\) 3.30391 0.144057
\(527\) 10.8853 0.474170
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 22.1992 0.964273
\(531\) 0 0
\(532\) 13.3044 0.576817
\(533\) 2.72630 0.118089
\(534\) 0 0
\(535\) −11.0644 −0.478355
\(536\) 39.8409 1.72086
\(537\) 0 0
\(538\) −24.8086 −1.06957
\(539\) −24.3689 −1.04964
\(540\) 0 0
\(541\) 17.4208 0.748979 0.374490 0.927231i \(-0.377818\pi\)
0.374490 + 0.927231i \(0.377818\pi\)
\(542\) 11.8751 0.510079
\(543\) 0 0
\(544\) 5.12522 0.219742
\(545\) 32.7239 1.40174
\(546\) 0 0
\(547\) 12.2981 0.525828 0.262914 0.964819i \(-0.415316\pi\)
0.262914 + 0.964819i \(0.415316\pi\)
\(548\) −4.12391 −0.176165
\(549\) 0 0
\(550\) −2.79319 −0.119102
\(551\) 7.02640 0.299335
\(552\) 0 0
\(553\) −48.2825 −2.05318
\(554\) 36.6680 1.55787
\(555\) 0 0
\(556\) −7.68326 −0.325843
\(557\) −27.2236 −1.15350 −0.576751 0.816920i \(-0.695680\pi\)
−0.576751 + 0.816920i \(0.695680\pi\)
\(558\) 0 0
\(559\) −6.92195 −0.292767
\(560\) −24.7705 −1.04675
\(561\) 0 0
\(562\) −34.0839 −1.43774
\(563\) −19.9191 −0.839491 −0.419745 0.907642i \(-0.637881\pi\)
−0.419745 + 0.907642i \(0.637881\pi\)
\(564\) 0 0
\(565\) 15.3911 0.647506
\(566\) −14.0381 −0.590065
\(567\) 0 0
\(568\) 29.5476 1.23979
\(569\) −0.396105 −0.0166056 −0.00830280 0.999966i \(-0.502643\pi\)
−0.00830280 + 0.999966i \(0.502643\pi\)
\(570\) 0 0
\(571\) −13.3273 −0.557729 −0.278864 0.960331i \(-0.589958\pi\)
−0.278864 + 0.960331i \(0.589958\pi\)
\(572\) 0.545166 0.0227945
\(573\) 0 0
\(574\) 25.7424 1.07447
\(575\) −1.02744 −0.0428473
\(576\) 0 0
\(577\) 42.4841 1.76864 0.884319 0.466884i \(-0.154623\pi\)
0.884319 + 0.466884i \(0.154623\pi\)
\(578\) 15.7981 0.657116
\(579\) 0 0
\(580\) 0.885084 0.0367511
\(581\) −29.0677 −1.20593
\(582\) 0 0
\(583\) −19.4605 −0.805974
\(584\) 21.7789 0.901217
\(585\) 0 0
\(586\) 15.4697 0.639049
\(587\) −39.3902 −1.62581 −0.812904 0.582397i \(-0.802115\pi\)
−0.812904 + 0.582397i \(0.802115\pi\)
\(588\) 0 0
\(589\) −36.7354 −1.51366
\(590\) 17.0772 0.703056
\(591\) 0 0
\(592\) 9.36810 0.385026
\(593\) 36.5618 1.50141 0.750707 0.660635i \(-0.229713\pi\)
0.750707 + 0.660635i \(0.229713\pi\)
\(594\) 0 0
\(595\) −17.6943 −0.725395
\(596\) −6.28875 −0.257597
\(597\) 0 0
\(598\) −0.702630 −0.0287327
\(599\) −8.57473 −0.350354 −0.175177 0.984537i \(-0.556050\pi\)
−0.175177 + 0.984537i \(0.556050\pi\)
\(600\) 0 0
\(601\) −6.97815 −0.284645 −0.142322 0.989820i \(-0.545457\pi\)
−0.142322 + 0.989820i \(0.545457\pi\)
\(602\) −65.3587 −2.66382
\(603\) 0 0
\(604\) 5.87797 0.239171
\(605\) 12.4570 0.506450
\(606\) 0 0
\(607\) 6.33213 0.257013 0.128507 0.991709i \(-0.458982\pi\)
0.128507 + 0.991709i \(0.458982\pi\)
\(608\) −17.2965 −0.701466
\(609\) 0 0
\(610\) 4.88105 0.197628
\(611\) −3.44458 −0.139353
\(612\) 0 0
\(613\) −26.5212 −1.07118 −0.535590 0.844478i \(-0.679911\pi\)
−0.535590 + 0.844478i \(0.679911\pi\)
\(614\) −2.84325 −0.114744
\(615\) 0 0
\(616\) 28.3314 1.14150
\(617\) 15.4097 0.620373 0.310186 0.950676i \(-0.399609\pi\)
0.310186 + 0.950676i \(0.399609\pi\)
\(618\) 0 0
\(619\) 15.1345 0.608306 0.304153 0.952623i \(-0.401627\pi\)
0.304153 + 0.952623i \(0.401627\pi\)
\(620\) −4.62740 −0.185841
\(621\) 0 0
\(622\) 41.6790 1.67117
\(623\) −23.0247 −0.922466
\(624\) 0 0
\(625\) −18.8071 −0.752286
\(626\) −4.93135 −0.197096
\(627\) 0 0
\(628\) 6.80078 0.271380
\(629\) 6.69190 0.266823
\(630\) 0 0
\(631\) 12.6845 0.504961 0.252480 0.967602i \(-0.418754\pi\)
0.252480 + 0.967602i \(0.418754\pi\)
\(632\) 34.5213 1.37318
\(633\) 0 0
\(634\) −42.0734 −1.67095
\(635\) 27.8940 1.10694
\(636\) 0 0
\(637\) 6.29826 0.249546
\(638\) 2.71858 0.107630
\(639\) 0 0
\(640\) 12.3139 0.486751
\(641\) −23.3330 −0.921597 −0.460799 0.887505i \(-0.652437\pi\)
−0.460799 + 0.887505i \(0.652437\pi\)
\(642\) 0 0
\(643\) −2.79864 −0.110368 −0.0551838 0.998476i \(-0.517574\pi\)
−0.0551838 + 0.998476i \(0.517574\pi\)
\(644\) 1.89348 0.0746136
\(645\) 0 0
\(646\) 18.2480 0.717958
\(647\) 5.87120 0.230821 0.115410 0.993318i \(-0.463182\pi\)
0.115410 + 0.993318i \(0.463182\pi\)
\(648\) 0 0
\(649\) −14.9704 −0.587639
\(650\) 0.721913 0.0283157
\(651\) 0 0
\(652\) 6.29844 0.246666
\(653\) 39.3801 1.54106 0.770532 0.637402i \(-0.219991\pi\)
0.770532 + 0.637402i \(0.219991\pi\)
\(654\) 0 0
\(655\) −21.7538 −0.849993
\(656\) −14.1069 −0.550781
\(657\) 0 0
\(658\) −32.5245 −1.26794
\(659\) 12.6740 0.493707 0.246854 0.969053i \(-0.420603\pi\)
0.246854 + 0.969053i \(0.420603\pi\)
\(660\) 0 0
\(661\) 42.7161 1.66146 0.830731 0.556674i \(-0.187923\pi\)
0.830731 + 0.556674i \(0.187923\pi\)
\(662\) 20.9925 0.815896
\(663\) 0 0
\(664\) 20.7830 0.806536
\(665\) 59.7145 2.31563
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −2.15110 −0.0832287
\(669\) 0 0
\(670\) 32.4901 1.25520
\(671\) −4.27888 −0.165184
\(672\) 0 0
\(673\) 18.6162 0.717602 0.358801 0.933414i \(-0.383186\pi\)
0.358801 + 0.933414i \(0.383186\pi\)
\(674\) 15.5375 0.598482
\(675\) 0 0
\(676\) 5.63198 0.216615
\(677\) −14.3352 −0.550948 −0.275474 0.961309i \(-0.588835\pi\)
−0.275474 + 0.961309i \(0.588835\pi\)
\(678\) 0 0
\(679\) 15.5727 0.597626
\(680\) 12.6512 0.485150
\(681\) 0 0
\(682\) −14.2133 −0.544255
\(683\) −28.8242 −1.10293 −0.551464 0.834199i \(-0.685930\pi\)
−0.551464 + 0.834199i \(0.685930\pi\)
\(684\) 0 0
\(685\) −18.5095 −0.707212
\(686\) 22.2386 0.849075
\(687\) 0 0
\(688\) 35.8167 1.36550
\(689\) 5.02967 0.191615
\(690\) 0 0
\(691\) 39.8007 1.51409 0.757045 0.653362i \(-0.226642\pi\)
0.757045 + 0.653362i \(0.226642\pi\)
\(692\) −9.10305 −0.346046
\(693\) 0 0
\(694\) −29.5527 −1.12180
\(695\) −34.4851 −1.30809
\(696\) 0 0
\(697\) −10.0769 −0.381691
\(698\) 19.2801 0.729763
\(699\) 0 0
\(700\) −1.94544 −0.0735309
\(701\) 46.5650 1.75874 0.879368 0.476144i \(-0.157966\pi\)
0.879368 + 0.476144i \(0.157966\pi\)
\(702\) 0 0
\(703\) −22.5837 −0.851761
\(704\) −19.3970 −0.731050
\(705\) 0 0
\(706\) 31.7932 1.19655
\(707\) −18.2248 −0.685415
\(708\) 0 0
\(709\) −11.8273 −0.444183 −0.222092 0.975026i \(-0.571288\pi\)
−0.222092 + 0.975026i \(0.571288\pi\)
\(710\) 24.0959 0.904303
\(711\) 0 0
\(712\) 16.4623 0.616952
\(713\) −5.22820 −0.195798
\(714\) 0 0
\(715\) 2.44689 0.0915085
\(716\) −4.15175 −0.155158
\(717\) 0 0
\(718\) −22.9780 −0.857532
\(719\) −43.6512 −1.62792 −0.813958 0.580923i \(-0.802692\pi\)
−0.813958 + 0.580923i \(0.802692\pi\)
\(720\) 0 0
\(721\) −44.6864 −1.66421
\(722\) −37.8831 −1.40986
\(723\) 0 0
\(724\) 2.18864 0.0813400
\(725\) −1.02744 −0.0381583
\(726\) 0 0
\(727\) −26.7061 −0.990473 −0.495236 0.868758i \(-0.664919\pi\)
−0.495236 + 0.868758i \(0.664919\pi\)
\(728\) −7.32237 −0.271385
\(729\) 0 0
\(730\) 17.7606 0.657350
\(731\) 25.5849 0.946292
\(732\) 0 0
\(733\) −1.08710 −0.0401531 −0.0200765 0.999798i \(-0.506391\pi\)
−0.0200765 + 0.999798i \(0.506391\pi\)
\(734\) −32.8544 −1.21268
\(735\) 0 0
\(736\) −2.46165 −0.0907375
\(737\) −28.4818 −1.04914
\(738\) 0 0
\(739\) 6.75646 0.248540 0.124270 0.992248i \(-0.460341\pi\)
0.124270 + 0.992248i \(0.460341\pi\)
\(740\) −2.84477 −0.104576
\(741\) 0 0
\(742\) 47.4913 1.74346
\(743\) 5.56646 0.204214 0.102107 0.994773i \(-0.467442\pi\)
0.102107 + 0.994773i \(0.467442\pi\)
\(744\) 0 0
\(745\) −28.2260 −1.03412
\(746\) −46.5348 −1.70376
\(747\) 0 0
\(748\) −2.01504 −0.0736772
\(749\) −23.6703 −0.864893
\(750\) 0 0
\(751\) −33.9034 −1.23715 −0.618577 0.785724i \(-0.712291\pi\)
−0.618577 + 0.785724i \(0.712291\pi\)
\(752\) 17.8235 0.649957
\(753\) 0 0
\(754\) −0.702630 −0.0255883
\(755\) 26.3823 0.960151
\(756\) 0 0
\(757\) −33.6145 −1.22174 −0.610869 0.791732i \(-0.709180\pi\)
−0.610869 + 0.791732i \(0.709180\pi\)
\(758\) −14.6697 −0.532829
\(759\) 0 0
\(760\) −42.6950 −1.54871
\(761\) −46.1969 −1.67464 −0.837319 0.546715i \(-0.815878\pi\)
−0.837319 + 0.546715i \(0.815878\pi\)
\(762\) 0 0
\(763\) 70.0070 2.53442
\(764\) 3.15921 0.114296
\(765\) 0 0
\(766\) 36.9589 1.33538
\(767\) 3.86916 0.139707
\(768\) 0 0
\(769\) −39.8972 −1.43873 −0.719364 0.694633i \(-0.755567\pi\)
−0.719364 + 0.694633i \(0.755567\pi\)
\(770\) 23.1041 0.832614
\(771\) 0 0
\(772\) 8.74432 0.314715
\(773\) −31.5932 −1.13633 −0.568164 0.822916i \(-0.692346\pi\)
−0.568164 + 0.822916i \(0.692346\pi\)
\(774\) 0 0
\(775\) 5.37168 0.192956
\(776\) −11.1343 −0.399697
\(777\) 0 0
\(778\) 36.5225 1.30940
\(779\) 34.0075 1.21845
\(780\) 0 0
\(781\) −21.1232 −0.755849
\(782\) 2.59706 0.0928707
\(783\) 0 0
\(784\) −32.5895 −1.16391
\(785\) 30.5242 1.08945
\(786\) 0 0
\(787\) 11.2307 0.400333 0.200166 0.979762i \(-0.435852\pi\)
0.200166 + 0.979762i \(0.435852\pi\)
\(788\) 8.86267 0.315719
\(789\) 0 0
\(790\) 28.1520 1.00160
\(791\) 32.9264 1.17073
\(792\) 0 0
\(793\) 1.10590 0.0392715
\(794\) 43.3575 1.53870
\(795\) 0 0
\(796\) −3.28178 −0.116320
\(797\) 39.7919 1.40950 0.704750 0.709456i \(-0.251059\pi\)
0.704750 + 0.709456i \(0.251059\pi\)
\(798\) 0 0
\(799\) 12.7318 0.450420
\(800\) 2.52920 0.0894207
\(801\) 0 0
\(802\) 20.4914 0.723578
\(803\) −15.5695 −0.549436
\(804\) 0 0
\(805\) 8.49858 0.299536
\(806\) 3.67349 0.129393
\(807\) 0 0
\(808\) 13.0305 0.458411
\(809\) −18.6090 −0.654259 −0.327129 0.944980i \(-0.606081\pi\)
−0.327129 + 0.944980i \(0.606081\pi\)
\(810\) 0 0
\(811\) 7.44117 0.261295 0.130647 0.991429i \(-0.458294\pi\)
0.130647 + 0.991429i \(0.458294\pi\)
\(812\) 1.89348 0.0664482
\(813\) 0 0
\(814\) −8.73786 −0.306262
\(815\) 28.2695 0.990239
\(816\) 0 0
\(817\) −86.3436 −3.02078
\(818\) −31.3418 −1.09584
\(819\) 0 0
\(820\) 4.28377 0.149596
\(821\) 19.1494 0.668318 0.334159 0.942517i \(-0.391548\pi\)
0.334159 + 0.942517i \(0.391548\pi\)
\(822\) 0 0
\(823\) −52.7502 −1.83876 −0.919379 0.393373i \(-0.871308\pi\)
−0.919379 + 0.393373i \(0.871308\pi\)
\(824\) 31.9502 1.11304
\(825\) 0 0
\(826\) 36.5336 1.27117
\(827\) 3.02517 0.105195 0.0525977 0.998616i \(-0.483250\pi\)
0.0525977 + 0.998616i \(0.483250\pi\)
\(828\) 0 0
\(829\) −28.9116 −1.00414 −0.502070 0.864827i \(-0.667428\pi\)
−0.502070 + 0.864827i \(0.667428\pi\)
\(830\) 16.9484 0.588288
\(831\) 0 0
\(832\) 5.01323 0.173802
\(833\) −23.2796 −0.806590
\(834\) 0 0
\(835\) −9.65488 −0.334121
\(836\) 6.80033 0.235194
\(837\) 0 0
\(838\) −43.6390 −1.50748
\(839\) 15.5459 0.536702 0.268351 0.963321i \(-0.413521\pi\)
0.268351 + 0.963321i \(0.413521\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −13.6938 −0.471920
\(843\) 0 0
\(844\) 5.63709 0.194036
\(845\) 25.2782 0.869598
\(846\) 0 0
\(847\) 26.6496 0.915690
\(848\) −26.0253 −0.893714
\(849\) 0 0
\(850\) −2.66833 −0.0915230
\(851\) −3.21412 −0.110179
\(852\) 0 0
\(853\) −25.6274 −0.877466 −0.438733 0.898617i \(-0.644573\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(854\) 10.4421 0.357322
\(855\) 0 0
\(856\) 16.9239 0.578447
\(857\) 30.2135 1.03207 0.516037 0.856566i \(-0.327407\pi\)
0.516037 + 0.856566i \(0.327407\pi\)
\(858\) 0 0
\(859\) −13.0782 −0.446221 −0.223111 0.974793i \(-0.571621\pi\)
−0.223111 + 0.974793i \(0.571621\pi\)
\(860\) −10.8763 −0.370879
\(861\) 0 0
\(862\) −33.6605 −1.14648
\(863\) −5.97393 −0.203355 −0.101678 0.994817i \(-0.532421\pi\)
−0.101678 + 0.994817i \(0.532421\pi\)
\(864\) 0 0
\(865\) −40.8576 −1.38920
\(866\) 6.61570 0.224811
\(867\) 0 0
\(868\) −9.89950 −0.336011
\(869\) −24.6789 −0.837175
\(870\) 0 0
\(871\) 7.36126 0.249427
\(872\) −50.0540 −1.69504
\(873\) 0 0
\(874\) −8.76453 −0.296465
\(875\) −51.2247 −1.73171
\(876\) 0 0
\(877\) 12.7561 0.430743 0.215372 0.976532i \(-0.430904\pi\)
0.215372 + 0.976532i \(0.430904\pi\)
\(878\) −20.0468 −0.676547
\(879\) 0 0
\(880\) −12.6611 −0.426806
\(881\) 17.1776 0.578728 0.289364 0.957219i \(-0.406556\pi\)
0.289364 + 0.957219i \(0.406556\pi\)
\(882\) 0 0
\(883\) 8.39238 0.282426 0.141213 0.989979i \(-0.454900\pi\)
0.141213 + 0.989979i \(0.454900\pi\)
\(884\) 0.520796 0.0175163
\(885\) 0 0
\(886\) −36.1696 −1.21514
\(887\) −13.0653 −0.438691 −0.219346 0.975647i \(-0.570392\pi\)
−0.219346 + 0.975647i \(0.570392\pi\)
\(888\) 0 0
\(889\) 59.6743 2.00141
\(890\) 13.4250 0.450006
\(891\) 0 0
\(892\) 4.68731 0.156943
\(893\) −42.9673 −1.43784
\(894\) 0 0
\(895\) −18.6345 −0.622882
\(896\) 26.3435 0.880074
\(897\) 0 0
\(898\) 20.7006 0.690789
\(899\) −5.22820 −0.174370
\(900\) 0 0
\(901\) −18.5906 −0.619344
\(902\) 13.1578 0.438108
\(903\) 0 0
\(904\) −23.5419 −0.782992
\(905\) 9.82334 0.326539
\(906\) 0 0
\(907\) −12.1824 −0.404510 −0.202255 0.979333i \(-0.564827\pi\)
−0.202255 + 0.979333i \(0.564827\pi\)
\(908\) 3.79399 0.125908
\(909\) 0 0
\(910\) −5.97136 −0.197949
\(911\) 48.5411 1.60824 0.804119 0.594468i \(-0.202637\pi\)
0.804119 + 0.594468i \(0.202637\pi\)
\(912\) 0 0
\(913\) −14.8575 −0.491712
\(914\) 18.8717 0.624220
\(915\) 0 0
\(916\) 0.432550 0.0142919
\(917\) −46.5385 −1.53684
\(918\) 0 0
\(919\) −47.2023 −1.55706 −0.778531 0.627606i \(-0.784035\pi\)
−0.778531 + 0.627606i \(0.784035\pi\)
\(920\) −6.07636 −0.200332
\(921\) 0 0
\(922\) 42.5875 1.40254
\(923\) 5.45940 0.179698
\(924\) 0 0
\(925\) 3.30233 0.108580
\(926\) −0.500699 −0.0164540
\(927\) 0 0
\(928\) −2.46165 −0.0808075
\(929\) −12.1402 −0.398306 −0.199153 0.979968i \(-0.563819\pi\)
−0.199153 + 0.979968i \(0.563819\pi\)
\(930\) 0 0
\(931\) 78.5637 2.57482
\(932\) 9.65989 0.316420
\(933\) 0 0
\(934\) −35.5957 −1.16473
\(935\) −9.04418 −0.295776
\(936\) 0 0
\(937\) −40.3140 −1.31700 −0.658501 0.752580i \(-0.728809\pi\)
−0.658501 + 0.752580i \(0.728809\pi\)
\(938\) 69.5068 2.26948
\(939\) 0 0
\(940\) −5.41239 −0.176533
\(941\) −57.8357 −1.88539 −0.942695 0.333654i \(-0.891718\pi\)
−0.942695 + 0.333654i \(0.891718\pi\)
\(942\) 0 0
\(943\) 4.83996 0.157611
\(944\) −20.0205 −0.651611
\(945\) 0 0
\(946\) −33.4072 −1.08616
\(947\) 44.4178 1.44338 0.721692 0.692214i \(-0.243365\pi\)
0.721692 + 0.692214i \(0.243365\pi\)
\(948\) 0 0
\(949\) 4.02401 0.130625
\(950\) 9.00505 0.292162
\(951\) 0 0
\(952\) 27.0649 0.877179
\(953\) −15.0278 −0.486798 −0.243399 0.969926i \(-0.578263\pi\)
−0.243399 + 0.969926i \(0.578263\pi\)
\(954\) 0 0
\(955\) 14.1796 0.458842
\(956\) 11.6057 0.375355
\(957\) 0 0
\(958\) 5.24397 0.169425
\(959\) −39.5978 −1.27868
\(960\) 0 0
\(961\) −3.66593 −0.118256
\(962\) 2.25834 0.0728118
\(963\) 0 0
\(964\) −9.72626 −0.313262
\(965\) 39.2475 1.26342
\(966\) 0 0
\(967\) −39.8659 −1.28200 −0.641001 0.767540i \(-0.721481\pi\)
−0.641001 + 0.767540i \(0.721481\pi\)
\(968\) −19.0541 −0.612421
\(969\) 0 0
\(970\) −9.07995 −0.291540
\(971\) 11.9856 0.384635 0.192318 0.981333i \(-0.438400\pi\)
0.192318 + 0.981333i \(0.438400\pi\)
\(972\) 0 0
\(973\) −73.7747 −2.36511
\(974\) −14.6855 −0.470553
\(975\) 0 0
\(976\) −5.72231 −0.183167
\(977\) −18.9625 −0.606664 −0.303332 0.952885i \(-0.598099\pi\)
−0.303332 + 0.952885i \(0.598099\pi\)
\(978\) 0 0
\(979\) −11.7688 −0.376131
\(980\) 9.89631 0.316126
\(981\) 0 0
\(982\) 29.2389 0.933052
\(983\) 34.5151 1.10086 0.550431 0.834881i \(-0.314464\pi\)
0.550431 + 0.834881i \(0.314464\pi\)
\(984\) 0 0
\(985\) 39.7786 1.26745
\(986\) 2.59706 0.0827073
\(987\) 0 0
\(988\) −1.75758 −0.0559160
\(989\) −12.2884 −0.390750
\(990\) 0 0
\(991\) 55.9207 1.77638 0.888191 0.459475i \(-0.151963\pi\)
0.888191 + 0.459475i \(0.151963\pi\)
\(992\) 12.8700 0.408622
\(993\) 0 0
\(994\) 51.5489 1.63503
\(995\) −14.7297 −0.466964
\(996\) 0 0
\(997\) 32.5201 1.02992 0.514961 0.857214i \(-0.327806\pi\)
0.514961 + 0.857214i \(0.327806\pi\)
\(998\) −12.0427 −0.381203
\(999\) 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 \(a_p\))