Properties

Label 8041.2.a.a.1.1
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -2.00000 q^{3} +2.00000 q^{4} +2.00000 q^{5} +4.00000 q^{6} +3.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -2.00000 q^{3} +2.00000 q^{4} +2.00000 q^{5} +4.00000 q^{6} +3.00000 q^{7} +1.00000 q^{9} -4.00000 q^{10} +1.00000 q^{11} -4.00000 q^{12} -2.00000 q^{13} -6.00000 q^{14} -4.00000 q^{15} -4.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} -8.00000 q^{19} +4.00000 q^{20} -6.00000 q^{21} -2.00000 q^{22} -4.00000 q^{23} -1.00000 q^{25} +4.00000 q^{26} +4.00000 q^{27} +6.00000 q^{28} -3.00000 q^{29} +8.00000 q^{30} +8.00000 q^{31} +8.00000 q^{32} -2.00000 q^{33} -2.00000 q^{34} +6.00000 q^{35} +2.00000 q^{36} +6.00000 q^{37} +16.0000 q^{38} +4.00000 q^{39} +11.0000 q^{41} +12.0000 q^{42} -1.00000 q^{43} +2.00000 q^{44} +2.00000 q^{45} +8.00000 q^{46} -5.00000 q^{47} +8.00000 q^{48} +2.00000 q^{49} +2.00000 q^{50} -2.00000 q^{51} -4.00000 q^{52} +1.00000 q^{53} -8.00000 q^{54} +2.00000 q^{55} +16.0000 q^{57} +6.00000 q^{58} -3.00000 q^{59} -8.00000 q^{60} +2.00000 q^{61} -16.0000 q^{62} +3.00000 q^{63} -8.00000 q^{64} -4.00000 q^{65} +4.00000 q^{66} -9.00000 q^{67} +2.00000 q^{68} +8.00000 q^{69} -12.0000 q^{70} +2.00000 q^{71} -7.00000 q^{73} -12.0000 q^{74} +2.00000 q^{75} -16.0000 q^{76} +3.00000 q^{77} -8.00000 q^{78} +4.00000 q^{79} -8.00000 q^{80} -11.0000 q^{81} -22.0000 q^{82} -12.0000 q^{84} +2.00000 q^{85} +2.00000 q^{86} +6.00000 q^{87} +11.0000 q^{89} -4.00000 q^{90} -6.00000 q^{91} -8.00000 q^{92} -16.0000 q^{93} +10.0000 q^{94} -16.0000 q^{95} -16.0000 q^{96} -8.00000 q^{97} -4.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 2.00000 1.00000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 4.00000 1.63299
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) −4.00000 −1.26491
\(11\) 1.00000 0.301511
\(12\) −4.00000 −1.15470
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −6.00000 −1.60357
\(15\) −4.00000 −1.03280
\(16\) −4.00000 −1.00000
\(17\) 1.00000 0.242536
\(18\) −2.00000 −0.471405
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 4.00000 0.894427
\(21\) −6.00000 −1.30931
\(22\) −2.00000 −0.426401
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 4.00000 0.784465
\(27\) 4.00000 0.769800
\(28\) 6.00000 1.13389
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 8.00000 1.46059
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 8.00000 1.41421
\(33\) −2.00000 −0.348155
\(34\) −2.00000 −0.342997
\(35\) 6.00000 1.01419
\(36\) 2.00000 0.333333
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 16.0000 2.59554
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 12.0000 1.85164
\(43\) −1.00000 −0.152499
\(44\) 2.00000 0.301511
\(45\) 2.00000 0.298142
\(46\) 8.00000 1.17954
\(47\) −5.00000 −0.729325 −0.364662 0.931140i \(-0.618816\pi\)
−0.364662 + 0.931140i \(0.618816\pi\)
\(48\) 8.00000 1.15470
\(49\) 2.00000 0.285714
\(50\) 2.00000 0.282843
\(51\) −2.00000 −0.280056
\(52\) −4.00000 −0.554700
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) −8.00000 −1.08866
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 16.0000 2.11925
\(58\) 6.00000 0.787839
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −8.00000 −1.03280
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −16.0000 −2.03200
\(63\) 3.00000 0.377964
\(64\) −8.00000 −1.00000
\(65\) −4.00000 −0.496139
\(66\) 4.00000 0.492366
\(67\) −9.00000 −1.09952 −0.549762 0.835321i \(-0.685282\pi\)
−0.549762 + 0.835321i \(0.685282\pi\)
\(68\) 2.00000 0.242536
\(69\) 8.00000 0.963087
\(70\) −12.0000 −1.43427
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −12.0000 −1.39497
\(75\) 2.00000 0.230940
\(76\) −16.0000 −1.83533
\(77\) 3.00000 0.341882
\(78\) −8.00000 −0.905822
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −8.00000 −0.894427
\(81\) −11.0000 −1.22222
\(82\) −22.0000 −2.42949
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −12.0000 −1.30931
\(85\) 2.00000 0.216930
\(86\) 2.00000 0.215666
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) −4.00000 −0.421637
\(91\) −6.00000 −0.628971
\(92\) −8.00000 −0.834058
\(93\) −16.0000 −1.65912
\(94\) 10.0000 1.03142
\(95\) −16.0000 −1.64157
\(96\) −16.0000 −1.63299
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −4.00000 −0.404061
\(99\) 1.00000 0.100504
\(100\) −2.00000 −0.200000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 4.00000 0.396059
\(103\) 1.00000 0.0985329 0.0492665 0.998786i \(-0.484312\pi\)
0.0492665 + 0.998786i \(0.484312\pi\)
\(104\) 0 0
\(105\) −12.0000 −1.17108
\(106\) −2.00000 −0.194257
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 8.00000 0.769800
\(109\) −11.0000 −1.05361 −0.526804 0.849987i \(-0.676610\pi\)
−0.526804 + 0.849987i \(0.676610\pi\)
\(110\) −4.00000 −0.381385
\(111\) −12.0000 −1.13899
\(112\) −12.0000 −1.13389
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) −32.0000 −2.99707
\(115\) −8.00000 −0.746004
\(116\) −6.00000 −0.557086
\(117\) −2.00000 −0.184900
\(118\) 6.00000 0.552345
\(119\) 3.00000 0.275010
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −4.00000 −0.362143
\(123\) −22.0000 −1.98367
\(124\) 16.0000 1.43684
\(125\) −12.0000 −1.07331
\(126\) −6.00000 −0.534522
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) 2.00000 0.176090
\(130\) 8.00000 0.701646
\(131\) 5.00000 0.436852 0.218426 0.975854i \(-0.429908\pi\)
0.218426 + 0.975854i \(0.429908\pi\)
\(132\) −4.00000 −0.348155
\(133\) −24.0000 −2.08106
\(134\) 18.0000 1.55496
\(135\) 8.00000 0.688530
\(136\) 0 0
\(137\) −15.0000 −1.28154 −0.640768 0.767734i \(-0.721384\pi\)
−0.640768 + 0.767734i \(0.721384\pi\)
\(138\) −16.0000 −1.36201
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) 12.0000 1.01419
\(141\) 10.0000 0.842152
\(142\) −4.00000 −0.335673
\(143\) −2.00000 −0.167248
\(144\) −4.00000 −0.333333
\(145\) −6.00000 −0.498273
\(146\) 14.0000 1.15865
\(147\) −4.00000 −0.329914
\(148\) 12.0000 0.986394
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −4.00000 −0.326599
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) 1.00000 0.0808452
\(154\) −6.00000 −0.483494
\(155\) 16.0000 1.28515
\(156\) 8.00000 0.640513
\(157\) 23.0000 1.83560 0.917800 0.397043i \(-0.129964\pi\)
0.917800 + 0.397043i \(0.129964\pi\)
\(158\) −8.00000 −0.636446
\(159\) −2.00000 −0.158610
\(160\) 16.0000 1.26491
\(161\) −12.0000 −0.945732
\(162\) 22.0000 1.72848
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 22.0000 1.71791
\(165\) −4.00000 −0.311400
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −4.00000 −0.306786
\(171\) −8.00000 −0.611775
\(172\) −2.00000 −0.152499
\(173\) −3.00000 −0.228086 −0.114043 0.993476i \(-0.536380\pi\)
−0.114043 + 0.993476i \(0.536380\pi\)
\(174\) −12.0000 −0.909718
\(175\) −3.00000 −0.226779
\(176\) −4.00000 −0.301511
\(177\) 6.00000 0.450988
\(178\) −22.0000 −1.64897
\(179\) 5.00000 0.373718 0.186859 0.982387i \(-0.440169\pi\)
0.186859 + 0.982387i \(0.440169\pi\)
\(180\) 4.00000 0.298142
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 12.0000 0.889499
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) 12.0000 0.882258
\(186\) 32.0000 2.34635
\(187\) 1.00000 0.0731272
\(188\) −10.0000 −0.729325
\(189\) 12.0000 0.872872
\(190\) 32.0000 2.32152
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 16.0000 1.15470
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 16.0000 1.14873
\(195\) 8.00000 0.572892
\(196\) 4.00000 0.285714
\(197\) 26.0000 1.85242 0.926212 0.377004i \(-0.123046\pi\)
0.926212 + 0.377004i \(0.123046\pi\)
\(198\) −2.00000 −0.142134
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 18.0000 1.26962
\(202\) 0 0
\(203\) −9.00000 −0.631676
\(204\) −4.00000 −0.280056
\(205\) 22.0000 1.53655
\(206\) −2.00000 −0.139347
\(207\) −4.00000 −0.278019
\(208\) 8.00000 0.554700
\(209\) −8.00000 −0.553372
\(210\) 24.0000 1.65616
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 2.00000 0.137361
\(213\) −4.00000 −0.274075
\(214\) 6.00000 0.410152
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) 24.0000 1.62923
\(218\) 22.0000 1.49003
\(219\) 14.0000 0.946032
\(220\) 4.00000 0.269680
\(221\) −2.00000 −0.134535
\(222\) 24.0000 1.61077
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 24.0000 1.60357
\(225\) −1.00000 −0.0666667
\(226\) 4.00000 0.266076
\(227\) −13.0000 −0.862840 −0.431420 0.902151i \(-0.641987\pi\)
−0.431420 + 0.902151i \(0.641987\pi\)
\(228\) 32.0000 2.11925
\(229\) 15.0000 0.991228 0.495614 0.868543i \(-0.334943\pi\)
0.495614 + 0.868543i \(0.334943\pi\)
\(230\) 16.0000 1.05501
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) −3.00000 −0.196537 −0.0982683 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) 4.00000 0.261488
\(235\) −10.0000 −0.652328
\(236\) −6.00000 −0.390567
\(237\) −8.00000 −0.519656
\(238\) −6.00000 −0.388922
\(239\) −14.0000 −0.905585 −0.452792 0.891616i \(-0.649572\pi\)
−0.452792 + 0.891616i \(0.649572\pi\)
\(240\) 16.0000 1.03280
\(241\) −27.0000 −1.73922 −0.869611 0.493737i \(-0.835631\pi\)
−0.869611 + 0.493737i \(0.835631\pi\)
\(242\) −2.00000 −0.128565
\(243\) 10.0000 0.641500
\(244\) 4.00000 0.256074
\(245\) 4.00000 0.255551
\(246\) 44.0000 2.80534
\(247\) 16.0000 1.01806
\(248\) 0 0
\(249\) 0 0
\(250\) 24.0000 1.51789
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 6.00000 0.377964
\(253\) −4.00000 −0.251478
\(254\) −32.0000 −2.00786
\(255\) −4.00000 −0.250490
\(256\) 16.0000 1.00000
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) −4.00000 −0.249029
\(259\) 18.0000 1.11847
\(260\) −8.00000 −0.496139
\(261\) −3.00000 −0.185695
\(262\) −10.0000 −0.617802
\(263\) −24.0000 −1.47990 −0.739952 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 48.0000 2.94307
\(267\) −22.0000 −1.34638
\(268\) −18.0000 −1.09952
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) −16.0000 −0.973729
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) −4.00000 −0.242536
\(273\) 12.0000 0.726273
\(274\) 30.0000 1.81237
\(275\) −1.00000 −0.0603023
\(276\) 16.0000 0.963087
\(277\) 1.00000 0.0600842 0.0300421 0.999549i \(-0.490436\pi\)
0.0300421 + 0.999549i \(0.490436\pi\)
\(278\) −14.0000 −0.839664
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −32.0000 −1.90896 −0.954480 0.298275i \(-0.903589\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) −20.0000 −1.19098
\(283\) −12.0000 −0.713326 −0.356663 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) 4.00000 0.237356
\(285\) 32.0000 1.89552
\(286\) 4.00000 0.236525
\(287\) 33.0000 1.94793
\(288\) 8.00000 0.471405
\(289\) 1.00000 0.0588235
\(290\) 12.0000 0.704664
\(291\) 16.0000 0.937937
\(292\) −14.0000 −0.819288
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 8.00000 0.466569
\(295\) −6.00000 −0.349334
\(296\) 0 0
\(297\) 4.00000 0.232104
\(298\) −12.0000 −0.695141
\(299\) 8.00000 0.462652
\(300\) 4.00000 0.230940
\(301\) −3.00000 −0.172917
\(302\) 4.00000 0.230174
\(303\) 0 0
\(304\) 32.0000 1.83533
\(305\) 4.00000 0.229039
\(306\) −2.00000 −0.114332
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 6.00000 0.341882
\(309\) −2.00000 −0.113776
\(310\) −32.0000 −1.81748
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) 0 0
\(313\) −2.00000 −0.113047 −0.0565233 0.998401i \(-0.518002\pi\)
−0.0565233 + 0.998401i \(0.518002\pi\)
\(314\) −46.0000 −2.59593
\(315\) 6.00000 0.338062
\(316\) 8.00000 0.450035
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 4.00000 0.224309
\(319\) −3.00000 −0.167968
\(320\) −16.0000 −0.894427
\(321\) 6.00000 0.334887
\(322\) 24.0000 1.33747
\(323\) −8.00000 −0.445132
\(324\) −22.0000 −1.22222
\(325\) 2.00000 0.110940
\(326\) −4.00000 −0.221540
\(327\) 22.0000 1.21660
\(328\) 0 0
\(329\) −15.0000 −0.826977
\(330\) 8.00000 0.440386
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 6.00000 0.328798
\(334\) 24.0000 1.31322
\(335\) −18.0000 −0.983445
\(336\) 24.0000 1.30931
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 18.0000 0.979071
\(339\) 4.00000 0.217250
\(340\) 4.00000 0.216930
\(341\) 8.00000 0.433224
\(342\) 16.0000 0.865181
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 16.0000 0.861411
\(346\) 6.00000 0.322562
\(347\) 7.00000 0.375780 0.187890 0.982190i \(-0.439835\pi\)
0.187890 + 0.982190i \(0.439835\pi\)
\(348\) 12.0000 0.643268
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 6.00000 0.320713
\(351\) −8.00000 −0.427008
\(352\) 8.00000 0.426401
\(353\) −25.0000 −1.33062 −0.665308 0.746569i \(-0.731700\pi\)
−0.665308 + 0.746569i \(0.731700\pi\)
\(354\) −12.0000 −0.637793
\(355\) 4.00000 0.212298
\(356\) 22.0000 1.16600
\(357\) −6.00000 −0.317554
\(358\) −10.0000 −0.528516
\(359\) −2.00000 −0.105556 −0.0527780 0.998606i \(-0.516808\pi\)
−0.0527780 + 0.998606i \(0.516808\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 4.00000 0.210235
\(363\) −2.00000 −0.104973
\(364\) −12.0000 −0.628971
\(365\) −14.0000 −0.732793
\(366\) 8.00000 0.418167
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) 16.0000 0.834058
\(369\) 11.0000 0.572637
\(370\) −24.0000 −1.24770
\(371\) 3.00000 0.155752
\(372\) −32.0000 −1.65912
\(373\) 38.0000 1.96757 0.983783 0.179364i \(-0.0574041\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) −2.00000 −0.103418
\(375\) 24.0000 1.23935
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) −24.0000 −1.23443
\(379\) −10.0000 −0.513665 −0.256833 0.966456i \(-0.582679\pi\)
−0.256833 + 0.966456i \(0.582679\pi\)
\(380\) −32.0000 −1.64157
\(381\) −32.0000 −1.63941
\(382\) −16.0000 −0.818631
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) 6.00000 0.305788
\(386\) 12.0000 0.610784
\(387\) −1.00000 −0.0508329
\(388\) −16.0000 −0.812277
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) −16.0000 −0.810191
\(391\) −4.00000 −0.202289
\(392\) 0 0
\(393\) −10.0000 −0.504433
\(394\) −52.0000 −2.61972
\(395\) 8.00000 0.402524
\(396\) 2.00000 0.100504
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 32.0000 1.60402
\(399\) 48.0000 2.40301
\(400\) 4.00000 0.200000
\(401\) −28.0000 −1.39825 −0.699127 0.714998i \(-0.746428\pi\)
−0.699127 + 0.714998i \(0.746428\pi\)
\(402\) −36.0000 −1.79552
\(403\) −16.0000 −0.797017
\(404\) 0 0
\(405\) −22.0000 −1.09319
\(406\) 18.0000 0.893325
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −12.0000 −0.593362 −0.296681 0.954977i \(-0.595880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(410\) −44.0000 −2.17301
\(411\) 30.0000 1.47979
\(412\) 2.00000 0.0985329
\(413\) −9.00000 −0.442861
\(414\) 8.00000 0.393179
\(415\) 0 0
\(416\) −16.0000 −0.784465
\(417\) −14.0000 −0.685583
\(418\) 16.0000 0.782586
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) −24.0000 −1.17108
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 2.00000 0.0973585
\(423\) −5.00000 −0.243108
\(424\) 0 0
\(425\) −1.00000 −0.0485071
\(426\) 8.00000 0.387601
\(427\) 6.00000 0.290360
\(428\) −6.00000 −0.290021
\(429\) 4.00000 0.193122
\(430\) 4.00000 0.192897
\(431\) 21.0000 1.01153 0.505767 0.862670i \(-0.331209\pi\)
0.505767 + 0.862670i \(0.331209\pi\)
\(432\) −16.0000 −0.769800
\(433\) 15.0000 0.720854 0.360427 0.932787i \(-0.382631\pi\)
0.360427 + 0.932787i \(0.382631\pi\)
\(434\) −48.0000 −2.30407
\(435\) 12.0000 0.575356
\(436\) −22.0000 −1.05361
\(437\) 32.0000 1.53077
\(438\) −28.0000 −1.33789
\(439\) −1.00000 −0.0477274 −0.0238637 0.999715i \(-0.507597\pi\)
−0.0238637 + 0.999715i \(0.507597\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 4.00000 0.190261
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −24.0000 −1.13899
\(445\) 22.0000 1.04290
\(446\) 32.0000 1.51524
\(447\) −12.0000 −0.567581
\(448\) −24.0000 −1.13389
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 2.00000 0.0942809
\(451\) 11.0000 0.517970
\(452\) −4.00000 −0.188144
\(453\) 4.00000 0.187936
\(454\) 26.0000 1.22024
\(455\) −12.0000 −0.562569
\(456\) 0 0
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) −30.0000 −1.40181
\(459\) 4.00000 0.186704
\(460\) −16.0000 −0.746004
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 12.0000 0.558291
\(463\) 31.0000 1.44069 0.720346 0.693615i \(-0.243983\pi\)
0.720346 + 0.693615i \(0.243983\pi\)
\(464\) 12.0000 0.557086
\(465\) −32.0000 −1.48396
\(466\) 6.00000 0.277945
\(467\) 21.0000 0.971764 0.485882 0.874024i \(-0.338498\pi\)
0.485882 + 0.874024i \(0.338498\pi\)
\(468\) −4.00000 −0.184900
\(469\) −27.0000 −1.24674
\(470\) 20.0000 0.922531
\(471\) −46.0000 −2.11957
\(472\) 0 0
\(473\) −1.00000 −0.0459800
\(474\) 16.0000 0.734904
\(475\) 8.00000 0.367065
\(476\) 6.00000 0.275010
\(477\) 1.00000 0.0457869
\(478\) 28.0000 1.28069
\(479\) −21.0000 −0.959514 −0.479757 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) −32.0000 −1.46059
\(481\) −12.0000 −0.547153
\(482\) 54.0000 2.45963
\(483\) 24.0000 1.09204
\(484\) 2.00000 0.0909091
\(485\) −16.0000 −0.726523
\(486\) −20.0000 −0.907218
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) −8.00000 −0.361403
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) −44.0000 −1.98367
\(493\) −3.00000 −0.135113
\(494\) −32.0000 −1.43975
\(495\) 2.00000 0.0898933
\(496\) −32.0000 −1.43684
\(497\) 6.00000 0.269137
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −24.0000 −1.07331
\(501\) 24.0000 1.07224
\(502\) −8.00000 −0.357057
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8.00000 0.355643
\(507\) 18.0000 0.799408
\(508\) 32.0000 1.41977
\(509\) −21.0000 −0.930809 −0.465404 0.885098i \(-0.654091\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(510\) 8.00000 0.354246
\(511\) −21.0000 −0.928985
\(512\) −32.0000 −1.41421
\(513\) −32.0000 −1.41283
\(514\) −42.0000 −1.85254
\(515\) 2.00000 0.0881305
\(516\) 4.00000 0.176090
\(517\) −5.00000 −0.219900
\(518\) −36.0000 −1.58175
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 6.00000 0.262613
\(523\) 6.00000 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) 10.0000 0.436852
\(525\) 6.00000 0.261861
\(526\) 48.0000 2.09290
\(527\) 8.00000 0.348485
\(528\) 8.00000 0.348155
\(529\) −7.00000 −0.304348
\(530\) −4.00000 −0.173749
\(531\) −3.00000 −0.130189
\(532\) −48.0000 −2.08106
\(533\) −22.0000 −0.952926
\(534\) 44.0000 1.90407
\(535\) −6.00000 −0.259403
\(536\) 0 0
\(537\) −10.0000 −0.431532
\(538\) 20.0000 0.862261
\(539\) 2.00000 0.0861461
\(540\) 16.0000 0.688530
\(541\) 43.0000 1.84871 0.924357 0.381528i \(-0.124602\pi\)
0.924357 + 0.381528i \(0.124602\pi\)
\(542\) 44.0000 1.88996
\(543\) 4.00000 0.171656
\(544\) 8.00000 0.342997
\(545\) −22.0000 −0.942376
\(546\) −24.0000 −1.02711
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −30.0000 −1.28154
\(549\) 2.00000 0.0853579
\(550\) 2.00000 0.0852803
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) −2.00000 −0.0849719
\(555\) −24.0000 −1.01874
\(556\) 14.0000 0.593732
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) −16.0000 −0.677334
\(559\) 2.00000 0.0845910
\(560\) −24.0000 −1.01419
\(561\) −2.00000 −0.0844401
\(562\) 64.0000 2.69968
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 20.0000 0.842152
\(565\) −4.00000 −0.168281
\(566\) 24.0000 1.00880
\(567\) −33.0000 −1.38587
\(568\) 0 0
\(569\) 4.00000 0.167689 0.0838444 0.996479i \(-0.473280\pi\)
0.0838444 + 0.996479i \(0.473280\pi\)
\(570\) −64.0000 −2.68067
\(571\) 31.0000 1.29731 0.648655 0.761083i \(-0.275332\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) −4.00000 −0.167248
\(573\) −16.0000 −0.668410
\(574\) −66.0000 −2.75479
\(575\) 4.00000 0.166812
\(576\) −8.00000 −0.333333
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) −2.00000 −0.0831890
\(579\) 12.0000 0.498703
\(580\) −12.0000 −0.498273
\(581\) 0 0
\(582\) −32.0000 −1.32644
\(583\) 1.00000 0.0414158
\(584\) 0 0
\(585\) −4.00000 −0.165380
\(586\) −8.00000 −0.330477
\(587\) −4.00000 −0.165098 −0.0825488 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) −8.00000 −0.329914
\(589\) −64.0000 −2.63707
\(590\) 12.0000 0.494032
\(591\) −52.0000 −2.13899
\(592\) −24.0000 −0.986394
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) −8.00000 −0.328244
\(595\) 6.00000 0.245976
\(596\) 12.0000 0.491539
\(597\) 32.0000 1.30967
\(598\) −16.0000 −0.654289
\(599\) −43.0000 −1.75693 −0.878466 0.477805i \(-0.841433\pi\)
−0.878466 + 0.477805i \(0.841433\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 6.00000 0.244542
\(603\) −9.00000 −0.366508
\(604\) −4.00000 −0.162758
\(605\) 2.00000 0.0813116
\(606\) 0 0
\(607\) −40.0000 −1.62355 −0.811775 0.583970i \(-0.801498\pi\)
−0.811775 + 0.583970i \(0.801498\pi\)
\(608\) −64.0000 −2.59554
\(609\) 18.0000 0.729397
\(610\) −8.00000 −0.323911
\(611\) 10.0000 0.404557
\(612\) 2.00000 0.0808452
\(613\) 42.0000 1.69636 0.848182 0.529705i \(-0.177697\pi\)
0.848182 + 0.529705i \(0.177697\pi\)
\(614\) −4.00000 −0.161427
\(615\) −44.0000 −1.77425
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 4.00000 0.160904
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 32.0000 1.28515
\(621\) −16.0000 −0.642058
\(622\) 60.0000 2.40578
\(623\) 33.0000 1.32212
\(624\) −16.0000 −0.640513
\(625\) −19.0000 −0.760000
\(626\) 4.00000 0.159872
\(627\) 16.0000 0.638978
\(628\) 46.0000 1.83560
\(629\) 6.00000 0.239236
\(630\) −12.0000 −0.478091
\(631\) −27.0000 −1.07485 −0.537427 0.843311i \(-0.680603\pi\)
−0.537427 + 0.843311i \(0.680603\pi\)
\(632\) 0 0
\(633\) 2.00000 0.0794929
\(634\) −24.0000 −0.953162
\(635\) 32.0000 1.26988
\(636\) −4.00000 −0.158610
\(637\) −4.00000 −0.158486
\(638\) 6.00000 0.237542
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −12.0000 −0.473602
\(643\) 6.00000 0.236617 0.118308 0.992977i \(-0.462253\pi\)
0.118308 + 0.992977i \(0.462253\pi\)
\(644\) −24.0000 −0.945732
\(645\) 4.00000 0.157500
\(646\) 16.0000 0.629512
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 0 0
\(649\) −3.00000 −0.117760
\(650\) −4.00000 −0.156893
\(651\) −48.0000 −1.88127
\(652\) 4.00000 0.156652
\(653\) −8.00000 −0.313064 −0.156532 0.987673i \(-0.550031\pi\)
−0.156532 + 0.987673i \(0.550031\pi\)
\(654\) −44.0000 −1.72054
\(655\) 10.0000 0.390732
\(656\) −44.0000 −1.71791
\(657\) −7.00000 −0.273096
\(658\) 30.0000 1.16952
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) −8.00000 −0.311400
\(661\) −29.0000 −1.12797 −0.563985 0.825785i \(-0.690732\pi\)
−0.563985 + 0.825785i \(0.690732\pi\)
\(662\) 16.0000 0.621858
\(663\) 4.00000 0.155347
\(664\) 0 0
\(665\) −48.0000 −1.86136
\(666\) −12.0000 −0.464991
\(667\) 12.0000 0.464642
\(668\) −24.0000 −0.928588
\(669\) 32.0000 1.23719
\(670\) 36.0000 1.39080
\(671\) 2.00000 0.0772091
\(672\) −48.0000 −1.85164
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) 18.0000 0.693334
\(675\) −4.00000 −0.153960
\(676\) −18.0000 −0.692308
\(677\) −23.0000 −0.883962 −0.441981 0.897024i \(-0.645724\pi\)
−0.441981 + 0.897024i \(0.645724\pi\)
\(678\) −8.00000 −0.307238
\(679\) −24.0000 −0.921035
\(680\) 0 0
\(681\) 26.0000 0.996322
\(682\) −16.0000 −0.612672
\(683\) 48.0000 1.83667 0.918334 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) −16.0000 −0.611775
\(685\) −30.0000 −1.14624
\(686\) 30.0000 1.14541
\(687\) −30.0000 −1.14457
\(688\) 4.00000 0.152499
\(689\) −2.00000 −0.0761939
\(690\) −32.0000 −1.21822
\(691\) 38.0000 1.44559 0.722794 0.691063i \(-0.242858\pi\)
0.722794 + 0.691063i \(0.242858\pi\)
\(692\) −6.00000 −0.228086
\(693\) 3.00000 0.113961
\(694\) −14.0000 −0.531433
\(695\) 14.0000 0.531050
\(696\) 0 0
\(697\) 11.0000 0.416655
\(698\) −16.0000 −0.605609
\(699\) 6.00000 0.226941
\(700\) −6.00000 −0.226779
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 16.0000 0.603881
\(703\) −48.0000 −1.81035
\(704\) −8.00000 −0.301511
\(705\) 20.0000 0.753244
\(706\) 50.0000 1.88177
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) −8.00000 −0.300235
\(711\) 4.00000 0.150012
\(712\) 0 0
\(713\) −32.0000 −1.19841
\(714\) 12.0000 0.449089
\(715\) −4.00000 −0.149592
\(716\) 10.0000 0.373718
\(717\) 28.0000 1.04568
\(718\) 4.00000 0.149279
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) −8.00000 −0.298142
\(721\) 3.00000 0.111726
\(722\) −90.0000 −3.34945
\(723\) 54.0000 2.00828
\(724\) −4.00000 −0.148659
\(725\) 3.00000 0.111417
\(726\) 4.00000 0.148454
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 28.0000 1.03633
\(731\) −1.00000 −0.0369863
\(732\) −8.00000 −0.295689
\(733\) 44.0000 1.62518 0.812589 0.582838i \(-0.198058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(734\) −56.0000 −2.06700
\(735\) −8.00000 −0.295084
\(736\) −32.0000 −1.17954
\(737\) −9.00000 −0.331519
\(738\) −22.0000 −0.809831
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 24.0000 0.882258
\(741\) −32.0000 −1.17555
\(742\) −6.00000 −0.220267
\(743\) −33.0000 −1.21065 −0.605326 0.795977i \(-0.706957\pi\)
−0.605326 + 0.795977i \(0.706957\pi\)
\(744\) 0 0
\(745\) 12.0000 0.439646
\(746\) −76.0000 −2.78256
\(747\) 0 0
\(748\) 2.00000 0.0731272
\(749\) −9.00000 −0.328853
\(750\) −48.0000 −1.75271
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 20.0000 0.729325
\(753\) −8.00000 −0.291536
\(754\) −12.0000 −0.437014
\(755\) −4.00000 −0.145575
\(756\) 24.0000 0.872872
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 20.0000 0.726433
\(759\) 8.00000 0.290382
\(760\) 0 0
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 64.0000 2.31848
\(763\) −33.0000 −1.19468
\(764\) 16.0000 0.578860
\(765\) 2.00000 0.0723102
\(766\) 32.0000 1.15621
\(767\) 6.00000 0.216647
\(768\) −32.0000 −1.15470
\(769\) −12.0000 −0.432731 −0.216366 0.976312i \(-0.569420\pi\)
−0.216366 + 0.976312i \(0.569420\pi\)
\(770\) −12.0000 −0.432450
\(771\) −42.0000 −1.51259
\(772\) −12.0000 −0.431889
\(773\) −34.0000 −1.22290 −0.611448 0.791285i \(-0.709412\pi\)
−0.611448 + 0.791285i \(0.709412\pi\)
\(774\) 2.00000 0.0718885
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) −36.0000 −1.29149
\(778\) −30.0000 −1.07555
\(779\) −88.0000 −3.15293
\(780\) 16.0000 0.572892
\(781\) 2.00000 0.0715656
\(782\) 8.00000 0.286079
\(783\) −12.0000 −0.428845
\(784\) −8.00000 −0.285714
\(785\) 46.0000 1.64181
\(786\) 20.0000 0.713376
\(787\) −23.0000 −0.819861 −0.409931 0.912117i \(-0.634447\pi\)
−0.409931 + 0.912117i \(0.634447\pi\)
\(788\) 52.0000 1.85242
\(789\) 48.0000 1.70885
\(790\) −16.0000 −0.569254
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) 36.0000 1.27759
\(795\) −4.00000 −0.141865
\(796\) −32.0000 −1.13421
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) −96.0000 −3.39836
\(799\) −5.00000 −0.176887
\(800\) −8.00000 −0.282843
\(801\) 11.0000 0.388666
\(802\) 56.0000 1.97743
\(803\) −7.00000 −0.247025
\(804\) 36.0000 1.26962
\(805\) −24.0000 −0.845889
\(806\) 32.0000 1.12715
\(807\) 20.0000 0.704033
\(808\) 0 0
\(809\) −19.0000 −0.668004 −0.334002 0.942572i \(-0.608399\pi\)
−0.334002 + 0.942572i \(0.608399\pi\)
\(810\) 44.0000 1.54600
\(811\) 40.0000 1.40459 0.702295 0.711886i \(-0.252159\pi\)
0.702295 + 0.711886i \(0.252159\pi\)
\(812\) −18.0000 −0.631676
\(813\) 44.0000 1.54315
\(814\) −12.0000 −0.420600
\(815\) 4.00000 0.140114
\(816\) 8.00000 0.280056
\(817\) 8.00000 0.279885
\(818\) 24.0000 0.839140
\(819\) −6.00000 −0.209657
\(820\) 44.0000 1.53655
\(821\) −26.0000 −0.907406 −0.453703 0.891153i \(-0.649897\pi\)
−0.453703 + 0.891153i \(0.649897\pi\)
\(822\) −60.0000 −2.09274
\(823\) 44.0000 1.53374 0.766872 0.641800i \(-0.221812\pi\)
0.766872 + 0.641800i \(0.221812\pi\)
\(824\) 0 0
\(825\) 2.00000 0.0696311
\(826\) 18.0000 0.626300
\(827\) −15.0000 −0.521601 −0.260801 0.965393i \(-0.583986\pi\)
−0.260801 + 0.965393i \(0.583986\pi\)
\(828\) −8.00000 −0.278019
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) 16.0000 0.554700
\(833\) 2.00000 0.0692959
\(834\) 28.0000 0.969561
\(835\) −24.0000 −0.830554
\(836\) −16.0000 −0.553372
\(837\) 32.0000 1.10608
\(838\) 80.0000 2.76355
\(839\) −34.0000 −1.17381 −0.586905 0.809656i \(-0.699654\pi\)
−0.586905 + 0.809656i \(0.699654\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −34.0000 −1.17172
\(843\) 64.0000 2.20428
\(844\) −2.00000 −0.0688428
\(845\) −18.0000 −0.619219
\(846\) 10.0000 0.343807
\(847\) 3.00000 0.103081
\(848\) −4.00000 −0.137361
\(849\) 24.0000 0.823678
\(850\) 2.00000 0.0685994
\(851\) −24.0000 −0.822709
\(852\) −8.00000 −0.274075
\(853\) 1.00000 0.0342393 0.0171197 0.999853i \(-0.494550\pi\)
0.0171197 + 0.999853i \(0.494550\pi\)
\(854\) −12.0000 −0.410632
\(855\) −16.0000 −0.547188
\(856\) 0 0
\(857\) 26.0000 0.888143 0.444072 0.895991i \(-0.353534\pi\)
0.444072 + 0.895991i \(0.353534\pi\)
\(858\) −8.00000 −0.273115
\(859\) 1.00000 0.0341196 0.0170598 0.999854i \(-0.494569\pi\)
0.0170598 + 0.999854i \(0.494569\pi\)
\(860\) −4.00000 −0.136399
\(861\) −66.0000 −2.24927
\(862\) −42.0000 −1.43053
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 32.0000 1.08866
\(865\) −6.00000 −0.204006
\(866\) −30.0000 −1.01944
\(867\) −2.00000 −0.0679236
\(868\) 48.0000 1.62923
\(869\) 4.00000 0.135691
\(870\) −24.0000 −0.813676
\(871\) 18.0000 0.609907
\(872\) 0 0
\(873\) −8.00000 −0.270759
\(874\) −64.0000 −2.16483
\(875\) −36.0000 −1.21702
\(876\) 28.0000 0.946032
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 2.00000 0.0674967
\(879\) −8.00000 −0.269833
\(880\) −8.00000 −0.269680
\(881\) −44.0000 −1.48240 −0.741199 0.671286i \(-0.765742\pi\)
−0.741199 + 0.671286i \(0.765742\pi\)
\(882\) −4.00000 −0.134687
\(883\) −41.0000 −1.37976 −0.689880 0.723924i \(-0.742337\pi\)
−0.689880 + 0.723924i \(0.742337\pi\)
\(884\) −4.00000 −0.134535
\(885\) 12.0000 0.403376
\(886\) 8.00000 0.268765
\(887\) 8.00000 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) 48.0000 1.60987
\(890\) −44.0000 −1.47488
\(891\) −11.0000 −0.368514
\(892\) −32.0000 −1.07144
\(893\) 40.0000 1.33855
\(894\) 24.0000 0.802680
\(895\) 10.0000 0.334263
\(896\) 0 0
\(897\) −16.0000 −0.534224
\(898\) −36.0000 −1.20134
\(899\) −24.0000 −0.800445
\(900\) −2.00000 −0.0666667
\(901\) 1.00000 0.0333148
\(902\) −22.0000 −0.732520
\(903\) 6.00000 0.199667
\(904\) 0 0
\(905\) −4.00000 −0.132964
\(906\) −8.00000 −0.265782
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) −26.0000 −0.862840
\(909\) 0 0
\(910\) 24.0000 0.795592
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) −64.0000 −2.11925
\(913\) 0 0
\(914\) −36.0000 −1.19077
\(915\) −8.00000 −0.264472
\(916\) 30.0000 0.991228
\(917\) 15.0000 0.495344
\(918\) −8.00000 −0.264039
\(919\) 26.0000 0.857661 0.428830 0.903385i \(-0.358926\pi\)
0.428830 + 0.903385i \(0.358926\pi\)
\(920\) 0 0
\(921\) −4.00000 −0.131804
\(922\) 0 0
\(923\) −4.00000 −0.131662
\(924\) −12.0000 −0.394771
\(925\) −6.00000 −0.197279
\(926\) −62.0000 −2.03745
\(927\) 1.00000 0.0328443
\(928\) −24.0000 −0.787839
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 64.0000 2.09864
\(931\) −16.0000 −0.524379
\(932\) −6.00000 −0.196537
\(933\) 60.0000 1.96431
\(934\) −42.0000 −1.37428
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 54.0000 1.76316
\(939\) 4.00000 0.130535
\(940\) −20.0000 −0.652328
\(941\) 15.0000 0.488986 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(942\) 92.0000 2.99752
\(943\) −44.0000 −1.43284
\(944\) 12.0000 0.390567
\(945\) 24.0000 0.780720
\(946\) 2.00000 0.0650256
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) −16.0000 −0.519656
\(949\) 14.0000 0.454459
\(950\) −16.0000 −0.519109
\(951\) −24.0000 −0.778253
\(952\) 0 0
\(953\) −44.0000 −1.42530 −0.712650 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) −2.00000 −0.0647524
\(955\) 16.0000 0.517748
\(956\) −28.0000 −0.905585
\(957\) 6.00000 0.193952
\(958\) 42.0000 1.35696
\(959\) −45.0000 −1.45313
\(960\) 32.0000 1.03280
\(961\) 33.0000 1.06452
\(962\) 24.0000 0.773791
\(963\) −3.00000 −0.0966736
\(964\) −54.0000 −1.73922
\(965\) −12.0000 −0.386294
\(966\) −48.0000 −1.54437
\(967\) 34.0000 1.09337 0.546683 0.837340i \(-0.315890\pi\)
0.546683 + 0.837340i \(0.315890\pi\)
\(968\) 0 0
\(969\) 16.0000 0.513994
\(970\) 32.0000 1.02746
\(971\) 20.0000 0.641831 0.320915 0.947108i \(-0.396010\pi\)
0.320915 + 0.947108i \(0.396010\pi\)
\(972\) 20.0000 0.641500
\(973\) 21.0000 0.673229
\(974\) −24.0000 −0.769010
\(975\) −4.00000 −0.128103
\(976\) −8.00000 −0.256074
\(977\) 7.00000 0.223950 0.111975 0.993711i \(-0.464282\pi\)
0.111975 + 0.993711i \(0.464282\pi\)
\(978\) 8.00000 0.255812
\(979\) 11.0000 0.351562
\(980\) 8.00000 0.255551
\(981\) −11.0000 −0.351203
\(982\) −12.0000 −0.382935
\(983\) −60.0000 −1.91370 −0.956851 0.290578i \(-0.906153\pi\)
−0.956851 + 0.290578i \(0.906153\pi\)
\(984\) 0 0
\(985\) 52.0000 1.65686
\(986\) 6.00000 0.191079
\(987\) 30.0000 0.954911
\(988\) 32.0000 1.01806
\(989\) 4.00000 0.127193
\(990\) −4.00000 −0.127128
\(991\) −58.0000 −1.84243 −0.921215 0.389053i \(-0.872802\pi\)
−0.921215 + 0.389053i \(0.872802\pi\)
\(992\) 64.0000 2.03200
\(993\) 16.0000 0.507745
\(994\) −12.0000 −0.380617
\(995\) −32.0000 −1.01447
\(996\) 0 0
\(997\) −5.00000 −0.158352 −0.0791758 0.996861i \(-0.525229\pi\)
−0.0791758 + 0.996861i \(0.525229\pi\)
\(998\) 40.0000 1.26618
\(999\) 24.0000 0.759326
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 \(a_p\))