Properties

Label 5077.2.a.a.1.1
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 3
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(3\)
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 \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +2.00000 q^{4} -4.00000 q^{5} +6.00000 q^{6} -4.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +2.00000 q^{4} -4.00000 q^{5} +6.00000 q^{6} -4.00000 q^{7} +6.00000 q^{9} +8.00000 q^{10} -6.00000 q^{11} -6.00000 q^{12} -4.00000 q^{13} +8.00000 q^{14} +12.0000 q^{15} -4.00000 q^{16} -4.00000 q^{17} -12.0000 q^{18} -7.00000 q^{19} -8.00000 q^{20} +12.0000 q^{21} +12.0000 q^{22} -6.00000 q^{23} +11.0000 q^{25} +8.00000 q^{26} -9.00000 q^{27} -8.00000 q^{28} -6.00000 q^{29} -24.0000 q^{30} -2.00000 q^{31} +8.00000 q^{32} +18.0000 q^{33} +8.00000 q^{34} +16.0000 q^{35} +12.0000 q^{36} +14.0000 q^{38} +12.0000 q^{39} -24.0000 q^{42} -8.00000 q^{43} -12.0000 q^{44} -24.0000 q^{45} +12.0000 q^{46} -9.00000 q^{47} +12.0000 q^{48} +9.00000 q^{49} -22.0000 q^{50} +12.0000 q^{51} -8.00000 q^{52} -9.00000 q^{53} +18.0000 q^{54} +24.0000 q^{55} +21.0000 q^{57} +12.0000 q^{58} -11.0000 q^{59} +24.0000 q^{60} -2.00000 q^{61} +4.00000 q^{62} -24.0000 q^{63} -8.00000 q^{64} +16.0000 q^{65} -36.0000 q^{66} -12.0000 q^{67} -8.00000 q^{68} +18.0000 q^{69} -32.0000 q^{70} -8.00000 q^{71} -14.0000 q^{73} -33.0000 q^{75} -14.0000 q^{76} +24.0000 q^{77} -24.0000 q^{78} +9.00000 q^{79} +16.0000 q^{80} +9.00000 q^{81} -2.00000 q^{83} +24.0000 q^{84} +16.0000 q^{85} +16.0000 q^{86} +18.0000 q^{87} +11.0000 q^{89} +48.0000 q^{90} +16.0000 q^{91} -12.0000 q^{92} +6.00000 q^{93} +18.0000 q^{94} +28.0000 q^{95} -24.0000 q^{96} +6.00000 q^{97} -18.0000 q^{98} -36.0000 q^{99} +O(q^{100})\)

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 \(0.750000\pi\)
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 2.00000 1.00000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 6.00000 2.44949
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 8.00000 2.52982
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) −6.00000 −1.73205
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 8.00000 2.13809
\(15\) 12.0000 3.09839
\(16\) −4.00000 −1.00000
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) −12.0000 −2.82843
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −8.00000 −1.78885
\(21\) 12.0000 2.61861
\(22\) 12.0000 2.55841
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 8.00000 1.56893
\(27\) −9.00000 −1.73205
\(28\) −8.00000 −1.51186
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −24.0000 −4.38178
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 8.00000 1.41421
\(33\) 18.0000 3.13340
\(34\) 8.00000 1.37199
\(35\) 16.0000 2.70449
\(36\) 12.0000 2.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 14.0000 2.27110
\(39\) 12.0000 1.92154
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −24.0000 −3.70328
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −12.0000 −1.80907
\(45\) −24.0000 −3.57771
\(46\) 12.0000 1.76930
\(47\) −9.00000 −1.31278 −0.656392 0.754420i \(-0.727918\pi\)
−0.656392 + 0.754420i \(0.727918\pi\)
\(48\) 12.0000 1.73205
\(49\) 9.00000 1.28571
\(50\) −22.0000 −3.11127
\(51\) 12.0000 1.68034
\(52\) −8.00000 −1.10940
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 18.0000 2.44949
\(55\) 24.0000 3.23616
\(56\) 0 0
\(57\) 21.0000 2.78152
\(58\) 12.0000 1.57568
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 24.0000 3.09839
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 4.00000 0.508001
\(63\) −24.0000 −3.02372
\(64\) −8.00000 −1.00000
\(65\) 16.0000 1.98456
\(66\) −36.0000 −4.43129
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) −8.00000 −0.970143
\(69\) 18.0000 2.16695
\(70\) −32.0000 −3.82473
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) −33.0000 −3.81051
\(76\) −14.0000 −1.60591
\(77\) 24.0000 2.73505
\(78\) −24.0000 −2.71746
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 16.0000 1.78885
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 24.0000 2.61861
\(85\) 16.0000 1.73544
\(86\) 16.0000 1.72532
\(87\) 18.0000 1.92980
\(88\) 0 0
\(89\) 11.0000 1.16600 0.582999 0.812473i \(-0.301879\pi\)
0.582999 + 0.812473i \(0.301879\pi\)
\(90\) 48.0000 5.05964
\(91\) 16.0000 1.67726
\(92\) −12.0000 −1.25109
\(93\) 6.00000 0.622171
\(94\) 18.0000 1.85656
\(95\) 28.0000 2.87274
\(96\) −24.0000 −2.44949
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −18.0000 −1.81827
\(99\) −36.0000 −3.61814
\(100\) 22.0000 2.20000
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) −24.0000 −2.37635
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) −48.0000 −4.68432
\(106\) 18.0000 1.74831
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −18.0000 −1.73205
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) −48.0000 −4.57662
\(111\) 0 0
\(112\) 16.0000 1.51186
\(113\) −5.00000 −0.470360 −0.235180 0.971952i \(-0.575568\pi\)
−0.235180 + 0.971952i \(0.575568\pi\)
\(114\) −42.0000 −3.93366
\(115\) 24.0000 2.23801
\(116\) −12.0000 −1.11417
\(117\) −24.0000 −2.21880
\(118\) 22.0000 2.02526
\(119\) 16.0000 1.46672
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 4.00000 0.362143
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −24.0000 −2.14663
\(126\) 48.0000 4.27618
\(127\) 7.00000 0.621150 0.310575 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 0 0
\(129\) 24.0000 2.11308
\(130\) −32.0000 −2.80659
\(131\) −7.00000 −0.611593 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) 36.0000 3.13340
\(133\) 28.0000 2.42791
\(134\) 24.0000 2.07328
\(135\) 36.0000 3.09839
\(136\) 0 0
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) −36.0000 −3.06452
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 32.0000 2.70449
\(141\) 27.0000 2.27381
\(142\) 16.0000 1.34269
\(143\) 24.0000 2.00698
\(144\) −24.0000 −2.00000
\(145\) 24.0000 1.99309
\(146\) 28.0000 2.31730
\(147\) −27.0000 −2.22692
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 66.0000 5.38888
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) 0 0
\(153\) −24.0000 −1.94029
\(154\) −48.0000 −3.86795
\(155\) 8.00000 0.642575
\(156\) 24.0000 1.92154
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) −18.0000 −1.43200
\(159\) 27.0000 2.14124
\(160\) −32.0000 −2.52982
\(161\) 24.0000 1.89146
\(162\) −18.0000 −1.41421
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) −72.0000 −5.60519
\(166\) 4.00000 0.310460
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −32.0000 −2.45429
\(171\) −42.0000 −3.21182
\(172\) −16.0000 −1.21999
\(173\) −9.00000 −0.684257 −0.342129 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) −36.0000 −2.72915
\(175\) −44.0000 −3.32609
\(176\) 24.0000 1.80907
\(177\) 33.0000 2.48043
\(178\) −22.0000 −1.64897
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) −48.0000 −3.57771
\(181\) 19.0000 1.41226 0.706129 0.708083i \(-0.250440\pi\)
0.706129 + 0.708083i \(0.250440\pi\)
\(182\) −32.0000 −2.37200
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) 0 0
\(186\) −12.0000 −0.879883
\(187\) 24.0000 1.75505
\(188\) −18.0000 −1.31278
\(189\) 36.0000 2.61861
\(190\) −56.0000 −4.06267
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 24.0000 1.73205
\(193\) −13.0000 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(194\) −12.0000 −0.861550
\(195\) −48.0000 −3.43735
\(196\) 18.0000 1.28571
\(197\) −20.0000 −1.42494 −0.712470 0.701702i \(-0.752424\pi\)
−0.712470 + 0.701702i \(0.752424\pi\)
\(198\) 72.0000 5.11682
\(199\) −13.0000 −0.921546 −0.460773 0.887518i \(-0.652428\pi\)
−0.460773 + 0.887518i \(0.652428\pi\)
\(200\) 0 0
\(201\) 36.0000 2.53924
\(202\) −8.00000 −0.562878
\(203\) 24.0000 1.68447
\(204\) 24.0000 1.68034
\(205\) 0 0
\(206\) 0 0
\(207\) −36.0000 −2.50217
\(208\) 16.0000 1.10940
\(209\) 42.0000 2.90520
\(210\) 96.0000 6.62463
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −18.0000 −1.23625
\(213\) 24.0000 1.64445
\(214\) −24.0000 −1.64061
\(215\) 32.0000 2.18238
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) −14.0000 −0.948200
\(219\) 42.0000 2.83810
\(220\) 48.0000 3.23616
\(221\) 16.0000 1.07628
\(222\) 0 0
\(223\) 21.0000 1.40626 0.703132 0.711059i \(-0.251784\pi\)
0.703132 + 0.711059i \(0.251784\pi\)
\(224\) −32.0000 −2.13809
\(225\) 66.0000 4.40000
\(226\) 10.0000 0.665190
\(227\) −26.0000 −1.72568 −0.862840 0.505477i \(-0.831317\pi\)
−0.862840 + 0.505477i \(0.831317\pi\)
\(228\) 42.0000 2.78152
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) −48.0000 −3.16503
\(231\) −72.0000 −4.73725
\(232\) 0 0
\(233\) 15.0000 0.982683 0.491341 0.870967i \(-0.336507\pi\)
0.491341 + 0.870967i \(0.336507\pi\)
\(234\) 48.0000 3.13786
\(235\) 36.0000 2.34838
\(236\) −22.0000 −1.43208
\(237\) −27.0000 −1.75384
\(238\) −32.0000 −2.07425
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) −48.0000 −3.09839
\(241\) −29.0000 −1.86805 −0.934027 0.357202i \(-0.883731\pi\)
−0.934027 + 0.357202i \(0.883731\pi\)
\(242\) −50.0000 −3.21412
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) −36.0000 −2.29996
\(246\) 0 0
\(247\) 28.0000 1.78160
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 48.0000 3.03579
\(251\) 8.00000 0.504956 0.252478 0.967603i \(-0.418755\pi\)
0.252478 + 0.967603i \(0.418755\pi\)
\(252\) −48.0000 −3.02372
\(253\) 36.0000 2.26330
\(254\) −14.0000 −0.878438
\(255\) −48.0000 −3.00588
\(256\) 16.0000 1.00000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) −48.0000 −2.98835
\(259\) 0 0
\(260\) 32.0000 1.98456
\(261\) −36.0000 −2.22834
\(262\) 14.0000 0.864923
\(263\) 2.00000 0.123325 0.0616626 0.998097i \(-0.480360\pi\)
0.0616626 + 0.998097i \(0.480360\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) −56.0000 −3.43358
\(267\) −33.0000 −2.01957
\(268\) −24.0000 −1.46603
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) −72.0000 −4.38178
\(271\) 18.0000 1.09342 0.546711 0.837321i \(-0.315880\pi\)
0.546711 + 0.837321i \(0.315880\pi\)
\(272\) 16.0000 0.970143
\(273\) −48.0000 −2.90509
\(274\) 6.00000 0.362473
\(275\) −66.0000 −3.97995
\(276\) 36.0000 2.16695
\(277\) −13.0000 −0.781094 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(278\) −8.00000 −0.479808
\(279\) −12.0000 −0.718421
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) −54.0000 −3.21565
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) −16.0000 −0.949425
\(285\) −84.0000 −4.97573
\(286\) −48.0000 −2.83830
\(287\) 0 0
\(288\) 48.0000 2.82843
\(289\) −1.00000 −0.0588235
\(290\) −48.0000 −2.81866
\(291\) −18.0000 −1.05518
\(292\) −28.0000 −1.63858
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 54.0000 3.14934
\(295\) 44.0000 2.56178
\(296\) 0 0
\(297\) 54.0000 3.13340
\(298\) −12.0000 −0.695141
\(299\) 24.0000 1.38796
\(300\) −66.0000 −3.81051
\(301\) 32.0000 1.84445
\(302\) −18.0000 −1.03578
\(303\) −12.0000 −0.689382
\(304\) 28.0000 1.60591
\(305\) 8.00000 0.458079
\(306\) 48.0000 2.74398
\(307\) −17.0000 −0.970241 −0.485121 0.874447i \(-0.661224\pi\)
−0.485121 + 0.874447i \(0.661224\pi\)
\(308\) 48.0000 2.73505
\(309\) 0 0
\(310\) −16.0000 −0.908739
\(311\) −32.0000 −1.81455 −0.907277 0.420534i \(-0.861843\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −8.00000 −0.451466
\(315\) 96.0000 5.40899
\(316\) 18.0000 1.01258
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) −54.0000 −3.02817
\(319\) 36.0000 2.01561
\(320\) 32.0000 1.78885
\(321\) −36.0000 −2.00932
\(322\) −48.0000 −2.67494
\(323\) 28.0000 1.55796
\(324\) 18.0000 1.00000
\(325\) −44.0000 −2.44068
\(326\) 8.00000 0.443079
\(327\) −21.0000 −1.16130
\(328\) 0 0
\(329\) 36.0000 1.98474
\(330\) 144.000 7.92694
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −4.00000 −0.219529
\(333\) 0 0
\(334\) 16.0000 0.875481
\(335\) 48.0000 2.62252
\(336\) −48.0000 −2.61861
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −6.00000 −0.326357
\(339\) 15.0000 0.814688
\(340\) 32.0000 1.73544
\(341\) 12.0000 0.649836
\(342\) 84.0000 4.54220
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) −72.0000 −3.87635
\(346\) 18.0000 0.967686
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 36.0000 1.92980
\(349\) −35.0000 −1.87351 −0.936754 0.349990i \(-0.886185\pi\)
−0.936754 + 0.349990i \(0.886185\pi\)
\(350\) 88.0000 4.70380
\(351\) 36.0000 1.92154
\(352\) −48.0000 −2.55841
\(353\) −34.0000 −1.80964 −0.904819 0.425797i \(-0.859994\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) −66.0000 −3.50786
\(355\) 32.0000 1.69838
\(356\) 22.0000 1.16600
\(357\) −48.0000 −2.54043
\(358\) −18.0000 −0.951330
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −38.0000 −1.99724
\(363\) −75.0000 −3.93648
\(364\) 32.0000 1.67726
\(365\) 56.0000 2.93117
\(366\) −12.0000 −0.627250
\(367\) 32.0000 1.67039 0.835193 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 24.0000 1.25109
\(369\) 0 0
\(370\) 0 0
\(371\) 36.0000 1.86903
\(372\) 12.0000 0.622171
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) −48.0000 −2.48202
\(375\) 72.0000 3.71806
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) −72.0000 −3.70328
\(379\) 15.0000 0.770498 0.385249 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 56.0000 2.87274
\(381\) −21.0000 −1.07586
\(382\) 32.0000 1.63726
\(383\) −27.0000 −1.37964 −0.689818 0.723983i \(-0.742309\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(384\) 0 0
\(385\) −96.0000 −4.89261
\(386\) 26.0000 1.32337
\(387\) −48.0000 −2.43998
\(388\) 12.0000 0.609208
\(389\) −3.00000 −0.152106 −0.0760530 0.997104i \(-0.524232\pi\)
−0.0760530 + 0.997104i \(0.524232\pi\)
\(390\) 96.0000 4.86115
\(391\) 24.0000 1.21373
\(392\) 0 0
\(393\) 21.0000 1.05931
\(394\) 40.0000 2.01517
\(395\) −36.0000 −1.81136
\(396\) −72.0000 −3.61814
\(397\) 10.0000 0.501886 0.250943 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) 26.0000 1.30326
\(399\) −84.0000 −4.20526
\(400\) −44.0000 −2.20000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) −72.0000 −3.59103
\(403\) 8.00000 0.398508
\(404\) 8.00000 0.398015
\(405\) −36.0000 −1.78885
\(406\) −48.0000 −2.38220
\(407\) 0 0
\(408\) 0 0
\(409\) −31.0000 −1.53285 −0.766426 0.642333i \(-0.777967\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 0 0
\(413\) 44.0000 2.16510
\(414\) 72.0000 3.53861
\(415\) 8.00000 0.392705
\(416\) −32.0000 −1.56893
\(417\) −12.0000 −0.587643
\(418\) −84.0000 −4.10857
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) −96.0000 −4.68432
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 24.0000 1.16830
\(423\) −54.0000 −2.62557
\(424\) 0 0
\(425\) −44.0000 −2.13431
\(426\) −48.0000 −2.32561
\(427\) 8.00000 0.387147
\(428\) 24.0000 1.16008
\(429\) −72.0000 −3.47619
\(430\) −64.0000 −3.08635
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 36.0000 1.73205
\(433\) 12.0000 0.576683 0.288342 0.957528i \(-0.406896\pi\)
0.288342 + 0.957528i \(0.406896\pi\)
\(434\) −16.0000 −0.768025
\(435\) −72.0000 −3.45214
\(436\) 14.0000 0.670478
\(437\) 42.0000 2.00913
\(438\) −84.0000 −4.01368
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 54.0000 2.57143
\(442\) −32.0000 −1.52208
\(443\) −32.0000 −1.52037 −0.760183 0.649709i \(-0.774891\pi\)
−0.760183 + 0.649709i \(0.774891\pi\)
\(444\) 0 0
\(445\) −44.0000 −2.08580
\(446\) −42.0000 −1.98876
\(447\) −18.0000 −0.851371
\(448\) 32.0000 1.51186
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) −132.000 −6.22254
\(451\) 0 0
\(452\) −10.0000 −0.470360
\(453\) −27.0000 −1.26857
\(454\) 52.0000 2.44048
\(455\) −64.0000 −3.00037
\(456\) 0 0
\(457\) −21.0000 −0.982339 −0.491169 0.871064i \(-0.663430\pi\)
−0.491169 + 0.871064i \(0.663430\pi\)
\(458\) 20.0000 0.934539
\(459\) 36.0000 1.68034
\(460\) 48.0000 2.23801
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 144.000 6.69949
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 24.0000 1.11417
\(465\) −24.0000 −1.11297
\(466\) −30.0000 −1.38972
\(467\) −11.0000 −0.509019 −0.254510 0.967070i \(-0.581914\pi\)
−0.254510 + 0.967070i \(0.581914\pi\)
\(468\) −48.0000 −2.21880
\(469\) 48.0000 2.21643
\(470\) −72.0000 −3.32111
\(471\) −12.0000 −0.552931
\(472\) 0 0
\(473\) 48.0000 2.20704
\(474\) 54.0000 2.48030
\(475\) −77.0000 −3.53300
\(476\) 32.0000 1.46672
\(477\) −54.0000 −2.47249
\(478\) 30.0000 1.37217
\(479\) −26.0000 −1.18797 −0.593985 0.804476i \(-0.702446\pi\)
−0.593985 + 0.804476i \(0.702446\pi\)
\(480\) 96.0000 4.38178
\(481\) 0 0
\(482\) 58.0000 2.64183
\(483\) −72.0000 −3.27611
\(484\) 50.0000 2.27273
\(485\) −24.0000 −1.08978
\(486\) 0 0
\(487\) −24.0000 −1.08754 −0.543772 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) 0 0
\(489\) 12.0000 0.542659
\(490\) 72.0000 3.25263
\(491\) 40.0000 1.80517 0.902587 0.430507i \(-0.141665\pi\)
0.902587 + 0.430507i \(0.141665\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) −56.0000 −2.51956
\(495\) 144.000 6.47232
\(496\) 8.00000 0.359211
\(497\) 32.0000 1.43540
\(498\) −12.0000 −0.537733
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) −48.0000 −2.14663
\(501\) 24.0000 1.07224
\(502\) −16.0000 −0.714115
\(503\) −41.0000 −1.82810 −0.914050 0.405602i \(-0.867062\pi\)
−0.914050 + 0.405602i \(0.867062\pi\)
\(504\) 0 0
\(505\) −16.0000 −0.711991
\(506\) −72.0000 −3.20079
\(507\) −9.00000 −0.399704
\(508\) 14.0000 0.621150
\(509\) 42.0000 1.86162 0.930809 0.365507i \(-0.119104\pi\)
0.930809 + 0.365507i \(0.119104\pi\)
\(510\) 96.0000 4.25095
\(511\) 56.0000 2.47729
\(512\) −32.0000 −1.41421
\(513\) 63.0000 2.78152
\(514\) 36.0000 1.58789
\(515\) 0 0
\(516\) 48.0000 2.11308
\(517\) 54.0000 2.37492
\(518\) 0 0
\(519\) 27.0000 1.18517
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 72.0000 3.15135
\(523\) 6.00000 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) −14.0000 −0.611593
\(525\) 132.000 5.76095
\(526\) −4.00000 −0.174408
\(527\) 8.00000 0.348485
\(528\) −72.0000 −3.13340
\(529\) 13.0000 0.565217
\(530\) −72.0000 −3.12748
\(531\) −66.0000 −2.86416
\(532\) 56.0000 2.42791
\(533\) 0 0
\(534\) 66.0000 2.85610
\(535\) −48.0000 −2.07522
\(536\) 0 0
\(537\) −27.0000 −1.16514
\(538\) 28.0000 1.20717
\(539\) −54.0000 −2.32594
\(540\) 72.0000 3.09839
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) −36.0000 −1.54633
\(543\) −57.0000 −2.44610
\(544\) −32.0000 −1.37199
\(545\) −28.0000 −1.19939
\(546\) 96.0000 4.10842
\(547\) 9.00000 0.384812 0.192406 0.981315i \(-0.438371\pi\)
0.192406 + 0.981315i \(0.438371\pi\)
\(548\) −6.00000 −0.256307
\(549\) −12.0000 −0.512148
\(550\) 132.000 5.62850
\(551\) 42.0000 1.78926
\(552\) 0 0
\(553\) −36.0000 −1.53088
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 17.0000 0.720313 0.360157 0.932892i \(-0.382723\pi\)
0.360157 + 0.932892i \(0.382723\pi\)
\(558\) 24.0000 1.01600
\(559\) 32.0000 1.35346
\(560\) −64.0000 −2.70449
\(561\) −72.0000 −3.03984
\(562\) −48.0000 −2.02476
\(563\) −33.0000 −1.39078 −0.695392 0.718631i \(-0.744769\pi\)
−0.695392 + 0.718631i \(0.744769\pi\)
\(564\) 54.0000 2.27381
\(565\) 20.0000 0.841406
\(566\) 32.0000 1.34506
\(567\) −36.0000 −1.51186
\(568\) 0 0
\(569\) 2.00000 0.0838444 0.0419222 0.999121i \(-0.486652\pi\)
0.0419222 + 0.999121i \(0.486652\pi\)
\(570\) 168.000 7.03675
\(571\) −31.0000 −1.29731 −0.648655 0.761083i \(-0.724668\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 48.0000 2.00698
\(573\) 48.0000 2.00523
\(574\) 0 0
\(575\) −66.0000 −2.75239
\(576\) −48.0000 −2.00000
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 2.00000 0.0831890
\(579\) 39.0000 1.62078
\(580\) 48.0000 1.99309
\(581\) 8.00000 0.331896
\(582\) 36.0000 1.49225
\(583\) 54.0000 2.23645
\(584\) 0 0
\(585\) 96.0000 3.96911
\(586\) −18.0000 −0.743573
\(587\) −26.0000 −1.07313 −0.536567 0.843857i \(-0.680279\pi\)
−0.536567 + 0.843857i \(0.680279\pi\)
\(588\) −54.0000 −2.22692
\(589\) 14.0000 0.576860
\(590\) −88.0000 −3.62290
\(591\) 60.0000 2.46807
\(592\) 0 0
\(593\) 5.00000 0.205325 0.102663 0.994716i \(-0.467264\pi\)
0.102663 + 0.994716i \(0.467264\pi\)
\(594\) −108.000 −4.43129
\(595\) −64.0000 −2.62374
\(596\) 12.0000 0.491539
\(597\) 39.0000 1.59616
\(598\) −48.0000 −1.96287
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −64.0000 −2.60845
\(603\) −72.0000 −2.93207
\(604\) 18.0000 0.732410
\(605\) −100.000 −4.06558
\(606\) 24.0000 0.974933
\(607\) 34.0000 1.38002 0.690009 0.723801i \(-0.257607\pi\)
0.690009 + 0.723801i \(0.257607\pi\)
\(608\) −56.0000 −2.27110
\(609\) −72.0000 −2.91759
\(610\) −16.0000 −0.647821
\(611\) 36.0000 1.45640
\(612\) −48.0000 −1.94029
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 34.0000 1.37213
\(615\) 0 0
\(616\) 0 0
\(617\) −4.00000 −0.161034 −0.0805170 0.996753i \(-0.525657\pi\)
−0.0805170 + 0.996753i \(0.525657\pi\)
\(618\) 0 0
\(619\) −3.00000 −0.120580 −0.0602901 0.998181i \(-0.519203\pi\)
−0.0602901 + 0.998181i \(0.519203\pi\)
\(620\) 16.0000 0.642575
\(621\) 54.0000 2.16695
\(622\) 64.0000 2.56617
\(623\) −44.0000 −1.76282
\(624\) −48.0000 −1.92154
\(625\) 41.0000 1.64000
\(626\) 28.0000 1.11911
\(627\) −126.000 −5.03196
\(628\) 8.00000 0.319235
\(629\) 0 0
\(630\) −192.000 −7.64946
\(631\) 47.0000 1.87104 0.935520 0.353273i \(-0.114931\pi\)
0.935520 + 0.353273i \(0.114931\pi\)
\(632\) 0 0
\(633\) 36.0000 1.43087
\(634\) 44.0000 1.74746
\(635\) −28.0000 −1.11115
\(636\) 54.0000 2.14124
\(637\) −36.0000 −1.42637
\(638\) −72.0000 −2.85051
\(639\) −48.0000 −1.89885
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 72.0000 2.84161
\(643\) −12.0000 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 48.0000 1.89146
\(645\) −96.0000 −3.78000
\(646\) −56.0000 −2.20329
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 0 0
\(649\) 66.0000 2.59073
\(650\) 88.0000 3.45164
\(651\) −24.0000 −0.940634
\(652\) −8.00000 −0.313304
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 42.0000 1.64233
\(655\) 28.0000 1.09405
\(656\) 0 0
\(657\) −84.0000 −3.27715
\(658\) −72.0000 −2.80685
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) −144.000 −5.60519
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) 8.00000 0.310929
\(663\) −48.0000 −1.86417
\(664\) 0 0
\(665\) −112.000 −4.34317
\(666\) 0 0
\(667\) 36.0000 1.39393
\(668\) −16.0000 −0.619059
\(669\) −63.0000 −2.43572
\(670\) −96.0000 −3.70880
\(671\) 12.0000 0.463255
\(672\) 96.0000 3.70328
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) −16.0000 −0.616297
\(675\) −99.0000 −3.81051
\(676\) 6.00000 0.230769
\(677\) −48.0000 −1.84479 −0.922395 0.386248i \(-0.873771\pi\)
−0.922395 + 0.386248i \(0.873771\pi\)
\(678\) −30.0000 −1.15214
\(679\) −24.0000 −0.921035
\(680\) 0 0
\(681\) 78.0000 2.98897
\(682\) −24.0000 −0.919007
\(683\) −45.0000 −1.72188 −0.860939 0.508709i \(-0.830123\pi\)
−0.860939 + 0.508709i \(0.830123\pi\)
\(684\) −84.0000 −3.21182
\(685\) 12.0000 0.458496
\(686\) 16.0000 0.610883
\(687\) 30.0000 1.14457
\(688\) 32.0000 1.21999
\(689\) 36.0000 1.37149
\(690\) 144.000 5.48199
\(691\) 2.00000 0.0760836 0.0380418 0.999276i \(-0.487888\pi\)
0.0380418 + 0.999276i \(0.487888\pi\)
\(692\) −18.0000 −0.684257
\(693\) 144.000 5.47011
\(694\) −24.0000 −0.911028
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 0 0
\(698\) 70.0000 2.64954
\(699\) −45.0000 −1.70206
\(700\) −88.0000 −3.32609
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) −72.0000 −2.71746
\(703\) 0 0
\(704\) 48.0000 1.80907
\(705\) −108.000 −4.06752
\(706\) 68.0000 2.55921
\(707\) −16.0000 −0.601742
\(708\) 66.0000 2.48043
\(709\) −8.00000 −0.300446 −0.150223 0.988652i \(-0.547999\pi\)
−0.150223 + 0.988652i \(0.547999\pi\)
\(710\) −64.0000 −2.40188
\(711\) 54.0000 2.02516
\(712\) 0 0
\(713\) 12.0000 0.449404
\(714\) 96.0000 3.59271
\(715\) −96.0000 −3.59020
\(716\) 18.0000 0.672692
\(717\) 45.0000 1.68056
\(718\) 30.0000 1.11959
\(719\) −10.0000 −0.372937 −0.186469 0.982461i \(-0.559704\pi\)
−0.186469 + 0.982461i \(0.559704\pi\)
\(720\) 96.0000 3.57771
\(721\) 0 0
\(722\) −60.0000 −2.23297
\(723\) 87.0000 3.23556
\(724\) 38.0000 1.41226
\(725\) −66.0000 −2.45118
\(726\) 150.000 5.56702
\(727\) −33.0000 −1.22390 −0.611951 0.790896i \(-0.709615\pi\)
−0.611951 + 0.790896i \(0.709615\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −112.000 −4.14531
\(731\) 32.0000 1.18356
\(732\) 12.0000 0.443533
\(733\) −18.0000 −0.664845 −0.332423 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) −64.0000 −2.36228
\(735\) 108.000 3.98364
\(736\) −48.0000 −1.76930
\(737\) 72.0000 2.65215
\(738\) 0 0
\(739\) 44.0000 1.61857 0.809283 0.587419i \(-0.199856\pi\)
0.809283 + 0.587419i \(0.199856\pi\)
\(740\) 0 0
\(741\) −84.0000 −3.08582
\(742\) −72.0000 −2.64320
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) −24.0000 −0.879292
\(746\) 0 0
\(747\) −12.0000 −0.439057
\(748\) 48.0000 1.75505
\(749\) −48.0000 −1.75388
\(750\) −144.000 −5.25814
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) 36.0000 1.31278
\(753\) −24.0000 −0.874609
\(754\) −48.0000 −1.74806
\(755\) −36.0000 −1.31017
\(756\) 72.0000 2.61861
\(757\) −33.0000 −1.19941 −0.599703 0.800223i \(-0.704714\pi\)
−0.599703 + 0.800223i \(0.704714\pi\)
\(758\) −30.0000 −1.08965
\(759\) −108.000 −3.92015
\(760\) 0 0
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 42.0000 1.52150
\(763\) −28.0000 −1.01367
\(764\) −32.0000 −1.15772
\(765\) 96.0000 3.47089
\(766\) 54.0000 1.95110
\(767\) 44.0000 1.58875
\(768\) −48.0000 −1.73205
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 192.000 6.91920
\(771\) 54.0000 1.94476
\(772\) −26.0000 −0.935760
\(773\) 3.00000 0.107903 0.0539513 0.998544i \(-0.482818\pi\)
0.0539513 + 0.998544i \(0.482818\pi\)
\(774\) 96.0000 3.45065
\(775\) −22.0000 −0.790263
\(776\) 0 0
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) −96.0000 −3.43735
\(781\) 48.0000 1.71758
\(782\) −48.0000 −1.71648
\(783\) 54.0000 1.92980
\(784\) −36.0000 −1.28571
\(785\) −16.0000 −0.571064
\(786\) −42.0000 −1.49809
\(787\) −1.00000 −0.0356462 −0.0178231 0.999841i \(-0.505674\pi\)
−0.0178231 + 0.999841i \(0.505674\pi\)
\(788\) −40.0000 −1.42494
\(789\) −6.00000 −0.213606
\(790\) 72.0000 2.56165
\(791\) 20.0000 0.711118
\(792\) 0 0
\(793\) 8.00000 0.284088
\(794\) −20.0000 −0.709773
\(795\) −108.000 −3.83037
\(796\) −26.0000 −0.921546
\(797\) 39.0000 1.38145 0.690725 0.723117i \(-0.257291\pi\)
0.690725 + 0.723117i \(0.257291\pi\)
\(798\) 168.000 5.94714
\(799\) 36.0000 1.27359
\(800\) 88.0000 3.11127
\(801\) 66.0000 2.33200
\(802\) 36.0000 1.27120
\(803\) 84.0000 2.96430
\(804\) 72.0000 2.53924
\(805\) −96.0000 −3.38356
\(806\) −16.0000 −0.563576
\(807\) 42.0000 1.47847
\(808\) 0 0
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) 72.0000 2.52982
\(811\) 16.0000 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) 48.0000 1.68447
\(813\) −54.0000 −1.89386
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) −48.0000 −1.68034
\(817\) 56.0000 1.95919
\(818\) 62.0000 2.16778
\(819\) 96.0000 3.35451
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) −18.0000 −0.627822
\(823\) −31.0000 −1.08059 −0.540296 0.841475i \(-0.681688\pi\)
−0.540296 + 0.841475i \(0.681688\pi\)
\(824\) 0 0
\(825\) 198.000 6.89348
\(826\) −88.0000 −3.06191
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) −72.0000 −2.50217
\(829\) −40.0000 −1.38926 −0.694629 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) −16.0000 −0.555368
\(831\) 39.0000 1.35290
\(832\) 32.0000 1.10940
\(833\) −36.0000 −1.24733
\(834\) 24.0000 0.831052
\(835\) 32.0000 1.10741
\(836\) 84.0000 2.90520
\(837\) 18.0000 0.622171
\(838\) 40.0000 1.38178
\(839\) 15.0000 0.517858 0.258929 0.965896i \(-0.416631\pi\)
0.258929 + 0.965896i \(0.416631\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −20.0000 −0.689246
\(843\) −72.0000 −2.47981
\(844\) −24.0000 −0.826114
\(845\) −12.0000 −0.412813
\(846\) 108.000 3.71312
\(847\) −100.000 −3.43604
\(848\) 36.0000 1.23625
\(849\) 48.0000 1.64736
\(850\) 88.0000 3.01838
\(851\) 0 0
\(852\) 48.0000 1.64445
\(853\) 15.0000 0.513590 0.256795 0.966466i \(-0.417333\pi\)
0.256795 + 0.966466i \(0.417333\pi\)
\(854\) −16.0000 −0.547509
\(855\) 168.000 5.74548
\(856\) 0 0
\(857\) −22.0000 −0.751506 −0.375753 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) 144.000 4.91608
\(859\) −41.0000 −1.39890 −0.699451 0.714681i \(-0.746572\pi\)
−0.699451 + 0.714681i \(0.746572\pi\)
\(860\) 64.0000 2.18238
\(861\) 0 0
\(862\) 60.0000 2.04361
\(863\) 21.0000 0.714848 0.357424 0.933942i \(-0.383655\pi\)
0.357424 + 0.933942i \(0.383655\pi\)
\(864\) −72.0000 −2.44949
\(865\) 36.0000 1.22404
\(866\) −24.0000 −0.815553
\(867\) 3.00000 0.101885
\(868\) 16.0000 0.543075
\(869\) −54.0000 −1.83182
\(870\) 144.000 4.88206
\(871\) 48.0000 1.62642
\(872\) 0 0
\(873\) 36.0000 1.21842
\(874\) −84.0000 −2.84134
\(875\) 96.0000 3.24539
\(876\) 84.0000 2.83810
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) −20.0000 −0.674967
\(879\) −27.0000 −0.910687
\(880\) −96.0000 −3.23616
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) −108.000 −3.63655
\(883\) −22.0000 −0.740359 −0.370179 0.928960i \(-0.620704\pi\)
−0.370179 + 0.928960i \(0.620704\pi\)
\(884\) 32.0000 1.07628
\(885\) −132.000 −4.43713
\(886\) 64.0000 2.15012
\(887\) 1.00000 0.0335767 0.0167884 0.999859i \(-0.494656\pi\)
0.0167884 + 0.999859i \(0.494656\pi\)
\(888\) 0 0
\(889\) −28.0000 −0.939090
\(890\) 88.0000 2.94977
\(891\) −54.0000 −1.80907
\(892\) 42.0000 1.40626
\(893\) 63.0000 2.10821
\(894\) 36.0000 1.20402
\(895\) −36.0000 −1.20335
\(896\) 0 0
\(897\) −72.0000 −2.40401
\(898\) −28.0000 −0.934372
\(899\) 12.0000 0.400222
\(900\) 132.000 4.40000
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) −96.0000 −3.19468
\(904\) 0 0
\(905\) −76.0000 −2.52633
\(906\) 54.0000 1.79403
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) −52.0000 −1.72568
\(909\) 24.0000 0.796030
\(910\) 128.000 4.24316
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) −84.0000 −2.78152
\(913\) 12.0000 0.397142
\(914\) 42.0000 1.38924
\(915\) −24.0000 −0.793416
\(916\) −20.0000 −0.660819
\(917\) 28.0000 0.924641
\(918\) −72.0000 −2.37635
\(919\) −25.0000 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 0 0
\(921\) 51.0000 1.68051
\(922\) 12.0000 0.395199
\(923\) 32.0000 1.05329
\(924\) −144.000 −4.73725
\(925\) 0 0
\(926\) −32.0000 −1.05159
\(927\) 0 0
\(928\) −48.0000 −1.57568
\(929\) −28.0000 −0.918650 −0.459325 0.888268i \(-0.651909\pi\)
−0.459325 + 0.888268i \(0.651909\pi\)
\(930\) 48.0000 1.57398
\(931\) −63.0000 −2.06474
\(932\) 30.0000 0.982683
\(933\) 96.0000 3.14290
\(934\) 22.0000 0.719862
\(935\) −96.0000 −3.13954
\(936\) 0 0
\(937\) 37.0000 1.20874 0.604369 0.796705i \(-0.293425\pi\)
0.604369 + 0.796705i \(0.293425\pi\)
\(938\) −96.0000 −3.13451
\(939\) 42.0000 1.37062
\(940\) 72.0000 2.34838
\(941\) 14.0000 0.456387 0.228193 0.973616i \(-0.426718\pi\)
0.228193 + 0.973616i \(0.426718\pi\)
\(942\) 24.0000 0.781962
\(943\) 0 0
\(944\) 44.0000 1.43208
\(945\) −144.000 −4.68432
\(946\) −96.0000 −3.12123
\(947\) −17.0000 −0.552426 −0.276213 0.961096i \(-0.589079\pi\)
−0.276213 + 0.961096i \(0.589079\pi\)
\(948\) −54.0000 −1.75384
\(949\) 56.0000 1.81784
\(950\) 154.000 4.99642
\(951\) 66.0000 2.14020
\(952\) 0 0
\(953\) 48.0000 1.55487 0.777436 0.628962i \(-0.216520\pi\)
0.777436 + 0.628962i \(0.216520\pi\)
\(954\) 108.000 3.49663
\(955\) 64.0000 2.07099
\(956\) −30.0000 −0.970269
\(957\) −108.000 −3.49114
\(958\) 52.0000 1.68004
\(959\) 12.0000 0.387500
\(960\) −96.0000 −3.09839
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 72.0000 2.32017
\(964\) −58.0000 −1.86805
\(965\) 52.0000 1.67394
\(966\) 144.000 4.63312
\(967\) −23.0000 −0.739630 −0.369815 0.929105i \(-0.620579\pi\)
−0.369815 + 0.929105i \(0.620579\pi\)
\(968\) 0 0
\(969\) −84.0000 −2.69847
\(970\) 48.0000 1.54119
\(971\) −2.00000 −0.0641831 −0.0320915 0.999485i \(-0.510217\pi\)
−0.0320915 + 0.999485i \(0.510217\pi\)
\(972\) 0 0
\(973\) −16.0000 −0.512936
\(974\) 48.0000 1.53802
\(975\) 132.000 4.22738
\(976\) 8.00000 0.256074
\(977\) 10.0000 0.319928 0.159964 0.987123i \(-0.448862\pi\)
0.159964 + 0.987123i \(0.448862\pi\)
\(978\) −24.0000 −0.767435
\(979\) −66.0000 −2.10937
\(980\) −72.0000 −2.29996
\(981\) 42.0000 1.34096
\(982\) −80.0000 −2.55290
\(983\) 17.0000 0.542216 0.271108 0.962549i \(-0.412610\pi\)
0.271108 + 0.962549i \(0.412610\pi\)
\(984\) 0 0
\(985\) 80.0000 2.54901
\(986\) −48.0000 −1.52863
\(987\) −108.000 −3.43768
\(988\) 56.0000 1.78160
\(989\) 48.0000 1.52631
\(990\) −288.000 −9.15324
\(991\) −13.0000 −0.412959 −0.206479 0.978451i \(-0.566201\pi\)
−0.206479 + 0.978451i \(0.566201\pi\)
\(992\) −16.0000 −0.508001
\(993\) 12.0000 0.380808
\(994\) −64.0000 −2.02996
\(995\) 52.0000 1.64851
\(996\) 12.0000 0.380235
\(997\) 49.0000 1.55185 0.775923 0.630828i \(-0.217285\pi\)
0.775923 + 0.630828i \(0.217285\pi\)
\(998\) −16.0000 −0.506471
\(999\) 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 \(a_p\))