Properties

Label 8001.2.a.z.1.19
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.903971 q^{2}\) \(-1.18284 q^{4}\) \(-2.97865 q^{5}\) \(-1.00000 q^{7}\) \(-2.87719 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.903971 q^{2}\) \(-1.18284 q^{4}\) \(-2.97865 q^{5}\) \(-1.00000 q^{7}\) \(-2.87719 q^{8}\) \(-2.69261 q^{10}\) \(-0.876539 q^{11}\) \(-1.42672 q^{13}\) \(-0.903971 q^{14}\) \(-0.235226 q^{16}\) \(+0.579876 q^{17}\) \(+7.77454 q^{19}\) \(+3.52326 q^{20}\) \(-0.792366 q^{22}\) \(+3.51820 q^{23}\) \(+3.87236 q^{25}\) \(-1.28972 q^{26}\) \(+1.18284 q^{28}\) \(-1.75016 q^{29}\) \(-5.47829 q^{31}\) \(+5.54175 q^{32}\) \(+0.524191 q^{34}\) \(+2.97865 q^{35}\) \(-8.19490 q^{37}\) \(+7.02796 q^{38}\) \(+8.57015 q^{40}\) \(+5.68670 q^{41}\) \(+7.37898 q^{43}\) \(+1.03680 q^{44}\) \(+3.18035 q^{46}\) \(+11.3105 q^{47}\) \(+1.00000 q^{49}\) \(+3.50050 q^{50}\) \(+1.68758 q^{52}\) \(+7.36292 q^{53}\) \(+2.61090 q^{55}\) \(+2.87719 q^{56}\) \(-1.58209 q^{58}\) \(+8.42438 q^{59}\) \(-14.0554 q^{61}\) \(-4.95221 q^{62}\) \(+5.48003 q^{64}\) \(+4.24971 q^{65}\) \(+1.17313 q^{67}\) \(-0.685899 q^{68}\) \(+2.69261 q^{70}\) \(-10.2426 q^{71}\) \(+11.1051 q^{73}\) \(-7.40795 q^{74}\) \(-9.19601 q^{76}\) \(+0.876539 q^{77}\) \(-1.45557 q^{79}\) \(+0.700655 q^{80}\) \(+5.14061 q^{82}\) \(-17.1757 q^{83}\) \(-1.72725 q^{85}\) \(+6.67039 q^{86}\) \(+2.52197 q^{88}\) \(-0.702467 q^{89}\) \(+1.42672 q^{91}\) \(-4.16145 q^{92}\) \(+10.2244 q^{94}\) \(-23.1576 q^{95}\) \(-17.4791 q^{97}\) \(+0.903971 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.903971 0.639204 0.319602 0.947552i \(-0.396451\pi\)
0.319602 + 0.947552i \(0.396451\pi\)
\(3\) 0 0
\(4\) −1.18284 −0.591418
\(5\) −2.97865 −1.33209 −0.666046 0.745910i \(-0.732015\pi\)
−0.666046 + 0.745910i \(0.732015\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −2.87719 −1.01724
\(9\) 0 0
\(10\) −2.69261 −0.851479
\(11\) −0.876539 −0.264286 −0.132143 0.991231i \(-0.542186\pi\)
−0.132143 + 0.991231i \(0.542186\pi\)
\(12\) 0 0
\(13\) −1.42672 −0.395701 −0.197851 0.980232i \(-0.563396\pi\)
−0.197851 + 0.980232i \(0.563396\pi\)
\(14\) −0.903971 −0.241596
\(15\) 0 0
\(16\) −0.235226 −0.0588064
\(17\) 0.579876 0.140641 0.0703203 0.997524i \(-0.477598\pi\)
0.0703203 + 0.997524i \(0.477598\pi\)
\(18\) 0 0
\(19\) 7.77454 1.78360 0.891801 0.452427i \(-0.149442\pi\)
0.891801 + 0.452427i \(0.149442\pi\)
\(20\) 3.52326 0.787824
\(21\) 0 0
\(22\) −0.792366 −0.168933
\(23\) 3.51820 0.733595 0.366798 0.930301i \(-0.380454\pi\)
0.366798 + 0.930301i \(0.380454\pi\)
\(24\) 0 0
\(25\) 3.87236 0.774471
\(26\) −1.28972 −0.252934
\(27\) 0 0
\(28\) 1.18284 0.223535
\(29\) −1.75016 −0.324997 −0.162498 0.986709i \(-0.551955\pi\)
−0.162498 + 0.986709i \(0.551955\pi\)
\(30\) 0 0
\(31\) −5.47829 −0.983929 −0.491965 0.870615i \(-0.663721\pi\)
−0.491965 + 0.870615i \(0.663721\pi\)
\(32\) 5.54175 0.979652
\(33\) 0 0
\(34\) 0.524191 0.0898981
\(35\) 2.97865 0.503484
\(36\) 0 0
\(37\) −8.19490 −1.34723 −0.673617 0.739081i \(-0.735260\pi\)
−0.673617 + 0.739081i \(0.735260\pi\)
\(38\) 7.02796 1.14009
\(39\) 0 0
\(40\) 8.57015 1.35506
\(41\) 5.68670 0.888114 0.444057 0.895999i \(-0.353539\pi\)
0.444057 + 0.895999i \(0.353539\pi\)
\(42\) 0 0
\(43\) 7.37898 1.12528 0.562642 0.826701i \(-0.309785\pi\)
0.562642 + 0.826701i \(0.309785\pi\)
\(44\) 1.03680 0.156304
\(45\) 0 0
\(46\) 3.18035 0.468917
\(47\) 11.3105 1.64980 0.824902 0.565275i \(-0.191230\pi\)
0.824902 + 0.565275i \(0.191230\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 3.50050 0.495045
\(51\) 0 0
\(52\) 1.68758 0.234025
\(53\) 7.36292 1.01138 0.505688 0.862717i \(-0.331239\pi\)
0.505688 + 0.862717i \(0.331239\pi\)
\(54\) 0 0
\(55\) 2.61090 0.352054
\(56\) 2.87719 0.384481
\(57\) 0 0
\(58\) −1.58209 −0.207739
\(59\) 8.42438 1.09676 0.548380 0.836229i \(-0.315245\pi\)
0.548380 + 0.836229i \(0.315245\pi\)
\(60\) 0 0
\(61\) −14.0554 −1.79961 −0.899803 0.436296i \(-0.856290\pi\)
−0.899803 + 0.436296i \(0.856290\pi\)
\(62\) −4.95221 −0.628932
\(63\) 0 0
\(64\) 5.48003 0.685004
\(65\) 4.24971 0.527111
\(66\) 0 0
\(67\) 1.17313 0.143320 0.0716602 0.997429i \(-0.477170\pi\)
0.0716602 + 0.997429i \(0.477170\pi\)
\(68\) −0.685899 −0.0831775
\(69\) 0 0
\(70\) 2.69261 0.321829
\(71\) −10.2426 −1.21558 −0.607789 0.794098i \(-0.707944\pi\)
−0.607789 + 0.794098i \(0.707944\pi\)
\(72\) 0 0
\(73\) 11.1051 1.29975 0.649874 0.760042i \(-0.274821\pi\)
0.649874 + 0.760042i \(0.274821\pi\)
\(74\) −7.40795 −0.861157
\(75\) 0 0
\(76\) −9.19601 −1.05485
\(77\) 0.876539 0.0998909
\(78\) 0 0
\(79\) −1.45557 −0.163764 −0.0818822 0.996642i \(-0.526093\pi\)
−0.0818822 + 0.996642i \(0.526093\pi\)
\(80\) 0.700655 0.0783356
\(81\) 0 0
\(82\) 5.14061 0.567686
\(83\) −17.1757 −1.88528 −0.942641 0.333807i \(-0.891667\pi\)
−0.942641 + 0.333807i \(0.891667\pi\)
\(84\) 0 0
\(85\) −1.72725 −0.187346
\(86\) 6.67039 0.719286
\(87\) 0 0
\(88\) 2.52197 0.268843
\(89\) −0.702467 −0.0744613 −0.0372307 0.999307i \(-0.511854\pi\)
−0.0372307 + 0.999307i \(0.511854\pi\)
\(90\) 0 0
\(91\) 1.42672 0.149561
\(92\) −4.16145 −0.433862
\(93\) 0 0
\(94\) 10.2244 1.05456
\(95\) −23.1576 −2.37592
\(96\) 0 0
\(97\) −17.4791 −1.77474 −0.887368 0.461062i \(-0.847469\pi\)
−0.887368 + 0.461062i \(0.847469\pi\)
\(98\) 0.903971 0.0913149
\(99\) 0 0
\(100\) −4.58036 −0.458036
\(101\) −3.51085 −0.349343 −0.174671 0.984627i \(-0.555886\pi\)
−0.174671 + 0.984627i \(0.555886\pi\)
\(102\) 0 0
\(103\) −5.78567 −0.570079 −0.285039 0.958516i \(-0.592007\pi\)
−0.285039 + 0.958516i \(0.592007\pi\)
\(104\) 4.10495 0.402524
\(105\) 0 0
\(106\) 6.65587 0.646475
\(107\) 13.8595 1.33985 0.669925 0.742428i \(-0.266326\pi\)
0.669925 + 0.742428i \(0.266326\pi\)
\(108\) 0 0
\(109\) −2.29482 −0.219804 −0.109902 0.993942i \(-0.535054\pi\)
−0.109902 + 0.993942i \(0.535054\pi\)
\(110\) 2.36018 0.225034
\(111\) 0 0
\(112\) 0.235226 0.0222267
\(113\) 6.62574 0.623297 0.311648 0.950198i \(-0.399119\pi\)
0.311648 + 0.950198i \(0.399119\pi\)
\(114\) 0 0
\(115\) −10.4795 −0.977217
\(116\) 2.07015 0.192209
\(117\) 0 0
\(118\) 7.61539 0.701054
\(119\) −0.579876 −0.0531572
\(120\) 0 0
\(121\) −10.2317 −0.930153
\(122\) −12.7057 −1.15032
\(123\) 0 0
\(124\) 6.47992 0.581914
\(125\) 3.35885 0.300425
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −6.12970 −0.541794
\(129\) 0 0
\(130\) 3.84161 0.336932
\(131\) 3.37363 0.294755 0.147378 0.989080i \(-0.452917\pi\)
0.147378 + 0.989080i \(0.452917\pi\)
\(132\) 0 0
\(133\) −7.77454 −0.674138
\(134\) 1.06047 0.0916110
\(135\) 0 0
\(136\) −1.66842 −0.143065
\(137\) −16.2096 −1.38488 −0.692439 0.721476i \(-0.743464\pi\)
−0.692439 + 0.721476i \(0.743464\pi\)
\(138\) 0 0
\(139\) 12.8614 1.09089 0.545445 0.838146i \(-0.316361\pi\)
0.545445 + 0.838146i \(0.316361\pi\)
\(140\) −3.52326 −0.297769
\(141\) 0 0
\(142\) −9.25906 −0.777003
\(143\) 1.25058 0.104579
\(144\) 0 0
\(145\) 5.21312 0.432926
\(146\) 10.0387 0.830805
\(147\) 0 0
\(148\) 9.69323 0.796778
\(149\) 13.9566 1.14337 0.571685 0.820473i \(-0.306290\pi\)
0.571685 + 0.820473i \(0.306290\pi\)
\(150\) 0 0
\(151\) −1.84657 −0.150272 −0.0751360 0.997173i \(-0.523939\pi\)
−0.0751360 + 0.997173i \(0.523939\pi\)
\(152\) −22.3689 −1.81435
\(153\) 0 0
\(154\) 0.792366 0.0638507
\(155\) 16.3179 1.31069
\(156\) 0 0
\(157\) 8.49539 0.678006 0.339003 0.940785i \(-0.389910\pi\)
0.339003 + 0.940785i \(0.389910\pi\)
\(158\) −1.31579 −0.104679
\(159\) 0 0
\(160\) −16.5069 −1.30499
\(161\) −3.51820 −0.277273
\(162\) 0 0
\(163\) −14.0518 −1.10062 −0.550311 0.834960i \(-0.685491\pi\)
−0.550311 + 0.834960i \(0.685491\pi\)
\(164\) −6.72644 −0.525247
\(165\) 0 0
\(166\) −15.5264 −1.20508
\(167\) 21.9372 1.69755 0.848776 0.528753i \(-0.177340\pi\)
0.848776 + 0.528753i \(0.177340\pi\)
\(168\) 0 0
\(169\) −10.9645 −0.843420
\(170\) −1.56138 −0.119753
\(171\) 0 0
\(172\) −8.72813 −0.665513
\(173\) −8.28652 −0.630013 −0.315006 0.949090i \(-0.602007\pi\)
−0.315006 + 0.949090i \(0.602007\pi\)
\(174\) 0 0
\(175\) −3.87236 −0.292723
\(176\) 0.206184 0.0155417
\(177\) 0 0
\(178\) −0.635009 −0.0475960
\(179\) −2.62195 −0.195974 −0.0979870 0.995188i \(-0.531240\pi\)
−0.0979870 + 0.995188i \(0.531240\pi\)
\(180\) 0 0
\(181\) −18.9051 −1.40520 −0.702601 0.711584i \(-0.747978\pi\)
−0.702601 + 0.711584i \(0.747978\pi\)
\(182\) 1.28972 0.0956001
\(183\) 0 0
\(184\) −10.1225 −0.746243
\(185\) 24.4097 1.79464
\(186\) 0 0
\(187\) −0.508284 −0.0371694
\(188\) −13.3785 −0.975724
\(189\) 0 0
\(190\) −20.9338 −1.51870
\(191\) 8.82348 0.638445 0.319222 0.947680i \(-0.396578\pi\)
0.319222 + 0.947680i \(0.396578\pi\)
\(192\) 0 0
\(193\) 16.4173 1.18174 0.590872 0.806765i \(-0.298784\pi\)
0.590872 + 0.806765i \(0.298784\pi\)
\(194\) −15.8006 −1.13442
\(195\) 0 0
\(196\) −1.18284 −0.0844883
\(197\) −23.4141 −1.66818 −0.834092 0.551626i \(-0.814008\pi\)
−0.834092 + 0.551626i \(0.814008\pi\)
\(198\) 0 0
\(199\) 6.84358 0.485128 0.242564 0.970135i \(-0.422011\pi\)
0.242564 + 0.970135i \(0.422011\pi\)
\(200\) −11.1415 −0.787824
\(201\) 0 0
\(202\) −3.17371 −0.223301
\(203\) 1.75016 0.122837
\(204\) 0 0
\(205\) −16.9387 −1.18305
\(206\) −5.23008 −0.364397
\(207\) 0 0
\(208\) 0.335602 0.0232698
\(209\) −6.81469 −0.471382
\(210\) 0 0
\(211\) 15.1368 1.04206 0.521029 0.853539i \(-0.325548\pi\)
0.521029 + 0.853539i \(0.325548\pi\)
\(212\) −8.70913 −0.598146
\(213\) 0 0
\(214\) 12.5286 0.856438
\(215\) −21.9794 −1.49898
\(216\) 0 0
\(217\) 5.47829 0.371890
\(218\) −2.07445 −0.140499
\(219\) 0 0
\(220\) −3.08827 −0.208211
\(221\) −0.827322 −0.0556517
\(222\) 0 0
\(223\) −13.0515 −0.873993 −0.436997 0.899463i \(-0.643958\pi\)
−0.436997 + 0.899463i \(0.643958\pi\)
\(224\) −5.54175 −0.370274
\(225\) 0 0
\(226\) 5.98947 0.398414
\(227\) −20.8243 −1.38216 −0.691078 0.722780i \(-0.742864\pi\)
−0.691078 + 0.722780i \(0.742864\pi\)
\(228\) 0 0
\(229\) −20.9369 −1.38355 −0.691776 0.722113i \(-0.743171\pi\)
−0.691776 + 0.722113i \(0.743171\pi\)
\(230\) −9.47315 −0.624641
\(231\) 0 0
\(232\) 5.03555 0.330600
\(233\) −11.8482 −0.776200 −0.388100 0.921617i \(-0.626868\pi\)
−0.388100 + 0.921617i \(0.626868\pi\)
\(234\) 0 0
\(235\) −33.6900 −2.19769
\(236\) −9.96466 −0.648644
\(237\) 0 0
\(238\) −0.524191 −0.0339783
\(239\) 8.77917 0.567877 0.283938 0.958842i \(-0.408359\pi\)
0.283938 + 0.958842i \(0.408359\pi\)
\(240\) 0 0
\(241\) −4.46764 −0.287786 −0.143893 0.989593i \(-0.545962\pi\)
−0.143893 + 0.989593i \(0.545962\pi\)
\(242\) −9.24914 −0.594557
\(243\) 0 0
\(244\) 16.6252 1.06432
\(245\) −2.97865 −0.190299
\(246\) 0 0
\(247\) −11.0921 −0.705774
\(248\) 15.7621 1.00089
\(249\) 0 0
\(250\) 3.03631 0.192033
\(251\) 23.4635 1.48101 0.740503 0.672053i \(-0.234587\pi\)
0.740503 + 0.672053i \(0.234587\pi\)
\(252\) 0 0
\(253\) −3.08384 −0.193879
\(254\) −0.903971 −0.0567202
\(255\) 0 0
\(256\) −16.5011 −1.03132
\(257\) −24.0009 −1.49714 −0.748569 0.663057i \(-0.769259\pi\)
−0.748569 + 0.663057i \(0.769259\pi\)
\(258\) 0 0
\(259\) 8.19490 0.509206
\(260\) −5.02671 −0.311743
\(261\) 0 0
\(262\) 3.04966 0.188409
\(263\) −4.99373 −0.307926 −0.153963 0.988077i \(-0.549204\pi\)
−0.153963 + 0.988077i \(0.549204\pi\)
\(264\) 0 0
\(265\) −21.9316 −1.34725
\(266\) −7.02796 −0.430912
\(267\) 0 0
\(268\) −1.38762 −0.0847623
\(269\) −12.9283 −0.788250 −0.394125 0.919057i \(-0.628952\pi\)
−0.394125 + 0.919057i \(0.628952\pi\)
\(270\) 0 0
\(271\) −23.0369 −1.39939 −0.699695 0.714441i \(-0.746681\pi\)
−0.699695 + 0.714441i \(0.746681\pi\)
\(272\) −0.136402 −0.00827057
\(273\) 0 0
\(274\) −14.6530 −0.885220
\(275\) −3.39427 −0.204682
\(276\) 0 0
\(277\) 21.4193 1.28696 0.643481 0.765462i \(-0.277490\pi\)
0.643481 + 0.765462i \(0.277490\pi\)
\(278\) 11.6263 0.697302
\(279\) 0 0
\(280\) −8.57015 −0.512164
\(281\) −9.53726 −0.568945 −0.284473 0.958684i \(-0.591818\pi\)
−0.284473 + 0.958684i \(0.591818\pi\)
\(282\) 0 0
\(283\) −15.7458 −0.935992 −0.467996 0.883731i \(-0.655024\pi\)
−0.467996 + 0.883731i \(0.655024\pi\)
\(284\) 12.1154 0.718915
\(285\) 0 0
\(286\) 1.13049 0.0668470
\(287\) −5.68670 −0.335675
\(288\) 0 0
\(289\) −16.6637 −0.980220
\(290\) 4.71251 0.276728
\(291\) 0 0
\(292\) −13.1355 −0.768695
\(293\) −30.0033 −1.75281 −0.876407 0.481572i \(-0.840066\pi\)
−0.876407 + 0.481572i \(0.840066\pi\)
\(294\) 0 0
\(295\) −25.0933 −1.46099
\(296\) 23.5783 1.37046
\(297\) 0 0
\(298\) 12.6164 0.730847
\(299\) −5.01949 −0.290285
\(300\) 0 0
\(301\) −7.37898 −0.425317
\(302\) −1.66925 −0.0960545
\(303\) 0 0
\(304\) −1.82877 −0.104887
\(305\) 41.8660 2.39724
\(306\) 0 0
\(307\) 22.2703 1.27103 0.635515 0.772088i \(-0.280788\pi\)
0.635515 + 0.772088i \(0.280788\pi\)
\(308\) −1.03680 −0.0590773
\(309\) 0 0
\(310\) 14.7509 0.837795
\(311\) 4.72911 0.268163 0.134082 0.990970i \(-0.457192\pi\)
0.134082 + 0.990970i \(0.457192\pi\)
\(312\) 0 0
\(313\) −4.61634 −0.260931 −0.130465 0.991453i \(-0.541647\pi\)
−0.130465 + 0.991453i \(0.541647\pi\)
\(314\) 7.67959 0.433384
\(315\) 0 0
\(316\) 1.72170 0.0968533
\(317\) 6.89241 0.387117 0.193558 0.981089i \(-0.437997\pi\)
0.193558 + 0.981089i \(0.437997\pi\)
\(318\) 0 0
\(319\) 1.53408 0.0858922
\(320\) −16.3231 −0.912489
\(321\) 0 0
\(322\) −3.18035 −0.177234
\(323\) 4.50827 0.250847
\(324\) 0 0
\(325\) −5.52478 −0.306459
\(326\) −12.7024 −0.703522
\(327\) 0 0
\(328\) −16.3617 −0.903426
\(329\) −11.3105 −0.623567
\(330\) 0 0
\(331\) 12.1593 0.668338 0.334169 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(332\) 20.3161 1.11499
\(333\) 0 0
\(334\) 19.8306 1.08508
\(335\) −3.49434 −0.190916
\(336\) 0 0
\(337\) 0.169189 0.00921633 0.00460817 0.999989i \(-0.498533\pi\)
0.00460817 + 0.999989i \(0.498533\pi\)
\(338\) −9.91156 −0.539118
\(339\) 0 0
\(340\) 2.04305 0.110800
\(341\) 4.80193 0.260039
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −21.2307 −1.14469
\(345\) 0 0
\(346\) −7.49078 −0.402707
\(347\) 6.13890 0.329553 0.164777 0.986331i \(-0.447310\pi\)
0.164777 + 0.986331i \(0.447310\pi\)
\(348\) 0 0
\(349\) 27.6545 1.48031 0.740157 0.672434i \(-0.234751\pi\)
0.740157 + 0.672434i \(0.234751\pi\)
\(350\) −3.50050 −0.187110
\(351\) 0 0
\(352\) −4.85756 −0.258909
\(353\) −27.7604 −1.47754 −0.738768 0.673959i \(-0.764592\pi\)
−0.738768 + 0.673959i \(0.764592\pi\)
\(354\) 0 0
\(355\) 30.5093 1.61926
\(356\) 0.830903 0.0440378
\(357\) 0 0
\(358\) −2.37017 −0.125267
\(359\) 4.10568 0.216689 0.108345 0.994113i \(-0.465445\pi\)
0.108345 + 0.994113i \(0.465445\pi\)
\(360\) 0 0
\(361\) 41.4435 2.18124
\(362\) −17.0896 −0.898211
\(363\) 0 0
\(364\) −1.68758 −0.0884531
\(365\) −33.0781 −1.73139
\(366\) 0 0
\(367\) −25.1833 −1.31456 −0.657278 0.753648i \(-0.728292\pi\)
−0.657278 + 0.753648i \(0.728292\pi\)
\(368\) −0.827571 −0.0431401
\(369\) 0 0
\(370\) 22.0657 1.14714
\(371\) −7.36292 −0.382264
\(372\) 0 0
\(373\) 25.8322 1.33754 0.668770 0.743469i \(-0.266821\pi\)
0.668770 + 0.743469i \(0.266821\pi\)
\(374\) −0.459474 −0.0237589
\(375\) 0 0
\(376\) −32.5424 −1.67825
\(377\) 2.49699 0.128602
\(378\) 0 0
\(379\) −3.13475 −0.161021 −0.0805107 0.996754i \(-0.525655\pi\)
−0.0805107 + 0.996754i \(0.525655\pi\)
\(380\) 27.3917 1.40516
\(381\) 0 0
\(382\) 7.97618 0.408097
\(383\) 29.1214 1.48804 0.744018 0.668159i \(-0.232918\pi\)
0.744018 + 0.668159i \(0.232918\pi\)
\(384\) 0 0
\(385\) −2.61090 −0.133064
\(386\) 14.8408 0.755376
\(387\) 0 0
\(388\) 20.6749 1.04961
\(389\) 0.482130 0.0244449 0.0122225 0.999925i \(-0.496109\pi\)
0.0122225 + 0.999925i \(0.496109\pi\)
\(390\) 0 0
\(391\) 2.04012 0.103173
\(392\) −2.87719 −0.145320
\(393\) 0 0
\(394\) −21.1656 −1.06631
\(395\) 4.33564 0.218150
\(396\) 0 0
\(397\) −34.2111 −1.71701 −0.858503 0.512808i \(-0.828605\pi\)
−0.858503 + 0.512808i \(0.828605\pi\)
\(398\) 6.18640 0.310096
\(399\) 0 0
\(400\) −0.910878 −0.0455439
\(401\) 15.7020 0.784123 0.392061 0.919939i \(-0.371762\pi\)
0.392061 + 0.919939i \(0.371762\pi\)
\(402\) 0 0
\(403\) 7.81599 0.389342
\(404\) 4.15276 0.206608
\(405\) 0 0
\(406\) 1.58209 0.0785180
\(407\) 7.18315 0.356056
\(408\) 0 0
\(409\) −18.6655 −0.922948 −0.461474 0.887154i \(-0.652679\pi\)
−0.461474 + 0.887154i \(0.652679\pi\)
\(410\) −15.3121 −0.756210
\(411\) 0 0
\(412\) 6.84350 0.337155
\(413\) −8.42438 −0.414537
\(414\) 0 0
\(415\) 51.1605 2.51137
\(416\) −7.90653 −0.387650
\(417\) 0 0
\(418\) −6.16028 −0.301309
\(419\) 31.6499 1.54620 0.773100 0.634284i \(-0.218705\pi\)
0.773100 + 0.634284i \(0.218705\pi\)
\(420\) 0 0
\(421\) −5.12267 −0.249664 −0.124832 0.992178i \(-0.539839\pi\)
−0.124832 + 0.992178i \(0.539839\pi\)
\(422\) 13.6832 0.666088
\(423\) 0 0
\(424\) −21.1845 −1.02881
\(425\) 2.24549 0.108922
\(426\) 0 0
\(427\) 14.0554 0.680187
\(428\) −16.3936 −0.792412
\(429\) 0 0
\(430\) −19.8687 −0.958156
\(431\) 26.8900 1.29525 0.647623 0.761961i \(-0.275763\pi\)
0.647623 + 0.761961i \(0.275763\pi\)
\(432\) 0 0
\(433\) 16.9919 0.816577 0.408289 0.912853i \(-0.366126\pi\)
0.408289 + 0.912853i \(0.366126\pi\)
\(434\) 4.95221 0.237714
\(435\) 0 0
\(436\) 2.71439 0.129996
\(437\) 27.3524 1.30844
\(438\) 0 0
\(439\) −12.5338 −0.598207 −0.299104 0.954221i \(-0.596688\pi\)
−0.299104 + 0.954221i \(0.596688\pi\)
\(440\) −7.51207 −0.358124
\(441\) 0 0
\(442\) −0.747875 −0.0355728
\(443\) −17.0518 −0.810154 −0.405077 0.914283i \(-0.632755\pi\)
−0.405077 + 0.914283i \(0.632755\pi\)
\(444\) 0 0
\(445\) 2.09240 0.0991894
\(446\) −11.7982 −0.558660
\(447\) 0 0
\(448\) −5.48003 −0.258907
\(449\) −14.3616 −0.677766 −0.338883 0.940829i \(-0.610049\pi\)
−0.338883 + 0.940829i \(0.610049\pi\)
\(450\) 0 0
\(451\) −4.98462 −0.234716
\(452\) −7.83716 −0.368629
\(453\) 0 0
\(454\) −18.8246 −0.883480
\(455\) −4.24971 −0.199229
\(456\) 0 0
\(457\) 2.47963 0.115992 0.0579960 0.998317i \(-0.481529\pi\)
0.0579960 + 0.998317i \(0.481529\pi\)
\(458\) −18.9264 −0.884372
\(459\) 0 0
\(460\) 12.3955 0.577944
\(461\) −8.87317 −0.413265 −0.206632 0.978419i \(-0.566250\pi\)
−0.206632 + 0.978419i \(0.566250\pi\)
\(462\) 0 0
\(463\) −27.1704 −1.26271 −0.631357 0.775492i \(-0.717502\pi\)
−0.631357 + 0.775492i \(0.717502\pi\)
\(464\) 0.411683 0.0191119
\(465\) 0 0
\(466\) −10.7104 −0.496150
\(467\) −6.99157 −0.323531 −0.161766 0.986829i \(-0.551719\pi\)
−0.161766 + 0.986829i \(0.551719\pi\)
\(468\) 0 0
\(469\) −1.17313 −0.0541700
\(470\) −30.4548 −1.40477
\(471\) 0 0
\(472\) −24.2386 −1.11567
\(473\) −6.46797 −0.297397
\(474\) 0 0
\(475\) 30.1058 1.38135
\(476\) 0.685899 0.0314381
\(477\) 0 0
\(478\) 7.93611 0.362989
\(479\) 19.6939 0.899837 0.449919 0.893070i \(-0.351453\pi\)
0.449919 + 0.893070i \(0.351453\pi\)
\(480\) 0 0
\(481\) 11.6918 0.533102
\(482\) −4.03862 −0.183954
\(483\) 0 0
\(484\) 12.1024 0.550109
\(485\) 52.0642 2.36411
\(486\) 0 0
\(487\) −22.9375 −1.03940 −0.519700 0.854349i \(-0.673956\pi\)
−0.519700 + 0.854349i \(0.673956\pi\)
\(488\) 40.4400 1.83063
\(489\) 0 0
\(490\) −2.69261 −0.121640
\(491\) 40.5985 1.83218 0.916092 0.400967i \(-0.131326\pi\)
0.916092 + 0.400967i \(0.131326\pi\)
\(492\) 0 0
\(493\) −1.01488 −0.0457078
\(494\) −10.0269 −0.451134
\(495\) 0 0
\(496\) 1.28863 0.0578614
\(497\) 10.2426 0.459446
\(498\) 0 0
\(499\) −15.2512 −0.682739 −0.341369 0.939929i \(-0.610891\pi\)
−0.341369 + 0.939929i \(0.610891\pi\)
\(500\) −3.97297 −0.177677
\(501\) 0 0
\(502\) 21.2104 0.946665
\(503\) −13.4918 −0.601571 −0.300786 0.953692i \(-0.597249\pi\)
−0.300786 + 0.953692i \(0.597249\pi\)
\(504\) 0 0
\(505\) 10.4576 0.465357
\(506\) −2.78770 −0.123928
\(507\) 0 0
\(508\) 1.18284 0.0524799
\(509\) −5.42460 −0.240441 −0.120221 0.992747i \(-0.538360\pi\)
−0.120221 + 0.992747i \(0.538360\pi\)
\(510\) 0 0
\(511\) −11.1051 −0.491259
\(512\) −2.65714 −0.117430
\(513\) 0 0
\(514\) −21.6962 −0.956976
\(515\) 17.2335 0.759398
\(516\) 0 0
\(517\) −9.91409 −0.436021
\(518\) 7.40795 0.325487
\(519\) 0 0
\(520\) −12.2272 −0.536199
\(521\) −31.9886 −1.40145 −0.700723 0.713433i \(-0.747139\pi\)
−0.700723 + 0.713433i \(0.747139\pi\)
\(522\) 0 0
\(523\) −42.1807 −1.84443 −0.922217 0.386672i \(-0.873625\pi\)
−0.922217 + 0.386672i \(0.873625\pi\)
\(524\) −3.99045 −0.174324
\(525\) 0 0
\(526\) −4.51418 −0.196828
\(527\) −3.17673 −0.138380
\(528\) 0 0
\(529\) −10.6223 −0.461838
\(530\) −19.8255 −0.861165
\(531\) 0 0
\(532\) 9.19601 0.398698
\(533\) −8.11334 −0.351428
\(534\) 0 0
\(535\) −41.2827 −1.78481
\(536\) −3.37531 −0.145791
\(537\) 0 0
\(538\) −11.6868 −0.503852
\(539\) −0.876539 −0.0377552
\(540\) 0 0
\(541\) −39.4783 −1.69731 −0.848653 0.528950i \(-0.822586\pi\)
−0.848653 + 0.528950i \(0.822586\pi\)
\(542\) −20.8247 −0.894496
\(543\) 0 0
\(544\) 3.21353 0.137779
\(545\) 6.83546 0.292799
\(546\) 0 0
\(547\) −6.56204 −0.280573 −0.140286 0.990111i \(-0.544802\pi\)
−0.140286 + 0.990111i \(0.544802\pi\)
\(548\) 19.1733 0.819042
\(549\) 0 0
\(550\) −3.06832 −0.130834
\(551\) −13.6067 −0.579665
\(552\) 0 0
\(553\) 1.45557 0.0618972
\(554\) 19.3624 0.822631
\(555\) 0 0
\(556\) −15.2129 −0.645173
\(557\) −8.00375 −0.339130 −0.169565 0.985519i \(-0.554236\pi\)
−0.169565 + 0.985519i \(0.554236\pi\)
\(558\) 0 0
\(559\) −10.5278 −0.445277
\(560\) −0.700655 −0.0296081
\(561\) 0 0
\(562\) −8.62141 −0.363672
\(563\) 17.6695 0.744680 0.372340 0.928096i \(-0.378556\pi\)
0.372340 + 0.928096i \(0.378556\pi\)
\(564\) 0 0
\(565\) −19.7357 −0.830289
\(566\) −14.2338 −0.598290
\(567\) 0 0
\(568\) 29.4701 1.23654
\(569\) 28.7821 1.20661 0.603305 0.797510i \(-0.293850\pi\)
0.603305 + 0.797510i \(0.293850\pi\)
\(570\) 0 0
\(571\) 12.4448 0.520798 0.260399 0.965501i \(-0.416146\pi\)
0.260399 + 0.965501i \(0.416146\pi\)
\(572\) −1.47923 −0.0618496
\(573\) 0 0
\(574\) −5.14061 −0.214565
\(575\) 13.6237 0.568148
\(576\) 0 0
\(577\) 46.9052 1.95269 0.976344 0.216222i \(-0.0693736\pi\)
0.976344 + 0.216222i \(0.0693736\pi\)
\(578\) −15.0635 −0.626561
\(579\) 0 0
\(580\) −6.16626 −0.256040
\(581\) 17.1757 0.712570
\(582\) 0 0
\(583\) −6.45389 −0.267293
\(584\) −31.9514 −1.32216
\(585\) 0 0
\(586\) −27.1221 −1.12041
\(587\) −11.4699 −0.473414 −0.236707 0.971581i \(-0.576068\pi\)
−0.236707 + 0.971581i \(0.576068\pi\)
\(588\) 0 0
\(589\) −42.5912 −1.75494
\(590\) −22.6836 −0.933869
\(591\) 0 0
\(592\) 1.92765 0.0792260
\(593\) 12.6400 0.519061 0.259530 0.965735i \(-0.416432\pi\)
0.259530 + 0.965735i \(0.416432\pi\)
\(594\) 0 0
\(595\) 1.72725 0.0708103
\(596\) −16.5084 −0.676210
\(597\) 0 0
\(598\) −4.53748 −0.185551
\(599\) 5.99492 0.244946 0.122473 0.992472i \(-0.460918\pi\)
0.122473 + 0.992472i \(0.460918\pi\)
\(600\) 0 0
\(601\) 40.2347 1.64121 0.820604 0.571498i \(-0.193637\pi\)
0.820604 + 0.571498i \(0.193637\pi\)
\(602\) −6.67039 −0.271865
\(603\) 0 0
\(604\) 2.18419 0.0888736
\(605\) 30.4766 1.23905
\(606\) 0 0
\(607\) −22.8886 −0.929020 −0.464510 0.885568i \(-0.653770\pi\)
−0.464510 + 0.885568i \(0.653770\pi\)
\(608\) 43.0846 1.74731
\(609\) 0 0
\(610\) 37.8457 1.53233
\(611\) −16.1369 −0.652830
\(612\) 0 0
\(613\) −44.0392 −1.77872 −0.889362 0.457203i \(-0.848851\pi\)
−0.889362 + 0.457203i \(0.848851\pi\)
\(614\) 20.1317 0.812448
\(615\) 0 0
\(616\) −2.52197 −0.101613
\(617\) 25.7540 1.03682 0.518408 0.855134i \(-0.326525\pi\)
0.518408 + 0.855134i \(0.326525\pi\)
\(618\) 0 0
\(619\) −1.87469 −0.0753501 −0.0376750 0.999290i \(-0.511995\pi\)
−0.0376750 + 0.999290i \(0.511995\pi\)
\(620\) −19.3014 −0.775163
\(621\) 0 0
\(622\) 4.27498 0.171411
\(623\) 0.702467 0.0281437
\(624\) 0 0
\(625\) −29.3666 −1.17467
\(626\) −4.17304 −0.166788
\(627\) 0 0
\(628\) −10.0487 −0.400985
\(629\) −4.75203 −0.189476
\(630\) 0 0
\(631\) 13.6693 0.544167 0.272083 0.962274i \(-0.412287\pi\)
0.272083 + 0.962274i \(0.412287\pi\)
\(632\) 4.18796 0.166588
\(633\) 0 0
\(634\) 6.23054 0.247446
\(635\) 2.97865 0.118204
\(636\) 0 0
\(637\) −1.42672 −0.0565288
\(638\) 1.38677 0.0549027
\(639\) 0 0
\(640\) 18.2582 0.721721
\(641\) −3.35578 −0.132545 −0.0662726 0.997802i \(-0.521111\pi\)
−0.0662726 + 0.997802i \(0.521111\pi\)
\(642\) 0 0
\(643\) 37.4676 1.47758 0.738788 0.673938i \(-0.235398\pi\)
0.738788 + 0.673938i \(0.235398\pi\)
\(644\) 4.16145 0.163984
\(645\) 0 0
\(646\) 4.07535 0.160342
\(647\) 22.3128 0.877208 0.438604 0.898680i \(-0.355473\pi\)
0.438604 + 0.898680i \(0.355473\pi\)
\(648\) 0 0
\(649\) −7.38430 −0.289859
\(650\) −4.99424 −0.195890
\(651\) 0 0
\(652\) 16.6210 0.650927
\(653\) 5.24950 0.205429 0.102714 0.994711i \(-0.467247\pi\)
0.102714 + 0.994711i \(0.467247\pi\)
\(654\) 0 0
\(655\) −10.0489 −0.392641
\(656\) −1.33766 −0.0522268
\(657\) 0 0
\(658\) −10.2244 −0.398587
\(659\) 23.8972 0.930904 0.465452 0.885073i \(-0.345892\pi\)
0.465452 + 0.885073i \(0.345892\pi\)
\(660\) 0 0
\(661\) −31.8842 −1.24015 −0.620076 0.784541i \(-0.712898\pi\)
−0.620076 + 0.784541i \(0.712898\pi\)
\(662\) 10.9917 0.427204
\(663\) 0 0
\(664\) 49.4179 1.91779
\(665\) 23.1576 0.898015
\(666\) 0 0
\(667\) −6.15741 −0.238416
\(668\) −25.9481 −1.00396
\(669\) 0 0
\(670\) −3.15878 −0.122034
\(671\) 12.3201 0.475612
\(672\) 0 0
\(673\) 29.9344 1.15389 0.576943 0.816785i \(-0.304246\pi\)
0.576943 + 0.816785i \(0.304246\pi\)
\(674\) 0.152942 0.00589112
\(675\) 0 0
\(676\) 12.9692 0.498814
\(677\) −10.5137 −0.404076 −0.202038 0.979378i \(-0.564756\pi\)
−0.202038 + 0.979378i \(0.564756\pi\)
\(678\) 0 0
\(679\) 17.4791 0.670787
\(680\) 4.96963 0.190576
\(681\) 0 0
\(682\) 4.34081 0.166218
\(683\) 3.60843 0.138073 0.0690363 0.997614i \(-0.478008\pi\)
0.0690363 + 0.997614i \(0.478008\pi\)
\(684\) 0 0
\(685\) 48.2827 1.84479
\(686\) −0.903971 −0.0345138
\(687\) 0 0
\(688\) −1.73573 −0.0661739
\(689\) −10.5048 −0.400203
\(690\) 0 0
\(691\) −29.5114 −1.12267 −0.561334 0.827589i \(-0.689712\pi\)
−0.561334 + 0.827589i \(0.689712\pi\)
\(692\) 9.80160 0.372601
\(693\) 0 0
\(694\) 5.54939 0.210652
\(695\) −38.3096 −1.45317
\(696\) 0 0
\(697\) 3.29758 0.124905
\(698\) 24.9989 0.946222
\(699\) 0 0
\(700\) 4.58036 0.173121
\(701\) 28.7494 1.08585 0.542924 0.839782i \(-0.317317\pi\)
0.542924 + 0.839782i \(0.317317\pi\)
\(702\) 0 0
\(703\) −63.7116 −2.40293
\(704\) −4.80346 −0.181037
\(705\) 0 0
\(706\) −25.0946 −0.944448
\(707\) 3.51085 0.132039
\(708\) 0 0
\(709\) −14.2070 −0.533555 −0.266777 0.963758i \(-0.585959\pi\)
−0.266777 + 0.963758i \(0.585959\pi\)
\(710\) 27.5795 1.03504
\(711\) 0 0
\(712\) 2.02113 0.0757451
\(713\) −19.2737 −0.721806
\(714\) 0 0
\(715\) −3.72503 −0.139308
\(716\) 3.10134 0.115903
\(717\) 0 0
\(718\) 3.71142 0.138509
\(719\) −49.3434 −1.84020 −0.920098 0.391688i \(-0.871891\pi\)
−0.920098 + 0.391688i \(0.871891\pi\)
\(720\) 0 0
\(721\) 5.78567 0.215470
\(722\) 37.4638 1.39426
\(723\) 0 0
\(724\) 22.3616 0.831062
\(725\) −6.77725 −0.251701
\(726\) 0 0
\(727\) −16.1812 −0.600128 −0.300064 0.953919i \(-0.597008\pi\)
−0.300064 + 0.953919i \(0.597008\pi\)
\(728\) −4.10495 −0.152140
\(729\) 0 0
\(730\) −29.9016 −1.10671
\(731\) 4.27890 0.158261
\(732\) 0 0
\(733\) 38.5103 1.42241 0.711206 0.702984i \(-0.248149\pi\)
0.711206 + 0.702984i \(0.248149\pi\)
\(734\) −22.7649 −0.840270
\(735\) 0 0
\(736\) 19.4970 0.718668
\(737\) −1.02829 −0.0378776
\(738\) 0 0
\(739\) −34.7101 −1.27683 −0.638416 0.769692i \(-0.720410\pi\)
−0.638416 + 0.769692i \(0.720410\pi\)
\(740\) −28.8727 −1.06138
\(741\) 0 0
\(742\) −6.65587 −0.244345
\(743\) −31.5544 −1.15762 −0.578810 0.815462i \(-0.696483\pi\)
−0.578810 + 0.815462i \(0.696483\pi\)
\(744\) 0 0
\(745\) −41.5719 −1.52308
\(746\) 23.3516 0.854962
\(747\) 0 0
\(748\) 0.601217 0.0219827
\(749\) −13.8595 −0.506416
\(750\) 0 0
\(751\) 19.5122 0.712011 0.356005 0.934484i \(-0.384139\pi\)
0.356005 + 0.934484i \(0.384139\pi\)
\(752\) −2.66052 −0.0970191
\(753\) 0 0
\(754\) 2.25721 0.0822027
\(755\) 5.50030 0.200176
\(756\) 0 0
\(757\) 17.6410 0.641174 0.320587 0.947219i \(-0.396120\pi\)
0.320587 + 0.947219i \(0.396120\pi\)
\(758\) −2.83372 −0.102925
\(759\) 0 0
\(760\) 66.6290 2.41689
\(761\) 14.6906 0.532534 0.266267 0.963899i \(-0.414210\pi\)
0.266267 + 0.963899i \(0.414210\pi\)
\(762\) 0 0
\(763\) 2.29482 0.0830780
\(764\) −10.4367 −0.377588
\(765\) 0 0
\(766\) 26.3249 0.951159
\(767\) −12.0192 −0.433990
\(768\) 0 0
\(769\) −28.0912 −1.01299 −0.506497 0.862242i \(-0.669060\pi\)
−0.506497 + 0.862242i \(0.669060\pi\)
\(770\) −2.36018 −0.0850550
\(771\) 0 0
\(772\) −19.4190 −0.698905
\(773\) 35.2304 1.26715 0.633574 0.773682i \(-0.281587\pi\)
0.633574 + 0.773682i \(0.281587\pi\)
\(774\) 0 0
\(775\) −21.2139 −0.762025
\(776\) 50.2908 1.80533
\(777\) 0 0
\(778\) 0.435831 0.0156253
\(779\) 44.2115 1.58404
\(780\) 0 0
\(781\) 8.97808 0.321261
\(782\) 1.84421 0.0659488
\(783\) 0 0
\(784\) −0.235226 −0.00840092
\(785\) −25.3048 −0.903167
\(786\) 0 0
\(787\) 31.1134 1.10907 0.554537 0.832159i \(-0.312896\pi\)
0.554537 + 0.832159i \(0.312896\pi\)
\(788\) 27.6950 0.986594
\(789\) 0 0
\(790\) 3.91929 0.139442
\(791\) −6.62574 −0.235584
\(792\) 0 0
\(793\) 20.0531 0.712107
\(794\) −30.9259 −1.09752
\(795\) 0 0
\(796\) −8.09483 −0.286914
\(797\) 21.6089 0.765428 0.382714 0.923867i \(-0.374989\pi\)
0.382714 + 0.923867i \(0.374989\pi\)
\(798\) 0 0
\(799\) 6.55869 0.232030
\(800\) 21.4596 0.758712
\(801\) 0 0
\(802\) 14.1942 0.501214
\(803\) −9.73402 −0.343506
\(804\) 0 0
\(805\) 10.4795 0.369353
\(806\) 7.06543 0.248869
\(807\) 0 0
\(808\) 10.1014 0.355366
\(809\) −13.2348 −0.465310 −0.232655 0.972559i \(-0.574741\pi\)
−0.232655 + 0.972559i \(0.574741\pi\)
\(810\) 0 0
\(811\) −6.57091 −0.230736 −0.115368 0.993323i \(-0.536805\pi\)
−0.115368 + 0.993323i \(0.536805\pi\)
\(812\) −2.07015 −0.0726481
\(813\) 0 0
\(814\) 6.49336 0.227592
\(815\) 41.8554 1.46613
\(816\) 0 0
\(817\) 57.3682 2.00706
\(818\) −16.8730 −0.589952
\(819\) 0 0
\(820\) 20.0357 0.699677
\(821\) 34.3943 1.20037 0.600184 0.799862i \(-0.295094\pi\)
0.600184 + 0.799862i \(0.295094\pi\)
\(822\) 0 0
\(823\) −8.93365 −0.311407 −0.155704 0.987804i \(-0.549764\pi\)
−0.155704 + 0.987804i \(0.549764\pi\)
\(824\) 16.6465 0.579908
\(825\) 0 0
\(826\) −7.61539 −0.264973
\(827\) 23.7127 0.824571 0.412285 0.911055i \(-0.364731\pi\)
0.412285 + 0.911055i \(0.364731\pi\)
\(828\) 0 0
\(829\) −47.6433 −1.65472 −0.827360 0.561672i \(-0.810158\pi\)
−0.827360 + 0.561672i \(0.810158\pi\)
\(830\) 46.2476 1.60528
\(831\) 0 0
\(832\) −7.81848 −0.271057
\(833\) 0.579876 0.0200915
\(834\) 0 0
\(835\) −65.3432 −2.26130
\(836\) 8.06066 0.278784
\(837\) 0 0
\(838\) 28.6106 0.988337
\(839\) −54.5101 −1.88190 −0.940948 0.338550i \(-0.890063\pi\)
−0.940948 + 0.338550i \(0.890063\pi\)
\(840\) 0 0
\(841\) −25.9369 −0.894377
\(842\) −4.63074 −0.159586
\(843\) 0 0
\(844\) −17.9043 −0.616293
\(845\) 32.6593 1.12351
\(846\) 0 0
\(847\) 10.2317 0.351565
\(848\) −1.73195 −0.0594754
\(849\) 0 0
\(850\) 2.02986 0.0696235
\(851\) −28.8313 −0.988324
\(852\) 0 0
\(853\) −38.9289 −1.33290 −0.666450 0.745550i \(-0.732187\pi\)
−0.666450 + 0.745550i \(0.732187\pi\)
\(854\) 12.7057 0.434778
\(855\) 0 0
\(856\) −39.8765 −1.36295
\(857\) −40.0166 −1.36694 −0.683471 0.729978i \(-0.739530\pi\)
−0.683471 + 0.729978i \(0.739530\pi\)
\(858\) 0 0
\(859\) −22.7166 −0.775079 −0.387540 0.921853i \(-0.626675\pi\)
−0.387540 + 0.921853i \(0.626675\pi\)
\(860\) 25.9980 0.886526
\(861\) 0 0
\(862\) 24.3078 0.827927
\(863\) 29.8714 1.01683 0.508417 0.861111i \(-0.330231\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(864\) 0 0
\(865\) 24.6827 0.839236
\(866\) 15.3602 0.521959
\(867\) 0 0
\(868\) −6.47992 −0.219943
\(869\) 1.27586 0.0432807
\(870\) 0 0
\(871\) −1.67373 −0.0567121
\(872\) 6.60263 0.223593
\(873\) 0 0
\(874\) 24.7258 0.836362
\(875\) −3.35885 −0.113550
\(876\) 0 0
\(877\) 16.3145 0.550901 0.275450 0.961315i \(-0.411173\pi\)
0.275450 + 0.961315i \(0.411173\pi\)
\(878\) −11.3302 −0.382377
\(879\) 0 0
\(880\) −0.614151 −0.0207030
\(881\) 17.3426 0.584286 0.292143 0.956375i \(-0.405632\pi\)
0.292143 + 0.956375i \(0.405632\pi\)
\(882\) 0 0
\(883\) 14.5659 0.490182 0.245091 0.969500i \(-0.421182\pi\)
0.245091 + 0.969500i \(0.421182\pi\)
\(884\) 0.978587 0.0329134
\(885\) 0 0
\(886\) −15.4143 −0.517854
\(887\) −26.8712 −0.902247 −0.451124 0.892461i \(-0.648977\pi\)
−0.451124 + 0.892461i \(0.648977\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 1.89147 0.0634022
\(891\) 0 0
\(892\) 15.4378 0.516895
\(893\) 87.9339 2.94260
\(894\) 0 0
\(895\) 7.80988 0.261056
\(896\) 6.12970 0.204779
\(897\) 0 0
\(898\) −12.9825 −0.433231
\(899\) 9.58788 0.319774
\(900\) 0 0
\(901\) 4.26958 0.142240
\(902\) −4.50595 −0.150032
\(903\) 0 0
\(904\) −19.0635 −0.634043
\(905\) 56.3116 1.87186
\(906\) 0 0
\(907\) 43.7507 1.45272 0.726358 0.687316i \(-0.241211\pi\)
0.726358 + 0.687316i \(0.241211\pi\)
\(908\) 24.6317 0.817433
\(909\) 0 0
\(910\) −3.84161 −0.127348
\(911\) 5.06252 0.167729 0.0838644 0.996477i \(-0.473274\pi\)
0.0838644 + 0.996477i \(0.473274\pi\)
\(912\) 0 0
\(913\) 15.0552 0.498255
\(914\) 2.24151 0.0741426
\(915\) 0 0
\(916\) 24.7650 0.818257
\(917\) −3.37363 −0.111407
\(918\) 0 0
\(919\) 26.4799 0.873492 0.436746 0.899585i \(-0.356131\pi\)
0.436746 + 0.899585i \(0.356131\pi\)
\(920\) 30.1515 0.994065
\(921\) 0 0
\(922\) −8.02109 −0.264160
\(923\) 14.6134 0.481006
\(924\) 0 0
\(925\) −31.7336 −1.04339
\(926\) −24.5612 −0.807132
\(927\) 0 0
\(928\) −9.69895 −0.318384
\(929\) −40.8254 −1.33944 −0.669719 0.742615i \(-0.733585\pi\)
−0.669719 + 0.742615i \(0.733585\pi\)
\(930\) 0 0
\(931\) 7.77454 0.254800
\(932\) 14.0144 0.459059
\(933\) 0 0
\(934\) −6.32018 −0.206802
\(935\) 1.51400 0.0495131
\(936\) 0 0
\(937\) −33.3098 −1.08818 −0.544092 0.839025i \(-0.683126\pi\)
−0.544092 + 0.839025i \(0.683126\pi\)
\(938\) −1.06047 −0.0346257
\(939\) 0 0
\(940\) 39.8497 1.29976
\(941\) −27.3790 −0.892528 −0.446264 0.894901i \(-0.647246\pi\)
−0.446264 + 0.894901i \(0.647246\pi\)
\(942\) 0 0
\(943\) 20.0070 0.651516
\(944\) −1.98163 −0.0644966
\(945\) 0 0
\(946\) −5.84685 −0.190098
\(947\) 10.3382 0.335948 0.167974 0.985791i \(-0.446278\pi\)
0.167974 + 0.985791i \(0.446278\pi\)
\(948\) 0 0
\(949\) −15.8438 −0.514313
\(950\) 27.2148 0.882964
\(951\) 0 0
\(952\) 1.66842 0.0540737
\(953\) −57.9009 −1.87559 −0.937796 0.347186i \(-0.887137\pi\)
−0.937796 + 0.347186i \(0.887137\pi\)
\(954\) 0 0
\(955\) −26.2821 −0.850468
\(956\) −10.3843 −0.335853
\(957\) 0 0
\(958\) 17.8027 0.575179
\(959\) 16.2096 0.523435
\(960\) 0 0
\(961\) −0.988371 −0.0318829
\(962\) 10.5691 0.340761
\(963\) 0 0
\(964\) 5.28448 0.170202
\(965\) −48.9015 −1.57419
\(966\) 0 0
\(967\) −47.6104 −1.53105 −0.765523 0.643408i \(-0.777520\pi\)
−0.765523 + 0.643408i \(0.777520\pi\)
\(968\) 29.4385 0.946189
\(969\) 0 0
\(970\) 47.0645 1.51115
\(971\) −18.1580 −0.582717 −0.291358 0.956614i \(-0.594107\pi\)
−0.291358 + 0.956614i \(0.594107\pi\)
\(972\) 0 0
\(973\) −12.8614 −0.412318
\(974\) −20.7349 −0.664388
\(975\) 0 0
\(976\) 3.30618 0.105828
\(977\) −53.1178 −1.69939 −0.849695 0.527274i \(-0.823214\pi\)
−0.849695 + 0.527274i \(0.823214\pi\)
\(978\) 0 0
\(979\) 0.615739 0.0196791
\(980\) 3.52326 0.112546
\(981\) 0 0
\(982\) 36.6999 1.17114
\(983\) 30.7192 0.979790 0.489895 0.871781i \(-0.337035\pi\)
0.489895 + 0.871781i \(0.337035\pi\)
\(984\) 0 0
\(985\) 69.7423 2.22217
\(986\) −0.917419 −0.0292166
\(987\) 0 0
\(988\) 13.1202 0.417408
\(989\) 25.9607 0.825503
\(990\) 0 0
\(991\) −36.4388 −1.15752 −0.578759 0.815499i \(-0.696463\pi\)
−0.578759 + 0.815499i \(0.696463\pi\)
\(992\) −30.3593 −0.963908
\(993\) 0 0
\(994\) 9.25906 0.293679
\(995\) −20.3846 −0.646236
\(996\) 0 0
\(997\) −37.1698 −1.17718 −0.588589 0.808432i \(-0.700316\pi\)
−0.588589 + 0.808432i \(0.700316\pi\)
\(998\) −13.7867 −0.436409
\(999\) 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 \(a_p\))