Properties

Label 8018.2.a.f.1.8
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.15742 q^{3} +1.00000 q^{4} -2.78011 q^{5} +2.15742 q^{6} -1.33229 q^{7} -1.00000 q^{8} +1.65446 q^{9} +2.78011 q^{10} -5.50011 q^{11} -2.15742 q^{12} -5.88689 q^{13} +1.33229 q^{14} +5.99787 q^{15} +1.00000 q^{16} -2.24200 q^{17} -1.65446 q^{18} -1.00000 q^{19} -2.78011 q^{20} +2.87432 q^{21} +5.50011 q^{22} -6.52318 q^{23} +2.15742 q^{24} +2.72902 q^{25} +5.88689 q^{26} +2.90289 q^{27} -1.33229 q^{28} +7.17506 q^{29} -5.99787 q^{30} +3.81787 q^{31} -1.00000 q^{32} +11.8661 q^{33} +2.24200 q^{34} +3.70393 q^{35} +1.65446 q^{36} +0.00121348 q^{37} +1.00000 q^{38} +12.7005 q^{39} +2.78011 q^{40} -0.0230918 q^{41} -2.87432 q^{42} -10.2247 q^{43} -5.50011 q^{44} -4.59959 q^{45} +6.52318 q^{46} -1.06053 q^{47} -2.15742 q^{48} -5.22499 q^{49} -2.72902 q^{50} +4.83693 q^{51} -5.88689 q^{52} +10.3892 q^{53} -2.90289 q^{54} +15.2909 q^{55} +1.33229 q^{56} +2.15742 q^{57} -7.17506 q^{58} +13.1194 q^{59} +5.99787 q^{60} +2.45924 q^{61} -3.81787 q^{62} -2.20423 q^{63} +1.00000 q^{64} +16.3662 q^{65} -11.8661 q^{66} +6.44973 q^{67} -2.24200 q^{68} +14.0732 q^{69} -3.70393 q^{70} +2.95646 q^{71} -1.65446 q^{72} -7.06136 q^{73} -0.00121348 q^{74} -5.88764 q^{75} -1.00000 q^{76} +7.32777 q^{77} -12.7005 q^{78} +4.54943 q^{79} -2.78011 q^{80} -11.2261 q^{81} +0.0230918 q^{82} -2.00252 q^{83} +2.87432 q^{84} +6.23300 q^{85} +10.2247 q^{86} -15.4796 q^{87} +5.50011 q^{88} +10.2497 q^{89} +4.59959 q^{90} +7.84307 q^{91} -6.52318 q^{92} -8.23675 q^{93} +1.06053 q^{94} +2.78011 q^{95} +2.15742 q^{96} +3.39933 q^{97} +5.22499 q^{98} -9.09974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.15742 −1.24559 −0.622794 0.782386i \(-0.714002\pi\)
−0.622794 + 0.782386i \(0.714002\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.78011 −1.24330 −0.621652 0.783294i \(-0.713538\pi\)
−0.621652 + 0.783294i \(0.713538\pi\)
\(6\) 2.15742 0.880763
\(7\) −1.33229 −0.503560 −0.251780 0.967784i \(-0.581016\pi\)
−0.251780 + 0.967784i \(0.581016\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.65446 0.551488
\(10\) 2.78011 0.879148
\(11\) −5.50011 −1.65835 −0.829173 0.558992i \(-0.811188\pi\)
−0.829173 + 0.558992i \(0.811188\pi\)
\(12\) −2.15742 −0.622794
\(13\) −5.88689 −1.63273 −0.816365 0.577536i \(-0.804014\pi\)
−0.816365 + 0.577536i \(0.804014\pi\)
\(14\) 1.33229 0.356071
\(15\) 5.99787 1.54864
\(16\) 1.00000 0.250000
\(17\) −2.24200 −0.543764 −0.271882 0.962331i \(-0.587646\pi\)
−0.271882 + 0.962331i \(0.587646\pi\)
\(18\) −1.65446 −0.389961
\(19\) −1.00000 −0.229416
\(20\) −2.78011 −0.621652
\(21\) 2.87432 0.627228
\(22\) 5.50011 1.17263
\(23\) −6.52318 −1.36018 −0.680089 0.733130i \(-0.738059\pi\)
−0.680089 + 0.733130i \(0.738059\pi\)
\(24\) 2.15742 0.440382
\(25\) 2.72902 0.545804
\(26\) 5.88689 1.15451
\(27\) 2.90289 0.558661
\(28\) −1.33229 −0.251780
\(29\) 7.17506 1.33238 0.666188 0.745784i \(-0.267925\pi\)
0.666188 + 0.745784i \(0.267925\pi\)
\(30\) −5.99787 −1.09506
\(31\) 3.81787 0.685710 0.342855 0.939388i \(-0.388606\pi\)
0.342855 + 0.939388i \(0.388606\pi\)
\(32\) −1.00000 −0.176777
\(33\) 11.8661 2.06562
\(34\) 2.24200 0.384499
\(35\) 3.70393 0.626078
\(36\) 1.65446 0.275744
\(37\) 0.00121348 0.000199495 0 9.97474e−5 1.00000i \(-0.499968\pi\)
9.97474e−5 1.00000i \(0.499968\pi\)
\(38\) 1.00000 0.162221
\(39\) 12.7005 2.03371
\(40\) 2.78011 0.439574
\(41\) −0.0230918 −0.00360634 −0.00180317 0.999998i \(-0.500574\pi\)
−0.00180317 + 0.999998i \(0.500574\pi\)
\(42\) −2.87432 −0.443517
\(43\) −10.2247 −1.55926 −0.779628 0.626243i \(-0.784592\pi\)
−0.779628 + 0.626243i \(0.784592\pi\)
\(44\) −5.50011 −0.829173
\(45\) −4.59959 −0.685667
\(46\) 6.52318 0.961791
\(47\) −1.06053 −0.154695 −0.0773474 0.997004i \(-0.524645\pi\)
−0.0773474 + 0.997004i \(0.524645\pi\)
\(48\) −2.15742 −0.311397
\(49\) −5.22499 −0.746427
\(50\) −2.72902 −0.385941
\(51\) 4.83693 0.677306
\(52\) −5.88689 −0.816365
\(53\) 10.3892 1.42707 0.713534 0.700621i \(-0.247094\pi\)
0.713534 + 0.700621i \(0.247094\pi\)
\(54\) −2.90289 −0.395033
\(55\) 15.2909 2.06183
\(56\) 1.33229 0.178035
\(57\) 2.15742 0.285757
\(58\) −7.17506 −0.942132
\(59\) 13.1194 1.70800 0.853998 0.520276i \(-0.174171\pi\)
0.853998 + 0.520276i \(0.174171\pi\)
\(60\) 5.99787 0.774322
\(61\) 2.45924 0.314874 0.157437 0.987529i \(-0.449677\pi\)
0.157437 + 0.987529i \(0.449677\pi\)
\(62\) −3.81787 −0.484870
\(63\) −2.20423 −0.277707
\(64\) 1.00000 0.125000
\(65\) 16.3662 2.02998
\(66\) −11.8661 −1.46061
\(67\) 6.44973 0.787960 0.393980 0.919119i \(-0.371098\pi\)
0.393980 + 0.919119i \(0.371098\pi\)
\(68\) −2.24200 −0.271882
\(69\) 14.0732 1.69422
\(70\) −3.70393 −0.442704
\(71\) 2.95646 0.350868 0.175434 0.984491i \(-0.443867\pi\)
0.175434 + 0.984491i \(0.443867\pi\)
\(72\) −1.65446 −0.194980
\(73\) −7.06136 −0.826470 −0.413235 0.910624i \(-0.635601\pi\)
−0.413235 + 0.910624i \(0.635601\pi\)
\(74\) −0.00121348 −0.000141064 0
\(75\) −5.88764 −0.679846
\(76\) −1.00000 −0.114708
\(77\) 7.32777 0.835077
\(78\) −12.7005 −1.43805
\(79\) 4.54943 0.511850 0.255925 0.966697i \(-0.417620\pi\)
0.255925 + 0.966697i \(0.417620\pi\)
\(80\) −2.78011 −0.310826
\(81\) −11.2261 −1.24735
\(82\) 0.0230918 0.00255006
\(83\) −2.00252 −0.219806 −0.109903 0.993942i \(-0.535054\pi\)
−0.109903 + 0.993942i \(0.535054\pi\)
\(84\) 2.87432 0.313614
\(85\) 6.23300 0.676064
\(86\) 10.2247 1.10256
\(87\) −15.4796 −1.65959
\(88\) 5.50011 0.586314
\(89\) 10.2497 1.08647 0.543235 0.839581i \(-0.317199\pi\)
0.543235 + 0.839581i \(0.317199\pi\)
\(90\) 4.59959 0.484840
\(91\) 7.84307 0.822178
\(92\) −6.52318 −0.680089
\(93\) −8.23675 −0.854112
\(94\) 1.06053 0.109386
\(95\) 2.78011 0.285233
\(96\) 2.15742 0.220191
\(97\) 3.39933 0.345150 0.172575 0.984996i \(-0.444791\pi\)
0.172575 + 0.984996i \(0.444791\pi\)
\(98\) 5.22499 0.527804
\(99\) −9.09974 −0.914558
\(100\) 2.72902 0.272902
\(101\) −4.60039 −0.457756 −0.228878 0.973455i \(-0.573506\pi\)
−0.228878 + 0.973455i \(0.573506\pi\)
\(102\) −4.83693 −0.478927
\(103\) −11.1268 −1.09636 −0.548180 0.836360i \(-0.684679\pi\)
−0.548180 + 0.836360i \(0.684679\pi\)
\(104\) 5.88689 0.577257
\(105\) −7.99093 −0.779835
\(106\) −10.3892 −1.00909
\(107\) 0.319302 0.0308681 0.0154340 0.999881i \(-0.495087\pi\)
0.0154340 + 0.999881i \(0.495087\pi\)
\(108\) 2.90289 0.279331
\(109\) −8.01354 −0.767558 −0.383779 0.923425i \(-0.625378\pi\)
−0.383779 + 0.923425i \(0.625378\pi\)
\(110\) −15.2909 −1.45793
\(111\) −0.00261799 −0.000248488 0
\(112\) −1.33229 −0.125890
\(113\) 7.93918 0.746855 0.373428 0.927659i \(-0.378182\pi\)
0.373428 + 0.927659i \(0.378182\pi\)
\(114\) −2.15742 −0.202061
\(115\) 18.1352 1.69111
\(116\) 7.17506 0.666188
\(117\) −9.73965 −0.900431
\(118\) −13.1194 −1.20774
\(119\) 2.98700 0.273818
\(120\) −5.99787 −0.547528
\(121\) 19.2512 1.75011
\(122\) −2.45924 −0.222649
\(123\) 0.0498188 0.00449201
\(124\) 3.81787 0.342855
\(125\) 6.31358 0.564704
\(126\) 2.20423 0.196369
\(127\) −15.8788 −1.40902 −0.704509 0.709695i \(-0.748833\pi\)
−0.704509 + 0.709695i \(0.748833\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 22.0590 1.94219
\(130\) −16.3662 −1.43541
\(131\) 11.8312 1.03369 0.516847 0.856078i \(-0.327106\pi\)
0.516847 + 0.856078i \(0.327106\pi\)
\(132\) 11.8661 1.03281
\(133\) 1.33229 0.115525
\(134\) −6.44973 −0.557172
\(135\) −8.07035 −0.694585
\(136\) 2.24200 0.192250
\(137\) −13.9862 −1.19492 −0.597459 0.801899i \(-0.703823\pi\)
−0.597459 + 0.801899i \(0.703823\pi\)
\(138\) −14.0732 −1.19799
\(139\) 5.22721 0.443366 0.221683 0.975119i \(-0.428845\pi\)
0.221683 + 0.975119i \(0.428845\pi\)
\(140\) 3.70393 0.313039
\(141\) 2.28802 0.192686
\(142\) −2.95646 −0.248101
\(143\) 32.3786 2.70763
\(144\) 1.65446 0.137872
\(145\) −19.9475 −1.65655
\(146\) 7.06136 0.584403
\(147\) 11.2725 0.929740
\(148\) 0.00121348 9.97474e−5 0
\(149\) −12.7346 −1.04326 −0.521630 0.853172i \(-0.674676\pi\)
−0.521630 + 0.853172i \(0.674676\pi\)
\(150\) 5.88764 0.480724
\(151\) −15.3227 −1.24694 −0.623471 0.781846i \(-0.714278\pi\)
−0.623471 + 0.781846i \(0.714278\pi\)
\(152\) 1.00000 0.0811107
\(153\) −3.70930 −0.299879
\(154\) −7.32777 −0.590489
\(155\) −10.6141 −0.852546
\(156\) 12.7005 1.01685
\(157\) 9.36503 0.747411 0.373705 0.927547i \(-0.378087\pi\)
0.373705 + 0.927547i \(0.378087\pi\)
\(158\) −4.54943 −0.361933
\(159\) −22.4139 −1.77754
\(160\) 2.78011 0.219787
\(161\) 8.69080 0.684931
\(162\) 11.2261 0.882009
\(163\) −10.5985 −0.830135 −0.415068 0.909791i \(-0.636242\pi\)
−0.415068 + 0.909791i \(0.636242\pi\)
\(164\) −0.0230918 −0.00180317
\(165\) −32.9890 −2.56819
\(166\) 2.00252 0.155426
\(167\) −24.5651 −1.90091 −0.950453 0.310869i \(-0.899380\pi\)
−0.950453 + 0.310869i \(0.899380\pi\)
\(168\) −2.87432 −0.221759
\(169\) 21.6555 1.66581
\(170\) −6.23300 −0.478049
\(171\) −1.65446 −0.126520
\(172\) −10.2247 −0.779628
\(173\) 18.5003 1.40655 0.703274 0.710919i \(-0.251721\pi\)
0.703274 + 0.710919i \(0.251721\pi\)
\(174\) 15.4796 1.17351
\(175\) −3.63586 −0.274845
\(176\) −5.50011 −0.414587
\(177\) −28.3040 −2.12746
\(178\) −10.2497 −0.768250
\(179\) 21.2926 1.59149 0.795743 0.605634i \(-0.207080\pi\)
0.795743 + 0.605634i \(0.207080\pi\)
\(180\) −4.59959 −0.342833
\(181\) −17.1761 −1.27669 −0.638346 0.769750i \(-0.720381\pi\)
−0.638346 + 0.769750i \(0.720381\pi\)
\(182\) −7.84307 −0.581367
\(183\) −5.30562 −0.392203
\(184\) 6.52318 0.480895
\(185\) −0.00337361 −0.000248033 0
\(186\) 8.23675 0.603948
\(187\) 12.3312 0.901749
\(188\) −1.06053 −0.0773474
\(189\) −3.86750 −0.281319
\(190\) −2.78011 −0.201690
\(191\) 8.30885 0.601208 0.300604 0.953749i \(-0.402812\pi\)
0.300604 + 0.953749i \(0.402812\pi\)
\(192\) −2.15742 −0.155698
\(193\) 25.4097 1.82903 0.914515 0.404551i \(-0.132572\pi\)
0.914515 + 0.404551i \(0.132572\pi\)
\(194\) −3.39933 −0.244058
\(195\) −35.3088 −2.52852
\(196\) −5.22499 −0.373214
\(197\) 1.65567 0.117962 0.0589808 0.998259i \(-0.481215\pi\)
0.0589808 + 0.998259i \(0.481215\pi\)
\(198\) 9.09974 0.646690
\(199\) −13.4727 −0.955057 −0.477529 0.878616i \(-0.658467\pi\)
−0.477529 + 0.878616i \(0.658467\pi\)
\(200\) −2.72902 −0.192971
\(201\) −13.9148 −0.981473
\(202\) 4.60039 0.323682
\(203\) −9.55930 −0.670931
\(204\) 4.83693 0.338653
\(205\) 0.0641978 0.00448377
\(206\) 11.1268 0.775243
\(207\) −10.7924 −0.750121
\(208\) −5.88689 −0.408182
\(209\) 5.50011 0.380451
\(210\) 7.99093 0.551427
\(211\) −1.00000 −0.0688428
\(212\) 10.3892 0.713534
\(213\) −6.37833 −0.437036
\(214\) −0.319302 −0.0218270
\(215\) 28.4259 1.93863
\(216\) −2.90289 −0.197517
\(217\) −5.08653 −0.345296
\(218\) 8.01354 0.542746
\(219\) 15.2343 1.02944
\(220\) 15.2909 1.03091
\(221\) 13.1984 0.887820
\(222\) 0.00261799 0.000175708 0
\(223\) −2.73815 −0.183360 −0.0916802 0.995789i \(-0.529224\pi\)
−0.0916802 + 0.995789i \(0.529224\pi\)
\(224\) 1.33229 0.0890177
\(225\) 4.51506 0.301004
\(226\) −7.93918 −0.528106
\(227\) 11.9544 0.793440 0.396720 0.917940i \(-0.370148\pi\)
0.396720 + 0.917940i \(0.370148\pi\)
\(228\) 2.15742 0.142879
\(229\) 23.1719 1.53124 0.765620 0.643293i \(-0.222432\pi\)
0.765620 + 0.643293i \(0.222432\pi\)
\(230\) −18.1352 −1.19580
\(231\) −15.8091 −1.04016
\(232\) −7.17506 −0.471066
\(233\) 0.0624516 0.00409134 0.00204567 0.999998i \(-0.499349\pi\)
0.00204567 + 0.999998i \(0.499349\pi\)
\(234\) 9.73965 0.636701
\(235\) 2.94840 0.192333
\(236\) 13.1194 0.853998
\(237\) −9.81503 −0.637554
\(238\) −2.98700 −0.193618
\(239\) 4.02893 0.260610 0.130305 0.991474i \(-0.458404\pi\)
0.130305 + 0.991474i \(0.458404\pi\)
\(240\) 5.99787 0.387161
\(241\) −15.1865 −0.978246 −0.489123 0.872215i \(-0.662683\pi\)
−0.489123 + 0.872215i \(0.662683\pi\)
\(242\) −19.2512 −1.23752
\(243\) 15.5108 0.995021
\(244\) 2.45924 0.157437
\(245\) 14.5261 0.928036
\(246\) −0.0498188 −0.00317633
\(247\) 5.88689 0.374574
\(248\) −3.81787 −0.242435
\(249\) 4.32029 0.273787
\(250\) −6.31358 −0.399306
\(251\) 8.49005 0.535887 0.267944 0.963435i \(-0.413656\pi\)
0.267944 + 0.963435i \(0.413656\pi\)
\(252\) −2.20423 −0.138854
\(253\) 35.8782 2.25565
\(254\) 15.8788 0.996327
\(255\) −13.4472 −0.842097
\(256\) 1.00000 0.0625000
\(257\) 0.782274 0.0487969 0.0243985 0.999702i \(-0.492233\pi\)
0.0243985 + 0.999702i \(0.492233\pi\)
\(258\) −22.0590 −1.37333
\(259\) −0.00161671 −0.000100458 0
\(260\) 16.3662 1.01499
\(261\) 11.8709 0.734789
\(262\) −11.8312 −0.730932
\(263\) 29.1044 1.79465 0.897327 0.441366i \(-0.145506\pi\)
0.897327 + 0.441366i \(0.145506\pi\)
\(264\) −11.8661 −0.730305
\(265\) −28.8832 −1.77428
\(266\) −1.33229 −0.0816882
\(267\) −22.1130 −1.35329
\(268\) 6.44973 0.393980
\(269\) 9.47053 0.577428 0.288714 0.957415i \(-0.406772\pi\)
0.288714 + 0.957415i \(0.406772\pi\)
\(270\) 8.07035 0.491146
\(271\) 10.9255 0.663675 0.331838 0.943336i \(-0.392331\pi\)
0.331838 + 0.943336i \(0.392331\pi\)
\(272\) −2.24200 −0.135941
\(273\) −16.9208 −1.02409
\(274\) 13.9862 0.844935
\(275\) −15.0099 −0.905131
\(276\) 14.0732 0.847110
\(277\) 25.6386 1.54047 0.770236 0.637759i \(-0.220138\pi\)
0.770236 + 0.637759i \(0.220138\pi\)
\(278\) −5.22721 −0.313507
\(279\) 6.31653 0.378161
\(280\) −3.70393 −0.221352
\(281\) 1.68999 0.100817 0.0504083 0.998729i \(-0.483948\pi\)
0.0504083 + 0.998729i \(0.483948\pi\)
\(282\) −2.28802 −0.136249
\(283\) 0.713173 0.0423937 0.0211969 0.999775i \(-0.493252\pi\)
0.0211969 + 0.999775i \(0.493252\pi\)
\(284\) 2.95646 0.175434
\(285\) −5.99787 −0.355283
\(286\) −32.3786 −1.91458
\(287\) 0.0307651 0.00181601
\(288\) −1.65446 −0.0974902
\(289\) −11.9735 −0.704321
\(290\) 19.9475 1.17136
\(291\) −7.33379 −0.429914
\(292\) −7.06136 −0.413235
\(293\) 2.86164 0.167179 0.0835894 0.996500i \(-0.473362\pi\)
0.0835894 + 0.996500i \(0.473362\pi\)
\(294\) −11.2725 −0.657426
\(295\) −36.4733 −2.12356
\(296\) −0.00121348 −7.05321e−5 0
\(297\) −15.9662 −0.926454
\(298\) 12.7346 0.737696
\(299\) 38.4013 2.22080
\(300\) −5.88764 −0.339923
\(301\) 13.6223 0.785179
\(302\) 15.3227 0.881722
\(303\) 9.92498 0.570175
\(304\) −1.00000 −0.0573539
\(305\) −6.83697 −0.391484
\(306\) 3.70930 0.212047
\(307\) −1.59554 −0.0910623 −0.0455311 0.998963i \(-0.514498\pi\)
−0.0455311 + 0.998963i \(0.514498\pi\)
\(308\) 7.32777 0.417539
\(309\) 24.0053 1.36561
\(310\) 10.6141 0.602841
\(311\) −15.4563 −0.876446 −0.438223 0.898866i \(-0.644392\pi\)
−0.438223 + 0.898866i \(0.644392\pi\)
\(312\) −12.7005 −0.719024
\(313\) −20.3537 −1.15046 −0.575230 0.817992i \(-0.695087\pi\)
−0.575230 + 0.817992i \(0.695087\pi\)
\(314\) −9.36503 −0.528499
\(315\) 6.12801 0.345274
\(316\) 4.54943 0.255925
\(317\) 15.3337 0.861225 0.430612 0.902537i \(-0.358298\pi\)
0.430612 + 0.902537i \(0.358298\pi\)
\(318\) 22.4139 1.25691
\(319\) −39.4636 −2.20954
\(320\) −2.78011 −0.155413
\(321\) −0.688869 −0.0384489
\(322\) −8.69080 −0.484319
\(323\) 2.24200 0.124748
\(324\) −11.2261 −0.623675
\(325\) −16.0654 −0.891150
\(326\) 10.5985 0.586994
\(327\) 17.2886 0.956061
\(328\) 0.0230918 0.00127503
\(329\) 1.41294 0.0778981
\(330\) 32.9890 1.81598
\(331\) 19.1231 1.05110 0.525552 0.850762i \(-0.323859\pi\)
0.525552 + 0.850762i \(0.323859\pi\)
\(332\) −2.00252 −0.109903
\(333\) 0.00200766 0.000110019 0
\(334\) 24.5651 1.34414
\(335\) −17.9310 −0.979673
\(336\) 2.87432 0.156807
\(337\) 12.7409 0.694042 0.347021 0.937857i \(-0.387193\pi\)
0.347021 + 0.937857i \(0.387193\pi\)
\(338\) −21.6555 −1.17790
\(339\) −17.1281 −0.930273
\(340\) 6.23300 0.338032
\(341\) −20.9987 −1.13714
\(342\) 1.65446 0.0894631
\(343\) 16.2873 0.879431
\(344\) 10.2247 0.551280
\(345\) −39.1252 −2.10643
\(346\) −18.5003 −0.994580
\(347\) −13.0802 −0.702179 −0.351090 0.936342i \(-0.614189\pi\)
−0.351090 + 0.936342i \(0.614189\pi\)
\(348\) −15.4796 −0.829795
\(349\) −14.1564 −0.757774 −0.378887 0.925443i \(-0.623693\pi\)
−0.378887 + 0.925443i \(0.623693\pi\)
\(350\) 3.63586 0.194345
\(351\) −17.0890 −0.912143
\(352\) 5.50011 0.293157
\(353\) −15.0701 −0.802102 −0.401051 0.916056i \(-0.631355\pi\)
−0.401051 + 0.916056i \(0.631355\pi\)
\(354\) 28.3040 1.50434
\(355\) −8.21929 −0.436235
\(356\) 10.2497 0.543235
\(357\) −6.44422 −0.341064
\(358\) −21.2926 −1.12535
\(359\) 22.9899 1.21336 0.606679 0.794947i \(-0.292501\pi\)
0.606679 + 0.794947i \(0.292501\pi\)
\(360\) 4.59959 0.242420
\(361\) 1.00000 0.0526316
\(362\) 17.1761 0.902758
\(363\) −41.5330 −2.17992
\(364\) 7.84307 0.411089
\(365\) 19.6314 1.02755
\(366\) 5.30562 0.277329
\(367\) −27.3145 −1.42581 −0.712903 0.701263i \(-0.752620\pi\)
−0.712903 + 0.701263i \(0.752620\pi\)
\(368\) −6.52318 −0.340044
\(369\) −0.0382046 −0.00198885
\(370\) 0.00337361 0.000175386 0
\(371\) −13.8415 −0.718614
\(372\) −8.23675 −0.427056
\(373\) 21.8061 1.12908 0.564538 0.825407i \(-0.309054\pi\)
0.564538 + 0.825407i \(0.309054\pi\)
\(374\) −12.3312 −0.637633
\(375\) −13.6211 −0.703388
\(376\) 1.06053 0.0546929
\(377\) −42.2388 −2.17541
\(378\) 3.86750 0.198923
\(379\) −30.5595 −1.56973 −0.784867 0.619664i \(-0.787269\pi\)
−0.784867 + 0.619664i \(0.787269\pi\)
\(380\) 2.78011 0.142617
\(381\) 34.2573 1.75506
\(382\) −8.30885 −0.425118
\(383\) 11.4871 0.586963 0.293481 0.955965i \(-0.405186\pi\)
0.293481 + 0.955965i \(0.405186\pi\)
\(384\) 2.15742 0.110095
\(385\) −20.3720 −1.03825
\(386\) −25.4097 −1.29332
\(387\) −16.9164 −0.859910
\(388\) 3.39933 0.172575
\(389\) −15.0418 −0.762651 −0.381326 0.924441i \(-0.624532\pi\)
−0.381326 + 0.924441i \(0.624532\pi\)
\(390\) 35.3088 1.78793
\(391\) 14.6250 0.739616
\(392\) 5.22499 0.263902
\(393\) −25.5248 −1.28756
\(394\) −1.65567 −0.0834115
\(395\) −12.6479 −0.636385
\(396\) −9.09974 −0.457279
\(397\) 28.2545 1.41805 0.709026 0.705182i \(-0.249135\pi\)
0.709026 + 0.705182i \(0.249135\pi\)
\(398\) 13.4727 0.675328
\(399\) −2.87432 −0.143896
\(400\) 2.72902 0.136451
\(401\) −0.492403 −0.0245894 −0.0122947 0.999924i \(-0.503914\pi\)
−0.0122947 + 0.999924i \(0.503914\pi\)
\(402\) 13.9148 0.694006
\(403\) −22.4754 −1.11958
\(404\) −4.60039 −0.228878
\(405\) 31.2099 1.55083
\(406\) 9.55930 0.474420
\(407\) −0.00667427 −0.000330831 0
\(408\) −4.83693 −0.239464
\(409\) 8.21722 0.406316 0.203158 0.979146i \(-0.434880\pi\)
0.203158 + 0.979146i \(0.434880\pi\)
\(410\) −0.0641978 −0.00317050
\(411\) 30.1740 1.48838
\(412\) −11.1268 −0.548180
\(413\) −17.4789 −0.860079
\(414\) 10.7924 0.530416
\(415\) 5.56724 0.273285
\(416\) 5.88689 0.288629
\(417\) −11.2773 −0.552251
\(418\) −5.50011 −0.269019
\(419\) −26.8072 −1.30962 −0.654808 0.755795i \(-0.727251\pi\)
−0.654808 + 0.755795i \(0.727251\pi\)
\(420\) −7.99093 −0.389917
\(421\) −29.2489 −1.42550 −0.712752 0.701416i \(-0.752552\pi\)
−0.712752 + 0.701416i \(0.752552\pi\)
\(422\) 1.00000 0.0486792
\(423\) −1.75461 −0.0853123
\(424\) −10.3892 −0.504545
\(425\) −6.11845 −0.296788
\(426\) 6.37833 0.309031
\(427\) −3.27644 −0.158558
\(428\) 0.319302 0.0154340
\(429\) −69.8542 −3.37259
\(430\) −28.4259 −1.37082
\(431\) 0.974703 0.0469498 0.0234749 0.999724i \(-0.492527\pi\)
0.0234749 + 0.999724i \(0.492527\pi\)
\(432\) 2.90289 0.139665
\(433\) −7.32945 −0.352231 −0.176115 0.984370i \(-0.556353\pi\)
−0.176115 + 0.984370i \(0.556353\pi\)
\(434\) 5.08653 0.244161
\(435\) 43.0351 2.06337
\(436\) −8.01354 −0.383779
\(437\) 6.52318 0.312046
\(438\) −15.2343 −0.727924
\(439\) −19.3320 −0.922665 −0.461333 0.887227i \(-0.652629\pi\)
−0.461333 + 0.887227i \(0.652629\pi\)
\(440\) −15.2909 −0.728966
\(441\) −8.64456 −0.411646
\(442\) −13.1984 −0.627783
\(443\) −30.3823 −1.44350 −0.721752 0.692152i \(-0.756663\pi\)
−0.721752 + 0.692152i \(0.756663\pi\)
\(444\) −0.00261799 −0.000124244 0
\(445\) −28.4954 −1.35081
\(446\) 2.73815 0.129655
\(447\) 27.4739 1.29947
\(448\) −1.33229 −0.0629450
\(449\) 38.4172 1.81302 0.906509 0.422186i \(-0.138737\pi\)
0.906509 + 0.422186i \(0.138737\pi\)
\(450\) −4.51506 −0.212842
\(451\) 0.127008 0.00598055
\(452\) 7.93918 0.373428
\(453\) 33.0575 1.55318
\(454\) −11.9544 −0.561047
\(455\) −21.8046 −1.02222
\(456\) −2.15742 −0.101030
\(457\) −1.48137 −0.0692958 −0.0346479 0.999400i \(-0.511031\pi\)
−0.0346479 + 0.999400i \(0.511031\pi\)
\(458\) −23.1719 −1.08275
\(459\) −6.50827 −0.303780
\(460\) 18.1352 0.845557
\(461\) −38.6136 −1.79841 −0.899207 0.437523i \(-0.855856\pi\)
−0.899207 + 0.437523i \(0.855856\pi\)
\(462\) 15.8091 0.735505
\(463\) −4.78767 −0.222502 −0.111251 0.993792i \(-0.535486\pi\)
−0.111251 + 0.993792i \(0.535486\pi\)
\(464\) 7.17506 0.333094
\(465\) 22.8991 1.06192
\(466\) −0.0624516 −0.00289301
\(467\) −16.0814 −0.744157 −0.372078 0.928201i \(-0.621355\pi\)
−0.372078 + 0.928201i \(0.621355\pi\)
\(468\) −9.73965 −0.450215
\(469\) −8.59294 −0.396785
\(470\) −2.94840 −0.136000
\(471\) −20.2043 −0.930966
\(472\) −13.1194 −0.603868
\(473\) 56.2371 2.58579
\(474\) 9.81503 0.450819
\(475\) −2.72902 −0.125216
\(476\) 2.98700 0.136909
\(477\) 17.1886 0.787010
\(478\) −4.02893 −0.184279
\(479\) 5.35999 0.244904 0.122452 0.992474i \(-0.460924\pi\)
0.122452 + 0.992474i \(0.460924\pi\)
\(480\) −5.99787 −0.273764
\(481\) −0.00714362 −0.000325721 0
\(482\) 15.1865 0.691725
\(483\) −18.7497 −0.853141
\(484\) 19.2512 0.875056
\(485\) −9.45052 −0.429126
\(486\) −15.5108 −0.703586
\(487\) −1.50511 −0.0682029 −0.0341014 0.999418i \(-0.510857\pi\)
−0.0341014 + 0.999418i \(0.510857\pi\)
\(488\) −2.45924 −0.111325
\(489\) 22.8653 1.03401
\(490\) −14.5261 −0.656220
\(491\) 10.0401 0.453102 0.226551 0.973999i \(-0.427255\pi\)
0.226551 + 0.973999i \(0.427255\pi\)
\(492\) 0.0498188 0.00224600
\(493\) −16.0865 −0.724498
\(494\) −5.88689 −0.264864
\(495\) 25.2983 1.13707
\(496\) 3.81787 0.171427
\(497\) −3.93888 −0.176683
\(498\) −4.32029 −0.193597
\(499\) 15.9373 0.713453 0.356727 0.934209i \(-0.383893\pi\)
0.356727 + 0.934209i \(0.383893\pi\)
\(500\) 6.31358 0.282352
\(501\) 52.9973 2.36774
\(502\) −8.49005 −0.378929
\(503\) 41.3289 1.84277 0.921383 0.388656i \(-0.127061\pi\)
0.921383 + 0.388656i \(0.127061\pi\)
\(504\) 2.20423 0.0981843
\(505\) 12.7896 0.569130
\(506\) −35.8782 −1.59498
\(507\) −46.7200 −2.07491
\(508\) −15.8788 −0.704509
\(509\) 18.4331 0.817031 0.408516 0.912751i \(-0.366047\pi\)
0.408516 + 0.912751i \(0.366047\pi\)
\(510\) 13.4472 0.595452
\(511\) 9.40782 0.416177
\(512\) −1.00000 −0.0441942
\(513\) −2.90289 −0.128166
\(514\) −0.782274 −0.0345046
\(515\) 30.9338 1.36311
\(516\) 22.0590 0.971094
\(517\) 5.83306 0.256538
\(518\) 0.00161671 7.10343e−5 0
\(519\) −39.9128 −1.75198
\(520\) −16.3662 −0.717706
\(521\) −40.0811 −1.75599 −0.877993 0.478674i \(-0.841118\pi\)
−0.877993 + 0.478674i \(0.841118\pi\)
\(522\) −11.8709 −0.519574
\(523\) −3.41281 −0.149232 −0.0746158 0.997212i \(-0.523773\pi\)
−0.0746158 + 0.997212i \(0.523773\pi\)
\(524\) 11.8312 0.516847
\(525\) 7.84407 0.342343
\(526\) −29.1044 −1.26901
\(527\) −8.55965 −0.372864
\(528\) 11.8661 0.516404
\(529\) 19.5519 0.850082
\(530\) 28.8832 1.25460
\(531\) 21.7055 0.941939
\(532\) 1.33229 0.0577623
\(533\) 0.135939 0.00588817
\(534\) 22.1130 0.956922
\(535\) −0.887695 −0.0383784
\(536\) −6.44973 −0.278586
\(537\) −45.9372 −1.98234
\(538\) −9.47053 −0.408304
\(539\) 28.7380 1.23783
\(540\) −8.07035 −0.347293
\(541\) 38.3046 1.64684 0.823422 0.567430i \(-0.192062\pi\)
0.823422 + 0.567430i \(0.192062\pi\)
\(542\) −10.9255 −0.469289
\(543\) 37.0561 1.59023
\(544\) 2.24200 0.0961248
\(545\) 22.2785 0.954308
\(546\) 16.9208 0.724144
\(547\) −2.03295 −0.0869226 −0.0434613 0.999055i \(-0.513839\pi\)
−0.0434613 + 0.999055i \(0.513839\pi\)
\(548\) −13.9862 −0.597459
\(549\) 4.06873 0.173649
\(550\) 15.0099 0.640025
\(551\) −7.17506 −0.305668
\(552\) −14.0732 −0.598997
\(553\) −6.06118 −0.257747
\(554\) −25.6386 −1.08928
\(555\) 0.00727829 0.000308946 0
\(556\) 5.22721 0.221683
\(557\) −26.4962 −1.12268 −0.561339 0.827586i \(-0.689714\pi\)
−0.561339 + 0.827586i \(0.689714\pi\)
\(558\) −6.31653 −0.267400
\(559\) 60.1918 2.54584
\(560\) 3.70393 0.156520
\(561\) −26.6037 −1.12321
\(562\) −1.68999 −0.0712881
\(563\) −7.76923 −0.327434 −0.163717 0.986507i \(-0.552348\pi\)
−0.163717 + 0.986507i \(0.552348\pi\)
\(564\) 2.28802 0.0963429
\(565\) −22.0718 −0.928568
\(566\) −0.713173 −0.0299769
\(567\) 14.9565 0.628115
\(568\) −2.95646 −0.124050
\(569\) 13.2614 0.555949 0.277974 0.960588i \(-0.410337\pi\)
0.277974 + 0.960588i \(0.410337\pi\)
\(570\) 5.99787 0.251223
\(571\) −9.12816 −0.382002 −0.191001 0.981590i \(-0.561173\pi\)
−0.191001 + 0.981590i \(0.561173\pi\)
\(572\) 32.3786 1.35382
\(573\) −17.9257 −0.748857
\(574\) −0.0307651 −0.00128411
\(575\) −17.8019 −0.742390
\(576\) 1.65446 0.0689360
\(577\) −18.3659 −0.764581 −0.382291 0.924042i \(-0.624865\pi\)
−0.382291 + 0.924042i \(0.624865\pi\)
\(578\) 11.9735 0.498030
\(579\) −54.8194 −2.27822
\(580\) −19.9475 −0.828273
\(581\) 2.66795 0.110685
\(582\) 7.33379 0.303995
\(583\) −57.1418 −2.36657
\(584\) 7.06136 0.292201
\(585\) 27.0773 1.11951
\(586\) −2.86164 −0.118213
\(587\) 14.5419 0.600210 0.300105 0.953906i \(-0.402978\pi\)
0.300105 + 0.953906i \(0.402978\pi\)
\(588\) 11.2725 0.464870
\(589\) −3.81787 −0.157313
\(590\) 36.4733 1.50158
\(591\) −3.57198 −0.146932
\(592\) 0.00121348 4.98737e−5 0
\(593\) −12.0601 −0.495249 −0.247625 0.968856i \(-0.579650\pi\)
−0.247625 + 0.968856i \(0.579650\pi\)
\(594\) 15.9662 0.655102
\(595\) −8.30419 −0.340439
\(596\) −12.7346 −0.521630
\(597\) 29.0664 1.18961
\(598\) −38.4013 −1.57034
\(599\) −9.07245 −0.370690 −0.185345 0.982673i \(-0.559340\pi\)
−0.185345 + 0.982673i \(0.559340\pi\)
\(600\) 5.88764 0.240362
\(601\) −0.942780 −0.0384568 −0.0192284 0.999815i \(-0.506121\pi\)
−0.0192284 + 0.999815i \(0.506121\pi\)
\(602\) −13.6223 −0.555205
\(603\) 10.6708 0.434550
\(604\) −15.3227 −0.623471
\(605\) −53.5206 −2.17592
\(606\) −9.92498 −0.403175
\(607\) 22.7710 0.924245 0.462122 0.886816i \(-0.347088\pi\)
0.462122 + 0.886816i \(0.347088\pi\)
\(608\) 1.00000 0.0405554
\(609\) 20.6234 0.835703
\(610\) 6.83697 0.276821
\(611\) 6.24325 0.252575
\(612\) −3.70930 −0.149940
\(613\) 48.0768 1.94180 0.970902 0.239476i \(-0.0769755\pi\)
0.970902 + 0.239476i \(0.0769755\pi\)
\(614\) 1.59554 0.0643908
\(615\) −0.138502 −0.00558493
\(616\) −7.32777 −0.295244
\(617\) 8.23906 0.331692 0.165846 0.986152i \(-0.446965\pi\)
0.165846 + 0.986152i \(0.446965\pi\)
\(618\) −24.0053 −0.965633
\(619\) −1.67620 −0.0673721 −0.0336860 0.999432i \(-0.510725\pi\)
−0.0336860 + 0.999432i \(0.510725\pi\)
\(620\) −10.6141 −0.426273
\(621\) −18.9361 −0.759878
\(622\) 15.4563 0.619741
\(623\) −13.6557 −0.547103
\(624\) 12.7005 0.508427
\(625\) −31.1976 −1.24790
\(626\) 20.3537 0.813498
\(627\) −11.8661 −0.473885
\(628\) 9.36503 0.373705
\(629\) −0.00272062 −0.000108478 0
\(630\) −6.12801 −0.244146
\(631\) −40.8749 −1.62721 −0.813603 0.581421i \(-0.802497\pi\)
−0.813603 + 0.581421i \(0.802497\pi\)
\(632\) −4.54943 −0.180966
\(633\) 2.15742 0.0857498
\(634\) −15.3337 −0.608978
\(635\) 44.1449 1.75184
\(636\) −22.4139 −0.888769
\(637\) 30.7590 1.21871
\(638\) 39.4636 1.56238
\(639\) 4.89136 0.193499
\(640\) 2.78011 0.109894
\(641\) −26.2565 −1.03707 −0.518535 0.855056i \(-0.673522\pi\)
−0.518535 + 0.855056i \(0.673522\pi\)
\(642\) 0.688869 0.0271875
\(643\) −24.4264 −0.963282 −0.481641 0.876369i \(-0.659959\pi\)
−0.481641 + 0.876369i \(0.659959\pi\)
\(644\) 8.69080 0.342466
\(645\) −61.3265 −2.41473
\(646\) −2.24200 −0.0882102
\(647\) −29.1756 −1.14701 −0.573505 0.819202i \(-0.694417\pi\)
−0.573505 + 0.819202i \(0.694417\pi\)
\(648\) 11.2261 0.441004
\(649\) −72.1580 −2.83245
\(650\) 16.0654 0.630138
\(651\) 10.9738 0.430097
\(652\) −10.5985 −0.415068
\(653\) −36.8413 −1.44171 −0.720855 0.693086i \(-0.756251\pi\)
−0.720855 + 0.693086i \(0.756251\pi\)
\(654\) −17.2886 −0.676037
\(655\) −32.8919 −1.28519
\(656\) −0.0230918 −0.000901584 0
\(657\) −11.6828 −0.455788
\(658\) −1.41294 −0.0550823
\(659\) −16.2993 −0.634930 −0.317465 0.948270i \(-0.602832\pi\)
−0.317465 + 0.948270i \(0.602832\pi\)
\(660\) −32.9890 −1.28409
\(661\) 45.4371 1.76730 0.883648 0.468151i \(-0.155080\pi\)
0.883648 + 0.468151i \(0.155080\pi\)
\(662\) −19.1231 −0.743242
\(663\) −28.4745 −1.10586
\(664\) 2.00252 0.0777130
\(665\) −3.70393 −0.143632
\(666\) −0.00200766 −7.77951e−5 0
\(667\) −46.8042 −1.81227
\(668\) −24.5651 −0.950453
\(669\) 5.90735 0.228391
\(670\) 17.9310 0.692734
\(671\) −13.5261 −0.522170
\(672\) −2.87432 −0.110879
\(673\) −42.1124 −1.62331 −0.811657 0.584134i \(-0.801434\pi\)
−0.811657 + 0.584134i \(0.801434\pi\)
\(674\) −12.7409 −0.490762
\(675\) 7.92203 0.304919
\(676\) 21.6555 0.832903
\(677\) −31.4073 −1.20708 −0.603539 0.797333i \(-0.706243\pi\)
−0.603539 + 0.797333i \(0.706243\pi\)
\(678\) 17.1281 0.657803
\(679\) −4.52891 −0.173804
\(680\) −6.23300 −0.239025
\(681\) −25.7906 −0.988299
\(682\) 20.9987 0.804083
\(683\) 9.75667 0.373329 0.186664 0.982424i \(-0.440232\pi\)
0.186664 + 0.982424i \(0.440232\pi\)
\(684\) −1.65446 −0.0632600
\(685\) 38.8831 1.48565
\(686\) −16.2873 −0.621852
\(687\) −49.9914 −1.90729
\(688\) −10.2247 −0.389814
\(689\) −61.1601 −2.33002
\(690\) 39.1252 1.48947
\(691\) 21.8118 0.829761 0.414881 0.909876i \(-0.363823\pi\)
0.414881 + 0.909876i \(0.363823\pi\)
\(692\) 18.5003 0.703274
\(693\) 12.1235 0.460535
\(694\) 13.0802 0.496516
\(695\) −14.5322 −0.551239
\(696\) 15.4796 0.586754
\(697\) 0.0517718 0.00196100
\(698\) 14.1564 0.535827
\(699\) −0.134734 −0.00509612
\(700\) −3.63586 −0.137422
\(701\) −4.43796 −0.167620 −0.0838098 0.996482i \(-0.526709\pi\)
−0.0838098 + 0.996482i \(0.526709\pi\)
\(702\) 17.0890 0.644982
\(703\) −0.00121348 −4.57672e−5 0
\(704\) −5.50011 −0.207293
\(705\) −6.36094 −0.239567
\(706\) 15.0701 0.567172
\(707\) 6.12908 0.230508
\(708\) −28.3040 −1.06373
\(709\) −18.3684 −0.689839 −0.344920 0.938632i \(-0.612094\pi\)
−0.344920 + 0.938632i \(0.612094\pi\)
\(710\) 8.21929 0.308465
\(711\) 7.52686 0.282279
\(712\) −10.2497 −0.384125
\(713\) −24.9047 −0.932687
\(714\) 6.44422 0.241169
\(715\) −90.0160 −3.36641
\(716\) 21.2926 0.795743
\(717\) −8.69210 −0.324612
\(718\) −22.9899 −0.857974
\(719\) 41.4738 1.54671 0.773356 0.633972i \(-0.218577\pi\)
0.773356 + 0.633972i \(0.218577\pi\)
\(720\) −4.59959 −0.171417
\(721\) 14.8242 0.552083
\(722\) −1.00000 −0.0372161
\(723\) 32.7636 1.21849
\(724\) −17.1761 −0.638346
\(725\) 19.5809 0.727215
\(726\) 41.5330 1.54144
\(727\) 20.1418 0.747018 0.373509 0.927627i \(-0.378155\pi\)
0.373509 + 0.927627i \(0.378155\pi\)
\(728\) −7.84307 −0.290684
\(729\) 0.215012 0.00796340
\(730\) −19.6314 −0.726590
\(731\) 22.9238 0.847867
\(732\) −5.30562 −0.196101
\(733\) 51.9726 1.91965 0.959825 0.280599i \(-0.0905330\pi\)
0.959825 + 0.280599i \(0.0905330\pi\)
\(734\) 27.3145 1.00820
\(735\) −31.3388 −1.15595
\(736\) 6.52318 0.240448
\(737\) −35.4742 −1.30671
\(738\) 0.0382046 0.00140633
\(739\) −37.8111 −1.39090 −0.695452 0.718573i \(-0.744796\pi\)
−0.695452 + 0.718573i \(0.744796\pi\)
\(740\) −0.00337361 −0.000124016 0
\(741\) −12.7005 −0.466565
\(742\) 13.8415 0.508137
\(743\) 0.661684 0.0242748 0.0121374 0.999926i \(-0.496136\pi\)
0.0121374 + 0.999926i \(0.496136\pi\)
\(744\) 8.23675 0.301974
\(745\) 35.4036 1.29709
\(746\) −21.8061 −0.798378
\(747\) −3.31310 −0.121220
\(748\) 12.3312 0.450875
\(749\) −0.425404 −0.0155439
\(750\) 13.6211 0.497371
\(751\) −1.74926 −0.0638315 −0.0319158 0.999491i \(-0.510161\pi\)
−0.0319158 + 0.999491i \(0.510161\pi\)
\(752\) −1.06053 −0.0386737
\(753\) −18.3166 −0.667494
\(754\) 42.2388 1.53825
\(755\) 42.5988 1.55033
\(756\) −3.86750 −0.140660
\(757\) −28.9312 −1.05152 −0.525761 0.850632i \(-0.676220\pi\)
−0.525761 + 0.850632i \(0.676220\pi\)
\(758\) 30.5595 1.10997
\(759\) −77.4044 −2.80960
\(760\) −2.78011 −0.100845
\(761\) 14.8160 0.537079 0.268540 0.963269i \(-0.413459\pi\)
0.268540 + 0.963269i \(0.413459\pi\)
\(762\) −34.2573 −1.24101
\(763\) 10.6764 0.386512
\(764\) 8.30885 0.300604
\(765\) 10.3123 0.372841
\(766\) −11.4871 −0.415045
\(767\) −77.2323 −2.78870
\(768\) −2.15742 −0.0778492
\(769\) 33.2703 1.19976 0.599880 0.800090i \(-0.295215\pi\)
0.599880 + 0.800090i \(0.295215\pi\)
\(770\) 20.3720 0.734157
\(771\) −1.68769 −0.0607808
\(772\) 25.4097 0.914515
\(773\) 11.0643 0.397957 0.198978 0.980004i \(-0.436238\pi\)
0.198978 + 0.980004i \(0.436238\pi\)
\(774\) 16.9164 0.608048
\(775\) 10.4190 0.374263
\(776\) −3.39933 −0.122029
\(777\) 0.00348793 0.000125129 0
\(778\) 15.0418 0.539276
\(779\) 0.0230918 0.000827350 0
\(780\) −35.3088 −1.26426
\(781\) −16.2609 −0.581860
\(782\) −14.6250 −0.522987
\(783\) 20.8284 0.744346
\(784\) −5.22499 −0.186607
\(785\) −26.0358 −0.929259
\(786\) 25.5248 0.910439
\(787\) 16.0464 0.571993 0.285996 0.958231i \(-0.407675\pi\)
0.285996 + 0.958231i \(0.407675\pi\)
\(788\) 1.65567 0.0589808
\(789\) −62.7904 −2.23540
\(790\) 12.6479 0.449992
\(791\) −10.5773 −0.376086
\(792\) 9.09974 0.323345
\(793\) −14.4773 −0.514104
\(794\) −28.2545 −1.00271
\(795\) 62.3131 2.21002
\(796\) −13.4727 −0.477529
\(797\) 41.5438 1.47156 0.735778 0.677223i \(-0.236817\pi\)
0.735778 + 0.677223i \(0.236817\pi\)
\(798\) 2.87432 0.101750
\(799\) 2.37771 0.0841175
\(800\) −2.72902 −0.0964854
\(801\) 16.9578 0.599175
\(802\) 0.492403 0.0173874
\(803\) 38.8383 1.37057
\(804\) −13.9148 −0.490736
\(805\) −24.1614 −0.851577
\(806\) 22.4754 0.791662
\(807\) −20.4319 −0.719238
\(808\) 4.60039 0.161841
\(809\) 29.7877 1.04728 0.523641 0.851939i \(-0.324573\pi\)
0.523641 + 0.851939i \(0.324573\pi\)
\(810\) −31.2099 −1.09660
\(811\) 46.3916 1.62903 0.814515 0.580142i \(-0.197003\pi\)
0.814515 + 0.580142i \(0.197003\pi\)
\(812\) −9.55930 −0.335466
\(813\) −23.5708 −0.826666
\(814\) 0.00667427 0.000233933 0
\(815\) 29.4649 1.03211
\(816\) 4.83693 0.169326
\(817\) 10.2247 0.357718
\(818\) −8.21722 −0.287309
\(819\) 12.9761 0.453421
\(820\) 0.0641978 0.00224188
\(821\) 0.984358 0.0343543 0.0171772 0.999852i \(-0.494532\pi\)
0.0171772 + 0.999852i \(0.494532\pi\)
\(822\) −30.1740 −1.05244
\(823\) −11.9961 −0.418157 −0.209078 0.977899i \(-0.567046\pi\)
−0.209078 + 0.977899i \(0.567046\pi\)
\(824\) 11.1268 0.387622
\(825\) 32.3827 1.12742
\(826\) 17.4789 0.608168
\(827\) −17.9525 −0.624270 −0.312135 0.950038i \(-0.601044\pi\)
−0.312135 + 0.950038i \(0.601044\pi\)
\(828\) −10.7924 −0.375061
\(829\) 33.9311 1.17848 0.589239 0.807959i \(-0.299428\pi\)
0.589239 + 0.807959i \(0.299428\pi\)
\(830\) −5.56724 −0.193242
\(831\) −55.3132 −1.91879
\(832\) −5.88689 −0.204091
\(833\) 11.7144 0.405880
\(834\) 11.2773 0.390501
\(835\) 68.2937 2.36340
\(836\) 5.50011 0.190225
\(837\) 11.0829 0.383079
\(838\) 26.8072 0.926039
\(839\) −20.1454 −0.695496 −0.347748 0.937588i \(-0.613054\pi\)
−0.347748 + 0.937588i \(0.613054\pi\)
\(840\) 7.99093 0.275713
\(841\) 22.4815 0.775224
\(842\) 29.2489 1.00798
\(843\) −3.64603 −0.125576
\(844\) −1.00000 −0.0344214
\(845\) −60.2047 −2.07110
\(846\) 1.75461 0.0603249
\(847\) −25.6483 −0.881287
\(848\) 10.3892 0.356767
\(849\) −1.53861 −0.0528051
\(850\) 6.11845 0.209861
\(851\) −0.00791575 −0.000271348 0
\(852\) −6.37833 −0.218518
\(853\) 9.31580 0.318967 0.159483 0.987201i \(-0.449017\pi\)
0.159483 + 0.987201i \(0.449017\pi\)
\(854\) 3.27644 0.112117
\(855\) 4.59959 0.157303
\(856\) −0.319302 −0.0109135
\(857\) 13.1804 0.450233 0.225116 0.974332i \(-0.427724\pi\)
0.225116 + 0.974332i \(0.427724\pi\)
\(858\) 69.8542 2.38478
\(859\) 15.0053 0.511975 0.255987 0.966680i \(-0.417599\pi\)
0.255987 + 0.966680i \(0.417599\pi\)
\(860\) 28.4259 0.969314
\(861\) −0.0663733 −0.00226199
\(862\) −0.974703 −0.0331985
\(863\) −47.7992 −1.62710 −0.813552 0.581493i \(-0.802469\pi\)
−0.813552 + 0.581493i \(0.802469\pi\)
\(864\) −2.90289 −0.0987583
\(865\) −51.4328 −1.74877
\(866\) 7.32945 0.249065
\(867\) 25.8318 0.877293
\(868\) −5.08653 −0.172648
\(869\) −25.0224 −0.848825
\(870\) −43.0351 −1.45903
\(871\) −37.9689 −1.28653
\(872\) 8.01354 0.271373
\(873\) 5.62407 0.190346
\(874\) −6.52318 −0.220650
\(875\) −8.41155 −0.284362
\(876\) 15.2343 0.514720
\(877\) −37.1911 −1.25585 −0.627927 0.778273i \(-0.716096\pi\)
−0.627927 + 0.778273i \(0.716096\pi\)
\(878\) 19.3320 0.652423
\(879\) −6.17376 −0.208236
\(880\) 15.2909 0.515457
\(881\) 7.44719 0.250902 0.125451 0.992100i \(-0.459962\pi\)
0.125451 + 0.992100i \(0.459962\pi\)
\(882\) 8.64456 0.291077
\(883\) −15.0947 −0.507976 −0.253988 0.967207i \(-0.581742\pi\)
−0.253988 + 0.967207i \(0.581742\pi\)
\(884\) 13.1984 0.443910
\(885\) 78.6883 2.64508
\(886\) 30.3823 1.02071
\(887\) −6.63936 −0.222928 −0.111464 0.993768i \(-0.535554\pi\)
−0.111464 + 0.993768i \(0.535554\pi\)
\(888\) 0.00261799 8.78538e−5 0
\(889\) 21.1553 0.709526
\(890\) 28.4954 0.955168
\(891\) 61.7450 2.06854
\(892\) −2.73815 −0.0916802
\(893\) 1.06053 0.0354894
\(894\) −27.4739 −0.918864
\(895\) −59.1959 −1.97870
\(896\) 1.33229 0.0445088
\(897\) −82.8477 −2.76620
\(898\) −38.4172 −1.28200
\(899\) 27.3935 0.913623
\(900\) 4.51506 0.150502
\(901\) −23.2926 −0.775988
\(902\) −0.127008 −0.00422889
\(903\) −29.3891 −0.978009
\(904\) −7.93918 −0.264053
\(905\) 47.7516 1.58732
\(906\) −33.0575 −1.09826
\(907\) −7.26465 −0.241219 −0.120609 0.992700i \(-0.538485\pi\)
−0.120609 + 0.992700i \(0.538485\pi\)
\(908\) 11.9544 0.396720
\(909\) −7.61118 −0.252447
\(910\) 21.8046 0.722816
\(911\) 24.7731 0.820770 0.410385 0.911912i \(-0.365394\pi\)
0.410385 + 0.911912i \(0.365394\pi\)
\(912\) 2.15742 0.0714393
\(913\) 11.0141 0.364514
\(914\) 1.48137 0.0489995
\(915\) 14.7502 0.487627
\(916\) 23.1719 0.765620
\(917\) −15.7626 −0.520527
\(918\) 6.50827 0.214805
\(919\) −21.0392 −0.694019 −0.347009 0.937862i \(-0.612803\pi\)
−0.347009 + 0.937862i \(0.612803\pi\)
\(920\) −18.1352 −0.597899
\(921\) 3.44225 0.113426
\(922\) 38.6136 1.27167
\(923\) −17.4044 −0.572872
\(924\) −15.8091 −0.520081
\(925\) 0.00331161 0.000108885 0
\(926\) 4.78767 0.157333
\(927\) −18.4089 −0.604629
\(928\) −7.17506 −0.235533
\(929\) −0.464932 −0.0152539 −0.00762697 0.999971i \(-0.502428\pi\)
−0.00762697 + 0.999971i \(0.502428\pi\)
\(930\) −22.8991 −0.750891
\(931\) 5.22499 0.171242
\(932\) 0.0624516 0.00204567
\(933\) 33.3457 1.09169
\(934\) 16.0814 0.526198
\(935\) −34.2822 −1.12115
\(936\) 9.73965 0.318350
\(937\) 39.4858 1.28995 0.644973 0.764206i \(-0.276869\pi\)
0.644973 + 0.764206i \(0.276869\pi\)
\(938\) 8.59294 0.280569
\(939\) 43.9115 1.43300
\(940\) 2.94840 0.0961663
\(941\) 49.5049 1.61381 0.806907 0.590678i \(-0.201140\pi\)
0.806907 + 0.590678i \(0.201140\pi\)
\(942\) 20.2043 0.658292
\(943\) 0.150632 0.00490526
\(944\) 13.1194 0.426999
\(945\) 10.7521 0.349765
\(946\) −56.2371 −1.82843
\(947\) −49.1586 −1.59744 −0.798720 0.601703i \(-0.794489\pi\)
−0.798720 + 0.601703i \(0.794489\pi\)
\(948\) −9.81503 −0.318777
\(949\) 41.5695 1.34940
\(950\) 2.72902 0.0885410
\(951\) −33.0812 −1.07273
\(952\) −2.98700 −0.0968092
\(953\) 12.7431 0.412791 0.206395 0.978469i \(-0.433827\pi\)
0.206395 + 0.978469i \(0.433827\pi\)
\(954\) −17.1886 −0.556500
\(955\) −23.0995 −0.747484
\(956\) 4.02893 0.130305
\(957\) 85.1397 2.75217
\(958\) −5.35999 −0.173174
\(959\) 18.6337 0.601713
\(960\) 5.99787 0.193580
\(961\) −16.4239 −0.529802
\(962\) 0.00714362 0.000230320 0
\(963\) 0.528274 0.0170234
\(964\) −15.1865 −0.489123
\(965\) −70.6418 −2.27404
\(966\) 18.7497 0.603262
\(967\) −39.0003 −1.25417 −0.627083 0.778953i \(-0.715751\pi\)
−0.627083 + 0.778953i \(0.715751\pi\)
\(968\) −19.2512 −0.618758
\(969\) −4.83693 −0.155385
\(970\) 9.45052 0.303438
\(971\) −6.69225 −0.214764 −0.107382 0.994218i \(-0.534247\pi\)
−0.107382 + 0.994218i \(0.534247\pi\)
\(972\) 15.5108 0.497511
\(973\) −6.96419 −0.223262
\(974\) 1.50511 0.0482267
\(975\) 34.6599 1.11001
\(976\) 2.45924 0.0787185
\(977\) 35.5370 1.13693 0.568465 0.822707i \(-0.307537\pi\)
0.568465 + 0.822707i \(0.307537\pi\)
\(978\) −22.8653 −0.731153
\(979\) −56.3747 −1.80174
\(980\) 14.5261 0.464018
\(981\) −13.2581 −0.423299
\(982\) −10.0401 −0.320392
\(983\) −21.5663 −0.687857 −0.343928 0.938996i \(-0.611758\pi\)
−0.343928 + 0.938996i \(0.611758\pi\)
\(984\) −0.0498188 −0.00158816
\(985\) −4.60295 −0.146662
\(986\) 16.0865 0.512297
\(987\) −3.04831 −0.0970289
\(988\) 5.88689 0.187287
\(989\) 66.6977 2.12086
\(990\) −25.2983 −0.804032
\(991\) 23.0864 0.733365 0.366682 0.930346i \(-0.380494\pi\)
0.366682 + 0.930346i \(0.380494\pi\)
\(992\) −3.81787 −0.121218
\(993\) −41.2567 −1.30924
\(994\) 3.93888 0.124934
\(995\) 37.4557 1.18743
\(996\) 4.32029 0.136894
\(997\) −43.6392 −1.38207 −0.691034 0.722823i \(-0.742844\pi\)
−0.691034 + 0.722823i \(0.742844\pi\)
\(998\) −15.9373 −0.504488
\(999\) 0.00352260 0.000111450 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 \(a_p\))