Properties

Label 8042.2.a.c.1.2
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.12962 q^{3} +1.00000 q^{4} +1.55366 q^{5} +3.12962 q^{6} +0.219811 q^{7} -1.00000 q^{8} +6.79451 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.12962 q^{3} +1.00000 q^{4} +1.55366 q^{5} +3.12962 q^{6} +0.219811 q^{7} -1.00000 q^{8} +6.79451 q^{9} -1.55366 q^{10} -3.38226 q^{11} -3.12962 q^{12} -1.24197 q^{13} -0.219811 q^{14} -4.86235 q^{15} +1.00000 q^{16} -6.07371 q^{17} -6.79451 q^{18} -4.37899 q^{19} +1.55366 q^{20} -0.687924 q^{21} +3.38226 q^{22} -0.273819 q^{23} +3.12962 q^{24} -2.58615 q^{25} +1.24197 q^{26} -11.8754 q^{27} +0.219811 q^{28} -9.14771 q^{29} +4.86235 q^{30} -0.0762978 q^{31} -1.00000 q^{32} +10.5852 q^{33} +6.07371 q^{34} +0.341511 q^{35} +6.79451 q^{36} -10.1804 q^{37} +4.37899 q^{38} +3.88690 q^{39} -1.55366 q^{40} -10.4153 q^{41} +0.687924 q^{42} -2.44954 q^{43} -3.38226 q^{44} +10.5563 q^{45} +0.273819 q^{46} -4.26477 q^{47} -3.12962 q^{48} -6.95168 q^{49} +2.58615 q^{50} +19.0084 q^{51} -1.24197 q^{52} +0.795398 q^{53} +11.8754 q^{54} -5.25487 q^{55} -0.219811 q^{56} +13.7046 q^{57} +9.14771 q^{58} -2.78406 q^{59} -4.86235 q^{60} -9.70482 q^{61} +0.0762978 q^{62} +1.49351 q^{63} +1.00000 q^{64} -1.92960 q^{65} -10.5852 q^{66} +5.80502 q^{67} -6.07371 q^{68} +0.856950 q^{69} -0.341511 q^{70} +4.38757 q^{71} -6.79451 q^{72} +1.82521 q^{73} +10.1804 q^{74} +8.09367 q^{75} -4.37899 q^{76} -0.743458 q^{77} -3.88690 q^{78} -2.72630 q^{79} +1.55366 q^{80} +16.7818 q^{81} +10.4153 q^{82} +9.27875 q^{83} -0.687924 q^{84} -9.43647 q^{85} +2.44954 q^{86} +28.6288 q^{87} +3.38226 q^{88} -12.0825 q^{89} -10.5563 q^{90} -0.272999 q^{91} -0.273819 q^{92} +0.238783 q^{93} +4.26477 q^{94} -6.80344 q^{95} +3.12962 q^{96} +10.0952 q^{97} +6.95168 q^{98} -22.9808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + O(q^{10}) \) \( 86q - 86q^{2} + 12q^{3} + 86q^{4} - 4q^{5} - 12q^{6} + 35q^{7} - 86q^{8} + 72q^{9} + 4q^{10} + 13q^{11} + 12q^{12} + 45q^{13} - 35q^{14} + 17q^{15} + 86q^{16} + 5q^{17} - 72q^{18} + 47q^{19} - 4q^{20} + 15q^{21} - 13q^{22} + 6q^{23} - 12q^{24} + 112q^{25} - 45q^{26} + 51q^{27} + 35q^{28} - 14q^{29} - 17q^{30} + 24q^{31} - 86q^{32} + 43q^{33} - 5q^{34} + 42q^{35} + 72q^{36} + 61q^{37} - 47q^{38} + 20q^{39} + 4q^{40} - 16q^{41} - 15q^{42} + 72q^{43} + 13q^{44} + 6q^{45} - 6q^{46} + 11q^{47} + 12q^{48} + 89q^{49} - 112q^{50} + 56q^{51} + 45q^{52} - 7q^{53} - 51q^{54} + 48q^{55} - 35q^{56} + 65q^{57} + 14q^{58} + 24q^{59} + 17q^{60} + 31q^{61} - 24q^{62} + 98q^{63} + 86q^{64} - 9q^{65} - 43q^{66} + 157q^{67} + 5q^{68} + q^{69} - 42q^{70} - 11q^{71} - 72q^{72} + 74q^{73} - 61q^{74} + 76q^{75} + 47q^{76} - 13q^{77} - 20q^{78} + 57q^{79} - 4q^{80} + 34q^{81} + 16q^{82} + 65q^{83} + 15q^{84} + 102q^{85} - 72q^{86} + 49q^{87} - 13q^{88} - 34q^{89} - 6q^{90} + 91q^{91} + 6q^{92} + 57q^{93} - 11q^{94} - 13q^{95} - 12q^{96} + 64q^{97} - 89q^{98} + 56q^{99} + O(q^{100}) \)

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
\(3\) −3.12962 −1.80689 −0.903443 0.428708i \(-0.858969\pi\)
−0.903443 + 0.428708i \(0.858969\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.55366 0.694816 0.347408 0.937714i \(-0.387062\pi\)
0.347408 + 0.937714i \(0.387062\pi\)
\(6\) 3.12962 1.27766
\(7\) 0.219811 0.0830807 0.0415403 0.999137i \(-0.486773\pi\)
0.0415403 + 0.999137i \(0.486773\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.79451 2.26484
\(10\) −1.55366 −0.491309
\(11\) −3.38226 −1.01979 −0.509895 0.860237i \(-0.670316\pi\)
−0.509895 + 0.860237i \(0.670316\pi\)
\(12\) −3.12962 −0.903443
\(13\) −1.24197 −0.344461 −0.172231 0.985057i \(-0.555097\pi\)
−0.172231 + 0.985057i \(0.555097\pi\)
\(14\) −0.219811 −0.0587469
\(15\) −4.86235 −1.25545
\(16\) 1.00000 0.250000
\(17\) −6.07371 −1.47309 −0.736546 0.676387i \(-0.763545\pi\)
−0.736546 + 0.676387i \(0.763545\pi\)
\(18\) −6.79451 −1.60148
\(19\) −4.37899 −1.00461 −0.502304 0.864691i \(-0.667514\pi\)
−0.502304 + 0.864691i \(0.667514\pi\)
\(20\) 1.55366 0.347408
\(21\) −0.687924 −0.150117
\(22\) 3.38226 0.721101
\(23\) −0.273819 −0.0570953 −0.0285477 0.999592i \(-0.509088\pi\)
−0.0285477 + 0.999592i \(0.509088\pi\)
\(24\) 3.12962 0.638831
\(25\) −2.58615 −0.517230
\(26\) 1.24197 0.243571
\(27\) −11.8754 −2.28541
\(28\) 0.219811 0.0415403
\(29\) −9.14771 −1.69869 −0.849344 0.527840i \(-0.823002\pi\)
−0.849344 + 0.527840i \(0.823002\pi\)
\(30\) 4.86235 0.887740
\(31\) −0.0762978 −0.0137035 −0.00685175 0.999977i \(-0.502181\pi\)
−0.00685175 + 0.999977i \(0.502181\pi\)
\(32\) −1.00000 −0.176777
\(33\) 10.5852 1.84264
\(34\) 6.07371 1.04163
\(35\) 0.341511 0.0577258
\(36\) 6.79451 1.13242
\(37\) −10.1804 −1.67365 −0.836823 0.547473i \(-0.815590\pi\)
−0.836823 + 0.547473i \(0.815590\pi\)
\(38\) 4.37899 0.710365
\(39\) 3.88690 0.622402
\(40\) −1.55366 −0.245655
\(41\) −10.4153 −1.62660 −0.813300 0.581845i \(-0.802331\pi\)
−0.813300 + 0.581845i \(0.802331\pi\)
\(42\) 0.687924 0.106149
\(43\) −2.44954 −0.373551 −0.186776 0.982403i \(-0.559804\pi\)
−0.186776 + 0.982403i \(0.559804\pi\)
\(44\) −3.38226 −0.509895
\(45\) 10.5563 1.57364
\(46\) 0.273819 0.0403725
\(47\) −4.26477 −0.622081 −0.311040 0.950397i \(-0.600677\pi\)
−0.311040 + 0.950397i \(0.600677\pi\)
\(48\) −3.12962 −0.451721
\(49\) −6.95168 −0.993098
\(50\) 2.58615 0.365737
\(51\) 19.0084 2.66171
\(52\) −1.24197 −0.172231
\(53\) 0.795398 0.109256 0.0546282 0.998507i \(-0.482603\pi\)
0.0546282 + 0.998507i \(0.482603\pi\)
\(54\) 11.8754 1.61603
\(55\) −5.25487 −0.708567
\(56\) −0.219811 −0.0293735
\(57\) 13.7046 1.81521
\(58\) 9.14771 1.20115
\(59\) −2.78406 −0.362453 −0.181227 0.983441i \(-0.558007\pi\)
−0.181227 + 0.983441i \(0.558007\pi\)
\(60\) −4.86235 −0.627727
\(61\) −9.70482 −1.24258 −0.621288 0.783583i \(-0.713390\pi\)
−0.621288 + 0.783583i \(0.713390\pi\)
\(62\) 0.0762978 0.00968983
\(63\) 1.49351 0.188164
\(64\) 1.00000 0.125000
\(65\) −1.92960 −0.239337
\(66\) −10.5852 −1.30295
\(67\) 5.80502 0.709196 0.354598 0.935019i \(-0.384618\pi\)
0.354598 + 0.935019i \(0.384618\pi\)
\(68\) −6.07371 −0.736546
\(69\) 0.856950 0.103165
\(70\) −0.341511 −0.0408183
\(71\) 4.38757 0.520709 0.260355 0.965513i \(-0.416161\pi\)
0.260355 + 0.965513i \(0.416161\pi\)
\(72\) −6.79451 −0.800741
\(73\) 1.82521 0.213625 0.106812 0.994279i \(-0.465936\pi\)
0.106812 + 0.994279i \(0.465936\pi\)
\(74\) 10.1804 1.18345
\(75\) 8.09367 0.934576
\(76\) −4.37899 −0.502304
\(77\) −0.743458 −0.0847249
\(78\) −3.88690 −0.440105
\(79\) −2.72630 −0.306733 −0.153366 0.988169i \(-0.549011\pi\)
−0.153366 + 0.988169i \(0.549011\pi\)
\(80\) 1.55366 0.173704
\(81\) 16.7818 1.86465
\(82\) 10.4153 1.15018
\(83\) 9.27875 1.01847 0.509237 0.860626i \(-0.329927\pi\)
0.509237 + 0.860626i \(0.329927\pi\)
\(84\) −0.687924 −0.0750587
\(85\) −9.43647 −1.02353
\(86\) 2.44954 0.264141
\(87\) 28.6288 3.06933
\(88\) 3.38226 0.360550
\(89\) −12.0825 −1.28074 −0.640370 0.768067i \(-0.721219\pi\)
−0.640370 + 0.768067i \(0.721219\pi\)
\(90\) −10.5563 −1.11274
\(91\) −0.272999 −0.0286181
\(92\) −0.273819 −0.0285477
\(93\) 0.238783 0.0247606
\(94\) 4.26477 0.439877
\(95\) −6.80344 −0.698018
\(96\) 3.12962 0.319415
\(97\) 10.0952 1.02501 0.512505 0.858684i \(-0.328718\pi\)
0.512505 + 0.858684i \(0.328718\pi\)
\(98\) 6.95168 0.702226
\(99\) −22.9808 −2.30966
\(100\) −2.58615 −0.258615
\(101\) 17.8857 1.77970 0.889849 0.456255i \(-0.150810\pi\)
0.889849 + 0.456255i \(0.150810\pi\)
\(102\) −19.0084 −1.88211
\(103\) 9.55210 0.941196 0.470598 0.882348i \(-0.344038\pi\)
0.470598 + 0.882348i \(0.344038\pi\)
\(104\) 1.24197 0.121785
\(105\) −1.06880 −0.104304
\(106\) −0.795398 −0.0772559
\(107\) 14.1746 1.37032 0.685158 0.728395i \(-0.259733\pi\)
0.685158 + 0.728395i \(0.259733\pi\)
\(108\) −11.8754 −1.14271
\(109\) 9.42284 0.902544 0.451272 0.892386i \(-0.350970\pi\)
0.451272 + 0.892386i \(0.350970\pi\)
\(110\) 5.25487 0.501032
\(111\) 31.8607 3.02409
\(112\) 0.219811 0.0207702
\(113\) −10.9128 −1.02659 −0.513293 0.858214i \(-0.671574\pi\)
−0.513293 + 0.858214i \(0.671574\pi\)
\(114\) −13.7046 −1.28355
\(115\) −0.425421 −0.0396707
\(116\) −9.14771 −0.849344
\(117\) −8.43859 −0.780148
\(118\) 2.78406 0.256293
\(119\) −1.33507 −0.122386
\(120\) 4.86235 0.443870
\(121\) 0.439694 0.0399722
\(122\) 9.70482 0.878633
\(123\) 32.5960 2.93908
\(124\) −0.0762978 −0.00685175
\(125\) −11.7863 −1.05420
\(126\) −1.49351 −0.133052
\(127\) 7.44426 0.660571 0.330286 0.943881i \(-0.392855\pi\)
0.330286 + 0.943881i \(0.392855\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.66612 0.674965
\(130\) 1.92960 0.169237
\(131\) 8.11615 0.709111 0.354556 0.935035i \(-0.384632\pi\)
0.354556 + 0.935035i \(0.384632\pi\)
\(132\) 10.5852 0.921322
\(133\) −0.962549 −0.0834636
\(134\) −5.80502 −0.501477
\(135\) −18.4502 −1.58794
\(136\) 6.07371 0.520817
\(137\) −17.5206 −1.49689 −0.748444 0.663198i \(-0.769199\pi\)
−0.748444 + 0.663198i \(0.769199\pi\)
\(138\) −0.856950 −0.0729484
\(139\) −3.70299 −0.314084 −0.157042 0.987592i \(-0.550196\pi\)
−0.157042 + 0.987592i \(0.550196\pi\)
\(140\) 0.341511 0.0288629
\(141\) 13.3471 1.12403
\(142\) −4.38757 −0.368197
\(143\) 4.20067 0.351278
\(144\) 6.79451 0.566209
\(145\) −14.2124 −1.18028
\(146\) −1.82521 −0.151055
\(147\) 21.7561 1.79441
\(148\) −10.1804 −0.836823
\(149\) −5.88730 −0.482306 −0.241153 0.970487i \(-0.577526\pi\)
−0.241153 + 0.970487i \(0.577526\pi\)
\(150\) −8.09367 −0.660845
\(151\) −4.04743 −0.329375 −0.164688 0.986346i \(-0.552662\pi\)
−0.164688 + 0.986346i \(0.552662\pi\)
\(152\) 4.37899 0.355183
\(153\) −41.2679 −3.33631
\(154\) 0.743458 0.0599095
\(155\) −0.118541 −0.00952141
\(156\) 3.88690 0.311201
\(157\) 10.9058 0.870378 0.435189 0.900339i \(-0.356682\pi\)
0.435189 + 0.900339i \(0.356682\pi\)
\(158\) 2.72630 0.216893
\(159\) −2.48929 −0.197414
\(160\) −1.55366 −0.122827
\(161\) −0.0601885 −0.00474352
\(162\) −16.7818 −1.31850
\(163\) 12.8049 1.00295 0.501477 0.865171i \(-0.332790\pi\)
0.501477 + 0.865171i \(0.332790\pi\)
\(164\) −10.4153 −0.813300
\(165\) 16.4457 1.28030
\(166\) −9.27875 −0.720171
\(167\) −7.34115 −0.568076 −0.284038 0.958813i \(-0.591674\pi\)
−0.284038 + 0.958813i \(0.591674\pi\)
\(168\) 0.687924 0.0530745
\(169\) −11.4575 −0.881347
\(170\) 9.43647 0.723744
\(171\) −29.7531 −2.27527
\(172\) −2.44954 −0.186776
\(173\) −17.3213 −1.31691 −0.658456 0.752619i \(-0.728790\pi\)
−0.658456 + 0.752619i \(0.728790\pi\)
\(174\) −28.6288 −2.17035
\(175\) −0.568464 −0.0429719
\(176\) −3.38226 −0.254948
\(177\) 8.71303 0.654912
\(178\) 12.0825 0.905620
\(179\) 6.26424 0.468211 0.234106 0.972211i \(-0.424784\pi\)
0.234106 + 0.972211i \(0.424784\pi\)
\(180\) 10.5563 0.786822
\(181\) 9.17332 0.681847 0.340924 0.940091i \(-0.389260\pi\)
0.340924 + 0.940091i \(0.389260\pi\)
\(182\) 0.272999 0.0202360
\(183\) 30.3724 2.24519
\(184\) 0.273819 0.0201862
\(185\) −15.8168 −1.16288
\(186\) −0.238783 −0.0175084
\(187\) 20.5429 1.50225
\(188\) −4.26477 −0.311040
\(189\) −2.61033 −0.189874
\(190\) 6.80344 0.493573
\(191\) −22.1924 −1.60579 −0.802894 0.596122i \(-0.796707\pi\)
−0.802894 + 0.596122i \(0.796707\pi\)
\(192\) −3.12962 −0.225861
\(193\) 1.84237 0.132616 0.0663082 0.997799i \(-0.478878\pi\)
0.0663082 + 0.997799i \(0.478878\pi\)
\(194\) −10.0952 −0.724791
\(195\) 6.03890 0.432455
\(196\) −6.95168 −0.496549
\(197\) 3.30779 0.235670 0.117835 0.993033i \(-0.462405\pi\)
0.117835 + 0.993033i \(0.462405\pi\)
\(198\) 22.9808 1.63317
\(199\) −4.01799 −0.284828 −0.142414 0.989807i \(-0.545486\pi\)
−0.142414 + 0.989807i \(0.545486\pi\)
\(200\) 2.58615 0.182869
\(201\) −18.1675 −1.28144
\(202\) −17.8857 −1.25844
\(203\) −2.01077 −0.141128
\(204\) 19.0084 1.33085
\(205\) −16.1818 −1.13019
\(206\) −9.55210 −0.665526
\(207\) −1.86047 −0.129312
\(208\) −1.24197 −0.0861153
\(209\) 14.8109 1.02449
\(210\) 1.06880 0.0737540
\(211\) 5.26154 0.362219 0.181110 0.983463i \(-0.442031\pi\)
0.181110 + 0.983463i \(0.442031\pi\)
\(212\) 0.795398 0.0546282
\(213\) −13.7314 −0.940862
\(214\) −14.1746 −0.968959
\(215\) −3.80574 −0.259550
\(216\) 11.8754 0.808016
\(217\) −0.0167711 −0.00113850
\(218\) −9.42284 −0.638195
\(219\) −5.71221 −0.385995
\(220\) −5.25487 −0.354283
\(221\) 7.54338 0.507423
\(222\) −31.8607 −2.13835
\(223\) −8.36690 −0.560289 −0.280144 0.959958i \(-0.590382\pi\)
−0.280144 + 0.959958i \(0.590382\pi\)
\(224\) −0.219811 −0.0146867
\(225\) −17.5716 −1.17144
\(226\) 10.9128 0.725905
\(227\) 8.48387 0.563094 0.281547 0.959547i \(-0.409152\pi\)
0.281547 + 0.959547i \(0.409152\pi\)
\(228\) 13.7046 0.907606
\(229\) 5.27650 0.348681 0.174340 0.984685i \(-0.444221\pi\)
0.174340 + 0.984685i \(0.444221\pi\)
\(230\) 0.425421 0.0280515
\(231\) 2.32674 0.153088
\(232\) 9.14771 0.600577
\(233\) 4.75489 0.311503 0.155752 0.987796i \(-0.450220\pi\)
0.155752 + 0.987796i \(0.450220\pi\)
\(234\) 8.43859 0.551648
\(235\) −6.62599 −0.432232
\(236\) −2.78406 −0.181227
\(237\) 8.53227 0.554231
\(238\) 1.33507 0.0865396
\(239\) −17.2172 −1.11369 −0.556844 0.830617i \(-0.687988\pi\)
−0.556844 + 0.830617i \(0.687988\pi\)
\(240\) −4.86235 −0.313863
\(241\) −7.68743 −0.495191 −0.247595 0.968864i \(-0.579640\pi\)
−0.247595 + 0.968864i \(0.579640\pi\)
\(242\) −0.439694 −0.0282646
\(243\) −16.8946 −1.08379
\(244\) −9.70482 −0.621288
\(245\) −10.8005 −0.690020
\(246\) −32.5960 −2.07824
\(247\) 5.43858 0.346049
\(248\) 0.0762978 0.00484492
\(249\) −29.0389 −1.84027
\(250\) 11.7863 0.745429
\(251\) −11.0951 −0.700316 −0.350158 0.936691i \(-0.613872\pi\)
−0.350158 + 0.936691i \(0.613872\pi\)
\(252\) 1.49351 0.0940821
\(253\) 0.926129 0.0582252
\(254\) −7.44426 −0.467094
\(255\) 29.5325 1.84940
\(256\) 1.00000 0.0625000
\(257\) −6.88536 −0.429497 −0.214749 0.976669i \(-0.568893\pi\)
−0.214749 + 0.976669i \(0.568893\pi\)
\(258\) −7.66612 −0.477272
\(259\) −2.23776 −0.139048
\(260\) −1.92960 −0.119669
\(261\) −62.1542 −3.84725
\(262\) −8.11615 −0.501417
\(263\) 1.08777 0.0670747 0.0335374 0.999437i \(-0.489323\pi\)
0.0335374 + 0.999437i \(0.489323\pi\)
\(264\) −10.5852 −0.651473
\(265\) 1.23578 0.0759131
\(266\) 0.962549 0.0590177
\(267\) 37.8135 2.31415
\(268\) 5.80502 0.354598
\(269\) −19.0127 −1.15922 −0.579611 0.814893i \(-0.696796\pi\)
−0.579611 + 0.814893i \(0.696796\pi\)
\(270\) 18.4502 1.12285
\(271\) −26.4945 −1.60943 −0.804714 0.593663i \(-0.797681\pi\)
−0.804714 + 0.593663i \(0.797681\pi\)
\(272\) −6.07371 −0.368273
\(273\) 0.854382 0.0517096
\(274\) 17.5206 1.05846
\(275\) 8.74704 0.527467
\(276\) 0.856950 0.0515823
\(277\) 24.1553 1.45135 0.725677 0.688036i \(-0.241527\pi\)
0.725677 + 0.688036i \(0.241527\pi\)
\(278\) 3.70299 0.222091
\(279\) −0.518406 −0.0310362
\(280\) −0.341511 −0.0204092
\(281\) −1.76711 −0.105417 −0.0527083 0.998610i \(-0.516785\pi\)
−0.0527083 + 0.998610i \(0.516785\pi\)
\(282\) −13.3471 −0.794808
\(283\) −4.06682 −0.241747 −0.120874 0.992668i \(-0.538570\pi\)
−0.120874 + 0.992668i \(0.538570\pi\)
\(284\) 4.38757 0.260355
\(285\) 21.2922 1.26124
\(286\) −4.20067 −0.248391
\(287\) −2.28940 −0.135139
\(288\) −6.79451 −0.400370
\(289\) 19.8900 1.17000
\(290\) 14.2124 0.834581
\(291\) −31.5940 −1.85208
\(292\) 1.82521 0.106812
\(293\) 29.4996 1.72338 0.861691 0.507433i \(-0.169405\pi\)
0.861691 + 0.507433i \(0.169405\pi\)
\(294\) −21.7561 −1.26884
\(295\) −4.32547 −0.251838
\(296\) 10.1804 0.591723
\(297\) 40.1656 2.33064
\(298\) 5.88730 0.341042
\(299\) 0.340076 0.0196671
\(300\) 8.09367 0.467288
\(301\) −0.538436 −0.0310349
\(302\) 4.04743 0.232903
\(303\) −55.9755 −3.21571
\(304\) −4.37899 −0.251152
\(305\) −15.0780 −0.863361
\(306\) 41.2679 2.35913
\(307\) 1.49105 0.0850989 0.0425495 0.999094i \(-0.486452\pi\)
0.0425495 + 0.999094i \(0.486452\pi\)
\(308\) −0.743458 −0.0423624
\(309\) −29.8944 −1.70063
\(310\) 0.118541 0.00673265
\(311\) −8.31280 −0.471376 −0.235688 0.971829i \(-0.575734\pi\)
−0.235688 + 0.971829i \(0.575734\pi\)
\(312\) −3.88690 −0.220052
\(313\) −5.24047 −0.296209 −0.148104 0.988972i \(-0.547317\pi\)
−0.148104 + 0.988972i \(0.547317\pi\)
\(314\) −10.9058 −0.615450
\(315\) 2.32040 0.130740
\(316\) −2.72630 −0.153366
\(317\) −0.491069 −0.0275812 −0.0137906 0.999905i \(-0.504390\pi\)
−0.0137906 + 0.999905i \(0.504390\pi\)
\(318\) 2.48929 0.139593
\(319\) 30.9400 1.73231
\(320\) 1.55366 0.0868520
\(321\) −44.3612 −2.47600
\(322\) 0.0601885 0.00335417
\(323\) 26.5967 1.47988
\(324\) 16.7818 0.932323
\(325\) 3.21193 0.178166
\(326\) −12.8049 −0.709195
\(327\) −29.4899 −1.63079
\(328\) 10.4153 0.575090
\(329\) −0.937443 −0.0516829
\(330\) −16.4457 −0.905308
\(331\) 22.2297 1.22185 0.610926 0.791688i \(-0.290797\pi\)
0.610926 + 0.791688i \(0.290797\pi\)
\(332\) 9.27875 0.509237
\(333\) −69.1708 −3.79054
\(334\) 7.34115 0.401690
\(335\) 9.01900 0.492761
\(336\) −0.687924 −0.0375293
\(337\) −3.14974 −0.171577 −0.0857886 0.996313i \(-0.527341\pi\)
−0.0857886 + 0.996313i \(0.527341\pi\)
\(338\) 11.4575 0.623206
\(339\) 34.1527 1.85492
\(340\) −9.43647 −0.511764
\(341\) 0.258059 0.0139747
\(342\) 29.7531 1.60886
\(343\) −3.06673 −0.165588
\(344\) 2.44954 0.132070
\(345\) 1.33141 0.0716805
\(346\) 17.3213 0.931198
\(347\) 10.2642 0.551012 0.275506 0.961299i \(-0.411155\pi\)
0.275506 + 0.961299i \(0.411155\pi\)
\(348\) 28.6288 1.53467
\(349\) −7.88385 −0.422013 −0.211007 0.977485i \(-0.567674\pi\)
−0.211007 + 0.977485i \(0.567674\pi\)
\(350\) 0.568464 0.0303857
\(351\) 14.7489 0.787236
\(352\) 3.38226 0.180275
\(353\) −4.02178 −0.214058 −0.107029 0.994256i \(-0.534134\pi\)
−0.107029 + 0.994256i \(0.534134\pi\)
\(354\) −8.71303 −0.463093
\(355\) 6.81678 0.361797
\(356\) −12.0825 −0.640370
\(357\) 4.17825 0.221137
\(358\) −6.26424 −0.331075
\(359\) 10.7412 0.566901 0.283450 0.958987i \(-0.408521\pi\)
0.283450 + 0.958987i \(0.408521\pi\)
\(360\) −10.5563 −0.556368
\(361\) 0.175525 0.00923817
\(362\) −9.17332 −0.482139
\(363\) −1.37607 −0.0722252
\(364\) −0.272999 −0.0143090
\(365\) 2.83575 0.148430
\(366\) −30.3724 −1.58759
\(367\) −11.0269 −0.575598 −0.287799 0.957691i \(-0.592924\pi\)
−0.287799 + 0.957691i \(0.592924\pi\)
\(368\) −0.273819 −0.0142738
\(369\) −70.7670 −3.68398
\(370\) 15.8168 0.822278
\(371\) 0.174837 0.00907709
\(372\) 0.238783 0.0123803
\(373\) 19.9346 1.03217 0.516086 0.856537i \(-0.327388\pi\)
0.516086 + 0.856537i \(0.327388\pi\)
\(374\) −20.5429 −1.06225
\(375\) 36.8865 1.90481
\(376\) 4.26477 0.219939
\(377\) 11.3612 0.585132
\(378\) 2.61033 0.134261
\(379\) −12.6839 −0.651530 −0.325765 0.945451i \(-0.605622\pi\)
−0.325765 + 0.945451i \(0.605622\pi\)
\(380\) −6.80344 −0.349009
\(381\) −23.2977 −1.19358
\(382\) 22.1924 1.13546
\(383\) −4.56730 −0.233378 −0.116689 0.993169i \(-0.537228\pi\)
−0.116689 + 0.993169i \(0.537228\pi\)
\(384\) 3.12962 0.159708
\(385\) −1.15508 −0.0588682
\(386\) −1.84237 −0.0937740
\(387\) −16.6434 −0.846033
\(388\) 10.0952 0.512505
\(389\) 2.20896 0.111999 0.0559993 0.998431i \(-0.482166\pi\)
0.0559993 + 0.998431i \(0.482166\pi\)
\(390\) −6.03890 −0.305792
\(391\) 1.66310 0.0841066
\(392\) 6.95168 0.351113
\(393\) −25.4005 −1.28128
\(394\) −3.30779 −0.166644
\(395\) −4.23573 −0.213123
\(396\) −22.9808 −1.15483
\(397\) −23.3040 −1.16960 −0.584798 0.811179i \(-0.698826\pi\)
−0.584798 + 0.811179i \(0.698826\pi\)
\(398\) 4.01799 0.201404
\(399\) 3.01241 0.150809
\(400\) −2.58615 −0.129308
\(401\) 15.6411 0.781077 0.390539 0.920587i \(-0.372289\pi\)
0.390539 + 0.920587i \(0.372289\pi\)
\(402\) 18.1675 0.906112
\(403\) 0.0947597 0.00472032
\(404\) 17.8857 0.889849
\(405\) 26.0732 1.29559
\(406\) 2.01077 0.0997927
\(407\) 34.4328 1.70677
\(408\) −19.0084 −0.941056
\(409\) 21.1945 1.04800 0.524000 0.851718i \(-0.324439\pi\)
0.524000 + 0.851718i \(0.324439\pi\)
\(410\) 16.1818 0.799163
\(411\) 54.8329 2.70471
\(412\) 9.55210 0.470598
\(413\) −0.611966 −0.0301129
\(414\) 1.86047 0.0914370
\(415\) 14.4160 0.707653
\(416\) 1.24197 0.0608927
\(417\) 11.5889 0.567513
\(418\) −14.8109 −0.724424
\(419\) 1.48447 0.0725212 0.0362606 0.999342i \(-0.488455\pi\)
0.0362606 + 0.999342i \(0.488455\pi\)
\(420\) −1.06880 −0.0521520
\(421\) 27.3072 1.33087 0.665435 0.746456i \(-0.268246\pi\)
0.665435 + 0.746456i \(0.268246\pi\)
\(422\) −5.26154 −0.256128
\(423\) −28.9770 −1.40891
\(424\) −0.795398 −0.0386279
\(425\) 15.7075 0.761928
\(426\) 13.7314 0.665290
\(427\) −2.13323 −0.103234
\(428\) 14.1746 0.685158
\(429\) −13.1465 −0.634719
\(430\) 3.80574 0.183529
\(431\) −20.5582 −0.990253 −0.495126 0.868821i \(-0.664878\pi\)
−0.495126 + 0.868821i \(0.664878\pi\)
\(432\) −11.8754 −0.571354
\(433\) −11.5076 −0.553021 −0.276510 0.961011i \(-0.589178\pi\)
−0.276510 + 0.961011i \(0.589178\pi\)
\(434\) 0.0167711 0.000805038 0
\(435\) 44.4794 2.13262
\(436\) 9.42284 0.451272
\(437\) 1.19905 0.0573584
\(438\) 5.71221 0.272940
\(439\) 13.6627 0.652085 0.326043 0.945355i \(-0.394285\pi\)
0.326043 + 0.945355i \(0.394285\pi\)
\(440\) 5.25487 0.250516
\(441\) −47.2333 −2.24920
\(442\) −7.54338 −0.358802
\(443\) −0.761260 −0.0361686 −0.0180843 0.999836i \(-0.505757\pi\)
−0.0180843 + 0.999836i \(0.505757\pi\)
\(444\) 31.8607 1.51204
\(445\) −18.7720 −0.889879
\(446\) 8.36690 0.396184
\(447\) 18.4250 0.871472
\(448\) 0.219811 0.0103851
\(449\) 39.8287 1.87963 0.939817 0.341677i \(-0.110995\pi\)
0.939817 + 0.341677i \(0.110995\pi\)
\(450\) 17.5716 0.828335
\(451\) 35.2273 1.65879
\(452\) −10.9128 −0.513293
\(453\) 12.6669 0.595143
\(454\) −8.48387 −0.398168
\(455\) −0.424147 −0.0198843
\(456\) −13.7046 −0.641775
\(457\) −5.39496 −0.252366 −0.126183 0.992007i \(-0.540273\pi\)
−0.126183 + 0.992007i \(0.540273\pi\)
\(458\) −5.27650 −0.246555
\(459\) 72.1276 3.36663
\(460\) −0.425421 −0.0198354
\(461\) −0.921782 −0.0429317 −0.0214658 0.999770i \(-0.506833\pi\)
−0.0214658 + 0.999770i \(0.506833\pi\)
\(462\) −2.32674 −0.108250
\(463\) −27.7349 −1.28895 −0.644475 0.764626i \(-0.722924\pi\)
−0.644475 + 0.764626i \(0.722924\pi\)
\(464\) −9.14771 −0.424672
\(465\) 0.370987 0.0172041
\(466\) −4.75489 −0.220266
\(467\) 12.2482 0.566779 0.283389 0.959005i \(-0.408541\pi\)
0.283389 + 0.959005i \(0.408541\pi\)
\(468\) −8.43859 −0.390074
\(469\) 1.27601 0.0589205
\(470\) 6.62599 0.305634
\(471\) −34.1310 −1.57267
\(472\) 2.78406 0.128147
\(473\) 8.28499 0.380944
\(474\) −8.53227 −0.391900
\(475\) 11.3247 0.519614
\(476\) −1.33507 −0.0611928
\(477\) 5.40434 0.247448
\(478\) 17.2172 0.787496
\(479\) 30.3247 1.38557 0.692785 0.721145i \(-0.256384\pi\)
0.692785 + 0.721145i \(0.256384\pi\)
\(480\) 4.86235 0.221935
\(481\) 12.6438 0.576506
\(482\) 7.68743 0.350153
\(483\) 0.188367 0.00857099
\(484\) 0.439694 0.0199861
\(485\) 15.6844 0.712194
\(486\) 16.8946 0.766355
\(487\) 7.93744 0.359680 0.179840 0.983696i \(-0.442442\pi\)
0.179840 + 0.983696i \(0.442442\pi\)
\(488\) 9.70482 0.439317
\(489\) −40.0743 −1.81222
\(490\) 10.8005 0.487918
\(491\) −35.2377 −1.59026 −0.795128 0.606441i \(-0.792596\pi\)
−0.795128 + 0.606441i \(0.792596\pi\)
\(492\) 32.5960 1.46954
\(493\) 55.5606 2.50232
\(494\) −5.43858 −0.244693
\(495\) −35.7043 −1.60479
\(496\) −0.0762978 −0.00342587
\(497\) 0.964436 0.0432609
\(498\) 29.0389 1.30127
\(499\) −16.3186 −0.730521 −0.365261 0.930905i \(-0.619020\pi\)
−0.365261 + 0.930905i \(0.619020\pi\)
\(500\) −11.7863 −0.527098
\(501\) 22.9750 1.02645
\(502\) 11.0951 0.495198
\(503\) −14.4790 −0.645585 −0.322792 0.946470i \(-0.604622\pi\)
−0.322792 + 0.946470i \(0.604622\pi\)
\(504\) −1.49351 −0.0665261
\(505\) 27.7883 1.23656
\(506\) −0.926129 −0.0411715
\(507\) 35.8576 1.59249
\(508\) 7.44426 0.330286
\(509\) 1.18958 0.0527272 0.0263636 0.999652i \(-0.491607\pi\)
0.0263636 + 0.999652i \(0.491607\pi\)
\(510\) −29.5325 −1.30772
\(511\) 0.401201 0.0177481
\(512\) −1.00000 −0.0441942
\(513\) 52.0021 2.29595
\(514\) 6.88536 0.303700
\(515\) 14.8407 0.653958
\(516\) 7.66612 0.337482
\(517\) 14.4246 0.634392
\(518\) 2.23776 0.0983216
\(519\) 54.2090 2.37951
\(520\) 1.92960 0.0846185
\(521\) −30.8116 −1.34988 −0.674939 0.737873i \(-0.735830\pi\)
−0.674939 + 0.737873i \(0.735830\pi\)
\(522\) 62.1542 2.72042
\(523\) −27.7969 −1.21547 −0.607736 0.794139i \(-0.707922\pi\)
−0.607736 + 0.794139i \(0.707922\pi\)
\(524\) 8.11615 0.354556
\(525\) 1.77908 0.0776452
\(526\) −1.08777 −0.0474290
\(527\) 0.463411 0.0201865
\(528\) 10.5852 0.460661
\(529\) −22.9250 −0.996740
\(530\) −1.23578 −0.0536786
\(531\) −18.9163 −0.820897
\(532\) −0.962549 −0.0417318
\(533\) 12.9355 0.560300
\(534\) −37.8135 −1.63635
\(535\) 22.0225 0.952117
\(536\) −5.80502 −0.250738
\(537\) −19.6047 −0.846004
\(538\) 19.0127 0.819694
\(539\) 23.5124 1.01275
\(540\) −18.4502 −0.793972
\(541\) −18.2859 −0.786171 −0.393085 0.919502i \(-0.628592\pi\)
−0.393085 + 0.919502i \(0.628592\pi\)
\(542\) 26.4945 1.13804
\(543\) −28.7090 −1.23202
\(544\) 6.07371 0.260408
\(545\) 14.6399 0.627103
\(546\) −0.854382 −0.0365642
\(547\) 10.7652 0.460288 0.230144 0.973157i \(-0.426080\pi\)
0.230144 + 0.973157i \(0.426080\pi\)
\(548\) −17.5206 −0.748444
\(549\) −65.9395 −2.81423
\(550\) −8.74704 −0.372975
\(551\) 40.0577 1.70652
\(552\) −0.856950 −0.0364742
\(553\) −0.599270 −0.0254836
\(554\) −24.1553 −1.02626
\(555\) 49.5006 2.10119
\(556\) −3.70299 −0.157042
\(557\) −8.56630 −0.362966 −0.181483 0.983394i \(-0.558090\pi\)
−0.181483 + 0.983394i \(0.558090\pi\)
\(558\) 0.518406 0.0219459
\(559\) 3.04226 0.128674
\(560\) 0.341511 0.0144315
\(561\) −64.2914 −2.71439
\(562\) 1.76711 0.0745409
\(563\) −10.9206 −0.460250 −0.230125 0.973161i \(-0.573913\pi\)
−0.230125 + 0.973161i \(0.573913\pi\)
\(564\) 13.3471 0.562014
\(565\) −16.9547 −0.713288
\(566\) 4.06682 0.170941
\(567\) 3.68883 0.154916
\(568\) −4.38757 −0.184099
\(569\) −7.06327 −0.296108 −0.148054 0.988979i \(-0.547301\pi\)
−0.148054 + 0.988979i \(0.547301\pi\)
\(570\) −21.2922 −0.891831
\(571\) 11.0907 0.464132 0.232066 0.972700i \(-0.425451\pi\)
0.232066 + 0.972700i \(0.425451\pi\)
\(572\) 4.20067 0.175639
\(573\) 69.4538 2.90147
\(574\) 2.28940 0.0955577
\(575\) 0.708139 0.0295314
\(576\) 6.79451 0.283105
\(577\) 1.35623 0.0564606 0.0282303 0.999601i \(-0.491013\pi\)
0.0282303 + 0.999601i \(0.491013\pi\)
\(578\) −19.8900 −0.827315
\(579\) −5.76590 −0.239623
\(580\) −14.2124 −0.590138
\(581\) 2.03957 0.0846156
\(582\) 31.5940 1.30962
\(583\) −2.69024 −0.111419
\(584\) −1.82521 −0.0755277
\(585\) −13.1107 −0.542059
\(586\) −29.4996 −1.21862
\(587\) 7.40091 0.305468 0.152734 0.988267i \(-0.451192\pi\)
0.152734 + 0.988267i \(0.451192\pi\)
\(588\) 21.7561 0.897207
\(589\) 0.334107 0.0137666
\(590\) 4.32547 0.178077
\(591\) −10.3521 −0.425829
\(592\) −10.1804 −0.418412
\(593\) −6.06585 −0.249095 −0.124547 0.992214i \(-0.539748\pi\)
−0.124547 + 0.992214i \(0.539748\pi\)
\(594\) −40.1656 −1.64801
\(595\) −2.07424 −0.0850355
\(596\) −5.88730 −0.241153
\(597\) 12.5748 0.514652
\(598\) −0.340076 −0.0139067
\(599\) −11.0821 −0.452802 −0.226401 0.974034i \(-0.572696\pi\)
−0.226401 + 0.974034i \(0.572696\pi\)
\(600\) −8.09367 −0.330423
\(601\) 24.8649 1.01426 0.507129 0.861870i \(-0.330707\pi\)
0.507129 + 0.861870i \(0.330707\pi\)
\(602\) 0.538436 0.0219450
\(603\) 39.4422 1.60621
\(604\) −4.04743 −0.164688
\(605\) 0.683133 0.0277733
\(606\) 55.9755 2.27385
\(607\) −37.8681 −1.53702 −0.768510 0.639838i \(-0.779001\pi\)
−0.768510 + 0.639838i \(0.779001\pi\)
\(608\) 4.37899 0.177591
\(609\) 6.29293 0.255002
\(610\) 15.0780 0.610489
\(611\) 5.29672 0.214283
\(612\) −41.2679 −1.66816
\(613\) 3.14628 0.127077 0.0635385 0.997979i \(-0.479761\pi\)
0.0635385 + 0.997979i \(0.479761\pi\)
\(614\) −1.49105 −0.0601740
\(615\) 50.6429 2.04212
\(616\) 0.743458 0.0299548
\(617\) 7.40240 0.298010 0.149005 0.988836i \(-0.452393\pi\)
0.149005 + 0.988836i \(0.452393\pi\)
\(618\) 29.8944 1.20253
\(619\) −11.1699 −0.448955 −0.224478 0.974479i \(-0.572068\pi\)
−0.224478 + 0.974479i \(0.572068\pi\)
\(620\) −0.118541 −0.00476070
\(621\) 3.25170 0.130486
\(622\) 8.31280 0.333313
\(623\) −2.65586 −0.106405
\(624\) 3.88690 0.155600
\(625\) −5.38106 −0.215242
\(626\) 5.24047 0.209451
\(627\) −46.3524 −1.85114
\(628\) 10.9058 0.435189
\(629\) 61.8328 2.46544
\(630\) −2.32040 −0.0924468
\(631\) 31.4977 1.25390 0.626951 0.779059i \(-0.284303\pi\)
0.626951 + 0.779059i \(0.284303\pi\)
\(632\) 2.72630 0.108446
\(633\) −16.4666 −0.654489
\(634\) 0.491069 0.0195028
\(635\) 11.5658 0.458975
\(636\) −2.48929 −0.0987069
\(637\) 8.63380 0.342083
\(638\) −30.9400 −1.22492
\(639\) 29.8114 1.17932
\(640\) −1.55366 −0.0614137
\(641\) 3.60696 0.142466 0.0712332 0.997460i \(-0.477307\pi\)
0.0712332 + 0.997460i \(0.477307\pi\)
\(642\) 44.3612 1.75080
\(643\) 20.4998 0.808433 0.404217 0.914663i \(-0.367544\pi\)
0.404217 + 0.914663i \(0.367544\pi\)
\(644\) −0.0601885 −0.00237176
\(645\) 11.9105 0.468976
\(646\) −26.5967 −1.04643
\(647\) 39.0587 1.53556 0.767779 0.640715i \(-0.221362\pi\)
0.767779 + 0.640715i \(0.221362\pi\)
\(648\) −16.7818 −0.659252
\(649\) 9.41641 0.369626
\(650\) −3.21193 −0.125982
\(651\) 0.0524871 0.00205713
\(652\) 12.8049 0.501477
\(653\) −6.28188 −0.245829 −0.122915 0.992417i \(-0.539224\pi\)
−0.122915 + 0.992417i \(0.539224\pi\)
\(654\) 29.4899 1.15315
\(655\) 12.6097 0.492702
\(656\) −10.4153 −0.406650
\(657\) 12.4014 0.483825
\(658\) 0.937443 0.0365453
\(659\) 8.49788 0.331030 0.165515 0.986207i \(-0.447071\pi\)
0.165515 + 0.986207i \(0.447071\pi\)
\(660\) 16.4457 0.640150
\(661\) −6.18180 −0.240444 −0.120222 0.992747i \(-0.538361\pi\)
−0.120222 + 0.992747i \(0.538361\pi\)
\(662\) −22.2297 −0.863980
\(663\) −23.6079 −0.916855
\(664\) −9.27875 −0.360085
\(665\) −1.49547 −0.0579918
\(666\) 69.1708 2.68031
\(667\) 2.50482 0.0969871
\(668\) −7.34115 −0.284038
\(669\) 26.1852 1.01238
\(670\) −9.01900 −0.348434
\(671\) 32.8243 1.26717
\(672\) 0.687924 0.0265372
\(673\) 34.3862 1.32549 0.662746 0.748845i \(-0.269391\pi\)
0.662746 + 0.748845i \(0.269391\pi\)
\(674\) 3.14974 0.121323
\(675\) 30.7115 1.18209
\(676\) −11.4575 −0.440673
\(677\) −2.44515 −0.0939748 −0.0469874 0.998895i \(-0.514962\pi\)
−0.0469874 + 0.998895i \(0.514962\pi\)
\(678\) −34.1527 −1.31163
\(679\) 2.21903 0.0851585
\(680\) 9.43647 0.361872
\(681\) −26.5513 −1.01745
\(682\) −0.258059 −0.00988160
\(683\) −38.7481 −1.48266 −0.741328 0.671143i \(-0.765804\pi\)
−0.741328 + 0.671143i \(0.765804\pi\)
\(684\) −29.7531 −1.13764
\(685\) −27.2210 −1.04006
\(686\) 3.06673 0.117088
\(687\) −16.5134 −0.630027
\(688\) −2.44954 −0.0933878
\(689\) −0.987862 −0.0376346
\(690\) −1.33141 −0.0506858
\(691\) −5.20610 −0.198049 −0.0990247 0.995085i \(-0.531572\pi\)
−0.0990247 + 0.995085i \(0.531572\pi\)
\(692\) −17.3213 −0.658456
\(693\) −5.05143 −0.191888
\(694\) −10.2642 −0.389624
\(695\) −5.75318 −0.218230
\(696\) −28.6288 −1.08517
\(697\) 63.2597 2.39613
\(698\) 7.88385 0.298408
\(699\) −14.8810 −0.562851
\(700\) −0.568464 −0.0214859
\(701\) −12.5641 −0.474539 −0.237270 0.971444i \(-0.576252\pi\)
−0.237270 + 0.971444i \(0.576252\pi\)
\(702\) −14.7489 −0.556660
\(703\) 44.5798 1.68136
\(704\) −3.38226 −0.127474
\(705\) 20.7368 0.780993
\(706\) 4.02178 0.151362
\(707\) 3.93148 0.147859
\(708\) 8.71303 0.327456
\(709\) −29.9877 −1.12621 −0.563106 0.826385i \(-0.690394\pi\)
−0.563106 + 0.826385i \(0.690394\pi\)
\(710\) −6.81678 −0.255829
\(711\) −18.5239 −0.694699
\(712\) 12.0825 0.452810
\(713\) 0.0208918 0.000782405 0
\(714\) −4.17825 −0.156367
\(715\) 6.52640 0.244074
\(716\) 6.26424 0.234106
\(717\) 53.8832 2.01231
\(718\) −10.7412 −0.400859
\(719\) −20.6031 −0.768364 −0.384182 0.923257i \(-0.625517\pi\)
−0.384182 + 0.923257i \(0.625517\pi\)
\(720\) 10.5563 0.393411
\(721\) 2.09965 0.0781952
\(722\) −0.175525 −0.00653237
\(723\) 24.0587 0.894753
\(724\) 9.17332 0.340924
\(725\) 23.6574 0.878613
\(726\) 1.37607 0.0510709
\(727\) 27.1998 1.00879 0.504393 0.863474i \(-0.331716\pi\)
0.504393 + 0.863474i \(0.331716\pi\)
\(728\) 0.272999 0.0101180
\(729\) 2.52818 0.0936364
\(730\) −2.83575 −0.104956
\(731\) 14.8778 0.550276
\(732\) 30.3724 1.12260
\(733\) 21.6061 0.798041 0.399021 0.916942i \(-0.369350\pi\)
0.399021 + 0.916942i \(0.369350\pi\)
\(734\) 11.0269 0.407009
\(735\) 33.8015 1.24679
\(736\) 0.273819 0.0100931
\(737\) −19.6341 −0.723231
\(738\) 70.7670 2.60497
\(739\) −19.2258 −0.707232 −0.353616 0.935391i \(-0.615048\pi\)
−0.353616 + 0.935391i \(0.615048\pi\)
\(740\) −15.8168 −0.581438
\(741\) −17.0207 −0.625270
\(742\) −0.174837 −0.00641847
\(743\) −2.22384 −0.0815846 −0.0407923 0.999168i \(-0.512988\pi\)
−0.0407923 + 0.999168i \(0.512988\pi\)
\(744\) −0.238783 −0.00875421
\(745\) −9.14684 −0.335114
\(746\) −19.9346 −0.729856
\(747\) 63.0445 2.30668
\(748\) 20.5429 0.751123
\(749\) 3.11574 0.113847
\(750\) −36.8865 −1.34691
\(751\) 47.4396 1.73110 0.865548 0.500825i \(-0.166970\pi\)
0.865548 + 0.500825i \(0.166970\pi\)
\(752\) −4.26477 −0.155520
\(753\) 34.7234 1.26539
\(754\) −11.3612 −0.413751
\(755\) −6.28831 −0.228855
\(756\) −2.61033 −0.0949369
\(757\) 19.0557 0.692592 0.346296 0.938125i \(-0.387439\pi\)
0.346296 + 0.938125i \(0.387439\pi\)
\(758\) 12.6839 0.460701
\(759\) −2.89843 −0.105206
\(760\) 6.80344 0.246787
\(761\) −25.8493 −0.937035 −0.468518 0.883454i \(-0.655212\pi\)
−0.468518 + 0.883454i \(0.655212\pi\)
\(762\) 23.2977 0.843986
\(763\) 2.07124 0.0749840
\(764\) −22.1924 −0.802894
\(765\) −64.1161 −2.31812
\(766\) 4.56730 0.165023
\(767\) 3.45772 0.124851
\(768\) −3.12962 −0.112930
\(769\) −13.3045 −0.479774 −0.239887 0.970801i \(-0.577110\pi\)
−0.239887 + 0.970801i \(0.577110\pi\)
\(770\) 1.15508 0.0416261
\(771\) 21.5486 0.776052
\(772\) 1.84237 0.0663082
\(773\) 23.4232 0.842474 0.421237 0.906951i \(-0.361596\pi\)
0.421237 + 0.906951i \(0.361596\pi\)
\(774\) 16.6434 0.598235
\(775\) 0.197318 0.00708786
\(776\) −10.0952 −0.362396
\(777\) 7.00334 0.251243
\(778\) −2.20896 −0.0791950
\(779\) 45.6085 1.63410
\(780\) 6.03890 0.216227
\(781\) −14.8399 −0.531014
\(782\) −1.66310 −0.0594724
\(783\) 108.632 3.88221
\(784\) −6.95168 −0.248274
\(785\) 16.9439 0.604753
\(786\) 25.4005 0.906004
\(787\) −39.9705 −1.42480 −0.712398 0.701776i \(-0.752391\pi\)
−0.712398 + 0.701776i \(0.752391\pi\)
\(788\) 3.30779 0.117835
\(789\) −3.40430 −0.121196
\(790\) 4.23573 0.150701
\(791\) −2.39874 −0.0852894
\(792\) 22.9808 0.816587
\(793\) 12.0531 0.428019
\(794\) 23.3040 0.827029
\(795\) −3.86750 −0.137166
\(796\) −4.01799 −0.142414
\(797\) −15.3193 −0.542638 −0.271319 0.962490i \(-0.587460\pi\)
−0.271319 + 0.962490i \(0.587460\pi\)
\(798\) −3.01241 −0.106638
\(799\) 25.9030 0.916382
\(800\) 2.58615 0.0914343
\(801\) −82.0945 −2.90067
\(802\) −15.6411 −0.552305
\(803\) −6.17334 −0.217852
\(804\) −18.1675 −0.640718
\(805\) −0.0935122 −0.00329587
\(806\) −0.0947597 −0.00333777
\(807\) 59.5024 2.09458
\(808\) −17.8857 −0.629218
\(809\) −24.5586 −0.863435 −0.431718 0.902009i \(-0.642092\pi\)
−0.431718 + 0.902009i \(0.642092\pi\)
\(810\) −26.0732 −0.916118
\(811\) 1.59901 0.0561487 0.0280743 0.999606i \(-0.491062\pi\)
0.0280743 + 0.999606i \(0.491062\pi\)
\(812\) −2.01077 −0.0705641
\(813\) 82.9177 2.90805
\(814\) −34.4328 −1.20687
\(815\) 19.8943 0.696868
\(816\) 19.0084 0.665427
\(817\) 10.7265 0.375273
\(818\) −21.1945 −0.741048
\(819\) −1.85489 −0.0648152
\(820\) −16.1818 −0.565094
\(821\) −26.2787 −0.917134 −0.458567 0.888660i \(-0.651637\pi\)
−0.458567 + 0.888660i \(0.651637\pi\)
\(822\) −54.8329 −1.91252
\(823\) −7.95634 −0.277341 −0.138670 0.990339i \(-0.544283\pi\)
−0.138670 + 0.990339i \(0.544283\pi\)
\(824\) −9.55210 −0.332763
\(825\) −27.3749 −0.953072
\(826\) 0.611966 0.0212930
\(827\) −54.3440 −1.88973 −0.944863 0.327465i \(-0.893806\pi\)
−0.944863 + 0.327465i \(0.893806\pi\)
\(828\) −1.86047 −0.0646558
\(829\) −44.8886 −1.55905 −0.779523 0.626374i \(-0.784538\pi\)
−0.779523 + 0.626374i \(0.784538\pi\)
\(830\) −14.4160 −0.500386
\(831\) −75.5970 −2.62243
\(832\) −1.24197 −0.0430576
\(833\) 42.2225 1.46292
\(834\) −11.5889 −0.401292
\(835\) −11.4056 −0.394708
\(836\) 14.8109 0.512245
\(837\) 0.906064 0.0313182
\(838\) −1.48447 −0.0512802
\(839\) −32.8818 −1.13521 −0.567603 0.823302i \(-0.692129\pi\)
−0.567603 + 0.823302i \(0.692129\pi\)
\(840\) 1.06880 0.0368770
\(841\) 54.6807 1.88554
\(842\) −27.3072 −0.941067
\(843\) 5.53037 0.190476
\(844\) 5.26154 0.181110
\(845\) −17.8010 −0.612374
\(846\) 28.9770 0.996250
\(847\) 0.0966495 0.00332092
\(848\) 0.795398 0.0273141
\(849\) 12.7276 0.436810
\(850\) −15.7075 −0.538765
\(851\) 2.78759 0.0955573
\(852\) −13.7314 −0.470431
\(853\) 23.6695 0.810429 0.405214 0.914222i \(-0.367197\pi\)
0.405214 + 0.914222i \(0.367197\pi\)
\(854\) 2.13323 0.0729975
\(855\) −46.2260 −1.58090
\(856\) −14.1746 −0.484480
\(857\) 17.6919 0.604343 0.302171 0.953254i \(-0.402288\pi\)
0.302171 + 0.953254i \(0.402288\pi\)
\(858\) 13.1465 0.448814
\(859\) −43.1607 −1.47262 −0.736312 0.676642i \(-0.763435\pi\)
−0.736312 + 0.676642i \(0.763435\pi\)
\(860\) −3.80574 −0.129775
\(861\) 7.16495 0.244181
\(862\) 20.5582 0.700215
\(863\) −1.23931 −0.0421867 −0.0210933 0.999778i \(-0.506715\pi\)
−0.0210933 + 0.999778i \(0.506715\pi\)
\(864\) 11.8754 0.404008
\(865\) −26.9113 −0.915012
\(866\) 11.5076 0.391045
\(867\) −62.2481 −2.11406
\(868\) −0.0167711 −0.000569248 0
\(869\) 9.22106 0.312803
\(870\) −44.4794 −1.50799
\(871\) −7.20967 −0.244290
\(872\) −9.42284 −0.319098
\(873\) 68.5918 2.32148
\(874\) −1.19905 −0.0405585
\(875\) −2.59075 −0.0875834
\(876\) −5.71221 −0.192998
\(877\) −32.2716 −1.08973 −0.544867 0.838522i \(-0.683420\pi\)
−0.544867 + 0.838522i \(0.683420\pi\)
\(878\) −13.6627 −0.461094
\(879\) −92.3224 −3.11396
\(880\) −5.25487 −0.177142
\(881\) −12.6428 −0.425945 −0.212973 0.977058i \(-0.568315\pi\)
−0.212973 + 0.977058i \(0.568315\pi\)
\(882\) 47.2333 1.59043
\(883\) −15.6762 −0.527546 −0.263773 0.964585i \(-0.584967\pi\)
−0.263773 + 0.964585i \(0.584967\pi\)
\(884\) 7.54338 0.253711
\(885\) 13.5371 0.455043
\(886\) 0.761260 0.0255750
\(887\) −42.6791 −1.43302 −0.716512 0.697575i \(-0.754263\pi\)
−0.716512 + 0.697575i \(0.754263\pi\)
\(888\) −31.8607 −1.06918
\(889\) 1.63633 0.0548807
\(890\) 18.7720 0.629239
\(891\) −56.7605 −1.90155
\(892\) −8.36690 −0.280144
\(893\) 18.6754 0.624947
\(894\) −18.4250 −0.616224
\(895\) 9.73247 0.325321
\(896\) −0.219811 −0.00734337
\(897\) −1.06431 −0.0355362
\(898\) −39.8287 −1.32910
\(899\) 0.697951 0.0232780
\(900\) −17.5716 −0.585721
\(901\) −4.83102 −0.160945
\(902\) −35.2273 −1.17294
\(903\) 1.68510 0.0560765
\(904\) 10.9128 0.362953
\(905\) 14.2522 0.473758
\(906\) −12.6669 −0.420830
\(907\) −55.9234 −1.85691 −0.928453 0.371450i \(-0.878861\pi\)
−0.928453 + 0.371450i \(0.878861\pi\)
\(908\) 8.48387 0.281547
\(909\) 121.525 4.03072
\(910\) 0.424147 0.0140603
\(911\) 0.460704 0.0152638 0.00763191 0.999971i \(-0.497571\pi\)
0.00763191 + 0.999971i \(0.497571\pi\)
\(912\) 13.7046 0.453803
\(913\) −31.3832 −1.03863
\(914\) 5.39496 0.178450
\(915\) 47.1883 1.56000
\(916\) 5.27650 0.174340
\(917\) 1.78402 0.0589135
\(918\) −72.1276 −2.38056
\(919\) −11.4287 −0.376998 −0.188499 0.982073i \(-0.560362\pi\)
−0.188499 + 0.982073i \(0.560362\pi\)
\(920\) 0.425421 0.0140257
\(921\) −4.66643 −0.153764
\(922\) 0.921782 0.0303573
\(923\) −5.44924 −0.179364
\(924\) 2.32674 0.0765441
\(925\) 26.3280 0.865661
\(926\) 27.7349 0.911425
\(927\) 64.9018 2.13166
\(928\) 9.14771 0.300288
\(929\) −27.4956 −0.902102 −0.451051 0.892498i \(-0.648951\pi\)
−0.451051 + 0.892498i \(0.648951\pi\)
\(930\) −0.370987 −0.0121651
\(931\) 30.4413 0.997674
\(932\) 4.75489 0.155752
\(933\) 26.0159 0.851722
\(934\) −12.2482 −0.400773
\(935\) 31.9166 1.04378
\(936\) 8.43859 0.275824
\(937\) 1.71085 0.0558911 0.0279455 0.999609i \(-0.491104\pi\)
0.0279455 + 0.999609i \(0.491104\pi\)
\(938\) −1.27601 −0.0416631
\(939\) 16.4007 0.535216
\(940\) −6.62599 −0.216116
\(941\) −59.5502 −1.94128 −0.970640 0.240537i \(-0.922677\pi\)
−0.970640 + 0.240537i \(0.922677\pi\)
\(942\) 34.1310 1.11205
\(943\) 2.85192 0.0928712
\(944\) −2.78406 −0.0906133
\(945\) −4.05556 −0.131927
\(946\) −8.28499 −0.269368
\(947\) 10.7417 0.349057 0.174529 0.984652i \(-0.444160\pi\)
0.174529 + 0.984652i \(0.444160\pi\)
\(948\) 8.53227 0.277115
\(949\) −2.26686 −0.0735854
\(950\) −11.3247 −0.367423
\(951\) 1.53686 0.0498360
\(952\) 1.33507 0.0432698
\(953\) 49.8715 1.61550 0.807748 0.589528i \(-0.200686\pi\)
0.807748 + 0.589528i \(0.200686\pi\)
\(954\) −5.40434 −0.174972
\(955\) −34.4794 −1.11573
\(956\) −17.2172 −0.556844
\(957\) −96.8303 −3.13008
\(958\) −30.3247 −0.979745
\(959\) −3.85123 −0.124363
\(960\) −4.86235 −0.156932
\(961\) −30.9942 −0.999812
\(962\) −12.6438 −0.407651
\(963\) 96.3098 3.10354
\(964\) −7.68743 −0.247595
\(965\) 2.86240 0.0921441
\(966\) −0.188367 −0.00606061
\(967\) 38.6912 1.24423 0.622113 0.782927i \(-0.286274\pi\)
0.622113 + 0.782927i \(0.286274\pi\)
\(968\) −0.439694 −0.0141323
\(969\) −83.2376 −2.67398
\(970\) −15.6844 −0.503597
\(971\) −0.377391 −0.0121110 −0.00605552 0.999982i \(-0.501928\pi\)
−0.00605552 + 0.999982i \(0.501928\pi\)
\(972\) −16.8946 −0.541895
\(973\) −0.813958 −0.0260943
\(974\) −7.93744 −0.254332
\(975\) −10.0521 −0.321925
\(976\) −9.70482 −0.310644
\(977\) −59.4031 −1.90047 −0.950237 0.311527i \(-0.899160\pi\)
−0.950237 + 0.311527i \(0.899160\pi\)
\(978\) 40.0743 1.28143
\(979\) 40.8661 1.30609
\(980\) −10.8005 −0.345010
\(981\) 64.0236 2.04412
\(982\) 35.2377 1.12448
\(983\) −12.9560 −0.413234 −0.206617 0.978422i \(-0.566245\pi\)
−0.206617 + 0.978422i \(0.566245\pi\)
\(984\) −32.5960 −1.03912
\(985\) 5.13917 0.163747
\(986\) −55.5606 −1.76941
\(987\) 2.93384 0.0933851
\(988\) 5.43858 0.173024
\(989\) 0.670732 0.0213280
\(990\) 35.7043 1.13476
\(991\) 36.2446 1.15135 0.575673 0.817680i \(-0.304740\pi\)
0.575673 + 0.817680i \(0.304740\pi\)
\(992\) 0.0762978 0.00242246
\(993\) −69.5703 −2.20775
\(994\) −0.964436 −0.0305901
\(995\) −6.24258 −0.197903
\(996\) −29.0389 −0.920134
\(997\) −28.8741 −0.914451 −0.457226 0.889351i \(-0.651157\pi\)
−0.457226 + 0.889351i \(0.651157\pi\)
\(998\) 16.3186 0.516557
\(999\) 120.896 3.82498
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 \(a_p\))