Properties

Label 5.8.a.b.1.1
Level 5
Weight 8
Character 5.1
Self dual Yes
Analytic conductor 1.562
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.56192512742\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{19}) \)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.35890\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.28220 q^{2} +79.7424 q^{3} -126.356 q^{4} -125.000 q^{5} +102.246 q^{6} -538.197 q^{7} -326.136 q^{8} +4171.85 q^{9} +O(q^{10})\) \(q+1.28220 q^{2} +79.7424 q^{3} -126.356 q^{4} -125.000 q^{5} +102.246 q^{6} -538.197 q^{7} -326.136 q^{8} +4171.85 q^{9} -160.275 q^{10} -1215.12 q^{11} -10075.9 q^{12} +7070.42 q^{13} -690.077 q^{14} -9967.80 q^{15} +15755.4 q^{16} -3348.13 q^{17} +5349.15 q^{18} +22169.7 q^{19} +15794.5 q^{20} -42917.1 q^{21} -1558.03 q^{22} -58513.1 q^{23} -26006.8 q^{24} +15625.0 q^{25} +9065.71 q^{26} +158276. q^{27} +68004.4 q^{28} -206301. q^{29} -12780.7 q^{30} +177822. q^{31} +61947.0 q^{32} -96896.5 q^{33} -4292.98 q^{34} +67274.6 q^{35} -527138. q^{36} -284128. q^{37} +28426.0 q^{38} +563812. q^{39} +40767.0 q^{40} +627353. q^{41} -55028.4 q^{42} -164889. q^{43} +153538. q^{44} -521481. q^{45} -75025.7 q^{46} -449355. q^{47} +1.25637e6 q^{48} -533887. q^{49} +20034.4 q^{50} -266988. q^{51} -893390. q^{52} -730190. q^{53} +202942. q^{54} +151890. q^{55} +175525. q^{56} +1.76786e6 q^{57} -264520. q^{58} +1.42202e6 q^{59} +1.25949e6 q^{60} -266326. q^{61} +228004. q^{62} -2.24527e6 q^{63} -1.93726e6 q^{64} -883803. q^{65} -124241. q^{66} +2.95028e6 q^{67} +423056. q^{68} -4.66598e6 q^{69} +86259.6 q^{70} +921138. q^{71} -1.36059e6 q^{72} +4.25657e6 q^{73} -364309. q^{74} +1.24597e6 q^{75} -2.80127e6 q^{76} +653973. q^{77} +722921. q^{78} +6.28551e6 q^{79} -1.96942e6 q^{80} +3.49751e6 q^{81} +804393. q^{82} -9.17165e6 q^{83} +5.42283e6 q^{84} +418516. q^{85} -211421. q^{86} -1.64510e7 q^{87} +396294. q^{88} +242643. q^{89} -668644. q^{90} -3.80528e6 q^{91} +7.39348e6 q^{92} +1.41799e7 q^{93} -576164. q^{94} -2.77121e6 q^{95} +4.93980e6 q^{96} -2.59198e6 q^{97} -684551. q^{98} -5.06929e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 20q^{2} + 20q^{3} + 96q^{4} - 250q^{5} - 1016q^{6} - 100q^{7} + 1440q^{8} + 5554q^{9} + O(q^{10}) \) \( 2q + 20q^{2} + 20q^{3} + 96q^{4} - 250q^{5} - 1016q^{6} - 100q^{7} + 1440q^{8} + 5554q^{9} - 2500q^{10} + 4544q^{11} - 23360q^{12} + 3540q^{13} + 7512q^{14} - 2500q^{15} + 20352q^{16} - 27340q^{17} + 31220q^{18} + 38760q^{19} - 12000q^{20} - 69096q^{21} + 106240q^{22} - 124140q^{23} - 131520q^{24} + 31250q^{25} - 57016q^{26} + 206360q^{27} + 165440q^{28} - 72260q^{29} + 127000q^{30} + 306824q^{31} - 78080q^{32} - 440960q^{33} - 453368q^{34} + 12500q^{35} - 219808q^{36} - 123020q^{37} + 338960q^{38} + 774728q^{39} - 180000q^{40} + 264364q^{41} - 545040q^{42} + 423300q^{43} + 1434112q^{44} - 694250q^{45} - 1303416q^{46} - 105460q^{47} + 981760q^{48} - 1165414q^{49} + 312500q^{50} + 1166344q^{51} - 1678400q^{52} - 2391580q^{53} + 1102960q^{54} - 568000q^{55} + 949440q^{56} + 776720q^{57} + 2244440q^{58} - 1120120q^{59} + 2920000q^{60} + 2257044q^{61} + 2642640q^{62} - 1639620q^{63} - 5146624q^{64} - 442500q^{65} - 6564352q^{66} + 4516460q^{67} - 4911680q^{68} - 745272q^{69} - 939000q^{70} + 621784q^{71} + 1080480q^{72} + 4569060q^{73} + 2651272q^{74} + 312500q^{75} + 887680q^{76} + 3177600q^{77} + 4670800q^{78} + 4333040q^{79} - 2544000q^{80} - 2397878q^{81} - 5989960q^{82} - 9793020q^{83} - 398208q^{84} + 3417500q^{85} + 10798184q^{86} - 24458920q^{87} + 10567680q^{88} + 6025620q^{89} - 3902500q^{90} - 5352296q^{91} - 7199040q^{92} + 6473040q^{93} + 5860792q^{94} - 4845000q^{95} + 13305344q^{96} + 4609540q^{97} - 12505340q^{98} + 2890688q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28220 0.113332 0.0566659 0.998393i \(-0.481953\pi\)
0.0566659 + 0.998393i \(0.481953\pi\)
\(3\) 79.7424 1.70516 0.852579 0.522598i \(-0.175037\pi\)
0.852579 + 0.522598i \(0.175037\pi\)
\(4\) −126.356 −0.987156
\(5\) −125.000 −0.447214
\(6\) 102.246 0.193249
\(7\) −538.197 −0.593059 −0.296529 0.955024i \(-0.595829\pi\)
−0.296529 + 0.955024i \(0.595829\pi\)
\(8\) −326.136 −0.225208
\(9\) 4171.85 1.90757
\(10\) −160.275 −0.0506835
\(11\) −1215.12 −0.275261 −0.137630 0.990484i \(-0.543949\pi\)
−0.137630 + 0.990484i \(0.543949\pi\)
\(12\) −10075.9 −1.68326
\(13\) 7070.42 0.892573 0.446286 0.894890i \(-0.352746\pi\)
0.446286 + 0.894890i \(0.352746\pi\)
\(14\) −690.077 −0.0672124
\(15\) −9967.80 −0.762570
\(16\) 15755.4 0.961633
\(17\) −3348.13 −0.165284 −0.0826420 0.996579i \(-0.526336\pi\)
−0.0826420 + 0.996579i \(0.526336\pi\)
\(18\) 5349.15 0.216188
\(19\) 22169.7 0.741519 0.370759 0.928729i \(-0.379097\pi\)
0.370759 + 0.928729i \(0.379097\pi\)
\(20\) 15794.5 0.441470
\(21\) −42917.1 −1.01126
\(22\) −1558.03 −0.0311958
\(23\) −58513.1 −1.00278 −0.501390 0.865221i \(-0.667178\pi\)
−0.501390 + 0.865221i \(0.667178\pi\)
\(24\) −26006.8 −0.384015
\(25\) 15625.0 0.200000
\(26\) 9065.71 0.101157
\(27\) 158276. 1.54754
\(28\) 68004.4 0.585442
\(29\) −206301. −1.57076 −0.785379 0.619015i \(-0.787532\pi\)
−0.785379 + 0.619015i \(0.787532\pi\)
\(30\) −12780.7 −0.0864234
\(31\) 177822. 1.07206 0.536030 0.844199i \(-0.319923\pi\)
0.536030 + 0.844199i \(0.319923\pi\)
\(32\) 61947.0 0.334191
\(33\) −96896.5 −0.469363
\(34\) −4292.98 −0.0187319
\(35\) 67274.6 0.265224
\(36\) −527138. −1.88307
\(37\) −284128. −0.922163 −0.461081 0.887358i \(-0.652538\pi\)
−0.461081 + 0.887358i \(0.652538\pi\)
\(38\) 28426.0 0.0840376
\(39\) 563812. 1.52198
\(40\) 40767.0 0.100716
\(41\) 627353. 1.42157 0.710785 0.703409i \(-0.248340\pi\)
0.710785 + 0.703409i \(0.248340\pi\)
\(42\) −55028.4 −0.114608
\(43\) −164889. −0.316266 −0.158133 0.987418i \(-0.550547\pi\)
−0.158133 + 0.987418i \(0.550547\pi\)
\(44\) 153538. 0.271725
\(45\) −521481. −0.853090
\(46\) −75025.7 −0.113647
\(47\) −449355. −0.631316 −0.315658 0.948873i \(-0.602225\pi\)
−0.315658 + 0.948873i \(0.602225\pi\)
\(48\) 1.25637e6 1.63974
\(49\) −533887. −0.648281
\(50\) 20034.4 0.0226663
\(51\) −266988. −0.281835
\(52\) −893390. −0.881108
\(53\) −730190. −0.673706 −0.336853 0.941557i \(-0.609362\pi\)
−0.336853 + 0.941557i \(0.609362\pi\)
\(54\) 202942. 0.175386
\(55\) 151890. 0.123100
\(56\) 175525. 0.133562
\(57\) 1.76786e6 1.26441
\(58\) −264520. −0.178017
\(59\) 1.42202e6 0.901412 0.450706 0.892673i \(-0.351172\pi\)
0.450706 + 0.892673i \(0.351172\pi\)
\(60\) 1.25949e6 0.752776
\(61\) −266326. −0.150231 −0.0751153 0.997175i \(-0.523932\pi\)
−0.0751153 + 0.997175i \(0.523932\pi\)
\(62\) 228004. 0.121498
\(63\) −2.24527e6 −1.13130
\(64\) −1.93726e6 −0.923758
\(65\) −883803. −0.399171
\(66\) −124241. −0.0531938
\(67\) 2.95028e6 1.19840 0.599200 0.800599i \(-0.295485\pi\)
0.599200 + 0.800599i \(0.295485\pi\)
\(68\) 423056. 0.163161
\(69\) −4.66598e6 −1.70990
\(70\) 86259.6 0.0300583
\(71\) 921138. 0.305436 0.152718 0.988270i \(-0.451197\pi\)
0.152718 + 0.988270i \(0.451197\pi\)
\(72\) −1.36059e6 −0.429599
\(73\) 4.25657e6 1.28065 0.640323 0.768105i \(-0.278800\pi\)
0.640323 + 0.768105i \(0.278800\pi\)
\(74\) −364309. −0.104510
\(75\) 1.24597e6 0.341032
\(76\) −2.80127e6 −0.731995
\(77\) 653973. 0.163246
\(78\) 722921. 0.172488
\(79\) 6.28551e6 1.43432 0.717159 0.696910i \(-0.245442\pi\)
0.717159 + 0.696910i \(0.245442\pi\)
\(80\) −1.96942e6 −0.430055
\(81\) 3.49751e6 0.731243
\(82\) 804393. 0.161109
\(83\) −9.17165e6 −1.76065 −0.880327 0.474367i \(-0.842677\pi\)
−0.880327 + 0.474367i \(0.842677\pi\)
\(84\) 5.42283e6 0.998271
\(85\) 418516. 0.0739172
\(86\) −211421. −0.0358430
\(87\) −1.64510e7 −2.67839
\(88\) 396294. 0.0619909
\(89\) 242643. 0.0364840 0.0182420 0.999834i \(-0.494193\pi\)
0.0182420 + 0.999834i \(0.494193\pi\)
\(90\) −668644. −0.0966821
\(91\) −3.80528e6 −0.529348
\(92\) 7.39348e6 0.989901
\(93\) 1.41799e7 1.82803
\(94\) −576164. −0.0715482
\(95\) −2.77121e6 −0.331617
\(96\) 4.93980e6 0.569849
\(97\) −2.59198e6 −0.288357 −0.144179 0.989552i \(-0.546054\pi\)
−0.144179 + 0.989552i \(0.546054\pi\)
\(98\) −684551. −0.0734708
\(99\) −5.06929e6 −0.525078
\(100\) −1.97431e6 −0.197431
\(101\) 3.69169e6 0.356534 0.178267 0.983982i \(-0.442951\pi\)
0.178267 + 0.983982i \(0.442951\pi\)
\(102\) −342332. −0.0319409
\(103\) 8.68203e6 0.782873 0.391436 0.920205i \(-0.371978\pi\)
0.391436 + 0.920205i \(0.371978\pi\)
\(104\) −2.30592e6 −0.201014
\(105\) 5.36464e6 0.452249
\(106\) −936251. −0.0763522
\(107\) 1.52118e7 1.20043 0.600216 0.799838i \(-0.295081\pi\)
0.600216 + 0.799838i \(0.295081\pi\)
\(108\) −1.99992e7 −1.52767
\(109\) −1.60843e6 −0.118963 −0.0594813 0.998229i \(-0.518945\pi\)
−0.0594813 + 0.998229i \(0.518945\pi\)
\(110\) 194754. 0.0139512
\(111\) −2.26570e7 −1.57243
\(112\) −8.47950e6 −0.570305
\(113\) −2.62766e7 −1.71315 −0.856574 0.516024i \(-0.827411\pi\)
−0.856574 + 0.516024i \(0.827411\pi\)
\(114\) 2.26676e6 0.143297
\(115\) 7.31414e6 0.448457
\(116\) 2.60674e7 1.55058
\(117\) 2.94967e7 1.70264
\(118\) 1.82332e6 0.102159
\(119\) 1.80195e6 0.0980231
\(120\) 3.25086e6 0.171737
\(121\) −1.80107e7 −0.924231
\(122\) −341483. −0.0170259
\(123\) 5.00266e7 2.42400
\(124\) −2.24688e7 −1.05829
\(125\) −1.95313e6 −0.0894427
\(126\) −2.87890e6 −0.128212
\(127\) −1.91864e7 −0.831152 −0.415576 0.909559i \(-0.636420\pi\)
−0.415576 + 0.909559i \(0.636420\pi\)
\(128\) −1.04132e7 −0.438882
\(129\) −1.31487e7 −0.539284
\(130\) −1.13321e6 −0.0452387
\(131\) 3.07018e7 1.19320 0.596602 0.802537i \(-0.296517\pi\)
0.596602 + 0.802537i \(0.296517\pi\)
\(132\) 1.22434e7 0.463335
\(133\) −1.19317e7 −0.439764
\(134\) 3.78286e6 0.135817
\(135\) −1.97846e7 −0.692083
\(136\) 1.09194e6 0.0372232
\(137\) −3.16847e7 −1.05276 −0.526378 0.850251i \(-0.676450\pi\)
−0.526378 + 0.850251i \(0.676450\pi\)
\(138\) −5.98273e6 −0.193786
\(139\) 2.07581e7 0.655596 0.327798 0.944748i \(-0.393693\pi\)
0.327798 + 0.944748i \(0.393693\pi\)
\(140\) −8.50054e6 −0.261817
\(141\) −3.58326e7 −1.07649
\(142\) 1.18108e6 0.0346156
\(143\) −8.59140e6 −0.245690
\(144\) 6.57291e7 1.83438
\(145\) 2.57877e7 0.702464
\(146\) 5.45778e6 0.145138
\(147\) −4.25734e7 −1.10542
\(148\) 3.59012e7 0.910318
\(149\) 2.94607e7 0.729611 0.364806 0.931084i \(-0.381135\pi\)
0.364806 + 0.931084i \(0.381135\pi\)
\(150\) 1.59759e6 0.0386497
\(151\) 4.60002e7 1.08728 0.543638 0.839320i \(-0.317046\pi\)
0.543638 + 0.839320i \(0.317046\pi\)
\(152\) −7.23033e6 −0.166996
\(153\) −1.39679e7 −0.315290
\(154\) 838526. 0.0185009
\(155\) −2.22277e7 −0.479440
\(156\) −7.12410e7 −1.50243
\(157\) 1.92998e7 0.398019 0.199010 0.979998i \(-0.436227\pi\)
0.199010 + 0.979998i \(0.436227\pi\)
\(158\) 8.05929e6 0.162554
\(159\) −5.82271e7 −1.14878
\(160\) −7.74337e6 −0.149455
\(161\) 3.14916e7 0.594708
\(162\) 4.48452e6 0.0828730
\(163\) 2.35624e7 0.426151 0.213076 0.977036i \(-0.431652\pi\)
0.213076 + 0.977036i \(0.431652\pi\)
\(164\) −7.92698e7 −1.40331
\(165\) 1.21121e7 0.209906
\(166\) −1.17599e7 −0.199538
\(167\) 2.18824e7 0.363570 0.181785 0.983338i \(-0.441813\pi\)
0.181785 + 0.983338i \(0.441813\pi\)
\(168\) 1.39968e7 0.227744
\(169\) −1.27577e7 −0.203314
\(170\) 536622. 0.00837717
\(171\) 9.24886e7 1.41450
\(172\) 2.08347e7 0.312204
\(173\) −9.62312e7 −1.41304 −0.706520 0.707693i \(-0.749736\pi\)
−0.706520 + 0.707693i \(0.749736\pi\)
\(174\) −2.10935e7 −0.303547
\(175\) −8.40932e6 −0.118612
\(176\) −1.91447e7 −0.264700
\(177\) 1.13395e8 1.53705
\(178\) 311117. 0.00413479
\(179\) 8.46776e7 1.10353 0.551763 0.834001i \(-0.313955\pi\)
0.551763 + 0.834001i \(0.313955\pi\)
\(180\) 6.58922e7 0.842132
\(181\) −9.65249e7 −1.20994 −0.604971 0.796248i \(-0.706815\pi\)
−0.604971 + 0.796248i \(0.706815\pi\)
\(182\) −4.87913e6 −0.0599919
\(183\) −2.12374e7 −0.256167
\(184\) 1.90832e7 0.225834
\(185\) 3.55160e7 0.412404
\(186\) 1.81815e7 0.207174
\(187\) 4.06837e6 0.0454962
\(188\) 5.67787e7 0.623208
\(189\) −8.51839e7 −0.917785
\(190\) −3.55325e6 −0.0375828
\(191\) −1.46467e8 −1.52098 −0.760491 0.649348i \(-0.775042\pi\)
−0.760491 + 0.649348i \(0.775042\pi\)
\(192\) −1.54482e8 −1.57515
\(193\) −8.53275e7 −0.854355 −0.427177 0.904168i \(-0.640492\pi\)
−0.427177 + 0.904168i \(0.640492\pi\)
\(194\) −3.32345e6 −0.0326800
\(195\) −7.04765e7 −0.680649
\(196\) 6.74598e7 0.639954
\(197\) 1.44802e8 1.34941 0.674705 0.738087i \(-0.264271\pi\)
0.674705 + 0.738087i \(0.264271\pi\)
\(198\) −6.49986e6 −0.0595080
\(199\) 1.26870e7 0.114123 0.0570617 0.998371i \(-0.481827\pi\)
0.0570617 + 0.998371i \(0.481827\pi\)
\(200\) −5.09587e6 −0.0450416
\(201\) 2.35263e8 2.04346
\(202\) 4.73349e6 0.0404066
\(203\) 1.11031e8 0.931552
\(204\) 3.37355e7 0.278215
\(205\) −7.84191e7 −0.635746
\(206\) 1.11321e7 0.0887243
\(207\) −2.44108e8 −1.91287
\(208\) 1.11397e8 0.858327
\(209\) −2.69388e7 −0.204111
\(210\) 6.87855e6 0.0512542
\(211\) −9.47331e7 −0.694246 −0.347123 0.937820i \(-0.612841\pi\)
−0.347123 + 0.937820i \(0.612841\pi\)
\(212\) 9.22638e7 0.665053
\(213\) 7.34537e7 0.520817
\(214\) 1.95046e7 0.136047
\(215\) 2.06111e7 0.141438
\(216\) −5.16196e7 −0.348519
\(217\) −9.57031e7 −0.635795
\(218\) −2.06234e6 −0.0134822
\(219\) 3.39429e8 2.18371
\(220\) −1.91922e7 −0.121519
\(221\) −2.36727e7 −0.147528
\(222\) −2.90509e7 −0.178207
\(223\) −2.28554e8 −1.38014 −0.690069 0.723744i \(-0.742420\pi\)
−0.690069 + 0.723744i \(0.742420\pi\)
\(224\) −3.33397e7 −0.198195
\(225\) 6.51851e7 0.381513
\(226\) −3.36919e7 −0.194154
\(227\) −3.00587e8 −1.70561 −0.852806 0.522229i \(-0.825101\pi\)
−0.852806 + 0.522229i \(0.825101\pi\)
\(228\) −2.23380e8 −1.24817
\(229\) −1.05343e8 −0.579669 −0.289835 0.957077i \(-0.593600\pi\)
−0.289835 + 0.957077i \(0.593600\pi\)
\(230\) 9.37821e6 0.0508244
\(231\) 5.21494e7 0.278360
\(232\) 6.72823e7 0.353747
\(233\) 3.27196e8 1.69458 0.847291 0.531130i \(-0.178232\pi\)
0.847291 + 0.531130i \(0.178232\pi\)
\(234\) 3.78208e7 0.192963
\(235\) 5.61694e7 0.282333
\(236\) −1.79681e8 −0.889834
\(237\) 5.01221e8 2.44574
\(238\) 2.31047e6 0.0111091
\(239\) −5.72888e7 −0.271442 −0.135721 0.990747i \(-0.543335\pi\)
−0.135721 + 0.990747i \(0.543335\pi\)
\(240\) −1.57047e8 −0.733312
\(241\) 2.84287e8 1.30827 0.654134 0.756379i \(-0.273033\pi\)
0.654134 + 0.756379i \(0.273033\pi\)
\(242\) −2.30933e7 −0.104745
\(243\) −6.72506e7 −0.300659
\(244\) 3.36518e7 0.148301
\(245\) 6.67359e7 0.289920
\(246\) 6.41442e7 0.274717
\(247\) 1.56749e8 0.661859
\(248\) −5.79941e7 −0.241436
\(249\) −7.31369e8 −3.00219
\(250\) −2.50430e6 −0.0101367
\(251\) −2.69178e7 −0.107444 −0.0537220 0.998556i \(-0.517108\pi\)
−0.0537220 + 0.998556i \(0.517108\pi\)
\(252\) 2.83704e8 1.11677
\(253\) 7.11004e7 0.276026
\(254\) −2.46008e7 −0.0941959
\(255\) 3.33735e7 0.126041
\(256\) 2.34618e8 0.874019
\(257\) −3.28749e8 −1.20809 −0.604044 0.796951i \(-0.706445\pi\)
−0.604044 + 0.796951i \(0.706445\pi\)
\(258\) −1.68592e7 −0.0611179
\(259\) 1.52917e8 0.546897
\(260\) 1.11674e8 0.394044
\(261\) −8.60658e8 −2.99632
\(262\) 3.93660e7 0.135228
\(263\) 1.85590e8 0.629084 0.314542 0.949244i \(-0.398149\pi\)
0.314542 + 0.949244i \(0.398149\pi\)
\(264\) 3.16014e7 0.105704
\(265\) 9.12737e7 0.301290
\(266\) −1.52988e7 −0.0498393
\(267\) 1.93489e7 0.0622109
\(268\) −3.72786e8 −1.18301
\(269\) 2.70876e8 0.848471 0.424236 0.905552i \(-0.360543\pi\)
0.424236 + 0.905552i \(0.360543\pi\)
\(270\) −2.53678e7 −0.0784350
\(271\) 2.30743e8 0.704263 0.352132 0.935950i \(-0.385457\pi\)
0.352132 + 0.935950i \(0.385457\pi\)
\(272\) −5.27511e7 −0.158942
\(273\) −3.03442e8 −0.902623
\(274\) −4.06262e7 −0.119311
\(275\) −1.89862e7 −0.0550522
\(276\) 5.89574e8 1.68794
\(277\) 1.42059e8 0.401595 0.200798 0.979633i \(-0.435647\pi\)
0.200798 + 0.979633i \(0.435647\pi\)
\(278\) 2.66161e7 0.0742998
\(279\) 7.41846e8 2.04503
\(280\) −2.19406e7 −0.0597305
\(281\) −1.15362e8 −0.310164 −0.155082 0.987902i \(-0.549564\pi\)
−0.155082 + 0.987902i \(0.549564\pi\)
\(282\) −4.59447e7 −0.122001
\(283\) 2.18080e8 0.571958 0.285979 0.958236i \(-0.407681\pi\)
0.285979 + 0.958236i \(0.407681\pi\)
\(284\) −1.16391e8 −0.301513
\(285\) −2.20983e8 −0.565460
\(286\) −1.10159e7 −0.0278445
\(287\) −3.37639e8 −0.843075
\(288\) 2.58433e8 0.637492
\(289\) −3.99129e8 −0.972681
\(290\) 3.30650e7 0.0796115
\(291\) −2.06691e8 −0.491695
\(292\) −5.37842e8 −1.26420
\(293\) 4.12384e8 0.957778 0.478889 0.877875i \(-0.341040\pi\)
0.478889 + 0.877875i \(0.341040\pi\)
\(294\) −5.45878e7 −0.125279
\(295\) −1.77752e8 −0.403124
\(296\) 9.26642e7 0.207678
\(297\) −1.92325e8 −0.425979
\(298\) 3.77746e7 0.0826881
\(299\) −4.13713e8 −0.895055
\(300\) −1.57436e8 −0.336652
\(301\) 8.87428e7 0.187564
\(302\) 5.89815e7 0.123223
\(303\) 2.94384e8 0.607946
\(304\) 3.49292e8 0.713069
\(305\) 3.32907e7 0.0671852
\(306\) −1.79096e7 −0.0357324
\(307\) 1.57983e8 0.311621 0.155810 0.987787i \(-0.450201\pi\)
0.155810 + 0.987787i \(0.450201\pi\)
\(308\) −8.26334e7 −0.161149
\(309\) 6.92326e8 1.33492
\(310\) −2.85004e7 −0.0543357
\(311\) −1.69169e8 −0.318904 −0.159452 0.987206i \(-0.550973\pi\)
−0.159452 + 0.987206i \(0.550973\pi\)
\(312\) −1.83879e8 −0.342761
\(313\) −5.22117e8 −0.962415 −0.481208 0.876607i \(-0.659802\pi\)
−0.481208 + 0.876607i \(0.659802\pi\)
\(314\) 2.47463e7 0.0451082
\(315\) 2.80659e8 0.505932
\(316\) −7.94211e8 −1.41590
\(317\) 4.73280e8 0.834470 0.417235 0.908799i \(-0.362999\pi\)
0.417235 + 0.908799i \(0.362999\pi\)
\(318\) −7.46589e7 −0.130193
\(319\) 2.50681e8 0.432368
\(320\) 2.42158e8 0.413117
\(321\) 1.21303e9 2.04693
\(322\) 4.03786e7 0.0673993
\(323\) −7.42270e7 −0.122561
\(324\) −4.41932e8 −0.721851
\(325\) 1.10475e8 0.178515
\(326\) 3.02118e7 0.0482965
\(327\) −1.28260e8 −0.202850
\(328\) −2.04602e8 −0.320149
\(329\) 2.41841e8 0.374408
\(330\) 1.55301e7 0.0237890
\(331\) −8.75892e7 −0.132756 −0.0663778 0.997795i \(-0.521144\pi\)
−0.0663778 + 0.997795i \(0.521144\pi\)
\(332\) 1.15889e9 1.73804
\(333\) −1.18534e9 −1.75909
\(334\) 2.80577e7 0.0412040
\(335\) −3.68785e8 −0.535941
\(336\) −6.76175e8 −0.972460
\(337\) −3.04119e8 −0.432851 −0.216426 0.976299i \(-0.569440\pi\)
−0.216426 + 0.976299i \(0.569440\pi\)
\(338\) −1.63579e7 −0.0230419
\(339\) −2.09536e9 −2.92119
\(340\) −5.28820e7 −0.0729678
\(341\) −2.16075e8 −0.295096
\(342\) 1.18589e8 0.160307
\(343\) 7.30565e8 0.977528
\(344\) 5.37762e7 0.0712256
\(345\) 5.83247e8 0.764691
\(346\) −1.23388e8 −0.160142
\(347\) 3.15347e8 0.405169 0.202584 0.979265i \(-0.435066\pi\)
0.202584 + 0.979265i \(0.435066\pi\)
\(348\) 2.07868e9 2.64399
\(349\) −5.23418e8 −0.659112 −0.329556 0.944136i \(-0.606899\pi\)
−0.329556 + 0.944136i \(0.606899\pi\)
\(350\) −1.07825e7 −0.0134425
\(351\) 1.11908e9 1.38130
\(352\) −7.52730e7 −0.0919898
\(353\) −4.13964e8 −0.500900 −0.250450 0.968130i \(-0.580579\pi\)
−0.250450 + 0.968130i \(0.580579\pi\)
\(354\) 1.45395e8 0.174197
\(355\) −1.15142e8 −0.136595
\(356\) −3.06593e7 −0.0360154
\(357\) 1.43692e8 0.167145
\(358\) 1.08574e8 0.125065
\(359\) −2.48768e8 −0.283768 −0.141884 0.989883i \(-0.545316\pi\)
−0.141884 + 0.989883i \(0.545316\pi\)
\(360\) 1.70074e8 0.192122
\(361\) −4.02376e8 −0.450150
\(362\) −1.23764e8 −0.137125
\(363\) −1.43621e9 −1.57596
\(364\) 4.80819e8 0.522549
\(365\) −5.32071e8 −0.572723
\(366\) −2.72307e7 −0.0290319
\(367\) 1.45884e9 1.54056 0.770278 0.637708i \(-0.220117\pi\)
0.770278 + 0.637708i \(0.220117\pi\)
\(368\) −9.21897e8 −0.964307
\(369\) 2.61722e9 2.71174
\(370\) 4.55386e7 0.0467384
\(371\) 3.92986e8 0.399547
\(372\) −1.79172e9 −1.80455
\(373\) 6.29125e8 0.627706 0.313853 0.949472i \(-0.398380\pi\)
0.313853 + 0.949472i \(0.398380\pi\)
\(374\) 5.21648e6 0.00515616
\(375\) −1.55747e8 −0.152514
\(376\) 1.46551e8 0.142177
\(377\) −1.45864e9 −1.40202
\(378\) −1.09223e8 −0.104014
\(379\) 8.54658e7 0.0806409 0.0403204 0.999187i \(-0.487162\pi\)
0.0403204 + 0.999187i \(0.487162\pi\)
\(380\) 3.50159e8 0.327358
\(381\) −1.52997e9 −1.41725
\(382\) −1.87801e8 −0.172376
\(383\) −7.56340e8 −0.687893 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(384\) −8.30371e8 −0.748364
\(385\) −8.17466e7 −0.0730058
\(386\) −1.09407e8 −0.0968255
\(387\) −6.87892e8 −0.603298
\(388\) 3.27512e8 0.284654
\(389\) 1.42837e9 1.23032 0.615160 0.788402i \(-0.289092\pi\)
0.615160 + 0.788402i \(0.289092\pi\)
\(390\) −9.03652e7 −0.0771392
\(391\) 1.95909e8 0.165744
\(392\) 1.74120e8 0.145998
\(393\) 2.44824e9 2.03460
\(394\) 1.85666e8 0.152931
\(395\) −7.85688e8 −0.641446
\(396\) 6.40535e8 0.518334
\(397\) −1.67152e8 −0.134074 −0.0670372 0.997750i \(-0.521355\pi\)
−0.0670372 + 0.997750i \(0.521355\pi\)
\(398\) 1.62673e7 0.0129338
\(399\) −9.51459e8 −0.749868
\(400\) 2.46178e8 0.192327
\(401\) 2.32051e9 1.79712 0.898561 0.438848i \(-0.144613\pi\)
0.898561 + 0.438848i \(0.144613\pi\)
\(402\) 3.01654e8 0.231589
\(403\) 1.25728e9 0.956892
\(404\) −4.66467e8 −0.351954
\(405\) −4.37189e8 −0.327022
\(406\) 1.42364e8 0.105574
\(407\) 3.45249e8 0.253835
\(408\) 8.70742e7 0.0634715
\(409\) −8.24735e8 −0.596050 −0.298025 0.954558i \(-0.596328\pi\)
−0.298025 + 0.954558i \(0.596328\pi\)
\(410\) −1.00549e8 −0.0720502
\(411\) −2.52661e9 −1.79512
\(412\) −1.09703e9 −0.772817
\(413\) −7.65326e8 −0.534590
\(414\) −3.12996e8 −0.216789
\(415\) 1.14646e9 0.787389
\(416\) 4.37991e8 0.298290
\(417\) 1.65530e9 1.11790
\(418\) −3.45410e7 −0.0231323
\(419\) 8.23968e8 0.547219 0.273610 0.961841i \(-0.411782\pi\)
0.273610 + 0.961841i \(0.411782\pi\)
\(420\) −6.77854e8 −0.446440
\(421\) −2.12046e8 −0.138498 −0.0692488 0.997599i \(-0.522060\pi\)
−0.0692488 + 0.997599i \(0.522060\pi\)
\(422\) −1.21467e8 −0.0786801
\(423\) −1.87464e9 −1.20428
\(424\) 2.38141e8 0.151724
\(425\) −5.23145e7 −0.0330568
\(426\) 9.41825e7 0.0590251
\(427\) 1.43336e8 0.0890956
\(428\) −1.92210e9 −1.18501
\(429\) −6.85099e8 −0.418941
\(430\) 2.64276e7 0.0160295
\(431\) 7.44023e8 0.447627 0.223813 0.974632i \(-0.428149\pi\)
0.223813 + 0.974632i \(0.428149\pi\)
\(432\) 2.49371e9 1.48817
\(433\) −1.93573e9 −1.14588 −0.572938 0.819598i \(-0.694197\pi\)
−0.572938 + 0.819598i \(0.694197\pi\)
\(434\) −1.22711e8 −0.0720557
\(435\) 2.05637e9 1.19781
\(436\) 2.03235e8 0.117435
\(437\) −1.29722e9 −0.743581
\(438\) 4.35216e8 0.247483
\(439\) −1.35485e9 −0.764300 −0.382150 0.924100i \(-0.624816\pi\)
−0.382150 + 0.924100i \(0.624816\pi\)
\(440\) −4.95367e7 −0.0277232
\(441\) −2.22730e9 −1.23664
\(442\) −3.03531e7 −0.0167196
\(443\) 1.05985e9 0.579203 0.289601 0.957147i \(-0.406477\pi\)
0.289601 + 0.957147i \(0.406477\pi\)
\(444\) 2.86285e9 1.55224
\(445\) −3.03303e7 −0.0163161
\(446\) −2.93053e8 −0.156413
\(447\) 2.34927e9 1.24410
\(448\) 1.04263e9 0.547843
\(449\) −1.70272e9 −0.887730 −0.443865 0.896094i \(-0.646393\pi\)
−0.443865 + 0.896094i \(0.646393\pi\)
\(450\) 8.35805e7 0.0432376
\(451\) −7.62309e8 −0.391303
\(452\) 3.32021e9 1.69114
\(453\) 3.66816e9 1.85398
\(454\) −3.85414e8 −0.193300
\(455\) 4.75660e8 0.236732
\(456\) −5.76564e8 −0.284754
\(457\) −3.76431e9 −1.84493 −0.922463 0.386085i \(-0.873827\pi\)
−0.922463 + 0.386085i \(0.873827\pi\)
\(458\) −1.35071e8 −0.0656949
\(459\) −5.29930e8 −0.255784
\(460\) −9.24185e8 −0.442697
\(461\) 3.59084e9 1.70704 0.853519 0.521062i \(-0.174464\pi\)
0.853519 + 0.521062i \(0.174464\pi\)
\(462\) 6.68660e7 0.0315470
\(463\) −2.45649e8 −0.115022 −0.0575111 0.998345i \(-0.518316\pi\)
−0.0575111 + 0.998345i \(0.518316\pi\)
\(464\) −3.25036e9 −1.51049
\(465\) −1.77249e9 −0.817521
\(466\) 4.19532e8 0.192050
\(467\) −4.04985e8 −0.184005 −0.0920025 0.995759i \(-0.529327\pi\)
−0.0920025 + 0.995759i \(0.529327\pi\)
\(468\) −3.72709e9 −1.68077
\(469\) −1.58783e9 −0.710722
\(470\) 7.20205e7 0.0319973
\(471\) 1.53901e9 0.678686
\(472\) −4.63771e8 −0.203005
\(473\) 2.00360e8 0.0870556
\(474\) 6.42667e8 0.277180
\(475\) 3.46401e8 0.148304
\(476\) −2.27687e8 −0.0967641
\(477\) −3.04624e9 −1.28514
\(478\) −7.34559e7 −0.0307630
\(479\) 4.18334e9 1.73920 0.869598 0.493760i \(-0.164378\pi\)
0.869598 + 0.493760i \(0.164378\pi\)
\(480\) −6.17475e8 −0.254844
\(481\) −2.00890e9 −0.823097
\(482\) 3.64513e8 0.148268
\(483\) 2.51121e9 1.01407
\(484\) 2.27575e9 0.912361
\(485\) 3.23998e8 0.128957
\(486\) −8.62289e7 −0.0340742
\(487\) 3.25089e9 1.27541 0.637706 0.770280i \(-0.279883\pi\)
0.637706 + 0.770280i \(0.279883\pi\)
\(488\) 8.68583e7 0.0338331
\(489\) 1.87893e9 0.726656
\(490\) 8.55689e7 0.0328571
\(491\) −3.37360e9 −1.28620 −0.643100 0.765782i \(-0.722352\pi\)
−0.643100 + 0.765782i \(0.722352\pi\)
\(492\) −6.32116e9 −2.39287
\(493\) 6.90723e8 0.259621
\(494\) 2.00984e8 0.0750097
\(495\) 6.33662e8 0.234822
\(496\) 2.80165e9 1.03093
\(497\) −4.95753e8 −0.181142
\(498\) −9.37763e8 −0.340244
\(499\) 3.74951e9 1.35090 0.675449 0.737406i \(-0.263950\pi\)
0.675449 + 0.737406i \(0.263950\pi\)
\(500\) 2.46789e8 0.0882939
\(501\) 1.74496e9 0.619945
\(502\) −3.45141e7 −0.0121768
\(503\) −3.09301e9 −1.08366 −0.541830 0.840488i \(-0.682268\pi\)
−0.541830 + 0.840488i \(0.682268\pi\)
\(504\) 7.32264e8 0.254777
\(505\) −4.61461e8 −0.159447
\(506\) 9.11651e7 0.0312825
\(507\) −1.01733e9 −0.346683
\(508\) 2.42432e9 0.820476
\(509\) 1.36862e9 0.460015 0.230007 0.973189i \(-0.426125\pi\)
0.230007 + 0.973189i \(0.426125\pi\)
\(510\) 4.27915e7 0.0142844
\(511\) −2.29087e9 −0.759499
\(512\) 1.63371e9 0.537937
\(513\) 3.50894e9 1.14753
\(514\) −4.21523e8 −0.136915
\(515\) −1.08525e9 −0.350111
\(516\) 1.66141e9 0.532357
\(517\) 5.46020e8 0.173777
\(518\) 1.96070e8 0.0619808
\(519\) −7.67371e9 −2.40946
\(520\) 2.88240e8 0.0898963
\(521\) −4.47414e9 −1.38604 −0.693022 0.720916i \(-0.743721\pi\)
−0.693022 + 0.720916i \(0.743721\pi\)
\(522\) −1.10354e9 −0.339579
\(523\) −3.01993e9 −0.923085 −0.461542 0.887118i \(-0.652704\pi\)
−0.461542 + 0.887118i \(0.652704\pi\)
\(524\) −3.87936e9 −1.17788
\(525\) −6.70579e8 −0.202252
\(526\) 2.37963e8 0.0712952
\(527\) −5.95370e8 −0.177194
\(528\) −1.52664e9 −0.451355
\(529\) 1.89619e7 0.00556913
\(530\) 1.17031e8 0.0341458
\(531\) 5.93244e9 1.71950
\(532\) 1.50764e9 0.434116
\(533\) 4.43565e9 1.26885
\(534\) 2.48092e7 0.00705047
\(535\) −1.90148e9 −0.536850
\(536\) −9.62193e8 −0.269889
\(537\) 6.75239e9 1.88169
\(538\) 3.47318e8 0.0961587
\(539\) 6.48737e8 0.178446
\(540\) 2.49990e9 0.683194
\(541\) 3.23946e9 0.879593 0.439796 0.898097i \(-0.355051\pi\)
0.439796 + 0.898097i \(0.355051\pi\)
\(542\) 2.95859e8 0.0798154
\(543\) −7.69713e9 −2.06314
\(544\) −2.07406e8 −0.0552365
\(545\) 2.01054e8 0.0532017
\(546\) −3.89074e8 −0.102296
\(547\) 4.25742e9 1.11222 0.556111 0.831108i \(-0.312293\pi\)
0.556111 + 0.831108i \(0.312293\pi\)
\(548\) 4.00355e9 1.03923
\(549\) −1.11107e9 −0.286575
\(550\) −2.43442e7 −0.00623916
\(551\) −4.57364e9 −1.16475
\(552\) 1.52174e9 0.385083
\(553\) −3.38284e9 −0.850635
\(554\) 1.82148e8 0.0455135
\(555\) 2.83213e9 0.703214
\(556\) −2.62291e9 −0.647175
\(557\) −5.65828e9 −1.38737 −0.693684 0.720280i \(-0.744013\pi\)
−0.693684 + 0.720280i \(0.744013\pi\)
\(558\) 9.51196e8 0.231766
\(559\) −1.16584e9 −0.282290
\(560\) 1.05994e9 0.255048
\(561\) 3.24422e8 0.0775783
\(562\) −1.47918e8 −0.0351515
\(563\) 4.37511e9 1.03326 0.516630 0.856209i \(-0.327186\pi\)
0.516630 + 0.856209i \(0.327186\pi\)
\(564\) 4.52767e9 1.06267
\(565\) 3.28458e9 0.766143
\(566\) 2.79623e8 0.0648210
\(567\) −1.88235e9 −0.433670
\(568\) −3.00416e8 −0.0687866
\(569\) 1.67226e9 0.380550 0.190275 0.981731i \(-0.439062\pi\)
0.190275 + 0.981731i \(0.439062\pi\)
\(570\) −2.83345e8 −0.0640846
\(571\) 6.39802e8 0.143820 0.0719100 0.997411i \(-0.477091\pi\)
0.0719100 + 0.997411i \(0.477091\pi\)
\(572\) 1.08558e9 0.242535
\(573\) −1.16797e10 −2.59352
\(574\) −4.32922e8 −0.0955472
\(575\) −9.14268e8 −0.200556
\(576\) −8.08196e9 −1.76213
\(577\) 4.87101e9 1.05561 0.527805 0.849366i \(-0.323015\pi\)
0.527805 + 0.849366i \(0.323015\pi\)
\(578\) −5.11764e8 −0.110236
\(579\) −6.80422e9 −1.45681
\(580\) −3.25843e9 −0.693442
\(581\) 4.93615e9 1.04417
\(582\) −2.65019e8 −0.0557246
\(583\) 8.87268e8 0.185445
\(584\) −1.38822e9 −0.288412
\(585\) −3.68709e9 −0.761444
\(586\) 5.28760e8 0.108547
\(587\) −2.32406e9 −0.474258 −0.237129 0.971478i \(-0.576206\pi\)
−0.237129 + 0.971478i \(0.576206\pi\)
\(588\) 5.37941e9 1.09122
\(589\) 3.94226e9 0.794953
\(590\) −2.27914e8 −0.0456867
\(591\) 1.15469e10 2.30096
\(592\) −4.47654e9 −0.886782
\(593\) 4.27080e9 0.841043 0.420522 0.907283i \(-0.361847\pi\)
0.420522 + 0.907283i \(0.361847\pi\)
\(594\) −2.46599e8 −0.0482769
\(595\) −2.25244e8 −0.0438373
\(596\) −3.72254e9 −0.720240
\(597\) 1.01169e9 0.194598
\(598\) −5.30463e8 −0.101438
\(599\) 3.50335e9 0.666023 0.333012 0.942923i \(-0.391935\pi\)
0.333012 + 0.942923i \(0.391935\pi\)
\(600\) −4.06357e8 −0.0768030
\(601\) 2.98866e9 0.561585 0.280792 0.959769i \(-0.409403\pi\)
0.280792 + 0.959769i \(0.409403\pi\)
\(602\) 1.13786e8 0.0212570
\(603\) 1.23081e10 2.28603
\(604\) −5.81240e9 −1.07331
\(605\) 2.25133e9 0.413329
\(606\) 3.77460e8 0.0688996
\(607\) −7.31901e9 −1.32829 −0.664143 0.747605i \(-0.731203\pi\)
−0.664143 + 0.747605i \(0.731203\pi\)
\(608\) 1.37335e9 0.247809
\(609\) 8.85386e9 1.58844
\(610\) 4.26854e7 0.00761421
\(611\) −3.17713e9 −0.563496
\(612\) 1.76492e9 0.311241
\(613\) −8.32799e9 −1.46026 −0.730128 0.683311i \(-0.760539\pi\)
−0.730128 + 0.683311i \(0.760539\pi\)
\(614\) 2.02566e8 0.0353165
\(615\) −6.25333e9 −1.08405
\(616\) −2.13284e8 −0.0367643
\(617\) −2.88456e9 −0.494403 −0.247201 0.968964i \(-0.579511\pi\)
−0.247201 + 0.968964i \(0.579511\pi\)
\(618\) 8.87702e8 0.151289
\(619\) −2.27213e9 −0.385049 −0.192525 0.981292i \(-0.561668\pi\)
−0.192525 + 0.981292i \(0.561668\pi\)
\(620\) 2.80861e9 0.473282
\(621\) −9.26125e9 −1.55185
\(622\) −2.16909e8 −0.0361420
\(623\) −1.30589e8 −0.0216371
\(624\) 8.88308e9 1.46358
\(625\) 2.44141e8 0.0400000
\(626\) −6.69459e8 −0.109072
\(627\) −2.14817e9 −0.348042
\(628\) −2.43865e9 −0.392907
\(629\) 9.51296e8 0.152419
\(630\) 3.59862e8 0.0573382
\(631\) −2.90856e7 −0.00460867 −0.00230434 0.999997i \(-0.500733\pi\)
−0.00230434 + 0.999997i \(0.500733\pi\)
\(632\) −2.04993e9 −0.323020
\(633\) −7.55424e9 −1.18380
\(634\) 6.06841e8 0.0945719
\(635\) 2.39830e9 0.371702
\(636\) 7.35734e9 1.13402
\(637\) −3.77481e9 −0.578638
\(638\) 3.21423e8 0.0490010
\(639\) 3.84285e9 0.582640
\(640\) 1.30165e9 0.196274
\(641\) −3.12634e9 −0.468849 −0.234424 0.972134i \(-0.575320\pi\)
−0.234424 + 0.972134i \(0.575320\pi\)
\(642\) 1.55534e9 0.231982
\(643\) 2.48120e9 0.368064 0.184032 0.982920i \(-0.441085\pi\)
0.184032 + 0.982920i \(0.441085\pi\)
\(644\) −3.97915e9 −0.587070
\(645\) 1.64358e9 0.241175
\(646\) −9.51740e7 −0.0138901
\(647\) 3.10080e9 0.450100 0.225050 0.974347i \(-0.427746\pi\)
0.225050 + 0.974347i \(0.427746\pi\)
\(648\) −1.14066e9 −0.164682
\(649\) −1.72792e9 −0.248123
\(650\) 1.41652e8 0.0202314
\(651\) −7.63159e9 −1.08413
\(652\) −2.97726e9 −0.420678
\(653\) 9.64911e8 0.135610 0.0678049 0.997699i \(-0.478400\pi\)
0.0678049 + 0.997699i \(0.478400\pi\)
\(654\) −1.64456e8 −0.0229894
\(655\) −3.83773e9 −0.533617
\(656\) 9.88419e9 1.36703
\(657\) 1.77577e10 2.44292
\(658\) 3.10089e8 0.0424323
\(659\) −7.70039e9 −1.04813 −0.524063 0.851679i \(-0.675584\pi\)
−0.524063 + 0.851679i \(0.675584\pi\)
\(660\) −1.53043e9 −0.207210
\(661\) 1.30650e10 1.75956 0.879779 0.475382i \(-0.157690\pi\)
0.879779 + 0.475382i \(0.157690\pi\)
\(662\) −1.12307e8 −0.0150454
\(663\) −1.88772e9 −0.251559
\(664\) 2.99120e9 0.396513
\(665\) 1.49146e9 0.196669
\(666\) −1.51984e9 −0.199360
\(667\) 1.20713e10 1.57513
\(668\) −2.76498e9 −0.358900
\(669\) −1.82255e10 −2.35335
\(670\) −4.72857e8 −0.0607391
\(671\) 3.23617e8 0.0413526
\(672\) −2.65858e9 −0.337954
\(673\) 1.31771e10 1.66636 0.833179 0.553003i \(-0.186518\pi\)
0.833179 + 0.553003i \(0.186518\pi\)
\(674\) −3.89942e8 −0.0490558
\(675\) 2.47307e9 0.309509
\(676\) 1.61201e9 0.200703
\(677\) −3.18151e9 −0.394069 −0.197035 0.980397i \(-0.563131\pi\)
−0.197035 + 0.980397i \(0.563131\pi\)
\(678\) −2.68667e9 −0.331063
\(679\) 1.39500e9 0.171013
\(680\) −1.36493e8 −0.0166467
\(681\) −2.39695e10 −2.90834
\(682\) −2.77051e8 −0.0334438
\(683\) −3.33139e8 −0.0400086 −0.0200043 0.999800i \(-0.506368\pi\)
−0.0200043 + 0.999800i \(0.506368\pi\)
\(684\) −1.16865e10 −1.39633
\(685\) 3.96059e9 0.470807
\(686\) 9.36731e8 0.110785
\(687\) −8.40028e9 −0.988428
\(688\) −2.59789e9 −0.304132
\(689\) −5.16275e9 −0.601331
\(690\) 7.47841e8 0.0866637
\(691\) −4.45248e9 −0.513368 −0.256684 0.966495i \(-0.582630\pi\)
−0.256684 + 0.966495i \(0.582630\pi\)
\(692\) 1.21594e10 1.39489
\(693\) 2.72828e9 0.311402
\(694\) 4.04339e8 0.0459185
\(695\) −2.59476e9 −0.293191
\(696\) 5.36525e9 0.603195
\(697\) −2.10046e9 −0.234963
\(698\) −6.71127e8 −0.0746983
\(699\) 2.60914e10 2.88953
\(700\) 1.06257e9 0.117088
\(701\) −1.91380e9 −0.209838 −0.104919 0.994481i \(-0.533458\pi\)
−0.104919 + 0.994481i \(0.533458\pi\)
\(702\) 1.43489e9 0.156545
\(703\) −6.29902e9 −0.683801
\(704\) 2.35400e9 0.254274
\(705\) 4.47908e9 0.481423
\(706\) −5.30785e8 −0.0567679
\(707\) −1.98686e9 −0.211445
\(708\) −1.43282e10 −1.51731
\(709\) 1.38704e9 0.146160 0.0730799 0.997326i \(-0.476717\pi\)
0.0730799 + 0.997326i \(0.476717\pi\)
\(710\) −1.47636e8 −0.0154806
\(711\) 2.62222e10 2.73606
\(712\) −7.91344e7 −0.00821647
\(713\) −1.04049e10 −1.07504
\(714\) 1.84242e8 0.0189428
\(715\) 1.07393e9 0.109876
\(716\) −1.06995e10 −1.08935
\(717\) −4.56835e9 −0.462852
\(718\) −3.18970e8 −0.0321599
\(719\) 9.42958e9 0.946109 0.473055 0.881033i \(-0.343151\pi\)
0.473055 + 0.881033i \(0.343151\pi\)
\(720\) −8.21614e9 −0.820359
\(721\) −4.67264e9 −0.464290
\(722\) −5.15928e8 −0.0510163
\(723\) 2.26697e10 2.23081
\(724\) 1.21965e10 1.19440
\(725\) −3.22346e9 −0.314152
\(726\) −1.84151e9 −0.178606
\(727\) −2.99387e9 −0.288976 −0.144488 0.989507i \(-0.546154\pi\)
−0.144488 + 0.989507i \(0.546154\pi\)
\(728\) 1.24104e9 0.119213
\(729\) −1.30118e10 −1.24391
\(730\) −6.82222e8 −0.0649076
\(731\) 5.52070e8 0.0522737
\(732\) 2.68348e9 0.252877
\(733\) 1.11711e10 1.04768 0.523842 0.851815i \(-0.324498\pi\)
0.523842 + 0.851815i \(0.324498\pi\)
\(734\) 1.87053e9 0.174594
\(735\) 5.32168e9 0.494360
\(736\) −3.62471e9 −0.335121
\(737\) −3.58495e9 −0.329873
\(738\) 3.35581e9 0.307326
\(739\) −6.96449e9 −0.634796 −0.317398 0.948292i \(-0.602809\pi\)
−0.317398 + 0.948292i \(0.602809\pi\)
\(740\) −4.48765e9 −0.407107
\(741\) 1.24995e10 1.12858
\(742\) 5.03887e8 0.0452814
\(743\) 1.27161e9 0.113734 0.0568672 0.998382i \(-0.481889\pi\)
0.0568672 + 0.998382i \(0.481889\pi\)
\(744\) −4.62458e9 −0.411687
\(745\) −3.68259e9 −0.326292
\(746\) 8.06666e8 0.0711390
\(747\) −3.82627e10 −3.35856
\(748\) −5.14063e8 −0.0449119
\(749\) −8.18695e9 −0.711927
\(750\) −1.99699e8 −0.0172847
\(751\) −1.70771e10 −1.47121 −0.735603 0.677413i \(-0.763101\pi\)
−0.735603 + 0.677413i \(0.763101\pi\)
\(752\) −7.07976e9 −0.607094
\(753\) −2.14649e9 −0.183209
\(754\) −1.87027e9 −0.158893
\(755\) −5.75002e9 −0.486245
\(756\) 1.07635e10 0.905997
\(757\) 1.37933e10 1.15567 0.577833 0.816155i \(-0.303899\pi\)
0.577833 + 0.816155i \(0.303899\pi\)
\(758\) 1.09584e8 0.00913917
\(759\) 5.66972e9 0.470669
\(760\) 9.03791e8 0.0746828
\(761\) 1.71364e10 1.40953 0.704765 0.709441i \(-0.251053\pi\)
0.704765 + 0.709441i \(0.251053\pi\)
\(762\) −1.96173e9 −0.160619
\(763\) 8.65654e8 0.0705518
\(764\) 1.85070e10 1.50145
\(765\) 1.74598e9 0.141002
\(766\) −9.69780e8 −0.0779602
\(767\) 1.00543e10 0.804575
\(768\) 1.87090e10 1.49034
\(769\) −4.41529e9 −0.350120 −0.175060 0.984558i \(-0.556012\pi\)
−0.175060 + 0.984558i \(0.556012\pi\)
\(770\) −1.04816e8 −0.00827387
\(771\) −2.62152e10 −2.05998
\(772\) 1.07816e10 0.843381
\(773\) −5.87300e8 −0.0457332 −0.0228666 0.999739i \(-0.507279\pi\)
−0.0228666 + 0.999739i \(0.507279\pi\)
\(774\) −8.82017e8 −0.0683728
\(775\) 2.77847e9 0.214412
\(776\) 8.45338e8 0.0649403
\(777\) 1.21939e10 0.932546
\(778\) 1.83146e9 0.139434
\(779\) 1.39082e10 1.05412
\(780\) 8.90513e9 0.671907
\(781\) −1.11929e9 −0.0840746
\(782\) 2.51195e8 0.0187840
\(783\) −3.26527e10 −2.43082
\(784\) −8.41160e9 −0.623408
\(785\) −2.41248e9 −0.178000
\(786\) 3.13914e9 0.230585
\(787\) −2.30069e10 −1.68247 −0.841235 0.540670i \(-0.818171\pi\)
−0.841235 + 0.540670i \(0.818171\pi\)
\(788\) −1.82967e10 −1.33208
\(789\) 1.47994e10 1.07269
\(790\) −1.00741e9 −0.0726962
\(791\) 1.41420e10 1.01600
\(792\) 1.65328e9 0.118252
\(793\) −1.88303e9 −0.134092
\(794\) −2.14323e8 −0.0151949
\(795\) 7.27838e9 0.513748
\(796\) −1.60308e9 −0.112658
\(797\) 2.49526e10 1.74587 0.872935 0.487836i \(-0.162213\pi\)
0.872935 + 0.487836i \(0.162213\pi\)
\(798\) −1.21996e9 −0.0849838
\(799\) 1.50450e9 0.104346
\(800\) 9.67921e8 0.0668383
\(801\) 1.01227e9 0.0695956
\(802\) 2.97536e9 0.203671
\(803\) −5.17223e9 −0.352512
\(804\) −2.97268e10 −2.01722
\(805\) −3.93645e9 −0.265962
\(806\) 1.61208e9 0.108446
\(807\) 2.16003e10 1.44678
\(808\) −1.20399e9 −0.0802942
\(809\) −1.29758e10 −0.861616 −0.430808 0.902443i \(-0.641771\pi\)
−0.430808 + 0.902443i \(0.641771\pi\)
\(810\) −5.60565e8 −0.0370620
\(811\) −2.04887e10 −1.34878 −0.674391 0.738374i \(-0.735594\pi\)
−0.674391 + 0.738374i \(0.735594\pi\)
\(812\) −1.40294e10 −0.919587
\(813\) 1.84000e10 1.20088
\(814\) 4.42679e8 0.0287676
\(815\) −2.94531e9 −0.190581
\(816\) −4.20649e9 −0.271022
\(817\) −3.65554e9 −0.234517
\(818\) −1.05748e9 −0.0675514
\(819\) −1.58750e10 −1.00977
\(820\) 9.90872e9 0.627580
\(821\) −7.97556e9 −0.502991 −0.251495 0.967858i \(-0.580922\pi\)
−0.251495 + 0.967858i \(0.580922\pi\)
\(822\) −3.23963e9 −0.203444
\(823\) 5.64462e9 0.352968 0.176484 0.984304i \(-0.443528\pi\)
0.176484 + 0.984304i \(0.443528\pi\)
\(824\) −2.83152e9 −0.176309
\(825\) −1.51401e9 −0.0938727
\(826\) −9.81302e8 −0.0605860
\(827\) 1.22946e10 0.755866 0.377933 0.925833i \(-0.376635\pi\)
0.377933 + 0.925833i \(0.376635\pi\)
\(828\) 3.08445e10 1.88830
\(829\) −1.72844e10 −1.05369 −0.526845 0.849962i \(-0.676625\pi\)
−0.526845 + 0.849962i \(0.676625\pi\)
\(830\) 1.46999e9 0.0892361
\(831\) 1.13281e10 0.684784
\(832\) −1.36973e10 −0.824521
\(833\) 1.78752e9 0.107150
\(834\) 2.12243e9 0.126693
\(835\) −2.73530e9 −0.162593
\(836\) 3.40388e9 0.201489
\(837\) 2.81450e10 1.65906
\(838\) 1.05649e9 0.0620173
\(839\) −4.87580e9 −0.285023 −0.142511 0.989793i \(-0.545518\pi\)
−0.142511 + 0.989793i \(0.545518\pi\)
\(840\) −1.74960e9 −0.101850
\(841\) 2.53104e10 1.46728
\(842\) −2.71885e8 −0.0156962
\(843\) −9.19927e9 −0.528879
\(844\) 1.19701e10 0.685329
\(845\) 1.59471e9 0.0909249
\(846\) −2.40367e9 −0.136483
\(847\) 9.69328e9 0.548124
\(848\) −1.15044e10 −0.647857
\(849\) 1.73903e10 0.975279
\(850\) −6.70777e7 −0.00374638
\(851\) 1.66252e10 0.924727
\(852\) −9.28132e9 −0.514128
\(853\) −1.67542e10 −0.924277 −0.462138 0.886808i \(-0.652918\pi\)
−0.462138 + 0.886808i \(0.652918\pi\)
\(854\) 1.83785e8 0.0100974
\(855\) −1.15611e10 −0.632582
\(856\) −4.96112e9 −0.270347
\(857\) −1.45198e10 −0.788001 −0.394001 0.919110i \(-0.628909\pi\)
−0.394001 + 0.919110i \(0.628909\pi\)
\(858\) −8.78435e8 −0.0474793
\(859\) 2.44108e10 1.31403 0.657016 0.753877i \(-0.271819\pi\)
0.657016 + 0.753877i \(0.271819\pi\)
\(860\) −2.60434e9 −0.139622
\(861\) −2.69242e10 −1.43758
\(862\) 9.53988e8 0.0507303
\(863\) −2.03914e10 −1.07996 −0.539981 0.841677i \(-0.681569\pi\)
−0.539981 + 0.841677i \(0.681569\pi\)
\(864\) 9.80475e9 0.517176
\(865\) 1.20289e10 0.631931
\(866\) −2.48200e9 −0.129864
\(867\) −3.18275e10 −1.65858
\(868\) 1.20927e10 0.627629
\(869\) −7.63764e9 −0.394812
\(870\) 2.63668e9 0.135750
\(871\) 2.08597e10 1.06966
\(872\) 5.24568e8 0.0267913
\(873\) −1.08134e10 −0.550061
\(874\) −1.66330e9 −0.0842713
\(875\) 1.05117e9 0.0530448
\(876\) −4.28888e10 −2.15566
\(877\) −3.75418e10 −1.87939 −0.939693 0.342018i \(-0.888890\pi\)
−0.939693 + 0.342018i \(0.888890\pi\)
\(878\) −1.73719e9 −0.0866194
\(879\) 3.28845e10 1.63316
\(880\) 2.39308e9 0.118377
\(881\) 1.05852e10 0.521533 0.260767 0.965402i \(-0.416025\pi\)
0.260767 + 0.965402i \(0.416025\pi\)
\(882\) −2.85584e9 −0.140150
\(883\) 3.45129e10 1.68702 0.843509 0.537116i \(-0.180486\pi\)
0.843509 + 0.537116i \(0.180486\pi\)
\(884\) 2.99118e9 0.145633
\(885\) −1.41744e10 −0.687390
\(886\) 1.35894e9 0.0656420
\(887\) 1.68685e10 0.811602 0.405801 0.913961i \(-0.366993\pi\)
0.405801 + 0.913961i \(0.366993\pi\)
\(888\) 7.38926e9 0.354124
\(889\) 1.03261e10 0.492922
\(890\) −3.88896e7 −0.00184913
\(891\) −4.24990e9 −0.201283
\(892\) 2.88792e10 1.36241
\(893\) −9.96206e9 −0.468133
\(894\) 3.01224e9 0.140996
\(895\) −1.05847e10 −0.493512
\(896\) 5.60434e9 0.260283
\(897\) −3.29904e10 −1.52621
\(898\) −2.18323e9 −0.100608
\(899\) −3.66849e10 −1.68395
\(900\) −8.23653e9 −0.376613
\(901\) 2.44477e9 0.111353
\(902\) −9.77434e8 −0.0443470
\(903\) 7.07656e9 0.319827
\(904\) 8.56974e9 0.385814
\(905\) 1.20656e10 0.541102
\(906\) 4.70333e9 0.210115
\(907\) −1.14713e10 −0.510492 −0.255246 0.966876i \(-0.582156\pi\)
−0.255246 + 0.966876i \(0.582156\pi\)
\(908\) 3.79810e10 1.68370
\(909\) 1.54012e10 0.680112
\(910\) 6.09892e8 0.0268292
\(911\) 1.62306e10 0.711248 0.355624 0.934629i \(-0.384268\pi\)
0.355624 + 0.934629i \(0.384268\pi\)
\(912\) 2.78534e10 1.21590
\(913\) 1.11446e10 0.484639
\(914\) −4.82661e9 −0.209089
\(915\) 2.65468e9 0.114561
\(916\) 1.33107e10 0.572224
\(917\) −1.65236e10 −0.707641
\(918\) −6.79477e8 −0.0289885
\(919\) −4.36259e10 −1.85413 −0.927065 0.374900i \(-0.877677\pi\)
−0.927065 + 0.374900i \(0.877677\pi\)
\(920\) −2.38540e9 −0.100996
\(921\) 1.25979e10 0.531363
\(922\) 4.60419e9 0.193462
\(923\) 6.51283e9 0.272624
\(924\) −6.58938e9 −0.274785
\(925\) −4.43950e9 −0.184433
\(926\) −3.14972e8 −0.0130357
\(927\) 3.62201e10 1.49338
\(928\) −1.27797e10 −0.524934
\(929\) 1.67801e10 0.686656 0.343328 0.939216i \(-0.388446\pi\)
0.343328 + 0.939216i \(0.388446\pi\)
\(930\) −2.27269e9 −0.0926511
\(931\) −1.18361e10 −0.480713
\(932\) −4.13432e10 −1.67282
\(933\) −1.34900e10 −0.543782
\(934\) −5.19273e8 −0.0208536
\(935\) −5.08547e8 −0.0203465
\(936\) −9.61993e9 −0.383448
\(937\) 1.94934e10 0.774105 0.387053 0.922058i \(-0.373493\pi\)
0.387053 + 0.922058i \(0.373493\pi\)
\(938\) −2.03592e9 −0.0805474
\(939\) −4.16348e10 −1.64107
\(940\) −7.09733e9 −0.278707
\(941\) −4.91523e10 −1.92300 −0.961502 0.274797i \(-0.911389\pi\)
−0.961502 + 0.274797i \(0.911389\pi\)
\(942\) 1.97333e9 0.0769167
\(943\) −3.67084e10 −1.42552
\(944\) 2.24045e10 0.866827
\(945\) 1.06480e10 0.410446
\(946\) 2.56902e8 0.00986617
\(947\) 3.01570e10 1.15389 0.576944 0.816784i \(-0.304245\pi\)
0.576944 + 0.816784i \(0.304245\pi\)
\(948\) −6.33323e10 −2.41433
\(949\) 3.00957e10 1.14307
\(950\) 4.44157e8 0.0168075
\(951\) 3.77405e10 1.42290
\(952\) −5.87681e8 −0.0220756
\(953\) −1.86916e10 −0.699554 −0.349777 0.936833i \(-0.613743\pi\)
−0.349777 + 0.936833i \(0.613743\pi\)
\(954\) −3.90590e9 −0.145647
\(955\) 1.83084e10 0.680204
\(956\) 7.23879e9 0.267956
\(957\) 1.99899e10 0.737256
\(958\) 5.36388e9 0.197106
\(959\) 1.70526e10 0.624346
\(960\) 1.93102e10 0.704430
\(961\) 4.10799e9 0.149313
\(962\) −2.57582e9 −0.0932830
\(963\) 6.34614e10 2.28990
\(964\) −3.59213e10 −1.29146
\(965\) 1.06659e10 0.382079
\(966\) 3.21988e9 0.114926
\(967\) −7.61328e9 −0.270757 −0.135378 0.990794i \(-0.543225\pi\)
−0.135378 + 0.990794i \(0.543225\pi\)
\(968\) 5.87392e9 0.208144
\(969\) −5.91903e9 −0.208986
\(970\) 4.15431e8 0.0146150
\(971\) −4.83242e10 −1.69394 −0.846969 0.531643i \(-0.821575\pi\)
−0.846969 + 0.531643i \(0.821575\pi\)
\(972\) 8.49752e9 0.296797
\(973\) −1.11720e10 −0.388807
\(974\) 4.16829e9 0.144545
\(975\) 8.80957e9 0.304396
\(976\) −4.19606e9 −0.144467
\(977\) 1.42491e9 0.0488829 0.0244414 0.999701i \(-0.492219\pi\)
0.0244414 + 0.999701i \(0.492219\pi\)
\(978\) 2.40916e9 0.0823531
\(979\) −2.94840e8 −0.0100426
\(980\) −8.43248e9 −0.286196
\(981\) −6.71014e9 −0.226929
\(982\) −4.32564e9 −0.145767
\(983\) 4.85675e10 1.63083 0.815415 0.578877i \(-0.196509\pi\)
0.815415 + 0.578877i \(0.196509\pi\)
\(984\) −1.63155e10 −0.545905
\(985\) −1.81003e10 −0.603475
\(986\) 8.85647e8 0.0294233
\(987\) 1.92850e10 0.638425
\(988\) −1.98062e10 −0.653358
\(989\) 9.64818e9 0.317145
\(990\) 8.12482e8 0.0266128
\(991\) −1.69341e10 −0.552719 −0.276360 0.961054i \(-0.589128\pi\)
−0.276360 + 0.961054i \(0.589128\pi\)
\(992\) 1.10155e10 0.358273
\(993\) −6.98457e9 −0.226369
\(994\) −6.35656e8 −0.0205291
\(995\) −1.58588e9 −0.0510375
\(996\) 9.24128e10 2.96363
\(997\) 2.36849e10 0.756900 0.378450 0.925622i \(-0.376457\pi\)
0.378450 + 0.925622i \(0.376457\pi\)
\(998\) 4.80763e9 0.153100
\(999\) −4.49707e10 −1.42709
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 \(a_p\))