Properties

Label 4017.2.a.j.1.14
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.506527 q^{2} -1.00000 q^{3} -1.74343 q^{4} +4.00697 q^{5} -0.506527 q^{6} +4.25155 q^{7} -1.89615 q^{8} +1.00000 q^{9} +2.02964 q^{10} -0.00859157 q^{11} +1.74343 q^{12} +1.00000 q^{13} +2.15352 q^{14} -4.00697 q^{15} +2.52641 q^{16} -2.55474 q^{17} +0.506527 q^{18} +5.31133 q^{19} -6.98588 q^{20} -4.25155 q^{21} -0.00435186 q^{22} +7.33175 q^{23} +1.89615 q^{24} +11.0558 q^{25} +0.506527 q^{26} -1.00000 q^{27} -7.41228 q^{28} -3.63092 q^{29} -2.02964 q^{30} -4.47636 q^{31} +5.07199 q^{32} +0.00859157 q^{33} -1.29404 q^{34} +17.0358 q^{35} -1.74343 q^{36} -4.40497 q^{37} +2.69033 q^{38} -1.00000 q^{39} -7.59781 q^{40} +10.3946 q^{41} -2.15352 q^{42} -8.16666 q^{43} +0.0149788 q^{44} +4.00697 q^{45} +3.71373 q^{46} +10.6650 q^{47} -2.52641 q^{48} +11.0757 q^{49} +5.60007 q^{50} +2.55474 q^{51} -1.74343 q^{52} -8.47563 q^{53} -0.506527 q^{54} -0.0344262 q^{55} -8.06157 q^{56} -5.31133 q^{57} -1.83916 q^{58} -9.30787 q^{59} +6.98588 q^{60} +9.90044 q^{61} -2.26740 q^{62} +4.25155 q^{63} -2.48372 q^{64} +4.00697 q^{65} +0.00435186 q^{66} -4.26929 q^{67} +4.45401 q^{68} -7.33175 q^{69} +8.62911 q^{70} -5.41974 q^{71} -1.89615 q^{72} +11.7345 q^{73} -2.23124 q^{74} -11.0558 q^{75} -9.25993 q^{76} -0.0365275 q^{77} -0.506527 q^{78} -10.8270 q^{79} +10.1233 q^{80} +1.00000 q^{81} +5.26515 q^{82} +4.73251 q^{83} +7.41228 q^{84} -10.2368 q^{85} -4.13663 q^{86} +3.63092 q^{87} +0.0162909 q^{88} +14.1868 q^{89} +2.02964 q^{90} +4.25155 q^{91} -12.7824 q^{92} +4.47636 q^{93} +5.40212 q^{94} +21.2823 q^{95} -5.07199 q^{96} -16.4976 q^{97} +5.61013 q^{98} -0.00859157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.506527 0.358169 0.179084 0.983834i \(-0.442687\pi\)
0.179084 + 0.983834i \(0.442687\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.74343 −0.871715
\(5\) 4.00697 1.79197 0.895986 0.444082i \(-0.146470\pi\)
0.895986 + 0.444082i \(0.146470\pi\)
\(6\) −0.506527 −0.206789
\(7\) 4.25155 1.60694 0.803468 0.595348i \(-0.202986\pi\)
0.803468 + 0.595348i \(0.202986\pi\)
\(8\) −1.89615 −0.670390
\(9\) 1.00000 0.333333
\(10\) 2.02964 0.641828
\(11\) −0.00859157 −0.00259045 −0.00129523 0.999999i \(-0.500412\pi\)
−0.00129523 + 0.999999i \(0.500412\pi\)
\(12\) 1.74343 0.503285
\(13\) 1.00000 0.277350
\(14\) 2.15352 0.575554
\(15\) −4.00697 −1.03460
\(16\) 2.52641 0.631603
\(17\) −2.55474 −0.619615 −0.309807 0.950799i \(-0.600265\pi\)
−0.309807 + 0.950799i \(0.600265\pi\)
\(18\) 0.506527 0.119390
\(19\) 5.31133 1.21850 0.609251 0.792977i \(-0.291470\pi\)
0.609251 + 0.792977i \(0.291470\pi\)
\(20\) −6.98588 −1.56209
\(21\) −4.25155 −0.927764
\(22\) −0.00435186 −0.000927819 0
\(23\) 7.33175 1.52878 0.764388 0.644756i \(-0.223041\pi\)
0.764388 + 0.644756i \(0.223041\pi\)
\(24\) 1.89615 0.387050
\(25\) 11.0558 2.21116
\(26\) 0.506527 0.0993381
\(27\) −1.00000 −0.192450
\(28\) −7.41228 −1.40079
\(29\) −3.63092 −0.674245 −0.337122 0.941461i \(-0.609454\pi\)
−0.337122 + 0.941461i \(0.609454\pi\)
\(30\) −2.02964 −0.370560
\(31\) −4.47636 −0.803978 −0.401989 0.915644i \(-0.631681\pi\)
−0.401989 + 0.915644i \(0.631681\pi\)
\(32\) 5.07199 0.896610
\(33\) 0.00859157 0.00149560
\(34\) −1.29404 −0.221927
\(35\) 17.0358 2.87958
\(36\) −1.74343 −0.290572
\(37\) −4.40497 −0.724173 −0.362086 0.932145i \(-0.617935\pi\)
−0.362086 + 0.932145i \(0.617935\pi\)
\(38\) 2.69033 0.436429
\(39\) −1.00000 −0.160128
\(40\) −7.59781 −1.20132
\(41\) 10.3946 1.62337 0.811683 0.584099i \(-0.198552\pi\)
0.811683 + 0.584099i \(0.198552\pi\)
\(42\) −2.15352 −0.332296
\(43\) −8.16666 −1.24540 −0.622702 0.782459i \(-0.713965\pi\)
−0.622702 + 0.782459i \(0.713965\pi\)
\(44\) 0.0149788 0.00225814
\(45\) 4.00697 0.597324
\(46\) 3.71373 0.547560
\(47\) 10.6650 1.55565 0.777827 0.628478i \(-0.216322\pi\)
0.777827 + 0.628478i \(0.216322\pi\)
\(48\) −2.52641 −0.364656
\(49\) 11.0757 1.58224
\(50\) 5.60007 0.791970
\(51\) 2.55474 0.357735
\(52\) −1.74343 −0.241770
\(53\) −8.47563 −1.16422 −0.582109 0.813111i \(-0.697772\pi\)
−0.582109 + 0.813111i \(0.697772\pi\)
\(54\) −0.506527 −0.0689296
\(55\) −0.0344262 −0.00464202
\(56\) −8.06157 −1.07727
\(57\) −5.31133 −0.703502
\(58\) −1.83916 −0.241493
\(59\) −9.30787 −1.21178 −0.605891 0.795548i \(-0.707183\pi\)
−0.605891 + 0.795548i \(0.707183\pi\)
\(60\) 6.98588 0.901873
\(61\) 9.90044 1.26762 0.633810 0.773488i \(-0.281490\pi\)
0.633810 + 0.773488i \(0.281490\pi\)
\(62\) −2.26740 −0.287960
\(63\) 4.25155 0.535645
\(64\) −2.48372 −0.310465
\(65\) 4.00697 0.497004
\(66\) 0.00435186 0.000535677 0
\(67\) −4.26929 −0.521577 −0.260789 0.965396i \(-0.583983\pi\)
−0.260789 + 0.965396i \(0.583983\pi\)
\(68\) 4.45401 0.540128
\(69\) −7.33175 −0.882639
\(70\) 8.62911 1.03138
\(71\) −5.41974 −0.643204 −0.321602 0.946875i \(-0.604221\pi\)
−0.321602 + 0.946875i \(0.604221\pi\)
\(72\) −1.89615 −0.223463
\(73\) 11.7345 1.37342 0.686708 0.726934i \(-0.259055\pi\)
0.686708 + 0.726934i \(0.259055\pi\)
\(74\) −2.23124 −0.259376
\(75\) −11.0558 −1.27662
\(76\) −9.25993 −1.06219
\(77\) −0.0365275 −0.00416269
\(78\) −0.506527 −0.0573529
\(79\) −10.8270 −1.21813 −0.609064 0.793121i \(-0.708455\pi\)
−0.609064 + 0.793121i \(0.708455\pi\)
\(80\) 10.1233 1.13181
\(81\) 1.00000 0.111111
\(82\) 5.26515 0.581438
\(83\) 4.73251 0.519461 0.259730 0.965681i \(-0.416366\pi\)
0.259730 + 0.965681i \(0.416366\pi\)
\(84\) 7.41228 0.808746
\(85\) −10.2368 −1.11033
\(86\) −4.13663 −0.446064
\(87\) 3.63092 0.389276
\(88\) 0.0162909 0.00173661
\(89\) 14.1868 1.50380 0.751901 0.659276i \(-0.229137\pi\)
0.751901 + 0.659276i \(0.229137\pi\)
\(90\) 2.02964 0.213943
\(91\) 4.25155 0.445684
\(92\) −12.7824 −1.33266
\(93\) 4.47636 0.464177
\(94\) 5.40212 0.557187
\(95\) 21.2823 2.18352
\(96\) −5.07199 −0.517658
\(97\) −16.4976 −1.67508 −0.837538 0.546379i \(-0.816006\pi\)
−0.837538 + 0.546379i \(0.816006\pi\)
\(98\) 5.61013 0.566709
\(99\) −0.00859157 −0.000863485 0
\(100\) −19.2751 −1.92751
\(101\) −13.0311 −1.29664 −0.648321 0.761367i \(-0.724529\pi\)
−0.648321 + 0.761367i \(0.724529\pi\)
\(102\) 1.29404 0.128129
\(103\) −1.00000 −0.0985329
\(104\) −1.89615 −0.185933
\(105\) −17.0358 −1.66253
\(106\) −4.29313 −0.416986
\(107\) −10.2303 −0.989005 −0.494503 0.869176i \(-0.664650\pi\)
−0.494503 + 0.869176i \(0.664650\pi\)
\(108\) 1.74343 0.167762
\(109\) −11.0315 −1.05662 −0.528312 0.849050i \(-0.677175\pi\)
−0.528312 + 0.849050i \(0.677175\pi\)
\(110\) −0.0174378 −0.00166263
\(111\) 4.40497 0.418101
\(112\) 10.7412 1.01494
\(113\) 0.592472 0.0557350 0.0278675 0.999612i \(-0.491128\pi\)
0.0278675 + 0.999612i \(0.491128\pi\)
\(114\) −2.69033 −0.251972
\(115\) 29.3781 2.73952
\(116\) 6.33026 0.587750
\(117\) 1.00000 0.0924500
\(118\) −4.71469 −0.434022
\(119\) −10.8616 −0.995681
\(120\) 7.59781 0.693582
\(121\) −10.9999 −0.999993
\(122\) 5.01484 0.454022
\(123\) −10.3946 −0.937250
\(124\) 7.80423 0.700840
\(125\) 24.2655 2.17037
\(126\) 2.15352 0.191851
\(127\) 17.4613 1.54944 0.774722 0.632303i \(-0.217890\pi\)
0.774722 + 0.632303i \(0.217890\pi\)
\(128\) −11.4021 −1.00781
\(129\) 8.16666 0.719034
\(130\) 2.02964 0.178011
\(131\) −12.1714 −1.06342 −0.531712 0.846925i \(-0.678451\pi\)
−0.531712 + 0.846925i \(0.678451\pi\)
\(132\) −0.0149788 −0.00130374
\(133\) 22.5814 1.95805
\(134\) −2.16251 −0.186813
\(135\) −4.00697 −0.344865
\(136\) 4.84416 0.415383
\(137\) −1.60038 −0.136730 −0.0683649 0.997660i \(-0.521778\pi\)
−0.0683649 + 0.997660i \(0.521778\pi\)
\(138\) −3.71373 −0.316134
\(139\) 12.6546 1.07335 0.536675 0.843789i \(-0.319680\pi\)
0.536675 + 0.843789i \(0.319680\pi\)
\(140\) −29.7008 −2.51018
\(141\) −10.6650 −0.898158
\(142\) −2.74524 −0.230376
\(143\) −0.00859157 −0.000718463 0
\(144\) 2.52641 0.210534
\(145\) −14.5490 −1.20823
\(146\) 5.94382 0.491914
\(147\) −11.0757 −0.913507
\(148\) 7.67976 0.631272
\(149\) 10.1161 0.828745 0.414372 0.910107i \(-0.364001\pi\)
0.414372 + 0.910107i \(0.364001\pi\)
\(150\) −5.60007 −0.457244
\(151\) 4.99137 0.406192 0.203096 0.979159i \(-0.434900\pi\)
0.203096 + 0.979159i \(0.434900\pi\)
\(152\) −10.0711 −0.816871
\(153\) −2.55474 −0.206538
\(154\) −0.0185022 −0.00149095
\(155\) −17.9367 −1.44071
\(156\) 1.74343 0.139586
\(157\) −5.97346 −0.476734 −0.238367 0.971175i \(-0.576612\pi\)
−0.238367 + 0.971175i \(0.576612\pi\)
\(158\) −5.48414 −0.436295
\(159\) 8.47563 0.672161
\(160\) 20.3233 1.60670
\(161\) 31.1713 2.45664
\(162\) 0.506527 0.0397965
\(163\) −3.22756 −0.252802 −0.126401 0.991979i \(-0.540343\pi\)
−0.126401 + 0.991979i \(0.540343\pi\)
\(164\) −18.1223 −1.41511
\(165\) 0.0344262 0.00268007
\(166\) 2.39714 0.186055
\(167\) 9.12586 0.706180 0.353090 0.935589i \(-0.385131\pi\)
0.353090 + 0.935589i \(0.385131\pi\)
\(168\) 8.06157 0.621964
\(169\) 1.00000 0.0769231
\(170\) −5.18519 −0.397686
\(171\) 5.31133 0.406167
\(172\) 14.2380 1.08564
\(173\) 3.89271 0.295957 0.147979 0.988991i \(-0.452723\pi\)
0.147979 + 0.988991i \(0.452723\pi\)
\(174\) 1.83916 0.139426
\(175\) 47.0044 3.55320
\(176\) −0.0217058 −0.00163614
\(177\) 9.30787 0.699623
\(178\) 7.18601 0.538614
\(179\) 15.1591 1.13305 0.566524 0.824045i \(-0.308288\pi\)
0.566524 + 0.824045i \(0.308288\pi\)
\(180\) −6.98588 −0.520697
\(181\) −17.0656 −1.26848 −0.634239 0.773137i \(-0.718687\pi\)
−0.634239 + 0.773137i \(0.718687\pi\)
\(182\) 2.15352 0.159630
\(183\) −9.90044 −0.731861
\(184\) −13.9021 −1.02488
\(185\) −17.6506 −1.29770
\(186\) 2.26740 0.166254
\(187\) 0.0219492 0.00160508
\(188\) −18.5937 −1.35609
\(189\) −4.25155 −0.309255
\(190\) 10.7801 0.782069
\(191\) −19.9820 −1.44585 −0.722925 0.690926i \(-0.757203\pi\)
−0.722925 + 0.690926i \(0.757203\pi\)
\(192\) 2.48372 0.179247
\(193\) 20.8721 1.50241 0.751203 0.660071i \(-0.229474\pi\)
0.751203 + 0.660071i \(0.229474\pi\)
\(194\) −8.35647 −0.599960
\(195\) −4.00697 −0.286945
\(196\) −19.3097 −1.37926
\(197\) −6.55617 −0.467108 −0.233554 0.972344i \(-0.575036\pi\)
−0.233554 + 0.972344i \(0.575036\pi\)
\(198\) −0.00435186 −0.000309273 0
\(199\) 6.22649 0.441384 0.220692 0.975344i \(-0.429168\pi\)
0.220692 + 0.975344i \(0.429168\pi\)
\(200\) −20.9635 −1.48234
\(201\) 4.26929 0.301133
\(202\) −6.60060 −0.464416
\(203\) −15.4370 −1.08347
\(204\) −4.45401 −0.311843
\(205\) 41.6509 2.90903
\(206\) −0.506527 −0.0352914
\(207\) 7.33175 0.509592
\(208\) 2.52641 0.175175
\(209\) −0.0456326 −0.00315647
\(210\) −8.62911 −0.595465
\(211\) −8.28439 −0.570321 −0.285160 0.958480i \(-0.592047\pi\)
−0.285160 + 0.958480i \(0.592047\pi\)
\(212\) 14.7767 1.01487
\(213\) 5.41974 0.371354
\(214\) −5.18195 −0.354231
\(215\) −32.7236 −2.23173
\(216\) 1.89615 0.129017
\(217\) −19.0315 −1.29194
\(218\) −5.58774 −0.378450
\(219\) −11.7345 −0.792942
\(220\) 0.0600196 0.00404652
\(221\) −2.55474 −0.171850
\(222\) 2.23124 0.149751
\(223\) 26.0408 1.74382 0.871910 0.489666i \(-0.162881\pi\)
0.871910 + 0.489666i \(0.162881\pi\)
\(224\) 21.5638 1.44079
\(225\) 11.0558 0.737055
\(226\) 0.300103 0.0199625
\(227\) −5.19680 −0.344924 −0.172462 0.985016i \(-0.555172\pi\)
−0.172462 + 0.985016i \(0.555172\pi\)
\(228\) 9.25993 0.613254
\(229\) 17.8295 1.17821 0.589104 0.808057i \(-0.299481\pi\)
0.589104 + 0.808057i \(0.299481\pi\)
\(230\) 14.8808 0.981212
\(231\) 0.0365275 0.00240333
\(232\) 6.88476 0.452007
\(233\) 16.5553 1.08457 0.542285 0.840194i \(-0.317559\pi\)
0.542285 + 0.840194i \(0.317559\pi\)
\(234\) 0.506527 0.0331127
\(235\) 42.7345 2.78769
\(236\) 16.2276 1.05633
\(237\) 10.8270 0.703286
\(238\) −5.50169 −0.356622
\(239\) 18.2439 1.18010 0.590050 0.807367i \(-0.299108\pi\)
0.590050 + 0.807367i \(0.299108\pi\)
\(240\) −10.1233 −0.653454
\(241\) 17.4518 1.12417 0.562083 0.827081i \(-0.310000\pi\)
0.562083 + 0.827081i \(0.310000\pi\)
\(242\) −5.57176 −0.358166
\(243\) −1.00000 −0.0641500
\(244\) −17.2607 −1.10500
\(245\) 44.3800 2.83533
\(246\) −5.26515 −0.335694
\(247\) 5.31133 0.337952
\(248\) 8.48785 0.538979
\(249\) −4.73251 −0.299911
\(250\) 12.2911 0.777359
\(251\) 24.8925 1.57120 0.785600 0.618735i \(-0.212355\pi\)
0.785600 + 0.618735i \(0.212355\pi\)
\(252\) −7.41228 −0.466930
\(253\) −0.0629912 −0.00396023
\(254\) 8.84464 0.554962
\(255\) 10.2368 0.641051
\(256\) −0.808001 −0.0505000
\(257\) −17.5455 −1.09446 −0.547229 0.836983i \(-0.684317\pi\)
−0.547229 + 0.836983i \(0.684317\pi\)
\(258\) 4.13663 0.257535
\(259\) −18.7280 −1.16370
\(260\) −6.98588 −0.433246
\(261\) −3.63092 −0.224748
\(262\) −6.16516 −0.380885
\(263\) 22.6846 1.39879 0.699397 0.714733i \(-0.253452\pi\)
0.699397 + 0.714733i \(0.253452\pi\)
\(264\) −0.0162909 −0.00100263
\(265\) −33.9616 −2.08624
\(266\) 11.4381 0.701313
\(267\) −14.1868 −0.868220
\(268\) 7.44322 0.454667
\(269\) 6.79797 0.414480 0.207240 0.978290i \(-0.433552\pi\)
0.207240 + 0.978290i \(0.433552\pi\)
\(270\) −2.02964 −0.123520
\(271\) 13.1078 0.796240 0.398120 0.917333i \(-0.369663\pi\)
0.398120 + 0.917333i \(0.369663\pi\)
\(272\) −6.45432 −0.391350
\(273\) −4.25155 −0.257316
\(274\) −0.810636 −0.0489723
\(275\) −0.0949868 −0.00572792
\(276\) 12.7824 0.769410
\(277\) −20.3224 −1.22105 −0.610526 0.791996i \(-0.709042\pi\)
−0.610526 + 0.791996i \(0.709042\pi\)
\(278\) 6.40990 0.384440
\(279\) −4.47636 −0.267993
\(280\) −32.3025 −1.93044
\(281\) −11.1509 −0.665210 −0.332605 0.943066i \(-0.607928\pi\)
−0.332605 + 0.943066i \(0.607928\pi\)
\(282\) −5.40212 −0.321692
\(283\) −15.4541 −0.918652 −0.459326 0.888268i \(-0.651909\pi\)
−0.459326 + 0.888268i \(0.651909\pi\)
\(284\) 9.44893 0.560691
\(285\) −21.2823 −1.26066
\(286\) −0.00435186 −0.000257331 0
\(287\) 44.1932 2.60864
\(288\) 5.07199 0.298870
\(289\) −10.4733 −0.616078
\(290\) −7.36946 −0.432749
\(291\) 16.4976 0.967106
\(292\) −20.4582 −1.19723
\(293\) 13.0203 0.760655 0.380327 0.924852i \(-0.375811\pi\)
0.380327 + 0.924852i \(0.375811\pi\)
\(294\) −5.61013 −0.327190
\(295\) −37.2964 −2.17148
\(296\) 8.35248 0.485478
\(297\) 0.00859157 0.000498533 0
\(298\) 5.12409 0.296830
\(299\) 7.33175 0.424006
\(300\) 19.2751 1.11285
\(301\) −34.7210 −2.00128
\(302\) 2.52826 0.145485
\(303\) 13.0311 0.748617
\(304\) 13.4186 0.769609
\(305\) 39.6708 2.27154
\(306\) −1.29404 −0.0739755
\(307\) 1.46207 0.0834446 0.0417223 0.999129i \(-0.486716\pi\)
0.0417223 + 0.999129i \(0.486716\pi\)
\(308\) 0.0636831 0.00362868
\(309\) 1.00000 0.0568880
\(310\) −9.08540 −0.516016
\(311\) 0.0221015 0.00125326 0.000626630 1.00000i \(-0.499801\pi\)
0.000626630 1.00000i \(0.499801\pi\)
\(312\) 1.89615 0.107348
\(313\) 14.6248 0.826641 0.413320 0.910586i \(-0.364369\pi\)
0.413320 + 0.910586i \(0.364369\pi\)
\(314\) −3.02572 −0.170751
\(315\) 17.0358 0.959861
\(316\) 18.8760 1.06186
\(317\) −7.50750 −0.421663 −0.210832 0.977522i \(-0.567617\pi\)
−0.210832 + 0.977522i \(0.567617\pi\)
\(318\) 4.29313 0.240747
\(319\) 0.0311953 0.00174660
\(320\) −9.95221 −0.556345
\(321\) 10.2303 0.571002
\(322\) 15.7891 0.879893
\(323\) −13.5690 −0.755002
\(324\) −1.74343 −0.0968573
\(325\) 11.0558 0.613267
\(326\) −1.63485 −0.0905458
\(327\) 11.0315 0.610042
\(328\) −19.7097 −1.08829
\(329\) 45.3429 2.49984
\(330\) 0.0174378 0.000959918 0
\(331\) −25.3692 −1.39442 −0.697209 0.716868i \(-0.745575\pi\)
−0.697209 + 0.716868i \(0.745575\pi\)
\(332\) −8.25081 −0.452822
\(333\) −4.40497 −0.241391
\(334\) 4.62249 0.252932
\(335\) −17.1069 −0.934652
\(336\) −10.7412 −0.585979
\(337\) 3.07697 0.167613 0.0838065 0.996482i \(-0.473292\pi\)
0.0838065 + 0.996482i \(0.473292\pi\)
\(338\) 0.506527 0.0275514
\(339\) −0.592472 −0.0321786
\(340\) 17.8471 0.967894
\(341\) 0.0384590 0.00208267
\(342\) 2.69033 0.145476
\(343\) 17.3280 0.935623
\(344\) 15.4852 0.834905
\(345\) −29.3781 −1.58167
\(346\) 1.97176 0.106003
\(347\) −12.1451 −0.651982 −0.325991 0.945373i \(-0.605698\pi\)
−0.325991 + 0.945373i \(0.605698\pi\)
\(348\) −6.33026 −0.339337
\(349\) −18.1385 −0.970930 −0.485465 0.874256i \(-0.661350\pi\)
−0.485465 + 0.874256i \(0.661350\pi\)
\(350\) 23.8090 1.27264
\(351\) −1.00000 −0.0533761
\(352\) −0.0435763 −0.00232263
\(353\) 13.6578 0.726931 0.363465 0.931608i \(-0.381594\pi\)
0.363465 + 0.931608i \(0.381594\pi\)
\(354\) 4.71469 0.250583
\(355\) −21.7167 −1.15260
\(356\) −24.7338 −1.31089
\(357\) 10.8616 0.574857
\(358\) 7.67852 0.405822
\(359\) 18.9649 1.00093 0.500466 0.865756i \(-0.333162\pi\)
0.500466 + 0.865756i \(0.333162\pi\)
\(360\) −7.59781 −0.400440
\(361\) 9.21020 0.484747
\(362\) −8.64420 −0.454329
\(363\) 10.9999 0.577346
\(364\) −7.41228 −0.388509
\(365\) 47.0197 2.46112
\(366\) −5.01484 −0.262130
\(367\) 20.2870 1.05897 0.529486 0.848319i \(-0.322385\pi\)
0.529486 + 0.848319i \(0.322385\pi\)
\(368\) 18.5230 0.965579
\(369\) 10.3946 0.541122
\(370\) −8.94050 −0.464794
\(371\) −36.0346 −1.87082
\(372\) −7.80423 −0.404630
\(373\) −1.32244 −0.0684732 −0.0342366 0.999414i \(-0.510900\pi\)
−0.0342366 + 0.999414i \(0.510900\pi\)
\(374\) 0.0111179 0.000574891 0
\(375\) −24.2655 −1.25307
\(376\) −20.2225 −1.04289
\(377\) −3.63092 −0.187002
\(378\) −2.15352 −0.110765
\(379\) 9.02528 0.463598 0.231799 0.972764i \(-0.425539\pi\)
0.231799 + 0.972764i \(0.425539\pi\)
\(380\) −37.1043 −1.90341
\(381\) −17.4613 −0.894571
\(382\) −10.1214 −0.517858
\(383\) −22.3456 −1.14181 −0.570903 0.821018i \(-0.693407\pi\)
−0.570903 + 0.821018i \(0.693407\pi\)
\(384\) 11.4021 0.581859
\(385\) −0.146365 −0.00745943
\(386\) 10.5723 0.538115
\(387\) −8.16666 −0.415134
\(388\) 28.7624 1.46019
\(389\) 18.9373 0.960159 0.480080 0.877225i \(-0.340608\pi\)
0.480080 + 0.877225i \(0.340608\pi\)
\(390\) −2.02964 −0.102775
\(391\) −18.7307 −0.947252
\(392\) −21.0011 −1.06072
\(393\) 12.1714 0.613968
\(394\) −3.32088 −0.167303
\(395\) −43.3833 −2.18285
\(396\) 0.0149788 0.000752713 0
\(397\) −27.9231 −1.40142 −0.700711 0.713445i \(-0.747134\pi\)
−0.700711 + 0.713445i \(0.747134\pi\)
\(398\) 3.15388 0.158090
\(399\) −22.5814 −1.13048
\(400\) 27.9316 1.39658
\(401\) −29.3659 −1.46646 −0.733232 0.679978i \(-0.761989\pi\)
−0.733232 + 0.679978i \(0.761989\pi\)
\(402\) 2.16251 0.107856
\(403\) −4.47636 −0.222983
\(404\) 22.7188 1.13030
\(405\) 4.00697 0.199108
\(406\) −7.81928 −0.388064
\(407\) 0.0378456 0.00187594
\(408\) −4.84416 −0.239822
\(409\) −16.0837 −0.795288 −0.397644 0.917540i \(-0.630172\pi\)
−0.397644 + 0.917540i \(0.630172\pi\)
\(410\) 21.0973 1.04192
\(411\) 1.60038 0.0789410
\(412\) 1.74343 0.0858927
\(413\) −39.5729 −1.94726
\(414\) 3.71373 0.182520
\(415\) 18.9630 0.930859
\(416\) 5.07199 0.248675
\(417\) −12.6546 −0.619699
\(418\) −0.0231141 −0.00113055
\(419\) 31.8611 1.55652 0.778259 0.627943i \(-0.216103\pi\)
0.778259 + 0.627943i \(0.216103\pi\)
\(420\) 29.7008 1.44925
\(421\) −8.15980 −0.397684 −0.198842 0.980032i \(-0.563718\pi\)
−0.198842 + 0.980032i \(0.563718\pi\)
\(422\) −4.19626 −0.204271
\(423\) 10.6650 0.518552
\(424\) 16.0710 0.780479
\(425\) −28.2447 −1.37007
\(426\) 2.74524 0.133007
\(427\) 42.0922 2.03698
\(428\) 17.8359 0.862131
\(429\) 0.00859157 0.000414805 0
\(430\) −16.5754 −0.799335
\(431\) 10.3519 0.498632 0.249316 0.968422i \(-0.419794\pi\)
0.249316 + 0.968422i \(0.419794\pi\)
\(432\) −2.52641 −0.121552
\(433\) −30.4781 −1.46469 −0.732343 0.680936i \(-0.761573\pi\)
−0.732343 + 0.680936i \(0.761573\pi\)
\(434\) −9.63996 −0.462733
\(435\) 14.5490 0.697571
\(436\) 19.2326 0.921075
\(437\) 38.9413 1.86282
\(438\) −5.94382 −0.284007
\(439\) 23.1848 1.10655 0.553274 0.832999i \(-0.313378\pi\)
0.553274 + 0.832999i \(0.313378\pi\)
\(440\) 0.0652771 0.00311196
\(441\) 11.0757 0.527414
\(442\) −1.29404 −0.0615513
\(443\) −1.18205 −0.0561607 −0.0280804 0.999606i \(-0.508939\pi\)
−0.0280804 + 0.999606i \(0.508939\pi\)
\(444\) −7.67976 −0.364465
\(445\) 56.8462 2.69477
\(446\) 13.1904 0.624581
\(447\) −10.1161 −0.478476
\(448\) −10.5597 −0.498898
\(449\) −19.6807 −0.928789 −0.464395 0.885628i \(-0.653728\pi\)
−0.464395 + 0.885628i \(0.653728\pi\)
\(450\) 5.60007 0.263990
\(451\) −0.0893060 −0.00420525
\(452\) −1.03293 −0.0485851
\(453\) −4.99137 −0.234515
\(454\) −2.63232 −0.123541
\(455\) 17.0358 0.798653
\(456\) 10.0711 0.471621
\(457\) −33.0186 −1.54454 −0.772272 0.635292i \(-0.780880\pi\)
−0.772272 + 0.635292i \(0.780880\pi\)
\(458\) 9.03113 0.421997
\(459\) 2.55474 0.119245
\(460\) −51.2187 −2.38809
\(461\) −13.0434 −0.607493 −0.303747 0.952753i \(-0.598238\pi\)
−0.303747 + 0.952753i \(0.598238\pi\)
\(462\) 0.0185022 0.000860798 0
\(463\) −20.3792 −0.947102 −0.473551 0.880766i \(-0.657028\pi\)
−0.473551 + 0.880766i \(0.657028\pi\)
\(464\) −9.17320 −0.425855
\(465\) 17.9367 0.831793
\(466\) 8.38568 0.388459
\(467\) 5.87118 0.271686 0.135843 0.990730i \(-0.456626\pi\)
0.135843 + 0.990730i \(0.456626\pi\)
\(468\) −1.74343 −0.0805901
\(469\) −18.1511 −0.838141
\(470\) 21.6462 0.998463
\(471\) 5.97346 0.275243
\(472\) 17.6491 0.812366
\(473\) 0.0701644 0.00322616
\(474\) 5.48414 0.251895
\(475\) 58.7211 2.69431
\(476\) 18.9364 0.867950
\(477\) −8.47563 −0.388072
\(478\) 9.24103 0.422675
\(479\) 21.3276 0.974484 0.487242 0.873267i \(-0.338003\pi\)
0.487242 + 0.873267i \(0.338003\pi\)
\(480\) −20.3233 −0.927629
\(481\) −4.40497 −0.200849
\(482\) 8.83979 0.402641
\(483\) −31.1713 −1.41834
\(484\) 19.1776 0.871709
\(485\) −66.1054 −3.00169
\(486\) −0.506527 −0.0229765
\(487\) 30.8957 1.40002 0.700008 0.714135i \(-0.253180\pi\)
0.700008 + 0.714135i \(0.253180\pi\)
\(488\) −18.7727 −0.849800
\(489\) 3.22756 0.145955
\(490\) 22.4796 1.01553
\(491\) 27.6350 1.24715 0.623576 0.781763i \(-0.285679\pi\)
0.623576 + 0.781763i \(0.285679\pi\)
\(492\) 18.1223 0.817015
\(493\) 9.27605 0.417772
\(494\) 2.69033 0.121044
\(495\) −0.0344262 −0.00154734
\(496\) −11.3091 −0.507795
\(497\) −23.0423 −1.03359
\(498\) −2.39714 −0.107419
\(499\) −40.3219 −1.80506 −0.902528 0.430630i \(-0.858291\pi\)
−0.902528 + 0.430630i \(0.858291\pi\)
\(500\) −42.3052 −1.89195
\(501\) −9.12586 −0.407713
\(502\) 12.6087 0.562754
\(503\) −6.57249 −0.293053 −0.146526 0.989207i \(-0.546809\pi\)
−0.146526 + 0.989207i \(0.546809\pi\)
\(504\) −8.06157 −0.359091
\(505\) −52.2152 −2.32355
\(506\) −0.0319068 −0.00141843
\(507\) −1.00000 −0.0444116
\(508\) −30.4426 −1.35067
\(509\) 6.69358 0.296688 0.148344 0.988936i \(-0.452606\pi\)
0.148344 + 0.988936i \(0.452606\pi\)
\(510\) 5.18519 0.229604
\(511\) 49.8897 2.20699
\(512\) 22.3948 0.989721
\(513\) −5.31133 −0.234501
\(514\) −8.88727 −0.392001
\(515\) −4.00697 −0.176568
\(516\) −14.2380 −0.626793
\(517\) −0.0916293 −0.00402985
\(518\) −9.48621 −0.416800
\(519\) −3.89271 −0.170871
\(520\) −7.59781 −0.333186
\(521\) 39.7298 1.74060 0.870298 0.492526i \(-0.163926\pi\)
0.870298 + 0.492526i \(0.163926\pi\)
\(522\) −1.83916 −0.0804978
\(523\) 30.0567 1.31429 0.657144 0.753765i \(-0.271765\pi\)
0.657144 + 0.753765i \(0.271765\pi\)
\(524\) 21.2201 0.927003
\(525\) −47.0044 −2.05144
\(526\) 11.4904 0.501004
\(527\) 11.4359 0.498157
\(528\) 0.0217058 0.000944625 0
\(529\) 30.7546 1.33716
\(530\) −17.2025 −0.747227
\(531\) −9.30787 −0.403927
\(532\) −39.3691 −1.70687
\(533\) 10.3946 0.450240
\(534\) −7.18601 −0.310969
\(535\) −40.9927 −1.77227
\(536\) 8.09521 0.349660
\(537\) −15.1591 −0.654166
\(538\) 3.44335 0.148454
\(539\) −0.0951575 −0.00409872
\(540\) 6.98588 0.300624
\(541\) −2.54647 −0.109481 −0.0547406 0.998501i \(-0.517433\pi\)
−0.0547406 + 0.998501i \(0.517433\pi\)
\(542\) 6.63943 0.285188
\(543\) 17.0656 0.732357
\(544\) −12.9576 −0.555553
\(545\) −44.2028 −1.89344
\(546\) −2.15352 −0.0921623
\(547\) −31.6332 −1.35254 −0.676269 0.736655i \(-0.736404\pi\)
−0.676269 + 0.736655i \(0.736404\pi\)
\(548\) 2.79015 0.119189
\(549\) 9.90044 0.422540
\(550\) −0.0481134 −0.00205156
\(551\) −19.2850 −0.821569
\(552\) 13.9021 0.591712
\(553\) −46.0314 −1.95745
\(554\) −10.2938 −0.437343
\(555\) 17.6506 0.749226
\(556\) −22.0624 −0.935656
\(557\) −32.1107 −1.36058 −0.680288 0.732945i \(-0.738145\pi\)
−0.680288 + 0.732945i \(0.738145\pi\)
\(558\) −2.26740 −0.0959866
\(559\) −8.16666 −0.345413
\(560\) 43.0396 1.81875
\(561\) −0.0219492 −0.000926696 0
\(562\) −5.64825 −0.238257
\(563\) −11.1913 −0.471656 −0.235828 0.971795i \(-0.575780\pi\)
−0.235828 + 0.971795i \(0.575780\pi\)
\(564\) 18.5937 0.782938
\(565\) 2.37402 0.0998756
\(566\) −7.82792 −0.329032
\(567\) 4.25155 0.178548
\(568\) 10.2766 0.431197
\(569\) −33.0632 −1.38608 −0.693041 0.720898i \(-0.743729\pi\)
−0.693041 + 0.720898i \(0.743729\pi\)
\(570\) −10.7801 −0.451528
\(571\) 22.4153 0.938053 0.469026 0.883184i \(-0.344605\pi\)
0.469026 + 0.883184i \(0.344605\pi\)
\(572\) 0.0149788 0.000626295 0
\(573\) 19.9820 0.834762
\(574\) 22.3850 0.934334
\(575\) 81.0586 3.38038
\(576\) −2.48372 −0.103488
\(577\) −11.8411 −0.492952 −0.246476 0.969149i \(-0.579273\pi\)
−0.246476 + 0.969149i \(0.579273\pi\)
\(578\) −5.30502 −0.220660
\(579\) −20.8721 −0.867415
\(580\) 25.3652 1.05323
\(581\) 20.1205 0.834740
\(582\) 8.35647 0.346387
\(583\) 0.0728189 0.00301585
\(584\) −22.2503 −0.920723
\(585\) 4.00697 0.165668
\(586\) 6.59514 0.272443
\(587\) −8.59238 −0.354646 −0.177323 0.984153i \(-0.556744\pi\)
−0.177323 + 0.984153i \(0.556744\pi\)
\(588\) 19.3097 0.796318
\(589\) −23.7754 −0.979649
\(590\) −18.8916 −0.777756
\(591\) 6.55617 0.269685
\(592\) −11.1288 −0.457390
\(593\) −30.4558 −1.25067 −0.625335 0.780356i \(-0.715038\pi\)
−0.625335 + 0.780356i \(0.715038\pi\)
\(594\) 0.00435186 0.000178559 0
\(595\) −43.5221 −1.78423
\(596\) −17.6368 −0.722430
\(597\) −6.22649 −0.254833
\(598\) 3.71373 0.151866
\(599\) −2.70297 −0.110440 −0.0552202 0.998474i \(-0.517586\pi\)
−0.0552202 + 0.998474i \(0.517586\pi\)
\(600\) 20.9635 0.855830
\(601\) −18.4778 −0.753726 −0.376863 0.926269i \(-0.622997\pi\)
−0.376863 + 0.926269i \(0.622997\pi\)
\(602\) −17.5871 −0.716796
\(603\) −4.26929 −0.173859
\(604\) −8.70211 −0.354084
\(605\) −44.0764 −1.79196
\(606\) 6.60060 0.268131
\(607\) 10.2233 0.414950 0.207475 0.978240i \(-0.433476\pi\)
0.207475 + 0.978240i \(0.433476\pi\)
\(608\) 26.9390 1.09252
\(609\) 15.4370 0.625541
\(610\) 20.0943 0.813595
\(611\) 10.6650 0.431461
\(612\) 4.45401 0.180043
\(613\) −34.8904 −1.40921 −0.704604 0.709601i \(-0.748875\pi\)
−0.704604 + 0.709601i \(0.748875\pi\)
\(614\) 0.740577 0.0298872
\(615\) −41.6509 −1.67953
\(616\) 0.0692615 0.00279063
\(617\) −46.4525 −1.87011 −0.935053 0.354508i \(-0.884648\pi\)
−0.935053 + 0.354508i \(0.884648\pi\)
\(618\) 0.506527 0.0203755
\(619\) −23.3126 −0.937012 −0.468506 0.883460i \(-0.655208\pi\)
−0.468506 + 0.883460i \(0.655208\pi\)
\(620\) 31.2713 1.25589
\(621\) −7.33175 −0.294213
\(622\) 0.0111950 0.000448878 0
\(623\) 60.3160 2.41651
\(624\) −2.52641 −0.101137
\(625\) 41.9521 1.67808
\(626\) 7.40784 0.296077
\(627\) 0.0456326 0.00182239
\(628\) 10.4143 0.415576
\(629\) 11.2535 0.448708
\(630\) 8.62911 0.343792
\(631\) −41.3825 −1.64741 −0.823706 0.567017i \(-0.808097\pi\)
−0.823706 + 0.567017i \(0.808097\pi\)
\(632\) 20.5295 0.816620
\(633\) 8.28439 0.329275
\(634\) −3.80275 −0.151027
\(635\) 69.9671 2.77656
\(636\) −14.7767 −0.585933
\(637\) 11.0757 0.438835
\(638\) 0.0158013 0.000625578 0
\(639\) −5.41974 −0.214401
\(640\) −45.6877 −1.80597
\(641\) −35.4437 −1.39994 −0.699971 0.714172i \(-0.746804\pi\)
−0.699971 + 0.714172i \(0.746804\pi\)
\(642\) 5.18195 0.204515
\(643\) −26.7711 −1.05575 −0.527874 0.849323i \(-0.677011\pi\)
−0.527874 + 0.849323i \(0.677011\pi\)
\(644\) −54.3450 −2.14149
\(645\) 32.7236 1.28849
\(646\) −6.87309 −0.270418
\(647\) 13.2253 0.519939 0.259970 0.965617i \(-0.416287\pi\)
0.259970 + 0.965617i \(0.416287\pi\)
\(648\) −1.89615 −0.0744877
\(649\) 0.0799692 0.00313907
\(650\) 5.60007 0.219653
\(651\) 19.0315 0.745903
\(652\) 5.62703 0.220372
\(653\) −6.90906 −0.270372 −0.135186 0.990820i \(-0.543163\pi\)
−0.135186 + 0.990820i \(0.543163\pi\)
\(654\) 5.58774 0.218498
\(655\) −48.7706 −1.90563
\(656\) 26.2611 1.02532
\(657\) 11.7345 0.457805
\(658\) 22.9674 0.895363
\(659\) 6.31810 0.246118 0.123059 0.992399i \(-0.460730\pi\)
0.123059 + 0.992399i \(0.460730\pi\)
\(660\) −0.0600196 −0.00233626
\(661\) −41.4314 −1.61149 −0.805747 0.592260i \(-0.798236\pi\)
−0.805747 + 0.592260i \(0.798236\pi\)
\(662\) −12.8502 −0.499436
\(663\) 2.55474 0.0992178
\(664\) −8.97355 −0.348241
\(665\) 90.4829 3.50878
\(666\) −2.23124 −0.0864586
\(667\) −26.6210 −1.03077
\(668\) −15.9103 −0.615588
\(669\) −26.0408 −1.00679
\(670\) −8.66512 −0.334763
\(671\) −0.0850603 −0.00328371
\(672\) −21.5638 −0.831843
\(673\) 12.1167 0.467064 0.233532 0.972349i \(-0.424972\pi\)
0.233532 + 0.972349i \(0.424972\pi\)
\(674\) 1.55857 0.0600337
\(675\) −11.0558 −0.425539
\(676\) −1.74343 −0.0670550
\(677\) −7.07689 −0.271987 −0.135994 0.990710i \(-0.543423\pi\)
−0.135994 + 0.990710i \(0.543423\pi\)
\(678\) −0.300103 −0.0115254
\(679\) −70.1403 −2.69174
\(680\) 19.4104 0.744355
\(681\) 5.19680 0.199142
\(682\) 0.0194805 0.000745947 0
\(683\) −4.37044 −0.167230 −0.0836151 0.996498i \(-0.526647\pi\)
−0.0836151 + 0.996498i \(0.526647\pi\)
\(684\) −9.25993 −0.354062
\(685\) −6.41268 −0.245016
\(686\) 8.77709 0.335111
\(687\) −17.8295 −0.680239
\(688\) −20.6323 −0.786600
\(689\) −8.47563 −0.322896
\(690\) −14.8808 −0.566503
\(691\) 5.57841 0.212213 0.106106 0.994355i \(-0.466162\pi\)
0.106106 + 0.994355i \(0.466162\pi\)
\(692\) −6.78667 −0.257991
\(693\) −0.0365275 −0.00138756
\(694\) −6.15181 −0.233519
\(695\) 50.7067 1.92341
\(696\) −6.88476 −0.260966
\(697\) −26.5555 −1.00586
\(698\) −9.18762 −0.347757
\(699\) −16.5553 −0.626177
\(700\) −81.9489 −3.09738
\(701\) −39.9798 −1.51001 −0.755007 0.655716i \(-0.772367\pi\)
−0.755007 + 0.655716i \(0.772367\pi\)
\(702\) −0.506527 −0.0191176
\(703\) −23.3962 −0.882406
\(704\) 0.0213391 0.000804247 0
\(705\) −42.7345 −1.60947
\(706\) 6.91804 0.260364
\(707\) −55.4023 −2.08362
\(708\) −16.2276 −0.609872
\(709\) −1.08728 −0.0408335 −0.0204168 0.999792i \(-0.506499\pi\)
−0.0204168 + 0.999792i \(0.506499\pi\)
\(710\) −11.0001 −0.412827
\(711\) −10.8270 −0.406043
\(712\) −26.9003 −1.00813
\(713\) −32.8196 −1.22910
\(714\) 5.50169 0.205896
\(715\) −0.0344262 −0.00128747
\(716\) −26.4289 −0.987695
\(717\) −18.2439 −0.681331
\(718\) 9.60625 0.358502
\(719\) 13.0425 0.486403 0.243201 0.969976i \(-0.421802\pi\)
0.243201 + 0.969976i \(0.421802\pi\)
\(720\) 10.1233 0.377272
\(721\) −4.25155 −0.158336
\(722\) 4.66521 0.173621
\(723\) −17.4518 −0.649038
\(724\) 29.7528 1.10575
\(725\) −40.1428 −1.49087
\(726\) 5.57176 0.206787
\(727\) −29.6388 −1.09924 −0.549621 0.835414i \(-0.685228\pi\)
−0.549621 + 0.835414i \(0.685228\pi\)
\(728\) −8.06157 −0.298782
\(729\) 1.00000 0.0370370
\(730\) 23.8167 0.881497
\(731\) 20.8637 0.771670
\(732\) 17.2607 0.637975
\(733\) −8.36554 −0.308988 −0.154494 0.987994i \(-0.549375\pi\)
−0.154494 + 0.987994i \(0.549375\pi\)
\(734\) 10.2759 0.379290
\(735\) −44.3800 −1.63698
\(736\) 37.1866 1.37072
\(737\) 0.0366799 0.00135112
\(738\) 5.26515 0.193813
\(739\) 29.3976 1.08141 0.540704 0.841213i \(-0.318158\pi\)
0.540704 + 0.841213i \(0.318158\pi\)
\(740\) 30.7726 1.13122
\(741\) −5.31133 −0.195116
\(742\) −18.2525 −0.670069
\(743\) −40.6657 −1.49188 −0.745940 0.666013i \(-0.768000\pi\)
−0.745940 + 0.666013i \(0.768000\pi\)
\(744\) −8.48785 −0.311180
\(745\) 40.5350 1.48509
\(746\) −0.669850 −0.0245249
\(747\) 4.73251 0.173154
\(748\) −0.0382669 −0.00139918
\(749\) −43.4948 −1.58927
\(750\) −12.2911 −0.448809
\(751\) −5.13585 −0.187410 −0.0937049 0.995600i \(-0.529871\pi\)
−0.0937049 + 0.995600i \(0.529871\pi\)
\(752\) 26.9443 0.982556
\(753\) −24.8925 −0.907132
\(754\) −1.83916 −0.0669782
\(755\) 20.0003 0.727885
\(756\) 7.41228 0.269582
\(757\) −18.1990 −0.661453 −0.330727 0.943727i \(-0.607294\pi\)
−0.330727 + 0.943727i \(0.607294\pi\)
\(758\) 4.57155 0.166046
\(759\) 0.0629912 0.00228644
\(760\) −40.3545 −1.46381
\(761\) 3.50791 0.127162 0.0635808 0.997977i \(-0.479748\pi\)
0.0635808 + 0.997977i \(0.479748\pi\)
\(762\) −8.84464 −0.320407
\(763\) −46.9009 −1.69793
\(764\) 34.8373 1.26037
\(765\) −10.2368 −0.370111
\(766\) −11.3186 −0.408959
\(767\) −9.30787 −0.336088
\(768\) 0.808001 0.0291562
\(769\) 45.7620 1.65022 0.825111 0.564971i \(-0.191113\pi\)
0.825111 + 0.564971i \(0.191113\pi\)
\(770\) −0.0741376 −0.00267173
\(771\) 17.5455 0.631886
\(772\) −36.3890 −1.30967
\(773\) 48.5204 1.74516 0.872578 0.488474i \(-0.162446\pi\)
0.872578 + 0.488474i \(0.162446\pi\)
\(774\) −4.13663 −0.148688
\(775\) −49.4899 −1.77773
\(776\) 31.2819 1.12295
\(777\) 18.7280 0.671862
\(778\) 9.59225 0.343899
\(779\) 55.2092 1.97807
\(780\) 6.98588 0.250135
\(781\) 0.0465640 0.00166619
\(782\) −9.48760 −0.339276
\(783\) 3.63092 0.129759
\(784\) 27.9817 0.999348
\(785\) −23.9355 −0.854294
\(786\) 6.16516 0.219904
\(787\) 36.3138 1.29445 0.647223 0.762300i \(-0.275930\pi\)
0.647223 + 0.762300i \(0.275930\pi\)
\(788\) 11.4302 0.407185
\(789\) −22.6846 −0.807594
\(790\) −21.9748 −0.781829
\(791\) 2.51892 0.0895626
\(792\) 0.0162909 0.000578871 0
\(793\) 9.90044 0.351575
\(794\) −14.1438 −0.501946
\(795\) 33.9616 1.20449
\(796\) −10.8555 −0.384761
\(797\) 2.10868 0.0746933 0.0373467 0.999302i \(-0.488109\pi\)
0.0373467 + 0.999302i \(0.488109\pi\)
\(798\) −11.4381 −0.404903
\(799\) −27.2464 −0.963907
\(800\) 56.0750 1.98255
\(801\) 14.1868 0.501267
\(802\) −14.8746 −0.525242
\(803\) −0.100817 −0.00355777
\(804\) −7.44322 −0.262502
\(805\) 124.903 4.40224
\(806\) −2.26740 −0.0798657
\(807\) −6.79797 −0.239300
\(808\) 24.7089 0.869255
\(809\) 11.4830 0.403719 0.201860 0.979414i \(-0.435301\pi\)
0.201860 + 0.979414i \(0.435301\pi\)
\(810\) 2.02964 0.0713142
\(811\) 22.9272 0.805083 0.402542 0.915402i \(-0.368127\pi\)
0.402542 + 0.915402i \(0.368127\pi\)
\(812\) 26.9134 0.944476
\(813\) −13.1078 −0.459709
\(814\) 0.0191698 0.000671901 0
\(815\) −12.9328 −0.453015
\(816\) 6.45432 0.225946
\(817\) −43.3758 −1.51753
\(818\) −8.14682 −0.284847
\(819\) 4.25155 0.148561
\(820\) −72.6155 −2.53584
\(821\) 4.37509 0.152692 0.0763459 0.997081i \(-0.475675\pi\)
0.0763459 + 0.997081i \(0.475675\pi\)
\(822\) 0.810636 0.0282742
\(823\) 16.2346 0.565903 0.282952 0.959134i \(-0.408686\pi\)
0.282952 + 0.959134i \(0.408686\pi\)
\(824\) 1.89615 0.0660554
\(825\) 0.0949868 0.00330702
\(826\) −20.0447 −0.697446
\(827\) 43.5291 1.51366 0.756828 0.653614i \(-0.226748\pi\)
0.756828 + 0.653614i \(0.226748\pi\)
\(828\) −12.7824 −0.444219
\(829\) −25.1296 −0.872786 −0.436393 0.899756i \(-0.643744\pi\)
−0.436393 + 0.899756i \(0.643744\pi\)
\(830\) 9.60529 0.333405
\(831\) 20.3224 0.704975
\(832\) −2.48372 −0.0861076
\(833\) −28.2955 −0.980380
\(834\) −6.40990 −0.221957
\(835\) 36.5671 1.26546
\(836\) 0.0795573 0.00275155
\(837\) 4.47636 0.154726
\(838\) 16.1385 0.557496
\(839\) −16.4830 −0.569055 −0.284527 0.958668i \(-0.591837\pi\)
−0.284527 + 0.958668i \(0.591837\pi\)
\(840\) 32.3025 1.11454
\(841\) −15.8164 −0.545394
\(842\) −4.13316 −0.142438
\(843\) 11.1509 0.384059
\(844\) 14.4433 0.497157
\(845\) 4.00697 0.137844
\(846\) 5.40212 0.185729
\(847\) −46.7667 −1.60692
\(848\) −21.4129 −0.735323
\(849\) 15.4541 0.530384
\(850\) −14.3067 −0.490716
\(851\) −32.2962 −1.10710
\(852\) −9.44893 −0.323715
\(853\) 9.71729 0.332714 0.166357 0.986066i \(-0.446800\pi\)
0.166357 + 0.986066i \(0.446800\pi\)
\(854\) 21.3208 0.729584
\(855\) 21.2823 0.727841
\(856\) 19.3983 0.663019
\(857\) −9.02043 −0.308132 −0.154066 0.988061i \(-0.549237\pi\)
−0.154066 + 0.988061i \(0.549237\pi\)
\(858\) 0.00435186 0.000148570 0
\(859\) −28.5445 −0.973927 −0.486964 0.873422i \(-0.661896\pi\)
−0.486964 + 0.873422i \(0.661896\pi\)
\(860\) 57.0513 1.94543
\(861\) −44.1932 −1.50610
\(862\) 5.24350 0.178594
\(863\) 14.5119 0.493991 0.246995 0.969017i \(-0.420557\pi\)
0.246995 + 0.969017i \(0.420557\pi\)
\(864\) −5.07199 −0.172553
\(865\) 15.5980 0.530348
\(866\) −15.4380 −0.524604
\(867\) 10.4733 0.355693
\(868\) 33.1801 1.12620
\(869\) 0.0930205 0.00315551
\(870\) 7.36946 0.249848
\(871\) −4.26929 −0.144659
\(872\) 20.9173 0.708350
\(873\) −16.4976 −0.558359
\(874\) 19.7248 0.667202
\(875\) 103.166 3.48765
\(876\) 20.4582 0.691219
\(877\) −20.7347 −0.700161 −0.350081 0.936720i \(-0.613846\pi\)
−0.350081 + 0.936720i \(0.613846\pi\)
\(878\) 11.7437 0.396331
\(879\) −13.0203 −0.439164
\(880\) −0.0869746 −0.00293191
\(881\) 12.5990 0.424471 0.212235 0.977219i \(-0.431926\pi\)
0.212235 + 0.977219i \(0.431926\pi\)
\(882\) 5.61013 0.188903
\(883\) 19.1594 0.644766 0.322383 0.946609i \(-0.395516\pi\)
0.322383 + 0.946609i \(0.395516\pi\)
\(884\) 4.45401 0.149804
\(885\) 37.2964 1.25370
\(886\) −0.598738 −0.0201150
\(887\) 19.5244 0.655567 0.327783 0.944753i \(-0.393698\pi\)
0.327783 + 0.944753i \(0.393698\pi\)
\(888\) −8.35248 −0.280291
\(889\) 74.2378 2.48985
\(890\) 28.7941 0.965182
\(891\) −0.00859157 −0.000287828 0
\(892\) −45.4003 −1.52011
\(893\) 56.6455 1.89557
\(894\) −5.12409 −0.171375
\(895\) 60.7423 2.03039
\(896\) −48.4764 −1.61948
\(897\) −7.33175 −0.244800
\(898\) −9.96880 −0.332663
\(899\) 16.2533 0.542078
\(900\) −19.2751 −0.642502
\(901\) 21.6530 0.721366
\(902\) −0.0452359 −0.00150619
\(903\) 34.7210 1.15544
\(904\) −1.12341 −0.0373642
\(905\) −68.3815 −2.27308
\(906\) −2.52826 −0.0839959
\(907\) 24.8627 0.825552 0.412776 0.910833i \(-0.364559\pi\)
0.412776 + 0.910833i \(0.364559\pi\)
\(908\) 9.06026 0.300675
\(909\) −13.0311 −0.432214
\(910\) 8.62911 0.286052
\(911\) 22.6448 0.750256 0.375128 0.926973i \(-0.377599\pi\)
0.375128 + 0.926973i \(0.377599\pi\)
\(912\) −13.4186 −0.444334
\(913\) −0.0406597 −0.00134564
\(914\) −16.7248 −0.553207
\(915\) −39.6708 −1.31148
\(916\) −31.0845 −1.02706
\(917\) −51.7475 −1.70885
\(918\) 1.29404 0.0427098
\(919\) 6.95440 0.229405 0.114702 0.993400i \(-0.463409\pi\)
0.114702 + 0.993400i \(0.463409\pi\)
\(920\) −55.7053 −1.83655
\(921\) −1.46207 −0.0481768
\(922\) −6.60685 −0.217585
\(923\) −5.41974 −0.178393
\(924\) −0.0636831 −0.00209502
\(925\) −48.7006 −1.60126
\(926\) −10.3226 −0.339222
\(927\) −1.00000 −0.0328443
\(928\) −18.4160 −0.604535
\(929\) −26.1620 −0.858348 −0.429174 0.903222i \(-0.641195\pi\)
−0.429174 + 0.903222i \(0.641195\pi\)
\(930\) 9.08540 0.297922
\(931\) 58.8266 1.92796
\(932\) −28.8629 −0.945437
\(933\) −0.0221015 −0.000723570 0
\(934\) 2.97391 0.0973093
\(935\) 0.0879498 0.00287627
\(936\) −1.89615 −0.0619775
\(937\) 22.7288 0.742516 0.371258 0.928530i \(-0.378926\pi\)
0.371258 + 0.928530i \(0.378926\pi\)
\(938\) −9.19403 −0.300196
\(939\) −14.6248 −0.477261
\(940\) −74.5046 −2.43007
\(941\) 52.5328 1.71252 0.856260 0.516545i \(-0.172782\pi\)
0.856260 + 0.516545i \(0.172782\pi\)
\(942\) 3.02572 0.0985832
\(943\) 76.2107 2.48176
\(944\) −23.5155 −0.765365
\(945\) −17.0358 −0.554176
\(946\) 0.0355401 0.00115551
\(947\) 41.9432 1.36297 0.681485 0.731832i \(-0.261334\pi\)
0.681485 + 0.731832i \(0.261334\pi\)
\(948\) −18.8760 −0.613066
\(949\) 11.7345 0.380917
\(950\) 29.7438 0.965017
\(951\) 7.50750 0.243447
\(952\) 20.5952 0.667494
\(953\) 5.12231 0.165928 0.0829639 0.996553i \(-0.473561\pi\)
0.0829639 + 0.996553i \(0.473561\pi\)
\(954\) −4.29313 −0.138995
\(955\) −80.0675 −2.59092
\(956\) −31.8070 −1.02871
\(957\) −0.0311953 −0.00100840
\(958\) 10.8030 0.349030
\(959\) −6.80410 −0.219716
\(960\) 9.95221 0.321206
\(961\) −10.9622 −0.353619
\(962\) −2.23124 −0.0719379
\(963\) −10.2303 −0.329668
\(964\) −30.4259 −0.979953
\(965\) 83.6339 2.69227
\(966\) −15.7891 −0.508006
\(967\) −36.6550 −1.17874 −0.589372 0.807861i \(-0.700625\pi\)
−0.589372 + 0.807861i \(0.700625\pi\)
\(968\) 20.8575 0.670385
\(969\) 13.5690 0.435901
\(970\) −33.4841 −1.07511
\(971\) −19.1260 −0.613784 −0.306892 0.951744i \(-0.599289\pi\)
−0.306892 + 0.951744i \(0.599289\pi\)
\(972\) 1.74343 0.0559206
\(973\) 53.8017 1.72480
\(974\) 15.6495 0.501442
\(975\) −11.0558 −0.354070
\(976\) 25.0126 0.800633
\(977\) −27.2464 −0.871690 −0.435845 0.900022i \(-0.643550\pi\)
−0.435845 + 0.900022i \(0.643550\pi\)
\(978\) 1.63485 0.0522767
\(979\) −0.121887 −0.00389553
\(980\) −77.3734 −2.47160
\(981\) −11.0315 −0.352208
\(982\) 13.9979 0.446691
\(983\) 52.7288 1.68179 0.840893 0.541201i \(-0.182030\pi\)
0.840893 + 0.541201i \(0.182030\pi\)
\(984\) 19.7097 0.628323
\(985\) −26.2704 −0.837045
\(986\) 4.69857 0.149633
\(987\) −45.3429 −1.44328
\(988\) −9.25993 −0.294598
\(989\) −59.8759 −1.90394
\(990\) −0.0174378 −0.000554209 0
\(991\) −34.3420 −1.09091 −0.545455 0.838140i \(-0.683643\pi\)
−0.545455 + 0.838140i \(0.683643\pi\)
\(992\) −22.7041 −0.720855
\(993\) 25.3692 0.805067
\(994\) −11.6715 −0.370199
\(995\) 24.9494 0.790948
\(996\) 8.25081 0.261437
\(997\) 17.7242 0.561330 0.280665 0.959806i \(-0.409445\pi\)
0.280665 + 0.959806i \(0.409445\pi\)
\(998\) −20.4241 −0.646515
\(999\) 4.40497 0.139367
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 \(a_p\))