Properties

Label 4003.2.a.b.1.19
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} +O(q^{10})\) \(q-2.36790 q^{2} -2.62074 q^{3} +3.60697 q^{4} +3.23023 q^{5} +6.20567 q^{6} +1.16162 q^{7} -3.80516 q^{8} +3.86830 q^{9} -7.64888 q^{10} -5.95997 q^{11} -9.45295 q^{12} -4.69577 q^{13} -2.75061 q^{14} -8.46560 q^{15} +1.79630 q^{16} +0.273086 q^{17} -9.15976 q^{18} +8.27742 q^{19} +11.6513 q^{20} -3.04431 q^{21} +14.1126 q^{22} +1.00000 q^{23} +9.97234 q^{24} +5.43438 q^{25} +11.1191 q^{26} -2.27558 q^{27} +4.18994 q^{28} -8.08895 q^{29} +20.0457 q^{30} +0.403546 q^{31} +3.35684 q^{32} +15.6195 q^{33} -0.646641 q^{34} +3.75230 q^{35} +13.9528 q^{36} +4.87945 q^{37} -19.6001 q^{38} +12.3064 q^{39} -12.2915 q^{40} +7.36311 q^{41} +7.20864 q^{42} -1.48896 q^{43} -21.4974 q^{44} +12.4955 q^{45} -2.36790 q^{46} -2.84372 q^{47} -4.70764 q^{48} -5.65064 q^{49} -12.8681 q^{50} -0.715688 q^{51} -16.9375 q^{52} -9.11543 q^{53} +5.38836 q^{54} -19.2521 q^{55} -4.42015 q^{56} -21.6930 q^{57} +19.1539 q^{58} +7.08591 q^{59} -30.5352 q^{60} +3.67954 q^{61} -0.955558 q^{62} +4.49350 q^{63} -11.5413 q^{64} -15.1684 q^{65} -36.9856 q^{66} +5.34809 q^{67} +0.985013 q^{68} -2.62074 q^{69} -8.88510 q^{70} +1.23645 q^{71} -14.7195 q^{72} -14.3861 q^{73} -11.5541 q^{74} -14.2421 q^{75} +29.8564 q^{76} -6.92323 q^{77} -29.1404 q^{78} +12.2858 q^{79} +5.80247 q^{80} -5.64117 q^{81} -17.4352 q^{82} +4.40796 q^{83} -10.9807 q^{84} +0.882130 q^{85} +3.52571 q^{86} +21.1991 q^{87} +22.6786 q^{88} +4.11367 q^{89} -29.5881 q^{90} -5.45471 q^{91} +3.60697 q^{92} -1.05759 q^{93} +6.73365 q^{94} +26.7380 q^{95} -8.79742 q^{96} +1.62836 q^{97} +13.3802 q^{98} -23.0549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36790 −1.67436 −0.837181 0.546926i \(-0.815798\pi\)
−0.837181 + 0.546926i \(0.815798\pi\)
\(3\) −2.62074 −1.51309 −0.756543 0.653943i \(-0.773113\pi\)
−0.756543 + 0.653943i \(0.773113\pi\)
\(4\) 3.60697 1.80349
\(5\) 3.23023 1.44460 0.722301 0.691578i \(-0.243084\pi\)
0.722301 + 0.691578i \(0.243084\pi\)
\(6\) 6.20567 2.53345
\(7\) 1.16162 0.439052 0.219526 0.975607i \(-0.429549\pi\)
0.219526 + 0.975607i \(0.429549\pi\)
\(8\) −3.80516 −1.34533
\(9\) 3.86830 1.28943
\(10\) −7.64888 −2.41879
\(11\) −5.95997 −1.79700 −0.898499 0.438976i \(-0.855341\pi\)
−0.898499 + 0.438976i \(0.855341\pi\)
\(12\) −9.45295 −2.72883
\(13\) −4.69577 −1.30237 −0.651186 0.758918i \(-0.725728\pi\)
−0.651186 + 0.758918i \(0.725728\pi\)
\(14\) −2.75061 −0.735131
\(15\) −8.46560 −2.18581
\(16\) 1.79630 0.449075
\(17\) 0.273086 0.0662330 0.0331165 0.999451i \(-0.489457\pi\)
0.0331165 + 0.999451i \(0.489457\pi\)
\(18\) −9.15976 −2.15898
\(19\) 8.27742 1.89897 0.949485 0.313813i \(-0.101606\pi\)
0.949485 + 0.313813i \(0.101606\pi\)
\(20\) 11.6513 2.60532
\(21\) −3.04431 −0.664323
\(22\) 14.1126 3.00882
\(23\) 1.00000 0.208514 0.104257 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 9.97234 2.03559
\(25\) 5.43438 1.08688
\(26\) 11.1191 2.18064
\(27\) −2.27558 −0.437936
\(28\) 4.18994 0.791823
\(29\) −8.08895 −1.50208 −0.751040 0.660257i \(-0.770448\pi\)
−0.751040 + 0.660257i \(0.770448\pi\)
\(30\) 20.0457 3.65983
\(31\) 0.403546 0.0724790 0.0362395 0.999343i \(-0.488462\pi\)
0.0362395 + 0.999343i \(0.488462\pi\)
\(32\) 3.35684 0.593411
\(33\) 15.6195 2.71901
\(34\) −0.646641 −0.110898
\(35\) 3.75230 0.634255
\(36\) 13.9528 2.32547
\(37\) 4.87945 0.802176 0.401088 0.916040i \(-0.368632\pi\)
0.401088 + 0.916040i \(0.368632\pi\)
\(38\) −19.6001 −3.17956
\(39\) 12.3064 1.97060
\(40\) −12.2915 −1.94346
\(41\) 7.36311 1.14993 0.574963 0.818180i \(-0.305017\pi\)
0.574963 + 0.818180i \(0.305017\pi\)
\(42\) 7.20864 1.11232
\(43\) −1.48896 −0.227064 −0.113532 0.993534i \(-0.536216\pi\)
−0.113532 + 0.993534i \(0.536216\pi\)
\(44\) −21.4974 −3.24086
\(45\) 12.4955 1.86272
\(46\) −2.36790 −0.349128
\(47\) −2.84372 −0.414799 −0.207399 0.978256i \(-0.566500\pi\)
−0.207399 + 0.978256i \(0.566500\pi\)
\(48\) −4.70764 −0.679490
\(49\) −5.65064 −0.807234
\(50\) −12.8681 −1.81982
\(51\) −0.715688 −0.100216
\(52\) −16.9375 −2.34881
\(53\) −9.11543 −1.25210 −0.626050 0.779783i \(-0.715330\pi\)
−0.626050 + 0.779783i \(0.715330\pi\)
\(54\) 5.38836 0.733263
\(55\) −19.2521 −2.59595
\(56\) −4.42015 −0.590667
\(57\) −21.6930 −2.87331
\(58\) 19.1539 2.51503
\(59\) 7.08591 0.922507 0.461254 0.887268i \(-0.347400\pi\)
0.461254 + 0.887268i \(0.347400\pi\)
\(60\) −30.5352 −3.94208
\(61\) 3.67954 0.471116 0.235558 0.971860i \(-0.424308\pi\)
0.235558 + 0.971860i \(0.424308\pi\)
\(62\) −0.955558 −0.121356
\(63\) 4.49350 0.566127
\(64\) −11.5413 −1.44266
\(65\) −15.1684 −1.88141
\(66\) −36.9856 −4.55261
\(67\) 5.34809 0.653374 0.326687 0.945133i \(-0.394068\pi\)
0.326687 + 0.945133i \(0.394068\pi\)
\(68\) 0.985013 0.119450
\(69\) −2.62074 −0.315500
\(70\) −8.88510 −1.06197
\(71\) 1.23645 0.146740 0.0733701 0.997305i \(-0.476625\pi\)
0.0733701 + 0.997305i \(0.476625\pi\)
\(72\) −14.7195 −1.73471
\(73\) −14.3861 −1.68377 −0.841884 0.539658i \(-0.818553\pi\)
−0.841884 + 0.539658i \(0.818553\pi\)
\(74\) −11.5541 −1.34313
\(75\) −14.2421 −1.64454
\(76\) 29.8564 3.42476
\(77\) −6.92323 −0.788975
\(78\) −29.1404 −3.29950
\(79\) 12.2858 1.38226 0.691128 0.722732i \(-0.257114\pi\)
0.691128 + 0.722732i \(0.257114\pi\)
\(80\) 5.80247 0.648735
\(81\) −5.64117 −0.626797
\(82\) −17.4352 −1.92539
\(83\) 4.40796 0.483836 0.241918 0.970297i \(-0.422223\pi\)
0.241918 + 0.970297i \(0.422223\pi\)
\(84\) −10.9807 −1.19810
\(85\) 0.882130 0.0956804
\(86\) 3.52571 0.380187
\(87\) 21.1991 2.27278
\(88\) 22.6786 2.41755
\(89\) 4.11367 0.436048 0.218024 0.975943i \(-0.430039\pi\)
0.218024 + 0.975943i \(0.430039\pi\)
\(90\) −29.5881 −3.11886
\(91\) −5.45471 −0.571809
\(92\) 3.60697 0.376053
\(93\) −1.05759 −0.109667
\(94\) 6.73365 0.694523
\(95\) 26.7380 2.74326
\(96\) −8.79742 −0.897883
\(97\) 1.62836 0.165335 0.0826673 0.996577i \(-0.473656\pi\)
0.0826673 + 0.996577i \(0.473656\pi\)
\(98\) 13.3802 1.35160
\(99\) −23.0549 −2.31711
\(100\) 19.6017 1.96017
\(101\) 0.409125 0.0407095 0.0203547 0.999793i \(-0.493520\pi\)
0.0203547 + 0.999793i \(0.493520\pi\)
\(102\) 1.69468 0.167798
\(103\) 15.9314 1.56977 0.784886 0.619640i \(-0.212721\pi\)
0.784886 + 0.619640i \(0.212721\pi\)
\(104\) 17.8681 1.75211
\(105\) −9.83383 −0.959683
\(106\) 21.5845 2.09647
\(107\) −9.82848 −0.950155 −0.475078 0.879944i \(-0.657580\pi\)
−0.475078 + 0.879944i \(0.657580\pi\)
\(108\) −8.20796 −0.789812
\(109\) −1.25265 −0.119982 −0.0599909 0.998199i \(-0.519107\pi\)
−0.0599909 + 0.998199i \(0.519107\pi\)
\(110\) 45.5870 4.34655
\(111\) −12.7878 −1.21376
\(112\) 2.08662 0.197167
\(113\) −9.36258 −0.880757 −0.440379 0.897812i \(-0.645156\pi\)
−0.440379 + 0.897812i \(0.645156\pi\)
\(114\) 51.3669 4.81095
\(115\) 3.23023 0.301220
\(116\) −29.1766 −2.70898
\(117\) −18.1646 −1.67932
\(118\) −16.7788 −1.54461
\(119\) 0.317222 0.0290797
\(120\) 32.2129 2.94063
\(121\) 24.5212 2.22920
\(122\) −8.71279 −0.788819
\(123\) −19.2968 −1.73994
\(124\) 1.45558 0.130715
\(125\) 1.40316 0.125503
\(126\) −10.6402 −0.947902
\(127\) −15.4924 −1.37472 −0.687362 0.726315i \(-0.741231\pi\)
−0.687362 + 0.726315i \(0.741231\pi\)
\(128\) 20.6150 1.82212
\(129\) 3.90217 0.343567
\(130\) 35.9174 3.15016
\(131\) −9.82582 −0.858486 −0.429243 0.903189i \(-0.641220\pi\)
−0.429243 + 0.903189i \(0.641220\pi\)
\(132\) 56.3392 4.90370
\(133\) 9.61523 0.833746
\(134\) −12.6638 −1.09398
\(135\) −7.35066 −0.632644
\(136\) −1.03913 −0.0891050
\(137\) −19.1051 −1.63226 −0.816129 0.577870i \(-0.803884\pi\)
−0.816129 + 0.577870i \(0.803884\pi\)
\(138\) 6.20567 0.528262
\(139\) −8.54556 −0.724825 −0.362413 0.932018i \(-0.618047\pi\)
−0.362413 + 0.932018i \(0.618047\pi\)
\(140\) 13.5345 1.14387
\(141\) 7.45266 0.627627
\(142\) −2.92781 −0.245696
\(143\) 27.9866 2.34036
\(144\) 6.94863 0.579052
\(145\) −26.1292 −2.16991
\(146\) 34.0650 2.81924
\(147\) 14.8089 1.22141
\(148\) 17.6000 1.44671
\(149\) 11.5712 0.947952 0.473976 0.880538i \(-0.342818\pi\)
0.473976 + 0.880538i \(0.342818\pi\)
\(150\) 33.7240 2.75355
\(151\) 11.8956 0.968054 0.484027 0.875053i \(-0.339174\pi\)
0.484027 + 0.875053i \(0.339174\pi\)
\(152\) −31.4969 −2.55473
\(153\) 1.05638 0.0854030
\(154\) 16.3935 1.32103
\(155\) 1.30355 0.104703
\(156\) 44.3889 3.55395
\(157\) −24.7242 −1.97321 −0.986604 0.163131i \(-0.947841\pi\)
−0.986604 + 0.163131i \(0.947841\pi\)
\(158\) −29.0915 −2.31440
\(159\) 23.8892 1.89454
\(160\) 10.8434 0.857243
\(161\) 1.16162 0.0915486
\(162\) 13.3578 1.04948
\(163\) −1.11031 −0.0869662 −0.0434831 0.999054i \(-0.513845\pi\)
−0.0434831 + 0.999054i \(0.513845\pi\)
\(164\) 26.5585 2.07387
\(165\) 50.4547 3.92789
\(166\) −10.4376 −0.810117
\(167\) −0.423596 −0.0327788 −0.0163894 0.999866i \(-0.505217\pi\)
−0.0163894 + 0.999866i \(0.505217\pi\)
\(168\) 11.5841 0.893731
\(169\) 9.05025 0.696173
\(170\) −2.08880 −0.160204
\(171\) 32.0195 2.44859
\(172\) −5.37062 −0.409506
\(173\) −1.60089 −0.121713 −0.0608565 0.998147i \(-0.519383\pi\)
−0.0608565 + 0.998147i \(0.519383\pi\)
\(174\) −50.1974 −3.80545
\(175\) 6.31270 0.477195
\(176\) −10.7059 −0.806987
\(177\) −18.5704 −1.39583
\(178\) −9.74077 −0.730101
\(179\) 11.1500 0.833388 0.416694 0.909047i \(-0.363189\pi\)
0.416694 + 0.909047i \(0.363189\pi\)
\(180\) 45.0709 3.35938
\(181\) −2.23764 −0.166323 −0.0831613 0.996536i \(-0.526502\pi\)
−0.0831613 + 0.996536i \(0.526502\pi\)
\(182\) 12.9162 0.957414
\(183\) −9.64312 −0.712840
\(184\) −3.80515 −0.280520
\(185\) 15.7617 1.15883
\(186\) 2.50427 0.183622
\(187\) −1.62758 −0.119021
\(188\) −10.2572 −0.748084
\(189\) −2.64337 −0.192277
\(190\) −63.3129 −4.59320
\(191\) 10.0081 0.724158 0.362079 0.932147i \(-0.382067\pi\)
0.362079 + 0.932147i \(0.382067\pi\)
\(192\) 30.2467 2.18287
\(193\) 16.8540 1.21318 0.606589 0.795016i \(-0.292537\pi\)
0.606589 + 0.795016i \(0.292537\pi\)
\(194\) −3.85580 −0.276830
\(195\) 39.7525 2.84674
\(196\) −20.3817 −1.45583
\(197\) −11.3691 −0.810012 −0.405006 0.914314i \(-0.632731\pi\)
−0.405006 + 0.914314i \(0.632731\pi\)
\(198\) 54.5918 3.87967
\(199\) 8.71490 0.617783 0.308892 0.951097i \(-0.400042\pi\)
0.308892 + 0.951097i \(0.400042\pi\)
\(200\) −20.6787 −1.46220
\(201\) −14.0160 −0.988611
\(202\) −0.968770 −0.0681624
\(203\) −9.39630 −0.659491
\(204\) −2.58147 −0.180739
\(205\) 23.7846 1.66119
\(206\) −37.7242 −2.62837
\(207\) 3.86830 0.268865
\(208\) −8.43502 −0.584863
\(209\) −49.3331 −3.41244
\(210\) 23.2856 1.60686
\(211\) 13.4361 0.924982 0.462491 0.886624i \(-0.346956\pi\)
0.462491 + 0.886624i \(0.346956\pi\)
\(212\) −32.8791 −2.25815
\(213\) −3.24043 −0.222031
\(214\) 23.2729 1.59090
\(215\) −4.80967 −0.328017
\(216\) 8.65895 0.589167
\(217\) 0.468768 0.0318220
\(218\) 2.96615 0.200893
\(219\) 37.7023 2.54769
\(220\) −69.4416 −4.68175
\(221\) −1.28235 −0.0862601
\(222\) 30.2802 2.03228
\(223\) −22.3198 −1.49464 −0.747321 0.664463i \(-0.768660\pi\)
−0.747321 + 0.664463i \(0.768660\pi\)
\(224\) 3.89938 0.260538
\(225\) 21.0218 1.40145
\(226\) 22.1697 1.47471
\(227\) −22.2610 −1.47752 −0.738758 0.673971i \(-0.764587\pi\)
−0.738758 + 0.673971i \(0.764587\pi\)
\(228\) −78.2460 −5.18197
\(229\) 5.15383 0.340574 0.170287 0.985394i \(-0.445530\pi\)
0.170287 + 0.985394i \(0.445530\pi\)
\(230\) −7.64887 −0.504352
\(231\) 18.1440 1.19379
\(232\) 30.7797 2.02079
\(233\) 0.303341 0.0198725 0.00993627 0.999951i \(-0.496837\pi\)
0.00993627 + 0.999951i \(0.496837\pi\)
\(234\) 43.0121 2.81179
\(235\) −9.18586 −0.599220
\(236\) 25.5587 1.66373
\(237\) −32.1978 −2.09147
\(238\) −0.751152 −0.0486900
\(239\) 6.94556 0.449271 0.224636 0.974443i \(-0.427881\pi\)
0.224636 + 0.974443i \(0.427881\pi\)
\(240\) −15.2068 −0.981593
\(241\) −13.1719 −0.848477 −0.424238 0.905551i \(-0.639458\pi\)
−0.424238 + 0.905551i \(0.639458\pi\)
\(242\) −58.0639 −3.73249
\(243\) 21.6108 1.38633
\(244\) 13.2720 0.849652
\(245\) −18.2529 −1.16613
\(246\) 45.6931 2.91328
\(247\) −38.8688 −2.47317
\(248\) −1.53555 −0.0975078
\(249\) −11.5521 −0.732086
\(250\) −3.32255 −0.210137
\(251\) 10.1886 0.643099 0.321550 0.946893i \(-0.395796\pi\)
0.321550 + 0.946893i \(0.395796\pi\)
\(252\) 16.2079 1.02100
\(253\) −5.95996 −0.374700
\(254\) 36.6844 2.30179
\(255\) −2.31184 −0.144773
\(256\) −25.7317 −1.60823
\(257\) −5.09460 −0.317792 −0.158896 0.987295i \(-0.550794\pi\)
−0.158896 + 0.987295i \(0.550794\pi\)
\(258\) −9.23997 −0.575256
\(259\) 5.66807 0.352197
\(260\) −54.7120 −3.39310
\(261\) −31.2905 −1.93683
\(262\) 23.2666 1.43742
\(263\) 8.99407 0.554598 0.277299 0.960784i \(-0.410561\pi\)
0.277299 + 0.960784i \(0.410561\pi\)
\(264\) −59.4348 −3.65796
\(265\) −29.4449 −1.80879
\(266\) −22.7679 −1.39599
\(267\) −10.7809 −0.659778
\(268\) 19.2904 1.17835
\(269\) −18.9194 −1.15353 −0.576767 0.816908i \(-0.695686\pi\)
−0.576767 + 0.816908i \(0.695686\pi\)
\(270\) 17.4057 1.05927
\(271\) −10.3231 −0.627084 −0.313542 0.949574i \(-0.601516\pi\)
−0.313542 + 0.949574i \(0.601516\pi\)
\(272\) 0.490544 0.0297436
\(273\) 14.2954 0.865196
\(274\) 45.2390 2.73299
\(275\) −32.3887 −1.95311
\(276\) −9.45295 −0.569000
\(277\) 23.3823 1.40491 0.702454 0.711730i \(-0.252088\pi\)
0.702454 + 0.711730i \(0.252088\pi\)
\(278\) 20.2351 1.21362
\(279\) 1.56104 0.0934567
\(280\) −14.2781 −0.853280
\(281\) −9.32947 −0.556550 −0.278275 0.960501i \(-0.589763\pi\)
−0.278275 + 0.960501i \(0.589763\pi\)
\(282\) −17.6472 −1.05087
\(283\) 9.07449 0.539422 0.269711 0.962941i \(-0.413072\pi\)
0.269711 + 0.962941i \(0.413072\pi\)
\(284\) 4.45986 0.264644
\(285\) −70.0733 −4.15079
\(286\) −66.2697 −3.91861
\(287\) 8.55315 0.504877
\(288\) 12.9853 0.765164
\(289\) −16.9254 −0.995613
\(290\) 61.8714 3.63321
\(291\) −4.26751 −0.250166
\(292\) −51.8903 −3.03665
\(293\) −0.732174 −0.0427740 −0.0213870 0.999771i \(-0.506808\pi\)
−0.0213870 + 0.999771i \(0.506808\pi\)
\(294\) −35.0660 −2.04509
\(295\) 22.8891 1.33266
\(296\) −18.5670 −1.07919
\(297\) 13.5624 0.786970
\(298\) −27.3996 −1.58721
\(299\) −4.69577 −0.271563
\(300\) −51.3710 −2.96590
\(301\) −1.72960 −0.0996927
\(302\) −28.1677 −1.62087
\(303\) −1.07221 −0.0615970
\(304\) 14.8687 0.852780
\(305\) 11.8857 0.680576
\(306\) −2.50140 −0.142996
\(307\) −8.27546 −0.472306 −0.236153 0.971716i \(-0.575887\pi\)
−0.236153 + 0.971716i \(0.575887\pi\)
\(308\) −24.9719 −1.42290
\(309\) −41.7522 −2.37520
\(310\) −3.08667 −0.175311
\(311\) −13.1401 −0.745106 −0.372553 0.928011i \(-0.621518\pi\)
−0.372553 + 0.928011i \(0.621518\pi\)
\(312\) −46.8278 −2.65110
\(313\) 12.0949 0.683644 0.341822 0.939765i \(-0.388956\pi\)
0.341822 + 0.939765i \(0.388956\pi\)
\(314\) 58.5446 3.30386
\(315\) 14.5150 0.817829
\(316\) 44.3144 2.49288
\(317\) −8.29138 −0.465690 −0.232845 0.972514i \(-0.574803\pi\)
−0.232845 + 0.972514i \(0.574803\pi\)
\(318\) −56.5674 −3.17214
\(319\) 48.2099 2.69923
\(320\) −37.2810 −2.08407
\(321\) 25.7579 1.43767
\(322\) −2.75061 −0.153285
\(323\) 2.26045 0.125775
\(324\) −20.3475 −1.13042
\(325\) −25.5186 −1.41552
\(326\) 2.62911 0.145613
\(327\) 3.28286 0.181543
\(328\) −28.0178 −1.54702
\(329\) −3.30332 −0.182118
\(330\) −119.472 −6.57671
\(331\) −4.88230 −0.268356 −0.134178 0.990957i \(-0.542839\pi\)
−0.134178 + 0.990957i \(0.542839\pi\)
\(332\) 15.8994 0.872592
\(333\) 18.8751 1.03435
\(334\) 1.00303 0.0548836
\(335\) 17.2756 0.943865
\(336\) −5.46850 −0.298331
\(337\) 16.9669 0.924244 0.462122 0.886816i \(-0.347088\pi\)
0.462122 + 0.886816i \(0.347088\pi\)
\(338\) −21.4301 −1.16565
\(339\) 24.5369 1.33266
\(340\) 3.18182 0.172558
\(341\) −2.40512 −0.130245
\(342\) −75.8191 −4.09983
\(343\) −14.6953 −0.793469
\(344\) 5.66571 0.305475
\(345\) −8.46560 −0.455773
\(346\) 3.79074 0.203792
\(347\) −32.7364 −1.75738 −0.878690 0.477392i \(-0.841582\pi\)
−0.878690 + 0.477392i \(0.841582\pi\)
\(348\) 76.4644 4.09892
\(349\) −19.7796 −1.05878 −0.529389 0.848379i \(-0.677579\pi\)
−0.529389 + 0.848379i \(0.677579\pi\)
\(350\) −14.9479 −0.798997
\(351\) 10.6856 0.570356
\(352\) −20.0067 −1.06636
\(353\) −20.9130 −1.11309 −0.556543 0.830819i \(-0.687873\pi\)
−0.556543 + 0.830819i \(0.687873\pi\)
\(354\) 43.9728 2.33713
\(355\) 3.99403 0.211981
\(356\) 14.8379 0.786406
\(357\) −0.831358 −0.0440002
\(358\) −26.4021 −1.39539
\(359\) 1.15416 0.0609142 0.0304571 0.999536i \(-0.490304\pi\)
0.0304571 + 0.999536i \(0.490304\pi\)
\(360\) −47.5473 −2.50596
\(361\) 49.5156 2.60609
\(362\) 5.29852 0.278484
\(363\) −64.2638 −3.37297
\(364\) −19.6750 −1.03125
\(365\) −46.4705 −2.43238
\(366\) 22.8340 1.19355
\(367\) −13.3643 −0.697610 −0.348805 0.937195i \(-0.613412\pi\)
−0.348805 + 0.937195i \(0.613412\pi\)
\(368\) 1.79630 0.0936387
\(369\) 28.4827 1.48275
\(370\) −37.3223 −1.94029
\(371\) −10.5887 −0.549737
\(372\) −3.81470 −0.197783
\(373\) 6.30895 0.326665 0.163332 0.986571i \(-0.447776\pi\)
0.163332 + 0.986571i \(0.447776\pi\)
\(374\) 3.85396 0.199283
\(375\) −3.67732 −0.189896
\(376\) 10.8208 0.558040
\(377\) 37.9838 1.95627
\(378\) 6.25924 0.321941
\(379\) −5.67432 −0.291470 −0.145735 0.989324i \(-0.546555\pi\)
−0.145735 + 0.989324i \(0.546555\pi\)
\(380\) 96.4431 4.94742
\(381\) 40.6015 2.08008
\(382\) −23.6981 −1.21250
\(383\) −34.4123 −1.75839 −0.879193 0.476466i \(-0.841917\pi\)
−0.879193 + 0.476466i \(0.841917\pi\)
\(384\) −54.0265 −2.75703
\(385\) −22.3636 −1.13975
\(386\) −39.9087 −2.03130
\(387\) −5.75973 −0.292783
\(388\) 5.87344 0.298179
\(389\) 24.7281 1.25376 0.626881 0.779115i \(-0.284331\pi\)
0.626881 + 0.779115i \(0.284331\pi\)
\(390\) −94.1302 −4.76647
\(391\) 0.273086 0.0138105
\(392\) 21.5015 1.08599
\(393\) 25.7509 1.29896
\(394\) 26.9209 1.35625
\(395\) 39.6858 1.99681
\(396\) −83.1584 −4.17887
\(397\) 0.200175 0.0100465 0.00502325 0.999987i \(-0.498401\pi\)
0.00502325 + 0.999987i \(0.498401\pi\)
\(398\) −20.6361 −1.03439
\(399\) −25.1990 −1.26153
\(400\) 9.76179 0.488090
\(401\) 20.6837 1.03290 0.516448 0.856319i \(-0.327254\pi\)
0.516448 + 0.856319i \(0.327254\pi\)
\(402\) 33.1885 1.65529
\(403\) −1.89496 −0.0943946
\(404\) 1.47570 0.0734190
\(405\) −18.2223 −0.905472
\(406\) 22.2495 1.10423
\(407\) −29.0813 −1.44151
\(408\) 2.72330 0.134824
\(409\) 20.0039 0.989130 0.494565 0.869141i \(-0.335327\pi\)
0.494565 + 0.869141i \(0.335327\pi\)
\(410\) −56.3195 −2.78142
\(411\) 50.0696 2.46975
\(412\) 57.4643 2.83106
\(413\) 8.23115 0.405028
\(414\) −9.15975 −0.450177
\(415\) 14.2387 0.698951
\(416\) −15.7630 −0.772842
\(417\) 22.3957 1.09672
\(418\) 116.816 5.71366
\(419\) 23.3874 1.14255 0.571274 0.820759i \(-0.306449\pi\)
0.571274 + 0.820759i \(0.306449\pi\)
\(420\) −35.4703 −1.73078
\(421\) −29.1388 −1.42014 −0.710070 0.704131i \(-0.751337\pi\)
−0.710070 + 0.704131i \(0.751337\pi\)
\(422\) −31.8155 −1.54875
\(423\) −11.0003 −0.534855
\(424\) 34.6856 1.68448
\(425\) 1.48405 0.0719872
\(426\) 7.67303 0.371759
\(427\) 4.27423 0.206844
\(428\) −35.4511 −1.71359
\(429\) −73.3458 −3.54117
\(430\) 11.3888 0.549219
\(431\) −26.1859 −1.26133 −0.630665 0.776055i \(-0.717218\pi\)
−0.630665 + 0.776055i \(0.717218\pi\)
\(432\) −4.08763 −0.196666
\(433\) 15.5373 0.746675 0.373337 0.927696i \(-0.378213\pi\)
0.373337 + 0.927696i \(0.378213\pi\)
\(434\) −1.11000 −0.0532816
\(435\) 68.4778 3.28326
\(436\) −4.51826 −0.216385
\(437\) 8.27741 0.395962
\(438\) −89.2755 −4.26575
\(439\) 18.6711 0.891122 0.445561 0.895252i \(-0.353004\pi\)
0.445561 + 0.895252i \(0.353004\pi\)
\(440\) 73.2571 3.49239
\(441\) −21.8583 −1.04087
\(442\) 3.03648 0.144431
\(443\) 37.3852 1.77622 0.888112 0.459627i \(-0.152017\pi\)
0.888112 + 0.459627i \(0.152017\pi\)
\(444\) −46.1251 −2.18900
\(445\) 13.2881 0.629916
\(446\) 52.8511 2.50257
\(447\) −30.3252 −1.43433
\(448\) −13.4066 −0.633402
\(449\) 23.9745 1.13143 0.565714 0.824602i \(-0.308601\pi\)
0.565714 + 0.824602i \(0.308601\pi\)
\(450\) −49.7776 −2.34654
\(451\) −43.8839 −2.06641
\(452\) −33.7705 −1.58843
\(453\) −31.1754 −1.46475
\(454\) 52.7120 2.47390
\(455\) −17.6200 −0.826036
\(456\) 82.5452 3.86553
\(457\) 29.2875 1.37001 0.685006 0.728537i \(-0.259800\pi\)
0.685006 + 0.728537i \(0.259800\pi\)
\(458\) −12.2038 −0.570245
\(459\) −0.621429 −0.0290058
\(460\) 11.6513 0.543247
\(461\) −23.4979 −1.09440 −0.547202 0.837000i \(-0.684307\pi\)
−0.547202 + 0.837000i \(0.684307\pi\)
\(462\) −42.9633 −1.99883
\(463\) −0.980451 −0.0455654 −0.0227827 0.999740i \(-0.507253\pi\)
−0.0227827 + 0.999740i \(0.507253\pi\)
\(464\) −14.5302 −0.674547
\(465\) −3.41626 −0.158425
\(466\) −0.718283 −0.0332738
\(467\) −16.5640 −0.766492 −0.383246 0.923646i \(-0.625194\pi\)
−0.383246 + 0.923646i \(0.625194\pi\)
\(468\) −65.5193 −3.02863
\(469\) 6.21246 0.286865
\(470\) 21.7512 1.00331
\(471\) 64.7959 2.98564
\(472\) −26.9630 −1.24107
\(473\) 8.87413 0.408033
\(474\) 76.2414 3.50188
\(475\) 44.9827 2.06395
\(476\) 1.14421 0.0524449
\(477\) −35.2612 −1.61450
\(478\) −16.4464 −0.752242
\(479\) −7.45352 −0.340560 −0.170280 0.985396i \(-0.554467\pi\)
−0.170280 + 0.985396i \(0.554467\pi\)
\(480\) −28.4177 −1.29708
\(481\) −22.9128 −1.04473
\(482\) 31.1898 1.42066
\(483\) −3.04431 −0.138521
\(484\) 88.4473 4.02033
\(485\) 5.25997 0.238843
\(486\) −51.1723 −2.32122
\(487\) 30.8128 1.39626 0.698130 0.715971i \(-0.254016\pi\)
0.698130 + 0.715971i \(0.254016\pi\)
\(488\) −14.0012 −0.633805
\(489\) 2.90984 0.131587
\(490\) 43.2210 1.95253
\(491\) −19.7841 −0.892843 −0.446421 0.894823i \(-0.647302\pi\)
−0.446421 + 0.894823i \(0.647302\pi\)
\(492\) −69.6031 −3.13795
\(493\) −2.20898 −0.0994873
\(494\) 92.0377 4.14097
\(495\) −74.4727 −3.34730
\(496\) 0.724890 0.0325485
\(497\) 1.43629 0.0644265
\(498\) 27.3543 1.22578
\(499\) −34.9866 −1.56622 −0.783108 0.621885i \(-0.786367\pi\)
−0.783108 + 0.621885i \(0.786367\pi\)
\(500\) 5.06116 0.226342
\(501\) 1.11014 0.0495972
\(502\) −24.1256 −1.07678
\(503\) −14.9569 −0.666896 −0.333448 0.942769i \(-0.608212\pi\)
−0.333448 + 0.942769i \(0.608212\pi\)
\(504\) −17.0985 −0.761626
\(505\) 1.32157 0.0588090
\(506\) 14.1126 0.627383
\(507\) −23.7184 −1.05337
\(508\) −55.8805 −2.47930
\(509\) −35.2583 −1.56280 −0.781399 0.624031i \(-0.785494\pi\)
−0.781399 + 0.624031i \(0.785494\pi\)
\(510\) 5.47421 0.242402
\(511\) −16.7112 −0.739261
\(512\) 19.7003 0.870639
\(513\) −18.8359 −0.831627
\(514\) 12.0635 0.532099
\(515\) 51.4622 2.26770
\(516\) 14.0750 0.619619
\(517\) 16.9485 0.745393
\(518\) −13.4214 −0.589704
\(519\) 4.19551 0.184162
\(520\) 57.7182 2.53111
\(521\) −25.2947 −1.10818 −0.554091 0.832456i \(-0.686934\pi\)
−0.554091 + 0.832456i \(0.686934\pi\)
\(522\) 74.0928 3.24295
\(523\) −7.08519 −0.309814 −0.154907 0.987929i \(-0.549508\pi\)
−0.154907 + 0.987929i \(0.549508\pi\)
\(524\) −35.4414 −1.54827
\(525\) −16.5440 −0.722038
\(526\) −21.2971 −0.928598
\(527\) 0.110203 0.00480050
\(528\) 28.0574 1.22104
\(529\) −22.0000 −0.956522
\(530\) 69.7228 3.02857
\(531\) 27.4104 1.18951
\(532\) 34.6818 1.50365
\(533\) −34.5755 −1.49763
\(534\) 25.5281 1.10471
\(535\) −31.7483 −1.37260
\(536\) −20.3503 −0.879000
\(537\) −29.2212 −1.26099
\(538\) 44.7993 1.93143
\(539\) 33.6776 1.45060
\(540\) −26.5136 −1.14096
\(541\) 42.4556 1.82531 0.912655 0.408731i \(-0.134029\pi\)
0.912655 + 0.408731i \(0.134029\pi\)
\(542\) 24.4441 1.04996
\(543\) 5.86428 0.251660
\(544\) 0.916706 0.0393034
\(545\) −4.04633 −0.173326
\(546\) −33.8501 −1.44865
\(547\) −26.1683 −1.11887 −0.559437 0.828873i \(-0.688983\pi\)
−0.559437 + 0.828873i \(0.688983\pi\)
\(548\) −68.9115 −2.94375
\(549\) 14.2335 0.607473
\(550\) 76.6935 3.27022
\(551\) −66.9556 −2.85240
\(552\) 9.97233 0.424451
\(553\) 14.2714 0.606882
\(554\) −55.3671 −2.35232
\(555\) −41.3075 −1.75340
\(556\) −30.8236 −1.30721
\(557\) −32.1710 −1.36313 −0.681565 0.731757i \(-0.738700\pi\)
−0.681565 + 0.731757i \(0.738700\pi\)
\(558\) −3.69638 −0.156480
\(559\) 6.99180 0.295721
\(560\) 6.74027 0.284828
\(561\) 4.26548 0.180089
\(562\) 22.0913 0.931865
\(563\) 1.40481 0.0592055 0.0296027 0.999562i \(-0.490576\pi\)
0.0296027 + 0.999562i \(0.490576\pi\)
\(564\) 26.8815 1.13192
\(565\) −30.2433 −1.27234
\(566\) −21.4875 −0.903188
\(567\) −6.55291 −0.275196
\(568\) −4.70490 −0.197413
\(569\) −18.5474 −0.777546 −0.388773 0.921334i \(-0.627101\pi\)
−0.388773 + 0.921334i \(0.627101\pi\)
\(570\) 165.927 6.94992
\(571\) −20.3961 −0.853551 −0.426775 0.904358i \(-0.640350\pi\)
−0.426775 + 0.904358i \(0.640350\pi\)
\(572\) 100.947 4.22080
\(573\) −26.2286 −1.09571
\(574\) −20.2530 −0.845346
\(575\) 5.43438 0.226629
\(576\) −44.6451 −1.86021
\(577\) −22.7231 −0.945974 −0.472987 0.881069i \(-0.656824\pi\)
−0.472987 + 0.881069i \(0.656824\pi\)
\(578\) 40.0778 1.66702
\(579\) −44.1700 −1.83564
\(580\) −94.2472 −3.91340
\(581\) 5.12038 0.212429
\(582\) 10.1051 0.418868
\(583\) 54.3277 2.25002
\(584\) 54.7414 2.26522
\(585\) −58.6759 −2.42595
\(586\) 1.73372 0.0716192
\(587\) −45.5761 −1.88113 −0.940564 0.339615i \(-0.889703\pi\)
−0.940564 + 0.339615i \(0.889703\pi\)
\(588\) 53.4152 2.20280
\(589\) 3.34032 0.137635
\(590\) −54.1993 −2.23135
\(591\) 29.7954 1.22562
\(592\) 8.76495 0.360237
\(593\) −22.0569 −0.905767 −0.452884 0.891570i \(-0.649605\pi\)
−0.452884 + 0.891570i \(0.649605\pi\)
\(594\) −32.1145 −1.31767
\(595\) 1.02470 0.0420086
\(596\) 41.7371 1.70962
\(597\) −22.8395 −0.934760
\(598\) 11.1191 0.454695
\(599\) −6.86560 −0.280521 −0.140260 0.990115i \(-0.544794\pi\)
−0.140260 + 0.990115i \(0.544794\pi\)
\(600\) 54.1935 2.21244
\(601\) 42.3508 1.72752 0.863762 0.503900i \(-0.168102\pi\)
0.863762 + 0.503900i \(0.168102\pi\)
\(602\) 4.09554 0.166922
\(603\) 20.6880 0.842481
\(604\) 42.9073 1.74587
\(605\) 79.2091 3.22031
\(606\) 2.53890 0.103136
\(607\) 36.4480 1.47938 0.739689 0.672949i \(-0.234972\pi\)
0.739689 + 0.672949i \(0.234972\pi\)
\(608\) 27.7860 1.12687
\(609\) 24.6253 0.997867
\(610\) −28.1443 −1.13953
\(611\) 13.3534 0.540223
\(612\) 3.81032 0.154023
\(613\) −33.1476 −1.33882 −0.669409 0.742895i \(-0.733452\pi\)
−0.669409 + 0.742895i \(0.733452\pi\)
\(614\) 19.5955 0.790810
\(615\) −62.3332 −2.51352
\(616\) 26.3439 1.06143
\(617\) −15.7496 −0.634057 −0.317028 0.948416i \(-0.602685\pi\)
−0.317028 + 0.948416i \(0.602685\pi\)
\(618\) 98.8653 3.97695
\(619\) 23.6842 0.951946 0.475973 0.879460i \(-0.342096\pi\)
0.475973 + 0.879460i \(0.342096\pi\)
\(620\) 4.70185 0.188831
\(621\) −2.27558 −0.0913160
\(622\) 31.1145 1.24758
\(623\) 4.77852 0.191447
\(624\) 22.1060 0.884949
\(625\) −22.6394 −0.905576
\(626\) −28.6396 −1.14467
\(627\) 129.289 5.16332
\(628\) −89.1796 −3.55865
\(629\) 1.33251 0.0531305
\(630\) −34.3702 −1.36934
\(631\) −21.7893 −0.867418 −0.433709 0.901053i \(-0.642795\pi\)
−0.433709 + 0.901053i \(0.642795\pi\)
\(632\) −46.7492 −1.85959
\(633\) −35.2127 −1.39958
\(634\) 19.6332 0.779733
\(635\) −50.0439 −1.98593
\(636\) 86.1677 3.41677
\(637\) 26.5341 1.05132
\(638\) −114.156 −4.51949
\(639\) 4.78297 0.189211
\(640\) 66.5911 2.63224
\(641\) −31.9045 −1.26015 −0.630075 0.776534i \(-0.716976\pi\)
−0.630075 + 0.776534i \(0.716976\pi\)
\(642\) −60.9923 −2.40717
\(643\) 7.18518 0.283356 0.141678 0.989913i \(-0.454750\pi\)
0.141678 + 0.989913i \(0.454750\pi\)
\(644\) 4.18993 0.165107
\(645\) 12.6049 0.496318
\(646\) −5.35252 −0.210592
\(647\) −1.64595 −0.0647088 −0.0323544 0.999476i \(-0.510301\pi\)
−0.0323544 + 0.999476i \(0.510301\pi\)
\(648\) 21.4655 0.843246
\(649\) −42.2318 −1.65774
\(650\) 60.4256 2.37009
\(651\) −1.22852 −0.0481495
\(652\) −4.00486 −0.156842
\(653\) −6.79202 −0.265792 −0.132896 0.991130i \(-0.542428\pi\)
−0.132896 + 0.991130i \(0.542428\pi\)
\(654\) −7.77351 −0.303968
\(655\) −31.7396 −1.24017
\(656\) 13.2264 0.516403
\(657\) −55.6498 −2.17111
\(658\) 7.82196 0.304932
\(659\) −31.3243 −1.22022 −0.610111 0.792316i \(-0.708875\pi\)
−0.610111 + 0.792316i \(0.708875\pi\)
\(660\) 181.989 7.08390
\(661\) −35.3664 −1.37559 −0.687796 0.725904i \(-0.741422\pi\)
−0.687796 + 0.725904i \(0.741422\pi\)
\(662\) 11.5608 0.449324
\(663\) 3.36071 0.130519
\(664\) −16.7730 −0.650917
\(665\) 31.0594 1.20443
\(666\) −44.6945 −1.73188
\(667\) −8.08895 −0.313205
\(668\) −1.52790 −0.0591162
\(669\) 58.4944 2.26152
\(670\) −40.9069 −1.58037
\(671\) −21.9299 −0.846595
\(672\) −10.2193 −0.394217
\(673\) −2.89140 −0.111455 −0.0557276 0.998446i \(-0.517748\pi\)
−0.0557276 + 0.998446i \(0.517748\pi\)
\(674\) −40.1759 −1.54752
\(675\) −12.3664 −0.475983
\(676\) 32.6440 1.25554
\(677\) 44.9906 1.72913 0.864565 0.502522i \(-0.167594\pi\)
0.864565 + 0.502522i \(0.167594\pi\)
\(678\) −58.1011 −2.23136
\(679\) 1.89154 0.0725905
\(680\) −3.35664 −0.128721
\(681\) 58.3404 2.23561
\(682\) 5.69509 0.218076
\(683\) −15.4299 −0.590409 −0.295204 0.955434i \(-0.595388\pi\)
−0.295204 + 0.955434i \(0.595388\pi\)
\(684\) 115.493 4.41600
\(685\) −61.7138 −2.35796
\(686\) 34.7969 1.32855
\(687\) −13.5069 −0.515319
\(688\) −2.67461 −0.101969
\(689\) 42.8040 1.63070
\(690\) 20.0457 0.763128
\(691\) −40.4436 −1.53855 −0.769274 0.638920i \(-0.779382\pi\)
−0.769274 + 0.638920i \(0.779382\pi\)
\(692\) −5.77435 −0.219508
\(693\) −26.7811 −1.01733
\(694\) 77.5166 2.94249
\(695\) −27.6041 −1.04708
\(696\) −80.6657 −3.05763
\(697\) 2.01076 0.0761630
\(698\) 46.8362 1.77278
\(699\) −0.794980 −0.0300689
\(700\) 22.7697 0.860615
\(701\) −46.0718 −1.74011 −0.870055 0.492955i \(-0.835917\pi\)
−0.870055 + 0.492955i \(0.835917\pi\)
\(702\) −25.3025 −0.954982
\(703\) 40.3892 1.52331
\(704\) 68.7856 2.59246
\(705\) 24.0738 0.906671
\(706\) 49.5200 1.86371
\(707\) 0.475249 0.0178736
\(708\) −66.9828 −2.51737
\(709\) −52.1758 −1.95950 −0.979752 0.200214i \(-0.935836\pi\)
−0.979752 + 0.200214i \(0.935836\pi\)
\(710\) −9.45748 −0.354933
\(711\) 47.5250 1.78233
\(712\) −15.6531 −0.586626
\(713\) 0.403546 0.0151129
\(714\) 1.96858 0.0736722
\(715\) 90.4032 3.38089
\(716\) 40.2176 1.50300
\(717\) −18.2025 −0.679786
\(718\) −2.73294 −0.101992
\(719\) −34.8949 −1.30136 −0.650680 0.759352i \(-0.725516\pi\)
−0.650680 + 0.759352i \(0.725516\pi\)
\(720\) 22.4457 0.836500
\(721\) 18.5063 0.689211
\(722\) −117.248 −4.36353
\(723\) 34.5202 1.28382
\(724\) −8.07111 −0.299960
\(725\) −43.9585 −1.63258
\(726\) 152.170 5.64758
\(727\) 43.8113 1.62487 0.812436 0.583051i \(-0.198141\pi\)
0.812436 + 0.583051i \(0.198141\pi\)
\(728\) 20.7560 0.769269
\(729\) −39.7129 −1.47085
\(730\) 110.038 4.07268
\(731\) −0.406613 −0.0150391
\(732\) −34.7825 −1.28560
\(733\) −40.3876 −1.49175 −0.745874 0.666087i \(-0.767968\pi\)
−0.745874 + 0.666087i \(0.767968\pi\)
\(734\) 31.6454 1.16805
\(735\) 47.8360 1.76446
\(736\) 3.35684 0.123735
\(737\) −31.8745 −1.17411
\(738\) −67.4443 −2.48266
\(739\) 11.0165 0.405250 0.202625 0.979256i \(-0.435053\pi\)
0.202625 + 0.979256i \(0.435053\pi\)
\(740\) 56.8521 2.08993
\(741\) 101.865 3.74211
\(742\) 25.0730 0.920458
\(743\) −33.8313 −1.24115 −0.620575 0.784147i \(-0.713101\pi\)
−0.620575 + 0.784147i \(0.713101\pi\)
\(744\) 4.02430 0.147538
\(745\) 37.3777 1.36941
\(746\) −14.9390 −0.546955
\(747\) 17.0513 0.623874
\(748\) −5.87064 −0.214652
\(749\) −11.4170 −0.417167
\(750\) 8.70755 0.317955
\(751\) 11.6347 0.424558 0.212279 0.977209i \(-0.431912\pi\)
0.212279 + 0.977209i \(0.431912\pi\)
\(752\) −5.10817 −0.186276
\(753\) −26.7017 −0.973065
\(754\) −89.9421 −3.27550
\(755\) 38.4257 1.39845
\(756\) −9.53455 −0.346768
\(757\) 19.0459 0.692236 0.346118 0.938191i \(-0.387500\pi\)
0.346118 + 0.938191i \(0.387500\pi\)
\(758\) 13.4363 0.488027
\(759\) 15.6195 0.566953
\(760\) −101.742 −3.69057
\(761\) 32.4268 1.17547 0.587736 0.809053i \(-0.300019\pi\)
0.587736 + 0.809053i \(0.300019\pi\)
\(762\) −96.1405 −3.48280
\(763\) −1.45510 −0.0526782
\(764\) 36.0988 1.30601
\(765\) 3.41234 0.123373
\(766\) 81.4850 2.94417
\(767\) −33.2738 −1.20145
\(768\) 67.4362 2.43340
\(769\) 32.9396 1.18783 0.593917 0.804526i \(-0.297581\pi\)
0.593917 + 0.804526i \(0.297581\pi\)
\(770\) 52.9549 1.90836
\(771\) 13.3516 0.480847
\(772\) 60.7919 2.18795
\(773\) 17.1105 0.615424 0.307712 0.951480i \(-0.400437\pi\)
0.307712 + 0.951480i \(0.400437\pi\)
\(774\) 13.6385 0.490225
\(775\) 2.19302 0.0787757
\(776\) −6.19615 −0.222429
\(777\) −14.8546 −0.532904
\(778\) −58.5537 −2.09925
\(779\) 60.9476 2.18367
\(780\) 143.386 5.13405
\(781\) −7.36923 −0.263692
\(782\) −0.646641 −0.0231238
\(783\) 18.4071 0.657815
\(784\) −10.1502 −0.362509
\(785\) −79.8650 −2.85050
\(786\) −60.9758 −2.17493
\(787\) −12.5717 −0.448134 −0.224067 0.974574i \(-0.571933\pi\)
−0.224067 + 0.974574i \(0.571933\pi\)
\(788\) −41.0079 −1.46085
\(789\) −23.5711 −0.839155
\(790\) −93.9723 −3.34338
\(791\) −10.8758 −0.386698
\(792\) 87.7275 3.11726
\(793\) −17.2783 −0.613569
\(794\) −0.473995 −0.0168215
\(795\) 77.1676 2.73685
\(796\) 31.4344 1.11416
\(797\) −27.2521 −0.965319 −0.482660 0.875808i \(-0.660329\pi\)
−0.482660 + 0.875808i \(0.660329\pi\)
\(798\) 59.6689 2.11226
\(799\) −0.776579 −0.0274734
\(800\) 18.2424 0.644965
\(801\) 15.9129 0.562254
\(802\) −48.9771 −1.72944
\(803\) 85.7408 3.02573
\(804\) −50.5552 −1.78295
\(805\) 3.75230 0.132251
\(806\) 4.48708 0.158051
\(807\) 49.5828 1.74540
\(808\) −1.55679 −0.0547675
\(809\) −47.4499 −1.66825 −0.834124 0.551577i \(-0.814026\pi\)
−0.834124 + 0.551577i \(0.814026\pi\)
\(810\) 43.1486 1.51609
\(811\) 26.7380 0.938897 0.469449 0.882960i \(-0.344453\pi\)
0.469449 + 0.882960i \(0.344453\pi\)
\(812\) −33.8922 −1.18938
\(813\) 27.0542 0.948832
\(814\) 68.8618 2.41361
\(815\) −3.58656 −0.125632
\(816\) −1.28559 −0.0450047
\(817\) −12.3247 −0.431187
\(818\) −47.3674 −1.65616
\(819\) −21.1004 −0.737309
\(820\) 85.7902 2.99592
\(821\) −18.1586 −0.633739 −0.316870 0.948469i \(-0.602632\pi\)
−0.316870 + 0.948469i \(0.602632\pi\)
\(822\) −118.560 −4.13525
\(823\) 31.4304 1.09560 0.547798 0.836611i \(-0.315466\pi\)
0.547798 + 0.836611i \(0.315466\pi\)
\(824\) −60.6216 −2.11185
\(825\) 84.8826 2.95523
\(826\) −19.4906 −0.678164
\(827\) 34.4447 1.19776 0.598879 0.800839i \(-0.295613\pi\)
0.598879 + 0.800839i \(0.295613\pi\)
\(828\) 13.9528 0.484894
\(829\) 7.54813 0.262157 0.131079 0.991372i \(-0.458156\pi\)
0.131079 + 0.991372i \(0.458156\pi\)
\(830\) −33.7159 −1.17030
\(831\) −61.2791 −2.12575
\(832\) 54.1952 1.87888
\(833\) −1.54311 −0.0534655
\(834\) −53.0309 −1.83631
\(835\) −1.36831 −0.0473524
\(836\) −177.943 −6.15429
\(837\) −0.918302 −0.0317412
\(838\) −55.3791 −1.91304
\(839\) −30.6368 −1.05770 −0.528849 0.848716i \(-0.677376\pi\)
−0.528849 + 0.848716i \(0.677376\pi\)
\(840\) 37.4192 1.29109
\(841\) 36.4311 1.25624
\(842\) 68.9980 2.37783
\(843\) 24.4502 0.842108
\(844\) 48.4638 1.66819
\(845\) 29.2344 1.00569
\(846\) 26.0478 0.895541
\(847\) 28.4843 0.978734
\(848\) −16.3741 −0.562288
\(849\) −23.7819 −0.816193
\(850\) −3.51410 −0.120533
\(851\) 4.87944 0.167265
\(852\) −11.6881 −0.400429
\(853\) −26.6251 −0.911625 −0.455813 0.890076i \(-0.650651\pi\)
−0.455813 + 0.890076i \(0.650651\pi\)
\(854\) −10.1210 −0.346332
\(855\) 103.430 3.53724
\(856\) 37.3989 1.27827
\(857\) 2.67059 0.0912255 0.0456128 0.998959i \(-0.485476\pi\)
0.0456128 + 0.998959i \(0.485476\pi\)
\(858\) 173.676 5.92919
\(859\) −55.1713 −1.88242 −0.941210 0.337823i \(-0.890310\pi\)
−0.941210 + 0.337823i \(0.890310\pi\)
\(860\) −17.3483 −0.591574
\(861\) −22.4156 −0.763922
\(862\) 62.0057 2.11192
\(863\) 33.3886 1.13656 0.568281 0.822835i \(-0.307609\pi\)
0.568281 + 0.822835i \(0.307609\pi\)
\(864\) −7.63877 −0.259876
\(865\) −5.17123 −0.175827
\(866\) −36.7908 −1.25020
\(867\) 44.3572 1.50645
\(868\) 1.69083 0.0573906
\(869\) −73.2227 −2.48391
\(870\) −162.149 −5.49737
\(871\) −25.1134 −0.850935
\(872\) 4.76651 0.161414
\(873\) 6.29897 0.213188
\(874\) −19.6001 −0.662984
\(875\) 1.62994 0.0551021
\(876\) 135.991 4.59472
\(877\) −31.1685 −1.05249 −0.526243 0.850334i \(-0.676400\pi\)
−0.526243 + 0.850334i \(0.676400\pi\)
\(878\) −44.2113 −1.49206
\(879\) 1.91884 0.0647208
\(880\) −34.5825 −1.16578
\(881\) 0.0372684 0.00125560 0.000627802 1.00000i \(-0.499800\pi\)
0.000627802 1.00000i \(0.499800\pi\)
\(882\) 51.7584 1.74280
\(883\) −32.3896 −1.09000 −0.544998 0.838437i \(-0.683470\pi\)
−0.544998 + 0.838437i \(0.683470\pi\)
\(884\) −4.62539 −0.155569
\(885\) −59.9865 −2.01643
\(886\) −88.5246 −2.97404
\(887\) −56.6582 −1.90240 −0.951198 0.308581i \(-0.900146\pi\)
−0.951198 + 0.308581i \(0.900146\pi\)
\(888\) 48.6595 1.63290
\(889\) −17.9963 −0.603575
\(890\) −31.4649 −1.05471
\(891\) 33.6212 1.12635
\(892\) −80.5068 −2.69557
\(893\) −23.5386 −0.787691
\(894\) 71.8073 2.40159
\(895\) 36.0170 1.20391
\(896\) 23.9468 0.800006
\(897\) 12.3064 0.410899
\(898\) −56.7694 −1.89442
\(899\) −3.26426 −0.108869
\(900\) 75.8251 2.52750
\(901\) −2.48930 −0.0829304
\(902\) 103.913 3.45992
\(903\) 4.53285 0.150844
\(904\) 35.6261 1.18490
\(905\) −7.22809 −0.240270
\(906\) 73.8204 2.45252
\(907\) −10.4365 −0.346538 −0.173269 0.984875i \(-0.555433\pi\)
−0.173269 + 0.984875i \(0.555433\pi\)
\(908\) −80.2949 −2.66468
\(909\) 1.58262 0.0524921
\(910\) 41.7224 1.38308
\(911\) 38.8754 1.28800 0.643999 0.765026i \(-0.277274\pi\)
0.643999 + 0.765026i \(0.277274\pi\)
\(912\) −38.9671 −1.29033
\(913\) −26.2713 −0.869452
\(914\) −69.3500 −2.29390
\(915\) −31.1495 −1.02977
\(916\) 18.5897 0.614221
\(917\) −11.4139 −0.376920
\(918\) 1.47149 0.0485663
\(919\) 18.5725 0.612649 0.306325 0.951927i \(-0.400901\pi\)
0.306325 + 0.951927i \(0.400901\pi\)
\(920\) −12.2915 −0.405240
\(921\) 21.6879 0.714639
\(922\) 55.6407 1.83243
\(923\) −5.80610 −0.191110
\(924\) 65.4449 2.15298
\(925\) 26.5168 0.871866
\(926\) 2.32161 0.0762930
\(927\) 61.6276 2.02412
\(928\) −27.1533 −0.891351
\(929\) 2.69095 0.0882872 0.0441436 0.999025i \(-0.485944\pi\)
0.0441436 + 0.999025i \(0.485944\pi\)
\(930\) 8.08938 0.265261
\(931\) −46.7727 −1.53291
\(932\) 1.09414 0.0358399
\(933\) 34.4368 1.12741
\(934\) 39.2220 1.28338
\(935\) −5.25746 −0.171937
\(936\) 69.1192 2.25923
\(937\) 49.5245 1.61790 0.808948 0.587881i \(-0.200038\pi\)
0.808948 + 0.587881i \(0.200038\pi\)
\(938\) −14.7105 −0.480315
\(939\) −31.6976 −1.03441
\(940\) −33.1331 −1.08068
\(941\) 12.4547 0.406010 0.203005 0.979178i \(-0.434929\pi\)
0.203005 + 0.979178i \(0.434929\pi\)
\(942\) −153.430 −4.99903
\(943\) 7.36311 0.239776
\(944\) 12.7284 0.414275
\(945\) −8.53868 −0.277763
\(946\) −21.0131 −0.683195
\(947\) −34.1295 −1.10906 −0.554530 0.832164i \(-0.687102\pi\)
−0.554530 + 0.832164i \(0.687102\pi\)
\(948\) −116.137 −3.77194
\(949\) 67.5539 2.19289
\(950\) −106.515 −3.45579
\(951\) 21.7296 0.704630
\(952\) −1.20708 −0.0391217
\(953\) −7.39659 −0.239599 −0.119800 0.992798i \(-0.538225\pi\)
−0.119800 + 0.992798i \(0.538225\pi\)
\(954\) 83.4951 2.70326
\(955\) 32.3283 1.04612
\(956\) 25.0524 0.810254
\(957\) −126.346 −4.08418
\(958\) 17.6492 0.570221
\(959\) −22.1929 −0.716646
\(960\) 97.7039 3.15338
\(961\) −30.8372 −0.994747
\(962\) 54.2552 1.74926
\(963\) −38.0195 −1.22516
\(964\) −47.5107 −1.53022
\(965\) 54.4423 1.75256
\(966\) 7.20864 0.231934
\(967\) −14.9572 −0.480991 −0.240495 0.970650i \(-0.577310\pi\)
−0.240495 + 0.970650i \(0.577310\pi\)
\(968\) −93.3070 −2.99900
\(969\) −5.92405 −0.190308
\(970\) −12.4551 −0.399909
\(971\) 54.4507 1.74741 0.873703 0.486459i \(-0.161712\pi\)
0.873703 + 0.486459i \(0.161712\pi\)
\(972\) 77.9496 2.50023
\(973\) −9.92671 −0.318236
\(974\) −72.9617 −2.33784
\(975\) 66.8777 2.14180
\(976\) 6.60956 0.211567
\(977\) −18.4733 −0.591012 −0.295506 0.955341i \(-0.595488\pi\)
−0.295506 + 0.955341i \(0.595488\pi\)
\(978\) −6.89022 −0.220325
\(979\) −24.5173 −0.783577
\(980\) −65.8375 −2.10310
\(981\) −4.84561 −0.154708
\(982\) 46.8468 1.49494
\(983\) 10.9429 0.349025 0.174513 0.984655i \(-0.444165\pi\)
0.174513 + 0.984655i \(0.444165\pi\)
\(984\) 73.4275 2.34078
\(985\) −36.7247 −1.17015
\(986\) 5.23065 0.166578
\(987\) 8.65717 0.275561
\(988\) −140.199 −4.46032
\(989\) −1.48896 −0.0473460
\(990\) 176.344 5.60459
\(991\) 7.24628 0.230186 0.115093 0.993355i \(-0.463283\pi\)
0.115093 + 0.993355i \(0.463283\pi\)
\(992\) 1.35464 0.0430098
\(993\) 12.7953 0.406046
\(994\) −3.40100 −0.107873
\(995\) 28.1511 0.892451
\(996\) −41.6682 −1.32031
\(997\) −11.4549 −0.362781 −0.181390 0.983411i \(-0.558060\pi\)
−0.181390 + 0.983411i \(0.558060\pi\)
\(998\) 82.8450 2.62241
\(999\) −11.1036 −0.351302
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 \(a_p\))