Properties

Label 4003.2.a.b.1.12
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 1.12
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} +O(q^{10})\) \(q-2.54789 q^{2} -3.05680 q^{3} +4.49172 q^{4} +1.69745 q^{5} +7.78837 q^{6} -1.95167 q^{7} -6.34863 q^{8} +6.34402 q^{9} -4.32491 q^{10} +1.27907 q^{11} -13.7303 q^{12} +2.11227 q^{13} +4.97263 q^{14} -5.18877 q^{15} +7.19214 q^{16} -4.74604 q^{17} -16.1638 q^{18} +6.91804 q^{19} +7.62448 q^{20} +5.96586 q^{21} -3.25894 q^{22} -0.312750 q^{23} +19.4065 q^{24} -2.11866 q^{25} -5.38182 q^{26} -10.2220 q^{27} -8.76636 q^{28} +2.76156 q^{29} +13.2204 q^{30} +6.09804 q^{31} -5.62749 q^{32} -3.90987 q^{33} +12.0924 q^{34} -3.31286 q^{35} +28.4956 q^{36} -5.58541 q^{37} -17.6264 q^{38} -6.45678 q^{39} -10.7765 q^{40} -8.81948 q^{41} -15.2003 q^{42} +2.76370 q^{43} +5.74525 q^{44} +10.7687 q^{45} +0.796852 q^{46} +1.05384 q^{47} -21.9849 q^{48} -3.19099 q^{49} +5.39810 q^{50} +14.5077 q^{51} +9.48773 q^{52} -0.198763 q^{53} +26.0445 q^{54} +2.17117 q^{55} +12.3904 q^{56} -21.1471 q^{57} -7.03613 q^{58} -1.29207 q^{59} -23.3065 q^{60} +1.28912 q^{61} -15.5371 q^{62} -12.3814 q^{63} -0.0460754 q^{64} +3.58547 q^{65} +9.96191 q^{66} +4.45843 q^{67} -21.3179 q^{68} +0.956014 q^{69} +8.44079 q^{70} -3.26402 q^{71} -40.2758 q^{72} -3.95016 q^{73} +14.2310 q^{74} +6.47632 q^{75} +31.0739 q^{76} -2.49633 q^{77} +16.4511 q^{78} -14.7462 q^{79} +12.2083 q^{80} +12.2145 q^{81} +22.4710 q^{82} -10.7341 q^{83} +26.7970 q^{84} -8.05616 q^{85} -7.04160 q^{86} -8.44152 q^{87} -8.12037 q^{88} -5.43628 q^{89} -27.4373 q^{90} -4.12245 q^{91} -1.40479 q^{92} -18.6405 q^{93} -2.68508 q^{94} +11.7430 q^{95} +17.2021 q^{96} -8.36985 q^{97} +8.13028 q^{98} +8.11447 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54789 −1.80163 −0.900814 0.434206i \(-0.857029\pi\)
−0.900814 + 0.434206i \(0.857029\pi\)
\(3\) −3.05680 −1.76484 −0.882422 0.470459i \(-0.844088\pi\)
−0.882422 + 0.470459i \(0.844088\pi\)
\(4\) 4.49172 2.24586
\(5\) 1.69745 0.759123 0.379562 0.925166i \(-0.376075\pi\)
0.379562 + 0.925166i \(0.376075\pi\)
\(6\) 7.78837 3.17959
\(7\) −1.95167 −0.737661 −0.368831 0.929497i \(-0.620242\pi\)
−0.368831 + 0.929497i \(0.620242\pi\)
\(8\) −6.34863 −2.24458
\(9\) 6.34402 2.11467
\(10\) −4.32491 −1.36766
\(11\) 1.27907 0.385655 0.192828 0.981233i \(-0.438234\pi\)
0.192828 + 0.981233i \(0.438234\pi\)
\(12\) −13.7303 −3.96359
\(13\) 2.11227 0.585838 0.292919 0.956137i \(-0.405373\pi\)
0.292919 + 0.956137i \(0.405373\pi\)
\(14\) 4.97263 1.32899
\(15\) −5.18877 −1.33973
\(16\) 7.19214 1.79803
\(17\) −4.74604 −1.15108 −0.575541 0.817773i \(-0.695209\pi\)
−0.575541 + 0.817773i \(0.695209\pi\)
\(18\) −16.1638 −3.80985
\(19\) 6.91804 1.58711 0.793554 0.608500i \(-0.208229\pi\)
0.793554 + 0.608500i \(0.208229\pi\)
\(20\) 7.62448 1.70489
\(21\) 5.96586 1.30186
\(22\) −3.25894 −0.694807
\(23\) −0.312750 −0.0652129 −0.0326065 0.999468i \(-0.510381\pi\)
−0.0326065 + 0.999468i \(0.510381\pi\)
\(24\) 19.4065 3.96133
\(25\) −2.11866 −0.423732
\(26\) −5.38182 −1.05546
\(27\) −10.2220 −1.96722
\(28\) −8.76636 −1.65669
\(29\) 2.76156 0.512808 0.256404 0.966570i \(-0.417462\pi\)
0.256404 + 0.966570i \(0.417462\pi\)
\(30\) 13.2204 2.41370
\(31\) 6.09804 1.09524 0.547621 0.836727i \(-0.315534\pi\)
0.547621 + 0.836727i \(0.315534\pi\)
\(32\) −5.62749 −0.994809
\(33\) −3.90987 −0.680621
\(34\) 12.0924 2.07382
\(35\) −3.31286 −0.559976
\(36\) 28.4956 4.74926
\(37\) −5.58541 −0.918235 −0.459118 0.888376i \(-0.651834\pi\)
−0.459118 + 0.888376i \(0.651834\pi\)
\(38\) −17.6264 −2.85938
\(39\) −6.45678 −1.03391
\(40\) −10.7765 −1.70391
\(41\) −8.81948 −1.37737 −0.688686 0.725060i \(-0.741812\pi\)
−0.688686 + 0.725060i \(0.741812\pi\)
\(42\) −15.2003 −2.34546
\(43\) 2.76370 0.421460 0.210730 0.977544i \(-0.432416\pi\)
0.210730 + 0.977544i \(0.432416\pi\)
\(44\) 5.74525 0.866129
\(45\) 10.7687 1.60530
\(46\) 0.796852 0.117489
\(47\) 1.05384 0.153719 0.0768595 0.997042i \(-0.475511\pi\)
0.0768595 + 0.997042i \(0.475511\pi\)
\(48\) −21.9849 −3.17325
\(49\) −3.19099 −0.455856
\(50\) 5.39810 0.763407
\(51\) 14.5077 2.03148
\(52\) 9.48773 1.31571
\(53\) −0.198763 −0.0273023 −0.0136511 0.999907i \(-0.504345\pi\)
−0.0136511 + 0.999907i \(0.504345\pi\)
\(54\) 26.0445 3.54420
\(55\) 2.17117 0.292760
\(56\) 12.3904 1.65574
\(57\) −21.1471 −2.80100
\(58\) −7.03613 −0.923889
\(59\) −1.29207 −0.168213 −0.0841064 0.996457i \(-0.526804\pi\)
−0.0841064 + 0.996457i \(0.526804\pi\)
\(60\) −23.3065 −3.00886
\(61\) 1.28912 0.165055 0.0825274 0.996589i \(-0.473701\pi\)
0.0825274 + 0.996589i \(0.473701\pi\)
\(62\) −15.5371 −1.97322
\(63\) −12.3814 −1.55991
\(64\) −0.0460754 −0.00575942
\(65\) 3.58547 0.444723
\(66\) 9.96191 1.22623
\(67\) 4.45843 0.544684 0.272342 0.962200i \(-0.412202\pi\)
0.272342 + 0.962200i \(0.412202\pi\)
\(68\) −21.3179 −2.58517
\(69\) 0.956014 0.115091
\(70\) 8.44079 1.00887
\(71\) −3.26402 −0.387367 −0.193684 0.981064i \(-0.562044\pi\)
−0.193684 + 0.981064i \(0.562044\pi\)
\(72\) −40.2758 −4.74655
\(73\) −3.95016 −0.462331 −0.231166 0.972914i \(-0.574254\pi\)
−0.231166 + 0.972914i \(0.574254\pi\)
\(74\) 14.2310 1.65432
\(75\) 6.47632 0.747821
\(76\) 31.0739 3.56442
\(77\) −2.49633 −0.284483
\(78\) 16.4511 1.86273
\(79\) −14.7462 −1.65908 −0.829539 0.558449i \(-0.811397\pi\)
−0.829539 + 0.558449i \(0.811397\pi\)
\(80\) 12.2083 1.36493
\(81\) 12.2145 1.35717
\(82\) 22.4710 2.48151
\(83\) −10.7341 −1.17822 −0.589110 0.808053i \(-0.700521\pi\)
−0.589110 + 0.808053i \(0.700521\pi\)
\(84\) 26.7970 2.92379
\(85\) −8.05616 −0.873814
\(86\) −7.04160 −0.759315
\(87\) −8.44152 −0.905026
\(88\) −8.12037 −0.865634
\(89\) −5.43628 −0.576245 −0.288122 0.957594i \(-0.593031\pi\)
−0.288122 + 0.957594i \(0.593031\pi\)
\(90\) −27.4373 −2.89215
\(91\) −4.12245 −0.432150
\(92\) −1.40479 −0.146459
\(93\) −18.6405 −1.93293
\(94\) −2.68508 −0.276945
\(95\) 11.7430 1.20481
\(96\) 17.2021 1.75568
\(97\) −8.36985 −0.849830 −0.424915 0.905233i \(-0.639696\pi\)
−0.424915 + 0.905233i \(0.639696\pi\)
\(98\) 8.13028 0.821282
\(99\) 8.11447 0.815535
\(100\) −9.51643 −0.951643
\(101\) −12.6494 −1.25866 −0.629332 0.777137i \(-0.716671\pi\)
−0.629332 + 0.777137i \(0.716671\pi\)
\(102\) −36.9639 −3.65997
\(103\) −2.52520 −0.248815 −0.124408 0.992231i \(-0.539703\pi\)
−0.124408 + 0.992231i \(0.539703\pi\)
\(104\) −13.4100 −1.31496
\(105\) 10.1268 0.988270
\(106\) 0.506427 0.0491885
\(107\) 5.53331 0.534925 0.267463 0.963568i \(-0.413815\pi\)
0.267463 + 0.963568i \(0.413815\pi\)
\(108\) −45.9143 −4.41811
\(109\) 9.10785 0.872373 0.436187 0.899856i \(-0.356329\pi\)
0.436187 + 0.899856i \(0.356329\pi\)
\(110\) −5.53188 −0.527444
\(111\) 17.0735 1.62054
\(112\) −14.0367 −1.32634
\(113\) 12.4667 1.17277 0.586384 0.810033i \(-0.300551\pi\)
0.586384 + 0.810033i \(0.300551\pi\)
\(114\) 53.8803 5.04635
\(115\) −0.530878 −0.0495046
\(116\) 12.4041 1.15170
\(117\) 13.4003 1.23886
\(118\) 3.29204 0.303057
\(119\) 9.26269 0.849109
\(120\) 32.9416 3.00714
\(121\) −9.36397 −0.851270
\(122\) −3.28453 −0.297367
\(123\) 26.9594 2.43085
\(124\) 27.3907 2.45976
\(125\) −12.0836 −1.08079
\(126\) 31.5464 2.81038
\(127\) 18.0879 1.60504 0.802521 0.596625i \(-0.203492\pi\)
0.802521 + 0.596625i \(0.203492\pi\)
\(128\) 11.3724 1.00519
\(129\) −8.44808 −0.743812
\(130\) −9.13538 −0.801226
\(131\) 21.2647 1.85790 0.928952 0.370199i \(-0.120711\pi\)
0.928952 + 0.370199i \(0.120711\pi\)
\(132\) −17.5621 −1.52858
\(133\) −13.5017 −1.17075
\(134\) −11.3596 −0.981318
\(135\) −17.3513 −1.49336
\(136\) 30.1308 2.58370
\(137\) 6.22612 0.531934 0.265967 0.963982i \(-0.414309\pi\)
0.265967 + 0.963982i \(0.414309\pi\)
\(138\) −2.43582 −0.207350
\(139\) 8.74712 0.741921 0.370961 0.928649i \(-0.379029\pi\)
0.370961 + 0.928649i \(0.379029\pi\)
\(140\) −14.8805 −1.25763
\(141\) −3.22139 −0.271290
\(142\) 8.31634 0.697892
\(143\) 2.70175 0.225932
\(144\) 45.6270 3.80225
\(145\) 4.68761 0.389284
\(146\) 10.0646 0.832948
\(147\) 9.75422 0.804514
\(148\) −25.0881 −2.06223
\(149\) 3.31093 0.271242 0.135621 0.990761i \(-0.456697\pi\)
0.135621 + 0.990761i \(0.456697\pi\)
\(150\) −16.5009 −1.34729
\(151\) −8.30448 −0.675809 −0.337905 0.941180i \(-0.609718\pi\)
−0.337905 + 0.941180i \(0.609718\pi\)
\(152\) −43.9201 −3.56239
\(153\) −30.1089 −2.43416
\(154\) 6.36036 0.512533
\(155\) 10.3511 0.831423
\(156\) −29.0021 −2.32203
\(157\) 22.8598 1.82441 0.912204 0.409737i \(-0.134379\pi\)
0.912204 + 0.409737i \(0.134379\pi\)
\(158\) 37.5717 2.98904
\(159\) 0.607580 0.0481842
\(160\) −9.55239 −0.755182
\(161\) 0.610385 0.0481050
\(162\) −31.1212 −2.44511
\(163\) 13.1912 1.03322 0.516609 0.856221i \(-0.327194\pi\)
0.516609 + 0.856221i \(0.327194\pi\)
\(164\) −39.6147 −3.09339
\(165\) −6.63682 −0.516676
\(166\) 27.3492 2.12271
\(167\) 3.38409 0.261869 0.130935 0.991391i \(-0.458202\pi\)
0.130935 + 0.991391i \(0.458202\pi\)
\(168\) −37.8750 −2.92212
\(169\) −8.53832 −0.656794
\(170\) 20.5262 1.57429
\(171\) 43.8882 3.35621
\(172\) 12.4138 0.946542
\(173\) −1.31951 −0.100320 −0.0501601 0.998741i \(-0.515973\pi\)
−0.0501601 + 0.998741i \(0.515973\pi\)
\(174\) 21.5080 1.63052
\(175\) 4.13492 0.312571
\(176\) 9.19928 0.693422
\(177\) 3.94959 0.296869
\(178\) 13.8510 1.03818
\(179\) 6.00066 0.448510 0.224255 0.974530i \(-0.428005\pi\)
0.224255 + 0.974530i \(0.428005\pi\)
\(180\) 48.3698 3.60528
\(181\) 1.58330 0.117686 0.0588429 0.998267i \(-0.481259\pi\)
0.0588429 + 0.998267i \(0.481259\pi\)
\(182\) 10.5035 0.778574
\(183\) −3.94058 −0.291296
\(184\) 1.98553 0.146376
\(185\) −9.48095 −0.697054
\(186\) 47.4939 3.48242
\(187\) −6.07053 −0.443921
\(188\) 4.73358 0.345232
\(189\) 19.9499 1.45114
\(190\) −29.9199 −2.17062
\(191\) −18.1483 −1.31317 −0.656583 0.754254i \(-0.727999\pi\)
−0.656583 + 0.754254i \(0.727999\pi\)
\(192\) 0.140843 0.0101645
\(193\) 20.5290 1.47771 0.738855 0.673865i \(-0.235367\pi\)
0.738855 + 0.673865i \(0.235367\pi\)
\(194\) 21.3254 1.53108
\(195\) −10.9601 −0.784867
\(196\) −14.3331 −1.02379
\(197\) −8.67871 −0.618332 −0.309166 0.951008i \(-0.600050\pi\)
−0.309166 + 0.951008i \(0.600050\pi\)
\(198\) −20.6747 −1.46929
\(199\) 20.9943 1.48825 0.744124 0.668042i \(-0.232867\pi\)
0.744124 + 0.668042i \(0.232867\pi\)
\(200\) 13.4506 0.951100
\(201\) −13.6285 −0.961283
\(202\) 32.2293 2.26764
\(203\) −5.38964 −0.378279
\(204\) 65.1645 4.56243
\(205\) −14.9706 −1.04559
\(206\) 6.43392 0.448273
\(207\) −1.98409 −0.137904
\(208\) 15.1917 1.05336
\(209\) 8.84869 0.612077
\(210\) −25.8018 −1.78049
\(211\) −18.3322 −1.26204 −0.631021 0.775766i \(-0.717364\pi\)
−0.631021 + 0.775766i \(0.717364\pi\)
\(212\) −0.892790 −0.0613171
\(213\) 9.97744 0.683643
\(214\) −14.0982 −0.963736
\(215\) 4.69125 0.319940
\(216\) 64.8956 4.41559
\(217\) −11.9014 −0.807917
\(218\) −23.2058 −1.57169
\(219\) 12.0748 0.815942
\(220\) 9.75228 0.657499
\(221\) −10.0249 −0.674348
\(222\) −43.5012 −2.91961
\(223\) −14.7292 −0.986339 −0.493170 0.869933i \(-0.664162\pi\)
−0.493170 + 0.869933i \(0.664162\pi\)
\(224\) 10.9830 0.733832
\(225\) −13.4408 −0.896054
\(226\) −31.7637 −2.11289
\(227\) −8.39648 −0.557294 −0.278647 0.960394i \(-0.589886\pi\)
−0.278647 + 0.960394i \(0.589886\pi\)
\(228\) −94.9867 −6.29065
\(229\) 20.6880 1.36710 0.683550 0.729904i \(-0.260435\pi\)
0.683550 + 0.729904i \(0.260435\pi\)
\(230\) 1.35262 0.0891889
\(231\) 7.63077 0.502068
\(232\) −17.5321 −1.15104
\(233\) −22.1788 −1.45298 −0.726492 0.687175i \(-0.758851\pi\)
−0.726492 + 0.687175i \(0.758851\pi\)
\(234\) −34.1424 −2.23196
\(235\) 1.78885 0.116692
\(236\) −5.80361 −0.377783
\(237\) 45.0762 2.92801
\(238\) −23.6003 −1.52978
\(239\) 2.61708 0.169285 0.0846425 0.996411i \(-0.473025\pi\)
0.0846425 + 0.996411i \(0.473025\pi\)
\(240\) −37.3183 −2.40889
\(241\) 3.88922 0.250527 0.125263 0.992124i \(-0.460022\pi\)
0.125263 + 0.992124i \(0.460022\pi\)
\(242\) 23.8583 1.53367
\(243\) −6.67131 −0.427965
\(244\) 5.79037 0.370690
\(245\) −5.41655 −0.346051
\(246\) −68.6894 −4.37948
\(247\) 14.6128 0.929788
\(248\) −38.7142 −2.45836
\(249\) 32.8119 2.07937
\(250\) 30.7876 1.94718
\(251\) −15.8612 −1.00115 −0.500576 0.865693i \(-0.666878\pi\)
−0.500576 + 0.865693i \(0.666878\pi\)
\(252\) −55.6139 −3.50335
\(253\) −0.400031 −0.0251497
\(254\) −46.0859 −2.89169
\(255\) 24.6261 1.54214
\(256\) −28.8834 −1.80521
\(257\) −13.8317 −0.862797 −0.431398 0.902162i \(-0.641980\pi\)
−0.431398 + 0.902162i \(0.641980\pi\)
\(258\) 21.5247 1.34007
\(259\) 10.9009 0.677347
\(260\) 16.1050 0.998787
\(261\) 17.5194 1.08442
\(262\) −54.1800 −3.34725
\(263\) −27.6002 −1.70190 −0.850949 0.525248i \(-0.823973\pi\)
−0.850949 + 0.525248i \(0.823973\pi\)
\(264\) 24.8223 1.52771
\(265\) −0.337391 −0.0207258
\(266\) 34.4008 2.10925
\(267\) 16.6176 1.01698
\(268\) 20.0261 1.22329
\(269\) −1.80058 −0.109783 −0.0548915 0.998492i \(-0.517481\pi\)
−0.0548915 + 0.998492i \(0.517481\pi\)
\(270\) 44.2092 2.69049
\(271\) −6.62851 −0.402653 −0.201327 0.979524i \(-0.564525\pi\)
−0.201327 + 0.979524i \(0.564525\pi\)
\(272\) −34.1341 −2.06969
\(273\) 12.6015 0.762677
\(274\) −15.8635 −0.958346
\(275\) −2.70992 −0.163415
\(276\) 4.29415 0.258478
\(277\) −15.9509 −0.958397 −0.479199 0.877706i \(-0.659073\pi\)
−0.479199 + 0.877706i \(0.659073\pi\)
\(278\) −22.2867 −1.33667
\(279\) 38.6861 2.31608
\(280\) 21.0321 1.25691
\(281\) −15.0481 −0.897695 −0.448848 0.893608i \(-0.648165\pi\)
−0.448848 + 0.893608i \(0.648165\pi\)
\(282\) 8.20774 0.488764
\(283\) 21.5951 1.28370 0.641849 0.766831i \(-0.278168\pi\)
0.641849 + 0.766831i \(0.278168\pi\)
\(284\) −14.6611 −0.869974
\(285\) −35.8961 −2.12630
\(286\) −6.88375 −0.407045
\(287\) 17.2127 1.01603
\(288\) −35.7009 −2.10369
\(289\) 5.52486 0.324992
\(290\) −11.9435 −0.701346
\(291\) 25.5850 1.49982
\(292\) −17.7430 −1.03833
\(293\) 17.2953 1.01040 0.505202 0.863001i \(-0.331418\pi\)
0.505202 + 0.863001i \(0.331418\pi\)
\(294\) −24.8526 −1.44943
\(295\) −2.19322 −0.127694
\(296\) 35.4597 2.06105
\(297\) −13.0747 −0.758670
\(298\) −8.43586 −0.488676
\(299\) −0.660613 −0.0382042
\(300\) 29.0898 1.67950
\(301\) −5.39383 −0.310895
\(302\) 21.1589 1.21756
\(303\) 38.6667 2.22134
\(304\) 49.7555 2.85367
\(305\) 2.18822 0.125297
\(306\) 76.7141 4.38546
\(307\) 8.47402 0.483638 0.241819 0.970321i \(-0.422256\pi\)
0.241819 + 0.970321i \(0.422256\pi\)
\(308\) −11.2128 −0.638910
\(309\) 7.71903 0.439120
\(310\) −26.3735 −1.49791
\(311\) −26.9798 −1.52988 −0.764941 0.644100i \(-0.777232\pi\)
−0.764941 + 0.644100i \(0.777232\pi\)
\(312\) 40.9917 2.32070
\(313\) −6.65398 −0.376105 −0.188053 0.982159i \(-0.560218\pi\)
−0.188053 + 0.982159i \(0.560218\pi\)
\(314\) −58.2441 −3.28690
\(315\) −21.0168 −1.18417
\(316\) −66.2359 −3.72606
\(317\) 1.90143 0.106795 0.0533974 0.998573i \(-0.482995\pi\)
0.0533974 + 0.998573i \(0.482995\pi\)
\(318\) −1.54804 −0.0868100
\(319\) 3.53224 0.197767
\(320\) −0.0782107 −0.00437211
\(321\) −16.9142 −0.944059
\(322\) −1.55519 −0.0866674
\(323\) −32.8333 −1.82689
\(324\) 54.8642 3.04801
\(325\) −4.47518 −0.248238
\(326\) −33.6098 −1.86147
\(327\) −27.8408 −1.53960
\(328\) 55.9916 3.09162
\(329\) −2.05676 −0.113393
\(330\) 16.9099 0.930857
\(331\) 16.8542 0.926390 0.463195 0.886256i \(-0.346703\pi\)
0.463195 + 0.886256i \(0.346703\pi\)
\(332\) −48.2146 −2.64612
\(333\) −35.4339 −1.94177
\(334\) −8.62229 −0.471791
\(335\) 7.56797 0.413483
\(336\) 42.9073 2.34078
\(337\) −13.7120 −0.746942 −0.373471 0.927642i \(-0.621832\pi\)
−0.373471 + 0.927642i \(0.621832\pi\)
\(338\) 21.7547 1.18330
\(339\) −38.1082 −2.06975
\(340\) −36.1861 −1.96246
\(341\) 7.79985 0.422386
\(342\) −111.822 −6.04664
\(343\) 19.8894 1.07393
\(344\) −17.5457 −0.946001
\(345\) 1.62279 0.0873679
\(346\) 3.36195 0.180739
\(347\) 2.62664 0.141006 0.0705028 0.997512i \(-0.477540\pi\)
0.0705028 + 0.997512i \(0.477540\pi\)
\(348\) −37.9170 −2.03256
\(349\) 18.1831 0.973319 0.486659 0.873592i \(-0.338215\pi\)
0.486659 + 0.873592i \(0.338215\pi\)
\(350\) −10.5353 −0.563136
\(351\) −21.5916 −1.15247
\(352\) −7.19798 −0.383653
\(353\) −29.0730 −1.54740 −0.773699 0.633553i \(-0.781596\pi\)
−0.773699 + 0.633553i \(0.781596\pi\)
\(354\) −10.0631 −0.534848
\(355\) −5.54051 −0.294060
\(356\) −24.4183 −1.29417
\(357\) −28.3142 −1.49854
\(358\) −15.2890 −0.808049
\(359\) −20.1578 −1.06389 −0.531945 0.846779i \(-0.678539\pi\)
−0.531945 + 0.846779i \(0.678539\pi\)
\(360\) −68.3662 −3.60322
\(361\) 28.8593 1.51891
\(362\) −4.03407 −0.212026
\(363\) 28.6238 1.50236
\(364\) −18.5169 −0.970550
\(365\) −6.70520 −0.350966
\(366\) 10.0401 0.524807
\(367\) 9.34111 0.487602 0.243801 0.969825i \(-0.421606\pi\)
0.243801 + 0.969825i \(0.421606\pi\)
\(368\) −2.24934 −0.117255
\(369\) −55.9509 −2.91269
\(370\) 24.1564 1.25583
\(371\) 0.387920 0.0201398
\(372\) −83.7279 −4.34109
\(373\) 15.1424 0.784043 0.392022 0.919956i \(-0.371776\pi\)
0.392022 + 0.919956i \(0.371776\pi\)
\(374\) 15.4670 0.799781
\(375\) 36.9371 1.90742
\(376\) −6.69047 −0.345035
\(377\) 5.83315 0.300423
\(378\) −50.8301 −2.61442
\(379\) −6.39086 −0.328277 −0.164138 0.986437i \(-0.552484\pi\)
−0.164138 + 0.986437i \(0.552484\pi\)
\(380\) 52.7465 2.70584
\(381\) −55.2910 −2.83265
\(382\) 46.2398 2.36584
\(383\) 0.122038 0.00623583 0.00311791 0.999995i \(-0.499008\pi\)
0.00311791 + 0.999995i \(0.499008\pi\)
\(384\) −34.7630 −1.77399
\(385\) −4.23740 −0.215958
\(386\) −52.3055 −2.66228
\(387\) 17.5330 0.891251
\(388\) −37.5951 −1.90860
\(389\) 6.44018 0.326530 0.163265 0.986582i \(-0.447797\pi\)
0.163265 + 0.986582i \(0.447797\pi\)
\(390\) 27.9250 1.41404
\(391\) 1.48432 0.0750655
\(392\) 20.2584 1.02320
\(393\) −65.0019 −3.27891
\(394\) 22.1124 1.11400
\(395\) −25.0310 −1.25944
\(396\) 36.4480 1.83158
\(397\) −21.3887 −1.07347 −0.536735 0.843751i \(-0.680342\pi\)
−0.536735 + 0.843751i \(0.680342\pi\)
\(398\) −53.4911 −2.68127
\(399\) 41.2720 2.06619
\(400\) −15.2377 −0.761885
\(401\) −1.20640 −0.0602445 −0.0301223 0.999546i \(-0.509590\pi\)
−0.0301223 + 0.999546i \(0.509590\pi\)
\(402\) 34.7239 1.73187
\(403\) 12.8807 0.641634
\(404\) −56.8177 −2.82678
\(405\) 20.7335 1.03026
\(406\) 13.7322 0.681517
\(407\) −7.14415 −0.354122
\(408\) −92.1039 −4.55982
\(409\) 28.2505 1.39690 0.698449 0.715660i \(-0.253874\pi\)
0.698449 + 0.715660i \(0.253874\pi\)
\(410\) 38.1435 1.88377
\(411\) −19.0320 −0.938779
\(412\) −11.3425 −0.558805
\(413\) 2.52169 0.124084
\(414\) 5.05524 0.248452
\(415\) −18.2206 −0.894414
\(416\) −11.8868 −0.582797
\(417\) −26.7382 −1.30937
\(418\) −22.5454 −1.10273
\(419\) 2.55944 0.125037 0.0625184 0.998044i \(-0.480087\pi\)
0.0625184 + 0.998044i \(0.480087\pi\)
\(420\) 45.4866 2.21952
\(421\) −31.2538 −1.52322 −0.761608 0.648038i \(-0.775590\pi\)
−0.761608 + 0.648038i \(0.775590\pi\)
\(422\) 46.7084 2.27373
\(423\) 6.68561 0.325065
\(424\) 1.26188 0.0612821
\(425\) 10.0552 0.487751
\(426\) −25.4214 −1.23167
\(427\) −2.51593 −0.121755
\(428\) 24.8541 1.20137
\(429\) −8.25870 −0.398734
\(430\) −11.9528 −0.576413
\(431\) 18.4718 0.889757 0.444878 0.895591i \(-0.353247\pi\)
0.444878 + 0.895591i \(0.353247\pi\)
\(432\) −73.5179 −3.53713
\(433\) 16.6879 0.801970 0.400985 0.916085i \(-0.368668\pi\)
0.400985 + 0.916085i \(0.368668\pi\)
\(434\) 30.3233 1.45557
\(435\) −14.3291 −0.687026
\(436\) 40.9099 1.95923
\(437\) −2.16362 −0.103500
\(438\) −30.7653 −1.47002
\(439\) 5.43370 0.259336 0.129668 0.991557i \(-0.458609\pi\)
0.129668 + 0.991557i \(0.458609\pi\)
\(440\) −13.7839 −0.657123
\(441\) −20.2437 −0.963986
\(442\) 25.5423 1.21492
\(443\) 20.2292 0.961117 0.480559 0.876963i \(-0.340434\pi\)
0.480559 + 0.876963i \(0.340434\pi\)
\(444\) 76.6893 3.63951
\(445\) −9.22782 −0.437441
\(446\) 37.5283 1.77702
\(447\) −10.1208 −0.478699
\(448\) 0.0899239 0.00424850
\(449\) −32.5339 −1.53537 −0.767684 0.640828i \(-0.778591\pi\)
−0.767684 + 0.640828i \(0.778591\pi\)
\(450\) 34.2457 1.61436
\(451\) −11.2808 −0.531191
\(452\) 55.9969 2.63387
\(453\) 25.3851 1.19270
\(454\) 21.3933 1.00404
\(455\) −6.99766 −0.328055
\(456\) 134.255 6.28706
\(457\) −8.38603 −0.392282 −0.196141 0.980576i \(-0.562841\pi\)
−0.196141 + 0.980576i \(0.562841\pi\)
\(458\) −52.7106 −2.46300
\(459\) 48.5139 2.26444
\(460\) −2.38456 −0.111181
\(461\) −28.8811 −1.34513 −0.672563 0.740040i \(-0.734807\pi\)
−0.672563 + 0.740040i \(0.734807\pi\)
\(462\) −19.4423 −0.904540
\(463\) −9.29190 −0.431831 −0.215916 0.976412i \(-0.569274\pi\)
−0.215916 + 0.976412i \(0.569274\pi\)
\(464\) 19.8615 0.922046
\(465\) −31.6413 −1.46733
\(466\) 56.5092 2.61774
\(467\) −1.33238 −0.0616553 −0.0308276 0.999525i \(-0.509814\pi\)
−0.0308276 + 0.999525i \(0.509814\pi\)
\(468\) 60.1903 2.78230
\(469\) −8.70138 −0.401793
\(470\) −4.55779 −0.210235
\(471\) −69.8777 −3.21979
\(472\) 8.20286 0.377567
\(473\) 3.53498 0.162539
\(474\) −114.849 −5.27519
\(475\) −14.6570 −0.672508
\(476\) 41.6054 1.90698
\(477\) −1.26096 −0.0577353
\(478\) −6.66803 −0.304988
\(479\) 21.5871 0.986340 0.493170 0.869933i \(-0.335838\pi\)
0.493170 + 0.869933i \(0.335838\pi\)
\(480\) 29.1997 1.33278
\(481\) −11.7979 −0.537937
\(482\) −9.90930 −0.451356
\(483\) −1.86582 −0.0848979
\(484\) −42.0604 −1.91183
\(485\) −14.2074 −0.645126
\(486\) 16.9977 0.771033
\(487\) 17.4192 0.789340 0.394670 0.918823i \(-0.370859\pi\)
0.394670 + 0.918823i \(0.370859\pi\)
\(488\) −8.18414 −0.370479
\(489\) −40.3230 −1.82347
\(490\) 13.8008 0.623455
\(491\) −1.85911 −0.0839006 −0.0419503 0.999120i \(-0.513357\pi\)
−0.0419503 + 0.999120i \(0.513357\pi\)
\(492\) 121.094 5.45934
\(493\) −13.1064 −0.590284
\(494\) −37.2317 −1.67513
\(495\) 13.7739 0.619091
\(496\) 43.8580 1.96928
\(497\) 6.37028 0.285746
\(498\) −83.6011 −3.74626
\(499\) −29.4259 −1.31728 −0.658641 0.752457i \(-0.728869\pi\)
−0.658641 + 0.752457i \(0.728869\pi\)
\(500\) −54.2761 −2.42730
\(501\) −10.3445 −0.462158
\(502\) 40.4126 1.80370
\(503\) 1.79364 0.0799743 0.0399872 0.999200i \(-0.487268\pi\)
0.0399872 + 0.999200i \(0.487268\pi\)
\(504\) 78.6050 3.50135
\(505\) −21.4718 −0.955481
\(506\) 1.01923 0.0453104
\(507\) 26.0999 1.15914
\(508\) 81.2458 3.60470
\(509\) −38.0802 −1.68787 −0.843937 0.536442i \(-0.819768\pi\)
−0.843937 + 0.536442i \(0.819768\pi\)
\(510\) −62.7444 −2.77837
\(511\) 7.70940 0.341044
\(512\) 50.8468 2.24713
\(513\) −70.7161 −3.12219
\(514\) 35.2416 1.55444
\(515\) −4.28640 −0.188882
\(516\) −37.9464 −1.67050
\(517\) 1.34795 0.0592826
\(518\) −27.7742 −1.22033
\(519\) 4.03346 0.177049
\(520\) −22.7628 −0.998217
\(521\) −14.8236 −0.649433 −0.324717 0.945811i \(-0.605269\pi\)
−0.324717 + 0.945811i \(0.605269\pi\)
\(522\) −44.6373 −1.95372
\(523\) −0.830678 −0.0363230 −0.0181615 0.999835i \(-0.505781\pi\)
−0.0181615 + 0.999835i \(0.505781\pi\)
\(524\) 95.5151 4.17260
\(525\) −12.6396 −0.551638
\(526\) 70.3220 3.06619
\(527\) −28.9415 −1.26071
\(528\) −28.1203 −1.22378
\(529\) −22.9022 −0.995747
\(530\) 0.859634 0.0373401
\(531\) −8.19690 −0.355715
\(532\) −60.6460 −2.62934
\(533\) −18.6291 −0.806917
\(534\) −42.3398 −1.83222
\(535\) 9.39252 0.406074
\(536\) −28.3049 −1.22259
\(537\) −18.3428 −0.791551
\(538\) 4.58766 0.197788
\(539\) −4.08151 −0.175803
\(540\) −77.9373 −3.35389
\(541\) 7.05717 0.303411 0.151706 0.988426i \(-0.451523\pi\)
0.151706 + 0.988426i \(0.451523\pi\)
\(542\) 16.8887 0.725431
\(543\) −4.83983 −0.207697
\(544\) 26.7083 1.14511
\(545\) 15.4601 0.662239
\(546\) −32.1072 −1.37406
\(547\) −37.1334 −1.58771 −0.793854 0.608109i \(-0.791928\pi\)
−0.793854 + 0.608109i \(0.791928\pi\)
\(548\) 27.9660 1.19465
\(549\) 8.17820 0.349037
\(550\) 6.90458 0.294412
\(551\) 19.1046 0.813881
\(552\) −6.06938 −0.258330
\(553\) 28.7797 1.22384
\(554\) 40.6411 1.72668
\(555\) 28.9814 1.23019
\(556\) 39.2897 1.66625
\(557\) 33.0107 1.39871 0.699355 0.714775i \(-0.253471\pi\)
0.699355 + 0.714775i \(0.253471\pi\)
\(558\) −98.5678 −4.17271
\(559\) 5.83768 0.246908
\(560\) −23.8266 −1.00686
\(561\) 18.5564 0.783452
\(562\) 38.3409 1.61731
\(563\) −0.884460 −0.0372755 −0.0186378 0.999826i \(-0.505933\pi\)
−0.0186378 + 0.999826i \(0.505933\pi\)
\(564\) −14.4696 −0.609280
\(565\) 21.1616 0.890275
\(566\) −55.0220 −2.31275
\(567\) −23.8387 −1.00113
\(568\) 20.7220 0.869477
\(569\) −5.12423 −0.214819 −0.107410 0.994215i \(-0.534256\pi\)
−0.107410 + 0.994215i \(0.534256\pi\)
\(570\) 91.4592 3.83080
\(571\) −0.674828 −0.0282407 −0.0141203 0.999900i \(-0.504495\pi\)
−0.0141203 + 0.999900i \(0.504495\pi\)
\(572\) 12.1355 0.507411
\(573\) 55.4757 2.31753
\(574\) −43.8560 −1.83051
\(575\) 0.662611 0.0276328
\(576\) −0.292303 −0.0121793
\(577\) −18.0723 −0.752362 −0.376181 0.926546i \(-0.622763\pi\)
−0.376181 + 0.926546i \(0.622763\pi\)
\(578\) −14.0767 −0.585514
\(579\) −62.7530 −2.60793
\(580\) 21.0554 0.874279
\(581\) 20.9494 0.869127
\(582\) −65.1876 −2.70211
\(583\) −0.254233 −0.0105293
\(584\) 25.0781 1.03774
\(585\) 22.7463 0.940444
\(586\) −44.0665 −1.82037
\(587\) −38.8470 −1.60339 −0.801693 0.597736i \(-0.796067\pi\)
−0.801693 + 0.597736i \(0.796067\pi\)
\(588\) 43.8132 1.80683
\(589\) 42.1865 1.73827
\(590\) 5.58808 0.230057
\(591\) 26.5291 1.09126
\(592\) −40.1710 −1.65102
\(593\) −28.1628 −1.15651 −0.578253 0.815858i \(-0.696265\pi\)
−0.578253 + 0.815858i \(0.696265\pi\)
\(594\) 33.3128 1.36684
\(595\) 15.7230 0.644579
\(596\) 14.8718 0.609171
\(597\) −64.1754 −2.62652
\(598\) 1.68317 0.0688298
\(599\) 8.01136 0.327335 0.163668 0.986516i \(-0.447668\pi\)
0.163668 + 0.986516i \(0.447668\pi\)
\(600\) −41.1157 −1.67854
\(601\) −31.6868 −1.29253 −0.646265 0.763113i \(-0.723670\pi\)
−0.646265 + 0.763113i \(0.723670\pi\)
\(602\) 13.7429 0.560117
\(603\) 28.2844 1.15183
\(604\) −37.3014 −1.51777
\(605\) −15.8949 −0.646219
\(606\) −98.5184 −4.00204
\(607\) −1.05334 −0.0427538 −0.0213769 0.999771i \(-0.506805\pi\)
−0.0213769 + 0.999771i \(0.506805\pi\)
\(608\) −38.9312 −1.57887
\(609\) 16.4750 0.667603
\(610\) −5.57533 −0.225739
\(611\) 2.22600 0.0900545
\(612\) −135.241 −5.46679
\(613\) −18.1006 −0.731075 −0.365538 0.930797i \(-0.619115\pi\)
−0.365538 + 0.930797i \(0.619115\pi\)
\(614\) −21.5908 −0.871335
\(615\) 45.7622 1.84531
\(616\) 15.8483 0.638545
\(617\) 4.02776 0.162152 0.0810758 0.996708i \(-0.474164\pi\)
0.0810758 + 0.996708i \(0.474164\pi\)
\(618\) −19.6672 −0.791131
\(619\) −25.7600 −1.03538 −0.517690 0.855568i \(-0.673208\pi\)
−0.517690 + 0.855568i \(0.673208\pi\)
\(620\) 46.4944 1.86726
\(621\) 3.19693 0.128288
\(622\) 68.7414 2.75628
\(623\) 10.6098 0.425073
\(624\) −46.4381 −1.85901
\(625\) −9.91798 −0.396719
\(626\) 16.9536 0.677601
\(627\) −27.0487 −1.08022
\(628\) 102.680 4.09737
\(629\) 26.5085 1.05696
\(630\) 53.5485 2.13342
\(631\) 5.70380 0.227065 0.113532 0.993534i \(-0.463783\pi\)
0.113532 + 0.993534i \(0.463783\pi\)
\(632\) 93.6182 3.72393
\(633\) 56.0379 2.22731
\(634\) −4.84462 −0.192404
\(635\) 30.7033 1.21842
\(636\) 2.72908 0.108215
\(637\) −6.74023 −0.267058
\(638\) −8.99973 −0.356303
\(639\) −20.7070 −0.819155
\(640\) 19.3040 0.763059
\(641\) 13.3053 0.525526 0.262763 0.964860i \(-0.415366\pi\)
0.262763 + 0.964860i \(0.415366\pi\)
\(642\) 43.0955 1.70084
\(643\) −6.25771 −0.246780 −0.123390 0.992358i \(-0.539377\pi\)
−0.123390 + 0.992358i \(0.539377\pi\)
\(644\) 2.74168 0.108037
\(645\) −14.3402 −0.564645
\(646\) 83.6554 3.29138
\(647\) −13.2687 −0.521646 −0.260823 0.965387i \(-0.583994\pi\)
−0.260823 + 0.965387i \(0.583994\pi\)
\(648\) −77.5453 −3.04627
\(649\) −1.65265 −0.0648722
\(650\) 11.4023 0.447233
\(651\) 36.3801 1.42585
\(652\) 59.2514 2.32047
\(653\) −35.0646 −1.37218 −0.686091 0.727516i \(-0.740675\pi\)
−0.686091 + 0.727516i \(0.740675\pi\)
\(654\) 70.9353 2.77379
\(655\) 36.0958 1.41038
\(656\) −63.4309 −2.47656
\(657\) −25.0599 −0.977679
\(658\) 5.24038 0.204291
\(659\) −17.9489 −0.699192 −0.349596 0.936901i \(-0.613681\pi\)
−0.349596 + 0.936901i \(0.613681\pi\)
\(660\) −29.8108 −1.16038
\(661\) 31.8572 1.23910 0.619551 0.784956i \(-0.287315\pi\)
0.619551 + 0.784956i \(0.287315\pi\)
\(662\) −42.9425 −1.66901
\(663\) 30.6441 1.19012
\(664\) 68.1468 2.64461
\(665\) −22.9185 −0.888742
\(666\) 90.2816 3.49834
\(667\) −0.863677 −0.0334417
\(668\) 15.2004 0.588122
\(669\) 45.0242 1.74073
\(670\) −19.2823 −0.744942
\(671\) 1.64888 0.0636543
\(672\) −33.5728 −1.29510
\(673\) −25.1467 −0.969334 −0.484667 0.874699i \(-0.661059\pi\)
−0.484667 + 0.874699i \(0.661059\pi\)
\(674\) 34.9367 1.34571
\(675\) 21.6569 0.833575
\(676\) −38.3518 −1.47507
\(677\) 29.6637 1.14007 0.570035 0.821621i \(-0.306930\pi\)
0.570035 + 0.821621i \(0.306930\pi\)
\(678\) 97.0952 3.72892
\(679\) 16.3352 0.626887
\(680\) 51.1456 1.96134
\(681\) 25.6664 0.983537
\(682\) −19.8731 −0.760982
\(683\) 13.3108 0.509325 0.254662 0.967030i \(-0.418036\pi\)
0.254662 + 0.967030i \(0.418036\pi\)
\(684\) 197.134 7.53759
\(685\) 10.5685 0.403803
\(686\) −50.6760 −1.93482
\(687\) −63.2389 −2.41272
\(688\) 19.8769 0.757800
\(689\) −0.419842 −0.0159947
\(690\) −4.13468 −0.157404
\(691\) 22.1038 0.840867 0.420433 0.907323i \(-0.361878\pi\)
0.420433 + 0.907323i \(0.361878\pi\)
\(692\) −5.92685 −0.225305
\(693\) −15.8368 −0.601588
\(694\) −6.69239 −0.254040
\(695\) 14.8478 0.563210
\(696\) 53.5921 2.03140
\(697\) 41.8576 1.58547
\(698\) −46.3285 −1.75356
\(699\) 67.7963 2.56429
\(700\) 18.5729 0.701991
\(701\) 33.2557 1.25605 0.628026 0.778192i \(-0.283863\pi\)
0.628026 + 0.778192i \(0.283863\pi\)
\(702\) 55.0129 2.07633
\(703\) −38.6401 −1.45734
\(704\) −0.0589339 −0.00222115
\(705\) −5.46815 −0.205943
\(706\) 74.0746 2.78784
\(707\) 24.6875 0.928467
\(708\) 17.7405 0.666727
\(709\) −21.4090 −0.804033 −0.402016 0.915633i \(-0.631690\pi\)
−0.402016 + 0.915633i \(0.631690\pi\)
\(710\) 14.1166 0.529786
\(711\) −93.5502 −3.50841
\(712\) 34.5129 1.29343
\(713\) −1.90716 −0.0714239
\(714\) 72.1413 2.69982
\(715\) 4.58609 0.171510
\(716\) 26.9533 1.00729
\(717\) −7.99989 −0.298761
\(718\) 51.3598 1.91673
\(719\) −34.4595 −1.28512 −0.642561 0.766234i \(-0.722128\pi\)
−0.642561 + 0.766234i \(0.722128\pi\)
\(720\) 77.4497 2.88638
\(721\) 4.92835 0.183541
\(722\) −73.5302 −2.73651
\(723\) −11.8886 −0.442141
\(724\) 7.11175 0.264306
\(725\) −5.85080 −0.217293
\(726\) −72.9301 −2.70669
\(727\) 0.0869977 0.00322657 0.00161328 0.999999i \(-0.499486\pi\)
0.00161328 + 0.999999i \(0.499486\pi\)
\(728\) 26.1719 0.969995
\(729\) −16.2507 −0.601876
\(730\) 17.0841 0.632310
\(731\) −13.1166 −0.485136
\(732\) −17.7000 −0.654211
\(733\) −30.1407 −1.11327 −0.556636 0.830757i \(-0.687908\pi\)
−0.556636 + 0.830757i \(0.687908\pi\)
\(734\) −23.8001 −0.878477
\(735\) 16.5573 0.610725
\(736\) 1.76000 0.0648744
\(737\) 5.70267 0.210060
\(738\) 142.557 5.24758
\(739\) −12.4239 −0.457021 −0.228510 0.973541i \(-0.573385\pi\)
−0.228510 + 0.973541i \(0.573385\pi\)
\(740\) −42.5858 −1.56549
\(741\) −44.6683 −1.64093
\(742\) −0.988377 −0.0362845
\(743\) −36.1729 −1.32705 −0.663527 0.748152i \(-0.730941\pi\)
−0.663527 + 0.748152i \(0.730941\pi\)
\(744\) 118.342 4.33861
\(745\) 5.62013 0.205906
\(746\) −38.5811 −1.41255
\(747\) −68.0972 −2.49155
\(748\) −27.2672 −0.996986
\(749\) −10.7992 −0.394594
\(750\) −94.1114 −3.43646
\(751\) 34.6758 1.26534 0.632670 0.774422i \(-0.281959\pi\)
0.632670 + 0.774422i \(0.281959\pi\)
\(752\) 7.57940 0.276392
\(753\) 48.4846 1.76688
\(754\) −14.8622 −0.541249
\(755\) −14.0965 −0.513023
\(756\) 89.6096 3.25907
\(757\) 7.74052 0.281334 0.140667 0.990057i \(-0.455075\pi\)
0.140667 + 0.990057i \(0.455075\pi\)
\(758\) 16.2832 0.591432
\(759\) 1.22281 0.0443853
\(760\) −74.5522 −2.70429
\(761\) −48.6175 −1.76238 −0.881191 0.472760i \(-0.843258\pi\)
−0.881191 + 0.472760i \(0.843258\pi\)
\(762\) 140.875 5.10337
\(763\) −17.7755 −0.643516
\(764\) −81.5172 −2.94919
\(765\) −51.1084 −1.84783
\(766\) −0.310938 −0.0112346
\(767\) −2.72919 −0.0985455
\(768\) 88.2906 3.18591
\(769\) 0.979541 0.0353231 0.0176616 0.999844i \(-0.494378\pi\)
0.0176616 + 0.999844i \(0.494378\pi\)
\(770\) 10.7964 0.389075
\(771\) 42.2807 1.52270
\(772\) 92.2106 3.31873
\(773\) 1.19604 0.0430186 0.0215093 0.999769i \(-0.493153\pi\)
0.0215093 + 0.999769i \(0.493153\pi\)
\(774\) −44.6720 −1.60570
\(775\) −12.9197 −0.464089
\(776\) 53.1371 1.90751
\(777\) −33.3217 −1.19541
\(778\) −16.4088 −0.588286
\(779\) −61.0135 −2.18604
\(780\) −49.2296 −1.76270
\(781\) −4.17492 −0.149390
\(782\) −3.78189 −0.135240
\(783\) −28.2286 −1.00881
\(784\) −22.9500 −0.819644
\(785\) 38.8033 1.38495
\(786\) 165.617 5.90738
\(787\) −22.6952 −0.808997 −0.404499 0.914539i \(-0.632554\pi\)
−0.404499 + 0.914539i \(0.632554\pi\)
\(788\) −38.9824 −1.38869
\(789\) 84.3681 3.00358
\(790\) 63.7761 2.26905
\(791\) −24.3308 −0.865105
\(792\) −51.5158 −1.83053
\(793\) 2.72297 0.0966954
\(794\) 54.4960 1.93399
\(795\) 1.03134 0.0365778
\(796\) 94.3007 3.34240
\(797\) 31.4101 1.11260 0.556301 0.830981i \(-0.312220\pi\)
0.556301 + 0.830981i \(0.312220\pi\)
\(798\) −105.156 −3.72250
\(799\) −5.00159 −0.176943
\(800\) 11.9227 0.421532
\(801\) −34.4879 −1.21857
\(802\) 3.07376 0.108538
\(803\) −5.05255 −0.178300
\(804\) −61.2156 −2.15891
\(805\) 1.03610 0.0365177
\(806\) −32.8186 −1.15599
\(807\) 5.50400 0.193750
\(808\) 80.3064 2.82517
\(809\) 19.1638 0.673764 0.336882 0.941547i \(-0.390628\pi\)
0.336882 + 0.941547i \(0.390628\pi\)
\(810\) −52.8266 −1.85614
\(811\) 39.6043 1.39070 0.695348 0.718673i \(-0.255250\pi\)
0.695348 + 0.718673i \(0.255250\pi\)
\(812\) −24.2088 −0.849562
\(813\) 20.2620 0.710620
\(814\) 18.2025 0.637997
\(815\) 22.3915 0.784340
\(816\) 104.341 3.65267
\(817\) 19.1194 0.668903
\(818\) −71.9791 −2.51669
\(819\) −26.1529 −0.913856
\(820\) −67.2440 −2.34826
\(821\) 36.9958 1.29116 0.645582 0.763691i \(-0.276615\pi\)
0.645582 + 0.763691i \(0.276615\pi\)
\(822\) 48.4914 1.69133
\(823\) 20.1681 0.703016 0.351508 0.936185i \(-0.385669\pi\)
0.351508 + 0.936185i \(0.385669\pi\)
\(824\) 16.0316 0.558486
\(825\) 8.28369 0.288401
\(826\) −6.42497 −0.223553
\(827\) 39.7977 1.38390 0.691951 0.721945i \(-0.256751\pi\)
0.691951 + 0.721945i \(0.256751\pi\)
\(828\) −8.91199 −0.309713
\(829\) 13.1943 0.458256 0.229128 0.973396i \(-0.426412\pi\)
0.229128 + 0.973396i \(0.426412\pi\)
\(830\) 46.4240 1.61140
\(831\) 48.7587 1.69142
\(832\) −0.0973236 −0.00337409
\(833\) 15.1446 0.524728
\(834\) 68.1259 2.35901
\(835\) 5.74434 0.198791
\(836\) 39.7459 1.37464
\(837\) −62.3341 −2.15458
\(838\) −6.52116 −0.225270
\(839\) 34.5099 1.19141 0.595707 0.803202i \(-0.296872\pi\)
0.595707 + 0.803202i \(0.296872\pi\)
\(840\) −64.2910 −2.21825
\(841\) −21.3738 −0.737028
\(842\) 79.6310 2.74427
\(843\) 45.9991 1.58429
\(844\) −82.3433 −2.83437
\(845\) −14.4934 −0.498587
\(846\) −17.0342 −0.585647
\(847\) 18.2754 0.627949
\(848\) −1.42953 −0.0490904
\(849\) −66.0120 −2.26553
\(850\) −25.6196 −0.878745
\(851\) 1.74684 0.0598808
\(852\) 44.8159 1.53537
\(853\) −19.8552 −0.679828 −0.339914 0.940456i \(-0.610398\pi\)
−0.339914 + 0.940456i \(0.610398\pi\)
\(854\) 6.41031 0.219356
\(855\) 74.4980 2.54778
\(856\) −35.1289 −1.20068
\(857\) −30.3386 −1.03635 −0.518173 0.855276i \(-0.673388\pi\)
−0.518173 + 0.855276i \(0.673388\pi\)
\(858\) 21.0422 0.718370
\(859\) −30.2650 −1.03263 −0.516315 0.856399i \(-0.672696\pi\)
−0.516315 + 0.856399i \(0.672696\pi\)
\(860\) 21.0718 0.718542
\(861\) −52.6158 −1.79314
\(862\) −47.0641 −1.60301
\(863\) −47.6875 −1.62330 −0.811651 0.584143i \(-0.801431\pi\)
−0.811651 + 0.584143i \(0.801431\pi\)
\(864\) 57.5241 1.95701
\(865\) −2.23980 −0.0761553
\(866\) −42.5189 −1.44485
\(867\) −16.8884 −0.573559
\(868\) −53.4576 −1.81447
\(869\) −18.8615 −0.639832
\(870\) 36.5088 1.23777
\(871\) 9.41741 0.319097
\(872\) −57.8223 −1.95811
\(873\) −53.0985 −1.79711
\(874\) 5.51265 0.186468
\(875\) 23.5831 0.797255
\(876\) 54.2368 1.83249
\(877\) 18.0714 0.610229 0.305115 0.952316i \(-0.401305\pi\)
0.305115 + 0.952316i \(0.401305\pi\)
\(878\) −13.8444 −0.467227
\(879\) −52.8683 −1.78320
\(880\) 15.6153 0.526392
\(881\) 16.2125 0.546213 0.273107 0.961984i \(-0.411949\pi\)
0.273107 + 0.961984i \(0.411949\pi\)
\(882\) 51.5786 1.73674
\(883\) 37.3852 1.25811 0.629056 0.777360i \(-0.283442\pi\)
0.629056 + 0.777360i \(0.283442\pi\)
\(884\) −45.0291 −1.51449
\(885\) 6.70423 0.225360
\(886\) −51.5417 −1.73158
\(887\) 4.92612 0.165403 0.0827014 0.996574i \(-0.473645\pi\)
0.0827014 + 0.996574i \(0.473645\pi\)
\(888\) −108.393 −3.63743
\(889\) −35.3016 −1.18398
\(890\) 23.5114 0.788105
\(891\) 15.6233 0.523399
\(892\) −66.1594 −2.21518
\(893\) 7.29054 0.243969
\(894\) 25.7867 0.862437
\(895\) 10.1858 0.340475
\(896\) −22.1951 −0.741486
\(897\) 2.01936 0.0674245
\(898\) 82.8926 2.76616
\(899\) 16.8401 0.561648
\(900\) −60.3724 −2.01241
\(901\) 0.943338 0.0314272
\(902\) 28.7421 0.957008
\(903\) 16.4878 0.548681
\(904\) −79.1464 −2.63237
\(905\) 2.68758 0.0893380
\(906\) −64.6784 −2.14880
\(907\) 28.4442 0.944474 0.472237 0.881472i \(-0.343447\pi\)
0.472237 + 0.881472i \(0.343447\pi\)
\(908\) −37.7147 −1.25161
\(909\) −80.2481 −2.66166
\(910\) 17.8292 0.591033
\(911\) −8.58577 −0.284459 −0.142230 0.989834i \(-0.545427\pi\)
−0.142230 + 0.989834i \(0.545427\pi\)
\(912\) −152.093 −5.03629
\(913\) −13.7297 −0.454387
\(914\) 21.3667 0.706746
\(915\) −6.68894 −0.221130
\(916\) 92.9246 3.07032
\(917\) −41.5016 −1.37050
\(918\) −123.608 −4.07967
\(919\) 23.6006 0.778513 0.389257 0.921129i \(-0.372732\pi\)
0.389257 + 0.921129i \(0.372732\pi\)
\(920\) 3.37035 0.111117
\(921\) −25.9034 −0.853545
\(922\) 73.5857 2.42342
\(923\) −6.89448 −0.226935
\(924\) 34.2753 1.12758
\(925\) 11.8336 0.389086
\(926\) 23.6747 0.777999
\(927\) −16.0199 −0.526163
\(928\) −15.5406 −0.510146
\(929\) 28.0146 0.919128 0.459564 0.888145i \(-0.348006\pi\)
0.459564 + 0.888145i \(0.348006\pi\)
\(930\) 80.6185 2.64358
\(931\) −22.0754 −0.723492
\(932\) −99.6213 −3.26320
\(933\) 82.4717 2.70000
\(934\) 3.39476 0.111080
\(935\) −10.3044 −0.336991
\(936\) −85.0734 −2.78071
\(937\) −34.4427 −1.12520 −0.562598 0.826731i \(-0.690198\pi\)
−0.562598 + 0.826731i \(0.690198\pi\)
\(938\) 22.1701 0.723881
\(939\) 20.3399 0.663767
\(940\) 8.03502 0.262074
\(941\) −9.61440 −0.313420 −0.156710 0.987645i \(-0.550089\pi\)
−0.156710 + 0.987645i \(0.550089\pi\)
\(942\) 178.040 5.80087
\(943\) 2.75829 0.0898224
\(944\) −9.29272 −0.302452
\(945\) 33.8640 1.10160
\(946\) −9.00672 −0.292834
\(947\) −31.7865 −1.03292 −0.516461 0.856310i \(-0.672751\pi\)
−0.516461 + 0.856310i \(0.672751\pi\)
\(948\) 202.470 6.57591
\(949\) −8.34380 −0.270851
\(950\) 37.3443 1.21161
\(951\) −5.81228 −0.188476
\(952\) −58.8054 −1.90589
\(953\) 48.9178 1.58460 0.792302 0.610129i \(-0.208882\pi\)
0.792302 + 0.610129i \(0.208882\pi\)
\(954\) 3.21278 0.104018
\(955\) −30.8059 −0.996855
\(956\) 11.7552 0.380191
\(957\) −10.7973 −0.349028
\(958\) −55.0015 −1.77702
\(959\) −12.1513 −0.392387
\(960\) 0.239074 0.00771609
\(961\) 6.18614 0.199553
\(962\) 30.0597 0.969163
\(963\) 35.1034 1.13119
\(964\) 17.4693 0.562649
\(965\) 34.8470 1.12176
\(966\) 4.75390 0.152954
\(967\) −35.3648 −1.13725 −0.568627 0.822595i \(-0.692525\pi\)
−0.568627 + 0.822595i \(0.692525\pi\)
\(968\) 59.4484 1.91074
\(969\) 100.365 3.22418
\(970\) 36.1989 1.16228
\(971\) 27.7055 0.889113 0.444556 0.895751i \(-0.353361\pi\)
0.444556 + 0.895751i \(0.353361\pi\)
\(972\) −29.9657 −0.961150
\(973\) −17.0715 −0.547286
\(974\) −44.3822 −1.42210
\(975\) 13.6797 0.438102
\(976\) 9.27153 0.296774
\(977\) 25.9738 0.830974 0.415487 0.909599i \(-0.363611\pi\)
0.415487 + 0.909599i \(0.363611\pi\)
\(978\) 102.738 3.28521
\(979\) −6.95341 −0.222232
\(980\) −24.3297 −0.777182
\(981\) 57.7803 1.84478
\(982\) 4.73681 0.151158
\(983\) −1.36130 −0.0434187 −0.0217094 0.999764i \(-0.506911\pi\)
−0.0217094 + 0.999764i \(0.506911\pi\)
\(984\) −171.155 −5.45623
\(985\) −14.7317 −0.469391
\(986\) 33.3937 1.06347
\(987\) 6.28709 0.200120
\(988\) 65.6365 2.08818
\(989\) −0.864348 −0.0274847
\(990\) −35.0944 −1.11537
\(991\) −7.15478 −0.227279 −0.113639 0.993522i \(-0.536251\pi\)
−0.113639 + 0.993522i \(0.536251\pi\)
\(992\) −34.3167 −1.08956
\(993\) −51.5198 −1.63493
\(994\) −16.2307 −0.514808
\(995\) 35.6368 1.12976
\(996\) 147.382 4.66998
\(997\) −41.9249 −1.32777 −0.663887 0.747833i \(-0.731094\pi\)
−0.663887 + 0.747833i \(0.731094\pi\)
\(998\) 74.9738 2.37325
\(999\) 57.0939 1.80637
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 \(a_p\))