Properties

Label 4003.2.a.b.1.2
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 1.2
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78616 q^{2} -2.78181 q^{3} +5.76271 q^{4} -2.35951 q^{5} +7.75059 q^{6} +2.45659 q^{7} -10.4835 q^{8} +4.73848 q^{9} +O(q^{10})\) \(q-2.78616 q^{2} -2.78181 q^{3} +5.76271 q^{4} -2.35951 q^{5} +7.75059 q^{6} +2.45659 q^{7} -10.4835 q^{8} +4.73848 q^{9} +6.57398 q^{10} -0.138384 q^{11} -16.0308 q^{12} -0.680783 q^{13} -6.84446 q^{14} +6.56371 q^{15} +17.6834 q^{16} -1.50415 q^{17} -13.2022 q^{18} +1.47256 q^{19} -13.5972 q^{20} -6.83377 q^{21} +0.385559 q^{22} +1.82601 q^{23} +29.1632 q^{24} +0.567284 q^{25} +1.89677 q^{26} -4.83613 q^{27} +14.1566 q^{28} +1.90185 q^{29} -18.2876 q^{30} +2.55278 q^{31} -28.3018 q^{32} +0.384957 q^{33} +4.19081 q^{34} -5.79634 q^{35} +27.3065 q^{36} +3.62223 q^{37} -4.10280 q^{38} +1.89381 q^{39} +24.7360 q^{40} +0.248958 q^{41} +19.0400 q^{42} -9.11424 q^{43} -0.797464 q^{44} -11.1805 q^{45} -5.08756 q^{46} -5.29370 q^{47} -49.1919 q^{48} -0.965176 q^{49} -1.58055 q^{50} +4.18426 q^{51} -3.92315 q^{52} +0.0647470 q^{53} +13.4743 q^{54} +0.326517 q^{55} -25.7537 q^{56} -4.09639 q^{57} -5.29887 q^{58} +3.82392 q^{59} +37.8248 q^{60} -2.71113 q^{61} -7.11247 q^{62} +11.6405 q^{63} +43.4866 q^{64} +1.60631 q^{65} -1.07255 q^{66} -10.4681 q^{67} -8.66798 q^{68} -5.07961 q^{69} +16.1496 q^{70} -9.64129 q^{71} -49.6760 q^{72} +2.70366 q^{73} -10.0921 q^{74} -1.57808 q^{75} +8.48595 q^{76} -0.339951 q^{77} -5.27647 q^{78} +15.7292 q^{79} -41.7241 q^{80} -0.762228 q^{81} -0.693638 q^{82} -8.01504 q^{83} -39.3810 q^{84} +3.54906 q^{85} +25.3938 q^{86} -5.29059 q^{87} +1.45075 q^{88} +3.06706 q^{89} +31.1507 q^{90} -1.67240 q^{91} +10.5228 q^{92} -7.10136 q^{93} +14.7491 q^{94} -3.47453 q^{95} +78.7302 q^{96} -3.37079 q^{97} +2.68914 q^{98} -0.655728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78616 −1.97012 −0.985058 0.172225i \(-0.944904\pi\)
−0.985058 + 0.172225i \(0.944904\pi\)
\(3\) −2.78181 −1.60608 −0.803040 0.595925i \(-0.796786\pi\)
−0.803040 + 0.595925i \(0.796786\pi\)
\(4\) 5.76271 2.88135
\(5\) −2.35951 −1.05520 −0.527602 0.849492i \(-0.676909\pi\)
−0.527602 + 0.849492i \(0.676909\pi\)
\(6\) 7.75059 3.16416
\(7\) 2.45659 0.928503 0.464251 0.885703i \(-0.346323\pi\)
0.464251 + 0.885703i \(0.346323\pi\)
\(8\) −10.4835 −3.70648
\(9\) 4.73848 1.57949
\(10\) 6.57398 2.07887
\(11\) −0.138384 −0.0417242 −0.0208621 0.999782i \(-0.506641\pi\)
−0.0208621 + 0.999782i \(0.506641\pi\)
\(12\) −16.0308 −4.62769
\(13\) −0.680783 −0.188815 −0.0944076 0.995534i \(-0.530096\pi\)
−0.0944076 + 0.995534i \(0.530096\pi\)
\(14\) −6.84446 −1.82926
\(15\) 6.56371 1.69474
\(16\) 17.6834 4.42085
\(17\) −1.50415 −0.364810 −0.182405 0.983223i \(-0.558388\pi\)
−0.182405 + 0.983223i \(0.558388\pi\)
\(18\) −13.2022 −3.11179
\(19\) 1.47256 0.337829 0.168915 0.985631i \(-0.445974\pi\)
0.168915 + 0.985631i \(0.445974\pi\)
\(20\) −13.5972 −3.04042
\(21\) −6.83377 −1.49125
\(22\) 0.385559 0.0822015
\(23\) 1.82601 0.380749 0.190375 0.981712i \(-0.439030\pi\)
0.190375 + 0.981712i \(0.439030\pi\)
\(24\) 29.1632 5.95291
\(25\) 0.567284 0.113457
\(26\) 1.89677 0.371988
\(27\) −4.83613 −0.930714
\(28\) 14.1566 2.67535
\(29\) 1.90185 0.353165 0.176582 0.984286i \(-0.443496\pi\)
0.176582 + 0.984286i \(0.443496\pi\)
\(30\) −18.2876 −3.33884
\(31\) 2.55278 0.458493 0.229247 0.973368i \(-0.426374\pi\)
0.229247 + 0.973368i \(0.426374\pi\)
\(32\) −28.3018 −5.00309
\(33\) 0.384957 0.0670125
\(34\) 4.19081 0.718718
\(35\) −5.79634 −0.979761
\(36\) 27.3065 4.55108
\(37\) 3.62223 0.595490 0.297745 0.954645i \(-0.403765\pi\)
0.297745 + 0.954645i \(0.403765\pi\)
\(38\) −4.10280 −0.665562
\(39\) 1.89381 0.303252
\(40\) 24.7360 3.91110
\(41\) 0.248958 0.0388807 0.0194404 0.999811i \(-0.493812\pi\)
0.0194404 + 0.999811i \(0.493812\pi\)
\(42\) 19.0400 2.93794
\(43\) −9.11424 −1.38991 −0.694955 0.719054i \(-0.744576\pi\)
−0.694955 + 0.719054i \(0.744576\pi\)
\(44\) −0.797464 −0.120222
\(45\) −11.1805 −1.66669
\(46\) −5.08756 −0.750119
\(47\) −5.29370 −0.772166 −0.386083 0.922464i \(-0.626172\pi\)
−0.386083 + 0.922464i \(0.626172\pi\)
\(48\) −49.1919 −7.10023
\(49\) −0.965176 −0.137882
\(50\) −1.58055 −0.223523
\(51\) 4.18426 0.585914
\(52\) −3.92315 −0.544043
\(53\) 0.0647470 0.00889369 0.00444684 0.999990i \(-0.498585\pi\)
0.00444684 + 0.999990i \(0.498585\pi\)
\(54\) 13.4743 1.83361
\(55\) 0.326517 0.0440276
\(56\) −25.7537 −3.44148
\(57\) −4.09639 −0.542581
\(58\) −5.29887 −0.695775
\(59\) 3.82392 0.497832 0.248916 0.968525i \(-0.419926\pi\)
0.248916 + 0.968525i \(0.419926\pi\)
\(60\) 37.8248 4.88316
\(61\) −2.71113 −0.347125 −0.173563 0.984823i \(-0.555528\pi\)
−0.173563 + 0.984823i \(0.555528\pi\)
\(62\) −7.11247 −0.903284
\(63\) 11.6405 1.46657
\(64\) 43.4866 5.43582
\(65\) 1.60631 0.199239
\(66\) −1.07255 −0.132022
\(67\) −10.4681 −1.27888 −0.639439 0.768842i \(-0.720833\pi\)
−0.639439 + 0.768842i \(0.720833\pi\)
\(68\) −8.66798 −1.05115
\(69\) −5.07961 −0.611514
\(70\) 16.1496 1.93024
\(71\) −9.64129 −1.14421 −0.572105 0.820180i \(-0.693873\pi\)
−0.572105 + 0.820180i \(0.693873\pi\)
\(72\) −49.6760 −5.85437
\(73\) 2.70366 0.316439 0.158220 0.987404i \(-0.449425\pi\)
0.158220 + 0.987404i \(0.449425\pi\)
\(74\) −10.0921 −1.17318
\(75\) −1.57808 −0.182221
\(76\) 8.48595 0.973405
\(77\) −0.339951 −0.0387411
\(78\) −5.27647 −0.597442
\(79\) 15.7292 1.76967 0.884835 0.465904i \(-0.154271\pi\)
0.884835 + 0.465904i \(0.154271\pi\)
\(80\) −41.7241 −4.66490
\(81\) −0.762228 −0.0846920
\(82\) −0.693638 −0.0765995
\(83\) −8.01504 −0.879765 −0.439882 0.898055i \(-0.644980\pi\)
−0.439882 + 0.898055i \(0.644980\pi\)
\(84\) −39.3810 −4.29682
\(85\) 3.54906 0.384949
\(86\) 25.3938 2.73828
\(87\) −5.29059 −0.567211
\(88\) 1.45075 0.154650
\(89\) 3.06706 0.325108 0.162554 0.986700i \(-0.448027\pi\)
0.162554 + 0.986700i \(0.448027\pi\)
\(90\) 31.1507 3.28357
\(91\) −1.67240 −0.175315
\(92\) 10.5228 1.09707
\(93\) −7.10136 −0.736377
\(94\) 14.7491 1.52126
\(95\) −3.47453 −0.356479
\(96\) 78.7302 8.03537
\(97\) −3.37079 −0.342251 −0.171126 0.985249i \(-0.554740\pi\)
−0.171126 + 0.985249i \(0.554740\pi\)
\(98\) 2.68914 0.271644
\(99\) −0.655728 −0.0659032
\(100\) 3.26909 0.326909
\(101\) 15.1986 1.51232 0.756161 0.654386i \(-0.227073\pi\)
0.756161 + 0.654386i \(0.227073\pi\)
\(102\) −11.6580 −1.15432
\(103\) 12.4258 1.22435 0.612175 0.790722i \(-0.290295\pi\)
0.612175 + 0.790722i \(0.290295\pi\)
\(104\) 7.13700 0.699840
\(105\) 16.1243 1.57357
\(106\) −0.180396 −0.0175216
\(107\) −10.1051 −0.976900 −0.488450 0.872592i \(-0.662438\pi\)
−0.488450 + 0.872592i \(0.662438\pi\)
\(108\) −27.8692 −2.68172
\(109\) −3.57337 −0.342267 −0.171133 0.985248i \(-0.554743\pi\)
−0.171133 + 0.985248i \(0.554743\pi\)
\(110\) −0.909731 −0.0867394
\(111\) −10.0764 −0.956406
\(112\) 43.4408 4.10477
\(113\) 5.74911 0.540831 0.270415 0.962744i \(-0.412839\pi\)
0.270415 + 0.962744i \(0.412839\pi\)
\(114\) 11.4132 1.06895
\(115\) −4.30848 −0.401768
\(116\) 10.9598 1.01759
\(117\) −3.22588 −0.298233
\(118\) −10.6541 −0.980786
\(119\) −3.69508 −0.338727
\(120\) −68.8108 −6.28154
\(121\) −10.9808 −0.998259
\(122\) 7.55367 0.683877
\(123\) −0.692555 −0.0624456
\(124\) 14.7109 1.32108
\(125\) 10.4590 0.935485
\(126\) −32.4323 −2.88930
\(127\) 0.775797 0.0688409 0.0344204 0.999407i \(-0.489041\pi\)
0.0344204 + 0.999407i \(0.489041\pi\)
\(128\) −64.5572 −5.70610
\(129\) 25.3541 2.23231
\(130\) −4.47545 −0.392523
\(131\) −17.1620 −1.49945 −0.749727 0.661748i \(-0.769815\pi\)
−0.749727 + 0.661748i \(0.769815\pi\)
\(132\) 2.21840 0.193087
\(133\) 3.61748 0.313675
\(134\) 29.1657 2.51954
\(135\) 11.4109 0.982094
\(136\) 15.7688 1.35216
\(137\) 22.1747 1.89451 0.947256 0.320477i \(-0.103843\pi\)
0.947256 + 0.320477i \(0.103843\pi\)
\(138\) 14.1526 1.20475
\(139\) −4.43049 −0.375789 −0.187895 0.982189i \(-0.560166\pi\)
−0.187895 + 0.982189i \(0.560166\pi\)
\(140\) −33.4026 −2.82304
\(141\) 14.7261 1.24016
\(142\) 26.8622 2.25423
\(143\) 0.0942092 0.00787817
\(144\) 83.7924 6.98270
\(145\) −4.48743 −0.372661
\(146\) −7.53283 −0.623421
\(147\) 2.68494 0.221450
\(148\) 20.8738 1.71582
\(149\) 4.14488 0.339562 0.169781 0.985482i \(-0.445694\pi\)
0.169781 + 0.985482i \(0.445694\pi\)
\(150\) 4.39678 0.358996
\(151\) 22.5025 1.83123 0.915615 0.402056i \(-0.131704\pi\)
0.915615 + 0.402056i \(0.131704\pi\)
\(152\) −15.4376 −1.25216
\(153\) −7.12739 −0.576215
\(154\) 0.947160 0.0763244
\(155\) −6.02331 −0.483804
\(156\) 10.9135 0.873777
\(157\) 3.20028 0.255410 0.127705 0.991812i \(-0.459239\pi\)
0.127705 + 0.991812i \(0.459239\pi\)
\(158\) −43.8241 −3.48645
\(159\) −0.180114 −0.0142840
\(160\) 66.7783 5.27928
\(161\) 4.48575 0.353527
\(162\) 2.12369 0.166853
\(163\) 4.14993 0.325048 0.162524 0.986705i \(-0.448037\pi\)
0.162524 + 0.986705i \(0.448037\pi\)
\(164\) 1.43467 0.112029
\(165\) −0.908310 −0.0707119
\(166\) 22.3312 1.73324
\(167\) 8.00279 0.619275 0.309637 0.950855i \(-0.399792\pi\)
0.309637 + 0.950855i \(0.399792\pi\)
\(168\) 71.6419 5.52730
\(169\) −12.5365 −0.964349
\(170\) −9.88825 −0.758394
\(171\) 6.97771 0.533599
\(172\) −52.5227 −4.00482
\(173\) 21.4081 1.62763 0.813814 0.581126i \(-0.197388\pi\)
0.813814 + 0.581126i \(0.197388\pi\)
\(174\) 14.7405 1.11747
\(175\) 1.39358 0.105345
\(176\) −2.44709 −0.184456
\(177\) −10.6374 −0.799558
\(178\) −8.54533 −0.640500
\(179\) 2.24317 0.167663 0.0838313 0.996480i \(-0.473284\pi\)
0.0838313 + 0.996480i \(0.473284\pi\)
\(180\) −64.4299 −4.80232
\(181\) 9.92890 0.738010 0.369005 0.929427i \(-0.379699\pi\)
0.369005 + 0.929427i \(0.379699\pi\)
\(182\) 4.65959 0.345392
\(183\) 7.54187 0.557511
\(184\) −19.1430 −1.41124
\(185\) −8.54668 −0.628364
\(186\) 19.7856 1.45075
\(187\) 0.208150 0.0152214
\(188\) −30.5060 −2.22488
\(189\) −11.8804 −0.864171
\(190\) 9.68060 0.702304
\(191\) −13.8419 −1.00157 −0.500783 0.865573i \(-0.666955\pi\)
−0.500783 + 0.865573i \(0.666955\pi\)
\(192\) −120.971 −8.73036
\(193\) 2.22573 0.160211 0.0801057 0.996786i \(-0.474474\pi\)
0.0801057 + 0.996786i \(0.474474\pi\)
\(194\) 9.39156 0.674275
\(195\) −4.46846 −0.319993
\(196\) −5.56202 −0.397287
\(197\) −6.14052 −0.437494 −0.218747 0.975782i \(-0.570197\pi\)
−0.218747 + 0.975782i \(0.570197\pi\)
\(198\) 1.82697 0.129837
\(199\) 4.08396 0.289504 0.144752 0.989468i \(-0.453762\pi\)
0.144752 + 0.989468i \(0.453762\pi\)
\(200\) −5.94713 −0.420526
\(201\) 29.1202 2.05398
\(202\) −42.3459 −2.97945
\(203\) 4.67206 0.327915
\(204\) 24.1127 1.68823
\(205\) −0.587419 −0.0410271
\(206\) −34.6203 −2.41211
\(207\) 8.65251 0.601391
\(208\) −12.0385 −0.834723
\(209\) −0.203779 −0.0140957
\(210\) −44.9250 −3.10012
\(211\) 4.17352 0.287317 0.143658 0.989627i \(-0.454113\pi\)
0.143658 + 0.989627i \(0.454113\pi\)
\(212\) 0.373118 0.0256259
\(213\) 26.8203 1.83769
\(214\) 28.1546 1.92461
\(215\) 21.5051 1.46664
\(216\) 50.6997 3.44968
\(217\) 6.27113 0.425712
\(218\) 9.95599 0.674305
\(219\) −7.52107 −0.508226
\(220\) 1.88162 0.126859
\(221\) 1.02400 0.0688817
\(222\) 28.0744 1.88423
\(223\) 3.28589 0.220039 0.110020 0.993929i \(-0.464909\pi\)
0.110020 + 0.993929i \(0.464909\pi\)
\(224\) −69.5258 −4.64539
\(225\) 2.68806 0.179204
\(226\) −16.0180 −1.06550
\(227\) 3.95863 0.262743 0.131372 0.991333i \(-0.458062\pi\)
0.131372 + 0.991333i \(0.458062\pi\)
\(228\) −23.6063 −1.56337
\(229\) 14.5005 0.958218 0.479109 0.877756i \(-0.340960\pi\)
0.479109 + 0.877756i \(0.340960\pi\)
\(230\) 12.0041 0.791530
\(231\) 0.945681 0.0622213
\(232\) −19.9381 −1.30900
\(233\) −15.9449 −1.04459 −0.522293 0.852766i \(-0.674923\pi\)
−0.522293 + 0.852766i \(0.674923\pi\)
\(234\) 8.98782 0.587552
\(235\) 12.4905 0.814793
\(236\) 22.0361 1.43443
\(237\) −43.7556 −2.84223
\(238\) 10.2951 0.667331
\(239\) 11.9436 0.772566 0.386283 0.922380i \(-0.373759\pi\)
0.386283 + 0.922380i \(0.373759\pi\)
\(240\) 116.069 7.49220
\(241\) −12.4483 −0.801865 −0.400933 0.916108i \(-0.631314\pi\)
−0.400933 + 0.916108i \(0.631314\pi\)
\(242\) 30.5944 1.96669
\(243\) 16.6288 1.06674
\(244\) −15.6235 −1.00019
\(245\) 2.27734 0.145494
\(246\) 1.92957 0.123025
\(247\) −1.00250 −0.0637873
\(248\) −26.7621 −1.69940
\(249\) 22.2963 1.41297
\(250\) −29.1406 −1.84301
\(251\) 21.6969 1.36950 0.684749 0.728779i \(-0.259912\pi\)
0.684749 + 0.728779i \(0.259912\pi\)
\(252\) 67.0808 4.22569
\(253\) −0.252690 −0.0158865
\(254\) −2.16150 −0.135624
\(255\) −9.87281 −0.618259
\(256\) 92.8937 5.80586
\(257\) 4.43881 0.276885 0.138443 0.990370i \(-0.455790\pi\)
0.138443 + 0.990370i \(0.455790\pi\)
\(258\) −70.6407 −4.39790
\(259\) 8.89832 0.552915
\(260\) 9.25671 0.574077
\(261\) 9.01189 0.557822
\(262\) 47.8162 2.95410
\(263\) 23.9884 1.47919 0.739595 0.673052i \(-0.235017\pi\)
0.739595 + 0.673052i \(0.235017\pi\)
\(264\) −4.03571 −0.248381
\(265\) −0.152771 −0.00938466
\(266\) −10.0789 −0.617977
\(267\) −8.53199 −0.522149
\(268\) −60.3244 −3.68490
\(269\) −17.2625 −1.05252 −0.526258 0.850325i \(-0.676405\pi\)
−0.526258 + 0.850325i \(0.676405\pi\)
\(270\) −31.7926 −1.93484
\(271\) 27.6909 1.68210 0.841050 0.540957i \(-0.181938\pi\)
0.841050 + 0.540957i \(0.181938\pi\)
\(272\) −26.5985 −1.61277
\(273\) 4.65231 0.281571
\(274\) −61.7824 −3.73241
\(275\) −0.0785028 −0.00473389
\(276\) −29.2723 −1.76199
\(277\) −25.2031 −1.51431 −0.757155 0.653236i \(-0.773411\pi\)
−0.757155 + 0.653236i \(0.773411\pi\)
\(278\) 12.3441 0.740348
\(279\) 12.0963 0.724187
\(280\) 60.7661 3.63147
\(281\) 13.8534 0.826425 0.413213 0.910635i \(-0.364407\pi\)
0.413213 + 0.910635i \(0.364407\pi\)
\(282\) −41.0293 −2.44326
\(283\) −23.8314 −1.41663 −0.708315 0.705897i \(-0.750544\pi\)
−0.708315 + 0.705897i \(0.750544\pi\)
\(284\) −55.5599 −3.29688
\(285\) 9.66548 0.572534
\(286\) −0.262482 −0.0155209
\(287\) 0.611588 0.0361009
\(288\) −134.107 −7.90235
\(289\) −14.7375 −0.866914
\(290\) 12.5027 0.734185
\(291\) 9.37689 0.549683
\(292\) 15.5804 0.911773
\(293\) −11.0617 −0.646232 −0.323116 0.946359i \(-0.604730\pi\)
−0.323116 + 0.946359i \(0.604730\pi\)
\(294\) −7.48068 −0.436282
\(295\) −9.02257 −0.525314
\(296\) −37.9737 −2.20718
\(297\) 0.669242 0.0388333
\(298\) −11.5483 −0.668976
\(299\) −1.24312 −0.0718912
\(300\) −9.09400 −0.525042
\(301\) −22.3899 −1.29053
\(302\) −62.6957 −3.60773
\(303\) −42.2798 −2.42891
\(304\) 26.0399 1.49349
\(305\) 6.39695 0.366288
\(306\) 19.8581 1.13521
\(307\) 5.73042 0.327053 0.163526 0.986539i \(-0.447713\pi\)
0.163526 + 0.986539i \(0.447713\pi\)
\(308\) −1.95904 −0.111627
\(309\) −34.5662 −1.96640
\(310\) 16.7819 0.953150
\(311\) −14.1231 −0.800847 −0.400423 0.916330i \(-0.631137\pi\)
−0.400423 + 0.916330i \(0.631137\pi\)
\(312\) −19.8538 −1.12400
\(313\) −10.2147 −0.577370 −0.288685 0.957424i \(-0.593218\pi\)
−0.288685 + 0.957424i \(0.593218\pi\)
\(314\) −8.91650 −0.503187
\(315\) −27.4659 −1.54753
\(316\) 90.6426 5.09905
\(317\) −14.8650 −0.834904 −0.417452 0.908699i \(-0.637077\pi\)
−0.417452 + 0.908699i \(0.637077\pi\)
\(318\) 0.501827 0.0281411
\(319\) −0.263185 −0.0147355
\(320\) −102.607 −5.73590
\(321\) 28.1106 1.56898
\(322\) −12.4980 −0.696488
\(323\) −2.21496 −0.123243
\(324\) −4.39250 −0.244028
\(325\) −0.386197 −0.0214224
\(326\) −11.5624 −0.640381
\(327\) 9.94044 0.549708
\(328\) −2.60996 −0.144111
\(329\) −13.0044 −0.716958
\(330\) 2.53070 0.139311
\(331\) −23.5116 −1.29231 −0.646157 0.763205i \(-0.723625\pi\)
−0.646157 + 0.763205i \(0.723625\pi\)
\(332\) −46.1883 −2.53491
\(333\) 17.1639 0.940574
\(334\) −22.2971 −1.22004
\(335\) 24.6995 1.34948
\(336\) −120.844 −6.59259
\(337\) 24.2855 1.32292 0.661459 0.749982i \(-0.269938\pi\)
0.661459 + 0.749982i \(0.269938\pi\)
\(338\) 34.9288 1.89988
\(339\) −15.9930 −0.868618
\(340\) 20.4522 1.10917
\(341\) −0.353263 −0.0191303
\(342\) −19.4411 −1.05125
\(343\) −19.5672 −1.05653
\(344\) 95.5493 5.15167
\(345\) 11.9854 0.645272
\(346\) −59.6465 −3.20661
\(347\) −22.5345 −1.20971 −0.604857 0.796334i \(-0.706770\pi\)
−0.604857 + 0.796334i \(0.706770\pi\)
\(348\) −30.4881 −1.63434
\(349\) −16.2237 −0.868433 −0.434217 0.900808i \(-0.642975\pi\)
−0.434217 + 0.900808i \(0.642975\pi\)
\(350\) −3.88275 −0.207542
\(351\) 3.29236 0.175733
\(352\) 3.91650 0.208750
\(353\) −21.3489 −1.13629 −0.568143 0.822930i \(-0.692338\pi\)
−0.568143 + 0.822930i \(0.692338\pi\)
\(354\) 29.6376 1.57522
\(355\) 22.7487 1.20738
\(356\) 17.6746 0.936750
\(357\) 10.2790 0.544023
\(358\) −6.24985 −0.330315
\(359\) 12.4901 0.659200 0.329600 0.944121i \(-0.393086\pi\)
0.329600 + 0.944121i \(0.393086\pi\)
\(360\) 117.211 6.17756
\(361\) −16.8316 −0.885871
\(362\) −27.6635 −1.45396
\(363\) 30.5467 1.60328
\(364\) −9.63757 −0.505146
\(365\) −6.37930 −0.333908
\(366\) −21.0129 −1.09836
\(367\) 34.3580 1.79347 0.896736 0.442566i \(-0.145932\pi\)
0.896736 + 0.442566i \(0.145932\pi\)
\(368\) 32.2900 1.68323
\(369\) 1.17968 0.0614119
\(370\) 23.8124 1.23795
\(371\) 0.159057 0.00825782
\(372\) −40.9231 −2.12176
\(373\) −32.2616 −1.67044 −0.835220 0.549916i \(-0.814660\pi\)
−0.835220 + 0.549916i \(0.814660\pi\)
\(374\) −0.579939 −0.0299879
\(375\) −29.0951 −1.50246
\(376\) 55.4966 2.86202
\(377\) −1.29475 −0.0666829
\(378\) 33.1007 1.70252
\(379\) 19.7648 1.01525 0.507624 0.861578i \(-0.330524\pi\)
0.507624 + 0.861578i \(0.330524\pi\)
\(380\) −20.0227 −1.02714
\(381\) −2.15812 −0.110564
\(382\) 38.5659 1.97320
\(383\) 24.7371 1.26401 0.632004 0.774965i \(-0.282233\pi\)
0.632004 + 0.774965i \(0.282233\pi\)
\(384\) 179.586 9.16446
\(385\) 0.802119 0.0408798
\(386\) −6.20124 −0.315635
\(387\) −43.1877 −2.19535
\(388\) −19.4248 −0.986147
\(389\) −33.1677 −1.68167 −0.840835 0.541291i \(-0.817936\pi\)
−0.840835 + 0.541291i \(0.817936\pi\)
\(390\) 12.4499 0.630424
\(391\) −2.74659 −0.138901
\(392\) 10.1184 0.511058
\(393\) 47.7415 2.40824
\(394\) 17.1085 0.861913
\(395\) −37.1131 −1.86736
\(396\) −3.77877 −0.189890
\(397\) −10.9404 −0.549082 −0.274541 0.961575i \(-0.588526\pi\)
−0.274541 + 0.961575i \(0.588526\pi\)
\(398\) −11.3786 −0.570357
\(399\) −10.0632 −0.503788
\(400\) 10.0315 0.501575
\(401\) −3.38038 −0.168808 −0.0844041 0.996432i \(-0.526899\pi\)
−0.0844041 + 0.996432i \(0.526899\pi\)
\(402\) −81.1336 −4.04658
\(403\) −1.73789 −0.0865705
\(404\) 87.5853 4.35753
\(405\) 1.79848 0.0893674
\(406\) −13.0171 −0.646029
\(407\) −0.501257 −0.0248464
\(408\) −43.8658 −2.17168
\(409\) 1.18141 0.0584170 0.0292085 0.999573i \(-0.490701\pi\)
0.0292085 + 0.999573i \(0.490701\pi\)
\(410\) 1.63665 0.0808282
\(411\) −61.6859 −3.04274
\(412\) 71.6062 3.52779
\(413\) 9.39379 0.462238
\(414\) −24.1073 −1.18481
\(415\) 18.9116 0.928332
\(416\) 19.2674 0.944660
\(417\) 12.3248 0.603548
\(418\) 0.567760 0.0277701
\(419\) −20.1230 −0.983072 −0.491536 0.870857i \(-0.663564\pi\)
−0.491536 + 0.870857i \(0.663564\pi\)
\(420\) 92.9198 4.53402
\(421\) −12.5742 −0.612830 −0.306415 0.951898i \(-0.599130\pi\)
−0.306415 + 0.951898i \(0.599130\pi\)
\(422\) −11.6281 −0.566047
\(423\) −25.0841 −1.21963
\(424\) −0.678777 −0.0329643
\(425\) −0.853280 −0.0413901
\(426\) −74.7257 −3.62047
\(427\) −6.66014 −0.322307
\(428\) −58.2329 −2.81480
\(429\) −0.262072 −0.0126530
\(430\) −59.9168 −2.88945
\(431\) 6.18173 0.297763 0.148882 0.988855i \(-0.452433\pi\)
0.148882 + 0.988855i \(0.452433\pi\)
\(432\) −85.5192 −4.11454
\(433\) 21.8245 1.04882 0.524410 0.851466i \(-0.324286\pi\)
0.524410 + 0.851466i \(0.324286\pi\)
\(434\) −17.4724 −0.838702
\(435\) 12.4832 0.598524
\(436\) −20.5923 −0.986191
\(437\) 2.68891 0.128628
\(438\) 20.9549 1.00126
\(439\) −34.0658 −1.62587 −0.812936 0.582353i \(-0.802132\pi\)
−0.812936 + 0.582353i \(0.802132\pi\)
\(440\) −3.42305 −0.163188
\(441\) −4.57347 −0.217784
\(442\) −2.85303 −0.135705
\(443\) −38.9813 −1.85206 −0.926028 0.377454i \(-0.876800\pi\)
−0.926028 + 0.377454i \(0.876800\pi\)
\(444\) −58.0671 −2.75574
\(445\) −7.23676 −0.343055
\(446\) −9.15501 −0.433502
\(447\) −11.5303 −0.545364
\(448\) 106.829 5.04718
\(449\) −9.15764 −0.432176 −0.216088 0.976374i \(-0.569330\pi\)
−0.216088 + 0.976374i \(0.569330\pi\)
\(450\) −7.48939 −0.353053
\(451\) −0.0344517 −0.00162227
\(452\) 33.1305 1.55833
\(453\) −62.5978 −2.94110
\(454\) −11.0294 −0.517635
\(455\) 3.94605 0.184994
\(456\) 42.9446 2.01107
\(457\) −36.7056 −1.71702 −0.858509 0.512799i \(-0.828609\pi\)
−0.858509 + 0.512799i \(0.828609\pi\)
\(458\) −40.4007 −1.88780
\(459\) 7.27427 0.339534
\(460\) −24.8285 −1.15764
\(461\) 23.1718 1.07922 0.539609 0.841916i \(-0.318572\pi\)
0.539609 + 0.841916i \(0.318572\pi\)
\(462\) −2.63482 −0.122583
\(463\) 12.7507 0.592575 0.296287 0.955099i \(-0.404251\pi\)
0.296287 + 0.955099i \(0.404251\pi\)
\(464\) 33.6311 1.56129
\(465\) 16.7557 0.777028
\(466\) 44.4251 2.05795
\(467\) −6.10730 −0.282612 −0.141306 0.989966i \(-0.545130\pi\)
−0.141306 + 0.989966i \(0.545130\pi\)
\(468\) −18.5898 −0.859313
\(469\) −25.7157 −1.18744
\(470\) −34.8007 −1.60524
\(471\) −8.90257 −0.410209
\(472\) −40.0881 −1.84521
\(473\) 1.26126 0.0579929
\(474\) 121.910 5.59953
\(475\) 0.835361 0.0383290
\(476\) −21.2936 −0.975993
\(477\) 0.306803 0.0140475
\(478\) −33.2768 −1.52204
\(479\) 34.2474 1.56480 0.782401 0.622774i \(-0.213995\pi\)
0.782401 + 0.622774i \(0.213995\pi\)
\(480\) −185.765 −8.47896
\(481\) −2.46595 −0.112438
\(482\) 34.6830 1.57977
\(483\) −12.4785 −0.567792
\(484\) −63.2794 −2.87634
\(485\) 7.95340 0.361145
\(486\) −46.3305 −2.10159
\(487\) −27.1478 −1.23018 −0.615091 0.788456i \(-0.710881\pi\)
−0.615091 + 0.788456i \(0.710881\pi\)
\(488\) 28.4222 1.28661
\(489\) −11.5443 −0.522053
\(490\) −6.34504 −0.286640
\(491\) 27.4521 1.23890 0.619448 0.785038i \(-0.287356\pi\)
0.619448 + 0.785038i \(0.287356\pi\)
\(492\) −3.99099 −0.179928
\(493\) −2.86067 −0.128838
\(494\) 2.79312 0.125668
\(495\) 1.54720 0.0695413
\(496\) 45.1418 2.02693
\(497\) −23.6847 −1.06240
\(498\) −62.1212 −2.78372
\(499\) −15.0332 −0.672976 −0.336488 0.941688i \(-0.609239\pi\)
−0.336488 + 0.941688i \(0.609239\pi\)
\(500\) 60.2724 2.69546
\(501\) −22.2623 −0.994605
\(502\) −60.4512 −2.69807
\(503\) 22.5820 1.00688 0.503441 0.864030i \(-0.332067\pi\)
0.503441 + 0.864030i \(0.332067\pi\)
\(504\) −122.033 −5.43580
\(505\) −35.8613 −1.59581
\(506\) 0.704035 0.0312982
\(507\) 34.8743 1.54882
\(508\) 4.47069 0.198355
\(509\) 6.76934 0.300046 0.150023 0.988683i \(-0.452065\pi\)
0.150023 + 0.988683i \(0.452065\pi\)
\(510\) 27.5073 1.21804
\(511\) 6.64177 0.293815
\(512\) −129.703 −5.73210
\(513\) −7.12151 −0.314422
\(514\) −12.3672 −0.545496
\(515\) −29.3188 −1.29194
\(516\) 146.108 6.43206
\(517\) 0.732561 0.0322180
\(518\) −24.7922 −1.08931
\(519\) −59.5533 −2.61410
\(520\) −16.8398 −0.738475
\(521\) 15.3206 0.671208 0.335604 0.942003i \(-0.391060\pi\)
0.335604 + 0.942003i \(0.391060\pi\)
\(522\) −25.1086 −1.09897
\(523\) −25.4831 −1.11430 −0.557149 0.830413i \(-0.688105\pi\)
−0.557149 + 0.830413i \(0.688105\pi\)
\(524\) −98.8997 −4.32046
\(525\) −3.87669 −0.169192
\(526\) −66.8357 −2.91418
\(527\) −3.83977 −0.167263
\(528\) 6.80735 0.296252
\(529\) −19.6657 −0.855030
\(530\) 0.425646 0.0184889
\(531\) 18.1196 0.786323
\(532\) 20.8465 0.903810
\(533\) −0.169486 −0.00734127
\(534\) 23.7715 1.02869
\(535\) 23.8432 1.03083
\(536\) 109.742 4.74014
\(537\) −6.24009 −0.269280
\(538\) 48.0962 2.07358
\(539\) 0.133564 0.00575303
\(540\) 65.7577 2.82976
\(541\) −6.68551 −0.287433 −0.143716 0.989619i \(-0.545905\pi\)
−0.143716 + 0.989619i \(0.545905\pi\)
\(542\) −77.1513 −3.31393
\(543\) −27.6204 −1.18530
\(544\) 42.5701 1.82518
\(545\) 8.43140 0.361161
\(546\) −12.9621 −0.554727
\(547\) 12.3659 0.528726 0.264363 0.964423i \(-0.414838\pi\)
0.264363 + 0.964423i \(0.414838\pi\)
\(548\) 127.786 5.45876
\(549\) −12.8467 −0.548282
\(550\) 0.218722 0.00932632
\(551\) 2.80059 0.119309
\(552\) 53.2522 2.26657
\(553\) 38.6401 1.64314
\(554\) 70.2200 2.98336
\(555\) 23.7753 1.00920
\(556\) −25.5316 −1.08278
\(557\) 6.92959 0.293616 0.146808 0.989165i \(-0.453100\pi\)
0.146808 + 0.989165i \(0.453100\pi\)
\(558\) −33.7023 −1.42673
\(559\) 6.20482 0.262436
\(560\) −102.499 −4.33137
\(561\) −0.579033 −0.0244468
\(562\) −38.5979 −1.62815
\(563\) 23.2223 0.978701 0.489351 0.872087i \(-0.337234\pi\)
0.489351 + 0.872087i \(0.337234\pi\)
\(564\) 84.8621 3.57334
\(565\) −13.5651 −0.570687
\(566\) 66.3982 2.79092
\(567\) −1.87248 −0.0786368
\(568\) 101.075 4.24100
\(569\) 24.0327 1.00750 0.503751 0.863849i \(-0.331953\pi\)
0.503751 + 0.863849i \(0.331953\pi\)
\(570\) −26.9296 −1.12796
\(571\) −3.11778 −0.130475 −0.0652376 0.997870i \(-0.520781\pi\)
−0.0652376 + 0.997870i \(0.520781\pi\)
\(572\) 0.542900 0.0226998
\(573\) 38.5056 1.60860
\(574\) −1.70398 −0.0711229
\(575\) 1.03586 0.0431985
\(576\) 206.060 8.58585
\(577\) −32.7678 −1.36414 −0.682071 0.731286i \(-0.738920\pi\)
−0.682071 + 0.731286i \(0.738920\pi\)
\(578\) 41.0612 1.70792
\(579\) −6.19156 −0.257312
\(580\) −25.8598 −1.07377
\(581\) −19.6896 −0.816864
\(582\) −26.1256 −1.08294
\(583\) −0.00895993 −0.000371082 0
\(584\) −28.3438 −1.17288
\(585\) 7.61149 0.314696
\(586\) 30.8197 1.27315
\(587\) −10.2378 −0.422559 −0.211280 0.977426i \(-0.567763\pi\)
−0.211280 + 0.977426i \(0.567763\pi\)
\(588\) 15.4725 0.638076
\(589\) 3.75913 0.154892
\(590\) 25.1384 1.03493
\(591\) 17.0818 0.702650
\(592\) 64.0532 2.63257
\(593\) 9.57768 0.393308 0.196654 0.980473i \(-0.436992\pi\)
0.196654 + 0.980473i \(0.436992\pi\)
\(594\) −1.86462 −0.0765062
\(595\) 8.71857 0.357426
\(596\) 23.8857 0.978398
\(597\) −11.3608 −0.464967
\(598\) 3.46352 0.141634
\(599\) −14.5078 −0.592771 −0.296386 0.955068i \(-0.595781\pi\)
−0.296386 + 0.955068i \(0.595781\pi\)
\(600\) 16.5438 0.675398
\(601\) 10.8864 0.444065 0.222032 0.975039i \(-0.428731\pi\)
0.222032 + 0.975039i \(0.428731\pi\)
\(602\) 62.3820 2.54250
\(603\) −49.6027 −2.01998
\(604\) 129.676 5.27642
\(605\) 25.9094 1.05337
\(606\) 117.798 4.78523
\(607\) −26.1804 −1.06263 −0.531314 0.847175i \(-0.678302\pi\)
−0.531314 + 0.847175i \(0.678302\pi\)
\(608\) −41.6761 −1.69019
\(609\) −12.9968 −0.526657
\(610\) −17.8229 −0.721630
\(611\) 3.60386 0.145797
\(612\) −41.0731 −1.66028
\(613\) 3.53300 0.142697 0.0713483 0.997451i \(-0.477270\pi\)
0.0713483 + 0.997451i \(0.477270\pi\)
\(614\) −15.9659 −0.644331
\(615\) 1.63409 0.0658929
\(616\) 3.56389 0.143593
\(617\) −27.1679 −1.09374 −0.546869 0.837218i \(-0.684180\pi\)
−0.546869 + 0.837218i \(0.684180\pi\)
\(618\) 96.3072 3.87404
\(619\) −18.0672 −0.726180 −0.363090 0.931754i \(-0.618278\pi\)
−0.363090 + 0.931754i \(0.618278\pi\)
\(620\) −34.7106 −1.39401
\(621\) −8.83082 −0.354369
\(622\) 39.3492 1.57776
\(623\) 7.53450 0.301863
\(624\) 33.4890 1.34063
\(625\) −27.5146 −1.10058
\(626\) 28.4599 1.13749
\(627\) 0.566874 0.0226388
\(628\) 18.4423 0.735926
\(629\) −5.44837 −0.217241
\(630\) 76.5244 3.04881
\(631\) −10.5147 −0.418582 −0.209291 0.977853i \(-0.567116\pi\)
−0.209291 + 0.977853i \(0.567116\pi\)
\(632\) −164.897 −6.55925
\(633\) −11.6099 −0.461454
\(634\) 41.4165 1.64486
\(635\) −1.83050 −0.0726412
\(636\) −1.03795 −0.0411572
\(637\) 0.657075 0.0260343
\(638\) 0.733276 0.0290307
\(639\) −45.6851 −1.80727
\(640\) 152.323 6.02110
\(641\) −37.3825 −1.47652 −0.738259 0.674517i \(-0.764352\pi\)
−0.738259 + 0.674517i \(0.764352\pi\)
\(642\) −78.3207 −3.09107
\(643\) 34.7285 1.36956 0.684779 0.728751i \(-0.259899\pi\)
0.684779 + 0.728751i \(0.259899\pi\)
\(644\) 25.8501 1.01864
\(645\) −59.8233 −2.35554
\(646\) 6.17123 0.242804
\(647\) 17.0898 0.671871 0.335936 0.941885i \(-0.390948\pi\)
0.335936 + 0.941885i \(0.390948\pi\)
\(648\) 7.99083 0.313909
\(649\) −0.529168 −0.0207716
\(650\) 1.07601 0.0422045
\(651\) −17.4451 −0.683728
\(652\) 23.9148 0.936577
\(653\) −13.3860 −0.523834 −0.261917 0.965090i \(-0.584355\pi\)
−0.261917 + 0.965090i \(0.584355\pi\)
\(654\) −27.6957 −1.08299
\(655\) 40.4940 1.58223
\(656\) 4.40242 0.171886
\(657\) 12.8112 0.499814
\(658\) 36.2325 1.41249
\(659\) −10.1851 −0.396755 −0.198378 0.980126i \(-0.563567\pi\)
−0.198378 + 0.980126i \(0.563567\pi\)
\(660\) −5.23433 −0.203746
\(661\) 43.2412 1.68189 0.840943 0.541124i \(-0.182001\pi\)
0.840943 + 0.541124i \(0.182001\pi\)
\(662\) 65.5071 2.54601
\(663\) −2.84857 −0.110629
\(664\) 84.0258 3.26083
\(665\) −8.53548 −0.330992
\(666\) −47.8213 −1.85304
\(667\) 3.47279 0.134467
\(668\) 46.1177 1.78435
\(669\) −9.14072 −0.353401
\(670\) −68.8168 −2.65863
\(671\) 0.375177 0.0144835
\(672\) 193.408 7.46086
\(673\) 16.7291 0.644858 0.322429 0.946594i \(-0.395501\pi\)
0.322429 + 0.946594i \(0.395501\pi\)
\(674\) −67.6635 −2.60630
\(675\) −2.74346 −0.105596
\(676\) −72.2444 −2.77863
\(677\) −35.7189 −1.37279 −0.686395 0.727229i \(-0.740808\pi\)
−0.686395 + 0.727229i \(0.740808\pi\)
\(678\) 44.5590 1.71128
\(679\) −8.28063 −0.317781
\(680\) −37.2066 −1.42681
\(681\) −11.0122 −0.421987
\(682\) 0.984249 0.0376888
\(683\) 9.02420 0.345302 0.172651 0.984983i \(-0.444767\pi\)
0.172651 + 0.984983i \(0.444767\pi\)
\(684\) 40.2105 1.53749
\(685\) −52.3214 −1.99910
\(686\) 54.5173 2.08148
\(687\) −40.3376 −1.53897
\(688\) −161.171 −6.14457
\(689\) −0.0440787 −0.00167926
\(690\) −33.3933 −1.27126
\(691\) −22.1594 −0.842985 −0.421492 0.906832i \(-0.638494\pi\)
−0.421492 + 0.906832i \(0.638494\pi\)
\(692\) 123.369 4.68977
\(693\) −1.61085 −0.0611913
\(694\) 62.7848 2.38328
\(695\) 10.4538 0.396535
\(696\) 55.4640 2.10236
\(697\) −0.374470 −0.0141841
\(698\) 45.2018 1.71091
\(699\) 44.3558 1.67769
\(700\) 8.03081 0.303536
\(701\) 24.9200 0.941216 0.470608 0.882342i \(-0.344035\pi\)
0.470608 + 0.882342i \(0.344035\pi\)
\(702\) −9.17305 −0.346214
\(703\) 5.33396 0.201174
\(704\) −6.01783 −0.226805
\(705\) −34.7463 −1.30862
\(706\) 59.4815 2.23862
\(707\) 37.3368 1.40419
\(708\) −61.3004 −2.30381
\(709\) 47.4707 1.78280 0.891400 0.453218i \(-0.149724\pi\)
0.891400 + 0.453218i \(0.149724\pi\)
\(710\) −63.3816 −2.37867
\(711\) 74.5324 2.79518
\(712\) −32.1536 −1.20501
\(713\) 4.66140 0.174571
\(714\) −28.6390 −1.07179
\(715\) −0.222287 −0.00831308
\(716\) 12.9267 0.483095
\(717\) −33.2248 −1.24080
\(718\) −34.7993 −1.29870
\(719\) −34.9420 −1.30312 −0.651558 0.758599i \(-0.725884\pi\)
−0.651558 + 0.758599i \(0.725884\pi\)
\(720\) −197.709 −7.36818
\(721\) 30.5251 1.13681
\(722\) 46.8955 1.74527
\(723\) 34.6288 1.28786
\(724\) 57.2174 2.12647
\(725\) 1.07889 0.0400689
\(726\) −85.1080 −3.15865
\(727\) −13.4471 −0.498725 −0.249362 0.968410i \(-0.580221\pi\)
−0.249362 + 0.968410i \(0.580221\pi\)
\(728\) 17.5327 0.649804
\(729\) −43.9715 −1.62857
\(730\) 17.7738 0.657837
\(731\) 13.7092 0.507053
\(732\) 43.4616 1.60639
\(733\) −37.8624 −1.39848 −0.699240 0.714887i \(-0.746478\pi\)
−0.699240 + 0.714887i \(0.746478\pi\)
\(734\) −95.7269 −3.53335
\(735\) −6.33514 −0.233675
\(736\) −51.6792 −1.90492
\(737\) 1.44861 0.0533602
\(738\) −3.28679 −0.120988
\(739\) −31.8895 −1.17307 −0.586537 0.809922i \(-0.699509\pi\)
−0.586537 + 0.809922i \(0.699509\pi\)
\(740\) −49.2520 −1.81054
\(741\) 2.78876 0.102447
\(742\) −0.443158 −0.0162689
\(743\) −9.02167 −0.330973 −0.165487 0.986212i \(-0.552919\pi\)
−0.165487 + 0.986212i \(0.552919\pi\)
\(744\) 74.4473 2.72937
\(745\) −9.77989 −0.358307
\(746\) 89.8860 3.29096
\(747\) −37.9791 −1.38958
\(748\) 1.19951 0.0438583
\(749\) −24.8242 −0.907055
\(750\) 81.0636 2.96003
\(751\) −1.61806 −0.0590438 −0.0295219 0.999564i \(-0.509398\pi\)
−0.0295219 + 0.999564i \(0.509398\pi\)
\(752\) −93.6105 −3.41362
\(753\) −60.3568 −2.19952
\(754\) 3.60738 0.131373
\(755\) −53.0949 −1.93232
\(756\) −68.4632 −2.48998
\(757\) 50.2345 1.82580 0.912902 0.408178i \(-0.133836\pi\)
0.912902 + 0.408178i \(0.133836\pi\)
\(758\) −55.0679 −2.00016
\(759\) 0.702935 0.0255149
\(760\) 36.4253 1.32128
\(761\) −34.8988 −1.26508 −0.632540 0.774527i \(-0.717988\pi\)
−0.632540 + 0.774527i \(0.717988\pi\)
\(762\) 6.01288 0.217824
\(763\) −8.77829 −0.317796
\(764\) −79.7669 −2.88587
\(765\) 16.8171 0.608025
\(766\) −68.9217 −2.49024
\(767\) −2.60326 −0.0939982
\(768\) −258.413 −9.32467
\(769\) 26.1574 0.943262 0.471631 0.881796i \(-0.343665\pi\)
0.471631 + 0.881796i \(0.343665\pi\)
\(770\) −2.23483 −0.0805378
\(771\) −12.3479 −0.444700
\(772\) 12.8262 0.461626
\(773\) −21.7709 −0.783044 −0.391522 0.920169i \(-0.628051\pi\)
−0.391522 + 0.920169i \(0.628051\pi\)
\(774\) 120.328 4.32510
\(775\) 1.44815 0.0520191
\(776\) 35.3377 1.26855
\(777\) −24.7535 −0.888025
\(778\) 92.4107 3.31308
\(779\) 0.366607 0.0131350
\(780\) −25.7504 −0.922014
\(781\) 1.33420 0.0477413
\(782\) 7.65245 0.273651
\(783\) −9.19760 −0.328696
\(784\) −17.0676 −0.609556
\(785\) −7.55108 −0.269510
\(786\) −133.016 −4.74451
\(787\) −15.4454 −0.550569 −0.275285 0.961363i \(-0.588772\pi\)
−0.275285 + 0.961363i \(0.588772\pi\)
\(788\) −35.3860 −1.26057
\(789\) −66.7314 −2.37570
\(790\) 103.403 3.67892
\(791\) 14.1232 0.502163
\(792\) 6.87434 0.244269
\(793\) 1.84569 0.0655425
\(794\) 30.4817 1.08175
\(795\) 0.424981 0.0150725
\(796\) 23.5347 0.834164
\(797\) −12.6298 −0.447371 −0.223685 0.974661i \(-0.571809\pi\)
−0.223685 + 0.974661i \(0.571809\pi\)
\(798\) 28.0376 0.992520
\(799\) 7.96252 0.281694
\(800\) −16.0551 −0.567634
\(801\) 14.5332 0.513506
\(802\) 9.41829 0.332571
\(803\) −0.374142 −0.0132032
\(804\) 167.811 5.91824
\(805\) −10.5842 −0.373043
\(806\) 4.84205 0.170554
\(807\) 48.0211 1.69042
\(808\) −159.335 −5.60539
\(809\) −12.8447 −0.451594 −0.225797 0.974174i \(-0.572499\pi\)
−0.225797 + 0.974174i \(0.572499\pi\)
\(810\) −5.01087 −0.176064
\(811\) −31.6401 −1.11104 −0.555518 0.831505i \(-0.687480\pi\)
−0.555518 + 0.831505i \(0.687480\pi\)
\(812\) 26.9237 0.944838
\(813\) −77.0308 −2.70159
\(814\) 1.39658 0.0489502
\(815\) −9.79180 −0.342992
\(816\) 73.9919 2.59024
\(817\) −13.4213 −0.469552
\(818\) −3.29160 −0.115088
\(819\) −7.92465 −0.276910
\(820\) −3.38512 −0.118214
\(821\) 16.8488 0.588026 0.294013 0.955801i \(-0.405009\pi\)
0.294013 + 0.955801i \(0.405009\pi\)
\(822\) 171.867 5.99455
\(823\) 20.9413 0.729967 0.364983 0.931014i \(-0.381075\pi\)
0.364983 + 0.931014i \(0.381075\pi\)
\(824\) −130.266 −4.53803
\(825\) 0.218380 0.00760302
\(826\) −26.1726 −0.910663
\(827\) 12.6356 0.439382 0.219691 0.975569i \(-0.429495\pi\)
0.219691 + 0.975569i \(0.429495\pi\)
\(828\) 49.8619 1.73282
\(829\) −34.4989 −1.19820 −0.599099 0.800675i \(-0.704474\pi\)
−0.599099 + 0.800675i \(0.704474\pi\)
\(830\) −52.6907 −1.82892
\(831\) 70.1104 2.43210
\(832\) −29.6049 −1.02637
\(833\) 1.45177 0.0503008
\(834\) −34.3389 −1.18906
\(835\) −18.8827 −0.653461
\(836\) −1.17432 −0.0406146
\(837\) −12.3456 −0.426726
\(838\) 56.0659 1.93676
\(839\) 53.6063 1.85069 0.925347 0.379122i \(-0.123774\pi\)
0.925347 + 0.379122i \(0.123774\pi\)
\(840\) −169.040 −5.83243
\(841\) −25.3830 −0.875275
\(842\) 35.0339 1.20735
\(843\) −38.5376 −1.32731
\(844\) 24.0508 0.827861
\(845\) 29.5801 1.01759
\(846\) 69.8884 2.40281
\(847\) −26.9754 −0.926887
\(848\) 1.14495 0.0393176
\(849\) 66.2945 2.27522
\(850\) 2.37738 0.0815434
\(851\) 6.61422 0.226732
\(852\) 154.557 5.29505
\(853\) −11.1450 −0.381599 −0.190799 0.981629i \(-0.561108\pi\)
−0.190799 + 0.981629i \(0.561108\pi\)
\(854\) 18.5562 0.634982
\(855\) −16.4640 −0.563056
\(856\) 105.937 3.62087
\(857\) 12.0748 0.412468 0.206234 0.978503i \(-0.433879\pi\)
0.206234 + 0.978503i \(0.433879\pi\)
\(858\) 0.730176 0.0249278
\(859\) 30.7872 1.05045 0.525223 0.850965i \(-0.323982\pi\)
0.525223 + 0.850965i \(0.323982\pi\)
\(860\) 123.928 4.22590
\(861\) −1.70132 −0.0579809
\(862\) −17.2233 −0.586628
\(863\) −52.4567 −1.78565 −0.892823 0.450407i \(-0.851279\pi\)
−0.892823 + 0.450407i \(0.851279\pi\)
\(864\) 136.871 4.65645
\(865\) −50.5126 −1.71748
\(866\) −60.8067 −2.06630
\(867\) 40.9971 1.39233
\(868\) 36.1387 1.22663
\(869\) −2.17666 −0.0738381
\(870\) −34.7802 −1.17916
\(871\) 7.12648 0.241472
\(872\) 37.4615 1.26861
\(873\) −15.9724 −0.540584
\(874\) −7.49175 −0.253412
\(875\) 25.6935 0.868600
\(876\) −43.3417 −1.46438
\(877\) 13.5145 0.456352 0.228176 0.973620i \(-0.426724\pi\)
0.228176 + 0.973620i \(0.426724\pi\)
\(878\) 94.9129 3.20316
\(879\) 30.7716 1.03790
\(880\) 5.77393 0.194639
\(881\) −34.2649 −1.15441 −0.577207 0.816598i \(-0.695857\pi\)
−0.577207 + 0.816598i \(0.695857\pi\)
\(882\) 12.7424 0.429060
\(883\) 29.3749 0.988545 0.494273 0.869307i \(-0.335434\pi\)
0.494273 + 0.869307i \(0.335434\pi\)
\(884\) 5.90101 0.198472
\(885\) 25.0991 0.843697
\(886\) 108.608 3.64877
\(887\) −18.2307 −0.612127 −0.306064 0.952011i \(-0.599012\pi\)
−0.306064 + 0.952011i \(0.599012\pi\)
\(888\) 105.636 3.54490
\(889\) 1.90581 0.0639189
\(890\) 20.1628 0.675858
\(891\) 0.105480 0.00353371
\(892\) 18.9356 0.634011
\(893\) −7.79531 −0.260860
\(894\) 32.1253 1.07443
\(895\) −5.29279 −0.176918
\(896\) −158.590 −5.29813
\(897\) 3.45811 0.115463
\(898\) 25.5147 0.851436
\(899\) 4.85501 0.161924
\(900\) 15.4905 0.516351
\(901\) −0.0973892 −0.00324451
\(902\) 0.0959881 0.00319606
\(903\) 62.2846 2.07270
\(904\) −60.2709 −2.00458
\(905\) −23.4273 −0.778751
\(906\) 174.408 5.79431
\(907\) 10.5749 0.351134 0.175567 0.984467i \(-0.443824\pi\)
0.175567 + 0.984467i \(0.443824\pi\)
\(908\) 22.8124 0.757057
\(909\) 72.0185 2.38870
\(910\) −10.9943 −0.364459
\(911\) 51.1619 1.69507 0.847535 0.530740i \(-0.178086\pi\)
0.847535 + 0.530740i \(0.178086\pi\)
\(912\) −72.4381 −2.39867
\(913\) 1.10915 0.0367075
\(914\) 102.268 3.38272
\(915\) −17.7951 −0.588288
\(916\) 83.5619 2.76096
\(917\) −42.1600 −1.39225
\(918\) −20.2673 −0.668921
\(919\) 29.2727 0.965619 0.482809 0.875725i \(-0.339616\pi\)
0.482809 + 0.875725i \(0.339616\pi\)
\(920\) 45.1681 1.48915
\(921\) −15.9410 −0.525273
\(922\) −64.5604 −2.12618
\(923\) 6.56363 0.216044
\(924\) 5.44969 0.179281
\(925\) 2.05483 0.0675624
\(926\) −35.5255 −1.16744
\(927\) 58.8794 1.93385
\(928\) −53.8257 −1.76692
\(929\) 18.8026 0.616892 0.308446 0.951242i \(-0.400191\pi\)
0.308446 + 0.951242i \(0.400191\pi\)
\(930\) −46.6842 −1.53084
\(931\) −1.42128 −0.0465806
\(932\) −91.8858 −3.00982
\(933\) 39.2878 1.28622
\(934\) 17.0159 0.556778
\(935\) −0.491131 −0.0160617
\(936\) 33.8185 1.10539
\(937\) 30.8288 1.00713 0.503567 0.863956i \(-0.332021\pi\)
0.503567 + 0.863956i \(0.332021\pi\)
\(938\) 71.6482 2.33940
\(939\) 28.4154 0.927303
\(940\) 71.9793 2.34771
\(941\) −45.9288 −1.49724 −0.748618 0.663002i \(-0.769282\pi\)
−0.748618 + 0.663002i \(0.769282\pi\)
\(942\) 24.8040 0.808159
\(943\) 0.454600 0.0148038
\(944\) 67.6198 2.20084
\(945\) 28.0319 0.911877
\(946\) −3.51408 −0.114253
\(947\) −6.31059 −0.205067 −0.102533 0.994730i \(-0.532695\pi\)
−0.102533 + 0.994730i \(0.532695\pi\)
\(948\) −252.151 −8.18948
\(949\) −1.84060 −0.0597485
\(950\) −2.32745 −0.0755125
\(951\) 41.3518 1.34092
\(952\) 38.7374 1.25549
\(953\) 9.91361 0.321133 0.160567 0.987025i \(-0.448668\pi\)
0.160567 + 0.987025i \(0.448668\pi\)
\(954\) −0.854803 −0.0276753
\(955\) 32.6601 1.05686
\(956\) 68.8274 2.22604
\(957\) 0.732131 0.0236664
\(958\) −95.4188 −3.08284
\(959\) 54.4741 1.75906
\(960\) 285.433 9.21232
\(961\) −24.4833 −0.789784
\(962\) 6.87054 0.221515
\(963\) −47.8830 −1.54301
\(964\) −71.7359 −2.31046
\(965\) −5.25163 −0.169056
\(966\) 34.7672 1.11862
\(967\) −1.46686 −0.0471710 −0.0235855 0.999722i \(-0.507508\pi\)
−0.0235855 + 0.999722i \(0.507508\pi\)
\(968\) 115.118 3.70003
\(969\) 6.16159 0.197939
\(970\) −22.1595 −0.711498
\(971\) −14.2073 −0.455935 −0.227967 0.973669i \(-0.573208\pi\)
−0.227967 + 0.973669i \(0.573208\pi\)
\(972\) 95.8268 3.07365
\(973\) −10.8839 −0.348922
\(974\) 75.6381 2.42360
\(975\) 1.07433 0.0344060
\(976\) −47.9420 −1.53459
\(977\) 8.22566 0.263162 0.131581 0.991305i \(-0.457995\pi\)
0.131581 + 0.991305i \(0.457995\pi\)
\(978\) 32.1644 1.02850
\(979\) −0.424431 −0.0135649
\(980\) 13.1236 0.419220
\(981\) −16.9323 −0.540608
\(982\) −76.4861 −2.44077
\(983\) 37.9111 1.20918 0.604588 0.796538i \(-0.293338\pi\)
0.604588 + 0.796538i \(0.293338\pi\)
\(984\) 7.26041 0.231453
\(985\) 14.4886 0.461646
\(986\) 7.97029 0.253826
\(987\) 36.1759 1.15149
\(988\) −5.77709 −0.183794
\(989\) −16.6427 −0.529207
\(990\) −4.31074 −0.137004
\(991\) −28.0450 −0.890879 −0.445440 0.895312i \(-0.646953\pi\)
−0.445440 + 0.895312i \(0.646953\pi\)
\(992\) −72.2482 −2.29388
\(993\) 65.4048 2.07556
\(994\) 65.9894 2.09306
\(995\) −9.63614 −0.305486
\(996\) 128.487 4.07127
\(997\) −21.2365 −0.672568 −0.336284 0.941761i \(-0.609170\pi\)
−0.336284 + 0.941761i \(0.609170\pi\)
\(998\) 41.8848 1.32584
\(999\) −17.5176 −0.554232
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 \(a_p\))