Properties

Label 5077.2.a.c.1.20
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +O(q^{10})\) \(q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +9.47483 q^{10} +1.22619 q^{11} -6.48530 q^{12} +5.68229 q^{13} +10.6770 q^{14} +6.94611 q^{15} +2.31159 q^{16} +0.875977 q^{17} -0.156736 q^{18} +0.266691 q^{19} -14.6944 q^{20} +7.82741 q^{21} -2.92850 q^{22} +4.72547 q^{23} +7.12553 q^{24} +10.7385 q^{25} -13.5710 q^{26} +5.13777 q^{27} -16.5588 q^{28} +3.52186 q^{29} -16.5894 q^{30} -5.19719 q^{31} +2.61854 q^{32} -2.14692 q^{33} -2.09210 q^{34} +17.7354 q^{35} +0.243080 q^{36} +0.569856 q^{37} -0.636938 q^{38} -9.94909 q^{39} +16.1451 q^{40} +7.28931 q^{41} -18.6942 q^{42} -1.60856 q^{43} +4.54179 q^{44} -0.260352 q^{45} -11.2858 q^{46} +6.34320 q^{47} -4.04734 q^{48} +12.9856 q^{49} -25.6468 q^{50} -1.53374 q^{51} +21.0472 q^{52} -6.00921 q^{53} -12.2706 q^{54} -4.86450 q^{55} +18.1935 q^{56} -0.466947 q^{57} -8.41127 q^{58} +10.6432 q^{59} +25.7283 q^{60} -14.5845 q^{61} +12.4125 q^{62} -0.293384 q^{63} -10.8770 q^{64} -22.5427 q^{65} +5.12750 q^{66} +1.39232 q^{67} +3.24462 q^{68} -8.27378 q^{69} -42.3574 q^{70} +2.69836 q^{71} -0.267077 q^{72} +5.82397 q^{73} -1.36099 q^{74} -18.8020 q^{75} +0.987820 q^{76} -5.48169 q^{77} +23.7614 q^{78} -14.5393 q^{79} -9.17048 q^{80} -9.19257 q^{81} -17.4091 q^{82} +4.36231 q^{83} +28.9927 q^{84} -3.47516 q^{85} +3.84173 q^{86} -6.16640 q^{87} -4.99015 q^{88} -3.79378 q^{89} +0.621799 q^{90} -25.4028 q^{91} +17.5031 q^{92} +9.09973 q^{93} -15.1495 q^{94} -1.05801 q^{95} -4.58479 q^{96} -2.58581 q^{97} -31.0135 q^{98} +0.0804702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38830 −1.68879 −0.844393 0.535724i \(-0.820039\pi\)
−0.844393 + 0.535724i \(0.820039\pi\)
\(3\) −1.75089 −1.01088 −0.505439 0.862862i \(-0.668670\pi\)
−0.505439 + 0.862862i \(0.668670\pi\)
\(4\) 3.70399 1.85200
\(5\) −3.96718 −1.77418 −0.887088 0.461600i \(-0.847276\pi\)
−0.887088 + 0.461600i \(0.847276\pi\)
\(6\) 4.18166 1.70716
\(7\) −4.47052 −1.68970 −0.844849 0.535004i \(-0.820310\pi\)
−0.844849 + 0.535004i \(0.820310\pi\)
\(8\) −4.06966 −1.43884
\(9\) 0.0656264 0.0218755
\(10\) 9.47483 2.99620
\(11\) 1.22619 0.369709 0.184854 0.982766i \(-0.440819\pi\)
0.184854 + 0.982766i \(0.440819\pi\)
\(12\) −6.48530 −1.87214
\(13\) 5.68229 1.57598 0.787992 0.615685i \(-0.211121\pi\)
0.787992 + 0.615685i \(0.211121\pi\)
\(14\) 10.6770 2.85354
\(15\) 6.94611 1.79348
\(16\) 2.31159 0.577896
\(17\) 0.875977 0.212456 0.106228 0.994342i \(-0.466123\pi\)
0.106228 + 0.994342i \(0.466123\pi\)
\(18\) −0.156736 −0.0369430
\(19\) 0.266691 0.0611830 0.0305915 0.999532i \(-0.490261\pi\)
0.0305915 + 0.999532i \(0.490261\pi\)
\(20\) −14.6944 −3.28577
\(21\) 7.82741 1.70808
\(22\) −2.92850 −0.624359
\(23\) 4.72547 0.985328 0.492664 0.870220i \(-0.336023\pi\)
0.492664 + 0.870220i \(0.336023\pi\)
\(24\) 7.12553 1.45449
\(25\) 10.7385 2.14770
\(26\) −13.5710 −2.66150
\(27\) 5.13777 0.988765
\(28\) −16.5588 −3.12932
\(29\) 3.52186 0.653993 0.326996 0.945026i \(-0.393963\pi\)
0.326996 + 0.945026i \(0.393963\pi\)
\(30\) −16.5894 −3.02880
\(31\) −5.19719 −0.933443 −0.466722 0.884404i \(-0.654565\pi\)
−0.466722 + 0.884404i \(0.654565\pi\)
\(32\) 2.61854 0.462897
\(33\) −2.14692 −0.373731
\(34\) −2.09210 −0.358792
\(35\) 17.7354 2.99782
\(36\) 0.243080 0.0405133
\(37\) 0.569856 0.0936837 0.0468418 0.998902i \(-0.485084\pi\)
0.0468418 + 0.998902i \(0.485084\pi\)
\(38\) −0.636938 −0.103325
\(39\) −9.94909 −1.59313
\(40\) 16.1451 2.55276
\(41\) 7.28931 1.13840 0.569200 0.822199i \(-0.307253\pi\)
0.569200 + 0.822199i \(0.307253\pi\)
\(42\) −18.6942 −2.88458
\(43\) −1.60856 −0.245303 −0.122651 0.992450i \(-0.539140\pi\)
−0.122651 + 0.992450i \(0.539140\pi\)
\(44\) 4.54179 0.684700
\(45\) −0.260352 −0.0388110
\(46\) −11.2858 −1.66401
\(47\) 6.34320 0.925251 0.462626 0.886554i \(-0.346907\pi\)
0.462626 + 0.886554i \(0.346907\pi\)
\(48\) −4.04734 −0.584183
\(49\) 12.9856 1.85508
\(50\) −25.6468 −3.62701
\(51\) −1.53374 −0.214767
\(52\) 21.0472 2.91872
\(53\) −6.00921 −0.825429 −0.412714 0.910861i \(-0.635419\pi\)
−0.412714 + 0.910861i \(0.635419\pi\)
\(54\) −12.2706 −1.66981
\(55\) −4.86450 −0.655929
\(56\) 18.1935 2.43121
\(57\) −0.466947 −0.0618486
\(58\) −8.41127 −1.10445
\(59\) 10.6432 1.38562 0.692812 0.721118i \(-0.256371\pi\)
0.692812 + 0.721118i \(0.256371\pi\)
\(60\) 25.7283 3.32152
\(61\) −14.5845 −1.86736 −0.933678 0.358115i \(-0.883420\pi\)
−0.933678 + 0.358115i \(0.883420\pi\)
\(62\) 12.4125 1.57639
\(63\) −0.293384 −0.0369630
\(64\) −10.8770 −1.35963
\(65\) −22.5427 −2.79608
\(66\) 5.12750 0.631151
\(67\) 1.39232 0.170099 0.0850495 0.996377i \(-0.472895\pi\)
0.0850495 + 0.996377i \(0.472895\pi\)
\(68\) 3.24462 0.393467
\(69\) −8.27378 −0.996047
\(70\) −42.3574 −5.06268
\(71\) 2.69836 0.320236 0.160118 0.987098i \(-0.448813\pi\)
0.160118 + 0.987098i \(0.448813\pi\)
\(72\) −0.267077 −0.0314753
\(73\) 5.82397 0.681644 0.340822 0.940128i \(-0.389295\pi\)
0.340822 + 0.940128i \(0.389295\pi\)
\(74\) −1.36099 −0.158212
\(75\) −18.8020 −2.17107
\(76\) 0.987820 0.113311
\(77\) −5.48169 −0.624697
\(78\) 23.7614 2.69045
\(79\) −14.5393 −1.63580 −0.817899 0.575361i \(-0.804861\pi\)
−0.817899 + 0.575361i \(0.804861\pi\)
\(80\) −9.17048 −1.02529
\(81\) −9.19257 −1.02140
\(82\) −17.4091 −1.92251
\(83\) 4.36231 0.478826 0.239413 0.970918i \(-0.423045\pi\)
0.239413 + 0.970918i \(0.423045\pi\)
\(84\) 28.9927 3.16336
\(85\) −3.47516 −0.376934
\(86\) 3.84173 0.414264
\(87\) −6.16640 −0.661107
\(88\) −4.99015 −0.531952
\(89\) −3.79378 −0.402140 −0.201070 0.979577i \(-0.564442\pi\)
−0.201070 + 0.979577i \(0.564442\pi\)
\(90\) 0.621799 0.0655434
\(91\) −25.4028 −2.66294
\(92\) 17.5031 1.82482
\(93\) 9.09973 0.943598
\(94\) −15.1495 −1.56255
\(95\) −1.05801 −0.108549
\(96\) −4.58479 −0.467933
\(97\) −2.58581 −0.262549 −0.131275 0.991346i \(-0.541907\pi\)
−0.131275 + 0.991346i \(0.541907\pi\)
\(98\) −31.0135 −3.13283
\(99\) 0.0804702 0.00808756
\(100\) 39.7754 3.97754
\(101\) −14.0545 −1.39848 −0.699238 0.714889i \(-0.746477\pi\)
−0.699238 + 0.714889i \(0.746477\pi\)
\(102\) 3.66304 0.362695
\(103\) 2.25317 0.222011 0.111006 0.993820i \(-0.464593\pi\)
0.111006 + 0.993820i \(0.464593\pi\)
\(104\) −23.1250 −2.26759
\(105\) −31.0527 −3.03044
\(106\) 14.3518 1.39397
\(107\) 14.0059 1.35400 0.677002 0.735981i \(-0.263279\pi\)
0.677002 + 0.735981i \(0.263279\pi\)
\(108\) 19.0303 1.83119
\(109\) 4.80541 0.460275 0.230138 0.973158i \(-0.426082\pi\)
0.230138 + 0.973158i \(0.426082\pi\)
\(110\) 11.6179 1.10772
\(111\) −0.997756 −0.0947028
\(112\) −10.3340 −0.976471
\(113\) 18.0303 1.69614 0.848072 0.529881i \(-0.177764\pi\)
0.848072 + 0.529881i \(0.177764\pi\)
\(114\) 1.11521 0.104449
\(115\) −18.7468 −1.74815
\(116\) 13.0449 1.21119
\(117\) 0.372909 0.0344754
\(118\) −25.4192 −2.34002
\(119\) −3.91608 −0.358986
\(120\) −28.2683 −2.58053
\(121\) −9.49647 −0.863315
\(122\) 34.8322 3.15356
\(123\) −12.7628 −1.15078
\(124\) −19.2504 −1.72873
\(125\) −22.7657 −2.03623
\(126\) 0.700691 0.0624225
\(127\) −9.09032 −0.806635 −0.403318 0.915060i \(-0.632143\pi\)
−0.403318 + 0.915060i \(0.632143\pi\)
\(128\) 20.7406 1.83323
\(129\) 2.81641 0.247971
\(130\) 53.8388 4.72197
\(131\) 8.77954 0.767072 0.383536 0.923526i \(-0.374706\pi\)
0.383536 + 0.923526i \(0.374706\pi\)
\(132\) −7.95218 −0.692148
\(133\) −1.19225 −0.103381
\(134\) −3.32528 −0.287261
\(135\) −20.3825 −1.75424
\(136\) −3.56493 −0.305690
\(137\) −2.42199 −0.206924 −0.103462 0.994633i \(-0.532992\pi\)
−0.103462 + 0.994633i \(0.532992\pi\)
\(138\) 19.7603 1.68211
\(139\) 10.1719 0.862768 0.431384 0.902168i \(-0.358025\pi\)
0.431384 + 0.902168i \(0.358025\pi\)
\(140\) 65.6917 5.55196
\(141\) −11.1063 −0.935317
\(142\) −6.44449 −0.540810
\(143\) 6.96755 0.582656
\(144\) 0.151701 0.0126418
\(145\) −13.9719 −1.16030
\(146\) −13.9094 −1.15115
\(147\) −22.7363 −1.87526
\(148\) 2.11074 0.173502
\(149\) −9.77994 −0.801204 −0.400602 0.916252i \(-0.631199\pi\)
−0.400602 + 0.916252i \(0.631199\pi\)
\(150\) 44.9049 3.66647
\(151\) 14.6506 1.19225 0.596124 0.802892i \(-0.296707\pi\)
0.596124 + 0.802892i \(0.296707\pi\)
\(152\) −1.08534 −0.0880326
\(153\) 0.0574873 0.00464757
\(154\) 13.0919 1.05498
\(155\) 20.6182 1.65609
\(156\) −36.8514 −2.95047
\(157\) −2.17862 −0.173873 −0.0869365 0.996214i \(-0.527708\pi\)
−0.0869365 + 0.996214i \(0.527708\pi\)
\(158\) 34.7243 2.76251
\(159\) 10.5215 0.834408
\(160\) −10.3882 −0.821262
\(161\) −21.1253 −1.66491
\(162\) 21.9547 1.72492
\(163\) 22.7026 1.77821 0.889103 0.457708i \(-0.151329\pi\)
0.889103 + 0.457708i \(0.151329\pi\)
\(164\) 26.9996 2.10831
\(165\) 8.51722 0.663065
\(166\) −10.4185 −0.808634
\(167\) 10.6426 0.823546 0.411773 0.911286i \(-0.364910\pi\)
0.411773 + 0.911286i \(0.364910\pi\)
\(168\) −31.8549 −2.45766
\(169\) 19.2885 1.48373
\(170\) 8.29974 0.636561
\(171\) 0.0175019 0.00133841
\(172\) −5.95809 −0.454300
\(173\) 3.89438 0.296085 0.148042 0.988981i \(-0.452703\pi\)
0.148042 + 0.988981i \(0.452703\pi\)
\(174\) 14.7272 1.11647
\(175\) −48.0068 −3.62897
\(176\) 2.83443 0.213653
\(177\) −18.6351 −1.40070
\(178\) 9.06071 0.679129
\(179\) −13.2651 −0.991481 −0.495741 0.868471i \(-0.665103\pi\)
−0.495741 + 0.868471i \(0.665103\pi\)
\(180\) −0.964342 −0.0718778
\(181\) −0.584514 −0.0434466 −0.0217233 0.999764i \(-0.506915\pi\)
−0.0217233 + 0.999764i \(0.506915\pi\)
\(182\) 60.6696 4.49713
\(183\) 25.5359 1.88767
\(184\) −19.2310 −1.41773
\(185\) −2.26072 −0.166211
\(186\) −21.7329 −1.59353
\(187\) 1.07411 0.0785468
\(188\) 23.4952 1.71356
\(189\) −22.9685 −1.67072
\(190\) 2.52685 0.183317
\(191\) −24.1022 −1.74397 −0.871986 0.489531i \(-0.837168\pi\)
−0.871986 + 0.489531i \(0.837168\pi\)
\(192\) 19.0445 1.37442
\(193\) 4.48141 0.322579 0.161290 0.986907i \(-0.448435\pi\)
0.161290 + 0.986907i \(0.448435\pi\)
\(194\) 6.17570 0.443389
\(195\) 39.4698 2.82649
\(196\) 48.0985 3.43561
\(197\) 9.85850 0.702389 0.351195 0.936302i \(-0.385776\pi\)
0.351195 + 0.936302i \(0.385776\pi\)
\(198\) −0.192187 −0.0136582
\(199\) −9.18896 −0.651388 −0.325694 0.945475i \(-0.605598\pi\)
−0.325694 + 0.945475i \(0.605598\pi\)
\(200\) −43.7021 −3.09020
\(201\) −2.43780 −0.171949
\(202\) 33.5665 2.36173
\(203\) −15.7446 −1.10505
\(204\) −5.68097 −0.397748
\(205\) −28.9180 −2.01972
\(206\) −5.38125 −0.374929
\(207\) 0.310115 0.0215545
\(208\) 13.1351 0.910756
\(209\) 0.327012 0.0226199
\(210\) 74.1633 5.11776
\(211\) 2.89258 0.199134 0.0995669 0.995031i \(-0.468254\pi\)
0.0995669 + 0.995031i \(0.468254\pi\)
\(212\) −22.2581 −1.52869
\(213\) −4.72453 −0.323720
\(214\) −33.4504 −2.28662
\(215\) 6.38144 0.435211
\(216\) −20.9090 −1.42268
\(217\) 23.2342 1.57724
\(218\) −11.4768 −0.777306
\(219\) −10.1971 −0.689059
\(220\) −18.0181 −1.21478
\(221\) 4.97756 0.334827
\(222\) 2.38294 0.159933
\(223\) 13.1510 0.880658 0.440329 0.897837i \(-0.354862\pi\)
0.440329 + 0.897837i \(0.354862\pi\)
\(224\) −11.7063 −0.782157
\(225\) 0.704731 0.0469820
\(226\) −43.0617 −2.86442
\(227\) −18.9061 −1.25484 −0.627419 0.778682i \(-0.715889\pi\)
−0.627419 + 0.778682i \(0.715889\pi\)
\(228\) −1.72957 −0.114543
\(229\) −4.98989 −0.329741 −0.164871 0.986315i \(-0.552721\pi\)
−0.164871 + 0.986315i \(0.552721\pi\)
\(230\) 44.7730 2.95224
\(231\) 9.59785 0.631492
\(232\) −14.3328 −0.940992
\(233\) −8.85678 −0.580227 −0.290113 0.956992i \(-0.593693\pi\)
−0.290113 + 0.956992i \(0.593693\pi\)
\(234\) −0.890619 −0.0582216
\(235\) −25.1646 −1.64156
\(236\) 39.4223 2.56617
\(237\) 25.4568 1.65359
\(238\) 9.35278 0.606251
\(239\) 21.5968 1.39698 0.698489 0.715620i \(-0.253856\pi\)
0.698489 + 0.715620i \(0.253856\pi\)
\(240\) 16.0565 1.03644
\(241\) −2.44494 −0.157492 −0.0787462 0.996895i \(-0.525092\pi\)
−0.0787462 + 0.996895i \(0.525092\pi\)
\(242\) 22.6805 1.45795
\(243\) 0.681888 0.0437432
\(244\) −54.0209 −3.45834
\(245\) −51.5161 −3.29124
\(246\) 30.4815 1.94343
\(247\) 1.51541 0.0964235
\(248\) 21.1508 1.34308
\(249\) −7.63793 −0.484034
\(250\) 54.3715 3.43875
\(251\) 9.13636 0.576682 0.288341 0.957528i \(-0.406896\pi\)
0.288341 + 0.957528i \(0.406896\pi\)
\(252\) −1.08669 −0.0684553
\(253\) 5.79430 0.364284
\(254\) 21.7104 1.36223
\(255\) 6.08463 0.381035
\(256\) −27.7808 −1.73630
\(257\) 9.89140 0.617009 0.308504 0.951223i \(-0.400172\pi\)
0.308504 + 0.951223i \(0.400172\pi\)
\(258\) −6.72645 −0.418771
\(259\) −2.54755 −0.158297
\(260\) −83.4980 −5.17832
\(261\) 0.231127 0.0143064
\(262\) −20.9682 −1.29542
\(263\) 10.6650 0.657634 0.328817 0.944394i \(-0.393350\pi\)
0.328817 + 0.944394i \(0.393350\pi\)
\(264\) 8.73723 0.537739
\(265\) 23.8396 1.46446
\(266\) 2.84745 0.174588
\(267\) 6.64251 0.406515
\(268\) 5.15715 0.315023
\(269\) 19.9580 1.21686 0.608431 0.793607i \(-0.291799\pi\)
0.608431 + 0.793607i \(0.291799\pi\)
\(270\) 48.6795 2.96254
\(271\) −0.516063 −0.0313486 −0.0156743 0.999877i \(-0.504989\pi\)
−0.0156743 + 0.999877i \(0.504989\pi\)
\(272\) 2.02490 0.122777
\(273\) 44.4776 2.69191
\(274\) 5.78444 0.349451
\(275\) 13.1674 0.794025
\(276\) −30.6461 −1.84468
\(277\) −6.75597 −0.405927 −0.202963 0.979186i \(-0.565057\pi\)
−0.202963 + 0.979186i \(0.565057\pi\)
\(278\) −24.2935 −1.45703
\(279\) −0.341073 −0.0204195
\(280\) −72.1768 −4.31339
\(281\) −22.8601 −1.36372 −0.681859 0.731484i \(-0.738828\pi\)
−0.681859 + 0.731484i \(0.738828\pi\)
\(282\) 26.5252 1.57955
\(283\) −9.64501 −0.573337 −0.286668 0.958030i \(-0.592548\pi\)
−0.286668 + 0.958030i \(0.592548\pi\)
\(284\) 9.99469 0.593076
\(285\) 1.85246 0.109730
\(286\) −16.6406 −0.983980
\(287\) −32.5870 −1.92355
\(288\) 0.171846 0.0101261
\(289\) −16.2327 −0.954863
\(290\) 33.3690 1.95950
\(291\) 4.52748 0.265405
\(292\) 21.5719 1.26240
\(293\) −19.0200 −1.11116 −0.555579 0.831464i \(-0.687503\pi\)
−0.555579 + 0.831464i \(0.687503\pi\)
\(294\) 54.3013 3.16692
\(295\) −42.2234 −2.45834
\(296\) −2.31912 −0.134796
\(297\) 6.29987 0.365555
\(298\) 23.3575 1.35306
\(299\) 26.8515 1.55286
\(300\) −69.6425 −4.02081
\(301\) 7.19110 0.414488
\(302\) −34.9901 −2.01345
\(303\) 24.6080 1.41369
\(304\) 0.616478 0.0353574
\(305\) 57.8594 3.31302
\(306\) −0.137297 −0.00784875
\(307\) −13.8217 −0.788847 −0.394424 0.918929i \(-0.629056\pi\)
−0.394424 + 0.918929i \(0.629056\pi\)
\(308\) −20.3042 −1.15694
\(309\) −3.94505 −0.224426
\(310\) −49.2425 −2.79679
\(311\) 25.7073 1.45773 0.728865 0.684658i \(-0.240048\pi\)
0.728865 + 0.684658i \(0.240048\pi\)
\(312\) 40.4894 2.29226
\(313\) −10.0156 −0.566116 −0.283058 0.959103i \(-0.591349\pi\)
−0.283058 + 0.959103i \(0.591349\pi\)
\(314\) 5.20321 0.293634
\(315\) 1.16391 0.0655788
\(316\) −53.8535 −3.02949
\(317\) −24.6014 −1.38175 −0.690876 0.722973i \(-0.742775\pi\)
−0.690876 + 0.722973i \(0.742775\pi\)
\(318\) −25.1285 −1.40914
\(319\) 4.31845 0.241787
\(320\) 43.1512 2.41223
\(321\) −24.5229 −1.36873
\(322\) 50.4536 2.81167
\(323\) 0.233615 0.0129987
\(324\) −34.0492 −1.89162
\(325\) 61.0194 3.38475
\(326\) −54.2207 −3.00301
\(327\) −8.41377 −0.465282
\(328\) −29.6650 −1.63798
\(329\) −28.3574 −1.56340
\(330\) −20.3417 −1.11977
\(331\) 2.06549 0.113530 0.0567649 0.998388i \(-0.481921\pi\)
0.0567649 + 0.998388i \(0.481921\pi\)
\(332\) 16.1580 0.886784
\(333\) 0.0373976 0.00204938
\(334\) −25.4177 −1.39079
\(335\) −5.52359 −0.301786
\(336\) 18.0937 0.987093
\(337\) 22.3314 1.21647 0.608235 0.793757i \(-0.291878\pi\)
0.608235 + 0.793757i \(0.291878\pi\)
\(338\) −46.0667 −2.50570
\(339\) −31.5690 −1.71460
\(340\) −12.8720 −0.698081
\(341\) −6.37272 −0.345102
\(342\) −0.0418000 −0.00226028
\(343\) −26.7586 −1.44483
\(344\) 6.54628 0.352952
\(345\) 32.8236 1.76716
\(346\) −9.30097 −0.500023
\(347\) −31.8775 −1.71128 −0.855638 0.517575i \(-0.826835\pi\)
−0.855638 + 0.517575i \(0.826835\pi\)
\(348\) −22.8403 −1.22437
\(349\) −33.5954 −1.79832 −0.899160 0.437620i \(-0.855822\pi\)
−0.899160 + 0.437620i \(0.855822\pi\)
\(350\) 114.655 6.12856
\(351\) 29.1943 1.55828
\(352\) 3.21082 0.171137
\(353\) 18.5922 0.989562 0.494781 0.869018i \(-0.335248\pi\)
0.494781 + 0.869018i \(0.335248\pi\)
\(354\) 44.5062 2.36548
\(355\) −10.7049 −0.568155
\(356\) −14.0522 −0.744763
\(357\) 6.85663 0.362891
\(358\) 31.6811 1.67440
\(359\) 28.5402 1.50629 0.753146 0.657853i \(-0.228535\pi\)
0.753146 + 0.657853i \(0.228535\pi\)
\(360\) 1.05954 0.0558428
\(361\) −18.9289 −0.996257
\(362\) 1.39600 0.0733720
\(363\) 16.6273 0.872707
\(364\) −94.0919 −4.93176
\(365\) −23.1047 −1.20936
\(366\) −60.9875 −3.18787
\(367\) 20.0744 1.04787 0.523936 0.851757i \(-0.324463\pi\)
0.523936 + 0.851757i \(0.324463\pi\)
\(368\) 10.9233 0.569417
\(369\) 0.478372 0.0249030
\(370\) 5.39929 0.280695
\(371\) 26.8643 1.39473
\(372\) 33.7053 1.74754
\(373\) −9.14764 −0.473647 −0.236823 0.971553i \(-0.576106\pi\)
−0.236823 + 0.971553i \(0.576106\pi\)
\(374\) −2.56530 −0.132649
\(375\) 39.8604 2.05838
\(376\) −25.8147 −1.33129
\(377\) 20.0122 1.03068
\(378\) 54.8558 2.82148
\(379\) 33.3064 1.71083 0.855416 0.517941i \(-0.173301\pi\)
0.855416 + 0.517941i \(0.173301\pi\)
\(380\) −3.91886 −0.201033
\(381\) 15.9162 0.815411
\(382\) 57.5633 2.94520
\(383\) −21.7060 −1.10912 −0.554561 0.832143i \(-0.687114\pi\)
−0.554561 + 0.832143i \(0.687114\pi\)
\(384\) −36.3146 −1.85317
\(385\) 21.7469 1.10832
\(386\) −10.7030 −0.544767
\(387\) −0.105564 −0.00536612
\(388\) −9.57783 −0.486240
\(389\) 17.8533 0.905198 0.452599 0.891714i \(-0.350497\pi\)
0.452599 + 0.891714i \(0.350497\pi\)
\(390\) −94.2659 −4.77334
\(391\) 4.13940 0.209339
\(392\) −52.8468 −2.66917
\(393\) −15.3720 −0.775417
\(394\) −23.5451 −1.18619
\(395\) 57.6800 2.90220
\(396\) 0.298061 0.0149781
\(397\) 9.44450 0.474006 0.237003 0.971509i \(-0.423835\pi\)
0.237003 + 0.971509i \(0.423835\pi\)
\(398\) 21.9460 1.10005
\(399\) 2.08750 0.104505
\(400\) 24.8230 1.24115
\(401\) −8.13671 −0.406328 −0.203164 0.979145i \(-0.565122\pi\)
−0.203164 + 0.979145i \(0.565122\pi\)
\(402\) 5.82222 0.290386
\(403\) −29.5320 −1.47109
\(404\) −52.0579 −2.58998
\(405\) 36.4686 1.81214
\(406\) 37.6028 1.86619
\(407\) 0.698749 0.0346357
\(408\) 6.24181 0.309015
\(409\) −13.0276 −0.644173 −0.322087 0.946710i \(-0.604384\pi\)
−0.322087 + 0.946710i \(0.604384\pi\)
\(410\) 69.0650 3.41088
\(411\) 4.24064 0.209175
\(412\) 8.34572 0.411164
\(413\) −47.5806 −2.34129
\(414\) −0.740650 −0.0364010
\(415\) −17.3061 −0.849521
\(416\) 14.8793 0.729519
\(417\) −17.8099 −0.872154
\(418\) −0.781004 −0.0382002
\(419\) 6.07588 0.296826 0.148413 0.988925i \(-0.452583\pi\)
0.148413 + 0.988925i \(0.452583\pi\)
\(420\) −115.019 −5.61236
\(421\) 7.86083 0.383113 0.191557 0.981482i \(-0.438646\pi\)
0.191557 + 0.981482i \(0.438646\pi\)
\(422\) −6.90837 −0.336294
\(423\) 0.416282 0.0202403
\(424\) 24.4554 1.18766
\(425\) 9.40670 0.456292
\(426\) 11.2836 0.546693
\(427\) 65.2004 3.15527
\(428\) 51.8779 2.50761
\(429\) −12.1994 −0.588994
\(430\) −15.2408 −0.734978
\(431\) −29.5516 −1.42345 −0.711726 0.702458i \(-0.752086\pi\)
−0.711726 + 0.702458i \(0.752086\pi\)
\(432\) 11.8764 0.571404
\(433\) −26.2418 −1.26110 −0.630550 0.776149i \(-0.717171\pi\)
−0.630550 + 0.776149i \(0.717171\pi\)
\(434\) −55.4902 −2.66362
\(435\) 24.4632 1.17292
\(436\) 17.7992 0.852428
\(437\) 1.26024 0.0602853
\(438\) 24.3539 1.16367
\(439\) 18.7901 0.896803 0.448401 0.893832i \(-0.351994\pi\)
0.448401 + 0.893832i \(0.351994\pi\)
\(440\) 19.7968 0.943777
\(441\) 0.852197 0.0405808
\(442\) −11.8879 −0.565451
\(443\) −25.0243 −1.18894 −0.594471 0.804117i \(-0.702638\pi\)
−0.594471 + 0.804117i \(0.702638\pi\)
\(444\) −3.69568 −0.175389
\(445\) 15.0506 0.713468
\(446\) −31.4086 −1.48724
\(447\) 17.1236 0.809920
\(448\) 48.6261 2.29737
\(449\) 26.6325 1.25686 0.628432 0.777864i \(-0.283697\pi\)
0.628432 + 0.777864i \(0.283697\pi\)
\(450\) −1.68311 −0.0793426
\(451\) 8.93805 0.420876
\(452\) 66.7840 3.14125
\(453\) −25.6516 −1.20522
\(454\) 45.1534 2.11915
\(455\) 100.778 4.72452
\(456\) 1.90031 0.0889903
\(457\) 38.9616 1.82255 0.911273 0.411802i \(-0.135101\pi\)
0.911273 + 0.411802i \(0.135101\pi\)
\(458\) 11.9174 0.556862
\(459\) 4.50057 0.210069
\(460\) −69.4379 −3.23756
\(461\) −2.03724 −0.0948837 −0.0474419 0.998874i \(-0.515107\pi\)
−0.0474419 + 0.998874i \(0.515107\pi\)
\(462\) −22.9226 −1.06646
\(463\) −31.5991 −1.46854 −0.734268 0.678860i \(-0.762474\pi\)
−0.734268 + 0.678860i \(0.762474\pi\)
\(464\) 8.14108 0.377940
\(465\) −36.1003 −1.67411
\(466\) 21.1527 0.979879
\(467\) 13.8274 0.639855 0.319927 0.947442i \(-0.396342\pi\)
0.319927 + 0.947442i \(0.396342\pi\)
\(468\) 1.38125 0.0638484
\(469\) −6.22440 −0.287416
\(470\) 60.1008 2.77224
\(471\) 3.81453 0.175764
\(472\) −43.3141 −1.99369
\(473\) −1.97239 −0.0906907
\(474\) −60.7985 −2.79257
\(475\) 2.86386 0.131403
\(476\) −14.5051 −0.664841
\(477\) −0.394363 −0.0180566
\(478\) −51.5796 −2.35920
\(479\) 27.6181 1.26190 0.630951 0.775822i \(-0.282665\pi\)
0.630951 + 0.775822i \(0.282665\pi\)
\(480\) 18.1887 0.830196
\(481\) 3.23809 0.147644
\(482\) 5.83926 0.265971
\(483\) 36.9881 1.68302
\(484\) −35.1749 −1.59886
\(485\) 10.2584 0.465809
\(486\) −1.62856 −0.0738728
\(487\) 1.88156 0.0852616 0.0426308 0.999091i \(-0.486426\pi\)
0.0426308 + 0.999091i \(0.486426\pi\)
\(488\) 59.3539 2.68683
\(489\) −39.7498 −1.79755
\(490\) 123.036 5.55820
\(491\) 14.5676 0.657425 0.328713 0.944430i \(-0.393385\pi\)
0.328713 + 0.944430i \(0.393385\pi\)
\(492\) −47.2734 −2.13125
\(493\) 3.08507 0.138945
\(494\) −3.61927 −0.162839
\(495\) −0.319240 −0.0143488
\(496\) −12.0138 −0.539434
\(497\) −12.0631 −0.541102
\(498\) 18.2417 0.817430
\(499\) 26.0109 1.16441 0.582203 0.813044i \(-0.302191\pi\)
0.582203 + 0.813044i \(0.302191\pi\)
\(500\) −84.3242 −3.77109
\(501\) −18.6340 −0.832505
\(502\) −21.8204 −0.973892
\(503\) −38.5668 −1.71961 −0.859805 0.510623i \(-0.829415\pi\)
−0.859805 + 0.510623i \(0.829415\pi\)
\(504\) 1.19397 0.0531838
\(505\) 55.7568 2.48115
\(506\) −13.8385 −0.615198
\(507\) −33.7720 −1.49987
\(508\) −33.6705 −1.49389
\(509\) −35.8752 −1.59014 −0.795070 0.606518i \(-0.792566\pi\)
−0.795070 + 0.606518i \(0.792566\pi\)
\(510\) −14.5320 −0.643486
\(511\) −26.0362 −1.15177
\(512\) 24.8677 1.09901
\(513\) 1.37020 0.0604956
\(514\) −23.6237 −1.04200
\(515\) −8.93872 −0.393887
\(516\) 10.4320 0.459242
\(517\) 7.77795 0.342074
\(518\) 6.08433 0.267330
\(519\) −6.81865 −0.299306
\(520\) 91.7410 4.02311
\(521\) 33.2903 1.45847 0.729236 0.684262i \(-0.239875\pi\)
0.729236 + 0.684262i \(0.239875\pi\)
\(522\) −0.552002 −0.0241605
\(523\) 18.2217 0.796781 0.398390 0.917216i \(-0.369569\pi\)
0.398390 + 0.917216i \(0.369569\pi\)
\(524\) 32.5194 1.42062
\(525\) 84.0547 3.66845
\(526\) −25.4713 −1.11060
\(527\) −4.55262 −0.198315
\(528\) −4.96279 −0.215978
\(529\) −0.669974 −0.0291293
\(530\) −56.9363 −2.47315
\(531\) 0.698474 0.0303112
\(532\) −4.41607 −0.191461
\(533\) 41.4200 1.79410
\(534\) −15.8643 −0.686517
\(535\) −55.5640 −2.40224
\(536\) −5.66627 −0.244745
\(537\) 23.2258 1.00227
\(538\) −47.6658 −2.05502
\(539\) 15.9227 0.685840
\(540\) −75.4966 −3.24886
\(541\) 44.9009 1.93044 0.965220 0.261437i \(-0.0841964\pi\)
0.965220 + 0.261437i \(0.0841964\pi\)
\(542\) 1.23251 0.0529410
\(543\) 1.02342 0.0439192
\(544\) 2.29378 0.0983452
\(545\) −19.0639 −0.816610
\(546\) −106.226 −4.54606
\(547\) 0.380055 0.0162500 0.00812499 0.999967i \(-0.497414\pi\)
0.00812499 + 0.999967i \(0.497414\pi\)
\(548\) −8.97103 −0.383223
\(549\) −0.957129 −0.0408493
\(550\) −31.4478 −1.34094
\(551\) 0.939247 0.0400133
\(552\) 33.6715 1.43315
\(553\) 64.9982 2.76401
\(554\) 16.1353 0.685523
\(555\) 3.95828 0.168020
\(556\) 37.6766 1.59784
\(557\) 39.4224 1.67038 0.835190 0.549962i \(-0.185358\pi\)
0.835190 + 0.549962i \(0.185358\pi\)
\(558\) 0.814586 0.0344842
\(559\) −9.14030 −0.386594
\(560\) 40.9968 1.73243
\(561\) −1.88065 −0.0794013
\(562\) 54.5968 2.30303
\(563\) −41.6216 −1.75414 −0.877070 0.480362i \(-0.840505\pi\)
−0.877070 + 0.480362i \(0.840505\pi\)
\(564\) −41.1376 −1.73220
\(565\) −71.5293 −3.00926
\(566\) 23.0352 0.968243
\(567\) 41.0956 1.72585
\(568\) −10.9814 −0.460768
\(569\) −16.2989 −0.683285 −0.341643 0.939830i \(-0.610983\pi\)
−0.341643 + 0.939830i \(0.610983\pi\)
\(570\) −4.42424 −0.185311
\(571\) −30.4043 −1.27238 −0.636191 0.771532i \(-0.719491\pi\)
−0.636191 + 0.771532i \(0.719491\pi\)
\(572\) 25.8078 1.07908
\(573\) 42.2003 1.76294
\(574\) 77.8277 3.24847
\(575\) 50.7445 2.11619
\(576\) −0.713822 −0.0297426
\(577\) −5.84694 −0.243411 −0.121706 0.992566i \(-0.538836\pi\)
−0.121706 + 0.992566i \(0.538836\pi\)
\(578\) 38.7685 1.61256
\(579\) −7.84647 −0.326088
\(580\) −51.7517 −2.14887
\(581\) −19.5018 −0.809071
\(582\) −10.8130 −0.448213
\(583\) −7.36841 −0.305168
\(584\) −23.7015 −0.980777
\(585\) −1.47940 −0.0611655
\(586\) 45.4254 1.87651
\(587\) 32.2394 1.33066 0.665331 0.746549i \(-0.268290\pi\)
0.665331 + 0.746549i \(0.268290\pi\)
\(588\) −84.2153 −3.47298
\(589\) −1.38604 −0.0571109
\(590\) 100.842 4.15162
\(591\) −17.2612 −0.710030
\(592\) 1.31727 0.0541395
\(593\) 17.5483 0.720621 0.360311 0.932832i \(-0.382671\pi\)
0.360311 + 0.932832i \(0.382671\pi\)
\(594\) −15.0460 −0.617345
\(595\) 15.5358 0.636905
\(596\) −36.2249 −1.48383
\(597\) 16.0889 0.658474
\(598\) −64.1295 −2.62245
\(599\) 5.08583 0.207801 0.103901 0.994588i \(-0.466868\pi\)
0.103901 + 0.994588i \(0.466868\pi\)
\(600\) 76.5177 3.12382
\(601\) 27.6760 1.12893 0.564463 0.825458i \(-0.309083\pi\)
0.564463 + 0.825458i \(0.309083\pi\)
\(602\) −17.1745 −0.699981
\(603\) 0.0913730 0.00372100
\(604\) 54.2657 2.20804
\(605\) 37.6742 1.53167
\(606\) −58.7713 −2.38742
\(607\) 21.5227 0.873580 0.436790 0.899564i \(-0.356115\pi\)
0.436790 + 0.899564i \(0.356115\pi\)
\(608\) 0.698341 0.0283215
\(609\) 27.5670 1.11707
\(610\) −138.186 −5.59498
\(611\) 36.0439 1.45818
\(612\) 0.212933 0.00860729
\(613\) 3.21425 0.129822 0.0649112 0.997891i \(-0.479324\pi\)
0.0649112 + 0.997891i \(0.479324\pi\)
\(614\) 33.0105 1.33219
\(615\) 50.6324 2.04169
\(616\) 22.3086 0.898839
\(617\) −17.2829 −0.695785 −0.347893 0.937534i \(-0.613103\pi\)
−0.347893 + 0.937534i \(0.613103\pi\)
\(618\) 9.42199 0.379008
\(619\) −18.1292 −0.728673 −0.364337 0.931267i \(-0.618704\pi\)
−0.364337 + 0.931267i \(0.618704\pi\)
\(620\) 76.3697 3.06708
\(621\) 24.2784 0.974258
\(622\) −61.3969 −2.46179
\(623\) 16.9602 0.679496
\(624\) −22.9982 −0.920664
\(625\) 36.6232 1.46493
\(626\) 23.9203 0.956049
\(627\) −0.572563 −0.0228660
\(628\) −8.06960 −0.322012
\(629\) 0.499181 0.0199036
\(630\) −2.77977 −0.110749
\(631\) −16.4951 −0.656660 −0.328330 0.944563i \(-0.606486\pi\)
−0.328330 + 0.944563i \(0.606486\pi\)
\(632\) 59.1699 2.35365
\(633\) −5.06461 −0.201300
\(634\) 58.7556 2.33348
\(635\) 36.0629 1.43111
\(636\) 38.9715 1.54532
\(637\) 73.7878 2.92358
\(638\) −10.3138 −0.408326
\(639\) 0.177083 0.00700531
\(640\) −82.2817 −3.25247
\(641\) −1.00007 −0.0395002 −0.0197501 0.999805i \(-0.506287\pi\)
−0.0197501 + 0.999805i \(0.506287\pi\)
\(642\) 58.5681 2.31150
\(643\) 26.8659 1.05949 0.529745 0.848157i \(-0.322288\pi\)
0.529745 + 0.848157i \(0.322288\pi\)
\(644\) −78.2480 −3.08340
\(645\) −11.1732 −0.439945
\(646\) −0.557943 −0.0219520
\(647\) 24.1605 0.949846 0.474923 0.880027i \(-0.342476\pi\)
0.474923 + 0.880027i \(0.342476\pi\)
\(648\) 37.4106 1.46963
\(649\) 13.0505 0.512278
\(650\) −145.733 −5.71611
\(651\) −40.6805 −1.59440
\(652\) 84.0903 3.29323
\(653\) 14.2181 0.556399 0.278200 0.960523i \(-0.410262\pi\)
0.278200 + 0.960523i \(0.410262\pi\)
\(654\) 20.0946 0.785762
\(655\) −34.8300 −1.36092
\(656\) 16.8499 0.657877
\(657\) 0.382206 0.0149113
\(658\) 67.7262 2.64024
\(659\) 47.6450 1.85598 0.927992 0.372600i \(-0.121534\pi\)
0.927992 + 0.372600i \(0.121534\pi\)
\(660\) 31.5477 1.22799
\(661\) 2.81472 0.109480 0.0547399 0.998501i \(-0.482567\pi\)
0.0547399 + 0.998501i \(0.482567\pi\)
\(662\) −4.93302 −0.191727
\(663\) −8.71518 −0.338469
\(664\) −17.7531 −0.688954
\(665\) 4.72985 0.183416
\(666\) −0.0893168 −0.00346096
\(667\) 16.6424 0.644397
\(668\) 39.4200 1.52520
\(669\) −23.0260 −0.890238
\(670\) 13.1920 0.509652
\(671\) −17.8833 −0.690378
\(672\) 20.4964 0.790666
\(673\) 23.2842 0.897541 0.448770 0.893647i \(-0.351862\pi\)
0.448770 + 0.893647i \(0.351862\pi\)
\(674\) −53.3342 −2.05436
\(675\) 55.1721 2.12357
\(676\) 71.4443 2.74786
\(677\) −0.235205 −0.00903967 −0.00451983 0.999990i \(-0.501439\pi\)
−0.00451983 + 0.999990i \(0.501439\pi\)
\(678\) 75.3965 2.89558
\(679\) 11.5599 0.443629
\(680\) 14.1427 0.542348
\(681\) 33.1025 1.26849
\(682\) 15.2200 0.582804
\(683\) 26.4028 1.01028 0.505138 0.863039i \(-0.331442\pi\)
0.505138 + 0.863039i \(0.331442\pi\)
\(684\) 0.0648271 0.00247873
\(685\) 9.60846 0.367120
\(686\) 63.9077 2.44001
\(687\) 8.73676 0.333328
\(688\) −3.71832 −0.141760
\(689\) −34.1461 −1.30086
\(690\) −78.3927 −2.98436
\(691\) −30.7440 −1.16956 −0.584779 0.811193i \(-0.698819\pi\)
−0.584779 + 0.811193i \(0.698819\pi\)
\(692\) 14.4248 0.548348
\(693\) −0.359744 −0.0136655
\(694\) 76.1332 2.88998
\(695\) −40.3537 −1.53070
\(696\) 25.0951 0.951228
\(697\) 6.38527 0.241859
\(698\) 80.2360 3.03698
\(699\) 15.5073 0.586539
\(700\) −177.817 −6.72085
\(701\) −22.4258 −0.847011 −0.423506 0.905893i \(-0.639201\pi\)
−0.423506 + 0.905893i \(0.639201\pi\)
\(702\) −69.7249 −2.63160
\(703\) 0.151975 0.00573185
\(704\) −13.3373 −0.502668
\(705\) 44.0606 1.65942
\(706\) −44.4038 −1.67116
\(707\) 62.8310 2.36300
\(708\) −69.0242 −2.59409
\(709\) −30.5979 −1.14913 −0.574565 0.818459i \(-0.694829\pi\)
−0.574565 + 0.818459i \(0.694829\pi\)
\(710\) 25.5665 0.959492
\(711\) −0.954162 −0.0357839
\(712\) 15.4394 0.578616
\(713\) −24.5592 −0.919747
\(714\) −16.3757 −0.612846
\(715\) −27.6415 −1.03373
\(716\) −49.1339 −1.83622
\(717\) −37.8136 −1.41218
\(718\) −68.1626 −2.54380
\(719\) 4.84100 0.180539 0.0902694 0.995917i \(-0.471227\pi\)
0.0902694 + 0.995917i \(0.471227\pi\)
\(720\) −0.601826 −0.0224287
\(721\) −10.0728 −0.375132
\(722\) 45.2079 1.68246
\(723\) 4.28083 0.159206
\(724\) −2.16504 −0.0804630
\(725\) 37.8196 1.40458
\(726\) −39.7110 −1.47382
\(727\) −1.97527 −0.0732586 −0.0366293 0.999329i \(-0.511662\pi\)
−0.0366293 + 0.999329i \(0.511662\pi\)
\(728\) 103.381 3.83154
\(729\) 26.3838 0.977178
\(730\) 55.1811 2.04234
\(731\) −1.40906 −0.0521160
\(732\) 94.5849 3.49596
\(733\) −21.1541 −0.781343 −0.390672 0.920530i \(-0.627757\pi\)
−0.390672 + 0.920530i \(0.627757\pi\)
\(734\) −47.9437 −1.76963
\(735\) 90.1992 3.32705
\(736\) 12.3738 0.456106
\(737\) 1.70724 0.0628871
\(738\) −1.14250 −0.0420559
\(739\) −30.0492 −1.10538 −0.552689 0.833387i \(-0.686398\pi\)
−0.552689 + 0.833387i \(0.686398\pi\)
\(740\) −8.37369 −0.307823
\(741\) −2.65333 −0.0974724
\(742\) −64.1601 −2.35539
\(743\) 0.927757 0.0340361 0.0170181 0.999855i \(-0.494583\pi\)
0.0170181 + 0.999855i \(0.494583\pi\)
\(744\) −37.0328 −1.35769
\(745\) 38.7988 1.42148
\(746\) 21.8473 0.799888
\(747\) 0.286283 0.0104745
\(748\) 3.97850 0.145468
\(749\) −62.6138 −2.28786
\(750\) −95.1987 −3.47616
\(751\) −1.39640 −0.0509553 −0.0254777 0.999675i \(-0.508111\pi\)
−0.0254777 + 0.999675i \(0.508111\pi\)
\(752\) 14.6629 0.534700
\(753\) −15.9968 −0.582955
\(754\) −47.7953 −1.74060
\(755\) −58.1215 −2.11526
\(756\) −85.0753 −3.09416
\(757\) −26.1273 −0.949612 −0.474806 0.880090i \(-0.657482\pi\)
−0.474806 + 0.880090i \(0.657482\pi\)
\(758\) −79.5457 −2.88923
\(759\) −10.1452 −0.368247
\(760\) 4.30573 0.156185
\(761\) 0.995374 0.0360823 0.0180411 0.999837i \(-0.494257\pi\)
0.0180411 + 0.999837i \(0.494257\pi\)
\(762\) −38.0127 −1.37705
\(763\) −21.4827 −0.777726
\(764\) −89.2743 −3.22983
\(765\) −0.228062 −0.00824561
\(766\) 51.8404 1.87307
\(767\) 60.4777 2.18372
\(768\) 48.6412 1.75519
\(769\) −36.2952 −1.30884 −0.654419 0.756132i \(-0.727087\pi\)
−0.654419 + 0.756132i \(0.727087\pi\)
\(770\) −51.9381 −1.87172
\(771\) −17.3188 −0.623721
\(772\) 16.5991 0.597416
\(773\) −38.5863 −1.38785 −0.693926 0.720046i \(-0.744121\pi\)
−0.693926 + 0.720046i \(0.744121\pi\)
\(774\) 0.252119 0.00906222
\(775\) −55.8101 −2.00476
\(776\) 10.5234 0.377767
\(777\) 4.46049 0.160019
\(778\) −42.6391 −1.52868
\(779\) 1.94399 0.0696507
\(780\) 146.196 5.23466
\(781\) 3.30869 0.118394
\(782\) −9.88615 −0.353528
\(783\) 18.0945 0.646645
\(784\) 30.0173 1.07204
\(785\) 8.64299 0.308481
\(786\) 36.7131 1.30951
\(787\) −16.3109 −0.581421 −0.290710 0.956811i \(-0.593892\pi\)
−0.290710 + 0.956811i \(0.593892\pi\)
\(788\) 36.5158 1.30082
\(789\) −18.6733 −0.664788
\(790\) −137.757 −4.90119
\(791\) −80.6047 −2.86597
\(792\) −0.327486 −0.0116367
\(793\) −82.8735 −2.94292
\(794\) −22.5563 −0.800494
\(795\) −41.7406 −1.48039
\(796\) −34.0359 −1.20637
\(797\) −5.43112 −0.192380 −0.0961900 0.995363i \(-0.530666\pi\)
−0.0961900 + 0.995363i \(0.530666\pi\)
\(798\) −4.98557 −0.176487
\(799\) 5.55650 0.196575
\(800\) 28.1193 0.994166
\(801\) −0.248972 −0.00879701
\(802\) 19.4329 0.686201
\(803\) 7.14127 0.252010
\(804\) −9.02961 −0.318450
\(805\) 83.8079 2.95384
\(806\) 70.5313 2.48436
\(807\) −34.9443 −1.23010
\(808\) 57.1971 2.01219
\(809\) −12.5539 −0.441372 −0.220686 0.975345i \(-0.570830\pi\)
−0.220686 + 0.975345i \(0.570830\pi\)
\(810\) −87.0981 −3.06031
\(811\) 27.3730 0.961194 0.480597 0.876941i \(-0.340420\pi\)
0.480597 + 0.876941i \(0.340420\pi\)
\(812\) −58.3177 −2.04655
\(813\) 0.903571 0.0316896
\(814\) −1.66882 −0.0584923
\(815\) −90.0653 −3.15485
\(816\) −3.54538 −0.124113
\(817\) −0.428987 −0.0150084
\(818\) 31.1139 1.08787
\(819\) −1.66710 −0.0582531
\(820\) −107.112 −3.74052
\(821\) 11.5797 0.404134 0.202067 0.979372i \(-0.435234\pi\)
0.202067 + 0.979372i \(0.435234\pi\)
\(822\) −10.1279 −0.353252
\(823\) −5.47179 −0.190734 −0.0953672 0.995442i \(-0.530403\pi\)
−0.0953672 + 0.995442i \(0.530403\pi\)
\(824\) −9.16961 −0.319439
\(825\) −23.0547 −0.802663
\(826\) 113.637 3.95393
\(827\) 11.2074 0.389719 0.194860 0.980831i \(-0.437575\pi\)
0.194860 + 0.980831i \(0.437575\pi\)
\(828\) 1.14867 0.0399189
\(829\) 31.7906 1.10413 0.552067 0.833800i \(-0.313839\pi\)
0.552067 + 0.833800i \(0.313839\pi\)
\(830\) 41.3321 1.43466
\(831\) 11.8290 0.410343
\(832\) −61.8066 −2.14276
\(833\) 11.3751 0.394123
\(834\) 42.5354 1.47288
\(835\) −42.2210 −1.46112
\(836\) 1.21125 0.0418920
\(837\) −26.7020 −0.922956
\(838\) −14.5111 −0.501276
\(839\) −21.3064 −0.735580 −0.367790 0.929909i \(-0.619885\pi\)
−0.367790 + 0.929909i \(0.619885\pi\)
\(840\) 126.374 4.36032
\(841\) −16.5965 −0.572293
\(842\) −18.7740 −0.646996
\(843\) 40.0256 1.37855
\(844\) 10.7141 0.368795
\(845\) −76.5208 −2.63239
\(846\) −0.994208 −0.0341816
\(847\) 42.4542 1.45874
\(848\) −13.8908 −0.477012
\(849\) 16.8874 0.579574
\(850\) −22.4661 −0.770579
\(851\) 2.69283 0.0923091
\(852\) −17.4996 −0.599528
\(853\) 33.3108 1.14054 0.570270 0.821458i \(-0.306839\pi\)
0.570270 + 0.821458i \(0.306839\pi\)
\(854\) −155.718 −5.32857
\(855\) −0.0694334 −0.00237457
\(856\) −56.9993 −1.94820
\(857\) 12.2290 0.417734 0.208867 0.977944i \(-0.433022\pi\)
0.208867 + 0.977944i \(0.433022\pi\)
\(858\) 29.1359 0.994685
\(859\) 8.43378 0.287757 0.143878 0.989595i \(-0.454043\pi\)
0.143878 + 0.989595i \(0.454043\pi\)
\(860\) 23.6368 0.806009
\(861\) 57.0564 1.94448
\(862\) 70.5782 2.40390
\(863\) −42.4917 −1.44643 −0.723217 0.690621i \(-0.757337\pi\)
−0.723217 + 0.690621i \(0.757337\pi\)
\(864\) 13.4535 0.457697
\(865\) −15.4497 −0.525306
\(866\) 62.6734 2.12973
\(867\) 28.4217 0.965250
\(868\) 86.0592 2.92104
\(869\) −17.8279 −0.604769
\(870\) −58.4256 −1.98081
\(871\) 7.91157 0.268073
\(872\) −19.5564 −0.662263
\(873\) −0.169697 −0.00574339
\(874\) −3.00983 −0.101809
\(875\) 101.775 3.44061
\(876\) −37.7702 −1.27614
\(877\) 35.9175 1.21285 0.606424 0.795142i \(-0.292603\pi\)
0.606424 + 0.795142i \(0.292603\pi\)
\(878\) −44.8765 −1.51451
\(879\) 33.3019 1.12325
\(880\) −11.2447 −0.379059
\(881\) −25.4978 −0.859044 −0.429522 0.903056i \(-0.641318\pi\)
−0.429522 + 0.903056i \(0.641318\pi\)
\(882\) −2.03530 −0.0685323
\(883\) −49.7463 −1.67410 −0.837048 0.547130i \(-0.815720\pi\)
−0.837048 + 0.547130i \(0.815720\pi\)
\(884\) 18.4369 0.620099
\(885\) 73.9287 2.48509
\(886\) 59.7657 2.00787
\(887\) 28.0467 0.941716 0.470858 0.882209i \(-0.343944\pi\)
0.470858 + 0.882209i \(0.343944\pi\)
\(888\) 4.06052 0.136262
\(889\) 40.6385 1.36297
\(890\) −35.9455 −1.20489
\(891\) −11.2718 −0.377620
\(892\) 48.7113 1.63098
\(893\) 1.69167 0.0566097
\(894\) −40.8964 −1.36778
\(895\) 52.6251 1.75906
\(896\) −92.7213 −3.09760
\(897\) −47.0141 −1.56975
\(898\) −63.6064 −2.12257
\(899\) −18.3038 −0.610465
\(900\) 2.61032 0.0870106
\(901\) −5.26393 −0.175367
\(902\) −21.3468 −0.710770
\(903\) −12.5908 −0.418997
\(904\) −73.3769 −2.44048
\(905\) 2.31887 0.0770819
\(906\) 61.2639 2.03536
\(907\) −49.1046 −1.63049 −0.815246 0.579114i \(-0.803398\pi\)
−0.815246 + 0.579114i \(0.803398\pi\)
\(908\) −70.0279 −2.32396
\(909\) −0.922348 −0.0305923
\(910\) −240.687 −7.97871
\(911\) −33.6278 −1.11414 −0.557069 0.830466i \(-0.688074\pi\)
−0.557069 + 0.830466i \(0.688074\pi\)
\(912\) −1.07939 −0.0357421
\(913\) 5.34900 0.177026
\(914\) −93.0521 −3.07789
\(915\) −101.306 −3.34906
\(916\) −18.4825 −0.610680
\(917\) −39.2491 −1.29612
\(918\) −10.7487 −0.354761
\(919\) −38.9312 −1.28422 −0.642112 0.766611i \(-0.721941\pi\)
−0.642112 + 0.766611i \(0.721941\pi\)
\(920\) 76.2929 2.51530
\(921\) 24.2004 0.797429
\(922\) 4.86555 0.160238
\(923\) 15.3328 0.504687
\(924\) 35.5504 1.16952
\(925\) 6.11940 0.201205
\(926\) 75.4683 2.48004
\(927\) 0.147867 0.00485660
\(928\) 9.22214 0.302732
\(929\) 17.3666 0.569780 0.284890 0.958560i \(-0.408043\pi\)
0.284890 + 0.958560i \(0.408043\pi\)
\(930\) 86.2184 2.82721
\(931\) 3.46313 0.113499
\(932\) −32.8055 −1.07458
\(933\) −45.0108 −1.47359
\(934\) −33.0240 −1.08058
\(935\) −4.26119 −0.139356
\(936\) −1.51761 −0.0496046
\(937\) −10.8030 −0.352920 −0.176460 0.984308i \(-0.556465\pi\)
−0.176460 + 0.984308i \(0.556465\pi\)
\(938\) 14.8658 0.485384
\(939\) 17.5363 0.572275
\(940\) −93.2097 −3.04016
\(941\) 25.7914 0.840774 0.420387 0.907345i \(-0.361894\pi\)
0.420387 + 0.907345i \(0.361894\pi\)
\(942\) −9.11027 −0.296829
\(943\) 34.4454 1.12170
\(944\) 24.6026 0.800748
\(945\) 91.1203 2.96414
\(946\) 4.71067 0.153157
\(947\) −21.5238 −0.699430 −0.349715 0.936856i \(-0.613722\pi\)
−0.349715 + 0.936856i \(0.613722\pi\)
\(948\) 94.2917 3.06245
\(949\) 33.0935 1.07426
\(950\) −6.83977 −0.221911
\(951\) 43.0744 1.39678
\(952\) 15.9371 0.516524
\(953\) −35.6681 −1.15540 −0.577702 0.816248i \(-0.696050\pi\)
−0.577702 + 0.816248i \(0.696050\pi\)
\(954\) 0.941859 0.0304938
\(955\) 95.6177 3.09412
\(956\) 79.9943 2.58720
\(957\) −7.56115 −0.244417
\(958\) −65.9604 −2.13108
\(959\) 10.8275 0.349640
\(960\) −75.5532 −2.43847
\(961\) −3.98920 −0.128684
\(962\) −7.73353 −0.249339
\(963\) 0.919159 0.0296195
\(964\) −9.05604 −0.291675
\(965\) −17.7786 −0.572312
\(966\) −88.3389 −2.84226
\(967\) 9.01500 0.289903 0.144951 0.989439i \(-0.453697\pi\)
0.144951 + 0.989439i \(0.453697\pi\)
\(968\) 38.6474 1.24217
\(969\) −0.409035 −0.0131401
\(970\) −24.5001 −0.786651
\(971\) 38.0223 1.22019 0.610096 0.792327i \(-0.291131\pi\)
0.610096 + 0.792327i \(0.291131\pi\)
\(972\) 2.52571 0.0810122
\(973\) −45.4736 −1.45782
\(974\) −4.49373 −0.143989
\(975\) −106.838 −3.42157
\(976\) −33.7133 −1.07914
\(977\) −2.12682 −0.0680429 −0.0340214 0.999421i \(-0.510831\pi\)
−0.0340214 + 0.999421i \(0.510831\pi\)
\(978\) 94.9347 3.03568
\(979\) −4.65188 −0.148675
\(980\) −190.815 −6.09537
\(981\) 0.315362 0.0100687
\(982\) −34.7918 −1.11025
\(983\) 6.58974 0.210180 0.105090 0.994463i \(-0.466487\pi\)
0.105090 + 0.994463i \(0.466487\pi\)
\(984\) 51.9402 1.65579
\(985\) −39.1105 −1.24616
\(986\) −7.36808 −0.234648
\(987\) 49.6508 1.58040
\(988\) 5.61308 0.178576
\(989\) −7.60119 −0.241704
\(990\) 0.762442 0.0242320
\(991\) −20.7147 −0.658025 −0.329012 0.944326i \(-0.606716\pi\)
−0.329012 + 0.944326i \(0.606716\pi\)
\(992\) −13.6091 −0.432088
\(993\) −3.61646 −0.114765
\(994\) 28.8102 0.913805
\(995\) 36.4543 1.15568
\(996\) −28.2909 −0.896430
\(997\) 47.8293 1.51477 0.757384 0.652969i \(-0.226477\pi\)
0.757384 + 0.652969i \(0.226477\pi\)
\(998\) −62.1218 −1.96643
\(999\) 2.92779 0.0926312
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 \(a_p\))