Properties

Label 5077.2.a.c.1.3
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 1.3
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} +O(q^{10})\) \(q-2.71273 q^{2} -1.56061 q^{3} +5.35892 q^{4} +1.41855 q^{5} +4.23352 q^{6} -1.24026 q^{7} -9.11187 q^{8} -0.564498 q^{9} -3.84815 q^{10} -1.09049 q^{11} -8.36319 q^{12} -1.70420 q^{13} +3.36451 q^{14} -2.21381 q^{15} +14.0002 q^{16} +0.0690599 q^{17} +1.53133 q^{18} -5.12812 q^{19} +7.60191 q^{20} +1.93557 q^{21} +2.95821 q^{22} +5.50957 q^{23} +14.2201 q^{24} -2.98771 q^{25} +4.62305 q^{26} +5.56279 q^{27} -6.64649 q^{28} -3.90043 q^{29} +6.00546 q^{30} -1.98239 q^{31} -19.7551 q^{32} +1.70183 q^{33} -0.187341 q^{34} -1.75938 q^{35} -3.02510 q^{36} +10.5208 q^{37} +13.9112 q^{38} +2.65959 q^{39} -12.9257 q^{40} -2.16444 q^{41} -5.25068 q^{42} -7.04361 q^{43} -5.84386 q^{44} -0.800770 q^{45} -14.9460 q^{46} -6.34939 q^{47} -21.8489 q^{48} -5.46174 q^{49} +8.10486 q^{50} -0.107775 q^{51} -9.13269 q^{52} -9.99502 q^{53} -15.0904 q^{54} -1.54692 q^{55} +11.3011 q^{56} +8.00299 q^{57} +10.5808 q^{58} -7.58854 q^{59} -11.8636 q^{60} -7.37657 q^{61} +5.37770 q^{62} +0.700127 q^{63} +25.5900 q^{64} -2.41750 q^{65} -4.61661 q^{66} +7.07625 q^{67} +0.370087 q^{68} -8.59829 q^{69} +4.77273 q^{70} +5.26521 q^{71} +5.14363 q^{72} +8.99661 q^{73} -28.5400 q^{74} +4.66265 q^{75} -27.4812 q^{76} +1.35250 q^{77} -7.21477 q^{78} +4.05163 q^{79} +19.8600 q^{80} -6.98785 q^{81} +5.87156 q^{82} +1.64902 q^{83} +10.3726 q^{84} +0.0979650 q^{85} +19.1074 q^{86} +6.08706 q^{87} +9.93641 q^{88} +8.31856 q^{89} +2.17228 q^{90} +2.11366 q^{91} +29.5254 q^{92} +3.09374 q^{93} +17.2242 q^{94} -7.27450 q^{95} +30.8301 q^{96} -7.87488 q^{97} +14.8163 q^{98} +0.615580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71273 −1.91819 −0.959096 0.283080i \(-0.908644\pi\)
−0.959096 + 0.283080i \(0.908644\pi\)
\(3\) −1.56061 −0.901018 −0.450509 0.892772i \(-0.648758\pi\)
−0.450509 + 0.892772i \(0.648758\pi\)
\(4\) 5.35892 2.67946
\(5\) 1.41855 0.634396 0.317198 0.948359i \(-0.397258\pi\)
0.317198 + 0.948359i \(0.397258\pi\)
\(6\) 4.23352 1.72833
\(7\) −1.24026 −0.468776 −0.234388 0.972143i \(-0.575309\pi\)
−0.234388 + 0.972143i \(0.575309\pi\)
\(8\) −9.11187 −3.22153
\(9\) −0.564498 −0.188166
\(10\) −3.84815 −1.21689
\(11\) −1.09049 −0.328795 −0.164398 0.986394i \(-0.552568\pi\)
−0.164398 + 0.986394i \(0.552568\pi\)
\(12\) −8.36319 −2.41424
\(13\) −1.70420 −0.472661 −0.236330 0.971673i \(-0.575945\pi\)
−0.236330 + 0.971673i \(0.575945\pi\)
\(14\) 3.36451 0.899203
\(15\) −2.21381 −0.571602
\(16\) 14.0002 3.50006
\(17\) 0.0690599 0.0167495 0.00837474 0.999965i \(-0.497334\pi\)
0.00837474 + 0.999965i \(0.497334\pi\)
\(18\) 1.53133 0.360939
\(19\) −5.12812 −1.17647 −0.588236 0.808690i \(-0.700177\pi\)
−0.588236 + 0.808690i \(0.700177\pi\)
\(20\) 7.60191 1.69984
\(21\) 1.93557 0.422376
\(22\) 2.95821 0.630693
\(23\) 5.50957 1.14882 0.574412 0.818566i \(-0.305231\pi\)
0.574412 + 0.818566i \(0.305231\pi\)
\(24\) 14.2201 2.90266
\(25\) −2.98771 −0.597542
\(26\) 4.62305 0.906654
\(27\) 5.56279 1.07056
\(28\) −6.64649 −1.25607
\(29\) −3.90043 −0.724293 −0.362146 0.932121i \(-0.617956\pi\)
−0.362146 + 0.932121i \(0.617956\pi\)
\(30\) 6.00546 1.09644
\(31\) −1.98239 −0.356048 −0.178024 0.984026i \(-0.556970\pi\)
−0.178024 + 0.984026i \(0.556970\pi\)
\(32\) −19.7551 −3.49225
\(33\) 1.70183 0.296251
\(34\) −0.187341 −0.0321287
\(35\) −1.75938 −0.297389
\(36\) −3.02510 −0.504184
\(37\) 10.5208 1.72960 0.864801 0.502115i \(-0.167445\pi\)
0.864801 + 0.502115i \(0.167445\pi\)
\(38\) 13.9112 2.25670
\(39\) 2.65959 0.425876
\(40\) −12.9257 −2.04373
\(41\) −2.16444 −0.338029 −0.169015 0.985614i \(-0.554059\pi\)
−0.169015 + 0.985614i \(0.554059\pi\)
\(42\) −5.25068 −0.810198
\(43\) −7.04361 −1.07414 −0.537070 0.843538i \(-0.680469\pi\)
−0.537070 + 0.843538i \(0.680469\pi\)
\(44\) −5.84386 −0.880995
\(45\) −0.800770 −0.119372
\(46\) −14.9460 −2.20367
\(47\) −6.34939 −0.926154 −0.463077 0.886318i \(-0.653255\pi\)
−0.463077 + 0.886318i \(0.653255\pi\)
\(48\) −21.8489 −3.15361
\(49\) −5.46174 −0.780249
\(50\) 8.10486 1.14620
\(51\) −0.107775 −0.0150916
\(52\) −9.13269 −1.26648
\(53\) −9.99502 −1.37292 −0.686461 0.727167i \(-0.740837\pi\)
−0.686461 + 0.727167i \(0.740837\pi\)
\(54\) −15.0904 −2.05354
\(55\) −1.54692 −0.208586
\(56\) 11.3011 1.51018
\(57\) 8.00299 1.06002
\(58\) 10.5808 1.38933
\(59\) −7.58854 −0.987943 −0.493972 0.869478i \(-0.664455\pi\)
−0.493972 + 0.869478i \(0.664455\pi\)
\(60\) −11.8636 −1.53159
\(61\) −7.37657 −0.944473 −0.472236 0.881472i \(-0.656553\pi\)
−0.472236 + 0.881472i \(0.656553\pi\)
\(62\) 5.37770 0.682969
\(63\) 0.700127 0.0882078
\(64\) 25.5900 3.19875
\(65\) −2.41750 −0.299854
\(66\) −4.61661 −0.568266
\(67\) 7.07625 0.864501 0.432251 0.901753i \(-0.357720\pi\)
0.432251 + 0.901753i \(0.357720\pi\)
\(68\) 0.370087 0.0448796
\(69\) −8.59829 −1.03511
\(70\) 4.77273 0.570450
\(71\) 5.26521 0.624865 0.312433 0.949940i \(-0.398856\pi\)
0.312433 + 0.949940i \(0.398856\pi\)
\(72\) 5.14363 0.606183
\(73\) 8.99661 1.05297 0.526487 0.850183i \(-0.323509\pi\)
0.526487 + 0.850183i \(0.323509\pi\)
\(74\) −28.5400 −3.31771
\(75\) 4.66265 0.538396
\(76\) −27.4812 −3.15231
\(77\) 1.35250 0.154131
\(78\) −7.21477 −0.816912
\(79\) 4.05163 0.455844 0.227922 0.973679i \(-0.426807\pi\)
0.227922 + 0.973679i \(0.426807\pi\)
\(80\) 19.8600 2.22042
\(81\) −6.98785 −0.776427
\(82\) 5.87156 0.648405
\(83\) 1.64902 0.181004 0.0905019 0.995896i \(-0.471153\pi\)
0.0905019 + 0.995896i \(0.471153\pi\)
\(84\) 10.3726 1.13174
\(85\) 0.0979650 0.0106258
\(86\) 19.1074 2.06041
\(87\) 6.08706 0.652601
\(88\) 9.93641 1.05922
\(89\) 8.31856 0.881765 0.440883 0.897565i \(-0.354666\pi\)
0.440883 + 0.897565i \(0.354666\pi\)
\(90\) 2.17228 0.228978
\(91\) 2.11366 0.221572
\(92\) 29.5254 3.07823
\(93\) 3.09374 0.320806
\(94\) 17.2242 1.77654
\(95\) −7.27450 −0.746348
\(96\) 30.8301 3.14658
\(97\) −7.87488 −0.799573 −0.399787 0.916608i \(-0.630916\pi\)
−0.399787 + 0.916608i \(0.630916\pi\)
\(98\) 14.8163 1.49667
\(99\) 0.615580 0.0618681
\(100\) −16.0109 −1.60109
\(101\) 9.96459 0.991514 0.495757 0.868461i \(-0.334891\pi\)
0.495757 + 0.868461i \(0.334891\pi\)
\(102\) 0.292366 0.0289486
\(103\) 2.20029 0.216801 0.108401 0.994107i \(-0.465427\pi\)
0.108401 + 0.994107i \(0.465427\pi\)
\(104\) 15.5285 1.52269
\(105\) 2.74570 0.267953
\(106\) 27.1138 2.63353
\(107\) 8.25043 0.797599 0.398800 0.917038i \(-0.369427\pi\)
0.398800 + 0.917038i \(0.369427\pi\)
\(108\) 29.8106 2.86852
\(109\) −15.6141 −1.49556 −0.747778 0.663949i \(-0.768879\pi\)
−0.747778 + 0.663949i \(0.768879\pi\)
\(110\) 4.19638 0.400109
\(111\) −16.4188 −1.55840
\(112\) −17.3640 −1.64074
\(113\) −3.89674 −0.366574 −0.183287 0.983059i \(-0.558674\pi\)
−0.183287 + 0.983059i \(0.558674\pi\)
\(114\) −21.7100 −2.03333
\(115\) 7.81561 0.728809
\(116\) −20.9021 −1.94071
\(117\) 0.962020 0.0889387
\(118\) 20.5857 1.89507
\(119\) −0.0856525 −0.00785175
\(120\) 20.1719 1.84143
\(121\) −9.81083 −0.891894
\(122\) 20.0107 1.81168
\(123\) 3.37785 0.304571
\(124\) −10.6235 −0.954017
\(125\) −11.3310 −1.01347
\(126\) −1.89926 −0.169199
\(127\) −21.5257 −1.91010 −0.955051 0.296443i \(-0.904200\pi\)
−0.955051 + 0.296443i \(0.904200\pi\)
\(128\) −29.9086 −2.64357
\(129\) 10.9923 0.967820
\(130\) 6.55803 0.575178
\(131\) 1.83015 0.159901 0.0799506 0.996799i \(-0.474524\pi\)
0.0799506 + 0.996799i \(0.474524\pi\)
\(132\) 9.11998 0.793792
\(133\) 6.36023 0.551502
\(134\) −19.1960 −1.65828
\(135\) 7.89111 0.679158
\(136\) −0.629264 −0.0539590
\(137\) 9.20913 0.786789 0.393394 0.919370i \(-0.371301\pi\)
0.393394 + 0.919370i \(0.371301\pi\)
\(138\) 23.3249 1.98554
\(139\) −2.40481 −0.203973 −0.101987 0.994786i \(-0.532520\pi\)
−0.101987 + 0.994786i \(0.532520\pi\)
\(140\) −9.42838 −0.796844
\(141\) 9.90892 0.834482
\(142\) −14.2831 −1.19861
\(143\) 1.85842 0.155409
\(144\) −7.90310 −0.658592
\(145\) −5.53297 −0.459488
\(146\) −24.4054 −2.01981
\(147\) 8.52365 0.703019
\(148\) 56.3799 4.63440
\(149\) −2.10140 −0.172153 −0.0860767 0.996289i \(-0.527433\pi\)
−0.0860767 + 0.996289i \(0.527433\pi\)
\(150\) −12.6485 −1.03275
\(151\) 1.80539 0.146921 0.0734604 0.997298i \(-0.476596\pi\)
0.0734604 + 0.997298i \(0.476596\pi\)
\(152\) 46.7268 3.79004
\(153\) −0.0389842 −0.00315168
\(154\) −3.66897 −0.295654
\(155\) −2.81212 −0.225875
\(156\) 14.2526 1.14112
\(157\) 7.36639 0.587902 0.293951 0.955821i \(-0.405030\pi\)
0.293951 + 0.955821i \(0.405030\pi\)
\(158\) −10.9910 −0.874396
\(159\) 15.5983 1.23703
\(160\) −28.0237 −2.21547
\(161\) −6.83332 −0.538541
\(162\) 18.9562 1.48934
\(163\) 16.9298 1.32605 0.663023 0.748599i \(-0.269273\pi\)
0.663023 + 0.748599i \(0.269273\pi\)
\(164\) −11.5991 −0.905737
\(165\) 2.41413 0.187940
\(166\) −4.47336 −0.347200
\(167\) 17.8943 1.38470 0.692350 0.721562i \(-0.256575\pi\)
0.692350 + 0.721562i \(0.256575\pi\)
\(168\) −17.6366 −1.36070
\(169\) −10.0957 −0.776592
\(170\) −0.265753 −0.0203823
\(171\) 2.89481 0.221372
\(172\) −37.7462 −2.87812
\(173\) 9.02172 0.685909 0.342954 0.939352i \(-0.388572\pi\)
0.342954 + 0.939352i \(0.388572\pi\)
\(174\) −16.5126 −1.25181
\(175\) 3.70555 0.280113
\(176\) −15.2671 −1.15080
\(177\) 11.8427 0.890155
\(178\) −22.5660 −1.69140
\(179\) 20.7408 1.55024 0.775121 0.631813i \(-0.217689\pi\)
0.775121 + 0.631813i \(0.217689\pi\)
\(180\) −4.29127 −0.319852
\(181\) 3.48264 0.258863 0.129431 0.991588i \(-0.458685\pi\)
0.129431 + 0.991588i \(0.458685\pi\)
\(182\) −5.73380 −0.425018
\(183\) 11.5119 0.850987
\(184\) −50.2025 −3.70098
\(185\) 14.9242 1.09725
\(186\) −8.39249 −0.615367
\(187\) −0.0753092 −0.00550715
\(188\) −34.0259 −2.48159
\(189\) −6.89933 −0.501853
\(190\) 19.7338 1.43164
\(191\) −1.74317 −0.126131 −0.0630656 0.998009i \(-0.520088\pi\)
−0.0630656 + 0.998009i \(0.520088\pi\)
\(192\) −39.9360 −2.88213
\(193\) −7.67337 −0.552341 −0.276171 0.961109i \(-0.589065\pi\)
−0.276171 + 0.961109i \(0.589065\pi\)
\(194\) 21.3625 1.53374
\(195\) 3.77277 0.270174
\(196\) −29.2691 −2.09065
\(197\) −1.20267 −0.0856864 −0.0428432 0.999082i \(-0.513642\pi\)
−0.0428432 + 0.999082i \(0.513642\pi\)
\(198\) −1.66991 −0.118675
\(199\) −4.30631 −0.305266 −0.152633 0.988283i \(-0.548775\pi\)
−0.152633 + 0.988283i \(0.548775\pi\)
\(200\) 27.2236 1.92500
\(201\) −11.0433 −0.778932
\(202\) −27.0313 −1.90191
\(203\) 4.83757 0.339531
\(204\) −0.577561 −0.0404373
\(205\) −3.07038 −0.214444
\(206\) −5.96881 −0.415867
\(207\) −3.11014 −0.216170
\(208\) −23.8592 −1.65434
\(209\) 5.59217 0.386818
\(210\) −7.44837 −0.513986
\(211\) −3.37008 −0.232006 −0.116003 0.993249i \(-0.537008\pi\)
−0.116003 + 0.993249i \(0.537008\pi\)
\(212\) −53.5626 −3.67869
\(213\) −8.21693 −0.563015
\(214\) −22.3812 −1.52995
\(215\) −9.99172 −0.681430
\(216\) −50.6874 −3.44884
\(217\) 2.45869 0.166907
\(218\) 42.3568 2.86876
\(219\) −14.0402 −0.948749
\(220\) −8.28982 −0.558899
\(221\) −0.117692 −0.00791682
\(222\) 44.5398 2.98932
\(223\) −11.8886 −0.796122 −0.398061 0.917359i \(-0.630317\pi\)
−0.398061 + 0.917359i \(0.630317\pi\)
\(224\) 24.5016 1.63708
\(225\) 1.68656 0.112437
\(226\) 10.5708 0.703160
\(227\) −7.46056 −0.495175 −0.247588 0.968866i \(-0.579638\pi\)
−0.247588 + 0.968866i \(0.579638\pi\)
\(228\) 42.8874 2.84029
\(229\) −30.1797 −1.99433 −0.997166 0.0752269i \(-0.976032\pi\)
−0.997166 + 0.0752269i \(0.976032\pi\)
\(230\) −21.2017 −1.39800
\(231\) −2.11072 −0.138875
\(232\) 35.5403 2.33333
\(233\) 11.9243 0.781189 0.390594 0.920563i \(-0.372270\pi\)
0.390594 + 0.920563i \(0.372270\pi\)
\(234\) −2.60970 −0.170602
\(235\) −9.00694 −0.587548
\(236\) −40.6664 −2.64716
\(237\) −6.32301 −0.410724
\(238\) 0.232352 0.0150612
\(239\) −13.9164 −0.900180 −0.450090 0.892983i \(-0.648608\pi\)
−0.450090 + 0.892983i \(0.648608\pi\)
\(240\) −30.9938 −2.00064
\(241\) −23.3562 −1.50451 −0.752253 0.658874i \(-0.771033\pi\)
−0.752253 + 0.658874i \(0.771033\pi\)
\(242\) 26.6142 1.71082
\(243\) −5.78307 −0.370984
\(244\) −39.5305 −2.53068
\(245\) −7.74777 −0.494987
\(246\) −9.16321 −0.584225
\(247\) 8.73936 0.556072
\(248\) 18.0633 1.14702
\(249\) −2.57348 −0.163088
\(250\) 30.7379 1.94404
\(251\) 25.2226 1.59204 0.796019 0.605271i \(-0.206935\pi\)
0.796019 + 0.605271i \(0.206935\pi\)
\(252\) 3.75193 0.236349
\(253\) −6.00814 −0.377728
\(254\) 58.3936 3.66394
\(255\) −0.152885 −0.00957404
\(256\) 29.9540 1.87213
\(257\) 26.4096 1.64739 0.823694 0.567035i \(-0.191910\pi\)
0.823694 + 0.567035i \(0.191910\pi\)
\(258\) −29.8192 −1.85646
\(259\) −13.0485 −0.810796
\(260\) −12.9552 −0.803447
\(261\) 2.20179 0.136287
\(262\) −4.96472 −0.306721
\(263\) 6.08434 0.375176 0.187588 0.982248i \(-0.439933\pi\)
0.187588 + 0.982248i \(0.439933\pi\)
\(264\) −15.5069 −0.954381
\(265\) −14.1785 −0.870976
\(266\) −17.2536 −1.05789
\(267\) −12.9820 −0.794486
\(268\) 37.9211 2.31640
\(269\) 7.04730 0.429682 0.214841 0.976649i \(-0.431077\pi\)
0.214841 + 0.976649i \(0.431077\pi\)
\(270\) −21.4065 −1.30276
\(271\) −1.49702 −0.0909375 −0.0454688 0.998966i \(-0.514478\pi\)
−0.0454688 + 0.998966i \(0.514478\pi\)
\(272\) 0.966854 0.0586241
\(273\) −3.29860 −0.199640
\(274\) −24.9819 −1.50921
\(275\) 3.25807 0.196469
\(276\) −46.0776 −2.77354
\(277\) 9.25506 0.556083 0.278041 0.960569i \(-0.410315\pi\)
0.278041 + 0.960569i \(0.410315\pi\)
\(278\) 6.52361 0.391260
\(279\) 1.11906 0.0669962
\(280\) 16.0312 0.958050
\(281\) 3.53201 0.210702 0.105351 0.994435i \(-0.466403\pi\)
0.105351 + 0.994435i \(0.466403\pi\)
\(282\) −26.8803 −1.60070
\(283\) −8.81917 −0.524245 −0.262123 0.965035i \(-0.584422\pi\)
−0.262123 + 0.965035i \(0.584422\pi\)
\(284\) 28.2159 1.67430
\(285\) 11.3527 0.672473
\(286\) −5.04139 −0.298104
\(287\) 2.68448 0.158460
\(288\) 11.1517 0.657123
\(289\) −16.9952 −0.999719
\(290\) 15.0095 0.881387
\(291\) 12.2896 0.720430
\(292\) 48.2122 2.82140
\(293\) −25.0376 −1.46271 −0.731357 0.681995i \(-0.761113\pi\)
−0.731357 + 0.681995i \(0.761113\pi\)
\(294\) −23.1224 −1.34853
\(295\) −10.7647 −0.626747
\(296\) −95.8638 −5.57197
\(297\) −6.06617 −0.351995
\(298\) 5.70054 0.330223
\(299\) −9.38942 −0.543004
\(300\) 24.9868 1.44261
\(301\) 8.73594 0.503531
\(302\) −4.89755 −0.281823
\(303\) −15.5508 −0.893372
\(304\) −71.7948 −4.11772
\(305\) −10.4640 −0.599169
\(306\) 0.105754 0.00604554
\(307\) −1.59450 −0.0910032 −0.0455016 0.998964i \(-0.514489\pi\)
−0.0455016 + 0.998964i \(0.514489\pi\)
\(308\) 7.24793 0.412989
\(309\) −3.43380 −0.195342
\(310\) 7.62855 0.433272
\(311\) 16.8063 0.952999 0.476499 0.879175i \(-0.341905\pi\)
0.476499 + 0.879175i \(0.341905\pi\)
\(312\) −24.2339 −1.37197
\(313\) −11.9435 −0.675085 −0.337543 0.941310i \(-0.609596\pi\)
−0.337543 + 0.941310i \(0.609596\pi\)
\(314\) −19.9830 −1.12771
\(315\) 0.993167 0.0559586
\(316\) 21.7124 1.22142
\(317\) −11.2285 −0.630654 −0.315327 0.948983i \(-0.602114\pi\)
−0.315327 + 0.948983i \(0.602114\pi\)
\(318\) −42.3141 −2.37286
\(319\) 4.25339 0.238144
\(320\) 36.3008 2.02927
\(321\) −12.8757 −0.718652
\(322\) 18.5370 1.03303
\(323\) −0.354147 −0.0197053
\(324\) −37.4473 −2.08041
\(325\) 5.09166 0.282435
\(326\) −45.9261 −2.54361
\(327\) 24.3675 1.34752
\(328\) 19.7221 1.08897
\(329\) 7.87493 0.434159
\(330\) −6.54890 −0.360505
\(331\) 4.88661 0.268592 0.134296 0.990941i \(-0.457123\pi\)
0.134296 + 0.990941i \(0.457123\pi\)
\(332\) 8.83699 0.484993
\(333\) −5.93895 −0.325452
\(334\) −48.5424 −2.65612
\(335\) 10.0380 0.548436
\(336\) 27.0984 1.47834
\(337\) 26.2853 1.43185 0.715927 0.698175i \(-0.246004\pi\)
0.715927 + 0.698175i \(0.246004\pi\)
\(338\) 27.3869 1.48965
\(339\) 6.08129 0.330290
\(340\) 0.524987 0.0284714
\(341\) 2.16178 0.117067
\(342\) −7.85286 −0.424634
\(343\) 15.4559 0.834538
\(344\) 64.1804 3.46038
\(345\) −12.1971 −0.656671
\(346\) −24.4735 −1.31570
\(347\) −24.5843 −1.31976 −0.659878 0.751373i \(-0.729392\pi\)
−0.659878 + 0.751373i \(0.729392\pi\)
\(348\) 32.6201 1.74862
\(349\) −6.61163 −0.353913 −0.176956 0.984219i \(-0.556625\pi\)
−0.176956 + 0.984219i \(0.556625\pi\)
\(350\) −10.0522 −0.537311
\(351\) −9.48012 −0.506011
\(352\) 21.5428 1.14824
\(353\) −25.4699 −1.35563 −0.677814 0.735233i \(-0.737073\pi\)
−0.677814 + 0.735233i \(0.737073\pi\)
\(354\) −32.1262 −1.70749
\(355\) 7.46897 0.396412
\(356\) 44.5785 2.36266
\(357\) 0.133670 0.00707457
\(358\) −56.2643 −2.97366
\(359\) 17.3540 0.915907 0.457954 0.888976i \(-0.348583\pi\)
0.457954 + 0.888976i \(0.348583\pi\)
\(360\) 7.29651 0.384560
\(361\) 7.29761 0.384085
\(362\) −9.44748 −0.496549
\(363\) 15.3109 0.803612
\(364\) 11.3270 0.593694
\(365\) 12.7622 0.668002
\(366\) −31.2288 −1.63236
\(367\) 11.0514 0.576881 0.288440 0.957498i \(-0.406863\pi\)
0.288440 + 0.957498i \(0.406863\pi\)
\(368\) 77.1352 4.02095
\(369\) 1.22182 0.0636057
\(370\) −40.4855 −2.10474
\(371\) 12.3965 0.643593
\(372\) 16.5791 0.859587
\(373\) 17.2130 0.891257 0.445628 0.895218i \(-0.352980\pi\)
0.445628 + 0.895218i \(0.352980\pi\)
\(374\) 0.204294 0.0105638
\(375\) 17.6832 0.913158
\(376\) 57.8548 2.98363
\(377\) 6.64713 0.342345
\(378\) 18.7161 0.962650
\(379\) 21.6062 1.10984 0.554919 0.831905i \(-0.312749\pi\)
0.554919 + 0.831905i \(0.312749\pi\)
\(380\) −38.9835 −1.99981
\(381\) 33.5933 1.72104
\(382\) 4.72875 0.241944
\(383\) 16.9682 0.867037 0.433518 0.901145i \(-0.357272\pi\)
0.433518 + 0.901145i \(0.357272\pi\)
\(384\) 46.6756 2.38191
\(385\) 1.91859 0.0977803
\(386\) 20.8158 1.05950
\(387\) 3.97610 0.202117
\(388\) −42.2009 −2.14243
\(389\) 3.91854 0.198678 0.0993388 0.995054i \(-0.468327\pi\)
0.0993388 + 0.995054i \(0.468327\pi\)
\(390\) −10.2345 −0.518246
\(391\) 0.380490 0.0192422
\(392\) 49.7667 2.51360
\(393\) −2.85615 −0.144074
\(394\) 3.26251 0.164363
\(395\) 5.74745 0.289185
\(396\) 3.29885 0.165773
\(397\) 28.6515 1.43798 0.718988 0.695023i \(-0.244606\pi\)
0.718988 + 0.695023i \(0.244606\pi\)
\(398\) 11.6819 0.585560
\(399\) −9.92583 −0.496913
\(400\) −41.8286 −2.09143
\(401\) 11.9504 0.596775 0.298388 0.954445i \(-0.403551\pi\)
0.298388 + 0.954445i \(0.403551\pi\)
\(402\) 29.9574 1.49414
\(403\) 3.37840 0.168290
\(404\) 53.3995 2.65672
\(405\) −9.91262 −0.492562
\(406\) −13.1230 −0.651286
\(407\) −11.4728 −0.568685
\(408\) 0.982036 0.0486180
\(409\) −22.8418 −1.12946 −0.564728 0.825277i \(-0.691019\pi\)
−0.564728 + 0.825277i \(0.691019\pi\)
\(410\) 8.32911 0.411346
\(411\) −14.3719 −0.708911
\(412\) 11.7912 0.580911
\(413\) 9.41179 0.463124
\(414\) 8.43699 0.414655
\(415\) 2.33922 0.114828
\(416\) 33.6668 1.65065
\(417\) 3.75297 0.183784
\(418\) −15.1701 −0.741992
\(419\) 6.95482 0.339765 0.169883 0.985464i \(-0.445661\pi\)
0.169883 + 0.985464i \(0.445661\pi\)
\(420\) 14.7140 0.717971
\(421\) 31.0666 1.51409 0.757046 0.653362i \(-0.226642\pi\)
0.757046 + 0.653362i \(0.226642\pi\)
\(422\) 9.14213 0.445032
\(423\) 3.58422 0.174271
\(424\) 91.0734 4.42291
\(425\) −0.206331 −0.0100085
\(426\) 22.2904 1.07997
\(427\) 9.14890 0.442746
\(428\) 44.2134 2.13714
\(429\) −2.90026 −0.140026
\(430\) 27.1049 1.30711
\(431\) 35.8846 1.72850 0.864249 0.503064i \(-0.167794\pi\)
0.864249 + 0.503064i \(0.167794\pi\)
\(432\) 77.8803 3.74702
\(433\) 35.6337 1.71244 0.856222 0.516608i \(-0.172805\pi\)
0.856222 + 0.516608i \(0.172805\pi\)
\(434\) −6.66977 −0.320159
\(435\) 8.63480 0.414007
\(436\) −83.6746 −4.00729
\(437\) −28.2537 −1.35156
\(438\) 38.0873 1.81988
\(439\) −32.3343 −1.54323 −0.771617 0.636088i \(-0.780552\pi\)
−0.771617 + 0.636088i \(0.780552\pi\)
\(440\) 14.0953 0.671968
\(441\) 3.08314 0.146816
\(442\) 0.319267 0.0151860
\(443\) −20.8139 −0.988898 −0.494449 0.869207i \(-0.664630\pi\)
−0.494449 + 0.869207i \(0.664630\pi\)
\(444\) −87.9871 −4.17568
\(445\) 11.8003 0.559388
\(446\) 32.2507 1.52711
\(447\) 3.27946 0.155113
\(448\) −31.7384 −1.49950
\(449\) −9.33986 −0.440775 −0.220388 0.975412i \(-0.570732\pi\)
−0.220388 + 0.975412i \(0.570732\pi\)
\(450\) −4.57518 −0.215676
\(451\) 2.36031 0.111142
\(452\) −20.8823 −0.982222
\(453\) −2.81751 −0.132378
\(454\) 20.2385 0.949841
\(455\) 2.99834 0.140564
\(456\) −72.9222 −3.41490
\(457\) −21.9286 −1.02578 −0.512888 0.858456i \(-0.671424\pi\)
−0.512888 + 0.858456i \(0.671424\pi\)
\(458\) 81.8696 3.82551
\(459\) 0.384166 0.0179313
\(460\) 41.8833 1.95282
\(461\) 19.2143 0.894899 0.447449 0.894309i \(-0.352332\pi\)
0.447449 + 0.894309i \(0.352332\pi\)
\(462\) 5.72582 0.266389
\(463\) −17.7095 −0.823030 −0.411515 0.911403i \(-0.635000\pi\)
−0.411515 + 0.911403i \(0.635000\pi\)
\(464\) −54.6070 −2.53506
\(465\) 4.38863 0.203518
\(466\) −32.3475 −1.49847
\(467\) −22.8629 −1.05797 −0.528984 0.848632i \(-0.677427\pi\)
−0.528984 + 0.848632i \(0.677427\pi\)
\(468\) 5.15539 0.238308
\(469\) −8.77642 −0.405258
\(470\) 24.4334 1.12703
\(471\) −11.4961 −0.529710
\(472\) 69.1458 3.18269
\(473\) 7.68099 0.353172
\(474\) 17.1526 0.787847
\(475\) 15.3213 0.702991
\(476\) −0.459005 −0.0210385
\(477\) 5.64217 0.258337
\(478\) 37.7516 1.72672
\(479\) 17.7932 0.812993 0.406496 0.913652i \(-0.366750\pi\)
0.406496 + 0.913652i \(0.366750\pi\)
\(480\) 43.7341 1.99618
\(481\) −17.9295 −0.817515
\(482\) 63.3592 2.88593
\(483\) 10.6642 0.485236
\(484\) −52.5755 −2.38980
\(485\) −11.1709 −0.507246
\(486\) 15.6879 0.711619
\(487\) 14.0626 0.637237 0.318618 0.947883i \(-0.396781\pi\)
0.318618 + 0.947883i \(0.396781\pi\)
\(488\) 67.2143 3.04265
\(489\) −26.4208 −1.19479
\(490\) 21.0176 0.949480
\(491\) −9.39146 −0.423831 −0.211915 0.977288i \(-0.567970\pi\)
−0.211915 + 0.977288i \(0.567970\pi\)
\(492\) 18.1017 0.816086
\(493\) −0.269364 −0.0121315
\(494\) −23.7075 −1.06665
\(495\) 0.873233 0.0392489
\(496\) −27.7539 −1.24619
\(497\) −6.53025 −0.292922
\(498\) 6.98117 0.312834
\(499\) −26.6825 −1.19447 −0.597237 0.802065i \(-0.703735\pi\)
−0.597237 + 0.802065i \(0.703735\pi\)
\(500\) −60.7219 −2.71557
\(501\) −27.9260 −1.24764
\(502\) −68.4223 −3.05384
\(503\) 35.4839 1.58215 0.791075 0.611720i \(-0.209522\pi\)
0.791075 + 0.611720i \(0.209522\pi\)
\(504\) −6.37947 −0.284164
\(505\) 14.1353 0.629012
\(506\) 16.2985 0.724555
\(507\) 15.7554 0.699723
\(508\) −115.355 −5.11804
\(509\) 26.8679 1.19090 0.595449 0.803393i \(-0.296974\pi\)
0.595449 + 0.803393i \(0.296974\pi\)
\(510\) 0.414737 0.0183648
\(511\) −11.1582 −0.493609
\(512\) −21.4401 −0.947527
\(513\) −28.5267 −1.25948
\(514\) −71.6423 −3.16001
\(515\) 3.12123 0.137538
\(516\) 58.9070 2.59324
\(517\) 6.92395 0.304515
\(518\) 35.3972 1.55526
\(519\) −14.0794 −0.618016
\(520\) 22.0279 0.965989
\(521\) 14.7647 0.646852 0.323426 0.946254i \(-0.395165\pi\)
0.323426 + 0.946254i \(0.395165\pi\)
\(522\) −5.97287 −0.261425
\(523\) 31.8730 1.39371 0.696855 0.717212i \(-0.254582\pi\)
0.696855 + 0.717212i \(0.254582\pi\)
\(524\) 9.80765 0.428449
\(525\) −5.78292 −0.252387
\(526\) −16.5052 −0.719661
\(527\) −0.136904 −0.00596362
\(528\) 23.8260 1.03689
\(529\) 7.35536 0.319798
\(530\) 38.4624 1.67070
\(531\) 4.28372 0.185897
\(532\) 34.0840 1.47773
\(533\) 3.68865 0.159773
\(534\) 35.2168 1.52398
\(535\) 11.7037 0.505994
\(536\) −64.4779 −2.78502
\(537\) −32.3683 −1.39680
\(538\) −19.1175 −0.824212
\(539\) 5.95598 0.256542
\(540\) 42.2878 1.81978
\(541\) −18.3107 −0.787237 −0.393618 0.919274i \(-0.628777\pi\)
−0.393618 + 0.919274i \(0.628777\pi\)
\(542\) 4.06102 0.174436
\(543\) −5.43505 −0.233240
\(544\) −1.36429 −0.0584934
\(545\) −22.1494 −0.948774
\(546\) 8.94823 0.382949
\(547\) 14.0980 0.602789 0.301394 0.953500i \(-0.402548\pi\)
0.301394 + 0.953500i \(0.402548\pi\)
\(548\) 49.3510 2.10817
\(549\) 4.16406 0.177718
\(550\) −8.83828 −0.376866
\(551\) 20.0019 0.852109
\(552\) 78.3465 3.33465
\(553\) −5.02509 −0.213689
\(554\) −25.1065 −1.06667
\(555\) −23.2909 −0.988644
\(556\) −12.8872 −0.546539
\(557\) 41.3339 1.75137 0.875687 0.482879i \(-0.160409\pi\)
0.875687 + 0.482879i \(0.160409\pi\)
\(558\) −3.03570 −0.128512
\(559\) 12.0037 0.507704
\(560\) −24.6317 −1.04088
\(561\) 0.117528 0.00496204
\(562\) −9.58140 −0.404167
\(563\) 36.3540 1.53214 0.766069 0.642758i \(-0.222210\pi\)
0.766069 + 0.642758i \(0.222210\pi\)
\(564\) 53.1012 2.23596
\(565\) −5.52773 −0.232553
\(566\) 23.9241 1.00560
\(567\) 8.66678 0.363971
\(568\) −47.9759 −2.01302
\(569\) 6.66130 0.279256 0.139628 0.990204i \(-0.455409\pi\)
0.139628 + 0.990204i \(0.455409\pi\)
\(570\) −30.7967 −1.28993
\(571\) 21.1023 0.883104 0.441552 0.897236i \(-0.354428\pi\)
0.441552 + 0.897236i \(0.354428\pi\)
\(572\) 9.95912 0.416412
\(573\) 2.72040 0.113646
\(574\) −7.28229 −0.303957
\(575\) −16.4610 −0.686471
\(576\) −14.4455 −0.601897
\(577\) 20.5777 0.856661 0.428331 0.903622i \(-0.359102\pi\)
0.428331 + 0.903622i \(0.359102\pi\)
\(578\) 46.1035 1.91765
\(579\) 11.9751 0.497670
\(580\) −29.6508 −1.23118
\(581\) −2.04523 −0.0848502
\(582\) −33.3385 −1.38192
\(583\) 10.8995 0.451410
\(584\) −81.9760 −3.39219
\(585\) 1.36467 0.0564224
\(586\) 67.9204 2.80577
\(587\) 11.6165 0.479464 0.239732 0.970839i \(-0.422940\pi\)
0.239732 + 0.970839i \(0.422940\pi\)
\(588\) 45.6776 1.88371
\(589\) 10.1659 0.418880
\(590\) 29.2019 1.20222
\(591\) 1.87689 0.0772050
\(592\) 147.293 6.05370
\(593\) −6.59952 −0.271010 −0.135505 0.990777i \(-0.543266\pi\)
−0.135505 + 0.990777i \(0.543266\pi\)
\(594\) 16.4559 0.675194
\(595\) −0.121503 −0.00498112
\(596\) −11.2612 −0.461278
\(597\) 6.72047 0.275051
\(598\) 25.4710 1.04159
\(599\) 24.9869 1.02094 0.510469 0.859896i \(-0.329472\pi\)
0.510469 + 0.859896i \(0.329472\pi\)
\(600\) −42.4855 −1.73446
\(601\) −14.4301 −0.588615 −0.294308 0.955711i \(-0.595089\pi\)
−0.294308 + 0.955711i \(0.595089\pi\)
\(602\) −23.6983 −0.965870
\(603\) −3.99453 −0.162670
\(604\) 9.67497 0.393669
\(605\) −13.9172 −0.565813
\(606\) 42.1853 1.71366
\(607\) −5.56243 −0.225772 −0.112886 0.993608i \(-0.536009\pi\)
−0.112886 + 0.993608i \(0.536009\pi\)
\(608\) 101.307 4.10853
\(609\) −7.54956 −0.305924
\(610\) 28.3862 1.14932
\(611\) 10.8206 0.437757
\(612\) −0.208913 −0.00844482
\(613\) −6.45541 −0.260731 −0.130366 0.991466i \(-0.541615\pi\)
−0.130366 + 0.991466i \(0.541615\pi\)
\(614\) 4.32547 0.174562
\(615\) 4.79166 0.193218
\(616\) −12.3238 −0.496539
\(617\) −4.53749 −0.182673 −0.0913363 0.995820i \(-0.529114\pi\)
−0.0913363 + 0.995820i \(0.529114\pi\)
\(618\) 9.31499 0.374704
\(619\) 18.6434 0.749341 0.374671 0.927158i \(-0.377756\pi\)
0.374671 + 0.927158i \(0.377756\pi\)
\(620\) −15.0700 −0.605224
\(621\) 30.6486 1.22988
\(622\) −45.5911 −1.82804
\(623\) −10.3172 −0.413350
\(624\) 37.2349 1.49059
\(625\) −1.13503 −0.0454013
\(626\) 32.3995 1.29494
\(627\) −8.72719 −0.348530
\(628\) 39.4759 1.57526
\(629\) 0.726562 0.0289699
\(630\) −2.69420 −0.107339
\(631\) 5.88623 0.234327 0.117163 0.993113i \(-0.462620\pi\)
0.117163 + 0.993113i \(0.462620\pi\)
\(632\) −36.9179 −1.46852
\(633\) 5.25938 0.209041
\(634\) 30.4598 1.20972
\(635\) −30.5354 −1.21176
\(636\) 83.5903 3.31457
\(637\) 9.30792 0.368793
\(638\) −11.5383 −0.456806
\(639\) −2.97220 −0.117578
\(640\) −42.4269 −1.67707
\(641\) 4.53080 0.178956 0.0894780 0.995989i \(-0.471480\pi\)
0.0894780 + 0.995989i \(0.471480\pi\)
\(642\) 34.9284 1.37851
\(643\) 42.2298 1.66538 0.832690 0.553740i \(-0.186800\pi\)
0.832690 + 0.553740i \(0.186800\pi\)
\(644\) −36.6193 −1.44300
\(645\) 15.5932 0.613981
\(646\) 0.960707 0.0377985
\(647\) −10.9571 −0.430768 −0.215384 0.976529i \(-0.569100\pi\)
−0.215384 + 0.976529i \(0.569100\pi\)
\(648\) 63.6723 2.50129
\(649\) 8.27523 0.324831
\(650\) −13.8123 −0.541764
\(651\) −3.83705 −0.150386
\(652\) 90.7256 3.55309
\(653\) −17.4560 −0.683104 −0.341552 0.939863i \(-0.610953\pi\)
−0.341552 + 0.939863i \(0.610953\pi\)
\(654\) −66.1024 −2.58481
\(655\) 2.59617 0.101441
\(656\) −30.3027 −1.18312
\(657\) −5.07857 −0.198134
\(658\) −21.3626 −0.832800
\(659\) −30.8964 −1.20355 −0.601776 0.798665i \(-0.705540\pi\)
−0.601776 + 0.798665i \(0.705540\pi\)
\(660\) 12.9372 0.503578
\(661\) −14.8210 −0.576472 −0.288236 0.957559i \(-0.593069\pi\)
−0.288236 + 0.957559i \(0.593069\pi\)
\(662\) −13.2561 −0.515212
\(663\) 0.183671 0.00713320
\(664\) −15.0257 −0.583110
\(665\) 9.02231 0.349870
\(666\) 16.1108 0.624280
\(667\) −21.4897 −0.832085
\(668\) 95.8940 3.71025
\(669\) 18.5535 0.717320
\(670\) −27.2305 −1.05201
\(671\) 8.04408 0.310538
\(672\) −38.2375 −1.47504
\(673\) −10.5034 −0.404876 −0.202438 0.979295i \(-0.564886\pi\)
−0.202438 + 0.979295i \(0.564886\pi\)
\(674\) −71.3051 −2.74657
\(675\) −16.6200 −0.639704
\(676\) −54.1021 −2.08085
\(677\) −16.3383 −0.627931 −0.313965 0.949434i \(-0.601658\pi\)
−0.313965 + 0.949434i \(0.601658\pi\)
\(678\) −16.4969 −0.633560
\(679\) 9.76694 0.374821
\(680\) −0.892644 −0.0342313
\(681\) 11.6430 0.446162
\(682\) −5.86433 −0.224557
\(683\) −46.8851 −1.79401 −0.897004 0.442023i \(-0.854261\pi\)
−0.897004 + 0.442023i \(0.854261\pi\)
\(684\) 15.5131 0.593158
\(685\) 13.0636 0.499135
\(686\) −41.9276 −1.60080
\(687\) 47.0988 1.79693
\(688\) −98.6121 −3.75955
\(689\) 17.0335 0.648926
\(690\) 33.0875 1.25962
\(691\) 36.4325 1.38596 0.692978 0.720959i \(-0.256298\pi\)
0.692978 + 0.720959i \(0.256298\pi\)
\(692\) 48.3467 1.83787
\(693\) −0.763482 −0.0290023
\(694\) 66.6907 2.53154
\(695\) −3.41135 −0.129400
\(696\) −55.4645 −2.10237
\(697\) −0.149476 −0.00566182
\(698\) 17.9356 0.678873
\(699\) −18.6092 −0.703865
\(700\) 19.8578 0.750553
\(701\) −34.2157 −1.29231 −0.646155 0.763206i \(-0.723624\pi\)
−0.646155 + 0.763206i \(0.723624\pi\)
\(702\) 25.7170 0.970627
\(703\) −53.9517 −2.03483
\(704\) −27.9057 −1.05173
\(705\) 14.0563 0.529391
\(706\) 69.0932 2.60036
\(707\) −12.3587 −0.464798
\(708\) 63.4644 2.38514
\(709\) 12.2729 0.460917 0.230459 0.973082i \(-0.425977\pi\)
0.230459 + 0.973082i \(0.425977\pi\)
\(710\) −20.2613 −0.760394
\(711\) −2.28714 −0.0857744
\(712\) −75.7976 −2.84063
\(713\) −10.9221 −0.409037
\(714\) −0.362611 −0.0135704
\(715\) 2.63626 0.0985906
\(716\) 111.149 4.15382
\(717\) 21.7181 0.811079
\(718\) −47.0767 −1.75689
\(719\) 24.9681 0.931152 0.465576 0.885008i \(-0.345847\pi\)
0.465576 + 0.885008i \(0.345847\pi\)
\(720\) −11.2110 −0.417808
\(721\) −2.72895 −0.101631
\(722\) −19.7965 −0.736749
\(723\) 36.4499 1.35559
\(724\) 18.6632 0.693613
\(725\) 11.6534 0.432795
\(726\) −41.5343 −1.54148
\(727\) −5.82767 −0.216136 −0.108068 0.994143i \(-0.534466\pi\)
−0.108068 + 0.994143i \(0.534466\pi\)
\(728\) −19.2594 −0.713801
\(729\) 29.9887 1.11069
\(730\) −34.6203 −1.28136
\(731\) −0.486431 −0.0179913
\(732\) 61.6916 2.28019
\(733\) 24.5041 0.905078 0.452539 0.891745i \(-0.350518\pi\)
0.452539 + 0.891745i \(0.350518\pi\)
\(734\) −29.9796 −1.10657
\(735\) 12.0912 0.445992
\(736\) −108.842 −4.01198
\(737\) −7.71659 −0.284244
\(738\) −3.31449 −0.122008
\(739\) 37.4422 1.37733 0.688666 0.725078i \(-0.258196\pi\)
0.688666 + 0.725078i \(0.258196\pi\)
\(740\) 79.9779 2.94004
\(741\) −13.6387 −0.501031
\(742\) −33.6283 −1.23454
\(743\) 20.1042 0.737551 0.368776 0.929518i \(-0.379777\pi\)
0.368776 + 0.929518i \(0.379777\pi\)
\(744\) −28.1897 −1.03349
\(745\) −2.98094 −0.109213
\(746\) −46.6944 −1.70960
\(747\) −0.930871 −0.0340588
\(748\) −0.403576 −0.0147562
\(749\) −10.2327 −0.373895
\(750\) −47.9699 −1.75161
\(751\) −38.3104 −1.39796 −0.698982 0.715139i \(-0.746363\pi\)
−0.698982 + 0.715139i \(0.746363\pi\)
\(752\) −88.8929 −3.24159
\(753\) −39.3627 −1.43446
\(754\) −18.0319 −0.656683
\(755\) 2.56105 0.0932060
\(756\) −36.9730 −1.34470
\(757\) 45.2296 1.64390 0.821949 0.569561i \(-0.192887\pi\)
0.821949 + 0.569561i \(0.192887\pi\)
\(758\) −58.6120 −2.12888
\(759\) 9.37635 0.340340
\(760\) 66.2843 2.40439
\(761\) −24.9525 −0.904527 −0.452264 0.891884i \(-0.649383\pi\)
−0.452264 + 0.891884i \(0.649383\pi\)
\(762\) −91.1296 −3.30128
\(763\) 19.3656 0.701081
\(764\) −9.34150 −0.337964
\(765\) −0.0553011 −0.00199941
\(766\) −46.0303 −1.66314
\(767\) 12.9324 0.466962
\(768\) −46.7465 −1.68682
\(769\) 34.7943 1.25471 0.627356 0.778732i \(-0.284137\pi\)
0.627356 + 0.778732i \(0.284137\pi\)
\(770\) −5.20462 −0.187561
\(771\) −41.2151 −1.48433
\(772\) −41.1210 −1.47998
\(773\) 46.3049 1.66547 0.832737 0.553669i \(-0.186773\pi\)
0.832737 + 0.553669i \(0.186773\pi\)
\(774\) −10.7861 −0.387699
\(775\) 5.92281 0.212754
\(776\) 71.7549 2.57585
\(777\) 20.3636 0.730542
\(778\) −10.6299 −0.381102
\(779\) 11.0995 0.397682
\(780\) 20.2180 0.723921
\(781\) −5.74166 −0.205453
\(782\) −1.03217 −0.0369103
\(783\) −21.6973 −0.775398
\(784\) −76.4656 −2.73092
\(785\) 10.4496 0.372962
\(786\) 7.74798 0.276361
\(787\) 32.5825 1.16144 0.580720 0.814103i \(-0.302771\pi\)
0.580720 + 0.814103i \(0.302771\pi\)
\(788\) −6.44500 −0.229594
\(789\) −9.49528 −0.338041
\(790\) −15.5913 −0.554713
\(791\) 4.83299 0.171841
\(792\) −5.60909 −0.199310
\(793\) 12.5712 0.446415
\(794\) −77.7238 −2.75831
\(795\) 22.1270 0.784765
\(796\) −23.0772 −0.817950
\(797\) 26.2477 0.929742 0.464871 0.885378i \(-0.346101\pi\)
0.464871 + 0.885378i \(0.346101\pi\)
\(798\) 26.9261 0.953175
\(799\) −0.438488 −0.0155126
\(800\) 59.0227 2.08677
\(801\) −4.69581 −0.165918
\(802\) −32.4183 −1.14473
\(803\) −9.81072 −0.346213
\(804\) −59.1800 −2.08712
\(805\) −9.69343 −0.341648
\(806\) −9.16469 −0.322812
\(807\) −10.9981 −0.387151
\(808\) −90.7960 −3.19419
\(809\) −44.4026 −1.56111 −0.780555 0.625087i \(-0.785064\pi\)
−0.780555 + 0.625087i \(0.785064\pi\)
\(810\) 26.8903 0.944829
\(811\) −9.46145 −0.332236 −0.166118 0.986106i \(-0.553123\pi\)
−0.166118 + 0.986106i \(0.553123\pi\)
\(812\) 25.9242 0.909760
\(813\) 2.33626 0.0819364
\(814\) 31.1226 1.09085
\(815\) 24.0158 0.841238
\(816\) −1.50888 −0.0528214
\(817\) 36.1205 1.26370
\(818\) 61.9638 2.16651
\(819\) −1.19316 −0.0416923
\(820\) −16.4539 −0.574596
\(821\) −36.4488 −1.27207 −0.636036 0.771659i \(-0.719427\pi\)
−0.636036 + 0.771659i \(0.719427\pi\)
\(822\) 38.9870 1.35983
\(823\) 42.2388 1.47235 0.736176 0.676790i \(-0.236630\pi\)
0.736176 + 0.676790i \(0.236630\pi\)
\(824\) −20.0488 −0.698433
\(825\) −5.08458 −0.177022
\(826\) −25.5317 −0.888361
\(827\) 23.5979 0.820579 0.410289 0.911955i \(-0.365428\pi\)
0.410289 + 0.911955i \(0.365428\pi\)
\(828\) −16.6670 −0.579219
\(829\) −4.28163 −0.148707 −0.0743537 0.997232i \(-0.523689\pi\)
−0.0743537 + 0.997232i \(0.523689\pi\)
\(830\) −6.34569 −0.220262
\(831\) −14.4435 −0.501041
\(832\) −43.6106 −1.51192
\(833\) −0.377187 −0.0130688
\(834\) −10.1808 −0.352532
\(835\) 25.3839 0.878448
\(836\) 29.9680 1.03647
\(837\) −11.0276 −0.381170
\(838\) −18.8666 −0.651735
\(839\) 7.84687 0.270904 0.135452 0.990784i \(-0.456751\pi\)
0.135452 + 0.990784i \(0.456751\pi\)
\(840\) −25.0185 −0.863220
\(841\) −13.7866 −0.475400
\(842\) −84.2753 −2.90432
\(843\) −5.51209 −0.189846
\(844\) −18.0600 −0.621651
\(845\) −14.3213 −0.492666
\(846\) −9.72304 −0.334285
\(847\) 12.1680 0.418098
\(848\) −139.933 −4.80531
\(849\) 13.7633 0.472354
\(850\) 0.559721 0.0191983
\(851\) 57.9648 1.98701
\(852\) −44.0339 −1.50858
\(853\) −32.1285 −1.10006 −0.550029 0.835146i \(-0.685383\pi\)
−0.550029 + 0.835146i \(0.685383\pi\)
\(854\) −24.8185 −0.849272
\(855\) 4.10645 0.140437
\(856\) −75.1769 −2.56949
\(857\) −34.6350 −1.18311 −0.591554 0.806265i \(-0.701485\pi\)
−0.591554 + 0.806265i \(0.701485\pi\)
\(858\) 7.86764 0.268597
\(859\) −0.335482 −0.0114465 −0.00572324 0.999984i \(-0.501822\pi\)
−0.00572324 + 0.999984i \(0.501822\pi\)
\(860\) −53.5449 −1.82587
\(861\) −4.18943 −0.142775
\(862\) −97.3453 −3.31559
\(863\) −22.5853 −0.768812 −0.384406 0.923164i \(-0.625594\pi\)
−0.384406 + 0.923164i \(0.625594\pi\)
\(864\) −109.894 −3.73866
\(865\) 12.7978 0.435137
\(866\) −96.6646 −3.28480
\(867\) 26.5229 0.900765
\(868\) 13.1759 0.447220
\(869\) −4.41826 −0.149879
\(870\) −23.4239 −0.794145
\(871\) −12.0594 −0.408616
\(872\) 142.273 4.81798
\(873\) 4.44536 0.150453
\(874\) 76.6449 2.59255
\(875\) 14.0534 0.475092
\(876\) −75.2404 −2.54214
\(877\) 43.6009 1.47230 0.736148 0.676820i \(-0.236643\pi\)
0.736148 + 0.676820i \(0.236643\pi\)
\(878\) 87.7145 2.96022
\(879\) 39.0740 1.31793
\(880\) −21.6572 −0.730064
\(881\) −28.0497 −0.945020 −0.472510 0.881325i \(-0.656652\pi\)
−0.472510 + 0.881325i \(0.656652\pi\)
\(882\) −8.36375 −0.281622
\(883\) −43.6356 −1.46845 −0.734227 0.678904i \(-0.762455\pi\)
−0.734227 + 0.678904i \(0.762455\pi\)
\(884\) −0.630703 −0.0212128
\(885\) 16.7995 0.564710
\(886\) 56.4625 1.89690
\(887\) −17.8638 −0.599808 −0.299904 0.953969i \(-0.596955\pi\)
−0.299904 + 0.953969i \(0.596955\pi\)
\(888\) 149.606 5.02044
\(889\) 26.6976 0.895410
\(890\) −32.0111 −1.07301
\(891\) 7.62018 0.255286
\(892\) −63.7103 −2.13318
\(893\) 32.5604 1.08959
\(894\) −8.89631 −0.297537
\(895\) 29.4219 0.983467
\(896\) 37.0946 1.23924
\(897\) 14.6532 0.489257
\(898\) 25.3366 0.845492
\(899\) 7.73219 0.257883
\(900\) 9.03814 0.301271
\(901\) −0.690255 −0.0229957
\(902\) −6.40288 −0.213193
\(903\) −13.6334 −0.453691
\(904\) 35.5066 1.18093
\(905\) 4.94031 0.164221
\(906\) 7.64317 0.253927
\(907\) −33.0466 −1.09729 −0.548647 0.836054i \(-0.684857\pi\)
−0.548647 + 0.836054i \(0.684857\pi\)
\(908\) −39.9806 −1.32680
\(909\) −5.62499 −0.186569
\(910\) −8.13370 −0.269629
\(911\) 29.3063 0.970961 0.485480 0.874248i \(-0.338645\pi\)
0.485480 + 0.874248i \(0.338645\pi\)
\(912\) 112.044 3.71014
\(913\) −1.79824 −0.0595132
\(914\) 59.4864 1.96764
\(915\) 16.3303 0.539863
\(916\) −161.731 −5.34374
\(917\) −2.26987 −0.0749578
\(918\) −1.04214 −0.0343957
\(919\) 9.46268 0.312145 0.156072 0.987746i \(-0.450117\pi\)
0.156072 + 0.987746i \(0.450117\pi\)
\(920\) −71.2148 −2.34788
\(921\) 2.48840 0.0819955
\(922\) −52.1233 −1.71659
\(923\) −8.97298 −0.295349
\(924\) −11.3112 −0.372111
\(925\) −31.4330 −1.03351
\(926\) 48.0412 1.57873
\(927\) −1.24206 −0.0407947
\(928\) 77.0537 2.52941
\(929\) −46.5486 −1.52721 −0.763605 0.645684i \(-0.776572\pi\)
−0.763605 + 0.645684i \(0.776572\pi\)
\(930\) −11.9052 −0.390386
\(931\) 28.0085 0.917941
\(932\) 63.9016 2.09317
\(933\) −26.2281 −0.858669
\(934\) 62.0209 2.02939
\(935\) −0.106830 −0.00349371
\(936\) −8.76580 −0.286519
\(937\) −25.3352 −0.827665 −0.413833 0.910353i \(-0.635810\pi\)
−0.413833 + 0.910353i \(0.635810\pi\)
\(938\) 23.8081 0.777362
\(939\) 18.6391 0.608264
\(940\) −48.2675 −1.57431
\(941\) −8.99616 −0.293266 −0.146633 0.989191i \(-0.546844\pi\)
−0.146633 + 0.989191i \(0.546844\pi\)
\(942\) 31.1857 1.01609
\(943\) −11.9252 −0.388336
\(944\) −106.241 −3.45786
\(945\) −9.78706 −0.318373
\(946\) −20.8365 −0.677453
\(947\) −3.44570 −0.111970 −0.0559852 0.998432i \(-0.517830\pi\)
−0.0559852 + 0.998432i \(0.517830\pi\)
\(948\) −33.8845 −1.10052
\(949\) −15.3321 −0.497699
\(950\) −41.5627 −1.34847
\(951\) 17.5233 0.568230
\(952\) 0.780455 0.0252947
\(953\) −24.5706 −0.795921 −0.397960 0.917403i \(-0.630282\pi\)
−0.397960 + 0.917403i \(0.630282\pi\)
\(954\) −15.3057 −0.495541
\(955\) −2.47277 −0.0800170
\(956\) −74.5772 −2.41200
\(957\) −6.63788 −0.214572
\(958\) −48.2683 −1.55948
\(959\) −11.4218 −0.368828
\(960\) −56.6513 −1.82841
\(961\) −27.0701 −0.873230
\(962\) 48.6380 1.56815
\(963\) −4.65735 −0.150081
\(964\) −125.164 −4.03127
\(965\) −10.8851 −0.350403
\(966\) −28.9290 −0.930775
\(967\) 46.0793 1.48181 0.740906 0.671609i \(-0.234396\pi\)
0.740906 + 0.671609i \(0.234396\pi\)
\(968\) 89.3950 2.87326
\(969\) 0.552686 0.0177548
\(970\) 30.3038 0.972995
\(971\) 16.7213 0.536612 0.268306 0.963334i \(-0.413536\pi\)
0.268306 + 0.963334i \(0.413536\pi\)
\(972\) −30.9910 −0.994038
\(973\) 2.98260 0.0956178
\(974\) −38.1481 −1.22234
\(975\) −7.94610 −0.254479
\(976\) −103.274 −3.30571
\(977\) −13.3636 −0.427538 −0.213769 0.976884i \(-0.568574\pi\)
−0.213769 + 0.976884i \(0.568574\pi\)
\(978\) 71.6727 2.29184
\(979\) −9.07131 −0.289920
\(980\) −41.5197 −1.32630
\(981\) 8.81411 0.281413
\(982\) 25.4765 0.812989
\(983\) 34.0887 1.08726 0.543631 0.839325i \(-0.317049\pi\)
0.543631 + 0.839325i \(0.317049\pi\)
\(984\) −30.7785 −0.981184
\(985\) −1.70604 −0.0543591
\(986\) 0.730712 0.0232706
\(987\) −12.2897 −0.391185
\(988\) 46.8336 1.48997
\(989\) −38.8072 −1.23400
\(990\) −2.36885 −0.0752869
\(991\) 26.0445 0.827332 0.413666 0.910429i \(-0.364248\pi\)
0.413666 + 0.910429i \(0.364248\pi\)
\(992\) 39.1624 1.24341
\(993\) −7.62609 −0.242007
\(994\) 17.7148 0.561880
\(995\) −6.10873 −0.193660
\(996\) −13.7911 −0.436987
\(997\) −42.0386 −1.33138 −0.665688 0.746230i \(-0.731862\pi\)
−0.665688 + 0.746230i \(0.731862\pi\)
\(998\) 72.3826 2.29123
\(999\) 58.5248 1.85164
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 \(a_p\))